LMFDB - Embedded newform 76.7.l.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(23,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	76.23
Dual form			76.7.l.a.43.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.01566 - 6.23243i) q^{2} +(22.9636 - 4.04910i) q^{3} +(-13.6863 + 62.5195i) q^{4} +(-26.2597 + 22.0345i) q^{5} +(-140.413 - 122.810i) q^{6} +(137.300 + 79.2704i) q^{7} +(458.294 - 228.277i) q^{8} +(-174.105 + 63.3690i) q^{9} +O(q^{10})$	\(q+(-5.01566 - 6.23243i) q^{2} +(22.9636 - 4.04910i) q^{3} +(-13.6863 + 62.5195i) q^{4} +(-26.2597 + 22.0345i) q^{5} +(-140.413 - 122.810i) q^{6} +(137.300 + 79.2704i) q^{7} +(458.294 - 228.277i) q^{8} +(-174.105 + 63.3690i) q^{9} +(269.038 + 53.1441i) q^{10} +(-1762.62 + 1017.65i) q^{11} +(-61.1394 + 1491.09i) q^{12} +(605.935 - 3436.43i) q^{13} +(-194.605 - 1253.31i) q^{14} +(-513.796 + 612.319i) q^{15} +(-3721.37 - 1711.32i) q^{16} +(-5578.27 - 2030.32i) q^{17} +(1268.19 + 767.259i) q^{18} +(-4091.55 - 5505.01i) q^{19} +(-1018.19 - 1943.31i) q^{20} +(3473.88 + 1264.39i) q^{21} +(15183.1 + 5881.22i) q^{22} +(7985.21 - 9516.40i) q^{23} +(9599.76 - 7097.74i) q^{24} +(-2509.20 + 14230.4i) q^{25} +(-24456.4 + 13459.5i) q^{26} +(-18462.8 + 10659.5i) q^{27} +(-6835.08 + 7499.03i) q^{28} +(-12815.3 + 4664.37i) q^{29} +(6393.26 + 131.017i) q^{30} +(-18754.4 - 10827.8i) q^{31} +(7999.42 + 31776.6i) q^{32} +(-36355.5 + 30505.9i) q^{33} +(15324.9 + 44949.6i) q^{34} +(-5352.15 + 943.728i) q^{35} +(-1578.94 - 11752.2i) q^{36} -43839.9 q^{37} +(-13787.8 + 53111.5i) q^{38} -81366.1i q^{39} +(-7004.68 + 16092.8i) q^{40} +(22431.6 + 127216. i) q^{41} +(-9543.59 - 27992.5i) q^{42} +(-44957.7 - 53578.5i) q^{43} +(-39499.1 - 124126. i) q^{44} +(3175.64 - 5500.36i) q^{45} +(-99361.4 - 2036.21i) q^{46} +(36523.6 + 100348. i) q^{47} +(-92385.3 - 24229.9i) q^{48} +(-46256.9 - 80119.3i) q^{49} +(101275. - 55736.3i) q^{50} +(-136318. - 24036.6i) q^{51} +(206551. + 84914.8i) q^{52} +(203930. + 171118. i) q^{53} +(159038. + 61603.6i) q^{54} +(23862.5 - 65561.6i) q^{55} +(81019.6 + 4986.59i) q^{56} +(-116247. - 109848. i) q^{57} +(93347.3 + 56475.2i) q^{58} +(132668. - 364504. i) q^{59} +(-31249.9 - 40502.7i) q^{60} +(-199260. - 167199. i) q^{61} +(26581.8 + 171194. i) q^{62} +(-28928.0 - 5100.78i) q^{63} +(157923. - 209236. i) q^{64} +(59808.2 + 103591. i) q^{65} +(372473. + 73575.9i) q^{66} +(23279.4 + 63959.7i) q^{67} +(203281. - 320963. i) q^{68} +(144836. - 250864. i) q^{69} +(32726.3 + 28623.5i) q^{70} +(-228033. - 271760. i) q^{71} +(-65325.6 + 68785.9i) q^{72} +(-29525.0 - 167444. i) q^{73} +(219886. + 273229. i) q^{74} +336941. i q^{75} +(400169. - 180458. i) q^{76} -322678. q^{77} +(-507109. + 408105. i) q^{78} +(-489959. + 86393.0i) q^{79} +(135430. - 37059.7i) q^{80} +(-277342. + 232718. i) q^{81} +(680354. - 777874. i) q^{82} +(-135706. - 78349.7i) q^{83} +(-126594. + 199881. i) q^{84} +(191221. - 69598.7i) q^{85} +(-108432. + 548927. i) q^{86} +(-275398. + 159001. i) q^{87} +(-575492. + 868749. i) q^{88} +(56501.7 - 320437. i) q^{89} +(-50208.5 + 7796.03i) q^{90} +(355602. - 423790. i) q^{91} +(485672. + 629476. i) q^{92} +(-474511. - 172708. i) q^{93} +(442220. - 730940. i) q^{94} +(228743. + 54404.7i) q^{95} +(312362. + 697314. i) q^{96} +(956525. + 348147. i) q^{97} +(-267329. + 690144. i) q^{98} +(242394. - 288873. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) $ 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.01566	−	6.23243i	−0.626957	−	0.779054i
$2$	−5.01566	−	6.23243i	−0.626957	−	0.779054i
$3$	22.9636	−	4.04910i	0.850503	−	0.149967i	0.268627	−	0.963244i	$-0.413430\pi$
$3$	22.9636	−	4.04910i	0.850503	−	0.149967i	0.581876	+	0.813278i	$0.302319\pi$
$4$	−13.6863	+	62.5195i	−0.213849	+	0.976867i
$5$	−26.2597	+	22.0345i	−0.210077	+	0.176276i	−0.741755	−	0.670671i	$-0.766006\pi$
$5$	−26.2597	+	22.0345i	−0.210077	+	0.176276i	0.531678	+	0.846947i	$0.321562\pi$
$6$	−140.413	−	122.810i	−0.650061	−	0.568565i
$7$	137.300	+	79.2704i	0.400293	+	0.231109i	0.686610	−	0.727026i	$-0.259098\pi$
$7$	137.300	+	79.2704i	0.400293	+	0.231109i	−0.286318	+	0.958135i	$0.592431\pi$
$8$	458.294	−	228.277i	0.895106	−	0.445854i
$9$	−174.105	+	63.3690i	−0.238827	+	0.0869260i
$10$	269.038	+	53.1441i	0.269038	+	0.0531441i
$11$	−1762.62	+	1017.65i	−1.32428	+	0.764575i	−0.984409	−	0.175896i	$-0.943718\pi$
$11$	−1762.62	+	1017.65i	−1.32428	+	0.764575i	−0.339874	+	0.940471i	$0.610384\pi$
$12$	−61.1394	+	1491.09i	−0.0353816	+	0.862898i
$13$	605.935	−	3436.43i	0.275801	−	1.56414i	−0.460605	−	0.887605i	$-0.652368\pi$
$13$	605.935	−	3436.43i	0.275801	−	1.56414i	0.736406	−	0.676540i	$-0.236521\pi$
$14$	−194.605	−	1253.31i	−0.0709201	−	0.456745i
$15$	−513.796	+	612.319i	−0.152236	+	0.181428i
$16$	−3721.37	−	1711.32i	−0.908537	−	0.417804i
$17$	−5578.27	−	2030.32i	−1.13541	−	0.413256i	−0.295157	−	0.955449i	$-0.595372\pi$
$17$	−5578.27	−	2030.32i	−1.13541	−	0.413256i	−0.840254	+	0.542193i	$0.817594\pi$
$18$	1268.19	+	767.259i	0.217454	+	0.131560i
$19$	−4091.55	−	5505.01i	−0.596522	−	0.802597i
$19$	−4091.55	−	5505.01i	−0.596522	−	0.802597i
$20$	−1018.19	−	1943.31i	−0.127273	−	0.242914i
$21$	3473.88	+	1264.39i	0.375109	+	0.136528i
$22$	15183.1	+	5881.22i	1.42591	+	0.552331i
$23$	7985.21	−	9516.40i	0.656301	−	0.782149i	−0.330549	−	0.943789i	$-0.607234\pi$
$23$	7985.21	−	9516.40i	0.656301	−	0.782149i	0.986850	+	0.161640i	$0.0516784\pi$
$24$	9599.76	−	7097.74i	0.694427	−	0.513436i
$25$	−2509.20	+	14230.4i	−0.160589	+	0.910745i
$26$	−24456.4	+	13459.5i	−1.39147	+	0.765789i
$27$	−18462.8	+	10659.5i	−0.938007	+	0.541559i
$28$	−6835.08	+	7499.03i	−0.311365	+	0.341610i
$29$	−12815.3	+	4664.37i	−0.525452	+	0.191249i	−0.591107	−	0.806593i	$-0.701309\pi$
$29$	−12815.3	+	4664.37i	−0.525452	+	0.191249i	0.0656544	+	0.997842i	$0.479087\pi$
$30$	6393.26	+	131.017i	0.236787	+	0.00485249i
$31$	−18754.4	−	10827.8i	−0.629532	−	0.363460i	0.151039	−	0.988528i	$-0.451738\pi$
$31$	−18754.4	−	10827.8i	−0.629532	−	0.363460i	−0.780571	+	0.625067i	$0.785071\pi$
$32$	7999.42	+	31776.6i	0.244123	+	0.969744i
$33$	−36355.5	+	30505.9i	−1.01165	+	0.848872i
$34$	15324.9	+	44949.6i	0.389906	+	1.14364i
$35$	−5352.15	+	943.728i	−0.124831	+	0.0220112i
$36$	−1578.94	−	11752.2i	−0.0338422	−	0.251891i
$37$	−43839.9			−0.865495			−0.432747	−	0.901515i	$-0.642456\pi$
$37$	−43839.9			−0.865495			−0.432747	+	0.901515i	$0.642456\pi$
$38$	−13787.8	+	53111.5i	−0.251272	+	0.967917i
$39$		−	81366.1i		−	1.37167i
$40$	−7004.68	+	16092.8i	−0.109448	+	0.251449i
$41$	22431.6	+	127216.i	0.325468	+	1.84582i	0.506367	+	0.862318i	$0.330988\pi$
$41$	22431.6	+	127216.i	0.325468	+	1.84582i	−0.180899	+	0.983502i	$0.557901\pi$
$42$	−9543.59	−	27992.5i	−0.128814	−	0.377827i
$43$	−44957.7	−	53578.5i	−0.565456	−	0.673884i	0.405236	−	0.914212i	$-0.367189\pi$
$43$	−44957.7	−	53578.5i	−0.565456	−	0.673884i	−0.970692	+	0.240328i	$0.922745\pi$
$44$	−39499.1	−	124126.i	−0.463692	−	1.45715i
$45$	3175.64	−	5500.36i	0.0348492	−	0.0603607i
$46$	−99361.4	−	2036.21i	−1.02081	−	0.0209194i
$47$	36523.6	+	100348.i	0.351787	+	0.966527i	0.981796	+	0.189939i	$0.0608290\pi$
$47$	36523.6	+	100348.i	0.351787	+	0.966527i	−0.630009	+	0.776588i	$0.716949\pi$
$48$	−92385.3	−	24229.9i	−0.835370	−	0.219093i
$49$	−46256.9	−	80119.3i	−0.393177	−	0.681003i
$50$	101275.	−	55736.3i	0.810201	−	0.445891i
$51$	−136318.	−	24036.6i	−1.02764	−	0.181201i
$52$	206551.	+	84914.8i	1.46898	+	0.603911i
$53$	203930.	+	171118.i	1.36979	+	1.14939i	0.972822	+	0.231556i	$0.0743816\pi$
$53$	203930.	+	171118.i	1.36979	+	1.14939i	0.396967	+	0.917833i	$0.370063\pi$
$54$	159038.	+	61603.6i	1.00999	+	0.391224i
$55$	23862.5	−	65561.6i	0.143426	−	0.394059i
$56$	81019.6	+	4986.59i	0.461345	+	0.0283949i
$57$	−116247.	−	109848.i	−0.627707	−	0.593152i
$58$	93347.3	+	56475.2i	0.478429	+	0.289450i
$59$	132668.	−	364504.i	0.645969	−	1.77479i	0.0138629	−	0.999904i	$-0.495587\pi$
$59$	132668.	−	364504.i	0.645969	−	1.77479i	0.632106	−	0.774882i	$-0.282191\pi$
$60$	−31249.9	−	40502.7i	−0.144675	−	0.187512i
$61$	−199260.	−	167199.i	−0.877870	−	0.736620i	0.0878704	−	0.996132i	$-0.471994\pi$
$61$	−199260.	−	167199.i	−0.877870	−	0.736620i	−0.965740	+	0.259512i	$0.916438\pi$
$62$	26581.8	+	171194.i	0.111535	+	0.718313i
$63$	−28928.0	−	5100.78i	−0.115690	−	0.0203993i
$64$	157923.	−	209236.i	0.602428	−	0.798173i
$65$	59808.2	+	103591.i	0.217781	+	0.377209i
$66$	372473.	+	73575.9i	1.29558	+	0.255920i
$67$	23279.4	+	63959.7i	0.0774013	+	0.212658i	0.972358	−	0.233494i	$-0.0750161\pi$
$67$	23279.4	+	63959.7i	0.0774013	+	0.212658i	−0.894957	+	0.446153i	$0.852794\pi$
$68$	203281.	−	320963.i	0.646502	−	1.02077i
$69$	144836.	−	250864.i	0.440890	−	0.763643i
$70$	32726.3	+	28623.5i	0.0954119	+	0.0834503i
$71$	−228033.	−	271760.i	−0.637123	−	0.759294i	0.346790	−	0.937943i	$-0.387272\pi$
$71$	−228033.	−	271760.i	−0.637123	−	0.759294i	−0.983913	+	0.178649i	$0.942827\pi$
$72$	−65325.6	+	68785.9i	−0.175019	+	0.184290i
$73$	−29525.0	−	167444.i	−0.0758963	−	0.430429i	−0.998952	−	0.0457638i	$-0.985428\pi$
$73$	−29525.0	−	167444.i	−0.0758963	−	0.430429i	0.923056	−	0.384666i	$-0.125683\pi$
$74$	219886.	+	273229.i	0.542628	+	0.674267i
$75$			336941.i			0.798674i
$76$	400169.	−	180458.i	0.911595	−	0.411088i
$77$	−322678.			−0.706801
$78$	−507109.	+	408105.i	−1.06861	+	0.859979i
$79$	−489959.	+	86393.0i	−0.993753	+	0.175225i	−0.646802	−	0.762658i	$-0.723894\pi$
$79$	−489959.	+	86393.0i	−0.993753	+	0.175225i	−0.346951	+	0.937883i	$0.612783\pi$
$80$	135430.	−	37059.7i	0.264512	−	0.0723821i
$81$	−277342.	+	232718.i	−0.521868	+	0.437900i
$82$	680354.	−	777874.i	1.23394	−	1.41081i
$83$	−135706.	−	78349.7i	−0.237336	−	0.137026i	0.376616	−	0.926370i	$-0.377088\pi$
$83$	−135706.	−	78349.7i	−0.237336	−	0.137026i	−0.613952	+	0.789344i	$0.710421\pi$
$84$	−126594.	+	199881.i	−0.213587	+	0.337235i
$85$	191221.	−	69598.7i	0.311371	−	0.113330i
$86$	−108432.	+	548927.i	−0.170475	+	0.863017i
$87$	−275398.	+	159001.i	−0.418218	+	0.241458i
$88$	−575492.	+	868749.i	−0.844484	+	1.27481i
$89$	56501.7	−	320437.i	0.0801478	−	0.454541i	−0.918151	−	0.396231i	$-0.870318\pi$
$89$	56501.7	−	320437.i	0.0801478	−	0.454541i	0.998299	−	0.0583095i	$-0.0185710\pi$
$90$	−50208.5	+	7796.03i	−0.0688732	+	0.0106941i
$91$	355602.	−	423790.i	0.471889	−	0.562376i
$92$	485672.	+	629476.i	0.623706	+	0.808380i
$93$	−474511.	−	172708.i	−0.589926	−	0.214715i
$94$	442220.	−	730940.i	0.532421	−	0.880032i
$95$	228743.	+	54404.7i	0.266794	+	0.0634550i
$96$	312362.	+	697314.i	0.353057	+	0.788160i
$97$	956525.	+	348147.i	1.04805	+	0.381458i	0.807926	−	0.589284i	$-0.200590\pi$
$97$	956525.	+	348147.i	1.04805	+	0.381458i	0.240122	+	0.970743i	$0.422812\pi$
$98$	−267329.	+	690144.i	−0.284032	+	0.733266i
$99$	242394.	−	288873.i	0.249813	−	0.297716i
$100$	−855334.	−	351636.i	−0.855334	−	0.351636i
$101$	−253043.	+	1.43508e6i	−0.245601	+	1.39287i	0.573492	+	0.819211i	$0.305588\pi$
$101$	−253043.	+	1.43508e6i	−0.245601	+	1.39287i	−0.819093	+	0.573661i	$0.805523\pi$
$102$	533919.	+	970152.i	0.503124	+	0.914196i
$103$	718882.	−	415047.i	0.657879	−	0.379826i	−0.133590	−	0.991037i	$-0.542650\pi$
$103$	718882.	−	415047.i	0.657879	−	0.379826i	0.791468	+	0.611210i	$0.209317\pi$
$104$	−506762.	−	1.71321e6i	−0.450510	−	1.52304i
$105$	−119083.	+	43342.8i	−0.102869	+	0.0374411i
$106$	43634.7	−	2.12925e6i	0.0366365	−	1.78776i
$107$	278814.	+	160973.i	0.227595	+	0.131402i	0.609462	−	0.792815i	$-0.291385\pi$
$107$	278814.	+	160973.i	0.227595	+	0.131402i	−0.381867	+	0.924217i	$0.624719\pi$
$108$	−413739.	−	1.30017e6i	−0.328439	−	1.03212i
$109$	−1.32565e6	+	1.11235e6i	−1.02365	+	0.858940i	−0.990081	−	0.140496i	$-0.955130\pi$
$109$	−1.32565e6	+	1.11235e6i	−1.02365	+	0.858940i	−0.0335640	+	0.999437i	$0.510686\pi$
$110$	−528294.	+	180113.i	−0.396915	+	0.135322i
$111$	−1.00672e6	+	177512.i	−0.736106	+	0.129795i
$112$	−375288.	−	529960.i	−0.267123	−	0.377215i
$113$	1.53447e6			1.06347			0.531733	−	0.846912i	$-0.321541\pi$
$113$	1.53447e6			1.06347			0.531733	+	0.846912i	$0.321541\pi$
$114$	−101563.	+	1.27546e6i	−0.0685522	+	0.860898i
$115$			425848.i			0.280002i
$116$	−116220.	−	865041.i	−0.0744574	−	0.554195i
$117$	112267.	+	636697.i	0.0700961	+	0.397535i
$118$	−2.93716e6	+	1.00138e6i	−1.78765	+	0.609470i
$119$	−604954.	−	720956.i	−0.358989	−	0.427827i
$120$	−95691.4	+	397910.i	−0.0553769	+	0.230272i
$121$	1.18544e6	−	2.05324e6i	0.669150	−	1.15900i
$122$	−42635.4	+	2.08048e6i	−0.0234796	+	1.14574i
$123$	1.03022e6	+	2.83050e6i	0.553623	+	1.52107i
$124$	933630.	−	1.02432e6i	0.489677	−	0.537243i
$125$	−515478.	−	892833.i	−0.263925	−	0.457131i
$126$	113303.	+	205875.i	0.0566407	+	0.102918i
$127$	518206.	+	91373.7i	0.252983	+	0.0446077i	0.298701	−	0.954347i	$-0.403447\pi$
$127$	518206.	+	91373.7i	0.252983	+	0.0446077i	−0.0457184	+	0.998954i	$0.514558\pi$
$128$	−2.09614e6	+	65215.0i	−0.999516	+	0.0310969i
$129$	−1.24933e6	−	1.04832e6i	−0.581982	−	0.488341i
$130$	345645.	−	892327.i	0.157326	−	0.406157i
$131$	556791.	−	1.52977e6i	0.247673	−	0.680476i	−0.752097	−	0.659052i	$-0.770958\pi$
$131$	556791.	−	1.52977e6i	0.247673	−	0.680476i	0.999770	−	0.0214241i	$-0.00682001\pi$
$132$	−1.40964e6	−	2.69044e6i	−0.612895	−	1.16977i
$133$	−125386.	−	1.08018e6i	−0.0532961	−	0.459135i
$134$	281863.	−	465888.i	0.117145	−	0.193627i
$135$	249950.	−	686733.i	0.101590	−	0.279117i
$136$	−3.01997e6	+	342907.i	−1.20056	+	0.136320i
$137$	274118.	+	230013.i	0.106605	+	0.0894519i	0.694532	−	0.719462i	$-0.255611\pi$
$137$	274118.	+	230013.i	0.106605	+	0.0894519i	−0.587927	+	0.808914i	$0.700056\pi$
$138$	−2.28994e6	+	355565.i	−0.871338	+	0.135295i
$139$	−1.79981e6	−	317356.i	−0.670167	−	0.118169i	−0.171796	−	0.985132i	$-0.554957\pi$
$139$	−1.79981e6	−	317356.i	−0.670167	−	0.118169i	−0.498371	+	0.866964i	$0.666068\pi$
$140$	14249.8	−	347530.i	0.00519309	−	0.126651i
$141$	1.24503e6	+	2.15645e6i	0.444143	+	0.769278i
$142$	−549984.	+	2.78426e6i	−0.192081	+	0.972398i
$143$	2.42904e6	+	6.67374e6i	0.830668	+	2.28224i
$144$	756354.	+	62130.4i	0.253301	+	0.0208073i
$145$	233747.	−	404862.i	0.0766730	−	0.132802i
$146$	−895498.	+	1.02386e6i	−0.287744	+	0.328988i
$147$	−1.38664e6	−	1.65253e6i	−0.436526	−	0.520231i
$148$	600007.	−	2.74085e6i	0.185085	−	0.845473i
$149$	527907.	+	2.99391e6i	0.159588	+	0.905066i	0.954471	+	0.298304i	$0.0964208\pi$
$149$	527907.	+	2.99391e6i	0.159588	+	0.905066i	−0.794883	+	0.606762i	$0.792468\pi$
$150$	2.09996e6	−	1.68998e6i	0.622210	−	0.500735i
$151$			1.17045e6i			0.339957i	0.985448	+	0.169978i	$0.0543698\pi$
$151$			1.17045e6i			0.339957i	−0.985448	+	0.169978i	$0.945630\pi$
$152$	−3.13180e6	−	1.58891e6i	−0.891791	−	0.452447i
$153$	1.09986e6			0.307089
$154$	1.61844e6	+	2.01107e6i	0.443134	+	0.550636i
$155$	731070.	−	128907.i	0.196320	−	0.0346165i
$156$	5.08697e6	+	1.11360e6i	1.33994	+	0.293330i
$157$	2.14183e6	−	1.79721e6i	0.553459	−	0.464407i	−0.322652	−	0.946518i	$-0.604574\pi$
$157$	2.14183e6	−	1.79721e6i	0.553459	−	0.464407i	0.876110	+	0.482111i	$0.160130\pi$
$158$	2.99590e6	+	2.62032e6i	0.759551	+	0.664328i
$159$	5.37583e6	+	3.10374e6i	1.33738	+	0.772136i
$160$	−910243.	−	658180.i	−0.222227	−	0.160688i
$161$	1.85074e6	−	673615.i	0.443474	−	0.161411i
$162$	2.84145e6	+	561283.i	0.668337	+	0.132019i
$163$	2.36083e6	−	1.36303e6i	0.545132	−	0.314732i	−0.202024	−	0.979381i	$-0.564752\pi$
$163$	2.36083e6	−	1.36303e6i	0.545132	−	0.314732i	0.747156	+	0.664648i	$0.231419\pi$
$164$	−8.26047e6	−	338706.i	−1.87272	−	0.0767876i
$165$	282502.	−	1.60215e6i	0.0628884	−	0.356658i
$166$	192344.	+	1.23875e6i	0.0420490	+	0.270807i
$167$	−181111.	+	215840.i	−0.0388863	+	0.0463429i	−0.785137	−	0.619322i	$-0.787408\pi$
$167$	−181111.	+	215840.i	−0.0388863	+	0.0463429i	0.746251	+	0.665665i	$0.231852\pi$
$168$	1.88069e6	−	213546.i	0.396634	−	0.0450365i
$169$	−6.90615e6	−	2.51363e6i	−1.43079	−	0.520765i
$170$	−1.39287e6	−	842686.i	−0.283506	−	0.171522i
$171$	1.06121e6	+	699173.i	0.212232	+	0.139829i
$172$	3.96500e6	−	2.07744e6i	0.779217	−	0.408266i
$173$	−1.94072e6	−	706366.i	−0.374822	−	0.136424i	0.147738	−	0.989027i	$-0.452801\pi$
$173$	−1.94072e6	−	706366.i	−0.374822	−	0.136424i	−0.522560	+	0.852602i	$0.675023\pi$
$174$	2.37226e6	+	918901.i	0.450313	+	0.174430i
$175$	−1.47256e6	+	1.75493e6i	−0.274764	+	0.327451i
$176$	8.30089e6	−	770636.i	1.52260	−	0.141355i
$177$	1.57063e6	−	8.90750e6i	0.283240	−	1.60633i
$178$	−2.28049e6	+	1.25506e6i	−0.404361	+	0.222538i
$179$	−8.88403e6	+	5.12919e6i	−1.54900	+	0.894314i	−0.550779	+	0.834651i	$0.685669\pi$
$179$	−8.88403e6	+	5.12919e6i	−1.54900	+	0.894314i	−0.998219	+	0.0596628i	$0.980997\pi$
$180$	300417.	+	273819.i	0.0515119	+	0.0469511i
$181$	1.10137e7	−	4.00867e6i	1.85737	−	0.676028i	0.876489	−	0.481421i	$-0.159879\pi$
$181$	1.10137e7	−	4.00867e6i	1.85737	−	0.676028i	0.980881	−	0.194606i	$-0.0623430\pi$
$182$	−4.42482e6	−	90677.9i	−0.733975	−	0.0150414i
$183$	−5.25272e6	−	3.03266e6i	−0.857099	−	0.494846i
$184$	1.48720e6	−	6.18415e6i	0.238734	−	0.992720i
$185$	1.15122e6	−	965990.i	0.181821	−	0.152566i
$186$	1.30360e6	+	3.82360e6i	0.202584	+	0.594201i
$187$	1.18985e7	−	2.09803e6i	1.81957	−	0.320839i
$188$	−6.77356e6	+	910044.i	−1.01940	+	0.136958i
$189$	−3.37993e6			−0.500637
$190$	−808222.	−	1.69850e6i	−0.117834	−	0.247631i
$191$		−	7.14595e6i		−	1.02556i	−0.858521	−	0.512778i	$-0.828616\pi$
$191$		−	7.14595e6i		−	1.02556i	0.858521	−	0.512778i	$-0.171384\pi$
$192$	2.77926e6	−	5.44426e6i	0.392668	−	0.769193i
$193$	885396.	+	5.02133e6i	0.123159	+	0.698468i	0.982384	+	0.186871i	$0.0598348\pi$
$193$	885396.	+	5.02133e6i	0.123159	+	0.698468i	−0.859226	+	0.511597i	$0.829054\pi$
$194$	−2.62780e6	−	7.70766e6i	−0.359905	−	1.05564i
$195$	1.79286e6	+	2.13665e6i	0.241793	+	0.288157i
$196$	5.64210e6	−	1.79542e6i	0.749329	−	0.238450i
$197$	−5.18463e6	+	8.98004e6i	−0.678139	+	1.17457i	0.297401	+	0.954753i	$0.403880\pi$
$197$	−5.18463e6	+	8.98004e6i	−0.678139	+	1.17457i	−0.975541	+	0.219819i	$0.929453\pi$
$198$	−3.01615e6	−	61809.9i	−0.388559	−	0.00796274i
$199$	−68632.5	−	188566.i	−0.00870904	−	0.0239279i	0.935262	−	0.353956i	$-0.115164\pi$
$199$	−68632.5	−	188566.i	−0.00870904	−	0.0239279i	−0.943971	+	0.330028i	$0.892942\pi$
$200$	2.09852e6	+	7.09449e6i	0.262315	+	0.886812i
$201$	793558.	+	1.37448e6i	0.0977216	+	0.169259i
$202$	1.02132e7	−	5.62079e6i	1.23910	−	0.681935i
$203$	−2.12929e6	−	375451.i	−0.254534	−	0.0448812i
$204$	3.36845e6	−	8.19356e6i	0.396770	−	0.965122i
$205$	−3.39218e6	−	2.84638e6i	−0.393747	−	0.330393i
$206$	−6.19241e6	−	2.39865e6i	−0.708367	−	0.274388i
$207$	−787220.	+	2.16287e6i	−0.0887534	+	0.243848i
$208$	−8.13574e6	+	1.17513e7i	−0.904081	+	1.30585i
$209$	1.28140e7	+	5.53948e6i	1.40361	+	0.606779i
$210$	867412.	+	524785.i	0.0936628	+	0.0566662i
$211$	−96709.0	+	265706.i	−0.0102948	+	0.0282848i	−0.944734	−	0.327839i	$-0.893680\pi$
$211$	−96709.0	+	265706.i	−0.0102948	+	0.0282848i	0.934439	+	0.356124i	$0.115902\pi$
$212$	−1.34892e7	+	1.04076e7i	−1.41573	+	1.09231i
$213$	−6.33685e6	−	5.31724e6i	−0.655744	−	0.550235i
$214$	−395181.	−	2.54507e6i	−0.0403232	−	0.259692i
$215$	2.36115e6	+	416334.i	0.237579	+	0.0418916i
$216$	−6.02807e6	+	9.09982e6i	−0.598159	+	0.902967i
$217$	−1.71666e6	−	2.97334e6i	−0.167998	−	0.290981i
$218$	1.35817e7	+	2.68284e6i	1.31094	+	0.258955i
$219$	−1.35600e6	−	3.72557e6i	−0.129100	−	0.354700i
$220$	3.77229e6	+	2.38917e6i	0.354272	+	0.224377i
$221$	−1.03571e7	+	1.79391e7i	−0.959539	+	1.66197i
$222$	6.15570e6	+	5.38398e6i	0.562625	+	0.492090i
$223$	−1.06832e7	−	1.27317e7i	−0.963353	−	1.14808i	−0.988927	−	0.148406i	$-0.952586\pi$
$223$	−1.06832e7	−	1.27317e7i	−0.963353	−	1.14808i	0.0255739	−	0.999673i	$-0.491859\pi$
$224$	−1.42062e6	+	4.99706e6i	−0.126396	+	0.444601i
$225$	−464901.	−	2.63659e6i	−0.0408144	−	0.231470i
$226$	−7.69639e6	−	9.56348e6i	−0.666748	−	0.828497i
$227$		−	1.75896e7i		−	1.50376i	−0.659299	−	0.751881i	$-0.729147\pi$
$227$		−	1.75896e7i		−	1.50376i	0.659299	−	0.751881i	$-0.270853\pi$
$228$	8.45861e6	−	5.76428e6i	0.713665	−	0.486341i
$229$	5.82357e6			0.484934			0.242467	−	0.970160i	$-0.422043\pi$
$229$	5.82357e6			0.484934			0.242467	+	0.970160i	$0.422043\pi$
$230$	2.65407e6	−	2.13591e6i	0.218136	−	0.175549i
$231$	−7.40984e6	+	1.30656e6i	−0.601137	+	0.105997i
$232$	−4.80838e6	+	5.06308e6i	−0.385066	+	0.405463i
$233$	−7.98105e6	+	6.69690e6i	−0.630946	+	0.529427i	−0.901223	−	0.433356i	$-0.857329\pi$
$233$	−7.98105e6	+	6.69690e6i	−0.630946	+	0.529427i	0.270277	+	0.962783i	$0.412885\pi$
$234$	3.40507e6	−	3.89315e6i	0.265753	−	0.303846i
$235$	−3.17021e6	−	1.83032e6i	−0.244278	−	0.141034i
$236$	2.09728e7	+	1.32831e7i	1.59559	+	1.01056i
$237$	−1.09014e7	+	3.96778e6i	−0.818912	+	0.298060i
$238$	−1.45906e6	+	7.38641e6i	−0.108229	+	0.547901i
$239$	7.70181e6	−	4.44664e6i	0.564156	−	0.325716i	−0.190656	−	0.981657i	$-0.561061\pi$
$239$	7.70181e6	−	4.44664e6i	0.564156	−	0.325716i	0.754812	+	0.655941i	$0.227728\pi$
$240$	2.95990e6	−	1.39939e6i	0.214113	−	0.101229i
$241$	−866995.	+	4.91697e6i	−0.0619392	+	0.351275i	0.938049	+	0.346501i	$0.112630\pi$
$241$	−866995.	+	4.91697e6i	−0.0619392	+	0.351275i	−0.999989	+	0.00477308i	$0.998481\pi$
$242$	−1.87425e7	+	2.91020e6i	−1.32245	+	0.205341i
$243$	4.56344e6	−	5.43850e6i	0.318034	−	0.379018i
$244$	1.31803e7	−	1.01693e7i	0.907311	−	0.700036i
$245$	2.98008e6	+	1.08466e6i	0.202642	+	0.0737557i
$246$	1.24737e7	−	2.06176e7i	0.837894	−	1.38495i
$247$	−2.13968e7	+	1.07246e7i	−1.41990	+	0.711690i
$248$	−1.10668e7	−	681137.i	−0.725548	−	0.0446560i
$249$	−3.43353e6	−	1.24970e6i	−0.222404	−	0.0809486i
$250$	−2.97906e6	+	7.69082e6i	−0.190660	+	0.492213i
$251$	−1.03703e7	+	1.23588e7i	−0.655797	+	0.781548i	−0.986776	−	0.162090i	$-0.948177\pi$
$251$	−1.03703e7	+	1.23588e7i	−0.655797	+	0.781548i	0.330979	+	0.943638i	$0.392621\pi$
$252$	714816.	−	1.73875e6i	0.0446676	−	0.108652i
$253$	−4.39053e6	+	2.49000e7i	−0.271116	+	1.53758i
$254$	−2.02966e6	−	3.68798e6i	−0.123858	−	0.225054i
$255$	4.10930e6	−	2.37251e6i	0.247826	−	0.143083i
$256$	1.09200e7	+	1.27369e7i	0.650880	+	0.759180i
$257$	−1.15668e7	+	4.20999e6i	−0.681421	+	0.248017i	−0.659458	−	0.751742i	$-0.729214\pi$
$257$	−1.15668e7	+	4.20999e6i	−0.681421	+	0.248017i	−0.0219635	+	0.999759i	$0.506992\pi$
$258$	−267319.	+	1.30444e7i	−0.0155657	+	0.759564i
$259$	−6.01924e6	−	3.47521e6i	−0.346451	−	0.200024i
$260$	−7.29500e6	+	2.32140e6i	−0.415055	+	0.132078i
$261$	1.93562e6	−	1.62418e6i	0.108868	−	0.0913509i
$262$	−1.23269e7	+	4.20265e6i	−0.685408	+	0.233679i
$263$	8.83780e6	−	1.55834e6i	0.485822	−	0.0856635i	0.0746281	−	0.997211i	$-0.476223\pi$
$263$	8.83780e6	−	1.55834e6i	0.485822	−	0.0856635i	0.411194	+	0.911548i	$0.365112\pi$
$264$	−9.69771e6	+	2.22798e7i	−0.527057	+	1.21088i
$265$	−9.12562e6			−0.490371
$266$	−6.10324e6	+	6.19927e6i	−0.324277	+	0.329379i
$267$		−	7.58716e6i		−	0.398608i
$268$	−4.31734e6	+	580045.i	−0.224291	+	0.0301340i
$269$	−1.73731e6	−	9.85277e6i	−0.0892525	−	0.506176i	−0.996358	−	0.0852720i	$-0.972824\pi$
$269$	−1.73731e6	−	9.85277e6i	−0.0892525	−	0.506176i	0.907105	−	0.420904i	$-0.138287\pi$
$270$	−5.53368e6	+	1.88662e6i	−0.281140	+	0.0958503i
$271$	−2.05126e6	−	2.44460e6i	−0.103065	−	0.122829i	0.712046	−	0.702133i	$-0.247769\pi$
$271$	−2.05126e6	−	2.44460e6i	−0.103065	−	0.122829i	−0.815111	+	0.579304i	$0.803324\pi$
$272$	1.72843e7	+	1.71018e7i	0.858903	+	0.849837i
$273$	6.44993e6	−	1.11716e7i	0.317006	−	0.549070i
$274$	58652.8	−	2.86209e6i	0.00285126	−	0.139133i
$275$	−1.00588e7	−	2.76363e7i	−0.483668	−	1.32887i
$276$	1.37016e7	+	1.24885e7i	0.651694	+	0.593994i
$277$	−1.05173e7	−	1.82166e7i	−0.494842	−	0.857091i	0.505140	−	0.863037i	$-0.331441\pi$
$277$	−1.05173e7	−	1.82166e7i	−0.494842	−	0.857091i	−0.999982	+	0.00594574i	$0.998107\pi$
$278$	7.04936e6	+	1.28090e7i	0.328107	+	0.596183i
$279$	3.95138e6	+	696735.i	0.181943	+	0.0320815i
$280$	−2.23743e6	+	1.65428e6i	−0.101924	+	0.0753589i
$281$	6.29394e6	+	5.28124e6i	0.283664	+	0.238022i	0.773506	−	0.633789i	$-0.218501\pi$
$281$	6.29394e6	+	5.28124e6i	0.283664	+	0.238022i	−0.489842	+	0.871811i	$0.662946\pi$
$282$	7.19530e6	−	1.85756e7i	0.320850	−	0.828315i
$283$	−5.46772e6	+	1.50224e7i	−0.241239	+	0.662798i	0.758697	+	0.651444i	$0.225836\pi$
$283$	−5.46772e6	+	1.50224e7i	−0.241239	+	0.662798i	−0.999936	+	0.0113539i	$0.996386\pi$
$284$	2.01112e7	−	1.05371e7i	0.877977	−	0.460010i
$285$	5.47304e6	+	323125.i	0.236425	+	0.0139584i
$286$	2.94104e7	−	4.86121e7i	1.25719	−	2.07800i
$287$	−7.00458e6	+	1.92449e7i	−0.296303	+	0.814087i
$288$	−3.40639e6	−	5.02555e6i	−0.142599	−	0.210381i
$289$	8.50444e6	+	7.13607e6i	0.352332	+	0.295642i
$290$	−3.69567e6	+	573838.i	−0.151530	+	0.0235285i
$291$	2.33749e7	+	4.12163e6i	0.948574	+	0.167259i
$292$	1.08726e7	+	445813.i	0.436703	+	0.0179062i
$293$	−5.92741e6	−	1.02666e7i	−0.235647	−	0.408153i	0.723813	−	0.689996i	$-0.242388\pi$
$293$	−5.92741e6	−	1.02666e7i	−0.235647	−	0.408153i	−0.959461	+	0.281843i	$0.909054\pi$
$294$	−3.34437e6	+	1.69306e7i	−0.131605	+	0.666240i
$295$	4.54782e6	+	1.24950e7i	0.177148	+	0.486711i
$296$	−2.00916e7	+	1.00077e7i	−0.774709	+	0.385884i
$297$	2.16953e7	−	3.75773e7i	0.828125	−	1.43435i
$298$	1.60115e7	−	1.83066e7i	0.605040	−	0.691765i
$299$	−2.78639e7	−	3.32069e7i	−1.04239	−	1.24227i
$300$	−2.10653e7	−	4.61148e6i	−0.780198	−	0.170795i
$301$	−1.92552e6	−	1.09202e7i	−0.0706071	−	0.400433i
$302$	7.29477e6	−	5.87060e6i	0.264844	−	0.213138i
$303$			3.39791e7i			1.22147i
$304$	5.80530e6	+	2.74881e7i	0.206635	+	0.978418i
$305$	8.91663e6			0.314269
$306$	−5.51655e6	−	6.85483e6i	−0.192532	−	0.239239i
$307$	2.37298e7	−	4.18421e6i	0.820124	−	0.144610i	0.252183	−	0.967680i	$-0.418851\pi$
$307$	2.37298e7	−	4.18421e6i	0.820124	−	0.144610i	0.567941	+	0.823070i	$0.307740\pi$
$308$	4.41628e6	−	2.01737e7i	0.151149	−	0.690451i
$309$	1.48275e7	−	1.24418e7i	0.502567	−	0.421703i
$310$	−4.47021e6	−	3.90979e6i	−0.150052	−	0.131241i
$311$	3.08896e7	+	1.78341e7i	1.02691	+	0.592886i	0.916098	−	0.400956i	$-0.131322\pi$
$311$	3.08896e7	+	1.78341e7i	1.02691	+	0.592886i	0.110811	+	0.993841i	$0.464655\pi$
$312$	−1.85740e7	−	3.72896e7i	−0.611565	−	1.22779i
$313$	−9.09016e6	+	3.30855e6i	−0.296441	+	0.107896i	−0.485959	−	0.873981i	$-0.661530\pi$
$313$	−9.09016e6	+	3.30855e6i	−0.296441	+	0.107896i	0.189518	+	0.981877i	$0.439307\pi$
$314$	−2.19436e7	−	4.33461e6i	−0.708793	−	0.140011i
$315$	872033.	−	503468.i	0.0278998	−	0.0161080i
$316$	1.30449e6	−	3.18144e7i	0.0413409	−	1.00824i
$317$	4.79402e6	−	2.71882e7i	0.150495	−	0.853499i	−0.812295	−	0.583247i	$-0.801782\pi$
$317$	4.79402e6	−	2.71882e7i	0.150495	−	0.853499i	0.962790	−	0.270252i	$-0.0871070\pi$
$318$	−7.61952e6	−	4.90718e7i	−0.236944	−	1.52599i
$319$	1.78417e7	−	2.12629e7i	0.549623	−	0.655015i
$320$	463410.	+	8.97423e6i	0.0141422	+	0.273872i
$321$	7.05436e6	+	2.56758e6i	0.213276	+	0.0776262i
$322$	−1.34809e7	−	8.15599e6i	−0.403787	−	0.244292i
$323$	1.16468e7	+	3.90156e7i	0.345620	+	1.15779i
$324$	−1.07536e7	−	2.05243e7i	−0.316169	−	0.603440i
$325$	4.73813e7	+	1.72454e7i	1.38025	+	0.502368i
$326$	−2.03361e7	−	7.87723e6i	−0.586968	−	0.227363i
$327$	−2.59377e7	+	3.09113e7i	−0.741801	+	0.884044i
$328$	3.93207e7	+	5.31816e7i	1.11429	+	1.50709i
$329$	−2.93990e6	+	1.66730e7i	−0.0825554	+	0.468195i
$330$	−1.14022e7	+	6.27516e6i	−0.317284	+	0.174616i
$331$	3.65162e7	−	2.10826e7i	1.00694	−	0.581354i	0.0966425	−	0.995319i	$-0.469190\pi$
$331$	3.65162e7	−	2.10826e7i	1.00694	−	0.581354i	0.910293	+	0.413965i	$0.135856\pi$
$332$	6.75569e6	−	7.41193e6i	0.184610	−	0.202543i
$333$	7.63275e6	−	2.77809e6i	0.206704	−	0.0752340i
$334$	2.25360e6	+	46183.1i	0.0604836	+	0.00123949i
$335$	−2.02063e6	−	1.16661e6i	−0.0537468	−	0.0310307i
$336$	−1.07638e7	−	1.06502e7i	−0.283758	−	0.280763i
$337$	−3.89522e7	+	3.26847e7i	−1.01775	+	0.853995i	−0.989343	−	0.145601i	$-0.953488\pi$
$337$	−3.89522e7	+	3.26847e7i	−1.01775	+	0.853995i	−0.0284085	+	0.999596i	$0.509044\pi$
$338$	1.89729e7	+	5.56496e7i	0.491341	+	1.44116i
$339$	3.52370e7	−	6.21323e6i	0.904481	−	0.159484i
$340$	1.73416e6	+	1.29076e7i	0.0441218	+	0.328403i
$341$	4.40758e7			1.11157
$342$	−965104.	−	1.01207e7i	−0.0241266	−	0.253007i
$343$		−	3.33194e7i		−	0.825686i
$344$	−3.28346e7	−	1.42919e7i	−0.806597	−	0.351086i
$345$	1.72430e6	+	9.77899e6i	0.0419909	+	0.238142i
$346$	5.33164e6	+	1.56383e7i	0.128716	+	0.377539i
$347$	1.67046e6	+	1.99077e6i	0.0399804	+	0.0476467i	0.785664	−	0.618653i	$-0.212321\pi$
$347$	1.67046e6	+	1.99077e6i	0.0399804	+	0.0476467i	−0.745684	+	0.666300i	$0.767877\pi$
$348$	−6.17147e6	−	1.93938e7i	−0.146437	−	0.460178i
$349$	2.06883e7	−	3.58333e7i	0.486687	−	0.842966i	−0.513196	−	0.858271i	$-0.671539\pi$
$349$	2.06883e7	−	3.58333e7i	0.486687	−	0.842966i	0.999883	+	0.0153052i	$0.00487198\pi$
$350$	1.83234e7	+	375501.i	0.427367	+	0.00875804i
$351$	2.54433e7	+	6.99050e7i	0.588373	+	1.61654i
$352$	−4.64374e7	−	4.78694e7i	−1.06473	−	1.09757i
$353$	2.70653e6	+	4.68785e6i	0.0615303	+	0.106574i	0.895150	−	0.445766i	$-0.147069\pi$
$353$	2.70653e6	+	4.68785e6i	0.0615303	+	0.106574i	−0.833619	+	0.552339i	$0.813735\pi$
$354$	−6.33931e7	+	3.48881e7i	−1.42900	+	0.786444i
$355$	1.19762e7	+	2.11172e6i	0.267690	+	0.0472010i
$356$	1.92603e7	+	7.91806e6i	0.426886	+	0.175497i
$357$	−1.68111e7	−	1.41062e7i	−0.369481	−	0.310032i
$358$	7.65266e7	+	2.96428e7i	1.66787	+	0.646055i
$359$	−2.75842e7	+	7.57869e7i	−0.596179	+	1.63799i	0.162638	+	0.986686i	$0.448000\pi$
$359$	−2.75842e7	+	7.57869e7i	−0.596179	+	1.63799i	−0.758818	+	0.651303i	$0.774223\pi$
$360$	199767.	−	3.24571e6i	0.00428170	−	0.0695668i
$361$	−1.35644e7	+	4.50480e7i	−0.288323	+	0.957533i
$362$	−8.02248e7	−	4.85361e7i	−1.69115	−	1.02315i
$363$	1.89082e7	−	5.19498e7i	0.395303	−	1.08609i
$364$	2.16282e7	+	2.80322e7i	0.448453	+	0.581236i
$365$	4.46487e6	+	3.74647e6i	0.0918184	+	0.0770448i
$366$	7.44502e6	+	4.79480e7i	0.151853	+	0.977974i
$367$	−4.41542e7	−	7.78558e6i	−0.893252	−	0.157504i	−0.291862	−	0.956460i	$-0.594275\pi$
$367$	−4.41542e7	−	7.78558e6i	−0.893252	−	0.157504i	−0.601390	+	0.798956i	$0.705386\pi$
$368$	−4.60016e7	+	2.17488e7i	−0.923058	+	0.436407i
$369$	−1.19670e7	−	2.07274e7i	−0.238180	−	0.412540i
$370$	−1.17946e7	−	2.32983e6i	−0.232851	−	0.0459959i
$371$	1.44351e7	+	3.96601e7i	0.282682	+	0.776663i
$372$	1.72919e7	−	2.73024e7i	0.335903	−	0.530362i
$373$	4.99206e6	−	8.64650e6i	0.0961952	−	0.166615i	−0.813912	−	0.580989i	$-0.802666\pi$
$373$	4.99206e6	−	8.64650e6i	0.0961952	−	0.166615i	0.910107	+	0.414374i	$0.135999\pi$
$374$	−7.27548e7	−	6.36337e7i	−1.39074	−	1.21639i
$375$	−1.54524e7	−	1.84154e7i	−0.293023	−	0.349211i
$376$	3.96456e7	+	3.76512e7i	0.745816	+	0.708298i
$377$	8.26356e6	+	4.68650e7i	0.154221	+	0.874630i
$378$	1.69526e7	+	2.10652e7i	0.313878	+	0.390023i
$379$		−	2.05787e7i		−	0.378007i	−0.981976	−	0.189003i	$-0.939474\pi$
$379$		−	2.05787e7i		−	0.378007i	0.981976	−	0.189003i	$-0.0605257\pi$
$380$	−6.53200e6	+	1.35563e7i	−0.119041	+	0.247053i
$381$	1.22698e7			0.221852
$382$	−4.45366e7	+	3.58416e7i	−0.798964	+	0.642981i
$383$	−1.45310e7	+	2.56220e6i	−0.258642	+	0.0456055i	−0.301465	−	0.953477i	$-0.597476\pi$
$383$	−1.45310e7	+	2.56220e6i	−0.258642	+	0.0456055i	0.0428236	+	0.999083i	$0.486365\pi$
$384$	−4.78708e7	+	9.98504e6i	−0.845428	+	0.176342i
$385$	8.47342e6	−	7.11005e6i	0.148483	−	0.124592i
$386$	2.68542e7	−	3.07034e7i	0.466929	−	0.533857i
$387$	1.12226e7	+	6.47936e6i	0.193624	+	0.111789i
$388$	−3.48573e7	+	5.50366e7i	−0.596758	+	0.942229i
$389$	−4.89238e7	+	1.78068e7i	−0.831135	+	0.302508i	−0.722325	−	0.691554i	$-0.756926\pi$
$389$	−4.89238e7	+	1.78068e7i	−0.831135	+	0.302508i	−0.108810	+	0.994063i	$0.534704\pi$
$390$	4.32413e6	−	2.18906e7i	0.0728962	−	0.369032i
$391$	−6.38651e7	+	3.68725e7i	−1.06840	+	0.616840i
$392$	−3.94887e7	−	2.61588e7i	−0.655563	−	0.434270i
$393$	6.59173e6	−	3.73835e7i	0.108598	−	0.615890i
$394$	8.19718e7	−	1.27280e7i	1.34022	−	0.208100i
$395$	1.09625e7	−	1.30646e7i	0.177877	−	0.211986i
$396$	1.47427e7	+	1.91079e7i	0.237407	+	0.307701i
$397$	−4.56013e7	−	1.65975e7i	−0.728796	−	0.265260i	−0.0491410	−	0.998792i	$-0.515648\pi$
$397$	−4.56013e7	−	1.65975e7i	−0.728796	−	0.265260i	−0.679655	+	0.733532i	$0.737871\pi$
$398$	−830988.	+	1.37353e6i	−0.0131809	+	0.0217866i
$399$	−7.25307e6	−	2.42971e7i	−0.114183	−	0.382503i
$400$	3.36905e7	−	4.86625e7i	0.526413	−	0.760351i
$401$	−7.13451e7	−	2.59675e7i	−1.10645	−	0.402714i	−0.276759	−	0.960939i	$-0.589260\pi$
$401$	−7.13451e7	−	2.59675e7i	−1.10645	−	0.402714i	−0.829690	+	0.558225i	$0.811483\pi$
$402$	4.58615e6	−	1.18397e7i	0.0705944	−	0.182248i
$403$	−4.85730e7	+	5.78871e7i	−0.742130	+	0.884436i
$404$	−8.62571e7	−	3.54610e7i	−1.30813	−	0.537783i
$405$	2.15510e6	−	1.22222e7i	0.0324416	−	0.183986i
$406$	8.33980e6	+	1.51538e7i	0.124617	+	0.226434i
$407$	7.72731e7	−	4.46137e7i	1.14616	−	0.661736i
$408$	−6.79608e7	+	2.01025e7i	−1.00064	+	0.295985i
$409$	−1.32964e7	+	4.83949e6i	−0.194341	+	0.0707343i	−0.437357	−	0.899288i	$-0.644085\pi$
$409$	−1.32964e7	+	4.83949e6i	−0.194341	+	0.0707343i	0.243016	+	0.970022i	$0.421863\pi$
$410$	−725821.	+	3.54180e7i	−0.0105312	+	0.513892i
$411$	7.22608e6	+	4.17198e6i	0.104082	+	0.0600920i
$412$	1.61096e7	+	5.06246e7i	0.230353	+	0.723885i
$413$	4.71098e7	−	3.95298e7i	0.668746	−	0.561144i
$414$	1.74283e7	−	5.94192e6i	0.245615	−	0.0837386i
$415$	5.28998e6	−	932766.i	0.0740133	−	0.0130505i
$416$	1.14045e8	−	8.23489e6i	1.58415	−	0.114387i
$417$	−4.26152e7			−0.587701
$418$	−2.97463e7	−	1.07647e8i	−0.407290	−	1.47391i
$419$		−	9.79005e7i		−	1.33089i	−0.746446	−	0.665446i	$-0.768242\pi$
$419$		−	9.79005e7i		−	1.33089i	0.746446	−	0.665446i	$-0.231758\pi$
$420$	−1.07995e6	−	8.03822e6i	−0.0145766	−	0.108496i
$421$	−2.14495e6	−	1.21646e7i	−0.0287456	−	0.163024i	0.967056	−	0.254564i	$-0.0819321\pi$
$421$	−2.14495e6	−	1.21646e7i	−0.0287456	−	0.163024i	−0.995801	+	0.0915402i	$0.970821\pi$
$422$	2.14105e6	−	729958.i	0.0284898	−	0.00971316i
$423$	−1.27179e7	−	1.51566e7i	−0.168033	−	0.200253i
$424$	1.32522e8	+	3.18696e7i	1.73856	+	0.418098i
$425$	4.28893e7	−	7.42864e7i	0.558705	−	0.967705i
$426$	−1.35589e6	+	6.61634e7i	−0.0175386	+	0.855833i
$427$	−1.41045e7	−	3.87519e7i	−0.181165	−	0.497747i
$428$	−1.38799e7	+	1.52282e7i	−0.177033	+	0.194230i
$429$	8.28022e7	+	1.43418e8i	1.04875	+	1.81648i
$430$	−9.24795e6	−	1.68039e7i	−0.116316	−	0.211351i
$431$	−6.01113e7	−	1.05992e7i	−0.750800	−	0.132386i	−0.214863	−	0.976644i	$-0.568930\pi$
$431$	−6.01113e7	−	1.05992e7i	−0.750800	−	0.132386i	−0.535937	+	0.844258i	$0.680042\pi$
$432$	8.69487e7	−	8.07212e6i	1.07848	−	0.100124i
$433$	3.39315e7	+	2.84719e7i	0.417965	+	0.350714i	0.827388	−	0.561630i	$-0.189826\pi$
$433$	3.39315e7	+	2.84719e7i	0.417965	+	0.350714i	−0.409424	+	0.912344i	$0.634270\pi$
$434$	−9.92094e6	+	2.56122e7i	−0.121362	+	0.313312i
$435$	3.72835e6	−	1.02436e7i	0.0452949	−	0.124447i
$436$	−5.14004e7	−	9.81030e7i	−0.620165	−	1.18365i
$437$	−8.50597e7	−	5.02187e6i	−1.01925	−	0.0601757i
$438$	−1.64181e7	+	2.71374e7i	−0.195390	+	0.322957i
$439$	−4.87655e7	+	1.33982e8i	−0.576394	+	1.58363i	0.217819	+	0.975989i	$0.430106\pi$
$439$	−4.87655e7	+	1.33982e8i	−0.576394	+	1.58363i	−0.794213	+	0.607640i	$0.792117\pi$
$440$	−4.03020e6	−	3.54937e7i	−0.0473117	−	0.416672i
$441$	1.31306e7	+	1.10179e7i	0.153098	+	0.128465i
$442$	1.63752e8	−	2.54262e7i	1.89635	−	0.294452i
$443$	7.01840e7	+	1.23753e7i	0.807285	+	0.142346i	0.562035	−	0.827114i	$-0.310019\pi$
$443$	7.01840e7	+	1.23753e7i	0.807285	+	0.142346i	0.245250	+	0.969460i	$0.421130\pi$
$444$	2.68035e6	−	6.53692e7i	0.0306226	−	0.746834i
$445$	5.57695e6	+	9.65956e6i	0.0632873	+	0.109617i
$446$	−2.57663e7	+	1.30440e8i	−0.290434	+	1.47030i
$447$	2.42453e7	+	6.66134e7i	0.271459	+	0.745829i
$448$	3.82691e7	−	1.62096e7i	0.425613	−	0.180276i
$449$	2.73555e6	−	4.73811e6i	0.0302208	−	0.0523439i	−0.850519	−	0.525944i	$-0.823712\pi$
$449$	2.73555e6	−	4.73811e6i	0.0302208	−	0.0523439i	0.880740	+	0.473600i	$0.157046\pi$
$450$	−1.41006e7	+	1.61217e7i	−0.154739	+	0.176918i
$451$	−1.68999e8	−	2.01406e8i	−1.84228	−	2.19554i
$452$	−2.10013e7	+	9.59343e7i	−0.227421	+	1.03886i
$453$	4.73928e6	+	2.68778e7i	0.0509821	+	0.289134i
$454$	−1.09626e8	+	8.82236e7i	−1.17151	+	0.942795i
$455$			1.89641e7i			0.201325i
$456$	−7.83510e7	−	2.38060e7i	−0.826323	−	0.251068i
$457$	−1.03224e8			−1.08151			−0.540757	−	0.841179i	$-0.681862\pi$
$457$	−1.03224e8			−1.08151			−0.540757	+	0.841179i	$0.681862\pi$
$458$	−2.92090e7	−	3.62950e7i	−0.304033	−	0.377790i
$459$	1.24633e8	−	2.19761e7i	1.28883	−	0.227255i
$460$	−2.66238e7	−	5.82829e6i	−0.273524	−	0.0598780i
$461$	−4.90852e7	+	4.11873e7i	−0.501011	+	0.420398i	−0.857953	−	0.513728i	$-0.828264\pi$
$461$	−4.90852e7	+	4.11873e7i	−0.501011	+	0.420398i	0.356942	+	0.934127i	$0.383819\pi$
$462$	4.53083e7	+	3.96281e7i	0.459464	+	0.401862i
$463$	−7.87920e7	−	4.54906e7i	−0.793851	−	0.458330i	0.0474656	−	0.998873i	$-0.484886\pi$
$463$	−7.87920e7	−	4.54906e7i	−0.793851	−	0.458330i	−0.841316	+	0.540543i	$0.818219\pi$
$464$	5.56725e7	+	4.57320e6i	0.557297	+	0.0457790i
$465$	1.62660e7	−	5.92035e6i	0.161779	−	0.0588828i
$466$	8.17681e7	+	1.61520e7i	0.808028	+	0.159613i
$467$	7.11132e7	−	4.10572e7i	0.698232	−	0.403124i	−0.108457	−	0.994101i	$-0.534591\pi$
$467$	7.11132e7	−	4.10572e7i	0.698232	−	0.403124i	0.806688	+	0.590977i	$0.201258\pi$
$468$	−4.13425e7	−	1.69517e6i	−0.403328	−	0.0165378i
$469$	−1.87384e6	+	1.06271e7i	−0.0181641	+	0.103014i
$470$	4.49334e6	+	2.89383e7i	0.0432789	+	0.278728i
$471$	4.19069e7	−	4.99427e7i	0.401073	−	0.477980i
$472$	−2.24068e7	−	1.97335e8i	−0.213085	−	1.87663i
$473$	1.33767e8	+	4.86874e7i	1.26406	+	0.460080i
$474$	7.94066e7	+	4.80411e7i	0.745627	+	0.451105i
$475$	8.86049e7	−	4.44111e7i	0.826755	−	0.414391i
$476$	5.33534e7	−	2.79542e7i	0.494699	−	0.259195i
$477$	−4.63488e7	−	1.68696e7i	−0.427054	−	0.155435i
$478$	−6.63430e7	−	2.56981e7i	−0.607452	−	0.235298i
$479$	−1.15118e8	+	1.37193e8i	−1.04746	+	1.24831i	−0.0795995	+	0.996827i	$0.525364\pi$
$479$	−1.15118e8	+	1.37193e8i	−1.04746	+	1.24831i	−0.967861	+	0.251487i	$0.919080\pi$
$480$	−2.35675e7	−	1.14285e7i	−0.213103	−	0.103339i
$481$	−2.65641e7	+	1.50653e8i	−0.238704	+	1.35376i
$482$	3.49932e7	−	1.92584e7i	0.312495	−	0.171980i
$483$	3.97721e7	−	2.29625e7i	0.352970	−	0.203787i
$484$	1.12143e8	+	1.02214e8i	0.989094	+	0.901522i
$485$	−3.27893e7	+	1.19343e7i	−0.287413	+	0.104610i
$486$	−5.67837e7	−	1.16367e6i	−0.494669	−	0.0101373i
$487$	9.16172e7	+	5.28952e7i	0.793214	+	0.457962i	0.841093	−	0.540891i	$-0.181913\pi$
$487$	9.16172e7	+	5.28952e7i	0.793214	+	0.457962i	−0.0478789	+	0.998853i	$0.515246\pi$
$488$	−1.29487e8	−	3.11397e7i	−1.11421	−	0.267951i
$489$	4.86941e7	−	4.08592e7i	0.416437	−	0.349432i
$490$	−8.18699e6	−	2.40134e7i	−0.0695883	−	0.204111i
$491$	−5.70375e7	+	1.00573e7i	−0.481855	+	0.0849640i	−0.409299	−	0.912400i	$-0.634227\pi$
$491$	−5.70375e7	+	1.00573e7i	−0.481855	+	0.0849640i	−0.0725558	+	0.997364i	$0.523116\pi$
$492$	−1.91061e8	+	2.56695e7i	−1.60427	+	0.215538i
$493$	8.09571e7			0.675638
$494$	1.74159e8	+	7.95628e7i	1.44466	+	0.659978i
$495$			1.29267e7i			0.106579i
$496$	5.12620e7	+	7.23892e7i	0.420098	+	0.593238i
$497$	−9.76658e6	−	5.53890e7i	−0.0795561	−	0.451185i
$498$	9.43274e6	+	2.76673e7i	0.0763748	+	0.224016i
$499$	−8.37312e7	−	9.97870e7i	−0.673885	−	0.803105i	0.315422	−	0.948951i	$-0.397854\pi$
$499$	−8.37312e7	−	9.97870e7i	−0.673885	−	0.803105i	−0.989307	+	0.145847i	$0.953409\pi$
$500$	6.28745e7	−	2.00078e7i	0.502996	−	0.160062i
$501$	−3.28501e6	+	5.68980e6i	−0.0261230	+	0.0452464i
$502$	1.29039e8	+	2.64440e6i	1.02002	+	0.0209034i
$503$	−1.08619e7	−	2.98429e7i	−0.0853498	−	0.234497i	0.889674	−	0.456596i	$-0.150931\pi$
$503$	−1.08619e7	−	2.98429e7i	−0.0853498	−	0.234497i	−0.975024	+	0.222099i	$0.928709\pi$
$504$	−1.44219e7	+	4.26594e6i	−0.112650	+	0.0333214i
$505$	−2.49764e7	−	4.32603e7i	−0.193935	−	0.335905i
$506$	1.77209e8	−	9.75260e7i	1.36783	−	0.752781i
$507$	−1.68768e8	−	2.97583e7i	−1.29499	−	0.228342i
$508$	−1.28050e7	+	3.11474e7i	−0.0976759	+	0.237591i
$509$	−1.77284e8	−	1.48759e8i	−1.34436	−	1.12805i	−0.980483	−	0.196606i	$-0.937008\pi$
$509$	−1.77284e8	−	1.48759e8i	−1.34436	−	1.12805i	−0.363878	−	0.931447i	$-0.618547\pi$
$510$	−3.53973e7	−	1.37112e7i	−0.266846	−	0.103363i
$511$	9.21960e6	−	2.53306e7i	0.0690954	−	0.189838i
$512$	2.46112e7	−	1.31942e8i	0.183368	−	0.983044i
$513$	1.34222e8	+	5.80240e7i	0.994195	+	0.429790i
$514$	8.42538e7	+	5.09737e7i	0.620441	+	0.375367i
$515$	−9.73227e6	+	2.67392e7i	−0.0712512	+	0.195761i
$516$	8.26389e7	−	6.37601e7i	0.601500	−	0.464088i
$517$	−1.66496e8	−	1.39707e8i	−1.20485	−	1.01099i
$518$	8.53146e6	+	5.49449e7i	0.0613810	+	0.395310i
$519$	−4.74261e7	−	8.36250e6i	−0.339247	−	0.0598183i
$520$	5.10572e7	+	3.38222e7i	0.363117	+	0.240543i
$521$	−1.87785e7	−	3.25254e7i	−0.132785	−	0.229990i	0.791964	−	0.610568i	$-0.209059\pi$
$521$	−1.87785e7	−	3.25254e7i	−0.132785	−	0.229990i	−0.924749	+	0.380577i	$0.875725\pi$
$522$	−1.98310e7	−	3.91729e6i	−0.139423	−	0.0275407i
$523$	−6.39735e7	−	1.75766e8i	−0.447193	−	1.22865i	−0.934670	−	0.355517i	$-0.884305\pi$
$523$	−6.39735e7	−	1.75766e8i	−0.447193	−	1.22865i	0.487477	−	0.873136i	$-0.337917\pi$
$524$	8.80201e7	+	5.57473e7i	0.611770	+	0.387462i
$525$	−2.67094e7	+	4.62621e7i	−0.184581	+	0.319703i
$526$	−5.40397e7	−	4.72649e7i	−0.371326	−	0.324774i
$527$	8.26330e7	+	9.84782e7i	0.564575	+	0.672834i
$528$	1.87498e8	−	5.13077e7i	1.27378	−	0.348562i
$529$	−1.09218e6	−	6.19407e6i	−0.00737781	−	0.0418416i
$530$	4.57710e7	+	5.68748e7i	0.307442	+	0.382025i
$531$			7.18690e7i			0.480019i
$532$	6.92483e7	+	6.94458e6i	0.459911	+	0.0461223i
$533$	4.50760e8			2.97689
$534$	−4.72865e7	+	3.80546e7i	−0.310537	+	0.249910i
$535$	−1.08685e7	+	1.91641e6i	−0.0709756	+	0.0125149i
$536$	2.52694e7	+	2.39982e7i	0.164097	+	0.155842i
$537$	−1.83240e8	+	1.53757e8i	−1.18331	+	0.992915i
$538$	−5.26929e7	+	6.02458e7i	−0.338381	+	0.386883i
$539$	1.63067e8	+	9.41466e7i	1.04136	+	0.601227i
$540$	3.95133e7	+	2.50256e7i	0.250935	+	0.158929i
$541$	−6.60585e7	+	2.40433e7i	−0.417193	+	0.151846i	−0.542083	−	0.840325i	$-0.682364\pi$
$541$	−6.60585e7	+	2.40433e7i	−0.417193	+	0.151846i	0.124890	+	0.992171i	$0.460142\pi$
$542$	−4.94735e6	+	2.50456e7i	−0.0310724	+	0.157302i
$543$	2.36683e8	−	1.36649e8i	1.47832	−	0.853507i
$544$	1.98938e7	−	1.93500e8i	0.123573	−	1.20194i
$545$	1.03010e7	−	5.84200e7i	0.0636343	−	0.360888i
$546$	−1.01977e8	+	1.58342e7i	−0.626504	+	0.0972791i
$547$	1.02473e8	−	1.22122e8i	0.626103	−	0.746161i	−0.356004	−	0.934485i	$-0.615861\pi$
$547$	1.02473e8	−	1.22122e8i	0.626103	−	0.746161i	0.982107	+	0.188324i	$0.0603054\pi$
$548$	−1.81319e7	+	1.39897e7i	−0.110180	+	0.0850094i
$549$	4.52873e7	+	1.64832e7i	0.273691	+	0.0996152i
$550$	−1.21790e8	+	2.01305e8i	−0.732019	+	1.20995i
$551$	7.81116e7	+	5.14636e7i	0.466940	+	0.307642i
$552$	9.11107e6	−	1.48032e8i	0.0541692	−	0.880114i
$553$	−7.41200e7	−	2.69775e7i	−0.438288	−	0.159524i
$554$	−6.07820e7	+	1.56917e8i	−0.357475	+	0.922868i
$555$	2.25248e7	−	2.68440e7i	0.131759	−	0.157025i
$556$	4.44738e7	−	1.08180e8i	0.258749	−	0.629394i
$557$	−7.69637e6	+	4.36483e7i	−0.0445369	+	0.252582i	−0.998945	−	0.0459237i	$-0.985377\pi$
$557$	−7.69637e6	+	4.36483e7i	−0.0445369	+	0.252582i	0.954408	+	0.298505i	$0.0964880\pi$
$558$	−1.54764e7	−	2.81213e7i	−0.0890776	−	0.161857i
$559$	−2.11360e8	+	1.22029e8i	−1.21001	+	0.698597i
$560$	2.15323e7	+	5.64730e6i	0.122610	+	0.0321571i
$561$	2.64738e8	−	9.63567e7i	1.49943	−	0.545749i
$562$	1.34671e6	−	6.57154e7i	0.00758690	−	0.370219i
$563$	−2.15947e8	−	1.24677e8i	−1.21010	−	0.698653i	−0.247321	−	0.968933i	$-0.579550\pi$
$563$	−2.15947e8	−	1.24677e8i	−1.21010	−	0.698653i	−0.962782	+	0.270280i	$0.912884\pi$
$564$	−1.51860e8	+	4.83247e7i	−0.846461	+	0.269359i
$565$	−4.02947e7	+	3.38113e7i	−0.223410	+	0.187463i
$566$	1.21050e8	−	4.12702e7i	0.667601	−	0.227608i
$567$	−5.65269e7	+	9.96721e6i	−0.310103	+	0.0546795i
$568$	−1.66543e8	−	7.24910e7i	−0.908827	−	0.395584i
$569$	−3.53328e8			−1.91797			−0.958984	−	0.283459i	$-0.908518\pi$
$569$	−3.53328e8			−1.91797			−0.958984	+	0.283459i	$0.908518\pi$
$570$	−2.54371e7	−	3.57310e7i	−0.137354	−	0.192939i
$571$			1.52193e8i			0.817496i	0.912647	+	0.408748i	$0.134035\pi$
$571$			1.52193e8i			0.817496i	−0.912647	+	0.408748i	$0.865965\pi$
$572$	−4.50484e8	+	6.05236e7i	−2.40708	+	0.323397i
$573$	−2.89347e7	−	1.64097e8i	−0.153799	−	0.872239i
$574$	1.55075e8	−	5.28705e7i	0.819987	−	0.279562i
$575$	1.15386e8	+	1.37511e8i	0.606943	+	0.723327i
$576$	−1.42361e7	+	4.64365e7i	−0.0744942	+	0.242992i
$577$	1.36786e8	−	2.36921e8i	0.712058	−	1.23332i	−0.252025	−	0.967721i	$-0.581097\pi$
$577$	1.36786e8	−	2.36921e8i	0.712058	−	1.23332i	0.964083	−	0.265600i	$-0.0855700\pi$
$578$	1.81969e6	−	8.87954e7i	0.00942351	−	0.459840i
$579$	4.06637e7	+	1.11723e8i	0.209494	+	0.575580i
$580$	2.21126e7	+	2.01548e7i	0.113333	+	0.103299i
$581$	−1.24216e7	−	2.15149e7i	−0.0633359	−	0.109701i
$582$	−9.15529e7	−	1.66355e8i	−0.464412	−	0.843854i
$583$	−5.33589e8	−	9.40861e7i	−2.69278	−	0.474810i
$584$	−5.17549e7	−	6.99989e7i	−0.259844	−	0.351441i
$585$	−1.69774e7	−	1.42457e7i	−0.0848014	−	0.0711568i
$586$	−3.42558e7	+	8.84358e7i	−0.170232	+	0.439476i
$587$	1.36605e7	−	3.75320e7i	0.0675388	−	0.185561i	−0.901332	−	0.433130i	$-0.857409\pi$
$587$	1.36605e7	−	3.75320e7i	0.0675388	−	0.185561i	0.968870	+	0.247568i	$0.0796315\pi$
$588$	1.22293e8	−	6.40747e7i	0.601547	−	0.315177i
$589$	1.71270e7	+	1.47546e8i	0.0838176	+	0.722072i
$590$	5.50641e7	−	9.10148e7i	0.268110	−	0.443155i
$591$	−8.26966e7	+	2.27207e8i	−0.400613	+	1.10068i
$592$	1.63144e8	+	7.50242e7i	0.786334	+	0.361607i
$593$	2.54392e7	+	2.13460e7i	0.121994	+	0.102365i	0.701744	−	0.712429i	$-0.252405\pi$
$593$	2.54392e7	+	2.13460e7i	0.121994	+	0.102365i	−0.579750	+	0.814795i	$0.696850\pi$
$594$	−3.43014e8	+	5.32608e7i	−1.63664	+	0.254125i
$595$	3.17718e7	+	5.60223e6i	0.150831	+	0.0265956i
$596$	−1.94403e8	−	7.97115e6i	−0.918256	−	0.0376515i
$597$	−2.33957e6	−	4.05225e6i	−0.0109955	−	0.0190447i
$598$	−6.72038e7	+	3.40214e8i	−0.314261	+	1.59092i
$599$	5.50991e7	+	1.51384e8i	0.256368	+	0.704366i	0.999384	+	0.0350922i	$0.0111725\pi$
$599$	5.50991e7	+	1.51384e8i	0.256368	+	0.704366i	−0.743016	+	0.669274i	$0.766605\pi$
$600$	7.69159e7	+	1.54418e8i	0.356092	+	0.714898i
$601$	−8.82073e7	+	1.52780e8i	−0.406332	+	0.703788i	−0.994476	−	0.104969i	$-0.966526\pi$
$601$	−8.82073e7	+	1.52780e8i	−0.406332	+	0.703788i	0.588143	+	0.808757i	$0.299859\pi$
$602$	−5.84014e7	+	6.67725e7i	−0.267691	+	0.306061i
$603$	−8.10613e6	−	9.66051e6i	−0.0369710	−	0.0440604i
$604$	−7.31762e7	−	1.60192e7i	−0.332092	−	0.0726993i
$605$	1.41129e7	+	8.00381e7i	0.0637308	+	0.361435i
$606$	2.11772e8	−	1.70428e8i	0.951594	−	0.765812i
$607$			3.59284e7i			0.160647i	0.996769	+	0.0803234i	$0.0255953\pi$
$607$			3.59284e7i			0.160647i	−0.996769	+	0.0803234i	$0.974405\pi$
$608$	1.42200e8	−	1.74052e8i	0.632689	−	0.774406i
$609$	−5.04163e7			−0.223213
$610$	−4.47228e7	−	5.55723e7i	−0.197033	−	0.244832i
$611$	3.66968e8	−	6.47064e7i	1.60881	−	0.283677i
$612$	−1.50531e7	+	6.87630e7i	−0.0656707	+	0.299986i
$613$	3.20170e7	−	2.68654e7i	0.138995	−	0.116631i	−0.570639	−	0.821201i	$-0.693305\pi$
$613$	3.20170e7	−	2.68654e7i	0.138995	−	0.116631i	0.709634	+	0.704570i	$0.248860\pi$
$614$	−1.45098e8	−	1.26908e8i	−0.626842	−	0.548256i
$615$	−8.94218e7	−	5.16277e7i	−0.384431	−	0.221951i
$616$	−1.47881e8	+	7.36601e7i	−0.632662	+	0.315130i
$617$	1.20943e8	−	4.40197e7i	0.514903	−	0.187409i	−0.0714821	−	0.997442i	$-0.522773\pi$
$617$	1.20943e8	−	4.40197e7i	0.514903	−	0.187409i	0.586385	+	0.810033i	$0.300551\pi$
$618$	−1.51912e8	−	3.00078e7i	−0.643617	−	0.127136i
$619$	2.23569e8	−	1.29078e8i	0.942628	−	0.544226i	0.0518447	−	0.998655i	$-0.483490\pi$
$619$	2.23569e8	−	1.29078e8i	0.942628	−	0.544226i	0.890783	+	0.454429i	$0.150157\pi$
$620$	−1.94644e6	+	4.74704e7i	−0.00816706	+	0.199181i
$621$	−4.59892e7	+	2.60818e8i	−0.192035	+	1.08909i
$622$	−4.37819e7	−	2.81968e8i	−0.181938	−	1.17173i
$623$	3.31589e7	−	3.95172e7i	0.137131	−	0.163426i
$624$	−1.39244e8	+	3.02793e8i	−0.573089	+	1.24621i
$625$	−1.78954e8	−	6.51340e7i	−0.732997	−	0.266789i
$626$	6.62134e7	+	4.00592e7i	0.269913	+	0.163298i
$627$	3.16686e8	+	7.53212e7i	1.28477	+	0.305573i
$628$	8.30466e7	+	1.58503e8i	0.335307	+	0.639968i
$629$	2.44551e8	+	8.90092e7i	0.982692	+	0.357671i
$630$	−7.51165e6	−	2.90966e6i	−0.0300409	−	0.0116364i
$631$	−7.05540e7	+	8.40830e7i	−0.280824	+	0.334673i	−0.887956	−	0.459928i	$-0.847875\pi$
$631$	−7.05540e7	+	8.40830e7i	−0.280824	+	0.334673i	0.607133	+	0.794601i	$0.292320\pi$
$632$	−2.04824e8	+	1.51440e8i	−0.811389	+	0.599914i
$633$	−1.14492e6	+	6.49314e6i	−0.00451401	+	0.0256002i
$634$	−1.93494e8	+	1.06489e8i	−0.759276	+	0.417864i
$635$	−1.56213e7	+	9.01896e6i	−0.0610093	+	0.0352237i
$636$	−2.67620e8	+	2.93616e8i	−1.04027	+	1.14132i
$637$	−3.03353e8	+	1.10411e8i	−1.17363	+	0.427165i
$638$	−2.22008e8	−	4.54961e6i	−0.854882	−	0.0175191i
$639$	5.69229e7	+	3.28645e7i	0.218165	+	0.125957i
$640$	5.36069e7	−	4.78998e7i	0.204494	−	0.182723i
$641$	2.90858e8	−	2.44059e8i	1.10435	−	0.926659i	0.106639	−	0.994298i	$-0.465991\pi$
$641$	2.90858e8	−	2.44059e8i	1.10435	−	0.926659i	0.997710	+	0.0676388i	$0.0215466\pi$
$642$	−1.93800e7	−	5.68439e7i	−0.0732402	−	0.214822i
$643$	5.13013e7	−	9.04580e6i	0.192972	−	0.0340262i	−0.0763266	−	0.997083i	$-0.524319\pi$
$643$	5.13013e7	−	9.04580e6i	0.192972	−	0.0340262i	0.269299	+	0.963057i	$0.413208\pi$
$644$	1.67842e7	+	1.24927e8i	0.0628410	+	0.467733i
$645$	5.59062e7			0.208344
$646$	1.84746e8	−	2.68277e8i	0.685293	−	0.995143i
$647$		−	2.25019e8i		−	0.830817i	−0.909635	−	0.415409i	$-0.863639\pi$
$647$		−	2.25019e8i		−	0.830817i	0.909635	−	0.415409i	$-0.136361\pi$
$648$	−7.39801e7	+	1.69964e8i	−0.271888	+	0.624644i
$649$	1.37093e8	+	7.77492e8i	0.501511	+	2.84421i
$650$	−1.30168e8	−	3.81797e8i	−0.473984	−	1.39025i
$651$	−5.14599e7	−	6.13275e7i	−0.186520	−	0.222286i
$652$	5.29046e7	+	1.66253e8i	0.190876	+	0.599827i
$653$	−1.58376e7	+	2.74315e7i	−0.0568786	+	0.0985167i	−0.893063	−	0.449932i	$-0.851448\pi$
$653$	−1.58376e7	+	2.74315e7i	−0.0568786	+	0.0985167i	0.836184	+	0.548449i	$0.184781\pi$
$654$	3.22747e8	+	6.61405e6i	1.15380	+	0.0236447i
$655$	1.90866e7	+	5.24399e7i	0.0679210	+	0.186611i
$656$	1.34231e8	−	5.11804e8i	0.475490	−	1.81298i
$657$	1.57512e7	+	2.72819e7i	0.0555416	+	0.0962009i
$658$	1.18659e8	−	6.53035e7i	0.416507	−	0.229223i
$659$	2.75150e8	+	4.85163e7i	0.961419	+	0.169524i	0.632265	−	0.774752i	$-0.282125\pi$
$659$	2.75150e8	+	4.85163e7i	0.961419	+	0.169524i	0.329154	+	0.944276i	$0.393237\pi$
$660$	9.62992e7	+	3.95894e7i	0.334958	+	0.137704i
$661$	2.28905e8	+	1.92074e8i	0.792596	+	0.665067i	0.946386	−	0.323037i	$-0.104704\pi$
$661$	2.28905e8	+	1.92074e8i	0.792596	+	0.665067i	−0.153791	+	0.988103i	$0.549148\pi$
$662$	−3.14549e8	−	1.21841e8i	−1.08421	−	0.419972i
$663$	−1.65200e8	+	4.53882e8i	−0.566851	+	1.55741i
$664$	−8.00785e7	−	4.92867e6i	−0.273534	−	0.0168355i
$665$	2.70938e7	+	2.56023e7i	0.0921308	+	0.0870592i
$666$	−5.55975e7	−	3.36366e7i	−0.188206	−	0.113865i
$667$	−5.79445e7	+	1.59201e8i	−0.195269	+	0.536498i
$668$	−1.10155e7	−	1.42770e7i	−0.0369550	−	0.0478971i
$669$	−2.96876e8	−	2.49108e8i	−0.991508	−	0.831974i
$670$	2.86397e6	+	1.84448e7i	0.00952235	+	0.0613265i
$671$	5.21369e8	+	9.19314e7i	1.72575	+	0.304296i
$672$	−1.23889e7	+	1.20503e8i	−0.0408250	+	0.397089i
$673$	1.16639e8	+	2.02025e8i	0.382647	+	0.662765i	0.991440	−	0.130565i	$-0.0416791\pi$
$673$	1.16639e8	+	2.02025e8i	0.382647	+	0.662765i	−0.608792	+	0.793330i	$0.708346\pi$
$674$	3.99076e8	+	7.88310e7i	1.30340	+	0.257465i
$675$	−1.05362e8	−	2.89479e8i	−0.342588	−	0.941253i
$676$	2.51671e8	−	3.97367e8i	0.814691	−	1.28633i
$677$	1.38214e8	−	2.39393e8i	0.445436	−	0.771518i	−0.552646	−	0.833416i	$-0.686382\pi$
$677$	1.38214e8	−	2.39393e8i	0.445436	−	0.771518i	0.998083	+	0.0618976i	$0.0197152\pi$
$678$	−2.15460e8	−	1.88448e8i	−0.691318	−	0.604649i
$679$	1.03734e8	+	1.23625e8i	0.331367	+	0.394908i
$680$	7.17475e7	−	7.55480e7i	0.228181	−	0.240268i
$681$	−7.12221e7	−	4.03921e8i	−0.225514	−	1.27895i
$682$	−2.21069e8	−	2.74699e8i	−0.696908	−	0.865973i
$683$		−	5.11706e7i		−	0.160605i	−0.996771	−	0.0803024i	$-0.974411\pi$
$683$		−	5.11706e7i		−	0.160605i	0.996771	−	0.0803024i	$-0.0255886\pi$
$684$	−5.82359e7	+	5.67769e7i	−0.181980	+	0.177420i
$685$	−1.22665e7			−0.0381635
$686$	−2.07661e8	+	1.67119e8i	−0.643253	+	0.517670i
$687$	1.33730e8	−	2.35802e7i	0.412438	−	0.0727239i
$688$	7.56140e7	+	2.76322e8i	0.232187	+	0.848498i
$689$	7.11601e8	−	5.97104e8i	2.17560	−	1.82554i
$690$	5.22983e7	−	5.97946e7i	0.159199	−	0.182018i
$691$	−5.05829e8	−	2.92040e8i	−1.53310	−	0.885133i	−0.999217	−	0.0395719i	$-0.987401\pi$
$691$	−5.05829e8	−	2.92040e8i	−1.53310	−	0.885133i	−0.533879	−	0.845561i	$-0.679266\pi$
$692$	7.07230e7	−	1.11665e8i	0.213424	−	0.336977i
$693$	5.61799e7	−	2.04478e7i	0.168803	−	0.0614394i
$694$	4.02891e6	−	2.03960e7i	0.0120534	−	0.0610193i
$695$	5.42553e7	−	3.13243e7i	0.161617	−	0.0933098i
$696$	−8.99168e7	+	1.35736e8i	−0.266694	+	0.402595i
$697$	1.33160e8	−	7.55187e8i	0.393256	−	2.23026i
$698$	−3.27094e8	+	5.07888e7i	−0.961848	+	0.149349i
$699$	−1.56157e8	+	1.86101e8i	−0.457225	+	0.544900i
$700$	−8.95635e7	−	1.16082e8i	−0.261118	−	0.338433i
$701$	−3.97515e8	−	1.44684e8i	−1.15398	−	0.420015i	−0.307038	−	0.951697i	$-0.599338\pi$
$701$	−3.97515e8	−	1.44684e8i	−1.15398	−	0.420015i	−0.846944	+	0.531682i	$0.821560\pi$
$702$	3.08063e8	−	5.09193e8i	0.890487	−	1.47188i
$703$	1.79373e8	+	2.41339e8i	0.516287	+	0.694643i
$704$	−6.54289e7	+	5.29514e8i	−0.187522	+	1.51761i
$705$	−8.02105e7	−	2.91942e7i	−0.228909	−	0.0833162i
$706$	1.56417e7	−	4.03809e7i	0.0444497	−	0.114753i
$707$	−1.48502e8	+	1.76978e8i	−0.420218	+	0.500796i
$708$	5.35396e8	+	2.20106e8i	1.50860	+	0.620201i
$709$	−3.75259e7	+	2.12820e8i	−0.105291	+	0.597137i	0.885812	+	0.464044i	$0.153602\pi$
$709$	−3.75259e7	+	2.12820e8i	−0.105291	+	0.597137i	−0.991104	+	0.133093i	$0.957509\pi$
$710$	−4.69072e7	−	8.52323e7i	−0.131058	−	0.238138i
$711$	7.98296e7	−	4.60897e7i	0.222104	−	0.128232i
$712$	−4.72541e7	−	1.59752e8i	−0.130918	−	0.442596i
$713$	−2.52800e8	+	9.20116e7i	−0.697442	+	0.253848i
$714$	−3.59706e6	+	1.75526e8i	−0.00988219	+	0.482222i
$715$	−2.10838e8	−	1.21728e8i	−0.576809	−	0.333021i
$716$	−1.99085e8	−	6.25624e8i	−0.542374	−	1.70441i
$717$	1.58856e8	−	1.33296e8i	0.430970	−	0.361627i
$718$	6.10689e8	−	2.08205e8i	1.64986	−	0.562494i
$719$	−2.47642e8	+	4.36660e7i	−0.666251	+	0.117478i	−0.496537	−	0.868015i	$-0.665395\pi$
$719$	−2.47642e8	+	4.36660e7i	−0.666251	+	0.117478i	−0.169714	+	0.985493i	$0.554284\pi$
$720$	−2.12306e7	+	1.50343e7i	−0.0568807	+	0.0402798i
$721$	1.31604e8			0.351125
$722$	3.48793e8	−	1.41406e8i	0.926736	−	0.375714i
$723$			1.16422e8i			0.308049i
$724$	9.98824e7	+	7.43436e8i	0.263192	+	1.95897i
$725$	−3.42197e7	−	1.94070e8i	−0.0897972	−	0.509265i
$726$	−4.18610e8	+	1.42719e8i	−1.09396	+	0.372967i
$727$	−2.59228e7	−	3.08936e7i	−0.0674650	−	0.0804017i	0.731256	−	0.682103i	$-0.238934\pi$
$727$	−2.59228e7	−	3.08936e7i	−0.0674650	−	0.0804017i	−0.798721	+	0.601701i	$0.794490\pi$
$728$	6.62286e7	−	2.75396e8i	0.171653	−	0.713780i
$729$	2.14737e8	−	3.71936e8i	0.554274	−	0.960031i
$730$	955342.	−	4.66180e7i	0.00245579	−	0.119835i
$731$	1.42004e8	+	3.90154e8i	0.363538	+	0.998813i
$732$	2.61491e8	−	2.86891e8i	0.666689	−	0.731449i
$733$	−1.18055e8	−	2.04478e8i	−0.299760	−	0.519200i	0.676321	−	0.736607i	$-0.263573\pi$
$733$	−1.18055e8	−	2.04478e8i	−0.299760	−	0.519200i	−0.976081	+	0.217407i	$0.930240\pi$
$734$	1.72939e8	+	3.14238e8i	0.437327	+	0.794640i
$735$	7.28252e7	+	1.28410e7i	0.183409	+	0.0323399i
$736$	3.66276e8	+	1.77617e8i	0.918702	+	0.445503i
$737$	−1.06121e8	−	8.90464e7i	−0.265094	−	0.222441i
$738$	−6.91599e7	+	1.78545e8i	−0.172062	+	0.444200i
$739$	2.13690e8	−	5.87109e8i	0.529482	−	1.45474i	−0.330200	−	0.943911i	$-0.607116\pi$
$739$	2.13690e8	−	5.87109e8i	0.529482	−	1.45474i	0.859682	−	0.510829i	$-0.170662\pi$
$740$	4.46372e7	+	8.51946e7i	0.110154	+	0.210241i
$741$	−4.47921e8	+	3.32913e8i	−1.10090	+	0.818232i
$742$	1.74777e8	−	2.88887e8i	0.427832	−	0.707159i
$743$	−1.10769e7	+	3.04336e7i	−0.0270055	+	0.0741971i	−0.952463	−	0.304655i	$-0.901459\pi$
$743$	−1.10769e7	+	3.04336e7i	−0.0270055	+	0.0741971i	0.925457	+	0.378852i	$0.123681\pi$
$744$	−2.56891e8	+	2.91691e7i	−0.623778	+	0.0708279i
$745$	−7.98320e7	−	6.69870e7i	−0.193067	−	0.162002i
$746$	−7.89272e7	+	1.22553e7i	−0.190112	+	0.0295193i
$747$	2.85920e7	+	5.04154e6i	0.0685934	+	0.0120949i
$748$	−3.16793e7	+	7.72604e8i	−0.0756956	+	1.84609i
$749$	2.55208e7	+	4.42034e7i	0.0607365	+	0.105199i
$750$	−3.72690e7	+	1.88671e8i	−0.0883413	+	0.447221i
$751$	−3.05731e7	−	8.39989e7i	−0.0721804	−	0.198314i	0.898356	−	0.439268i	$-0.144762\pi$
$751$	−3.05731e7	−	8.39989e7i	−0.0721804	−	0.198314i	−0.970537	+	0.240954i	$0.922540\pi$
$752$	3.58096e7	−	4.35934e8i	0.0842067	−	1.02510i
$753$	−1.88097e8	+	3.25793e8i	−0.440551	+	0.763057i
$754$	2.50635e8	−	2.86561e8i	0.584694	−	0.668502i
$755$	−2.57903e7	−	3.07357e7i	−0.0599261	−	0.0714172i
$756$	4.62588e7	−	2.11312e8i	0.107061	−	0.489055i
$757$	1.36660e8	+	7.75039e8i	0.315032	+	1.78663i	0.572040	+	0.820226i	$0.306152\pi$
$757$	1.36660e8	+	7.75039e8i	0.315032	+	1.78663i	−0.257008	+	0.966409i	$0.582737\pi$
$758$	−1.28255e8	+	1.03216e8i	−0.294488	+	0.236994i
$759$			5.89570e8i			1.34837i
$760$	1.17251e8	−	2.72834e7i	0.267101	−	0.0621525i
$761$	−3.39622e8			−0.770623			−0.385312	−	0.922786i	$-0.625906\pi$
$761$	−3.39622e8			−0.770623			−0.385312	+	0.922786i	$0.625906\pi$
$762$	−6.15414e7	−	7.64709e7i	−0.139092	−	0.172835i
$763$	−2.70189e8	+	4.76416e7i	−0.608267	+	0.107254i
$764$	4.46761e8	+	9.78018e7i	1.00183	+	0.219314i
$765$	−2.88821e7	+	2.42350e7i	−0.0645126	+	0.0541325i
$766$	8.88512e7	+	7.77122e7i	0.197687	+	0.172903i
$767$	−1.17220e9	−	6.76771e8i	−2.59786	−	1.49988i
$768$	3.02335e8	+	2.48270e8i	0.667427	+	0.548075i
$769$	1.49038e8	−	5.42455e7i	0.327732	−	0.119285i	−0.172914	−	0.984937i	$-0.555318\pi$
$769$	1.49038e8	−	5.42455e7i	0.327732	−	0.119285i	0.500646	+	0.865652i	$0.333096\pi$
$770$	−8.68126e7	−	1.71484e7i	−0.190156	−	0.0375623i
$771$	−2.48570e8	+	1.43512e8i	−0.542356	+	0.313130i
$772$	−3.26049e8	−	1.33691e7i	−0.708648	−	0.0290569i
$773$	2.70373e7	−	1.53336e8i	0.0585361	−	0.331975i	−0.941450	−	0.337151i	$-0.890537\pi$
$773$	2.70373e7	−	1.53336e8i	0.0585361	−	0.331975i	0.999987	+	0.00517640i	$0.00164771\pi$
$774$	−1.59065e7	−	1.02442e8i	−0.0343045	−	0.220931i
$775$	2.01143e8	−	2.39713e8i	0.432115	−	0.514975i
$776$	5.17844e8	−	5.87995e7i	1.10819	−	0.125831i
$777$	−1.52295e8	−	5.54307e7i	−0.324655	−	0.118165i
$778$	3.56365e8	+	2.15601e8i	0.756756	+	0.457839i
$779$	6.08544e8	−	6.43995e8i	1.28730	−	1.36229i
$780$	−1.58120e8	+	8.28459e7i	−0.333198	+	0.174577i
$781$	6.78492e8	+	2.46951e8i	1.42427	+	0.518391i
$782$	5.50131e8	+	2.13094e8i	1.15039	+	0.445607i
$783$	1.86885e8	−	2.22721e8i	0.389305	−	0.463956i
$784$	3.50290e7	+	3.77314e8i	0.0726908	+	0.782987i
$785$	−1.66432e7	+	9.43881e7i	−0.0344054	+	0.195123i
$786$	−2.66052e8	+	1.46421e8i	−0.547897	+	0.301533i
$787$	4.78810e8	−	2.76441e8i	0.982289	−	0.567125i	0.0793287	−	0.996849i	$-0.474722\pi$
$787$	4.78810e8	−	2.76441e8i	0.982289	−	0.567125i	0.902960	+	0.429724i	$0.141389\pi$
$788$	−4.90469e8	−	4.47044e8i	−1.00238	−	0.913633i
$789$	1.96638e8	−	7.15703e7i	0.400346	−	0.145714i
$790$	−1.36409e8	−	2.79543e6i	−0.276669	−	0.00566979i
$791$	2.10684e8	+	1.21638e8i	0.425698	+	0.245777i
$792$	4.51443e7	−	1.87722e8i	0.0908714	−	0.377867i
$793$	−6.95305e8	+	5.83430e8i	−1.39430	+	1.16995i
$794$	1.25278e8	+	3.67455e8i	0.250272	+	0.734078i
$795$	−2.09557e8	+	3.69506e7i	−0.417062	+	0.0735393i
$796$	1.27284e7	−	1.71009e6i	0.0252368	−	0.00339062i
$797$	−5.50424e8			−1.08723			−0.543616	−	0.839334i	$-0.682945\pi$
$797$	−5.50424e8			−1.08723			−0.543616	+	0.839334i	$0.682945\pi$
$798$	−1.15051e8	+	1.67070e8i	−0.226402	+	0.328768i
$799$		−	6.33921e8i		−	1.24278i
$800$	−4.72265e8	+	3.41010e7i	−0.922393	+	0.0666035i
$801$	1.04686e7	+	5.93702e7i	0.0203699	+	0.115524i
$802$	1.96002e8	+	5.74898e8i	0.379960	+	1.11447i
$803$	2.22441e8	+	2.65095e8i	0.429604	+	0.511982i
$804$	−9.67929e7	+	3.08012e7i	−0.186241	+	0.0592652i
$805$	−3.37571e7	+	5.84691e7i	−0.0647110	+	0.112083i
$806$	6.04403e8	+	1.23860e7i	1.15431	+	0.0236552i
$807$	−7.97897e7	−	2.19220e8i	−0.151819	−	0.417119i
$808$	2.11628e8	+	7.15451e8i	0.401179	+	1.35627i
$809$	4.74163e8	+	8.21274e8i	0.895534	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$809$	4.74163e8	+	8.21274e8i	0.895534	+	1.55111i	0.0623911	+	0.998052i	$0.480127\pi$
$810$	−8.69832e7	+	4.78708e7i	−0.163674	+	0.0900774i
$811$	−8.80931e8	−	1.55332e8i	−1.65150	−	0.291204i	−0.731127	−	0.682241i	$-0.761005\pi$
$811$	−8.80931e8	−	1.55332e8i	−1.65150	−	0.291204i	−0.920375	+	0.391037i	$0.872117\pi$
$812$	5.26151e7	−	1.27983e8i	0.0982748	−	0.239048i
$813$	−5.70027e7	−	4.78310e7i	−0.106078	−	0.0890097i
$814$	−6.65627e8	−	2.57832e8i	−1.23412	−	0.478040i
$815$	−3.19611e7	+	8.78123e7i	−0.0590403	+	0.162212i
$816$	4.66156e8	+	3.22733e8i	0.857947	+	0.593982i
$817$	−1.11004e8	+	4.66711e8i	−0.203550	+	0.855820i
$818$	9.68520e7	+	5.85956e7i	0.176949	+	0.107055i
$819$	−3.50569e7	+	9.63181e7i	−0.0638149	+	0.175330i
$820$	2.24380e8	−	1.73121e8i	0.406952	−	0.313984i
$821$	−6.14754e8	−	5.15840e8i	−1.11089	−	0.932150i	−0.112784	−	0.993620i	$-0.535977\pi$
$821$	−6.14754e8	−	5.15840e8i	−1.11089	−	0.932150i	−0.998109	+	0.0614699i	$0.980421\pi$
$822$	−1.02420e7	−	6.59613e7i	−0.0184403	−	0.118761i
$823$	−3.41659e8	−	6.02437e7i	−0.612905	−	0.108072i	−0.141426	−	0.989949i	$-0.545169\pi$
$823$	−3.41659e8	−	6.02437e7i	−0.612905	−	0.108072i	−0.471479	+	0.881877i	$0.656280\pi$
$824$	2.34714e8	−	3.54318e8i	0.419524	−	0.633303i
$825$	−3.42887e8	−	5.93898e8i	−0.610646	−	1.05767i
$826$	−4.82654e8	−	9.53404e7i	−0.856437	−	0.169175i
$827$	−9.08111e7	−	2.49501e8i	−0.160554	−	0.441120i	0.833164	−	0.553025i	$-0.186527\pi$
$827$	−9.08111e7	−	2.49501e8i	−0.160554	−	0.441120i	−0.993719	+	0.111906i	$0.964305\pi$
$828$	−1.24447e8	−	7.88183e7i	−0.219227	−	0.138847i
$829$	−2.42980e8	+	4.20853e8i	−0.426488	+	0.738699i	−0.996558	−	0.0828974i	$-0.973583\pi$
$829$	−2.42980e8	+	4.20853e8i	−0.426488	+	0.738699i	0.570070	+	0.821596i	$0.306916\pi$
$830$	−3.23461e7	−	2.82910e7i	−0.0565703	−	0.0494782i
$831$	−3.15276e8	−	3.75732e8i	−0.549400	−	0.654749i
$832$	−6.23334e8	−	6.69474e8i	−1.08231	−	1.16242i
$833$	9.53653e7	+	5.40844e8i	0.164989	+	0.935700i
$834$	2.13743e8	+	2.65596e8i	0.368463	+	0.457850i
$835$		−	9.65859e6i		−	0.0165903i
$836$	−5.21702e8	+	7.25310e8i	−0.892902	+	1.24138i
$837$	4.61678e8			0.787341
$838$	−6.10158e8	+	4.91035e8i	−1.03684	+	0.834412i
$839$	6.19125e7	−	1.09168e7i	0.104832	−	0.0184846i	−0.120986	−	0.992654i	$-0.538606\pi$
$839$	6.19125e7	−	1.09168e7i	0.104832	−	0.0184846i	0.225818	+	0.974170i	$0.427495\pi$
$840$	−4.46810e7	+	4.70477e7i	−0.0753850	+	0.0793781i
$841$	−3.13187e8	+	2.62795e8i	−0.526521	+	0.441803i
$842$	−6.50567e7	+	7.43818e7i	−0.108982	+	0.124604i
$843$	1.65916e8	+	9.57915e7i	0.276952	+	0.159898i
$844$	−1.52882e7	−	9.68273e6i	−0.0254290	−	0.0161054i
$845$	2.36740e8	−	8.61663e7i	0.392375	−	0.142813i
$846$	−3.06737e7	+	1.55283e8i	−0.0506589	+	0.256457i
$847$	3.25523e8	−	1.87941e8i	0.535712	−	0.309293i
$848$	−4.66061e8	−	9.85782e8i	−0.764285	−	1.61657i
$849$	−6.47311e7	+	3.67108e8i	−0.105777	+	0.599889i
$850$	−6.78103e8	+	1.05291e8i	−1.10418	+	0.171449i
$851$	−3.50071e8	+	4.17198e8i	−0.568025	+	0.676946i
$852$	4.19159e8	−	3.23403e8i	0.677736	−	0.522908i
$853$	1.34475e8	+	4.89448e7i	0.216667	+	0.0788604i	0.448073	−	0.893997i	$-0.352110\pi$
$853$	1.34475e8	+	4.89448e7i	0.216667	+	0.0788604i	−0.231406	+	0.972857i	$0.574333\pi$
$854$	−1.70775e8	+	2.82272e8i	−0.274189	+	0.453204i
$855$	−4.32728e7	+	5.02308e6i	−0.0692336	+	0.00803659i
$856$	1.64525e8	+	1.01262e7i	0.262308	+	0.0161445i
$857$	−3.24297e8	−	1.18034e8i	−0.515229	−	0.187528i	0.0713023	−	0.997455i	$-0.477285\pi$
$857$	−3.24297e8	−	1.18034e8i	−0.515229	−	0.187528i	−0.586531	+	0.809927i	$0.699507\pi$
$858$	4.78532e8	−	1.23539e9i	0.757617	−	1.95588i
$859$	−1.63411e8	+	1.94746e8i	−0.257811	+	0.307247i	−0.879388	−	0.476106i	$-0.842048\pi$
$859$	−1.63411e8	+	1.94746e8i	−0.257811	+	0.307247i	0.621577	+	0.783353i	$0.286492\pi$
$860$	−5.83444e7	+	1.41920e8i	−0.0917285	+	0.223125i
$861$	−8.29257e7	+	4.70295e8i	−0.129921	+	0.736819i
$862$	2.35439e8	+	4.27802e8i	0.367584	+	0.667914i
$863$	−7.31349e8	+	4.22244e8i	−1.13787	+	0.656949i	−0.945902	−	0.324453i	$-0.894820\pi$
$863$	−7.31349e8	+	4.22244e8i	−1.13787	+	0.656949i	−0.191967	+	0.981401i	$0.561487\pi$
$864$	−4.86414e8	−	5.01415e8i	−0.754162	−	0.777420i
$865$	6.65272e7	−	2.42139e7i	0.102790	−	0.0374125i
$866$	7.26029e6	−	3.54281e8i	0.0111789	−	0.545500i
$867$	2.24187e8	+	1.29434e8i	0.343996	+	0.198606i
$868$	2.09386e8	−	6.66304e7i	0.320176	−	0.101886i
$869$	7.75694e8	−	6.50884e8i	1.18204	−	0.991847i
$870$	−8.25424e7	+	2.81415e7i	−0.125348	+	0.0427356i
$871$	2.33899e8	−	4.12426e7i	0.353976	−	0.0624154i
$872$	−3.53613e8	+	8.12401e8i	−0.533308	+	1.22524i
$873$	−1.88597e8			−0.283461
$874$	3.95332e8	+	5.55317e8i	0.592145	+	0.831776i
$875$		−	1.63449e8i		−	0.243981i
$876$	2.51479e8	−	3.37869e7i	0.374102	−	0.0502615i
$877$	6.96416e7	+	3.94957e8i	0.103245	+	0.585533i	0.991907	+	0.126969i	$0.0405249\pi$
$877$	6.96416e7	+	3.94957e8i	0.103245	+	0.585533i	−0.888661	+	0.458564i	$0.848364\pi$
$878$	1.07963e9	−	3.68081e8i	1.59511	−	0.543826i
$879$	−1.77685e8	−	2.11757e8i	−0.261628	−	0.311796i
$880$	−2.00998e8	+	2.03142e8i	−0.294947	+	0.298094i
$881$	−1.79414e8	+	3.10754e8i	−0.262378	+	0.454452i	−0.966873	−	0.255256i	$-0.917840\pi$
$881$	−1.79414e8	+	3.10754e8i	−0.262378	+	0.454452i	0.704495	+	0.709709i	$0.251173\pi$
$882$	2.80955e6	−	1.37098e8i	0.00409478	−	0.199814i
$883$	1.21233e8	+	3.33084e8i	0.176091	+	0.483807i	0.996068	−	0.0885897i	$-0.0282360\pi$
$883$	1.21233e8	+	3.33084e8i	0.176091	+	0.483807i	−0.819977	+	0.572397i	$0.806014\pi$
$884$	−9.79790e8	−	8.93042e8i	−1.41833	−	1.29275i
$885$	1.55028e8	+	2.68516e8i	0.223656	+	0.387383i
$886$	−2.74891e8	−	4.99487e8i	−0.395238	−	0.718163i
$887$	8.44145e8	+	1.48846e8i	1.20961	+	0.213287i	0.741849	−	0.670567i	$-0.233949\pi$
$887$	8.44145e8	+	1.48846e8i	1.20961	+	0.213287i	0.467763	+	0.883854i	$0.345060\pi$
$888$	−4.20852e8	+	3.11164e8i	−0.601023	+	0.444376i
$889$	6.39067e7	+	5.36241e7i	0.0909580	+	0.0763228i
$890$	3.22304e7	−	8.32070e7i	0.0457189	−	0.118029i
$891$	2.52024e8	−	6.92430e8i	0.356294	−	0.978911i
$892$	9.42192e8	−	4.93656e8i	1.32753	−	0.695552i
$893$	4.02977e8	−	6.11640e8i	0.565882	−	0.858898i
$894$	2.93557e8	−	4.85217e8i	0.410847	−	0.679084i
$895$	1.20272e8	−	3.30446e8i	0.167763	−	0.460926i
$896$	−2.92970e8	−	1.57208e8i	−0.407286	−	0.218549i
$897$	−7.74313e8	−	6.49726e8i	−1.07285	−	0.900229i
$898$	−4.32505e7	+	6.71563e6i	−0.0597258	+	0.00927380i
$899$	2.90847e8	+	5.12842e7i	0.400300	+	0.0705837i
$900$	1.71201e8	+	7.01979e6i	0.234843	+	0.00962934i
$901$	−7.90152e8	−	1.36858e9i	−1.08028	−	1.87110i
$902$	−4.07603e8	+	2.06346e9i	−0.555415	+	2.81175i
$903$	−8.84337e7	−	2.42969e8i	−0.120103	−	0.329981i
$904$	7.03239e8	−	3.50285e8i	0.951914	−	0.474151i
$905$	−2.00888e8	+	3.47948e8i	−0.271024	+	0.469428i
$906$	1.43743e8	−	1.64347e8i	0.193287	−	0.220993i
$907$	2.14190e8	+	2.55262e8i	0.287063	+	0.342109i	0.890234	−	0.455503i	$-0.150541\pi$
$907$	2.14190e8	+	2.55262e8i	0.287063	+	0.342109i	−0.603171	+	0.797612i	$0.706096\pi$
$908$	1.09969e9	+	2.40737e8i	1.46898	+	0.321578i
$909$	−4.68835e7	−	2.65889e8i	−0.0624206	−	0.354005i
$910$	1.18192e8	−	9.51175e7i	0.156843	−	0.126222i
$911$			3.44274e8i			0.455354i	0.973737	+	0.227677i	$0.0731130\pi$
$911$			3.44274e8i			0.455354i	−0.973737	+	0.227677i	$0.926887\pi$
$912$	2.44613e8	+	6.07720e8i	0.322474	+	0.801159i
$913$	3.18930e8			0.419067
$914$	5.17737e8	+	6.43337e8i	0.678064	+	0.842558i
$915$	2.04758e8	−	3.61043e7i	0.267287	−	0.0471299i
$916$	−7.97032e7	+	3.64086e8i	−0.103703	+	0.473716i
$917$	1.97713e8	−	1.65901e8i	0.256406	−	0.215150i
$918$	−7.62080e8	−	6.66540e8i	−0.985082	−	0.861585i
$919$	−6.30709e8	−	3.64140e8i	−0.812611	−	0.469161i	0.0352510	−	0.999378i	$-0.488777\pi$
$919$	−6.30709e8	−	3.64140e8i	−0.812611	−	0.469161i	−0.847862	+	0.530217i	$0.822110\pi$
$920$	9.72114e7	+	1.95163e8i	0.124840	+	0.250631i
$921$	5.27979e8	−	1.92169e8i	0.675831	−	0.245982i
$922$	5.02892e8	+	9.93381e7i	0.641625	+	0.126743i
$923$	−1.07206e9	+	6.18951e8i	−1.36336	+	0.787139i
$924$	1.97284e7	−	4.81141e8i	0.0250078	−	0.609898i
$925$	1.10003e8	−	6.23859e8i	0.138989	−	0.788245i
$926$	1.11677e8	+	7.19230e8i	0.140647	+	0.905806i
$927$	−9.88598e7	+	1.17817e8i	−0.124103	+	0.147900i
$928$	−2.50732e8	−	3.69913e8i	−0.313737	−	0.462866i
$929$	7.11366e8	+	2.58916e8i	0.887250	+	0.322933i	0.745132	−	0.666917i	$-0.232386\pi$
$929$	7.11366e8	+	2.58916e8i	0.887250	+	0.322933i	0.142118	+	0.989850i	$0.454609\pi$
$930$	−1.18483e8	−	7.16824e7i	−0.147302	−	0.0891177i
$931$	−2.51795e8	+	5.82456e8i	−0.312032	+	0.721796i
$932$	−3.09455e8	−	5.90627e8i	−0.382252	−	0.729567i
$933$	7.81549e8	+	2.84461e8i	0.962302	+	0.350249i
$934$	−6.12566e8	−	2.37279e8i	−0.751817	−	0.291218i
$935$	−2.66223e8	+	3.17272e8i	−0.325694	+	0.388147i
$936$	1.96795e8	+	2.66166e8i	0.239986	+	0.324583i
$937$	2.49449e8	−	1.41470e9i	0.303224	−	1.71967i	−0.328524	−	0.944496i	$-0.606551\pi$
$937$	2.49449e8	−	1.41470e9i	0.303224	−	1.71967i	0.631748	−	0.775174i	$-0.282338\pi$
$938$	7.56310e7	−	4.16232e7i	0.0916413	−	0.0504344i
$939$	−1.95346e8	+	1.12783e8i	−0.235943	+	0.136222i
$940$	1.57819e8	−	1.73149e8i	0.190010	−	0.208467i
$941$	6.36447e7	−	2.31648e7i	0.0763824	−	0.0278009i	−0.303546	−	0.952817i	$-0.598171\pi$
$941$	6.36447e7	−	2.31648e7i	0.0763824	−	0.0278009i	0.379929	+	0.925016i	$0.375949\pi$
$942$	−5.21455e8	−	1.06862e7i	−0.623828	−	0.0127841i
$943$	1.38976e9	+	8.02377e8i	1.65731	+	0.956848i
$944$	−1.11749e9	+	1.12941e9i	−1.32840	+	1.34257i
$945$	8.87559e7	−	7.44751e7i	0.105172	−	0.0882502i
$946$	−3.67491e8	−	1.07790e9i	−0.434084	−	1.27322i
$947$	1.60153e9	−	2.82393e8i	1.88576	−	0.332510i	0.892749	−	0.450554i	$-0.148774\pi$
$947$	1.60153e9	−	2.82393e8i	1.88576	−	0.332510i	0.993008	+	0.118044i	$0.0376625\pi$
$948$	−9.88637e7	−	7.35854e8i	−0.116041	−	0.863707i
$949$	−5.93300e8			−0.694186
$950$	−7.21201e8	−	3.29473e8i	−0.841173	−	0.384281i
$951$		−	6.43751e8i		−	0.748473i
$952$	−4.41825e8	−	1.92313e8i	−0.512082	−	0.222893i
$953$	2.63024e8	+	1.49168e9i	0.303890	+	1.72345i	0.628682	+	0.777662i	$0.283595\pi$
$953$	2.63024e8	+	1.49168e9i	0.303890	+	1.72345i	−0.324792	+	0.945785i	$0.605294\pi$
$954$	1.27331e8	+	3.73478e8i	0.146653	+	0.430149i
$955$	1.57457e8	+	1.87650e8i	0.180781	+	0.215446i
$956$	1.72592e8	+	5.42371e8i	0.197537	+	0.620759i
$957$	3.23614e8	−	5.60516e8i	0.369226	−	0.639518i
$958$	1.43244e9	+	2.93549e7i	1.62922	+	0.0333875i
$959$	1.94034e7	+	5.33103e7i	0.0219999	+	0.0604443i
$960$	4.69791e7	+	2.04204e8i	0.0530996	+	0.230808i
$961$	−2.09267e8	−	3.62461e8i	−0.235793	−	0.408406i
$962$	1.07217e9	−	5.90063e8i	1.20431	−	0.662786i
$963$	−5.87436e7	−	1.03581e7i	−0.0657782	−	0.0115985i
$964$	−2.95541e8	−	1.21499e8i	−0.329903	−	0.135626i
$965$	−1.33893e8	−	1.12349e8i	−0.148996	−	0.125023i
$966$	−3.42595e8	−	1.32705e8i	−0.380058	−	0.147216i
$967$	−4.32613e8	+	1.18859e9i	−0.478432	+	1.31448i	0.432392	+	0.901686i	$0.357670\pi$
$967$	−4.32613e8	+	1.18859e9i	−0.478432	+	1.31448i	−0.910824	+	0.412796i	$0.864552\pi$
$968$	7.45714e7	−	1.21160e9i	0.0822141	−	1.33577i
$969$	4.25430e8	+	8.48779e8i	0.467581	+	0.932875i
$970$	2.38840e8	+	1.44498e8i	0.261692	+	0.158324i
$971$	2.60035e8	−	7.14442e8i	0.284037	−	0.780385i	−0.712833	−	0.701333i	$-0.752588\pi$
$971$	2.60035e8	−	7.14442e8i	0.284037	−	0.780385i	0.996870	−	0.0790520i	$-0.0251893\pi$
$972$	2.77555e8	+	3.59737e8i	0.302239	+	0.391729i
$973$	−2.21958e8	−	1.86245e8i	−0.240953	−	0.202184i
$974$	−1.29855e8	−	8.36302e8i	−0.140534	−	0.905079i
$975$	1.15787e9	+	2.04164e8i	1.24924	+	0.220275i
$976$	4.55388e8	+	9.63206e8i	0.489815	+	1.03602i
$977$	−1.15533e8	−	2.00109e8i	−0.123886	−	0.214577i	0.797411	−	0.603437i	$-0.206202\pi$
$977$	−1.15533e8	−	2.00109e8i	−0.123886	−	0.214577i	−0.921297	+	0.388860i	$0.872869\pi$
$978$	−4.98885e8	−	9.85466e7i	−0.533315	−	0.105348i
$979$	2.26502e8	+	6.22308e8i	0.241392	+	0.663219i
$980$	−1.08599e8	+	1.71468e8i	−0.115384	+	0.182182i
$981$	1.60314e8	−	2.77671e8i	0.169810	−	0.294120i
$982$	3.48762e8	+	3.05038e8i	0.368294	+	0.322122i
$983$	6.75312e7	+	8.04805e7i	0.0710957	+	0.0847286i	0.800420	−	0.599440i	$-0.204610\pi$
$983$	6.75312e7	+	8.04805e7i	0.0710957	+	0.0847286i	−0.729324	+	0.684168i	$0.760165\pi$
$984$	1.11828e9	+	1.06203e9i	1.17372	+	1.11468i
$985$	−6.17239e7	−	3.50054e8i	−0.0645869	−	0.366291i
$986$	−4.06053e8	−	5.04560e8i	−0.423597	−	0.526359i
$987$			3.94776e8i			0.410582i
$988$	−3.77654e8	−	1.48450e9i	−0.391583	−	1.53925i
$989$	−8.68871e8			−0.898186
$990$	8.05650e7	−	6.48361e7i	0.0830311	−	0.0668208i
$991$	−1.72416e8	+	3.04016e7i	−0.177156	+	0.0312374i	−0.261522	−	0.965197i	$-0.584225\pi$
$991$	−1.72416e8	+	3.04016e7i	−0.177156	+	0.0312374i	0.0843663	+	0.996435i	$0.473113\pi$
$992$	1.94048e8	−	6.82567e8i	0.198780	−	0.699214i
$993$	7.53177e8	−	6.31991e8i	0.769218	−	0.645450i
$994$	−2.96222e8	+	3.38682e8i	−0.301619	+	0.344852i
$995$	5.95722e6	+	3.43941e6i	0.00604748	+	0.00349152i
$996$	1.25123e8	−	1.97559e8i	0.126637	−	0.199949i
$997$	8.81927e8	−	3.20995e8i	0.889912	−	0.323902i	0.143709	−	0.989620i	$-0.454097\pi$
$997$	8.81927e8	−	3.20995e8i	0.889912	−	0.323902i	0.746203	+	0.665718i	$0.231875\pi$
$998$	−2.01948e8	+	1.02235e9i	−0.203164	+	1.02850i
$999$	8.09407e8	−	4.67311e8i	0.811840	−	0.468716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.l.a.23.16	yes	348
4.3	odd	2	inner	76.7.l.a.23.3	✓	348
19.5	even	9	inner	76.7.l.a.43.3	yes	348
76.43	odd	18	inner	76.7.l.a.43.16	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.l.a.23.3	✓	348	4.3	odd	2	inner
76.7.l.a.23.16	yes	348	1.1	even	1	trivial
76.7.l.a.43.3	yes	348	19.5	even	9	inner
76.7.l.a.43.16	yes	348	76.43	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.01566 - 6.23243i) q^{2} +(22.9636 - 4.04910i) q^{3} +(-13.6863 + 62.5195i) q^{4} +(-26.2597 + 22.0345i) q^{5} +(-140.413 - 122.810i) q^{6} +(137.300 + 79.2704i) q^{7} +(458.294 - 228.277i) q^{8} +(-174.105 + 63.3690i) q^{9} +O(q^{10})\)	\(q+(-5.01566 - 6.23243i) q^{2} +(22.9636 - 4.04910i) q^{3} +(-13.6863 + 62.5195i) q^{4} +(-26.2597 + 22.0345i) q^{5} +(-140.413 - 122.810i) q^{6} +(137.300 + 79.2704i) q^{7} +(458.294 - 228.277i) q^{8} +(-174.105 + 63.3690i) q^{9} +(269.038 + 53.1441i) q^{10} +(-1762.62 + 1017.65i) q^{11} +(-61.1394 + 1491.09i) q^{12} +(605.935 - 3436.43i) q^{13} +(-194.605 - 1253.31i) q^{14} +(-513.796 + 612.319i) q^{15} +(-3721.37 - 1711.32i) q^{16} +(-5578.27 - 2030.32i) q^{17} +(1268.19 + 767.259i) q^{18} +(-4091.55 - 5505.01i) q^{19} +(-1018.19 - 1943.31i) q^{20} +(3473.88 + 1264.39i) q^{21} +(15183.1 + 5881.22i) q^{22} +(7985.21 - 9516.40i) q^{23} +(9599.76 - 7097.74i) q^{24} +(-2509.20 + 14230.4i) q^{25} +(-24456.4 + 13459.5i) q^{26} +(-18462.8 + 10659.5i) q^{27} +(-6835.08 + 7499.03i) q^{28} +(-12815.3 + 4664.37i) q^{29} +(6393.26 + 131.017i) q^{30} +(-18754.4 - 10827.8i) q^{31} +(7999.42 + 31776.6i) q^{32} +(-36355.5 + 30505.9i) q^{33} +(15324.9 + 44949.6i) q^{34} +(-5352.15 + 943.728i) q^{35} +(-1578.94 - 11752.2i) q^{36} -43839.9 q^{37} +(-13787.8 + 53111.5i) q^{38} -81366.1i q^{39} +(-7004.68 + 16092.8i) q^{40} +(22431.6 + 127216. i) q^{41} +(-9543.59 - 27992.5i) q^{42} +(-44957.7 - 53578.5i) q^{43} +(-39499.1 - 124126. i) q^{44} +(3175.64 - 5500.36i) q^{45} +(-99361.4 - 2036.21i) q^{46} +(36523.6 + 100348. i) q^{47} +(-92385.3 - 24229.9i) q^{48} +(-46256.9 - 80119.3i) q^{49} +(101275. - 55736.3i) q^{50} +(-136318. - 24036.6i) q^{51} +(206551. + 84914.8i) q^{52} +(203930. + 171118. i) q^{53} +(159038. + 61603.6i) q^{54} +(23862.5 - 65561.6i) q^{55} +(81019.6 + 4986.59i) q^{56} +(-116247. - 109848. i) q^{57} +(93347.3 + 56475.2i) q^{58} +(132668. - 364504. i) q^{59} +(-31249.9 - 40502.7i) q^{60} +(-199260. - 167199. i) q^{61} +(26581.8 + 171194. i) q^{62} +(-28928.0 - 5100.78i) q^{63} +(157923. - 209236. i) q^{64} +(59808.2 + 103591. i) q^{65} +(372473. + 73575.9i) q^{66} +(23279.4 + 63959.7i) q^{67} +(203281. - 320963. i) q^{68} +(144836. - 250864. i) q^{69} +(32726.3 + 28623.5i) q^{70} +(-228033. - 271760. i) q^{71} +(-65325.6 + 68785.9i) q^{72} +(-29525.0 - 167444. i) q^{73} +(219886. + 273229. i) q^{74} +336941. i q^{75} +(400169. - 180458. i) q^{76} -322678. q^{77} +(-507109. + 408105. i) q^{78} +(-489959. + 86393.0i) q^{79} +(135430. - 37059.7i) q^{80} +(-277342. + 232718. i) q^{81} +(680354. - 777874. i) q^{82} +(-135706. - 78349.7i) q^{83} +(-126594. + 199881. i) q^{84} +(191221. - 69598.7i) q^{85} +(-108432. + 548927. i) q^{86} +(-275398. + 159001. i) q^{87} +(-575492. + 868749. i) q^{88} +(56501.7 - 320437. i) q^{89} +(-50208.5 + 7796.03i) q^{90} +(355602. - 423790. i) q^{91} +(485672. + 629476. i) q^{92} +(-474511. - 172708. i) q^{93} +(442220. - 730940. i) q^{94} +(228743. + 54404.7i) q^{95} +(312362. + 697314. i) q^{96} +(956525. + 348147. i) q^{97} +(-267329. + 690144. i) q^{98} +(242394. - 288873. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Introduction

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