LMFDB - Embedded newform 930.2.j.h.497.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.10
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.69956 + 0.333903i) q^{3} -1.00000i q^{4} +(1.37834 + 1.76073i) q^{5} +(-1.43788 + 0.965667i) q^{6} +(-2.07397 - 2.07397i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77702 + 1.13498i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.69956 + 0.333903i) q^{3} -1.00000i q^{4} +(1.37834 + 1.76073i) q^{5} +(-1.43788 + 0.965667i) q^{6} +(-2.07397 - 2.07397i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77702 + 1.13498i) q^{9} +(-2.21966 - 0.270390i) q^{10} -3.16919i q^{11} +(0.333903 - 1.69956i) q^{12} +(4.31493 - 4.31493i) q^{13} +2.93304 q^{14} +(1.75466 + 3.45270i) q^{15} -1.00000 q^{16} +(1.60510 - 1.60510i) q^{17} +(-2.76620 + 1.16110i) q^{18} -4.20927i q^{19} +(1.76073 - 1.37834i) q^{20} +(-2.83234 - 4.21735i) q^{21} +(2.24096 + 2.24096i) q^{22} +(-1.74467 - 1.74467i) q^{23} +(0.965667 + 1.43788i) q^{24} +(-1.20035 + 4.85378i) q^{25} +6.10223i q^{26} +(4.34074 + 2.85621i) q^{27} +(-2.07397 + 2.07397i) q^{28} +6.90768 q^{29} +(-3.68216 - 1.20069i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.05820 - 5.38623i) q^{33} +2.26995i q^{34} +(0.793064 - 6.51035i) q^{35} +(1.13498 - 2.77702i) q^{36} +(5.96913 + 5.96913i) q^{37} +(2.97641 + 2.97641i) q^{38} +(8.77425 - 5.89272i) q^{39} +(-0.270390 + 2.21966i) q^{40} +9.79654i q^{41} +(4.98488 + 0.979350i) q^{42} +(-7.01443 + 7.01443i) q^{43} -3.16919 q^{44} +(1.82929 + 6.45397i) q^{45} +2.46733 q^{46} +(-3.86329 + 3.86329i) q^{47} +(-1.69956 - 0.333903i) q^{48} +1.60273i q^{49} +(-2.58337 - 4.28091i) q^{50} +(3.26391 - 2.19202i) q^{51} +(-4.31493 - 4.31493i) q^{52} +(-5.48692 - 5.48692i) q^{53} +(-5.08902 + 1.04972i) q^{54} +(5.58009 - 4.36823i) q^{55} -2.93304i q^{56} +(1.40549 - 7.15392i) q^{57} +(-4.88446 + 4.88446i) q^{58} -1.65624 q^{59} +(3.45270 - 1.75466i) q^{60} -5.62235 q^{61} +(0.707107 - 0.707107i) q^{62} +(-3.40555 - 8.11337i) q^{63} +1.00000i q^{64} +(13.5449 + 1.64998i) q^{65} +(3.06038 + 4.55690i) q^{66} +(-11.1009 - 11.1009i) q^{67} +(-1.60510 - 1.60510i) q^{68} +(-2.38262 - 3.54772i) q^{69} +(4.04273 + 5.16430i) q^{70} +6.44184i q^{71} +(1.16110 + 2.76620i) q^{72} +(11.3843 - 11.3843i) q^{73} -8.44163 q^{74} +(-3.66075 + 7.84850i) q^{75} -4.20927 q^{76} +(-6.57282 + 6.57282i) q^{77} +(-2.03755 + 10.3711i) q^{78} +11.1919i q^{79} +(-1.37834 - 1.76073i) q^{80} +(6.42366 + 6.30370i) q^{81} +(-6.92720 - 6.92720i) q^{82} +(5.80418 + 5.80418i) q^{83} +(-4.21735 + 2.83234i) q^{84} +(5.03852 + 0.613771i) q^{85} -9.91991i q^{86} +(11.7400 + 2.30649i) q^{87} +(2.24096 - 2.24096i) q^{88} +12.5769 q^{89} +(-5.85715 - 3.27014i) q^{90} -17.8981 q^{91} +(-1.74467 + 1.74467i) q^{92} +(-1.69956 - 0.333903i) q^{93} -5.46352i q^{94} +(7.41140 - 5.80182i) q^{95} +(1.43788 - 0.965667i) q^{96} +(-6.14577 - 6.14577i) q^{97} +(-1.13330 - 1.13330i) q^{98} +(3.59695 - 8.80090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.69956	+	0.333903i	0.981242	+	0.192779i
$3$	1.69956	+	0.333903i	0.981242	+	0.192779i
$4$		−	1.00000i		−	0.500000i
$5$	1.37834	+	1.76073i	0.616413	+	0.787423i
$5$	1.37834	+	1.76073i	0.616413	+	0.787423i
$6$	−1.43788	+	0.965667i	−0.587010	+	0.394232i
$7$	−2.07397	−	2.07397i	−0.783888	−	0.783888i	0.196596	−	0.980485i	$-0.437011\pi$
$7$	−2.07397	−	2.07397i	−0.783888	−	0.783888i	−0.980485	+	0.196596i	$0.937011\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.77702	+	1.13498i	0.925673	+	0.378325i
$10$	−2.21966	−	0.270390i	−0.701918	−	0.0855047i
$11$		−	3.16919i		−	0.955547i	−0.878483	−	0.477773i	$-0.841444\pi$
$11$		−	3.16919i		−	0.955547i	0.878483	−	0.477773i	$-0.158556\pi$
$12$	0.333903	−	1.69956i	0.0963894	−	0.490621i
$13$	4.31493	−	4.31493i	1.19675	−	1.19675i	0.221611	−	0.975135i	$-0.428869\pi$
$13$	4.31493	−	4.31493i	1.19675	−	1.19675i	0.975135	−	0.221611i	$-0.0711314\pi$
$14$	2.93304			0.783888
$15$	1.75466	+	3.45270i	0.453052	+	0.891484i
$16$	−1.00000			−0.250000
$17$	1.60510	−	1.60510i	0.389293	−	0.389293i	−0.485142	−	0.874435i	$-0.661232\pi$
$17$	1.60510	−	1.60510i	0.389293	−	0.389293i	0.874435	+	0.485142i	$0.161232\pi$
$18$	−2.76620	+	1.16110i	−0.651999	+	0.273674i
$19$		−	4.20927i		−	0.965674i	−0.875710	−	0.482837i	$-0.839606\pi$
$19$		−	4.20927i		−	0.965674i	0.875710	−	0.482837i	$-0.160394\pi$
$20$	1.76073	−	1.37834i	0.393711	−	0.308207i
$21$	−2.83234	−	4.21735i	−0.618067	−	0.920301i
$22$	2.24096	+	2.24096i	0.477773	+	0.477773i
$23$	−1.74467	−	1.74467i	−0.363789	−	0.363789i	0.501417	−	0.865206i	$-0.332812\pi$
$23$	−1.74467	−	1.74467i	−0.363789	−	0.363789i	−0.865206	+	0.501417i	$0.832812\pi$
$24$	0.965667	+	1.43788i	0.197116	+	0.293505i
$25$	−1.20035	+	4.85378i	−0.240069	+	0.970756i
$26$			6.10223i			1.19675i
$27$	4.34074	+	2.85621i	0.835376	+	0.549679i
$28$	−2.07397	+	2.07397i	−0.391944	+	0.391944i
$29$	6.90768			1.28272			0.641362	−	0.767239i	$-0.278370\pi$
$29$	6.90768			1.28272			0.641362	+	0.767239i	$0.278370\pi$
$30$	−3.68216	−	1.20069i	−0.672268	−	0.219216i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.05820	−	5.38623i	0.184209	−	0.937623i
$34$			2.26995i			0.389293i
$35$	0.793064	−	6.51035i	0.134052	−	1.10045i
$36$	1.13498	−	2.77702i	0.189163	−	0.462836i
$37$	5.96913	+	5.96913i	0.981319	+	0.981319i	0.999829	−	0.0185095i	$-0.00589208\pi$
$37$	5.96913	+	5.96913i	0.981319	+	0.981319i	−0.0185095	+	0.999829i	$0.505892\pi$
$38$	2.97641	+	2.97641i	0.482837	+	0.482837i
$39$	8.77425	−	5.89272i	1.40500	−	0.943591i
$40$	−0.270390	+	2.21966i	−0.0427523	+	0.350959i
$41$			9.79654i			1.52996i	0.644053	+	0.764981i	$0.277252\pi$
$41$			9.79654i			1.52996i	−0.644053	+	0.764981i	$0.722748\pi$
$42$	4.98488	+	0.979350i	0.769184	+	0.151117i
$43$	−7.01443	+	7.01443i	−1.06969	+	1.06969i	−0.0723088	+	0.997382i	$0.523037\pi$
$43$	−7.01443	+	7.01443i	−1.06969	+	1.06969i	−0.997382	+	0.0723088i	$0.976963\pi$
$44$	−3.16919			−0.477773
$45$	1.82929	+	6.45397i	0.272695	+	0.962101i
$46$	2.46733			0.363789
$47$	−3.86329	+	3.86329i	−0.563519	+	0.563519i	−0.930305	−	0.366786i	$-0.880458\pi$
$47$	−3.86329	+	3.86329i	−0.563519	+	0.563519i	0.366786	+	0.930305i	$0.380458\pi$
$48$	−1.69956	−	0.333903i	−0.245311	−	0.0481947i
$49$			1.60273i			0.228962i
$50$	−2.58337	−	4.28091i	−0.365343	−	0.605412i
$51$	3.26391	−	2.19202i	0.457039	−	0.306944i
$52$	−4.31493	−	4.31493i	−0.598373	−	0.598373i
$53$	−5.48692	−	5.48692i	−0.753687	−	0.753687i	0.221479	−	0.975165i	$-0.428912\pi$
$53$	−5.48692	−	5.48692i	−0.753687	−	0.753687i	−0.975165	+	0.221479i	$0.928912\pi$
$54$	−5.08902	+	1.04972i	−0.692527	+	0.142849i
$55$	5.58009	−	4.36823i	0.752419	−	0.589012i
$56$		−	2.93304i		−	0.391944i
$57$	1.40549	−	7.15392i	0.186161	−	0.947560i
$58$	−4.88446	+	4.88446i	−0.641362	+	0.641362i
$59$	−1.65624			−0.215623			−0.107812	−	0.994171i	$-0.534384\pi$
$59$	−1.65624			−0.215623			−0.107812	+	0.994171i	$0.534384\pi$
$60$	3.45270	−	1.75466i	0.445742	−	0.226526i
$61$	−5.62235			−0.719868			−0.359934	−	0.932978i	$-0.617201\pi$
$61$	−5.62235			−0.719868			−0.359934	+	0.932978i	$0.617201\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	−3.40555	−	8.11337i	−0.429059	−	1.02219i
$64$			1.00000i			0.125000i
$65$	13.5449	+	1.64998i	1.68004	+	0.204655i
$66$	3.06038	+	4.55690i	0.376707	+	0.560916i
$67$	−11.1009	−	11.1009i	−1.35619	−	1.35619i	−0.878557	−	0.477638i	$-0.841493\pi$
$67$	−11.1009	−	11.1009i	−1.35619	−	1.35619i	−0.477638	−	0.878557i	$-0.658507\pi$
$68$	−1.60510	−	1.60510i	−0.194647	−	0.194647i
$69$	−2.38262	−	3.54772i	−0.286834	−	0.427095i
$70$	4.04273	+	5.16430i	0.483199	+	0.617251i
$71$			6.44184i			0.764506i	0.924058	+	0.382253i	$0.124852\pi$
$71$			6.44184i			0.764506i	−0.924058	+	0.382253i	$0.875148\pi$
$72$	1.16110	+	2.76620i	0.136837	+	0.325999i
$73$	11.3843	−	11.3843i	1.33243	−	1.33243i	0.429241	−	0.903190i	$-0.358781\pi$
$73$	11.3843	−	11.3843i	1.33243	−	1.33243i	0.903190	−	0.429241i	$-0.141219\pi$
$74$	−8.44163			−0.981319
$75$	−3.66075	+	7.84850i	−0.422707	+	0.906266i
$76$	−4.20927			−0.482837
$77$	−6.57282	+	6.57282i	−0.749042	+	0.749042i
$78$	−2.03755	+	10.3711i	−0.230707	+	1.17430i
$79$			11.1919i			1.25918i	0.776926	+	0.629592i	$0.216778\pi$
$79$			11.1919i			1.25918i	−0.776926	+	0.629592i	$0.783222\pi$
$80$	−1.37834	−	1.76073i	−0.154103	−	0.196856i
$81$	6.42366	+	6.30370i	0.713740	+	0.700411i
$82$	−6.92720	−	6.92720i	−0.764981	−	0.764981i
$83$	5.80418	+	5.80418i	0.637091	+	0.637091i	0.949837	−	0.312746i	$-0.101249\pi$
$83$	5.80418	+	5.80418i	0.637091	+	0.637091i	−0.312746	+	0.949837i	$0.601249\pi$
$84$	−4.21735	+	2.83234i	−0.460151	+	0.309034i
$85$	5.03852	+	0.613771i	0.546504	+	0.0665728i
$86$		−	9.91991i		−	1.06969i
$87$	11.7400	+	2.30649i	1.25866	+	0.247282i
$88$	2.24096	−	2.24096i	0.238887	−	0.238887i
$89$	12.5769			1.33315			0.666577	−	0.745436i	$-0.267759\pi$
$89$	12.5769			1.33315			0.666577	+	0.745436i	$0.267759\pi$
$90$	−5.85715	−	3.27014i	−0.617398	−	0.344703i
$91$	−17.8981			−1.87623
$92$	−1.74467	+	1.74467i	−0.181894	+	0.181894i
$93$	−1.69956	−	0.333903i	−0.176236	−	0.0346241i
$94$		−	5.46352i		−	0.563519i
$95$	7.41140	−	5.80182i	0.760393	−	0.595254i
$96$	1.43788	−	0.965667i	0.146753	−	0.0985579i
$97$	−6.14577	−	6.14577i	−0.624009	−	0.624009i	0.322545	−	0.946554i	$-0.395462\pi$
$97$	−6.14577	−	6.14577i	−0.624009	−	0.624009i	−0.946554	+	0.322545i	$0.895462\pi$
$98$	−1.13330	−	1.13330i	−0.114481	−	0.114481i
$99$	3.59695	−	8.80090i	0.361507	−	0.884524i
$100$	4.85378	+	1.20035i	0.485378	+	0.120035i
$101$			9.38137i			0.933481i	0.884394	+	0.466740i	$0.154572\pi$
$101$			9.38137i			0.933481i	−0.884394	+	0.466740i	$0.845428\pi$
$102$	−0.757943	+	3.85792i	−0.0750475	+	0.381991i
$103$	−6.72419	+	6.72419i	−0.662554	+	0.662554i	−0.955981	−	0.293427i	$-0.905204\pi$
$103$	−6.72419	+	6.72419i	−0.662554	+	0.662554i	0.293427	+	0.955981i	$0.405204\pi$
$104$	6.10223			0.598373
$105$	3.52168	−	10.7999i	0.343681	−	1.05397i
$106$	7.75968			0.753687
$107$	4.35496	−	4.35496i	0.421010	−	0.421010i	−0.464542	−	0.885551i	$-0.653781\pi$
$107$	4.35496	−	4.35496i	0.421010	−	0.421010i	0.885551	+	0.464542i	$0.153781\pi$
$108$	2.85621	−	4.34074i	0.274839	−	0.417688i
$109$		−	5.72516i		−	0.548371i	−0.961677	−	0.274186i	$-0.911592\pi$
$109$		−	5.72516i		−	0.548371i	0.961677	−	0.274186i	$-0.0884082\pi$
$110$	−0.856916	+	7.03452i	−0.0817037	+	0.670715i
$111$	8.15180	+	12.1380i	0.773734	+	1.15209i
$112$	2.07397	+	2.07397i	0.195972	+	0.195972i
$113$	1.89039	+	1.89039i	0.177833	+	0.177833i	0.790410	−	0.612578i	$-0.209867\pi$
$113$	1.89039	+	1.89039i	0.177833	+	0.177833i	−0.612578	+	0.790410i	$0.709867\pi$
$114$	4.06476	+	6.05241i	0.380699	+	0.566861i
$115$	0.667141	−	5.47664i	0.0622113	−	0.510700i
$116$		−	6.90768i		−	0.641362i
$117$	16.8800	−	7.08530i	1.56055	−	0.655036i
$118$	1.17114	−	1.17114i	0.107812	−	0.107812i
$119$	−6.65786			−0.610325
$120$	−1.20069	+	3.68216i	−0.109608	+	0.336134i
$121$	0.956236			0.0869305
$122$	3.97560	−	3.97560i	0.359934	−	0.359934i
$123$	−3.27109	+	16.6498i	−0.294944	+	1.50126i
$124$			1.00000i			0.0898027i
$125$	−10.2007	+	4.57668i	−0.912377	+	0.409351i
$126$	8.14511	+	3.32893i	0.725624	+	0.296565i
$127$	−3.08903	−	3.08903i	−0.274107	−	0.274107i	0.556644	−	0.830751i	$-0.312089\pi$
$127$	−3.08903	−	3.08903i	−0.274107	−	0.274107i	−0.830751	+	0.556644i	$0.812089\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−14.2636	+	9.57932i	−1.25584	+	0.843412i
$130$	−10.7444	+	8.41096i	−0.942345	+	0.737690i
$131$			0.589172i			0.0514762i	0.999669	+	0.0257381i	$0.00819360\pi$
$131$			0.589172i			0.0514762i	−0.999669	+	0.0257381i	$0.991806\pi$
$132$	−5.38623	−	1.05820i	−0.468811	−	0.0921045i
$133$	−8.72992	+	8.72992i	−0.756980	+	0.756980i
$134$	15.6991			1.35619
$135$	0.954002	+	11.5797i	0.0821075	+	0.996623i
$136$	2.26995			0.194647
$137$	−7.96363	+	7.96363i	−0.680378	+	0.680378i	−0.960085	−	0.279707i	$-0.909763\pi$
$137$	−7.96363	+	7.96363i	−0.680378	+	0.680378i	0.279707	+	0.960085i	$0.409763\pi$
$138$	4.19339	+	0.823849i	0.356965	+	0.0701307i
$139$			16.3935i			1.39048i	0.718777	+	0.695240i	$0.244702\pi$
$139$			16.3935i			1.39048i	−0.718777	+	0.695240i	$0.755298\pi$
$140$	−6.51035	−	0.793064i	−0.550225	−	0.0670261i
$141$	−7.85586	+	5.27594i	−0.661583	+	0.444314i
$142$	−4.55507	−	4.55507i	−0.382253	−	0.382253i
$143$	−13.6748	−	13.6748i	−1.14355	−	1.14355i
$144$	−2.77702	−	1.13498i	−0.231418	−	0.0945813i
$145$	9.52114	+	12.1626i	0.790688	+	1.01005i
$146$			16.0998i			1.33243i
$147$	−0.535156	+	2.72394i	−0.0441389	+	0.224667i
$148$	5.96913	−	5.96913i	0.490660	−	0.490660i
$149$	3.69544			0.302742			0.151371	−	0.988477i	$-0.451631\pi$
$149$	3.69544			0.302742			0.151371	+	0.988477i	$0.451631\pi$
$150$	−2.96118	−	8.13827i	−0.241780	−	0.664487i
$151$	9.74536			0.793066			0.396533	−	0.918020i	$-0.370213\pi$
$151$	9.74536			0.793066			0.396533	+	0.918020i	$0.370213\pi$
$152$	2.97641	−	2.97641i	0.241418	−	0.241418i
$153$	6.27913	−	2.63564i	0.507638	−	0.213079i
$154$		−	9.29536i		−	0.749042i
$155$	−1.37834	−	1.76073i	−0.110711	−	0.141425i
$156$	−5.89272	−	8.77425i	−0.471795	−	0.702502i
$157$	−10.7909	−	10.7909i	−0.861208	−	0.861208i	0.130270	−	0.991479i	$-0.458415\pi$
$157$	−10.7909	−	10.7909i	−0.861208	−	0.861208i	−0.991479	+	0.130270i	$0.958415\pi$
$158$	−7.91385	−	7.91385i	−0.629592	−	0.629592i
$159$	−7.49326	−	11.1575i	−0.594254	−	0.884844i
$160$	2.21966	+	0.270390i	0.175480	+	0.0213762i
$161$			7.23679i			0.570339i
$162$	−8.99960	+	0.0848267i	−0.707075	+	0.00666462i
$163$	9.92465	−	9.92465i	0.777359	−	0.777359i	−0.202022	−	0.979381i	$-0.564751\pi$
$163$	9.92465	−	9.92465i	0.777359	−	0.777359i	0.979381	+	0.202022i	$0.0647513\pi$
$164$	9.79654			0.764981
$165$	10.9423	−	5.56087i	0.851854	−	0.432913i
$166$	−8.20835			−0.637091
$167$	1.43445	−	1.43445i	0.111001	−	0.111001i	−0.649425	−	0.760426i	$-0.724990\pi$
$167$	1.43445	−	1.43445i	0.111001	−	0.111001i	0.760426	+	0.649425i	$0.224990\pi$
$168$	0.979350	−	4.98488i	0.0755585	−	0.384592i
$169$		−	24.2372i		−	1.86440i
$170$	−3.99677	+	3.12877i	−0.306539	+	0.239966i
$171$	4.77742	−	11.6892i	0.365339	−	0.893898i
$172$	7.01443	+	7.01443i	0.534846	+	0.534846i
$173$	−6.36976	−	6.36976i	−0.484284	−	0.484284i	0.422213	−	0.906497i	$-0.361253\pi$
$173$	−6.36976	−	6.36976i	−0.484284	−	0.484284i	−0.906497	+	0.422213i	$0.861253\pi$
$174$	−9.93238	+	6.67051i	−0.752972	+	0.505690i
$175$	12.5561	−	7.57712i	0.949151	−	0.572777i
$176$			3.16919i			0.238887i
$177$	−2.81487	−	0.553021i	−0.211579	−	0.0415676i
$178$	−8.89325	+	8.89325i	−0.666577	+	0.666577i
$179$	16.9715			1.26851			0.634253	−	0.773126i	$-0.281308\pi$
$179$	16.9715			1.26851			0.634253	+	0.773126i	$0.281308\pi$
$180$	6.45397	−	1.82929i	0.481050	−	0.136348i
$181$	−16.6154			−1.23501			−0.617505	−	0.786567i	$-0.711856\pi$
$181$	−16.6154			−1.23501			−0.617505	+	0.786567i	$0.711856\pi$
$182$	12.6559	−	12.6559i	0.938115	−	0.938115i
$183$	−9.55552	−	1.87732i	−0.706365	−	0.138775i
$184$		−	2.46733i		−	0.181894i
$185$	−2.28253	+	18.7375i	−0.167815	+	1.37761i
$186$	1.43788	−	0.965667i	0.105430	−	0.0708061i
$187$	−5.08686	−	5.08686i	−0.371988	−	0.371988i
$188$	3.86329	+	3.86329i	0.281759	+	0.281759i
$189$	−3.07887	−	14.9263i	−0.223955	−	1.08573i
$190$	−1.13814	+	9.34316i	−0.0825696	+	0.677824i
$191$			16.5986i			1.20103i	0.799613	+	0.600515i	$0.205038\pi$
$191$			16.5986i			1.20103i	−0.799613	+	0.600515i	$0.794962\pi$
$192$	−0.333903	+	1.69956i	−0.0240973	+	0.122655i
$193$	7.25915	−	7.25915i	0.522525	−	0.522525i	−0.395808	−	0.918333i	$-0.629535\pi$
$193$	7.25915	−	7.25915i	0.522525	−	0.522525i	0.918333	+	0.395808i	$0.129535\pi$
$194$	8.69144			0.624009
$195$	22.4694	+	7.32691i	1.60907	+	0.524691i
$196$	1.60273			0.114481
$197$	−10.2617	+	10.2617i	−0.731114	+	0.731114i	−0.970840	−	0.239727i	$-0.922942\pi$
$197$	−10.2617	+	10.2617i	−0.731114	+	0.731114i	0.239727	+	0.970840i	$0.422942\pi$
$198$	3.67974	+	8.76660i	0.261508	+	0.623015i
$199$			2.14395i			0.151981i	0.997109	+	0.0759903i	$0.0242118\pi$
$199$			2.14395i			0.151981i	−0.997109	+	0.0759903i	$0.975788\pi$
$200$	−4.28091	+	2.58337i	−0.302706	+	0.182672i
$201$	−15.1601	−	22.5733i	−1.06931	−	1.59220i
$202$	−6.63363	−	6.63363i	−0.466740	−	0.466740i
$203$	−14.3263	−	14.3263i	−1.00551	−	1.00551i
$204$	−2.19202	−	3.26391i	−0.153472	−	0.228519i
$205$	−17.2491	+	13.5030i	−1.20473	+	0.943089i
$206$		−	9.50944i		−	0.662554i
$207$	−2.86482	−	6.82513i	−0.199119	−	0.474380i
$208$	−4.31493	+	4.31493i	−0.299187	+	0.299187i
$209$	−13.3400			−0.922746
$210$	5.14650	+	10.1269i	0.355143	+	0.698824i
$211$	5.11243			0.351954			0.175977	−	0.984394i	$-0.443692\pi$
$211$	5.11243			0.351954			0.175977	+	0.984394i	$0.443692\pi$
$212$	−5.48692	+	5.48692i	−0.376843	+	0.376843i
$213$	−2.15095	+	10.9483i	−0.147380	+	0.750166i
$214$			6.15884i			0.421010i
$215$	−22.0188	−	2.68224i	−1.50167	−	0.182927i
$216$	1.04972	+	5.08902i	0.0714243	+	0.346264i
$217$	2.07397	+	2.07397i	0.140790	+	0.140790i
$218$	4.04830	+	4.04830i	0.274186	+	0.274186i
$219$	23.1496	−	15.5471i	1.56430	−	1.05057i
$220$	−4.36823	−	5.58009i	−0.294506	−	0.376210i
$221$		−	13.8518i		−	0.931771i
$222$	−14.3471	−	2.81868i	−0.962912	−	0.189177i
$223$	−12.3678	+	12.3678i	−0.828209	+	0.828209i	−0.987269	−	0.159060i	$-0.949154\pi$
$223$	−12.3678	+	12.3678i	−0.828209	+	0.828209i	0.159060	+	0.987269i	$0.449154\pi$
$224$	−2.93304			−0.195972
$225$	−8.84230	+	12.1167i	−0.589487	+	0.807778i
$226$	−2.67341			−0.177833
$227$	−3.51012	+	3.51012i	−0.232975	+	0.232975i	−0.813933	−	0.580959i	$-0.802678\pi$
$227$	−3.51012	+	3.51012i	−0.232975	+	0.232975i	0.580959	+	0.813933i	$0.302678\pi$
$228$	−7.15392	−	1.40549i	−0.473780	−	0.0930807i
$229$		−	26.6631i		−	1.76195i	−0.473165	−	0.880974i	$-0.656889\pi$
$229$		−	26.6631i		−	1.76195i	0.473165	−	0.880974i	$-0.343111\pi$
$230$	3.40083	+	4.34431i	0.224244	+	0.286455i
$231$	−13.3656	+	8.97622i	−0.879391	+	0.590592i
$232$	4.88446	+	4.88446i	0.320681	+	0.320681i
$233$	−15.1000	−	15.1000i	−0.989236	−	0.989236i	0.0107066	−	0.999943i	$-0.496592\pi$
$233$	−15.1000	−	15.1000i	−0.989236	−	0.989236i	−0.999943	+	0.0107066i	$0.996592\pi$
$234$	−6.92588	+	16.9460i	−0.452759	+	1.10780i
$235$	−12.1271	−	1.47728i	−0.791088	−	0.0963670i
$236$			1.65624i			0.107812i
$237$	−3.73700	+	19.0213i	−0.242744	+	1.23556i
$238$	4.70782	−	4.70782i	0.305163	−	0.305163i
$239$	12.7150			0.822465			0.411233	−	0.911530i	$-0.365098\pi$
$239$	12.7150			0.822465			0.411233	+	0.911530i	$0.365098\pi$
$240$	−1.75466	−	3.45270i	−0.113263	−	0.222871i
$241$	19.9468			1.28489			0.642444	−	0.766333i	$-0.277920\pi$
$241$	19.9468			1.28489			0.642444	+	0.766333i	$0.277920\pi$
$242$	−0.676161	+	0.676161i	−0.0434653	+	0.0434653i
$243$	8.81258	+	12.8584i	0.565328	+	0.824867i
$244$			5.62235i			0.359934i
$245$	−2.82198	+	2.20911i	−0.180290	+	0.141135i
$246$	−9.46019	−	14.0862i	−0.603160	−	0.898104i
$247$	−18.1627	−	18.1627i	−1.15567	−	1.15567i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	7.92653	+	11.8026i	0.502323	+	0.747958i
$250$	3.97677	−	10.4492i	0.251513	−	0.660864i
$251$			2.24110i			0.141457i	0.997496	+	0.0707285i	$0.0225324\pi$
$251$			2.24110i			0.141457i	−0.997496	+	0.0707285i	$0.977468\pi$
$252$	−8.11337	+	3.40555i	−0.511094	+	0.214530i
$253$	−5.52919	+	5.52919i	−0.347617	+	0.347617i
$254$	4.36855			0.274107
$255$	8.35833	+	2.72552i	0.523419	+	0.170678i
$256$	1.00000			0.0625000
$257$	−12.5226	+	12.5226i	−0.781138	+	0.781138i	−0.980023	−	0.198885i	$-0.936268\pi$
$257$	−12.5226	+	12.5226i	−0.781138	+	0.781138i	0.198885	+	0.980023i	$0.436268\pi$
$258$	3.31228	−	16.8595i	0.206214	−	1.04963i
$259$		−	24.7596i		−	1.53849i
$260$	1.64998	−	13.5449i	0.102327	−	0.840018i
$261$	19.1827	+	7.84005i	1.18738	+	0.485287i
$262$	−0.416608	−	0.416608i	−0.0257381	−	0.0257381i
$263$	−18.0535	−	18.0535i	−1.11323	−	1.11323i	−0.992711	−	0.120517i	$-0.961545\pi$
$263$	−18.0535	−	18.0535i	−1.11323	−	1.11323i	−0.120517	−	0.992711i	$-0.538455\pi$
$264$	4.55690	−	3.06038i	0.280458	−	0.188353i
$265$	2.09814	−	17.2238i	0.128888	−	1.05805i
$266$		−	12.3460i		−	0.756980i
$267$	21.3753	+	4.19948i	1.30815	+	0.257004i
$268$	−11.1009	+	11.1009i	−0.678097	+	0.678097i
$269$	−27.3712			−1.66885			−0.834427	−	0.551119i	$-0.814201\pi$
$269$	−27.3712			−1.66885			−0.834427	+	0.551119i	$0.814201\pi$
$270$	−8.86268	−	7.51352i	−0.539365	−	0.457258i
$271$	−16.6558			−1.01177			−0.505883	−	0.862602i	$-0.668833\pi$
$271$	−16.6558			−1.01177			−0.505883	+	0.862602i	$0.668833\pi$
$272$	−1.60510	+	1.60510i	−0.0973234	+	0.0973234i
$273$	−30.4189	−	5.97622i	−1.84104	−	0.361697i
$274$		−	11.2623i		−	0.680378i
$275$	15.3825	+	3.80412i	0.927602	+	0.229397i
$276$	−3.54772	+	2.38262i	−0.213548	+	0.143417i
$277$	13.8768	+	13.8768i	0.833775	+	0.833775i	0.988031	−	0.154256i	$-0.0492981\pi$
$277$	13.8768	+	13.8768i	0.833775	+	0.833775i	−0.154256	+	0.988031i	$0.549298\pi$
$278$	−11.5920	−	11.5920i	−0.695240	−	0.695240i
$279$	−2.77702	−	1.13498i	−0.166256	−	0.0679492i
$280$	5.16430	−	4.04273i	0.308626	−	0.241600i
$281$		−	7.80902i		−	0.465847i	−0.972495	−	0.232923i	$-0.925171\pi$
$281$		−	7.80902i		−	0.465847i	0.972495	−	0.232923i	$-0.0748292\pi$
$282$	1.82428	−	9.28558i	0.108634	−	0.552948i
$283$	−1.99750	+	1.99750i	−0.118739	+	0.118739i	−0.763980	−	0.645240i	$-0.776757\pi$
$283$	−1.99750	+	1.99750i	−0.118739	+	0.118739i	0.645240	+	0.763980i	$0.276757\pi$
$284$	6.44184			0.382253
$285$	14.5334	−	7.38586i	0.860882	−	0.437501i
$286$	19.3391			1.14355
$287$	20.3178	−	20.3178i	1.19932	−	1.19932i
$288$	2.76620	−	1.16110i	0.163000	−	0.0684184i
$289$			11.8473i			0.696901i
$290$	−15.3327	−	1.86776i	−0.900367	−	0.109679i
$291$	−8.39303	−	12.4972i	−0.492008	−	0.732599i
$292$	−11.3843	−	11.3843i	−0.666215	−	0.666215i
$293$	−4.08601	−	4.08601i	−0.238707	−	0.238707i	0.577607	−	0.816315i	$-0.303986\pi$
$293$	−4.08601	−	4.08601i	−0.238707	−	0.238707i	−0.816315	+	0.577607i	$0.803986\pi$
$294$	−1.54770	−	2.30453i	−0.0902640	−	0.134403i
$295$	−2.28286	−	2.91618i	−0.132913	−	0.169787i
$296$			8.44163i			0.490660i
$297$	9.05189	−	13.7566i	0.525244	−	0.798241i
$298$	−2.61307	+	2.61307i	−0.151371	+	0.151371i
$299$	−15.0562			−0.870725
$300$	7.84850	+	3.66075i	0.453133	+	0.211354i
$301$	29.0955			1.67704
$302$	−6.89101	+	6.89101i	−0.396533	+	0.396533i
$303$	−3.13246	+	15.9442i	−0.179955	+	0.915971i
$304$			4.20927i			0.241418i
$305$	−7.74952	−	9.89944i	−0.443736	−	0.566840i
$306$	−2.57634	+	6.30370i	−0.147280	+	0.360358i
$307$	−8.01309	−	8.01309i	−0.457331	−	0.457331i	0.440447	−	0.897779i	$-0.354820\pi$
$307$	−8.01309	−	8.01309i	−0.457331	−	0.457331i	−0.897779	+	0.440447i	$0.854820\pi$
$308$	6.57282	+	6.57282i	0.374521	+	0.374521i
$309$	−13.6734	+	9.18295i	−0.777853	+	0.522400i
$310$	2.21966	+	0.270390i	0.126068	+	0.0153571i
$311$			13.9211i			0.789392i	0.918812	+	0.394696i	$0.129150\pi$
$311$			13.9211i			0.789392i	−0.918812	+	0.394696i	$0.870850\pi$
$312$	10.3711	+	2.03755i	0.587149	+	0.115354i
$313$	3.73351	−	3.73351i	0.211031	−	0.211031i	−0.593675	−	0.804705i	$-0.702323\pi$
$313$	3.73351	−	3.73351i	0.211031	−	0.211031i	0.804705	+	0.593675i	$0.202323\pi$
$314$	15.2606			0.861208
$315$	9.59145	−	17.1793i	0.540417	−	0.967942i
$316$	11.1919			0.629592
$317$	−22.2577	+	22.2577i	−1.25012	+	1.25012i	−0.294449	+	0.955667i	$0.595136\pi$
$317$	−22.2577	+	22.2577i	−1.25012	+	1.25012i	−0.955667	+	0.294449i	$0.904864\pi$
$318$	13.1881	+	2.59098i	0.739549	+	0.145295i
$319$		−	21.8917i		−	1.22570i
$320$	−1.76073	+	1.37834i	−0.0984278	+	0.0770517i
$321$	8.85565	−	5.94739i	0.494274	−	0.331951i
$322$	−5.11719	−	5.11719i	−0.285170	−	0.285170i
$323$	−6.75630	−	6.75630i	−0.375930	−	0.375930i
$324$	6.30370	−	6.42366i	0.350205	−	0.356870i
$325$	15.7643	+	26.1231i	0.874446	+	1.44905i
$326$			14.0356i			0.777359i
$327$	1.91165	−	9.73026i	0.105714	−	0.538085i
$328$	−6.92720	+	6.92720i	−0.382491	+	0.382491i
$329$	16.0247			0.883471
$330$	−3.80523	+	11.6695i	−0.209471	+	0.642384i
$331$	−0.441739			−0.0242802			−0.0121401	−	0.999926i	$-0.503864\pi$
$331$	−0.441739			−0.0242802			−0.0121401	+	0.999926i	$0.503864\pi$
$332$	5.80418	−	5.80418i	0.318546	−	0.318546i
$333$	9.80157	+	23.3512i	0.537123	+	1.27964i
$334$			2.02862i			0.111001i
$335$	4.24487	−	34.8466i	0.231922	−	1.90388i
$336$	2.83234	+	4.21735i	0.154517	+	0.230075i
$337$	−1.39208	−	1.39208i	−0.0758314	−	0.0758314i	0.668174	−	0.744005i	$-0.267076\pi$
$337$	−1.39208	−	1.39208i	−0.0758314	−	0.0758314i	−0.744005	+	0.668174i	$0.767076\pi$
$338$	17.1383	+	17.1383i	0.932201	+	0.932201i
$339$	2.58162	+	3.84403i	0.140215	+	0.208779i
$340$	0.613771	−	5.03852i	0.0332864	−	0.273252i
$341$			3.16919i			0.171621i
$342$	4.88738	+	11.6437i	0.264280	+	0.629618i
$343$	−11.1938	+	11.1938i	−0.604408	+	0.604408i
$344$	−9.91991			−0.534846
$345$	2.96251	−	9.08513i	0.159496	−	0.489127i
$346$	9.00820			0.484284
$347$	−6.21440	+	6.21440i	−0.333606	+	0.333606i	−0.853954	−	0.520348i	$-0.825802\pi$
$347$	−6.21440	+	6.21440i	−0.333606	+	0.333606i	0.520348	+	0.853954i	$0.325802\pi$
$348$	2.30649	−	11.7400i	0.123641	−	0.629331i
$349$			32.6162i			1.74591i	0.487804	+	0.872953i	$0.337798\pi$
$349$			32.6162i			1.74591i	−0.487804	+	0.872953i	$0.662202\pi$
$350$	−3.52066	+	14.2363i	−0.188187	+	0.760964i
$351$	31.0544	−	6.40563i	1.65756	−	0.341907i
$352$	−2.24096	−	2.24096i	−0.119443	−	0.119443i
$353$	13.3734	+	13.3734i	0.711795	+	0.711795i	0.966911	−	0.255116i	$-0.0821135\pi$
$353$	13.3734	+	13.3734i	0.711795	+	0.711795i	−0.255116	+	0.966911i	$0.582113\pi$
$354$	2.38146	−	1.59937i	0.126573	−	0.0850056i
$355$	−11.3423	+	8.87906i	−0.601989	+	0.471252i
$356$		−	12.5769i		−	0.666577i
$357$	−11.3154	−	2.22308i	−0.598877	−	0.117658i
$358$	−12.0006	+	12.0006i	−0.634253	+	0.634253i
$359$	4.20091			0.221716			0.110858	−	0.993836i	$-0.464640\pi$
$359$	4.20091			0.221716			0.110858	+	0.993836i	$0.464640\pi$
$360$	−3.27014	+	5.85715i	−0.172351	+	0.308699i
$361$	1.28202			0.0674745
$362$	11.7488	−	11.7488i	0.617505	−	0.617505i
$363$	1.62518	+	0.319290i	0.0852999	+	0.0167584i
$364$			17.8981i			0.938115i
$365$	35.7361	+	4.35323i	1.87051	+	0.227858i
$366$	8.08424	−	5.42931i	0.422570	−	0.283795i
$367$	16.1338	+	16.1338i	0.842178	+	0.842178i	0.989142	−	0.146964i	$-0.0469501\pi$
$367$	16.1338	+	16.1338i	0.842178	+	0.842178i	−0.146964	+	0.989142i	$0.546950\pi$
$368$	1.74467	+	1.74467i	0.0909471	+	0.0909471i
$369$	−11.1188	+	27.2052i	−0.578823	+	1.41624i
$370$	−11.6355	−	14.8634i	−0.604898	−	0.772713i
$371$			22.7595i			1.18161i
$372$	−0.333903	+	1.69956i	−0.0173120	+	0.0881182i
$373$	−7.12949	+	7.12949i	−0.369151	+	0.369151i	−0.867168	−	0.498016i	$-0.834062\pi$
$373$	−7.12949	+	7.12949i	−0.369151	+	0.369151i	0.498016	+	0.867168i	$0.334062\pi$
$374$	7.19391			0.371988
$375$	−18.8649	+	4.37232i	−0.974177	+	0.225786i
$376$	−5.46352			−0.281759
$377$	29.8061	−	29.8061i	1.53509	−	1.53509i
$378$	12.7316	+	8.37740i	0.654842	+	0.430887i
$379$			3.15744i			0.162187i	0.996707	+	0.0810933i	$0.0258412\pi$
$379$			3.15744i			0.162187i	−0.996707	+	0.0810933i	$0.974159\pi$
$380$	−5.80182	−	7.41140i	−0.297627	−	0.380197i
$381$	−4.21857	−	6.28144i	−0.216124	−	0.321808i
$382$	−11.7370	−	11.7370i	−0.600515	−	0.600515i
$383$	−10.1021	−	10.1021i	−0.516194	−	0.516194i	0.400224	−	0.916417i	$-0.368932\pi$
$383$	−10.1021	−	10.1021i	−0.516194	−	0.516194i	−0.916417	+	0.400224i	$0.868932\pi$
$384$	−0.965667	−	1.43788i	−0.0492790	−	0.0733763i
$385$	−20.6325	−	2.51337i	−1.05153	−	0.128093i
$386$			10.2660i			0.522525i
$387$	−27.4404	+	11.5180i	−1.39488	+	0.585493i
$388$	−6.14577	+	6.14577i	−0.312004	+	0.312004i
$389$	−20.2441			−1.02642			−0.513208	−	0.858265i	$-0.671543\pi$
$389$	−20.2441			−1.02642			−0.513208	+	0.858265i	$0.671543\pi$
$390$	−21.0692	+	10.7074i	−1.06688	+	0.542189i
$391$	−5.60073			−0.283241
$392$	−1.13330	+	1.13330i	−0.0572404	+	0.0572404i
$393$	−0.196726	+	1.00133i	−0.00992352	+	0.0505106i
$394$		−	14.5122i		−	0.731114i
$395$	−19.7059	+	15.4262i	−0.991510	+	0.776178i
$396$	−8.80090	−	3.59695i	−0.442262	−	0.180754i
$397$	6.50451	+	6.50451i	0.326452	+	0.326452i	0.851236	−	0.524784i	$-0.175854\pi$
$397$	6.50451	+	6.50451i	0.326452	+	0.326452i	−0.524784	+	0.851236i	$0.675854\pi$
$398$	−1.51600	−	1.51600i	−0.0759903	−	0.0759903i
$399$	−17.7520	+	11.9221i	−0.888711	+	0.596851i
$400$	1.20035	−	4.85378i	0.0600173	−	0.242689i
$401$			3.90591i			0.195052i	0.995233	+	0.0975258i	$0.0310929\pi$
$401$			3.90591i			0.195052i	−0.995233	+	0.0975258i	$0.968907\pi$
$402$	26.6816	+	5.24197i	1.33076	+	0.261446i
$403$	−4.31493	+	4.31493i	−0.214942	+	0.214942i
$404$	9.38137			0.466740
$405$	−2.24511	+	19.9990i	−0.111560	+	0.993758i
$406$	20.2605			1.00551
$407$	18.9173	−	18.9173i	0.937696	−	0.937696i
$408$	3.85792	+	0.757943i	0.190996	+	0.0375238i
$409$			4.32068i			0.213644i	0.994278	+	0.106822i	$0.0340675\pi$
$409$			4.32068i			0.213644i	−0.994278	+	0.106822i	$0.965933\pi$
$410$	2.64888	−	21.7450i	0.130819	−	1.07391i
$411$	−16.1937	+	10.8756i	−0.798779	+	0.536454i
$412$	6.72419	+	6.72419i	0.331277	+	0.331277i
$413$	3.43499	+	3.43499i	0.169025	+	0.169025i
$414$	6.85183	+	2.80036i	0.336749	+	0.137630i
$415$	−2.21945	+	18.2197i	−0.108949	+	0.894372i
$416$		−	6.10223i		−	0.299187i
$417$	−5.47384	+	27.8618i	−0.268055	+	1.36440i
$418$	9.43280	−	9.43280i	0.461373	−	0.461373i
$419$	18.0892			0.883717			0.441859	−	0.897085i	$-0.354319\pi$
$419$	18.0892			0.883717			0.441859	+	0.897085i	$0.354319\pi$
$420$	−10.7999	−	3.52168i	−0.526983	−	0.171841i
$421$	8.55912			0.417146			0.208573	−	0.978007i	$-0.433118\pi$
$421$	8.55912			0.417146			0.208573	+	0.978007i	$0.433118\pi$
$422$	−3.61503	+	3.61503i	−0.175977	+	0.175977i
$423$	−15.1132	+	6.34369i	−0.734827	+	0.308441i
$424$		−	7.75968i		−	0.376843i
$425$	5.86412	+	9.71746i	0.284452	+	0.471366i
$426$	−6.22067	−	9.26257i	−0.301393	−	0.448773i
$427$	11.6606	+	11.6606i	0.564296	+	0.564296i
$428$	−4.35496	−	4.35496i	−0.210505	−	0.210505i
$429$	−18.6752	−	27.8073i	−0.901645	−	1.34255i
$430$	17.4663	−	13.6730i	0.842299	−	0.659372i
$431$		−	0.986613i		−	0.0475235i	−0.999718	−	0.0237617i	$-0.992436\pi$
$431$		−	0.986613i		−	0.0475235i	0.999718	−	0.0237617i	$-0.00756431\pi$
$432$	−4.34074	−	2.85621i	−0.208844	−	0.137420i
$433$	−0.288054	+	0.288054i	−0.0138430	+	0.0138430i	−0.713994	−	0.700151i	$-0.753116\pi$
$433$	−0.288054	+	0.288054i	−0.0138430	+	0.0138430i	0.700151	+	0.713994i	$0.253116\pi$
$434$	−2.93304			−0.140790
$435$	12.1207	+	23.8501i	0.581141	+	1.14353i
$436$	−5.72516			−0.274186
$437$	−7.34379	+	7.34379i	−0.351301	+	0.351301i
$438$	−5.37577	+	27.3626i	−0.256864	+	1.30744i
$439$		−	15.7966i		−	0.753930i	−0.926227	−	0.376965i	$-0.876968\pi$
$439$		−	15.7966i		−	0.753930i	0.926227	−	0.376965i	$-0.123032\pi$
$440$	7.03452	+	0.856916i	0.335358	+	0.0408519i
$441$	−1.81906	+	4.45081i	−0.0866220	+	0.211944i
$442$	9.79468	+	9.79468i	0.465885	+	0.465885i
$443$	−9.92788	−	9.92788i	−0.471688	−	0.471688i	0.430773	−	0.902460i	$-0.358241\pi$
$443$	−9.92788	−	9.92788i	−0.471688	−	0.471688i	−0.902460	+	0.430773i	$0.858241\pi$
$444$	12.1380	−	8.15180i	0.576045	−	0.386867i
$445$	17.3353	+	22.1446i	0.821774	+	1.04976i
$446$		−	17.4907i		−	0.828209i
$447$	6.28062	+	1.23392i	0.297063	+	0.0583622i
$448$	2.07397	−	2.07397i	0.0979860	−	0.0979860i
$449$	−10.8832			−0.513609			−0.256805	−	0.966463i	$-0.582670\pi$
$449$	−10.8832			−0.513609			−0.256805	+	0.966463i	$0.582670\pi$
$450$	−2.31533	−	14.8202i	−0.109146	−	0.698632i
$451$	31.0471			1.46195
$452$	1.89039	−	1.89039i	0.0889163	−	0.0889163i
$453$	16.5628	+	3.25400i	0.778190	+	0.152886i
$454$		−	4.96405i		−	0.232975i
$455$	−24.6697	−	31.5137i	−1.15653	−	1.47739i
$456$	6.05241	−	4.06476i	0.283430	−	0.190350i
$457$	−0.0245420	−	0.0245420i	−0.00114803	−	0.00114803i	0.706533	−	0.707681i	$-0.250258\pi$
$457$	−0.0245420	−	0.0245420i	−0.00114803	−	0.00114803i	−0.707681	+	0.706533i	$0.750258\pi$
$458$	18.8537	+	18.8537i	0.880974	+	0.880974i
$459$	11.5518	−	2.38281i	0.539193	−	0.111220i
$460$	−5.47664	−	0.667141i	−0.255350	−	0.0311056i
$461$		−	2.11772i		−	0.0986322i	−0.998783	−	0.0493161i	$-0.984296\pi$
$461$		−	2.11772i		−	0.0986322i	0.998783	−	0.0493161i	$-0.0157042\pi$
$462$	3.10375	−	15.7980i	0.144399	−	0.734992i
$463$	14.3450	−	14.3450i	0.666668	−	0.666668i	−0.290275	−	0.956943i	$-0.593747\pi$
$463$	14.3450	−	14.3450i	0.666668	−	0.666668i	0.956943	+	0.290275i	$0.0937468\pi$
$464$	−6.90768			−0.320681
$465$	−1.75466	−	3.45270i	−0.0813706	−	0.160115i
$466$	21.3547			0.989236
$467$	−13.7070	+	13.7070i	−0.634285	+	0.634285i	−0.949140	−	0.314855i	$-0.898044\pi$
$467$	−13.7070	+	13.7070i	−0.634285	+	0.634285i	0.314855	+	0.949140i	$0.398044\pi$
$468$	−7.08530	−	16.8800i	−0.327518	−	0.780277i
$469$			46.0461i			2.12621i
$470$	9.61978	−	7.53060i	0.443727	−	0.347360i
$471$	−14.7367	−	21.9429i	−0.679031	−	1.01108i
$472$	−1.17114	−	1.17114i	−0.0539059	−	0.0539059i
$473$	22.2301	+	22.2301i	1.02214	+	1.02214i
$474$	−10.8076	−	16.0925i	−0.496410	−	0.739154i
$475$	20.4309	+	5.05258i	0.937433	+	0.231828i
$476$			6.65786i			0.305163i
$477$	−9.00976	−	21.4648i	−0.412528	−	0.982806i
$478$	−8.99086	+	8.99086i	−0.411233	+	0.411233i
$479$	5.82049			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$479$	5.82049			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$480$	3.68216	+	1.20069i	0.168067	+	0.0548039i
$481$	51.5128			2.34878
$482$	−14.1045	+	14.1045i	−0.642444	+	0.642444i
$483$	−2.41638	+	12.2994i	−0.109949	+	0.559641i
$484$		−	0.956236i		−	0.0434653i
$485$	2.35007	−	19.2920i	0.106711	−	0.876006i
$486$	−15.3237	−	2.86082i	−0.695097	−	0.129769i
$487$	10.3617	+	10.3617i	0.469533	+	0.469533i	0.901763	−	0.432231i	$-0.142273\pi$
$487$	10.3617	+	10.3617i	0.469533	+	0.469533i	−0.432231	+	0.901763i	$0.642273\pi$
$488$	−3.97560	−	3.97560i	−0.179967	−	0.179967i
$489$	20.1814	−	13.5537i	0.912636	−	0.612919i
$490$	0.433362	−	3.55752i	0.0195773	−	0.160712i
$491$		−	3.65977i		−	0.165163i	−0.996584	−	0.0825816i	$-0.973683\pi$
$491$		−	3.65977i		−	0.165163i	0.996584	−	0.0825816i	$-0.0263165\pi$
$492$	16.6498	+	3.27109i	0.750632	+	0.147472i
$493$	11.0875	−	11.0875i	0.499356	−	0.499356i
$494$	25.6860			1.15567
$495$	20.4538	−	5.79738i	0.919332	−	0.260573i
$496$	1.00000			0.0449013
$497$	13.3602	−	13.3602i	0.599287	−	0.599287i
$498$	−13.9506	−	2.74079i	−0.625141	−	0.122818i
$499$			5.06240i			0.226624i	0.993559	+	0.113312i	$0.0361460\pi$
$499$			5.06240i			0.226624i	−0.993559	+	0.113312i	$0.963854\pi$
$500$	4.57668	+	10.2007i	0.204675	+	0.456189i
$501$	2.91691	−	1.95897i	0.130318	−	0.0875205i
$502$	−1.58470	−	1.58470i	−0.0707285	−	0.0707285i
$503$	20.5910	+	20.5910i	0.918106	+	0.918106i	0.996892	−	0.0787858i	$-0.0251043\pi$
$503$	20.5910	+	20.5910i	0.918106	+	0.918106i	−0.0787858	+	0.996892i	$0.525104\pi$
$504$	3.32893	−	8.14511i	0.148282	−	0.362812i
$505$	−16.5181	+	12.9307i	−0.735044	+	0.575410i
$506$		−	7.81945i		−	0.347617i
$507$	8.09287	−	41.1927i	0.359417	−	1.82943i
$508$	−3.08903	+	3.08903i	−0.137054	+	0.137054i
$509$	33.7265			1.49490			0.747449	−	0.664319i	$-0.231278\pi$
$509$	33.7265			1.49490			0.747449	+	0.664319i	$0.231278\pi$
$510$	−7.83747	+	3.98300i	−0.347049	+	0.176370i
$511$	−47.2215			−2.08895
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	12.0226	−	18.2714i	0.530810	−	0.806701i
$514$		−	17.7096i		−	0.781138i
$515$	−21.1077	−	2.57125i	−0.930118	−	0.113303i
$516$	9.57932	+	14.2636i	0.421706	+	0.627920i
$517$	12.2435	+	12.2435i	0.538468	+	0.538468i
$518$	17.5077	+	17.5077i	0.769245	+	0.769245i
$519$	−8.69892	−	12.9527i	−0.381840	−	0.568559i
$520$	8.41096	+	10.7444i	0.368845	+	0.471173i
$521$			11.1221i			0.487268i	0.969867	+	0.243634i	$0.0783395\pi$
$521$			11.1221i			0.487268i	−0.969867	+	0.243634i	$0.921661\pi$
$522$	−19.1080	+	8.02050i	−0.836334	+	0.351048i
$523$	16.3679	−	16.3679i	0.715720	−	0.715720i	−0.252006	−	0.967726i	$-0.581090\pi$
$523$	16.3679	−	16.3679i	0.715720	−	0.715720i	0.967726	+	0.252006i	$0.0810902\pi$
$524$	0.589172			0.0257381
$525$	23.8699	−	8.68527i	1.04177	−	0.379056i
$526$	25.5315			1.11323
$527$	−1.60510	+	1.60510i	−0.0699192	+	0.0699192i
$528$	−1.05820	+	5.38623i	−0.0460523	+	0.234406i
$529$		−	16.9123i		−	0.735316i
$530$	10.6955	+	13.6627i	0.464583	+	0.593470i
$531$	−4.59940	−	1.87979i	−0.199597	−	0.0815758i
$532$	8.72992	+	8.72992i	0.378490	+	0.378490i
$533$	42.2714	+	42.2714i	1.83098	+	1.83098i
$534$	−18.0841	+	12.1451i	−0.782575	+	0.525572i
$535$	13.6705	+	1.66529i	0.591029	+	0.0719966i
$536$		−	15.6991i		−	0.678097i
$537$	28.8440	+	5.66681i	1.24471	+	0.244541i
$538$	19.3544	−	19.3544i	0.834427	−	0.834427i
$539$	5.07936			0.218784
$540$	11.5797	−	0.954002i	0.498312	−	0.0410537i
$541$	−27.6996			−1.19090			−0.595450	−	0.803392i	$-0.703026\pi$
$541$	−27.6996			−1.19090			−0.595450	+	0.803392i	$0.703026\pi$
$542$	11.7774	−	11.7774i	0.505883	−	0.505883i
$543$	−28.2388	−	5.54791i	−1.21184	−	0.238084i
$544$		−	2.26995i		−	0.0973234i
$545$	10.0805	−	7.89123i	0.431800	−	0.338023i
$546$	25.7352	−	17.2836i	1.10137	−	0.739670i
$547$	−27.1830	−	27.1830i	−1.16226	−	1.16226i	−0.983980	−	0.178280i	$-0.942947\pi$
$547$	−27.1830	−	27.1830i	−1.16226	−	1.16226i	−0.178280	−	0.983980i	$-0.557053\pi$
$548$	7.96363	+	7.96363i	0.340189	+	0.340189i
$549$	−15.6134	−	6.38123i	−0.666362	−	0.272344i
$550$	−13.5670	+	8.18718i	−0.578500	+	0.349103i
$551$		−	29.0763i		−	1.23869i
$552$	0.823849	−	4.19339i	0.0350653	−	0.178482i
$553$	23.2117	−	23.2117i	0.987060	−	0.987060i
$554$	−19.6247			−0.833775
$555$	−10.1358	+	31.0835i	−0.430241	+	1.31942i
$556$	16.3935			0.695240
$557$	19.9953	−	19.9953i	0.847226	−	0.847226i	−0.142560	−	0.989786i	$-0.545533\pi$
$557$	19.9953	−	19.9953i	0.847226	−	0.847226i	0.989786	+	0.142560i	$0.0455333\pi$
$558$	2.76620	−	1.16110i	0.117102	−	0.0491533i
$559$			60.5336i			2.56030i
$560$	−0.793064	+	6.51035i	−0.0335131	+	0.275113i
$561$	−6.94692	−	10.3439i	−0.293299	−	0.436722i
$562$	5.52181	+	5.52181i	0.232923	+	0.232923i
$563$	13.9356	+	13.9356i	0.587315	+	0.587315i	0.936903	−	0.349588i	$-0.113679\pi$
$563$	13.9356	+	13.9356i	0.587315	+	0.587315i	−0.349588	+	0.936903i	$0.613679\pi$
$564$	5.27594	+	7.85586i	0.222157	+	0.330791i
$565$	−0.722862	+	5.93406i	−0.0304111	+	0.249648i
$566$		−	2.82490i		−	0.118739i
$567$	−0.248800	−	26.3962i	−0.0104486	−	1.10854i
$568$	−4.55507	+	4.55507i	−0.191126	+	0.191126i
$569$	−35.4249			−1.48509			−0.742545	−	0.669796i	$-0.766382\pi$
$569$	−35.4249			−1.48509			−0.742545	+	0.669796i	$0.766382\pi$
$570$	−5.05405	+	15.4992i	−0.211691	+	0.649192i
$571$	−9.31804			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$571$	−9.31804			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$572$	−13.6748	+	13.6748i	−0.571773	+	0.571773i
$573$	−5.54231	+	28.2103i	−0.231533	+	1.17850i
$574$			28.7337i			1.19932i
$575$	10.5624	−	6.37403i	0.440484	−	0.265815i
$576$	−1.13498	+	2.77702i	−0.0472907	+	0.115709i
$577$	19.0628	+	19.0628i	0.793596	+	0.793596i	0.982077	−	0.188481i	$-0.0603563\pi$
$577$	19.0628	+	19.0628i	0.793596	+	0.793596i	−0.188481	+	0.982077i	$0.560356\pi$
$578$	−8.37732	−	8.37732i	−0.348451	−	0.348451i
$579$	14.7612	−	9.91353i	0.613456	−	0.411992i
$580$	12.1626	−	9.52114i	0.505023	−	0.395344i
$581$		−	24.0754i		−	0.998817i
$582$	14.7716	+	2.90209i	0.612304	+	0.120296i
$583$	−17.3891	+	17.3891i	−0.720183	+	0.720183i
$584$	16.0998			0.666215
$585$	35.7417	+	19.9551i	1.47774	+	0.825043i
$586$	5.77849			0.238707
$587$	11.5456	−	11.5456i	0.476540	−	0.476540i	−0.427483	−	0.904023i	$-0.640600\pi$
$587$	11.5456	−	11.5456i	0.476540	−	0.476540i	0.904023	+	0.427483i	$0.140600\pi$
$588$	2.72394	+	0.535156i	0.112333	+	0.0220695i
$589$			4.20927i			0.173440i
$590$	3.67628	+	0.447829i	0.151350	+	0.0184368i
$591$	−20.8667	+	14.0139i	−0.858343	+	0.576457i
$592$	−5.96913	−	5.96913i	−0.245330	−	0.245330i
$593$	−26.6497	−	26.6497i	−1.09437	−	1.09437i	−0.995056	−	0.0993142i	$-0.968335\pi$
$593$	−26.6497	−	26.6497i	−1.09437	−	1.09437i	−0.0993142	−	0.995056i	$-0.531665\pi$
$594$	3.32676	+	16.1281i	0.136499	+	0.661742i
$595$	−9.17681	−	11.7227i	−0.376213	−	0.480584i
$596$		−	3.69544i		−	0.151371i
$597$	−0.715871	+	3.64378i	−0.0292986	+	0.149130i
$598$	10.6464	−	10.6464i	0.435363	−	0.435363i
$599$	−36.6290			−1.49662			−0.748310	−	0.663349i	$-0.769135\pi$
$599$	−36.6290			−1.49662			−0.748310	+	0.663349i	$0.769135\pi$
$600$	−8.13827	+	2.96118i	−0.332243	+	0.120890i
$601$	−21.4952			−0.876809			−0.438405	−	0.898778i	$-0.644456\pi$
$601$	−21.4952			−0.876809			−0.438405	+	0.898778i	$0.644456\pi$
$602$	−20.5736	+	20.5736i	−0.838518	+	0.838518i
$603$	−18.2282	−	43.4268i	−0.742310	−	1.76848i
$604$		−	9.74536i		−	0.396533i
$605$	1.31802	+	1.68367i	0.0535851	+	0.0684511i
$606$	−9.05927	−	13.4892i	−0.368008	−	0.547963i
$607$	25.1298	+	25.1298i	1.01999	+	1.01999i	0.999796	+	0.0201911i	$0.00642748\pi$
$607$	25.1298	+	25.1298i	1.01999	+	1.01999i	0.0201911	+	0.999796i	$0.493573\pi$
$608$	−2.97641	−	2.97641i	−0.120709	−	0.120709i
$609$	−19.5649	−	29.1321i	−0.792809	−	1.18049i
$610$	12.4797	+	1.52022i	0.505288	+	0.0615521i
$611$			33.3396i			1.34878i
$612$	−2.63564	−	6.27913i	−0.106539	−	0.253819i
$613$	2.52556	−	2.52556i	0.102006	−	0.102006i	−0.654262	−	0.756268i	$-0.727021\pi$
$613$	2.52556	−	2.52556i	0.102006	−	0.102006i	0.756268	+	0.654262i	$0.227021\pi$
$614$	11.3322			0.457331
$615$	−33.8245	+	17.1896i	−1.36394	+	0.693153i
$616$	−9.29536			−0.374521
$617$	21.3997	−	21.3997i	0.861519	−	0.861519i	−0.129995	−	0.991515i	$-0.541496\pi$
$617$	21.3997	−	21.3997i	0.861519	−	0.861519i	0.991515	+	0.129995i	$0.0414963\pi$
$618$	3.17523	−	16.1619i	0.127726	−	0.650126i
$619$			10.6214i			0.426911i	0.976953	+	0.213455i	$0.0684718\pi$
$619$			10.6214i			0.426911i	−0.976953	+	0.213455i	$0.931528\pi$
$620$	−1.76073	+	1.37834i	−0.0707126	+	0.0553556i
$621$	−2.59001	−	12.5563i	−0.103933	−	0.503867i
$622$	−9.84369	−	9.84369i	−0.394696	−	0.394696i
$623$	−26.0843	−	26.0843i	−1.04504	−	1.04504i
$624$	−8.77425	+	5.89272i	−0.351251	+	0.235898i
$625$	−22.1183	−	11.6524i	−0.884734	−	0.466097i
$626$			5.27998i			0.211031i
$627$	−22.6721	−	4.45426i	−0.905438	−	0.177886i
$628$	−10.7909	+	10.7909i	−0.430604	+	0.430604i
$629$	19.1621			0.764042
$630$	5.36540	+	18.9298i	0.213763	+	0.754179i
$631$	−28.0689			−1.11741			−0.558703	−	0.829368i	$-0.688701\pi$
$631$	−28.0689			−1.11741			−0.558703	+	0.829368i	$0.688701\pi$
$632$	−7.91385	+	7.91385i	−0.314796	+	0.314796i
$633$	8.68889	+	1.70705i	0.345352	+	0.0678493i
$634$		−	31.4771i		−	1.25012i
$635$	1.18121	−	9.69670i	0.0468749	−	0.384802i
$636$	−11.1575	+	7.49326i	−0.442422	+	0.297127i
$637$	6.91567	+	6.91567i	0.274009	+	0.274009i
$638$	15.4798	+	15.4798i	0.612851	+	0.612851i
$639$	−7.31133	+	17.8891i	−0.289232	+	0.707682i
$640$	0.270390	−	2.21966i	0.0106881	−	0.0877398i
$641$			33.9076i			1.33927i	0.742690	+	0.669635i	$0.233550\pi$
$641$			33.9076i			1.33927i	−0.742690	+	0.669635i	$0.766450\pi$
$642$	−2.05645	+	10.4673i	−0.0811617	+	0.413113i
$643$	32.1371	−	32.1371i	1.26736	−	1.26736i	0.319920	−	0.947445i	$-0.396344\pi$
$643$	32.1371	−	32.1371i	1.26736	−	1.26736i	0.947445	−	0.319920i	$-0.103656\pi$
$644$	7.23679			0.285170
$645$	−36.5267	−	11.9108i	−1.43824	−	0.468986i
$646$	9.55485			0.375930
$647$	8.86360	−	8.86360i	0.348464	−	0.348464i	−0.511073	−	0.859537i	$-0.670752\pi$
$647$	8.86360	−	8.86360i	0.348464	−	0.348464i	0.859537	+	0.511073i	$0.170752\pi$
$648$	0.0848267	+	8.99960i	0.00333231	+	0.353538i
$649$			5.24892i			0.206038i
$650$	−29.6189	−	7.32479i	−1.16175	−	0.287302i
$651$	2.83234	+	4.21735i	0.111008	+	0.165291i
$652$	−9.92465	−	9.92465i	−0.388679	−	0.388679i
$653$	23.5223	+	23.5223i	0.920498	+	0.920498i	0.997064	−	0.0765665i	$-0.0243958\pi$
$653$	23.5223	+	23.5223i	0.920498	+	0.920498i	−0.0765665	+	0.997064i	$0.524396\pi$
$654$	5.52860	+	8.23207i	0.216185	+	0.321900i
$655$	−1.03737	+	0.812081i	−0.0405335	+	0.0317306i
$656$		−	9.79654i		−	0.382491i
$657$	44.5353	−	18.6935i	1.73749	−	0.729303i
$658$	−11.3312	+	11.3312i	−0.441736	+	0.441736i
$659$	42.9702			1.67388			0.836940	−	0.547295i	$-0.184342\pi$
$659$	42.9702			1.67388			0.836940	+	0.547295i	$0.184342\pi$
$660$	−5.56087	−	10.9423i	−0.216456	−	0.425927i
$661$	−34.7752			−1.35260			−0.676300	−	0.736627i	$-0.736418\pi$
$661$	−34.7752			−1.35260			−0.676300	+	0.736627i	$0.736418\pi$
$662$	0.312357	−	0.312357i	0.0121401	−	0.0121401i
$663$	4.62514	−	23.5419i	0.179626	−	0.914293i
$664$			8.20835i			0.318546i
$665$	−27.4039	−	3.33822i	−1.06268	−	0.129451i
$666$	−23.4426	−	9.58104i	−0.908380	−	0.371258i
$667$	−12.0516	−	12.0516i	−0.466640	−	0.466640i
$668$	−1.43445	−	1.43445i	−0.0555006	−	0.0555006i
$669$	−25.1495	+	16.8902i	−0.972335	+	0.653013i
$670$	21.6387	+	27.6419i	0.835977	+	1.06790i
$671$			17.8183i			0.687867i
$672$	−4.98488	−	0.979350i	−0.192296	−	0.0377792i
$673$	−0.216881	+	0.216881i	−0.00836014	+	0.00836014i	−0.711274	−	0.702914i	$-0.751882\pi$
$673$	−0.216881	+	0.216881i	−0.00836014	+	0.00836014i	0.702914	+	0.711274i	$0.251882\pi$
$674$	1.96870			0.0758314
$675$	−19.0738	+	17.6406i	−0.734152	+	0.678985i
$676$	−24.2372			−0.932201
$677$	−32.3769	+	32.3769i	−1.24435	+	1.24435i	−0.286165	+	0.958180i	$0.592381\pi$
$677$	−32.3769	+	32.3769i	−1.24435	+	1.24435i	−0.958180	+	0.286165i	$0.907619\pi$
$678$	−4.54363	−	0.892659i	−0.174497	−	0.0342824i
$679$			25.4923i			0.978306i
$680$	3.12877	+	3.99677i	0.119983	+	0.153269i
$681$	−7.13769	+	4.79362i	−0.273517	+	0.183692i
$682$	−2.24096	−	2.24096i	−0.0858106	−	0.0858106i
$683$	−15.6080	−	15.6080i	−0.597225	−	0.597225i	0.342348	−	0.939573i	$-0.388778\pi$
$683$	−15.6080	−	15.6080i	−0.597225	−	0.597225i	−0.939573	+	0.342348i	$0.888778\pi$
$684$	−11.6892	−	4.77742i	−0.446949	−	0.182669i
$685$	−24.9984	−	3.04520i	−0.955140	−	0.116351i
$686$		−	15.8304i		−	0.604408i
$687$	8.90288	−	45.3156i	0.339666	−	1.72890i
$688$	7.01443	−	7.01443i	0.267423	−	0.267423i
$689$	−47.3514			−1.80394
$690$	4.32934	+	8.51897i	0.164815	+	0.324312i
$691$	16.7511			0.637241			0.318620	−	0.947882i	$-0.396780\pi$
$691$	16.7511			0.637241			0.318620	+	0.947882i	$0.396780\pi$
$692$	−6.36976	+	6.36976i	−0.242142	+	0.242142i
$693$	−25.7128	+	10.7928i	−0.976749	+	0.409986i
$694$		−	8.78848i		−	0.333606i
$695$	−28.8646	+	22.5959i	−1.09490	+	0.857111i
$696$	6.67051	+	9.93238i	0.252845	+	0.376486i
$697$	15.7244	+	15.7244i	0.595604	+	0.595604i
$698$	−23.0631	−	23.0631i	−0.872953	−	0.872953i
$699$	−20.6215	−	30.7054i	−0.779977	−	1.16138i
$700$	−7.57712	−	12.5561i	−0.286388	−	0.474576i
$701$		−	16.5878i		−	0.626513i	−0.949669	−	0.313256i	$-0.898580\pi$
$701$		−	16.5878i		−	0.626513i	0.949669	−	0.313256i	$-0.101420\pi$
$702$	−17.4293	+	26.4882i	−0.657826	+	0.999733i
$703$	25.1257	−	25.1257i	0.947634	−	0.947634i
$704$	3.16919			0.119443
$705$	−20.1176	−	6.56001i	−0.757671	−	0.247064i
$706$	−18.9129			−0.711795
$707$	19.4567	−	19.4567i	0.731745	−	0.731745i
$708$	−0.553021	+	2.81487i	−0.0207838	+	0.105789i
$709$		−	16.3120i		−	0.612609i	−0.951934	−	0.306305i	$-0.900907\pi$
$709$		−	16.3120i		−	0.612609i	0.951934	−	0.306305i	$-0.0990926\pi$
$710$	1.74181	−	14.2987i	0.0653689	−	0.536621i
$711$	−12.7025	+	31.0800i	−0.476381	+	1.16559i
$712$	8.89325	+	8.89325i	0.333288	+	0.333288i
$713$	1.74467	+	1.74467i	0.0653384	+	0.0653384i
$714$	9.57318	−	6.42928i	0.358267	−	0.240610i
$715$	5.22910	−	42.9263i	0.195557	−	1.60535i
$716$		−	16.9715i		−	0.634253i
$717$	21.6099	+	4.24557i	0.807037	+	0.158554i
$718$	−2.97049	+	2.97049i	−0.110858	+	0.110858i
$719$	25.5866			0.954220			0.477110	−	0.878843i	$-0.341684\pi$
$719$	25.5866			0.954220			0.477110	+	0.878843i	$0.341684\pi$
$720$	−1.82929	−	6.45397i	−0.0681738	−	0.240525i
$721$	27.8916			1.03874
$722$	−0.906522	+	0.906522i	−0.0337372	+	0.0337372i
$723$	33.9009	+	6.66030i	1.26079	+	0.247699i
$724$			16.6154i			0.617505i
$725$	−8.29160	+	33.5283i	−0.307942	+	1.24521i
$726$	−1.37495	+	0.923405i	−0.0510291	+	0.0342708i
$727$	−6.38648	−	6.38648i	−0.236861	−	0.236861i	0.578688	−	0.815549i	$-0.303565\pi$
$727$	−6.38648	−	6.38648i	−0.236861	−	0.236861i	−0.815549	+	0.578688i	$0.803565\pi$
$728$	−12.6559	−	12.6559i	−0.469058	−	0.469058i
$729$	10.6841	+	24.7962i	0.395707	+	0.918377i
$730$	−28.3475	+	22.1911i	−1.04919	+	0.821328i
$731$			22.5177i			0.832848i
$732$	−1.87732	+	9.55552i	−0.0693876	+	0.353182i
$733$	−11.2841	+	11.2841i	−0.416787	+	0.416787i	−0.884095	−	0.467308i	$-0.845224\pi$
$733$	−11.2841	+	11.2841i	−0.416787	+	0.416787i	0.467308	+	0.884095i	$0.345224\pi$
$734$	−22.8166			−0.842178
$735$	−5.53375	+	2.81226i	−0.204116	+	0.103732i
$736$	−2.46733			−0.0909471
$737$	−35.1810	+	35.1810i	−1.29591	+	1.29591i
$738$	−11.3748	−	27.0992i	−0.418711	−	0.997534i
$739$		−	1.82029i		−	0.0669604i	−0.999439	−	0.0334802i	$-0.989341\pi$
$739$		−	1.82029i		−	0.0669604i	0.999439	−	0.0334802i	$-0.0106591\pi$
$740$	18.7375	+	2.28253i	0.688806	+	0.0839074i
$741$	−24.8041	−	36.9332i	−0.911201	−	1.35678i
$742$	−16.0934	−	16.0934i	−0.590806	−	0.590806i
$743$	−7.39599	−	7.39599i	−0.271332	−	0.271332i	0.558304	−	0.829636i	$-0.311452\pi$
$743$	−7.39599	−	7.39599i	−0.271332	−	0.271332i	−0.829636	+	0.558304i	$0.811452\pi$
$744$	−0.965667	−	1.43788i	−0.0354031	−	0.0527151i
$745$	5.09357	+	6.50667i	0.186614	+	0.238386i
$746$		−	10.0826i		−	0.369151i
$747$	9.53071	+	22.7059i	0.348710	+	0.830766i
$748$	−5.08686	+	5.08686i	−0.185994	+	0.185994i
$749$	−18.0641			−0.660049
$750$	10.2478	−	16.4312i	0.374196	−	0.599981i
$751$	7.65051			0.279171			0.139585	−	0.990210i	$-0.455423\pi$
$751$	7.65051			0.279171			0.139585	+	0.990210i	$0.455423\pi$
$752$	3.86329	−	3.86329i	0.140880	−	0.140880i
$753$	−0.748309	+	3.80889i	−0.0272699	+	0.138804i
$754$			42.1522i			1.53509i
$755$	13.4324	+	17.1590i	0.488857	+	0.624478i
$756$	−14.9263	+	3.07887i	−0.542864	+	0.111977i
$757$	−6.58416	−	6.58416i	−0.239305	−	0.239305i	0.577257	−	0.816562i	$-0.304123\pi$
$757$	−6.58416	−	6.58416i	−0.239305	−	0.239305i	−0.816562	+	0.577257i	$0.804123\pi$
$758$	−2.23265	−	2.23265i	−0.0810933	−	0.0810933i
$759$	−11.2434	+	7.55098i	−0.408110	+	0.274083i
$760$	9.34316	+	1.13814i	0.338912	+	0.0412848i
$761$			32.2036i			1.16738i	0.811977	+	0.583689i	$0.198391\pi$
$761$			32.2036i			1.16738i	−0.811977	+	0.583689i	$0.801609\pi$
$762$	7.42463	+	1.45867i	0.268966	+	0.0528421i
$763$	−11.8738	+	11.8738i	−0.429862	+	0.429862i
$764$	16.5986			0.600515
$765$	13.2954	+	7.42305i	0.480698	+	0.268381i
$766$	14.2865			0.516194
$767$	−7.14654	+	7.14654i	−0.258047	+	0.258047i
$768$	1.69956	+	0.333903i	0.0613276	+	0.0120487i
$769$		−	1.05661i		−	0.0381022i	−0.999819	−	0.0190511i	$-0.993935\pi$
$769$		−	1.05661i		−	0.0381022i	0.999819	−	0.0190511i	$-0.00606453\pi$
$770$	16.3666	−	12.8122i	0.589813	−	0.461719i
$771$	−25.4642	+	17.1016i	−0.917073	+	0.615899i
$772$	−7.25915	−	7.25915i	−0.261263	−	0.261263i
$773$	2.59876	+	2.59876i	0.0934708	+	0.0934708i	0.752296	−	0.658825i	$-0.228946\pi$
$773$	2.59876	+	2.59876i	0.0934708	+	0.0934708i	−0.658825	+	0.752296i	$0.728946\pi$
$774$	11.2589	−	27.5478i	0.404691	−	0.990184i
$775$	1.20035	−	4.85378i	0.0431177	−	0.174353i
$776$		−	8.69144i		−	0.312004i
$777$	8.26731	−	42.0805i	0.296588	−	1.50963i
$778$	14.3147	−	14.3147i	0.513208	−	0.513208i
$779$	41.2363			1.47744
$780$	7.32691	−	22.4694i	0.262345	−	0.804534i
$781$	20.4154			0.730521
$782$	3.96031	−	3.96031i	0.141621	−	0.141621i
$783$	29.9844	+	19.7298i	1.07156	+	0.705086i
$784$		−	1.60273i		−	0.0572404i
$785$	4.12632	−	33.8734i	0.147275	−	1.20900i
$786$	−0.568944	−	0.847156i	−0.0202936	−	0.0302171i
$787$	−20.3838	−	20.3838i	−0.726605	−	0.726605i	0.243337	−	0.969942i	$-0.421758\pi$
$787$	−20.3838	−	20.3838i	−0.726605	−	0.726605i	−0.969942	+	0.243337i	$0.921758\pi$
$788$	10.2617	+	10.2617i	0.365557	+	0.365557i
$789$	−24.6550	−	36.7112i	−0.877740	−	1.30695i
$790$	3.02617	−	24.8422i	0.107666	−	0.883844i
$791$		−	7.84122i		−	0.278802i
$792$	8.76660	−	3.67974i	0.311508	−	0.130754i
$793$	−24.2600	+	24.2600i	−0.861499	+	0.861499i
$794$	−9.19877			−0.326452
$795$	9.31700	−	28.5724i	0.330440	−	1.01336i
$796$	2.14395			0.0759903
$797$	−2.61813	+	2.61813i	−0.0927388	+	0.0927388i	−0.751954	−	0.659215i	$-0.770889\pi$
$797$	−2.61813	+	2.61813i	−0.0927388	+	0.0927388i	0.659215	+	0.751954i	$0.270889\pi$
$798$	4.12235	−	20.9827i	0.145930	−	0.742781i
$799$			12.4019i			0.438748i
$800$	2.58337	+	4.28091i	0.0913358	+	0.151353i
$801$	34.9264	+	14.2745i	1.23406	+	0.504366i
$802$	−2.76189	−	2.76189i	−0.0975258	−	0.0975258i
$803$	−36.0790	−	36.0790i	−1.27320	−	1.27320i
$804$	−22.5733	+	15.1601i	−0.796101	+	0.534655i
$805$	−12.7420	+	9.97478i	−0.449098	+	0.351565i
$806$		−	6.10223i		−	0.214942i
$807$	−46.5191	−	9.13932i	−1.63755	−	0.321719i
$808$	−6.63363	+	6.63363i	−0.233370	+	0.233370i
$809$	−13.3464			−0.469235			−0.234618	−	0.972088i	$-0.575384\pi$
$809$	−13.3464			−0.469235			−0.234618	+	0.972088i	$0.575384\pi$
$810$	−12.5539	−	15.7290i	−0.441099	−	0.552659i
$811$	37.2577			1.30830			0.654148	−	0.756367i	$-0.273027\pi$
$811$	37.2577			1.30830			0.654148	+	0.756367i	$0.273027\pi$
$812$	−14.3263	+	14.3263i	−0.502756	+	0.502756i
$813$	−28.3075	−	5.56141i	−0.992789	−	0.195047i
$814$			26.7531i			0.937696i
$815$	31.1542	+	3.79507i	1.09128	+	0.132936i
$816$	−3.26391	+	2.19202i	−0.114260	+	0.0767359i
$817$	29.5257	+	29.5257i	1.03297	+	1.03297i
$818$	−3.05518	−	3.05518i	−0.106822	−	0.106822i
$819$	−49.7033	−	20.3139i	−1.73678	−	0.709825i
$820$	13.5030	+	17.2491i	0.471545	+	0.602364i
$821$			46.3102i			1.61624i	0.589019	+	0.808119i	$0.299514\pi$
$821$			46.3102i			1.61624i	−0.589019	+	0.808119i	$0.700486\pi$
$822$	3.76050	−	19.1409i	0.131162	−	0.667616i
$823$	28.2044	−	28.2044i	0.983145	−	0.983145i	−0.0167154	−	0.999860i	$-0.505321\pi$
$823$	28.2044	−	28.2044i	0.983145	−	0.983145i	0.999860	+	0.0167154i	$0.00532094\pi$
$824$	−9.50944			−0.331277
$825$	24.8734	+	11.6016i	0.865980	+	0.403916i
$826$	−4.85781			−0.169025
$827$	−4.46508	+	4.46508i	−0.155266	+	0.155266i	−0.780465	−	0.625199i	$-0.785018\pi$
$827$	−4.46508	+	4.46508i	−0.155266	+	0.155266i	0.625199	+	0.780465i	$0.285018\pi$
$828$	−6.82513	+	2.86482i	−0.237190	+	0.0995594i
$829$		−	31.2864i		−	1.08662i	−0.839532	−	0.543311i	$-0.817171\pi$
$829$		−	31.2864i		−	1.08662i	0.839532	−	0.543311i	$-0.182829\pi$
$830$	−11.3139	−	14.4527i	−0.392712	−	0.501660i
$831$	18.9509	+	28.2179i	0.657401	+	0.978869i
$832$	4.31493	+	4.31493i	0.149593	+	0.149593i
$833$	2.57254	+	2.57254i	0.0891333	+	0.0891333i
$834$	−15.8307	−	23.5719i	−0.548172	−	0.816227i
$835$	4.50285	+	0.548518i	0.155828	+	0.0189823i
$836$			13.3400i			0.461373i
$837$	−4.34074	−	2.85621i	−0.150038	−	0.0987252i
$838$	−12.7910	+	12.7910i	−0.441859	+	0.441859i
$839$	−52.2405			−1.80354			−0.901771	−	0.432214i	$-0.857732\pi$
$839$	−52.2405			−1.80354			−0.901771	+	0.432214i	$0.857732\pi$
$840$	10.1269	−	5.14650i	0.349412	−	0.177571i
$841$	18.7160			0.645379
$842$	−6.05221	+	6.05221i	−0.208573	+	0.208573i
$843$	2.60745	−	13.2719i	0.0898054	−	0.457109i
$844$		−	5.11243i		−	0.175977i
$845$	42.6752	−	33.4072i	1.46807	−	1.14924i
$846$	6.20096	−	15.1723i	0.213193	−	0.521634i
$847$	−1.98321	−	1.98321i	−0.0681438	−	0.0681438i
$848$	5.48692	+	5.48692i	0.188422	+	0.188422i
$849$	−4.06185	+	2.72791i	−0.139402	+	0.0936216i
$850$	−11.0178	−	2.72473i	−0.377909	−	0.0934574i
$851$		−	20.8283i		−	0.713985i
$852$	10.9483	+	2.15095i	0.375083	+	0.0736902i
$853$	15.4713	−	15.4713i	0.529728	−	0.529728i	−0.390763	−	0.920491i	$-0.627789\pi$
$853$	15.4713	−	15.4713i	0.529728	−	0.529728i	0.920491	+	0.390763i	$0.127789\pi$
$854$	−16.4906			−0.564296
$855$	27.1665	−	7.70000i	0.929075	−	0.263334i
$856$	6.15884			0.210505
$857$	−27.3706	+	27.3706i	−0.934963	+	0.934963i	−0.998011	−	0.0630476i	$-0.979918\pi$
$857$	−27.3706	+	27.3706i	−0.934963	+	0.934963i	0.0630476	+	0.998011i	$0.479918\pi$
$858$	32.8680	+	6.45738i	1.12210	+	0.220451i
$859$		−	8.43565i		−	0.287821i	−0.989591	−	0.143910i	$-0.954032\pi$
$859$		−	8.43565i		−	0.287821i	0.989591	−	0.143910i	$-0.0459677\pi$
$860$	−2.68224	+	22.0188i	−0.0914636	+	0.750836i
$861$	41.3154	−	27.7471i	1.40803	−	0.945620i
$862$	0.697641	+	0.697641i	0.0237617	+	0.0237617i
$863$	4.29463	+	4.29463i	0.146191	+	0.146191i	0.776414	−	0.630223i	$-0.217037\pi$
$863$	4.29463	+	4.29463i	0.146191	+	0.146191i	−0.630223	+	0.776414i	$0.717037\pi$
$864$	5.08902	−	1.04972i	0.173132	−	0.0357122i
$865$	2.43572	−	19.9951i	0.0828171	−	0.679855i
$866$		−	0.407370i		−	0.0138430i
$867$	−3.95585	+	20.1352i	−0.134348	+	0.683829i
$868$	2.07397	−	2.07397i	0.0703952	−	0.0703952i
$869$	35.4692			1.20321
$870$	−25.4352	−	8.29400i	−0.862334	−	0.281193i
$871$	−95.7995			−3.24604
$872$	4.04830	−	4.04830i	0.137093	−	0.137093i
$873$	−10.0916	−	24.0422i	−0.341550	−	0.813706i
$874$		−	10.3857i		−	0.351301i
$875$	30.6479	+	11.6640i	1.03609	+	0.394316i
$876$	−15.5471	−	23.1496i	−0.525287	−	0.782151i
$877$	−0.124584	−	0.124584i	−0.00420690	−	0.00420690i	0.705000	−	0.709207i	$-0.250947\pi$
$877$	−0.124584	−	0.124584i	−0.00420690	−	0.00420690i	−0.709207	+	0.705000i	$0.750947\pi$
$878$	11.1699	+	11.1699i	0.376965	+	0.376965i
$879$	−5.58010	−	8.30876i	−0.188212	−	0.280248i
$880$	−5.58009	+	4.36823i	−0.188105	+	0.147253i
$881$			17.3926i			0.585973i	0.956117	+	0.292986i	$0.0946491\pi$
$881$			17.3926i			0.585973i	−0.956117	+	0.292986i	$0.905351\pi$
$882$	−1.86093	−	4.43347i	−0.0626608	−	0.149283i
$883$	25.4674	−	25.4674i	0.857047	−	0.857047i	−0.133942	−	0.990989i	$-0.542764\pi$
$883$	25.4674	−	25.4674i	0.857047	−	0.857047i	0.990989	+	0.133942i	$0.0427636\pi$
$884$	−13.8518			−0.465885
$885$	−2.90614	−	5.71849i	−0.0976887	−	0.192225i
$886$	14.0401			0.471688
$887$	15.2739	−	15.2739i	0.512847	−	0.512847i	−0.402551	−	0.915398i	$-0.631876\pi$
$887$	15.2739	−	15.2739i	0.512847	−	0.512847i	0.915398	+	0.402551i	$0.131876\pi$
$888$	−2.81868	+	14.3471i	−0.0945887	+	0.481456i
$889$			12.8131i			0.429739i
$890$	−27.9165	−	3.40068i	−0.935765	−	0.113991i
$891$	19.9776	−	20.3578i	0.669275	−	0.682012i
$892$	12.3678	+	12.3678i	0.414104	+	0.414104i
$893$	16.2616	+	16.2616i	0.544175	+	0.544175i
$894$	−5.31358	+	3.56856i	−0.177713	+	0.119350i
$895$	23.3925	+	29.8822i	0.781924	+	0.998851i
$896$			2.93304i			0.0979860i
$897$	−25.5890	−	5.02732i	−0.854392	−	0.167857i
$898$	7.69558	−	7.69558i	0.256805	−	0.256805i
$899$	−6.90768			−0.230384
$900$	12.1167	+	8.84230i	0.403889	+	0.294743i
$901$	−17.6141			−0.586811
$902$	−21.9536	+	21.9536i	−0.730975	+	0.730975i
$903$	49.4496	+	9.71506i	1.64558	+	0.323297i
$904$			2.67341i			0.0889163i
$905$	−22.9016	−	29.2552i	−0.761276	−	0.972475i
$906$	−14.0126	+	9.41077i	−0.465538	+	0.312652i
$907$	−3.32527	−	3.32527i	−0.110414	−	0.110414i	0.649741	−	0.760155i	$-0.274877\pi$
$907$	−3.32527	−	3.32527i	−0.110414	−	0.110414i	−0.760155	+	0.649741i	$0.774877\pi$
$908$	3.51012	+	3.51012i	0.116487	+	0.116487i
$909$	−10.6476	+	26.0522i	−0.353159	+	0.864098i
$910$	39.7277	+	4.83946i	1.31696	+	0.160427i
$911$		−	2.53184i		−	0.0838837i	−0.999120	−	0.0419418i	$-0.986646\pi$
$911$		−	2.53184i		−	0.0838837i	0.999120	−	0.0419418i	$-0.0133544\pi$
$912$	−1.40549	+	7.15392i	−0.0465403	+	0.236890i
$913$	18.3945	−	18.3945i	0.608770	−	0.608770i
$914$	0.0347077			0.00114803
$915$	−9.86533	−	19.4123i	−0.326138	−	0.641750i
$916$	−26.6631			−0.880974
$917$	1.22193	−	1.22193i	0.0403516	−	0.0403516i
$918$	−6.48347	+	9.85327i	−0.213986	+	0.325206i
$919$			19.4202i			0.640615i	0.947314	+	0.320307i	$0.103786\pi$
$919$			19.4202i			0.640615i	−0.947314	+	0.320307i	$0.896214\pi$
$920$	4.34431	−	3.40083i	0.143228	−	0.112122i
$921$	−10.9432	−	16.2943i	−0.360589	−	0.536917i
$922$	1.49746	+	1.49746i	0.0493161	+	0.0493161i
$923$	27.7961	+	27.7961i	0.914919	+	0.914919i
$924$	8.97622	+	13.3656i	0.295296	+	0.439695i
$925$	−36.1379	+	21.8078i	−1.18821	+	0.717037i
$926$			20.2869i			0.666668i
$927$	−26.3050	+	11.0414i	−0.863970	+	0.362647i
$928$	4.88446	−	4.88446i	0.160340	−	0.160340i
$929$	55.2551			1.81286			0.906430	−	0.422356i	$-0.138797\pi$
$929$	55.2551			1.81286			0.906430	+	0.422356i	$0.138797\pi$
$930$	3.68216	+	1.20069i	0.120743	+	0.0393723i
$931$	6.74634			0.221102
$932$	−15.1000	+	15.1000i	−0.494618	+	0.494618i
$933$	−4.64829	+	23.6597i	−0.152178	+	0.774585i
$934$		−	19.3847i		−	0.634285i
$935$	1.94516	−	15.9680i	0.0636135	−	0.522210i
$936$	16.9460	+	6.92588i	0.553898	+	0.226380i
$937$	11.1658	+	11.1658i	0.364771	+	0.364771i	0.865566	−	0.500795i	$-0.166959\pi$
$937$	11.1658	+	11.1658i	0.364771	+	0.364771i	−0.500795	+	0.865566i	$0.666959\pi$
$938$	−32.5595	−	32.5595i	−1.06311	−	1.06311i
$939$	7.59196	−	5.09870i	0.247754	−	0.166390i
$940$	−1.47728	+	12.1271i	−0.0481835	+	0.395544i
$941$		−	30.0282i		−	0.978891i	−0.872034	−	0.489445i	$-0.837199\pi$
$941$		−	30.0282i		−	0.978891i	0.872034	−	0.489445i	$-0.162801\pi$
$942$	25.9364	+	5.09557i	0.845054	+	0.166023i
$943$	17.0917	−	17.0917i	0.556583	−	0.556583i
$944$	1.65624			0.0539059
$945$	22.0375	−	25.9946i	0.716878	−	0.845605i
$946$	−31.4381			−1.02214
$947$	−40.1925	+	40.1925i	−1.30608	+	1.30608i	−0.381863	+	0.924219i	$0.624717\pi$
$947$	−40.1925	+	40.1925i	−1.30608	+	1.30608i	−0.924219	+	0.381863i	$0.875283\pi$
$948$	19.0213	+	3.73700i	0.617782	+	0.121372i
$949$		−	98.2449i		−	3.18916i
$950$	−18.0195	+	10.8741i	−0.584631	+	0.352802i
$951$	−45.2602	+	30.3964i	−1.46766	+	0.985671i
$952$	−4.70782	−	4.70782i	−0.152581	−	0.152581i
$953$	−12.1437	−	12.1437i	−0.393372	−	0.393372i	0.482515	−	0.875888i	$-0.339723\pi$
$953$	−12.1437	−	12.1437i	−0.393372	−	0.393372i	−0.875888	+	0.482515i	$0.839723\pi$
$954$	21.5488	+	8.80705i	0.697667	+	0.285139i
$955$	−29.2256	+	22.8785i	−0.945719	+	0.740332i
$956$		−	12.7150i		−	0.411233i
$957$	7.30971	−	37.2064i	0.236289	−	1.20271i
$958$	−4.11571	+	4.11571i	−0.132973	+	0.132973i
$959$	33.0327			1.06668
$960$	−3.45270	+	1.75466i	−0.111435	+	0.0566316i
$961$	1.00000			0.0322581
$962$	−36.4250	+	36.4250i	−1.17439	+	1.17439i
$963$	17.0366	−	7.15103i	0.548996	−	0.230439i
$964$		−	19.9468i		−	0.642444i
$965$	22.7870	+	2.77582i	0.733540	+	0.0893567i
$966$	−6.98833	−	10.4056i	−0.224846	−	0.334795i
$967$	29.2305	+	29.2305i	0.939989	+	0.939989i	0.998299	−	0.0583099i	$-0.0185712\pi$
$967$	29.2305	+	29.2305i	0.939989	+	0.939989i	−0.0583099	+	0.998299i	$0.518571\pi$
$968$	0.676161	+	0.676161i	0.0217326	+	0.0217326i
$969$	−9.22680	−	13.7387i	−0.296407	−	0.441350i
$970$	11.9798	+	15.3033i	0.384647	+	0.491359i
$971$			4.43992i			0.142484i	0.997459	+	0.0712420i	$0.0226963\pi$
$971$			4.43992i			0.142484i	−0.997459	+	0.0712420i	$0.977304\pi$
$972$	12.8584	−	8.81258i	0.412433	−	0.282664i
$973$	33.9997	−	33.9997i	1.08998	−	1.08998i
$974$	−14.6536			−0.469533
$975$	18.0698	+	49.6616i	0.578698	+	1.59044i
$976$	5.62235			0.179967
$977$	−28.8331	+	28.8331i	−0.922452	+	0.922452i	−0.997202	−	0.0747501i	$-0.976184\pi$
$977$	−28.8331	+	28.8331i	−0.922452	+	0.922452i	0.0747501	+	0.997202i	$0.476184\pi$
$978$	−4.68652	+	23.8543i	−0.149858	+	0.762777i
$979$		−	39.8587i		−	1.27389i
$980$	2.20911	+	2.82198i	0.0705675	+	0.0901448i
$981$	6.49792	−	15.8989i	0.207463	−	0.507612i
$982$	2.58785	+	2.58785i	0.0825816	+	0.0825816i
$983$	−12.2264	−	12.2264i	−0.389961	−	0.389961i	0.484713	−	0.874673i	$-0.338924\pi$
$983$	−12.2264	−	12.2264i	−0.389961	−	0.389961i	−0.874673	+	0.484713i	$0.838924\pi$
$984$	−14.0862	+	9.46019i	−0.449052	+	0.301580i
$985$	−32.2121	−	3.92395i	−1.02636	−	0.125027i
$986$			15.6801i			0.499356i
$987$	27.2350	+	5.35069i	0.866899	+	0.170314i
$988$	−18.1627	+	18.1627i	−0.577833	+	0.577833i
$989$	24.4757			0.778283
$990$	−10.3637	+	18.5624i	−0.329380	+	0.589952i
$991$	15.0472			0.477990			0.238995	−	0.971021i	$-0.423182\pi$
$991$	15.0472			0.477990			0.238995	+	0.971021i	$0.423182\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	−0.750763	−	0.147498i	−0.0238247	−	0.00468070i
$994$			18.8942i			0.599287i
$995$	−3.77492	+	2.95510i	−0.119673	+	0.0936829i
$996$	11.8026	−	7.92653i	0.373979	−	0.251162i
$997$	14.4470	+	14.4470i	0.457540	+	0.457540i	0.897847	−	0.440307i	$-0.145130\pi$
$997$	14.4470	+	14.4470i	0.457540	+	0.457540i	−0.440307	+	0.897847i	$0.645130\pi$
$998$	−3.57965	−	3.57965i	−0.113312	−	0.113312i
$999$	8.86134	+	42.9596i	0.280360	+	1.35918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.10	✓	40
3.2	odd	2	inner	930.2.j.h.497.15	yes	40
5.3	odd	4	inner	930.2.j.h.683.15	yes	40
15.8	even	4	inner	930.2.j.h.683.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.10	✓	40	1.1	even	1	trivial
930.2.j.h.497.15	yes	40	3.2	odd	2	inner
930.2.j.h.683.10	yes	40	15.8	even	4	inner
930.2.j.h.683.15	yes	40	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.69956 + 0.333903i) q^{3} -1.00000i q^{4} +(1.37834 + 1.76073i) q^{5} +(-1.43788 + 0.965667i) q^{6} +(-2.07397 - 2.07397i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77702 + 1.13498i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.69956 + 0.333903i) q^{3} -1.00000i q^{4} +(1.37834 + 1.76073i) q^{5} +(-1.43788 + 0.965667i) q^{6} +(-2.07397 - 2.07397i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77702 + 1.13498i) q^{9} +(-2.21966 - 0.270390i) q^{10} -3.16919i q^{11} +(0.333903 - 1.69956i) q^{12} +(4.31493 - 4.31493i) q^{13} +2.93304 q^{14} +(1.75466 + 3.45270i) q^{15} -1.00000 q^{16} +(1.60510 - 1.60510i) q^{17} +(-2.76620 + 1.16110i) q^{18} -4.20927i q^{19} +(1.76073 - 1.37834i) q^{20} +(-2.83234 - 4.21735i) q^{21} +(2.24096 + 2.24096i) q^{22} +(-1.74467 - 1.74467i) q^{23} +(0.965667 + 1.43788i) q^{24} +(-1.20035 + 4.85378i) q^{25} +6.10223i q^{26} +(4.34074 + 2.85621i) q^{27} +(-2.07397 + 2.07397i) q^{28} +6.90768 q^{29} +(-3.68216 - 1.20069i) q^{30} -1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.05820 - 5.38623i) q^{33} +2.26995i q^{34} +(0.793064 - 6.51035i) q^{35} +(1.13498 - 2.77702i) q^{36} +(5.96913 + 5.96913i) q^{37} +(2.97641 + 2.97641i) q^{38} +(8.77425 - 5.89272i) q^{39} +(-0.270390 + 2.21966i) q^{40} +9.79654i q^{41} +(4.98488 + 0.979350i) q^{42} +(-7.01443 + 7.01443i) q^{43} -3.16919 q^{44} +(1.82929 + 6.45397i) q^{45} +2.46733 q^{46} +(-3.86329 + 3.86329i) q^{47} +(-1.69956 - 0.333903i) q^{48} +1.60273i q^{49} +(-2.58337 - 4.28091i) q^{50} +(3.26391 - 2.19202i) q^{51} +(-4.31493 - 4.31493i) q^{52} +(-5.48692 - 5.48692i) q^{53} +(-5.08902 + 1.04972i) q^{54} +(5.58009 - 4.36823i) q^{55} -2.93304i q^{56} +(1.40549 - 7.15392i) q^{57} +(-4.88446 + 4.88446i) q^{58} -1.65624 q^{59} +(3.45270 - 1.75466i) q^{60} -5.62235 q^{61} +(0.707107 - 0.707107i) q^{62} +(-3.40555 - 8.11337i) q^{63} +1.00000i q^{64} +(13.5449 + 1.64998i) q^{65} +(3.06038 + 4.55690i) q^{66} +(-11.1009 - 11.1009i) q^{67} +(-1.60510 - 1.60510i) q^{68} +(-2.38262 - 3.54772i) q^{69} +(4.04273 + 5.16430i) q^{70} +6.44184i q^{71} +(1.16110 + 2.76620i) q^{72} +(11.3843 - 11.3843i) q^{73} -8.44163 q^{74} +(-3.66075 + 7.84850i) q^{75} -4.20927 q^{76} +(-6.57282 + 6.57282i) q^{77} +(-2.03755 + 10.3711i) q^{78} +11.1919i q^{79} +(-1.37834 - 1.76073i) q^{80} +(6.42366 + 6.30370i) q^{81} +(-6.92720 - 6.92720i) q^{82} +(5.80418 + 5.80418i) q^{83} +(-4.21735 + 2.83234i) q^{84} +(5.03852 + 0.613771i) q^{85} -9.91991i q^{86} +(11.7400 + 2.30649i) q^{87} +(2.24096 - 2.24096i) q^{88} +12.5769 q^{89} +(-5.85715 - 3.27014i) q^{90} -17.8981 q^{91} +(-1.74467 + 1.74467i) q^{92} +(-1.69956 - 0.333903i) q^{93} -5.46352i q^{94} +(7.41140 - 5.80182i) q^{95} +(1.43788 - 0.965667i) q^{96} +(-6.14577 - 6.14577i) q^{97} +(-1.13330 - 1.13330i) q^{98} +(3.59695 - 8.80090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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