LMFDB - Embedded newform 416.2.bg.a.77.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(77,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 4]))

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

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

chi := DirichletCharacter("416.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.3
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40524 + 0.159029i) q^{2} +(-0.700567 + 1.69132i) q^{3} +(1.94942 - 0.446949i) q^{4} +(-0.175581 - 0.423890i) q^{5} +(0.715499 - 2.48813i) q^{6} +(-0.506941 - 0.506941i) q^{7} +(-2.66833 + 0.938086i) q^{8} +(-0.248445 - 0.248445i) q^{9} +(0.314145 + 0.567746i) q^{10} +(2.80869 - 1.16340i) q^{11} +(-0.609767 + 3.61021i) q^{12} +(0.593888 + 3.55630i) q^{13} +(0.792994 + 0.631757i) q^{14} +0.839940 q^{15} +(3.60047 - 1.74258i) q^{16} +7.47949i q^{17} +(0.388636 + 0.309616i) q^{18} +(-0.221460 + 0.534652i) q^{19} +(-0.531738 - 0.747864i) q^{20} +(1.21255 - 0.502253i) q^{21} +(-3.76188 + 2.08152i) q^{22} +(-4.70684 - 4.70684i) q^{23} +(0.282743 - 5.17019i) q^{24} +(3.38668 - 3.38668i) q^{25} +(-1.40011 - 4.90303i) q^{26} +(-4.47970 + 1.85555i) q^{27} +(-1.21482 - 0.761664i) q^{28} +(-1.96036 + 4.73273i) q^{29} +(-1.18032 + 0.133575i) q^{30} +1.65672i q^{31} +(-4.78242 + 3.02133i) q^{32} +5.56542i q^{33} +(-1.18946 - 10.5105i) q^{34} +(-0.125878 + 0.303896i) q^{35} +(-0.595367 - 0.373282i) q^{36} +(3.18043 + 7.67825i) q^{37} +(0.226180 - 0.786535i) q^{38} +(-6.43090 - 1.48698i) q^{39} +(0.866154 + 0.966369i) q^{40} +(-5.59227 + 5.59227i) q^{41} +(-1.62405 + 0.898617i) q^{42} +(1.85495 + 4.47824i) q^{43} +(4.95533 - 3.52329i) q^{44} +(-0.0616912 + 0.148936i) q^{45} +(7.36278 + 5.86573i) q^{46} -10.1095 q^{47} +(0.424887 + 7.31035i) q^{48} -6.48602i q^{49} +(-4.22053 + 5.29769i) q^{50} +(-12.6502 - 5.23989i) q^{51} +(2.74722 + 6.66729i) q^{52} +(-1.65199 - 3.98827i) q^{53} +(5.99999 - 3.31991i) q^{54} +(-0.986304 - 0.986304i) q^{55} +(1.82824 + 0.877132i) q^{56} +(-0.749120 - 0.749120i) q^{57} +(2.00214 - 6.96239i) q^{58} +(4.82597 + 11.6509i) q^{59} +(1.63739 - 0.375410i) q^{60} +(-1.04472 + 2.52218i) q^{61} +(-0.263467 - 2.32810i) q^{62} +0.251894i q^{63} +(6.23999 - 5.00625i) q^{64} +(1.40321 - 0.876163i) q^{65} +(-0.885063 - 7.82078i) q^{66} +(12.9725 + 5.37337i) q^{67} +(3.34295 + 14.5807i) q^{68} +(11.2582 - 4.66331i) q^{69} +(0.128561 - 0.447067i) q^{70} +(-3.76193 - 3.76193i) q^{71} +(0.895998 + 0.429872i) q^{72} +(1.03025 - 1.03025i) q^{73} +(-5.69035 - 10.2840i) q^{74} +(3.35536 + 8.10055i) q^{75} +(-0.192757 + 1.14124i) q^{76} +(-2.01361 - 0.834065i) q^{77} +(9.27346 + 1.06686i) q^{78} -2.10903i q^{79} +(-1.37084 - 1.22024i) q^{80} -9.93061i q^{81} +(6.96917 - 8.74783i) q^{82} +(5.22750 - 12.6203i) q^{83} +(2.13928 - 1.52105i) q^{84} +(3.17048 - 1.31326i) q^{85} +(-3.31882 - 5.99803i) q^{86} +(-6.63119 - 6.63119i) q^{87} +(-6.40314 + 5.73912i) q^{88} +(6.45097 + 6.45097i) q^{89} +(0.0630061 - 0.219102i) q^{90} +(1.50177 - 2.10390i) q^{91} +(-11.2793 - 7.07189i) q^{92} +(-2.80205 - 1.16065i) q^{93} +(14.2063 - 1.60770i) q^{94} +0.265518 q^{95} +(-1.75963 - 10.2052i) q^{96} +2.02880i q^{97} +(1.03147 + 9.11444i) q^{98} +(-0.986846 - 0.408765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	−1.40524	+	0.159029i	−0.993657	+	0.112450i
$2$	−1.40524	+	0.159029i	−0.993657	+	0.112450i
$3$	−0.700567	+	1.69132i	−0.404473	+	0.976484i	0.582094	+	0.813122i	$0.302234\pi$
$3$	−0.700567	+	1.69132i	−0.404473	+	0.976484i	−0.986566	+	0.163362i	$0.947766\pi$
$4$	1.94942	−	0.446949i	0.974710	−	0.223474i
$5$	−0.175581	−	0.423890i	−0.0785222	−	0.189569i	0.879743	−	0.475449i	$-0.157714\pi$
$5$	−0.175581	−	0.423890i	−0.0785222	−	0.189569i	−0.958266	+	0.285879i	$0.907714\pi$
$6$	0.715499	−	2.48813i	0.292101	−	1.01577i
$7$	−0.506941	−	0.506941i	−0.191606	−	0.191606i	0.604784	−	0.796390i	$-0.293259\pi$
$7$	−0.506941	−	0.506941i	−0.191606	−	0.191606i	−0.796390	+	0.604784i	$0.793259\pi$
$8$	−2.66833	+	0.938086i	−0.943398	+	0.331664i
$9$	−0.248445	−	0.248445i	−0.0828151	−	0.0828151i
$10$	0.314145	+	0.567746i	0.0993413	+	0.179537i
$11$	2.80869	−	1.16340i	0.846851	−	0.350777i	0.0832998	−	0.996525i	$-0.473454\pi$
$11$	2.80869	−	1.16340i	0.846851	−	0.350777i	0.763551	+	0.645747i	$0.223454\pi$
$12$	−0.609767	+	3.61021i	−0.176024	+	1.04218i
$13$	0.593888	+	3.55630i	0.164715	+	0.986341i
$13$	0.593888	+	3.55630i	0.164715	+	0.986341i
$14$	0.792994	+	0.631757i	0.211936	+	0.168844i
$15$	0.839940			0.216871
$16$	3.60047	−	1.74258i	0.900118	−	0.435645i
$17$			7.47949i			1.81404i	0.421084	+	0.907022i	$0.361650\pi$
$17$			7.47949i			1.81404i	−0.421084	+	0.907022i	$0.638350\pi$
$18$	0.388636	+	0.309616i	0.0916025	+	0.0729773i
$19$	−0.221460	+	0.534652i	−0.0508065	+	0.122658i	−0.947245	−	0.320511i	$-0.896146\pi$
$19$	−0.221460	+	0.534652i	−0.0508065	+	0.122658i	0.896438	+	0.443168i	$0.146146\pi$
$20$	−0.531738	−	0.747864i	−0.118900	−	0.167227i
$21$	1.21255	−	0.502253i	0.264599	−	0.109601i
$22$	−3.76188	+	2.08152i	−0.802035	+	0.443781i
$23$	−4.70684	−	4.70684i	−0.981444	−	0.981444i	0.0183869	−	0.999831i	$-0.494147\pi$
$23$	−4.70684	−	4.70684i	−0.981444	−	0.981444i	−0.999831	+	0.0183869i	$0.994147\pi$
$24$	0.282743	−	5.17019i	0.0577147	−	1.05536i
$25$	3.38668	−	3.38668i	0.677336	−	0.677336i
$26$	−1.40011	−	4.90303i	−0.274585	−	0.961563i
$27$	−4.47970	+	1.85555i	−0.862119	+	0.357102i
$28$	−1.21482	−	0.761664i	−0.229579	−	0.143941i
$29$	−1.96036	+	4.73273i	−0.364030	+	0.878846i	0.630672	+	0.776049i	$0.282779\pi$
$29$	−1.96036	+	4.73273i	−0.364030	+	0.878846i	−0.994702	+	0.102797i	$0.967221\pi$
$30$	−1.18032	+	0.133575i	−0.215496	+	0.0243873i
$31$			1.65672i			0.297556i	0.988871	+	0.148778i	$0.0475340\pi$
$31$			1.65672i			0.297556i	−0.988871	+	0.148778i	$0.952466\pi$
$32$	−4.78242	+	3.02133i	−0.845421	+	0.534101i
$33$			5.56542i			0.968816i
$34$	−1.18946	−	10.5105i	−0.203990	−	1.80254i
$35$	−0.125878	+	0.303896i	−0.0212773	+	0.0513679i
$36$	−0.595367	−	0.373282i	−0.0992278	−	0.0622137i
$37$	3.18043	+	7.67825i	0.522860	+	1.26230i	0.936119	+	0.351683i	$0.114390\pi$
$37$	3.18043	+	7.67825i	0.522860	+	1.26230i	−0.413259	+	0.910613i	$0.635610\pi$
$38$	0.226180	−	0.786535i	0.0366913	−	0.127593i
$39$	−6.43090	−	1.48698i	−1.02977	−	0.238107i
$40$	0.866154	+	0.966369i	0.136951	+	0.152796i
$41$	−5.59227	+	5.59227i	−0.873366	+	0.873366i	−0.992838	−	0.119472i	$-0.961880\pi$
$41$	−5.59227	+	5.59227i	−0.873366	+	0.873366i	0.119472	+	0.992838i	$0.461880\pi$
$42$	−1.62405	+	0.898617i	−0.250596	+	0.138660i
$43$	1.85495	+	4.47824i	0.282877	+	0.682925i	0.999900	−	0.0141239i	$-0.00449594\pi$
$43$	1.85495	+	4.47824i	0.282877	+	0.682925i	−0.717023	+	0.697049i	$0.754496\pi$
$44$	4.95533	−	3.52329i	0.747044	−	0.531155i
$45$	−0.0616912	+	0.148936i	−0.00919639	+	0.0222020i
$46$	7.36278	+	5.86573i	1.08558	+	0.864855i
$47$	−10.1095			−1.47462			−0.737309	−	0.675555i	$-0.763904\pi$
$47$	−10.1095			−1.47462			−0.737309	+	0.675555i	$0.763904\pi$
$48$	0.424887	+	7.31035i	0.0613272	+	1.05516i
$49$		−	6.48602i		−	0.926575i
$50$	−4.22053	+	5.29769i	−0.596873	+	0.749207i
$51$	−12.6502	−	5.23989i	−1.77138	−	0.733731i
$52$	2.74722	+	6.66729i	0.380971	+	0.924587i
$53$	−1.65199	−	3.98827i	−0.226919	−	0.547830i	0.768881	−	0.639392i	$-0.220814\pi$
$53$	−1.65199	−	3.98827i	−0.226919	−	0.547830i	−0.995799	+	0.0915620i	$0.970814\pi$
$54$	5.99999	−	3.31991i	0.816495	−	0.451782i
$55$	−0.986304	−	0.986304i	−0.132993	−	0.132993i
$56$	1.82824	+	0.877132i	0.244309	+	0.117212i
$57$	−0.749120	−	0.749120i	−0.0992233	−	0.0992233i
$58$	2.00214	−	6.96239i	0.262894	−	0.914207i
$59$	4.82597	+	11.6509i	0.628288	+	1.51682i	0.841748	+	0.539870i	$0.181527\pi$
$59$	4.82597	+	11.6509i	0.628288	+	1.51682i	−0.213460	+	0.976952i	$0.568473\pi$
$60$	1.63739	−	0.375410i	0.211387	−	0.0484652i
$61$	−1.04472	+	2.52218i	−0.133763	+	0.322932i	−0.976542	−	0.215328i	$-0.930918\pi$
$61$	−1.04472	+	2.52218i	−0.133763	+	0.322932i	0.842779	+	0.538259i	$0.180918\pi$
$62$	−0.263467	−	2.32810i	−0.0334603	−	0.295669i
$63$			0.251894i			0.0317357i
$64$	6.23999	−	5.00625i	0.779999	−	0.625781i
$65$	1.40321	−	0.876163i	0.174046	−	0.108675i
$66$	−0.885063	−	7.82078i	−0.108944	−	0.962671i
$67$	12.9725	+	5.37337i	1.58484	+	0.656461i	0.989171	−	0.146771i	$-0.0468879\pi$
$67$	12.9725	+	5.37337i	1.58484	+	0.656461i	0.595667	+	0.803232i	$0.296888\pi$
$68$	3.34295	+	14.5807i	0.405392	+	1.76817i
$69$	11.2582	−	4.66331i	1.35533	−	0.561397i
$70$	0.128561	−	0.447067i	0.0153660	−	0.0534347i
$71$	−3.76193	−	3.76193i	−0.446458	−	0.446458i	0.447717	−	0.894175i	$-0.352237\pi$
$71$	−3.76193	−	3.76193i	−0.446458	−	0.446458i	−0.894175	+	0.447717i	$0.852237\pi$
$72$	0.895998	+	0.429872i	0.105594	+	0.0506609i
$73$	1.03025	−	1.03025i	0.120581	−	0.120581i	−0.644241	−	0.764822i	$-0.722827\pi$
$73$	1.03025	−	1.03025i	0.120581	−	0.120581i	0.764822	+	0.644241i	$0.222827\pi$
$74$	−5.69035	−	10.2840i	−0.661489	−	1.19549i
$75$	3.35536	+	8.10055i	0.387443	+	0.935371i
$76$	−0.192757	+	1.14124i	−0.0221107	+	0.130910i
$77$	−2.01361	−	0.834065i	−0.229472	−	0.0950505i
$78$	9.27346	+	1.06686i	1.05001	+	0.120799i
$79$		−	2.10903i		−	0.237285i	−0.992937	−	0.118642i	$-0.962146\pi$
$79$		−	2.10903i		−	0.237285i	0.992937	−	0.118642i	$-0.0378542\pi$
$80$	−1.37084	−	1.22024i	−0.153264	−	0.136427i
$81$		−	9.93061i		−	1.10340i
$82$	6.96917	−	8.74783i	0.769616	−	0.966037i
$83$	5.22750	−	12.6203i	0.573792	−	1.38526i	−0.324511	−	0.945882i	$-0.605200\pi$
$83$	5.22750	−	12.6203i	0.573792	−	1.38526i	0.898303	−	0.439376i	$-0.144800\pi$
$84$	2.13928	−	1.52105i	0.233414	−	0.165960i
$85$	3.17048	−	1.31326i	0.343887	−	0.142443i
$86$	−3.31882	−	5.99803i	−0.357878	−	0.646784i
$87$	−6.63119	−	6.63119i	−0.710938	−	0.710938i
$88$	−6.40314	+	5.73912i	−0.682577	+	0.611792i
$89$	6.45097	+	6.45097i	0.683802	+	0.683802i	0.960855	−	0.277053i	$-0.0893577\pi$
$89$	6.45097	+	6.45097i	0.683802	+	0.683802i	−0.277053	+	0.960855i	$0.589358\pi$
$90$	0.0630061	−	0.219102i	0.00664143	−	0.0230954i
$91$	1.50177	−	2.10390i	0.157428	−	0.220549i
$92$	−11.2793	−	7.07189i	−1.17595	−	0.737296i
$93$	−2.80205	−	1.16065i	−0.290559	−	0.120353i
$94$	14.2063	−	1.60770i	1.46527	−	0.165821i
$95$	0.265518			0.0272416
$96$	−1.75963	−	10.2052i	−0.179591	−	1.04157i
$97$			2.02880i			0.205993i	0.994682	+	0.102996i	$0.0328430\pi$
$97$			2.02880i			0.205993i	−0.994682	+	0.102996i	$0.967157\pi$
$98$	1.03147	+	9.11444i	0.104194	+	0.920698i
$99$	−0.986846	−	0.408765i	−0.0991817	−	0.0410824i
$100$	5.08839	−	8.11573i	0.508839	−	0.811573i
$101$	13.3773	−	5.54107i	1.33109	−	0.551357i	0.400127	−	0.916460i	$-0.368966\pi$
$101$	13.3773	−	5.54107i	1.33109	−	0.551357i	0.930967	+	0.365102i	$0.118966\pi$
$102$	18.6099	+	5.35157i	1.84266	+	0.529885i
$103$	2.38776	−	2.38776i	0.235273	−	0.235273i	−0.579616	−	0.814890i	$-0.696798\pi$
$103$	2.38776	−	2.38776i	0.235273	−	0.235273i	0.814890	+	0.579616i	$0.196798\pi$
$104$	−4.92081	−	8.93228i	−0.482525	−	0.875882i
$105$	−0.425800	−	0.425800i	−0.0415538	−	0.0415538i
$106$	2.95570	+	5.34177i	0.287083	+	0.518839i
$107$	−2.21975	−	5.35895i	−0.214591	−	0.518069i	0.779527	−	0.626368i	$-0.215459\pi$
$107$	−2.21975	−	5.35895i	−0.214591	−	0.518069i	−0.994118	+	0.108300i	$0.965459\pi$
$108$	−7.90349	+	5.61945i	−0.760513	+	0.540732i
$109$	2.27691	−	5.49694i	0.218088	−	0.526511i	−0.776535	−	0.630074i	$-0.783024\pi$
$109$	2.27691	−	5.49694i	0.218088	−	0.526511i	0.994623	+	0.103563i	$0.0330244\pi$
$110$	1.54285	+	1.22915i	0.147105	+	0.117195i
$111$	−15.2145			−1.44409
$112$	−2.70861	−	0.941841i	−0.255940	−	0.0889957i
$113$			3.04289i			0.286251i	0.989705	+	0.143125i	$0.0457152\pi$
$113$			3.04289i			0.286251i	−0.989705	+	0.143125i	$0.954285\pi$
$114$	1.17183	+	0.933564i	0.109752	+	0.0874363i
$115$	−1.16875	+	2.82161i	−0.108987	+	0.263117i
$116$	−1.70628	+	10.1023i	−0.158424	+	0.937971i
$117$	0.735999	−	1.03110i	0.0680431	−	0.0953249i
$118$	−8.63450	−	15.6049i	−0.794871	−	1.43655i
$119$	3.79166	−	3.79166i	0.347581	−	0.347581i
$120$	−2.24124	+	0.787936i	−0.204596	+	0.0719284i
$121$	−1.24294	+	1.24294i	−0.112995	+	0.112995i
$122$	1.06699	−	3.71041i	0.0966004	−	0.335925i
$123$	−5.54055	−	13.3761i	−0.499575	−	1.20608i
$124$	0.740470	+	3.22965i	0.0664961	+	0.290031i
$125$	−4.14967	−	1.71885i	−0.371157	−	0.153738i
$126$	−0.0400585	−	0.353973i	−0.00356869	−	0.0315344i
$127$	10.1645			0.901951			0.450975	−	0.892536i	$-0.351076\pi$
$127$	10.1645			0.901951			0.450975	+	0.892536i	$0.351076\pi$
$128$	−7.97257	+	8.02734i	−0.704682	+	0.709523i
$129$	−8.87365			−0.781281
$130$	−1.83251	+	1.45437i	−0.160722	+	0.127557i
$131$	−6.67537	+	16.1158i	−0.583230	+	1.40804i	0.306639	+	0.951826i	$0.400796\pi$
$131$	−6.67537	+	16.1158i	−0.583230	+	1.40804i	−0.889869	+	0.456216i	$0.849204\pi$
$132$	2.48746	+	10.8493i	0.216506	+	0.944314i
$133$	0.383304	−	0.158770i	0.0332367	−	0.0137671i
$134$	−19.0840	−	5.48789i	−1.64860	−	0.474082i
$135$	1.57310	+	1.57310i	0.135391	+	0.135391i
$136$	−7.01641	−	19.9578i	−0.601652	−	1.71136i
$137$	11.0554	−	11.0554i	0.944529	−	0.944529i	−0.0540116	−	0.998540i	$-0.517201\pi$
$137$	11.0554	−	11.0554i	0.944529	−	0.944529i	0.998540	+	0.0540116i	$0.0172008\pi$
$138$	−15.0790	+	8.34347i	−1.28361	+	0.710243i
$139$	1.56726	+	3.78370i	0.132933	+	0.320929i	0.976304	−	0.216403i	$-0.0694324\pi$
$139$	1.56726	+	3.78370i	0.132933	+	0.320929i	−0.843371	+	0.537332i	$0.819432\pi$
$140$	−0.109563	+	0.648683i	−0.00925976	+	0.0548237i
$141$	7.08237	−	17.0983i	0.596443	−	1.43994i
$142$	5.88468	+	4.68817i	0.493831	+	0.393422i
$143$	5.80544	+	9.29762i	0.485475	+	0.777506i
$144$	−1.32746	−	0.461585i	−0.110621	−	0.0384654i
$145$	2.35036			0.195187
$146$	−1.28391	+	1.61159i	−0.106257	+	0.133376i
$147$	10.9699	+	4.54389i	0.904785	+	0.374774i
$148$	9.63178	+	13.5466i	0.791728	+	1.11353i
$149$	15.7948	−	6.54242i	1.29396	−	0.535976i	0.373796	−	0.927511i	$-0.378056\pi$
$149$	15.7948	−	6.54242i	1.29396	−	0.535976i	0.920163	+	0.391535i	$0.128056\pi$
$150$	−6.00332	−	10.8497i	−0.490169	−	0.885870i
$151$	7.38587	−	7.38587i	0.601054	−	0.601054i	−0.339539	−	0.940592i	$-0.610271\pi$
$151$	7.38587	−	7.38587i	0.601054	−	0.601054i	0.940592	+	0.339539i	$0.110271\pi$
$152$	0.0893795	−	1.63438i	0.00724964	−	0.132566i
$153$	1.85825	−	1.85825i	0.150230	−	0.150230i
$154$	2.96226	+	0.851842i	0.238705	+	0.0686434i
$155$	0.702268	−	0.290889i	0.0564075	−	0.0233648i
$156$	−13.2011	−	0.0244562i	−1.05694	−	0.00195807i
$157$	−4.75046	+	11.4686i	−0.379128	+	0.915295i	0.613002	+	0.790081i	$0.289962\pi$
$157$	−4.75046	+	11.4686i	−0.379128	+	0.915295i	−0.992130	+	0.125214i	$0.960038\pi$
$158$	0.335397	+	2.96370i	0.0266828	+	0.235780i
$159$	7.90276			0.626730
$160$	2.12041	+	1.49673i	0.167633	+	0.118327i
$161$			4.77218i			0.376100i
$162$	1.57925	+	13.9549i	0.124078	+	1.09640i
$163$	−9.30261	−	3.85327i	−0.728636	−	0.301811i	−0.0126449	−	0.999920i	$-0.504025\pi$
$163$	−9.30261	−	3.85327i	−0.728636	−	0.301811i	−0.715992	+	0.698109i	$0.754025\pi$
$164$	−8.40222	+	13.4011i	−0.656103	+	1.04645i
$165$	2.35913	−	0.977183i	0.183658	−	0.0760736i
$166$	−5.33892	+	18.5659i	−0.414380	+	1.44099i
$167$	−9.11401	−	9.11401i	−0.705263	−	0.705263i	0.260272	−	0.965535i	$-0.416188\pi$
$167$	−9.11401	−	9.11401i	−0.705263	−	0.705263i	−0.965535	+	0.260272i	$0.916188\pi$
$168$	−2.76432	+	2.47765i	−0.213272	+	0.191155i
$169$	−12.2946	+	4.22409i	−0.945738	+	0.324930i
$170$	−4.24646	+	2.34964i	−0.325688	+	0.180210i
$171$	0.187853	−	0.0778111i	0.0143655	−	0.00595037i
$172$	5.61762	+	7.90090i	0.428339	+	0.602438i
$173$	19.9138	+	8.24857i	1.51402	+	0.627127i	0.976382	−	0.216050i	$-0.0693175\pi$
$173$	19.9138	+	8.24857i	1.51402	+	0.627127i	0.537636	+	0.843177i	$0.319317\pi$
$174$	10.3730	+	8.26389i	0.786375	+	0.626484i
$175$	−3.43369			−0.259563
$176$	8.08529	−	9.08314i	0.609452	−	0.684668i
$177$	−23.0864			−1.73528
$178$	−10.0911	−	8.03930i	−0.756359	−	0.602571i
$179$	−5.73403	−	2.37511i	−0.428581	−	0.177524i	0.157956	−	0.987446i	$-0.449509\pi$
$179$	−5.73403	−	2.37511i	−0.428581	−	0.177524i	−0.586538	+	0.809922i	$0.699509\pi$
$180$	−0.0536954	+	0.317911i	−0.00400222	+	0.0236957i
$181$	−5.33988	−	12.8916i	−0.396910	−	0.958225i	−0.988395	−	0.151909i	$-0.951458\pi$
$181$	−5.33988	−	12.8916i	−0.396910	−	0.958225i	0.591485	−	0.806316i	$-0.298542\pi$
$182$	−1.77577	+	3.19532i	−0.131629	+	0.236853i
$183$	−3.53391	−	3.53391i	−0.261234	−	0.261234i
$184$	16.9748	+	8.14399i	1.25140	+	0.600383i
$185$	2.69631	−	2.69631i	0.198237	−	0.198237i
$186$	4.12213	+	1.18538i	0.302249	+	0.0869165i
$187$	8.70161	+	21.0076i	0.636325	+	1.53622i
$188$	−19.7076	+	4.51842i	−1.43733	+	0.329539i
$189$	3.21160	+	1.33029i	0.233610	+	0.0967643i
$190$	−0.373117	+	0.0422250i	−0.0270688	+	0.00306333i
$191$	8.55602			0.619092			0.309546	−	0.950884i	$-0.399823\pi$
$191$	8.55602			0.619092			0.309546	+	0.950884i	$0.399823\pi$
$192$	4.09563	+	14.0610i	0.295577	+	1.01477i
$193$		−	4.53748i		−	0.326615i	−0.986575	−	0.163308i	$-0.947784\pi$
$193$		−	4.53748i		−	0.326615i	0.986575	−	0.163308i	$-0.0522163\pi$
$194$	−0.322637	−	2.85095i	−0.0231640	−	0.204686i
$195$	0.498830	+	2.98708i	0.0357220	+	0.213909i
$196$	−2.89892	−	12.6440i	−0.207066	−	0.903141i
$197$	2.86811	+	6.92422i	0.204344	+	0.493331i	0.992515	−	0.122127i	$-0.0389714\pi$
$197$	2.86811	+	6.92422i	0.204344	+	0.493331i	−0.788170	+	0.615457i	$0.788971\pi$
$198$	1.45176	+	0.417477i	0.103172	+	0.0296688i
$199$	3.26730	−	3.26730i	0.231613	−	0.231613i	−0.581753	−	0.813366i	$-0.697633\pi$
$199$	3.26730	−	3.26730i	0.231613	−	0.231613i	0.813366	+	0.581753i	$0.197633\pi$
$200$	−5.85979	+	12.2138i	−0.414350	+	0.863645i
$201$	−18.1762	+	18.1762i	−1.28205	+	1.28205i
$202$	−17.9172	+	9.91394i	−1.26065	+	0.697543i
$203$	3.39300	−	1.40543i	0.238142	−	0.0986417i
$204$	−27.0025	−	4.56075i	−1.89056	−	0.319316i
$205$	3.35240	+	1.38861i	0.234142	+	0.0969848i
$206$	−2.97567	+	3.73511i	−0.207325	+	0.260238i
$207$			2.33879i			0.162557i
$208$	8.33543	+	11.7695i	0.577958	+	0.816067i
$209$			1.75932i			0.121694i
$210$	0.666067	+	0.530638i	0.0459630	+	0.0366175i
$211$	−16.4456	−	6.81199i	−1.13216	−	0.468957i	−0.263646	−	0.964619i	$-0.584925\pi$
$211$	−16.4456	−	6.81199i	−1.13216	−	0.468957i	−0.868515	+	0.495663i	$0.834925\pi$
$212$	−5.00298	−	7.03645i	−0.343606	−	0.483265i
$213$	8.99810	−	3.72713i	0.616539	−	0.255379i
$214$	3.97151	+	7.17762i	0.271487	+	0.490652i
$215$	1.57259	−	1.57259i	0.107250	−	0.107250i
$216$	10.2127	−	9.15358i	0.694884	−	0.622822i
$217$	0.839860	−	0.839860i	0.0570134	−	0.0570134i
$218$	−2.32544	+	8.08663i	−0.157498	+	0.547696i
$219$	1.02072	+	2.46423i	0.0689737	+	0.166517i
$220$	−2.36355	−	1.48189i	−0.159350	−	0.0999092i
$221$	−26.5994	+	4.44198i	−1.78927	+	0.298800i
$222$	21.3800	−	2.41954i	1.43493	−	0.162389i
$223$		−	6.85054i		−	0.458746i	−0.973339	−	0.229373i	$-0.926332\pi$
$223$		−	6.85054i		−	0.458746i	0.973339	−	0.229373i	$-0.0736675\pi$
$224$	3.95604	+	0.892769i	0.264324	+	0.0596506i
$225$	−1.68281			−0.112187
$226$	−0.483907	−	4.27600i	−0.0321890	−	0.284435i
$227$	−3.00941	−	1.24654i	−0.199742	−	0.0827357i	0.280570	−	0.959834i	$-0.409476\pi$
$227$	−3.00941	−	1.24654i	−0.199742	−	0.0827357i	−0.480312	+	0.877098i	$0.659476\pi$
$228$	−1.79517	−	1.12553i	−0.118888	−	0.0745401i
$229$	−8.55595	−	20.6559i	−0.565393	−	1.36498i	−0.905401	−	0.424557i	$-0.860430\pi$
$229$	−8.55595	−	20.6559i	−0.565393	−	1.36498i	0.340008	−	0.940422i	$-0.389570\pi$
$230$	1.19366	−	4.15092i	0.0787077	−	0.273704i
$231$	2.82134	−	2.82134i	0.185631	−	0.185631i
$232$	0.791186	−	14.4675i	0.0519439	−	0.949837i
$233$	9.88307	+	9.88307i	0.647462	+	0.647462i	0.952379	−	0.304917i	$-0.0986288\pi$
$233$	9.88307	+	9.88307i	0.647462	+	0.647462i	−0.304917	+	0.952379i	$0.598629\pi$
$234$	−0.870283	+	1.56599i	−0.0568922	+	0.102372i
$235$	1.77503	+	4.28531i	0.115790	+	0.279543i
$236$	14.6152	+	20.5556i	0.951370	+	1.33806i
$237$	3.56705	+	1.47752i	0.231704	+	0.0959751i
$238$	−4.72522	+	5.93119i	−0.306291	+	0.384462i
$239$	7.85411			0.508040			0.254020	−	0.967199i	$-0.418247\pi$
$239$	7.85411			0.508040			0.254020	+	0.967199i	$0.418247\pi$
$240$	3.02418	−	1.46366i	0.195210	−	0.0944791i
$241$	12.2226			0.787330			0.393665	−	0.919254i	$-0.371207\pi$
$241$	12.2226			0.787330			0.393665	+	0.919254i	$0.371207\pi$
$242$	1.54897	−	1.94430i	0.0995718	−	0.124984i
$243$	3.35673	+	1.39040i	0.215334	+	0.0891943i
$244$	−0.909313	+	5.38372i	−0.0582128	+	0.344657i
$245$	−2.74936	+	1.13882i	−0.175650	+	0.0727567i
$246$	9.91301	+	17.9155i	0.632030	+	1.14225i
$247$	−2.03291	−	0.470056i	−0.129351	−	0.0299090i
$248$	−1.55415	−	4.42068i	−0.0986885	−	0.280714i
$249$	17.6827	+	17.6827i	1.12060	+	1.12060i
$250$	6.10464	+	1.75548i	0.386091	+	0.111027i
$251$	17.8379	−	7.38868i	1.12592	−	0.466369i	0.259525	−	0.965736i	$-0.416434\pi$
$251$	17.8379	−	7.38868i	1.12592	−	0.466369i	0.866391	+	0.499367i	$0.166434\pi$
$252$	0.112584	+	0.491048i	0.00709212	+	0.0309331i
$253$	−18.6960	−	7.74412i	−1.17540	−	0.486869i
$254$	−14.2836	+	1.61644i	−0.896230	+	0.101425i
$255$			6.28232i			0.393414i
$256$	9.92682	−	12.5482i	0.620426	−	0.784265i
$257$	−17.0900			−1.06605			−0.533023	−	0.846101i	$-0.678944\pi$
$257$	−17.0900			−1.06605			−0.533023	+	0.846101i	$0.678944\pi$
$258$	12.4696	−	1.41117i	0.776326	−	0.0878554i
$259$	2.28013	−	5.50471i	0.141680	−	0.342046i
$260$	2.34384	−	2.33517i	0.145359	−	0.144821i
$261$	1.66287	−	0.688783i	0.102929	−	0.0426346i
$262$	6.81765	−	23.7082i	0.421196	−	1.46470i
$263$	−2.63987	+	2.63987i	−0.162781	+	0.162781i	−0.783798	−	0.621016i	$-0.786720\pi$
$263$	−2.63987	+	2.63987i	−0.162781	+	0.162781i	0.621016	+	0.783798i	$0.286720\pi$
$264$	−5.22085	−	14.8504i	−0.321321	−	0.913979i
$265$	−1.40053	+	1.40053i	−0.0860337	+	0.0860337i
$266$	−0.513387	+	0.284067i	−0.0314778	+	0.0174173i
$267$	−15.4300	+	6.39131i	−0.944300	+	0.391142i
$268$	27.6904	+	4.67692i	1.69146	+	0.285688i
$269$	−11.0876	−	4.59264i	−0.676023	−	0.280018i	0.0181401	−	0.999835i	$-0.494225\pi$
$269$	−11.0876	−	4.59264i	−0.676023	−	0.280018i	−0.694163	+	0.719817i	$0.744225\pi$
$270$	−2.46076	−	1.96042i	−0.149757	−	0.119308i
$271$	−13.4345			−0.816088			−0.408044	−	0.912962i	$-0.633789\pi$
$271$	−13.4345			−0.816088			−0.408044	+	0.912962i	$0.633789\pi$
$272$	13.0336	+	26.9297i	0.790280	+	1.63285i
$273$	2.50628	+	4.01390i	0.151687	+	0.242932i
$274$	−13.7774	+	17.2937i	−0.832325	+	1.04475i
$275$	5.57207	−	13.4522i	0.336009	−	0.811197i
$276$	19.8627	−	14.1226i	1.19560	−	0.850081i
$277$	4.25991	+	10.2843i	0.255953	+	0.617925i	0.998663	−	0.0516878i	$-0.0164601\pi$
$277$	4.25991	+	10.2843i	0.255953	+	0.617925i	−0.742710	+	0.669613i	$0.766460\pi$
$278$	−2.80410	−	5.06778i	−0.168179	−	0.303945i
$279$	0.411605	−	0.411605i	0.0246421	−	0.0246421i
$280$	0.0508033	−	0.928981i	0.00303608	−	0.0555172i
$281$	−9.45491	−	9.45491i	−0.564032	−	0.564032i	0.366418	−	0.930450i	$-0.380584\pi$
$281$	−9.45491	−	9.45491i	−0.564032	−	0.564032i	−0.930450	+	0.366418i	$0.880584\pi$
$282$	−7.23332	+	25.1536i	−0.430738	+	1.49788i
$283$	20.2771	−	8.39905i	1.20535	−	0.499272i	0.312625	−	0.949877i	$-0.398792\pi$
$283$	20.2771	−	8.39905i	1.20535	−	0.499272i	0.892724	+	0.450605i	$0.148792\pi$
$284$	−9.01496	−	5.65218i	−0.534939	−	0.335395i
$285$	−0.186013	+	0.449076i	−0.0110185	+	0.0266009i
$286$	−9.63664	−	12.1422i	−0.569827	−	0.717982i
$287$	5.66990			0.334684
$288$	1.93881	+	0.437535i	0.114245	+	0.0257820i
$289$	−38.9428			−2.29075
$290$	−3.30283	+	0.373775i	−0.193949	+	0.0219488i
$291$	−3.43134	−	1.42131i	−0.201149	−	0.0833185i
$292$	1.54791	−	2.46885i	0.0905848	−	0.144478i
$293$	−10.1272	−	24.4493i	−0.591638	−	1.42834i	−0.881920	−	0.471399i	$-0.843749\pi$
$293$	−10.1272	−	24.4493i	−0.591638	−	1.42834i	0.290282	−	0.956941i	$-0.406251\pi$
$294$	−16.1380	−	4.64074i	−0.941190	−	0.270654i
$295$	4.09136	−	4.09136i	0.238208	−	0.238208i
$296$	−15.6893	−	17.5046i	−0.911923	−	1.01743i
$297$	−10.4233	+	10.4233i	−0.604824	+	0.604824i
$298$	−21.1551	+	11.7055i	−1.22548	+	0.678082i
$299$	13.9436	−	19.5343i	0.806380	−	1.12970i
$300$	10.1615	+	14.2917i	0.586677	+	0.825132i
$301$	1.32985	−	3.21055i	0.0766515	−	0.185053i
$302$	−9.20438	+	11.5535i	−0.529653	+	0.664830i
$303$			26.5072i			1.52280i
$304$	0.134313	+	2.31091i	0.00770340	+	0.132540i
$305$	1.25256			0.0717213
$306$	−2.31577	+	2.90680i	−0.132384	+	0.166171i
$307$	−3.83288	+	9.25340i	−0.218754	+	0.528120i	−0.994717	−	0.102660i	$-0.967265\pi$
$307$	−3.83288	+	9.25340i	−0.218754	+	0.528120i	0.775962	+	0.630779i	$0.217265\pi$
$308$	−4.29816	−	0.725962i	−0.244910	−	0.0413655i
$309$	2.36568	+	5.71126i	0.134579	+	0.324902i
$310$	−0.940598	+	0.520451i	−0.0534224	+	0.0295596i
$311$	−24.0387	−	24.0387i	−1.36311	−	1.36311i	−0.869923	−	0.493188i	$-0.835831\pi$
$311$	−24.0387	−	24.0387i	−1.36311	−	1.36311i	−0.493188	−	0.869923i	$-0.664169\pi$
$312$	18.5547	−	2.06499i	1.05045	−	0.116907i
$313$	−2.39237	+	2.39237i	−0.135225	+	0.135225i	−0.771479	−	0.636255i	$-0.780483\pi$
$313$	−2.39237	+	2.39237i	−0.135225	+	0.135225i	0.636255	+	0.771479i	$0.280483\pi$
$314$	4.85171	−	16.8717i	0.273798	−	0.952123i
$315$	0.106775	−	0.0442279i	0.00601612	−	0.00249196i
$316$	−0.942629	−	4.11139i	−0.0530270	−	0.231284i
$317$	14.5862	+	6.04181i	0.819243	+	0.339342i	0.752635	−	0.658437i	$-0.228782\pi$
$317$	14.5862	+	6.04181i	0.819243	+	0.339342i	0.0666080	+	0.997779i	$0.478782\pi$
$318$	−11.1053	+	1.25677i	−0.622755	+	0.0704760i
$319$			15.5734i			0.871945i
$320$	−3.21772	−	1.76607i	−0.179876	−	0.0987261i
$321$	10.6188			0.592682
$322$	−0.758915	−	6.70608i	−0.0422927	−	0.373715i
$323$	−3.99893	−	1.65641i	−0.222506	−	0.0921651i
$324$	−4.43848	−	19.3589i	−0.246582	−	1.07550i
$325$	14.0554	+	10.0328i	0.779652	+	0.556517i
$326$	13.6852	+	3.93539i	0.757954	+	0.217961i
$327$	7.70195	+	7.70195i	0.425919	+	0.425919i
$328$	9.67600	−	20.1681i	0.534268	−	1.11359i
$329$	5.12491	+	5.12491i	0.282545	+	0.282545i
$330$	−3.15975	+	1.74835i	−0.173938	+	0.0962435i
$331$	−0.516513	+	0.213947i	−0.0283901	+	0.0117596i	−0.396833	−	0.917891i	$-0.629891\pi$
$331$	−0.516513	+	0.213947i	−0.0283901	+	0.0117596i	0.368443	+	0.929650i	$0.379891\pi$
$332$	4.54996	−	26.9387i	0.249712	−	1.47845i
$333$	1.11746	−	2.69779i	0.0612365	−	0.147838i
$334$	14.2568	+	11.3580i	0.780097	+	0.621483i
$335$		−	6.44235i		−	0.351983i
$336$	3.49052	−	3.92131i	0.190423	−	0.213925i
$337$		−	6.06960i		−	0.330632i	−0.986241	−	0.165316i	$-0.947136\pi$
$337$		−	6.06960i		−	0.330632i	0.986241	−	0.165316i	$-0.0528645\pi$
$338$	16.6051	−	7.89107i	0.903201	−	0.429218i
$339$	−5.14649	−	2.13175i	−0.279519	−	0.115781i
$340$	5.59364	−	3.97713i	0.303358	−	0.215690i
$341$	1.92742	+	4.65321i	0.104376	+	0.251986i
$342$	−0.251605	+	0.139218i	−0.0136052	+	0.00752803i
$343$	−6.83662	+	6.83662i	−0.369143	+	0.369143i
$344$	−9.15059	−	10.2093i	−0.493367	−	0.550450i
$345$	−3.95346	−	3.95346i	−0.212847	−	0.212847i
$346$	−29.2955	−	8.42438i	−1.57494	−	0.452897i
$347$	6.60641	−	2.73646i	0.354651	−	0.146901i	−0.198243	−	0.980153i	$-0.563524\pi$
$347$	6.60641	−	2.73646i	0.354651	−	0.146901i	0.552894	+	0.833252i	$0.313524\pi$
$348$	−15.8908	−	9.96317i	−0.851835	−	0.534082i
$349$	13.1592	+	5.45071i	0.704394	+	0.291770i	0.705983	−	0.708229i	$-0.250506\pi$
$349$	13.1592	+	5.45071i	0.704394	+	0.291770i	−0.00158843	+	0.999999i	$0.500506\pi$
$350$	4.82518	−	0.546057i	0.257916	−	0.0291879i
$351$	−9.25936	−	14.8292i	−0.494228	−	0.791524i
$352$	−9.91732	+	14.0498i	−0.528595	+	0.748858i
$353$		−	16.7790i		−	0.893056i	−0.894770	−	0.446528i	$-0.852660\pi$
$353$		−	16.7790i		−	0.893056i	0.894770	−	0.446528i	$-0.147340\pi$
$354$	32.4420	−	3.67140i	1.72427	−	0.195133i
$355$	−0.934120	+	2.25517i	−0.0495779	+	0.119692i
$356$	15.4589	+	9.69240i	0.819321	+	0.513696i
$357$	3.75660	+	9.06922i	0.198820	+	0.479994i
$358$	8.43542	+	2.42573i	0.445826	+	0.128204i
$359$	22.2755	+	22.2755i	1.17566	+	1.17566i	0.980840	+	0.194815i	$0.0624107\pi$
$359$	22.2755	+	22.2755i	1.17566	+	1.17566i	0.194815	+	0.980840i	$0.437589\pi$
$360$	0.0248981	−	0.455282i	0.00131224	−	0.0239955i
$361$	13.1982	+	13.1982i	0.694643	+	0.694643i
$362$	9.55396	+	17.2666i	0.502145	+	0.907515i
$363$	−1.23145	−	2.97298i	−0.0646343	−	0.156041i
$364$	1.98724	−	4.77260i	0.104160	−	0.250152i
$365$	−0.617603	−	0.255819i	−0.0323268	−	0.0133902i
$366$	5.52800	+	4.40401i	0.288953	+	0.230201i
$367$			3.18172i			0.166084i	0.996546	+	0.0830422i	$0.0264636\pi$
$367$			3.18172i			0.166084i	−0.996546	+	0.0830422i	$0.973536\pi$
$368$	−25.1489	−	8.74480i	−1.31098	−	0.455854i
$369$	2.77875			0.144656
$370$	−3.36018	+	4.21776i	−0.174687	+	0.219271i
$371$	−1.18435	+	2.85928i	−0.0614885	+	0.148446i
$372$	−5.98111	−	1.01021i	−0.310106	−	0.0523771i
$373$	−9.99656	−	24.1338i	−0.517602	−	1.24960i	−0.939372	−	0.342900i	$-0.888591\pi$
$373$	−9.99656	−	24.1338i	−0.517602	−	1.24960i	0.421770	−	0.906703i	$-0.361409\pi$
$374$	−15.5687	−	28.1369i	−0.805038	−	1.45493i
$375$	5.81424	−	5.81424i	0.300246	−	0.300246i
$376$	26.9754	−	9.48356i	1.39115	−	0.489077i
$377$	−17.9953	−	4.16093i	−0.926803	−	0.214299i
$378$	−4.72464	−	1.35864i	−0.243009	−	0.0698810i
$379$	8.97361	+	21.6642i	0.460943	+	1.11282i	0.968011	+	0.250909i	$0.0807295\pi$
$379$	8.97361	+	21.6642i	0.460943	+	1.11282i	−0.507067	+	0.861906i	$0.669270\pi$
$380$	0.517606	−	0.118673i	0.0265526	−	0.00608779i
$381$	−7.12090	+	17.1914i	−0.364815	+	0.880740i
$382$	−12.0233	+	1.36066i	−0.615165	+	0.0696172i
$383$		−	16.5744i		−	0.846914i	−0.905916	−	0.423457i	$-0.860816\pi$
$383$		−	16.5744i		−	0.846914i	0.905916	−	0.423457i	$-0.139184\pi$
$384$	−7.99147	−	19.1078i	−0.407813	−	0.975093i
$385$			0.999996i			0.0509645i
$386$	0.721591	+	6.37627i	0.0367280	+	0.324544i
$387$	0.651745	−	1.57345i	0.0331301	−	0.0799830i
$388$	0.906768	+	3.95497i	0.0460341	+	0.200783i
$389$	−19.1205	+	7.91999i	−0.969450	+	0.401559i	−0.810507	−	0.585729i	$-0.800808\pi$
$389$	−19.1205	+	7.91999i	−0.969450	+	0.401559i	−0.158942	+	0.987288i	$0.550808\pi$
$390$	−1.17601	−	4.11825i	−0.0595496	−	0.208536i
$391$	35.2048	−	35.2048i	1.78038	−	1.78038i
$392$	6.08445	+	17.3069i	0.307311	+	0.874128i
$393$	−22.5804	−	22.5804i	−1.13903	−	1.13903i
$394$	−5.13154	−	9.27411i	−0.258523	−	0.467223i
$395$	−0.893997	+	0.370306i	−0.0449819	+	0.0186321i
$396$	−2.10647	−	0.355785i	−0.105854	−	0.0178789i
$397$	2.96082	−	7.14805i	0.148599	−	0.358751i	−0.831999	−	0.554777i	$-0.812804\pi$
$397$	2.96082	−	7.14805i	0.148599	−	0.358751i	0.980599	+	0.196026i	$0.0628037\pi$
$398$	−4.07175	+	5.11094i	−0.204099	+	0.256188i
$399$			0.759519i			0.0380235i
$400$	6.29209	−	18.0952i	0.314604	−	0.904761i
$401$	20.3932			1.01839			0.509194	−	0.860652i	$-0.329944\pi$
$401$	20.3932			1.01839			0.509194	+	0.860652i	$0.329944\pi$
$402$	22.6514	−	28.4325i	1.12975	−	1.41808i
$403$	−5.89181	+	0.983907i	−0.293492	+	0.0490119i
$404$	23.6015	−	16.7809i	1.17422	−	0.834879i
$405$	−4.20949	+	1.74363i	−0.209171	+	0.0866415i
$406$	−4.54449	+	2.51455i	−0.225539	+	0.124795i
$407$	17.8657	+	17.8657i	0.885569	+	0.885569i
$408$	38.6704	+	2.11478i	1.91447	+	0.104697i
$409$	8.99182	+	8.99182i	0.444617	+	0.444617i	0.893560	−	0.448943i	$-0.148200\pi$
$409$	8.99182	+	8.99182i	0.444617	+	0.444617i	−0.448943	+	0.893560i	$0.648200\pi$
$410$	−4.93177	−	1.41821i	−0.243563	−	0.0700403i
$411$	10.9532	+	26.4433i	0.540281	+	1.30435i
$412$	3.58755	−	5.72196i	0.176746	−	0.281901i
$413$	3.45985	−	8.35282i	0.170248	−	0.411015i
$414$	−0.371935	−	3.28656i	−0.0182796	−	0.161526i
$415$	−6.26747			−0.307658
$416$	−13.5850	−	15.2134i	−0.666059	−	0.745899i
$417$	−7.49741			−0.367150
$418$	−0.279782	−	2.47227i	−0.0136846	−	0.120923i
$419$	−3.33268	+	8.04580i	−0.162812	+	0.393063i	−0.984140	−	0.177393i	$-0.943234\pi$
$419$	−3.33268	+	8.04580i	−0.162812	+	0.393063i	0.821328	+	0.570456i	$0.193234\pi$
$420$	−1.02037	−	0.639752i	−0.0497891	−	0.0312167i
$421$	1.64925	+	3.98164i	0.0803795	+	0.194053i	0.958960	−	0.283541i	$-0.0915091\pi$
$421$	1.64925	+	3.98164i	0.0803795	+	0.194053i	−0.878581	+	0.477594i	$0.841509\pi$
$422$	24.1934	+	6.95718i	1.17772	+	0.338670i
$423$	2.51165	+	2.51165i	0.122121	+	0.122121i
$424$	8.14940	+	9.09230i	0.395770	+	0.441561i
$425$	25.3307	+	25.3307i	1.22872	+	1.22872i
$426$	−12.0518	+	6.66849i	−0.583911	+	0.323089i
$427$	1.80821	−	0.748983i	0.0875052	−	0.0362458i
$428$	−6.72240	−	9.45472i	−0.324939	−	0.457011i
$429$	−19.7923	+	3.30524i	−0.955583	+	0.159578i
$430$	−1.95978	+	2.45996i	−0.0945091	+	0.118630i
$431$	38.5679			1.85775			0.928874	−	0.370395i	$-0.120778\pi$
$431$	38.5679			1.85775			0.928874	+	0.370395i	$0.120778\pi$
$432$	−12.8956	+	14.4871i	−0.620440	+	0.697012i
$433$		−	36.5545i		−	1.75670i	−0.478022	−	0.878348i	$-0.658646\pi$
$433$		−	36.5545i		−	1.75670i	0.478022	−	0.878348i	$-0.341354\pi$
$434$	−1.04665	+	1.31377i	−0.0502406	+	0.0630630i
$435$	−1.64659	+	3.97521i	−0.0789477	+	0.190597i
$436$	1.98180	−	11.7335i	0.0949108	−	0.561933i
$437$	3.55890	−	1.47414i	0.170245	−	0.0705179i
$438$	−1.82624	−	3.30052i	−0.0872612	−	0.157705i
$439$	11.9277	+	11.9277i	0.569276	+	0.569276i	0.931926	−	0.362649i	$-0.118128\pi$
$439$	11.9277	+	11.9277i	0.569276	+	0.569276i	−0.362649	+	0.931926i	$0.618128\pi$
$440$	3.55703	+	1.70655i	0.169575	+	0.0813565i
$441$	−1.61142	+	1.61142i	−0.0767344	+	0.0767344i
$442$	36.6722	−	10.4721i	1.74432	−	0.498109i
$443$	−0.0395774	+	0.0163935i	−0.00188038	+	0.000778879i	−0.383623	−	0.923490i	$-0.625324\pi$
$443$	−0.0395774	+	0.0163935i	−0.00188038	+	0.000778879i	0.381743	+	0.924268i	$0.375324\pi$
$444$	−29.6594	+	6.80009i	−1.40757	+	0.322718i
$445$	1.60184	−	3.86717i	0.0759343	−	0.183322i
$446$	1.08943	+	9.62667i	0.0515862	+	0.455836i
$447$			31.2974i			1.48032i
$448$	−5.70118	−	0.625433i	−0.269355	−	0.0295489i
$449$		−	36.0879i		−	1.70309i	−0.524278	−	0.851547i	$-0.675665\pi$
$449$		−	36.0879i		−	1.70309i	0.524278	−	0.851547i	$-0.324335\pi$
$450$	2.36476	−	0.267616i	0.111476	−	0.0126155i
$451$	−9.20091	+	22.2130i	−0.433254	+	1.04597i
$452$	1.36002	+	5.93187i	0.0639697	+	0.279011i
$453$	7.31756	+	17.6662i	0.343809	+	0.830029i
$454$	4.42719	+	1.27311i	0.207778	+	0.0597499i
$455$	−1.15551	−	0.267180i	−0.0541709	−	0.0125256i
$456$	2.70164	+	1.29616i	0.126516	+	0.0606983i
$457$	−6.27526	+	6.27526i	−0.293544	+	0.293544i	−0.838479	−	0.544934i	$-0.816555\pi$
$457$	−6.27526	+	6.27526i	−0.293544	+	0.293544i	0.544934	+	0.838479i	$0.316555\pi$
$458$	15.3081	+	27.6659i	0.715299	+	1.29274i
$459$	−13.8786	−	33.5059i	−0.647798	−	1.56392i
$460$	−1.01727	+	6.02288i	−0.0474304	+	0.280818i
$461$	−13.3447	+	32.2169i	−0.621524	+	1.50049i	0.228389	+	0.973570i	$0.426654\pi$
$461$	−13.3447	+	32.2169i	−0.621524	+	1.50049i	−0.849913	+	0.526923i	$0.823346\pi$
$462$	−3.51600	+	4.41335i	−0.163579	+	0.205327i
$463$	−35.3169			−1.64132			−0.820658	−	0.571419i	$-0.806393\pi$
$463$	−35.3169			−1.64132			−0.820658	+	0.571419i	$0.806393\pi$
$464$	1.18894	+	20.4562i	0.0551951	+	0.949653i
$465$			1.39155i			0.0645314i
$466$	−15.4598	−	12.3164i	−0.716162	−	0.570548i
$467$	30.9379	+	12.8149i	1.43164	+	0.593003i	0.957755	−	0.287585i	$-0.0928525\pi$
$467$	30.9379	+	12.8149i	1.43164	+	0.593003i	0.473882	+	0.880589i	$0.342852\pi$
$468$	0.973923	−	2.33899i	0.0450196	−	0.108120i
$469$	−3.85229	−	9.30024i	−0.177882	−	0.429445i
$470$	−3.17584	−	5.73962i	−0.146491	−	0.264749i
$471$	−16.0691	−	16.0691i	−0.740424	−	0.740424i
$472$	−23.8069	−	26.5614i	−1.09580	−	1.22259i
$473$	10.4199	+	10.4199i	0.479109	+	0.479109i
$474$	−5.24754	−	1.50901i	−0.241027	−	0.0693111i
$475$	1.06068	+	2.56071i	0.0486674	+	0.117493i
$476$	5.69686	−	9.08622i	0.261115	−	0.416466i
$477$	−0.580436	+	1.40130i	−0.0265763	+	0.0641610i
$478$	−11.0369	+	1.24903i	−0.504818	+	0.0571293i
$479$			7.79173i			0.356013i	0.984029	+	0.178007i	$0.0569649\pi$
$479$			7.79173i			0.356013i	−0.984029	+	0.178007i	$0.943035\pi$
$480$	−4.01695	+	2.53774i	−0.183348	+	0.115831i
$481$	−25.4174	+	15.8706i	−1.15893	+	0.723637i
$482$	−17.1758	+	1.94375i	−0.782336	+	0.0885355i
$483$	−8.07128	−	3.34323i	−0.367256	−	0.152122i
$484$	−1.86749	+	2.97855i	−0.0848857	+	0.135389i
$485$	0.859986	−	0.356218i	0.0390500	−	0.0161750i
$486$	−4.93813	−	1.42004i	−0.223998	−	0.0644142i
$487$	14.0224	+	14.0224i	0.635416	+	0.635416i	0.949421	−	0.314005i	$-0.101671\pi$
$487$	14.0224	+	14.0224i	0.635416	+	0.635416i	−0.314005	+	0.949421i	$0.601671\pi$
$488$	0.421640	−	7.71004i	0.0190868	−	0.349017i
$489$	13.0342	−	13.0342i	0.589427	−	0.589427i
$490$	3.68242	−	2.03755i	0.166355	−	0.0920472i
$491$	1.46846	+	3.54518i	0.0662707	+	0.159992i	0.953545	−	0.301250i	$-0.0974040\pi$
$491$	1.46846	+	3.54518i	0.0662707	+	0.159992i	−0.887274	+	0.461242i	$0.847404\pi$
$492$	−16.7793	−	23.5992i	−0.756468	−	1.06394i
$493$	−35.3984	−	14.6625i	−1.59427	−	0.660366i
$494$	2.93148	+	0.337252i	0.131894	+	0.0151737i
$495$			0.490086i			0.0220277i
$496$	2.88697	+	5.96498i	0.129629	+	0.267836i
$497$			3.81415i			0.171088i
$498$	−27.6606	−	22.0365i	−1.23950	−	0.987478i
$499$	−2.91724	+	7.04284i	−0.130594	+	0.315281i	−0.975628	−	0.219431i	$-0.929580\pi$
$499$	−2.91724	+	7.04284i	−0.130594	+	0.315281i	0.845034	+	0.534712i	$0.179580\pi$
$500$	−8.85768	−	1.49607i	−0.396127	−	0.0669062i
$501$	21.7997	−	9.02972i	0.973938	−	0.403418i
$502$	−23.8915	+	13.2196i	−1.06633	+	0.590021i
$503$	16.3861	+	16.3861i	0.730621	+	0.730621i	0.970743	−	0.240122i	$-0.0771873\pi$
$503$	16.3861	+	16.3861i	0.730621	+	0.730621i	−0.240122	+	0.970743i	$0.577187\pi$
$504$	−0.236299	−	0.672138i	−0.0105256	−	0.0299394i
$505$	−4.69761	−	4.69761i	−0.209041	−	0.209041i
$506$	27.5039	+	7.90918i	1.22270	+	0.351606i
$507$	1.46890	−	23.7533i	0.0652363	−	1.05492i
$508$	19.8148	−	4.54300i	0.879140	−	0.201563i
$509$	0.175619	+	0.0727436i	0.00778416	+	0.00322431i	0.386572	−	0.922259i	$-0.373659\pi$
$509$	0.175619	+	0.0727436i	0.00778416	+	0.00322431i	−0.378788	+	0.925483i	$0.623659\pi$
$510$	−0.999071	−	8.82820i	−0.0442396	−	0.390919i
$511$	−1.04455			−0.0462081
$512$	−11.9541	+	19.2120i	−0.528300	+	0.849058i
$513$		−	2.80602i		−	0.123889i
$514$	24.0156	−	2.71781i	1.05928	−	0.119877i
$515$	−1.43140	−	0.592903i	−0.0630748	−	0.0261264i
$516$	−17.2985	+	3.96607i	−0.761522	+	0.174596i
$517$	−28.3944	+	11.7613i	−1.24878	+	0.517263i
$518$	−2.32872	+	8.09806i	−0.102318	+	0.355808i
$519$	−27.9019	+	27.9019i	−1.22476	+	1.22476i
$520$	−2.92230	+	3.65422i	−0.128152	+	0.160248i
$521$	15.6642	+	15.6642i	0.686260	+	0.686260i	0.961403	−	0.275144i	$-0.0887254\pi$
$521$	15.6642	+	15.6642i	0.686260	+	0.686260i	−0.275144	+	0.961403i	$0.588725\pi$
$522$	−2.22720	+	1.23235i	−0.0974818	+	0.0539386i
$523$	0.950538	+	2.29480i	0.0415641	+	0.100345i	0.943298	−	0.331946i	$-0.107705\pi$
$523$	0.950538	+	2.29480i	0.0415641	+	0.100345i	−0.901734	+	0.432291i	$0.857705\pi$
$524$	−5.81018	+	34.4000i	−0.253819	+	1.50277i
$525$	2.40553	−	5.80747i	0.104986	−	0.253459i
$526$	3.28985	−	4.12948i	0.143444	−	0.180054i
$527$	−12.3914			−0.539780
$528$	9.69820	+	20.0382i	0.422060	+	0.872049i
$529$			21.3087i			0.926465i
$530$	1.74536	−	2.19081i	0.0758135	−	0.0951626i
$531$	1.69563	−	4.09361i	0.0735841	−	0.177648i
$532$	0.676259	−	0.480826i	0.0293195	−	0.0208465i
$533$	−23.2090	−	16.5666i	−1.00529	−	0.717580i
$534$	20.6665	−	11.4352i	0.894327	−	0.494848i
$535$	−1.88186	+	1.88186i	−0.0813598	+	0.0813598i
$536$	−39.6555	−	2.16865i	−1.71286	−	0.0936712i
$537$	8.03414	−	8.03414i	0.346699	−	0.346699i
$538$	16.3112	+	4.69052i	0.703224	+	0.202223i
$539$	−7.54581	−	18.2172i	−0.325021	−	0.784671i
$540$	3.76973	+	2.36354i	0.162223	+	0.101711i
$541$	−14.1477	−	5.86018i	−0.608258	−	0.251949i	0.0572256	−	0.998361i	$-0.481775\pi$
$541$	−14.1477	−	5.86018i	−0.608258	−	0.251949i	−0.665483	+	0.746413i	$0.731775\pi$
$542$	18.8787	−	2.13647i	0.810911	−	0.0917694i
$543$	25.5448			1.09623
$544$	−22.5980	−	35.7701i	−0.968882	−	1.53363i
$545$	−2.72988			−0.116935
$546$	−4.16026	−	5.24193i	−0.178043	−	0.224334i
$547$	−13.6172	+	32.8748i	−0.582228	+	1.40562i	0.308560	+	0.951205i	$0.400153\pi$
$547$	−13.6172	+	32.8748i	−0.582228	+	1.40562i	−0.890788	+	0.454419i	$0.849847\pi$
$548$	16.6105	−	26.4929i	0.709563	−	1.13172i
$549$	0.886179	−	0.367067i	0.0378212	−	0.0156661i
$550$	−5.69084	+	19.7897i	−0.242658	+	0.843836i
$551$	−2.09622	−	2.09622i	−0.0893021	−	0.0893021i
$552$	−25.6661	+	23.0044i	−1.09242	+	0.979134i
$553$	−1.06915	+	1.06915i	−0.0454651	+	0.0454651i
$554$	−7.62171	−	13.7745i	−0.323815	−	0.585224i
$555$	2.67137	+	6.44926i	0.113393	+	0.273756i
$556$	4.74636	+	6.67553i	0.201291	+	0.283106i
$557$	−10.3593	+	25.0095i	−0.438937	+	1.05969i	0.537380	+	0.843340i	$0.319414\pi$
$557$	−10.3593	+	25.0095i	−0.438937	+	1.05969i	−0.976317	+	0.216347i	$0.930586\pi$
$558$	−0.512948	+	0.643862i	−0.0217148	+	0.0272569i
$559$	−14.8244	+	9.25633i	−0.627003	+	0.391501i
$560$	0.0763438	+	1.31352i	0.00322611	+	0.0555065i
$561$	−41.6265			−1.75747
$562$	14.7900	+	11.7828i	0.623881	+	0.497029i
$563$	−6.34489	−	2.62814i	−0.267405	−	0.110763i	0.244952	−	0.969535i	$-0.421228\pi$
$563$	−6.34489	−	2.62814i	−0.267405	−	0.110763i	−0.512357	+	0.858772i	$0.671228\pi$
$564$	6.16442	−	36.4973i	0.259569	−	1.53681i
$565$	1.28985	−	0.534273i	0.0542644	−	0.0224770i
$566$	−27.1586	+	15.0274i	−1.14156	+	0.631647i
$567$	−5.03423	+	5.03423i	−0.211418	+	0.211418i
$568$	13.5671	+	6.50905i	0.569262	+	0.273114i
$569$	12.1057	−	12.1057i	0.507498	−	0.507498i	−0.406259	−	0.913758i	$-0.633167\pi$
$569$	12.1057	−	12.1057i	0.507498	−	0.507498i	0.913758	+	0.406259i	$0.133167\pi$
$570$	0.189978	−	0.660642i	0.00795730	−	0.0276713i
$571$	21.8489	−	9.05013i	0.914350	−	0.378736i	0.124630	−	0.992203i	$-0.460226\pi$
$571$	21.8489	−	9.05013i	0.914350	−	0.378736i	0.789720	+	0.613467i	$0.210226\pi$
$572$	15.4728	+	15.5302i	0.646950	+	0.649351i
$573$	−5.99407	+	14.4710i	−0.250406	+	0.604533i
$574$	−7.96759	+	0.901678i	−0.332561	+	0.0376353i
$575$	−31.8811			−1.32953
$576$	−2.79408	−	0.306517i	−0.116420	−	0.0127715i
$577$		−	44.9896i		−	1.87294i	−0.350748	−	0.936470i	$-0.614073\pi$
$577$		−	44.9896i		−	1.87294i	0.350748	−	0.936470i	$-0.385927\pi$
$578$	54.7242	−	6.19304i	2.27622	−	0.257596i
$579$	7.67433	+	3.17881i	0.318934	+	0.132107i
$580$	4.58184	−	1.05049i	0.190250	−	0.0436192i
$581$	−9.04778	+	3.74771i	−0.375365	+	0.155481i
$582$	5.04790	+	1.45160i	0.209242	+	0.0601708i
$583$	−9.27987	−	9.27987i	−0.384333	−	0.384333i
$584$	−1.78258	+	3.71550i	−0.0737636	+	0.153748i
$585$	−0.566299	−	0.130942i	−0.0234136	−	0.00541377i
$586$	18.1193	+	32.7466i	0.748503	+	1.35275i
$587$	6.14474	−	2.54523i	0.253620	−	0.105053i	−0.252251	−	0.967662i	$-0.581171\pi$
$587$	6.14474	−	2.54523i	0.253620	−	0.105053i	0.505872	+	0.862609i	$0.331171\pi$
$588$	23.4159	+	3.95496i	0.965655	+	0.163100i
$589$	−0.885770	−	0.366898i	−0.0364975	−	0.0151178i
$590$	−5.09872	+	6.40001i	−0.209911	+	0.263484i
$591$	−13.7204			−0.564381
$592$	24.8310	+	22.1032i	1.02055	+	0.908434i
$593$	43.5965			1.79029			0.895146	−	0.445773i	$-0.147071\pi$
$593$	43.5965			1.79029			0.895146	+	0.445773i	$0.147071\pi$
$594$	12.9897	−	16.3049i	0.532975	−	0.669000i
$595$	−2.27299	−	0.941504i	−0.0931836	−	0.0385979i
$596$	27.8665	−	19.8134i	1.14146	−	0.811587i
$597$	3.23708	+	7.81501i	0.132485	+	0.319847i
$598$	−16.4877	+	29.6679i	−0.674231	+	1.21321i
$599$	−6.56778	−	6.56778i	−0.268352	−	0.268352i	0.560084	−	0.828436i	$-0.310769\pi$
$599$	−6.56778	−	6.56778i	−0.268352	−	0.268352i	−0.828436	+	0.560084i	$0.810769\pi$
$600$	−16.5522	−	18.4673i	−0.675742	−	0.753926i
$601$	−15.0617	+	15.0617i	−0.614379	+	0.614379i	−0.944084	−	0.329705i	$-0.893051\pi$
$601$	−15.0617	+	15.0617i	−0.614379	+	0.614379i	0.329705	+	0.944084i	$0.393051\pi$
$602$	−1.35820	+	4.72309i	−0.0553560	+	0.192499i
$603$	−1.88796	−	4.55793i	−0.0768836	−	0.185613i
$604$	11.0971	−	17.6993i	0.451533	−	0.720173i
$605$	0.745108	+	0.308634i	0.0302930	+	0.0125478i
$606$	−4.21542	−	37.2491i	−0.171240	−	1.51314i
$607$	5.35938			0.217531			0.108765	−	0.994067i	$-0.465310\pi$
$607$	5.35938			0.217531			0.108765	+	0.994067i	$0.465310\pi$
$608$	−0.556245	−	3.22604i	−0.0225587	−	0.130833i
$609$			6.72325i			0.272440i
$610$	−1.76015	+	0.199193i	−0.0712664	+	0.00806509i
$611$	−6.00390	−	35.9524i	−0.242892	−	1.45448i
$612$	2.79196	−	4.45304i	0.112858	−	0.180004i
$613$	−3.41173	−	8.23664i	−0.137798	−	0.332675i	0.839883	−	0.542767i	$-0.182623\pi$
$613$	−3.41173	−	8.23664i	−0.137798	−	0.332675i	−0.977681	+	0.210093i	$0.932623\pi$
$614$	3.91458	−	13.6128i	0.157980	−	0.549369i
$615$	−4.69717	+	4.69717i	−0.189408	+	0.189408i
$616$	6.15541	+	0.336622i	0.248008	+	0.0135629i
$617$	19.3559	−	19.3559i	0.779239	−	0.779239i	−0.200463	−	0.979701i	$-0.564245\pi$
$617$	19.3559	−	19.3559i	0.779239	−	0.779239i	0.979701	+	0.200463i	$0.0642445\pi$
$618$	−4.23261	−	7.64950i	−0.170261	−	0.307708i
$619$	−4.03091	+	1.66966i	−0.162016	+	0.0671092i	−0.462217	−	0.886767i	$-0.652946\pi$
$619$	−4.03091	+	1.66966i	−0.162016	+	0.0671092i	0.300202	+	0.953876i	$0.402946\pi$
$620$	1.23900	−	0.880942i	0.0497595	−	0.0353795i
$621$	29.8190	+	12.3515i	1.19660	+	0.495647i
$622$	37.6031	+	29.9574i	1.50775	+	1.20118i
$623$		−	6.54052i		−	0.262041i
$624$	−25.7455	+	5.85255i	−1.03064	+	0.234290i
$625$		−	21.8866i		−	0.875466i
$626$	2.98141	−	3.74232i	0.119161	−	0.149573i
$627$	−2.97557	−	1.23252i	−0.118833	−	0.0492221i
$628$	−4.13475	+	24.4804i	−0.164994	+	0.976873i
$629$	−57.4294	+	23.7880i	−2.28986	+	0.948491i
$630$	−0.143012	+	0.0791313i	−0.00569774	+	0.00315267i
$631$	−22.6765	+	22.6765i	−0.902739	+	0.902739i	−0.995672	−	0.0929332i	$-0.970376\pi$
$631$	−22.6765	+	22.6765i	−0.902739	+	0.902739i	0.0929332	+	0.995672i	$0.470376\pi$
$632$	1.97845	+	5.62760i	0.0786986	+	0.223854i
$633$	23.0425	−	23.0425i	0.915857	−	0.915857i
$634$	−21.4580	−	6.17058i	−0.852206	−	0.245065i
$635$	−1.78469	−	4.30862i	−0.0708232	−	0.170982i
$636$	15.4058	−	3.53213i	0.610880	−	0.140058i
$637$	23.0663	−	3.85197i	0.913919	−	0.152621i
$638$	−2.47663	−	21.8845i	−0.0980506	−	0.866415i
$639$			1.86927i			0.0739470i
$640$	4.80254	+	1.97004i	0.189837	+	0.0778728i
$641$	3.10301			0.122561			0.0612807	−	0.998121i	$-0.480482\pi$
$641$	3.10301			0.122561			0.0612807	+	0.998121i	$0.480482\pi$
$642$	−14.9220	+	1.68869i	−0.588923	+	0.0666473i
$643$	2.32900	+	0.964705i	0.0918469	+	0.0380442i	0.428134	−	0.903715i	$-0.359171\pi$
$643$	2.32900	+	0.964705i	0.0918469	+	0.0380442i	−0.336287	+	0.941760i	$0.609171\pi$
$644$	2.13292	+	9.30298i	0.0840488	+	0.366589i
$645$	1.55804	+	3.76145i	0.0613479	+	0.148107i
$646$	5.88289	+	1.69171i	0.231459	+	0.0665596i
$647$	4.68376	−	4.68376i	0.184138	−	0.184138i	−0.609018	−	0.793156i	$-0.708436\pi$
$647$	4.68376	−	4.68376i	0.184138	−	0.184138i	0.793156	+	0.609018i	$0.208436\pi$
$648$	9.31577	+	26.4982i	0.365958	+	1.04095i
$649$	27.1093	+	27.1093i	1.06413	+	1.06413i
$650$	−21.3467	−	11.8633i	−0.837287	−	0.465315i
$651$	0.832093	+	2.00885i	0.0326123	+	0.0787330i
$652$	−19.8569	−	3.35384i	−0.777656	−	0.131347i
$653$	26.5009	+	10.9770i	1.03706	+	0.429565i	0.835257	−	0.549860i	$-0.185319\pi$
$653$	26.5009	+	10.9770i	1.03706	+	0.429565i	0.201806	+	0.979426i	$0.435319\pi$
$654$	−12.0479	−	9.59828i	−0.471112	−	0.375322i
$655$	8.00339			0.312718
$656$	−10.3898	+	29.8798i	−0.405655	+	1.16661i
$657$	−0.511920			−0.0199719
$658$	−8.01675	−	6.38673i	−0.312525	−	0.248981i
$659$	3.13368	+	1.29801i	0.122071	+	0.0505635i	0.442883	−	0.896579i	$-0.353956\pi$
$659$	3.13368	+	1.29801i	0.122071	+	0.0505635i	−0.320812	+	0.947143i	$0.603956\pi$
$660$	4.16218	−	2.95935i	0.162013	−	0.115192i
$661$	−1.23577	+	0.511874i	−0.0480660	+	0.0199096i	−0.406587	−	0.913612i	$-0.633281\pi$
$661$	−1.23577	+	0.511874i	−0.0480660	+	0.0199096i	0.358521	+	0.933522i	$0.383281\pi$
$662$	0.691803	−	0.382788i	0.0268877	−	0.0148775i
$663$	11.1218	−	48.0999i	0.431936	−	1.86805i
$664$	−2.10977	+	38.5790i	−0.0818751	+	1.49715i
$665$	−0.134602	−	0.134602i	−0.00521964	−	0.00521964i
$666$	−1.14128	+	3.96876i	−0.0442236	+	0.153786i
$667$	31.5033	−	13.0491i	1.21981	−	0.505263i
$668$	−21.8405	−	13.6935i	−0.845036	−	0.529819i
$669$	11.5864	+	4.79926i	0.447958	+	0.185550i
$670$	1.02452	+	9.05308i	0.0395807	+	0.349751i
$671$			8.29942i			0.320396i
$672$	−4.28143	+	6.06548i	−0.165160	+	0.233981i
$673$	20.1322			0.776038			0.388019	−	0.921651i	$-0.373159\pi$
$673$	20.1322			0.776038			0.388019	+	0.921651i	$0.373159\pi$
$674$	0.965243	+	8.52927i	0.0371798	+	0.328535i
$675$	−8.88716	+	21.4555i	−0.342067	+	0.825822i
$676$	−22.0794	+	13.7296i	−0.849207	+	0.528061i
$677$	−4.76953	+	1.97560i	−0.183308	+	0.0759286i	−0.472450	−	0.881358i	$-0.656630\pi$
$677$	−4.76953	+	1.97560i	−0.183308	+	0.0759286i	0.289142	+	0.957286i	$0.406630\pi$
$678$	7.57109	+	2.17718i	0.290766	+	0.0836142i
$679$	1.02848	−	1.02848i	0.0394694	−	0.0394694i
$680$	−7.22795	+	6.47839i	−0.277179	+	0.248435i
$681$	4.21659	−	4.21659i	0.161580	−	0.161580i
$682$	−3.44850	−	6.23238i	−0.132050	−	0.238650i
$683$	−10.3738	+	4.29696i	−0.396942	+	0.164419i	−0.572220	−	0.820100i	$-0.693918\pi$
$683$	−10.3738	+	4.29696i	−0.396942	+	0.164419i	0.175278	+	0.984519i	$0.443918\pi$
$684$	0.331426	−	0.235647i	0.0126724	−	0.00901019i
$685$	−6.62741	−	2.74516i	−0.253220	−	0.104887i
$686$	8.51989	−	10.6943i	0.325291	−	0.408311i
$687$	40.9297			1.56157
$688$	14.4824	+	12.8914i	0.552136	+	0.491480i
$689$	13.2024	−	8.24357i	0.502971	−	0.314055i
$690$	6.18429	+	4.92686i	0.235432	+	0.187562i
$691$	12.9512	−	31.2671i	0.492688	−	1.18946i	−0.460658	−	0.887578i	$-0.652387\pi$
$691$	12.9512	−	31.2671i	0.492688	−	1.18946i	0.953347	−	0.301878i	$-0.0976134\pi$
$692$	42.5070	+	7.17947i	1.61588	+	0.272922i
$693$	0.293053	+	0.707492i	0.0111322	+	0.0268754i
$694$	−8.84843	+	4.89601i	−0.335882	+	0.185850i
$695$	1.32869	−	1.32869i	0.0504001	−	0.0504001i
$696$	23.9149	+	11.4736i	0.906490	+	0.434905i
$697$	−41.8273	−	41.8273i	−1.58432	−	1.58432i
$698$	−19.3587	−	5.56688i	−0.732736	−	0.210710i
$699$	−23.6392	+	9.79167i	−0.894116	+	0.370355i
$700$	−6.69371	+	1.53468i	−0.252998	+	0.0580056i
$701$	14.4084	−	34.7848i	0.544196	−	1.31381i	−0.377542	−	0.925992i	$-0.623231\pi$
$701$	14.4084	−	34.7848i	0.544196	−	1.31381i	0.921738	−	0.387813i	$-0.126769\pi$
$702$	15.3699	+	19.3661i	0.580100	+	0.730928i
$703$	−4.80953			−0.181395
$704$	11.7019	−	21.3206i	0.441033	−	0.803549i
$705$	−8.49135			−0.319803
$706$	2.66835	+	23.5786i	0.100424	+	0.887391i
$707$	−9.59052	−	3.97252i	−0.360688	−	0.149402i
$708$	−45.0050	+	10.3184i	−1.69139	+	0.387790i
$709$	12.7079	+	30.6797i	0.477257	+	1.15220i	0.960890	+	0.276929i	$0.0893166\pi$
$709$	12.7079	+	30.6797i	0.477257	+	1.15220i	−0.483634	+	0.875270i	$0.660683\pi$
$710$	0.954030	−	3.31761i	0.0358041	−	0.124508i
$711$	−0.523979	+	0.523979i	−0.0196508	+	0.0196508i
$712$	−23.2649	−	11.1618i	−0.871889	−	0.418305i
$713$	7.79792	−	7.79792i	0.292035	−	0.292035i
$714$	−6.72120	−	12.1471i	−0.251535	−	0.454592i
$715$	2.92184	−	4.09335i	0.109271	−	0.153083i
$716$	−12.2396	−	2.06727i	−0.457415	−	0.0772576i
$717$	−5.50233	+	13.2838i	−0.205488	+	0.496093i
$718$	−34.8449	−	27.7600i	−1.30040	−	1.03600i
$719$			7.04807i			0.262848i	0.991326	+	0.131424i	$0.0419550\pi$
$719$			7.04807i			0.262848i	−0.991326	+	0.131424i	$0.958045\pi$
$720$	0.0374151	+	0.643742i	0.00139438	+	0.0239908i
$721$	−2.42091			−0.0901594
$722$	−20.6456	−	16.4478i	−0.768350	−	0.612124i
$723$	−8.56278	+	20.6724i	−0.318453	+	0.768814i
$724$	−16.1715	−	22.7445i	−0.601011	−	0.845292i
$725$	9.38913	+	22.6674i	0.348703	+	0.841845i
$726$	2.20327	+	3.98192i	0.0817712	+	0.147783i
$727$	31.9228	+	31.9228i	1.18395	+	1.18395i	0.978712	+	0.205238i	$0.0657967\pi$
$727$	31.9228	+	31.9228i	1.18395	+	1.18395i	0.205238	+	0.978712i	$0.434203\pi$
$728$	−2.03358	+	7.02270i	−0.0753695	+	0.260278i
$729$	16.3628	−	16.3628i	0.606029	−	0.606029i
$730$	0.908565	+	0.261272i	0.0336275	+	0.00967010i
$731$	−33.4950	+	13.8741i	−1.23886	+	0.513151i
$732$	−8.46855	−	5.30959i	−0.313006	−	0.196248i
$733$	−16.0717	−	6.65711i	−0.593621	−	0.245886i	0.0655866	−	0.997847i	$-0.479108\pi$
$733$	−16.0717	−	6.65711i	−0.593621	−	0.245886i	−0.659208	+	0.751961i	$0.729108\pi$
$734$	−0.505985	−	4.47109i	−0.0186763	−	0.165031i
$735$		−	5.44787i		−	0.200948i
$736$	36.7310	+	8.28917i	1.35392	+	0.305543i
$737$	42.6869			1.57239
$738$	−3.90482	+	0.441901i	−0.143738	+	0.0162666i
$739$	−36.4457	−	15.0963i	−1.34068	−	0.555326i	−0.406995	−	0.913430i	$-0.633423\pi$
$739$	−36.4457	−	15.0963i	−1.34068	−	0.555326i	−0.933682	+	0.358104i	$0.883423\pi$
$740$	4.05112	−	6.46135i	0.148922	−	0.237524i
$741$	2.21920	−	3.10899i	0.0815245	−	0.114212i
$742$	1.20959	−	4.20633i	0.0444056	−	0.154419i
$743$	−28.1734	−	28.1734i	−1.03358	−	1.03358i	−0.999416	−	0.0341664i	$-0.989122\pi$
$743$	−28.1734	−	28.1734i	−1.03358	−	1.03358i	−0.0341664	−	0.999416i	$-0.510878\pi$
$744$	8.56557	+	0.468427i	0.314029	+	0.0171734i
$745$	−5.54653	−	5.54653i	−0.203209	−	0.203209i
$746$	17.8856	+	32.3242i	0.654838	+	1.18347i
$747$	−4.43420	+	1.83671i	−0.162239	+	0.0672016i
$748$	26.3524	+	37.0634i	0.963539	+	1.35517i
$749$	−1.59139	+	3.84195i	−0.0581480	+	0.140382i
$750$	−7.24579	+	9.09506i	−0.264579	+	0.332105i
$751$			41.7567i			1.52372i	0.647739	+	0.761862i	$0.275715\pi$
$751$			41.7567i			1.52372i	−0.647739	+	0.761862i	$0.724285\pi$
$752$	−36.3989	+	17.6166i	−1.32733	+	0.642411i
$753$			35.3458i			1.28807i
$754$	25.9494	+	2.98535i	0.945023	+	0.108720i
$755$	−4.42762	−	1.83398i	−0.161137	−	0.0667453i
$756$	6.85533	+	1.15787i	0.249326	+	0.0421113i
$757$	1.36517	+	3.29582i	0.0496181	+	0.119789i	0.946745	−	0.321984i	$-0.104350\pi$
$757$	1.36517	+	3.29582i	0.0496181	+	0.119789i	−0.897127	+	0.441773i	$0.854350\pi$
$758$	−16.0553	−	29.0164i	−0.583156	−	1.05392i
$759$	26.1956	−	26.1956i	0.950839	−	0.950839i
$760$	−0.708490	+	0.249079i	−0.0256996	+	0.00903503i
$761$	15.3702	+	15.3702i	0.557168	+	0.557168i	0.928500	−	0.371332i	$-0.121099\pi$
$761$	15.3702	+	15.3702i	0.557168	+	0.557168i	−0.371332	+	0.928500i	$0.621099\pi$
$762$	7.27267	−	25.2905i	0.263461	−	0.916178i
$763$	−3.94088	+	1.63237i	−0.142669	+	0.0590956i
$764$	16.6793	−	3.82410i	0.603435	−	0.138351i
$765$	−1.11396	−	0.461419i	−0.0402755	−	0.0166827i
$766$	2.63582	+	23.2911i	0.0952359	+	0.841543i
$767$	−38.5682	+	24.0820i	−1.39262	+	0.869550i
$768$	14.2687	+	25.5803i	0.514876	+	0.923050i
$769$		−	25.6520i		−	0.925035i	−0.886610	−	0.462517i	$-0.846946\pi$
$769$		−	25.6520i		−	0.925035i	0.886610	−	0.462517i	$-0.153054\pi$
$770$	−0.159028	−	1.40524i	−0.00573098	−	0.0506413i
$771$	11.9727	−	28.9047i	0.431187	−	1.04098i
$772$	−2.02802	−	8.84546i	−0.0729902	−	0.318355i
$773$	7.33460	+	17.7073i	0.263807	+	0.636887i	0.999168	−	0.0407891i	$-0.0129872\pi$
$773$	7.33460	+	17.7073i	0.263807	+	0.636887i	−0.735361	+	0.677676i	$0.762987\pi$
$774$	−0.665636	+	2.31473i	−0.0239258	+	0.0832012i
$775$	5.61079	+	5.61079i	0.201545	+	0.201545i
$776$	−1.90318	−	5.41350i	−0.0683203	−	0.194333i
$777$	7.71284	+	7.71284i	0.276697	+	0.276697i
$778$	25.6095	−	14.1702i	0.918145	−	0.508027i
$779$	−1.75145	−	4.22838i	−0.0627524	−	0.151498i
$780$	2.30750	+	5.60012i	0.0826218	+	0.200517i
$781$	−14.9427	−	6.18946i	−0.534691	−	0.221476i
$782$	−43.8727	+	55.0699i	−1.56889	+	1.96929i
$783$		−	24.8388i		−	0.887666i
$784$	−11.3024	−	23.3528i	−0.403658	−	0.834027i
$785$	5.69552			0.203282
$786$	35.3219	+	28.1400i	1.25989	+	1.00372i
$787$	−11.0222	+	26.6100i	−0.392900	+	0.948545i	0.596405	+	0.802684i	$0.296595\pi$
$787$	−11.0222	+	26.6100i	−0.392900	+	0.948545i	−0.989305	+	0.145861i	$0.953405\pi$
$788$	8.68592	+	12.2163i	0.309423	+	0.435188i
$789$	−2.61546	−	6.31427i	−0.0931127	−	0.224794i
$790$	1.19739	−	0.662541i	0.0426014	−	0.0235722i
$791$	1.54256	−	1.54256i	0.0548473	−	0.0548473i
$792$	3.01669	+	0.164974i	0.107193	+	0.00586210i
$793$	−9.59007	−	2.21745i	−0.340553	−	0.0787440i
$794$	−3.02393	+	10.5156i	−0.107315	+	0.373185i
$795$	−1.38758	−	3.34990i	−0.0492122	−	0.118809i
$796$	4.90902	−	7.82965i	0.173996	−	0.277515i
$797$	10.5395	−	25.4445i	0.373327	−	0.901290i	−0.619855	−	0.784716i	$-0.712809\pi$
$797$	10.5395	−	25.4445i	0.373327	−	0.901290i	0.993182	−	0.116574i	$-0.0371912\pi$
$798$	−0.120785	−	1.06731i	−0.00427576	−	0.0377823i
$799$		−	75.6138i		−	2.67502i
$800$	−5.96425	+	26.4288i	−0.210868	+	0.934400i
$801$		−	3.20543i		−	0.113258i
$802$	−28.6574	+	3.24311i	−1.01193	+	0.114518i
$803$	1.69505	−	4.09222i	0.0598171	−	0.144411i
$804$	−27.3091	+	43.5568i	−0.963119	+	1.53613i
$805$	2.02288	−	0.837904i	0.0712971	−	0.0295322i
$806$	8.12295	−	2.31960i	0.286119	−	0.0817043i
$807$	15.5352	−	15.5352i	0.546866	−	0.546866i
$808$	−30.4972	+	27.3345i	−1.07289	+	0.961625i
$809$	−13.6869	−	13.6869i	−0.481204	−	0.481204i	0.424312	−	0.905516i	$-0.360516\pi$
$809$	−13.6869	−	13.6869i	−0.481204	−	0.481204i	−0.905516	+	0.424312i	$0.860516\pi$
$810$	5.63807	−	3.11965i	0.198102	−	0.109613i
$811$	−1.10728	+	0.458652i	−0.0388820	+	0.0161055i	−0.402040	−	0.915622i	$-0.631699\pi$
$811$	−1.10728	+	0.458652i	−0.0388820	+	0.0161055i	0.363158	+	0.931728i	$0.381699\pi$
$812$	5.98623	−	4.25627i	0.210076	−	0.149366i
$813$	9.41177	−	22.7220i	0.330085	−	0.796896i
$814$	−27.9468	−	22.2645i	−0.979535	−	0.780370i
$815$			4.61984i			0.161826i
$816$	−54.6777	+	3.17794i	−1.91410	+	0.111250i
$817$	−2.80510			−0.0981380
$818$	−14.0657	−	11.2057i	−0.491794	−	0.391799i
$819$	−0.895813	+	0.149597i	−0.0313022	+	0.00522734i
$820$	7.15588	+	1.20863i	0.249894	+	0.0422073i
$821$	−37.4174	+	15.4988i	−1.30588	+	0.540912i	−0.923679	−	0.383168i	$-0.874833\pi$
$821$	−37.4174	+	15.4988i	−1.30588	+	0.540912i	−0.382199	+	0.924080i	$0.624833\pi$
$822$	−19.5971	−	35.4174i	−0.683529	−	1.23533i
$823$	−10.0562	−	10.0562i	−0.350539	−	0.350539i	0.509771	−	0.860310i	$-0.329730\pi$
$823$	−10.0562	−	10.0562i	−0.350539	−	0.350539i	−0.860310	+	0.509771i	$0.829730\pi$
$824$	−4.13142	+	8.61128i	−0.143925	+	0.299988i
$825$	18.8483	+	18.8483i	0.656214	+	0.656214i
$826$	−3.53359	+	12.2880i	−0.122949	+	0.427553i
$827$	−15.6959	−	37.8931i	−0.545798	−	1.31767i	−0.920578	−	0.390560i	$-0.872281\pi$
$827$	−15.6959	−	37.8931i	−0.545798	−	1.31767i	0.374779	−	0.927114i	$-0.377719\pi$
$828$	1.04532	+	4.55928i	0.0363273	+	0.158446i
$829$	−15.9577	+	38.5252i	−0.554233	+	1.33804i	0.360040	+	0.932937i	$0.382763\pi$
$829$	−15.9577	+	38.5252i	−0.554233	+	1.33804i	−0.914273	+	0.405099i	$0.867237\pi$
$830$	8.80732	−	0.996709i	0.305706	−	0.0345963i
$831$	−20.3784			−0.706920
$832$	21.5096	+	19.2181i	0.745711	+	0.666269i
$833$	48.5122			1.68085
$834$	10.5357	−	1.19231i	0.364821	−	0.0412861i
$835$	−2.26309	+	5.46359i	−0.0783175	+	0.189075i
$836$	0.786325	+	3.42965i	0.0271956	+	0.118617i
$837$	−3.07414	−	7.42162i	−0.106258	−	0.256529i
$838$	3.40371	−	11.8363i	0.117579	−	0.408878i
$839$	38.6410	+	38.6410i	1.33404	+	1.33404i	0.901724	+	0.432313i	$0.142302\pi$
$839$	38.6410	+	38.6410i	1.33404	+	1.33404i	0.432313	+	0.901724i	$0.357698\pi$
$840$	1.53561	+	0.736738i	0.0529836	+	0.0254199i
$841$	1.95037	+	1.95037i	0.0672543	+	0.0672543i
$842$	−2.95079	−	5.33289i	−0.101691	−	0.183784i
$843$	22.6151	−	9.36746i	0.778904	−	0.322633i
$844$	−35.1040	−	5.92909i	−1.20833	−	0.204088i
$845$	3.94925	+	4.46989i	0.135858	+	0.153769i
$846$	−3.92891	−	3.13006i	−0.135079	−	0.107614i
$847$	1.26020			0.0433009
$848$	−12.8978	−	11.4809i	−0.442914	−	0.394256i
$849$			40.1792i			1.37895i
$850$	−39.6240	−	31.5674i	−1.35909	−	1.08275i
$851$	21.1705	−	51.1101i	0.725715	−	1.75203i
$852$	15.8752	−	11.2874i	0.543876	−	0.386701i
$853$	47.6009	−	19.7169i	1.62982	−	0.675095i	0.634612	−	0.772831i	$-0.281160\pi$
$853$	47.6009	−	19.7169i	1.62982	−	0.675095i	0.995212	+	0.0977361i	$0.0311601\pi$
$854$	−2.42186	+	1.34006i	−0.0828743	+	0.0458559i
$855$	−0.0659667	−	0.0659667i	−0.00225601	−	0.00225601i
$856$	10.9502	+	12.2171i	0.374269	+	0.417573i
$857$	−5.36732	+	5.36732i	−0.183344	+	0.183344i	−0.792811	−	0.609467i	$-0.791383\pi$
$857$	−5.36732	+	5.36732i	−0.183344	+	0.183344i	0.609467	+	0.792811i	$0.291383\pi$
$858$	27.2874	−	7.79222i	0.931577	−	0.266022i
$859$	−26.6983	+	11.0588i	−0.910933	+	0.377321i	−0.788414	−	0.615145i	$-0.789097\pi$
$859$	−26.6983	+	11.0588i	−0.910933	+	0.377321i	−0.122519	+	0.992466i	$0.539097\pi$
$860$	2.36277	−	3.76850i	0.0805697	−	0.128505i
$861$	−3.97215	+	9.58961i	−0.135370	+	0.326813i
$862$	−54.1972	+	6.13341i	−1.84597	+	0.208905i
$863$		−	5.13854i		−	0.174918i	−0.996168	−	0.0874590i	$-0.972125\pi$
$863$		−	5.13854i		−	0.174918i	0.996168	−	0.0874590i	$-0.0278747\pi$
$864$	15.8176	−	22.4087i	0.538125	−	0.762360i
$865$		−	9.88955i		−	0.336255i
$866$	5.81322	+	51.3679i	0.197541	+	1.74555i
$867$	27.2821	−	65.8647i	0.926548	−	2.23688i
$868$	1.26187	−	2.01261i	0.0428305	−	0.0683126i
$869$	−2.45364	−	5.92361i	−0.0832340	−	0.200945i
$870$	1.68168	−	5.84799i	0.0570143	−	0.198265i
$871$	−11.4051	+	49.3252i	−0.386448	+	1.67132i
$872$	−0.918940	+	16.8036i	−0.0311192	+	0.569041i
$873$	0.504045	−	0.504045i	0.0170593	−	0.0170593i
$874$	−4.76669	+	2.63750i	−0.161236	+	0.0892148i
$875$	1.23228	+	2.97499i	0.0416587	+	0.100573i
$876$	3.09119	+	4.34761i	0.104442	+	0.146892i
$877$	−13.5619	+	32.7413i	−0.457953	+	1.10560i	0.511272	+	0.859419i	$0.329174\pi$
$877$	−13.5619	+	32.7413i	−0.457953	+	1.10560i	−0.969225	+	0.246177i	$0.920826\pi$
$878$	−18.6581	−	14.8644i	−0.629681	−	0.501650i
$879$	48.4463			1.63405
$880$	−5.26988	−	1.83245i	−0.177648	−	0.0617718i
$881$			4.96957i			0.167429i	0.996490	+	0.0837146i	$0.0266784\pi$
$881$			4.96957i			0.167429i	−0.996490	+	0.0837146i	$0.973322\pi$
$882$	2.00818	−	2.52070i	0.0676189	−	0.0848765i
$883$	−49.7122	−	20.5915i	−1.67295	−	0.692958i	−0.673996	−	0.738735i	$-0.735424\pi$
$883$	−49.7122	−	20.5915i	−1.67295	−	0.692958i	−0.998952	+	0.0457770i	$0.985424\pi$
$884$	−49.8680	+	20.5478i	−1.67724	+	0.691098i
$885$	4.05353	+	9.78608i	0.136258	+	0.328955i
$886$	0.0530089	−	0.0293308i	0.00178087	−	0.000985388i
$887$	7.26922	+	7.26922i	0.244076	+	0.244076i	0.818534	−	0.574458i	$-0.194787\pi$
$887$	7.26922	+	7.26922i	0.244076	+	0.244076i	−0.574458	+	0.818534i	$0.694787\pi$
$888$	40.5973	−	14.2725i	1.36235	−	0.478953i
$889$	−5.15279	−	5.15279i	−0.172819	−	0.172819i
$890$	−1.63598	+	5.68906i	−0.0548381	+	0.190698i
$891$	−11.5532	−	27.8920i	−0.387048	−	0.934417i
$892$	−3.06184	−	13.3546i	−0.102518	−	0.447144i
$893$	2.23885	−	5.40505i	0.0749201	−	0.180873i
$894$	−4.97720	−	43.9805i	−0.166462	−	1.47093i
$895$			2.84762i			0.0951855i
$896$	8.11101	−	0.0277666i	0.270970	−	0.000927616i
$897$	23.2703	+	37.2682i	0.776972	+	1.24435i
$898$	5.73903	+	50.7123i	0.191514	+	1.69229i
$899$	−7.84082	−	3.24777i	−0.261506	−	0.108319i
$900$	−3.28050	+	0.752130i	−0.109350	+	0.0250710i
$901$	29.8302	−	12.3561i	0.993788	−	0.411641i
$902$	9.39702	−	32.6778i	0.312886	−	1.08805i
$903$	4.49842	+	4.49842i	0.149698	+	0.149698i
$904$	−2.85449	−	8.11944i	−0.0949390	−	0.270048i
$905$	−4.52704	+	4.52704i	−0.150484	+	0.150484i
$906$	−13.0924	−	23.6616i	−0.434966	−	0.786103i
$907$	4.47008	+	10.7917i	0.148426	+	0.358333i	0.980554	−	0.196252i	$-0.0628770\pi$
$907$	4.47008	+	10.7917i	0.148426	+	0.358333i	−0.832127	+	0.554585i	$0.812877\pi$
$908$	−6.42375	−	1.08497i	−0.213179	−	0.0360062i
$909$	−4.70019	−	1.94688i	−0.155896	−	0.0645741i
$910$	1.66626	+	0.191694i	0.0552358	+	0.00635460i
$911$		−	51.8459i		−	1.71773i	−0.512201	−	0.858865i	$-0.671170\pi$
$911$		−	51.8459i		−	1.71773i	0.512201	−	0.858865i	$-0.328830\pi$
$912$	−4.00259	−	1.39178i	−0.132539	−	0.0460866i
$913$		−	41.5281i		−	1.37438i
$914$	7.82032	−	9.81622i	0.258673	−	0.324692i
$915$	−0.877501	+	2.11848i	−0.0290093	+	0.0700346i
$916$	−25.9113	−	36.4429i	−0.856132	−	1.20411i
$917$	11.5538	−	4.78573i	0.381539	−	0.158039i
$918$	24.8312	+	44.8769i	0.819553	+	1.48116i
$919$	−24.6672	−	24.6672i	−0.813696	−	0.813696i	0.171490	−	0.985186i	$-0.445142\pi$
$919$	−24.6672	−	24.6672i	−0.813696	−	0.813696i	−0.985186	+	0.171490i	$0.945142\pi$
$920$	0.471698	−	8.62539i	0.0155514	−	0.284371i
$921$	−12.9653	−	12.9653i	−0.427220	−	0.427220i
$922$	13.6291	−	47.3949i	0.448851	−	1.56087i
$923$	11.1444	−	15.6127i	0.366822	−	0.513899i
$924$	4.23898	−	6.76097i	0.139452	−	0.222420i
$925$	36.7749	+	15.2327i	1.20915	+	0.500846i
$926$	49.6289	−	5.61641i	1.63091	−	0.184567i
$927$	−1.18646			−0.0389684
$928$	−4.92387	−	28.5568i	−0.161634	−	0.937423i
$929$			46.0283i			1.51014i	0.655644	+	0.755071i	$0.272397\pi$
$929$			46.0283i			1.51014i	−0.655644	+	0.755071i	$0.727603\pi$
$930$	−0.221296	−	1.95546i	−0.00725659	−	0.0641221i
$931$	3.46777	+	1.43640i	0.113651	+	0.0470760i
$932$	23.6835	+	14.8490i	0.775778	+	0.486396i
$933$	57.4979	−	23.8164i	1.88240	−	0.779714i
$934$	−45.5133	−	13.0880i	−1.48924	−	0.428254i
$935$	7.37706	−	7.37706i	0.241256	−	0.241256i
$936$	−0.996632	+	3.44174i	−0.0325759	+	0.112497i
$937$	−19.1542	−	19.1542i	−0.625742	−	0.625742i	0.321252	−	0.946994i	$-0.395896\pi$
$937$	−19.1542	−	19.1542i	−0.625742	−	0.625742i	−0.946994	+	0.321252i	$0.895896\pi$
$938$	6.89241	+	12.4565i	0.225045	+	0.406719i
$939$	−2.37024	−	5.72228i	−0.0773500	−	0.186739i
$940$	5.37559	+	7.56051i	0.175333	+	0.246597i
$941$	11.6321	−	28.0823i	0.379195	−	0.915458i	−0.612922	−	0.790144i	$-0.710006\pi$
$941$	11.6321	−	28.0823i	0.379195	−	0.915458i	0.992117	−	0.125315i	$-0.0399941\pi$
$942$	25.1364	+	20.0255i	0.818989	+	0.652467i
$943$	52.6438			1.71432
$944$	37.6785	+	33.5392i	1.22633	+	1.09161i
$945$		−	1.59494i		−	0.0518834i
$946$	−16.2996	−	12.9855i	−0.529946	−	0.422194i
$947$	10.6289	−	25.6604i	0.345392	−	0.833851i	−0.651759	−	0.758426i	$-0.725969\pi$
$947$	10.6289	−	25.6604i	0.345392	−	0.833851i	0.997151	−	0.0754251i	$-0.0240314\pi$
$948$	7.61404	+	1.28602i	0.247293	+	0.0417679i
$949$	4.27572	+	3.05202i	0.138796	+	0.0990726i
$950$	−1.89774	−	3.42974i	−0.0615709	−	0.111276i
$951$	−20.4373	+	20.4373i	−0.662723	+	0.662723i
$952$	−6.56051	+	13.6743i	−0.212627	+	0.443187i
$953$	−0.756999	+	0.756999i	−0.0245216	+	0.0245216i	−0.719261	−	0.694740i	$-0.755520\pi$
$953$	−0.756999	+	0.756999i	−0.0245216	+	0.0245216i	0.694740	+	0.719261i	$0.255520\pi$
$954$	0.592807	−	2.06147i	0.0191928	−	0.0667425i
$955$	−1.50228	−	3.62681i	−0.0486125	−	0.117361i
$956$	15.3110	−	3.51039i	0.495192	−	0.113534i
$957$	−26.3396	−	10.9102i	−0.851440	−	0.352678i
$958$	−1.23911	−	10.9493i	−0.0400339	−	0.353755i
$959$	−11.2089			−0.361954
$960$	5.24121	−	4.20495i	0.169159	−	0.135714i
$961$	28.2553			0.911460
$962$	33.1937	−	26.3442i	1.07021	−	0.849370i
$963$	−0.779919	+	1.88289i	−0.0251326	+	0.0606753i
$964$	23.8271	−	5.46289i	0.767418	−	0.175948i
$965$	−1.92339	+	0.796696i	−0.0619163	+	0.0256466i
$966$	11.8738	+	3.41449i	0.382033	+	0.109859i
$967$	−27.6643	−	27.6643i	−0.889625	−	0.889625i	0.104862	−	0.994487i	$-0.466560\pi$
$967$	−27.6643	−	27.6643i	−0.889625	−	0.889625i	−0.994487	+	0.104862i	$0.966560\pi$
$968$	2.15060	−	4.48257i	0.0691228	−	0.144075i
$969$	5.60304	−	5.60304i	0.179995	−	0.179995i
$970$	−1.15184	+	0.637336i	−0.0369834	+	0.0204636i
$971$	−0.346724	−	0.837066i	−0.0111269	−	0.0268627i	0.918218	−	0.396074i	$-0.129628\pi$
$971$	−0.346724	−	0.837066i	−0.0111269	−	0.0268627i	−0.929345	+	0.369212i	$0.879628\pi$
$972$	7.16511	+	1.21019i	0.229821	+	0.0388169i
$973$	1.12360	−	2.71262i	0.0360211	−	0.0869626i
$974$	−21.9349	−	17.4749i	−0.702839	−	0.559933i
$975$	−26.8153	+	16.7435i	−0.858778	+	0.536221i
$976$	0.633612	+	10.9015i	0.0202814	+	0.348950i
$977$	−8.81166			−0.281910			−0.140955	−	0.990016i	$-0.545017\pi$
$977$	−8.81166			−0.281910			−0.140955	+	0.990016i	$0.545017\pi$
$978$	−16.2434	+	20.3890i	−0.519407	+	0.651970i
$979$	25.6238	+	10.6137i	0.818940	+	0.339216i
$980$	−4.85066	+	3.44887i	−0.154949	+	0.110170i
$981$	−1.93138	+	0.800002i	−0.0616641	+	0.0255421i
$982$	−2.62733	−	4.74831i	−0.0838416	−	0.151525i
$983$	−11.8199	+	11.8199i	−0.376997	+	0.376997i	−0.870017	−	0.493021i	$-0.835893\pi$
$983$	−11.8199	+	11.8199i	−0.376997	+	0.376997i	0.493021	+	0.870017i	$0.335893\pi$
$984$	27.3319	+	30.4943i	0.871310	+	0.972122i
$985$	2.43152	−	2.43152i	0.0774748	−	0.0774748i
$986$	52.0752	+	14.9750i	1.65841	+	0.476902i
$987$	−12.2582	+	5.07751i	−0.390183	+	0.161619i
$988$	−4.17308	−	0.00773100i	−0.132763	−	0.000245956i
$989$	12.3474	−	29.8093i	0.392625	−	0.947881i
$990$	−0.0779378	−	0.688690i	−0.00247703	−	0.0218880i
$991$	46.1162			1.46493			0.732465	−	0.680805i	$-0.238370\pi$
$991$	46.1162			1.46493			0.732465	+	0.680805i	$0.238370\pi$
$992$	−5.00550	−	7.92314i	−0.158925	−	0.251560i
$993$		−	1.02347i		−	0.0324789i
$994$	−0.606560	−	5.35981i	−0.0192389	−	0.170003i
$995$	−1.95865	−	0.811300i	−0.0620934	−	0.0257199i
$996$	42.3743	+	26.5678i	1.34268	+	0.841833i
$997$	−20.9763	+	8.68866i	−0.664326	+	0.275173i	−0.689258	−	0.724516i	$-0.742063\pi$
$997$	−20.9763	+	8.68866i	−0.664326	+	0.275173i	0.0249318	+	0.999689i	$0.492063\pi$
$998$	2.97942	−	10.3608i	0.0943118	−	0.327966i
$999$	−28.4948	−	28.4948i	−0.901536	−	0.901536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.3	✓	216
13.12	even	2	inner	416.2.bg.a.77.52	yes	216
32.5	even	8	inner	416.2.bg.a.389.52	yes	216
416.389	even	8	inner	416.2.bg.a.389.3	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.3	✓	216	1.1	even	1	trivial
416.2.bg.a.77.52	yes	216	13.12	even	2	inner
416.2.bg.a.389.3	yes	216	416.389	even	8	inner
416.2.bg.a.389.52	yes	216	32.5	even	8	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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40524 + 0.159029i) q^{2} +(-0.700567 + 1.69132i) q^{3} +(1.94942 - 0.446949i) q^{4} +(-0.175581 - 0.423890i) q^{5} +(0.715499 - 2.48813i) q^{6} +(-0.506941 - 0.506941i) q^{7} +(-2.66833 + 0.938086i) q^{8} +(-0.248445 - 0.248445i) q^{9} +(0.314145 + 0.567746i) q^{10} +(2.80869 - 1.16340i) q^{11} +(-0.609767 + 3.61021i) q^{12} +(0.593888 + 3.55630i) q^{13} +(0.792994 + 0.631757i) q^{14} +0.839940 q^{15} +(3.60047 - 1.74258i) q^{16} +7.47949i q^{17} +(0.388636 + 0.309616i) q^{18} +(-0.221460 + 0.534652i) q^{19} +(-0.531738 - 0.747864i) q^{20} +(1.21255 - 0.502253i) q^{21} +(-3.76188 + 2.08152i) q^{22} +(-4.70684 - 4.70684i) q^{23} +(0.282743 - 5.17019i) q^{24} +(3.38668 - 3.38668i) q^{25} +(-1.40011 - 4.90303i) q^{26} +(-4.47970 + 1.85555i) q^{27} +(-1.21482 - 0.761664i) q^{28} +(-1.96036 + 4.73273i) q^{29} +(-1.18032 + 0.133575i) q^{30} +1.65672i q^{31} +(-4.78242 + 3.02133i) q^{32} +5.56542i q^{33} +(-1.18946 - 10.5105i) q^{34} +(-0.125878 + 0.303896i) q^{35} +(-0.595367 - 0.373282i) q^{36} +(3.18043 + 7.67825i) q^{37} +(0.226180 - 0.786535i) q^{38} +(-6.43090 - 1.48698i) q^{39} +(0.866154 + 0.966369i) q^{40} +(-5.59227 + 5.59227i) q^{41} +(-1.62405 + 0.898617i) q^{42} +(1.85495 + 4.47824i) q^{43} +(4.95533 - 3.52329i) q^{44} +(-0.0616912 + 0.148936i) q^{45} +(7.36278 + 5.86573i) q^{46} -10.1095 q^{47} +(0.424887 + 7.31035i) q^{48} -6.48602i q^{49} +(-4.22053 + 5.29769i) q^{50} +(-12.6502 - 5.23989i) q^{51} +(2.74722 + 6.66729i) q^{52} +(-1.65199 - 3.98827i) q^{53} +(5.99999 - 3.31991i) q^{54} +(-0.986304 - 0.986304i) q^{55} +(1.82824 + 0.877132i) q^{56} +(-0.749120 - 0.749120i) q^{57} +(2.00214 - 6.96239i) q^{58} +(4.82597 + 11.6509i) q^{59} +(1.63739 - 0.375410i) q^{60} +(-1.04472 + 2.52218i) q^{61} +(-0.263467 - 2.32810i) q^{62} +0.251894i q^{63} +(6.23999 - 5.00625i) q^{64} +(1.40321 - 0.876163i) q^{65} +(-0.885063 - 7.82078i) q^{66} +(12.9725 + 5.37337i) q^{67} +(3.34295 + 14.5807i) q^{68} +(11.2582 - 4.66331i) q^{69} +(0.128561 - 0.447067i) q^{70} +(-3.76193 - 3.76193i) q^{71} +(0.895998 + 0.429872i) q^{72} +(1.03025 - 1.03025i) q^{73} +(-5.69035 - 10.2840i) q^{74} +(3.35536 + 8.10055i) q^{75} +(-0.192757 + 1.14124i) q^{76} +(-2.01361 - 0.834065i) q^{77} +(9.27346 + 1.06686i) q^{78} -2.10903i q^{79} +(-1.37084 - 1.22024i) q^{80} -9.93061i q^{81} +(6.96917 - 8.74783i) q^{82} +(5.22750 - 12.6203i) q^{83} +(2.13928 - 1.52105i) q^{84} +(3.17048 - 1.31326i) q^{85} +(-3.31882 - 5.99803i) q^{86} +(-6.63119 - 6.63119i) q^{87} +(-6.40314 + 5.73912i) q^{88} +(6.45097 + 6.45097i) q^{89} +(0.0630061 - 0.219102i) q^{90} +(1.50177 - 2.10390i) q^{91} +(-11.2793 - 7.07189i) q^{92} +(-2.80205 - 1.16065i) q^{93} +(14.2063 - 1.60770i) q^{94} +0.265518 q^{95} +(-1.75963 - 10.2052i) q^{96} +2.02880i q^{97} +(1.03147 + 9.11444i) q^{98} +(-0.986846 - 0.408765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more