LMFDB - Embedded newform 750.2.m.c.721.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			721.6
Character	$\chi$	$=$	750.721
Dual form			750.2.m.c.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929776 + 0.368125i) q^{2} +(-0.876307 + 0.481754i) q^{3} +(0.728969 + 0.684547i) q^{4} +(2.23586 - 0.0305203i) q^{5} +(-0.992115 + 0.125333i) q^{6} +(-1.03403 - 0.751268i) q^{7} +(0.425779 + 0.904827i) q^{8} +(0.535827 - 0.844328i) q^{9} +O(q^{10})$	\(q+(0.929776 + 0.368125i) q^{2} +(-0.876307 + 0.481754i) q^{3} +(0.728969 + 0.684547i) q^{4} +(2.23586 - 0.0305203i) q^{5} +(-0.992115 + 0.125333i) q^{6} +(-1.03403 - 0.751268i) q^{7} +(0.425779 + 0.904827i) q^{8} +(0.535827 - 0.844328i) q^{9} +(2.09009 + 0.794698i) q^{10} +(1.96720 + 0.778870i) q^{11} +(-0.968583 - 0.248690i) q^{12} +(2.64793 - 4.17248i) q^{13} +(-0.684858 - 1.07916i) q^{14} +(-1.94460 + 1.10388i) q^{15} +(0.0627905 + 0.998027i) q^{16} +(0.883873 - 0.830012i) q^{17} +(0.809017 - 0.587785i) q^{18} +(4.91268 + 2.70077i) q^{19} +(1.65076 + 1.50830i) q^{20} +(1.26805 + 0.160193i) q^{21} +(1.54234 + 1.44835i) q^{22} +(-4.31515 + 5.21612i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(4.99814 - 0.136478i) q^{25} +(3.99798 - 2.90470i) q^{26} +(-0.0627905 + 0.998027i) q^{27} +(-0.239498 - 1.25549i) q^{28} +(-0.355196 - 1.86200i) q^{29} +(-2.21440 + 0.310507i) q^{30} +(-3.32039 + 3.11806i) q^{31} +(-0.309017 + 0.951057i) q^{32} +(-2.09910 + 0.265177i) q^{33} +(1.12735 - 0.446350i) q^{34} +(-2.33488 - 1.64817i) q^{35} +(0.968583 - 0.248690i) q^{36} +(0.173620 + 2.75961i) q^{37} +(3.57347 + 4.31959i) q^{38} +(-0.310297 + 4.93202i) q^{39} +(0.979598 + 2.01007i) q^{40} +(0.791526 + 0.956790i) q^{41} +(1.12004 + 0.615745i) q^{42} +(-0.165715 - 0.510018i) q^{43} +(0.900855 + 1.91441i) q^{44} +(1.17226 - 1.90415i) q^{45} +(-5.93231 + 3.26132i) q^{46} +(2.89033 - 6.14227i) q^{47} +(-0.535827 - 0.844328i) q^{48} +(-1.65830 - 5.10373i) q^{49} +(4.69739 + 1.71304i) q^{50} +(-0.374682 + 1.15315i) q^{51} +(4.78652 - 1.22897i) q^{52} +(0.414760 + 0.0523964i) q^{53} +(-0.425779 + 0.904827i) q^{54} +(4.42216 + 1.68140i) q^{55} +(0.239498 - 1.25549i) q^{56} -5.60612 q^{57} +(0.355196 - 1.86200i) q^{58} +(11.9598 + 3.07076i) q^{59} +(-2.17321 - 0.526474i) q^{60} +(-6.11122 + 7.38720i) q^{61} +(-4.23505 + 1.67678i) q^{62} +(-1.18838 + 0.470512i) q^{63} +(-0.637424 + 0.770513i) q^{64} +(5.79306 - 9.40989i) q^{65} +(-2.04931 - 0.526173i) q^{66} +(2.23635 - 11.7234i) q^{67} +1.21250 q^{68} +(1.26851 - 6.64976i) q^{69} +(-1.56418 - 2.39196i) q^{70} +(-5.58733 + 11.8737i) q^{71} +(0.992115 + 0.125333i) q^{72} +(-12.9512 + 3.32530i) q^{73} +(-0.854453 + 2.62974i) q^{74} +(-4.31415 + 2.52747i) q^{75} +(1.73239 + 5.33174i) q^{76} +(-1.44901 - 2.28327i) q^{77} +(-2.10410 + 4.47145i) q^{78} +(-6.84969 + 3.76565i) q^{79} +(0.170851 + 2.22953i) q^{80} +(-0.425779 - 0.904827i) q^{81} +(0.383724 + 1.18098i) q^{82} +(-1.36379 - 0.749751i) q^{83} +(0.814712 + 0.984818i) q^{84} +(1.95088 - 1.88277i) q^{85} +(0.0336723 - 0.535206i) q^{86} +(1.20829 + 1.46057i) q^{87} +(0.132851 + 2.11160i) q^{88} +(6.44498 - 1.65479i) q^{89} +(1.79091 - 1.33890i) q^{90} +(-5.87269 + 2.32516i) q^{91} +(-6.71629 + 0.848465i) q^{92} +(1.40755 - 4.33198i) q^{93} +(4.94848 - 4.64694i) q^{94} +(11.0665 + 5.88860i) q^{95} +(-0.187381 - 0.982287i) q^{96} +(-2.19331 - 11.4977i) q^{97} +(0.336958 - 5.35579i) q^{98} +(1.71170 - 1.24362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) $ 120 * q + 20 * q^5 - 5 * q^7	$ 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) $ 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{25}\right)$	$1$

Coefficient data

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

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

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

$2$	0.929776	+	0.368125i	0.657451	+	0.260303i
$2$	0.929776	+	0.368125i	0.657451	+	0.260303i
$3$	−0.876307	+	0.481754i	−0.505936	+	0.278141i
$3$	−0.876307	+	0.481754i	−0.505936	+	0.278141i
$4$	0.728969	+	0.684547i	0.364484	+	0.342274i
$5$	2.23586	−	0.0305203i	0.999907	−	0.0136491i
$5$	2.23586	−	0.0305203i	0.999907	−	0.0136491i
$6$	−0.992115	+	0.125333i	−0.405029	+	0.0511671i
$7$	−1.03403	−	0.751268i	−0.390827	−	0.283952i	0.374967	−	0.927038i	$-0.377654\pi$
$7$	−1.03403	−	0.751268i	−0.390827	−	0.283952i	−0.765794	+	0.643086i	$0.777654\pi$
$8$	0.425779	+	0.904827i	0.150536	+	0.319905i
$9$	0.535827	−	0.844328i	0.178609	−	0.281443i
$10$	2.09009	+	0.794698i	0.660943	+	0.251305i
$11$	1.96720	+	0.778870i	0.593133	+	0.234838i	0.645463	−	0.763792i	$-0.276665\pi$
$11$	1.96720	+	0.778870i	0.593133	+	0.234838i	−0.0523293	+	0.998630i	$0.516665\pi$
$12$	−0.968583	−	0.248690i	−0.279606	−	0.0717906i
$13$	2.64793	−	4.17248i	0.734405	−	1.15724i	−0.247688	−	0.968840i	$-0.579671\pi$
$13$	2.64793	−	4.17248i	0.734405	−	1.15724i	0.982093	−	0.188397i	$-0.0603292\pi$
$14$	−0.684858	−	1.07916i	−0.183036	−	0.288418i
$15$	−1.94460	+	1.10388i	−0.502092	+	0.285020i
$16$	0.0627905	+	0.998027i	0.0156976	+	0.249507i
$17$	0.883873	−	0.830012i	0.214371	−	0.201307i	−0.569921	−	0.821699i	$-0.693026\pi$
$17$	0.883873	−	0.830012i	0.214371	−	0.201307i	0.784292	+	0.620392i	$0.213026\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	4.91268	+	2.70077i	1.12705	+	0.619599i	0.932455	−	0.361286i	$-0.117662\pi$
$19$	4.91268	+	2.70077i	1.12705	+	0.619599i	0.194591	+	0.980885i	$0.437662\pi$
$20$	1.65076	+	1.50830i	0.369122	+	0.337267i
$21$	1.26805	+	0.160193i	0.276712	+	0.0349569i
$22$	1.54234	+	1.44835i	0.328827	+	0.308789i
$23$	−4.31515	+	5.21612i	−0.899772	+	1.08764i	0.0959641	+	0.995385i	$0.469407\pi$
$23$	−4.31515	+	5.21612i	−0.899772	+	1.08764i	−0.995736	+	0.0922522i	$0.970593\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	4.99814	−	0.136478i	0.999627	−	0.0272957i
$26$	3.99798	−	2.90470i	0.784068	−	0.569659i
$27$	−0.0627905	+	0.998027i	−0.0120840	+	0.192070i
$28$	−0.239498	−	1.25549i	−0.0452609	−	0.237266i
$29$	−0.355196	−	1.86200i	−0.0659582	−	0.345765i	0.933975	−	0.357339i	$-0.116316\pi$
$29$	−0.355196	−	1.86200i	−0.0659582	−	0.345765i	−0.999933	+	0.0115738i	$0.996316\pi$
$30$	−2.21440	+	0.310507i	−0.404293	+	0.0566906i
$31$	−3.32039	+	3.11806i	−0.596360	+	0.560019i	−0.922839	−	0.385185i	$-0.874138\pi$
$31$	−3.32039	+	3.11806i	−0.596360	+	0.560019i	0.326479	+	0.945204i	$0.394138\pi$
$32$	−0.309017	+	0.951057i	−0.0546270	+	0.168125i
$33$	−2.09910	+	0.265177i	−0.365406	+	0.0461615i
$34$	1.12735	−	0.446350i	0.193339	−	0.0765484i
$35$	−2.33488	−	1.64817i	−0.394666	−	0.278592i
$36$	0.968583	−	0.248690i	0.161431	−	0.0414483i
$37$	0.173620	+	2.75961i	0.0285430	+	0.453678i	0.986178	+	0.165692i	$0.0529856\pi$
$37$	0.173620	+	2.75961i	0.0285430	+	0.453678i	−0.957635	+	0.287986i	$0.907014\pi$
$38$	3.57347	+	4.31959i	0.579694	+	0.700730i
$39$	−0.310297	+	4.93202i	−0.0496872	+	0.789756i
$40$	0.979598	+	2.01007i	0.154888	+	0.317820i
$41$	0.791526	+	0.956790i	0.123616	+	0.149426i	0.828690	−	0.559708i	$-0.189087\pi$
$41$	0.791526	+	0.956790i	0.123616	+	0.149426i	−0.705075	+	0.709133i	$0.749087\pi$
$42$	1.12004	+	0.615745i	0.172825	+	0.0950115i
$43$	−0.165715	−	0.510018i	−0.0252713	−	0.0777770i	0.937625	−	0.347647i	$-0.113019\pi$
$43$	−0.165715	−	0.510018i	−0.0252713	−	0.0777770i	−0.962897	+	0.269870i	$0.913019\pi$
$44$	0.900855	+	1.91441i	0.135809	+	0.288609i
$45$	1.17226	−	1.90415i	0.174751	−	0.283854i
$46$	−5.93231	+	3.26132i	−0.874672	+	0.480855i
$47$	2.89033	−	6.14227i	0.421598	−	0.895942i	−0.575352	−	0.817906i	$-0.695135\pi$
$47$	2.89033	−	6.14227i	0.421598	−	0.895942i	0.996951	−	0.0780363i	$-0.0248650\pi$
$48$	−0.535827	−	0.844328i	−0.0773399	−	0.121868i
$49$	−1.65830	−	5.10373i	−0.236900	−	0.729104i
$50$	4.69739	+	1.71304i	0.664311	+	0.242261i
$51$	−0.374682	+	1.15315i	−0.0524660	+	0.161474i
$52$	4.78652	−	1.22897i	0.663771	−	0.170427i
$53$	0.414760	+	0.0523964i	0.0569717	+	0.00719720i	0.153767	−	0.988107i	$-0.450859\pi$
$53$	0.414760	+	0.0523964i	0.0569717	+	0.00719720i	−0.0967957	+	0.995304i	$0.530859\pi$
$54$	−0.425779	+	0.904827i	−0.0579412	+	0.123131i
$55$	4.42216	+	1.68140i	0.596284	+	0.226721i
$56$	0.239498	−	1.25549i	0.0320043	−	0.167772i
$57$	−5.60612			−0.742548
$58$	0.355196	−	1.86200i	0.0466395	−	0.244493i
$59$	11.9598	+	3.07076i	1.55703	+	0.399778i	0.926473	−	0.376361i	$-0.122825\pi$
$59$	11.9598	+	3.07076i	1.55703	+	0.399778i	0.630561	+	0.776140i	$0.282825\pi$
$60$	−2.17321	−	0.526474i	−0.280560	−	0.0679675i
$61$	−6.11122	+	7.38720i	−0.782462	+	0.945834i	−0.999540	−	0.0303204i	$-0.990347\pi$
$61$	−6.11122	+	7.38720i	−0.782462	+	0.945834i	0.217078	+	0.976154i	$0.430347\pi$
$62$	−4.23505	+	1.67678i	−0.537852	+	0.212951i
$63$	−1.18838	+	0.470512i	−0.149722	+	0.0592789i
$64$	−0.637424	+	0.770513i	−0.0796780	+	0.0963142i
$65$	5.79306	−	9.40989i	0.718541	−	1.16715i
$66$	−2.04931	−	0.526173i	−0.252252	−	0.0647674i
$67$	2.23635	−	11.7234i	0.273214	−	1.43224i	−0.535749	−	0.844377i	$-0.679971\pi$
$67$	2.23635	−	11.7234i	0.273214	−	1.43224i	0.808963	−	0.587860i	$-0.200029\pi$
$68$	1.21250			0.147037
$69$	1.26851	−	6.64976i	0.152711	−	0.800538i
$70$	−1.56418	−	2.39196i	−0.186956	−	0.285893i
$71$	−5.58733	+	11.8737i	−0.663094	+	1.40915i	0.236158	+	0.971715i	$0.424112\pi$
$71$	−5.58733	+	11.8737i	−0.663094	+	1.40915i	−0.899252	+	0.437431i	$0.855888\pi$
$72$	0.992115	+	0.125333i	0.116922	+	0.0147707i
$73$	−12.9512	+	3.32530i	−1.51582	+	0.389197i	−0.912760	−	0.408497i	$-0.866053\pi$
$73$	−12.9512	+	3.32530i	−1.51582	+	0.389197i	−0.603062	+	0.797694i	$0.706053\pi$
$74$	−0.854453	+	2.62974i	−0.0993282	+	0.305701i
$75$	−4.31415	+	2.52747i	−0.498155	+	0.291847i
$76$	1.73239	+	5.33174i	0.198718	+	0.611592i
$77$	−1.44901	−	2.28327i	−0.165130	−	0.260203i
$78$	−2.10410	+	4.47145i	−0.238243	+	0.506292i
$79$	−6.84969	+	3.76565i	−0.770650	+	0.423669i	−0.818006	−	0.575209i	$-0.804921\pi$
$79$	−6.84969	+	3.76565i	−0.770650	+	0.423669i	0.0473558	+	0.998878i	$0.484921\pi$
$80$	0.170851	+	2.22953i	0.0191017	+	0.249269i
$81$	−0.425779	−	0.904827i	−0.0473088	−	0.100536i
$82$	0.383724	+	1.18098i	0.0423752	+	0.130418i
$83$	−1.36379	−	0.749751i	−0.149696	−	0.0822959i	0.405145	−	0.914252i	$-0.367221\pi$
$83$	−1.36379	−	0.749751i	−0.149696	−	0.0822959i	−0.554841	+	0.831956i	$0.687221\pi$
$84$	0.814712	+	0.984818i	0.0888924	+	0.107452i
$85$	1.95088	−	1.88277i	0.211603	−	0.204215i
$86$	0.0336723	−	0.535206i	0.00363098	−	0.0577128i
$87$	1.20829	+	1.46057i	0.129542	+	0.156589i
$88$	0.132851	+	2.11160i	0.0141619	+	0.225098i
$89$	6.44498	−	1.65479i	0.683167	−	0.175407i	0.108872	−	0.994056i	$-0.465276\pi$
$89$	6.44498	−	1.65479i	0.683167	−	0.175407i	0.574295	+	0.818648i	$0.305276\pi$
$90$	1.79091	−	1.33890i	0.188778	−	0.141132i
$91$	−5.87269	+	2.32516i	−0.615626	+	0.243743i
$92$	−6.71629	+	0.848465i	−0.700222	+	0.0884586i
$93$	1.40755	−	4.33198i	0.145956	−	0.449206i
$94$	4.94848	−	4.64694i	0.510397	−	0.479295i
$95$	11.0665	+	5.88860i	1.13540	+	0.604158i
$96$	−0.187381	−	0.982287i	−0.0191245	−	0.100254i
$97$	−2.19331	−	11.4977i	−0.222697	−	1.16742i	−0.901394	−	0.433001i	$-0.857455\pi$
$97$	−2.19331	−	11.4977i	−0.222697	−	1.16742i	0.678696	−	0.734419i	$-0.262545\pi$
$98$	0.336958	−	5.35579i	0.0340379	−	0.541016i
$99$	1.71170	−	1.24362i	0.172032	−	0.124989i
$100$	3.73691	+	3.32197i	0.373691	+	0.332197i
$101$	2.67466	+	1.94325i	0.266138	+	0.193361i	0.712849	−	0.701318i	$-0.247405\pi$
$101$	2.67466	+	1.94325i	0.266138	+	0.193361i	−0.446711	+	0.894679i	$0.647405\pi$
$102$	−0.772875	+	0.934246i	−0.0765260	+	0.0925041i
$103$	−0.357630	−	0.335837i	−0.0352383	−	0.0330910i	0.666728	−	0.745301i	$-0.267694\pi$
$103$	−0.357630	−	0.335837i	−0.0352383	−	0.0330910i	−0.701966	+	0.712210i	$0.747694\pi$
$104$	4.90281	+	0.619368i	0.480760	+	0.0607341i
$105$	2.84008	+	0.319467i	0.277163	+	0.0311767i
$106$	0.366346	+	0.201400i	0.0355826	+	0.0195617i
$107$	3.08066	−	2.23823i	0.297819	−	0.216378i	−0.428833	−	0.903384i	$-0.641075\pi$
$107$	3.08066	−	2.23823i	0.297819	−	0.216378i	0.726652	+	0.687005i	$0.241075\pi$
$108$	−0.728969	+	0.684547i	−0.0701450	+	0.0658706i
$109$	−0.948439	−	15.0750i	−0.0908440	−	1.44392i	−0.734500	−	0.678609i	$-0.762583\pi$
$109$	−0.948439	−	15.0750i	−0.0908440	−	1.44392i	0.643656	−	0.765315i	$-0.277417\pi$
$110$	3.49265	+	3.19124i	0.333011	+	0.304272i
$111$	−1.48160	−	2.33463i	−0.140627	−	0.221593i
$112$	0.684858	−	1.07916i	0.0647130	−	0.101971i
$113$	−9.08741	−	2.33325i	−0.854871	−	0.219494i	−0.204271	−	0.978914i	$-0.565483\pi$
$113$	−9.08741	−	2.33325i	−0.854871	−	0.219494i	−0.650600	+	0.759421i	$0.725483\pi$
$114$	−5.21244	−	2.06375i	−0.488189	−	0.193288i
$115$	−9.48888	+	11.7942i	−0.884842	+	1.09982i
$116$	1.01570	−	1.60049i	0.0943055	−	0.148602i
$117$	−2.10410	−	4.47145i	−0.194525	−	0.413386i
$118$	9.98952	+	7.25781i	0.919610	+	0.668136i
$119$	−1.53751	+	0.194233i	−0.140944	+	0.0178053i
$120$	−1.82679	−	1.28951i	−0.166762	−	0.117716i
$121$	−4.75541	−	4.46563i	−0.432310	−	0.405966i
$122$	−8.40148	+	4.61875i	−0.760634	+	0.418162i
$123$	−1.15456	−	0.457121i	−0.104103	−	0.0412172i
$124$	−4.55492			−0.409044
$125$	11.1710	−	0.457691i	0.999162	−	0.0409372i
$126$	−1.27813			−0.113865
$127$	−7.98538	−	3.16164i	−0.708588	−	0.280550i	−0.0139432	−	0.999903i	$-0.504438\pi$
$127$	−7.98538	−	3.16164i	−0.708588	−	0.280550i	−0.694645	+	0.719353i	$0.744438\pi$
$128$	−0.876307	+	0.481754i	−0.0774553	+	0.0425814i
$129$	0.390920	+	0.367098i	0.0344186	+	0.0323212i
$130$	8.85027	−	6.61652i	0.776220	−	0.580308i
$131$	−1.61504	+	0.204027i	−0.141107	+	0.0178259i	−0.195569	−	0.980690i	$-0.562655\pi$
$131$	−1.61504	+	0.204027i	−0.141107	+	0.0178259i	0.0544625	+	0.998516i	$0.482655\pi$
$132$	−1.71170	−	1.24362i	−0.148984	−	0.108244i
$133$	−3.05086	−	6.48341i	−0.264543	−	0.562183i
$134$	6.39497	−	10.0769i	0.552441	−	0.870508i
$135$	−0.109931	+	2.23336i	−0.00946133	+	0.192217i
$136$	1.12735	+	0.446350i	0.0966696	+	0.0382742i
$137$	−6.39931	−	1.64306i	−0.546730	−	0.140376i	−0.0347853	−	0.999395i	$-0.511075\pi$
$137$	−6.39931	−	1.64306i	−0.546730	−	0.140376i	−0.511945	+	0.859018i	$0.671075\pi$
$138$	3.62737	−	5.71583i	0.308782	−	0.486563i
$139$	−12.1414	−	19.1319i	−1.02982	−	1.62274i	−0.748505	−	0.663129i	$-0.769228\pi$
$139$	−12.1414	−	19.1319i	−1.02982	−	1.62274i	−0.281319	−	0.959614i	$-0.590772\pi$
$140$	−0.573802	−	2.79980i	−0.0484952	−	0.236626i
$141$	0.426243	+	6.77494i	0.0358961	+	0.570553i
$142$	−9.56595	+	8.98303i	−0.802757	+	0.753839i
$143$	8.45884	−	6.14571i	0.707364	−	0.513930i
$144$	0.876307	+	0.481754i	0.0730256	+	0.0401461i
$145$	−0.850997	−	4.15233i	−0.0706714	−	0.344833i
$146$	−13.2658	−	1.67586i	−1.09789	−	0.138696i
$147$	3.91192	+	3.67354i	0.322650	+	0.302988i
$148$	−1.76252	+	2.13052i	−0.144878	+	0.175128i
$149$	−3.75285	−	2.72660i	−0.307445	−	0.223372i	0.423354	−	0.905964i	$-0.360853\pi$
$149$	−3.75285	−	2.72660i	−0.307445	−	0.223372i	−0.730799	+	0.682592i	$0.760853\pi$
$150$	−4.94162	+	0.761835i	−0.403482	+	0.0622036i
$151$	−6.14439	+	4.46416i	−0.500023	+	0.363288i	−0.809026	−	0.587773i	$-0.800005\pi$
$151$	−6.14439	+	4.46416i	−0.500023	+	0.363288i	0.309003	+	0.951061i	$0.400005\pi$
$152$	−0.352011	+	5.59506i	−0.0285519	+	0.453819i
$153$	−0.227199	−	1.19102i	−0.0183680	−	0.0962884i
$154$	−0.506725	−	2.65635i	−0.0408331	−	0.214054i
$155$	−7.32877	+	7.07287i	−0.588661	+	0.568107i
$156$	−3.60240	+	3.38288i	−0.288423	+	0.270847i
$157$	−0.685058	+	2.10839i	−0.0546736	+	0.168268i	−0.974665	−	0.223672i	$-0.928196\pi$
$157$	−0.685058	+	2.10839i	−0.0546736	+	0.168268i	0.919991	+	0.391939i	$0.128196\pi$
$158$	−7.75491	+	0.979673i	−0.616947	+	0.0779386i
$159$	−0.388699	+	0.153897i	−0.0308258	+	0.0122048i
$160$	−0.661892	+	2.13586i	−0.0523272	+	0.168855i
$161$	8.38071	−	2.15180i	0.660492	−	0.169586i
$162$	−0.0627905	−	0.998027i	−0.00493329	−	0.0784124i
$163$	−10.4780	−	12.6658i	−0.820702	−	0.992059i	−0.999966	−	0.00825763i	$-0.997371\pi$
$163$	−10.4780	−	12.6658i	−0.820702	−	0.992059i	0.179264	−	0.983801i	$-0.442629\pi$
$164$	−0.0779706	+	1.23931i	−0.00608848	+	0.0967736i
$165$	−4.68519	+	0.656964i	−0.364741	+	0.0511446i
$166$	−0.992020	−	1.19915i	−0.0769957	−	0.0930718i
$167$	−14.0631	−	7.73123i	−1.08823	−	0.598261i	−0.166482	−	0.986045i	$-0.553241\pi$
$167$	−14.0631	−	7.73123i	−1.08823	−	0.598261i	−0.921750	+	0.387784i	$0.873241\pi$
$168$	0.394965	+	1.21558i	0.0304722	+	0.0937838i
$169$	−4.86288	−	10.3341i	−0.374068	−	0.794934i
$170$	2.50698	−	1.03238i	0.192276	−	0.0791802i
$171$	4.91268	−	2.70077i	0.375682	−	0.206533i
$172$	0.228330	−	0.485227i	0.0174100	−	0.0369982i
$173$	−5.87268	−	9.25386i	−0.446491	−	0.703558i	0.544310	−	0.838884i	$-0.316792\pi$
$173$	−5.87268	−	9.25386i	−0.446491	−	0.703558i	−0.990801	+	0.135327i	$0.956792\pi$
$174$	0.585766	+	1.80280i	0.0444068	+	0.136670i
$175$	−5.27076	−	3.61382i	−0.398432	−	0.273179i
$176$	−0.653812	+	2.01223i	−0.0492829	+	0.151677i
$177$	−11.9598	+	3.07076i	−0.898954	+	0.230812i
$178$	6.60156	+	0.833971i	0.494808	+	0.0625088i
$179$	2.09761	−	4.45765i	0.156783	−	0.333181i	−0.810968	−	0.585091i	$-0.801059\pi$
$179$	2.09761	−	4.45765i	0.156783	−	0.333181i	0.967751	+	0.251910i	$0.0810588\pi$
$180$	2.15803	−	0.585597i	0.160850	−	0.0436478i
$181$	−2.39069	+	12.5325i	−0.177699	+	0.931530i	0.775992	+	0.630742i	$0.217250\pi$
$181$	−2.39069	+	12.5325i	−0.177699	+	0.931530i	−0.953691	+	0.300788i	$0.902750\pi$
$182$	−6.31624			−0.468191
$183$	1.79649	−	9.41755i	0.132801	−	0.696166i
$184$	−6.55699	−	1.68355i	−0.483388	−	0.124113i
$185$	0.472415	+	6.16481i	0.0347326	+	0.453246i
$186$	2.90341	−	3.50962i	0.212889	−	0.257338i
$187$	2.38523	−	0.944378i	0.174425	−	0.0690598i
$188$	6.31164	−	2.49895i	0.460323	−	0.182255i
$189$	0.814712	−	0.984818i	0.0592616	−	0.0716350i
$190$	8.12162	+	9.54893i	0.589204	+	0.692752i
$191$	11.8376	+	3.03938i	0.856539	+	0.219922i	0.651329	−	0.758796i	$-0.274212\pi$
$191$	11.8376	+	3.03938i	0.856539	+	0.219922i	0.205211	+	0.978718i	$0.434212\pi$
$192$	0.187381	−	0.982287i	0.0135231	−	0.0708905i
$193$	10.2566			0.738288			0.369144	−	0.929372i	$-0.379651\pi$
$193$	10.2566			0.738288			0.369144	+	0.929372i	$0.379651\pi$
$194$	2.19331	−	11.4977i	0.157471	−	0.825490i
$195$	−0.543252	+	11.0368i	−0.0389031	+	0.790360i
$196$	2.28489	−	4.85564i	0.163207	−	0.346832i
$197$	9.13793	+	1.15439i	0.651050	+	0.0822468i	0.443920	−	0.896067i	$-0.353587\pi$
$197$	9.13793	+	1.15439i	0.651050	+	0.0822468i	0.207131	+	0.978313i	$0.433587\pi$
$198$	2.04931	−	0.526173i	0.145638	−	0.0373935i
$199$	−5.61840	+	17.2916i	−0.398277	+	1.22577i	0.528102	+	0.849181i	$0.322904\pi$
$199$	−5.61840	+	17.2916i	−0.398277	+	1.22577i	−0.926380	+	0.376591i	$0.877096\pi$
$200$	2.25159	+	4.46434i	0.159212	+	0.315677i
$201$	3.68804	+	11.3506i	0.260135	+	0.800612i
$202$	1.77147	+	2.79140i	0.124640	+	0.196402i
$203$	−1.03158	+	2.19221i	−0.0724026	+	0.153863i
$204$	−1.06252	+	0.584125i	−0.0743913	+	0.0408970i
$205$	1.79894	+	2.11509i	0.125644	+	0.147724i
$206$	−0.208886	−	0.443905i	−0.0145538	−	0.0309284i
$207$	2.09194	+	6.43834i	0.145400	+	0.447496i
$208$	4.33051	+	2.38072i	0.300267	+	0.165073i
$209$	7.56068	+	9.13929i	0.522983	+	0.632178i
$210$	2.52304	+	1.34254i	0.174106	+	0.0926438i
$211$	−1.10862	+	17.6210i	−0.0763206	+	1.21308i	0.754409	+	0.656405i	$0.227924\pi$
$211$	−1.10862	+	17.6210i	−0.0763206	+	1.21308i	−0.830730	+	0.556676i	$0.812076\pi$
$212$	0.266479	+	0.322118i	0.0183019	+	0.0221232i
$213$	−0.823974	−	13.0967i	−0.0564578	−	0.897371i
$214$	3.68828	−	0.946989i	0.252125	−	0.0647348i
$215$	−0.386081	−	1.13527i	−0.0263305	−	0.0774248i
$216$	−0.929776	+	0.368125i	−0.0632633	+	0.0250477i
$217$	5.77588	−	0.729664i	0.392092	−	0.0495328i
$218$	4.66764	−	14.3655i	0.316133	−	0.972956i
$219$	9.74724	−	9.15327i	0.658657	−	0.618520i
$220$	2.07261	+	4.25287i	0.139736	+	0.286728i
$221$	−1.12277	−	5.88576i	−0.0755256	−	0.395919i
$222$	−0.518122	−	2.71609i	−0.0347741	−	0.182292i
$223$	−0.108814	+	1.72955i	−0.00728672	+	0.115819i	−0.999989	−	0.00477514i	$-0.998480\pi$
$223$	−0.108814	+	1.72955i	−0.00728672	+	0.115819i	0.992702	+	0.120594i	$0.0384800\pi$
$224$	1.03403	−	0.751268i	0.0690891	−	0.0501962i
$225$	2.56290	−	4.29320i	0.170860	−	0.286213i
$226$	−7.59033	−	5.51470i	−0.504901	−	0.366832i
$227$	−14.4473	+	17.4638i	−0.958903	+	1.15911i	0.0282930	+	0.999600i	$0.490993\pi$
$227$	−14.4473	+	17.4638i	−0.958903	+	1.15911i	−0.987196	+	0.159514i	$0.949007\pi$
$228$	−4.08668	−	3.83765i	−0.270647	−	0.254155i
$229$	12.6765	+	1.60142i	0.837689	+	0.105825i	0.532461	−	0.846455i	$-0.321267\pi$
$229$	12.6765	+	1.60142i	0.837689	+	0.105825i	0.305228	+	0.952279i	$0.401267\pi$
$230$	−13.1643	+	7.47290i	−0.868027	+	0.492748i
$231$	2.36975	+	1.30278i	0.155918	+	0.0857167i
$232$	1.53355	−	1.11419i	0.100683	−	0.0731503i
$233$	2.84267	−	2.66945i	0.186230	−	0.174881i	−0.585825	−	0.810438i	$-0.699229\pi$
$233$	2.84267	−	2.66945i	0.186230	−	0.174881i	0.772054	+	0.635556i	$0.219229\pi$
$234$	−0.310297	−	4.93202i	−0.0202847	−	0.322416i
$235$	6.27491	−	13.8215i	0.409330	−	0.901613i
$236$	6.61624	+	10.4255i	0.430681	+	0.678644i
$237$	4.18831	−	6.59973i	0.272060	−	0.428698i
$238$	−1.50105	−	0.385403i	−0.0972983	−	0.0249820i
$239$	23.2296	+	9.19724i	1.50260	+	0.594920i	0.968170	−	0.250294i	$-0.0805273\pi$
$239$	23.2296	+	9.19724i	1.50260	+	0.594920i	0.534427	+	0.845214i	$0.320527\pi$
$240$	−1.22380	−	1.87145i	−0.0789961	−	0.120801i
$241$	−11.1090	+	17.5050i	−0.715594	+	1.12760i	0.270711	+	0.962661i	$0.412741\pi$
$241$	−11.1090	+	17.5050i	−0.715594	+	1.12760i	−0.986304	+	0.164935i	$0.947259\pi$
$242$	−2.77756	−	5.90262i	−0.178549	−	0.379435i
$243$	0.809017	+	0.587785i	0.0518985	+	0.0377064i
$244$	−9.51177	+	1.20162i	−0.608929	+	0.0769256i
$245$	−3.86350	−	11.3606i	−0.246830	−	0.725803i
$246$	−0.905202	−	0.850041i	−0.0577136	−	0.0541966i
$247$	24.2773	−	13.3466i	1.54473	−	0.849223i
$248$	−4.23505	−	1.67678i	−0.268926	−	0.106475i
$249$	1.55630			0.0986263
$250$	10.5550	+	3.68676i	0.667556	+	0.233171i
$251$	−17.9679			−1.13413			−0.567063	−	0.823675i	$-0.691920\pi$
$251$	−17.9679			−1.13413			−0.567063	+	0.823675i	$0.691920\pi$
$252$	−1.18838	−	0.470512i	−0.0748608	−	0.0296395i
$253$	−12.5515	+	6.90022i	−0.789103	+	0.433813i
$254$	−6.26074	−	5.87923i	−0.392834	−	0.368896i
$255$	−0.802543	+	2.58973i	−0.0502572	+	0.162175i
$256$	−0.992115	+	0.125333i	−0.0620072	+	0.00783333i
$257$	16.9656	+	12.3262i	1.05828	+	0.768887i	0.973770	−	0.227535i	$-0.0730666\pi$
$257$	16.9656	+	12.3262i	1.05828	+	0.768887i	0.0845127	+	0.996422i	$0.473067\pi$
$258$	0.228330	+	0.485227i	0.0142152	+	0.0302089i
$259$	1.89368	−	2.98396i	0.117668	−	0.185414i
$260$	10.6645	−	2.89389i	0.661383	−	0.179471i
$261$	−1.76246	−	0.697809i	−0.109094	−	0.0431933i
$262$	−1.57674	−	0.404837i	−0.0974110	−	0.0250109i
$263$	−7.82540	+	12.3309i	−0.482535	+	0.760353i	−0.995161	−	0.0982590i	$-0.968673\pi$
$263$	−7.82540	+	12.3309i	−0.482535	+	0.760353i	0.512626	+	0.858612i	$0.328673\pi$
$264$	−1.13369	−	1.78641i	−0.0697739	−	0.109946i
$265$	0.928944	+	0.104492i	0.0570646	+	0.00641891i
$266$	−0.449917	−	7.15122i	−0.0275862	−	0.438470i
$267$	−4.85058	+	4.55500i	−0.296851	+	0.278761i
$268$	9.65543	−	7.01508i	0.589799	−	0.428514i
$269$	12.3975	+	6.81560i	0.755891	+	0.415554i	0.812589	−	0.582837i	$-0.198057\pi$
$269$	12.3975	+	6.81560i	0.755891	+	0.415554i	−0.0566984	+	0.998391i	$0.518057\pi$
$270$	−0.924367	+	2.03606i	−0.0562552	+	0.123911i
$271$	−4.05468	−	0.512225i	−0.246304	−	0.0311154i	0.00121183	−	0.999999i	$-0.499614\pi$
$271$	−4.05468	−	0.512225i	−0.246304	−	0.0311154i	−0.247516	+	0.968884i	$0.579614\pi$
$272$	0.883873	+	0.830012i	0.0535927	+	0.0503269i
$273$	4.02612	−	4.86675i	0.243672	−	0.294549i
$274$	−5.34508	−	3.88343i	−0.322908	−	0.234606i
$275$	9.93864	+	3.62442i	0.599323	+	0.218561i
$276$	5.47678	−	3.97911i	0.329664	−	0.239515i
$277$	−1.30524	+	20.7462i	−0.0784244	+	1.24652i	0.740277	+	0.672302i	$0.234694\pi$
$277$	−1.30524	+	20.7462i	−0.0784244	+	1.24652i	−0.818702	+	0.574219i	$0.805306\pi$
$278$	−4.24592	−	22.2579i	−0.254654	−	1.33494i
$279$	0.853506	+	4.47424i	0.0510981	+	0.267866i
$280$	0.497166	−	2.81442i	0.0297114	−	0.168194i
$281$	17.8236	−	16.7375i	1.06327	−	0.998474i	0.0632664	−	0.997997i	$-0.479848\pi$
$281$	17.8236	−	16.7375i	1.06327	−	0.998474i	1.00000		0.000476847i	$-0.000151785\pi$
$282$	−2.09771	+	6.45609i	−0.124917	+	0.384455i
$283$	−20.0334	+	2.53080i	−1.19086	+	0.150441i	−0.695682	−	0.718350i	$-0.744898\pi$
$283$	−20.0334	+	2.53080i	−1.19086	+	0.150441i	−0.495179	+	0.868791i	$0.664898\pi$
$284$	−12.2011	+	4.83075i	−0.724000	+	0.286652i
$285$	−12.5345	+	0.171101i	−0.742479	+	0.0101351i
$286$	10.1272	−	2.60023i	0.598835	−	0.153755i
$287$	−0.0996567	−	1.58400i	−0.00588255	−	0.0935005i
$288$	0.637424	+	0.770513i	0.0375606	+	0.0454029i
$289$	−0.975127	+	15.4992i	−0.0573604	+	0.911718i
$290$	0.737339	−	4.17401i	0.0432980	−	0.245107i
$291$	7.46110	+	9.01892i	0.437377	+	0.528698i
$292$	−11.7173	−	6.44166i	−0.685705	−	0.376970i
$293$	8.12552	+	25.0078i	0.474698	+	1.46097i	0.846365	+	0.532603i	$0.178786\pi$
$293$	8.12552	+	25.0078i	0.474698	+	1.46097i	−0.371667	+	0.928366i	$0.621214\pi$
$294$	2.28489	+	4.85564i	0.133258	+	0.283187i
$295$	26.8342	+	6.50076i	1.56235	+	0.378489i
$296$	−2.42305	+	1.33208i	−0.140837	+	0.0774257i
$297$	−0.900855	+	1.91441i	−0.0522729	+	0.111086i
$298$	−2.48558	−	3.91665i	−0.143986	−	0.226885i
$299$	10.3379	+	31.8168i	0.597857	+	1.84001i
$300$	−4.87505	−	1.11080i	−0.281461	−	0.0641318i
$301$	−0.211806	+	0.651870i	−0.0122083	+	0.0375732i
$302$	−7.35628	+	1.88877i	−0.423306	+	0.108687i
$303$	−3.27999	−	0.414359i	−0.188430	−	0.0238043i
$304$	−2.38697	+	5.07257i	−0.136902	+	0.290932i
$305$	−13.4384	+	16.7033i	−0.769479	+	0.956426i
$306$	0.227199	−	1.19102i	0.0129881	−	0.0680861i
$307$	−26.3804			−1.50561			−0.752805	−	0.658244i	$-0.771300\pi$
$307$	−26.3804			−1.50561			−0.752805	+	0.658244i	$0.771300\pi$
$308$	0.506725	−	2.65635i	0.0288733	−	0.151359i
$309$	0.475184	+	0.122006i	0.0270323	+	0.00694071i
$310$	−9.41781	+	3.87829i	−0.534896	+	0.220272i
$311$	16.9388	−	20.4755i	0.960510	−	1.16106i	−0.0263782	−	0.999652i	$-0.508397\pi$
$311$	16.9388	−	20.4755i	0.960510	−	1.16106i	0.986888	−	0.161405i	$-0.0516026\pi$
$312$	−4.59474	+	1.81919i	−0.260126	+	0.102991i
$313$	13.3783	−	5.29684i	0.756185	−	0.299395i	0.0417797	−	0.999127i	$-0.486697\pi$
$313$	13.3783	−	5.29684i	0.756185	−	0.299395i	0.714405	+	0.699732i	$0.246697\pi$
$314$	−1.41310	+	1.70815i	−0.0797459	+	0.0963962i
$315$	−2.64269	+	1.08827i	−0.148898	+	0.0613170i
$316$	−7.57097	−	1.94390i	−0.425901	−	0.109353i
$317$	1.38395	−	7.25494i	0.0777306	−	0.407478i	−0.922061	−	0.387045i	$-0.873496\pi$
$317$	1.38395	−	7.25494i	0.0777306	−	0.407478i	0.999791	−	0.0204326i	$-0.00650436\pi$
$318$	−0.418056			−0.0234434
$319$	0.751516	−	3.93958i	0.0420768	−	0.220574i
$320$	−1.40167	+	1.74221i	−0.0783560	+	0.0973927i
$321$	−1.62133	+	3.44550i	−0.0904938	+	0.192309i
$322$	8.58431	+	1.08445i	0.478385	+	0.0604341i
$323$	6.58385	−	1.69045i	0.366335	−	0.0940589i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	12.6653	−	21.2160i	0.702544	−	1.17685i
$326$	−5.07965	−	15.6335i	−0.281336	−	0.865862i
$327$	8.09356	+	12.7534i	0.447575	+	0.705265i
$328$	−0.528714	+	1.12358i	−0.0291934	+	0.0620391i
$329$	−7.60318	+	4.17988i	−0.419177	+	0.230445i
$330$	−4.59802	−	1.11390i	−0.253113	−	0.0613183i
$331$	−7.59109	−	16.1319i	−0.417244	−	0.886689i	−0.997392	−	0.0721773i	$-0.977005\pi$
$331$	−7.59109	−	16.1319i	−0.417244	−	0.886689i	0.580148	−	0.814511i	$-0.302995\pi$
$332$	−0.480922	−	1.48013i	−0.0263940	−	0.0812324i
$333$	2.42305	+	1.33208i	0.132782	+	0.0729977i
$334$	−10.2294	−	12.3653i	−0.559730	−	0.676598i
$335$	4.64237	−	26.2801i	0.253640	−	1.43583i
$336$	−0.0802546	+	1.27561i	−0.00437825	+	0.0695903i
$337$	−12.8197	−	15.4964i	−0.698334	−	0.844141i	0.295462	−	0.955354i	$-0.404526\pi$
$337$	−12.8197	−	15.4964i	−0.698334	−	0.844141i	−0.993797	+	0.111213i	$0.964526\pi$
$338$	−0.717138	−	11.3986i	−0.0390072	−	0.620001i
$339$	9.08741	−	2.33325i	0.493560	−	0.126725i
$340$	2.71098	−	0.0370058i	0.147023	−	0.00200692i
$341$	−8.96044	+	3.54769i	−0.485235	+	0.192118i
$342$	5.56191	−	0.702633i	0.300754	−	0.0379940i
$343$	−4.88428	+	15.0323i	−0.263726	+	0.811667i
$344$	0.390920	−	0.367098i	0.0210770	−	0.0197926i
$345$	2.63326	−	14.9067i	0.141770	−	0.802547i
$346$	−2.05370	−	10.7659i	−0.110408	−	0.578778i
$347$	−1.42769	−	7.48419i	−0.0766422	−	0.401772i	−0.999847	−	0.0174653i	$-0.994440\pi$
$347$	−1.42769	−	7.48419i	−0.0766422	−	0.401772i	0.923205	−	0.384307i	$-0.125560\pi$
$348$	−0.119024	+	1.89184i	−0.00638037	+	0.101413i
$349$	3.09387	−	2.24783i	0.165611	−	0.120324i	−0.501893	−	0.864930i	$-0.667363\pi$
$349$	3.09387	−	2.24783i	0.165611	−	0.120324i	0.667504	+	0.744606i	$0.267363\pi$
$350$	−3.57030	−	5.30034i	−0.190840	−	0.283315i
$351$	3.99798	+	2.90470i	0.213396	+	0.155041i
$352$	−1.34865	+	1.63024i	−0.0718832	+	0.0868918i
$353$	−11.0754	−	10.4005i	−0.589482	−	0.553560i	0.331356	−	0.943506i	$-0.392494\pi$
$353$	−11.0754	−	10.4005i	−0.589482	−	0.553560i	−0.920838	+	0.389945i	$0.872494\pi$
$354$	−12.2504	−	1.54758i	−0.651100	−	0.0822530i
$355$	−12.1301	+	26.7184i	−0.643798	+	1.41807i
$356$	5.83097	+	3.20560i	0.309041	+	0.169897i
$357$	1.25376	−	0.910910i	0.0663560	−	0.0482105i
$358$	3.59128	−	3.37244i	0.189805	−	0.178239i
$359$	−1.44829	−	23.0199i	−0.0764378	−	1.21494i	−0.830074	−	0.557653i	$-0.811702\pi$
$359$	−1.44829	−	23.0199i	−0.0764378	−	1.21494i	0.753636	−	0.657292i	$-0.228298\pi$
$360$	2.22205	+	0.249948i	0.117113	+	0.0131734i
$361$	6.65955	+	10.4938i	0.350503	+	0.552304i
$362$	−6.83632	+	10.7723i	−0.359309	+	0.566180i
$363$	6.31853	+	1.62232i	0.331637	+	0.0851499i
$364$	−5.87269	−	2.32516i	−0.307813	−	0.121872i
$365$	−28.8556	+	7.83018i	−1.51037	+	0.409850i
$366$	5.13717	−	8.09489i	0.268524	−	0.423127i
$367$	9.08599	+	19.3087i	0.474285	+	1.00791i	0.988636	+	0.150327i	$0.0480327\pi$
$367$	9.08599	+	19.3087i	0.474285	+	1.00791i	−0.514351	+	0.857579i	$0.671967\pi$
$368$	−5.47678	−	3.97911i	−0.285497	−	0.207426i
$369$	1.23197	−	0.155633i	0.0641336	−	0.00810195i
$370$	−1.83018	+	5.90580i	−0.0951464	+	0.307028i
$371$	−0.389511	−	0.365775i	−0.0202224	−	0.0189901i
$372$	3.99150	−	2.19435i	0.206950	−	0.113772i
$373$	23.7828	+	9.41626i	1.23142	+	0.487555i	0.891553	−	0.452917i	$-0.149616\pi$
$373$	23.7828	+	9.41626i	1.23142	+	0.487555i	0.339871	+	0.940472i	$0.389616\pi$
$374$	2.56538			0.132652
$375$	−9.56870	+	5.78273i	−0.494125	+	0.298619i
$376$	6.78834			0.350082
$377$	−8.70969	−	3.44841i	−0.448572	−	0.177602i
$378$	1.12004	−	0.615745i	0.0576084	−	0.0316705i
$379$	−11.6670	−	10.9560i	−0.599294	−	0.562774i	0.324393	−	0.945922i	$-0.394840\pi$
$379$	−11.6670	−	10.9560i	−0.599294	−	0.562774i	−0.923687	+	0.383148i	$0.874840\pi$
$380$	4.03610	+	11.8681i	0.207047	+	0.608823i
$381$	8.52077	−	1.07642i	0.436532	−	0.0551469i
$382$	9.88746	+	7.18366i	0.505886	+	0.367548i
$383$	−0.637920	−	1.35565i	−0.0325962	−	0.0692705i	0.887866	−	0.460102i	$-0.152187\pi$
$383$	−0.637920	−	1.35565i	−0.0325962	−	0.0692705i	−0.920462	+	0.390832i	$0.872187\pi$
$384$	0.535827	−	0.844328i	0.0273438	−	0.0430869i
$385$	−3.30946	−	5.06085i	−0.168666	−	0.257925i
$386$	9.53637	+	3.77571i	0.485388	+	0.192179i
$387$	−0.519417	−	0.133364i	−0.0264034	−	0.00677925i
$388$	6.27189	−	9.88292i	0.318407	−	0.501729i
$389$	−6.82096	−	10.7481i	−0.345836	−	0.544951i	0.626236	−	0.779634i	$-0.284595\pi$
$389$	−6.82096	−	10.7481i	−0.345836	−	0.544951i	−0.972072	+	0.234683i	$0.924595\pi$
$390$	−4.56801	+	10.0618i	−0.231310	+	0.509497i
$391$	0.515398	+	8.19202i	0.0260648	+	0.414288i
$392$	3.91192	−	3.67354i	0.197582	−	0.185542i
$393$	1.31698	−	0.956843i	0.0664329	−	0.0482663i
$394$	8.07127	+	4.43722i	0.406625	+	0.223544i
$395$	−15.2000	+	8.62852i	−0.764796	+	0.434148i
$396$	2.09910	+	0.265177i	0.105483	+	0.0133257i
$397$	1.24438	+	1.16855i	0.0624536	+	0.0586478i	0.715146	−	0.698976i	$-0.246360\pi$
$397$	1.24438	+	1.16855i	0.0624536	+	0.0586478i	−0.652692	+	0.757623i	$0.726360\pi$
$398$	−11.5893	+	14.0091i	−0.580921	+	0.702212i
$399$	5.79690	+	4.21169i	0.290208	+	0.210848i
$400$	0.450045	+	4.97970i	0.0225022	+	0.248985i
$401$	29.3901	−	21.3532i	1.46767	−	1.06633i	0.486391	−	0.873741i	$-0.338313\pi$
$401$	29.3901	−	21.3532i	1.46767	−	1.06633i	0.981280	−	0.192584i	$-0.0616869\pi$
$402$	−0.749390	+	11.9112i	−0.0373762	+	0.594077i
$403$	4.21783	+	22.1107i	0.210105	+	1.10141i
$404$	0.619493	+	3.24750i	0.0308209	+	0.161569i
$405$	−0.979598	−	2.01007i	−0.0486766	−	0.0998813i
$406$	−1.76614	+	1.65852i	−0.0876523	+	0.0823110i
$407$	−1.80783	+	5.56394i	−0.0896110	+	0.275794i
$408$	−1.20294	+	0.151966i	−0.0595543	+	0.00752345i
$409$	24.6707	−	9.76783i	1.21989	−	0.482988i	0.332102	−	0.943243i	$-0.392242\pi$
$409$	24.6707	−	9.76783i	1.21989	−	0.482988i	0.887787	+	0.460255i	$0.152242\pi$
$410$	0.893997	+	2.62880i	0.0441514	+	0.129827i
$411$	6.39931	−	1.64306i	0.315655	−	0.0810464i
$412$	−0.0308048	−	0.489629i	−0.00151765	−	0.0241223i
$413$	−10.0598	−	12.1603i	−0.495013	−	0.598368i
$414$	−0.425071	+	6.75632i	−0.0208911	+	0.332055i
$415$	−3.07213	−	1.63472i	−0.150805	−	0.0802450i
$416$	3.15000	+	3.80770i	0.154442	+	0.186688i
$417$	19.8565	+	10.9162i	0.972376	+	0.534568i
$418$	3.66534	+	11.2808i	0.179278	+	0.551761i
$419$	4.84825	+	10.3031i	0.236853	+	0.503338i	0.987549	−	0.157309i	$-0.0502820\pi$
$419$	4.84825	+	10.3031i	0.236853	+	0.503338i	−0.750697	+	0.660647i	$0.770282\pi$
$420$	1.85164	+	2.17705i	0.0903508	+	0.106229i
$421$	−30.8110	+	16.9385i	−1.50164	+	0.825531i	−0.999235	−	0.0391044i	$-0.987549\pi$
$421$	−30.8110	+	16.9385i	−1.50164	+	0.825531i	−0.502400	+	0.864635i	$0.667549\pi$
$422$	−7.51750	+	15.9755i	−0.365946	+	0.777675i
$423$	−3.63737	−	5.73158i	−0.176855	−	0.278679i
$424$	0.129187	+	0.397595i	0.00627385	+	0.0193089i
$425$	4.30444	−	4.26914i	0.208796	−	0.207084i
$426$	4.05510	−	12.4803i	0.196470	−	0.604674i
$427$	11.8690	−	3.04743i	0.574379	−	0.147475i
$428$	3.77788	+	0.477258i	0.182611	+	0.0230691i
$429$	−4.45182	+	9.46060i	−0.214936	+	0.456762i
$430$	0.0589519	−	1.19767i	0.00284291	−	0.0577570i
$431$	−0.539250	+	2.82685i	−0.0259748	+	0.136164i	−0.992912	−	0.118848i	$-0.962080\pi$
$431$	−0.539250	+	2.82685i	−0.0259748	+	0.136164i	0.966938	+	0.255013i	$0.0820797\pi$
$432$	−1.00000			−0.0481125
$433$	−2.88126	+	15.1041i	−0.138465	+	0.725857i	0.843550	+	0.537051i	$0.180462\pi$
$433$	−2.88126	+	15.1041i	−0.138465	+	0.725857i	−0.982014	+	0.188806i	$0.939538\pi$
$434$	5.63889	+	1.44782i	0.270675	+	0.0694976i
$435$	2.74614	+	3.22875i	0.131667	+	0.154807i
$436$	9.62817	−	11.6385i	0.461106	−	0.557381i
$437$	−35.2865	+	13.9709i	−1.68798	+	0.668319i
$438$	12.4323	−	4.92229i	0.594038	−	0.235196i
$439$	15.1446	−	18.3067i	0.722813	−	0.873730i	−0.273290	−	0.961932i	$-0.588112\pi$
$439$	15.1446	−	18.3067i	0.722813	−	0.873730i	0.996103	+	0.0882013i	$0.0281119\pi$
$440$	0.361483	+	4.71719i	0.0172330	+	0.224883i
$441$	−5.19778	−	1.33456i	−0.247513	−	0.0635506i
$442$	1.12277	−	5.88576i	0.0534046	−	0.279957i
$443$	28.0497			1.33268			0.666341	−	0.745647i	$-0.267859\pi$
$443$	28.0497			1.33268			0.666341	+	0.745647i	$0.267859\pi$
$444$	0.518122	−	2.71609i	0.0245890	−	0.128900i
$445$	14.3596	−	3.89658i	0.680709	−	0.184716i
$446$	−0.737862	+	1.56804i	−0.0349388	+	0.0742487i
$447$	4.60220	+	0.581392i	0.217676	+	0.0274989i
$448$	1.23798	−	0.317859i	0.0584890	−	0.0150174i
$449$	−11.6451	+	35.8401i	−0.549568	+	1.69140i	0.160304	+	0.987068i	$0.448753\pi$
$449$	−11.6451	+	35.8401i	−0.549568	+	1.69140i	−0.709873	+	0.704330i	$0.751247\pi$
$450$	3.96336	−	3.04824i	0.186834	−	0.143696i
$451$	0.811875	+	2.49869i	0.0382297	+	0.117659i
$452$	−5.02722	−	7.92162i	−0.236460	−	0.372602i
$453$	3.23374	−	6.87206i	0.151935	−	0.322877i
$454$	−19.8616	+	10.9190i	−0.932153	+	0.512455i
$455$	−13.0596	+	5.37798i	−0.612241	+	0.252123i
$456$	−2.38697	−	5.07257i	−0.111780	−	0.237545i
$457$	−11.7716	−	36.2292i	−0.550652	−	1.69473i	−0.707158	−	0.707055i	$-0.750023\pi$
$457$	−11.7716	−	36.2292i	−0.550652	−	1.69473i	0.156506	−	0.987677i	$-0.449977\pi$
$458$	11.1968	+	6.15551i	0.523193	+	0.287628i
$459$	0.772875	+	0.934246i	0.0360747	+	0.0436069i
$460$	−14.9908	+	2.10203i	−0.698949	+	0.0980078i
$461$	−1.21132	+	19.2534i	−0.0564168	+	0.896720i	0.863436	+	0.504458i	$0.168308\pi$
$461$	−1.21132	+	19.2534i	−0.0564168	+	0.896720i	−0.919853	+	0.392263i	$0.871692\pi$
$462$	1.72375	+	2.08366i	0.0801962	+	0.0969405i
$463$	−1.86117	−	29.5825i	−0.0864960	−	1.37481i	−0.766801	−	0.641885i	$-0.778153\pi$
$463$	−1.86117	−	29.5825i	−0.0864960	−	1.37481i	0.680305	−	0.732929i	$-0.261847\pi$
$464$	1.83602	−	0.471411i	0.0852353	−	0.0218847i
$465$	3.01486	−	9.72867i	0.139811	−	0.451156i
$466$	3.62574	−	1.43553i	0.167959	−	0.0664997i
$467$	0.492935	−	0.0622722i	0.0228103	−	0.00288161i	−0.113920	−	0.993490i	$-0.536341\pi$
$467$	0.492935	−	0.0622722i	0.0228103	−	0.00288161i	0.136730	+	0.990608i	$0.456341\pi$
$468$	1.52709	−	4.69991i	0.0705899	−	0.217253i
$469$	−11.1198	+	10.4422i	−0.513467	+	0.482177i
$470$	10.9223	−	10.5409i	0.503808	−	0.486217i
$471$	−0.415404	−	2.17763i	−0.0191408	−	0.100340i
$472$	2.31373	+	12.1290i	0.106498	+	0.558283i
$473$	0.0712432	−	1.13238i	0.00327576	−	0.0520668i
$474$	6.32372	−	4.59445i	0.290458	−	0.211030i
$475$	24.9228	+	12.8283i	1.14354	+	0.588604i
$476$	−1.25376	−	0.910910i	−0.0574660	−	0.0417515i
$477$	0.266479	−	0.322118i	0.0122012	−	0.0147488i
$478$	18.2126	+	17.1028i	0.833025	+	0.782262i
$479$	1.64406	+	0.207693i	0.0751190	+	0.00948973i	0.162803	−	0.986659i	$-0.447947\pi$
$479$	1.64406	+	0.207693i	0.0751190	+	0.00948973i	−0.0876839	+	0.996148i	$0.527947\pi$
$480$	−0.448938	−	2.19054i	−0.0204911	−	0.0999839i
$481$	11.9742	+	6.58285i	0.545975	+	0.300152i
$482$	−16.7729	+	12.1862i	−0.763985	+	0.555068i
$483$	−6.30743	+	5.92307i	−0.286998	+	0.269509i
$484$	−0.409613	−	6.51061i	−0.0186188	−	0.295937i
$485$	−5.25485	−	25.6404i	−0.238611	−	1.16427i
$486$	0.535827	+	0.844328i	0.0243056	+	0.0382995i
$487$	2.89706	−	4.56504i	0.131278	−	0.206862i	−0.772330	−	0.635222i	$-0.780909\pi$
$487$	2.89706	−	4.56504i	0.131278	−	0.206862i	0.903608	+	0.428360i	$0.140909\pi$
$488$	−9.28617	−	2.38428i	−0.420365	−	0.107931i
$489$	15.2837	+	6.05126i	0.691155	+	0.273647i
$490$	0.589929	−	11.9851i	0.0266503	−	0.541430i
$491$	−12.8949	+	20.3191i	−0.581939	+	0.916990i	0.418024	+	0.908436i	$0.362723\pi$
$491$	−12.8949	+	20.3191i	−0.581939	+	0.916990i	−0.999963	+	0.00855373i	$0.997277\pi$
$492$	−0.528714	−	1.12358i	−0.0238363	−	0.0506547i
$493$	−1.85943	−	1.35096i	−0.0837446	−	0.0608440i
$494$	27.4857	−	3.47225i	1.23664	−	0.156224i
$495$	3.78917	−	2.83281i	0.170310	−	0.127325i
$496$	−3.32039	−	3.11806i	−0.149090	−	0.140005i
$497$	14.6978	−	8.08017i	0.659285	−	0.362445i
$498$	1.44701	+	0.572911i	0.0648420	+	0.0256727i
$499$	31.5203			1.41104			0.705522	−	0.708688i	$-0.250712\pi$
$499$	31.5203			1.41104			0.705522	+	0.708688i	$0.250712\pi$
$500$	8.45660	+	7.31341i	0.378190	+	0.327066i
$501$	16.0481			0.716976
$502$	−16.7062	−	6.61444i	−0.745632	−	0.295217i
$503$	−26.5168	+	14.5777i	−1.18232	+	0.649989i	−0.946782	−	0.321875i	$-0.895687\pi$
$503$	−26.5168	+	14.5777i	−1.18232	+	0.649989i	−0.235543	+	0.971864i	$0.575687\pi$
$504$	−0.931719	−	0.874942i	−0.0415020	−	0.0389730i
$505$	6.03946	+	4.26321i	0.268753	+	0.189710i
$506$	−14.2102	+	1.79516i	−0.631720	+	0.0798048i
$507$	9.23988	+	6.71317i	0.410358	+	0.298142i
$508$	−3.65680	−	7.77110i	−0.162244	−	0.344787i
$509$	−9.26963	+	14.6066i	−0.410869	+	0.647426i	−0.985242	−	0.171168i	$-0.945246\pi$
$509$	−9.26963	+	14.6066i	−0.410869	+	0.647426i	0.574373	+	0.818594i	$0.305246\pi$
$510$	−1.69953	+	2.11243i	−0.0752563	+	0.0935400i
$511$	15.8901	+	6.29135i	0.702938	+	0.278313i
$512$	−0.968583	−	0.248690i	−0.0428057	−	0.0109906i
$513$	−3.00391	+	4.73340i	−0.132626	+	0.208985i
$514$	11.2366	+	17.7061i	0.495625	+	0.780980i
$515$	−0.809860	−	0.739969i	−0.0356867	−	0.0326069i
$516$	0.0336723	+	0.535206i	0.00148234	+	0.0235611i
$517$	10.4699	−	9.83189i	0.460466	−	0.432406i
$518$	2.85917	−	2.07731i	0.125625	−	0.0912716i
$519$	9.60434	+	5.28003i	0.421584	+	0.231768i
$520$	10.9809	+	1.23519i	0.481544	+	0.0541665i
$521$	−16.0749	−	2.03073i	−0.704254	−	0.0889680i	−0.234954	−	0.972007i	$-0.575494\pi$
$521$	−16.0749	−	2.03073i	−0.704254	−	0.0889680i	−0.469300	+	0.883039i	$0.655494\pi$
$522$	−1.38182	−	1.29761i	−0.0604805	−	0.0567949i
$523$	−2.13192	+	2.57705i	−0.0932223	+	0.112686i	−0.815062	−	0.579374i	$-0.803297\pi$
$523$	−2.13192	+	2.57705i	−0.0932223	+	0.112686i	0.721839	+	0.692061i	$0.243297\pi$
$524$	−1.31698	−	0.956843i	−0.0575326	−	0.0417999i
$525$	6.35977	+	0.627602i	0.277563	+	0.0273908i
$526$	−11.8152	+	8.58421i	−0.515165	+	0.374290i
$527$	−0.346781	+	5.51193i	−0.0151060	+	0.240103i
$528$	−0.396457	−	2.07830i	−0.0172536	−	0.0904465i
$529$	−4.27763	−	22.4241i	−0.185984	−	0.974962i
$530$	0.825244	+	0.439122i	0.0358463	+	0.0190742i
$531$	9.00111	−	8.45260i	0.390615	−	0.366812i
$532$	2.21422	−	6.81467i	0.0959986	−	0.295453i
$533$	6.08809	−	0.769105i	0.263705	−	0.0333136i
$534$	−6.18676	+	2.44951i	−0.267727	+	0.106001i
$535$	6.81962	−	5.09840i	0.294838	−	0.220423i
$536$	11.5598	−	2.96805i	0.499308	−	0.128200i
$537$	0.309339	+	4.91680i	0.0133490	+	0.212176i
$538$	9.01794	+	10.9008i	0.388791	+	0.469968i
$539$	0.712928	−	11.3317i	0.0307080	−	0.488089i
$540$	−1.60898	+	1.55280i	−0.0692394	+	0.0668219i
$541$	13.4829	+	16.2980i	0.579676	+	0.700708i	0.976091	−	0.217364i	$-0.0697458\pi$
$541$	13.4829	+	16.2980i	0.579676	+	0.700708i	−0.396415	+	0.918072i	$0.629746\pi$
$542$	−3.58138	−	1.96888i	−0.153833	−	0.0845707i
$543$	−3.94258	−	12.1340i	−0.169192	−	0.520720i
$544$	0.516256	+	1.09710i	0.0221343	+	0.0470378i
$545$	−2.58067	−	33.6766i	−0.110544	−	1.44255i
$546$	5.53497	−	3.04287i	0.236875	−	0.130223i
$547$	11.2583	−	23.9252i	0.481372	−	1.02297i	−0.505703	−	0.862708i	$-0.668767\pi$
$547$	11.2583	−	23.9252i	0.481372	−	1.02297i	0.987075	−	0.160260i	$-0.0512332\pi$
$548$	−3.54014	−	5.57837i	−0.151227	−	0.238296i
$549$	2.96266	+	9.11813i	0.126443	+	0.389152i
$550$	7.90648	+	7.02856i	0.337133	+	0.299699i
$551$	3.28387	−	10.1067i	0.139898	−	0.430561i
$552$	6.55699	−	1.68355i	0.279084	−	0.0716566i
$553$	9.91180	+	1.25215i	0.421493	+	0.0532469i
$554$	−8.85078	+	18.8089i	−0.376034	+	0.799112i
$555$	−3.38390	−	5.17468i	−0.143639	−	0.219653i
$556$	4.24592	−	22.2579i	0.180067	−	0.943946i
$557$	5.14911			0.218175			0.109087	−	0.994032i	$-0.465207\pi$
$557$	5.14911			0.218175			0.109087	+	0.994032i	$0.465207\pi$
$558$	−0.853506	+	4.47424i	−0.0361318	+	0.189410i
$559$	−2.56684	−	0.659052i	−0.108566	−	0.0278749i
$560$	1.49831	−	2.43376i	0.0633151	−	0.102845i
$561$	−1.63523	+	1.97666i	−0.0690396	+	0.0834545i
$562$	22.7334	−	9.00080i	0.958952	−	0.379676i
$563$	−30.4753	+	12.0660i	−1.28438	+	0.508523i	−0.908399	−	0.418103i	$-0.862695\pi$
$563$	−30.4753	+	12.0660i	−1.28438	+	0.508523i	−0.375983	+	0.926626i	$0.622695\pi$
$564$	−4.32705	+	5.23050i	−0.182202	+	0.220244i
$565$	−20.3894	−	4.93947i	−0.857788	−	0.207805i
$566$	−19.5582	−	5.02170i	−0.822093	−	0.211078i
$567$	−0.239498	+	1.25549i	−0.0100580	+	0.0527258i
$568$	−13.1226			−0.550612
$569$	−1.46792	+	7.69511i	−0.0615385	+	0.322596i	−0.999723	−	0.0235399i	$-0.992506\pi$
$569$	−1.46792	+	7.69511i	−0.0615385	+	0.322596i	0.938184	+	0.346136i	$0.112506\pi$
$570$	−11.7173	−	4.45517i	−0.490782	−	0.186607i
$571$	16.4522	−	34.9627i	0.688503	−	1.46314i	−0.188209	−	0.982129i	$-0.560268\pi$
$571$	16.4522	−	34.9627i	0.688503	−	1.46314i	0.876712	−	0.481015i	$-0.159732\pi$
$572$	10.3733	+	1.31045i	0.433727	+	0.0547925i
$573$	−11.8376	+	3.03938i	−0.494523	+	0.126972i
$574$	0.490450	−	1.50945i	0.0204710	−	0.0630033i
$575$	−20.8558	+	26.6598i	−0.869749	+	1.11179i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	4.92170	+	7.75535i	0.204893	+	0.322860i	0.931199	−	0.364512i	$-0.118764\pi$
$577$	4.92170	+	7.75535i	0.204893	+	0.322860i	−0.726306	+	0.687372i	$0.758764\pi$
$578$	−6.61229	+	14.0518i	−0.275035	+	0.584479i
$579$	−8.98795	+	4.94117i	−0.373526	+	0.205348i
$580$	2.22212	−	3.60947i	0.0922684	−	0.149875i
$581$	0.846940	+	1.79984i	0.0351370	+	0.0746699i
$582$	3.61707	+	11.1322i	0.149932	+	0.461444i
$583$	0.775106	+	0.426118i	0.0321016	+	0.0176480i
$584$	−8.52317	−	10.3027i	−0.352691	−	0.426331i
$585$	−4.84095	−	9.93332i	−0.200149	−	0.410692i
$586$	−1.65106	+	26.2428i	−0.0682046	+	1.08408i
$587$	24.7664	+	29.9374i	1.02222	+	1.23565i	0.971525	+	0.236935i	$0.0761429\pi$
$587$	24.7664	+	29.9374i	1.02222	+	1.23565i	0.0506927	+	0.998714i	$0.483857\pi$
$588$	0.336958	+	5.35579i	0.0138959	+	0.220869i
$589$	−24.7332	+	6.35040i	−1.01911	+	0.261664i
$590$	22.5567	+	15.9226i	0.928644	+	0.655522i
$591$	−8.56376	+	3.39063i	−0.352266	+	0.139472i
$592$	−2.74327	+	0.346555i	−0.112748	+	0.0142433i
$593$	1.03637	−	3.18963i	0.0425587	−	0.130982i	−0.927520	−	0.373775i	$-0.878063\pi$
$593$	1.03637	−	3.18963i	0.0425587	−	0.130982i	0.970078	+	0.242792i	$0.0780633\pi$
$594$	−1.54234	+	1.44835i	−0.0632828	+	0.0594265i
$595$	−3.43174	+	0.481203i	−0.140687	+	0.0197274i
$596$	−0.869219	−	4.55661i	−0.0356046	−	0.186646i
$597$	−3.40688	−	17.8595i	−0.139434	−	0.730939i
$598$	−2.10061	+	33.3882i	−0.0859002	+	1.36534i
$599$	−9.34701	+	6.79100i	−0.381908	+	0.277473i	−0.762132	−	0.647422i	$-0.775847\pi$
$599$	−9.34701	+	6.79100i	−0.381908	+	0.277473i	0.380223	+	0.924895i	$0.375847\pi$
$600$	−4.12380	−	2.82742i	−0.168353	−	0.115429i
$601$	23.4752	+	17.0557i	0.957573	+	0.695718i	0.952586	−	0.304270i	$-0.0984125\pi$
$601$	23.4752	+	17.0557i	0.957573	+	0.695718i	0.00498732	+	0.999988i	$0.498412\pi$
$602$	−0.436901	+	0.528123i	−0.0178068	+	0.0215247i
$603$	−8.70007	−	8.16991i	−0.354294	−	0.332704i
$604$	−7.53500	−	0.951891i	−0.306595	−	0.0387319i
$605$	−10.7687	−	9.83939i	−0.437811	−	0.400028i
$606$	−2.89712	−	1.59270i	−0.117687	−	0.0646992i
$607$	−4.88631	+	3.55011i	−0.198329	+	0.144095i	−0.682518	−	0.730869i	$-0.739115\pi$
$607$	−4.88631	+	3.55011i	−0.198329	+	0.144095i	0.484188	+	0.874964i	$0.339115\pi$
$608$	−4.08668	+	3.83765i	−0.165737	+	0.155637i
$609$	−0.152129	−	2.41802i	−0.00616457	−	0.0979831i
$610$	−18.6436	+	10.5833i	−0.754856	+	0.428505i
$611$	−17.9751	−	28.3242i	−0.727193	−	1.14587i
$612$	0.649689	−	1.02375i	0.0262621	−	0.0413825i
$613$	−2.56135	−	0.657642i	−0.103452	−	0.0265619i	0.196609	−	0.980482i	$-0.437007\pi$
$613$	−2.56135	−	0.657642i	−0.103452	−	0.0265619i	−0.300061	+	0.953920i	$0.597007\pi$
$614$	−24.5279	−	9.71128i	−0.989865	−	0.391915i
$615$	−2.59538	−	0.986822i	−0.104656	−	0.0397925i
$616$	1.44901	−	2.28327i	0.0583822	−	0.0919956i
$617$	−17.8164	−	37.8619i	−0.717263	−	1.52426i	−0.846349	−	0.532629i	$-0.821204\pi$
$617$	−17.8164	−	37.8619i	−0.717263	−	1.52426i	0.129086	−	0.991633i	$-0.458796\pi$
$618$	0.396901	+	0.288366i	0.0159657	+	0.0115998i
$619$	25.2885	−	3.19468i	1.01643	−	0.128405i	0.400575	−	0.916264i	$-0.368810\pi$
$619$	25.2885	−	3.19468i	1.01643	−	0.128405i	0.615856	+	0.787859i	$0.288810\pi$
$620$	−10.1842	+	0.139018i	−0.409006	+	0.00558308i
$621$	−4.93488	−	4.63416i	−0.198030	−	0.185962i
$622$	23.2868	−	12.8020i	0.933716	−	0.513315i
$623$	−7.90750	−	3.13080i	−0.316807	−	0.125433i
$624$	−4.94177			−0.197829
$625$	24.9627	−	1.36428i	0.998510	−	0.0545710i
$626$	14.3887			0.575088
$627$	−11.0284	−	4.36644i	−0.440430	−	0.174379i
$628$	−1.94268	+	1.06800i	−0.0775213	+	0.0426177i
$629$	2.44397	+	2.29504i	0.0974475	+	0.0915093i
$630$	−2.85773	+	0.0390090i	−0.113855	+	0.00155416i
$631$	−5.21391	+	0.658670i	−0.207562	+	0.0262212i	−0.228427	−	0.973561i	$-0.573358\pi$
$631$	−5.21391	+	0.658670i	−0.207562	+	0.0262212i	0.0208644	+	0.999782i	$0.493358\pi$
$632$	−6.32372	−	4.59445i	−0.251544	−	0.182757i
$633$	−7.51750	−	15.9755i	−0.298794	−	0.634969i
$634$	3.95749	−	6.23601i	0.157172	−	0.247663i
$635$	−17.9507	−	6.82526i	−0.712351	−	0.270852i
$636$	−0.388699	−	0.153897i	−0.0154129	−	0.00610241i
$637$	−25.6863	−	6.59511i	−1.01773	−	0.261308i
$638$	2.14900	−	3.38628i	0.0850797	−	0.134064i
$639$	7.03143	+	11.0798i	0.278159	+	0.438309i
$640$	−1.94460	+	1.10388i	−0.0768669	+	0.0436346i
$641$	−2.19034	−	34.8145i	−0.0865132	−	1.37509i	−0.766679	−	0.642030i	$-0.778092\pi$
$641$	−2.19034	−	34.8145i	−0.0865132	−	1.37509i	0.680166	−	0.733058i	$-0.261908\pi$
$642$	−2.77585	+	2.60669i	−0.109554	+	0.102878i
$643$	−0.918750	+	0.667511i	−0.0362320	+	0.0263241i	−0.605754	−	0.795652i	$-0.707128\pi$
$643$	−0.918750	+	0.667511i	−0.0362320	+	0.0263241i	0.569522	+	0.821976i	$0.307128\pi$
$644$	7.58228	+	4.16839i	0.298784	+	0.164258i
$645$	0.885246	+	0.808849i	0.0348565	+	0.0318484i
$646$	6.74381	+	0.851941i	0.265332	+	0.0335192i
$647$	27.8964	+	26.1964i	1.09672	+	1.02989i	0.999400	+	0.0346353i	$0.0110270\pi$
$647$	27.8964	+	26.1964i	1.09672	+	1.02989i	0.0973198	+	0.995253i	$0.468973\pi$
$648$	0.637424	−	0.770513i	0.0250404	−	0.0302686i
$649$	21.1356	+	15.3559i	0.829646	+	0.602773i
$650$	19.5860	−	15.0637i	0.768227	−	0.590848i
$651$	−4.70993	+	3.42196i	−0.184597	+	0.134117i
$652$	1.03216	−	16.4056i	0.0404223	−	0.642495i
$653$	0.848654	+	4.44880i	0.0332104	+	0.174095i	0.995028	−	0.0995966i	$-0.0317552\pi$
$653$	0.848654	+	4.44880i	0.0332104	+	0.174095i	−0.961817	+	0.273692i	$0.911755\pi$
$654$	2.83036	+	14.8373i	0.110676	+	0.580183i
$655$	−3.60478	+	0.505468i	−0.140850	+	0.0197503i
$656$	−0.905202	+	0.850041i	−0.0353422	+	0.0331885i
$657$	−4.13195	+	12.7168i	−0.161203	+	0.496131i
$658$	−8.60798	+	1.08744i	−0.335574	+	0.0423928i
$659$	−31.1638	+	12.3386i	−1.21397	+	0.480644i	−0.885841	−	0.463989i	$-0.846418\pi$
$659$	−31.1638	+	12.3386i	−1.21397	+	0.480644i	−0.328128	+	0.944633i	$0.606418\pi$
$660$	−3.86508	−	2.72833i	−0.150448	−	0.106200i
$661$	11.4951	−	2.95143i	0.447106	−	0.114797i	−0.0184225	−	0.999830i	$-0.505864\pi$
$661$	11.4951	−	2.95143i	0.447106	−	0.114797i	0.465528	+	0.885033i	$0.345864\pi$
$662$	−1.11947	−	17.7935i	−0.0435095	−	0.691564i
$663$	3.81937	+	4.61683i	0.148332	+	0.179303i
$664$	0.0977206	−	1.55322i	0.00379230	−	0.0602768i
$665$	−7.01918	−	14.4029i	−0.272192	−	0.558520i
$666$	1.76252	+	2.13052i	0.0682963	+	0.0825561i
$667$	11.2452	+	6.18208i	0.435414	+	0.239371i
$668$	−4.95913	−	15.2626i	−0.191875	−	0.590530i
$669$	−0.737862	−	1.56804i	−0.0285274	−	0.0606238i
$670$	13.9907	−	22.7256i	0.540508	−	0.877967i
$671$	−17.7757	+	9.77226i	−0.686222	+	0.377254i
$672$	−0.544202	+	1.15649i	−0.0209931	+	0.0446125i
$673$	21.2489	+	33.4829i	0.819085	+	1.29067i	0.953998	+	0.299814i	$0.0969247\pi$
$673$	21.2489	+	33.4829i	0.819085	+	1.29067i	−0.134912	+	0.990858i	$0.543075\pi$
$674$	−6.21487	−	19.1274i	−0.239388	−	0.736760i
$675$	−0.177627	+	4.99684i	−0.00683685	+	0.192329i
$676$	3.52932	−	10.8621i	0.135743	−	0.417774i
$677$	16.0962	−	4.13279i	0.618626	−	0.158836i	0.0736448	−	0.997285i	$-0.476537\pi$
$677$	16.0962	−	4.13279i	0.618626	−	0.158836i	0.544981	+	0.838448i	$0.316537\pi$
$678$	9.30818	+	1.17590i	0.357479	+	0.0451601i
$679$	−6.36993	+	13.5368i	−0.244456	+	0.519494i
$680$	2.53422	+	0.963569i	0.0971830	+	0.0369512i
$681$	4.24703	−	22.2637i	0.162747	−	0.853147i
$682$	−9.63720			−0.369027
$683$	−1.86424	+	9.77267i	−0.0713330	+	0.373941i	0.928662	+	0.370926i	$0.120960\pi$
$683$	−1.86424	+	9.77267i	−0.0713330	+	0.373941i	−0.999995	+	0.00301488i	$0.999040\pi$
$684$	5.42999	+	1.39418i	0.207621	+	0.0533080i
$685$	−14.3581	−	3.47835i	−0.548595	−	0.132901i
$686$	−10.0750	+	12.1786i	−0.384667	+	0.464982i
$687$	−11.8800	+	4.70363i	−0.453251	+	0.179455i
$688$	0.498606	−	0.197412i	0.0190092	−	0.00752627i
$689$	1.31688	−	1.59183i	0.0501691	−	0.0606441i
$690$	7.93585	−	12.8905i	0.302113	−	0.490733i
$691$	−36.0582	−	9.25817i	−1.37172	−	0.352197i	−0.510257	−	0.860022i	$-0.670450\pi$
$691$	−36.0582	−	9.25817i	−1.37172	−	0.352197i	−0.861461	+	0.507824i	$0.830450\pi$
$692$	2.05370	−	10.7659i	0.0780701	−	0.409258i
$693$	−2.70425			−0.102726
$694$	1.42769	−	7.48419i	0.0541942	−	0.284096i
$695$	−27.7305	−	42.4056i	−1.05188	−	1.60854i
$696$	−0.807098	+	1.71517i	−0.0305930	+	0.0650133i
$697$	1.49376	+	0.188705i	0.0565800	+	0.00714772i
$698$	3.70409	−	0.951049i	0.140202	−	0.0359977i
$699$	−1.20504	+	3.70872i	−0.0455787	+	0.140277i
$700$	−1.36839	−	6.24244i	−0.0517204	−	0.235942i
$701$	−2.41305	−	7.42661i	−0.0911397	−	0.280499i	0.895089	−	0.445888i	$-0.147112\pi$
$701$	−2.41305	−	7.42661i	−0.0911397	−	0.280499i	−0.986228	+	0.165389i	$0.947112\pi$
$702$	2.64793	+	4.17248i	0.0999399	+	0.157480i
$703$	−6.60013	+	14.0260i	−0.248929	+	0.529001i
$704$	−1.85407	+	1.01928i	−0.0698779	+	0.0384157i
$705$	1.15979	+	15.1348i	0.0436803	+	0.570010i
$706$	−6.46895	−	13.7472i	−0.243462	−	0.517383i
$707$	−1.30578	−	4.01876i	−0.0491087	−	0.151141i
$708$	−10.8204	−	5.94856i	−0.406655	−	0.223561i
$709$	−19.5767	−	23.6642i	−0.735219	−	0.888727i	0.261860	−	0.965106i	$-0.415664\pi$
$709$	−19.5767	−	23.6642i	−0.735219	−	0.888727i	−0.997079	+	0.0763790i	$0.975664\pi$
$710$	−21.1140	+	20.3767i	−0.792393	+	0.764726i
$711$	−0.490805	+	7.80112i	−0.0184066	+	0.292565i
$712$	4.24144	+	5.12702i	0.158955	+	0.192143i
$713$	−1.93616	−	30.7745i	−0.0725099	−	1.15251i
$714$	1.50105	−	0.385403i	0.0561752	−	0.0144233i
$715$	18.7252	−	13.9991i	0.700283	−	0.523537i
$716$	4.58057	−	1.81358i	0.171184	−	0.0677765i
$717$	−24.7870	+	3.13133i	−0.925689	+	0.116942i
$718$	7.12761	−	21.9365i	0.266000	−	0.818664i
$719$	6.28225	−	5.89943i	0.234289	−	0.220012i	−0.558506	−	0.829500i	$-0.688625\pi$
$719$	6.28225	−	5.89943i	0.234289	−	0.220012i	0.792795	+	0.609489i	$0.208625\pi$
$720$	1.97400	+	1.05039i	0.0735667	+	0.0391457i
$721$	0.117497	+	0.615941i	0.00437582	+	0.0229389i
$722$	2.32888	+	12.2084i	0.0866719	+	0.454350i
$723$	1.30180	−	20.6915i	0.0484145	−	0.769527i
$724$	−10.3218	+	7.49923i	−0.383607	+	0.278707i
$725$	−2.02944	−	9.25806i	−0.0753715	−	0.343836i
$726$	5.27761	+	3.83441i	0.195870	+	0.142308i
$727$	16.9831	−	20.5291i	0.629870	−	0.761382i	−0.354964	−	0.934880i	$-0.615507\pi$
$727$	16.9831	−	20.5291i	0.629870	−	0.761382i	0.984834	+	0.173498i	$0.0555069\pi$
$728$	−4.60434	−	4.32377i	−0.170648	−	0.160249i
$729$	−0.992115	−	0.125333i	−0.0367450	−	0.00464197i
$730$	−29.7117	−	3.34212i	−1.09968	−	0.123697i
$731$	−0.569792	−	0.313246i	−0.0210745	−	0.0115858i
$732$	7.75635	−	5.63532i	0.286683	−	0.208287i
$733$	3.90158	−	3.66383i	0.144108	−	0.135327i	−0.609141	−	0.793062i	$-0.708486\pi$
$733$	3.90158	−	3.66383i	0.144108	−	0.135327i	0.753249	+	0.657736i	$0.228486\pi$
$734$	1.33993	+	21.2976i	0.0494577	+	0.786107i
$735$	8.85862	+	8.09412i	0.326755	+	0.298556i
$736$	−3.62737	−	5.71583i	−0.133707	−	0.210688i
$737$	13.5303	−	21.3204i	0.498396	−	0.785347i
$738$	1.20275	+	0.308812i	0.0442737	+	0.0113675i
$739$	−20.6202	−	8.16412i	−0.758527	−	0.300322i	−0.0431575	−	0.999068i	$-0.513742\pi$
$739$	−20.6202	−	8.16412i	−0.758527	−	0.300322i	−0.715370	+	0.698746i	$0.753742\pi$
$740$	−3.87573	+	4.81734i	−0.142475	+	0.177089i
$741$	−14.8446	+	23.3914i	−0.545331	+	0.859305i
$742$	−0.227507	−	0.483478i	−0.00835206	−	0.0177490i
$743$	21.4595	+	15.5912i	0.787273	+	0.571987i	0.907153	−	0.420801i	$-0.138251\pi$
$743$	21.4595	+	15.5912i	0.787273	+	0.571987i	−0.119880	+	0.992788i	$0.538251\pi$
$744$	4.51900	−	0.570882i	0.165675	−	0.0209296i
$745$	−8.47406	−	5.98176i	−0.310465	−	0.219155i
$746$	18.6463	+	17.5100i	0.682689	+	0.641088i
$747$	−1.36379	+	0.749751i	−0.0498986	+	0.0274320i
$748$	2.38523	+	0.944378i	0.0872125	+	0.0345299i
$749$	−4.86702			−0.177837
$750$	−11.0255	+	1.85418i	−0.402595	+	0.0677049i
$751$	−32.7335			−1.19446			−0.597231	−	0.802070i	$-0.703732\pi$
$751$	−32.7335			−1.19446			−0.597231	+	0.802070i	$0.703732\pi$
$752$	6.31164	+	2.49895i	0.230162	+	0.0911274i
$753$	15.7454	−	8.65612i	0.573795	−	0.315446i
$754$	−6.82862	−	6.41250i	−0.248684	−	0.233530i
$755$	−13.6017	+	10.1688i	−0.495018	+	0.370079i
$756$	1.26805	−	0.160193i	0.0461187	−	0.00582615i
$757$	35.7672	+	25.9864i	1.29998	+	0.944490i	0.999955	−	0.00944148i	$-0.00300536\pi$
$757$	35.7672	+	25.9864i	1.29998	+	0.944490i	0.300024	+	0.953932i	$0.403005\pi$
$758$	−6.81451	−	14.4816i	−0.247514	−	0.525995i
$759$	7.67472	−	12.0934i	0.278575	−	0.438963i
$760$	−0.616284	+	12.5205i	−0.0223550	+	0.454166i
$761$	−6.64717	−	2.63180i	−0.240960	−	0.0954027i	0.244541	−	0.969639i	$-0.421363\pi$
$761$	−6.64717	−	2.63180i	−0.240960	−	0.0954027i	−0.485501	+	0.874236i	$0.661363\pi$
$762$	8.31867	+	2.13587i	0.301354	+	0.0773745i
$763$	−10.3446	+	16.3006i	−0.374501	+	0.590120i
$764$	6.54865	+	10.3190i	0.236922	+	0.373329i
$765$	−0.544336	−	2.65602i	−0.0196805	−	0.0960287i
$766$	−0.0940754	−	1.49529i	−0.00339908	−	0.0540269i
$767$	44.4814	−	41.7708i	1.60613	−	1.50826i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−31.0142	−	17.0502i	−1.11840	−	0.614845i	−0.188284	−	0.982115i	$-0.560293\pi$
$769$	−31.0142	−	17.0502i	−1.11840	−	0.614845i	−0.930115	+	0.367270i	$0.880293\pi$
$770$	−1.21404	−	5.92375i	−0.0437509	−	0.213477i
$771$	−20.8052	−	2.62831i	−0.749282	−	0.0946563i
$772$	7.47676	+	7.02114i	0.269094	+	0.252696i
$773$	−15.7841	+	19.0797i	−0.567716	+	0.686250i	−0.973753	−	0.227606i	$-0.926910\pi$
$773$	−15.7841	+	19.0797i	−0.567716	+	0.686250i	0.406038	+	0.913856i	$0.366910\pi$
$774$	−0.433847	−	0.315208i	−0.0155943	−	0.0113299i
$775$	−16.1702	+	16.0376i	−0.580852	+	0.576089i
$776$	9.46961	−	6.88007i	0.339939	−	0.246980i
$777$	−0.221910	+	3.52715i	−0.00796096	+	0.126536i
$778$	−2.38532	−	12.5043i	−0.0855180	−	0.448301i
$779$	1.30444	+	6.83813i	0.0467365	+	0.245001i
$780$	−7.95121	+	7.67358i	−0.284699	+	0.274758i
$781$	−20.2394	+	19.0061i	−0.724224	+	0.680092i
$782$	−2.53648	+	7.80648i	−0.0907043	+	0.279159i
$783$	1.88063	−	0.237579i	0.0672082	−	0.00849037i
$784$	4.98953	−	1.97550i	0.178198	−	0.0705534i
$785$	−1.46734	+	4.73497i	−0.0523718	+	0.168998i
$786$	1.57674	−	0.404837i	0.0562403	−	0.0144401i
$787$	−2.05453	−	32.6558i	−0.0732361	−	1.16405i	−0.847359	−	0.531020i	$-0.821809\pi$
$787$	−2.05453	−	32.6558i	−0.0732361	−	1.16405i	0.774123	−	0.633035i	$-0.218191\pi$
$788$	5.87103	+	7.09686i	0.209147	+	0.252815i
$789$	0.917014	−	14.5755i	0.0326466	−	0.518902i
$790$	−17.3090	+	2.42709i	−0.615826	+	0.0863521i
$791$	7.64377	+	9.23973i	0.271781	+	0.328527i
$792$	1.85407	+	1.01928i	0.0658815	+	0.0362187i
$793$	14.6408	+	45.0598i	0.519910	+	1.60012i
$794$	0.726823	+	1.54458i	0.0257940	+	0.0548150i
$795$	−0.864380	+	0.355955i	−0.0306564	+	0.0126244i
$796$	−15.9326	+	8.75901i	−0.564715	+	0.310455i
$797$	−20.8397	+	44.2866i	−0.738180	+	1.56871i	0.0820163	+	0.996631i	$0.473864\pi$
$797$	−20.8397	+	44.2866i	−0.738180	+	1.56871i	−0.820197	+	0.572082i	$0.806136\pi$
$798$	3.83939	+	6.04992i	0.135913	+	0.214165i
$799$	−2.54347	−	7.82800i	−0.0899815	−	0.276935i
$800$	−1.41471	+	4.79568i	−0.0500176	+	0.169553i
$801$	2.05621	−	6.32836i	0.0726526	−	0.223602i
$802$	35.1868	−	9.03444i	1.24249	−	0.319017i
$803$	−28.0676	−	3.54576i	−0.990483	−	0.125127i
$804$	−5.08157	+	10.7989i	−0.179213	+	0.380848i
$805$	18.6724	−	5.06690i	0.658116	−	0.178585i
$806$	−4.21783	+	22.1107i	−0.148567	+	0.778815i
$807$	−14.1475			−0.498015
$808$	−0.619493	+	3.24750i	−0.0217937	+	0.114247i
$809$	−47.2541	−	12.1328i	−1.66137	−	0.426566i	−0.702788	−	0.711399i	$-0.748062\pi$
$809$	−47.2541	−	12.1328i	−1.66137	−	0.426566i	−0.958577	+	0.284833i	$0.908062\pi$
$810$	−0.170851	−	2.22953i	−0.00600309	−	0.0783377i
$811$	6.17792	−	7.46782i	0.216936	−	0.262231i	−0.650808	−	0.759243i	$-0.725570\pi$
$811$	6.17792	−	7.46782i	0.216936	−	0.262231i	0.867744	+	0.497012i	$0.165570\pi$
$812$	−2.25266	+	0.891892i	−0.0790529	+	0.0312993i
$813$	3.79991	−	1.50449i	0.133269	−	0.0527648i
$814$	−3.72911	+	4.50771i	−0.130705	+	0.157995i
$815$	−23.8140	−	27.9991i	−0.834167	−	0.980764i
$816$	−1.17440	−	0.301536i	−0.0411124	−	0.0105559i
$817$	0.563336	−	2.95311i	0.0197086	−	0.103316i
$818$	26.5340			0.927741
$819$	−1.18355	+	6.20436i	−0.0413564	+	0.216798i
$820$	−0.136507	+	2.77330i	−0.00476704	+	0.0968477i
$821$	13.3943	−	28.4644i	0.467465	−	0.993414i	−0.522571	−	0.852596i	$-0.675027\pi$
$821$	13.3943	−	28.4644i	0.467465	−	0.993414i	0.990036	−	0.140818i	$-0.0449731\pi$
$822$	6.55478	+	0.828061i	0.228624	+	0.0288820i
$823$	−3.92672	+	1.00821i	−0.136877	+	0.0351440i	−0.316507	−	0.948590i	$-0.602510\pi$
$823$	−3.92672	+	1.00821i	−0.136877	+	0.0351440i	0.179630	+	0.983734i	$0.442510\pi$
$824$	0.151603	−	0.466585i	0.00528133	−	0.0162543i
$825$	−10.4554	+	1.61187i	−0.364009	+	0.0561182i
$826$	−4.87692	−	15.0096i	−0.169690	−	0.522251i
$827$	18.9013	+	29.7838i	0.657264	+	1.03568i	0.995513	+	0.0946260i	$0.0301655\pi$
$827$	18.9013	+	29.7838i	0.657264	+	1.03568i	−0.338249	+	0.941057i	$0.609834\pi$
$828$	−2.88239	+	6.12538i	−0.100170	+	0.212872i
$829$	−41.5153	+	22.8232i	−1.44188	+	0.792683i	−0.994804	−	0.101811i	$-0.967536\pi$
$829$	−41.5153	+	22.8232i	−1.44188	+	0.792683i	−0.447081	+	0.894494i	$0.647536\pi$
$830$	−2.25462	−	2.65085i	−0.0782589	−	0.0920122i
$831$	−8.85078	−	18.8089i	−0.307030	−	0.652473i
$832$	1.52709	+	4.69991i	0.0529424	+	0.162940i
$833$	−5.70188	−	3.13464i	−0.197559	−	0.108609i
$834$	14.4436	+	17.4593i	0.500140	+	0.604565i
$835$	−31.6790	−	16.8567i	−1.09630	−	0.583351i
$836$	−0.744777	+	11.8379i	−0.0257587	+	0.409422i
$837$	−2.90341	−	3.50962i	−0.100357	−	0.121310i
$838$	0.714982	+	11.3643i	0.0246986	+	0.392573i
$839$	17.8115	−	4.57322i	0.614922	−	0.157885i	0.0716330	−	0.997431i	$-0.477179\pi$
$839$	17.8115	−	4.57322i	0.614922	−	0.157885i	0.543289	+	0.839546i	$0.317179\pi$
$840$	0.920186	+	2.70580i	0.0317494	+	0.0933591i
$841$	23.6226	−	9.35286i	0.814574	−	0.322512i
$842$	−34.8828	+	4.40672i	−1.20214	+	0.151866i
$843$	−7.55560	+	23.2537i	−0.260229	+	0.800901i
$844$	−12.8706	+	12.0863i	−0.443023	+	0.416026i
$845$	−11.1881	−	22.9573i	−0.384883	−	0.789754i
$846$	−1.27201	−	6.66810i	−0.0437325	−	0.229254i
$847$	1.56236	+	8.19019i	0.0536834	+	0.281418i
$848$	−0.0262500	+	0.417232i	−0.000901428	+	0.0143278i
$849$	16.3362	−	11.8689i	0.560656	−	0.407340i
$850$	5.57374	−	2.38478i	0.191178	−	0.0817972i
$851$	−15.1437	−	11.0025i	−0.519119	−	0.377162i
$852$	8.36465	−	10.1111i	0.286568	−	0.346402i
$853$	14.9776	+	14.0649i	0.512823	+	0.481573i	0.897213	−	0.441598i	$-0.145588\pi$
$853$	14.9776	+	14.0649i	0.512823	+	0.481573i	−0.384390	+	0.923171i	$0.625588\pi$
$854$	12.1573	+	1.53583i	0.416015	+	0.0525549i
$855$	10.9016	−	6.18847i	0.372828	−	0.211641i
$856$	3.33690	+	1.83447i	0.114053	+	0.0627011i
$857$	−3.35215	+	2.43548i	−0.114507	+	0.0831943i	−0.643565	−	0.765391i	$-0.722545\pi$
$857$	−3.35215	+	2.43548i	−0.114507	+	0.0831943i	0.529058	+	0.848586i	$0.322545\pi$
$858$	−7.62188	+	7.15742i	−0.260207	+	0.244350i
$859$	−0.742483	−	11.8014i	−0.0253332	−	0.402660i	−0.990175	−	0.139830i	$-0.955344\pi$
$859$	−0.742483	−	11.8014i	−0.0253332	−	0.402660i	0.964842	−	0.262830i	$-0.0846557\pi$
$860$	0.495705	−	1.09187i	0.0169034	−	0.0372324i
$861$	0.850427	+	1.34006i	0.0289825	+	0.0456691i
$862$	−1.54201	+	2.42983i	−0.0525212	+	0.0827602i
$863$	13.6516	+	3.50512i	0.464704	+	0.119316i	0.473780	−	0.880643i	$-0.342889\pi$
$863$	13.6516	+	3.50512i	0.464704	+	0.119316i	−0.00907601	+	0.999959i	$0.502889\pi$
$864$	−0.929776	−	0.368125i	−0.0316316	−	0.0125239i
$865$	−13.4129	−	20.5111i	−0.456053	−	0.697398i
$866$	−8.23912	+	12.9828i	−0.279977	+	0.441173i
$867$	−6.61229	−	14.0518i	−0.224565	−	0.477225i
$868$	4.70993	+	3.42196i	0.159865	+	0.116149i
$869$	−16.4077	+	2.07277i	−0.556592	+	0.0703139i
$870$	1.36471	+	4.01293i	0.0462681	+	0.136051i
$871$	−42.9938	−	40.3738i	−1.45679	−	1.36802i
$872$	13.2364	−	7.27680i	0.448243	−	0.246423i
$873$	−10.8831	−	4.30893i	−0.368337	−	0.145835i
$874$	−37.9516			−1.28373
$875$	−11.8950	−	7.91912i	−0.402124	−	0.267715i
$876$	13.3713			0.451773
$877$	12.1481	+	4.80978i	0.410213	+	0.162415i	0.564162	−	0.825664i	$-0.309199\pi$
$877$	12.1481	+	4.80978i	0.410213	+	0.162415i	−0.153949	+	0.988079i	$0.549199\pi$
$878$	20.8202	−	11.4460i	0.702649	−	0.386285i
$879$	−19.1680	−	18.0000i	−0.646522	−	0.607124i
$880$	−1.40042	+	4.51901i	−0.0472081	+	0.152336i
$881$	53.4285	−	6.74958i	1.80005	−	0.227399i	0.847292	−	0.531128i	$-0.178232\pi$
$881$	53.4285	−	6.74958i	1.80005	−	0.227399i	0.952759	+	0.303729i	$0.0982316\pi$
$882$	−4.34149	−	3.15428i	−0.146186	−	0.106210i
$883$	−11.6678	−	24.7954i	−0.392653	−	0.834431i	−0.999223	−	0.0394011i	$-0.987455\pi$
$883$	−11.6678	−	24.7954i	−0.392653	−	0.834431i	0.606570	−	0.795030i	$-0.292545\pi$
$884$	3.21062	−	5.05912i	0.107985	−	0.170157i
$885$	−26.6467	+	7.23080i	−0.895720	+	0.243061i
$886$	26.0800	+	10.3258i	0.876174	+	0.346902i
$887$	14.0768	+	3.61431i	0.472652	+	0.121356i	0.477500	−	0.878632i	$-0.341543\pi$
$887$	14.0768	+	3.61431i	0.472652	+	0.121356i	−0.00484765	+	0.999988i	$0.501543\pi$
$888$	1.48160	−	2.33463i	0.0497192	−	0.0783449i
$889$	5.88190	+	9.26839i	0.197272	+	0.310852i
$890$	14.7856	+	1.66316i	0.495615	+	0.0557493i
$891$	−0.132851	−	2.11160i	−0.00445067	−	0.0707414i
$892$	−1.26328	+	1.18630i	−0.0422977	+	0.0397202i
$893$	30.7881	−	22.3689i	1.03029	−	0.748546i
$894$	4.06499	+	2.23475i	0.135954	+	0.0747411i
$895$	4.55392	−	10.0307i	0.152221	−	0.335290i
$896$	1.26805	+	0.160193i	0.0423627	+	0.00535166i
$897$	−24.3871	−	22.9010i	−0.814260	−	0.764641i
$898$	−24.0210	+	29.0364i	−0.801591	+	0.968957i
$899$	6.98521	+	5.07505i	0.232970	+	0.169263i
$900$	4.80717	−	1.37518i	0.160239	−	0.0458392i
$901$	0.410085	−	0.297944i	0.0136619	−	0.00992595i
$902$	−0.164968	+	2.62210i	−0.00549285	+	0.0873063i
$903$	−0.128434	−	0.673276i	−0.00427403	−	0.0224052i
$904$	−1.75804	−	9.21598i	−0.0584716	−	0.306519i
$905$	−4.96276	+	28.0938i	−0.164968	+	0.933869i
$906$	5.53643	−	5.19906i	0.183936	−	0.172727i
$907$	16.5832	−	51.0379i	0.550637	−	1.69469i	−0.156558	−	0.987669i	$-0.550040\pi$
$907$	16.5832	−	51.0379i	0.550637	−	1.69469i	0.707195	−	0.707018i	$-0.249960\pi$
$908$	−22.4864	+	2.84070i	−0.746239	+	0.0942719i
$909$	3.07389	−	1.21704i	0.101955	−	0.0403667i
$910$	−14.1222	+	0.192774i	−0.468147	+	0.00639039i
$911$	−0.340570	+	0.0874435i	−0.0112836	+	0.00289713i	−0.254327	−	0.967118i	$-0.581854\pi$
$911$	−0.340570	+	0.0874435i	−0.0112836	+	0.00289713i	0.243044	+	0.970015i	$0.421854\pi$
$912$	−0.352011	−	5.59506i	−0.0116563	−	0.185271i
$913$	−2.09890	−	2.53713i	−0.0694633	−	0.0839667i
$914$	2.39192	−	38.0185i	0.0791177	−	1.25754i
$915$	3.72928	−	21.1112i	0.123286	−	0.697913i
$916$	8.14455	+	9.84507i	0.269104	+	0.325290i
$917$	1.82328	+	1.00236i	0.0602101	+	0.0331008i
$918$	0.374682	+	1.15315i	0.0123664	+	0.0380598i
$919$	−19.2781	−	40.9680i	−0.635925	−	1.35141i	−0.919739	−	0.392531i	$-0.871600\pi$
$919$	−19.2781	−	40.9680i	−0.635925	−	1.35141i	0.283813	−	0.958880i	$-0.408400\pi$
$920$	−14.7119	−	3.56406i	−0.485037	−	0.117504i
$921$	23.1173	−	12.7089i	0.761742	−	0.418771i
$922$	−8.21391	+	17.4554i	−0.270511	+	0.574864i
$923$	34.7478	+	54.7537i	1.14374	+	1.80224i
$924$	0.835658	+	2.57189i	0.0274911	+	0.0846090i
$925$	1.24440	+	13.7692i	0.0409158	+	0.452729i
$926$	9.15956	−	28.1902i	0.301002	−	0.926388i
$927$	−0.475184	+	0.122006i	−0.0156071	+	0.00400722i
$928$	1.88063	+	0.237579i	0.0617347	+	0.00779891i
$929$	4.00418	−	8.50932i	0.131373	−	0.279182i	−0.828308	−	0.560273i	$-0.810696\pi$
$929$	4.00418	−	8.50932i	0.131373	−	0.279182i	0.959681	+	0.281091i	$0.0906963\pi$
$930$	6.38451	−	7.93564i	0.209356	−	0.260220i
$931$	5.63728	−	29.5517i	0.184754	−	0.968517i
$932$	3.89958			0.127735
$933$	−4.97943	+	26.1031i	−0.163019	+	0.854577i
$934$	0.481243	+	0.123562i	0.0157468	+	0.00404308i
$935$	5.30421	−	2.18430i	0.173466	−	0.0714341i
$936$	3.15000	−	3.80770i	0.102961	−	0.124459i
$937$	−44.8287	+	17.7489i	−1.46449	+	0.579832i	−0.959102	−	0.283060i	$-0.908650\pi$
$937$	−44.8287	+	17.7489i	−1.46449	+	0.579832i	−0.505387	+	0.862893i	$0.668650\pi$
$938$	−14.1830	+	5.61545i	−0.463092	+	0.183351i
$939$	−9.17171	+	11.0867i	−0.299307	+	0.361800i
$940$	14.0357	−	5.77994i	0.457793	−	0.188521i
$941$	6.70022	+	1.72032i	0.218421	+	0.0560810i	0.356315	−	0.934366i	$-0.384033\pi$
$941$	6.70022	+	1.72032i	0.218421	+	0.0560810i	−0.137894	+	0.990447i	$0.544033\pi$
$942$	0.415404	−	2.17763i	0.0135346	−	0.0709509i
$943$	−8.40629			−0.273747
$944$	−2.31373	+	12.1290i	−0.0753056	+	0.394766i
$945$	1.79153	−	2.22678i	0.0582783	−	0.0724372i
$946$	0.483096	−	1.02663i	0.0157068	−	0.0333787i
$947$	32.6360	+	4.12288i	1.06053	+	0.133976i	0.636193	−	0.771530i	$-0.280508\pi$
$947$	32.6360	+	4.12288i	1.06053	+	0.133976i	0.424334	+	0.905506i	$0.360508\pi$
$948$	7.57097	−	1.94390i	0.245894	−	0.0631348i
$949$	−20.4192	+	62.8437i	−0.662834	+	2.03999i
$950$	18.4502	+	21.1022i	0.598605	+	0.684645i
$951$	2.28233	+	7.02428i	0.0740095	+	0.227778i
$952$	−0.830389	−	1.30848i	−0.0269130	−	0.0424082i
$953$	−9.25262	+	19.6628i	−0.299722	+	0.636941i	−0.996790	−	0.0800638i	$-0.974488\pi$
$953$	−9.25262	+	19.6628i	−0.299722	+	0.636941i	0.697068	+	0.717005i	$0.254488\pi$
$954$	0.366346	−	0.201400i	0.0118609	−	0.00652057i
$955$	26.5600	+	6.43434i	0.859461	+	0.208210i
$956$	10.6377	+	22.6062i	0.344048	+	0.731138i
$957$	1.23935	+	3.81433i	0.0400625	+	0.123300i
$958$	1.45215	+	0.798327i	0.0469169	+	0.0257928i
$959$	5.38271	+	6.50657i	0.173817	+	0.210108i
$960$	0.388979	−	2.20198i	0.0125542	−	0.0710685i
$961$	−0.643774	+	10.2325i	−0.0207669	+	0.330081i
$962$	8.70998	+	10.5286i	0.280821	+	0.339454i
$963$	−0.239101	−	3.80040i	−0.00770491	−	0.122466i
$964$	−20.0811	+	5.15595i	−0.646769	+	0.166062i
$965$	22.9324	−	0.313036i	0.738219	−	0.0100770i
$966$	−8.04493	+	3.18521i	−0.258841	+	0.102483i
$967$	3.25786	−	0.411564i	0.104766	−	0.0132350i	−0.0727755	−	0.997348i	$-0.523186\pi$
$967$	3.25786	−	0.411564i	0.104766	−	0.0132350i	0.177541	+	0.984113i	$0.443186\pi$
$968$	2.01587	−	6.20420i	0.0647924	−	0.199411i
$969$	−4.95510	+	4.65314i	−0.159181	+	0.149481i
$970$	4.55302	−	25.7743i	0.146189	−	0.827563i
$971$	−4.52895	−	23.7416i	−0.145341	−	0.761903i	−0.978079	−	0.208236i	$-0.933228\pi$
$971$	−4.52895	−	23.7416i	−0.145341	−	0.761903i	0.832738	−	0.553668i	$-0.186772\pi$
$972$	0.187381	+	0.982287i	0.00601026	+	0.0315069i
$973$	−1.81851	+	28.9044i	−0.0582988	+	0.926633i
$974$	4.37412	−	3.17799i	0.140156	−	0.101829i
$975$	−0.877790	+	24.6933i	−0.0281118	+	0.790818i
$976$	−7.75635	−	5.63532i	−0.248275	−	0.180382i
$977$	−1.89979	+	2.29645i	−0.0607797	+	0.0734700i	−0.800027	−	0.599964i	$-0.795182\pi$
$977$	−1.89979	+	2.29645i	−0.0607797	+	0.0734700i	0.739247	+	0.673434i	$0.235182\pi$
$978$	11.9828	+	11.2526i	0.383169	+	0.359820i
$979$	13.9674	+	1.76450i	0.446402	+	0.0563936i
$980$	4.96050	−	10.9263i	0.158457	−	0.349027i
$981$	−13.2364	−	7.27680i	−0.422607	−	0.232330i
$982$	−19.4694	+	14.1453i	−0.621292	+	0.451395i
$983$	32.6579	−	30.6678i	1.04162	−	0.978150i	0.0418444	−	0.999124i	$-0.486677\pi$
$983$	32.6579	−	30.6678i	1.04162	−	0.978150i	0.999780	+	0.0209737i	$0.00667662\pi$
$984$	−0.0779706	−	1.23931i	−0.00248561	−	0.0395077i
$985$	20.4664	+	2.30216i	0.652112	+	0.0733529i
$986$	−1.23154	−	1.94059i	−0.0392201	−	0.0618010i
$987$	4.64904	−	7.32572i	0.147981	−	0.233180i
$988$	26.8338	+	6.88975i	0.853697	+	0.219192i
$989$	3.37540	+	1.33642i	0.107331	+	0.0424955i
$990$	4.56591	−	1.23899i	0.145114	−	0.0393778i
$991$	−24.5510	+	38.6861i	−0.779887	+	1.22890i	0.189140	+	0.981950i	$0.439430\pi$
$991$	−24.5510	+	38.6861i	−0.779887	+	1.22890i	−0.969027	+	0.246955i	$0.920570\pi$
$992$	−1.93939	−	4.12141i	−0.0615757	−	0.130855i
$993$	14.4237	+	10.4794i	0.457723	+	0.332555i
$994$	16.6402	−	2.10214i	0.527794	−	0.0666758i
$995$	−12.0342	+	38.8332i	−0.381510	+	1.23109i
$996$	1.13449	+	1.06536i	0.0359477	+	0.0337572i
$997$	39.9749	−	21.9764i	1.26602	−	0.695999i	0.299867	−	0.953981i	$-0.403058\pi$
$997$	39.9749	−	21.9764i	1.26602	−	0.695999i	0.966150	+	0.257982i	$0.0830576\pi$
$998$	29.3069	+	11.6034i	0.927693	+	0.367300i
$999$	−2.76507			−0.0874829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.c.721.6	yes	120
125.56	even	25	inner	750.2.m.c.181.6	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.c.181.6	✓	120	125.56	even	25	inner
750.2.m.c.721.6	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929776 + 0.368125i) q^{2} +(-0.876307 + 0.481754i) q^{3} +(0.728969 + 0.684547i) q^{4} +(2.23586 - 0.0305203i) q^{5} +(-0.992115 + 0.125333i) q^{6} +(-1.03403 - 0.751268i) q^{7} +(0.425779 + 0.904827i) q^{8} +(0.535827 - 0.844328i) q^{9} +O(q^{10})\)	\(q+(0.929776 + 0.368125i) q^{2} +(-0.876307 + 0.481754i) q^{3} +(0.728969 + 0.684547i) q^{4} +(2.23586 - 0.0305203i) q^{5} +(-0.992115 + 0.125333i) q^{6} +(-1.03403 - 0.751268i) q^{7} +(0.425779 + 0.904827i) q^{8} +(0.535827 - 0.844328i) q^{9} +(2.09009 + 0.794698i) q^{10} +(1.96720 + 0.778870i) q^{11} +(-0.968583 - 0.248690i) q^{12} +(2.64793 - 4.17248i) q^{13} +(-0.684858 - 1.07916i) q^{14} +(-1.94460 + 1.10388i) q^{15} +(0.0627905 + 0.998027i) q^{16} +(0.883873 - 0.830012i) q^{17} +(0.809017 - 0.587785i) q^{18} +(4.91268 + 2.70077i) q^{19} +(1.65076 + 1.50830i) q^{20} +(1.26805 + 0.160193i) q^{21} +(1.54234 + 1.44835i) q^{22} +(-4.31515 + 5.21612i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(4.99814 - 0.136478i) q^{25} +(3.99798 - 2.90470i) q^{26} +(-0.0627905 + 0.998027i) q^{27} +(-0.239498 - 1.25549i) q^{28} +(-0.355196 - 1.86200i) q^{29} +(-2.21440 + 0.310507i) q^{30} +(-3.32039 + 3.11806i) q^{31} +(-0.309017 + 0.951057i) q^{32} +(-2.09910 + 0.265177i) q^{33} +(1.12735 - 0.446350i) q^{34} +(-2.33488 - 1.64817i) q^{35} +(0.968583 - 0.248690i) q^{36} +(0.173620 + 2.75961i) q^{37} +(3.57347 + 4.31959i) q^{38} +(-0.310297 + 4.93202i) q^{39} +(0.979598 + 2.01007i) q^{40} +(0.791526 + 0.956790i) q^{41} +(1.12004 + 0.615745i) q^{42} +(-0.165715 - 0.510018i) q^{43} +(0.900855 + 1.91441i) q^{44} +(1.17226 - 1.90415i) q^{45} +(-5.93231 + 3.26132i) q^{46} +(2.89033 - 6.14227i) q^{47} +(-0.535827 - 0.844328i) q^{48} +(-1.65830 - 5.10373i) q^{49} +(4.69739 + 1.71304i) q^{50} +(-0.374682 + 1.15315i) q^{51} +(4.78652 - 1.22897i) q^{52} +(0.414760 + 0.0523964i) q^{53} +(-0.425779 + 0.904827i) q^{54} +(4.42216 + 1.68140i) q^{55} +(0.239498 - 1.25549i) q^{56} -5.60612 q^{57} +(0.355196 - 1.86200i) q^{58} +(11.9598 + 3.07076i) q^{59} +(-2.17321 - 0.526474i) q^{60} +(-6.11122 + 7.38720i) q^{61} +(-4.23505 + 1.67678i) q^{62} +(-1.18838 + 0.470512i) q^{63} +(-0.637424 + 0.770513i) q^{64} +(5.79306 - 9.40989i) q^{65} +(-2.04931 - 0.526173i) q^{66} +(2.23635 - 11.7234i) q^{67} +1.21250 q^{68} +(1.26851 - 6.64976i) q^{69} +(-1.56418 - 2.39196i) q^{70} +(-5.58733 + 11.8737i) q^{71} +(0.992115 + 0.125333i) q^{72} +(-12.9512 + 3.32530i) q^{73} +(-0.854453 + 2.62974i) q^{74} +(-4.31415 + 2.52747i) q^{75} +(1.73239 + 5.33174i) q^{76} +(-1.44901 - 2.28327i) q^{77} +(-2.10410 + 4.47145i) q^{78} +(-6.84969 + 3.76565i) q^{79} +(0.170851 + 2.22953i) q^{80} +(-0.425779 - 0.904827i) q^{81} +(0.383724 + 1.18098i) q^{82} +(-1.36379 - 0.749751i) q^{83} +(0.814712 + 0.984818i) q^{84} +(1.95088 - 1.88277i) q^{85} +(0.0336723 - 0.535206i) q^{86} +(1.20829 + 1.46057i) q^{87} +(0.132851 + 2.11160i) q^{88} +(6.44498 - 1.65479i) q^{89} +(1.79091 - 1.33890i) q^{90} +(-5.87269 + 2.32516i) q^{91} +(-6.71629 + 0.848465i) q^{92} +(1.40755 - 4.33198i) q^{93} +(4.94848 - 4.64694i) q^{94} +(11.0665 + 5.88860i) q^{95} +(-0.187381 - 0.982287i) q^{96} +(-2.19331 - 11.4977i) q^{97} +(0.336958 - 5.35579i) q^{98} +(1.71170 - 1.24362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) \) 120 * q + 20 * q^5 - 5 * q^7	\( 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) \) 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

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