LMFDB - Embedded newform 570.2.k.b.533.15

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			533.15
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.08861 + 1.34719i) q^{3} +1.00000i q^{4} +(0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 - 2.86820i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.629843 + 2.93314i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.08861 + 1.34719i) 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} +(-1.34719 + 1.08861i) q^{12} +(1.32932 + 1.32932i) q^{13} +4.05624 q^{14} +(3.51052 - 1.63592i) q^{15} -1.00000 q^{16} +(3.40435 + 3.40435i) q^{17} +(-2.51941 + 1.62868i) 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} +(-4.63715 + 2.34453i) q^{27} +(2.86820 + 2.86820i) q^{28} -6.21092 q^{29} +(3.63908 + 1.32554i) q^{30} -3.91496 q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.20008 - 5.01005i) 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} +(4.41568 + 5.46453i) q^{42} +(8.19327 + 8.19327i) q^{43} +4.60223 q^{44} +(6.02550 + 2.94846i) q^{45} -2.83687 q^{46} +(-5.22236 - 5.22236i) q^{47} +(-1.08861 - 1.34719i) 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} +(-1.34719 + 1.08861i) q^{57} +(-4.39178 - 4.39178i) q^{58} +5.08697 q^{59} +(1.63592 + 3.51052i) q^{60} -0.446018 q^{61} +(-2.76830 - 2.76830i) q^{62} +(6.60631 + 10.2193i) 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} +(-1.62868 - 2.51941i) q^{72} +(-6.36719 - 6.36719i) q^{73} -6.06094 q^{74} +(-1.65707 - 8.50024i) q^{75} -1.00000 q^{76} +(-13.2001 - 13.2001i) q^{77} +(-2.53264 + 2.04653i) 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} +(-6.76129 - 8.36729i) q^{87} +(3.25427 + 3.25427i) q^{88} +2.07373 q^{89} +(2.17579 + 6.34554i) q^{90} +7.62551 q^{91} +(-2.00597 - 2.00597i) q^{92} +(-4.26188 - 5.27420i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.08861	+	1.34719i	0.628511	+	0.777801i
$3$	1.08861	+	1.34719i	0.628511	+	0.777801i
$4$			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	0.0879519	−	0.996125i	$-0.471968\pi$
$7$	2.86820	−	2.86820i	1.08408	−	1.08408i	0.996125	−	0.0879519i	$-0.0280322\pi$
$8$	−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	$-0.244070\pi$
$12$	−1.34719	+	1.08861i	−0.388900	+	0.314256i
$13$	1.32932	+	1.32932i	0.368687	+	0.368687i	0.866998	−	0.498311i	$-0.166046\pi$
$13$	1.32932	+	1.32932i	0.368687	+	0.368687i	−0.498311	+	0.866998i	$0.666046\pi$
$14$	4.05624			1.08408
$15$	3.51052	−	1.63592i	0.906413	−	0.422393i
$16$	−1.00000			−0.250000
$17$	3.40435	+	3.40435i	0.825677	+	0.825677i	0.986915	−	0.161239i	$-0.0515489\pi$
$17$	3.40435	+	3.40435i	0.825677	+	0.825677i	−0.161239	+	0.986915i	$0.551549\pi$
$18$	−2.51941	+	1.62868i	−0.593830	+	0.383883i
$19$			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	$-0.845574\pi$
$23$	−2.00597	+	2.00597i	−0.418274	+	0.418274i	0.466334	+	0.884609i	$0.345574\pi$
$24$	−1.72237	−	0.182842i	−0.351578	−	0.0373224i
$25$	−4.41845	−	2.34036i	−0.883690	−	0.468073i
$26$			1.87994i			0.368687i
$27$	−4.63715	+	2.34453i	−0.892420	+	0.451206i
$28$	2.86820	+	2.86820i	0.542038	+	0.542038i
$29$	−6.21092			−1.15334			−0.576670	−	0.816978i	$-0.695648\pi$
$29$	−6.21092			−1.15334			−0.576670	+	0.816978i	$0.695648\pi$
$30$	3.63908	+	1.32554i	0.664403	+	0.242010i
$31$	−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
$33$	6.20008	−	5.01005i	1.07930	−	0.872138i
$34$			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	−0.965388	−	0.260818i	$-0.916008\pi$
$37$	−4.28573	+	4.28573i	−0.704570	+	0.704570i	0.260818	+	0.965388i	$0.416008\pi$
$38$	−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	$-0.0434440\pi$
$42$	4.41568	+	5.46453i	0.681354	+	0.843195i
$43$	8.19327	+	8.19327i	1.24946	+	1.24946i	0.955958	+	0.293504i	$0.0948215\pi$
$43$	8.19327	+	8.19327i	1.24946	+	1.24946i	0.293504	+	0.955958i	$0.405178\pi$
$44$	4.60223			0.693813
$45$	6.02550	+	2.94846i	0.898228	+	0.439530i
$46$	−2.83687			−0.418274
$47$	−5.22236	−	5.22236i	−0.761759	−	0.761759i	0.214881	−	0.976640i	$-0.431064\pi$
$47$	−5.22236	−	5.22236i	−0.761759	−	0.761759i	−0.976640	+	0.214881i	$0.931064\pi$
$48$	−1.08861	−	1.34719i	−0.157128	−	0.194450i
$49$		−	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	$-0.910058\pi$
$53$	−4.96160	+	4.96160i	−0.681527	+	0.681527i	0.278817	+	0.960344i	$0.410058\pi$
$54$	−4.93680	−	1.62112i	−0.671813	−	0.220607i
$55$	−9.98719	−	2.48169i	−1.34667	−	0.334631i
$56$			4.05624i			0.542038i
$57$	−1.34719	+	1.08861i	−0.178440	+	0.144190i
$58$	−4.39178	−	4.39178i	−0.576670	−	0.576670i
$59$	5.08697			0.662268			0.331134	−	0.943584i	$-0.392569\pi$
$59$	5.08697			0.662268			0.331134	+	0.943584i	$0.392569\pi$
$60$	1.63592	+	3.51052i	0.211196	+	0.453207i
$61$	−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
$63$	6.60631	+	10.2193i	0.832316	+	1.28751i
$64$		−	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	−0.210427	−	0.977610i	$-0.567485\pi$
$67$	6.27966	−	6.27966i	0.767183	−	0.767183i	0.977610	+	0.210427i	$0.0674854\pi$
$68$	−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	$0.626965\pi$
$72$	−1.62868	−	2.51941i	−0.191941	−	0.296915i
$73$	−6.36719	−	6.36719i	−0.745223	−	0.745223i	0.228355	−	0.973578i	$-0.426665\pi$
$73$	−6.36719	−	6.36719i	−0.745223	−	0.745223i	−0.973578	+	0.228355i	$0.926665\pi$
$74$	−6.06094			−0.704570
$75$	−1.65707	−	8.50024i	−0.191342	−	0.981523i
$76$	−1.00000			−0.114708
$77$	−13.2001	−	13.2001i	−1.50429	−	1.50429i
$78$	−2.53264	+	2.04653i	−0.286765	+	0.231724i
$79$			10.4449i			1.17514i	0.809173	+	0.587571i	$0.199916\pi$
$79$			10.4449i			1.17514i	−0.809173	+	0.587571i	$0.800084\pi$
$80$	−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	$-0.652679\pi$
$83$	3.87813	−	3.87813i	0.425680	−	0.425680i	0.887154	+	0.461474i	$0.152679\pi$
$84$	−0.741650	+	6.98636i	−0.0809206	+	0.762275i
$85$	9.22345	−	5.55195i	1.00042	−	0.602194i
$86$			11.5870i			1.24946i
$87$	−6.76129	−	8.36729i	−0.724886	−	0.897068i
$88$	3.25427	+	3.25427i	0.346906	+	0.346906i
$89$	2.07373			0.219814			0.109907	−	0.993942i	$-0.464945\pi$
$89$	2.07373			0.219814			0.109907	+	0.993942i	$0.464945\pi$
$90$	2.17579	+	6.34554i	0.229349	+	0.668879i
$91$	7.62551			0.799370
$92$	−2.00597	−	2.00597i	−0.209137	−	0.209137i
$93$	−4.26188	−	5.27420i	−0.441936	−	0.546909i
$94$		−	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	0.323828	−	0.946116i	$-0.395030\pi$
$97$	12.5075	−	12.5075i	1.26994	−	1.26994i	0.946116	−	0.323828i	$-0.104970\pi$
$98$	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	$0.970592\pi$
$102$	−6.48602	+	5.24111i	−0.642212	+	0.518947i
$103$	−11.4600	−	11.4600i	−1.12919	−	1.12919i	−0.990309	−	0.138882i	$-0.955649\pi$
$103$	−11.4600	−	11.4600i	−1.12919	−	1.12919i	−0.138882	−	0.990309i	$-0.544351\pi$
$104$	−1.87994			−0.184344
$105$	5.37673	−	14.7610i	0.524715	−	1.44053i
$106$	−7.01675			−0.681527
$107$	8.61306	+	8.61306i	0.832656	+	0.832656i	0.987879	−	0.155223i	$-0.0496097\pi$
$107$	8.61306	+	8.61306i	0.832656	+	0.832656i	−0.155223	+	0.987879i	$0.549610\pi$
$108$	−2.34453	−	4.63715i	−0.225603	−	0.446210i
$109$		−	6.32736i		−	0.606051i	−0.952982	−	0.303025i	$-0.902003\pi$
$109$		−	6.32736i		−	0.606051i	0.952982	−	0.303025i	$-0.0979967\pi$
$110$	−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	$-0.770866\pi$
$113$	−0.984759	+	0.984759i	−0.0926383	+	0.0926383i	0.659269	+	0.751907i	$0.270866\pi$
$114$	−1.72237	−	0.182842i	−0.161315	−	0.0171247i
$115$	3.27142	+	5.43480i	0.305061	+	0.506798i
$116$		−	6.21092i		−	0.576670i
$117$	−4.73634	+	3.06182i	−0.437875	+	0.283065i
$118$	3.59703	+	3.59703i	0.331134	+	0.331134i
$119$	19.5287			1.79019
$120$	−1.32554	+	3.63908i	−0.121005	+	0.332201i
$121$	−10.1805			−0.925503
$122$	−0.315382	−	0.315382i	−0.0285534	−	0.0285534i
$123$	2.34737	−	1.89682i	0.211655	−	0.171030i
$124$		−	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	−0.233886	−	0.972264i	$-0.575144\pi$
$127$	8.32109	−	8.32109i	0.738378	−	0.738378i	0.972264	+	0.233886i	$0.0751443\pi$
$128$	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	$0.696211\pi$
$132$	5.01005	+	6.20008i	0.436069	+	0.539648i
$133$	2.86820	+	2.86820i	0.248704	+	0.248704i
$134$	8.88078			0.767183
$135$	2.58730	+	11.3272i	0.222679	+	0.974892i
$136$	−4.81448			−0.412838
$137$	−14.3208	−	14.3208i	−1.22351	−	1.22351i	−0.966375	−	0.257137i	$-0.917221\pi$
$137$	−14.3208	−	14.3208i	−1.22351	−	1.22351i	−0.257137	−	0.966375i	$-0.582779\pi$
$138$	−3.08826	−	3.82181i	−0.262890	−	0.325334i
$139$		−	11.2626i		−	0.955283i	−0.878555	−	0.477642i	$-0.841492\pi$
$139$		−	11.2626i		−	0.955283i	0.878555	−	0.477642i	$-0.158508\pi$
$140$	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
$147$	12.7351	−	10.2908i	1.05038	−	0.848769i
$148$	−4.28573	−	4.28573i	−0.352285	−	0.352285i
$149$	5.59268			0.458170			0.229085	−	0.973406i	$-0.426427\pi$
$149$	5.59268			0.458170			0.229085	+	0.973406i	$0.426427\pi$
$150$	4.83885	−	7.18230i	0.395091	−	0.586433i
$151$	−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
$153$	−12.1296	+	7.84123i	−0.980623	+	0.633926i
$154$		−	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	−0.986484	−	0.163858i	$-0.947606\pi$
$157$	−10.3075	+	10.3075i	−0.822626	+	0.822626i	0.163858	+	0.986484i	$0.447606\pi$
$158$	−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
$162$	−3.19030	−	8.41558i	−0.250654	−	0.661190i
$163$	−11.0783	−	11.0783i	−0.867718	−	0.867718i	0.124502	−	0.992219i	$-0.460267\pi$
$163$	−11.0783	−	11.0783i	−0.867718	−	0.867718i	−0.992219	+	0.124502i	$0.960267\pi$
$164$	1.74242			0.136060
$165$	−7.52888	−	16.1562i	−0.586122	−	1.25776i
$166$	5.48450			0.425680
$167$	−4.00388	−	4.00388i	−0.309830	−	0.309830i	0.535014	−	0.844843i	$-0.320306\pi$
$167$	−4.00388	−	4.00388i	−0.309830	−	0.309830i	−0.844843	+	0.535014i	$0.820306\pi$
$168$	−5.46453	+	4.41568i	−0.421598	+	0.340677i
$169$		−	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	$-0.895171\pi$
$173$	−8.19231	+	8.19231i	−0.622850	+	0.622850i	0.323409	+	0.946259i	$0.395171\pi$
$174$	1.13561	−	10.6975i	0.0860907	−	0.810977i
$175$	−19.3856	+	5.96036i	−1.46541	+	0.450561i
$176$			4.60223i			0.346906i
$177$	5.53775	+	6.85312i	0.416243	+	0.515112i
$178$	1.46635	+	1.46635i	0.109907	+	0.109907i
$179$	5.97757			0.446784			0.223392	−	0.974729i	$-0.428287\pi$
$179$	5.97757			0.446784			0.223392	+	0.974729i	$0.428287\pi$
$180$	−2.94846	+	6.02550i	−0.219765	+	0.449114i
$181$	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
$183$	−0.485541	−	0.600871i	−0.0358922	−	0.0444177i
$184$		−	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	$-0.0750572\pi$
$192$	1.34719	−	1.08861i	0.0972251	−	0.0785639i
$193$	4.32749	+	4.32749i	0.311500	+	0.311500i	0.845490	−	0.533991i	$-0.179308\pi$
$193$	4.32749	+	4.32749i	0.311500	+	0.311500i	−0.533991	+	0.845490i	$0.679308\pi$
$194$	17.6883			1.26994
$195$	6.84127	+	2.49195i	0.489914	+	0.178452i
$196$	9.45311			0.675222
$197$	−14.8702	−	14.8702i	−1.05946	−	1.05946i	−0.998117	−	0.0613383i	$-0.980463\pi$
$197$	−14.8702	−	14.8702i	−1.05946	−	1.05946i	−0.0613383	−	0.998117i	$-0.519537\pi$
$198$	7.49554	+	11.5949i	0.532685	+	0.824014i
$199$			0.789726i			0.0559822i	0.999608	+	0.0279911i	$0.00891101\pi$
$199$			0.789726i			0.0559822i	−0.999608	+	0.0279911i	$0.991089\pi$
$200$	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
$207$	−4.62035	−	7.14724i	−0.321136	−	0.496768i
$208$	−1.32932	−	1.32932i	−0.0921718	−	0.0921718i
$209$	4.60223			0.318343
$210$	14.2395	−	6.63569i	0.982621	−	0.457906i
$211$	−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
$213$	−20.9210	+	16.9055i	−1.43349	+	1.15834i
$214$			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
$222$	−6.59802	−	8.16524i	−0.442830	−	0.548015i
$223$	10.1226	+	10.1226i	0.677856	+	0.677856i	0.959515	−	0.281659i	$-0.0908845\pi$
$223$	10.1226	+	10.1226i	0.677856	+	0.677856i	−0.281659	+	0.959515i	$0.590885\pi$
$224$	−4.05624			−0.271019
$225$	9.64754	−	11.4859i	0.643169	−	0.765724i
$226$	−1.39266			−0.0926383
$227$	13.7553	+	13.7553i	0.912969	+	0.912969i	0.996505	−	0.0835359i	$-0.0266213\pi$
$227$	13.7553	+	13.7553i	0.912969	+	0.912969i	−0.0835359	+	0.996505i	$0.526621\pi$
$228$	−1.08861	−	1.34719i	−0.0720952	−	0.0892198i
$229$			6.47050i			0.427583i	0.976879	+	0.213791i	$0.0685813\pi$
$229$			6.47050i			0.427583i	−0.976879	+	0.213791i	$0.931419\pi$
$230$	−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	$-0.809399\pi$
$233$	−4.00499	+	4.00499i	−0.262376	+	0.262376i	0.563643	+	0.826019i	$0.309399\pi$
$234$	−5.51413	−	1.18407i	−0.360470	−	0.0774050i
$235$	−14.1490	+	8.51682i	−0.922978	+	0.555576i
$236$			5.08697i			0.331134i
$237$	−14.0713	+	11.3704i	−0.914026	+	0.738590i
$238$	13.8089	+	13.8089i	0.895097	+	0.895097i
$239$	1.96845			0.127329			0.0636643	−	0.997971i	$-0.479721\pi$
$239$	1.96845			0.127329			0.0636643	+	0.997971i	$0.479721\pi$
$240$	−3.51052	+	1.63592i	−0.226603	+	0.105598i
$241$	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
$243$	−3.95617	−	15.0781i	−0.253788	−	0.967260i
$244$		−	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	$-0.0641837\pi$
$252$	−10.2193	+	6.60631i	−0.643757	+	0.416158i
$253$	9.23195	+	9.23195i	0.580408	+	0.580408i
$254$	11.7678			0.738378
$255$	17.5203	+	6.38181i	1.09716	+	0.399644i
$256$	1.00000			0.0625000
$257$	3.25382	+	3.25382i	0.202968	+	0.202968i	0.801270	−	0.598302i	$-0.204158\pi$
$257$	3.25382	+	3.25382i	0.202968	+	0.202968i	−0.598302	+	0.801270i	$0.704158\pi$
$258$	−15.6099	+	12.6138i	−0.971832	+	0.785301i
$259$			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	0.294183	−	0.955749i	$-0.404952\pi$
$263$	20.2705	−	20.2705i	1.24993	−	1.24993i	0.955749	−	0.294183i	$-0.0950475\pi$
$264$	−0.841479	+	7.92676i	−0.0517895	+	0.487858i
$265$	8.09156	+	13.4425i	0.497061	+	0.825766i
$266$			4.05624i			0.248704i
$267$	2.25748	+	2.79370i	0.138156	+	0.170972i
$268$	6.27966	+	6.27966i	0.383591	+	0.383591i
$269$	−16.9049			−1.03071			−0.515354	−	0.856977i	$-0.672340\pi$
$269$	−16.9049			−1.03071			−0.515354	+	0.856977i	$0.672340\pi$
$270$	−6.18006	+	9.83905i	−0.376106	+	0.598786i
$271$	−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
$273$	8.30123	+	10.2730i	0.502413	+	0.621751i
$274$		−	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	−0.817949	−	0.575291i	$-0.804889\pi$
$277$	−4.03864	+	4.03864i	−0.242659	+	0.242659i	0.575291	+	0.817949i	$0.304889\pi$
$278$	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	$0.861960\pi$
$282$	9.94971	−	8.03998i	0.592496	−	0.478774i
$283$	15.0689	+	15.0689i	0.895756	+	0.895756i	0.995057	−	0.0993018i	$-0.0316609\pi$
$283$	15.0689	+	15.0689i	0.895756	+	0.895756i	−0.0993018	+	0.995057i	$0.531661\pi$
$284$	−15.5294			−0.921499
$285$	1.63592	+	3.51052i	0.0969035	+	0.207945i
$286$	8.65193			0.511600
$287$	−4.99760	−	4.99760i	−0.294999	−	0.294999i
$288$	2.51941	−	1.62868i	0.148458	−	0.0959706i
$289$			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	$-0.684798\pi$
$293$	4.92404	−	4.92404i	0.287665	−	0.287665i	0.836156	+	0.548491i	$0.184798\pi$
$294$	16.2818	+	1.72842i	0.949573	+	0.100804i
$295$	2.74308	−	11.0391i	0.159708	−	0.642722i
$296$		−	6.06094i		−	0.352285i
$297$	10.7901	+	21.3412i	0.626105	+	1.23834i
$298$	3.95462	+	3.95462i	0.229085	+	0.229085i
$299$	−5.33316			−0.308425
$300$	8.50024	−	1.65707i	0.490762	−	0.0956709i
$301$	46.9998			2.70903
$302$	−3.26781	−	3.26781i	−0.188041	−	0.188041i
$303$	−2.49816	+	2.01866i	−0.143515	+	0.115969i
$304$		−	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	−0.886235	−	0.463237i	$-0.846688\pi$
$307$	−7.41152	+	7.41152i	−0.422998	+	0.422998i	0.463237	+	0.886235i	$0.346688\pi$
$308$	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	$0.778548\pi$
$312$	−2.04653	−	2.53264i	−0.115862	−	0.143383i
$313$	−17.6638	−	17.6638i	−0.998419	−	0.998419i	0.00158010	−	0.999999i	$-0.499497\pi$
$313$	−17.6638	−	17.6638i	−0.998419	−	0.998419i	−0.999999	+	0.00158010i	$0.999497\pi$
$314$	−14.5770			−0.822626
$315$	25.7391	−	8.82555i	1.45023	−	0.497263i
$316$	−10.4449			−0.587571
$317$	0.617852	+	0.617852i	0.0347020	+	0.0347020i	0.724245	−	0.689543i	$-0.242189\pi$
$317$	0.617852	+	0.617852i	0.0347020	+	0.0347020i	−0.689543	+	0.724245i	$0.742189\pi$
$318$	−7.63853	−	9.45290i	−0.428348	−	0.530092i
$319$			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
$327$	8.52415	−	6.88804i	0.471387	−	0.380910i
$328$	1.23207	+	1.23207i	0.0680300	+	0.0680300i
$329$	−29.9575			−1.65161
$330$	6.10046	−	16.7479i	0.335819	−	0.921942i
$331$	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
$333$	−9.87131	−	15.2700i	−0.540944	−	0.836790i
$334$		−	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	0.0535356	−	0.998566i	$-0.482951\pi$
$337$	19.3140	−	19.3140i	1.05210	−	1.05210i	0.998566	−	0.0535356i	$-0.0170491\pi$
$338$	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
$342$	−1.62868	−	2.51941i	−0.0880687	−	0.136234i
$343$	−7.03600	−	7.03600i	−0.379908	−	0.379908i
$344$	−11.5870			−0.624731
$345$	−3.76040	+	10.3236i	−0.202453	+	0.555805i
$346$	−11.5857			−0.622850
$347$	−20.8770	−	20.8770i	−1.12074	−	1.12074i	−0.991631	−	0.129107i	$-0.958789\pi$
$347$	−20.8770	−	20.8770i	−1.12074	−	1.12074i	−0.129107	−	0.991631i	$-0.541211\pi$
$348$	8.36729	−	6.76129i	0.448534	−	0.362443i
$349$			11.2937i			0.604537i	0.953223	+	0.302269i	$0.0977440\pi$
$349$			11.2937i			0.604537i	−0.953223	+	0.302269i	$0.902256\pi$
$350$	−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	$-0.758669\pi$
$353$	−0.723576	+	0.723576i	−0.0385121	+	0.0385121i	0.687589	+	0.726101i	$0.258669\pi$
$354$	−0.930110	+	8.76167i	−0.0494348	+	0.465677i
$355$	33.6999	+	8.37399i	1.78861	+	0.444445i
$356$			2.07373i			0.109907i
$357$	21.2592	+	26.3089i	1.12516	+	1.39241i
$358$	4.22678	+	4.22678i	0.223392	+	0.223392i
$359$	25.4403			1.34269			0.671345	−	0.741145i	$-0.265717\pi$
$359$	25.4403			1.34269			0.671345	+	0.741145i	$0.265717\pi$
$360$	−6.34554	+	2.17579i	−0.334439	+	0.114674i
$361$	−1.00000			−0.0526316
$362$	5.99334	+	5.99334i	0.315003	+	0.315003i
$363$	−11.0827	−	13.7151i	−0.581689	−	0.719857i
$364$			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	−0.237737	−	0.971330i	$-0.576406\pi$
$367$	14.0536	−	14.0536i	0.733593	−	0.733593i	0.971330	+	0.237737i	$0.0764055\pi$
$368$	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
$372$	5.27420	−	4.26188i	0.273454	−	0.220968i
$373$	5.52563	+	5.52563i	0.286106	+	0.286106i	0.835538	−	0.549432i	$-0.185156\pi$
$373$	5.52563	+	5.52563i	0.286106	+	0.286106i	−0.549432	+	0.835538i	$0.685156\pi$
$374$	22.1574			1.14573
$375$	−19.3397	−	0.987670i	−0.998698	−	0.0510031i
$376$	7.38553			0.380879
$377$	−8.25630	−	8.25630i	−0.425221	−	0.425221i
$378$	−18.8094	+	9.51000i	−0.967452	+	0.489142i
$379$			8.19606i			0.421003i	0.977593	+	0.210502i	$0.0675098\pi$
$379$			8.19606i			0.421003i	−0.977593	+	0.210502i	$0.932490\pi$
$380$	−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	$-0.888445\pi$
$383$	−11.6617	+	11.6617i	−0.595886	+	0.595886i	0.343329	+	0.939215i	$0.388445\pi$
$384$	1.72237	+	0.182842i	0.0878945	+	0.00933059i
$385$	−35.7632	+	21.5273i	−1.82266	+	1.09713i
$386$			6.12000i			0.311500i
$387$	−29.1925	+	18.8715i	−1.48394	+	0.959293i
$388$	12.5075	+	12.5075i	0.634972	+	0.634972i
$389$	15.6133			0.791625			0.395813	−	0.918331i	$-0.370463\pi$
$389$	15.6133			0.791625			0.395813	+	0.918331i	$0.370463\pi$
$390$	3.07543	+	6.59958i	0.155731	+	0.334183i
$391$	−13.6581			−0.690719
$392$	6.68436	+	6.68436i	0.337611	+	0.337611i
$393$	−25.1629	+	20.3332i	−1.26930	+	1.02567i
$394$		−	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	−0.193114	+	0.981176i	$0.561859\pi$
$397$	−23.3976	+	23.3976i	−1.17429	+	1.17429i	−0.981176	+	0.193114i	$0.938141\pi$
$398$	−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	$-0.0391844\pi$
$402$	9.66774	+	11.9641i	0.482183	+	0.596715i
$403$	−5.20424	−	5.20424i	−0.259242	−	0.259242i
$404$	−1.85435			−0.0922571
$405$	−12.4433	+	15.8165i	−0.618315	+	0.785930i
$406$	−25.1930			−1.25031
$407$	19.7239	+	19.7239i	0.977679	+	0.977679i
$408$	−5.24111	−	6.48602i	−0.259473	−	0.321106i
$409$		−	3.39494i		−	0.167869i	−0.996471	−	0.0839345i	$-0.973251\pi$
$409$		−	3.39494i		−	0.167869i	0.996471	−	0.0839345i	$-0.0267487\pi$
$410$	−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
$417$	15.1729	−	12.2606i	0.743020	−	0.600406i
$418$	3.25427	+	3.25427i	0.159172	+	0.159172i
$419$	12.5500			0.613105			0.306553	−	0.951854i	$-0.400824\pi$
$419$	12.5500			0.613105			0.306553	+	0.951854i	$0.400824\pi$
$420$	14.7610	+	5.37673i	0.720264	+	0.262358i
$421$	−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
$423$	18.6072	−	12.0286i	0.904711	−	0.584852i
$424$		−	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	$-0.0640735\pi$
$432$	4.63715	−	2.34453i	0.223105	−	0.112801i
$433$	−10.8163	−	10.8163i	−0.519799	−	0.519799i	0.397712	−	0.917510i	$-0.369804\pi$
$433$	−10.8163	−	10.8163i	−0.519799	−	0.519799i	−0.917510	+	0.397712i	$0.869804\pi$
$434$	−15.8800			−0.762266
$435$	−21.8036	+	10.1606i	−1.04540	+	0.487162i
$436$	6.32736			0.303025
$437$	−2.00597	−	2.00597i	−0.0959587	−	0.0959587i
$438$	12.1309	−	9.80248i	0.579635	−	0.468381i
$439$			17.0396i			0.813258i	0.913593	+	0.406629i	$0.133296\pi$
$439$			17.0396i			0.813258i	−0.913593	+	0.406629i	$0.866704\pi$
$440$	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	0.239884	−	0.970802i	$-0.422891\pi$
$443$	25.4820	−	25.4820i	1.21069	−	1.21069i	0.970802	−	0.239884i	$-0.0771094\pi$
$444$	1.10819	−	10.4392i	0.0525924	−	0.495422i
$445$	1.11823	−	4.50014i	0.0530090	−	0.213327i
$446$			14.3154i			0.677856i
$447$	6.08827	+	7.53441i	0.287965	+	0.356365i
$448$	−2.86820	−	2.86820i	−0.135510	−	0.135510i
$449$	−7.40137			−0.349292			−0.174646	−	0.984631i	$-0.555878\pi$
$449$	−7.40137			−0.349292			−0.174646	+	0.984631i	$0.555878\pi$
$450$	14.9436	−	1.29989i	0.704447	−	0.0612776i
$451$	−8.01901			−0.377600
$452$	−0.984759	−	0.984759i	−0.0463192	−	0.0463192i
$453$	−5.03090	−	6.22588i	−0.236372	−	0.292517i
$454$			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	−0.274220	−	0.961667i	$-0.588420\pi$
$457$	14.6959	−	14.6959i	0.687447	−	0.687447i	0.961667	+	0.274220i	$0.0884196\pi$
$458$	−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	$-0.342696\pi$
$462$	25.1490	−	20.3220i	1.17004	−	0.945464i
$463$	−0.789669	−	0.789669i	−0.0366990	−	0.0366990i	0.688519	−	0.725218i	$-0.258261\pi$
$463$	−0.789669	−	0.789669i	−0.0366990	−	0.0366990i	−0.725218	+	0.688519i	$0.758261\pi$
$464$	6.21092			0.288335
$465$	−13.7436	+	6.40456i	−0.637342	+	0.297004i
$466$	−5.66392			−0.262376
$467$	28.1504	+	28.1504i	1.30265	+	1.30265i	0.926601	+	0.376045i	$0.122716\pi$
$467$	28.1504	+	28.1504i	1.30265	+	1.30265i	0.376045	+	0.926601i	$0.377284\pi$
$468$	−3.06182	−	4.73634i	−0.141533	−	0.218938i
$469$		−	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
$477$	−11.4280	−	17.6781i	−0.523253	−	0.809423i
$478$	1.39191	+	1.39191i	0.0636643	+	0.0636643i
$479$	23.0077			1.05125			0.525624	−	0.850717i	$-0.323832\pi$
$479$	23.0077			1.05125			0.525624	+	0.850717i	$0.323832\pi$
$480$	−3.63908	−	1.32554i	−0.166101	−	0.0605026i
$481$	−11.3942			−0.519532
$482$	16.9005	+	16.9005i	0.769794	+	0.769794i
$483$	−15.5022	+	12.5267i	−0.705374	+	0.569986i
$484$		−	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	−0.0685156	−	0.997650i	$-0.521826\pi$
$487$	20.5042	−	20.5042i	0.929134	−	0.929134i	0.997650	+	0.0685156i	$0.0218263\pi$
$488$	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	$-0.124692\pi$
$492$	1.89682	+	2.34737i	0.0855152	+	0.105827i
$493$	−21.1442	−	21.1442i	−0.952285	−	0.952285i
$494$	−1.87994			−0.0845826
$495$	13.5695	−	27.7307i	0.609903	−	1.24640i
$496$	3.91496			0.175787
$497$	44.5413	+	44.5413i	1.99795	+	1.99795i
$498$	5.97050	+	7.38866i	0.267544	+	0.331094i
$499$			26.0020i			1.16401i	0.813185	+	0.582005i	$0.197732\pi$
$499$			26.0020i			1.16401i	−0.813185	+	0.582005i	$0.802268\pi$
$500$	−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	$-0.788284\pi$
$503$	−3.80551	+	3.80551i	−0.169679	+	0.169679i	0.617159	+	0.786838i	$0.288284\pi$
$504$	−11.8975	−	2.55479i	−0.529958	−	0.113800i
$505$	4.02407	+	0.999929i	0.179069	+	0.0444963i
$506$			13.0560i			0.580408i
$507$	12.7523	−	10.3046i	0.566347	−	0.457644i
$508$	8.32109	+	8.32109i	0.369189	+	0.369189i
$509$	7.97379			0.353432			0.176716	−	0.984262i	$-0.443453\pi$
$509$	7.97379			0.353432			0.176716	+	0.984262i	$0.443453\pi$
$510$	7.87610	+	16.9013i	0.348760	+	0.748404i
$511$	−36.5247			−1.61576
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.34453	−	4.63715i	−0.103514	−	0.204735i
$514$			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	$-0.157674\pi$
$522$	15.6478	−	10.1156i	0.684887	−	0.442747i
$523$	−24.3202	−	24.3202i	−1.06345	−	1.06345i	−0.997846	−	0.0656023i	$-0.979103\pi$
$523$	−24.3202	−	24.3202i	−1.06345	−	1.06345i	−0.0656023	−	0.997846i	$-0.520897\pi$
$524$	−18.6781			−0.815955
$525$	−29.1332	−	19.6276i	−1.27148	−	0.856617i
$526$	28.6668			1.24993
$527$	−13.3279	−	13.3279i	−0.580573	−	0.580573i
$528$	−6.20008	+	5.01005i	−0.269824	+	0.218034i
$529$			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
$537$	6.50726	+	8.05292i	0.280809	+	0.347509i
$538$	−11.9535	−	11.9535i	−0.515354	−	0.515354i
$539$	−43.5054			−1.87391
$540$	−11.3272	+	2.58730i	−0.487446	+	0.111340i
$541$	−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
$543$	9.22694	+	11.4186i	0.395966	+	0.490019i
$544$		−	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	−0.345984	−	0.938240i	$-0.612455\pi$
$547$	13.8517	−	13.8517i	0.592256	−	0.592256i	0.938240	+	0.345984i	$0.112455\pi$
$548$	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
$552$	3.82181	−	3.08826i	0.162667	−	0.131445i
$553$	29.9580	+	29.9580i	1.27394	+	1.27394i
$554$	−5.71150			−0.242659
$555$	−8.03405	+	22.0563i	−0.341026	+	0.936236i
$556$	11.2626			0.477642
$557$	−15.4865	−	15.4865i	−0.656182	−	0.656182i	0.298292	−	0.954475i	$-0.403583\pi$
$557$	−15.4865	−	15.4865i	−0.656182	−	0.656182i	−0.954475	+	0.298292i	$0.903583\pi$
$558$	9.86338	−	6.37620i	0.417550	−	0.269926i
$559$			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	$-0.974312\pi$
$563$	−21.7376	+	21.7376i	−0.916131	+	0.916131i	0.0806140	+	0.996745i	$0.474312\pi$
$564$	12.7206	+	1.35038i	0.535635	+	0.0568613i
$565$	1.60598	+	2.66802i	0.0675642	+	0.112244i
$566$			21.3107i			0.895756i
$567$	−34.1356	+	12.9406i	−1.43356	+	0.543456i
$568$	−10.9809	−	10.9809i	−0.460750	−	0.460750i
$569$	−33.8572			−1.41937			−0.709684	−	0.704520i	$-0.751162\pi$
$569$	−33.8572			−1.41937			−0.709684	+	0.704520i	$0.751162\pi$
$570$	−1.32554	+	3.63908i	−0.0555210	+	0.152424i
$571$	−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
$573$	8.69933	−	7.02960i	0.363420	−	0.293666i
$574$		−	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	−0.935375	−	0.353658i	$-0.884938\pi$
$577$	−13.9733	+	13.9733i	−0.581717	+	0.581717i	0.353658	+	0.935375i	$0.384938\pi$
$578$	−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
$582$	19.2557	+	23.8295i	0.798174	+	0.987763i
$583$	22.8344	+	22.8344i	0.945705	+	0.945705i
$584$	9.00456			0.372611
$585$	4.09037	+	11.9293i	0.169116	+	0.493214i
$586$	6.96364			0.287665
$587$	22.9650	+	22.9650i	0.947869	+	0.947869i	0.998707	−	0.0508382i	$-0.0161893\pi$
$587$	22.9650	+	22.9650i	0.947869	+	0.947869i	−0.0508382	+	0.998707i	$0.516189\pi$
$588$	10.2908	+	12.7351i	0.424385	+	0.525188i
$589$		−	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	$-0.730179\pi$
$593$	2.14305	−	2.14305i	0.0880044	−	0.0880044i	0.749739	+	0.661734i	$0.230179\pi$
$594$	−7.46079	+	22.7203i	−0.306120	+	0.932224i
$595$	10.5306	−	42.3788i	0.431711	−	1.73736i
$596$			5.59268i			0.229085i
$597$	−1.06391	+	0.859707i	−0.0435430	+	0.0351855i
$598$	−3.77111	−	3.77111i	−0.154212	−	0.154212i
$599$	28.0055			1.14427			0.572137	−	0.820158i	$-0.306115\pi$
$599$	28.0055			1.14427			0.572137	+	0.820158i	$0.306115\pi$
$600$	7.18230	+	4.83885i	0.293216	+	0.197545i
$601$	−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
$603$	14.4639	+	22.3743i	0.589016	+	0.911152i
$604$		−	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	−0.0308996	+	0.999522i	$0.509837\pi$
$607$	−25.3869	+	25.3869i	−1.03042	+	1.03042i	−0.999522	+	0.0308996i	$0.990163\pi$
$608$	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
$612$	−7.84123	−	12.1296i	−0.316963	−	0.490312i
$613$	−3.65006	−	3.65006i	−0.147425	−	0.147425i	0.629542	−	0.776967i	$-0.283243\pi$
$613$	−3.65006	−	3.65006i	−0.147425	−	0.147425i	−0.776967	+	0.629542i	$0.783243\pi$
$614$	−10.4815			−0.422998
$615$	−2.85045	−	6.11679i	−0.114941	−	0.246653i
$616$	18.6678			0.752146
$617$	−25.7417	−	25.7417i	−1.03632	−	1.03632i	−0.999315	−	0.0370077i	$-0.988217\pi$
$617$	−25.7417	−	25.7417i	−1.03632	−	1.03632i	−0.0370077	−	0.999315i	$-0.511783\pi$
$618$	21.8338	−	17.6431i	0.878286	−	0.709709i
$619$			26.4712i			1.06397i	0.846755	+	0.531984i	$0.178553\pi$
$619$			26.4712i			1.06397i	−0.846755	+	0.531984i	$0.821447\pi$
$620$	−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
$627$	5.01005	+	6.20008i	0.200082	+	0.247607i
$628$	−10.3075	−	10.3075i	−0.411313	−	0.411313i
$629$	−29.1803			−1.16349
$630$	24.4409	+	11.9597i	0.973748	+	0.476484i
$631$	−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
$633$	−21.6292	−	26.7668i	−0.859683	−	1.06388i
$634$			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	$0.940784\pi$
$642$	−16.4097	+	13.2601i	−0.647640	+	0.523334i
$643$	−21.9899	−	21.9899i	−0.867197	−	0.867197i	0.124964	−	0.992161i	$-0.460118\pi$
$643$	−21.9899	−	21.9899i	−0.867197	−	0.867197i	−0.992161	+	0.124964i	$0.960118\pi$
$644$	−11.5071			−0.453441
$645$	42.1662	+	15.3591i	1.66029	+	0.604765i
$646$	−4.81448			−0.189423
$647$	6.75416	+	6.75416i	0.265533	+	0.265533i	0.827297	−	0.561764i	$-0.189877\pi$
$647$	6.75416	+	6.75416i	0.265533	+	0.265533i	−0.561764	+	0.827297i	$0.689877\pi$
$648$	8.41558	−	3.19030i	0.330595	−	0.125327i
$649$		−	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	$-0.873162\pi$
$653$	−13.6366	+	13.6366i	−0.533643	+	0.533643i	0.388011	+	0.921655i	$0.373162\pi$
$654$	10.8981	+	1.15690i	0.426148	+	0.0452385i
$655$	40.5328	+	10.0719i	1.58375	+	0.393541i
$656$			1.74242i			0.0680300i
$657$	22.6862	−	14.6655i	0.885071	−	0.572156i
$658$	−21.1831	−	21.1831i	−0.825805	−	0.825805i
$659$	−10.2941			−0.401002			−0.200501	−	0.979694i	$-0.564257\pi$
$659$	−10.2941			−0.401002			−0.200501	+	0.979694i	$0.564257\pi$
$660$	16.1562	−	7.52888i	0.628881	−	0.293061i
$661$	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
$663$	−12.1933	+	9.85298i	−0.473550	+	0.382658i
$664$			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
$672$	−4.41568	−	5.46453i	−0.170339	−	0.210799i
$673$	2.16629	+	2.16629i	0.0835045	+	0.0835045i	0.747625	−	0.664121i	$-0.231194\pi$
$673$	2.16629	+	2.16629i	0.0835045	+	0.0835045i	−0.664121	+	0.747625i	$0.731194\pi$
$674$	27.3141			1.05210
$675$	25.9761	+	0.493404i	0.999820	+	0.0189911i
$676$	9.46581			0.364070
$677$	−6.41647	−	6.41647i	−0.246605	−	0.246605i	0.572971	−	0.819576i	$-0.305791\pi$
$677$	−6.41647	−	6.41647i	−0.246605	−	0.246605i	−0.819576	+	0.572971i	$0.805791\pi$
$678$	−1.51607	−	1.87618i	−0.0582242	−	0.0720541i
$679$		−	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	$-0.570087\pi$
$683$	19.7954	−	19.7954i	0.757448	−	0.757448i	0.975857	+	0.218409i	$0.0700867\pi$
$684$	0.629843	−	2.93314i	0.0240826	−	0.112151i
$685$	−38.7996	+	23.3550i	−1.48246	+	0.892348i
$686$		−	9.95041i		−	0.379908i
$687$	−8.71699	+	7.04387i	−0.332574	+	0.268740i
$688$	−8.19327	−	8.19327i	−0.312366	−	0.312366i
$689$	−13.1911			−0.502541
$690$	−9.95891	+	4.64090i	−0.379129	+	0.176676i
$691$	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
$693$	47.0317	−	30.4037i	1.78659	−	1.15494i
$694$		−	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	$-0.182776\pi$
$702$	−4.40759	−	8.71758i	−0.166354	−	0.329024i
$703$	−4.28573	−	4.28573i	−0.161639	−	0.161639i
$704$	−4.60223			−0.173453
$705$	−26.8765	−	9.78984i	−1.01223	−	0.368707i
$706$	−1.02329			−0.0385121
$707$	5.31863	+	5.31863i	0.200028	+	0.200028i
$708$	−6.85312	+	5.53775i	−0.257556	+	0.208121i
$709$			15.0208i			0.564119i	0.959397	+	0.282060i	$0.0910176\pi$
$709$			15.0208i			0.564119i	−0.959397	+	0.282060i	$0.908982\pi$
$710$	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
$717$	2.14288	+	2.65188i	0.0800274	+	0.0990362i
$718$	17.9890	+	17.9890i	0.671345	+	0.671345i
$719$	0.237709			0.00886505			0.00443253	−	0.999990i	$-0.498589\pi$
$719$	0.237709			0.00886505			0.00443253	+	0.999990i	$0.498589\pi$
$720$	−6.02550	−	2.94846i	−0.224557	−	0.109883i
$721$	−65.7393			−2.44826
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	26.0188	+	32.1990i	0.967649	+	1.19749i
$724$			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	0.103098	−	0.994671i	$-0.467125\pi$
$727$	29.5991	−	29.5991i	1.09777	−	1.09777i	0.994671	−	0.103098i	$-0.0328754\pi$
$728$	−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
$732$	0.600871	−	0.485541i	0.0222088	−	0.0179461i
$733$	20.2570	+	20.2570i	0.748209	+	0.748209i	0.974143	−	0.225933i	$-0.0725432\pi$
$733$	20.2570	+	20.2570i	0.748209	+	0.748209i	−0.225933	+	0.974143i	$0.572543\pi$
$734$	19.8748			0.733593
$735$	−15.4645	−	33.1854i	−0.570418	−	1.22406i
$736$	2.83687			0.104569
$737$	−28.9005	−	28.9005i	−1.06456	−	1.06456i
$738$	2.83783	+	4.38986i	0.104462	+	0.161593i
$739$			48.1026i			1.76948i	0.466081	+	0.884742i	$0.345666\pi$
$739$			48.1026i			1.76948i	−0.466081	+	0.884742i	$0.654334\pi$
$740$	−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	0.225817	−	0.974170i	$-0.427495\pi$
$743$	32.7093	−	32.7093i	1.19999	−	1.19999i	0.974170	−	0.225817i	$-0.0725052\pi$
$744$	6.74302	+	0.715817i	0.247211	+	0.0262431i
$745$	3.01577	−	12.1365i	0.110489	−	0.444648i
$746$			7.81442i			0.286106i
$747$	8.93247	+	13.8177i	0.326822	+	0.505563i
$748$	15.6676	+	15.6676i	0.572865	+	0.572865i
$749$	49.4079			1.80533
$750$	−12.9769	−	14.3736i	−0.473848	−	0.524851i
$751$	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
$753$	8.54916	−	6.90825i	0.311549	−	0.251751i
$754$		−	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	0.396477	−	0.918045i	$-0.370233\pi$
$757$	36.1673	−	36.1673i	1.31452	−	1.31452i	0.918045	−	0.396477i	$-0.129767\pi$
$758$	−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	$-0.119689\pi$
$762$	12.8106	+	15.8535i	0.464079	+	0.574311i
$763$	−18.1481	−	18.1481i	−0.657006	−	0.657006i
$764$	6.45739			0.233620
$765$	10.4753	+	30.5505i	0.378736	+	1.10456i
$766$	−16.4922			−0.595886
$767$	6.76222	+	6.76222i	0.244170	+	0.244170i
$768$	1.08861	+	1.34719i	0.0392819	+	0.0486125i
$769$			10.8266i			0.390416i	0.980762	+	0.195208i	$0.0625382\pi$
$769$			10.8266i			0.390416i	−0.980762	+	0.195208i	$0.937462\pi$
$770$	−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	$-0.621872\pi$
$773$	15.4031	−	15.4031i	0.554011	−	0.554011i	0.927596	+	0.373585i	$0.121872\pi$
$774$	−33.9864	−	7.29801i	−1.22161	−	0.262321i
$775$	17.2981	+	9.16243i	0.621365	+	0.329124i
$776$			17.6883i			0.634972i
$777$	−33.1202	+	26.7632i	−1.18818	+	0.960123i
$778$	11.0403	+	11.0403i	0.395813	+	0.395813i
$779$	1.74242			0.0624286
$780$	−2.49195	+	6.84127i	−0.0892261	+	0.244957i
$781$	71.4698			2.55739
$782$	−9.65772	−	9.65772i	−0.345359	−	0.345359i
$783$	28.8010	−	14.5617i	1.02926	−	0.520393i
$784$			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	−0.137895	−	0.990447i	$-0.544034\pi$
$787$	23.9171	−	23.9171i	0.852552	−	0.852552i	0.990447	+	0.137895i	$0.0440337\pi$
$788$	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
$792$	−11.5949	+	7.49554i	−0.412007	+	0.266343i
$793$	−0.592901	−	0.592901i	−0.0210545	−	0.0210545i
$794$	−33.0892			−1.17429
$795$	−9.30102	+	25.5346i	−0.329873	+	0.905618i
$796$	−0.789726			−0.0279911
$797$	21.0294	+	21.0294i	0.744901	+	0.744901i	0.973517	−	0.228616i	$-0.0734199\pi$
$797$	21.0294	+	21.0294i	0.744901	+	0.744901i	−0.228616	+	0.973517i	$0.573420\pi$
$798$	−5.46453	+	4.41568i	−0.193442	+	0.156313i
$799$		−	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
$807$	−18.4029	−	22.7741i	−0.647811	−	0.801685i
$808$	−1.31122	−	1.31122i	−0.0461286	−	0.0461286i
$809$	55.3606			1.94637			0.973187	−	0.230016i	$-0.0738780\pi$
$809$	55.3606			1.94637			0.973187	+	0.230016i	$0.0738780\pi$
$810$	−19.9828	+	2.38521i	−0.702123	+	0.0838078i
$811$	−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
$813$	−3.19761	−	3.95714i	−0.112145	−	0.138783i
$814$			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	$0.855225\pi$
$822$	27.2843	−	22.0474i	0.951648	−	0.768991i
$823$	−8.56588	−	8.56588i	−0.298588	−	0.298588i	0.541873	−	0.840460i	$-0.317715\pi$
$823$	−8.56588	−	8.56588i	−0.298588	−	0.298588i	−0.840460	+	0.541873i	$0.817715\pi$
$824$	16.2069			0.564596
$825$	−39.1201	+	7.62621i	−1.36199	+	0.265511i
$826$	20.6340			0.717949
$827$	11.7327	+	11.7327i	0.407986	+	0.407986i	0.881036	−	0.473050i	$-0.156847\pi$
$827$	11.7327	+	11.7327i	0.407986	+	0.407986i	−0.473050	+	0.881036i	$0.656847\pi$
$828$	7.14724	−	4.62035i	0.248384	−	0.160568i
$829$		−	2.19216i		−	0.0761369i	−0.999275	−	0.0380684i	$-0.987880\pi$
$829$		−	2.19216i		−	0.0761369i	0.999275	−	0.0380684i	$-0.0121205\pi$
$830$	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
$837$	18.1543	−	9.17876i	0.627503	−	0.317264i
$838$	8.87416	+	8.87416i	0.306553	+	0.306553i
$839$	−23.1579			−0.799501			−0.399750	−	0.916624i	$-0.630903\pi$
$839$	−23.1579			−0.799501			−0.399750	+	0.916624i	$0.630903\pi$
$840$	6.63569	+	14.2395i	0.228953	+	0.491311i
$841$	9.57554			0.330191
$842$	−10.1279	−	10.1279i	−0.349030	−	0.349030i
$843$	−18.9788	+	15.3360i	−0.653664	+	0.528201i
$844$		−	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
$852$	−16.9055	−	20.9210i	−0.579172	−	0.716743i
$853$	28.3401	+	28.3401i	0.970346	+	0.970346i	0.999573	−	0.0292268i	$-0.00930451\pi$
$853$	28.3401	+	28.3401i	0.970346	+	0.970346i	−0.0292268	+	0.999573i	$0.509305\pi$
$854$	−1.80916			−0.0619081
$855$	−2.94846	+	6.02550i	−0.100835	+	0.206068i
$856$	−12.1807			−0.416328
$857$	37.5618	+	37.5618i	1.28309	+	1.28309i	0.938903	+	0.344182i	$0.111844\pi$
$857$	37.5618	+	37.5618i	1.28309	+	1.28309i	0.344182	+	0.938903i	$0.388156\pi$
$858$	9.41861	+	11.6558i	0.321546	+	0.397922i
$859$			21.0474i			0.718128i	0.933313	+	0.359064i	$0.116904\pi$
$859$			21.0474i			0.718128i	−0.933313	+	0.359064i	$0.883096\pi$
$860$	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	$-0.882522\pi$
$863$	−16.8012	+	16.8012i	−0.571918	+	0.571918i	0.360746	+	0.932664i	$0.382522\pi$
$864$	4.93680	+	1.62112i	0.167953	+	0.0551517i
$865$	13.3603	+	22.1955i	0.454265	+	0.754670i
$866$		−	15.2966i		−	0.519799i
$867$	−8.32460	+	6.72679i	−0.282718	+	0.228454i
$868$	−11.2289	−	11.2289i	−0.381133	−	0.381133i
$869$	48.0698			1.63066
$870$	−22.6021	−	8.23285i	−0.766282	−	0.279120i
$871$	16.6954			0.565701
$872$	4.47412	+	4.47412i	0.151513	+	0.151513i
$873$	28.8085	+	44.5640i	0.975019	+	1.50826i
$874$		−	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	−0.936897	−	0.349606i	$-0.886316\pi$
$877$	−17.3922	+	17.3922i	−0.587291	+	0.587291i	0.349606	+	0.936897i	$0.386316\pi$
$878$	−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	$-0.00867894\pi$
$882$	15.3961	+	23.8162i	0.518412	+	0.801934i
$883$	9.09541	+	9.09541i	0.306085	+	0.306085i	0.843389	−	0.537304i	$-0.180557\pi$
$883$	9.09541	+	9.09541i	0.306085	+	0.306085i	−0.537304	+	0.843389i	$0.680557\pi$
$884$	−9.05095			−0.304416
$885$	17.8579	−	8.32188i	0.600288	−	0.279737i
$886$	36.0370			1.21069
$887$	−31.1947	−	31.1947i	−1.04742	−	1.04742i	−0.998818	−	0.0485966i	$-0.984525\pi$
$887$	−31.1947	−	31.1947i	−1.04742	−	1.04742i	−0.0485966	−	0.998818i	$-0.515475\pi$
$888$	8.16524	−	6.59802i	0.274007	−	0.221415i
$889$		−	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
$897$	−5.80575	−	7.18478i	−0.193848	−	0.239893i
$898$	−5.23356	−	5.23356i	−0.174646	−	0.174646i
$899$	24.3155			0.810968
$900$	11.4859	+	9.64754i	0.382862	+	0.321585i
$901$	−33.7820			−1.12544
$902$	−5.67029	−	5.67029i	−0.188800	−	0.188800i
$903$	51.1646	+	63.3177i	1.70265	+	2.10708i
$904$		−	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	−0.889711	−	0.456524i	$-0.849094\pi$
$907$	−13.0460	+	13.0460i	−0.433187	+	0.433187i	0.456524	+	0.889711i	$0.349094\pi$
$908$	−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	$-0.317503\pi$
$912$	1.34719	−	1.08861i	0.0446099	−	0.0360476i
$913$	−17.8480	−	17.8480i	−0.590684	−	0.590684i
$914$	20.7832			0.687447
$915$	−1.56576	+	0.729649i	−0.0517623	+	0.0241215i
$916$	−6.47050			−0.213791
$917$	53.5724	+	53.5724i	1.76912	+	1.76912i
$918$	−11.2877	−	22.3255i	−0.372550	−	0.736850i
$919$			20.6702i			0.681847i	0.940091	+	0.340924i	$0.110740\pi$
$919$			20.6702i			0.681847i	−0.940091	+	0.340924i	$0.889260\pi$
$920$	−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
$927$	40.8319	−	26.3959i	1.34110	−	0.866954i
$928$	4.39178	+	4.39178i	0.144167	+	0.144167i
$929$	24.9065			0.817156			0.408578	−	0.912723i	$-0.366025\pi$
$929$	24.9065			0.817156			0.408578	+	0.912723i	$0.366025\pi$
$930$	−14.2469	−	5.18946i	−0.467173	−	0.170169i
$931$	9.45311			0.309813
$932$	−4.00499	−	4.00499i	−0.131188	−	0.131188i
$933$	−30.4544	+	24.6091i	−0.997034	+	0.805665i
$934$			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	0.0957973	−	0.995401i	$-0.469460\pi$
$937$	33.4021	−	33.4021i	1.09120	−	1.09120i	0.995401	−	0.0957973i	$-0.0305401\pi$
$938$	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	$-0.0104948\pi$
$942$	−15.8687	−	19.6380i	−0.517030	−	0.639839i
$943$	3.49524	+	3.49524i	0.113821	+	0.113821i
$944$	−5.08697			−0.165567
$945$	39.9096	+	25.0678i	1.29826	+	0.815456i
$946$	53.3262			1.73378
$947$	−7.33043	−	7.33043i	−0.238207	−	0.238207i	0.577900	−	0.816107i	$-0.303872\pi$
$947$	−7.33043	−	7.33043i	−0.238207	−	0.238207i	−0.816107	+	0.577900i	$0.803872\pi$
$948$	−11.3704	−	14.0713i	−0.369295	−	0.457013i
$949$		−	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	$-0.884744\pi$
$953$	−17.9338	+	17.9338i	−0.580934	+	0.580934i	0.354226	+	0.935160i	$0.384744\pi$
$954$	4.41945	−	20.5811i	0.143085	−	0.666338i
$955$	−14.0130	−	3.48205i	−0.453451	−	0.112677i
$956$			1.96845i			0.0636643i
$957$	−38.5082	+	31.1170i	−1.24479	+	1.00587i
$958$	16.2689	+	16.2689i	0.525624	+	0.525624i
$959$	−82.1500			−2.65276
$960$	−1.63592	−	3.51052i	−0.0527991	−	0.113302i
$961$	−15.6731			−0.505583
$962$	−8.05693	−	8.05693i	−0.259766	−	0.259766i
$963$	−30.6882	+	19.8384i	−0.988913	+	0.639284i
$964$			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	−0.812486	−	0.582980i	$-0.801886\pi$
$967$	−7.13685	+	7.13685i	−0.229506	+	0.229506i	0.582980	+	0.812486i	$0.301886\pi$
$968$	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	$-0.00126576\pi$
$972$	15.0781	−	3.95617i	0.483630	−	0.126894i
$973$	−32.3034	−	32.3034i	−1.03560	−	1.03560i
$974$	28.9973			0.929134
$975$	9.09677	−	13.5023i	0.291330	−	0.432420i
$976$	0.446018			0.0142767
$977$	14.2133	+	14.2133i	0.454724	+	0.454724i	0.896919	−	0.442195i	$-0.145800\pi$
$977$	14.2133	+	14.2133i	0.454724	+	0.454724i	−0.442195	+	0.896919i	$0.645800\pi$
$978$	21.1065	−	17.0554i	0.674911	−	0.545370i
$979$		−	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	0.173617	−	0.984813i	$-0.444455\pi$
$983$	36.3201	−	36.3201i	1.15843	−	1.15843i	0.984813	−	0.173617i	$-0.0555454\pi$
$984$	−0.318586	+	3.00109i	−0.0101562	+	0.0956713i
$985$	−40.2879	+	24.2508i	−1.28368	+	0.772696i
$986$		−	29.9024i		−	0.952285i
$987$	−32.6121	−	40.3584i	−1.03806	−	1.28462i
$988$	−1.32932	−	1.32932i	−0.0422913	−	0.0422913i
$989$	−32.8710			−1.04524
$990$	29.2037	−	10.0135i	0.928153	−	0.318250i
$991$	−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
$993$	18.2636	+	22.6017i	0.579577	+	0.717243i
$994$			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	−0.562579	−	0.826744i	$-0.690191\pi$
$997$	8.34108	−	8.34108i	0.264165	−	0.264165i	0.826744	+	0.562579i	$0.190191\pi$
$998$	−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.533.15	yes	36
3.2	odd	2	inner	570.2.k.b.533.8	yes	36
5.2	odd	4	inner	570.2.k.b.77.8	✓	36
15.2	even	4	inner	570.2.k.b.77.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.8	✓	36	5.2	odd	4	inner
570.2.k.b.77.15	yes	36	15.2	even	4	inner
570.2.k.b.533.8	yes	36	3.2	odd	2	inner
570.2.k.b.533.15	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.08861 + 1.34719i) q^{3} +1.00000i q^{4} +(0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 - 2.86820i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.629843 + 2.93314i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.08861 + 1.34719i) 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} +(-1.34719 + 1.08861i) q^{12} +(1.32932 + 1.32932i) q^{13} +4.05624 q^{14} +(3.51052 - 1.63592i) q^{15} -1.00000 q^{16} +(3.40435 + 3.40435i) q^{17} +(-2.51941 + 1.62868i) 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} +(-4.63715 + 2.34453i) q^{27} +(2.86820 + 2.86820i) q^{28} -6.21092 q^{29} +(3.63908 + 1.32554i) q^{30} -3.91496 q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.20008 - 5.01005i) 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} +(4.41568 + 5.46453i) q^{42} +(8.19327 + 8.19327i) q^{43} +4.60223 q^{44} +(6.02550 + 2.94846i) q^{45} -2.83687 q^{46} +(-5.22236 - 5.22236i) q^{47} +(-1.08861 - 1.34719i) 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} +(-1.34719 + 1.08861i) q^{57} +(-4.39178 - 4.39178i) q^{58} +5.08697 q^{59} +(1.63592 + 3.51052i) q^{60} -0.446018 q^{61} +(-2.76830 - 2.76830i) q^{62} +(6.60631 + 10.2193i) 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} +(-1.62868 - 2.51941i) q^{72} +(-6.36719 - 6.36719i) q^{73} -6.06094 q^{74} +(-1.65707 - 8.50024i) q^{75} -1.00000 q^{76} +(-13.2001 - 13.2001i) q^{77} +(-2.53264 + 2.04653i) 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} +(-6.76129 - 8.36729i) q^{87} +(3.25427 + 3.25427i) q^{88} +2.07373 q^{89} +(2.17579 + 6.34554i) q^{90} +7.62551 q^{91} +(-2.00597 - 2.00597i) q^{92} +(-4.26188 - 5.27420i) 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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