LMFDB - Embedded newform 690.2.n.a.89.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.13
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.0575173 + 1.73110i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22287 - 1.87206i) q^{5} +(1.70529 - 0.303292i) q^{6} +(1.08447 - 0.696948i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.99338 + 0.199136i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.0575173 + 1.73110i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22287 - 1.87206i) q^{5} +(1.70529 - 0.303292i) q^{6} +(1.08447 - 0.696948i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.99338 + 0.199136i) q^{9} +(-1.67897 + 1.47684i) q^{10} +(-0.894396 + 6.22066i) q^{11} +(-0.542893 - 1.64477i) q^{12} +(1.25371 - 1.95081i) q^{13} +(-0.844191 - 0.974248i) q^{14} +(3.17037 - 2.22458i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0693233 - 0.236094i) q^{17} +(0.623112 + 2.93458i) q^{18} +(1.55224 + 5.28644i) q^{19} +(1.70075 + 1.45170i) q^{20} +(1.26886 + 1.83724i) q^{21} +6.28463 q^{22} +(-0.433107 + 4.77623i) q^{23} +(-1.55077 + 0.771443i) q^{24} +(-2.00918 + 4.57856i) q^{25} +(-2.10938 - 0.963320i) q^{26} +(-0.516895 - 5.17038i) q^{27} +(-0.844191 + 0.974248i) q^{28} +(1.83687 - 6.25580i) q^{29} +(-2.65313 - 2.82151i) q^{30} +(3.36003 + 7.35743i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-10.8200 - 1.19049i) q^{33} +(-0.243556 - 0.0350181i) q^{34} +(-2.63089 - 1.17792i) q^{35} +(2.81603 - 1.03440i) q^{36} +(0.444500 + 0.512980i) q^{37} +(5.01173 - 2.28878i) q^{38} +(3.44915 + 2.05809i) q^{39} +(1.19488 - 1.89004i) q^{40} +(2.46674 + 2.13745i) q^{41} +(1.63796 - 1.51741i) q^{42} +(-3.28717 + 7.19790i) q^{43} +(-0.894396 - 6.22066i) q^{44} +(4.03331 + 5.36026i) q^{45} +(4.78926 - 0.251030i) q^{46} -0.182036 q^{47} +(0.984288 + 1.42519i) q^{48} +(-2.21756 + 4.85578i) q^{49} +(4.81789 + 1.33713i) q^{50} +(0.412688 + 0.106426i) q^{51} +(-0.653319 + 2.22500i) q^{52} +(3.24409 + 5.04791i) q^{53} +(-5.04419 + 1.24746i) q^{54} +(12.7392 - 5.93270i) q^{55} +(1.08447 + 0.696948i) q^{56} +(-9.06206 + 2.99114i) q^{57} +(-6.45354 - 0.927879i) q^{58} +(-5.43699 + 8.46012i) q^{59} +(-2.41521 + 3.02766i) q^{60} +(2.48161 - 1.13331i) q^{61} +(6.80436 - 4.37290i) q^{62} +(-3.10745 + 2.30219i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-5.18515 + 0.0385728i) q^{65} +(0.361475 + 10.8793i) q^{66} +(0.138700 + 0.964679i) q^{67} +0.246061i q^{68} +(-8.29303 - 0.475033i) q^{69} +(-0.791511 + 2.77175i) q^{70} +(-7.87233 + 1.13187i) q^{71} +(-1.42464 - 2.64015i) q^{72} +(-2.31983 - 7.90061i) q^{73} +(0.444500 - 0.512980i) q^{74} +(-8.04148 - 3.21474i) q^{75} +(-2.97873 - 4.63499i) q^{76} +(3.36553 + 7.36948i) q^{77} +(1.54627 - 3.70694i) q^{78} +(-1.97047 + 3.06611i) q^{79} +(-2.04085 - 0.913740i) q^{80} +(8.92069 - 1.19218i) q^{81} +(1.76463 - 2.74583i) q^{82} +(1.81014 - 1.56849i) q^{83} +(-1.73507 - 1.40534i) q^{84} +(-0.526753 + 0.158934i) q^{85} +(7.59245 + 2.22934i) q^{86} +(10.9350 + 2.81998i) q^{87} +(-6.03006 + 1.77059i) q^{88} +(7.11816 - 15.5866i) q^{89} +(4.73170 - 4.75510i) q^{90} -2.98937i q^{91} +(-0.930058 - 4.70478i) q^{92} +(-12.5432 + 6.23971i) q^{93} +(0.0259065 + 0.180183i) q^{94} +(7.99833 - 9.37051i) q^{95} +(1.27061 - 1.17710i) q^{96} +(-5.26602 + 6.07732i) q^{97} +(5.12195 + 1.50394i) q^{98} +(1.43851 - 18.7989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.0575173	+	1.73110i	0.0332077	+	0.999448i
$3$	0.0575173	+	1.73110i	0.0332077	+	0.999448i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−1.22287	−	1.87206i	−0.546884	−	0.837208i
$5$	−1.22287	−	1.87206i	−0.546884	−	0.837208i
$6$	1.70529	−	0.303292i	0.696182	−	0.123819i
$7$	1.08447	−	0.696948i	0.409892	−	0.263422i	−0.319406	−	0.947618i	$-0.603483\pi$
$7$	1.08447	−	0.696948i	0.409892	−	0.263422i	0.729298	+	0.684196i	$0.239847\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−2.99338	+	0.199136i	−0.997795	+	0.0663787i
$10$	−1.67897	+	1.47684i	−0.530936	+	0.467019i
$11$	−0.894396	+	6.22066i	−0.269671	+	1.87560i	0.181831	+	0.983330i	$0.441798\pi$
$11$	−0.894396	+	6.22066i	−0.269671	+	1.87560i	−0.451501	+	0.892270i	$0.649111\pi$
$12$	−0.542893	−	1.64477i	−0.156720	−	0.474804i
$13$	1.25371	−	1.95081i	0.347717	−	0.541058i	−0.622710	−	0.782452i	$-0.713968\pi$
$13$	1.25371	−	1.95081i	0.347717	−	0.541058i	0.970427	+	0.241395i	$0.0776048\pi$
$14$	−0.844191	−	0.974248i	−0.225619	−	0.260379i
$15$	3.17037	−	2.22458i	0.818586	−	0.574384i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.0693233	−	0.236094i	0.0168134	−	0.0572611i	−0.950659	−	0.310238i	$-0.899591\pi$
$17$	0.0693233	−	0.236094i	0.0168134	−	0.0572611i	0.967472	+	0.252977i	$0.0814096\pi$
$18$	0.623112	+	2.93458i	0.146869	+	0.691686i
$19$	1.55224	+	5.28644i	0.356108	+	1.21279i	0.921633	+	0.388062i	$0.126855\pi$
$19$	1.55224	+	5.28644i	0.356108	+	1.21279i	−0.565525	+	0.824731i	$0.691326\pi$
$20$	1.70075	+	1.45170i	0.380300	+	0.324610i
$21$	1.26886	+	1.83724i	0.276888	+	0.400918i
$22$	6.28463			1.33989
$23$	−0.433107	+	4.77623i	−0.0903091	+	0.995914i
$23$	−0.433107	+	4.77623i	−0.0903091	+	0.995914i
$24$	−1.55077	+	0.771443i	−0.316549	+	0.157470i
$25$	−2.00918	+	4.57856i	−0.401836	+	0.915712i
$26$	−2.10938	−	0.963320i	−0.413683	−	0.188923i
$27$	−0.516895	−	5.17038i	−0.0994765	−	0.995040i
$28$	−0.844191	+	0.974248i	−0.159537	+	0.184116i
$29$	1.83687	−	6.25580i	0.341098	−	1.16167i	−0.593162	−	0.805083i	$-0.702121\pi$
$29$	1.83687	−	6.25580i	0.341098	−	1.16167i	0.934261	−	0.356591i	$-0.116061\pi$
$30$	−2.65313	−	2.82151i	−0.484393	−	0.515135i
$31$	3.36003	+	7.35743i	0.603479	+	1.32143i	0.926946	+	0.375195i	$0.122424\pi$
$31$	3.36003	+	7.35743i	0.603479	+	1.32143i	−0.323467	+	0.946239i	$0.604849\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−10.8200	−	1.19049i	−1.88352	−	0.207238i
$34$	−0.243556	−	0.0350181i	−0.0417695	−	0.00600555i
$35$	−2.63089	−	1.17792i	−0.444702	−	0.199104i
$36$	2.81603	−	1.03440i	0.469338	−	0.172401i
$37$	0.444500	+	0.512980i	0.0730753	+	0.0843334i	0.791110	−	0.611674i	$-0.209504\pi$
$37$	0.444500	+	0.512980i	0.0730753	+	0.0843334i	−0.718035	+	0.696007i	$0.754958\pi$
$38$	5.01173	−	2.28878i	0.813010	−	0.371289i
$39$	3.44915	+	2.05809i	0.552306	+	0.329558i
$40$	1.19488	−	1.89004i	0.188928	−	0.298842i
$41$	2.46674	+	2.13745i	0.385241	+	0.333813i	0.825854	−	0.563884i	$-0.190694\pi$
$41$	2.46674	+	2.13745i	0.385241	+	0.333813i	−0.440613	+	0.897697i	$0.645239\pi$
$42$	1.63796	−	1.51741i	0.252743	−	0.234142i
$43$	−3.28717	+	7.19790i	−0.501289	+	1.09767i	0.474759	+	0.880116i	$0.342535\pi$
$43$	−3.28717	+	7.19790i	−0.501289	+	1.09767i	−0.976048	+	0.217554i	$0.930192\pi$
$44$	−0.894396	−	6.22066i	−0.134835	−	0.937800i
$45$	4.03331	+	5.36026i	0.601250	+	0.799061i
$46$	4.78926	−	0.251030i	0.706137	−	0.0370124i
$47$	−0.182036			−0.0265527			−0.0132764	−	0.999912i	$-0.504226\pi$
$47$	−0.182036			−0.0265527			−0.0132764	+	0.999912i	$0.504226\pi$
$48$	0.984288	+	1.42519i	0.142070	+	0.205709i
$49$	−2.21756	+	4.85578i	−0.316795	+	0.693683i
$50$	4.81789	+	1.33713i	0.681353	+	0.189099i
$51$	0.412688	+	0.106426i	0.0577878	+	0.0149026i
$52$	−0.653319	+	2.22500i	−0.0905991	+	0.308552i
$53$	3.24409	+	5.04791i	0.445611	+	0.693384i	0.989299	−	0.145904i	$-0.0466089\pi$
$53$	3.24409	+	5.04791i	0.445611	+	0.693384i	−0.543688	+	0.839287i	$0.682973\pi$
$54$	−5.04419	+	1.24746i	−0.686427	+	0.169757i
$55$	12.7392	−	5.93270i	1.71775	−	0.799965i
$56$	1.08447	+	0.696948i	0.144919	+	0.0931336i
$57$	−9.06206	+	2.99114i	−1.20030	+	0.396186i
$58$	−6.45354	−	0.927879i	−0.847392	−	0.121837i
$59$	−5.43699	+	8.46012i	−0.707835	+	1.10141i	0.282030	+	0.959406i	$0.408992\pi$
$59$	−5.43699	+	8.46012i	−0.707835	+	1.10141i	−0.989866	+	0.142008i	$0.954644\pi$
$60$	−2.41521	+	3.02766i	−0.311802	+	0.390870i
$61$	2.48161	−	1.13331i	0.317738	−	0.145106i	−0.250161	−	0.968204i	$-0.580484\pi$
$61$	2.48161	−	1.13331i	0.317738	−	0.145106i	0.567899	+	0.823098i	$0.307756\pi$
$62$	6.80436	−	4.37290i	0.864155	−	0.555359i
$63$	−3.10745	+	2.30219i	−0.391502	+	0.290049i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−5.18515	+	0.0385728i	−0.643139	+	0.00478437i
$66$	0.361475	+	10.8793i	0.0444945	+	1.33915i
$67$	0.138700	+	0.964679i	0.0169449	+	0.117854i	0.996538	−	0.0831353i	$-0.0264934\pi$
$67$	0.138700	+	0.964679i	0.0169449	+	0.117854i	−0.979593	+	0.200990i	$0.935584\pi$
$68$			0.246061i			0.0298392i
$69$	−8.29303	−	0.475033i	−0.998363	−	0.0571873i
$70$	−0.791511	+	2.77175i	−0.0946036	+	0.331287i
$71$	−7.87233	+	1.13187i	−0.934274	+	0.134328i	−0.592606	−	0.805492i	$-0.701901\pi$
$71$	−7.87233	+	1.13187i	−0.934274	+	0.134328i	−0.341668	+	0.939821i	$0.610992\pi$
$72$	−1.42464	−	2.64015i	−0.167895	−	0.311145i
$73$	−2.31983	−	7.90061i	−0.271516	−	0.924697i	−0.976508	−	0.215482i	$-0.930868\pi$
$73$	−2.31983	−	7.90061i	−0.271516	−	0.924697i	0.704992	−	0.709215i	$-0.250950\pi$
$74$	0.444500	−	0.512980i	0.0516720	−	0.0596327i
$75$	−8.04148	−	3.21474i	−0.928551	−	0.371206i
$76$	−2.97873	−	4.63499i	−0.341683	−	0.531670i
$77$	3.36553	+	7.36948i	0.383538	+	0.839831i
$78$	1.54627	−	3.70694i	0.175081	−	0.419728i
$79$	−1.97047	+	3.06611i	−0.221695	+	0.344964i	−0.934229	−	0.356673i	$-0.883911\pi$
$79$	−1.97047	+	3.06611i	−0.221695	+	0.344964i	0.712534	+	0.701637i	$0.247547\pi$
$80$	−2.04085	−	0.913740i	−0.228174	−	0.102159i
$81$	8.92069	−	1.19218i	0.991188	−	0.132465i
$82$	1.76463	−	2.74583i	0.194871	−	0.303226i
$83$	1.81014	−	1.56849i	0.198688	−	0.172164i	−0.549834	−	0.835274i	$-0.685309\pi$
$83$	1.81014	−	1.56849i	0.198688	−	0.172164i	0.748522	+	0.663109i	$0.230764\pi$
$84$	−1.73507	−	1.40534i	−0.189312	−	0.153335i
$85$	−0.526753	+	0.158934i	−0.0571344	+	0.0172389i
$86$	7.59245	+	2.22934i	0.818715	+	0.240396i
$87$	10.9350	+	2.81998i	1.17236	+	0.302334i
$88$	−6.03006	+	1.77059i	−0.642806	+	0.188745i
$89$	7.11816	−	15.5866i	0.754524	−	1.65218i	−0.00353850	−	0.999994i	$-0.501126\pi$
$89$	7.11816	−	15.5866i	0.754524	−	1.65218i	0.758062	−	0.652182i	$-0.226146\pi$
$90$	4.73170	−	4.75510i	0.498765	−	0.501232i
$91$		−	2.98937i		−	0.313371i
$92$	−0.930058	−	4.70478i	−0.0969652	−	0.490508i
$93$	−12.5432	+	6.23971i	−1.30066	+	0.647027i
$94$	0.0259065	+	0.180183i	0.00267205	+	0.0185845i
$95$	7.99833	−	9.37051i	0.820611	−	0.961394i
$96$	1.27061	−	1.17710i	0.129681	−	0.120137i
$97$	−5.26602	+	6.07732i	−0.534684	+	0.617058i	−0.957246	−	0.289276i	$-0.906585\pi$
$97$	−5.26602	+	6.07732i	−0.534684	+	0.617058i	0.422562	+	0.906334i	$0.361131\pi$
$98$	5.12195	+	1.50394i	0.517395	+	0.151921i
$99$	1.43851	−	18.7989i	0.144576	−	1.88936i
$100$	0.637866	−	4.95915i	0.0637866	−	0.495915i
$101$	8.69786	−	7.53674i	0.865469	−	0.749933i	−0.104148	−	0.994562i	$-0.533211\pi$
$101$	8.69786	−	7.53674i	0.865469	−	0.749933i	0.969617	+	0.244629i	$0.0786660\pi$
$102$	0.0466110	−	0.423633i	0.00461517	−	0.0419459i
$103$	1.26519	−	8.79960i	0.124663	−	0.867050i	−0.827501	−	0.561464i	$-0.810238\pi$
$103$	1.26519	−	8.79960i	0.124663	−	0.867050i	0.952164	−	0.305586i	$-0.0988525\pi$
$104$	2.29533	+	0.330019i	0.225076	+	0.0323610i
$105$	1.88776	−	4.62208i	0.184227	−	0.451069i
$106$	4.53485	−	3.92947i	0.440463	−	0.381664i
$107$	13.4769	−	6.15471i	1.30287	−	0.594999i	0.361495	−	0.932374i	$-0.382266\pi$
$107$	13.4769	−	6.15471i	1.30287	−	0.594999i	0.941370	+	0.337375i	$0.109539\pi$
$108$	1.95262	+	4.81532i	0.187891	+	0.463354i
$109$	2.90431	−	9.89119i	0.278183	−	0.947404i	−0.695314	−	0.718706i	$-0.744735\pi$
$109$	2.90431	−	9.89119i	0.278183	−	0.947404i	0.973497	−	0.228698i	$-0.0734469\pi$
$110$	−7.68528	−	11.7652i	−0.732763	−	1.12177i
$111$	−0.862451	+	0.798977i	−0.0818602	+	0.0758355i
$112$	0.535518	−	1.17262i	0.0506017	−	0.110802i
$113$	−3.59329	+	0.516638i	−0.338029	+	0.0486012i	−0.309239	−	0.950984i	$-0.600074\pi$
$113$	−3.59329	+	0.516638i	−0.338029	+	0.0486012i	−0.0287895	+	0.999585i	$0.509165\pi$
$114$	4.25036	+	8.54414i	0.398083	+	0.800232i
$115$	9.47101	−	5.02991i	0.883176	−	0.469042i
$116$			6.51991i			0.605358i
$117$	−3.36436	+	6.08919i	−0.311035	+	0.562945i
$118$	9.14777	+	4.17765i	0.842120	+	0.384583i
$119$	−0.0893657	−	0.304352i	−0.00819214	−	0.0278999i
$120$	3.34057	+	1.95975i	0.304951	+	0.178900i
$121$	−27.3423	−	8.02842i	−2.48566	−	0.729856i
$122$	−1.47495	−	2.29507i	−0.133536	−	0.207785i
$123$	−3.55824	+	4.39311i	−0.320836	+	0.396113i
$124$	−5.29675	−	6.11278i	−0.475662	−	0.548943i
$125$	11.0283	−	1.83768i	0.986399	−	0.164367i
$126$	2.72099	+	2.74819i	0.242405	+	0.244828i
$127$	−12.7204	−	1.82891i	−1.12875	−	0.162290i	−0.447461	−	0.894304i	$-0.647672\pi$
$127$	−12.7204	−	1.82891i	−1.12875	−	0.162290i	−0.681290	+	0.732014i	$0.738581\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−12.6493	−	5.27640i	−1.11371	−	0.464561i
$130$	0.776104	+	5.12688i	0.0680688	+	0.449657i
$131$	−10.6094	−	16.5086i	−0.926951	−	1.44236i	−0.896608	−	0.442824i	$-0.853977\pi$
$131$	−10.6094	−	16.5086i	−0.926951	−	1.44236i	−0.0303425	−	0.999540i	$-0.509660\pi$
$132$	10.7171	−	1.90608i	0.932805	−	0.165903i
$133$	5.36774	+	4.65117i	0.465442	+	0.403308i
$134$	0.935121	−	0.274576i	0.0807822	−	0.0237198i
$135$	−9.04714	+	7.29035i	−0.778654	+	0.627454i
$136$	0.243556	−	0.0350181i	0.0208848	−	0.00300278i
$137$			7.93214i			0.677688i	0.940843	+	0.338844i	$0.110036\pi$
$137$			7.93214i			0.677688i	−0.940843	+	0.338844i	$0.889964\pi$
$138$	0.710023	+	8.27622i	0.0604412	+	0.704519i
$139$	7.60519			0.645064			0.322532	−	0.946559i	$-0.395466\pi$
$139$	7.60519			0.645064			0.322532	+	0.946559i	$0.395466\pi$
$140$	2.85618	+	0.388993i	0.241391	+	0.0328759i
$141$	−0.0104702	−	0.315122i	−0.000881754	−	0.0265381i
$142$	2.24070	+	7.63112i	0.188035	+	0.640389i
$143$	11.0140	+	9.54371i	0.921039	+	0.798085i
$144$	−2.41053	+	1.78587i	−0.200878	+	0.148822i
$145$	−13.9575	+	4.21131i	−1.15910	+	0.349730i
$146$	−7.49005	+	3.42059i	−0.619881	+	0.283090i
$147$	−8.53337	−	3.55952i	−0.703821	−	0.293584i
$148$	−0.571017	−	0.366971i	−0.0469373	−	0.0301648i
$149$	0.597972	−	4.15899i	0.0489878	−	0.340718i	−0.950557	−	0.310550i	$-0.899487\pi$
$149$	0.597972	−	4.15899i	0.0489878	−	0.340718i	0.999545	−	0.0301676i	$-0.00960410\pi$
$150$	−2.03759	+	8.41714i	−0.166369	+	0.687256i
$151$	−3.33889	−	2.14577i	−0.271715	−	0.174620i	0.397687	−	0.917521i	$-0.369813\pi$
$151$	−3.33889	−	2.14577i	−0.271715	−	0.174620i	−0.669402	+	0.742901i	$0.733449\pi$
$152$	−4.16390	+	3.60804i	−0.337737	+	0.292650i
$153$	−0.160497	+	0.720523i	−0.0129754	+	0.0582508i
$154$	6.81551	−	4.38006i	0.549209	−	0.352955i
$155$	9.66464	−	15.2873i	0.776283	−	1.22791i
$156$	−3.88927	−	1.00298i	−0.311391	−	0.0803028i
$157$	5.56583	−	1.63428i	0.444202	−	0.130429i	−0.0519798	−	0.998648i	$-0.516553\pi$
$157$	5.56583	−	1.63428i	0.444202	−	0.130429i	0.496182	+	0.868219i	$0.334735\pi$
$158$	3.31532	+	1.51406i	0.263753	+	0.120452i
$159$	−8.55182	+	5.90618i	−0.678204	+	0.468391i
$160$	−0.613996	+	2.15012i	−0.0485406	+	0.169982i
$161$	2.85909	+	5.48155i	0.225328	+	0.432006i
$162$	−2.44959	−	8.66022i	−0.192458	−	0.680412i
$163$	7.37131	−	1.05983i	0.577365	−	0.0830126i	0.152555	−	0.988295i	$-0.451250\pi$
$163$	7.37131	−	1.05983i	0.577365	−	0.0830126i	0.424810	+	0.905282i	$0.360341\pi$
$164$	−2.96901	−	1.35590i	−0.231841	−	0.105878i
$165$	11.0028	+	21.7115i	0.856566	+	1.69023i
$166$	−1.81014	−	1.56849i	−0.140494	−	0.121739i
$167$	−21.9863	−	6.45577i	−1.70135	−	0.499562i	−0.720359	−	0.693601i	$-0.756023\pi$
$167$	−21.9863	−	6.45577i	−1.70135	−	0.499562i	−0.980994	+	0.194039i	$0.937841\pi$
$168$	−1.14411	+	1.91741i	−0.0882698	+	0.147932i
$169$	3.16652	+	6.93371i	0.243578	+	0.533362i
$170$	0.232282	+	0.498773i	0.0178152	+	0.0382542i
$171$	−5.69917	−	15.5152i	−0.435827	−	1.18648i
$172$	1.12613	−	7.83244i	0.0858670	−	0.597218i
$173$	−2.83697	+	19.7316i	−0.215691	+	1.50016i	0.538006	+	0.842941i	$0.319178\pi$
$173$	−2.83697	+	19.7316i	−0.215691	+	1.50016i	−0.753697	+	0.657222i	$0.771732\pi$
$174$	1.23506	−	11.2251i	0.0936294	−	0.850970i
$175$	1.01212	+	6.36561i	0.0765088	+	0.481195i
$176$	2.61073	+	5.71670i	0.196791	+	0.430913i
$177$	−14.9580	−	8.92534i	−1.12431	−	0.670870i
$178$	−16.4410	−	4.82750i	−1.23230	−	0.361837i
$179$	16.8971	+	14.6414i	1.26295	+	1.09435i	0.991254	+	0.131969i	$0.0421299\pi$
$179$	16.8971	+	14.6414i	1.26295	+	1.09435i	0.271696	+	0.962383i	$0.412416\pi$
$180$	−5.38009	−	4.00682i	−0.401009	−	0.298651i
$181$	4.91707	+	2.24555i	0.365483	+	0.166910i	0.589687	−	0.807632i	$-0.299251\pi$
$181$	4.91707	+	2.24555i	0.365483	+	0.166910i	−0.224204	+	0.974542i	$0.571978\pi$
$182$	−2.95894	+	0.425432i	−0.219332	+	0.0315351i
$183$	2.10461	+	4.23072i	0.155577	+	0.312744i
$184$	−4.52454	+	1.59015i	−0.333553	+	0.117228i
$185$	0.416762	−	1.45944i	0.0306409	−	0.107300i
$186$	7.96127	+	11.5275i	0.583749	+	0.845236i
$187$	1.40666	+	0.642398i	0.102865	+	0.0469768i
$188$	0.174663	−	0.0512856i	0.0127386	−	0.00374038i
$189$	−4.16404	−	5.24688i	−0.302890	−	0.381655i
$190$	−10.4134	−	6.58335i	−0.755468	−	0.477607i
$191$	19.6467	−	12.6261i	1.42158	−	0.913595i	0.421605	−	0.906780i	$-0.361467\pi$
$191$	19.6467	−	12.6261i	1.42158	−	0.913595i	0.999977	−	0.00681553i	$-0.00216947\pi$
$192$	−1.34594	−	1.09016i	−0.0971349	−	0.0786754i
$193$	−4.12080	+	3.57070i	−0.296622	+	0.257024i	−0.790438	−	0.612542i	$-0.790147\pi$
$193$	−4.12080	+	3.57070i	−0.296622	+	0.257024i	0.493816	+	0.869566i	$0.335602\pi$
$194$	6.76489	+	4.34753i	0.485691	+	0.312135i
$195$	−0.365009	−	8.97377i	−0.0261389	−	0.642625i
$196$	0.759703	−	5.28385i	0.0542645	−	0.377418i
$197$	2.40604	+	1.54627i	0.171423	+	0.110167i	0.623539	−	0.781792i	$-0.285694\pi$
$197$	2.40604	+	1.54627i	0.171423	+	0.110167i	−0.452116	+	0.891959i	$0.649331\pi$
$198$	−18.8123	+	1.25150i	−1.33693	+	0.0889400i
$199$	12.8219	−	5.85556i	0.908919	−	0.415089i	0.0946055	−	0.995515i	$-0.469841\pi$
$199$	12.8219	−	5.85556i	0.908919	−	0.415089i	0.814313	+	0.580426i	$0.197114\pi$
$200$	−4.99945	+	0.0743868i	−0.353514	+	0.00525994i
$201$	−1.66197	+	0.295589i	−0.117227	+	0.0208492i
$202$	−8.69786	−	7.53674i	−0.611979	−	0.530283i
$203$	−2.36794	−	8.06445i	−0.166197	−	0.566013i
$204$	−0.425955	+	0.0141528i	−0.0298228	+	0.000990891i
$205$	0.984910	−	7.23170i	0.0687891	−	0.505083i
$206$	−8.89009			−0.619402
$207$	0.345335	−	14.3833i	0.0240024	−	0.999712i
$208$		−	2.31893i		−	0.160789i
$209$	−34.2735	+	4.92779i	−2.37075	+	0.340862i
$210$	−4.84369	−	1.21076i	−0.334246	−	0.0835502i
$211$	−20.6808	+	6.07243i	−1.42372	+	0.418043i	−0.900762	−	0.434313i	$-0.856991\pi$
$211$	−20.6808	+	6.07243i	−1.42372	+	0.418043i	−0.522962	+	0.852356i	$0.675173\pi$
$212$	−4.53485	−	3.92947i	−0.311455	−	0.269877i
$213$	−2.41217	−	13.5627i	−0.165279	−	0.929298i
$214$	−8.01004	−	12.4639i	−0.547555	−	0.852012i
$215$	17.4947	−	2.64833i	1.19313	−	0.180614i
$216$	4.48842	−	2.61804i	0.305398	−	0.178135i
$217$	8.77160	+	5.63717i	0.595455	+	0.382676i
$218$	−10.2038	−	1.46709i	−0.691091	−	0.0993639i
$219$	13.5433	−	4.47027i	0.915171	−	0.302073i
$220$	−10.5517	+	9.28142i	−0.711395	+	0.625753i
$221$	−0.373663	−	0.431230i	−0.0251353	−	0.0290076i
$222$	0.913584	+	0.739966i	0.0613157	+	0.0496633i
$223$	3.09550	+	4.81670i	0.207290	+	0.322550i	0.929295	−	0.369338i	$-0.120416\pi$
$223$	3.09550	+	4.81670i	0.207290	+	0.322550i	−0.722005	+	0.691888i	$0.756779\pi$
$224$	−1.23690	−	0.363186i	−0.0826436	−	0.0242664i
$225$	5.10249	−	14.1055i	0.340166	−	0.940365i
$226$	1.02276	+	3.48319i	0.0680329	+	0.231699i
$227$	3.34827	+	1.52911i	0.222233	+	0.101490i	0.523420	−	0.852075i	$-0.324656\pi$
$227$	3.34827	+	1.52911i	0.222233	+	0.101490i	−0.301188	+	0.953565i	$0.597383\pi$
$228$	7.85228	−	5.42305i	0.520030	−	0.359151i
$229$			15.5478i			1.02743i	0.857961	+	0.513714i	$0.171731\pi$
$229$			15.5478i			1.02743i	−0.857961	+	0.513714i	$0.828269\pi$
$230$	−6.32658	−	8.65878i	−0.417162	−	0.570943i
$231$	−12.5637	+	6.24993i	−0.826631	+	0.411215i
$232$	6.45354	−	0.927879i	0.423696	−	0.0609183i
$233$	−6.70270	+	14.6769i	−0.439108	+	0.961513i	0.552653	+	0.833412i	$0.313616\pi$
$233$	−6.70270	+	14.6769i	−0.439108	+	0.961513i	−0.991761	+	0.128101i	$0.959112\pi$
$234$	6.50601	+	2.46353i	0.425311	+	0.161046i
$235$	0.222607	+	0.340782i	0.0145213	+	0.0222302i
$236$	2.83326	−	9.64920i	0.184430	−	0.628109i
$237$	−5.42106	−	3.23471i	−0.352136	−	0.210117i
$238$	−0.288536	+	0.131770i	−0.0187030	+	0.00854137i
$239$	−14.7856	+	12.8118i	−0.956398	+	0.828724i	−0.985296	−	0.170858i	$-0.945346\pi$
$239$	−14.7856	+	12.8118i	−0.956398	+	0.828724i	0.0288972	+	0.999582i	$0.490800\pi$
$240$	1.46439	−	3.58547i	0.0945257	−	0.231441i
$241$	−8.77817	−	1.26211i	−0.565452	−	0.0812997i	−0.146340	−	0.989234i	$-0.546749\pi$
$241$	−8.77817	−	1.26211i	−0.565452	−	0.0812997i	−0.419112	+	0.907935i	$0.637658\pi$
$242$	−4.05549	+	28.2065i	−0.260697	+	1.81318i
$243$	2.57687	+	15.3740i	0.165307	+	0.986242i
$244$	−2.06180	+	1.78656i	−0.131993	+	0.114373i
$245$	11.8021	−	1.78659i	0.754007	−	0.114141i
$246$	4.85478	+	2.89682i	0.309530	+	0.184694i
$247$	12.2589	+	3.59954i	0.780016	+	0.229033i
$248$	−5.29675	+	6.11278i	−0.336344	+	0.388162i
$249$	2.81933	+	3.04331i	0.178667	+	0.192862i
$250$	−3.38846	−	10.6545i	−0.214305	−	0.673850i
$251$	−1.86497	−	12.9712i	−0.117716	−	0.818734i	−0.960060	−	0.279794i	$-0.909734\pi$
$251$	−1.86497	−	12.9712i	−0.117716	−	0.818734i	0.842344	−	0.538940i	$-0.181175\pi$
$252$	2.33298	−	3.08441i	0.146964	−	0.194299i
$253$	−29.3240	−	6.96606i	−1.84358	−	0.437952i
$254$			12.8512i			0.806355i
$255$	−0.305428	−	0.902719i	−0.0191267	−	0.0565305i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	0.0327583	−	0.00961870i	0.00204341	−	0.000599998i	−0.280711	−	0.959792i	$-0.590570\pi$
$257$	0.0327583	−	0.00961870i	0.00204341	−	0.000599998i	0.282754	+	0.959192i	$0.408752\pi$
$258$	−3.42251	+	13.2715i	−0.213076	+	0.826247i
$259$	0.839568	+	0.246519i	0.0521682	+	0.0153180i
$260$	4.96425	−	1.49784i	0.307870	−	0.0928919i
$261$	−4.25270	+	19.0918i	−0.263236	+	1.18175i
$262$	−14.8307	+	12.8509i	−0.916243	+	0.793929i
$263$	0.153594	−	0.238997i	0.00947100	−	0.0147372i	−0.836486	−	0.547989i	$-0.815394\pi$
$263$	0.153594	−	0.238997i	0.00947100	−	0.0147372i	0.845957	+	0.533251i	$0.179030\pi$
$264$	−3.41189	−	10.3368i	−0.209987	−	0.636184i
$265$	5.48286	−	12.2461i	0.336810	−	0.752269i
$266$	3.83992	−	5.97503i	0.235441	−	0.366353i
$267$	27.3913	+	11.4257i	1.67632	+	0.699243i
$268$	−0.404863	−	0.886527i	−0.0247310	−	0.0541532i
$269$	13.2214	+	20.5729i	0.806123	+	1.25435i	0.963738	+	0.266851i	$0.0859830\pi$
$269$	13.2214	+	20.5729i	0.806123	+	1.25435i	−0.157615	+	0.987501i	$0.550381\pi$
$270$	8.50369	+	7.91753i	0.517518	+	0.481845i
$271$	0.830102	−	0.957988i	0.0504251	−	0.0581936i	−0.729977	−	0.683472i	$-0.760469\pi$
$271$	0.830102	−	0.957988i	0.0504251	−	0.0581936i	0.780402	+	0.625278i	$0.215015\pi$
$272$	−0.0693233	−	0.236094i	−0.00420334	−	0.0143153i
$273$	5.17489	−	0.171941i	0.313199	−	0.0104063i
$274$	7.85140	−	1.12886i	0.474320	−	0.0681970i
$275$	−26.6847	−	16.5935i	−1.60915	−	1.00062i
$276$	8.09094	−	1.88063i	0.487017	−	0.113200i
$277$		−	28.7488i		−	1.72735i	−0.504050	−	0.863675i	$-0.668157\pi$
$277$		−	28.7488i		−	1.72735i	0.504050	−	0.863675i	$-0.331843\pi$
$278$	−1.08233	−	7.52778i	−0.0649139	−	0.451486i
$279$	−11.5230	−	21.3545i	−0.689863	−	1.27846i
$280$	−0.0214429	−	2.88247i	−0.00128146	−	0.172260i
$281$	8.76713	−	10.1178i	0.523003	−	0.603577i	−0.431377	−	0.902172i	$-0.641972\pi$
$281$	8.76713	−	10.1178i	0.523003	−	0.603577i	0.954380	+	0.298594i	$0.0965177\pi$
$282$	−0.310425	+	0.0552102i	−0.0184855	+	0.00328772i
$283$	−11.5584	+	7.42815i	−0.687077	+	0.441558i	−0.837046	−	0.547133i	$-0.815719\pi$
$283$	−11.5584	+	7.42815i	−0.687077	+	0.441558i	0.149968	+	0.988691i	$0.452083\pi$
$284$	7.23456	−	3.30391i	0.429292	−	0.196051i
$285$	16.6813	+	13.3069i	0.988115	+	0.788233i
$286$	7.87911	−	12.2601i	0.465901	−	0.724957i
$287$	4.16480	+	0.598808i	0.245841	+	0.0353465i
$288$	2.11075	+	2.13184i	0.124377	+	0.125620i
$289$	14.2504	+	9.15816i	0.838257	+	0.538715i
$290$	6.15480	+	13.2161i	0.361422	+	0.776074i
$291$	−10.8233	−	8.76644i	−0.634473	−	0.513898i
$292$	4.45172	+	6.92701i	0.260517	+	0.405373i
$293$	6.72038	−	22.8875i	0.392609	−	1.33710i	−0.491930	−	0.870635i	$-0.663708\pi$
$293$	6.72038	−	22.8875i	0.392609	−	1.33710i	0.884538	−	0.466467i	$-0.154474\pi$
$294$	−2.30886	+	8.95309i	−0.134656	+	0.522155i
$295$	22.4865	−	0.167279i	1.30922	−	0.00973938i
$296$	−0.281971	+	0.617431i	−0.0163892	+	0.0358874i
$297$	32.6255	+	1.40894i	1.89312	+	0.0817549i
$298$	−4.20175			−0.243401
$299$	8.77454	+	6.83293i	0.507445	+	0.395158i
$300$	8.62144	+	0.818970i	0.497759	+	0.0472832i
$301$	1.45172	+	10.0969i	0.0836756	+	0.581976i
$302$	−1.64876	+	3.61028i	−0.0948753	+	0.207748i
$303$	13.5471	+	14.6233i	0.778260	+	0.840088i
$304$	4.16390	+	3.60804i	0.238816	+	0.206935i
$305$	−5.15631	−	3.25982i	−0.295250	−	0.186657i
$306$	0.736030	+	0.0563218i	0.0420761	+	0.00321970i
$307$	11.3141	−	5.16696i	0.645728	−	0.294894i	−0.0655033	−	0.997852i	$-0.520865\pi$
$307$	11.3141	−	5.16696i	0.645728	−	0.294894i	0.711231	+	0.702958i	$0.248138\pi$
$308$	−5.30543	−	6.12279i	−0.302305	−	0.348878i
$309$	15.3057	+	1.68404i	0.870712	+	0.0958015i
$310$	−16.5072	−	7.39066i	−0.937543	−	0.419761i
$311$	−12.5793	−	1.80863i	−0.713305	−	0.102558i	−0.223897	−	0.974613i	$-0.571878\pi$
$311$	−12.5793	−	1.80863i	−0.713305	−	0.102558i	−0.489408	+	0.872055i	$0.662787\pi$
$312$	−0.439273	+	3.99242i	−0.0248689	+	0.226026i
$313$	1.20283	+	1.38814i	0.0679879	+	0.0784622i	0.788725	−	0.614747i	$-0.210742\pi$
$313$	1.20283	+	1.38814i	0.0679879	+	0.0784622i	−0.720737	+	0.693209i	$0.756196\pi$
$314$	−2.40974	−	5.27660i	−0.135990	−	0.297776i
$315$	8.10984	+	3.00205i	0.456938	+	0.169146i
$316$	1.02683	−	3.49705i	0.0577635	−	0.196724i
$317$	0.159009	−	0.183506i	0.00893083	−	0.0103067i	−0.751267	−	0.659999i	$-0.770557\pi$
$317$	0.159009	−	0.183506i	0.00893083	−	0.0103067i	0.760197	+	0.649692i	$0.225102\pi$
$318$	7.06312	+	7.62424i	0.396080	+	0.427546i
$319$	37.2724	+	17.0217i	2.08685	+	0.953033i
$320$	2.21561	+	0.301752i	0.123857	+	0.0168685i
$321$	11.4296	+	22.9759i	0.637936	+	1.28239i
$322$	5.01886	−	3.61010i	0.279690	−	0.201183i
$323$	1.35570			0.0754333
$324$	−8.22346	+	3.65714i	−0.456859	+	0.203174i
$325$	6.41297	+	9.65972i	0.355728	+	0.535825i
$326$	−2.09809	−	7.14545i	−0.116203	−	0.395750i
$327$	17.2896	+	4.45873i	0.956119	+	0.246568i
$328$	−0.919566	+	3.13176i	−0.0507746	+	0.172922i
$329$	−0.197413	+	0.126870i	−0.0108837	+	0.00699456i
$330$	19.9246	−	13.9807i	1.09681	−	0.769610i
$331$	−7.53043	−	8.69058i	−0.413910	−	0.477677i	0.510062	−	0.860138i	$-0.329622\pi$
$331$	−7.53043	−	8.69058i	−0.413910	−	0.477677i	−0.923972	+	0.382460i	$0.875077\pi$
$332$	−1.29492	+	2.01493i	−0.0710679	+	0.110584i
$333$	−1.43271	−	1.44703i	−0.0785121	−	0.0792967i
$334$	−3.26108	+	22.6813i	−0.178438	+	1.24107i
$335$	1.63632	−	1.43933i	0.0894018	−	0.0786390i
$336$	2.06072	+	0.859586i	0.112421	+	0.0468943i
$337$	11.1770	+	24.4741i	0.608848	+	1.33319i	0.923359	+	0.383938i	$0.125432\pi$
$337$	11.1770	+	24.4741i	0.608848	+	1.33319i	−0.314511	+	0.949254i	$0.601840\pi$
$338$	6.41249	−	4.12106i	0.348794	−	0.224156i
$339$	−1.10103	−	6.19062i	−0.0597995	−	0.336228i
$340$	0.460639	−	0.300900i	0.0249817	−	0.0163186i
$341$	−48.7733	+	14.3211i	−2.64122	+	0.775533i
$342$	−14.5463	+	7.84921i	−0.786571	+	0.424437i
$343$	2.26356	+	15.7434i	0.122221	+	0.850066i
$344$	−7.91298			−0.426639
$345$	9.25200	+	16.1059i	0.498111	+	0.867113i
$346$	19.9345			1.07168
$347$	−4.13815	−	28.7814i	−0.222147	−	1.54507i	−0.729893	−	0.683561i	$-0.760430\pi$
$347$	−4.13815	−	28.7814i	−0.222147	−	1.54507i	0.507746	−	0.861507i	$-0.330479\pi$
$348$	−11.2866	+	0.375008i	−0.605024	+	0.0201025i
$349$	24.8039	−	7.28308i	1.32772	−	0.389854i	0.460449	−	0.887686i	$-0.347688\pi$
$349$	24.8039	−	7.28308i	1.32772	−	0.389854i	0.867274	+	0.497832i	$0.165870\pi$
$350$	6.15678	−	1.90774i	0.329094	−	0.101973i
$351$	−10.7345	−	5.47379i	−0.572964	−	0.292169i
$352$	5.28697	−	3.39773i	0.281796	−	0.181100i
$353$	15.1427	+	33.1580i	0.805967	+	1.76482i	0.623851	+	0.781544i	$0.285567\pi$
$353$	15.1427	+	33.1580i	0.805967	+	1.76482i	0.182116	+	0.983277i	$0.441705\pi$
$354$	−6.70575	+	16.0759i	−0.356407	+	0.854427i
$355$	11.7458	+	13.3533i	0.623400	+	0.708720i
$356$	−2.43857	+	16.9606i	−0.129244	+	0.898913i
$357$	0.521722	−	0.172206i	0.0276124	−	0.00911411i
$358$	12.0877	−	18.8088i	0.638855	−	0.994077i
$359$	−19.8702	−	22.9315i	−1.04871	−	1.21028i	−0.977086	−	0.212844i	$-0.931727\pi$
$359$	−19.8702	−	22.9315i	−1.04871	−	1.21028i	−0.0716239	−	0.997432i	$-0.522818\pi$
$360$	−3.20037	+	5.89556i	−0.168674	+	0.310723i
$361$	−9.55323	+	6.13949i	−0.502802	+	0.323131i
$362$	1.52292	−	5.18659i	0.0800429	−	0.272601i
$363$	12.3253	−	47.7939i	0.646910	−	2.50853i
$364$	0.842203	+	2.86828i	0.0441435	+	0.150339i
$365$	−11.9535	+	14.0043i	−0.625677	+	0.733017i
$366$	3.88814	−	2.68528i	0.203236	−	0.140362i
$367$	−30.6724			−1.60109			−0.800543	−	0.599275i	$-0.795456\pi$
$367$	−30.6724			−1.60109			−0.800543	+	0.599275i	$0.795456\pi$
$368$	2.21787	+	4.25218i	0.115615	+	0.221660i
$369$	−7.80955	−	5.90698i	−0.406549	−	0.307505i
$370$	−1.50389	−	0.204820i	−0.0781836	−	0.0106481i
$371$	7.03626	+	3.21335i	0.365305	+	0.166829i
$372$	10.2771	−	9.52077i	0.532845	−	0.493629i
$373$	7.37935	−	8.51622i	0.382088	−	0.440953i	−0.531830	−	0.846851i	$-0.678496\pi$
$373$	7.37935	−	8.51622i	0.382088	−	0.440953i	0.913919	+	0.405898i	$0.133041\pi$
$374$	0.435671	−	1.48376i	0.0225280	−	0.0767234i
$375$	3.81552	+	18.9853i	0.197033	+	0.980397i
$376$	−0.0756206	−	0.165586i	−0.00389984	−	0.00853945i
$377$	−9.90099	−	11.4264i	−0.509927	−	0.588487i
$378$	−4.60087	+	4.86837i	−0.236643	+	0.250402i
$379$	18.8303	+	2.70738i	0.967246	+	0.139069i	0.607794	−	0.794095i	$-0.292055\pi$
$379$	18.8303	+	2.70738i	0.967246	+	0.139069i	0.359452	+	0.933164i	$0.382964\pi$
$380$	−5.03436	+	11.2443i	−0.258257	+	0.576822i
$381$	2.43438	−	22.1254i	0.124717	−	1.13352i
$382$	−15.2936	−	17.6498i	−0.782490	−	0.903042i
$383$	−17.6547	+	8.06263i	−0.902113	+	0.411981i	−0.811802	−	0.583932i	$-0.801513\pi$
$383$	−17.6547	+	8.06263i	−0.902113	+	0.411981i	−0.0903107	+	0.995914i	$0.528786\pi$
$384$	−0.887514	+	1.48739i	−0.0452908	+	0.0759029i
$385$	9.68047	−	15.3124i	0.493363	−	0.780391i
$386$	4.12080	+	3.57070i	0.209743	+	0.181744i
$387$	8.40640	−	22.2007i	0.427322	−	1.12852i
$388$	3.34054	−	7.31475i	0.169590	−	0.371350i
$389$	0.957239	+	6.65775i	0.0485340	+	0.337561i	0.999592	+	0.0285499i	$0.00908896\pi$
$389$	0.957239	+	6.65775i	0.0485340	+	0.337561i	−0.951058	+	0.309011i	$0.900002\pi$
$390$	−8.83049	+	1.63840i	−0.447149	+	0.0829634i
$391$	1.09761	+	0.433358i	0.0555087	+	0.0219159i
$392$	−5.33818			−0.269619
$393$	27.9678	−	19.3155i	1.41079	−	0.974337i
$394$	1.18811	−	2.60161i	0.0598564	−	0.131067i
$395$	8.14954	−	0.0606252i	0.410048	−	0.00305038i
$396$	3.91603	+	18.4427i	0.196788	+	0.926782i
$397$	−3.69826	+	12.5951i	−0.185610	+	0.632131i	0.813136	+	0.582074i	$0.197759\pi$
$397$	−3.69826	+	12.5951i	−0.185610	+	0.632131i	−0.998746	+	0.0500572i	$0.984060\pi$
$398$	−7.62070	−	11.8580i	−0.381991	−	0.594390i
$399$	−7.74289	+	9.55959i	−0.387629	+	0.478578i
$400$	0.785125	+	4.93797i	0.0392563	+	0.246899i
$401$	18.6090	+	11.9593i	0.929289	+	0.597218i	0.915339	−	0.402685i	$-0.131923\pi$
$401$	18.6090	+	11.9593i	0.929289	+	0.597218i	0.0139502	+	0.999903i	$0.495559\pi$
$402$	0.529104	+	1.60299i	0.0263893	+	0.0799499i
$403$	18.5655	+	2.66931i	0.924812	+	0.132968i
$404$	−6.22219	+	9.68191i	−0.309565	+	0.481693i
$405$	−13.1407	−	15.2421i	−0.652965	−	0.757388i
$406$	−7.64537	+	3.49152i	−0.379433	+	0.173281i
$407$	−3.58863	+	2.30627i	−0.177882	+	0.114318i
$408$	0.0746284	+	0.419605i	0.00369465	+	0.0207735i
$409$	1.77718	−	2.05098i	0.0878759	−	0.101414i	−0.710109	−	0.704092i	$-0.751354\pi$
$409$	1.77718	−	2.05098i	0.0878759	−	0.101414i	0.797985	+	0.602678i	$0.205900\pi$
$410$	−7.29825	+	0.0542924i	−0.360435	+	0.00268131i
$411$	−13.7313	+	0.456235i	−0.677314	+	0.0225044i
$412$	1.26519	+	8.79960i	0.0623315	+	0.433525i
$413$			12.9641i			0.637920i
$414$	−14.2861	+	1.70514i	−0.702123	+	0.0838033i
$415$	−5.14987	−	1.47061i	−0.252797	−	0.0721896i
$416$	−2.29533	+	0.330019i	−0.112538	+	0.0161805i
$417$	0.437431	+	13.1653i	0.0214211	+	0.644708i
$418$	9.75526	+	33.2234i	0.477145	+	1.62501i
$419$	3.90481	−	4.50640i	0.190763	−	0.220152i	−0.652309	−	0.757953i	$-0.726200\pi$
$419$	3.90481	−	4.50640i	0.190763	−	0.220152i	0.843072	+	0.537801i	$0.180745\pi$
$420$	−0.509105	+	4.96670i	−0.0248418	+	0.242350i
$421$	−0.630107	−	0.980466i	−0.0307095	−	0.0477850i	0.825559	−	0.564315i	$-0.190860\pi$
$421$	−0.630107	−	0.980466i	−0.0307095	−	0.0477850i	−0.856269	+	0.516530i	$0.827223\pi$
$422$	8.95380	+	19.6061i	0.435864	+	0.954409i
$423$	0.544904	−	0.0362500i	0.0264942	−	0.00176253i
$424$	−3.24409	+	5.04791i	−0.157547	+	0.245148i
$425$	0.941685	+	0.791755i	0.0456784	+	0.0384058i
$426$	−13.0813	+	4.31779i	−0.633792	+	0.209197i
$427$	1.90138	−	2.95860i	0.0920142	−	0.143177i
$428$	−11.1970	+	9.70230i	−0.541230	+	0.468978i
$429$	−15.8876	+	19.6153i	−0.767059	+	0.947034i
$430$	−5.11112	−	16.9397i	−0.246480	−	0.816904i
$431$	2.76353	+	0.811446i	0.133115	+	0.0390860i	0.347611	−	0.937639i	$-0.386993\pi$
$431$	2.76353	+	0.811446i	0.133115	+	0.0390860i	−0.214497	+	0.976725i	$0.568811\pi$
$432$	−3.23016	−	4.07015i	−0.155411	−	0.195825i
$433$	19.7842	−	5.80915i	0.950766	−	0.279170i	0.230660	−	0.973034i	$-0.425911\pi$
$433$	19.7842	−	5.80915i	0.950766	−	0.279170i	0.720106	+	0.693864i	$0.244093\pi$
$434$	4.33146	−	9.48457i	0.207917	−	0.455274i
$435$	−8.09298	−	23.9195i	−0.388029	−	1.14685i
$436$			10.3088i			0.493700i
$437$	−25.9216	+	5.12427i	−1.24000	+	0.245127i
$438$	−6.35218	−	12.7693i	−0.303519	−	0.610138i
$439$	2.54426	+	17.6957i	0.121431	+	0.844571i	0.955937	+	0.293572i	$0.0948441\pi$
$439$	2.54426	+	17.6957i	0.121431	+	0.844571i	−0.834506	+	0.550999i	$0.814247\pi$
$440$	10.6886	+	9.12341i	0.509559	+	0.434941i
$441$	5.67105	−	14.9768i	0.270050	−	0.713182i
$442$	−0.373663	+	0.431230i	−0.0177733	+	0.0205115i
$443$	−19.8673	−	5.83357i	−0.943924	−	0.277161i	−0.226669	−	0.973972i	$-0.572784\pi$
$443$	−19.8673	−	5.83357i	−0.943924	−	0.277161i	−0.717255	+	0.696811i	$0.754602\pi$
$444$	0.602418	−	1.00959i	0.0285895	−	0.0479132i
$445$	−37.8836	+	5.73479i	−1.79585	+	0.271855i
$446$	4.32713	−	3.74948i	0.204896	−	0.177543i
$447$	7.23400	+	0.795933i	0.342156	+	0.0376463i
$448$	−0.183460	+	1.27599i	−0.00866768	+	0.0602850i
$449$	27.5767	+	3.96493i	1.30142	+	0.187116i	0.757952	−	0.652311i	$-0.226200\pi$
$449$	27.5767	+	3.96493i	1.30142	+	0.187116i	0.543472	+	0.839427i	$0.317109\pi$
$450$	−14.6881	−	3.04314i	−0.692402	−	0.143455i
$451$	−15.5026	+	13.4331i	−0.729987	+	0.632538i
$452$	3.30219	−	1.50806i	0.155322	−	0.0709331i
$453$	3.52249	−	5.90335i	0.165501	−	0.277364i
$454$	1.03703	−	3.53181i	0.0486703	−	0.165756i
$455$	−5.59627	+	3.65561i	−0.262357	+	0.171378i
$456$	−6.48535	−	7.00058i	−0.303704	−	0.327832i
$457$	12.6846	−	27.7754i	0.593361	−	1.29928i	−0.340029	−	0.940415i	$-0.610437\pi$
$457$	12.6846	−	27.7754i	0.593361	−	1.29928i	0.933390	−	0.358864i	$-0.116836\pi$
$458$	15.3896	−	2.21268i	0.719107	−	0.103392i
$459$	−1.25653	−	0.236392i	−0.0586496	−	0.0110338i
$460$	−7.67028	+	7.49446i	−0.357628	+	0.349431i
$461$			1.99913i			0.0931087i	0.998916	+	0.0465543i	$0.0148241\pi$
$461$			1.99913i			0.0931087i	−0.998916	+	0.0465543i	$0.985176\pi$
$462$	7.97431	+	11.5464i	0.370999	+	0.537186i
$463$	−33.3228	−	15.2180i	−1.54864	−	0.707240i	−0.556324	−	0.830966i	$-0.687789\pi$
$463$	−33.3228	−	15.2180i	−1.54864	−	0.707240i	−0.992316	+	0.123725i	$0.960516\pi$
$464$	−1.83687	−	6.25580i	−0.0852745	−	0.290418i
$465$	27.0197	+	15.8511i	1.25301	+	0.735079i
$466$	15.4814	+	4.54574i	0.717160	+	0.210577i
$467$	7.72391	+	12.0186i	0.357420	+	0.556157i	0.972675	−	0.232172i	$-0.0745832\pi$
$467$	7.72391	+	12.0186i	0.357420	+	0.556157i	−0.615255	+	0.788328i	$0.710947\pi$
$468$	1.51256	−	6.79038i	0.0699180	−	0.313885i
$469$	0.822748	+	0.949501i	0.0379910	+	0.0438439i
$470$	0.305633	−	0.268839i	0.0140978	−	0.0124006i
$471$	3.14922	+	9.54099i	0.145108	+	0.439626i
$472$	−9.95420	−	1.43120i	−0.458179	−	0.0658762i
$473$	−41.8357	−	26.8862i	−1.92361	−	1.23623i
$474$	−2.43029	+	5.82623i	−0.111627	+	0.267607i
$475$	−27.3230	−	3.51440i	−1.25367	−	0.161252i
$476$	0.171492	+	0.266846i	0.00786030	+	0.0122309i
$477$	−10.7160	−	14.4643i	−0.490654	−	0.662276i
$478$	14.7856	+	12.8118i	0.676276	+	0.585996i
$479$	28.4537	−	8.35476i	1.30008	−	0.381739i	0.442817	−	0.896612i	$-0.353979\pi$
$479$	28.4537	−	8.35476i	1.30008	−	0.381739i	0.857266	+	0.514873i	$0.172161\pi$
$480$	−3.75738	−	0.939216i	−0.171500	−	0.0428692i
$481$	1.55800	−	0.224007i	0.0710387	−	0.0102138i
$482$			8.86844i			0.403946i
$483$	−9.32463	+	5.26465i	−0.424286	+	0.239550i
$484$	28.4966			1.29530
$485$	17.8167	+	2.42652i	0.809016	+	0.110183i
$486$	14.8508	−	4.73859i	0.673645	−	0.214947i
$487$	−0.555668	−	1.89243i	−0.0251797	−	0.0857542i	0.945945	−	0.324328i	$-0.105138\pi$
$487$	−0.555668	−	1.89243i	−0.0251797	−	0.0857542i	−0.971124	+	0.238574i	$0.923320\pi$
$488$	2.06180	+	1.78656i	0.0933332	+	0.0808737i
$489$	2.25865	+	12.6995i	0.102140	+	0.574290i
$490$	−3.44802	−	11.4277i	−0.155766	−	0.516251i
$491$	−4.38831	+	2.00408i	−0.198042	+	0.0904426i	−0.511967	−	0.859005i	$-0.671083\pi$
$491$	−4.38831	+	2.00408i	−0.198042	+	0.0904426i	0.313925	+	0.949448i	$0.398356\pi$
$492$	2.17643	−	5.21763i	0.0981208	−	0.235229i
$493$	−1.34962	−	0.867346i	−0.0607837	−	0.0390633i
$494$	1.81828	−	12.6464i	0.0818082	−	0.568989i
$495$	−36.9518	+	20.2957i	−1.66086	+	0.912222i
$496$	6.80436	+	4.37290i	0.305525	+	0.196349i
$497$	−7.74847	+	6.71409i	−0.347566	+	0.301168i
$498$	2.61110	−	3.22374i	0.117006	−	0.144459i
$499$	12.1326	−	7.79717i	0.543131	−	0.349049i	−0.240131	−	0.970740i	$-0.577190\pi$
$499$	12.1326	−	7.79717i	0.543131	−	0.349049i	0.783262	+	0.621691i	$0.213554\pi$
$500$	−10.0638	+	4.87027i	−0.450068	+	0.217805i
$501$	9.91096	−	38.4318i	0.442789	−	1.71700i
$502$	−12.5737	+	3.69198i	−0.561193	+	0.164781i
$503$	34.2837	+	15.6568i	1.52863	+	0.698103i	0.989555	−	0.144153i	$-0.0460458\pi$
$503$	34.2837	+	15.6568i	1.52863	+	0.698103i	0.539077	+	0.842256i	$0.318773\pi$
$504$	−3.38503	−	1.87028i	−0.150781	−	0.0833087i
$505$	−24.7455	−	7.06642i	−1.10116	−	0.314452i
$506$	−2.72192	+	30.0169i	−0.121004	+	1.33441i
$507$	−11.8208	+	5.88036i	−0.524979	+	0.261156i
$508$	12.7204	−	1.82891i	0.564375	−	0.0811449i
$509$	15.2350	+	6.95758i	0.675279	+	0.308389i	0.723377	−	0.690453i	$-0.242589\pi$
$509$	15.2350	+	6.95758i	0.675279	+	0.308389i	−0.0480985	+	0.998843i	$0.515316\pi$
$510$	−0.850064	+	0.430790i	−0.0376415	+	0.0190757i
$511$	−8.02211	−	6.95120i	−0.354877	−	0.307503i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	26.5306	−	10.7582i	1.17135	−	0.474986i
$514$	−0.0141828	−	0.0310560i	−0.000625576	−	0.00136982i
$515$	−18.0205	+	8.39225i	−0.794078	+	0.369807i
$516$	13.6235	+	1.49895i	0.599740	+	0.0659874i
$517$	0.162813	−	1.13239i	0.00716049	−	0.0498023i
$518$	0.124527	−	0.866106i	0.00547141	−	0.0380545i
$519$	−34.3204	−	3.77616i	−1.50650	−	0.165755i
$520$	−2.18908	−	4.70056i	−0.0959974	−	0.206133i
$521$	−1.98564	−	4.34794i	−0.0869924	−	0.190487i	0.861136	−	0.508375i	$-0.169754\pi$
$521$	−1.98564	−	4.34794i	−0.0869924	−	0.190487i	−0.948128	+	0.317888i	$0.897026\pi$
$522$	19.5027	+	1.49237i	0.853610	+	0.0653191i
$523$	13.9264	+	4.08917i	0.608960	+	0.178807i	0.571651	−	0.820497i	$-0.306303\pi$
$523$	13.9264	+	4.08917i	0.608960	+	0.178807i	0.0373093	+	0.999304i	$0.488121\pi$
$524$	14.8307	+	12.8509i	0.647882	+	0.561393i
$525$	−10.9613	+	2.11820i	−0.478389	+	0.0924460i
$526$	−0.258423	−	0.118018i	−0.0112678	−	0.00514581i
$527$	1.96997	−	0.283239i	0.0858133	−	0.0123381i
$528$	−9.74599	+	4.84823i	−0.424140	+	0.210992i
$529$	−22.6248	−	4.13724i	−0.983689	−	0.179880i
$530$	−12.9017	−	3.68426i	−0.560414	−	0.160034i
$531$	14.5903	−	26.4071i	0.633164	−	1.14597i
$532$	−6.46069	−	2.95050i	−0.280107	−	0.127920i
$533$	7.26233	−	2.13241i	0.314567	−	0.0923651i
$534$	7.41123	−	28.7386i	0.320715	−	1.24364i
$535$	−28.0025	−	17.7032i	−1.21065	−	0.765375i
$536$	−0.819885	+	0.526908i	−0.0354136	+	0.0227590i
$537$	−24.3738	+	30.0927i	−1.05181	+	1.29859i
$538$	18.4819	−	16.0146i	0.796811	−	0.690440i
$539$	−28.2228	−	18.1377i	−1.21564	−	0.781246i
$540$	6.62674	−	9.54392i	0.285169	−	0.410705i
$541$	2.93302	−	20.3996i	0.126101	−	0.877048i	−0.824330	−	0.566110i	$-0.808448\pi$
$541$	2.93302	−	20.3996i	0.126101	−	0.877048i	0.950430	−	0.310938i	$-0.100643\pi$
$542$	−1.06637	−	0.685316i	−0.0458046	−	0.0294369i
$543$	−3.60444	+	8.64107i	−0.154681	+	0.370824i
$544$	−0.223825	+	0.102217i	−0.00959640	+	0.00438253i
$545$	−22.0684	+	6.65859i	−0.945308	+	0.285223i
$546$	−0.906654	−	5.09775i	−0.0388012	−	0.218163i
$547$	4.68351	+	4.05828i	0.200252	+	0.173520i	0.749214	−	0.662328i	$-0.230431\pi$
$547$	4.68351	+	4.05828i	0.200252	+	0.173520i	−0.548962	+	0.835847i	$0.684977\pi$
$548$	−2.23474	−	7.61083i	−0.0954634	−	0.325119i
$549$	−7.20273	+	3.88662i	−0.307405	+	0.165877i
$550$	−12.6270	+	28.7745i	−0.538415	+	1.22695i
$551$	35.9222			1.53034
$552$	−3.01294	−	7.74094i	−0.128239	−	0.329476i
$553$			4.69842i			0.199797i
$554$	−28.4562	+	4.09138i	−1.20899	+	0.173826i
$555$	2.55039	+	0.637511i	0.108258	+	0.0270608i
$556$	−7.29713	+	2.14263i	−0.309467	+	0.0908678i
$557$	−0.332356	−	0.287988i	−0.0140824	−	0.0122024i	0.647791	−	0.761818i	$-0.275693\pi$
$557$	−0.332356	−	0.287988i	−0.0140824	−	0.0122024i	−0.661873	+	0.749616i	$0.730238\pi$
$558$	−19.4973	+	14.4448i	−0.825385	+	0.611495i
$559$	9.92059	+	15.4367i	0.419596	+	0.652904i
$560$	−2.85008	+	0.431443i	−0.120438	+	0.0182318i
$561$	−1.03115	+	2.47200i	−0.0435350	+	0.104368i
$562$	−11.2625	−	7.23798i	−0.475080	−	0.305316i
$563$	−30.8547	−	4.43624i	−1.30037	−	0.186965i	−0.542880	−	0.839810i	$-0.682666\pi$
$563$	−30.8547	−	4.43624i	−1.30037	−	0.186965i	−0.757492	+	0.652845i	$0.773575\pi$
$564$	0.0988263	+	0.299408i	0.00416134	+	0.0126073i
$565$	5.36130	+	6.09506i	0.225552	+	0.256421i
$566$	8.99748	+	10.3836i	0.378192	+	0.436457i
$567$	8.84335	−	7.51014i	0.371386	−	0.315396i
$568$	−4.29987	−	6.69073i	−0.180419	−	0.280737i
$569$	−15.1172	−	4.43880i	−0.633745	−	0.186084i	−0.0509468	−	0.998701i	$-0.516224\pi$
$569$	−15.1172	−	4.43880i	−0.633745	−	0.186084i	−0.582798	+	0.812617i	$0.698042\pi$
$570$	10.7975	−	18.4053i	0.452256	−	0.770912i
$571$	10.4927	+	35.7349i	0.439106	+	1.49546i	0.820825	+	0.571180i	$0.193514\pi$
$571$	10.4927	+	35.7349i	0.439106	+	1.49546i	−0.381719	+	0.924278i	$0.624668\pi$
$572$	−13.2567	−	6.05411i	−0.554289	−	0.253135i
$573$	22.9871	+	33.2840i	0.960299	+	1.39046i
$574$		−	4.20763i		−	0.175623i
$575$	−20.9981	−	11.5793i	−0.875680	−	0.482891i
$576$	1.80975	−	2.39265i	0.0754063	−	0.0996939i
$577$	−15.4156	+	2.21643i	−0.641761	+	0.0922713i	−0.455510	−	0.890231i	$-0.650543\pi$
$577$	−15.4156	+	2.21643i	−0.641761	+	0.0922713i	−0.186251	+	0.982502i	$0.559634\pi$
$578$	7.03690	−	15.4087i	0.292697	−	0.640916i
$579$	−6.41824	−	6.92813i	−0.266733	−	0.287923i
$580$	12.2056	−	7.97299i	0.506811	−	0.331061i
$581$	0.869886	−	2.96256i	0.0360889	−	0.122908i
$582$	−7.13689	+	11.9607i	−0.295834	+	0.495788i
$583$	−34.3029	+	15.6656i	−1.42068	+	0.648802i
$584$	6.22296	−	5.39223i	0.257508	−	0.223132i
$585$	15.5135	−	1.14801i	0.641403	−	0.0474645i
$586$	−23.6110	−	3.39474i	−0.975360	−	0.140236i
$587$	−2.40652	+	16.7377i	−0.0993278	+	0.690840i	0.877931	+	0.478788i	$0.158924\pi$
$587$	−2.40652	+	16.7377i	−0.0993278	+	0.690840i	−0.977258	+	0.212052i	$0.931985\pi$
$588$	9.19054	+	1.01121i	0.379012	+	0.0417014i
$589$	−33.6791	+	29.1831i	−1.38772	+	1.20247i
$590$	−3.36574	−	22.2338i	−0.138565	−	0.915353i
$591$	−2.53835	+	4.25402i	−0.104414	+	0.174987i
$592$	0.651275	+	0.191232i	0.0267672	+	0.00785957i
$593$	1.86022	−	2.14680i	0.0763899	−	0.0881586i	−0.716268	−	0.697825i	$-0.754151\pi$
$593$	1.86022	−	2.14680i	0.0763899	−	0.0881586i	0.792658	+	0.609667i	$0.208697\pi$
$594$	−3.24849	−	32.4939i	−0.133287	−	1.33324i
$595$	−0.460480	+	0.539480i	−0.0188779	+	0.0221165i
$596$	0.597972	+	4.15899i	0.0244939	+	0.170359i
$597$	10.8740	+	21.8591i	0.445043	+	0.894633i
$598$	5.51463	−	9.65766i	0.225510	−	0.394931i
$599$		−	8.90466i		−	0.363834i	−0.983314	−	0.181917i	$-0.941770\pi$
$599$		−	8.90466i		−	0.363834i	0.983314	−	0.181917i	$-0.0582303\pi$
$600$	−0.416325	−	8.65024i	−0.0169964	−	0.353145i
$601$	6.76727	−	14.8183i	0.276043	−	0.604449i	−0.719936	−	0.694041i	$-0.755829\pi$
$601$	6.76727	−	14.8183i	0.276043	−	0.604449i	0.995979	+	0.0895914i	$0.0285561\pi$
$602$	9.78754	−	2.87388i	0.398910	−	0.117131i
$603$	−0.607285	−	2.86003i	−0.0247305	−	0.116470i
$604$	3.80817	+	1.11818i	0.154952	+	0.0454981i
$605$	18.4064	+	61.0039i	0.748326	+	2.48016i
$606$	12.5465	−	15.4903i	0.509668	−	0.629251i
$607$	30.7899	−	26.6796i	1.24972	−	1.08289i	0.256516	−	0.966540i	$-0.417425\pi$
$607$	30.7899	−	26.6796i	1.24972	−	1.08289i	0.993208	−	0.116352i	$-0.0371201\pi$
$608$	2.97873	−	4.63499i	0.120803	−	0.187974i
$609$	13.8241	−	4.56297i	0.560182	−	0.184901i
$610$	−2.49282	+	5.56775i	−0.100931	+	0.225432i
$611$	−0.228221	+	0.355119i	−0.00923283	+	0.0143666i
$612$	−0.0489996	−	0.736554i	−0.00198069	−	0.0297734i
$613$	−9.77007	−	21.3935i	−0.394609	−	0.864074i	−0.997789	−	0.0664684i	$-0.978827\pi$
$613$	−9.77007	−	21.3935i	−0.394609	−	0.864074i	0.603179	−	0.797606i	$-0.293900\pi$
$614$	−6.72453	−	10.4636i	−0.271380	−	0.422275i
$615$	12.5754	+	1.28903i	0.507089	+	0.0519785i
$616$	−5.30543	+	6.12279i	−0.213762	+	0.246694i
$617$	−2.58807	−	8.81415i	−0.104192	−	0.354844i	0.890851	−	0.454296i	$-0.150109\pi$
$617$	−2.58807	−	8.81415i	−0.104192	−	0.354844i	−0.995042	+	0.0994519i	$0.968291\pi$
$618$	−0.511334	−	15.3896i	−0.0205689	−	0.619060i
$619$	44.0020	−	6.32653i	1.76859	−	0.254285i	0.820355	−	0.571855i	$-0.193776\pi$
$619$	44.0020	−	6.32653i	1.76859	−	0.254285i	0.948235	+	0.317570i	$0.102867\pi$
$620$	−4.96622	+	17.3909i	−0.199448	+	0.698437i
$621$	24.9188	−	0.229484i	0.999958	−	0.00920888i
$622$			12.7086i			0.509570i
$623$	−3.14360	−	21.8642i	−0.125946	−	0.875972i
$624$	4.01430	−	0.133379i	0.160700	−	0.00533943i
$625$	−16.9264	−	18.3983i	−0.677055	−	0.735932i
$626$	1.20283	−	1.38814i	0.0480747	−	0.0554811i
$627$	−10.5018	−	59.0473i	−0.419401	−	2.35812i
$628$	−4.87995	+	3.13615i	−0.194731	+	0.125146i
$629$	0.151925	−	0.0693820i	0.00605766	−	0.00276644i
$630$	1.81734	−	8.45453i	0.0724046	−	0.336836i
$631$	−14.0369	+	21.8418i	−0.558800	+	0.869509i	−0.999605	−	0.0280933i	$-0.991056\pi$
$631$	−14.0369	+	21.8418i	−0.558800	+	0.869509i	0.440806	+	0.897603i	$0.354693\pi$
$632$	−3.60759	−	0.518693i	−0.143502	−	0.0206325i
$633$	−11.7015	−	35.4511i	−0.465091	−	1.40906i
$634$	−0.204268	−	0.131275i	−0.00811250	−	0.00521359i
$635$	12.1315	+	26.0498i	0.481425	+	1.03375i
$636$	6.54145	−	8.07627i	0.259385	−	0.320245i
$637$	6.69254	+	10.4138i	0.265168	+	0.412609i
$638$	11.5440	−	39.3154i	0.457033	−	1.55651i
$639$	23.3395	−	4.95579i	0.923297	−	0.196048i
$640$	−0.0166338	−	2.23601i	−0.000657511	−	0.0883859i
$641$	−13.0538	+	28.5838i	−0.515594	+	1.12899i	0.455487	+	0.890243i	$0.349465\pi$
$641$	−13.0538	+	28.5838i	−0.515594	+	1.12899i	−0.971081	+	0.238751i	$0.923262\pi$
$642$	21.1154	−	14.5830i	0.833359	−	0.575546i
$643$	45.0590			1.77695			0.888477	−	0.458922i	$-0.151764\pi$
$643$	45.0590			1.77695			0.888477	+	0.458922i	$0.151764\pi$
$644$	−4.28761	−	4.45401i	−0.168956	−	0.175512i
$645$	5.59075	+	30.1326i	0.220136	+	1.18647i
$646$	−0.192936	−	1.34190i	−0.00759098	−	0.0527965i
$647$	−16.8740	+	36.9490i	−0.663387	+	1.45262i	0.215944	+	0.976406i	$0.430717\pi$
$647$	−16.8740	+	36.9490i	−0.663387	+	1.45262i	−0.879332	+	0.476210i	$0.842010\pi$
$648$	4.79023	+	7.61929i	0.188178	+	0.299314i
$649$	−47.7647	−	41.3884i	−1.87493	−	1.62464i
$650$	8.64874	−	7.72242i	0.339231	−	0.302898i
$651$	−9.25396	+	15.5087i	−0.362691	+	0.607835i
$652$	−6.77413	+	3.09364i	−0.265295	+	0.121156i
$653$	−31.5683	−	36.4317i	−1.23536	−	1.42568i	−0.868708	−	0.495325i	$-0.835049\pi$
$653$	−31.5683	−	36.4317i	−1.23536	−	1.42568i	−0.366654	−	0.930357i	$-0.619497\pi$
$654$	1.95278	−	17.7482i	0.0763596	−	0.694009i
$655$	−17.9311	+	40.0493i	−0.700625	+	1.56486i
$656$	3.23075	+	0.464511i	0.126139	+	0.0181361i
$657$	8.51744	+	23.1876i	0.332297	+	0.904635i
$658$	0.153673	+	0.177348i	0.00599081	+	0.00691376i
$659$	−8.60340	−	18.8388i	−0.335141	−	0.733856i	0.664772	−	0.747046i	$-0.268529\pi$
$659$	−8.60340	−	18.8388i	−0.335141	−	0.733856i	−0.999913	+	0.0131899i	$0.995801\pi$
$660$	−16.6739	−	17.7321i	−0.649032	−	0.690223i
$661$	4.81472	−	16.3974i	0.187271	−	0.637786i	−0.811314	−	0.584610i	$-0.801247\pi$
$661$	4.81472	−	16.3974i	0.187271	−	0.637786i	0.998585	−	0.0531759i	$-0.0169344\pi$
$662$	−7.53043	+	8.69058i	−0.292678	+	0.337769i
$663$	0.725008	−	0.671649i	0.0281570	−	0.0260847i
$664$	2.17871	+	0.994983i	0.0845503	+	0.0386128i
$665$	2.14321	−	15.7365i	0.0831100	−	0.610234i
$666$	−1.22840	+	1.62406i	−0.0475997	+	0.0629311i
$667$	29.0836	+	11.4828i	1.12612	+	0.444614i
$668$	22.9145			0.886590
$669$	−8.16012	+	5.63566i	−0.315488	+	0.217887i
$670$	−1.65755	−	1.41483i	−0.0640369	−	0.0546595i
$671$	4.83042	+	16.4509i	0.186476	+	0.635080i
$672$	0.557566	−	2.16208i	0.0215086	−	0.0834039i
$673$	1.35231	−	4.60555i	0.0521278	−	0.177531i	−0.929314	−	0.369290i	$-0.879601\pi$
$673$	1.35231	−	4.60555i	0.0521278	−	0.177531i	0.981442	+	0.191759i	$0.0614191\pi$
$674$	22.6344	−	14.5462i	0.871844	−	0.560300i
$675$	24.7114	+	8.02159i	0.951143	+	0.308751i
$676$	−4.99170	−	5.76073i	−0.191989	−	0.221567i
$677$	14.2467	−	22.1682i	0.547543	−	0.851994i	−0.451648	−	0.892196i	$-0.649164\pi$
$677$	14.2467	−	22.1682i	0.547543	−	0.851994i	0.999192	+	0.0402020i	$0.0128001\pi$
$678$	−5.97092	+	1.97084i	−0.229312	+	0.0756895i
$679$	−1.47528	+	10.2608i	−0.0566162	+	0.393774i
$680$	−0.363393	−	0.413128i	−0.0139355	−	0.0158427i
$681$	−2.45444	+	5.88413i	−0.0940545	+	0.225480i
$682$	21.1165	+	46.2387i	0.808594	+	1.77057i
$683$	30.9376	−	19.8824i	1.18379	−	0.760778i	0.207714	−	0.978190i	$-0.433398\pi$
$683$	30.9376	−	19.8824i	1.18379	−	0.760778i	0.976080	+	0.217411i	$0.0697612\pi$
$684$	9.83947	+	13.2811i	0.376221	+	0.507817i
$685$	14.8494	−	9.69997i	0.567366	−	0.370617i
$686$	15.2611	−	4.48105i	0.582670	−	0.171087i
$687$	−26.9147	+	0.894269i	−1.02686	+	0.0341185i
$688$	1.12613	+	7.83244i	0.0429335	+	0.298609i
$689$	13.9147			0.530107
$690$	14.6253	−	11.4499i	0.556775	−	0.435892i
$691$	3.45706			0.131513			0.0657564	−	0.997836i	$-0.479054\pi$
$691$	3.45706			0.131513			0.0657564	+	0.997836i	$0.479054\pi$
$692$	−2.83697	−	19.7316i	−0.107845	−	0.750081i
$693$	−11.5419	−	21.3895i	−0.438439	−	0.812520i
$694$	−27.8996	+	8.19205i	−1.05905	+	0.310966i
$695$	−9.30016	−	14.2373i	−0.352775	−	0.540053i
$696$	1.97744	+	11.1183i	0.0749546	+	0.421439i
$697$	0.675640	−	0.434207i	0.0255917	−	0.0164468i
$698$	−10.7389	−	23.5149i	−0.406474	−	0.890054i
$699$	−25.7926	−	10.7588i	−0.975565	−	0.406937i
$700$	−2.76452	−	5.82262i	−0.104489	−	0.220074i
$701$	3.10574	−	21.6009i	0.117302	−	0.815855i	−0.843204	−	0.537595i	$-0.819333\pi$
$701$	3.10574	−	21.6009i	0.117302	−	0.815855i	0.960506	−	0.278260i	$-0.0897578\pi$
$702$	−3.89040	+	11.4042i	−0.146834	+	0.430424i
$703$	−2.02187	+	3.14609i	−0.0762563	+	0.118657i
$704$	−4.11556	−	4.74961i	−0.155111	−	0.179008i
$705$	−0.577122	+	0.404954i	−0.0217357	+	0.0152515i
$706$	30.6654	−	19.7075i	1.15411	−	0.741701i
$707$	4.17987	−	14.2353i	0.157200	−	0.535375i
$708$	16.8666	+	4.34965i	0.633887	+	0.163470i
$709$	−0.653430	−	2.22538i	−0.0245401	−	0.0835759i	0.946313	−	0.323253i	$-0.104777\pi$
$709$	−0.653430	−	2.22538i	−0.0245401	−	0.0835759i	−0.970853	+	0.239677i	$0.922958\pi$
$710$	11.5458	−	13.5266i	0.433306	−	0.507643i
$711$	5.28779	−	9.57042i	0.198308	−	0.358919i
$712$	17.1351			0.642164
$713$	−36.5961	+	12.8617i	−1.37053	+	0.481675i
$714$	−0.244702	−	0.491904i	−0.00915774	−	0.0184090i
$715$	4.39763	−	32.2896i	0.164462	−	1.20756i
$716$	−20.3376	−	9.28789i	−0.760053	−	0.347105i
$717$	−23.0288	−	24.8583i	−0.860027	−	0.928351i
$718$	−19.8702	+	22.9315i	−0.741550	+	0.855794i
$719$	−10.3905	+	35.3868i	−0.387500	+	1.31971i	0.502828	+	0.864386i	$0.332293\pi$
$719$	−10.3905	+	35.3868i	−0.387500	+	1.31971i	−0.890329	+	0.455319i	$0.849525\pi$
$720$	6.29101	+	2.32877i	0.234452	+	0.0867880i
$721$	−4.76080	−	10.4247i	−0.177301	−	0.388236i
$722$	7.43657	+	8.58225i	0.276760	+	0.319398i
$723$	1.67994	−	15.2684i	0.0624775	−	0.567840i
$724$	−5.35053	−	0.769291i	−0.198851	−	0.0285905i
$725$	24.9520	+	20.9793i	0.926692	+	0.779150i
$726$	−49.0615	−	5.39807i	−1.82084	−	0.200341i
$727$	−3.70264	−	4.27308i	−0.137323	−	0.158480i	0.682922	−	0.730491i	$-0.260709\pi$
$727$	−3.70264	−	4.27308i	−0.137323	−	0.158480i	−0.820246	+	0.572011i	$0.806163\pi$
$728$	2.71923	−	1.24183i	0.100781	−	0.0460253i
$729$	−26.4656	+	5.34509i	−0.980209	+	0.197966i
$730$	15.5629	+	9.83885i	0.576008	+	0.364152i
$731$	1.47150	+	1.27506i	0.0544254	+	0.0471599i
$732$	−3.21129	−	3.46641i	−0.118693	−	0.128122i
$733$	−12.2467	+	26.8165i	−0.452341	+	0.990489i	0.536826	+	0.843693i	$0.319623\pi$
$733$	−12.2467	+	26.8165i	−0.452341	+	0.990489i	−0.989167	+	0.146796i	$0.953104\pi$
$734$	4.36514	+	30.3602i	0.161120	+	1.12062i
$735$	3.77158	+	20.3278i	0.139117	+	0.749801i
$736$	3.89326	−	2.80045i	0.143508	−	0.103226i
$737$	−6.12500			−0.225617
$738$	−4.73544	+	8.57071i	−0.174314	+	0.315492i
$739$	14.0481	−	30.7609i	0.516766	−	1.13156i	−0.453883	−	0.891061i	$-0.649962\pi$
$739$	14.0481	−	30.7609i	0.516766	−	1.13156i	0.970649	−	0.240499i	$-0.0773110\pi$
$740$	0.0112906	+	1.51773i	0.000415049	+	0.0557930i
$741$	−5.52605	+	21.4284i	−0.203005	+	0.787192i
$742$	2.17928	−	7.42195i	0.0800039	−	0.272468i
$743$	13.7622	+	21.4143i	0.504885	+	0.785616i	0.996357	−	0.0852770i	$-0.0271775\pi$
$743$	13.7622	+	21.4143i	0.504885	+	0.785616i	−0.491472	+	0.870893i	$0.663541\pi$
$744$	−10.8865	−	8.81759i	−0.399117	−	0.323269i
$745$	−8.51709	+	3.96646i	−0.312042	+	0.145320i
$746$	−9.47973	−	6.09225i	−0.347078	−	0.223053i
$747$	−5.10609	+	5.05556i	−0.186822	+	0.184973i
$748$	−1.53066	−	0.220076i	−0.0559665	−	0.00804677i
$749$	10.3259	−	16.0673i	0.377299	−	0.587088i
$750$	18.2491	−	6.47857i	0.666361	−	0.236564i
$751$	37.5031	−	17.1271i	1.36851	−	0.624977i	0.410537	−	0.911844i	$-0.365341\pi$
$751$	37.5031	−	17.1271i	1.36851	−	0.624977i	0.957970	+	0.286867i	$0.0926138\pi$
$752$	−0.153139	+	0.0984162i	−0.00558439	+	0.00358887i
$753$	22.3471	−	3.97452i	0.814373	−	0.144839i
$754$	−9.90099	+	11.4264i	−0.360573	+	0.416123i
$755$	0.0660188	+	8.87458i	0.00240267	+	0.322979i
$756$	5.47359	+	3.86120i	0.199072	+	0.140431i
$757$	2.88087	+	20.0369i	0.104707	+	0.728253i	0.972766	+	0.231791i	$0.0744587\pi$
$757$	2.88087	+	20.0369i	0.104707	+	0.728253i	−0.868058	+	0.496462i	$0.834632\pi$
$758$		−	19.0239i		−	0.690980i
$759$	10.3723	−	51.1633i	0.376490	−	1.85711i
$760$	11.8463	+	3.38288i	0.429712	+	0.122710i
$761$	16.1644	−	2.32409i	0.585958	−	0.0842481i	0.157041	−	0.987592i	$-0.449804\pi$
$761$	16.1644	−	2.32409i	0.585958	−	0.0842481i	0.428917	+	0.903344i	$0.358895\pi$
$762$	−22.2466	+	0.739166i	−0.805910	+	0.0267772i
$763$	−3.74399	−	12.7509i	−0.135542	−	0.461613i
$764$	−15.2936	+	17.6498i	−0.553304	+	0.638547i
$765$	1.54513	−	0.580647i	0.0558641	−	0.0209934i
$766$	10.4931	+	16.3276i	0.379131	+	0.589939i
$767$	9.68769	+	21.2131i	0.349802	+	0.765960i
$768$	1.59855	+	0.666803i	0.0576828	+	0.0240612i
$769$	−10.8173	+	16.8321i	−0.390082	+	0.606980i	−0.979644	−	0.200744i	$-0.935664\pi$
$769$	−10.8173	+	16.8321i	−0.390082	+	0.606980i	0.589562	+	0.807723i	$0.299300\pi$
$770$	−16.5342	−	7.40276i	−0.595851	−	0.266777i
$771$	0.0185351	+	0.0561545i	0.000667524	+	0.00202235i
$772$	2.94790	−	4.58702i	0.106097	−	0.165091i
$773$	11.3512	−	9.83588i	0.408275	−	0.353772i	−0.426381	−	0.904543i	$-0.640212\pi$
$773$	11.3512	−	9.83588i	0.408275	−	0.353772i	0.834656	+	0.550771i	$0.185666\pi$
$774$	−23.1711	−	5.16135i	−0.832867	−	0.185521i
$775$	−40.4373	+	0.601667i	−1.45255	+	0.0216125i
$776$	−7.71571	−	2.26554i	−0.276978	−	0.0813280i
$777$	−0.378459	+	1.46755i	−0.0135771	+	0.0526481i
$778$	6.45375	−	1.89499i	0.231378	−	0.0679387i
$779$	−7.47051	+	16.3581i	−0.267659	+	0.586091i
$780$	2.87843	+	8.50744i	0.103064	+	0.304615i
$781$		−	49.9835i		−	1.78855i
$782$	0.272741	−	1.14811i	0.00975318	−	0.0410565i
$783$	−33.2943	−	6.26372i	−1.18984	−	0.223847i
$784$	0.759703	+	5.28385i	0.0271322	+	0.188709i
$785$	−9.86574	−	8.42104i	−0.352123	−	0.300560i
$786$	−23.0991	−	24.9342i	−0.823918	−	0.889373i
$787$	−27.3205	+	31.5296i	−0.973871	+	1.12391i	0.0184011	+	0.999831i	$0.494142\pi$
$787$	−27.3205	+	31.5296i	−0.973871	+	1.12391i	−0.992273	+	0.124077i	$0.960403\pi$
$788$	−2.74421	−	0.805774i	−0.0977586	−	0.0287045i
$789$	0.422560	+	0.252139i	0.0150435	+	0.00897639i
$790$	−1.21981	−	8.05796i	−0.0433988	−	0.286689i
$791$	−3.53676	+	3.06462i	−0.125753	+	0.108965i
$792$	17.6977	−	6.50084i	0.628860	−	0.230997i
$793$	0.900341	−	6.26201i	0.0319720	−	0.222370i
$794$	12.9932	+	1.86815i	0.461113	+	0.0662980i
$795$	21.5145	+	8.78700i	0.763039	+	0.311643i
$796$	−10.6528	+	9.23070i	−0.377579	+	0.327174i
$797$	37.8938	−	17.3055i	1.34227	−	0.612993i	0.390725	−	0.920508i	$-0.372224\pi$
$797$	37.8938	−	17.3055i	1.34227	−	0.612993i	0.951544	+	0.307514i	$0.0994971\pi$
$798$	10.5642	+	6.30360i	0.373969	+	0.223145i
$799$	−0.0126194	+	0.0429776i	−0.000446441	+	0.00152044i
$800$	4.77598	−	1.47988i	0.168856	−	0.0523217i
$801$	−18.2035	+	48.0741i	−0.643190	+	1.69862i
$802$	9.18921	−	20.1216i	0.324482	−	0.710517i
$803$	51.2219	−	7.36460i	1.80758	−	0.259891i
$804$	1.51138	−	0.751848i	0.0533021	−	0.0265156i
$805$	6.76546	−	12.0556i	0.238451	−	0.424904i
$806$		−	18.7564i		−	0.660665i
$807$	−34.8532	+	24.0708i	−1.22689	+	0.847332i
$808$	10.4689	+	4.78098i	0.368294	+	0.168194i
$809$	−4.34848	−	14.8095i	−0.152884	−	0.520676i	0.847057	−	0.531502i	$-0.178372\pi$
$809$	−4.34848	−	14.8095i	−0.152884	−	0.520676i	−0.999941	+	0.0108258i	$0.996554\pi$
$810$	−13.2169	+	15.1761i	−0.464394	+	0.533234i
$811$	0.697915	+	0.204926i	0.0245071	+	0.00719593i	0.293963	−	0.955817i	$-0.405026\pi$
$811$	0.697915	+	0.204926i	0.0245071	+	0.00719593i	−0.269456	+	0.963013i	$0.586844\pi$
$812$	4.54404	+	7.07066i	0.159464	+	0.248131i
$813$	1.70611	+	1.38188i	0.0598360	+	0.0484648i
$814$	2.79352	+	3.22389i	0.0979127	+	0.112997i
$815$	−10.9982	−	12.5035i	−0.385251	−	0.437977i
$816$	0.404713	−	0.133585i	0.0141678	−	0.00467640i
$817$	−43.1538	−	6.20458i	−1.50976	−	0.217071i
$818$	−2.28302	−	1.46721i	−0.0798239	−	0.0512997i
$819$	0.595292	+	8.94834i	0.0208012	+	0.312680i
$820$	1.09239	+	7.21624i	0.0381479	+	0.252002i
$821$	−14.2318	−	22.1450i	−0.496692	−	0.772867i	0.498900	−	0.866660i	$-0.333737\pi$
$821$	−14.2318	−	22.1450i	−0.496692	−	0.772867i	−0.995592	+	0.0937921i	$0.970101\pi$
$822$	2.40576	+	13.5266i	0.0839104	+	0.471794i
$823$	−0.923367	−	0.800102i	−0.0321866	−	0.0278898i	0.638619	−	0.769523i	$-0.279506\pi$
$823$	−0.923367	−	0.800102i	−0.0321866	−	0.0278898i	−0.670806	+	0.741633i	$0.734051\pi$
$824$	8.52997	−	2.50463i	0.297156	−	0.0872528i
$825$	27.1901	−	47.1481i	0.946637	−	1.64149i
$826$	12.8321	−	1.84498i	0.446486	−	0.0641950i
$827$			23.9022i			0.831161i	0.909556	+	0.415581i	$0.136422\pi$
$827$			23.9022i			0.831161i	−0.909556	+	0.415581i	$0.863578\pi$
$828$	3.72091	+	13.8980i	0.129311	+	0.482989i
$829$	−17.9119			−0.622105			−0.311052	−	0.950393i	$-0.600681\pi$
$829$	−17.9119			−0.622105			−0.311052	+	0.950393i	$0.600681\pi$
$830$	−0.722744	+	5.30674i	−0.0250868	+	0.184200i
$831$	49.7670	−	1.65356i	1.72640	−	0.0573612i
$832$	0.653319	+	2.22500i	0.0226498	+	0.0771380i
$833$	0.992690	+	0.860171i	0.0343947	+	0.0298032i
$834$	12.9691	−	2.30660i	0.449082	−	0.0798710i
$835$	14.8009	+	49.0542i	0.512205	+	1.69759i
$836$	31.4969	−	14.3841i	1.08934	−	0.497486i
$837$	36.3039	−	21.1756i	1.25485	−	0.731937i
$838$	−5.01624	−	3.22374i	−0.173283	−	0.111362i
$839$	−4.98055	+	34.6405i	−0.171948	+	1.19592i	0.702815	+	0.711372i	$0.251926\pi$
$839$	−4.98055	+	34.6405i	−0.171948	+	1.19592i	−0.874763	+	0.484551i	$0.838983\pi$
$840$	4.98859	−	0.202912i	0.172123	−	0.00700112i
$841$	−11.3646	−	7.30361i	−0.391884	−	0.251849i
$842$	−0.880812	+	0.763228i	−0.0303548	+	0.0263026i
$843$	18.0191	+	14.5948i	0.620612	+	0.502671i
$844$	18.1323	−	11.6529i	0.624138	−	0.401109i
$845$	9.10805	−	14.4069i	0.313326	−	0.495613i
$846$	−0.113429	−	0.534199i	−0.00389977	−	0.0183661i
$847$	−35.2473	+	10.3495i	−1.21111	+	0.355615i
$848$	5.45821	+	2.49268i	0.187436	+	0.0855991i
$849$	−13.5236	−	19.5815i	−0.464130	−	0.672035i
$850$	0.649681	−	1.04478i	0.0222839	−	0.0358356i
$851$	−2.64263	+	1.90086i	−0.0905881	+	0.0651606i
$852$	6.13550	+	12.3337i	0.210199	+	0.422545i
$853$	28.6651	−	4.12143i	0.981476	−	0.141115i	0.367145	−	0.930164i	$-0.380335\pi$
$853$	28.6651	−	4.12143i	0.981476	−	0.141115i	0.614331	+	0.789049i	$0.289426\pi$
$854$	−3.19908	−	1.46097i	−0.109470	−	0.0499934i
$855$	−22.0761	+	29.6423i	−0.754985	+	1.01374i
$856$	11.1970	+	9.70230i	0.382707	+	0.331618i
$857$	−24.7011	−	7.25291i	−0.843775	−	0.247755i	−0.168851	−	0.985642i	$-0.554006\pi$
$857$	−24.7011	−	7.25291i	−0.843775	−	0.247755i	−0.674924	+	0.737887i	$0.735824\pi$
$858$	21.6766	+	12.9343i	0.740028	+	0.441570i
$859$	−12.4759	−	27.3183i	−0.425671	−	0.932089i	−0.994009	−	0.109295i	$-0.965141\pi$
$859$	−12.4759	−	27.3183i	−0.425671	−	0.932089i	0.568338	−	0.822795i	$-0.307586\pi$
$860$	−16.0399	+	7.46986i	−0.546955	+	0.254720i
$861$	−0.797046	+	7.24411i	−0.0271632	+	0.246879i
$862$	0.409895	−	2.85088i	0.0139611	−	0.0971015i
$863$	−4.29193	+	29.8510i	−0.146099	+	1.01614i	0.776428	+	0.630207i	$0.217030\pi$
$863$	−4.29193	+	29.8510i	−0.146099	+	1.01614i	−0.922526	+	0.385934i	$0.873879\pi$
$864$	−3.56902	+	3.77652i	−0.121420	+	0.128480i
$865$	40.4078	−	18.8182i	1.37391	−	0.639836i
$866$	−8.56561	−	18.7561i	−0.291071	−	0.637357i
$867$	−15.0340	+	25.1955i	−0.510582	+	0.855685i
$868$	−10.0045	−	2.93758i	−0.339574	−	0.0997078i
$869$	−17.3108	−	14.9999i	−0.587230	−	0.508837i
$870$	−22.5243	+	11.4147i	−0.763644	+	0.386995i
$871$	2.05580	+	0.938851i	0.0696580	+	0.0318118i
$872$	10.2038	−	1.46709i	0.345545	−	0.0496819i
$873$	14.5530	−	19.2404i	0.492545	−	0.651189i
$874$	8.76114	+	24.9285i	0.296350	+	0.843219i
$875$	10.6791	−	9.67905i	0.361019	−	0.327212i
$876$	−11.7353	+	8.10478i	−0.396498	+	0.273835i
$877$	−13.3529	−	6.09807i	−0.450896	−	0.205917i	0.177006	−	0.984210i	$-0.443359\pi$
$877$	−13.3529	−	6.09807i	−0.450896	−	0.205917i	−0.627902	+	0.778293i	$0.716086\pi$
$878$	17.1535	−	5.03673i	0.578903	−	0.169981i
$879$	40.0070	+	10.3172i	1.34940	+	0.347990i
$880$	7.50940	−	11.8782i	0.253142	−	0.400414i
$881$	8.30378	−	5.33651i	0.279761	−	0.179792i	−0.393234	−	0.919438i	$-0.628644\pi$
$881$	8.30378	−	5.33651i	0.279761	−	0.179792i	0.672995	+	0.739647i	$0.265007\pi$
$882$	−15.6314	−	3.48190i	−0.526338	−	0.117242i
$883$	38.4263	−	33.2966i	1.29315	−	1.12052i	0.307530	−	0.951539i	$-0.400498\pi$
$883$	38.4263	−	33.2966i	1.29315	−	1.12052i	0.985619	−	0.168981i	$-0.0540477\pi$
$884$	0.480018	+	0.308489i	0.0161448	+	0.0103756i
$885$	1.58294	+	38.9167i	0.0532100	+	1.30817i
$886$	−2.94678	+	20.4953i	−0.0989989	+	0.688553i
$887$	15.5758	+	10.0099i	0.522984	+	0.336101i	0.775351	−	0.631530i	$-0.217573\pi$
$887$	15.5758	+	10.0099i	0.522984	+	0.336101i	−0.252368	+	0.967631i	$0.581209\pi$
$888$	−1.08505	−	0.452606i	−0.0364119	−	0.0151885i
$889$	−15.0696	+	6.88203i	−0.505417	+	0.230816i
$890$	11.0678	+	36.6818i	0.370994	+	1.22958i
$891$	−0.562475	+	56.5589i	−0.0188436	+	1.89479i
$892$	−4.32713	−	3.74948i	−0.144883	−	0.125542i
$893$	−0.282564	−	0.962325i	−0.00945565	−	0.0322030i
$894$	−0.241674	−	7.27364i	−0.00808278	−	0.243267i
$895$	6.74660	−	49.5369i	0.225514	−	1.65584i
$896$	1.28911			0.0430663
$897$	−11.3238	+	15.5826i	−0.378089	+	0.520287i
$898$		−	27.8603i		−	0.929709i
$899$	52.1986	−	7.50502i	1.74092	−	0.250307i
$900$	−0.921832	+	14.9716i	−0.0307277	+	0.499055i
$901$	1.41667	−	0.415972i	0.0471961	−	0.0138580i
$902$	15.5026	+	13.4331i	0.516179	+	0.447272i
$903$	−17.3952	+	3.09381i	−0.578877	+	0.102955i
$904$	−1.96266	−	3.05396i	−0.0652770	−	0.101573i
$905$	−1.80914	−	11.9510i	−0.0601378	−	0.397266i
$906$	−6.34456	−	2.64650i	−0.210784	−	0.0879242i
$907$	−29.0317	−	18.6576i	−0.963983	−	0.619514i	−0.0388851	−	0.999244i	$-0.512381\pi$
$907$	−29.0317	−	18.6576i	−0.963983	−	0.619514i	−0.925098	+	0.379730i	$0.876017\pi$
$908$	−3.64344	−	0.523848i	−0.120912	−	0.0173845i
$909$	−24.5352	+	24.2924i	−0.813781	+	0.805728i
$910$	4.41484	+	5.01906i	0.146350	+	0.166380i
$911$	−10.7755	−	12.4356i	−0.357010	−	0.412011i	0.548626	−	0.836068i	$-0.315151\pi$
$911$	−10.7755	−	12.4356i	−0.357010	−	0.412011i	−0.905636	+	0.424057i	$0.860606\pi$
$912$	−6.00636	+	7.41563i	−0.198890	+	0.245556i
$913$	8.13808	+	12.6631i	0.269331	+	0.419088i
$914$	−29.2979	−	8.60264i	−0.969089	−	0.284550i
$915$	5.34648	−	9.11357i	0.176749	−	0.301285i
$916$	−4.38032	−	14.9180i	−0.144730	−	0.492905i
$917$	−23.0113	−	10.5089i	−0.759900	−	0.347034i
$918$	−0.0551638	+	1.27738i	−0.00182068	+	0.0421598i
$919$		−	44.0756i		−	1.45392i	−0.686681	−	0.726959i	$-0.740933\pi$
$919$		−	44.0756i		−	1.45392i	0.686681	−	0.726959i	$-0.259067\pi$
$920$	8.50977	+	6.52563i	0.280559	+	0.215144i
$921$	9.59526	+	19.2885i	0.316174	+	0.635579i
$922$	1.97878	−	0.284506i	0.0651677	−	0.00936969i
$923$	−7.66156	+	16.7765i	−0.252183	+	0.552204i
$924$	10.2940	−	9.53637i	0.338647	−	0.313723i
$925$	−3.24179	+	1.00450i	−0.106589	+	0.0330277i
$926$	−10.3208	+	35.1493i	−0.339162	+	1.15508i
$927$	−2.03489	+	26.5925i	−0.0668344	+	0.873413i
$928$	−5.93072	+	2.70847i	−0.194685	+	0.0889098i
$929$	3.63156	−	3.14676i	0.119147	−	0.103242i	−0.593249	−	0.805019i	$-0.702155\pi$
$929$	3.63156	−	3.14676i	0.119147	−	0.103242i	0.712397	+	0.701777i	$0.247610\pi$
$930$	11.8445	−	29.0006i	0.388396	−	0.950966i
$931$	−29.1120	−	4.18568i	−0.954108	−	0.137180i
$932$	2.29624	−	15.9707i	0.0752159	−	0.523138i
$933$	2.40738	−	21.8800i	0.0788141	−	0.716318i
$934$	10.7971	−	9.35573i	0.353291	−	0.306129i
$935$	−0.517552	−	3.41891i	−0.0169257	−	0.111810i
$936$	−6.93652	−	0.530790i	−0.226727	−	0.0173494i
$937$	−25.8605	−	7.59332i	−0.844824	−	0.248063i	−0.169451	−	0.985539i	$-0.554199\pi$
$937$	−25.8605	−	7.59332i	−0.844824	−	0.248063i	−0.675374	+	0.737476i	$0.736018\pi$
$938$	0.822748	−	0.949501i	0.0268637	−	0.0310023i
$939$	−2.33382	+	2.16205i	−0.0761612	+	0.0705559i
$940$	−0.309599	−	0.264262i	−0.0100980	−	0.00861929i
$941$	3.99713	+	27.8007i	0.130303	+	0.906275i	0.945159	+	0.326612i	$0.105907\pi$
$941$	3.99713	+	27.8007i	0.130303	+	0.906275i	−0.814856	+	0.579664i	$0.803184\pi$
$942$	8.99570	−	4.47499i	0.293096	−	0.145803i
$943$	−11.2773	+	10.8560i	−0.367240	+	0.353520i
$944$			10.0566i			0.327313i
$945$	−4.73037	+	14.2116i	−0.153879	+	0.462303i
$946$	−20.6587	+	45.2362i	−0.671671	+	1.47075i
$947$	28.6264	−	8.40547i	0.930234	−	0.273141i	0.218699	−	0.975792i	$-0.429819\pi$
$947$	28.6264	−	8.40547i	0.930234	−	0.273141i	0.711535	+	0.702651i	$0.248001\pi$
$948$	6.11279	+	1.57639i	0.198534	+	0.0511989i
$949$	−18.3210	−	5.37953i	−0.594725	−	0.174627i
$950$	0.409843	+	27.5451i	0.0132971	+	0.893680i
$951$	0.326812	+	0.264705i	0.0105976	+	0.00858364i
$952$	0.239724	−	0.207722i	0.00776950	−	0.00673231i
$953$	8.42763	−	13.1137i	0.272998	−	0.424793i	−0.677501	−	0.735522i	$-0.736937\pi$
$953$	8.42763	−	13.1137i	0.272998	−	0.424793i	0.950498	+	0.310729i	$0.100573\pi$
$954$	−12.7920	+	12.6655i	−0.414158	+	0.410059i
$955$	−47.6621	−	21.3395i	−1.54231	−	0.690530i
$956$	10.5772	−	16.4584i	0.342090	−	0.532302i
$957$	−27.3224	+	65.5011i	−0.883208	+	2.11735i
$958$	−12.3191	−	26.9751i	−0.398012	−	0.871525i
$959$	5.52829	+	8.60218i	0.178518	+	0.277779i
$960$	−0.394926	+	3.85280i	−0.0127462	+	0.124348i
$961$	−22.5413	+	26.0141i	−0.727140	+	0.839165i
$962$	−0.443453	−	1.51026i	−0.0142975	−	0.0486928i
$963$	−39.1160	+	21.1072i	−1.26050	+	0.680169i
$964$	8.77817	−	1.26211i	0.282726	−	0.0406498i
$965$	11.7237	+	3.34788i	0.377401	+	0.107772i
$966$	6.53810	+	8.48049i	0.210360	+	0.272855i
$967$		−	0.693162i		−	0.0222906i	−0.999938	−	0.0111453i	$-0.996452\pi$
$967$		−	0.693162i		−	0.0222906i	0.999938	−	0.0111453i	$-0.00354773\pi$
$968$	−4.05549	−	28.2065i	−0.130348	−	0.906592i
$969$	0.0779764	+	2.34685i	0.00250496	+	0.0753917i
$970$	−0.133760	−	17.9807i	−0.00429478	−	0.577326i
$971$	−20.9124	+	24.1342i	−0.671111	+	0.774503i	−0.984550	−	0.175105i	$-0.943973\pi$
$971$	−20.9124	+	24.1342i	−0.671111	+	0.774503i	0.313439	+	0.949608i	$0.398519\pi$
$972$	−6.80385	−	14.0253i	−0.218234	−	0.449860i
$973$	8.24762	−	5.30042i	0.264407	−	0.169924i
$974$	−1.79409	+	0.819332i	−0.0574863	+	0.0262531i
$975$	−16.3530	+	11.6571i	−0.523716	+	0.373325i
$976$	1.47495	−	2.29507i	0.0472120	−	0.0734633i
$977$	50.9037	+	7.31885i	1.62855	+	0.234151i	0.895190	−	0.445684i	$-0.147040\pi$
$977$	50.9037	+	7.31885i	1.62855	+	0.234151i	0.733365	+	0.679835i	$0.237949\pi$
$978$	12.2488	−	4.04299i	0.391673	−	0.129280i
$979$	90.5925	+	58.2203i	2.89535	+	1.86073i
$980$	−10.8207	+	5.03925i	−0.345654	+	0.160973i
$981$	−6.72404	+	30.1865i	−0.214682	+	0.963780i
$982$	2.60820	+	4.05844i	0.0832310	+	0.129510i
$983$	−15.1927	+	51.7416i	−0.484572	+	1.65030i	0.247359	+	0.968924i	$0.420437\pi$
$983$	−15.1927	+	51.7416i	−0.484572	+	1.65030i	−0.731932	+	0.681378i	$0.761381\pi$
$984$	−5.47426	−	1.41173i	−0.174513	−	0.0450042i
$985$	−0.0475739	−	6.39513i	−0.00151583	−	0.203766i
$986$	−0.666447	+	1.45932i	−0.0212240	+	0.0464741i
$987$	−0.230978	−	0.334444i	−0.00735213	−	0.0106455i
$988$	−12.7765			−0.406473
$989$	−32.9552	−	18.8178i	−1.04791	−	0.598370i
$990$	25.3479	+	33.6873i	0.805608	+	1.07065i
$991$	−6.51082	−	45.2837i	−0.206823	−	1.43849i	−0.783438	−	0.621469i	$-0.786536\pi$
$991$	−6.51082	−	45.2837i	−0.206823	−	1.43849i	0.576615	−	0.817016i	$-0.304373\pi$
$992$	3.36003	−	7.35743i	0.106681	−	0.233599i
$993$	14.6111	−	13.5358i	0.463669	−	0.429544i
$994$	7.74847	+	6.71409i	0.245767	+	0.212958i
$995$	−26.6414	−	16.8427i	−0.844589	−	0.533949i
$996$	−3.56252	−	2.12573i	−0.112883	−	0.0673565i
$997$	29.6476	−	13.5396i	0.938949	−	0.428803i	0.113663	−	0.993519i	$-0.463742\pi$
$997$	29.6476	−	13.5396i	0.938949	−	0.428803i	0.825285	+	0.564716i	$0.191014\pi$
$998$	−9.44446	−	10.8995i	−0.298959	−	0.345017i
$999$	2.42254	−	2.56339i	0.0766458	−	0.0811020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.89.13	yes	240
3.2	odd	2		690.2.n.b.89.19	yes	240
5.4	even	2		690.2.n.b.89.12	yes	240
15.14	odd	2	inner	690.2.n.a.89.6	✓	240
23.15	odd	22	inner	690.2.n.a.659.6	yes	240
69.38	even	22		690.2.n.b.659.12	yes	240
115.84	odd	22		690.2.n.b.659.19	yes	240
345.314	even	22	inner	690.2.n.a.659.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.6	✓	240	15.14	odd	2	inner
690.2.n.a.89.13	yes	240	1.1	even	1	trivial
690.2.n.a.659.6	yes	240	23.15	odd	22	inner
690.2.n.a.659.13	yes	240	345.314	even	22	inner
690.2.n.b.89.12	yes	240	5.4	even	2
690.2.n.b.89.19	yes	240	3.2	odd	2
690.2.n.b.659.12	yes	240	69.38	even	22
690.2.n.b.659.19	yes	240	115.84	odd	22

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.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.0575173 + 1.73110i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22287 - 1.87206i) q^{5} +(1.70529 - 0.303292i) q^{6} +(1.08447 - 0.696948i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.99338 + 0.199136i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.0575173 + 1.73110i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22287 - 1.87206i) q^{5} +(1.70529 - 0.303292i) q^{6} +(1.08447 - 0.696948i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.99338 + 0.199136i) q^{9} +(-1.67897 + 1.47684i) q^{10} +(-0.894396 + 6.22066i) q^{11} +(-0.542893 - 1.64477i) q^{12} +(1.25371 - 1.95081i) q^{13} +(-0.844191 - 0.974248i) q^{14} +(3.17037 - 2.22458i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.0693233 - 0.236094i) q^{17} +(0.623112 + 2.93458i) q^{18} +(1.55224 + 5.28644i) q^{19} +(1.70075 + 1.45170i) q^{20} +(1.26886 + 1.83724i) q^{21} +6.28463 q^{22} +(-0.433107 + 4.77623i) q^{23} +(-1.55077 + 0.771443i) q^{24} +(-2.00918 + 4.57856i) q^{25} +(-2.10938 - 0.963320i) q^{26} +(-0.516895 - 5.17038i) q^{27} +(-0.844191 + 0.974248i) q^{28} +(1.83687 - 6.25580i) q^{29} +(-2.65313 - 2.82151i) q^{30} +(3.36003 + 7.35743i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-10.8200 - 1.19049i) q^{33} +(-0.243556 - 0.0350181i) q^{34} +(-2.63089 - 1.17792i) q^{35} +(2.81603 - 1.03440i) q^{36} +(0.444500 + 0.512980i) q^{37} +(5.01173 - 2.28878i) q^{38} +(3.44915 + 2.05809i) q^{39} +(1.19488 - 1.89004i) q^{40} +(2.46674 + 2.13745i) q^{41} +(1.63796 - 1.51741i) q^{42} +(-3.28717 + 7.19790i) q^{43} +(-0.894396 - 6.22066i) q^{44} +(4.03331 + 5.36026i) q^{45} +(4.78926 - 0.251030i) q^{46} -0.182036 q^{47} +(0.984288 + 1.42519i) q^{48} +(-2.21756 + 4.85578i) q^{49} +(4.81789 + 1.33713i) q^{50} +(0.412688 + 0.106426i) q^{51} +(-0.653319 + 2.22500i) q^{52} +(3.24409 + 5.04791i) q^{53} +(-5.04419 + 1.24746i) q^{54} +(12.7392 - 5.93270i) q^{55} +(1.08447 + 0.696948i) q^{56} +(-9.06206 + 2.99114i) q^{57} +(-6.45354 - 0.927879i) q^{58} +(-5.43699 + 8.46012i) q^{59} +(-2.41521 + 3.02766i) q^{60} +(2.48161 - 1.13331i) q^{61} +(6.80436 - 4.37290i) q^{62} +(-3.10745 + 2.30219i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-5.18515 + 0.0385728i) q^{65} +(0.361475 + 10.8793i) q^{66} +(0.138700 + 0.964679i) q^{67} +0.246061i q^{68} +(-8.29303 - 0.475033i) q^{69} +(-0.791511 + 2.77175i) q^{70} +(-7.87233 + 1.13187i) q^{71} +(-1.42464 - 2.64015i) q^{72} +(-2.31983 - 7.90061i) q^{73} +(0.444500 - 0.512980i) q^{74} +(-8.04148 - 3.21474i) q^{75} +(-2.97873 - 4.63499i) q^{76} +(3.36553 + 7.36948i) q^{77} +(1.54627 - 3.70694i) q^{78} +(-1.97047 + 3.06611i) q^{79} +(-2.04085 - 0.913740i) q^{80} +(8.92069 - 1.19218i) q^{81} +(1.76463 - 2.74583i) q^{82} +(1.81014 - 1.56849i) q^{83} +(-1.73507 - 1.40534i) q^{84} +(-0.526753 + 0.158934i) q^{85} +(7.59245 + 2.22934i) q^{86} +(10.9350 + 2.81998i) q^{87} +(-6.03006 + 1.77059i) q^{88} +(7.11816 - 15.5866i) q^{89} +(4.73170 - 4.75510i) q^{90} -2.98937i q^{91} +(-0.930058 - 4.70478i) q^{92} +(-12.5432 + 6.23971i) q^{93} +(0.0259065 + 0.180183i) q^{94} +(7.99833 - 9.37051i) q^{95} +(1.27061 - 1.17710i) q^{96} +(-5.26602 + 6.07732i) q^{97} +(5.12195 + 1.50394i) q^{98} +(1.43851 - 18.7989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

Modular forms

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