LMFDB - Embedded newform 690.2.n.a.659.13

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			659.13
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.13

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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	0.729298	−	0.684196i	$-0.239847\pi$
$7$	1.08447	+	0.696948i	0.409892	+	0.263422i	−0.319406	+	0.947618i	$0.603483\pi$
$8$	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	−0.451501	−	0.892270i	$-0.649111\pi$
$11$	−0.894396	−	6.22066i	−0.269671	−	1.87560i	0.181831	−	0.983330i	$-0.441798\pi$
$12$	−0.542893	+	1.64477i	−0.156720	+	0.474804i
$13$	1.25371	+	1.95081i	0.347717	+	0.541058i	0.970427	−	0.241395i	$-0.0776048\pi$
$13$	1.25371	+	1.95081i	0.347717	+	0.541058i	−0.622710	+	0.782452i	$0.713968\pi$
$14$	−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	0.967472	−	0.252977i	$-0.0814096\pi$
$17$	0.0693233	+	0.236094i	0.0168134	+	0.0572611i	−0.950659	+	0.310238i	$0.899591\pi$
$18$	0.623112	−	2.93458i	0.146869	−	0.691686i
$19$	1.55224	−	5.28644i	0.356108	−	1.21279i	−0.565525	−	0.824731i	$-0.691326\pi$
$19$	1.55224	−	5.28644i	0.356108	−	1.21279i	0.921633	−	0.388062i	$-0.126855\pi$
$20$	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	0.934261	+	0.356591i	$0.116061\pi$
$29$	1.83687	+	6.25580i	0.341098	+	1.16167i	−0.593162	+	0.805083i	$0.702121\pi$
$30$	−2.65313	+	2.82151i	−0.484393	+	0.515135i
$31$	3.36003	−	7.35743i	0.603479	−	1.32143i	−0.323467	−	0.946239i	$-0.604849\pi$
$31$	3.36003	−	7.35743i	0.603479	−	1.32143i	0.926946	−	0.375195i	$-0.122424\pi$
$32$	−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	−0.718035	−	0.696007i	$-0.754958\pi$
$37$	0.444500	−	0.512980i	0.0730753	−	0.0843334i	0.791110	+	0.611674i	$0.209504\pi$
$38$	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	−0.440613	−	0.897697i	$-0.645239\pi$
$41$	2.46674	−	2.13745i	0.385241	−	0.333813i	0.825854	+	0.563884i	$0.190694\pi$
$42$	1.63796	+	1.51741i	0.252743	+	0.234142i
$43$	−3.28717	−	7.19790i	−0.501289	−	1.09767i	−0.976048	−	0.217554i	$-0.930192\pi$
$43$	−3.28717	−	7.19790i	−0.501289	−	1.09767i	0.474759	−	0.880116i	$-0.342535\pi$
$44$	−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	−0.543688	−	0.839287i	$-0.682973\pi$
$53$	3.24409	−	5.04791i	0.445611	−	0.693384i	0.989299	+	0.145904i	$0.0466089\pi$
$54$	−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	−0.989866	−	0.142008i	$-0.954644\pi$
$59$	−5.43699	−	8.46012i	−0.707835	−	1.10141i	0.282030	−	0.959406i	$-0.408992\pi$
$60$	−2.41521	−	3.02766i	−0.311802	−	0.390870i
$61$	2.48161	+	1.13331i	0.317738	+	0.145106i	0.567899	−	0.823098i	$-0.307756\pi$
$61$	2.48161	+	1.13331i	0.317738	+	0.145106i	−0.250161	+	0.968204i	$0.580484\pi$
$62$	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	−0.979593	−	0.200990i	$-0.935584\pi$
$67$	0.138700	−	0.964679i	0.0169449	−	0.117854i	0.996538	+	0.0831353i	$0.0264934\pi$
$68$		−	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	−0.341668	−	0.939821i	$-0.610992\pi$
$71$	−7.87233	−	1.13187i	−0.934274	−	0.134328i	−0.592606	+	0.805492i	$0.701901\pi$
$72$	−1.42464	+	2.64015i	−0.167895	+	0.311145i
$73$	−2.31983	+	7.90061i	−0.271516	+	0.924697i	0.704992	+	0.709215i	$0.250950\pi$
$73$	−2.31983	+	7.90061i	−0.271516	+	0.924697i	−0.976508	+	0.215482i	$0.930868\pi$
$74$	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	0.712534	−	0.701637i	$-0.247547\pi$
$79$	−1.97047	−	3.06611i	−0.221695	−	0.344964i	−0.934229	+	0.356673i	$0.883911\pi$
$80$	−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	0.748522	−	0.663109i	$-0.230764\pi$
$83$	1.81014	+	1.56849i	0.198688	+	0.172164i	−0.549834	+	0.835274i	$0.685309\pi$
$84$	−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	0.758062	+	0.652182i	$0.226146\pi$
$89$	7.11816	+	15.5866i	0.754524	+	1.65218i	−0.00353850	+	0.999994i	$0.501126\pi$
$90$	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	0.422562	−	0.906334i	$-0.361131\pi$
$97$	−5.26602	−	6.07732i	−0.534684	−	0.617058i	−0.957246	+	0.289276i	$0.906585\pi$
$98$	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	0.969617	−	0.244629i	$-0.0786660\pi$
$101$	8.69786	+	7.53674i	0.865469	+	0.749933i	−0.104148	+	0.994562i	$0.533211\pi$
$102$	0.0466110	+	0.423633i	0.00461517	+	0.0419459i
$103$	1.26519	+	8.79960i	0.124663	+	0.867050i	0.952164	+	0.305586i	$0.0988525\pi$
$103$	1.26519	+	8.79960i	0.124663	+	0.867050i	−0.827501	+	0.561464i	$0.810238\pi$
$104$	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	0.941370	−	0.337375i	$-0.109539\pi$
$107$	13.4769	+	6.15471i	1.30287	+	0.594999i	0.361495	+	0.932374i	$0.382266\pi$
$108$	1.95262	−	4.81532i	0.187891	−	0.463354i
$109$	2.90431	+	9.89119i	0.278183	+	0.947404i	0.973497	+	0.228698i	$0.0734469\pi$
$109$	2.90431	+	9.89119i	0.278183	+	0.947404i	−0.695314	+	0.718706i	$0.744735\pi$
$110$	−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	−0.0287895	−	0.999585i	$-0.509165\pi$
$113$	−3.59329	−	0.516638i	−0.338029	−	0.0486012i	−0.309239	+	0.950984i	$0.600074\pi$
$114$	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	−0.681290	−	0.732014i	$-0.738581\pi$
$127$	−12.7204	+	1.82891i	−1.12875	+	0.162290i	−0.447461	+	0.894304i	$0.647672\pi$
$128$	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	−0.0303425	+	0.999540i	$0.509660\pi$
$131$	−10.6094	+	16.5086i	−0.926951	+	1.44236i	−0.896608	+	0.442824i	$0.853977\pi$
$132$	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	$-0.889964\pi$
$137$		−	7.93214i		−	0.677688i	0.940843	−	0.338844i	$-0.110036\pi$
$138$	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	0.999545	+	0.0301676i	$0.00960410\pi$
$149$	0.597972	+	4.15899i	0.0489878	+	0.340718i	−0.950557	+	0.310550i	$0.899487\pi$
$150$	−2.03759	−	8.41714i	−0.166369	−	0.687256i
$151$	−3.33889	+	2.14577i	−0.271715	+	0.174620i	−0.669402	−	0.742901i	$-0.733449\pi$
$151$	−3.33889	+	2.14577i	−0.271715	+	0.174620i	0.397687	+	0.917521i	$0.369813\pi$
$152$	−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	0.496182	−	0.868219i	$-0.334735\pi$
$157$	5.56583	+	1.63428i	0.444202	+	0.130429i	−0.0519798	+	0.998648i	$0.516553\pi$
$158$	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	0.424810	−	0.905282i	$-0.360341\pi$
$163$	7.37131	+	1.05983i	0.577365	+	0.0830126i	0.152555	+	0.988295i	$0.451250\pi$
$164$	−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	−0.980994	−	0.194039i	$-0.937841\pi$
$167$	−21.9863	+	6.45577i	−1.70135	+	0.499562i	−0.720359	+	0.693601i	$0.756023\pi$
$168$	−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	−0.753697	−	0.657222i	$-0.771732\pi$
$173$	−2.83697	−	19.7316i	−0.215691	−	1.50016i	0.538006	−	0.842941i	$-0.319178\pi$
$174$	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	0.271696	−	0.962383i	$-0.412416\pi$
$179$	16.8971	−	14.6414i	1.26295	−	1.09435i	0.991254	−	0.131969i	$-0.0421299\pi$
$180$	−5.38009	+	4.00682i	−0.401009	+	0.298651i
$181$	4.91707	−	2.24555i	0.365483	−	0.166910i	−0.224204	−	0.974542i	$-0.571978\pi$
$181$	4.91707	−	2.24555i	0.365483	−	0.166910i	0.589687	+	0.807632i	$0.299251\pi$
$182$	−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	0.999977	+	0.00681553i	$0.00216947\pi$
$191$	19.6467	+	12.6261i	1.42158	+	0.913595i	0.421605	+	0.906780i	$0.361467\pi$
$192$	−1.34594	+	1.09016i	−0.0971349	+	0.0786754i
$193$	−4.12080	−	3.57070i	−0.296622	−	0.257024i	0.493816	−	0.869566i	$-0.335602\pi$
$193$	−4.12080	−	3.57070i	−0.296622	−	0.257024i	−0.790438	+	0.612542i	$0.790147\pi$
$194$	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	−0.452116	−	0.891959i	$-0.649331\pi$
$197$	2.40604	−	1.54627i	0.171423	−	0.110167i	0.623539	+	0.781792i	$0.285694\pi$
$198$	−18.8123	−	1.25150i	−1.33693	−	0.0889400i
$199$	12.8219	+	5.85556i	0.908919	+	0.415089i	0.814313	−	0.580426i	$-0.197114\pi$
$199$	12.8219	+	5.85556i	0.908919	+	0.415089i	0.0946055	+	0.995515i	$0.469841\pi$
$200$	−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	−0.522962	−	0.852356i	$-0.675173\pi$
$211$	−20.6808	−	6.07243i	−1.42372	−	0.418043i	−0.900762	+	0.434313i	$0.856991\pi$
$212$	−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	−0.722005	−	0.691888i	$-0.756779\pi$
$223$	3.09550	−	4.81670i	0.207290	−	0.322550i	0.929295	+	0.369338i	$0.120416\pi$
$224$	−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	−0.301188	−	0.953565i	$-0.597383\pi$
$227$	3.34827	−	1.52911i	0.222233	−	0.101490i	0.523420	+	0.852075i	$0.324656\pi$
$228$	7.85228	+	5.42305i	0.520030	+	0.359151i
$229$		−	15.5478i		−	1.02743i	−0.857961	−	0.513714i	$-0.828269\pi$
$229$		−	15.5478i		−	1.02743i	0.857961	−	0.513714i	$-0.171731\pi$
$230$	−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	−0.991761	−	0.128101i	$-0.959112\pi$
$233$	−6.70270	−	14.6769i	−0.439108	−	0.961513i	0.552653	−	0.833412i	$-0.313616\pi$
$234$	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	0.0288972	−	0.999582i	$-0.490800\pi$
$239$	−14.7856	−	12.8118i	−0.956398	−	0.828724i	−0.985296	+	0.170858i	$0.945346\pi$
$240$	1.46439	+	3.58547i	0.0945257	+	0.231441i
$241$	−8.77817	+	1.26211i	−0.565452	+	0.0812997i	−0.419112	−	0.907935i	$-0.637658\pi$
$241$	−8.77817	+	1.26211i	−0.565452	+	0.0812997i	−0.146340	+	0.989234i	$0.546749\pi$
$242$	−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	0.842344	+	0.538940i	$0.181175\pi$
$251$	−1.86497	+	12.9712i	−0.117716	+	0.818734i	−0.960060	+	0.279794i	$0.909734\pi$
$252$	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	0.282754	−	0.959192i	$-0.408752\pi$
$257$	0.0327583	+	0.00961870i	0.00204341	+	0.000599998i	−0.280711	+	0.959792i	$0.590570\pi$
$258$	−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	0.845957	−	0.533251i	$-0.179030\pi$
$263$	0.153594	+	0.238997i	0.00947100	+	0.0147372i	−0.836486	+	0.547989i	$0.815394\pi$
$264$	−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	−0.157615	−	0.987501i	$-0.550381\pi$
$269$	13.2214	−	20.5729i	0.806123	−	1.25435i	0.963738	−	0.266851i	$-0.0859830\pi$
$270$	8.50369	−	7.91753i	0.517518	−	0.481845i
$271$	0.830102	+	0.957988i	0.0504251	+	0.0581936i	0.780402	−	0.625278i	$-0.215015\pi$
$271$	0.830102	+	0.957988i	0.0504251	+	0.0581936i	−0.729977	+	0.683472i	$0.760469\pi$
$272$	−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	$0.331843\pi$
$277$			28.7488i			1.72735i	−0.504050	+	0.863675i	$0.668157\pi$
$278$	−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	0.954380	−	0.298594i	$-0.0965177\pi$
$281$	8.76713	+	10.1178i	0.523003	+	0.603577i	−0.431377	+	0.902172i	$0.641972\pi$
$282$	−0.310425	−	0.0552102i	−0.0184855	−	0.00328772i
$283$	−11.5584	−	7.42815i	−0.687077	−	0.441558i	0.149968	−	0.988691i	$-0.452083\pi$
$283$	−11.5584	−	7.42815i	−0.687077	−	0.441558i	−0.837046	+	0.547133i	$0.815719\pi$
$284$	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	0.884538	+	0.466467i	$0.154474\pi$
$293$	6.72038	+	22.8875i	0.392609	+	1.33710i	−0.491930	+	0.870635i	$0.663708\pi$
$294$	−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	0.711231	−	0.702958i	$-0.248138\pi$
$307$	11.3141	+	5.16696i	0.645728	+	0.294894i	−0.0655033	+	0.997852i	$0.520865\pi$
$308$	−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	−0.489408	−	0.872055i	$-0.662787\pi$
$311$	−12.5793	+	1.80863i	−0.713305	+	0.102558i	−0.223897	+	0.974613i	$0.571878\pi$
$312$	−0.439273	−	3.99242i	−0.0248689	−	0.226026i
$313$	1.20283	−	1.38814i	0.0679879	−	0.0784622i	−0.720737	−	0.693209i	$-0.756196\pi$
$313$	1.20283	−	1.38814i	0.0679879	−	0.0784622i	0.788725	+	0.614747i	$0.210742\pi$
$314$	−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	0.760197	−	0.649692i	$-0.225102\pi$
$317$	0.159009	+	0.183506i	0.00893083	+	0.0103067i	−0.751267	+	0.659999i	$0.770557\pi$
$318$	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	−0.923972	−	0.382460i	$-0.875077\pi$
$331$	−7.53043	+	8.69058i	−0.413910	+	0.477677i	0.510062	+	0.860138i	$0.329622\pi$
$332$	−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	−0.314511	−	0.949254i	$-0.601840\pi$
$337$	11.1770	−	24.4741i	0.608848	−	1.33319i	0.923359	−	0.383938i	$-0.125432\pi$
$338$	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	0.507746	+	0.861507i	$0.330479\pi$
$347$	−4.13815	+	28.7814i	−0.222147	+	1.54507i	−0.729893	+	0.683561i	$0.760430\pi$
$348$	−11.2866	−	0.375008i	−0.605024	−	0.0201025i
$349$	24.8039	+	7.28308i	1.32772	+	0.389854i	0.867274	−	0.497832i	$-0.165870\pi$
$349$	24.8039	+	7.28308i	1.32772	+	0.389854i	0.460449	+	0.887686i	$0.347688\pi$
$350$	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	0.182116	−	0.983277i	$-0.441705\pi$
$353$	15.1427	−	33.1580i	0.805967	−	1.76482i	0.623851	−	0.781544i	$-0.285567\pi$
$354$	−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	−0.0716239	+	0.997432i	$0.522818\pi$
$359$	−19.8702	+	22.9315i	−1.04871	+	1.21028i	−0.977086	+	0.212844i	$0.931727\pi$
$360$	−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	0.913919	−	0.405898i	$-0.133041\pi$
$373$	7.37935	+	8.51622i	0.382088	+	0.440953i	−0.531830	+	0.846851i	$0.678496\pi$
$374$	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	0.359452	−	0.933164i	$-0.382964\pi$
$379$	18.8303	−	2.70738i	0.967246	−	0.139069i	0.607794	+	0.794095i	$0.292055\pi$
$380$	−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	−0.0903107	−	0.995914i	$-0.528786\pi$
$383$	−17.6547	−	8.06263i	−0.902113	−	0.411981i	−0.811802	+	0.583932i	$0.801513\pi$
$384$	−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	−0.951058	−	0.309011i	$-0.900002\pi$
$389$	0.957239	−	6.65775i	0.0485340	−	0.337561i	0.999592	−	0.0285499i	$-0.00908896\pi$
$390$	−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	−0.998746	−	0.0500572i	$-0.984060\pi$
$397$	−3.69826	−	12.5951i	−0.185610	−	0.632131i	0.813136	−	0.582074i	$-0.197759\pi$
$398$	−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	0.0139502	−	0.999903i	$-0.495559\pi$
$401$	18.6090	−	11.9593i	0.929289	−	0.597218i	0.915339	+	0.402685i	$0.131923\pi$
$402$	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	0.797985	−	0.602678i	$-0.205900\pi$
$409$	1.77718	+	2.05098i	0.0878759	+	0.101414i	−0.710109	+	0.704092i	$0.751354\pi$
$410$	−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	0.843072	−	0.537801i	$-0.180745\pi$
$419$	3.90481	+	4.50640i	0.190763	+	0.220152i	−0.652309	+	0.757953i	$0.726200\pi$
$420$	−0.509105	−	4.96670i	−0.0248418	−	0.242350i
$421$	−0.630107	+	0.980466i	−0.0307095	+	0.0477850i	−0.856269	−	0.516530i	$-0.827223\pi$
$421$	−0.630107	+	0.980466i	−0.0307095	+	0.0477850i	0.825559	+	0.564315i	$0.190860\pi$
$422$	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	−0.214497	−	0.976725i	$-0.568811\pi$
$431$	2.76353	−	0.811446i	0.133115	−	0.0390860i	0.347611	+	0.937639i	$0.386993\pi$
$432$	−3.23016	+	4.07015i	−0.155411	+	0.195825i
$433$	19.7842	+	5.80915i	0.950766	+	0.279170i	0.720106	−	0.693864i	$-0.244093\pi$
$433$	19.7842	+	5.80915i	0.950766	+	0.279170i	0.230660	+	0.973034i	$0.425911\pi$
$434$	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	−0.834506	−	0.550999i	$-0.814247\pi$
$439$	2.54426	−	17.6957i	0.121431	−	0.844571i	0.955937	−	0.293572i	$-0.0948441\pi$
$440$	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	−0.717255	−	0.696811i	$-0.754602\pi$
$443$	−19.8673	+	5.83357i	−0.943924	+	0.277161i	−0.226669	+	0.973972i	$0.572784\pi$
$444$	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	0.543472	−	0.839427i	$-0.317109\pi$
$449$	27.5767	−	3.96493i	1.30142	−	0.187116i	0.757952	+	0.652311i	$0.226200\pi$
$450$	−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	0.933390	+	0.358864i	$0.116836\pi$
$457$	12.6846	+	27.7754i	0.593361	+	1.29928i	−0.340029	+	0.940415i	$0.610437\pi$
$458$	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	$-0.985176\pi$
$461$		−	1.99913i		−	0.0931087i	0.998916	−	0.0465543i	$-0.0148241\pi$
$462$	7.97431	−	11.5464i	0.370999	−	0.537186i
$463$	−33.3228	+	15.2180i	−1.54864	+	0.707240i	−0.992316	−	0.123725i	$-0.960516\pi$
$463$	−33.3228	+	15.2180i	−1.54864	+	0.707240i	−0.556324	+	0.830966i	$0.687789\pi$
$464$	−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	−0.615255	−	0.788328i	$-0.710947\pi$
$467$	7.72391	−	12.0186i	0.357420	−	0.556157i	0.972675	+	0.232172i	$0.0745832\pi$
$468$	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	0.857266	−	0.514873i	$-0.172161\pi$
$479$	28.4537	+	8.35476i	1.30008	+	0.381739i	0.442817	+	0.896612i	$0.353979\pi$
$480$	−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	−0.971124	−	0.238574i	$-0.923320\pi$
$487$	−0.555668	+	1.89243i	−0.0251797	+	0.0857542i	0.945945	+	0.324328i	$0.105138\pi$
$488$	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	0.313925	−	0.949448i	$-0.398356\pi$
$491$	−4.38831	−	2.00408i	−0.198042	−	0.0904426i	−0.511967	+	0.859005i	$0.671083\pi$
$492$	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	0.783262	−	0.621691i	$-0.213554\pi$
$499$	12.1326	+	7.79717i	0.543131	+	0.349049i	−0.240131	+	0.970740i	$0.577190\pi$
$500$	−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	0.539077	−	0.842256i	$-0.318773\pi$
$503$	34.2837	−	15.6568i	1.52863	−	0.698103i	0.989555	+	0.144153i	$0.0460458\pi$
$504$	−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	−0.0480985	−	0.998843i	$-0.515316\pi$
$509$	15.2350	−	6.95758i	0.675279	−	0.308389i	0.723377	+	0.690453i	$0.242589\pi$
$510$	−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	−0.948128	−	0.317888i	$-0.897026\pi$
$521$	−1.98564	+	4.34794i	−0.0869924	+	0.190487i	0.861136	+	0.508375i	$0.169754\pi$
$522$	19.5027	−	1.49237i	0.853610	−	0.0653191i
$523$	13.9264	−	4.08917i	0.608960	−	0.178807i	0.0373093	−	0.999304i	$-0.488121\pi$
$523$	13.9264	−	4.08917i	0.608960	−	0.178807i	0.571651	+	0.820497i	$0.306303\pi$
$524$	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	0.950430	+	0.310938i	$0.100643\pi$
$541$	2.93302	+	20.3996i	0.126101	+	0.877048i	−0.824330	+	0.566110i	$0.808448\pi$
$542$	−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	−0.548962	−	0.835847i	$-0.684977\pi$
$547$	4.68351	−	4.05828i	0.200252	−	0.173520i	0.749214	+	0.662328i	$0.230431\pi$
$548$	−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	−0.661873	−	0.749616i	$-0.730238\pi$
$557$	−0.332356	+	0.287988i	−0.0140824	+	0.0122024i	0.647791	+	0.761818i	$0.275693\pi$
$558$	−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	−0.757492	−	0.652845i	$-0.773575\pi$
$563$	−30.8547	+	4.43624i	−1.30037	+	0.186965i	−0.542880	+	0.839810i	$0.682666\pi$
$564$	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	−0.582798	−	0.812617i	$-0.698042\pi$
$569$	−15.1172	+	4.43880i	−0.633745	+	0.186084i	−0.0509468	+	0.998701i	$0.516224\pi$
$570$	10.7975	+	18.4053i	0.452256	+	0.770912i
$571$	10.4927	−	35.7349i	0.439106	−	1.49546i	−0.381719	−	0.924278i	$-0.624668\pi$
$571$	10.4927	−	35.7349i	0.439106	−	1.49546i	0.820825	−	0.571180i	$-0.193514\pi$
$572$	−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	−0.186251	−	0.982502i	$-0.559634\pi$
$577$	−15.4156	−	2.21643i	−0.641761	−	0.0922713i	−0.455510	+	0.890231i	$0.650543\pi$
$578$	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	−0.977258	−	0.212052i	$-0.931985\pi$
$587$	−2.40652	−	16.7377i	−0.0993278	−	0.690840i	0.877931	−	0.478788i	$-0.158924\pi$
$588$	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	0.792658	−	0.609667i	$-0.208697\pi$
$593$	1.86022	+	2.14680i	0.0763899	+	0.0881586i	−0.716268	+	0.697825i	$0.754151\pi$
$594$	−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	$0.0582303\pi$
$599$			8.90466i			0.363834i	−0.983314	+	0.181917i	$0.941770\pi$
$600$	−0.416325	+	8.65024i	−0.0169964	+	0.353145i
$601$	6.76727	+	14.8183i	0.276043	+	0.604449i	0.995979	−	0.0895914i	$-0.0285561\pi$
$601$	6.76727	+	14.8183i	0.276043	+	0.604449i	−0.719936	+	0.694041i	$0.755829\pi$
$602$	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	0.993208	+	0.116352i	$0.0371201\pi$
$607$	30.7899	+	26.6796i	1.24972	+	1.08289i	0.256516	+	0.966540i	$0.417425\pi$
$608$	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	0.603179	+	0.797606i	$0.293900\pi$
$613$	−9.77007	+	21.3935i	−0.394609	+	0.864074i	−0.997789	+	0.0664684i	$0.978827\pi$
$614$	−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	−0.995042	−	0.0994519i	$-0.968291\pi$
$617$	−2.58807	+	8.81415i	−0.104192	+	0.354844i	0.890851	+	0.454296i	$0.150109\pi$
$618$	−0.511334	+	15.3896i	−0.0205689	+	0.619060i
$619$	44.0020	+	6.32653i	1.76859	+	0.254285i	0.948235	−	0.317570i	$-0.102867\pi$
$619$	44.0020	+	6.32653i	1.76859	+	0.254285i	0.820355	+	0.571855i	$0.193776\pi$
$620$	−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	0.440806	−	0.897603i	$-0.354693\pi$
$631$	−14.0369	−	21.8418i	−0.558800	−	0.869509i	−0.999605	+	0.0280933i	$0.991056\pi$
$632$	−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	−0.971081	−	0.238751i	$-0.923262\pi$
$641$	−13.0538	−	28.5838i	−0.515594	−	1.12899i	0.455487	−	0.890243i	$-0.349465\pi$
$642$	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	−0.879332	−	0.476210i	$-0.842010\pi$
$647$	−16.8740	−	36.9490i	−0.663387	−	1.45262i	0.215944	−	0.976406i	$-0.430717\pi$
$648$	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	−0.366654	+	0.930357i	$0.619497\pi$
$653$	−31.5683	+	36.4317i	−1.23536	+	1.42568i	−0.868708	+	0.495325i	$0.835049\pi$
$654$	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	−0.999913	−	0.0131899i	$-0.995801\pi$
$659$	−8.60340	+	18.8388i	−0.335141	+	0.733856i	0.664772	+	0.747046i	$0.268529\pi$
$660$	−16.6739	+	17.7321i	−0.649032	+	0.690223i
$661$	4.81472	+	16.3974i	0.187271	+	0.637786i	0.998585	+	0.0531759i	$0.0169344\pi$
$661$	4.81472	+	16.3974i	0.187271	+	0.637786i	−0.811314	+	0.584610i	$0.801247\pi$
$662$	−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	0.981442	−	0.191759i	$-0.0614191\pi$
$673$	1.35231	+	4.60555i	0.0521278	+	0.177531i	−0.929314	+	0.369290i	$0.879601\pi$
$674$	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	0.999192	−	0.0402020i	$-0.0128001\pi$
$677$	14.2467	+	22.1682i	0.547543	+	0.851994i	−0.451648	+	0.892196i	$0.649164\pi$
$678$	−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	0.976080	−	0.217411i	$-0.0697612\pi$
$683$	30.9376	+	19.8824i	1.18379	+	0.760778i	0.207714	+	0.978190i	$0.433398\pi$
$684$	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	0.960506	+	0.278260i	$0.0897578\pi$
$701$	3.10574	+	21.6009i	0.117302	+	0.815855i	−0.843204	+	0.537595i	$0.819333\pi$
$702$	−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	−0.970853	−	0.239677i	$-0.922958\pi$
$709$	−0.653430	+	2.22538i	−0.0245401	+	0.0835759i	0.946313	+	0.323253i	$0.104777\pi$
$710$	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	−0.890329	−	0.455319i	$-0.849525\pi$
$719$	−10.3905	−	35.3868i	−0.387500	−	1.31971i	0.502828	−	0.864386i	$-0.332293\pi$
$720$	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	−0.820246	−	0.572011i	$-0.806163\pi$
$727$	−3.70264	+	4.27308i	−0.137323	+	0.158480i	0.682922	+	0.730491i	$0.260709\pi$
$728$	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	−0.989167	−	0.146796i	$-0.953104\pi$
$733$	−12.2467	−	26.8165i	−0.452341	−	0.990489i	0.536826	−	0.843693i	$-0.319623\pi$
$734$	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	0.970649	+	0.240499i	$0.0773110\pi$
$739$	14.0481	+	30.7609i	0.516766	+	1.13156i	−0.453883	+	0.891061i	$0.649962\pi$
$740$	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	−0.491472	−	0.870893i	$-0.663541\pi$
$743$	13.7622	−	21.4143i	0.504885	−	0.785616i	0.996357	+	0.0852770i	$0.0271775\pi$
$744$	−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	0.957970	−	0.286867i	$-0.0926138\pi$
$751$	37.5031	+	17.1271i	1.36851	+	0.624977i	0.410537	+	0.911844i	$0.365341\pi$
$752$	−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	−0.868058	−	0.496462i	$-0.834632\pi$
$757$	2.88087	−	20.0369i	0.104707	−	0.728253i	0.972766	−	0.231791i	$-0.0744587\pi$
$758$			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	0.428917	−	0.903344i	$-0.358895\pi$
$761$	16.1644	+	2.32409i	0.585958	+	0.0842481i	0.157041	+	0.987592i	$0.449804\pi$
$762$	−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	0.589562	−	0.807723i	$-0.299300\pi$
$769$	−10.8173	−	16.8321i	−0.390082	−	0.606980i	−0.979644	+	0.200744i	$0.935664\pi$
$770$	−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	0.834656	−	0.550771i	$-0.185666\pi$
$773$	11.3512	+	9.83588i	0.408275	+	0.353772i	−0.426381	+	0.904543i	$0.640212\pi$
$774$	−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	−0.992273	−	0.124077i	$-0.960403\pi$
$787$	−27.3205	−	31.5296i	−0.973871	−	1.12391i	0.0184011	−	0.999831i	$-0.494142\pi$
$788$	−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	0.951544	−	0.307514i	$-0.0994971\pi$
$797$	37.8938	+	17.3055i	1.34227	+	0.612993i	0.390725	+	0.920508i	$0.372224\pi$
$798$	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	−0.999941	−	0.0108258i	$-0.996554\pi$
$809$	−4.34848	+	14.8095i	−0.152884	+	0.520676i	0.847057	+	0.531502i	$0.178372\pi$
$810$	−13.2169	−	15.1761i	−0.464394	−	0.533234i
$811$	0.697915	−	0.204926i	0.0245071	−	0.00719593i	−0.269456	−	0.963013i	$-0.586844\pi$
$811$	0.697915	−	0.204926i	0.0245071	−	0.00719593i	0.293963	+	0.955817i	$0.405026\pi$
$812$	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	−0.995592	−	0.0937921i	$-0.970101\pi$
$821$	−14.2318	+	22.1450i	−0.496692	+	0.772867i	0.498900	+	0.866660i	$0.333737\pi$
$822$	2.40576	−	13.5266i	0.0839104	−	0.471794i
$823$	−0.923367	+	0.800102i	−0.0321866	+	0.0278898i	−0.670806	−	0.741633i	$-0.734051\pi$
$823$	−0.923367	+	0.800102i	−0.0321866	+	0.0278898i	0.638619	+	0.769523i	$0.279506\pi$
$824$	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	$-0.863578\pi$
$827$		−	23.9022i		−	0.831161i	0.909556	−	0.415581i	$-0.136422\pi$
$828$	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	−0.874763	−	0.484551i	$-0.838983\pi$
$839$	−4.98055	−	34.6405i	−0.171948	−	1.19592i	0.702815	−	0.711372i	$-0.251926\pi$
$840$	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	0.614331	−	0.789049i	$-0.289426\pi$
$853$	28.6651	+	4.12143i	0.981476	+	0.141115i	0.367145	+	0.930164i	$0.380335\pi$
$854$	−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	−0.674924	−	0.737887i	$-0.735824\pi$
$857$	−24.7011	+	7.25291i	−0.843775	+	0.247755i	−0.168851	+	0.985642i	$0.554006\pi$
$858$	21.6766	−	12.9343i	0.740028	−	0.441570i
$859$	−12.4759	+	27.3183i	−0.425671	+	0.932089i	0.568338	+	0.822795i	$0.307586\pi$
$859$	−12.4759	+	27.3183i	−0.425671	+	0.932089i	−0.994009	+	0.109295i	$0.965141\pi$
$860$	−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	−0.922526	−	0.385934i	$-0.873879\pi$
$863$	−4.29193	−	29.8510i	−0.146099	−	1.01614i	0.776428	−	0.630207i	$-0.217030\pi$
$864$	−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	−0.627902	−	0.778293i	$-0.716086\pi$
$877$	−13.3529	+	6.09807i	−0.450896	+	0.205917i	0.177006	+	0.984210i	$0.443359\pi$
$878$	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	0.672995	−	0.739647i	$-0.265007\pi$
$881$	8.30378	+	5.33651i	0.279761	+	0.179792i	−0.393234	+	0.919438i	$0.628644\pi$
$882$	−15.6314	+	3.48190i	−0.526338	+	0.117242i
$883$	38.4263	+	33.2966i	1.29315	+	1.12052i	0.985619	+	0.168981i	$0.0540477\pi$
$883$	38.4263	+	33.2966i	1.29315	+	1.12052i	0.307530	+	0.951539i	$0.400498\pi$
$884$	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	−0.252368	−	0.967631i	$-0.581209\pi$
$887$	15.5758	−	10.0099i	0.522984	−	0.336101i	0.775351	+	0.631530i	$0.217573\pi$
$888$	−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	−0.925098	−	0.379730i	$-0.876017\pi$
$907$	−29.0317	+	18.6576i	−0.963983	+	0.619514i	−0.0388851	+	0.999244i	$0.512381\pi$
$908$	−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	−0.905636	−	0.424057i	$-0.860606\pi$
$911$	−10.7755	+	12.4356i	−0.357010	+	0.412011i	0.548626	+	0.836068i	$0.315151\pi$
$912$	−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	$0.259067\pi$
$919$			44.0756i			1.45392i	−0.686681	+	0.726959i	$0.740933\pi$
$920$	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	0.712397	−	0.701777i	$-0.247610\pi$
$929$	3.63156	+	3.14676i	0.119147	+	0.103242i	−0.593249	+	0.805019i	$0.702155\pi$
$930$	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	−0.675374	−	0.737476i	$-0.736018\pi$
$937$	−25.8605	+	7.59332i	−0.844824	+	0.248063i	−0.169451	+	0.985539i	$0.554199\pi$
$938$	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	−0.814856	−	0.579664i	$-0.803184\pi$
$941$	3.99713	−	27.8007i	0.130303	−	0.906275i	0.945159	−	0.326612i	$-0.105907\pi$
$942$	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	0.711535	−	0.702651i	$-0.248001\pi$
$947$	28.6264	+	8.40547i	0.930234	+	0.273141i	0.218699	+	0.975792i	$0.429819\pi$
$948$	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	0.950498	−	0.310729i	$-0.100573\pi$
$953$	8.42763	+	13.1137i	0.272998	+	0.424793i	−0.677501	+	0.735522i	$0.736937\pi$
$954$	−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	$0.00354773\pi$
$967$			0.693162i			0.0222906i	−0.999938	+	0.0111453i	$0.996452\pi$
$968$	−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	0.313439	−	0.949608i	$-0.398519\pi$
$971$	−20.9124	−	24.1342i	−0.671111	−	0.774503i	−0.984550	+	0.175105i	$0.943973\pi$
$972$	−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	0.733365	−	0.679835i	$-0.237949\pi$
$977$	50.9037	−	7.31885i	1.62855	−	0.234151i	0.895190	+	0.445684i	$0.147040\pi$
$978$	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	−0.731932	−	0.681378i	$-0.761381\pi$
$983$	−15.1927	−	51.7416i	−0.484572	−	1.65030i	0.247359	−	0.968924i	$-0.420437\pi$
$984$	−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	0.576615	+	0.817016i	$0.304373\pi$
$991$	−6.51082	+	45.2837i	−0.206823	+	1.43849i	−0.783438	+	0.621469i	$0.786536\pi$
$992$	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	0.825285	−	0.564716i	$-0.191014\pi$
$997$	29.6476	+	13.5396i	0.938949	+	0.428803i	0.113663	+	0.993519i	$0.463742\pi$
$998$	−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.659.13	yes	240
3.2	odd	2		690.2.n.b.659.19	yes	240
5.4	even	2		690.2.n.b.659.12	yes	240
15.14	odd	2	inner	690.2.n.a.659.6	yes	240
23.20	odd	22	inner	690.2.n.a.89.6	✓	240
69.20	even	22		690.2.n.b.89.12	yes	240
115.89	odd	22		690.2.n.b.89.19	yes	240
345.89	even	22	inner	690.2.n.a.89.13	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.6	✓	240	23.20	odd	22	inner
690.2.n.a.89.13	yes	240	345.89	even	22	inner
690.2.n.a.659.6	yes	240	15.14	odd	2	inner
690.2.n.a.659.13	yes	240	1.1	even	1	trivial
690.2.n.b.89.12	yes	240	69.20	even	22
690.2.n.b.89.19	yes	240	115.89	odd	22
690.2.n.b.659.12	yes	240	5.4	even	2
690.2.n.b.659.19	yes	240	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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

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