LMFDB - Embedded newform 105.2.j.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(8,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("105.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.4
Character	$\chi$	$=$	105.8
Dual form			105.2.j.a.92.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.800553 - 0.800553i) q^{2} +(-1.34285 - 1.09397i) q^{3} -0.718229i q^{4} +(-2.10480 + 0.754855i) q^{5} +(0.199242 + 1.95080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +O(q^{10})$	\(q+(-0.800553 - 0.800553i) q^{2} +(-1.34285 - 1.09397i) q^{3} -0.718229i q^{4} +(-2.10480 + 0.754855i) q^{5} +(0.199242 + 1.95080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +(2.28931 + 1.08070i) q^{10} -5.20191i q^{11} +(-0.785718 + 0.964471i) q^{12} +(-3.24693 - 3.24693i) q^{13} +1.13215 q^{14} +(3.65221 + 1.28893i) q^{15} +2.04769 q^{16} +(-0.844232 - 0.844232i) q^{17} +(1.86656 - 2.83759i) q^{18} +1.32025i q^{19} +(0.542159 + 1.51173i) q^{20} +(1.72309 - 0.175985i) q^{21} +(-4.16440 + 4.16440i) q^{22} +(5.62910 - 5.62910i) q^{23} +(5.30272 - 0.541586i) q^{24} +(3.86039 - 3.17764i) q^{25} +5.19868i q^{26} +(2.39973 - 4.60883i) q^{27} +(0.507864 + 0.507864i) q^{28} -4.38282 q^{29} +(-1.89194 - 3.95565i) q^{30} -1.70499 q^{31} +(2.71289 + 2.71289i) q^{32} +(-5.69071 + 6.98536i) q^{33} +1.35170i q^{34} +(0.954557 - 2.02208i) q^{35} +(2.11020 - 0.435588i) q^{36} +(-1.71171 + 1.71171i) q^{37} +(1.05693 - 1.05693i) q^{38} +(0.808099 + 7.91217i) q^{39} +(2.93760 - 6.22286i) q^{40} -1.82176i q^{41} +(-1.52031 - 1.23854i) q^{42} +(-0.281771 - 0.281771i) q^{43} -3.73616 q^{44} +(-3.49432 - 5.72623i) q^{45} -9.01279 q^{46} +(3.39588 + 3.39588i) q^{47} +(-2.74973 - 2.24010i) q^{48} -1.00000i q^{49} +(-5.63432 - 0.546575i) q^{50} +(0.210113 + 2.05723i) q^{51} +(-2.33204 + 2.33204i) q^{52} +(-3.51059 + 3.51059i) q^{53} +(-5.61073 + 1.76850i) q^{54} +(3.92668 + 10.9490i) q^{55} -3.07745i q^{56} +(1.44431 - 1.77289i) q^{57} +(3.50868 + 3.50868i) q^{58} -1.81772 q^{59} +(0.925745 - 2.62313i) q^{60} -2.47514 q^{61} +(1.36494 + 1.36494i) q^{62} +(-2.50636 - 1.64868i) q^{63} -8.43900i q^{64} +(9.28511 + 4.38319i) q^{65} +(10.1479 - 1.03644i) q^{66} +(7.92132 - 7.92132i) q^{67} +(-0.606352 + 0.606352i) q^{68} +(-13.7171 + 1.40098i) q^{69} +(-2.38296 + 0.854612i) q^{70} +9.06358i q^{71} +(-7.71322 - 5.07373i) q^{72} +(-1.33856 - 1.33856i) q^{73} +2.74064 q^{74} +(-8.66014 + 0.0439525i) q^{75} +0.948239 q^{76} +(3.67830 + 3.67830i) q^{77} +(5.68718 - 6.98104i) q^{78} -11.5015i q^{79} +(-4.30998 + 1.54571i) q^{80} +(-8.26437 + 3.56372i) q^{81} +(-1.45841 + 1.45841i) q^{82} +(5.46196 - 5.46196i) q^{83} +(-0.126398 - 1.23757i) q^{84} +(2.41421 + 1.13967i) q^{85} +0.451146i q^{86} +(5.88546 + 4.79466i) q^{87} +(11.3198 + 11.3198i) q^{88} +9.43116 q^{89} +(-1.78676 + 7.38154i) q^{90} +4.59186 q^{91} +(-4.04298 - 4.04298i) q^{92} +(2.28954 + 1.86520i) q^{93} -5.43717i q^{94} +(-0.996595 - 2.77886i) q^{95} +(-0.675186 - 6.61080i) q^{96} +(-3.06315 + 3.06315i) q^{97} +(-0.800553 + 0.800553i) q^{98} +(15.2835 - 3.15483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.800553	−	0.800553i	−0.566077	−	0.566077i	0.364950	−	0.931027i	$-0.381086\pi$
$2$	−0.800553	−	0.800553i	−0.566077	−	0.566077i	−0.931027	+	0.364950i	$0.881086\pi$
$3$	−1.34285	−	1.09397i	−0.775293	−	0.631602i
$3$	−1.34285	−	1.09397i	−0.775293	−	0.631602i
$4$		−	0.718229i		−	0.359114i
$5$	−2.10480	+	0.754855i	−0.941296	+	0.337581i
$5$	−2.10480	+	0.754855i	−0.941296	+	0.337581i
$6$	0.199242	+	1.95080i	0.0813403	+	0.796410i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.17609	+	2.17609i	−0.769363	+	0.769363i
$9$	0.606476	+	2.93806i	0.202159	+	0.979353i
$10$	2.28931	+	1.08070i	0.723943	+	0.341749i
$11$		−	5.20191i		−	1.56843i	−0.620487	−	0.784217i	$-0.713065\pi$
$11$		−	5.20191i		−	1.56843i	0.620487	−	0.784217i	$-0.286935\pi$
$12$	−0.785718	+	0.964471i	−0.226817	+	0.278419i
$13$	−3.24693	−	3.24693i	−0.900537	−	0.900537i	0.0949456	−	0.995482i	$-0.469732\pi$
$13$	−3.24693	−	3.24693i	−0.900537	−	0.900537i	−0.995482	+	0.0949456i	$0.969732\pi$
$14$	1.13215			0.302581
$15$	3.65221	+	1.28893i	0.942997	+	0.332800i
$16$	2.04769			0.511922
$17$	−0.844232	−	0.844232i	−0.204756	−	0.204756i	0.597278	−	0.802034i	$-0.296249\pi$
$17$	−0.844232	−	0.844232i	−0.204756	−	0.204756i	−0.802034	+	0.597278i	$0.796249\pi$
$18$	1.86656	−	2.83759i	0.439951	−	0.668826i
$19$			1.32025i			0.302885i	0.988466	+	0.151443i	$0.0483919\pi$
$19$			1.32025i			0.302885i	−0.988466	+	0.151443i	$0.951608\pi$
$20$	0.542159	+	1.51173i	0.121230	+	0.338033i
$21$	1.72309	−	0.175985i	0.376008	−	0.0384031i
$22$	−4.16440	+	4.16440i	−0.887854	+	0.887854i
$23$	5.62910	−	5.62910i	1.17375	−	1.17375i	0.192440	−	0.981309i	$-0.438360\pi$
$23$	5.62910	−	5.62910i	1.17375	−	1.17375i	0.981309	−	0.192440i	$-0.0616401\pi$
$24$	5.30272	−	0.541586i	1.08241	−	0.110551i
$25$	3.86039	−	3.17764i	0.772078	−	0.635528i
$26$			5.19868i			1.01955i
$27$	2.39973	−	4.60883i	0.461829	−	0.886969i
$28$	0.507864	+	0.507864i	0.0959774	+	0.0959774i
$29$	−4.38282			−0.813870			−0.406935	−	0.913457i	$-0.633402\pi$
$29$	−4.38282			−0.813870			−0.406935	+	0.913457i	$0.633402\pi$
$30$	−1.89194	−	3.95565i	−0.345419	−	0.722199i
$31$	−1.70499			−0.306225			−0.153113	−	0.988209i	$-0.548930\pi$
$31$	−1.70499			−0.306225			−0.153113	+	0.988209i	$0.548930\pi$
$32$	2.71289	+	2.71289i	0.479576	+	0.479576i
$33$	−5.69071	+	6.98536i	−0.990625	+	1.21600i
$34$			1.35170i			0.231815i
$35$	0.954557	−	2.02208i	0.161350	−	0.341794i
$36$	2.11020	−	0.435588i	0.351700	−	0.0725981i
$37$	−1.71171	+	1.71171i	−0.281404	+	0.281404i	−0.833669	−	0.552265i	$-0.813764\pi$
$37$	−1.71171	+	1.71171i	−0.281404	+	0.281404i	0.552265	+	0.833669i	$0.313764\pi$
$38$	1.05693	−	1.05693i	0.171456	−	0.171456i
$39$	0.808099	+	7.91217i	0.129399	+	1.26696i
$40$	2.93760	−	6.22286i	0.464476	−	0.983921i
$41$		−	1.82176i		−	0.284511i	−0.989830	−	0.142255i	$-0.954565\pi$
$41$		−	1.82176i		−	0.284511i	0.989830	−	0.142255i	$-0.0454354\pi$
$42$	−1.52031	−	1.23854i	−0.234589	−	0.191110i
$43$	−0.281771	−	0.281771i	−0.0429697	−	0.0429697i	0.685295	−	0.728265i	$-0.259673\pi$
$43$	−0.281771	−	0.281771i	−0.0429697	−	0.0429697i	−0.728265	+	0.685295i	$0.759673\pi$
$44$	−3.73616			−0.563247
$45$	−3.49432	−	5.72623i	−0.520902	−	0.853616i
$46$	−9.01279			−1.32886
$47$	3.39588	+	3.39588i	0.495340	+	0.495340i	0.909984	−	0.414644i	$-0.136094\pi$
$47$	3.39588	+	3.39588i	0.495340	+	0.495340i	−0.414644	+	0.909984i	$0.636094\pi$
$48$	−2.74973	−	2.24010i	−0.396890	−	0.323331i
$49$		−	1.00000i		−	0.142857i
$50$	−5.63432	−	0.546575i	−0.796813	−	0.0772973i
$51$	0.210113	+	2.05723i	0.0294217	+	0.288071i
$52$	−2.33204	+	2.33204i	−0.323396	+	0.323396i
$53$	−3.51059	+	3.51059i	−0.482216	+	0.482216i	−0.905839	−	0.423623i	$-0.860758\pi$
$53$	−3.51059	+	3.51059i	−0.482216	+	0.482216i	0.423623	+	0.905839i	$0.360758\pi$
$54$	−5.61073	+	1.76850i	−0.763523	+	0.240662i
$55$	3.92668	+	10.9490i	0.529474	+	1.47636i
$56$		−	3.07745i		−	0.411242i
$57$	1.44431	−	1.77289i	0.191303	−	0.234825i
$58$	3.50868	+	3.50868i	0.460713	+	0.460713i
$59$	−1.81772			−0.236647			−0.118323	−	0.992975i	$-0.537752\pi$
$59$	−1.81772			−0.236647			−0.118323	+	0.992975i	$0.537752\pi$
$60$	0.925745	−	2.62313i	0.119513	−	0.338644i
$61$	−2.47514			−0.316909			−0.158455	−	0.987366i	$-0.550651\pi$
$61$	−2.47514			−0.316909			−0.158455	+	0.987366i	$0.550651\pi$
$62$	1.36494	+	1.36494i	0.173347	+	0.173347i
$63$	−2.50636	−	1.64868i	−0.315772	−	0.207714i
$64$		−	8.43900i		−	1.05488i
$65$	9.28511	+	4.38319i	1.15168	+	0.543668i
$66$	10.1479	−	1.03644i	1.24912	−	0.127577i
$67$	7.92132	−	7.92132i	0.967743	−	0.967743i	−0.0317530	−	0.999496i	$-0.510109\pi$
$67$	7.92132	−	7.92132i	0.967743	−	0.967743i	0.999496	+	0.0317530i	$0.0101090\pi$
$68$	−0.606352	+	0.606352i	−0.0735309	+	0.0735309i
$69$	−13.7171	+	1.40098i	−1.65134	+	0.168658i
$70$	−2.38296	+	0.854612i	−0.284818	+	0.102146i
$71$			9.06358i			1.07565i	0.843057	+	0.537825i	$0.180754\pi$
$71$			9.06358i			1.07565i	−0.843057	+	0.537825i	$0.819246\pi$
$72$	−7.71322	−	5.07373i	−0.909011	−	0.597944i
$73$	−1.33856	−	1.33856i	−0.156666	−	0.156666i	0.624422	−	0.781088i	$-0.285335\pi$
$73$	−1.33856	−	1.33856i	−0.156666	−	0.156666i	−0.781088	+	0.624422i	$0.785335\pi$
$74$	2.74064			0.318592
$75$	−8.66014	+	0.0439525i	−0.999987	+	0.00507520i
$76$	0.948239			0.108771
$77$	3.67830	+	3.67830i	0.419182	+	0.419182i
$78$	5.68718	−	6.98104i	0.643947	−	0.790447i
$79$		−	11.5015i		−	1.29402i	−0.762481	−	0.647011i	$-0.776019\pi$
$79$		−	11.5015i		−	1.29402i	0.762481	−	0.647011i	$-0.223981\pi$
$80$	−4.30998	+	1.54571i	−0.481871	+	0.172815i
$81$	−8.26437	+	3.56372i	−0.918264	+	0.395969i
$82$	−1.45841	+	1.45841i	−0.161055	+	0.161055i
$83$	5.46196	−	5.46196i	0.599528	−	0.599528i	−0.340659	−	0.940187i	$-0.610650\pi$
$83$	5.46196	−	5.46196i	0.599528	−	0.599528i	0.940187	+	0.340659i	$0.110650\pi$
$84$	−0.126398	−	1.23757i	−0.0137911	−	0.135030i
$85$	2.41421	+	1.13967i	0.261858	+	0.123614i
$86$			0.451146i			0.0486483i
$87$	5.88546	+	4.79466i	0.630988	+	0.514041i
$88$	11.3198	+	11.3198i	1.20669	+	1.20669i
$89$	9.43116			0.999701			0.499850	−	0.866112i	$-0.333388\pi$
$89$	9.43116			0.999701			0.499850	+	0.866112i	$0.333388\pi$
$90$	−1.78676	+	7.38154i	−0.188341	+	0.778083i
$91$	4.59186			0.481357
$92$	−4.04298	−	4.04298i	−0.421510	−	0.421510i
$93$	2.28954	+	1.86520i	0.237414	+	0.193412i
$94$		−	5.43717i		−	0.560801i
$95$	−0.996595	−	2.77886i	−0.102248	−	0.285105i
$96$	−0.675186	−	6.61080i	−0.0689109	−	0.674712i
$97$	−3.06315	+	3.06315i	−0.311016	+	0.311016i	−0.845303	−	0.534287i	$-0.820580\pi$
$97$	−3.06315	+	3.06315i	−0.311016	+	0.311016i	0.534287	+	0.845303i	$0.320580\pi$
$98$	−0.800553	+	0.800553i	−0.0808681	+	0.0808681i
$99$	15.2835	−	3.15483i	1.53605	−	0.317072i
$100$	−2.28227	−	2.77264i	−0.228227	−	0.277264i
$101$		−	3.71640i		−	0.369796i	−0.982758	−	0.184898i	$-0.940805\pi$
$101$		−	3.71640i		−	0.369796i	0.982758	−	0.184898i	$-0.0591954\pi$
$102$	1.47872	−	1.81513i	0.146415	−	0.179725i
$103$	1.18049	+	1.18049i	0.116317	+	0.116317i	0.762869	−	0.646553i	$-0.223790\pi$
$103$	1.18049	+	1.18049i	0.116317	+	0.116317i	−0.646553	+	0.762869i	$0.723790\pi$
$104$	14.1312			1.38568
$105$	−3.49391	+	1.67110i	−0.340971	+	0.163082i
$106$	5.62082			0.545943
$107$	1.38009	+	1.38009i	0.133418	+	0.133418i	0.770662	−	0.637244i	$-0.219926\pi$
$107$	1.38009	+	1.38009i	0.133418	+	0.133418i	−0.637244	+	0.770662i	$0.719926\pi$
$108$	−3.31019	−	1.72356i	−0.318523	−	0.165849i
$109$			5.93506i			0.568475i	0.958754	+	0.284238i	$0.0917405\pi$
$109$			5.93506i			0.568475i	−0.958754	+	0.284238i	$0.908260\pi$
$110$	5.62173	−	11.9088i	0.536011	−	1.13546i
$111$	4.17113	−	0.426013i	0.395906	−	0.0404353i
$112$	−1.44794	+	1.44794i	−0.136817	+	0.136817i
$113$	−0.240664	+	0.240664i	−0.0226398	+	0.0226398i	−0.718336	−	0.695696i	$-0.755096\pi$
$113$	−0.240664	+	0.240664i	−0.0226398	+	0.0226398i	0.695696	+	0.718336i	$0.255096\pi$
$114$	−2.57554	+	0.263049i	−0.241221	+	0.0246368i
$115$	−7.59899	+	16.0973i	−0.708610	+	1.50108i
$116$			3.14787i			0.292272i
$117$	7.57049	−	11.5089i	0.699892	−	1.06399i
$118$	1.45518	+	1.45518i	0.133960	+	0.133960i
$119$	1.19392			0.109447
$120$	−10.7524	+	5.14271i	−0.981551	+	0.469463i
$121$	−16.0598			−1.45998
$122$	1.98148	+	1.98148i	0.179395	+	0.179395i
$123$	−1.99294	+	2.44634i	−0.179697	+	0.220579i
$124$			1.22457i			0.109970i
$125$	−5.72670	+	9.60234i	−0.512211	+	0.858860i
$126$	0.686624	+	3.32633i	0.0611693	+	0.296333i
$127$	−4.55939	+	4.55939i	−0.404581	+	0.404581i	−0.879844	−	0.475263i	$-0.842353\pi$
$127$	−4.55939	+	4.55939i	−0.404581	+	0.404581i	0.475263	+	0.879844i	$0.342353\pi$
$128$	−1.33009	+	1.33009i	−0.117565	+	0.117565i
$129$	0.0701274	+	0.686624i	0.00617437	+	0.0604538i
$130$	−3.92425	−	10.9422i	−0.344180	−	0.959695i
$131$		−	13.6784i		−	1.19509i	−0.801837	−	0.597543i	$-0.796144\pi$
$131$		−	13.6784i		−	1.19509i	0.801837	−	0.597543i	$-0.203856\pi$
$132$	5.01709	+	4.08723i	0.436682	+	0.355748i
$133$	−0.933556	−	0.933556i	−0.0809495	−	0.0809495i
$134$	−12.6829			−1.09563
$135$	−1.57197	+	11.5121i	−0.135293	+	0.990806i
$136$	3.67424			0.315064
$137$	−10.0232	−	10.0232i	−0.856337	−	0.856337i	0.134567	−	0.990904i	$-0.457036\pi$
$137$	−10.0232	−	10.0232i	−0.856337	−	0.856337i	−0.990904	+	0.134567i	$0.957036\pi$
$138$	12.1028	+	9.85969i	1.03026	+	0.839313i
$139$		−	15.8262i		−	1.34236i	−0.741292	−	0.671182i	$-0.765787\pi$
$139$		−	15.8262i		−	1.34236i	0.741292	−	0.671182i	$-0.234213\pi$
$140$	−1.45232	−	0.685590i	−0.122743	−	0.0579430i
$141$	−0.845170	−	8.27513i	−0.0711761	−	0.696892i
$142$	7.25588	−	7.25588i	0.608900	−	0.608900i
$143$	−16.8902	+	16.8902i	−1.41243	+	1.41243i
$144$	1.24187	+	6.01623i	0.103490	+	0.501353i
$145$	9.22498	−	3.30840i	0.766093	−	0.274747i
$146$			2.14317i			0.177370i
$147$	−1.09397	+	1.34285i	−0.0902288	+	0.110756i
$148$	1.22940	+	1.22940i	0.101056	+	0.101056i
$149$	−9.30594			−0.762373			−0.381186	−	0.924498i	$-0.624484\pi$
$149$	−9.30594			−0.762373			−0.381186	+	0.924498i	$0.624484\pi$
$150$	6.96809	+	6.89772i	0.568942	+	0.563196i
$151$	−16.8274			−1.36939			−0.684697	−	0.728827i	$-0.740066\pi$
$151$	−16.8274			−1.36939			−0.684697	+	0.728827i	$0.740066\pi$
$152$	−2.87297	−	2.87297i	−0.233029	−	0.233029i
$153$	1.96840	−	2.99241i	0.159135	−	0.241922i
$154$		−	5.88936i		−	0.474578i
$155$	3.58867	−	1.28702i	0.288249	−	0.103376i
$156$	5.68275	−	0.580400i	0.454984	−	0.0464692i
$157$	6.80647	−	6.80647i	0.543216	−	0.543216i	−0.381255	−	0.924470i	$-0.624508\pi$
$157$	6.80647	−	6.80647i	0.543216	−	0.543216i	0.924470	+	0.381255i	$0.124508\pi$
$158$	−9.20757	+	9.20757i	−0.732515	+	0.732515i
$159$	8.55464	−	0.873717i	0.678427	−	0.0692903i
$160$	−7.75793	−	3.66226i	−0.613319	−	0.289527i
$161$			7.96075i			0.627395i
$162$	9.46902	+	3.76312i	0.743957	+	0.295659i
$163$	8.77966	+	8.77966i	0.687676	+	0.687676i	0.961718	−	0.274042i	$-0.0883607\pi$
$163$	8.77966	+	8.77966i	0.687676	+	0.687676i	−0.274042	+	0.961718i	$0.588361\pi$
$164$	−1.30844			−0.102172
$165$	6.70488	−	18.9985i	0.521974	−	1.47903i
$166$	−8.74519			−0.678758
$167$	−12.4516	−	12.4516i	−0.963532	−	0.963532i	0.0358258	−	0.999358i	$-0.488594\pi$
$167$	−12.4516	−	12.4516i	−0.963532	−	0.963532i	−0.999358	+	0.0358258i	$0.988594\pi$
$168$	−3.36663	+	4.13255i	−0.259741	+	0.318833i
$169$			8.08513i			0.621933i
$170$	−1.02034	−	2.84507i	−0.0782566	−	0.218207i
$171$	−3.87896	+	0.800698i	−0.296632	+	0.0612309i
$172$	−0.202376	+	0.202376i	−0.0154310	+	0.0154310i
$173$	13.7966	−	13.7966i	1.04894	−	1.04894i	0.0501977	−	0.998739i	$-0.484015\pi$
$173$	13.7966	−	13.7966i	1.04894	−	1.04894i	0.998739	−	0.0501977i	$-0.0159851\pi$
$174$	−0.873244	−	8.55000i	−0.0662004	−	0.648174i
$175$	−0.482774	+	4.97664i	−0.0364943	+	0.376198i
$176$		−	10.6519i		−	0.802916i
$177$	2.44092	+	1.98852i	0.183471	+	0.149466i
$178$	−7.55015	−	7.55015i	−0.565907	−	0.565907i
$179$	−7.03160			−0.525567			−0.262783	−	0.964855i	$-0.584640\pi$
$179$	−7.03160			−0.525567			−0.262783	+	0.964855i	$0.584640\pi$
$180$	−4.11274	+	2.50972i	−0.306546	+	0.187064i
$181$	14.1873			1.05454			0.527268	−	0.849699i	$-0.323216\pi$
$181$	14.1873			1.05454			0.527268	+	0.849699i	$0.323216\pi$
$182$	−3.67602	−	3.67602i	−0.272485	−	0.272485i
$183$	3.32374	+	2.70772i	0.245698	+	0.200161i
$184$			24.4988i			1.80608i
$185$	2.31072	−	4.89492i	0.169888	−	0.359881i
$186$	−0.339706	−	3.32609i	−0.0249085	−	0.243881i
$187$	−4.39161	+	4.39161i	−0.321147	+	0.321147i
$188$	2.43902	−	2.43902i	0.177884	−	0.177884i
$189$	1.56207	+	4.95580i	0.113624	+	0.360481i
$190$	−1.42680	+	3.02245i	−0.103511	+	0.219272i
$191$			15.6450i			1.13203i	0.824394	+	0.566017i	$0.191516\pi$
$191$			15.6450i			1.13203i	−0.824394	+	0.566017i	$0.808484\pi$
$192$	−9.23199	+	11.3323i	−0.666261	+	0.817838i
$193$	9.00959	+	9.00959i	0.648525	+	0.648525i	0.952636	−	0.304112i	$-0.0983596\pi$
$193$	9.00959	+	9.00959i	0.648525	+	0.648525i	−0.304112	+	0.952636i	$0.598360\pi$
$194$	4.90443			0.352118
$195$	−7.67343	−	16.0436i	−0.549506	−	1.14890i
$196$	−0.718229			−0.0513021
$197$	−2.78986	−	2.78986i	−0.198769	−	0.198769i	0.600703	−	0.799472i	$-0.294887\pi$
$197$	−2.78986	−	2.78986i	−0.198769	−	0.198769i	−0.799472	+	0.600703i	$0.794887\pi$
$198$	−14.7609	−	9.70965i	−1.04901	−	0.690035i
$199$		−	14.4320i		−	1.02306i	−0.859266	−	0.511528i	$-0.829080\pi$
$199$		−	14.4320i		−	1.02306i	0.859266	−	0.511528i	$-0.170920\pi$
$200$	−1.48572	+	15.3154i	−0.105056	+	1.08296i
$201$	−19.3028	+	1.97146i	−1.36151	+	0.139056i
$202$	−2.97518	+	2.97518i	−0.209333	+	0.209333i
$203$	3.09912	−	3.09912i	0.217516	−	0.217516i
$204$	1.47757	−	0.150909i	0.103450	−	0.0105658i
$205$	1.37516	+	3.83444i	0.0960455	+	0.267809i
$206$		−	1.89009i		−	0.131689i
$207$	19.9525	+	13.1247i	1.38680	+	0.912231i
$208$	−6.64871	−	6.64871i	−0.461005	−	0.461005i
$209$	6.86780			0.475056
$210$	4.13487	+	1.45926i	0.285333	+	0.100699i
$211$	11.9845			0.825049			0.412524	−	0.910947i	$-0.364647\pi$
$211$	11.9845			0.825049			0.412524	+	0.910947i	$0.364647\pi$
$212$	2.52140	+	2.52140i	0.173171	+	0.173171i
$213$	9.91525	−	12.1710i	0.679382	−	0.833943i
$214$		−	2.20967i		−	0.151050i
$215$	0.805769	+	0.380376i	0.0549530	+	0.0259414i
$216$	4.80718	+	15.2512i	0.327087	+	1.03772i
$217$	1.20561	−	1.20561i	0.0818422	−	0.0818422i
$218$	4.75133	−	4.75133i	0.321801	−	0.321801i
$219$	0.333141	+	3.26181i	0.0225116	+	0.220413i
$220$	7.86388	−	2.82026i	0.530182	−	0.190142i
$221$			5.48233i			0.368781i
$222$	−3.68025	−	2.99816i	−0.247003	−	0.201224i
$223$	−12.1834	−	12.1834i	−0.815858	−	0.815858i	0.169647	−	0.985505i	$-0.445737\pi$
$223$	−12.1834	−	12.1834i	−0.815858	−	0.815858i	−0.985505	+	0.169647i	$0.945737\pi$
$224$	−3.83661			−0.256344
$225$	11.6773	+	9.41488i	0.778489	+	0.627659i
$226$	0.385328			0.0256317
$227$	−4.17335	−	4.17335i	−0.276995	−	0.276995i	0.554913	−	0.831908i	$-0.312751\pi$
$227$	−4.17335	−	4.17335i	−0.276995	−	0.276995i	−0.831908	+	0.554913i	$0.812751\pi$
$228$	−1.27334	−	1.03734i	−0.0843290	−	0.0686996i
$229$			27.2705i			1.80209i	0.433730	+	0.901043i	$0.357197\pi$
$229$			27.2705i			1.80209i	−0.433730	+	0.901043i	$0.642803\pi$
$230$	18.9701	−	6.80335i	1.25085	−	0.448600i
$231$	−0.915459	−	8.96334i	−0.0602328	−	0.589744i
$232$	9.53740	−	9.53740i	0.626161	−	0.626161i
$233$	−1.96791	+	1.96791i	−0.128922	+	0.128922i	−0.768624	−	0.639701i	$-0.779058\pi$
$233$	−1.96791	+	1.96791i	−0.128922	+	0.128922i	0.639701	+	0.768624i	$0.279058\pi$
$234$	−15.2740	+	3.15288i	−0.998495	+	0.206110i
$235$	−9.71106	−	4.58426i	−0.633480	−	0.299044i
$236$			1.30554i			0.0849832i
$237$	−12.5823	+	15.4448i	−0.817306	+	1.00325i
$238$	−0.955800	−	0.955800i	−0.0619553	−	0.0619553i
$239$	1.42942			0.0924613			0.0462307	−	0.998931i	$-0.485279\pi$
$239$	1.42942			0.0924613			0.0462307	+	0.998931i	$0.485279\pi$
$240$	7.47860	+	2.63932i	0.482742	+	0.170368i
$241$	29.1319			1.87655			0.938274	−	0.345893i	$-0.112424\pi$
$241$	29.1319			1.87655			0.938274	+	0.345893i	$0.112424\pi$
$242$	12.8567	+	12.8567i	0.826463	+	0.826463i
$243$	14.9964	+	4.25541i	0.962018	+	0.272985i
$244$			1.77772i			0.113807i
$245$	0.754855	+	2.10480i	0.0482259	+	0.134471i
$246$	3.55388	−	0.362971i	0.226587	−	0.0231422i
$247$	4.28675	−	4.28675i	0.272759	−	0.272759i
$248$	3.71021	−	3.71021i	0.235598	−	0.235598i
$249$	−13.3098	+	1.35938i	−0.843473	+	0.0861470i
$250$	12.2717	−	3.10266i	0.776131	−	0.196230i
$251$		−	12.3977i		−	0.782538i	−0.920276	−	0.391269i	$-0.872036\pi$
$251$		−	12.3977i		−	0.782538i	0.920276	−	0.391269i	$-0.127964\pi$
$252$	−1.18413	+	1.80014i	−0.0745931	+	0.113398i
$253$	−29.2821	−	29.2821i	−1.84095	−	1.84095i
$254$	7.30007			0.458047
$255$	−1.99516	−	4.17147i	−0.124942	−	0.261227i
$256$	−14.7484			−0.921774
$257$	13.8717	+	13.8717i	0.865290	+	0.865290i	0.991947	−	0.126657i	$-0.0404246\pi$
$257$	13.8717	+	13.8717i	0.865290	+	0.865290i	−0.126657	+	0.991947i	$0.540425\pi$
$258$	0.493538	−	0.605820i	0.0307263	−	0.0377167i
$259$		−	2.42073i		−	0.150417i
$260$	3.14813	−	6.66884i	0.195239	−	0.413584i
$261$	−2.65808	−	12.8770i	−0.164531	−	0.797066i
$262$	−10.9503	+	10.9503i	−0.676511	+	0.676511i
$263$	12.2912	−	12.2912i	0.757909	−	0.757909i	−0.218032	−	0.975942i	$-0.569964\pi$
$263$	12.2912	−	12.2912i	0.757909	−	0.757909i	0.975942	+	0.218032i	$0.0699639\pi$
$264$	−2.81728	−	27.5842i	−0.173392	−	1.69769i
$265$	4.73911	−	10.0391i	0.291121	−	0.616695i
$266$			1.49472i			0.0916473i
$267$	−12.6646	−	10.3174i	−0.775061	−	0.631413i
$268$	−5.68932	−	5.68932i	−0.347530	−	0.347530i
$269$	19.1535			1.16781			0.583906	−	0.811822i	$-0.301524\pi$
$269$	19.1535			1.16781			0.583906	+	0.811822i	$0.301524\pi$
$270$	10.4745	−	7.95762i	0.637458	−	0.484286i
$271$	18.4629			1.12154			0.560771	−	0.827971i	$-0.310505\pi$
$271$	18.4629			1.12154			0.560771	+	0.827971i	$0.310505\pi$
$272$	−1.72872	−	1.72872i	−0.104819	−	0.104819i
$273$	−6.16616	−	5.02333i	−0.373193	−	0.304026i
$274$			16.0482i			0.969505i
$275$	−16.5298	−	20.0814i	−0.996784	−	1.21095i
$276$	1.00622	+	9.85200i	0.0605674	+	0.593020i
$277$	−7.66076	+	7.66076i	−0.460290	+	0.460290i	−0.898751	−	0.438460i	$-0.855524\pi$
$277$	−7.66076	+	7.66076i	−0.460290	+	0.460290i	0.438460	+	0.898751i	$0.355524\pi$
$278$	−12.6698	+	12.6698i	−0.759881	+	0.759881i
$279$	−1.03404	−	5.00936i	−0.0619061	−	0.299903i
$280$	2.32303	+	6.47743i	0.138828	+	0.387100i
$281$			20.4646i			1.22082i	0.792087	+	0.610408i	$0.208995\pi$
$281$			20.4646i			1.22082i	−0.792087	+	0.610408i	$0.791005\pi$
$282$	−5.94808	+	7.30129i	−0.354203	+	0.434785i
$283$	8.24528	+	8.24528i	0.490131	+	0.490131i	0.908347	−	0.418216i	$-0.137345\pi$
$283$	8.24528	+	8.24528i	0.490131	+	0.490131i	−0.418216	+	0.908347i	$0.637345\pi$
$284$	6.50972			0.386281
$285$	−1.70170	+	4.82182i	−0.100800	+	0.285620i
$286$	27.0431			1.59909
$287$	1.28818	+	1.28818i	0.0760387	+	0.0760387i
$288$	−6.32533	+	9.61593i	−0.372723	+	0.566624i
$289$		−	15.5745i		−	0.916150i
$290$	−10.0336	−	4.73654i	−0.589195	−	0.278139i
$291$	7.46433	−	0.762360i	0.437567	−	0.0446903i
$292$	−0.961389	+	0.961389i	−0.0562610	+	0.0562610i
$293$	−19.7225	+	19.7225i	−1.15220	+	1.15220i	−0.166088	+	0.986111i	$0.553114\pi$
$293$	−19.7225	+	19.7225i	−1.15220	+	1.15220i	−0.986111	+	0.166088i	$0.946886\pi$
$294$	1.95080	−	0.199242i	0.113773	−	0.0116200i
$295$	3.82594	−	1.37211i	0.222755	−	0.0798875i
$296$		−	7.44968i		−	0.433004i
$297$	−23.9747	−	12.4832i	−1.39115	−	0.724348i
$298$	7.44990	+	7.44990i	0.431561	+	0.431561i
$299$	−36.5546			−2.11401
$300$	0.0315680	+	6.21996i	0.00182258	+	0.359110i
$301$	0.398485			0.0229683
$302$	13.4712	+	13.4712i	0.775182	+	0.775182i
$303$	−4.06562	+	4.99056i	−0.233564	+	0.286700i
$304$			2.70346i			0.155054i
$305$	5.20968	−	1.86837i	0.298306	−	0.106983i
$306$	−3.97139	+	0.819776i	−0.227029	+	0.0468635i
$307$	−13.2997	+	13.2997i	−0.759057	+	0.759057i	−0.976151	−	0.217094i	$-0.930342\pi$
$307$	−13.2997	+	13.2997i	−0.759057	+	0.759057i	0.217094	+	0.976151i	$0.430342\pi$
$308$	2.64186	−	2.64186i	0.150534	−	0.150534i
$309$	−0.293801	−	2.87663i	−0.0167137	−	0.163646i
$310$	−3.90325	−	1.84259i	−0.221690	−	0.104652i
$311$			23.8049i			1.34985i	0.737885	+	0.674926i	$0.235824\pi$
$311$			23.8049i			1.34985i	−0.737885	+	0.674926i	$0.764176\pi$
$312$	−18.9761	−	15.4591i	−1.07431	−	0.875197i
$313$	−18.9352	−	18.9352i	−1.07028	−	1.07028i	−0.997336	−	0.0729475i	$-0.976759\pi$
$313$	−18.9352	−	18.9352i	−1.07028	−	1.07028i	−0.0729475	−	0.997336i	$-0.523241\pi$
$314$	−10.8979			−0.615003
$315$	6.51991	+	1.57820i	0.367356	+	0.0889215i
$316$	−8.26072			−0.464702
$317$	11.6929	+	11.6929i	0.656739	+	0.656739i	0.954607	−	0.297868i	$-0.0962755\pi$
$317$	11.6929	+	11.6929i	0.656739	+	0.656739i	−0.297868	+	0.954607i	$0.596275\pi$
$318$	−7.54790	−	6.14899i	−0.423265	−	0.344818i
$319$			22.7990i			1.27650i
$320$	6.37022	+	17.7624i	0.356106	+	0.992950i
$321$	−0.343478	−	3.36302i	−0.0191711	−	0.187706i
$322$	6.37301	−	6.37301i	0.355154	−	0.355154i
$323$	1.11459	−	1.11459i	0.0620177	−	0.0620177i
$324$	2.55957	+	5.93571i	0.142198	+	0.329762i
$325$	−22.8520	−	2.21683i	−1.26760	−	0.122968i
$326$		−	14.0572i		−	0.778555i
$327$	6.49275	−	7.96987i	0.359050	−	0.440735i
$328$	3.96430	+	3.96430i	0.218892	+	0.218892i
$329$	−4.80250			−0.264771
$330$	−20.5769	+	9.84167i	−1.13272	+	0.541766i
$331$	−11.5898			−0.637031			−0.318516	−	0.947918i	$-0.603184\pi$
$331$	−11.5898			−0.637031			−0.318516	+	0.947918i	$0.603184\pi$
$332$	−3.92294	−	3.92294i	−0.215299	−	0.215299i
$333$	−6.06723	−	3.99100i	−0.332482	−	0.218706i
$334$			19.9363i			1.09087i
$335$	−10.6934	+	22.6523i	−0.584241	+	1.23762i
$336$	3.52835	−	0.360363i	0.192487	−	0.0196594i
$337$	−5.46127	+	5.46127i	−0.297494	+	0.297494i	−0.840032	−	0.542537i	$-0.817464\pi$
$337$	−5.46127	+	5.46127i	−0.297494	+	0.297494i	0.542537	+	0.840032i	$0.317464\pi$
$338$	6.47258	−	6.47258i	0.352062	−	0.352062i
$339$	0.586453	−	0.0598966i	0.0318517	−	0.00325314i
$340$	0.818543	−	1.73396i	0.0443917	−	0.0940371i
$341$			8.86920i			0.480294i
$342$	3.74632	+	2.46431i	0.202578	+	0.133255i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.22632			0.0661186
$345$	27.8142	−	13.3032i	1.49747	−	0.716219i
$346$	−22.0898			−1.18756
$347$	−20.1982	−	20.1982i	−1.08430	−	1.08430i	−0.996103	−	0.0881938i	$-0.971891\pi$
$347$	−20.1982	−	20.1982i	−1.08430	−	1.08430i	−0.0881938	−	0.996103i	$-0.528109\pi$
$348$	3.44366	−	4.22711i	0.184600	−	0.226597i
$349$			11.9748i			0.640997i	0.947249	+	0.320498i	$0.103850\pi$
$349$			11.9748i			0.640997i	−0.947249	+	0.320498i	$0.896150\pi$
$350$	4.37055	−	3.59758i	0.233616	−	0.192299i
$351$	−22.7563	+	7.17278i	−1.21464	+	0.382855i
$352$	14.1122	−	14.1122i	0.752183	−	0.752183i
$353$	24.3423	−	24.3423i	1.29561	−	1.29561i	0.364345	−	0.931264i	$-0.381293\pi$
$353$	24.3423	−	24.3423i	1.29561	−	1.29561i	0.931264	−	0.364345i	$-0.118707\pi$
$354$	−0.362166	−	3.54600i	−0.0192489	−	0.188468i
$355$	−6.84169	−	19.0770i	−0.363119	−	1.01250i
$356$		−	6.77373i		−	0.359007i
$357$	−1.60326	−	1.30611i	−0.0848534	−	0.0691268i
$358$	5.62917	+	5.62917i	0.297511	+	0.297511i
$359$	14.2164			0.750314			0.375157	−	0.926961i	$-0.377589\pi$
$359$	14.2164			0.750314			0.375157	+	0.926961i	$0.377589\pi$
$360$	20.0647	+	4.85683i	1.05750	+	0.255978i
$361$	17.2569			0.908260
$362$	−11.3577	−	11.3577i	−0.596948	−	0.596948i
$363$	21.5659	+	17.5689i	1.13192	+	0.922129i
$364$		−	3.29800i		−	0.172862i
$365$	3.82781	+	1.80698i	0.200357	+	0.0945816i
$366$	−0.493153	−	4.82850i	−0.0257775	−	0.252390i
$367$	16.7024	−	16.7024i	0.871859	−	0.871859i	−0.120816	−	0.992675i	$-0.538551\pi$
$367$	16.7024	−	16.7024i	0.871859	−	0.871859i	0.992675	+	0.120816i	$0.0385512\pi$
$368$	11.5267	−	11.5267i	0.600868	−	0.600868i
$369$	5.35243	−	1.10485i	0.278636	−	0.0575163i
$370$	−5.76850	+	2.06878i	−0.299890	+	0.107551i
$371$		−	4.96472i		−	0.257755i
$372$	1.33964	−	1.64441i	0.0694572	−	0.0852589i
$373$	4.57877	+	4.57877i	0.237080	+	0.237080i	0.815640	−	0.578560i	$-0.196385\pi$
$373$	4.57877	+	4.57877i	0.237080	+	0.237080i	−0.578560	+	0.815640i	$0.696385\pi$
$374$	7.03144			0.363587
$375$	18.1947	−	6.62966i	0.939571	−	0.342354i
$376$	−14.7795			−0.762193
$377$	14.2307	+	14.2307i	0.732920	+	0.732920i
$378$	2.71686	−	5.21790i	0.139740	−	0.268380i
$379$		−	12.6506i		−	0.649816i	−0.945746	−	0.324908i	$-0.894667\pi$
$379$		−	12.6506i		−	0.649816i	0.945746	−	0.324908i	$-0.105333\pi$
$380$	−1.99586	+	0.715783i	−0.102385	+	0.0367189i
$381$	11.1104	−	1.13474i	0.569202	−	0.0581347i
$382$	12.5247	−	12.5247i	0.640818	−	0.640818i
$383$	−18.0165	+	18.0165i	−0.920601	+	0.920601i	−0.997072	−	0.0764705i	$-0.975635\pi$
$383$	−18.0165	+	18.0165i	−0.920601	+	0.920601i	0.0764705	+	0.997072i	$0.475635\pi$
$384$	3.24119	−	0.331035i	0.165401	−	0.0168930i
$385$	−10.5187	−	4.96552i	−0.536082	−	0.253066i
$386$		−	14.4253i		−	0.734229i
$387$	0.656973	−	0.998748i	0.0333958	−	0.0507692i
$388$	2.20004	+	2.20004i	0.111690	+	0.111690i
$389$	17.7215			0.898517			0.449259	−	0.893402i	$-0.351688\pi$
$389$	17.7215			0.898517			0.449259	+	0.893402i	$0.351688\pi$
$390$	−6.70073	+	18.9867i	−0.339305	+	0.961429i
$391$	−9.50453			−0.480665
$392$	2.17609	+	2.17609i	0.109909	+	0.109909i
$393$	−14.9637	+	18.3680i	−0.754819	+	0.926543i
$394$			4.46686i			0.225037i
$395$	8.68197	+	24.2084i	0.436838	+	1.21806i
$396$	−2.26589	−	10.9771i	−0.113865	−	0.551618i
$397$	4.43035	−	4.43035i	0.222353	−	0.222353i	−0.587136	−	0.809489i	$-0.699745\pi$
$397$	4.43035	−	4.43035i	0.222353	−	0.222353i	0.809489	+	0.587136i	$0.199745\pi$
$398$	−11.5536	+	11.5536i	−0.579128	+	0.579128i
$399$	0.232344	+	2.27490i	0.0116317	+	0.113887i
$400$	7.90488	−	6.50682i	0.395244	−	0.325341i
$401$		−	34.4780i		−	1.72175i	−0.508818	−	0.860874i	$-0.669918\pi$
$401$		−	34.4780i		−	1.72175i	0.508818	−	0.860874i	$-0.330082\pi$
$402$	17.0312	+	13.8746i	0.849437	+	0.692004i
$403$	5.53599	+	5.53599i	0.275767	+	0.275767i
$404$	−2.66923			−0.132799
$405$	14.7048	−	13.7393i	0.730686	−	0.682713i
$406$	−4.96203			−0.246261
$407$	8.90417	+	8.90417i	0.441364	+	0.441364i
$408$	−4.93395	−	4.01950i	−0.244267	−	0.198995i
$409$			19.5663i			0.967490i	0.875209	+	0.483745i	$0.160724\pi$
$409$			19.5663i			0.967490i	−0.875209	+	0.483745i	$0.839276\pi$
$410$	1.96878	−	4.17056i	0.0972312	−	0.205969i
$411$	2.49457	+	24.4246i	0.123048	+	1.20478i
$412$	0.847860	−	0.847860i	0.0417711	−	0.0417711i
$413$	1.28532	−	1.28532i	0.0632465	−	0.0632465i
$414$	−5.46604	−	26.4801i	−0.268641	−	1.30143i
$415$	−7.37336	+	15.6193i	−0.361944	+	0.766723i
$416$		−	17.6171i		−	0.863751i
$417$	−17.3134	+	21.2522i	−0.847840	+	1.04073i
$418$	−5.49804	−	5.49804i	−0.268918	−	0.268918i
$419$	17.0209			0.831524			0.415762	−	0.909474i	$-0.363515\pi$
$419$	17.0209			0.831524			0.415762	+	0.909474i	$0.363515\pi$
$420$	1.20023	+	2.50943i	0.0585652	+	0.122448i
$421$	21.7474			1.05990			0.529951	−	0.848028i	$-0.322210\pi$
$421$	21.7474			1.05990			0.529951	+	0.848028i	$0.322210\pi$
$422$	−9.59425	−	9.59425i	−0.467041	−	0.467041i
$423$	−7.91778	+	12.0368i	−0.384976	+	0.585250i
$424$		−	15.2787i		−	0.741998i
$425$	−5.94173	−	0.576396i	−0.288216	−	0.0279593i
$426$	−17.6812	+	1.80585i	−0.856658	+	0.0874936i
$427$	1.75019	−	1.75019i	0.0846976	−	0.0846976i
$428$	0.991221	−	0.991221i	0.0479125	−	0.0479125i
$429$	41.1583	−	4.20365i	1.98714	−	0.202954i
$430$	−0.340550	−	0.949573i	−0.0164228	−	0.0457925i
$431$		−	10.7912i		−	0.519796i	−0.965636	−	0.259898i	$-0.916311\pi$
$431$		−	10.7912i		−	0.519796i	0.965636	−	0.259898i	$-0.0836889\pi$
$432$	4.91391	−	9.43745i	0.236420	−	0.454059i
$433$	0.466927	+	0.466927i	0.0224391	+	0.0224391i	0.718237	−	0.695798i	$-0.244949\pi$
$433$	0.466927	+	0.466927i	0.0224391	+	0.0224391i	−0.695798	+	0.718237i	$0.744949\pi$
$434$	−1.93031			−0.0926579
$435$	−16.0070	−	5.64914i	−0.767477	−	0.270856i
$436$	4.26273			0.204148
$437$	7.43180	+	7.43180i	0.355511	+	0.355511i
$438$	2.34456	−	2.87795i	0.112027	−	0.137514i
$439$		−	9.43662i		−	0.450385i	−0.974314	−	0.225193i	$-0.927699\pi$
$439$		−	9.43662i		−	0.450385i	0.974314	−	0.225193i	$-0.0723011\pi$
$440$	−32.3708	−	15.2811i	−1.54322	−	0.728500i
$441$	2.93806	−	0.606476i	0.139908	−	0.0288798i
$442$	4.38889	−	4.38889i	0.208758	−	0.208758i
$443$	−16.8956	+	16.8956i	−0.802734	+	0.802734i	−0.983522	−	0.180788i	$-0.942135\pi$
$443$	−16.8956	+	16.8956i	−0.802734	+	0.802734i	0.180788	+	0.983522i	$0.442135\pi$
$444$	−0.305975	−	2.99582i	−0.0145209	−	0.142175i
$445$	−19.8507	+	7.11916i	−0.941015	+	0.337480i
$446$			19.5068i			0.923676i
$447$	12.4965	+	10.1804i	0.591062	+	0.481516i
$448$	5.96728	+	5.96728i	0.281927	+	0.281927i
$449$	11.5643			0.545753			0.272876	−	0.962049i	$-0.412025\pi$
$449$	11.5643			0.545753			0.272876	+	0.962049i	$0.412025\pi$
$450$	−1.81121	−	16.8854i	−0.0853812	−	0.795987i
$451$	−9.47661			−0.446236
$452$	0.172852	+	0.172852i	0.00813026	+	0.00813026i
$453$	22.5966	+	18.4086i	1.06168	+	0.864912i
$454$			6.68197i			0.313601i
$455$	−9.66495	+	3.46618i	−0.453100	+	0.162497i
$456$	0.715027	+	7.00090i	0.0334842	+	0.327847i
$457$	−17.8413	+	17.8413i	−0.834580	+	0.834580i	−0.988139	−	0.153560i	$-0.950926\pi$
$457$	−17.8413	+	17.8413i	−0.834580	+	0.834580i	0.153560	+	0.988139i	$0.450926\pi$
$458$	21.8315	−	21.8315i	1.02012	−	1.02012i
$459$	−5.91685	+	1.86499i	−0.276175	+	0.0870502i
$460$	11.5615	+	5.45782i	0.539060	+	0.254472i
$461$			13.0571i			0.608129i	0.952651	+	0.304064i	$0.0983438\pi$
$461$			13.0571i			0.608129i	−0.952651	+	0.304064i	$0.901656\pi$
$462$	−6.44276	+	7.90850i	−0.299744	+	0.367937i
$463$	17.3925	+	17.3925i	0.808298	+	0.808298i	0.984376	−	0.176079i	$-0.0563413\pi$
$463$	17.3925	+	17.3925i	0.808298	+	0.808298i	−0.176079	+	0.984376i	$0.556341\pi$
$464$	−8.97466			−0.416638
$465$	−6.22699	−	2.19761i	−0.288770	−	0.101912i
$466$	3.15084			0.145960
$467$	−9.40605	−	9.40605i	−0.435260	−	0.435260i	0.455153	−	0.890413i	$-0.349585\pi$
$467$	−9.40605	−	9.40605i	−0.435260	−	0.435260i	−0.890413	+	0.455153i	$0.849585\pi$
$468$	−8.26600	−	5.43734i	−0.382096	−	0.251341i
$469$			11.2024i			0.517280i
$470$	4.10427	+	11.4442i	0.189316	+	0.527880i
$471$	−16.5861	+	1.69400i	−0.764247	+	0.0780554i
$472$	3.95551	−	3.95551i	0.182067	−	0.182067i
$473$	−1.46575	+	1.46575i	−0.0673951	+	0.0673951i
$474$	22.4371	−	2.29159i	1.03057	−	0.105256i
$475$	4.19527	+	5.09667i	0.192492	+	0.233851i
$476$		−	0.857511i		−	0.0393039i
$477$	−12.4434	−	8.18522i	−0.569744	−	0.374776i
$478$	−1.14432	−	1.14432i	−0.0523402	−	0.0523402i
$479$	−38.8689			−1.77596			−0.887982	−	0.459879i	$-0.847893\pi$
$479$	−38.8689			−1.77596			−0.887982	+	0.459879i	$0.847893\pi$
$480$	6.41133	+	13.4048i	0.292636	+	0.611841i
$481$	11.1156			0.506829
$482$	−23.3216	−	23.3216i	−1.06227	−	1.06227i
$483$	8.70879	−	10.6901i	0.396264	−	0.486415i
$484$			11.5346i			0.524301i
$485$	4.13509	−	8.75957i	0.187765	−	0.397751i
$486$	−8.59872	−	15.4121i	−0.390046	−	0.699106i
$487$	23.9549	−	23.9549i	1.08550	−	1.08550i	0.0895148	−	0.995985i	$-0.471468\pi$
$487$	23.9549	−	23.9549i	1.08550	−	1.08550i	0.995985	−	0.0895148i	$-0.0285316\pi$
$488$	5.38612	−	5.38612i	0.243818	−	0.243818i
$489$	−2.18509	−	21.3944i	−0.0988131	−	0.967488i
$490$	1.08070	−	2.28931i	0.0488213	−	0.103420i
$491$		−	25.6453i		−	1.15736i	−0.815556	−	0.578678i	$-0.803569\pi$
$491$		−	25.6453i		−	1.15736i	0.815556	−	0.578678i	$-0.196431\pi$
$492$	1.75703	+	1.43139i	0.0792132	+	0.0645319i
$493$	3.70012	+	3.70012i	0.166645	+	0.166645i
$494$	−6.86355			−0.308806
$495$	−29.7873	+	18.1771i	−1.33884	+	0.817001i
$496$	−3.49129			−0.156764
$497$	−6.40892	−	6.40892i	−0.287479	−	0.287479i
$498$	11.7434	+	9.56694i	0.526236	+	0.428705i
$499$		−	29.1057i		−	1.30295i	−0.758669	−	0.651476i	$-0.774150\pi$
$499$		−	29.1057i		−	1.30295i	0.758669	−	0.651476i	$-0.225850\pi$
$500$	6.89668	+	4.11308i	0.308429	+	0.183942i
$501$	3.09896	+	30.3422i	0.138451	+	1.35559i
$502$	−9.92505	+	9.92505i	−0.442976	+	0.442976i
$503$	10.1763	−	10.1763i	0.453738	−	0.453738i	−0.442855	−	0.896593i	$-0.646035\pi$
$503$	10.1763	−	10.1763i	0.453738	−	0.453738i	0.896593	+	0.442855i	$0.146035\pi$
$504$	9.04173	−	1.86640i	0.402751	−	0.0831361i
$505$	2.80534	+	7.82229i	0.124836	+	0.348087i
$506$			46.8837i			2.08423i
$507$	8.84486	−	10.8571i	0.392814	−	0.482181i
$508$	3.27469	+	3.27469i	0.145291	+	0.145291i
$509$	−31.2970			−1.38721			−0.693607	−	0.720354i	$-0.743979\pi$
$509$	−31.2970			−1.38721			−0.693607	+	0.720354i	$0.743979\pi$
$510$	−1.74225	+	4.93672i	−0.0771481	+	0.218601i
$511$	1.89300			0.0837415
$512$	14.4671	+	14.4671i	0.639360	+	0.639360i
$513$	6.08479	+	3.16824i	0.268650	+	0.139881i
$514$		−	22.2100i		−	0.979641i
$515$	−3.37579	−	1.59360i	−0.148755	−	0.0702222i
$516$	0.493153	−	0.0503675i	0.0217098	−	0.00221731i
$517$	17.6651	−	17.6651i	0.776908	−	0.776908i
$518$	−1.93792	+	1.93792i	−0.0851474	+	0.0851474i
$519$	−33.6198	+	3.43371i	−1.47574	+	0.150723i
$520$	−29.7434	+	10.6670i	−1.30433	+	0.467780i
$521$		−	24.4644i		−	1.07180i	−0.844280	−	0.535902i	$-0.819972\pi$
$521$		−	24.4644i		−	1.07180i	0.844280	−	0.535902i	$-0.180028\pi$
$522$	−8.18078	+	12.4366i	−0.358063	+	0.544337i
$523$	1.82790	+	1.82790i	0.0799284	+	0.0799284i	0.745941	−	0.666012i	$-0.232000\pi$
$523$	1.82790	+	1.82790i	0.0799284	+	0.0799284i	−0.666012	+	0.745941i	$0.732000\pi$
$524$	−9.82422			−0.429173
$525$	6.09257	−	6.15472i	0.265901	−	0.268614i
$526$	−19.6796			−0.858069
$527$	1.43941	+	1.43941i	0.0627015	+	0.0627015i
$528$	−11.6528	+	14.3039i	−0.507123	+	0.622495i
$529$		−	40.3736i		−	1.75537i
$530$	−11.8307	+	4.24291i	−0.513894	+	0.184300i
$531$	−1.10240	−	5.34056i	−0.0478402	−	0.231761i
$532$	−0.670507	+	0.670507i	−0.0290701	+	0.0290701i
$533$	−5.91512	+	5.91512i	−0.256212	+	0.256212i
$534$	1.87909	+	18.3983i	0.0813160	+	0.796172i
$535$	−3.94659	−	1.86305i	−0.170626	−	0.0805467i
$536$			34.4749i			1.48909i
$537$	9.44237	+	7.69234i	0.407468	+	0.331949i
$538$	−15.3334	−	15.3334i	−0.661071	−	0.661071i
$539$	−5.20191			−0.224062
$540$	8.26834	+	1.12903i	0.355813	+	0.0485858i
$541$	41.8839			1.80073			0.900364	−	0.435137i	$-0.143300\pi$
$541$	41.8839			1.80073			0.900364	+	0.435137i	$0.143300\pi$
$542$	−14.7805	−	14.7805i	−0.634879	−	0.634879i
$543$	−19.0514	−	15.5205i	−0.817575	−	0.666047i
$544$		−	4.58061i		−	0.196392i
$545$	−4.48011	−	12.4921i	−0.191907	−	0.535104i
$546$	0.914892	+	8.95779i	0.0391538	+	0.383358i
$547$	−21.6813	+	21.6813i	−0.927024	+	0.927024i	−0.997513	−	0.0704885i	$-0.977544\pi$
$547$	−21.6813	+	21.6813i	−0.927024	+	0.927024i	0.0704885	+	0.997513i	$0.477544\pi$
$548$	−7.19893	+	7.19893i	−0.307523	+	0.307523i
$549$	−1.50111	−	7.27211i	−0.0640660	−	0.310366i
$550$	−2.84323	+	29.3092i	−0.121236	+	1.24975i
$551$		−	5.78641i		−	0.246509i
$552$	26.8009	−	32.8982i	1.14072	−	1.40024i
$553$	8.13280	+	8.13280i	0.345842	+	0.345842i
$554$	12.2657			0.521119
$555$	−8.45782	+	4.04527i	−0.359014	+	0.171712i
$556$	−11.3669			−0.482063
$557$	13.1204	+	13.1204i	0.555929	+	0.555929i	0.928146	−	0.372217i	$-0.121402\pi$
$557$	13.1204	+	13.1204i	0.555929	+	0.555929i	−0.372217	+	0.928146i	$0.621402\pi$
$558$	−3.18246	+	4.83806i	−0.134724	+	0.204811i
$559$			1.82978i			0.0773916i
$560$	1.95464	−	4.14060i	0.0825985	−	0.174972i
$561$	10.7015	−	1.09299i	0.451819	−	0.0461460i
$562$	16.3830	−	16.3830i	0.691076	−	0.691076i
$563$	−15.9166	+	15.9166i	−0.670804	+	0.670804i	−0.957901	−	0.287097i	$-0.907310\pi$
$563$	−15.9166	+	15.9166i	−0.670804	+	0.670804i	0.287097	+	0.957901i	$0.407310\pi$
$564$	−5.94344	+	0.607025i	−0.250264	+	0.0255604i
$565$	0.324884	−	0.688216i	0.0136680	−	0.0289535i
$566$		−	13.2016i		−	0.554903i
$567$	3.32386	−	8.36373i	0.139589	−	0.351244i
$568$	−19.7231	−	19.7231i	−0.827565	−	0.827565i
$569$	−27.8303			−1.16671			−0.583354	−	0.812218i	$-0.698260\pi$
$569$	−27.8303			−1.16671			−0.583354	+	0.812218i	$0.698260\pi$
$570$	5.22243	−	2.49782i	0.218744	−	0.104622i
$571$	−4.11555			−0.172230			−0.0861151	−	0.996285i	$-0.527445\pi$
$571$	−4.11555			−0.172230			−0.0861151	+	0.996285i	$0.527445\pi$
$572$	12.1311	+	12.1311i	0.507225	+	0.507225i
$573$	17.1151	−	21.0089i	0.714994	−	0.877658i
$574$		−	2.06251i		−	0.0860874i
$575$	3.84325	−	39.6178i	0.160275	−	1.65218i
$576$	24.7943	−	5.11805i	1.03310	−	0.213252i
$577$	−15.3143	+	15.3143i	−0.637542	+	0.637542i	−0.949949	−	0.312406i	$-0.898865\pi$
$577$	−15.3143	+	15.3143i	−0.637542	+	0.637542i	0.312406	+	0.949949i	$0.398865\pi$
$578$	−12.4683	+	12.4683i	−0.518611	+	0.518611i
$579$	−2.24231	−	21.9547i	−0.0931874	−	0.912406i
$580$	−2.37619	−	6.62564i	−0.0986657	−	0.275115i
$581$			7.72438i			0.320461i
$582$	−6.58590	−	5.36528i	−0.272994	−	0.222398i
$583$	18.2617	+	18.2617i	0.756324	+	0.756324i
$584$	5.82563			0.241066
$585$	−7.24686	+	29.9385i	−0.299621	+	1.23780i
$586$	31.5778			1.30447
$587$	23.2211	+	23.2211i	0.958439	+	0.958439i	0.999170	−	0.0407314i	$-0.0129688\pi$
$587$	23.2211	+	23.2211i	0.958439	+	0.958439i	−0.0407314	+	0.999170i	$0.512969\pi$
$588$	0.964471	+	0.785718i	0.0397741	+	0.0324025i
$589$		−	2.25101i		−	0.0927512i
$590$	−4.16132	−	1.96442i	−0.171319	−	0.0808737i
$591$	0.694342	+	6.79837i	0.0285614	+	0.279647i
$592$	−3.50506	+	3.50506i	−0.144057	+	0.144057i
$593$	24.2941	−	24.2941i	0.997641	−	0.997641i	−0.00235668	−	0.999997i	$-0.500750\pi$
$593$	24.2941	−	24.2941i	0.997641	−	0.997641i	0.999997	+	0.00235668i	$0.000750155\pi$
$594$	9.19956	+	29.1865i	0.377463	+	1.19754i
$595$	−2.51297	+	0.901239i	−0.103022	+	0.0369472i
$596$			6.68380i			0.273779i
$597$	−15.7881	+	19.3799i	−0.646164	+	0.793169i
$598$	29.2639	+	29.2639i	1.19669	+	1.19669i
$599$	22.7865			0.931029			0.465515	−	0.885040i	$-0.345869\pi$
$599$	22.7865			0.931029			0.465515	+	0.885040i	$0.345869\pi$
$600$	18.7496	−	18.9409i	0.765448	−	0.773258i
$601$	−41.7276			−1.70210			−0.851052	−	0.525082i	$-0.824035\pi$
$601$	−41.7276			−1.70210			−0.851052	+	0.525082i	$0.824035\pi$
$602$	−0.319008	−	0.319008i	−0.0130018	−	0.0130018i
$603$	28.0774	+	18.4692i	1.14340	+	0.752124i
$604$			12.0859i			0.491769i
$605$	33.8028	−	12.1228i	1.37428	−	0.492864i
$606$	7.24995	−	0.740464i	0.294509	−	0.0300793i
$607$	−17.5164	+	17.5164i	−0.710968	+	0.710968i	−0.966738	−	0.255770i	$-0.917671\pi$
$607$	−17.5164	+	17.5164i	−0.710968	+	0.710968i	0.255770	+	0.966738i	$0.417671\pi$
$608$	−3.58168	+	3.58168i	−0.145256	+	0.145256i
$609$	−7.55198	+	0.771312i	−0.306022	+	0.0312551i
$610$	−5.66636	−	2.67490i	−0.229424	−	0.108303i
$611$		−	22.0524i		−	0.892144i
$612$	−2.14923	−	1.41376i	−0.0868776	−	0.0571478i
$613$	−25.9860	−	25.9860i	−1.04956	−	1.04956i	−0.998706	−	0.0508591i	$-0.983804\pi$
$613$	−25.9860	−	25.9860i	−1.04956	−	1.04956i	−0.0508591	−	0.998706i	$-0.516196\pi$
$614$	21.2943			0.859369
$615$	2.34811	−	6.65345i	0.0946851	−	0.268293i
$616$	−16.0086			−0.645005
$617$	−8.12737	−	8.12737i	−0.327196	−	0.327196i	0.524323	−	0.851519i	$-0.324318\pi$
$617$	−8.12737	−	8.12737i	−0.327196	−	0.327196i	−0.851519	+	0.524323i	$0.824318\pi$
$618$	−2.06769	+	2.53810i	−0.0831747	+	0.102097i
$619$			7.20599i			0.289633i	0.989459	+	0.144817i	$0.0462592\pi$
$619$			7.20599i			0.289633i	−0.989459	+	0.144817i	$0.953741\pi$
$620$	−0.924375	−	2.57748i	−0.0371238	−	0.103514i
$621$	−12.4352	−	39.4519i	−0.499008	−	1.58315i
$622$	19.0571	−	19.0571i	0.764120	−	0.764120i
$623$	−6.66884	+	6.66884i	−0.267181	+	0.267181i
$624$	1.65474	+	16.2017i	0.0662424	+	0.648586i
$625$	4.80519	−	24.5339i	0.192208	−	0.981354i
$626$			30.3173i			1.21172i
$627$	−9.22241	−	7.51314i	−0.368307	−	0.300046i
$628$	−4.88860	−	4.88860i	−0.195077	−	0.195077i
$629$	2.89017			0.115238
$630$	−3.95611	−	6.48297i	−0.157615	−	0.258288i
$631$	−29.8770			−1.18938			−0.594692	−	0.803954i	$-0.702726\pi$
$631$	−29.8770			−1.18938			−0.594692	+	0.803954i	$0.702726\pi$
$632$	25.0283	+	25.0283i	0.995572	+	0.995572i
$633$	−16.0934	−	13.1107i	−0.639655	−	0.521102i
$634$		−	18.7216i		−	0.743530i
$635$	6.15494	−	13.0383i	0.244251	−	0.517409i
$636$	−0.627529	−	6.14419i	−0.0248831	−	0.243633i
$637$	−3.24693	+	3.24693i	−0.128648	+	0.128648i
$638$	18.2518	−	18.2518i	0.722597	−	0.722597i
$639$	−26.6293	+	5.49684i	−1.05344	+	0.217452i
$640$	1.79556	−	3.80361i	0.0709756	−	0.150351i
$641$		−	19.3661i		−	0.764917i	−0.923973	−	0.382458i	$-0.875078\pi$
$641$		−	19.3661i		−	0.764917i	0.923973	−	0.382458i	$-0.124922\pi$
$642$	−2.41731	+	2.96725i	−0.0954035	+	0.117108i
$643$	11.6091	+	11.6091i	0.457819	+	0.457819i	0.897939	−	0.440120i	$-0.145064\pi$
$643$	11.6091	+	11.6091i	0.457819	+	0.457819i	−0.440120	+	0.897939i	$0.645064\pi$
$644$	5.71764			0.225307
$645$	−0.665906	−	1.39227i	−0.0262200	−	0.0548206i
$646$	−1.78458			−0.0702135
$647$	10.6517	+	10.6517i	0.418760	+	0.418760i	0.884776	−	0.466016i	$-0.154311\pi$
$647$	10.6517	+	10.6517i	0.418760	+	0.418760i	−0.466016	+	0.884776i	$0.654311\pi$
$648$	10.2290	−	25.7390i	0.401834	−	1.01112i
$649$			9.45560i			0.371165i
$650$	16.5196	+	20.0689i	0.647950	+	0.787168i
$651$	−2.93785	+	0.300053i	−0.115143	+	0.0117600i
$652$	6.30580	−	6.30580i	0.246954	−	0.246954i
$653$	3.67307	−	3.67307i	0.143738	−	0.143738i	−0.631576	−	0.775314i	$-0.717592\pi$
$653$	3.67307	−	3.67307i	0.143738	−	0.143738i	0.775314	+	0.631576i	$0.217592\pi$
$654$	−11.5781	+	1.18251i	−0.452740	+	0.0462400i
$655$	10.3252	+	28.7903i	0.403439	+	1.12493i
$656$		−	3.73039i		−	0.145647i
$657$	3.12095	−	4.74456i	0.121760	−	0.185103i
$658$	3.84466	+	3.84466i	0.149880	+	0.149880i
$659$	45.6844			1.77961			0.889807	−	0.456338i	$-0.150839\pi$
$659$	45.6844			1.77961			0.889807	+	0.456338i	$0.150839\pi$
$660$	−13.6453	−	4.81564i	−0.531141	−	0.187449i
$661$	−21.8518			−0.849935			−0.424968	−	0.905209i	$-0.639715\pi$
$661$	−21.8518			−0.849935			−0.424968	+	0.905209i	$0.639715\pi$
$662$	9.27823	+	9.27823i	0.360609	+	0.360609i
$663$	5.99748	−	7.36192i	0.232923	−	0.285913i
$664$			23.7714i			0.922510i
$665$	2.66965	+	1.26025i	0.103525	+	0.0488704i
$666$	1.66213	+	8.05215i	0.0644062	+	0.312014i
$667$	−24.6714	+	24.6714i	−0.955279	+	0.955279i
$668$	−8.94308	+	8.94308i	−0.346018	+	0.346018i
$669$	3.03220	+	29.6886i	0.117232	+	1.14783i
$670$	26.6949	−	9.57373i	1.03132	−	0.369865i
$671$			12.8755i			0.497051i
$672$	5.15197	+	4.19712i	0.198742	+	0.161907i
$673$	12.1963	+	12.1963i	0.470132	+	0.470132i	0.901957	−	0.431825i	$-0.142130\pi$
$673$	12.1963	+	12.1963i	0.470132	+	0.470132i	−0.431825	+	0.901957i	$0.642130\pi$
$674$	8.74408			0.336809
$675$	−5.38130	−	25.4173i	−0.207126	−	0.978314i
$676$	5.80698			0.223345
$677$	−30.0858	−	30.0858i	−1.15629	−	1.15629i	−0.985267	−	0.171025i	$-0.945292\pi$
$677$	−30.0858	−	30.0858i	−1.15629	−	1.15629i	−0.171025	−	0.985267i	$-0.554708\pi$
$678$	−0.517437	−	0.421536i	−0.0198721	−	0.0161890i
$679$		−	4.33195i		−	0.166245i
$680$	−7.73356	+	2.77352i	−0.296568	+	0.106360i
$681$	1.03867	+	10.1697i	0.0398018	+	0.389703i
$682$	7.10027	−	7.10027i	0.271883	−	0.271883i
$683$	1.48486	−	1.48486i	0.0568166	−	0.0568166i	−0.678128	−	0.734944i	$-0.737208\pi$
$683$	1.48486	−	1.48486i	0.0568166	−	0.0568166i	0.734944	+	0.678128i	$0.237208\pi$
$684$	0.575084	+	2.78598i	0.0219889	+	0.106525i
$685$	28.6628	+	13.5308i	1.09515	+	0.516984i
$686$		−	1.13215i		−	0.0432258i
$687$	29.8330	−	36.6201i	1.13820	−	1.39714i
$688$	−0.576980	−	0.576980i	−0.0219972	−	0.0219972i
$689$	22.7973			0.868507
$690$	−32.9166	−	11.6168i	−1.25312	−	0.442246i
$691$	42.2833			1.60853			0.804267	−	0.594269i	$-0.202558\pi$
$691$	42.2833			1.60853			0.804267	+	0.594269i	$0.202558\pi$
$692$	−9.90912	−	9.90912i	−0.376688	−	0.376688i
$693$	−8.57627	+	13.0379i	−0.325785	+	0.495268i
$694$			32.3395i			1.22759i
$695$	11.9465	+	33.3111i	0.453157	+	1.26356i
$696$	−23.2409	+	2.37368i	−0.880943	+	0.0899740i
$697$	−1.53799	+	1.53799i	−0.0582553	+	0.0582553i
$698$	9.58647	−	9.58647i	0.362853	−	0.362853i
$699$	4.79544	−	0.489776i	0.181380	−	0.0185250i
$700$	3.57437	+	0.346743i	0.135098	+	0.0131056i
$701$			42.8399i			1.61804i	0.587781	+	0.809020i	$0.300002\pi$
$701$			42.8399i			1.61804i	−0.587781	+	0.809020i	$0.699998\pi$
$702$	23.9598	+	12.4755i	0.904306	+	0.470856i
$703$	−2.25988	−	2.25988i	−0.0852332	−	0.0852332i
$704$	−43.8989			−1.65450
$705$	8.02544	+	16.7795i	0.302255	+	0.631954i
$706$	−38.9746			−1.46683
$707$	2.62789	+	2.62789i	0.0988320	+	0.0988320i
$708$	1.42821	−	1.75314i	0.0536756	−	0.0658869i
$709$		−	21.7856i		−	0.818175i	−0.912495	−	0.409087i	$-0.865847\pi$
$709$		−	21.7856i		−	0.818175i	0.912495	−	0.409087i	$-0.134153\pi$
$710$	−9.79506	+	20.7493i	−0.367602	+	0.778708i
$711$	33.7921	−	6.97539i	1.26730	−	0.261598i
$712$	−20.5230	+	20.5230i	−0.769133	+	0.769133i
$713$	−9.59756	+	9.59756i	−0.359432	+	0.359432i
$714$	0.237880	+	2.32911i	0.00890244	+	0.0871646i
$715$	22.8009	−	48.3003i	0.852706	−	1.80633i
$716$			5.05030i			0.188739i
$717$	−1.91949	−	1.56373i	−0.0716846	−	0.0583987i
$718$	−11.3810	−	11.3810i	−0.424735	−	0.424735i
$719$	45.9617			1.71408			0.857041	−	0.515249i	$-0.172301\pi$
$719$	45.9617			1.71408			0.857041	+	0.515249i	$0.172301\pi$
$720$	−7.15528	−	11.7255i	−0.266662	−	0.436985i
$721$	−1.66946			−0.0621740
$722$	−13.8151	−	13.8151i	−0.514145	−	0.514145i
$723$	−39.1196	−	31.8693i	−1.45487	−	1.18523i
$724$		−	10.1898i		−	0.378699i
$725$	−16.9194	+	13.9270i	−0.628371	+	0.517237i
$726$	−3.19980	−	31.3295i	−0.118756	−	1.16275i
$727$	−4.37251	+	4.37251i	−0.162168	+	0.162168i	−0.783526	−	0.621359i	$-0.786581\pi$
$727$	−4.37251	+	4.37251i	−0.162168	+	0.162168i	0.621359	+	0.783526i	$0.286581\pi$
$728$	−9.99228	+	9.99228i	−0.370338	+	0.370338i
$729$	−15.4826	−	22.1199i	−0.573428	−	0.819256i
$730$	−1.61778	−	4.51095i	−0.0598768	−	0.166958i
$731$			0.475760i			0.0175966i
$732$	1.94476	−	2.38720i	0.0718805	−	0.0882336i
$733$	−32.0267	−	32.0267i	−1.18293	−	1.18293i	−0.978981	−	0.203952i	$-0.934621\pi$
$733$	−32.0267	−	32.0267i	−1.18293	−	1.18293i	−0.203952	−	0.978981i	$-0.565379\pi$
$734$	−26.7423			−0.987078
$735$	1.28893	−	3.65221i	0.0475428	−	0.134714i
$736$	30.5423			1.12580
$737$	−41.2059	−	41.2059i	−1.51784	−	1.51784i
$738$	−5.16940	−	3.40041i	−0.190288	−	0.125171i
$739$		−	19.8100i		−	0.728722i	−0.931258	−	0.364361i	$-0.881287\pi$
$739$		−	19.8100i		−	0.728722i	0.931258	−	0.364361i	$-0.118713\pi$
$740$	−3.51567	−	1.65963i	−0.129239	−	0.0610092i
$741$	−10.4460	+	1.06689i	−0.383744	+	0.0391932i
$742$	−3.97452	+	3.97452i	−0.145909	+	0.145909i
$743$	14.6828	−	14.6828i	0.538660	−	0.538660i	−0.384475	−	0.923135i	$-0.625618\pi$
$743$	14.6828	−	14.6828i	0.538660	−	0.538660i	0.923135	+	0.384475i	$0.125618\pi$
$744$	−9.04108	+	0.923399i	−0.331462	+	0.0338535i
$745$	19.5872	−	7.02464i	0.717619	−	0.257363i
$746$		−	7.33110i		−	0.268411i
$747$	19.3601	+	12.7350i	0.708350	+	0.465950i
$748$	3.15418	+	3.15418i	0.115328	+	0.115328i
$749$	−1.95174			−0.0713151
$750$	−19.8732	−	9.25844i	−0.725668	−	0.338070i
$751$	−26.6832			−0.973682			−0.486841	−	0.873491i	$-0.661851\pi$
$751$	−26.6832			−0.973682			−0.486841	+	0.873491i	$0.661851\pi$
$752$	6.95371	+	6.95371i	0.253576	+	0.253576i
$753$	−13.5627	+	16.6483i	−0.494252	+	0.606696i
$754$		−	22.7849i		−	0.829777i
$755$	35.4184	−	12.7023i	1.28901	−	0.462282i
$756$	3.55940	−	1.12192i	0.129454	−	0.0408039i
$757$	−4.11078	+	4.11078i	−0.149409	+	0.149409i	−0.777854	−	0.628445i	$-0.783692\pi$
$757$	−4.11078	+	4.11078i	−0.149409	+	0.149409i	0.628445	+	0.777854i	$0.283692\pi$
$758$	−10.1275	+	10.1275i	−0.367846	+	0.367846i
$759$	7.28774	+	71.3549i	0.264528	+	2.59002i
$760$	8.21572	+	3.87836i	0.298015	+	0.140683i
$761$		−	22.2859i		−	0.807862i	−0.914789	−	0.403931i	$-0.867644\pi$
$761$		−	22.2859i		−	0.807862i	0.914789	−	0.403931i	$-0.132356\pi$
$762$	−9.80288	−	7.98603i	−0.355121	−	0.289303i
$763$	−4.19672	−	4.19672i	−0.151931	−	0.151931i
$764$	11.2367			0.406530
$765$	−1.88425	+	7.78428i	−0.0681252	+	0.281441i
$766$	28.8464			1.04226
$767$	5.90201	+	5.90201i	0.213109	+	0.213109i
$768$	19.8048	+	16.1342i	0.714645	+	0.582194i
$769$			37.7021i			1.35957i	0.733410	+	0.679786i	$0.237927\pi$
$769$			37.7021i			1.35957i	−0.733410	+	0.679786i	$0.762073\pi$
$770$	4.44561	+	12.3959i	0.160209	+	0.446718i
$771$	−3.45239	−	33.8026i	−0.124335	−	1.21737i
$772$	6.47095	−	6.47095i	0.232895	−	0.232895i
$773$	−20.5564	+	20.5564i	−0.739362	+	0.739362i	−0.972455	−	0.233093i	$-0.925116\pi$
$773$	−20.5564	+	20.5564i	−0.739362	+	0.739362i	0.233093	+	0.972455i	$0.425116\pi$
$774$	−1.32549	+	0.273609i	−0.0476438	+	0.00983467i
$775$	−6.58192	+	5.41785i	−0.236430	+	0.194615i
$776$		−	13.3314i		−	0.478568i
$777$	−2.64820	+	3.25067i	−0.0950035	+	0.116617i
$778$	−14.1870	−	14.1870i	−0.508630	−	0.508630i
$779$	2.40517			0.0861741
$780$	−11.5229	+	5.51128i	−0.412587	+	0.197335i
$781$	47.1479			1.68708
$782$	7.60888	+	7.60888i	0.272093	+	0.272093i
$783$	−10.5176	+	20.1997i	−0.375868	+	0.721877i
$784$		−	2.04769i		−	0.0731318i
$785$	−9.18838	+	19.4642i	−0.327947	+	0.694706i
$786$	26.6838	−	2.72531i	0.951779	−	0.0972088i
$787$	9.45113	−	9.45113i	0.336896	−	0.336896i	−0.518302	−	0.855198i	$-0.673436\pi$
$787$	9.45113	−	9.45113i	0.336896	−	0.336896i	0.855198	+	0.518302i	$0.173436\pi$
$788$	−2.00376	+	2.00376i	−0.0713809	+	0.0713809i
$789$	−29.9514	+	3.05905i	−1.06630	+	0.108905i
$790$	12.4297	−	26.3305i	0.442230	−	0.936797i
$791$		−	0.340350i		−	0.0121015i
$792$	−26.3930	+	40.1234i	−0.937836	+	1.42572i
$793$	8.03662	+	8.03662i	0.285389	+	0.285389i
$794$	−7.09346			−0.251737
$795$	−17.3463	+	8.29652i	−0.615210	+	0.294247i
$796$	−10.3655			−0.367394
$797$	−5.16008	−	5.16008i	−0.182779	−	0.182779i	0.609786	−	0.792566i	$-0.291255\pi$
$797$	−5.16008	−	5.16008i	−0.182779	−	0.182779i	−0.792566	+	0.609786i	$0.791255\pi$
$798$	1.63518	−	2.00718i	0.0578846	−	0.0710535i
$799$		−	5.73382i		−	0.202848i
$800$	19.0934	+	1.85221i	0.675053	+	0.0654857i
$801$	5.71977	+	27.7093i	0.202098	+	0.979060i
$802$	−27.6015	+	27.6015i	−0.974641	+	0.974641i
$803$	−6.96304	+	6.96304i	−0.245720	+	0.245720i
$804$	1.41596	+	13.8638i	0.0499371	+	0.488939i
$805$	−6.00921	−	16.7558i	−0.211797	−	0.590565i
$806$		−	8.86371i		−	0.312211i
$807$	−25.7203	−	20.9533i	−0.905396	−	0.737592i
$808$	8.08721	+	8.08721i	0.284507	+	0.284507i
$809$	−12.8615			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$809$	−12.8615			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$810$	−22.7710	−	0.772890i	−0.800093	−	0.0271566i
$811$	0.485057			0.0170327			0.00851633	−	0.999964i	$-0.497289\pi$
$811$	0.485057			0.0170327			0.00851633	+	0.999964i	$0.497289\pi$
$812$	−2.22588	−	2.22588i	−0.0781131	−	0.0781131i
$813$	−24.7929	−	20.1978i	−0.869524	−	0.708368i
$814$		−	14.2565i		−	0.499691i
$815$	−25.1068	−	11.8521i	−0.879454	−	0.415160i
$816$	0.430246	+	4.21258i	0.0150616	+	0.147470i
$817$	0.372008	−	0.372008i	0.0130149	−	0.0130149i
$818$	15.6638	−	15.6638i	0.547673	−	0.547673i
$819$	2.78485	+	13.4911i	0.0973105	+	0.471419i
$820$	2.75401	−	0.987682i	0.0961740	−	0.0344913i
$821$			28.1679i			0.983066i	0.870859	+	0.491533i	$0.163563\pi$
$821$			28.1679i			0.983066i	−0.870859	+	0.491533i	$0.836437\pi$
$822$	17.5562	−	21.5502i	0.612341	−	0.751651i
$823$	7.62024	+	7.62024i	0.265625	+	0.265625i	0.827334	−	0.561710i	$-0.189856\pi$
$823$	7.62024	+	7.62024i	0.265625	+	0.265625i	−0.561710	+	0.827334i	$0.689856\pi$
$824$	−5.13769			−0.178980
$825$	0.228637	+	45.0492i	0.00796012	+	1.56841i
$826$	−2.05794			−0.0716047
$827$	−24.0314	−	24.0314i	−0.835652	−	0.835652i	0.152631	−	0.988283i	$-0.451225\pi$
$827$	−24.0314	−	24.0314i	−0.835652	−	0.835652i	−0.988283	+	0.152631i	$0.951225\pi$
$828$	9.42655	−	14.3305i	0.327595	−	0.498019i
$829$			18.7082i			0.649763i	0.945755	+	0.324881i	$0.105324\pi$
$829$			18.7082i			0.649763i	−0.945755	+	0.324881i	$0.894676\pi$
$830$	18.4069	−	6.60135i	0.638912	−	0.229136i
$831$	18.6678	−	1.90661i	0.647580	−	0.0661397i
$832$	−27.4009	+	27.4009i	−0.949954	+	0.949954i
$833$	−0.844232	+	0.844232i	−0.0292509	+	0.0292509i
$834$	30.8738	−	3.15326i	1.06907	−	0.109188i
$835$	35.6073	+	16.8090i	1.23224	+	0.581699i
$836$		−	4.93265i		−	0.170599i
$837$	−4.09152	+	7.85801i	−0.141424	+	0.271612i
$838$	−13.6261	−	13.6261i	−0.470706	−	0.470706i
$839$	1.64172			0.0566785			0.0283392	−	0.999598i	$-0.490978\pi$
$839$	1.64172			0.0566785			0.0283392	+	0.999598i	$0.490978\pi$
$840$	3.96661	−	11.2395i	0.136861	−	0.387800i
$841$	−9.79087			−0.337616
$842$	−17.4099	−	17.4099i	−0.599986	−	0.599986i
$843$	22.3876	−	27.4809i	0.771070	−	0.946491i
$844$		−	8.60763i		−	0.296287i
$845$	−6.10310	−	17.0176i	−0.209953	−	0.585424i
$846$	15.9747	−	3.29751i	0.549222	−	0.113371i
$847$	11.3560	−	11.3560i	0.390197	−	0.390197i
$848$	−7.18859	+	7.18859i	−0.246857	+	0.246857i
$849$	−2.05209	−	20.0922i	−0.0704276	−	0.689563i
$850$	4.29523	+	5.21811i	0.147325	+	0.178980i
$851$			19.2708i			0.660595i
$852$	−8.74156	−	7.12142i	−0.299481	−	0.243976i
$853$	3.77850	+	3.77850i	0.129373	+	0.129373i	0.768828	−	0.639455i	$-0.220840\pi$
$853$	3.77850	+	3.77850i	0.129373	+	0.129373i	−0.639455	+	0.768828i	$0.720840\pi$
$854$	−2.80224			−0.0958907
$855$	7.56004	−	4.61337i	0.258548	−	0.157774i
$856$	−6.00639			−0.205294
$857$	8.38908	+	8.38908i	0.286566	+	0.286566i	0.835721	−	0.549155i	$-0.185050\pi$
$857$	8.38908	+	8.38908i	0.286566	+	0.286566i	−0.549155	+	0.835721i	$0.685050\pi$
$858$	−36.3147	−	29.5842i	−1.23976	−	1.00999i
$859$			12.4393i			0.424424i	0.977224	+	0.212212i	$0.0680668\pi$
$859$			12.4393i			0.424424i	−0.977224	+	0.212212i	$0.931933\pi$
$860$	0.273197	−	0.578727i	0.00931595	−	0.0197344i
$861$	−0.320602	−	3.13905i	−0.0109261	−	0.106978i
$862$	−8.63896	+	8.63896i	−0.294244	+	0.294244i
$863$	8.43057	−	8.43057i	0.286980	−	0.286980i	−0.548905	−	0.835885i	$-0.684955\pi$
$863$	8.43057	−	8.43057i	0.286980	−	0.286980i	0.835885	+	0.548905i	$0.184955\pi$
$864$	19.0134	−	5.99303i	0.646851	−	0.203887i
$865$	−18.6247	+	39.4536i	−0.633259	+	1.34146i
$866$		−	0.747600i		−	0.0254045i
$867$	−17.0380	+	20.9142i	−0.578642	+	0.710285i
$868$	−0.865904	−	0.865904i	−0.0293907	−	0.0293907i
$869$	−59.8298			−2.02959
$870$	8.29202	+	17.3369i	0.281126	+	0.587776i
$871$	−51.4399			−1.74298
$872$	−12.9152	−	12.9152i	−0.437364	−	0.437364i
$873$	−10.8574	−	7.14199i	−0.367469	−	0.241720i
$874$		−	11.8991i		−	0.402493i
$875$	−2.74050	−	10.8393i	−0.0926457	−	0.366434i
$876$	2.34273	−	0.239271i	0.0791534	−	0.00808423i
$877$	−2.56130	+	2.56130i	−0.0864889	+	0.0864889i	−0.749028	−	0.662539i	$-0.769479\pi$
$877$	−2.56130	+	2.56130i	−0.0864889	+	0.0864889i	0.662539	+	0.749028i	$0.269479\pi$
$878$	−7.55451	+	7.55451i	−0.254953	+	0.254953i
$879$	48.0600	−	4.90854i	1.62102	−	0.165561i
$880$	8.04063	+	22.4201i	0.271050	+	0.755782i
$881$			16.9744i			0.571882i	0.958247	+	0.285941i	$0.0923061\pi$
$881$			16.9744i			0.571882i	−0.958247	+	0.285941i	$0.907694\pi$
$882$	−2.83759	−	1.86656i	−0.0955466	−	0.0628502i
$883$	21.2023	+	21.2023i	0.713513	+	0.713513i	0.967268	−	0.253756i	$-0.0816660\pi$
$883$	21.2023	+	21.2023i	0.713513	+	0.713513i	−0.253756	+	0.967268i	$0.581666\pi$
$884$	3.93756			0.132435
$885$	−6.63869	−	2.34291i	−0.223157	−	0.0787560i
$886$	27.0517			0.908818
$887$	12.5527	+	12.5527i	0.421480	+	0.421480i	0.885713	−	0.464233i	$-0.153670\pi$
$887$	12.5527	+	12.5527i	0.421480	+	0.421480i	−0.464233	+	0.885713i	$0.653670\pi$
$888$	−8.14969	+	10.0038i	−0.273486	+	0.335705i
$889$		−	6.44795i		−	0.216257i
$890$	21.5908	+	10.1923i	0.723726	+	0.341647i
$891$	18.5382	+	42.9905i	0.621051	+	1.44024i
$892$	−8.75044	+	8.75044i	−0.292986	+	0.292986i
$893$	−4.48340	+	4.48340i	−0.150031	+	0.150031i
$894$	−1.85414	−	18.1540i	−0.0620116	−	0.607161i
$895$	14.8001	−	5.30784i	0.494714	−	0.177422i
$896$		−	1.88104i		−	0.0628410i
$897$	49.0873	+	39.9895i	1.63898	+	1.33521i
$898$	−9.25783	−	9.25783i	−0.308938	−	0.308938i
$899$	7.47267			0.249227
$900$	6.76204	−	8.38699i	0.225401	−	0.279566i
$901$	5.92750			0.197474
$902$	7.58653	+	7.58653i	0.252604	+	0.252604i
$903$	−0.535104	−	0.435929i	−0.0178071	−	0.0145068i
$904$		−	1.04741i		−	0.0348364i
$905$	−29.8615	+	10.7094i	−0.992631	+	0.355992i
$906$	−3.35273	−	32.8269i	−0.111387	−	1.09060i
$907$	−8.60959	+	8.60959i	−0.285877	+	0.285877i	−0.835447	−	0.549571i	$-0.814791\pi$
$907$	−8.60959	+	8.60959i	−0.285877	+	0.285877i	0.549571	+	0.835447i	$0.314791\pi$
$908$	−2.99742	+	2.99742i	−0.0994728	+	0.0994728i
$909$	10.9190	−	2.25391i	0.362160	−	0.0747574i
$910$	10.5122	+	4.96244i	0.348475	+	0.164503i
$911$		−	23.0151i		−	0.762525i	−0.924467	−	0.381263i	$-0.875489\pi$
$911$		−	23.0151i		−	0.762525i	0.924467	−	0.381263i	$-0.124511\pi$
$912$	2.95749	−	3.63033i	0.0979323	−	0.120212i
$913$	−28.4126	−	28.4126i	−0.940320	−	0.940320i
$914$	28.5658			0.944872
$915$	−9.03975	−	3.19028i	−0.298845	−	0.105467i
$916$	19.5865			0.647155
$917$	9.67209	+	9.67209i	0.319400	+	0.319400i
$918$	6.22977	+	3.24373i	0.205613	+	0.107059i
$919$		−	22.0977i		−	0.728935i	−0.931216	−	0.364468i	$-0.881251\pi$
$919$		−	22.0977i		−	0.728935i	0.931216	−	0.364468i	$-0.118749\pi$
$920$	−18.4931	−	51.5652i	−0.609698	−	1.70005i
$921$	32.4090	−	3.31005i	1.06791	−	0.109070i
$922$	10.4529	−	10.4529i	0.344248	−	0.344248i
$923$	29.4288	−	29.4288i	0.968662	−	0.968662i
$924$	−6.43773	+	0.657509i	−0.211786	+	0.0216305i
$925$	−1.16867	+	12.0471i	−0.0384255	+	0.396106i
$926$		−	27.8472i		−	0.915117i
$927$	−2.75240	+	4.18428i	−0.0904008	+	0.137430i
$928$	−11.8901	−	11.8901i	−0.390312	−	0.390312i
$929$	51.7684			1.69846			0.849232	−	0.528019i	$-0.177065\pi$
$929$	51.7684			1.69846			0.849232	+	0.528019i	$0.177065\pi$
$930$	3.22573	+	6.74434i	0.105776	+	0.221156i
$931$	1.32025			0.0432693
$932$	1.41341	+	1.41341i	0.0462979	+	0.0462979i
$933$	26.0418	−	31.9663i	0.852569	−	1.04653i
$934$			15.0601i			0.492781i
$935$	5.92845	−	12.5585i	0.193881	−	0.410707i
$936$	8.57024	+	41.5183i	0.280127	+	1.35707i
$937$	32.8470	−	32.8470i	1.07307	−	1.07307i	0.0759541	−	0.997111i	$-0.475800\pi$
$937$	32.8470	−	32.8470i	1.07307	−	1.07307i	0.997111	−	0.0759541i	$-0.0242002\pi$
$938$	8.96814	−	8.96814i	0.292820	−	0.292820i
$939$	4.71262	+	46.1417i	0.153790	+	1.50578i
$940$	−3.29255	+	6.97476i	−0.107391	+	0.227492i
$941$		−	15.0930i		−	0.492018i	−0.969268	−	0.246009i	$-0.920881\pi$
$941$		−	15.0930i		−	0.492018i	0.969268	−	0.246009i	$-0.0791193\pi$
$942$	14.6342	+	11.9219i	0.476808	+	0.388437i
$943$	−10.2549	−	10.2549i	−0.333944	−	0.333944i
$944$	−3.72212			−0.121145
$945$	−7.02875	−	9.25185i	−0.228645	−	0.300963i
$946$	2.34682			0.0763016
$947$	27.9272	+	27.9272i	0.907512	+	0.907512i	0.996071	−	0.0885587i	$-0.0282261\pi$
$947$	27.9272	+	27.9272i	0.907512	+	0.907512i	−0.0885587	+	0.996071i	$0.528226\pi$
$948$	11.0929	+	9.03695i	0.360280	+	0.293506i
$949$			8.69240i			0.282167i
$950$	0.721614	−	7.43869i	0.0234122	−	0.241343i
$951$	−2.91014	−	28.4934i	−0.0943678	−	0.923963i
$952$	−2.59808	+	2.59808i	−0.0842043	+	0.0842043i
$953$	−11.2553	+	11.2553i	−0.364595	+	0.364595i	−0.865501	−	0.500906i	$-0.833000\pi$
$953$	−11.2553	+	11.2553i	−0.364595	+	0.364595i	0.500906	+	0.865501i	$0.333000\pi$
$954$	3.40889	+	16.5143i	0.110367	+	0.534670i
$955$	−11.8097	−	32.9297i	−0.382153	−	1.06558i
$956$		−	1.02665i		−	0.0332042i
$957$	24.9414	−	30.6156i	0.806240	−	0.989662i
$958$	31.1166	+	31.1166i	1.00533	+	1.00533i
$959$	14.1749			0.457732
$960$	10.8773	−	30.8210i	0.351062	−	0.994745i
$961$	−28.0930			−0.906226
$962$	−8.89866	−	8.89866i	−0.286904	−	0.286904i
$963$	−3.21779	+	4.89178i	−0.103692	+	0.157635i
$964$		−	20.9233i		−	0.673896i
$965$	−25.7643	−	12.1625i	−0.829384	−	0.391524i
$966$	−15.5298	+	1.58612i	−0.499664	+	0.0510325i
$967$	21.6914	−	21.6914i	0.697548	−	0.697548i	−0.266333	−	0.963881i	$-0.585812\pi$
$967$	21.6914	−	21.6914i	0.697548	−	0.697548i	0.963881	+	0.266333i	$0.0858122\pi$
$968$	34.9476	−	34.9476i	1.12326	−	1.12326i
$969$	−2.71606	+	0.277401i	−0.0872524	+	0.00891141i
$970$	−10.3229	+	3.70214i	−0.331447	+	0.118868i
$971$			57.5902i			1.84816i	0.382201	+	0.924079i	$0.375166\pi$
$971$			57.5902i			1.84816i	−0.382201	+	0.924079i	$0.624834\pi$
$972$	3.05636	−	10.7708i	0.0980328	−	0.345475i
$973$	11.1908	+	11.1908i	0.358762	+	0.358762i
$974$	−38.3544			−1.22895
$975$	28.2616	+	27.9762i	0.905096	+	0.895955i
$976$	−5.06832			−0.162233
$977$	7.49722	+	7.49722i	0.239857	+	0.239857i	0.816791	−	0.576934i	$-0.195751\pi$
$977$	7.49722	+	7.49722i	0.239857	+	0.239857i	−0.576934	+	0.816791i	$0.695751\pi$
$978$	−15.3781	+	18.8766i	−0.491736	+	0.603608i
$979$		−	49.0600i		−	1.56796i
$980$	1.51173	−	0.542159i	0.0482904	−	0.0173186i
$981$	−17.4375	+	3.59947i	−0.556738	+	0.114922i
$982$	−20.5304	+	20.5304i	−0.655152	+	0.655152i
$983$	1.92238	−	1.92238i	0.0613143	−	0.0613143i	−0.675785	−	0.737099i	$-0.736195\pi$
$983$	1.92238	−	1.92238i	0.0613143	−	0.0613143i	0.737099	+	0.675785i	$0.236195\pi$
$984$	−0.986639	−	9.66026i	−0.0314529	−	0.307958i
$985$	7.97804	+	3.76616i	0.254202	+	0.120000i
$986$		−	5.92428i		−	0.188668i
$987$	6.44903	+	5.25377i	0.205275	+	0.167229i
$988$	−3.07887	−	3.07887i	−0.0979519	−	0.0979519i
$989$	−3.17224			−0.100871
$990$	38.3981	+	9.29458i	1.22037	+	0.295401i
$991$	−31.7442			−1.00839			−0.504194	−	0.863591i	$-0.668210\pi$
$991$	−31.7442			−1.00839			−0.504194	+	0.863591i	$0.668210\pi$
$992$	−4.62545	−	4.62545i	−0.146858	−	0.146858i
$993$	15.5633	+	12.6788i	0.493886	+	0.402350i
$994$			10.2614i			0.325471i
$995$	10.8941	+	30.3765i	0.345365	+	0.962999i
$996$	0.976344	+	9.55947i	0.0309366	+	0.302903i
$997$	12.7289	−	12.7289i	0.403128	−	0.403128i	−0.476206	−	0.879334i	$-0.657988\pi$
$997$	12.7289	−	12.7289i	0.403128	−	0.403128i	0.879334	+	0.476206i	$0.157988\pi$
$998$	−23.3007	+	23.3007i	−0.737571	+	0.737571i
$999$	3.78134	+	11.9966i	0.119636	+	0.379557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.j.a.8.4	✓	24
3.2	odd	2	inner	105.2.j.a.8.9	yes	24
5.2	odd	4	inner	105.2.j.a.92.9	yes	24
5.3	odd	4		525.2.j.b.407.4		24
5.4	even	2		525.2.j.b.218.9		24
7.2	even	3		735.2.y.j.263.4		48
7.3	odd	6		735.2.y.g.128.9		48
7.4	even	3		735.2.y.j.128.9		48
7.5	odd	6		735.2.y.g.263.4		48
7.6	odd	2		735.2.j.h.638.4		24
15.2	even	4	inner	105.2.j.a.92.4	yes	24
15.8	even	4		525.2.j.b.407.9		24
15.14	odd	2		525.2.j.b.218.4		24
21.2	odd	6		735.2.y.j.263.9		48
21.5	even	6		735.2.y.g.263.9		48
21.11	odd	6		735.2.y.j.128.4		48
21.17	even	6		735.2.y.g.128.4		48
21.20	even	2		735.2.j.h.638.9		24
35.2	odd	12		735.2.y.j.557.4		48
35.12	even	12		735.2.y.g.557.4		48
35.17	even	12		735.2.y.g.422.9		48
35.27	even	4		735.2.j.h.197.9		24
35.32	odd	12		735.2.y.j.422.9		48
105.2	even	12		735.2.y.j.557.9		48
105.17	odd	12		735.2.y.g.422.4		48
105.32	even	12		735.2.y.j.422.4		48
105.47	odd	12		735.2.y.g.557.9		48
105.62	odd	4		735.2.j.h.197.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.4	✓	24	1.1	even	1	trivial
105.2.j.a.8.9	yes	24	3.2	odd	2	inner
105.2.j.a.92.4	yes	24	15.2	even	4	inner
105.2.j.a.92.9	yes	24	5.2	odd	4	inner
525.2.j.b.218.4		24	15.14	odd	2
525.2.j.b.218.9		24	5.4	even	2
525.2.j.b.407.4		24	5.3	odd	4
525.2.j.b.407.9		24	15.8	even	4
735.2.j.h.197.4		24	105.62	odd	4
735.2.j.h.197.9		24	35.27	even	4
735.2.j.h.638.4		24	7.6	odd	2
735.2.j.h.638.9		24	21.20	even	2
735.2.y.g.128.4		48	21.17	even	6
735.2.y.g.128.9		48	7.3	odd	6
735.2.y.g.263.4		48	7.5	odd	6
735.2.y.g.263.9		48	21.5	even	6
735.2.y.g.422.4		48	105.17	odd	12
735.2.y.g.422.9		48	35.17	even	12
735.2.y.g.557.4		48	35.12	even	12
735.2.y.g.557.9		48	105.47	odd	12
735.2.y.j.128.4		48	21.11	odd	6
735.2.y.j.128.9		48	7.4	even	3
735.2.y.j.263.4		48	7.2	even	3
735.2.y.j.263.9		48	21.2	odd	6
735.2.y.j.422.4		48	105.32	even	12
735.2.y.j.422.9		48	35.32	odd	12
735.2.y.j.557.4		48	35.2	odd	12
735.2.y.j.557.9		48	105.2	even	12

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.800553 - 0.800553i) q^{2} +(-1.34285 - 1.09397i) q^{3} -0.718229i q^{4} +(-2.10480 + 0.754855i) q^{5} +(0.199242 + 1.95080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +O(q^{10})\)	\(q+(-0.800553 - 0.800553i) q^{2} +(-1.34285 - 1.09397i) q^{3} -0.718229i q^{4} +(-2.10480 + 0.754855i) q^{5} +(0.199242 + 1.95080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.17609 + 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +(2.28931 + 1.08070i) q^{10} -5.20191i q^{11} +(-0.785718 + 0.964471i) q^{12} +(-3.24693 - 3.24693i) q^{13} +1.13215 q^{14} +(3.65221 + 1.28893i) q^{15} +2.04769 q^{16} +(-0.844232 - 0.844232i) q^{17} +(1.86656 - 2.83759i) q^{18} +1.32025i q^{19} +(0.542159 + 1.51173i) q^{20} +(1.72309 - 0.175985i) q^{21} +(-4.16440 + 4.16440i) q^{22} +(5.62910 - 5.62910i) q^{23} +(5.30272 - 0.541586i) q^{24} +(3.86039 - 3.17764i) q^{25} +5.19868i q^{26} +(2.39973 - 4.60883i) q^{27} +(0.507864 + 0.507864i) q^{28} -4.38282 q^{29} +(-1.89194 - 3.95565i) q^{30} -1.70499 q^{31} +(2.71289 + 2.71289i) q^{32} +(-5.69071 + 6.98536i) q^{33} +1.35170i q^{34} +(0.954557 - 2.02208i) q^{35} +(2.11020 - 0.435588i) q^{36} +(-1.71171 + 1.71171i) q^{37} +(1.05693 - 1.05693i) q^{38} +(0.808099 + 7.91217i) q^{39} +(2.93760 - 6.22286i) q^{40} -1.82176i q^{41} +(-1.52031 - 1.23854i) q^{42} +(-0.281771 - 0.281771i) q^{43} -3.73616 q^{44} +(-3.49432 - 5.72623i) q^{45} -9.01279 q^{46} +(3.39588 + 3.39588i) q^{47} +(-2.74973 - 2.24010i) q^{48} -1.00000i q^{49} +(-5.63432 - 0.546575i) q^{50} +(0.210113 + 2.05723i) q^{51} +(-2.33204 + 2.33204i) q^{52} +(-3.51059 + 3.51059i) q^{53} +(-5.61073 + 1.76850i) q^{54} +(3.92668 + 10.9490i) q^{55} -3.07745i q^{56} +(1.44431 - 1.77289i) q^{57} +(3.50868 + 3.50868i) q^{58} -1.81772 q^{59} +(0.925745 - 2.62313i) q^{60} -2.47514 q^{61} +(1.36494 + 1.36494i) q^{62} +(-2.50636 - 1.64868i) q^{63} -8.43900i q^{64} +(9.28511 + 4.38319i) q^{65} +(10.1479 - 1.03644i) q^{66} +(7.92132 - 7.92132i) q^{67} +(-0.606352 + 0.606352i) q^{68} +(-13.7171 + 1.40098i) q^{69} +(-2.38296 + 0.854612i) q^{70} +9.06358i q^{71} +(-7.71322 - 5.07373i) q^{72} +(-1.33856 - 1.33856i) q^{73} +2.74064 q^{74} +(-8.66014 + 0.0439525i) q^{75} +0.948239 q^{76} +(3.67830 + 3.67830i) q^{77} +(5.68718 - 6.98104i) q^{78} -11.5015i q^{79} +(-4.30998 + 1.54571i) q^{80} +(-8.26437 + 3.56372i) q^{81} +(-1.45841 + 1.45841i) q^{82} +(5.46196 - 5.46196i) q^{83} +(-0.126398 - 1.23757i) q^{84} +(2.41421 + 1.13967i) q^{85} +0.451146i q^{86} +(5.88546 + 4.79466i) q^{87} +(11.3198 + 11.3198i) q^{88} +9.43116 q^{89} +(-1.78676 + 7.38154i) q^{90} +4.59186 q^{91} +(-4.04298 - 4.04298i) q^{92} +(2.28954 + 1.86520i) q^{93} -5.43717i q^{94} +(-0.996595 - 2.77886i) q^{95} +(-0.675186 - 6.61080i) q^{96} +(-3.06315 + 3.06315i) q^{97} +(-0.800553 + 0.800553i) q^{98} +(15.2835 - 3.15483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more