LMFDB - Embedded newform 570.2.u.f.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(-1.85844 - 3.21891i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.09240 + 1.12554i) q^{13} +(-0.0923963 - 0.524005i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.624485 + 0.524005i) q^{17} -1.00000 q^{18} +(4.21688 + 1.10359i) q^{19} -1.00000 q^{20} +(0.407604 - 0.342020i) q^{21} +(3.49273 + 1.27125i) q^{22} +(-1.01367 + 5.74881i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.64543 - 2.84997i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.407604 + 0.342020i) q^{28} +(-7.68139 - 6.44545i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.70574 + 8.15058i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.645430 + 3.66041i) q^{33} +(0.141559 - 0.802823i) q^{34} +(0.500000 + 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} -8.04189 q^{37} +(-3.93969 + 1.86516i) q^{38} +3.29086 q^{39} +(0.766044 - 0.642788i) q^{40} +(-9.69119 - 3.52730i) q^{41} +(-0.0923963 + 0.524005i) q^{42} +(0.768571 + 4.35878i) q^{43} +(-3.49273 + 1.27125i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-2.91875 - 5.05542i) q^{46} +(-8.35117 - 7.00746i) q^{47} +(0.766044 + 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.766044 - 0.278817i) q^{51} +(0.571452 + 3.24086i) q^{52} +(-0.180922 + 1.02606i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-2.84730 + 2.38917i) q^{55} -0.532089 q^{56} +(-3.58512 - 2.47929i) q^{57} +10.0273 q^{58} +(5.09627 - 4.27628i) q^{59} +(0.939693 + 0.342020i) q^{60} +(2.48886 - 14.1150i) q^{61} +(-1.63429 - 9.26849i) q^{62} +(-0.500000 + 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.64543 + 2.84997i) q^{65} +(-2.84730 - 2.38917i) q^{66} +(3.91740 + 3.28709i) q^{67} +(0.407604 + 0.705990i) q^{68} +(2.91875 - 5.05542i) q^{69} +(-0.500000 + 0.181985i) q^{70} +(0.595800 + 3.37895i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-1.02094 - 0.371593i) q^{73} +(6.16044 - 5.16923i) q^{74} +1.00000 q^{75} +(1.81908 - 3.96118i) q^{76} +1.97771 q^{77} +(-2.52094 + 2.11532i) q^{78} +(-11.8623 - 4.31753i) q^{79} +(-0.173648 + 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(9.69119 - 3.52730i) q^{82} +(-9.02141 + 15.6255i) q^{83} +(-0.266044 - 0.460802i) q^{84} +(0.624485 + 0.524005i) q^{85} +(-3.39053 - 2.84499i) q^{86} +(5.01367 + 8.68393i) q^{87} +(1.85844 - 3.21891i) q^{88} +(-3.60607 + 1.31250i) q^{89} +(0.173648 + 0.984808i) q^{90} +(0.304063 - 1.72443i) q^{91} +(5.48545 + 1.99654i) q^{92} +(7.20961 - 6.04958i) q^{93} +10.9017 q^{94} +(0.354570 - 4.34445i) q^{95} -1.00000 q^{96} +(2.01501 - 1.69080i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(0.645430 - 3.66041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 15 q^{13} + 3 q^{14} + 9 q^{17} - 6 q^{18} + 9 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{30} - 18 q^{31} - 12 q^{33} + 9 q^{34} + 3 q^{35} - 42 q^{37} - 18 q^{38} - 12 q^{39} - 12 q^{41} + 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} - 15 q^{46} - 24 q^{47} + 12 q^{49} + 3 q^{50} + 3 q^{52} - 18 q^{53} - 15 q^{55} + 6 q^{56} + 18 q^{58} + 3 q^{59} + 21 q^{61} - 3 q^{63} - 3 q^{64} - 6 q^{65} - 15 q^{66} + 30 q^{67} + 6 q^{68} + 15 q^{69} - 3 q^{70} + 42 q^{71} - 3 q^{73} - 9 q^{74} + 6 q^{75} - 6 q^{76} + 24 q^{77} - 12 q^{78} - 39 q^{79} + 12 q^{82} + 15 q^{83} + 3 q^{84} - 9 q^{85} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 3 q^{89} + 15 q^{91} - 3 q^{92} + 9 q^{93} + 42 q^{94} + 18 q^{95} - 6 q^{96} - 18 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 15 * q^13 + 3 * q^14 + 9 * q^17 - 6 * q^18 + 9 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^30 - 18 * q^31 - 12 * q^33 + 9 * q^34 + 3 * q^35 - 42 * q^37 - 18 * q^38 - 12 * q^39 - 12 * q^41 + 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 - 15 * q^46 - 24 * q^47 + 12 * q^49 + 3 * q^50 + 3 * q^52 - 18 * q^53 - 15 * q^55 + 6 * q^56 + 18 * q^58 + 3 * q^59 + 21 * q^61 - 3 * q^63 - 3 * q^64 - 6 * q^65 - 15 * q^66 + 30 * q^67 + 6 * q^68 + 15 * q^69 - 3 * q^70 + 42 * q^71 - 3 * q^73 - 9 * q^74 + 6 * q^75 - 6 * q^76 + 24 * q^77 - 12 * q^78 - 39 * q^79 + 12 * q^82 + 15 * q^83 + 3 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 3 * q^89 + 15 * q^91 - 3 * q^92 + 9 * q^93 + 42 * q^94 + 18 * q^95 - 6 * q^96 - 18 * q^97 - 3 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	0.766044	+	0.642788i	0.242245	+	0.203267i
$11$	−1.85844	−	3.21891i	−0.560341	−	0.970539i	−0.997466	−	0.0711385i	$-0.977337\pi$
$11$	−1.85844	−	3.21891i	−0.560341	−	0.970539i	0.437125	−	0.899401i	$-0.355997\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−3.09240	+	1.12554i	−0.857676	+	0.312169i	−0.733166	−	0.680050i	$-0.761958\pi$
$13$	−3.09240	+	1.12554i	−0.857676	+	0.312169i	−0.124510	+	0.992218i	$0.539736\pi$
$14$	−0.0923963	−	0.524005i	−0.0246939	−	0.140046i
$15$	−0.173648	+	0.984808i	−0.0448358	+	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.624485	+	0.524005i	−0.151460	+	0.127090i	−0.715369	−	0.698747i	$-0.753741\pi$
$17$	−0.624485	+	0.524005i	−0.151460	+	0.127090i	0.563909	+	0.825837i	$0.309297\pi$
$18$	−1.00000			−0.235702
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$19$	4.21688	+	1.10359i	0.967419	+	0.253181i
$20$	−1.00000			−0.223607
$21$	0.407604	−	0.342020i	0.0889464	−	0.0746349i
$22$	3.49273	+	1.27125i	0.744652	+	0.271031i
$23$	−1.01367	+	5.74881i	−0.211365	+	1.19871i	0.675739	+	0.737141i	$0.263825\pi$
$23$	−1.01367	+	5.74881i	−0.211365	+	1.19871i	−0.887104	+	0.461569i	$0.847287\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	1.64543	−	2.84997i	0.322695	−	0.558925i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.407604	+	0.342020i	0.0770299	+	0.0646357i
$29$	−7.68139	−	6.44545i	−1.42640	−	1.19689i	−0.947804	−	0.318854i	$-0.896702\pi$
$29$	−7.68139	−	6.44545i	−1.42640	−	1.19689i	−0.478594	−	0.878036i	$-0.658854\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.70574	+	8.15058i	−0.845175	+	1.46389i	0.0402935	+	0.999188i	$0.487171\pi$
$31$	−4.70574	+	8.15058i	−0.845175	+	1.46389i	−0.885469	+	0.464699i	$0.846163\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.645430	+	3.66041i	0.112355	+	0.637196i
$34$	0.141559	−	0.802823i	0.0242772	−	0.137683i
$35$	0.500000	+	0.181985i	0.0845154	+	0.0307611i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−8.04189			−1.32208			−0.661039	−	0.750351i	$-0.729884\pi$
$37$	−8.04189			−1.32208			−0.661039	+	0.750351i	$0.729884\pi$
$38$	−3.93969	+	1.86516i	−0.639103	+	0.302569i
$39$	3.29086			0.526959
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	−9.69119	−	3.52730i	−1.51351	−	0.550872i	−0.553992	−	0.832522i	$-0.686896\pi$
$41$	−9.69119	−	3.52730i	−1.51351	−	0.550872i	−0.959517	+	0.281650i	$0.909118\pi$
$42$	−0.0923963	+	0.524005i	−0.0142571	+	0.0808558i
$43$	0.768571	+	4.35878i	0.117206	+	0.664708i	0.985634	+	0.168893i	$0.0540193\pi$
$43$	0.768571	+	4.35878i	0.117206	+	0.664708i	−0.868428	+	0.495815i	$0.834870\pi$
$44$	−3.49273	+	1.27125i	−0.526548	+	0.191648i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−2.91875	−	5.05542i	−0.430346	−	0.745381i
$47$	−8.35117	−	7.00746i	−1.21814	−	1.02214i	−0.998920	−	0.0464685i	$-0.985203\pi$
$47$	−8.35117	−	7.00746i	−1.21814	−	1.02214i	−0.219223	−	0.975675i	$-0.570352\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.766044	−	0.278817i	0.107268	−	0.0390422i
$52$	0.571452	+	3.24086i	0.0792461	+	0.449427i
$53$	−0.180922	+	1.02606i	−0.0248516	+	0.140940i	−0.994709	−	0.102733i	$-0.967241\pi$
$53$	−0.180922	+	1.02606i	−0.0248516	+	0.140940i	0.969857	+	0.243673i	$0.0783524\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	−2.84730	+	2.38917i	−0.383929	+	0.322155i
$56$	−0.532089			−0.0711034
$57$	−3.58512	−	2.47929i	−0.474861	−	0.328390i
$58$	10.0273			1.31665
$59$	5.09627	−	4.27628i	0.663477	−	0.556724i	−0.247649	−	0.968850i	$-0.579658\pi$
$59$	5.09627	−	4.27628i	0.663477	−	0.556724i	0.911127	+	0.412126i	$0.135214\pi$
$60$	0.939693	+	0.342020i	0.121314	+	0.0441546i
$61$	2.48886	−	14.1150i	0.318665	−	1.80724i	−0.232224	−	0.972662i	$-0.574600\pi$
$61$	2.48886	−	14.1150i	0.318665	−	1.80724i	0.550889	−	0.834578i	$-0.314289\pi$
$62$	−1.63429	−	9.26849i	−0.207554	−	1.17710i
$63$	−0.500000	+	0.181985i	−0.0629941	+	0.0229280i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.64543	+	2.84997i	0.204090	+	0.353495i
$66$	−2.84730	−	2.38917i	−0.350478	−	0.294086i
$67$	3.91740	+	3.28709i	0.478587	+	0.401582i	0.849915	−	0.526919i	$-0.176653\pi$
$67$	3.91740	+	3.28709i	0.478587	+	0.401582i	−0.371328	+	0.928502i	$0.621098\pi$
$68$	0.407604	+	0.705990i	0.0494292	+	0.0856139i
$69$	2.91875	−	5.05542i	0.351376	−	0.608601i
$70$	−0.500000	+	0.181985i	−0.0597614	+	0.0217514i
$71$	0.595800	+	3.37895i	0.0707084	+	0.401007i	0.999535	+	0.0304926i	$0.00970761\pi$
$71$	0.595800	+	3.37895i	0.0707084	+	0.401007i	−0.928827	+	0.370515i	$0.879181\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	−1.02094	−	0.371593i	−0.119493	−	0.0434917i	0.281582	−	0.959537i	$-0.409141\pi$
$73$	−1.02094	−	0.371593i	−0.119493	−	0.0434917i	−0.401074	+	0.916045i	$0.631363\pi$
$74$	6.16044	−	5.16923i	0.716137	−	0.600910i
$75$	1.00000			0.115470
$76$	1.81908	−	3.96118i	0.208663	−	0.454379i
$77$	1.97771			0.225381
$78$	−2.52094	+	2.11532i	−0.285441	+	0.239513i
$79$	−11.8623	−	4.31753i	−1.33461	−	0.485760i	−0.426502	−	0.904487i	$-0.640254\pi$
$79$	−11.8623	−	4.31753i	−1.33461	−	0.485760i	−0.908112	+	0.418727i	$0.862477\pi$
$80$	−0.173648	+	0.984808i	−0.0194145	+	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	9.69119	−	3.52730i	1.07021	−	0.389526i
$83$	−9.02141	+	15.6255i	−0.990229	+	1.71513i	−0.374344	+	0.927290i	$0.622132\pi$
$83$	−9.02141	+	15.6255i	−0.990229	+	1.71513i	−0.615885	+	0.787836i	$0.711201\pi$
$84$	−0.266044	−	0.460802i	−0.0290278	−	0.0502777i
$85$	0.624485	+	0.524005i	0.0677349	+	0.0568364i
$86$	−3.39053	−	2.84499i	−0.365610	−	0.306783i
$87$	5.01367	+	8.68393i	0.537522	+	0.931015i
$88$	1.85844	−	3.21891i	0.198110	−	0.343137i
$89$	−3.60607	+	1.31250i	−0.382242	+	0.139125i	−0.525993	−	0.850489i	$-0.676306\pi$
$89$	−3.60607	+	1.31250i	−0.382242	+	0.139125i	0.143750	+	0.989614i	$0.454084\pi$
$90$	0.173648	+	0.984808i	0.0183041	+	0.103808i
$91$	0.304063	−	1.72443i	0.0318745	−	0.180769i
$92$	5.48545	+	1.99654i	0.571898	+	0.208154i
$93$	7.20961	−	6.04958i	0.747601	−	0.627312i
$94$	10.9017			1.12442
$95$	0.354570	−	4.34445i	0.0363781	−	0.445732i
$96$	−1.00000			−0.102062
$97$	2.01501	−	1.69080i	0.204594	−	0.171675i	−0.534734	−	0.845021i	$-0.679588\pi$
$97$	2.01501	−	1.69080i	0.204594	−	0.171675i	0.739327	+	0.673346i	$0.235144\pi$
$98$	−6.31180	−	2.29731i	−0.637588	−	0.232063i
$99$	0.645430	−	3.66041i	0.0648681	−	0.367885i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	12.1074	−	4.40674i	1.20473	−	0.438487i	0.339859	−	0.940476i	$-0.389621\pi$
$101$	12.1074	−	4.40674i	1.20473	−	0.438487i	0.864874	+	0.501990i	$0.167398\pi$
$102$	−0.407604	+	0.705990i	−0.0403588	+	0.0699035i
$103$	5.26264	+	9.11516i	0.518543	+	0.898144i	0.999768	+	0.0215461i	$0.00685887\pi$
$103$	5.26264	+	9.11516i	0.518543	+	0.898144i	−0.481224	+	0.876597i	$0.659808\pi$
$104$	−2.52094	−	2.11532i	−0.247199	−	0.207425i
$105$	−0.407604	−	0.342020i	−0.0397781	−	0.0333777i
$106$	−0.520945	−	0.902302i	−0.0505986	−	0.0876394i
$107$	−3.31908	+	5.74881i	−0.320867	+	0.555759i	−0.980667	−	0.195683i	$-0.937308\pi$
$107$	−3.31908	+	5.74881i	−0.320867	+	0.555759i	0.659800	+	0.751441i	$0.270641\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	1.97565	+	11.2045i	0.189233	+	1.07319i	0.920395	+	0.390990i	$0.127867\pi$
$109$	1.97565	+	11.2045i	0.189233	+	1.07319i	−0.731162	+	0.682204i	$0.761022\pi$
$110$	0.645430	−	3.66041i	0.0615393	−	0.349007i
$111$	7.55690	+	2.75049i	0.717270	+	0.261065i
$112$	0.407604	−	0.342020i	0.0385149	−	0.0323179i
$113$	2.45336			0.230793			0.115396	−	0.993320i	$-0.463186\pi$
$113$	2.45336			0.230793			0.115396	+	0.993320i	$0.463186\pi$
$114$	4.34002	−	0.405223i	0.406480	−	0.0379526i
$115$	5.83750			0.544349
$116$	−7.68139	+	6.44545i	−0.713199	+	0.598445i
$117$	−3.09240	−	1.12554i	−0.285892	−	0.104056i
$118$	−1.15523	+	6.55163i	−0.106348	+	0.603127i
$119$	−0.0753221	−	0.427173i	−0.00690477	−	0.0391589i
$120$	−0.939693	+	0.342020i	−0.0857818	+	0.0312220i
$121$	−1.40760	+	2.43804i	−0.127964	+	0.221640i
$122$	7.16637	+	12.4125i	0.648813	+	1.12378i
$123$	7.90033	+	6.62916i	0.712349	+	0.597732i
$124$	7.20961	+	6.04958i	0.647442	+	0.543268i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	0.266044	−	0.460802i	0.0237011	−	0.0410515i
$127$	2.31268	−	0.841747i	0.205217	−	0.0746930i	−0.237366	−	0.971420i	$-0.576284\pi$
$127$	2.31268	−	0.841747i	0.205217	−	0.0746930i	0.442584	+	0.896727i	$0.354062\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.768571	−	4.35878i	0.0676689	−	0.383769i
$130$	−3.09240	−	1.12554i	−0.271221	−	0.0987164i
$131$	4.34730	−	3.64781i	0.379825	−	0.318711i	−0.432809	−	0.901486i	$-0.642477\pi$
$131$	4.34730	−	3.64781i	0.379825	−	0.318711i	0.812634	+	0.582775i	$0.198033\pi$
$132$	3.71688			0.323513
$133$	−1.63041	+	1.64955i	−0.141375	+	0.143034i
$134$	−5.11381			−0.441766
$135$	−0.766044	+	0.642788i	−0.0659306	+	0.0553223i
$136$	−0.766044	−	0.278817i	−0.0656878	−	0.0239084i
$137$	3.47653	−	19.7164i	0.297020	−	1.68448i	−0.361857	−	0.932233i	$-0.617857\pi$
$137$	3.47653	−	19.7164i	0.297020	−	1.68448i	0.658877	−	0.752250i	$-0.271032\pi$
$138$	1.01367	+	5.74881i	0.0862894	+	0.489371i
$139$	10.0753	−	3.66712i	0.854578	−	0.311041i	0.122672	−	0.992447i	$-0.460854\pi$
$139$	10.0753	−	3.66712i	0.854578	−	0.311041i	0.731905	+	0.681406i	$0.238631\pi$
$140$	0.266044	−	0.460802i	0.0224849	−	0.0389449i
$141$	5.45084	+	9.44113i	0.459043	+	0.795086i
$142$	−2.62836	−	2.20545i	−0.220567	−	0.185077i
$143$	9.37005	+	7.86241i	0.783563	+	0.657488i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−5.01367	+	8.68393i	−0.416363	+	0.721161i
$146$	1.02094	−	0.371593i	0.0844940	−	0.0307533i
$147$	−1.16637	−	6.61484i	−0.0962009	−	0.545583i
$148$	−1.39646	+	7.91971i	−0.114788	+	0.650997i
$149$	0.405078	+	0.147436i	0.0331852	+	0.0120784i	0.358559	−	0.933507i	$-0.383268\pi$
$149$	0.405078	+	0.147436i	0.0331852	+	0.0120784i	−0.325374	+	0.945585i	$0.605490\pi$
$150$	−0.766044	+	0.642788i	−0.0625473	+	0.0524834i
$151$	11.1061			0.903799			0.451899	−	0.892069i	$-0.350747\pi$
$151$	11.1061			0.903799			0.451899	+	0.892069i	$0.350747\pi$
$152$	1.15270	+	4.20372i	0.0934966	+	0.340967i
$153$	−0.815207			−0.0659056
$154$	−1.51501	+	1.27125i	−0.122083	+	0.102440i
$155$	8.84389	+	3.21891i	0.710359	+	0.258549i
$156$	0.571452	−	3.24086i	0.0457528	−	0.259477i
$157$	−2.83363	−	16.0703i	−0.226148	−	1.28255i	−0.860478	−	0.509487i	$-0.829835\pi$
$157$	−2.83363	−	16.0703i	−0.226148	−	1.28255i	0.634331	−	0.773062i	$-0.281276\pi$
$158$	11.8623	−	4.31753i	0.943715	−	0.343484i
$159$	0.520945	−	0.902302i	0.0413136	−	0.0715572i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.37939	−	1.99654i	−0.187522	−	0.157349i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	−10.5778	−	18.3214i	−0.828521	−	1.43504i	−0.899198	−	0.437541i	$-0.855849\pi$
$163$	−10.5778	−	18.3214i	−0.828521	−	1.43504i	0.0706773	−	0.997499i	$-0.477484\pi$
$164$	−5.15657	+	8.93145i	−0.402661	+	0.697429i
$165$	3.49273	−	1.27125i	0.271908	−	0.0989665i
$166$	−3.13310	−	17.7687i	−0.243176	−	1.37912i
$167$	1.05556	−	5.98638i	0.0816817	−	0.463240i	−0.916342	−	0.400397i	$-0.868872\pi$
$167$	1.05556	−	5.98638i	0.0816817	−	0.463240i	0.998023	−	0.0628427i	$-0.0200167\pi$
$168$	0.500000	+	0.181985i	0.0385758	+	0.0140405i
$169$	−1.66250	+	1.39501i	−0.127885	+	0.107308i
$170$	−0.815207			−0.0625236
$171$	2.52094	+	3.55596i	0.192781	+	0.271931i
$172$	4.42602			0.337481
$173$	−11.2456	+	9.43615i	−0.854985	+	0.717417i	−0.960881	−	0.276960i	$-0.910673\pi$
$173$	−11.2456	+	9.43615i	−0.854985	+	0.717417i	0.105897	+	0.994377i	$0.466229\pi$
$174$	−9.42262	−	3.42955i	−0.714327	−	0.259994i
$175$	0.0923963	−	0.524005i	0.00698450	−	0.0396111i
$176$	0.645430	+	3.66041i	0.0486511	+	0.275914i
$177$	−6.25150	+	2.27536i	−0.469891	+	0.171026i
$178$	1.91875	−	3.32337i	0.143816	−	0.249097i
$179$	5.51754	+	9.55666i	0.412400	+	0.714298i	0.995152	−	0.0983522i	$-0.0313572\pi$
$179$	5.51754	+	9.55666i	0.412400	+	0.714298i	−0.582751	+	0.812651i	$0.698024\pi$
$180$	−0.766044	−	0.642788i	−0.0570976	−	0.0479106i
$181$	1.89053	+	1.58634i	0.140522	+	0.117912i	0.710339	−	0.703860i	$-0.248542\pi$
$181$	1.89053	+	1.58634i	0.140522	+	0.117912i	−0.569817	+	0.821771i	$0.692986\pi$
$182$	0.875515	+	1.51644i	0.0648975	+	0.112406i
$183$	−7.16637	+	12.4125i	−0.529754	+	0.917560i
$184$	−5.48545	+	1.99654i	−0.404393	+	0.147187i
$185$	1.39646	+	7.91971i	0.102670	+	0.582269i
$186$	−1.63429	+	9.26849i	−0.119832	+	0.679599i
$187$	2.84730	+	1.03633i	0.208215	+	0.0757840i
$188$	−8.35117	+	7.00746i	−0.609071	+	0.511072i
$189$	0.532089			0.0387038
$190$	2.52094	+	3.55596i	0.182889	+	0.257976i
$191$	6.14796			0.444850			0.222425	−	0.974950i	$-0.428603\pi$
$191$	6.14796			0.444850			0.222425	+	0.974950i	$0.428603\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	3.05051	+	1.11029i	0.219580	+	0.0799207i	0.449468	−	0.893296i	$-0.351614\pi$
$193$	3.05051	+	1.11029i	0.219580	+	0.0799207i	−0.229888	+	0.973217i	$0.573836\pi$
$194$	−0.456767	+	2.59045i	−0.0327939	+	0.185984i
$195$	−0.571452	−	3.24086i	−0.0409225	−	0.232083i
$196$	6.31180	−	2.29731i	0.450843	−	0.164093i
$197$	5.98932	−	10.3738i	0.426722	−	0.739103i	−0.569858	−	0.821743i	$-0.693002\pi$
$197$	5.98932	−	10.3738i	0.426722	−	0.739103i	0.996579	+	0.0826398i	$0.0263351\pi$
$198$	1.85844	+	3.21891i	0.132074	+	0.228758i
$199$	−13.0307	−	10.9341i	−0.923725	−	0.775097i	0.0509552	−	0.998701i	$-0.483773\pi$
$199$	−13.0307	−	10.9341i	−0.923725	−	0.775097i	−0.974680	+	0.223604i	$0.928218\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	−2.55690	−	4.42869i	−0.180350	−	0.312376i
$202$	−6.44222	+	11.1583i	−0.453273	+	0.785092i
$203$	5.01367	−	1.82483i	0.351891	−	0.128078i
$204$	−0.141559	−	0.802823i	−0.00991113	−	0.0562088i
$205$	−1.79086	+	10.1565i	−0.125079	+	0.709359i
$206$	−9.89053	−	3.59986i	−0.689106	−	0.250814i
$207$	−4.47178	+	3.75227i	−0.310810	+	0.260801i
$208$	3.29086			0.228180
$209$	−4.28446	−	15.6247i	−0.296362	−	1.08079i
$210$	0.532089			0.0367176
$211$	6.47178	−	5.43047i	0.445536	−	0.373849i	−0.392240	−	0.919863i	$-0.628300\pi$
$211$	6.47178	−	5.43047i	0.445536	−	0.373849i	0.837776	+	0.546014i	$0.183855\pi$
$212$	0.979055	+	0.356347i	0.0672418	+	0.0244740i
$213$	0.595800	−	3.37895i	0.0408235	−	0.231522i
$214$	−1.15270	−	6.53731i	−0.0787972	−	0.446881i
$215$	4.15910	−	1.51379i	0.283648	−	0.103240i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−2.50387	−	4.33683i	−0.169974	−	0.294403i
$218$	−8.71554	−	7.31320i	−0.590291	−	0.495313i
$219$	0.832282	+	0.698367i	0.0562404	+	0.0471913i
$220$	1.85844	+	3.21891i	0.125296	+	0.217019i
$221$	1.34137	−	2.32332i	0.0902301	−	0.156283i
$222$	−7.55690	+	2.75049i	−0.507186	+	0.184601i
$223$	−1.19800	−	6.79417i	−0.0802238	−	0.454972i	−0.998285	−	0.0585339i	$-0.981357\pi$
$223$	−1.19800	−	6.79417i	−0.0802238	−	0.454972i	0.918062	−	0.396438i	$-0.129754\pi$
$224$	−0.0923963	+	0.524005i	−0.00617349	+	0.0350116i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	−1.87939	+	1.57699i	−0.125015	+	0.104900i
$227$	14.3182			0.950332			0.475166	−	0.879896i	$-0.342388\pi$
$227$	14.3182			0.950332			0.475166	+	0.879896i	$0.342388\pi$
$228$	−3.06418	+	3.10013i	−0.202930	+	0.205311i
$229$	−14.6236			−0.966355			−0.483178	−	0.875522i	$-0.660517\pi$
$229$	−14.6236			−0.966355			−0.483178	+	0.875522i	$0.660517\pi$
$230$	−4.47178	+	3.75227i	−0.294861	+	0.247417i
$231$	−1.85844	−	0.676417i	−0.122276	−	0.0445050i
$232$	1.74123	−	9.87500i	0.114317	−	0.648326i
$233$	0.554378	+	3.14403i	0.0363185	+	0.205972i	0.997567	−	0.0697099i	$-0.0222074\pi$
$233$	0.554378	+	3.14403i	0.0363185	+	0.205972i	−0.961249	+	0.275682i	$0.911096\pi$
$234$	3.09240	−	1.12554i	0.202156	−	0.0735789i
$235$	−5.45084	+	9.44113i	−0.355573	+	0.615871i
$236$	−3.32635	−	5.76141i	−0.216527	−	0.375036i
$237$	9.67024	+	8.11430i	0.628150	+	0.527080i
$238$	0.332282	+	0.278817i	0.0215386	+	0.0180730i
$239$	9.84002	+	17.0434i	0.636498	+	1.10245i	0.986196	+	0.165584i	$0.0529510\pi$
$239$	9.84002	+	17.0434i	0.636498	+	1.10245i	−0.349697	+	0.936863i	$0.613716\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−11.0287	+	4.01411i	−0.710420	+	0.258572i	−0.671853	−	0.740684i	$-0.734501\pi$
$241$	−11.0287	+	4.01411i	−0.710420	+	0.258572i	−0.0385668	+	0.999256i	$0.512279\pi$
$242$	−0.488856	−	2.77244i	−0.0314248	−	0.178219i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	−13.4684	−	4.90209i	−0.862225	−	0.313824i
$245$	5.14543	−	4.31753i	0.328729	−	0.275837i
$246$	−10.3131			−0.657542
$247$	−14.2824	+	1.33353i	−0.908768	+	0.0848506i
$248$	−9.41147			−0.597629
$249$	13.8216	−	11.5977i	0.875909	−	0.734975i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	−3.12108	+	17.7005i	−0.197001	+	1.11725i	0.712539	+	0.701632i	$0.247545\pi$
$251$	−3.12108	+	17.7005i	−0.197001	+	1.11725i	−0.909540	+	0.415616i	$0.863566\pi$
$252$	0.0923963	+	0.524005i	0.00582042	+	0.0330092i
$253$	20.3888	−	7.42091i	1.28183	−	0.466548i
$254$	−1.23055	+	2.13138i	−0.0772117	+	0.133735i
$255$	−0.407604	−	0.705990i	−0.0255251	−	0.0442108i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−23.2108	−	19.4762i	−1.44785	−	1.21489i	−0.934131	−	0.356931i	$-0.883823\pi$
$257$	−23.2108	−	19.4762i	−1.44785	−	1.21489i	−0.513719	−	0.857959i	$-0.671732\pi$
$258$	2.21301	+	3.83305i	0.137776	+	0.238635i
$259$	2.13950	−	3.70572i	0.132942	−	0.230262i
$260$	3.09240	−	1.12554i	0.191782	−	0.0698030i
$261$	−1.74123	−	9.87500i	−0.107779	−	0.611247i
$262$	−0.985452	+	5.58878i	−0.0608814	+	0.345276i
$263$	14.6420	+	5.32926i	0.902866	+	0.328616i	0.751401	−	0.659846i	$-0.229379\pi$
$263$	14.6420	+	5.32926i	0.902866	+	0.328616i	0.151465	+	0.988463i	$0.451601\pi$
$264$	−2.84730	+	2.38917i	−0.175239	+	0.147043i
$265$	1.04189			0.0640027
$266$	0.188663	−	2.31164i	0.0115677	−	0.141735i
$267$	3.83750			0.234851
$268$	3.91740	−	3.28709i	0.239294	−	0.200791i
$269$	−24.2592	−	8.82964i	−1.47911	−	0.538353i	−0.528554	−	0.848900i	$-0.677266\pi$
$269$	−24.2592	−	8.82964i	−1.47911	−	0.538353i	−0.950558	+	0.310547i	$0.899488\pi$
$270$	0.173648	−	0.984808i	0.0105679	−	0.0599335i
$271$	−2.19846	−	12.4681i	−0.133547	−	0.757383i	−0.975860	−	0.218395i	$-0.929918\pi$
$271$	−2.19846	−	12.4681i	−0.133547	−	0.757383i	0.842313	−	0.538988i	$-0.181193\pi$
$272$	0.766044	−	0.278817i	0.0464483	−	0.0169058i
$273$	−0.875515	+	1.51644i	−0.0529886	+	0.0917789i
$274$	10.0103	+	17.3383i	0.604742	+	1.04744i
$275$	2.84730	+	2.38917i	0.171698	+	0.144072i
$276$	−4.47178	−	3.75227i	−0.269170	−	0.225860i
$277$	−10.7267	−	18.5792i	−0.644504	−	1.11631i	−0.984416	−	0.175856i	$-0.943731\pi$
$277$	−10.7267	−	18.5792i	−0.644504	−	1.11631i	0.339912	−	0.940457i	$-0.389603\pi$
$278$	−5.36097	+	9.28547i	−0.321529	+	0.556905i
$279$	−8.84389	+	3.21891i	−0.529470	+	0.192711i
$280$	0.0923963	+	0.524005i	0.00552173	+	0.0313153i
$281$	1.57604	−	8.93815i	0.0940185	−	0.533205i	−0.901025	−	0.433767i	$-0.857184\pi$
$281$	1.57604	−	8.93815i	0.0940185	−	0.533205i	0.995044	−	0.0994387i	$-0.0317047\pi$
$282$	−10.2442	−	3.72859i	−0.610035	−	0.222034i
$283$	15.0025	−	12.5886i	0.891808	−	0.748315i	−0.0767643	−	0.997049i	$-0.524459\pi$
$283$	15.0025	−	12.5886i	0.891808	−	0.748315i	0.968572	+	0.248734i	$0.0800144\pi$
$284$	3.43107			0.203597
$285$	−1.81908	+	3.96118i	−0.107753	+	0.234640i
$286$	−12.2317			−0.723278
$287$	4.20368	−	3.52730i	0.248135	−	0.208210i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	−2.83662	+	16.0873i	−0.166860	+	0.946310i
$290$	−1.74123	−	9.87500i	−0.102249	−	0.579880i
$291$	−2.47178	+	0.899655i	−0.144898	+	0.0527387i
$292$	−0.543233	+	0.940908i	−0.0317903	+	0.0550625i
$293$	4.17365	+	7.22897i	0.243827	+	0.422321i	0.961801	−	0.273749i	$-0.0882637\pi$
$293$	4.17365	+	7.22897i	0.243827	+	0.422321i	−0.717974	+	0.696070i	$0.754930\pi$
$294$	5.14543	+	4.31753i	0.300088	+	0.251803i
$295$	−5.09627	−	4.27628i	−0.296716	−	0.248974i
$296$	−4.02094	−	6.96448i	−0.233713	−	0.404802i
$297$	−1.85844	+	3.21891i	−0.107838	+	0.186780i
$298$	−0.405078	+	0.147436i	−0.0234655	+	0.00854075i
$299$	−3.33585	−	18.9185i	−0.192917	−	1.09409i
$300$	0.173648	−	0.984808i	0.0100256	−	0.0568579i
$301$	−2.21301	−	0.805470i	−0.127556	−	0.0464265i
$302$	−8.50774	+	7.13884i	−0.489565	+	0.410794i
$303$	−12.8844			−0.740192
$304$	−3.58512	−	2.47929i	−0.205621	−	0.142197i
$305$	−14.3327			−0.820691
$306$	0.624485	−	0.524005i	0.0356994	−	0.0299554i
$307$	−18.2160	−	6.63008i	−1.03964	−	0.378399i	−0.234898	−	0.972020i	$-0.575476\pi$
$307$	−18.2160	−	6.63008i	−1.03964	−	0.378399i	−0.804745	+	0.593621i	$0.797698\pi$
$308$	0.343426	−	1.94767i	0.0195685	−	0.110979i
$309$	−1.82770	−	10.3654i	−0.103974	−	0.589666i
$310$	−8.84389	+	3.21891i	−0.502299	+	0.182822i
$311$	−10.3045	+	17.8480i	−0.584316	+	1.01207i	0.410644	+	0.911796i	$0.365304\pi$
$311$	−10.3045	+	17.8480i	−0.584316	+	1.01207i	−0.994960	+	0.100270i	$0.968029\pi$
$312$	1.64543	+	2.84997i	0.0931541	+	0.161348i
$313$	−17.4179	−	14.6153i	−0.984516	−	0.826107i	0.000248337	−	1.00000i	$-0.499921\pi$
$313$	−17.4179	−	14.6153i	−0.984516	−	0.826107i	−0.984765	+	0.173893i	$0.944365\pi$
$314$	12.5005	+	10.4891i	0.705442	+	0.591936i
$315$	0.266044	+	0.460802i	0.0149899	+	0.0259633i
$316$	−6.31180	+	10.9324i	−0.355067	+	0.614994i
$317$	7.24422	−	2.63668i	0.406876	−	0.148091i	−0.130471	−	0.991452i	$-0.541649\pi$
$317$	7.24422	−	2.63668i	0.406876	−	0.148091i	0.537347	+	0.843361i	$0.319427\pi$
$318$	0.180922	+	1.02606i	0.0101456	+	0.0575386i
$319$	−6.47194	+	36.7042i	−0.362359	+	2.05504i
$320$	0.939693	+	0.342020i	0.0525304	+	0.0191195i
$321$	5.08512	−	4.26692i	0.283824	−	0.238156i
$322$	3.10607			0.173094
$323$	−3.21167	+	1.52049i	−0.178702	+	0.0846025i
$324$	1.00000			0.0555556
$325$	2.52094	−	2.11532i	0.139837	−	0.117337i
$326$	19.8799	+	7.23567i	1.10104	+	0.400747i
$327$	1.97565	−	11.2045i	0.109254	−	0.619609i
$328$	−1.79086	−	10.1565i	−0.0988837	−	0.560797i
$329$	5.45084	−	1.98394i	0.300514	−	0.109378i
$330$	−1.85844	+	3.21891i	−0.102304	+	0.177195i
$331$	−3.48633	−	6.03850i	−0.191626	−	0.331906i	0.754163	−	0.656687i	$-0.228043\pi$
$331$	−3.48633	−	6.03850i	−0.191626	−	0.331906i	−0.945789	+	0.324781i	$0.894709\pi$
$332$	13.8216	+	11.5977i	0.758559	+	0.636507i
$333$	−6.16044	−	5.16923i	−0.337590	−	0.283272i
$334$	3.03936	+	5.26433i	0.166307	+	0.288051i
$335$	2.55690	−	4.42869i	0.139699	−	0.241965i
$336$	−0.500000	+	0.181985i	−0.0272772	+	0.00992810i
$337$	4.02734	+	22.8402i	0.219383	+	1.24418i	0.873136	+	0.487476i	$0.162082\pi$
$337$	4.02734	+	22.8402i	0.219383	+	1.24418i	−0.653753	+	0.756708i	$0.726806\pi$
$338$	0.376859	−	2.13727i	0.0204984	−	0.116252i
$339$	−2.30541	−	0.839100i	−0.125213	−	0.0455736i
$340$	0.624485	−	0.524005i	0.0338675	−	0.0284182i
$341$	34.9813			1.89435
$342$	−4.21688	−	1.10359i	−0.228023	−	0.0596753i
$343$	−7.29860			−0.394087
$344$	−3.39053	+	2.84499i	−0.182805	+	0.153392i
$345$	−5.48545	−	1.99654i	−0.295327	−	0.107490i
$346$	2.54916	−	14.4570i	0.137044	−	0.777214i
$347$	−0.192066	−	1.08926i	−0.0103107	−	0.0584747i	0.979218	−	0.202809i	$-0.0650071\pi$
$347$	−0.192066	−	1.08926i	−0.0103107	−	0.0584747i	−0.989529	+	0.144334i	$0.953896\pi$
$348$	9.42262	−	3.42955i	0.505105	−	0.183843i
$349$	−13.8293	+	23.9531i	−0.740268	+	1.28218i	0.212105	+	0.977247i	$0.431968\pi$
$349$	−13.8293	+	23.9531i	−0.740268	+	1.28218i	−0.952373	+	0.304935i	$0.901365\pi$
$350$	0.266044	+	0.460802i	0.0142207	+	0.0246309i
$351$	2.52094	+	2.11532i	0.134558	+	0.112908i
$352$	−2.84730	−	2.38917i	−0.151761	−	0.127343i
$353$	5.02734	+	8.70761i	0.267578	+	0.463459i	0.968236	−	0.250038i	$-0.0804432\pi$
$353$	5.02734	+	8.70761i	0.267578	+	0.463459i	−0.700658	+	0.713498i	$0.747110\pi$
$354$	3.32635	−	5.76141i	0.176794	−	0.306216i
$355$	3.22416	−	1.17350i	0.171120	−	0.0622827i
$356$	0.666374	+	3.77920i	0.0353178	+	0.200297i
$357$	−0.0753221	+	0.427173i	−0.00398647	+	0.0226084i
$358$	−10.3696	−	3.77422i	−0.548050	−	0.199474i
$359$	14.3537	−	12.0442i	0.757559	−	0.635667i	−0.179931	−	0.983679i	$-0.557588\pi$
$359$	14.3537	−	12.0442i	0.757559	−	0.635667i	0.937490	+	0.348012i	$0.113143\pi$
$360$	1.00000			0.0527046
$361$	16.5642	+	9.30742i	0.871799	+	0.489864i
$362$	−2.46791			−0.129711
$363$	2.15657	−	1.80958i	0.113191	−	0.0949783i
$364$	−1.64543	−	0.598887i	−0.0862439	−	0.0313902i
$365$	−0.188663	+	1.06996i	−0.00987507	+	0.0560043i
$366$	−2.48886	−	14.1150i	−0.130095	−	0.737803i
$367$	−31.8187	+	11.5810i	−1.66092	+	0.604526i	−0.990507	−	0.137462i	$-0.956106\pi$
$367$	−31.8187	+	11.5810i	−1.66092	+	0.604526i	−0.670414	+	0.741987i	$0.733883\pi$
$368$	2.91875	−	5.05542i	0.152150	−	0.263532i
$369$	−5.15657	−	8.93145i	−0.268441	−	0.464953i
$370$	−6.16044	−	5.16923i	−0.320266	−	0.268735i
$371$	−0.424678	−	0.356347i	−0.0220482	−	0.0185006i
$372$	−4.70574	−	8.15058i	−0.243981	−	0.422588i
$373$	0.300660	−	0.520758i	0.0155676	−	0.0269638i	−0.858137	−	0.513421i	$-0.828378\pi$
$373$	0.300660	−	0.520758i	0.0155676	−	0.0269638i	0.873704	+	0.486458i	$0.161711\pi$
$374$	−2.84730	+	1.03633i	−0.147230	+	0.0535874i
$375$	−0.173648	−	0.984808i	−0.00896715	−	0.0508553i
$376$	1.89306	−	10.7361i	0.0976269	−	0.553670i
$377$	31.0085	+	11.2862i	1.59702	+	0.581268i
$378$	−0.407604	+	0.342020i	−0.0209649	+	0.0175916i
$379$	1.82976			0.0939882			0.0469941	−	0.998895i	$-0.485036\pi$
$379$	1.82976			0.0939882			0.0469941	+	0.998895i	$0.485036\pi$
$380$	−4.21688	−	1.10359i	−0.216321	−	0.0566130i
$381$	−2.46110			−0.126086
$382$	−4.70961	+	3.95183i	−0.240964	+	0.202193i
$383$	−28.3653	−	10.3241i	−1.44940	−	0.527538i	−0.506976	−	0.861960i	$-0.669237\pi$
$383$	−28.3653	−	10.3241i	−1.44940	−	0.527538i	−0.942423	+	0.334422i	$0.891459\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−0.343426	−	1.94767i	−0.0175026	−	0.0992622i
$386$	−3.05051	+	1.11029i	−0.155267	+	0.0565125i
$387$	−2.21301	+	3.83305i	−0.112494	+	0.194845i
$388$	−1.31521	−	2.27801i	−0.0667695	−	0.115648i
$389$	−2.17886	−	1.82828i	−0.110473	−	0.0926976i	0.585878	−	0.810399i	$-0.300750\pi$
$389$	−2.17886	−	1.82828i	−0.110473	−	0.0926976i	−0.696351	+	0.717702i	$0.745194\pi$
$390$	2.52094	+	2.11532i	0.127653	+	0.107114i
$391$	−2.37939	−	4.12122i	−0.120331	−	0.208419i
$392$	−3.35844	+	5.81699i	−0.169627	+	0.293802i
$393$	−5.33275	+	1.94096i	−0.269002	+	0.0979086i
$394$	2.08007	+	11.7967i	0.104792	+	0.594307i
$395$	−2.19207	+	12.4318i	−0.110295	+	0.625513i
$396$	−3.49273	−	1.27125i	−0.175516	−	0.0638826i
$397$	7.22462	−	6.06218i	0.362593	−	0.304252i	−0.443230	−	0.896408i	$-0.646168\pi$
$397$	7.22462	−	6.06218i	0.362593	−	0.304252i	0.805823	+	0.592156i	$0.201723\pi$
$398$	17.0104			0.852656
$399$	2.09627	−	0.992431i	0.104945	−	0.0496837i
$400$	1.00000			0.0500000
$401$	8.69640	−	7.29715i	0.434278	−	0.364402i	−0.399285	−	0.916827i	$-0.630742\pi$
$401$	8.69640	−	7.29715i	0.434278	−	0.364402i	0.833563	+	0.552425i	$0.186297\pi$
$402$	4.80541	+	1.74903i	0.239672	+	0.0872334i
$403$	5.37820	−	30.5013i	0.267907	−	1.51938i
$404$	−2.23736	−	12.6887i	−0.111313	−	0.631286i
$405$	0.939693	−	0.342020i	0.0466937	−	0.0169951i
$406$	−2.66772	+	4.62062i	−0.132397	+	0.229318i
$407$	14.9454	+	25.8861i	0.740815	+	1.28313i
$408$	0.624485	+	0.524005i	0.0309166	+	0.0259421i
$409$	12.6079	+	10.5793i	0.623419	+	0.523111i	0.898876	−	0.438202i	$-0.144385\pi$
$409$	12.6079	+	10.5793i	0.623419	+	0.523111i	−0.275457	+	0.961313i	$0.588829\pi$
$410$	−5.15657	−	8.93145i	−0.254665	−	0.441093i
$411$	−10.0103	+	17.3383i	−0.493770	+	0.855235i
$412$	9.89053	−	3.59986i	0.487271	−	0.177352i
$413$	0.614685	+	3.48605i	0.0302467	+	0.171537i
$414$	1.01367	−	5.74881i	0.0498192	−	0.282539i
$415$	16.9547	+	6.17101i	0.832274	+	0.302923i
$416$	−2.52094	+	2.11532i	−0.123599	+	0.103712i
$417$	−10.7219			−0.525055
$418$	13.3255	+	9.21524i	0.651770	+	0.450732i
$419$	0.00505244			0.000246828			0.000123414	−	1.00000i	$-0.499961\pi$
$419$	0.00505244			0.000246828			0.000123414		1.00000i	$0.499961\pi$
$420$	−0.407604	+	0.342020i	−0.0198890	+	0.0166889i
$421$	−10.3366	−	3.76222i	−0.503776	−	0.183359i	0.0776156	−	0.996983i	$-0.475269\pi$
$421$	−10.3366	−	3.76222i	−0.503776	−	0.183359i	−0.581392	+	0.813624i	$0.697492\pi$
$422$	−1.46703	+	8.31996i	−0.0714141	+	0.405009i
$423$	−1.89306	−	10.7361i	−0.0920435	−	0.522005i
$424$	−0.979055	+	0.356347i	−0.0475471	+	0.0173057i
$425$	0.407604	−	0.705990i	0.0197717	−	0.0342456i
$426$	1.71554	+	2.97140i	0.0831181	+	0.143965i
$427$	5.84208	+	4.90209i	0.282718	+	0.237229i
$428$	5.08512	+	4.26692i	0.245799	+	0.206250i
$429$	−6.11587	−	10.5930i	−0.295277	−	0.511434i
$430$	−2.21301	+	3.83305i	−0.106721	+	0.184846i
$431$	−33.6313	+	12.2408i	−1.61997	+	0.589619i	−0.983375	−	0.181584i	$-0.941878\pi$
$431$	−33.6313	+	12.2408i	−1.61997	+	0.589619i	−0.636590	+	0.771203i	$0.719655\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	4.05762	−	23.0119i	0.194997	−	1.10588i	−0.717427	−	0.696634i	$-0.754680\pi$
$433$	4.05762	−	23.0119i	0.194997	−	1.10588i	0.912423	−	0.409247i	$-0.134209\pi$
$434$	4.70574	+	1.71275i	0.225883	+	0.0822145i
$435$	7.68139	−	6.44545i	0.368294	−	0.309036i
$436$	11.3773			0.544875
$437$	−10.6189	+	23.1234i	−0.507969	+	1.10614i
$438$	−1.08647			−0.0519134
$439$	14.3229	−	12.0184i	0.683597	−	0.573606i	−0.233458	−	0.972367i	$-0.575004\pi$
$439$	14.3229	−	12.0184i	0.683597	−	0.573606i	0.917055	+	0.398761i	$0.130560\pi$
$440$	−3.49273	−	1.27125i	−0.166509	−	0.0606044i
$441$	−1.16637	+	6.61484i	−0.0555416	+	0.314992i
$442$	0.465852	+	2.64198i	0.0221583	+	0.125666i
$443$	10.4667	−	3.80958i	0.497289	−	0.180999i	−0.0811851	−	0.996699i	$-0.525870\pi$
$443$	10.4667	−	3.80958i	0.497289	−	0.180999i	0.578474	+	0.815701i	$0.303648\pi$
$444$	4.02094	−	6.96448i	0.190826	−	0.330520i
$445$	1.91875	+	3.32337i	0.0909574	+	0.157543i
$446$	5.28493	+	4.43458i	0.250249	+	0.209984i
$447$	−0.330222	−	0.277089i	−0.0156190	−	0.0131059i
$448$	−0.266044	−	0.460802i	−0.0125694	−	0.0217709i
$449$	−17.8576	+	30.9302i	−0.842751	+	1.45969i	0.0448100	+	0.998996i	$0.485732\pi$
$449$	−17.8576	+	30.9302i	−0.842751	+	1.45969i	−0.887560	+	0.460691i	$0.847602\pi$
$450$	0.939693	−	0.342020i	0.0442975	−	0.0161230i
$451$	6.65641	+	37.7504i	0.313438	+	1.77760i
$452$	0.426022	−	2.41609i	0.0200384	−	0.113643i
$453$	−10.4363	−	3.79850i	−0.490340	−	0.178469i
$454$	−10.9684	+	9.20356i	−0.514771	+	0.431945i
$455$	−1.75103			−0.0820895
$456$	0.354570	−	4.34445i	0.0166043	−	0.203448i
$457$	30.8161			1.44152			0.720759	−	0.693186i	$-0.243793\pi$
$457$	30.8161			1.44152			0.720759	+	0.693186i	$0.243793\pi$
$458$	11.2023	−	9.39987i	0.523451	−	0.439227i
$459$	0.766044	+	0.278817i	0.0357559	+	0.0130141i
$460$	1.01367	−	5.74881i	0.0472626	−	0.268040i
$461$	0.509962	+	2.89214i	0.0237513	+	0.134700i	0.994378	−	0.105891i	$-0.0337696\pi$
$461$	0.509962	+	2.89214i	0.0237513	+	0.134700i	−0.970626	+	0.240592i	$0.922658\pi$
$462$	1.85844	−	0.676417i	0.0864625	−	0.0314698i
$463$	3.82753	−	6.62948i	0.177881	−	0.308098i	−0.763274	−	0.646075i	$-0.776409\pi$
$463$	3.82753	−	6.62948i	0.177881	−	0.308098i	0.941154	+	0.337977i	$0.109743\pi$
$464$	5.01367	+	8.68393i	0.232754	+	0.403141i
$465$	−7.20961	−	6.04958i	−0.334338	−	0.280543i
$466$	−2.44562	−	2.05212i	−0.113291	−	0.0950627i
$467$	−5.92649	−	10.2650i	−0.274245	−	0.475007i	0.695699	−	0.718333i	$-0.255095\pi$
$467$	−5.92649	−	10.2650i	−0.274245	−	0.475007i	−0.969944	+	0.243327i	$0.921761\pi$
$468$	−1.64543	+	2.84997i	−0.0760600	+	0.131740i
$469$	−2.55690	+	0.930637i	−0.118067	+	0.0429728i
$470$	−1.89306	−	10.7361i	−0.0873202	−	0.495217i
$471$	−2.83363	+	16.0703i	−0.130567	+	0.740480i
$472$	6.25150	+	2.27536i	0.287748	+	0.104732i
$473$	12.6022	−	10.5745i	0.579450	−	0.486216i
$474$	−12.6236			−0.579822
$475$	−4.34002	+	0.405223i	−0.199134	+	0.0185929i
$476$	−0.433763			−0.0198815
$477$	−0.798133	+	0.669713i	−0.0365440	+	0.0306641i
$478$	−18.4932	−	6.73097i	−0.845859	−	0.307867i
$479$	−1.34848	+	7.64760i	−0.0616136	+	0.349428i	0.938379	+	0.345608i	$0.112327\pi$
$479$	−1.34848	+	7.64760i	−0.0616136	+	0.349428i	−0.999993	+	0.00382028i	$0.998784\pi$
$480$	0.173648	+	0.984808i	0.00792592	+	0.0449501i
$481$	24.8687	−	9.05147i	1.13392	−	0.412711i
$482$	5.86824	−	10.1641i	0.267291	−	0.462962i
$483$	1.55303	+	2.68993i	0.0706655	+	0.122396i
$484$	2.15657	+	1.80958i	0.0980261	+	0.0822537i
$485$	−2.01501	−	1.69080i	−0.0914971	−	0.0767752i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−0.476529	+	0.825373i	−0.0215936	+	0.0374012i	−0.876620	−	0.481183i	$-0.840207\pi$
$487$	−0.476529	+	0.825373i	−0.0215936	+	0.0374012i	0.855027	+	0.518584i	$0.173541\pi$
$488$	13.4684	−	4.90209i	0.609685	−	0.221907i
$489$	3.67365	+	20.8343i	0.166128	+	0.942159i
$490$	−1.16637	+	6.61484i	−0.0526914	+	0.298828i
$491$	19.5116	+	7.10165i	0.880547	+	0.320493i	0.742430	−	0.669923i	$-0.233673\pi$
$491$	19.5116	+	7.10165i	0.880547	+	0.320493i	0.138116	+	0.990416i	$0.455895\pi$
$492$	7.90033	−	6.62916i	0.356174	−	0.298866i
$493$	8.17436			0.368155
$494$	10.0838	−	10.2021i	0.453691	−	0.459014i
$495$	−3.71688			−0.167061
$496$	7.20961	−	6.04958i	0.323721	−	0.271634i
$497$	−1.71554	−	0.624404i	−0.0769524	−	0.0280084i
$498$	−3.13310	+	17.7687i	−0.140398	+	0.796235i
$499$	0.980238	+	5.55920i	0.0438815	+	0.248864i	0.998856	−	0.0478244i	$-0.0152288\pi$
$499$	0.980238	+	5.55920i	0.0438815	+	0.248864i	−0.954974	+	0.296689i	$0.904118\pi$
$500$	0.939693	−	0.342020i	0.0420243	−	0.0152956i
$501$	−3.03936	+	5.26433i	−0.135789	+	0.235193i
$502$	−8.98680	−	15.5656i	−0.401100	−	0.694726i
$503$	7.12701	+	5.98027i	0.317778	+	0.266647i	0.787698	−	0.616062i	$-0.211273\pi$
$503$	7.12701	+	5.98027i	0.317778	+	0.266647i	−0.469920	+	0.882709i	$0.655717\pi$
$504$	−0.407604	−	0.342020i	−0.0181561	−	0.0152348i
$505$	−6.44222	−	11.1583i	−0.286675	−	0.496536i
$506$	−10.8486	+	18.7904i	−0.482281	+	0.835335i
$507$	2.03936	−	0.742267i	0.0905713	−	0.0329653i
$508$	−0.427366	−	2.42371i	−0.0189613	−	0.107535i
$509$	4.31315	−	24.4611i	0.191177	−	1.08422i	−0.726582	−	0.687080i	$-0.758892\pi$
$509$	4.31315	−	24.4611i	0.191177	−	1.08422i	0.917759	−	0.397138i	$-0.129997\pi$
$510$	0.766044	+	0.278817i	0.0339210	+	0.0123462i
$511$	0.442848	−	0.371593i	0.0195904	−	0.0164383i
$512$	−1.00000			−0.0441942
$513$	−1.15270	−	4.20372i	−0.0508931	−	0.185599i
$514$	30.2995			1.33646
$515$	8.06283	−	6.76552i	0.355291	−	0.298124i
$516$	−4.15910	−	1.51379i	−0.183094	−	0.0666408i
$517$	−7.03626	+	39.9046i	−0.309455	+	1.75500i
$518$	0.743041	+	4.21399i	0.0326473	+	0.185152i
$519$	13.7947	−	5.02087i	0.605521	−	0.220392i
$520$	−1.64543	+	2.84997i	−0.0721569	+	0.124979i
$521$	0.896926	+	1.55352i	0.0392951	+	0.0680610i	0.885004	−	0.465583i	$-0.154155\pi$
$521$	0.896926	+	1.55352i	0.0392951	+	0.0680610i	−0.845709	+	0.533644i	$0.820822\pi$
$522$	7.68139	+	6.44545i	0.336205	+	0.282110i
$523$	−21.5089	−	18.0481i	−0.940520	−	0.789190i	0.0371561	−	0.999309i	$-0.488170\pi$
$523$	−21.5089	−	18.0481i	−0.940520	−	0.789190i	−0.977676	+	0.210120i	$0.932615\pi$
$524$	−2.83750	−	4.91469i	−0.123957	−	0.214699i
$525$	−0.266044	+	0.460802i	−0.0116111	+	0.0201111i
$526$	−14.6420	+	5.32926i	−0.638423	+	0.232367i
$527$	−1.33228	−	7.55574i	−0.0580351	−	0.329133i
$528$	0.645430	−	3.66041i	0.0280887	−	0.159299i
$529$	−10.4084	−	3.78834i	−0.452538	−	0.164710i
$530$	−0.798133	+	0.669713i	−0.0346687	+	0.0290905i
$531$	6.65270			0.288703
$532$	1.34137	+	1.89209i	0.0581556	+	0.0820323i
$533$	33.9391			1.47007
$534$	−2.93969	+	2.46669i	−0.127213	+	0.106744i
$535$	6.23783	+	2.27038i	0.269685	+	0.0981572i
$536$	−0.888003	+	5.03612i	−0.0383559	+	0.217527i
$537$	−1.91622	−	10.8674i	−0.0826911	−	0.468964i
$538$	24.2592	−	8.82964i	1.04589	−	0.380673i
$539$	12.4829	−	21.6211i	0.537678	−	0.931285i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	29.4085	+	24.6767i	1.26437	+	1.06093i	0.995202	+	0.0978411i	$0.0311937\pi$
$541$	29.4085	+	24.6767i	1.26437	+	1.06093i	0.269170	+	0.963093i	$0.413251\pi$
$542$	9.69846	+	8.13798i	0.416585	+	0.349556i
$543$	−1.23396	−	2.13727i	−0.0529541	−	0.0917192i
$544$	−0.407604	+	0.705990i	−0.0174759	+	0.0302691i
$545$	10.6912	−	3.89127i	0.457960	−	0.166684i
$546$	−0.304063	−	1.72443i	−0.0130127	−	0.0737987i
$547$	0.762174	−	4.32250i	0.0325882	−	0.184817i	−0.964169	−	0.265290i	$-0.914532\pi$
$547$	0.762174	−	4.32250i	0.0325882	−	0.184817i	0.996757	+	0.0804736i	$0.0256433\pi$
$548$	−18.8131	−	6.84743i	−0.803658	−	0.292508i
$549$	10.9795	−	9.21291i	0.468595	−	0.393198i
$550$	−3.71688			−0.158488
$551$	−25.2784	−	35.6568i	−1.07689	−	1.51903i
$552$	5.83750			0.248460
$553$	5.14543	−	4.31753i	0.218806	−	0.183600i
$554$	20.1596	+	7.33748i	0.856498	+	0.311740i
$555$	1.39646	−	7.91971i	0.0592764	−	0.336173i
$556$	−1.86184	−	10.5590i	−0.0789598	−	0.447803i
$557$	16.8182	−	6.12132i	0.712610	−	0.259369i	0.0398248	−	0.999207i	$-0.487320\pi$
$557$	16.8182	−	6.12132i	0.712610	−	0.259369i	0.672785	+	0.739838i	$0.265098\pi$
$558$	4.70574	−	8.15058i	0.199210	−	0.345041i
$559$	−7.28271	−	12.6140i	−0.308026	−	0.533516i
$560$	−0.407604	−	0.342020i	−0.0172244	−	0.0144530i
$561$	−2.32114	−	1.94767i	−0.0979985	−	0.0822305i
$562$	4.53802	+	7.86008i	0.191425	+	0.331557i
$563$	−12.6322	+	21.8797i	−0.532385	+	0.922118i	0.466900	+	0.884310i	$0.345371\pi$
$563$	−12.6322	+	21.8797i	−0.532385	+	0.922118i	−0.999285	+	0.0378076i	$0.987963\pi$
$564$	10.2442	−	3.72859i	0.431360	−	0.157002i
$565$	−0.426022	−	2.41609i	−0.0179229	−	0.101646i
$566$	−3.40080	+	19.2869i	−0.142946	+	0.810688i
$567$	−0.500000	−	0.181985i	−0.0209980	−	0.00764266i
$568$	−2.62836	+	2.20545i	−0.110283	+	0.0925387i
$569$	−4.44562			−0.186370			−0.0931851	−	0.995649i	$-0.529705\pi$
$569$	−4.44562			−0.186370			−0.0931851	+	0.995649i	$0.529705\pi$
$570$	−1.15270	−	4.20372i	−0.0482814	−	0.176075i
$571$	5.02641			0.210349			0.105174	−	0.994454i	$-0.466460\pi$
$571$	5.02641			0.210349			0.105174	+	0.994454i	$0.466460\pi$
$572$	9.37005	−	7.86241i	0.391782	−	0.328744i
$573$	−5.77719	−	2.10272i	−0.241346	−	0.0878426i
$574$	−0.952896	+	5.40414i	−0.0397731	+	0.225565i
$575$	−1.01367	−	5.74881i	−0.0422730	−	0.239742i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−10.4693	+	18.1333i	−0.435841	+	0.754898i	−0.997364	−	0.0725627i	$-0.976882\pi$
$577$	−10.4693	+	18.1333i	−0.435841	+	0.754898i	0.561523	+	0.827461i	$0.310216\pi$
$578$	−8.16772	−	14.1469i	−0.339732	−	0.588434i
$579$	−2.48680	−	2.08667i	−0.103348	−	0.0867190i
$580$	7.68139	+	6.44545i	0.318952	+	0.267633i
$581$	−4.80019	−	8.31418i	−0.199146	−	0.344930i
$582$	1.31521	−	2.27801i	0.0545171	−	0.0944264i
$583$	3.63903	−	1.32450i	0.150713	−	0.0548552i
$584$	−0.188663	−	1.06996i	−0.00780693	−	0.0442753i
$585$	−0.571452	+	3.24086i	−0.0236266	+	0.133993i
$586$	−7.84389	−	2.85494i	−0.324028	−	0.117937i
$587$	−22.4618	+	18.8477i	−0.927098	+	0.777928i	−0.975294	−	0.220910i	$-0.929097\pi$
$587$	−22.4618	+	18.8477i	−0.927098	+	0.777928i	0.0481957	+	0.998838i	$0.484653\pi$
$588$	−6.71688			−0.277000
$589$	−28.8384	+	29.1768i	−1.18827	+	1.20221i
$590$	6.65270			0.273887
$591$	−9.17617	+	7.69972i	−0.377457	+	0.316724i
$592$	7.55690	+	2.75049i	0.310587	+	0.113044i
$593$	−4.92309	+	27.9202i	−0.202167	+	1.14655i	0.699669	+	0.714467i	$0.253331\pi$
$593$	−4.92309	+	27.9202i	−0.202167	+	1.14655i	−0.901836	+	0.432078i	$0.857780\pi$
$594$	−0.645430	−	3.66041i	−0.0264823	−	0.150189i
$595$	−0.407604	+	0.148356i	−0.0167101	+	0.00608199i
$596$	0.215537	−	0.373321i	0.00882875	−	0.0152918i
$597$	8.50521	+	14.7315i	0.348095	+	0.602919i
$598$	14.7160	+	12.3482i	0.601782	+	0.504955i
$599$	3.16637	+	2.65690i	0.129375	+	0.108558i	0.705179	−	0.709029i	$-0.250867\pi$
$599$	3.16637	+	2.65690i	0.129375	+	0.108558i	−0.575804	+	0.817587i	$0.695311\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	6.69001	−	11.5874i	0.272891	−	0.472661i	−0.696710	−	0.717353i	$-0.745353\pi$
$601$	6.69001	−	11.5874i	0.272891	−	0.472661i	0.969601	+	0.244692i	$0.0786868\pi$
$602$	2.21301	−	0.805470i	0.0901956	−	0.0328285i
$603$	0.888003	+	5.03612i	0.0361623	+	0.205087i
$604$	1.92855	−	10.9373i	0.0784715	−	0.445034i
$605$	2.64543	+	0.962858i	0.107552	+	0.0391457i
$606$	9.87005	−	8.28196i	0.400943	−	0.336432i
$607$	44.3688			1.80087			0.900436	−	0.434988i	$-0.143247\pi$
$607$	44.3688			1.80087			0.900436	+	0.434988i	$0.143247\pi$
$608$	4.34002	−	0.405223i	0.176011	−	0.0164340i
$609$	−5.33544			−0.216203
$610$	10.9795	−	9.21291i	0.444548	−	0.373020i
$611$	33.7123	+	12.2703i	1.36385	+	0.496402i
$612$	−0.141559	+	0.802823i	−0.00572220	+	0.0324522i
$613$	−1.61510	−	9.15966i	−0.0652331	−	0.369955i	−0.999896	−	0.0144202i	$-0.995410\pi$
$613$	−1.61510	−	9.15966i	−0.0652331	−	0.369955i	0.934663	−	0.355535i	$-0.115701\pi$
$614$	18.2160	−	6.63008i	0.735138	−	0.267568i
$615$	5.15657	−	8.93145i	0.207933	−	0.360151i
$616$	0.988856	+	1.71275i	0.0398421	+	0.0690086i
$617$	−15.3150	−	12.8508i	−0.616557	−	0.517353i	0.280162	−	0.959953i	$-0.409612\pi$
$617$	−15.3150	−	12.8508i	−0.616557	−	0.517353i	−0.896719	+	0.442600i	$0.854056\pi$
$618$	8.06283	+	6.76552i	0.324335	+	0.272149i
$619$	8.34255	+	14.4497i	0.335315	+	0.580783i	0.983545	−	0.180661i	$-0.0578238\pi$
$619$	8.34255	+	14.4497i	0.335315	+	0.580783i	−0.648230	+	0.761445i	$0.724490\pi$
$620$	4.70574	−	8.15058i	0.188987	−	0.327335i
$621$	5.48545	−	1.99654i	0.220124	−	0.0801184i
$622$	−3.57873	−	20.2960i	−0.143494	−	0.813794i
$623$	0.354570	−	2.01087i	0.0142056	−	0.0805637i
$624$	−3.09240	−	1.12554i	−0.123795	−	0.0450577i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	22.7374			0.908770
$627$	−1.31790	+	16.1478i	−0.0526317	+	0.644882i
$628$	−16.3182			−0.651167
$629$	5.02204	−	4.21399i	0.200242	−	0.168023i
$630$	−0.500000	−	0.181985i	−0.0199205	−	0.00725046i
$631$	5.69341	−	32.2889i	0.226651	−	1.28540i	−0.632852	−	0.774272i	$-0.718116\pi$
$631$	5.69341	−	32.2889i	0.226651	−	1.28540i	0.859504	−	0.511130i	$-0.170773\pi$
$632$	−2.19207	−	12.4318i	−0.0871957	−	0.494512i
$633$	−7.93882	+	2.88949i	−0.315540	+	0.114847i
$634$	−3.85457	+	6.67631i	−0.153085	+	0.265150i
$635$	−1.23055	−	2.13138i	−0.0488330	−	0.0845812i
$636$	−0.798133	−	0.669713i	−0.0316480	−	0.0265559i
$637$	−16.9329	−	14.2084i	−0.670905	−	0.562956i
$638$	−18.6352	−	32.2771i	−0.737775	−	1.27786i
$639$	−1.71554	+	2.97140i	−0.0678656	+	0.117547i
$640$	−0.939693	+	0.342020i	−0.0371446	+	0.0135195i
$641$	−0.434640	−	2.46497i	−0.0171673	−	0.0973603i	0.975020	−	0.222116i	$-0.0712964\pi$
$641$	−0.434640	−	2.46497i	−0.0171673	−	0.0973603i	−0.992187	+	0.124756i	$0.960185\pi$
$642$	−1.15270	+	6.53731i	−0.0454936	+	0.258007i
$643$	4.62284	+	1.68257i	0.182307	+	0.0663543i	0.431561	−	0.902084i	$-0.357963\pi$
$643$	4.62284	+	1.68257i	0.182307	+	0.0663543i	−0.249254	+	0.968438i	$0.580185\pi$
$644$	−2.37939	+	1.99654i	−0.0937609	+	0.0786747i
$645$	−4.42602			−0.174274
$646$	1.48293	−	3.22918i	0.0583449	−	0.127051i
$647$	−36.4807			−1.43420			−0.717102	−	0.696968i	$-0.754532\pi$
$647$	−36.4807			−1.43420			−0.717102	+	0.696968i	$0.754532\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	−23.2361	−	8.45724i	−0.912096	−	0.331976i
$650$	−0.571452	+	3.24086i	−0.0224142	+	0.127117i
$651$	0.869585	+	4.93166i	0.0340817	+	0.193287i
$652$	−19.8799	+	7.23567i	−0.778555	+	0.283371i
$653$	8.54488	−	14.8002i	0.334387	−	0.579175i	−0.648980	−	0.760806i	$-0.724804\pi$
$653$	8.54488	−	14.8002i	0.334387	−	0.579175i	0.983367	+	0.181630i	$0.0581374\pi$
$654$	5.68866	+	9.85305i	0.222444	+	0.385285i
$655$	−4.34730	−	3.64781i	−0.169863	−	0.142532i
$656$	7.90033	+	6.62916i	0.308456	+	0.258825i
$657$	−0.543233	−	0.940908i	−0.0211935	−	0.0367083i
$658$	−2.90033	+	5.02352i	−0.113067	+	0.195837i
$659$	6.21688	−	2.26276i	0.242175	−	0.0881446i	−0.218081	−	0.975931i	$-0.569980\pi$
$659$	6.21688	−	2.26276i	0.242175	−	0.0881446i	0.460256	+	0.887786i	$0.347757\pi$
$660$	−0.645430	−	3.66041i	−0.0251233	−	0.142481i
$661$	−6.75578	+	38.3139i	−0.262769	+	1.49024i	0.512544	+	0.858661i	$0.328703\pi$
$661$	−6.75578	+	38.3139i	−0.262769	+	1.49024i	−0.775313	+	0.631577i	$0.782408\pi$
$662$	6.55216	+	2.38479i	0.254657	+	0.0926875i
$663$	−2.05509	+	1.72443i	−0.0798132	+	0.0669712i
$664$	−18.0428			−0.700197
$665$	1.90760	+	1.31920i	0.0739737	+	0.0511566i
$666$	8.04189			0.311617
$667$	44.8401	−	37.6253i	1.73621	−	1.45686i
$668$	−5.71213	−	2.07905i	−0.221009	−	0.0804407i
$669$	−1.19800	+	6.79417i	−0.0463172	+	0.262678i
$670$	0.888003	+	5.03612i	0.0343066	+	0.194562i
$671$	−50.0604	+	18.2205i	−1.93256	+	0.703394i
$672$	0.266044	−	0.460802i	0.0102629	−	0.0177758i
$673$	1.36366	+	2.36192i	0.0525650	+	0.0910453i	0.891111	−	0.453786i	$-0.149927\pi$
$673$	1.36366	+	2.36192i	0.0525650	+	0.0910453i	−0.838546	+	0.544831i	$0.816594\pi$
$674$	−17.7665	−	14.9079i	−0.684340	−	0.574230i
$675$	0.766044	+	0.642788i	0.0294851	+	0.0247409i
$676$	1.08512	+	1.87949i	0.0417355	+	0.0722880i
$677$	−16.5082	+	28.5931i	−0.634462	+	1.09892i	0.352167	+	0.935937i	$0.385445\pi$
$677$	−16.5082	+	28.5931i	−0.634462	+	1.09892i	−0.986629	+	0.162983i	$0.947888\pi$
$678$	2.30541	−	0.839100i	0.0885386	−	0.0322254i
$679$	0.243041	+	1.37835i	0.00932704	+	0.0528963i
$680$	−0.141559	+	0.802823i	−0.00542855	+	0.0307868i
$681$	−13.4547	−	4.89711i	−0.515586	−	0.187658i
$682$	−26.7973	+	22.4856i	−1.02612	+	0.861017i
$683$	25.3746			0.970934			0.485467	−	0.874255i	$-0.338650\pi$
$683$	25.3746			0.970934			0.485467	+	0.874255i	$0.338650\pi$
$684$	3.93969	−	1.86516i	0.150638	−	0.0713162i
$685$	−20.0205			−0.764945
$686$	5.59105	−	4.69145i	0.213467	−	0.179120i
$687$	13.7417	+	5.00157i	0.524278	+	0.190822i
$688$	0.768571	−	4.35878i	0.0293015	−	0.166177i
$689$	−0.595389	−	3.37662i	−0.0226825	−	0.128639i
$690$	5.48545	−	1.99654i	0.208828	−	0.0760070i
$691$	−18.4770	+	32.0031i	−0.702898	+	1.21746i	0.264547	+	0.964373i	$0.414778\pi$
$691$	−18.4770	+	32.0031i	−0.702898	+	1.21746i	−0.967445	+	0.253082i	$0.918556\pi$
$692$	7.34002	+	12.7133i	0.279026	+	0.483287i
$693$	1.51501	+	1.27125i	0.0575507	+	0.0482907i
$694$	0.847296	+	0.710966i	0.0321629	+	0.0269879i
$695$	−5.36097	−	9.28547i	−0.203353	−	0.352218i
$696$	−5.01367	+	8.68393i	−0.190043	+	0.329164i
$697$	7.90033	−	2.87548i	0.299246	−	0.108917i
$698$	−4.80288	−	27.2385i	−0.181792	−	1.03099i
$699$	0.554378	−	3.14403i	0.0209685	−	0.118918i
$700$	−0.500000	−	0.181985i	−0.0188982	−	0.00687839i
$701$	−22.8102	+	19.1400i	−0.861530	+	0.722909i	−0.962297	−	0.272001i	$-0.912315\pi$
$701$	−22.8102	+	19.1400i	−0.861530	+	0.722909i	0.100767	+	0.994910i	$0.467870\pi$
$702$	−3.29086			−0.124205
$703$	−33.9117	−	8.87495i	−1.27900	−	0.334725i
$704$	3.71688			0.140085
$705$	8.35117	−	7.00746i	0.314523	−	0.263916i
$706$	−9.44831	−	3.43890i	−0.355592	−	0.129425i
$707$	−1.19047	+	6.75151i	−0.0447724	+	0.253917i
$708$	1.15523	+	6.55163i	0.0434162	+	0.246225i
$709$	4.92427	−	1.79229i	0.184935	−	0.0673107i	−0.247893	−	0.968787i	$-0.579738\pi$
$709$	4.92427	−	1.79229i	0.184935	−	0.0673107i	0.432828	+	0.901477i	$0.357516\pi$
$710$	−1.71554	+	2.97140i	−0.0643830	+	0.111515i
$711$	−6.31180	−	10.9324i	−0.236711	−	0.409996i
$712$	−2.93969	−	2.46669i	−0.110170	−	0.0924433i
$713$	−42.0861	−	35.3144i	−1.57614	−	1.32253i
$714$	−0.216881	−	0.375650i	−0.00811658	−	0.0140583i
$715$	6.11587	−	10.5930i	0.228720	−	0.396155i
$716$	10.3696	−	3.77422i	0.387530	−	0.141049i
$717$	−3.41740	−	19.3811i	−0.127625	−	0.723799i
$718$	−3.25372	+	18.4528i	−0.121428	+	0.688651i
$719$	37.6874	+	13.7171i	1.40550	+	0.511561i	0.929806	−	0.368049i	$-0.119974\pi$
$719$	37.6874	+	13.7171i	1.40550	+	0.511561i	0.475696	+	0.879610i	$0.342196\pi$
$720$	−0.766044	+	0.642788i	−0.0285488	+	0.0239553i
$721$	−5.60039			−0.208569
$722$	−18.6716	+	3.51735i	−0.694885	+	0.130902i
$723$	11.7365			0.436484
$724$	1.89053	−	1.58634i	0.0702610	−	0.0589560i
$725$	9.42262	+	3.42955i	0.349947	+	0.127370i
$726$	−0.488856	+	2.77244i	−0.0181431	+	0.102895i
$727$	−7.10725	−	40.3072i	−0.263593	−	1.49491i	−0.773011	−	0.634392i	$-0.781250\pi$
$727$	−7.10725	−	40.3072i	−0.263593	−	1.49491i	0.509418	−	0.860519i	$-0.329861\pi$
$728$	1.64543	−	0.598887i	0.0609837	−	0.0221962i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.543233	−	0.940908i	−0.0201060	−	0.0348246i
$731$	−2.76399	−	2.31926i	−0.102230	−	0.0857809i
$732$	10.9795	+	9.21291i	0.405815	+	0.340519i
$733$	−19.4918	−	33.7609i	−0.719948	−	1.24699i	−0.961020	−	0.276479i	$-0.910832\pi$
$733$	−19.4918	−	33.7609i	−0.719948	−	1.24699i	0.241072	−	0.970507i	$-0.422501\pi$
$734$	16.9304	−	29.3242i	0.624911	−	1.08238i
$735$	−6.31180	+	2.29731i	−0.232814	+	0.0847375i
$736$	1.01367	+	5.74881i	0.0373644	+	0.211904i
$737$	3.30060	−	18.7187i	0.121579	−	0.689510i
$738$	9.69119	+	3.52730i	0.356738	+	0.129842i
$739$	21.7310	−	18.2345i	0.799388	−	0.670767i	−0.148661	−	0.988888i	$-0.547496\pi$
$739$	21.7310	−	18.2345i	0.799388	−	0.670767i	0.948050	+	0.318122i	$0.103052\pi$
$740$	8.04189			0.295626
$741$	13.8772	+	3.63176i	0.509790	+	0.133416i
$742$	0.554378			0.0203518
$743$	−38.4372	+	32.2527i	−1.41012	+	1.18324i	−0.453737	+	0.891136i	$0.649909\pi$
$743$	−38.4372	+	32.2527i	−1.41012	+	1.18324i	−0.956388	+	0.292100i	$0.905646\pi$
$744$	8.84389	+	3.21891i	0.324233	+	0.118011i
$745$	0.0748553	−	0.424525i	0.00274249	−	0.0155534i
$746$	0.104418	+	0.592184i	0.00382301	+	0.0216814i
$747$	−16.9547	+	6.17101i	−0.620340	+	0.225785i
$748$	1.51501	−	2.62408i	0.0553944	−	0.0959460i
$749$	−1.76604	−	3.05888i	−0.0645299	−	0.111769i
$750$	0.766044	+	0.642788i	0.0279720	+	0.0234713i
$751$	−12.8038	−	10.7437i	−0.467218	−	0.392042i	0.378561	−	0.925576i	$-0.376419\pi$
$751$	−12.8038	−	10.7437i	−0.467218	−	0.392042i	−0.845779	+	0.533534i	$0.820864\pi$
$752$	5.45084	+	9.44113i	0.198772	+	0.344282i
$753$	8.98680	−	15.5656i	0.327497	−	0.567242i
$754$	−31.0085	+	11.2862i	−1.12926	+	0.411018i
$755$	−1.92855	−	10.9373i	−0.0701871	−	0.398051i
$756$	0.0923963	−	0.524005i	0.00336042	−	0.0190579i
$757$	23.6805	+	8.61900i	0.860683	+	0.313263i	0.734388	−	0.678730i	$-0.237469\pi$
$757$	23.6805	+	8.61900i	0.860683	+	0.313263i	0.126295	+	0.991993i	$0.459691\pi$
$758$	−1.40167	+	1.17614i	−0.0509111	+	0.0427195i
$759$	−21.6973			−0.787561
$760$	3.93969	−	1.86516i	0.142908	−	0.0676565i
$761$	−39.0164			−1.41434			−0.707172	−	0.707042i	$-0.750029\pi$
$761$	−39.0164			−1.41434			−0.707172	+	0.707042i	$0.750029\pi$
$762$	1.88532	−	1.58197i	0.0682978	−	0.0573086i
$763$	−5.68866	−	2.07050i	−0.205943	−	0.0749573i
$764$	1.06758	−	6.05455i	0.0386237	−	0.219046i
$765$	0.141559	+	0.802823i	0.00511809	+	0.0290261i
$766$	28.3653	−	10.3241i	1.02488	−	0.373026i
$767$	−10.9466	+	18.9600i	−0.395257	+	0.684606i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	37.1523	+	31.1745i	1.33975	+	1.12418i	0.981691	+	0.190480i	$0.0610044\pi$
$769$	37.1523	+	31.1745i	1.33975	+	1.12418i	0.358055	+	0.933701i	$0.383440\pi$
$770$	1.51501	+	1.27125i	0.0545973	+	0.0458126i
$771$	15.1498	+	26.2402i	0.545606	+	0.945016i
$772$	1.62314	−	2.81136i	0.0584181	−	0.101183i
$773$	−14.1591	+	5.15349i	−0.509267	+	0.185358i	−0.583858	−	0.811856i	$-0.698457\pi$
$773$	−14.1591	+	5.15349i	−0.509267	+	0.185358i	0.0745902	+	0.997214i	$0.476235\pi$
$774$	−0.768571	−	4.35878i	−0.0276257	−	0.156673i
$775$	1.63429	−	9.26849i	0.0587053	−	0.332934i
$776$	2.47178	+	0.899655i	0.0887318	+	0.0322957i
$777$	−3.27790	+	2.75049i	−0.117594	+	0.0986732i
$778$	2.84430			0.101973
$779$	−36.9739	−	25.5693i	−1.32473	−	0.916116i
$780$	−3.29086			−0.117832
$781$	9.76929	−	8.19740i	0.349573	−	0.293326i
$782$	4.47178	+	1.62760i	0.159911	+	0.0582027i
$783$	−1.74123	+	9.87500i	−0.0622265	+	0.352904i
$784$	−1.16637	−	6.61484i	−0.0416562	−	0.236244i
$785$	−15.3341	+	5.58115i	−0.547297	+	0.199200i
$786$	2.83750	−	4.91469i	0.101210	−	0.175301i
$787$	10.3610	+	17.9457i	0.369329	+	0.639696i	0.989461	−	0.144802i	$-0.0462544\pi$
$787$	10.3610	+	17.9457i	0.369329	+	0.639696i	−0.620132	+	0.784497i	$0.712921\pi$
$788$	−9.17617	−	7.69972i	−0.326888	−	0.274291i
$789$	−11.9363	−	10.0157i	−0.424943	−	0.356570i
$790$	−6.31180	−	10.9324i	−0.224564	−	0.388956i
$791$	−0.652704	+	1.13052i	−0.0232075	+	0.0401965i
$792$	3.49273	−	1.27125i	0.124109	−	0.0451718i
$793$	8.19047	+	46.4505i	0.290852	+	1.64951i
$794$	−1.63769	+	9.28780i	−0.0581194	+	0.329612i
$795$	−0.979055	−	0.356347i	−0.0347235	−	0.0126383i
$796$	−13.0307	+	10.9341i	−0.461863	+	0.387549i
$797$	16.9685			0.601057			0.300528	−	0.953773i	$-0.402837\pi$
$797$	16.9685			0.601057			0.300528	+	0.953773i	$0.402837\pi$
$798$	−0.967911	+	2.10770i	−0.0342637	+	0.0746118i
$799$	8.88713			0.314404
$800$	−0.766044	+	0.642788i	−0.0270838	+	0.0227260i
$801$	−3.60607	−	1.31250i	−0.127414	−	0.0463749i
$802$	−1.97131	+	11.1799i	−0.0696095	+	0.394775i
$803$	0.701238	+	3.97692i	0.0247461	+	0.140342i
$804$	−4.80541	+	1.74903i	−0.169474	+	0.0616834i
$805$	−1.55303	+	2.68993i	−0.0547372	+	0.0948077i
$806$	15.4859	+	26.8224i	0.545468	+	0.944779i
$807$	19.7763	+	16.5943i	0.696159	+	0.584147i
$808$	9.87005	+	8.28196i	0.347227	+	0.291358i
$809$	9.40033	+	16.2818i	0.330498	+	0.572439i	0.982610	−	0.185684i	$-0.0594500\pi$
$809$	9.40033	+	16.2818i	0.330498	+	0.572439i	−0.652112	+	0.758123i	$0.726117\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	8.55216	−	3.11273i	0.300307	−	0.109303i	−0.187472	−	0.982270i	$-0.560029\pi$
$811$	8.55216	−	3.11273i	0.300307	−	0.109303i	0.487779	+	0.872967i	$0.337807\pi$
$812$	−0.926489	−	5.25438i	−0.0325134	−	0.184393i
$813$	−2.19846	+	12.4681i	−0.0771035	+	0.437275i
$814$	−28.0881	−	10.2232i	−0.984488	−	0.358324i
$815$	−16.2062	+	13.5986i	−0.567679	+	0.476339i
$816$	−0.815207			−0.0285380
$817$	−1.56934	+	19.2286i	−0.0549041	+	0.672725i
$818$	−16.4584			−0.575455
$819$	1.34137	−	1.12554i	0.0468711	−	0.0393296i
$820$	9.69119	+	3.52730i	0.338431	+	0.123179i
$821$	0.275434	−	1.56206i	0.00961272	−	0.0545164i	−0.979624	−	0.200840i	$-0.935633\pi$
$821$	0.275434	−	1.56206i	0.00961272	−	0.0545164i	0.989237	+	0.146323i	$0.0467440\pi$
$822$	−3.47653	−	19.7164i	−0.121258	−	0.687688i
$823$	−30.8692	+	11.2355i	−1.07603	+	0.391644i	−0.818429	−	0.574607i	$-0.805155\pi$
$823$	−30.8692	+	11.2355i	−1.07603	+	0.391644i	−0.257603	+	0.966251i	$0.582933\pi$
$824$	−5.26264	+	9.11516i	−0.183333	+	0.317542i
$825$	−1.85844	−	3.21891i	−0.0647026	−	0.112068i
$826$	−2.71167	−	2.27536i	−0.0943510	−	0.0791699i
$827$	0.950122	+	0.797247i	0.0330390	+	0.0277230i	0.659158	−	0.752005i	$-0.270913\pi$
$827$	0.950122	+	0.797247i	0.0330390	+	0.0277230i	−0.626119	+	0.779728i	$0.715357\pi$
$828$	2.91875	+	5.05542i	0.101434	+	0.175688i
$829$	22.9736	−	39.7914i	0.797906	−	1.38201i	−0.123072	−	0.992398i	$-0.539275\pi$
$829$	22.9736	−	39.7914i	0.797906	−	1.38201i	0.920978	−	0.389616i	$-0.127392\pi$
$830$	−16.9547	+	6.17101i	−0.588506	+	0.214199i
$831$	3.72534	+	21.1274i	0.129231	+	0.732903i
$832$	0.571452	−	3.24086i	0.0198115	−	0.112357i
$833$	−5.14543	−	1.87278i	−0.178279	−	0.0648881i
$834$	8.21348	−	6.89193i	0.284409	−	0.238648i
$835$	−6.07873			−0.210363
$836$	−16.1313	+	1.50617i	−0.557914	+	0.0520918i
$837$	9.41147			0.325308
$838$	−0.00387039	+	0.00324765i	−0.000133701	+	0.000112188i
$839$	−49.5249	−	18.0256i	−1.70979	−	0.622312i	−0.712909	−	0.701256i	$-0.752623\pi$
$839$	−49.5249	−	18.0256i	−1.70979	−	0.622312i	−0.996879	+	0.0789441i	$0.974845\pi$
$840$	0.0923963	−	0.524005i	0.00318797	−	0.0180799i
$841$	12.4241	+	70.4606i	0.428417	+	2.42968i
$842$	10.3366	−	3.76222i	0.356223	−	0.129655i
$843$	−4.53802	+	7.86008i	−0.156298	+	0.270715i
$844$	−4.22416	−	7.31645i	−0.145401	−	0.251843i
$845$	1.66250	+	1.39501i	0.0571919	+	0.0479897i
$846$	8.35117	+	7.00746i	0.287119	+	0.240921i
$847$	−0.748970	−	1.29725i	−0.0257349	−	0.0445742i
$848$	0.520945	−	0.902302i	0.0178893	−	0.0309852i
$849$	−18.4033	+	6.69826i	−0.631600	+	0.229884i
$850$	0.141559	+	0.802823i	0.00485544	+	0.0275366i
$851$	8.15183	−	46.2313i	0.279441	−	1.58479i
$852$	−3.22416	−	1.17350i	−0.110458	−	0.0402033i
$853$	−0.605600	+	0.508159i	−0.0207353	+	0.0173990i	−0.653096	−	0.757275i	$-0.726530\pi$
$853$	−0.605600	+	0.508159i	−0.0207353	+	0.0173990i	0.632361	+	0.774674i	$0.282086\pi$
$854$	−7.62630			−0.260966
$855$	3.06418	−	3.10013i	0.104793	−	0.106022i
$856$	−6.63816			−0.226887
$857$	1.23467	−	1.03601i	0.0421756	−	0.0353895i	−0.621456	−	0.783449i	$-0.713459\pi$
$857$	1.23467	−	1.03601i	0.0421756	−	0.0353895i	0.663632	+	0.748059i	$0.269014\pi$
$858$	11.4941	+	4.18350i	0.392401	+	0.142822i
$859$	5.75150	−	32.6184i	0.196239	−	1.11292i	−0.714405	−	0.699732i	$-0.753303\pi$
$859$	5.75150	−	32.6184i	0.196239	−	1.11292i	0.910644	−	0.413192i	$-0.135586\pi$
$860$	−0.768571	−	4.35878i	−0.0262080	−	0.148633i
$861$	−5.15657	+	1.87684i	−0.175736	+	0.0639625i
$862$	17.8949	−	30.9948i	0.609502	−	1.05569i
$863$	2.49525	+	4.32190i	0.0849394	+	0.147119i	0.905365	−	0.424633i	$-0.139597\pi$
$863$	2.49525	+	4.32190i	0.0849394	+	0.147119i	−0.820426	+	0.571753i	$0.806264\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	11.2456	+	9.43615i	0.382361	+	0.320839i
$866$	11.6834	+	20.2363i	0.397020	+	0.687658i
$867$	8.16772	−	14.1469i	0.277390	−	0.480454i
$868$	−4.70574	+	1.71275i	−0.159723	+	0.0581345i
$869$	8.14765	+	46.2076i	0.276390	+	1.56749i
$870$	−1.74123	+	9.87500i	−0.0590332	+	0.334794i
$871$	−15.8139	−	5.75580i	−0.535834	−	0.195028i
$872$	−8.71554	+	7.31320i	−0.295145	+	0.247656i
$873$	2.63041			0.0890261
$874$	−6.72890	−	24.5392i	−0.227609	−	0.830051i
$875$	−0.532089			−0.0179879
$876$	0.832282	−	0.698367i	0.0281202	−	0.0235956i
$877$	−14.9329	−	5.43513i	−0.504248	−	0.183531i	0.0773558	−	0.997004i	$-0.475352\pi$
$877$	−14.9329	−	5.43513i	−0.504248	−	0.183531i	−0.581604	+	0.813472i	$0.697574\pi$
$878$	−3.24675	+	18.4132i	−0.109572	+	0.621416i
$879$	−1.44949	−	8.22048i	−0.0488902	−	0.277270i
$880$	3.49273	−	1.27125i	0.117740	−	0.0428538i
$881$	−2.00475	+	3.47232i	−0.0675417	+	0.116986i	−0.897819	−	0.440365i	$-0.854849\pi$
$881$	−2.00475	+	3.47232i	−0.0675417	+	0.116986i	0.830277	+	0.557351i	$0.188182\pi$
$882$	−3.35844	−	5.81699i	−0.113085	−	0.195868i
$883$	−10.3418	−	8.67783i	−0.348030	−	0.292032i	0.451968	−	0.892034i	$-0.350722\pi$
$883$	−10.3418	−	8.67783i	−0.348030	−	0.292032i	−0.799999	+	0.600002i	$0.795166\pi$
$884$	−2.05509	−	1.72443i	−0.0691203	−	0.0579988i
$885$	3.32635	+	5.76141i	0.111814	+	0.193668i
$886$	−5.56923	+	9.64619i	−0.187102	+	0.324070i
$887$	−26.2545	+	9.55585i	−0.881539	+	0.320854i	−0.742831	−	0.669479i	$-0.766517\pi$
$887$	−26.2545	+	9.55585i	−0.881539	+	0.320854i	−0.138709	+	0.990333i	$0.544295\pi$
$888$	1.39646	+	7.91971i	0.0468621	+	0.265768i
$889$	−0.227397	+	1.28963i	−0.00762664	+	0.0432529i
$890$	−3.60607	−	1.31250i	−0.120876	−	0.0439951i
$891$	2.84730	−	2.38917i	0.0953880	−	0.0800400i
$892$	−6.89899			−0.230995
$893$	−27.4825	−	38.7659i	−0.919667	−	1.29725i
$894$	0.431074			0.0144173
$895$	8.45336	−	7.09321i	0.282565	−	0.237100i
$896$	0.500000	+	0.181985i	0.0167038	+	0.00607970i
$897$	−3.33585	+	18.9185i	−0.111381	+	0.631671i
$898$	−6.20187	−	35.1725i	−0.206959	−	1.17372i
$899$	88.6807	−	32.2771i	2.95767	−	1.07650i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−0.424678	−	0.735564i	−0.0141481	−	0.0245052i
$902$	−29.3646	−	24.6398i	−0.977734	−	0.820416i
$903$	1.80406	+	1.51379i	0.0600355	+	0.0503757i
$904$	1.22668	+	2.12467i	0.0407988	+	0.0706656i
$905$	1.23396	−	2.13727i	0.0410181	−	0.0710454i
$906$	10.4363	−	3.79850i	0.346722	−	0.126197i
$907$	−3.09089	−	17.5293i	−0.102631	−	0.582051i	−0.992140	−	0.125133i	$-0.960064\pi$
$907$	−3.09089	−	17.5293i	−0.102631	−	0.582051i	0.889509	−	0.456918i	$-0.151047\pi$
$908$	2.48633	−	14.1007i	0.0825117	−	0.467947i
$909$	12.1074	+	4.40674i	0.401577	+	0.146162i
$910$	1.34137	−	1.12554i	0.0444659	−	0.0373113i
$911$	38.2012			1.26566			0.632831	−	0.774290i	$-0.281893\pi$
$911$	38.2012			1.26566			0.632831	+	0.774290i	$0.281893\pi$
$912$	2.52094	+	3.55596i	0.0834768	+	0.117750i
$913$	67.0630			2.21946
$914$	−23.6065	+	19.8082i	−0.780835	+	0.655198i
$915$	13.4684	+	4.90209i	0.445251	+	0.162058i
$916$	−2.53936	+	14.4014i	−0.0839029	+	0.475837i
$917$	0.524348	+	2.97373i	0.0173155	+	0.0982011i
$918$	−0.766044	+	0.278817i	−0.0252832	+	0.00920234i
$919$	−14.9802	+	25.9465i	−0.494152	+	0.855897i	−0.999977	−	0.00673907i	$-0.997855\pi$
$919$	−14.9802	+	25.9465i	−0.494152	+	0.855897i	0.505825	+	0.862636i	$0.331188\pi$
$920$	2.91875	+	5.05542i	0.0962283	+	0.166672i
$921$	14.8498	+	12.4605i	0.489318	+	0.410587i
$922$	−2.24969	−	1.88771i	−0.0740894	−	0.0621684i
$923$	−5.64559	−	9.77845i	−0.185827	−	0.321862i
$924$	−0.988856	+	1.71275i	−0.0325310	+	0.0563453i
$925$	7.55690	−	2.75049i	0.248469	−	0.0904355i
$926$	1.32929	+	7.53877i	0.0436831	+	0.247739i
$927$	−1.82770	+	10.3654i	−0.0600294	+	0.340444i
$928$	−9.42262	−	3.42955i	−0.309313	−	0.112581i
$929$	−36.4044	+	30.5469i	−1.19439	+	1.00221i	−0.194618	+	0.980879i	$0.562347\pi$
$929$	−36.4044	+	30.5469i	−1.19439	+	1.00221i	−0.999772	+	0.0213333i	$0.993209\pi$
$930$	9.41147			0.308614
$931$	7.74257	+	28.2359i	0.253753	+	0.925394i
$932$	3.19253			0.104575
$933$	15.7875	−	13.2472i	0.516858	−	0.433695i
$934$	11.1382	+	4.05396i	0.364452	+	0.132650i
$935$	0.526159	−	2.98400i	0.0172072	−	0.0975871i
$936$	−0.571452	−	3.24086i	−0.0186785	−	0.105931i
$937$	−6.42514	+	2.33856i	−0.209900	+	0.0763975i	−0.444830	−	0.895615i	$-0.646736\pi$
$937$	−6.42514	+	2.33856i	−0.209900	+	0.0763975i	0.234930	+	0.972012i	$0.424514\pi$
$938$	1.36050	−	2.35646i	0.0444219	−	0.0769410i
$939$	11.3687	+	19.6912i	0.371004	+	0.642597i
$940$	8.35117	+	7.00746i	0.272385	+	0.228558i
$941$	−30.4197	−	25.5251i	−0.991653	−	0.832096i	−0.00584704	−	0.999983i	$-0.501861\pi$
$941$	−30.4197	−	25.5251i	−0.991653	−	0.832096i	−0.985806	+	0.167887i	$0.946306\pi$
$942$	−8.15910	−	14.1320i	−0.265838	−	0.460445i
$943$	30.1015	−	52.1373i	0.980239	−	1.69782i
$944$	−6.25150	+	2.27536i	−0.203469	+	0.0740566i
$945$	−0.0923963	−	0.524005i	−0.00300565	−	0.0170459i
$946$	−2.85669	+	16.2011i	−0.0928789	+	0.526742i
$947$	−47.8379	−	17.4116i	−1.55452	−	0.565800i	−0.585049	−	0.810998i	$-0.698925\pi$
$947$	−47.8379	−	17.4116i	−1.55452	−	0.565800i	−0.969473	+	0.245199i	$0.921147\pi$
$948$	9.67024	−	8.11430i	0.314075	−	0.263540i
$949$	3.57541			0.116063
$950$	3.06418	−	3.10013i	0.0994151	−	0.100582i
$951$	−7.70914			−0.249986
$952$	0.332282	−	0.278817i	0.0107693	−	0.00903652i
$953$	38.5026	+	14.0138i	1.24722	+	0.453951i	0.879462	−	0.475970i	$-0.157903\pi$
$953$	38.5026	+	14.0138i	1.24722	+	0.453951i	0.367759	+	0.929921i	$0.380125\pi$
$954$	0.180922	−	1.02606i	0.00585757	−	0.0332199i
$955$	−1.06758	−	6.05455i	−0.0345461	−	0.195921i
$956$	18.4932	−	6.73097i	0.598113	−	0.217695i
$957$	18.6352	−	32.2771i	0.602391	−	1.04337i
$958$	−3.88279	−	6.72519i	−0.125447	−	0.217281i
$959$	8.16044	+	6.84743i	0.263514	+	0.221115i
$960$	−0.766044	−	0.642788i	−0.0247240	−	0.0207459i
$961$	−28.7879	−	49.8621i	−0.928643	−	1.60846i
$962$	−13.2324	+	22.9191i	−0.426629	+	0.738942i
$963$	−6.23783	+	2.27038i	−0.201011	+	0.0731621i
$964$	2.03802	+	11.5582i	0.0656402	+	0.372264i
$965$	0.563711	−	3.19696i	0.0181465	−	0.102914i
$966$	−2.91875	−	1.06234i	−0.0939092	−	0.0341801i
$967$	−28.3862	+	23.8189i	−0.912840	+	0.765964i	−0.972657	−	0.232245i	$-0.925393\pi$
$967$	−28.3862	+	23.8189i	−0.912840	+	0.765964i	0.0598170	+	0.998209i	$0.480948\pi$
$968$	−2.81521			−0.0904842
$969$	3.53802	−	0.330341i	0.113658	−	0.0106121i
$970$	2.63041			0.0844575
$971$	−7.45883	+	6.25870i	−0.239365	+	0.200851i	−0.754577	−	0.656212i	$-0.772158\pi$
$971$	−7.45883	+	6.25870i	−0.239365	+	0.200851i	0.515212	+	0.857063i	$0.327713\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	−0.990667	+	5.61835i	−0.0317593	+	0.180116i
$974$	−0.165497	−	0.938579i	−0.00530286	−	0.0300740i
$975$	−3.09240	+	1.12554i	−0.0990359	+	0.0360461i
$976$	−7.16637	+	12.4125i	−0.229390	+	0.397315i
$977$	2.12196	+	3.67534i	0.0678875	+	0.117585i	0.897971	−	0.440054i	$-0.145041\pi$
$977$	2.12196	+	3.67534i	0.0678875	+	0.117585i	−0.830084	+	0.557639i	$0.811707\pi$
$978$	−16.2062	−	13.5986i	−0.518217	−	0.434836i
$979$	10.9265	+	9.16841i	0.349212	+	0.293024i
$980$	−3.35844	−	5.81699i	−0.107281	−	0.185817i
$981$	−5.68866	+	9.85305i	−0.181625	+	0.314584i
$982$	−19.5116	+	7.10165i	−0.622641	+	0.226623i
$983$	1.81655	+	10.3022i	0.0579390	+	0.328588i	0.999976	−	0.00692046i	$-0.00220287\pi$
$983$	1.81655	+	10.3022i	0.0579390	+	0.328588i	−0.942037	+	0.335509i	$0.891092\pi$
$984$	−1.79086	+	10.1565i	−0.0570905	+	0.323776i
$985$	−11.2562	−	4.09694i	−0.358654	−	0.130539i
$986$	−6.26193	+	5.25438i	−0.199420	+	0.167334i
$987$	−5.80066			−0.184637
$988$	−1.16684	+	14.2970i	−0.0371222	+	0.454848i
$989$	−25.8369			−0.821565
$990$	2.84730	−	2.38917i	0.0904930	−	0.0759327i
$991$	−10.8174	−	3.93722i	−0.343627	−	0.125070i	0.164441	−	0.986387i	$-0.447418\pi$
$991$	−10.8174	−	3.93722i	−0.343627	−	0.125070i	−0.508068	+	0.861317i	$0.669640\pi$
$992$	−1.63429	+	9.26849i	−0.0518886	+	0.294275i
$993$	1.21079	+	6.86673i	0.0384232	+	0.217909i
$994$	1.71554	−	0.624404i	0.0544135	−	0.0198049i
$995$	−8.50521	+	14.7315i	−0.269633	+	0.467019i
$996$	−9.02141	−	15.6255i	−0.285854	−	0.495114i
$997$	2.01186	+	1.68815i	0.0637162	+	0.0534643i	0.674090	−	0.738650i	$-0.264536\pi$
$997$	2.01186	+	1.68815i	0.0637162	+	0.0534643i	−0.610373	+	0.792114i	$0.708981\pi$
$998$	−4.32429	−	3.62851i	−0.136883	−	0.114859i
$999$	4.02094	+	6.96448i	0.127217	+	0.220346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.f.481.1	yes	6
19.16	even	9	inner	570.2.u.f.301.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.f.301.1	✓	6	19.16	even	9	inner
570.2.u.f.481.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(-1.85844 - 3.21891i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-3.09240 + 1.12554i) q^{13} +(-0.0923963 - 0.524005i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.624485 + 0.524005i) q^{17} -1.00000 q^{18} +(4.21688 + 1.10359i) q^{19} -1.00000 q^{20} +(0.407604 - 0.342020i) q^{21} +(3.49273 + 1.27125i) q^{22} +(-1.01367 + 5.74881i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.64543 - 2.84997i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.407604 + 0.342020i) q^{28} +(-7.68139 - 6.44545i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-4.70574 + 8.15058i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.645430 + 3.66041i) q^{33} +(0.141559 - 0.802823i) q^{34} +(0.500000 + 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} -8.04189 q^{37} +(-3.93969 + 1.86516i) q^{38} +3.29086 q^{39} +(0.766044 - 0.642788i) q^{40} +(-9.69119 - 3.52730i) q^{41} +(-0.0923963 + 0.524005i) q^{42} +(0.768571 + 4.35878i) q^{43} +(-3.49273 + 1.27125i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-2.91875 - 5.05542i) q^{46} +(-8.35117 - 7.00746i) q^{47} +(0.766044 + 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.766044 - 0.278817i) q^{51} +(0.571452 + 3.24086i) q^{52} +(-0.180922 + 1.02606i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-2.84730 + 2.38917i) q^{55} -0.532089 q^{56} +(-3.58512 - 2.47929i) q^{57} +10.0273 q^{58} +(5.09627 - 4.27628i) q^{59} +(0.939693 + 0.342020i) q^{60} +(2.48886 - 14.1150i) q^{61} +(-1.63429 - 9.26849i) q^{62} +(-0.500000 + 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.64543 + 2.84997i) q^{65} +(-2.84730 - 2.38917i) q^{66} +(3.91740 + 3.28709i) q^{67} +(0.407604 + 0.705990i) q^{68} +(2.91875 - 5.05542i) q^{69} +(-0.500000 + 0.181985i) q^{70} +(0.595800 + 3.37895i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-1.02094 - 0.371593i) q^{73} +(6.16044 - 5.16923i) q^{74} +1.00000 q^{75} +(1.81908 - 3.96118i) q^{76} +1.97771 q^{77} +(-2.52094 + 2.11532i) q^{78} +(-11.8623 - 4.31753i) q^{79} +(-0.173648 + 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(9.69119 - 3.52730i) q^{82} +(-9.02141 + 15.6255i) q^{83} +(-0.266044 - 0.460802i) q^{84} +(0.624485 + 0.524005i) q^{85} +(-3.39053 - 2.84499i) q^{86} +(5.01367 + 8.68393i) q^{87} +(1.85844 - 3.21891i) q^{88} +(-3.60607 + 1.31250i) q^{89} +(0.173648 + 0.984808i) q^{90} +(0.304063 - 1.72443i) q^{91} +(5.48545 + 1.99654i) q^{92} +(7.20961 - 6.04958i) q^{93} +10.9017 q^{94} +(0.354570 - 4.34445i) q^{95} -1.00000 q^{96} +(2.01501 - 1.69080i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(0.645430 - 3.66041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{7} + 3 q^{8} - 3 q^{11} - 3 q^{12} - 15 q^{13} + 3 q^{14} + 9 q^{17} - 6 q^{18} + 9 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 3 q^{29} - 3 q^{30} - 18 q^{31} - 12 q^{33} + 9 q^{34} + 3 q^{35} - 42 q^{37} - 18 q^{38} - 12 q^{39} - 12 q^{41} + 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} - 15 q^{46} - 24 q^{47} + 12 q^{49} + 3 q^{50} + 3 q^{52} - 18 q^{53} - 15 q^{55} + 6 q^{56} + 18 q^{58} + 3 q^{59} + 21 q^{61} - 3 q^{63} - 3 q^{64} - 6 q^{65} - 15 q^{66} + 30 q^{67} + 6 q^{68} + 15 q^{69} - 3 q^{70} + 42 q^{71} - 3 q^{73} - 9 q^{74} + 6 q^{75} - 6 q^{76} + 24 q^{77} - 12 q^{78} - 39 q^{79} + 12 q^{82} + 15 q^{83} + 3 q^{84} - 9 q^{85} - 3 q^{86} + 9 q^{87} + 3 q^{88} + 3 q^{89} + 15 q^{91} - 3 q^{92} + 9 q^{93} + 42 q^{94} + 18 q^{95} - 6 q^{96} - 18 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^11 - 3 * q^12 - 15 * q^13 + 3 * q^14 + 9 * q^17 - 6 * q^18 + 9 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 3 * q^29 - 3 * q^30 - 18 * q^31 - 12 * q^33 + 9 * q^34 + 3 * q^35 - 42 * q^37 - 18 * q^38 - 12 * q^39 - 12 * q^41 + 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 - 15 * q^46 - 24 * q^47 + 12 * q^49 + 3 * q^50 + 3 * q^52 - 18 * q^53 - 15 * q^55 + 6 * q^56 + 18 * q^58 + 3 * q^59 + 21 * q^61 - 3 * q^63 - 3 * q^64 - 6 * q^65 - 15 * q^66 + 30 * q^67 + 6 * q^68 + 15 * q^69 - 3 * q^70 + 42 * q^71 - 3 * q^73 - 9 * q^74 + 6 * q^75 - 6 * q^76 + 24 * q^77 - 12 * q^78 - 39 * q^79 + 12 * q^82 + 15 * q^83 + 3 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 + 3 * q^88 + 3 * q^89 + 15 * q^91 - 3 * q^92 + 9 * q^93 + 42 * q^94 + 18 * q^95 - 6 * q^96 - 18 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

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