LMFDB - Embedded newform 465.2.k.b.32.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(32,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, 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("465.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.14
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.195513 + 0.195513i) q^{2} +(-1.67938 + 0.423882i) q^{3} +1.92355i q^{4} +(2.09279 - 0.787555i) q^{5} +(0.245466 - 0.411215i) q^{6} +(-2.75743 - 2.75743i) q^{7} +(-0.767103 - 0.767103i) q^{8} +(2.64065 - 1.42372i) q^{9} +O(q^{10})$	\(q+(-0.195513 + 0.195513i) q^{2} +(-1.67938 + 0.423882i) q^{3} +1.92355i q^{4} +(2.09279 - 0.787555i) q^{5} +(0.245466 - 0.411215i) q^{6} +(-2.75743 - 2.75743i) q^{7} +(-0.767103 - 0.767103i) q^{8} +(2.64065 - 1.42372i) q^{9} +(-0.255189 + 0.563143i) q^{10} -1.30222i q^{11} +(-0.815358 - 3.23037i) q^{12} +(3.21824 - 3.21824i) q^{13} +1.07822 q^{14} +(-3.18076 + 2.20970i) q^{15} -3.54714 q^{16} +(1.44041 - 1.44041i) q^{17} +(-0.237925 + 0.794635i) q^{18} +1.91179i q^{19} +(1.51490 + 4.02558i) q^{20} +(5.79960 + 3.46195i) q^{21} +(0.254601 + 0.254601i) q^{22} +(0.841570 + 0.841570i) q^{23} +(1.61342 + 0.963098i) q^{24} +(3.75951 - 3.29637i) q^{25} +1.25841i q^{26} +(-3.83117 + 3.51029i) q^{27} +(5.30405 - 5.30405i) q^{28} +10.6272 q^{29} +(0.189854 - 1.05390i) q^{30} -1.00000 q^{31} +(2.22772 - 2.22772i) q^{32} +(0.551989 + 2.18693i) q^{33} +0.563238i q^{34} +(-7.94234 - 3.59909i) q^{35} +(2.73859 + 5.07942i) q^{36} +(-2.30971 - 2.30971i) q^{37} +(-0.373779 - 0.373779i) q^{38} +(-4.04050 + 6.76881i) q^{39} +(-2.20952 - 1.00125i) q^{40} -2.71829i q^{41} +(-1.81075 + 0.457040i) q^{42} +(1.08844 - 1.08844i) q^{43} +2.50489 q^{44} +(4.40506 - 5.05920i) q^{45} -0.329075 q^{46} +(6.09812 - 6.09812i) q^{47} +(5.95701 - 1.50357i) q^{48} +8.20684i q^{49} +(-0.0905505 + 1.37951i) q^{50} +(-1.80844 + 3.02957i) q^{51} +(6.19045 + 6.19045i) q^{52} +(-2.73996 - 2.73996i) q^{53} +(0.0627356 - 1.43535i) q^{54} +(-1.02557 - 2.72528i) q^{55} +4.23047i q^{56} +(-0.810372 - 3.21062i) q^{57} +(-2.07775 + 2.07775i) q^{58} +10.0143 q^{59} +(-4.25047 - 6.11835i) q^{60} -14.1143 q^{61} +(0.195513 - 0.195513i) q^{62} +(-11.2072 - 3.35560i) q^{63} -6.22319i q^{64} +(4.20055 - 9.26964i) q^{65} +(-0.535494 - 0.319652i) q^{66} +(5.05747 + 5.05747i) q^{67} +(2.77071 + 2.77071i) q^{68} +(-1.77004 - 1.05659i) q^{69} +(2.25649 - 0.849161i) q^{70} -13.0255i q^{71} +(-3.11779 - 0.933510i) q^{72} +(-5.56117 + 5.56117i) q^{73} +0.903157 q^{74} +(-4.91639 + 7.12945i) q^{75} -3.67742 q^{76} +(-3.59079 + 3.59079i) q^{77} +(-0.533419 - 2.11336i) q^{78} +7.10626i q^{79} +(-7.42341 + 2.79357i) q^{80} +(4.94605 - 7.51908i) q^{81} +(0.531459 + 0.531459i) q^{82} +(2.09111 + 2.09111i) q^{83} +(-6.65924 + 11.1558i) q^{84} +(1.88007 - 4.14888i) q^{85} +0.425607i q^{86} +(-17.8471 + 4.50466i) q^{87} +(-0.998940 + 0.998940i) q^{88} -13.6995 q^{89} +(0.127893 + 1.85038i) q^{90} -17.7482 q^{91} +(-1.61880 + 1.61880i) q^{92} +(1.67938 - 0.423882i) q^{93} +2.38452i q^{94} +(1.50564 + 4.00097i) q^{95} +(-2.79690 + 4.68548i) q^{96} +(-0.122463 - 0.122463i) q^{97} +(-1.60454 - 1.60454i) q^{98} +(-1.85400 - 3.43872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6}+O(q^{10}) $ 60 * q - 4 * q^6	$ 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.195513	+	0.195513i	−0.138248	+	0.138248i	−0.772844	−	0.634596i	$-0.781167\pi$
$2$	−0.195513	+	0.195513i	−0.138248	+	0.138248i	0.634596	+	0.772844i	$0.281167\pi$
$3$	−1.67938	+	0.423882i	−0.969592	+	0.244728i
$3$	−1.67938	+	0.423882i	−0.969592	+	0.244728i
$4$			1.92355i			0.961775i
$5$	2.09279	−	0.787555i	0.935923	−	0.352205i
$5$	2.09279	−	0.787555i	0.935923	−	0.352205i
$6$	0.245466	−	0.411215i	0.100211	−	0.167878i
$7$	−2.75743	−	2.75743i	−1.04221	−	1.04221i	−0.999069	−	0.0431418i	$-0.986263\pi$
$7$	−2.75743	−	2.75743i	−1.04221	−	1.04221i	−0.0431418	−	0.999069i	$-0.513737\pi$
$8$	−0.767103	−	0.767103i	−0.271212	−	0.271212i
$9$	2.64065	−	1.42372i	0.880216	−	0.474573i
$10$	−0.255189	+	0.563143i	−0.0806979	+	0.178081i
$11$		−	1.30222i		−	0.392635i	−0.980540	−	0.196318i	$-0.937102\pi$
$11$		−	1.30222i		−	0.392635i	0.980540	−	0.196318i	$-0.0628984\pi$
$12$	−0.815358	−	3.23037i	−0.235374	−	0.932529i
$13$	3.21824	−	3.21824i	0.892579	−	0.892579i	−0.102186	−	0.994765i	$-0.532584\pi$
$13$	3.21824	−	3.21824i	0.892579	−	0.892579i	0.994765	+	0.102186i	$0.0325836\pi$
$14$	1.07822			0.288168
$15$	−3.18076	+	2.20970i	−0.821268	+	0.570542i
$16$	−3.54714			−0.886786
$17$	1.44041	−	1.44041i	0.349351	−	0.349351i	−0.510517	−	0.859868i	$-0.670546\pi$
$17$	1.44041	−	1.44041i	0.349351	−	0.349351i	0.859868	+	0.510517i	$0.170546\pi$
$18$	−0.237925	+	0.794635i	−0.0560795	+	0.187297i
$19$			1.91179i			0.438594i	0.975658	+	0.219297i	$0.0703764\pi$
$19$			1.91179i			0.438594i	−0.975658	+	0.219297i	$0.929624\pi$
$20$	1.51490	+	4.02558i	0.338742	+	0.900147i
$21$	5.79960	+	3.46195i	1.26558	+	0.755460i
$22$	0.254601	+	0.254601i	0.0542812	+	0.0542812i
$23$	0.841570	+	0.841570i	0.175480	+	0.175480i	0.789382	−	0.613902i	$-0.210401\pi$
$23$	0.841570	+	0.841570i	0.175480	+	0.175480i	−0.613902	+	0.789382i	$0.710401\pi$
$24$	1.61342	+	0.963098i	0.329338	+	0.196592i
$25$	3.75951	−	3.29637i	0.751903	−	0.659274i
$26$			1.25841i			0.246795i
$27$	−3.83117	+	3.51029i	−0.737309	+	0.675556i
$28$	5.30405	−	5.30405i	1.00237	−	1.00237i
$29$	10.6272			1.97342			0.986708	−	0.162505i	$-0.0519574\pi$
$29$	10.6272			1.97342			0.986708	+	0.162505i	$0.0519574\pi$
$30$	0.189854	−	1.05390i	0.0346625	−	0.192415i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	2.22772	−	2.22772i	0.393809	−	0.393809i
$33$	0.551989	+	2.18693i	0.0960890	+	0.380696i
$34$			0.563238i			0.0965945i
$35$	−7.94234	−	3.59909i	−1.34250	−	0.608357i
$36$	2.73859	+	5.07942i	0.456432	+	0.846570i
$37$	−2.30971	−	2.30971i	−0.379715	−	0.379715i	0.491284	−	0.870999i	$-0.336528\pi$
$37$	−2.30971	−	2.30971i	−0.379715	−	0.379715i	−0.870999	+	0.491284i	$0.836528\pi$
$38$	−0.373779	−	0.373779i	−0.0606349	−	0.0606349i
$39$	−4.04050	+	6.76881i	−0.646998	+	1.08388i
$40$	−2.20952	−	1.00125i	−0.349356	−	0.158311i
$41$		−	2.71829i		−	0.424525i	−0.977213	−	0.212263i	$-0.931917\pi$
$41$		−	2.71829i		−	0.424525i	0.977213	−	0.212263i	$-0.0680832\pi$
$42$	−1.81075	+	0.457040i	−0.279405	+	0.0705228i
$43$	1.08844	−	1.08844i	0.165985	−	0.165985i	−0.619227	−	0.785212i	$-0.712554\pi$
$43$	1.08844	−	1.08844i	0.165985	−	0.165985i	0.785212	+	0.619227i	$0.212554\pi$
$44$	2.50489			0.377627
$45$	4.40506	−	5.05920i	0.656667	−	0.754181i
$46$	−0.329075			−0.0485195
$47$	6.09812	−	6.09812i	0.889503	−	0.889503i	−0.104972	−	0.994475i	$-0.533475\pi$
$47$	6.09812	−	6.09812i	0.889503	−	0.889503i	0.994475	+	0.104972i	$0.0334754\pi$
$48$	5.95701	−	1.50357i	0.859820	−	0.217022i
$49$			8.20684i			1.17241i
$50$	−0.0905505	+	1.37951i	−0.0128058	+	0.195093i
$51$	−1.80844	+	3.02957i	−0.253232	+	0.424224i
$52$	6.19045	+	6.19045i	0.858460	+	0.858460i
$53$	−2.73996	−	2.73996i	−0.376362	−	0.376362i	0.493426	−	0.869788i	$-0.335744\pi$
$53$	−2.73996	−	2.73996i	−0.376362	−	0.376362i	−0.869788	+	0.493426i	$0.835744\pi$
$54$	0.0627356	−	1.43535i	0.00853723	−	0.195326i
$55$	−1.02557	−	2.72528i	−0.138288	−	0.367476i
$56$			4.23047i			0.565320i
$57$	−0.810372	−	3.21062i	−0.107336	−	0.425257i
$58$	−2.07775	+	2.07775i	−0.272821	+	0.272821i
$59$	10.0143			1.30375			0.651873	−	0.758328i	$-0.273984\pi$
$59$	10.0143			1.30375			0.651873	+	0.758328i	$0.273984\pi$
$60$	−4.25047	−	6.11835i	−0.548733	−	0.789875i
$61$	−14.1143			−1.80715			−0.903575	−	0.428430i	$-0.859067\pi$
$61$	−14.1143			−1.80715			−0.903575	+	0.428430i	$0.859067\pi$
$62$	0.195513	−	0.195513i	0.0248301	−	0.0248301i
$63$	−11.2072	−	3.35560i	−1.41198	−	0.422766i
$64$		−	6.22319i		−	0.777899i
$65$	4.20055	−	9.26964i	0.521014	−	1.14976i
$66$	−0.535494	−	0.319652i	−0.0659147	−	0.0393464i
$67$	5.05747	+	5.05747i	0.617868	+	0.617868i	0.944984	−	0.327116i	$-0.106077\pi$
$67$	5.05747	+	5.05747i	0.617868	+	0.617868i	−0.327116	+	0.944984i	$0.606077\pi$
$68$	2.77071	+	2.77071i	0.335997	+	0.335997i
$69$	−1.77004	−	1.05659i	−0.213088	−	0.127199i
$70$	2.25649	−	0.849161i	0.269703	−	0.101494i
$71$		−	13.0255i		−	1.54584i	−0.634505	−	0.772918i	$-0.718796\pi$
$71$		−	13.0255i		−	1.54584i	0.634505	−	0.772918i	$-0.281204\pi$
$72$	−3.11779	−	0.933510i	−0.367435	−	0.110015i
$73$	−5.56117	+	5.56117i	−0.650886	+	0.650886i	−0.953206	−	0.302320i	$-0.902239\pi$
$73$	−5.56117	+	5.56117i	−0.650886	+	0.650886i	0.302320	+	0.953206i	$0.402239\pi$
$74$	0.903157			0.104990
$75$	−4.91639	+	7.12945i	−0.567696	+	0.823238i
$76$	−3.67742			−0.421829
$77$	−3.59079	+	3.59079i	−0.409209	+	0.409209i
$78$	−0.533419	−	2.11336i	−0.0603978	−	0.239291i
$79$			7.10626i			0.799516i	0.916621	+	0.399758i	$0.130906\pi$
$79$			7.10626i			0.799516i	−0.916621	+	0.399758i	$0.869094\pi$
$80$	−7.42341	+	2.79357i	−0.829963	+	0.312331i
$81$	4.94605	−	7.51908i	0.549561	−	0.835454i
$82$	0.531459	+	0.531459i	0.0586899	+	0.0586899i
$83$	2.09111	+	2.09111i	0.229529	+	0.229529i	0.812496	−	0.582967i	$-0.198108\pi$
$83$	2.09111	+	2.09111i	0.229529	+	0.229529i	−0.582967	+	0.812496i	$0.698108\pi$
$84$	−6.65924	+	11.1558i	−0.726583	+	1.21720i
$85$	1.88007	−	4.14888i	0.203923	−	0.450009i
$86$			0.425607i			0.0458944i
$87$	−17.8471	+	4.50466i	−1.91341	+	0.482951i
$88$	−0.998940	+	0.998940i	−0.106487	+	0.106487i
$89$	−13.6995			−1.45214			−0.726072	−	0.687619i	$-0.758656\pi$
$89$	−13.6995			−1.45214			−0.726072	+	0.687619i	$0.758656\pi$
$90$	0.127893	+	1.85038i	0.0134811	+	0.195047i
$91$	−17.7482			−1.86051
$92$	−1.61880	+	1.61880i	−0.168772	+	0.168772i
$93$	1.67938	−	0.423882i	0.174144	−	0.0439545i
$94$			2.38452i			0.245944i
$95$	1.50564	+	4.00097i	0.154475	+	0.410490i
$96$	−2.79690	+	4.68548i	−0.285457	+	0.478210i
$97$	−0.122463	−	0.122463i	−0.0124343	−	0.0124343i	0.700862	−	0.713297i	$-0.252799\pi$
$97$	−0.122463	−	0.122463i	−0.0124343	−	0.0124343i	−0.713297	+	0.700862i	$0.752799\pi$
$98$	−1.60454	−	1.60454i	−0.162083	−	0.162083i
$99$	−1.85400	−	3.43872i	−0.186334	−	0.345604i
$100$	6.34073	+	7.23161i	0.634073	+	0.723161i
$101$			15.1427i			1.50675i	0.657588	+	0.753377i	$0.271577\pi$
$101$			15.1427i			1.50675i	−0.657588	+	0.753377i	$0.728423\pi$
$102$	−0.238746	−	0.945891i	−0.0236394	−	0.0936572i
$103$	2.14405	−	2.14405i	0.211259	−	0.211259i	−0.593543	−	0.804802i	$-0.702271\pi$
$103$	2.14405	−	2.14405i	0.211259	−	0.211259i	0.804802	+	0.593543i	$0.202271\pi$
$104$	−4.93745			−0.484157
$105$	14.8638	+	2.67763i	1.45056	+	0.261309i
$106$	1.07139			0.104063
$107$	−6.98208	+	6.98208i	−0.674983	+	0.674983i	−0.958861	−	0.283878i	$-0.908379\pi$
$107$	−6.98208	+	6.98208i	−0.674983	+	0.674983i	0.283878	+	0.958861i	$0.408379\pi$
$108$	−6.75222	−	7.36944i	−0.649733	−	0.709125i
$109$		−	6.65004i		−	0.636958i	−0.947930	−	0.318479i	$-0.896828\pi$
$109$		−	6.65004i		−	0.636958i	0.947930	−	0.318479i	$-0.103172\pi$
$110$	0.733339	+	0.332314i	0.0699211	+	0.0316849i
$111$	4.85794	+	2.89985i	0.461095	+	0.275241i
$112$	9.78100	+	9.78100i	0.924218	+	0.924218i
$113$	−6.41597	−	6.41597i	−0.603564	−	0.603564i	0.337692	−	0.941257i	$-0.390354\pi$
$113$	−6.41597	−	6.41597i	−0.603564	−	0.603564i	−0.941257	+	0.337692i	$0.890354\pi$
$114$	0.786155	+	0.469279i	0.0736302	+	0.0439520i
$115$	2.42401	+	1.09844i	0.226040	+	0.102430i
$116$			20.4419i			1.89798i
$117$	3.91637	−	13.0801i	0.362069	−	1.20926i
$118$	−1.95791	+	1.95791i	−0.180241	+	0.180241i
$119$	−7.94368			−0.728196
$120$	4.13504	+	0.744902i	0.377476	+	0.0679999i
$121$	9.30421			0.845838
$122$	2.75952	−	2.75952i	0.249835	−	0.249835i
$123$	1.15223	+	4.56504i	0.103893	+	0.411616i
$124$		−	1.92355i		−	0.172740i
$125$	5.27179	−	9.85942i	0.471523	−	0.881854i
$126$	2.84721	−	1.53509i	0.253650	−	0.136757i
$127$	−8.76187	−	8.76187i	−0.777490	−	0.777490i	0.201913	−	0.979403i	$-0.435284\pi$
$127$	−8.76187	−	8.76187i	−0.777490	−	0.777490i	−0.979403	+	0.201913i	$0.935284\pi$
$128$	5.67215	+	5.67215i	0.501352	+	0.501352i
$129$	−1.36654	+	2.28928i	−0.120317	+	0.201559i
$130$	0.991070	+	2.63359i	0.0869226	+	0.230981i
$131$		−	17.5330i		−	1.53187i	−0.642921	−	0.765933i	$-0.722277\pi$
$131$		−	17.5330i		−	1.53187i	0.642921	−	0.765933i	$-0.277723\pi$
$132$	−4.20667	+	1.06178i	−0.366144	+	0.0924160i
$133$	5.27162	−	5.27162i	0.457108	−	0.457108i
$134$	−1.97760			−0.170838
$135$	−5.25327	+	10.3635i	−0.452130	+	0.891952i
$136$	−2.20989			−0.189497
$137$	−8.51816	+	8.51816i	−0.727756	+	0.727756i	−0.970172	−	0.242416i	$-0.922060\pi$
$137$	−8.51816	+	8.51816i	−0.727756	+	0.727756i	0.242416	+	0.970172i	$0.422060\pi$
$138$	0.552643	−	0.139489i	0.0470441	−	0.0118741i
$139$			13.1336i			1.11398i	0.830520	+	0.556989i	$0.188043\pi$
$139$			13.1336i			1.11398i	−0.830520	+	0.556989i	$0.811957\pi$
$140$	6.92302	−	15.2775i	0.585102	−	1.29118i
$141$	−7.65620	+	12.8260i	−0.644768	+	1.08014i
$142$	2.54664	+	2.54664i	0.213709	+	0.213709i
$143$	−4.19087	−	4.19087i	−0.350458	−	0.350458i
$144$	−9.36676	+	5.05013i	−0.780563	+	0.420845i
$145$	22.2404	−	8.36948i	1.84696	−	0.695047i
$146$		−	2.17456i		−	0.179968i
$147$	−3.47873	−	13.7824i	−0.286921	−	1.13676i
$148$	4.44285	−	4.44285i	0.365200	−	0.365200i
$149$	20.6009			1.68769			0.843845	−	0.536587i	$-0.180287\pi$
$149$	20.6009			1.68769			0.843845	+	0.536587i	$0.180287\pi$
$150$	−0.432682	−	2.35511i	−0.0353284	−	0.192294i
$151$	8.37216			0.681317			0.340658	−	0.940187i	$-0.389350\pi$
$151$	8.37216			0.681317			0.340658	+	0.940187i	$0.389350\pi$
$152$	1.46654	−	1.46654i	0.118952	−	0.118952i
$153$	1.75288	−	5.85437i	0.141712	−	0.473298i
$154$		−	1.40409i		−	0.113145i
$155$	−2.09279	+	0.787555i	−0.168097	+	0.0632579i
$156$	−13.0201	−	7.77211i	−1.04245	−	0.622267i
$157$	−5.29676	−	5.29676i	−0.422728	−	0.422728i	0.463414	−	0.886142i	$-0.346624\pi$
$157$	−5.29676	−	5.29676i	−0.422728	−	0.422728i	−0.886142	+	0.463414i	$0.846624\pi$
$158$	−1.38936	−	1.38936i	−0.110532	−	0.110532i
$159$	5.76285	+	3.44001i	0.457024	+	0.272811i
$160$	2.90769	−	6.41659i	0.229873	−	0.507276i
$161$		−	4.64114i		−	0.365773i
$162$	0.503061	+	2.43709i	0.0395242	+	0.191476i
$163$	8.07724	−	8.07724i	0.632658	−	0.632658i	−0.316076	−	0.948734i	$-0.602365\pi$
$163$	8.07724	−	8.07724i	0.632658	−	0.632658i	0.948734	+	0.316076i	$0.102365\pi$
$164$	5.22876			0.408298
$165$	2.87752	+	4.14206i	0.224015	+	0.322459i
$166$	−0.817677			−0.0634640
$167$	3.04388	−	3.04388i	0.235543	−	0.235543i	−0.579459	−	0.815001i	$-0.696736\pi$
$167$	3.04388	−	3.04388i	0.235543	−	0.235543i	0.815001	+	0.579459i	$0.196736\pi$
$168$	−1.79322	−	7.10457i	−0.138350	−	0.548130i
$169$		−	7.71415i		−	0.593396i
$170$	0.443581	+	1.17874i	0.0340211	+	0.0904050i
$171$	2.72185	+	5.04836i	0.208145	+	0.386058i
$172$	2.09367	+	2.09367i	0.159641	+	0.159641i
$173$	4.02272	+	4.02272i	0.305842	+	0.305842i	0.843294	−	0.537452i	$-0.180613\pi$
$173$	4.02272	+	4.02272i	0.305842	+	0.305842i	−0.537452	+	0.843294i	$0.680613\pi$
$174$	2.60861	−	4.37005i	0.197758	−	0.331292i
$175$	−19.4561	−	1.27709i	−1.47074	−	0.0965387i
$176$			4.61917i			0.348183i
$177$	−16.8178	+	4.24486i	−1.26410	+	0.319064i
$178$	2.67842	−	2.67842i	0.200756	−	0.200756i
$179$	−3.29569			−0.246331			−0.123166	−	0.992386i	$-0.539305\pi$
$179$	−3.29569			−0.246331			−0.123166	+	0.992386i	$0.539305\pi$
$180$	9.73162	+	8.47335i	0.725352	+	0.631566i
$181$	−0.276350			−0.0205409			−0.0102705	−	0.999947i	$-0.503269\pi$
$181$	−0.276350			−0.0205409			−0.0102705	+	0.999947i	$0.503269\pi$
$182$	3.46999	−	3.46999i	0.257213	−	0.257213i
$183$	23.7033	−	5.98279i	1.75220	−	0.442261i
$184$		−	1.29114i		−	0.0951843i
$185$	−6.65277	−	3.01471i	−0.489121	−	0.221646i
$186$	−0.245466	+	0.411215i	−0.0179984	+	0.0301517i
$187$	−1.87574	−	1.87574i	−0.137168	−	0.137168i
$188$	11.7300	+	11.7300i	0.855501	+	0.855501i
$189$	20.2436	+	0.884797i	1.47250	+	0.0643595i
$190$	−1.07661	−	0.487868i	−0.0781055	−	0.0353937i
$191$		−	7.91815i		−	0.572937i	−0.958090	−	0.286469i	$-0.907519\pi$
$191$		−	7.91815i		−	0.572937i	0.958090	−	0.286469i	$-0.0924814\pi$
$192$	2.63790	+	10.4511i	0.190374	+	0.754244i
$193$	−15.7911	+	15.7911i	−1.13667	+	1.13667i	−0.147628	+	0.989043i	$0.547164\pi$
$193$	−15.7911	+	15.7911i	−1.13667	+	1.13667i	−0.989043	+	0.147628i	$0.952836\pi$
$194$	0.0478863			0.00343803
$195$	−3.12510	+	17.3478i	−0.223793	+	1.24230i
$196$	−15.7863			−1.12759
$197$	−9.48753	+	9.48753i	−0.675958	+	0.675958i	−0.959083	−	0.283125i	$-0.908629\pi$
$197$	−9.48753	+	9.48753i	−0.675958	+	0.675958i	0.283125	+	0.959083i	$0.408629\pi$
$198$	1.03479	+	0.309832i	0.0735395	+	0.0220188i
$199$			25.3657i			1.79812i	0.437821	+	0.899062i	$0.355750\pi$
$199$			25.3657i			1.79812i	−0.437821	+	0.899062i	$0.644250\pi$
$200$	−5.41259	−	0.355279i	−0.382728	−	0.0251220i
$201$	−10.6372	−	6.34965i	−0.750290	−	0.447870i
$202$	−2.96059	−	2.96059i	−0.208306	−	0.208306i
$203$	−29.3037	−	29.3037i	−2.05671	−	2.05671i
$204$	−5.82753	−	3.47862i	−0.408008	−	0.243552i
$205$	−2.14080	−	5.68880i	−0.149520	−	0.397323i
$206$			0.838376i			0.0584124i
$207$	3.42045	+	1.02413i	0.237738	+	0.0711821i
$208$	−11.4156	+	11.4156i	−0.791527	+	0.791527i
$209$	2.48958			0.172208
$210$	−3.42957	+	2.38255i	−0.236663	+	0.164412i
$211$	21.0663			1.45026			0.725131	−	0.688611i	$-0.241779\pi$
$211$	21.0663			1.45026			0.725131	+	0.688611i	$0.241779\pi$
$212$	5.27044	−	5.27044i	0.361975	−	0.361975i
$213$	5.52125	+	21.8747i	0.378310	+	1.49883i
$214$		−	2.73017i		−	0.186630i
$215$	1.42067	−	3.13508i	0.0968886	−	0.213811i
$216$	5.63166	+	0.246146i	0.383186	+	0.0167481i
$217$	2.75743	+	2.75743i	0.187187	+	0.187187i
$218$	1.30017	+	1.30017i	0.0880584	+	0.0880584i
$219$	6.98205	−	11.6966i	0.471803	−	0.790384i
$220$	5.24221	−	1.97274i	0.353429	−	0.133002i
$221$		−	9.27119i		−	0.623648i
$222$	−1.51675	+	0.382832i	−0.101797	+	0.0256940i
$223$	−1.88522	+	1.88522i	−0.126244	+	0.126244i	−0.767406	−	0.641162i	$-0.778453\pi$
$223$	−1.88522	+	1.88522i	−0.126244	+	0.126244i	0.641162	+	0.767406i	$0.278453\pi$
$224$	−12.2856			−0.820863
$225$	5.23445	−	14.0570i	0.348963	−	0.937136i
$226$	2.50881			0.166883
$227$	−5.20858	+	5.20858i	−0.345706	+	0.345706i	−0.858507	−	0.512802i	$-0.828608\pi$
$227$	−5.20858	+	5.20858i	−0.345706	+	0.345706i	0.512802	+	0.858507i	$0.328608\pi$
$228$	6.17579	−	1.55879i	0.409002	−	0.103233i
$229$		−	9.94908i		−	0.657453i	−0.944425	−	0.328727i	$-0.893381\pi$
$229$		−	9.94908i		−	0.657453i	0.944425	−	0.328727i	$-0.106619\pi$
$230$	−0.688684	+	0.259165i	−0.0454105	+	0.0170888i
$231$	4.50824	−	7.55238i	0.296620	−	0.496910i
$232$	−8.15214	−	8.15214i	−0.535214	−	0.535214i
$233$	18.7234	+	18.7234i	1.22661	+	1.22661i	0.965237	+	0.261376i	$0.0841764\pi$
$233$	18.7234	+	18.7234i	1.22661	+	1.22661i	0.261376	+	0.965237i	$0.415824\pi$
$234$	1.79163	+	3.32303i	0.117122	+	0.217233i
$235$	7.95946	−	17.5647i	0.519218	−	1.14579i
$236$			19.2629i			1.25391i
$237$	−3.01221	−	11.9341i	−0.195664	−	0.775204i
$238$	1.55309	−	1.55309i	0.100672	−	0.100672i
$239$	−8.72591			−0.564432			−0.282216	−	0.959351i	$-0.591070\pi$
$239$	−8.72591			−0.564432			−0.282216	+	0.959351i	$0.591070\pi$
$240$	11.2826	−	7.83812i	0.728289	−	0.505949i
$241$	−17.6390			−1.13623			−0.568115	−	0.822950i	$-0.692327\pi$
$241$	−17.6390			−1.13623			−0.568115	+	0.822950i	$0.692327\pi$
$242$	−1.81909	+	1.81909i	−0.116936	+	0.116936i
$243$	−5.11910	+	14.7240i	−0.328390	+	0.944542i
$244$		−	27.1495i		−	1.73807i
$245$	6.46334	+	17.1752i	0.412928	+	1.09728i
$246$	−1.11780	−	0.667247i	−0.0712683	−	0.0425421i
$247$	6.15260	+	6.15260i	0.391480	+	0.391480i
$248$	0.767103	+	0.767103i	0.0487111	+	0.0487111i
$249$	−4.39816	−	2.62539i	−0.278722	−	0.166377i
$250$	0.896941	+	2.95834i	0.0567275	+	0.187102i
$251$		−	23.6565i		−	1.49319i	−0.665281	−	0.746593i	$-0.731688\pi$
$251$		−	23.6565i		−	1.49319i	0.665281	−	0.746593i	$-0.268312\pi$
$252$	6.45466	−	21.5576i	0.406605	−	1.35800i
$253$	1.09591	−	1.09591i	0.0688995	−	0.0688995i
$254$	3.42611			0.214973
$255$	−1.39872	+	7.76449i	−0.0875915	+	0.486231i
$256$	10.2284			0.639277
$257$	0.0842873	−	0.0842873i	0.00525770	−	0.00525770i	−0.704473	−	0.709731i	$-0.748817\pi$
$257$	0.0842873	−	0.0842873i	0.00525770	−	0.00525770i	0.709731	+	0.704473i	$0.248817\pi$
$258$	−0.180407	−	0.714757i	−0.0112317	−	0.0444988i
$259$			12.7378i			0.791486i
$260$	17.8306	+	8.07997i	1.10581	+	0.501098i
$261$	28.0626	−	15.1301i	1.73703	−	0.936530i
$262$	3.42792	+	3.42792i	0.211778	+	0.211778i
$263$	9.75609	+	9.75609i	0.601586	+	0.601586i	0.940733	−	0.339147i	$-0.110138\pi$
$263$	9.75609	+	9.75609i	0.601586	+	0.601586i	−0.339147	+	0.940733i	$0.610138\pi$
$264$	1.25417	−	2.10104i	0.0771888	−	0.129310i
$265$	−7.89201	−	3.57628i	−0.484802	−	0.219689i
$266$			2.06134i			0.126389i
$267$	23.0067	−	5.80697i	1.40799	−	0.355381i
$268$	−9.72829	+	9.72829i	−0.594250	+	0.594250i
$269$	3.68241			0.224520			0.112260	−	0.993679i	$-0.464191\pi$
$269$	3.68241			0.224520			0.112260	+	0.993679i	$0.464191\pi$
$270$	−0.999123	−	3.05329i	−0.0608047	−	0.185817i
$271$	10.5118			0.638547			0.319274	−	0.947663i	$-0.396561\pi$
$271$	10.5118			0.638547			0.319274	+	0.947663i	$0.396561\pi$
$272$	−5.10935	+	5.10935i	−0.309800	+	0.309800i
$273$	29.8059	−	7.52312i	1.80394	−	0.455320i
$274$		−	3.33082i		−	0.201222i
$275$	−4.29261	−	4.89573i	−0.258854	−	0.295224i
$276$	2.03241	−	3.40477i	0.122337	−	0.204943i
$277$	13.1707	+	13.1707i	0.791353	+	0.791353i	0.981714	−	0.190361i	$-0.0609659\pi$
$277$	13.1707	+	13.1707i	0.791353	+	0.791353i	−0.190361	+	0.981714i	$0.560966\pi$
$278$	−2.56778	−	2.56778i	−0.154005	−	0.154005i
$279$	−2.64065	+	1.42372i	−0.158091	+	0.0852358i
$280$	3.33173	+	8.85347i	0.199109	+	0.529096i
$281$			14.0284i			0.836865i	0.908248	+	0.418433i	$0.137420\pi$
$281$			14.0284i			0.836865i	−0.908248	+	0.418433i	$0.862580\pi$
$282$	−1.01075	−	4.00452i	−0.0601896	−	0.238466i
$283$	−19.4633	+	19.4633i	−1.15697	+	1.15697i	−0.171852	+	0.985123i	$0.554975\pi$
$283$	−19.4633	+	19.4633i	−1.15697	+	1.15697i	−0.985123	+	0.171852i	$0.945025\pi$
$284$	25.0551			1.48675
$285$	−4.22448	−	6.08094i	−0.250237	−	0.360204i
$286$	1.63874			0.0969005
$287$	−7.49549	+	7.49549i	−0.442445	+	0.442445i
$288$	2.71097	−	9.05426i	0.159746	−	0.533528i
$289$			12.8504i			0.755907i
$290$	−2.71194	+	5.98462i	−0.159251	+	0.351429i
$291$	0.257573	+	0.153753i	0.0150992	+	0.00901315i
$292$	−10.6972	−	10.6972i	−0.626006	−	0.626006i
$293$	15.8297	+	15.8297i	0.924784	+	0.924784i	0.997363	−	0.0725790i	$-0.0231229\pi$
$293$	15.8297	+	15.8297i	0.924784	+	0.924784i	−0.0725790	+	0.997363i	$0.523123\pi$
$294$	3.37477	+	2.01450i	0.196821	+	0.117488i
$295$	20.9577	−	7.88678i	1.22021	−	0.459186i
$296$			3.54358i			0.205966i
$297$	4.57119	+	4.98904i	0.265247	+	0.289493i
$298$	−4.02773	+	4.02773i	−0.233320	+	0.233320i
$299$	5.41675			0.313259
$300$	−13.7139	−	9.45692i	−0.791770	−	0.545995i
$301$	−6.00259			−0.345984
$302$	−1.63686	+	1.63686i	−0.0941909	+	0.0941909i
$303$	−6.41871	−	25.4304i	−0.368746	−	1.46094i
$304$		−	6.78139i		−	0.388939i
$305$	−29.5382	+	11.1158i	−1.69135	+	0.636488i
$306$	0.801892	+	1.48731i	0.0458411	+	0.0850240i
$307$	−13.8516	−	13.8516i	−0.790552	−	0.790552i	0.191032	−	0.981584i	$-0.438817\pi$
$307$	−13.8516	−	13.8516i	−0.790552	−	0.790552i	−0.981584	+	0.191032i	$0.938817\pi$
$308$	−6.90707	−	6.90707i	−0.393567	−	0.393567i
$309$	−2.69185	+	4.50949i	−0.153134	+	0.256536i
$310$	0.255189	−	0.563143i	0.0144938	−	0.0319844i
$311$			10.3583i			0.587366i	0.955903	+	0.293683i	$0.0948811\pi$
$311$			10.3583i			0.587366i	−0.955903	+	0.293683i	$0.905119\pi$
$312$	8.29186	−	2.09289i	0.469434	−	0.118487i
$313$	2.92740	−	2.92740i	0.165466	−	0.165466i	−0.619517	−	0.784983i	$-0.712672\pi$
$313$	2.92740	−	2.92740i	0.165466	−	0.165466i	0.784983	+	0.619517i	$0.212672\pi$
$314$	2.07117			0.116883
$315$	−26.0970	+	1.80375i	−1.47040	+	0.101630i
$316$	−13.6692			−0.768955
$317$	−6.36072	+	6.36072i	−0.357254	+	0.357254i	−0.862800	−	0.505546i	$-0.831291\pi$
$317$	−6.36072	+	6.36072i	−0.357254	+	0.357254i	0.505546	+	0.862800i	$0.331291\pi$
$318$	−1.79928	+	0.454143i	−0.100898	+	0.0254671i
$319$		−	13.8390i		−	0.774833i
$320$	−4.90111	−	13.0238i	−0.273980	−	0.728053i
$321$	8.76600	−	14.6852i	0.489270	−	0.819645i
$322$	0.907402	+	0.907402i	0.0505675	+	0.0505675i
$323$	2.75376	+	2.75376i	0.153224	+	0.153224i
$324$	14.4633	+	9.51397i	0.803518	+	0.528554i
$325$	1.49051	−	22.7075i	0.0826786	−	1.25959i
$326$			3.15840i			0.174928i
$327$	2.81883	+	11.1680i	0.155882	+	0.617589i
$328$	−2.08521	+	2.08521i	−0.115136	+	0.115136i
$329$	−33.6303			−1.85410
$330$	−1.37242	−	0.247233i	−0.0755491	−	0.0136097i
$331$	−11.6823			−0.642118			−0.321059	−	0.947059i	$-0.604039\pi$
$331$	−11.6823			−0.642118			−0.321059	+	0.947059i	$0.604039\pi$
$332$	−4.02235	+	4.02235i	−0.220755	+	0.220755i
$333$	−9.38753	−	2.81076i	−0.514433	−	0.154029i
$334$			1.19023i			0.0651267i
$335$	14.5672	+	6.60117i	0.795893	+	0.360660i
$336$	−20.5720	−	12.2800i	−1.12230	−	0.669931i
$337$	14.2967	+	14.2967i	0.778790	+	0.778790i	0.979625	−	0.200835i	$-0.0643654\pi$
$337$	14.2967	+	14.2967i	0.778790	+	0.778790i	−0.200835	+	0.979625i	$0.564365\pi$
$338$	1.50821	+	1.50821i	0.0820360	+	0.0820360i
$339$	13.4945	+	8.05526i	0.732920	+	0.437502i
$340$	7.98058	+	3.61641i	0.432808	+	0.196128i
$341$			1.30222i			0.0705194i
$342$	−1.51917	−	0.454862i	−0.0821475	−	0.0245961i
$343$	3.32779	−	3.32779i	0.179684	−	0.179684i
$344$	−1.66989			−0.0900345
$345$	−4.53645	−	0.817214i	−0.244234	−	0.0439973i
$346$	−1.57299			−0.0845642
$347$	−10.8386	+	10.8386i	−0.581845	+	0.581845i	−0.935410	−	0.353565i	$-0.884969\pi$
$347$	−10.8386	+	10.8386i	−0.581845	+	0.581845i	0.353565	+	0.935410i	$0.384969\pi$
$348$	−8.66494	−	34.3297i	−0.464490	−	1.84027i
$349$			1.17973i			0.0631493i	0.999501	+	0.0315747i	$0.0100522\pi$
$349$			1.17973i			0.0631493i	−0.999501	+	0.0315747i	$0.989948\pi$
$350$	4.05360	−	3.55423i	0.216674	−	0.189981i
$351$	−1.03266	+	23.6266i	−0.0551193	+	1.26109i
$352$	−2.90099	−	2.90099i	−0.154623	−	0.154623i
$353$	12.7383	+	12.7383i	0.677990	+	0.677990i	0.959545	−	0.281555i	$-0.0908502\pi$
$353$	12.7383	+	12.7383i	0.677990	+	0.677990i	−0.281555	+	0.959545i	$0.590850\pi$
$354$	2.45816	−	4.11801i	0.130650	−	0.218870i
$355$	−10.2583	−	27.2595i	−0.544452	−	1.44678i
$356$		−	26.3516i		−	1.39663i
$357$	13.3405	−	3.36718i	0.706052	−	0.178210i
$358$	0.644348	−	0.644348i	0.0340548	−	0.0340548i
$359$	15.0864			0.796228			0.398114	−	0.917336i	$-0.369665\pi$
$359$	15.0864			0.796228			0.398114	+	0.917336i	$0.369665\pi$
$360$	−7.26006	+	0.501793i	−0.382639	+	0.0264468i
$361$	15.3451			0.807635
$362$	0.0540298	−	0.0540298i	0.00283974	−	0.00283974i
$363$	−15.6253	+	3.94389i	−0.820117	+	0.207000i
$364$		−	34.1395i		−	1.78939i
$365$	−7.25862	+	16.0181i	−0.379933	+	0.838425i
$366$	−3.46458	+	5.80400i	−0.181097	+	0.303380i
$367$	26.4459	+	26.4459i	1.38046	+	1.38046i	0.843791	+	0.536672i	$0.180319\pi$
$367$	26.4459	+	26.4459i	1.38046	+	1.38046i	0.536672	+	0.843791i	$0.319681\pi$
$368$	−2.98517	−	2.98517i	−0.155613	−	0.155613i
$369$	−3.87008	−	7.17804i	−0.201468	−	0.373674i
$370$	1.89011	−	0.711286i	0.0982624	−	0.0369780i
$371$			15.1105i			0.784497i
$372$	0.815358	+	3.23037i	0.0422743	+	0.167487i
$373$	−2.15911	+	2.15911i	−0.111794	+	0.111794i	−0.760791	−	0.648997i	$-0.775189\pi$
$373$	−2.15911	+	2.15911i	−0.111794	+	0.111794i	0.648997	+	0.760791i	$0.275189\pi$
$374$	0.733462			0.0379264
$375$	−4.67412	+	18.7924i	−0.241370	+	0.970433i
$376$	−9.35578			−0.482488
$377$	34.2008	−	34.2008i	1.76143	−	1.76143i
$378$	−4.13086	+	3.78488i	−0.212469	+	0.194673i
$379$			16.8796i			0.867049i	0.901142	+	0.433525i	$0.142730\pi$
$379$			16.8796i			0.867049i	−0.901142	+	0.433525i	$0.857270\pi$
$380$	−7.69606	+	2.89617i	−0.394799	+	0.148570i
$381$	18.4285	+	11.0005i	0.944122	+	0.563574i
$382$	1.54810	+	1.54810i	0.0792076	+	0.0792076i
$383$	−14.7580	−	14.7580i	−0.754100	−	0.754100i	0.221142	−	0.975242i	$-0.429022\pi$
$383$	−14.7580	−	14.7580i	−0.754100	−	0.754100i	−0.975242	+	0.221142i	$0.929022\pi$
$384$	−11.9300	−	7.12138i	−0.608801	−	0.363412i
$385$	−4.68682	+	10.3427i	−0.238862	+	0.527113i
$386$		−	6.17473i		−	0.314286i
$387$	1.32455	−	4.42382i	0.0673308	−	0.224875i
$388$	0.235564	−	0.235564i	0.0119590	−	0.0119590i
$389$	−17.4161			−0.883030			−0.441515	−	0.897254i	$-0.645559\pi$
$389$	−17.4161			−0.883030			−0.441515	+	0.897254i	$0.645559\pi$
$390$	−2.78072	−	4.00271i	−0.140807	−	0.202685i
$391$	2.42442			0.122608
$392$	6.29550	−	6.29550i	0.317971	−	0.317971i
$393$	7.43192	+	29.4446i	0.374891	+	1.48528i
$394$		−	3.70986i		−	0.186900i
$395$	5.59657	+	14.8719i	0.281594	+	0.748285i
$396$	6.61454	−	3.56626i	0.332393	−	0.179211i
$397$	−14.4374	−	14.4374i	−0.724591	−	0.724591i	0.244946	−	0.969537i	$-0.421230\pi$
$397$	−14.4374	−	14.4374i	−0.724591	−	0.724591i	−0.969537	+	0.244946i	$0.921230\pi$
$398$	−4.95931	−	4.95931i	−0.248588	−	0.248588i
$399$	−6.61852	+	11.0876i	−0.331341	+	0.555075i
$400$	−13.3355	+	11.6927i	−0.666777	+	0.584635i
$401$			39.1449i			1.95480i	0.211392	+	0.977401i	$0.432200\pi$
$401$			39.1449i			1.95480i	−0.211392	+	0.977401i	$0.567800\pi$
$402$	3.32114	−	0.838268i	0.165644	−	0.0418090i
$403$	−3.21824	+	3.21824i	−0.160312	+	0.160312i
$404$	−29.1277			−1.44916
$405$	4.42933	−	19.6311i	0.220095	−	0.975478i
$406$	11.4585			0.568675
$407$	−3.00777	+	3.00777i	−0.149089	+	0.149089i
$408$	3.71125	−	0.936733i	0.183734	−	0.0463752i
$409$		−	3.18530i		−	0.157503i	−0.996894	−	0.0787516i	$-0.974907\pi$
$409$		−	3.18530i		−	0.157503i	0.996894	−	0.0787516i	$-0.0250934\pi$
$410$	1.53078	+	0.693678i	0.0756001	+	0.0342583i
$411$	10.6946	−	17.9159i	0.527524	−	0.883728i
$412$	4.12418	+	4.12418i	0.203184	+	0.203184i
$413$	−27.6136	−	27.6136i	−1.35878	−	1.35878i
$414$	−0.868972	+	0.468511i	−0.0427076	+	0.0230260i
$415$	6.02311	+	2.72938i	0.295663	+	0.133980i
$416$		−	14.3387i		−	0.703011i
$417$	−5.56710	−	22.0563i	−0.272622	−	1.08010i
$418$	−0.486744	+	0.486744i	−0.0238074	+	0.0238074i
$419$	−28.2490			−1.38005			−0.690027	−	0.723783i	$-0.742401\pi$
$419$	−28.2490			−1.38005			−0.690027	+	0.723783i	$0.742401\pi$
$420$	−5.15055	+	28.5913i	−0.251321	+	1.39511i
$421$	−9.84827			−0.479975			−0.239988	−	0.970776i	$-0.577143\pi$
$421$	−9.84827			−0.479975			−0.239988	+	0.970776i	$0.577143\pi$
$422$	−4.11872	+	4.11872i	−0.200496	+	0.200496i
$423$	7.42098	−	24.7850i	0.360821	−	1.20509i
$424$			4.20366i			0.204148i
$425$	0.667119	−	10.1634i	0.0323600	−	0.492997i
$426$	−5.35626	−	3.19731i	−0.259511	−	0.154910i
$427$	38.9192	+	38.9192i	1.88343	+	1.88343i
$428$	−13.4304	−	13.4304i	−0.649182	−	0.649182i
$429$	8.81451	+	5.26164i	0.425568	+	0.254034i
$430$	0.335189	+	0.890705i	0.0161643	+	0.0429536i
$431$			8.68487i			0.418335i	0.977880	+	0.209168i	$0.0670754\pi$
$431$			8.68487i			0.418335i	−0.977880	+	0.209168i	$0.932925\pi$
$432$	13.5897	−	12.4515i	0.653835	−	0.599073i
$433$	−17.6974	+	17.6974i	−0.850482	+	0.850482i	−0.990192	−	0.139711i	$-0.955383\pi$
$433$	−17.6974	+	17.6974i	−0.850482	+	0.850482i	0.139711	+	0.990192i	$0.455383\pi$
$434$	−1.07822			−0.0517564
$435$	−33.8025	+	23.4829i	−1.62070	+	1.12592i
$436$	12.7917			0.612610
$437$	−1.60890	+	1.60890i	−0.0769643	+	0.0769643i
$438$	0.921756	+	3.65191i	0.0440432	+	0.174495i
$439$		−	21.6287i		−	1.03228i	−0.856503	−	0.516141i	$-0.827368\pi$
$439$		−	21.6287i		−	1.03228i	0.856503	−	0.516141i	$-0.172632\pi$
$440$	−1.30385	+	2.87729i	−0.0621586	+	0.137169i
$441$	11.6842	+	21.6714i	0.556393	+	1.03197i
$442$	1.81263	+	1.81263i	0.0862182	+	0.0862182i
$443$	−1.31942	−	1.31942i	−0.0626877	−	0.0626877i	0.675068	−	0.737756i	$-0.264114\pi$
$443$	−1.31942	−	1.31942i	−0.0626877	−	0.0626877i	−0.737756	+	0.675068i	$0.764114\pi$
$444$	−5.57800	+	9.34449i	−0.264720	+	0.443470i
$445$	−28.6701	+	10.7891i	−1.35909	+	0.511453i
$446$		−	0.737168i		−	0.0349059i
$447$	−34.5968	+	8.73234i	−1.63637	+	0.413026i
$448$	−17.1600	+	17.1600i	−0.810735	+	0.810735i
$449$	31.7021			1.49611			0.748057	−	0.663634i	$-0.230987\pi$
$449$	31.7021			1.49611			0.748057	+	0.663634i	$0.230987\pi$
$450$	1.72493	+	3.77173i	0.0813139	+	0.177801i
$451$	−3.53982			−0.166684
$452$	12.3414	−	12.3414i	0.580493	−	0.580493i
$453$	−14.0601	+	3.54881i	−0.660599	+	0.166737i
$454$		−	2.03669i		−	0.0955864i
$455$	−37.1431	+	13.9776i	−1.74130	+	0.655282i
$456$	−1.84124	+	3.08452i	−0.0862240	+	0.144446i
$457$	23.3151	+	23.3151i	1.09063	+	1.09063i	0.995461	+	0.0951712i	$0.0303398\pi$
$457$	23.3151	+	23.3151i	1.09063	+	1.09063i	0.0951712	+	0.995461i	$0.469660\pi$
$458$	1.94517	+	1.94517i	0.0908918	+	0.0908918i
$459$	−0.462196	+	10.5747i	−0.0215735	+	0.493586i
$460$	−2.11291	+	4.66270i	−0.0985150	+	0.217400i
$461$		−	35.3362i		−	1.64577i	−0.568207	−	0.822886i	$-0.692363\pi$
$461$		−	35.3362i		−	1.64577i	0.568207	−	0.822886i	$-0.307637\pi$
$462$	0.595168	+	2.35800i	0.0276897	+	0.109704i
$463$	4.40729	−	4.40729i	0.204824	−	0.204824i	−0.597239	−	0.802063i	$-0.703736\pi$
$463$	4.40729	−	4.40729i	0.204824	−	0.204824i	0.802063	+	0.597239i	$0.203736\pi$
$464$	−37.6961			−1.75000
$465$	3.18076	−	2.20970i	0.147504	−	0.102472i
$466$	−7.32134			−0.339154
$467$	22.1966	−	22.1966i	1.02714	−	1.02714i	0.0275140	−	0.999621i	$-0.491241\pi$
$467$	22.1966	−	22.1966i	1.02714	−	1.02714i	0.999621	−	0.0275140i	$-0.00875909\pi$
$468$	25.1603	+	7.53333i	1.16303	+	0.348229i
$469$		−	27.8912i		−	1.28790i
$470$	1.87794	+	4.99029i	0.0866230	+	0.230185i
$471$	11.1405	+	6.65008i	0.513327	+	0.306420i
$472$	−7.68197	−	7.68197i	−0.353592	−	0.353592i
$473$	−1.41739	−	1.41739i	−0.0651718	−	0.0651718i
$474$	2.92220	+	1.74435i	0.134221	+	0.0801204i
$475$	6.30196	+	7.18740i	0.289154	+	0.329780i
$476$		−	15.2801i		−	0.700360i
$477$	−11.1362	−	3.33433i	−0.509891	−	0.152669i
$478$	1.70603	−	1.70603i	0.0780318	−	0.0780318i
$479$	−0.388520			−0.0177519			−0.00887597	−	0.999961i	$-0.502825\pi$
$479$	−0.388520			−0.0177519			−0.00887597	+	0.999961i	$0.502825\pi$
$480$	−2.16324	+	12.0084i	−0.0987381	+	0.548107i
$481$	−14.8664			−0.677851
$482$	3.44865	−	3.44865i	0.157082	−	0.157082i
$483$	1.96730	+	7.79425i	0.0895151	+	0.354651i
$484$			17.8971i			0.813505i
$485$	−0.352736	−	0.159843i	−0.0160169	−	0.00725810i
$486$	−1.87787	−	3.87957i	−0.0851819	−	0.175981i
$487$	10.2168	+	10.2168i	0.462968	+	0.462968i	0.899627	−	0.436659i	$-0.143838\pi$
$487$	10.2168	+	10.2168i	0.462968	+	0.462968i	−0.436659	+	0.899627i	$0.643838\pi$
$488$	10.8271	+	10.8271i	0.490121	+	0.490121i
$489$	−10.1410	+	16.9886i	−0.458591	+	0.768249i
$490$	−4.62163	−	2.09430i	−0.208784	−	0.0946108i
$491$			14.4555i			0.652367i	0.945307	+	0.326183i	$0.105763\pi$
$491$			14.4555i			0.652367i	−0.945307	+	0.326183i	$0.894237\pi$
$492$	−8.78109	+	2.21638i	−0.395882	+	0.0999220i
$493$	15.3075	−	15.3075i	0.689416	−	0.689416i
$494$	−2.40582			−0.108243
$495$	−6.58821	−	5.73637i	−0.296118	−	0.257831i
$496$	3.54714			0.159271
$497$	−35.9168	+	35.9168i	−1.61109	+	1.61109i
$498$	1.37319	−	0.346598i	0.0615342	−	0.0155314i
$499$		−	28.4627i		−	1.27416i	−0.770796	−	0.637082i	$-0.780141\pi$
$499$		−	28.4627i		−	1.27416i	0.770796	−	0.637082i	$-0.219859\pi$
$500$	18.9651	+	10.1405i	0.848145	+	0.453499i
$501$	−3.82159	+	6.40208i	−0.170736	+	0.286024i
$502$	4.62515	+	4.62515i	0.206430	+	0.206430i
$503$	−18.5498	−	18.5498i	−0.827095	−	0.827095i	0.160019	−	0.987114i	$-0.448845\pi$
$503$	−18.5498	−	18.5498i	−0.827095	−	0.827095i	−0.987114	+	0.160019i	$0.948845\pi$
$504$	6.02300	+	11.1712i	0.268286	+	0.497604i
$505$	11.9257	+	31.6904i	0.530687	+	1.41021i
$506$			0.428530i			0.0190505i
$507$	3.26989	+	12.9550i	0.145221	+	0.575352i
$508$	16.8539	−	16.8539i	0.747771	−	0.747771i
$509$	4.45556			0.197489			0.0987447	−	0.995113i	$-0.468517\pi$
$509$	4.45556			0.197489			0.0987447	+	0.995113i	$0.468517\pi$
$510$	−1.24459	−	1.79152i	−0.0551112	−	0.0793300i
$511$	30.6691			1.35672
$512$	−13.3441	+	13.3441i	−0.589731	+	0.589731i
$513$	−6.71093	−	7.32438i	−0.296295	−	0.323379i
$514$			0.0329585i			0.00145374i
$515$	2.79848	−	6.17558i	0.123316	−	0.272129i
$516$	−4.40353	−	2.62860i	−0.193855	−	0.115718i
$517$	−7.94112	−	7.94112i	−0.349250	−	0.349250i
$518$	−2.49039	−	2.49039i	−0.109422	−	0.109422i
$519$	−8.46085	−	5.05053i	−0.371390	−	0.221694i
$520$	−10.3330	+	3.88851i	−0.453133	+	0.170523i
$521$		−	21.2147i		−	0.929435i	−0.885459	−	0.464717i	$-0.846156\pi$
$521$		−	21.2147i		−	0.929435i	0.885459	−	0.464717i	$-0.153844\pi$
$522$	−2.52847	+	8.44472i	−0.110668	+	0.369615i
$523$	−24.9549	+	24.9549i	−1.09120	+	1.09120i	−0.0958005	+	0.995401i	$0.530541\pi$
$523$	−24.9549	+	24.9549i	−1.09120	+	1.09120i	−0.995401	+	0.0958005i	$0.969459\pi$
$524$	33.7256			1.47331
$525$	33.2156	−	6.10237i	1.44965	−	0.266329i
$526$	−3.81488			−0.166337
$527$	−1.44041	+	1.44041i	−0.0627454	+	0.0627454i
$528$	−1.95798	−	7.75736i	−0.0852103	−	0.337596i
$529$		−	21.5835i		−	0.938414i
$530$	2.24219	−	0.843780i	0.0973947	−	0.0366515i
$531$	26.4441	−	14.2575i	1.14758	−	0.618723i
$532$	10.1402	+	10.1402i	0.439635	+	0.439635i
$533$	−8.74810	−	8.74810i	−0.378922	−	0.378922i
$534$	−3.36276	+	5.63343i	−0.145521	+	0.243782i
$535$	−9.11323	+	20.1108i	−0.393999	+	0.869464i
$536$		−	7.75920i		−	0.335147i
$537$	5.53471	−	1.39698i	0.238841	−	0.0602842i
$538$	−0.719957	+	0.719957i	−0.0310395	+	0.0310395i
$539$	10.6872			0.460328
$540$	−19.9348	−	10.1049i	−0.857857	−	0.434847i
$541$	−0.579882			−0.0249311			−0.0124655	−	0.999922i	$-0.503968\pi$
$541$	−0.579882			−0.0249311			−0.0124655	+	0.999922i	$0.503968\pi$
$542$	−2.05519	+	2.05519i	−0.0882780	+	0.0882780i
$543$	0.464097	−	0.117140i	0.0199163	−	0.00502694i
$544$		−	6.41767i		−	0.275155i
$545$	−5.23727	−	13.9171i	−0.224340	−	0.596144i
$546$	−4.35657	+	7.29830i	−0.186444	+	0.312338i
$547$	−5.43168	−	5.43168i	−0.232242	−	0.232242i	0.581386	−	0.813628i	$-0.302511\pi$
$547$	−5.43168	−	5.43168i	−0.232242	−	0.232242i	−0.813628	+	0.581386i	$0.802511\pi$
$548$	−16.3851	−	16.3851i	−0.699937	−	0.699937i
$549$	−37.2709	+	20.0948i	−1.59068	+	0.857625i
$550$	1.79644	+	0.117917i	0.0766003	+	0.00502800i
$551$			20.3169i			0.865529i
$552$	0.547292	+	2.16832i	0.0232943	+	0.0922899i
$553$	19.5950	−	19.5950i	0.833264	−	0.833264i
$554$	−5.15009			−0.218806
$555$	12.4504	+	2.24287i	0.528491	+	0.0952044i
$556$	−25.2631			−1.07140
$557$	25.5071	−	25.5071i	1.08077	−	1.08077i	0.0843317	−	0.996438i	$-0.473124\pi$
$557$	25.5071	−	25.5071i	1.08077	−	1.08077i	0.996438	−	0.0843317i	$-0.0268755\pi$
$558$	0.237925	−	0.794635i	0.0100722	−	0.0336396i
$559$		−	7.00572i		−	0.296310i
$560$	28.1726	+	12.7665i	1.19051	+	0.539482i
$561$	3.94518	+	2.35499i	0.166566	+	0.0994279i
$562$	−2.74273	−	2.74273i	−0.115695	−	0.115695i
$563$	19.6179	+	19.6179i	0.826795	+	0.826795i	0.987072	−	0.160277i	$-0.0512387\pi$
$563$	19.6179	+	19.6179i	0.826795	+	0.826795i	−0.160277	+	0.987072i	$0.551239\pi$
$564$	−24.6714	−	14.7271i	−1.03885	−	0.620122i
$565$	−18.4802	−	8.37433i	−0.777468	−	0.352311i
$566$		−	7.61065i		−	0.319900i
$567$	−34.3717	+	7.09497i	−1.44348	+	0.297961i
$568$	−9.99187	+	9.99187i	−0.419249	+	0.419249i
$569$	−8.20848			−0.344117			−0.172059	−	0.985087i	$-0.555042\pi$
$569$	−8.20848			−0.344117			−0.172059	+	0.985087i	$0.555042\pi$
$570$	2.01484	+	0.362961i	0.0843923	+	0.0152028i
$571$	−2.50950			−0.105019			−0.0525097	−	0.998620i	$-0.516722\pi$
$571$	−2.50950			−0.105019			−0.0525097	+	0.998620i	$0.516722\pi$
$572$	8.06135	−	8.06135i	0.337062	−	0.337062i
$573$	3.35636	+	13.2976i	0.140214	+	0.555515i
$574$		−	2.93092i		−	0.122334i
$575$	5.93802	+	0.389768i	0.247633	+	0.0162545i
$576$	−8.86008	−	16.4333i	−0.369170	−	0.684719i
$577$	−30.7665	−	30.7665i	−1.28083	−	1.28083i	−0.940198	−	0.340629i	$-0.889360\pi$
$577$	−30.7665	−	30.7665i	−1.28083	−	1.28083i	−0.340629	−	0.940198i	$-0.610640\pi$
$578$	−2.51242	−	2.51242i	−0.104503	−	0.104503i
$579$	19.8258	−	33.2129i	0.823931	−	1.38028i
$580$	16.0991	+	42.7805i	0.668479	+	1.77636i
$581$		−	11.5322i		−	0.478436i
$582$	−0.0804193	+	0.0202981i	−0.00333349	+	0.000841384i
$583$	−3.56804	+	3.56804i	−0.147773	+	0.147773i
$584$	8.53199			0.353056
$585$	−2.10518	−	30.4583i	−0.0870385	−	1.25929i
$586$	−6.18983			−0.255700
$587$	26.6194	−	26.6194i	1.09870	−	1.09870i	0.104138	−	0.994563i	$-0.466791\pi$
$587$	26.6194	−	26.6194i	1.09870	−	1.09870i	0.994563	−	0.104138i	$-0.0332085\pi$
$588$	26.5112	−	6.69152i	1.09330	−	0.275953i
$589$		−	1.91179i		−	0.0787739i
$590$	−2.55553	+	5.63946i	−0.105210	+	0.232173i
$591$	11.9116	−	19.9548i	0.489978	−	0.820830i
$592$	8.19289	+	8.19289i	0.336726	+	0.336726i
$593$	28.7743	+	28.7743i	1.18162	+	1.18162i	0.979325	+	0.202292i	$0.0648392\pi$
$593$	28.7743	+	28.7743i	1.18162	+	1.18162i	0.202292	+	0.979325i	$0.435161\pi$
$594$	−1.86914	−	0.0816957i	−0.0766919	−	0.00335202i
$595$	−16.6244	+	6.25608i	−0.681535	+	0.256474i
$596$			39.6268i			1.62318i
$597$	−10.7520	−	42.5986i	−0.440052	−	1.74345i
$598$	−1.05904	+	1.05904i	−0.0433075	+	0.0433075i
$599$	−19.9639			−0.815701			−0.407851	−	0.913049i	$-0.633722\pi$
$599$	−19.9639			−0.815701			−0.407851	+	0.913049i	$0.633722\pi$
$600$	9.24041	−	1.69765i	0.377238	−	0.0693063i
$601$	−23.2645			−0.948978			−0.474489	−	0.880261i	$-0.657367\pi$
$601$	−23.2645			−0.948978			−0.474489	+	0.880261i	$0.657367\pi$
$602$	1.17358	−	1.17358i	0.0478316	−	0.0478316i
$603$	20.5554	+	6.15458i	0.837081	+	0.250634i
$604$			16.1043i			0.655273i
$605$	19.4717	−	7.32758i	0.791639	−	0.297908i
$606$	6.22690	+	3.71702i	0.252950	+	0.150994i
$607$	−19.3390	−	19.3390i	−0.784946	−	0.784946i	0.195715	−	0.980661i	$-0.437297\pi$
$607$	−19.3390	−	19.3390i	−0.784946	−	0.784946i	−0.980661	+	0.195715i	$0.937297\pi$
$608$	4.25893	+	4.25893i	0.172722	+	0.172722i
$609$	61.6334	+	36.7908i	2.49751	+	1.49084i
$610$	3.60182	−	7.94837i	0.145833	−	0.321820i
$611$		−	39.2505i		−	1.58790i
$612$	11.2612	+	3.37175i	0.455206	+	0.136295i
$613$	11.0324	−	11.0324i	0.445596	−	0.445596i	−0.448291	−	0.893887i	$-0.647967\pi$
$613$	11.0324	−	11.0324i	0.445596	−	0.445596i	0.893887	+	0.448291i	$0.147967\pi$
$614$	5.41632			0.218585
$615$	6.00660	+	8.64621i	0.242209	+	0.348649i
$616$	5.50902			0.221965
$617$	5.36102	−	5.36102i	0.215826	−	0.215826i	−0.590911	−	0.806737i	$-0.701231\pi$
$617$	5.36102	−	5.36102i	0.215826	−	0.215826i	0.806737	+	0.590911i	$0.201231\pi$
$618$	−0.355372	−	1.40795i	−0.0142952	−	0.0566362i
$619$		−	35.5265i		−	1.42793i	−0.700181	−	0.713965i	$-0.746898\pi$
$619$		−	35.5265i		−	1.42793i	0.700181	−	0.713965i	$-0.253102\pi$
$620$	−1.51490	−	4.02558i	−0.0608399	−	0.161671i
$621$	−6.17836	−	0.270041i	−0.247929	−	0.0108364i
$622$	−2.02518	−	2.02518i	−0.0812024	−	0.0812024i
$623$	37.7754	+	37.7754i	1.51344	+	1.51344i
$624$	14.3322	−	24.0099i	0.573749	−	0.961167i
$625$	3.26789	−	24.7855i	0.130716	−	0.991420i
$626$			1.14469i			0.0457508i
$627$	−4.18095	+	1.05529i	−0.166971	+	0.0421441i
$628$	10.1886	−	10.1886i	0.406569	−	0.406569i
$629$	−6.65389			−0.265308
$630$	4.74964	−	5.45495i	0.189230	−	0.217330i
$631$	30.4926			1.21389			0.606946	−	0.794743i	$-0.292394\pi$
$631$	30.4926			1.21389			0.606946	+	0.794743i	$0.292394\pi$
$632$	5.45123	−	5.45123i	0.216838	−	0.216838i
$633$	−35.3783	+	8.92961i	−1.40616	+	0.354920i
$634$		−	2.48720i		−	0.0987794i
$635$	−25.2372	−	11.4363i	−1.00151	−	0.453835i
$636$	−6.61704	+	11.0851i	−0.262383	+	0.439554i
$637$	26.4116	+	26.4116i	1.04647	+	1.04647i
$638$	2.70569	+	2.70569i	0.107119	+	0.107119i
$639$	−18.5446	−	34.3956i	−0.733612	−	1.36067i
$640$	16.3377	+	7.40347i	0.645805	+	0.292648i
$641$		−	1.65769i		−	0.0654749i	−0.999464	−	0.0327375i	$-0.989577\pi$
$641$		−	1.65769i		−	0.0654749i	0.999464	−	0.0327375i	$-0.0104225\pi$
$642$	1.15727	+	4.58500i	0.0456738	+	0.180955i
$643$	−4.84062	+	4.84062i	−0.190895	+	0.190895i	−0.796083	−	0.605188i	$-0.793098\pi$
$643$	−4.84062	+	4.84062i	−0.190895	+	0.190895i	0.605188	+	0.796083i	$0.293098\pi$
$644$	8.92747			0.351792
$645$	−1.05694	+	5.86719i	−0.0416169	+	0.231020i
$646$	−1.07679			−0.0423658
$647$	−15.2649	+	15.2649i	−0.600126	+	0.600126i	−0.940346	−	0.340220i	$-0.889498\pi$
$647$	−15.2649	+	15.2649i	−0.600126	+	0.600126i	0.340220	+	0.940346i	$0.389498\pi$
$648$	−9.56204	+	1.97378i	−0.375633	+	0.0775376i
$649$		−	13.0408i		−	0.511897i
$650$	4.14820	+	4.73102i	0.162706	+	0.185566i
$651$	−5.79960	−	3.46195i	−0.227304	−	0.135685i
$652$	15.5370	+	15.5370i	0.608475	+	0.608475i
$653$	2.63146	+	2.63146i	0.102977	+	0.102977i	0.756718	−	0.653741i	$-0.226802\pi$
$653$	2.63146	+	2.63146i	0.102977	+	0.102977i	−0.653741	+	0.756718i	$0.726802\pi$
$654$	−2.73459	−	1.63236i	−0.106931	−	0.0638303i
$655$	−13.8082	−	36.6928i	−0.539531	−	1.43371i
$656$			9.64215i			0.376463i
$657$	−6.76755	+	22.6026i	−0.264027	+	0.881813i
$658$	6.57515	−	6.57515i	0.256326	−	0.256326i
$659$	−18.1892			−0.708552			−0.354276	−	0.935141i	$-0.615273\pi$
$659$	−18.1892			−0.708552			−0.354276	+	0.935141i	$0.615273\pi$
$660$	−7.96746	+	5.53506i	−0.310133	+	0.215452i
$661$	19.5650			0.760990			0.380495	−	0.924783i	$-0.375754\pi$
$661$	19.5650			0.760990			0.380495	+	0.924783i	$0.375754\pi$
$662$	2.28404	−	2.28404i	0.0887718	−	0.0887718i
$663$	3.92989	+	15.5699i	0.152624	+	0.604684i
$664$		−	3.20820i		−	0.124502i
$665$	6.88069	−	15.1841i	0.266822	−	0.588813i
$666$	2.38492	−	1.28584i	0.0924137	−	0.0498253i
$667$	8.94351	+	8.94351i	0.346294	+	0.346294i
$668$	5.85506	+	5.85506i	0.226539	+	0.226539i
$669$	2.36689	−	3.96511i	0.0915093	−	0.153300i
$670$	−4.13869	+	1.55747i	−0.159892	+	0.0601702i
$671$			18.3800i			0.709551i
$672$	20.6321	−	5.20762i	0.795902	−	0.200888i
$673$	0.155305	−	0.155305i	0.00598658	−	0.00598658i	−0.704107	−	0.710094i	$-0.748653\pi$
$673$	0.155305	−	0.155305i	0.00598658	−	0.00598658i	0.710094	+	0.704107i	$0.248653\pi$
$674$	−5.59037			−0.215333
$675$	−2.83211	+	25.8259i	−0.109008	+	0.994041i
$676$	14.8386			0.570714
$677$	−1.73057	+	1.73057i	−0.0665114	+	0.0665114i	−0.739580	−	0.673069i	$-0.764976\pi$
$677$	−1.73057	+	1.73057i	−0.0665114	+	0.0665114i	0.673069	+	0.739580i	$0.264976\pi$
$678$	−4.21325	+	1.06344i	−0.161809	+	0.0408411i
$679$			0.675368i			0.0259183i
$680$	−4.62483	+	1.74041i	−0.177354	+	0.0667417i
$681$	6.53937	−	10.9550i	0.250589	−	0.419797i
$682$	−0.254601	−	0.254601i	−0.00974918	−	0.00974918i
$683$	9.85086	+	9.85086i	0.376933	+	0.376933i	0.869994	−	0.493062i	$-0.164122\pi$
$683$	9.85086	+	9.85086i	0.376933	+	0.376933i	−0.493062	+	0.869994i	$0.664122\pi$
$684$	−9.71077	+	5.23561i	−0.371301	+	0.200189i
$685$	−11.1182	+	24.5352i	−0.424804	+	0.937443i
$686$			1.30125i			0.0496820i
$687$	4.21723	+	16.7083i	0.160897	+	0.637461i
$688$	−3.86085	+	3.86085i	−0.147194	+	0.147194i
$689$	−17.6357			−0.671866
$690$	1.04671	−	0.727158i	0.0398475	−	0.0276824i
$691$	−19.0820			−0.725915			−0.362958	−	0.931806i	$-0.618233\pi$
$691$	−19.0820			−0.725915			−0.362958	+	0.931806i	$0.618233\pi$
$692$	−7.73790	+	7.73790i	−0.294151	+	0.294151i
$693$	−4.36974	+	14.5943i	−0.165993	+	0.554392i
$694$		−	4.23815i		−	0.160878i
$695$	10.3434	+	27.4858i	0.392349	+	1.04260i
$696$	17.1461	+	10.2350i	0.649921	+	0.387957i
$697$	−3.91546	−	3.91546i	−0.148308	−	0.148308i
$698$	−0.230651	−	0.230651i	−0.00873029	−	0.00873029i
$699$	−39.3803	−	23.5073i	−1.48950	−	0.889127i
$700$	2.45654	−	37.4248i	0.0928485	−	1.41452i
$701$		−	5.06789i		−	0.191411i	−0.995410	−	0.0957057i	$-0.969489\pi$
$701$		−	5.06789i		−	0.191411i	0.995410	−	0.0957057i	$-0.0305108\pi$
$702$	−4.41740	−	4.82119i	−0.166724	−	0.181964i
$703$	4.41569	−	4.41569i	0.166541	−	0.166541i
$704$	−8.10399			−0.305431
$705$	−5.92163	+	32.8717i	−0.223022	+	1.23802i
$706$	−4.98099			−0.187462
$707$	41.7549	−	41.7549i	1.57036	−	1.57036i
$708$	−8.16521	−	32.3498i	−0.306867	−	1.21578i
$709$			25.3000i			0.950162i	0.879942	+	0.475081i	$0.157581\pi$
$709$			25.3000i			0.950162i	−0.879942	+	0.475081i	$0.842419\pi$
$710$	7.33519	+	3.32396i	0.275285	+	0.124746i
$711$	10.1173	+	18.7651i	0.379429	+	0.703747i
$712$	10.5089	+	10.5089i	0.393839	+	0.393839i
$713$	−0.841570	−	0.841570i	−0.0315171	−	0.0315171i
$714$	−1.94990	+	3.26656i	−0.0729733	+	0.122248i
$715$	−12.0711	−	5.47006i	−0.451435	−	0.204569i
$716$		−	6.33941i		−	0.236915i
$717$	14.6541	−	3.69875i	0.547269	−	0.138133i
$718$	−2.94957	+	2.94957i	−0.110077	+	0.110077i
$719$	18.3859			0.685677			0.342839	−	0.939394i	$-0.388612\pi$
$719$	18.3859			0.685677			0.342839	+	0.939394i	$0.388612\pi$
$720$	−15.6254	+	17.9457i	−0.582323	+	0.668796i
$721$	−11.8241			−0.440353
$722$	−3.00015	+	3.00015i	−0.111654	+	0.111654i
$723$	29.6227	−	7.47686i	1.10168	−	0.278067i
$724$		−	0.531572i		−	0.0197557i
$725$	39.9530	−	35.0311i	1.48382	−	1.30102i
$726$	2.28387	−	3.82603i	0.0847623	−	0.141997i
$727$	26.0950	+	26.0950i	0.967809	+	0.967809i	0.999498	−	0.0316889i	$-0.0100886\pi$
$727$	26.0950	+	26.0950i	0.967809	+	0.967809i	−0.0316889	+	0.999498i	$0.510089\pi$
$728$	13.6147	+	13.6147i	0.504593	+	0.504593i
$729$	2.35571	−	26.8970i	0.0872484	−	0.996187i
$730$	−1.71258	−	4.55089i	−0.0633856	−	0.168436i
$731$		−	3.13560i		−	0.115975i
$732$	11.5082	+	45.5945i	0.425355	+	1.68522i
$733$	35.0168	−	35.0168i	1.29338	−	1.29338i	0.360691	−	0.932685i	$-0.382541\pi$
$733$	35.0168	−	35.0168i	1.29338	−	1.29338i	0.932685	−	0.360691i	$-0.117459\pi$
$734$	−10.3410			−0.381693
$735$	−18.1347	−	26.1040i	−0.668907	−	0.962860i
$736$	3.74956			0.138211
$737$	6.58596	−	6.58596i	0.242597	−	0.242597i
$738$	2.16005	+	0.646748i	0.0795124	+	0.0238071i
$739$			19.3366i			0.711309i	0.934618	+	0.355654i	$0.115742\pi$
$739$			19.3366i			0.711309i	−0.934618	+	0.355654i	$0.884258\pi$
$740$	5.79895	−	12.7969i	0.213174	−	0.470424i
$741$	−12.9405	−	7.72459i	−0.475382	−	0.283770i
$742$	−2.95429	−	2.95429i	−0.108455	−	0.108455i
$743$	5.90304	+	5.90304i	0.216561	+	0.216561i	0.807048	−	0.590486i	$-0.201064\pi$
$743$	5.90304	+	5.90304i	0.216561	+	0.216561i	−0.590486	+	0.807048i	$0.701064\pi$
$744$	−1.61342	−	0.963098i	−0.0591509	−	0.0353089i
$745$	43.1133	−	16.2243i	1.57955	−	0.594414i
$746$		−	0.844265i		−	0.0309107i
$747$	8.49904	+	2.54473i	0.310964	+	0.0931069i
$748$	3.60808	−	3.60808i	0.131924	−	0.131924i
$749$	38.5052			1.40695
$750$	−2.76029	−	4.58799i	−0.100792	−	0.167530i
$751$	−13.6195			−0.496981			−0.248491	−	0.968634i	$-0.579935\pi$
$751$	−13.6195			−0.496981			−0.248491	+	0.968634i	$0.579935\pi$
$752$	−21.6309	+	21.6309i	−0.788798	+	0.788798i
$753$	10.0276	+	39.7283i	0.365425	+	1.44778i
$754$			13.3734i			0.487029i
$755$	17.5211	−	6.59354i	0.637660	−	0.239963i
$756$	−1.70195	+	38.9395i	−0.0618993	+	1.41622i
$757$	1.79426	+	1.79426i	0.0652134	+	0.0652134i	0.738961	−	0.673748i	$-0.235317\pi$
$757$	1.79426	+	1.79426i	0.0652134	+	0.0652134i	−0.673748	+	0.738961i	$0.735317\pi$
$758$	−3.30018	−	3.30018i	−0.119868	−	0.119868i
$759$	−1.37592	+	2.30499i	−0.0499427	+	0.0836660i
$760$	1.91417	−	4.22414i	0.0694344	−	0.153225i
$761$		−	25.0126i		−	0.906708i	−0.891331	−	0.453354i	$-0.850227\pi$
$761$		−	25.0126i		−	0.906708i	0.891331	−	0.453354i	$-0.149773\pi$
$762$	−5.75375	+	1.45227i	−0.208436	+	0.0526101i
$763$	−18.3370	+	18.3370i	−0.663845	+	0.663845i
$764$	15.2310			0.551037
$765$	−0.942232	−	13.6324i	−0.0340665	−	0.492882i
$766$	5.77076			0.208506
$767$	32.2283	−	32.2283i	1.16370	−	1.16370i
$768$	−17.1774	+	4.33565i	−0.619838	+	0.156449i
$769$			13.4564i			0.485249i	0.970120	+	0.242624i	$0.0780083\pi$
$769$			13.4564i			0.485249i	−0.970120	+	0.242624i	$0.921992\pi$
$770$	−1.10580	−	2.93846i	−0.0398502	−	0.105895i
$771$	−0.105823	+	0.177278i	−0.00381111	+	0.00638453i
$772$	−30.3750	−	30.3750i	−1.09322	−	1.09322i
$773$	7.47981	+	7.47981i	0.269030	+	0.269030i	0.828709	−	0.559679i	$-0.189076\pi$
$773$	7.47981	+	7.47981i	0.269030	+	0.269030i	−0.559679	+	0.828709i	$0.689076\pi$
$774$	0.605945	+	1.12388i	0.0217803	+	0.0403970i
$775$	−3.75951	+	3.29637i	−0.135046	+	0.118409i
$776$			0.187884i			0.00674465i
$777$	−5.39930	−	21.3916i	−0.193699	−	0.767418i
$778$	3.40506	−	3.40506i	0.122077	−	0.122077i
$779$	5.19679			0.186194
$780$	−33.3693	−	6.01128i	−1.19481	−	0.215238i
$781$	−16.9621			−0.606950
$782$	−0.474004	+	0.474004i	−0.0169504	+	0.0169504i
$783$	−40.7145	+	37.3045i	−1.45502	+	1.33315i
$784$		−	29.1108i		−	1.03967i
$785$	−15.2565	−	6.91350i	−0.544527	−	0.246753i
$786$	−7.20983	−	4.30376i	−0.257166	−	0.153510i
$787$	−19.0064	−	19.0064i	−0.677505	−	0.677505i	0.281930	−	0.959435i	$-0.409026\pi$
$787$	−19.0064	−	19.0064i	−0.677505	−	0.677505i	−0.959435	+	0.281930i	$0.909026\pi$
$788$	−18.2497	−	18.2497i	−0.650120	−	0.650120i
$789$	−20.5196	−	12.2488i	−0.730518	−	0.436068i
$790$	−4.00184	−	1.81344i	−0.142379	−	0.0645193i
$791$			35.3832i			1.25808i
$792$	−1.21564	+	4.06006i	−0.0431959	+	0.144268i
$793$	−45.4232	+	45.4232i	−1.61302	+	1.61302i
$794$	5.64537			0.200347
$795$	14.7696	+	2.66066i	0.523824	+	0.0943637i
$796$	−48.7921			−1.72939
$797$	−10.2094	+	10.2094i	−0.361636	+	0.361636i	−0.864415	−	0.502779i	$-0.832311\pi$
$797$	−10.2094	+	10.2094i	−0.361636	+	0.361636i	0.502779	+	0.864415i	$0.332311\pi$
$798$	−0.873764	−	3.46177i	−0.0309309	−	0.122545i
$799$		−	17.5676i		−	0.621498i
$800$	1.03175	−	15.7185i	0.0364780	−	0.555734i
$801$	−36.1755	+	19.5042i	−1.27820	+	0.689148i
$802$	−7.65332	−	7.65332i	−0.270248	−	0.270248i
$803$	7.24189	+	7.24189i	0.255561	+	0.255561i
$804$	12.2139	−	20.4612i	0.430750	−	0.721610i
$805$	−3.65516	−	9.71292i	−0.128827	−	0.342336i
$806$		−	1.25841i		−	0.0443257i
$807$	−6.18417	+	1.56091i	−0.217693	+	0.0549465i
$808$	11.6160	−	11.6160i	0.408650	−	0.408650i
$809$	−7.10033			−0.249634			−0.124817	−	0.992180i	$-0.539834\pi$
$809$	−7.10033			−0.249634			−0.124817	+	0.992180i	$0.539834\pi$
$810$	2.97214	+	4.70412i	0.104430	+	0.165286i
$811$	16.5900			0.582555			0.291278	−	0.956639i	$-0.405920\pi$
$811$	16.5900			0.582555			0.291278	+	0.956639i	$0.405920\pi$
$812$	56.3671	−	56.3671i	1.97810	−	1.97810i
$813$	−17.6533	+	4.45577i	−0.619130	+	0.156271i
$814$		−	1.17611i		−	0.0412227i
$815$	10.5427	−	23.2652i	0.369294	−	0.814945i
$816$	6.41479	−	10.7463i	0.224563	−	0.376196i
$817$	2.08087	+	2.08087i	0.0728003	+	0.0728003i
$818$	0.622767	+	0.622767i	0.0217745	+	0.0217745i
$819$	−46.8666	+	25.2684i	−1.63765	+	0.882949i
$820$	10.9427	−	4.11794i	0.382135	−	0.143805i
$821$			8.33701i			0.290964i	0.989361	+	0.145482i	$0.0464732\pi$
$821$			8.33701i			0.290964i	−0.989361	+	0.145482i	$0.953527\pi$
$822$	1.41187	+	5.59371i	0.0492447	+	0.195103i
$823$	−23.4837	+	23.4837i	−0.818590	+	0.818590i	−0.985904	−	0.167314i	$-0.946491\pi$
$823$	−23.4837	+	23.4837i	−0.818590	+	0.818590i	0.167314	+	0.985904i	$0.446491\pi$
$824$	−3.28941			−0.114592
$825$	9.28415	+	6.40224i	0.323232	+	0.222897i
$826$	10.7976			0.375697
$827$	−12.4519	+	12.4519i	−0.432996	+	0.432996i	−0.889646	−	0.456650i	$-0.849049\pi$
$827$	−12.4519	+	12.4519i	−0.432996	+	0.432996i	0.456650	+	0.889646i	$0.349049\pi$
$828$	−1.96997	+	6.57941i	−0.0684611	+	0.228650i
$829$			30.6849i			1.06573i	0.846200	+	0.532866i	$0.178885\pi$
$829$			30.6849i			1.06573i	−0.846200	+	0.532866i	$0.821115\pi$
$830$	−1.71122	+	0.643966i	−0.0593974	+	0.0223524i
$831$	−27.7015	−	16.5359i	−0.960956	−	0.573623i
$832$	−20.0277	−	20.0277i	−0.694337	−	0.694337i
$833$	11.8212	+	11.8212i	0.409582	+	0.409582i
$834$	5.40073	+	3.22385i	0.187012	+	0.111633i
$835$	3.97297	−	8.76742i	0.137490	−	0.303409i
$836$			4.78882i			0.165625i
$837$	3.83117	−	3.51029i	0.132425	−	0.121333i
$838$	5.52304	−	5.52304i	0.190790	−	0.190790i
$839$	52.1445			1.80023			0.900113	−	0.435656i	$-0.143483\pi$
$839$	52.1445			1.80023			0.900113	+	0.435656i	$0.143483\pi$
$840$	−9.34807	−	13.4561i	−0.322539	−	0.464279i
$841$	83.9367			2.89437
$842$	1.92546	−	1.92546i	0.0663558	−	0.0663558i
$843$	−5.94639	−	23.5591i	−0.204805	−	0.811417i
$844$			40.5220i			1.39483i
$845$	−6.07532	−	16.1441i	−0.208997	−	0.555373i
$846$	3.39489	+	6.29668i	0.116719	+	0.216484i
$847$	−25.6557	−	25.6557i	−0.881541	−	0.881541i
$848$	9.71901	+	9.71901i	0.333752	+	0.333752i
$849$	24.4362	−	40.9365i	0.838649	−	1.40494i
$850$	1.85664	+	2.11750i	0.0636822	+	0.0726297i
$851$		−	3.88757i		−	0.133264i
$852$	−42.0771	+	10.6204i	−1.44154	+	0.363849i
$853$	−3.54410	+	3.54410i	−0.121348	+	0.121348i	−0.765173	−	0.643825i	$-0.777346\pi$
$853$	−3.54410	+	3.54410i	−0.121348	+	0.121348i	0.643825	+	0.765173i	$0.277346\pi$
$854$	−15.2184			−0.520762
$855$	9.67211	+	8.42154i	0.330779	+	0.288010i
$856$	10.7120			0.366127
$857$	−35.5654	+	35.5654i	−1.21489	+	1.21489i	−0.245493	+	0.969398i	$0.578950\pi$
$857$	−35.5654	+	35.5654i	−1.21489	+	1.21489i	−0.969398	+	0.245493i	$0.921050\pi$
$858$	−2.75206	+	0.694630i	−0.0939539	+	0.0237143i
$859$		−	28.2204i		−	0.962867i	−0.876483	−	0.481433i	$-0.840116\pi$
$859$		−	28.2204i		−	0.962867i	0.876483	−	0.481433i	$-0.159884\pi$
$860$	6.03048	+	2.73272i	0.205638	+	0.0931850i
$861$	9.41059	−	15.7650i	0.320712	−	0.537269i
$862$	−1.69800	−	1.69800i	−0.0578341	−	0.0578341i
$863$	−20.6246	−	20.6246i	−0.702071	−	0.702071i	0.262784	−	0.964855i	$-0.415359\pi$
$863$	−20.6246	−	20.6246i	−0.702071	−	0.702071i	−0.964855	+	0.262784i	$0.915359\pi$
$864$	−0.714824	+	16.3547i	−0.0243188	+	0.556398i
$865$	11.5868	+	5.25058i	0.393963	+	0.178525i
$866$		−	6.92012i		−	0.235155i
$867$	−5.44706	−	21.5808i	−0.184992	−	0.732921i
$868$	−5.30405	+	5.30405i	−0.180031	+	0.180031i
$869$	9.25394			0.313918
$870$	2.01761	−	11.2000i	0.0684034	−	0.379716i
$871$	32.5523			1.10299
$872$	−5.10127	+	5.10127i	−0.172751	+	0.172751i
$873$	−0.497736	−	0.149029i	−0.0168458	−	0.00504388i
$874$		−	0.629122i		−	0.0212804i
$875$	−41.7233	+	12.6501i	−1.41050	+	0.427651i
$876$	22.4990	+	13.4303i	0.760171	+	0.453769i
$877$	−9.16867	−	9.16867i	−0.309604	−	0.309604i	0.535152	−	0.844756i	$-0.320254\pi$
$877$	−9.16867	−	9.16867i	−0.309604	−	0.309604i	−0.844756	+	0.535152i	$0.820254\pi$
$878$	4.22869	+	4.22869i	0.142711	+	0.142711i
$879$	−33.2941	−	19.8743i	−1.12298	−	0.670342i
$880$	3.63785	+	9.66695i	0.122632	+	0.325873i
$881$		−	6.91859i		−	0.233093i	−0.993185	−	0.116547i	$-0.962818\pi$
$881$		−	6.91859i		−	0.233093i	0.993185	−	0.116547i	$-0.0371824\pi$
$882$	−6.52145	−	1.95261i	−0.219589	−	0.0657479i
$883$	4.33450	−	4.33450i	0.145867	−	0.145867i	−0.630402	−	0.776269i	$-0.717110\pi$
$883$	4.33450	−	4.33450i	0.145867	−	0.145867i	0.776269	+	0.630402i	$0.217110\pi$
$884$	17.8336			0.599809
$885$	−31.8529	+	22.1285i	−1.07073	+	0.743842i
$886$	0.515928			0.0173329
$887$	−11.7332	+	11.7332i	−0.393961	+	0.393961i	−0.876097	−	0.482135i	$-0.839861\pi$
$887$	−11.7332	+	11.7332i	−0.393961	+	0.393961i	0.482135	+	0.876097i	$0.339861\pi$
$888$	−1.50206	−	5.95102i	−0.0504058	−	0.199703i
$889$			48.3205i			1.62062i
$890$	3.49596	−	7.71477i	0.117185	−	0.258600i
$891$	−9.79153	−	6.44086i	−0.328029	−	0.215777i
$892$	−3.62631	−	3.62631i	−0.121418	−	0.121418i
$893$	11.6583	+	11.6583i	0.390131	+	0.390131i
$894$	5.05682	−	8.47139i	0.169125	−	0.283326i
$895$	−6.89717	+	2.59553i	−0.230547	+	0.0867591i
$896$		−	31.2811i		−	1.04503i
$897$	−9.09680	+	2.29606i	−0.303733	+	0.0766633i
$898$	−6.19816	+	6.19816i	−0.206835	+	0.206835i
$899$	−10.6272			−0.354436
$900$	27.0394	+	10.0687i	0.901314	+	0.335624i
$901$	−7.89333			−0.262965
$902$	0.692079	−	0.692079i	0.0230437	−	0.0230437i
$903$	10.0806	−	2.54439i	0.335463	−	0.0846720i
$904$			9.84343i			0.327388i
$905$	−0.578341	+	0.217641i	−0.0192247	+	0.00723462i
$906$	2.05508	−	3.44275i	0.0682755	−	0.114378i
$907$	−3.53335	−	3.53335i	−0.117323	−	0.117323i	0.646008	−	0.763331i	$-0.276437\pi$
$907$	−3.53335	−	3.53335i	−0.117323	−	0.117323i	−0.763331	+	0.646008i	$0.776437\pi$
$908$	−10.0190	−	10.0190i	−0.332491	−	0.332491i
$909$	21.5589	+	39.9865i	0.715065	+	1.32627i
$910$	4.52914	−	9.99475i	0.150139	−	0.331323i
$911$		−	9.32251i		−	0.308868i	−0.988003	−	0.154434i	$-0.950645\pi$
$911$		−	9.32251i		−	0.308868i	0.988003	−	0.154434i	$-0.0493555\pi$
$912$	2.87451	+	11.3885i	0.0951844	+	0.377112i
$913$	2.72309	−	2.72309i	0.0901213	−	0.0901213i
$914$	−9.11677			−0.301556
$915$	44.8942	−	31.1884i	1.48415	−	1.03106i
$916$	19.1375			0.632322
$917$	−48.3460	+	48.3460i	−1.59653	+	1.59653i
$918$	−1.97713	−	2.15786i	−0.0652550	−	0.0712200i
$919$			40.7720i			1.34494i	0.740122	+	0.672472i	$0.234768\pi$
$919$			40.7720i			1.34494i	−0.740122	+	0.672472i	$0.765232\pi$
$920$	−1.01685	−	2.70209i	−0.0335244	−	0.0890852i
$921$	29.1335	+	17.3907i	0.959983	+	0.573042i
$922$	6.90867	+	6.90867i	0.227525	+	0.227525i
$923$	−41.9190	−	41.9190i	−1.37978	−	1.37978i
$924$	14.5274	+	8.67182i	0.477916	+	0.285282i
$925$	−16.2971	−	1.06973i	−0.535845	−	0.0351725i
$926$			1.72336i			0.0566332i
$927$	2.60915	−	8.71419i	0.0856958	−	0.286212i
$928$	23.6743	−	23.6743i	0.777148	−	0.777148i
$929$	2.88821			0.0947591			0.0473795	−	0.998877i	$-0.484913\pi$
$929$	2.88821			0.0947591			0.0473795	+	0.998877i	$0.484913\pi$
$930$	−0.189854	+	1.05390i	−0.00622556	+	0.0345588i
$931$	−15.6898			−0.514211
$932$	−36.0155	+	36.0155i	−1.17973	+	1.17973i
$933$	−4.39070	−	17.3956i	−0.143745	−	0.569506i
$934$			8.67942i			0.283999i
$935$	−5.40277	−	2.44828i	−0.176690	−	0.0800672i
$936$	−13.0381	+	7.02954i	−0.426162	+	0.229768i
$937$	8.88659	+	8.88659i	0.290312	+	0.290312i	0.837204	−	0.546891i	$-0.184189\pi$
$937$	8.88659	+	8.88659i	0.290312	+	0.290312i	−0.546891	+	0.837204i	$0.684189\pi$
$938$	5.45309	+	5.45309i	0.178050	+	0.178050i
$939$	−3.67535	+	6.15709i	−0.119940	+	0.200929i
$940$	33.7865	+	15.3104i	1.10200	+	0.499371i
$941$		−	15.9068i		−	0.518546i	−0.965804	−	0.259273i	$-0.916517\pi$
$941$		−	15.9068i		−	0.518546i	0.965804	−	0.259273i	$-0.0834829\pi$
$942$	−3.47828	+	0.877930i	−0.113329	+	0.0286045i
$943$	2.28763	−	2.28763i	0.0744955	−	0.0744955i
$944$	−35.5220			−1.15614
$945$	43.0623	−	14.0912i	1.40082	−	0.458388i
$946$	0.554236			0.0180198
$947$	30.9163	−	30.9163i	1.00465	−	1.00465i	0.00465593	−	0.999989i	$-0.498518\pi$
$947$	30.9163	−	30.9163i	1.00465	−	1.00465i	0.999989	−	0.00465593i	$-0.00148204\pi$
$948$	22.9559	−	5.79414i	0.745572	−	0.188185i
$949$			35.7944i			1.16193i
$950$	−2.63734	−	0.173113i	−0.0855666	−	0.00561654i
$951$	7.98588	−	13.3783i	0.258960	−	0.433820i
$952$	6.09362	+	6.09362i	0.197495	+	0.197495i
$953$	−11.5932	−	11.5932i	−0.375541	−	0.375541i	0.493949	−	0.869491i	$-0.335553\pi$
$953$	−11.5932	−	11.5932i	−0.375541	−	0.375541i	−0.869491	+	0.493949i	$0.835553\pi$
$954$	2.82917	−	1.52536i	0.0915977	−	0.0493854i
$955$	−6.23598	−	16.5710i	−0.201792	−	0.536225i
$956$		−	16.7847i		−	0.542857i
$957$	5.86608	+	23.2409i	0.189623	+	0.751271i
$958$	0.0759606	−	0.0759606i	0.00245417	−	0.00245417i
$959$	46.9765			1.51695
$960$	13.7514	+	19.7945i	0.443824	+	0.638864i
$961$	1.00000			0.0322581
$962$	2.90658	−	2.90658i	0.0937118	−	0.0937118i
$963$	−8.49669	+	28.3777i	−0.273802	+	0.914460i
$964$		−	33.9295i		−	1.09280i
$965$	−20.6111	+	45.4839i	−0.663495	+	1.46418i
$966$	−1.90851	−	1.13924i	−0.0614052	−	0.0366546i
$967$	26.9351	+	26.9351i	0.866175	+	0.866175i	0.992047	−	0.125871i	$-0.0401726\pi$
$967$	26.9351	+	26.9351i	0.866175	+	0.866175i	−0.125871	+	0.992047i	$0.540173\pi$
$968$	−7.13729	−	7.13729i	−0.229401	−	0.229401i
$969$	−5.79189	−	3.45735i	−0.186062	−	0.111066i
$970$	0.100216	−	0.0377131i	0.00321773	−	0.00121089i
$971$			5.22062i			0.167538i	0.996485	+	0.0837689i	$0.0266957\pi$
$971$			5.22062i			0.167538i	−0.996485	+	0.0837689i	$0.973304\pi$
$972$	−28.3223	−	9.84684i	−0.908437	−	0.315838i
$973$	36.2150	−	36.2150i	1.16100	−	1.16100i
$974$	−3.99503			−0.128009
$975$	7.12218	+	38.7664i	0.228092	+	1.24152i
$976$	50.0654			1.60255
$977$	−19.6221	+	19.6221i	−0.627767	+	0.627767i	−0.947506	−	0.319739i	$-0.896405\pi$
$977$	−19.6221	+	19.6221i	−0.627767	+	0.627767i	0.319739	+	0.947506i	$0.396405\pi$
$978$	−1.33879	−	5.30417i	−0.0428098	−	0.169609i
$979$			17.8398i			0.570163i
$980$	−33.0373	+	12.4326i	−1.05534	+	0.397144i
$981$	−9.46779	−	17.5604i	−0.302283	−	0.560661i
$982$	−2.82623	−	2.82623i	−0.0901886	−	0.0901886i
$983$	27.1611	+	27.1611i	0.866304	+	0.866304i	0.992061	−	0.125757i	$-0.0401359\pi$
$983$	27.1611	+	27.1611i	0.866304	+	0.866304i	−0.125757	+	0.992061i	$0.540136\pi$
$984$	2.61798	−	4.38574i	0.0834581	−	0.139812i
$985$	−12.3834	+	27.3273i	−0.394569	+	0.870721i
$986$			5.98562i			0.190621i
$987$	56.4781	−	14.2553i	1.79772	−	0.453750i
$988$	−11.8348	+	11.8348i	−0.376516	+	0.376516i
$989$	1.83200			0.0582541
$990$	2.40961	−	0.166545i	0.0765824	−	0.00529314i
$991$	−23.4936			−0.746300			−0.373150	−	0.927771i	$-0.621722\pi$
$991$	−23.4936			−0.746300			−0.373150	+	0.927771i	$0.621722\pi$
$992$	−2.22772	+	2.22772i	−0.0707301	+	0.0707301i
$993$	19.6191	−	4.95192i	0.622593	−	0.157145i
$994$		−	14.0444i		−	0.445460i
$995$	19.9769	+	53.0849i	0.633309	+	1.68291i
$996$	5.05007	−	8.46007i	0.160018	−	0.268068i
$997$	−24.1362	−	24.1362i	−0.764401	−	0.764401i	0.212713	−	0.977115i	$-0.431770\pi$
$997$	−24.1362	−	24.1362i	−0.764401	−	0.764401i	−0.977115	+	0.212713i	$0.931770\pi$
$998$	5.56481	+	5.56481i	0.176151	+	0.176151i
$999$	16.9567	+	0.741135i	0.536486	+	0.0234485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.32.14	✓	60
3.2	odd	2	inner	465.2.k.b.32.17	yes	60
5.3	odd	4	inner	465.2.k.b.218.17	yes	60
15.8	even	4	inner	465.2.k.b.218.14	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.14	✓	60	1.1	even	1	trivial
465.2.k.b.32.17	yes	60	3.2	odd	2	inner
465.2.k.b.218.14	yes	60	15.8	even	4	inner
465.2.k.b.218.17	yes	60	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.195513 + 0.195513i) q^{2} +(-1.67938 + 0.423882i) q^{3} +1.92355i q^{4} +(2.09279 - 0.787555i) q^{5} +(0.245466 - 0.411215i) q^{6} +(-2.75743 - 2.75743i) q^{7} +(-0.767103 - 0.767103i) q^{8} +(2.64065 - 1.42372i) q^{9} +O(q^{10})\)	\(q+(-0.195513 + 0.195513i) q^{2} +(-1.67938 + 0.423882i) q^{3} +1.92355i q^{4} +(2.09279 - 0.787555i) q^{5} +(0.245466 - 0.411215i) q^{6} +(-2.75743 - 2.75743i) q^{7} +(-0.767103 - 0.767103i) q^{8} +(2.64065 - 1.42372i) q^{9} +(-0.255189 + 0.563143i) q^{10} -1.30222i q^{11} +(-0.815358 - 3.23037i) q^{12} +(3.21824 - 3.21824i) q^{13} +1.07822 q^{14} +(-3.18076 + 2.20970i) q^{15} -3.54714 q^{16} +(1.44041 - 1.44041i) q^{17} +(-0.237925 + 0.794635i) q^{18} +1.91179i q^{19} +(1.51490 + 4.02558i) q^{20} +(5.79960 + 3.46195i) q^{21} +(0.254601 + 0.254601i) q^{22} +(0.841570 + 0.841570i) q^{23} +(1.61342 + 0.963098i) q^{24} +(3.75951 - 3.29637i) q^{25} +1.25841i q^{26} +(-3.83117 + 3.51029i) q^{27} +(5.30405 - 5.30405i) q^{28} +10.6272 q^{29} +(0.189854 - 1.05390i) q^{30} -1.00000 q^{31} +(2.22772 - 2.22772i) q^{32} +(0.551989 + 2.18693i) q^{33} +0.563238i q^{34} +(-7.94234 - 3.59909i) q^{35} +(2.73859 + 5.07942i) q^{36} +(-2.30971 - 2.30971i) q^{37} +(-0.373779 - 0.373779i) q^{38} +(-4.04050 + 6.76881i) q^{39} +(-2.20952 - 1.00125i) q^{40} -2.71829i q^{41} +(-1.81075 + 0.457040i) q^{42} +(1.08844 - 1.08844i) q^{43} +2.50489 q^{44} +(4.40506 - 5.05920i) q^{45} -0.329075 q^{46} +(6.09812 - 6.09812i) q^{47} +(5.95701 - 1.50357i) q^{48} +8.20684i q^{49} +(-0.0905505 + 1.37951i) q^{50} +(-1.80844 + 3.02957i) q^{51} +(6.19045 + 6.19045i) q^{52} +(-2.73996 - 2.73996i) q^{53} +(0.0627356 - 1.43535i) q^{54} +(-1.02557 - 2.72528i) q^{55} +4.23047i q^{56} +(-0.810372 - 3.21062i) q^{57} +(-2.07775 + 2.07775i) q^{58} +10.0143 q^{59} +(-4.25047 - 6.11835i) q^{60} -14.1143 q^{61} +(0.195513 - 0.195513i) q^{62} +(-11.2072 - 3.35560i) q^{63} -6.22319i q^{64} +(4.20055 - 9.26964i) q^{65} +(-0.535494 - 0.319652i) q^{66} +(5.05747 + 5.05747i) q^{67} +(2.77071 + 2.77071i) q^{68} +(-1.77004 - 1.05659i) q^{69} +(2.25649 - 0.849161i) q^{70} -13.0255i q^{71} +(-3.11779 - 0.933510i) q^{72} +(-5.56117 + 5.56117i) q^{73} +0.903157 q^{74} +(-4.91639 + 7.12945i) q^{75} -3.67742 q^{76} +(-3.59079 + 3.59079i) q^{77} +(-0.533419 - 2.11336i) q^{78} +7.10626i q^{79} +(-7.42341 + 2.79357i) q^{80} +(4.94605 - 7.51908i) q^{81} +(0.531459 + 0.531459i) q^{82} +(2.09111 + 2.09111i) q^{83} +(-6.65924 + 11.1558i) q^{84} +(1.88007 - 4.14888i) q^{85} +0.425607i q^{86} +(-17.8471 + 4.50466i) q^{87} +(-0.998940 + 0.998940i) q^{88} -13.6995 q^{89} +(0.127893 + 1.85038i) q^{90} -17.7482 q^{91} +(-1.61880 + 1.61880i) q^{92} +(1.67938 - 0.423882i) q^{93} +2.38452i q^{94} +(1.50564 + 4.00097i) q^{95} +(-2.79690 + 4.68548i) q^{96} +(-0.122463 - 0.122463i) q^{97} +(-1.60454 - 1.60454i) q^{98} +(-1.85400 - 3.43872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40} - 12 q^{42} - 24 q^{43} - 58 q^{45} + 8 q^{46} + 80 q^{48} + 32 q^{51} + 52 q^{52} + 64 q^{55} - 14 q^{57} - 48 q^{58} - 108 q^{60} - 56 q^{61} + 62 q^{63} + 40 q^{66} + 104 q^{67} + 108 q^{70} - 76 q^{72} - 108 q^{73} - 38 q^{75} - 120 q^{76} + 112 q^{78} + 60 q^{81} + 20 q^{82} + 48 q^{85} - 110 q^{87} - 28 q^{88} - 82 q^{90} - 32 q^{91} + 120 q^{96} + 56 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more