LMFDB - Embedded newform 76.7.b.a.39.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, 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:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.12
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.52919 + 4.62273i) q^{2} -11.8519i q^{3} +(21.2607 - 60.3654i) q^{4} +179.762 q^{5} +(54.7881 + 77.3834i) q^{6} -39.4677i q^{7} +(140.237 + 492.420i) q^{8} +588.532 q^{9} +O(q^{10})$	\(q+(-6.52919 + 4.62273i) q^{2} -11.8519i q^{3} +(21.2607 - 60.3654i) q^{4} +179.762 q^{5} +(54.7881 + 77.3834i) q^{6} -39.4677i q^{7} +(140.237 + 492.420i) q^{8} +588.532 q^{9} +(-1173.70 + 830.991i) q^{10} -536.570i q^{11} +(-715.445 - 251.980i) q^{12} -1508.07 q^{13} +(182.448 + 257.692i) q^{14} -2130.52i q^{15} +(-3191.96 - 2566.83i) q^{16} +2145.25 q^{17} +(-3842.64 + 2720.63i) q^{18} -1573.56i q^{19} +(3821.87 - 10851.4i) q^{20} -467.767 q^{21} +(2480.42 + 3503.37i) q^{22} +261.443i q^{23} +(5836.11 - 1662.08i) q^{24} +16689.4 q^{25} +(9846.47 - 6971.39i) q^{26} -15615.3i q^{27} +(-2382.48 - 839.112i) q^{28} +40536.1 q^{29} +(9848.83 + 13910.6i) q^{30} +26418.9i q^{31} +(32706.7 + 2003.73i) q^{32} -6359.37 q^{33} +(-14006.8 + 9916.92i) q^{34} -7094.79i q^{35} +(12512.6 - 35527.0i) q^{36} +17559.3 q^{37} +(7274.15 + 10274.1i) q^{38} +17873.5i q^{39} +(25209.4 + 88518.4i) q^{40} +30619.5 q^{41} +(3054.14 - 2162.36i) q^{42} -131724. i q^{43} +(-32390.2 - 11407.9i) q^{44} +105796. q^{45} +(-1208.58 - 1707.01i) q^{46} -198201. i q^{47} +(-30421.8 + 37830.8i) q^{48} +116091. q^{49} +(-108968. + 77150.5i) q^{50} -25425.3i q^{51} +(-32062.6 + 91035.1i) q^{52} -128125. q^{53} +(72185.1 + 101955. i) q^{54} -96454.9i q^{55} +(19434.7 - 5534.84i) q^{56} -18649.7 q^{57} +(-264668. + 187388. i) q^{58} +18873.2i q^{59} +(-128610. - 45296.5i) q^{60} -166795. q^{61} +(-122127. - 172494. i) q^{62} -23228.0i q^{63} +(-222811. + 138111. i) q^{64} -271093. q^{65} +(41521.6 - 29397.7i) q^{66} +267170. i q^{67} +(45609.6 - 129499. i) q^{68} +3098.60 q^{69} +(32797.3 + 46323.2i) q^{70} -104773. i q^{71} +(82534.3 + 289805. i) q^{72} +263046. q^{73} +(-114648. + 81172.0i) q^{74} -197801. i q^{75} +(-94988.7 - 33455.1i) q^{76} -21177.1 q^{77} +(-82624.2 - 116699. i) q^{78} -48638.0i q^{79} +(-573794. - 461418. i) q^{80} +243970. q^{81} +(-199921. + 141546. i) q^{82} +317734. i q^{83} +(-9945.07 + 28236.9i) q^{84} +385635. q^{85} +(608924. + 860051. i) q^{86} -480430. i q^{87} +(264218. - 75247.1i) q^{88} +30232.1 q^{89} +(-690761. + 489065. i) q^{90} +59519.9i q^{91} +(15782.1 + 5558.47i) q^{92} +313114. q^{93} +(916228. + 1.29409e6i) q^{94} -282867. i q^{95} +(23748.0 - 387636. i) q^{96} +666671. q^{97} +(-757983. + 536659. i) q^{98} -315789. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−6.52919	+	4.62273i	−0.816149	+	0.577841i
$2$	−6.52919	+	4.62273i	−0.816149	+	0.577841i
$3$		−	11.8519i		−	0.438959i	−0.975617	−	0.219480i	$-0.929564\pi$
$3$		−	11.8519i		−	0.438959i	0.975617	−	0.219480i	$-0.0704359\pi$
$4$	21.2607	−	60.3654i	0.332199	−	0.943209i
$5$	179.762			1.43810			0.719048	−	0.694960i	$-0.244578\pi$
$5$	179.762			1.43810			0.719048	+	0.694960i	$0.244578\pi$
$6$	54.7881	+	77.3834i	0.253649	+	0.358256i
$7$		−	39.4677i		−	0.115066i	−0.998344	−	0.0575330i	$-0.981677\pi$
$7$		−	39.4677i		−	0.115066i	0.998344	−	0.0575330i	$-0.0183234\pi$
$8$	140.237	+	492.420i	0.273901	+	0.961758i
$9$	588.532			0.807315
$10$	−1173.70	+	830.991i	−1.17370	+	0.830991i
$11$		−	536.570i		−	0.403133i	−0.979475	−	0.201566i	$-0.935397\pi$
$11$		−	536.570i		−	0.403133i	0.979475	−	0.201566i	$-0.0646032\pi$
$12$	−715.445	−	251.980i	−0.414030	−	0.145822i
$13$	−1508.07			−0.686421			−0.343211	−	0.939258i	$-0.611515\pi$
$13$	−1508.07			−0.686421			−0.343211	+	0.939258i	$0.611515\pi$
$14$	182.448	+	257.692i	0.0664899	+	0.0939111i
$15$		−	2130.52i		−	0.631266i
$16$	−3191.96	−	2566.83i	−0.779288	−	0.626667i
$17$	2145.25			0.436648			0.218324	−	0.975876i	$-0.429941\pi$
$17$	2145.25			0.436648			0.218324	+	0.975876i	$0.429941\pi$
$18$	−3842.64	+	2720.63i	−0.658889	+	0.466500i
$19$		−	1573.56i		−	0.229416i
$19$		−	1573.56i		−	0.229416i
$20$	3821.87	−	10851.4i	0.477734	−	1.35643i
$21$	−467.767			−0.0505093
$22$	2480.42	+	3503.37i	0.232947	+	0.329016i
$23$			261.443i			0.0214879i	0.999942	+	0.0107439i	$0.00341997\pi$
$23$			261.443i			0.0214879i	−0.999942	+	0.0107439i	$0.996580\pi$
$24$	5836.11	−	1662.08i	0.422173	−	0.120231i
$25$	16689.4			1.06812
$26$	9846.47	−	6971.39i	0.560222	−	0.396643i
$27$		−	15615.3i		−	0.793338i
$28$	−2382.48	−	839.112i	−0.108531	−	0.0382248i
$29$	40536.1			1.66207			0.831033	−	0.556223i	$-0.187750\pi$
$29$	40536.1			1.66207			0.831033	+	0.556223i	$0.187750\pi$
$30$	9848.83	+	13910.6i	0.364771	+	0.515207i
$31$			26418.9i			0.886807i	0.896322	+	0.443404i	$0.146229\pi$
$31$			26418.9i			0.886807i	−0.896322	+	0.443404i	$0.853771\pi$
$32$	32706.7	+	2003.73i	0.998129	+	0.0611489i
$33$	−6359.37			−0.176959
$34$	−14006.8	+	9916.92i	−0.356370	+	0.252313i
$35$		−	7094.79i		−	0.165476i
$36$	12512.6	−	35527.0i	0.268189	−	0.761467i
$37$	17559.3			0.346659			0.173330	−	0.984864i	$-0.444547\pi$
$37$	17559.3			0.346659			0.173330	+	0.984864i	$0.444547\pi$
$38$	7274.15	+	10274.1i	0.132566	+	0.187237i
$39$			17873.5i			0.301311i
$40$	25209.4	+	88518.4i	0.393896	+	1.38310i
$41$	30619.5			0.444270			0.222135	−	0.975016i	$-0.428697\pi$
$41$	30619.5			0.444270			0.222135	+	0.975016i	$0.428697\pi$
$42$	3054.14	−	2162.36i	0.0412231	−	0.0291864i
$43$		−	131724.i		−	1.65676i	−0.560167	−	0.828380i	$-0.689263\pi$
$43$		−	131724.i		−	1.65676i	0.560167	−	0.828380i	$-0.310737\pi$
$44$	−32390.2	−	11407.9i	−0.380239	−	0.133920i
$45$	105796.			1.16100
$46$	−1208.58	−	1707.01i	−0.0124166	−	0.0175373i
$47$		−	198201.i		−	1.90902i	−0.298172	−	0.954512i	$-0.596377\pi$
$47$		−	198201.i		−	1.90902i	0.298172	−	0.954512i	$-0.403623\pi$
$48$	−30421.8	+	37830.8i	−0.275081	+	0.342075i
$49$	116091.			0.986760
$50$	−108968.	+	77150.5i	−0.871746	+	0.617204i
$51$		−	25425.3i		−	0.191671i
$52$	−32062.6	+	91035.1i	−0.228029	+	0.647439i
$53$	−128125.			−0.860607			−0.430304	−	0.902684i	$-0.641593\pi$
$53$	−128125.			−0.860607			−0.430304	+	0.902684i	$0.641593\pi$
$54$	72185.1	+	101955.i	0.458423	+	0.647482i
$55$		−	96454.9i		−	0.579744i
$56$	19434.7	−	5534.84i	0.110666	−	0.0315167i
$57$	−18649.7			−0.100704
$58$	−264668.	+	187388.i	−1.35649	+	0.960410i
$59$			18873.2i			0.0918947i	0.998944	+	0.0459474i	$0.0146306\pi$
$59$			18873.2i			0.0918947i	−0.998944	+	0.0459474i	$0.985369\pi$
$60$	−128610.	−	45296.5i	−0.595416	−	0.209706i
$61$	−166795.			−0.734841			−0.367421	−	0.930055i	$-0.619759\pi$
$61$	−166795.			−0.734841			−0.367421	+	0.930055i	$0.619759\pi$
$62$	−122127.	−	172494.i	−0.512434	−	0.723767i
$63$		−	23228.0i		−	0.0928945i
$64$	−222811.	+	138111.i	−0.849956	+	0.526853i
$65$	−271093.			−0.987140
$66$	41521.6	−	29397.7i	0.144425	−	0.102254i
$67$			267170.i			0.888307i	0.895951	+	0.444154i	$0.146496\pi$
$67$			267170.i			0.888307i	−0.895951	+	0.444154i	$0.853504\pi$
$68$	45609.6	−	129499.i	0.145054	−	0.411850i
$69$	3098.60			0.00943231
$70$	32797.3	+	46323.2i	0.0956189	+	0.135053i
$71$		−	104773.i		−	0.292736i	−0.989230	−	0.146368i	$-0.953242\pi$
$71$		−	104773.i		−	0.292736i	0.989230	−	0.146368i	$-0.0467583\pi$
$72$	82534.3	+	289805.i	0.221124	+	0.776441i
$73$	263046.			0.676180			0.338090	−	0.941114i	$-0.390219\pi$
$73$	263046.			0.676180			0.338090	+	0.941114i	$0.390219\pi$
$74$	−114648.	+	81172.0i	−0.282926	+	0.200314i
$75$		−	197801.i		−	0.468862i
$76$	−94988.7	−	33455.1i	−0.216387	−	0.0762117i
$77$	−21177.1			−0.0463869
$78$	−82624.2	−	116699.i	−0.174110	−	0.245915i
$79$		−	48638.0i		−	0.0986495i	−0.998783	−	0.0493247i	$-0.984293\pi$
$79$		−	48638.0i		−	0.0986495i	0.998783	−	0.0493247i	$-0.0157069\pi$
$80$	−573794.	−	461418.i	−1.12069	−	0.901207i
$81$	243970.			0.459072
$82$	−199921.	+	141546.i	−0.362591	+	0.256718i
$83$			317734.i			0.555686i	0.960626	+	0.277843i	$0.0896195\pi$
$83$			317734.i			0.555686i	−0.960626	+	0.277843i	$0.910380\pi$
$84$	−9945.07	+	28236.9i	−0.0167791	+	0.0476408i
$85$	385635.			0.627942
$86$	608924.	+	860051.i	0.957344	+	1.35216i
$87$		−	480430.i		−	0.729579i
$88$	264218.	−	75247.1i	0.387716	−	0.110419i
$89$	30232.1			0.0428843			0.0214421	−	0.999770i	$-0.493174\pi$
$89$	30232.1			0.0428843			0.0214421	+	0.999770i	$0.493174\pi$
$90$	−690761.	+	489065.i	−0.947546	+	0.670872i
$91$			59519.9i			0.0789838i
$92$	15782.1	+	5558.47i	0.0202676	+	0.00713826i
$93$	313114.			0.389272
$94$	916228.	+	1.29409e6i	1.10311	+	1.55805i
$95$		−	282867.i		−	0.329922i
$96$	23748.0	−	387636.i	0.0268419	−	0.438138i
$97$	666671.			0.730460			0.365230	−	0.930917i	$-0.380990\pi$
$97$	666671.			0.730460			0.365230	+	0.930917i	$0.380990\pi$
$98$	−757983.	+	536659.i	−0.805343	+	0.570190i
$99$		−	315789.i		−	0.325455i
$100$	354829.	−	1.00746e6i	0.354829	−	1.00746i
$101$	57446.0			0.0557565			0.0278782	−	0.999611i	$-0.491125\pi$
$101$	57446.0			0.0557565			0.0278782	+	0.999611i	$0.491125\pi$
$102$	117534.	+	166007.i	0.110755	+	0.156432i
$103$		−	1.33511e6i		−	1.22182i	−0.791701	−	0.610909i	$-0.790804\pi$
$103$		−	1.33511e6i		−	1.22182i	0.791701	−	0.610909i	$-0.209196\pi$
$104$	−211488.	−	742603.i	−0.188012	−	0.660171i
$105$	−84086.7			−0.0726372
$106$	836550.	−	592285.i	0.702384	−	0.497294i
$107$			1.95799e6i			1.59830i	0.601130	+	0.799151i	$0.294717\pi$
$107$			1.95799e6i			1.59830i	−0.601130	+	0.799151i	$0.705283\pi$
$108$	−942622.	−	331992.i	−0.748283	−	0.263546i
$109$	−160354.			−0.123823			−0.0619114	−	0.998082i	$-0.519720\pi$
$109$	−160354.			−0.123823			−0.0619114	+	0.998082i	$0.519720\pi$
$110$	445885.	+	629773.i	0.335000	+	0.473157i
$111$		−	208111.i		−	0.152169i
$112$	−101307.	+	125979.i	−0.0721080	+	0.0896695i
$113$	−1.35711e6			−0.940547			−0.470274	−	0.882521i	$-0.655845\pi$
$113$	−1.35711e6			−0.940547			−0.470274	+	0.882521i	$0.655845\pi$
$114$	121768.	−	86212.5i	0.0821896	−	0.0581910i
$115$			46997.5i			0.0309016i
$116$	861828.	−	2.44698e6i	0.552137	−	1.56768i
$117$	−887547.			−0.554158
$118$	−87245.9	−	123227.i	−0.0531005	−	0.0749998i
$119$		−	84668.0i		−	0.0502434i
$120$	1.04911e6	−	298779.i	0.607125	−	0.172904i
$121$	1.48365e6			0.837484
$122$	1.08904e6	−	771048.i	0.599740	−	0.424622i
$123$		−	362900.i		−	0.195017i
$124$	1.59479e6	+	561685.i	0.836445	+	0.294597i
$125$	191337.			0.0979645
$126$	107377.	+	151660.i	0.0536783	+	0.0758158i
$127$			1.61576e6i			0.788799i	0.918939	+	0.394400i	$0.129047\pi$
$127$			1.61576e6i			0.788799i	−0.918939	+	0.394400i	$0.870953\pi$
$128$	816324.	−	1.93175e6i	0.389254	−	0.921131i
$129$	−1.56118e6			−0.727250
$130$	1.77002e6	−	1.25319e6i	0.805654	−	0.570410i
$131$			3.34081e6i			1.48606i	0.669256	+	0.743032i	$0.266613\pi$
$131$			3.34081e6i			1.48606i	−0.669256	+	0.743032i	$0.733387\pi$
$132$	−135205.	+	383886.i	−0.0587856	+	0.166909i
$133$	−62104.8			−0.0263980
$134$	−1.23505e6	−	1.74440e6i	−0.513301	−	0.724991i
$135$		−	2.80703e6i		−	1.14090i
$136$	300845.	+	1.05636e6i	0.119598	+	0.419950i
$137$	−4.68940e6			−1.82371			−0.911856	−	0.410511i	$-0.865350\pi$
$137$	−4.68940e6			−1.82371			−0.911856	+	0.410511i	$0.865350\pi$
$138$	−20231.3	+	14324.0i	−0.00769817	+	0.00545037i
$139$			1.72450e6i			0.642125i	0.947058	+	0.321063i	$0.104040\pi$
$139$			1.72450e6i			0.642125i	−0.947058	+	0.321063i	$0.895960\pi$
$140$	−428280.	−	150840.i	−0.156079	−	0.0549710i
$141$	−2.34905e6			−0.837984
$142$	484339.	+	684085.i	0.169155	+	0.238916i
$143$			809184.i			0.276719i
$144$	−1.87857e6	−	1.51066e6i	−0.629130	−	0.505917i
$145$	7.28686e6			2.39021
$146$	−1.71748e6	+	1.21599e6i	−0.551864	+	0.390725i
$147$		−	1.37590e6i		−	0.433147i
$148$	373324.	−	1.05998e6i	0.115160	−	0.326972i
$149$	−2.31907e6			−0.701060			−0.350530	−	0.936551i	$-0.613999\pi$
$149$	−2.31907e6			−0.701060			−0.350530	+	0.936551i	$0.613999\pi$
$150$	914380.	+	1.29148e6i	0.270928	+	0.382661i
$151$			4.41731e6i			1.28300i	0.767122	+	0.641501i	$0.221688\pi$
$151$			4.41731e6i			1.28300i	−0.767122	+	0.641501i	$0.778312\pi$
$152$	774854.	−	220672.i	0.220642	−	0.0628372i
$153$	1.26255e6			0.352512
$154$	138270.	−	97896.2i	0.0378586	−	0.0268043i
$155$			4.74911e6i			1.27531i
$156$	1.07894e6	+	380003.i	0.284199	+	0.100095i
$157$	4.01544e6			1.03761			0.518804	−	0.854893i	$-0.326377\pi$
$157$	4.01544e6			1.03761			0.518804	+	0.854893i	$0.326377\pi$
$158$	224840.	+	317567.i	0.0570037	+	0.0805127i
$159$			1.51852e6i			0.377771i
$160$	5.87942e6	+	360194.i	1.43541	+	0.0879381i
$161$	10318.5			0.00247253
$162$	−1.59293e6	+	1.12781e6i	−0.374671	+	0.265271i
$163$		−	4.61245e6i		−	1.06505i	−0.846415	−	0.532524i	$-0.821244\pi$
$163$		−	4.61245e6i		−	1.06505i	0.846415	−	0.532524i	$-0.178756\pi$
$164$	650994.	−	1.84836e6i	0.147586	−	0.419040i
$165$	−1.14317e6			−0.254484
$166$	−1.46880e6	−	2.07455e6i	−0.321098	−	0.453523i
$167$			1.92901e6i			0.414175i	0.978322	+	0.207088i	$0.0663985\pi$
$167$			1.92901e6i			0.414175i	−0.978322	+	0.207088i	$0.933601\pi$
$168$	−65598.4	−	230338.i	−0.0138346	−	0.0485777i
$169$	−2.55254e6			−0.528826
$170$	−2.51788e6	+	1.78269e6i	−0.512494	+	0.362851i
$171$		−	926093.i		−	0.185211i
$172$	−7.95157e6	−	2.80055e6i	−1.56267	−	0.550374i
$173$	−4.01149e6			−0.774761			−0.387381	−	0.921920i	$-0.626620\pi$
$173$	−4.01149e6			−0.774761			−0.387381	+	0.921920i	$0.626620\pi$
$174$	2.22090e6	+	3.13682e6i	0.421581	+	0.595445i
$175$		−	658691.i		−	0.122904i
$176$	−1.37728e6	+	1.71271e6i	−0.252630	+	0.314156i
$177$	223684.			0.0403380
$178$	−197391.	+	139755.i	−0.0350000	+	0.0247803i
$179$		−	8.33008e6i		−	1.45241i	−0.687477	−	0.726206i	$-0.741282\pi$
$179$		−	8.33008e6i		−	1.45241i	0.687477	−	0.726206i	$-0.258718\pi$
$180$	2.24930e6	−	6.38640e6i	0.385682	−	1.09506i
$181$	−7.40325e6			−1.24849			−0.624247	−	0.781227i	$-0.714594\pi$
$181$	−7.40325e6			−1.24849			−0.624247	+	0.781227i	$0.714594\pi$
$182$	−275144.	−	388617.i	−0.0456401	−	0.0644626i
$183$			1.97684e6i			0.322565i
$184$	−128740.	+	36664.1i	−0.0206661	+	0.00588556i
$185$	3.15650e6			0.498529
$186$	−2.04438e6	+	1.44744e6i	−0.317704	+	0.224938i
$187$		−	1.15108e6i		−	0.176027i
$188$	−1.19645e7	−	4.21389e6i	−1.80061	−	0.634176i
$189$	−616298.			−0.0912862
$190$	1.30762e6	+	1.84689e6i	0.190642	+	0.269266i
$191$			1.18467e7i			1.70019i	0.526626	+	0.850097i	$0.323457\pi$
$191$			1.18467e7i			1.70019i	−0.526626	+	0.850097i	$0.676543\pi$
$192$	1.63688e6	+	2.64073e6i	0.231267	+	0.373096i
$193$	−1.00117e7			−1.39264			−0.696318	−	0.717733i	$-0.745180\pi$
$193$	−1.00117e7			−1.39264			−0.696318	+	0.717733i	$0.745180\pi$
$194$	−4.35283e6	+	3.08184e6i	−0.596164	+	0.422090i
$195$			3.21297e6i			0.433314i
$196$	2.46819e6	−	7.00790e6i	0.327801	−	0.930721i
$197$	−3.12661e6			−0.408954			−0.204477	−	0.978871i	$-0.565549\pi$
$197$	−3.12661e6			−0.408954			−0.204477	+	0.978871i	$0.565549\pi$
$198$	1.45981e6	+	2.06185e6i	0.188061	+	0.265620i
$199$		−	546538.i		−	0.0693523i	−0.999399	−	0.0346762i	$-0.988960\pi$
$199$		−	546538.i		−	0.0693523i	0.999399	−	0.0346762i	$-0.0110400\pi$
$200$	2.34048e6	+	8.21819e6i	0.292560	+	1.02727i
$201$	3.16647e6			0.389931
$202$	−375076.	+	265557.i	−0.0455056	+	0.0322184i
$203$		−	1.59987e6i		−	0.191247i
$204$	−1.53481e6	−	540561.i	−0.180786	−	0.0636728i
$205$	5.50423e6			0.638903
$206$	6.17187e6	+	8.71722e6i	0.706017	+	0.997186i
$207$			153868.i			0.0173475i
$208$	4.81370e6	+	3.87095e6i	0.534920	+	0.430157i
$209$	−844326.			−0.0924850
$210$	549018.	−	388710.i	0.0592828	−	0.0419728i
$211$			3.19130e6i			0.339719i	0.985468	+	0.169859i	$0.0543314\pi$
$211$			3.19130e6i			0.339719i	−0.985468	+	0.169859i	$0.945669\pi$
$212$	−2.72402e6	+	7.73429e6i	−0.285893	+	0.811733i
$213$	−1.24176e6			−0.128499
$214$	−9.05125e6	−	1.27841e7i	−0.923565	−	1.30445i
$215$		−	2.36790e7i		−	2.38258i
$216$	7.68927e6	−	2.18984e6i	0.762999	−	0.217296i
$217$	1.04269e6			0.102041
$218$	1.04698e6	−	741273.i	0.101058	−	0.0715499i
$219$		−	3.11759e6i		−	0.296815i
$220$	−5.82254e6	−	2.05070e6i	−0.546820	−	0.192590i
$221$	−3.23519e6			−0.299725
$222$	962042.	+	1.35880e6i	0.0879296	+	0.124193i
$223$			1.82721e7i			1.64768i	0.566821	+	0.823841i	$0.308173\pi$
$223$			1.82721e7i			1.64768i	−0.566821	+	0.823841i	$0.691827\pi$
$224$	79082.5	−	1.29086e6i	0.00703617	−	0.114851i
$225$	9.82225e6			0.862310
$226$	8.86085e6	−	6.27357e6i	0.767627	−	0.543487i
$227$		−	1.50032e7i		−	1.28265i	−0.767271	−	0.641323i	$-0.778386\pi$
$227$		−	1.50032e7i		−	1.28265i	0.767271	−	0.641323i	$-0.221614\pi$
$228$	−396507.	+	1.12580e6i	−0.0334538	+	0.0949851i
$229$	1.07397e7			0.894308			0.447154	−	0.894457i	$-0.352438\pi$
$229$	1.07397e7			0.894308			0.447154	+	0.894457i	$0.352438\pi$
$230$	−217257.	−	306856.i	−0.0178562	−	0.0252204i
$231$			250989.i			0.0203620i
$232$	5.68468e6	+	1.99608e7i	0.455242	+	1.59850i
$233$	2.09886e7			1.65926			0.829631	−	0.558312i	$-0.188551\pi$
$233$	2.09886e7			1.65926			0.829631	+	0.558312i	$0.188551\pi$
$234$	5.79497e6	−	4.10289e6i	0.452276	−	0.320215i
$235$		−	3.56290e7i		−	2.74536i
$236$	1.13929e6	+	401259.i	0.0866759	+	0.0305273i
$237$	−576453.			−0.0433031
$238$	391398.	+	552814.i	0.0290327	+	0.0410061i
$239$		−	1.23002e6i		−	0.0900990i	−0.998985	−	0.0450495i	$-0.985655\pi$
$239$		−	1.23002e6i		−	0.0900990i	0.998985	−	0.0450495i	$-0.0143446\pi$
$240$	−5.46868e6	+	6.80054e6i	−0.395593	+	0.491937i
$241$	1.95724e7			1.39828			0.699139	−	0.714985i	$-0.253567\pi$
$241$	1.95724e7			1.39828			0.699139	+	0.714985i	$0.253567\pi$
$242$	−9.68706e6	+	6.85853e6i	−0.683512	+	0.483933i
$243$		−	1.42750e7i		−	0.994851i
$244$	−3.54619e6	+	1.00686e7i	−0.244114	+	0.693109i
$245$	2.08688e7			1.41906
$246$	1.67759e6	+	2.36944e6i	0.112689	+	0.159163i
$247$			2.37304e6i			0.157476i
$248$	−1.30092e7	+	3.70491e6i	−0.852894	+	0.242898i
$249$	3.76575e6			0.243924
$250$	−1.24928e6	+	884499.i	−0.0799537	+	0.0566079i
$251$		−	1.20797e6i		−	0.0763897i	−0.999270	−	0.0381949i	$-0.987839\pi$
$251$		−	1.20797e6i		−	0.0763897i	0.999270	−	0.0381949i	$-0.0121608\pi$
$252$	−1.40217e6	−	493844.i	−0.0876190	−	0.0308595i
$253$	140282.			0.00866247
$254$	−7.46924e6	−	1.05496e7i	−0.455801	−	0.643778i
$255$		−	4.57051e6i		−	0.275641i
$256$	3.60002e6	+	1.63864e7i	0.214578	+	0.976707i
$257$	−2.44754e7			−1.44189			−0.720943	−	0.692994i	$-0.756291\pi$
$257$	−2.44754e7			−1.44189			−0.720943	+	0.692994i	$0.756291\pi$
$258$	1.01932e7	−	7.21691e6i	0.593544	−	0.420235i
$259$		−	693025.i		−	0.0398887i
$260$	−5.76365e6	+	1.63647e7i	−0.327927	+	0.931080i
$261$	2.38568e7			1.34181
$262$	−1.54437e7	−	2.18128e7i	−0.858709	−	1.21285i
$263$			8.19021e6i			0.450223i	0.974333	+	0.225111i	$0.0722746\pi$
$263$			8.19021e6i			0.450223i	−0.974333	+	0.225111i	$0.927725\pi$
$264$	−891822.	−	3.13148e6i	−0.0484692	−	0.170192i
$265$	−2.30319e7			−1.23764
$266$	405494.	−	287094.i	0.0215447	−	0.0152538i
$267$		−	358308.i		−	0.0188244i
$268$	1.61278e7	+	5.68023e6i	0.837860	+	0.295095i
$269$	4.43886e6			0.228042			0.114021	−	0.993478i	$-0.463627\pi$
$269$	4.43886e6			0.228042			0.114021	+	0.993478i	$0.463627\pi$
$270$	1.29761e7	+	1.83277e7i	0.659257	+	0.931141i
$271$			3.52126e7i			1.76925i	0.466301	+	0.884626i	$0.345586\pi$
$271$			3.52126e7i			1.76925i	−0.466301	+	0.884626i	$0.654414\pi$
$272$	−6.84756e6	−	5.50649e6i	−0.340274	−	0.273633i
$273$	705424.			0.0346707
$274$	3.06180e7	−	2.16779e7i	1.48842	−	1.05382i
$275$		−	8.95502e6i		−	0.430595i
$276$	65878.5	−	187048.i	0.00313340	−	0.00889664i
$277$	1.56422e7			0.735965			0.367983	−	0.929833i	$-0.380049\pi$
$277$	1.56422e7			0.735965			0.367983	+	0.929833i	$0.380049\pi$
$278$	−7.97191e6	−	1.12596e7i	−0.371046	−	0.524070i
$279$			1.55484e7i			0.715932i
$280$	3.49361e6	−	994954.i	0.159148	−	0.0453241i
$281$	2.32657e7			1.04857			0.524285	−	0.851543i	$-0.324333\pi$
$281$	2.32657e7			1.04857			0.524285	+	0.851543i	$0.324333\pi$
$282$	1.53374e7	−	1.08590e7i	0.683920	−	0.484222i
$283$			1.17289e7i			0.517486i	0.965946	+	0.258743i	$0.0833083\pi$
$283$			1.17289e7i			0.517486i	−0.965946	+	0.258743i	$0.916692\pi$
$284$	−6.32468e6	−	2.22756e6i	−0.276111	−	0.0972465i
$285$	−3.35251e6			−0.144822
$286$	−3.74064e6	−	5.28332e6i	−0.159900	−	0.225844i
$287$		−	1.20848e6i		−	0.0511204i
$288$	1.92489e7	+	1.17926e6i	0.805804	+	0.0493664i
$289$	−1.95355e7			−0.809339
$290$	−4.75773e7	+	3.36852e7i	−1.95077	+	1.38116i
$291$		−	7.90132e6i		−	0.320642i
$292$	5.59254e6	−	1.58788e7i	0.224626	−	0.637779i
$293$	−4.52757e7			−1.79996			−0.899979	−	0.435934i	$-0.856418\pi$
$293$	−4.52757e7			−1.79996			−0.899979	+	0.435934i	$0.856418\pi$
$294$	6.36043e6	+	8.98353e6i	0.250290	+	0.353513i
$295$			3.39269e6i			0.132153i
$296$	2.46247e6	+	8.64656e6i	0.0949503	+	0.333402i
$297$	−8.37868e6			−0.319820
$298$	1.51417e7	−	1.07204e7i	0.572170	−	0.405102i
$299$		−	394274.i		−	0.0147497i
$300$	−1.19403e7	−	4.20540e6i	−0.442235	−	0.155755i
$301$	−5.19884e6			−0.190637
$302$	−2.04200e7	−	2.88415e7i	−0.741372	−	1.04712i
$303$		−	680844.i		−	0.0244748i
$304$	−4.03906e6	+	5.02275e6i	−0.143767	+	0.178781i
$305$	−2.99834e7			−1.05677
$306$	−8.24344e6	+	5.83643e6i	−0.287703	+	0.203696i
$307$			3.91648e7i			1.35357i	0.736181	+	0.676785i	$0.236627\pi$
$307$			3.91648e7i			1.35357i	−0.736181	+	0.676785i	$0.763373\pi$
$308$	−450242.	+	1.27837e6i	−0.0154097	+	0.0437525i
$309$	−1.58236e7			−0.536329
$310$	−2.19539e7	−	3.10079e7i	−0.736929	−	1.04085i
$311$		−	3.14497e7i		−	1.04553i	−0.852478	−	0.522763i	$-0.824901\pi$
$311$		−	3.14497e7i		−	1.04553i	0.852478	−	0.522763i	$-0.175099\pi$
$312$	−8.80125e6	+	2.50653e6i	−0.289788	+	0.0825295i
$313$	−2.43745e7			−0.794883			−0.397441	−	0.917628i	$-0.630102\pi$
$313$	−2.43745e7			−0.794883			−0.397441	+	0.917628i	$0.630102\pi$
$314$	−2.62176e7	+	1.85623e7i	−0.846844	+	0.599573i
$315$		−	4.17551e6i		−	0.133591i
$316$	−2.93605e6	−	1.03408e6i	−0.0930471	−	0.0327713i
$317$	−3.40937e7			−1.07028			−0.535139	−	0.844764i	$-0.679741\pi$
$317$	−3.40937e7			−1.07028			−0.535139	+	0.844764i	$0.679741\pi$
$318$	−7.01971e6	−	9.91471e6i	−0.218292	−	0.308318i
$319$		−	2.17505e7i		−	0.670033i
$320$	−4.00529e7	+	2.48272e7i	−1.22232	+	0.757666i
$321$	2.32059e7			0.701589
$322$	−67371.8	+	47699.8i	−0.00201795	+	0.00142873i
$323$		−	3.37569e6i		−	0.100174i
$324$	5.18698e6	−	1.47273e7i	0.152503	−	0.433001i
$325$	−2.51687e7			−0.733181
$326$	2.13221e7	+	3.01156e7i	0.615429	+	0.869238i
$327$			1.90050e6i			0.0543531i
$328$	4.29401e6	+	1.50777e7i	0.121686	+	0.427280i
$329$	−7.82251e6			−0.219664
$330$	7.46400e6	−	5.28458e6i	0.207697	−	0.147051i
$331$		−	1.75934e7i		−	0.485139i	−0.970134	−	0.242569i	$-0.922010\pi$
$331$		−	1.75934e7i		−	0.485139i	0.970134	−	0.242569i	$-0.0779902\pi$
$332$	1.91801e7	+	6.75526e6i	0.524128	+	0.184598i
$333$	1.03342e7			0.279863
$334$	−8.91727e6	−	1.25949e7i	−0.239328	−	0.338029i
$335$			4.80270e7i			1.27747i
$336$	1.49309e6	+	1.20068e6i	0.0393613	+	0.0316525i
$337$	1.32250e7			0.345546			0.172773	−	0.984962i	$-0.444727\pi$
$337$	1.32250e7			0.345546			0.172773	+	0.984962i	$0.444727\pi$
$338$	1.66660e7	−	1.17997e7i	0.431601	−	0.305577i
$339$			1.60844e7i			0.412862i
$340$	8.19888e6	−	2.32790e7i	0.208602	−	0.592281i
$341$	1.41756e7			0.357501
$342$	4.28108e6	+	6.04664e6i	0.107022	+	0.151160i
$343$		−	9.22518e6i		−	0.228609i
$344$	6.48635e7	−	1.84726e7i	1.59340	−	0.453788i
$345$	557010.			0.0135646
$346$	2.61918e7	−	1.85440e7i	0.632321	−	0.447689i
$347$			5.96821e7i			1.42842i	0.699932	+	0.714209i	$0.253214\pi$
$347$			5.96821e7i			1.42842i	−0.699932	+	0.714209i	$0.746786\pi$
$348$	−2.90013e7	−	1.02143e7i	−0.688146	−	0.242366i
$349$	−4.24552e6			−0.0998745			−0.0499372	−	0.998752i	$-0.515902\pi$
$349$	−4.24552e6			−0.0998745			−0.0499372	+	0.998752i	$0.515902\pi$
$350$	3.04495e6	+	4.30072e6i	0.0710193	+	0.100308i
$351$			2.35489e7i			0.544564i
$352$	1.07514e6	−	1.75494e7i	0.0246511	−	0.402378i
$353$	1.08089e7			0.245729			0.122864	−	0.992423i	$-0.460792\pi$
$353$	1.08089e7			0.245729			0.122864	+	0.992423i	$0.460792\pi$
$354$	−1.46047e6	+	1.03403e6i	−0.0329219	+	0.0233090i
$355$		−	1.88343e7i		−	0.420982i
$356$	642757.	−	1.82497e6i	0.0142461	−	0.0404488i
$357$	−1.00348e6			−0.0220548
$358$	3.85077e7	+	5.43887e7i	0.839264	+	1.18539i
$359$			2.56464e7i			0.554299i	0.960827	+	0.277149i	$0.0893897\pi$
$359$			2.56464e7i			0.554299i	−0.960827	+	0.277149i	$0.910610\pi$
$360$	1.48365e7	+	5.20960e7i	0.317998	+	1.11660i
$361$	−2.47610e6			−0.0526316
$362$	4.83372e7	−	3.42232e7i	1.01896	−	0.721432i
$363$		−	1.75841e7i		−	0.367621i
$364$	3.59294e6	+	1.26544e6i	0.0744983	+	0.0262383i
$365$	4.72856e7			0.972412
$366$	−9.13839e6	−	1.29072e7i	−0.186392	−	0.263261i
$367$		−	1.00057e7i		−	0.202418i	−0.994865	−	0.101209i	$-0.967729\pi$
$367$		−	1.00057e7i		−	0.202418i	0.994865	−	0.101209i	$-0.0322711\pi$
$368$	671079.	−	834516.i	0.0134657	−	0.0167452i
$369$	1.80206e7			0.358666
$370$	−2.06094e7	+	1.45916e7i	−0.406874	+	0.288071i
$371$			5.05678e6i			0.0990266i
$372$	6.65703e6	−	1.89012e7i	0.129316	−	0.367165i
$373$	−1.42935e7			−0.275430			−0.137715	−	0.990472i	$-0.543976\pi$
$373$	−1.42935e7			−0.275430			−0.137715	+	0.990472i	$0.543976\pi$
$374$	5.32112e6	+	7.51561e6i	0.101716	+	0.143664i
$375$		−	2.26771e6i		−	0.0430024i
$376$	9.75980e7	−	2.77951e7i	1.83602	−	0.522884i
$377$	−6.11312e7			−1.14088
$378$	4.02393e6	−	2.84898e6i	0.0745032	−	0.0527489i
$379$			7.62386e7i			1.40042i	0.713938	+	0.700209i	$0.246910\pi$
$379$			7.62386e7i			1.40042i	−0.713938	+	0.700209i	$0.753090\pi$
$380$	−1.70754e7	−	6.01396e6i	−0.311185	−	0.109600i
$381$	1.91499e7			0.346251
$382$	−5.47642e7	−	7.73496e7i	−0.982442	−	1.38761i
$383$			1.02902e8i			1.83158i	0.401654	+	0.915791i	$0.368435\pi$
$383$			1.02902e8i			1.83158i	−0.401654	+	0.915791i	$0.631565\pi$
$384$	−2.28949e7	−	9.67499e6i	−0.404339	−	0.170866i
$385$	−3.80685e6			−0.0667088
$386$	6.53686e7	−	4.62816e7i	1.13660	−	0.804723i
$387$		−	7.75238e7i		−	1.33753i
$388$	1.41739e7	−	4.02439e7i	0.242658	−	0.688977i
$389$	3.71426e7			0.630991			0.315496	−	0.948927i	$-0.397829\pi$
$389$	3.71426e7			0.630991			0.315496	+	0.948927i	$0.397829\pi$
$390$	−1.48527e7	−	2.09781e7i	−0.250387	−	0.353649i
$391$			560861.i			0.00938264i
$392$	1.62803e7	+	5.71657e7i	0.270275	+	0.949024i
$393$	3.95949e7			0.652322
$394$	2.04142e7	−	1.44535e7i	0.333768	−	0.236311i
$395$		−	8.74327e6i		−	0.141867i
$396$	−1.90627e7	−	6.71390e6i	−0.306972	−	0.108116i
$397$	−7.61528e7			−1.21707			−0.608533	−	0.793528i	$-0.708242\pi$
$397$	−7.61528e7			−1.21707			−0.608533	+	0.793528i	$0.708242\pi$
$398$	2.52650e6	+	3.56845e6i	0.0400746	+	0.0566019i
$399$			736060.i			0.0115876i
$400$	−5.32719e7	−	4.28388e7i	−0.832373	−	0.669356i
$401$	−5.07560e7			−0.787144			−0.393572	−	0.919294i	$-0.628761\pi$
$401$	−5.07560e7			−0.787144			−0.393572	+	0.919294i	$0.628761\pi$
$402$	−2.06745e7	+	1.46377e7i	−0.318242	+	0.225318i
$403$		−	3.98415e7i		−	0.608723i
$404$	1.22134e6	−	3.46775e6i	0.0185223	−	0.0525900i
$405$	4.38565e7			0.660190
$406$	7.39575e6	+	1.04458e7i	0.110511	+	0.156086i
$407$		−	9.42180e6i		−	0.139750i
$408$	1.25199e7	−	3.56558e6i	0.184341	−	0.0524988i
$409$	−3.37620e7			−0.493467			−0.246733	−	0.969083i	$-0.579357\pi$
$409$	−3.37620e7			−0.493467			−0.246733	+	0.969083i	$0.579357\pi$
$410$	−3.59382e7	+	2.54446e7i	−0.521440	+	0.369185i
$411$			5.55784e7i			0.800535i
$412$	−8.05947e7	−	2.83855e7i	−1.15243	−	0.405887i
$413$	744883.			0.0105740
$414$	−711289.	−	1.00463e6i	−0.0100241	−	0.0141581i
$415$			5.71165e7i			0.799130i
$416$	−4.93239e7	−	3.02176e6i	−0.685137	−	0.0419739i
$417$	2.04386e7			0.281867
$418$	5.51277e6	−	3.90309e6i	0.0754816	−	0.0534416i
$419$		−	1.08092e8i		−	1.46943i	−0.678373	−	0.734717i	$-0.737315\pi$
$419$		−	1.08092e8i		−	1.46943i	0.678373	−	0.734717i	$-0.262685\pi$
$420$	−1.78775e6	+	5.07593e6i	−0.0241300	+	0.0685121i
$421$	6.92888e7			0.928574			0.464287	−	0.885685i	$-0.346311\pi$
$421$	6.92888e7			0.928574			0.464287	+	0.885685i	$0.346311\pi$
$422$	−1.47525e7	−	2.08366e7i	−0.196304	−	0.277261i
$423$		−	1.16648e8i		−	1.54118i
$424$	−1.79679e7	−	6.30911e7i	−0.235721	−	0.827696i
$425$	3.58029e7			0.466393
$426$	8.10771e6	−	5.74034e6i	0.104874	−	0.0742521i
$427$			6.58301e6i			0.0845553i
$428$	1.18195e8	+	4.16283e7i	1.50753	+	0.530954i
$429$	9.59036e6			0.121468
$430$	1.09461e8	+	1.54605e8i	1.37675	+	1.94454i
$431$		−	6.55929e7i		−	0.819266i	−0.912250	−	0.409633i	$-0.865657\pi$
$431$		−	6.55929e7i		−	0.819266i	0.912250	−	0.409633i	$-0.134343\pi$
$432$	−4.00817e7	+	4.98433e7i	−0.497158	+	0.618238i
$433$	2.87571e7			0.354227			0.177114	−	0.984190i	$-0.443324\pi$
$433$	2.87571e7			0.354227			0.177114	+	0.984190i	$0.443324\pi$
$434$	−6.80793e6	+	4.82008e6i	−0.0832810	+	0.0589637i
$435$		−	8.63631e7i		−	1.04921i
$436$	−3.40925e6	+	9.67983e6i	−0.0411338	+	0.116791i
$437$	411397.			0.00492966
$438$	1.44118e7	+	2.03553e7i	0.171512	+	0.242246i
$439$			7.76307e7i			0.917571i	0.888547	+	0.458786i	$0.151715\pi$
$439$			7.76307e7i			0.917571i	−0.888547	+	0.458786i	$0.848285\pi$
$440$	4.74963e7	−	1.35266e7i	0.557573	−	0.158792i
$441$	6.83235e7			0.796626
$442$	2.11232e7	−	1.49554e7i	0.244620	−	0.173193i
$443$		−	5.26161e7i		−	0.605212i	−0.953116	−	0.302606i	$-0.902143\pi$
$443$		−	5.26161e7i		−	0.605212i	0.953116	−	0.302606i	$-0.0978567\pi$
$444$	−1.25627e7	−	4.42460e6i	−0.143527	−	0.0505505i
$445$	5.43458e6			0.0616717
$446$	−8.44669e7	−	1.19302e8i	−0.952098	−	1.34475i
$447$			2.74854e7i			0.307737i
$448$	5.45093e6	+	8.79382e6i	0.0606229	+	0.0978011i
$449$	5.92286e7			0.654323			0.327161	−	0.944968i	$-0.393908\pi$
$449$	5.92286e7			0.654323			0.327161	+	0.944968i	$0.393908\pi$
$450$	−6.41314e7	+	4.54056e7i	−0.703773	+	0.498278i
$451$		−	1.64295e7i		−	0.179100i
$452$	−2.88532e7	+	8.19227e7i	−0.312449	+	0.887133i
$453$	5.23536e7			0.563186
$454$	6.93558e7	+	9.79589e7i	0.741166	+	1.04683i
$455$			1.06994e7i			0.113586i
$456$	−2.61539e6	−	9.18349e6i	−0.0275830	−	0.0968530i
$457$	−1.52328e8			−1.59600			−0.797999	−	0.602659i	$-0.794108\pi$
$457$	−1.52328e8			−1.59600			−0.797999	+	0.602659i	$0.794108\pi$
$458$	−7.01218e7	+	4.96469e7i	−0.729888	+	0.516768i
$459$		−	3.34987e7i		−	0.346409i
$460$	2.83703e6	+	999203.i	0.0291467	+	0.0102655i
$461$	−1.17190e7			−0.119616			−0.0598078	−	0.998210i	$-0.519049\pi$
$461$	−1.17190e7			−0.119616			−0.0598078	+	0.998210i	$0.519049\pi$
$462$	−1.16026e6	−	1.63876e6i	−0.0117660	−	0.0166184i
$463$			6.00475e7i			0.604995i	0.953150	+	0.302497i	$0.0978204\pi$
$463$			6.00475e7i			0.604995i	−0.953150	+	0.302497i	$0.902180\pi$
$464$	−1.29390e8	−	1.04049e8i	−1.29523	−	1.04156i
$465$	5.62860e7			0.559811
$466$	−1.37038e8	+	9.70245e7i	−1.35421	+	0.958790i
$467$		−	9.87028e7i		−	0.969123i	−0.874757	−	0.484562i	$-0.838979\pi$
$467$		−	9.87028e7i		−	0.969123i	0.874757	−	0.484562i	$-0.161021\pi$
$468$	−1.88699e7	+	5.35771e7i	−0.184091	+	0.522687i
$469$	1.05446e7			0.102214
$470$	1.64703e8	+	2.32628e8i	1.58638	+	2.24062i
$471$		−	4.75905e7i		−	0.455468i
$472$	−9.29356e6	+	2.64673e6i	−0.0883805	+	0.0251701i
$473$	−7.06791e7			−0.667894
$474$	3.76377e6	−	2.66479e6i	0.0353418	−	0.0250223i
$475$		−	2.62618e7i		−	0.245044i
$476$	−5.11102e6	−	1.80011e6i	−0.0473900	−	0.0166908i
$477$	−7.54055e7			−0.694781
$478$	5.68607e6	+	8.03107e6i	0.0520629	+	0.0735343i
$479$		−	2.40198e7i		−	0.218556i	−0.994011	−	0.109278i	$-0.965146\pi$
$479$		−	2.40198e7i		−	0.218556i	0.994011	−	0.109278i	$-0.0348539\pi$
$480$	4.26899e6	−	6.96823e7i	0.0386012	−	0.630084i
$481$	−2.64807e7			−0.237954
$482$	−1.27792e8	+	9.04781e7i	−1.14120	+	0.807983i
$483$		−	122294.i		−	0.00108534i
$484$	3.15436e7	−	8.95614e7i	0.278211	−	0.789923i
$485$	1.19842e8			1.05047
$486$	6.59896e7	+	9.32044e7i	0.574866	+	0.811947i
$487$			1.88299e8i			1.63028i	0.579266	+	0.815139i	$0.303339\pi$
$487$			1.88299e8i			1.63028i	−0.579266	+	0.815139i	$0.696661\pi$
$488$	−2.33909e7	−	8.21332e7i	−0.201274	−	0.706739i
$489$	−5.46663e7			−0.467513
$490$	−1.36256e8	+	9.64709e7i	−1.15816	+	0.819989i
$491$			1.38868e8i			1.17316i	0.809890	+	0.586582i	$0.199527\pi$
$491$			1.38868e8i			1.17316i	−0.809890	+	0.586582i	$0.800473\pi$
$492$	−2.19066e7	−	7.71552e6i	−0.183941	−	0.0647843i
$493$	8.69602e7			0.725738
$494$	−1.09699e7	−	1.54940e7i	−0.0909961	−	0.128524i
$495$		−	5.67668e7i		−	0.468036i
$496$	6.78126e7	−	8.43280e7i	0.555732	−	0.691078i
$497$	−4.13516e6			−0.0336839
$498$	−2.45873e7	+	1.74081e7i	−0.199078	+	0.140949i
$499$		−	2.11975e8i		−	1.70602i	−0.521896	−	0.853009i	$-0.674775\pi$
$499$		−	2.11975e8i		−	1.70602i	0.521896	−	0.853009i	$-0.325225\pi$
$500$	4.06797e6	−	1.15501e7i	0.0325437	−	0.0924010i
$501$	2.28624e7			0.181806
$502$	5.58412e6	+	7.88707e6i	0.0441411	+	0.0623454i
$503$			5.05810e7i			0.397451i	0.980055	+	0.198726i	$0.0636802\pi$
$503$			5.05810e7i			0.397451i	−0.980055	+	0.198726i	$0.936320\pi$
$504$	1.14379e7	−	3.25743e6i	0.0893420	−	0.0254439i
$505$	1.03266e7			0.0801832
$506$	−915931.	+	648488.i	−0.00706987	+	0.00500553i
$507$			3.02524e7i			0.232133i
$508$	9.75362e7	+	3.43523e7i	0.744003	+	0.262038i
$509$	−2.28416e8			−1.73210			−0.866050	−	0.499957i	$-0.833349\pi$
$509$	−2.28416e8			−1.73210			−0.866050	+	0.499957i	$0.833349\pi$
$510$	2.11282e7	+	2.98417e7i	0.159277	+	0.224964i
$511$		−	1.03818e7i		−	0.0778054i
$512$	−9.92552e7	−	9.03482e7i	−0.739509	−	0.673146i
$513$	−2.45716e7			−0.182004
$514$	1.59805e8	−	1.13143e8i	1.17679	−	0.833182i
$515$		−	2.40003e8i		−	1.75709i
$516$	−3.31918e7	+	9.42412e7i	−0.241592	+	0.685949i
$517$	−1.06348e8			−0.769590
$518$	3.20367e6	+	4.52490e6i	0.0230493	+	0.0325551i
$519$			4.75438e7i			0.340089i
$520$	−3.80174e7	−	1.33492e8i	−0.270379	−	0.949390i
$521$	1.65550e8			1.17062			0.585310	−	0.810809i	$-0.300973\pi$
$521$	1.65550e8			1.17062			0.585310	+	0.810809i	$0.300973\pi$
$522$	−1.55766e8	+	1.10284e8i	−1.09512	+	0.775353i
$523$		−	1.35143e8i		−	0.944686i	−0.881415	−	0.472343i	$-0.843408\pi$
$523$		−	1.35143e8i		−	0.944686i	0.881415	−	0.472343i	$-0.156592\pi$
$524$	2.01669e8	+	7.10281e7i	1.40167	+	0.493669i
$525$	−7.80674e6			−0.0539500
$526$	−3.78611e7	−	5.34754e7i	−0.260157	−	0.367449i
$527$			5.66751e7i			0.387223i
$528$	2.02989e7	+	1.63234e7i	0.137902	+	0.110894i
$529$	1.47968e8			0.999538
$530$	1.50380e8	−	1.06470e8i	1.01010	−	0.715157i
$531$			1.11075e7i			0.0741880i
$532$	−1.32039e6	+	3.74898e6i	−0.00876938	+	0.0248988i
$533$	−4.61764e7			−0.304957
$534$	1.65636e6	+	2.33946e6i	0.0108775	+	0.0153636i
$535$			3.51972e8i			2.29851i
$536$	−1.31560e8	+	3.74672e7i	−0.854337	+	0.243308i
$537$	−9.87272e7			−0.637550
$538$	−2.89822e7	+	2.05197e7i	−0.186116	+	0.131772i
$539$		−	6.22911e7i		−	0.397795i
$540$	−1.69448e8	−	5.96796e7i	−1.07610	−	0.379005i
$541$	1.34292e8			0.848121			0.424060	−	0.905634i	$-0.360604\pi$
$541$	1.34292e8			0.848121			0.424060	+	0.905634i	$0.360604\pi$
$542$	−1.62778e8	−	2.29910e8i	−1.02235	−	1.44397i
$543$			8.77426e7i			0.548038i
$544$	7.01641e7	+	4.29850e6i	0.435831	+	0.0267006i
$545$	−2.88256e7			−0.178069
$546$	−4.60585e6	+	3.26098e6i	−0.0282964	+	0.0200341i
$547$			6.77658e7i			0.414046i	0.978336	+	0.207023i	$0.0663775\pi$
$547$			6.77658e7i			0.414046i	−0.978336	+	0.207023i	$0.933623\pi$
$548$	−9.97002e7	+	2.83078e8i	−0.605835	+	1.72014i
$549$	−9.81643e7			−0.593248
$550$	4.13966e7	+	5.84691e7i	0.248815	+	0.351429i
$551$		−	6.37861e7i		−	0.381304i
$552$	434539.	+	1.52581e6i	0.00258352	+	0.00907159i
$553$	−1.91963e6			−0.0113512
$554$	−1.02131e8	+	7.23094e7i	−0.600657	+	0.425271i
$555$		−	3.74105e7i		−	0.218834i
$556$	1.04100e8	+	3.66642e7i	0.605658	+	0.213313i
$557$	4.33122e7			0.250637			0.125318	−	0.992117i	$-0.460005\pi$
$557$	4.33122e7			0.250637			0.125318	+	0.992117i	$0.460005\pi$
$558$	−7.18759e7	−	1.01518e8i	−0.413695	−	0.584308i
$559$			1.98649e8i			1.13724i
$560$	−1.82111e7	+	2.26463e7i	−0.103698	+	0.128953i
$561$	−1.36425e7			−0.0772687
$562$	−1.51906e8	+	1.07551e8i	−0.855790	+	0.605907i
$563$		−	2.30319e8i		−	1.29064i	−0.763913	−	0.645319i	$-0.776724\pi$
$563$		−	2.30319e8i		−	1.29064i	0.763913	−	0.645319i	$-0.223276\pi$
$564$	−4.99426e7	+	1.41802e8i	−0.278377	+	0.790394i
$565$	−2.43957e8			−1.35260
$566$	−5.42196e7	−	7.65804e7i	−0.299025	−	0.422346i
$567$		−	9.62891e6i		−	0.0528236i
$568$	5.15925e7	−	1.46931e7i	0.281541	−	0.0801807i
$569$	3.28302e8			1.78212			0.891059	−	0.453887i	$-0.149963\pi$
$569$	3.28302e8			1.78212			0.891059	+	0.453887i	$0.149963\pi$
$570$	2.18892e7	−	1.54977e7i	0.118197	−	0.0836843i
$571$		−	3.59864e8i		−	1.93299i	−0.256683	−	0.966496i	$-0.582630\pi$
$571$		−	3.59864e8i		−	1.93299i	0.256683	−	0.966496i	$-0.417370\pi$
$572$	4.88467e7	+	1.72038e7i	0.261004	+	0.0919258i
$573$	1.40406e8			0.746316
$574$	5.58648e6	+	7.89041e6i	0.0295395	+	0.0417219i
$575$			4.36333e6i			0.0229517i
$576$	−1.31131e8	+	8.12830e7i	−0.686182	+	0.425336i
$577$	9.65385e6			0.0502543			0.0251271	−	0.999684i	$-0.492001\pi$
$577$	9.65385e6			0.0502543			0.0251271	+	0.999684i	$0.492001\pi$
$578$	1.27551e8	−	9.03072e7i	0.660541	−	0.467669i
$579$			1.18658e8i			0.611311i
$580$	1.54924e8	−	4.39874e8i	0.794026	−	2.25447i
$581$	1.25402e7			0.0639406
$582$	3.65257e7	+	5.15892e7i	0.185280	+	0.261692i
$583$			6.87478e7i			0.346939i
$584$	3.68888e7	+	1.29529e8i	0.185207	+	0.650321i
$585$	−1.59547e8			−0.796933
$586$	2.95614e8	−	2.09297e8i	1.46903	−	1.04009i
$587$		−	2.03874e8i		−	1.00797i	−0.863712	−	0.503986i	$-0.831866\pi$
$587$		−	2.03874e8i		−	1.00797i	0.863712	−	0.503986i	$-0.168134\pi$
$588$	−8.30569e7	−	2.92527e7i	−0.408549	−	0.143891i
$589$	4.15717e7			0.203448
$590$	−1.56835e7	−	2.21515e7i	−0.0763637	−	0.107857i
$591$			3.70562e7i			0.179514i
$592$	−5.60487e7	−	4.50717e7i	−0.270147	−	0.217240i
$593$	1.07600e8			0.515997			0.257998	−	0.966145i	$-0.416937\pi$
$593$	1.07600e8			0.515997			0.257998	+	0.966145i	$0.416937\pi$
$594$	5.47060e7	−	3.87324e7i	0.261021	−	0.184805i
$595$		−	1.52201e7i		−	0.0722548i
$596$	−4.93052e7	+	1.39992e8i	−0.232892	+	0.661247i
$597$	−6.47751e6			−0.0304429
$598$	1.82262e6	+	2.57429e6i	0.00852301	+	0.0120380i
$599$		−	3.19378e8i		−	1.48602i	−0.669280	−	0.743010i	$-0.733397\pi$
$599$		−	3.19378e8i		−	1.48602i	0.669280	−	0.743010i	$-0.266603\pi$
$600$	9.74012e7	−	2.77391e7i	0.450931	−	0.128422i
$601$	−2.26861e8			−1.04505			−0.522524	−	0.852625i	$-0.675009\pi$
$601$	−2.26861e8			−1.04505			−0.522524	+	0.852625i	$0.675009\pi$
$602$	3.39442e7	−	2.40328e7i	0.155588	−	0.110158i
$603$			1.57238e8i			0.717144i
$604$	2.66653e8	+	9.39154e7i	1.21014	+	0.426212i
$605$	2.66705e8			1.20438
$606$	3.14736e6	+	4.44536e6i	0.0141426	+	0.0199751i
$607$			2.08398e8i			0.931810i	0.884835	+	0.465905i	$0.154271\pi$
$607$			2.08398e8i			0.931810i	−0.884835	+	0.465905i	$0.845729\pi$
$608$	3.15299e6	−	5.14660e7i	0.0140285	−	0.228986i
$609$	−1.89614e7			−0.0839498
$610$	1.95768e8	−	1.38605e8i	0.862484	−	0.610647i
$611$			2.98900e8i			1.31040i
$612$	2.68428e7	−	7.62143e7i	0.117104	−	0.332493i
$613$	1.66040e8			0.720828			0.360414	−	0.932792i	$-0.382635\pi$
$613$	1.66040e8			0.720828			0.360414	+	0.932792i	$0.382635\pi$
$614$	−1.81048e8	−	2.55714e8i	−0.782148	−	1.10471i
$615$		−	6.52356e7i		−	0.280453i
$616$	−2.96983e6	−	1.04281e7i	−0.0127054	−	0.0446130i
$617$	1.10651e8			0.471084			0.235542	−	0.971864i	$-0.424314\pi$
$617$	1.10651e8			0.471084			0.235542	+	0.971864i	$0.424314\pi$
$618$	1.03316e8	−	7.31484e7i	0.437724	−	0.309913i
$619$			4.44270e8i			1.87316i	0.350452	+	0.936581i	$0.386028\pi$
$619$			4.44270e8i			1.87316i	−0.350452	+	0.936581i	$0.613972\pi$
$620$	2.86682e8	+	1.00970e8i	1.20289	+	0.423658i
$621$	4.08250e6			0.0170471
$622$	1.45383e8	+	2.05341e8i	0.604148	+	0.853305i
$623$		−	1.19319e6i		−	0.00493452i
$624$	4.58781e7	−	5.70514e7i	0.188822	−	0.234808i
$625$	−2.26377e8			−0.927239
$626$	1.59146e8	−	1.12677e8i	0.648743	−	0.459316i
$627$			1.00069e7i			0.0405971i
$628$	8.53711e7	−	2.42393e8i	0.344693	−	0.978682i
$629$	3.76692e7			0.151368
$630$	1.93023e7	+	2.72627e7i	0.0771945	+	0.109030i
$631$			4.95484e8i			1.97216i	0.166280	+	0.986078i	$0.446824\pi$
$631$			4.95484e8i			1.97216i	−0.166280	+	0.986078i	$0.553176\pi$
$632$	2.39503e7	−	6.82087e6i	0.0948769	−	0.0270202i
$633$	3.78229e7			0.149123
$634$	2.22604e8	−	1.57606e8i	0.873506	−	0.618450i
$635$			2.90453e8i			1.13437i
$636$	9.16660e7	+	3.22849e7i	0.356318	+	0.125495i
$637$	−1.75074e8			−0.677333
$638$	1.00546e8	+	1.42013e8i	0.387173	+	0.546847i
$639$		−	6.16625e7i		−	0.236330i
$640$	1.46744e8	−	3.47255e8i	0.559784	−	1.32467i
$641$	7.93560e7			0.301305			0.150652	−	0.988587i	$-0.451863\pi$
$641$	7.93560e7			0.301305			0.150652	+	0.988587i	$0.451863\pi$
$642$	−1.51516e8	+	1.07275e8i	−0.572602	+	0.405407i
$643$		−	2.02965e8i		−	0.763465i	−0.924273	−	0.381732i	$-0.875328\pi$
$643$		−	2.02965e8i		−	0.763465i	0.924273	−	0.381732i	$-0.124672\pi$
$644$	219380.	−	622883.i	0.000821371	−	0.00233211i
$645$	−2.80641e8			−1.04586
$646$	1.56049e7	+	2.20405e7i	0.0578846	+	0.0817569i
$647$		−	3.38684e8i		−	1.25050i	−0.780427	−	0.625248i	$-0.784998\pi$
$647$		−	3.38684e8i		−	1.25050i	0.780427	−	0.625248i	$-0.215002\pi$
$648$	3.42137e7	+	1.20136e8i	0.125740	+	0.441516i
$649$	1.01268e7			0.0370458
$650$	1.64332e8	−	1.16348e8i	0.598385	−	0.423662i
$651$		−	1.23579e7i		−	0.0447920i
$652$	−2.78433e8	−	9.80642e7i	−1.00456	−	0.353808i
$653$	−5.27856e8			−1.89573			−0.947864	−	0.318676i	$-0.896762\pi$
$653$	−5.27856e8			−1.89573			−0.947864	+	0.318676i	$0.896762\pi$
$654$	−8.78550e6	−	1.24087e7i	−0.0314075	−	0.0443603i
$655$			6.00551e8i			2.13710i
$656$	−9.77364e7	−	7.85950e7i	−0.346214	−	0.278409i
$657$	1.54811e8			0.545890
$658$	5.10747e7	−	3.61614e7i	0.179278	−	0.126931i
$659$		−	1.03582e8i		−	0.361933i	−0.983489	−	0.180967i	$-0.942077\pi$
$659$		−	1.03582e8i		−	0.361933i	0.983489	−	0.180967i	$-0.0579226\pi$
$660$	−2.43047e7	+	6.90081e7i	−0.0845393	+	0.240032i
$661$	2.81482e7			0.0974646			0.0487323	−	0.998812i	$-0.484482\pi$
$661$	2.81482e7			0.0974646			0.0487323	+	0.998812i	$0.484482\pi$
$662$	8.13296e7	+	1.14871e8i	0.280333	+	0.395946i
$663$			3.83431e7i			0.131567i
$664$	−1.56459e8	+	4.45582e7i	−0.534436	+	0.152203i
$665$	−1.11641e7			−0.0379628
$666$	−6.74742e7	+	4.77724e7i	−0.228410	+	0.161716i
$667$			1.05979e7i			0.0357143i
$668$	1.16445e8	+	4.10121e7i	0.390654	+	0.137589i
$669$	2.16559e8			0.723265
$670$	−2.22016e8	−	3.13578e8i	−0.738176	−	1.04261i
$671$			8.94972e7i			0.296239i
$672$	−1.52991e7	−	937277.i	−0.0504148	−	0.00308859i
$673$	−1.18540e8			−0.388883			−0.194441	−	0.980914i	$-0.562289\pi$
$673$	−1.18540e8			−0.388883			−0.194441	+	0.980914i	$0.562289\pi$
$674$	−8.63485e7	+	6.11356e7i	−0.282017	+	0.199671i
$675$		−	2.60609e8i		−	0.847380i
$676$	−5.42689e7	+	1.54085e8i	−0.175675	+	0.498793i
$677$	7.24887e6			0.0233617			0.0116809	−	0.999932i	$-0.496282\pi$
$677$	7.24887e6			0.0233617			0.0116809	+	0.999932i	$0.496282\pi$
$678$	−7.43537e7	−	1.05018e8i	−0.238569	−	0.336957i
$679$		−	2.63119e7i		−	0.0840511i
$680$	5.40804e7	+	1.89894e8i	0.171994	+	0.603928i
$681$	−1.77817e8			−0.563029
$682$	−9.25550e7	+	6.55298e7i	−0.291774	+	0.206579i
$683$		−	3.89119e8i		−	1.22130i	−0.791903	−	0.610648i	$-0.790909\pi$
$683$		−	3.89119e8i		−	1.22130i	0.791903	−	0.610648i	$-0.209091\pi$
$684$	−5.59039e7	−	1.96894e7i	−0.174692	−	0.0615268i
$685$	−8.42977e8			−2.62267
$686$	4.26455e7	+	6.02330e7i	0.132099	+	0.186579i
$687$		−	1.27286e8i		−	0.392565i
$688$	−3.38112e8	+	4.20458e8i	−1.03824	+	1.29109i
$689$	1.93221e8			0.590739
$690$	−3.63683e6	+	2.57491e6i	−0.0110707	+	0.00783816i
$691$		−	1.28087e8i		−	0.388214i	−0.980980	−	0.194107i	$-0.937819\pi$
$691$		−	1.28087e8i		−	0.388214i	0.980980	−	0.194107i	$-0.0621810\pi$
$692$	−8.52873e7	+	2.42155e8i	−0.257375	+	0.730762i
$693$	−1.24634e7			−0.0374488
$694$	−2.75894e8	−	3.89676e8i	−0.825399	−	1.16580i
$695$			3.10000e8i			0.923438i
$696$	2.36573e8	−	6.73743e7i	0.701678	−	0.199833i
$697$	6.56866e7			0.193990
$698$	2.77198e7	−	1.96259e7i	0.0815125	−	0.0577116i
$699$		−	2.48754e8i		−	0.728348i
$700$	−3.97621e7	−	1.40043e7i	−0.115925	−	0.0408287i
$701$	5.13901e8			1.49185			0.745926	−	0.666029i	$-0.232007\pi$
$701$	5.13901e8			1.49185			0.745926	+	0.666029i	$0.232007\pi$
$702$	−1.08860e8	−	1.53755e8i	−0.314671	−	0.444445i
$703$		−	2.76307e7i		−	0.0795291i
$704$	7.41064e7	+	1.19554e8i	0.212392	+	0.342645i
$705$	−4.22271e8			−1.20510
$706$	−7.05732e7	+	4.99665e7i	−0.200551	+	0.141992i
$707$		−	2.26726e6i		−	0.00641568i
$708$	4.75568e6	−	1.35028e7i	0.0134003	−	0.0380472i
$709$	1.30532e7			0.0366250			0.0183125	−	0.999832i	$-0.494171\pi$
$709$	1.30532e7			0.0366250			0.0183125	+	0.999832i	$0.494171\pi$
$710$	8.70657e7	+	1.22973e8i	0.243261	+	0.343584i
$711$		−	2.86251e7i		−	0.0796412i
$712$	4.23967e6	+	1.48869e7i	0.0117461	+	0.0412443i
$713$	−6.90703e6			−0.0190556
$714$	6.55190e6	−	4.63880e6i	0.0180000	−	0.0127442i
$715$			1.45460e8i			0.397949i
$716$	−5.02848e8	−	1.77104e8i	−1.36993	−	0.482490i
$717$	−1.45781e7			−0.0395498
$718$	−1.18557e8	−	1.67451e8i	−0.320297	−	0.452390i
$719$			3.77365e8i			1.01525i	0.861577	+	0.507627i	$0.169477\pi$
$719$			3.77365e8i			1.01525i	−0.861577	+	0.507627i	$0.830523\pi$
$720$	−3.37696e8	−	2.71559e8i	−0.904750	−	0.727558i
$721$	−5.26938e7			−0.140590
$722$	1.61669e7	−	1.14463e7i	0.0429552	−	0.0304127i
$723$		−	2.31971e8i		−	0.613787i
$724$	−1.57399e8	+	4.46900e8i	−0.414749	+	1.17759i
$725$	6.76523e8			1.77529
$726$	8.12866e7	+	1.14810e8i	0.212427	+	0.300034i
$727$			3.44700e8i			0.897094i	0.893759	+	0.448547i	$0.148058\pi$
$727$			3.44700e8i			0.897094i	−0.893759	+	0.448547i	$0.851942\pi$
$728$	−2.93088e7	+	8.34692e6i	−0.0759633	+	0.0216338i
$729$	8.66763e6			0.0223727
$730$	−3.08737e8	+	2.18589e8i	−0.793633	+	0.561900i
$731$		−	2.82581e8i		−	0.723421i
$732$	1.19333e8	+	4.20290e7i	0.304247	+	0.107156i
$733$	−5.51510e8			−1.40036			−0.700182	−	0.713964i	$-0.746898\pi$
$733$	−5.51510e8			−1.40036			−0.700182	+	0.713964i	$0.746898\pi$
$734$	4.62536e7	+	6.53291e7i	0.116965	+	0.165203i
$735$		−	2.47335e8i		−	0.622908i
$736$	−523861.	+	8.55093e6i	−0.00131396	+	0.0214477i
$737$	1.43355e8			0.358106
$738$	−1.17660e8	+	8.33043e7i	−0.292725	+	0.207252i
$739$			3.56434e8i			0.883173i	0.897219	+	0.441587i	$0.145584\pi$
$739$			3.56434e8i			0.883173i	−0.897219	+	0.441587i	$0.854416\pi$
$740$	6.71095e7	−	1.90543e8i	0.165611	−	0.470217i
$741$	2.81250e7			0.0691255
$742$	−2.33761e7	−	3.30167e7i	−0.0572217	−	0.0808205i
$743$		−	5.02630e8i		−	1.22541i	−0.790311	−	0.612706i	$-0.790081\pi$
$743$		−	5.02630e8i		−	1.22541i	0.790311	−	0.612706i	$-0.209919\pi$
$744$	4.39103e7	+	1.54184e8i	0.106622	+	0.374386i
$745$	−4.16881e8			−1.00819
$746$	9.33248e7	−	6.60748e7i	0.224792	−	0.159155i
$747$			1.86997e8i			0.448614i
$748$	−6.94852e7	−	2.44728e7i	−0.166030	−	0.0584761i
$749$	7.72772e7			0.183910
$750$	1.04830e7	+	1.48063e7i	0.0248486	+	0.0350964i
$751$		−	6.61475e8i		−	1.56169i	−0.624727	−	0.780843i	$-0.714790\pi$
$751$		−	6.61475e8i		−	1.56169i	0.624727	−	0.780843i	$-0.285210\pi$
$752$	−5.08747e8	+	6.32649e8i	−1.19632	+	1.48768i
$753$	−1.43167e7			−0.0335320
$754$	3.99138e8	−	2.82593e8i	0.931126	−	0.659246i
$755$			7.94065e8i			1.84508i
$756$	−1.31029e7	+	3.72031e7i	−0.0303252	+	0.0861020i
$757$	−5.73592e8			−1.32226			−0.661128	−	0.750273i	$-0.729922\pi$
$757$	−5.73592e8			−1.32226			−0.661128	+	0.750273i	$0.729922\pi$
$758$	−3.52431e8	−	4.97777e8i	−0.809219	−	1.14295i
$759$		−	1.66261e6i		−	0.00380247i
$760$	1.39289e8	−	3.96685e7i	0.317305	−	0.0903660i
$761$	2.81973e7			0.0639814			0.0319907	−	0.999488i	$-0.489815\pi$
$761$	2.81973e7			0.0639814			0.0319907	+	0.999488i	$0.489815\pi$
$762$	−1.25033e8	+	8.85246e7i	−0.282592	+	0.200078i
$763$			6.32880e6i			0.0142478i
$764$	7.15133e8	+	2.51870e8i	1.60364	+	0.564803i
$765$	2.26959e8			0.506947
$766$	−4.75687e8	−	6.71866e8i	−1.05836	−	1.49484i
$767$		−	2.84621e7i		−	0.0630785i
$768$	1.94210e8	−	4.26671e7i	0.428735	−	0.0941911i
$769$	4.90996e8			1.07969			0.539844	−	0.841765i	$-0.318483\pi$
$769$	4.90996e8			1.07969			0.539844	+	0.841765i	$0.318483\pi$
$770$	2.48556e7	−	1.75980e7i	0.0544444	−	0.0385471i
$771$			2.90080e8i			0.632930i
$772$	−2.12857e8	+	6.04363e8i	−0.462633	+	1.31355i
$773$	8.28311e8			1.79331			0.896654	−	0.442731i	$-0.145990\pi$
$773$	8.28311e8			1.79331			0.896654	+	0.442731i	$0.145990\pi$
$774$	3.58372e8	+	5.06168e8i	0.772878	+	1.09162i
$775$			4.40915e8i			0.947217i
$776$	9.34922e7	+	3.28282e8i	0.200074	+	0.702526i
$777$	−8.21367e6			−0.0175095
$778$	−2.42511e8	+	1.71700e8i	−0.514983	+	0.364613i
$779$		−	4.81818e7i		−	0.101923i
$780$	1.93952e8	+	6.83102e7i	0.408706	+	0.143947i
$781$	−5.62182e7			−0.118011
$782$	−2.59271e6	−	3.66197e6i	−0.00542168	−	0.00765764i
$783$		−	6.32982e8i		−	1.31858i
$784$	−3.70559e8	−	2.97986e8i	−0.768970	−	0.618369i
$785$	7.21823e8			1.49218
$786$	−2.58523e8	+	1.83037e8i	−0.532392	+	0.376938i
$787$		−	5.08364e8i		−	1.04292i	−0.853276	−	0.521459i	$-0.825388\pi$
$787$		−	5.08364e8i		−	1.04292i	0.853276	−	0.521459i	$-0.174612\pi$
$788$	−6.64740e7	+	1.88739e8i	−0.135854	+	0.385729i
$789$	9.70695e7			0.197630
$790$	4.04178e7	+	5.70865e7i	0.0819768	+	0.115785i
$791$			5.35621e7i			0.108225i
$792$	1.55501e8	−	4.42854e7i	0.313009	−	0.0891425i
$793$	2.51538e8			0.504411
$794$	4.97216e8	−	3.52034e8i	0.993308	−	0.703271i
$795$			2.72972e8i			0.543272i
$796$	−3.29920e7	−	1.16198e7i	−0.0654138	−	0.0230388i
$797$	−1.24758e8			−0.246431			−0.123215	−	0.992380i	$-0.539321\pi$
$797$	−1.24758e8			−0.246431			−0.123215	+	0.992380i	$0.539321\pi$
$798$	−3.40261e6	−	4.80588e6i	−0.00669581	−	0.00945723i
$799$		−	4.25190e8i		−	0.833572i
$800$	5.45855e8	+	3.34410e7i	1.06612	+	0.0653145i
$801$	1.77926e7			0.0346211
$802$	3.31396e8	−	2.34631e8i	0.642427	−	0.454844i
$803$		−	1.41142e8i		−	0.272590i
$804$	6.73215e7	−	1.91145e8i	0.129535	−	0.367786i
$805$	1.85488e6			0.00355573
$806$	1.84176e8	+	2.60133e8i	0.351745	+	0.496809i
$807$		−	5.26090e7i		−	0.100101i
$808$	8.05607e6	+	2.82875e7i	0.0152718	+	0.0536242i
$809$	7.72600e7			0.145918			0.0729591	−	0.997335i	$-0.476756\pi$
$809$	7.72600e7			0.145918			0.0729591	+	0.997335i	$0.476756\pi$
$810$	−2.86347e8	+	2.02737e8i	−0.538813	+	0.381485i
$811$		−	5.47814e8i		−	1.02700i	−0.858090	−	0.513500i	$-0.828349\pi$
$811$		−	5.47814e8i		−	1.02700i	0.858090	−	0.513500i	$-0.171651\pi$
$812$	−9.65765e7	−	3.40143e7i	−0.180386	−	0.0635322i
$813$	4.17336e8			0.776629
$814$	4.35544e7	+	6.15168e7i	0.0807531	+	0.114057i
$815$		−	8.29144e8i		−	1.53164i
$816$	−6.52623e7	+	8.11566e7i	−0.120114	+	0.149367i
$817$	−2.07276e8			−0.380087
$818$	2.20438e8	−	1.56072e8i	0.402743	−	0.285145i
$819$			3.50294e7i			0.0637648i
$820$	1.17024e8	−	3.32265e8i	0.212243	−	0.602620i
$821$	−7.87142e8			−1.42241			−0.711203	−	0.702987i	$-0.751849\pi$
$821$	−7.87142e8			−1.42241			−0.711203	+	0.702987i	$0.751849\pi$
$822$	−2.56924e8	−	3.62882e8i	−0.462582	−	0.653356i
$823$			3.81472e7i			0.0684326i	0.999414	+	0.0342163i	$0.0108935\pi$
$823$			3.81472e7i			0.0684326i	−0.999414	+	0.0342163i	$0.989106\pi$
$824$	6.57437e8	−	1.87233e8i	1.17509	−	0.334658i
$825$	−1.06134e8			−0.189013
$826$	−4.86348e6	+	3.44339e6i	−0.00862993	+	0.00611007i
$827$			3.67173e8i			0.649164i	0.945858	+	0.324582i	$0.105224\pi$
$827$			3.67173e8i			0.649164i	−0.945858	+	0.324582i	$0.894776\pi$
$828$	9.28829e6	+	3.27134e6i	0.0163623	+	0.00576282i
$829$	6.07250e8			1.06587			0.532935	−	0.846156i	$-0.321089\pi$
$829$	6.07250e8			1.06587			0.532935	+	0.846156i	$0.321089\pi$
$830$	−2.64034e8	−	3.72925e8i	−0.461770	−	0.652210i
$831$		−	1.85389e8i		−	0.323059i
$832$	3.36014e8	−	2.08281e8i	0.583428	−	0.361643i
$833$	2.49045e8			0.430867
$834$	−1.33448e8	+	9.44823e7i	−0.230045	+	0.162874i
$835$			3.46762e8i			0.595624i
$836$	−1.79510e7	+	5.09681e7i	−0.0307234	+	0.0872327i
$837$	4.12538e8			0.703537
$838$	4.99679e8	+	7.05752e8i	0.849100	+	1.19928i
$839$		−	2.91590e8i		−	0.493728i	−0.969050	−	0.246864i	$-0.920600\pi$
$839$		−	2.91590e8i		−	0.493728i	0.969050	−	0.246864i	$-0.0794000\pi$
$840$	−1.17921e7	−	4.14060e7i	−0.0198954	−	0.0698594i
$841$	1.04835e9			1.76246
$842$	−4.52400e8	+	3.20303e8i	−0.757855	+	0.536568i
$843$		−	2.75743e8i		−	0.460280i
$844$	1.92644e8	+	6.78493e7i	0.320426	+	0.112854i
$845$	−4.58850e8			−0.760502
$846$	5.39230e8	+	7.61614e8i	0.890559	+	1.25784i
$847$		−	5.85563e7i		−	0.0963660i
$848$	4.08969e8	+	3.28874e8i	0.670660	+	0.539314i
$849$	1.39010e8			0.227155
$850$	−2.33764e8	+	1.65507e8i	−0.380646	+	0.269501i
$851$			4.59076e6i			0.00744897i
$852$	−2.64008e7	+	7.49595e7i	−0.0426873	+	0.121202i
$853$	1.01563e9			1.63640			0.818198	−	0.574937i	$-0.194973\pi$
$853$	1.01563e9			1.63640			0.818198	+	0.574937i	$0.194973\pi$
$854$	−3.04315e7	−	4.29817e7i	−0.0488595	−	0.0690097i
$855$		−	1.66476e8i		−	0.266351i
$856$	−9.64153e8	+	2.74583e8i	−1.53718	+	0.437777i
$857$	−6.83024e8			−1.08516			−0.542580	−	0.840004i	$-0.682552\pi$
$857$	−6.83024e8			−1.08516			−0.542580	+	0.840004i	$0.682552\pi$
$858$	−6.26173e7	+	4.43337e7i	−0.0991363	+	0.0701894i
$859$		−	5.32877e8i		−	0.840713i	−0.907359	−	0.420356i	$-0.861905\pi$
$859$		−	5.32877e8i		−	0.840713i	0.907359	−	0.420356i	$-0.138095\pi$
$860$	−1.42939e9	−	5.03432e8i	−2.24727	−	0.791491i
$861$	−1.43228e7			−0.0224398
$862$	3.03218e8	+	4.28269e8i	0.473406	+	0.668643i
$863$		−	7.75563e8i		−	1.20666i	−0.797492	−	0.603330i	$-0.793840\pi$
$863$		−	7.75563e8i		−	1.20666i	0.797492	−	0.603330i	$-0.206160\pi$
$864$	3.12887e7	−	5.10723e8i	0.0485117	−	0.791853i
$865$	−7.21114e8			−1.11418
$866$	−1.87761e8	+	1.32936e8i	−0.289102	+	0.204687i
$867$			2.31532e8i			0.355267i
$868$	2.21684e7	−	6.29424e7i	0.0338981	−	0.0962464i
$869$	−2.60977e7			−0.0397688
$870$	3.99233e8	+	5.63881e8i	0.606274	+	0.856308i
$871$		−	4.02910e8i		−	0.609753i
$872$	−2.24876e7	−	7.89615e7i	−0.0339152	−	0.119087i
$873$	3.92358e8			0.589711
$874$	−2.68609e6	+	1.90178e6i	−0.00402334	+	0.00284856i
$875$		−	7.55162e6i		−	0.0112724i
$876$	−1.88195e8	−	6.62823e7i	−0.279959	−	0.0986018i
$877$	4.34542e8			0.644218			0.322109	−	0.946703i	$-0.395608\pi$
$877$	4.34542e8			0.644218			0.322109	+	0.946703i	$0.395608\pi$
$878$	−3.58866e8	−	5.06866e8i	−0.530211	−	0.748875i
$879$			5.36603e8i			0.790108i
$880$	−2.47583e8	+	3.07880e8i	−0.363306	+	0.451787i
$881$	−7.44134e8			−1.08824			−0.544118	−	0.839009i	$-0.683136\pi$
$881$	−7.44134e8			−1.08824			−0.544118	+	0.839009i	$0.683136\pi$
$882$	−4.46097e8	+	3.15841e8i	−0.650165	+	0.460323i
$883$			4.95209e8i			0.719295i	0.933088	+	0.359647i	$0.117103\pi$
$883$			4.95209e8i			0.719295i	−0.933088	+	0.359647i	$0.882897\pi$
$884$	−6.87824e7	+	1.95293e8i	−0.0995682	+	0.282703i
$885$	4.02099e7			0.0580100
$886$	2.43230e8	+	3.43541e8i	0.349717	+	0.493944i
$887$			1.36360e9i			1.95397i	0.213311	+	0.976984i	$0.431575\pi$
$887$			1.36360e9i			1.95397i	−0.213311	+	0.976984i	$0.568425\pi$
$888$	1.02478e8	−	2.91850e7i	0.146350	−	0.0416793i
$889$	6.37704e7			0.0907640
$890$	−3.54834e7	+	2.51226e7i	−0.0503333	+	0.0356365i
$891$		−	1.30907e8i		−	0.185067i
$892$	1.10300e9	+	3.88478e8i	1.55411	+	0.547358i
$893$	−3.11881e8			−0.437960
$894$	−1.27058e8	−	1.79458e8i	−0.177823	−	0.251159i
$895$		−	1.49743e9i		−	2.08871i
$896$	−7.62417e7	−	3.22184e7i	−0.105991	−	0.0447899i
$897$	−4.67290e6			−0.00647454
$898$	−3.86715e8	+	2.73798e8i	−0.534025	+	0.378095i
$899$			1.07092e9i			1.47393i
$900$	2.08828e8	−	5.92924e8i	0.286459	−	0.813339i
$901$	−2.74860e8			−0.375782
$902$	7.59492e7	+	1.07272e8i	0.103491	+	0.146172i
$903$			6.16161e7i			0.0836818i
$904$	−1.90318e8	−	6.68270e8i	−0.257617	−	0.904579i
$905$	−1.33082e9			−1.79546
$906$	−3.41827e8	+	2.42016e8i	−0.459644	+	0.325432i
$907$		−	8.48842e8i		−	1.13764i	−0.822462	−	0.568820i	$-0.807400\pi$
$907$		−	8.48842e8i		−	1.13764i	0.822462	−	0.568820i	$-0.192600\pi$
$908$	−9.05675e8	−	3.18980e8i	−1.20980	−	0.426094i
$909$	3.38088e7			0.0450130
$910$	−4.94605e7	−	6.98586e7i	−0.0656349	−	0.0927034i
$911$			5.90719e8i			0.781315i	0.920536	+	0.390657i	$0.127752\pi$
$911$			5.90719e8i			0.781315i	−0.920536	+	0.390657i	$0.872248\pi$
$912$	5.95291e7	+	4.78706e7i	0.0784775	+	0.0631079i
$913$	1.70487e8			0.224015
$914$	9.94581e8	−	7.04173e8i	1.30257	−	0.922233i
$915$			3.55360e8i			0.463880i
$916$	2.28335e8	−	6.48308e8i	0.297088	−	0.843519i
$917$	1.31854e8			0.170996
$918$	1.54855e8	+	2.18719e8i	0.200170	+	0.282722i
$919$			4.57837e8i			0.589881i	0.955516	+	0.294940i	$0.0952998\pi$
$919$			4.57837e8i			0.589881i	−0.955516	+	0.294940i	$0.904700\pi$
$920$	−2.31425e7	+	6.59081e6i	−0.0297199	+	0.00846400i
$921$	4.64177e8			0.594162
$922$	7.65157e7	−	5.41738e7i	0.0976242	−	0.0691189i
$923$			1.58005e8i			0.200940i
$924$	1.51511e7	+	5.33622e6i	0.0192056	+	0.00676422i
$925$	2.93054e8			0.370274
$926$	−2.77583e8	−	3.92062e8i	−0.349591	−	0.493766i
$927$		−	7.85758e8i		−	0.986392i
$928$	1.32580e9	+	8.12234e7i	1.65896	+	0.101634i
$929$	3.31295e7			0.0413207			0.0206604	−	0.999787i	$-0.493423\pi$
$929$	3.31295e7			0.0413207			0.0206604	+	0.999787i	$0.493423\pi$
$930$	−3.67502e8	+	2.60195e8i	−0.456889	+	0.323482i
$931$		−	1.82677e8i		−	0.226378i
$932$	4.46232e8	−	1.26698e9i	0.551205	−	1.56503i
$933$	−3.72738e8			−0.458943
$934$	4.56276e8	+	6.44450e8i	0.559999	+	0.790949i
$935$		−	2.06920e8i		−	0.253144i
$936$	−1.24467e8	−	4.37046e8i	−0.151785	−	0.532966i
$937$	−2.76382e8			−0.335962			−0.167981	−	0.985790i	$-0.553725\pi$
$937$	−2.76382e8			−0.335962			−0.167981	+	0.985790i	$0.553725\pi$
$938$	−6.88476e7	+	4.87447e7i	−0.0834219	+	0.0590635i
$939$			2.88884e8i			0.348921i
$940$	−2.15076e9	−	7.57498e8i	−2.58945	−	0.912006i
$941$	−4.58833e8			−0.550663			−0.275331	−	0.961349i	$-0.588788\pi$
$941$	−4.58833e8			−0.550663			−0.275331	+	0.961349i	$0.588788\pi$
$942$	2.19998e8	+	3.10728e8i	0.263188	+	0.371730i
$943$			8.00527e6i			0.00954643i
$944$	4.84443e7	−	6.02427e7i	0.0575873	−	0.0716124i
$945$	−1.10787e8			−0.131278
$946$	4.61477e8	−	3.26730e8i	0.545101	−	0.385937i
$947$			1.75733e8i			0.206921i	0.994634	+	0.103460i	$0.0329915\pi$
$947$			1.75733e8i			0.206921i	−0.994634	+	0.103460i	$0.967009\pi$
$948$	−1.22558e7	+	3.47978e7i	−0.0143852	+	0.0408439i
$949$	−3.96691e8			−0.464144
$950$	1.21401e8	+	1.71468e8i	0.141596	+	0.199992i
$951$			4.04075e8i			0.469808i
$952$	4.16922e7	−	1.18736e7i	0.0483219	−	0.0137617i
$953$	−1.55427e7			−0.0179576			−0.00897879	−	0.999960i	$-0.502858\pi$
$953$	−1.55427e7			−0.0179576			−0.00897879	+	0.999960i	$0.502858\pi$
$954$	4.92337e8	−	3.48579e8i	0.567045	−	0.401473i
$955$			2.12959e9i			2.44504i
$956$	−7.42509e7	−	2.61512e7i	−0.0849823	−	0.0299308i
$957$	−2.57784e8			−0.294117
$958$	1.11037e8	+	1.56830e8i	0.126291	+	0.178374i
$959$			1.85080e8i			0.209847i
$960$	2.94249e8	+	4.74704e8i	0.332584	+	0.536548i
$961$	1.89547e8			0.213573
$962$	1.72897e8	−	1.22413e8i	0.194206	−	0.137500i
$963$			1.15234e9i			1.29033i
$964$	4.16124e8	−	1.18150e9i	0.464507	−	1.31887i
$965$	−1.79973e9			−2.00275
$966$	565334.	+	798484.i	0.000627153	+	0.000885798i
$967$			1.66888e9i			1.84564i	0.385236	+	0.922818i	$0.374120\pi$
$967$			1.66888e9i			1.84564i	−0.385236	+	0.922818i	$0.625880\pi$
$968$	2.08064e8	+	7.30581e8i	0.229388	+	0.805457i
$969$	−4.00083e7			−0.0439723
$970$	−7.82473e8	+	5.53998e8i	−0.857342	+	0.607006i
$971$		−	1.09973e9i		−	1.20124i	−0.799535	−	0.600620i	$-0.794921\pi$
$971$		−	1.09973e9i		−	1.20124i	0.799535	−	0.600620i	$-0.205079\pi$
$972$	−8.61718e8	−	3.03498e8i	−0.938353	−	0.330489i
$973$	6.80621e7			0.0738868
$974$	−8.70456e8	−	1.22944e9i	−0.942042	−	1.33055i
$975$			2.98297e8i			0.321837i
$976$	5.32403e8	+	4.28134e8i	0.572653	+	0.460500i
$977$	−3.80732e8			−0.408259			−0.204129	−	0.978944i	$-0.565436\pi$
$977$	−3.80732e8			−0.408259			−0.204129	+	0.978944i	$0.565436\pi$
$978$	3.56927e8	−	2.52708e8i	0.381560	−	0.270148i
$979$		−	1.62216e7i		−	0.0172881i
$980$	4.43686e8	−	1.25975e9i	0.471409	−	1.33847i
$981$	−9.43736e7			−0.0999639
$982$	−6.41951e8	−	9.06698e8i	−0.677902	−	0.957477i
$983$		−	5.81394e7i		−	0.0612083i	−0.999532	−	0.0306041i	$-0.990257\pi$
$983$		−	5.81394e7i		−	0.0612083i	0.999532	−	0.0306041i	$-0.00974312\pi$
$984$	1.78699e8	−	5.08921e7i	0.187559	−	0.0534153i
$985$	−5.62045e8			−0.588115
$986$	−5.67780e8	+	4.01993e8i	−0.592310	+	0.419361i
$987$			9.27117e7i			0.0964235i
$988$	1.43249e8	+	5.04526e7i	0.148533	+	0.0523133i
$989$	3.44383e7			0.0356002
$990$	2.62418e8	+	3.70642e8i	0.270450	+	0.381987i
$991$			5.54527e8i			0.569773i	0.958561	+	0.284887i	$0.0919559\pi$
$991$			5.54527e8i			0.569773i	−0.958561	+	0.284887i	$0.908044\pi$
$992$	−5.29362e7	+	8.64074e8i	−0.0542273	+	0.885148i
$993$	−2.08515e8			−0.212956
$994$	2.69992e7	−	1.91157e7i	0.0274911	−	0.0194640i
$995$		−	9.82468e7i		−	0.0997354i
$996$	8.00627e7	−	2.27321e8i	0.0810312	−	0.230071i
$997$	1.07984e9			1.08961			0.544807	−	0.838561i	$-0.316603\pi$
$997$	1.07984e9			1.08961			0.544807	+	0.838561i	$0.316603\pi$
$998$	9.79905e8	+	1.38403e9i	0.985808	+	1.39237i
$999$		−	2.74193e8i		−	0.275018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.12	yes	54
4.3	odd	2	inner	76.7.b.a.39.11	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.11	✓	54	4.3	odd	2	inner
76.7.b.a.39.12	yes	54	1.1	even	1	trivial

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.52919 + 4.62273i) q^{2} -11.8519i q^{3} +(21.2607 - 60.3654i) q^{4} +179.762 q^{5} +(54.7881 + 77.3834i) q^{6} -39.4677i q^{7} +(140.237 + 492.420i) q^{8} +588.532 q^{9} +O(q^{10})\)	\(q+(-6.52919 + 4.62273i) q^{2} -11.8519i q^{3} +(21.2607 - 60.3654i) q^{4} +179.762 q^{5} +(54.7881 + 77.3834i) q^{6} -39.4677i q^{7} +(140.237 + 492.420i) q^{8} +588.532 q^{9} +(-1173.70 + 830.991i) q^{10} -536.570i q^{11} +(-715.445 - 251.980i) q^{12} -1508.07 q^{13} +(182.448 + 257.692i) q^{14} -2130.52i q^{15} +(-3191.96 - 2566.83i) q^{16} +2145.25 q^{17} +(-3842.64 + 2720.63i) q^{18} -1573.56i q^{19} +(3821.87 - 10851.4i) q^{20} -467.767 q^{21} +(2480.42 + 3503.37i) q^{22} +261.443i q^{23} +(5836.11 - 1662.08i) q^{24} +16689.4 q^{25} +(9846.47 - 6971.39i) q^{26} -15615.3i q^{27} +(-2382.48 - 839.112i) q^{28} +40536.1 q^{29} +(9848.83 + 13910.6i) q^{30} +26418.9i q^{31} +(32706.7 + 2003.73i) q^{32} -6359.37 q^{33} +(-14006.8 + 9916.92i) q^{34} -7094.79i q^{35} +(12512.6 - 35527.0i) q^{36} +17559.3 q^{37} +(7274.15 + 10274.1i) q^{38} +17873.5i q^{39} +(25209.4 + 88518.4i) q^{40} +30619.5 q^{41} +(3054.14 - 2162.36i) q^{42} -131724. i q^{43} +(-32390.2 - 11407.9i) q^{44} +105796. q^{45} +(-1208.58 - 1707.01i) q^{46} -198201. i q^{47} +(-30421.8 + 37830.8i) q^{48} +116091. q^{49} +(-108968. + 77150.5i) q^{50} -25425.3i q^{51} +(-32062.6 + 91035.1i) q^{52} -128125. q^{53} +(72185.1 + 101955. i) q^{54} -96454.9i q^{55} +(19434.7 - 5534.84i) q^{56} -18649.7 q^{57} +(-264668. + 187388. i) q^{58} +18873.2i q^{59} +(-128610. - 45296.5i) q^{60} -166795. q^{61} +(-122127. - 172494. i) q^{62} -23228.0i q^{63} +(-222811. + 138111. i) q^{64} -271093. q^{65} +(41521.6 - 29397.7i) q^{66} +267170. i q^{67} +(45609.6 - 129499. i) q^{68} +3098.60 q^{69} +(32797.3 + 46323.2i) q^{70} -104773. i q^{71} +(82534.3 + 289805. i) q^{72} +263046. q^{73} +(-114648. + 81172.0i) q^{74} -197801. i q^{75} +(-94988.7 - 33455.1i) q^{76} -21177.1 q^{77} +(-82624.2 - 116699. i) q^{78} -48638.0i q^{79} +(-573794. - 461418. i) q^{80} +243970. q^{81} +(-199921. + 141546. i) q^{82} +317734. i q^{83} +(-9945.07 + 28236.9i) q^{84} +385635. q^{85} +(608924. + 860051. i) q^{86} -480430. i q^{87} +(264218. - 75247.1i) q^{88} +30232.1 q^{89} +(-690761. + 489065. i) q^{90} +59519.9i q^{91} +(15782.1 + 5558.47i) q^{92} +313114. q^{93} +(916228. + 1.29409e6i) q^{94} -282867. i q^{95} +(23748.0 - 387636. i) q^{96} +666671. q^{97} +(-757983. + 536659. i) q^{98} -315789. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more