LMFDB - Embedded newform 22.6.c.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,6,Mod(3,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, 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:	$3.52844403589$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 329 x^{10} + 1365 x^{9} + 52729 x^{8} + 242031 x^{7} + 7017903 x^{6} + \cdots + 93740681241 $ x^12 - 2x^11 + 329x^10 + 1365x^9 + 52729x^8 + 242031x^7 + 7017903x^6 + 130221686x^5 + 2541092161x^4 + 14394729912x^3 + 45294850764x^2 + 76920871185*x + 93740681241
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-8.87706 - 6.44956i$ of defining polynomial
Character	$\chi$	$=$	22.9
Dual form			22.6.c.b.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 - 3.80423i) q^{2} +(-15.7161 + 11.4184i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(32.8187 + 101.006i) q^{5} +(24.0121 + 73.9017i) q^{6} +(-39.7423 - 28.8745i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(41.5249 - 127.801i) q^{9} +O(q^{10})$	\(q+(1.23607 - 3.80423i) q^{2} +(-15.7161 + 11.4184i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(32.8187 + 101.006i) q^{5} +(24.0121 + 73.9017i) q^{6} +(-39.7423 - 28.8745i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(41.5249 - 127.801i) q^{9} +424.814 q^{10} +(-342.914 + 208.474i) q^{11} +310.819 q^{12} +(10.6356 - 32.7331i) q^{13} +(-158.969 + 115.498i) q^{14} +(-1669.11 - 1212.68i) q^{15} +(79.1084 + 243.470i) q^{16} +(149.664 + 460.619i) q^{17} +(-434.855 - 315.941i) q^{18} +(2063.87 - 1499.49i) q^{19} +(525.099 - 1616.09i) q^{20} +954.296 q^{21} +(369.217 + 1562.21i) q^{22} +1687.31 q^{23} +(384.194 - 1182.43i) q^{24} +(-6596.88 + 4792.91i) q^{25} +(-111.378 - 80.9207i) q^{26} +(-652.064 - 2006.85i) q^{27} +(242.883 + 747.518i) q^{28} +(6284.59 + 4566.02i) q^{29} +(-6676.44 + 4850.71i) q^{30} +(-1578.27 + 4857.42i) q^{31} +1024.00 q^{32} +(3008.83 - 7191.94i) q^{33} +1937.29 q^{34} +(1612.19 - 4961.81i) q^{35} +(-1739.42 + 1263.76i) q^{36} +(4646.30 + 3375.73i) q^{37} +(-3153.31 - 9704.91i) q^{38} +(206.610 + 635.880i) q^{39} +(-5498.91 - 3995.19i) q^{40} +(867.129 - 630.006i) q^{41} +(1179.57 - 3630.36i) q^{42} -9063.00 q^{43} +(6399.37 + 526.411i) q^{44} +14271.4 q^{45} +(2085.62 - 6418.89i) q^{46} +(-6164.76 + 4478.96i) q^{47} +(-4023.33 - 2923.12i) q^{48} +(-4447.93 - 13689.3i) q^{49} +(10079.1 + 31020.4i) q^{50} +(-7611.69 - 5530.21i) q^{51} +(-445.511 + 323.683i) q^{52} +(6691.63 - 20594.7i) q^{53} -8440.49 q^{54} +(-32311.0 - 27794.3i) q^{55} +3143.95 q^{56} +(-15314.2 + 47132.4i) q^{57} +(25138.4 - 18264.1i) q^{58} +(13425.8 + 9754.38i) q^{59} +(10200.7 + 31394.5i) q^{60} +(11957.4 + 36801.1i) q^{61} +(16527.9 + 12008.2i) q^{62} +(-5340.47 + 3880.08i) q^{63} +(1265.73 - 3895.53i) q^{64} +3655.28 q^{65} +(-23640.6 - 20336.0i) q^{66} +7618.44 q^{67} +(2394.63 - 7369.90i) q^{68} +(-26517.9 + 19266.4i) q^{69} +(-16883.1 - 12266.3i) q^{70} +(10654.4 + 32790.7i) q^{71} +(2657.60 + 8179.24i) q^{72} +(-12333.0 - 8960.43i) q^{73} +(18585.2 - 13502.9i) q^{74} +(48949.9 - 150652. i) q^{75} -40817.4 q^{76} +(19647.7 + 1616.22i) q^{77} +2674.42 q^{78} +(-3090.54 + 9511.72i) q^{79} +(-21995.6 + 15980.8i) q^{80} +(59580.4 + 43287.7i) q^{81} +(-1324.85 - 4077.48i) q^{82} +(-17737.0 - 54589.0i) q^{83} +(-12352.7 - 8974.74i) q^{84} +(-41613.3 + 30233.8i) q^{85} +(-11202.5 + 34477.7i) q^{86} -150906. q^{87} +(9912.64 - 23694.0i) q^{88} +76175.8 q^{89} +(17640.4 - 54291.5i) q^{90} +(-1367.84 + 993.791i) q^{91} +(-21840.9 - 15868.4i) q^{92} +(-30659.9 - 94361.3i) q^{93} +(9418.91 + 28988.4i) q^{94} +(219190. + 159251. i) q^{95} +(-16093.3 + 11692.5i) q^{96} +(-5383.44 + 16568.5i) q^{97} -57575.3 q^{98} +(12403.6 + 52481.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9	\( 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18} + 7535 q^{19} + 704 q^{20} - 3368 q^{21} + 484 q^{22} + 15732 q^{23} - 1600 q^{24} - 19283 q^{25} - 984 q^{26} - 27411 q^{27} + 3264 q^{28} - 2504 q^{29} + 448 q^{30} + 15336 q^{31} + 12288 q^{32} + 26213 q^{33} + 24600 q^{34} - 33916 q^{35} - 5664 q^{36} - 116 q^{37} - 34880 q^{38} + 4690 q^{39} - 3584 q^{40} - 38836 q^{41} + 19808 q^{42} + 42230 q^{43} - 4704 q^{44} + 139932 q^{45} - 35232 q^{46} - 57840 q^{47} - 125521 q^{49} + 26268 q^{50} + 16467 q^{51} - 3936 q^{52} + 131934 q^{53} + 60176 q^{54} - 53082 q^{55} + 15616 q^{56} - 90021 q^{57} - 10016 q^{58} + 36585 q^{59} - 37248 q^{60} + 43146 q^{61} - 40016 q^{62} - 52922 q^{63} - 12288 q^{64} - 133772 q^{65} - 211008 q^{66} + 325206 q^{67} + 6400 q^{68} - 103894 q^{69} + 68216 q^{70} - 172806 q^{71} - 4416 q^{72} + 49436 q^{73} - 464 q^{74} + 263915 q^{75} + 37920 q^{76} - 207094 q^{77} + 330000 q^{78} + 58364 q^{79} - 14336 q^{80} + 341038 q^{81} + 82836 q^{82} + 82035 q^{83} - 52288 q^{84} - 317604 q^{85} - 104380 q^{86} - 572732 q^{87} - 38336 q^{88} + 97958 q^{89} - 151672 q^{90} - 22162 q^{91} + 15072 q^{92} - 271316 q^{93} + 153720 q^{94} + 549736 q^{95} + 76403 q^{97} + 198656 q^{98} - 199487 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$	−15.7161	+	11.4184i	−1.00819	+	0.732493i	−0.963829	−	0.266522i	$-0.914125\pi$
$3$	−15.7161	+	11.4184i	−1.00819	+	0.732493i	−0.0443616	+	0.999016i	$0.514125\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	32.8187	+	101.006i	0.587079	+	1.80684i	0.590757	+	0.806849i	$0.298829\pi$
$5$	32.8187	+	101.006i	0.587079	+	1.80684i	−0.00367835	+	0.999993i	$0.501171\pi$
$6$	24.0121	+	73.9017i	0.272303	+	0.838062i
$7$	−39.7423	−	28.8745i	−0.306554	−	0.222725i	0.423862	−	0.905727i	$-0.360674\pi$
$7$	−39.7423	−	28.8745i	−0.306554	−	0.222725i	−0.730417	+	0.683002i	$0.760674\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	41.5249	−	127.801i	0.170885	−	0.525929i
$10$	424.814			1.34338
$11$	−342.914	+	208.474i	−0.854482	+	0.519481i
$11$	−342.914	+	208.474i	−0.854482	+	0.519481i
$12$	310.819			0.623096
$13$	10.6356	−	32.7331i	0.0174544	−	0.0537191i	−0.941950	−	0.335753i	$-0.891009\pi$
$13$	10.6356	−	32.7331i	0.0174544	−	0.0537191i	0.959404	+	0.282034i	$0.0910092\pi$
$14$	−158.969	+	115.498i	−0.216767	+	0.157490i
$15$	−1669.11	−	1212.68i	−1.91539	−	1.39161i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	149.664	+	460.619i	0.125602	+	0.386562i	0.994010	−	0.109287i	$-0.0348568\pi$
$17$	149.664	+	460.619i	0.125602	+	0.386562i	−0.868409	+	0.495849i	$0.834857\pi$
$18$	−434.855	−	315.941i	−0.316346	−	0.229839i
$19$	2063.87	−	1499.49i	1.31159	−	0.952927i	0.311595	−	0.950215i	$-0.399137\pi$
$19$	2063.87	−	1499.49i	1.31159	−	0.952927i	0.999996	−	0.00271212i	$-0.000863296\pi$
$20$	525.099	−	1616.09i	0.293539	−	0.903421i
$21$	954.296			0.472210
$22$	369.217	+	1562.21i	0.162639	+	0.688149i
$23$	1687.31			0.665080			0.332540	−	0.943089i	$-0.392094\pi$
$23$	1687.31			0.665080			0.332540	+	0.943089i	$0.392094\pi$
$24$	384.194	−	1182.43i	0.136151	−	0.419031i
$25$	−6596.88	+	4792.91i	−2.11100	+	1.53373i
$26$	−111.378	−	80.9207i	−0.0323121	−	0.0234761i
$27$	−652.064	−	2006.85i	−0.172140	−	0.529791i
$28$	242.883	+	747.518i	0.0585467	+	0.180188i
$29$	6284.59	+	4566.02i	1.38766	+	1.00819i	0.996118	+	0.0880300i	$0.0280572\pi$
$29$	6284.59	+	4566.02i	1.38766	+	1.00819i	0.391539	+	0.920162i	$0.371943\pi$
$30$	−6676.44	+	4850.71i	−1.35438	+	0.984017i
$31$	−1578.27	+	4857.42i	−0.294970	+	0.907824i	0.688262	+	0.725463i	$0.258374\pi$
$31$	−1578.27	+	4857.42i	−0.294970	+	0.907824i	−0.983232	+	0.182362i	$0.941626\pi$
$32$	1024.00			0.176777
$33$	3008.83	−	7191.94i	0.480964	−	1.14964i
$34$	1937.29			0.287407
$35$	1612.19	−	4961.81i	0.222457	−	0.684653i
$36$	−1739.42	+	1263.76i	−0.223691	+	0.162521i
$37$	4646.30	+	3375.73i	0.557959	+	0.405381i	0.830712	−	0.556703i	$-0.187934\pi$
$37$	4646.30	+	3375.73i	0.557959	+	0.405381i	−0.272752	+	0.962084i	$0.587934\pi$
$38$	−3153.31	−	9704.91i	−0.354249	−	1.09027i
$39$	206.610	+	635.880i	0.0217515	+	0.0669444i
$40$	−5498.91	−	3995.19i	−0.543409	−	0.394810i
$41$	867.129	−	630.006i	0.0805608	−	0.0585309i	−0.546776	−	0.837279i	$-0.684145\pi$
$41$	867.129	−	630.006i	0.0805608	−	0.0585309i	0.627337	+	0.778748i	$0.284145\pi$
$42$	1179.57	−	3630.36i	0.103182	−	0.317560i
$43$	−9063.00			−0.747482			−0.373741	−	0.927533i	$-0.621925\pi$
$43$	−9063.00			−0.747482			−0.373741	+	0.927533i	$0.621925\pi$
$44$	6399.37	+	526.411i	0.498317	+	0.0409915i
$45$	14271.4			1.05059
$46$	2085.62	−	6418.89i	0.145325	−	0.447266i
$47$	−6164.76	+	4478.96i	−0.407072	+	0.295755i	−0.772415	−	0.635118i	$-0.780952\pi$
$47$	−6164.76	+	4478.96i	−0.407072	+	0.295755i	0.365343	+	0.930873i	$0.380952\pi$
$48$	−4023.33	−	2923.12i	−0.252048	−	0.183123i
$49$	−4447.93	−	13689.3i	−0.264648	−	0.814502i
$50$	10079.1	+	31020.4i	0.570162	+	1.75478i
$51$	−7611.69	−	5530.21i	−0.409784	−	0.297726i
$52$	−445.511	+	323.683i	−0.0228481	+	0.0166001i
$53$	6691.63	−	20594.7i	0.327222	−	1.00709i	−0.643206	−	0.765693i	$-0.722396\pi$
$53$	6691.63	−	20594.7i	0.327222	−	1.00709i	0.970428	−	0.241392i	$-0.0776040\pi$
$54$	−8440.49			−0.393898
$55$	−32311.0	−	27794.3i	−1.44027	−	1.23894i
$56$	3143.95			0.133969
$57$	−15314.2	+	47132.4i	−0.624321	+	1.92146i
$58$	25138.4	−	18264.1i	0.981221	−	0.712899i
$59$	13425.8	+	9754.38i	0.502121	+	0.364812i	0.809827	−	0.586669i	$-0.199561\pi$
$59$	13425.8	+	9754.38i	0.502121	+	0.364812i	−0.307705	+	0.951482i	$0.599561\pi$
$60$	10200.7	+	31394.5i	0.365806	+	1.12584i
$61$	11957.4	+	36801.1i	0.411445	+	1.26630i	0.915392	+	0.402564i	$0.131881\pi$
$61$	11957.4	+	36801.1i	0.411445	+	1.26630i	−0.503947	+	0.863735i	$0.668119\pi$
$62$	16527.9	+	12008.2i	0.546057	+	0.396734i
$63$	−5340.47	+	3880.08i	−0.169523	+	0.123165i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	3655.28			0.107309
$66$	−23640.6	−	20336.0i	−0.668035	−	0.574653i
$67$	7618.44			0.207338			0.103669	−	0.994612i	$-0.466942\pi$
$67$	7618.44			0.207338			0.103669	+	0.994612i	$0.466942\pi$
$68$	2394.63	−	7369.90i	0.0628008	−	0.193281i
$69$	−26517.9	+	19266.4i	−0.670528	+	0.487167i
$70$	−16883.1	−	12266.3i	−0.411819	−	0.299204i
$71$	10654.4	+	32790.7i	0.250831	+	0.771978i	0.994623	+	0.103567i	$0.0330255\pi$
$71$	10654.4	+	32790.7i	0.250831	+	0.771978i	−0.743792	+	0.668412i	$0.766974\pi$
$72$	2657.60	+	8179.24i	0.0604168	+	0.185944i
$73$	−12333.0	−	8960.43i	−0.270870	−	0.196798i	0.444055	−	0.895999i	$-0.353539\pi$
$73$	−12333.0	−	8960.43i	−0.270870	−	0.196798i	−0.714925	+	0.699201i	$0.753539\pi$
$74$	18585.2	−	13502.9i	0.394537	−	0.286648i
$75$	48949.9	−	150652.i	1.00484	−	3.09259i
$76$	−40817.4			−0.810608
$77$	19647.7	+	1616.22i	0.377647	+	0.0310651i
$78$	2674.42			0.0497729
$79$	−3090.54	+	9511.72i	−0.0557144	+	0.171471i	−0.975041	−	0.222023i	$-0.928734\pi$
$79$	−3090.54	+	9511.72i	−0.0557144	+	0.171471i	0.919327	+	0.393494i	$0.128734\pi$
$80$	−21995.6	+	15980.8i	−0.384248	+	0.279173i
$81$	59580.4	+	43287.7i	1.00900	+	0.733081i
$82$	−1324.85	−	4077.48i	−0.0217587	−	0.0669665i
$83$	−17737.0	−	54589.0i	−0.282609	−	0.869780i	−0.987105	−	0.160073i	$-0.948827\pi$
$83$	−17737.0	−	54589.0i	−0.282609	−	0.869780i	0.704496	−	0.709707i	$-0.251173\pi$
$84$	−12352.7	−	8974.74i	−0.191013	−	0.138779i
$85$	−41613.3	+	30233.8i	−0.624719	+	0.453885i
$86$	−11202.5	+	34477.7i	−0.163331	+	0.502681i
$87$	−150906.			−2.13752
$88$	9912.64	−	23694.0i	0.136453	−	0.326160i
$89$	76175.8			1.01939			0.509697	−	0.860354i	$-0.329758\pi$
$89$	76175.8			1.01939			0.509697	+	0.860354i	$0.329758\pi$
$90$	17640.4	−	54291.5i	0.229563	−	0.706522i
$91$	−1367.84	+	993.791i	−0.0173153	+	0.0125803i
$92$	−21840.9	−	15868.4i	−0.269031	−	0.195462i
$93$	−30659.9	−	94361.3i	−0.367589	−	1.13132i
$94$	9418.91	+	28988.4i	0.109946	+	0.338380i
$95$	219190.	+	159251.i	2.49180	+	1.81040i
$96$	−16093.3	+	11692.5i	−0.178225	+	0.129488i
$97$	−5383.44	+	16568.5i	−0.0580939	+	0.178794i	−0.975893	−	0.218252i	$-0.929965\pi$
$97$	−5383.44	+	16568.5i	−0.0580939	+	0.178794i	0.917799	+	0.397046i	$0.129965\pi$
$98$	−57575.3			−0.605579
$99$	12403.6	+	52481.4i	0.127192	+	0.538168i
$100$	130467.			1.30467
$101$	49916.4	−	153627.i	0.486900	−	1.49853i	−0.342309	−	0.939587i	$-0.611209\pi$
$101$	49916.4	−	153627.i	0.486900	−	1.49853i	0.829210	−	0.558938i	$-0.188791\pi$
$102$	−30446.7	+	22120.9i	−0.289761	+	0.210524i
$103$	−802.651	−	583.160i	−0.00745477	−	0.00541620i	0.584052	−	0.811717i	$-0.301467\pi$
$103$	−802.651	−	583.160i	−0.00745477	−	0.00541620i	−0.591506	+	0.806300i	$0.701467\pi$
$104$	680.681	+	2094.92i	0.00617106	+	0.0189926i
$105$	31318.8	+	96389.2i	0.277224	+	0.853209i
$106$	−70075.7	−	50913.0i	−0.605763	−	0.440112i
$107$	−93158.7	+	67683.7i	−0.786618	+	0.571511i	−0.906958	−	0.421221i	$-0.861602\pi$
$107$	−93158.7	+	67683.7i	−0.786618	+	0.571511i	0.120340	+	0.992733i	$0.461602\pi$
$108$	−10433.0	+	32109.5i	−0.0860698	+	0.264896i
$109$	−23507.5			−0.189513			−0.0947567	−	0.995500i	$-0.530207\pi$
$109$	−23507.5			−0.189513			−0.0947567	+	0.995500i	$0.530207\pi$
$110$	−145675.	+	88562.6i	−1.14789	+	0.697861i
$111$	−111567.			−0.859468
$112$	3886.13	−	11960.3i	0.0292733	−	0.0900941i
$113$	−119028.	+	86479.2i	−0.876909	+	0.637112i	−0.932432	−	0.361346i	$-0.882317\pi$
$113$	−119028.	+	86479.2i	−0.876909	+	0.637112i	0.0555229	+	0.998457i	$0.482317\pi$
$114$	160373.	+	116518.i	1.15576	+	0.839710i
$115$	55375.2	+	170427.i	0.390455	+	1.20170i
$116$	−38408.0	−	118208.i	−0.265019	−	0.815644i
$117$	−3741.67	−	2718.48i	−0.0252697	−	0.0183595i
$118$	53703.0	−	39017.5i	0.355053	−	0.257961i
$119$	7352.12	−	22627.5i	0.0475932	−	0.146477i
$120$	132040.			0.837055
$121$	74128.4	−	142977.i	0.460279	−	0.887774i
$122$	154780.			0.941488
$123$	−6434.23	+	19802.5i	−0.0383472	+	0.118020i
$124$	66111.5	−	48032.9i	0.386121	−	0.280533i
$125$	−432111.	−	313947.i	−2.47355	−	1.79714i
$126$	8159.51	+	25112.4i	0.0457865	+	0.140916i
$127$	−33487.3	−	103063.i	−0.184234	−	0.567015i	0.815700	−	0.578475i	$-0.196352\pi$
$127$	−33487.3	−	103063.i	−0.184234	−	0.567015i	−0.999934	+	0.0114599i	$0.996352\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	142435.	−	103485.i	0.753604	−	0.547526i
$130$	4518.17	−	13905.5i	0.0234479	−	0.0721652i
$131$	210721.			1.07283			0.536413	−	0.843955i	$-0.319779\pi$
$131$	210721.			1.07283			0.536413	+	0.843955i	$0.319779\pi$
$132$	−106584.	+	64797.7i	−0.532424	+	0.323686i
$133$	−125320.			−0.614315
$134$	9416.91	−	28982.3i	0.0453050	−	0.139435i
$135$	181303.	−	131724.i	0.856190	−	0.622058i
$136$	−25076.8	−	18219.4i	−0.116259	−	0.0844669i
$137$	−101411.	−	312112.i	−0.461621	−	1.42072i	−0.863183	−	0.504891i	$-0.831533\pi$
$137$	−101411.	−	312112.i	−0.461621	−	1.42072i	0.401563	−	0.915832i	$-0.368467\pi$
$138$	40515.8	+	124695.i	0.181103	+	0.557379i
$139$	120541.	+	87578.2i	0.529173	+	0.384467i	0.820048	−	0.572294i	$-0.193946\pi$
$139$	120541.	+	87578.2i	0.529173	+	0.384467i	−0.290875	+	0.956761i	$0.593946\pi$
$140$	−67532.3	+	49065.1i	−0.291200	+	0.211569i
$141$	45743.4	−	140784.i	0.193767	−	0.596355i
$142$	137913.			0.573963
$143$	3176.89	+	13441.9i	0.0129916	+	0.0549693i
$144$	34400.6			0.138248
$145$	−254942.	+	784630.i	−1.00698	+	3.09917i
$146$	−49331.9	+	35841.7i	−0.191534	+	0.139157i
$147$	226215.	+	164355.i	0.863432	+	0.627320i
$148$	−28395.6	−	87392.8i	−0.106561	−	0.327960i
$149$	34016.8	+	104693.i	0.125524	+	0.386324i	0.993996	−	0.109415i	$-0.0348976\pi$
$149$	34016.8	+	104693.i	0.125524	+	0.386324i	−0.868472	+	0.495738i	$0.834898\pi$
$150$	−512610.	−	372433.i	−1.86020	−	1.35151i
$151$	−10892.1	+	7913.55i	−0.0388748	+	0.0282442i	−0.607053	−	0.794661i	$-0.707648\pi$
$151$	−10892.1	+	7913.55i	−0.0388748	+	0.0282442i	0.568178	+	0.822906i	$0.307648\pi$
$152$	−50453.0	+	155278.i	−0.177124	+	0.545133i
$153$	65082.1			0.224767
$154$	30434.4	−	72746.6i	0.103410	−	0.247179i
$155$	−542424.			−1.81347
$156$	3305.76	−	10174.1i	0.0108758	−	0.0334722i
$157$	120339.	−	87431.4i	0.389634	−	0.283086i	−0.375671	−	0.926753i	$-0.622588\pi$
$157$	120339.	−	87431.4i	0.389634	−	0.283086i	0.765306	+	0.643667i	$0.222588\pi$
$158$	32364.6	+	23514.3i	0.103140	+	0.0749357i
$159$	129993.	+	400077.i	0.407781	+	1.25502i
$160$	33606.3	+	103430.i	0.103782	+	0.319408i
$161$	−67057.4	−	48720.0i	−0.203883	−	0.148130i
$162$	238322.	−	173151.i	0.713470	−	0.518366i
$163$	−66291.5	+	204024.i	−0.195429	+	0.601469i	0.804542	+	0.593895i	$0.202411\pi$
$163$	−66291.5	+	204024.i	−0.195429	+	0.601469i	−0.999971	+	0.00757323i	$0.997589\pi$
$164$	−17149.3			−0.0497893
$165$	825172.	+	67878.5i	2.35958	+	0.194099i
$166$	−229593.			−0.646678
$167$	139984.	−	430827.i	0.388407	−	1.19539i	−0.545571	−	0.838065i	$-0.683687\pi$
$167$	139984.	−	430827.i	0.388407	−	1.19539i	0.933978	−	0.357330i	$-0.116313\pi$
$168$	−49410.7	+	35899.0i	−0.135066	+	0.0981315i
$169$	299424.	+	217544.i	0.806436	+	0.585910i
$170$	63579.4	+	195677.i	0.168731	+	0.519300i
$171$	−105934.	−	326030.i	−0.277041	−	0.852644i
$172$	117314.	+	85233.6i	0.302363	+	0.219679i
$173$	25565.7	−	18574.6i	0.0649446	−	0.0471850i	−0.554839	−	0.831958i	$-0.687220\pi$
$173$	25565.7	−	18574.6i	0.0649446	−	0.0471850i	0.619784	+	0.784773i	$0.287220\pi$
$174$	−186530.	+	574082.i	−0.467064	+	1.43748i
$175$	400568.			0.988737
$176$	−77884.5	−	66997.3i	−0.189526	−	0.163033i
$177$	−322381.			−0.773456
$178$	94158.5	−	289790.i	0.222746	−	0.685541i
$179$	−175526.	+	127527.i	−0.409458	+	0.297489i	−0.773382	−	0.633940i	$-0.781437\pi$
$179$	−175526.	+	127527.i	−0.409458	+	0.297489i	0.363924	+	0.931429i	$0.381437\pi$
$180$	−184733.	−	134216.i	−0.424974	−	0.308761i
$181$	−208578.	−	641938.i	−0.473231	−	1.45645i	−0.848329	−	0.529469i	$-0.822391\pi$
$181$	−208578.	−	641938.i	−0.473231	−	1.45645i	0.375098	−	0.926985i	$-0.377609\pi$
$182$	2089.87	+	6431.95i	0.00467671	+	0.0143934i
$183$	−608135.	−	441836.i	−1.34237	−	0.975289i
$184$	−87363.8	+	63473.5i	−0.190233	+	0.138213i
$185$	−188482.	+	580089.i	−0.404894	+	1.24614i
$186$	−396869.			−0.841134
$187$	−147349.	−	126751.i	−0.308136	−	0.265063i
$188$	121921.			0.251584
$189$	−32032.1	+	98584.6i	−0.0652275	+	0.200750i
$190$	876762.	−	637005.i	1.76197	−	1.28014i
$191$	475165.	+	345227.i	0.942455	+	0.684734i	0.949010	−	0.315245i	$-0.102087\pi$
$191$	475165.	+	345227.i	0.942455	+	0.684734i	−0.00655501	+	0.999979i	$0.502087\pi$
$192$	24588.4	+	75675.3i	0.0481368	+	0.148150i
$193$	−220023.	−	677162.i	−0.425183	−	1.30858i	−0.902819	−	0.430020i	$-0.858506\pi$
$193$	−220023.	−	677162.i	−0.425183	−	1.30858i	0.477636	−	0.878558i	$-0.341494\pi$
$194$	56376.1	+	40959.6i	0.107545	+	0.0781361i
$195$	−57446.8	+	41737.5i	−0.108188	+	0.0786032i
$196$	−71166.9	+	219029.i	−0.132324	+	0.407251i
$197$	444246.			0.815564			0.407782	−	0.913079i	$-0.366302\pi$
$197$	444246.			0.815564			0.407782	+	0.913079i	$0.366302\pi$
$198$	214983.	+	17684.5i	0.389709	+	0.0320574i
$199$	117983.			0.211197			0.105598	−	0.994409i	$-0.466324\pi$
$199$	117983.			0.211197			0.105598	+	0.994409i	$0.466324\pi$
$200$	161266.	−	496326.i	0.285081	−	0.877389i
$201$	−119732.	+	86990.7i	−0.209036	+	0.151874i
$202$	−522732.	−	379787.i	−0.901364	−	0.654879i
$203$	−117923.	−	362928.i	−0.200843	−	0.618131i
$204$	46518.5	+	143169.i	0.0782619	+	0.240865i
$205$	92092.1	+	66908.9i	0.153052	+	0.111198i
$206$	−3210.61	+	2332.64i	−0.00527131	+	0.00382983i
$207$	70065.3	−	215639.i	0.113652	−	0.349785i
$208$	8810.92			0.0141209
$209$	−395125.	+	944459.i	−0.625704	+	1.49561i
$210$	405398.			0.634357
$211$	−161153.	+	495978.i	−0.249191	+	0.766931i	0.745728	+	0.666251i	$0.232102\pi$
$211$	−161153.	+	495978.i	−0.249191	+	0.766931i	−0.994919	+	0.100681i	$0.967898\pi$
$212$	−280303.	+	203652.i	−0.428339	+	0.311206i
$213$	−541864.	−	393687.i	−0.818354	−	0.594569i
$214$	142334.	+	438058.i	0.212458	+	0.653879i
$215$	−297436.	−	915413.i	−0.438831	−	1.35058i
$216$	109256.	+	79379.1i	0.159335	+	0.115764i
$217$	202980.	−	147473.i	0.292619	−	0.212600i
$218$	−29056.8	+	89427.8i	−0.0414102	+	0.127447i
$219$	296141.			0.417242
$220$	156849.	+	663648.i	0.218486	+	0.924445i
$221$	16669.3			0.0229581
$222$	−137905.	+	424428.i	−0.187801	+	0.577991i
$223$	−488187.	+	354688.i	−0.657391	+	0.477623i	−0.865781	−	0.500423i	$-0.833178\pi$
$223$	−488187.	+	354688.i	−0.657391	+	0.477623i	0.208390	+	0.978046i	$0.433178\pi$
$224$	−40696.1	−	29567.4i	−0.0541917	−	0.0393726i
$225$	338602.	+	1.04211e6i	0.445896	+	1.37233i
$226$	181859.	+	559705.i	0.236845	+	0.728934i
$227$	1.04095e6	+	756298.i	1.34081	+	0.974156i	0.999414	+	0.0342361i	$0.0108998\pi$
$227$	1.04095e6	+	756298.i	1.34081	+	0.974156i	0.341396	+	0.939919i	$0.389100\pi$
$228$	641491.	−	466071.i	0.817247	−	0.593765i
$229$	168190.	−	517635.i	0.211939	−	0.652281i	−0.787418	−	0.616420i	$-0.788583\pi$
$229$	168190.	−	517635.i	0.211939	−	0.652281i	0.999357	−	0.0358613i	$-0.0114175\pi$
$230$	716791.			0.893456
$231$	−327241.	+	198946.i	−0.403495	+	0.245304i
$232$	−497164.			−0.606428
$233$	−102624.	+	315844.i	−0.123839	+	0.381138i	−0.993688	−	0.112181i	$-0.964216\pi$
$233$	−102624.	+	315844.i	−0.123839	+	0.381138i	0.869848	+	0.493319i	$0.164216\pi$
$234$	−14966.7	+	10873.9i	−0.0178684	+	0.0129822i
$235$	−654719.	−	475681.i	−0.773366	−	0.561883i
$236$	−82050.9	−	252527.i	−0.0958966	−	0.295139i
$237$	−60037.6	−	184777.i	−0.0694308	−	0.213686i
$238$	−76992.4	−	55938.3i	−0.0881060	−	0.0640128i
$239$	−243522.	+	176929.i	−0.275768	+	0.200357i	−0.717069	−	0.697002i	$-0.754517\pi$
$239$	−243522.	+	176929.i	−0.275768	+	0.200357i	0.441301	+	0.897359i	$0.354517\pi$
$240$	163211.	−	502312.i	0.182903	−	0.562918i
$241$	−422764.			−0.468873			−0.234436	−	0.972131i	$-0.575324\pi$
$241$	−422764.			−0.468873			−0.234436	+	0.972131i	$0.575324\pi$
$242$	−452289.	−	458730.i	−0.496452	−	0.503523i
$243$	−917891.			−0.997185
$244$	191318.	−	588817.i	0.205723	−	0.633149i
$245$	1.23672e6	−	898532.i	1.31631	−	0.956354i
$246$	67380.1	+	48954.5i	0.0709894	+	0.0515768i
$247$	−27132.4	−	83505.0i	−0.0282974	−	0.0870904i
$248$	−101009.	−	310875.i	−0.104288	−	0.320964i
$249$	902078.	+	655398.i	0.922031	+	0.669895i
$250$	−1.72844e6	+	1.25579e6i	−1.74906	+	1.27077i
$251$	−19264.8	+	59291.0i	−0.0193010	+	0.0594024i	−0.960243	−	0.279165i	$-0.909942\pi$
$251$	−19264.8	+	59291.0i	−0.0193010	+	0.0594024i	0.940942	+	0.338567i	$0.109942\pi$
$252$	105619.			0.104771
$253$	−578600.	+	351759.i	−0.568299	+	0.345497i
$254$	−433469.			−0.421574
$255$	308777.	−	950317.i	0.297368	−	0.915204i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	270639.	+	196630.i	0.255598	+	0.185703i	0.708204	−	0.706008i	$-0.249506\pi$
$257$	270639.	+	196630.i	0.255598	+	0.185703i	−0.452606	+	0.891710i	$0.649506\pi$
$258$	−217622.	−	669771.i	−0.203542	−	0.626436i
$259$	−87182.0	−	268319.i	−0.0807565	−	0.248543i
$260$	−47314.9	−	34376.3i	−0.0434075	−	0.0315374i
$261$	844508.	−	613571.i	0.767366	−	0.557524i
$262$	260466.	−	801631.i	0.234421	−	0.721475i
$263$	320685.			0.285884			0.142942	−	0.989731i	$-0.454344\pi$
$263$	320685.			0.285884			0.142942	+	0.989731i	$0.454344\pi$
$264$	114760.	+	485565.i	0.101340	+	0.428783i
$265$	2.29979e6			2.01175
$266$	−154904.	+	476745.i	−0.134233	+	0.413126i
$267$	−1.19719e6	+	869809.i	−1.02774	+	0.746699i
$268$	−98615.2	−	71648.1i	−0.0838700	−	0.0609352i
$269$	245417.	+	755317.i	0.206788	+	0.636427i	0.999635	+	0.0270068i	$0.00859759\pi$
$269$	245417.	+	755317.i	0.206788	+	0.636427i	−0.792848	+	0.609420i	$0.791402\pi$
$270$	−277006.	−	852537.i	−0.231249	−	0.711711i
$271$	−698565.	−	507537.i	−0.577808	−	0.419802i	0.260125	−	0.965575i	$-0.416236\pi$
$271$	−698565.	−	507537.i	−0.577808	−	0.419802i	−0.837933	+	0.545773i	$0.816236\pi$
$272$	−100307.	+	72877.6i	−0.0822073	+	0.0597271i
$273$	10149.5	−	31237.1i	0.00824214	−	0.0253667i
$274$	−1.31270e6			−1.05630
$275$	1.26296e6	−	3.01883e6i	1.00707	−	2.40717i
$276$	524447.			0.414409
$277$	58812.8	−	181007.i	0.0460545	−	0.141741i	−0.925385	−	0.379028i	$-0.876258\pi$
$277$	58812.8	−	181007.i	0.0460545	−	0.141741i	0.971440	+	0.237287i	$0.0762583\pi$
$278$	482164.	−	350313.i	0.374182	−	0.271859i
$279$	555244.	+	403409.i	0.427045	+	0.310266i
$280$	103180.	+	317556.i	0.0786505	+	0.242061i
$281$	794259.	+	2.44448e6i	0.600063	+	1.84680i	0.527712	+	0.849423i	$0.323050\pi$
$281$	794259.	+	2.44448e6i	0.600063	+	1.84680i	0.0723502	+	0.997379i	$0.476950\pi$
$282$	−479031.	−	348037.i	−0.358708	−	0.260617i
$283$	966774.	−	702402.i	0.717561	−	0.521338i	−0.168043	−	0.985780i	$-0.553745\pi$
$283$	966774.	−	702402.i	0.717561	−	0.521338i	0.885604	+	0.464441i	$0.153745\pi$
$284$	170470.	−	524651.i	0.125415	−	0.385989i
$285$	−5.26323e6			−3.83831
$286$	55062.8	+	4529.46i	0.0398055	+	0.00327440i
$287$	−52652.7			−0.0377326
$288$	42521.5	−	130868.i	0.0302084	−	0.0929719i
$289$	958918.	−	696695.i	0.675363	−	0.490680i
$290$	2.66978e6	+	1.93971e6i	1.86415	+	1.35438i
$291$	−104580.	−	321863.i	−0.0723961	−	0.222812i
$292$	75372.4	+	231972.i	0.0517315	+	0.159213i
$293$	−1.25081e6	−	908765.i	−0.851181	−	0.618419i	0.0742908	−	0.997237i	$-0.476331\pi$
$293$	−1.25081e6	−	908765.i	−0.851181	−	0.618419i	−0.925471	+	0.378818i	$0.876331\pi$
$294$	904861.	−	657420.i	0.610539	−	0.443582i
$295$	−544631.	+	1.67620e6i	−0.364374	+	1.12143i
$296$	−367561.			−0.243837
$297$	641976.	+	552236.i	0.422307	+	0.363274i
$298$	440322.			0.287230
$299$	17945.6	−	55230.8i	0.0116086	−	0.0357275i
$300$	−2.05044e6	+	1.48973e6i	−1.31536	+	0.955663i
$301$	360184.	+	261689.i	0.229144	+	0.166483i
$302$	16641.6	+	51217.6i	0.0104997	+	0.0323148i
$303$	969687.	+	2.98439e6i	0.606771	+	1.86745i
$304$	528351.	+	383870.i	0.327898	+	0.238232i
$305$	−3.32469e6	+	2.41553e6i	−2.04645	+	1.48683i
$306$	80446.0	−	247587.i	0.0491135	−	0.151156i
$307$	1.73245e6			1.04909			0.524547	−	0.851381i	$-0.324235\pi$
$307$	1.73245e6			1.04909			0.524547	+	0.851381i	$0.324235\pi$
$308$	−239126.	−	205699.i	−0.143631	−	0.123554i
$309$	19273.4			0.0114832
$310$	−670473.	+	2.06350e6i	−0.396257	+	1.21955i
$311$	72580.7	−	52733.0i	0.0425520	−	0.0309159i	−0.566306	−	0.824195i	$-0.691628\pi$
$311$	72580.7	−	52733.0i	0.0425520	−	0.0309159i	0.608858	+	0.793279i	$0.291628\pi$
$312$	−34618.4	−	25151.7i	−0.0201335	−	0.0146279i
$313$	−385297.	−	1.18582e6i	−0.222297	−	0.684161i	−0.998555	−	0.0537450i	$-0.982884\pi$
$313$	−385297.	−	1.18582e6i	−0.222297	−	0.684161i	0.776257	−	0.630416i	$-0.217116\pi$
$314$	−183862.	−	565868.i	−0.105237	−	0.323885i
$315$	−567177.	−	412078.i	−0.322064	−	0.233993i
$316$	129458.	−	94057.0i	0.0729311	−	0.0529875i
$317$	630485.	−	1.94043e6i	0.352393	−	1.08455i	−0.605113	−	0.796139i	$-0.706872\pi$
$317$	630485.	−	1.94043e6i	0.352393	−	1.08455i	0.957506	−	0.288414i	$-0.0931278\pi$
$318$	1.68266e6			0.933104
$319$	−3.10697e6	−	255579.i	−1.70946	−	0.140620i
$320$	435010.			0.237478
$321$	691251.	−	2.12745e6i	0.374432	−	1.15238i
$322$	−268229.	+	194880.i	−0.144167	+	0.104744i
$323$	999581.	+	726238.i	0.533103	+	0.387322i
$324$	−364123.	−	1.12066e6i	−0.192702	−	0.593075i
$325$	86725.0	+	266912.i	0.0455445	+	0.140172i
$326$	694214.	+	504376.i	0.361784	+	0.262851i
$327$	369447.	−	268419.i	0.191066	−	0.138817i
$328$	−21197.7	+	65239.7i	−0.0108794	+	0.0334832i
$329$	374329.			0.190662
$330$	1.27819e6	−	3.05524e6i	0.646118	−	1.54440i
$331$	1.77377e6			0.889871			0.444935	−	0.895563i	$-0.353227\pi$
$331$	1.77377e6			0.889871			0.444935	+	0.895563i	$0.353227\pi$
$332$	−283792.	+	873423.i	−0.141304	+	0.434890i
$333$	624358.	−	453622.i	0.308548	−	0.224173i
$334$	−1.46593e6	−	1.06506e6i	−0.719031	−	0.522407i
$335$	250027.	+	769505.i	0.121724	+	0.374627i
$336$	75492.8	+	232343.i	0.0364802	+	0.112275i
$337$	352264.	+	255935.i	0.168964	+	0.122759i	0.669054	−	0.743214i	$-0.266700\pi$
$337$	352264.	+	255935.i	0.168964	+	0.122759i	−0.500090	+	0.865974i	$0.666700\pi$
$338$	1.19770e6	−	870177.i	0.570236	−	0.414301i
$339$	883209.	−	2.71824e6i	0.417411	−	1.28466i
$340$	822989.			0.386097
$341$	−471434.	−	1.99470e6i	−0.219551	−	0.928951i
$342$	−1.37123e6			−0.633937
$343$	−473635.	+	1.45770e6i	−0.217374	+	0.669009i
$344$	469256.	−	340934.i	0.213803	−	0.155337i
$345$	−2.81630e6	−	2.04616e6i	−1.27389	−	0.925533i
$346$	−39061.0	−	120217.i	−0.0175409	−	0.0539854i
$347$	1.00037e6	+	3.07881e6i	0.446001	+	1.37265i	0.881383	+	0.472403i	$0.156613\pi$
$347$	1.00037e6	+	3.07881e6i	0.446001	+	1.37265i	−0.435382	+	0.900246i	$0.643387\pi$
$348$	1.95337e6	+	1.41921e6i	0.864643	+	0.628200i
$349$	324589.	−	235828.i	0.142649	−	0.103641i	−0.514172	−	0.857687i	$-0.671901\pi$
$349$	324589.	−	235828.i	0.142649	−	0.103641i	0.656821	+	0.754046i	$0.271901\pi$
$350$	495129.	−	1.52385e6i	0.216047	−	0.664924i
$351$	−72625.4			−0.0314645
$352$	−351143.	+	213477.i	−0.151053	+	0.0918321i
$353$	−2.54234e6			−1.08592			−0.542958	−	0.839760i	$-0.682696\pi$
$353$	−2.54234e6			−1.08592			−0.542958	+	0.839760i	$0.682696\pi$
$354$	−398484.	+	1.22641e6i	−0.169006	+	0.520148i
$355$	−2.96238e6	+	2.15230e6i	−1.24759	+	0.906424i
$356$	−986040.	−	716400.i	−0.412354	−	0.299592i
$357$	142824.	+	439567.i	0.0593103	+	0.182538i
$358$	268180.	+	825374.i	0.110591	+	0.340364i
$359$	−2.07270e6	−	1.50590e6i	−0.848790	−	0.616682i	0.0760220	−	0.997106i	$-0.475778\pi$
$359$	−2.07270e6	−	1.50590e6i	−0.848790	−	0.616682i	−0.924812	+	0.380424i	$0.875778\pi$
$360$	−738930.	+	536864.i	−0.300502	+	0.218327i
$361$	1.24594e6	−	3.83460e6i	0.503185	−	1.54865i
$362$	−2.69990e6			−1.08287
$363$	467562.	+	3.09347e6i	0.186240	+	1.23220i
$364$	27051.8			0.0107015
$365$	500301.	−	1.53977e6i	0.196562	−	0.604955i
$366$	−2.43254e6	+	1.76734e6i	−0.949199	+	0.689633i
$367$	−2.07779e6	−	1.50960e6i	−0.805261	−	0.585056i	0.107192	−	0.994238i	$-0.465814\pi$
$367$	−2.07779e6	−	1.50960e6i	−0.805261	−	0.585056i	−0.912453	+	0.409182i	$0.865814\pi$
$368$	133480.	+	410809.i	0.0513803	+	0.158132i
$369$	−44507.7	−	136981.i	−0.0170165	−	0.0523712i
$370$	1.97381e6	+	1.43406e6i	0.749552	+	0.544581i
$371$	−860602.	+	625264.i	−0.324614	+	0.235846i
$372$	−490558.	+	1.50978e6i	−0.183795	+	0.565662i
$373$	4.73013e6			1.76036			0.880180	−	0.474640i	$-0.157422\pi$
$373$	4.73013e6			1.76036			0.880180	+	0.474640i	$0.157422\pi$
$374$	−664324.	+	403875.i	−0.245584	+	0.149303i
$375$	1.03759e7			3.81020
$376$	150703.	−	463815.i	0.0549732	−	0.169190i
$377$	216301.	−	157152.i	0.0783799	−	0.0569463i
$378$	335444.	+	243715.i	0.120751	+	0.0877308i
$379$	−950597.	−	2.92564e6i	−0.339937	−	1.04622i	−0.964239	−	0.265035i	$-0.914616\pi$
$379$	−950597.	−	2.92564e6i	−0.339937	−	1.04622i	0.624302	−	0.781183i	$-0.285384\pi$
$380$	−1.33957e6	−	4.12278e6i	−0.475891	−	1.46464i
$381$	1.70311e6	+	1.23738e6i	0.601078	+	0.436709i
$382$	1.90066e6	−	1.38091e6i	0.666417	−	0.484180i
$383$	−1.76030e6	+	5.41764e6i	−0.613182	+	1.88718i	−0.187647	+	0.982237i	$0.560086\pi$
$383$	−1.76030e6	+	5.41764e6i	−0.613182	+	1.88718i	−0.425534	+	0.904942i	$0.639914\pi$
$384$	318279.			0.110149
$385$	481566.	+	2.03757e6i	0.165578	+	0.700586i
$386$	−2.84804e6			−0.972923
$387$	−376341.	+	1.15826e6i	−0.127733	+	0.393122i
$388$	225504.	−	163838.i	0.0760458	−	0.0552505i
$389$	854257.	+	620654.i	0.286230	+	0.207958i	0.721630	−	0.692279i	$-0.243393\pi$
$389$	854257.	+	620654.i	0.286230	+	0.207958i	−0.435400	+	0.900237i	$0.643393\pi$
$390$	87770.9	+	270131.i	0.0292206	+	0.0899317i
$391$	252529.	+	777204.i	0.0835352	+	0.257095i
$392$	745270.	+	541470.i	0.244962	+	0.177975i
$393$	−3.31172e6	+	2.40611e6i	−1.08161	+	0.785838i
$394$	549118.	−	1.69001e6i	0.178207	−	0.548465i
$395$	−1.06216e6			−0.342530
$396$	333009.	−	795984.i	0.106713	−	0.255074i
$397$	−483703.			−0.154029			−0.0770145	−	0.997030i	$-0.524539\pi$
$397$	−483703.			−0.154029			−0.0770145	+	0.997030i	$0.524539\pi$
$398$	145835.	−	448834.i	0.0461482	−	0.142029i
$399$	1.96954e6	−	1.43096e6i	0.619346	−	0.449981i
$400$	−1.68880e6	−	1.22699e6i	−0.527750	−	0.383433i
$401$	−16447.6	−	50620.4i	−0.00510788	−	0.0157204i	0.948470	−	0.316867i	$-0.102631\pi$
$401$	−16447.6	−	50620.4i	−0.00510788	−	0.0157204i	−0.953578	+	0.301146i	$0.902631\pi$
$402$	182935.	+	563016.i	0.0564588	+	0.173762i
$403$	142213.	+	103324.i	0.0436190	+	0.0316911i
$404$	−2.09093e6	+	1.51915e6i	−0.637361	+	0.463070i
$405$	−2.41695e6	+	7.43860e6i	−0.732200	+	2.25348i
$406$	−1.52642e6			−0.459578
$407$	−2.29703e6	−	188953.i	−0.687354	−	0.0565416i
$408$	602148.			0.179082
$409$	1.38734e6	−	4.26978e6i	0.410084	−	1.26211i	−0.506490	−	0.862246i	$-0.669057\pi$
$409$	1.38734e6	−	4.26978e6i	0.410084	−	1.26211i	0.916574	−	0.399864i	$-0.130943\pi$
$410$	368369.	−	267635.i	0.108224	−	0.0786292i
$411$	5.15763e6	+	3.74724e6i	1.50607	+	1.09422i
$412$	4905.37	+	15097.2i	0.00142373	+	0.00438180i
$413$	−251918.	−	775323.i	−0.0726747	−	0.223670i
$414$	−733733.	−	533088.i	−0.210396	−	0.152862i
$415$	4.93168e6	−	3.58308e6i	1.40564	−	1.02126i
$416$	10890.9	−	33518.7i	0.00308553	−	0.00949629i
$417$	−2.89444e6			−0.815126
$418$	3.10453e6	+	2.67056e6i	0.869071	+	0.747587i
$419$	−2.70506e6			−0.752735			−0.376368	−	0.926470i	$-0.622827\pi$
$419$	−2.70506e6			−0.752735			−0.376368	+	0.926470i	$0.622827\pi$
$420$	501100.	−	1.54223e6i	0.138612	−	0.426604i
$421$	−2.12946e6	+	1.54714e6i	−0.585549	+	0.425427i	−0.840720	−	0.541469i	$-0.817868\pi$
$421$	−2.12946e6	+	1.54714e6i	−0.585549	+	0.425427i	0.255171	+	0.966896i	$0.417868\pi$
$422$	1.68762e6	+	1.22613e6i	0.461310	+	0.335161i
$423$	316422.	+	973848.i	0.0859837	+	0.264631i
$424$	428264.	+	1.31806e6i	0.115690	+	0.356058i
$425$	−3.19502e6	−	2.32132e6i	−0.858028	−	0.623394i
$426$	−2.16746e6	+	1.57475e6i	−0.578664	+	0.420424i
$427$	587397.	−	1.80782e6i	0.155906	−	0.479829i
$428$	1.84241e6			0.486157
$429$	−203414.	−	174979.i	−0.0533626	−	0.0459032i
$430$	−3.85009e6			−1.00415
$431$	1.88536e6	−	5.80253e6i	0.488878	−	1.50461i	−0.337408	−	0.941359i	$-0.609550\pi$
$431$	1.88536e6	−	5.80253e6i	0.488878	−	1.50461i	0.826285	−	0.563252i	$-0.190450\pi$
$432$	437024.	−	317517.i	0.112667	−	0.0818572i
$433$	−749597.	−	544614.i	−0.192136	−	0.139595i	0.487559	−	0.873090i	$-0.337888\pi$
$433$	−749597.	−	544614.i	−0.192136	−	0.139595i	−0.679694	+	0.733495i	$0.737888\pi$
$434$	−310125.	−	954467.i	−0.0790338	−	0.243241i
$435$	−4.95255e6	−	1.52424e7i	−1.25489	−	3.86215i
$436$	304287.	+	221078.i	0.0766598	+	0.0556966i
$437$	3.48238e6	−	2.53010e6i	0.872314	−	0.633773i
$438$	366050.	−	1.12659e6i	0.0911707	−	0.280594i
$439$	−4.65632e6			−1.15314			−0.576569	−	0.817048i	$-0.695609\pi$
$439$	−4.65632e6			−1.15314			−0.576569	+	0.817048i	$0.695609\pi$
$440$	2.71854e6	+	223627.i	0.669429	+	0.0550671i
$441$	−1.93421e6			−0.473594
$442$	20604.3	−	63413.6i	0.00501653	−	0.0154393i
$443$	−460906.	+	334868.i	−0.111584	+	0.0810707i	−0.642178	−	0.766556i	$-0.721969\pi$
$443$	−460906.	+	334868.i	−0.111584	+	0.0810707i	0.530594	+	0.847626i	$0.321969\pi$
$444$	1.44416e6	+	1.04924e6i	0.347662	+	0.252591i
$445$	2.49999e6	+	7.69418e6i	0.598465	+	1.84188i
$446$	745883.	+	2.29559e6i	0.177555	+	0.546459i
$447$	−1.73004e6	−	1.25695e6i	−0.409532	−	0.297542i
$448$	−162784.	+	118270.i	−0.0383193	+	0.0278406i
$449$	−609436.	+	1.87565e6i	−0.142663	+	0.439073i	−0.996703	−	0.0811351i	$-0.974145\pi$
$449$	−609436.	+	1.87565e6i	−0.142663	+	0.439073i	0.854040	+	0.520208i	$0.174145\pi$
$450$	4.38296e6			1.02032
$451$	−166010.	+	396811.i	−0.0384321	+	0.0918634i
$452$	2.35404e6			0.541960
$453$	80820.8	−	248741.i	0.0185045	−	0.0569510i
$454$	4.16382e6	−	3.02519e6i	0.948096	−	0.688832i
$455$	−145269.	−	105544.i	−0.0328961	−	0.0239004i
$456$	−980111.	−	3.01647e6i	−0.220731	−	0.679340i
$457$	2.21650e6	+	6.82169e6i	0.496452	+	1.52792i	0.814681	+	0.579909i	$0.196912\pi$
$457$	2.21650e6	+	6.82169e6i	0.496452	+	1.52792i	−0.318229	+	0.948014i	$0.603088\pi$
$458$	−1.76131e6	−	1.27966e6i	−0.392348	−	0.285057i
$459$	826800.	−	600705.i	0.183176	−	0.133085i
$460$	886003.	−	2.72684e6i	0.195227	−	0.600848i
$461$	161519.			0.0353974			0.0176987	−	0.999843i	$-0.494366\pi$
$461$	161519.			0.0353974			0.0176987	+	0.999843i	$0.494366\pi$
$462$	352342.	+	1.49081e6i	0.0767997	+	0.324950i
$463$	−6.62659e6			−1.43661			−0.718303	−	0.695730i	$-0.755081\pi$
$463$	−6.62659e6			−1.43661			−0.718303	+	0.695730i	$0.755081\pi$
$464$	−614528.	+	1.89132e6i	−0.132509	+	0.407822i
$465$	8.52480e6	−	6.19363e6i	1.82832	−	1.32835i
$466$	1.07469e6	+	780809.i	0.229255	+	0.166564i
$467$	815758.	+	2.51065e6i	0.173089	+	0.532713i	0.999541	−	0.0302941i	$-0.00964437\pi$
$467$	815758.	+	2.51065e6i	0.173089	+	0.532713i	−0.826452	+	0.563007i	$0.809644\pi$
$468$	22867.0	+	70377.5i	0.00482609	+	0.0148532i
$469$	−302774.	−	219978.i	−0.0635604	−	0.0461794i
$470$	−2.61888e6	+	1.90272e6i	−0.546853	+	0.397312i
$471$	−892933.	+	2.74817e6i	−0.185467	+	0.570809i
$472$	−1.06209e6			−0.219435
$473$	3.10783e6	−	1.88940e6i	0.638710	−	0.388303i
$474$	−777142.			−0.158875
$475$	−6.42818e6	+	1.97839e7i	−1.30724	+	4.02326i
$476$	−307970.	+	223753.i	−0.0623004	+	0.0452639i
$477$	−2.35415e6	−	1.71039e6i	−0.473738	−	0.344191i
$478$	372069.	+	1.14511e6i	0.0744824	+	0.229233i
$479$	−2.17473e6	−	6.69314e6i	−0.433079	−	1.33288i	−0.895042	−	0.445981i	$-0.852855\pi$
$479$	−2.17473e6	−	6.69314e6i	−0.433079	−	1.33288i	0.461963	−	0.886899i	$-0.347145\pi$
$480$	−1.70917e6	−	1.24178e6i	−0.338596	−	0.246004i
$481$	159915.	−	116185.i	0.0315156	−	0.0228974i
$482$	−522565.	+	1.60829e6i	−0.102453	+	0.315316i
$483$	1.61019e6			0.314057
$484$	−2.30417e6	+	1.15359e6i	−0.447097	+	0.223840i
$485$	−1.85019e6			−0.357159
$486$	−1.13458e6	+	3.49187e6i	−0.217893	+	0.670605i
$487$	4.84321e6	−	3.51880e6i	0.925361	−	0.672314i	−0.0194914	−	0.999810i	$-0.506205\pi$
$487$	4.84321e6	−	3.51880e6i	0.925361	−	0.672314i	0.944853	+	0.327496i	$0.106205\pi$
$488$	−2.00351e6	−	1.45564e6i	−0.380840	−	0.276696i
$489$	−1.28779e6	−	3.96342e6i	−0.243542	−	0.749545i
$490$	−1.88955e6	−	5.81542e6i	−0.355523	−	1.09419i
$491$	6.42229e6	+	4.66607e6i	1.20223	+	0.873469i	0.994502	−	0.104719i	$-0.0333942\pi$
$491$	6.42229e6	+	4.66607e6i	1.20223	+	0.873469i	0.207725	+	0.978187i	$0.433394\pi$
$492$	269520.	−	195818.i	0.0501971	−	0.0364703i
$493$	−1.16262e6	+	3.57817e6i	−0.215437	+	0.663046i
$494$	−351209.			−0.0647513
$495$	−4.89385e6	+	2.97521e6i	−0.897713	+	0.545763i
$496$	−1.30749e6			−0.238636
$497$	523386.	−	1.61082e6i	0.0950454	−	0.292520i
$498$	3.60831e6	−	2.62159e6i	0.651975	−	0.473687i
$499$	−2.74045e6	−	1.99105e6i	−0.492686	−	0.357958i	0.313530	−	0.949578i	$-0.398488\pi$
$499$	−2.74045e6	−	1.99105e6i	−0.492686	−	0.357958i	−0.806216	+	0.591621i	$0.798488\pi$
$500$	2.64083e6	+	8.12763e6i	0.472405	+	1.45391i
$501$	2.71936e6	+	8.36933e6i	0.484030	+	1.48969i
$502$	201744.	+	146575.i	0.0357306	+	0.0259598i
$503$	8.29113e6	−	6.02386e6i	1.46115	−	1.06158i	0.478083	−	0.878315i	$-0.341332\pi$
$503$	8.29113e6	−	6.02386e6i	1.46115	−	1.06158i	0.983063	−	0.183270i	$-0.0586682\pi$
$504$	130552.	−	401798.i	0.0228933	−	0.0704582i
$505$	1.71554e7			2.99345
$506$	622982.	+	2.63592e6i	0.108168	+	0.457674i
$507$	−7.18980e6			−1.24222
$508$	−535797.	+	1.64901e6i	−0.0921172	+	0.283508i
$509$	−4.67922e6	+	3.39965e6i	−0.800532	+	0.581621i	−0.911070	−	0.412251i	$-0.864743\pi$
$509$	−4.67922e6	+	3.39965e6i	−0.800532	+	0.581621i	0.110538	+	0.993872i	$0.464743\pi$
$510$	−3.23355e6	−	2.34931e6i	−0.550496	−	0.399959i
$511$	231413.	+	712216.i	0.0392044	+	0.120659i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	−4.35502e6	−	3.16411e6i	−0.730629	−	0.530833i
$514$	1.08255e6	−	786522.i	0.180735	−	0.131312i
$515$	32560.5	−	100211.i	0.00540969	−	0.0166493i
$516$	−2.81696e6			−0.465753
$517$	1.18023e6	−	2.82108e6i	0.194197	−	0.464184i
$518$	−1.12851e6			−0.184791
$519$	−189702.	+	583841.i	−0.0309138	+	0.0951429i
$520$	−189260.	+	137505.i	−0.0306937	+	0.0223003i
$521$	1.95010e6	+	1.41683e6i	0.314747	+	0.228677i	0.733931	−	0.679224i	$-0.237684\pi$
$521$	1.95010e6	+	1.41683e6i	0.314747	+	0.228677i	−0.419184	+	0.907902i	$0.637684\pi$
$522$	−1.29029e6	−	3.97111e6i	−0.207258	−	0.637876i
$523$	−1.95252e6	−	6.00924e6i	−0.312134	−	0.960650i	−0.976918	−	0.213614i	$-0.931476\pi$
$523$	−1.95252e6	−	6.00924e6i	−0.312134	−	0.960650i	0.664784	−	0.747036i	$-0.268524\pi$
$524$	−2.72763e6	−	1.98174e6i	−0.433968	−	0.315296i
$525$	−6.29538e6	+	4.57386e6i	−0.996836	+	0.724243i
$526$	396389.	−	1.21996e6i	0.0624679	−	0.192256i
$527$	−2.47363e6			−0.387979
$528$	1.98905e6	+	163619.i	0.310499	+	0.0255416i
$529$	−3.58934e6			−0.557668
$530$	2.84270e6	−	8.74893e6i	0.439583	−	1.35290i
$531$	1.80412e6	−	1.31077e6i	0.277670	−	0.201739i
$532$	1.62217e6	+	1.17858e6i	0.248496	+	0.180543i
$533$	−11399.6	−	35084.3i	−0.00173809	−	0.00534928i
$534$	1.82914e6	+	5.62952e6i	0.277584	+	0.854315i
$535$	−9.89378e6	−	7.18825e6i	−1.49444	−	1.08577i
$536$	−394461.	+	286593.i	−0.0593051	+	0.0430877i
$537$	1.30243e6	−	4.00847e6i	0.194903	−	0.599851i
$538$	3.17675e6			0.473181
$539$	4.37912e6	+	3.76698e6i	0.649255	+	0.558498i
$540$	−3.58564e6			−0.529154
$541$	1.92626e6	−	5.92841e6i	0.282957	−	0.870853i	−0.704046	−	0.710154i	$-0.748625\pi$
$541$	1.92626e6	−	5.92841e6i	0.282957	−	0.870853i	0.987003	−	0.160699i	$-0.0513748\pi$
$542$	−2.79426e6	+	2.03015e6i	−0.408572	+	0.296845i
$543$	1.06080e7	+	7.70715e6i	1.54395	+	1.12175i
$544$	153256.	+	471674.i	0.0222034	+	0.0683352i
$545$	−771485.	−	2.37439e6i	−0.111259	−	0.342421i
$546$	−106287.	−	77222.3i	−0.0152581	−	0.0110857i
$547$	1.26423e6	−	918514.i	0.180658	−	0.131255i	−0.493781	−	0.869586i	$-0.664386\pi$
$547$	1.26423e6	−	918514.i	0.180658	−	0.131255i	0.674439	+	0.738331i	$0.264386\pi$
$548$	−1.62258e6	+	4.99379e6i	−0.230810	+	0.710361i
$549$	5.19973e6			0.736292
$550$	−9.92321e6	−	8.53608e6i	−1.39877	−	1.20324i
$551$	1.98173e7			2.78077
$552$	648252.	−	1.99512e6i	0.0905517	−	0.278689i
$553$	397471.	−	288780.i	0.0552704	−	0.0401563i
$554$	−615895.	−	447474.i	−0.0852575	−	0.0619432i
$555$	−3.66150e6	−	1.12689e7i	−0.504576	−	1.55292i
$556$	−736681.	−	2.26727e6i	−0.101063	−	0.311040i
$557$	9.30106e6	+	6.75761e6i	1.27027	+	0.922902i	0.999213	−	0.0396631i	$-0.0126285\pi$
$557$	9.30106e6	+	6.75761e6i	1.27027	+	0.922902i	0.271052	+	0.962565i	$0.412628\pi$
$558$	2.22098e6	−	1.61363e6i	0.301966	−	0.219391i
$559$	−96390.8	+	296660.i	−0.0130469	+	0.0401541i
$560$	1.33559e6			0.179972
$561$	3.76305e6	+	309548.i	0.504816	+	0.0415261i
$562$	1.02811e7			1.37309
$563$	2.43597e6	−	7.49716e6i	0.323893	−	0.996841i	−0.648045	−	0.761602i	$-0.724413\pi$
$563$	2.43597e6	−	7.49716e6i	0.323893	−	0.996841i	0.971938	−	0.235238i	$-0.0755871\pi$
$564$	−1.91613e6	+	1.39215e6i	−0.253645	+	0.184284i
$565$	−1.26412e7	−	9.18440e6i	−1.66598	−	1.21040i
$566$	−1.47710e6	−	4.54604e6i	−0.193807	−	0.596475i
$567$	−1.11795e6	−	3.44070e6i	−0.146038	−	0.449458i
$568$	−1.78518e6	−	1.29701e6i	−0.232173	−	0.168683i
$569$	−1.14371e7	+	8.30951e6i	−1.48093	+	1.07596i	−0.503670	+	0.863896i	$0.668017\pi$
$569$	−1.14371e7	+	8.30951e6i	−1.48093	+	1.07596i	−0.977257	+	0.212060i	$0.931983\pi$
$570$	−6.50571e6	+	2.00225e7i	−0.838701	+	2.58126i
$571$	−1.16438e7			−1.49452			−0.747262	−	0.664530i	$-0.768632\pi$
$571$	−1.16438e7			−1.49452			−0.747262	+	0.664530i	$0.768632\pi$
$572$	85292.5	−	203873.i	0.0108999	−	0.0260537i
$573$	−1.14097e7			−1.45174
$574$	−65082.4	+	200303.i	−0.00824487	+	0.0253751i
$575$	−1.11310e7	+	8.08711e6i	−1.40399	+	1.02006i
$576$	−445291.	−	323523.i	−0.0559227	−	0.0406302i
$577$	181736.	+	559326.i	0.0227249	+	0.0699400i	0.961776	−	0.273838i	$-0.0882932\pi$
$577$	181736.	+	559326.i	0.0227249	+	0.0699400i	−0.939051	+	0.343778i	$0.888293\pi$
$578$	−1.46510e6	−	4.50910e6i	−0.182409	−	0.561398i
$579$	1.11901e7	+	8.13005e6i	1.38719	+	1.00785i
$580$	1.06791e7	−	7.75885e6i	1.31815	−	0.957695i
$581$	−871316.	+	2.68164e6i	−0.107087	+	0.329579i
$582$	−1.35371e6			−0.165660
$583$	1.99881e6	+	8.45724e6i	0.243557	+	1.03052i
$584$	975641.			0.118374
$585$	151785.	−	467147.i	0.0183375	−	0.0564369i
$586$	−5.00323e6	+	3.63506e6i	−0.601876	+	0.437288i
$587$	−1.22894e6	−	892879.i	−0.147210	−	0.106954i	0.511743	−	0.859139i	$-0.329000\pi$
$587$	−1.22894e6	−	892879.i	−0.147210	−	0.106954i	−0.658952	+	0.752185i	$0.729000\pi$
$588$	−1.38250e6	−	4.25491e6i	−0.164901	−	0.507513i
$589$	4.02631e6	+	1.23917e7i	0.478210	+	1.47178i
$590$	5.70345e6	+	4.14380e6i	0.674540	+	0.490082i
$591$	−6.98183e6	+	5.07259e6i	−0.822243	+	0.597395i
$592$	−454330.	+	1.39828e6i	−0.0532804	+	0.163980i
$593$	1.99219e6			0.232646			0.116323	−	0.993211i	$-0.462889\pi$
$593$	1.99219e6			0.232646			0.116323	+	0.993211i	$0.462889\pi$
$594$	2.89436e6	−	1.75962e6i	0.336578	−	0.204622i
$595$	2.52679e6			0.292602
$596$	544268.	−	1.67508e6i	0.0627621	−	0.193162i
$597$	−1.85424e6	+	1.34718e6i	−0.212926	+	0.154700i
$598$	−187928.	−	136538.i	−0.0214902	−	0.0156135i
$599$	−2.22011e6	−	6.83279e6i	−0.252818	−	0.778092i	−0.994252	−	0.107067i	$-0.965854\pi$
$599$	−2.22011e6	−	6.83279e6i	−0.252818	−	0.778092i	0.741434	−	0.671025i	$-0.234146\pi$
$600$	3.13279e6	+	9.64174e6i	0.355266	+	1.09340i
$601$	−8.16993e6	−	5.93580e6i	−0.922640	−	0.670337i	0.0215396	−	0.999768i	$-0.493143\pi$
$601$	−8.16993e6	−	5.93580e6i	−0.922640	−	0.670337i	−0.944180	+	0.329431i	$0.893143\pi$
$602$	1.44074e6	−	1.04676e6i	0.162029	−	0.117721i
$603$	316355.	−	973642.i	0.0354309	−	0.109045i
$604$	215413.			0.0240259
$605$	1.68743e7	+	2.79506e6i	1.87429	+	0.310458i
$606$	1.25519e7			1.38844
$607$	−1.33448e6	+	4.10712e6i	−0.147008	+	0.452445i	−0.997264	−	0.0739253i	$-0.976447\pi$
$607$	−1.33448e6	+	4.10712e6i	−0.147008	+	0.452445i	0.850256	+	0.526370i	$0.176447\pi$
$608$	2.11340e6	−	1.53548e6i	0.231859	−	0.168455i
$609$	5.99736e6	+	4.35734e6i	0.655265	+	0.476078i
$610$	5.07967e6	+	1.56336e7i	0.552728	+	1.70112i
$611$	81044.2	+	249428.i	0.00878251	+	0.0270298i
$612$	−842441.	−	612069.i	−0.0909203	−	0.0660575i
$613$	−5.54932e6	+	4.03182e6i	−0.596470	+	0.433361i	−0.844624	−	0.535360i	$-0.820176\pi$
$613$	−5.54932e6	+	4.03182e6i	−0.596470	+	0.433361i	0.248154	+	0.968721i	$0.420176\pi$
$614$	2.14143e6	−	6.59063e6i	0.229236	−	0.705515i
$615$	−2.21133e6			−0.235757
$616$	−1.07810e6	+	655430.i	−0.114474	+	0.0695945i
$617$	−2.91426e6			−0.308188			−0.154094	−	0.988056i	$-0.549246\pi$
$617$	−2.91426e6			−0.308188			−0.154094	+	0.988056i	$0.549246\pi$
$618$	23823.2	−	73320.2i	0.00250916	−	0.00772240i
$619$	−5.75418e6	+	4.18065e6i	−0.603610	+	0.438549i	−0.847159	−	0.531340i	$-0.821689\pi$
$619$	−5.75418e6	+	4.18065e6i	−0.603610	+	0.438549i	0.243548	+	0.969889i	$0.421689\pi$
$620$	7.02128e6	+	5.10126e6i	0.733563	+	0.532964i
$621$	−1.10023e6	−	3.38616e6i	−0.114487	−	0.352354i
$622$	−110894.	−	341295.i	−0.0114929	−	0.0353716i
$623$	−3.02740e6	−	2.19953e6i	−0.312500	−	0.227044i
$624$	−138474.	+	100607.i	−0.0142366	+	0.0103435i
$625$	9.65474e6	−	2.97142e7i	0.988645	−	3.04274i
$626$	−4.98739e6			−0.508671
$627$	−4.57440e6	−	1.93549e7i	−0.464693	−	1.96618i
$628$	−2.37995e6			−0.240807
$629$	−859541.	+	2.64540e6i	−0.0866244	+	0.266602i
$630$	−2.26871e6	+	1.64831e6i	−0.227734	+	0.165458i
$631$	−6.31153e6	−	4.58559e6i	−0.631046	−	0.458482i	0.225716	−	0.974193i	$-0.427528\pi$
$631$	−6.31153e6	−	4.58559e6i	−0.631046	−	0.458482i	−0.856762	+	0.515711i	$0.827528\pi$
$632$	−197795.	−	608750.i	−0.0196980	−	0.0606242i
$633$	−3.13059e6	−	9.63498e6i	−0.310540	−	0.955744i
$634$	−6.60253e6	−	4.79702e6i	−0.652360	−	0.473967i
$635$	9.31096e6	−	6.76481e6i	0.916348	−	0.665765i
$636$	2.07989e6	−	6.40124e6i	0.203891	−	0.627511i
$637$	−495401.			−0.0483736
$638$	−4.81270e6	+	1.15037e7i	−0.468098	+	1.11889i
$639$	4.63310e6			0.448868
$640$	537702.	−	1.65488e6i	0.0518909	−	0.159704i
$641$	−9.13371e6	+	6.63603e6i	−0.878015	+	0.637915i	−0.932726	−	0.360587i	$-0.882576\pi$
$641$	−9.13371e6	+	6.63603e6i	−0.878015	+	0.637915i	0.0547103	+	0.998502i	$0.482576\pi$
$642$	−7.23888e6	−	5.25935e6i	−0.693160	−	0.503610i
$643$	5.49127e6	+	1.69004e7i	0.523776	+	1.61202i	0.766723	+	0.641978i	$0.221886\pi$
$643$	5.49127e6	+	1.69004e7i	0.523776	+	1.61202i	−0.242947	+	0.970039i	$0.578114\pi$
$644$	409818.	+	1.26129e6i	0.0389383	+	0.119840i
$645$	1.51271e7	+	1.09905e7i	1.43172	+	1.04020i
$646$	3.99832e6	−	2.90495e6i	0.376961	−	0.273878i
$647$	−116419.	+	358301.i	−0.0109336	+	0.0336502i	−0.956374	−	0.292144i	$-0.905631\pi$
$647$	−116419.	+	358301.i	−0.0109336	+	0.0336502i	0.945441	+	0.325794i	$0.105631\pi$
$648$	−4.71331e6			−0.440949
$649$	−6.63740e6	−	545992.i	−0.618567	−	0.0508832i
$650$	1.12259e6			0.104217
$651$	−1.50614e6	+	4.63542e6i	−0.139288	+	0.428683i
$652$	2.77685e6	−	2.01750e6i	0.255820	−	0.185864i
$653$	−1.25074e7	−	9.08716e6i	−1.14785	−	0.833960i	−0.159654	−	0.987173i	$-0.551038\pi$
$653$	−1.25074e7	−	9.08716e6i	−1.14785	−	0.833960i	−0.988193	+	0.153213i	$0.951038\pi$
$654$	−564464.	−	1.73724e6i	−0.0516050	−	0.158824i
$655$	6.91559e6	+	2.12840e7i	0.629834	+	1.93843i
$656$	221985.	+	161281.i	0.0201402	+	0.0146327i
$657$	−1.65727e6	+	1.20408e6i	−0.149789	+	0.108828i
$658$	462696.	−	1.42403e6i	0.0416611	−	0.128220i
$659$	1.28179e7			1.14975			0.574875	−	0.818241i	$-0.305051\pi$
$659$	1.28179e7			1.14975			0.574875	+	0.818241i	$0.305051\pi$
$660$	−1.00429e7	−	8.63902e6i	−0.897426	−	0.771977i
$661$	−8.19562e6			−0.729589			−0.364794	−	0.931088i	$-0.618861\pi$
$661$	−8.19562e6			−0.729589			−0.364794	+	0.931088i	$0.618861\pi$
$662$	2.19250e6	−	6.74781e6i	0.194444	−	0.598437i
$663$	−261976.	+	190337.i	−0.0231461	+	0.0168166i
$664$	2.97191e6	+	2.15922e6i	0.261587	+	0.190054i
$665$	−4.11284e6	−	1.26580e7i	−0.360651	−	1.10997i
$666$	−953934.	−	2.93591e6i	−0.0833360	−	0.256482i
$667$	1.06040e7	+	7.70428e6i	0.922903	+	0.670528i
$668$	−5.86373e6	+	4.26025e6i	−0.508432	+	0.369397i
$669$	3.62242e6	−	1.11487e7i	0.312920	−	0.963069i
$670$	3.23642e6			0.278534
$671$	−1.17724e7	−	1.01268e7i	−1.00939	−	0.868291i
$672$	977199.			0.0834757
$673$	−1.42854e6	+	4.39660e6i	−0.121578	+	0.374179i	−0.993262	−	0.115890i	$-0.963028\pi$
$673$	−1.42854e6	+	4.39660e6i	−0.121578	+	0.374179i	0.871684	+	0.490068i	$0.163028\pi$
$674$	1.40906e6	−	1.02374e6i	0.119475	−	0.0868039i
$675$	1.39202e7	+	1.01136e7i	1.17594	+	0.854374i
$676$	−1.82992e6	−	5.63190e6i	−0.154016	−	0.474011i
$677$	3.29823e6	+	1.01509e7i	0.276572	+	0.851202i	0.988799	+	0.149253i	$0.0476868\pi$
$677$	3.29823e6	+	1.01509e7i	0.276572	+	0.851202i	−0.712227	+	0.701950i	$0.752313\pi$
$678$	−9.24908e6	−	6.71985e6i	−0.772724	−	0.561417i
$679$	692357.	−	503027.i	0.0576309	−	0.0418713i
$680$	1.01727e6	−	3.13084e6i	0.0843654	−	0.259650i
$681$	−2.49955e7			−2.06535
$682$	−8.17103e6	−	672148.i	−0.672692	−	0.0553355i
$683$	−8.53950e6			−0.700456			−0.350228	−	0.936665i	$-0.613896\pi$
$683$	−8.53950e6			−0.700456			−0.350228	+	0.936665i	$0.613896\pi$
$684$	−1.69494e6	+	5.21648e6i	−0.138520	+	0.426322i
$685$	2.81969e7	−	2.04862e7i	2.29601	−	1.66815i
$686$	4.95997e6	+	3.60363e6i	0.402410	+	0.292368i
$687$	3.26729e6	+	1.00557e7i	0.264117	+	0.812867i
$688$	−716959.	−	2.20657e6i	−0.0577462	−	0.177724i
$689$	−602960.	−	438076.i	−0.0483883	−	0.0351562i
$690$	−1.12652e7	+	8.18464e6i	−0.900774	+	0.654450i
$691$	6.62949e6	−	2.04035e7i	0.528184	−	1.62558i	−0.229749	−	0.973250i	$-0.573791\pi$
$691$	6.62949e6	−	2.04035e7i	0.528184	−	1.62558i	0.757933	−	0.652332i	$-0.226209\pi$
$692$	−505616.			−0.0401380
$693$	1.02242e6	−	2.44388e6i	0.0808720	−	0.193307i
$694$	1.29490e7			1.02056
$695$	−4.88988e6	+	1.50495e7i	−0.384005	+	1.18184i
$696$	7.81349e6	−	5.67683e6i	0.611395	−	0.444205i
$697$	419970.	+	305126.i	0.0327444	+	0.0237902i
$698$	−495927.	−	1.52631e6i	−0.0385283	−	0.118578i
$699$	−1.99359e6	−	6.13565e6i	−0.154328	−	0.474971i
$700$	−5.18506e6	−	3.76717e6i	−0.399953	−	0.290583i
$701$	9.60626e6	−	6.97936e6i	0.738345	−	0.536439i	−0.153847	−	0.988095i	$-0.549166\pi$
$701$	9.60626e6	−	6.97936e6i	0.738345	−	0.536439i	0.892192	+	0.451656i	$0.149166\pi$
$702$	−89770.0	+	276284.i	−0.00687525	+	0.0211598i
$703$	1.46512e7			1.11811
$704$	378078.	+	1.59970e6i	0.0287508	+	0.121649i
$705$	1.57212e7			1.19128
$706$	−3.14250e6	+	9.67162e6i	−0.237281	+	0.730277i
$707$	−6.41969e6	+	4.66418e6i	−0.483020	+	0.350935i
$708$	4.17298e6	+	3.03185e6i	0.312870	+	0.227313i
$709$	5.26958e6	+	1.62181e7i	0.393695	+	1.21167i	0.929973	+	0.367628i	$0.119830\pi$
$709$	5.26958e6	+	1.62181e7i	0.393695	+	1.21167i	−0.536278	+	0.844042i	$0.680170\pi$
$710$	4.52612e6	+	1.39300e7i	0.336961	+	1.03706i
$711$	1.08727e6	+	789947.i	0.0806609	+	0.0586036i
$712$	−3.94416e6	+	2.86560e6i	−0.291578	+	0.211844i
$713$	−2.66303e6	+	8.19596e6i	−0.196179	+	0.603776i
$714$	1.84875e6			0.135717
$715$	−1.25344e6	+	762029.i	−0.0916937	+	0.0557451i
$716$	3.47140e6			0.253059
$717$	1.80697e6	−	5.56129e6i	0.131266	−	0.403996i
$718$	−8.29080e6	+	6.02362e6i	−0.600185	+	0.436060i
$719$	1.60460e7	+	1.16581e7i	1.15756	+	0.841020i	0.989468	−	0.144751i	$-0.0462380\pi$
$719$	1.60460e7	+	1.16581e7i	1.15756	+	0.841020i	0.168097	+	0.985771i	$0.446238\pi$
$720$	1.12898e6	+	3.47466e6i	0.0811628	+	0.249793i
$721$	15060.8	+	46352.2i	0.00107897	+	0.00332072i
$722$	−1.30476e7	−	9.47965e6i	−0.931512	−	0.676783i
$723$	6.64421e6	−	4.82730e6i	0.472713	−	0.343446i
$724$	−3.33725e6	+	1.02710e7i	−0.236615	+	0.728227i
$725$	−6.33433e7			−4.47564
$726$	1.23462e7	+	2.04503e6i	0.869345	+	0.143999i
$727$	6.10145e6			0.428151			0.214075	−	0.976817i	$-0.431326\pi$
$727$	6.10145e6			0.428151			0.214075	+	0.976817i	$0.431326\pi$
$728$	33437.9	−	102911.i	0.00233835	−	0.00719671i
$729$	−52333.9	+	38022.8i	−0.00364724	+	0.00264988i
$730$	−5.23922e6	−	3.80652e6i	−0.363881	−	0.264375i
$731$	−1.35641e6	−	4.17459e6i	−0.0938850	−	0.288948i
$732$	3.71659e6	+	1.14385e7i	0.256370	+	0.789025i
$733$	8.69742e6	+	6.31905e6i	0.597903	+	0.434402i	0.845134	−	0.534555i	$-0.179521\pi$
$733$	8.69742e6	+	6.31905e6i	0.597903	+	0.434402i	−0.247231	+	0.968957i	$0.579521\pi$
$734$	−8.31116e6	+	6.03841e6i	−0.569405	+	0.413697i
$735$	−9.17668e6	+	2.82429e7i	−0.626566	+	1.92837i
$736$	1.72780e6			0.117571
$737$	−2.61247e6	+	1.58825e6i	−0.177167	+	0.107708i
$738$	−576119.			−0.0389378
$739$	−2.90563e6	+	8.94260e6i	−0.195717	+	0.602356i	0.804250	+	0.594291i	$0.202567\pi$
$739$	−2.90563e6	+	8.94260e6i	−0.195717	+	0.602356i	−0.999967	+	0.00806482i	$0.997433\pi$
$740$	7.89525e6	−	5.73623e6i	0.530013	−	0.385077i
$741$	1.37991e6	+	1.00257e6i	0.0923222	+	0.0670760i
$742$	1.31488e6	+	4.04679e6i	0.0876753	+	0.269837i
$743$	−7.48649e6	−	2.30410e7i	−0.497515	−	1.53119i	−0.813000	−	0.582263i	$-0.802167\pi$
$743$	−7.48649e6	−	2.30410e7i	−0.497515	−	1.53119i	0.315485	−	0.948930i	$-0.397833\pi$
$744$	5.13719e6	+	3.73238e6i	0.340246	+	0.247203i
$745$	−9.45817e6	+	6.87176e6i	−0.624333	+	0.453605i
$746$	5.84677e6	−	1.79945e7i	0.384653	−	1.18384i
$747$	−7.71303e6			−0.505736
$748$	715281.	+	3.02645e6i	0.0467437	+	0.197779i
$749$	5.65667e6			0.368431
$750$	1.28253e7	−	3.94722e7i	0.832558	−	2.56235i
$751$	−1.21659e7	+	8.83906e6i	−0.787127	+	0.571882i	−0.907110	−	0.420894i	$-0.861716\pi$
$751$	−1.21659e7	+	8.83906e6i	−0.787127	+	0.571882i	0.119982	+	0.992776i	$0.461716\pi$
$752$	−1.57818e6	−	1.14661e6i	−0.101768	−	0.0739388i
$753$	−374242.	−	1.15180e6i	−0.0240528	−	0.0740268i
$754$	−330478.	−	1.01711e6i	−0.0211697	−	0.0651536i
$755$	−1.15678e6	−	840447.i	−0.0738554	−	0.0536591i
$756$	1.34178e6	−	974858.i	0.0853839	−	0.0620350i
$757$	−759850.	+	2.33858e6i	−0.0481935	+	0.148324i	−0.972257	−	0.233914i	$-0.924847\pi$
$757$	−759850.	+	2.33858e6i	−0.0481935	+	0.148324i	0.924064	+	0.382238i	$0.124847\pi$
$758$	−1.23048e7			−0.777860
$759$	5.07681e6	−	1.21350e7i	0.319880	−	0.764602i
$760$	−1.73398e7			−1.08896
$761$	2.81469e6	−	8.66271e6i	0.176185	−	0.542241i	−0.823501	−	0.567315i	$-0.807982\pi$
$761$	2.81469e6	−	8.66271e6i	0.176185	−	0.542241i	0.999686	+	0.0250741i	$0.00798217\pi$
$762$	6.81245e6	−	4.94954e6i	0.425027	−	0.308800i
$763$	934241.	+	678766.i	0.0580962	+	0.0422093i
$764$	−2.90395e6	−	8.93744e6i	−0.179993	−	0.553961i
$765$	2.13591e6	+	6.57366e6i	0.131956	+	0.406119i
$766$	1.84341e7	+	1.33931e7i	1.13514	+	0.824727i
$767$	462083.	−	335723.i	0.0283616	−	0.0206059i
$768$	393414.	−	1.21081e6i	0.0240684	−	0.0740749i
$769$	2.72483e7			1.66159			0.830794	−	0.556580i	$-0.187887\pi$
$769$	2.72483e7			1.66159			0.830794	+	0.556580i	$0.187887\pi$
$770$	8.34663e6	+	686593.i	0.507323	+	0.0417323i
$771$	−6.49861e6			−0.393717
$772$	−3.52037e6	+	1.08346e7i	−0.212591	+	0.654289i
$773$	2.13447e7	−	1.55078e7i	1.28481	−	0.933472i	0.285128	−	0.958490i	$-0.407964\pi$
$773$	2.13447e7	−	1.55078e7i	1.28481	−	0.933472i	0.999687	+	0.0250172i	$0.00796405\pi$
$774$	3.94109e6	+	2.86337e6i	0.236463	+	0.171801i
$775$	−1.28695e7	−	3.96084e7i	−0.769678	−	2.36882i
$776$	−344540.	−	1.06038e6i	−0.0205393	−	0.0632134i
$777$	4.43394e6	+	3.22145e6i	0.263474	+	0.191425i
$778$	3.41703e6	−	2.48262e6i	0.202395	−	0.147049i
$779$	844954.	−	2.60050e6i	0.0498872	−	0.153537i
$780$	1.13613e6			0.0668639
$781$	−1.04895e7	−	9.02323e6i	−0.615359	−	0.529340i
$782$	3.26880e6			0.191149
$783$	5.06535e6	−	1.55895e7i	0.295260	−	0.908718i
$784$	2.98108e6	−	2.16588e6i	0.173214	−	0.125847i
$785$	1.27804e7	+	9.28552e6i	0.740238	+	0.537814i
$786$	5.05986e6	+	1.55726e7i	0.292134	+	0.899096i
$787$	−6.78839e6	−	2.08925e7i	−0.390688	−	1.20241i	−0.932269	−	0.361765i	$-0.882174\pi$
$787$	−6.78839e6	−	2.08925e7i	−0.390688	−	1.20241i	0.541581	−	0.840648i	$-0.317826\pi$
$788$	−5.75044e6	−	4.17794e6i	−0.329902	−	0.239688i
$789$	−5.03993e6	+	3.66173e6i	−0.288225	+	0.209408i
$790$	−1.31291e6	+	4.04071e6i	−0.0748456	+	0.230351i
$791$	7.22750e6			0.410721
$792$	−2.61648e6	−	2.25073e6i	−0.148219	−	0.127500i
$793$	1.33179e6			0.0752060
$794$	−597889.	+	1.84011e6i	−0.0336566	+	0.103584i
$795$	−3.61438e7	+	2.62600e7i	−2.02823	+	1.47359i
$796$	−1.52721e6	−	1.10958e6i	−0.0854309	−	0.0620692i
$797$	1.44527e6	+	4.44809e6i	0.0805942	+	0.248043i	0.983232	−	0.182357i	$-0.0583725\pi$
$797$	1.44527e6	+	4.44809e6i	0.0805942	+	0.248043i	−0.902638	+	0.430400i	$0.858373\pi$
$798$	−3.00920e6	−	9.26135e6i	−0.167280	−	0.514834i
$799$	−2.98573e6	−	2.16926e6i	−0.165457	−	0.120211i
$800$	−6.75521e6	+	4.90794e6i	−0.373176	+	0.271128i
$801$	3.16320e6	−	9.73532e6i	0.174199	−	0.536128i
$802$	−212902.			−0.0116881
$803$	6.09716e6	+	501551.i	0.333686	+	0.0274490i
$804$	2.36796e6			0.129192
$805$	2.72026e6	−	8.37210e6i	0.147952	−	0.455349i
$806$	568851.	−	413294.i	0.0308433	−	0.0224090i
$807$	−1.24815e7	−	9.06838e6i	−0.674659	−	0.490169i
$808$	3.19465e6	+	9.83213e6i	0.172145	+	0.529809i
$809$	717208.	+	2.20734e6i	0.0385278	+	0.118576i	0.968471	−	0.249128i	$-0.0801439\pi$
$809$	717208.	+	2.20734e6i	0.0385278	+	0.118576i	−0.929943	+	0.367704i	$0.880144\pi$
$810$	2.53106e7	+	1.83892e7i	1.35547	+	0.984806i
$811$	−1.10118e7	+	8.00052e6i	−0.587902	+	0.427136i	−0.841564	−	0.540157i	$-0.818365\pi$
$811$	−1.10118e7	+	8.00052e6i	−0.587902	+	0.427136i	0.253662	+	0.967293i	$0.418365\pi$
$812$	−1.88676e6	+	5.80685e6i	−0.100422	+	0.309066i
$813$	1.67740e7			0.890042
$814$	−3.55811e6	+	8.50486e6i	−0.188217	+	0.449890i
$815$	−2.27832e7			−1.20149
$816$	744296.	−	2.29071e6i	0.0391309	−	0.120433i
$817$	−1.87049e7	+	1.35899e7i	−0.980391	+	0.712296i
$818$	−1.45284e7	−	1.05555e7i	−0.759160	−	0.551562i
$819$	70207.8	+	216077.i	0.00365743	+	0.0112564i
$820$	−562817.	−	1.73217e6i	−0.0292303	−	0.0899615i
$821$	−8.41165e6	−	6.11142e6i	−0.435535	−	0.316435i	0.348323	−	0.937375i	$-0.386751\pi$
$821$	−8.41165e6	−	6.11142e6i	−0.435535	−	0.316435i	−0.783858	+	0.620940i	$0.786751\pi$
$822$	2.06305e7	−	1.49889e7i	1.06495	−	0.773734i
$823$	9.19863e6	−	2.83105e7i	0.473395	−	1.45696i	−0.374715	−	0.927140i	$-0.622259\pi$
$823$	9.19863e6	−	2.83105e7i	0.473395	−	1.45696i	0.848110	−	0.529820i	$-0.177741\pi$
$824$	63496.4			0.00325785
$825$	1.46215e7	+	6.18654e7i	0.747921	+	3.16456i
$826$	−3.26089e6			−0.166298
$827$	−1.07855e6	+	3.31942e6i	−0.0548372	+	0.168771i	−0.974724	−	0.223412i	$-0.928280\pi$
$827$	−1.07855e6	+	3.31942e6i	−0.0548372	+	0.168771i	0.919887	+	0.392184i	$0.128280\pi$
$828$	−2.93493e6	+	2.13235e6i	−0.148772	+	0.108089i
$829$	−2.33190e7	−	1.69422e7i	−1.17848	−	0.856218i	−0.186483	−	0.982458i	$-0.559709\pi$
$829$	−2.33190e7	−	1.69422e7i	−1.17848	−	0.856218i	−0.992000	+	0.126241i	$0.959709\pi$
$830$	−7.53494e6	−	2.31902e7i	−0.379651	−	1.16845i
$831$	1.14251e6	+	3.51628e6i	0.0573928	+	0.176637i
$832$	−114051.	−	82862.8i	−0.00571203	−	0.00415003i
$833$	5.63987e6	−	4.09760e6i	0.281615	−	0.204606i
$834$	−3.57773e6	+	1.10111e7i	−0.178112	+	0.548171i
$835$	4.81100e7			2.38792
$836$	1.39968e7	−	8.50935e6i	0.692650	−	0.421096i
$837$	1.07772e7			0.531733
$838$	−3.34364e6	+	1.02907e7i	−0.164479	+	0.506213i
$839$	3.63948e6	−	2.64423e6i	0.178498	−	0.129687i	−0.494949	−	0.868922i	$-0.664813\pi$
$839$	3.63948e6	−	2.64423e6i	0.178498	−	0.129687i	0.673447	+	0.739236i	$0.264813\pi$
$840$	−5.24759e6	−	3.81260e6i	−0.256603	−	0.186433i
$841$	1.23092e7	+	3.78839e7i	0.600124	+	1.84699i
$842$	3.25352e6	+	1.00133e7i	0.158151	+	0.486740i
$843$	−4.03948e7	−	2.93485e7i	−1.95775	−	1.42239i
$844$	6.75047e6	−	4.90450e6i	0.326195	−	0.236995i
$845$	−1.21465e7	+	3.73830e7i	−0.585206	+	1.80108i
$846$	4.09586e6			0.196752
$847$	−7.07441e6	+	3.54181e6i	−0.338830	+	0.169636i
$848$	5.54357e6			0.264728
$849$	−7.17361e6	+	2.20781e7i	−0.341561	+	1.05122i
$850$	−1.27801e7	+	9.28528e6i	−0.606718	+	0.440806i
$851$	7.83972e6	+	5.69589e6i	0.371088	+	0.269611i
$852$	3.31158e6	+	1.01920e7i	0.156292	+	0.481016i
$853$	−8.22027e6	−	2.52994e7i	−0.386824	−	1.19052i	−0.935148	−	0.354256i	$-0.884734\pi$
$853$	−8.22027e6	−	2.52994e7i	−0.386824	−	1.19052i	0.548324	−	0.836266i	$-0.315266\pi$
$854$	−6.15130e6	−	4.46918e6i	−0.288617	−	0.209693i
$855$	2.94543e7	−	2.13998e7i	1.37795	−	1.00114i
$856$	2.27734e6	−	7.00893e6i	0.106229	−	0.326940i
$857$	−5.90140e6			−0.274475			−0.137238	−	0.990538i	$-0.543822\pi$
$857$	−5.90140e6			−0.274475			−0.137238	+	0.990538i	$0.543822\pi$
$858$	−917094.	+	557546.i	−0.0425300	+	0.0258561i
$859$	2.40070e7			1.11008			0.555042	−	0.831822i	$-0.312702\pi$
$859$	2.40070e7			1.11008			0.555042	+	0.831822i	$0.312702\pi$
$860$	−4.75897e6	+	1.46466e7i	−0.219415	+	0.675291i
$861$	827497.	−	601212.i	0.0380416	−	0.0276388i
$862$	−1.97437e7	−	1.43446e7i	−0.905025	−	0.657539i
$863$	6.73711e6	+	2.07347e7i	0.307926	+	0.947699i	0.978569	+	0.205919i	$0.0660184\pi$
$863$	6.73711e6	+	2.07347e7i	0.307926	+	0.947699i	−0.670643	+	0.741780i	$0.733982\pi$
$864$	−667713.	−	2.05501e6i	−0.0304303	−	0.0936547i
$865$	2.71517e6	+	1.97269e6i	0.123383	+	0.0896433i
$866$	−2.99839e6	+	2.17846e6i	−0.135861	+	0.0987085i
$867$	−7.11532e6	+	2.18987e7i	−0.321475	+	0.989397i
$868$	−4.01435e6			−0.180849
$869$	−923154.	−	3.90599e6i	−0.0414691	−	0.175462i
$870$	−6.41071e7			−2.87150
$871$	81027.0	−	249375.i	0.00361896	−	0.0111380i
$872$	1.21715e6	−	884310.i	0.0542066	−	0.0393834i
$873$	1.89392e6	+	1.37601e6i	0.0841058	+	0.0611064i
$874$	−5.32061e6	−	1.63751e7i	−0.235604	−	0.725114i
$875$	8.10802e6	+	2.49539e7i	0.358010	+	1.10184i
$876$	−3.83333e6	−	2.78507e6i	−0.168778	−	0.122624i
$877$	1.74907e7	−	1.27077e7i	0.767906	−	0.557917i	−0.133419	−	0.991060i	$-0.542596\pi$
$877$	1.74907e7	−	1.27077e7i	0.767906	−	0.557917i	0.901325	+	0.433143i	$0.142596\pi$
$878$	−5.75553e6	+	1.77137e7i	−0.251970	+	0.775484i
$879$	3.00345e7			1.31114
$880$	4.21103e6	−	1.00655e7i	0.183308	−	0.438157i
$881$	2.21376e7			0.960929			0.480465	−	0.877014i	$-0.340468\pi$
$881$	2.21376e7			0.960929			0.480465	+	0.877014i	$0.340468\pi$
$882$	−2.39081e6	+	7.35816e6i	−0.103484	+	0.318491i
$883$	1.58774e7	−	1.15356e7i	0.685297	−	0.497897i	−0.189814	−	0.981820i	$-0.560788\pi$
$883$	1.58774e7	−	1.15356e7i	0.685297	−	0.497897i	0.875111	+	0.483923i	$0.160788\pi$
$884$	−215771.	−	156767.i	−0.00928674	−	0.00674721i
$885$	−1.05801e7	−	3.25622e7i	−0.454080	−	1.39751i
$886$	704201.	+	2.16731e6i	0.0301379	+	0.0927548i
$887$	1.35387e7	+	9.83645e6i	0.577788	+	0.419787i	0.837926	−	0.545784i	$-0.183768\pi$
$887$	1.35387e7	+	9.83645e6i	0.577788	+	0.419787i	−0.260138	+	0.965571i	$0.583768\pi$
$888$	5.77663e6	−	4.19697e6i	0.245834	−	0.178609i
$889$	−1.64504e6	+	5.06290e6i	−0.0698105	+	0.214855i
$890$	3.23606e7			1.36943
$891$	−2.94553e7	−	2.42299e6i	−1.24299	−	0.102248i
$892$	9.65491e6			0.406290
$893$	−6.00711e6	+	1.84880e7i	−0.252079	+	0.775820i
$894$	−6.92016e6	+	5.02779e6i	−0.289583	+	0.210394i
$895$	−1.86415e7	−	1.35439e7i	−0.777900	−	0.565177i
$896$	248712.	+	765458.i	0.0103497	+	0.0318531i
$897$	348614.	+	1.07292e6i	0.0144665	+	0.0445234i
$898$	6.38210e6	+	4.63687e6i	0.264103	+	0.191882i
$899$	−3.20979e7	+	2.33205e7i	−1.32458	+	0.962362i
$900$	5.41764e6	−	1.66738e7i	0.222948	−	0.686164i
$901$	1.04878e7			0.430401
$902$	1.30436e6	+	1.12203e6i	0.0533803	+	0.0459184i
$903$	−8.64878e6			−0.352968
$904$	2.90975e6	−	8.95528e6i	0.118423	−	0.364467i
$905$	5.79941e7	−	4.21352e7i	2.35376	−	1.71011i
$906$	−846366.	−	614921.i	−0.0342561	−	0.0248885i
$907$	1.78714e6	+	5.50027e6i	0.0721343	+	0.222006i	0.980624	−	0.195902i	$-0.0627634\pi$
$907$	1.78714e6	+	5.50027e6i	0.0721343	+	0.222006i	−0.908489	+	0.417908i	$0.862763\pi$
$908$	−6.36175e6	−	1.95795e7i	−0.256072	−	0.788108i
$909$	−1.75608e7	−	1.27587e7i	−0.704913	−	0.512150i
$910$	−581076.	+	422176.i	−0.0232611	+	0.0169001i
$911$	−7.66762e6	+	2.35985e7i	−0.306101	+	0.942081i	0.673163	+	0.739494i	$0.264935\pi$
$911$	−7.66762e6	+	2.35985e7i	−0.306101	+	0.942081i	−0.979264	+	0.202588i	$0.935065\pi$
$912$	−1.26868e7			−0.505087
$913$	1.74626e7	+	1.50216e7i	0.693318	+	0.596402i
$914$	2.86910e7			1.13601
$915$	2.46697e7	−	7.59255e7i	0.974117	−	2.99802i
$916$	−7.04522e6	+	5.11865e6i	−0.277432	+	0.201566i
$917$	−8.37453e6	−	6.08446e6i	−0.328880	−	0.238945i
$918$	−1.26324e6	−	3.88785e6i	−0.0494742	−	0.152266i
$919$	339089.	+	1.04361e6i	0.0132442	+	0.0407613i	0.957460	−	0.288565i	$-0.0931783\pi$
$919$	339089.	+	1.04361e6i	0.0132442	+	0.0407613i	−0.944216	+	0.329327i	$0.893178\pi$
$920$	−9.27834e6	−	6.74111e6i	−0.361411	−	0.262580i
$921$	−2.72274e7	+	1.97819e7i	−1.05769	+	0.768455i
$922$	199648.	−	614455.i	0.00773461	−	0.0238047i
$923$	1.18666e6			0.0458481
$924$	6.10689e6	+	502352.i	0.235310	+	0.0193566i
$925$	−4.68307e7			−1.79960
$926$	−8.19092e6	+	2.52091e7i	−0.313910	+	0.966116i
$927$	−107858.	+	78363.7i	−0.00412244	+	0.00299513i
$928$	6.43542e6	+	4.67561e6i	0.245305	+	0.178225i
$929$	−1.59166e7	−	4.89864e7i	−0.605079	−	1.86224i	−0.496249	−	0.868180i	$-0.665290\pi$
$929$	−1.59166e7	−	4.89864e7i	−0.605079	−	1.86224i	−0.108830	−	0.994060i	$-0.534710\pi$
$930$	−1.30247e7	−	4.00860e7i	−0.493812	−	1.51980i
$931$	−2.97070e7	−	2.15834e7i	−1.12327	−	0.816104i
$932$	4.29876e6	−	3.12324e6i	0.162108	−	0.117778i
$933$	−538560.	+	1.65752e6i	−0.0202549	+	0.0623382i
$934$	1.05594e7			0.396070
$935$	7.96680e6	−	1.90429e7i	0.298026	−	0.712366i
$936$	295997.			0.0110433
$937$	1.57086e6	−	4.83460e6i	0.0584504	−	0.179892i	−0.917568	−	0.397578i	$-0.869851\pi$
$937$	1.57086e6	−	4.83460e6i	0.0584504	−	0.179892i	0.976019	+	0.217686i	$0.0698509\pi$
$938$	−1.21110e6	+	879914.i	−0.0449440	+	0.0326537i
$939$	1.95956e7	+	1.42370e7i	0.725262	+	0.526933i
$940$	4.00129e6	+	1.23147e7i	0.147700	+	0.454573i
$941$	5.13936e6	+	1.58173e7i	0.189206	+	0.582316i	0.999995	−	0.00302165i	$-0.000961824\pi$
$941$	5.13936e6	+	1.58173e7i	0.189206	+	0.582316i	−0.810789	+	0.585338i	$0.800962\pi$
$942$	9.35092e6	+	6.79384e6i	0.343342	+	0.249453i
$943$	1.46311e6	−	1.06301e6i	0.0535794	−	0.0389277i
$944$	−1.31281e6	+	4.04043e6i	−0.0479483	+	0.147570i
$945$	−1.10088e7			−0.401017
$946$	−3.34621e6	−	1.41583e7i	−0.121570	−	0.514379i
$947$	−3.41176e7			−1.23624			−0.618120	−	0.786083i	$-0.712106\pi$
$947$	−3.41176e7			−1.23624			−0.618120	+	0.786083i	$0.712106\pi$
$948$	−960601.	+	2.95643e6i	−0.0347154	+	0.106843i
$949$	−424472.	+	308397.i	−0.0152997	+	0.0111159i
$950$	6.73168e7	+	4.89085e7i	2.42000	+	1.75823i
$951$	1.22479e7	+	3.76953e7i	0.439149	+	1.35156i
$952$	470536.	+	1.44816e6i	0.0168268	+	0.0517874i
$953$	−1.90484e7	−	1.38394e7i	−0.679400	−	0.493613i	0.193759	−	0.981049i	$-0.437932\pi$
$953$	−1.90484e7	−	1.38394e7i	−0.679400	−	0.493613i	−0.873158	+	0.487436i	$0.837932\pi$
$954$	−9.41660e6	+	6.84156e6i	−0.334983	+	0.243380i
$955$	−1.92756e7	+	5.93242e7i	−0.683911	+	2.10486i
$956$	4.81616e6			0.170434
$957$	5.17478e7	−	3.14600e7i	1.82647	−	1.11040i
$958$	−2.81503e7			−0.990991
$959$	−4.98175e6	+	1.53322e7i	−0.174918	+	0.538343i
$960$	−6.83667e6	+	4.96713e6i	−0.239423	+	0.173951i
$961$	2.05785e6	+	1.49511e6i	0.0718794	+	0.0522234i
$962$	−244328.	−	751963.i	−0.00851207	−	0.0261974i
$963$	4.78162e6	+	1.47163e7i	0.166153	+	0.511367i
$964$	5.47237e6	+	3.97591e6i	0.189663	+	0.137798i
$965$	6.11763e7	−	4.44472e7i	2.11478	−	1.53648i
$966$	1.99030e6	−	6.12552e6i	0.0686241	−	0.211203i
$967$	−4.88313e7			−1.67931			−0.839657	−	0.543116i	$-0.817244\pi$
$967$	−4.88313e7			−1.67931			−0.839657	+	0.543116i	$0.817244\pi$
$968$	1.54039e6	+	1.01915e7i	0.0528376	+	0.349583i
$969$	−2.40020e7			−0.821181
$970$	−2.28696e6	+	7.03854e6i	−0.0780421	+	0.240189i
$971$	3.29244e7	−	2.39210e7i	1.12065	−	0.814200i	0.136343	−	0.990662i	$-0.456465\pi$
$971$	3.29244e7	−	2.39210e7i	1.12065	−	0.814200i	0.984308	+	0.176461i	$0.0564651\pi$
$972$	1.18814e7	+	8.63237e6i	0.403370	+	0.293065i
$973$	−2.26180e6	−	6.96111e6i	−0.0765901	−	0.235720i
$974$	−7.39977e6	−	2.27742e7i	−0.249932	−	0.769210i
$975$	−4.41070e6	−	3.20456e6i	−0.148592	−	0.107959i
$976$	−8.01405e6	+	5.82255e6i	−0.269294	+	0.195654i
$977$	−6.84578e6	+	2.10691e7i	−0.229449	+	0.706172i	0.768360	+	0.640018i	$0.221073\pi$
$977$	−6.84578e6	+	2.10691e7i	−0.229449	+	0.706172i	−0.997809	+	0.0661544i	$0.978927\pi$
$978$	−1.66695e7			−0.557284
$979$	−2.61217e7	+	1.58807e7i	−0.871054	+	0.529556i
$980$	−2.44588e7			−0.813523
$981$	−976147.	+	3.00427e6i	−0.0323849	+	0.0996705i
$982$	2.56892e7	−	1.86643e7i	0.850102	−	0.617636i
$983$	1.10788e7	+	8.04921e6i	0.365686	+	0.265687i	0.755420	−	0.655241i	$-0.227433\pi$
$983$	1.10788e7	+	8.04921e6i	0.365686	+	0.265687i	−0.389734	+	0.920928i	$0.627433\pi$
$984$	−411790.	−	1.26736e6i	−0.0135578	−	0.0417265i
$985$	1.45796e7	+	4.48713e7i	0.478800	+	1.47360i
$986$	1.21751e7	+	8.84572e6i	0.398823	+	0.289762i
$987$	−5.88300e6	+	4.27425e6i	−0.192223	+	0.139658i
$988$	−434119.	+	1.33608e6i	−0.0141487	+	0.0435452i
$989$	−1.52920e7			−0.497136
$990$	5.26923e6	+	2.22949e7i	0.170867	+	0.722964i
$991$	1.38832e7			0.449061			0.224531	−	0.974467i	$-0.427915\pi$
$991$	1.38832e7			0.449061			0.224531	+	0.974467i	$0.427915\pi$
$992$	−1.61615e6	+	4.97400e6i	−0.0521438	+	0.160482i
$993$	−2.78768e7	+	2.02537e7i	−0.897159	+	0.651824i
$994$	−5.48097e6	−	3.98216e6i	−0.175951	−	0.127836i
$995$	3.87205e6	+	1.19170e7i	0.123989	+	0.381599i
$996$	−5.51301e6	−	1.69673e7i	−0.176092	−	0.541956i
$997$	2.13366e7	+	1.55019e7i	0.679810	+	0.493911i	0.873295	−	0.487193i	$-0.161979\pi$
$997$	2.13366e7	+	1.55019e7i	0.679810	+	0.493911i	−0.193485	+	0.981103i	$0.561979\pi$
$998$	−1.09618e7	+	7.96421e6i	−0.348382	+	0.253114i
$999$	3.74489e6	−	1.15256e7i	0.118720	−	0.365384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.c.b.9.1	yes	12
3.2	odd	2		198.6.f.e.163.1		12
11.4	even	5		242.6.a.p.1.5		6
11.5	even	5	inner	22.6.c.b.5.1	✓	12
11.7	odd	10		242.6.a.o.1.5		6
33.5	odd	10		198.6.f.e.181.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.c.b.5.1	✓	12	11.5	even	5	inner
22.6.c.b.9.1	yes	12	1.1	even	1	trivial
198.6.f.e.163.1		12	3.2	odd	2
198.6.f.e.181.1		12	33.5	odd	10
242.6.a.o.1.5		6	11.7	odd	10
242.6.a.p.1.5		6	11.4	even	5

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(-15.7161 + 11.4184i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(32.8187 + 101.006i) q^{5} +(24.0121 + 73.9017i) q^{6} +(-39.7423 - 28.8745i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(41.5249 - 127.801i) q^{9} +O(q^{10})\)	\(q+(1.23607 - 3.80423i) q^{2} +(-15.7161 + 11.4184i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(32.8187 + 101.006i) q^{5} +(24.0121 + 73.9017i) q^{6} +(-39.7423 - 28.8745i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(41.5249 - 127.801i) q^{9} +424.814 q^{10} +(-342.914 + 208.474i) q^{11} +310.819 q^{12} +(10.6356 - 32.7331i) q^{13} +(-158.969 + 115.498i) q^{14} +(-1669.11 - 1212.68i) q^{15} +(79.1084 + 243.470i) q^{16} +(149.664 + 460.619i) q^{17} +(-434.855 - 315.941i) q^{18} +(2063.87 - 1499.49i) q^{19} +(525.099 - 1616.09i) q^{20} +954.296 q^{21} +(369.217 + 1562.21i) q^{22} +1687.31 q^{23} +(384.194 - 1182.43i) q^{24} +(-6596.88 + 4792.91i) q^{25} +(-111.378 - 80.9207i) q^{26} +(-652.064 - 2006.85i) q^{27} +(242.883 + 747.518i) q^{28} +(6284.59 + 4566.02i) q^{29} +(-6676.44 + 4850.71i) q^{30} +(-1578.27 + 4857.42i) q^{31} +1024.00 q^{32} +(3008.83 - 7191.94i) q^{33} +1937.29 q^{34} +(1612.19 - 4961.81i) q^{35} +(-1739.42 + 1263.76i) q^{36} +(4646.30 + 3375.73i) q^{37} +(-3153.31 - 9704.91i) q^{38} +(206.610 + 635.880i) q^{39} +(-5498.91 - 3995.19i) q^{40} +(867.129 - 630.006i) q^{41} +(1179.57 - 3630.36i) q^{42} -9063.00 q^{43} +(6399.37 + 526.411i) q^{44} +14271.4 q^{45} +(2085.62 - 6418.89i) q^{46} +(-6164.76 + 4478.96i) q^{47} +(-4023.33 - 2923.12i) q^{48} +(-4447.93 - 13689.3i) q^{49} +(10079.1 + 31020.4i) q^{50} +(-7611.69 - 5530.21i) q^{51} +(-445.511 + 323.683i) q^{52} +(6691.63 - 20594.7i) q^{53} -8440.49 q^{54} +(-32311.0 - 27794.3i) q^{55} +3143.95 q^{56} +(-15314.2 + 47132.4i) q^{57} +(25138.4 - 18264.1i) q^{58} +(13425.8 + 9754.38i) q^{59} +(10200.7 + 31394.5i) q^{60} +(11957.4 + 36801.1i) q^{61} +(16527.9 + 12008.2i) q^{62} +(-5340.47 + 3880.08i) q^{63} +(1265.73 - 3895.53i) q^{64} +3655.28 q^{65} +(-23640.6 - 20336.0i) q^{66} +7618.44 q^{67} +(2394.63 - 7369.90i) q^{68} +(-26517.9 + 19266.4i) q^{69} +(-16883.1 - 12266.3i) q^{70} +(10654.4 + 32790.7i) q^{71} +(2657.60 + 8179.24i) q^{72} +(-12333.0 - 8960.43i) q^{73} +(18585.2 - 13502.9i) q^{74} +(48949.9 - 150652. i) q^{75} -40817.4 q^{76} +(19647.7 + 1616.22i) q^{77} +2674.42 q^{78} +(-3090.54 + 9511.72i) q^{79} +(-21995.6 + 15980.8i) q^{80} +(59580.4 + 43287.7i) q^{81} +(-1324.85 - 4077.48i) q^{82} +(-17737.0 - 54589.0i) q^{83} +(-12352.7 - 8974.74i) q^{84} +(-41613.3 + 30233.8i) q^{85} +(-11202.5 + 34477.7i) q^{86} -150906. q^{87} +(9912.64 - 23694.0i) q^{88} +76175.8 q^{89} +(17640.4 - 54291.5i) q^{90} +(-1367.84 + 993.791i) q^{91} +(-21840.9 - 15868.4i) q^{92} +(-30659.9 - 94361.3i) q^{93} +(9418.91 + 28988.4i) q^{94} +(219190. + 159251. i) q^{95} +(-16093.3 + 11692.5i) q^{96} +(-5383.44 + 16568.5i) q^{97} -57575.3 q^{98} +(12403.6 + 52481.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9	\( 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18} + 7535 q^{19} + 704 q^{20} - 3368 q^{21} + 484 q^{22} + 15732 q^{23} - 1600 q^{24} - 19283 q^{25} - 984 q^{26} - 27411 q^{27} + 3264 q^{28} - 2504 q^{29} + 448 q^{30} + 15336 q^{31} + 12288 q^{32} + 26213 q^{33} + 24600 q^{34} - 33916 q^{35} - 5664 q^{36} - 116 q^{37} - 34880 q^{38} + 4690 q^{39} - 3584 q^{40} - 38836 q^{41} + 19808 q^{42} + 42230 q^{43} - 4704 q^{44} + 139932 q^{45} - 35232 q^{46} - 57840 q^{47} - 125521 q^{49} + 26268 q^{50} + 16467 q^{51} - 3936 q^{52} + 131934 q^{53} + 60176 q^{54} - 53082 q^{55} + 15616 q^{56} - 90021 q^{57} - 10016 q^{58} + 36585 q^{59} - 37248 q^{60} + 43146 q^{61} - 40016 q^{62} - 52922 q^{63} - 12288 q^{64} - 133772 q^{65} - 211008 q^{66} + 325206 q^{67} + 6400 q^{68} - 103894 q^{69} + 68216 q^{70} - 172806 q^{71} - 4416 q^{72} + 49436 q^{73} - 464 q^{74} + 263915 q^{75} + 37920 q^{76} - 207094 q^{77} + 330000 q^{78} + 58364 q^{79} - 14336 q^{80} + 341038 q^{81} + 82836 q^{82} + 82035 q^{83} - 52288 q^{84} - 317604 q^{85} - 104380 q^{86} - 572732 q^{87} - 38336 q^{88} + 97958 q^{89} - 151672 q^{90} - 22162 q^{91} + 15072 q^{92} - 271316 q^{93} + 153720 q^{94} + 549736 q^{95} + 76403 q^{97} + 198656 q^{98} - 199487 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 48 * q^4 + 44 * q^5 - 100 * q^6 - 326 * q^7 - 192 * q^8 - 69 * q^9 + 96 * q^10 + 1011 * q^11 + 800 * q^12 - 246 * q^13 - 1304 * q^14 + 112 * q^15 - 768 * q^16 + 400 * q^17 - 1416 * q^18 + 7535 * q^19 + 704 * q^20 - 3368 * q^21 + 484 * q^22 + 15732 * q^23 - 1600 * q^24 - 19283 * q^25 - 984 * q^26 - 27411 * q^27 + 3264 * q^28 - 2504 * q^29 + 448 * q^30 + 15336 * q^31 + 12288 * q^32 + 26213 * q^33 + 24600 * q^34 - 33916 * q^35 - 5664 * q^36 - 116 * q^37 - 34880 * q^38 + 4690 * q^39 - 3584 * q^40 - 38836 * q^41 + 19808 * q^42 + 42230 * q^43 - 4704 * q^44 + 139932 * q^45 - 35232 * q^46 - 57840 * q^47 - 125521 * q^49 + 26268 * q^50 + 16467 * q^51 - 3936 * q^52 + 131934 * q^53 + 60176 * q^54 - 53082 * q^55 + 15616 * q^56 - 90021 * q^57 - 10016 * q^58 + 36585 * q^59 - 37248 * q^60 + 43146 * q^61 - 40016 * q^62 - 52922 * q^63 - 12288 * q^64 - 133772 * q^65 - 211008 * q^66 + 325206 * q^67 + 6400 * q^68 - 103894 * q^69 + 68216 * q^70 - 172806 * q^71 - 4416 * q^72 + 49436 * q^73 - 464 * q^74 + 263915 * q^75 + 37920 * q^76 - 207094 * q^77 + 330000 * q^78 + 58364 * q^79 - 14336 * q^80 + 341038 * q^81 + 82836 * q^82 + 82035 * q^83 - 52288 * q^84 - 317604 * q^85 - 104380 * q^86 - 572732 * q^87 - 38336 * q^88 + 97958 * q^89 - 151672 * q^90 - 22162 * q^91 + 15072 * q^92 - 271316 * q^93 + 153720 * q^94 + 549736 * q^95 + 76403 * q^97 + 198656 * q^98 - 199487 * q^99

Introduction

L-functions

Modular forms

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