LMFDB - Embedded newform 690.2.m.g.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	690.271
Dual form			690.2.m.g.331.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.117211 - 0.256656i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.117211 - 0.256656i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-1.39757 + 0.410362i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(2.84180 - 6.22268i) q^{13} +(0.0401546 + 0.279282i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.16135 - 2.03168i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(2.46452 + 1.58385i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(0.270724 + 0.0794918i) q^{21} +1.45657 q^{22} +(1.94865 + 4.38210i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-4.47982 + 5.16999i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.0401546 - 0.279282i) q^{28} +(-0.776666 + 0.499133i) q^{29} +(0.415415 + 0.909632i) q^{30} +(2.55288 + 2.94618i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.605080 - 1.32494i) q^{33} +(-3.60568 + 1.05872i) q^{34} +(0.270724 - 0.0794918i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.362593 - 2.52189i) q^{37} +(-1.91846 - 2.21403i) q^{38} +(2.84180 + 6.22268i) q^{39} +(0.841254 - 0.540641i) q^{40} +(-1.56584 + 10.8906i) q^{41} +(-0.237363 - 0.152544i) q^{42} +(2.09148 - 2.41370i) q^{43} +(-1.39757 - 0.410362i) q^{44} +1.00000 q^{45} +(-0.635134 - 4.75359i) q^{46} +10.9883 q^{47} +(-0.959493 - 0.281733i) q^{48} +(4.53189 - 5.23008i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.534805 + 3.71965i) q^{51} +(5.75491 - 3.69846i) q^{52} +(-0.896767 - 1.96365i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.207291 - 1.44174i) q^{55} +(-0.117211 + 0.256656i) q^{56} +(-2.81091 + 0.825357i) q^{57} +(0.885828 - 0.260102i) q^{58} +(-1.09762 + 2.40345i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(6.99617 + 8.07400i) q^{61} +(-1.61944 - 3.54607i) q^{62} +(-0.237363 + 0.152544i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(5.75491 + 3.69846i) q^{65} +(-0.953848 + 1.10080i) q^{66} +(13.2343 + 3.88595i) q^{67} +3.75790 q^{68} +(-4.58786 - 1.39697i) q^{69} -0.282154 q^{70} +(-2.52713 - 0.742033i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-3.47667 - 2.23432i) q^{73} +(-0.362593 + 2.52189i) q^{74} +(0.841254 - 0.540641i) q^{75} +(1.21699 + 2.66484i) q^{76} +(0.269132 + 0.310595i) q^{77} +(-0.973558 - 6.77125i) q^{78} +(2.75667 - 6.03626i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.57066 - 10.0083i) q^{82} +(-0.722593 - 5.02574i) q^{83} +(0.184771 + 0.213237i) q^{84} +(1.56109 + 3.41831i) q^{85} +(-2.68678 + 1.72669i) q^{86} +(0.131389 - 0.913828i) q^{87} +(1.22534 + 0.787479i) q^{88} +(2.50730 - 2.89357i) q^{89} +(-0.959493 - 0.281733i) q^{90} -1.93018 q^{91} +(-0.729834 + 4.73997i) q^{92} -3.89836 q^{93} +(-10.5432 - 3.09575i) q^{94} +(-1.91846 + 2.21403i) q^{95} +(0.841254 + 0.540641i) q^{96} +(0.686509 - 4.77478i) q^{97} +(-5.82180 + 3.74144i) q^{98} +(0.605080 + 1.32494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	−0.117211	−	0.256656i	−0.0443015	−	0.0970068i	0.886187	−	0.463327i	$-0.153345\pi$
$7$	−0.117211	−	0.256656i	−0.0443015	−	0.0970068i	−0.930489	+	0.366321i	$0.880617\pi$
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.415415	−	0.909632i	0.131366	−	0.287651i
$11$	−1.39757	+	0.410362i	−0.421382	+	0.123729i	−0.485547	−	0.874210i	$-0.661380\pi$
$11$	−1.39757	+	0.410362i	−0.421382	+	0.123729i	0.0641654	+	0.997939i	$0.479561\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	2.84180	−	6.22268i	0.788175	−	1.72586i	0.106370	−	0.994327i	$-0.466077\pi$
$13$	2.84180	−	6.22268i	0.788175	−	1.72586i	0.681804	−	0.731535i	$-0.261196\pi$
$14$	0.0401546	+	0.279282i	0.0107318	+	0.0746412i
$15$	−0.654861	−	0.755750i	−0.169084	−	0.195134i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	3.16135	−	2.03168i	0.766740	−	0.492754i	−0.0978692	−	0.995199i	$-0.531203\pi$
$17$	3.16135	−	2.03168i	0.766740	−	0.492754i	0.864609	+	0.502446i	$0.167566\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	2.46452	+	1.58385i	0.565399	+	0.363360i	0.791900	−	0.610651i	$-0.209092\pi$
$19$	2.46452	+	1.58385i	0.565399	+	0.363360i	−0.226501	+	0.974011i	$0.572729\pi$
$20$	−0.654861	+	0.755750i	−0.146431	+	0.168991i
$21$	0.270724	+	0.0794918i	0.0590769	+	0.0173465i
$22$	1.45657			0.310541
$23$	1.94865	+	4.38210i	0.406321	+	0.913730i
$23$	1.94865	+	4.38210i	0.406321	+	0.913730i
$24$	1.00000			0.204124
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	−4.47982	+	5.16999i	−0.878565	+	1.01392i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.0401546	−	0.279282i	0.00758851	−	0.0527793i
$29$	−0.776666	+	0.499133i	−0.144223	+	0.0926867i	−0.610763	−	0.791814i	$-0.709137\pi$
$29$	−0.776666	+	0.499133i	−0.144223	+	0.0926867i	0.466539	+	0.884500i	$0.345501\pi$
$30$	0.415415	+	0.909632i	0.0758441	+	0.166075i
$31$	2.55288	+	2.94618i	0.458511	+	0.529150i	0.937180	−	0.348845i	$-0.113426\pi$
$31$	2.55288	+	2.94618i	0.458511	+	0.529150i	−0.478669	+	0.877995i	$0.658881\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	0.605080	−	1.32494i	0.105331	−	0.230642i
$34$	−3.60568	+	1.05872i	−0.618369	+	0.181570i
$35$	0.270724	−	0.0794918i	0.0457608	−	0.0134366i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−0.362593	−	2.52189i	−0.0596099	−	0.414596i	−0.997676	−	0.0681393i	$-0.978294\pi$
$37$	−0.362593	−	2.52189i	−0.0596099	−	0.414596i	0.938066	−	0.346457i	$-0.112615\pi$
$38$	−1.91846	−	2.21403i	−0.311216	−	0.359162i
$39$	2.84180	+	6.22268i	0.455053	+	0.996427i
$40$	0.841254	−	0.540641i	0.133014	−	0.0854828i
$41$	−1.56584	+	10.8906i	−0.244543	+	1.70083i	0.384226	+	0.923239i	$0.374468\pi$
$41$	−1.56584	+	10.8906i	−0.244543	+	1.70083i	−0.628768	+	0.777593i	$0.716441\pi$
$42$	−0.237363	−	0.152544i	−0.0366259	−	0.0235380i
$43$	2.09148	−	2.41370i	0.318948	−	0.368086i	−0.573524	−	0.819189i	$-0.694424\pi$
$43$	2.09148	−	2.41370i	0.318948	−	0.368086i	0.892472	+	0.451103i	$0.148969\pi$
$44$	−1.39757	−	0.410362i	−0.210691	−	0.0618644i
$45$	1.00000			0.149071
$46$	−0.635134	−	4.75359i	−0.0936454	−	0.700878i
$47$	10.9883			1.60280			0.801401	−	0.598127i	$-0.204088\pi$
$47$	10.9883			1.60280			0.801401	+	0.598127i	$0.204088\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	4.53189	−	5.23008i	0.647413	−	0.747154i
$50$	0.841254	+	0.540641i	0.118971	+	0.0764582i
$51$	−0.534805	+	3.71965i	−0.0748877	+	0.520855i
$52$	5.75491	−	3.69846i	0.798063	−	0.512884i
$53$	−0.896767	−	1.96365i	−0.123180	−	0.269727i	0.837989	−	0.545688i	$-0.183731\pi$
$53$	−0.896767	−	1.96365i	−0.123180	−	0.269727i	−0.961169	+	0.275960i	$0.911004\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−0.207291	−	1.44174i	−0.0279511	−	0.194404i
$56$	−0.117211	+	0.256656i	−0.0156630	+	0.0342971i
$57$	−2.81091	+	0.825357i	−0.372314	+	0.109321i
$58$	0.885828	−	0.260102i	0.116315	−	0.0341531i
$59$	−1.09762	+	2.40345i	−0.142898	+	0.312903i	−0.967526	−	0.252773i	$-0.918657\pi$
$59$	−1.09762	+	2.40345i	−0.142898	+	0.312903i	0.824628	+	0.565676i	$0.191385\pi$
$60$	−0.142315	−	0.989821i	−0.0183728	−	0.127785i
$61$	6.99617	+	8.07400i	0.895767	+	1.03377i	0.999234	+	0.0391375i	$0.0124610\pi$
$61$	6.99617	+	8.07400i	0.895767	+	1.03377i	−0.103467	+	0.994633i	$0.532994\pi$
$62$	−1.61944	−	3.54607i	−0.205669	−	0.450351i
$63$	−0.237363	+	0.152544i	−0.0299049	+	0.0192187i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	5.75491	+	3.69846i	0.713809	+	0.458737i
$66$	−0.953848	+	1.10080i	−0.117411	+	0.135499i
$67$	13.2343	+	3.88595i	1.61683	+	0.474744i	0.960164	−	0.279437i	$-0.0901479\pi$
$67$	13.2343	+	3.88595i	1.61683	+	0.474744i	0.656666	+	0.754181i	$0.271966\pi$
$68$	3.75790			0.455713
$69$	−4.58786	−	1.39697i	−0.552314	−	0.168176i
$70$	−0.282154			−0.0337238
$71$	−2.52713	−	0.742033i	−0.299915	−	0.0880631i	0.128313	−	0.991734i	$-0.459044\pi$
$71$	−2.52713	−	0.742033i	−0.299915	−	0.0880631i	−0.428228	+	0.903671i	$0.640862\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	−3.47667	−	2.23432i	−0.406914	−	0.261507i	0.321134	−	0.947034i	$-0.395936\pi$
$73$	−3.47667	−	2.23432i	−0.406914	−	0.261507i	−0.728048	+	0.685526i	$0.759572\pi$
$74$	−0.362593	+	2.52189i	−0.0421506	+	0.293164i
$75$	0.841254	−	0.540641i	0.0971396	−	0.0624278i
$76$	1.21699	+	2.66484i	0.139598	+	0.305678i
$77$	0.269132	+	0.310595i	0.0306704	+	0.0353955i
$78$	−0.973558	−	6.77125i	−0.110234	−	0.766693i
$79$	2.75667	−	6.03626i	0.310149	−	0.679132i	−0.688800	−	0.724951i	$-0.741862\pi$
$79$	2.75667	−	6.03626i	0.310149	−	0.679132i	0.998950	+	0.0458187i	$0.0145896\pi$
$80$	−0.959493	+	0.281733i	−0.107275	+	0.0314987i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	4.57066	−	10.0083i	0.504745	−	1.10524i
$83$	−0.722593	−	5.02574i	−0.0793149	−	0.551647i	−0.990272	−	0.139146i	$-0.955564\pi$
$83$	−0.722593	−	5.02574i	−0.0793149	−	0.551647i	0.910957	−	0.412501i	$-0.135345\pi$
$84$	0.184771	+	0.213237i	0.0201602	+	0.0232661i
$85$	1.56109	+	3.41831i	0.169324	+	0.370768i
$86$	−2.68678	+	1.72669i	−0.289723	+	0.186194i
$87$	0.131389	−	0.913828i	0.0140863	−	0.0979726i
$88$	1.22534	+	0.787479i	0.130622	+	0.0839456i
$89$	2.50730	−	2.89357i	0.265773	−	0.306718i	−0.607140	−	0.794595i	$-0.707683\pi$
$89$	2.50730	−	2.89357i	0.265773	−	0.306718i	0.872912	+	0.487877i	$0.162229\pi$
$90$	−0.959493	−	0.281733i	−0.101139	−	0.0296972i
$91$	−1.93018			−0.202338
$92$	−0.729834	+	4.73997i	−0.0760904	+	0.494176i
$93$	−3.89836			−0.404241
$94$	−10.5432	−	3.09575i	−1.08744	−	0.319302i
$95$	−1.91846	+	2.21403i	−0.196830	+	0.227154i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	0.686509	−	4.77478i	0.0697044	−	0.484805i	−0.924829	−	0.380384i	$-0.875792\pi$
$97$	0.686509	−	4.77478i	0.0697044	−	0.484805i	0.994533	−	0.104421i	$-0.0332990\pi$
$98$	−5.82180	+	3.74144i	−0.588091	+	0.377943i
$99$	0.605080	+	1.32494i	0.0608128	+	0.133161i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−0.482825	−	3.35812i	−0.0480429	−	0.334146i	−0.999641	−	0.0267999i	$-0.991468\pi$
$101$	−0.482825	−	3.35812i	−0.0480429	−	0.334146i	0.951598	−	0.307346i	$-0.0994408\pi$
$102$	1.56109	−	3.41831i	0.154571	−	0.338463i
$103$	7.15522	−	2.10096i	0.705025	−	0.207014i	0.0904828	−	0.995898i	$-0.471159\pi$
$103$	7.15522	−	2.10096i	0.705025	−	0.207014i	0.614542	+	0.788884i	$0.289341\pi$
$104$	−6.56377	+	1.92730i	−0.643631	+	0.188987i
$105$	−0.117211	+	0.256656i	−0.0114386	+	0.0250471i
$106$	0.307219	+	2.13675i	0.0298397	+	0.207540i
$107$	0.679994	+	0.784755i	0.0657375	+	0.0758652i	0.787666	−	0.616103i	$-0.211289\pi$
$107$	0.679994	+	0.784755i	0.0657375	+	0.0758652i	−0.721928	+	0.691968i	$0.756744\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	9.59837	−	6.16850i	0.919358	−	0.590835i	0.00688638	−	0.999976i	$-0.497808\pi$
$109$	9.59837	−	6.16850i	0.919358	−	0.590835i	0.912471	+	0.409141i	$0.134172\pi$
$110$	−0.207291	+	1.44174i	−0.0197644	+	0.137465i
$111$	2.14337	+	1.37746i	0.203439	+	0.130742i
$112$	0.184771	−	0.213237i	0.0174592	−	0.0201490i
$113$	−5.50858	−	1.61747i	−0.518204	−	0.152158i	0.0121639	−	0.999926i	$-0.496128\pi$
$113$	−5.50858	−	1.61747i	−0.518204	−	0.152158i	−0.530368	+	0.847768i	$0.677946\pi$
$114$	2.92958			0.274380
$115$	−4.61481	+	1.30518i	−0.430334	+	0.121708i
$116$	−0.923225			−0.0857193
$117$	−6.56377	−	1.92730i	−0.606821	−	0.178179i
$118$	1.73029	−	1.99686i	0.159286	−	0.183826i
$119$	−0.891986	−	0.573244i	−0.0817682	−	0.0525492i
$120$	−0.142315	+	0.989821i	−0.0129915	+	0.0903579i
$121$	−7.46900	+	4.80003i	−0.679000	+	0.436367i
$122$	−4.43806	−	9.71800i	−0.401803	−	0.879826i
$123$	−7.20519	−	8.31523i	−0.649670	−	0.749759i
$124$	0.554794	+	3.85868i	0.0498220	+	0.346519i
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$	0.270724	−	0.0794918i	0.0241180	−	0.00708170i
$127$	−13.7715	+	4.04367i	−1.22202	+	0.358817i	−0.828233	−	0.560384i	$-0.810653\pi$
$127$	−13.7715	+	4.04367i	−1.22202	+	0.358817i	−0.393787	+	0.919202i	$0.628835\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.454523	+	3.16128i	0.0400185	+	0.278335i
$130$	−4.47982	−	5.16999i	−0.392906	−	0.453438i
$131$	0.0682194	+	0.149380i	0.00596036	+	0.0130514i	0.912589	−	0.408879i	$-0.134080\pi$
$131$	0.0682194	+	0.149380i	0.00596036	+	0.0130514i	−0.906628	+	0.421930i	$0.861353\pi$
$132$	1.22534	−	0.787479i	0.106652	−	0.0685413i
$133$	0.117636	−	0.818177i	0.0102003	−	0.0709449i
$134$	−11.6034	−	7.45708i	−1.00238	−	0.644194i
$135$	−0.654861	+	0.755750i	−0.0563614	+	0.0650446i
$136$	−3.60568	−	1.05872i	−0.309185	−	0.0907848i
$137$	−20.6419			−1.76355			−0.881777	−	0.471667i	$-0.843652\pi$
$137$	−20.6419			−1.76355			−0.881777	+	0.471667i	$0.843652\pi$
$138$	4.00845	+	2.63294i	0.341222	+	0.224130i
$139$	9.96149			0.844923			0.422461	−	0.906381i	$-0.361166\pi$
$139$	9.96149			0.844923			0.422461	+	0.906381i	$0.361166\pi$
$140$	0.270724	+	0.0794918i	0.0228804	+	0.00671829i
$141$	−7.19578	+	8.30437i	−0.605994	+	0.699354i
$142$	2.21571	+	1.42395i	0.185938	+	0.119495i
$143$	−1.41805	+	9.86277i	−0.118584	+	0.824767i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−0.383521	−	0.839795i	−0.0318497	−	0.0697412i
$146$	2.70636	+	3.12331i	0.223980	+	0.258487i
$147$	0.984874	+	6.84995i	0.0812310	+	0.564974i
$148$	1.05840	−	2.31758i	0.0870003	−	0.190504i
$149$	19.0515	−	5.59401i	1.56076	−	0.458279i	0.616463	−	0.787384i	$-0.288565\pi$
$149$	19.0515	−	5.59401i	1.56076	−	0.458279i	0.944293	+	0.329105i	$0.106747\pi$
$150$	−0.959493	+	0.281733i	−0.0783423	+	0.0230034i
$151$	−9.19350	+	20.1310i	−0.748157	+	1.63823i	0.0214939	+	0.999769i	$0.493158\pi$
$151$	−9.19350	+	20.1310i	−0.748157	+	1.63823i	−0.769650	+	0.638465i	$0.779570\pi$
$152$	−0.416922	−	2.89976i	−0.0338168	−	0.235201i
$153$	−2.46090	−	2.84003i	−0.198952	−	0.229603i
$154$	−0.170725	−	0.373836i	−0.0137574	−	0.0301246i
$155$	−3.27951	+	2.10761i	−0.263416	+	0.169287i
$156$	−0.973558	+	6.77125i	−0.0779471	+	0.542134i
$157$	−15.1306	−	9.72386i	−1.20755	−	0.776048i	−0.227307	−	0.973823i	$-0.572992\pi$
$157$	−15.1306	−	9.72386i	−1.20755	−	0.776048i	−0.980247	+	0.197775i	$0.936629\pi$
$158$	−4.34561	+	5.01511i	−0.345719	+	0.398980i
$159$	2.07128	+	0.608183i	0.164263	+	0.0482321i
$160$	1.00000			0.0790569
$161$	0.896289	−	1.01376i	0.0706374	−	0.0798956i
$162$	1.00000			0.0785674
$163$	−4.59445	−	1.34905i	−0.359865	−	0.105666i	0.0968016	−	0.995304i	$-0.469139\pi$
$163$	−4.59445	−	1.34905i	−0.359865	−	0.105666i	−0.456667	+	0.889638i	$0.650957\pi$
$164$	−7.20519	+	8.31523i	−0.562631	+	0.649311i
$165$	1.22534	+	0.787479i	0.0953927	+	0.0613052i
$166$	−0.722593	+	5.02574i	−0.0560841	+	0.390073i
$167$	−7.12892	+	4.58148i	−0.551653	+	0.354526i	−0.786581	−	0.617487i	$-0.788151\pi$
$167$	−7.12892	+	4.58148i	−0.551653	+	0.354526i	0.234928	+	0.972013i	$0.424514\pi$
$168$	−0.117211	−	0.256656i	−0.00904301	−	0.0198014i
$169$	−22.1327	−	25.5425i	−1.70252	−	1.96481i
$170$	−0.534805	−	3.71965i	−0.0410177	−	0.285284i
$171$	1.21699	−	2.66484i	0.0930655	−	0.203785i
$172$	3.06441	−	0.899793i	0.233659	−	0.0686086i
$173$	17.5778	−	5.16129i	1.33641	−	0.392406i	0.466024	−	0.884772i	$-0.345686\pi$
$173$	17.5778	−	5.16129i	1.33641	−	0.392406i	0.870388	+	0.492366i	$0.163868\pi$
$174$	−0.383521	+	0.839795i	−0.0290747	+	0.0636647i
$175$	0.0401546	+	0.279282i	0.00303541	+	0.0211117i
$176$	−0.953848	−	1.10080i	−0.0718990	−	0.0829759i
$177$	−1.09762	−	2.40345i	−0.0825021	−	0.180654i
$178$	−3.22095	+	2.06998i	−0.241420	+	0.155151i
$179$	0.157157	−	1.09305i	0.0117465	−	0.0816985i	−0.983105	−	0.183043i	$-0.941405\pi$
$179$	0.157157	−	1.09305i	0.0117465	−	0.0816985i	0.994851	+	0.101344i	$0.0323144\pi$
$180$	0.841254	+	0.540641i	0.0627033	+	0.0402970i
$181$	−6.39736	+	7.38295i	−0.475512	+	0.548770i	−0.941937	−	0.335791i	$-0.890997\pi$
$181$	−6.39736	+	7.38295i	−0.475512	+	0.548770i	0.466424	+	0.884561i	$0.345542\pi$
$182$	1.85199	+	0.543794i	0.137279	+	0.0403087i
$183$	−10.6834			−0.789743
$184$	2.03568	−	4.34235i	0.150072	−	0.320122i
$185$	2.54782			0.187320
$186$	3.74045	+	1.09829i	0.274263	+	0.0805308i
$187$	−3.58447	+	4.13670i	−0.262122	+	0.302505i
$188$	9.24391	+	5.94070i	0.674182	+	0.433270i
$189$	0.0401546	−	0.279282i	0.00292082	−	0.0203148i
$190$	2.46452	−	1.58385i	0.178795	−	0.114904i
$191$	−4.38511	−	9.60206i	−0.317296	−	0.694780i	0.682037	−	0.731318i	$-0.261094\pi$
$191$	−4.38511	−	9.60206i	−0.317296	−	0.694780i	−0.999332	+	0.0365375i	$0.988367\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	−0.146114	−	1.01624i	−0.0105175	−	0.0731509i	0.983887	−	0.178793i	$-0.0572193\pi$
$193$	−0.146114	−	1.01624i	−0.0105175	−	0.0731509i	−0.994404	+	0.105642i	$0.966310\pi$
$194$	−2.00391	+	4.38795i	−0.143872	+	0.315037i
$195$	−6.56377	+	1.92730i	−0.470042	+	0.138017i
$196$	6.64006	−	1.94970i	0.474290	−	0.139264i
$197$	2.64771	−	5.79768i	0.188642	−	0.413067i	−0.791554	−	0.611099i	$-0.790728\pi$
$197$	2.64771	−	5.79768i	0.188642	−	0.413067i	0.980196	+	0.198032i	$0.0634549\pi$
$198$	−0.207291	−	1.44174i	−0.0147315	−	0.102460i
$199$	−5.33218	−	6.15366i	−0.377988	−	0.436222i	0.534598	−	0.845107i	$-0.320463\pi$
$199$	−5.33218	−	6.15366i	−0.377988	−	0.436222i	−0.912586	+	0.408885i	$0.865918\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	−11.6034	+	7.45708i	−0.818444	+	0.525982i
$202$	−0.482825	+	3.35812i	−0.0339714	+	0.236277i
$203$	0.219139	+	0.140832i	0.0153805	+	0.00988448i
$204$	−2.46090	+	2.84003i	−0.172298	+	0.198842i
$205$	−10.5569	−	3.09980i	−0.737329	−	0.216499i
$206$	−7.45729			−0.519574
$207$	4.06017	−	2.55245i	0.282201	−	0.177408i
$208$	6.84088			0.474330
$209$	−4.09427	−	1.20219i	−0.283207	−	0.0831570i
$210$	0.184771	−	0.213237i	0.0127504	−	0.0147148i
$211$	15.8791	+	10.2049i	1.09316	+	0.702532i	0.957561	−	0.288231i	$-0.0930672\pi$
$211$	15.8791	+	10.2049i	1.09316	+	0.702532i	0.135601	+	0.990764i	$0.456704\pi$
$212$	0.307219	−	2.13675i	0.0210999	−	0.146753i
$213$	2.21571	−	1.42395i	0.151818	−	0.0975675i
$214$	−0.431359	−	0.944544i	−0.0294871	−	0.0645677i
$215$	2.09148	+	2.41370i	0.142638	+	0.164613i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	0.456930	−	1.00054i	0.0310184	−	0.0679208i
$218$	−10.9474	+	3.21446i	−0.741454	+	0.217711i
$219$	3.96532	−	1.16432i	0.267952	−	0.0786777i
$220$	0.605080	−	1.32494i	0.0407945	−	0.0893274i
$221$	−3.65854	−	25.4457i	−0.246100	−	1.71166i
$222$	−1.66847	−	1.92552i	−0.111980	−	0.129232i
$223$	8.46305	+	18.5315i	0.566728	+	1.24096i	0.948521	+	0.316713i	$0.102579\pi$
$223$	8.46305	+	18.5315i	0.566728	+	1.24096i	−0.381793	+	0.924248i	$0.624693\pi$
$224$	−0.237363	+	0.152544i	−0.0158595	+	0.0101923i
$225$	−0.142315	+	0.989821i	−0.00948766	+	0.0659881i
$226$	4.82975	+	3.10389i	0.321270	+	0.206468i
$227$	4.85944	−	5.60809i	0.322532	−	0.372222i	−0.571209	−	0.820805i	$-0.693525\pi$
$227$	4.85944	−	5.60809i	0.322532	−	0.372222i	0.893742	+	0.448582i	$0.148071\pi$
$228$	−2.81091	−	0.825357i	−0.186157	−	0.0546606i
$229$	−17.4880			−1.15564			−0.577818	−	0.816165i	$-0.696096\pi$
$229$	−17.4880			−1.15564			−0.577818	+	0.816165i	$0.696096\pi$
$230$	4.79559	+	0.0478368i	0.316212	+	0.00315426i
$231$	−0.410976			−0.0270402
$232$	0.885828	+	0.260102i	0.0581574	+	0.0170766i
$233$	4.60286	−	5.31199i	0.301544	−	0.348000i	−0.584675	−	0.811268i	$-0.698778\pi$
$233$	4.60286	−	5.31199i	0.301544	−	0.348000i	0.886218	+	0.463268i	$0.153323\pi$
$234$	5.75491	+	3.69846i	0.376210	+	0.241776i
$235$	−1.56379	+	10.8764i	−0.102011	+	0.709499i
$236$	−2.22278	+	1.42849i	−0.144691	+	0.0929870i
$237$	2.75667	+	6.03626i	0.179065	+	0.392097i
$238$	0.694352	+	0.801325i	0.0450082	+	0.0519422i
$239$	−0.748544	−	5.20624i	−0.0484193	−	0.336764i	−0.999604	−	0.0281413i	$-0.991041\pi$
$239$	−0.748544	−	5.20624i	−0.0484193	−	0.336764i	0.951185	−	0.308622i	$-0.0998679\pi$
$240$	0.415415	−	0.909632i	0.0268149	−	0.0587165i
$241$	18.6608	−	5.47930i	1.20205	−	0.352953i	0.381411	−	0.924405i	$-0.375438\pi$
$241$	18.6608	−	5.47930i	1.20205	−	0.352953i	0.820635	+	0.571453i	$0.193620\pi$
$242$	8.51878	−	2.50134i	0.547608	−	0.160792i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	1.52041	+	10.5747i	0.0973344	+	0.676976i
$245$	4.53189	+	5.23008i	0.289532	+	0.334138i
$246$	4.57066	+	10.0083i	0.291414	+	0.638109i
$247$	16.8595	−	10.8349i	1.07274	−	0.689409i
$248$	0.554794	−	3.85868i	0.0352295	−	0.245026i
$249$	4.27140	+	2.74506i	0.270689	+	0.173961i
$250$	−0.654861	+	0.755750i	−0.0414170	+	0.0477978i
$251$	−25.7570	−	7.56292i	−1.62576	−	0.477368i	−0.663205	−	0.748438i	$-0.730804\pi$
$251$	−25.7570	−	7.56292i	−1.62576	−	0.477368i	−0.962560	+	0.271070i	$0.912622\pi$
$252$	−0.282154			−0.0177740
$253$	−4.52161	−	5.32462i	−0.284271	−	0.334756i
$254$	14.3529			0.900578
$255$	−3.60568	−	1.05872i	−0.225796	−	0.0662998i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−0.667304	−	0.428850i	−0.0416253	−	0.0267510i	0.519663	−	0.854372i	$-0.326058\pi$
$257$	−0.667304	−	0.428850i	−0.0416253	−	0.0267510i	−0.561288	+	0.827621i	$0.689694\pi$
$258$	0.454523	−	3.16128i	0.0282974	−	0.196812i
$259$	−0.604758	+	0.388655i	−0.0375779	+	0.0241498i
$260$	2.84180	+	6.22268i	0.176241	+	0.385914i
$261$	0.604584	+	0.697727i	0.0374228	+	0.0431882i
$262$	−0.0233709	−	0.162548i	−0.00144386	−	0.0100423i
$263$	−12.6066	+	27.6047i	−0.777358	+	1.70218i	−0.0676196	+	0.997711i	$0.521540\pi$
$263$	−12.6066	+	27.6047i	−0.777358	+	1.70218i	−0.709738	+	0.704465i	$0.751187\pi$
$264$	−1.39757	+	0.410362i	−0.0860142	+	0.0252561i
$265$	2.07128	−	0.608183i	0.127238	−	0.0373604i
$266$	−0.343378	+	0.751893i	−0.0210539	+	0.0461015i
$267$	0.544887	+	3.78977i	0.0333466	+	0.231930i
$268$	9.03252	+	10.4241i	0.551749	+	0.636752i
$269$	−11.1841	−	24.4897i	−0.681906	−	1.49317i	−0.860611	−	0.509263i	$-0.829918\pi$
$269$	−11.1841	−	24.4897i	−0.681906	−	1.49317i	0.178705	−	0.983903i	$-0.442809\pi$
$270$	0.841254	−	0.540641i	0.0511971	−	0.0329024i
$271$	−3.72391	+	25.9004i	−0.226211	+	1.57333i	0.487645	+	0.873042i	$0.337856\pi$
$271$	−3.72391	+	25.9004i	−0.226211	+	1.57333i	−0.713856	+	0.700292i	$0.753053\pi$
$272$	3.16135	+	2.03168i	0.191685	+	0.123188i
$273$	1.26400	−	1.45873i	0.0765006	−	0.0882864i
$274$	19.8057	+	5.81549i	1.19651	+	0.351326i
$275$	1.45657			0.0878343
$276$	−3.10429	−	3.65559i	−0.186856	−	0.220041i
$277$	7.15030			0.429620			0.214810	−	0.976656i	$-0.431087\pi$
$277$	7.15030			0.429620			0.214810	+	0.976656i	$0.431087\pi$
$278$	−9.55798	−	2.80648i	−0.573250	−	0.168321i
$279$	2.55288	−	2.94618i	0.152837	−	0.176383i
$280$	−0.237363	−	0.152544i	−0.0141851	−	0.00911623i
$281$	−2.54015	+	17.6671i	−0.151532	+	1.05393i	0.762120	+	0.647435i	$0.224158\pi$
$281$	−2.54015	+	17.6671i	−0.151532	+	1.05393i	−0.913653	+	0.406496i	$0.866751\pi$
$282$	9.24391	−	5.94070i	0.550467	−	0.353764i
$283$	−3.27495	−	7.17113i	−0.194675	−	0.426279i	0.786971	−	0.616990i	$-0.211648\pi$
$283$	−3.27495	−	7.17113i	−0.194675	−	0.426279i	−0.981646	+	0.190710i	$0.938921\pi$
$284$	−1.72479	−	1.99051i	−0.102347	−	0.118115i
$285$	−0.416922	−	2.89976i	−0.0246963	−	0.171767i
$286$	4.13928	−	9.06375i	0.244761	−	0.535951i
$287$	2.97868	−	0.874619i	0.175826	−	0.0516271i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	−1.19564	+	2.61808i	−0.0703315	+	0.154005i
$290$	0.131389	+	0.913828i	0.00771540	+	0.0536618i
$291$	3.15897	+	3.64564i	0.185182	+	0.213711i
$292$	−1.71680	−	3.75926i	−0.100468	−	0.219994i
$293$	24.9644	−	16.0437i	1.45844	−	0.937281i	0.459647	−	0.888102i	$-0.347976\pi$
$293$	24.9644	−	16.0437i	1.45844	−	0.937281i	0.998790	−	0.0491788i	$-0.0156604\pi$
$294$	0.984874	−	6.84995i	0.0574390	−	0.399497i
$295$	−2.22278	−	1.42849i	−0.129415	−	0.0831701i
$296$	−1.66847	+	1.92552i	−0.0969778	+	0.111918i
$297$	−1.39757	−	0.410362i	−0.0810950	−	0.0238116i
$298$	−19.8558			−1.15021
$299$	32.8061	+	0.327246i	1.89722	+	0.0189251i
$300$	1.00000			0.0577350
$301$	−0.864635	−	0.253880i	−0.0498368	−	0.0146334i
$302$	14.4926	−	16.7254i	0.833958	−	0.962439i
$303$	2.85408	+	1.83421i	0.163963	+	0.105372i
$304$	−0.416922	+	2.89976i	−0.0239121	+	0.166312i
$305$	−8.98748	+	5.77590i	−0.514622	+	0.330727i
$306$	1.56109	+	3.41831i	0.0892415	+	0.195412i
$307$	−11.7834	−	13.5988i	−0.672514	−	0.776122i	0.312254	−	0.949999i	$-0.398916\pi$
$307$	−11.7834	−	13.5988i	−0.672514	−	0.776122i	−0.984767	+	0.173877i	$0.944371\pi$
$308$	0.0584879	+	0.406792i	0.00333266	+	0.0231791i
$309$	−3.09787	+	6.78339i	−0.176232	+	0.385894i
$310$	3.74045	−	1.09829i	0.212443	−	0.0623789i
$311$	30.3197	−	8.90267i	1.71927	−	0.504824i	0.734491	−	0.678618i	$-0.237421\pi$
$311$	30.3197	−	8.90267i	1.71927	−	0.504824i	0.984782	+	0.173794i	$0.0556028\pi$
$312$	2.84180	−	6.22268i	0.160885	−	0.352290i
$313$	−0.417265	−	2.90214i	−0.0235852	−	0.164039i	0.974625	−	0.223845i	$-0.0718609\pi$
$313$	−0.417265	−	2.90214i	−0.0235852	−	0.164039i	−0.998210	+	0.0598060i	$0.980952\pi$
$314$	11.7782	+	13.5928i	0.664682	+	0.767084i
$315$	−0.117211	−	0.256656i	−0.00660408	−	0.0144609i
$316$	5.58251	−	3.58766i	0.314040	−	0.201822i
$317$	1.34567	−	9.35936i	0.0755805	−	0.525674i	−0.916497	−	0.400043i	$-0.868995\pi$
$317$	1.34567	−	9.35936i	0.0755805	−	0.525674i	0.992077	−	0.125631i	$-0.0400956\pi$
$318$	−1.81603	−	1.16709i	−0.101838	−	0.0654474i
$319$	0.880616	−	1.01629i	0.0493050	−	0.0569011i
$320$	−0.959493	−	0.281733i	−0.0536373	−	0.0157493i
$321$	−1.03838			−0.0579567
$322$	−1.14559	+	0.720183i	−0.0638414	+	0.0401342i
$323$	11.0091			0.612560
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−4.47982	+	5.16999i	−0.248496	+	0.286779i
$326$	4.02827	+	2.58881i	0.223105	+	0.143381i
$327$	−1.62376	+	11.2935i	−0.0897940	+	0.624531i
$328$	9.25600	−	5.94847i	0.511077	−	0.328449i
$329$	−1.28794	−	2.82020i	−0.0710066	−	0.155483i
$330$	−0.953848	−	1.10080i	−0.0525076	−	0.0605970i
$331$	−2.58079	−	17.9498i	−0.141853	−	0.986610i	−0.929062	−	0.369924i	$-0.879384\pi$
$331$	−2.58079	−	17.9498i	−0.141853	−	0.986610i	0.787209	−	0.616686i	$-0.211525\pi$
$332$	2.10924	−	4.61859i	0.115760	−	0.253478i
$333$	−2.44462	+	0.717805i	−0.133964	+	0.0393355i
$334$	8.13091	−	2.38745i	0.444903	−	0.130635i
$335$	−5.72984	+	12.5466i	−0.313054	+	0.685494i
$336$	0.0401546	+	0.279282i	0.00219062	+	0.0152361i
$337$	11.5503	+	13.3298i	0.629185	+	0.726118i	0.977424	−	0.211288i	$-0.0677657\pi$
$337$	11.5503	+	13.3298i	0.629185	+	0.726118i	−0.348239	+	0.937406i	$0.613220\pi$
$338$	14.0400	+	30.7434i	0.763677	+	1.67222i
$339$	4.82975	−	3.10389i	0.262316	−	0.168580i
$340$	−0.534805	+	3.71965i	−0.0290039	+	0.201726i
$341$	−4.77682	−	3.06988i	−0.258679	−	0.166243i
$342$	−1.91846	+	2.21403i	−0.103739	+	0.119721i
$343$	−3.76859	−	1.10656i	−0.203485	−	0.0597485i
$344$	−3.19378			−0.172197
$345$	2.03568	−	4.34235i	0.109597	−	0.233784i
$346$	−18.3198			−0.984880
$347$	−5.97284	−	1.75378i	−0.320639	−	0.0941480i	0.117453	−	0.993078i	$-0.462527\pi$
$347$	−5.97284	−	1.75378i	−0.320639	−	0.0941480i	−0.438091	+	0.898930i	$0.644345\pi$
$348$	0.604584	−	0.697727i	0.0324091	−	0.0374021i
$349$	−5.54950	−	3.56645i	−0.297058	−	0.190908i	0.383619	−	0.923492i	$-0.374678\pi$
$349$	−5.54950	−	3.56645i	−0.297058	−	0.190908i	−0.680677	+	0.732584i	$0.738314\pi$
$350$	0.0401546	−	0.279282i	0.00214636	−	0.0149282i
$351$	5.75491	−	3.69846i	0.307175	−	0.197409i
$352$	0.605080	+	1.32494i	0.0322509	+	0.0706195i
$353$	15.4227	+	17.7987i	0.820866	+	0.947330i	0.999329	−	0.0366164i	$-0.0116580\pi$
$353$	15.4227	+	17.7987i	0.820866	+	0.947330i	−0.178463	+	0.983947i	$0.557113\pi$
$354$	0.376027	+	2.61533i	0.0199856	+	0.139003i
$355$	1.09413	−	2.39581i	0.0580703	−	0.127156i
$356$	3.67365	−	1.07868i	0.194703	−	0.0571700i
$357$	1.01736	−	0.298723i	0.0538442	−	0.0158101i
$358$	−0.458739	+	1.00450i	−0.0242451	+	0.0530894i
$359$	−2.54832	−	17.7239i	−0.134495	−	0.935433i	−0.939594	−	0.342292i	$-0.888797\pi$
$359$	−2.54832	−	17.7239i	−0.134495	−	0.935433i	0.805099	−	0.593141i	$-0.202112\pi$
$360$	−0.654861	−	0.755750i	−0.0345142	−	0.0398315i
$361$	−4.32762	−	9.47617i	−0.227770	−	0.498746i
$362$	8.21824	−	5.28154i	0.431941	−	0.277592i
$363$	1.26353	−	8.78804i	0.0663181	−	0.461253i
$364$	−1.62377	−	1.04353i	−0.0851086	−	0.0546960i
$365$	2.70636	−	3.12331i	0.141657	−	0.163481i
$366$	10.2507	+	3.00987i	0.535812	+	0.157329i
$367$	−19.6644			−1.02647			−0.513237	−	0.858247i	$-0.671554\pi$
$367$	−19.6644			−1.02647			−0.513237	+	0.858247i	$0.671554\pi$
$368$	−3.17660	+	3.59294i	−0.165592	+	0.187295i
$369$	11.0026			0.572774
$370$	−2.44462	−	0.717805i	−0.127090	−	0.0373169i
$371$	−0.398870	+	0.460321i	−0.0207083	+	0.0238987i
$372$	−3.27951	−	2.10761i	−0.170035	−	0.109275i
$373$	−2.99771	+	20.8495i	−0.155215	+	1.07955i	0.752086	+	0.659065i	$0.229048\pi$
$373$	−2.99771	+	20.8495i	−0.155215	+	1.07955i	−0.907301	+	0.420482i	$0.861861\pi$
$374$	4.60471	−	2.95927i	0.238104	−	0.153020i
$375$	0.415415	+	0.909632i	0.0214519	+	0.0469732i
$376$	−7.19578	−	8.30437i	−0.371094	−	0.428265i
$377$	0.898813	+	6.25138i	0.0462912	+	0.321963i
$378$	−0.117211	+	0.256656i	−0.00602867	+	0.0132010i
$379$	13.2968	−	3.90430i	0.683013	−	0.200551i	0.0782231	−	0.996936i	$-0.475075\pi$
$379$	13.2968	−	3.90430i	0.683013	−	0.200551i	0.604790	+	0.796385i	$0.293257\pi$
$380$	−2.81091	+	0.825357i	−0.144196	+	0.0423399i
$381$	5.96239	−	13.0558i	0.305463	−	0.668870i
$382$	1.50227	+	10.4485i	0.0768630	+	0.534594i
$383$	−5.20951	−	6.01210i	−0.266194	−	0.307204i	0.606879	−	0.794794i	$-0.292421\pi$
$383$	−5.20951	−	6.01210i	−0.266194	−	0.307204i	−0.873072	+	0.487591i	$0.837876\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	−0.345735	+	0.222190i	−0.0176203	+	0.0113239i
$386$	−0.146114	+	1.01624i	−0.00743700	+	0.0517255i
$387$	−2.68678	−	1.72669i	−0.136577	−	0.0877726i
$388$	3.15897	−	3.64564i	0.160372	−	0.185079i
$389$	19.4781	+	5.71928i	0.987578	+	0.289979i	0.735349	−	0.677689i	$-0.237018\pi$
$389$	19.4781	+	5.71928i	0.987578	+	0.289979i	0.252229	+	0.967668i	$0.418836\pi$
$390$	6.84088			0.346401
$391$	15.0634	+	9.89432i	0.761786	+	0.500377i
$392$	−6.92039			−0.349532
$393$	−0.157568	−	0.0462661i	−0.00794825	−	0.00233382i
$394$	−4.17385	+	4.81688i	−0.210276	+	0.242671i
$395$	5.58251	+	3.58766i	0.280886	+	0.180515i
$396$	−0.207291	+	1.44174i	−0.0104168	+	0.0724502i
$397$	−28.9534	+	18.6073i	−1.45313	+	0.933871i	−0.454052	+	0.890975i	$0.650022\pi$
$397$	−28.9534	+	18.6073i	−1.45313	+	0.933871i	−0.999080	+	0.0428962i	$0.986342\pi$
$398$	3.38250	+	7.40665i	0.169550	+	0.371262i
$399$	0.541301	+	0.624695i	0.0270990	+	0.0312739i
$400$	−0.142315	−	0.989821i	−0.00711574	−	0.0494911i
$401$	9.48035	−	20.7591i	0.473426	−	1.03666i	−0.510793	−	0.859704i	$-0.670648\pi$
$401$	9.48035	−	20.7591i	0.473426	−	1.03666i	0.984219	−	0.176955i	$-0.0566246\pi$
$402$	13.2343	−	3.88595i	0.660068	−	0.193814i
$403$	25.5879	−	7.51330i	1.27463	−	0.374264i
$404$	1.40936	−	3.08607i	0.0701182	−	0.153538i
$405$	−0.142315	−	0.989821i	−0.00707168	−	0.0491846i
$406$	−0.170585	−	0.196866i	−0.00846601	−	0.00977030i
$407$	1.54164	+	3.37571i	0.0764161	+	0.167328i
$408$	3.16135	−	2.03168i	0.156510	−	0.100583i
$409$	−3.83749	+	26.6903i	−0.189752	+	1.31975i	0.642898	+	0.765952i	$0.277732\pi$
$409$	−3.83749	+	26.6903i	−0.189752	+	1.31975i	−0.832650	+	0.553800i	$0.813177\pi$
$410$	9.25600	+	5.94847i	0.457121	+	0.293774i
$411$	13.5175	−	15.6001i	0.666771	−	0.769495i
$412$	7.15522	+	2.10096i	0.352512	+	0.103507i
$413$	0.745512			0.0366843
$414$	−4.61481	+	1.30518i	−0.226806	+	0.0641459i
$415$	5.07743			0.249241
$416$	−6.56377	−	1.92730i	−0.321816	−	0.0944936i
$417$	−6.52339	+	7.52839i	−0.319452	+	0.368667i
$418$	3.58973	+	2.30698i	0.175579	+	0.112838i
$419$	−2.61432	+	18.1830i	−0.127718	+	0.888297i	0.820719	+	0.571332i	$0.193573\pi$
$419$	−2.61432	+	18.1830i	−0.127718	+	0.888297i	−0.948437	+	0.316965i	$0.897336\pi$
$420$	−0.237363	+	0.152544i	−0.0115821	+	0.00744337i
$421$	10.6849	+	23.3966i	0.520749	+	1.14028i	0.969155	+	0.246451i	$0.0792645\pi$
$421$	10.6849	+	23.3966i	0.520749	+	1.14028i	−0.448406	+	0.893830i	$0.648008\pi$
$422$	−12.3608	−	14.2652i	−0.601716	−	0.694417i
$423$	−1.56379	−	10.8764i	−0.0760342	−	0.528829i
$424$	−0.896767	+	1.96365i	−0.0435508	+	0.0953630i
$425$	−3.60568	+	1.05872i	−0.174901	+	0.0513556i
$426$	−2.52713	+	0.742033i	−0.122440	+	0.0359516i
$427$	1.25221	−	2.74197i	0.0605989	−	0.132693i
$428$	0.147777	+	1.02781i	0.00714307	+	0.0496811i
$429$	−6.52516	−	7.53044i	−0.315038	−	0.363573i
$430$	−1.32675	−	2.90517i	−0.0639814	−	0.140100i
$431$	−9.30161	+	5.97778i	−0.448043	+	0.287940i	−0.745141	−	0.666907i	$-0.767618\pi$
$431$	−9.30161	+	5.97778i	−0.448043	+	0.287940i	0.297098	+	0.954847i	$0.403981\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	−32.1362	−	20.6527i	−1.54437	−	0.992504i	−0.986721	−	0.162426i	$-0.948068\pi$
$433$	−32.1362	−	20.6527i	−1.54437	−	0.992504i	−0.557646	−	0.830079i	$-0.688295\pi$
$434$	−0.720305	+	0.831276i	−0.0345757	+	0.0399025i
$435$	0.885828	+	0.260102i	0.0424722	+	0.0124710i
$436$	11.4096			0.546421
$437$	−2.13810	+	13.8861i	−0.102279	+	0.664263i
$438$	−4.13273			−0.197469
$439$	−20.9948	−	6.16464i	−1.00203	−	0.294222i	−0.260740	−	0.965409i	$-0.583967\pi$
$439$	−20.9948	−	6.16464i	−1.00203	−	0.294222i	−0.741288	+	0.671187i	$0.765785\pi$
$440$	−0.953848	+	1.10080i	−0.0454729	+	0.0524786i
$441$	−5.82180	−	3.74144i	−0.277229	−	0.178164i
$442$	−3.65854	+	25.4457i	−0.174019	+	1.21033i
$443$	16.1353	−	10.3696i	0.766613	−	0.492672i	−0.0979533	−	0.995191i	$-0.531230\pi$
$443$	16.1353	−	10.3696i	0.766613	−	0.492672i	0.864566	+	0.502519i	$0.167593\pi$
$444$	1.05840	+	2.31758i	0.0502296	+	0.109988i
$445$	2.50730	+	2.89357i	0.118857	+	0.137169i
$446$	−2.89931	−	20.1652i	−0.137286	−	0.954848i
$447$	−8.24838	+	18.0614i	−0.390135	+	0.854276i
$448$	0.270724	−	0.0794918i	0.0127905	−	0.00375564i
$449$	21.5909	−	6.33967i	1.01894	−	0.299188i	0.270734	−	0.962654i	$-0.412734\pi$
$449$	21.5909	−	6.33967i	1.01894	−	0.299188i	0.748206	+	0.663467i	$0.230916\pi$
$450$	0.415415	−	0.909632i	0.0195829	−	0.0428805i
$451$	−2.28075	−	15.8629i	−0.107396	−	0.746957i
$452$	−3.75965	−	4.33886i	−0.176839	−	0.204083i
$453$	−9.19350	−	20.1310i	−0.431948	−	0.945835i
$454$	−6.24258	+	4.01186i	−0.292979	+	0.188286i
$455$	0.274693	−	1.91053i	0.0128778	−	0.0895671i
$456$	2.46452	+	1.58385i	0.115412	+	0.0741705i
$457$	10.6503	−	12.2911i	0.498201	−	0.574955i	−0.449837	−	0.893111i	$-0.648518\pi$
$457$	10.6503	−	12.2911i	0.498201	−	0.574955i	0.948038	+	0.318156i	$0.103063\pi$
$458$	16.7796	+	4.92693i	0.784058	+	0.230220i
$459$	3.75790			0.175404
$460$	−4.58786	−	1.39697i	−0.213910	−	0.0651342i
$461$	−23.1320			−1.07737			−0.538683	−	0.842509i	$-0.681078\pi$
$461$	−23.1320			−1.07737			−0.538683	+	0.842509i	$0.681078\pi$
$462$	0.394328	+	0.115785i	0.0183458	+	0.00538681i
$463$	−11.8052	+	13.6239i	−0.548634	+	0.633157i	−0.960564	−	0.278058i	$-0.910309\pi$
$463$	−11.8052	+	13.6239i	−0.548634	+	0.633157i	0.411930	+	0.911215i	$0.364855\pi$
$464$	−0.776666	−	0.499133i	−0.0360558	−	0.0231717i
$465$	0.554794	−	3.85868i	0.0257280	−	0.178942i
$466$	−5.91297	+	3.80004i	−0.273913	+	0.176033i
$467$	−12.1233	−	26.5462i	−0.560998	−	1.22841i	−0.951454	−	0.307792i	$-0.900410\pi$
$467$	−12.1233	−	26.5462i	−0.560998	−	1.22841i	0.390456	−	0.920622i	$-0.372317\pi$
$468$	−4.47982	−	5.16999i	−0.207080	−	0.238983i
$469$	−0.553855	−	3.85214i	−0.0255746	−	0.177875i
$470$	4.56469	−	9.99527i	0.210553	−	0.461048i
$471$	17.2572	−	5.06719i	0.795172	−	0.233484i
$472$	2.53519	−	0.744400i	0.116692	−	0.0342638i
$473$	−1.93249	+	4.23157i	−0.0888562	+	0.194568i
$474$	−0.944392	−	6.56839i	−0.0433774	−	0.301696i
$475$	−1.91846	−	2.21403i	−0.0880252	−	0.101586i
$476$	−0.440467	−	0.964488i	−0.0201888	−	0.0442072i
$477$	−1.81603	+	1.16709i	−0.0831505	+	0.0534376i
$478$	−0.748544	+	5.20624i	−0.0342376	+	0.238128i
$479$	9.49229	+	6.10032i	0.433714	+	0.278731i	0.739226	−	0.673457i	$-0.235191\pi$
$479$	9.49229	+	6.10032i	0.433714	+	0.278731i	−0.305513	+	0.952188i	$0.598828\pi$
$480$	−0.654861	+	0.755750i	−0.0298902	+	0.0344951i
$481$	−16.7233	−	4.91042i	−0.762519	−	0.223896i
$482$	−19.4486			−0.885859
$483$	0.179205	+	1.34124i	0.00815413	+	0.0610286i
$484$	−8.87841			−0.403564
$485$	4.62848	+	1.35904i	0.210168	+	0.0617110i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	29.7797	+	19.1383i	1.34945	+	0.867238i	0.997628	−	0.0688301i	$-0.0219266\pi$
$487$	29.7797	+	19.1383i	1.34945	+	0.867238i	0.351820	+	0.936068i	$0.385563\pi$
$488$	1.52041	−	10.5747i	0.0688258	−	0.478694i
$489$	4.02827	−	2.58881i	0.182165	−	0.117070i
$490$	−2.87483	−	6.29501i	−0.129872	−	0.284379i
$491$	−8.70307	−	10.0439i	−0.392764	−	0.453274i	0.524585	−	0.851358i	$-0.324221\pi$
$491$	−8.70307	−	10.0439i	−0.392764	−	0.453274i	−0.917349	+	0.398084i	$0.869675\pi$
$492$	−1.56584	−	10.8906i	−0.0705934	−	0.490988i
$493$	−1.44124	+	3.15587i	−0.0649100	+	0.142133i
$494$	−19.2291	+	5.64616i	−0.865157	+	0.254033i
$495$	−1.39757	+	0.410362i	−0.0628159	+	0.0184444i
$496$	−1.61944	+	3.54607i	−0.0727148	+	0.159223i
$497$	0.105760	+	0.735578i	0.00474399	+	0.0329952i
$498$	−3.32501	−	3.83726i	−0.148997	−	0.171952i
$499$	2.26974	+	4.97004i	0.101608	+	0.222489i	0.953608	−	0.301052i	$-0.0973378\pi$
$499$	2.26974	+	4.97004i	0.101608	+	0.222489i	−0.852000	+	0.523541i	$0.824611\pi$
$500$	0.841254	−	0.540641i	0.0376220	−	0.0241782i
$501$	1.20600	−	8.38791i	0.0538801	−	0.374744i
$502$	22.5829	+	14.5131i	1.00792	+	0.647753i
$503$	−22.6596	+	26.1506i	−1.01034	+	1.16600i	−0.0242653	+	0.999706i	$0.507725\pi$
$503$	−22.6596	+	26.1506i	−1.01034	+	1.16600i	−0.986077	+	0.166291i	$0.946821\pi$
$504$	0.270724	+	0.0794918i	0.0120590	+	0.00354085i
$505$	3.39265			0.150971
$506$	2.83833	+	6.38282i	0.126179	+	0.283751i
$507$	33.7976			1.50100
$508$	−13.7715	−	4.04367i	−0.611010	−	0.179409i
$509$	−20.8599	+	24.0736i	−0.924597	+	1.06704i	0.0729706	+	0.997334i	$0.476752\pi$
$509$	−20.8599	+	24.0736i	−0.924597	+	1.06704i	−0.997567	+	0.0697076i	$0.977793\pi$
$510$	3.16135	+	2.03168i	0.139987	+	0.0899641i
$511$	−0.165948	+	1.15419i	−0.00734112	+	0.0510586i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	1.21699	+	2.66484i	0.0537314	+	0.117655i
$514$	0.519453	+	0.599480i	0.0229121	+	0.0264419i
$515$	1.06128	+	7.38139i	0.0467657	+	0.325263i
$516$	−1.32675	+	2.90517i	−0.0584067	+	0.127893i
$517$	−15.3568	+	4.50917i	−0.675392	+	0.198313i
$518$	0.689758	−	0.202531i	0.0303062	−	0.00889871i
$519$	−7.61033	+	16.6643i	−0.334057	+	0.731482i
$520$	−0.973558	−	6.77125i	−0.0426934	−	0.296939i
$521$	−18.3923	−	21.2259i	−0.805782	−	0.929922i	0.192901	−	0.981218i	$-0.438210\pi$
$521$	−18.3923	−	21.2259i	−0.805782	−	0.929922i	−0.998684	+	0.0512958i	$0.983665\pi$
$522$	−0.383521	−	0.839795i	−0.0167863	−	0.0367568i
$523$	−5.84185	+	3.75433i	−0.255446	+	0.164165i	−0.662096	−	0.749419i	$-0.730333\pi$
$523$	−5.84185	+	3.75433i	−0.255446	+	0.164165i	0.406650	+	0.913584i	$0.366697\pi$
$524$	−0.0233709	+	0.162548i	−0.00102096	+	0.00710096i
$525$	−0.237363	−	0.152544i	−0.0103594	−	0.00665755i
$526$	19.8731	−	22.9348i	0.866508	−	1.00000i
$527$	14.0562	+	4.12728i	0.612299	+	0.179787i
$528$	1.45657			0.0633889
$529$	−15.4055	+	17.0783i	−0.669806	+	0.742536i
$530$	−2.15872			−0.0937690
$531$	2.53519	+	0.744400i	0.110018	+	0.0323042i
$532$	0.541301	−	0.624695i	0.0234684	−	0.0270840i
$533$	63.3192	+	40.6928i	2.74266	+	1.76260i
$534$	0.544887	−	3.78977i	0.0235796	−	0.164000i
$535$	−0.873541	+	0.561391i	−0.0377665	+	0.0242710i
$536$	−5.72984	−	12.5466i	−0.247491	−	0.541930i
$537$	0.723157	+	0.834568i	0.0312065	+	0.0360143i
$538$	3.83150	+	26.6487i	0.165188	+	1.14891i
$539$	−4.18739	+	9.16910i	−0.180364	+	0.394941i
$540$	−0.959493	+	0.281733i	−0.0412900	+	0.0121238i
$541$	18.9307	−	5.55855i	0.813894	−	0.238981i	0.151809	−	0.988410i	$-0.451490\pi$
$541$	18.9307	−	5.55855i	0.813894	−	0.238981i	0.662085	+	0.749429i	$0.269672\pi$
$542$	10.8700	−	23.8021i	0.466908	−	1.02239i
$543$	−1.39028	−	9.66961i	−0.0596626	−	0.414963i
$544$	−2.46090	−	2.84003i	−0.105510	−	0.121765i
$545$	4.73972	+	10.3785i	0.203027	+	0.444568i
$546$	−1.62377	+	1.04353i	−0.0694909	+	0.0446591i
$547$	−3.86900	+	26.9095i	−0.165426	+	1.15057i	0.722765	+	0.691093i	$0.242871\pi$
$547$	−3.86900	+	26.9095i	−0.165426	+	1.15057i	−0.888192	+	0.459473i	$0.848038\pi$
$548$	−17.3650	−	11.1598i	−0.741798	−	0.476725i
$549$	6.99617	−	8.07400i	0.298589	−	0.344590i
$550$	−1.39757	−	0.410362i	−0.0595924	−	0.0174979i
$551$	−2.70466			−0.115222
$552$	1.94865	+	4.38210i	0.0829399	+	0.186514i
$553$	−1.87235			−0.0796206
$554$	−6.86066	−	2.01447i	−0.291481	−	0.0855867i
$555$	−1.66847	+	1.92552i	−0.0708226	+	0.0817336i
$556$	8.38014	+	5.38559i	0.355397	+	0.228400i
$557$	−2.58240	+	17.9610i	−0.109420	+	0.761030i	0.859049	+	0.511894i	$0.171056\pi$
$557$	−2.58240	+	17.9610i	−0.109420	+	0.761030i	−0.968468	+	0.249136i	$0.919853\pi$
$558$	−3.27951	+	2.10761i	−0.138833	+	0.0892223i
$559$	−9.07611	−	19.8739i	−0.383878	−	0.840577i
$560$	0.184771	+	0.213237i	0.00780801	+	0.00901093i
$561$	−0.778979	−	5.41792i	−0.0328885	−	0.228745i
$562$	7.41465	−	16.2358i	0.312768	−	0.684867i
$563$	−45.0754	+	13.2353i	−1.89970	+	0.557803i	−0.910010	+	0.414586i	$0.863926\pi$
$563$	−45.0754	+	13.2353i	−1.89970	+	0.557803i	−0.989691	+	0.143216i	$0.954256\pi$
$564$	−10.5432	+	3.09575i	−0.443947	+	0.130355i
$565$	2.38496	−	5.22232i	0.100336	−	0.219705i
$566$	1.12195	+	7.80331i	0.0471589	+	0.327998i
$567$	0.184771	+	0.213237i	0.00775967	+	0.00895513i
$568$	1.09413	+	2.39581i	0.0459086	+	0.100526i
$569$	−6.21297	+	3.99284i	−0.260461	+	0.167388i	−0.664354	−	0.747418i	$-0.731293\pi$
$569$	−6.21297	+	3.99284i	−0.260461	+	0.167388i	0.403893	+	0.914806i	$0.367657\pi$
$570$	−0.416922	+	2.89976i	−0.0174629	+	0.121457i
$571$	5.40551	+	3.47391i	0.226214	+	0.145379i	0.648839	−	0.760926i	$-0.275255\pi$
$571$	5.40551	+	3.47391i	0.226214	+	0.145379i	−0.422625	+	0.906305i	$0.638891\pi$
$572$	−6.52516	+	7.53044i	−0.272831	+	0.314863i
$573$	10.1284	+	2.97396i	0.423120	+	0.124239i
$574$	−3.10443			−0.129576
$575$	−0.635134	−	4.75359i	−0.0264869	−	0.198238i
$576$	1.00000			0.0416667
$577$	1.53711	+	0.451337i	0.0639909	+	0.0187894i	0.313571	−	0.949565i	$-0.398475\pi$
$577$	1.53711	+	0.451337i	0.0639909	+	0.0187894i	−0.249580	+	0.968354i	$0.580293\pi$
$578$	1.88480	−	2.17518i	0.0783974	−	0.0904755i
$579$	0.863711	+	0.555073i	0.0358946	+	0.0230681i
$580$	0.131389	−	0.913828i	0.00545561	−	0.0379446i
$581$	−1.20519	+	0.774529i	−0.0499998	+	0.0321329i
$582$	−2.00391	−	4.38795i	−0.0830648	−	0.181886i
$583$	2.05910	+	2.37632i	0.0852790	+	0.0984173i
$584$	0.588148	+	4.09066i	0.0243378	+	0.169273i
$585$	2.84180	−	6.22268i	0.117494	−	0.257276i
$586$	−28.4732	+	8.36049i	−1.17622	+	0.345369i
$587$	−9.22083	+	2.70748i	−0.380584	+	0.111750i	−0.466428	−	0.884559i	$-0.654459\pi$
$587$	−9.22083	+	2.70748i	−0.380584	+	0.111750i	0.0858441	+	0.996309i	$0.472641\pi$
$588$	−2.87483	+	6.29501i	−0.118556	+	0.259602i
$589$	1.62531	+	11.3043i	0.0669698	+	0.465785i
$590$	1.73029	+	1.99686i	0.0712348	+	0.0822094i
$591$	2.64771	+	5.79768i	0.108912	+	0.238485i
$592$	2.14337	−	1.37746i	0.0880918	−	0.0566132i
$593$	−0.904385	+	6.29013i	−0.0371386	+	0.258305i	−0.999929	−	0.0119458i	$-0.996197\pi$
$593$	−0.904385	+	6.29013i	−0.0371386	+	0.258305i	0.962790	+	0.270251i	$0.0871065\pi$
$594$	1.22534	+	0.787479i	0.0502764	+	0.0323107i
$595$	0.694352	−	0.801325i	0.0284657	−	0.0328511i
$596$	19.0515	+	5.59401i	0.780378	+	0.229140i
$597$	8.14246			0.333249
$598$	−31.3850	−	9.55653i	−1.28343	−	0.390795i
$599$	−21.3664			−0.873008			−0.436504	−	0.899702i	$-0.643784\pi$
$599$	−21.3664			−0.873008			−0.436504	+	0.899702i	$0.643784\pi$
$600$	−0.959493	−	0.281733i	−0.0391711	−	0.0115017i
$601$	−21.1358	+	24.3921i	−0.862149	+	0.994973i	0.137841	+	0.990454i	$0.455984\pi$
$601$	−21.1358	+	24.3921i	−0.862149	+	0.994973i	−0.999990	+	0.00451841i	$0.998562\pi$
$602$	0.758085	+	0.487192i	0.0308972	+	0.0198565i
$603$	1.96295	−	13.6526i	0.0799377	−	0.555979i
$604$	−18.6177	+	11.9649i	−0.757543	+	0.486843i
$605$	−3.68823	−	8.07609i	−0.149948	−	0.328340i
$606$	−2.22172	−	2.56400i	−0.0902510	−	0.104155i
$607$	1.61903	+	11.2606i	0.0657144	+	0.457054i	0.995937	+	0.0900571i	$0.0287049\pi$
$607$	1.61903	+	11.2606i	0.0657144	+	0.457054i	−0.930222	+	0.366997i	$0.880386\pi$
$608$	1.21699	−	2.66484i	0.0493554	−	0.108073i
$609$	−0.249939	+	0.0733888i	−0.0101281	+	0.00297387i
$610$	10.2507	−	3.00987i	0.415038	−	0.121866i
$611$	31.2265	−	68.3764i	1.26329	−	2.76621i
$612$	−0.534805	−	3.71965i	−0.0216182	−	0.150358i
$613$	−28.9419	−	33.4007i	−1.16895	−	1.34904i	−0.925325	−	0.379174i	$-0.876208\pi$
$613$	−28.9419	−	33.4007i	−1.16895	−	1.34904i	−0.243627	−	0.969869i	$-0.578337\pi$
$614$	7.47487	+	16.3677i	0.301661	+	0.660546i
$615$	9.25600	−	5.94847i	0.373238	−	0.239865i
$616$	0.0584879	−	0.406792i	0.00235655	−	0.0163901i
$617$	−20.9852	−	13.4864i	−0.844832	−	0.542940i	0.0451272	−	0.998981i	$-0.485631\pi$
$617$	−20.9852	−	13.4864i	−0.844832	−	0.542940i	−0.889959	+	0.456041i	$0.849267\pi$
$618$	4.88349	−	5.63585i	0.196443	−	0.226707i
$619$	−8.49720	−	2.49500i	−0.341531	−	0.100283i	0.106469	−	0.994316i	$-0.466045\pi$
$619$	−8.49720	−	2.49500i	−0.341531	−	0.100283i	−0.448000	+	0.894033i	$0.647864\pi$
$620$	−3.89836			−0.156562
$621$	−0.729834	+	4.73997i	−0.0292872	+	0.190209i
$622$	−31.5997			−1.26703
$623$	−1.03653	−	0.304354i	−0.0415279	−	0.0121937i
$624$	−4.47982	+	5.16999i	−0.179336	+	0.206965i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−0.417265	+	2.90214i	−0.0166773	+	0.115993i
$627$	3.58973	−	2.30698i	0.143360	−	0.0921319i
$628$	−7.47157	−	16.3605i	−0.298148	−	0.652853i
$629$	−6.26995	−	7.23590i	−0.249999	−	0.288514i
$630$	0.0401546	+	0.279282i	0.00159980	+	0.0111268i
$631$	−3.20001	+	7.00704i	−0.127390	+	0.278946i	−0.962571	−	0.271030i	$-0.912636\pi$
$631$	−3.20001	+	7.00704i	−0.127390	+	0.278946i	0.835181	+	0.549976i	$0.185363\pi$
$632$	−6.36713	+	1.86956i	−0.253271	+	0.0743671i
$633$	−18.1109	+	5.31785i	−0.719844	+	0.211365i
$634$	−3.92800	+	8.60112i	−0.156001	+	0.341594i
$635$	−2.04262	−	14.2068i	−0.0810591	−	0.563778i
$636$	1.41366	+	1.63146i	0.0560554	+	0.0646914i
$637$	−19.6664	−	43.0634i	−0.779211	−	1.70623i
$638$	−1.13127	+	0.727020i	−0.0447872	+	0.0287830i
$639$	−0.374832	+	2.60701i	−0.0148281	+	0.103132i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	20.5991	−	23.7727i	0.813616	−	0.938963i	−0.185428	−	0.982658i	$-0.559367\pi$
$641$	20.5991	−	23.7727i	0.813616	−	0.938963i	0.999045	+	0.0436943i	$0.0139128\pi$
$642$	0.996319	+	0.292546i	0.0393216	+	0.0115459i
$643$	−9.43504			−0.372082			−0.186041	−	0.982542i	$-0.559566\pi$
$643$	−9.43504			−0.372082			−0.186041	+	0.982542i	$0.559566\pi$
$644$	1.30209	−	0.368260i	0.0513094	−	0.0145115i
$645$	−3.19378			−0.125755
$646$	−10.5631	−	3.10161i	−0.415600	−	0.122031i
$647$	−13.5963	+	15.6910i	−0.534525	+	0.616875i	−0.957207	−	0.289403i	$-0.906543\pi$
$647$	−13.5963	+	15.6910i	−0.534525	+	0.616875i	0.422682	+	0.906278i	$0.361089\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	0.547709	−	3.80940i	0.0214995	−	0.149532i
$650$	5.75491	−	3.69846i	0.225726	−	0.145065i
$651$	0.456930	+	1.00054i	0.0179085	+	0.0392141i
$652$	−3.13575	−	3.61885i	−0.122805	−	0.141725i
$653$	0.327256	+	2.27611i	0.0128065	+	0.0890713i	0.995222	−	0.0976351i	$-0.0311278\pi$
$653$	0.327256	+	2.27611i	0.0128065	+	0.0890713i	−0.982416	+	0.186706i	$0.940219\pi$
$654$	4.73972	−	10.3785i	0.185338	−	0.405833i
$655$	−0.157568	+	0.0462661i	−0.00615669	+	0.00180777i
$656$	−10.5569	+	3.09980i	−0.412179	+	0.121027i
$657$	−1.71680	+	3.75926i	−0.0669786	+	0.146663i
$658$	0.441230	+	3.06882i	0.0172009	+	0.119635i
$659$	−13.0752	−	15.0896i	−0.509338	−	0.587808i	0.441591	−	0.897217i	$-0.354414\pi$
$659$	−13.0752	−	15.0896i	−0.509338	−	0.587808i	−0.950929	+	0.309409i	$0.899869\pi$
$660$	0.605080	+	1.32494i	0.0235527	+	0.0515732i
$661$	8.31494	−	5.34369i	0.323414	−	0.207845i	−0.368852	−	0.929488i	$-0.620249\pi$
$661$	8.31494	−	5.34369i	0.323414	−	0.207845i	0.692266	+	0.721643i	$0.256613\pi$
$662$	−2.58079	+	17.9498i	−0.100305	+	0.697639i
$663$	21.6264	+	13.8984i	0.839900	+	0.539771i
$664$	−3.32501	+	3.83726i	−0.129035	+	0.148915i
$665$	0.793107	+	0.232877i	0.0307554	+	0.00903060i
$666$	2.54782			0.0987262
$667$	−3.70070	−	2.43079i	−0.143292	−	0.0941206i
$668$	−8.47417			−0.327875
$669$	−19.5473	−	5.73960i	−0.755742	−	0.221906i
$670$	9.03252	−	10.4241i	0.348957	−	0.402718i
$671$	−13.0909	−	8.41299i	−0.505367	−	0.324780i
$672$	0.0401546	−	0.279282i	0.00154900	−	0.0107735i
$673$	14.5768	−	9.36795i	0.561895	−	0.361108i	−0.228653	−	0.973508i	$-0.573432\pi$
$673$	14.5768	−	9.36795i	0.561895	−	0.361108i	0.790548	+	0.612400i	$0.209796\pi$
$674$	−7.32700	−	16.0439i	−0.282226	−	0.617988i
$675$	−0.654861	−	0.755750i	−0.0252056	−	0.0290888i
$676$	−4.80990	−	33.4536i	−0.184996	−	1.28668i
$677$	−2.23128	+	4.88583i	−0.0857552	+	0.187778i	−0.947651	−	0.319307i	$-0.896550\pi$
$677$	−2.23128	+	4.88583i	−0.0857552	+	0.187778i	0.861896	+	0.507085i	$0.169277\pi$
$678$	−5.50858	+	1.61747i	−0.211556	+	0.0621184i
$679$	−1.30594	+	0.383459i	−0.0501174	+	0.0147158i
$680$	1.56109	−	3.41831i	0.0598650	−	0.131086i
$681$	1.05606	+	7.34504i	0.0404682	+	0.281463i
$682$	3.71844	+	4.29131i	0.142386	+	0.164323i
$683$	−7.81598	−	17.1146i	−0.299070	−	0.654873i	0.699120	−	0.715004i	$-0.253575\pi$
$683$	−7.81598	−	17.1146i	−0.299070	−	0.654873i	−0.998190	+	0.0601315i	$0.980848\pi$
$684$	2.46452	−	1.58385i	0.0942331	−	0.0605599i
$685$	2.93764	−	20.4318i	0.112242	−	0.780657i
$686$	3.30418	+	2.12347i	0.126154	+	0.0810744i
$687$	11.4522	−	13.2165i	0.436928	−	0.504241i
$688$	3.06441	+	0.899793i	0.116830	+	0.0343043i
$689$	−14.7676			−0.562600
$690$	−3.17660	+	3.59294i	−0.120931	+	0.136781i
$691$	6.65156			0.253037			0.126519	−	0.991964i	$-0.459620\pi$
$691$	6.65156			0.253037			0.126519	+	0.991964i	$0.459620\pi$
$692$	17.5778	+	5.16129i	0.668206	+	0.196203i
$693$	0.269132	−	0.310595i	0.0102235	−	0.0117985i
$694$	5.23680	+	3.36549i	0.198786	+	0.127752i
$695$	−1.41767	+	9.86010i	−0.0537752	+	0.374015i
$696$	−0.776666	+	0.499133i	−0.0294394	+	0.0189196i
$697$	17.1761	+	37.6104i	0.650591	+	1.42459i
$698$	4.31992	+	4.98546i	0.163511	+	0.188702i
$699$	1.00030	+	6.95722i	0.0378347	+	0.263146i
$700$	−0.117211	+	0.256656i	−0.00443015	+	0.00970068i
$701$	−7.14922	+	2.09920i	−0.270022	+	0.0792857i	−0.413941	−	0.910304i	$-0.635848\pi$
$701$	−7.14922	+	2.09920i	−0.270022	+	0.0792857i	0.143918	+	0.989590i	$0.454030\pi$
$702$	−6.56377	+	1.92730i	−0.247734	+	0.0727412i
$703$	3.10067	−	6.78953i	0.116944	−	0.256072i
$704$	−0.207291	−	1.44174i	−0.00781258	−	0.0543377i
$705$	−7.19578	−	8.30437i	−0.271009	−	0.312761i
$706$	−9.78347	−	21.4228i	−0.368206	−	0.806258i
$707$	−0.805289	+	0.517528i	−0.0302860	+	0.0194636i
$708$	0.376027	−	2.61533i	0.0141320	−	0.0982901i
$709$	25.0073	+	16.0712i	0.939170	+	0.603568i	0.918159	−	0.396212i	$-0.129675\pi$
$709$	25.0073	+	16.0712i	0.939170	+	0.603568i	0.0210103	+	0.999779i	$0.493312\pi$
$710$	−1.72479	+	1.99051i	−0.0647300	+	0.0747024i
$711$	−6.36713	−	1.86956i	−0.238786	−	0.0701140i
$712$	−3.82875			−0.143488
$713$	−7.93579	+	16.9280i	−0.297198	+	0.633960i
$714$	−1.06031			−0.0396809
$715$	−9.56058	−	2.80724i	−0.357545	−	0.104985i
$716$	0.723157	−	0.834568i	0.0270257	−	0.0311893i
$717$	4.42480	+	2.84365i	0.165247	+	0.106198i
$718$	−2.54832	+	17.7239i	−0.0951023	+	0.661451i
$719$	−5.47787	+	3.52041i	−0.204290	+	0.131289i	−0.638786	−	0.769385i	$-0.720563\pi$
$719$	−5.47787	+	3.52041i	−0.204290	+	0.131289i	0.434496	+	0.900674i	$0.356927\pi$
$720$	0.415415	+	0.909632i	0.0154816	+	0.0339000i
$721$	−1.37789	−	1.59017i	−0.0513155	−	0.0592212i
$722$	1.48258	+	10.3116i	0.0551758	+	0.383756i
$723$	−8.07923	+	17.6910i	−0.300470	+	0.657937i
$724$	−9.37333	+	2.75226i	−0.348357	+	0.102287i
$725$	0.885828	−	0.260102i	0.0328988	−	0.00965996i
$726$	−3.68823	+	8.07609i	−0.136883	+	0.299732i
$727$	0.544460	+	3.78680i	0.0201929	+	0.140445i	0.997424	−	0.0717339i	$-0.0228532\pi$
$727$	0.544460	+	3.78680i	0.0201929	+	0.140445i	−0.977231	+	0.212179i	$0.931944\pi$
$728$	1.26400	+	1.45873i	0.0468469	+	0.0540642i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−3.47667	+	2.23432i	−0.128677	+	0.0826959i
$731$	1.70805	−	11.8798i	0.0631746	−	0.439389i
$732$	−8.98748	−	5.77590i	−0.332187	−	0.213484i
$733$	23.0417	−	26.5915i	0.851064	−	0.982181i	−0.148913	−	0.988850i	$-0.547578\pi$
$733$	23.0417	−	26.5915i	0.851064	−	0.982181i	0.999978	+	0.00666962i	$0.00212302\pi$
$734$	18.8679	+	5.54011i	0.696426	+	0.204489i
$735$	−6.92039			−0.255262
$736$	4.06017	−	2.55245i	0.149660	−	0.0940846i
$737$	−20.0905			−0.740042
$738$	−10.5569	−	3.09980i	−0.388607	−	0.114105i
$739$	11.5868	−	13.3718i	0.426226	−	0.491891i	−0.501498	−	0.865159i	$-0.667217\pi$
$739$	11.5868	−	13.3718i	0.426226	−	0.491891i	0.927723	+	0.373268i	$0.121763\pi$
$740$	2.14337	+	1.37746i	0.0787917	+	0.0506363i
$741$	−2.85211	+	19.8369i	−0.104775	+	0.728726i
$742$	0.512401	−	0.329300i	0.0188108	−	0.0120890i
$743$	4.17787	+	9.14826i	0.153271	+	0.335617i	0.970655	−	0.240476i	$-0.0773037\pi$
$743$	4.17787	+	9.14826i	0.153271	+	0.335617i	−0.817384	+	0.576093i	$0.804576\pi$
$744$	2.55288	+	2.94618i	0.0935932	+	0.108012i
$745$	2.82577	+	19.6536i	0.103528	+	0.720054i
$746$	8.75027	−	19.1604i	0.320370	−	0.701512i
$747$	−4.87175	+	1.43048i	−0.178248	+	0.0523384i
$748$	−5.25191	+	1.54210i	−0.192029	+	0.0563848i
$749$	0.121709	−	0.266506i	0.00444717	−	0.00973793i
$750$	−0.142315	−	0.989821i	−0.00519660	−	0.0361432i
$751$	21.1717	+	24.4334i	0.772566	+	0.891589i	0.996549	−	0.0830042i	$-0.0264515\pi$
$751$	21.1717	+	24.4334i	0.772566	+	0.891589i	−0.223983	+	0.974593i	$0.571906\pi$
$752$	4.56469	+	9.99527i	0.166457	+	0.364490i
$753$	22.5829	−	14.5131i	0.822966	−	0.528888i
$754$	0.898813	−	6.25138i	0.0327328	−	0.227662i
$755$	−18.6177	−	11.9649i	−0.677567	−	0.435446i
$756$	0.184771	−	0.213237i	0.00672007	−	0.00775537i
$757$	1.42967	+	0.419789i	0.0519622	+	0.0152575i	0.307610	−	0.951512i	$-0.400471\pi$
$757$	1.42967	+	0.419789i	0.0519622	+	0.0152575i	−0.255648	+	0.966770i	$0.582289\pi$
$758$	−13.8582			−0.503352
$759$	6.98510	+	0.0696775i	0.253543	+	0.00252913i
$760$	2.92958			0.106267
$761$	3.07157	+	0.901895i	0.111344	+	0.0326937i	0.336930	−	0.941530i	$-0.390611\pi$
$761$	3.07157	+	0.901895i	0.111344	+	0.0326937i	−0.225586	+	0.974223i	$0.572430\pi$
$762$	−9.39912	+	10.8472i	−0.340494	+	0.392951i
$763$	−2.70822	−	1.74046i	−0.0980440	−	0.0630090i
$764$	1.50227	−	10.4485i	0.0543503	−	0.378015i
$765$	3.16135	−	2.03168i	0.114299	−	0.0734554i
$766$	3.30469	+	7.23625i	0.119403	+	0.261456i
$767$	11.8367	+	13.6603i	0.427398	+	0.493244i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	5.98946	−	13.1151i	0.215986	−	0.472943i	−0.770365	−	0.637604i	$-0.779926\pi$
$769$	5.98946	−	13.1151i	0.215986	−	0.472943i	0.986350	+	0.164661i	$0.0526530\pi$
$770$	0.394328	−	0.115785i	0.0142106	−	0.00417261i
$771$	0.761095	−	0.223478i	0.0274102	−	0.00804835i
$772$	0.426505	−	0.933915i	0.0153502	−	0.0336123i
$773$	3.79568	+	26.3995i	0.136521	+	0.949524i	0.936792	+	0.349886i	$0.113780\pi$
$773$	3.79568	+	26.3995i	0.136521	+	0.949524i	−0.800271	+	0.599638i	$0.795311\pi$
$774$	2.09148	+	2.41370i	0.0751768	+	0.0867587i
$775$	−1.61944	−	3.54607i	−0.0581719	−	0.127379i
$776$	−4.05810	+	2.60798i	−0.145677	+	0.0936212i
$777$	0.102307	−	0.711560i	0.00367024	−	0.0255271i
$778$	−17.0778	−	10.9752i	−0.612268	−	0.393481i
$779$	−21.1081	+	24.3601i	−0.756278	+	0.872791i
$780$	−6.56377	−	1.92730i	−0.235021	−	0.0690083i
$781$	3.83633			0.137275
$782$	−11.6656	−	13.7374i	−0.417162	−	0.491247i
$783$	−0.923225			−0.0329934
$784$	6.64006	+	1.94970i	0.237145	+	0.0696321i
$785$	11.7782	−	13.5928i	0.420382	−	0.485146i
$786$	0.138151	+	0.0887840i	0.00492767	+	0.00316682i
$787$	1.59855	−	11.1182i	0.0569823	−	0.396321i	−0.941292	−	0.337594i	$-0.890387\pi$
$787$	1.59855	−	11.1182i	0.0569823	−	0.396321i	0.998274	−	0.0587266i	$-0.0187040\pi$
$788$	5.36186	−	3.44586i	0.191008	−	0.122754i
$789$	−12.6066	−	27.6047i	−0.448808	−	0.982752i
$790$	−4.34561	−	5.01511i	−0.154610	−	0.178429i
$791$	0.230533	+	1.60340i	0.00819683	+	0.0570102i
$792$	0.605080	−	1.32494i	0.0215006	−	0.0470797i
$793$	70.1237	−	20.5902i	2.49017	−	0.731179i
$794$	33.0229	−	9.69640i	1.17194	−	0.344112i
$795$	−0.896767	+	1.96365i	−0.0318050	+	0.0696433i
$796$	−1.15879	−	8.05959i	−0.0410723	−	0.285664i
$797$	30.8606	+	35.6150i	1.09314	+	1.26155i	0.962840	+	0.270074i	$0.0870481\pi$
$797$	30.8606	+	35.6150i	1.09314	+	1.26155i	0.130298	+	0.991475i	$0.458406\pi$
$798$	−0.343378	−	0.751893i	−0.0121554	−	0.0266167i
$799$	34.7377	−	22.3246i	1.22893	−	0.789787i
$800$	−0.142315	+	0.989821i	−0.00503159	+	0.0349955i
$801$	−3.22095	−	2.06998i	−0.113807	−	0.0731390i
$802$	−14.9448	+	17.2473i	−0.527720	+	0.609022i
$803$	5.77576	+	1.69592i	0.203822	+	0.0598476i
$804$	−13.7930			−0.486443
$805$	0.875887	+	1.03144i	0.0308710	+	0.0363534i
$806$	−26.6682			−0.939347
$807$	25.8321	+	7.58500i	0.909334	+	0.267005i
$808$	−2.22172	+	2.56400i	−0.0781597	+	0.0902011i
$809$	20.5200	+	13.1874i	0.721446	+	0.463645i	0.849140	−	0.528168i	$-0.177121\pi$
$809$	20.5200	+	13.1874i	0.721446	+	0.463645i	−0.127693	+	0.991814i	$0.540757\pi$
$810$	−0.142315	+	0.989821i	−0.00500043	+	0.0347788i
$811$	−30.3347	+	19.4949i	−1.06519	+	0.684559i	−0.951091	−	0.308910i	$-0.900036\pi$
$811$	−30.3347	+	19.4949i	−1.06519	+	0.684559i	−0.114103	+	0.993469i	$0.536399\pi$
$812$	0.108212	+	0.236951i	0.00379749	+	0.00831535i
$813$	−17.1355	−	19.7755i	−0.600970	−	0.693556i
$814$	−0.528141	−	3.67330i	−0.0185113	−	0.128749i
$815$	1.98918	−	4.35570i	0.0696780	−	0.152573i
$816$	−3.60568	+	1.05872i	−0.126224	+	0.0370627i
$817$	8.97743	−	2.63601i	0.314081	−	0.0922224i
$818$	11.2016	−	24.5280i	0.391654	−	0.857603i
$819$	0.274693	+	1.91053i	0.00959855	+	0.0667594i
$820$	−7.20519	−	8.31523i	−0.251616	−	0.290381i
$821$	10.0712	+	22.0529i	0.351488	+	0.769651i	0.999965	+	0.00841677i	$0.00267917\pi$
$821$	10.0712	+	22.0529i	0.351488	+	0.769651i	−0.648477	+	0.761235i	$0.724594\pi$
$822$	−17.3650	+	11.1598i	−0.605675	+	0.389244i
$823$	−4.51325	+	31.3903i	−0.157322	+	1.09420i	0.746220	+	0.665699i	$0.231866\pi$
$823$	−4.51325	+	31.3903i	−0.157322	+	1.09420i	−0.903542	+	0.428499i	$0.859043\pi$
$824$	−6.27348	−	4.03172i	−0.218547	−	0.140452i
$825$	−0.953848	+	1.10080i	−0.0332087	+	0.0383249i
$826$	−0.715314	−	0.210035i	−0.0248890	−	0.00730806i
$827$	−54.6304			−1.89968			−0.949842	−	0.312729i	$-0.898757\pi$
$827$	−54.6304			−1.89968			−0.949842	+	0.312729i	$0.898757\pi$
$828$	4.79559	+	0.0478368i	0.166658	+	0.00166244i
$829$	7.64632			0.265568			0.132784	−	0.991145i	$-0.457608\pi$
$829$	7.64632			0.265568			0.132784	+	0.991145i	$0.457608\pi$
$830$	−4.87175	−	1.43048i	−0.169101	−	0.0496525i
$831$	−4.68245	+	5.40383i	−0.162432	+	0.187457i
$832$	5.75491	+	3.69846i	0.199516	+	0.128221i
$833$	3.70106	−	25.7414i	0.128234	−	0.891888i
$834$	8.38014	−	5.38559i	0.290181	−	0.186488i
$835$	−3.52030	−	7.70838i	−0.121825	−	0.266759i
$836$	−2.79437	−	3.22488i	−0.0966453	−	0.111535i
$837$	0.554794	+	3.85868i	0.0191765	+	0.133375i
$838$	7.63116	−	16.7099i	0.263614	−	0.577234i
$839$	−16.3760	+	4.80842i	−0.565362	+	0.166005i	−0.551909	−	0.833904i	$-0.686100\pi$
$839$	−16.3760	+	4.80842i	−0.565362	+	0.166005i	−0.0134527	+	0.999910i	$0.504282\pi$
$840$	0.270724	−	0.0794918i	0.00934088	−	0.00274273i
$841$	−11.6930	+	25.6040i	−0.403205	+	0.882897i
$842$	−3.66047	−	25.4592i	−0.126148	−	0.877380i
$843$	−11.6885	−	13.4892i	−0.402572	−	0.464593i
$844$	7.84117	+	17.1698i	0.269904	+	0.591008i
$845$	28.4324	−	18.2724i	0.978103	−	0.628589i
$846$	−1.56379	+	10.8764i	−0.0537643	+	0.373939i
$847$	2.10740	+	1.35435i	0.0724113	+	0.0465359i
$848$	1.41366	−	1.63146i	0.0485454	−	0.0560244i
$849$	7.56421	+	2.22105i	0.259603	+	0.0762264i
$850$	3.75790			0.128895
$851$	10.3446	−	6.50319i	0.354608	−	0.222927i
$852$	2.63382			0.0902332
$853$	2.31400	+	0.679451i	0.0792298	+	0.0232640i	0.321107	−	0.947043i	$-0.395945\pi$
$853$	2.31400	+	0.679451i	0.0792298	+	0.0232640i	−0.241877	+	0.970307i	$0.577763\pi$
$854$	−1.97399	+	2.27811i	−0.0675487	+	0.0779553i
$855$	2.46452	+	1.58385i	0.0842847	+	0.0541665i
$856$	0.147777	−	1.02781i	0.00505091	−	0.0351299i
$857$	3.18662	−	2.04791i	0.108853	−	0.0699554i	−0.485082	−	0.874469i	$-0.661210\pi$
$857$	3.18662	−	2.04791i	0.108853	−	0.0699554i	0.593935	+	0.804513i	$0.297574\pi$
$858$	4.13928	+	9.06375i	0.141313	+	0.309431i
$859$	7.83010	+	9.03642i	0.267160	+	0.308319i	0.873439	−	0.486933i	$-0.161884\pi$
$859$	7.83010	+	9.03642i	0.267160	+	0.308319i	−0.606280	+	0.795251i	$0.707339\pi$
$860$	0.454523	+	3.16128i	0.0154991	+	0.107799i
$861$	−1.28963	+	2.82389i	−0.0439504	+	0.0962379i
$862$	10.6090	−	3.11507i	0.361343	−	0.106100i
$863$	22.2266	−	6.52633i	0.756603	−	0.222159i	0.119391	−	0.992847i	$-0.461906\pi$
$863$	22.2266	−	6.52633i	0.756603	−	0.222159i	0.637212	+	0.770689i	$0.280088\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	2.60718	+	18.1334i	0.0886469	+	0.616553i
$866$	25.0159	+	28.8699i	0.850076	+	0.981040i
$867$	−1.19564	−	2.61808i	−0.0406059	−	0.0889146i
$868$	0.925325	−	0.594670i	0.0314076	−	0.0201844i
$869$	−1.37557	+	9.56730i	−0.0466630	+	0.324548i
$870$	−0.776666	−	0.499133i	−0.0263314	−	0.0169222i
$871$	61.7904	−	71.3099i	2.09369	−	2.41624i
$872$	−10.9474	−	3.21446i	−0.370727	−	0.108855i
$873$	−4.82388			−0.163263
$874$	5.96366	−	12.7212i	0.201724	−	0.430303i
$875$	−0.282154			−0.00953853
$876$	3.96532	+	1.16432i	0.133976	+	0.0393389i
$877$	−10.1374	+	11.6992i	−0.342315	+	0.395052i	−0.900637	−	0.434572i	$-0.856900\pi$
$877$	−10.1374	+	11.6992i	−0.342315	+	0.395052i	0.558322	+	0.829624i	$0.311445\pi$
$878$	18.4076	+	11.8299i	0.621227	+	0.399238i
$879$	−4.22323	+	29.3732i	−0.142446	+	0.990734i
$880$	1.22534	−	0.787479i	0.0413063	−	0.0265459i
$881$	−6.28913	−	13.7713i	−0.211886	−	0.463966i	0.773610	−	0.633662i	$-0.218449\pi$
$881$	−6.28913	−	13.7713i	−0.211886	−	0.463966i	−0.985497	+	0.169696i	$0.945722\pi$
$882$	4.53189	+	5.23008i	0.152597	+	0.176106i
$883$	−5.24746	−	36.4969i	−0.176591	−	1.22822i	−0.864579	−	0.502496i	$-0.832415\pi$
$883$	−5.24746	−	36.4969i	−0.176591	−	1.22822i	0.687988	−	0.725722i	$-0.258494\pi$
$884$	10.6792	−	23.3842i	0.359181	−	0.786497i
$885$	2.53519	−	0.744400i	0.0852196	−	0.0250227i
$886$	−18.4032	+	5.40366i	−0.618267	+	0.181540i
$887$	−19.1704	+	41.9773i	−0.643679	+	1.40946i	0.253301	+	0.967388i	$0.418484\pi$
$887$	−19.1704	+	41.9773i	−0.643679	+	1.40946i	−0.896979	+	0.442072i	$0.854244\pi$
$888$	−0.362593	−	2.52189i	−0.0121678	−	0.0846291i
$889$	2.65200	+	3.06057i	0.0889451	+	0.102648i
$890$	−1.59052	−	3.48275i	−0.0533143	−	0.116742i
$891$	1.22534	−	0.787479i	0.0410505	−	0.0263816i
$892$	−2.89931	+	20.1652i	−0.0970762	+	0.675180i
$893$	27.0807	+	17.4037i	0.906222	+	0.582394i
$894$	13.0028	−	15.0060i	0.434877	−	0.501875i
$895$	1.05956	+	0.311115i	0.0354172	+	0.0103994i
$896$	−0.282154			−0.00942609
$897$	−21.7307	+	24.5789i	−0.725568	+	0.820665i
$898$	−22.5024			−0.750916
$899$	−3.45327	−	1.01397i	−0.115173	−	0.0338179i
$900$	−0.654861	+	0.755750i	−0.0218287	+	0.0251917i
$901$	−6.82448	−	4.38583i	−0.227356	−	0.146113i
$902$	−2.28075	+	15.8629i	−0.0759406	+	0.528178i
$903$	0.758085	−	0.487192i	0.0252275	−	0.0162127i
$904$	2.38496	+	5.22232i	0.0793225	+	0.173692i
$905$	−6.39736	−	7.38295i	−0.212656	−	0.245418i
$906$	3.14955	+	21.9056i	0.104637	+	0.727766i
$907$	9.20088	−	20.1471i	0.305510	−	0.668974i	−0.693146	−	0.720797i	$-0.743776\pi$
$907$	9.20088	−	20.1471i	0.305510	−	0.668974i	0.998656	+	0.0518231i	$0.0165032\pi$
$908$	7.11999	−	2.09062i	0.236285	−	0.0693796i
$909$	−3.25523	+	0.955821i	−0.107969	+	0.0317026i
$910$	−0.801825	+	1.75575i	−0.0265802	+	0.0582026i
$911$	−1.93284	−	13.4432i	−0.0640380	−	0.445394i	−0.996463	−	0.0840307i	$-0.973221\pi$
$911$	−1.93284	−	13.4432i	−0.0640380	−	0.445394i	0.932425	−	0.361363i	$-0.117688\pi$
$912$	−1.91846	−	2.21403i	−0.0635267	−	0.0733137i
$913$	3.07225	+	6.72728i	0.101677	+	0.222641i
$914$	−13.6817	+	8.79271i	−0.452551	+	0.290837i
$915$	1.52041	−	10.5747i	0.0502633	−	0.349589i
$916$	−14.7118	−	9.45470i	−0.486092	−	0.312392i
$917$	0.0303431	−	0.0350178i	0.00100202	−	0.00115639i
$918$	−3.60568	−	1.05872i	−0.119005	−	0.0349431i
$919$	23.8798			0.787723			0.393862	−	0.919170i	$-0.371139\pi$
$919$	23.8798			0.787723			0.393862	+	0.919170i	$0.371139\pi$
$920$	4.00845	+	2.63294i	0.132155	+	0.0868053i
$921$	17.9937			0.592914
$922$	22.1950	+	6.51704i	0.730954	+	0.214627i
$923$	−11.7990	+	13.6168i	−0.388370	+	0.448203i
$924$	−0.345735	−	0.222190i	−0.0113738	−	0.00730952i
$925$	−0.362593	+	2.52189i	−0.0119220	+	0.0829193i
$926$	15.1653	−	9.74615i	0.498363	−	0.320278i
$927$	−3.09787	−	6.78339i	−0.101747	−	0.222796i
$928$	0.604584	+	0.697727i	0.0198464	+	0.0229040i
$929$	5.84318	+	40.6402i	0.191709	+	1.33336i	0.827484	+	0.561489i	$0.189771\pi$
$929$	5.84318	+	40.6402i	0.191709	+	1.33336i	−0.635776	+	0.771874i	$0.719320\pi$
$930$	−1.61944	+	3.54607i	−0.0531034	+	0.116280i
$931$	19.4526	−	5.71179i	0.637532	−	0.187196i
$932$	6.74405	−	1.98023i	0.220909	−	0.0648647i
$933$	−13.1270	+	28.7441i	−0.429759	+	0.941040i
$934$	4.15324	+	28.8864i	0.135898	+	0.945193i
$935$	−3.58447	−	4.13670i	−0.117225	−	0.135284i
$936$	2.84180	+	6.22268i	0.0928873	+	0.203395i
$937$	−15.0448	+	9.66870i	−0.491492	+	0.315863i	−0.762805	−	0.646628i	$-0.776178\pi$
$937$	−15.0448	+	9.66870i	−0.491492	+	0.315863i	0.271313	+	0.962491i	$0.412542\pi$
$938$	−0.553855	+	3.85214i	−0.0180840	+	0.125777i
$939$	2.46654	+	1.58515i	0.0804926	+	0.0517295i
$940$	−7.19578	+	8.30437i	−0.234700	+	0.270859i
$941$	26.9508	+	7.91348i	0.878573	+	0.257972i	0.689757	−	0.724040i	$-0.257717\pi$
$941$	26.9508	+	7.91348i	0.878573	+	0.257972i	0.188815	+	0.982013i	$0.439535\pi$
$942$	−17.9858			−0.586009
$943$	−50.7751	+	14.3604i	−1.65346	+	0.467638i
$944$	−2.64222			−0.0859970
$945$	0.270724	+	0.0794918i	0.00880666	+	0.00258587i
$946$	3.04639	−	3.51572i	0.0990466	−	0.114306i
$947$	26.7172	+	17.1701i	0.868192	+	0.557953i	0.897199	−	0.441626i	$-0.145598\pi$
$947$	26.7172	+	17.1701i	0.868192	+	0.557953i	−0.0290072	+	0.999579i	$0.509235\pi$
$948$	−0.944392	+	6.56839i	−0.0306724	+	0.213331i
$949$	−23.7835	+	15.2847i	−0.772045	+	0.496163i
$950$	1.21699	+	2.66484i	0.0394844	+	0.0864587i
$951$	6.19210	+	7.14607i	0.200793	+	0.231727i
$952$	0.150897	+	1.04951i	0.00489061	+	0.0340149i
$953$	9.79030	−	21.4378i	0.317139	−	0.694438i	−0.682186	−	0.731179i	$-0.738970\pi$
$953$	9.79030	−	21.4378i	0.317139	−	0.694438i	0.999325	+	0.0367413i	$0.0116978\pi$
$954$	2.07128	−	0.608183i	0.0670602	−	0.0196907i
$955$	10.1284	−	2.97396i	0.327747	−	0.0962352i
$956$	2.18499	−	4.78446i	0.0706676	−	0.154741i
$957$	0.191376	+	1.33105i	0.00618631	+	0.0430268i
$958$	−7.38912	−	8.52750i	−0.238732	−	0.275511i
$959$	2.41945	+	5.29786i	0.0781281	+	0.171077i
$960$	0.841254	−	0.540641i	0.0271513	−	0.0174491i
$961$	2.24897	−	15.6420i	0.0725476	−	0.504579i
$962$	14.6625	+	9.42302i	0.472738	+	0.303810i
$963$	0.679994	−	0.784755i	0.0219125	−	0.0252884i
$964$	18.6608	+	5.47930i	0.601023	+	0.176476i
$965$	1.02670			0.0330505
$966$	0.205925	−	1.33740i	0.00662554	−	0.0430301i
$967$	56.3595			1.81240			0.906199	−	0.422851i	$-0.138971\pi$
$967$	56.3595			1.81240			0.906199	+	0.422851i	$0.138971\pi$
$968$	8.51878	+	2.50134i	0.273804	+	0.0803961i
$969$	−7.20940	+	8.32009i	−0.231599	+	0.267280i
$970$	−4.05810	−	2.60798i	−0.130298	−	0.0837373i
$971$	−2.31330	+	16.0893i	−0.0742373	+	0.516331i	0.918442	+	0.395555i	$0.129448\pi$
$971$	−2.31330	+	16.0893i	−0.0742373	+	0.516331i	−0.992680	+	0.120777i	$0.961461\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−1.16759	−	2.55668i	−0.0374314	−	0.0819633i
$974$	−23.1816	−	26.7530i	−0.742785	−	0.857220i
$975$	−0.973558	−	6.77125i	−0.0311788	−	0.216853i
$976$	−4.43806	+	9.71800i	−0.142059	+	0.311066i
$977$	15.6545	−	4.59658i	0.500832	−	0.147058i	−0.0215522	−	0.999768i	$-0.506861\pi$
$977$	15.6545	−	4.59658i	0.500832	−	0.147058i	0.522384	+	0.852710i	$0.325043\pi$
$978$	−4.59445	+	1.34905i	−0.146914	+	0.0431380i
$979$	−2.31670	+	5.07286i	−0.0740419	+	0.162129i
$980$	0.984874	+	6.84995i	0.0314606	+	0.218814i
$981$	−7.47171	−	8.62281i	−0.238553	−	0.275305i
$982$	5.52085	+	12.0890i	0.176177	+	0.385775i
$983$	22.6891	−	14.5814i	0.723671	−	0.465075i	−0.126241	−	0.992000i	$-0.540291\pi$
$983$	22.6891	−	14.5814i	0.723671	−	0.465075i	0.849912	+	0.526924i	$0.176655\pi$
$984$	−1.56584	+	10.8906i	−0.0499171	+	0.347181i
$985$	5.36186	+	3.44586i	0.170843	+	0.109794i
$986$	2.27197	−	2.62199i	0.0723541	−	0.0835011i
$987$	2.97479	+	0.873477i	0.0946886	+	0.0278031i
$988$	20.0409			0.637585
$989$	14.6526	+	4.46163i	0.465927	+	0.141872i
$990$	1.45657			0.0462927
$991$	10.3885	+	3.05034i	0.330001	+	0.0968972i	0.442536	−	0.896751i	$-0.354079\pi$
$991$	10.3885	+	3.05034i	0.330001	+	0.0968972i	−0.112535	+	0.993648i	$0.535897\pi$
$992$	2.55288	−	2.94618i	0.0810541	−	0.0935414i
$993$	15.2556	+	9.80419i	0.484122	+	0.311126i
$994$	0.105760	−	0.735578i	0.00335451	−	0.0233311i
$995$	6.84988	−	4.40215i	0.217156	−	0.139557i
$996$	2.10924	+	4.61859i	0.0668338	+	0.146346i
$997$	−26.8716	−	31.0115i	−0.851033	−	0.982144i	0.148945	−	0.988845i	$-0.452412\pi$
$997$	−26.8716	−	31.0115i	−0.851033	−	0.982144i	−0.999978	+	0.00670156i	$0.997867\pi$
$998$	−0.777578	−	5.40817i	−0.0246138	−	0.171193i
$999$	1.05840	−	2.31758i	0.0334864	−	0.0733250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.271.2	✓	30
23.9	even	11	inner	690.2.m.g.331.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.271.2	✓	30	1.1	even	1	trivial
690.2.m.g.331.2	yes	30	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.117211 - 0.256656i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.142315 + 0.989821i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.117211 - 0.256656i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.415415 - 0.909632i) q^{10} +(-1.39757 + 0.410362i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(2.84180 - 6.22268i) q^{13} +(0.0401546 + 0.279282i) q^{14} +(-0.654861 - 0.755750i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.16135 - 2.03168i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(2.46452 + 1.58385i) q^{19} +(-0.654861 + 0.755750i) q^{20} +(0.270724 + 0.0794918i) q^{21} +1.45657 q^{22} +(1.94865 + 4.38210i) q^{23} +1.00000 q^{24} +(-0.959493 - 0.281733i) q^{25} +(-4.47982 + 5.16999i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.0401546 - 0.279282i) q^{28} +(-0.776666 + 0.499133i) q^{29} +(0.415415 + 0.909632i) q^{30} +(2.55288 + 2.94618i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.605080 - 1.32494i) q^{33} +(-3.60568 + 1.05872i) q^{34} +(0.270724 - 0.0794918i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.362593 - 2.52189i) q^{37} +(-1.91846 - 2.21403i) q^{38} +(2.84180 + 6.22268i) q^{39} +(0.841254 - 0.540641i) q^{40} +(-1.56584 + 10.8906i) q^{41} +(-0.237363 - 0.152544i) q^{42} +(2.09148 - 2.41370i) q^{43} +(-1.39757 - 0.410362i) q^{44} +1.00000 q^{45} +(-0.635134 - 4.75359i) q^{46} +10.9883 q^{47} +(-0.959493 - 0.281733i) q^{48} +(4.53189 - 5.23008i) q^{49} +(0.841254 + 0.540641i) q^{50} +(-0.534805 + 3.71965i) q^{51} +(5.75491 - 3.69846i) q^{52} +(-0.896767 - 1.96365i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.207291 - 1.44174i) q^{55} +(-0.117211 + 0.256656i) q^{56} +(-2.81091 + 0.825357i) q^{57} +(0.885828 - 0.260102i) q^{58} +(-1.09762 + 2.40345i) q^{59} +(-0.142315 - 0.989821i) q^{60} +(6.99617 + 8.07400i) q^{61} +(-1.61944 - 3.54607i) q^{62} +(-0.237363 + 0.152544i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(5.75491 + 3.69846i) q^{65} +(-0.953848 + 1.10080i) q^{66} +(13.2343 + 3.88595i) q^{67} +3.75790 q^{68} +(-4.58786 - 1.39697i) q^{69} -0.282154 q^{70} +(-2.52713 - 0.742033i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(-3.47667 - 2.23432i) q^{73} +(-0.362593 + 2.52189i) q^{74} +(0.841254 - 0.540641i) q^{75} +(1.21699 + 2.66484i) q^{76} +(0.269132 + 0.310595i) q^{77} +(-0.973558 - 6.77125i) q^{78} +(2.75667 - 6.03626i) q^{79} +(-0.959493 + 0.281733i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.57066 - 10.0083i) q^{82} +(-0.722593 - 5.02574i) q^{83} +(0.184771 + 0.213237i) q^{84} +(1.56109 + 3.41831i) q^{85} +(-2.68678 + 1.72669i) q^{86} +(0.131389 - 0.913828i) q^{87} +(1.22534 + 0.787479i) q^{88} +(2.50730 - 2.89357i) q^{89} +(-0.959493 - 0.281733i) q^{90} -1.93018 q^{91} +(-0.729834 + 4.73997i) q^{92} -3.89836 q^{93} +(-10.5432 - 3.09575i) q^{94} +(-1.91846 + 2.21403i) q^{95} +(0.841254 + 0.540641i) q^{96} +(0.686509 - 4.77478i) q^{97} +(-5.82180 + 3.74144i) q^{98} +(0.605080 + 1.32494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

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