LMFDB - Embedded newform 48.7.l.a.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	48.19
Dual form			48.7.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)

$f(q)$	$=$	$q+(3.36544 - 7.25767i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-41.3476 - 48.8505i) q^{4} +(-26.6395 + 26.6395i) q^{5} +(-42.9029 - 117.095i) q^{6} -403.840 q^{7} +(-493.694 + 135.684i) q^{8} -243.000i q^{9} +O(q^{10})$	\(q+(3.36544 - 7.25767i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-41.3476 - 48.8505i) q^{4} +(-26.6395 + 26.6395i) q^{5} +(-42.9029 - 117.095i) q^{6} -403.840 q^{7} +(-493.694 + 135.684i) q^{8} -243.000i q^{9} +(103.687 + 282.994i) q^{10} +(152.675 + 152.675i) q^{11} +(-994.227 - 82.7024i) q^{12} +(-1728.86 - 1728.86i) q^{13} +(-1359.10 + 2930.94i) q^{14} +587.279i q^{15} +(-676.749 + 4039.71i) q^{16} +110.784 q^{17} +(-1763.61 - 817.802i) q^{18} +(3293.87 - 3293.87i) q^{19} +(2402.83 + 199.874i) q^{20} +(-4451.41 + 4451.41i) q^{21} +(1621.89 - 594.248i) q^{22} -4142.48 q^{23} +(-3946.24 + 6937.45i) q^{24} +14205.7i q^{25} +(-18365.9 + 6729.13i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(16697.8 + 19727.8i) q^{28} +(-26256.6 - 26256.6i) q^{29} +(4262.28 + 1976.45i) q^{30} -15500.0i q^{31} +(27041.3 + 18507.0i) q^{32} +3365.79 q^{33} +(372.835 - 804.031i) q^{34} +(10758.1 - 10758.1i) q^{35} +(-11870.7 + 10047.5i) q^{36} +(41837.5 - 41837.5i) q^{37} +(-12820.5 - 34991.1i) q^{38} -38113.5 q^{39} +(9537.21 - 16766.3i) q^{40} -135328. i q^{41} +(17325.9 + 47287.8i) q^{42} +(25578.8 + 25578.8i) q^{43} +(1145.51 - 13771.0i) q^{44} +(6473.40 + 6473.40i) q^{45} +(-13941.3 + 30064.7i) q^{46} -36531.8i q^{47} +(37068.9 + 51988.1i) q^{48} +45437.8 q^{49} +(103100. + 47808.4i) q^{50} +(1221.13 - 1221.13i) q^{51} +(-12971.5 + 155940. i) q^{52} +(115323. - 115323. i) q^{53} +(-28454.2 + 10425.4i) q^{54} -8134.39 q^{55} +(199373. - 54794.6i) q^{56} -72614.7i q^{57} +(-278927. + 102197. i) q^{58} +(71056.8 + 71056.8i) q^{59} +(28688.9 - 24282.6i) q^{60} +(-96379.6 - 96379.6i) q^{61} +(-112494. - 52164.4i) q^{62} +98133.1i q^{63} +(225324. - 133973. i) q^{64} +92112.0 q^{65} +(11327.4 - 24427.8i) q^{66} +(-266382. + 266382. i) q^{67} +(-4580.64 - 5411.84i) q^{68} +(-45661.3 + 45661.3i) q^{69} +(-41873.0 - 114285. i) q^{70} -416772. q^{71} +(32971.2 + 119968. i) q^{72} +202516. i q^{73} +(-162841. - 444444. i) q^{74} +(156585. + 156585. i) q^{75} +(-297101. - 24713.6i) q^{76} +(-61656.4 - 61656.4i) q^{77} +(-128269. + 276615. i) q^{78} +832723. i q^{79} +(-89587.5 - 125644. i) q^{80} -59049.0 q^{81} +(-982165. - 455438. i) q^{82} +(-157114. + 157114. i) q^{83} +(401509. + 33398.5i) q^{84} +(-2951.22 + 2951.22i) q^{85} +(271726. - 99558.5i) q^{86} -578837. q^{87} +(-96090.5 - 54659.3i) q^{88} -985026. i q^{89} +(68767.6 - 25196.0i) q^{90} +(698184. + 698184. i) q^{91} +(171282. + 202362. i) q^{92} +(-170852. - 170852. i) q^{93} +(-265136. - 122945. i) q^{94} +175494. i q^{95} +(502066. - 94071.0i) q^{96} +1.46802e6 q^{97} +(152918. - 329773. i) q^{98} +(37100.1 - 37100.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) $ 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	3.36544	−	7.25767i	0.420680	−	0.907209i
$2$	3.36544	−	7.25767i	0.420680	−	0.907209i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$4$	−41.3476	−	48.8505i	−0.646057	−	0.763290i
$5$	−26.6395	+	26.6395i	−0.213116	+	0.213116i	−0.805590	−	0.592474i	$-0.798151\pi$
$5$	−26.6395	+	26.6395i	−0.213116	+	0.213116i	0.592474	+	0.805590i	$0.298151\pi$
$6$	−42.9029	−	117.095i	−0.198625	−	0.542108i
$7$	−403.840			−1.17738			−0.588688	−	0.808360i	$-0.700355\pi$
$7$	−403.840			−1.17738			−0.588688	+	0.808360i	$0.700355\pi$
$8$	−493.694	+	135.684i	−0.964246	+	0.265008i
$9$		−	243.000i		−	0.333333i
$10$	103.687	+	282.994i	0.103687	+	0.282994i
$11$	152.675	+	152.675i	0.114707	+	0.114707i	0.762131	−	0.647423i	$-0.224153\pi$
$11$	152.675	+	152.675i	0.114707	+	0.114707i	−0.647423	+	0.762131i	$0.724153\pi$
$12$	−994.227	−	82.7024i	−0.575363	−	0.0478602i
$13$	−1728.86	−	1728.86i	−0.786919	−	0.786919i	0.194069	−	0.980988i	$-0.437832\pi$
$13$	−1728.86	−	1728.86i	−0.786919	−	0.786919i	−0.980988	+	0.194069i	$0.937832\pi$
$14$	−1359.10	+	2930.94i	−0.495299	+	1.06813i
$15$			587.279i			0.174008i
$16$	−676.749	+	4039.71i	−0.165222	+	0.986256i
$17$	110.784			0.0225491			0.0112745	−	0.999936i	$-0.496411\pi$
$17$	110.784			0.0225491			0.0112745	+	0.999936i	$0.496411\pi$
$18$	−1763.61	−	817.802i	−0.302403	−	0.140227i
$19$	3293.87	−	3293.87i	0.480226	−	0.480226i	−0.424978	−	0.905204i	$-0.639718\pi$
$19$	3293.87	−	3293.87i	0.480226	−	0.480226i	0.905204	+	0.424978i	$0.139718\pi$
$20$	2402.83	+	199.874i	0.300354	+	0.0249842i
$21$	−4451.41	+	4451.41i	−0.480662	+	0.480662i
$22$	1621.89	−	594.248i	0.152318	−	0.0558084i
$23$	−4142.48			−0.340468			−0.170234	−	0.985404i	$-0.554452\pi$
$23$	−4142.48			−0.340468			−0.170234	+	0.985404i	$0.554452\pi$
$24$	−3946.24	+	6937.45i	−0.285463	+	0.501841i
$25$			14205.7i			0.909163i
$26$	−18365.9	+	6729.13i	−1.04494	+	0.382859i
$27$	−2678.52	−	2678.52i	−0.136083	−	0.136083i
$28$	16697.8	+	19727.8i	0.760652	+	0.898679i
$29$	−26256.6	−	26256.6i	−1.07658	−	1.07658i	−0.996814	−	0.0797613i	$-0.974584\pi$
$29$	−26256.6	−	26256.6i	−1.07658	−	1.07658i	−0.0797613	−	0.996814i	$-0.525416\pi$
$30$	4262.28	+	1976.45i	0.157862	+	0.0732019i
$31$		−	15500.0i		−	0.520293i	−0.965569	−	0.260146i	$-0.916229\pi$
$31$		−	15500.0i		−	0.520293i	0.965569	−	0.260146i	$-0.0837708\pi$
$32$	27041.3	+	18507.0i	0.825235	+	0.564789i
$33$	3365.79			0.0936580
$34$	372.835	−	804.031i	0.00948594	−	0.0204567i
$35$	10758.1	−	10758.1i	0.250918	−	0.250918i
$36$	−11870.7	+	10047.5i	−0.254430	+	0.215352i
$37$	41837.5	−	41837.5i	0.825963	−	0.825963i	−0.160993	−	0.986956i	$-0.551470\pi$
$37$	41837.5	−	41837.5i	0.825963	−	0.825963i	0.986956	+	0.160993i	$0.0514696\pi$
$38$	−12820.5	−	34991.1i	−0.233644	−	0.637686i
$39$	−38113.5			−0.642517
$40$	9537.21	−	16766.3i	0.149019	−	0.261974i
$41$		−	135328.i		−	1.96352i	−0.190121	−	0.981761i	$-0.560888\pi$
$41$		−	135328.i		−	1.96352i	0.190121	−	0.981761i	$-0.439112\pi$
$42$	17325.9	+	47287.8i	0.233856	+	0.638266i
$43$	25578.8	+	25578.8i	0.321717	+	0.321717i	0.849426	−	0.527708i	$-0.176949\pi$
$43$	25578.8	+	25578.8i	0.321717	+	0.321717i	−0.527708	+	0.849426i	$0.676949\pi$
$44$	1145.51	−	13771.0i	0.0134475	−	0.161662i
$45$	6473.40	+	6473.40i	0.0710387	+	0.0710387i
$46$	−13941.3	+	30064.7i	−0.143228	+	0.308876i
$47$		−	36531.8i		−	0.351866i	−0.984402	−	0.175933i	$-0.943706\pi$
$47$		−	36531.8i		−	0.351866i	0.984402	−	0.175933i	$-0.0562942\pi$
$48$	37068.9	+	51988.1i	0.335186	+	0.470089i
$49$	45437.8			0.386215
$50$	103100.	+	47808.4i	0.824801	+	0.382467i
$51$	1221.13	−	1221.13i	0.00920562	−	0.00920562i
$52$	−12971.5	+	155940.i	−0.0922529	+	1.10904i
$53$	115323.	−	115323.i	0.774619	−	0.774619i	−0.204291	−	0.978910i	$-0.565489\pi$
$53$	115323.	−	115323.i	0.774619	−	0.774619i	0.978910	+	0.204291i	$0.0654888\pi$
$54$	−28454.2	+	10425.4i	−0.180703	+	0.0662082i
$55$	−8134.39			−0.0488919
$56$	199373.	−	54794.6i	1.13528	−	0.312014i
$57$		−	72614.7i		−	0.392103i
$58$	−278927.	+	102197.i	−1.42957	+	0.523785i
$59$	71056.8	+	71056.8i	0.345979	+	0.345979i	0.858609	−	0.512630i	$-0.171329\pi$
$59$	71056.8	+	71056.8i	0.345979	+	0.345979i	−0.512630	+	0.858609i	$0.671329\pi$
$60$	28688.9	−	24282.6i	0.132819	−	0.112419i
$61$	−96379.6	−	96379.6i	−0.424615	−	0.424615i	0.462174	−	0.886789i	$-0.347070\pi$
$61$	−96379.6	−	96379.6i	−0.424615	−	0.424615i	−0.886789	+	0.462174i	$0.847070\pi$
$62$	−112494.	−	52164.4i	−0.472014	−	0.218877i
$63$			98133.1i			0.392459i
$64$	225324.	−	133973.i	0.859542	−	0.511065i
$65$	92112.0			0.335410
$66$	11327.4	−	24427.8i	0.0394001	−	0.0849674i
$67$	−266382.	+	266382.i	−0.885688	+	0.885688i	−0.994105	−	0.108417i	$-0.965422\pi$
$67$	−266382.	+	266382.i	−0.885688	+	0.885688i	0.108417	+	0.994105i	$0.465422\pi$
$68$	−4580.64	−	5411.84i	−0.0145680	−	0.0172115i
$69$	−45661.3	+	45661.3i	−0.138996	+	0.138996i
$70$	−41873.0	−	114285.i	−0.122079	−	0.333191i
$71$	−416772.			−1.16446			−0.582229	−	0.813025i	$-0.697819\pi$
$71$	−416772.			−1.16446			−0.582229	+	0.813025i	$0.697819\pi$
$72$	32971.2	+	119968.i	0.0883359	+	0.321415i
$73$			202516.i			0.520584i	0.965530	+	0.260292i	$0.0838189\pi$
$73$			202516.i			0.520584i	−0.965530	+	0.260292i	$0.916181\pi$
$74$	−162841.	−	444444.i	−0.401855	−	1.09679i
$75$	156585.	+	156585.i	0.371164	+	0.371164i
$76$	−297101.	−	24713.6i	−0.676804	−	0.0562983i
$77$	−61656.4	−	61656.4i	−0.135054	−	0.135054i
$78$	−128269.	+	276615.i	−0.270294	+	0.582897i
$79$			832723.i			1.68896i	0.535588	+	0.844479i	$0.320090\pi$
$79$			832723.i			1.68896i	−0.535588	+	0.844479i	$0.679910\pi$
$80$	−89587.5	−	125644.i	−0.174976	−	0.245398i
$81$	−59049.0			−0.111111
$82$	−982165.	−	455438.i	−1.78132	−	0.826014i
$83$	−157114.	+	157114.i	−0.274777	+	0.274777i	−0.831020	−	0.556243i	$-0.812243\pi$
$83$	−157114.	+	157114.i	−0.274777	+	0.274777i	0.556243	+	0.831020i	$0.312243\pi$
$84$	401509.	+	33398.5i	0.677419	+	0.0563495i
$85$	−2951.22	+	2951.22i	−0.00480557	+	0.00480557i
$86$	271726.	−	99558.5i	0.427205	−	0.156525i
$87$	−578837.			−0.879020
$88$	−96090.5	−	54659.3i	−0.141004	−	0.0802077i
$89$		−	985026.i		−	1.39726i	−0.715483	−	0.698631i	$-0.753793\pi$
$89$		−	985026.i		−	1.39726i	0.715483	−	0.698631i	$-0.246207\pi$
$90$	68767.6	−	25196.0i	0.0943315	−	0.0345624i
$91$	698184.	+	698184.i	0.926500	+	0.926500i
$92$	171282.	+	202362.i	0.219962	+	0.259876i
$93$	−170852.	−	170852.i	−0.212409	−	0.212409i
$94$	−265136.	−	122945.i	−0.319216	−	0.148023i
$95$			175494.i			0.204688i
$96$	502066.	−	94071.0i	0.567475	−	0.106327i
$97$	1.46802e6			1.60848			0.804239	−	0.594305i	$-0.202573\pi$
$97$	1.46802e6			1.60848			0.804239	+	0.594305i	$0.202573\pi$
$98$	152918.	−	329773.i	0.162473	−	0.350378i
$99$	37100.1	−	37100.1i	0.0382357	−	0.0382357i
$100$	693955.	−	587371.i	0.693955	−	0.587371i
$101$	−653326.	+	653326.i	−0.634112	+	0.634112i	−0.949097	−	0.314985i	$-0.898001\pi$
$101$	−653326.	+	653326.i	−0.634112	+	0.634112i	0.314985	+	0.949097i	$0.398001\pi$
$102$	−4752.94	−	12972.2i	−0.00447880	−	0.0122240i
$103$	697466.			0.638280			0.319140	−	0.947708i	$-0.396606\pi$
$103$	697466.			0.638280			0.319140	+	0.947708i	$0.396606\pi$
$104$	1.08811e6	+	618950.i	0.967324	+	0.550244i
$105$		−	237167.i		−	0.204873i
$106$	−448864.	−	1.22509e6i	−0.376875	−	1.02861i
$107$	1.08466e6	+	1.08466e6i	0.885408	+	0.885408i	0.994078	−	0.108670i	$-0.0346591\pi$
$107$	1.08466e6	+	1.08466e6i	0.885408	+	0.885408i	−0.108670	+	0.994078i	$0.534659\pi$
$108$	−20096.7	+	241597.i	−0.0159534	+	0.191788i
$109$	1.10911e6	+	1.10911e6i	0.856434	+	0.856434i	0.990916	−	0.134482i	$-0.0429370\pi$
$109$	1.10911e6	+	1.10911e6i	0.856434	+	0.856434i	−0.134482	+	0.990916i	$0.542937\pi$
$110$	−27375.8	+	59036.7i	−0.0205678	+	0.0443552i
$111$		−	922325.i		−	0.674396i
$112$	273298.	−	1.63140e6i	0.194528	−	1.16120i
$113$	−383617.			−0.265866			−0.132933	−	0.991125i	$-0.542439\pi$
$113$	−383617.			−0.265866			−0.132933	+	0.991125i	$0.542439\pi$
$114$	−527013.	−	244380.i	−0.355719	−	0.164950i
$115$	110354.	−	110354.i	0.0725592	−	0.0725592i
$116$	−197001.	+	2.36830e6i	−0.126210	+	1.51727i
$117$	−420113.	+	420113.i	−0.262306	+	0.262306i
$118$	754844.	−	276569.i	0.459422	−	0.168329i
$119$	−44738.8			−0.0265487
$120$	−79684.3	−	289936.i	−0.0461136	−	0.167787i
$121$		−	1.72494e6i		−	0.973685i
$122$	−1.02385e6	+	375132.i	−0.563842	+	0.206588i
$123$	−1.49168e6	−	1.49168e6i	−0.801604	−	0.801604i
$124$	−757185.	+	640890.i	−0.397134	+	0.336138i
$125$	−794674.	−	794674.i	−0.406873	−	0.406873i
$126$	712218.	+	330261.i	0.356042	+	0.165100i
$127$		−	3.40598e6i		−	1.66277i	−0.555699	−	0.831383i	$-0.687549\pi$
$127$		−	3.40598e6i		−	1.66277i	0.555699	−	0.831383i	$-0.312451\pi$
$128$	−214016.	−	2.08620e6i	−0.102051	−	0.994779i
$129$	563894.			0.262681
$130$	309998.	−	668519.i	0.141100	−	0.304287i
$131$	−1.96163e6	+	1.96163e6i	−0.872577	+	0.872577i	−0.992753	−	0.120176i	$-0.961654\pi$
$131$	−1.96163e6	+	1.96163e6i	−0.872577	+	0.872577i	0.120176	+	0.992753i	$0.461654\pi$
$132$	−139167.	−	164421.i	−0.0605084	−	0.0714882i
$133$	−1.33020e6	+	1.33020e6i	−0.565406	+	0.565406i
$134$	1.03682e6	+	2.82981e6i	0.430913	+	1.17610i
$135$	142709.			0.0580028
$136$	−54693.2	+	15031.5i	−0.0217429	+	0.00597567i
$137$		−	3.22491e6i		−	1.25417i	−0.778952	−	0.627084i	$-0.784248\pi$
$137$		−	3.22491e6i		−	1.25417i	0.778952	−	0.627084i	$-0.215752\pi$
$138$	177724.	+	485065.i	0.0676254	+	0.184571i
$139$	2.53730e6	+	2.53730e6i	0.944774	+	0.944774i	0.998553	−	0.0537786i	$-0.0171265\pi$
$139$	2.53730e6	+	2.53730e6i	0.944774	+	0.944774i	−0.0537786	+	0.998553i	$0.517127\pi$
$140$	−970361.	−	80717.1i	−0.353630	−	0.0294159i
$141$	−402679.	−	402679.i	−0.143649	−	0.143649i
$142$	−1.40262e6	+	3.02480e6i	−0.489864	+	1.05641i
$143$		−	527909.i		−	0.180531i
$144$	981649.	+	164450.i	0.328752	+	0.0550740i
$145$	1.39893e6			0.458871
$146$	1.46980e6	+	681556.i	0.472279	+	0.218999i
$147$	500848.	−	500848.i	0.157672	−	0.157672i
$148$	−3.77367e6	−	313903.i	−1.16407	−	0.0968301i
$149$	−2.49552e6	+	2.49552e6i	−0.754400	+	0.754400i	−0.975297	−	0.220897i	$-0.929101\pi$
$149$	−2.49552e6	+	2.49552e6i	−0.754400	+	0.754400i	0.220897	+	0.975297i	$0.429101\pi$
$150$	1.66342e6	−	609465.i	0.492865	−	0.180582i
$151$	−6.26921e6			−1.82088			−0.910441	−	0.413640i	$-0.864257\pi$
$151$	−6.26921e6			−1.82088			−0.910441	+	0.413640i	$0.864257\pi$
$152$	−1.17924e6	+	2.07309e6i	−0.335792	+	0.590319i
$153$		−	26920.4i		−	0.00751635i
$154$	−654983.	+	239981.i	−0.179336	+	0.0657075i
$155$	412913.	+	412913.i	0.110883	+	0.110883i
$156$	1.57590e6	+	1.86186e6i	0.415102	+	0.490426i
$157$	2.79743e6	+	2.79743e6i	0.722871	+	0.722871i	0.969189	−	0.246318i	$-0.0792209\pi$
$157$	2.79743e6	+	2.79743e6i	0.722871	+	0.722871i	−0.246318	+	0.969189i	$0.579221\pi$
$158$	6.04363e6	+	2.80248e6i	1.53224	+	0.710511i
$159$		−	2.54234e6i		−	0.632474i
$160$	−1.21338e6	+	227349.i	−0.296236	+	0.0555052i
$161$	1.67290e6			0.400859
$162$	−198726.	+	428558.i	−0.0467422	+	0.100801i
$163$	4.03319e6	−	4.03319e6i	0.931291	−	0.931291i	−0.0664955	−	0.997787i	$-0.521182\pi$
$163$	4.03319e6	−	4.03319e6i	0.931291	−	0.931291i	0.997787	+	0.0664955i	$0.0211818\pi$
$164$	−6.61084e6	+	5.59548e6i	−1.49874	+	1.26855i
$165$	−89662.9	+	89662.9i	−0.0199600	+	0.0199600i
$166$	611524.	+	1.66904e6i	0.133687	+	0.364874i
$167$	−1.19127e6			−0.255777			−0.127889	−	0.991789i	$-0.540820\pi$
$167$	−1.19127e6			−0.255777			−0.127889	+	0.991789i	$0.540820\pi$
$168$	1.59365e6	−	2.80162e6i	0.336097	−	0.590856i
$169$			1.15112e6i			0.238484i
$170$	11486.8	+	31351.1i	0.00233805	+	0.00638126i
$171$	−800410.	−	800410.i	−0.160075	−	0.160075i
$172$	191915.	−	2.30716e6i	0.0377159	−	0.453411i
$173$	−4.28834e6	−	4.28834e6i	−0.828230	−	0.828230i	0.159042	−	0.987272i	$-0.449160\pi$
$173$	−4.28834e6	−	4.28834e6i	−0.828230	−	0.828230i	−0.987272	+	0.159042i	$0.949160\pi$
$174$	−1.94804e6	+	4.20101e6i	−0.369786	+	0.797455i
$175$		−	5.73682e6i		−	1.07043i
$176$	−720086.	+	513441.i	−0.132083	+	0.0941786i
$177$	1.56648e6			0.282491
$178$	−7.14900e6	−	3.31505e6i	−1.26761	−	0.587800i
$179$	6.40473e6	−	6.40473e6i	1.11671	−	1.11671i	0.124494	−	0.992220i	$-0.460269\pi$
$179$	6.40473e6	−	6.40473e6i	1.11671	−	1.11671i	0.992220	−	0.124494i	$-0.0397306\pi$
$180$	48569.4	−	583889.i	0.00832808	−	0.100118i
$181$	−6.09230e6	+	6.09230e6i	−1.02741	+	1.02741i	−0.0278011	+	0.999613i	$0.508850\pi$
$181$	−6.09230e6	+	6.09230e6i	−1.02741	+	1.02741i	−0.999613	+	0.0278011i	$0.991150\pi$
$182$	7.41688e6	−	2.71749e6i	1.23029	−	0.450769i
$183$	−2.12473e6			−0.346697
$184$	2.04512e6	−	562067.i	0.328295	−	0.0902267i
$185$			2.22906e6i			0.352052i
$186$	−1.81498e6	+	664997.i	−0.282055	+	0.103343i
$187$	16913.9	+	16913.9i	0.00258654	+	0.00258654i
$188$	−1.78460e6	+	1.51050e6i	−0.268575	+	0.227325i
$189$	1.08169e6	+	1.08169e6i	0.160221	+	0.160221i
$190$	1.27368e6	+	590615.i	0.185694	+	0.0861080i
$191$		−	2.73988e6i		−	0.393216i	−0.980482	−	0.196608i	$-0.937007\pi$
$191$		−	2.73988e6i		−	0.393216i	0.980482	−	0.196608i	$-0.0629927\pi$
$192$	1.00694e6	−	3.96042e6i	0.142265	−	0.559548i
$193$	−234810.			−0.0326622			−0.0163311	−	0.999867i	$-0.505199\pi$
$193$	−234810.			−0.0326622			−0.0163311	+	0.999867i	$0.505199\pi$
$194$	4.94052e6	−	1.06544e7i	0.676655	−	1.45923i
$195$	1.01532e6	−	1.01532e6i	0.136931	−	0.136931i
$196$	−1.87875e6	−	2.21966e6i	−0.249517	−	0.294794i
$197$	−1.24528e6	+	1.24528e6i	−0.162881	+	0.162881i	−0.783842	−	0.620961i	$-0.786743\pi$
$197$	−1.24528e6	+	1.24528e6i	−0.162881	+	0.162881i	0.620961	+	0.783842i	$0.286743\pi$
$198$	−144402.	−	394119.i	−0.0186028	−	0.0507728i
$199$	3.73945e6			0.474513			0.237257	−	0.971447i	$-0.423752\pi$
$199$	3.73945e6			0.474513			0.237257	+	0.971447i	$0.423752\pi$
$200$	−1.92748e6	−	7.01326e6i	−0.240935	−	0.876657i
$201$			5.87250e6i			0.723161i
$202$	2.54290e6	+	6.94036e6i	0.308514	+	0.842031i
$203$	1.06035e7	+	1.06035e7i	1.26753	+	1.26753i
$204$	−110144.	−	9162.07i	−0.0129739	−	0.00107920i
$205$	3.60507e6	+	3.60507e6i	0.418458	+	0.418458i
$206$	2.34728e6	−	5.06198e6i	0.268512	−	0.579053i
$207$			1.00662e6i			0.113489i
$208$	8.15410e6	−	5.81409e6i	0.906120	−	0.646088i
$209$	1.00578e6			0.110171
$210$	−1.72128e6	−	798170.i	−0.185863	−	0.0861862i
$211$	−3.39522e6	+	3.39522e6i	−0.361427	+	0.361427i	−0.864338	−	0.502911i	$-0.832262\pi$
$211$	−3.39522e6	+	3.39522e6i	−0.361427	+	0.361427i	0.502911	+	0.864338i	$0.332262\pi$
$212$	−1.04019e7	−	865259.i	−1.09171	−	0.0908110i
$213$	−4.59396e6	+	4.59396e6i	−0.475388	+	0.475388i
$214$	1.15225e7	−	4.22176e6i	1.17572	−	0.430777i
$215$	−1.36281e6			−0.137126
$216$	1.68580e6	+	958936.i	0.167280	+	0.0951543i
$217$			6.25954e6i			0.612580i
$218$	1.17822e7	−	4.31690e6i	1.13725	−	0.416680i
$219$	2.23228e6	+	2.23228e6i	0.212528	+	0.212528i
$220$	336338.	+	397369.i	0.0315869	+	0.0373187i
$221$	−191529.	−	191529.i	−0.0177443	−	0.0177443i
$222$	−6.69393e6	−	3.10403e6i	−0.611818	−	0.283705i
$223$		−	1.00504e7i		−	0.906295i	−0.891435	−	0.453148i	$-0.850301\pi$
$223$		−	1.00504e7i		−	0.906295i	0.891435	−	0.453148i	$-0.149699\pi$
$224$	−1.09204e7	−	7.47387e6i	−0.971612	−	0.664970i
$225$	3.45198e6			0.303054
$226$	−1.29104e6	+	2.78417e6i	−0.111844	+	0.241196i
$227$	−3.03181e6	+	3.03181e6i	−0.259194	+	0.259194i	−0.824726	−	0.565532i	$-0.808671\pi$
$227$	−3.03181e6	+	3.03181e6i	−0.259194	+	0.259194i	0.565532	+	0.824726i	$0.308671\pi$
$228$	−3.54726e6	+	3.00244e6i	−0.299288	+	0.253320i
$229$	449030.	−	449030.i	0.0373911	−	0.0373911i	−0.688164	−	0.725555i	$-0.741583\pi$
$229$	449030.	−	449030.i	0.0373911	−	0.0373911i	0.725555	+	0.688164i	$0.241583\pi$
$230$	−429521.	−	1.17230e6i	−0.0353022	−	0.0963506i
$231$	−1.35924e6			−0.110271
$232$	1.65253e7	+	9.40013e6i	1.32338	+	0.752783i
$233$		−	1.61678e7i		−	1.27816i	−0.769142	−	0.639078i	$-0.779316\pi$
$233$		−	1.61678e7i		−	1.27816i	0.769142	−	0.639078i	$-0.220684\pi$
$234$	1.63518e6	+	4.46291e6i	0.127620	+	0.348314i
$235$	973188.	+	973188.i	0.0749882	+	0.0749882i
$236$	533133.	−	6.40919e6i	0.0405602	−	0.487604i
$237$	9.17885e6	+	9.17885e6i	0.689515	+	0.689515i
$238$	−150566.	+	324700.i	−0.0111685	+	0.0240853i
$239$			1.69324e7i			1.24029i	0.784486	+	0.620146i	$0.212927\pi$
$239$			1.69324e7i			1.24029i	−0.784486	+	0.620146i	$0.787073\pi$
$240$	−2.37243e6	−	397440.i	−0.171617	−	0.0287500i
$241$	−6.23137e6			−0.445177			−0.222588	−	0.974913i	$-0.571451\pi$
$241$	−6.23137e6			−0.445177			−0.222588	+	0.974913i	$0.571451\pi$
$242$	−1.25191e7	−	5.80519e6i	−0.883335	−	0.409610i
$243$	−650880.	+	650880.i	−0.0453609	+	0.0453609i
$244$	−723128.	+	8.69326e6i	−0.0497789	+	0.598430i
$245$	−1.21044e6	+	1.21044e6i	−0.0823086	+	0.0823086i
$246$	−1.58463e7	+	5.80596e6i	−1.06444	+	0.390004i
$247$	−1.13893e7			−0.755798
$248$	2.10311e6	+	7.65228e6i	0.137881	+	0.501690i
$249$			3.46364e6i			0.224355i
$250$	−8.44191e6	+	3.09306e6i	−0.540283	+	0.197956i
$251$	2.89165e6	+	2.89165e6i	0.182863	+	0.182863i	0.792602	−	0.609739i	$-0.208726\pi$
$251$	2.89165e6	+	2.89165e6i	0.182863	+	0.182863i	−0.609739	+	0.792602i	$0.708726\pi$
$252$	4.79386e6	−	4.05757e6i	0.299560	−	0.253551i
$253$	−632454.	−	632454.i	−0.0390542	−	0.0390542i
$254$	−2.47195e7	−	1.14626e7i	−1.50848	−	0.699493i
$255$			65060.8i			0.00392373i
$256$	−1.58612e7	−	5.46773e6i	−0.945403	−	0.325902i
$257$	3.03086e6			0.178552			0.0892762	−	0.996007i	$-0.471545\pi$
$257$	3.03086e6			0.178552			0.0892762	+	0.996007i	$0.471545\pi$
$258$	1.89775e6	−	4.09256e6i	0.110505	−	0.238307i
$259$	−1.68957e7	+	1.68957e7i	−0.972469	+	0.972469i
$260$	−3.80861e6	−	4.49972e6i	−0.216694	−	0.256015i
$261$	−6.38035e6	+	6.38035e6i	−0.358858	+	0.358858i
$262$	7.63513e6	+	2.08386e7i	0.424534	+	1.15869i
$263$	1.28970e7			0.708958			0.354479	−	0.935064i	$-0.384658\pi$
$263$	1.28970e7			0.708958			0.354479	+	0.935064i	$0.384658\pi$
$264$	−1.66167e6	+	456683.i	−0.0903094	+	0.0248201i
$265$			6.14430e6i			0.330168i
$266$	5.17743e6	+	1.41308e7i	0.275087	+	0.750797i
$267$	−1.08576e7	−	1.08576e7i	−0.570430	−	0.570430i
$268$	2.40272e7	+	1.99864e6i	1.24824	+	0.103832i
$269$	−1.99946e7	−	1.99946e7i	−1.02720	−	1.02720i	−0.999620	−	0.0275804i	$-0.991220\pi$
$269$	−1.99946e7	−	1.99946e7i	−1.02720	−	1.02720i	−0.0275804	−	0.999620i	$-0.508780\pi$
$270$	480278.	−	1.03573e6i	0.0244006	−	0.0526207i
$271$		−	1.61595e7i		−	0.811935i	−0.913887	−	0.405968i	$-0.866935\pi$
$271$		−	1.61595e7i		−	0.811935i	0.913887	−	0.405968i	$-0.133065\pi$
$272$	−74972.7	+	447533.i	−0.00372560	+	0.0222392i
$273$	1.53917e7			0.756484
$274$	−2.34053e7	−	1.08532e7i	−1.13779	−	0.527603i
$275$	−2.16886e6	+	2.16886e6i	−0.104288	+	0.104288i
$276$	4.11856e6	+	342593.i	0.195893	+	0.0162949i
$277$	2.71035e7	−	2.71035e7i	1.27522	−	1.27522i	0.331911	−	0.943311i	$-0.392307\pi$
$277$	2.71035e7	−	2.71035e7i	1.27522	−	1.27522i	0.943311	−	0.331911i	$-0.107693\pi$
$278$	2.69541e7	−	9.87577e6i	1.25456	−	0.459660i
$279$	−3.76651e6			−0.173431
$280$	−3.85151e6	+	6.77091e6i	−0.175451	+	0.308442i
$281$		−	2.50197e7i		−	1.12762i	−0.825905	−	0.563810i	$-0.809335\pi$
$281$		−	2.50197e7i		−	1.12762i	0.825905	−	0.563810i	$-0.190665\pi$
$282$	−4.27770e6	+	1.56732e6i	−0.190749	+	0.0698892i
$283$	−1.99085e7	−	1.99085e7i	−0.878376	−	0.878376i	0.114991	−	0.993367i	$-0.463316\pi$
$283$	−1.99085e7	−	1.99085e7i	−0.878376	−	0.878376i	−0.993367	+	0.114991i	$0.963316\pi$
$284$	1.72325e7	+	2.03596e7i	0.752306	+	0.888819i
$285$	1.93442e6	+	1.93442e6i	0.0835633	+	0.0835633i
$286$	−3.83139e6	−	1.77665e6i	−0.163779	−	0.0759456i
$287$			5.46508e7i			2.31180i
$288$	4.49720e6	−	6.57104e6i	0.188263	−	0.275078i
$289$	−2.41253e7			−0.999492
$290$	4.70800e6	−	1.01529e7i	0.193038	−	0.416292i
$291$	1.61815e7	−	1.61815e7i	0.656659	−	0.656659i
$292$	9.89302e6	−	8.37356e6i	0.397357	−	0.336327i
$293$	1.84063e7	−	1.84063e7i	0.731750	−	0.731750i	−0.239216	−	0.970966i	$-0.576890\pi$
$293$	1.84063e7	−	1.84063e7i	0.731750	−	0.731750i	0.970966	+	0.239216i	$0.0768905\pi$
$294$	−1.94942e6	−	5.32056e6i	−0.0767118	−	0.209371i
$295$	−3.78583e6			−0.147467
$296$	−1.49783e7	+	2.63316e7i	−0.577545	+	1.01532i
$297$		−	817887.i		−	0.0312193i
$298$	9.71313e6	+	2.65101e7i	0.367037	+	1.00176i
$299$	7.16177e6	+	7.16177e6i	0.267921	+	0.267921i
$300$	1.17484e6	−	1.41237e7i	0.0435127	−	0.523099i
$301$	−1.03297e7	−	1.03297e7i	−0.378782	−	0.378782i
$302$	−2.10986e7	+	4.54998e7i	−0.766009	+	1.65192i
$303$			1.44028e7i			0.517750i
$304$	1.10771e7	+	1.55354e7i	0.394282	+	0.552969i
$305$	5.13501e6			0.180985
$306$	−195379.	−	90599.0i	−0.00681890	−	0.00316198i
$307$	−8.59455e6	+	8.59455e6i	−0.297035	+	0.297035i	−0.839852	−	0.542816i	$-0.817358\pi$
$307$	−8.59455e6	+	8.59455e6i	−0.297035	+	0.297035i	0.542816	+	0.839852i	$0.317358\pi$
$308$	−462603.	+	5.56129e6i	−0.0158327	+	0.190337i
$309$	7.68796e6	−	7.68796e6i	0.260577	−	0.260577i
$310$	4.38642e6	−	1.60715e6i	0.147240	−	0.0539476i
$311$	2.28440e7			0.759436			0.379718	−	0.925102i	$-0.376021\pi$
$311$	2.28440e7			0.759436			0.379718	+	0.925102i	$0.376021\pi$
$312$	1.88164e7	−	5.17138e6i	0.619544	−	0.170272i
$313$		−	3.00742e7i		−	0.980755i	−0.871510	−	0.490377i	$-0.836859\pi$
$313$		−	3.00742e7i		−	0.980755i	0.871510	−	0.490377i	$-0.163141\pi$
$314$	2.97174e7	−	1.08883e7i	0.959892	−	0.351698i
$315$	−2.61422e6	−	2.61422e6i	−0.0836393	−	0.0836393i
$316$	4.06789e7	−	3.44311e7i	1.28916	−	1.09116i
$317$	6.07210e6	+	6.07210e6i	0.190617	+	0.190617i	0.795963	−	0.605346i	$-0.206965\pi$
$317$	6.07210e6	+	6.07210e6i	0.190617	+	0.190617i	−0.605346	+	0.795963i	$0.706965\pi$
$318$	−1.84515e7	−	8.55610e6i	−0.573786	−	0.266069i
$319$		−	8.01747e6i		−	0.246982i
$320$	−2.43355e6	+	9.57148e6i	−0.0742660	+	0.292098i
$321$	2.39118e7			0.722933
$322$	5.63004e6	−	1.21413e7i	0.168633	−	0.363663i
$323$	364906.	−	364906.i	0.0108286	−	0.0108286i
$324$	2.44154e6	+	2.88458e6i	0.0717841	+	0.0848100i
$325$	2.45596e7	−	2.45596e7i	0.715438	−	0.715438i
$326$	−1.56981e7	−	4.28450e7i	−0.453100	−	1.23665i
$327$	2.44507e7			0.699275
$328$	1.83618e7	+	6.68106e7i	0.520348	+	1.89332i
$329$			1.47530e7i			0.414278i
$330$	348989.	+	952500.i	0.00971113	+	0.0265047i
$331$	−9.24350e6	−	9.24350e6i	−0.254890	−	0.254890i	0.568082	−	0.822972i	$-0.307686\pi$
$331$	−9.24350e6	−	9.24350e6i	−0.254890	−	0.254890i	−0.822972	+	0.568082i	$0.807686\pi$
$332$	1.41714e7	+	1.17881e6i	0.387256	+	0.0322130i
$333$	−1.01665e7	−	1.01665e7i	−0.275321	−	0.275321i
$334$	−4.00916e6	+	8.64588e6i	−0.107601	+	0.232044i
$335$		−	1.41926e7i		−	0.377509i
$336$	−1.49699e7	−	2.09949e7i	−0.394640	−	0.553472i
$337$	−6.00061e7			−1.56785			−0.783927	−	0.620853i	$-0.786786\pi$
$337$	−6.00061e7			−1.56785			−0.783927	+	0.620853i	$0.786786\pi$
$338$	8.35442e6	+	3.87401e6i	0.216355	+	0.100325i
$339$	−4.22850e6	+	4.22850e6i	−0.108539	+	0.108539i
$340$	266194.	+	22142.7i	0.00677271	+	0.000563371i
$341$	2.36647e6	−	2.36647e6i	0.0596813	−	0.0596813i
$342$	−8.50284e6	+	3.11538e6i	−0.212562	+	0.0778812i
$343$	2.91618e7			0.722656
$344$	−1.60987e7	−	9.15746e6i	−0.395472	−	0.224957i
$345$		−	2.43279e6i		−	0.0592444i
$346$	−4.55555e7	+	1.66912e7i	−1.09980	+	0.402958i
$347$	−4.30217e7	−	4.30217e7i	−1.02967	−	1.02967i	−0.999546	−	0.0301258i	$-0.990409\pi$
$347$	−4.30217e7	−	4.30217e7i	−1.02967	−	1.02967i	−0.0301258	−	0.999546i	$-0.509591\pi$
$348$	2.39335e7	+	2.82765e7i	0.567897	+	0.670947i
$349$	2.63834e7	+	2.63834e7i	0.620662	+	0.620662i	0.945701	−	0.325039i	$-0.105377\pi$
$349$	2.63834e7	+	2.63834e7i	0.620662	+	0.620662i	−0.325039	+	0.945701i	$0.605377\pi$
$350$	−4.16360e7	−	1.93069e7i	−0.971101	−	0.450307i
$351$			9.26157e6i			0.214172i
$352$	1.30298e6	+	6.95410e6i	0.0298750	+	0.159446i
$353$	−2.69154e7			−0.611894			−0.305947	−	0.952049i	$-0.598973\pi$
$353$	−2.69154e7			−0.611894			−0.305947	+	0.952049i	$0.598973\pi$
$354$	5.27188e6	−	1.13690e7i	0.118838	−	0.256278i
$355$	1.11026e7	−	1.11026e7i	0.248165	−	0.248165i
$356$	−4.81190e7	+	4.07285e7i	−1.06651	+	0.902710i
$357$	−493143.	+	493143.i	−0.0108385	+	0.0108385i
$358$	−2.49287e7	−	6.80382e7i	−0.543314	−	1.48287i
$359$	1.32413e7			0.286185			0.143092	−	0.989709i	$-0.454295\pi$
$359$	1.32413e7			0.286185			0.143092	+	0.989709i	$0.454295\pi$
$360$	−4.07421e6	−	2.31754e6i	−0.0873246	−	0.0496730i
$361$			2.53468e7i			0.538767i
$362$	2.37127e7	+	6.47192e7i	0.499867	+	1.36429i
$363$	−1.90135e7	−	1.90135e7i	−0.397505	−	0.397505i
$364$	5.23841e6	−	6.29749e7i	0.108616	−	1.30576i
$365$	−5.39493e6	−	5.39493e6i	−0.110945	−	0.110945i
$366$	−7.15064e6	+	1.54206e7i	−0.145848	+	0.314527i
$367$		−	1.01398e7i		−	0.205131i	−0.994726	−	0.102566i	$-0.967295\pi$
$367$		−	1.01398e7i		−	0.205131i	0.994726	−	0.102566i	$-0.0327052\pi$
$368$	2.80342e6	−	1.67344e7i	0.0562528	−	0.335789i
$369$	−3.28847e7			−0.654507
$370$	1.61778e7	+	7.50177e6i	0.319385	+	0.148101i
$371$	−4.65721e7	+	4.65721e7i	−0.912019	+	0.912019i
$372$	−1.28189e6	+	1.54106e7i	−0.0249013	+	0.299357i
$373$	2.01133e7	−	2.01133e7i	0.387577	−	0.387577i	−0.486245	−	0.873822i	$-0.661634\pi$
$373$	2.01133e7	−	2.01133e7i	0.387577	−	0.387577i	0.873822	+	0.486245i	$0.161634\pi$
$374$	179678.	−	65832.9i	0.00343464	−	0.00125843i
$375$	−1.75189e7			−0.332211
$376$	4.95677e6	+	1.80355e7i	0.0932471	+	0.339285i
$377$			9.07880e7i			1.69436i
$378$	1.14909e7	−	4.21020e6i	0.212755	−	0.0779520i
$379$	5.39896e7	+	5.39896e7i	0.991728	+	0.991728i	0.999966	−	0.00823775i	$-0.00262219\pi$
$379$	5.39896e7	+	5.39896e7i	0.991728	+	0.991728i	−0.00823775	+	0.999966i	$0.502622\pi$
$380$	8.57297e6	−	7.25626e6i	0.156236	−	0.132240i
$381$	−3.75431e7	−	3.75431e7i	−0.678822	−	0.678822i
$382$	−1.98852e7	−	9.22090e6i	−0.356729	−	0.165418i
$383$			1.00149e8i			1.78258i	0.453436	+	0.891289i	$0.350198\pi$
$383$			1.00149e8i			1.78258i	−0.453436	+	0.891289i	$0.649802\pi$
$384$	−2.53546e7	−	2.06366e7i	−0.447779	−	0.364455i
$385$	3.28499e6			0.0575642
$386$	−790239.	+	1.70417e6i	−0.0137403	+	0.0296314i
$387$	6.21564e6	−	6.21564e6i	0.107239	−	0.107239i
$388$	−6.06989e7	−	7.17133e7i	−1.03917	−	1.22774i
$389$	513308.	−	513308.i	0.00872025	−	0.00872025i	−0.702733	−	0.711453i	$-0.748037\pi$
$389$	513308.	−	513308.i	0.00872025	−	0.00872025i	0.711453	+	0.702733i	$0.248037\pi$
$390$	−3.95187e6	−	1.07859e7i	−0.0666207	−	0.181829i
$391$	−458918.			−0.00767724
$392$	−2.24324e7	+	6.16518e6i	−0.372407	+	0.102350i
$393$			4.32450e7i			0.712456i
$394$	4.84693e6	+	1.32288e7i	0.0792461	+	0.216287i
$395$	−2.21833e7	−	2.21833e7i	−0.359944	−	0.359944i
$396$	−3.34636e6	−	278359.i	−0.0538874	−	0.00448249i
$397$	7.43291e7	+	7.43291e7i	1.18792	+	1.18792i	0.977641	+	0.210280i	$0.0674374\pi$
$397$	7.43291e7	+	7.43291e7i	1.18792	+	1.18792i	0.210280	+	0.977641i	$0.432563\pi$
$398$	1.25849e7	−	2.71397e7i	0.199618	−	0.430483i
$399$			2.93247e7i			0.461652i
$400$	−5.73867e7	−	9.61368e6i	−0.896668	−	0.150214i
$401$	4.28921e6			0.0665187			0.0332594	−	0.999447i	$-0.489411\pi$
$401$	4.28921e6			0.0665187			0.0332594	+	0.999447i	$0.489411\pi$
$402$	4.26207e7	+	1.97636e7i	0.656058	+	0.304220i
$403$	−2.67974e7	+	2.67974e7i	−0.409428	+	0.409428i
$404$	5.89288e7	+	4.90185e6i	0.893684	+	0.0743389i
$405$	1.57304e6	−	1.57304e6i	0.0236796	−	0.0236796i
$406$	1.12642e8	−	4.12711e7i	1.68315	−	0.616692i
$407$	1.27751e7			0.189488
$408$	−437179.	+	768555.i	−0.00643692	+	0.0113160i
$409$			7.90997e7i			1.15613i	0.815992	+	0.578063i	$0.196191\pi$
$409$			7.90997e7i			1.15613i	−0.815992	+	0.578063i	$0.803809\pi$
$410$	3.82970e7	−	1.40318e7i	0.555666	−	0.203592i
$411$	−3.55472e7	−	3.55472e7i	−0.512012	−	0.512012i
$412$	−2.88386e7	−	3.40716e7i	−0.412365	−	0.487193i
$413$	−2.86956e7	−	2.86956e7i	−0.407347	−	0.407347i
$414$	7.30573e6	+	3.38773e6i	0.102959	+	0.0477427i
$415$		−	8.37088e6i		−	0.117119i
$416$	−1.47546e7	−	7.87467e7i	−0.204950	−	1.09384i
$417$	5.59359e7			0.771405
$418$	3.38491e6	−	7.29965e6i	0.0463466	−	0.0999478i
$419$	9.85115e7	−	9.85115e7i	1.33920	−	1.33920i	0.442361	−	0.896837i	$-0.354141\pi$
$419$	9.85115e7	−	9.85115e7i	1.33920	−	1.33920i	0.896837	−	0.442361i	$-0.145859\pi$
$420$	−1.15857e7	+	9.80628e6i	−0.156378	+	0.132360i
$421$	−8.68766e6	+	8.68766e6i	−0.116428	+	0.116428i	−0.762920	−	0.646493i	$-0.776235\pi$
$421$	−8.68766e6	+	8.68766e6i	−0.116428	+	0.116428i	0.646493	+	0.762920i	$0.276235\pi$
$422$	1.32150e7	+	3.60678e7i	0.175844	+	0.479934i
$423$	−8.87722e6			−0.117289
$424$	−4.12868e7	+	7.25818e7i	−0.541644	+	0.952204i
$425$			1.57375e6i			0.0205008i
$426$	1.78808e7	+	4.88021e7i	0.231290	+	0.631263i
$427$	3.89219e7	+	3.89219e7i	0.499932	+	0.499932i
$428$	8.13813e6	−	9.78346e7i	0.103799	−	1.24785i
$429$	−5.81898e6	−	5.81898e6i	−0.0737013	−	0.0737013i
$430$	−4.58646e6	+	9.89084e6i	−0.0576863	+	0.124402i
$431$		−	9.13408e7i		−	1.14086i	−0.821346	−	0.570431i	$-0.806776\pi$
$431$		−	9.13408e7i		−	1.14086i	0.821346	−	0.570431i	$-0.193224\pi$
$432$	1.26331e7	−	9.00774e6i	0.156696	−	0.111729i
$433$	−5.70687e7			−0.702965			−0.351483	−	0.936194i	$-0.614322\pi$
$433$	−5.70687e7			−0.702965			−0.351483	+	0.936194i	$0.614322\pi$
$434$	4.54297e7	+	2.10661e7i	0.555738	+	0.257700i
$435$	1.54199e7	−	1.54199e7i	0.187333	−	0.187333i
$436$	8.32153e6	−	1.00039e8i	0.100402	−	1.20701i
$437$	−1.36448e7	+	1.36448e7i	−0.163502	+	0.163502i
$438$	2.37137e7	−	8.68853e6i	0.282213	−	0.103401i
$439$	−1.29673e7			−0.153269			−0.0766347	−	0.997059i	$-0.524418\pi$
$439$	−1.29673e7			−0.153269			−0.0766347	+	0.997059i	$0.524418\pi$
$440$	4.01590e6	−	1.10371e6i	0.0471438	−	0.0129567i
$441$		−	1.10414e7i		−	0.128738i
$442$	−2.03464e6	+	745477.i	−0.0235625	+	0.00863311i
$443$	−4.74461e7	−	4.74461e7i	−0.545745	−	0.545745i	0.379462	−	0.925207i	$-0.376109\pi$
$443$	−4.74461e7	−	4.74461e7i	−0.545745	−	0.545745i	−0.925207	+	0.379462i	$0.876109\pi$
$444$	−4.50561e7	+	3.81359e7i	−0.514759	+	0.435698i
$445$	2.62406e7	+	2.62406e7i	0.297779	+	0.297779i
$446$	−7.29427e7	−	3.38241e7i	−0.822199	−	0.381260i
$447$			5.50147e7i			0.615965i
$448$	−9.09948e7	+	5.41035e7i	−1.01200	+	0.601716i
$449$	3.70427e7			0.409226			0.204613	−	0.978843i	$-0.434406\pi$
$449$	3.70427e7			0.409226			0.204613	+	0.978843i	$0.434406\pi$
$450$	1.16174e7	−	2.50533e7i	0.127489	−	0.274934i
$451$	2.06612e7	−	2.06612e7i	0.225230	−	0.225230i
$452$	1.58617e7	+	1.87399e7i	0.171764	+	0.202933i
$453$	−6.91036e7	+	6.91036e7i	−0.743372	+	0.743372i
$454$	1.18005e7	+	3.22073e7i	0.126105	+	0.344181i
$455$	−3.71985e7			−0.394904
$456$	9.85264e6	+	3.58494e7i	0.103910	+	0.378083i
$457$			7.63145e7i			0.799573i	0.916608	+	0.399787i	$0.130916\pi$
$457$			7.63145e7i			0.799573i	−0.916608	+	0.399787i	$0.869084\pi$
$458$	−1.74773e6	−	4.77010e6i	−0.0181919	−	0.0496513i
$459$	−296736.	−	296736.i	−0.00306854	−	0.00306854i
$460$	−9.95368e6	−	827973.i	−0.102261	−	0.00850634i
$461$	−2.82948e7	−	2.82948e7i	−0.288804	−	0.288804i	0.547803	−	0.836607i	$-0.315464\pi$
$461$	−2.82948e7	−	2.82948e7i	−0.288804	−	0.288804i	−0.836607	+	0.547803i	$0.815464\pi$
$462$	−4.57444e6	+	9.86492e6i	−0.0463887	+	0.100039i
$463$		−	1.01789e8i		−	1.02555i	−0.858523	−	0.512776i	$-0.828617\pi$
$463$		−	1.01789e8i		−	1.02555i	0.858523	−	0.512776i	$-0.171383\pi$
$464$	1.23838e8	−	8.82998e7i	1.23965	−	0.883905i
$465$	9.10284e6			0.0905353
$466$	−1.17341e8	−	5.44118e7i	−1.15955	−	0.537695i
$467$	9.43637e7	−	9.43637e7i	0.926519	−	0.926519i	−0.0709599	−	0.997479i	$-0.522606\pi$
$467$	9.43637e7	−	9.43637e7i	0.926519	−	0.926519i	0.997479	+	0.0709599i	$0.0226062\pi$
$468$	3.78934e7	+	3.15207e6i	0.369681	+	0.0307510i
$469$	1.07576e8	−	1.07576e8i	1.04279	−	1.04279i
$470$	1.03383e7	−	3.78787e6i	0.0995760	−	0.0364839i
$471$	6.16705e7			0.590221
$472$	−4.47216e7	−	2.54391e7i	−0.425296	−	0.241922i
$473$			7.81049e6i			0.0738066i
$474$	9.75080e7	−	3.57262e7i	0.915599	−	0.335469i
$475$	4.67916e7	+	4.67916e7i	0.436603	+	0.436603i
$476$	1.84984e6	+	2.18552e6i	0.0171520	+	0.0202644i
$477$	−2.80235e7	−	2.80235e7i	−0.258206	−	0.258206i
$478$	1.22890e8	+	5.69849e7i	1.12520	+	0.521766i
$479$		−	1.11086e8i		−	1.01077i	−0.862893	−	0.505387i	$-0.831350\pi$
$479$		−	1.11086e8i		−	1.01077i	0.862893	−	0.505387i	$-0.168650\pi$
$480$	−1.08688e7	+	1.58808e7i	−0.0982781	+	0.143598i
$481$	−1.44662e8			−1.29993
$482$	−2.09713e7	+	4.52252e7i	−0.187277	+	0.403868i
$483$	1.84399e7	−	1.84399e7i	0.163650	−	0.163650i
$484$	−8.42643e7	+	7.13222e7i	−0.743203	+	0.629055i
$485$	−3.91072e7	+	3.91072e7i	−0.342793	+	0.342793i
$486$	2.53337e6	+	6.91437e6i	0.0220694	+	0.0602343i
$487$	1.62475e8			1.40669			0.703347	−	0.710846i	$-0.251688\pi$
$487$	1.62475e8			1.40669			0.703347	+	0.710846i	$0.251688\pi$
$488$	6.06592e7	+	3.45049e7i	0.521960	+	0.296907i
$489$		−	8.89132e7i		−	0.760396i
$490$	4.71132e6	+	1.28587e7i	0.0400455	+	0.109297i
$491$	−1.59056e8	−	1.59056e8i	−1.34371	−	1.34371i	−0.892332	−	0.451379i	$-0.850932\pi$
$491$	−1.59056e8	−	1.59056e8i	−1.34371	−	1.34371i	−0.451379	−	0.892332i	$-0.649068\pi$
$492$	−1.11919e7	+	1.34547e8i	−0.0939745	+	1.12974i
$493$	−2.90880e6	−	2.90880e6i	−0.0242758	−	0.0242758i
$494$	−3.83300e7	+	8.26597e7i	−0.317949	+	0.685666i
$495$			1.97666e6i			0.0162973i
$496$	6.26156e7	+	1.04896e7i	0.513142	+	0.0859637i
$497$	1.68309e8			1.37101
$498$	2.51380e7	+	1.16567e7i	0.203537	+	0.0943816i
$499$	−1.52626e8	+	1.52626e8i	−1.22836	+	1.22836i	−0.263778	+	0.964583i	$0.584969\pi$
$499$	−1.52626e8	+	1.52626e8i	−1.22836	+	1.22836i	−0.964583	+	0.263778i	$0.915031\pi$
$500$	−5.96237e6	+	7.16782e7i	−0.0476990	+	0.573425i
$501$	−1.31311e7	+	1.31311e7i	−0.104421	+	0.104421i
$502$	3.07184e7	−	1.12550e7i	0.242821	−	0.0889680i
$503$	−2.80504e7			−0.220412			−0.110206	−	0.993909i	$-0.535151\pi$
$503$	−2.80504e7			−0.220412			−0.110206	+	0.993909i	$0.535151\pi$
$504$	−1.33151e7	−	4.84478e7i	−0.104005	−	0.378427i
$505$		−	3.48086e7i		−	0.270279i
$506$	−6.71863e6	+	2.46166e6i	−0.0518596	+	0.0190010i
$507$	1.26884e7	+	1.26884e7i	0.0973605	+	0.0973605i
$508$	−1.66384e8	+	1.40829e8i	−1.26917	+	1.07424i
$509$	1.33201e8	+	1.33201e8i	1.01008	+	1.01008i	0.999949	+	0.0101280i	$0.00322389\pi$
$509$	1.33201e8	+	1.33201e8i	1.01008	+	1.01008i	0.0101280	+	0.999949i	$0.496776\pi$
$510$	472190.	+	218958.i	0.00355964	+	0.00165063i
$511$		−	8.17841e7i		−	0.612924i
$512$	−9.30631e7	+	9.67143e7i	−0.693374	+	0.720578i
$513$	−1.76454e7			−0.130701
$514$	1.02002e7	−	2.19970e7i	0.0751135	−	0.161984i
$515$	−1.85801e7	+	1.85801e7i	−0.136028	+	0.136028i
$516$	−2.33157e7	−	2.75465e7i	−0.169707	−	0.200502i
$517$	5.57750e6	−	5.57750e6i	0.0403615	−	0.0403615i
$518$	6.57618e7	+	1.79485e8i	0.473134	+	1.29133i
$519$	−9.45382e7			−0.676247
$520$	−4.54752e7	+	1.24981e7i	−0.323418	+	0.0888862i
$521$		−	1.63500e8i		−	1.15612i	−0.815993	−	0.578061i	$-0.803809\pi$
$521$		−	1.63500e8i		−	1.15612i	0.815993	−	0.578061i	$-0.196191\pi$
$522$	2.48338e7	+	6.77792e7i	0.174595	+	0.476524i
$523$	1.51209e8	+	1.51209e8i	1.05700	+	1.05700i	0.998274	+	0.0587229i	$0.0187028\pi$
$523$	1.51209e8	+	1.51209e8i	1.05700	+	1.05700i	0.0587229	+	0.998274i	$0.481297\pi$
$524$	1.76936e8	+	1.47180e7i	1.22976	+	0.102295i
$525$	−6.32353e7	−	6.32353e7i	−0.437000	−	0.437000i
$526$	4.34040e7	−	9.36021e7i	0.298245	−	0.643173i
$527$		−	1.71715e6i		−	0.0117321i
$528$	−2.27779e6	+	1.35968e7i	−0.0154744	+	0.0923709i
$529$	−1.30876e8			−0.884081
$530$	4.45933e7	+	2.06783e7i	0.299531	+	0.138895i
$531$	1.72668e7	−	1.72668e7i	0.115326	−	0.115326i
$532$	1.19981e8	+	9.98035e6i	0.796853	+	0.0662843i
$533$	−2.33963e8	+	2.33963e8i	−1.54513	+	1.54513i
$534$	−1.15342e8	+	4.22605e7i	−0.757467	+	0.277530i
$535$	−5.77898e7			−0.377389
$536$	9.53675e7	−	1.67655e8i	0.619307	−	1.08874i
$537$		−	1.41195e8i		−	0.911793i
$538$	−2.12404e8	+	7.78235e7i	−1.36401	+	0.499763i
$539$	6.93723e6	+	6.93723e6i	0.0443017	+	0.0443017i
$540$	−5.90067e6	−	6.97140e6i	−0.0374731	−	0.0442730i
$541$	3.15433e7	+	3.15433e7i	0.199212	+	0.199212i	0.799662	−	0.600450i	$-0.205012\pi$
$541$	3.15433e7	+	3.15433e7i	0.199212	+	0.199212i	−0.600450	+	0.799662i	$0.705012\pi$
$542$	−1.17281e8	−	5.43840e7i	−0.736595	−	0.341565i
$543$			1.34307e8i			0.838880i
$544$	2.99573e6	+	2.05027e6i	0.0186083	+	0.0127355i
$545$	−5.90921e7			−0.365040
$546$	5.18000e7	−	1.11708e8i	0.318238	−	0.686289i
$547$	−6.10938e7	+	6.10938e7i	−0.373280	+	0.373280i	−0.868671	−	0.495390i	$-0.835025\pi$
$547$	−6.10938e7	+	6.10938e7i	−0.373280	+	0.373280i	0.495390	+	0.868671i	$0.335025\pi$
$548$	−1.57538e8	+	1.33342e8i	−0.957293	+	0.810263i
$549$	−2.34202e7	+	2.34202e7i	−0.141538	+	0.141538i
$550$	8.44169e6	+	2.30400e7i	0.0507389	+	0.138482i
$551$	−1.72971e8			−1.03400
$552$	1.63472e7	−	2.87382e7i	0.0971911	−	0.170861i
$553$		−	3.36287e8i		−	1.98854i
$554$	−1.05493e8	−	2.87923e8i	−0.620432	−	1.69335i
$555$	2.45703e7	+	2.45703e7i	0.143725	+	0.143725i
$556$	1.90372e7	−	2.28860e8i	0.110759	−	1.33151i
$557$	−3.82316e7	−	3.82316e7i	−0.221236	−	0.221236i	0.587783	−	0.809019i	$-0.300001\pi$
$557$	−3.82316e7	−	3.82316e7i	−0.221236	−	0.221236i	−0.809019	+	0.587783i	$0.800001\pi$
$558$	−1.26760e7	+	2.73361e7i	−0.0729589	+	0.157338i
$559$		−	8.84443e7i		−	0.506331i
$560$	3.61790e7	+	5.07401e7i	0.206012	+	0.288926i
$561$	372874.			0.00211190
$562$	−1.81585e8	−	8.42022e7i	−1.02299	−	0.474367i
$563$	1.98038e7	−	1.98038e7i	0.110974	−	0.110974i	−0.649439	−	0.760414i	$-0.724996\pi$
$563$	1.98038e7	−	1.98038e7i	0.110974	−	0.110974i	0.760414	+	0.649439i	$0.224996\pi$
$564$	−3.02126e6	+	3.63209e7i	−0.0168404	+	0.202451i
$565$	1.02194e7	−	1.02194e7i	0.0566603	−	0.0566603i
$566$	−2.11491e8	+	7.74887e7i	−1.16639	+	0.427355i
$567$	2.38464e7			0.130820
$568$	2.05758e8	−	5.65493e7i	1.12282	−	0.308590i
$569$			3.17667e8i			1.72439i	0.506578	+	0.862194i	$0.330910\pi$
$569$			3.17667e8i			1.72439i	−0.506578	+	0.862194i	$0.669090\pi$
$570$	2.05495e7	−	7.52920e6i	0.110963	−	0.0406560i
$571$	−1.14822e7	−	1.14822e7i	−0.0616759	−	0.0616759i	0.675596	−	0.737272i	$-0.263886\pi$
$571$	−1.14822e7	−	1.14822e7i	−0.0616759	−	0.0616759i	−0.737272	+	0.675596i	$0.763886\pi$
$572$	−2.57886e7	+	2.18278e7i	−0.137797	+	0.116633i
$573$	−3.02009e7	−	3.02009e7i	−0.160530	−	0.160530i
$574$	3.96638e8	+	1.83924e8i	2.09729	+	0.972530i
$575$		−	5.88467e7i		−	0.309541i
$576$	−3.25554e7	−	5.47537e7i	−0.170355	−	0.286514i
$577$	2.85865e8			1.48810			0.744052	−	0.668122i	$-0.232902\pi$
$577$	2.85865e8			1.48810			0.744052	+	0.668122i	$0.232902\pi$
$578$	−8.11923e7	+	1.75093e8i	−0.420466	+	0.906748i
$579$	−2.58824e6	+	2.58824e6i	−0.0133343	+	0.0133343i
$580$	−5.78422e7	−	6.83382e7i	−0.296457	−	0.350251i
$581$	6.34490e7	−	6.34490e7i	0.323516	−	0.323516i
$582$	−6.29821e7	−	1.71898e8i	−0.319484	−	0.871970i
$583$	3.52140e7			0.177709
$584$	−2.74782e7	−	9.99810e7i	−0.137959	−	0.501972i
$585$		−	2.23832e7i		−	0.111803i
$586$	−7.16414e7	−	1.95532e8i	−0.356018	−	0.971683i
$587$	1.94525e8	+	1.94525e8i	0.961749	+	0.961749i	0.999295	−	0.0375461i	$-0.0119541\pi$
$587$	1.94525e8	+	1.94525e8i	0.961749	+	0.961749i	−0.0375461	+	0.999295i	$0.511954\pi$
$588$	−4.51755e7	−	3.75782e6i	−0.222214	−	0.0184843i
$589$	−5.10551e7	−	5.10551e7i	−0.249858	−	0.249858i
$590$	−1.27410e7	+	2.74763e7i	−0.0620365	+	0.133784i
$591$			2.74528e7i			0.132991i
$592$	1.40698e8	+	1.97325e8i	0.678144	+	0.951078i
$593$	3.72075e8			1.78429			0.892147	−	0.451745i	$-0.149198\pi$
$593$	3.72075e8			1.78429			0.892147	+	0.451745i	$0.149198\pi$
$594$	−5.93595e6	−	2.75255e6i	−0.0283225	−	0.0131334i
$595$	1.19182e6	−	1.19182e6i	0.00565796	−	0.00565796i
$596$	2.25091e8	+	1.87236e7i	1.06321	+	0.0884406i
$597$	4.12188e7	−	4.12188e7i	0.193719	−	0.193719i
$598$	7.60803e7	−	2.78753e7i	0.355769	−	0.130351i
$599$	−2.67399e8			−1.24417			−0.622084	−	0.782951i	$-0.713714\pi$
$599$	−2.67399e8			−1.24417			−0.622084	+	0.782951i	$0.713714\pi$
$600$	−9.85511e7	−	5.60590e7i	−0.456255	−	0.259532i
$601$		−	1.80794e8i		−	0.832836i	−0.909173	−	0.416418i	$-0.863285\pi$
$601$		−	1.80794e8i		−	0.832836i	0.909173	−	0.416418i	$-0.136715\pi$
$602$	−1.09734e8	+	4.02057e7i	−0.502981	+	0.184289i
$603$	6.47309e7	+	6.47309e7i	0.295229	+	0.295229i
$604$	2.59217e8	+	3.06254e8i	1.17639	+	1.38986i
$605$	4.59516e7	+	4.59516e7i	0.207508	+	0.207508i
$606$	1.04531e8	+	4.84719e7i	0.469708	+	0.217807i
$607$		−	5.44539e7i		−	0.243480i	−0.992562	−	0.121740i	$-0.961153\pi$
$607$		−	5.44539e7i		−	0.243480i	0.992562	−	0.121740i	$-0.0388473\pi$
$608$	1.50030e8	−	2.81108e7i	0.667525	−	0.125073i
$609$	2.33758e8			1.03494
$610$	1.72816e7	−	3.72682e7i	0.0761366	−	0.164191i
$611$	−6.31583e7	+	6.31583e7i	−0.276890	+	0.276890i
$612$	−1.31508e6	+	1.11309e6i	−0.00573715	+	0.00485599i
$613$	−2.02723e7	+	2.02723e7i	−0.0880079	+	0.0880079i	−0.749740	−	0.661732i	$-0.769822\pi$
$613$	−2.02723e7	+	2.02723e7i	−0.0880079	+	0.0880079i	0.661732	+	0.749740i	$0.269822\pi$
$614$	3.34520e7	+	9.13009e7i	0.144516	+	0.394430i
$615$	7.94752e7			0.341669
$616$	3.88052e7	+	2.20736e7i	0.166015	+	0.0944347i
$617$		−	1.68371e8i		−	0.716821i	−0.933564	−	0.358410i	$-0.883319\pi$
$617$		−	1.68371e8i		−	0.716821i	0.933564	−	0.358410i	$-0.116681\pi$
$618$	−2.99233e7	−	8.16701e7i	−0.126778	−	0.346017i
$619$	2.13535e8	+	2.13535e8i	0.900319	+	0.900319i	0.995463	−	0.0951444i	$-0.0303313\pi$
$619$	2.13535e8	+	2.13535e8i	0.900319	+	0.900319i	−0.0951444	+	0.995463i	$0.530331\pi$
$620$	3.09805e6	−	3.72440e7i	0.0129991	−	0.156272i
$621$	1.10957e7	+	1.10957e7i	0.0463319	+	0.0463319i
$622$	7.68801e7	−	1.65794e8i	0.319479	−	0.688967i
$623$			3.97793e8i			1.64510i
$624$	2.57932e7	−	1.53967e8i	0.106158	−	0.633686i
$625$	−1.79624e8			−0.735741
$626$	−2.18268e8	−	1.01213e8i	−0.889750	−	0.412584i
$627$	1.10865e7	−	1.10865e7i	0.0449770	−	0.0449770i
$628$	2.09889e7	−	2.52323e8i	0.0847443	−	1.01877i
$629$	4.63491e6	−	4.63491e6i	0.0186247	−	0.0186247i
$630$	−2.77711e7	+	1.01751e7i	−0.111064	+	0.0406929i
$631$	−3.27286e8			−1.30269			−0.651343	−	0.758783i	$-0.725794\pi$
$631$	−3.27286e8			−1.30269			−0.651343	+	0.758783i	$0.725794\pi$
$632$	−1.12987e8	−	4.11110e8i	−0.447587	−	1.62857i
$633$			7.48489e7i			0.295104i
$634$	6.45046e7	−	2.36340e7i	0.253118	−	0.0927406i
$635$	9.07337e7	+	9.07337e7i	0.354362	+	0.354362i
$636$	−1.24195e8	+	1.05120e8i	−0.482761	+	0.408614i
$637$	−7.85557e7	−	7.85557e7i	−0.303920	−	0.303920i
$638$	−5.81881e7	−	2.69823e7i	−0.224064	−	0.103900i
$639$			1.01276e8i			0.388153i
$640$	6.12767e7	+	4.98741e7i	0.233752	+	0.190255i
$641$	3.54495e8			1.34597			0.672986	−	0.739655i	$-0.265011\pi$
$641$	3.54495e8			1.34597			0.672986	+	0.739655i	$0.265011\pi$
$642$	8.04739e7	−	1.73544e8i	0.304123	−	0.655851i
$643$	−2.20361e8	+	2.20361e8i	−0.828898	+	0.828898i	−0.987364	−	0.158466i	$-0.949345\pi$
$643$	−2.20361e8	+	2.20361e8i	−0.828898	+	0.828898i	0.158466	+	0.987364i	$0.449345\pi$
$644$	−6.91704e7	−	8.17220e7i	−0.258978	−	0.305972i
$645$	−1.50219e7	+	1.50219e7i	−0.0559815	+	0.0559815i
$646$	−1.42030e6	−	3.87644e6i	−0.00526845	−	0.0143792i
$647$	2.98046e8			1.10045			0.550225	−	0.835017i	$-0.314542\pi$
$647$	2.98046e8			1.10045			0.550225	+	0.835017i	$0.314542\pi$
$648$	2.91521e7	−	8.01200e6i	0.107138	−	0.0294453i
$649$			2.16972e7i			0.0793725i
$650$	−9.55918e7	−	2.60900e8i	−0.348081	−	0.950022i
$651$	6.89970e7	+	6.89970e7i	0.250085	+	0.250085i
$652$	−3.63786e8	−	3.02607e7i	−1.31251	−	0.109178i
$653$	−4.46026e7	−	4.46026e7i	−0.160185	−	0.160185i	0.622464	−	0.782648i	$-0.286132\pi$
$653$	−4.46026e7	−	4.46026e7i	−0.160185	−	0.160185i	−0.782648	+	0.622464i	$0.786132\pi$
$654$	8.22874e7	−	1.77455e8i	0.294171	−	0.634389i
$655$		−	1.04514e8i		−	0.371920i
$656$	5.46685e8	+	9.15830e7i	1.93654	+	0.324417i
$657$	4.92114e7			0.173528
$658$	1.07072e8	+	4.96503e7i	0.375837	+	0.174279i
$659$	−1.68168e8	+	1.68168e8i	−0.587607	+	0.587607i	−0.936983	−	0.349375i	$-0.886394\pi$
$659$	−1.68168e8	+	1.68168e8i	−0.587607	+	0.587607i	0.349375	+	0.936983i	$0.386394\pi$
$660$	8.08743e6	+	672733.i	0.0281306	+	0.00233997i
$661$	9.57897e7	−	9.57897e7i	0.331676	−	0.331676i	−0.521547	−	0.853223i	$-0.674645\pi$
$661$	9.57897e7	−	9.57897e7i	0.331676	−	0.331676i	0.853223	+	0.521547i	$0.174645\pi$
$662$	−9.81947e7	+	3.59778e7i	−0.338465	+	0.124011i
$663$	−4.22234e6			−0.0144882
$664$	5.62484e7	−	9.88841e7i	0.192135	−	0.337771i
$665$		−	7.08715e7i		−	0.240994i
$666$	−1.08000e8	+	3.95704e7i	−0.365596	+	0.133952i
$667$	1.08767e8	+	1.08767e8i	0.366540	+	0.366540i
$668$	4.92564e7	+	5.81944e7i	0.165247	+	0.195232i
$669$	−1.10783e8	−	1.10783e8i	−0.369993	−	0.369993i
$670$	−1.03005e8	−	4.77643e7i	−0.342479	−	0.158810i
$671$		−	2.94296e7i		−	0.0974129i
$672$	−2.02754e8	+	3.79896e7i	−0.668132	+	0.125186i
$673$	−3.40113e8			−1.11578			−0.557889	−	0.829916i	$-0.688389\pi$
$673$	−3.40113e8			−1.11578			−0.557889	+	0.829916i	$0.688389\pi$
$674$	−2.01947e8	+	4.35504e8i	−0.659565	+	1.42237i
$675$	3.80501e7	−	3.80501e7i	0.123721	−	0.123721i
$676$	5.62326e7	−	4.75959e7i	0.182032	−	0.154074i
$677$	−3.07721e8	+	3.07721e8i	−0.991724	+	0.991724i	−0.999966	−	0.00824207i	$-0.997376\pi$
$677$	−3.07721e8	+	3.07721e8i	−0.991724	+	0.991724i	0.00824207	+	0.999966i	$0.497376\pi$
$678$	1.64583e7	+	4.49198e7i	0.0528075	+	0.144128i
$679$	−5.92843e8			−1.89379
$680$	1.05657e6	−	1.85743e6i	0.00336024	−	0.00590726i
$681$			6.68375e7i			0.211631i
$682$	−9.21086e6	−	2.51393e7i	−0.0290367	−	0.0792502i
$683$	−3.12833e7	−	3.12833e7i	−0.0981862	−	0.0981862i	0.656307	−	0.754494i	$-0.272117\pi$
$683$	−3.12833e7	−	3.12833e7i	−0.0981862	−	0.0981862i	−0.754494	+	0.656307i	$0.772117\pi$
$684$	−6.00541e6	+	7.21955e7i	−0.0187661	+	0.225601i
$685$	8.59099e7	+	8.59099e7i	0.267283	+	0.267283i
$686$	9.81422e7	−	2.11647e8i	0.304007	−	0.655600i
$687$		−	9.89905e6i		−	0.0305297i
$688$	−1.20641e8	+	8.60203e7i	−0.370450	+	0.264141i
$689$	−3.98755e8			−1.21913
$690$	−1.76564e7	−	8.18740e6i	−0.0537470	−	0.0249229i
$691$	3.09028e8	−	3.09028e8i	0.936620	−	0.936620i	−0.0614883	−	0.998108i	$-0.519585\pi$
$691$	3.09028e8	−	3.09028e8i	0.936620	−	0.936620i	0.998108	+	0.0614883i	$0.0195847\pi$
$692$	−3.21751e7	+	3.86800e8i	−0.0970959	+	1.16726i
$693$	−1.49825e7	+	1.49825e7i	−0.0450179	+	0.0450179i
$694$	−4.57024e8	+	1.67450e8i	−1.36729	+	0.500965i
$695$	−1.35185e8			−0.402693
$696$	2.85769e8	−	7.85389e7i	0.847592	−	0.232947i
$697$		−	1.49921e7i		−	0.0442756i
$698$	2.80274e8	−	1.02690e8i	0.824170	−	0.301970i
$699$	−1.78213e8	−	1.78213e8i	−0.521805	−	0.521805i
$700$	−2.80247e8	+	2.37204e8i	−0.817046	+	0.691556i
$701$	2.16593e8	+	2.16593e8i	0.628767	+	0.628767i	0.947758	−	0.318991i	$-0.103344\pi$
$701$	2.16593e8	+	2.16593e8i	0.628767	+	0.628767i	−0.318991	+	0.947758i	$0.603344\pi$
$702$	6.72174e7	+	3.11693e7i	0.194299	+	0.0900980i
$703$		−	2.75614e8i		−	0.793297i
$704$	5.48557e7	+	1.39471e7i	0.157219	+	0.0399728i
$705$	2.14543e7			0.0612276
$706$	−9.05821e7	+	1.95343e8i	−0.257412	+	0.555116i
$707$	2.63839e8	−	2.63839e8i	0.746589	−	0.746589i
$708$	−6.47700e7	−	7.65232e7i	−0.182505	−	0.215622i
$709$	−3.07048e8	+	3.07048e8i	−0.861524	+	0.861524i	−0.991515	−	0.129991i	$-0.958505\pi$
$709$	−3.07048e8	+	3.07048e8i	−0.861524	+	0.861524i	0.129991	+	0.991515i	$0.458505\pi$
$710$	−4.32139e7	−	1.17944e8i	−0.120739	−	0.329535i
$711$	2.02352e8			0.562986
$712$	1.33652e8	+	4.86301e8i	0.370285	+	1.34730i
$713$			6.42085e7i			0.177143i
$714$	1.91943e6	+	5.23871e6i	0.00527323	+	0.0143923i
$715$	1.40632e7	+	1.40632e7i	0.0384740	+	0.0384740i
$716$	−5.77695e8	−	4.80542e7i	−1.57384	−	0.130916i
$717$	1.86641e8	+	1.86641e8i	0.506347	+	0.506347i
$718$	4.45627e7	−	9.61008e7i	0.120392	−	0.259629i
$719$		−	3.88723e8i		−	1.04581i	−0.852390	−	0.522906i	$-0.824848\pi$
$719$		−	3.88723e8i		−	1.04581i	0.852390	−	0.522906i	$-0.175152\pi$
$720$	−3.05315e7	+	2.17698e7i	−0.0817995	+	0.0583252i
$721$	−2.81665e8			−0.751496
$722$	1.83958e8	+	8.53030e7i	0.488774	+	0.226648i
$723$	−6.86865e7	+	6.86865e7i	−0.181743	+	0.181743i
$724$	5.49514e8	+	4.57100e7i	1.44798	+	0.120447i
$725$	3.72993e8	−	3.72993e8i	0.978783	−	0.978783i
$726$	−2.01983e8	+	7.40050e7i	−0.527843	+	0.193398i
$727$	2.19025e8			0.570019			0.285010	−	0.958525i	$-0.408003\pi$
$727$	2.19025e8			0.570019			0.285010	+	0.958525i	$0.408003\pi$
$728$	−4.39421e8	−	2.49957e8i	−1.13890	−	0.647845i
$729$			1.43489e7i			0.0370370i
$730$	−5.73109e7	+	2.09983e7i	−0.147322	+	0.0539779i
$731$	2.83371e6	+	2.83371e6i	0.00725442	+	0.00725442i
$732$	8.78524e7	+	1.03794e8i	0.223986	+	0.264630i
$733$	−3.39039e7	−	3.39039e7i	−0.0860870	−	0.0860870i	0.662752	−	0.748839i	$-0.269388\pi$
$733$	−3.39039e7	−	3.39039e7i	−0.0860870	−	0.0860870i	−0.748839	+	0.662752i	$0.769388\pi$
$734$	−7.35915e7	−	3.41250e7i	−0.186097	−	0.0862947i
$735$			2.66847e7i			0.0672047i
$736$	−1.12018e8	−	7.66649e7i	−0.280966	−	0.192293i
$737$	−8.13400e7			−0.203190
$738$	−1.10671e8	+	2.38666e8i	−0.275338	+	0.593775i
$739$	−1.32965e8	+	1.32965e8i	−0.329461	+	0.329461i	−0.852382	−	0.522920i	$-0.824843\pi$
$739$	−1.32965e8	+	1.32965e8i	−0.329461	+	0.329461i	0.522920	+	0.852382i	$0.324843\pi$
$740$	1.08891e8	−	9.21663e7i	0.268718	−	0.227445i
$741$	−1.25541e8	+	1.25541e8i	−0.308553	+	0.308553i
$742$	1.81269e8	+	4.94740e8i	0.443724	+	1.21106i
$743$	4.53728e8			1.10619			0.553094	−	0.833119i	$-0.313447\pi$
$743$	4.53728e8			1.10619			0.553094	+	0.833119i	$0.313447\pi$
$744$	1.07531e8	+	6.11669e7i	0.261104	+	0.148524i
$745$		−	1.32959e8i		−	0.321549i
$746$	−7.82858e7	−	2.13666e8i	−0.188567	−	0.514659i
$747$	3.81787e7	+	3.81787e7i	0.0915924	+	0.0915924i
$748$	126904.	−	1.52560e6i	0.000303228	−	0.00364533i
$749$	−4.38030e8	−	4.38030e8i	−1.04246	−	1.04246i
$750$	−5.89589e7	+	1.27147e8i	−0.139754	+	0.301384i
$751$			5.32097e7i			0.125623i	0.998025	+	0.0628117i	$0.0200068\pi$
$751$			5.32097e7i			0.125623i	−0.998025	+	0.0628117i	$0.979993\pi$
$752$	1.47578e8	+	2.47228e7i	0.347030	+	0.0581359i
$753$	6.37477e7			0.149307
$754$	6.58910e8	+	3.05542e8i	1.53713	+	0.712782i
$755$	1.67009e8	−	1.67009e8i	0.388059	−	0.388059i
$756$	8.11585e6	−	9.75667e7i	0.0187832	−	0.225806i
$757$	2.48819e8	−	2.48819e8i	0.573583	−	0.573583i	−0.359545	−	0.933128i	$-0.617068\pi$
$757$	2.48819e8	−	2.48819e8i	0.573583	−	0.573583i	0.933128	+	0.359545i	$0.117068\pi$
$758$	5.73538e8	−	2.10140e8i	1.31691	−	0.482505i
$759$	−1.39427e7			−0.0318876
$760$	−2.38117e7	−	8.66403e7i	−0.0542438	−	0.197369i
$761$			1.77622e8i			0.403035i	0.979485	+	0.201517i	$0.0645872\pi$
$761$			1.77622e8i			0.403035i	−0.979485	+	0.201517i	$0.935413\pi$
$762$	−3.98825e8	+	1.46127e8i	−0.901400	+	0.330266i
$763$	−4.47902e8	−	4.47902e8i	−1.00835	−	1.00835i
$764$	−1.33845e8	+	1.13288e8i	−0.300138	+	0.254040i
$765$	717146.	+	717146.i	0.00160186	+	0.00160186i
$766$	7.26846e8	+	3.37044e8i	1.61717	+	0.749895i
$767$		−	2.45695e8i		−	0.544515i
$768$	−2.35103e8	+	1.14565e8i	−0.519008	+	0.252910i
$769$	5.49859e8			1.20913			0.604564	−	0.796556i	$-0.293347\pi$
$769$	5.49859e8			1.20913			0.604564	+	0.796556i	$0.293347\pi$
$770$	1.10554e7	−	2.38414e7i	0.0242161	−	0.0522227i
$771$	3.34082e7	−	3.34082e7i	0.0728937	−	0.0728937i
$772$	9.70884e6	+	1.14706e7i	0.0211016	+	0.0249307i
$773$	1.63126e8	−	1.63126e8i	0.353170	−	0.353170i	−0.508118	−	0.861288i	$-0.669658\pi$
$773$	1.63126e8	−	1.63126e8i	0.353170	−	0.353170i	0.861288	+	0.508118i	$0.169658\pi$
$774$	−2.41927e7	−	6.60295e7i	−0.0521749	−	0.142402i
$775$	2.20188e8			0.473031
$776$	−7.24751e8	+	1.99186e8i	−1.55097	+	0.426259i
$777$			3.72472e8i			0.794018i
$778$	−1.99791e6	−	5.45292e6i	−0.00424265	−	0.0115795i
$779$	−4.45752e8	−	4.45752e8i	−0.942933	−	0.942933i
$780$	−9.15803e7	−	7.61789e6i	−0.192983	−	0.0160528i
$781$	−6.36309e7	−	6.36309e7i	−0.133572	−	0.133572i
$782$	−1.54446e6	+	3.33068e6i	−0.00322966	+	0.00696486i
$783$			1.40657e8i			0.293007i
$784$	−3.07500e7	+	1.83556e8i	−0.0638112	+	0.380907i
$785$	−1.49044e8			−0.308111
$786$	3.13858e8	+	1.45538e8i	0.646346	+	0.299716i
$787$	3.65012e8	−	3.65012e8i	0.748829	−	0.748829i	−0.225431	−	0.974259i	$-0.572379\pi$
$787$	3.65012e8	−	3.65012e8i	0.748829	−	0.748829i	0.974259	+	0.225431i	$0.0723789\pi$
$788$	1.12322e8	+	9.34325e6i	0.229555	+	0.0190950i
$789$	1.42160e8	−	1.42160e8i	0.289431	−	0.289431i
$790$	−2.35656e8	+	8.63426e7i	−0.477966	+	0.175123i
$791$	1.54920e8			0.313024
$792$	−1.32822e7	+	2.33500e7i	−0.0267359	+	0.0470014i
$793$			3.33254e8i			0.668276i
$794$	7.89607e8	−	2.89306e8i	1.57743	−	0.577958i
$795$	6.77268e7	+	6.77268e7i	0.134790	+	0.134790i
$796$	−1.54617e8	−	1.82674e8i	−0.306562	−	0.362191i
$797$	1.74396e8	+	1.74396e8i	0.344479	+	0.344479i	0.858048	−	0.513569i	$-0.171677\pi$
$797$	1.74396e8	+	1.74396e8i	0.344479	+	0.344479i	−0.513569	+	0.858048i	$0.671677\pi$
$798$	2.12829e8	+	9.86906e7i	0.418815	+	0.194208i
$799$		−	4.04712e6i		−	0.00793424i
$800$	−2.62905e8	+	3.84140e8i	−0.513486	+	0.750273i
$801$	−2.39361e8			−0.465754
$802$	1.44351e7	−	3.11297e7i	0.0279831	−	0.0603464i
$803$	−3.09192e7	+	3.09192e7i	−0.0597148	+	0.0597148i
$804$	2.86875e8	−	2.42814e8i	0.551981	−	0.467203i
$805$	−4.45652e7	+	4.45652e7i	−0.0854295	+	0.0854295i
$806$	1.04302e8	+	2.84672e8i	0.199199	+	0.543675i
$807$	−4.40788e8			−0.838705
$808$	2.33898e8	−	4.11189e8i	0.443396	−	0.779485i
$809$		−	5.26702e8i		−	0.994762i	−0.867532	−	0.497381i	$-0.834295\pi$
$809$		−	5.26702e8i		−	0.994762i	0.867532	−	0.497381i	$-0.165705\pi$
$810$	−6.12262e6	−	1.67105e7i	−0.0115208	−	0.0314438i
$811$	−2.56605e8	−	2.56605e8i	−0.481063	−	0.481063i	0.424408	−	0.905471i	$-0.360482\pi$
$811$	−2.56605e8	−	2.56605e8i	−0.481063	−	0.481063i	−0.905471	+	0.424408i	$0.860482\pi$
$812$	7.95569e7	−	9.56413e8i	0.148597	−	1.78639i
$813$	−1.78122e8	−	1.78122e8i	−0.331471	−	0.331471i
$814$	4.29939e7	−	9.27175e7i	0.0797137	−	0.171905i
$815$			2.14884e8i			0.396946i
$816$	4.10662e6	+	5.75942e6i	0.00755813	+	0.0106001i
$817$	1.68506e8			0.308994
$818$	5.74080e8	+	2.66205e8i	1.04885	+	0.486359i
$819$	1.69659e8	−	1.69659e8i	0.308833	−	0.308833i
$820$	2.70485e7	−	3.25170e8i	0.0490571	−	0.589752i
$821$	−4.69870e7	+	4.69870e7i	−0.0849080	+	0.0849080i	−0.748285	−	0.663377i	$-0.769123\pi$
$821$	−4.69870e7	+	4.69870e7i	−0.0849080	+	0.0849080i	0.663377	+	0.748285i	$0.269123\pi$
$822$	−3.77622e8	+	1.38358e8i	−0.679895	+	0.249109i
$823$	6.05096e8			1.08549			0.542744	−	0.839898i	$-0.317385\pi$
$823$	6.05096e8			1.08549			0.542744	+	0.839898i	$0.317385\pi$
$824$	−3.44335e8	+	9.46349e7i	−0.615459	+	0.169149i
$825$			4.78133e7i			0.0851504i
$826$	−3.04836e8	+	1.11690e8i	−0.540912	+	0.198186i
$827$	5.66395e7	+	5.66395e7i	0.100139	+	0.100139i	0.755401	−	0.655262i	$-0.227442\pi$
$827$	5.66395e7	+	5.66395e7i	0.100139	+	0.100139i	−0.655262	+	0.755401i	$0.727442\pi$
$828$	4.91740e7	−	4.16214e7i	0.0866253	−	0.0733206i
$829$	2.70924e8	+	2.70924e8i	0.475537	+	0.475537i	0.903701	−	0.428164i	$-0.140839\pi$
$829$	2.70924e8	+	2.70924e8i	0.475537	+	0.475537i	−0.428164	+	0.903701i	$0.640839\pi$
$830$	−6.07531e7	−	2.81717e7i	−0.106251	−	0.0492696i
$831$		−	5.97507e8i		−	1.04121i
$832$	−6.21174e8	−	1.57933e8i	−1.07856	−	0.274223i
$833$	5.03376e6			0.00870879
$834$	1.88249e8	−	4.05964e8i	0.324515	−	0.699826i
$835$	3.17350e7	−	3.17350e7i	0.0545103	−	0.0545103i
$836$	−4.15868e7	−	4.91331e7i	−0.0711765	−	0.0840921i
$837$	−4.15171e7	+	4.15171e7i	−0.0708028	+	0.0708028i
$838$	−3.83430e8	−	1.04650e9i	−0.651559	−	1.77831i
$839$	−3.64457e8			−0.617107			−0.308554	−	0.951207i	$-0.599845\pi$
$839$	−3.64457e8			−0.617107			−0.308554	+	0.951207i	$0.599845\pi$
$840$	3.21797e7	+	1.17088e8i	0.0542930	+	0.197549i
$841$			7.83994e8i			1.31803i
$842$	3.38144e7	+	9.22900e7i	0.0566455	+	0.154603i
$843$	−2.75784e8	−	2.75784e8i	−0.460349	−	0.460349i
$844$	3.06242e8	+	2.54740e7i	0.509375	+	0.0423711i
$845$	−3.06651e7	−	3.06651e7i	−0.0508247	−	0.0508247i
$846$	−2.98757e7	+	6.44279e7i	−0.0493410	+	0.106405i
$847$			6.96601e8i			1.14639i
$848$	3.87826e8	+	5.43916e8i	0.635989	+	0.891958i
$849$	−4.38892e8			−0.717191
$850$	1.14218e7	+	5.29638e6i	0.0185985	+	0.00862427i
$851$	−1.73311e8	+	1.73311e8i	−0.281214	+	0.281214i
$852$	4.14367e8	+	3.44681e7i	0.669986	+	0.0557312i
$853$	−2.02133e8	+	2.02133e8i	−0.325679	+	0.325679i	−0.850941	−	0.525262i	$-0.823967\pi$
$853$	−2.02133e8	+	2.02133e8i	−0.325679	+	0.325679i	0.525262	+	0.850941i	$0.323967\pi$
$854$	4.13472e8	−	1.51493e8i	0.663854	−	0.243231i
$855$	4.26450e7			0.0682292
$856$	−6.82663e8	−	3.88320e8i	−1.08839	−	0.619112i
$857$			3.51121e8i			0.557846i	0.960314	+	0.278923i	$0.0899774\pi$
$857$			3.51121e8i			0.557846i	−0.960314	+	0.278923i	$0.910023\pi$
$858$	−6.18157e7	+	2.26488e7i	−0.0978672	+	0.0358578i
$859$	−3.33973e8	−	3.33973e8i	−0.526904	−	0.526904i	0.392744	−	0.919648i	$-0.371526\pi$
$859$	−3.33973e8	−	3.33973e8i	−0.526904	−	0.526904i	−0.919648	+	0.392744i	$0.871526\pi$
$860$	5.63490e7	+	6.65741e7i	0.0885913	+	0.104667i
$861$	6.02400e8	+	6.02400e8i	0.943790	+	0.943790i
$862$	−6.62921e8	−	3.07402e8i	−1.03500	−	0.479938i
$863$			3.35360e8i			0.521769i	0.965370	+	0.260885i	$0.0840142\pi$
$863$			3.35360e8i			0.521769i	−0.965370	+	0.260885i	$0.915986\pi$
$864$	−2.28592e7	−	1.22002e8i	−0.0354422	−	0.189158i
$865$	2.28479e8			0.353018
$866$	−1.92061e8	+	4.14186e8i	−0.295724	+	0.637737i
$867$	−2.65926e8	+	2.65926e8i	−0.408041	+	0.408041i
$868$	3.05782e8	−	2.58817e8i	0.467576	−	0.395761i
$869$	−1.27136e8	+	1.27136e8i	−0.193736	+	0.193736i
$870$	−6.00180e7	−	1.63808e8i	−0.0911430	−	0.248758i
$871$	9.21076e8			1.39393
$872$	−6.98048e8	−	3.97072e8i	−1.05277	−	0.598852i
$873$		−	3.56728e8i		−	0.536160i
$874$	5.31086e7	+	1.44950e8i	0.0795482	+	0.217112i
$875$	3.20921e8	+	3.20921e8i	0.479043	+	0.479043i
$876$	1.67486e7	−	2.01347e8i	0.0249153	−	0.299525i
$877$	48710.2	+	48710.2i	7.22139e−5	+	7.22139e-5i	0.707143	−	0.707071i	$-0.249984\pi$
$877$	48710.2	+	48710.2i	7.22139e−5	+	7.22139e-5i	−0.707071	+	0.707143i	$0.749984\pi$
$878$	−4.36406e7	+	9.41123e7i	−0.0644774	+	0.139047i
$879$		−	4.05774e8i		−	0.597471i
$880$	5.50494e6	−	3.28605e7i	0.00807801	−	0.0482199i
$881$	−1.26485e9			−1.84974			−0.924868	−	0.380288i	$-0.875825\pi$
$881$	−1.26485e9			−1.84974			−0.924868	+	0.380288i	$0.875825\pi$
$882$	−8.01348e7	−	3.71592e7i	−0.116793	−	0.0541577i
$883$	−2.69441e8	+	2.69441e8i	−0.391364	+	0.391364i	−0.875173	−	0.483809i	$-0.839253\pi$
$883$	−2.69441e8	+	2.69441e8i	−0.391364	+	0.391364i	0.483809	+	0.875173i	$0.339253\pi$
$884$	−1.43703e6	+	1.72756e7i	−0.00208022	+	0.0250078i
$885$	−4.17301e7	+	4.17301e7i	−0.0602033	+	0.0602033i
$886$	−5.04026e8	+	1.84671e8i	−0.724689	+	0.265521i
$887$	9.42264e8			1.35021			0.675106	−	0.737721i	$-0.264098\pi$
$887$	9.42264e8			1.35021			0.675106	+	0.737721i	$0.264098\pi$
$888$	1.25145e8	+	4.55346e8i	0.178720	+	0.650284i
$889$			1.37547e9i			1.95770i
$890$	2.78757e8	−	1.02134e8i	0.395417	−	0.144878i
$891$	−9.01532e6	−	9.01532e6i	−0.0127452	−	0.0127452i
$892$	−4.90968e8	+	4.15561e8i	−0.691766	+	0.585518i
$893$	−1.20331e8	−	1.20331e8i	−0.168975	−	0.168975i
$894$	3.99278e8	+	1.85149e8i	0.558809	+	0.259124i
$895$			3.41238e8i			0.475979i
$896$	8.64283e7	+	8.42493e8i	0.120152	+	1.17123i
$897$	1.57884e8			0.218757
$898$	1.24665e8	−	2.68844e8i	0.172153	−	0.371254i
$899$	−4.06978e8	+	4.06978e8i	−0.560134	+	0.560134i
$900$	−1.42731e8	−	1.68631e8i	−0.195790	−	0.231318i
$901$	1.27759e7	−	1.27759e7i	0.0174669	−	0.0174669i
$902$	−8.04183e7	−	2.19486e8i	−0.109581	−	0.299081i
$903$	−2.27723e8			−0.309274
$904$	1.89389e8	−	5.20507e7i	0.256360	−	0.0704565i
$905$		−	3.24592e8i		−	0.437917i
$906$	2.68967e8	+	7.34095e8i	0.361672	+	0.987115i
$907$	−6.98350e8	−	6.98350e8i	−0.935946	−	0.935946i	0.0621221	−	0.998069i	$-0.480213\pi$
$907$	−6.98350e8	−	6.98350e8i	−0.935946	−	0.935946i	−0.998069	+	0.0621221i	$0.980213\pi$
$908$	2.73464e8	+	2.27474e7i	0.365294	+	0.0303861i
$909$	1.58758e8	+	1.58758e8i	0.211371	+	0.211371i
$910$	−1.25189e8	+	2.69975e8i	−0.166128	+	0.358260i
$911$			8.33932e8i			1.10300i	0.834175	+	0.551500i	$0.185944\pi$
$911$			8.33932e8i			1.10300i	−0.834175	+	0.551500i	$0.814056\pi$
$912$	2.93342e8	+	4.91419e7i	0.386714	+	0.0647839i
$913$	−4.79749e7			−0.0630379
$914$	5.53865e8	+	2.56832e8i	0.725380	+	0.336365i
$915$	5.66017e7	−	5.66017e7i	0.0738867	−	0.0738867i
$916$	−4.05017e7	−	3.36903e6i	−0.0526971	−	0.00438348i
$917$	7.92186e8	−	7.92186e8i	1.02735	−	1.02735i
$918$	−3.15226e6	+	1.15496e6i	−0.00407468	+	0.00149293i
$919$	9.76779e7			0.125849			0.0629245	−	0.998018i	$-0.479957\pi$
$919$	9.76779e7			0.125849			0.0629245	+	0.998018i	$0.479957\pi$
$920$	−3.95077e7	+	6.94541e7i	−0.0507362	+	0.0891937i
$921$			1.89470e8i			0.242528i
$922$	−3.00578e8	+	1.10130e8i	−0.383500	+	0.140512i
$923$	7.20542e8	+	7.20542e8i	0.916335	+	0.916335i
$924$	5.62014e7	+	6.63996e7i	0.0712412	+	0.0841685i
$925$	5.94330e8	+	5.94330e8i	0.750935	+	0.750935i
$926$	−7.38751e8	−	3.42565e8i	−0.930390	−	0.431429i
$927$		−	1.69484e8i		−	0.212760i
$928$	−2.24081e8	−	1.19594e9i	−0.280390	−	1.49647i
$929$	−9.74514e8			−1.21546			−0.607731	−	0.794143i	$-0.707920\pi$
$929$	−9.74514e8			−1.21546			−0.607731	+	0.794143i	$0.707920\pi$
$930$	3.06351e7	−	6.60654e7i	0.0380864	−	0.0821345i
$931$	1.49666e8	−	1.49666e8i	0.185470	−	0.185470i
$932$	−7.89807e8	+	6.68501e8i	−0.975603	+	0.825761i
$933$	2.51803e8	−	2.51803e8i	0.310038	−	0.310038i
$934$	−3.67286e8	−	1.00244e9i	−0.450778	−	1.23031i
$935$	−901156.			−0.00110247
$936$	1.50405e8	−	2.64410e8i	0.183415	−	0.322441i
$937$		−	2.77324e8i		−	0.337107i	−0.985692	−	0.168554i	$-0.946090\pi$
$937$		−	2.77324e8i		−	0.337107i	0.985692	−	0.168554i	$-0.0539097\pi$
$938$	−4.18710e8	−	1.14279e9i	−0.507347	−	1.38471i
$939$	−3.31499e8	−	3.31499e8i	−0.400391	−	0.400391i
$940$	7.30174e6	−	8.77797e7i	0.00879110	−	0.105684i
$941$	−5.23882e8	−	5.23882e8i	−0.628730	−	0.628730i	0.319018	−	0.947749i	$-0.396647\pi$
$941$	−5.23882e8	−	5.23882e8i	−0.628730	−	0.628730i	−0.947749	+	0.319018i	$0.896647\pi$
$942$	2.07549e8	−	4.47585e8i	0.248294	−	0.535454i
$943$			5.60592e8i			0.668517i
$944$	−3.35136e8	+	2.38961e8i	−0.398387	+	0.284061i
$945$	−5.76315e7			−0.0682912
$946$	5.66860e7	+	2.62858e7i	0.0669580	+	0.0310490i
$947$	−4.98354e8	+	4.98354e8i	−0.586798	+	0.586798i	−0.936763	−	0.349965i	$-0.886193\pi$
$947$	−4.98354e8	+	4.98354e8i	−0.586798	+	0.586798i	0.349965	+	0.936763i	$0.386193\pi$
$948$	6.88682e7	−	8.27916e8i	0.0808339	−	0.971765i
$949$	3.50122e8	−	3.50122e8i	0.409658	−	0.409658i
$950$	4.97073e8	−	1.82124e8i	0.579761	−	0.212420i
$951$	1.33862e8			0.155638
$952$	2.20873e7	−	6.07034e6i	0.0255995	−	0.00703562i
$953$		−	1.60833e8i		−	0.185821i	−0.995674	−	0.0929107i	$-0.970383\pi$
$953$		−	1.60833e8i		−	0.185821i	0.995674	−	0.0929107i	$-0.0296171\pi$
$954$	−2.97697e8	+	1.09074e8i	−0.342870	+	0.125625i
$955$	7.29890e7	+	7.29890e7i	0.0838007	+	0.0838007i
$956$	8.27155e8	−	7.00113e8i	0.946702	−	0.801299i
$957$	−8.83742e7	−	8.83742e7i	−0.100830	−	0.100830i
$958$	−8.06228e8	−	3.73854e8i	−0.916983	−	0.425212i
$959$			1.30235e9i			1.47663i
$960$	7.86793e7	+	1.32328e8i	0.0889297	+	0.149568i
$961$	6.47253e8			0.729296
$962$	−4.86853e8	+	1.04991e9i	−0.546856	+	1.17931i
$963$	2.63573e8	−	2.63573e8i	0.295136	−	0.295136i
$964$	2.57652e8	+	3.04406e8i	0.287609	+	0.339799i
$965$	6.25522e6	−	6.25522e6i	0.00696083	−	0.00696083i
$966$	−7.17722e7	−	1.95889e8i	−0.0796205	−	0.217309i
$967$	−3.65197e8			−0.403875			−0.201938	−	0.979398i	$-0.564724\pi$
$967$	−3.65197e8			−0.403875			−0.201938	+	0.979398i	$0.564724\pi$
$968$	2.34047e8	+	8.51593e8i	0.258034	+	0.938872i
$969$		−	8.04451e6i		−	0.00884155i
$970$	1.52214e8	+	4.15440e8i	0.166779	+	0.455191i
$971$	−2.95923e7	−	2.95923e7i	−0.0323237	−	0.0323237i	0.690760	−	0.723084i	$-0.257276\pi$
$971$	−2.95923e7	−	2.95923e7i	−0.0323237	−	0.0323237i	−0.723084	+	0.690760i	$0.757276\pi$
$972$	5.87081e7	+	4.88349e6i	0.0639292	+	0.00531780i
$973$	−1.02467e9	−	1.02467e9i	−1.11235	−	1.11235i
$974$	5.46800e8	−	1.17919e9i	0.591768	−	1.27617i
$975$		−	5.41427e8i		−	0.584153i
$976$	4.54570e8	−	3.24120e8i	0.488935	−	0.348624i
$977$	−2.96856e7			−0.0318319			−0.0159159	−	0.999873i	$-0.505066\pi$
$977$	−2.96856e7			−0.0318319			−0.0159159	+	0.999873i	$0.505066\pi$
$978$	−6.45303e8	−	2.99232e8i	−0.689838	−	0.319883i
$979$	1.50389e8	−	1.50389e8i	0.160276	−	0.160276i
$980$	1.09180e8	+	9.08184e6i	0.116001	+	0.00964929i
$981$	2.69513e8	−	2.69513e8i	0.285478	−	0.285478i
$982$	−1.68967e9	+	6.19083e8i	−1.78430	+	0.653754i
$983$	5.48457e7			0.0577407			0.0288704	−	0.999583i	$-0.490809\pi$
$983$	5.48457e7			0.0577407			0.0288704	+	0.999583i	$0.490809\pi$
$984$	9.38830e8	+	5.34036e8i	0.985375	+	0.560513i
$985$		−	6.63474e7i		−	0.0694249i
$986$	−3.09005e7	+	1.13217e7i	−0.0322355	+	0.0118109i
$987$	1.62618e8	+	1.62618e8i	0.169128	+	0.169128i
$988$	4.70920e8	+	5.56372e8i	0.488288	+	0.576892i
$989$	−1.05959e8	−	1.05959e8i	−0.109534	−	0.109534i
$990$	1.43459e7	+	6.65232e6i	0.0147851	+	0.00685595i
$991$			2.73901e8i			0.281431i	0.990050	+	0.140716i	$0.0449404\pi$
$991$			2.73901e8i			0.281431i	−0.990050	+	0.140716i	$0.955060\pi$
$992$	2.86859e8	−	4.19141e8i	0.293856	−	0.429364i
$993$	−2.03777e8			−0.208117
$994$	5.66435e8	−	1.22153e9i	0.576755	−	1.24379i
$995$	−9.96170e7	+	9.96170e7i	−0.101126	+	0.101126i
$996$	1.69201e8	−	1.43213e8i	0.171248	−	0.144946i
$997$	1.69342e8	−	1.69342e8i	0.170875	−	0.170875i	−0.616489	−	0.787364i	$-0.711445\pi$
$997$	1.69342e8	−	1.69342e8i	0.170875	−	0.170875i	0.787364	+	0.616489i	$0.211445\pi$
$998$	5.94055e8	+	1.62136e9i	0.597633	+	1.63113i
$999$	−2.24125e8			−0.224799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.l.a.19.16	✓	48
4.3	odd	2		192.7.l.a.175.5		48
8.3	odd	2		384.7.l.a.223.20		48
8.5	even	2		384.7.l.b.223.5		48
16.3	odd	4		384.7.l.b.31.5		48
16.5	even	4		192.7.l.a.79.5		48
16.11	odd	4	inner	48.7.l.a.43.16	yes	48
16.13	even	4		384.7.l.a.31.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.16	✓	48	1.1	even	1	trivial
48.7.l.a.43.16	yes	48	16.11	odd	4	inner
192.7.l.a.79.5		48	16.5	even	4
192.7.l.a.175.5		48	4.3	odd	2
384.7.l.a.31.20		48	16.13	even	4
384.7.l.a.223.20		48	8.3	odd	2
384.7.l.b.31.5		48	16.3	odd	4
384.7.l.b.223.5		48	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.36544 - 7.25767i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-41.3476 - 48.8505i) q^{4} +(-26.6395 + 26.6395i) q^{5} +(-42.9029 - 117.095i) q^{6} -403.840 q^{7} +(-493.694 + 135.684i) q^{8} -243.000i q^{9} +O(q^{10})\)	\(q+(3.36544 - 7.25767i) q^{2} +(11.0227 - 11.0227i) q^{3} +(-41.3476 - 48.8505i) q^{4} +(-26.6395 + 26.6395i) q^{5} +(-42.9029 - 117.095i) q^{6} -403.840 q^{7} +(-493.694 + 135.684i) q^{8} -243.000i q^{9} +(103.687 + 282.994i) q^{10} +(152.675 + 152.675i) q^{11} +(-994.227 - 82.7024i) q^{12} +(-1728.86 - 1728.86i) q^{13} +(-1359.10 + 2930.94i) q^{14} +587.279i q^{15} +(-676.749 + 4039.71i) q^{16} +110.784 q^{17} +(-1763.61 - 817.802i) q^{18} +(3293.87 - 3293.87i) q^{19} +(2402.83 + 199.874i) q^{20} +(-4451.41 + 4451.41i) q^{21} +(1621.89 - 594.248i) q^{22} -4142.48 q^{23} +(-3946.24 + 6937.45i) q^{24} +14205.7i q^{25} +(-18365.9 + 6729.13i) q^{26} +(-2678.52 - 2678.52i) q^{27} +(16697.8 + 19727.8i) q^{28} +(-26256.6 - 26256.6i) q^{29} +(4262.28 + 1976.45i) q^{30} -15500.0i q^{31} +(27041.3 + 18507.0i) q^{32} +3365.79 q^{33} +(372.835 - 804.031i) q^{34} +(10758.1 - 10758.1i) q^{35} +(-11870.7 + 10047.5i) q^{36} +(41837.5 - 41837.5i) q^{37} +(-12820.5 - 34991.1i) q^{38} -38113.5 q^{39} +(9537.21 - 16766.3i) q^{40} -135328. i q^{41} +(17325.9 + 47287.8i) q^{42} +(25578.8 + 25578.8i) q^{43} +(1145.51 - 13771.0i) q^{44} +(6473.40 + 6473.40i) q^{45} +(-13941.3 + 30064.7i) q^{46} -36531.8i q^{47} +(37068.9 + 51988.1i) q^{48} +45437.8 q^{49} +(103100. + 47808.4i) q^{50} +(1221.13 - 1221.13i) q^{51} +(-12971.5 + 155940. i) q^{52} +(115323. - 115323. i) q^{53} +(-28454.2 + 10425.4i) q^{54} -8134.39 q^{55} +(199373. - 54794.6i) q^{56} -72614.7i q^{57} +(-278927. + 102197. i) q^{58} +(71056.8 + 71056.8i) q^{59} +(28688.9 - 24282.6i) q^{60} +(-96379.6 - 96379.6i) q^{61} +(-112494. - 52164.4i) q^{62} +98133.1i q^{63} +(225324. - 133973. i) q^{64} +92112.0 q^{65} +(11327.4 - 24427.8i) q^{66} +(-266382. + 266382. i) q^{67} +(-4580.64 - 5411.84i) q^{68} +(-45661.3 + 45661.3i) q^{69} +(-41873.0 - 114285. i) q^{70} -416772. q^{71} +(32971.2 + 119968. i) q^{72} +202516. i q^{73} +(-162841. - 444444. i) q^{74} +(156585. + 156585. i) q^{75} +(-297101. - 24713.6i) q^{76} +(-61656.4 - 61656.4i) q^{77} +(-128269. + 276615. i) q^{78} +832723. i q^{79} +(-89587.5 - 125644. i) q^{80} -59049.0 q^{81} +(-982165. - 455438. i) q^{82} +(-157114. + 157114. i) q^{83} +(401509. + 33398.5i) q^{84} +(-2951.22 + 2951.22i) q^{85} +(271726. - 99558.5i) q^{86} -578837. q^{87} +(-96090.5 - 54659.3i) q^{88} -985026. i q^{89} +(68767.6 - 25196.0i) q^{90} +(698184. + 698184. i) q^{91} +(171282. + 202362. i) q^{92} +(-170852. - 170852. i) q^{93} +(-265136. - 122945. i) q^{94} +175494. i q^{95} +(502066. - 94071.0i) q^{96} +1.46802e6 q^{97} +(152918. - 329773. i) q^{98} +(37100.1 - 37100.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 180 q^{4} - 1932 q^{8}+O(q^{10}) \) 48 * q - 180 * q^4 - 1932 * q^8	\( 48 q - 180 q^{4} - 1932 q^{8} + 744 q^{10} - 2720 q^{11} - 1944 q^{12} - 15388 q^{14} + 3744 q^{16} + 4860 q^{18} - 3936 q^{19} - 14000 q^{20} - 41184 q^{22} + 26240 q^{23} + 18468 q^{24} - 5300 q^{26} - 96120 q^{28} + 66400 q^{29} - 33048 q^{30} - 52960 q^{32} + 122208 q^{34} + 162336 q^{35} + 32076 q^{36} - 7200 q^{37} + 16968 q^{38} - 309072 q^{40} - 231660 q^{42} + 340704 q^{43} - 193192 q^{44} - 450264 q^{46} + 299376 q^{48} + 806736 q^{49} + 537764 q^{50} + 80352 q^{51} + 1126224 q^{52} + 443680 q^{53} + 78732 q^{54} + 232704 q^{55} - 420448 q^{56} - 1295664 q^{58} - 886144 q^{59} - 627912 q^{60} - 326496 q^{61} - 719652 q^{62} - 192024 q^{64} - 372832 q^{65} + 775656 q^{66} - 962112 q^{67} + 3197632 q^{68} + 541728 q^{69} + 642816 q^{70} + 534016 q^{71} + 82620 q^{72} - 4894836 q^{74} - 1073088 q^{75} - 3162552 q^{76} - 932960 q^{77} - 337284 q^{78} + 4668072 q^{80} - 2834352 q^{81} + 5077560 q^{82} - 2497760 q^{83} + 1312200 q^{84} - 372000 q^{85} + 4142928 q^{86} - 2794272 q^{88} - 507384 q^{90} + 775008 q^{91} - 9470992 q^{92} - 5050728 q^{94} + 1879200 q^{96} + 12708584 q^{98} - 660960 q^{99}+O(q^{100}) \) 48 * q - 180 * q^4 - 1932 * q^8 + 744 * q^10 - 2720 * q^11 - 1944 * q^12 - 15388 * q^14 + 3744 * q^16 + 4860 * q^18 - 3936 * q^19 - 14000 * q^20 - 41184 * q^22 + 26240 * q^23 + 18468 * q^24 - 5300 * q^26 - 96120 * q^28 + 66400 * q^29 - 33048 * q^30 - 52960 * q^32 + 122208 * q^34 + 162336 * q^35 + 32076 * q^36 - 7200 * q^37 + 16968 * q^38 - 309072 * q^40 - 231660 * q^42 + 340704 * q^43 - 193192 * q^44 - 450264 * q^46 + 299376 * q^48 + 806736 * q^49 + 537764 * q^50 + 80352 * q^51 + 1126224 * q^52 + 443680 * q^53 + 78732 * q^54 + 232704 * q^55 - 420448 * q^56 - 1295664 * q^58 - 886144 * q^59 - 627912 * q^60 - 326496 * q^61 - 719652 * q^62 - 192024 * q^64 - 372832 * q^65 + 775656 * q^66 - 962112 * q^67 + 3197632 * q^68 + 541728 * q^69 + 642816 * q^70 + 534016 * q^71 + 82620 * q^72 - 4894836 * q^74 - 1073088 * q^75 - 3162552 * q^76 - 932960 * q^77 - 337284 * q^78 + 4668072 * q^80 - 2834352 * q^81 + 5077560 * q^82 - 2497760 * q^83 + 1312200 * q^84 - 372000 * q^85 + 4142928 * q^86 - 2794272 * q^88 - 507384 * q^90 + 775008 * q^91 - 9470992 * q^92 - 5050728 * q^94 + 1879200 * q^96 + 12708584 * q^98 - 660960 * q^99

Introduction

L-functions

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