LMFDB - Embedded newform 465.2.k.a.32.13

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			32.13
Character	$\chi$	$=$	465.32
Dual form			465.2.k.a.218.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522133 + 0.522133i) q^{2} +(0.999094 - 1.41485i) q^{3} +1.45476i q^{4} +(-2.19887 - 0.406185i) q^{5} +(0.217082 + 1.26040i) q^{6} +(-1.35198 - 1.35198i) q^{7} +(-1.80384 - 1.80384i) q^{8} +(-1.00362 - 2.82714i) q^{9} +O(q^{10})$	\(q+(-0.522133 + 0.522133i) q^{2} +(0.999094 - 1.41485i) q^{3} +1.45476i q^{4} +(-2.19887 - 0.406185i) q^{5} +(0.217082 + 1.26040i) q^{6} +(-1.35198 - 1.35198i) q^{7} +(-1.80384 - 1.80384i) q^{8} +(-1.00362 - 2.82714i) q^{9} +(1.36018 - 0.936017i) q^{10} +4.17180i q^{11} +(2.05827 + 1.45344i) q^{12} +(-2.74614 + 2.74614i) q^{13} +1.41183 q^{14} +(-2.77157 + 2.70526i) q^{15} -1.02582 q^{16} +(-2.92209 + 2.92209i) q^{17} +(2.00017 + 0.952120i) q^{18} +4.74303i q^{19} +(0.590900 - 3.19881i) q^{20} +(-3.26362 + 0.562101i) q^{21} +(-2.17824 - 2.17824i) q^{22} +(-5.03865 - 5.03865i) q^{23} +(-4.35438 + 0.749965i) q^{24} +(4.67003 + 1.78629i) q^{25} -2.86770i q^{26} +(-5.00271 - 1.40460i) q^{27} +(1.96680 - 1.96680i) q^{28} +1.00949 q^{29} +(0.0346223 - 2.85963i) q^{30} +1.00000 q^{31} +(4.14330 - 4.14330i) q^{32} +(5.90249 + 4.16802i) q^{33} -3.05143i q^{34} +(2.42368 + 3.52199i) q^{35} +(4.11280 - 1.46003i) q^{36} +(-7.63858 - 7.63858i) q^{37} +(-2.47649 - 2.47649i) q^{38} +(1.14173 + 6.62904i) q^{39} +(3.23371 + 4.69910i) q^{40} -0.218381i q^{41} +(1.41055 - 1.99753i) q^{42} +(-8.99500 + 8.99500i) q^{43} -6.06895 q^{44} +(1.05849 + 6.62417i) q^{45} +5.26169 q^{46} +(5.87242 - 5.87242i) q^{47} +(-1.02489 + 1.45139i) q^{48} -3.34428i q^{49} +(-3.37106 + 1.50569i) q^{50} +(1.21489 + 7.05376i) q^{51} +(-3.99496 - 3.99496i) q^{52} +(9.70078 + 9.70078i) q^{53} +(3.34547 - 1.87869i) q^{54} +(1.69453 - 9.17324i) q^{55} +4.87752i q^{56} +(6.71069 + 4.73873i) q^{57} +(-0.527087 + 0.527087i) q^{58} -2.31265 q^{59} +(-3.93549 - 4.03195i) q^{60} -2.92893 q^{61} +(-0.522133 + 0.522133i) q^{62} +(-2.46537 + 5.17913i) q^{63} +2.27506i q^{64} +(7.15384 - 4.92295i) q^{65} +(-5.25815 + 0.905623i) q^{66} +(-3.57864 - 3.57864i) q^{67} +(-4.25092 - 4.25092i) q^{68} +(-12.1630 + 2.09487i) q^{69} +(-3.10442 - 0.573464i) q^{70} -11.3175i q^{71} +(-3.28934 + 6.91009i) q^{72} +(6.34526 - 6.34526i) q^{73} +7.97670 q^{74} +(7.19314 - 4.82273i) q^{75} -6.89994 q^{76} +(5.64021 - 5.64021i) q^{77} +(-4.05737 - 2.86510i) q^{78} +12.9361i q^{79} +(2.25565 + 0.416674i) q^{80} +(-6.98548 + 5.67477i) q^{81} +(0.114024 + 0.114024i) q^{82} +(3.65131 + 3.65131i) q^{83} +(-0.817719 - 4.74776i) q^{84} +(7.61219 - 5.23837i) q^{85} -9.39316i q^{86} +(1.00857 - 1.42828i) q^{87} +(7.52527 - 7.52527i) q^{88} -10.8720 q^{89} +(-4.01137 - 2.90602i) q^{90} +7.42547 q^{91} +(7.33000 - 7.33000i) q^{92} +(0.999094 - 1.41485i) q^{93} +6.13236i q^{94} +(1.92655 - 10.4293i) q^{95} +(-1.72262 - 10.0017i) q^{96} +(6.68329 + 6.68329i) q^{97} +(1.74616 + 1.74616i) q^{98} +(11.7943 - 4.18692i) 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} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * 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 $

$2$	−0.522133	+	0.522133i	−0.369204	+	0.369204i	−0.867187	−	0.497983i	$-0.834074\pi$
$2$	−0.522133	+	0.522133i	−0.369204	+	0.369204i	0.497983	+	0.867187i	$0.334074\pi$
$3$	0.999094	−	1.41485i	0.576827	−	0.816866i
$3$	0.999094	−	1.41485i	0.576827	−	0.816866i
$4$			1.45476i			0.727378i
$5$	−2.19887	−	0.406185i	−0.983363	−	0.181652i
$5$	−2.19887	−	0.406185i	−0.983363	−	0.181652i
$6$	0.217082	+	1.26040i	0.0886233	+	0.514557i
$7$	−1.35198	−	1.35198i	−0.511002	−	0.511002i	0.403832	−	0.914833i	$-0.367678\pi$
$7$	−1.35198	−	1.35198i	−0.511002	−	0.511002i	−0.914833	+	0.403832i	$0.867678\pi$
$8$	−1.80384	−	1.80384i	−0.637754	−	0.637754i
$9$	−1.00362	−	2.82714i	−0.334541	−	0.942381i
$10$	1.36018	−	0.936017i	0.430127	−	0.295995i
$11$			4.17180i			1.25785i	0.777467	+	0.628923i	$0.216504\pi$
$11$			4.17180i			1.25785i	−0.777467	+	0.628923i	$0.783496\pi$
$12$	2.05827	+	1.45344i	0.594170	+	0.419571i
$13$	−2.74614	+	2.74614i	−0.761642	+	0.761642i	−0.976619	−	0.214977i	$-0.931032\pi$
$13$	−2.74614	+	2.74614i	−0.761642	+	0.761642i	0.214977	+	0.976619i	$0.431032\pi$
$14$	1.41183			0.377327
$15$	−2.77157	+	2.70526i	−0.715615	+	0.698494i
$16$	−1.02582			−0.256456
$17$	−2.92209	+	2.92209i	−0.708710	+	0.708710i	−0.966264	−	0.257554i	$-0.917083\pi$
$17$	−2.92209	+	2.92209i	−0.708710	+	0.708710i	0.257554	+	0.966264i	$0.417083\pi$
$18$	2.00017	+	0.952120i	0.471444	+	0.224417i
$19$			4.74303i			1.08813i	0.839045	+	0.544063i	$0.183115\pi$
$19$			4.74303i			1.08813i	−0.839045	+	0.544063i	$0.816885\pi$
$20$	0.590900	−	3.19881i	0.132129	−	0.715276i
$21$	−3.26362	+	0.562101i	−0.712180	+	0.122660i
$22$	−2.17824	−	2.17824i	−0.464401	−	0.464401i
$23$	−5.03865	−	5.03865i	−1.05063	−	1.05063i	−0.998648	−	0.0519827i	$-0.983446\pi$
$23$	−5.03865	−	5.03865i	−1.05063	−	1.05063i	−0.0519827	−	0.998648i	$-0.516554\pi$
$24$	−4.35438	+	0.749965i	−0.888833	+	0.153086i
$25$	4.67003	+	1.78629i	0.934005	+	0.357259i
$26$		−	2.86770i		−	0.562402i
$27$	−5.00271	−	1.40460i	−0.962772	−	0.270316i
$28$	1.96680	−	1.96680i	0.371691	−	0.371691i
$29$	1.00949			0.187457			0.0937287	−	0.995598i	$-0.470121\pi$
$29$	1.00949			0.187457			0.0937287	+	0.995598i	$0.470121\pi$
$30$	0.0346223	−	2.85963i	0.00632114	−	0.522094i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	4.14330	−	4.14330i	0.732438	−	0.732438i
$33$	5.90249	+	4.16802i	1.02749	+	0.725560i
$34$		−	3.05143i		−	0.523316i
$35$	2.42368	+	3.52199i	0.409676	+	0.595324i
$36$	4.11280	−	1.46003i	0.685467	−	0.243338i
$37$	−7.63858	−	7.63858i	−1.25577	−	1.25577i	−0.953091	−	0.302684i	$-0.902117\pi$
$37$	−7.63858	−	7.63858i	−1.25577	−	1.25577i	−0.302684	−	0.953091i	$-0.597883\pi$
$38$	−2.47649	−	2.47649i	−0.401740	−	0.401740i
$39$	1.14173	+	6.62904i	0.182824	+	1.06150i
$40$	3.23371	+	4.69910i	0.511295	+	0.742993i
$41$		−	0.218381i		−	0.0341054i	−0.999855	−	0.0170527i	$-0.994572\pi$
$41$		−	0.218381i		−	0.0341054i	0.999855	−	0.0170527i	$-0.00542831\pi$
$42$	1.41055	−	1.99753i	0.217653	−	0.308226i
$43$	−8.99500	+	8.99500i	−1.37172	+	1.37172i	−0.513835	+	0.857889i	$0.671776\pi$
$43$	−8.99500	+	8.99500i	−1.37172	+	1.37172i	−0.857889	+	0.513835i	$0.828224\pi$
$44$	−6.06895			−0.914929
$45$	1.05849	+	6.62417i	0.157790	+	0.987473i
$46$	5.26169			0.775793
$47$	5.87242	−	5.87242i	0.856580	−	0.856580i	−0.134354	−	0.990933i	$-0.542896\pi$
$47$	5.87242	−	5.87242i	0.856580	−	0.856580i	0.990933	+	0.134354i	$0.0428958\pi$
$48$	−1.02489	+	1.45139i	−0.147931	+	0.209490i
$49$		−	3.34428i		−	0.477754i
$50$	−3.37106	+	1.50569i	−0.476739	+	0.212937i
$51$	1.21489	+	7.05376i	0.170118	+	0.987724i
$52$	−3.99496	−	3.99496i	−0.554001	−	0.554001i
$53$	9.70078	+	9.70078i	1.33250	+	1.33250i	0.903123	+	0.429382i	$0.141268\pi$
$53$	9.70078	+	9.70078i	1.33250	+	1.33250i	0.429382	+	0.903123i	$0.358732\pi$
$54$	3.34547	−	1.87869i	0.455260	−	0.255657i
$55$	1.69453	−	9.17324i	0.228490	−	1.23692i
$56$			4.87752i			0.651787i
$57$	6.71069	+	4.73873i	0.888853	+	0.627660i
$58$	−0.527087	+	0.527087i	−0.0692099	+	0.0692099i
$59$	−2.31265			−0.301081			−0.150541	−	0.988604i	$-0.548101\pi$
$59$	−2.31265			−0.301081			−0.150541	+	0.988604i	$0.548101\pi$
$60$	−3.93549	−	4.03195i	−0.508069	−	0.520523i
$61$	−2.92893			−0.375011			−0.187506	−	0.982264i	$-0.560040\pi$
$61$	−2.92893			−0.375011			−0.187506	+	0.982264i	$0.560040\pi$
$62$	−0.522133	+	0.522133i	−0.0663109	+	0.0663109i
$63$	−2.46537	+	5.17913i	−0.310607	+	0.652509i
$64$			2.27506i			0.284382i
$65$	7.15384	−	4.92295i	0.887324	−	0.610617i
$66$	−5.25815	+	0.905623i	−0.647233	+	0.111474i
$67$	−3.57864	−	3.57864i	−0.437200	−	0.437200i	0.453869	−	0.891069i	$-0.350044\pi$
$67$	−3.57864	−	3.57864i	−0.437200	−	0.437200i	−0.891069	+	0.453869i	$0.850044\pi$
$68$	−4.25092	−	4.25092i	−0.515500	−	0.515500i
$69$	−12.1630	+	2.09487i	−1.46426	+	0.252192i
$70$	−3.10442	−	0.573464i	−0.371050	−	0.0685421i
$71$		−	11.3175i		−	1.34314i	−0.740939	−	0.671572i	$-0.765619\pi$
$71$		−	11.3175i		−	1.34314i	0.740939	−	0.671572i	$-0.234381\pi$
$72$	−3.28934	+	6.91009i	−0.387653	+	0.814362i
$73$	6.34526	−	6.34526i	0.742656	−	0.742656i	−0.230432	−	0.973088i	$-0.574014\pi$
$73$	6.34526	−	6.34526i	0.742656	−	0.742656i	0.973088	+	0.230432i	$0.0740140\pi$
$74$	7.97670			0.927273
$75$	7.19314	−	4.82273i	0.830592	−	0.556881i
$76$	−6.89994			−0.791478
$77$	5.64021	−	5.64021i	0.642762	−	0.642762i
$78$	−4.05737	−	2.86510i	−0.459407	−	0.324409i
$79$			12.9361i			1.45542i	0.685882	+	0.727712i	$0.259416\pi$
$79$			12.9361i			1.45542i	−0.685882	+	0.727712i	$0.740584\pi$
$80$	2.25565	+	0.416674i	0.252189	+	0.0465856i
$81$	−6.98548	+	5.67477i	−0.776165	+	0.630530i
$82$	0.114024	+	0.114024i	0.0125918	+	0.0125918i
$83$	3.65131	+	3.65131i	0.400784	+	0.400784i	0.878509	−	0.477725i	$-0.158539\pi$
$83$	3.65131	+	3.65131i	0.400784	+	0.400784i	−0.477725	+	0.878509i	$0.658539\pi$
$84$	−0.817719	−	4.74776i	−0.0892204	−	0.518024i
$85$	7.61219	−	5.23837i	0.825657	−	0.568181i
$86$		−	9.39316i		−	1.01289i
$87$	1.00857	−	1.42828i	0.108130	−	0.153128i
$88$	7.52527	−	7.52527i	0.802196	−	0.802196i
$89$	−10.8720			−1.15243			−0.576213	−	0.817300i	$-0.695470\pi$
$89$	−10.8720			−1.15243			−0.576213	+	0.817300i	$0.695470\pi$
$90$	−4.01137	−	2.90602i	−0.422835	−	0.306322i
$91$	7.42547			0.778401
$92$	7.33000	−	7.33000i	0.764205	−	0.764205i
$93$	0.999094	−	1.41485i	0.103601	−	0.146714i
$94$			6.13236i			0.632505i
$95$	1.92655	−	10.4293i	0.197660	−	1.07002i
$96$	−1.72262	−	10.0017i	−0.175814	−	1.02079i
$97$	6.68329	+	6.68329i	0.678586	+	0.678586i	0.959680	−	0.281094i	$-0.0906974\pi$
$97$	6.68329	+	6.68329i	0.678586	+	0.678586i	−0.281094	+	0.959680i	$0.590697\pi$
$98$	1.74616	+	1.74616i	0.176389	+	0.176389i
$99$	11.7943	−	4.18692i	1.18537	−	0.420801i
$100$	−2.59862	+	6.79375i	−0.259862	+	0.679375i
$101$			2.79460i			0.278073i	0.990287	+	0.139036i	$0.0444005\pi$
$101$			2.79460i			0.278073i	−0.990287	+	0.139036i	$0.955600\pi$
$102$	−4.31733	−	3.04867i	−0.427480	−	0.301863i
$103$	0.203238	−	0.203238i	0.0200257	−	0.0200257i	−0.697023	−	0.717049i	$-0.745492\pi$
$103$	0.203238	−	0.203238i	0.0200257	−	0.0200257i	0.717049	+	0.697023i	$0.245492\pi$
$104$	9.90720			0.971481
$105$	7.40458	+	0.0896493i	0.722613	+	0.00874887i
$106$	−10.1302			−0.983931
$107$	−1.35951	+	1.35951i	−0.131429	+	0.131429i	−0.769761	−	0.638332i	$-0.779625\pi$
$107$	−1.35951	+	1.35951i	−0.131429	+	0.131429i	0.638332	+	0.769761i	$0.279625\pi$
$108$	2.04335	−	7.27772i	0.196622	−	0.700298i
$109$			4.55839i			0.436615i	0.975880	+	0.218307i	$0.0700535\pi$
$109$			4.55839i			0.436615i	−0.975880	+	0.218307i	$0.929946\pi$
$110$	3.90488	+	5.67442i	0.372316	+	0.541034i
$111$	−18.4391	+	3.17582i	−1.75017	+	0.301435i
$112$	1.38689	+	1.38689i	0.131049	+	0.131049i
$113$	4.31736	+	4.31736i	0.406143	+	0.406143i	0.880391	−	0.474248i	$-0.157280\pi$
$113$	4.31736	+	4.31736i	0.406143	+	0.406143i	−0.474248	+	0.880391i	$0.657280\pi$
$114$	−5.97812	+	1.02963i	−0.559902	+	0.0964333i
$115$	9.03269	+	13.1259i	0.842303	+	1.22400i
$116$			1.46856i			0.136352i
$117$	10.5198	+	5.00764i	0.972558	+	0.462957i
$118$	1.20751	−	1.20751i	0.111160	−	0.111160i
$119$	7.90122			0.724304
$120$	9.87932	+	0.119612i	0.901854	+	0.0109190i
$121$	−6.40396			−0.582178
$122$	1.52929	−	1.52929i	0.138456	−	0.138456i
$123$	−0.308977	−	0.218183i	−0.0278596	−	0.0196729i
$124$			1.45476i			0.130641i
$125$	−9.54320	−	5.82472i	−0.853570	−	0.520979i
$126$	−1.41694	−	3.99144i	−0.126231	−	0.355586i
$127$	−1.86731	−	1.86731i	−0.165697	−	0.165697i	0.619388	−	0.785085i	$-0.287381\pi$
$127$	−1.86731	−	1.86731i	−0.165697	−	0.165697i	−0.785085	+	0.619388i	$0.787381\pi$
$128$	7.09871	+	7.09871i	0.627443	+	0.627443i
$129$	3.73976	+	21.7134i	0.329267	+	1.91176i
$130$	−1.16482	+	6.30569i	−0.102161	+	0.553045i
$131$		−	0.737629i		−	0.0644469i	−0.999481	−	0.0322235i	$-0.989741\pi$
$131$		−	0.737629i		−	0.0644469i	0.999481	−	0.0322235i	$-0.0102588\pi$
$132$	−6.06346	+	8.58668i	−0.527756	+	0.747375i
$133$	6.41250	−	6.41250i	0.556034	−	0.556034i
$134$	3.73705			0.322832
$135$	10.4298	+	5.12056i	0.897651	+	0.440708i
$136$	10.5420			0.903965
$137$	−7.90994	+	7.90994i	−0.675791	+	0.675791i	−0.959045	−	0.283254i	$-0.908586\pi$
$137$	−7.90994	+	7.90994i	−0.675791	+	0.675791i	0.283254	+	0.959045i	$0.408586\pi$
$138$	5.25692	−	7.44452i	0.447499	−	0.633719i
$139$		−	11.0888i		−	0.940536i	−0.882524	−	0.470268i	$-0.844157\pi$
$139$		−	11.0888i		−	0.940536i	0.882524	−	0.470268i	$-0.155843\pi$
$140$	−5.12363	+	3.52585i	−0.433026	+	0.297989i
$141$	−2.44152	−	14.1757i	−0.205613	−	1.19381i
$142$	5.90925	+	5.90925i	0.495893	+	0.495893i
$143$	−11.4564	−	11.4564i	−0.958029	−	0.958029i
$144$	1.02954	+	2.90015i	0.0857949	+	0.241679i
$145$	−2.21973	−	0.410039i	−0.184339	−	0.0340519i
$146$			6.62613i			0.548383i
$147$	−4.73167	−	3.34125i	−0.390261	−	0.275582i
$148$	11.1123	−	11.1123i	0.913422	−	0.913422i
$149$	6.04498			0.495224			0.247612	−	0.968859i	$-0.420354\pi$
$149$	6.04498			0.495224			0.247612	+	0.968859i	$0.420354\pi$
$150$	−1.23767	+	6.27388i	−0.101055	+	0.512260i
$151$	11.9566			0.973013			0.486507	−	0.873677i	$-0.338271\pi$
$151$	11.9566			0.973013			0.486507	+	0.873677i	$0.338271\pi$
$152$	8.55567	−	8.55567i	0.693956	−	0.693956i
$153$	11.1938	+	5.32849i	0.904967	+	0.430782i
$154$			5.88988i			0.474620i
$155$	−2.19887	−	0.406185i	−0.176617	−	0.0326256i
$156$	−9.64363	+	1.66094i	−0.772108	+	0.132982i
$157$	−3.13766	−	3.13766i	−0.250413	−	0.250413i	0.570727	−	0.821140i	$-0.306661\pi$
$157$	−3.13766	−	3.13766i	−0.250413	−	0.250413i	−0.821140	+	0.570727i	$0.806661\pi$
$158$	−6.75436	−	6.75436i	−0.537348	−	0.537348i
$159$	23.4172	−	4.03320i	1.85710	−	0.319853i
$160$	−10.7935	+	7.42761i	−0.853301	+	0.587204i
$161$			13.6243i			1.07375i
$162$	0.684365	−	6.61033i	0.0537688	−	0.519357i
$163$	0.295787	−	0.295787i	0.0231679	−	0.0231679i	−0.695428	−	0.718596i	$-0.744785\pi$
$163$	0.295787	−	0.295787i	0.0231679	−	0.0231679i	0.718596	+	0.695428i	$0.244785\pi$
$164$	0.317691			0.0248075
$165$	−11.2858	−	11.5624i	−0.878599	−	0.900134i
$166$	−3.81294			−0.295942
$167$	13.8968	−	13.8968i	1.07537	−	1.07537i	0.0784477	−	0.996918i	$-0.475004\pi$
$167$	13.8968	−	13.8968i	1.07537	−	1.07537i	0.996918	−	0.0784477i	$-0.0249964\pi$
$168$	6.90098	+	4.87311i	0.532423	+	0.375968i
$169$		−	2.08257i		−	0.160198i
$170$	−1.23945	+	6.70969i	−0.0950613	+	0.514610i
$171$	13.4092	−	4.76021i	1.02543	−	0.364022i
$172$	−13.0855	−	13.0855i	−0.997761	−	0.997761i
$173$	0.499269	+	0.499269i	0.0379587	+	0.0379587i	0.725831	−	0.687873i	$-0.241455\pi$
$173$	0.499269	+	0.499269i	0.0379587	+	0.0379587i	−0.687873	+	0.725831i	$0.741455\pi$
$174$	0.219142	+	1.27236i	0.0166131	+	0.0964574i
$175$	−3.89876	−	8.72884i	−0.294718	−	0.659838i
$176$		−	4.27953i		−	0.322582i
$177$	−2.31055	+	3.27206i	−0.173672	+	0.245943i
$178$	5.67661	−	5.67661i	0.425480	−	0.425480i
$179$	−24.2909			−1.81559			−0.907795	−	0.419414i	$-0.862235\pi$
$179$	−24.2909			−1.81559			−0.907795	+	0.419414i	$0.862235\pi$
$180$	−9.63654	+	1.53984i	−0.718265	+	0.114773i
$181$	−15.4602			−1.14915			−0.574575	−	0.818452i	$-0.694833\pi$
$181$	−15.4602			−1.14915			−0.574575	+	0.818452i	$0.694833\pi$
$182$	−3.87708	+	3.87708i	−0.287388	+	0.287388i
$183$	−2.92628	+	4.14401i	−0.216317	+	0.306334i
$184$			18.1778i			1.34009i
$185$	13.6935	+	19.8989i	1.00677	+	1.46300i
$186$	0.217082	+	1.26040i	0.0159172	+	0.0924171i
$187$	−12.1904	−	12.1904i	−0.891448	−	0.891448i
$188$	8.54293	+	8.54293i	0.623057	+	0.623057i
$189$	4.86458	+	8.66258i	0.353846	+	0.630110i
$190$	4.43956	+	6.45138i	0.322079	+	0.468033i
$191$			8.45088i			0.611484i	0.952114	+	0.305742i	$0.0989045\pi$
$191$			8.45088i			0.611484i	−0.952114	+	0.305742i	$0.901095\pi$
$192$	3.21887	+	2.27299i	0.232302	+	0.164039i
$193$	−9.33662	+	9.33662i	−0.672065	+	0.672065i	−0.958192	−	0.286127i	$-0.907632\pi$
$193$	−9.33662	+	9.33662i	−0.672065	+	0.672065i	0.286127	+	0.958192i	$0.407632\pi$
$194$	−6.97913			−0.501072
$195$	0.182095	−	15.0401i	0.0130401	−	1.07705i
$196$	4.86511			0.347508
$197$	−10.8528	+	10.8528i	−0.773231	+	0.773231i	−0.978670	−	0.205439i	$-0.934138\pi$
$197$	−10.8528	+	10.8528i	−0.773231	+	0.773231i	0.205439	+	0.978670i	$0.434138\pi$
$198$	−3.97206	+	8.34431i	−0.282282	+	0.593004i
$199$		−	5.00245i		−	0.354614i	−0.984156	−	0.177307i	$-0.943261\pi$
$199$		−	5.00245i		−	0.354614i	0.984156	−	0.177307i	$-0.0567385\pi$
$200$	−5.20179	−	11.6462i	−0.367822	−	0.823509i
$201$	−8.63864	+	1.48785i	−0.609323	+	0.104945i
$202$	−1.45915	−	1.45915i	−0.102665	−	0.102665i
$203$	−1.36481	−	1.36481i	−0.0957910	−	0.0957910i
$204$	−10.2615	+	1.76736i	−0.718448	+	0.123740i
$205$	−0.0887032	+	0.480191i	−0.00619530	+	0.0335380i
$206$			0.212235i			0.0147871i
$207$	−9.18808	+	19.3019i	−0.638616	+	1.34157i
$208$	2.81705	−	2.81705i	0.195327	−	0.195327i
$209$	−19.7870			−1.36869
$210$	−3.91298	+	3.81936i	−0.270021	+	0.263561i
$211$	6.61082			0.455107			0.227554	−	0.973766i	$-0.426927\pi$
$211$	6.61082			0.455107			0.227554	+	0.973766i	$0.426927\pi$
$212$	−14.1123	+	14.1123i	−0.969234	+	0.969234i
$213$	−16.0126	−	11.3073i	−1.09717	−	0.774762i
$214$		−	1.41969i		−	0.0970483i
$215$	23.4324	−	16.1252i	1.59808	−	1.09973i
$216$	6.49041	+	11.5578i	0.441616	+	0.786406i
$217$	−1.35198	−	1.35198i	−0.0917786	−	0.0917786i
$218$	−2.38008	−	2.38008i	−0.161200	−	0.161200i
$219$	−2.63810	−	15.3171i	−0.178267	−	1.03504i
$220$	13.3448	+	2.46512i	0.899708	+	0.166198i
$221$		−	16.0489i		−	1.07957i
$222$	7.96948	−	11.2859i	0.534876	−	0.757458i
$223$	7.24109	−	7.24109i	0.484899	−	0.484899i	−0.421793	−	0.906692i	$-0.638599\pi$
$223$	7.24109	−	7.24109i	0.484899	−	0.484899i	0.906692	+	0.421793i	$0.138599\pi$
$224$	−11.2033			−0.748554
$225$	0.363165	−	14.9956i	0.0242110	−	0.999707i
$226$	−4.50847			−0.299899
$227$	−5.04027	+	5.04027i	−0.334534	+	0.334534i	−0.854306	−	0.519771i	$-0.826017\pi$
$227$	−5.04027	+	5.04027i	−0.334534	+	0.334534i	0.519771	+	0.854306i	$0.326017\pi$
$228$	−6.89369	+	9.76241i	−0.456546	+	0.646532i
$229$			12.2628i			0.810349i	0.914239	+	0.405174i	$0.132789\pi$
$229$			12.2628i			0.810349i	−0.914239	+	0.405174i	$0.867211\pi$
$230$	−11.5697	−	2.13722i	−0.762886	−	0.140924i
$231$	−2.34497	−	13.6152i	−0.154288	−	0.895813i
$232$	−1.82096	−	1.82096i	−0.119552	−	0.119552i
$233$	−16.4997	−	16.4997i	−1.08093	−	1.08093i	−0.996423	−	0.0845071i	$-0.973068\pi$
$233$	−16.4997	−	16.4997i	−1.08093	−	1.08093i	−0.0845071	−	0.996423i	$-0.526932\pi$
$234$	−8.10740	+	2.87809i	−0.529997	+	0.188146i
$235$	−15.2979	+	10.5274i	−0.997928	+	0.686730i
$236$		−	3.36434i		−	0.219000i
$237$	18.3027	+	12.9244i	1.18889	+	0.839529i
$238$	−4.12549	+	4.12549i	−0.267416	+	0.267416i
$239$	−30.5763			−1.97782			−0.988910	−	0.148517i	$-0.952550\pi$
$239$	−30.5763			−1.97782			−0.988910	+	0.148517i	$0.952550\pi$
$240$	2.84313	−	2.77511i	0.183524	−	0.179133i
$241$	−4.44180			−0.286121			−0.143061	−	0.989714i	$-0.545694\pi$
$241$	−4.44180			−0.286121			−0.143061	+	0.989714i	$0.545694\pi$
$242$	3.34371	−	3.34371i	0.214942	−	0.214942i
$243$	1.04982	+	15.5531i	0.0673459	+	0.997730i
$244$		−	4.26088i		−	0.272775i
$245$	−1.35840	+	7.35363i	−0.0867848	+	0.469806i
$246$	0.275248	−	0.0474066i	0.0175492	−	0.00302253i
$247$	−13.0250	−	13.0250i	−0.828762	−	0.828762i
$248$	−1.80384	−	1.80384i	−0.114544	−	0.114544i
$249$	8.81408	−	1.51807i	0.558570	−	0.0962038i
$250$	8.02409	−	1.94154i	0.507488	−	0.122794i
$251$			11.9817i			0.756280i	0.925748	+	0.378140i	$0.123436\pi$
$251$			11.9817i			0.756280i	−0.925748	+	0.378140i	$0.876564\pi$
$252$	−7.53437	−	3.58651i	−0.474621	−	0.225929i
$253$	21.0203	−	21.0203i	1.32153	−	1.32153i
$254$	1.94997			0.122352
$255$	0.193762	−	16.0038i	0.0121338	−	1.00219i
$256$	−11.9630			−0.747691
$257$	−18.1822	+	18.1822i	−1.13417	+	1.13417i	−0.144696	+	0.989476i	$0.546220\pi$
$257$	−18.1822	+	18.1822i	−1.13417	+	1.13417i	−0.989476	+	0.144696i	$0.953780\pi$
$258$	−13.2900	−	9.38465i	−0.827396	−	0.584263i
$259$			20.6545i			1.28341i
$260$	7.16169	+	10.4071i	0.444149	+	0.645420i
$261$	−1.01315	−	2.85397i	−0.0627121	−	0.176656i
$262$	0.385140	+	0.385140i	0.0237940	+	0.0237940i
$263$	6.20459	+	6.20459i	0.382591	+	0.382591i	0.872035	−	0.489444i	$-0.162800\pi$
$263$	6.20459	+	6.20459i	0.382591	+	0.382591i	−0.489444	+	0.872035i	$0.662800\pi$
$264$	−3.12871	−	18.1656i	−0.192559	−	1.11802i
$265$	−17.3904	−	25.2710i	−1.06828	−	1.55239i
$266$			6.69635i			0.410579i
$267$	−10.8621	+	15.3822i	−0.664751	+	0.941378i
$268$	5.20604	−	5.20604i	0.318009	−	0.318009i
$269$	6.71866			0.409644			0.204822	−	0.978799i	$-0.434338\pi$
$269$	6.71866			0.409644			0.204822	+	0.978799i	$0.434338\pi$
$270$	−8.11933	+	2.77211i	−0.494127	+	0.168705i
$271$	18.1486			1.10245			0.551223	−	0.834358i	$-0.314161\pi$
$271$	18.1486			1.10245			0.551223	+	0.834358i	$0.314161\pi$
$272$	2.99754	−	2.99754i	0.181753	−	0.181753i
$273$	7.41874	−	10.5060i	0.449003	−	0.635849i
$274$		−	8.26007i		−	0.499009i
$275$	−7.45207	+	19.4824i	−0.449377	+	1.17484i
$276$	−3.04752	−	17.6942i	−0.183439	−	1.06507i
$277$	4.97647	+	4.97647i	0.299007	+	0.299007i	0.840625	−	0.541618i	$-0.182188\pi$
$277$	4.97647	+	4.97647i	0.299007	+	0.299007i	−0.541618	+	0.840625i	$0.682188\pi$
$278$	5.78980	+	5.78980i	0.347249	+	0.347249i
$279$	−1.00362	−	2.82714i	−0.0600853	−	0.169257i
$280$	1.98118	−	10.7250i	0.118398	−	0.640943i
$281$		−	10.3189i		−	0.615574i	−0.951455	−	0.307787i	$-0.900412\pi$
$281$		−	10.3189i		−	0.615574i	0.951455	−	0.307787i	$-0.0995884\pi$
$282$	8.67639	+	6.12680i	0.516672	+	0.364846i
$283$	−5.38915	+	5.38915i	−0.320352	+	0.320352i	−0.848902	−	0.528550i	$-0.822736\pi$
$283$	−5.38915	+	5.38915i	−0.320352	+	0.320352i	0.528550	+	0.848902i	$0.322736\pi$
$284$	16.4642			0.976972
$285$	−12.8311	−	13.1456i	−0.760050	−	0.778679i
$286$	11.9635			0.707415
$287$	−0.295248	+	0.295248i	−0.0174279	+	0.0174279i
$288$	−15.8720	−	7.55539i	−0.935267	−	0.445205i
$289$		−	0.0771738i		−	0.00453964i
$290$	1.37309	−	0.944899i	0.0806305	−	0.0554864i
$291$	16.1331	−	2.77865i	0.945740	−	0.162887i
$292$	9.23080	+	9.23080i	0.540192	+	0.540192i
$293$	−7.96883	−	7.96883i	−0.465544	−	0.465544i	0.434923	−	0.900467i	$-0.356775\pi$
$293$	−7.96883	−	7.96883i	−0.465544	−	0.465544i	−0.900467	+	0.434923i	$0.856775\pi$
$294$	4.21514	−	0.725983i	0.245832	−	0.0423402i
$295$	5.08521	+	0.939364i	0.296072	+	0.0546919i
$296$			27.5576i			1.60175i
$297$	5.85973	−	20.8703i	0.340016	−	1.21102i
$298$	−3.15628	+	3.15628i	−0.182838	+	0.182838i
$299$	27.6737			1.60041
$300$	7.01589	+	10.4643i	0.405063	+	0.604154i
$301$	24.3222			1.40191
$302$	−6.24292	+	6.24292i	−0.359240	+	0.359240i
$303$	3.95395	+	2.79206i	0.227148	+	0.160400i
$304$		−	4.86550i		−	0.279056i
$305$	6.44033	+	1.18969i	0.368772	+	0.0681214i
$306$	−8.62684	+	3.06249i	−0.493164	+	0.175071i
$307$	11.3761	+	11.3761i	0.649271	+	0.649271i	0.952817	−	0.303546i	$-0.0981706\pi$
$307$	11.3761	+	11.3761i	0.649271	+	0.649271i	−0.303546	+	0.952817i	$0.598171\pi$
$308$	8.20513	+	8.20513i	0.467530	+	0.467530i
$309$	−0.0844984	−	0.490607i	−0.00480695	−	0.0279097i
$310$	1.36018	−	0.936017i	0.0772532	−	0.0531622i
$311$			16.7415i			0.949324i	0.880168	+	0.474662i	$0.157430\pi$
$311$			16.7415i			0.949324i	−0.880168	+	0.474662i	$0.842570\pi$
$312$	9.89822	−	14.0172i	0.560376	−	0.793570i
$313$	−3.26569	+	3.26569i	−0.184588	+	0.184588i	−0.793351	−	0.608764i	$-0.791666\pi$
$313$	−3.26569	+	3.26569i	−0.184588	+	0.184588i	0.608764	+	0.793351i	$0.291666\pi$
$314$	3.27655			0.184906
$315$	7.52471	−	10.3868i	0.423969	−	0.585231i
$316$	−18.8189			−1.05864
$317$	−19.8572	+	19.8572i	−1.11529	+	1.11529i	−0.122867	+	0.992423i	$0.539209\pi$
$317$	−19.8572	+	19.8572i	−1.11529	+	1.11529i	−0.992423	+	0.122867i	$0.960791\pi$
$318$	−10.1210	+	14.3327i	−0.567558	+	0.803740i
$319$			4.21139i			0.235793i
$320$	0.924094	−	5.00254i	0.0516584	−	0.279651i
$321$	0.565232	+	3.28180i	0.0315482	+	0.183172i
$322$	−7.11371	−	7.11371i	−0.396432	−	0.396432i
$323$	−13.8595	−	13.8595i	−0.771165	−	0.771165i
$324$	−8.25540	−	10.1622i	−0.458633	−	0.564565i
$325$	−17.7300	+	7.91913i	−0.983481	+	0.439275i
$326$			0.308881i			0.0171073i
$327$	6.44946	+	4.55426i	0.356656	+	0.251851i
$328$	−0.393925	+	0.393925i	−0.0217509	+	0.0217509i
$329$	−15.8788			−0.875428
$330$	11.9298	+	0.144438i	0.656715	+	0.00795103i
$331$	9.49043			0.521641			0.260821	−	0.965387i	$-0.416007\pi$
$331$	9.49043			0.521641			0.260821	+	0.965387i	$0.416007\pi$
$332$	−5.31177	+	5.31177i	−0.291521	+	0.291521i
$333$	−13.9291	+	29.2616i	−0.763311	+	1.60353i
$334$			14.5119i			0.794058i
$335$	6.41535	+	9.32253i	0.350508	+	0.509344i
$336$	3.34789	−	0.576615i	0.182642	−	0.0314569i
$337$	−15.6779	−	15.6779i	−0.854030	−	0.854030i	0.136597	−	0.990627i	$-0.456384\pi$
$337$	−15.6779	−	15.6779i	−0.854030	−	0.854030i	−0.990627	+	0.136597i	$0.956384\pi$
$338$	1.08738	+	1.08738i	0.0591455	+	0.0591455i
$339$	10.4219	−	1.79499i	0.566039	−	0.0974902i
$340$	7.62054	+	11.0739i	0.413282	+	0.600565i
$341$			4.17180i			0.225916i
$342$	−4.51593	+	9.48686i	−0.244194	+	0.512990i
$343$	−13.9853	+	13.9853i	−0.755135	+	0.755135i
$344$	32.4511			1.74964
$345$	27.5958	+	0.334110i	1.48571	+	0.0179879i
$346$	−0.521369			−0.0280290
$347$	−4.37265	+	4.37265i	−0.234736	+	0.234736i	−0.814666	−	0.579930i	$-0.803080\pi$
$347$	−4.37265	+	4.37265i	−0.234736	+	0.234736i	0.579930	+	0.814666i	$0.303080\pi$
$348$	2.07780	+	1.46723i	0.111382	+	0.0786517i
$349$		−	31.7143i		−	1.69763i	−0.528692	−	0.848814i	$-0.677317\pi$
$349$		−	31.7143i		−	1.69763i	0.528692	−	0.848814i	$-0.322683\pi$
$350$	6.59328	+	2.52194i	0.352426	+	0.134804i
$351$	17.5954	−	9.88090i	0.939171	−	0.527404i
$352$	17.2850	+	17.2850i	0.921295	+	0.921295i
$353$	13.7588	+	13.7588i	0.732307	+	0.732307i	0.971076	−	0.238769i	$-0.0767439\pi$
$353$	13.7588	+	13.7588i	0.732307	+	0.732307i	−0.238769	+	0.971076i	$0.576744\pi$
$354$	−0.502034	−	2.91486i	−0.0266828	−	0.154923i
$355$	−4.59701	+	24.8857i	−0.243984	+	1.32080i
$356$		−	15.8160i		−	0.838249i
$357$	7.89407	−	11.1791i	0.417798	−	0.591660i
$358$	12.6831	−	12.6831i	0.670322	−	0.670322i
$359$	6.61652			0.349206			0.174603	−	0.984639i	$-0.444136\pi$
$359$	6.61652			0.349206			0.174603	+	0.984639i	$0.444136\pi$
$360$	10.0396	−	13.8583i	0.529133	−	0.730396i
$361$	−3.49632			−0.184017
$362$	8.07229	−	8.07229i	0.424270	−	0.424270i
$363$	−6.39815	+	9.06066i	−0.335816	+	0.475561i
$364$			10.8022i			0.566191i
$365$	−16.5297	+	11.3750i	−0.865205	+	0.595396i
$366$	−0.635818	−	3.69163i	−0.0332347	−	0.192965i
$367$	−4.18279	−	4.18279i	−0.218340	−	0.218340i	0.589459	−	0.807799i	$-0.299341\pi$
$367$	−4.18279	−	4.18279i	−0.218340	−	0.218340i	−0.807799	+	0.589459i	$0.799341\pi$
$368$	5.16876	+	5.16876i	0.269440	+	0.269440i
$369$	−0.617395	+	0.219172i	−0.0321403	+	0.0114097i
$370$	−17.5397	−	3.24002i	−0.911846	−	0.168441i
$371$		−	26.2306i		−	1.36182i
$372$	2.05827	+	1.45344i	0.106716	+	0.0753572i
$373$	−20.4444	+	20.4444i	−1.05857	+	1.05857i	−0.0603939	+	0.998175i	$0.519236\pi$
$373$	−20.4444	+	20.4444i	−1.05857	+	1.05857i	−0.998175	+	0.0603939i	$0.980764\pi$
$374$	12.7300			0.658252
$375$	−17.7757	+	7.68279i	−0.917932	+	0.396738i
$376$	−21.1858			−1.09257
$377$	−2.77220	+	2.77220i	−0.142775	+	0.142775i
$378$	−7.06297	−	1.98306i	−0.363280	−	0.101998i
$379$		−	13.7695i		−	0.707293i	−0.935379	−	0.353647i	$-0.884942\pi$
$379$		−	13.7695i		−	0.707293i	0.935379	−	0.353647i	$-0.115058\pi$
$380$	15.1721	+	2.80266i	0.778310	+	0.143773i
$381$	−4.50759	+	0.776353i	−0.230931	+	0.0397738i
$382$	−4.41248	−	4.41248i	−0.225762	−	0.225762i
$383$	2.49388	+	2.49388i	0.127431	+	0.127431i	0.767946	−	0.640515i	$-0.221279\pi$
$383$	2.49388	+	2.49388i	0.127431	+	0.127431i	−0.640515	+	0.767946i	$0.721279\pi$
$384$	17.1359	−	2.95136i	0.874464	−	0.150611i
$385$	−14.6930	+	10.1111i	−0.748827	+	0.515309i
$386$		−	9.74991i		−	0.496257i
$387$	34.4577	+	16.4026i	1.75158	+	0.833789i
$388$	−9.72255	+	9.72255i	−0.493588	+	0.493588i
$389$	−18.5595			−0.941002			−0.470501	−	0.882400i	$-0.655927\pi$
$389$	−18.5595			−0.941002			−0.470501	+	0.882400i	$0.655927\pi$
$390$	7.75786	+	7.94802i	0.392835	+	0.402464i
$391$	29.4467			1.48918
$392$	−6.03255	+	6.03255i	−0.304690	+	0.304690i
$393$	−1.04364	−	0.736961i	−0.0526445	−	0.0371747i
$394$		−	11.3332i		−	0.570959i
$395$	5.25445	−	28.4448i	0.264380	−	1.43121i
$396$	6.09094	+	17.1578i	0.306081	+	0.862212i
$397$	1.61527	+	1.61527i	0.0810681	+	0.0810681i	0.746478	−	0.665410i	$-0.231743\pi$
$397$	1.61527	+	1.61527i	0.0810681	+	0.0810681i	−0.665410	+	0.746478i	$0.731743\pi$
$398$	2.61194	+	2.61194i	0.130925	+	0.130925i
$399$	−2.66606	−	15.4794i	−0.133470	−	0.774941i
$400$	−4.79062	−	1.83242i	−0.239531	−	0.0916210i
$401$			9.73586i			0.486186i	0.970003	+	0.243093i	$0.0781620\pi$
$401$			9.73586i			0.486186i	−0.970003	+	0.243093i	$0.921838\pi$
$402$	3.73366	−	5.28737i	0.186218	−	0.263710i
$403$	−2.74614	+	2.74614i	−0.136795	+	0.136795i
$404$	−4.06545			−0.202264
$405$	17.6652	−	9.64066i	0.877788	−	0.479048i
$406$	1.42523			0.0707328
$407$	31.8667	−	31.8667i	1.57957	−	1.57957i
$408$	10.5324	−	14.9153i	0.521432	−	0.738419i
$409$			19.7281i			0.975492i	0.872985	+	0.487746i	$0.162181\pi$
$409$			19.7281i			0.975492i	−0.872985	+	0.487746i	$0.837819\pi$
$410$	−0.204409	−	0.297038i	−0.0100950	−	0.0146697i
$411$	3.28863	+	19.0942i	0.162216	+	0.941846i
$412$	0.295662	+	0.295662i	0.0145662	+	0.0145662i
$413$	3.12666	+	3.12666i	0.153853	+	0.153853i
$414$	−5.28075	−	14.8755i	−0.259535	−	0.731093i
$415$	−6.54564	−	9.51186i	−0.321313	−	0.466919i
$416$			22.7561i			1.11571i
$417$	−15.6890	−	11.0787i	−0.768292	−	0.542527i
$418$	10.3314	−	10.3314i	0.505327	−	0.505327i
$419$	18.5719			0.907299			0.453649	−	0.891180i	$-0.350122\pi$
$419$	18.5719			0.907299			0.453649	+	0.891180i	$0.350122\pi$
$420$	−0.130418	+	10.7718i	−0.00636373	+	0.525612i
$421$	24.9114			1.21411			0.607054	−	0.794661i	$-0.292351\pi$
$421$	24.9114			1.21411			0.607054	+	0.794661i	$0.292351\pi$
$422$	−3.45172	+	3.45172i	−0.168027	+	0.168027i
$423$	−22.4959	−	10.7085i	−1.09379	−	0.520664i
$424$		−	34.9973i		−	1.69962i
$425$	−18.8659	+	8.42652i	−0.915132	+	0.408746i
$426$	14.2646	−	2.45683i	0.691123	−	0.119034i
$427$	3.95987	+	3.95987i	0.191632	+	0.191632i
$428$	−1.97776	−	1.97776i	−0.0955987	−	0.0955987i
$429$	−27.6551	+	4.76310i	−1.33520	+	0.229964i
$430$	−3.81536	+	20.6543i	−0.183993	+	0.996039i
$431$		−	27.1185i		−	1.30625i	−0.757248	−	0.653127i	$-0.773457\pi$
$431$		−	27.1185i		−	1.30625i	0.757248	−	0.653127i	$-0.226543\pi$
$432$	5.13189	+	1.44087i	0.246908	+	0.0693240i
$433$	−15.8354	+	15.8354i	−0.761001	+	0.761001i	−0.976503	−	0.215503i	$-0.930861\pi$
$433$	−15.8354	+	15.8354i	−0.761001	+	0.761001i	0.215503	+	0.976503i	$0.430861\pi$
$434$	1.41183			0.0677700
$435$	−2.79786	+	2.73093i	−0.134147	+	0.130938i
$436$	−6.63134			−0.317584
$437$	23.8985	−	23.8985i	1.14322	−	1.14322i
$438$	9.37501	+	6.62013i	0.447955	+	0.316322i
$439$			4.08025i			0.194740i	0.995248	+	0.0973699i	$0.0310430\pi$
$439$			4.08025i			0.194740i	−0.995248	+	0.0973699i	$0.968957\pi$
$440$	−19.6037	+	13.4904i	−0.934571	+	0.643130i
$441$	−9.45476	+	3.35640i	−0.450227	+	0.159828i
$442$	8.37966	+	8.37966i	0.398580	+	0.398580i
$443$	14.6229	+	14.6229i	0.694756	+	0.694756i	0.963274	−	0.268519i	$-0.0865341\pi$
$443$	14.6229	+	14.6229i	0.694756	+	0.694756i	−0.268519	+	0.963274i	$0.586534\pi$
$444$	−4.62003	−	26.8244i	−0.219257	−	1.27303i
$445$	23.9060	+	4.41603i	1.13325	+	0.209340i
$446$			7.56161i			0.358053i
$447$	6.03950	−	8.55276i	0.285659	−	0.404532i
$448$	3.07584	−	3.07584i	0.145320	−	0.145320i
$449$	−12.7395			−0.601214			−0.300607	−	0.953748i	$-0.597189\pi$
$449$	−12.7395			−0.601214			−0.300607	+	0.953748i	$0.597189\pi$
$450$	7.64007	+	8.01931i	0.360157	+	0.378034i
$451$	0.911044			0.0428994
$452$	−6.28070	+	6.28070i	−0.295419	+	0.295419i
$453$	11.9458	−	16.9168i	0.561260	−	0.794822i
$454$		−	5.26338i		−	0.247023i
$455$	−16.3276	−	3.01612i	−0.765451	−	0.141398i
$456$	−3.55710	−	20.6529i	−0.166577	−	0.967162i
$457$	−22.3969	−	22.3969i	−1.04768	−	1.04768i	−0.998805	−	0.0488796i	$-0.984435\pi$
$457$	−22.3969	−	22.3969i	−1.04768	−	1.04768i	−0.0488796	−	0.998805i	$-0.515565\pi$
$458$	−6.40281	−	6.40281i	−0.299184	−	0.299184i
$459$	18.7227	−	10.5140i	0.873901	−	0.490750i
$460$	−19.0950	+	13.1403i	−0.890310	+	0.612672i
$461$		−	9.45291i		−	0.440266i	−0.975470	−	0.220133i	$-0.929351\pi$
$461$		−	9.45291i		−	0.440266i	0.975470	−	0.220133i	$-0.0706491\pi$
$462$	8.33332	+	5.88454i	0.387701	+	0.273774i
$463$	5.17828	−	5.17828i	0.240655	−	0.240655i	−0.576466	−	0.817121i	$-0.695569\pi$
$463$	5.17828	−	5.17828i	0.240655	−	0.240655i	0.817121	+	0.576466i	$0.195569\pi$
$464$	−1.03556			−0.0480745
$465$	−2.77157	+	2.70526i	−0.128528	+	0.125453i
$466$	17.2300			0.798166
$467$	26.5579	−	26.5579i	1.22895	−	1.22895i	0.264594	−	0.964360i	$-0.414762\pi$
$467$	26.5579	−	26.5579i	1.22895	−	1.22895i	0.964360	−	0.264594i	$-0.0852378\pi$
$468$	−7.28489	+	15.3038i	−0.336744	+	0.707417i
$469$			9.67651i			0.446820i
$470$	2.49087	−	13.4842i	0.114895	−	0.621982i
$471$	−7.57415	+	1.30451i	−0.348998	+	0.0601088i
$472$	4.17165	+	4.17165i	0.192016	+	0.192016i
$473$	−37.5254	−	37.5254i	−1.72542	−	1.72542i
$474$	−16.3047	+	2.80819i	−0.748898	+	0.128985i
$475$	−8.47245	+	22.1501i	−0.388742	+	1.01632i
$476$			11.4943i			0.526842i
$477$	17.6896	−	37.1614i	0.809950	−	1.70150i
$478$	15.9649	−	15.9649i	0.730218	−	0.730218i
$479$	36.4277			1.66442			0.832212	−	0.554457i	$-0.187074\pi$
$479$	36.4277			1.66442			0.832212	+	0.554457i	$0.187074\pi$
$480$	−0.274740	+	22.6921i	−0.0125401	+	1.03575i
$481$	41.9532			1.91290
$482$	2.31921	−	2.31921i	0.105637	−	0.105637i
$483$	19.2764	+	13.6120i	0.877109	+	0.619367i
$484$		−	9.31619i		−	0.423463i
$485$	−11.9810	−	17.4103i	−0.544030	−	0.790562i
$486$	−8.66891	−	7.57262i	−0.393230	−	0.343501i
$487$	−9.19245	−	9.19245i	−0.416550	−	0.416550i	0.467463	−	0.884013i	$-0.345168\pi$
$487$	−9.19245	−	9.19245i	−0.416550	−	0.416550i	−0.884013	+	0.467463i	$0.845168\pi$
$488$	5.28333	+	5.28333i	0.239165	+	0.239165i
$489$	−0.122977	−	0.714015i	−0.00556119	−	0.0322889i
$490$	−3.13031	−	4.54883i	−0.141413	−	0.205495i
$491$		−	11.4212i		−	0.515430i	−0.966221	−	0.257715i	$-0.917031\pi$
$491$		−	11.4212i		−	0.515430i	0.966221	−	0.257715i	$-0.0829695\pi$
$492$	0.317403	−	0.449487i	0.0143096	−	0.0202644i
$493$	−2.94981	+	2.94981i	−0.132853	+	0.132853i
$494$	13.6016			0.611964
$495$	−27.6347	+	4.41581i	−1.24209	+	0.198476i
$496$	−1.02582			−0.0460608
$497$	−15.3011	+	15.3011i	−0.686349	+	0.686349i
$498$	−3.80948	+	5.39475i	−0.170707	+	0.241745i
$499$		−	8.38472i		−	0.375352i	−0.982231	−	0.187676i	$-0.939905\pi$
$499$		−	8.38472i		−	0.375352i	0.982231	−	0.187676i	$-0.0600954\pi$
$500$	8.47354	−	13.8830i	0.378948	−	0.620867i
$501$	−5.77773	−	33.5461i	−0.258130	−	1.49873i
$502$	−6.25605	−	6.25605i	−0.279221	−	0.279221i
$503$	0.860090	+	0.860090i	0.0383495	+	0.0383495i	0.726022	−	0.687672i	$-0.241367\pi$
$503$	0.860090	+	0.860090i	0.0383495	+	0.0383495i	−0.687672	+	0.726022i	$0.741367\pi$
$504$	13.7895	−	4.89519i	0.614232	−	0.218049i
$505$	1.13512	−	6.14494i	0.0505123	−	0.273446i
$506$			21.9507i			0.975829i
$507$	−2.94653	−	2.08068i	−0.130860	−	0.0924063i
$508$	2.71648	−	2.71648i	0.120524	−	0.120524i
$509$	−11.5435			−0.511656			−0.255828	−	0.966722i	$-0.582348\pi$
$509$	−11.5435			−0.511656			−0.255828	+	0.966722i	$0.582348\pi$
$510$	8.25491	+	8.45725i	0.365534	+	0.374493i
$511$	−17.1574			−0.758997
$512$	−7.95112	+	7.95112i	−0.351393	+	0.351393i
$513$	6.66207	−	23.7280i	0.294138	−	1.04762i
$514$		−	18.9870i		−	0.837480i
$515$	−0.529447	+	0.364342i	−0.0233302	+	0.0160548i
$516$	−31.5877	+	5.44043i	−1.39057	+	0.239502i
$517$	24.4986	+	24.4986i	1.07745	+	1.07745i
$518$	−10.7844	−	10.7844i	−0.473838	−	0.473838i
$519$	1.20521	−	0.207576i	0.0529028	−	0.00911157i
$520$	−21.7846	−	4.02416i	−0.955318	−	0.176471i
$521$		−	2.13177i		−	0.0933947i	−0.998909	−	0.0466973i	$-0.985130\pi$
$521$		−	2.13177i		−	0.0933947i	0.998909	−	0.0466973i	$-0.0148696\pi$
$522$	2.01915	+	0.961154i	0.0883757	+	0.0420686i
$523$	5.10557	−	5.10557i	0.223251	−	0.223251i	−0.586615	−	0.809866i	$-0.699540\pi$
$523$	5.10557	−	5.10557i	0.223251	−	0.223251i	0.809866	+	0.586615i	$0.199540\pi$
$524$	1.07307			0.0468773
$525$	−16.2453	−	3.20476i	−0.709001	−	0.139867i
$526$	−6.47923			−0.282508
$527$	−2.92209	+	2.92209i	−0.127288	+	0.127288i
$528$	−6.05491	−	4.27565i	−0.263506	−	0.186074i
$529$			27.7759i			1.20765i
$530$	22.2749	+	4.11473i	0.967561	+	0.178733i
$531$	2.32103	+	6.53819i	0.100724	+	0.283733i
$532$	9.32861	+	9.32861i	0.404447	+	0.404447i
$533$	0.599705	+	0.599705i	0.0259761	+	0.0259761i
$534$	−2.36011	−	13.7030i	−0.102132	−	0.592988i
$535$	3.54161	−	2.43718i	0.153117	−	0.105368i
$536$			12.9106i			0.557652i
$537$	−24.2689	+	34.3681i	−1.04728	+	1.48309i
$538$	−3.50803	+	3.50803i	−0.151242	+	0.151242i
$539$	13.9517			0.600942
$540$	−7.44916	+	15.1727i	−0.320561	+	0.652931i
$541$	−6.52868			−0.280690			−0.140345	−	0.990103i	$-0.544821\pi$
$541$	−6.52868			−0.280690			−0.140345	+	0.990103i	$0.544821\pi$
$542$	−9.47596	+	9.47596i	−0.407027	+	0.407027i
$543$	−15.4462	+	21.8740i	−0.662861	+	0.938701i
$544$			24.2141i			1.03817i
$545$	1.85155	−	10.0233i	0.0793117	−	0.429351i
$546$	1.61194	+	9.35907i	0.0689845	+	0.400531i
$547$	6.27857	+	6.27857i	0.268452	+	0.268452i	0.828476	−	0.560024i	$-0.189208\pi$
$547$	6.27857	+	6.27857i	0.268452	+	0.268452i	−0.560024	+	0.828476i	$0.689208\pi$
$548$	−11.5070	−	11.5070i	−0.491556	−	0.491556i
$549$	2.93954	+	8.28052i	0.125457	+	0.353404i
$550$	−6.28145	−	14.0634i	−0.267842	−	0.599665i
$551$			4.78803i			0.203977i
$552$	25.7190	+	18.1614i	1.09467	+	0.772999i
$553$	17.4894	−	17.4894i	0.743725	−	0.743725i
$554$	−5.19676			−0.220789
$555$	41.8352	+	0.506510i	1.77580	+	0.0215001i
$556$	16.1314			0.684125
$557$	−22.2299	+	22.2299i	−0.941911	+	0.941911i	−0.998403	−	0.0564924i	$-0.982008\pi$
$557$	−22.2299	+	22.2299i	−0.941911	+	0.941911i	0.0564924	+	0.998403i	$0.482008\pi$
$558$	2.00017	+	0.952120i	0.0846739	+	0.0403064i
$559$		−	49.4030i		−	2.08953i
$560$	−2.48626	−	3.61293i	−0.105064	−	0.152674i
$561$	−29.4269	+	5.06827i	−1.24241	+	0.213982i
$562$	5.38784	+	5.38784i	0.227272	+	0.227272i
$563$	17.1185	+	17.1185i	0.721461	+	0.721461i	0.968903	−	0.247442i	$-0.0795900\pi$
$563$	17.1185	+	17.1185i	0.721461	+	0.721461i	−0.247442	+	0.968903i	$0.579590\pi$
$564$	20.6222	−	3.55181i	0.868350	−	0.149558i
$565$	−7.73965	−	11.2469i	−0.325610	−	0.473163i
$566$		−	5.62770i		−	0.236550i
$567$	17.1165	+	1.77206i	0.718824	+	0.0744195i
$568$	−20.4150	+	20.4150i	−0.856595	+	0.856595i
$569$	0.657081			0.0275463			0.0137731	−	0.999905i	$-0.495616\pi$
$569$	0.657081			0.0275463			0.0137731	+	0.999905i	$0.495616\pi$
$570$	13.5633	+	0.164215i	0.568104	+	0.00687820i
$571$	−4.01066			−0.167841			−0.0839204	−	0.996472i	$-0.526744\pi$
$571$	−4.01066			−0.167841			−0.0839204	+	0.996472i	$0.526744\pi$
$572$	16.6662	−	16.6662i	0.696849	−	0.696849i
$573$	11.9568	+	8.44322i	0.499501	+	0.352721i
$574$		−	0.308317i		−	0.0128689i
$575$	−14.5301	−	32.5311i	−0.605948	−	1.35664i
$576$	6.43191	−	2.28330i	0.267996	−	0.0951374i
$577$	−10.9689	−	10.9689i	−0.456641	−	0.456641i	0.440910	−	0.897551i	$-0.354656\pi$
$577$	−10.9689	−	10.9689i	−0.456641	−	0.456641i	−0.897551	+	0.440910i	$0.854656\pi$
$578$	0.0402950	+	0.0402950i	0.00167605	+	0.00167605i
$579$	3.88179	+	22.5381i	0.161322	+	0.936652i
$580$	0.596507	−	3.22916i	0.0247686	−	0.134084i
$581$		−	9.87303i		−	0.409602i
$582$	−6.97281	+	9.87445i	−0.289032	+	0.409309i
$583$	−40.4698	+	40.4698i	−1.67609	+	1.67609i
$584$	−22.8917			−0.947264
$585$	−21.0976	−	15.2841i	−0.872280	−	0.631921i
$586$	8.32157			0.343761
$587$	−1.87138	+	1.87138i	−0.0772402	+	0.0772402i	−0.744671	−	0.667431i	$-0.767394\pi$
$587$	−1.87138	+	1.87138i	−0.0772402	+	0.0772402i	0.667431	+	0.744671i	$0.267394\pi$
$588$	4.86070	−	6.88342i	0.200452	−	0.283867i
$589$			4.74303i			0.195433i
$590$	−3.14562	+	2.16468i	−0.129503	+	0.0891184i
$591$	4.51216	+	26.1981i	0.185606	+	1.07765i
$592$	7.83582	+	7.83582i	0.322050	+	0.322050i
$593$	10.9258	+	10.9258i	0.448670	+	0.448670i	0.894912	−	0.446242i	$-0.147238\pi$
$593$	10.9258	+	10.9258i	0.448670	+	0.448670i	−0.446242	+	0.894912i	$0.647238\pi$
$594$	7.83752	+	13.9566i	0.321577	+	0.572648i
$595$	−17.3737	−	3.20936i	−0.712254	−	0.131571i
$596$			8.79396i			0.360215i
$597$	−7.07773	−	4.99791i	−0.289672	−	0.204551i
$598$	−14.4493	+	14.4493i	−0.590877	+	0.590877i
$599$	−33.1261			−1.35349			−0.676747	−	0.736216i	$-0.736611\pi$
$599$	−33.1261			−1.35349			−0.676747	+	0.736216i	$0.736611\pi$
$600$	−21.6747	−	4.27584i	−0.884866	−	0.174561i
$601$	38.2939			1.56204			0.781021	−	0.624504i	$-0.214699\pi$
$601$	38.2939			1.56204			0.781021	+	0.624504i	$0.214699\pi$
$602$	−12.6994	+	12.6994i	−0.517589	+	0.517589i
$603$	−6.52572	+	13.7089i	−0.265748	+	0.558270i
$604$			17.3939i			0.707748i
$605$	14.0814	+	2.60119i	0.572492	+	0.105754i
$606$	−3.52231	+	0.606656i	−0.143084	+	0.0246437i
$607$	−7.59229	−	7.59229i	−0.308162	−	0.308162i	0.536034	−	0.844196i	$-0.319922\pi$
$607$	−7.59229	−	7.59229i	−0.308162	−	0.308162i	−0.844196	+	0.536034i	$0.819922\pi$
$608$	19.6518	+	19.6518i	0.796985	+	0.796985i
$609$	−3.29458	+	0.567434i	−0.133503	+	0.0229936i
$610$	−3.98388	+	2.74153i	−0.161303	+	0.111001i
$611$			32.2530i			1.30481i
$612$	−7.75164	+	16.2843i	−0.313341	+	0.658253i
$613$	16.2601	−	16.2601i	0.656740	−	0.656740i	−0.297868	−	0.954607i	$-0.596275\pi$
$613$	16.2601	−	16.2601i	0.656740	−	0.656740i	0.954607	+	0.297868i	$0.0962754\pi$
$614$	−11.8797			−0.479426
$615$	0.590777	+	0.605258i	0.0238224	+	0.0244064i
$616$	−20.3481			−0.819848
$617$	3.63475	−	3.63475i	0.146329	−	0.146329i	−0.630147	−	0.776476i	$-0.717005\pi$
$617$	3.63475	−	3.63475i	0.146329	−	0.146329i	0.776476	+	0.630147i	$0.217005\pi$
$618$	0.300281	+	0.212043i	0.0120791	+	0.00852960i
$619$		−	10.6386i		−	0.427602i	−0.976877	−	0.213801i	$-0.931416\pi$
$619$		−	10.6386i		−	0.427602i	0.976877	−	0.213801i	$-0.0685844\pi$
$620$	0.590900	−	3.19881i	0.0237311	−	0.128467i
$621$	18.1296	+	32.2842i	0.727515	+	1.29552i
$622$	−8.74129	−	8.74129i	−0.350494	−	0.350494i
$623$	14.6987	+	14.6987i	0.588892	+	0.588892i
$624$	−1.17122	−	6.80021i	−0.0468862	−	0.272226i
$625$	18.6183	+	16.6841i	0.744732	+	0.667363i
$626$		−	3.41024i		−	0.136301i
$627$	−19.7691	+	27.9957i	−0.789500	+	1.11804i
$628$	4.56453	−	4.56453i	0.182145	−	0.182145i
$629$	44.6412			1.77996
$630$	1.49440	+	9.35220i	0.0595385	+	0.372600i
$631$	−11.6592			−0.464147			−0.232073	−	0.972698i	$-0.574551\pi$
$631$	−11.6592			−0.464147			−0.232073	+	0.972698i	$0.574551\pi$
$632$	23.3347	−	23.3347i	0.928203	−	0.928203i
$633$	6.60483	−	9.35334i	0.262518	−	0.371762i
$634$		−	20.7362i		−	0.823538i
$635$	3.34749	+	4.86444i	0.132841	+	0.193040i
$636$	5.86731	+	34.0663i	0.232654	+	1.35081i
$637$	9.18386	+	9.18386i	0.363878	+	0.363878i
$638$	−2.19890	−	2.19890i	−0.0870554	−	0.0870554i
$639$	−31.9963	+	11.3585i	−1.26575	+	0.449336i
$640$	−12.7257	−	18.4925i	−0.503028	−	0.730981i
$641$			1.08212i			0.0427412i	0.999772	+	0.0213706i	$0.00680299\pi$
$641$			1.08212i			0.0427412i	−0.999772	+	0.0213706i	$0.993197\pi$
$642$	−2.00866	−	1.41841i	−0.0792755	−	0.0559801i
$643$	20.4401	−	20.4401i	0.806078	−	0.806078i	−0.177960	−	0.984038i	$-0.556950\pi$
$643$	20.4401	−	20.4401i	0.806078	−	0.806078i	0.984038	+	0.177960i	$0.0569497\pi$
$644$	−19.8201			−0.781020
$645$	0.596453	−	49.2640i	0.0234853	−	1.93977i
$646$	14.4730			0.569434
$647$	22.1672	−	22.1672i	0.871482	−	0.871482i	−0.121152	−	0.992634i	$-0.538659\pi$
$647$	22.1672	−	22.1672i	0.871482	−	0.871482i	0.992634	+	0.121152i	$0.0386588\pi$
$648$	22.8371	+	2.36431i	0.897125	+	0.0928790i
$649$		−	9.64792i		−	0.378714i
$650$	5.12255	−	13.3922i	0.200923	−	0.525286i
$651$	−3.26362	+	0.562101i	−0.127911	+	0.0220305i
$652$	0.430298	+	0.430298i	0.0168518	+	0.0168518i
$653$	−8.61746	−	8.61746i	−0.337227	−	0.337227i	0.518096	−	0.855323i	$-0.326641\pi$
$653$	−8.61746	−	8.61746i	−0.337227	−	0.337227i	−0.855323	+	0.518096i	$0.826641\pi$
$654$	−5.74540	+	0.989544i	−0.224663	+	0.0386942i
$655$	−0.299614	+	1.62195i	−0.0117069	+	0.0633747i
$656$			0.224020i			0.00874652i
$657$	−24.3072	−	11.5707i	−0.948314	−	0.451416i
$658$	8.29085	−	8.29085i	0.323211	−	0.323211i
$659$	31.8035			1.23889			0.619444	−	0.785041i	$-0.287358\pi$
$659$	31.8035			1.23889			0.619444	+	0.785041i	$0.287358\pi$
$660$	16.8205	−	16.4181i	0.654738	−	0.639073i
$661$	−6.53074			−0.254016			−0.127008	−	0.991902i	$-0.540537\pi$
$661$	−6.53074			−0.254016			−0.127008	+	0.991902i	$0.540537\pi$
$662$	−4.95526	+	4.95526i	−0.192592	+	0.192592i
$663$	−22.7069	−	16.0344i	−0.881862	−	0.622723i
$664$		−	13.1728i		−	0.511203i
$665$	−16.7049	+	11.4956i	−0.647788	+	0.445779i
$666$	−8.00560	−	22.5513i	−0.310211	−	0.873845i
$667$	−5.08646	−	5.08646i	−0.196948	−	0.196948i
$668$	20.2164	+	20.2164i	0.782197	+	0.782197i
$669$	−3.01055	−	17.4796i	−0.116395	−	0.675800i
$670$	−8.21726	−	1.51793i	−0.317461	−	0.0586429i
$671$		−	12.2189i		−	0.471707i
$672$	−11.1932	+	15.8511i	−0.431786	+	0.611469i
$673$	−25.4200	+	25.4200i	−0.979871	+	0.979871i	−0.999801	−	0.0199306i	$-0.993655\pi$
$673$	−25.4200	+	25.4200i	−0.979871	+	0.979871i	0.0199306	+	0.999801i	$0.493655\pi$
$674$	16.3719			0.630622
$675$	−20.8538	−	15.4958i	−0.802661	−	0.596435i
$676$	3.02963			0.116524
$677$	2.40727	−	2.40727i	0.0925189	−	0.0925189i	−0.659333	−	0.751851i	$-0.729161\pi$
$677$	2.40727	−	2.40727i	0.0925189	−	0.0925189i	0.751851	+	0.659333i	$0.229161\pi$
$678$	−4.50438	+	6.37882i	−0.172990	+	0.244977i
$679$		−	18.0714i		−	0.693517i
$680$	−23.1803	−	4.28199i	−0.888926	−	0.164207i
$681$	2.09554	+	12.1669i	0.0803013	+	0.466238i
$682$	−2.17824	−	2.17824i	−0.0834090	−	0.0834090i
$683$	−3.67357	−	3.67357i	−0.140565	−	0.140565i	0.633323	−	0.773888i	$-0.281691\pi$
$683$	−3.67357	−	3.67357i	−0.140565	−	0.140565i	−0.773888	+	0.633323i	$0.781691\pi$
$684$	6.92494	+	19.5071i	0.264782	+	0.745874i
$685$	20.6058	−	14.1800i	0.787307	−	0.541790i
$686$		−	14.6044i		−	0.557597i
$687$	17.3501	+	12.2517i	0.661947	+	0.467431i
$688$	9.22727	−	9.22727i	0.351786	−	0.351786i
$689$	−53.2794			−2.02978
$690$	−14.5831	+	14.2342i	−0.555170	+	0.541887i
$691$	12.3025			0.468008			0.234004	−	0.972236i	$-0.424817\pi$
$691$	12.3025			0.468008			0.234004	+	0.972236i	$0.424817\pi$
$692$	−0.726314	+	0.726314i	−0.0276103	+	0.0276103i
$693$	−21.6063	−	10.2850i	−0.820757	−	0.390697i
$694$		−	4.56620i		−	0.173331i
$695$	−4.50409	+	24.3827i	−0.170850	+	0.924888i
$696$	−4.39569	+	0.757081i	−0.166618	+	0.0286971i
$697$	0.638129	+	0.638129i	0.0241708	+	0.0241708i
$698$	16.5591	+	16.5591i	0.626770	+	0.626770i
$699$	−39.8294	+	6.85991i	−1.50648	+	0.259465i
$700$	12.6983	−	5.67174i	0.479952	−	0.214372i
$701$			6.70690i			0.253316i	0.991946	+	0.126658i	$0.0404251\pi$
$701$			6.70690i			0.253316i	−0.991946	+	0.126658i	$0.959575\pi$
$702$	−4.02798	+	14.3463i	−0.152026	+	0.541465i
$703$	36.2300	−	36.2300i	1.36644	−	1.36644i
$704$	−9.49109			−0.357709
$705$	−0.389397	+	32.1622i	−0.0146655	+	1.21130i
$706$	−14.3678			−0.540741
$707$	3.77825	−	3.77825i	0.142096	−	0.142096i
$708$	−4.76005	−	3.36129i	−0.178893	−	0.126325i
$709$		−	8.60191i		−	0.323052i	−0.986868	−	0.161526i	$-0.948359\pi$
$709$		−	8.60191i		−	0.323052i	0.986868	−	0.161526i	$-0.0516415\pi$
$710$	−10.5934	−	15.3939i	−0.397563	−	0.577723i
$711$	36.5722	−	12.9830i	1.37157	−	0.486899i
$712$	19.6113	+	19.6113i	0.734964	+	0.734964i
$713$	−5.03865	−	5.03865i	−0.188699	−	0.188699i
$714$	1.71521	+	9.95871i	0.0641902	+	0.372695i
$715$	20.5376	+	29.8444i	0.768063	+	1.11612i
$716$		−	35.3374i		−	1.32062i
$717$	−30.5486	+	43.2611i	−1.14086	+	1.61561i
$718$	−3.45470	+	3.45470i	−0.128928	+	0.128928i
$719$	−24.4922			−0.913403			−0.456702	−	0.889620i	$-0.650969\pi$
$719$	−24.4922			−0.913403			−0.456702	+	0.889620i	$0.650969\pi$
$720$	−1.08582	−	6.79522i	−0.0404661	−	0.253243i
$721$	−0.549550			−0.0204663
$722$	1.82554	−	1.82554i	0.0679397	−	0.0679397i
$723$	−4.43777	+	6.28450i	−0.165043	+	0.233723i
$724$		−	22.4908i		−	0.835866i
$725$	4.71434	+	1.80324i	0.175086	+	0.0669708i
$726$	−1.39018	−	8.07155i	−0.0515945	−	0.299563i
$727$	10.3579	+	10.3579i	0.384153	+	0.384153i	0.872596	−	0.488443i	$-0.162435\pi$
$727$	10.3579	+	10.3579i	0.384153	+	0.384153i	−0.488443	+	0.872596i	$0.662435\pi$
$728$	−13.3944	−	13.3944i	−0.496428	−	0.496428i
$729$	23.0542	+	14.0536i	0.853859	+	0.520505i
$730$	2.69144	−	14.5700i	0.0996146	−	0.539259i
$731$		−	52.5683i		−	1.94431i
$732$	−6.02852	−	4.25702i	−0.222821	−	0.157344i
$733$	13.0858	−	13.0858i	0.483336	−	0.483336i	−0.422860	−	0.906195i	$-0.638974\pi$
$733$	13.0858	−	13.0858i	0.483336	−	0.483336i	0.906195	+	0.422860i	$0.138974\pi$
$734$	4.36794			0.161224
$735$	9.04714	+	9.26890i	0.333709	+	0.341888i
$736$	−41.7532			−1.53904
$737$	14.9294	−	14.9294i	0.549931	−	0.549931i
$738$	0.207925	−	0.436799i	0.00765383	−	0.0160788i
$739$			34.0687i			1.25324i	0.779327	+	0.626618i	$0.215561\pi$
$739$			34.0687i			1.25324i	−0.779327	+	0.626618i	$0.784439\pi$
$740$	−28.9480	+	19.9207i	−1.06415	+	0.732301i
$741$	−31.4417	+	5.41528i	−1.15504	+	0.198935i
$742$	13.6958	+	13.6958i	0.502790	+	0.502790i
$743$	−27.3150	−	27.3150i	−1.00209	−	1.00209i	−0.999998	−	0.00209141i	$-0.999334\pi$
$743$	−27.3150	−	27.3150i	−1.00209	−	1.00209i	−0.00209141	−	0.999998i	$-0.500666\pi$
$744$	−4.35438	+	0.749965i	−0.159639	+	0.0274950i
$745$	−13.2921	−	2.45538i	−0.486985	−	0.0899582i
$746$		−	21.3493i		−	0.781655i
$747$	6.65825	−	13.9873i	0.243612	−	0.511770i
$748$	17.7340	−	17.7340i	0.648419	−	0.648419i
$749$	3.67608			0.134321
$750$	5.26983	−	13.2927i	0.192427	−	0.485381i
$751$	−21.3547			−0.779243			−0.389621	−	0.920975i	$-0.627394\pi$
$751$	−21.3547			−0.779243			−0.389621	+	0.920975i	$0.627394\pi$
$752$	−6.02405	+	6.02405i	−0.219675	+	0.219675i
$753$	16.9524	+	11.9709i	0.617780	+	0.436243i
$754$		−	2.89491i		−	0.105426i
$755$	−26.2909	−	4.85659i	−0.956825	−	0.176749i
$756$	−12.6019	+	7.07677i	−0.458328	+	0.257380i
$757$	35.6978	+	35.6978i	1.29746	+	1.29746i	0.930067	+	0.367391i	$0.119749\pi$
$757$	35.6978	+	35.6978i	1.29746	+	1.29746i	0.367391	+	0.930067i	$0.380251\pi$
$758$	7.18952	+	7.18952i	0.261135	+	0.261135i
$759$	−8.73938	−	50.7418i	−0.317219	−	1.84181i
$760$	−22.2880	+	15.3376i	−0.808469	+	0.556353i
$761$			24.0797i			0.872888i	0.899731	+	0.436444i	$0.143762\pi$
$761$			24.0797i			0.872888i	−0.899731	+	0.436444i	$0.856238\pi$
$762$	1.94820	−	2.75892i	0.0705759	−	0.0999452i
$763$	6.16287	−	6.16287i	0.223111	−	0.223111i
$764$	−12.2940			−0.444780
$765$	−22.4494	−	16.2634i	−0.811659	−	0.588004i
$766$	−2.60427			−0.0940960
$767$	6.35086	−	6.35086i	0.229316	−	0.229316i
$768$	−11.9522	+	16.9260i	−0.431288	+	0.610763i
$769$		−	10.6113i		−	0.382655i	−0.981526	−	0.191327i	$-0.938721\pi$
$769$		−	10.6113i		−	0.382655i	0.981526	−	0.191327i	$-0.0612792\pi$
$770$	2.39238	−	12.9511i	0.0862154	−	0.466724i
$771$	7.55941	+	43.8908i	0.272246	+	1.58069i
$772$	−13.5825	−	13.5825i	−0.488845	−	0.488845i
$773$	−5.35202	−	5.35202i	−0.192499	−	0.192499i	0.604276	−	0.796775i	$-0.293462\pi$
$773$	−5.35202	−	5.35202i	−0.192499	−	0.192499i	−0.796775	+	0.604276i	$0.793462\pi$
$774$	−26.5558	+	9.42719i	−0.954529	+	0.338853i
$775$	4.67003	+	1.78629i	0.167752	+	0.0641656i
$776$		−	24.1112i		−	0.865541i
$777$	29.2231	+	20.6358i	1.04837	+	0.740304i
$778$	9.69050	−	9.69050i	0.347421	−	0.347421i
$779$	1.03579			0.0371110
$780$	21.8797	+	0.264904i	0.783419	+	0.00948507i
$781$	47.2145			1.68947
$782$	−15.3751	+	15.3751i	−0.549812	+	0.549812i
$783$	−5.05018	−	1.41793i	−0.180479	−	0.0506727i
$784$			3.43064i			0.122523i
$785$	5.62483	+	8.17377i	0.200759	+	0.291734i
$786$	0.929708	−	0.160126i	0.0331616	−	0.00571150i
$787$	11.2511	+	11.2511i	0.401059	+	0.401059i	0.878606	−	0.477547i	$-0.158474\pi$
$787$	11.2511	+	11.2511i	0.401059	+	0.401059i	−0.477547	+	0.878606i	$0.658474\pi$
$788$	−15.7882	−	15.7882i	−0.562430	−	0.562430i
$789$	14.9775	−	2.57962i	0.533215	−	0.0918368i
$790$	12.1084	+	17.5955i	0.430798	+	0.626018i
$791$		−	11.6740i		−	0.415080i
$792$	−28.8276	−	13.7225i	−1.02434	−	0.487607i
$793$	8.04326	−	8.04326i	0.285625	−	0.285625i
$794$	−1.68677			−0.0598612
$795$	−53.1295	−	0.643253i	−1.88431	−	0.0228138i
$796$	7.27733			0.257938
$797$	−36.9795	+	36.9795i	−1.30988	+	1.30988i	−0.388383	+	0.921498i	$0.626966\pi$
$797$	−36.9795	+	36.9795i	−1.30988	+	1.30988i	−0.921498	+	0.388383i	$0.873034\pi$
$798$	9.47435	+	6.69028i	0.335388	+	0.236833i
$799$			34.3194i			1.21413i
$800$	26.7505	−	11.9482i	0.945771	−	0.422431i
$801$	10.9114	+	30.7366i	0.385534	+	1.08602i
$802$	−5.08341	−	5.08341i	−0.179501	−	0.179501i
$803$	26.4712	+	26.4712i	0.934148	+	0.934148i
$804$	−2.16446	−	12.5671i	−0.0763347	−	0.443208i
$805$	5.53401	−	29.9581i	0.195048	−	1.05588i
$806$		−	2.86770i		−	0.101010i
$807$	6.71257	−	9.50592i	0.236294	−	0.334624i
$808$	5.04101	−	5.04101i	0.177342	−	0.177342i
$809$	7.18319			0.252547			0.126274	−	0.991995i	$-0.459698\pi$
$809$	7.18319			0.252547			0.126274	+	0.991995i	$0.459698\pi$
$810$	−4.18985	+	14.2573i	−0.147216	+	0.500949i
$811$	−21.2797			−0.747231			−0.373616	−	0.927584i	$-0.621882\pi$
$811$	−21.2797			−0.747231			−0.373616	+	0.927584i	$0.621882\pi$
$812$	1.98547	−	1.98547i	0.0696762	−	0.0696762i
$813$	18.1321	−	25.6776i	0.635921	−	0.900552i
$814$			33.2773i			1.16637i
$815$	−0.770542	+	0.530253i	−0.0269909	+	0.0185739i
$816$	−1.24626	−	7.23591i	−0.0436277	−	0.253307i
$817$	−42.6635	−	42.6635i	−1.49261	−	1.49261i
$818$	−10.3007	−	10.3007i	−0.360155	−	0.360155i
$819$	−7.45237	−	20.9929i	−0.260407	−	0.733550i
$820$	−0.698560	−	0.129041i	−0.0243948	−	0.00450632i
$821$			39.8034i			1.38915i	0.719422	+	0.694573i	$0.244407\pi$
$821$			39.8034i			1.38915i	−0.719422	+	0.694573i	$0.755593\pi$
$822$	−11.6868	−	8.25259i	−0.407624	−	0.287842i
$823$	−31.8774	+	31.8774i	−1.11118	+	1.11118i	−0.118183	+	0.992992i	$0.537707\pi$
$823$	−31.8774	+	31.8774i	−1.11118	+	1.11118i	−0.992992	+	0.118183i	$0.962293\pi$
$824$	−0.733219			−0.0255429
$825$	20.1195	+	30.0084i	0.700471	+	1.04476i
$826$	−3.26507			−0.113606
$827$	29.9815	−	29.9815i	1.04256	−	1.04256i	0.0435054	−	0.999053i	$-0.486147\pi$
$827$	29.9815	−	29.9815i	1.04256	−	1.04256i	0.999053	−	0.0435054i	$-0.0138526\pi$
$828$	−28.0795	−	13.3664i	−0.975830	−	0.464515i
$829$			47.7414i			1.65813i	0.559154	+	0.829064i	$0.311126\pi$
$829$			47.7414i			1.65813i	−0.559154	+	0.829064i	$0.688874\pi$
$830$	8.38415	+	1.54876i	0.291018	+	0.0537582i
$831$	12.0129	−	2.06902i	0.416725	−	0.0717735i
$832$	−6.24762	−	6.24762i	−0.216597	−	0.216597i
$833$	9.77228	+	9.77228i	0.338589	+	0.338589i
$834$	13.9763	−	2.40717i	0.483959	−	0.0833534i
$835$	−36.2019	+	24.9125i	−1.25282	+	0.862133i
$836$		−	28.7852i		−	0.995558i
$837$	−5.00271	−	1.40460i	−0.172919	−	0.0485502i
$838$	−9.69702	+	9.69702i	−0.334978	+	0.334978i
$839$	27.3182			0.943130			0.471565	−	0.881831i	$-0.343689\pi$
$839$	27.3182			0.943130			0.471565	+	0.881831i	$0.343689\pi$
$840$	−13.1950	−	13.5184i	−0.455269	−	0.466429i
$841$	−27.9809			−0.964860
$842$	−13.0071	+	13.0071i	−0.448253	+	0.448253i
$843$	−14.5997	−	10.3096i	−0.502842	−	0.355080i
$844$			9.61712i			0.331035i
$845$	−0.845909	+	4.57929i	−0.0291001	+	0.157532i
$846$	17.3371	−	6.15458i	0.596061	−	0.211599i
$847$	8.65804	+	8.65804i	0.297494	+	0.297494i
$848$	−9.95128	−	9.95128i	−0.341728	−	0.341728i
$849$	2.24059	+	13.0091i	0.0768969	+	0.446472i
$850$	5.45076	−	14.2503i	0.186959	−	0.488780i
$851$			76.9762i			2.63871i
$852$	16.4493	−	23.2945i	0.563544	−	0.798056i
$853$	−25.5944	+	25.5944i	−0.876337	+	0.876337i	−0.993154	−	0.116817i	$-0.962731\pi$
$853$	−25.5944	+	25.5944i	−0.876337	+	0.876337i	0.116817	+	0.993154i	$0.462731\pi$
$854$	−4.13515			−0.141502
$855$	−31.4186	+	5.02044i	−1.07449	+	0.171695i
$856$	4.90470			0.167639
$857$	18.2737	−	18.2737i	0.624217	−	0.624217i	−0.322390	−	0.946607i	$-0.604486\pi$
$857$	18.2737	−	18.2737i	0.624217	−	0.624217i	0.946607	+	0.322390i	$0.104486\pi$
$858$	11.9526	−	16.9266i	0.408056	−	0.577864i
$859$		−	54.2844i		−	1.85216i	−0.377327	−	0.926080i	$-0.623157\pi$
$859$		−	54.2844i		−	1.85216i	0.377327	−	0.926080i	$-0.376843\pi$
$860$	23.4582	+	34.0884i	0.799916	+	1.16241i
$861$	0.122752	+	0.712713i	0.00418338	+	0.0242892i
$862$	14.1595	+	14.1595i	0.482274	+	0.482274i
$863$	−17.9753	−	17.9753i	−0.611887	−	0.611887i	0.331551	−	0.943437i	$-0.392428\pi$
$863$	−17.9753	−	17.9753i	−0.611887	−	0.611887i	−0.943437	+	0.331551i	$0.892428\pi$
$864$	−26.5474	+	14.9080i	−0.903160	+	0.507181i
$865$	−0.895030	−	1.30062i	−0.0304319	−	0.0442224i
$866$		−	16.5364i		−	0.561928i
$867$	−0.109190	−	0.0771039i	−0.00370827	−	0.00261858i
$868$	1.96680	−	1.96680i	0.0667577	−	0.0667577i
$869$	−53.9669			−1.83070
$870$	0.0349508	−	2.88676i	0.00118494	−	0.0978704i
$871$	19.6549			0.665980
$872$	8.22261	−	8.22261i	0.278453	−	0.278453i
$873$	12.1871	−	25.6021i	0.412472	−	0.866501i
$874$			24.9563i			0.844160i
$875$	5.02732	+	20.7772i	0.169955	+	0.702397i
$876$	22.2827	−	3.83780i	0.752861	−	0.129667i
$877$	−32.5455	−	32.5455i	−1.09898	−	1.09898i	−0.994530	−	0.104455i	$-0.966690\pi$
$877$	−32.5455	−	32.5455i	−1.09898	−	1.09898i	−0.104455	−	0.994530i	$-0.533310\pi$
$878$	−2.13043	−	2.13043i	−0.0718986	−	0.0718986i
$879$	−19.2363	+	3.31312i	−0.648826	+	0.111749i
$880$	−1.73828	+	9.41011i	−0.0585975	+	0.317215i
$881$		−	3.85023i		−	0.129718i	−0.997894	−	0.0648588i	$-0.979340\pi$
$881$		−	3.85023i		−	0.129718i	0.997894	−	0.0648588i	$-0.0206597\pi$
$882$	3.18416	−	6.68912i	0.107216	−	0.225235i
$883$	−13.5611	+	13.5611i	−0.456368	+	0.456368i	−0.897461	−	0.441094i	$-0.854591\pi$
$883$	−13.5611	+	13.5611i	−0.456368	+	0.456368i	0.441094	+	0.897461i	$0.354591\pi$
$884$	23.3472			0.785253
$885$	6.40966	−	6.25631i	0.215458	−	0.210304i
$886$	−15.2702			−0.513013
$887$	2.61563	−	2.61563i	0.0878242	−	0.0878242i	−0.661830	−	0.749654i	$-0.730220\pi$
$887$	2.61563	−	2.61563i	0.0878242	−	0.0878242i	0.749654	+	0.661830i	$0.230220\pi$
$888$	38.9899	+	27.5326i	1.30842	+	0.923933i
$889$			5.04915i			0.169343i
$890$	−14.7879	+	10.1763i	−0.495690	+	0.341112i
$891$	−23.6740	−	29.1421i	−0.793110	−	0.976296i
$892$	10.5340	+	10.5340i	0.352705	+	0.352705i
$893$	27.8530	+	27.8530i	0.932066	+	0.932066i
$894$	1.31226	+	7.61910i	0.0438884	+	0.254821i
$895$	53.4125	+	9.86662i	1.78538	+	0.329805i
$896$		−	19.1947i		−	0.641249i
$897$	27.6486	−	39.1542i	0.923160	−	1.30732i
$898$	6.65171	−	6.65171i	0.221970	−	0.221970i
$899$	1.00949			0.0336683
$900$	21.8149	+	0.528316i	0.727164	+	0.0176105i
$901$	−56.6930			−1.88872
$902$	−0.475686	+	0.475686i	−0.0158386	+	0.0158386i
$903$	24.3001	−	34.4123i	0.808658	−	1.14517i
$904$		−	15.5757i		−	0.518039i
$905$	33.9950	+	6.27972i	1.13003	+	0.208745i
$906$	2.59556	+	15.0701i	0.0862316	+	0.500670i
$907$	−10.5504	−	10.5504i	−0.350321	−	0.350321i	0.509908	−	0.860229i	$-0.329679\pi$
$907$	−10.5504	−	10.5504i	−0.350321	−	0.350321i	−0.860229	+	0.509908i	$0.829679\pi$
$908$	−7.33236	−	7.33236i	−0.243333	−	0.243333i
$909$	7.90073	−	2.80472i	0.262051	−	0.0930267i
$910$	10.1000	−	6.95037i	0.334812	−	0.230403i
$911$		−	25.4140i		−	0.842002i	−0.907060	−	0.421001i	$-0.861679\pi$
$911$		−	25.4140i		−	0.842002i	0.907060	−	0.421001i	$-0.138321\pi$
$912$	−6.88398	−	4.86110i	−0.227951	−	0.160967i
$913$	−15.2326	+	15.2326i	−0.504124	+	0.504124i
$914$	23.3883			0.773617
$915$	8.11773	−	7.92352i	0.268364	−	0.261943i
$916$	−17.8394			−0.589430
$917$	−0.997262	+	0.997262i	−0.0329325	+	0.0329325i
$918$	−4.28605	+	15.2654i	−0.141461	+	0.503834i
$919$			44.9227i			1.48186i	0.671581	+	0.740931i	$0.265616\pi$
$919$			44.9227i			1.48186i	−0.671581	+	0.740931i	$0.734384\pi$
$920$	7.38357	−	39.9706i	0.243429	−	1.31779i
$921$	27.4614	−	4.72974i	0.904884	−	0.155850i
$922$	4.93567	+	4.93567i	0.162548	+	0.162548i
$923$	31.0795	+	31.0795i	1.02299	+	1.02299i
$924$	19.8067	−	3.41136i	0.651594	−	0.112226i
$925$	−22.0276	−	49.3171i	−0.724264	−	1.62154i
$926$			5.40749i			0.177701i
$927$	−0.778559	−	0.370610i	−0.0255712	−	0.0121724i
$928$	4.18261	−	4.18261i	0.137301	−	0.137301i
$929$	24.6695			0.809380			0.404690	−	0.914454i	$-0.367380\pi$
$929$	24.6695			0.809380			0.404690	+	0.914454i	$0.367380\pi$
$930$	0.0346223	−	2.85963i	0.00113531	−	0.0937709i
$931$	15.8620			0.519857
$932$	24.0030	−	24.0030i	0.786244	−	0.786244i
$933$	23.6868	+	16.7263i	0.775471	+	0.547596i
$934$			27.7335i			0.907468i
$935$	21.8535	+	31.7566i	0.714684	+	1.03855i
$936$	−9.94309	−	28.0091i	−0.325000	−	0.915505i
$937$	4.45887	+	4.45887i	0.145665	+	0.145665i	0.776178	−	0.630513i	$-0.217156\pi$
$937$	4.45887	+	4.45887i	0.145665	+	0.145665i	−0.630513	+	0.776178i	$0.717156\pi$
$938$	−5.05242	−	5.05242i	−0.164967	−	0.164967i
$939$	1.35774	+	7.88320i	0.0443082	+	0.257258i
$940$	−15.3147	−	22.2548i	−0.499512	−	0.725870i
$941$		−	45.2186i		−	1.47408i	−0.675847	−	0.737042i	$-0.736222\pi$
$941$		−	45.2186i		−	1.47408i	0.675847	−	0.737042i	$-0.263778\pi$
$942$	3.27358	−	4.63584i	0.106659	−	0.151044i
$943$	−1.10035	+	1.10035i	−0.0358322	+	0.0358322i
$944$	2.37237			0.0772139
$945$	−7.17795	−	21.0238i	−0.233499	−	0.683903i
$946$	39.1864			1.27406
$947$	−3.08532	+	3.08532i	−0.100259	+	0.100259i	−0.755457	−	0.655198i	$-0.772585\pi$
$947$	−3.08532	+	3.08532i	−0.100259	+	0.100259i	0.655198	+	0.755457i	$0.272585\pi$
$948$	−18.8018	+	26.6259i	−0.610654	+	0.864770i
$949$			34.8499i			1.13128i
$950$	−7.14154	−	15.9890i	−0.231702	−	0.518752i
$951$	8.25582	+	47.9342i	0.267713	+	1.55437i
$952$	−14.2525	−	14.2525i	−0.461928	−	0.461928i
$953$	−5.07876	−	5.07876i	−0.164517	−	0.164517i	0.620047	−	0.784564i	$-0.287113\pi$
$953$	−5.07876	−	5.07876i	−0.164517	−	0.164517i	−0.784564	+	0.620047i	$0.787113\pi$
$954$	10.1669	+	28.6395i	0.329165	+	0.927238i
$955$	3.43262	−	18.5824i	0.111077	−	0.601311i
$956$		−	44.4811i		−	1.43862i
$957$	5.95850	+	4.20757i	0.192611	+	0.136012i
$958$	−19.0201	+	19.0201i	−0.614511	+	0.614511i
$959$	21.3882			0.690661
$960$	−6.15461	−	6.30547i	−0.198639	−	0.203508i
$961$	1.00000			0.0322581
$962$	−21.9051	+	21.9051i	−0.706250	+	0.706250i
$963$	5.20798	+	2.47910i	0.167825	+	0.0798880i
$964$		−	6.46173i		−	0.208118i
$965$	24.3224	−	16.7376i	0.782965	−	0.538802i
$966$	−17.1721	+	2.95760i	−0.552504	+	0.0951591i
$967$	2.03208	+	2.03208i	0.0653473	+	0.0653473i	0.739025	−	0.673678i	$-0.235286\pi$
$967$	2.03208	+	2.03208i	0.0653473	+	0.0653473i	−0.673678	+	0.739025i	$0.735286\pi$
$968$	11.5517	+	11.5517i	0.371286	+	0.371286i
$969$	−33.4562	+	5.76224i	−1.07477	+	0.185110i
$970$	15.3462	+	2.83482i	0.492736	+	0.0910206i
$971$		−	9.38119i		−	0.301057i	−0.988606	−	0.150528i	$-0.951903\pi$
$971$		−	9.38119i		−	0.301057i	0.988606	−	0.150528i	$-0.0480975\pi$
$972$	−22.6259	+	1.52723i	−0.725726	+	0.0489859i
$973$	−14.9918	+	14.9918i	−0.480616	+	0.480616i
$974$	9.59936			0.307583
$975$	−6.50948	+	32.9973i	−0.208470	+	1.05676i
$976$	3.00456			0.0961738
$977$	27.6860	−	27.6860i	0.885755	−	0.885755i	−0.108357	−	0.994112i	$-0.534559\pi$
$977$	27.6860	−	27.6860i	0.885755	−	0.885755i	0.994112	+	0.108357i	$0.0345591\pi$
$978$	0.437021	+	0.308601i	0.0139744	+	0.00986796i
$979$		−	45.3557i		−	1.44958i
$980$	−10.6977	−	1.97614i	−0.341726	−	0.0631253i
$981$	12.8872	−	4.57490i	0.411457	−	0.146065i
$982$	5.96336	+	5.96336i	0.190298	+	0.190298i
$983$	−31.3073	−	31.3073i	−0.998549	−	0.998549i	0.00145006	−	0.999999i	$-0.499538\pi$
$983$	−31.3073	−	31.3073i	−0.998549	−	0.998549i	−0.999999	+	0.00145006i	$0.999538\pi$
$984$	0.163778	+	0.950914i	0.00522106	+	0.0303140i
$985$	28.2721	−	19.4556i	0.900825	−	0.619908i
$986$		−	3.08039i		−	0.0980995i
$987$	−15.8644	+	22.4662i	−0.504970	+	0.715107i
$988$	18.9482	−	18.9482i	0.602823	−	0.602823i
$989$	90.6452			2.88235
$990$	12.1234	−	16.7346i	0.385306	−	0.531862i
$991$	33.8908			1.07658			0.538289	−	0.842760i	$-0.319071\pi$
$991$	33.8908			1.07658			0.538289	+	0.842760i	$0.319071\pi$
$992$	4.14330	−	4.14330i	0.131550	−	0.131550i
$993$	9.48183	−	13.4276i	0.300897	−	0.426111i
$994$		−	15.9784i		−	0.506805i
$995$	−2.03192	+	10.9997i	−0.0644162	+	0.348714i
$996$	2.20842	+	12.8223i	0.0699765	+	0.406291i
$997$	−27.1088	−	27.1088i	−0.858544	−	0.858544i	0.132623	−	0.991167i	$-0.457660\pi$
$997$	−27.1088	−	27.1088i	−0.858544	−	0.858544i	−0.991167	+	0.132623i	$0.957660\pi$
$998$	4.37794	+	4.37794i	0.138581	+	0.138581i
$999$	27.4844	+	48.9428i	0.869569	+	1.54848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.32.13	✓	60
3.2	odd	2	inner	465.2.k.a.32.18	yes	60
5.3	odd	4	inner	465.2.k.a.218.18	yes	60
15.8	even	4	inner	465.2.k.a.218.13	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.13	✓	60	1.1	even	1	trivial
465.2.k.a.32.18	yes	60	3.2	odd	2	inner
465.2.k.a.218.13	yes	60	15.8	even	4	inner
465.2.k.a.218.18	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)

\(f(q)\)	\(=\)	\(q+(-0.522133 + 0.522133i) q^{2} +(0.999094 - 1.41485i) q^{3} +1.45476i q^{4} +(-2.19887 - 0.406185i) q^{5} +(0.217082 + 1.26040i) q^{6} +(-1.35198 - 1.35198i) q^{7} +(-1.80384 - 1.80384i) q^{8} +(-1.00362 - 2.82714i) q^{9} +O(q^{10})\)	\(q+(-0.522133 + 0.522133i) q^{2} +(0.999094 - 1.41485i) q^{3} +1.45476i q^{4} +(-2.19887 - 0.406185i) q^{5} +(0.217082 + 1.26040i) q^{6} +(-1.35198 - 1.35198i) q^{7} +(-1.80384 - 1.80384i) q^{8} +(-1.00362 - 2.82714i) q^{9} +(1.36018 - 0.936017i) q^{10} +4.17180i q^{11} +(2.05827 + 1.45344i) q^{12} +(-2.74614 + 2.74614i) q^{13} +1.41183 q^{14} +(-2.77157 + 2.70526i) q^{15} -1.02582 q^{16} +(-2.92209 + 2.92209i) q^{17} +(2.00017 + 0.952120i) q^{18} +4.74303i q^{19} +(0.590900 - 3.19881i) q^{20} +(-3.26362 + 0.562101i) q^{21} +(-2.17824 - 2.17824i) q^{22} +(-5.03865 - 5.03865i) q^{23} +(-4.35438 + 0.749965i) q^{24} +(4.67003 + 1.78629i) q^{25} -2.86770i q^{26} +(-5.00271 - 1.40460i) q^{27} +(1.96680 - 1.96680i) q^{28} +1.00949 q^{29} +(0.0346223 - 2.85963i) q^{30} +1.00000 q^{31} +(4.14330 - 4.14330i) q^{32} +(5.90249 + 4.16802i) q^{33} -3.05143i q^{34} +(2.42368 + 3.52199i) q^{35} +(4.11280 - 1.46003i) q^{36} +(-7.63858 - 7.63858i) q^{37} +(-2.47649 - 2.47649i) q^{38} +(1.14173 + 6.62904i) q^{39} +(3.23371 + 4.69910i) q^{40} -0.218381i q^{41} +(1.41055 - 1.99753i) q^{42} +(-8.99500 + 8.99500i) q^{43} -6.06895 q^{44} +(1.05849 + 6.62417i) q^{45} +5.26169 q^{46} +(5.87242 - 5.87242i) q^{47} +(-1.02489 + 1.45139i) q^{48} -3.34428i q^{49} +(-3.37106 + 1.50569i) q^{50} +(1.21489 + 7.05376i) q^{51} +(-3.99496 - 3.99496i) q^{52} +(9.70078 + 9.70078i) q^{53} +(3.34547 - 1.87869i) q^{54} +(1.69453 - 9.17324i) q^{55} +4.87752i q^{56} +(6.71069 + 4.73873i) q^{57} +(-0.527087 + 0.527087i) q^{58} -2.31265 q^{59} +(-3.93549 - 4.03195i) q^{60} -2.92893 q^{61} +(-0.522133 + 0.522133i) q^{62} +(-2.46537 + 5.17913i) q^{63} +2.27506i q^{64} +(7.15384 - 4.92295i) q^{65} +(-5.25815 + 0.905623i) q^{66} +(-3.57864 - 3.57864i) q^{67} +(-4.25092 - 4.25092i) q^{68} +(-12.1630 + 2.09487i) q^{69} +(-3.10442 - 0.573464i) q^{70} -11.3175i q^{71} +(-3.28934 + 6.91009i) q^{72} +(6.34526 - 6.34526i) q^{73} +7.97670 q^{74} +(7.19314 - 4.82273i) q^{75} -6.89994 q^{76} +(5.64021 - 5.64021i) q^{77} +(-4.05737 - 2.86510i) q^{78} +12.9361i q^{79} +(2.25565 + 0.416674i) q^{80} +(-6.98548 + 5.67477i) q^{81} +(0.114024 + 0.114024i) q^{82} +(3.65131 + 3.65131i) q^{83} +(-0.817719 - 4.74776i) q^{84} +(7.61219 - 5.23837i) q^{85} -9.39316i q^{86} +(1.00857 - 1.42828i) q^{87} +(7.52527 - 7.52527i) q^{88} -10.8720 q^{89} +(-4.01137 - 2.90602i) q^{90} +7.42547 q^{91} +(7.33000 - 7.33000i) q^{92} +(0.999094 - 1.41485i) q^{93} +6.13236i q^{94} +(1.92655 - 10.4293i) q^{95} +(-1.72262 - 10.0017i) q^{96} +(6.68329 + 6.68329i) q^{97} +(1.74616 + 1.74616i) q^{98} +(11.7943 - 4.18692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6}+O(q^{10}) \) 60 * q - 4 * q^6	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40} + 44 q^{42} + 16 q^{43} + 14 q^{45} + 40 q^{46} - 104 q^{48} - 48 q^{51} - 12 q^{52} - 48 q^{55} + 42 q^{57} + 80 q^{58} + 60 q^{60} - 8 q^{61} - 10 q^{63} - 24 q^{66} - 88 q^{67} - 84 q^{70} + 84 q^{72} + 60 q^{73} + 14 q^{75} + 72 q^{76} - 152 q^{78} - 132 q^{81} - 60 q^{82} - 16 q^{85} + 34 q^{87} + 124 q^{88} + 190 q^{90} + 64 q^{91} - 88 q^{96} - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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