LMFDB - Embedded newform 465.2.k.b.32.15

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			32.15
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150369 + 0.150369i) q^{2} +(0.591574 + 1.62789i) q^{3} +1.95478i q^{4} +(0.684260 - 2.12880i) q^{5} +(-0.333740 - 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(-0.594677 - 0.594677i) q^{8} +(-2.30008 + 1.92604i) q^{9} +O(q^{10})$	\(q+(-0.150369 + 0.150369i) q^{2} +(0.591574 + 1.62789i) q^{3} +1.95478i q^{4} +(0.684260 - 2.12880i) q^{5} +(-0.333740 - 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(-0.594677 - 0.594677i) q^{8} +(-2.30008 + 1.92604i) q^{9} +(0.217214 + 0.422998i) q^{10} +5.94154i q^{11} +(-3.18217 + 1.15640i) q^{12} +(-2.75083 + 2.75083i) q^{13} +0.116445 q^{14} +(3.87025 - 0.145439i) q^{15} -3.73071 q^{16} +(4.13991 - 4.13991i) q^{17} +(0.0562442 - 0.635479i) q^{18} +1.21724i q^{19} +(4.16133 + 1.33758i) q^{20} +(0.401260 - 0.859371i) q^{21} +(-0.893425 - 0.893425i) q^{22} +(6.27242 + 6.27242i) q^{23} +(0.616276 - 1.31987i) q^{24} +(-4.06358 - 2.91331i) q^{25} -0.827280i q^{26} +(-4.49606 - 2.60489i) q^{27} +(0.756883 - 0.756883i) q^{28} -2.83642 q^{29} +(-0.560097 + 0.603836i) q^{30} -1.00000 q^{31} +(1.75034 - 1.75034i) q^{32} +(-9.67221 + 3.51486i) q^{33} +1.24503i q^{34} +(-1.08921 + 0.559321i) q^{35} +(-3.76498 - 4.49615i) q^{36} +(3.46533 + 3.46533i) q^{37} +(-0.183035 - 0.183035i) q^{38} +(-6.10537 - 2.85074i) q^{39} +(-1.67286 + 0.859035i) q^{40} -6.88424i q^{41} +(0.0688858 + 0.189560i) q^{42} +(-4.32117 + 4.32117i) q^{43} -11.6144 q^{44} +(2.52630 + 6.21432i) q^{45} -1.88636 q^{46} +(3.93745 - 3.93745i) q^{47} +(-2.20699 - 6.07321i) q^{48} -6.70016i q^{49} +(1.04911 - 0.172965i) q^{50} +(9.18839 + 4.29027i) q^{51} +(-5.37726 - 5.37726i) q^{52} +(4.51366 + 4.51366i) q^{53} +(1.06776 - 0.284373i) q^{54} +(12.6484 + 4.06556i) q^{55} +0.460514i q^{56} +(-1.98154 + 0.720087i) q^{57} +(0.426510 - 0.426510i) q^{58} +4.65734 q^{59} +(0.284301 + 7.56548i) q^{60} +0.744831 q^{61} +(0.150369 - 0.150369i) q^{62} +(1.63634 + 0.144827i) q^{63} -6.93503i q^{64} +(3.97368 + 7.73824i) q^{65} +(0.925875 - 1.98293i) q^{66} +(5.51708 + 5.51708i) q^{67} +(8.09260 + 8.09260i) q^{68} +(-6.50024 + 13.9214i) q^{69} +(0.0796786 - 0.247888i) q^{70} -4.91796i q^{71} +(2.51318 + 0.222433i) q^{72} +(9.51707 - 9.51707i) q^{73} -1.04216 q^{74} +(2.33865 - 8.33851i) q^{75} -2.37943 q^{76} +(2.30055 - 2.30055i) q^{77} +(1.34672 - 0.489397i) q^{78} +3.31966i q^{79} +(-2.55278 + 7.94194i) q^{80} +(1.58074 - 8.86009i) q^{81} +(1.03518 + 1.03518i) q^{82} +(-4.12394 - 4.12394i) q^{83} +(1.67988 + 0.784374i) q^{84} +(-5.98026 - 11.6458i) q^{85} -1.29954i q^{86} +(-1.67795 - 4.61739i) q^{87} +(3.53330 - 3.53330i) q^{88} +3.87913 q^{89} +(-1.31432 - 0.554565i) q^{90} +2.13022 q^{91} +(-12.2612 + 12.2612i) q^{92} +(-0.591574 - 1.62789i) q^{93} +1.18414i q^{94} +(2.59126 + 0.832908i) q^{95} +(3.88482 + 1.81391i) q^{96} +(5.32691 + 5.32691i) q^{97} +(1.00750 + 1.00750i) q^{98} +(-11.4436 - 13.6660i) 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 $

$2$	−0.150369	+	0.150369i	−0.106327	+	0.106327i	−0.758269	−	0.651942i	$-0.773955\pi$
$2$	−0.150369	+	0.150369i	−0.106327	+	0.106327i	0.651942	+	0.758269i	$0.273955\pi$
$3$	0.591574	+	1.62789i	0.341545	+	0.939865i
$3$	0.591574	+	1.62789i	0.341545	+	0.939865i
$4$			1.95478i			0.977389i
$5$	0.684260	−	2.12880i	0.306010	−	0.952028i
$5$	0.684260	−	2.12880i	0.306010	−	0.952028i
$6$	−0.333740	−	0.155831i	−0.136249	−	0.0636176i
$7$	−0.387197	−	0.387197i	−0.146347	−	0.146347i	0.630137	−	0.776484i	$-0.282999\pi$
$7$	−0.387197	−	0.387197i	−0.146347	−	0.146347i	−0.776484	+	0.630137i	$0.782999\pi$
$8$	−0.594677	−	0.594677i	−0.210250	−	0.210250i
$9$	−2.30008	+	1.92604i	−0.766694	+	0.642013i
$10$	0.217214	+	0.422998i	0.0686892	+	0.133764i
$11$			5.94154i			1.79144i	0.444616	+	0.895721i	$0.353340\pi$
$11$			5.94154i			1.79144i	−0.444616	+	0.895721i	$0.646660\pi$
$12$	−3.18217	+	1.15640i	−0.918614	+	0.333823i
$13$	−2.75083	+	2.75083i	−0.762942	+	0.762942i	−0.976853	−	0.213911i	$-0.931380\pi$
$13$	−2.75083	+	2.75083i	−0.762942	+	0.762942i	0.213911	+	0.976853i	$0.431380\pi$
$14$	0.116445			0.0311212
$15$	3.87025	−	0.145439i	0.999295	−	0.0375522i
$16$	−3.73071			−0.932679
$17$	4.13991	−	4.13991i	1.00408	−	1.00408i	0.00408352	−	0.999992i	$-0.498700\pi$
$17$	4.13991	−	4.13991i	1.00408	−	1.00408i	0.999992	−	0.00408352i	$-0.00129983\pi$
$18$	0.0562442	−	0.635479i	0.0132569	−	0.149784i
$19$			1.21724i			0.279254i	0.990204	+	0.139627i	$0.0445903\pi$
$19$			1.21724i			0.279254i	−0.990204	+	0.139627i	$0.955410\pi$
$20$	4.16133	+	1.33758i	0.930502	+	0.299091i
$21$	0.401260	−	0.859371i	0.0875621	−	0.187530i
$22$	−0.893425	−	0.893425i	−0.190479	−	0.190479i
$23$	6.27242	+	6.27242i	1.30789	+	1.30789i	0.922936	+	0.384954i	$0.125783\pi$
$23$	6.27242	+	6.27242i	1.30789	+	1.30789i	0.384954	+	0.922936i	$0.374217\pi$
$24$	0.616276	−	1.31987i	0.125797	−	0.269417i
$25$	−4.06358	−	2.91331i	−0.812715	−	0.582661i
$26$		−	0.827280i		−	0.162243i
$27$	−4.49606	−	2.60489i	−0.865267	−	0.501312i
$28$	0.756883	−	0.756883i	0.143038	−	0.143038i
$29$	−2.83642			−0.526709			−0.263355	−	0.964699i	$-0.584829\pi$
$29$	−2.83642			−0.526709			−0.263355	+	0.964699i	$0.584829\pi$
$30$	−0.560097	+	0.603836i	−0.102259	+	0.110245i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	1.75034	−	1.75034i	0.309419	−	0.309419i
$33$	−9.67221	+	3.51486i	−1.68371	+	0.611859i
$34$			1.24503i			0.213521i
$35$	−1.08921	+	0.559321i	−0.184110	+	0.0945425i
$36$	−3.76498	−	4.49615i	−0.627497	−	0.749358i
$37$	3.46533	+	3.46533i	0.569697	+	0.569697i	0.932043	−	0.362347i	$-0.118024\pi$
$37$	3.46533	+	3.46533i	0.569697	+	0.569697i	−0.362347	+	0.932043i	$0.618024\pi$
$38$	−0.183035	−	0.183035i	−0.0296922	−	0.0296922i
$39$	−6.10537	−	2.85074i	−0.977642	−	0.456483i
$40$	−1.67286	+	0.859035i	−0.264503	+	0.135825i
$41$		−	6.88424i		−	1.07514i	−0.843220	−	0.537568i	$-0.819343\pi$
$41$		−	6.88424i		−	1.07514i	0.843220	−	0.537568i	$-0.180657\pi$
$42$	0.0688858	+	0.189560i	0.0106293	+	0.0292498i
$43$	−4.32117	+	4.32117i	−0.658972	+	0.658972i	−0.955137	−	0.296165i	$-0.904292\pi$
$43$	−4.32117	+	4.32117i	−0.658972	+	0.658972i	0.296165	+	0.955137i	$0.404292\pi$
$44$	−11.6144			−1.75094
$45$	2.52630	+	6.21432i	0.376598	+	0.926377i
$46$	−1.88636			−0.278128
$47$	3.93745	−	3.93745i	0.574335	−	0.574335i	−0.359002	−	0.933337i	$-0.616883\pi$
$47$	3.93745	−	3.93745i	0.574335	−	0.574335i	0.933337	+	0.359002i	$0.116883\pi$
$48$	−2.20699	−	6.07321i	−0.318552	−	0.876592i
$49$		−	6.70016i		−	0.957165i
$50$	1.04911	−	0.172965i	0.148366	−	0.0244610i
$51$	9.18839	+	4.29027i	1.28663	+	0.600758i
$52$	−5.37726	−	5.37726i	−0.745691	−	0.745691i
$53$	4.51366	+	4.51366i	0.619999	+	0.619999i	0.945531	−	0.325532i	$-0.105543\pi$
$53$	4.51366	+	4.51366i	0.619999	+	0.619999i	−0.325532	+	0.945531i	$0.605543\pi$
$54$	1.06776	−	0.284373i	0.145304	−	0.0386982i
$55$	12.6484	+	4.06556i	1.70550	+	0.548200i
$56$			0.460514i			0.0615388i
$57$	−1.98154	+	0.720087i	−0.262461	+	0.0953778i
$58$	0.426510	−	0.426510i	0.0560035	−	0.0560035i
$59$	4.65734			0.606334			0.303167	−	0.952937i	$-0.401956\pi$
$59$	4.65734			0.606334			0.303167	+	0.952937i	$0.401956\pi$
$60$	0.284301	+	7.56548i	0.0367031	+	0.976700i
$61$	0.744831			0.0953658			0.0476829	−	0.998863i	$-0.484816\pi$
$61$	0.744831			0.0953658			0.0476829	+	0.998863i	$0.484816\pi$
$62$	0.150369	−	0.150369i	0.0190969	−	0.0190969i
$63$	1.63634	+	0.144827i	0.206159	+	0.0182465i
$64$		−	6.93503i		−	0.866879i
$65$	3.97368	+	7.73824i	0.492874	+	0.959811i
$66$	0.925875	−	1.98293i	0.113967	−	0.244082i
$67$	5.51708	+	5.51708i	0.674019	+	0.674019i	0.958640	−	0.284621i	$-0.0918677\pi$
$67$	5.51708	+	5.51708i	0.674019	+	0.674019i	−0.284621	+	0.958640i	$0.591868\pi$
$68$	8.09260	+	8.09260i	0.981372	+	0.981372i
$69$	−6.50024	+	13.9214i	−0.782537	+	1.67594i
$70$	0.0796786	−	0.247888i	0.00952342	−	0.0296283i
$71$		−	4.91796i		−	0.583655i	−0.956471	−	0.291827i	$-0.905737\pi$
$71$		−	4.91796i		−	0.583655i	0.956471	−	0.291827i	$-0.0942633\pi$
$72$	2.51318	+	0.222433i	0.296181	+	0.0262140i
$73$	9.51707	−	9.51707i	1.11389	−	1.11389i	0.121270	−	0.992620i	$-0.461303\pi$
$73$	9.51707	−	9.51707i	1.11389	−	1.11389i	0.992620	−	0.121270i	$-0.0386966\pi$
$74$	−1.04216			−0.121148
$75$	2.33865	−	8.33851i	0.270044	−	0.962848i
$76$	−2.37943			−0.272940
$77$	2.30055	−	2.30055i	0.262171	−	0.262171i
$78$	1.34672	−	0.489397i	0.152486	−	0.0554133i
$79$			3.31966i			0.373491i	0.982408	+	0.186745i	$0.0597939\pi$
$79$			3.31966i			0.373491i	−0.982408	+	0.186745i	$0.940206\pi$
$80$	−2.55278	+	7.94194i	−0.285409	+	0.887936i
$81$	1.58074	−	8.86009i	0.175638	−	0.984455i
$82$	1.03518	+	1.03518i	0.114316	+	0.114316i
$83$	−4.12394	−	4.12394i	−0.452661	−	0.452661i	0.443576	−	0.896237i	$-0.353710\pi$
$83$	−4.12394	−	4.12394i	−0.452661	−	0.452661i	−0.896237	+	0.443576i	$0.853710\pi$
$84$	1.67988	+	0.784374i	0.183290	+	0.0855822i
$85$	−5.98026	−	11.6458i	−0.648650	−	1.26317i
$86$		−	1.29954i		−	0.140133i
$87$	−1.67795	−	4.61739i	−0.179895	−	0.495036i
$88$	3.53330	−	3.53330i	0.376651	−	0.376651i
$89$	3.87913			0.411187			0.205593	−	0.978638i	$-0.434088\pi$
$89$	3.87913			0.411187			0.205593	+	0.978638i	$0.434088\pi$
$90$	−1.31432	−	0.554565i	−0.138542	−	0.0584563i
$91$	2.13022			0.223308
$92$	−12.2612	+	12.2612i	−1.27832	+	1.27832i
$93$	−0.591574	−	1.62789i	−0.0613434	−	0.168805i
$94$			1.18414i			0.122135i
$95$	2.59126	+	0.832908i	0.265857	+	0.0854546i
$96$	3.88482	+	1.81391i	0.396493	+	0.185132i
$97$	5.32691	+	5.32691i	0.540865	+	0.540865i	0.923783	−	0.382917i	$-0.125081\pi$
$97$	5.32691	+	5.32691i	0.540865	+	0.540865i	−0.382917	+	0.923783i	$0.625081\pi$
$98$	1.00750	+	1.00750i	0.101773	+	0.101773i
$99$	−11.4436	−	13.6660i	−1.15013	−	1.37349i
$100$	5.69487	−	7.94339i	0.569487	−	0.794339i
$101$		−	3.06803i		−	0.305280i	−0.988282	−	0.152640i	$-0.951223\pi$
$101$		−	3.06803i		−	0.305280i	0.988282	−	0.152640i	$-0.0487775\pi$
$102$	−2.02678	+	0.736527i	−0.200681	+	0.0729271i
$103$	6.09837	−	6.09837i	0.600890	−	0.600890i	−0.339658	−	0.940549i	$-0.610311\pi$
$103$	6.09837	−	6.09837i	0.600890	−	0.600890i	0.940549	+	0.339658i	$0.110311\pi$
$104$	3.27171			0.320817
$105$	−1.55486	−	1.44223i	−0.151739	−	0.140748i
$106$	−1.35743			−0.131845
$107$	6.95342	−	6.95342i	0.672212	−	0.672212i	−0.286013	−	0.958226i	$-0.592330\pi$
$107$	6.95342	−	6.95342i	0.672212	−	0.672212i	0.958226	+	0.286013i	$0.0923302\pi$
$108$	5.09199	−	8.78879i	0.489977	−	0.845702i
$109$			18.0090i			1.72495i	0.506103	+	0.862473i	$0.331085\pi$
$109$			18.0090i			1.72495i	−0.506103	+	0.862473i	$0.668915\pi$
$110$	−2.51326	+	1.29059i	−0.239630	+	0.123053i
$111$	−3.59119	+	7.69119i	−0.340861	+	0.730016i
$112$	1.44452	+	1.44452i	0.136494	+	0.136494i
$113$	5.26302	+	5.26302i	0.495104	+	0.495104i	0.909910	−	0.414806i	$-0.136151\pi$
$113$	5.26302	+	5.26302i	0.495104	+	0.495104i	−0.414806	+	0.909910i	$0.636151\pi$
$114$	0.189683	−	0.406241i	0.0177655	−	0.0380480i
$115$	17.6447	−	9.06076i	1.64538	−	0.844920i
$116$		−	5.54457i		−	0.514800i
$117$	1.02892	−	11.6253i	0.0951238	−	1.07476i
$118$	−0.700320	+	0.700320i	−0.0644697	+	0.0644697i
$119$	−3.20592			−0.293886
$120$	−2.38804	−	2.21506i	−0.217997	−	0.202206i
$121$	−24.3019			−2.20927
$122$	−0.112000	+	0.112000i	−0.0101400	+	0.0101400i
$123$	11.2068	−	4.07253i	1.01048	−	0.367208i
$124$		−	1.95478i		−	0.175544i
$125$	−8.98239	+	6.65708i	−0.803409	+	0.595427i
$126$	−0.267833	+	0.224278i	−0.0238604	+	0.0199802i
$127$	4.38475	+	4.38475i	0.389084	+	0.389084i	0.874361	−	0.485277i	$-0.161281\pi$
$127$	4.38475	+	4.38475i	0.389084	+	0.389084i	−0.485277	+	0.874361i	$0.661281\pi$
$128$	4.54349	+	4.54349i	0.401592	+	0.401592i
$129$	−9.59070	−	4.47812i	−0.844414	−	0.394276i
$130$	−1.76111	−	0.566075i	−0.154460	−	0.0496480i
$131$		−	12.5892i		−	1.09993i	−0.835189	−	0.549963i	$-0.814642\pi$
$131$		−	12.5892i		−	1.09993i	0.835189	−	0.549963i	$-0.185358\pi$
$132$	−6.87078	−	18.9070i	−0.598024	−	1.64564i
$133$	0.471311	−	0.471311i	0.0408678	−	0.0408678i
$134$	−1.65920			−0.143333
$135$	−8.62177	+	7.78878i	−0.742044	+	0.670351i
$136$	−4.92382			−0.422214
$137$	7.88928	−	7.88928i	0.674027	−	0.674027i	−0.284615	−	0.958642i	$-0.591866\pi$
$137$	7.88928	−	7.88928i	0.674027	−	0.674027i	0.958642	+	0.284615i	$0.0918657\pi$
$138$	−1.11592	−	3.07079i	−0.0949935	−	0.261403i
$139$			17.9929i			1.52614i	0.646316	+	0.763070i	$0.276309\pi$
$139$			17.9929i			1.52614i	−0.646316	+	0.763070i	$0.723691\pi$
$140$	−1.09335	−	2.12916i	−0.0924048	−	0.179947i
$141$	8.73904	+	4.08046i	0.735960	+	0.343636i
$142$	0.739510	+	0.739510i	0.0620583	+	0.0620583i
$143$	−16.3442	−	16.3442i	−1.36677	−	1.36677i
$144$	8.58094	−	7.18550i	0.715079	−	0.598792i
$145$	−1.94085	+	6.03816i	−0.161179	+	0.501442i
$146$			2.86215i			0.236873i
$147$	10.9071	−	3.96364i	0.899607	−	0.326915i
$148$	−6.77395	+	6.77395i	−0.556816	+	0.556816i
$149$	−4.60051			−0.376888			−0.188444	−	0.982084i	$-0.560344\pi$
$149$	−4.60051			−0.376888			−0.188444	+	0.982084i	$0.560344\pi$
$150$	0.902195	+	1.60552i	0.0736639	+	0.131090i
$151$	6.31707			0.514076			0.257038	−	0.966401i	$-0.417253\pi$
$151$	6.31707			0.514076			0.257038	+	0.966401i	$0.417253\pi$
$152$	0.723864	−	0.723864i	0.0587131	−	0.0587131i
$153$	−1.54849	+	17.4957i	−0.125188	+	1.41445i
$154$			0.691863i			0.0557519i
$155$	−0.684260	+	2.12880i	−0.0549611	+	0.170989i
$156$	5.57256	−	11.9347i	0.446162	−	0.955537i
$157$	−7.07817	−	7.07817i	−0.564899	−	0.564899i	0.365796	−	0.930695i	$-0.380797\pi$
$157$	−7.07817	−	7.07817i	−0.564899	−	0.564899i	−0.930695	+	0.365796i	$0.880797\pi$
$158$	−0.499174	−	0.499174i	−0.0397122	−	0.0397122i
$159$	−4.67760	+	10.0179i	−0.370958	+	0.794473i
$160$	−2.52843	−	4.92381i	−0.199890	−	0.389261i
$161$		−	4.85732i		−	0.382810i
$162$	1.09459	+	1.56998i	0.0859992	+	0.123349i
$163$	−6.57855	+	6.57855i	−0.515272	+	0.515272i	−0.916137	−	0.400865i	$-0.868710\pi$
$163$	−6.57855	+	6.57855i	−0.515272	+	0.515272i	0.400865	+	0.916137i	$0.368710\pi$
$164$	13.4572			1.05083
$165$	0.864132	+	22.9953i	0.0672726	+	1.79018i
$166$	1.24023			0.0962603
$167$	−0.410469	+	0.410469i	−0.0317630	+	0.0317630i	−0.722810	−	0.691047i	$-0.757150\pi$
$167$	−0.410469	+	0.410469i	−0.0317630	+	0.0317630i	0.691047	+	0.722810i	$0.257150\pi$
$168$	−0.749668	+	0.272428i	−0.0578381	+	0.0210183i
$169$		−	2.13410i		−	0.164161i
$170$	2.65042	+	0.851924i	0.203278	+	0.0653396i
$171$	−2.34445	−	2.79975i	−0.179285	−	0.214102i
$172$	−8.44693	−	8.44693i	−0.644072	−	0.644072i
$173$	−15.4838	−	15.4838i	−1.17721	−	1.17721i	−0.980453	−	0.196756i	$-0.936959\pi$
$173$	−15.4838	−	15.4838i	−1.17721	−	1.17721i	−0.196756	−	0.980453i	$-0.563041\pi$
$174$	0.946625	+	0.442001i	0.0717635	+	0.0335080i
$175$	0.445381	+	2.70142i	0.0336676	+	0.204209i
$176$		−	22.1662i		−	1.67084i
$177$	2.75516	+	7.58165i	0.207090	+	0.569872i
$178$	−0.583302	+	0.583302i	−0.0437203	+	0.0437203i
$179$	12.8633			0.961447			0.480723	−	0.876872i	$-0.340374\pi$
$179$	12.8633			0.961447			0.480723	+	0.876872i	$0.340374\pi$
$180$	−12.1476	+	4.93835i	−0.905430	+	0.368083i
$181$	1.90600			0.141672			0.0708359	−	0.997488i	$-0.477433\pi$
$181$	1.90600			0.141672			0.0708359	+	0.997488i	$0.477433\pi$
$182$	−0.320320	+	0.320320i	−0.0237437	+	0.0237437i
$183$	0.440622	+	1.21251i	0.0325717	+	0.0896310i
$184$		−	7.46013i		−	0.549968i
$185$	9.74818	−	5.00581i	0.716701	−	0.368034i
$186$	0.333740	+	0.155831i	0.0244710	+	0.0114261i
$187$	24.5974	+	24.5974i	1.79874	+	1.79874i
$188$	7.69683	+	7.69683i	0.561349	+	0.561349i
$189$	0.732252	+	2.74946i	0.0532635	+	0.199994i
$190$	−0.514889	+	0.264402i	−0.0373540	+	0.0191817i
$191$			22.1386i			1.60189i	0.598738	+	0.800945i	$0.295669\pi$
$191$			22.1386i			1.60189i	−0.598738	+	0.800945i	$0.704331\pi$
$192$	11.2895	−	4.10259i	0.814750	−	0.296079i
$193$	11.1630	−	11.1630i	0.803532	−	0.803532i	−0.180114	−	0.983646i	$-0.557647\pi$
$193$	11.1630	−	11.1630i	0.803532	−	0.803532i	0.983646	+	0.180114i	$0.0576466\pi$
$194$	−1.60201			−0.115017
$195$	−10.2463	+	11.0465i	−0.733754	+	0.791054i
$196$	13.0973			0.935523
$197$	−3.08689	+	3.08689i	−0.219932	+	0.219932i	−0.808470	−	0.588538i	$-0.799704\pi$
$197$	−3.08689	+	3.08689i	−0.219932	+	0.219932i	0.588538	+	0.808470i	$0.299704\pi$
$198$	3.77572	+	0.334178i	0.268329	+	0.0237490i
$199$		−	26.9148i		−	1.90794i	−0.299907	−	0.953968i	$-0.596956\pi$
$199$		−	26.9148i		−	1.90794i	0.299907	−	0.953968i	$-0.403044\pi$
$200$	0.684039	+	4.14899i	0.0483689	+	0.293378i
$201$	−5.71747	+	12.2450i	−0.403279	+	0.863695i
$202$	0.461337	+	0.461337i	0.0324595	+	0.0324595i
$203$	1.09825	+	1.09825i	0.0770821	+	0.0770821i
$204$	−8.38653	+	17.9613i	−0.587174	+	1.25754i
$205$	−14.6552	−	4.71061i	−1.02356	−	0.329003i
$206$			1.83402i			0.127782i
$207$	−26.5080	−	2.34614i	−1.84243	−	0.163068i
$208$	10.2625	−	10.2625i	0.711580	−	0.711580i
$209$	−7.23228			−0.500267
$210$	0.450671	−	0.0169356i	0.0310993	−	0.00116867i
$211$	−16.3188			−1.12344			−0.561718	−	0.827329i	$-0.689859\pi$
$211$	−16.3188			−1.12344			−0.561718	+	0.827329i	$0.689859\pi$
$212$	−8.82320	+	8.82320i	−0.605980	+	0.605980i
$213$	8.00592	−	2.90934i	0.548557	−	0.199345i
$214$			2.09116i			0.142949i
$215$	6.24210	+	12.1557i	0.425708	+	0.829012i
$216$	1.12463	+	4.22277i	0.0765215	+	0.287323i
$217$	0.387197	+	0.387197i	0.0262846	+	0.0262846i
$218$	−2.70799	−	2.70799i	−0.183408	−	0.183408i
$219$	21.1228	+	9.86274i	1.42735	+	0.666462i
$220$	−7.94727	+	24.7247i	−0.535805	+	1.66694i
$221$			22.7763i			1.53210i
$222$	−0.616514	−	1.69652i	−0.0413777	−	0.113863i
$223$	−2.38293	+	2.38293i	−0.159573	+	0.159573i	−0.782377	−	0.622805i	$-0.785993\pi$
$223$	−2.38293	+	2.38293i	−0.159573	+	0.159573i	0.622805	+	0.782377i	$0.285993\pi$
$224$	−1.35545			−0.0905649
$225$	14.9577	−	1.12577i	0.997180	−	0.0750514i
$226$	−1.58279			−0.105286
$227$	5.53741	−	5.53741i	0.367531	−	0.367531i	−0.499045	−	0.866576i	$-0.666316\pi$
$227$	5.53741	−	5.53741i	0.367531	−	0.367531i	0.866576	+	0.499045i	$0.166316\pi$
$228$	−1.40761	−	3.87346i	−0.0932212	−	0.256526i
$229$			16.0544i			1.06090i	0.847715	+	0.530452i	$0.177978\pi$
$229$			16.0544i			1.06090i	−0.847715	+	0.530452i	$0.822022\pi$
$230$	−1.29076	+	4.01568i	−0.0851102	+	0.264786i
$231$	5.10599	+	2.38410i	0.335949	+	0.156862i
$232$	1.68675	+	1.68675i	0.110741	+	0.110741i
$233$	−3.58715	−	3.58715i	−0.235002	−	0.235002i	0.579775	−	0.814777i	$-0.303141\pi$
$233$	−3.58715	−	3.58715i	−0.235002	−	0.235002i	−0.814777	+	0.579775i	$0.803141\pi$
$234$	1.59337	+	1.90281i	0.104162	+	0.124391i
$235$	−5.68780	−	11.0763i	−0.371031	−	0.722536i
$236$			9.10406i			0.592624i
$237$	−5.40405	+	1.96382i	−0.351031	+	0.127564i
$238$	0.482071	−	0.482071i	0.0312480	−	0.0312480i
$239$	−12.0021			−0.776352			−0.388176	−	0.921585i	$-0.626895\pi$
$239$	−12.0021			−0.776352			−0.388176	+	0.921585i	$0.626895\pi$
$240$	−14.4388	+	0.542591i	−0.932021	+	0.0350241i
$241$	−14.8788			−0.958430			−0.479215	−	0.877698i	$-0.659079\pi$
$241$	−14.8788			−0.958430			−0.479215	+	0.877698i	$0.659079\pi$
$242$	3.65426	−	3.65426i	0.234905	−	0.234905i
$243$	15.3584	−	2.66812i	0.985243	−	0.171160i
$244$			1.45598i			0.0932095i
$245$	−14.2633	−	4.58465i	−0.911248	−	0.292903i
$246$	−1.07278	+	2.29754i	−0.0683977	+	0.146486i
$247$	−3.34841	−	3.34841i	−0.213054	−	0.213054i
$248$	0.594677	+	0.594677i	0.0377620	+	0.0377620i
$249$	4.27372	−	9.15295i	0.270836	−	0.580045i
$250$	0.349655	−	2.35170i	0.0221141	−	0.148734i
$251$		−	25.4696i		−	1.60763i	−0.594882	−	0.803813i	$-0.702801\pi$
$251$		−	25.4696i		−	1.60763i	0.594882	−	0.803813i	$-0.297199\pi$
$252$	−0.283105	+	3.19868i	−0.0178340	+	0.201498i
$253$	−37.2679	+	37.2679i	−2.34301	+	2.34301i
$254$	−1.31866			−0.0827404
$255$	15.4204	−	16.6246i	0.965662	−	1.04107i
$256$	12.5037			0.781479
$257$	10.4714	−	10.4714i	0.653188	−	0.653188i	−0.300572	−	0.953759i	$-0.597177\pi$
$257$	10.4714	−	10.4714i	0.653188	−	0.653188i	0.953759	+	0.300572i	$0.0971774\pi$
$258$	2.11552	−	0.768775i	0.131706	−	0.0478619i
$259$		−	2.68353i		−	0.166746i
$260$	−15.1265	+	7.76766i	−0.938108	+	0.481730i
$261$	6.52399	−	5.46305i	0.403825	−	0.338154i
$262$	1.89303	+	1.89303i	0.116952	+	0.116952i
$263$	3.06882	+	3.06882i	0.189232	+	0.189232i	0.795364	−	0.606132i	$-0.207280\pi$
$263$	3.06882	+	3.06882i	0.189232	+	0.189232i	−0.606132	+	0.795364i	$0.707280\pi$
$264$	7.84205	+	3.66163i	0.482645	+	0.225358i
$265$	12.6972	−	6.52016i	0.779983	−	0.400530i
$266$			0.141741i			0.00869072i
$267$	2.29479	+	6.31481i	0.140439	+	0.386460i
$268$	−10.7847	+	10.7847i	−0.658779	+	0.658779i
$269$	−25.2332			−1.53850			−0.769248	−	0.638950i	$-0.779369\pi$
$269$	−25.2332			−1.53850			−0.769248	+	0.638950i	$0.779369\pi$
$270$	0.125256	−	2.46764i	0.00762283	−	0.150176i
$271$	−12.5505			−0.762388			−0.381194	−	0.924495i	$-0.624487\pi$
$271$	−12.5505			−0.762388			−0.381194	+	0.924495i	$0.624487\pi$
$272$	−15.4448	+	15.4448i	−0.936479	+	0.936479i
$273$	1.26018	+	3.46778i	0.0762698	+	0.209879i
$274$			2.37261i			0.143335i
$275$	17.3095	−	24.1439i	1.04380	−	1.45593i
$276$	−27.2133	−	12.7065i	−1.63805	−	0.764843i
$277$	−8.03940	−	8.03940i	−0.483041	−	0.483041i	0.423061	−	0.906101i	$-0.360956\pi$
$277$	−8.03940	−	8.03940i	−0.483041	−	0.483041i	−0.906101	+	0.423061i	$0.860956\pi$
$278$	−2.70558	−	2.70558i	−0.162270	−	0.162270i
$279$	2.30008	−	1.92604i	0.137702	−	0.115309i
$280$	0.980342	+	0.315111i	0.0585866	+	0.0188315i
$281$			25.6247i			1.52864i	0.644835	+	0.764322i	$0.276926\pi$
$281$			25.6247i			1.52864i	−0.644835	+	0.764322i	$0.723074\pi$
$282$	−1.92766	+	0.700507i	−0.114790	+	0.0417146i
$283$	5.80564	−	5.80564i	0.345109	−	0.345109i	−0.513175	−	0.858284i	$-0.671531\pi$
$283$	5.80564	−	5.80564i	0.345109	−	0.345109i	0.858284	+	0.513175i	$0.171531\pi$
$284$	9.61353			0.570458
$285$	0.177034	+	4.71102i	0.0104866	+	0.279057i
$286$	4.91532			0.290649
$287$	−2.66555	+	2.66555i	−0.157343	+	0.157343i
$288$	−0.654698	+	7.39714i	−0.0385785	+	0.435881i
$289$		−	17.2777i		−	1.01633i
$290$	−0.616111	−	1.19980i	−0.0361793	−	0.0704546i
$291$	−5.52038	+	11.8229i	−0.323611	+	0.693071i
$292$	18.6038	+	18.6038i	1.08870	+	1.08870i
$293$	−3.49594	−	3.49594i	−0.204235	−	0.204235i	0.597577	−	0.801812i	$-0.296130\pi$
$293$	−3.49594	−	3.49594i	−0.204235	−	0.204235i	−0.801812	+	0.597577i	$0.796130\pi$
$294$	−1.04409	+	2.23611i	−0.0608926	+	0.130413i
$295$	3.18683	−	9.91454i	0.185544	−	0.577247i
$296$		−	4.12151i		−	0.239558i
$297$	15.4771	−	26.7135i	0.898072	−	1.55008i
$298$	0.691775	−	0.691775i	0.0400734	−	0.0400734i
$299$	−34.5087			−1.99569
$300$	16.2999	+	4.57154i	0.941077	+	0.263938i
$301$	3.34628			0.192877
$302$	−0.949893	+	0.949893i	−0.0546602	+	0.0546602i
$303$	4.99442	−	1.81496i	0.286922	−	0.104267i
$304$		−	4.54117i		−	0.260454i
$305$	0.509658	−	1.58560i	0.0291829	−	0.0907909i
$306$	−2.39798	−	2.86367i	−0.137083	−	0.163705i
$307$	−21.3502	−	21.3502i	−1.21852	−	1.21852i	−0.968150	−	0.250370i	$-0.919448\pi$
$307$	−21.3502	−	21.3502i	−1.21852	−	1.21852i	−0.250370	−	0.968150i	$-0.580552\pi$
$308$	4.49706	+	4.49706i	0.256244	+	0.256244i
$309$	13.5351	+	6.31987i	0.769987	+	0.359525i
$310$	−0.217214	−	0.422998i	−0.0123369	−	0.0240247i
$311$			14.4807i			0.821128i	0.911832	+	0.410564i	$0.134668\pi$
$311$			14.4807i			0.821128i	−0.911832	+	0.410564i	$0.865332\pi$
$312$	1.93546	+	5.32599i	0.109574	+	0.301525i
$313$	−15.6700	+	15.6700i	−0.885720	+	0.885720i	−0.994109	−	0.108389i	$-0.965431\pi$
$313$	−15.6700	+	15.6700i	−0.885720	+	0.885720i	0.108389	+	0.994109i	$0.465431\pi$
$314$	2.12868			0.120128
$315$	1.42799	−	3.38434i	0.0804581	−	0.190686i
$316$	−6.48919			−0.365046
$317$	−1.91432	+	1.91432i	−0.107519	+	0.107519i	−0.758820	−	0.651301i	$-0.774224\pi$
$317$	−1.91432	+	1.91432i	−0.107519	+	0.107519i	0.651301	+	0.758820i	$0.274224\pi$
$318$	−0.803021	−	2.20976i	−0.0450312	−	0.123917i
$319$		−	16.8527i		−	0.943570i
$320$	−14.7633	−	4.74537i	−0.825293	−	0.265274i
$321$	15.4329	+	7.20597i	0.861380	+	0.402198i
$322$	0.730392	+	0.730392i	0.0407031	+	0.0407031i
$323$	5.03926	+	5.03926i	0.280392	+	0.280392i
$324$	17.3195	+	3.09000i	0.962195	+	0.171667i
$325$	19.1922	−	3.16419i	1.06459	−	0.175518i
$326$		−	1.97842i		−	0.109575i
$327$	−29.3167	+	10.6536i	−1.62122	+	0.589147i
$328$	−4.09390	+	4.09390i	−0.226048	+	0.226048i
$329$	−3.04913			−0.168104
$330$	−3.58772	−	3.32784i	−0.197497	−	0.183192i
$331$	−19.9462			−1.09634			−0.548170	−	0.836367i	$-0.684675\pi$
$331$	−19.9462			−1.09634			−0.548170	+	0.836367i	$0.684675\pi$
$332$	8.06139	−	8.06139i	0.442426	−	0.442426i
$333$	−14.6449	−	1.29618i	−0.802536	−	0.0710300i
$334$		−	0.123444i		−	0.00675454i
$335$	15.5199	−	7.96965i	0.847942	−	0.435428i
$336$	−1.49699	+	3.20607i	−0.0816673	+	0.174905i
$337$	−3.51648	−	3.51648i	−0.191555	−	0.191555i	0.604813	−	0.796368i	$-0.293248\pi$
$337$	−3.51648	−	3.51648i	−0.191555	−	0.191555i	−0.796368	+	0.604813i	$0.793248\pi$
$338$	0.320903	+	0.320903i	0.0174548	+	0.0174548i
$339$	−5.45418	+	11.6811i	−0.296230	+	0.634431i
$340$	22.7650	−	11.6901i	1.23460	−	0.633984i
$341$		−	5.94154i		−	0.321753i
$342$	0.773529	+	0.0684627i	0.0418277	+	0.00370204i
$343$	−5.30465	+	5.30465i	−0.286424	+	0.286424i
$344$	5.13940			0.277098
$345$	25.1881	+	23.3636i	1.35608	+	1.25785i
$346$	4.65656			0.250338
$347$	−5.30489	+	5.30489i	−0.284781	+	0.284781i	−0.835012	−	0.550231i	$-0.814540\pi$
$347$	−5.30489	+	5.30489i	−0.284781	+	0.284781i	0.550231	+	0.835012i	$0.314540\pi$
$348$	9.02597	−	3.28002i	0.483843	−	0.175828i
$349$			18.3193i			0.980610i	0.871551	+	0.490305i	$0.163115\pi$
$349$			18.3193i			0.980610i	−0.871551	+	0.490305i	$0.836885\pi$
$350$	−0.473183	−	0.339240i	−0.0252927	−	0.0181331i
$351$	19.5335	−	5.20226i	1.04262	−	0.277676i
$352$	10.3997	+	10.3997i	0.554307	+	0.554307i
$353$	22.8752	+	22.8752i	1.21752	+	1.21752i	0.968497	+	0.249024i	$0.0801099\pi$
$353$	22.8752	+	22.8752i	1.21752	+	1.21752i	0.249024	+	0.968497i	$0.419890\pi$
$354$	−1.55434	−	0.725756i	−0.0826122	−	0.0385735i
$355$	−10.4694	−	3.36517i	−0.555656	−	0.178604i
$356$			7.58284i			0.401889i
$357$	−1.89654	−	5.21889i	−0.100375	−	0.276213i
$358$	−1.93424	+	1.93424i	−0.102228	+	0.102228i
$359$	15.1609			0.800161			0.400080	−	0.916480i	$-0.368982\pi$
$359$	15.1609			0.800161			0.400080	+	0.916480i	$0.368982\pi$
$360$	2.19318	−	5.19785i	0.115591	−	0.273951i
$361$	17.5183			0.922017
$362$	−0.286603	+	0.286603i	−0.0150635	+	0.0150635i
$363$	−14.3764	−	39.5610i	−0.754565	−	2.07641i
$364$			4.16411i			0.218259i
$365$	−13.7478	−	26.7721i	−0.719592	−	1.40132i
$366$	−0.248580	−	0.116068i	−0.0129935	−	0.00606695i
$367$	1.01193	+	1.01193i	0.0528225	+	0.0528225i	0.733025	−	0.680202i	$-0.238108\pi$
$367$	1.01193	+	1.01193i	0.0528225	+	0.0528225i	−0.680202	+	0.733025i	$0.738108\pi$
$368$	−23.4006	−	23.4006i	−1.21984	−	1.21984i
$369$	13.2593	+	15.8343i	0.690252	+	0.824301i
$370$	−0.713108	+	2.21855i	−0.0370727	+	0.115337i
$371$		−	3.49535i		−	0.181469i
$372$	3.18217	−	1.15640i	0.164988	−	0.0599563i
$373$	15.2384	−	15.2384i	0.789015	−	0.789015i	−0.192317	−	0.981333i	$-0.561600\pi$
$373$	15.2384	−	15.2384i	0.789015	−	0.789015i	0.981333	+	0.192317i	$0.0616003\pi$
$374$	−7.39740			−0.382510
$375$	−16.1508	−	10.6842i	−0.834022	−	0.551731i
$376$	−4.68302			−0.241508
$377$	7.80249	−	7.80249i	0.401849	−	0.401849i
$378$	−0.523543	−	0.303327i	−0.0269282	−	0.0156014i
$379$		−	12.6527i		−	0.649926i	−0.945727	−	0.324963i	$-0.894648\pi$
$379$		−	12.6527i		−	0.649926i	0.945727	−	0.324963i	$-0.105352\pi$
$380$	−1.62815	+	5.06533i	−0.0835224	+	0.259846i
$381$	−4.54401	+	9.73182i	−0.232797	+	0.498576i
$382$	−3.32896	−	3.32896i	−0.170324	−	0.170324i
$383$	−15.8313	−	15.8313i	−0.808941	−	0.808941i	0.175533	−	0.984474i	$-0.443835\pi$
$383$	−15.8313	−	15.8313i	−0.808941	−	0.808941i	−0.984474	+	0.175533i	$0.943835\pi$
$384$	−4.70852	+	10.0841i	−0.240280	+	0.514604i
$385$	−3.32323	−	6.47157i	−0.169367	−	0.329822i
$386$			3.35715i			0.170874i
$387$	1.61629	−	18.2618i	0.0821608	−	0.928299i
$388$	−10.4129	+	10.4129i	−0.528636	+	0.528636i
$389$	15.1891			0.770119			0.385059	−	0.922892i	$-0.374181\pi$
$389$	15.1891			0.770119			0.385059	+	0.922892i	$0.374181\pi$
$390$	−0.120319	−	3.20178i	−0.00609258	−	0.162128i
$391$	51.9345			2.62644
$392$	−3.98443	+	3.98443i	−0.201244	+	0.201244i
$393$	20.4939	−	7.44745i	1.03378	−	0.375674i
$394$		−	0.928346i		−	0.0467694i
$395$	7.06689	+	2.27151i	0.355574	+	0.114292i
$396$	26.7141	−	22.3698i	1.34243	−	1.12412i
$397$	−0.341751	−	0.341751i	−0.0171520	−	0.0171520i	0.698479	−	0.715631i	$-0.253861\pi$
$397$	−0.341751	−	0.341751i	−0.0171520	−	0.0171520i	−0.715631	+	0.698479i	$0.753861\pi$
$398$	4.04715	+	4.04715i	0.202865	+	0.202865i
$399$	1.04606	+	0.488429i	0.0523685	+	0.0244520i
$400$	15.1600	+	10.8687i	0.758002	+	0.543436i
$401$		−	24.8749i		−	1.24219i	−0.783733	−	0.621097i	$-0.786687\pi$
$401$		−	24.8749i		−	1.24219i	0.783733	−	0.621097i	$-0.213313\pi$
$402$	−0.981539	−	2.70100i	−0.0489547	−	0.134714i
$403$	2.75083	−	2.75083i	0.137028	−	0.137028i
$404$	5.99731			0.298377
$405$	−17.7797	−	9.42769i	−0.883482	−	0.468466i
$406$	−0.330286			−0.0163918
$407$	−20.5894	+	20.5894i	−1.02058	+	1.02058i
$408$	−2.91280	−	8.01545i	−0.144205	−	0.396824i
$409$		−	35.0261i		−	1.73193i	−0.500107	−	0.865964i	$-0.666706\pi$
$409$		−	35.0261i		−	1.73193i	0.500107	−	0.865964i	$-0.333294\pi$
$410$	2.91202	−	1.49535i	0.143814	−	0.0738503i
$411$	17.5100	+	8.17583i	0.863706	+	0.403284i
$412$	11.9210	+	11.9210i	0.587304	+	0.587304i
$413$	−1.80331	−	1.80331i	−0.0887349	−	0.0887349i
$414$	4.33878	−	3.63320i	0.213239	−	0.178562i
$415$	−11.6009	+	5.95719i	−0.569465	+	0.292427i
$416$			9.62976i			0.472138i
$417$	−29.2906	+	10.6441i	−1.43437	+	0.521246i
$418$	1.08751	−	1.08751i	0.0531920	−	0.0531920i
$419$	11.3426			0.554122			0.277061	−	0.960852i	$-0.410640\pi$
$419$	11.3426			0.554122			0.277061	+	0.960852i	$0.410640\pi$
$420$	2.81925	−	3.03941i	0.137565	−	0.148308i
$421$	7.44294			0.362747			0.181373	−	0.983414i	$-0.441946\pi$
$421$	7.44294			0.362747			0.181373	+	0.983414i	$0.441946\pi$
$422$	2.45385	−	2.45385i	0.119452	−	0.119452i
$423$	−1.47277	+	16.6401i	−0.0716083	+	0.809070i
$424$		−	5.36834i		−	0.260710i
$425$	−28.8836	+	4.76201i	−1.40106	+	0.230992i
$426$	−0.766370	+	1.64132i	−0.0371307	+	0.0795222i
$427$	−0.288396	−	0.288396i	−0.0139565	−	0.0139565i
$428$	13.5924	+	13.5924i	0.657013	+	0.657013i
$429$	16.9378	−	36.2753i	0.817764	−	1.75139i
$430$	−2.76647	−	0.889225i	−0.133411	−	0.0428822i
$431$			22.7224i			1.09450i	0.836970	+	0.547249i	$0.184325\pi$
$431$			22.7224i			1.09450i	−0.836970	+	0.547249i	$0.815675\pi$
$432$	16.7735	+	9.71811i	0.807016	+	0.467563i
$433$	−5.15688	+	5.15688i	−0.247824	+	0.247824i	−0.820077	−	0.572253i	$-0.806069\pi$
$433$	−5.15688	+	5.15688i	−0.247824	+	0.247824i	0.572253	+	0.820077i	$0.306069\pi$
$434$	−0.116445			−0.00558954
$435$	−10.9776	+	0.412526i	−0.526338	+	0.0197791i
$436$	−35.2035			−1.68594
$437$	−7.63503	+	7.63503i	−0.365233	+	0.365233i
$438$	−4.65928	+	1.69317i	−0.222629	+	0.0809030i
$439$		−	14.9779i		−	0.714858i	−0.933940	−	0.357429i	$-0.883653\pi$
$439$		−	14.9779i		−	0.714858i	0.933940	−	0.357429i	$-0.116347\pi$
$440$	−5.10399	−	9.93938i	−0.243323	−	0.473841i
$441$	12.9048	+	15.4109i	0.614513	+	0.733852i
$442$	−3.42486	−	3.42486i	−0.162904	−	0.162904i
$443$	−13.6735	−	13.6735i	−0.649648	−	0.649648i	0.303260	−	0.952908i	$-0.401925\pi$
$443$	−13.6735	−	13.6735i	−0.649648	−	0.649648i	−0.952908	+	0.303260i	$0.901925\pi$
$444$	−15.0346	−	7.01999i	−0.713509	−	0.333154i
$445$	2.65433	−	8.25789i	0.125827	−	0.391461i
$446$		−	0.716638i		−	0.0339338i
$447$	−2.72154	−	7.48914i	−0.128724	−	0.354224i
$448$	−2.68522	+	2.68522i	−0.126865	+	0.126865i
$449$	1.47057			0.0694006			0.0347003	−	0.999398i	$-0.488952\pi$
$449$	1.47057			0.0694006			0.0347003	+	0.999398i	$0.488952\pi$
$450$	−2.07990	+	2.41846i	−0.0980472	+	0.114007i
$451$	40.9030			1.92605
$452$	−10.2880	+	10.2880i	−0.483909	+	0.483909i
$453$	3.73701	+	10.2835i	0.175580	+	0.483162i
$454$			1.66531i			0.0781569i
$455$	1.45763	−	4.53482i	0.0683346	−	0.212595i
$456$	1.60659	+	0.750155i	0.0752356	+	0.0351292i
$457$	12.9890	+	12.9890i	0.607602	+	0.607602i	0.942319	−	0.334717i	$-0.108641\pi$
$457$	12.9890	+	12.9890i	0.607602	+	0.607602i	−0.334717	+	0.942319i	$0.608641\pi$
$458$	−2.41408	−	2.41408i	−0.112803	−	0.112803i
$459$	−29.3973	+	7.82924i	−1.37215	+	0.365438i
$460$	17.7118	+	34.4915i	0.825816	+	1.60817i
$461$			16.5999i			0.773133i	0.922262	+	0.386567i	$0.126339\pi$
$461$			16.5999i			0.773133i	−0.922262	+	0.386567i	$0.873661\pi$
$462$	−1.12628	+	0.409288i	−0.0523993	+	0.0190418i
$463$	−2.21616	+	2.21616i	−0.102994	+	0.102994i	−0.756726	−	0.653732i	$-0.773202\pi$
$463$	−2.21616	+	2.21616i	−0.102994	+	0.102994i	0.653732	+	0.756726i	$0.273202\pi$
$464$	10.5819			0.491251
$465$	−3.87025	+	0.145439i	−0.179479	+	0.00674457i
$466$	1.07879			0.0499742
$467$	−6.70869	+	6.70869i	−0.310441	+	0.310441i	−0.845080	−	0.534639i	$-0.820447\pi$
$467$	−6.70869	+	6.70869i	−0.310441	+	0.310441i	0.534639	+	0.845080i	$0.320447\pi$
$468$	22.7249	+	2.01131i	1.05046	+	0.0929730i
$469$		−	4.27239i		−	0.197281i
$470$	2.52080	+	0.810261i	0.116276	+	0.0373745i
$471$	7.33525	−	15.7098i	0.337991	−	0.723868i
$472$	−2.76961	−	2.76961i	−0.127482	−	0.127482i
$473$	−25.6744	−	25.6744i	−1.18051	−	1.18051i
$474$	0.517305	−	1.10790i	0.0237606	−	0.0508876i
$475$	3.54619	−	4.94634i	0.162710	−	0.226954i
$476$		−	6.26686i		−	0.287241i
$477$	−19.0753	−	1.68829i	−0.873397	−	0.0773016i
$478$	1.80475	−	1.80475i	0.0825473	−	0.0825473i
$479$	−17.5332			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$479$	−17.5332			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$480$	6.51968	−	7.02882i	0.297582	−	0.320820i
$481$	−19.0651			−0.869292
$482$	2.23732	−	2.23732i	0.101907	−	0.101907i
$483$	7.90720	−	2.87346i	0.359790	−	0.130747i
$484$		−	47.5049i		−	2.15931i
$485$	14.9849	−	7.69493i	0.680430	−	0.349409i
$486$	−1.90823	+	2.71064i	−0.0865591	+	0.122957i
$487$	16.5622	+	16.5622i	0.750506	+	0.750506i	0.974574	−	0.224067i	$-0.0719336\pi$
$487$	16.5622	+	16.5622i	0.750506	+	0.750506i	−0.224067	+	0.974574i	$0.571934\pi$
$488$	−0.442934	−	0.442934i	−0.0200507	−	0.0200507i
$489$	−14.6009	−	6.81749i	−0.660275	−	0.308298i
$490$	2.83415	−	1.45537i	0.128034	−	0.0657469i
$491$		−	43.8967i		−	1.98103i	−0.137409	−	0.990514i	$-0.543877\pi$
$491$		−	43.8967i		−	1.98103i	0.137409	−	0.990514i	$-0.456123\pi$
$492$	7.96090	+	21.9068i	0.358905	+	0.987636i
$493$	−11.7425	+	11.7425i	−0.528856	+	0.528856i
$494$	1.00700			0.0453069
$495$	−36.9227	+	15.0101i	−1.65955	+	0.674655i
$496$	3.73071			0.167514
$497$	−1.90422	+	1.90422i	−0.0854159	+	0.0854159i
$498$	0.733686	+	2.01896i	0.0328773	+	0.0904717i
$499$			2.06424i			0.0924083i	0.998932	+	0.0462041i	$0.0147125\pi$
$499$			2.06424i			0.0924083i	−0.998932	+	0.0462041i	$0.985288\pi$
$500$	−13.0131	−	17.5586i	−0.581964	−	0.785243i
$501$	−0.911023	−	0.425377i	−0.0407015	−	0.0190045i
$502$	3.82984	+	3.82984i	0.170934	+	0.170934i
$503$	3.64758	+	3.64758i	0.162637	+	0.162637i	0.783734	−	0.621097i	$-0.213313\pi$
$503$	3.64758	+	3.64758i	0.162637	+	0.162637i	−0.621097	+	0.783734i	$0.713313\pi$
$504$	−0.886968	−	1.05922i	−0.0395087	−	0.0471814i
$505$	−6.53121	−	2.09933i	−0.290635	−	0.0934189i
$506$		−	11.2079i		−	0.498251i
$507$	3.47409	−	1.26248i	0.154290	−	0.0560686i
$508$	−8.57122	+	8.57122i	−0.380286	+	0.380286i
$509$	−2.71268			−0.120237			−0.0601187	−	0.998191i	$-0.519148\pi$
$509$	−2.71268			−0.120237			−0.0601187	+	0.998191i	$0.519148\pi$
$510$	0.181076	+	4.81858i	0.00801818	+	0.213370i
$511$	−7.36996			−0.326028
$512$	−10.9672	+	10.9672i	−0.484684	+	0.484684i
$513$	3.17078	−	5.47278i	0.139993	−	0.241629i
$514$			3.14915i			0.138903i
$515$	−8.80934	−	17.1551i	−0.388186	−	0.755943i
$516$	8.75373	−	18.7477i	0.385361	−	0.825321i
$517$	23.3945	+	23.3945i	1.02889	+	1.02889i
$518$	0.403520	+	0.403520i	0.0177297	+	0.0177297i
$519$	16.0461	−	34.3657i	0.704347	−	1.50849i
$520$	2.23870	−	6.96481i	0.0981735	−	0.305427i
$521$			2.76763i			0.121252i	0.998161	+	0.0606260i	$0.0193097\pi$
$521$			2.76763i			0.121252i	−0.998161	+	0.0606260i	$0.980690\pi$
$522$	−0.159532	+	1.80248i	−0.00698253	+	0.0788925i
$523$	19.8821	−	19.8821i	0.869385	−	0.869385i	−0.123019	−	0.992404i	$-0.539258\pi$
$523$	19.8821	−	19.8821i	0.869385	−	0.869385i	0.992404	+	0.123019i	$0.0392576\pi$
$524$	24.6091			1.07506
$525$	−4.13416	+	2.32313i	−0.180429	+	0.101390i
$526$	−0.922914			−0.0402410
$527$	−4.13991	+	4.13991i	−0.180337	+	0.180337i
$528$	36.0842	−	13.1129i	1.57036	−	0.570668i
$529$			55.6865i			2.42115i
$530$	−0.928836	+	2.88970i	−0.0403461	+	0.125521i
$531$	−10.7123	+	8.97022i	−0.464872	+	0.389274i
$532$	0.921308	+	0.921308i	0.0399438	+	0.0399438i
$533$	18.9373	+	18.9373i	0.820267	+	0.820267i
$534$	−1.29462	−	0.604487i	−0.0560237	−	0.0261587i
$535$	−10.0445	−	19.5604i	−0.434261	−	0.845669i
$536$		−	6.56177i		−	0.283425i
$537$	7.60958	+	20.9401i	0.328378	+	0.903630i
$538$	3.79430	−	3.79430i	0.163584	−	0.163584i
$539$	39.8093			1.71471
$540$	−15.2253	−	16.8536i	−0.655194	−	0.725265i
$541$	−21.0674			−0.905757			−0.452879	−	0.891572i	$-0.649603\pi$
$541$	−21.0674			−0.905757			−0.452879	+	0.891572i	$0.649603\pi$
$542$	1.88721	−	1.88721i	0.0810625	−	0.0810625i
$543$	1.12754	+	3.10276i	0.0483873	+	0.133152i
$544$		−	14.4925i		−	0.621360i
$545$	38.3375	+	12.3228i	1.64220	+	0.527851i
$546$	−0.710940	−	0.331954i	−0.0304254	−	0.0142063i
$547$	−7.80186	−	7.80186i	−0.333584	−	0.333584i	0.520362	−	0.853946i	$-0.325797\pi$
$547$	−7.80186	−	7.80186i	−0.333584	−	0.333584i	−0.853946	+	0.520362i	$0.825797\pi$
$548$	15.4218	+	15.4218i	0.658787	+	0.658787i
$549$	−1.71317	+	1.43457i	−0.0731163	+	0.0612261i
$550$	1.02768	+	6.23332i	0.0438205	+	0.265790i
$551$		−	3.45260i		−	0.147086i
$552$	12.1443	−	4.41322i	0.516896	−	0.187839i
$553$	1.28536	−	1.28536i	0.0546591	−	0.0546591i
$554$	2.41776			0.102721
$555$	13.9157	+	12.9077i	0.590688	+	0.547902i
$556$	−35.1722			−1.49163
$557$	−2.73515	+	2.73515i	−0.115892	+	0.115892i	−0.762675	−	0.646782i	$-0.776114\pi$
$557$	−2.73515	+	2.73515i	−0.115892	+	0.115892i	0.646782	+	0.762675i	$0.276114\pi$
$558$	−0.0562442	+	0.635479i	−0.00238101	+	0.0269020i
$559$		−	23.7736i		−	1.00552i
$560$	4.06352	−	2.08667i	0.171715	−	0.0881777i
$561$	−25.4908	+	54.5932i	−1.07622	+	2.30493i
$562$	−3.85317	−	3.85317i	−0.162536	−	0.162536i
$563$	18.9526	+	18.9526i	0.798756	+	0.798756i	0.982899	−	0.184144i	$-0.0589511\pi$
$563$	18.9526	+	18.9526i	0.798756	+	0.798756i	−0.184144	+	0.982899i	$0.558951\pi$
$564$	−7.97639	+	17.0829i	−0.335866	+	0.719319i
$565$	14.8052	−	7.60264i	0.622859	−	0.319846i
$566$			1.74598i			0.0733890i
$567$	−4.04266	+	2.81854i	−0.169776	+	0.118368i
$568$	−2.92460	+	2.92460i	−0.122713	+	0.122713i
$569$	10.1657			0.426168			0.213084	−	0.977034i	$-0.431649\pi$
$569$	10.1657			0.426168			0.213084	+	0.977034i	$0.431649\pi$
$570$	−0.735013	−	0.681772i	−0.0307863	−	0.0285563i
$571$	34.6026			1.44808			0.724038	−	0.689760i	$-0.242284\pi$
$571$	34.6026			1.44808			0.724038	+	0.689760i	$0.242284\pi$
$572$	31.9492	−	31.9492i	1.33586	−	1.33586i
$573$	−36.0392	+	13.0966i	−1.50556	+	0.547118i
$574$		−	0.801634i		−	0.0334596i
$575$	−7.21498	−	43.7619i	−0.300885	−	1.82500i
$576$	13.3572	+	15.9511i	0.556548	+	0.664631i
$577$	−2.15736	−	2.15736i	−0.0898119	−	0.0898119i	0.660773	−	0.750585i	$-0.270228\pi$
$577$	−2.15736	−	2.15736i	−0.0898119	−	0.0898119i	−0.750585	+	0.660773i	$0.770228\pi$
$578$	2.59803	+	2.59803i	0.108064	+	0.108064i
$579$	24.7760	+	11.5685i	1.02965	+	0.480769i
$580$	−11.8033	−	3.79393i	−0.490104	−	0.157534i
$581$			3.19355i			0.132491i
$582$	−0.947705	−	2.60790i	−0.0392836	−	0.108101i
$583$	−26.8181	+	26.8181i	−1.11069	+	1.11069i
$584$	−11.3192			−0.468391
$585$	−24.0439	−	10.1451i	−0.994095	−	0.419449i
$586$	1.05136			0.0434315
$587$	−14.1634	+	14.1634i	−0.584588	+	0.584588i	−0.936161	−	0.351573i	$-0.885647\pi$
$587$	−14.1634	+	14.1634i	−0.584588	+	0.584588i	0.351573	+	0.936161i	$0.385647\pi$
$588$	7.74803	+	21.3211i	0.319524	+	0.879266i
$589$		−	1.21724i		−	0.0501555i
$590$	1.01164	+	1.97004i	0.0416486	+	0.0811054i
$591$	−6.85125	−	3.19901i	−0.281823	−	0.131589i
$592$	−12.9282	−	12.9282i	−0.531344	−	0.531344i
$593$	−19.3823	−	19.3823i	−0.795937	−	0.795937i	0.186515	−	0.982452i	$-0.440281\pi$
$593$	−19.3823	−	19.3823i	−0.795937	−	0.795937i	−0.982452	+	0.186515i	$0.940281\pi$
$594$	1.68961	+	6.34417i	0.0693257	+	0.260304i
$595$	−2.19368	+	6.82475i	−0.0899322	+	0.279788i
$596$		−	8.99297i		−	0.368366i
$597$	43.8144	−	15.9221i	1.79320	−	0.651647i
$598$	5.18905	−	5.18905i	0.212196	−	0.212196i
$599$	−14.3410			−0.585959			−0.292979	−	0.956119i	$-0.594647\pi$
$599$	−14.3410			−0.585959			−0.292979	+	0.956119i	$0.594647\pi$
$600$	−6.34946	+	3.56798i	−0.259216	+	0.145662i
$601$	−34.6467			−1.41327			−0.706634	−	0.707579i	$-0.749787\pi$
$601$	−34.6467			−1.41327			−0.706634	+	0.707579i	$0.749787\pi$
$602$	−0.503178	+	0.503178i	−0.0205080	+	0.0205080i
$603$	−23.3159	−	2.06361i	−0.949495	−	0.0840369i
$604$			12.3485i			0.502452i
$605$	−16.6288	+	51.7340i	−0.676059	+	2.10328i
$606$	−0.478093	+	1.02392i	−0.0194212	+	0.0415940i
$607$	11.0616	+	11.0616i	0.448977	+	0.448977i	0.895014	−	0.446037i	$-0.147165\pi$
$607$	11.0616	+	11.0616i	0.448977	+	0.448977i	−0.446037	+	0.895014i	$0.647165\pi$
$608$	2.13058	+	2.13058i	0.0864065	+	0.0864065i
$609$	−1.13814	+	2.43753i	−0.0461198	+	0.0987739i
$610$	0.161788	+	0.315062i	0.00655060	+	0.0127565i
$611$			21.6625i			0.876369i
$612$	−34.2003	−	3.02696i	−1.38247	−	0.122358i
$613$	27.2713	−	27.2713i	1.10148	−	1.10148i	0.107245	−	0.994233i	$-0.465797\pi$
$613$	27.2713	−	27.2713i	1.10148	−	1.10148i	0.994233	−	0.107245i	$-0.0342029\pi$
$614$	6.42083			0.259124
$615$	−1.00124	−	26.6437i	−0.0403738	−	1.07438i
$616$	−2.73616			−0.110243
$617$	−4.99456	+	4.99456i	−0.201073	+	0.201073i	−0.800460	−	0.599387i	$-0.795411\pi$
$617$	−4.99456	+	4.99456i	−0.201073	+	0.201073i	0.599387	+	0.800460i	$0.295411\pi$
$618$	−2.98558	+	1.08496i	−0.120098	+	0.0436433i
$619$		−	5.68333i		−	0.228432i	−0.993456	−	0.114216i	$-0.963564\pi$
$619$		−	5.68333i		−	0.228432i	0.993456	−	0.114216i	$-0.0364357\pi$
$620$	−4.16133	−	1.33758i	−0.167123	−	0.0537184i
$621$	−11.8622	−	44.5401i	−0.476013	−	1.78733i
$622$	−2.17746	−	2.17746i	−0.0873082	−	0.0873082i
$623$	−1.50199	−	1.50199i	−0.0601758	−	0.0601758i
$624$	22.7774	+	10.6353i	0.911826	+	0.425752i
$625$	8.02530	+	23.6769i	0.321012	+	0.947075i
$626$		−	4.71257i		−	0.188352i
$627$	−4.27843	−	11.7734i	−0.170864	−	0.470184i
$628$	13.8363	−	13.8363i	0.552127	−	0.552127i
$629$	28.6923			1.14404
$630$	0.294175	+	0.723626i	0.0117202	+	0.0288300i
$631$	−3.36174			−0.133829			−0.0669144	−	0.997759i	$-0.521315\pi$
$631$	−3.36174			−0.133829			−0.0669144	+	0.997759i	$0.521315\pi$
$632$	1.97412	−	1.97412i	0.0785264	−	0.0785264i
$633$	−9.65380	−	26.5654i	−0.383704	−	1.05588i
$634$		−	0.575710i		−	0.0228644i
$635$	12.3346	−	6.33395i	0.489483	−	0.251355i
$636$	−19.5828	−	9.14367i	−0.776509	−	0.362570i
$637$	18.4310	+	18.4310i	0.730262	+	0.730262i
$638$	2.53413	+	2.53413i	0.100327	+	0.100327i
$639$	9.47219	+	11.3117i	0.374714	+	0.447484i
$640$	12.7811	−	6.56326i	0.505218	−	0.259435i
$641$			15.8897i			0.627606i	0.949488	+	0.313803i	$0.101603\pi$
$641$			15.8897i			0.627606i	−0.949488	+	0.313803i	$0.898397\pi$
$642$	−3.40419	+	1.23708i	−0.134353	+	0.0488235i
$643$	−18.6741	+	18.6741i	−0.736436	+	0.736436i	−0.971886	−	0.235450i	$-0.924344\pi$
$643$	−18.6741	+	18.6741i	−0.736436	+	0.736436i	0.235450	+	0.971886i	$0.424344\pi$
$644$	9.49498			0.374155
$645$	−16.0955	+	17.3525i	−0.633762	+	0.683253i
$646$	−1.51550			−0.0596265
$647$	7.58920	−	7.58920i	0.298362	−	0.298362i	−0.542010	−	0.840372i	$-0.682336\pi$
$647$	7.58920	−	7.58920i	0.298362	−	0.298362i	0.840372	+	0.542010i	$0.182336\pi$
$648$	−6.20893	+	4.32886i	−0.243910	+	0.170054i
$649$			27.6718i			1.08621i
$650$	−2.41012	+	3.36171i	−0.0945326	+	0.131857i
$651$	−0.401260	+	0.859371i	−0.0157266	+	0.0336814i
$652$	−12.8596	−	12.8596i	−0.503621	−	0.503621i
$653$	−26.7830	−	26.7830i	−1.04810	−	1.04810i	−0.998783	−	0.0493152i	$-0.984296\pi$
$653$	−26.7830	−	26.7830i	−1.04810	−	1.04810i	−0.0493152	−	0.998783i	$-0.515704\pi$
$654$	2.80635	−	6.01031i	0.109737	−	0.235022i
$655$	−26.7999	−	8.61430i	−1.04716	−	0.336589i
$656$			25.6831i			1.00276i
$657$	−3.55977	+	40.2203i	−0.138880	+	1.56914i
$658$	0.458496	−	0.458496i	0.0178740	−	0.0178740i
$659$	18.9035			0.736377			0.368189	−	0.929751i	$-0.379978\pi$
$659$	18.9035			0.736377			0.368189	+	0.929751i	$0.379978\pi$
$660$	−44.9506	+	1.68919i	−1.74970	+	0.0657515i
$661$	−7.52825			−0.292815			−0.146408	−	0.989224i	$-0.546771\pi$
$661$	−7.52825			−0.292815			−0.146408	+	0.989224i	$0.546771\pi$
$662$	2.99929	−	2.99929i	0.116571	−	0.116571i
$663$	−37.0775	+	13.4739i	−1.43997	+	0.523283i
$664$			4.90482i			0.190344i
$665$	−0.680827	−	1.32583i	−0.0264013	−	0.0514133i
$666$	2.39705	−	2.00724i	0.0928838	−	0.0777789i
$667$	−17.7912	−	17.7912i	−0.688878	−	0.688878i
$668$	−0.802376	−	0.802376i	−0.0310448	−	0.0310448i
$669$	−5.28883	−	2.46948i	−0.204478	−	0.0954754i
$670$	−1.13532	+	3.53210i	−0.0438614	+	0.136457i
$671$			4.42544i			0.170842i
$672$	−0.801849	−	2.20653i	−0.0309320	−	0.0851188i
$673$	27.1168	−	27.1168i	1.04527	−	1.04527i	0.0463492	−	0.998925i	$-0.485241\pi$
$673$	27.1168	−	27.1168i	1.04527	−	1.04527i	0.998925	−	0.0463492i	$-0.0147587\pi$
$674$	1.05754			0.0407349
$675$	10.6812	+	23.6836i	0.411120	+	0.911581i
$676$	4.17169			0.160450
$677$	−11.0573	+	11.0573i	−0.424965	+	0.424965i	−0.886909	−	0.461944i	$-0.847152\pi$
$677$	−11.0573	+	11.0573i	−0.424965	+	0.424965i	0.461944	+	0.886909i	$0.347152\pi$
$678$	−0.936340	−	2.57662i	−0.0359599	−	0.0989545i
$679$		−	4.12512i		−	0.158308i
$680$	−3.36917	+	10.4818i	−0.129202	+	0.401959i
$681$	12.2901	+	5.73853i	0.470958	+	0.219901i
$682$	0.893425	+	0.893425i	0.0342110	+	0.0342110i
$683$	5.35568	+	5.35568i	0.204930	+	0.204930i	0.802108	−	0.597179i	$-0.203712\pi$
$683$	5.35568	+	5.35568i	0.204930	+	0.204930i	−0.597179	+	0.802108i	$0.703712\pi$
$684$	5.47289	−	4.58288i	0.209261	−	0.175231i
$685$	−11.3964	−	22.1930i	−0.435433	−	0.847952i
$686$		−	1.59531i		−	0.0609094i
$687$	−26.1348	+	9.49735i	−0.997106	+	0.362347i
$688$	16.1210	−	16.1210i	0.614609	−	0.614609i
$689$	−24.8326			−0.946047
$690$	−7.30068	+	0.274350i	−0.277932	+	0.0104443i
$691$	−45.9628			−1.74851			−0.874254	−	0.485469i	$-0.838649\pi$
$691$	−45.9628			−1.74851			−0.874254	+	0.485469i	$0.838649\pi$
$692$	30.2673	−	30.2673i	1.15059	−	1.15059i
$693$	−0.860498	+	9.72238i	−0.0326876	+	0.369323i
$694$		−	1.59538i		−	0.0605599i
$695$	38.3033	+	12.3118i	1.45293	+	0.467015i
$696$	−1.74802	+	3.74369i	−0.0662584	+	0.141904i
$697$	−28.5001	−	28.5001i	−1.07952	−	1.07952i
$698$	−2.75466	−	2.75466i	−0.104265	−	0.104265i
$699$	3.71744	−	7.96157i	0.140606	−	0.301134i
$700$	−5.28069	+	0.870621i	−0.199591	+	0.0329064i
$701$			16.2166i			0.612492i	0.951952	+	0.306246i	$0.0990730\pi$
$701$			16.2166i			0.612492i	−0.951952	+	0.306246i	$0.900927\pi$
$702$	−2.15498	+	3.71950i	−0.0813343	+	0.140383i
$703$	−4.21814	+	4.21814i	−0.159090	+	0.159090i
$704$	41.2048			1.55296
$705$	14.6662	−	15.8116i	0.552363	−	0.595498i
$706$	−6.87944			−0.258911
$707$	−1.18793	+	1.18793i	−0.0446767	+	0.0446767i
$708$	−14.8205	+	5.38573i	−0.556987	+	0.202408i
$709$			10.3445i			0.388495i	0.980953	+	0.194248i	$0.0622266\pi$
$709$			10.3445i			0.388495i	−0.980953	+	0.194248i	$0.937773\pi$
$710$	2.08029	−	1.06825i	0.0780718	−	0.0400908i
$711$	−6.39379	−	7.63548i	−0.239786	−	0.286353i
$712$	−2.30683	−	2.30683i	−0.0864521	−	0.0864521i
$713$	−6.27242	−	6.27242i	−0.234904	−	0.234904i
$714$	1.06994	+	0.499580i	0.0400416	+	0.0186963i
$715$	−45.9771	+	23.6098i	−1.71945	+	0.882956i
$716$			25.1449i			0.939708i
$717$	−7.10014	−	19.5382i	−0.265160	−	0.729667i
$718$	−2.27973	+	2.27973i	−0.0850788	+	0.0850788i
$719$	47.9026			1.78647			0.893233	−	0.449595i	$-0.148432\pi$
$719$	47.9026			1.78647			0.893233	+	0.449595i	$0.148432\pi$
$720$	−9.42490	−	23.1839i	−0.351245	−	0.864012i
$721$	−4.72254			−0.175877
$722$	−2.63422	+	2.63422i	−0.0980355	+	0.0980355i
$723$	−8.80193	−	24.2212i	−0.327347	−	0.900795i
$724$			3.72580i			0.138468i
$725$	11.5260	+	8.26335i	0.428065	+	0.306893i
$726$	8.11052	+	3.78699i	0.301010	+	0.140548i
$727$	19.1390	+	19.1390i	0.709826	+	0.709826i	0.966498	−	0.256672i	$-0.0826261\pi$
$727$	19.1390	+	19.1390i	0.709826	+	0.709826i	−0.256672	+	0.966498i	$0.582626\pi$
$728$	−1.26679	−	1.26679i	−0.0469505	−	0.0469505i
$729$	13.4291	+	23.4235i	0.497373	+	0.867537i
$730$	6.09295	+	1.95846i	0.225510	+	0.0724857i
$731$			35.7785i			1.32332i
$732$	−2.37018	+	0.861319i	−0.0876044	+	0.0318353i
$733$	−16.4809	+	16.4809i	−0.608734	+	0.608734i	−0.942615	−	0.333881i	$-0.891642\pi$
$733$	−16.4809	+	16.4809i	−0.608734	+	0.608734i	0.333881	+	0.942615i	$0.391642\pi$
$734$	−0.304327			−0.0112329
$735$	−0.974464	−	25.9313i	−0.0359437	−	0.956490i
$736$	21.9577			0.809372
$737$	−32.7800	+	32.7800i	−1.20747	+	1.20747i
$738$	−4.37478	−	0.387199i	−0.161038	−	0.0142530i
$739$		−	10.1260i		−	0.372491i	−0.982503	−	0.186245i	$-0.940368\pi$
$739$		−	10.1260i		−	0.372491i	0.982503	−	0.186245i	$-0.0596319\pi$
$740$	9.78524	+	19.0555i	0.359713	+	0.700495i
$741$	3.47003	−	7.43170i	0.127475	−	0.273010i
$742$	0.525593	+	0.525593i	0.0192951	+	0.0192951i
$743$	−25.7772	−	25.7772i	−0.945673	−	0.945673i	0.0529252	−	0.998598i	$-0.483146\pi$
$743$	−25.7772	−	25.7772i	−0.945673	−	0.945673i	−0.998598	+	0.0529252i	$0.983146\pi$
$744$	−0.616276	+	1.31987i	−0.0225938	+	0.0483887i
$745$	−3.14794	+	9.79356i	−0.115332	+	0.358808i
$746$			4.58278i			0.167787i
$747$	17.4283	+	1.54252i	0.637667	+	0.0564379i
$748$	−48.0825	+	48.0825i	−1.75807	+	1.75807i
$749$	−5.38468			−0.196752
$750$	4.03516	−	0.822001i	0.147343	−	0.0300152i
$751$	49.0297			1.78912			0.894560	−	0.446948i	$-0.147489\pi$
$751$	49.0297			1.78912			0.894560	+	0.446948i	$0.147489\pi$
$752$	−14.6895	+	14.6895i	−0.535670	+	0.535670i
$753$	41.4618	−	15.0672i	1.51095	−	0.549077i
$754$			2.34651i			0.0854549i
$755$	4.32252	−	13.4478i	0.157313	−	0.489415i
$756$	−5.37459	+	1.43139i	−0.195472	+	0.0520592i
$757$	−17.5977	−	17.5977i	−0.639599	−	0.639599i	0.310858	−	0.950456i	$-0.399384\pi$
$757$	−17.5977	−	17.5977i	−0.639599	−	0.639599i	−0.950456	+	0.310858i	$0.899384\pi$
$758$	1.90258	+	1.90258i	0.0691047	+	0.0691047i
$759$	−82.7148	−	38.6214i	−3.00236	−	1.40187i
$760$	−1.04565	−	2.03627i	−0.0379297	−	0.0738634i
$761$		−	12.2728i		−	0.444890i	−0.974945	−	0.222445i	$-0.928596\pi$
$761$		−	12.2728i		−	0.444890i	0.974945	−	0.222445i	$-0.0714038\pi$
$762$	−0.780087	−	2.14665i	−0.0282596	−	0.0777648i
$763$	6.97301	−	6.97301i	0.252440	−	0.252440i
$764$	−43.2760			−1.56567
$765$	36.1854	+	15.2681i	1.30828	+	0.552019i
$766$	4.76108			0.172025
$767$	−12.8115	+	12.8115i	−0.462598	+	0.462598i
$768$	7.39684	+	20.3546i	0.266911	+	0.734485i
$769$			34.1804i			1.23258i	0.787520	+	0.616289i	$0.211365\pi$
$769$			34.1804i			1.23258i	−0.787520	+	0.616289i	$0.788635\pi$
$770$	1.47284	+	0.473414i	0.0530774	+	0.0170607i
$771$	23.2409	+	10.8517i	0.837002	+	0.390815i
$772$	21.8212	+	21.8212i	0.785363	+	0.785363i
$773$	28.9943	+	28.9943i	1.04285	+	1.04285i	0.999040	+	0.0438138i	$0.0139508\pi$
$773$	28.9943	+	28.9943i	1.04285	+	1.04285i	0.0438138	+	0.999040i	$0.486049\pi$
$774$	2.50297	+	2.98905i	0.0899674	+	0.107439i
$775$	4.06358	+	2.91331i	0.145968	+	0.104649i
$776$		−	6.33558i		−	0.227434i
$777$	4.36850	−	1.58751i	0.156719	−	0.0569515i
$778$	−2.28398	+	2.28398i	−0.0818845	+	0.0818845i
$779$	8.37976			0.300236
$780$	−21.5934	−	20.0293i	−0.773168	−	0.717163i
$781$	29.2203			1.04558
$782$	−7.80935	+	7.80935i	−0.279262	+	0.279262i
$783$	12.7527	+	7.38857i	0.455744	+	0.264046i
$784$			24.9964i			0.892728i
$785$	−19.9113	+	10.2247i	−0.710665	+	0.364935i
$786$	−1.96179	+	4.20152i	−0.0699747	+	0.149863i
$787$	28.9823	+	28.9823i	1.03311	+	1.03311i	0.999433	+	0.0336749i	$0.0107211\pi$
$787$	28.9823	+	28.9823i	1.03311	+	1.03311i	0.0336749	+	0.999433i	$0.489279\pi$
$788$	−6.03418	−	6.03418i	−0.214959	−	0.214959i
$789$	−3.18029	+	6.81116i	−0.113221	+	0.242484i
$790$	−1.40421	+	0.721077i	−0.0499595	+	0.0256548i
$791$		−	4.07565i		−	0.144913i
$792$	−1.32160	+	14.9321i	−0.0469609	+	0.530591i
$793$	−2.04890	+	2.04890i	−0.0727586	+	0.0727586i
$794$	0.102778			0.00364744
$795$	18.1255	+	16.8125i	0.642844	+	0.596279i
$796$	52.6124			1.86480
$797$	38.6866	−	38.6866i	1.37035	−	1.37035i	0.510428	−	0.859921i	$-0.329487\pi$
$797$	38.6866	−	38.6866i	1.37035	−	1.37035i	0.859921	−	0.510428i	$-0.170513\pi$
$798$	−0.230740	+	0.0838505i	−0.00816810	+	0.00296827i
$799$		−	32.6013i		−	1.15335i
$800$	−12.2119	+	2.01336i	−0.431756	+	0.0711831i
$801$	−8.92231	+	7.47136i	−0.315254	+	0.263987i
$802$	3.74043	+	3.74043i	0.132079	+	0.132079i
$803$	56.5461	+	56.5461i	1.99547	+	1.99547i
$804$	−23.9362	−	11.1764i	−0.844166	−	0.394161i
$805$	−10.3403	−	3.32367i	−0.364446	−	0.117144i
$806$			0.827280i			0.0291397i
$807$	−14.9273	−	41.0770i	−0.525466	−	1.44598i
$808$	−1.82448	+	1.82448i	−0.0641851	+	0.0641851i
$809$	28.5690			1.00443			0.502216	−	0.864742i	$-0.332518\pi$
$809$	28.5690			1.00443			0.502216	+	0.864742i	$0.332518\pi$
$810$	4.09116	−	1.25589i	0.143749	−	0.0441275i
$811$	−16.6652			−0.585196			−0.292598	−	0.956236i	$-0.594520\pi$
$811$	−16.6652			−0.585196			−0.292598	+	0.956236i	$0.594520\pi$
$812$	−2.14684	+	2.14684i	−0.0753392	+	0.0753392i
$813$	−7.42454	−	20.4309i	−0.260390	−	0.716542i
$814$		−	6.19203i		−	0.217031i
$815$	9.50298	+	18.5059i	0.332875	+	0.648232i
$816$	−34.2793	−	16.0058i	−1.20001	−	0.560314i
$817$	−5.25990	−	5.25990i	−0.184020	−	0.184020i
$818$	5.26684	+	5.26684i	0.184151	+	0.184151i
$819$	−4.89968	+	4.10289i	−0.171209	+	0.143367i
$820$	9.20819	−	28.6476i	0.321564	−	1.00042i
$821$		−	4.02639i		−	0.140522i	−0.997529	−	0.0702609i	$-0.977617\pi$
$821$		−	4.02639i		−	0.140522i	0.997529	−	0.0702609i	$-0.0223832\pi$
$822$	−3.86236	+	1.40358i	−0.134715	+	0.0489553i
$823$	−16.6083	+	16.6083i	−0.578928	+	0.578928i	−0.934608	−	0.355680i	$-0.884249\pi$
$823$	−16.6083	+	16.6083i	−0.578928	+	0.578928i	0.355680	+	0.934608i	$0.384249\pi$
$824$	−7.25312			−0.252675
$825$	49.5436	+	13.8952i	1.72489	+	0.483768i
$826$	0.542323			0.0188698
$827$	32.5604	−	32.5604i	1.13224	−	1.13224i	0.142433	−	0.989804i	$-0.454507\pi$
$827$	32.5604	−	32.5604i	1.13224	−	1.13224i	0.989804	−	0.142433i	$-0.0454926\pi$
$828$	4.58618	−	51.8173i	0.159381	−	1.80077i
$829$			39.3477i			1.36660i	0.730137	+	0.683301i	$0.239456\pi$
$829$			39.3477i			1.36660i	−0.730137	+	0.683301i	$0.760544\pi$
$830$	0.848638	−	2.64020i	0.0294567	−	0.0916425i
$831$	8.33140	−	17.8432i	0.289013	−	0.618974i
$832$	19.0771	+	19.0771i	0.661379	+	0.661379i
$833$	−27.7380	−	27.7380i	−0.961066	−	0.961066i
$834$	2.80385	−	6.00496i	0.0970894	−	0.207935i
$835$	0.592939	+	1.15467i	0.0205195	+	0.0399591i
$836$		−	14.1375i		−	0.488956i
$837$	4.49606	+	2.60489i	0.155406	+	0.0900383i
$838$	−1.70558	+	1.70558i	−0.0589182	+	0.0589182i
$839$	23.7421			0.819667			0.409834	−	0.912160i	$-0.365587\pi$
$839$	23.7421			0.819667			0.409834	+	0.912160i	$0.365587\pi$
$840$	0.0669767	+	1.78230i	0.00231092	+	0.0614954i
$841$	−20.9547			−0.722577
$842$	−1.11919	+	1.11919i	−0.0385698	+	0.0385698i
$843$	−41.7144	+	15.1589i	−1.43672	+	0.522101i
$844$		−	31.8997i		−	1.09803i
$845$	−4.54307	−	1.46028i	−0.156286	−	0.0502351i
$846$	−2.28070	−	2.72362i	−0.0784122	−	0.0936400i
$847$	9.40963	+	9.40963i	0.323319	+	0.323319i
$848$	−16.8392	−	16.8392i	−0.578260	−	0.578260i
$849$	12.8854	+	6.01650i	0.442227	+	0.206486i
$850$	3.62715	−	5.05927i	0.124410	−	0.173532i
$851$			43.4720i			1.49020i
$852$	5.68711	+	15.6498i	0.194837	+	0.536153i
$853$	31.5646	−	31.5646i	1.08075	−	1.08075i	0.0843126	−	0.996439i	$-0.473131\pi$
$853$	31.5646	−	31.5646i	1.08075	−	1.08075i	0.996439	−	0.0843126i	$-0.0268694\pi$
$854$	0.0867318			0.00296790
$855$	−7.56432	+	3.07511i	−0.258694	+	0.105167i
$856$	−8.27008			−0.282665
$857$	35.6222	−	35.6222i	1.21683	−	1.21683i	0.248098	−	0.968735i	$-0.420195\pi$
$857$	35.6222	−	35.6222i	1.21683	−	1.21683i	0.968735	−	0.248098i	$-0.0798054\pi$
$858$	2.90777	+	8.00162i	0.0992698	+	0.273171i
$859$			32.8366i			1.12037i	0.828368	+	0.560184i	$0.189270\pi$
$859$			32.8366i			1.12037i	−0.828368	+	0.560184i	$0.810730\pi$
$860$	−23.7617	+	12.2019i	−0.810268	+	0.416082i
$861$	−5.91611	−	2.76237i	−0.201620	−	0.0941412i
$862$	−3.41674	−	3.41674i	−0.116375	−	0.116375i
$863$	−7.37506	−	7.37506i	−0.251050	−	0.251050i	0.570351	−	0.821401i	$-0.306807\pi$
$863$	−7.37506	−	7.37506i	−0.251050	−	0.251050i	−0.821401	+	0.570351i	$0.806807\pi$
$864$	−12.4291	+	3.31018i	−0.422846	+	0.112615i
$865$	−43.5567	+	22.3669i	−1.48097	+	0.760497i
$866$		−	1.55087i		−	0.0527008i
$867$	28.1262	−	10.2210i	0.955217	−	0.347124i
$868$	−0.756883	+	0.756883i	−0.0256903	+	0.0256903i
$869$	−19.7239			−0.669087
$870$	1.58867	−	1.71273i	0.0538609	−	0.0580671i
$871$	−30.3531			−1.02848
$872$	10.7095	−	10.7095i	0.362670	−	0.362670i
$873$	−22.5122	−	1.99248i	−0.761921	−	0.0674352i
$874$		−	2.29615i		−	0.0776684i
$875$	6.05555	+	0.900351i	0.204715	+	0.0304374i
$876$	−19.2795	+	41.2905i	−0.651393	+	1.39508i
$877$	12.7700	+	12.7700i	0.431213	+	0.431213i	0.889041	−	0.457828i	$-0.151373\pi$
$877$	12.7700	+	12.7700i	0.431213	+	0.431213i	−0.457828	+	0.889041i	$0.651373\pi$
$878$	2.25222	+	2.25222i	0.0760088	+	0.0760088i
$879$	3.62292	−	7.75913i	0.122198	−	0.261709i
$880$	−47.1874	−	15.1674i	−1.59069	−	0.511295i
$881$			0.0959314i			0.00323201i	0.999999	+	0.00161601i	$0.000514391\pi$
$881$			0.0959314i			0.00323201i	−0.999999	+	0.00161601i	$0.999486\pi$
$882$	−4.25781	−	0.376845i	−0.143368	−	0.0126890i
$883$	2.39245	−	2.39245i	0.0805123	−	0.0805123i	−0.665704	−	0.746216i	$-0.731869\pi$
$883$	2.39245	−	2.39245i	0.0805123	−	0.0805123i	0.746216	+	0.665704i	$0.231869\pi$
$884$	−44.5227			−1.49746
$885$	18.0251	−	0.677359i	0.605906	−	0.0227692i
$886$	4.11215			0.138150
$887$	−10.2230	+	10.2230i	−0.343256	+	0.343256i	−0.857590	−	0.514334i	$-0.828039\pi$
$887$	−10.2230	+	10.2230i	−0.343256	+	0.343256i	0.514334	+	0.857590i	$0.328039\pi$
$888$	6.70938	−	2.43818i	0.225152	−	0.0818198i
$889$		−	3.39552i		−	0.113882i
$890$	0.842602	+	1.64086i	0.0282441	+	0.0550018i
$891$	52.6426	+	9.39204i	1.76359	+	0.314645i
$892$	−4.65809	−	4.65809i	−0.155964	−	0.155964i
$893$	4.79281	+	4.79281i	0.160385	+	0.160385i
$894$	1.53537	+	0.716901i	0.0513505	+	0.0239767i
$895$	8.80183	−	27.3833i	0.294213	−	0.915324i
$896$		−	3.51845i		−	0.117543i
$897$	−20.4144	−	56.1765i	−0.681618	−	1.87568i
$898$	−0.221129	+	0.221129i	−0.00737917	+	0.00737917i
$899$	2.83642			0.0945998
$900$	2.20063	+	29.2390i	0.0733544	+	0.974633i
$901$	37.3723			1.24505
$902$	−6.15055	+	6.15055i	−0.204791	+	0.204791i
$903$	1.97957	+	5.44740i	0.0658761	+	0.181278i
$904$		−	6.25960i		−	0.208191i
$905$	1.30420	−	4.05749i	0.0433530	−	0.134875i
$906$	−2.10826	−	0.984394i	−0.0700422	−	0.0327043i
$907$	33.6412	+	33.6412i	1.11704	+	1.11704i	0.992174	+	0.124865i	$0.0398499\pi$
$907$	33.6412	+	33.6412i	1.11704	+	1.11704i	0.124865	+	0.992174i	$0.460150\pi$
$908$	10.8244	+	10.8244i	0.359220	+	0.359220i
$909$	5.90914	+	7.05671i	0.195994	+	0.234056i
$910$	0.462715	+	0.901079i	0.0153388	+	0.0298705i
$911$		−	19.7839i		−	0.655470i	−0.944770	−	0.327735i	$-0.893715\pi$
$911$		−	19.7839i		−	0.655470i	0.944770	−	0.327735i	$-0.106285\pi$
$912$	7.39255	−	2.68644i	0.244792	−	0.0889569i
$913$	24.5026	−	24.5026i	0.810916	−	0.810916i
$914$	−3.90631			−0.129209
$915$	2.88268	−	0.108327i	0.0952985	−	0.00358120i
$916$	−31.3827			−1.03692
$917$	−4.87450	+	4.87450i	−0.160970	+	0.160970i
$918$	3.24317	−	5.59773i	0.107041	−	0.184752i
$919$			6.29613i			0.207690i	0.994593	+	0.103845i	$0.0331146\pi$
$919$			6.29613i			0.207690i	−0.994593	+	0.103845i	$0.966885\pi$
$920$	−15.8811	−	5.10467i	−0.523585	−	0.168296i
$921$	22.1257	−	47.3861i	0.729065	−	1.56142i
$922$	−2.49611	−	2.49611i	−0.0822050	−	0.0822050i
$923$	13.5285	+	13.5285i	0.445295	+	0.445295i
$924$	−4.66039	+	9.98107i	−0.153316	+	0.328353i
$925$	−3.98607	−	24.1772i	−0.131061	−	0.794942i
$926$		−	0.666486i		−	0.0219021i
$927$	−2.28104	+	25.7725i	−0.0749192	+	0.846479i
$928$	−4.96469	+	4.96469i	−0.162974	+	0.162974i
$929$	−28.8485			−0.946487			−0.473244	−	0.880932i	$-0.656917\pi$
$929$	−28.8485			−0.946487			−0.473244	+	0.880932i	$0.656917\pi$
$930$	0.560097	−	0.603836i	0.0183663	−	0.0198006i
$931$	8.15569			0.267292
$932$	7.01209	−	7.01209i	0.229689	−	0.229689i
$933$	−23.5731	+	8.56643i	−0.771750	+	0.280452i
$934$		−	2.01756i		−	0.0660166i
$935$	69.1941	−	35.5320i	2.26289	−	1.16202i
$936$	−7.52519	+	6.30144i	−0.245969	+	0.205969i
$937$	−9.12232	−	9.12232i	−0.298013	−	0.298013i	0.542222	−	0.840235i	$-0.317583\pi$
$937$	−9.12232	−	9.12232i	−0.298013	−	0.298013i	−0.840235	+	0.542222i	$0.817583\pi$
$938$	0.642437	+	0.642437i	0.0209763	+	0.0209763i
$939$	−34.7790	−	16.2391i	−1.13497	−	0.529944i
$940$	21.6517	−	11.1184i	0.706199	−	0.362642i
$941$			6.71081i			0.218766i	0.994000	+	0.109383i	$0.0348875\pi$
$941$			6.71081i			0.218766i	−0.994000	+	0.109383i	$0.965112\pi$
$942$	1.25927	+	3.46526i	0.0410293	+	0.112904i
$943$	43.1808	−	43.1808i	1.40616	−	1.40616i
$944$	−17.3752			−0.565514
$945$	6.35411	+	0.322531i	0.206699	+	0.0104919i
$946$	7.72129			0.251041
$947$	−2.03973	+	2.03973i	−0.0662825	+	0.0662825i	−0.739471	−	0.673188i	$-0.764924\pi$
$947$	−2.03973	+	2.03973i	−0.0662825	+	0.0662825i	0.673188	+	0.739471i	$0.264924\pi$
$948$	−3.83884	−	10.5637i	−0.124680	−	0.343094i
$949$			52.3596i			1.69967i
$950$	0.210540	+	1.27702i	0.00683082	+	0.0414319i
$951$	−4.24877	−	1.98385i	−0.137776	−	0.0643307i
$952$	1.90649	+	1.90649i	0.0617895	+	0.0617895i
$953$	−5.00183	−	5.00183i	−0.162025	−	0.162025i	0.621438	−	0.783463i	$-0.286549\pi$
$953$	−5.00183	−	5.00183i	−0.162025	−	0.162025i	−0.783463	+	0.621438i	$0.786549\pi$
$954$	3.12220	−	2.61447i	0.101085	−	0.0846465i
$955$	47.1286	+	15.1485i	1.52504	+	0.490195i
$956$		−	23.4615i		−	0.758798i
$957$	27.4344	−	9.96962i	0.886829	−	0.322272i
$958$	2.63645	−	2.63645i	0.0851800	−	0.0851800i
$959$	−6.10941			−0.197283
$960$	−1.00862	−	26.8403i	−0.0325532	−	0.866268i
$961$	1.00000			0.0322581
$962$	2.86680	−	2.86680i	0.0924293	−	0.0924293i
$963$	−2.60086	+	29.3860i	−0.0838116	+	0.946950i
$964$		−	29.0848i		−	0.936759i
$965$	−16.1254	−	31.4023i	−0.519096	−	1.01087i
$966$	−0.756920	+	1.62108i	−0.0243535	+	0.0521574i
$967$	−33.2417	−	33.2417i	−1.06898	−	1.06898i	−0.997437	−	0.0715442i	$-0.977207\pi$
$967$	−33.2417	−	33.2417i	−1.06898	−	1.06898i	−0.0715442	−	0.997437i	$-0.522793\pi$
$968$	14.4518	+	14.4518i	0.464499	+	0.464499i
$969$	−5.22229	+	11.1845i	−0.167764	+	0.359297i
$970$	−1.09619	+	3.41035i	−0.0351965	+	0.109500i
$971$		−	10.7794i		−	0.345926i	−0.984928	−	0.172963i	$-0.944666\pi$
$971$		−	10.7794i		−	0.345926i	0.984928	−	0.172963i	$-0.0553342\pi$
$972$	5.21558	+	30.0223i	0.167290	+	0.962966i
$973$	6.96680	−	6.96680i	0.223345	−	0.223345i
$974$	−4.98090			−0.159598
$975$	16.5046	+	29.3710i	0.528569	+	0.940625i
$976$	−2.77875			−0.0889456
$977$	28.5232	−	28.5232i	0.912536	−	0.912536i	−0.0839348	−	0.996471i	$-0.526749\pi$
$977$	28.5232	−	28.5232i	0.912536	−	0.912536i	0.996471	+	0.0839348i	$0.0267487\pi$
$978$	3.22067	−	1.17038i	0.102986	−	0.0374248i
$979$			23.0480i			0.736618i
$980$	8.96198	−	27.8816i	0.286280	−	0.890644i
$981$	−34.6860	−	41.4221i	−1.10744	−	1.32250i
$982$	6.60071	+	6.60071i	0.210637	+	0.210637i
$983$	−6.03258	−	6.03258i	−0.192409	−	0.192409i	0.604327	−	0.796736i	$-0.293442\pi$
$983$	−6.03258	−	6.03258i	−0.192409	−	0.192409i	−0.796736	+	0.604327i	$0.793442\pi$
$984$	−9.08627	−	4.24259i	−0.289660	−	0.135249i
$985$	4.45913	+	8.68360i	0.142080	+	0.276683i
$986$		−	3.53142i		−	0.112463i
$987$	−1.80379	−	4.96366i	−0.0574152	−	0.157995i
$988$	6.54541	−	6.54541i	0.208237	−	0.208237i
$989$	−54.2084			−1.72373
$990$	3.29497	−	7.80909i	0.104721	−	0.248189i
$991$	−41.5159			−1.31880			−0.659399	−	0.751793i	$-0.729189\pi$
$991$	−41.5159			−1.31880			−0.659399	+	0.751793i	$0.729189\pi$
$992$	−1.75034	+	1.75034i	−0.0555733	+	0.0555733i
$993$	−11.7996	−	32.4702i	−0.374450	−	1.03041i
$994$		−	0.572672i		−	0.0181640i
$995$	−57.2961	−	18.4167i	−1.81641	−	0.583849i
$996$	17.8920	+	8.35418i	0.566929	+	0.264712i
$997$	−22.6987	−	22.6987i	−0.718876	−	0.718876i	0.249499	−	0.968375i	$-0.419734\pi$
$997$	−22.6987	−	22.6987i	−0.718876	−	0.718876i	−0.968375	+	0.249499i	$0.919734\pi$
$998$	−0.310399	−	0.310399i	−0.00982550	−	0.00982550i
$999$	−6.55351	−	24.6071i	−0.207344	−	0.778536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.32.15	✓	60
3.2	odd	2	inner	465.2.k.b.32.16	yes	60
5.3	odd	4	inner	465.2.k.b.218.16	yes	60
15.8	even	4	inner	465.2.k.b.218.15	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.15	✓	60	1.1	even	1	trivial
465.2.k.b.32.16	yes	60	3.2	odd	2	inner
465.2.k.b.218.15	yes	60	15.8	even	4	inner
465.2.k.b.218.16	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)

\(f(q)\)	\(=\)	\(q+(-0.150369 + 0.150369i) q^{2} +(0.591574 + 1.62789i) q^{3} +1.95478i q^{4} +(0.684260 - 2.12880i) q^{5} +(-0.333740 - 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(-0.594677 - 0.594677i) q^{8} +(-2.30008 + 1.92604i) q^{9} +O(q^{10})\)	\(q+(-0.150369 + 0.150369i) q^{2} +(0.591574 + 1.62789i) q^{3} +1.95478i q^{4} +(0.684260 - 2.12880i) q^{5} +(-0.333740 - 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(-0.594677 - 0.594677i) q^{8} +(-2.30008 + 1.92604i) q^{9} +(0.217214 + 0.422998i) q^{10} +5.94154i q^{11} +(-3.18217 + 1.15640i) q^{12} +(-2.75083 + 2.75083i) q^{13} +0.116445 q^{14} +(3.87025 - 0.145439i) q^{15} -3.73071 q^{16} +(4.13991 - 4.13991i) q^{17} +(0.0562442 - 0.635479i) q^{18} +1.21724i q^{19} +(4.16133 + 1.33758i) q^{20} +(0.401260 - 0.859371i) q^{21} +(-0.893425 - 0.893425i) q^{22} +(6.27242 + 6.27242i) q^{23} +(0.616276 - 1.31987i) q^{24} +(-4.06358 - 2.91331i) q^{25} -0.827280i q^{26} +(-4.49606 - 2.60489i) q^{27} +(0.756883 - 0.756883i) q^{28} -2.83642 q^{29} +(-0.560097 + 0.603836i) q^{30} -1.00000 q^{31} +(1.75034 - 1.75034i) q^{32} +(-9.67221 + 3.51486i) q^{33} +1.24503i q^{34} +(-1.08921 + 0.559321i) q^{35} +(-3.76498 - 4.49615i) q^{36} +(3.46533 + 3.46533i) q^{37} +(-0.183035 - 0.183035i) q^{38} +(-6.10537 - 2.85074i) q^{39} +(-1.67286 + 0.859035i) q^{40} -6.88424i q^{41} +(0.0688858 + 0.189560i) q^{42} +(-4.32117 + 4.32117i) q^{43} -11.6144 q^{44} +(2.52630 + 6.21432i) q^{45} -1.88636 q^{46} +(3.93745 - 3.93745i) q^{47} +(-2.20699 - 6.07321i) q^{48} -6.70016i q^{49} +(1.04911 - 0.172965i) q^{50} +(9.18839 + 4.29027i) q^{51} +(-5.37726 - 5.37726i) q^{52} +(4.51366 + 4.51366i) q^{53} +(1.06776 - 0.284373i) q^{54} +(12.6484 + 4.06556i) q^{55} +0.460514i q^{56} +(-1.98154 + 0.720087i) q^{57} +(0.426510 - 0.426510i) q^{58} +4.65734 q^{59} +(0.284301 + 7.56548i) q^{60} +0.744831 q^{61} +(0.150369 - 0.150369i) q^{62} +(1.63634 + 0.144827i) q^{63} -6.93503i q^{64} +(3.97368 + 7.73824i) q^{65} +(0.925875 - 1.98293i) q^{66} +(5.51708 + 5.51708i) q^{67} +(8.09260 + 8.09260i) q^{68} +(-6.50024 + 13.9214i) q^{69} +(0.0796786 - 0.247888i) q^{70} -4.91796i q^{71} +(2.51318 + 0.222433i) q^{72} +(9.51707 - 9.51707i) q^{73} -1.04216 q^{74} +(2.33865 - 8.33851i) q^{75} -2.37943 q^{76} +(2.30055 - 2.30055i) q^{77} +(1.34672 - 0.489397i) q^{78} +3.31966i q^{79} +(-2.55278 + 7.94194i) q^{80} +(1.58074 - 8.86009i) q^{81} +(1.03518 + 1.03518i) q^{82} +(-4.12394 - 4.12394i) q^{83} +(1.67988 + 0.784374i) q^{84} +(-5.98026 - 11.6458i) q^{85} -1.29954i q^{86} +(-1.67795 - 4.61739i) q^{87} +(3.53330 - 3.53330i) q^{88} +3.87913 q^{89} +(-1.31432 - 0.554565i) q^{90} +2.13022 q^{91} +(-12.2612 + 12.2612i) q^{92} +(-0.591574 - 1.62789i) q^{93} +1.18414i q^{94} +(2.59126 + 0.832908i) q^{95} +(3.88482 + 1.81391i) q^{96} +(5.32691 + 5.32691i) q^{97} +(1.00750 + 1.00750i) q^{98} +(-11.4436 - 13.6660i) 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

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