LMFDB - Embedded newform 570.2.k.b.77.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.8
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +(1.91577 + 1.15318i) q^{10} -4.60223i q^{11} +(-1.08861 - 1.34719i) q^{12} +(1.32932 - 1.32932i) q^{13} -4.05624 q^{14} +(-3.08883 - 2.33648i) q^{15} -1.00000 q^{16} +(-3.40435 + 3.40435i) q^{17} +(1.62868 + 2.51941i) q^{18} -1.00000i q^{19} +(-2.17007 + 0.539236i) q^{20} +(6.98636 + 0.741650i) q^{21} +(3.25427 + 3.25427i) q^{22} +(2.00597 + 2.00597i) q^{23} +(1.72237 + 0.182842i) q^{24} +(-4.41845 + 2.34036i) q^{25} +1.87994i q^{26} +(-2.34453 - 4.63715i) q^{27} +(2.86820 - 2.86820i) q^{28} +6.21092 q^{29} +(3.83627 - 0.531985i) q^{30} -3.91496 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.01005 - 6.20008i) q^{33} -4.81448i q^{34} +(4.67757 - 7.77084i) q^{35} +(-2.93314 - 0.629843i) q^{36} +(-4.28573 - 4.28573i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.343732 - 3.23796i) q^{39} +(1.15318 - 1.91577i) q^{40} -1.74242i q^{41} +(-5.46453 + 4.41568i) q^{42} +(8.19327 - 8.19327i) q^{43} -4.60223 q^{44} +(-6.70476 + 0.214847i) q^{45} -2.83687 q^{46} +(5.22236 - 5.22236i) q^{47} +(-1.34719 + 1.08861i) q^{48} +9.45311i q^{49} +(1.46943 - 4.77920i) q^{50} +(-0.880287 + 8.29233i) q^{51} +(-1.32932 - 1.32932i) q^{52} +(4.96160 + 4.96160i) q^{53} +(4.93680 + 1.62112i) q^{54} +(-9.98719 + 2.48169i) q^{55} +4.05624i q^{56} +(-1.08861 - 1.34719i) q^{57} +(-4.39178 + 4.39178i) q^{58} -5.08697 q^{59} +(-2.33648 + 3.08883i) q^{60} -0.446018 q^{61} +(2.76830 - 2.76830i) q^{62} +(10.2193 - 6.60631i) q^{63} +1.00000i q^{64} +(-3.60154 - 2.16791i) q^{65} +(7.92676 + 0.841479i) q^{66} +(6.27966 + 6.27966i) q^{67} +(3.40435 + 3.40435i) q^{68} +(4.88616 + 0.518698i) q^{69} +(2.18727 + 8.80235i) q^{70} +15.5294i q^{71} +(2.51941 - 1.62868i) q^{72} +(-6.36719 + 6.36719i) q^{73} +6.06094 q^{74} +(-3.40474 + 7.96290i) q^{75} -1.00000 q^{76} +(13.2001 - 13.2001i) q^{77} +(2.04653 + 2.53264i) q^{78} -10.4449i q^{79} +(0.539236 + 2.17007i) q^{80} +(-8.20660 - 3.69483i) q^{81} +(1.23207 + 1.23207i) q^{82} +(-3.87813 - 3.87813i) q^{83} +(0.741650 - 6.98636i) q^{84} +(9.22345 + 5.55195i) q^{85} +11.5870i q^{86} +(8.36729 - 6.76129i) q^{87} +(3.25427 - 3.25427i) q^{88} -2.07373 q^{89} +(4.58906 - 4.89290i) q^{90} +7.62551 q^{91} +(2.00597 - 2.00597i) q^{92} +(-5.27420 + 4.26188i) q^{93} +7.38553i q^{94} +(-2.17007 + 0.539236i) q^{95} +(0.182842 - 1.72237i) q^{96} +(12.5075 + 12.5075i) q^{97} +(-6.68436 - 6.68436i) q^{98} +(-13.4990 - 2.89868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.34719	−	1.08861i	0.777801	−	0.628511i
$3$	1.34719	−	1.08861i	0.777801	−	0.628511i
$4$		−	1.00000i		−	0.500000i
$5$	−0.539236	−	2.17007i	−0.241153	−	0.970487i
$5$	−0.539236	−	2.17007i	−0.241153	−	0.970487i
$6$	−0.182842	+	1.72237i	−0.0746447	+	0.703156i
$7$	2.86820	+	2.86820i	1.08408	+	1.08408i	0.996125	+	0.0879519i	$0.0280322\pi$
$7$	2.86820	+	2.86820i	1.08408	+	1.08408i	0.0879519	+	0.996125i	$0.471968\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.629843	−	2.93314i	0.209948	−	0.977713i
$10$	1.91577	+	1.15318i	0.605820	+	0.364667i
$11$		−	4.60223i		−	1.38763i	−0.720156	−	0.693813i	$-0.755930\pi$
$11$		−	4.60223i		−	1.38763i	0.720156	−	0.693813i	$-0.244070\pi$
$12$	−1.08861	−	1.34719i	−0.314256	−	0.388900i
$13$	1.32932	−	1.32932i	0.368687	−	0.368687i	−0.498311	−	0.866998i	$-0.666046\pi$
$13$	1.32932	−	1.32932i	0.368687	−	0.368687i	0.866998	+	0.498311i	$0.166046\pi$
$14$	−4.05624			−1.08408
$15$	−3.08883	−	2.33648i	−0.797531	−	0.603278i
$16$	−1.00000			−0.250000
$17$	−3.40435	+	3.40435i	−0.825677	+	0.825677i	−0.986915	−	0.161239i	$-0.948451\pi$
$17$	−3.40435	+	3.40435i	−0.825677	+	0.825677i	0.161239	+	0.986915i	$0.448451\pi$
$18$	1.62868	+	2.51941i	0.383883	+	0.593830i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−2.17007	+	0.539236i	−0.485243	+	0.120577i
$21$	6.98636	+	0.741650i	1.52455	+	0.161841i
$22$	3.25427	+	3.25427i	0.693813	+	0.693813i
$23$	2.00597	+	2.00597i	0.418274	+	0.418274i	0.884609	−	0.466334i	$-0.154426\pi$
$23$	2.00597	+	2.00597i	0.418274	+	0.418274i	−0.466334	+	0.884609i	$0.654426\pi$
$24$	1.72237	+	0.182842i	0.351578	+	0.0373224i
$25$	−4.41845	+	2.34036i	−0.883690	+	0.468073i
$26$			1.87994i			0.368687i
$27$	−2.34453	−	4.63715i	−0.451206	−	0.892420i
$28$	2.86820	−	2.86820i	0.542038	−	0.542038i
$29$	6.21092			1.15334			0.576670	−	0.816978i	$-0.304352\pi$
$29$	6.21092			1.15334			0.576670	+	0.816978i	$0.304352\pi$
$30$	3.83627	−	0.531985i	0.700404	−	0.0971267i
$31$	−3.91496			−0.703148			−0.351574	−	0.936160i	$-0.614353\pi$
$31$	−3.91496			−0.703148			−0.351574	+	0.936160i	$0.614353\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.01005	−	6.20008i	−0.872138	−	1.07930i
$34$		−	4.81448i		−	0.825677i
$35$	4.67757	−	7.77084i	0.790653	−	1.31351i
$36$	−2.93314	−	0.629843i	−0.488856	−	0.104974i
$37$	−4.28573	−	4.28573i	−0.704570	−	0.704570i	0.260818	−	0.965388i	$-0.416008\pi$
$37$	−4.28573	−	4.28573i	−0.704570	−	0.704570i	−0.965388	+	0.260818i	$0.916008\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	0.343732	−	3.23796i	0.0550411	−	0.518489i
$40$	1.15318	−	1.91577i	0.182333	−	0.302910i
$41$		−	1.74242i		−	0.272120i	−0.990701	−	0.136060i	$-0.956556\pi$
$41$		−	1.74242i		−	0.272120i	0.990701	−	0.136060i	$-0.0434440\pi$
$42$	−5.46453	+	4.41568i	−0.843195	+	0.681354i
$43$	8.19327	−	8.19327i	1.24946	−	1.24946i	0.293504	−	0.955958i	$-0.405178\pi$
$43$	8.19327	−	8.19327i	1.24946	−	1.24946i	0.955958	−	0.293504i	$-0.0948215\pi$
$44$	−4.60223			−0.693813
$45$	−6.70476	+	0.214847i	−0.999487	+	0.0320275i
$46$	−2.83687			−0.418274
$47$	5.22236	−	5.22236i	0.761759	−	0.761759i	−0.214881	−	0.976640i	$-0.568936\pi$
$47$	5.22236	−	5.22236i	0.761759	−	0.761759i	0.976640	+	0.214881i	$0.0689365\pi$
$48$	−1.34719	+	1.08861i	−0.194450	+	0.157128i
$49$			9.45311i			1.35044i
$50$	1.46943	−	4.77920i	0.207809	−	0.675881i
$51$	−0.880287	+	8.29233i	−0.123265	+	1.16116i
$52$	−1.32932	−	1.32932i	−0.184344	−	0.184344i
$53$	4.96160	+	4.96160i	0.681527	+	0.681527i	0.960344	−	0.278817i	$-0.0899422\pi$
$53$	4.96160	+	4.96160i	0.681527	+	0.681527i	−0.278817	+	0.960344i	$0.589942\pi$
$54$	4.93680	+	1.62112i	0.671813	+	0.220607i
$55$	−9.98719	+	2.48169i	−1.34667	+	0.334631i
$56$			4.05624i			0.542038i
$57$	−1.08861	−	1.34719i	−0.144190	−	0.178440i
$58$	−4.39178	+	4.39178i	−0.576670	+	0.576670i
$59$	−5.08697			−0.662268			−0.331134	−	0.943584i	$-0.607431\pi$
$59$	−5.08697			−0.662268			−0.331134	+	0.943584i	$0.607431\pi$
$60$	−2.33648	+	3.08883i	−0.301639	+	0.398766i
$61$	−0.446018			−0.0571067			−0.0285534	−	0.999592i	$-0.509090\pi$
$61$	−0.446018			−0.0571067			−0.0285534	+	0.999592i	$0.509090\pi$
$62$	2.76830	−	2.76830i	0.351574	−	0.351574i
$63$	10.2193	−	6.60631i	1.28751	−	0.832316i
$64$			1.00000i			0.125000i
$65$	−3.60154	−	2.16791i	−0.446716	−	0.268896i
$66$	7.92676	+	0.841479i	0.975717	+	0.103579i
$67$	6.27966	+	6.27966i	0.767183	+	0.767183i	0.977610	−	0.210427i	$-0.0674854\pi$
$67$	6.27966	+	6.27966i	0.767183	+	0.767183i	−0.210427	+	0.977610i	$0.567485\pi$
$68$	3.40435	+	3.40435i	0.412838	+	0.412838i
$69$	4.88616	+	0.518698i	0.588224	+	0.0624440i
$70$	2.18727	+	8.80235i	0.261429	+	1.05208i
$71$			15.5294i			1.84300i	0.388380	+	0.921499i	$0.373035\pi$
$71$			15.5294i			1.84300i	−0.388380	+	0.921499i	$0.626965\pi$
$72$	2.51941	−	1.62868i	0.296915	−	0.191941i
$73$	−6.36719	+	6.36719i	−0.745223	+	0.745223i	−0.973578	−	0.228355i	$-0.926665\pi$
$73$	−6.36719	+	6.36719i	−0.745223	+	0.745223i	0.228355	+	0.973578i	$0.426665\pi$
$74$	6.06094			0.704570
$75$	−3.40474	+	7.96290i	−0.393146	+	0.919476i
$76$	−1.00000			−0.114708
$77$	13.2001	−	13.2001i	1.50429	−	1.50429i
$78$	2.04653	+	2.53264i	0.231724	+	0.286765i
$79$		−	10.4449i		−	1.17514i	−0.809173	−	0.587571i	$-0.800084\pi$
$79$		−	10.4449i		−	1.17514i	0.809173	−	0.587571i	$-0.199916\pi$
$80$	0.539236	+	2.17007i	0.0602884	+	0.242622i
$81$	−8.20660	−	3.69483i	−0.911844	−	0.410537i
$82$	1.23207	+	1.23207i	0.136060	+	0.136060i
$83$	−3.87813	−	3.87813i	−0.425680	−	0.425680i	0.461474	−	0.887154i	$-0.347321\pi$
$83$	−3.87813	−	3.87813i	−0.425680	−	0.425680i	−0.887154	+	0.461474i	$0.847321\pi$
$84$	0.741650	−	6.98636i	0.0809206	−	0.762275i
$85$	9.22345	+	5.55195i	1.00042	+	0.602194i
$86$			11.5870i			1.24946i
$87$	8.36729	−	6.76129i	0.897068	−	0.724886i
$88$	3.25427	−	3.25427i	0.346906	−	0.346906i
$89$	−2.07373			−0.219814			−0.109907	−	0.993942i	$-0.535055\pi$
$89$	−2.07373			−0.219814			−0.109907	+	0.993942i	$0.535055\pi$
$90$	4.58906	−	4.89290i	0.483730	−	0.515757i
$91$	7.62551			0.799370
$92$	2.00597	−	2.00597i	0.209137	−	0.209137i
$93$	−5.27420	+	4.26188i	−0.546909	+	0.441936i
$94$			7.38553i			0.761759i
$95$	−2.17007	+	0.539236i	−0.222645	+	0.0553244i
$96$	0.182842	−	1.72237i	0.0186612	−	0.175789i
$97$	12.5075	+	12.5075i	1.26994	+	1.26994i	0.946116	+	0.323828i	$0.104970\pi$
$97$	12.5075	+	12.5075i	1.26994	+	1.26994i	0.323828	+	0.946116i	$0.395030\pi$
$98$	−6.68436	−	6.68436i	−0.675222	−	0.675222i
$99$	−13.4990	−	2.89868i	−1.35670	−	0.291328i
$100$	2.34036	+	4.41845i	0.234036	+	0.441845i
$101$			1.85435i			0.184514i	0.995735	+	0.0922571i	$0.0294082\pi$
$101$			1.85435i			0.184514i	−0.995735	+	0.0922571i	$0.970592\pi$
$102$	−5.24111	−	6.48602i	−0.518947	−	0.642212i
$103$	−11.4600	+	11.4600i	−1.12919	+	1.12919i	−0.138882	+	0.990309i	$0.544351\pi$
$103$	−11.4600	+	11.4600i	−1.12919	+	1.12919i	−0.990309	+	0.138882i	$0.955649\pi$
$104$	1.87994			0.184344
$105$	−2.15786	−	15.5609i	−0.210586	−	1.51858i
$106$	−7.01675			−0.681527
$107$	−8.61306	+	8.61306i	−0.832656	+	0.832656i	−0.987879	−	0.155223i	$-0.950390\pi$
$107$	−8.61306	+	8.61306i	−0.832656	+	0.832656i	0.155223	+	0.987879i	$0.450390\pi$
$108$	−4.63715	+	2.34453i	−0.446210	+	0.225603i
$109$			6.32736i			0.606051i	0.952982	+	0.303025i	$0.0979967\pi$
$109$			6.32736i			0.606051i	−0.952982	+	0.303025i	$0.902003\pi$
$110$	5.30719	−	8.81683i	0.506021	−	0.840651i
$111$	−10.4392	−	1.10819i	−0.990845	−	0.105185i
$112$	−2.86820	−	2.86820i	−0.271019	−	0.271019i
$113$	0.984759	+	0.984759i	0.0926383	+	0.0926383i	0.751907	−	0.659269i	$-0.229134\pi$
$113$	0.984759	+	0.984759i	0.0926383	+	0.0926383i	−0.659269	+	0.751907i	$0.729134\pi$
$114$	1.72237	+	0.182842i	0.161315	+	0.0171247i
$115$	3.27142	−	5.43480i	0.305061	−	0.506798i
$116$		−	6.21092i		−	0.576670i
$117$	−3.06182	−	4.73634i	−0.283065	−	0.437875i
$118$	3.59703	−	3.59703i	0.331134	−	0.331134i
$119$	−19.5287			−1.79019
$120$	−0.531985	−	3.83627i	−0.0485634	−	0.350202i
$121$	−10.1805			−0.925503
$122$	0.315382	−	0.315382i	0.0285534	−	0.0285534i
$123$	−1.89682	−	2.34737i	−0.171030	−	0.211655i
$124$			3.91496i			0.351574i
$125$	7.46135	+	8.32636i	0.667363	+	0.744732i
$126$	−2.55479	+	11.8975i	−0.227599	+	1.05992i
$127$	8.32109	+	8.32109i	0.738378	+	0.738378i	0.972264	−	0.233886i	$-0.0751443\pi$
$127$	8.32109	+	8.32109i	0.738378	+	0.738378i	−0.233886	+	0.972264i	$0.575144\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	2.11859	−	19.9572i	0.186532	−	1.75713i
$130$	4.07962	−	1.01373i	0.357806	−	0.0889102i
$131$			18.6781i			1.63191i	0.578115	+	0.815955i	$0.303789\pi$
$131$			18.6781i			1.63191i	−0.578115	+	0.815955i	$0.696211\pi$
$132$	−6.20008	+	5.01005i	−0.539648	+	0.436069i
$133$	2.86820	−	2.86820i	0.248704	−	0.248704i
$134$	−8.88078			−0.767183
$135$	−8.79871	+	7.58833i	−0.757272	+	0.653100i
$136$	−4.81448			−0.412838
$137$	14.3208	−	14.3208i	1.22351	−	1.22351i	0.257137	−	0.966375i	$-0.417221\pi$
$137$	14.3208	−	14.3208i	1.22351	−	1.22351i	0.966375	−	0.257137i	$-0.0827792\pi$
$138$	−3.82181	+	3.08826i	−0.325334	+	0.262890i
$139$			11.2626i			0.955283i	0.878555	+	0.477642i	$0.158508\pi$
$139$			11.2626i			0.955283i	−0.878555	+	0.477642i	$0.841492\pi$
$140$	−7.77084	−	4.67757i	−0.656756	−	0.395327i
$141$	1.35038	−	12.7206i	0.113723	−	1.07127i
$142$	−10.9809	−	10.9809i	−0.921499	−	0.921499i
$143$	−6.11784	−	6.11784i	−0.511600	−	0.511600i
$144$	−0.629843	+	2.93314i	−0.0524869	+	0.244428i
$145$	−3.34915	−	13.4782i	−0.278132	−	1.11930i
$146$		−	9.00456i		−	0.745223i
$147$	10.2908	+	12.7351i	0.848769	+	1.05038i
$148$	−4.28573	+	4.28573i	−0.352285	+	0.352285i
$149$	−5.59268			−0.458170			−0.229085	−	0.973406i	$-0.573573\pi$
$149$	−5.59268			−0.458170			−0.229085	+	0.973406i	$0.573573\pi$
$150$	−3.22310	−	8.03813i	−0.263165	−	0.656311i
$151$	−4.62138			−0.376083			−0.188041	−	0.982161i	$-0.560214\pi$
$151$	−4.62138			−0.376083			−0.188041	+	0.982161i	$0.560214\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	7.84123	+	12.1296i	0.633926	+	0.980623i
$154$			18.6678i			1.50429i
$155$	2.11109	+	8.49576i	0.169567	+	0.682396i
$156$	−3.23796	−	0.343732i	−0.259245	−	0.0275206i
$157$	−10.3075	−	10.3075i	−0.822626	−	0.822626i	0.163858	−	0.986484i	$-0.447606\pi$
$157$	−10.3075	−	10.3075i	−0.822626	−	0.822626i	−0.986484	+	0.163858i	$0.947606\pi$
$158$	7.38565	+	7.38565i	0.587571	+	0.587571i
$159$	12.0855	+	1.28295i	0.958440	+	0.101745i
$160$	−1.91577	−	1.15318i	−0.151455	−	0.0911667i
$161$			11.5071i			0.906883i
$162$	8.41558	−	3.19030i	0.661190	−	0.250654i
$163$	−11.0783	+	11.0783i	−0.867718	+	0.867718i	−0.992219	−	0.124502i	$-0.960267\pi$
$163$	−11.0783	+	11.0783i	−0.867718	+	0.867718i	0.124502	+	0.992219i	$0.460267\pi$
$164$	−1.74242			−0.136060
$165$	−10.7530	+	14.2155i	−0.837123	+	1.10667i
$166$	5.48450			0.425680
$167$	4.00388	−	4.00388i	0.309830	−	0.309830i	−0.535014	−	0.844843i	$-0.679694\pi$
$167$	4.00388	−	4.00388i	0.309830	−	0.309830i	0.844843	+	0.535014i	$0.179694\pi$
$168$	4.41568	+	5.46453i	0.340677	+	0.421598i
$169$			9.46581i			0.728140i
$170$	−10.4478	+	2.59614i	−0.801308	+	0.199115i
$171$	−2.93314	−	0.629843i	−0.224303	−	0.0481653i
$172$	−8.19327	−	8.19327i	−0.624731	−	0.624731i
$173$	8.19231	+	8.19231i	0.622850	+	0.622850i	0.946259	−	0.323409i	$-0.104829\pi$
$173$	8.19231	+	8.19231i	0.622850	+	0.622850i	−0.323409	+	0.946259i	$0.604829\pi$
$174$	−1.13561	+	10.6975i	−0.0860907	+	0.810977i
$175$	−19.3856	−	5.96036i	−1.46541	−	0.450561i
$176$			4.60223i			0.346906i
$177$	−6.85312	+	5.53775i	−0.515112	+	0.416243i
$178$	1.46635	−	1.46635i	0.109907	−	0.109907i
$179$	−5.97757			−0.446784			−0.223392	−	0.974729i	$-0.571713\pi$
$179$	−5.97757			−0.446784			−0.223392	+	0.974729i	$0.571713\pi$
$180$	0.214847	+	6.70476i	0.0160137	+	0.499743i
$181$	8.47586			0.630006			0.315003	−	0.949091i	$-0.397994\pi$
$181$	8.47586			0.630006			0.315003	+	0.949091i	$0.397994\pi$
$182$	−5.39205	+	5.39205i	−0.399685	+	0.399685i
$183$	−0.600871	+	0.485541i	−0.0444177	+	0.0358922i
$184$			2.83687i			0.209137i
$185$	−6.98934	+	11.6114i	−0.513866	+	0.853685i
$186$	0.715817	−	6.74302i	0.0524863	−	0.494422i
$187$	15.6676	+	15.6676i	1.14573	+	1.14573i
$188$	−5.22236	−	5.22236i	−0.380879	−	0.380879i
$189$	6.57567	−	20.0248i	0.478310	−	1.45659i
$190$	1.15318	−	1.91577i	0.0836603	−	0.138985i
$191$		−	6.45739i		−	0.467240i	−0.972328	−	0.233620i	$-0.924943\pi$
$191$		−	6.45739i		−	0.467240i	0.972328	−	0.233620i	$-0.0750572\pi$
$192$	1.08861	+	1.34719i	0.0785639	+	0.0972251i
$193$	4.32749	−	4.32749i	0.311500	−	0.311500i	−0.533991	−	0.845490i	$-0.679308\pi$
$193$	4.32749	−	4.32749i	0.311500	−	0.311500i	0.845490	+	0.533991i	$0.179308\pi$
$194$	−17.6883			−1.26994
$195$	−7.21197	+	1.00010i	−0.516460	+	0.0716188i
$196$	9.45311			0.675222
$197$	14.8702	−	14.8702i	1.05946	−	1.05946i	0.0613383	−	0.998117i	$-0.480463\pi$
$197$	14.8702	−	14.8702i	1.05946	−	1.05946i	0.998117	−	0.0613383i	$-0.0195368\pi$
$198$	11.5949	−	7.49554i	0.824014	−	0.532685i
$199$		−	0.789726i		−	0.0559822i	−0.999608	−	0.0279911i	$-0.991089\pi$
$199$		−	0.789726i		−	0.0559822i	0.999608	−	0.0279911i	$-0.00891101\pi$
$200$	−4.77920	−	1.46943i	−0.337941	−	0.103904i
$201$	15.2960	+	1.62378i	1.07890	+	0.114532i
$202$	−1.31122	−	1.31122i	−0.0922571	−	0.0922571i
$203$	17.8141	+	17.8141i	1.25031	+	1.25031i
$204$	8.29233	+	0.880287i	0.580579	+	0.0616324i
$205$	−3.78118	+	0.939573i	−0.264089	+	0.0656226i
$206$		−	16.2069i		−	1.12919i
$207$	7.14724	−	4.62035i	0.496768	−	0.321136i
$208$	−1.32932	+	1.32932i	−0.0921718	+	0.0921718i
$209$	−4.60223			−0.318343
$210$	12.5290	+	9.47735i	0.864585	+	0.653999i
$211$	−19.8686			−1.36781			−0.683905	−	0.729571i	$-0.739720\pi$
$211$	−19.8686			−1.36781			−0.683905	+	0.729571i	$0.739720\pi$
$212$	4.96160	−	4.96160i	0.340764	−	0.340764i
$213$	16.9055	+	20.9210i	1.15834	+	1.43349i
$214$		−	12.1807i		−	0.832656i
$215$	−22.1981	−	13.3619i	−1.51390	−	0.911275i
$216$	1.62112	−	4.93680i	0.110303	−	0.335906i
$217$	−11.2289	−	11.2289i	−0.762266	−	0.762266i
$218$	−4.47412	−	4.47412i	−0.303025	−	0.303025i
$219$	−1.64641	+	15.5092i	−0.111254	+	1.04802i
$220$	2.48169	+	9.98719i	0.167315	+	0.673336i
$221$			9.05095i			0.608833i
$222$	8.16524	−	6.59802i	0.548015	−	0.442830i
$223$	10.1226	−	10.1226i	0.677856	−	0.677856i	−0.281659	−	0.959515i	$-0.590885\pi$
$223$	10.1226	−	10.1226i	0.677856	−	0.677856i	0.959515	+	0.281659i	$0.0908845\pi$
$224$	4.05624			0.271019
$225$	4.08168	+	14.4340i	0.272112	+	0.962266i
$226$	−1.39266			−0.0926383
$227$	−13.7553	+	13.7553i	−0.912969	+	0.912969i	−0.996505	−	0.0835359i	$-0.973379\pi$
$227$	−13.7553	+	13.7553i	−0.912969	+	0.912969i	0.0835359	+	0.996505i	$0.473379\pi$
$228$	−1.34719	+	1.08861i	−0.0892198	+	0.0720952i
$229$		−	6.47050i		−	0.427583i	−0.976879	−	0.213791i	$-0.931419\pi$
$229$		−	6.47050i		−	0.427583i	0.976879	−	0.213791i	$-0.0685813\pi$
$230$	1.52974	+	6.15623i	0.100868	+	0.405930i
$231$	3.41324	−	32.1529i	0.224575	−	2.11550i
$232$	4.39178	+	4.39178i	0.288335	+	0.288335i
$233$	4.00499	+	4.00499i	0.262376	+	0.262376i	0.826019	−	0.563643i	$-0.190601\pi$
$233$	4.00499	+	4.00499i	0.262376	+	0.262376i	−0.563643	+	0.826019i	$0.690601\pi$
$234$	5.51413	+	1.18407i	0.360470	+	0.0774050i
$235$	−14.1490	−	8.51682i	−0.922978	−	0.555576i
$236$			5.08697i			0.331134i
$237$	−11.3704	−	14.0713i	−0.738590	−	0.914026i
$238$	13.8089	−	13.8089i	0.895097	−	0.895097i
$239$	−1.96845			−0.127329			−0.0636643	−	0.997971i	$-0.520279\pi$
$239$	−1.96845			−0.127329			−0.0636643	+	0.997971i	$0.520279\pi$
$240$	3.08883	+	2.33648i	0.199383	+	0.150819i
$241$	23.9008			1.53959			0.769794	−	0.638292i	$-0.220359\pi$
$241$	23.9008			1.53959			0.769794	+	0.638292i	$0.220359\pi$
$242$	7.19873	−	7.19873i	0.462752	−	0.462752i
$243$	−15.0781	+	3.95617i	−0.967260	+	0.253788i
$244$			0.446018i			0.0285534i
$245$	20.5140	−	5.09745i	1.31059	−	0.325664i
$246$	3.00109	+	0.318586i	0.191343	+	0.0203123i
$247$	−1.32932	−	1.32932i	−0.0845826	−	0.0845826i
$248$	−2.76830	−	2.76830i	−0.175787	−	0.175787i
$249$	−9.44635	−	1.00279i	−0.598638	−	0.0635495i
$250$	−11.1636	−	0.611655i	−0.706048	−	0.0386845i
$251$		−	6.34592i		−	0.400551i	−0.979740	−	0.200275i	$-0.935816\pi$
$251$		−	6.34592i		−	0.400551i	0.979740	−	0.200275i	$-0.0641837\pi$
$252$	−6.60631	−	10.2193i	−0.416158	−	0.643757i
$253$	9.23195	−	9.23195i	0.580408	−	0.580408i
$254$	−11.7678			−0.738378
$255$	18.4697	−	2.56123i	1.15662	−	0.160391i
$256$	1.00000			0.0625000
$257$	−3.25382	+	3.25382i	−0.202968	+	0.202968i	−0.801270	−	0.598302i	$-0.795842\pi$
$257$	−3.25382	+	3.25382i	−0.202968	+	0.202968i	0.598302	+	0.801270i	$0.295842\pi$
$258$	12.6138	+	15.6099i	0.785301	+	0.971832i
$259$		−	24.5846i		−	1.52762i
$260$	−2.16791	+	3.60154i	−0.134448	+	0.223358i
$261$	3.91190	−	18.2175i	0.242141	−	1.12763i
$262$	−13.2074	−	13.2074i	−0.815955	−	0.815955i
$263$	−20.2705	−	20.2705i	−1.24993	−	1.24993i	−0.955749	−	0.294183i	$-0.904952\pi$
$263$	−20.2705	−	20.2705i	−1.24993	−	1.24993i	−0.294183	−	0.955749i	$-0.595048\pi$
$264$	0.841479	−	7.92676i	0.0517895	−	0.487858i
$265$	8.09156	−	13.4425i	0.497061	−	0.825766i
$266$			4.05624i			0.248704i
$267$	−2.79370	+	2.25748i	−0.170972	+	0.138156i
$268$	6.27966	−	6.27966i	0.383591	−	0.383591i
$269$	16.9049			1.03071			0.515354	−	0.856977i	$-0.327660\pi$
$269$	16.9049			1.03071			0.515354	+	0.856977i	$0.327660\pi$
$270$	0.855863	−	11.5874i	0.0520861	−	0.705186i
$271$	−2.93733			−0.178430			−0.0892149	−	0.996012i	$-0.528436\pi$
$271$	−2.93733			−0.178430			−0.0892149	+	0.996012i	$0.528436\pi$
$272$	3.40435	−	3.40435i	0.206419	−	0.206419i
$273$	10.2730	−	8.30123i	0.621751	−	0.502413i
$274$			20.2527i			1.22351i
$275$	10.7709	+	20.3347i	0.649509	+	1.22623i
$276$	0.518698	−	4.88616i	0.0312220	−	0.294112i
$277$	−4.03864	−	4.03864i	−0.242659	−	0.242659i	0.575291	−	0.817949i	$-0.304889\pi$
$277$	−4.03864	−	4.03864i	−0.242659	−	0.242659i	−0.817949	+	0.575291i	$0.804889\pi$
$278$	−7.96388	−	7.96388i	−0.477642	−	0.477642i
$279$	−2.46581	+	11.4831i	−0.147624	+	0.687476i
$280$	8.80235	−	2.18727i	0.526041	−	0.130714i
$281$			14.0877i			0.840400i	0.907431	+	0.420200i	$0.138040\pi$
$281$			14.0877i			0.840400i	−0.907431	+	0.420200i	$0.861960\pi$
$282$	8.03998	+	9.94971i	0.478774	+	0.592496i
$283$	15.0689	−	15.0689i	0.895756	−	0.895756i	−0.0993018	−	0.995057i	$-0.531661\pi$
$283$	15.0689	−	15.0689i	0.895756	−	0.895756i	0.995057	+	0.0993018i	$0.0316609\pi$
$284$	15.5294			0.921499
$285$	−2.33648	+	3.08883i	−0.138401	+	0.182966i
$286$	8.65193			0.511600
$287$	4.99760	−	4.99760i	0.294999	−	0.294999i
$288$	−1.62868	−	2.51941i	−0.0959706	−	0.148458i
$289$		−	6.17923i		−	0.363484i
$290$	11.8987	+	7.16229i	0.698716	+	0.420584i
$291$	30.4658	+	3.23415i	1.78594	+	0.189589i
$292$	6.36719	+	6.36719i	0.372611	+	0.372611i
$293$	−4.92404	−	4.92404i	−0.287665	−	0.287665i	0.548491	−	0.836156i	$-0.315202\pi$
$293$	−4.92404	−	4.92404i	−0.287665	−	0.287665i	−0.836156	+	0.548491i	$0.815202\pi$
$294$	−16.2818	−	1.72842i	−0.949573	−	0.100804i
$295$	2.74308	+	11.0391i	0.159708	+	0.642722i
$296$		−	6.06094i		−	0.352285i
$297$	−21.3412	+	10.7901i	−1.23834	+	0.626105i
$298$	3.95462	−	3.95462i	0.229085	−	0.229085i
$299$	5.33316			0.308425
$300$	7.96290	+	3.40474i	0.459738	+	0.196573i
$301$	46.9998			2.70903
$302$	3.26781	−	3.26781i	0.188041	−	0.188041i
$303$	2.01866	+	2.49816i	0.115969	+	0.143515i
$304$			1.00000i			0.0573539i
$305$	0.240509	+	0.967892i	0.0137715	+	0.0554214i
$306$	−14.1215	−	3.03237i	−0.807275	−	0.173349i
$307$	−7.41152	−	7.41152i	−0.422998	−	0.422998i	0.463237	−	0.886235i	$-0.346688\pi$
$307$	−7.41152	−	7.41152i	−0.422998	−	0.422998i	−0.886235	+	0.463237i	$0.846688\pi$
$308$	−13.2001	−	13.2001i	−0.752146	−	0.752146i
$309$	−2.96330	+	27.9144i	−0.168576	+	1.58799i
$310$	−7.50017	−	4.51465i	−0.425981	−	0.256415i
$311$			22.6059i			1.28186i	0.767598	+	0.640931i	$0.221452\pi$
$311$			22.6059i			1.28186i	−0.767598	+	0.640931i	$0.778548\pi$
$312$	2.53264	−	2.04653i	0.143383	−	0.115862i
$313$	−17.6638	+	17.6638i	−0.998419	+	0.998419i	−0.999999	−	0.00158010i	$-0.999497\pi$
$313$	−17.6638	+	17.6638i	−0.998419	+	0.998419i	0.00158010	+	0.999999i	$0.499497\pi$
$314$	14.5770			0.822626
$315$	−19.8468	−	18.6144i	−1.11824	−	1.04880i
$316$	−10.4449			−0.587571
$317$	−0.617852	+	0.617852i	−0.0347020	+	0.0347020i	−0.724245	−	0.689543i	$-0.757811\pi$
$317$	−0.617852	+	0.617852i	−0.0347020	+	0.0347020i	0.689543	+	0.724245i	$0.257811\pi$
$318$	−9.45290	+	7.63853i	−0.530092	+	0.428348i
$319$		−	28.5841i		−	1.60040i
$320$	2.17007	−	0.539236i	0.121311	−	0.0301442i
$321$	−2.22714	+	20.9797i	−0.124307	+	1.17097i
$322$	−8.13672	−	8.13672i	−0.453441	−	0.453441i
$323$	3.40435	+	3.40435i	0.189423	+	0.189423i
$324$	−3.69483	+	8.20660i	−0.205268	+	0.455922i
$325$	−2.76244	+	8.98463i	−0.153233	+	0.498377i
$326$		−	15.6671i		−	0.867718i
$327$	6.88804	+	8.52415i	0.380910	+	0.471387i
$328$	1.23207	−	1.23207i	0.0680300	−	0.0680300i
$329$	29.9575			1.65161
$330$	−2.44832	−	17.6554i	−0.134776	−	0.971899i
$331$	16.7769			0.922142			0.461071	−	0.887363i	$-0.347465\pi$
$331$	16.7769			0.922142			0.461071	+	0.887363i	$0.347465\pi$
$332$	−3.87813	+	3.87813i	−0.212840	+	0.212840i
$333$	−15.2700	+	9.87131i	−0.836790	+	0.540944i
$334$			5.66235i			0.309830i
$335$	10.2411	−	17.0135i	0.559532	−	0.929550i
$336$	−6.98636	−	0.741650i	−0.381137	−	0.0404603i
$337$	19.3140	+	19.3140i	1.05210	+	1.05210i	0.998566	+	0.0535356i	$0.0170491\pi$
$337$	19.3140	+	19.3140i	1.05210	+	1.05210i	0.0535356	+	0.998566i	$0.482951\pi$
$338$	−6.69334	−	6.69334i	−0.364070	−	0.364070i
$339$	2.39868	+	0.254636i	0.130278	+	0.0138299i
$340$	5.55195	−	9.22345i	0.301097	−	0.500212i
$341$			18.0176i			0.975706i
$342$	2.51941	−	1.62868i	0.136234	−	0.0880687i
$343$	−7.03600	+	7.03600i	−0.379908	+	0.379908i
$344$	11.5870			0.624731
$345$	−1.50917	−	10.8830i	−0.0812512	−	0.585922i
$346$	−11.5857			−0.622850
$347$	20.8770	−	20.8770i	1.12074	−	1.12074i	0.129107	−	0.991631i	$-0.458789\pi$
$347$	20.8770	−	20.8770i	1.12074	−	1.12074i	0.991631	−	0.129107i	$-0.0412109\pi$
$348$	−6.76129	−	8.36729i	−0.362443	−	0.448534i
$349$		−	11.2937i		−	0.604537i	−0.953223	−	0.302269i	$-0.902256\pi$
$349$		−	11.2937i		−	0.604537i	0.953223	−	0.302269i	$-0.0977440\pi$
$350$	17.9223	−	9.49308i	0.957988	−	0.507427i
$351$	−9.28090	−	3.04762i	−0.495378	−	0.162670i
$352$	−3.25427	−	3.25427i	−0.173453	−	0.173453i
$353$	0.723576	+	0.723576i	0.0385121	+	0.0385121i	0.726101	−	0.687589i	$-0.241331\pi$
$353$	0.723576	+	0.723576i	0.0385121	+	0.0385121i	−0.687589	+	0.726101i	$0.741331\pi$
$354$	0.930110	−	8.76167i	0.0494348	−	0.465677i
$355$	33.6999	−	8.37399i	1.78861	−	0.444445i
$356$			2.07373i			0.109907i
$357$	−26.3089	+	21.2592i	−1.39241	+	1.12516i
$358$	4.22678	−	4.22678i	0.223392	−	0.223392i
$359$	−25.4403			−1.34269			−0.671345	−	0.741145i	$-0.734283\pi$
$359$	−25.4403			−1.34269			−0.671345	+	0.741145i	$0.734283\pi$
$360$	−4.89290	−	4.58906i	−0.257879	−	0.241865i
$361$	−1.00000			−0.0526316
$362$	−5.99334	+	5.99334i	−0.315003	+	0.315003i
$363$	−13.7151	+	11.0827i	−0.719857	+	0.581689i
$364$		−	7.62551i		−	0.399685i
$365$	17.2507	+	10.3839i	0.902942	+	0.543516i
$366$	0.0815506	−	0.768209i	0.00426272	−	0.0401549i
$367$	14.0536	+	14.0536i	0.733593	+	0.733593i	0.971330	−	0.237737i	$-0.0764055\pi$
$367$	14.0536	+	14.0536i	0.733593	+	0.733593i	−0.237737	+	0.971330i	$0.576406\pi$
$368$	−2.00597	−	2.00597i	−0.104569	−	0.104569i
$369$	−5.11075	−	1.09745i	−0.266055	−	0.0571309i
$370$	−3.26827	−	13.1527i	−0.169910	−	0.683776i
$371$			28.4617i			1.47766i
$372$	4.26188	+	5.27420i	0.220968	+	0.273454i
$373$	5.52563	−	5.52563i	0.286106	−	0.286106i	−0.549432	−	0.835538i	$-0.685156\pi$
$373$	5.52563	−	5.52563i	0.286106	−	0.286106i	0.835538	+	0.549432i	$0.185156\pi$
$374$	−22.1574			−1.14573
$375$	19.1160	+	3.09467i	0.987148	+	0.159808i
$376$	7.38553			0.380879
$377$	8.25630	−	8.25630i	0.425221	−	0.425221i
$378$	9.51000	+	18.8094i	0.489142	+	0.967452i
$379$		−	8.19606i		−	0.421003i	−0.977593	−	0.210502i	$-0.932490\pi$
$379$		−	8.19606i		−	0.421003i	0.977593	−	0.210502i	$-0.0675098\pi$
$380$	0.539236	+	2.17007i	0.0276622	+	0.111322i
$381$	20.2685	+	2.15164i	1.03839	+	0.110232i
$382$	4.56606	+	4.56606i	0.233620	+	0.233620i
$383$	11.6617	+	11.6617i	0.595886	+	0.595886i	0.939215	−	0.343329i	$-0.111555\pi$
$383$	11.6617	+	11.6617i	0.595886	+	0.595886i	−0.343329	+	0.939215i	$0.611555\pi$
$384$	−1.72237	−	0.182842i	−0.0878945	−	0.00933059i
$385$	−35.7632	−	21.5273i	−1.82266	−	1.09713i
$386$			6.12000i			0.311500i
$387$	−18.8715	−	29.1925i	−0.959293	−	1.48394i
$388$	12.5075	−	12.5075i	0.634972	−	0.634972i
$389$	−15.6133			−0.791625			−0.395813	−	0.918331i	$-0.629537\pi$
$389$	−15.6133			−0.791625			−0.395813	+	0.918331i	$0.629537\pi$
$390$	4.39246	−	5.80681i	0.222421	−	0.294039i
$391$	−13.6581			−0.690719
$392$	−6.68436	+	6.68436i	−0.337611	+	0.337611i
$393$	20.3332	+	25.1629i	1.02567	+	1.26930i
$394$			21.0296i			1.05946i
$395$	−22.6662	+	5.63226i	−1.14046	+	0.283390i
$396$	−2.89868	+	13.4990i	−0.145664	+	0.678349i
$397$	−23.3976	−	23.3976i	−1.17429	−	1.17429i	−0.981176	−	0.193114i	$-0.938141\pi$
$397$	−23.3976	−	23.3976i	−1.17429	−	1.17429i	−0.193114	−	0.981176i	$-0.561859\pi$
$398$	0.558421	+	0.558421i	0.0279911	+	0.0279911i
$399$	0.741650	−	6.98636i	0.0371289	−	0.349756i
$400$	4.41845	−	2.34036i	0.220922	−	0.117018i
$401$		−	4.91777i		−	0.245582i	−0.992433	−	0.122791i	$-0.960816\pi$
$401$		−	4.91777i		−	0.245582i	0.992433	−	0.122791i	$-0.0391844\pi$
$402$	−11.9641	+	9.66774i	−0.596715	+	0.482183i
$403$	−5.20424	+	5.20424i	−0.259242	+	0.259242i
$404$	1.85435			0.0922571
$405$	−3.59277	+	19.8013i	−0.178526	+	0.983935i
$406$	−25.1930			−1.25031
$407$	−19.7239	+	19.7239i	−0.977679	+	0.977679i
$408$	−6.48602	+	5.24111i	−0.321106	+	0.259473i
$409$			3.39494i			0.167869i	0.996471	+	0.0839345i	$0.0267487\pi$
$409$			3.39494i			0.167869i	−0.996471	+	0.0839345i	$0.973251\pi$
$410$	2.00932	−	3.33807i	0.0992331	−	0.164856i
$411$	3.70304	−	34.8828i	0.182657	−	1.72064i
$412$	11.4600	+	11.4600i	0.564596	+	0.564596i
$413$	−14.5904	−	14.5904i	−0.717949	−	0.717949i
$414$	−1.78678	+	8.32094i	−0.0878157	+	0.408952i
$415$	−6.32460	+	10.5070i	−0.310462	+	0.515771i
$416$		−	1.87994i		−	0.0921718i
$417$	12.2606	+	15.1729i	0.600406	+	0.743020i
$418$	3.25427	−	3.25427i	0.159172	−	0.159172i
$419$	−12.5500			−0.613105			−0.306553	−	0.951854i	$-0.599176\pi$
$419$	−12.5500			−0.613105			−0.306553	+	0.951854i	$0.599176\pi$
$420$	−15.5609	+	2.15786i	−0.759292	+	0.105293i
$421$	−14.3230			−0.698060			−0.349030	−	0.937112i	$-0.613489\pi$
$421$	−14.3230			−0.698060			−0.349030	+	0.937112i	$0.613489\pi$
$422$	14.0492	−	14.0492i	0.683905	−	0.683905i
$423$	−12.0286	−	18.6072i	−0.584852	−	0.904711i
$424$			7.01675i			0.340764i
$425$	7.07454	−	23.0094i	0.343166	−	1.11612i
$426$	−26.7474	−	2.83942i	−1.29591	−	0.137570i
$427$	−1.27927	−	1.27927i	−0.0619081	−	0.0619081i
$428$	8.61306	+	8.61306i	0.416328	+	0.416328i
$429$	−14.9019	−	1.58193i	−0.719468	−	0.0763764i
$430$	25.1447	−	6.24814i	1.21259	−	0.301312i
$431$		−	8.30157i		−	0.399873i	−0.979809	−	0.199936i	$-0.935926\pi$
$431$		−	8.30157i		−	0.399873i	0.979809	−	0.199936i	$-0.0640735\pi$
$432$	2.34453	+	4.63715i	0.112801	+	0.223105i
$433$	−10.8163	+	10.8163i	−0.519799	+	0.519799i	−0.917510	−	0.397712i	$-0.869804\pi$
$433$	−10.8163	+	10.8163i	−0.519799	+	0.519799i	0.397712	+	0.917510i	$0.369804\pi$
$434$	15.8800			0.762266
$435$	−19.1844	−	14.5117i	−0.919824	−	0.695784i
$436$	6.32736			0.303025
$437$	2.00597	−	2.00597i	0.0959587	−	0.0959587i
$438$	−9.80248	−	12.1309i	−0.468381	−	0.579635i
$439$		−	17.0396i		−	0.813258i	−0.913593	−	0.406629i	$-0.866704\pi$
$439$		−	17.0396i		−	0.813258i	0.913593	−	0.406629i	$-0.133296\pi$
$440$	−8.81683	−	5.30719i	−0.420326	−	0.253010i
$441$	27.7273	+	5.95397i	1.32035	+	0.283522i
$442$	−6.39999	−	6.39999i	−0.304416	−	0.304416i
$443$	−25.4820	−	25.4820i	−1.21069	−	1.21069i	−0.970802	−	0.239884i	$-0.922891\pi$
$443$	−25.4820	−	25.4820i	−1.21069	−	1.21069i	−0.239884	−	0.970802i	$-0.577109\pi$
$444$	−1.10819	+	10.4392i	−0.0525924	+	0.495422i
$445$	1.11823	+	4.50014i	0.0530090	+	0.213327i
$446$			14.3154i			0.677856i
$447$	−7.53441	+	6.08827i	−0.356365	+	0.287965i
$448$	−2.86820	+	2.86820i	−0.135510	+	0.135510i
$449$	7.40137			0.349292			0.174646	−	0.984631i	$-0.444122\pi$
$449$	7.40137			0.349292			0.174646	+	0.984631i	$0.444122\pi$
$450$	−13.0926	−	7.32018i	−0.617189	−	0.345077i
$451$	−8.01901			−0.377600
$452$	0.984759	−	0.984759i	0.0463192	−	0.0463192i
$453$	−6.22588	+	5.03090i	−0.292517	+	0.236372i
$454$		−	19.4529i		−	0.912969i
$455$	−4.11194	−	16.5479i	−0.192771	−	0.775778i
$456$	0.182842	−	1.72237i	0.00856234	−	0.0806575i
$457$	14.6959	+	14.6959i	0.687447	+	0.687447i	0.961667	−	0.274220i	$-0.0884196\pi$
$457$	14.6959	+	14.6959i	0.687447	+	0.687447i	−0.274220	+	0.961667i	$0.588420\pi$
$458$	4.57533	+	4.57533i	0.213791	+	0.213791i
$459$	23.7681	+	7.80487i	1.10940	+	0.364300i
$460$	−5.43480	−	3.27142i	−0.253399	−	0.152531i
$461$		−	37.8041i		−	1.76071i	−0.474314	−	0.880356i	$-0.657304\pi$
$461$		−	37.8041i		−	1.76071i	0.474314	−	0.880356i	$-0.342696\pi$
$462$	20.3220	+	25.1490i	0.945464	+	1.17004i
$463$	−0.789669	+	0.789669i	−0.0366990	+	0.0366990i	−0.725218	−	0.688519i	$-0.758261\pi$
$463$	−0.789669	+	0.789669i	−0.0366990	+	0.0366990i	0.688519	+	0.725218i	$0.258261\pi$
$464$	−6.21092			−0.288335
$465$	12.0926	+	9.14725i	0.560782	+	0.424193i
$466$	−5.66392			−0.262376
$467$	−28.1504	+	28.1504i	−1.30265	+	1.30265i	−0.376045	+	0.926601i	$0.622716\pi$
$467$	−28.1504	+	28.1504i	−1.30265	+	1.30265i	−0.926601	+	0.376045i	$0.877284\pi$
$468$	−4.73634	+	3.06182i	−0.218938	+	0.141533i
$469$			36.0226i			1.66337i
$470$	16.0271	−	3.98254i	0.739277	−	0.183701i
$471$	−25.1070	−	2.66528i	−1.15687	−	0.122809i
$472$	−3.59703	−	3.59703i	−0.165567	−	0.165567i
$473$	−37.7073	−	37.7073i	−1.73378	−	1.73378i
$474$	17.9900	+	1.90976i	0.826308	+	0.0877182i
$475$	2.34036	+	4.41845i	0.107383	+	0.202732i
$476$			19.5287i			0.895097i
$477$	17.6781	−	11.4280i	0.809423	−	0.523253i
$478$	1.39191	−	1.39191i	0.0636643	−	0.0636643i
$479$	−23.0077			−1.05125			−0.525624	−	0.850717i	$-0.676168\pi$
$479$	−23.0077			−1.05125			−0.525624	+	0.850717i	$0.676168\pi$
$480$	−3.83627	+	0.531985i	−0.175101	+	0.0242817i
$481$	−11.3942			−0.519532
$482$	−16.9005	+	16.9005i	−0.769794	+	0.769794i
$483$	12.5267	+	15.5022i	0.569986	+	0.705374i
$484$			10.1805i			0.462752i
$485$	20.3977	−	33.8867i	0.926213	−	1.53872i
$486$	7.86438	−	13.4593i	0.356736	−	0.610524i
$487$	20.5042	+	20.5042i	0.929134	+	0.929134i	0.997650	−	0.0685156i	$-0.0218263\pi$
$487$	20.5042	+	20.5042i	0.929134	+	0.929134i	−0.0685156	+	0.997650i	$0.521826\pi$
$488$	−0.315382	−	0.315382i	−0.0142767	−	0.0142767i
$489$	−2.86459	+	26.9845i	−0.129541	+	1.22028i
$490$	−10.9011	+	18.1100i	−0.492462	+	0.818126i
$491$		−	16.9198i		−	0.763581i	−0.924249	−	0.381791i	$-0.875308\pi$
$491$		−	16.9198i		−	0.763581i	0.924249	−	0.381791i	$-0.124692\pi$
$492$	−2.34737	+	1.89682i	−0.105827	+	0.0855152i
$493$	−21.1442	+	21.1442i	−0.952285	+	0.952285i
$494$	1.87994			0.0845826
$495$	0.988774	+	30.8569i	0.0444421	+	1.38691i
$496$	3.91496			0.175787
$497$	−44.5413	+	44.5413i	−1.99795	+	1.99795i
$498$	7.38866	−	5.97050i	0.331094	−	0.267544i
$499$		−	26.0020i		−	1.16401i	−0.813185	−	0.582005i	$-0.802268\pi$
$499$		−	26.0020i		−	1.16401i	0.813185	−	0.582005i	$-0.197732\pi$
$500$	8.32636	−	7.46135i	0.372366	−	0.333682i
$501$	1.03531	−	9.75267i	0.0462543	−	0.435717i
$502$	4.48724	+	4.48724i	0.200275	+	0.200275i
$503$	3.80551	+	3.80551i	0.169679	+	0.169679i	0.786838	−	0.617159i	$-0.211716\pi$
$503$	3.80551	+	3.80551i	0.169679	+	0.169679i	−0.617159	+	0.786838i	$0.711716\pi$
$504$	11.8975	+	2.55479i	0.529958	+	0.113800i
$505$	4.02407	−	0.999929i	0.179069	−	0.0444963i
$506$			13.0560i			0.580408i
$507$	10.3046	+	12.7523i	0.457644	+	0.566347i
$508$	8.32109	−	8.32109i	0.369189	−	0.369189i
$509$	−7.97379			−0.353432			−0.176716	−	0.984262i	$-0.556547\pi$
$509$	−7.97379			−0.353432			−0.176716	+	0.984262i	$0.556547\pi$
$510$	−11.2490	+	14.8711i	−0.498112	+	0.658503i
$511$	−36.5247			−1.61576
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.63715	+	2.34453i	−0.204735	+	0.103514i
$514$		−	4.60160i		−	0.202968i
$515$	31.0488	+	18.6895i	1.36817	+	0.823557i
$516$	−19.9572	−	2.11859i	−0.878567	−	0.0932658i
$517$	−24.0345	−	24.0345i	−1.05704	−	1.05704i
$518$	17.3840	+	17.3840i	0.763808	+	0.763808i
$519$	19.9549	+	2.11834i	0.875921	+	0.0929849i
$520$	−1.01373	−	4.07962i	−0.0444551	−	0.178903i
$521$		−	21.6995i		−	0.950673i	−0.879804	−	0.475336i	$-0.842326\pi$
$521$		−	21.6995i		−	0.950673i	0.879804	−	0.475336i	$-0.157674\pi$
$522$	10.1156	+	15.6478i	0.442747	+	0.684887i
$523$	−24.3202	+	24.3202i	−1.06345	+	1.06345i	−0.0656023	+	0.997846i	$0.520897\pi$
$523$	−24.3202	+	24.3202i	−1.06345	+	1.06345i	−0.997846	+	0.0656023i	$0.979103\pi$
$524$	18.6781			0.815955
$525$	−32.6046	+	13.0737i	−1.42298	+	0.570583i
$526$	28.6668			1.24993
$527$	13.3279	−	13.3279i	0.580573	−	0.580573i
$528$	5.01005	+	6.20008i	0.218034	+	0.269824i
$529$		−	14.9521i		−	0.650093i
$530$	3.78368	+	15.2269i	0.164353	+	0.661414i
$531$	−3.20399	+	14.9208i	−0.139041	+	0.647507i
$532$	−2.86820	−	2.86820i	−0.124352	−	0.124352i
$533$	−2.31623	−	2.31623i	−0.100327	−	0.100327i
$534$	0.379163	−	3.57173i	0.0164080	−	0.154564i
$535$	23.3355	+	14.0465i	1.00888	+	0.607284i
$536$			8.88078i			0.383591i
$537$	−8.05292	+	6.50726i	−0.347509	+	0.280809i
$538$	−11.9535	+	11.9535i	−0.515354	+	0.515354i
$539$	43.5054			1.87391
$540$	7.58833	+	8.79871i	0.326550	+	0.378636i
$541$	−14.0695			−0.604893			−0.302447	−	0.953166i	$-0.597803\pi$
$541$	−14.0695			−0.604893			−0.302447	+	0.953166i	$0.597803\pi$
$542$	2.07700	−	2.07700i	0.0892149	−	0.0892149i
$543$	11.4186	−	9.22694i	0.490019	−	0.395966i
$544$			4.81448i			0.206419i
$545$	13.7308	−	3.41194i	0.588164	−	0.146151i
$546$	−1.39426	+	13.1340i	−0.0596688	+	0.562082i
$547$	13.8517	+	13.8517i	0.592256	+	0.592256i	0.938240	−	0.345984i	$-0.112455\pi$
$547$	13.8517	+	13.8517i	0.592256	+	0.592256i	−0.345984	+	0.938240i	$0.612455\pi$
$548$	−14.3208	−	14.3208i	−0.611756	−	0.611756i
$549$	−0.280921	+	1.30823i	−0.0119894	+	0.0558340i
$550$	−21.9950	−	6.76265i	−0.937870	−	0.288361i
$551$		−	6.21092i		−	0.264594i
$552$	3.08826	+	3.82181i	0.131445	+	0.162667i
$553$	29.9580	−	29.9580i	1.27394	−	1.27394i
$554$	5.71150			0.242659
$555$	3.22433	+	23.2514i	0.136865	+	0.986968i
$556$	11.2626			0.477642
$557$	15.4865	−	15.4865i	0.656182	−	0.656182i	−0.298292	−	0.954475i	$-0.596417\pi$
$557$	15.4865	−	15.4865i	0.656182	−	0.656182i	0.954475	+	0.298292i	$0.0964170\pi$
$558$	−6.37620	−	9.86338i	−0.269926	−	0.417550i
$559$		−	21.7830i		−	0.921321i
$560$	−4.67757	+	7.77084i	−0.197663	+	0.328378i
$561$	38.1632	+	4.05129i	1.61125	+	0.171045i
$562$	−9.96149	−	9.96149i	−0.420200	−	0.420200i
$563$	21.7376	+	21.7376i	0.916131	+	0.916131i	0.996745	−	0.0806140i	$-0.0256881\pi$
$563$	21.7376	+	21.7376i	0.916131	+	0.916131i	−0.0806140	+	0.996745i	$0.525688\pi$
$564$	−12.7206	−	1.35038i	−0.535635	−	0.0568613i
$565$	1.60598	−	2.66802i	0.0675642	−	0.112244i
$566$			21.3107i			0.895756i
$567$	−12.9406	−	34.1356i	−0.543456	−	1.43356i
$568$	−10.9809	+	10.9809i	−0.460750	+	0.460750i
$569$	33.8572			1.41937			0.709684	−	0.704520i	$-0.248838\pi$
$569$	33.8572			1.41937			0.709684	+	0.704520i	$0.248838\pi$
$570$	−0.531985	−	3.83627i	−0.0222824	−	0.160684i
$571$	−10.2627			−0.429480			−0.214740	−	0.976671i	$-0.568890\pi$
$571$	−10.2627			−0.429480			−0.214740	+	0.976671i	$0.568890\pi$
$572$	−6.11784	+	6.11784i	−0.255800	+	0.255800i
$573$	−7.02960	−	8.69933i	−0.293666	−	0.363420i
$574$			7.06767i			0.294999i
$575$	−13.5580	−	4.16859i	−0.565408	−	0.173842i
$576$	2.93314	+	0.629843i	0.122214	+	0.0262434i
$577$	−13.9733	−	13.9733i	−0.581717	−	0.581717i	0.353658	−	0.935375i	$-0.384938\pi$
$577$	−13.9733	−	13.9733i	−0.581717	−	0.581717i	−0.935375	+	0.353658i	$0.884938\pi$
$578$	4.36937	+	4.36937i	0.181742	+	0.181742i
$579$	1.11899	−	10.5409i	0.0465036	−	0.438066i
$580$	−13.4782	+	3.34915i	−0.559650	+	0.139066i
$581$		−	22.2465i		−	0.922939i
$582$	−23.8295	+	19.2557i	−0.987763	+	0.798174i
$583$	22.8344	−	22.8344i	0.945705	−	0.945705i
$584$	−9.00456			−0.372611
$585$	−8.62718	+	9.19838i	−0.356690	+	0.380306i
$586$	6.96364			0.287665
$587$	−22.9650	+	22.9650i	−0.947869	+	0.947869i	−0.998707	−	0.0508382i	$-0.983811\pi$
$587$	−22.9650	+	22.9650i	−0.947869	+	0.947869i	0.0508382	+	0.998707i	$0.483811\pi$
$588$	12.7351	−	10.2908i	0.525188	−	0.424385i
$589$			3.91496i			0.161313i
$590$	−9.74548	−	5.86618i	−0.401215	−	0.241507i
$591$	3.84508	−	36.2208i	0.158166	−	1.48992i
$592$	4.28573	+	4.28573i	0.176142	+	0.176142i
$593$	−2.14305	−	2.14305i	−0.0880044	−	0.0880044i	0.661734	−	0.749739i	$-0.269821\pi$
$593$	−2.14305	−	2.14305i	−0.0880044	−	0.0880044i	−0.749739	+	0.661734i	$0.769821\pi$
$594$	7.46079	−	22.7203i	0.306120	−	0.932224i
$595$	10.5306	+	42.3788i	0.431711	+	1.73736i
$596$			5.59268i			0.229085i
$597$	−0.859707	−	1.06391i	−0.0351855	−	0.0435430i
$598$	−3.77111	+	3.77111i	−0.154212	+	0.154212i
$599$	−28.0055			−1.14427			−0.572137	−	0.820158i	$-0.693885\pi$
$599$	−28.0055			−1.14427			−0.572137	+	0.820158i	$0.693885\pi$
$600$	−8.03813	+	3.22310i	−0.328155	+	0.131583i
$601$	−10.4827			−0.427599			−0.213800	−	0.976878i	$-0.568584\pi$
$601$	−10.4827			−0.427599			−0.213800	+	0.976878i	$0.568584\pi$
$602$	−33.2339	+	33.2339i	−1.35451	+	1.35451i
$603$	22.3743	−	14.4639i	0.911152	−	0.589016i
$604$			4.62138i			0.188041i
$605$	5.48971	+	22.0925i	0.223188	+	0.898189i
$606$	−3.19387	−	0.339051i	−0.129742	−	0.0137730i
$607$	−25.3869	−	25.3869i	−1.03042	−	1.03042i	−0.999522	−	0.0308996i	$-0.990163\pi$
$607$	−25.3869	−	25.3869i	−1.03042	−	1.03042i	−0.0308996	−	0.999522i	$-0.509837\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	43.3918	+	4.60633i	1.75832	+	0.186658i
$610$	−0.854469	−	0.514338i	−0.0345964	−	0.0208249i
$611$		−	13.8844i		−	0.561701i
$612$	12.1296	−	7.84123i	0.490312	−	0.316963i
$613$	−3.65006	+	3.65006i	−0.147425	+	0.147425i	−0.776967	−	0.629542i	$-0.783243\pi$
$613$	−3.65006	+	3.65006i	−0.147425	+	0.147425i	0.629542	+	0.776967i	$0.283243\pi$
$614$	10.4815			0.422998
$615$	−4.07113	+	5.38202i	−0.164164	+	0.217024i
$616$	18.6678			0.752146
$617$	25.7417	−	25.7417i	1.03632	−	1.03632i	0.0370077	−	0.999315i	$-0.488217\pi$
$617$	25.7417	−	25.7417i	1.03632	−	1.03632i	0.999315	−	0.0370077i	$-0.0117826\pi$
$618$	−17.6431	−	21.8338i	−0.709709	−	0.878286i
$619$		−	26.4712i		−	1.06397i	−0.846755	−	0.531984i	$-0.821447\pi$
$619$		−	26.4712i		−	1.06397i	0.846755	−	0.531984i	$-0.178553\pi$
$620$	8.49576	−	2.11109i	0.341198	−	0.0847833i
$621$	4.59892	−	14.0051i	0.184548	−	0.562004i
$622$	−15.9848	−	15.9848i	−0.640931	−	0.640931i
$623$	−5.94785	−	5.94785i	−0.238296	−	0.238296i
$624$	−0.343732	+	3.23796i	−0.0137603	+	0.129622i
$625$	14.0454	−	20.6816i	0.561816	−	0.827262i
$626$		−	24.9804i		−	0.998419i
$627$	−6.20008	+	5.01005i	−0.247607	+	0.200082i
$628$	−10.3075	+	10.3075i	−0.411313	+	0.411313i
$629$	29.1803			1.16349
$630$	27.1961	−	0.871471i	1.08352	−	0.0347202i
$631$	−0.953154			−0.0379445			−0.0189722	−	0.999820i	$-0.506039\pi$
$631$	−0.953154			−0.0379445			−0.0189722	+	0.999820i	$0.506039\pi$
$632$	7.38565	−	7.38565i	0.293786	−	0.293786i
$633$	−26.7668	+	21.6292i	−1.06388	+	0.859683i
$634$		−	0.873774i		−	0.0347020i
$635$	13.5704	−	22.5444i	0.538524	−	0.894648i
$636$	1.28295	−	12.0855i	0.0508724	−	0.479220i
$637$	12.5662	+	12.5662i	0.497891	+	0.497891i
$638$	20.2120	+	20.2120i	0.800201	+	0.800201i
$639$	45.5498	+	9.78106i	1.80192	+	0.386933i
$640$	−1.15318	+	1.91577i	−0.0455833	+	0.0757275i
$641$			9.36570i			0.369923i	0.982746	+	0.184961i	$0.0592160\pi$
$641$			9.36570i			0.369923i	−0.982746	+	0.184961i	$0.940784\pi$
$642$	−13.2601	−	16.4097i	−0.523334	−	0.647640i
$643$	−21.9899	+	21.9899i	−0.867197	+	0.867197i	−0.992161	−	0.124964i	$-0.960118\pi$
$643$	−21.9899	+	21.9899i	−0.867197	+	0.867197i	0.124964	+	0.992161i	$0.460118\pi$
$644$	11.5071			0.453441
$645$	−44.4510	+	6.16413i	−1.75026	+	0.242712i
$646$	−4.81448			−0.189423
$647$	−6.75416	+	6.75416i	−0.265533	+	0.265533i	−0.827297	−	0.561764i	$-0.810123\pi$
$647$	−6.75416	+	6.75416i	−0.265533	+	0.265533i	0.561764	+	0.827297i	$0.310123\pi$
$648$	−3.19030	−	8.41558i	−0.125327	−	0.330595i
$649$			23.4114i			0.918979i
$650$	−4.39975	−	8.30643i	−0.172572	−	0.325805i
$651$	−27.3513	−	2.90353i	−1.07198	−	0.113798i
$652$	11.0783	+	11.0783i	0.433859	+	0.433859i
$653$	13.6366	+	13.6366i	0.533643	+	0.533643i	0.921655	−	0.388011i	$-0.126838\pi$
$653$	13.6366	+	13.6366i	0.533643	+	0.533643i	−0.388011	+	0.921655i	$0.626838\pi$
$654$	−10.8981	−	1.15690i	−0.426148	−	0.0452385i
$655$	40.5328	−	10.0719i	1.58375	−	0.393541i
$656$			1.74242i			0.0680300i
$657$	14.6655	+	22.6862i	0.572156	+	0.885071i
$658$	−21.1831	+	21.1831i	−0.825805	+	0.825805i
$659$	10.2941			0.401002			0.200501	−	0.979694i	$-0.435743\pi$
$659$	10.2941			0.401002			0.200501	+	0.979694i	$0.435743\pi$
$660$	14.2155	+	10.7530i	0.553337	+	0.418562i
$661$	3.04994			0.118629			0.0593145	−	0.998239i	$-0.481109\pi$
$661$	3.04994			0.118629			0.0593145	+	0.998239i	$0.481109\pi$
$662$	−11.8631	+	11.8631i	−0.461071	+	0.461071i
$663$	9.85298	+	12.1933i	0.382658	+	0.473550i
$664$		−	5.48450i		−	0.212840i
$665$	−7.77084	−	4.67757i	−0.301340	−	0.181388i
$666$	3.81744	−	17.7776i	0.147923	−	0.688867i
$667$	12.4589	+	12.4589i	0.482412	+	0.482412i
$668$	−4.00388	−	4.00388i	−0.154915	−	0.154915i
$669$	2.61746	−	24.6565i	0.101197	−	0.953277i
$670$	4.78883	+	19.2720i	0.185009	+	0.744541i
$671$			2.05268i			0.0792427i
$672$	5.46453	−	4.41568i	0.210799	−	0.170339i
$673$	2.16629	−	2.16629i	0.0835045	−	0.0835045i	−0.664121	−	0.747625i	$-0.731194\pi$
$673$	2.16629	−	2.16629i	0.0835045	−	0.0835045i	0.747625	+	0.664121i	$0.231194\pi$
$674$	−27.3141			−1.05210
$675$	21.2118	+	15.0020i	0.816444	+	0.577425i
$676$	9.46581			0.364070
$677$	6.41647	−	6.41647i	0.246605	−	0.246605i	−0.572971	−	0.819576i	$-0.694209\pi$
$677$	6.41647	−	6.41647i	0.246605	−	0.246605i	0.819576	+	0.572971i	$0.194209\pi$
$678$	−1.87618	+	1.51607i	−0.0720541	+	0.0582242i
$679$			71.7479i			2.75343i
$680$	2.59614	+	10.4478i	0.0995574	+	0.400654i
$681$	−3.55679	+	33.5051i	−0.136297	+	1.28392i
$682$	−12.7403	−	12.7403i	−0.487853	−	0.487853i
$683$	−19.7954	−	19.7954i	−0.757448	−	0.757448i	0.218409	−	0.975857i	$-0.429913\pi$
$683$	−19.7954	−	19.7954i	−0.757448	−	0.757448i	−0.975857	+	0.218409i	$0.929913\pi$
$684$	−0.629843	+	2.93314i	−0.0240826	+	0.112151i
$685$	−38.7996	−	23.3550i	−1.48246	−	0.892348i
$686$		−	9.95041i		−	0.379908i
$687$	−7.04387	−	8.71699i	−0.268740	−	0.332574i
$688$	−8.19327	+	8.19327i	−0.312366	+	0.312366i
$689$	13.1911			0.502541
$690$	8.76261	+	6.62831i	0.333587	+	0.252336i
$691$	7.17293			0.272871			0.136436	−	0.990649i	$-0.456435\pi$
$691$	7.17293			0.272871			0.136436	+	0.990649i	$0.456435\pi$
$692$	8.19231	−	8.19231i	0.311425	−	0.311425i
$693$	−30.4037	−	47.0317i	−1.15494	−	1.78659i
$694$			29.5246i			1.12074i
$695$	24.4407	−	6.07321i	0.927090	−	0.230370i
$696$	10.6975	+	1.13561i	0.405489	+	0.0430453i
$697$	5.93180	+	5.93180i	0.224683	+	0.224683i
$698$	7.98584	+	7.98584i	0.302269	+	0.302269i
$699$	9.75538	+	1.03560i	0.368982	+	0.0391700i
$700$	−5.96036	+	19.3856i	−0.225281	+	0.732707i
$701$		−	28.7624i		−	1.08634i	−0.839623	−	0.543170i	$-0.817224\pi$
$701$		−	28.7624i		−	1.08634i	0.839623	−	0.543170i	$-0.182776\pi$
$702$	8.71758	−	4.40759i	0.329024	−	0.166354i
$703$	−4.28573	+	4.28573i	−0.161639	+	0.161639i
$704$	4.60223			0.173453
$705$	−28.3329	+	3.92899i	−1.06708	+	0.147974i
$706$	−1.02329			−0.0385121
$707$	−5.31863	+	5.31863i	−0.200028	+	0.200028i
$708$	5.53775	+	6.85312i	0.208121	+	0.257556i
$709$		−	15.0208i		−	0.564119i	−0.959397	−	0.282060i	$-0.908982\pi$
$709$		−	15.0208i		−	0.564119i	0.959397	−	0.282060i	$-0.0910176\pi$
$710$	−17.9081	+	29.7507i	−0.672080	+	1.11653i
$711$	−30.6363	−	6.57864i	−1.14895	−	0.246718i
$712$	−1.46635	−	1.46635i	−0.0549536	−	0.0549536i
$713$	−7.85331	−	7.85331i	−0.294109	−	0.294109i
$714$	3.57066	−	33.6357i	0.133629	−	1.25879i
$715$	−9.97721	+	16.5751i	−0.373127	+	0.619875i
$716$			5.97757i			0.223392i
$717$	−2.65188	+	2.14288i	−0.0990362	+	0.0800274i
$718$	17.9890	−	17.9890i	0.671345	−	0.671345i
$719$	−0.237709			−0.00886505			−0.00443253	−	0.999990i	$-0.501411\pi$
$719$	−0.237709			−0.00886505			−0.00443253	+	0.999990i	$0.501411\pi$
$720$	6.70476	−	0.214847i	0.249872	−	0.00800686i
$721$	−65.7393			−2.44826
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	32.1990	−	26.0188i	1.19749	−	0.967649i
$724$		−	8.47586i		−	0.315003i
$725$	−27.4426	+	14.5358i	−1.01919	+	0.539846i
$726$	1.86143	−	17.5347i	0.0690840	−	0.650773i
$727$	29.5991	+	29.5991i	1.09777	+	1.09777i	0.994671	+	0.103098i	$0.0328754\pi$
$727$	29.5991	+	29.5991i	1.09777	+	1.09777i	0.103098	+	0.994671i	$0.467125\pi$
$728$	5.39205	+	5.39205i	0.199843	+	0.199843i
$729$	−16.0063	+	21.7439i	−0.592826	+	0.805330i
$730$	−19.5406	+	4.85558i	−0.723229	+	0.179713i
$731$			55.7856i			2.06330i
$732$	0.485541	+	0.600871i	0.0179461	+	0.0222088i
$733$	20.2570	−	20.2570i	0.748209	−	0.748209i	−0.225933	−	0.974143i	$-0.572543\pi$
$733$	20.2570	−	20.2570i	0.748209	−	0.748209i	0.974143	+	0.225933i	$0.0725432\pi$
$734$	−19.8748			−0.733593
$735$	22.0870	−	29.1990i	0.814693	−	1.07702i
$736$	2.83687			0.104569
$737$	28.9005	−	28.9005i	1.06456	−	1.06456i
$738$	4.38986	−	2.83783i	0.161593	−	0.104462i
$739$		−	48.1026i		−	1.76948i	−0.466081	−	0.884742i	$-0.654334\pi$
$739$		−	48.1026i		−	1.76948i	0.466081	−	0.884742i	$-0.345666\pi$
$740$	11.6114	+	6.98934i	0.426843	+	0.256933i
$741$	−3.23796	−	0.343732i	−0.118950	−	0.0126273i
$742$	−20.1254	−	20.1254i	−0.738828	−	0.738828i
$743$	−32.7093	−	32.7093i	−1.19999	−	1.19999i	−0.974170	−	0.225817i	$-0.927495\pi$
$743$	−32.7093	−	32.7093i	−1.19999	−	1.19999i	−0.225817	−	0.974170i	$-0.572505\pi$
$744$	−6.74302	−	0.715817i	−0.247211	−	0.0262431i
$745$	3.01577	+	12.1365i	0.110489	+	0.444648i
$746$			7.81442i			0.286106i
$747$	−13.8177	+	8.93247i	−0.505563	+	0.326822i
$748$	15.6676	−	15.6676i	0.572865	−	0.572865i
$749$	−49.4079			−1.80533
$750$	−15.7053	+	11.3288i	−0.573478	+	0.413670i
$751$	20.7531			0.757292			0.378646	−	0.925542i	$-0.376390\pi$
$751$	20.7531			0.757292			0.378646	+	0.925542i	$0.376390\pi$
$752$	−5.22236	+	5.22236i	−0.190440	+	0.190440i
$753$	−6.90825	−	8.54916i	−0.251751	−	0.311549i
$754$			11.6762i			0.425221i
$755$	2.49201	+	10.0287i	0.0906937	+	0.364983i
$756$	−20.0248	−	6.57567i	−0.728297	−	0.239155i
$757$	36.1673	+	36.1673i	1.31452	+	1.31452i	0.918045	+	0.396477i	$0.129767\pi$
$757$	36.1673	+	36.1673i	1.31452	+	1.31452i	0.396477	+	0.918045i	$0.370233\pi$
$758$	5.79549	+	5.79549i	0.210502	+	0.210502i
$759$	2.38717	−	22.4872i	0.0866488	−	0.816234i
$760$	−1.91577	−	1.15318i	−0.0694923	−	0.0418301i
$761$		−	20.2602i		−	0.734432i	−0.930136	−	0.367216i	$-0.880311\pi$
$761$		−	20.2602i		−	0.734432i	0.930136	−	0.367216i	$-0.119689\pi$
$762$	−15.8535	+	12.8106i	−0.574311	+	0.464079i
$763$	−18.1481	+	18.1481i	−0.657006	+	0.657006i
$764$	−6.45739			−0.233620
$765$	22.0940	−	23.5568i	0.798809	−	0.851697i
$766$	−16.4922			−0.595886
$767$	−6.76222	+	6.76222i	−0.244170	+	0.244170i
$768$	1.34719	−	1.08861i	0.0486125	−	0.0392819i
$769$		−	10.8266i		−	0.390416i	−0.980762	−	0.195208i	$-0.937462\pi$
$769$		−	10.8266i		−	0.390416i	0.980762	−	0.195208i	$-0.0625382\pi$
$770$	40.5105	−	10.0663i	1.45990	−	0.362765i
$771$	−0.841363	+	7.92567i	−0.0303010	+	0.285436i
$772$	−4.32749	−	4.32749i	−0.155750	−	0.155750i
$773$	−15.4031	−	15.4031i	−0.554011	−	0.554011i	0.373585	−	0.927596i	$-0.378128\pi$
$773$	−15.4031	−	15.4031i	−0.554011	−	0.554011i	−0.927596	+	0.373585i	$0.878128\pi$
$774$	33.9864	+	7.29801i	1.22161	+	0.262321i
$775$	17.2981	−	9.16243i	0.621365	−	0.329124i
$776$			17.6883i			0.634972i
$777$	−26.7632	−	33.1202i	−0.960123	−	1.18818i
$778$	11.0403	−	11.0403i	0.395813	−	0.395813i
$779$	−1.74242			−0.0624286
$780$	1.00010	+	7.21197i	0.0358094	+	0.258230i
$781$	71.4698			2.55739
$782$	9.65772	−	9.65772i	0.345359	−	0.345359i
$783$	−14.5617	−	28.8010i	−0.520393	−	1.02926i
$784$		−	9.45311i		−	0.337611i
$785$	−16.8098	+	27.9262i	−0.599969	+	0.996727i
$786$	−32.1706	−	3.41513i	−1.14749	−	0.121814i
$787$	23.9171	+	23.9171i	0.852552	+	0.852552i	0.990447	−	0.137895i	$-0.0440337\pi$
$787$	23.9171	+	23.9171i	0.852552	+	0.852552i	−0.137895	+	0.990447i	$0.544034\pi$
$788$	−14.8702	−	14.8702i	−0.529728	−	0.529728i
$789$	−49.3749	−	5.24148i	−1.75779	−	0.186602i
$790$	12.0448	−	20.0100i	0.428535	−	0.711925i
$791$			5.64896i			0.200854i
$792$	−7.49554	−	11.5949i	−0.266343	−	0.412007i
$793$	−0.592901	+	0.592901i	−0.0210545	+	0.0210545i
$794$	33.0892			1.17429
$795$	−3.73281	−	26.9182i	−0.132389	−	0.954690i
$796$	−0.789726			−0.0279911
$797$	−21.0294	+	21.0294i	−0.744901	+	0.744901i	−0.973517	−	0.228616i	$-0.926580\pi$
$797$	−21.0294	+	21.0294i	−0.744901	+	0.744901i	0.228616	+	0.973517i	$0.426580\pi$
$798$	4.41568	+	5.46453i	0.156313	+	0.193442i
$799$			35.5575i			1.25793i
$800$	−1.46943	+	4.77920i	−0.0519522	+	0.168970i
$801$	−1.30612	+	6.08252i	−0.0461495	+	0.214915i
$802$	3.47739	+	3.47739i	0.122791	+	0.122791i
$803$	29.3033	+	29.3033i	1.03409	+	1.03409i
$804$	1.62378	−	15.2960i	0.0572661	−	0.539449i
$805$	24.9712	−	6.20501i	0.880118	−	0.218698i
$806$		−	7.35990i		−	0.259242i
$807$	22.7741	−	18.4029i	0.801685	−	0.647811i
$808$	−1.31122	+	1.31122i	−0.0461286	+	0.0461286i
$809$	−55.3606			−1.94637			−0.973187	−	0.230016i	$-0.926122\pi$
$809$	−55.3606			−1.94637			−0.973187	+	0.230016i	$0.926122\pi$
$810$	−11.4612	−	16.5421i	−0.402704	−	0.581231i
$811$	−48.8943			−1.71691			−0.858455	−	0.512889i	$-0.828575\pi$
$811$	−48.8943			−1.71691			−0.858455	+	0.512889i	$0.828575\pi$
$812$	17.8141	−	17.8141i	0.625154	−	0.625154i
$813$	−3.95714	+	3.19761i	−0.138783	+	0.112145i
$814$		−	27.8939i		−	0.977679i
$815$	30.0145	+	18.0669i	1.05136	+	0.632856i
$816$	0.880287	−	8.29233i	0.0308162	−	0.290290i
$817$	−8.19327	−	8.19327i	−0.286646	−	0.286646i
$818$	−2.40059	−	2.40059i	−0.0839345	−	0.0839345i
$819$	4.80287	−	22.3667i	0.167826	−	0.781554i
$820$	0.939573	+	3.78118i	0.0328113	+	0.132044i
$821$			25.1748i			0.878606i	0.898339	+	0.439303i	$0.144775\pi$
$821$			25.1748i			0.878606i	−0.898339	+	0.439303i	$0.855225\pi$
$822$	22.0474	+	27.2843i	0.768991	+	0.951648i
$823$	−8.56588	+	8.56588i	−0.298588	+	0.298588i	−0.840460	−	0.541873i	$-0.817715\pi$
$823$	−8.56588	+	8.56588i	−0.298588	+	0.298588i	0.541873	+	0.840460i	$0.317715\pi$
$824$	−16.2069			−0.564596
$825$	36.6471	+	15.6694i	1.27589	+	0.545539i
$826$	20.6340			0.717949
$827$	−11.7327	+	11.7327i	−0.407986	+	0.407986i	−0.881036	−	0.473050i	$-0.843153\pi$
$827$	−11.7327	+	11.7327i	−0.407986	+	0.407986i	0.473050	+	0.881036i	$0.343153\pi$
$828$	−4.62035	−	7.14724i	−0.160568	−	0.248384i
$829$			2.19216i			0.0761369i	0.999275	+	0.0380684i	$0.0121205\pi$
$829$			2.19216i			0.0761369i	−0.999275	+	0.0380684i	$0.987880\pi$
$830$	−2.95744	−	11.9018i	−0.102654	−	0.413117i
$831$	−9.83734	−	1.04430i	−0.341254	−	0.0362264i
$832$	1.32932	+	1.32932i	0.0460859	+	0.0460859i
$833$	−32.1817	−	32.1817i	−1.11503	−	1.11503i
$834$	−19.3984	−	2.05927i	−0.671713	−	0.0713069i
$835$	−10.8478	−	6.52969i	−0.375402	−	0.225969i
$836$			4.60223i			0.159172i
$837$	9.17876	+	18.1543i	0.317264	+	0.627503i
$838$	8.87416	−	8.87416i	0.306553	−	0.306553i
$839$	23.1579			0.799501			0.399750	−	0.916624i	$-0.369097\pi$
$839$	23.1579			0.799501			0.399750	+	0.916624i	$0.369097\pi$
$840$	9.47735	−	12.5290i	0.327000	−	0.432292i
$841$	9.57554			0.330191
$842$	10.1279	−	10.1279i	0.349030	−	0.349030i
$843$	15.3360	+	18.9788i	0.528201	+	0.653664i
$844$			19.8686i			0.683905i
$845$	20.5415	−	5.10430i	0.706650	−	0.175593i
$846$	21.6628	+	4.65172i	0.744781	+	0.159929i
$847$	−29.1998	−	29.1998i	−1.00332	−	1.00332i
$848$	−4.96160	−	4.96160i	−0.170382	−	0.170382i
$849$	3.89648	−	36.7050i	0.133727	−	1.25971i
$850$	11.2676	+	21.2725i	0.386477	+	0.729642i
$851$		−	17.1941i		−	0.589407i
$852$	20.9210	−	16.9055i	0.716743	−	0.579172i
$853$	28.3401	−	28.3401i	0.970346	−	0.970346i	−0.0292268	−	0.999573i	$-0.509305\pi$
$853$	28.3401	−	28.3401i	0.970346	−	0.970346i	0.999573	+	0.0292268i	$0.00930451\pi$
$854$	1.80916			0.0619081
$855$	0.214847	+	6.70476i	0.00734760	+	0.229298i
$856$	−12.1807			−0.416328
$857$	−37.5618	+	37.5618i	−1.28309	+	1.28309i	−0.344182	+	0.938903i	$0.611844\pi$
$857$	−37.5618	+	37.5618i	−1.28309	+	1.28309i	−0.938903	+	0.344182i	$0.888156\pi$
$858$	11.6558	−	9.41861i	0.397922	−	0.321546i
$859$		−	21.0474i		−	0.718128i	−0.933313	−	0.359064i	$-0.883096\pi$
$859$		−	21.0474i		−	0.718128i	0.933313	−	0.359064i	$-0.116904\pi$
$860$	−13.3619	+	22.1981i	−0.455637	+	0.756949i
$861$	1.29226	−	12.1732i	0.0440402	−	0.414860i
$862$	5.87010	+	5.87010i	0.199936	+	0.199936i
$863$	16.8012	+	16.8012i	0.571918	+	0.571918i	0.932664	−	0.360746i	$-0.117478\pi$
$863$	16.8012	+	16.8012i	0.571918	+	0.571918i	−0.360746	+	0.932664i	$0.617478\pi$
$864$	−4.93680	−	1.62112i	−0.167953	−	0.0551517i
$865$	13.3603	−	22.1955i	0.454265	−	0.754670i
$866$		−	15.2966i		−	0.519799i
$867$	−6.72679	−	8.32460i	−0.228454	−	0.282718i
$868$	−11.2289	+	11.2289i	−0.381133	+	0.381133i
$869$	−48.0698			−1.63066
$870$	23.8268	−	3.30412i	0.807804	−	0.112020i
$871$	16.6954			0.565701
$872$	−4.47412	+	4.47412i	−0.151513	+	0.151513i
$873$	44.5640	−	28.8085i	1.50826	−	0.975019i
$874$			2.83687i			0.0959587i
$875$	−2.48102	+	45.2823i	−0.0838739	+	1.53082i
$876$	15.5092	+	1.64641i	0.524008	+	0.0556270i
$877$	−17.3922	−	17.3922i	−0.587291	−	0.587291i	0.349606	−	0.936897i	$-0.386316\pi$
$877$	−17.3922	−	17.3922i	−0.587291	−	0.587291i	−0.936897	+	0.349606i	$0.886316\pi$
$878$	12.0488	+	12.0488i	0.406629	+	0.406629i
$879$	−11.9940	−	1.27324i	−0.404547	−	0.0429454i
$880$	9.98719	−	2.48169i	0.336668	−	0.0836577i
$881$		−	1.61838i		−	0.0545246i	−0.999628	−	0.0272623i	$-0.991321\pi$
$881$		−	1.61838i		−	0.0545246i	0.999628	−	0.0272623i	$-0.00867894\pi$
$882$	−23.8162	+	15.3961i	−0.801934	+	0.518412i
$883$	9.09541	−	9.09541i	0.306085	−	0.306085i	−0.537304	−	0.843389i	$-0.680557\pi$
$883$	9.09541	−	9.09541i	0.306085	−	0.306085i	0.843389	+	0.537304i	$0.180557\pi$
$884$	9.05095			0.304416
$885$	15.7128	+	11.8856i	0.528179	+	0.399531i
$886$	36.0370			1.21069
$887$	31.1947	−	31.1947i	1.04742	−	1.04742i	0.0485966	−	0.998818i	$-0.484525\pi$
$887$	31.1947	−	31.1947i	1.04742	−	1.04742i	0.998818	−	0.0485966i	$-0.0154749\pi$
$888$	−6.59802	−	8.16524i	−0.221415	−	0.274007i
$889$			47.7331i			1.60092i
$890$	−3.97278	−	2.39137i	−0.133168	−	0.0801590i
$891$	−17.0045	+	37.7687i	−0.569671	+	1.26530i
$892$	−10.1226	−	10.1226i	−0.338928	−	0.338928i
$893$	−5.22236	−	5.22236i	−0.174759	−	0.174759i
$894$	1.02257	−	9.63269i	0.0342000	−	0.322165i
$895$	3.22332	+	12.9718i	0.107744	+	0.433598i
$896$		−	4.05624i		−	0.135510i
$897$	7.18478	−	5.80575i	0.239893	−	0.193848i
$898$	−5.23356	+	5.23356i	−0.174646	+	0.174646i
$899$	−24.3155			−0.810968
$900$	14.4340	−	4.08168i	0.481133	−	0.136056i
$901$	−33.7820			−1.12544
$902$	5.67029	−	5.67029i	0.188800	−	0.188800i
$903$	63.3177	−	51.1646i	2.10708	−	1.70265i
$904$			1.39266i			0.0463192i
$905$	−4.57049	−	18.3933i	−0.151928	−	0.611413i
$906$	0.844980	−	7.95974i	0.0280726	−	0.264445i
$907$	−13.0460	−	13.0460i	−0.433187	−	0.433187i	0.456524	−	0.889711i	$-0.349094\pi$
$907$	−13.0460	−	13.0460i	−0.433187	−	0.433187i	−0.889711	+	0.456524i	$0.849094\pi$
$908$	13.7553	+	13.7553i	0.456484	+	0.456484i
$909$	5.43905	+	1.16795i	0.180402	+	0.0387383i
$910$	14.6087	+	8.79356i	0.484275	+	0.291504i
$911$		−	50.7130i		−	1.68020i	−0.542434	−	0.840098i	$-0.682497\pi$
$911$		−	50.7130i		−	1.68020i	0.542434	−	0.840098i	$-0.317503\pi$
$912$	1.08861	+	1.34719i	0.0360476	+	0.0446099i
$913$	−17.8480	+	17.8480i	−0.590684	+	0.590684i
$914$	−20.7832			−0.687447
$915$	1.37767	+	1.04211i	0.0455444	+	0.0344512i
$916$	−6.47050			−0.213791
$917$	−53.5724	+	53.5724i	−1.76912	+	1.76912i
$918$	−22.3255	+	11.2877i	−0.736850	+	0.372550i
$919$		−	20.6702i		−	0.681847i	−0.940091	−	0.340924i	$-0.889260\pi$
$919$		−	20.6702i		−	0.681847i	0.940091	−	0.340924i	$-0.110740\pi$
$920$	6.15623	−	1.52974i	0.202965	−	0.0504342i
$921$	−18.0530	−	1.91645i	−0.594867	−	0.0631491i
$922$	26.7315	+	26.7315i	0.880356	+	0.880356i
$923$	20.6435	+	20.6435i	0.679490	+	0.679490i
$924$	−32.1529	−	3.41324i	−1.05775	−	0.112287i
$925$	28.9665	+	8.90612i	0.952411	+	0.292831i
$926$		−	1.11676i		−	0.0366990i
$927$	26.3959	+	40.8319i	0.866954	+	1.34110i
$928$	4.39178	−	4.39178i	0.144167	−	0.144167i
$929$	−24.9065			−0.817156			−0.408578	−	0.912723i	$-0.633975\pi$
$929$	−24.9065			−0.817156			−0.408578	+	0.912723i	$0.633975\pi$
$930$	−15.0189	+	2.08270i	−0.492488	+	0.0682945i
$931$	9.45311			0.309813
$932$	4.00499	−	4.00499i	0.131188	−	0.131188i
$933$	24.6091	+	30.4544i	0.805665	+	0.997034i
$934$		−	39.8107i		−	1.30265i
$935$	25.5514	−	42.4484i	0.835619	−	1.38821i
$936$	1.18407	−	5.51413i	0.0387025	−	0.180235i
$937$	33.4021	+	33.4021i	1.09120	+	1.09120i	0.995401	+	0.0957973i	$0.0305401\pi$
$937$	33.4021	+	33.4021i	1.09120	+	1.09120i	0.0957973	+	0.995401i	$0.469460\pi$
$938$	−25.4718	−	25.4718i	−0.831685	−	0.831685i
$939$	−4.56746	+	43.0256i	−0.149053	+	1.40409i
$940$	−8.51682	+	14.1490i	−0.277788	+	0.461489i
$941$		−	2.02241i		−	0.0659288i	−0.999457	−	0.0329644i	$-0.989505\pi$
$941$		−	2.02241i		−	0.0659288i	0.999457	−	0.0329644i	$-0.0104948\pi$
$942$	19.6380	−	15.8687i	0.639839	−	0.517030i
$943$	3.49524	−	3.49524i	0.113821	−	0.113821i
$944$	5.08697			0.165567
$945$	−47.0013	−	3.47159i	−1.52895	−	0.112931i
$946$	53.3262			1.73378
$947$	7.33043	−	7.33043i	0.238207	−	0.238207i	−0.577900	−	0.816107i	$-0.696128\pi$
$947$	7.33043	−	7.33043i	0.238207	−	0.238207i	0.816107	+	0.577900i	$0.196128\pi$
$948$	−14.0713	+	11.3704i	−0.457013	+	0.369295i
$949$			16.9281i			0.549508i
$950$	−4.77920	−	1.46943i	−0.155058	−	0.0476746i
$951$	−0.159762	+	1.50497i	−0.00518064	+	0.0488018i
$952$	−13.8089	−	13.8089i	−0.447548	−	0.447548i
$953$	17.9338	+	17.9338i	0.580934	+	0.580934i	0.935160	−	0.354226i	$-0.115256\pi$
$953$	17.9338	+	17.9338i	0.580934	+	0.580934i	−0.354226	+	0.935160i	$0.615256\pi$
$954$	−4.41945	+	20.5811i	−0.143085	+	0.666338i
$955$	−14.0130	+	3.48205i	−0.453451	+	0.112677i
$956$			1.96845i			0.0636643i
$957$	−31.1170	−	38.5082i	−1.00587	−	1.24479i
$958$	16.2689	−	16.2689i	0.525624	−	0.525624i
$959$	82.1500			2.65276
$960$	2.33648	−	3.08883i	0.0754097	−	0.0996914i
$961$	−15.6731			−0.505583
$962$	8.05693	−	8.05693i	0.259766	−	0.259766i
$963$	19.8384	+	30.6882i	0.639284	+	0.988913i
$964$		−	23.9008i		−	0.769794i
$965$	−11.7245	−	7.05744i	−0.377426	−	0.227187i
$966$	−19.8194	−	2.10397i	−0.637680	−	0.0676940i
$967$	−7.13685	−	7.13685i	−0.229506	−	0.229506i	0.582980	−	0.812486i	$-0.301886\pi$
$967$	−7.13685	−	7.13685i	−0.229506	−	0.229506i	−0.812486	+	0.582980i	$0.801886\pi$
$968$	−7.19873	−	7.19873i	−0.231376	−	0.231376i
$969$	8.29233	+	0.880287i	0.266388	+	0.0282789i
$970$	9.53815	+	38.3849i	0.306251	+	1.23246i
$971$		−	0.247821i		−	0.00795295i	−0.999992	−	0.00397648i	$-0.998734\pi$
$971$		−	0.247821i		−	0.00795295i	0.999992	−	0.00397648i	$-0.00126576\pi$
$972$	3.95617	+	15.0781i	0.126894	+	0.483630i
$973$	−32.3034	+	32.3034i	−1.03560	+	1.03560i
$974$	−28.9973			−0.929134
$975$	6.05925	+	15.1112i	0.194051	+	0.483947i
$976$	0.446018			0.0142767
$977$	−14.2133	+	14.2133i	−0.454724	+	0.454724i	−0.896919	−	0.442195i	$-0.854200\pi$
$977$	−14.2133	+	14.2133i	−0.454724	+	0.454724i	0.442195	+	0.896919i	$0.354200\pi$
$978$	−17.0554	−	21.1065i	−0.545370	−	0.674911i
$979$			9.54376i			0.305020i
$980$	−5.09745	−	20.5140i	−0.162832	−	0.655294i
$981$	18.5590	+	3.98524i	0.592544	+	0.127239i
$982$	11.9641	+	11.9641i	0.381791	+	0.381791i
$983$	−36.3201	−	36.3201i	−1.15843	−	1.15843i	−0.984813	−	0.173617i	$-0.944455\pi$
$983$	−36.3201	−	36.3201i	−1.15843	−	1.15843i	−0.173617	−	0.984813i	$-0.555545\pi$
$984$	0.318586	−	3.00109i	0.0101562	−	0.0956713i
$985$	−40.2879	−	24.2508i	−1.28368	−	0.772696i
$986$		−	29.9024i		−	0.952285i
$987$	40.3584	−	32.6121i	1.28462	−	1.03806i
$988$	−1.32932	+	1.32932i	−0.0422913	+	0.0422913i
$989$	32.8710			1.04524
$990$	−22.5183	−	21.1199i	−0.715678	−	0.671236i
$991$	−10.0851			−0.320364			−0.160182	−	0.987088i	$-0.551208\pi$
$991$	−10.0851			−0.320364			−0.160182	+	0.987088i	$0.551208\pi$
$992$	−2.76830	+	2.76830i	−0.0878935	+	0.0878935i
$993$	22.6017	−	18.2636i	0.717243	−	0.579577i
$994$		−	62.9909i		−	1.99795i
$995$	−1.71377	+	0.425849i	−0.0543300	+	0.0135003i
$996$	−1.00279	+	9.44635i	−0.0317747	+	0.299319i
$997$	8.34108	+	8.34108i	0.264165	+	0.264165i	0.826744	−	0.562579i	$-0.190191\pi$
$997$	8.34108	+	8.34108i	0.264165	+	0.264165i	−0.562579	+	0.826744i	$0.690191\pi$
$998$	18.3862	+	18.3862i	0.582005	+	0.582005i
$999$	−9.82553	+	29.9216i	−0.310866	+	0.946678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.8	✓	36
3.2	odd	2	inner	570.2.k.b.77.15	yes	36
5.3	odd	4	inner	570.2.k.b.533.15	yes	36
15.8	even	4	inner	570.2.k.b.533.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.8	✓	36	1.1	even	1	trivial
570.2.k.b.77.15	yes	36	3.2	odd	2	inner
570.2.k.b.533.8	yes	36	15.8	even	4	inner
570.2.k.b.533.15	yes	36	5.3	odd	4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +(1.91577 + 1.15318i) q^{10} -4.60223i q^{11} +(-1.08861 - 1.34719i) q^{12} +(1.32932 - 1.32932i) q^{13} -4.05624 q^{14} +(-3.08883 - 2.33648i) q^{15} -1.00000 q^{16} +(-3.40435 + 3.40435i) q^{17} +(1.62868 + 2.51941i) q^{18} -1.00000i q^{19} +(-2.17007 + 0.539236i) q^{20} +(6.98636 + 0.741650i) q^{21} +(3.25427 + 3.25427i) q^{22} +(2.00597 + 2.00597i) q^{23} +(1.72237 + 0.182842i) q^{24} +(-4.41845 + 2.34036i) q^{25} +1.87994i q^{26} +(-2.34453 - 4.63715i) q^{27} +(2.86820 - 2.86820i) q^{28} +6.21092 q^{29} +(3.83627 - 0.531985i) q^{30} -3.91496 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.01005 - 6.20008i) q^{33} -4.81448i q^{34} +(4.67757 - 7.77084i) q^{35} +(-2.93314 - 0.629843i) q^{36} +(-4.28573 - 4.28573i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.343732 - 3.23796i) q^{39} +(1.15318 - 1.91577i) q^{40} -1.74242i q^{41} +(-5.46453 + 4.41568i) q^{42} +(8.19327 - 8.19327i) q^{43} -4.60223 q^{44} +(-6.70476 + 0.214847i) q^{45} -2.83687 q^{46} +(5.22236 - 5.22236i) q^{47} +(-1.34719 + 1.08861i) q^{48} +9.45311i q^{49} +(1.46943 - 4.77920i) q^{50} +(-0.880287 + 8.29233i) q^{51} +(-1.32932 - 1.32932i) q^{52} +(4.96160 + 4.96160i) q^{53} +(4.93680 + 1.62112i) q^{54} +(-9.98719 + 2.48169i) q^{55} +4.05624i q^{56} +(-1.08861 - 1.34719i) q^{57} +(-4.39178 + 4.39178i) q^{58} -5.08697 q^{59} +(-2.33648 + 3.08883i) q^{60} -0.446018 q^{61} +(2.76830 - 2.76830i) q^{62} +(10.2193 - 6.60631i) q^{63} +1.00000i q^{64} +(-3.60154 - 2.16791i) q^{65} +(7.92676 + 0.841479i) q^{66} +(6.27966 + 6.27966i) q^{67} +(3.40435 + 3.40435i) q^{68} +(4.88616 + 0.518698i) q^{69} +(2.18727 + 8.80235i) q^{70} +15.5294i q^{71} +(2.51941 - 1.62868i) q^{72} +(-6.36719 + 6.36719i) q^{73} +6.06094 q^{74} +(-3.40474 + 7.96290i) q^{75} -1.00000 q^{76} +(13.2001 - 13.2001i) q^{77} +(2.04653 + 2.53264i) q^{78} -10.4449i q^{79} +(0.539236 + 2.17007i) q^{80} +(-8.20660 - 3.69483i) q^{81} +(1.23207 + 1.23207i) q^{82} +(-3.87813 - 3.87813i) q^{83} +(0.741650 - 6.98636i) q^{84} +(9.22345 + 5.55195i) q^{85} +11.5870i q^{86} +(8.36729 - 6.76129i) q^{87} +(3.25427 - 3.25427i) q^{88} -2.07373 q^{89} +(4.58906 - 4.89290i) q^{90} +7.62551 q^{91} +(2.00597 - 2.00597i) q^{92} +(-5.27420 + 4.26188i) q^{93} +7.38553i q^{94} +(-2.17007 + 0.539236i) q^{95} +(0.182842 - 1.72237i) q^{96} +(12.5075 + 12.5075i) q^{97} +(-6.68436 - 6.68436i) q^{98} +(-13.4990 - 2.89868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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