LMFDB - Embedded newform 460.2.w.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35719 - 0.397537i) q^{2} +(0.361954 + 0.970436i) q^{3} +(1.68393 + 1.07907i) q^{4} +(-0.0598253 - 2.23527i) q^{5} +(-0.105456 - 1.46096i) q^{6} +(-3.20911 - 0.698099i) q^{7} +(-1.85644 - 2.13392i) q^{8} +(1.45651 - 1.26208i) q^{9} +O(q^{10})$	\(q+(-1.35719 - 0.397537i) q^{2} +(0.361954 + 0.970436i) q^{3} +(1.68393 + 1.07907i) q^{4} +(-0.0598253 - 2.23527i) q^{5} +(-0.105456 - 1.46096i) q^{6} +(-3.20911 - 0.698099i) q^{7} +(-1.85644 - 2.13392i) q^{8} +(1.45651 - 1.26208i) q^{9} +(-0.807408 + 3.05746i) q^{10} +(-5.55071 - 0.798071i) q^{11} +(-0.437661 + 2.02472i) q^{12} +(1.32587 + 6.09493i) q^{13} +(4.07785 + 2.22319i) q^{14} +(2.14753 - 0.867120i) q^{15} +(1.67123 + 3.63414i) q^{16} +(-4.38202 + 2.39276i) q^{17} +(-2.47849 + 1.13386i) q^{18} +(-2.72336 + 0.799650i) q^{19} +(2.31126 - 3.82859i) q^{20} +(-0.484089 - 3.36691i) q^{21} +(7.21610 + 3.28975i) q^{22} +(-2.02743 + 4.34621i) q^{23} +(1.39889 - 2.57394i) q^{24} +(-4.99284 + 0.267451i) q^{25} +(0.623504 - 8.79906i) q^{26} +(4.47909 + 2.44577i) q^{27} +(-4.65061 - 4.63839i) q^{28} +(1.97087 - 6.71217i) q^{29} +(-3.25932 + 0.323123i) q^{30} +(-0.167851 + 0.0766549i) q^{31} +(-0.823466 - 5.59660i) q^{32} +(-1.23462 - 5.67547i) q^{33} +(6.89845 - 1.50542i) q^{34} +(-1.36845 + 7.21498i) q^{35} +(3.81453 - 0.553570i) q^{36} +(-4.32167 - 0.309092i) q^{37} +(4.01400 - 0.00264039i) q^{38} +(-5.43484 + 3.49276i) q^{39} +(-4.65883 + 4.27730i) q^{40} +(-2.93013 + 3.38155i) q^{41} +(-0.681473 + 4.76198i) q^{42} +(-1.00810 - 2.70283i) q^{43} +(-8.48582 - 7.33348i) q^{44} +(-2.90821 - 3.18019i) q^{45} +(4.47939 - 5.09265i) q^{46} +(-2.88853 - 2.88853i) q^{47} +(-2.92179 + 2.93721i) q^{48} +(3.44361 + 1.57265i) q^{49} +(6.88256 + 1.62186i) q^{50} +(-3.90811 - 3.38640i) q^{51} +(-4.34417 + 11.6941i) q^{52} +(-1.81674 - 0.395207i) q^{53} +(-5.10670 - 5.09998i) q^{54} +(-1.45183 + 12.4551i) q^{55} +(4.46783 + 8.14397i) q^{56} +(-1.76174 - 2.35341i) q^{57} +(-5.34318 + 8.32619i) q^{58} +(-0.118997 - 0.0764745i) q^{59} +(4.55197 + 0.857161i) q^{60} +(2.06052 + 4.51191i) q^{61} +(0.258279 - 0.0373083i) q^{62} +(-5.55517 + 3.03335i) q^{63} +(-1.10726 + 7.92300i) q^{64} +(13.5445 - 3.32831i) q^{65} +(-0.580594 + 8.19350i) q^{66} +(6.09409 - 8.14074i) q^{67} +(-9.96096 - 0.699252i) q^{68} +(-4.95155 - 0.394368i) q^{69} +(4.72547 - 9.24809i) q^{70} +(9.29961 - 1.33708i) q^{71} +(-5.39711 - 0.765119i) q^{72} +(-11.6268 - 6.34870i) q^{73} +(5.74245 + 2.13752i) q^{74} +(-2.06672 - 4.74843i) q^{75} +(-5.44881 - 1.59213i) q^{76} +(17.2557 + 6.43604i) q^{77} +(8.76460 - 2.57978i) q^{78} +(-0.180453 - 0.115970i) q^{79} +(8.02330 - 3.95306i) q^{80} +(0.0705885 - 0.490954i) q^{81} +(5.32103 - 3.42457i) q^{82} +(-7.40350 - 0.529509i) q^{83} +(2.81795 - 6.19200i) q^{84} +(5.61062 + 9.65184i) q^{85} +(0.293712 + 4.06901i) q^{86} +(7.22709 - 0.516892i) q^{87} +(8.60153 + 13.3264i) q^{88} +(-4.38438 - 2.00228i) q^{89} +(2.68275 + 5.47225i) q^{90} -20.4849i q^{91} +(-8.10390 + 5.13096i) q^{92} +(-0.135143 - 0.135143i) q^{93} +(2.77199 + 5.06859i) q^{94} +(1.95036 + 6.03959i) q^{95} +(5.13308 - 2.82483i) q^{96} +(-0.147267 - 2.05906i) q^{97} +(-4.04845 - 3.50334i) q^{98} +(-9.09191 + 5.84302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	−1.35719	−	0.397537i	−0.959678	−	0.281101i
$2$	−1.35719	−	0.397537i	−0.959678	−	0.281101i
$3$	0.361954	+	0.970436i	0.208974	+	0.560281i	0.998577	−	0.0533375i	$-0.0169859\pi$
$3$	0.361954	+	0.970436i	0.208974	+	0.560281i	−0.789602	+	0.613619i	$0.789713\pi$
$4$	1.68393	+	1.07907i	0.841964	+	0.539534i
$5$	−0.0598253	−	2.23527i	−0.0267547	−	0.999642i
$5$	−0.0598253	−	2.23527i	−0.0267547	−	0.999642i
$6$	−0.105456	−	1.46096i	−0.0430521	−	0.596433i
$7$	−3.20911	−	0.698099i	−1.21293	−	0.263857i	−0.439794	−	0.898098i	$-0.644949\pi$
$7$	−3.20911	−	0.698099i	−1.21293	−	0.263857i	−0.773135	+	0.634242i	$0.781312\pi$
$8$	−1.85644	−	2.13392i	−0.656351	−	0.754456i
$9$	1.45651	−	1.26208i	0.485505	−	0.420692i
$10$	−0.807408	+	3.05746i	−0.255325	+	0.966855i
$11$	−5.55071	−	0.798071i	−1.67360	−	0.240628i	−0.760787	−	0.649002i	$-0.775187\pi$
$11$	−5.55071	−	0.798071i	−1.67360	−	0.240628i	−0.912814	+	0.408374i	$0.866096\pi$
$12$	−0.437661	+	2.02472i	−0.126342	+	0.584485i
$13$	1.32587	+	6.09493i	0.367731	+	1.69043i	0.674199	+	0.738549i	$0.264489\pi$
$13$	1.32587	+	6.09493i	0.367731	+	1.69043i	−0.306469	+	0.951881i	$0.599147\pi$
$14$	4.07785	+	2.22319i	1.08985	+	0.594173i
$15$	2.14753	−	0.867120i	0.554490	−	0.223889i
$16$	1.67123	+	3.63414i	0.417807	+	0.908536i
$17$	−4.38202	+	2.39276i	−1.06280	+	0.580331i	−0.912821	−	0.408359i	$-0.866101\pi$
$17$	−4.38202	+	2.39276i	−1.06280	+	0.580331i	−0.149975	+	0.988690i	$0.547919\pi$
$18$	−2.47849	+	1.13386i	−0.584185	+	0.267253i
$19$	−2.72336	+	0.799650i	−0.624781	+	0.183452i	−0.578773	−	0.815489i	$-0.696468\pi$
$19$	−2.72336	+	0.799650i	−0.624781	+	0.183452i	−0.0460081	+	0.998941i	$0.514650\pi$
$20$	2.31126	−	3.82859i	0.516814	−	0.856098i
$21$	−0.484089	−	3.36691i	−0.105637	−	0.734721i
$22$	7.21610	+	3.28975i	1.53848	+	0.701377i
$23$	−2.02743	+	4.34621i	−0.422749	+	0.906247i
$23$	−2.02743	+	4.34621i	−0.422749	+	0.906247i
$24$	1.39889	−	2.57394i	0.285547	−	0.525403i
$25$	−4.99284	+	0.267451i	−0.998568	+	0.0534902i
$26$	0.623504	−	8.79906i	0.122279	−	1.72564i
$27$	4.47909	+	2.44577i	0.862002	+	0.470689i
$28$	−4.65061	−	4.63839i	−0.878883	−	0.876574i
$29$	1.97087	−	6.71217i	0.365981	−	1.24642i	−0.546555	−	0.837423i	$-0.684061\pi$
$29$	1.97087	−	6.71217i	0.365981	−	1.24642i	0.912537	−	0.408995i	$-0.134121\pi$
$30$	−3.25932	+	0.323123i	−0.595067	+	0.0589940i
$31$	−0.167851	+	0.0766549i	−0.0301469	+	0.0137676i	−0.430431	−	0.902623i	$-0.641639\pi$
$31$	−0.167851	+	0.0766549i	−0.0301469	+	0.0137676i	0.400285	+	0.916391i	$0.368911\pi$
$32$	−0.823466	−	5.59660i	−0.145570	−	0.989348i
$33$	−1.23462	−	5.67547i	−0.214920	−	0.987972i
$34$	6.89845	−	1.50542i	1.18307	−	0.258177i
$35$	−1.36845	+	7.21498i	−0.231311	+	1.21955i
$36$	3.81453	−	0.553570i	0.635755	−	0.0922616i
$37$	−4.32167	−	0.309092i	−0.710478	−	0.0508144i	−0.288577	−	0.957457i	$-0.593182\pi$
$37$	−4.32167	−	0.309092i	−0.710478	−	0.0508144i	−0.421900	+	0.906642i	$0.638637\pi$
$38$	4.01400	−	0.00264039i	0.651157	−	0.000428328i
$39$	−5.43484	+	3.49276i	−0.870270	+	0.559289i
$40$	−4.65883	+	4.27730i	−0.736625	+	0.676301i
$41$	−2.93013	+	3.38155i	−0.457609	+	0.528109i	−0.936924	−	0.349534i	$-0.886340\pi$
$41$	−2.93013	+	3.38155i	−0.457609	+	0.528109i	0.479314	+	0.877643i	$0.340885\pi$
$42$	−0.681473	+	4.76198i	−0.105154	+	0.734790i
$43$	−1.00810	−	2.70283i	−0.153734	−	0.412177i	0.837136	−	0.546994i	$-0.184228\pi$
$43$	−1.00810	−	2.70283i	−0.153734	−	0.412177i	−0.990871	+	0.134817i	$0.956955\pi$
$44$	−8.48582	−	7.33348i	−1.27929	−	1.10556i
$45$	−2.90821	−	3.18019i	−0.433531	−	0.474075i
$46$	4.47939	−	5.09265i	0.660450	−	0.750870i
$47$	−2.88853	−	2.88853i	−0.421336	−	0.421336i	0.464328	−	0.885663i	$-0.346296\pi$
$47$	−2.88853	−	2.88853i	−0.421336	−	0.421336i	−0.885663	+	0.464328i	$0.846296\pi$
$48$	−2.92179	+	2.93721i	−0.421725	+	0.423950i
$49$	3.44361	+	1.57265i	0.491945	+	0.224664i
$50$	6.88256	+	1.62186i	0.973340	+	0.229366i
$51$	−3.90811	−	3.38640i	−0.547245	−	0.474191i
$52$	−4.34417	+	11.6941i	−0.602428	+	1.62168i
$53$	−1.81674	−	0.395207i	−0.249548	−	0.0542859i	0.0860512	−	0.996291i	$-0.472575\pi$
$53$	−1.81674	−	0.395207i	−0.249548	−	0.0542859i	−0.335599	+	0.942005i	$0.608939\pi$
$54$	−5.10670	−	5.09998i	−0.694933	−	0.694020i
$55$	−1.45183	+	12.4551i	−0.195765	+	1.67944i
$56$	4.46783	+	8.14397i	0.597039	+	1.08828i
$57$	−1.76174	−	2.35341i	−0.233348	−	0.311716i
$58$	−5.34318	+	8.32619i	−0.701594	+	1.09328i
$59$	−0.118997	−	0.0764745i	−0.0154921	−	0.00995614i	0.532872	−	0.846196i	$-0.321113\pi$
$59$	−0.118997	−	0.0764745i	−0.0154921	−	0.00995614i	−0.548364	+	0.836240i	$0.684749\pi$
$60$	4.55197	+	0.857161i	0.587656	+	0.110659i
$61$	2.06052	+	4.51191i	0.263823	+	0.577691i	0.994465	−	0.105069i	$-0.0335065\pi$
$61$	2.06052	+	4.51191i	0.263823	+	0.577691i	−0.730642	+	0.682761i	$0.760779\pi$
$62$	0.258279	−	0.0373083i	0.0328014	−	0.00473816i
$63$	−5.55517	+	3.03335i	−0.699885	+	0.382166i
$64$	−1.10726	+	7.92300i	−0.138407	+	0.990375i
$65$	13.5445	−	3.32831i	1.67999	−	0.412826i
$66$	−0.580594	+	8.19350i	−0.0714661	+	1.00855i
$67$	6.09409	−	8.14074i	0.744511	−	0.994550i	−0.255107	−	0.966913i	$-0.582111\pi$
$67$	6.09409	−	8.14074i	0.744511	−	0.994550i	0.999618	−	0.0276375i	$-0.00879840\pi$
$68$	−9.96096	−	0.699252i	−1.20794	−	0.0847967i
$69$	−4.95155	−	0.394368i	−0.596097	−	0.0474763i
$70$	4.72547	−	9.24809i	0.564802	−	1.10536i
$71$	9.29961	−	1.33708i	1.10366	−	0.158682i	0.433684	−	0.901065i	$-0.357213\pi$
$71$	9.29961	−	1.33708i	1.10366	−	0.158682i	0.669976	+	0.742383i	$0.266304\pi$
$72$	−5.39711	−	0.765119i	−0.636055	−	0.0901701i
$73$	−11.6268	−	6.34870i	−1.36081	−	0.743059i	−0.377676	−	0.925938i	$-0.623277\pi$
$73$	−11.6268	−	6.34870i	−1.36081	−	0.743059i	−0.983136	+	0.182878i	$0.941459\pi$
$74$	5.74245	+	2.13752i	0.667546	+	0.248482i
$75$	−2.06672	−	4.74843i	−0.238644	−	0.548301i
$76$	−5.44881	−	1.59213i	−0.625022	−	0.182630i
$77$	17.2557	+	6.43604i	1.96647	+	0.733455i
$78$	8.76460	−	2.57978i	0.992396	−	0.292103i
$79$	−0.180453	−	0.115970i	−0.0203026	−	0.0130477i	0.530450	−	0.847716i	$-0.322023\pi$
$79$	−0.180453	−	0.115970i	−0.0203026	−	0.0130477i	−0.550753	+	0.834668i	$0.685659\pi$
$80$	8.02330	−	3.95306i	0.897032	−	0.441965i
$81$	0.0705885	−	0.490954i	0.00784316	−	0.0545504i
$82$	5.32103	−	3.42457i	0.587610	−	0.378180i
$83$	−7.40350	−	0.529509i	−0.812640	−	0.0581212i	−0.341168	−	0.940002i	$-0.610823\pi$
$83$	−7.40350	−	0.529509i	−0.812640	−	0.0581212i	−0.471472	+	0.881881i	$0.656277\pi$
$84$	2.81795	−	6.19200i	0.307464	−	0.675603i
$85$	5.61062	+	9.65184i	0.608558	+	1.04689i
$86$	0.293712	+	4.06901i	0.0316717	+	0.438772i
$87$	7.22709	−	0.516892i	0.774825	−	0.0554166i
$88$	8.60153	+	13.3264i	0.916927	+	1.42059i
$89$	−4.38438	−	2.00228i	−0.464744	−	0.212241i	0.169260	−	0.985571i	$-0.445862\pi$
$89$	−4.38438	−	2.00228i	−0.464744	−	0.212241i	−0.634004	+	0.773330i	$0.718590\pi$
$90$	2.68275	+	5.47225i	0.282787	+	0.576826i
$91$		−	20.4849i		−	2.14740i
$92$	−8.10390	+	5.13096i	−0.844890	+	0.534940i
$93$	−0.135143	−	0.135143i	−0.0140137	−	0.0140137i
$94$	2.77199	+	5.06859i	0.285909	+	0.522785i
$95$	1.95036	+	6.03959i	0.200102	+	0.619649i
$96$	5.13308	−	2.82483i	0.523893	−	0.288308i
$97$	−0.147267	−	2.05906i	−0.0149527	−	0.209066i	−0.999436	−	0.0335866i	$-0.989307\pi$
$97$	−0.147267	−	2.05906i	−0.0149527	−	0.209066i	0.984483	−	0.175479i	$-0.0561475\pi$
$98$	−4.04845	−	3.50334i	−0.408955	−	0.353891i
$99$	−9.09191	+	5.84302i	−0.913771	+	0.587245i
$100$	−8.69618	−	4.93724i	−0.869618	−	0.493724i
$101$	−3.18553	−	3.67630i	−0.316972	−	0.365805i	0.574797	−	0.818296i	$-0.305081\pi$
$101$	−3.18553	−	3.67630i	−0.316972	−	0.365805i	−0.891769	+	0.452491i	$0.850536\pi$
$102$	3.95783	+	6.14961i	0.391884	+	0.608902i
$103$	6.60843	+	8.82782i	0.651148	+	0.869831i	0.997671	−	0.0682099i	$-0.0217288\pi$
$103$	6.60843	+	8.82782i	0.651148	+	0.869831i	−0.346523	+	0.938041i	$0.612638\pi$
$104$	10.5447	−	14.1442i	1.03399	−	1.38695i
$105$	−7.49699	+	1.28349i	−0.731631	+	0.125256i
$106$	2.30855	+	1.25859i	0.224226	+	0.122245i
$107$	3.52128	−	9.44093i	0.340415	−	0.912689i	−0.648098	−	0.761557i	$-0.724435\pi$
$107$	3.52128	−	9.44093i	0.340415	−	0.912689i	0.988514	−	0.151132i	$-0.0482919\pi$
$108$	4.90332	+	8.95175i	0.471822	+	0.861382i
$109$	0.0577719	−	0.196753i	0.00553354	−	0.0188455i	−0.956680	−	0.291142i	$-0.905965\pi$
$109$	0.0577719	−	0.196753i	0.00553354	−	0.0188455i	0.962213	+	0.272296i	$0.0877831\pi$
$110$	6.92176	−	16.3267i	0.659964	−	1.55669i
$111$	−1.26429	−	4.30578i	−0.120001	−	0.408686i
$112$	−2.82616	−	12.8290i	−0.267047	−	1.21223i
$113$	8.19738	−	10.9504i	0.771145	−	1.03013i	−0.227270	−	0.973832i	$-0.572980\pi$
$113$	8.19738	−	10.9504i	0.771145	−	1.03013i	0.998414	−	0.0562966i	$-0.0179292\pi$
$114$	1.45545	+	3.89438i	0.136315	+	0.364742i
$115$	9.83623	+	4.27184i	0.917233	+	0.398351i
$116$	10.5617	−	9.17611i	0.980628	−	0.851980i
$117$	9.62342	+	7.20400i	0.889686	+	0.666010i
$118$	0.131100	+	0.151096i	0.0120687	+	0.0139095i
$119$	15.7328	−	4.61956i	1.44222	−	0.423474i
$120$	−5.83713	−	2.97291i	−0.532854	−	0.271388i
$121$	19.6190	+	5.76066i	1.78355	+	0.523696i
$122$	−1.00286	−	6.94265i	−0.0907951	−	0.628558i
$123$	−4.34215	−	1.61954i	−0.391518	−	0.146029i
$124$	−0.365365	−	0.0520410i	−0.0328107	−	0.00467342i
$125$	0.896522	+	11.1443i	0.0801874	+	0.996780i
$126$	8.74528	−	1.90845i	0.779092	−	0.170018i
$127$	−2.09151	+	1.56568i	−0.185591	+	0.138932i	−0.688033	−	0.725679i	$-0.741526\pi$
$127$	−2.09151	+	1.56568i	−0.185591	+	0.138932i	0.502442	+	0.864611i	$0.332435\pi$
$128$	4.65245	−	10.3128i	0.411222	−	0.911535i
$129$	2.25803	−	1.95660i	0.198809	−	0.172269i
$130$	−19.7056	−	0.867292i	−1.72829	−	0.0760666i
$131$	−3.51006	−	5.46176i	−0.306675	−	0.477196i	0.653371	−	0.757038i	$-0.273354\pi$
$131$	−3.51006	−	5.46176i	−0.306675	−	0.477196i	−0.960046	+	0.279842i	$0.909718\pi$
$132$	4.04520	−	10.8893i	0.352089	−	0.947794i
$133$	9.29778	−	0.664991i	0.806220	−	0.0576620i
$134$	−11.5071	+	8.62591i	−0.994060	+	0.745165i
$135$	5.19899	−	10.1583i	0.447458	−	0.874287i
$136$	13.2409	+	4.90887i	1.13540	+	0.420932i
$137$	−3.20719	+	3.20719i	−0.274009	+	0.274009i	−0.830712	−	0.556703i	$-0.812066\pi$
$137$	−3.20719	+	3.20719i	−0.274009	+	0.274009i	0.556703	+	0.830712i	$0.312066\pi$
$138$	6.56342	+	2.50366i	0.558715	+	0.213126i
$139$	−6.93426			−0.588156			−0.294078	−	0.955781i	$-0.595013\pi$
$139$	−6.93426			−0.588156			−0.294078	+	0.955781i	$0.595013\pi$
$140$	−10.0898	+	10.6729i	−0.852746	+	0.902021i
$141$	1.75762	−	3.84865i	0.148018	−	0.324115i
$142$	−13.1529	−	1.88227i	−1.10376	−	0.157956i
$143$	−2.49533	−	34.8893i	−0.208670	−	2.91759i
$144$	7.02073	+	3.18396i	0.585061	+	0.265330i
$145$	−15.1214	−	4.00386i	−1.25576	−	0.332503i
$146$	13.2559	+	13.2385i	1.09707	+	1.09562i
$147$	−0.279722	+	3.91103i	−0.0230711	+	0.322576i
$148$	−6.94385	−	5.18386i	−0.570781	−	0.426111i
$149$	9.99740	+	1.43741i	0.819019	+	0.117757i	0.539073	−	0.842259i	$-0.318775\pi$
$149$	9.99740	+	1.43741i	0.819019	+	0.117757i	0.279946	+	0.960016i	$0.409684\pi$
$150$	0.917257	+	7.26612i	0.0748937	+	0.593276i
$151$	−10.5936	+	16.4839i	−0.862092	+	1.34144i	0.0767343	+	0.997052i	$0.475551\pi$
$151$	−10.5936	+	16.4839i	−0.862092	+	1.34144i	−0.938827	+	0.344390i	$0.888086\pi$
$152$	6.76214	+	4.32693i	0.548482	+	0.350961i
$153$	−3.36262	+	9.01554i	−0.271852	+	0.728863i
$154$	−20.8607	−	15.5947i	−1.68100	−	1.25666i
$155$	0.181386	+	0.370606i	0.0145693	+	0.0297678i
$156$	−12.9208	+	0.0169985i	−1.03449	+	0.00136097i
$157$	−6.56861	+	12.0295i	−0.524232	+	0.960059i	0.472658	+	0.881246i	$0.343295\pi$
$157$	−6.56861	+	12.0295i	−0.524232	+	0.960059i	−0.996889	+	0.0788127i	$0.974887\pi$
$158$	0.198807	+	0.229131i	0.0158162	+	0.0182286i
$159$	−0.274052	−	1.90607i	−0.0217337	−	0.151161i
$160$	−12.4606	+	2.17548i	−0.985099	+	0.171987i
$161$	9.54034	−	12.5321i	0.751884	−	0.987668i
$162$	−0.290974	+	0.638256i	−0.0228611	+	0.0501461i
$163$	−2.31297	−	1.73147i	−0.181166	−	0.135619i	0.504846	−	0.863209i	$-0.331549\pi$
$163$	−2.31297	−	1.73147i	−0.181166	−	0.135619i	−0.686012	+	0.727590i	$0.740640\pi$
$164$	−8.58305	+	2.53248i	−0.670223	+	0.197753i
$165$	−12.6123	+	3.09925i	−0.981869	+	0.241276i
$166$	9.83746	+	3.66181i	0.763535	+	0.284212i
$167$	10.8246	+	19.8237i	0.837629	+	1.53400i	0.845463	+	0.534034i	$0.179325\pi$
$167$	10.8246	+	19.8237i	0.837629	+	1.53400i	−0.00783365	+	0.999969i	$0.502494\pi$
$168$	−6.28605	+	7.28348i	−0.484979	+	0.561933i
$169$	−23.5651	+	10.7618i	−1.81270	+	0.827831i
$170$	−3.77771	−	15.3298i	−0.289737	−	1.17574i
$171$	−2.95739	+	4.60179i	−0.226157	+	0.351907i
$172$	1.21896	−	5.63918i	0.0929449	−	0.429983i
$173$	−6.53286	+	4.89044i	−0.496684	+	0.371813i	−0.818055	−	0.575140i	$-0.804947\pi$
$173$	−6.53286	+	4.89044i	−0.496684	+	0.371813i	0.321370	+	0.946954i	$0.395857\pi$
$174$	−10.0140	−	2.17152i	−0.759161	−	0.164622i
$175$	16.2093	+	2.62722i	1.22531	+	0.198599i
$176$	−6.37619	−	21.5058i	−0.480624	−	1.62106i
$177$	0.0311423	−	0.143159i	0.00234080	−	0.0107605i
$178$	5.15446	+	4.46043i	0.386343	+	0.334324i
$179$	6.95273	−	8.02387i	0.519671	−	0.599732i	−0.433877	−	0.900972i	$-0.642855\pi$
$179$	6.95273	−	8.02387i	0.519671	−	0.599732i	0.953549	+	0.301240i	$0.0974004\pi$
$180$	−1.46558	−	8.49338i	−0.109238	−	0.633059i
$181$	1.91566	−	4.19472i	0.142390	−	0.311791i	−0.824978	−	0.565164i	$-0.808813\pi$
$181$	1.91566	−	4.19472i	0.142390	−	0.311791i	0.967369	+	0.253373i	$0.0815401\pi$
$182$	−8.14351	+	27.8019i	−0.603637	+	2.06081i
$183$	−3.63271	+	3.63271i	−0.268537	+	0.268537i
$184$	13.0383	−	3.74209i	0.961195	−	0.275870i
$185$	−0.432358	+	9.67858i	−0.0317876	+	0.711583i
$186$	0.129690	+	0.237139i	0.00950935	+	0.0173879i
$187$	26.2329	−	9.78437i	1.91834	−	0.715504i
$188$	−1.74716	−	7.98100i	−0.127425	−	0.582074i
$189$	−12.6665	−	10.9756i	−0.921353	−	0.798357i
$190$	−0.246041	−	8.97221i	−0.0178497	−	0.650913i
$191$	7.65791	+	11.9159i	0.554107	+	0.862207i	0.999450	−	0.0331530i	$-0.0105549\pi$
$191$	7.65791	+	11.9159i	0.554107	+	0.862207i	−0.445344	+	0.895360i	$0.646918\pi$
$192$	−8.08954	+	1.79324i	−0.583812	+	0.129416i
$193$	0.148040	−	2.06987i	0.0106561	−	0.148992i	−0.989338	−	0.145636i	$-0.953477\pi$
$193$	0.148040	−	2.06987i	0.0106561	−	0.148992i	0.999994	−	0.00335621i	$-0.00106832\pi$
$194$	−0.618684	+	2.85308i	−0.0444189	+	0.204839i
$195$	8.13239	+	11.9394i	0.582372	+	0.854995i
$196$	4.10181	+	6.36411i	0.292986	+	0.454579i
$197$	−9.45609	+	2.05705i	−0.673718	+	0.146558i	−0.536394	−	0.843968i	$-0.680214\pi$
$197$	−9.45609	+	2.05705i	−0.673718	+	0.146558i	−0.137324	+	0.990526i	$0.543850\pi$
$198$	14.6623	−	4.31571i	1.04200	−	0.306704i
$199$	7.66109	+	16.7754i	0.543080	+	1.18918i	0.959939	+	0.280208i	$0.0904036\pi$
$199$	7.66109	+	16.7754i	0.543080	+	1.18918i	−0.416859	+	0.908971i	$0.636869\pi$
$200$	9.83963	+	10.1578i	0.695767	+	0.718267i
$201$	10.1058	+	2.96734i	0.712811	+	0.209300i
$202$	2.86190	+	6.25580i	0.201363	+	0.440156i
$203$	−11.0105	+	20.1642i	−0.772785	+	1.41525i
$204$	−2.92683	−	9.91957i	−0.204919	−	0.694509i
$205$	7.73396	+	6.34732i	0.540163	+	0.443316i
$206$	−5.45950	−	14.6081i	−0.380381	−	1.01780i
$207$	2.53226	+	8.88909i	0.176004	+	0.617834i
$208$	−19.9340	+	15.0044i	−1.38218	+	1.04037i
$209$	15.7547	−	2.26519i	1.08978	−	0.156686i
$210$	10.6851	+	1.23839i	0.737340	+	0.0854569i
$211$	−3.80471	−	12.9577i	−0.261927	−	0.892042i	−0.980488	−	0.196578i	$-0.937017\pi$
$211$	−3.80471	−	12.9577i	−0.261927	−	0.892042i	0.718561	−	0.695464i	$-0.244801\pi$
$212$	−2.63280	−	2.62588i	−0.180821	−	0.180346i
$213$	4.66358	+	8.54071i	0.319543	+	0.585200i
$214$	−8.53217	+	11.4133i	−0.583247	+	0.780196i
$215$	−5.98123	+	2.41508i	−0.407917	+	0.164707i
$216$	−3.09609	−	14.0985i	−0.210662	−	0.959280i
$217$	0.592165	−	0.128818i	0.0401987	−	0.00874470i
$218$	−0.156624	+	0.244065i	−0.0106079	+	0.0165301i
$219$	1.95265	−	13.5810i	0.131948	−	0.917718i
$220$	−15.8846	+	19.4068i	−1.07094	+	1.30841i
$221$	−20.3937	−	23.5356i	−1.37183	−	1.58318i
$222$	0.00417460	+	6.34636i	0.000280181	+	0.425940i
$223$	4.66469	−	21.4432i	0.312371	−	1.43594i	−0.506636	−	0.862160i	$-0.669111\pi$
$223$	4.66469	−	21.4432i	0.312371	−	1.43594i	0.819007	−	0.573784i	$-0.194525\pi$
$224$	−1.26439	+	18.5350i	−0.0844804	+	1.23842i
$225$	−6.93460	+	6.69089i	−0.462307	+	0.446060i
$226$	−15.4786	+	11.6030i	−1.02962	+	0.771822i
$227$	−12.5180	+	4.66898i	−0.830850	+	0.309891i	−0.728661	−	0.684874i	$-0.759857\pi$
$227$	−12.5180	+	4.66898i	−0.830850	+	0.309891i	−0.102188	+	0.994765i	$0.532584\pi$
$228$	−0.427156	−	5.86400i	−0.0282891	−	0.388353i
$229$		−	3.08799i		−	0.204060i	−0.994781	−	0.102030i	$-0.967466\pi$
$229$		−	3.08799i		−	0.204060i	0.994781	−	0.102030i	$-0.0325337\pi$
$230$	−11.6514	−	9.70797i	−0.768271	−	0.640125i
$231$			19.0751i			1.25505i
$232$	−17.9821	+	8.25505i	−1.18058	+	0.541971i
$233$	4.06013	−	1.51435i	0.265988	−	0.0992083i	−0.212932	−	0.977067i	$-0.568301\pi$
$233$	4.06013	−	1.51435i	0.265988	−	0.0992083i	0.478920	+	0.877859i	$0.341029\pi$
$234$	−10.1969	−	13.6029i	−0.666595	−	0.889247i
$235$	−6.28384	+	6.62945i	−0.409912	+	0.432458i
$236$	−0.117861	−	0.257183i	−0.00767208	−	0.0167412i
$237$	0.0472259	−	0.217094i	0.00306765	−	0.0141018i
$238$	−23.1888	+	0.0152535i	−1.50311	+	0.000988736i
$239$	−1.97566	−	2.28004i	−0.127795	−	0.147483i	0.688246	−	0.725478i	$-0.258381\pi$
$239$	−1.97566	−	2.28004i	−0.127795	−	0.147483i	−0.816041	+	0.577994i	$0.803836\pi$
$240$	6.74025	+	6.35527i	0.435081	+	0.410231i
$241$	−2.54722	+	17.7163i	−0.164081	+	1.14121i	0.726759	+	0.686892i	$0.241026\pi$
$241$	−2.54722	+	17.7163i	−0.164081	+	1.14121i	−0.890840	+	0.454316i	$0.849884\pi$
$242$	−24.3366	−	15.6176i	−1.56442	−	1.00394i
$243$	15.4621	−	3.36358i	0.991896	−	0.215774i
$244$	−1.39889	+	9.82118i	−0.0895545	+	0.628736i
$245$	3.30927	−	7.79148i	0.211421	−	0.497779i
$246$	5.24929	+	3.92419i	0.334683	+	0.250197i
$247$	−8.48463	−	15.5384i	−0.539864	−	0.988687i
$248$	0.475181	+	0.215876i	0.0301740	+	0.0137081i
$249$	−2.16587	−	7.37628i	−0.137257	−	0.467453i
$250$	3.21354	−	15.4814i	0.203242	−	0.979129i
$251$	−2.53193	+	0.364036i	−0.159814	+	0.0229777i	−0.221757	−	0.975102i	$-0.571179\pi$
$251$	−2.53193	+	0.364036i	−0.159814	+	0.0229777i	0.0619435	+	0.998080i	$0.480270\pi$
$252$	−12.6277	−	0.886454i	−0.795470	−	0.0558413i
$253$	14.7223	−	22.5065i	0.925581	−	1.41497i
$254$	3.46099	−	1.29348i	0.217162	−	0.0811598i
$255$	−7.33570	+	8.93827i	−0.459380	+	0.559736i
$256$	−10.4140	+	12.1470i	−0.650875	+	0.759185i
$257$	−10.8837	+	19.9320i	−0.678905	+	1.24332i	0.280110	+	0.959968i	$0.409629\pi$
$257$	−10.8837	+	19.9320i	−0.678905	+	1.24332i	−0.959015	+	0.283354i	$0.908553\pi$
$258$	−3.84240	+	1.75782i	−0.239217	+	0.109437i
$259$	13.6529	+	4.00886i	0.848352	+	0.249099i
$260$	26.3994	+	9.01078i	1.63722	+	0.558825i
$261$	−5.60067	−	12.2638i	−0.346673	−	0.759107i
$262$	2.59256	+	8.80803i	0.160169	+	0.544162i
$263$	−20.9631	+	4.56025i	−1.29264	+	0.281197i	−0.805746	−	0.592262i	$-0.798235\pi$
$263$	−20.9631	+	4.56025i	−1.29264	+	0.281197i	−0.486898	+	0.873459i	$0.661872\pi$
$264$	−9.81901	+	13.1708i	−0.604318	+	0.810604i
$265$	−0.774707	+	4.08454i	−0.0475898	+	0.250911i
$266$	−12.8832	−	2.79370i	−0.789920	−	0.171293i
$267$	0.356141	−	4.97950i	0.0217954	−	0.304740i
$268$	19.0464	−	7.13250i	1.16344	−	0.435687i
$269$	3.50387	+	5.45212i	0.213635	+	0.332422i	0.931488	−	0.363773i	$-0.118511\pi$
$269$	3.50387	+	5.45212i	0.213635	+	0.332422i	−0.717853	+	0.696194i	$0.754875\pi$
$270$	−11.0943	+	11.7199i	−0.675179	+	0.713253i
$271$	−8.80946	−	7.63344i	−0.535136	−	0.463698i	0.344876	−	0.938648i	$-0.387921\pi$
$271$	−8.80946	−	7.63344i	−0.535136	−	0.463698i	−0.880013	+	0.474950i	$0.842466\pi$
$272$	−16.0190	−	11.9260i	−0.971295	−	0.723122i
$273$	19.8793	−	7.41458i	1.20315	−	0.448751i
$274$	5.62775	−	3.07779i	0.339985	−	0.185936i
$275$	27.9272	+	2.50010i	1.68408	+	0.150762i
$276$	−7.91251	−	6.00714i	−0.476277	−	0.361588i
$277$	19.1572	−	19.1572i	1.15104	−	1.15104i	0.164698	−	0.986344i	$-0.447335\pi$
$277$	19.1572	−	19.1572i	1.15104	−	1.15104i	0.986344	−	0.164698i	$-0.0526649\pi$
$278$	9.41110	+	2.75663i	0.564440	+	0.165331i
$279$	−0.147733	+	0.323490i	−0.00884453	+	0.0193668i
$280$	17.9367	−	10.4740i	1.07192	−	0.625942i
$281$	−20.5732	+	23.7428i	−1.22730	+	1.41637i	−0.349776	+	0.936833i	$0.613742\pi$
$281$	−20.5732	+	23.7428i	−1.22730	+	1.41637i	−0.877520	+	0.479541i	$0.840803\pi$
$282$	−3.91541	+	4.52463i	−0.233159	+	0.269438i
$283$	6.32894	−	29.0937i	0.376216	−	1.72944i	−0.266948	−	0.963711i	$-0.586015\pi$
$283$	6.32894	−	29.0937i	0.376216	−	1.72944i	0.643165	−	0.765728i	$-0.277621\pi$
$284$	17.1027	+	7.78335i	1.01486	+	0.461857i
$285$	−5.15510	+	4.07875i	−0.305362	+	0.241604i
$286$	−10.4832	+	48.3434i	−0.619883	+	2.85861i
$287$	11.7638	−	8.80624i	0.694393	−	0.519816i
$288$	−8.26272	−	7.11225i	−0.486886	−	0.419093i
$289$	4.28589	−	6.66897i	0.252111	−	0.392293i
$290$	18.9309	+	11.4453i	1.11166	+	0.672093i
$291$	1.94488	−	0.888197i	0.114011	−	0.0520671i
$292$	−12.7280	−	23.2368i	−0.744849	−	1.35983i
$293$	1.09085	+	1.99774i	0.0637280	+	0.116709i	0.907601	−	0.419834i	$-0.137912\pi$
$293$	1.09085	+	1.99774i	0.0637280	+	0.116709i	−0.843873	+	0.536543i	$0.819730\pi$
$294$	1.93442	−	5.19681i	0.112817	−	0.303084i
$295$	−0.163822	+	0.270565i	−0.00953809	+	0.0157529i
$296$	7.36334	+	9.79592i	0.427986	+	0.569376i
$297$	−22.9102	−	17.1504i	−1.32939	−	0.995167i
$298$	−12.9969	−	5.92518i	−0.752893	−	0.343236i
$299$	−29.1780	−	6.59456i	−1.68740	−	0.381373i
$300$	1.64366	−	10.2261i	0.0948968	−	0.590407i
$301$	1.34827	+	9.37742i	0.0777130	+	0.540506i
$302$	20.9305	−	18.1605i	1.20441	−	1.04502i
$303$	2.41459	−	4.42200i	0.138715	−	0.254037i
$304$	−7.45739	−	8.56067i	−0.427711	−	0.490988i
$305$	9.96206	−	4.87574i	0.570426	−	0.279184i
$306$	8.14773	−	10.8990i	0.465775	−	0.623056i
$307$	4.11159	−	11.0236i	0.234661	−	0.629150i	−0.765232	−	0.643754i	$-0.777376\pi$
$307$	4.11159	−	11.0236i	0.234661	−	0.629150i	0.999893	+	0.0146037i	$0.00464868\pi$
$308$	22.1124	+	29.4579i	1.25997	+	1.67852i
$309$	−6.17489	+	9.60832i	−0.351277	+	0.546598i
$310$	−0.0988456	−	0.575090i	−0.00561405	−	0.0326629i
$311$	−33.8947	−	4.87333i	−1.92199	−	0.276341i	−0.926903	−	0.375301i	$-0.877539\pi$
$311$	−33.8947	−	4.87333i	−1.92199	−	0.276341i	−0.995091	+	0.0989604i	$0.968448\pi$
$312$	17.5427	+	5.11343i	0.993161	+	0.289491i
$313$	0.735827	−	10.2882i	0.0415914	−	0.581524i	−0.933336	−	0.359003i	$-0.883117\pi$
$313$	0.735827	−	10.2882i	0.0415914	−	0.581524i	0.974928	−	0.222521i	$-0.0714286\pi$
$314$	13.6970	−	13.7151i	0.772968	−	0.773985i
$315$	7.11269	+	12.2358i	0.400755	+	0.689410i
$316$	−0.178731	−	0.390007i	−0.0100544	−	0.0219396i
$317$	−1.89395	−	26.4809i	−0.106375	−	1.48731i	−0.717932	−	0.696113i	$-0.754911\pi$
$317$	−1.89395	−	26.4809i	−0.106375	−	1.48731i	0.611557	−	0.791200i	$-0.290543\pi$
$318$	−0.385795	+	2.69585i	−0.0216343	+	0.151176i
$319$	−16.2965	+	35.6844i	−0.912429	+	1.99794i
$320$	17.7763	+	2.00102i	0.993724	+	0.111860i
$321$	10.4364			0.582500
$322$	−17.9300	+	13.2158i	−0.999201	+	0.736488i
$323$	10.0204	−	10.0204i	0.557552	−	0.557552i
$324$	0.648638	−	0.750561i	0.0360354	−	0.0416978i
$325$	−8.24996	−	30.0764i	−0.457626	−	1.66834i
$326$	2.45081	+	3.26942i	0.135738	+	0.181076i
$327$	0.211847	−	0.0151516i	0.0117152	−	0.000837884i
$328$	12.6556	−	0.0249744i	0.698787	−	0.00137898i
$329$	7.25313	+	11.2861i	0.399878	+	0.622223i
$330$	18.3494	+	0.807604i	1.01010	+	0.0444571i
$331$	21.7740	−	18.8673i	1.19681	−	1.03704i	0.198427	−	0.980116i	$-0.436417\pi$
$331$	21.7740	−	18.8673i	1.19681	−	1.03704i	0.998379	−	0.0569224i	$-0.0181288\pi$
$332$	−11.8956	−	8.88053i	−0.652856	−	0.487383i
$333$	−6.68467	+	5.00408i	−0.366318	+	0.274222i
$334$	−6.81032	−	31.2077i	−0.372644	−	1.70761i
$335$	−18.5613	−	13.1349i	−1.01411	−	0.717636i
$336$	11.4268	−	7.38613i	0.623384	−	0.402946i
$337$	−15.5227	−	5.78965i	−0.845573	−	0.315382i	−0.110923	−	0.993829i	$-0.535381\pi$
$337$	−15.5227	−	5.78965i	−0.845573	−	0.315382i	−0.734650	+	0.678447i	$0.762653\pi$
$338$	36.2605	−	5.23782i	1.97231	−	0.284900i
$339$	13.5937	+	3.99148i	0.738311	+	0.216788i
$340$	−0.967097	+	22.3072i	−0.0524482	+	1.20978i
$341$	0.992867	−	0.291532i	0.0537668	−	0.0157874i
$342$	5.84312	−	5.06982i	0.315960	−	0.274145i
$343$	8.45068	+	6.32610i	0.456294	+	0.341577i
$344$	−3.89614	+	7.16885i	−0.210066	+	0.386519i
$345$	−0.585289	+	11.0916i	−0.0315109	+	0.597154i
$346$	10.8105	−	4.04020i	0.581174	−	0.217202i
$347$	8.91700	−	11.9117i	0.478690	−	0.639455i	−0.494577	−	0.869134i	$-0.664677\pi$
$347$	8.91700	−	11.9117i	0.478690	−	0.639455i	0.973266	+	0.229679i	$0.0737678\pi$
$348$	12.7277	+	6.92811i	0.682274	+	0.371386i
$349$	4.18281	+	14.2453i	0.223900	+	0.762535i	0.992440	+	0.122732i	$0.0391657\pi$
$349$	4.18281	+	14.2453i	0.223900	+	0.762535i	−0.768539	+	0.639803i	$0.779016\pi$
$350$	−20.9547	−	10.0094i	−1.12007	−	0.535026i
$351$	−8.96810	+	30.5426i	−0.478682	+	1.63024i
$352$	0.104334	+	31.7223i	0.00556102	+	1.69080i
$353$	−9.82947	+	26.3538i	−0.523170	+	1.40267i	0.359706	+	0.933066i	$0.382877\pi$
$353$	−9.82947	+	26.3538i	−0.523170	+	1.40267i	−0.882876	+	0.469607i	$0.844396\pi$
$354$	−0.0991770	+	0.181914i	−0.00527120	+	0.00966860i
$355$	−3.54509	−	20.7071i	−0.188154	−	1.09902i
$356$	−5.22239	−	8.10274i	−0.276786	−	0.429445i
$357$	10.1775	+	13.5956i	0.538651	+	0.719554i
$358$	−12.6260	+	8.12595i	−0.667303	+	0.429470i
$359$	5.86217	+	6.76530i	0.309393	+	0.357059i	0.889057	−	0.457797i	$-0.151361\pi$
$359$	5.86217	+	6.76530i	0.309393	+	0.357059i	−0.579663	+	0.814856i	$0.696816\pi$
$360$	−1.38736	+	12.1097i	−0.0731204	+	0.638240i
$361$	−9.20659	+	5.91671i	−0.484557	+	0.311406i
$362$	−4.26748	+	4.93148i	−0.224294	+	0.259193i
$363$	1.51082	+	21.1241i	0.0792977	+	1.10873i
$364$	22.1046	−	34.4951i	1.15859	−	1.80803i
$365$	−13.4955	+	26.3688i	−0.706385	+	1.38020i
$366$	6.37441	−	3.48614i	0.333196	−	0.182223i
$367$	10.7681	+	10.7681i	0.562090	+	0.562090i	0.929901	−	0.367810i	$-0.119892\pi$
$367$	10.7681	+	10.7681i	0.562090	+	0.562090i	−0.367810	+	0.929901i	$0.619892\pi$
$368$	−19.1830	−	0.104481i	−0.999985	−	0.00544647i
$369$			8.62332i			0.448912i
$370$	4.43439	−	12.9638i	0.230533	−	0.673955i
$371$	5.55421	+	2.53652i	0.288360	+	0.131690i
$372$	−0.0817427	−	0.373399i	−0.00423816	−	0.0193599i
$373$	8.90728	−	0.637061i	0.461201	−	0.0329858i	0.161194	−	0.986923i	$-0.448465\pi$
$373$	8.90728	−	0.637061i	0.461201	−	0.0329858i	0.300007	+	0.953937i	$0.403011\pi$
$374$	−39.4927	+	2.85068i	−2.04212	+	0.147405i
$375$	−10.4904	+	4.90375i	−0.541720	+	0.253229i
$376$	−0.801518	+	11.5263i	−0.0413351	+	0.594423i
$377$	43.5233	+	3.11285i	2.24157	+	0.160320i
$378$	12.8277	+	19.9314i	0.659783	+	1.02516i
$379$	−1.88342	+	13.0995i	−0.0967448	+	0.672875i	0.882518	+	0.470279i	$0.155847\pi$
$379$	−1.88342	+	13.0995i	−0.0967448	+	0.672875i	−0.979262	+	0.202596i	$0.935062\pi$
$380$	−3.23286	+	12.2748i	−0.165842	+	0.629684i
$381$	−2.27642	−	1.46297i	−0.116625	−	0.0749501i
$382$	−5.65620	−	19.2165i	−0.289397	−	0.983201i
$383$	−0.644020	−	0.240207i	−0.0329079	−	0.0122740i	0.332956	−	0.942942i	$-0.391954\pi$
$383$	−0.644020	−	0.240207i	−0.0329079	−	0.0122740i	−0.365864	+	0.930668i	$0.619227\pi$
$384$	11.6919	+	0.782129i	0.596651	+	0.0399128i
$385$	13.3539	−	38.9561i	0.680580	−	1.98539i
$386$	−1.02377	+	2.75035i	−0.0521084	+	0.139989i
$387$	−4.87949	−	2.66440i	−0.248038	−	0.135439i
$388$	1.97388	−	3.62622i	0.100208	−	0.184093i
$389$	−29.1176	+	4.18648i	−1.47632	+	0.212263i	−0.832974	−	0.553313i	$-0.813363\pi$
$389$	−29.1176	+	4.18648i	−1.47632	+	0.212263i	−0.643346	+	0.765575i	$0.722454\pi$
$390$	−6.29085	−	19.4369i	−0.318550	−	0.984226i
$391$	−1.51519	−	23.8963i	−0.0766266	−	1.20849i
$392$	−3.03696	−	10.2679i	−0.153390	−	0.518609i
$393$	4.02981	−	5.38319i	0.203277	−	0.271546i
$394$	13.6515	+	0.967346i	0.687750	+	0.0487342i
$395$	−0.248429	+	0.410299i	−0.0124998	+	0.0206444i
$396$	−21.6151	+	0.0284367i	−1.08620	+	0.00142900i
$397$	23.3484	−	12.7492i	1.17182	−	0.639862i	0.229086	−	0.973406i	$-0.426426\pi$
$397$	23.3484	−	12.7492i	1.17182	−	0.639862i	0.942735	+	0.333544i	$0.108245\pi$
$398$	−3.72869	−	25.8130i	−0.186902	−	1.29389i
$399$	4.01070	+	8.78220i	0.200786	+	0.439660i
$400$	−9.31613	−	17.6977i	−0.465807	−	0.884887i
$401$	−5.63071	−	3.61864i	−0.281184	−	0.180706i	0.392445	−	0.919775i	$-0.371629\pi$
$401$	−5.63071	−	3.61864i	−0.281184	−	0.180706i	−0.673630	+	0.739069i	$0.735266\pi$
$402$	−12.5359	−	8.04470i	−0.625235	−	0.401233i
$403$	−0.689755	−	0.921405i	−0.0343592	−	0.0458985i
$404$	−1.39723	−	9.62802i	−0.0695148	−	0.479012i
$405$	−1.10164	−	0.128413i	−0.0547407	−	0.00638088i
$406$	22.9594	−	22.9896i	1.13945	−	1.14095i
$407$	23.7416	+	5.16468i	1.17683	+	0.256004i
$408$	0.0288633	+	14.6263i	0.00142894	+	0.724108i
$409$	8.66519	+	7.50843i	0.428466	+	0.371268i	0.842232	−	0.539115i	$-0.181241\pi$
$409$	8.66519	+	7.50843i	0.428466	+	0.371268i	−0.413766	+	0.910383i	$0.635787\pi$
$410$	−7.97316	−	11.6891i	−0.393766	−	0.577281i
$411$	−4.27323	−	1.95152i	−0.210783	−	0.0962614i
$412$	1.60230	+	21.9964i	0.0789396	+	1.08368i
$413$	0.328487	+	0.328487i	0.0161638	+	0.0161638i
$414$	0.0969859	−	13.0708i	0.00476660	−	0.642397i
$415$	−0.740678	+	16.5805i	−0.0363585	+	0.813904i
$416$	33.0191	−	12.4393i	1.61889	−	0.609889i
$417$	−2.50988	−	6.72925i	−0.122909	−	0.329533i
$418$	−22.2827	−	3.18880i	−1.08988	−	0.155969i
$419$	−4.20663	+	4.85471i	−0.205507	+	0.237168i	−0.849142	−	0.528165i	$-0.822880\pi$
$419$	−4.20663	+	4.85471i	−0.205507	+	0.237168i	0.643634	+	0.765333i	$0.277426\pi$
$420$	−14.0094	−	5.92844i	−0.683587	−	0.289278i
$421$	8.79526	−	5.65237i	0.428655	−	0.275480i	−0.308473	−	0.951233i	$-0.599818\pi$
$421$	8.79526	−	5.65237i	0.428655	−	0.275480i	0.737128	+	0.675753i	$0.236182\pi$
$422$	0.0125629	+	19.0985i	0.000611553	+	0.929701i
$423$	−7.85274	−	0.561639i	−0.381813	−	0.0273078i
$424$	2.52932	+	4.61046i	0.122835	+	0.223904i
$425$	21.2388	−	13.1187i	1.03023	−	0.636349i
$426$	−2.93411	−	13.4453i	−0.142158	−	0.651427i
$427$	−3.46268	−	15.9177i	−0.167571	−	0.770310i
$428$	16.1170	−	12.0981i	0.779044	−	0.584786i
$429$	32.9547	−	15.0499i	1.59107	−	0.726615i
$430$	9.07775	−	0.899953i	0.437768	−	0.0433996i
$431$	−5.08502	+	17.3180i	−0.244937	+	0.834178i	0.741629	+	0.670811i	$0.234054\pi$
$431$	−5.08502	+	17.3180i	−0.244937	+	0.834178i	−0.986565	+	0.163367i	$0.947764\pi$
$432$	−1.40269	+	20.3651i	−0.0674871	+	0.979817i
$433$	−6.06058	−	3.30933i	−0.291253	−	0.159036i	0.326980	−	0.945031i	$-0.393969\pi$
$433$	−6.06058	−	3.30933i	−0.291253	−	0.159036i	−0.618232	+	0.785995i	$0.712151\pi$
$434$	−0.854889	−	0.0605777i	−0.0410360	−	0.00290782i
$435$	−1.58775	−	16.1236i	−0.0761270	−	0.773065i
$436$	0.309593	−	0.268978i	0.0148268	−	0.0128817i
$437$	2.04598	−	13.4575i	0.0978726	−	0.643760i
$438$	−8.04906	+	17.6557i	−0.384599	+	0.843623i
$439$	−3.13985	−	21.8381i	−0.149857	−	1.04228i	−0.916452	−	0.400145i	$-0.868960\pi$
$439$	−3.13985	−	21.8381i	−0.149857	−	1.04228i	0.766595	−	0.642131i	$-0.221949\pi$
$440$	29.2734	−	20.0240i	1.39555	−	0.954606i
$441$	7.00047	−	2.05552i	0.333356	−	0.0978821i
$442$	18.3219	+	40.0496i	0.871483	+	1.90496i
$443$	−20.8586	+	11.3897i	−0.991024	+	0.541140i	−0.891077	−	0.453853i	$-0.850049\pi$
$443$	−20.8586	+	11.3897i	−0.991024	+	0.541140i	−0.0999471	+	0.994993i	$0.531867\pi$
$444$	2.51725	−	8.61487i	0.119463	−	0.408844i
$445$	−4.21334	+	9.92006i	−0.199731	+	0.470256i
$446$	−14.8553	+	27.2481i	−0.703421	+	1.29024i
$447$	2.22368	+	10.2221i	0.105177	+	0.483489i
$448$	9.08435	−	24.6528i	0.429195	−	1.16474i
$449$	14.5975	+	2.09881i	0.688899	+	0.0990487i	0.477869	−	0.878431i	$-0.341409\pi$
$449$	14.5975	+	2.09881i	0.688899	+	0.0990487i	0.211030	+	0.977480i	$0.432318\pi$
$450$	12.0714	−	6.32405i	0.569054	−	0.298119i
$451$	18.9630	−	16.4315i	0.892933	−	0.773731i
$452$	25.6200	−	9.59419i	1.20506	−	0.451273i
$453$	−19.8310	−	4.31396i	−0.931740	−	0.202688i
$454$	18.8454	−	1.36031i	0.884459	−	0.0638426i
$455$	−45.7892	+	1.22551i	−2.14663	+	0.0574530i
$456$	−1.75143	+	8.12837i	−0.0820181	+	0.380646i
$457$	10.4521	+	28.0231i	0.488928	+	1.31087i	0.914002	+	0.405709i	$0.132975\pi$
$457$	10.4521	+	28.0231i	0.488928	+	1.31087i	−0.425074	+	0.905158i	$0.639752\pi$
$458$	−1.22759	+	4.19098i	−0.0573615	+	0.195832i
$459$	−25.4796			−1.18929
$460$	11.9539	+	17.8074i	0.557353	+	0.830276i
$461$	−4.99997			−0.232872			−0.116436	−	0.993198i	$-0.537147\pi$
$461$	−4.99997			−0.232872			−0.116436	+	0.993198i	$0.537147\pi$
$462$	7.58306	−	25.8885i	0.352796	−	1.20444i
$463$	−5.57695	−	14.9524i	−0.259183	−	0.694896i	−0.999738	−	0.0228999i	$-0.992710\pi$
$463$	−5.57695	−	14.9524i	−0.259183	−	0.694896i	0.740555	−	0.671996i	$-0.234563\pi$
$464$	27.6867	−	4.05514i	1.28533	−	0.188255i
$465$	−0.293996	+	0.310166i	−0.0136337	+	0.0143836i
$466$	−6.11237	+	0.441207i	−0.283150	+	0.0204385i
$467$	−26.6149	−	5.78971i	−1.23159	−	0.267916i	−0.450752	−	0.892649i	$-0.648844\pi$
$467$	−26.6149	−	5.78971i	−1.23159	−	0.267916i	−0.780838	+	0.624733i	$0.785208\pi$
$468$	8.43155	+	22.5153i	0.389748	+	1.04077i
$469$	−25.2396	+	21.8703i	−1.16546	+	1.00987i
$470$	11.1638	−	6.49936i	0.514948	−	0.299793i
$471$	−14.0514	−	2.02028i	−0.647454	−	0.0930898i
$472$	0.0577195	+	0.395900i	0.00265676	+	0.0182228i
$473$	3.43863	+	15.8071i	0.158109	+	0.726813i
$474$	−0.150398	+	0.275864i	−0.00690799	+	0.0126708i
$475$	13.3834	−	4.72089i	0.614074	−	0.216609i
$476$	31.4777	+	9.19771i	1.44278	+	0.421576i
$477$	−3.14488	+	1.71724i	−0.143994	+	0.0786269i
$478$	1.77495	+	3.87984i	0.0811843	+	0.177460i
$479$	37.3606	−	10.9700i	1.70705	−	0.501234i	0.724821	−	0.688937i	$-0.241922\pi$
$479$	37.3606	−	10.9700i	1.70705	−	0.501234i	0.982226	+	0.187702i	$0.0601041\pi$
$480$	−6.62134	−	11.3048i	−0.302221	−	0.515992i
$481$	−3.84608	−	26.7501i	−0.175366	−	1.21970i
$482$	10.5000	−	23.0318i	0.478260	−	1.04907i
$483$	15.6148	+	4.72224i	0.710496	+	0.214869i
$484$	26.8209	+	30.8708i	1.21913	+	1.40322i
$485$	−4.59374	+	0.452365i	−0.208591	+	0.0205408i
$486$	−22.3222	−	1.58176i	−1.01256	−	0.0717499i
$487$	−24.4419	−	13.3463i	−1.10757	−	0.604779i	−0.181978	−	0.983303i	$-0.558250\pi$
$487$	−24.4419	−	13.3463i	−1.10757	−	0.604779i	−0.925592	+	0.378524i	$0.876432\pi$
$488$	5.80284	−	12.7731i	0.262682	−	0.578211i
$489$	0.843089	−	2.87130i	0.0381258	−	0.129845i
$490$	−7.58871	+	9.25896i	−0.342823	+	0.418277i
$491$	−28.2444	+	12.8988i	−1.27465	+	0.582113i	−0.933730	−	0.357979i	$-0.883466\pi$
$491$	−28.2444	+	12.8988i	−1.27465	+	0.582113i	−0.340920	+	0.940092i	$0.610739\pi$
$492$	−5.56427	−	7.41265i	−0.250857	−	0.334188i
$493$	7.42424	+	34.1287i	0.334371	+	1.53708i
$494$	5.33814	+	24.4616i	0.240174	+	1.10058i
$495$	13.6046	+	19.9733i	0.611483	+	0.897733i
$496$	−0.559092	−	0.481886i	−0.0251040	−	0.0216373i
$497$	−30.7769	−	2.20121i	−1.38053	−	0.0987375i
$498$	0.00715157	+	10.8720i	0.000320469	+	0.487187i
$499$	−16.6957	+	10.7297i	−0.747403	+	0.480327i	−0.858071	−	0.513531i	$-0.828337\pi$
$499$	−16.6957	+	10.7297i	−0.747403	+	0.480327i	0.110668	+	0.993857i	$0.464701\pi$
$500$	−10.5158	+	19.7337i	−0.470281	+	0.882517i
$501$	−15.3196	+	17.6798i	−0.684431	+	0.789875i
$502$	3.58102	+	0.512469i	0.159829	+	0.0228726i
$503$	11.8990	+	31.9024i	0.530549	+	1.42246i	0.875216	+	0.483733i	$0.160719\pi$
$503$	11.8990	+	31.9024i	0.530549	+	1.42246i	−0.344666	+	0.938725i	$0.612008\pi$
$504$	16.7858	+	6.22306i	0.747698	+	0.277197i
$505$	−8.02693	+	7.34044i	−0.357194	+	0.326645i
$506$	−28.9281	+	24.6929i	−1.28601	+	1.09773i
$507$	−18.9731	−	18.9731i	−0.842625	−	0.842625i
$508$	−5.21142	+	0.379620i	−0.231219	+	0.0168429i
$509$	−10.8737	−	4.96583i	−0.481966	−	0.220107i	0.159589	−	0.987184i	$-0.448983\pi$
$509$	−10.8737	−	4.96583i	−0.481966	−	0.220107i	−0.641555	+	0.767077i	$0.721710\pi$
$510$	13.5092	−	9.21471i	0.598199	−	0.408034i
$511$	32.8796	+	28.4903i	1.45451	+	1.26034i
$512$	18.9626	−	12.3458i	0.838038	−	0.545612i
$513$	−14.1539	−	3.07900i	−0.624911	−	0.135941i
$514$	22.6949	−	22.7248i	1.00103	−	1.00235i
$515$	19.3372	−	15.2997i	0.852099	−	0.674187i
$516$	5.91367	−	0.858199i	0.260335	−	0.0377801i
$517$	13.7281	+	18.3387i	0.603763	+	0.806533i
$518$	−16.9359	−	10.8683i	−0.744123	−	0.477527i
$519$	−7.11045	−	4.56961i	−0.312114	−	0.200584i
$520$	−32.2469	−	22.7241i	−1.41412	−	0.996517i
$521$	−17.8582	−	39.1041i	−0.782383	−	1.71318i	−0.697270	−	0.716808i	$-0.745602\pi$
$521$	−17.8582	−	39.1041i	−0.782383	−	1.71318i	−0.0851127	−	0.996371i	$-0.527125\pi$
$522$	2.72587	+	18.8707i	0.119308	+	0.825949i
$523$	−9.02744	+	4.92935i	−0.394742	+	0.215546i	−0.664345	−	0.747426i	$-0.731289\pi$
$523$	−9.02744	+	4.92935i	−0.394742	+	0.215546i	0.269603	+	0.962972i	$0.413108\pi$
$524$	−0.0170827	−	12.9848i	−0.000746260	−	0.567244i
$525$	3.31746	+	16.6810i	0.144786	+	0.728018i
$526$	30.2638	+	2.14450i	1.31957	+	0.0935048i
$527$	0.552109	−	0.737531i	0.0240502	−	0.0321274i
$528$	18.5621	−	13.9718i	0.807813	−	0.608044i
$529$	−14.7790	−	17.6233i	−0.642566	−	0.766230i
$530$	2.67518	−	5.23552i	0.116202	−	0.227416i
$531$	−0.269837	+	0.0387967i	−0.0117099	+	0.00168363i
$532$	16.3744	+	8.91314i	0.709919	+	0.386433i
$533$	−24.4953	−	13.3754i	−1.06101	−	0.579355i
$534$	−2.46289	+	6.61654i	−0.106579	+	0.286326i
$535$	−21.3137	−	7.30620i	−0.921470	−	0.315875i
$536$	−28.6850	+	2.10850i	−1.23900	+	0.0910733i
$537$	10.3032	+	3.84290i	0.444617	+	0.165833i
$538$	−2.58799	−	8.79249i	−0.111576	−	0.379071i
$539$	−17.8594	−	11.4775i	−0.769259	−	0.494373i
$540$	19.7162	−	11.4958i	0.848450	−	0.494700i
$541$	−3.46847	+	24.1238i	−0.149121	+	1.03716i	0.768541	+	0.639801i	$0.220983\pi$
$541$	−3.46847	+	24.1238i	−0.149121	+	1.03716i	−0.917662	+	0.397361i	$0.869926\pi$
$542$	8.92153	+	13.8621i	0.383213	+	0.595429i
$543$	4.76409	+	0.340734i	0.204447	+	0.0146223i
$544$	16.9998	+	22.5540i	0.728860	+	0.966997i
$545$	−0.443252	−	0.117365i	−0.0189868	−	0.00502736i
$546$	−29.9275	+	2.16025i	−1.28078	+	0.0924500i
$547$	−29.3101	+	2.09630i	−1.25321	+	0.0896312i	−0.682109	−	0.731250i	$-0.738937\pi$
$547$	−29.3101	+	2.09630i	−1.25321	+	0.0896312i	−0.571098	+	0.820882i	$0.693483\pi$
$548$	−8.86146	+	1.93991i	−0.378543	+	0.0828687i
$549$	8.69556	+	3.97113i	0.371117	+	0.169484i
$550$	−36.9087	−	14.4952i	−1.57379	−	0.618079i
$551$			19.8556i			0.845878i
$552$	8.35071	+	11.2984i	0.355430	+	0.480890i
$553$	0.498135	+	0.498135i	0.0211829	+	0.0211829i
$554$	−33.6156	+	18.3842i	−1.42819	+	0.781070i
$555$	−9.54893	+	3.08362i	−0.405329	+	0.130892i
$556$	−11.6768	−	7.48253i	−0.495206	−	0.317330i
$557$	−1.81518	−	25.3796i	−0.0769118	−	1.07537i	−0.878579	−	0.477597i	$-0.841508\pi$
$557$	−1.81518	−	25.3796i	−0.0769118	−	1.07537i	0.801667	−	0.597770i	$-0.203947\pi$
$558$	0.329101	−	0.380308i	0.0139319	−	0.0160997i
$559$	15.1369	−	9.72792i	0.640224	−	0.411447i
$560$	−28.5073	+	7.08473i	−1.20465	+	0.299384i
$561$	18.9902	+	21.9159i	0.801767	+	0.925288i
$562$	37.3604	−	24.0448i	1.57595	−	1.01427i
$563$	0.280125	+	0.374203i	0.0118059	+	0.0157708i	0.806405	−	0.591363i	$-0.201410\pi$
$563$	0.280125	+	0.374203i	0.0118059	+	0.0157708i	−0.794599	+	0.607134i	$0.792319\pi$
$564$	7.11266	−	4.58426i	0.299497	−	0.193032i
$565$	−24.9675	−	17.6682i	−1.05039	−	0.743308i
$566$	−20.1554	+	36.9696i	−0.847194	+	1.55395i
$567$	−0.569260	+	1.52625i	−0.0239067	+	0.0640963i
$568$	−20.1174	−	17.3624i	−0.844107	−	0.728512i
$569$	−0.987452	+	3.36295i	−0.0413961	+	0.140982i	−0.977598	−	0.210480i	$-0.932497\pi$
$569$	−0.987452	+	3.36295i	−0.0413961	+	0.140982i	0.936202	+	0.351462i	$0.114315\pi$
$570$	8.61790	−	3.48629i	0.360964	−	0.146025i
$571$	6.24708	+	21.2756i	0.261432	+	0.890356i	0.980683	+	0.195605i	$0.0626671\pi$
$571$	6.24708	+	21.2756i	0.261432	+	0.890356i	−0.719251	+	0.694751i	$0.755515\pi$
$572$	33.4460	−	61.4438i	1.39845	−	2.56909i
$573$	−8.79184	+	11.7445i	−0.367284	+	0.490634i
$574$	−19.4665	+	7.27521i	−0.812514	+	0.303661i
$575$	8.96026	−	22.2422i	0.373669	−	0.927562i
$576$	8.38670	+	12.9374i	0.349446	+	0.539059i
$577$	9.65202	+	7.22541i	0.401819	+	0.300798i	0.781008	−	0.624521i	$-0.214706\pi$
$577$	9.65202	+	7.22541i	0.401819	+	0.300798i	−0.379189	+	0.925319i	$0.623797\pi$
$578$	−8.46793	+	7.34726i	−0.352219	+	0.305606i
$579$	2.06226	−	0.605533i	0.0857045	−	0.0251651i
$580$	−21.1429	−	23.0592i	−0.877911	−	0.957482i
$581$	23.3890	+	6.86763i	0.970339	+	0.284917i
$582$	−2.99266	+	0.432290i	−0.124050	+	0.0179190i
$583$	9.76877	+	3.64356i	0.404581	+	0.150901i
$584$	8.03678	+	36.5966i	0.332564	+	1.51438i
$585$	15.5272	−	21.9419i	0.641969	−	0.907186i
$586$	−0.686312	−	3.14496i	−0.0283513	−	0.129917i
$587$	0.0178586	−	0.0133688i	0.000737104	−	0.000551789i	−0.598909	−	0.800817i	$-0.704399\pi$
$587$	0.0178586	−	0.0133688i	0.000737104	−	0.000551789i	0.599646	+	0.800265i	$0.295308\pi$
$588$	−4.69130	+	6.28405i	−0.193466	+	0.259150i
$589$	0.395821	−	0.342981i	0.0163095	−	0.0141323i
$590$	0.329897	−	0.302082i	0.0135816	−	0.0124365i
$591$	−5.41890	−	8.43197i	−0.222904	−	0.346845i
$592$	−6.09921	−	16.2221i	−0.250676	−	0.666725i
$593$	−24.7646	+	1.77120i	−1.01696	+	0.0727344i	−0.569853	−	0.821747i	$-0.693000\pi$
$593$	−24.7646	+	1.77120i	−1.01696	+	0.0727344i	−0.447106	+	0.894481i	$0.647545\pi$
$594$	24.2756	+	32.3840i	0.996041	+	1.32873i
$595$	−11.2672	−	34.8906i	−0.461909	−	1.43037i
$596$	15.2838	+	13.2084i	0.626051	+	0.541036i
$597$	−13.5065	+	13.5065i	−0.552785	+	0.552785i
$598$	36.9784	+	20.5494i	1.51216	+	0.840327i
$599$	14.0750			0.575088			0.287544	−	0.957767i	$-0.407161\pi$
$599$	14.0750			0.575088			0.287544	+	0.957767i	$0.407161\pi$
$600$	−6.29603	+	13.2254i	−0.257034	+	0.539925i
$601$	6.97366	−	15.2702i	0.284461	−	0.622884i	−0.712424	−	0.701750i	$-0.752403\pi$
$601$	6.97366	−	15.2702i	0.284461	−	0.622884i	0.996885	+	0.0788657i	$0.0251298\pi$
$602$	1.89802	−	13.2629i	0.0773574	−	0.540557i
$603$	−1.39812	−	19.5483i	−0.0569360	−	0.796069i
$604$	−35.6261	+	16.3266i	−1.44960	+	0.664318i
$605$	11.7029	−	44.1984i	0.475791	−	1.79692i
$606$	−5.03497	+	5.04160i	−0.204532	+	0.204801i
$607$	−2.29295	+	32.0596i	−0.0930680	+	1.30126i	0.709502	+	0.704703i	$0.248920\pi$
$607$	−2.29295	+	32.0596i	−0.0930680	+	1.30126i	−0.802570	+	0.596558i	$0.796535\pi$
$608$	6.71791	+	14.5830i	0.272447	+	0.591421i
$609$	−23.5534	−	3.38646i	−0.954430	−	0.137226i
$610$	−15.4587	+	2.65702i	−0.625904	+	0.107579i
$611$	13.7756	−	21.4352i	0.557301	−	0.867177i
$612$	−15.3908	+	11.5530i	−0.622136	+	0.467003i
$613$	2.45400	−	6.57943i	0.0991161	−	0.265741i	−0.877923	−	0.478803i	$-0.841071\pi$
$613$	2.45400	−	6.57943i	0.0991161	−	0.265741i	0.977039	+	0.213062i	$0.0683437\pi$
$614$	−9.96251	+	13.3266i	−0.402054	+	0.537818i
$615$	−3.36033	+	9.80275i	−0.135502	+	0.395285i
$616$	−18.3001	−	48.7704i	−0.737334	−	1.96502i
$617$	12.9651	−	23.7439i	0.521957	−	0.955892i	−0.475152	−	0.879904i	$-0.657607\pi$
$617$	12.9651	−	23.7439i	0.521957	−	0.955892i	0.997109	−	0.0759886i	$-0.0242113\pi$
$618$	12.2002	−	10.5856i	0.490763	−	0.425814i
$619$	−0.760372	−	5.28850i	−0.0305619	−	0.212563i	0.968818	−	0.247773i	$-0.0796989\pi$
$619$	−0.760372	−	5.28850i	−0.0305619	−	0.212563i	−0.999380	+	0.0352107i	$0.988790\pi$
$620$	−0.0944675	+	0.819801i	−0.00379391	+	0.0329240i
$621$	−19.7109	+	14.5084i	−0.790971	+	0.582203i
$622$	44.0643	+	20.0885i	1.76682	+	0.805474i
$623$	12.6722	+	9.48627i	0.507700	+	0.380059i
$624$	−21.7760	−	13.9138i	−0.871739	−	0.556997i
$625$	24.8569	−	2.67068i	0.994278	−	0.106827i
$626$	−5.08860	+	13.6705i	−0.203382	+	0.546384i
$627$	7.90070	+	14.4691i	0.315524	+	0.577839i
$628$	−24.0417	+	13.1689i	−0.959368	+	0.525494i
$629$	19.6772	−	8.98629i	0.784582	−	0.358307i
$630$	−4.78908	−	19.4339i	−0.190801	−	0.774264i
$631$	−6.50361	+	10.1198i	−0.258905	+	0.402864i	−0.946234	−	0.323482i	$-0.895146\pi$
$631$	−6.50361	+	10.1198i	−0.258905	+	0.402864i	0.687330	+	0.726346i	$0.258783\pi$
$632$	0.0875291	+	0.600365i	0.00348172	+	0.0238812i
$633$	11.1974	−	8.38230i	0.445058	−	0.333167i
$634$	−7.95668	+	36.6925i	−0.316000	+	1.45724i
$635$	3.62484	+	4.58141i	0.143847	+	0.181808i
$636$	1.59530	−	3.50541i	0.0632576	−	0.138999i
$637$	−5.01938	+	23.0737i	−0.198875	+	0.914214i
$638$	36.3033	−	41.9520i	1.43726	−	1.66090i
$639$	11.8575	−	13.6843i	0.469076	−	0.541342i
$640$	−23.3303	−	9.78250i	−0.922211	−	0.386687i
$641$	4.69230	−	10.2747i	0.185335	−	0.405827i	−0.794044	−	0.607861i	$-0.792028\pi$
$641$	4.69230	−	10.2747i	0.185335	−	0.405827i	0.979378	+	0.202034i	$0.0647552\pi$
$642$	−14.1641	−	4.14884i	−0.559013	−	0.163742i
$643$	14.0059	−	14.0059i	0.552337	−	0.552337i	−0.374778	−	0.927115i	$-0.622281\pi$
$643$	14.0059	−	14.0059i	0.552337	−	0.552337i	0.927115	+	0.374778i	$0.122281\pi$
$644$	29.5882	−	10.8085i	1.16594	−	0.425914i
$645$	−4.50861	−	4.93026i	−0.177526	−	0.194129i
$646$	−17.5831	+	9.61613i	−0.691799	+	0.378342i
$647$	−23.8466	+	8.89431i	−0.937505	+	0.349671i	−0.771338	−	0.636426i	$-0.780412\pi$
$647$	−23.8466	+	8.89431i	−0.937505	+	0.349671i	−0.166167	+	0.986098i	$0.553139\pi$
$648$	−1.17870	+	0.760796i	−0.0463037	+	0.0298869i
$649$	0.599484	+	0.519456i	0.0235318	+	0.0203904i
$650$	−0.759740	+	44.0991i	−0.0297995	+	1.72971i
$651$	0.339345	+	0.528032i	0.0133000	+	0.0206952i
$652$	−2.02650	−	5.41151i	−0.0793640	−	0.211931i
$653$	2.42126	−	33.8537i	0.0947513	−	1.32480i	−0.698372	−	0.715735i	$-0.746092\pi$
$653$	2.42126	−	33.8537i	0.0947513	−	1.32480i	0.793123	−	0.609062i	$-0.208454\pi$
$654$	−0.293540	−	0.0636534i	−0.0114783	−	0.00248905i
$655$	−11.9985	+	8.17268i	−0.468820	+	0.319333i
$656$	−17.1859	−	4.99717i	−0.670999	−	0.195107i
$657$	−24.9471	+	5.42691i	−0.973280	+	0.211724i
$658$	−5.35723	−	18.2008i	−0.208847	−	0.709540i
$659$	15.5242	+	33.9932i	0.604736	+	1.32419i	0.926117	+	0.377237i	$0.123126\pi$
$659$	15.5242	+	33.9932i	0.604736	+	1.32419i	−0.321381	+	0.946950i	$0.604147\pi$
$660$	−24.5826	−	8.39064i	−0.956875	−	0.326605i
$661$	45.8647	+	13.4671i	1.78393	+	0.523809i	0.995788	−	0.0916848i	$-0.0292252\pi$
$661$	45.8647	+	13.4671i	1.78393	+	0.523809i	0.788142	+	0.615494i	$0.211043\pi$
$662$	−37.0518	+	16.9505i	−1.44006	+	0.658799i
$663$	15.4582	−	28.3096i	0.600347	−	1.09945i
$664$	12.6142	+	16.7815i	0.489527	+	0.651249i
$665$	−2.04267	−	20.7432i	−0.0792115	−	0.804389i
$666$	11.0617	−	4.13408i	0.428631	−	0.160192i
$667$	25.1767	+	22.1743i	0.974844	+	0.858592i
$668$	−3.16332	+	45.0621i	−0.122393	+	1.74350i
$669$	22.4977	−	3.23468i	0.869810	−	0.125060i
$670$	19.9696	+	25.2054i	0.771494	+	0.973768i
$671$	−7.83652	−	26.6887i	−0.302526	−	1.03031i
$672$	−18.4446	+	5.48179i	−0.711517	+	0.211465i
$673$	23.6602	+	43.3305i	0.912035	+	1.67027i	0.725965	+	0.687732i	$0.241394\pi$
$673$	23.6602	+	43.3305i	0.912035	+	1.67027i	0.186071	+	0.982536i	$0.440425\pi$
$674$	18.7656	+	14.0285i	0.722823	+	0.540357i
$675$	−23.0175	−	11.0134i	−0.885945	−	0.423906i
$676$	−51.2946	−	7.30618i	−1.97287	−	0.281007i
$677$	−17.5131	+	3.80975i	−0.673085	+	0.146421i	−0.536102	−	0.844153i	$-0.680104\pi$
$677$	−17.5131	+	3.80975i	−0.673085	+	0.146421i	−0.136982	+	0.990574i	$0.543740\pi$
$678$	−16.8625	−	10.8212i	−0.647602	−	0.415587i
$679$	−0.964832	+	6.71055i	−0.0370269	+	0.257527i
$680$	10.1805	−	29.8907i	0.390404	−	1.14626i
$681$	−9.06189	−	10.4580i	−0.347252	−	0.400750i
$682$	−1.46340		0.000962620i	−0.0560366		3.68606e-5i
$683$	−8.14249	+	37.4304i	−0.311564	+	1.43224i	0.509042	+	0.860741i	$0.330000\pi$
$683$	−8.14249	+	37.4304i	−0.311564	+	1.43224i	−0.820606	+	0.571494i	$0.806364\pi$
$684$	−9.94566	+	4.55786i	−0.380282	+	0.174274i
$685$	7.36081	+	6.97707i	0.281242	+	0.266580i
$686$	−8.95432	−	11.9452i	−0.341877	−	0.456069i
$687$	2.99669	−	1.11771i	0.114331	−	0.0426432i
$688$	8.13769	−	8.18063i	0.310247	−	0.311884i
$689$		−	11.5969i		−	0.441806i
$690$	5.20369	−	14.8208i	0.198101	−	0.564217i
$691$			25.6337i			0.975152i	0.873080	+	0.487576i	$0.162119\pi$
$691$			25.6337i			0.975152i	−0.873080	+	0.487576i	$0.837881\pi$
$692$	−16.2780	+	1.18575i	−0.618796	+	0.0450755i
$693$	33.2559	−	12.4038i	1.26329	−	0.471182i
$694$	−16.8374	+	12.6216i	−0.639140	+	0.479110i
$695$	0.414844	+	15.4999i	0.0157359	+	0.587945i
$696$	−14.5197	−	14.4625i	−0.550367	−	0.548199i
$697$	4.74864	−	21.8291i	0.179867	−	0.826837i
$698$	−0.0138113	−	20.9964i	−0.000522767	−	0.794727i
$699$	2.93916	+	3.39197i	0.111169	+	0.128296i
$700$	24.4603	+	21.9149i	0.924513	+	0.828307i
$701$	6.26189	−	43.5524i	0.236508	−	1.64495i	−0.432455	−	0.901655i	$-0.642353\pi$
$701$	6.26189	−	43.5524i	0.236508	−	1.64495i	0.668963	−	0.743295i	$-0.266738\pi$
$702$	24.3132	−	37.8869i	0.917644	−	1.42995i
$703$	12.0166	−	2.61405i	0.453215	−	0.0985909i
$704$	12.4692	−	43.0946i	0.469950	−	1.62419i
$705$	−8.70791	−	3.69850i	−0.327959	−	0.139294i
$706$	23.8171	−	31.8596i	0.896368	−	1.19905i
$707$	7.65629	+	14.0214i	0.287944	+	0.527331i
$708$	0.206919	−	0.207465i	0.00777651	−	0.00779700i
$709$	−3.70683	−	12.6243i	−0.139213	−	0.474115i	0.860141	−	0.510056i	$-0.170375\pi$
$709$	−3.70683	−	12.6243i	−0.139213	−	0.474115i	−0.999354	+	0.0359409i	$0.988557\pi$
$710$	−3.42050	+	29.5128i	−0.128369	+	1.10760i
$711$	−0.409196	+	0.0588335i	−0.0153460	+	0.00220643i
$712$	3.86663	+	13.0731i	0.144908	+	0.489933i
$713$	0.00714832	−	0.884927i	0.000267707	−	0.0331408i
$714$	−8.40807	−	22.4977i	−0.314664	−	0.841956i
$715$	−77.8377	+	7.66500i	−2.91096	+	0.286655i
$716$	20.3662	−	6.00917i	0.761120	−	0.224573i
$717$	1.49753	−	2.74252i	0.0559263	−	0.102421i
$718$	−5.26661	−	11.5122i	−0.196548	−	0.429632i
$719$	−2.94928	−	0.865986i	−0.109990	−	0.0322958i	0.226275	−	0.974064i	$-0.427345\pi$
$719$	−2.94928	−	0.865986i	−0.109990	−	0.0322958i	−0.336264	+	0.941768i	$0.609163\pi$
$720$	6.69699	−	15.8837i	0.249582	−	0.591951i
$721$	−15.0445	−	32.9428i	−0.560285	−	1.22685i
$722$	14.8472	−	4.37014i	0.552555	−	0.162640i
$723$	−18.1145	+	3.94057i	−0.673687	+	0.146552i
$724$	7.75223	−	4.99648i	0.288109	−	0.185693i
$725$	−8.04507	+	34.0399i	−0.298786	+	1.26421i
$726$	6.34714	−	29.2700i	0.235564	−	1.08631i
$727$	3.35212	−	46.8688i	0.124323	−	1.73827i	−0.427243	−	0.904137i	$-0.640515\pi$
$727$	3.35212	−	46.8688i	0.124323	−	1.73827i	0.551566	−	0.834131i	$-0.314030\pi$
$728$	−43.7132	+	38.0290i	−1.62012	+	1.40945i
$729$	8.05624	+	12.5357i	0.298379	+	0.464287i
$730$	28.7985	−	30.4225i	1.06588	−	1.12599i
$731$	10.8848	+	9.43169i	0.402587	+	0.348844i
$732$	−10.0372	+	2.19728i	−0.370984	+	0.0812139i
$733$	−17.2374	+	6.42921i	−0.636677	+	0.237468i	−0.647014	−	0.762478i	$-0.723982\pi$
$733$	−17.2374	+	6.42921i	−0.636677	+	0.237468i	0.0103365	+	0.999947i	$0.496710\pi$
$734$	−10.3336	−	18.8951i	−0.381422	−	0.697430i
$735$	8.75893	+	0.391276i	0.323078	+	0.0144324i
$736$	25.9935	+	7.76778i	0.958133	+	0.286324i
$737$	−40.3234	+	40.3234i	−1.48533	+	1.48533i
$738$	3.42809	−	11.7035i	0.126190	−	0.430811i
$739$	12.4503	−	27.2623i	0.457990	−	1.00286i	−0.529951	−	0.848028i	$-0.677790\pi$
$739$	12.4503	−	27.2623i	0.457990	−	1.00286i	0.987941	−	0.154830i	$-0.0494830\pi$
$740$	−11.1719	+	15.8315i	−0.410687	+	0.581977i
$741$	12.0080	−	13.8580i	0.441125	−	0.509086i
$742$	−6.52976	−	5.65055i	−0.239715	−	0.207438i
$743$	−5.36590	+	24.6666i	−0.196856	+	0.904931i	0.767650	+	0.640869i	$0.221426\pi$
$743$	−5.36590	+	24.6666i	−0.196856	+	0.904931i	−0.964506	+	0.264062i	$0.914938\pi$
$744$	−0.0374998	+	0.539270i	−0.00137481	+	0.0197706i
$745$	2.61490	−	22.4329i	0.0958024	−	0.821876i
$746$	−12.3421	−	2.67636i	−0.451877	−	0.0979886i
$747$	−11.4516	+	8.57255i	−0.418992	+	0.313653i
$748$	54.7323	+	11.8309i	2.00121	+	0.432580i
$749$	−17.8909	+	27.8388i	−0.653719	+	1.01721i
$750$	16.1868	−	2.48501i	0.591060	−	0.0907398i
$751$	27.1767	−	12.4112i	0.991690	−	0.452890i	0.147575	−	0.989051i	$-0.452853\pi$
$751$	27.1767	−	12.4112i	0.991690	−	0.452890i	0.844116	+	0.536161i	$0.180126\pi$
$752$	5.66994	−	15.3247i	0.206762	−	0.558836i
$753$	−1.26971	−	2.32531i	−0.0462709	−	0.0847389i
$754$	−57.8319	−	21.5269i	−2.10611	−	0.783963i
$755$	37.4797	+	22.6933i	1.36403	+	0.825894i
$756$	−9.48609	−	32.1501i	−0.345006	−	1.16929i
$757$	11.2286	+	8.40561i	0.408109	+	0.305507i	0.783537	−	0.621345i	$-0.213413\pi$
$757$	11.2286	+	8.40561i	0.408109	+	0.305507i	−0.375428	+	0.926852i	$0.622504\pi$
$758$	7.76369	−	17.0297i	0.281990	−	0.618548i
$759$	27.1699	+	6.14071i	0.986204	+	0.222894i
$760$	9.26730	−	15.3741i	0.336160	−	0.557676i
$761$	4.22660	+	29.3967i	0.153214	+	1.06563i	0.910787	+	0.412877i	$0.135476\pi$
$761$	4.22660	+	29.3967i	0.153214	+	1.06563i	−0.757572	+	0.652751i	$0.773615\pi$
$762$	2.50795	+	2.89049i	0.0908535	+	0.104711i
$763$	−0.322749	+	0.591071i	−0.0116843	+	0.0213982i
$764$	0.0372693	+	28.3290i	0.00134836	+	1.02491i
$765$	20.3533	+	6.97700i	0.735876	+	0.252254i
$766$	0.778566	+	0.582029i	0.0281307	+	0.0210295i
$767$	0.308333	−	0.826672i	0.0111333	−	0.0298494i
$768$	−15.5572	−	5.70947i	−0.561373	−	0.206023i
$769$	−11.6378	+	18.1087i	−0.419669	+	0.653018i	−0.985141	−	0.171750i	$-0.945058\pi$
$769$	−11.6378	+	18.1087i	−0.419669	+	0.653018i	0.565471	+	0.824768i	$0.308694\pi$
$770$	−33.6104	+	47.5622i	−1.21123	+	1.71402i
$771$	−23.2821	−	3.34746i	−0.838483	−	0.120556i
$772$	2.48281	−	3.32576i	0.0893584	−	0.119697i
$773$	−0.741239	+	10.3639i	−0.0266605	+	0.372763i	0.966554	+	0.256464i	$0.0825576\pi$
$773$	−0.741239	+	10.3639i	−0.0266605	+	0.372763i	−0.993214	+	0.116299i	$0.962897\pi$
$774$	5.56319	+	5.55588i	0.199965	+	0.199702i
$775$	0.817552	−	0.427618i	0.0293673	−	0.0153605i
$776$	−4.12048	+	4.13678i	−0.147917	+	0.148502i
$777$	1.05139	+	14.7003i	0.0377183	+	0.527371i
$778$	41.1824	+	5.89348i	1.47646	+	0.211292i
$779$	5.27573	−	11.5522i	0.189023	−	0.413902i
$780$	0.810986	+	28.8804i	0.0290380	+	1.03408i
$781$	−52.6865			−1.88527
$782$	−7.44328	+	33.0342i	−0.266171	+	1.18130i
$783$	25.2441	−	25.2441i	0.902152	−	0.902152i
$784$	0.0398436	+	15.1428i	0.00142299	+	0.540815i
$785$	27.2821	+	13.9629i	0.973741	+	0.498358i
$786$	−7.60923	+	5.70402i	−0.271412	+	0.203455i
$787$	−2.31103	+	0.165288i	−0.0823792	+	0.00589187i	−0.112468	−	0.993655i	$-0.535876\pi$
$787$	−2.31103	+	0.165288i	−0.0823792	+	0.00589187i	0.0300888	+	0.999547i	$0.490421\pi$
$788$	−18.1431	−	6.73984i	−0.646320	−	0.240097i
$789$	−12.0131	−	18.6928i	−0.427679	−	0.665481i
$790$	0.500274	−	0.458094i	0.0177990	−	0.0162983i
$791$	−33.9508	+	29.4185i	−1.20715	+	1.04600i
$792$	29.3471	+	8.55423i	1.04281	+	0.303961i
$793$	−24.7678	+	18.5410i	−0.879531	+	0.658409i
$794$	−36.7564	+	8.02119i	−1.30444	+	0.284662i
$795$	−4.24419	+	0.726611i	−0.150526	+	0.0257702i
$796$	−5.20111	+	36.5155i	−0.184348	+	1.29426i
$797$	−4.53648	−	1.69202i	−0.160690	−	0.0599344i	0.267832	−	0.963466i	$-0.413693\pi$
$797$	−4.53648	−	1.69202i	−0.160690	−	0.0599344i	−0.428522	+	0.903531i	$0.640966\pi$
$798$	−1.95202	−	13.5135i	−0.0691009	−	0.478373i
$799$	19.5692	+	5.74603i	0.692308	+	0.203280i
$800$	5.60825	+	27.7227i	0.198282	+	0.980145i
$801$	−8.91295	+	2.61708i	−0.314924	+	0.0924699i
$802$	6.20340	+	7.14960i	0.219050	+	0.252461i
$803$	59.4701	+	44.5188i	2.09866	+	1.57103i
$804$	13.8156	+	15.9017i	0.487237	+	0.560809i
$805$	−28.5834	−	20.5755i	−1.00743	−	0.725190i
$806$	0.569836	+	1.52473i	0.0200716	+	0.0537062i
$807$	−4.02270	+	5.37369i	−0.141606	+	0.189163i
$808$	−1.93119	+	13.6225i	−0.0679390	+	0.479238i
$809$	−0.463497	−	1.57853i	−0.0162957	−	0.0554981i	0.950944	−	0.309364i	$-0.100116\pi$
$809$	−0.463497	−	1.57853i	−0.0162957	−	0.0554981i	−0.967239	+	0.253866i	$0.918298\pi$
$810$	1.44408	+	0.612222i	0.0507398	+	0.0215113i
$811$	10.8689	−	37.0159i	0.381657	−	1.29980i	−0.515042	−	0.857165i	$-0.672224\pi$
$811$	10.8689	−	37.0159i	0.381657	−	1.29980i	0.896699	−	0.442640i	$-0.145958\pi$
$812$	−40.2994	+	22.0740i	−1.41423	+	0.774646i
$813$	4.21914	−	11.3120i	0.147972	−	0.396728i
$814$	−30.1688	−	16.4476i	−1.05741	−	0.576489i
$815$	−3.73192	+	5.27369i	−0.130723	+	0.184729i
$816$	5.77531	−	19.8621i	0.202176	−	0.695312i
$817$	4.90674	+	6.55463i	0.171665	+	0.229318i
$818$	−8.77542	−	13.6351i	−0.306825	−	0.476740i
$819$	−25.8535	−	29.8365i	−0.903394	−	1.04257i
$820$	6.17425	+	19.0339i	0.215614	+	0.664693i
$821$	−27.2495	+	17.5122i	−0.951013	+	0.611179i	−0.921497	−	0.388385i	$-0.873033\pi$
$821$	−27.2495	+	17.5122i	−0.951013	+	0.611179i	−0.0295158	+	0.999564i	$0.509397\pi$
$822$	5.02378	+	4.34735i	0.175225	+	0.151631i
$823$	−1.27907	−	17.8837i	−0.0445856	−	0.623388i	−0.969793	−	0.243927i	$-0.921564\pi$
$823$	−1.27907	−	17.8837i	−0.0445856	−	0.623388i	0.925208	−	0.379461i	$-0.123890\pi$
$824$	6.56975	−	30.4902i	0.228868	−	1.06218i
$825$	7.68219	+	28.0065i	0.267459	+	0.975062i
$826$	−0.315233	−	0.576404i	−0.0109684	−	0.0200557i
$827$	1.67125	+	1.67125i	0.0581149	+	0.0581149i	0.735567	−	0.677452i	$-0.236916\pi$
$827$	1.67125	+	1.67125i	0.0581149	+	0.0581149i	−0.677452	+	0.735567i	$0.736916\pi$
$828$	−5.32778	+	17.7011i	−0.185153	+	0.615154i
$829$			8.68817i			0.301753i	0.988553	+	0.150876i	$0.0482095\pi$
$829$			8.68817i			0.301753i	−0.988553	+	0.150876i	$0.951790\pi$
$830$	7.59661	−	22.2084i	0.263682	−	0.770866i
$831$	25.5248	+	11.6568i	0.885445	+	0.404369i
$832$	−49.7583	+	3.75623i	−1.72506	+	0.130224i
$833$	−18.8530	+	1.34839i	−0.653216	+	0.0467189i
$834$	0.731256	+	10.1306i	0.0253213	+	0.350795i
$835$	43.6637	−	25.3817i	1.51104	−	0.878371i
$836$	28.9741	+	13.1860i	1.00209	+	0.456047i
$837$	−0.939300	−	0.0671801i	−0.0324670	−	0.00232208i
$838$	7.63912	−	4.91647i	0.263889	−	0.169837i
$839$	6.51209	−	45.2925i	0.224822	−	1.56367i	−0.494613	−	0.869113i	$-0.664690\pi$
$839$	6.51209	−	45.2925i	0.224822	−	1.56367i	0.719435	−	0.694559i	$-0.244401\pi$
$840$	16.6566	+	13.6153i	0.574707	+	0.469771i
$841$	−16.7725	−	10.7790i	−0.578362	−	0.371691i
$842$	−14.1839	+	4.17489i	−0.488808	+	0.143876i
$843$	−30.4874	−	11.3712i	−1.05004	−	0.391645i
$844$	7.57532	−	25.9253i	0.260753	−	0.892386i
$845$	25.4653	+	52.0304i	0.876032	+	1.78990i
$846$	10.4344	+	3.88401i	0.358741	+	0.133535i
$847$	−58.9380	−	32.1826i	−2.02513	−	1.10581i
$848$	−1.59994	−	7.26276i	−0.0549423	−	0.249404i
$849$	30.5243	−	4.38873i	1.04759	−	0.150621i
$850$	−34.0402	+	9.36131i	−1.16757	+	0.321090i
$851$	10.1053	−	18.1562i	0.346404	−	0.622387i
$852$	−1.36287	+	19.4143i	−0.0466910	+	0.665122i
$853$	−9.89395	+	13.2168i	−0.338762	+	0.452534i	−0.937281	−	0.348576i	$-0.886665\pi$
$853$	−9.89395	+	13.2168i	−0.338762	+	0.452534i	0.598518	+	0.801109i	$0.295756\pi$
$854$	−1.62836	+	22.9798i	−0.0557212	+	0.786354i
$855$	10.4631	+	6.33525i	0.357832	+	0.216661i
$856$	−26.6833	+	10.0124i	−0.912015	+	0.342216i
$857$	39.8880	−	21.7805i	1.36255	−	0.744007i	0.379126	−	0.925345i	$-0.376225\pi$
$857$	39.8880	−	21.7805i	1.36255	−	0.744007i	0.983421	+	0.181338i	$0.0580429\pi$
$858$	−50.7086	+	7.32485i	−1.73116	+	0.250066i
$859$	2.01915	+	4.42133i	0.0688927	+	0.150854i	0.940946	−	0.338557i	$-0.109939\pi$
$859$	2.01915	+	4.42133i	0.0688927	+	0.150854i	−0.872053	+	0.489411i	$0.837212\pi$
$860$	−12.6780	−	2.38734i	−0.432316	−	0.0814075i
$861$	12.8038	+	8.22852i	0.436353	+	0.280427i
$862$	13.7859	−	21.4823i	0.469549	−	0.731690i
$863$	−2.88054	−	3.84795i	−0.0980547	−	0.130986i	0.748830	−	0.662762i	$-0.230616\pi$
$863$	−2.88054	−	3.84795i	−0.0980547	−	0.130986i	−0.846885	+	0.531776i	$0.821525\pi$
$864$	9.99961	−	27.0817i	0.340194	−	0.921338i
$865$	11.3223	+	14.3101i	0.384969	+	0.486559i
$866$	6.90977	+	6.90069i	0.234804	+	0.234495i
$867$	8.02310	+	1.74532i	0.272479	+	0.0592741i
$868$	1.13617	+	0.422066i	0.0385640	+	0.0143258i
$869$	0.909090	+	0.787731i	0.0308388	+	0.0267220i
$870$	−4.25483	+	22.5139i	−0.144252	+	0.763293i
$871$	57.6973	+	26.3495i	1.95500	+	0.892817i
$872$	−0.527106	+	0.241979i	−0.0178501	+	0.00819446i
$873$	−2.81319	−	2.81319i	−0.0952120	−	0.0952120i
$874$	−8.12665	+	17.4510i	−0.274888	+	0.590290i
$875$	4.90281	−	36.3893i	0.165745	−	1.23018i
$876$	17.9429	−	20.7624i	0.606235	−	0.701495i
$877$	0.279408	+	0.749122i	0.00943494	+	0.0252960i	0.941582	−	0.336784i	$-0.109339\pi$
$877$	0.279408	+	0.749122i	0.00943494	+	0.0252960i	−0.932147	+	0.362080i	$0.882067\pi$
$878$	−4.42010	+	30.8867i	−0.149171	+	1.04237i
$879$	−1.54384	+	1.78169i	−0.0520725	+	0.0600948i
$880$	−47.6898	+	15.5391i	−1.60762	+	0.523822i
$881$	−23.2574	+	14.9466i	−0.783563	+	0.503565i	−0.870214	−	0.492673i	$-0.836020\pi$
$881$	−23.2574	+	14.9466i	−0.783563	+	0.503565i	0.0866514	+	0.996239i	$0.472383\pi$
$882$	−10.3181	+	0.00678720i	−0.347429	+	0.000228537i
$883$	−25.0540	−	1.79190i	−0.843136	−	0.0603022i	−0.356913	−	0.934137i	$-0.616171\pi$
$883$	−25.0540	−	1.79190i	−0.843136	−	0.0603022i	−0.486222	+	0.873835i	$0.661625\pi$
$884$	−8.94506	−	61.6385i	−0.300855	−	2.07313i
$885$	−0.321861	−	0.0610469i	−0.0108193	−	0.00205207i
$886$	32.8370	−	7.16587i	1.10318	−	0.240742i
$887$	7.29865	+	33.5513i	0.245065	+	1.12654i	0.920994	+	0.389577i	$0.127379\pi$
$887$	7.29865	+	33.5513i	0.245065	+	1.12654i	−0.675929	+	0.736966i	$0.736258\pi$
$888$	−6.84112	+	10.6913i	−0.229573	+	0.358777i
$889$	7.80487	−	3.56436i	0.261767	−	0.119545i
$890$	9.66189	−	11.7884i	0.323867	−	0.395150i
$891$	−0.783632	+	2.66880i	−0.0262527	+	0.0894083i
$892$	30.9937	−	31.0753i	1.03774	−	1.04048i
$893$	10.1763	+	5.55669i	0.340537	+	0.185948i
$894$	1.04571	−	14.7573i	0.0349738	−	0.493559i
$895$	−18.3515	−	15.0612i	−0.613421	−	0.503439i
$896$	−22.1296	+	29.8472i	−0.739298	+	0.997124i
$897$	−4.16148	−	30.7023i	−0.138948	−	1.02512i
$898$	−18.9772	−	8.65153i	−0.633279	−	0.288705i
$899$	0.183708	+	1.27772i	0.00612702	+	0.0426144i
$900$	−18.8973	+	3.78409i	−0.629910	+	0.126136i
$901$	8.90662	−	2.61522i	0.296722	−	0.0871256i
$902$	−32.2685	+	14.7622i	−1.07443	+	0.491528i
$903$	−8.61217	+	4.70260i	−0.286595	+	0.156493i
$904$	−38.5853	+	2.83622i	−1.28333	+	0.0943312i
$905$	−9.49093	−	4.03107i	−0.315489	−	0.133997i
$906$	25.1994	+	13.7384i	0.837194	+	0.456428i
$907$	8.02829	+	36.9055i	0.266575	+	1.22543i	0.894470	+	0.447128i	$0.147553\pi$
$907$	8.02829	+	36.9055i	0.266575	+	1.22543i	−0.627895	+	0.778298i	$0.716083\pi$
$908$	−26.1176	−	5.64556i	−0.866742	−	0.187354i
$909$	−9.27953	−	1.33420i	−0.307783	−	0.0442525i
$910$	62.6318	+	16.5397i	2.07623	+	0.548285i
$911$	18.3127	−	15.8681i	0.606728	−	0.525733i	−0.296422	−	0.955057i	$-0.595794\pi$
$911$	18.3127	−	15.8681i	0.606728	−	0.525733i	0.903151	+	0.429324i	$0.141248\pi$
$912$	5.60835	−	10.3355i	0.185711	−	0.342242i
$913$	40.6721	+	8.84767i	1.34605	+	0.292815i
$914$	−3.04523	−	42.1878i	−0.100727	−	1.39545i
$915$	8.33740	+	7.90274i	0.275626	+	0.261257i
$916$	3.33214	−	5.19995i	0.110097	−	0.171811i
$917$	7.45132	+	19.9778i	0.246064	+	0.659724i
$918$	34.5807	+	10.1291i	1.14133	+	0.334310i
$919$	−21.7321			−0.716875			−0.358438	−	0.933554i	$-0.616690\pi$
$919$	−21.7321			−0.716875			−0.358438	+	0.933554i	$0.616690\pi$
$920$	−9.14458	−	28.9202i	−0.301488	−	0.953470i
$921$	12.1859			0.401539
$922$	6.78591	+	1.98767i	0.223482	+	0.0654606i
$923$	20.4795	+	54.9077i	0.674091	+	1.80731i
$924$	−20.5833	+	32.1211i	−0.677141	+	1.05671i
$925$	21.6601	+	0.387412i	0.712179	+	0.0127380i
$926$	1.62485	+	22.5102i	0.0533958	+	0.739733i
$927$	20.7667	+	4.51751i	0.682066	+	0.148374i
$928$	−39.1882	−	5.50293i	−1.28642	−	0.180642i
$929$	−4.16929	+	3.61271i	−0.136790	+	0.118529i	−0.720568	−	0.693384i	$-0.756119\pi$
$929$	−4.16929	+	3.61271i	−0.136790	+	0.118529i	0.583779	+	0.811913i	$0.301574\pi$
$930$	0.522310	−	0.304079i	0.0171272	−	0.00997115i
$931$	−10.6358	−	1.52919i	−0.348573	−	0.0501172i
$932$	8.47104	+	1.83109i	0.277478	+	0.0599795i
$933$	−7.53908	−	34.6566i	−0.246818	−	1.13461i
$934$	33.8198	+	18.4382i	1.10662	+	0.603315i
$935$	−23.4401	−	58.0522i	−0.766572	−	1.89851i
$936$	−2.49252	−	33.9094i	−0.0814706	−	1.10836i
$937$	23.0717	−	12.5981i	0.753721	−	0.411563i	−0.0559600	−	0.998433i	$-0.517822\pi$
$937$	23.0717	−	12.5981i	0.753721	−	0.411563i	0.809681	+	0.586870i	$0.199640\pi$
$938$	42.9492	−	19.6484i	1.40234	−	0.641543i
$939$	10.2504	−	3.00978i	0.334509	−	0.0982206i
$940$	−17.7351	+	4.38284i	−0.578457	+	0.142952i
$941$	1.22186	+	8.49820i	0.0398314	+	0.277033i	0.999997	−	0.00239777i	$-0.000763234\pi$
$941$	1.22186	+	8.49820i	0.0398314	+	0.277033i	−0.960166	+	0.279431i	$0.909854\pi$
$942$	18.2673	+	8.32786i	0.595180	+	0.271336i
$943$	−8.75627	−	19.5908i	−0.285143	−	0.637965i
$944$	0.0790488	−	0.560257i	0.00257282	−	0.0182348i
$945$	−23.7756	+	28.9697i	−0.773421	+	0.942383i
$946$	1.61705	−	22.8203i	0.0525749	−	0.741951i
$947$	26.3014	+	14.3617i	0.854681	+	0.466691i	0.845945	−	0.533270i	$-0.179037\pi$
$947$	26.3014	+	14.3617i	0.854681	+	0.466691i	0.00873660	+	0.999962i	$0.497219\pi$
$948$	0.313784	−	0.314611i	0.0101912	−	0.0102181i
$949$	23.2793	−	79.2820i	0.755678	−	2.57360i
$950$	−20.0406	+	1.08673i	−0.650202	+	0.0352582i
$951$	25.0124	−	11.4228i	0.811084	−	0.370410i
$952$	−39.0647	−	24.9966i	−1.26610	−	0.810144i
$953$	−4.36840	−	20.0812i	−0.141506	−	0.650494i	−0.992182	−	0.124802i	$-0.960170\pi$
$953$	−4.36840	−	20.0812i	−0.141506	−	0.650494i	0.850675	−	0.525691i	$-0.176193\pi$
$954$	4.95087	−	1.08041i	0.160290	−	0.0349795i
$955$	26.1772	−	17.8303i	0.847073	−	0.576976i
$956$	−0.866561	−	5.97129i	−0.0280266	−	0.193125i
$957$	−40.5280	−	2.89862i	−1.31008	−	0.0936990i
$958$	−55.0664	+	0.0362224i	−1.77911	+	0.00117029i
$959$	12.5312	−	8.05330i	0.404653	−	0.260055i
$960$	4.49233	+	17.9750i	0.144989	+	0.580141i
$961$	−20.2784	+	23.4025i	−0.654141	+	0.754919i
$962$	−5.41430	+	37.8339i	−0.174564	+	1.21981i
$963$	−6.78637	−	18.1950i	−0.218688	−	0.586325i
$964$	−23.4064	+	27.0844i	−0.753871	+	0.872329i
$965$	−4.63556	−	0.207078i	−0.149224	−	0.00666609i
$966$	−19.3149	−	12.6164i	−0.621447	−	0.405927i
$967$	−3.02684	−	3.02684i	−0.0973366	−	0.0973366i	0.656762	−	0.754098i	$-0.271926\pi$
$967$	−3.02684	−	3.02684i	−0.0973366	−	0.0973366i	−0.754098	+	0.656762i	$0.771926\pi$
$968$	−24.1287	−	52.5598i	−0.775526	−	1.68934i
$969$	13.3511	+	6.09725i	0.428900	+	0.195872i
$970$	6.41441	+	1.21224i	0.205954	+	0.0389226i
$971$	12.0849	+	10.4716i	0.387822	+	0.336050i	0.826849	−	0.562424i	$-0.190131\pi$
$971$	12.0849	+	10.4716i	0.387822	+	0.336050i	−0.439026	+	0.898474i	$0.644677\pi$
$972$	29.6666	+	11.0206i	0.951558	+	0.353487i
$973$	22.2528	+	4.84080i	0.713391	+	0.155189i
$974$	27.8667	+	27.8301i	0.892906	+	0.891733i
$975$	26.2011	−	18.8923i	0.839108	−	0.605039i
$976$	−12.9533	+	15.0287i	−0.414626	+	0.481056i
$977$	8.05892	+	10.7655i	0.257828	+	0.344417i	0.910713	−	0.413039i	$-0.135533\pi$
$977$	8.05892	+	10.7655i	0.257828	+	0.344417i	−0.652886	+	0.757456i	$0.726442\pi$
$978$	−2.28568	+	3.56174i	−0.0730880	+	0.113892i
$979$	22.7385	+	14.6131i	0.726725	+	0.467038i
$980$	13.9801	−	9.54937i	0.446578	−	0.305043i
$981$	−0.164172	−	0.359486i	−0.00524160	−	0.0114775i
$982$	43.4607	−	6.27789i	1.38689	−	0.200335i
$983$	−2.40575	+	1.31364i	−0.0767316	+	0.0418986i	−0.517157	−	0.855891i	$-0.673010\pi$
$983$	−2.40575	+	1.31364i	−0.0767316	+	0.0418986i	0.440425	+	0.897789i	$0.354828\pi$
$984$	4.60497	+	12.2724i	0.146801	+	0.391229i
$985$	5.16376	+	21.0138i	0.164531	+	0.669556i
$986$	3.49132	−	49.2705i	0.111186	−	1.56909i
$987$	−8.32713	+	11.1237i	−0.265055	+	0.354073i
$988$	2.47951	−	35.3211i	0.0788839	−	1.12371i
$989$	13.7909	+	1.09838i	0.438525	+	0.0349265i
$990$	−10.5239	−	32.5159i	−0.334473	−	1.03342i
$991$	−19.2849	+	2.77275i	−0.612604	+	0.0880792i	−0.441631	−	0.897197i	$-0.645600\pi$
$991$	−19.2849	+	2.77275i	−0.612604	+	0.0880792i	−0.170973	+	0.985276i	$0.554691\pi$
$992$	0.567226	+	0.876271i	0.0180095	+	0.0278216i
$993$	26.1906	+	14.3012i	0.831134	+	0.453834i
$994$	40.8950	+	15.2224i	1.29711	+	0.482825i
$995$	37.0393	−	18.1282i	1.17422	−	0.574702i
$996$	4.31233	−	14.7583i	0.136641	−	0.467633i
$997$	−44.0730	−	16.4384i	−1.39581	−	0.520609i	−0.464736	−	0.885449i	$-0.653851\pi$
$997$	−44.0730	−	16.4384i	−1.39581	−	0.520609i	−0.931070	+	0.364840i	$0.881124\pi$
$998$	26.9247	−	7.92505i	0.852287	−	0.250863i
$999$	−18.6012	−	11.9543i	−0.588516	−	0.378216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.7	✓	1360
4.3	odd	2	inner	460.2.w.a.3.23	yes	1360
5.2	odd	4	inner	460.2.w.a.187.39	yes	1360
20.7	even	4	inner	460.2.w.a.187.56	yes	1360
23.8	even	11	inner	460.2.w.a.123.56	yes	1360
92.31	odd	22	inner	460.2.w.a.123.39	yes	1360
115.77	odd	44	inner	460.2.w.a.307.23	yes	1360
460.307	even	44	inner	460.2.w.a.307.7	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.7	✓	1360	1.1	even	1	trivial
460.2.w.a.3.23	yes	1360	4.3	odd	2	inner
460.2.w.a.123.39	yes	1360	92.31	odd	22	inner
460.2.w.a.123.56	yes	1360	23.8	even	11	inner
460.2.w.a.187.39	yes	1360	5.2	odd	4	inner
460.2.w.a.187.56	yes	1360	20.7	even	4	inner
460.2.w.a.307.7	yes	1360	460.307	even	44	inner
460.2.w.a.307.23	yes	1360	115.77	odd	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35719 - 0.397537i) q^{2} +(0.361954 + 0.970436i) q^{3} +(1.68393 + 1.07907i) q^{4} +(-0.0598253 - 2.23527i) q^{5} +(-0.105456 - 1.46096i) q^{6} +(-3.20911 - 0.698099i) q^{7} +(-1.85644 - 2.13392i) q^{8} +(1.45651 - 1.26208i) q^{9} +O(q^{10})\)	\(q+(-1.35719 - 0.397537i) q^{2} +(0.361954 + 0.970436i) q^{3} +(1.68393 + 1.07907i) q^{4} +(-0.0598253 - 2.23527i) q^{5} +(-0.105456 - 1.46096i) q^{6} +(-3.20911 - 0.698099i) q^{7} +(-1.85644 - 2.13392i) q^{8} +(1.45651 - 1.26208i) q^{9} +(-0.807408 + 3.05746i) q^{10} +(-5.55071 - 0.798071i) q^{11} +(-0.437661 + 2.02472i) q^{12} +(1.32587 + 6.09493i) q^{13} +(4.07785 + 2.22319i) q^{14} +(2.14753 - 0.867120i) q^{15} +(1.67123 + 3.63414i) q^{16} +(-4.38202 + 2.39276i) q^{17} +(-2.47849 + 1.13386i) q^{18} +(-2.72336 + 0.799650i) q^{19} +(2.31126 - 3.82859i) q^{20} +(-0.484089 - 3.36691i) q^{21} +(7.21610 + 3.28975i) q^{22} +(-2.02743 + 4.34621i) q^{23} +(1.39889 - 2.57394i) q^{24} +(-4.99284 + 0.267451i) q^{25} +(0.623504 - 8.79906i) q^{26} +(4.47909 + 2.44577i) q^{27} +(-4.65061 - 4.63839i) q^{28} +(1.97087 - 6.71217i) q^{29} +(-3.25932 + 0.323123i) q^{30} +(-0.167851 + 0.0766549i) q^{31} +(-0.823466 - 5.59660i) q^{32} +(-1.23462 - 5.67547i) q^{33} +(6.89845 - 1.50542i) q^{34} +(-1.36845 + 7.21498i) q^{35} +(3.81453 - 0.553570i) q^{36} +(-4.32167 - 0.309092i) q^{37} +(4.01400 - 0.00264039i) q^{38} +(-5.43484 + 3.49276i) q^{39} +(-4.65883 + 4.27730i) q^{40} +(-2.93013 + 3.38155i) q^{41} +(-0.681473 + 4.76198i) q^{42} +(-1.00810 - 2.70283i) q^{43} +(-8.48582 - 7.33348i) q^{44} +(-2.90821 - 3.18019i) q^{45} +(4.47939 - 5.09265i) q^{46} +(-2.88853 - 2.88853i) q^{47} +(-2.92179 + 2.93721i) q^{48} +(3.44361 + 1.57265i) q^{49} +(6.88256 + 1.62186i) q^{50} +(-3.90811 - 3.38640i) q^{51} +(-4.34417 + 11.6941i) q^{52} +(-1.81674 - 0.395207i) q^{53} +(-5.10670 - 5.09998i) q^{54} +(-1.45183 + 12.4551i) q^{55} +(4.46783 + 8.14397i) q^{56} +(-1.76174 - 2.35341i) q^{57} +(-5.34318 + 8.32619i) q^{58} +(-0.118997 - 0.0764745i) q^{59} +(4.55197 + 0.857161i) q^{60} +(2.06052 + 4.51191i) q^{61} +(0.258279 - 0.0373083i) q^{62} +(-5.55517 + 3.03335i) q^{63} +(-1.10726 + 7.92300i) q^{64} +(13.5445 - 3.32831i) q^{65} +(-0.580594 + 8.19350i) q^{66} +(6.09409 - 8.14074i) q^{67} +(-9.96096 - 0.699252i) q^{68} +(-4.95155 - 0.394368i) q^{69} +(4.72547 - 9.24809i) q^{70} +(9.29961 - 1.33708i) q^{71} +(-5.39711 - 0.765119i) q^{72} +(-11.6268 - 6.34870i) q^{73} +(5.74245 + 2.13752i) q^{74} +(-2.06672 - 4.74843i) q^{75} +(-5.44881 - 1.59213i) q^{76} +(17.2557 + 6.43604i) q^{77} +(8.76460 - 2.57978i) q^{78} +(-0.180453 - 0.115970i) q^{79} +(8.02330 - 3.95306i) q^{80} +(0.0705885 - 0.490954i) q^{81} +(5.32103 - 3.42457i) q^{82} +(-7.40350 - 0.529509i) q^{83} +(2.81795 - 6.19200i) q^{84} +(5.61062 + 9.65184i) q^{85} +(0.293712 + 4.06901i) q^{86} +(7.22709 - 0.516892i) q^{87} +(8.60153 + 13.3264i) q^{88} +(-4.38438 - 2.00228i) q^{89} +(2.68275 + 5.47225i) q^{90} -20.4849i q^{91} +(-8.10390 + 5.13096i) q^{92} +(-0.135143 - 0.135143i) q^{93} +(2.77199 + 5.06859i) q^{94} +(1.95036 + 6.03959i) q^{95} +(5.13308 - 2.82483i) q^{96} +(-0.147267 - 2.05906i) q^{97} +(-4.04845 - 3.50334i) q^{98} +(-9.09191 + 5.84302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

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