LMFDB - Embedded newform 231.2.n.a.89.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(89,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("231.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.n (of order $6$, degree $2$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.10
Character	$\chi$	$=$	231.89
Dual form			231.2.n.a.122.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.872412 - 0.503687i) q^{2} +(1.39293 + 1.02944i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(0.168910 - 0.292561i) q^{5} +(-0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} +3.00721i q^{8} +(0.880503 + 2.86788i) q^{9} +O(q^{10})$	\(q+(-0.872412 - 0.503687i) q^{2} +(1.39293 + 1.02944i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(0.168910 - 0.292561i) q^{5} +(-0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} +3.00721i q^{8} +(0.880503 + 2.86788i) q^{9} +(-0.294718 + 0.170156i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.192170 - 1.69556i) q^{12} -6.18751i q^{13} +(-2.20211 - 1.50144i) q^{14} +(0.536454 - 0.233634i) q^{15} +(0.529497 - 0.917116i) q^{16} +(0.517054 + 0.895564i) q^{17} +(0.676351 - 2.94547i) q^{18} +(4.76552 + 2.75137i) q^{19} -0.332819 q^{20} +(3.47144 + 2.99151i) q^{21} -1.00737 q^{22} +(-0.780699 - 0.450737i) q^{23} +(-3.09575 + 4.18883i) q^{24} +(2.44294 + 4.23129i) q^{25} +(-3.11657 + 5.39806i) q^{26} +(-1.72583 + 4.90117i) q^{27} +(-1.13090 - 2.34848i) q^{28} -10.4471i q^{29} +(-0.585687 - 0.0663803i) q^{30} +(-2.82520 + 1.63113i) q^{31} +(4.28476 - 2.47381i) q^{32} +(1.72103 + 0.195057i) q^{33} -1.04173i q^{34} +(0.503505 - 0.738472i) q^{35} +(2.01315 - 2.16396i) q^{36} +(-1.95816 + 3.39162i) q^{37} +(-2.77166 - 4.80066i) q^{38} +(6.36968 - 8.61877i) q^{39} +(0.879793 + 0.507948i) q^{40} -11.2247 q^{41} +(-1.52174 - 4.35835i) q^{42} -6.76228 q^{43} +(-0.853205 - 0.492598i) q^{44} +(0.987755 + 0.226813i) q^{45} +(0.454061 + 0.786456i) q^{46} +(-3.61562 + 6.26243i) q^{47} +(1.68167 - 0.732392i) q^{48} +(6.92177 + 1.04359i) q^{49} -4.92191i q^{50} +(-0.201710 + 1.77973i) q^{51} +(-5.27922 + 3.04796i) q^{52} +(-7.55149 + 4.35985i) q^{53} +(3.97429 - 3.40656i) q^{54} -0.337820i q^{55} +(-0.594748 + 7.93407i) q^{56} +(3.80565 + 8.73829i) q^{57} +(-5.26205 + 9.11414i) q^{58} +(2.65866 + 4.60494i) q^{59} +(-0.463594 - 0.342618i) q^{60} +(-2.79724 - 1.61499i) q^{61} +3.28632 q^{62} +(1.75588 + 7.74060i) q^{63} -7.10209 q^{64} +(-1.81023 - 1.04513i) q^{65} +(-1.40320 - 1.03703i) q^{66} +(-5.29852 - 9.17731i) q^{67} +(0.509400 - 0.882306i) q^{68} +(-0.623452 - 1.43153i) q^{69} +(-0.811223 + 0.390643i) q^{70} -9.05873i q^{71} +(-8.62431 + 2.64786i) q^{72} +(-3.38869 + 1.95646i) q^{73} +(3.41664 - 1.97260i) q^{74} +(-0.953026 + 8.40875i) q^{75} -5.42129i q^{76} +(2.38376 - 1.14790i) q^{77} +(-9.89815 + 4.31079i) q^{78} +(-2.94659 + 5.10365i) q^{79} +(-0.178875 - 0.309821i) q^{80} +(-7.44943 + 5.05035i) q^{81} +(9.79259 + 5.65376i) q^{82} +6.94128 q^{83} +(0.842347 - 4.43546i) q^{84} +0.349343 q^{85} +(5.89950 + 3.40608i) q^{86} +(10.7546 - 14.5520i) q^{87} +(1.50361 + 2.60432i) q^{88} +(-1.82637 + 3.16337i) q^{89} +(-0.747486 - 0.695393i) q^{90} +(1.22373 - 16.3248i) q^{91} +0.888129i q^{92} +(-5.61445 - 0.636327i) q^{93} +(6.30861 - 3.64228i) q^{94} +(1.60989 - 0.929470i) q^{95} +(8.51501 + 0.965069i) q^{96} +9.23676i q^{97} +(-5.51299 - 4.39685i) q^{98} +(2.19648 + 2.04340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	$ 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) $ 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.872412	−	0.503687i	−0.616888	−	0.356161i	0.158768	−	0.987316i	$-0.449248\pi$
$2$	−0.872412	−	0.503687i	−0.616888	−	0.356161i	−0.775657	+	0.631155i	$0.782581\pi$
$3$	1.39293	+	1.02944i	0.804208	+	0.594348i
$3$	1.39293	+	1.02944i	0.804208	+	0.594348i
$4$	−0.492598	−	0.853205i	−0.246299	−	0.426603i
$5$	0.168910	−	0.292561i	0.0755389	−	0.130837i	−0.825782	−	0.563990i	$-0.809266\pi$
$5$	0.168910	−	0.292561i	0.0755389	−	0.130837i	0.901321	+	0.433153i	$0.142599\pi$
$6$	−0.696692	−	1.59970i	−0.284423	−	0.653074i
$7$	2.63835	+	0.197774i	0.997202	+	0.0747515i
$7$	2.63835	+	0.197774i	0.997202	+	0.0747515i
$8$			3.00721i			1.06321i
$9$	0.880503	+	2.86788i	0.293501	+	0.955959i
$10$	−0.294718	+	0.170156i	−0.0931982	+	0.0538080i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	0.192170	−	1.69556i	0.0554747	−	0.489465i
$13$		−	6.18751i		−	1.71611i	−0.513560	−	0.858054i	$-0.671674\pi$
$13$		−	6.18751i		−	1.71611i	0.513560	−	0.858054i	$-0.328326\pi$
$14$	−2.20211	−	1.50144i	−0.588539	−	0.401278i
$15$	0.536454	−	0.233634i	0.138512	−	0.0603240i
$16$	0.529497	−	0.917116i	0.132374	−	0.229279i
$17$	0.517054	+	0.895564i	0.125404	+	0.217206i	0.921891	−	0.387450i	$-0.126644\pi$
$17$	0.517054	+	0.895564i	0.125404	+	0.217206i	−0.796487	+	0.604656i	$0.793311\pi$
$18$	0.676351	−	2.94547i	0.159418	−	0.694253i
$19$	4.76552	+	2.75137i	1.09329	+	0.631209i	0.934449	−	0.356096i	$-0.115893\pi$
$19$	4.76552	+	2.75137i	1.09329	+	0.631209i	0.158836	+	0.987305i	$0.449226\pi$
$20$	−0.332819			−0.0744207
$21$	3.47144	+	2.99151i	0.757530	+	0.652801i
$22$	−1.00737			−0.214773
$23$	−0.780699	−	0.450737i	−0.162787	−	0.0939851i	0.416393	−	0.909185i	$-0.363294\pi$
$23$	−0.780699	−	0.450737i	−0.162787	−	0.0939851i	−0.579180	+	0.815199i	$0.696627\pi$
$24$	−3.09575	+	4.18883i	−0.631916	+	0.855042i
$25$	2.44294	+	4.23129i	0.488588	+	0.846259i
$26$	−3.11657	+	5.39806i	−0.611210	+	1.05865i
$27$	−1.72583	+	4.90117i	−0.332136	+	0.943231i
$28$	−1.13090	−	2.34848i	−0.213721	−	0.443820i
$29$		−	10.4471i		−	1.93997i	−0.243163	−	0.969985i	$-0.578185\pi$
$29$		−	10.4471i		−	1.93997i	0.243163	−	0.969985i	$-0.421815\pi$
$30$	−0.585687	−	0.0663803i	−0.106931	−	0.0121193i
$31$	−2.82520	+	1.63113i	−0.507421	+	0.292959i	−0.731773	−	0.681549i	$-0.761307\pi$
$31$	−2.82520	+	1.63113i	−0.507421	+	0.292959i	0.224352	+	0.974508i	$0.427973\pi$
$32$	4.28476	−	2.47381i	0.757446	−	0.437312i
$33$	1.72103	+	0.195057i	0.299593	+	0.0339551i
$34$		−	1.04173i		−	0.178656i
$35$	0.503505	−	0.738472i	0.0851079	−	0.124825i
$36$	2.01315	−	2.16396i	0.335525	−	0.360660i
$37$	−1.95816	+	3.39162i	−0.321919	+	0.557580i	−0.980884	−	0.194594i	$-0.937661\pi$
$37$	−1.95816	+	3.39162i	−0.321919	+	0.557580i	0.658965	+	0.752173i	$0.270994\pi$
$38$	−2.77166	−	4.80066i	−0.449623	−	0.778770i
$39$	6.36968	−	8.61877i	1.01997	−	1.38011i
$40$	0.879793	+	0.507948i	0.139107	+	0.0803137i
$41$	−11.2247			−1.75301			−0.876504	−	0.481394i	$-0.840131\pi$
$41$	−11.2247			−1.75301			−0.876504	+	0.481394i	$0.840131\pi$
$42$	−1.52174	−	4.35835i	−0.234809	−	0.672508i
$43$	−6.76228			−1.03124			−0.515619	−	0.856818i	$-0.672438\pi$
$43$	−6.76228			−1.03124			−0.515619	+	0.856818i	$0.672438\pi$
$44$	−0.853205	−	0.492598i	−0.128626	−	0.0742620i
$45$	0.987755	+	0.226813i	0.147246	+	0.0338112i
$46$	0.454061	+	0.786456i	0.0669476	+	0.115957i
$47$	−3.61562	+	6.26243i	−0.527392	+	0.913469i	0.472098	+	0.881546i	$0.343497\pi$
$47$	−3.61562	+	6.26243i	−0.527392	+	0.913469i	−0.999490	+	0.0319237i	$0.989837\pi$
$48$	1.68167	−	0.732392i	0.242728	−	0.105712i
$49$	6.92177	+	1.04359i	0.988824	+	0.149085i
$50$		−	4.92191i		−	0.696063i
$51$	−0.201710	+	1.77973i	−0.0282451	+	0.249213i
$52$	−5.27922	+	3.04796i	−0.732096	+	0.422676i
$53$	−7.55149	+	4.35985i	−1.03728	+	0.598872i	−0.919061	−	0.394116i	$-0.871051\pi$
$53$	−7.55149	+	4.35985i	−1.03728	+	0.598872i	−0.118216	+	0.992988i	$0.537718\pi$
$54$	3.97429	−	3.40656i	0.540833	−	0.463575i
$55$		−	0.337820i		−	0.0455517i
$56$	−0.594748	+	7.93407i	−0.0794765	+	1.06023i
$57$	3.80565	+	8.73829i	0.504071	+	1.15741i
$58$	−5.26205	+	9.11414i	−0.690941	+	1.19675i
$59$	2.65866	+	4.60494i	0.346128	+	0.599512i	0.985558	−	0.169338i	$-0.0541629\pi$
$59$	2.65866	+	4.60494i	0.346128	+	0.599512i	−0.639430	+	0.768849i	$0.720830\pi$
$60$	−0.463594	−	0.342618i	−0.0598497	−	0.0442318i
$61$	−2.79724	−	1.61499i	−0.358150	−	0.206778i	0.310119	−	0.950698i	$-0.399631\pi$
$61$	−2.79724	−	1.61499i	−0.358150	−	0.206778i	−0.668269	+	0.743920i	$0.732964\pi$
$62$	3.28632			0.417362
$63$	1.75588	+	7.74060i	0.221221	+	0.975224i
$64$	−7.10209			−0.887762
$65$	−1.81023	−	1.04513i	−0.224531	−	0.129633i
$66$	−1.40320	−	1.03703i	−0.172722	−	0.127650i
$67$	−5.29852	−	9.17731i	−0.647318	−	1.12119i	−0.983761	−	0.179484i	$-0.942557\pi$
$67$	−5.29852	−	9.17731i	−0.647318	−	1.12119i	0.336443	−	0.941704i	$-0.390776\pi$
$68$	0.509400	−	0.882306i	0.0617738	−	0.106995i
$69$	−0.623452	−	1.43153i	−0.0750547	−	0.172336i
$70$	−0.811223	+	0.390643i	−0.0969596	+	0.0466907i
$71$		−	9.05873i		−	1.07507i	−0.843240	−	0.537537i	$-0.819355\pi$
$71$		−	9.05873i		−	1.07507i	0.843240	−	0.537537i	$-0.180645\pi$
$72$	−8.62431	+	2.64786i	−1.01638	+	0.312053i
$73$	−3.38869	+	1.95646i	−0.396616	+	0.228987i	−0.685023	−	0.728522i	$-0.740208\pi$
$73$	−3.38869	+	1.95646i	−0.396616	+	0.228987i	0.288407	+	0.957508i	$0.406875\pi$
$74$	3.41664	−	1.97260i	0.397176	−	0.229310i
$75$	−0.953026	+	8.40875i	−0.110046	+	0.970959i
$76$		−	5.42129i		−	0.621864i
$77$	2.38376	−	1.14790i	0.271655	−	0.130815i
$78$	−9.89815	+	4.31079i	−1.12074	+	0.488101i
$79$	−2.94659	+	5.10365i	−0.331518	+	0.574205i	−0.982810	−	0.184622i	$-0.940894\pi$
$79$	−2.94659	+	5.10365i	−0.331518	+	0.574205i	0.651292	+	0.758827i	$0.274227\pi$
$80$	−0.178875	−	0.309821i	−0.0199988	−	0.0346390i
$81$	−7.44943	+	5.05035i	−0.827714	+	0.561150i
$82$	9.79259	+	5.65376i	1.08141	+	0.624353i
$83$	6.94128			0.761904			0.380952	−	0.924595i	$-0.375596\pi$
$83$	6.94128			0.761904			0.380952	+	0.924595i	$0.375596\pi$
$84$	0.842347	−	4.43546i	0.0919076	−	0.483948i
$85$	0.349343			0.0378915
$86$	5.89950	+	3.40608i	0.636159	+	0.367287i
$87$	10.7546	−	14.5520i	1.15302	−	1.56014i
$88$	1.50361	+	2.60432i	0.160285	+	0.277622i
$89$	−1.82637	+	3.16337i	−0.193595	+	0.335317i	−0.946439	−	0.322882i	$-0.895348\pi$
$89$	−1.82637	+	3.16337i	−0.193595	+	0.335317i	0.752844	+	0.658199i	$0.228681\pi$
$90$	−0.747486	−	0.695393i	−0.0787920	−	0.0733009i
$91$	1.22373	−	16.3248i	0.128282	−	1.71131i
$92$			0.888129i			0.0925938i
$93$	−5.61445	−	0.636327i	−0.582191	−	0.0659841i
$94$	6.30861	−	3.64228i	0.650684	−	0.375672i
$95$	1.60989	−	0.929470i	0.165171	−	0.0953616i
$96$	8.51501	+	0.965069i	0.869060	+	0.0984970i
$97$			9.23676i			0.937851i	0.883238	+	0.468925i	$0.155359\pi$
$97$			9.23676i			0.937851i	−0.883238	+	0.468925i	$0.844641\pi$
$98$	−5.51299	−	4.39685i	−0.556896	−	0.444149i
$99$	2.19648	+	2.04340i	0.220754	+	0.205370i
$100$	2.40677	−	4.16866i	0.240677	−	0.416866i
$101$	0.464343	+	0.804266i	0.0462039	+	0.0800275i	0.888202	−	0.459452i	$-0.151954\pi$
$101$	0.464343	+	0.804266i	0.0462039	+	0.0800275i	−0.841999	+	0.539480i	$0.818621\pi$
$102$	1.07240	−	1.45106i	0.106184	−	0.143677i
$103$	−2.16678	−	1.25099i	−0.213499	−	0.123264i	0.389438	−	0.921053i	$-0.372669\pi$
$103$	−2.16678	−	1.25099i	−0.213499	−	0.123264i	−0.602936	+	0.797789i	$0.706003\pi$
$104$	18.6072			1.82458
$105$	1.46156	−	0.510311i	0.142634	−	0.0498012i
$106$	8.78401			0.853179
$107$	7.12304	+	4.11249i	0.688611	+	0.397570i	0.803091	−	0.595856i	$-0.203187\pi$
$107$	7.12304	+	4.11249i	0.688611	+	0.397570i	−0.114481	+	0.993425i	$0.536520\pi$
$108$	5.03185	−	0.941822i	0.484190	−	0.0906269i
$109$	−2.32520	−	4.02736i	−0.222714	−	0.385751i	0.732917	−	0.680318i	$-0.238158\pi$
$109$	−2.32520	−	4.02736i	−0.222714	−	0.385751i	−0.955631	+	0.294566i	$0.904825\pi$
$110$	−0.170156	+	0.294718i	−0.0162237	+	0.0281003i
$111$	−6.21905	+	2.70849i	−0.590286	+	0.257078i
$112$	1.57838	−	2.31495i	0.149143	−	0.218742i
$113$		−	4.52821i		−	0.425978i	−0.977055	−	0.212989i	$-0.931680\pi$
$113$		−	4.52821i		−	0.425978i	0.977055	−	0.212989i	$-0.0683198\pi$
$114$	1.08127	−	9.54025i	0.101270	−	0.893526i
$115$	−0.263736	+	0.152268i	−0.0245935	+	0.0141991i
$116$	−8.91349	+	5.14620i	−0.827597	+	0.477813i
$117$	17.7450	−	5.44813i	1.64053	−	0.503679i
$118$		−	5.35654i		−	0.493109i
$119$	1.18705	+	2.46507i	0.108817	+	0.225973i
$120$	0.702586	+	1.61323i	0.0641370	+	0.147267i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	1.62690	+	2.81787i	0.147292	+	0.255118i
$123$	−15.6353	−	11.5552i	−1.40978	−	1.04190i
$124$	2.78338	+	1.60698i	0.249954	+	0.144311i
$125$	3.33965			0.298707
$126$	2.36699	−	7.63741i	0.210868	−	0.680394i
$127$	10.9941			0.975572			0.487786	−	0.872963i	$-0.337805\pi$
$127$	10.9941			0.975572			0.487786	+	0.872963i	$0.337805\pi$
$128$	−2.37357	−	1.37038i	−0.209796	−	0.121126i
$129$	−9.41938	−	6.96137i	−0.829330	−	0.612915i
$130$	1.05284	+	1.82357i	0.0923403	+	0.159938i
$131$	7.13990	−	12.3667i	0.623816	−	1.08048i	−0.364952	−	0.931026i	$-0.618915\pi$
$131$	7.13990	−	12.3667i	0.623816	−	1.08048i	0.988768	−	0.149455i	$-0.0477520\pi$
$132$	−0.681354	−	1.56448i	−0.0593042	−	0.136170i
$133$	12.0290	+	8.20158i	1.04304	+	0.711167i
$134$			10.6752i			0.922197i
$135$	1.14238	+	1.33277i	0.0983206	+	0.114706i
$136$	−2.69315	+	1.55489i	−0.230936	+	0.133331i
$137$	4.49906	−	2.59753i	0.384381	−	0.221922i	−0.295342	−	0.955392i	$-0.595434\pi$
$137$	4.49906	−	2.59753i	0.384381	−	0.221922i	0.679722	+	0.733469i	$0.262100\pi$
$138$	−0.177136	+	1.56291i	−0.0150788	+	0.133043i
$139$			0.823165i			0.0698199i	0.999390	+	0.0349100i	$0.0111144\pi$
$139$			0.823165i			0.0698199i	−0.999390	+	0.0349100i	$0.988886\pi$
$140$	−0.878094	−	0.0658230i	−0.0742125	−	0.00556306i
$141$	−11.4831	+	5.00106i	−0.967051	+	0.421165i
$142$	−4.56277	+	7.90295i	−0.382899	+	0.663201i
$143$	−3.09376	−	5.35854i	−0.258713	−	0.448104i
$144$	3.09640	+	0.711009i	0.258033	+	0.0592508i
$145$	−3.05640	−	1.76461i	−0.253820	−	0.146543i
$146$	3.94178			0.326224
$147$	8.56722	+	8.57920i	0.706612	+	0.707601i
$148$	3.85834			0.317153
$149$	0.992777	+	0.573180i	0.0813314	+	0.0469567i	0.540114	−	0.841592i	$-0.318381\pi$
$149$	0.992777	+	0.573180i	0.0813314	+	0.0469567i	−0.458783	+	0.888548i	$0.651714\pi$
$150$	5.06681	−	6.85587i	0.413704	−	0.559779i
$151$	−7.29020	−	12.6270i	−0.593268	−	1.02757i	−0.993789	−	0.111282i	$-0.964504\pi$
$151$	−7.29020	−	12.6270i	−0.593268	−	1.02757i	0.400521	−	0.916288i	$-0.368829\pi$
$152$	−8.27396	+	14.3309i	−0.671107	+	1.16239i
$153$	−2.11310	+	2.27139i	−0.170834	+	0.183631i
$154$	−2.65781	−	0.199232i	−0.214172	−	0.0160546i
$155$			1.10206i			0.0885193i
$156$	−10.4913	−	1.18905i	−0.839974	−	0.0952005i
$157$	10.2799	−	5.93507i	0.820421	−	0.473671i	−0.0301404	−	0.999546i	$-0.509595\pi$
$157$	10.2799	−	5.93507i	0.820421	−	0.473671i	0.850562	+	0.525875i	$0.176262\pi$
$158$	5.14129	−	2.96832i	0.409019	−	0.236147i
$159$	−15.0069	−	1.70084i	−1.19012	−	0.134886i
$160$		−	1.67141i		−	0.132136i
$161$	−1.97061	−	1.34360i	−0.155306	−	0.105891i
$162$	9.04277	−	0.653802i	0.710467	−	0.0513675i
$163$	7.27542	−	12.6014i	0.569855	−	0.987017i	−0.426725	−	0.904381i	$-0.640333\pi$
$163$	7.27542	−	12.6014i	0.569855	−	0.987017i	0.996580	−	0.0826359i	$-0.0263339\pi$
$164$	5.52928	+	9.57700i	0.431765	+	0.747838i
$165$	0.347766	−	0.470560i	0.0270735	−	0.0366330i
$166$	−6.05565	−	3.49623i	−0.470010	−	0.271360i
$167$	19.1863			1.48468			0.742342	−	0.670021i	$-0.233715\pi$
$167$	19.1863			1.48468			0.742342	+	0.670021i	$0.233715\pi$
$168$	−8.99610	+	10.4393i	−0.694064	+	0.805413i
$169$	−25.2853			−1.94503
$170$	−0.304771	−	0.175959i	−0.0233748	−	0.0134955i
$171$	−3.69455	+	16.0895i	−0.282529	+	1.23040i
$172$	3.33109	+	5.76962i	0.253993	+	0.439929i
$173$	−10.3037	+	17.8464i	−0.783372	+	1.35684i	0.146595	+	0.989197i	$0.453169\pi$
$173$	−10.3037	+	17.8464i	−0.783372	+	1.35684i	−0.929967	+	0.367644i	$0.880165\pi$
$174$	−16.7121	+	7.27838i	−1.26694	+	0.551773i
$175$	5.60849	+	11.6468i	0.423962	+	0.880414i
$176$		−	1.05899i		−	0.0798247i
$177$	−1.03718	+	9.15129i	−0.0779594	+	0.687853i
$178$	3.18670	−	1.83984i	0.238853	−	0.137902i
$179$	−0.717382	+	0.414181i	−0.0536197	+	0.0309573i	−0.526570	−	0.850132i	$-0.676522\pi$
$179$	−0.717382	+	0.414181i	−0.0536197	+	0.0309573i	0.472951	+	0.881089i	$0.343189\pi$
$180$	−0.293049	−	0.954485i	−0.0218425	−	0.0711431i
$181$			8.14952i			0.605749i	0.953030	+	0.302875i	$0.0979463\pi$
$181$			8.14952i			0.605749i	−0.953030	+	0.302875i	$0.902054\pi$
$182$	−9.29020	+	13.6256i	−0.688635	+	1.01000i
$183$	−2.23383	−	5.12916i	−0.165129	−	0.379158i
$184$	1.35546	−	2.34773i	0.0999259	−	0.173077i
$185$	0.661505	+	1.14576i	0.0486348	+	0.0842379i
$186$	4.57760	+	3.38307i	0.335646	+	0.248059i
$187$	0.895564	+	0.517054i	0.0654901	+	0.0378107i
$188$	7.12419			0.519585
$189$	−5.52267	+	12.5897i	−0.401715	+	0.915765i
$190$	−1.87265			−0.135856
$191$	−16.8944	−	9.75398i	−1.22244	−	0.705773i	−0.256999	−	0.966412i	$-0.582734\pi$
$191$	−16.8944	−	9.75398i	−1.22244	−	0.705773i	−0.965437	+	0.260638i	$0.916067\pi$
$192$	−9.89271	−	7.31119i	−0.713945	−	0.527639i
$193$	8.67207	+	15.0205i	0.624230	+	1.08120i	0.988689	+	0.149978i	$0.0479204\pi$
$193$	8.67207	+	15.0205i	0.624230	+	1.08120i	−0.364460	+	0.931219i	$0.618746\pi$
$194$	4.65244	−	8.05826i	0.334026	−	0.578549i
$195$	−1.44561	−	3.31932i	−0.103522	−	0.237701i
$196$	−2.51925	−	6.41976i	−0.179947	−	0.458555i
$197$			5.76409i			0.410675i	0.978691	+	0.205337i	$0.0658292\pi$
$197$			5.76409i			0.410675i	−0.978691	+	0.205337i	$0.934171\pi$
$198$	−0.886996	−	2.88903i	−0.0630361	−	0.205314i
$199$	−11.2355	+	6.48682i	−0.796464	+	0.459839i	−0.842233	−	0.539113i	$-0.818759\pi$
$199$	−11.2355	+	6.48682i	−0.796464	+	0.459839i	0.0457694	+	0.998952i	$0.485426\pi$
$200$	−12.7244	+	7.34643i	−0.899751	+	0.519471i
$201$	2.06703	−	18.2379i	0.145797	−	1.28640i
$202$		−	0.935535i		−	0.0658240i
$203$	2.06616	−	27.5630i	0.145016	−	1.93454i
$204$	1.61784	−	0.704593i	0.113271	−	0.0493314i
$205$	−1.89597	+	3.28392i	−0.132420	+	0.229359i
$206$	1.26021	+	2.18275i	0.0878033	+	0.152080i
$207$	0.605249	−	2.63582i	0.0420677	−	0.183202i
$208$	−5.67467	−	3.27627i	−0.393468	−	0.227169i
$209$	5.50275			0.380633
$210$	−1.53212	−	0.290968i	−0.105726	−	0.0200787i
$211$	−5.58202			−0.384282			−0.192141	−	0.981367i	$-0.561543\pi$
$211$	−5.58202			−0.384282			−0.192141	+	0.981367i	$0.561543\pi$
$212$	7.43970	+	4.29531i	0.510961	+	0.295003i
$213$	9.32543	−	12.6182i	0.638968	−	0.864583i
$214$	−4.14282	−	7.17557i	−0.283197	−	0.490512i
$215$	−1.14222	+	1.97838i	−0.0778987	+	0.134924i
$216$	−14.7389	−	5.18994i	−1.00285	−	0.353130i
$217$	−7.77645	+	3.74474i	−0.527900	+	0.254209i
$218$			4.68469i			0.317287i
$219$	−6.73427	−	0.763244i	−0.455060	−	0.0515753i
$220$	−0.288230	+	0.166410i	−0.0194325	+	0.0112193i
$221$	5.54131	−	3.19928i	0.372749	−	0.215207i
$222$	6.78980	+	0.769539i	0.455702	+	0.0516481i
$223$		−	2.32096i		−	0.155423i	−0.996976	−	0.0777116i	$-0.975239\pi$
$223$		−	2.32096i		−	0.155423i	0.996976	−	0.0777116i	$-0.0247613\pi$
$224$	11.7940	−	5.67936i	0.788017	−	0.379468i
$225$	−9.98381	+	10.7317i	−0.665587	+	0.715448i
$226$	−2.28080	+	3.95046i	−0.151717	+	0.262781i
$227$	0.207712	+	0.359767i	0.0137863	+	0.0238786i	0.872836	−	0.488013i	$-0.162278\pi$
$227$	0.207712	+	0.359767i	0.0137863	+	0.0238786i	−0.859050	+	0.511892i	$0.828945\pi$
$228$	5.58090	−	7.55147i	0.369604	−	0.500108i
$229$	5.54470	+	3.20124i	0.366404	+	0.211544i	0.671886	−	0.740654i	$-0.265484\pi$
$229$	5.54470	+	3.20124i	0.366404	+	0.211544i	−0.305482	+	0.952198i	$0.598818\pi$
$230$	0.306782			0.0202286
$231$	4.50211	+	0.855004i	0.296217	+	0.0562552i
$232$	31.4165			2.06260
$233$	0.676221	+	0.390416i	0.0443007	+	0.0255770i	0.521987	−	0.852954i	$-0.325191\pi$
$233$	0.676221	+	0.390416i	0.0443007	+	0.0255770i	−0.477686	+	0.878531i	$0.658524\pi$
$234$	−18.2251	−	4.18493i	−1.19141	−	0.273578i
$235$	1.22143	+	2.11558i	0.0796772	+	0.138005i
$236$	2.61930	−	4.53677i	0.170502	−	0.295318i
$237$	−9.35830	+	4.07568i	−0.607887	+	0.264744i
$238$	0.206028	−	2.74846i	0.0133548	−	0.178156i
$239$		−	27.1066i		−	1.75338i	−0.481056	−	0.876690i	$-0.659747\pi$
$239$		−	27.1066i		−	1.75338i	0.481056	−	0.876690i	$-0.340253\pi$
$240$	0.0697818	−	0.615699i	0.00450439	−	0.0397432i
$241$	−10.7835	+	6.22588i	−0.694629	+	0.401044i	−0.805344	−	0.592808i	$-0.798019\pi$
$241$	−10.7835	+	6.22588i	−0.694629	+	0.401044i	0.110715	+	0.993852i	$0.464686\pi$
$242$	−0.872412	+	0.503687i	−0.0560808	+	0.0323782i
$243$	−15.5756	−	0.633969i	−0.999173	−	0.0406691i
$244$			3.18216i			0.203717i
$245$	1.47447	−	1.84877i	0.0942006	−	0.118113i
$246$	7.82018	+	17.9562i	0.498596	+	1.14484i
$247$	17.0242	−	29.4867i	1.08322	−	1.87620i
$248$	−4.90515	−	8.49597i	−0.311477	−	0.539494i
$249$	9.66871	+	7.14563i	0.612729	+	0.452836i
$250$	−2.91355	−	1.68214i	−0.184269	−	0.106388i
$251$	6.22012			0.392610			0.196305	−	0.980543i	$-0.437106\pi$
$251$	6.22012			0.392610			0.196305	+	0.980543i	$0.437106\pi$
$252$	5.73937	−	5.31113i	0.361547	−	0.334570i
$253$	−0.901474			−0.0566752
$254$	−9.59142	−	5.53761i	−0.601819	−	0.347460i
$255$	0.486610	+	0.359628i	0.0304727	+	0.0225208i
$256$	8.48258	+	14.6923i	0.530161	+	0.918267i
$257$	0.261862	−	0.453557i	0.0163345	−	0.0282921i	−0.857743	−	0.514079i	$-0.828134\pi$
$257$	0.261862	−	0.453557i	0.0163345	−	0.0282921i	0.874077	+	0.485787i	$0.161467\pi$
$258$	4.71123	+	10.8176i	0.293308	+	0.673475i
$259$	−5.83707	+	8.56102i	−0.362698	+	0.531956i
$260$			2.05932i			0.127714i
$261$	29.9609	−	9.19867i	1.85453	−	0.569383i
$262$	−12.4579	+	7.19256i	−0.769650	+	0.444358i
$263$	−0.672889	+	0.388493i	−0.0414921	+	0.0239555i	−0.520603	−	0.853799i	$-0.674293\pi$
$263$	−0.672889	+	0.388493i	−0.0414921	+	0.0239555i	0.479110	+	0.877755i	$0.340959\pi$
$264$	−0.586579	+	5.17551i	−0.0361014	+	0.318530i
$265$			2.94569i			0.180953i
$266$	−6.36317	−	13.2140i	−0.390151	−	0.810202i
$267$	−5.80051	+	2.52621i	−0.354986	+	0.154601i
$268$	−5.22009	+	9.04146i	−0.318868	+	0.552295i
$269$	5.98065	+	10.3588i	0.364646	+	0.631586i	0.988719	−	0.149780i	$-0.0478565\pi$
$269$	5.98065	+	10.3588i	0.364646	+	0.631586i	−0.624073	+	0.781366i	$0.714523\pi$
$270$	−0.325329	−	1.73813i	−0.0197989	−	0.105779i
$271$	−9.58028	−	5.53117i	−0.581960	−	0.335995i	0.179952	−	0.983675i	$-0.442406\pi$
$271$	−9.58028	−	5.53117i	−0.581960	−	0.335995i	−0.761912	+	0.647681i	$0.775739\pi$
$272$	1.09511			0.0664011
$273$	18.5100	−	21.4796i	1.12028	−	1.30000i
$274$	−5.23338			−0.316160
$275$	4.23129	+	2.44294i	0.255157	+	0.147315i
$276$	−0.914276	+	1.23710i	−0.0550329	+	0.0744647i
$277$	5.92603	+	10.2642i	0.356061	+	0.616716i	0.987299	−	0.158874i	$-0.0507862\pi$
$277$	5.92603	+	10.2642i	0.356061	+	0.616716i	−0.631238	+	0.775589i	$0.717453\pi$
$278$	0.414618	−	0.718139i	0.0248671	−	0.0430711i
$279$	−7.16547	−	6.66610i	−0.428986	−	0.399089i
$280$	2.22074	+	1.51415i	0.132715	+	0.0904875i
$281$		−	11.8914i		−	0.709379i	−0.934984	−	0.354689i	$-0.884587\pi$
$281$		−	11.8914i		−	0.709379i	0.934984	−	0.354689i	$-0.115413\pi$
$282$	12.5370	+	1.42091i	0.746565	+	0.0846138i
$283$	−23.9902	+	13.8507i	−1.42607	+	0.823341i	−0.996808	−	0.0798405i	$-0.974559\pi$
$283$	−23.9902	+	13.8507i	−1.42607	+	0.823341i	−0.429260	+	0.903181i	$0.641226\pi$
$284$	−7.72896	+	4.46232i	−0.458629	+	0.264790i
$285$	3.19930	+	0.362600i	0.189510	+	0.0214786i
$286$			6.23314i			0.368574i
$287$	−29.6148	−	2.21996i	−1.74810	−	0.131040i
$288$	10.8673	+	10.1100i	0.640363	+	0.595736i
$289$	7.96531	−	13.7963i	0.468548	−	0.811548i
$290$	1.77763	+	3.07894i	0.104386	+	0.180802i
$291$	−9.50870	+	12.8662i	−0.557410	+	0.754227i
$292$	3.33853	+	1.92750i	0.195372	+	0.112798i
$293$	−10.5335			−0.615376			−0.307688	−	0.951487i	$-0.599555\pi$
$293$	−10.5335			−0.615376			−0.307688	+	0.951487i	$0.599555\pi$
$294$	−3.15291	−	11.7998i	−0.183881	−	0.688178i
$295$	1.79630			0.104585
$296$	−10.1993	−	5.88859i	−0.592824	−	0.342267i
$297$	0.955974	+	5.10746i	0.0554712	+	0.296365i
$298$	−0.577407	−	1.00010i	−0.0334483	−	0.0579341i
$299$	−2.78894	+	4.83059i	−0.161289	+	0.279360i
$300$	7.64385	−	3.32901i	0.441318	−	0.192201i
$301$	−17.8413	−	1.33740i	−1.02835	−	0.0770866i
$302$			14.6879i			0.845195i
$303$	−0.181147	+	1.59830i	−0.0104066	+	0.0918199i
$304$	5.04666	−	2.91369i	0.289446	−	0.167112i
$305$	−0.944965	+	0.545576i	−0.0541086	+	0.0312396i
$306$	2.98756	−	0.917250i	0.170788	−	0.0524357i
$307$			1.47636i			0.0842604i	0.999112	+	0.0421302i	$0.0134144\pi$
$307$			1.47636i			0.0842604i	−0.999112	+	0.0421302i	$0.986586\pi$
$308$	−2.15363	−	1.46839i	−0.122714	−	0.0836692i
$309$	−1.73035	−	3.97311i	−0.0984360	−	0.226022i
$310$	0.555092	−	0.961448i	0.0315271	−	0.0546066i
$311$	11.1828	+	19.3692i	0.634118	+	1.09832i	0.986701	+	0.162544i	$0.0519698\pi$
$311$	11.1828	+	19.3692i	0.634118	+	1.09832i	−0.352584	+	0.935780i	$0.614697\pi$
$312$	25.9185	+	19.1550i	1.46734	+	1.08444i
$313$	1.53205	+	0.884531i	0.0865967	+	0.0499967i	0.542673	−	0.839944i	$-0.317412\pi$
$313$	1.53205	+	0.884531i	0.0865967	+	0.0499967i	−0.456076	+	0.889941i	$0.650746\pi$
$314$	−11.9577			−0.674811
$315$	2.56118	+	0.793763i	0.144306	+	0.0447235i
$316$	5.80595			0.326610
$317$	9.92682	+	5.73125i	0.557546	+	0.321899i	0.752160	−	0.658981i	$-0.229012\pi$
$317$	9.92682	+	5.73125i	0.557546	+	0.321899i	−0.194614	+	0.980880i	$0.562345\pi$
$318$	12.2355	+	9.04262i	0.686133	+	0.507085i
$319$	−5.22353	−	9.04742i	−0.292462	−	0.506558i
$320$	−1.19962	+	2.07780i	−0.0670606	+	0.116152i
$321$	5.68833	+	13.0612i	0.317492	+	0.729003i
$322$	1.04243	+	2.16475i	0.0580924	+	0.120637i
$323$			5.69044i			0.316624i
$324$	7.97856	+	3.86810i	0.443253	+	0.214894i
$325$	26.1812	−	15.1157i	1.45227	−	0.838469i
$326$	−12.6943	+	7.32907i	−0.703074	+	0.405920i
$327$	0.907094	−	8.00349i	0.0501624	−	0.442594i
$328$		−	33.7551i		−	1.86382i
$329$	−10.7778	+	15.8074i	−0.594199	+	0.871490i
$330$	−0.540410	+	0.235357i	−0.0297486	+	0.0129560i
$331$	2.04107	−	3.53524i	0.112187	−	0.194314i	−0.804465	−	0.594001i	$-0.797548\pi$
$331$	2.04107	−	3.53524i	0.112187	−	0.194314i	0.916652	+	0.399686i	$0.130881\pi$
$332$	−3.41926	−	5.92233i	−0.187656	−	0.325030i
$333$	−11.4509	−	2.62941i	−0.627507	−	0.144091i
$334$	−16.7384	−	9.66391i	−0.915884	−	0.528786i
$335$	−3.57990			−0.195591
$336$	4.58168	−	1.59972i	0.249951	−	0.0872716i
$337$	−28.2782			−1.54041			−0.770207	−	0.637795i	$-0.779847\pi$
$337$	−28.2782			−1.54041			−0.770207	+	0.637795i	$0.779847\pi$
$338$	22.0592	+	12.7359i	1.19986	+	0.692742i
$339$	4.66152	−	6.30747i	0.253179	−	0.342575i
$340$	−0.172086	−	0.298061i	−0.00933265	−	0.0161646i
$341$	−1.63113	+	2.82520i	−0.0883306	+	0.152993i
$342$	11.3272	−	12.1758i	0.612508	−	0.658391i
$343$	18.0557	+	4.12231i	0.974914	+	0.222584i
$344$		−	20.3356i		−	1.09642i
$345$	−0.524116	−	0.0594020i	−0.0282175	−	0.00319810i
$346$	17.9781	−	10.3796i	0.966506	−	0.558013i
$347$	16.7024	−	9.64311i	0.896629	−	0.517669i	0.0205242	−	0.999789i	$-0.493466\pi$
$347$	16.7024	−	9.64311i	0.896629	−	0.517669i	0.876105	+	0.482120i	$0.160133\pi$
$348$	−17.7136	−	2.00761i	−0.949547	−	0.107619i
$349$		−	5.54773i		−	0.296963i	−0.988915	−	0.148482i	$-0.952561\pi$
$349$		−	5.54773i		−	0.296963i	0.988915	−	0.148482i	$-0.0474386\pi$
$350$	0.973425	−	12.9857i	0.0520317	−	0.694116i
$351$	30.3261	+	10.6786i	1.61869	+	0.569982i
$352$	2.47381	−	4.28476i	0.131854	−	0.228379i
$353$	7.60042	+	13.1643i	0.404529	+	0.700665i	0.994267	−	0.106930i	$-0.0341020\pi$
$353$	7.60042	+	13.1643i	0.404529	+	0.700665i	−0.589737	+	0.807595i	$0.700769\pi$
$354$	5.51424	−	7.46127i	0.293078	−	0.396562i
$355$	−2.65023	−	1.53011i	−0.140660	−	0.0812099i
$356$	3.59867			0.190729
$357$	−0.884167	+	4.65566i	−0.0467951	+	0.246404i
$358$	0.834471			0.0441031
$359$	21.0219	+	12.1370i	1.10949	+	0.640567i	0.938698	−	0.344740i	$-0.112033\pi$
$359$	21.0219	+	12.1370i	1.10949	+	0.640567i	0.170796	+	0.985306i	$0.445366\pi$
$360$	−0.682073	+	2.97039i	−0.0359484	+	0.156553i
$361$	5.64012	+	9.76897i	0.296848	+	0.514157i
$362$	4.10481	−	7.10974i	0.215744	−	0.373680i
$363$	1.58799	−	0.691592i	0.0833477	−	0.0362991i
$364$	−14.5312	+	6.99749i	−0.761643	+	0.366768i
$365$			1.32186i			0.0691896i
$366$	−0.634677	+	5.59989i	−0.0331751	+	0.292711i
$367$	28.6358	−	16.5329i	1.49478	−	0.863010i	0.494794	−	0.869010i	$-0.335243\pi$
$367$	28.6358	−	16.5329i	1.49478	−	0.863010i	0.999982	+	0.00600056i	$0.00191005\pi$
$368$	−0.826756	+	0.477328i	−0.0430976	+	0.0248824i
$369$	−9.88341	−	32.1911i	−0.514510	−	1.67580i
$370$		−	1.33277i		−	0.0692872i
$371$	−20.7857	+	10.0093i	−1.07914	+	0.519659i
$372$	2.22275	+	5.10373i	0.115244	+	0.264616i
$373$	−3.11212	+	5.39035i	−0.161140	+	0.279102i	−0.935278	−	0.353915i	$-0.884850\pi$
$373$	−3.11212	+	5.39035i	−0.161140	+	0.279102i	0.774138	+	0.633017i	$0.218184\pi$
$374$	−0.520867	−	0.902168i	−0.0269334	−	0.0466500i
$375$	4.65190	+	3.43797i	0.240223	+	0.177536i
$376$	−18.8325	−	10.8729i	−0.971210	−	0.560728i
$377$	−64.6413			−3.32920
$378$	11.1593	−	8.20169i	0.573973	−	0.421850i
$379$	4.68995			0.240907			0.120453	−	0.992719i	$-0.461565\pi$
$379$	4.68995			0.240907			0.120453	+	0.992719i	$0.461565\pi$
$380$	−1.58606	−	0.915711i	−0.0813630	−	0.0469750i
$381$	15.3141	+	11.3178i	0.784563	+	0.579829i
$382$	9.82591	+	17.0190i	0.502737	+	0.870767i
$383$	15.1879	−	26.3062i	0.776066	−	1.34419i	−0.158127	−	0.987419i	$-0.550545\pi$
$383$	15.1879	−	26.3062i	0.776066	−	1.34419i	0.934193	−	0.356768i	$-0.116121\pi$
$384$	−1.89549	−	4.35230i	−0.0967289	−	0.222102i
$385$	0.0668120	−	0.891288i	0.00340506	−	0.0454242i
$386$		−	17.4721i		−	0.889304i
$387$	−5.95421	−	19.3934i	−0.302670	−	0.985822i
$388$	7.88085	−	4.55001i	0.400090	−	0.230992i
$389$	−13.3267	+	7.69415i	−0.675688	+	0.390109i	−0.798228	−	0.602355i	$-0.794229\pi$
$389$	−13.3267	+	7.69415i	−0.675688	+	0.390109i	0.122540	+	0.992464i	$0.460896\pi$
$390$	−0.410729	+	3.62395i	−0.0207981	+	0.183506i
$391$		−	0.932221i		−	0.0471444i
$392$	−3.13830	+	20.8152i	−0.158508	+	1.05133i
$393$	22.6761	−	9.87580i	1.14386	−	0.498168i
$394$	2.90330	−	5.02867i	0.146266	−	0.253340i
$395$	0.995419	+	1.72412i	0.0500850	+	0.0867497i
$396$	0.661461	−	2.88062i	0.0332397	−	0.144757i
$397$	17.0604	+	9.84982i	0.856236	+	0.494348i	0.862750	−	0.505631i	$-0.168740\pi$
$397$	17.0604	+	9.84982i	0.856236	+	0.494348i	−0.00651405	+	0.999979i	$0.502074\pi$
$398$	13.0693			0.655106
$399$	8.31244	+	23.8073i	0.416143	+	1.19186i
$400$	5.17412			0.258706
$401$	−30.2790	−	17.4816i	−1.51206	−	0.872990i	−0.999901	−	0.0141006i	$-0.995511\pi$
$401$	−30.2790	−	17.4816i	−1.51206	−	0.872990i	−0.512162	−	0.858889i	$-0.671155\pi$
$402$	−10.9895	+	14.8698i	−0.548106	+	0.741638i
$403$	10.0926	+	17.4810i	0.502750	+	0.870788i
$404$	0.457469	−	0.792360i	0.0227600	−	0.0394214i
$405$	0.219251	+	3.03247i	0.0108946	+	0.150685i
$406$	−15.6857	+	23.0056i	−0.778467	+	1.14175i
$407$			3.91631i			0.194124i
$408$	−5.35203	−	0.606586i	−0.264965	−	0.0300305i
$409$	2.18524	−	1.26165i	0.108053	−	0.0623844i	−0.445000	−	0.895531i	$-0.646796\pi$
$409$	2.18524	−	1.26165i	0.108053	−	0.0623844i	0.553053	+	0.833146i	$0.313463\pi$
$410$	3.30814	−	1.90995i	0.163377	−	0.0943259i
$411$	8.94088	+	1.01334i	0.441021	+	0.0499842i
$412$			2.46494i			0.121439i
$413$	6.10374	+	12.6752i	0.300345	+	0.623708i
$414$	−1.85566	+	1.99467i	−0.0912006	+	0.0980325i
$415$	1.17245	−	2.03075i	0.0575534	−	0.0996854i
$416$	−15.3067	−	26.5120i	−0.750474	−	1.29986i
$417$	−0.847400	+	1.14661i	−0.0414973	+	0.0561498i
$418$	−4.80066	−	2.77166i	−0.234808	−	0.135567i
$419$	15.0762			0.736521			0.368260	−	0.929723i	$-0.379954\pi$
$419$	15.0762			0.736521			0.368260	+	0.929723i	$0.379954\pi$
$420$	−1.15536	−	0.995632i	−0.0563759	−	0.0485819i
$421$	16.4642			0.802416			0.401208	−	0.915987i	$-0.368590\pi$
$421$	16.4642			0.802416			0.401208	+	0.915987i	$0.368590\pi$
$422$	4.86982	+	2.81159i	0.237059	+	0.136866i
$423$	−21.1434	−	4.85505i	−1.02803	−	0.236061i
$424$	−13.1110	−	22.7089i	−0.636726	−	1.10284i
$425$	−2.52626	+	4.37561i	−0.122542	+	0.212248i
$426$	−14.4912	+	6.31114i	−0.702102	+	0.305776i
$427$	−7.06070	−	4.81413i	−0.341691	−	0.232972i
$428$		−	8.10323i		−	0.391684i
$429$	1.20692	−	10.6489i	0.0582707	−	0.514134i
$430$	1.99297	−	1.15064i	0.0961096	−	0.0554889i
$431$	15.1701	−	8.75845i	0.730717	−	0.421880i	−0.0879672	−	0.996123i	$-0.528037\pi$
$431$	15.1701	−	8.75845i	0.730717	−	0.421880i	0.818685	+	0.574243i	$0.194704\pi$
$432$	3.58112	+	4.17795i	0.172297	+	0.201012i
$433$			37.2422i			1.78974i	0.446322	+	0.894872i	$0.352733\pi$
$433$			37.2422i			1.78974i	−0.446322	+	0.894872i	$0.647267\pi$
$434$	8.67045	+	0.649947i	0.416195	+	0.0311985i
$435$	−2.44079	−	5.60437i	−0.117027	−	0.268709i
$436$	−2.29078	+	3.96774i	−0.109708	+	0.190020i
$437$	−2.48029	−	4.29599i	−0.118648	−	0.205505i
$438$	5.49062	+	4.05783i	0.262352	+	0.193891i
$439$	−23.4810	−	13.5567i	−1.12069	−	0.647028i	−0.179110	−	0.983829i	$-0.557322\pi$
$439$	−23.4810	−	13.5567i	−1.12069	−	0.647028i	−0.941576	+	0.336801i	$0.890655\pi$
$440$	1.01590			0.0484310
$441$	3.10175	+	20.7697i	0.147702	+	0.989032i
$442$	−6.44574			−0.306593
$443$	15.4316	+	8.90943i	0.733177	+	0.423300i	0.819583	−	0.572960i	$-0.194205\pi$
$443$	15.4316	+	8.90943i	0.733177	+	0.423300i	−0.0864065	+	0.996260i	$0.527538\pi$
$444$	5.37439	+	3.97193i	0.255057	+	0.188499i
$445$	0.616986	+	1.06865i	0.0292479	+	0.0506589i
$446$	−1.16904	+	2.02484i	−0.0553557	+	0.0958788i
$447$	0.792813	+	1.82040i	0.0374988	+	0.0861022i
$448$	−18.7378	−	1.40461i	−0.885278	−	0.0663615i
$449$		−	27.7358i		−	1.30893i	−0.756092	−	0.654466i	$-0.772894\pi$
$449$		−	27.7358i		−	1.30893i	0.756092	−	0.654466i	$-0.227106\pi$
$450$	14.1154	−	4.33376i	0.665408	−	0.204295i
$451$	−9.72090	+	5.61237i	−0.457740	+	0.264276i
$452$	−3.86349	+	2.23059i	−0.181723	+	0.104918i
$453$	2.84401	−	25.0933i	0.133623	−	1.17899i
$454$		−	0.418487i		−	0.0196406i
$455$	−4.56931	−	3.11544i	−0.214212	−	0.146054i
$456$	−26.2779	+	11.4444i	−1.23057	+	0.535933i
$457$	1.13233	−	1.96125i	0.0529682	−	0.0917436i	−0.838326	−	0.545170i	$-0.816465\pi$
$457$	1.13233	−	1.96125i	0.0529682	−	0.0917436i	0.891294	+	0.453426i	$0.149798\pi$
$458$	−3.22484	−	5.58559i	−0.150687	−	0.260998i
$459$	−5.28166	+	0.988580i	−0.246527	+	0.0461430i
$460$	0.259832	+	0.150014i	0.0121147	+	0.00699444i
$461$	20.6585			0.962161			0.481081	−	0.876676i	$-0.340244\pi$
$461$	20.6585			0.962161			0.481081	+	0.876676i	$0.340244\pi$
$462$	−3.49704	−	3.01357i	−0.162697	−	0.140204i
$463$	29.3828			1.36554			0.682768	−	0.730635i	$-0.260776\pi$
$463$	29.3828			1.36554			0.682768	+	0.730635i	$0.260776\pi$
$464$	−9.58117	−	5.53169i	−0.444795	−	0.256802i
$465$	−1.13450	+	1.53509i	−0.0526113	+	0.0711880i
$466$	−0.393295	−	0.681208i	−0.0182191	−	0.0315563i
$467$	−20.3668	+	35.2764i	−0.942464	+	1.63240i	−0.181714	+	0.983351i	$0.558164\pi$
$467$	−20.3668	+	35.2764i	−0.942464	+	1.63240i	−0.760750	+	0.649045i	$0.775169\pi$
$468$	−13.3895	−	12.4564i	−0.618932	−	0.575798i
$469$	−12.1643	−	25.2609i	−0.561696	−	1.16644i
$470$		−	2.46087i		−	0.113512i
$471$	20.4289	+	2.31536i	0.941315	+	0.106686i
$472$	−13.8480	+	7.99516i	−0.637407	+	0.368007i
$473$	−5.85631	+	3.38114i	−0.269273	+	0.155465i
$474$	10.2172	+	1.15799i	0.469290	+	0.0531881i
$475$			26.8858i			1.23360i
$476$	1.51847	−	2.22709i	0.0695990	−	0.102078i
$477$	−19.1526	−	17.8179i	−0.876939	−	0.815824i
$478$	−13.6532	+	23.6481i	−0.624485	+	1.08164i
$479$	8.33913	+	14.4438i	0.381025	+	0.659954i	0.991209	−	0.132306i	$-0.0422380\pi$
$479$	8.33913	+	14.4438i	0.381025	+	0.659954i	−0.610184	+	0.792259i	$0.708905\pi$
$480$	1.72061	−	2.32815i	0.0785349	−	0.106265i
$481$	20.9857	+	12.1161i	0.956867	+	0.552447i
$482$	12.5436			0.571345
$483$	−1.36176	−	3.90017i	−0.0619624	−	0.177464i
$484$	−0.985197			−0.0447817
$485$	2.70232	+	1.56018i	0.122706	+	0.0708442i
$486$	13.2690	+	8.39829i	0.601893	+	0.380954i
$487$	0.404579	+	0.700752i	0.0183332	+	0.0317541i	0.875046	−	0.484039i	$-0.160831\pi$
$487$	0.404579	+	0.700752i	0.0183332	+	0.0317541i	−0.856713	+	0.515793i	$0.827497\pi$
$488$	4.85661	−	8.41190i	0.219848	−	0.380789i
$489$	23.1065	−	10.0632i	1.04491	−	0.455075i
$490$	−2.21755	+	0.870213i	−0.100179	+	0.0393122i
$491$		−	2.13467i		−	0.0963365i	−0.998839	−	0.0481682i	$-0.984662\pi$
$491$		−	2.13467i		−	0.0963365i	0.998839	−	0.0481682i	$-0.0153384\pi$
$492$	−2.15706	+	19.0322i	−0.0972476	+	0.858036i
$493$	9.35601	−	5.40169i	0.421374	−	0.243280i
$494$	−29.7042	+	17.1497i	−1.33645	+	0.771602i
$495$	0.968827	−	0.297452i	0.0435455	−	0.0133695i
$496$			3.45471i			0.155121i
$497$	1.79158	−	23.9001i	0.0803633	−	1.07207i
$498$	−4.83593	−	11.1039i	−0.216703	−	0.497579i
$499$	−0.305648	+	0.529398i	−0.0136827	+	0.0236991i	−0.872786	−	0.488104i	$-0.837689\pi$
$499$	−0.305648	+	0.529398i	−0.0136827	+	0.0236991i	0.859103	+	0.511803i	$0.171022\pi$
$500$	−1.64511	−	2.84941i	−0.0735714	−	0.127429i
$501$	26.7252	+	19.7512i	1.19399	+	0.882419i
$502$	−5.42651	−	3.13299i	−0.242197	−	0.139832i
$503$	−29.3406			−1.30823			−0.654116	−	0.756394i	$-0.726959\pi$
$503$	−29.3406			−1.30823			−0.654116	+	0.756394i	$0.726959\pi$
$504$	−23.2776	+	5.28031i	−1.03687	+	0.235204i
$505$	0.313729			0.0139608
$506$	0.786456	+	0.454061i	0.0349622	+	0.0201855i
$507$	−35.2207	−	26.0298i	−1.56421	−	1.15602i
$508$	−5.41569	−	9.38025i	−0.240283	−	0.416182i
$509$	−2.26128	+	3.91665i	−0.100229	+	0.173602i	−0.911779	−	0.410681i	$-0.865291\pi$
$509$	−2.26128	+	3.91665i	−0.100229	+	0.173602i	0.811550	+	0.584283i	$0.198624\pi$
$510$	−0.243384	−	0.558842i	−0.0107772	−	0.0247460i
$511$	−9.32749	+	4.49163i	−0.412624	+	0.198698i
$512$		−	11.6087i		−	0.513039i
$513$	−21.7094	+	18.6082i	−0.958495	+	0.821574i
$514$	−0.456902	+	0.263793i	−0.0201531	+	0.0116354i
$515$	−0.731981	+	0.422609i	−0.0322549	+	0.0186224i
$516$	−1.29951	+	11.4658i	−0.0572076	+	0.504755i
$517$			7.23123i			0.318029i
$518$	9.40441	−	4.52868i	0.413206	−	0.198979i
$519$	−32.7241	+	14.2518i	−1.43643	+	0.625586i
$520$	3.14294	−	5.44373i	0.137827	−	0.238723i
$521$	−5.56886	−	9.64555i	−0.243976	−	0.422579i	0.717867	−	0.696180i	$-0.245119\pi$
$521$	−5.56886	−	9.64555i	−0.243976	−	0.422579i	−0.961843	+	0.273601i	$0.911785\pi$
$522$	−30.7715	−	7.06588i	−1.34683	−	0.309265i
$523$	5.05795	+	2.92021i	0.221169	+	0.127692i	0.606491	−	0.795090i	$-0.292577\pi$
$523$	5.05795	+	2.92021i	0.221169	+	0.127692i	−0.385323	+	0.922782i	$0.625910\pi$
$524$	−14.0684			−0.614582
$525$	−4.17745	+	21.9967i	−0.182319	+	0.960017i
$526$	0.782716			0.0341280
$527$	−2.92156	−	1.68676i	−0.127265	−	0.0734766i
$528$	1.09017	−	1.47510i	0.0474437	−	0.0641957i
$529$	−11.0937	−	19.2148i	−0.482334	−	0.835426i
$530$	1.48371	−	2.56986i	0.0644482	−	0.111628i
$531$	−10.8654	+	11.6794i	−0.471519	+	0.506842i
$532$	1.07219	−	14.3033i	0.0464853	−	0.620125i
$533$			69.4532i			3.00835i
$534$	6.33285	+	0.717749i	0.274049	+	0.0310600i
$535$	2.40631	−	1.38928i	0.104034	−	0.0600640i
$536$	27.5981	−	15.9338i	1.19206	−	0.688235i
$537$	−1.42564	−	0.161578i	−0.0615208	−	0.00697261i
$538$		−	12.0495i		−	0.519491i
$539$	6.51623	−	2.55711i	0.280674	−	0.110142i
$540$	0.574390	−	1.63121i	0.0247178	−	0.0701959i
$541$	15.8159	−	27.3939i	0.679978	−	1.17776i	−0.295009	−	0.955494i	$-0.595323\pi$
$541$	15.8159	−	27.3939i	0.679978	−	1.17776i	0.974987	−	0.222262i	$-0.0713439\pi$
$542$	5.57196	+	9.65093i	0.239336	+	0.414543i
$543$	−8.38945	+	11.3517i	−0.360026	+	0.487148i
$544$	4.43091	+	2.55819i	0.189974	+	0.109681i
$545$	−1.57100			−0.0672942
$546$	−26.9673	+	9.41577i	−1.15410	+	0.402958i
$547$	6.31442			0.269985			0.134993	−	0.990847i	$-0.456899\pi$
$547$	6.31442			0.269985			0.134993	+	0.990847i	$0.456899\pi$
$548$	−4.43246	−	2.55908i	−0.189345	−	0.109319i
$549$	2.16861	−	9.44415i	0.0925539	−	0.403066i
$550$	−2.46095	−	4.26250i	−0.104935	−	0.181754i
$551$	28.7438	−	49.7857i	1.22453	−	2.12094i
$552$	4.30491	−	1.87485i	0.183229	−	0.0797989i
$553$	−8.78351	+	12.8824i	−0.373513	+	0.547817i
$554$		−	11.9395i		−	0.507260i
$555$	−0.258063	+	2.27694i	−0.0109542	+	0.0966508i
$556$	0.702329	−	0.405490i	0.0297854	−	0.0171966i
$557$	−1.41798	+	0.818668i	−0.0600815	+	0.0346881i	−0.529740	−	0.848160i	$-0.677710\pi$
$557$	−1.41798	+	0.818668i	−0.0600815	+	0.0346881i	0.469658	+	0.882848i	$0.344377\pi$
$558$	2.89361	+	9.42475i	0.122496	+	0.398981i
$559$			41.8417i			1.76972i
$560$	−0.410660	−	0.852791i	−0.0173536	−	0.0360370i
$561$	0.715180	+	1.64215i	0.0301949	+	0.0693316i
$562$	−5.98952	+	10.3742i	−0.252653	+	0.437608i
$563$	−10.6341	−	18.4189i	−0.448175	−	0.776263i	0.550092	−	0.835104i	$-0.314593\pi$
$563$	−10.6341	−	18.4189i	−0.448175	−	0.776263i	−0.998267	+	0.0588414i	$0.981259\pi$
$564$	9.92349	+	7.33393i	0.417854	+	0.308814i
$565$	−1.32478	−	0.764860i	−0.0557338	−	0.0321779i
$566$	27.9057			1.17297
$567$	−20.6530	+	11.8513i	−0.867345	+	0.497707i
$568$	27.2415			1.14303
$569$	5.93181	+	3.42473i	0.248674	+	0.143572i	0.619157	−	0.785267i	$-0.287474\pi$
$569$	5.93181	+	3.42473i	0.248674	+	0.143572i	−0.370483	+	0.928839i	$0.620808\pi$
$570$	−2.60847	−	1.92778i	−0.109257	−	0.0807459i
$571$	−10.7464	−	18.6134i	−0.449725	−	0.778946i	0.548643	−	0.836057i	$-0.315145\pi$
$571$	−10.7464	−	18.6134i	−0.449725	−	0.778946i	−0.998368	+	0.0571108i	$0.981811\pi$
$572$	−3.04796	+	5.27922i	−0.127442	+	0.220735i
$573$	−13.4915	−	30.9784i	−0.563617	−	1.29414i
$574$	24.7181	+	16.8533i	1.03171	+	0.703443i
$575$		−	4.40449i		−	0.183680i
$576$	−6.25342	−	20.3679i	−0.260559	−	0.848664i
$577$	2.43897	−	1.40814i	0.101536	−	0.0586216i	−0.448372	−	0.893847i	$-0.647996\pi$
$577$	2.43897	−	1.40814i	0.101536	−	0.0586216i	0.549908	+	0.835225i	$0.314663\pi$
$578$	−13.8981	+	8.02405i	−0.578083	+	0.333757i
$579$	−3.38310	+	29.8498i	−0.140597	+	1.24052i
$580$			3.47699i			0.144374i
$581$	18.3135	+	1.37280i	0.759772	+	0.0569534i
$582$	14.7760	−	6.43517i	0.612486	−	0.266747i
$583$	−4.35985	+	7.55149i	−0.180567	+	0.312751i
$584$	−5.88349	−	10.1905i	−0.243461	−	0.421686i
$585$	1.40341	−	6.11175i	0.0580237	−	0.252690i
$586$	9.18959	+	5.30561i	0.379619	+	0.219173i
$587$	35.6049			1.46957			0.734785	−	0.678300i	$-0.237283\pi$
$587$	35.6049			1.46957			0.734785	+	0.678300i	$0.237283\pi$
$588$	3.09962	−	11.5357i	0.127826	−	0.475724i
$589$	−17.9514			−0.739674
$590$	−1.56711	−	0.904773i	−0.0645170	−	0.0372489i
$591$	−5.93379	+	8.02898i	−0.244084	+	0.330268i
$592$	2.07368	+	3.59171i	0.0852276	+	0.147618i
$593$	−11.0826	+	19.1956i	−0.455107	+	0.788269i	−0.998694	−	0.0510837i	$-0.983732\pi$
$593$	−11.0826	+	19.1956i	−0.455107	+	0.788269i	0.543587	+	0.839353i	$0.317066\pi$
$594$	1.73856	−	4.93732i	0.0713339	−	0.202581i
$595$	0.921688	+	0.0690908i	0.0377855	+	0.00283245i
$596$		−	1.12939i		−	0.0462616i
$597$	−22.3281	−	2.53060i	−0.913827	−	0.103571i
$598$	4.86621	−	2.80951i	0.198994	−	0.114889i
$599$	−24.1121	+	13.9211i	−0.985193	+	0.568802i	−0.903834	−	0.427883i	$-0.859259\pi$
$599$	−24.1121	+	13.9211i	−0.985193	+	0.568802i	−0.0813594	+	0.996685i	$0.525926\pi$
$600$	−25.2869	−	2.86595i	−1.03233	−	0.117002i
$601$		−	28.3202i		−	1.15521i	−0.816318	−	0.577603i	$-0.803988\pi$
$601$		−	28.3202i		−	1.15521i	0.816318	−	0.577603i	$-0.196012\pi$
$602$	14.8913	+	10.1532i	0.606924	+	0.413813i
$603$	21.6540	−	23.2762i	0.881820	−	0.947879i
$604$	−7.18228	+	12.4401i	−0.292243	+	0.506179i
$605$	−0.168910	−	0.292561i	−0.00686717	−	0.0118943i
$606$	0.963078	−	1.30313i	0.0391224	−	0.0529362i
$607$	22.3848	+	12.9239i	0.908573	+	0.524565i	0.879972	−	0.475026i	$-0.157561\pi$
$607$	22.3848	+	12.9239i	0.908573	+	0.524565i	0.0286011	+	0.999591i	$0.490895\pi$
$608$	27.2255			1.10414
$609$	31.2525	−	36.2663i	1.26641	−	1.46959i
$610$	1.09920			0.0445053
$611$	38.7489	+	22.3717i	1.56761	+	0.905061i
$612$	2.97887	+	0.684022i	0.120414	+	0.0276500i
$613$	−9.15558	−	15.8579i	−0.369790	−	0.640496i	0.619742	−	0.784805i	$-0.287237\pi$
$613$	−9.15558	−	15.8579i	−0.369790	−	0.640496i	−0.989533	+	0.144310i	$0.953904\pi$
$614$	0.743624	−	1.28799i	0.0300102	−	0.0519792i
$615$	−6.02155	+	2.62248i	−0.242813	+	0.105748i
$616$	3.45197	+	7.16848i	0.139084	+	0.288826i
$617$			41.3739i			1.66565i	0.553537	+	0.832825i	$0.313278\pi$
$617$			41.3739i			1.66565i	−0.553537	+	0.832825i	$0.686722\pi$
$618$	−0.491628	+	4.33774i	−0.0197762	+	0.174489i
$619$	−14.6907	+	8.48170i	−0.590470	+	0.340908i	−0.765284	−	0.643693i	$-0.777401\pi$
$619$	−14.6907	+	8.48170i	−0.590470	+	0.340908i	0.174813	+	0.984602i	$0.444068\pi$
$620$	0.940281	−	0.542871i	0.0377626	−	0.0218022i
$621$	3.55649	−	3.04845i	0.142717	−	0.122330i
$622$		−	22.5305i		−	0.903391i
$623$	−5.44424	+	7.98487i	−0.218119	+	0.319907i
$624$	−4.53168	−	10.4054i	−0.181413	−	0.416547i
$625$	−11.6506	+	20.1794i	−0.466024	+	0.807177i
$626$	−0.891054	−	1.54335i	−0.0356137	−	0.0616847i
$627$	7.66494	+	5.66475i	0.306108	+	0.226228i
$628$	−10.1277	−	5.84721i	−0.404138	−	0.233329i
$629$	−4.04989			−0.161480
$630$	−1.83460	−	1.98252i	−0.0730922	−	0.0789856i
$631$	0.630437			0.0250973			0.0125487	−	0.999921i	$-0.496006\pi$
$631$	0.630437			0.0250973			0.0125487	+	0.999921i	$0.496006\pi$
$632$	−15.3477	−	8.86103i	−0.610501	−	0.352473i
$633$	−7.77536	−	5.74636i	−0.309043	−	0.228397i
$634$	−5.77352	−	10.0000i	−0.229296	−	0.397152i
$635$	1.85702	−	3.21646i	0.0736936	−	0.127641i
$636$	5.94120	+	13.6418i	0.235584	+	0.540932i
$637$	6.45724	−	42.8286i	0.255845	−	1.69693i
$638$			10.5241i			0.416653i
$639$	25.9793	−	7.97624i	1.02773	−	0.315535i
$640$	−0.801841	+	0.462943i	−0.0316956	+	0.0182994i
$641$	11.7256	−	6.76979i	0.463134	−	0.267391i	−0.250227	−	0.968187i	$-0.580505\pi$
$641$	11.7256	−	6.76979i	0.463134	−	0.267391i	0.713361	+	0.700797i	$0.247172\pi$
$642$	1.61617	−	14.2599i	0.0637853	−	0.562792i
$643$			1.36678i			0.0539005i	0.999637	+	0.0269503i	$0.00857958\pi$
$643$			1.36678i			0.0539005i	−0.999637	+	0.0269503i	$0.991420\pi$
$644$	−0.175649	+	2.34319i	−0.00692152	+	0.0923347i
$645$	−3.62766	+	1.57990i	−0.142839	+	0.0622084i
$646$	2.86620	−	4.96440i	0.112769	−	0.195322i
$647$	7.64192	+	13.2362i	0.300435	+	0.520368i	0.976234	−	0.216717i	$-0.0695349\pi$
$647$	7.64192	+	13.2362i	0.300435	+	0.520368i	−0.675800	+	0.737085i	$0.736202\pi$
$648$	−15.1875	−	22.4020i	−0.596620	−	0.880034i
$649$	4.60494	+	2.65866i	0.180760	+	0.104362i
$650$	−30.4544			−1.19452
$651$	−14.6870	−	2.78924i	−0.575630	−	0.109319i
$652$	−14.3354			−0.561419
$653$	−7.60587	−	4.39125i	−0.297641	−	0.171843i	0.343742	−	0.939064i	$-0.388305\pi$
$653$	−7.60587	−	4.39125i	−0.297641	−	0.171843i	−0.641382	+	0.767221i	$0.721639\pi$
$654$	−4.82261	+	6.52545i	−0.188579	+	0.255165i
$655$	−2.41200	−	4.17771i	−0.0942448	−	0.163237i
$656$	−5.94347	+	10.2944i	−0.232053	+	0.401928i
$657$	−8.59464	−	7.99568i	−0.335309	−	0.311941i
$658$	17.3647	−	8.36193i	0.676945	−	0.325982i
$659$			16.6074i			0.646932i	0.946240	+	0.323466i	$0.104848\pi$
$659$			16.6074i			0.646932i	−0.946240	+	0.323466i	$0.895152\pi$
$660$	−0.572793	−	0.0649189i	−0.0222959	−	0.00252696i
$661$	30.8566	−	17.8151i	1.20018	−	0.692927i	0.239588	−	0.970875i	$-0.422988\pi$
$661$	30.8566	−	17.8151i	1.20018	−	0.692927i	0.960596	+	0.277948i	$0.0896542\pi$
$662$	−3.56131	+	2.05612i	−0.138414	+	0.0799135i
$663$	11.0121	+	1.24809i	0.427675	+	0.0484716i
$664$			20.8739i			0.810064i
$665$	4.43128	−	2.13387i	0.171837	−	0.0827480i
$666$	8.66552	+	8.06161i	0.335782	+	0.312381i
$667$	−4.70888	+	8.15601i	−0.182328	+	0.315802i
$668$	−9.45116	−	16.3699i	−0.365676	−	0.633370i
$669$	2.38930	−	3.23294i	0.0923755	−	0.124993i
$670$	3.12315	+	1.80315i	0.120658	+	0.0696617i
$671$	−3.22998			−0.124692
$672$	22.2747	+	4.23024i	0.859265	+	0.163185i
$673$	−3.23910			−0.124858			−0.0624290	−	0.998049i	$-0.519885\pi$
$673$	−3.23910			−0.124858			−0.0624290	+	0.998049i	$0.519885\pi$
$674$	24.6703	+	14.2434i	0.950263	+	0.548635i
$675$	−24.9544	+	4.67077i	−0.960496	+	0.179778i
$676$	12.4555	+	21.5736i	0.479058	+	0.829753i
$677$	9.42272	−	16.3206i	0.362145	−	0.627253i	−0.626169	−	0.779687i	$-0.715378\pi$
$677$	9.42272	−	16.3206i	0.362145	−	0.627253i	0.988314	+	0.152435i	$0.0487113\pi$
$678$	−7.24376	+	3.15476i	−0.278195	+	0.121158i
$679$	−1.82679	+	24.3698i	−0.0701057	+	0.935227i
$680$			1.05055i			0.0402866i
$681$	−0.0810314	+	0.714957i	−0.00310513	+	0.0273972i
$682$	2.84603	−	1.64316i	0.108980	−	0.0629198i
$683$	25.0963	−	14.4894i	0.960284	−	0.554420i	0.0640233	−	0.997948i	$-0.479607\pi$
$683$	25.0963	−	14.4894i	0.960284	−	0.554420i	0.896260	+	0.443528i	$0.146273\pi$
$684$	15.5476	−	4.77346i	0.594477	−	0.182518i
$685$		−	1.75500i		−	0.0670551i
$686$	−13.6756	−	12.6908i	−0.522137	−	0.484535i
$687$	4.42790	+	10.1670i	0.168935	+	0.387897i
$688$	−3.58061	+	6.20180i	−0.136510	+	0.236441i
$689$	26.9767	+	46.7249i	1.02773	+	1.78008i
$690$	0.427325	+	0.315814i	0.0162680	+	0.0120228i
$691$	17.6136	+	10.1692i	0.670052	+	0.386855i	0.796096	−	0.605170i	$-0.206895\pi$
$691$	17.6136	+	10.1692i	0.670052	+	0.386855i	−0.126044	+	0.992025i	$0.540228\pi$
$692$	20.3022			0.771775
$693$	5.39094	+	5.82561i	0.204785	+	0.221297i
$694$	−19.4284			−0.737494
$695$	0.240826	+	0.139041i	0.00913505	+	0.00527412i
$696$	43.7610	+	32.3414i	1.65876	+	1.22590i
$697$	−5.80379	−	10.0525i	−0.219834	−	0.380764i
$698$	−2.79432	+	4.83991i	−0.105767	+	0.183193i
$699$	0.540017	+	1.23995i	0.0204253	+	0.0468993i
$700$	7.17436	−	10.5224i	0.271165	−	0.397708i
$701$		−	16.8832i		−	0.637670i	−0.947810	−	0.318835i	$-0.896708\pi$
$701$		−	16.8832i		−	0.637670i	0.947810	−	0.318835i	$-0.103292\pi$
$702$	−21.0782	−	24.5910i	−0.795544	−	0.928128i
$703$	−18.6633	+	10.7752i	−0.703898	+	0.406396i
$704$	−6.15059	+	3.55105i	−0.231809	+	0.133835i
$705$	−0.476497	+	4.20424i	−0.0179459	+	0.158341i
$706$		−	15.3129i		−	0.576310i
$707$	1.06604	+	2.21377i	0.0400924	+	0.0832574i
$708$	8.31884	−	3.62298i	0.312641	−	0.136160i
$709$	20.7229	−	35.8931i	0.778264	−	1.34799i	−0.154677	−	0.987965i	$-0.549434\pi$
$709$	20.7229	−	35.8931i	0.778264	−	1.34799i	0.932941	−	0.360028i	$-0.117233\pi$
$710$	1.54140	+	2.66978i	0.0578476	+	0.100195i
$711$	−17.2311	−	3.95668i	−0.646217	−	0.148387i
$712$	−9.51292	−	5.49229i	−0.356512	−	0.205832i
$713$	2.94084			0.110135
$714$	3.11636	−	3.61631i	0.116627	−	0.135337i
$715$	−2.09027			−0.0781716
$716$	0.706763	+	0.408050i	0.0264130	+	0.0152495i
$717$	27.9046	−	37.7576i	1.04212	−	1.41008i
$718$	−12.2265	−	21.1769i	−0.456289	−	0.790316i
$719$	−11.4358	+	19.8073i	−0.426482	+	0.738689i	−0.996558	−	0.0829037i	$-0.973581\pi$
$719$	−11.4358	+	19.8073i	−0.426482	+	0.738689i	0.570075	+	0.821592i	$0.306914\pi$
$720$	0.731027	−	0.785789i	0.0272438	−	0.0292846i
$721$	−5.46930	−	3.72908i	−0.203687	−	0.138878i
$722$		−	11.3634i		−	0.422903i
$723$	−21.4299	−	2.42881i	−0.796986	−	0.0903283i
$724$	6.95321	−	4.01444i	0.258414	−	0.149196i
$725$	44.2046	−	25.5215i	1.64172	−	0.947846i
$726$	−1.73372	−	0.196496i	−0.0643445	−	0.00729264i
$727$		−	6.85223i		−	0.254135i	−0.991894	−	0.127067i	$-0.959444\pi$
$727$		−	6.85223i		−	0.254135i	0.991894	−	0.127067i	$-0.0405565\pi$
$728$	49.0922	+	3.68001i	1.81948	+	0.136390i
$729$	−21.0430	−	16.9172i	−0.779371	−	0.626563i
$730$	0.665807	−	1.15321i	0.0246426	−	0.0426822i
$731$	−3.49647	−	6.05606i	−0.129321	−	0.223991i
$732$	−3.27585	+	4.43253i	−0.121079	+	0.163831i
$733$	−8.40368	−	4.85187i	−0.310397	−	0.179208i	0.336707	−	0.941609i	$-0.390687\pi$
$733$	−8.40368	−	4.85187i	−0.310397	−	0.179208i	−0.647104	+	0.762402i	$0.724020\pi$
$734$	−33.3096			−1.22948
$735$	3.95703	−	1.05732i	0.145957	−	0.0389998i
$736$	−4.46015			−0.164403
$737$	−9.17731	−	5.29852i	−0.338051	−	0.195174i
$738$	−7.59186	+	33.0621i	−0.279460	+	1.21703i
$739$	−7.19141	−	12.4559i	−0.264540	−	0.458197i	0.702903	−	0.711286i	$-0.251887\pi$
$739$	−7.19141	−	12.4559i	−0.264540	−	0.458197i	−0.967443	+	0.253089i	$0.918554\pi$
$740$	0.651712	−	1.12880i	0.0239574	−	0.0414955i
$741$	54.0683	−	23.5475i	1.98625	−	0.865041i
$742$	23.1753	+	1.73725i	0.850792	+	0.0637764i
$743$		−	13.4799i		−	0.494531i	−0.968948	−	0.247265i	$-0.920468\pi$
$743$		−	13.4799i		−	0.494531i	0.968948	−	0.247265i	$-0.0795319\pi$
$744$	1.91357	−	16.8838i	0.0701549	−	0.618992i
$745$	0.335380	−	0.193632i	0.0122874	−	0.00709412i
$746$	5.43010	−	3.13507i	0.198810	−	0.114783i
$747$	6.11182	+	19.9067i	0.223620	+	0.728349i
$748$		−	1.01880i		−	0.0372510i
$749$	17.9797	+	12.2589i	0.656965	+	0.447932i
$750$	−2.32671	−	5.34243i	−0.0849593	−	0.195078i
$751$	−8.97435	+	15.5440i	−0.327479	+	0.567209i	−0.982011	−	0.188825i	$-0.939532\pi$
$751$	−8.97435	+	15.5440i	−0.327479	+	0.567209i	0.654532	+	0.756034i	$0.272866\pi$
$752$	3.82892	+	6.63188i	0.139626	+	0.241840i
$753$	8.66418	+	6.40324i	0.315740	+	0.233347i
$754$	56.3939	+	32.5590i	2.05374	+	1.18573i
$755$	−4.92555			−0.179259
$756$	13.4620	−	1.48969i	0.489610	−	0.0541794i
$757$	−6.03729			−0.219429			−0.109714	−	0.993963i	$-0.534994\pi$
$757$	−6.03729			−0.219429			−0.109714	+	0.993963i	$0.534994\pi$
$758$	−4.09157	−	2.36227i	−0.148612	−	0.0858015i
$759$	−1.25569	−	0.928014i	−0.0455786	−	0.0336848i
$760$	2.79511	+	4.84128i	0.101389	+	0.175612i
$761$	−18.9559	+	32.8326i	−0.687151	+	1.19018i	0.285605	+	0.958348i	$0.407806\pi$
$761$	−18.9559	+	32.8326i	−0.687151	+	1.19018i	−0.972756	+	0.231833i	$0.925528\pi$
$762$	−7.65952	−	17.5873i	−0.277475	−	0.637120i
$763$	−5.33818	−	11.0855i	−0.193255	−	0.401320i
$764$			19.2192i			0.695326i
$765$	0.307597	+	1.00187i	0.0111212	+	0.0362227i
$766$	−26.5002	+	15.2999i	−0.957493	+	0.552809i
$767$	28.4931	−	16.4505i	1.02883	−	0.593993i
$768$	−3.30918	+	29.1976i	−0.119410	+	1.05358i
$769$		−	9.07800i		−	0.327361i	−0.986513	−	0.163681i	$-0.947663\pi$
$769$		−	9.07800i		−	0.327361i	0.986513	−	0.163681i	$-0.0523366\pi$
$770$	−0.507218	+	0.743918i	−0.0182789	+	0.0268089i
$771$	0.831665	−	0.362202i	0.0299517	−	0.0130444i
$772$	8.54370	−	14.7981i	0.307494	−	0.532596i
$773$	−24.1552	−	41.8380i	−0.868802	−	1.50481i	−0.863222	−	0.504824i	$-0.831557\pi$
$773$	−24.1552	−	41.8380i	−0.868802	−	1.50481i	−0.00557968	−	0.999984i	$-0.501776\pi$
$774$	−4.57368	+	19.9181i	−0.164398	+	0.715941i
$775$	−13.8036	−	7.96950i	−0.495839	−	0.286273i
$776$	−27.7769			−0.997132
$777$	−16.9437	+	5.91597i	−0.607851	+	0.212234i
$778$	15.5018			0.555766
$779$	−53.4917	−	30.8834i	−1.91654	−	1.10651i
$780$	−2.11995	+	2.86849i	−0.0759065	+	0.102709i
$781$	−4.52937	−	7.84509i	−0.162073	−	0.280720i
$782$	−0.469548	+	0.813281i	−0.0167910	+	0.0290829i
$783$	51.2029	+	18.0299i	1.82984	+	0.644335i
$784$	4.62216	−	5.79549i	0.165077	−	0.206982i
$785$		−	4.00998i		−	0.143122i
$786$	−24.7572	−	2.80592i	−0.883062	−	0.100084i
$787$	−1.67827	+	0.968947i	−0.0598237	+	0.0345392i	−0.529614	−	0.848239i	$-0.677663\pi$
$787$	−1.67827	+	0.968947i	−0.0598237	+	0.0345392i	0.469790	+	0.882778i	$0.344330\pi$
$788$	4.91796	−	2.83938i	0.175195	−	0.101149i
$789$	−1.33722	−	0.151557i	−0.0476062	−	0.00539556i
$790$		−	2.00552i		−	0.0713532i
$791$	0.895560	−	11.9470i	0.0318425	−	0.424786i
$792$	−6.14494	+	6.60527i	−0.218351	+	0.234708i
$793$	−9.99277	+	17.3080i	−0.354854	+	0.614624i
$794$	−9.92245	−	17.1862i	−0.352135	−	0.609915i
$795$	−3.03242	+	4.10314i	−0.107549	+	0.145524i
$796$	11.0692	+	6.39079i	0.392337	+	0.226516i
$797$	21.5831			0.764512			0.382256	−	0.924057i	$-0.375147\pi$
$797$	21.5831			0.764512			0.382256	+	0.924057i	$0.375147\pi$
$798$	4.73957	−	24.9567i	0.167779	−	0.883456i
$799$	−7.47788			−0.264548
$800$	20.9348	+	12.0867i	0.740158	+	0.427330i
$801$	−10.6803	−	2.45245i	−0.377369	−	0.0866532i
$802$	17.6105	+	30.5023i	0.621849	+	1.07707i
$803$	−1.95646	+	3.38869i	−0.0690420	+	0.119584i
$804$	−16.5789	+	7.22034i	−0.584691	+	0.254642i
$805$	−0.725942	+	0.349576i	−0.0255861	+	0.0123209i
$806$		−	20.3341i		−	0.716239i
$807$	−2.33314	+	20.5858i	−0.0821304	+	0.724654i
$808$	−2.41860	+	1.39638i	−0.0850860	+	0.0491244i
$809$	8.50377	−	4.90965i	0.298977	−	0.172614i	−0.343006	−	0.939333i	$-0.611445\pi$
$809$	8.50377	−	4.90965i	0.298977	−	0.172614i	0.641983	+	0.766719i	$0.278112\pi$
$810$	1.33614	−	2.75599i	0.0469471	−	0.0968358i
$811$		−	32.6254i		−	1.14563i	−0.819684	−	0.572817i	$-0.805851\pi$
$811$		−	32.6254i		−	1.14563i	0.819684	−	0.572817i	$-0.194149\pi$
$812$	−24.5347	+	11.8146i	−0.860998	+	0.414612i
$813$	−7.65063	−	17.5669i	−0.268319	−	0.616097i
$814$	1.97260	−	3.41664i	0.0691394	−	0.119753i
$815$	−2.45778	−	4.25701i	−0.0860924	−	0.149116i
$816$	1.52542	+	1.12736i	0.0534003	+	0.0394654i
$817$	−32.2258	−	18.6056i	−1.12744	−	0.650927i
$818$	−2.54190			−0.0888755
$819$	47.8951	−	10.8646i	1.67359	−	0.379638i
$820$	3.73581			0.130460
$821$	0.270687	+	0.156281i	0.00944703	+	0.00545425i	0.504716	−	0.863285i	$-0.331597\pi$
$821$	0.270687	+	0.156281i	0.00944703	+	0.00545425i	−0.495269	+	0.868740i	$0.664931\pi$
$822$	−7.28972	−	5.38745i	−0.254258	−	0.187909i
$823$	14.3081	+	24.7823i	0.498749	+	0.863858i	0.999999	−	0.00144440i	$-0.000459768\pi$
$823$	14.3081	+	24.7823i	0.498749	+	0.863858i	−0.501250	+	0.865302i	$0.667126\pi$
$824$	3.76199	−	6.51595i	0.131055	−	0.226994i
$825$	3.37903	+	7.75871i	0.117643	+	0.270124i
$826$	1.05938	−	14.1324i	0.0368606	−	0.491729i
$827$			50.6285i			1.76052i	0.474487	+	0.880262i	$0.342634\pi$
$827$			50.6285i			1.76052i	−0.474487	+	0.880262i	$0.657366\pi$
$828$	−2.54704	+	0.782000i	−0.0885159	+	0.0271764i
$829$	8.10428	−	4.67901i	0.281473	−	0.162509i	−0.352617	−	0.935768i	$-0.614708\pi$
$829$	8.10428	−	4.67901i	0.281473	−	0.162509i	0.634090	+	0.773259i	$0.281375\pi$
$830$	−2.04572	+	1.18110i	−0.0710081	+	0.0409965i
$831$	−2.31183	+	20.3978i	−0.0801966	+	0.707592i
$832$			43.9443i			1.52349i
$833$	2.64433	+	6.73848i	0.0916204	+	0.233475i
$834$	1.31681	−	0.573492i	0.0455976	−	0.0198584i
$835$	3.24077	−	5.61317i	0.112151	−	0.194252i
$836$	−2.71064	−	4.69497i	−0.0937496	−	0.162379i
$837$	−3.11863	−	16.6618i	−0.107796	−	0.575917i
$838$	−13.1527	−	7.59369i	−0.454351	−	0.262320i
$839$	−14.1563			−0.488730			−0.244365	−	0.969683i	$-0.578579\pi$
$839$	−14.1563			−0.488730			−0.244365	+	0.969683i	$0.578579\pi$
$840$	1.53461	+	4.39522i	0.0529491	+	0.151649i
$841$	−80.1411			−2.76349
$842$	−14.3636	−	8.29281i	−0.495001	−	0.285789i
$843$	12.2414	−	16.5638i	0.421618	−	0.570488i
$844$	2.74969	+	4.76261i	0.0946483	+	0.163936i
$845$	−4.27095	+	7.39750i	−0.146925	+	0.254482i
$846$	16.0004	+	14.8853i	0.550104	+	0.511767i
$847$	1.49045	−	2.18599i	0.0512125	−	0.0751115i
$848$			9.23412i			0.317101i
$849$	−47.6751	−	5.40337i	−1.63621	−	0.185443i
$850$	4.40788	−	2.54489i	0.151189	−	0.0872891i
$851$	3.05746	−	1.76523i	0.104808	−	0.0605111i
$852$	−15.3596	−	1.74082i	−0.526211	−	0.0596393i
$853$			8.47986i			0.290345i	0.989406	+	0.145172i	$0.0463737\pi$
$853$			8.47986i			0.290345i	−0.989406	+	0.145172i	$0.953626\pi$
$854$	3.73503	+	7.75628i	0.127810	+	0.265415i
$855$	4.08312	+	3.79856i	0.139640	+	0.129908i
$856$	−12.3671	+	21.4205i	−0.422700	+	0.732138i
$857$	12.7652	+	22.1100i	0.436050	+	0.755262i	0.997381	−	0.0723303i	$-0.0230436\pi$
$857$	12.7652	+	22.1100i	0.436050	+	0.755262i	−0.561330	+	0.827592i	$0.689710\pi$
$858$	−6.41665	+	8.68233i	−0.219061	+	0.296410i
$859$	21.5846	+	12.4619i	0.736458	+	0.425195i	0.820780	−	0.571244i	$-0.193539\pi$
$859$	21.5846	+	12.4619i	0.736458	+	0.425195i	−0.0843218	+	0.996439i	$0.526872\pi$
$860$	2.25062			0.0767455
$861$	−38.9660	−	33.5789i	−1.32796	−	1.14437i
$862$	−17.6461			−0.601028
$863$	−18.7071	−	10.8006i	−0.636799	−	0.367656i	0.146582	−	0.989199i	$-0.453173\pi$
$863$	−18.7071	−	10.8006i	−0.636799	−	0.367656i	−0.783380	+	0.621543i	$0.786506\pi$
$864$	4.72979	+	25.2697i	0.160911	+	0.859694i
$865$	3.48078	+	6.02889i	0.118350	+	0.204988i
$866$	18.7584	−	32.4905i	0.637437	−	1.10407i
$867$	25.2976	−	11.0175i	0.859152	−	0.374173i
$868$	7.02570	+	4.79026i	0.238468	+	0.162592i
$869$			5.89319i			0.199913i
$870$	−0.693479	+	6.11871i	−0.0235111	+	0.207444i
$871$	−56.7848	+	32.7847i	−1.92408	+	1.11087i
$872$	12.1111	−	6.99237i	0.410135	−	0.236791i
$873$	−26.4899	+	8.13300i	−0.896547	+	0.275260i
$874$			4.99716i			0.169032i
$875$	8.81116	+	0.660495i	0.297872	+	0.0223288i
$876$	2.66608	+	6.12169i	0.0900786	+	0.206833i
$877$	−19.1285	+	33.1315i	−0.645924	+	1.11877i	0.338164	+	0.941087i	$0.390194\pi$
$877$	−19.1285	+	33.1315i	−0.645924	+	1.11877i	−0.984087	+	0.177685i	$0.943139\pi$
$878$	13.6567	+	23.6541i	0.460892	+	0.798288i
$879$	−14.6725	−	10.8437i	−0.494891	−	0.365748i
$880$	−0.309821	−	0.178875i	−0.0104440	−	0.00602987i
$881$	5.41544			0.182451			0.0912255	−	0.995830i	$-0.470922\pi$
$881$	5.41544			0.182451			0.0912255	+	0.995830i	$0.470922\pi$
$882$	7.75542	−	19.6820i	0.261138	−	0.662728i
$883$	39.9085			1.34303			0.671514	−	0.740992i	$-0.265645\pi$
$883$	39.9085			1.34303			0.671514	+	0.740992i	$0.265645\pi$
$884$	−5.45928	−	3.15192i	−0.183616	−	0.106010i
$885$	2.50212	+	1.84918i	0.0841078	+	0.0621597i
$886$	−8.97513	−	15.5454i	−0.301525	−	0.522257i
$887$	−9.36502	+	16.2207i	−0.314447	+	0.544638i	−0.979320	−	0.202319i	$-0.935152\pi$
$887$	−9.36502	+	16.2207i	−0.314447	+	0.544638i	0.664873	+	0.746956i	$0.268486\pi$
$888$	−8.14499	−	18.7020i	−0.273328	−	0.627598i
$889$	29.0064	+	2.17435i	0.972842	+	0.0729254i
$890$		−	1.24307i		−	0.0416679i
$891$	−3.92622	+	8.09844i	−0.131533	+	0.271308i
$892$	−1.98026	+	1.14330i	−0.0663040	+	0.0382806i
$893$	−34.4606	+	19.8958i	−1.15318	+	0.665788i
$894$	0.225255	−	1.98747i	0.00753365	−	0.0664710i
$895$			0.279837i			0.00935394i
$896$	−5.99129	−	4.08498i	−0.200155	−	0.136470i
$897$	−8.85760	+	3.85762i	−0.295747	+	0.128802i
$898$	−13.9702	+	24.1970i	−0.466190	+	0.807465i
$899$	17.0405	+	29.5150i	0.568333	+	0.984381i
$900$	14.0744	+	3.23182i	0.469145	+	0.107727i
$901$	−7.80905	−	4.50856i	−0.260157	−	0.150202i
$902$	11.3075			0.376499
$903$	−23.4748	−	20.2294i	−0.781194	−	0.673193i
$904$	13.6173			0.452904
$905$	2.38423	+	1.37654i	0.0792546	+	0.0457576i
$906$	−15.1203	+	20.4592i	−0.502340	+	0.679712i
$907$	−17.1561	−	29.7152i	−0.569658	−	0.986677i	−0.996600	−	0.0823976i	$-0.973742\pi$
$907$	−17.1561	−	29.7152i	−0.569658	−	0.986677i	0.426941	−	0.904279i	$-0.359591\pi$
$908$	0.204637	−	0.354441i	0.00679111	−	0.0117625i
$909$	−1.89768	+	2.03984i	−0.0629421	+	0.0676572i
$910$	2.41711	+	5.01945i	0.0801263	+	0.166393i
$911$			40.7756i			1.35095i	0.737381	+	0.675477i	$0.236062\pi$
$911$			40.7756i			1.35095i	−0.737381	+	0.675477i	$0.763938\pi$
$912$	10.0291	+	1.13667i	0.332097	+	0.0376390i
$913$	6.01132	−	3.47064i	0.198946	−	0.114861i
$914$	−1.97572	+	1.14068i	−0.0653509	+	0.0377304i
$915$	−1.87791	−	0.212837i	−0.0620817	−	0.00703618i
$916$		−	6.30769i		−	0.208412i
$917$	21.2834	−	31.2155i	0.702839	−	1.03083i
$918$	5.10572	+	1.79786i	0.168514	+	0.0593381i
$919$	−16.9993	+	29.4436i	−0.560754	+	0.971254i	0.436677	+	0.899618i	$0.356155\pi$
$919$	−16.9993	+	29.4436i	−0.560754	+	0.971254i	−0.997431	+	0.0716354i	$0.977178\pi$
$920$	−0.457902	−	0.793110i	−0.0150966	−	0.0261481i
$921$	−1.51983	+	2.05647i	−0.0500800	+	0.0677629i
$922$	−18.0227	−	10.4054i	−0.593546	−	0.342684i
$923$	−56.0510			−1.84494
$924$	−1.48824	−	4.26239i	−0.0489594	−	0.140222i
$925$	−19.1346			−0.629142
$926$	−25.6339	−	14.7998i	−0.842383	−	0.486350i
$927$	1.67983	−	7.31554i	0.0551728	−	0.240274i
$928$	−25.8440	−	44.7632i	−0.848372	−	1.46942i
$929$	26.6421	−	46.1454i	0.874098	−	1.51398i	0.0163773	−	0.999866i	$-0.494787\pi$
$929$	26.6421	−	46.1454i	0.874098	−	1.51398i	0.857721	−	0.514116i	$-0.171880\pi$
$930$	1.76296	−	0.767794i	0.0578096	−	0.0251770i
$931$	30.1145	+	24.0176i	0.986964	+	0.787146i
$932$		−	0.769273i		−	0.0251984i
$933$	−4.36257	+	38.4919i	−0.142824	+	1.26017i
$934$	35.5365	−	20.5170i	1.16279	−	0.671337i
$935$	0.302540	−	0.174671i	0.00989410	−	0.00571236i
$936$	16.3837	+	53.3630i	0.535517	+	1.74423i
$937$		−	45.4029i		−	1.48325i	−0.670816	−	0.741623i	$-0.734056\pi$
$937$		−	45.4029i		−	1.48325i	0.670816	−	0.741623i	$-0.265944\pi$
$938$	−2.11127	+	28.1649i	−0.0689356	+	0.919617i
$939$	1.22347	+	2.80925i	0.0399264	+	0.0916763i
$940$	1.20335	−	2.08426i	0.0392489	−	0.0679810i
$941$	−18.0339	−	31.2356i	−0.587888	−	1.01825i	−0.994509	−	0.104655i	$-0.966626\pi$
$941$	−18.0339	−	31.2356i	−0.587888	−	1.01825i	0.406620	−	0.913597i	$-0.366707\pi$
$942$	−16.6562	−	12.3097i	−0.542689	−	0.401073i
$943$	8.76314	+	5.05940i	0.285367	+	0.164757i
$944$	5.63102			0.183274
$945$	2.75042	+	3.74224i	0.0894710	+	0.121735i
$946$	6.81215			0.221482
$947$	−32.9502	−	19.0238i	−1.07074	−	0.618191i	−0.142355	−	0.989816i	$-0.545467\pi$
$947$	−32.9502	−	19.0238i	−1.07074	−	0.618191i	−0.928383	+	0.371625i	$0.878801\pi$
$948$	8.08727	+	5.97688i	0.262662	+	0.194120i
$949$	12.1056	+	20.9676i	0.392965	+	0.680636i
$950$	13.5420	−	23.4555i	0.439361	−	0.760995i
$951$	7.92738	+	18.2023i	0.257063	+	0.590250i
$952$	−7.41298	+	3.56971i	−0.240256	+	0.115695i
$953$		−	48.8499i		−	1.58241i	−0.611554	−	0.791203i	$-0.709455\pi$
$953$		−	48.8499i		−	1.58241i	0.611554	−	0.791203i	$-0.290545\pi$
$954$	7.73435	+	25.1915i	0.250409	+	0.815604i
$955$	−5.70727	+	3.29509i	−0.184683	+	0.106627i
$956$	−23.1275	+	13.3527i	−0.747996	+	0.431856i
$957$	2.03778	−	17.9797i	0.0658720	−	0.581202i
$958$		−	16.8013i		−	0.542824i
$959$	12.3838	−	5.96340i	0.399894	−	0.192568i
$960$	−3.80995	+	1.65929i	−0.122966	+	0.0535533i
$961$	−10.1788	+	17.6303i	−0.328350	+	0.568718i
$962$	−12.2055	−	21.1405i	−0.393520	−	0.681597i
$963$	−5.52225	+	24.0491i	−0.177952	+	0.774971i
$964$	10.6239	+	6.13371i	0.342173	+	0.197554i
$965$	5.85921			0.188615
$966$	−0.776448	+	4.08846i	−0.0249818	+	0.131544i
$967$	−39.0059			−1.25435			−0.627173	−	0.778880i	$-0.715788\pi$
$967$	−39.0059			−1.25435			−0.627173	+	0.778880i	$0.715788\pi$
$968$	2.60432	+	1.50361i	0.0837061	+	0.0483277i
$969$	−5.85797	+	7.92637i	−0.188185	+	0.254632i
$970$	−1.57169	−	2.72224i	−0.0504639	−	0.0874060i
$971$	6.71773	−	11.6354i	0.215582	−	0.373399i	−0.737870	−	0.674943i	$-0.764168\pi$
$971$	6.71773	−	11.6354i	0.215582	−	0.373399i	0.953453	+	0.301543i	$0.0975017\pi$
$972$	7.13159	+	13.6014i	0.228746	+	0.436266i
$973$	−0.162800	+	2.17180i	−0.00521914	+	0.0696246i
$974$		−	0.815126i		−	0.0261183i
$975$	52.0293	+	5.89686i	1.66627	+	0.188851i
$976$	−2.96227	+	1.71026i	−0.0948198	+	0.0547442i
$977$	6.62790	−	3.82662i	0.212045	−	0.122424i	−0.390216	−	0.920723i	$-0.627600\pi$
$977$	6.62790	−	3.82662i	0.212045	−	0.122424i	0.602262	+	0.798299i	$0.294266\pi$
$978$	−25.2271	−	2.85918i	−0.806675	−	0.0914264i
$979$			3.65275i			0.116742i
$980$	−2.30370	−	0.347328i	−0.0735890	−	0.0110950i
$981$	9.50263	−	10.2145i	0.303396	−	0.326124i
$982$	−1.07521	+	1.86231i	−0.0343113	+	0.0594289i
$983$	4.30533	+	7.45706i	0.137319	+	0.237843i	0.926481	−	0.376342i	$-0.122818\pi$
$983$	4.30533	+	7.45706i	0.137319	+	0.237843i	−0.789162	+	0.614185i	$0.789485\pi$
$984$	34.7489	−	47.0185i	1.10776	−	1.49890i
$985$	1.68635	+	0.973614i	0.0537316	+	0.0310219i
$986$	−10.8831			−0.346587
$987$	−31.2855	+	10.9235i	−0.995829	+	0.347698i
$988$	−33.5443			−1.06719
$989$	5.27931	+	3.04801i	0.167872	+	0.0969211i
$990$	−0.995039	−	0.228485i	−0.0316244	−	0.00726174i
$991$	9.55178	+	16.5442i	0.303422	+	0.525543i	0.976909	−	0.213657i	$-0.0685374\pi$
$991$	9.55178	+	16.5442i	0.303422	+	0.525543i	−0.673486	+	0.739200i	$0.735204\pi$
$992$	−8.07020	+	13.9780i	−0.256229	+	0.443802i
$993$	6.48239	−	2.82317i	0.205712	−	0.0895907i
$994$	−13.6012	+	19.9483i	−0.431403	+	0.632723i
$995$			4.38276i			0.138943i
$996$	1.33390	−	11.7693i	0.0422664	−	0.372925i
$997$	−14.5101	+	8.37740i	−0.459539	+	0.265315i	−0.711850	−	0.702331i	$-0.752143\pi$
$997$	−14.5101	+	8.37740i	−0.459539	+	0.265315i	0.252311	+	0.967646i	$0.418809\pi$
$998$	0.533302	−	0.307902i	0.0168814	−	0.00974648i
$999$	−13.2435	−	15.4506i	−0.419006	−	0.488836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.n.a.89.10	✓	52
3.2	odd	2	inner	231.2.n.a.89.17	yes	52
7.3	odd	6	inner	231.2.n.a.122.17	yes	52
21.17	even	6	inner	231.2.n.a.122.10	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.n.a.89.10	✓	52	1.1	even	1	trivial
231.2.n.a.89.17	yes	52	3.2	odd	2	inner
231.2.n.a.122.10	yes	52	21.17	even	6	inner
231.2.n.a.122.17	yes	52	7.3	odd	6	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.872412 - 0.503687i) q^{2} +(1.39293 + 1.02944i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(0.168910 - 0.292561i) q^{5} +(-0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} +3.00721i q^{8} +(0.880503 + 2.86788i) q^{9} +O(q^{10})\)	\(q+(-0.872412 - 0.503687i) q^{2} +(1.39293 + 1.02944i) q^{3} +(-0.492598 - 0.853205i) q^{4} +(0.168910 - 0.292561i) q^{5} +(-0.696692 - 1.59970i) q^{6} +(2.63835 + 0.197774i) q^{7} +3.00721i q^{8} +(0.880503 + 2.86788i) q^{9} +(-0.294718 + 0.170156i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.192170 - 1.69556i) q^{12} -6.18751i q^{13} +(-2.20211 - 1.50144i) q^{14} +(0.536454 - 0.233634i) q^{15} +(0.529497 - 0.917116i) q^{16} +(0.517054 + 0.895564i) q^{17} +(0.676351 - 2.94547i) q^{18} +(4.76552 + 2.75137i) q^{19} -0.332819 q^{20} +(3.47144 + 2.99151i) q^{21} -1.00737 q^{22} +(-0.780699 - 0.450737i) q^{23} +(-3.09575 + 4.18883i) q^{24} +(2.44294 + 4.23129i) q^{25} +(-3.11657 + 5.39806i) q^{26} +(-1.72583 + 4.90117i) q^{27} +(-1.13090 - 2.34848i) q^{28} -10.4471i q^{29} +(-0.585687 - 0.0663803i) q^{30} +(-2.82520 + 1.63113i) q^{31} +(4.28476 - 2.47381i) q^{32} +(1.72103 + 0.195057i) q^{33} -1.04173i q^{34} +(0.503505 - 0.738472i) q^{35} +(2.01315 - 2.16396i) q^{36} +(-1.95816 + 3.39162i) q^{37} +(-2.77166 - 4.80066i) q^{38} +(6.36968 - 8.61877i) q^{39} +(0.879793 + 0.507948i) q^{40} -11.2247 q^{41} +(-1.52174 - 4.35835i) q^{42} -6.76228 q^{43} +(-0.853205 - 0.492598i) q^{44} +(0.987755 + 0.226813i) q^{45} +(0.454061 + 0.786456i) q^{46} +(-3.61562 + 6.26243i) q^{47} +(1.68167 - 0.732392i) q^{48} +(6.92177 + 1.04359i) q^{49} -4.92191i q^{50} +(-0.201710 + 1.77973i) q^{51} +(-5.27922 + 3.04796i) q^{52} +(-7.55149 + 4.35985i) q^{53} +(3.97429 - 3.40656i) q^{54} -0.337820i q^{55} +(-0.594748 + 7.93407i) q^{56} +(3.80565 + 8.73829i) q^{57} +(-5.26205 + 9.11414i) q^{58} +(2.65866 + 4.60494i) q^{59} +(-0.463594 - 0.342618i) q^{60} +(-2.79724 - 1.61499i) q^{61} +3.28632 q^{62} +(1.75588 + 7.74060i) q^{63} -7.10209 q^{64} +(-1.81023 - 1.04513i) q^{65} +(-1.40320 - 1.03703i) q^{66} +(-5.29852 - 9.17731i) q^{67} +(0.509400 - 0.882306i) q^{68} +(-0.623452 - 1.43153i) q^{69} +(-0.811223 + 0.390643i) q^{70} -9.05873i q^{71} +(-8.62431 + 2.64786i) q^{72} +(-3.38869 + 1.95646i) q^{73} +(3.41664 - 1.97260i) q^{74} +(-0.953026 + 8.40875i) q^{75} -5.42129i q^{76} +(2.38376 - 1.14790i) q^{77} +(-9.89815 + 4.31079i) q^{78} +(-2.94659 + 5.10365i) q^{79} +(-0.178875 - 0.309821i) q^{80} +(-7.44943 + 5.05035i) q^{81} +(9.79259 + 5.65376i) q^{82} +6.94128 q^{83} +(0.842347 - 4.43546i) q^{84} +0.349343 q^{85} +(5.89950 + 3.40608i) q^{86} +(10.7546 - 14.5520i) q^{87} +(1.50361 + 2.60432i) q^{88} +(-1.82637 + 3.16337i) q^{89} +(-0.747486 - 0.695393i) q^{90} +(1.22373 - 16.3248i) q^{91} +0.888129i q^{92} +(-5.61445 - 0.636327i) q^{93} +(6.30861 - 3.64228i) q^{94} +(1.60989 - 0.929470i) q^{95} +(8.51501 + 0.965069i) q^{96} +9.23676i q^{97} +(-5.51299 - 4.39685i) q^{98} +(2.19648 + 2.04340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9	\( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) 52 * q + 24 * q^4 - 6 * q^7 - 4 * q^9 - 30 * q^12 - 4 * q^15 - 20 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^21 + 36 * q^24 - 22 * q^25 - 40 * q^28 - 20 * q^30 - 54 * q^31 + 36 * q^36 + 2 * q^37 + 20 * q^39 + 60 * q^40 - 36 * q^42 + 36 * q^43 - 54 * q^45 + 4 * q^46 + 22 * q^49 - 16 * q^51 + 12 * q^52 + 66 * q^54 - 44 * q^57 - 16 * q^58 + 20 * q^60 - 36 * q^61 - 24 * q^63 - 48 * q^64 - 30 * q^66 - 6 * q^67 - 116 * q^70 + 36 * q^72 - 6 * q^73 + 72 * q^75 + 112 * q^78 + 14 * q^79 + 52 * q^81 - 84 * q^82 + 8 * q^84 + 8 * q^85 + 18 * q^87 - 12 * q^88 + 46 * q^91 + 6 * q^93 + 48 * q^94 - 18 * q^96

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