LMFDB - Embedded newform 429.2.bb.a.64.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.6
Character	$\chi$	$=$	429.64
Dual form			429.2.bb.a.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.605812 - 0.196840i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.28977 - 0.937075i) q^{4} +(-4.01620 + 1.30494i) q^{5} +(0.605812 - 0.196840i) q^{6} +(0.707733 - 0.974111i) q^{7} +(1.34573 + 1.85224i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.605812 - 0.196840i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.28977 - 0.937075i) q^{4} +(-4.01620 + 1.30494i) q^{5} +(0.605812 - 0.196840i) q^{6} +(0.707733 - 0.974111i) q^{7} +(1.34573 + 1.85224i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.68992 q^{10} +(-2.53836 + 2.13465i) q^{11} +1.59425 q^{12} +(3.55318 + 0.612293i) q^{13} +(-0.620497 + 0.450817i) q^{14} +(2.48215 - 3.41638i) q^{15} +(0.534635 + 1.64544i) q^{16} +(-1.68497 - 5.18581i) q^{17} +(-0.374412 + 0.515334i) q^{18} +(-2.11004 - 2.90422i) q^{19} +(6.40281 + 2.08040i) q^{20} +1.20407i q^{21} +(1.95795 - 0.793547i) q^{22} +9.22169 q^{23} +(-2.17744 - 0.707492i) q^{24} +(10.3819 - 7.54288i) q^{25} +(-2.03203 - 1.07034i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.82563 + 0.593183i) q^{28} +(1.42209 + 1.03321i) q^{29} +(-2.17619 + 1.58110i) q^{30} +(3.81219 + 1.23866i) q^{31} -5.68105i q^{32} +(0.798856 - 3.21898i) q^{33} +3.47329i q^{34} +(-1.57124 + 4.83577i) q^{35} +(-1.28977 + 0.937075i) q^{36} +(-0.542859 + 0.747182i) q^{37} +(0.706618 + 2.17475i) q^{38} +(-3.23448 + 1.59315i) q^{39} +(-7.82178 - 5.68285i) q^{40} +(3.73058 + 5.13470i) q^{41} +(0.237009 - 0.729438i) q^{42} -2.73908 q^{43} +(5.27423 - 0.374588i) q^{44} +4.22288i q^{45} +(-5.58661 - 1.81520i) q^{46} +(-3.78830 - 5.21414i) q^{47} +(-1.39969 - 1.01694i) q^{48} +(1.71511 + 5.27858i) q^{49} +(-7.77420 + 2.52599i) q^{50} +(4.41131 + 3.20500i) q^{51} +(-4.00903 - 4.11931i) q^{52} +(-3.16857 + 9.75186i) q^{53} -0.636988i q^{54} +(7.40894 - 11.8856i) q^{55} +2.75670 q^{56} +(3.41411 + 1.10931i) q^{57} +(-0.658142 - 0.905855i) q^{58} +(2.90550 - 3.99907i) q^{59} +(-6.40281 + 2.08040i) q^{60} +(-2.24716 - 6.91605i) q^{61} +(-2.06565 - 1.50079i) q^{62} +(-0.707733 - 0.974111i) q^{63} +(-0.0489881 + 0.150770i) q^{64} +(-15.0693 + 2.17760i) q^{65} +(-1.11758 + 1.79285i) q^{66} +0.872982i q^{67} +(-2.68626 + 8.26745i) q^{68} +(-7.46050 + 5.42037i) q^{69} +(1.90375 - 2.62028i) q^{70} +(4.31019 - 1.40047i) q^{71} +(2.17744 - 0.707492i) q^{72} +(5.03640 - 6.93200i) q^{73} +(0.475946 - 0.345795i) q^{74} +(-3.96552 + 12.2046i) q^{75} +5.72304i q^{76} +(0.282910 + 3.98340i) q^{77} +(2.27308 - 0.328475i) q^{78} +(-0.193365 + 0.595115i) q^{79} +(-4.29440 - 5.91073i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.24931 - 3.84499i) q^{82} +(6.10312 - 1.98303i) q^{83} +(1.12830 - 1.55297i) q^{84} +(13.5343 + 18.6284i) q^{85} +(1.65937 + 0.539161i) q^{86} -1.75780 q^{87} +(-7.36983 - 1.82897i) q^{88} -13.3930i q^{89} +(0.831232 - 2.55827i) q^{90} +(3.11114 - 3.02785i) q^{91} +(-11.8939 - 8.64141i) q^{92} +(-3.81219 + 1.23866i) q^{93} +(1.26864 + 3.90448i) q^{94} +(12.2642 + 8.91043i) q^{95} +(3.33923 + 4.59606i) q^{96} +(6.12875 + 1.99135i) q^{97} -3.53542i q^{98} +(1.24578 + 3.07376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.605812	−	0.196840i	−0.428373	−	0.139187i	0.0868918	−	0.996218i	$-0.472307\pi$
$2$	−0.605812	−	0.196840i	−0.428373	−	0.139187i	−0.515265	+	0.857031i	$0.672307\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−1.28977	−	0.937075i	−0.644886	−	0.468537i
$5$	−4.01620	+	1.30494i	−1.79610	+	0.583588i	−0.999774	−	0.0212825i	$-0.993225\pi$
$5$	−4.01620	+	1.30494i	−1.79610	+	0.583588i	−0.796324	+	0.604870i	$0.793225\pi$
$6$	0.605812	−	0.196840i	0.247322	−	0.0803596i
$7$	0.707733	−	0.974111i	0.267498	−	0.368179i	−0.654045	−	0.756456i	$-0.726929\pi$
$7$	0.707733	−	0.974111i	0.267498	−	0.368179i	0.921543	+	0.388276i	$0.126929\pi$
$8$	1.34573	+	1.85224i	0.475787	+	0.654865i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.68992			0.850628
$11$	−2.53836	+	2.13465i	−0.765343	+	0.643622i
$11$	−2.53836	+	2.13465i	−0.765343	+	0.643622i
$12$	1.59425			0.460219
$13$	3.55318	+	0.612293i	0.985475	+	0.169819i
$13$	3.55318	+	0.612293i	0.985475	+	0.169819i
$14$	−0.620497	+	0.450817i	−0.165835	+	0.120486i
$15$	2.48215	−	3.41638i	0.640887	−	0.882106i
$16$	0.534635	+	1.64544i	0.133659	+	0.411359i
$17$	−1.68497	−	5.18581i	−0.408665	−	1.25774i	−0.917796	−	0.397053i	$-0.870033\pi$
$17$	−1.68497	−	5.18581i	−0.408665	−	1.25774i	0.509130	−	0.860690i	$-0.329967\pi$
$18$	−0.374412	+	0.515334i	−0.0882498	+	0.121465i
$19$	−2.11004	−	2.90422i	−0.484076	−	0.666273i	0.495206	−	0.868776i	$-0.335093\pi$
$19$	−2.11004	−	2.90422i	−0.484076	−	0.666273i	−0.979282	+	0.202502i	$0.935093\pi$
$20$	6.40281	+	2.08040i	1.43171	+	0.465191i
$21$			1.20407i			0.262749i
$22$	1.95795	−	0.793547i	0.417437	−	0.169185i
$23$	9.22169			1.92286			0.961428	−	0.275058i	$-0.0886970\pi$
$23$	9.22169			1.92286			0.961428	+	0.275058i	$0.0886970\pi$
$24$	−2.17744	−	0.707492i	−0.444467	−	0.144416i
$25$	10.3819	−	7.54288i	2.07638	−	1.50858i
$26$	−2.03203	−	1.07034i	−0.398515	−	0.209911i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.82563	+	0.593183i	−0.345011	+	0.112101i
$29$	1.42209	+	1.03321i	0.264076	+	0.191862i	0.711942	−	0.702238i	$-0.247816\pi$
$29$	1.42209	+	1.03321i	0.264076	+	0.191862i	−0.447866	+	0.894101i	$0.647816\pi$
$30$	−2.17619	+	1.58110i	−0.397317	+	0.288668i
$31$	3.81219	+	1.23866i	0.684690	+	0.222469i	0.630648	−	0.776069i	$-0.282789\pi$
$31$	3.81219	+	1.23866i	0.684690	+	0.222469i	0.0540425	+	0.998539i	$0.482789\pi$
$32$		−	5.68105i		−	1.00428i
$33$	0.798856	−	3.21898i	0.139063	−	0.560352i
$34$			3.47329i			0.595665i
$35$	−1.57124	+	4.83577i	−0.265588	+	0.817394i
$36$	−1.28977	+	0.937075i	−0.214962	+	0.156179i
$37$	−0.542859	+	0.747182i	−0.0892455	+	0.122836i	−0.851305	−	0.524671i	$-0.824188\pi$
$37$	−0.542859	+	0.747182i	−0.0892455	+	0.122836i	0.762060	+	0.647507i	$0.224188\pi$
$38$	0.706618	+	2.17475i	0.114629	+	0.352791i
$39$	−3.23448	+	1.59315i	−0.517931	+	0.255109i
$40$	−7.82178	−	5.68285i	−1.23673	−	0.898538i
$41$	3.73058	+	5.13470i	0.582618	+	0.801905i	0.993979	−	0.109567i	$-0.0349465\pi$
$41$	3.73058	+	5.13470i	0.582618	+	0.801905i	−0.411361	+	0.911472i	$0.634946\pi$
$42$	0.237009	−	0.729438i	0.0365712	−	0.112555i
$43$	−2.73908			−0.417706			−0.208853	−	0.977947i	$-0.566973\pi$
$43$	−2.73908			−0.417706			−0.208853	+	0.977947i	$0.566973\pi$
$44$	5.27423	−	0.374588i	0.795120	−	0.0564713i
$45$			4.22288i			0.629510i
$46$	−5.58661	−	1.81520i	−0.823700	−	0.267636i
$47$	−3.78830	−	5.21414i	−0.552580	−	0.760561i	0.437780	−	0.899082i	$-0.355765\pi$
$47$	−3.78830	−	5.21414i	−0.552580	−	0.760561i	−0.990359	+	0.138521i	$0.955765\pi$
$48$	−1.39969	−	1.01694i	−0.202028	−	0.146782i
$49$	1.71511	+	5.27858i	0.245016	+	0.754082i
$50$	−7.77420	+	2.52599i	−1.09944	+	0.357229i
$51$	4.41131	+	3.20500i	0.617707	+	0.448790i
$52$	−4.00903	−	4.11931i	−0.555953	−	0.571246i
$53$	−3.16857	+	9.75186i	−0.435237	+	1.33952i	0.457607	+	0.889154i	$0.348707\pi$
$53$	−3.16857	+	9.75186i	−0.435237	+	1.33952i	−0.892844	+	0.450366i	$0.851293\pi$
$54$		−	0.636988i		−	0.0866831i
$55$	7.40894	−	11.8856i	0.999021	−	1.60265i
$56$	2.75670			0.368380
$57$	3.41411	+	1.10931i	0.452210	+	0.146932i
$58$	−0.658142	−	0.905855i	−0.0864183	−	0.118945i
$59$	2.90550	−	3.99907i	0.378264	−	0.520635i	−0.576860	−	0.816843i	$-0.695722\pi$
$59$	2.90550	−	3.99907i	0.378264	−	0.520635i	0.955123	+	0.296208i	$0.0957221\pi$
$60$	−6.40281	+	2.08040i	−0.826599	+	0.268578i
$61$	−2.24716	−	6.91605i	−0.287720	−	0.885510i	−0.985570	−	0.169266i	$-0.945860\pi$
$61$	−2.24716	−	6.91605i	−0.287720	−	0.885510i	0.697851	−	0.716243i	$-0.254140\pi$
$62$	−2.06565	−	1.50079i	−0.262338	−	0.190600i
$63$	−0.707733	−	0.974111i	−0.0891660	−	0.122726i
$64$	−0.0489881	+	0.150770i	−0.00612351	+	0.0188462i
$65$	−15.0693	+	2.17760i	−1.86911	+	0.270099i
$66$	−1.11758	+	1.79285i	−0.137565	+	0.220684i
$67$			0.872982i			0.106652i	0.998577	+	0.0533259i	$0.0169822\pi$
$67$			0.872982i			0.106652i	−0.998577	+	0.0533259i	$0.983018\pi$
$68$	−2.68626	+	8.26745i	−0.325757	+	1.00258i
$69$	−7.46050	+	5.42037i	−0.898139	+	0.652536i
$70$	1.90375	−	2.62028i	0.227541	−	0.313184i
$71$	4.31019	−	1.40047i	0.511525	−	0.166205i	−0.0418706	−	0.999123i	$-0.513332\pi$
$71$	4.31019	−	1.40047i	0.511525	−	0.166205i	0.553396	+	0.832918i	$0.313332\pi$
$72$	2.17744	−	0.707492i	0.256613	−	0.0833787i
$73$	5.03640	−	6.93200i	0.589466	−	0.811330i	−0.405228	−	0.914216i	$-0.632808\pi$
$73$	5.03640	−	6.93200i	0.589466	−	0.811330i	0.994693	+	0.102886i	$0.0328077\pi$
$74$	0.475946	−	0.345795i	0.0553276	−	0.0401978i
$75$	−3.96552	+	12.2046i	−0.457899	+	1.40927i
$76$			5.72304i			0.656478i
$77$	0.282910	+	3.98340i	0.0322406	+	0.453951i
$78$	2.27308	−	0.328475i	0.257376	−	0.0371924i
$79$	−0.193365	+	0.595115i	−0.0217552	+	0.0669557i	−0.961345	−	0.275348i	$-0.911207\pi$
$79$	−0.193365	+	0.595115i	−0.0217552	+	0.0669557i	0.939590	+	0.342303i	$0.111207\pi$
$80$	−4.29440	−	5.91073i	−0.480128	−	0.660840i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.24931	−	3.84499i	−0.137963	−	0.424608i
$83$	6.10312	−	1.98303i	0.669905	−	0.217665i	0.0457346	−	0.998954i	$-0.485437\pi$
$83$	6.10312	−	1.98303i	0.669905	−	0.217665i	0.624170	+	0.781288i	$0.285437\pi$
$84$	1.12830	−	1.55297i	0.123108	−	0.169443i
$85$	13.5343	+	18.6284i	1.46801	+	2.02054i
$86$	1.65937	+	0.539161i	0.178934	+	0.0581392i
$87$	−1.75780			−0.188456
$88$	−7.36983	−	1.82897i	−0.785626	−	0.194969i
$89$		−	13.3930i		−	1.41966i	−0.704375	−	0.709828i	$-0.748773\pi$
$89$		−	13.3930i		−	1.41966i	0.704375	−	0.709828i	$-0.251227\pi$
$90$	0.831232	−	2.55827i	0.0876195	−	0.269665i
$91$	3.11114	−	3.02785i	0.326137	−	0.317405i
$92$	−11.8939	−	8.64141i	−1.24002	−	0.900929i
$93$	−3.81219	+	1.23866i	−0.395306	+	0.128443i
$94$	1.26864	+	3.90448i	0.130850	+	0.402716i
$95$	12.2642	+	8.91043i	1.25828	+	0.914191i
$96$	3.33923	+	4.59606i	0.340809	+	0.469084i
$97$	6.12875	+	1.99135i	0.622280	+	0.202191i	0.603152	−	0.797626i	$-0.293911\pi$
$97$	6.12875	+	1.99135i	0.622280	+	0.202191i	0.0191278	+	0.999817i	$0.493911\pi$
$98$		−	3.53542i		−	0.357132i
$99$	1.24578	+	3.07376i	0.125206	+	0.308925i
$100$	−20.4585			−2.04585
$101$	5.20012	−	16.0043i	0.517431	−	1.59249i	−0.261384	−	0.965235i	$-0.584179\pi$
$101$	5.20012	−	16.0043i	0.517431	−	1.59249i	0.778815	−	0.627253i	$-0.215821\pi$
$102$	−2.04155	−	2.80995i	−0.202144	−	0.278227i
$103$	5.54726	+	4.03032i	0.546588	+	0.397119i	0.826526	−	0.562899i	$-0.190314\pi$
$103$	5.54726	+	4.03032i	0.546588	+	0.397119i	−0.279938	+	0.960018i	$0.590314\pi$
$104$	3.64751	+	7.40532i	0.357668	+	0.726151i
$105$	−1.57124	−	4.83577i	−0.153337	−	0.471923i
$106$	3.83911	−	5.28409i	0.372888	−	0.513236i
$107$	−7.90891	+	5.74616i	−0.764583	+	0.555502i	−0.900313	−	0.435244i	$-0.856662\pi$
$107$	−7.90891	+	5.74616i	−0.764583	+	0.555502i	0.135730	+	0.990746i	$0.456662\pi$
$108$	0.492649	−	1.51622i	0.0474052	−	0.145898i
$109$		−	7.80886i		−	0.747953i	−0.927438	−	0.373976i	$-0.877994\pi$
$109$		−	7.80886i		−	0.747953i	0.927438	−	0.373976i	$-0.122006\pi$
$110$	−6.82798	+	5.74205i	−0.651023	+	0.547483i
$111$		−	0.923568i		−	0.0876612i
$112$	1.98122	+	0.643736i	0.187207	+	0.0608273i
$113$	−8.52883	+	6.19656i	−0.802325	+	0.582923i	−0.911595	−	0.411089i	$-0.865149\pi$
$113$	−8.52883	+	6.19656i	−0.802325	+	0.582923i	0.109270	+	0.994012i	$0.465149\pi$
$114$	−1.84995	−	1.34407i	−0.173264	−	0.125884i
$115$	−37.0361	+	12.0338i	−3.45364	+	1.12215i
$116$	−0.865980	−	2.66521i	−0.0804042	−	0.247459i
$117$	1.68032	−	3.19007i	0.155345	−	0.294922i
$118$	−2.54736	+	1.85077i	−0.234504	+	0.170377i
$119$	−6.24406	−	2.02882i	−0.572392	−	0.185981i
$120$	9.66825			0.882586
$121$	1.88651	−	10.8370i	0.171501	−	0.985184i
$122$			4.63216i			0.419376i
$123$	−6.03620	−	1.96128i	−0.544266	−	0.176843i
$124$	−3.75615	−	5.16989i	−0.337312	−	0.464270i
$125$	−19.4419	+	26.7595i	−1.73894	+	2.39344i
$126$	0.237009	+	0.729438i	0.0211144	+	0.0649835i
$127$	3.19839	+	9.84362i	0.283811	+	0.873480i	0.986753	+	0.162233i	$0.0518695\pi$
$127$	3.19839	+	9.84362i	0.283811	+	0.873480i	−0.702942	+	0.711247i	$0.748131\pi$
$128$	−6.61911	+	9.11043i	−0.585053	+	0.805256i
$129$	2.21596	−	1.60999i	0.195105	−	0.141752i
$130$	9.55778	+	1.64702i	0.838273	+	0.144453i
$131$	19.6186			1.71408			0.857041	−	0.515249i	$-0.172301\pi$
$131$	19.6186			1.71408			0.857041	+	0.515249i	$0.172301\pi$
$132$	−4.04677	+	3.40316i	−0.352226	+	0.296207i
$133$	−4.32237			−0.374797
$134$	0.171838	−	0.528863i	0.0148445	−	0.0456868i
$135$	−2.48215	−	3.41638i	−0.213629	−	0.294035i
$136$	7.33783	−	10.0997i	0.629214	−	0.866039i
$137$	6.07480	−	1.97382i	0.519005	−	0.168635i	−0.0377886	−	0.999286i	$-0.512031\pi$
$137$	6.07480	−	1.97382i	0.519005	−	0.168635i	0.556794	+	0.830651i	$0.312031\pi$
$138$	5.58661	−	1.81520i	0.475564	−	0.154520i
$139$	10.6129	+	7.71075i	0.900178	+	0.654017i	0.938512	−	0.345248i	$-0.112205\pi$
$139$	10.6129	+	7.71075i	0.900178	+	0.654017i	−0.0383340	+	0.999265i	$0.512205\pi$
$140$	6.55801	−	4.76468i	0.554253	−	0.402689i
$141$	6.12959	+	1.99163i	0.516205	+	0.167725i
$142$	−2.88683			−0.242257
$143$	−10.3263	+	6.03059i	−0.863526	+	0.504304i
$144$	1.73011			0.144176
$145$	−7.05968	−	2.29383i	−0.586274	−	0.190492i
$146$	−4.41560	+	3.20812i	−0.365438	+	0.265506i
$147$	−4.49022	−	3.26234i	−0.370347	−	0.269073i
$148$	1.40033	−	0.454995i	0.115106	−	0.0374003i
$149$	−4.10265	+	1.33303i	−0.336102	+	0.109206i	−0.472206	−	0.881488i	$-0.656542\pi$
$149$	−4.10265	+	1.33303i	−0.336102	+	0.109206i	0.136103	+	0.990695i	$0.456542\pi$
$150$	4.80472	−	6.61313i	0.392304	−	0.539960i
$151$	−4.53759	−	6.24546i	−0.369264	−	0.508249i	0.583436	−	0.812159i	$-0.301708\pi$
$151$	−4.53759	−	6.24546i	−0.369264	−	0.508249i	−0.952701	+	0.303910i	$0.901708\pi$
$152$	2.53976	−	7.81658i	0.206002	−	0.634008i
$153$	−5.45268			−0.440823
$154$	0.612703	−	2.46888i	0.0493730	−	0.198948i
$155$	−16.9269			−1.35960
$156$	5.66465	+	0.976146i	0.453535	+	0.0781542i
$157$	5.39899	−	3.92260i	0.430886	−	0.313057i	−0.351117	−	0.936332i	$-0.614198\pi$
$157$	5.39899	−	3.92260i	0.430886	−	0.313057i	0.782003	+	0.623274i	$0.214198\pi$
$158$	0.234285	−	0.322466i	0.0186387	−	0.0256540i
$159$	−3.16857	−	9.75186i	−0.251284	−	0.773373i
$160$	7.41343	+	22.8162i	0.586083	+	1.80378i
$161$	6.52649	−	8.98295i	0.514360	−	0.707955i
$162$	0.374412	+	0.515334i	0.0294166	+	0.0404885i
$163$	8.93484	+	2.90310i	0.699830	+	0.227389i	0.637257	−	0.770652i	$-0.280069\pi$
$163$	8.93484	+	2.90310i	0.699830	+	0.227389i	0.0625738	+	0.998040i	$0.480069\pi$
$164$		−	10.1184i		−	0.790116i
$165$	0.992218	+	13.9705i	0.0772441	+	1.08760i
$166$	−4.08768			−0.317266
$167$	13.8879	+	4.51246i	1.07468	+	0.349185i	0.792309	−	0.610120i	$-0.208879\pi$
$167$	13.8879	+	4.51246i	1.07468	+	0.349185i	0.282371	+	0.959305i	$0.408879\pi$
$168$	−2.23022	+	1.62035i	−0.172065	+	0.125013i
$169$	12.2502	+	4.35117i	0.942323	+	0.334706i
$170$	−4.53244	−	13.9494i	−0.347622	−	1.06987i
$171$	−3.41411	+	1.10931i	−0.261084	+	0.0848312i
$172$	3.53279	+	2.56672i	0.269373	+	0.195711i
$173$	10.3602	−	7.52713i	0.787672	−	0.572277i	−0.119599	−	0.992822i	$-0.538161\pi$
$173$	10.3602	−	7.52713i	0.787672	−	0.572277i	0.907272	+	0.420545i	$0.138161\pi$
$174$	1.06490	+	0.346006i	0.0807296	+	0.0262306i
$175$		−	15.4514i		−	1.16802i
$176$	−4.86953	−	3.03544i	−0.367055	−	0.228805i
$177$			4.94313i			0.371548i
$178$	−2.63628	+	8.11364i	−0.197598	+	0.608143i
$179$	3.12447	−	2.27006i	0.233534	−	0.169672i	−0.464864	−	0.885382i	$-0.653897\pi$
$179$	3.12447	−	2.27006i	0.233534	−	0.169672i	0.698398	+	0.715710i	$0.253897\pi$
$180$	3.95715	−	5.44655i	0.294949	−	0.405962i
$181$	−0.117347	−	0.361158i	−0.00872236	−	0.0268447i	0.946601	−	0.322409i	$-0.104492\pi$
$181$	−0.117347	−	0.361158i	−0.00872236	−	0.0268447i	−0.955323	+	0.295564i	$0.904492\pi$
$182$	−2.48077	+	1.22191i	−0.183887	+	0.0905740i
$183$	5.88314	+	4.27435i	0.434895	+	0.315969i
$184$	12.4099	+	17.0808i	0.914870	+	1.25921i
$185$	1.20520	−	3.70923i	0.0886082	−	0.272708i
$186$	2.55329			0.187216
$187$	15.3470	+	9.56660i	1.12228	+	0.699579i
$188$			10.2750i			0.749380i
$189$	1.14514	+	0.372077i	0.0832964	+	0.0270646i
$190$	−5.67584	−	7.81212i	−0.411769	−	0.566751i
$191$	12.7791	+	9.28459i	0.924667	+	0.671810i	0.944681	−	0.327990i	$-0.106371\pi$
$191$	12.7791	+	9.28459i	0.924667	+	0.671810i	−0.0200146	+	0.999800i	$0.506371\pi$
$192$	−0.0489881	−	0.150770i	−0.00353541	−	0.0108809i
$193$	−14.8571	+	4.82735i	−1.06944	+	0.347481i	−0.790268	−	0.612762i	$-0.790058\pi$
$193$	−14.8571	+	4.82735i	−1.06944	+	0.347481i	−0.279167	+	0.960242i	$0.590058\pi$
$194$	−3.32089	−	2.41277i	−0.238426	−	0.173227i
$195$	10.9113	−	10.6192i	0.781377	−	0.760458i
$196$	2.73431	−	8.41535i	0.195308	−	0.601096i
$197$		−	24.0171i		−	1.71114i	−0.517684	−	0.855572i	$-0.673206\pi$
$197$		−	24.0171i		−	1.71114i	0.517684	−	0.855572i	$-0.326794\pi$
$198$	−0.149668	−	2.10734i	−0.0106365	−	0.149762i
$199$	−0.129925			−0.00921013			−0.00460506	−	0.999989i	$-0.501466\pi$
$199$	−0.129925			−0.00921013			−0.00460506	+	0.999989i	$0.501466\pi$
$200$	27.9424	+	9.07903i	1.97583	+	0.641985i
$201$	−0.513126	−	0.706257i	−0.0361931	−	0.0498155i
$202$	−6.30058	+	8.67200i	−0.443307	+	0.610160i
$203$	2.01292	−	0.654038i	0.141279	−	0.0459045i
$204$	−2.68626	−	8.26745i	−0.188076	−	0.578838i
$205$	−21.6832	−	15.7538i	−1.51442	−	1.10029i
$206$	−2.56726	−	3.53354i	−0.178870	−	0.246193i
$207$	2.84966	−	8.77035i	0.198065	−	0.609581i
$208$	0.892165	+	6.17389i	0.0618605	+	0.428082i
$209$	11.5555	+	2.86774i	0.799312	+	0.198366i
$210$			3.23885i			0.223502i
$211$	0.591078	−	1.81915i	0.0406915	−	0.125236i	−0.928647	−	0.370964i	$-0.879027\pi$
$211$	0.591078	−	1.81915i	0.0406915	−	0.125236i	0.969339	+	0.245729i	$0.0790272\pi$
$212$	13.2250	−	9.60849i	0.908294	−	0.659914i
$213$	−2.66384	+	3.66647i	−0.182524	+	0.251222i
$214$	5.92238	−	1.92430i	0.404846	−	0.131542i
$215$	11.0007	−	3.57434i	0.750240	−	0.243768i
$216$	−1.34573	+	1.85224i	−0.0915653	+	0.126029i
$217$	3.90460	−	2.83686i	0.265062	−	0.192579i
$218$	−1.53710	+	4.73070i	−0.104105	+	0.320403i
$219$			8.56843i			0.579001i
$220$	−20.6935	+	8.38698i	−1.39516	+	0.565450i
$221$	−2.81177	−	19.4578i	−0.189140	−	1.30887i
$222$	−0.181795	+	0.559508i	−0.0122013	+	0.0375517i
$223$	0.962165	+	1.32431i	0.0644313	+	0.0886821i	0.840017	−	0.542561i	$-0.182545\pi$
$223$	0.962165	+	1.32431i	0.0644313	+	0.0886821i	−0.775585	+	0.631243i	$0.782545\pi$
$224$	−5.53397	−	4.02066i	−0.369754	−	0.268642i
$225$	−3.96552	−	12.2046i	−0.264368	−	0.813642i
$226$	6.38659	−	2.07513i	0.424830	−	0.138036i
$227$	6.02940	−	8.29876i	0.400186	−	0.550808i	−0.560605	−	0.828083i	$-0.689431\pi$
$227$	6.02940	−	8.29876i	0.400186	−	0.550808i	0.960791	+	0.277275i	$0.0894313\pi$
$228$	−3.36392	−	4.63004i	−0.222781	−	0.306632i
$229$	−8.65999	−	2.81380i	−0.572268	−	0.185941i	0.00856580	−	0.999963i	$-0.497273\pi$
$229$	−8.65999	−	2.81380i	−0.572268	−	0.185941i	−0.580834	+	0.814022i	$0.697273\pi$
$230$	24.8056			1.63564
$231$	−2.57027	−	3.05635i	−0.169111	−	0.201093i
$232$			4.02447i			0.264220i
$233$	4.49874	−	13.8457i	0.294722	−	0.907061i	−0.688593	−	0.725148i	$-0.741771\pi$
$233$	4.49874	−	13.8457i	0.294722	−	0.907061i	0.983315	−	0.181913i	$-0.0582289\pi$
$234$	−1.64589	+	1.60183i	−0.107595	+	0.104715i
$235$	22.0187	+	15.9975i	1.43634	+	1.04356i
$236$	−7.49486	+	2.43523i	−0.487874	+	0.158520i
$237$	−0.193365	−	0.595115i	−0.0125604	−	0.0386569i
$238$	3.38337	+	2.45816i	0.219311	+	0.159339i
$239$	6.42888	+	8.84859i	0.415849	+	0.572368i	0.964633	−	0.263597i	$-0.0849088\pi$
$239$	6.42888	+	8.84859i	0.415849	+	0.572368i	−0.548783	+	0.835965i	$0.684909\pi$
$240$	6.94848	+	2.25770i	0.448522	+	0.145734i
$241$			18.2102i			1.17302i	0.809941	+	0.586511i	$0.199499\pi$
$241$			18.2102i			1.17302i	−0.809941	+	0.586511i	$0.800501\pi$
$242$	−3.27603	+	6.19385i	−0.210591	+	0.398156i
$243$	1.00000			0.0641500
$244$	−3.58253	+	11.0259i	−0.229348	+	0.705860i
$245$	−13.7765	−	18.9617i	−0.880146	−	1.21142i
$246$	3.27074	+	2.37633i	0.208535	+	0.151509i
$247$	−5.71911	−	11.6112i	−0.363898	−	0.738801i
$248$	2.83589	+	8.72798i	0.180079	+	0.554228i
$249$	−3.77194	+	5.19163i	−0.239037	+	0.329006i
$250$	17.0455	−	12.3843i	1.07805	−	0.783250i
$251$	2.05156	−	6.31405i	0.129493	−	0.398539i	−0.865200	−	0.501428i	$-0.832808\pi$
$251$	2.05156	−	6.31405i	0.129493	−	0.398539i	0.994693	+	0.102888i	$0.0328084\pi$
$252$			1.91958i			0.120922i
$253$	−23.4079	+	19.6851i	−1.47164	+	1.23759i
$254$		−	6.59295i		−	0.413678i
$255$	−21.8990	−	7.11543i	−1.37137	−	0.445585i
$256$	6.05974	−	4.40266i	0.378734	−	0.275166i
$257$	−9.45964	−	6.87283i	−0.590076	−	0.428716i	0.252266	−	0.967658i	$-0.418824\pi$
$257$	−9.45964	−	6.87283i	−0.590076	−	0.428716i	−0.842343	+	0.538942i	$0.818824\pi$
$258$	−1.65937	+	0.539161i	−0.103308	+	0.0335667i
$259$	0.343638	+	1.05761i	0.0213527	+	0.0657167i
$260$	21.4765	+	11.3124i	1.33192	+	0.701567i
$261$	1.42209	−	1.03321i	0.0880253	−	0.0639541i
$262$	−11.8851	−	3.86172i	−0.734267	−	0.238578i
$263$	−25.3204			−1.56132			−0.780660	−	0.624956i	$-0.785117\pi$
$263$	−25.3204			−1.56132			−0.780660	+	0.624956i	$0.785117\pi$
$264$	7.03736	−	2.85220i	0.433119	−	0.175541i
$265$		−	43.3002i		−	2.65991i
$266$	2.61854	+	0.850816i	0.160553	+	0.0521669i
$267$	7.87222	+	10.8352i	0.481772	+	0.663102i
$268$	0.818049	−	1.12595i	0.0499703	−	0.0687782i
$269$	−7.42871	−	22.8632i	−0.452936	−	1.39399i	−0.873541	−	0.486751i	$-0.838182\pi$
$269$	−7.42871	−	22.8632i	−0.452936	−	1.39399i	0.420604	−	0.907244i	$-0.361818\pi$
$270$	0.831232	+	2.55827i	0.0505872	+	0.155691i
$271$	6.29399	−	8.66294i	0.382333	−	0.526236i	−0.573868	−	0.818948i	$-0.694558\pi$
$271$	6.29399	−	8.66294i	0.382333	−	0.526236i	0.956201	+	0.292712i	$0.0945577\pi$
$272$	7.63207	−	5.54502i	0.462762	−	0.336216i
$273$	−0.737242	+	4.27827i	−0.0446199	+	0.258933i
$274$	−4.06871			−0.245800
$275$	−10.2515	+	41.3082i	−0.618188	+	2.49098i
$276$	14.7016			0.884935
$277$	1.38349	−	4.25794i	0.0831258	−	0.255835i	−0.900852	−	0.434127i	$-0.857057\pi$
$277$	1.38349	−	4.25794i	0.0831258	−	0.255835i	0.983978	+	0.178292i	$0.0570571\pi$
$278$	−4.91165	−	6.76031i	−0.294581	−	0.405457i
$279$	2.35607	−	3.24285i	0.141054	−	0.194144i
$280$	−11.0715	+	3.59733i	−0.661646	+	0.214982i
$281$	−8.33269	+	2.70745i	−0.497087	+	0.161513i	−0.546821	−	0.837249i	$-0.684162\pi$
$281$	−8.33269	+	2.70745i	−0.497087	+	0.161513i	0.0497349	+	0.998762i	$0.484162\pi$
$282$	−3.32135	−	2.41310i	−0.197783	−	0.143698i
$283$	−17.1904	+	12.4895i	−1.02186	+	0.742425i	−0.966664	−	0.256050i	$-0.917579\pi$
$283$	−17.1904	+	12.4895i	−1.02186	+	0.742425i	−0.0551975	+	0.998475i	$0.517579\pi$
$284$	−6.87150	−	2.23269i	−0.407749	−	0.132486i
$285$	−15.1593			−0.897961
$286$	7.44284	−	1.62078i	0.440104	−	0.0958386i
$287$	7.64202			0.451094
$288$	−5.40299	−	1.75554i	−0.318375	−	0.103446i
$289$	−10.3002	+	7.48352i	−0.605893	+	0.440207i
$290$	3.82532	+	2.77926i	0.224630	+	0.163203i
$291$	−6.12875	+	1.99135i	−0.359274	+	0.116735i
$292$	−12.9916	+	4.22123i	−0.760276	+	0.247029i
$293$	17.0910	−	23.5238i	0.998467	−	1.37427i	0.0722062	−	0.997390i	$-0.476996\pi$
$293$	17.0910	−	23.5238i	0.998467	−	1.37427i	0.926261	−	0.376883i	$-0.123004\pi$
$294$	2.07807	+	2.86022i	0.121196	+	0.166811i
$295$	−6.45049	+	19.8526i	−0.375562	+	1.15586i
$296$	−2.11450			−0.122903
$297$	−2.81457	−	1.75448i	−0.163318	−	0.101805i
$298$	2.74783			0.159177
$299$	32.7663	+	5.64637i	1.89493	+	0.326538i
$300$	16.5513	−	12.0252i	0.955588	−	0.694275i
$301$	−1.93854	+	2.66817i	−0.111735	+	0.153791i
$302$	1.51957	+	4.67675i	0.0874414	+	0.269117i
$303$	5.20012	+	16.0043i	0.298739	+	0.919424i
$304$	3.65061	−	5.02463i	0.209377	−	0.288182i
$305$	18.0501	+	24.8438i	1.03354	+	1.42255i
$306$	3.30330	+	1.07331i	0.188837	+	0.0613568i
$307$			10.8673i			0.620231i	0.950699	+	0.310115i	$0.100368\pi$
$307$			10.8673i			0.620231i	−0.950699	+	0.310115i	$0.899632\pi$
$308$	3.36786	−	5.40279i	0.191901	−	0.307853i
$309$	−6.85679			−0.390069
$310$	10.2545	+	3.33189i	0.582417	+	0.189239i
$311$	3.89208	−	2.82776i	0.220700	−	0.160348i	−0.471942	−	0.881630i	$-0.656447\pi$
$311$	3.89208	−	2.82776i	0.220700	−	0.160348i	0.692642	+	0.721282i	$0.256447\pi$
$312$	−7.30363	−	3.84708i	−0.413487	−	0.217798i
$313$	6.25015	+	19.2360i	0.353279	+	1.08728i	0.957001	+	0.290086i	$0.0936840\pi$
$313$	6.25015	+	19.2360i	0.353279	+	1.08728i	−0.603721	+	0.797195i	$0.706316\pi$
$314$	−4.04289	+	1.31362i	−0.228154	+	0.0741316i
$315$	4.11355	+	2.98867i	0.231772	+	0.168392i
$316$	0.807063	−	0.586366i	0.0454009	−	0.0329857i
$317$	−15.1143	−	4.91094i	−0.848904	−	0.275826i	−0.147917	−	0.989000i	$-0.547257\pi$
$317$	−15.1143	−	4.91094i	−0.848904	−	0.275826i	−0.700987	+	0.713174i	$0.747257\pi$
$318$			6.53149i			0.366268i
$319$	−5.81532	+	0.413017i	−0.325595	+	0.0231245i
$320$		−	0.669448i		−	0.0374233i
$321$	3.02093	−	9.29748i	0.168612	−	0.518934i
$322$	−5.72203	+	4.15730i	−0.318876	+	0.231677i
$323$	−11.5054	+	15.8358i	−0.640175	+	0.881126i
$324$	0.492649	+	1.51622i	0.0273694	+	0.0842344i
$325$	41.5071	−	20.4445i	2.30240	−	1.13405i
$326$	−4.84138	−	3.51747i	−0.268139	−	0.194815i
$327$	4.58993	+	6.31750i	0.253824	+	0.349358i
$328$	−4.49034	+	13.8198i	−0.247937	+	0.763073i
$329$	−7.76025			−0.427837
$330$	2.14886	−	8.65881i	0.118291	−	0.476652i
$331$			25.6083i			1.40756i	0.710419	+	0.703779i	$0.248505\pi$
$331$			25.6083i			1.40756i	−0.710419	+	0.703779i	$0.751495\pi$
$332$	−9.72988	−	3.16143i	−0.533997	−	0.173506i
$333$	0.542859	+	0.747182i	0.0297485	+	0.0409453i
$334$	−7.52523	−	5.46740i	−0.411762	−	0.299163i
$335$	−1.13919	−	3.50607i	−0.0622406	−	0.191557i
$336$	−1.98122	+	0.643736i	−0.108084	+	0.0351187i
$337$	5.45343	+	3.96215i	0.297067	+	0.215832i	0.726327	−	0.687349i	$-0.241226\pi$
$337$	5.45343	+	3.96215i	0.297067	+	0.215832i	−0.429260	+	0.903181i	$0.641226\pi$
$338$	−6.56482	−	5.04732i	−0.357079	−	0.274538i
$339$	3.25772	−	10.0262i	0.176935	−	0.544551i
$340$		−	36.7091i		−	1.99083i
$341$	−12.3208	+	4.99356i	−0.667209	+	0.270416i
$342$	2.28667			0.123649
$343$	14.3717	+	4.66965i	0.775999	+	0.252137i
$344$	−3.68606	−	5.07342i	−0.198739	−	0.273541i
$345$	22.8896	−	31.5048i	1.23233	−	1.69616i
$346$	−7.75798	+	2.52072i	−0.417071	+	0.135515i
$347$	7.35464	+	22.6352i	0.394818	+	1.21512i	0.929104	+	0.369820i	$0.120581\pi$
$347$	7.35464	+	22.6352i	0.394818	+	1.21512i	−0.534286	+	0.845304i	$0.679419\pi$
$348$	2.26716	+	1.64719i	0.121533	+	0.0882987i
$349$	−1.02350	−	1.40873i	−0.0547868	−	0.0754075i	0.780745	−	0.624850i	$-0.214840\pi$
$349$	−1.02350	−	1.40873i	−0.0547868	−	0.0754075i	−0.835531	+	0.549443i	$0.814840\pi$
$350$	−3.04146	+	9.36066i	−0.162573	+	0.500348i
$351$	0.515668	+	3.56849i	0.0275243	+	0.190472i
$352$	12.1271	+	14.4205i	0.646375	+	0.768616i
$353$			22.5232i			1.19879i	0.800455	+	0.599393i	$0.204591\pi$
$353$			22.5232i			1.19879i	−0.800455	+	0.599393i	$0.795409\pi$
$354$	0.973006	−	2.99460i	0.0517147	−	0.159161i
$355$	−15.4830	+	11.2491i	−0.821754	+	0.597040i
$356$	−12.5503	+	17.2739i	−0.665162	+	0.915517i
$357$	6.24406	−	2.02882i	0.330471	−	0.107376i
$358$	−2.33968	+	0.760208i	−0.123656	+	0.0401782i
$359$	−2.06369	+	2.84043i	−0.108917	+	0.149912i	−0.859996	−	0.510301i	$-0.829534\pi$
$359$	−2.06369	+	2.84043i	−0.108917	+	0.149912i	0.751078	+	0.660213i	$0.229534\pi$
$360$	−7.82178	+	5.68285i	−0.412244	+	0.299513i
$361$	1.88910	−	5.81406i	0.0994265	−	0.306003i
$362$			0.241892i			0.0127136i
$363$	4.84363	+	9.87620i	0.254224	+	0.518366i
$364$	−6.84999	+	0.989866i	−0.359037	+	0.0518831i
$365$	−11.1813	+	34.4125i	−0.585256	+	1.80123i
$366$	−2.72271	−	3.74749i	−0.142318	−	0.195885i
$367$	−19.4293	−	14.1162i	−1.01420	−	0.736862i	−0.0491167	−	0.998793i	$-0.515641\pi$
$367$	−19.4293	−	14.1162i	−1.01420	−	0.736862i	−0.965087	+	0.261931i	$0.915641\pi$
$368$	4.93024	+	15.1737i	0.257006	+	0.790984i
$369$	6.03620	−	1.96128i	0.314232	−	0.102100i
$370$	−1.46025	+	2.00986i	−0.0759148	+	0.104488i
$371$	7.25689	+	9.98825i	0.376759	+	0.518564i
$372$	6.07758	+	1.97472i	0.315108	+	0.102385i
$373$	0.284970			0.0147552			0.00737758	−	0.999973i	$-0.497652\pi$
$373$	0.284970			0.0147552			0.00737758	+	0.999973i	$0.497652\pi$
$374$	−7.41427	−	8.81645i	−0.383383	−	0.455888i
$375$		−	33.0766i		−	1.70807i
$376$	4.55981	−	14.0337i	0.235154	−	0.723730i
$377$	4.42032	+	4.54192i	0.227658	+	0.233921i
$378$	−0.620497	−	0.450817i	−0.0319149	−	0.0231875i
$379$	18.1779	−	5.90635i	0.933735	−	0.303389i	0.197646	−	0.980274i	$-0.436670\pi$
$379$	18.1779	−	5.90635i	0.933735	−	0.303389i	0.736089	+	0.676885i	$0.236670\pi$
$380$	−7.46823	−	22.9849i	−0.383112	−	1.17910i
$381$	−8.37348	−	6.08369i	−0.428987	−	0.311677i
$382$	−5.91417	−	8.14016i	−0.302595	−	0.416487i
$383$	−10.5137	−	3.41612i	−0.537227	−	0.174556i	0.0278219	−	0.999613i	$-0.491143\pi$
$383$	−10.5137	−	3.41612i	−0.537227	−	0.174556i	−0.565049	+	0.825057i	$0.691143\pi$
$384$		−	11.2611i		−	0.574666i
$385$	−6.33433	−	15.6290i	−0.322828	−	0.796525i
$386$	9.95080			0.506482
$387$	−0.846422	+	2.60502i	−0.0430260	+	0.132421i
$388$	−6.03865	−	8.31149i	−0.306566	−	0.421952i
$389$	−9.32097	−	6.77208i	−0.472592	−	0.343358i	0.325859	−	0.945418i	$-0.394347\pi$
$389$	−9.32097	−	6.77208i	−0.472592	−	0.343358i	−0.798450	+	0.602060i	$0.794347\pi$
$390$	−8.70050	+	4.28546i	−0.440567	+	0.217003i
$391$	−15.5383	−	47.8219i	−0.785805	−	2.41846i
$392$	−7.46910	+	10.2803i	−0.377246	+	0.519235i
$393$	−15.8717	+	11.5315i	−0.800624	+	0.581687i
$394$	−4.72752	+	14.5498i	−0.238169	+	0.733009i
$395$		−	2.64243i		−	0.132955i
$396$	1.27357	−	5.13185i	0.0639994	−	0.257885i
$397$			14.9174i			0.748683i	0.927291	+	0.374342i	$0.122131\pi$
$397$			14.9174i			0.748683i	−0.927291	+	0.374342i	$0.877869\pi$
$398$	0.0787099	+	0.0255744i	0.00394537	+	0.00128193i
$399$	3.49687	−	2.54063i	0.175063	−	0.127190i
$400$	17.9618	+	13.0500i	0.898092	+	0.652502i
$401$	−25.0299	+	8.13271i	−1.24993	+	0.406128i	−0.857897	−	0.513822i	$-0.828229\pi$
$401$	−25.0299	+	8.13271i	−1.24993	+	0.406128i	−0.392036	+	0.919950i	$0.628229\pi$
$402$	0.171838	+	0.528863i	0.00857049	+	0.0263773i
$403$	12.7870	+	6.73535i	0.636966	+	0.335512i
$404$	−21.7042	+	15.7690i	−1.07982	+	0.784538i
$405$	4.01620	+	1.30494i	0.199566	+	0.0648431i
$406$	−1.34819			−0.0669097
$407$	−0.217004	−	3.05543i	−0.0107565	−	0.151452i
$408$			12.4839i			0.618043i
$409$	−25.3934	−	8.25080i	−1.25562	−	0.407976i	−0.395689	−	0.918385i	$-0.629494\pi$
$409$	−25.3934	−	8.25080i	−1.25562	−	0.407976i	−0.859932	+	0.510409i	$0.829494\pi$
$410$	10.0350	+	13.8119i	0.495592	+	0.682123i
$411$	−3.75443	+	5.16753i	−0.185193	+	0.254896i
$412$	−3.37799	−	10.3964i	−0.166422	−	0.512193i
$413$	−1.83923	−	5.66055i	−0.0905024	−	0.278538i
$414$	−3.45271	+	4.75225i	−0.169692	+	0.233560i
$415$	−21.9236	+	15.9284i	−1.07619	+	0.781896i
$416$	3.47846	−	20.1858i	0.170546	−	0.989689i
$417$	−13.1183			−0.642406
$418$	−6.43598	−	4.01190i	−0.314794	−	0.196228i
$419$	24.8778			1.21536			0.607681	−	0.794181i	$-0.292100\pi$
$419$	24.8778			1.21536			0.607681	+	0.794181i	$0.292100\pi$
$420$	−2.50494	+	7.70941i	−0.122228	+	0.376181i
$421$	−3.69123	−	5.08054i	−0.179900	−	0.247610i	0.709538	−	0.704667i	$-0.248904\pi$
$421$	−3.69123	−	5.08054i	−0.179900	−	0.247610i	−0.889438	+	0.457057i	$0.848904\pi$
$422$	−0.716164	+	0.985716i	−0.0348623	+	0.0479839i
$423$	−6.12959	+	1.99163i	−0.298031	+	0.0968361i
$424$	−22.3268	+	7.25442i	−1.08429	+	0.352306i
$425$	−56.6091	−	41.1289i	−2.74594	−	1.99504i
$426$	2.33549	−	1.69684i	0.113155	−	0.0822120i
$427$	−8.32739	−	2.70573i	−0.402991	−	0.130940i
$428$	15.5853			0.753342
$429$	4.80944	−	10.9485i	0.232202	−	0.528598i
$430$	−7.36791			−0.355312
$431$	−5.10509	−	1.65875i	−0.245904	−	0.0798990i	0.183472	−	0.983025i	$-0.441266\pi$
$431$	−5.10509	−	1.65875i	−0.245904	−	0.0798990i	−0.429376	+	0.903126i	$0.641266\pi$
$432$	−1.39969	+	1.01694i	−0.0673427	+	0.0489273i
$433$	−22.1133	−	16.0663i	−1.06270	−	0.772096i	−0.0881132	−	0.996110i	$-0.528084\pi$
$433$	−22.1133	−	16.0663i	−1.06270	−	0.772096i	−0.974586	+	0.224014i	$0.928084\pi$
$434$	−2.92386	+	0.950020i	−0.140350	+	0.0456024i
$435$	7.05968	−	2.29383i	0.338486	−	0.109981i
$436$	−7.31748	+	10.0717i	−0.350444	+	0.482345i
$437$	−19.4581	−	26.7818i	−0.930808	−	1.28115i
$438$	1.68661	−	5.19085i	0.0805894	−	0.248029i
$439$	23.1013			1.10257			0.551283	−	0.834318i	$-0.314138\pi$
$439$	23.1013			1.10257			0.551283	+	0.834318i	$0.314138\pi$
$440$	31.9854	−	2.27167i	1.52484	−	0.108298i
$441$	5.55022			0.264296
$442$	−2.12667	+	12.3412i	−0.101155	+	0.587013i
$443$	−24.3428	+	17.6861i	−1.15656	+	0.840291i	−0.989339	−	0.145628i	$-0.953480\pi$
$443$	−24.3428	+	17.6861i	−1.15656	+	0.840291i	−0.167222	+	0.985919i	$0.553480\pi$
$444$	−0.865452	+	1.19119i	−0.0410725	+	0.0565315i
$445$	17.4771	+	53.7890i	0.828494	+	2.54984i
$446$	−0.322214	−	0.991673i	−0.0152573	−	0.0469571i
$447$	2.53558	−	3.48992i	0.119929	−	0.165068i
$448$	0.112196	+	0.154425i	0.00530076	+	0.00729587i
$449$	−8.82406	−	2.86711i	−0.416433	−	0.135307i	0.0933037	−	0.995638i	$-0.470257\pi$
$449$	−8.82406	−	2.86711i	−0.416433	−	0.135307i	−0.509737	+	0.860330i	$0.670257\pi$
$450$			8.17428i			0.385339i
$451$	−20.4303	−	5.07021i	−0.962027	−	0.238747i
$452$	16.8069			0.790529
$453$	7.34198	+	2.38555i	0.344956	+	0.112083i
$454$	−5.28621	+	3.84066i	−0.248094	+	0.180251i
$455$	−8.54380	+	16.2203i	−0.400539	+	0.760420i
$456$	2.53976	+	7.81658i	0.118935	+	0.366045i
$457$	23.1758	−	7.53027i	1.08412	−	0.352251i	0.288147	−	0.957586i	$-0.406961\pi$
$457$	23.1758	−	7.53027i	1.08412	−	0.352251i	0.795971	+	0.605335i	$0.206961\pi$
$458$	4.69245	+	3.40927i	0.219264	+	0.159304i
$459$	4.41131	−	3.20500i	0.205902	−	0.149597i
$460$	59.0447	+	19.1848i	2.75297	+	0.894495i
$461$		−	30.1958i		−	1.40636i	−0.711013	−	0.703179i	$-0.751763\pi$
$461$		−	30.1958i		−	1.40636i	0.711013	−	0.703179i	$-0.248237\pi$
$462$	0.955484	+	2.35750i	0.0444531	+	0.109681i
$463$		−	28.4931i		−	1.32419i	−0.749421	−	0.662093i	$-0.769668\pi$
$463$		−	28.4931i		−	1.32419i	0.749421	−	0.662093i	$-0.230332\pi$
$464$	−0.939782	+	2.89235i	−0.0436283	+	0.134274i
$465$	13.6941	−	9.94938i	0.635051	−	0.461391i
$466$	−5.45077	+	7.50235i	−0.252502	+	0.347539i
$467$	0.908566	+	2.79628i	0.0420434	+	0.129396i	0.969875	−	0.243603i	$-0.0783294\pi$
$467$	0.908566	+	2.79628i	0.0420434	+	0.129396i	−0.927832	+	0.372999i	$0.878329\pi$
$468$	−5.15656	+	2.53988i	−0.238362	+	0.117406i
$469$	0.850381	+	0.617838i	0.0392670	+	0.0285291i
$470$	−10.1902	−	14.0256i	−0.470040	−	0.646955i
$471$	−2.06223	+	6.34689i	−0.0950226	+	0.292449i
$472$	11.3172			0.520919
$473$	6.95276	−	5.84698i	0.319688	−	0.268845i
$474$			0.398589i			0.0183078i
$475$	−43.8123	−	14.2355i	−2.01025	−	0.653169i
$476$	6.15226	+	8.46786i	0.281988	+	0.388124i
$477$	8.29543	+	6.02698i	0.379821	+	0.275956i
$478$	−2.15293	−	6.62604i	−0.0984727	−	0.303068i
$479$	29.4117	−	9.55643i	1.34385	−	0.436645i	0.453233	−	0.891392i	$-0.350270\pi$
$479$	29.4117	−	9.55643i	1.34385	−	0.436645i	0.890620	+	0.454747i	$0.150270\pi$
$480$	−19.4086	−	14.1012i	−0.885878	−	0.643628i
$481$	−2.38637	+	2.32248i	−0.108809	+	0.105896i
$482$	3.58450	−	11.0319i	0.163269	−	0.502491i
$483$			11.1035i			0.505228i
$484$	−12.5883	+	12.2095i	−0.572194	+	0.554977i
$485$	−27.2129			−1.23567
$486$	−0.605812	−	0.196840i	−0.0274802	−	0.00892885i
$487$	16.8245	+	23.1570i	0.762391	+	1.04934i	0.997011	+	0.0772545i	$0.0246154\pi$
$487$	16.8245	+	23.1570i	0.762391	+	1.04934i	−0.234620	+	0.972087i	$0.575385\pi$
$488$	9.78610	−	13.4694i	0.442996	−	0.609732i
$489$	−8.93484	+	2.90310i	−0.404047	+	0.131283i
$490$	4.61352	+	14.1990i	0.208418	+	0.641444i
$491$	26.2154	+	19.0466i	1.18308	+	0.859560i	0.992516	−	0.122114i	$-0.0389674\pi$
$491$	26.2154	+	19.0466i	1.18308	+	0.859560i	0.190567	+	0.981674i	$0.438967\pi$
$492$	5.94746	+	8.18598i	0.268132	+	0.369052i
$493$	2.96184	−	9.11562i	0.133395	−	0.410547i
$494$	1.17916	+	8.15993i	0.0530530	+	0.367133i
$495$	−9.01438	−	10.7192i	−0.405166	−	0.481791i
$496$			6.93495i			0.311388i
$497$	1.68625	−	5.18976i	0.0756388	−	0.232792i
$498$	3.30700	−	2.40268i	0.148190	−	0.107667i
$499$	14.5748	−	20.0605i	0.652459	−	0.898033i	−0.346743	−	0.937960i	$-0.612712\pi$
$499$	14.5748	−	20.0605i	0.652459	−	0.898033i	0.999203	+	0.0399268i	$0.0127125\pi$
$500$	50.1513	−	16.2951i	2.24283	−	0.728741i
$501$	−13.8879	+	4.51246i	−0.620467	+	0.201602i
$502$	−2.48572	+	3.42130i	−0.110943	+	0.152700i
$503$	−17.4739	+	12.6955i	−0.779123	+	0.566066i	−0.904716	−	0.426016i	$-0.859917\pi$
$503$	−17.4739	+	12.6955i	−0.779123	+	0.566066i	0.125593	+	0.992082i	$0.459917\pi$
$504$	0.851868	−	2.62178i	0.0379452	−	0.116783i
$505$			71.0623i			3.16223i
$506$	18.0556	−	7.31785i	0.802670	−	0.325318i
$507$	−12.4682	+	3.68031i	−0.553731	+	0.163448i
$508$	5.09902	−	15.6932i	0.226232	−	0.696271i
$509$	4.35225	+	5.99036i	0.192910	+	0.265518i	0.894505	−	0.447058i	$-0.147528\pi$
$509$	4.35225	+	5.99036i	0.192910	+	0.265518i	−0.701595	+	0.712576i	$0.747528\pi$
$510$	11.8661	+	8.62122i	0.525439	+	0.381754i
$511$	−3.18812	−	9.81201i	−0.141034	−	0.434058i
$512$	16.8822	−	5.48537i	0.746096	−	0.242421i
$513$	2.11004	−	2.90422i	0.0931604	−	0.128224i
$514$	4.37791	+	6.02568i	0.193101	+	0.265781i
$515$	−27.5382	−	8.94771i	−1.21348	−	0.394283i
$516$	−4.36677			−0.192236
$517$	20.7464	+	5.14865i	0.912427	+	0.226438i
$518$		−	0.708354i		−	0.0311233i
$519$	−3.95725	+	12.1792i	−0.173704	+	0.534606i
$520$	−24.3126	−	24.9814i	−1.06618	−	1.09551i
$521$	−0.458317	−	0.332987i	−0.0200792	−	0.0145884i	0.577700	−	0.816249i	$-0.303950\pi$
$521$	−0.458317	−	0.332987i	−0.0200792	−	0.0145884i	−0.597780	+	0.801660i	$0.703950\pi$
$522$	−1.06490	+	0.346006i	−0.0466093	+	0.0151443i
$523$	−6.73496	−	20.7281i	−0.294499	−	0.906376i	−0.983389	−	0.181510i	$-0.941902\pi$
$523$	−6.73496	−	20.7281i	−0.294499	−	0.906376i	0.688890	−	0.724866i	$-0.258098\pi$
$524$	−25.3035	−	18.3840i	−1.10539	−	0.803111i
$525$	9.08213	+	12.5005i	0.396377	+	0.545566i
$526$	15.3394	+	4.98406i	0.668828	+	0.217315i
$527$		−	21.8564i		−	0.952080i
$528$	5.72372	−	0.406512i	0.249093	−	0.0176912i
$529$	62.0396			2.69737
$530$	−8.52321	+	26.2317i	−0.370225	+	1.13943i
$531$	−2.90550	−	3.99907i	−0.126088	−	0.173545i
$532$	5.57488	+	4.05038i	0.241702	+	0.175606i
$533$	10.1115	+	20.5287i	0.437977	+	0.889198i
$534$	−2.63628	−	8.11364i	−0.114083	−	0.351112i
$535$	24.2653	−	33.3983i	1.04908	−	1.44394i
$536$	−1.61697	+	1.17480i	−0.0698425	+	0.0507435i
$537$	−1.19344	+	3.67304i	−0.0515008	+	0.158503i
$538$			15.3131i			0.660193i
$539$	−15.6215	−	9.73773i	−0.672866	−	0.419434i
$540$			6.73231i			0.289712i
$541$	21.9089	+	7.11862i	0.941935	+	0.306053i	0.739434	−	0.673229i	$-0.235093\pi$
$541$	21.9089	+	7.11862i	0.941935	+	0.306053i	0.202501	+	0.979282i	$0.435093\pi$
$542$	−5.51819	+	4.00920i	−0.237026	+	0.172210i
$543$	0.307219	+	0.223208i	0.0131840	+	0.00957877i
$544$	−29.4608	+	9.57239i	−1.26312	+	0.410413i
$545$	10.1901	+	31.3619i	0.436496	+	1.34340i
$546$	1.28876	−	2.44671i	0.0551540	−	0.104709i
$547$	−35.1738	+	25.5553i	−1.50392	+	1.09266i	−0.535138	+	0.844765i	$0.679740\pi$
$547$	−35.1738	+	25.5553i	−1.50392	+	1.09266i	−0.968786	+	0.247899i	$0.920260\pi$
$548$	−9.68473	−	3.14676i	−0.413711	−	0.134423i
$549$	−7.27197			−0.310360
$550$	14.3416	−	23.0071i	0.611527	−	0.981026i
$551$		−	6.31017i		−	0.268822i
$552$	−20.0796	−	6.52427i	−0.854646	−	0.277691i
$553$	0.442857	+	0.609541i	0.0188322	+	0.0259203i
$554$	−1.67627	+	2.30718i	−0.0712178	+	0.0980228i
$555$	1.20520	+	3.70923i	0.0511580	+	0.157448i
$556$	−6.46273	−	19.8902i	−0.274081	−	0.843533i
$557$	−1.79788	+	2.47457i	−0.0761785	+	0.104851i	−0.845406	−	0.534124i	$-0.820641\pi$
$557$	−1.79788	+	2.47457i	−0.0761785	+	0.104851i	0.769227	+	0.638975i	$0.220641\pi$
$558$	−2.06565	+	1.50079i	−0.0874461	+	0.0635333i
$559$	−9.73244	−	1.67712i	−0.411639	−	0.0709345i
$560$	−8.79699			−0.371741
$561$	−18.0391	+	1.28117i	−0.761609	+	0.0540912i
$562$	5.58098			0.235419
$563$	−11.5556	+	35.5646i	−0.487012	+	1.49887i	0.342032	+	0.939688i	$0.388885\pi$
$563$	−11.5556	+	35.5646i	−0.487012	+	1.49887i	−0.829045	+	0.559182i	$0.811115\pi$
$564$	−6.03948	−	8.31263i	−0.254308	−	0.350025i
$565$	26.1673	−	36.0162i	1.10087	−	1.51521i
$566$	12.8726	−	4.18255i	0.541074	−	0.175806i
$567$	−1.14514	+	0.372077i	−0.0480912	+	0.0156258i
$568$	8.39434	+	6.09885i	0.352219	+	0.255902i
$569$	6.52194	−	4.73847i	0.273414	−	0.198647i	−0.442626	−	0.896707i	$-0.645953\pi$
$569$	6.52194	−	4.73847i	0.273414	−	0.198647i	0.716040	+	0.698060i	$0.245953\pi$
$570$	9.18370	+	2.98396i	0.384663	+	0.124985i
$571$	18.4686			0.772888			0.386444	−	0.922313i	$-0.373703\pi$
$571$	18.4686			0.772888			0.386444	+	0.922313i	$0.373703\pi$
$572$	18.9697	+	1.89840i	0.793161	+	0.0793759i
$573$	−15.7959			−0.659883
$574$	−4.62962	−	1.50426i	−0.193237	−	0.0627864i
$575$	95.7385	−	69.5581i	3.99257	−	2.90077i
$576$	0.128252	+	0.0931808i	0.00534385	+	0.00388253i
$577$	−33.4438	+	10.8666i	−1.39228	+	0.452380i	−0.906688	−	0.421803i	$-0.861397\pi$
$577$	−33.4438	+	10.8666i	−1.39228	+	0.452380i	−0.485596	+	0.874183i	$0.661397\pi$
$578$	7.71302	−	2.50611i	0.320819	−	0.104241i
$579$	9.18217	−	12.6382i	0.381598	−	0.525225i
$580$	6.95589	+	9.57396i	0.288828	+	0.397537i
$581$	2.38770	−	7.34857i	0.0990583	−	0.304870i
$582$	4.10485			0.170151
$583$	−12.7739	−	31.5175i	−0.529040	−	1.30532i
$584$	19.6173			0.811771
$585$	−2.58564	+	15.0047i	−0.106903	+	0.620366i
$586$	−14.9843	+	10.8868i	−0.618998	+	0.449728i
$587$	−5.78870	+	7.96746i	−0.238925	+	0.328852i	−0.911594	−	0.411091i	$-0.865148\pi$
$587$	−5.78870	+	7.96746i	−0.238925	+	0.328852i	0.672669	+	0.739943i	$0.265148\pi$
$588$	2.73431	+	8.41535i	0.112761	+	0.347043i
$589$	−4.44654	−	13.6850i	−0.183217	−	0.563883i
$590$	7.81557	−	10.7572i	0.321762	−	0.442867i
$591$	14.1169	+	19.4302i	0.580690	+	0.799252i
$592$	−1.51967	−	0.493771i	−0.0624581	−	0.0202939i
$593$			5.19058i			0.213151i	0.994305	+	0.106576i	$0.0339887\pi$
$593$			5.19058i			0.213151i	−0.994305	+	0.106576i	$0.966011\pi$
$594$	1.35975	+	1.61690i	0.0557912	+	0.0663423i
$595$	27.7249			1.13661
$596$	6.54064	+	2.12518i	0.267915	+	0.0870509i
$597$	0.105111	−	0.0763679i	0.00430192	−	0.00312553i
$598$	−18.7388	−	9.87037i	−0.766286	−	0.403629i
$599$	−6.32944	−	19.4800i	−0.258614	−	0.795932i	−0.993096	−	0.117304i	$-0.962575\pi$
$599$	−6.32944	−	19.4800i	−0.258614	−	0.795932i	0.734482	−	0.678628i	$-0.237425\pi$
$600$	−27.9424	+	9.07903i	−1.14074	+	0.370650i
$601$	−0.898798	−	0.653015i	−0.0366627	−	0.0266370i	0.569303	−	0.822128i	$-0.307213\pi$
$601$	−0.898798	−	0.653015i	−0.0366627	−	0.0266370i	−0.605966	+	0.795491i	$0.707213\pi$
$602$	1.69959	−	1.23482i	0.0692701	−	0.0503277i
$603$	0.830255	+	0.269766i	0.0338106	+	0.0109857i
$604$			12.3073i			0.500777i
$605$	6.56509	+	45.9854i	0.266909	+	1.86957i
$606$		−	10.7192i		−	0.435437i
$607$	11.9772	−	36.8621i	0.486140	−	1.49619i	−0.344183	−	0.938903i	$-0.611844\pi$
$607$	11.9772	−	36.8621i	0.486140	−	1.49619i	0.830323	−	0.557283i	$-0.188156\pi$
$608$	−16.4990	+	11.9872i	−0.669122	+	0.486146i
$609$	−1.24405	+	1.71229i	−0.0504116	+	0.0693856i
$610$	−6.04469	−	18.6036i	−0.244742	−	0.753240i
$611$	−10.2679	−	20.8463i	−0.415396	−	0.843353i
$612$	7.03272	+	5.10957i	0.284281	+	0.206542i
$613$	13.2441	+	18.2290i	0.534925	+	0.736261i	0.987871	−	0.155277i	$-0.0496269\pi$
$613$	13.2441	+	18.2290i	0.534925	+	0.736261i	−0.452946	+	0.891538i	$0.649627\pi$
$614$	2.13913	−	6.58355i	0.0863281	−	0.265690i
$615$	26.8019			1.08076
$616$	−6.99749	+	5.88460i	−0.281937	+	0.237097i
$617$			22.1474i			0.891619i	0.895128	+	0.445809i	$0.147084\pi$
$617$			22.1474i			0.891619i	−0.895128	+	0.445809i	$0.852916\pi$
$618$	4.15392	+	1.34969i	0.167095	+	0.0542925i
$619$	25.9710	+	35.7460i	1.04386	+	1.43675i	0.894012	+	0.448042i	$0.147879\pi$
$619$	25.9710	+	35.7460i	1.04386	+	1.43675i	0.149848	+	0.988709i	$0.452121\pi$
$620$	21.8318	+	15.8618i	0.876788	+	0.637024i
$621$	2.84966	+	8.77035i	0.114353	+	0.351942i
$622$	−2.91449	+	0.946974i	−0.116860	+	0.0379702i
$623$	−13.0463	−	9.47868i	−0.522688	−	0.379755i
$624$	−4.35070	−	4.47038i	−0.174167	−	0.178958i
$625$	23.3354	−	71.8189i	0.933415	−	2.87275i
$626$		−	12.8837i		−	0.514934i
$627$	−11.0342	+	4.47212i	−0.440665	+	0.178599i
$628$	−10.6392			−0.424552
$629$	4.78944	+	1.55618i	0.190968	+	0.0620491i
$630$	−1.90375	−	2.62028i	−0.0758471	−	0.104395i
$631$	−13.3503	+	18.3751i	−0.531467	+	0.731501i	−0.987353	−	0.158537i	$-0.949322\pi$
$631$	−13.3503	+	18.3751i	−0.531467	+	0.731501i	0.455886	+	0.890038i	$0.349322\pi$
$632$	−1.36251	+	0.442707i	−0.0541978	+	0.0176099i
$633$	0.591078	+	1.81915i	0.0234933	+	0.0723048i
$634$	8.18975	+	5.95021i	0.325257	+	0.236313i
$635$	−25.6907	−	35.3602i	−1.01950	−	1.40323i
$636$	−5.05148	+	15.5469i	−0.200304	+	0.616473i
$637$	2.86207	+	19.8059i	0.113400	+	0.784738i
$638$	3.60429	+	0.894478i	0.142695	+	0.0354127i
$639$		−	4.53200i		−	0.179283i
$640$	14.6951	−	45.2268i	0.580874	−	1.78775i
$641$	−30.6243	+	22.2498i	−1.20959	+	0.878815i	−0.995193	−	0.0979326i	$-0.968777\pi$
$641$	−30.6243	+	22.2498i	−1.20959	+	0.878815i	−0.214392	+	0.976748i	$0.568777\pi$
$642$	−3.66023	+	5.03788i	−0.144458	+	0.198829i
$643$	3.67155	−	1.19296i	0.144792	−	0.0470457i	−0.235725	−	0.971820i	$-0.575746\pi$
$643$	3.67155	−	1.19296i	0.144792	−	0.0470457i	0.380516	+	0.924774i	$0.375746\pi$
$644$	−16.8354	+	5.47015i	−0.663407	+	0.215554i
$645$	−6.79879	+	9.35774i	−0.267702	+	0.368461i
$646$	10.0872	−	7.32877i	0.396875	−	0.288347i
$647$	−2.55092	+	7.85091i	−0.100287	+	0.308651i	−0.988595	−	0.150596i	$-0.951881\pi$
$647$	−2.55092	+	7.85091i	−0.100287	+	0.308651i	0.888309	+	0.459247i	$0.151881\pi$
$648$		−	2.28949i		−	0.0899397i
$649$	1.16145	+	16.3533i	0.0455909	+	0.641923i
$650$	−29.1698	+	4.21522i	−1.14413	+	0.165334i
$651$	−1.49143	+	4.59014i	−0.0584536	+	0.179902i
$652$	−8.80348	−	12.1170i	−0.344771	−	0.474536i
$653$	22.8374	+	16.5924i	0.893697	+	0.649309i	0.936839	−	0.349760i	$-0.113737\pi$
$653$	22.8374	+	16.5924i	0.893697	+	0.649309i	−0.0431420	+	0.999069i	$0.513737\pi$
$654$	−1.53710	−	4.73070i	−0.0601052	−	0.184985i
$655$	−78.7920	+	25.6011i	−3.07866	+	1.00032i
$656$	−6.45433	+	8.88362i	−0.251999	+	0.346847i
$657$	−5.03640	−	6.93200i	−0.196489	−	0.270443i
$658$	4.70125	+	1.52753i	0.183274	+	0.0595493i
$659$	20.2434			0.788569			0.394285	−	0.918988i	$-0.370992\pi$
$659$	20.2434			0.788569			0.394285	+	0.918988i	$0.370992\pi$
$660$	11.8117	−	18.9486i	0.459769	−	0.737572i
$661$			12.0241i			0.467685i	0.972274	+	0.233843i	$0.0751300\pi$
$661$			12.0241i			0.467685i	−0.972274	+	0.233843i	$0.924870\pi$
$662$	5.04073	−	15.5138i	0.195914	−	0.602960i
$663$	13.7118	+	14.0890i	0.532522	+	0.547171i
$664$	11.8862	+	8.63582i	0.461274	+	0.335135i
$665$	17.3595	−	5.64044i	0.673172	−	0.218727i
$666$	−0.181795	−	0.559508i	−0.00704442	−	0.0216805i
$667$	13.1141	+	9.52794i	0.507780	+	0.368923i
$668$	−13.6838	−	18.8341i	−0.529440	−	0.728712i
$669$	−1.55682	−	0.505840i	−0.0601900	−	0.0195569i
$670$			2.34825i			0.0907210i
$671$	20.4675	+	12.7585i	0.790138	+	0.492536i
$672$	6.84036			0.263873
$673$	13.8281	−	42.5586i	0.533035	−	1.64051i	−0.214823	−	0.976653i	$-0.568917\pi$
$673$	13.8281	−	42.5586i	0.533035	−	1.64051i	0.747858	−	0.663859i	$-0.231083\pi$
$674$	−2.52384	−	3.47377i	−0.0972148	−	0.133805i
$675$	10.3819	+	7.54288i	0.399599	+	0.290325i
$676$	−11.7226	−	17.0914i	−0.450869	−	0.657360i
$677$	−2.38191	−	7.33076i	−0.0915442	−	0.281744i	0.894793	−	0.446480i	$-0.147323\pi$
$677$	−2.38191	−	7.33076i	−0.0915442	−	0.281744i	−0.986338	+	0.164736i	$0.947323\pi$
$678$	−3.94713	+	5.43276i	−0.151589	+	0.208644i
$679$	6.27731	−	4.56074i	0.240901	−	0.175025i
$680$	−16.2907	+	50.1377i	−0.624720	+	1.92269i
$681$			10.2578i			0.393081i
$682$	8.44702	−	0.599927i	0.323453	−	0.0229724i
$683$		−	12.4467i		−	0.476260i	−0.971233	−	0.238130i	$-0.923466\pi$
$683$		−	12.4467i		−	0.476260i	0.971233	−	0.238130i	$-0.0765345\pi$
$684$	5.44294	+	1.76852i	0.208116	+	0.0676209i
$685$	−21.8219	+	15.8545i	−0.833771	+	0.605770i
$686$	−7.78737	−	5.65786i	−0.297323	−	0.216018i
$687$	8.65999	−	2.81380i	0.330399	−	0.107353i
$688$	−1.46441	−	4.50698i	−0.0558300	−	0.171827i
$689$	−17.2295	+	32.7100i	−0.656392	+	1.24615i
$690$	−20.0682	+	14.5804i	−0.763983	+	0.555066i
$691$	8.22070	+	2.67107i	0.312730	+	0.101612i	0.461177	−	0.887308i	$-0.347427\pi$
$691$	8.22070	+	2.67107i	0.312730	+	0.101612i	−0.148447	+	0.988920i	$0.547427\pi$
$692$	−20.4158			−0.776092
$693$	3.87587	+	0.961876i	0.147232	+	0.0365386i
$694$		−	15.1604i		−	0.575480i
$695$	−52.6857	−	17.1186i	−1.99848	−	0.649347i
$696$	−2.36553	−	3.25587i	−0.0896650	−	0.123413i
$697$	20.3416	−	27.9979i	0.770495	−	1.06050i
$698$	0.342755	+	1.05489i	0.0129735	+	0.0399282i
$699$	4.49874	+	13.8457i	0.170158	+	0.523692i
$700$	−14.4792	+	19.9288i	−0.547260	+	0.753239i
$701$	4.33399	−	3.14882i	0.163692	−	0.118929i	−0.502923	−	0.864331i	$-0.667742\pi$
$701$	4.33399	−	3.14882i	0.163692	−	0.118929i	0.666616	+	0.745402i	$0.267742\pi$
$702$	0.390023	−	2.26333i	0.0147205	−	0.0854240i
$703$	3.31543			0.125044
$704$	−0.197492	−	0.487280i	−0.00744326	−	0.0183651i
$705$	−27.2166			−1.02504
$706$	4.43346	−	13.6448i	0.166855	−	0.513528i
$707$	−11.9097	−	16.3923i	−0.447909	−	0.616495i
$708$	4.63208	−	6.37551i	0.174084	−	0.239606i
$709$	27.3506	−	8.88676i	1.02718	−	0.333749i	0.253502	−	0.967335i	$-0.418417\pi$
$709$	27.3506	−	8.88676i	1.02718	−	0.333749i	0.773673	+	0.633585i	$0.218417\pi$
$710$	11.5941	−	3.76714i	0.435118	−	0.141378i
$711$	0.506235	+	0.367801i	0.0189853	+	0.0137936i
$712$	24.8070	−	18.0234i	0.929683	−	0.675454i
$713$	35.1549	+	11.4225i	1.31656	+	0.427776i
$714$	−4.18208			−0.156510
$715$	33.6028	−	37.6952i	1.25667	−	1.40972i
$716$	−6.15707			−0.230101
$717$	−10.4021	−	3.37986i	−0.388475	−	0.126223i
$718$	1.80932	−	1.31455i	0.0675232	−	0.0490585i
$719$	−26.9941	−	19.6123i	−1.00671	−	0.731417i	−0.0431923	−	0.999067i	$-0.513753\pi$
$719$	−26.9941	−	19.6123i	−1.00671	−	0.731417i	−0.963516	+	0.267650i	$0.913753\pi$
$720$	−6.94848	+	2.25770i	−0.258955	+	0.0841394i
$721$	7.85195	−	2.55125i	0.292422	−	0.0950137i
$722$	−2.28888	+	3.15037i	−0.0851833	+	0.117245i
$723$	−10.7037	−	14.7324i	−0.398074	−	0.547902i
$724$	−0.187081	+	0.575775i	−0.00695279	+	0.0213985i
$725$	22.5574			0.837759
$726$	−0.990292	−	6.93653i	−0.0367532	−	0.257439i
$727$	6.82305			0.253053			0.126527	−	0.991963i	$-0.459617\pi$
$727$	6.82305			0.253053			0.126527	+	0.991963i	$0.459617\pi$
$728$	9.79506	+	1.68791i	0.363029	+	0.0625581i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	13.5475	−	18.6466i	0.501416	−	0.690140i
$731$	4.61527	+	14.2043i	0.170702	+	0.525366i
$732$	−3.58253	−	11.0259i	−0.132414	−	0.407529i
$733$	−22.4865	+	30.9500i	−0.830558	+	1.14317i	0.157261	+	0.987557i	$0.449734\pi$
$733$	−22.4865	+	30.9500i	−0.830558	+	1.14317i	−0.987819	+	0.155608i	$0.950266\pi$
$734$	8.99187	+	12.3763i	0.331896	+	0.456816i
$735$	22.2908	+	7.24271i	0.822208	+	0.267152i
$736$		−	52.3888i		−	1.93108i
$737$	−1.86351	−	2.21594i	−0.0686434	−	0.0816252i
$738$	−4.04286			−0.148820
$739$	0.0394336	+	0.0128127i	0.00145059	+	0.000471324i	0.309742	−	0.950821i	$-0.399757\pi$
$739$	0.0394336	+	0.0128127i	0.00145059	+	0.000471324i	−0.308292	+	0.951292i	$0.599757\pi$
$740$	−5.03026	+	3.65470i	−0.184916	+	0.134349i
$741$	11.4517	+	6.03202i	0.420690	+	0.221592i
$742$	−2.43022	−	7.47944i	−0.0892161	−	0.274579i
$743$	8.43301	−	2.74005i	0.309377	−	0.100523i	−0.150214	−	0.988654i	$-0.547996\pi$
$743$	8.43301	−	2.74005i	0.309377	−	0.100523i	0.459591	+	0.888131i	$0.347996\pi$
$744$	−7.42447	−	5.39419i	−0.272194	−	0.197761i
$745$	14.7375	−	10.7074i	0.539941	−	0.392290i
$746$	−0.172638	−	0.0560934i	−0.00632072	−	0.00205373i
$747$		−	6.41720i		−	0.234793i
$748$	−10.8295	−	26.7200i	−0.395965	−	0.976979i
$749$			11.7709i			0.430099i
$750$	−6.51080	+	20.0382i	−0.237741	+	0.731690i
$751$	−15.5708	+	11.3129i	−0.568187	+	0.412812i	−0.834446	−	0.551090i	$-0.814212\pi$
$751$	−15.5708	+	11.3129i	−0.568187	+	0.412812i	0.266259	+	0.963901i	$0.414212\pi$
$752$	6.55419	−	9.02106i	0.239007	−	0.328964i
$753$	2.05156	+	6.31405i	0.0747630	+	0.230097i
$754$	−1.78385	−	3.62164i	−0.0649640	−	0.131892i
$755$	26.3738	+	19.1617i	0.959842	+	0.697366i
$756$	−1.12830	−	1.55297i	−0.0410359	−	0.0564811i
$757$	0.275956	−	0.849305i	0.0100298	−	0.0308685i	−0.945916	−	0.324411i	$-0.894834\pi$
$757$	0.275956	−	0.849305i	0.0100298	−	0.0308685i	0.955946	+	0.293542i	$0.0948341\pi$
$758$	−12.1750			−0.442215
$759$	7.36680	−	29.6844i	0.267398	−	1.07748i
$760$			34.7072i			1.25896i
$761$	46.0488	+	14.9622i	1.66927	+	0.542378i	0.982783	−	0.184766i	$-0.0591528\pi$
$761$	46.0488	+	14.9622i	1.66927	+	0.542378i	0.686485	+	0.727144i	$0.259153\pi$
$762$	3.87524	+	5.33381i	0.140385	+	0.193223i
$763$	−7.60669	−	5.52659i	−0.275381	−	0.200076i
$764$	−7.78183	−	23.9500i	−0.281537	−	0.866481i
$765$	21.8990	−	7.11543i	0.791761	−	0.257259i
$766$	5.69692	+	4.13905i	0.205838	+	0.149550i
$767$	12.7724	−	12.4304i	0.461183	−	0.448837i
$768$	−2.31461	+	7.12365i	−0.0835214	+	0.257053i
$769$		−	12.4532i		−	0.449073i	−0.974466	−	0.224537i	$-0.927913\pi$
$769$		−	12.4532i		−	0.449073i	0.974466	−	0.224537i	$-0.0720868\pi$
$770$	0.761007	+	10.7151i	0.0274248	+	0.386144i
$771$	11.6928			0.421105
$772$	23.6858	+	7.69599i	0.852471	+	0.276985i
$773$	−0.375473	−	0.516795i	−0.0135048	−	0.0185878i	0.802211	−	0.597040i	$-0.203657\pi$
$773$	−0.375473	−	0.516795i	−0.0135048	−	0.0185878i	−0.815716	+	0.578453i	$0.803657\pi$
$774$	1.02554	−	1.41154i	0.0368624	−	0.0507368i
$775$	48.9208	−	15.8953i	1.75729	−	0.570977i
$776$	4.55918	+	14.0317i	0.163665	+	0.503709i
$777$	−0.899657	−	0.653639i	−0.0322750	−	0.0234492i
$778$	4.31373	+	5.93734i	0.154655	+	0.212864i
$779$	7.04062	−	21.6688i	0.252257	−	0.776366i
$780$	−24.0241	+	3.47164i	−0.860202	+	0.124305i
$781$	−7.95129	+	12.7556i	−0.284519	+	0.456433i
$782$			32.0296i			1.14538i
$783$	−0.543191	+	1.67177i	−0.0194121	+	0.0597441i
$784$	−7.76860	+	5.64422i	−0.277450	+	0.201579i
$785$	−16.5646	+	22.7993i	−0.591218	+	0.813741i
$786$	11.8851	−	3.86172i	0.423929	−	0.137743i
$787$	16.1314	−	5.24142i	0.575023	−	0.186836i	−0.00704651	−	0.999975i	$-0.502243\pi$
$787$	16.1314	−	5.24142i	0.575023	−	0.186836i	0.582070	+	0.813139i	$0.302243\pi$
$788$	−22.5058	+	30.9765i	−0.801735	+	1.10349i
$789$	20.4846	−	14.8829i	0.729271	−	0.529846i
$790$	−0.520136	+	1.60081i	−0.0185056	+	0.0569544i
$791$			12.6935i			0.451330i
$792$	−4.01686	+	6.44394i	−0.142733	+	0.228975i
$793$	−3.74992	−	25.9499i	−0.133164	−	0.921508i
$794$	2.93634	−	9.03713i	0.104207	−	0.320716i
$795$	25.4512	+	35.0306i	0.902661	+	1.24241i
$796$	0.167573	+	0.121749i	0.00593948	+	0.00431529i
$797$	−2.08122	−	6.40535i	−0.0737207	−	0.226889i	0.907406	−	0.420255i	$-0.138059\pi$
$797$	−2.08122	−	6.40535i	−0.0737207	−	0.226889i	−0.981127	+	0.193366i	$0.938059\pi$
$798$	−2.61854	+	0.850816i	−0.0926954	+	0.0301186i
$799$	−20.6564	+	28.4311i	−0.730770	+	1.00582i
$800$	−42.8514	−	58.9799i	−1.51503	−	2.08525i
$801$	−12.7375	−	4.13867i	−0.450058	−	0.146233i
$802$	16.7642			0.591966
$803$	2.01326	+	28.3469i	0.0710463	+	1.00034i
$804$			1.39175i			0.0490832i
$805$	−14.4895	+	44.5940i	−0.510686	+	1.57173i
$806$	−6.42072	−	6.59735i	−0.226160	−	0.232382i
$807$	19.4486	+	14.1302i	0.684624	+	0.497408i
$808$	36.6417	−	11.9056i	1.28905	−	0.418838i
$809$	8.37454	+	25.7742i	0.294433	+	0.906172i	0.983411	+	0.181390i	$0.0580596\pi$
$809$	8.37454	+	25.7742i	0.294433	+	0.906172i	−0.688978	+	0.724782i	$0.741940\pi$
$810$	−2.17619	−	1.58110i	−0.0764636	−	0.0555541i
$811$	−19.5931	−	26.9676i	−0.688008	−	0.946962i	0.311987	−	0.950086i	$-0.399005\pi$
$811$	−19.5931	−	26.9676i	−0.688008	−	0.946962i	−0.999995	+	0.00312437i	$0.999005\pi$
$812$	−3.20909	−	1.04270i	−0.112617	−	0.0365915i
$813$			10.7080i			0.375545i
$814$	−0.469968	+	1.89373i	−0.0164724	+	0.0663752i
$815$	−39.6724			−1.38966
$816$	−2.91519	+	8.97204i	−0.102052	+	0.314084i
$817$	5.77956	+	7.95488i	0.202201	+	0.278306i
$818$	13.7595	+	9.99686i	0.481090	+	0.349532i
$819$	−1.91826	−	3.89453i	−0.0670295	−	0.136086i
$820$	13.2039	+	40.6376i	0.461102	+	1.41913i
$821$	18.3586	−	25.2685i	0.640721	−	0.881877i	−0.357933	−	0.933747i	$-0.616518\pi$
$821$	18.3586	−	25.2685i	0.640721	−	0.881877i	0.998654	+	0.0518707i	$0.0165184\pi$
$822$	3.29166	−	2.39153i	0.114810	−	0.0834141i
$823$	−6.29420	+	19.3716i	−0.219402	+	0.675250i	0.779410	+	0.626515i	$0.215519\pi$
$823$	−6.29420	+	19.3716i	−0.219402	+	0.675250i	−0.998812	+	0.0487355i	$0.984481\pi$
$824$			15.6986i			0.546885i
$825$	−15.9867	−	39.4447i	−0.556587	−	1.37329i
$826$			3.79126i			0.131915i
$827$	−2.80285	−	0.910702i	−0.0974647	−	0.0316682i	0.259879	−	0.965641i	$-0.416317\pi$
$827$	−2.80285	−	0.910702i	−0.0974647	−	0.0316682i	−0.357343	+	0.933973i	$0.616317\pi$
$828$	−11.8939	+	8.64141i	−0.413341	+	0.300310i
$829$	−28.1777	−	20.4723i	−0.978652	−	0.711032i	−0.0212449	−	0.999774i	$-0.506763\pi$
$829$	−28.1777	−	20.4723i	−0.978652	−	0.711032i	−0.957407	+	0.288742i	$0.906763\pi$
$830$	16.4169	−	5.33418i	0.569840	−	0.185152i
$831$	1.38349	+	4.25794i	0.0479927	+	0.147706i
$832$	−0.266379	+	0.505717i	−0.00923502	+	0.0175326i
$833$	24.4838	−	17.7885i	0.848312	−	0.616335i
$834$	7.94722	+	2.58221i	0.275190	+	0.0894146i
$835$	−61.6651			−2.13401
$836$	−12.2167	−	14.5271i	−0.422524	−	0.502431i
$837$			4.00838i			0.138550i
$838$	−15.0713	−	4.89696i	−0.520629	−	0.169163i
$839$	16.8708	+	23.2207i	0.582446	+	0.801668i	0.993961	−	0.109735i	$-0.0350001\pi$
$839$	16.8708	+	23.2207i	0.582446	+	0.801668i	−0.411515	+	0.911403i	$0.635000\pi$
$840$	6.84254	−	9.41794i	0.236090	−	0.324950i
$841$	−8.00667	−	24.6420i	−0.276092	−	0.849724i
$842$	1.23614	+	3.80443i	0.0426000	+	0.131109i
$843$	5.14989	−	7.08821i	0.177371	−	0.244131i
$844$	−2.46704	+	1.79241i	−0.0849189	+	0.0616972i
$845$	−54.8772	−	1.48939i	−1.88783	−	0.0512365i
$846$	4.10541			0.141147
$847$	−9.22132	−	9.50739i	−0.316848	−	0.326678i
$848$	−17.7401			−0.609197
$849$	6.56613	−	20.2085i	0.225349	−	0.693553i
$850$	26.1986	+	36.0593i	0.898605	+	1.23682i
$851$	−5.00608	+	6.89028i	−0.171606	+	0.236196i
$852$	6.87150	−	2.23269i	0.235414	−	0.0764906i
$853$	−14.4426	+	4.69267i	−0.494504	+	0.160674i	−0.545643	−	0.838017i	$-0.683715\pi$
$853$	−14.4426	+	4.69267i	−0.494504	+	0.160674i	0.0511394	+	0.998692i	$0.483715\pi$
$854$	4.51223	+	3.27833i	0.154405	+	0.112182i
$855$	12.2642	−	8.91043i	0.419425	−	0.304730i
$856$	−21.2865	−	6.91640i	−0.727557	−	0.236398i
$857$	−30.3756			−1.03761			−0.518805	−	0.854893i	$-0.673623\pi$
$857$	−30.3756			−1.03761			−0.518805	+	0.854893i	$0.673623\pi$
$858$	−5.06871	+	5.68603i	−0.173043	+	0.194118i
$859$	−18.6617			−0.636728			−0.318364	−	0.947969i	$-0.603133\pi$
$859$	−18.6617			−0.636728			−0.318364	+	0.947969i	$0.603133\pi$
$860$	−17.5378	−	5.69837i	−0.598034	−	0.194313i
$861$	−6.18252	+	4.49187i	−0.210700	+	0.153082i
$862$	2.76622	+	2.00977i	0.0942177	+	0.0684532i
$863$	−39.2897	+	12.7660i	−1.33744	+	0.434560i	−0.888448	−	0.458977i	$-0.848216\pi$
$863$	−39.2897	+	12.7660i	−1.33744	+	0.434560i	−0.448990	+	0.893537i	$0.648216\pi$
$864$	5.40299	−	1.75554i	0.183814	−	0.0597247i
$865$	−31.7862	+	43.7499i	−1.08076	+	1.48754i
$866$	10.2340	+	14.0859i	0.347766	+	0.478659i
$867$	3.93432	−	12.1086i	0.133616	−	0.411229i
$868$	−7.69440			−0.261165
$869$	−0.779536	−	1.92338i	−0.0264439	−	0.0652462i
$870$	−4.72835			−0.160306
$871$	−0.534521	+	3.10186i	−0.0181115	+	0.105103i
$872$	14.4639	−	10.5086i	0.489808	−	0.355866i
$873$	3.78778	−	5.21343i	0.128197	−	0.176448i
$874$	6.51622	+	20.0549i	0.220414	+	0.678366i
$875$	12.3070	+	37.8772i	0.416054	+	1.28048i
$876$	8.02926	−	11.0513i	0.271283	−	0.373390i
$877$	−26.7872	−	36.8694i	−0.904538	−	1.24499i	−0.968998	−	0.247070i	$-0.920532\pi$
$877$	−26.7872	−	36.8694i	−0.904538	−	1.24499i	0.0644595	−	0.997920i	$-0.479468\pi$
$878$	−13.9951	−	4.54727i	−0.472310	−	0.153463i
$879$			29.0770i			0.980741i
$880$	23.5181	+	5.83649i	0.792794	+	0.196748i
$881$	−8.81924			−0.297128			−0.148564	−	0.988903i	$-0.547465\pi$
$881$	−8.81924			−0.297128			−0.148564	+	0.988903i	$0.547465\pi$
$882$	−3.36239	−	1.09251i	−0.113218	−	0.0367866i
$883$	27.3236	−	19.8518i	0.919513	−	0.668065i	−0.0238900	−	0.999715i	$-0.507605\pi$
$883$	27.3236	−	19.8518i	0.919513	−	0.668065i	0.943403	+	0.331650i	$0.107605\pi$
$884$	−14.6069	+	27.7310i	−0.491282	+	0.932694i
$885$	−6.45049	−	19.8526i	−0.216831	−	0.667337i
$886$	18.2285	−	5.92279i	0.612398	−	0.198980i
$887$	−4.41929	−	3.21080i	−0.148385	−	0.107808i	0.511116	−	0.859512i	$-0.329232\pi$
$887$	−4.41929	−	3.21080i	−0.148385	−	0.107808i	−0.659501	+	0.751704i	$0.729232\pi$
$888$	1.71067	−	1.24287i	0.0574062	−	0.0417081i
$889$	11.8524	+	3.85107i	0.397516	+	0.129161i
$890$		−	36.0262i		−	1.20760i
$891$	3.30829	−	0.234962i	0.110832	−	0.00787154i
$892$		−	2.60967i		−	0.0873784i
$893$	−7.14956	+	22.0041i	−0.239251	+	0.736338i
$894$	−2.22304	+	1.61513i	−0.0743496	+	0.0540181i
$895$	−9.58619	+	13.1943i	−0.320431	+	0.441036i
$896$	4.19000	+	12.8955i	0.139978	+	0.430808i
$897$	−29.8274	+	14.6916i	−0.995907	+	0.490537i
$898$	4.78136	+	3.47386i	0.159556	+	0.115924i
$899$	4.14150	+	5.70028i	0.138127	+	0.190115i
$900$	−6.32202	+	19.4572i	−0.210734	+	0.648573i
$901$	55.9102			1.86264
$902$	11.3789	+	7.09310i	0.378876	+	0.236174i
$903$		−	3.29803i		−	0.109752i
$904$	−22.9550	−	7.45853i	−0.763472	−	0.248067i
$905$	0.942580	+	1.29735i	0.0313324	+	0.0431254i
$906$	−3.97828	−	2.89039i	−0.132170	−	0.0960269i
$907$	−4.35838	−	13.4137i	−0.144718	−	0.445395i	0.852257	−	0.523123i	$-0.175233\pi$
$907$	−4.35838	−	13.4137i	−0.144718	−	0.445395i	−0.996975	+	0.0777283i	$0.975233\pi$
$908$	−15.5531	+	5.05351i	−0.516148	+	0.167707i
$909$	−13.6141	−	9.89121i	−0.451550	−	0.328071i
$910$	8.36874	−	8.14469i	0.277421	−	0.269994i
$911$	10.1885	−	31.3570i	0.337561	−	1.03891i	−0.627886	−	0.778305i	$-0.716080\pi$
$911$	10.1885	−	31.3570i	0.337561	−	1.03891i	0.965447	−	0.260600i	$-0.0839203\pi$
$912$			6.21078i			0.205660i
$913$	−11.2588	+	18.0617i	−0.372613	+	0.597754i
$914$	−15.5224			−0.513436
$915$	−29.2056	−	9.48949i	−0.965509	−	0.313713i
$916$	8.53267	+	11.7442i	0.281927	+	0.388040i
$917$	13.8847	−	19.1106i	0.458513	−	0.631089i
$918$	−3.30330	+	1.07331i	−0.109025	+	0.0354244i
$919$	2.87808	+	8.85781i	0.0949390	+	0.292192i	0.987238	−	0.159253i	$-0.0509086\pi$
$919$	2.87808	+	8.85781i	0.0949390	+	0.292192i	−0.892299	+	0.451445i	$0.850909\pi$
$920$	−72.1300	−	52.4055i	−2.37806	−	1.72776i
$921$	−6.38765	−	8.79185i	−0.210480	−	0.289701i
$922$	−5.94374	+	18.2930i	−0.195747	+	0.602447i
$923$	16.1724	−	2.33701i	0.532320	−	0.0769236i
$924$	0.451029	+	6.35053i	0.0148378	+	0.208917i
$925$			11.8519i			0.389687i
$926$	−5.60858	+	17.2614i	−0.184310	+	0.567246i
$927$	5.54726	−	4.03032i	0.182196	−	0.132373i
$928$	5.86971	−	8.07897i	0.192683	−	0.265205i
$929$	19.7092	−	6.40390i	0.646637	−	0.210105i	0.0327063	−	0.999465i	$-0.489587\pi$
$929$	19.7092	−	6.40390i	0.646637	−	0.210105i	0.613931	+	0.789360i	$0.289587\pi$
$930$	−10.2545	+	3.33189i	−0.336259	+	0.109257i
$931$	11.7112	−	16.1191i	0.383818	−	0.528281i
$932$	−18.7768	+	13.6421i	−0.615054	+	0.446863i
$933$	−1.48664	+	4.57542i	−0.0486705	+	0.149792i
$934$		−	1.87286i		−	0.0612818i
$935$	−74.1202	−	18.3945i	−2.42399	−	0.601563i
$936$	8.17002	−	1.18062i	0.267045	−	0.0385897i
$937$	−9.43791	+	29.0469i	−0.308323	+	0.948921i	0.670093	+	0.742277i	$0.266254\pi$
$937$	−9.43791	+	29.0469i	−0.308323	+	0.948921i	−0.978416	+	0.206644i	$0.933746\pi$
$938$	−0.393555	−	0.541682i	−0.0128500	−	0.0176866i
$939$	−16.3631	−	11.8885i	−0.533990	−	0.387966i
$940$	−13.4082	−	41.2663i	−0.437329	−	1.34596i
$941$	41.0233	−	13.3293i	1.33732	−	0.434522i	0.448913	−	0.893575i	$-0.351811\pi$
$941$	41.0233	−	13.3293i	1.33732	−	0.434522i	0.888409	+	0.459053i	$0.151811\pi$
$942$	2.49865	−	3.43909i	0.0814103	−	0.112052i
$943$	34.4022	+	47.3506i	1.12029	+	1.54195i
$944$	8.13360	+	2.64277i	0.264726	+	0.0860148i
$945$	−5.08463			−0.165403
$946$	−5.36298	+	2.17359i	−0.174366	+	0.0706695i
$947$		−	33.1068i		−	1.07583i	−0.843000	−	0.537913i	$-0.819213\pi$
$947$		−	33.1068i		−	1.07583i	0.843000	−	0.537913i	$-0.180787\pi$
$948$	−0.308271	+	0.948760i	−0.0100122	+	0.0308143i
$949$	22.1396	−	21.5469i	0.718683	−	0.699443i
$950$	23.7399	+	17.2480i	0.770223	+	0.559600i
$951$	15.1143	−	4.91094i	0.490115	−	0.159248i
$952$	−4.64496	−	14.2957i	−0.150544	−	0.463327i
$953$	40.3910	+	29.3457i	1.30839	+	0.950602i	1.00000		0.000657461i	$-0.000209276\pi$
$953$	40.3910	+	29.3457i	1.30839	+	0.950602i	0.308392	+	0.951259i	$0.400209\pi$
$954$	−3.83911	−	5.28409i	−0.124296	−	0.171079i
$955$	−63.4394	−	20.6127i	−2.05285	−	0.667012i
$956$		−	17.4370i		−	0.563953i
$957$	4.46193	−	3.75230i	0.144234	−	0.121295i
$958$	−19.6990			−0.636447
$959$	2.37661	−	7.31447i	0.0767449	−	0.236196i
$960$	0.393491	+	0.541594i	0.0126999	+	0.0174799i
$961$	−12.0810	−	8.77734i	−0.389709	−	0.283140i
$962$	1.90285	−	0.937254i	0.0613503	−	0.0302183i
$963$	3.02093	+	9.29748i	0.0973482	+	0.299607i
$964$	17.0643	−	23.4870i	0.549604	−	0.756466i
$965$	53.3695	−	38.7752i	1.71802	−	1.24822i
$966$	2.18562	−	6.72665i	0.0703212	−	0.216426i
$967$			29.6508i			0.953505i	0.879038	+	0.476752i	$0.158186\pi$
$967$			29.6508i			0.953505i	−0.879038	+	0.476752i	$0.841814\pi$
$968$	22.6115	−	11.0894i	0.726760	−	0.356428i
$969$		−	19.5741i		−	0.628810i
$970$	16.4859	+	5.35658i	0.529329	+	0.171989i
$971$	4.52604	−	3.28836i	0.145248	−	0.105529i	−0.512788	−	0.858515i	$-0.671387\pi$
$971$	4.52604	−	3.28836i	0.145248	−	0.105529i	0.658036	+	0.752987i	$0.271387\pi$
$972$	−1.28977	−	0.937075i	−0.0413695	−	0.0300567i
$973$	15.0222	−	4.88102i	0.481591	−	0.156478i
$974$	−5.63427	−	17.3405i	−0.180534	−	0.555625i
$975$	−21.5630	+	40.9372i	−0.690570	+	1.31104i
$976$	10.1785	−	7.39512i	0.325806	−	0.236712i
$977$	14.8444	+	4.82323i	0.474913	+	0.154309i	0.536687	−	0.843781i	$-0.319676\pi$
$977$	14.8444	+	4.82323i	0.474913	+	0.154309i	−0.0617734	+	0.998090i	$0.519676\pi$
$978$	5.98427			0.191356
$979$	28.5894	+	33.9962i	0.913723	+	1.08652i
$980$			37.3658i			1.19361i
$981$	−7.42667	−	2.41307i	−0.237115	−	0.0770434i
$982$	−12.1324	−	16.6989i	−0.387162	−	0.532882i
$983$	4.73450	−	6.51648i	0.151007	−	0.207843i	−0.726811	−	0.686837i	$-0.758998\pi$
$983$	4.73450	−	6.51648i	0.151007	−	0.207843i	0.877818	+	0.478994i	$0.158998\pi$
$984$	−4.49034	−	13.8198i	−0.143147	−	0.440560i
$985$	31.3408	+	96.4572i	0.998602	+	3.07338i
$986$	−3.58864	+	4.93934i	−0.114286	+	0.157301i
$987$	6.27818	−	4.56136i	0.199837	−	0.145190i
$988$	−3.50418	+	20.3350i	−0.111483	+	0.646943i
$989$	−25.2589			−0.803187
$990$	3.35105	+	8.26819i	0.106504	+	0.262780i
$991$	−31.7496			−1.00856			−0.504280	−	0.863540i	$-0.668242\pi$
$991$	−31.7496			−1.00856			−0.504280	+	0.863540i	$0.668242\pi$
$992$	7.03686	−	21.6572i	0.223421	−	0.687618i
$993$	−15.0522	−	20.7175i	−0.477666	−	0.657450i
$994$	−2.04310	+	2.81209i	−0.0648033	+	0.0891941i
$995$	0.521804	−	0.169544i	0.0165423	−	0.00537491i
$996$	9.72988	−	3.16143i	0.308303	−	0.100174i
$997$	−4.18368	−	3.03962i	−0.132499	−	0.0962658i	0.519562	−	0.854433i	$-0.326095\pi$
$997$	−4.18368	−	3.03962i	−0.132499	−	0.0962658i	−0.652060	+	0.758167i	$0.726095\pi$
$998$	−12.7783	+	9.28400i	−0.404491	+	0.293880i
$999$	−0.878365	−	0.285398i	−0.0277902	−	0.00902960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.64.6	✓	56
11.5	even	5	inner	429.2.bb.a.181.9	yes	56
13.12	even	2	inner	429.2.bb.a.64.9	yes	56
143.38	even	10	inner	429.2.bb.a.181.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.64.6	✓	56	1.1	even	1	trivial
429.2.bb.a.64.9	yes	56	13.12	even	2	inner
429.2.bb.a.181.6	yes	56	143.38	even	10	inner
429.2.bb.a.181.9	yes	56	11.5	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.605812 - 0.196840i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.28977 - 0.937075i) q^{4} +(-4.01620 + 1.30494i) q^{5} +(0.605812 - 0.196840i) q^{6} +(0.707733 - 0.974111i) q^{7} +(1.34573 + 1.85224i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.605812 - 0.196840i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.28977 - 0.937075i) q^{4} +(-4.01620 + 1.30494i) q^{5} +(0.605812 - 0.196840i) q^{6} +(0.707733 - 0.974111i) q^{7} +(1.34573 + 1.85224i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.68992 q^{10} +(-2.53836 + 2.13465i) q^{11} +1.59425 q^{12} +(3.55318 + 0.612293i) q^{13} +(-0.620497 + 0.450817i) q^{14} +(2.48215 - 3.41638i) q^{15} +(0.534635 + 1.64544i) q^{16} +(-1.68497 - 5.18581i) q^{17} +(-0.374412 + 0.515334i) q^{18} +(-2.11004 - 2.90422i) q^{19} +(6.40281 + 2.08040i) q^{20} +1.20407i q^{21} +(1.95795 - 0.793547i) q^{22} +9.22169 q^{23} +(-2.17744 - 0.707492i) q^{24} +(10.3819 - 7.54288i) q^{25} +(-2.03203 - 1.07034i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.82563 + 0.593183i) q^{28} +(1.42209 + 1.03321i) q^{29} +(-2.17619 + 1.58110i) q^{30} +(3.81219 + 1.23866i) q^{31} -5.68105i q^{32} +(0.798856 - 3.21898i) q^{33} +3.47329i q^{34} +(-1.57124 + 4.83577i) q^{35} +(-1.28977 + 0.937075i) q^{36} +(-0.542859 + 0.747182i) q^{37} +(0.706618 + 2.17475i) q^{38} +(-3.23448 + 1.59315i) q^{39} +(-7.82178 - 5.68285i) q^{40} +(3.73058 + 5.13470i) q^{41} +(0.237009 - 0.729438i) q^{42} -2.73908 q^{43} +(5.27423 - 0.374588i) q^{44} +4.22288i q^{45} +(-5.58661 - 1.81520i) q^{46} +(-3.78830 - 5.21414i) q^{47} +(-1.39969 - 1.01694i) q^{48} +(1.71511 + 5.27858i) q^{49} +(-7.77420 + 2.52599i) q^{50} +(4.41131 + 3.20500i) q^{51} +(-4.00903 - 4.11931i) q^{52} +(-3.16857 + 9.75186i) q^{53} -0.636988i q^{54} +(7.40894 - 11.8856i) q^{55} +2.75670 q^{56} +(3.41411 + 1.10931i) q^{57} +(-0.658142 - 0.905855i) q^{58} +(2.90550 - 3.99907i) q^{59} +(-6.40281 + 2.08040i) q^{60} +(-2.24716 - 6.91605i) q^{61} +(-2.06565 - 1.50079i) q^{62} +(-0.707733 - 0.974111i) q^{63} +(-0.0489881 + 0.150770i) q^{64} +(-15.0693 + 2.17760i) q^{65} +(-1.11758 + 1.79285i) q^{66} +0.872982i q^{67} +(-2.68626 + 8.26745i) q^{68} +(-7.46050 + 5.42037i) q^{69} +(1.90375 - 2.62028i) q^{70} +(4.31019 - 1.40047i) q^{71} +(2.17744 - 0.707492i) q^{72} +(5.03640 - 6.93200i) q^{73} +(0.475946 - 0.345795i) q^{74} +(-3.96552 + 12.2046i) q^{75} +5.72304i q^{76} +(0.282910 + 3.98340i) q^{77} +(2.27308 - 0.328475i) q^{78} +(-0.193365 + 0.595115i) q^{79} +(-4.29440 - 5.91073i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.24931 - 3.84499i) q^{82} +(6.10312 - 1.98303i) q^{83} +(1.12830 - 1.55297i) q^{84} +(13.5343 + 18.6284i) q^{85} +(1.65937 + 0.539161i) q^{86} -1.75780 q^{87} +(-7.36983 - 1.82897i) q^{88} -13.3930i q^{89} +(0.831232 - 2.55827i) q^{90} +(3.11114 - 3.02785i) q^{91} +(-11.8939 - 8.64141i) q^{92} +(-3.81219 + 1.23866i) q^{93} +(1.26864 + 3.90448i) q^{94} +(12.2642 + 8.91043i) q^{95} +(3.33923 + 4.59606i) q^{96} +(6.12875 + 1.99135i) q^{97} -3.53542i q^{98} +(1.24578 + 3.07376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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