LMFDB - Embedded newform 429.2.bb.b.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.b.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.975059 - 0.316816i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.767667 - 0.557743i) q^{4} +(3.70008 - 1.20223i) q^{5} +(-0.975059 + 0.316816i) q^{6} +(1.98998 - 2.73897i) q^{7} +(1.77706 + 2.44591i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.975059 - 0.316816i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.767667 - 0.557743i) q^{4} +(3.70008 - 1.20223i) q^{5} +(-0.975059 + 0.316816i) q^{6} +(1.98998 - 2.73897i) q^{7} +(1.77706 + 2.44591i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.98868 q^{10} +(-0.561230 - 3.26880i) q^{11} -0.948888 q^{12} +(-2.50546 + 2.59281i) q^{13} +(-2.80810 + 2.04020i) q^{14} +(2.28678 - 3.14748i) q^{15} +(-0.371387 - 1.14301i) q^{16} +(1.31180 + 4.03730i) q^{17} +(-0.602619 + 0.829434i) q^{18} +(4.63399 + 6.37814i) q^{19} +(-3.51097 - 1.14078i) q^{20} -3.38556i q^{21} +(-0.488374 + 3.36507i) q^{22} -4.16221 q^{23} +(2.87534 + 0.934254i) q^{24} +(8.20018 - 5.95778i) q^{25} +(3.26442 - 1.73437i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.05528 + 0.992722i) q^{28} +(-7.33545 - 5.32952i) q^{29} +(-3.22691 + 2.34449i) q^{30} +(-1.22565 - 0.398237i) q^{31} -4.81446i q^{32} +(-2.37539 - 2.31463i) q^{33} -4.35220i q^{34} +(4.07022 - 12.5268i) q^{35} +(-0.767667 + 0.557743i) q^{36} +(-1.98070 + 2.72619i) q^{37} +(-2.49772 - 7.68718i) q^{38} +(-0.502948 + 3.57030i) q^{39} +(9.51581 + 6.91364i) q^{40} +(2.33852 + 3.21870i) q^{41} +(-1.07260 + 3.30112i) q^{42} +4.99247 q^{43} +(-1.39231 + 2.82237i) q^{44} -3.89050i q^{45} +(4.05840 + 1.31865i) q^{46} +(-6.21760 - 8.55779i) q^{47} +(-0.972304 - 0.706420i) q^{48} +(-1.37883 - 4.24362i) q^{49} +(-9.88318 + 3.21124i) q^{50} +(3.43433 + 2.49519i) q^{51} +(3.36948 - 0.593009i) q^{52} +(-2.55452 + 7.86201i) q^{53} +1.02524i q^{54} +(-6.00644 - 11.4201i) q^{55} +10.2356 q^{56} +(7.49795 + 2.43623i) q^{57} +(5.46402 + 7.52058i) q^{58} +(1.99949 - 2.75207i) q^{59} +(-3.51097 + 1.14078i) q^{60} +(0.721013 + 2.21905i) q^{61} +(1.06891 + 0.776608i) q^{62} +(-1.98998 - 2.73897i) q^{63} +(-2.26807 + 6.98040i) q^{64} +(-6.15327 + 12.6058i) q^{65} +(1.58284 + 3.00946i) q^{66} +2.88602i q^{67} +(1.24475 - 3.83095i) q^{68} +(-3.36730 + 2.44649i) q^{69} +(-7.93741 + 10.9249i) q^{70} +(3.85724 - 1.25329i) q^{71} +(2.87534 - 0.934254i) q^{72} +(-2.43247 + 3.34800i) q^{73} +(2.79500 - 2.03068i) q^{74} +(3.13219 - 9.63989i) q^{75} -7.48086i q^{76} +(-10.0700 - 4.96765i) q^{77} +(1.62153 - 3.32191i) q^{78} +(-2.89995 + 8.92514i) q^{79} +(-2.74833 - 3.78275i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.26046 - 3.87930i) q^{82} +(5.79804 - 1.88390i) q^{83} +(-1.88827 + 2.59898i) q^{84} +(9.70753 + 13.3613i) q^{85} +(-4.86795 - 1.58169i) q^{86} -9.06712 q^{87} +(6.99784 - 7.18155i) q^{88} -10.3837i q^{89} +(-1.23257 + 3.79346i) q^{90} +(2.11581 + 12.0220i) q^{91} +(3.19519 + 2.32144i) q^{92} +(-1.22565 + 0.398237i) q^{93} +(3.35128 + 10.3142i) q^{94} +(24.8141 + 18.0285i) q^{95} +(-2.82987 - 3.89498i) q^{96} +(-5.32888 - 1.73146i) q^{97} +4.57461i q^{98} +(-3.28224 - 0.476352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * 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 $

$2$	−0.975059	−	0.316816i	−0.689471	−	0.224023i	−0.0567336	−	0.998389i	$-0.518069\pi$
$2$	−0.975059	−	0.316816i	−0.689471	−	0.224023i	−0.632737	+	0.774367i	$0.718069\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.767667	−	0.557743i	−0.383833	−	0.278871i
$5$	3.70008	−	1.20223i	1.65473	−	0.537654i	0.674971	−	0.737844i	$-0.264156\pi$
$5$	3.70008	−	1.20223i	1.65473	−	0.537654i	0.979757	+	0.200191i	$0.0641561\pi$
$6$	−0.975059	+	0.316816i	−0.398066	+	0.129339i
$7$	1.98998	−	2.73897i	0.752142	−	1.03523i	−0.245685	−	0.969350i	$-0.579013\pi$
$7$	1.98998	−	2.73897i	0.752142	−	1.03523i	0.997827	−	0.0658851i	$-0.0209871\pi$
$8$	1.77706	+	2.44591i	0.628285	+	0.864760i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.98868			−1.26133
$11$	−0.561230	−	3.26880i	−0.169217	−	0.985579i
$11$	−0.561230	−	3.26880i	−0.169217	−	0.985579i
$12$	−0.948888			−0.273920
$13$	−2.50546	+	2.59281i	−0.694891	+	0.719116i
$13$	−2.50546	+	2.59281i	−0.694891	+	0.719116i
$14$	−2.80810	+	2.04020i	−0.750496	+	0.545267i
$15$	2.28678	−	3.14748i	0.590443	−	0.812676i
$16$	−0.371387	−	1.14301i	−0.0928468	−	0.285753i
$17$	1.31180	+	4.03730i	0.318158	+	0.979189i	0.974435	+	0.224669i	$0.0721302\pi$
$17$	1.31180	+	4.03730i	0.318158	+	0.979189i	−0.656277	+	0.754520i	$0.727870\pi$
$18$	−0.602619	+	0.829434i	−0.142039	+	0.195500i
$19$	4.63399	+	6.37814i	1.06311	+	1.46324i	0.876862	+	0.480742i	$0.159633\pi$
$19$	4.63399	+	6.37814i	1.06311	+	1.46324i	0.186247	+	0.982503i	$0.440367\pi$
$20$	−3.51097	−	1.14078i	−0.785076	−	0.255087i
$21$		−	3.38556i		−	0.738789i
$22$	−0.488374	+	3.36507i	−0.104122	+	0.717436i
$23$	−4.16221			−0.867881			−0.433941	−	0.900941i	$-0.642877\pi$
$23$	−4.16221			−0.867881			−0.433941	+	0.900941i	$0.642877\pi$
$24$	2.87534	+	0.934254i	0.586926	+	0.190704i
$25$	8.20018	−	5.95778i	1.64004	−	1.19156i
$26$	3.26442	−	1.73437i	0.640205	−	0.340138i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−3.05528	+	0.992722i	−0.577395	+	0.187607i
$29$	−7.33545	−	5.32952i	−1.36216	−	0.989667i	−0.998304	−	0.0582113i	$-0.981460\pi$
$29$	−7.33545	−	5.32952i	−1.36216	−	0.989667i	−0.363855	−	0.931456i	$-0.618540\pi$
$30$	−3.22691	+	2.34449i	−0.589151	+	0.428043i
$31$	−1.22565	−	0.398237i	−0.220133	−	0.0715254i	0.196874	−	0.980429i	$-0.436921\pi$
$31$	−1.22565	−	0.398237i	−0.220133	−	0.0715254i	−0.417007	+	0.908903i	$0.636921\pi$
$32$		−	4.81446i		−	0.851084i
$33$	−2.37539	−	2.31463i	−0.413503	−	0.402925i
$34$		−	4.35220i		−	0.746397i
$35$	4.07022	−	12.5268i	0.687993	−	2.11742i
$36$	−0.767667	+	0.557743i	−0.127944	+	0.0929571i
$37$	−1.98070	+	2.72619i	−0.325624	+	0.448184i	−0.940174	−	0.340695i	$-0.889338\pi$
$37$	−1.98070	+	2.72619i	−0.325624	+	0.448184i	0.614550	+	0.788878i	$0.289338\pi$
$38$	−2.49772	−	7.68718i	−0.405183	−	1.24702i
$39$	−0.502948	+	3.57030i	−0.0805362	+	0.571706i
$40$	9.51581	+	6.91364i	1.50458	+	1.09314i
$41$	2.33852	+	3.21870i	0.365216	+	0.502676i	0.951593	−	0.307362i	$-0.0994463\pi$
$41$	2.33852	+	3.21870i	0.365216	+	0.502676i	−0.586377	+	0.810038i	$0.699446\pi$
$42$	−1.07260	+	3.30112i	−0.165505	+	0.509373i
$43$	4.99247			0.761344			0.380672	−	0.924710i	$-0.375693\pi$
$43$	4.99247			0.761344			0.380672	+	0.924710i	$0.375693\pi$
$44$	−1.39231	+	2.82237i	−0.209898	+	0.425488i
$45$		−	3.89050i		−	0.579961i
$46$	4.05840	+	1.31865i	0.598379	+	0.194425i
$47$	−6.21760	−	8.55779i	−0.906930	−	1.24828i	−0.968204	−	0.250161i	$-0.919516\pi$
$47$	−6.21760	−	8.55779i	−0.906930	−	1.24828i	0.0612741	−	0.998121i	$-0.480484\pi$
$48$	−0.972304	−	0.706420i	−0.140340	−	0.101963i
$49$	−1.37883	−	4.24362i	−0.196976	−	0.606231i
$50$	−9.88318	+	3.21124i	−1.39769	+	0.454138i
$51$	3.43433	+	2.49519i	0.480903	+	0.349396i
$52$	3.36948	−	0.593009i	0.467263	−	0.0822355i
$53$	−2.55452	+	7.86201i	−0.350890	+	1.07993i	0.607464	+	0.794347i	$0.292187\pi$
$53$	−2.55452	+	7.86201i	−0.350890	+	1.07993i	−0.958354	+	0.285582i	$0.907813\pi$
$54$			1.02524i			0.139517i
$55$	−6.00644	−	11.4201i	−0.809908	−	1.53988i
$56$	10.2356			1.36779
$57$	7.49795	+	2.43623i	0.993128	+	0.322687i
$58$	5.46402	+	7.52058i	0.717461	+	0.987501i
$59$	1.99949	−	2.75207i	0.260312	−	0.358289i	−0.658777	−	0.752338i	$-0.728926\pi$
$59$	1.99949	−	2.75207i	0.260312	−	0.358289i	0.919089	+	0.394049i	$0.128926\pi$
$60$	−3.51097	+	1.14078i	−0.453264	+	0.147274i
$61$	0.721013	+	2.21905i	0.0923162	+	0.284120i	0.986545	−	0.163490i	$-0.0522752\pi$
$61$	0.721013	+	2.21905i	0.0923162	+	0.284120i	−0.894229	+	0.447610i	$0.852275\pi$
$62$	1.06891	+	0.776608i	0.135752	+	0.0986293i
$63$	−1.98998	−	2.73897i	−0.250714	−	0.345078i
$64$	−2.26807	+	6.98040i	−0.283509	+	0.872550i
$65$	−6.15327	+	12.6058i	−0.763220	+	1.56355i
$66$	1.58284	+	3.00946i	0.194834	+	0.370439i
$67$			2.88602i			0.352584i	0.984338	+	0.176292i	$0.0564103\pi$
$67$			2.88602i			0.352584i	−0.984338	+	0.176292i	$0.943590\pi$
$68$	1.24475	−	3.83095i	0.150948	−	0.464571i
$69$	−3.36730	+	2.44649i	−0.405375	+	0.294522i
$70$	−7.93741	+	10.9249i	−0.948702	+	1.30578i
$71$	3.85724	−	1.25329i	0.457771	−	0.148739i	−0.0710491	−	0.997473i	$-0.522635\pi$
$71$	3.85724	−	1.25329i	0.457771	−	0.148739i	0.528820	+	0.848734i	$0.322635\pi$
$72$	2.87534	−	0.934254i	0.338862	−	0.110103i
$73$	−2.43247	+	3.34800i	−0.284699	+	0.391854i	−0.927283	−	0.374361i	$-0.877862\pi$
$73$	−2.43247	+	3.34800i	−0.284699	+	0.391854i	0.642584	+	0.766215i	$0.277862\pi$
$74$	2.79500	−	2.03068i	0.324912	−	0.236062i
$75$	3.13219	−	9.63989i	0.361674	−	1.11312i
$76$		−	7.48086i		−	0.858113i
$77$	−10.0700	−	4.96765i	−1.14758	−	0.566116i
$78$	1.62153	−	3.32191i	0.183602	−	0.376132i
$79$	−2.89995	+	8.92514i	−0.326270	+	1.00416i	0.644594	+	0.764525i	$0.277027\pi$
$79$	−2.89995	+	8.92514i	−0.326270	+	1.00416i	−0.970864	+	0.239631i	$0.922973\pi$
$80$	−2.74833	−	3.78275i	−0.307272	−	0.422924i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.26046	−	3.87930i	−0.139195	−	0.428397i
$83$	5.79804	−	1.88390i	0.636418	−	0.206785i	0.0270017	−	0.999635i	$-0.491404\pi$
$83$	5.79804	−	1.88390i	0.636418	−	0.206785i	0.609416	+	0.792851i	$0.291404\pi$
$84$	−1.88827	+	2.59898i	−0.206027	+	0.283572i
$85$	9.70753	+	13.3613i	1.05293	+	1.44923i
$86$	−4.86795	−	1.58169i	−0.524924	−	0.170558i
$87$	−9.06712			−0.972097
$88$	6.99784	−	7.18155i	0.745972	−	0.765556i
$89$		−	10.3837i		−	1.10067i	−0.834943	−	0.550336i	$-0.814500\pi$
$89$		−	10.3837i		−	1.10067i	0.834943	−	0.550336i	$-0.185500\pi$
$90$	−1.23257	+	3.79346i	−0.129924	+	0.399866i
$91$	2.11581	+	12.0220i	0.221797	+	1.26025i
$92$	3.19519	+	2.32144i	0.333122	+	0.242027i
$93$	−1.22565	+	0.398237i	−0.127094	+	0.0412952i
$94$	3.35128	+	10.3142i	0.345658	+	1.06383i
$95$	24.8141	+	18.0285i	2.54588	+	1.84969i
$96$	−2.82987	−	3.89498i	−0.288822	−	0.397529i
$97$	−5.32888	−	1.73146i	−0.541066	−	0.175803i	0.0257182	−	0.999669i	$-0.491813\pi$
$97$	−5.32888	−	1.73146i	−0.541066	−	0.175803i	−0.566784	+	0.823866i	$0.691813\pi$
$98$			4.57461i			0.462105i
$99$	−3.28224	−	0.476352i	−0.329877	−	0.0478752i
$100$	−9.61791			−0.961791
$101$	−3.23017	+	9.94145i	−0.321414	+	0.989212i	0.651619	+	0.758547i	$0.274090\pi$
$101$	−3.23017	+	9.94145i	−0.321414	+	0.989212i	−0.973033	+	0.230665i	$0.925910\pi$
$102$	−2.55816	−	3.52101i	−0.253296	−	0.348632i
$103$	12.9357	+	9.39832i	1.27459	+	0.926044i	0.999375	−	0.0353386i	$-0.0112510\pi$
$103$	12.9357	+	9.39832i	1.27459	+	0.926044i	0.275215	+	0.961383i	$0.411251\pi$
$104$	−10.7941	−	1.52057i	−1.05845	−	0.149104i
$105$	−4.07022	−	12.5268i	−0.397213	−	1.22250i
$106$	4.98161	−	6.85660i	0.483857	−	0.665972i
$107$	−6.64667	+	4.82909i	−0.642558	+	0.466845i	−0.860728	−	0.509065i	$-0.829991\pi$
$107$	−6.64667	+	4.82909i	−0.642558	+	0.466845i	0.218170	+	0.975911i	$0.429991\pi$
$108$	−0.293223	+	0.902446i	−0.0282154	+	0.0868380i
$109$			2.22902i			0.213502i	0.994286	+	0.106751i	$0.0340447\pi$
$109$			2.22902i			0.213502i	−0.994286	+	0.106751i	$0.965955\pi$
$110$	2.23857	+	13.0382i	0.213439	+	1.24314i
$111$			3.36976i			0.319844i
$112$	−3.86973	−	1.25735i	−0.365655	−	0.118809i
$113$	−0.168971	+	0.122764i	−0.0158954	+	0.0115487i	−0.595705	−	0.803204i	$-0.703127\pi$
$113$	−0.168971	+	0.122764i	−0.0158954	+	0.0115487i	0.579809	+	0.814752i	$0.303127\pi$
$114$	−6.53910	−	4.75094i	−0.612443	−	0.444966i
$115$	−15.4005	+	5.00394i	−1.43611	+	0.466620i
$116$	2.65868	+	8.18259i	0.246853	+	0.759734i
$117$	1.69168	+	3.18406i	0.156396	+	0.294366i
$118$	−2.82152	+	2.04996i	−0.259742	+	0.188714i
$119$	13.6685	+	4.44117i	1.25299	+	0.407121i
$120$	11.7622			1.07374
$121$	−10.3700	+	3.66909i	−0.942731	+	0.333554i
$122$		−	2.39213i		−	0.216573i
$123$	3.78381	+	1.22943i	0.341174	+	0.110854i
$124$	0.718774	+	0.989308i	0.0645478	+	0.0888425i
$125$	11.7448	−	16.1654i	1.05049	−	1.44588i
$126$	1.07260	+	3.30112i	0.0955546	+	0.294087i
$127$	−3.45568	−	10.6355i	−0.306642	−	0.943746i	−0.979059	−	0.203574i	$-0.934744\pi$
$127$	−3.45568	−	10.6355i	−0.306642	−	0.943746i	0.672418	−	0.740172i	$-0.265256\pi$
$128$	−1.23673	+	1.70221i	−0.109313	+	0.150456i
$129$	4.03899	−	2.93450i	0.355613	−	0.258368i
$130$	9.99350	−	10.3419i	0.876488	−	0.907044i
$131$	8.73798			0.763441			0.381720	−	0.924278i	$-0.375332\pi$
$131$	8.73798			0.763441			0.381720	+	0.924278i	$0.375332\pi$
$132$	0.532545	+	3.10172i	0.0463521	+	0.269970i
$133$	26.6911			2.31441
$134$	0.914338	−	2.81404i	0.0789867	−	0.243096i
$135$	−2.28678	−	3.14748i	−0.196814	−	0.270892i
$136$	−7.54373	+	10.3831i	−0.646869	+	0.890339i
$137$	−5.65511	+	1.83746i	−0.483148	+	0.156984i	−0.540456	−	0.841372i	$-0.681748\pi$
$137$	−5.65511	+	1.83746i	−0.483148	+	0.156984i	0.0573078	+	0.998357i	$0.481748\pi$
$138$	4.05840	−	1.31865i	0.345474	−	0.112251i
$139$	−5.31630	−	3.86252i	−0.450923	−	0.327615i	0.339037	−	0.940773i	$-0.389899\pi$
$139$	−5.31630	−	3.86252i	−0.450923	−	0.327615i	−0.789960	+	0.613158i	$0.789899\pi$
$140$	−10.1113	+	7.34631i	−0.854563	+	0.620877i
$141$	−10.0603	−	3.26879i	−0.847229	−	0.275281i
$142$	−4.15810			−0.348940
$143$	9.88150	+	6.73469i	0.826332	+	0.563183i
$144$	−1.20183			−0.100153
$145$	−33.5491	−	10.9008i	−2.78610	−	0.905259i
$146$	3.43250	−	2.49386i	0.284076	−	0.206393i
$147$	−3.60984	−	2.62270i	−0.297734	−	0.216317i
$148$	3.04103	−	0.988090i	0.249971	−	0.0812205i
$149$	−9.59083	+	3.11625i	−0.785711	+	0.255293i	−0.674277	−	0.738479i	$-0.735545\pi$
$149$	−9.59083	+	3.11625i	−0.785711	+	0.255293i	−0.111434	+	0.993772i	$0.535545\pi$
$150$	−6.10814	+	8.40713i	−0.498727	+	0.686439i
$151$	3.65761	+	5.03427i	0.297652	+	0.409683i	0.931481	−	0.363791i	$-0.118518\pi$
$151$	3.65761	+	5.03427i	0.297652	+	0.409683i	−0.633829	+	0.773473i	$0.718518\pi$
$152$	−7.36548	+	22.6686i	−0.597420	+	1.83867i
$153$	4.24507			0.343193
$154$	8.24499	+	8.03407i	0.664401	+	0.647404i
$155$	−5.01377			−0.402715
$156$	2.37741	−	2.46029i	0.190345	−	0.196980i
$157$	12.3191	−	8.95033i	0.983169	−	0.714314i	0.0247540	−	0.999694i	$-0.492120\pi$
$157$	12.3191	−	8.95033i	0.983169	−	0.714314i	0.958415	+	0.285380i	$0.0921197\pi$
$158$	5.65525	−	7.78379i	0.449908	−	0.619245i
$159$	2.55452	+	7.86201i	0.202587	+	0.623498i
$160$	−5.78808	−	17.8139i	−0.457588	−	1.40831i
$161$	−8.28272	+	11.4002i	−0.652770	+	0.898461i
$162$	0.602619	+	0.829434i	0.0473463	+	0.0651665i
$163$	10.0240	+	3.25698i	0.785137	+	0.255107i	0.674032	−	0.738702i	$-0.264561\pi$
$163$	10.0240	+	3.25698i	0.785137	+	0.255107i	0.111105	+	0.993809i	$0.464561\pi$
$164$		−	3.77518i		−	0.294792i
$165$	−11.5719	−	5.70855i	−0.900869	−	0.444410i
$166$	−6.25028			−0.485116
$167$	5.19330	+	1.68741i	0.401870	+	0.130575i	0.502976	−	0.864300i	$-0.332238\pi$
$167$	5.19330	+	1.68741i	0.401870	+	0.130575i	−0.101107	+	0.994876i	$0.532238\pi$
$168$	8.28077	−	6.01633i	0.638875	−	0.464170i
$169$	−0.445305	−	12.9924i	−0.0342543	−	0.999413i
$170$	−5.23235	−	16.1035i	−0.401303	−	1.23508i
$171$	7.49795	−	2.43623i	0.573382	−	0.186303i
$172$	−3.83255	−	2.78451i	−0.292229	−	0.212317i
$173$	−7.23199	+	5.25435i	−0.549838	+	0.399481i	−0.827726	−	0.561133i	$-0.810366\pi$
$173$	−7.23199	+	5.25435i	−0.549838	+	0.399481i	0.277888	+	0.960614i	$0.410366\pi$
$174$	8.84097	+	2.87261i	0.670232	+	0.217772i
$175$		−	34.3159i		−	2.59404i
$176$	−3.52784	+	1.85548i	−0.265921	+	0.139862i
$177$		−	3.40174i		−	0.255691i
$178$	−3.28972	+	10.1247i	−0.246575	+	0.758881i
$179$	9.60571	−	6.97896i	0.717965	−	0.521632i	−0.167769	−	0.985826i	$-0.553656\pi$
$179$	9.60571	−	6.97896i	0.717965	−	0.521632i	0.885733	+	0.464195i	$0.153656\pi$
$180$	−2.16990	+	2.98661i	−0.161735	+	0.222609i
$181$	1.24704	+	3.83800i	0.0926920	+	0.285277i	0.986645	−	0.162884i	$-0.0520795\pi$
$181$	1.24704	+	3.83800i	0.0926920	+	0.285277i	−0.893953	+	0.448160i	$0.852079\pi$
$182$	1.74573	−	12.3925i	0.129402	−	0.918594i
$183$	1.88764	+	1.37145i	0.139538	+	0.101380i
$184$	−7.39649	−	10.1804i	−0.545277	−	0.750509i
$185$	−4.05123	+	12.4684i	−0.297852	+	0.916695i
$186$	1.32124			0.0968784
$187$	12.4609	−	6.55385i	0.911230	−	0.479265i
$188$			10.0374i			0.732049i
$189$	−3.21986	−	1.04619i	−0.234210	−	0.0760995i
$190$	−18.4835	−	25.4404i	−1.34094	−	1.84564i
$191$	−4.91371	−	3.57002i	−0.355544	−	0.258318i	0.395647	−	0.918403i	$-0.370520\pi$
$191$	−4.91371	−	3.57002i	−0.355544	−	0.258318i	−0.751191	+	0.660085i	$0.770520\pi$
$192$	2.26807	+	6.98040i	0.163684	+	0.503767i
$193$	12.9611	−	4.21131i	0.932959	−	0.303137i	0.197187	−	0.980366i	$-0.436819\pi$
$193$	12.9611	−	4.21131i	0.932959	−	0.303137i	0.735772	+	0.677229i	$0.236819\pi$
$194$	4.64742	+	3.37655i	0.333665	+	0.242422i
$195$	2.43137	+	13.8151i	0.174114	+	0.989318i
$196$	−1.30836	+	4.02672i	−0.0934543	+	0.287623i
$197$			8.22224i			0.585810i	0.956141	+	0.292905i	$0.0946220\pi$
$197$			8.22224i			0.585810i	−0.956141	+	0.292905i	$0.905378\pi$
$198$	3.04946	+	1.50434i	0.216716	+	0.106908i
$199$	−8.43611			−0.598020			−0.299010	−	0.954250i	$-0.596656\pi$
$199$	−8.43611			−0.598020			−0.299010	+	0.954250i	$0.596656\pi$
$200$	29.1444	+	9.46958i	2.06082	+	0.669601i
$201$	1.69636	+	2.33484i	0.119652	+	0.164687i
$202$	6.29922	−	8.67013i	0.443211	−	0.610028i
$203$	−29.1948	+	9.48597i	−2.04907	+	0.665785i
$204$	−1.24475	−	3.83095i	−0.0871499	−	0.268220i
$205$	12.5223	+	9.09801i	0.874598	+	0.635433i
$206$	−9.63551	−	13.2621i	−0.671338	−	0.924017i
$207$	−1.28619	+	3.95850i	−0.0893967	+	0.275135i
$208$	3.89411	+	1.90084i	0.270008	+	0.131800i
$209$	18.2481	−	18.7272i	1.26225	−	1.29538i
$210$			13.5039i			0.931859i
$211$	−2.51264	+	7.73311i	−0.172977	+	0.532369i	−0.999535	−	0.0304821i	$-0.990296\pi$
$211$	−2.51264	+	7.73311i	−0.172977	+	0.532369i	0.826558	+	0.562852i	$0.190296\pi$
$212$	6.34600	−	4.61064i	0.435845	−	0.316660i
$213$	2.38391	−	3.28117i	0.163343	−	0.224822i
$214$	8.01082	−	2.60287i	0.547609	−	0.177929i
$215$	18.4725	−	6.00209i	1.25982	−	0.409339i
$216$	1.77706	−	2.44591i	0.120913	−	0.166423i
$217$	−3.52977	+	2.56453i	−0.239617	+	0.174092i
$218$	0.706190	−	2.17343i	0.0478292	−	0.147203i
$219$			4.13836i			0.279644i
$220$	−1.75852	+	12.1169i	−0.118560	+	0.816919i
$221$	−13.7546	−	6.71407i	−0.925235	−	0.451637i
$222$	1.06759	−	3.28571i	0.0716522	−	0.220523i
$223$	13.3843	+	18.4220i	0.896281	+	1.23363i	0.971639	+	0.236469i	$0.0759901\pi$
$223$	13.3843	+	18.4220i	0.896281	+	1.23363i	−0.0753577	+	0.997157i	$0.524010\pi$
$224$	−13.1867	−	9.58068i	−0.881071	−	0.640136i
$225$	−3.13219	−	9.63989i	−0.208813	−	0.642659i
$226$	0.203650	−	0.0661699i	0.0135466	−	0.00440155i
$227$	13.5339	−	18.6278i	0.898277	−	1.23637i	−0.0727370	−	0.997351i	$-0.523173\pi$
$227$	13.5339	−	18.6278i	0.898277	−	1.23637i	0.971014	−	0.239021i	$-0.0768266\pi$
$228$	−4.39714	−	6.05214i	−0.291207	−	0.400813i
$229$	−15.5109	−	5.03978i	−1.02499	−	0.333038i	−0.252180	−	0.967680i	$-0.581148\pi$
$229$	−15.5109	−	5.03978i	−1.02499	−	0.333038i	−0.772806	+	0.634642i	$0.781148\pi$
$230$	16.6018			1.09469
$231$	−11.0667	+	1.90008i	−0.728135	+	0.125016i
$232$		−	27.4127i		−	1.79973i
$233$	2.03639	−	6.26736i	0.133408	−	0.410588i	−0.861931	−	0.507026i	$-0.830745\pi$
$233$	2.03639	−	6.26736i	0.133408	−	0.410588i	0.995339	+	0.0964377i	$0.0307449\pi$
$234$	−0.640723	−	3.64059i	−0.0418854	−	0.237993i
$235$	−33.2941	−	24.1896i	−2.17187	−	1.57795i
$236$	−3.06989	+	0.997467i	−0.199833	+	0.0649296i
$237$	2.89995	+	8.92514i	0.188372	+	0.579750i
$238$	−11.9206	−	8.66080i	−0.772696	−	0.561396i
$239$	−0.806223	−	1.10967i	−0.0521502	−	0.0717786i	0.782145	−	0.623096i	$-0.214125\pi$
$239$	−0.806223	−	1.10967i	−0.0521502	−	0.0717786i	−0.834296	+	0.551317i	$0.814125\pi$
$240$	−4.44689	−	1.44488i	−0.287045	−	0.0932667i
$241$		−	9.73667i		−	0.627194i	−0.949556	−	0.313597i	$-0.898466\pi$
$241$		−	9.73667i		−	0.627194i	0.949556	−	0.313597i	$-0.101534\pi$
$242$	11.2738	−	0.292186i	0.724709	−	0.0187824i
$243$	−1.00000			−0.0641500
$244$	0.684160	−	2.10563i	0.0437989	−	0.134799i
$245$	−10.2036	−	14.0441i	−0.651884	−	0.897242i
$246$	−3.29993	−	2.39754i	−0.210396	−	0.152862i
$247$	−28.1476	−	3.96515i	−1.79099	−	0.252296i
$248$	−1.20399	−	3.70551i	−0.0764536	−	0.235300i
$249$	3.58339	−	4.93211i	0.227088	−	0.312560i
$250$	−16.5734	+	12.0413i	−1.04819	+	0.761556i
$251$	8.75043	−	26.9311i	0.552322	−	1.69987i	−0.150589	−	0.988596i	$-0.548117\pi$
$251$	8.75043	−	26.9311i	0.552322	−	1.69987i	0.702912	−	0.711277i	$-0.251883\pi$
$252$			3.21252i			0.202370i
$253$	2.33596	+	13.6054i	0.146860	+	0.855365i
$254$			11.4650i			0.719380i
$255$	15.7071	+	5.10355i	0.983617	+	0.319597i
$256$	13.6209	−	9.89619i	0.851309	−	0.618512i
$257$	15.2576	+	11.0853i	0.951746	+	0.691484i	0.951219	−	0.308516i	$-0.0998324\pi$
$257$	15.2576	+	11.0853i	0.951746	+	0.691484i	0.000526552		1.00000i	$0.499832\pi$
$258$	−4.86795	+	1.58169i	−0.303065	+	0.0984719i
$259$	3.52543	+	10.8501i	0.219059	+	0.674195i
$260$	11.7544	−	6.24507i	0.728979	−	0.387303i
$261$	−7.33545	+	5.32952i	−0.454053	+	0.329889i
$262$	−8.52004	−	2.76833i	−0.526370	−	0.171028i
$263$	−9.18106			−0.566128			−0.283064	−	0.959101i	$-0.591351\pi$
$263$	−9.18106			−0.566128			−0.283064	+	0.959101i	$0.591351\pi$
$264$	1.44016	−	9.92323i	0.0886357	−	0.610732i
$265$			32.1612i			1.97565i
$266$	−26.0254	−	8.45616i	−1.59572	−	0.518480i
$267$	−6.10339	−	8.40060i	−0.373522	−	0.514108i
$268$	1.60966	−	2.21550i	0.0983255	−	0.135333i
$269$	−8.60779	−	26.4921i	−0.524826	−	1.61525i	−0.764659	−	0.644435i	$-0.777093\pi$
$269$	−8.60779	−	26.4921i	−0.524826	−	1.61525i	0.239833	−	0.970814i	$-0.422907\pi$
$270$	1.23257	+	3.79346i	0.0750119	+	0.230863i
$271$	11.6456	−	16.0287i	0.707417	−	0.973676i	−0.292431	−	0.956286i	$-0.594464\pi$
$271$	11.6456	−	16.0287i	0.707417	−	0.973676i	0.999849	−	0.0173900i	$-0.00553567\pi$
$272$	4.12750	−	2.99880i	0.250266	−	0.181829i
$273$	8.77810	+	8.48239i	0.531275	+	0.513378i
$274$	6.09620			0.368285
$275$	−24.0769	−	23.4610i	−1.45189	−	1.41475i
$276$	3.94948			0.237730
$277$	−9.62941	+	29.6363i	−0.578575	+	1.78067i	0.0450942	+	0.998983i	$0.485641\pi$
$277$	−9.62941	+	29.6363i	−0.578575	+	1.78067i	−0.623669	+	0.781688i	$0.714359\pi$
$278$	3.96000	+	5.45047i	0.237505	+	0.326898i
$279$	−0.757491	+	1.04260i	−0.0453498	+	0.0624186i
$280$	37.8726	−	12.3055i	2.26332	−	0.735397i
$281$	10.1103	−	3.28504i	0.603132	−	0.195969i	0.00849496	−	0.999964i	$-0.497296\pi$
$281$	10.1103	−	3.28504i	0.603132	−	0.195969i	0.594637	+	0.803995i	$0.297296\pi$
$282$	8.77377	+	6.37452i	0.522470	+	0.379597i
$283$	−5.51499	+	4.00688i	−0.327832	+	0.238184i	−0.739510	−	0.673145i	$-0.764943\pi$
$283$	−5.51499	+	4.00688i	−0.327832	+	0.238184i	0.411678	+	0.911329i	$0.364943\pi$
$284$	−3.66009	−	1.18924i	−0.217187	−	0.0705682i
$285$	30.6720			1.81685
$286$	−7.50139	−	9.69733i	−0.443566	−	0.573415i
$287$	13.4695			0.795082
$288$	−4.57882	−	1.48775i	−0.269810	−	0.0876664i
$289$	−0.825686	+	0.599896i	−0.0485698	+	0.0352880i
$290$	29.2588	+	21.2578i	1.71814	+	1.24830i
$291$	−5.32888	+	1.73146i	−0.312385	+	0.101500i
$292$	3.73465	−	1.21346i	0.218554	−	0.0710124i
$293$	−8.64950	+	11.9050i	−0.505309	+	0.695499i	−0.983120	−	0.182964i	$-0.941431\pi$
$293$	−8.64950	+	11.9050i	−0.505309	+	0.695499i	0.477810	+	0.878463i	$0.341431\pi$
$294$	2.68889	+	3.70094i	0.156819	+	0.215843i
$295$	4.08968	−	12.5867i	0.238110	−	0.732828i
$296$	−10.1878			−0.592156
$297$	−2.93538	+	1.54387i	−0.170328	+	0.0895847i
$298$	10.3389			0.598916
$299$	10.4283	−	10.7918i	0.603083	−	0.624107i
$300$	−7.78106	+	5.65327i	−0.449239	+	0.326392i
$301$	9.93491	−	13.6742i	0.572639	−	0.788170i
$302$	−1.97145	−	6.06749i	−0.113444	−	0.349145i
$303$	3.23017	+	9.94145i	0.185569	+	0.571122i
$304$	5.56928	−	7.66546i	0.319420	−	0.439644i
$305$	5.33561	+	7.34384i	0.305516	+	0.420507i
$306$	−4.13919	−	1.34490i	−0.236622	−	0.0768831i
$307$		−	2.74791i		−	0.156832i	−0.996921	−	0.0784158i	$-0.975014\pi$
$307$		−	2.74791i		−	0.156832i	0.996921	−	0.0784158i	$-0.0249862\pi$
$308$	4.95972	+	9.42995i	0.282606	+	0.537321i
$309$	15.9894			0.909604
$310$	4.88872	+	1.58844i	0.277660	+	0.0902173i
$311$	−21.6054	+	15.6972i	−1.22513	+	0.890107i	−0.996515	−	0.0834107i	$-0.973419\pi$
$311$	−21.6054	+	15.6972i	−1.22513	+	0.890107i	−0.228612	+	0.973518i	$0.573419\pi$
$312$	−9.62640	+	5.11446i	−0.544988	+	0.289549i
$313$	6.98450	+	21.4961i	0.394787	+	1.21503i	0.929127	+	0.369761i	$0.120560\pi$
$313$	6.98450	+	21.4961i	0.394787	+	1.21503i	−0.534340	+	0.845270i	$0.679440\pi$
$314$	−14.8474	+	4.82422i	−0.837888	+	0.272246i
$315$	−10.6560	−	7.74202i	−0.600396	−	0.436213i
$316$	7.20413	−	5.23411i	0.405264	−	0.294442i
$317$	9.97401	+	3.24075i	0.560196	+	0.182019i	0.575410	−	0.817865i	$-0.304843\pi$
$317$	9.97401	+	3.24075i	0.560196	+	0.182019i	−0.0152132	+	0.999884i	$0.504843\pi$
$318$		−	8.47523i		−	0.475267i
$319$	−13.3042	+	26.9692i	−0.744894	+	1.50998i
$320$			28.5548i			1.59626i
$321$	−2.53880	+	7.81363i	−0.141702	+	0.436114i
$322$	11.6879	−	8.49176i	0.651341	−	0.473227i
$323$	−19.6716	+	27.0756i	−1.09456	+	1.50653i
$324$	0.293223	+	0.902446i	0.0162901	+	0.0501359i
$325$	−5.09787	+	36.1885i	−0.282779	+	2.00738i
$326$	−8.74209	−	6.35150i	−0.484179	−	0.351777i
$327$	1.31019	+	1.80332i	0.0724535	+	0.0997237i
$328$	−3.71696	+	11.4396i	−0.205235	+	0.631647i
$329$	−35.8125			−1.97441
$330$	9.47470	+	9.23232i	0.521565	+	0.508223i
$331$			22.2193i			1.22129i	0.791906	+	0.610643i	$0.209089\pi$
$331$			22.2193i			1.22129i	−0.791906	+	0.610643i	$0.790911\pi$
$332$	−5.50169	−	1.78761i	−0.301945	−	0.0981077i
$333$	1.98070	+	2.72619i	0.108541	+	0.149395i
$334$	−4.52918	−	3.29064i	−0.247826	−	0.180056i
$335$	3.46966	+	10.6785i	0.189568	+	0.583430i
$336$	−3.86973	+	1.25735i	−0.211111	+	0.0685942i
$337$	−3.13140	−	2.27510i	−0.170578	−	0.123932i	0.499221	−	0.866475i	$-0.333620\pi$
$337$	−3.13140	−	2.27510i	−0.170578	−	0.123932i	−0.669799	+	0.742543i	$0.733620\pi$
$338$	−3.68199	+	12.8094i	−0.200274	+	0.696740i
$339$	−0.0645410	+	0.198637i	−0.00350539	+	0.0107885i
$340$		−	15.6713i		−	0.849896i
$341$	−0.613884	+	4.22989i	−0.0332437	+	0.229061i
$342$	−8.08278			−0.437066
$343$	8.17199	+	2.65524i	0.441246	+	0.143370i
$344$	8.87190	+	12.2111i	0.478341	+	0.658380i
$345$	−9.51806	+	13.1005i	−0.512435	+	0.705306i
$346$	8.71628	−	2.83209i	0.468590	−	0.152254i
$347$	−0.382362	−	1.17679i	−0.0205263	−	0.0631734i	0.940269	−	0.340433i	$-0.110574\pi$
$347$	−0.382362	−	1.17679i	−0.0205263	−	0.0631734i	−0.960795	+	0.277260i	$0.910574\pi$
$348$	6.96053	+	5.05712i	0.373123	+	0.271090i
$349$	−16.8413	−	23.1800i	−0.901492	−	1.24080i	−0.969990	−	0.243146i	$-0.921821\pi$
$349$	−16.8413	−	23.1800i	−0.901492	−	1.24080i	0.0684980	−	0.997651i	$-0.478179\pi$
$350$	−10.8718	+	33.4601i	−0.581124	+	1.78852i
$351$	3.24014	+	1.58162i	0.172946	+	0.0844204i
$352$	−15.7375	+	2.70202i	−0.838810	+	0.144018i
$353$		−	5.71281i		−	0.304062i	−0.988376	−	0.152031i	$-0.951419\pi$
$353$		−	5.71281i		−	0.304062i	0.988376	−	0.152031i	$-0.0485814\pi$
$354$	−1.07773	+	3.31690i	−0.0572805	+	0.176291i
$355$	12.7654	−	9.27459i	0.677516	−	0.492244i
$356$	−5.79144	+	7.97123i	−0.306946	+	0.422474i
$357$	13.6685	−	4.44117i	0.723414	−	0.235052i
$358$	−11.5772	+	3.76165i	−0.611873	+	0.198810i
$359$	−1.07510	+	1.47975i	−0.0567416	+	0.0780982i	−0.836445	−	0.548051i	$-0.815370\pi$
$359$	−1.07510	+	1.47975i	−0.0567416	+	0.0780982i	0.779703	+	0.626149i	$0.215370\pi$
$360$	9.51581	−	6.91364i	0.501527	−	0.364381i
$361$	−13.3355	+	41.0423i	−0.701866	+	2.16012i
$362$		−	4.13736i		−	0.217455i
$363$	−6.23290	+	9.06371i	−0.327143	+	0.475722i
$364$	5.08097	−	10.4090i	0.266315	−	0.545580i
$365$	−4.97526	+	15.3123i	−0.260417	+	0.801481i
$366$	−1.40606	−	1.93527i	−0.0734959	−	0.101158i
$367$	1.44935	+	1.05301i	0.0756554	+	0.0549669i	0.624970	−	0.780649i	$-0.285111\pi$
$367$	1.44935	+	1.05301i	0.0756554	+	0.0549669i	−0.549315	+	0.835616i	$0.685111\pi$
$368$	1.54579	+	4.75746i	0.0805800	+	0.248000i
$369$	3.78381	−	1.22943i	0.196977	−	0.0640017i
$370$	7.90037	−	10.8739i	0.410721	−	0.565309i
$371$	16.4504	+	22.6420i	0.854061	+	1.17551i
$372$	1.16300	+	0.377882i	0.0602988	+	0.0195923i
$373$	−1.61341			−0.0835389			−0.0417695	−	0.999127i	$-0.513300\pi$
$373$	−1.61341			−0.0835389			−0.0417695	+	0.999127i	$0.513300\pi$
$374$	−14.2265	+	2.44259i	−0.735633	+	0.126303i
$375$		−	19.9815i		−	1.03184i
$376$	9.88255	−	30.4154i	0.509654	−	1.56855i
$377$	32.1971	−	5.66651i	1.65824	−	0.291840i
$378$	2.80810	+	2.04020i	0.144433	+	0.104937i
$379$	17.9892	−	5.84503i	0.924041	−	0.300239i	0.191918	−	0.981411i	$-0.438529\pi$
$379$	17.9892	−	5.84503i	0.924041	−	0.300239i	0.732124	+	0.681172i	$0.238529\pi$
$380$	−8.99371	−	27.6798i	−0.461368	−	1.41994i
$381$	−9.04708	−	6.57309i	−0.463496	−	0.336750i
$382$	3.66012	+	5.03772i	0.187268	+	0.257752i
$383$	11.9443	+	3.88095i	0.610327	+	0.198307i	0.597841	−	0.801615i	$-0.296026\pi$
$383$	11.9443	+	3.88095i	0.610327	+	0.198307i	0.0124859	+	0.999922i	$0.496026\pi$
$384$			2.10405i			0.107372i
$385$	−43.2320	−	6.27427i	−2.20331	−	0.319767i
$386$	−13.9720			−0.711157
$387$	1.54276	−	4.74812i	0.0784227	−	0.241360i
$388$	3.12510	+	4.30133i	0.158653	+	0.218367i
$389$	−6.25728	−	4.54618i	−0.317257	−	0.230501i	0.417747	−	0.908563i	$-0.362820\pi$
$389$	−6.25728	−	4.54618i	−0.317257	−	0.230501i	−0.735004	+	0.678063i	$0.762820\pi$
$390$	2.00610	−	14.2408i	0.101583	−	0.721111i
$391$	−5.45998	−	16.8041i	−0.276123	−	0.849820i
$392$	7.92923	−	10.9137i	0.400487	−	0.551223i
$393$	7.06917	−	5.13606i	0.356593	−	0.259080i
$394$	2.60494	−	8.01717i	0.131235	−	0.403899i
$395$			36.5102i			1.83703i
$396$	2.25398	+	2.19632i	0.113267	+	0.110369i
$397$			10.4805i			0.526004i	0.964795	+	0.263002i	$0.0847125\pi$
$397$			10.4805i			0.526004i	−0.964795	+	0.263002i	$0.915287\pi$
$398$	8.22570	+	2.67269i	0.412317	+	0.133970i
$399$	21.5935	−	15.6886i	1.08103	−	0.785414i
$400$	−9.85526	−	7.16026i	−0.492763	−	0.358013i
$401$	−7.61083	+	2.47291i	−0.380067	+	0.123491i	−0.492819	−	0.870132i	$-0.664033\pi$
$401$	−7.61083	+	2.47291i	−0.380067	+	0.123491i	0.112752	+	0.993623i	$0.464033\pi$
$402$	−0.914338	−	2.81404i	−0.0456030	−	0.140352i
$403$	4.10336	−	2.18010i	0.204403	−	0.108598i
$404$	8.02447	−	5.83012i	0.399232	−	0.290059i
$405$	−3.70008	−	1.20223i	−0.183859	−	0.0597393i
$406$	31.4720			1.56193
$407$	10.0230	+	4.94447i	0.496821	+	0.245088i
$408$			12.8342i			0.635386i
$409$	−34.0246	−	11.0553i	−1.68241	−	0.546647i	−0.697031	−	0.717041i	$-0.745496\pi$
$409$	−34.0246	−	11.0553i	−1.68241	−	0.546647i	−0.985376	+	0.170394i	$0.945496\pi$
$410$	−9.32762	−	12.8384i	−0.460658	−	0.634042i
$411$	−3.49505	+	4.81052i	−0.172398	+	0.237286i
$412$	−4.68845	−	14.4296i	−0.230983	−	0.710893i
$413$	−3.55888	−	10.9531i	−0.175121	−	0.538968i
$414$	2.50823	−	3.45228i	0.123273	−	0.169670i
$415$	19.1884	−	13.9412i	0.941919	−	0.684344i
$416$	12.4830	+	12.0624i	0.612027	+	0.591410i
$417$	−6.57131			−0.321799
$418$	−23.7260	+	12.4788i	−1.16048	+	0.610358i
$419$	21.6763			1.05896			0.529478	−	0.848324i	$-0.322388\pi$
$419$	21.6763			1.05896			0.529478	+	0.848324i	$0.322388\pi$
$420$	−3.86218	+	11.8866i	−0.188455	+	0.580006i
$421$	−9.31275	−	12.8179i	−0.453876	−	0.624706i	0.519349	−	0.854562i	$-0.326174\pi$
$421$	−9.31275	−	12.8179i	−0.453876	−	0.624706i	−0.973225	+	0.229856i	$0.926174\pi$
$422$	4.89994	−	6.74420i	0.238526	−	0.328302i
$423$	−10.0603	+	3.26879i	−0.489148	+	0.158934i
$424$	−23.7693	+	7.72311i	−1.15434	+	0.375067i
$425$	34.8103	+	25.2912i	1.68855	+	1.22680i
$426$	−3.36398	+	2.44407i	−0.162985	+	0.118416i
$427$	7.51272	+	2.44103i	0.363566	+	0.118130i
$428$	7.79581			0.376825
$429$	11.9528	−	0.359724i	0.577089	−	0.0173677i
$430$	−19.9134			−0.960308
$431$	−23.0767	−	7.49808i	−1.11157	−	0.361170i	−0.305023	−	0.952345i	$-0.598664\pi$
$431$	−23.0767	−	7.49808i	−1.11157	−	0.361170i	−0.806543	+	0.591175i	$0.798664\pi$
$432$	−0.972304	+	0.706420i	−0.0467800	+	0.0339877i
$433$	7.38895	+	5.36838i	0.355090	+	0.257988i	0.751001	−	0.660301i	$-0.229571\pi$
$433$	7.38895	+	5.36838i	0.355090	+	0.257988i	−0.395911	+	0.918289i	$0.629571\pi$
$434$	4.25422	−	1.38228i	0.204209	−	0.0663515i
$435$	−33.5491	+	10.9008i	−1.60856	+	0.522652i
$436$	1.24322	−	1.71115i	0.0595395	−	0.0819491i
$437$	−19.2876	−	26.5472i	−0.922653	−	1.26992i
$438$	1.31110	−	4.03514i	0.0626467	−	0.192807i
$439$	17.0843			0.815391			0.407695	−	0.913118i	$-0.366333\pi$
$439$	17.0843			0.815391			0.407695	+	0.913118i	$0.366333\pi$
$440$	17.2587	−	34.9854i	0.822777	−	1.66786i
$441$	−4.46200			−0.212476
$442$	11.2844	+	10.9043i	0.536745	+	0.518664i
$443$	2.49844	−	1.81523i	0.118705	−	0.0862440i	−0.526849	−	0.849959i	$-0.676627\pi$
$443$	2.49844	−	1.81523i	0.118705	−	0.0862440i	0.645554	+	0.763715i	$0.276627\pi$
$444$	1.87946	−	2.58685i	0.0891952	−	0.122767i
$445$	−12.4836	−	38.4206i	−0.591780	−	1.82131i
$446$	−7.21415	−	22.2029i	−0.341600	−	1.05134i
$447$	−5.92746	+	8.15845i	−0.280359	+	0.385881i
$448$	14.6057	+	20.1030i	0.690055	+	0.949780i
$449$	−29.4434	−	9.56675i	−1.38952	−	0.451483i	−0.483734	−	0.875215i	$-0.660720\pi$
$449$	−29.4434	−	9.56675i	−1.38952	−	0.451483i	−0.905788	+	0.423732i	$0.860720\pi$
$450$			10.3918i			0.489873i
$451$	9.20882	−	9.45058i	0.433626	−	0.445010i
$452$	0.198184			0.00932179
$453$	5.91814	+	1.92292i	0.278058	+	0.0903466i
$454$	−19.0979	+	13.8755i	−0.896311	+	0.651208i
$455$	22.2819	+	41.9389i	1.04459	+	1.96612i
$456$	7.36548	+	22.6686i	0.344920	+	1.06156i
$457$	−14.5797	+	4.73722i	−0.682008	+	0.221598i	−0.629474	−	0.777021i	$-0.716730\pi$
$457$	−14.5797	+	4.73722i	−0.682008	+	0.221598i	−0.0525337	+	0.998619i	$0.516730\pi$
$458$	13.5273	+	9.82817i	0.632090	+	0.459240i
$459$	3.43433	−	2.49519i	0.160301	−	0.116465i
$460$	14.6134	+	4.74818i	0.681353	+	0.221385i
$461$		−	35.6981i		−	1.66262i	−0.555805	−	0.831312i	$-0.687590\pi$
$461$		−	35.6981i		−	1.66262i	0.555805	−	0.831312i	$-0.312410\pi$
$462$	11.3927	+	1.65342i	0.530034	+	0.0769239i
$463$		−	21.0114i		−	0.976481i	−0.872709	−	0.488240i	$-0.837639\pi$
$463$		−	21.0114i		−	0.976481i	0.872709	−	0.488240i	$-0.162361\pi$
$464$	−3.36741	+	10.3638i	−0.156328	+	0.481129i
$465$	−4.05622	+	2.94702i	−0.188103	+	0.136665i
$466$	−3.97119	+	5.46588i	−0.183962	+	0.253202i
$467$	−7.62585	−	23.4700i	−0.352882	−	1.08606i	−0.957227	−	0.289337i	$-0.906565\pi$
$467$	−7.62585	−	23.4700i	−0.352882	−	1.08606i	0.604345	−	0.796723i	$-0.293435\pi$
$468$	0.477242	−	3.38782i	0.0220605	−	0.156602i
$469$	7.90474	+	5.74313i	0.365007	+	0.265193i
$470$	24.8000	+	34.1343i	1.14394	+	1.57450i
$471$	4.70546	−	14.4819i	0.216816	−	0.667292i
$472$	10.2845			0.473383
$473$	−2.80192	−	16.3194i	−0.128832	−	0.750365i
$474$		−	9.62129i		−	0.441920i
$475$	75.9991	+	24.6936i	3.48708	+	1.13302i
$476$	−8.01583	−	11.0328i	−0.367405	−	0.505690i
$477$	6.68782	+	4.85899i	0.306214	+	0.222478i
$478$	0.434553	+	1.33742i	0.0198760	+	0.0611721i
$479$	−18.5570	+	6.02955i	−0.847893	+	0.275497i	−0.700563	−	0.713590i	$-0.747068\pi$
$479$	−18.5570	+	6.02955i	−0.847893	+	0.275497i	−0.147330	+	0.989087i	$0.547068\pi$
$480$	−15.1534	−	11.0096i	−0.691655	−	0.502517i
$481$	−2.10594	−	11.9659i	−0.0960224	−	0.545600i
$482$	−3.08473	+	9.49383i	−0.140506	+	0.432432i
$483$			14.0914i			0.641181i
$484$	10.0071	+	2.96717i	0.454870	+	0.134872i
$485$	−21.7989			−0.989838
$486$	0.975059	+	0.316816i	0.0442296	+	0.0143711i
$487$	−13.6745	−	18.8213i	−0.619651	−	0.852876i	0.377677	−	0.925938i	$-0.376723\pi$
$487$	−13.6745	−	18.8213i	−0.619651	−	0.852876i	−0.997327	+	0.0730615i	$0.976723\pi$
$488$	−4.14631	+	5.70691i	−0.187695	+	0.258340i
$489$	10.0240	−	3.25698i	0.453299	−	0.147286i
$490$	5.49974	+	16.9264i	0.248453	+	0.764659i
$491$	−27.6486	−	20.0879i	−1.24776	−	0.906553i	−0.249673	−	0.968330i	$-0.580323\pi$
$491$	−27.6486	−	20.0879i	−1.24776	−	0.906553i	−0.998090	+	0.0617772i	$0.980323\pi$
$492$	−2.21900	−	3.05419i	−0.100040	−	0.137693i
$493$	11.8942	−	36.6067i	0.535689	−	1.64868i
$494$	26.1893	+	12.7838i	1.17831	+	0.575172i
$495$	−12.7172	+	2.18346i	−0.571598	+	0.0981394i
$496$			1.54883i			0.0695445i
$497$	4.24310	−	13.0589i	0.190329	−	0.585773i
$498$	−5.05658	+	3.67382i	−0.226591	+	0.164628i
$499$	4.57702	−	6.29972i	0.204895	−	0.282014i	−0.694186	−	0.719796i	$-0.744236\pi$
$499$	4.57702	−	6.29972i	0.204895	−	0.282014i	0.899082	+	0.437781i	$0.144236\pi$
$500$	−18.0323	+	5.85904i	−0.806427	+	0.262024i
$501$	5.19330	−	1.68741i	0.232020	−	0.0753877i
$502$	−17.0644	+	23.4871i	−0.761620	+	1.04828i
$503$	−19.3837	+	14.0831i	−0.864278	+	0.627935i	−0.929045	−	0.369966i	$-0.879369\pi$
$503$	−19.3837	+	14.0831i	−0.864278	+	0.627935i	0.0647673	+	0.997900i	$0.479369\pi$
$504$	3.16297	−	9.73463i	0.140890	−	0.433615i
$505$			40.6676i			1.80969i
$506$	2.03272	−	14.0062i	0.0903652	−	0.622649i
$507$	−7.99698	−	10.2493i	−0.355159	−	0.455188i
$508$	−3.27905	+	10.0919i	−0.145484	+	0.447755i
$509$	18.1224	+	24.9434i	0.803262	+	1.10560i	0.992328	+	0.123631i	$0.0394540\pi$
$509$	18.1224	+	24.9434i	0.803262	+	1.10560i	−0.189066	+	0.981964i	$0.560546\pi$
$510$	−13.6985	−	9.95252i	−0.606578	−	0.440705i
$511$	4.32953	+	13.3249i	0.191527	+	0.589460i
$512$	−12.4143	+	4.03366i	−0.548642	+	0.178264i
$513$	4.63399	−	6.37814i	0.204596	−	0.281602i
$514$	−11.3651	−	15.6427i	−0.501293	−	0.689970i
$515$	59.1621	+	19.2229i	2.60699	+	0.847063i
$516$	−4.73729			−0.208548
$517$	−24.4842	+	25.1269i	−1.07681	+	1.10508i
$518$		−	11.6964i		−	0.513912i
$519$	−2.76238	+	8.50172i	−0.121255	+	0.373184i
$520$	−41.7672	+	7.35079i	−1.83161	+	0.322354i
$521$	35.9371	+	26.1099i	1.57443	+	1.14389i	0.922747	+	0.385406i	$0.125939\pi$
$521$	35.9371	+	26.1099i	1.57443	+	1.14389i	0.651688	+	0.758487i	$0.274061\pi$
$522$	8.84097	−	2.87261i	0.386959	−	0.125731i
$523$	−0.913410	−	2.81119i	−0.0399406	−	0.122925i	0.929098	−	0.369833i	$-0.120585\pi$
$523$	−0.913410	−	2.81119i	−0.0399406	−	0.122925i	−0.969039	+	0.246909i	$0.920585\pi$
$524$	−6.70786	−	4.87354i	−0.293034	−	0.212902i
$525$	−20.1704	−	27.7622i	−0.880309	−	1.21164i
$526$	8.95207	+	2.90870i	0.390329	+	0.126826i
$527$		−	5.47071i		−	0.238308i
$528$	−1.76346	+	3.57473i	−0.0767446	+	0.155570i
$529$	−5.67598			−0.246782
$530$	10.1892	−	31.3591i	0.442590	−	1.36215i
$531$	−1.99949	−	2.75207i	−0.0867706	−	0.119430i
$532$	−20.4899	−	14.8868i	−0.888348	−	0.645423i
$533$	−14.2045	−	2.00099i	−0.615267	−	0.0866727i
$534$	3.28972	+	10.1247i	0.142360	+	0.438140i
$535$	−18.7876	+	25.8589i	−0.812257	+	1.11798i
$536$	−7.05895	+	5.12863i	−0.304900	+	0.221523i
$537$	3.66906	−	11.2922i	0.158331	−	0.487294i
$538$			28.5584i			1.23124i
$539$	−13.0977	+	6.88877i	−0.564156	+	0.296720i
$540$			3.69165i			0.158863i
$541$	3.92569	+	1.27553i	0.168779	+	0.0548395i	0.392187	−	0.919885i	$-0.371718\pi$
$541$	3.92569	+	1.27553i	0.168779	+	0.0548395i	−0.223409	+	0.974725i	$0.571718\pi$
$542$	−16.4333	+	11.9395i	−0.705869	+	0.512844i
$543$	3.26480	+	2.37202i	0.140106	+	0.101793i
$544$	19.4374	−	6.31559i	0.833372	−	0.270779i
$545$	2.67980	+	8.24757i	0.114790	+	0.353287i
$546$	−5.87181	−	11.0519i	−0.251290	−	0.472976i
$547$	−5.70367	+	4.14396i	−0.243871	+	0.177183i	−0.703006	−	0.711184i	$-0.748159\pi$
$547$	−5.70367	+	4.14396i	−0.243871	+	0.177183i	0.459135	+	0.888367i	$0.348159\pi$
$548$	5.36607	+	1.74354i	0.229227	+	0.0744803i
$549$	2.33325			0.0995805
$550$	16.0436	+	30.5038i	0.684102	+	1.30069i
$551$		−	71.4834i		−	3.04530i
$552$	−11.9678	−	3.88857i	−0.509382	−	0.165508i
$553$	18.6749	+	25.7038i	0.794136	+	1.09304i
$554$	18.7785	−	25.8464i	0.797821	−	1.09811i
$555$	4.05123	+	12.4684i	0.171965	+	0.529254i
$556$	1.92686	+	5.93026i	0.0817170	+	0.251499i
$557$	−2.93560	+	4.04050i	−0.124385	+	0.171201i	−0.866668	−	0.498885i	$-0.833743\pi$
$557$	−2.93560	+	4.04050i	−0.124385	+	0.171201i	0.742283	+	0.670086i	$0.233743\pi$
$558$	1.06891	−	0.776608i	0.0452505	−	0.0328764i
$559$	−12.5084	+	12.9445i	−0.529051	+	0.547494i
$560$	−15.8300			−0.668938
$561$	6.22881	−	12.6265i	0.262981	−	0.533091i
$562$	−10.8989			−0.459743
$563$	12.3096	−	37.8852i	0.518790	−	1.59667i	−0.257489	−	0.966281i	$-0.582895\pi$
$563$	12.3096	−	37.8852i	0.518790	−	1.59667i	0.776279	−	0.630389i	$-0.217105\pi$
$564$	5.89981	+	8.12039i	0.248427	+	0.341930i
$565$	−0.477614	+	0.657380i	−0.0200934	+	0.0276562i
$566$	6.64689	−	2.15970i	0.279389	−	0.0907791i
$567$	−3.21986	+	1.04619i	−0.135221	+	0.0439361i
$568$	9.91999	+	7.20730i	0.416234	+	0.302411i
$569$	−11.6373	+	8.45496i	−0.487859	+	0.354451i	−0.804360	−	0.594142i	$-0.797492\pi$
$569$	−11.6373	+	8.45496i	−0.487859	+	0.354451i	0.316501	+	0.948592i	$0.397492\pi$
$570$	−29.9070	−	9.71736i	−1.25266	−	0.407015i
$571$	−36.5584			−1.52992			−0.764960	−	0.644078i	$-0.777241\pi$
$571$	−36.5584			−1.52992			−0.764960	+	0.644078i	$0.777241\pi$
$572$	−3.82948	−	10.6813i	−0.160119	−	0.446609i
$573$	−6.07368			−0.253732
$574$	−13.1336	−	4.26736i	−0.548186	−	0.178116i
$575$	−34.1309	+	24.7975i	−1.42336	+	1.03413i
$576$	5.93788	+	4.31413i	0.247412	+	0.179755i
$577$	−21.8346	+	7.09450i	−0.908987	+	0.295348i	−0.725941	−	0.687757i	$-0.758596\pi$
$577$	−21.8346	+	7.09450i	−0.908987	+	0.295348i	−0.183046	+	0.983104i	$0.558596\pi$
$578$	0.995149	−	0.323343i	0.0413927	−	0.0134493i
$579$	8.01039	−	11.0254i	0.332900	−	0.458198i
$580$	19.6747	+	27.0799i	0.816948	+	1.12443i
$581$	6.37804	−	19.6296i	0.264606	−	0.814373i
$582$	5.74453			0.238118
$583$	27.1330	+	3.93781i	1.12373	+	0.163087i
$584$	−12.5115			−0.517732
$585$	10.0873	+	9.74750i	0.417059	+	0.403010i
$586$	12.2055	−	8.86779i	0.504203	−	0.366325i
$587$	−8.23457	+	11.3339i	−0.339877	+	0.467801i	−0.944406	−	0.328783i	$-0.893362\pi$
$587$	−8.23457	+	11.3339i	−0.339877	+	0.467801i	0.604528	+	0.796584i	$0.293362\pi$
$588$	1.30836	+	4.02672i	0.0539559	+	0.166059i
$589$	−3.13962	−	9.66276i	−0.129366	−	0.398147i
$590$	−7.97535	+	10.9771i	−0.328340	+	0.451921i
$591$	4.83291	+	6.65193i	0.198799	+	0.273624i
$592$	3.85168	+	1.25149i	0.158303	+	0.0514358i
$593$			3.94409i			0.161965i	0.996716	+	0.0809823i	$0.0258057\pi$
$593$			3.94409i			0.161965i	−0.996716	+	0.0809823i	$0.974194\pi$
$594$	3.35129	−	0.575394i	0.137505	−	0.0236087i
$595$	55.9140			2.29225
$596$	9.10063	+	2.95697i	0.372776	+	0.121122i
$597$	−6.82495	+	4.95862i	−0.279327	+	0.202943i
$598$	−13.5872	+	7.21881i	−0.555622	+	0.295199i
$599$	4.37080	+	13.4519i	0.178586	+	0.549631i	0.999779	−	0.0210194i	$-0.00669117\pi$
$599$	4.37080	+	13.4519i	0.178586	+	0.549631i	−0.821193	+	0.570650i	$0.806691\pi$
$600$	29.1444	−	9.46958i	1.18981	−	0.386594i
$601$	−2.50916	−	1.82301i	−0.102351	−	0.0743623i	0.535433	−	0.844578i	$-0.320149\pi$
$601$	−2.50916	−	1.82301i	−0.102351	−	0.0743623i	−0.637784	+	0.770216i	$0.720149\pi$
$602$	−14.0193	+	10.1856i	−0.571386	+	0.415136i
$603$	2.74477	+	0.891830i	0.111776	+	0.0363181i
$604$		−	5.90464i		−	0.240257i
$605$	−33.9589	+	26.0431i	−1.38063	+	1.05880i
$606$		−	10.7169i		−	0.435343i
$607$	−1.35288	+	4.16374i	−0.0549117	+	0.169001i	−0.974751	−	0.223294i	$-0.928319\pi$
$607$	−1.35288	+	4.16374i	−0.0549117	+	0.169001i	0.919839	+	0.392295i	$0.128319\pi$
$608$	30.7073	−	22.3101i	1.24534	−	0.904795i
$609$	−18.0434	+	24.8346i	−0.731155	+	1.00635i
$610$	−2.87589	−	8.85108i	−0.116441	−	0.358370i
$611$	37.7667	+	5.32019i	1.52788	+	0.215232i
$612$	−3.25880	−	2.36766i	−0.131729	−	0.0957068i
$613$	−16.4448	−	22.6343i	−0.664197	−	0.914189i	0.335414	−	0.942071i	$-0.391124\pi$
$613$	−16.4448	−	22.6343i	−0.664197	−	0.914189i	−0.999611	+	0.0278818i	$0.991124\pi$
$614$	−0.870582	+	2.67938i	−0.0351338	+	0.108131i
$615$	15.4785			0.624152
$616$	−5.74452	−	33.4581i	−0.231453	−	1.34806i
$617$		−	7.42496i		−	0.298918i	−0.988768	−	0.149459i	$-0.952247\pi$
$617$		−	7.42496i		−	0.298918i	0.988768	−	0.149459i	$-0.0477531\pi$
$618$	−15.5906	−	5.06569i	−0.627145	−	0.203772i
$619$	−22.9952	−	31.6502i	−0.924256	−	1.27213i	−0.962058	−	0.272844i	$-0.912036\pi$
$619$	−22.9952	−	31.6502i	−0.924256	−	1.27213i	0.0378028	−	0.999285i	$-0.487964\pi$
$620$	3.84890	+	2.79639i	0.154576	+	0.112306i
$621$	1.28619	+	3.95850i	0.0516132	+	0.158849i
$622$	26.0396	−	8.46078i	1.04409	−	0.339246i
$623$	−28.4407	−	20.6634i	−1.13945	−	0.827861i
$624$	4.26769	−	0.751088i	0.170844	−	0.0300676i
$625$	8.36144	−	25.7339i	0.334458	−	1.02935i
$626$		−	23.1727i		−	0.926169i
$627$	3.75547	−	25.8765i	0.149979	−	1.03341i
$628$	−14.4489			−0.576575
$629$	−13.6047	−	4.42045i	−0.542456	−	0.176255i
$630$	7.93741	+	10.9249i	0.316234	+	0.435259i
$631$	2.46413	−	3.39158i	0.0980954	−	0.135017i	−0.757148	−	0.653244i	$-0.773408\pi$
$631$	2.46413	−	3.39158i	0.0980954	−	0.135017i	0.855243	+	0.518227i	$0.173408\pi$
$632$	−26.9835	+	8.76746i	−1.07334	+	0.348751i
$633$	2.51264	+	7.73311i	0.0998685	+	0.307364i
$634$	−8.69853	−	6.31985i	−0.345463	−	0.250993i
$635$	−25.5726	−	35.1977i	−1.01482	−	1.39678i
$636$	2.42395	−	7.46017i	0.0961161	−	0.295815i
$637$	14.4575	+	7.05717i	0.572827	+	0.279615i
$638$	21.5167	−	22.0815i	0.851853	−	0.874217i
$639$		−	4.05575i		−	0.160443i
$640$	−2.52955	+	7.78516i	−0.0999894	+	0.307736i
$641$	−0.521742	+	0.379068i	−0.0206076	+	0.0149723i	−0.598041	−	0.801465i	$-0.704054\pi$
$641$	−0.521742	+	0.379068i	−0.0206076	+	0.0149723i	0.577434	+	0.816438i	$0.304054\pi$
$642$	4.95096	−	6.81441i	0.195399	−	0.268943i
$643$	35.2904	−	11.4665i	1.39172	−	0.452196i	0.485213	−	0.874396i	$-0.338742\pi$
$643$	35.2904	−	11.4665i	1.39172	−	0.452196i	0.906503	+	0.422200i	$0.138742\pi$
$644$	12.7167	−	4.13192i	0.501110	−	0.162820i
$645$	11.4167	−	15.7137i	0.449531	−	0.618726i
$646$	27.7589	−	20.1681i	1.09216	−	0.793501i
$647$	0.297662	−	0.916110i	0.0117023	−	0.0360160i	−0.945035	−	0.326970i	$-0.893973\pi$
$647$	0.297662	−	0.916110i	0.0117023	−	0.0360160i	0.956737	+	0.290954i	$0.0939725\pi$
$648$		−	3.02331i		−	0.118767i
$649$	−10.1181	−	4.99139i	−0.397171	−	0.195929i
$650$	16.4358	−	33.6708i	0.644666	−	1.32068i
$651$	−1.34825	+	4.14950i	−0.0528422	+	0.162632i
$652$	−5.87851	−	8.09107i	−0.230220	−	0.316871i
$653$	24.8118	+	18.0268i	0.970960	+	0.705444i	0.955670	−	0.294439i	$-0.0951328\pi$
$653$	24.8118	+	18.0268i	0.970960	+	0.705444i	0.0152900	+	0.999883i	$0.495133\pi$
$654$	−0.706190	−	2.17343i	−0.0276142	−	0.0849878i
$655$	32.3313	−	10.5051i	1.26329	−	0.410467i
$656$	2.81051	−	3.86834i	0.109732	−	0.151033i
$657$	2.43247	+	3.34800i	0.0948996	+	0.130618i
$658$	34.9193	+	11.3460i	1.36129	+	0.442311i
$659$	−25.9052			−1.00912			−0.504562	−	0.863375i	$-0.668346\pi$
$659$	−25.9052			−1.00912			−0.504562	+	0.863375i	$0.668346\pi$
$660$	5.69944	+	10.8364i	0.221851	+	0.421806i
$661$			15.5470i			0.604709i	0.953196	+	0.302355i	$0.0977727\pi$
$661$			15.5470i			0.604709i	−0.953196	+	0.302355i	$0.902227\pi$
$662$	7.03944	−	21.6652i	0.273596	−	0.842040i
$663$	−15.0741	+	2.65296i	−0.585431	+	0.103032i
$664$	14.9113	+	10.8337i	0.578670	+	0.420429i
$665$	98.7593	−	32.0888i	3.82972	−	1.24435i
$666$	−1.06759	−	3.28571i	−0.0413684	−	0.127319i
$667$	30.5317	+	22.1826i	1.18219	+	0.858913i
$668$	−3.04559	−	4.19189i	−0.117837	−	0.162189i
$669$	21.6563	+	7.03656i	0.837281	+	0.272049i
$670$		−	11.5114i		−	0.444726i
$671$	6.84896	−	3.60224i	0.264401	−	0.139063i
$672$	−16.2996			−0.628771
$673$	15.7030	−	48.3290i	0.605308	−	1.86295i	0.110646	−	0.993860i	$-0.464708\pi$
$673$	15.7030	−	48.3290i	0.605308	−	1.86295i	0.494662	−	0.869086i	$-0.335292\pi$
$674$	2.33251	+	3.21043i	0.0898450	+	0.123661i
$675$	−8.20018	−	5.95778i	−0.315625	−	0.229315i
$676$	−6.90455	+	10.2222i	−0.265560	+	0.393161i
$677$	11.7842	+	36.2680i	0.452903	+	1.39389i	0.873580	+	0.486681i	$0.161793\pi$
$677$	11.7842	+	36.2680i	0.452903	+	1.39389i	−0.420677	+	0.907211i	$0.638207\pi$
$678$	0.125863	−	0.173235i	0.00483372	−	0.00665305i
$679$	−15.3468	+	11.1501i	−0.588956	+	0.427902i
$680$	−15.4296	+	47.4875i	−0.591699	+	1.82106i
$681$		−	23.0253i		−	0.882330i
$682$	1.93867	−	3.92990i	0.0742355	−	0.150484i
$683$			6.04140i			0.231168i	0.993298	+	0.115584i	$0.0368739\pi$
$683$			6.04140i			0.231168i	−0.993298	+	0.115584i	$0.963126\pi$
$684$	−7.11472	−	2.31171i	−0.272038	−	0.0883905i
$685$	−18.7153	+	13.5975i	−0.715076	+	0.519533i
$686$	−7.12695	−	5.17803i	−0.272108	−	0.197698i
$687$	−15.5109	+	5.03978i	−0.591776	+	0.192280i
$688$	−1.85414	−	5.70645i	−0.0706884	−	0.217556i
$689$	−13.9844	−	26.3213i	−0.532764	−	1.00276i
$690$	13.4311	−	9.75827i	0.511313	−	0.371491i
$691$	−40.3547	−	13.1120i	−1.53517	−	0.498806i	−0.585128	−	0.810941i	$-0.698956\pi$
$691$	−40.3547	−	13.1120i	−1.53517	−	0.498806i	−0.950038	+	0.312135i	$0.898956\pi$
$692$	8.48234			0.322450
$693$	−7.83631	+	8.04203i	−0.297677	+	0.305492i
$694$			1.26858i			0.0481546i
$695$	−24.3144	−	7.90023i	−0.922298	−	0.299673i
$696$	−16.1128	−	22.1774i	−0.610754	−	0.840630i
$697$	−9.92718	+	13.6636i	−0.376019	+	0.517546i
$698$	9.07742	+	27.9374i	0.343586	+	1.05745i
$699$	−2.03639	−	6.26736i	−0.0770232	−	0.237053i
$700$	−19.1395	+	26.3432i	−0.723404	+	0.995680i
$701$	−4.82796	+	3.50772i	−0.182349	+	0.132485i	−0.675215	−	0.737621i	$-0.735949\pi$
$701$	−4.82796	+	3.50772i	−0.182349	+	0.132485i	0.492866	+	0.870105i	$0.335949\pi$
$702$	−2.65824	−	2.56869i	−0.100329	−	0.0969491i
$703$	−26.5666			−1.00198
$704$	24.0904	+	3.49625i	0.907941	+	0.131770i
$705$	−41.1537			−1.54994
$706$	−1.80991	+	5.57033i	−0.0681168	+	0.209642i
$707$	20.8014	+	28.6307i	0.782317	+	1.07677i
$708$	−1.89730	+	2.61140i	−0.0713047	+	0.0981426i
$709$	19.9412	−	6.47930i	0.748909	−	0.243335i	0.0903975	−	0.995906i	$-0.471186\pi$
$709$	19.9412	−	6.47930i	0.748909	−	0.243335i	0.658512	+	0.752570i	$0.271186\pi$
$710$	−15.3853	+	4.99900i	−0.577401	+	0.187609i
$711$	7.59218	+	5.51604i	0.284729	+	0.206868i
$712$	25.3976	−	18.4525i	0.951816	−	0.691535i
$713$	5.10140	+	1.65755i	0.191049	+	0.0620756i
$714$	−14.7346			−0.551430
$715$	44.6590	+	13.0391i	1.67015	+	0.487633i
$716$	−11.2664			−0.421047
$717$	−1.30450	−	0.423856i	−0.0487173	−	0.0158292i
$718$	1.51709	−	1.10223i	0.0566174	−	0.0411350i
$719$	−35.5462	−	25.8258i	−1.32565	−	0.963140i	−0.999843	−	0.0177025i	$-0.994365\pi$
$719$	−35.5462	−	25.8258i	−1.32565	−	0.963140i	−0.325805	−	0.945437i	$-0.605635\pi$
$720$	−4.44689	+	1.44488i	−0.165726	+	0.0538475i
$721$	51.4835	−	16.7280i	1.91735	−	0.622984i
$722$	26.0057	−	35.7938i	0.967832	−	1.33211i
$723$	−5.72307	−	7.87713i	−0.212843	−	0.292954i
$724$	1.18330	−	3.64184i	0.0439772	−	0.135348i
$725$	−91.9041			−3.41323
$726$	8.94897	−	6.86297i	0.332128	−	0.254709i
$727$	−1.19901			−0.0444689			−0.0222345	−	0.999753i	$-0.507078\pi$
$727$	−1.19901			−0.0444689			−0.0222345	+	0.999753i	$0.507078\pi$
$728$	−25.6449	+	26.5389i	−0.950463	+	0.983598i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	9.70234	−	13.3541i	0.359100	−	0.494259i
$731$	6.54911	+	20.1561i	0.242228	+	0.745500i
$732$	−0.684160	−	2.10563i	−0.0252873	−	0.0778263i
$733$	−24.0396	+	33.0877i	−0.887923	+	1.22212i	0.0862400	+	0.996274i	$0.472515\pi$
$733$	−24.0396	+	33.0877i	−0.887923	+	1.22212i	−0.974163	+	0.225847i	$0.927485\pi$
$734$	−1.07959	−	1.48593i	−0.0398484	−	0.0548466i
$735$	−16.5098	−	5.36435i	−0.608972	−	0.197867i
$736$			20.0388i			0.738640i
$737$	9.43382	−	1.61972i	0.347499	−	0.0596632i
$738$	−4.07894			−0.150148
$739$	17.3365	+	5.63297i	0.637733	+	0.207212i	0.609998	−	0.792403i	$-0.291170\pi$
$739$	17.3365	+	5.63297i	0.637733	+	0.207212i	0.0277356	+	0.999615i	$0.491170\pi$
$740$	10.0642	−	7.31203i	0.369966	−	0.268796i
$741$	−25.1025	+	13.3369i	−0.922164	+	0.489942i
$742$	−8.86674	−	27.2890i	−0.325508	−	1.00181i
$743$	0.992694	−	0.322546i	0.0364184	−	0.0118331i	−0.290751	−	0.956799i	$-0.593905\pi$
$743$	0.992694	−	0.322546i	0.0364184	−	0.0118331i	0.327170	+	0.944966i	$0.393905\pi$
$744$	−3.15209	−	2.29013i	−0.115561	−	0.0839603i
$745$	−31.7404	+	23.0608i	−1.16288	+	0.844881i
$746$	1.57316	+	0.511152i	0.0575976	+	0.0187146i
$747$		−	6.09642i		−	0.223056i
$748$	−13.2212	−	1.91879i	−0.483414	−	0.0701579i
$749$			27.8148i			1.01633i
$750$	−6.33046	+	19.4832i	−0.231156	+	0.711424i
$751$	−0.591981	+	0.430099i	−0.0216017	+	0.0156945i	−0.598534	−	0.801098i	$-0.704250\pi$
$751$	−0.591981	+	0.430099i	−0.0216017	+	0.0156945i	0.576932	+	0.816792i	$0.304250\pi$
$752$	−7.47252	+	10.2850i	−0.272495	+	0.375057i
$753$	−8.75043	−	26.9311i	−0.318883	−	0.981422i
$754$	−33.1893	−	4.67538i	−1.20868	−	0.170267i
$755$	19.5858	+	14.2299i	0.712801	+	0.517880i
$756$	1.88827	+	2.59898i	0.0686757	+	0.0945240i
$757$	10.7098	−	32.9613i	0.389254	−	1.19800i	−0.544093	−	0.839025i	$-0.683126\pi$
$757$	10.7098	−	32.9613i	0.389254	−	1.19800i	0.933347	−	0.358975i	$-0.116874\pi$
$758$	−19.3923			−0.704360
$759$	9.88690	+	9.63397i	0.358872	+	0.349691i
$760$			92.7308i			3.36370i
$761$	−24.5436	−	7.97470i	−0.889705	−	0.289083i	−0.171724	−	0.985145i	$-0.554934\pi$
$761$	−24.5436	−	7.97470i	−0.889705	−	0.289083i	−0.717981	+	0.696062i	$0.754934\pi$
$762$	6.73898	+	9.27540i	0.244127	+	0.336012i
$763$	6.10524	+	4.43571i	0.221024	+	0.160584i
$764$	1.78094	+	5.48117i	0.0644322	+	0.198302i
$765$	15.7071	−	5.10355i	0.567892	−	0.184519i
$766$	−10.4169	−	7.56830i	−0.376377	−	0.273454i
$767$	2.12592	+	12.0795i	0.0767626	+	0.436166i
$768$	5.20274	−	16.0124i	0.187738	−	0.577797i
$769$		−	12.7944i		−	0.461379i	−0.973027	−	0.230690i	$-0.925902\pi$
$769$		−	12.7944i		−	0.461379i	0.973027	−	0.230690i	$-0.0740982\pi$
$770$	40.1660	+	19.8144i	1.44748	+	0.714060i
$771$	18.8595			0.679208
$772$	−12.2986	−	3.99606i	−0.442637	−	0.143821i
$773$	8.83438	+	12.1595i	0.317750	+	0.437346i	0.937779	−	0.347233i	$-0.112879\pi$
$773$	8.83438	+	12.1595i	0.317750	+	0.437346i	−0.620028	+	0.784580i	$0.712879\pi$
$774$	−3.00856	+	4.14092i	−0.108140	+	0.148842i
$775$	−12.4231	+	4.03652i	−0.446252	+	0.144996i
$776$	−5.23474	−	16.1109i	−0.187916	−	0.578347i
$777$	9.22969	+	6.70576i	0.331113	+	0.240568i
$778$	4.66092	+	6.41520i	0.167102	+	0.229996i
$779$	−9.69262	+	29.8308i	−0.347274	+	1.06880i
$780$	5.83877	−	11.9615i	0.209061	−	0.428289i
$781$	−6.26156	−	11.9052i	−0.224056	−	0.426000i
$782$			18.1148i			0.647784i
$783$	−2.80189	+	8.62334i	−0.100132	+	0.308173i
$784$	−4.33842	+	3.15205i	−0.154944	+	0.112573i
$785$	34.8212	−	47.9273i	1.24282	−	1.71060i
$786$	−8.52004	+	2.76833i	−0.303900	+	0.0987430i
$787$	6.16025	−	2.00159i	0.219589	−	0.0713489i	−0.197156	−	0.980372i	$-0.563171\pi$
$787$	6.16025	−	2.00159i	0.219589	−	0.0713489i	0.416746	+	0.909023i	$0.363171\pi$
$788$	4.58589	−	6.31194i	0.163366	−	0.224854i
$789$	−7.42763	+	5.39649i	−0.264431	+	0.192120i
$790$	11.5670	−	35.5996i	0.411536	−	1.26658i
$791$			0.707105i			0.0251417i
$792$	−4.66761	−	8.87456i	−0.165856	−	0.315344i
$793$	−7.56004	−	3.69030i	−0.268465	−	0.131046i
$794$	3.32040	−	10.2191i	0.117837	−	0.362664i
$795$	18.9039	+	26.0190i	0.670452	+	0.922797i
$796$	6.47612	+	4.70518i	0.229540	+	0.166771i
$797$	−1.23129	−	3.78953i	−0.0436146	−	0.134232i	0.926878	−	0.375363i	$-0.122482\pi$
$797$	−1.23129	−	3.78953i	−0.0436146	−	0.134232i	−0.970493	+	0.241131i	$0.922482\pi$
$798$	−26.0254	+	8.45616i	−0.921289	+	0.299345i
$799$	26.3941	−	36.3284i	0.933757	−	1.28521i
$800$	−28.6835	−	39.4794i	−1.01411	−	1.39581i
$801$	−9.87550	−	3.20874i	−0.348934	−	0.113375i
$802$	8.20447			0.289710
$803$	12.3091	+	6.07224i	0.434379	+	0.214285i
$804$		−	2.73851i		−	0.0965799i
$805$	−16.9411	+	52.1394i	−0.597096	+	1.83767i
$806$	−4.69171	+	0.825713i	−0.165258	+	0.0290845i
$807$	−22.5355	−	16.3730i	−0.793287	−	0.576356i
$808$	−30.0561	+	9.76582i	−1.05737	+	0.343560i
$809$	7.40149	+	22.7795i	0.260223	+	0.800883i	0.992756	+	0.120151i	$0.0383380\pi$
$809$	7.40149	+	22.7795i	0.260223	+	0.800883i	−0.732533	+	0.680732i	$0.761662\pi$
$810$	3.22691	+	2.34449i	0.113382	+	0.0823770i
$811$	8.75170	+	12.0457i	0.307314	+	0.422981i	0.934541	−	0.355855i	$-0.115810\pi$
$811$	8.75170	+	12.0457i	0.307314	+	0.422981i	−0.627227	+	0.778836i	$0.715810\pi$
$812$	27.7026	+	9.00113i	0.972172	+	0.315878i
$813$		−	19.8126i		−	0.694859i
$814$	−8.20652	−	7.99659i	−0.287638	−	0.280280i
$815$	41.0051			1.43635
$816$	1.57656	−	4.85216i	0.0551908	−	0.169860i
$817$	23.1350	+	31.8426i	0.809392	+	1.11403i
$818$	29.6735	+	21.5590i	1.03751	+	0.753794i
$819$	12.0875	+	1.70276i	0.422370	+	0.0594993i
$820$	−4.53864	−	13.9685i	−0.158496	−	0.487801i
$821$	−26.7683	+	36.8435i	−0.934222	+	1.28585i	0.0239680	+	0.999713i	$0.492370\pi$
$821$	−26.7683	+	36.8435i	−0.934222	+	1.28585i	−0.958190	+	0.286133i	$0.907630\pi$
$822$	4.93193	−	3.58325i	0.172021	−	0.124980i
$823$	16.3066	−	50.1865i	0.568411	−	1.74939i	−0.0891806	−	0.996015i	$-0.528425\pi$
$823$	16.3066	−	50.1865i	0.568411	−	1.74939i	0.657592	−	0.753374i	$-0.271575\pi$
$824$			48.3409i			1.68403i
$825$	−33.2687	−	4.82829i	−1.15827	−	0.168100i
$826$			11.8074i			0.410834i
$827$	−1.03059	−	0.334861i	−0.0358373	−	0.0116442i	0.291043	−	0.956710i	$-0.405998\pi$
$827$	−1.03059	−	0.334861i	−0.0358373	−	0.0116442i	−0.326881	+	0.945066i	$0.605998\pi$
$828$	3.19519	−	2.32144i	0.111041	−	0.0806757i
$829$	−15.3142	−	11.1264i	−0.531886	−	0.386438i	0.289177	−	0.957276i	$-0.406618\pi$
$829$	−15.3142	−	11.1264i	−0.531886	−	0.386438i	−0.821063	+	0.570838i	$0.806618\pi$
$830$	−23.1266	+	7.51427i	−0.802734	+	0.260824i
$831$	9.62941	+	29.6363i	0.334040	+	1.02807i
$832$	−12.4163	−	23.3698i	−0.430457	−	0.810202i
$833$	15.3240	−	11.1335i	0.530945	−	0.385754i
$834$	6.40742	+	2.08190i	0.221871	+	0.0720901i
$835$	21.2443			0.735189
$836$	−24.4534	+	4.19848i	−0.845738	+	0.145207i
$837$			1.28872i			0.0445447i
$838$	−21.1356	−	6.86739i	−0.730119	−	0.237230i
$839$	−5.35304	−	7.36783i	−0.184807	−	0.254366i	0.706554	−	0.707659i	$-0.250249\pi$
$839$	−5.35304	−	7.36783i	−0.184807	−	0.254366i	−0.891361	+	0.453294i	$0.850249\pi$
$840$	23.4065	−	32.2163i	0.807602	−	1.11157i
$841$	16.4436	+	50.6082i	0.567021	+	1.74511i
$842$	5.01956	+	15.4486i	0.172986	+	0.532395i
$843$	6.24853	−	8.60036i	0.215211	−	0.296212i
$844$	6.24196	−	4.53505i	0.214857	−	0.156103i
$845$	−17.2675	−	47.5375i	−0.594020	−	1.63534i
$846$	10.8450			0.372858
$847$	−10.5866	+	35.7047i	−0.363761	+	1.22683i
$848$	9.93508			0.341172
$849$	−2.10654	+	6.48326i	−0.0722963	+	0.222505i
$850$	−25.9295	−	35.6888i	−0.889373	−	1.22412i
$851$	8.24408	−	11.3470i	0.282603	−	0.388970i
$852$	−3.66009	+	1.18924i	−0.125393	+	0.0407426i
$853$	32.0643	−	10.4183i	1.09786	−	0.356716i	0.296581	−	0.955008i	$-0.404154\pi$
$853$	32.0643	−	10.4183i	1.09786	−	0.356716i	0.801278	+	0.598292i	$0.204154\pi$
$854$	−6.55198	−	4.76029i	−0.224204	−	0.162894i
$855$	24.8141	−	18.0285i	0.848625	−	0.616562i
$856$	−23.6230	−	7.67558i	−0.807418	−	0.262346i
$857$	15.9471			0.544743			0.272372	−	0.962192i	$-0.412192\pi$
$857$	15.9471			0.544743			0.272372	+	0.962192i	$0.412192\pi$
$858$	−11.7687	−	3.43610i	−0.401777	−	0.117306i
$859$	33.8355			1.15445			0.577226	−	0.816584i	$-0.304135\pi$
$859$	33.8355			1.15445			0.577226	+	0.816584i	$0.304135\pi$
$860$	−17.5284	−	5.69532i	−0.597713	−	0.194209i
$861$	10.8971	−	7.91720i	0.371372	−	0.269817i
$862$	20.1256	+	14.6221i	0.685482	+	0.498032i
$863$	−20.3915	+	6.62560i	−0.694135	+	0.225538i	−0.634773	−	0.772698i	$-0.718907\pi$
$863$	−20.3915	+	6.62560i	−0.694135	+	0.225538i	−0.0593617	+	0.998237i	$0.518907\pi$
$864$	−4.57882	+	1.48775i	−0.155775	+	0.0506142i
$865$	−20.4420	+	28.1361i	−0.695050	+	0.956655i
$866$	−5.50387	−	7.57542i	−0.187029	−	0.257423i
$867$	−0.315384	+	0.970652i	−0.0107110	+	0.0329651i
$868$	4.14004			0.140522
$869$	30.8020	+	4.47030i	1.04489	+	0.151645i
$870$	36.1659			1.22614
$871$	−7.48290	−	7.23083i	−0.253549	−	0.245007i
$872$	−5.45199	+	3.96110i	−0.184628	+	0.134140i
$873$	−3.29343	+	4.53302i	−0.111466	+	0.153419i
$874$	10.3960	+	31.9957i	0.351651	+	1.08227i
$875$	−20.9046	−	64.3376i	−0.706703	−	2.17501i
$876$	2.30814	−	3.17688i	0.0779848	−	0.107337i
$877$	14.4891	+	19.9425i	0.489262	+	0.673411i	0.980252	−	0.197754i	$-0.0633647\pi$
$877$	14.4891	+	19.9425i	0.489262	+	0.673411i	−0.490990	+	0.871165i	$0.663365\pi$
$878$	−16.6582	−	5.41259i	−0.562188	−	0.182666i
$879$			14.7154i			0.496339i
$880$	−10.8226	+	11.1067i	−0.364829	+	0.374407i
$881$	18.0332			0.607553			0.303777	−	0.952743i	$-0.401752\pi$
$881$	18.0332			0.607553			0.303777	+	0.952743i	$0.401752\pi$
$882$	4.35071	+	1.41363i	0.146496	+	0.0475995i
$883$	0.0868389	−	0.0630922i	0.00292236	−	0.00212322i	−0.586323	−	0.810077i	$-0.699425\pi$
$883$	0.0868389	−	0.0630922i	0.00292236	−	0.00212322i	0.589245	+	0.807954i	$0.299425\pi$
$884$	6.81423	+	12.8257i	0.229187	+	0.431375i
$885$	−4.08968	−	12.5867i	−0.137473	−	0.423098i
$886$	−3.01122	+	0.978405i	−0.101164	+	0.0328702i
$887$	−24.6385	−	17.9009i	−0.827280	−	0.601054i	0.0915088	−	0.995804i	$-0.470831\pi$
$887$	−24.6385	−	17.9009i	−0.827280	−	0.601054i	−0.918788	+	0.394750i	$0.870831\pi$
$888$	−8.24213	+	5.98826i	−0.276588	+	0.200953i
$889$	−36.0070	−	11.6994i	−1.20764	−	0.392385i
$890$			41.4174i			1.38831i
$891$	−1.46730	+	2.97439i	−0.0491566	+	0.0996459i
$892$		−	21.6069i		−	0.723454i
$893$	25.7705	−	79.3134i	0.862376	−	2.65412i
$894$	8.36434	−	6.07705i	0.279746	−	0.203247i
$895$	27.1516	−	37.3710i	0.907579	−	1.24918i
$896$	2.20125	+	6.77474i	0.0735385	+	0.226328i
$897$	2.09338	−	14.8603i	0.0698959	−	0.496173i
$898$	25.6782	+	18.6563i	0.856892	+	0.622569i
$899$	6.86826	+	9.45335i	0.229069	+	0.315287i
$900$	−2.97210	+	9.14718i	−0.0990700	+	0.304906i
$901$	−35.0923			−1.16909
$902$	−11.9732	+	6.29737i	−0.398665	+	0.209679i
$903$		−	16.9023i		−	0.562473i
$904$	−0.600541	−	0.195128i	−0.0199737	−	0.00648985i
$905$	9.22833	+	12.7017i	0.306760	+	0.422219i
$906$	−5.16132	−	3.74992i	−0.171473	−	0.124583i
$907$	16.9500	+	52.1668i	0.562816	+	1.73217i	0.674353	+	0.738409i	$0.264423\pi$
$907$	16.9500	+	52.1668i	0.562816	+	1.73217i	−0.111537	+	0.993760i	$0.535577\pi$
$908$	−20.7791	+	6.75153i	−0.689578	+	0.224057i
$909$	8.45671	+	6.14416i	0.280491	+	0.203789i
$910$	−8.43929	−	47.9521i	−0.279760	−	1.58960i
$911$	1.49366	−	4.59703i	0.0494873	−	0.152306i	−0.923259	−	0.384178i	$-0.874485\pi$
$911$	1.49366	−	4.59703i	0.0494873	−	0.152306i	0.972746	+	0.231872i	$0.0744849\pi$
$912$		−	9.47503i		−	0.313750i
$913$	−9.41211	−	17.8953i	−0.311495	−	0.592248i
$914$	15.7169			0.519867
$915$	8.63321	+	2.80510i	0.285405	+	0.0927337i
$916$	9.09627	+	12.5199i	0.300549	+	0.413670i
$917$	17.3884	−	23.9331i	0.574216	−	0.790340i
$918$	−4.13919	+	1.34490i	−0.136614	+	0.0443885i
$919$	−2.94870	−	9.07518i	−0.0972687	−	0.299362i	0.890570	−	0.454847i	$-0.150306\pi$
$919$	−2.94870	−	9.07518i	−0.0972687	−	0.299362i	−0.987838	+	0.155485i	$0.950306\pi$
$920$	−39.6068	−	28.7760i	−1.30580	−	0.948718i
$921$	−1.61518	−	2.22311i	−0.0532221	−	0.0732539i
$922$	−11.3097	+	34.8077i	−0.372466	+	1.14633i
$923$	−6.41463	+	13.1412i	−0.211140	+	0.432547i
$924$	9.55529	+	4.71374i	0.314346	+	0.155071i
$925$			34.1558i			1.12304i
$926$	−6.65673	+	20.4873i	−0.218754	+	0.673255i
$927$	12.9357	−	9.39832i	0.424863	−	0.308681i
$928$	−25.6587	+	35.3162i	−0.842289	+	1.15931i
$929$	−0.0779364	+	0.0253231i	−0.00255701	+	0.000830823i	−0.310295	−	0.950640i	$-0.600428\pi$
$929$	−0.0779364	+	0.0253231i	−0.00255701	+	0.000830823i	0.307738	+	0.951471i	$0.400428\pi$
$930$	4.88872	−	1.58844i	0.160307	−	0.0520870i
$931$	20.6769	−	28.4593i	0.677657	−	0.932714i
$932$	−5.05884	+	3.67546i	−0.165708	+	0.120394i
$933$	−8.25251	+	25.3986i	−0.270175	+	0.831513i
$934$			25.3006i			0.827860i
$935$	38.2271	−	39.2307i	1.25016	−	1.28298i
$936$	−4.78172	+	9.79594i	−0.156295	+	0.320190i
$937$	7.85991	−	24.1903i	0.256772	−	0.790264i	−0.736703	−	0.676216i	$-0.763618\pi$
$937$	7.85991	−	24.1903i	0.256772	−	0.790264i	0.993475	−	0.114047i	$-0.0363815\pi$
$938$	−5.88807	−	8.10424i	−0.192252	−	0.264613i
$939$	18.2857	+	13.2853i	0.596730	+	0.433550i
$940$	12.0672	+	37.1390i	0.393589	+	1.21134i
$941$	−22.5092	+	7.31369i	−0.733779	+	0.238419i	−0.651987	−	0.758230i	$-0.726064\pi$
$941$	−22.5092	+	7.31369i	−0.733779	+	0.238419i	−0.0817923	+	0.996649i	$0.526064\pi$
$942$	−9.17621	+	12.6300i	−0.298977	+	0.411507i
$943$	−9.73342	−	13.3969i	−0.316964	−	0.436263i
$944$	−3.88823	−	1.26336i	−0.126551	−	0.0411190i
$945$	−13.1715			−0.428469
$946$	−2.43819	+	16.8000i	−0.0792724	+	0.546216i
$947$			19.2452i			0.625384i	0.949855	+	0.312692i	$0.101231\pi$
$947$			19.2452i			0.625384i	−0.949855	+	0.312692i	$0.898769\pi$
$948$	2.75173	−	8.46896i	0.0893721	−	0.275059i
$949$	−2.58627	−	14.6952i	−0.0839540	−	0.477027i
$950$	−66.2802	−	48.1554i	−2.15041	−	1.56237i
$951$	9.97401	−	3.24075i	0.323429	−	0.105089i
$952$	13.4270	+	41.3242i	0.435173	+	1.33932i
$953$	−7.83479	−	5.69231i	−0.253794	−	0.184392i	0.453613	−	0.891199i	$-0.350135\pi$
$953$	−7.83479	−	5.69231i	−0.253794	−	0.184392i	−0.707407	+	0.706807i	$0.750135\pi$
$954$	−4.98161	−	6.85660i	−0.161286	−	0.221991i
$955$	−22.4731	−	7.30196i	−0.727214	−	0.236286i
$956$			1.30152i			0.0420942i
$957$	5.08874	+	29.6386i	0.164496	+	0.958078i
$958$	20.0045			0.646315
$959$	−6.22081	+	19.1457i	−0.200881	+	0.618247i
$960$	16.7841	+	23.1013i	0.541704	+	0.745592i
$961$	−23.7359	−	17.2451i	−0.765675	−	0.556295i
$962$	−1.73759	+	12.3347i	−0.0560221	+	0.397686i
$963$	2.53880	+	7.81363i	0.0818117	+	0.251791i
$964$	−5.43056	+	7.47452i	−0.174906	+	0.240738i
$965$	42.8941	−	31.1644i	1.38081	−	1.00322i
$966$	4.46438	−	13.7400i	0.143639	−	0.442076i
$967$		−	40.5642i		−	1.30446i	−0.758023	−	0.652228i	$-0.773835\pi$
$967$		−	40.5642i		−	1.30446i	0.758023	−	0.652228i	$-0.226165\pi$
$968$	−27.4024	−	18.8440i	−0.880747	−	0.605669i
$969$			33.4673i			1.07512i
$970$	21.2552	+	6.90624i	0.682465	+	0.221746i
$971$	−46.1691	+	33.5438i	−1.48164	+	1.07647i	−0.504614	+	0.863345i	$0.668365\pi$
$971$	−46.1691	+	33.5438i	−1.48164	+	1.07647i	−0.977024	+	0.213128i	$0.931635\pi$
$972$	0.767667	+	0.557743i	0.0246229	+	0.0178896i
$973$	−21.1587	+	6.87487i	−0.678316	+	0.220398i
$974$	7.37054	+	22.6842i	0.236167	+	0.726849i
$975$	17.1468	+	32.2736i	0.549137	+	1.03358i
$976$	2.26862	−	1.64825i	0.0726169	−	0.0527593i
$977$	−22.6984	−	7.37515i	−0.726186	−	0.235952i	−0.0774827	−	0.996994i	$-0.524688\pi$
$977$	−22.6984	−	7.37515i	−0.726186	−	0.235952i	−0.648703	+	0.761042i	$0.724688\pi$
$978$	−10.8058			−0.345532
$979$	−33.9422	+	5.82765i	−1.08480	+	0.186253i
$980$			16.4721i			0.526183i
$981$	2.11993	+	0.688806i	0.0676841	+	0.0219919i
$982$	20.5948	+	28.3464i	0.657208	+	0.904569i
$983$	−15.3530	+	21.1316i	−0.489685	+	0.673994i	−0.980330	−	0.197366i	$-0.936761\pi$
$983$	−15.3530	+	21.1316i	−0.489685	+	0.673994i	0.490645	+	0.871360i	$0.336761\pi$
$984$	3.71696	+	11.4396i	0.118492	+	0.364682i
$985$	9.88503	+	30.4230i	0.314963	+	0.969357i
$986$	−23.1951	+	31.9254i	−0.738684	+	1.01671i
$987$	−28.9729	+	21.0500i	−0.922217	+	0.670030i
$988$	19.3964	+	18.7430i	0.617082	+	0.596295i
$989$	−20.7797			−0.660756
$990$	13.0918	+	1.90002i	0.416085	+	0.0603865i
$991$	−52.6923			−1.67383			−0.836913	−	0.547336i	$-0.815642\pi$
$991$	−52.6923			−1.67383			−0.836913	+	0.547336i	$0.815642\pi$
$992$	−1.91729	+	5.90082i	−0.0608741	+	0.187351i
$993$	13.0602	+	17.9758i	0.414453	+	0.570446i
$994$	−8.27455	+	11.3889i	−0.262453	+	0.361235i
$995$	−31.2143	+	10.1421i	−0.989560	+	0.321527i
$996$	−5.50169	+	1.78761i	−0.174328	+	0.0566425i
$997$	−31.1250	−	22.6137i	−0.985739	−	0.716182i	−0.0267555	−	0.999642i	$-0.508518\pi$
$997$	−31.1250	−	22.6137i	−0.985739	−	0.716182i	−0.958984	+	0.283460i	$0.908518\pi$
$998$	−6.45871	+	4.69253i	−0.204447	+	0.148539i
$999$	3.20483	+	1.04131i	0.101396	+	0.0329457i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.64.6	✓	56	1.1	even	1	trivial
429.2.bb.b.64.9	yes	56	13.12	even	2	inner
429.2.bb.b.181.6	yes	56	143.38	even	10	inner
429.2.bb.b.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)

\(f(q)\)	\(=\)	\(q+(-0.975059 - 0.316816i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.767667 - 0.557743i) q^{4} +(3.70008 - 1.20223i) q^{5} +(-0.975059 + 0.316816i) q^{6} +(1.98998 - 2.73897i) q^{7} +(1.77706 + 2.44591i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.975059 - 0.316816i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.767667 - 0.557743i) q^{4} +(3.70008 - 1.20223i) q^{5} +(-0.975059 + 0.316816i) q^{6} +(1.98998 - 2.73897i) q^{7} +(1.77706 + 2.44591i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.98868 q^{10} +(-0.561230 - 3.26880i) q^{11} -0.948888 q^{12} +(-2.50546 + 2.59281i) q^{13} +(-2.80810 + 2.04020i) q^{14} +(2.28678 - 3.14748i) q^{15} +(-0.371387 - 1.14301i) q^{16} +(1.31180 + 4.03730i) q^{17} +(-0.602619 + 0.829434i) q^{18} +(4.63399 + 6.37814i) q^{19} +(-3.51097 - 1.14078i) q^{20} -3.38556i q^{21} +(-0.488374 + 3.36507i) q^{22} -4.16221 q^{23} +(2.87534 + 0.934254i) q^{24} +(8.20018 - 5.95778i) q^{25} +(3.26442 - 1.73437i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.05528 + 0.992722i) q^{28} +(-7.33545 - 5.32952i) q^{29} +(-3.22691 + 2.34449i) q^{30} +(-1.22565 - 0.398237i) q^{31} -4.81446i q^{32} +(-2.37539 - 2.31463i) q^{33} -4.35220i q^{34} +(4.07022 - 12.5268i) q^{35} +(-0.767667 + 0.557743i) q^{36} +(-1.98070 + 2.72619i) q^{37} +(-2.49772 - 7.68718i) q^{38} +(-0.502948 + 3.57030i) q^{39} +(9.51581 + 6.91364i) q^{40} +(2.33852 + 3.21870i) q^{41} +(-1.07260 + 3.30112i) q^{42} +4.99247 q^{43} +(-1.39231 + 2.82237i) q^{44} -3.89050i q^{45} +(4.05840 + 1.31865i) q^{46} +(-6.21760 - 8.55779i) q^{47} +(-0.972304 - 0.706420i) q^{48} +(-1.37883 - 4.24362i) q^{49} +(-9.88318 + 3.21124i) q^{50} +(3.43433 + 2.49519i) q^{51} +(3.36948 - 0.593009i) q^{52} +(-2.55452 + 7.86201i) q^{53} +1.02524i q^{54} +(-6.00644 - 11.4201i) q^{55} +10.2356 q^{56} +(7.49795 + 2.43623i) q^{57} +(5.46402 + 7.52058i) q^{58} +(1.99949 - 2.75207i) q^{59} +(-3.51097 + 1.14078i) q^{60} +(0.721013 + 2.21905i) q^{61} +(1.06891 + 0.776608i) q^{62} +(-1.98998 - 2.73897i) q^{63} +(-2.26807 + 6.98040i) q^{64} +(-6.15327 + 12.6058i) q^{65} +(1.58284 + 3.00946i) q^{66} +2.88602i q^{67} +(1.24475 - 3.83095i) q^{68} +(-3.36730 + 2.44649i) q^{69} +(-7.93741 + 10.9249i) q^{70} +(3.85724 - 1.25329i) q^{71} +(2.87534 - 0.934254i) q^{72} +(-2.43247 + 3.34800i) q^{73} +(2.79500 - 2.03068i) q^{74} +(3.13219 - 9.63989i) q^{75} -7.48086i q^{76} +(-10.0700 - 4.96765i) q^{77} +(1.62153 - 3.32191i) q^{78} +(-2.89995 + 8.92514i) q^{79} +(-2.74833 - 3.78275i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.26046 - 3.87930i) q^{82} +(5.79804 - 1.88390i) q^{83} +(-1.88827 + 2.59898i) q^{84} +(9.70753 + 13.3613i) q^{85} +(-4.86795 - 1.58169i) q^{86} -9.06712 q^{87} +(6.99784 - 7.18155i) q^{88} -10.3837i q^{89} +(-1.23257 + 3.79346i) q^{90} +(2.11581 + 12.0220i) q^{91} +(3.19519 + 2.32144i) q^{92} +(-1.22565 + 0.398237i) q^{93} +(3.35128 + 10.3142i) q^{94} +(24.8141 + 18.0285i) q^{95} +(-2.82987 - 3.89498i) q^{96} +(-5.32888 - 1.73146i) q^{97} +4.57461i q^{98} +(-3.28224 - 0.476352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

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