LMFDB - Embedded newform 475.2.u.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.2
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	475.149
Dual form			475.2.u.a.424.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62760 - 1.93969i) q^{2} +(-0.223238 - 0.613341i) q^{3} +(-0.766044 - 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(1.32683 - 0.766044i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(1.97178 - 1.65452i) q^{9} +O(q^{10})$	\(q+(1.62760 - 1.93969i) q^{2} +(-0.223238 - 0.613341i) q^{3} +(-0.766044 - 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(1.32683 - 0.766044i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(1.97178 - 1.65452i) q^{9} +(0.592396 - 1.02606i) q^{11} +(-2.49362 + 1.43969i) q^{12} +(-0.929228 + 2.55303i) q^{13} +(0.673648 - 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.49362 + 2.97178i) q^{17} -6.51754i q^{18} +(-0.819078 + 4.28125i) q^{19} +(-0.766044 - 0.642788i) q^{21} +(-1.02606 - 2.81908i) q^{22} +(-4.98724 + 0.879385i) q^{23} +(-0.692066 + 3.92490i) q^{24} +(3.43969 + 5.95772i) q^{26} +(-3.15074 - 1.81908i) q^{27} +(-4.34445 - 5.17752i) q^{28} +(3.56418 - 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-1.57202 + 4.31908i) q^{32} +(-0.761570 - 0.134285i) q^{33} +(1.70574 + 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} -4.10607i q^{37} +(6.97118 + 8.55690i) q^{38} +1.77332 q^{39} +(9.38326 - 3.41523i) q^{41} +(-2.49362 + 0.439693i) q^{42} +(8.57013 + 1.51114i) q^{43} +(-4.91147 - 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(0.368946 + 0.439693i) q^{47} +(2.78504 + 3.31908i) q^{48} +(-2.32635 + 4.02936i) q^{49} +(2.37939 + 0.866025i) q^{51} +(11.8034 + 2.08125i) q^{52} +(2.89884 - 0.511144i) q^{53} +(-8.65657 + 3.15074i) q^{54} -9.35504 q^{56} +(2.80872 - 0.453363i) q^{57} -11.7811i q^{58} +(3.01501 + 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(9.56926 + 1.68732i) q^{62} +(1.34878 - 3.70574i) q^{63} +(-0.819078 - 1.41868i) q^{64} +(-1.50000 + 1.25865i) q^{66} +(-2.49860 - 2.97771i) q^{67} +(14.8210 + 8.55690i) q^{68} +(1.65270 + 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(-15.4781 + 2.72921i) q^{72} +(2.09602 + 5.75877i) q^{73} +(-7.96451 - 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} -1.81521i q^{77} +(2.88624 - 3.43969i) q^{78} +(9.21688 - 3.35467i) q^{79} +(0.928548 - 5.26606i) q^{81} +(8.64766 - 23.7592i) q^{82} +(-10.6679 + 6.15910i) q^{83} +(-2.20574 + 3.82045i) q^{84} +(16.8799 - 14.1639i) q^{86} +(-2.62998 - 1.51842i) q^{87} +(-6.26519 + 3.61721i) q^{88} +(-2.27972 - 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(7.64090 + 20.9932i) q^{92} +(1.61002 - 1.91875i) q^{93} +1.45336 q^{94} +3.00000 q^{96} +(-4.73708 + 5.64543i) q^{97} +(4.02936 + 11.0706i) q^{98} +(-0.529563 - 3.00330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 - 6 * q^9	$ 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.62760	−	1.93969i	1.15088	−	1.37157i	0.234087	−	0.972216i	$-0.424790\pi$
$2$	1.62760	−	1.93969i	1.15088	−	1.37157i	0.916797	−	0.399354i	$-0.130766\pi$
$3$	−0.223238	−	0.613341i	−0.128886	−	0.354112i	0.858418	−	0.512950i	$-0.171448\pi$
$3$	−0.223238	−	0.613341i	−0.128886	−	0.354112i	−0.987305	+	0.158838i	$0.949225\pi$
$4$	−0.766044	−	4.34445i	−0.383022	−	2.17223i
$5$		0			0
$5$		0			0
$6$	−1.55303	−	0.565258i	−0.634023	−	0.230766i
$7$	1.32683	−	0.766044i	0.501494	−	0.289538i	−0.227836	−	0.973699i	$-0.573165\pi$
$7$	1.32683	−	0.766044i	0.501494	−	0.289538i	0.729330	+	0.684162i	$0.239832\pi$
$8$	−5.28801	−	3.05303i	−1.86959	−	1.07941i
$9$	1.97178	−	1.65452i	0.657261	−	0.551507i
$10$		0			0
$11$	0.592396	−	1.02606i	0.178614	−	0.309369i	−0.762792	−	0.646644i	$-0.776172\pi$
$11$	0.592396	−	1.02606i	0.178614	−	0.309369i	0.941406	+	0.337275i	$0.109505\pi$
$12$	−2.49362	+	1.43969i	−0.719846	+	0.415603i
$13$	−0.929228	+	2.55303i	−0.257722	+	0.708084i	0.741585	+	0.670859i	$0.234074\pi$
$13$	−0.929228	+	2.55303i	−0.257722	+	0.708084i	−0.999307	+	0.0372256i	$0.988148\pi$
$14$	0.673648	−	3.82045i	0.180040	−	1.02106i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−2.49362	+	2.97178i	−0.604792	+	0.720763i	−0.978376	−	0.206833i	$-0.933684\pi$
$17$	−2.49362	+	2.97178i	−0.604792	+	0.720763i	0.373584	+	0.927596i	$0.378129\pi$
$18$		−	6.51754i		−	1.53620i
$19$	−0.819078	+	4.28125i	−0.187909	+	0.982186i
$19$	−0.819078	+	4.28125i	−0.187909	+	0.982186i
$20$		0			0
$21$	−0.766044	−	0.642788i	−0.167165	−	0.140268i
$22$	−1.02606	−	2.81908i	−0.218757	−	0.601029i
$23$	−4.98724	+	0.879385i	−1.03991	+	0.183364i	−0.667428	−	0.744674i	$-0.732605\pi$
$23$	−4.98724	+	0.879385i	−1.03991	+	0.183364i	−0.372484	+	0.928039i	$0.621494\pi$
$24$	−0.692066	+	3.92490i	−0.141267	+	0.801168i
$25$		0			0
$26$	3.43969	+	5.95772i	0.674579	+	1.16841i
$27$	−3.15074	−	1.81908i	−0.606359	−	0.350082i
$28$	−4.34445	−	5.17752i	−0.821025	−	0.978459i
$29$	3.56418	−	2.99070i	0.661851	−	0.555359i	−0.248790	−	0.968557i	$-0.580033\pi$
$29$	3.56418	−	2.99070i	0.661851	−	0.555359i	0.910641	+	0.413198i	$0.135588\pi$
$30$		0			0
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	0.985284	−	0.170924i	$-0.0546753\pi$
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	−0.640667	+	0.767819i	$0.721342\pi$
$32$	−1.57202	+	4.31908i	−0.277896	+	0.763512i
$33$	−0.761570	−	0.134285i	−0.132572	−	0.0233761i
$34$	1.70574	+	9.67372i	0.292531	+	1.65903i
$35$		0			0
$36$	−8.69846	−	7.29888i	−1.44974	−	1.21648i
$37$		−	4.10607i		−	0.675033i	−0.941320	−	0.337517i	$-0.890413\pi$
$37$		−	4.10607i		−	0.675033i	0.941320	−	0.337517i	$-0.109587\pi$
$38$	6.97118	+	8.55690i	1.13088	+	1.38811i
$39$	1.77332			0.283958
$40$		0			0
$41$	9.38326	−	3.41523i	1.46542	−	0.533369i	0.518566	−	0.855038i	$-0.326466\pi$
$41$	9.38326	−	3.41523i	1.46542	−	0.533369i	0.946852	+	0.321669i	$0.104244\pi$
$42$	−2.49362	+	0.439693i	−0.384774	+	0.0678460i
$43$	8.57013	+	1.51114i	1.30693	+	0.230447i	0.783378	−	0.621545i	$-0.213495\pi$
$43$	8.57013	+	1.51114i	1.30693	+	0.230447i	0.523554	+	0.851993i	$0.324606\pi$
$44$	−4.91147	−	1.78763i	−0.740433	−	0.269495i
$45$		0			0
$46$	−6.41147	+	11.1050i	−0.945320	+	1.63734i
$47$	0.368946	+	0.439693i	0.0538163	+	0.0641358i	0.792281	−	0.610156i	$-0.208893\pi$
$47$	0.368946	+	0.439693i	0.0538163	+	0.0641358i	−0.738465	+	0.674292i	$0.764449\pi$
$48$	2.78504	+	3.31908i	0.401985	+	0.479068i
$49$	−2.32635	+	4.02936i	−0.332336	+	0.575623i
$50$		0			0
$51$	2.37939	+	0.866025i	0.333181	+	0.121268i
$52$	11.8034	+	2.08125i	1.63683	+	0.288618i
$53$	2.89884	−	0.511144i	0.398187	−	0.0702111i	0.0290308	−	0.999579i	$-0.490758\pi$
$53$	2.89884	−	0.511144i	0.398187	−	0.0702111i	0.369156	+	0.929367i	$0.379647\pi$
$54$	−8.65657	+	3.15074i	−1.17801	+	0.428761i
$55$		0			0
$56$	−9.35504			−1.25012
$57$	2.80872	−	0.453363i	0.372023	−	0.0600494i
$58$		−	11.7811i		−	1.54693i
$59$	3.01501	+	2.52990i	0.392521	+	0.329365i	0.817595	−	0.575794i	$-0.195307\pi$
$59$	3.01501	+	2.52990i	0.392521	+	0.329365i	−0.425073	+	0.905159i	$0.639752\pi$
$60$		0			0
$61$	−0.784463	−	4.44891i	−0.100440	−	0.569624i	−0.992944	−	0.118585i	$-0.962164\pi$
$61$	−0.784463	−	4.44891i	−0.100440	−	0.569624i	0.892504	−	0.451040i	$-0.148947\pi$
$62$	9.56926	+	1.68732i	1.21530	+	0.214290i
$63$	1.34878	−	3.70574i	0.169930	−	0.466879i
$64$	−0.819078	−	1.41868i	−0.102385	−	0.177336i
$65$		0			0
$66$	−1.50000	+	1.25865i	−0.184637	+	0.154929i
$67$	−2.49860	−	2.97771i	−0.305252	−	0.363785i	0.591510	−	0.806297i	$-0.298532\pi$
$67$	−2.49860	−	2.97771i	−0.305252	−	0.363785i	−0.896763	+	0.442512i	$0.854087\pi$
$68$	14.8210	+	8.55690i	1.79731	+	1.03768i
$69$	1.65270	+	2.86257i	0.198962	+	0.344613i
$70$		0			0
$71$	−1.20439	+	6.83045i	−0.142935	+	0.810625i	0.826067	+	0.563572i	$0.190573\pi$
$71$	−1.20439	+	6.83045i	−0.142935	+	0.810625i	−0.969002	+	0.247053i	$0.920538\pi$
$72$	−15.4781	+	2.72921i	−1.82411	+	0.321640i
$73$	2.09602	+	5.75877i	0.245321	+	0.674013i	0.999843	+	0.0177383i	$0.00564657\pi$
$73$	2.09602	+	5.75877i	0.245321	+	0.674013i	−0.754522	+	0.656275i	$0.772131\pi$
$74$	−7.96451	−	6.68302i	−0.925855	−	0.776885i
$75$		0			0
$76$	19.2271	+	0.278817i	2.20551	+	0.0319825i
$77$		−	1.81521i		−	0.206862i
$78$	2.88624	−	3.43969i	0.326803	−	0.389468i
$79$	9.21688	−	3.35467i	1.03698	−	0.377430i	0.233246	−	0.972418i	$-0.425065\pi$
$79$	9.21688	−	3.35467i	1.03698	−	0.377430i	0.803735	+	0.594988i	$0.202843\pi$
$80$		0			0
$81$	0.928548	−	5.26606i	0.103172	−	0.585118i
$82$	8.64766	−	23.7592i	0.954974	−	2.62377i
$83$	−10.6679	+	6.15910i	−1.17095	+	0.676049i	−0.953904	−	0.300112i	$-0.902976\pi$
$83$	−10.6679	+	6.15910i	−1.17095	+	0.676049i	−0.217047	+	0.976161i	$0.569643\pi$
$84$	−2.20574	+	3.82045i	−0.240666	+	0.416845i
$85$		0			0
$86$	16.8799	−	14.1639i	1.82020	−	1.52733i
$87$	−2.62998	−	1.51842i	−0.281963	−	0.162792i
$88$	−6.26519	+	3.61721i	−0.667872	+	0.385596i
$89$	−2.27972	−	0.829748i	−0.241649	−	0.0879532i	0.218356	−	0.975869i	$-0.429930\pi$
$89$	−2.27972	−	0.829748i	−0.241649	−	0.0879532i	−0.460006	+	0.887916i	$0.652153\pi$
$90$		0			0
$91$	0.722811	+	4.09927i	0.0757712	+	0.429720i
$92$	7.64090	+	20.9932i	0.796619	+	2.18869i
$93$	1.61002	−	1.91875i	0.166951	−	0.198965i
$94$	1.45336			0.149903
$95$		0			0
$96$	3.00000			0.306186
$97$	−4.73708	+	5.64543i	−0.480977	+	0.573207i	−0.950899	−	0.309502i	$-0.899838\pi$
$97$	−4.73708	+	5.64543i	−0.480977	+	0.573207i	0.469922	+	0.882708i	$0.344282\pi$
$98$	4.02936	+	11.0706i	0.407027	+	1.11830i
$99$	−0.529563	−	3.00330i	−0.0532231	−	0.301843i
$100$		0			0
$101$	−2.03936	−	0.742267i	−0.202924	−	0.0738584i	0.238559	−	0.971128i	$-0.423325\pi$
$101$	−2.03936	−	0.742267i	−0.202924	−	0.0738584i	−0.441483	+	0.897270i	$0.645547\pi$
$102$	5.55250	−	3.20574i	0.549779	−	0.317415i
$103$	−10.8042	−	6.23783i	−1.06457	−	0.614631i	−0.137879	−	0.990449i	$-0.544029\pi$
$103$	−10.8042	−	6.23783i	−1.06457	−	0.614631i	−0.926694	+	0.375818i	$0.877362\pi$
$104$	12.7083	−	10.6635i	1.24615	−	1.04564i
$105$		0			0
$106$	3.72668	−	6.45480i	0.361967	−	0.626946i
$107$	−5.78509	+	3.34002i	−0.559266	+	0.322892i	−0.752851	−	0.658191i	$-0.771322\pi$
$107$	−5.78509	+	3.34002i	−0.559266	+	0.322892i	0.193585	+	0.981083i	$0.437988\pi$
$108$	−5.48930	+	15.0817i	−0.528208	+	1.45124i
$109$	−1.64156	+	9.30975i	−0.157233	+	0.891712i	0.799483	+	0.600689i	$0.205107\pi$
$109$	−1.64156	+	9.30975i	−0.157233	+	0.891712i	−0.956716	+	0.291023i	$0.906004\pi$
$110$		0			0
$111$	−2.51842	+	0.916629i	−0.239038	+	0.0870026i
$112$	−6.53731	+	7.79086i	−0.617717	+	0.736167i
$113$		−	1.31046i		−	0.123278i	−0.998099	−	0.0616388i	$-0.980367\pi$
$113$		−	1.31046i		−	0.123278i	0.998099	−	0.0616388i	$-0.0196327\pi$
$114$	3.69207	−	6.18594i	0.345794	−	0.579366i
$115$		0			0
$116$	−15.7233	−	13.1934i	−1.45987	−	1.22498i
$117$	2.39181	+	6.57145i	0.221123	+	0.607531i
$118$	9.81445	−	1.73055i	0.903493	−	0.159310i
$119$	−1.03209	+	5.85327i	−0.0946114	+	0.536568i
$120$		0			0
$121$	4.79813	+	8.31061i	0.436194	+	0.755510i
$122$	−9.90630	−	5.71941i	−0.896875	−	0.517811i
$123$	−4.18939	−	4.99273i	−0.377745	−	0.450179i
$124$	12.9684	−	10.8818i	1.16459	−	0.977211i
$125$		0			0
$126$	−4.99273	−	8.64766i	−0.444787	−	0.770394i
$127$	−4.96032	+	13.6284i	−0.440157	+	1.20932i	0.499232	+	0.866468i	$0.333615\pi$
$127$	−4.96032	+	13.6284i	−0.440157	+	1.20932i	−0.939389	+	0.342853i	$0.888607\pi$
$128$	−13.1378	−	2.31655i	−1.16123	−	0.204756i
$129$	−0.986329	−	5.59375i	−0.0868415	−	0.492502i
$130$		0			0
$131$	−15.1741	−	12.7326i	−1.32577	−	1.11245i	−0.985047	−	0.172288i	$-0.944884\pi$
$131$	−15.1741	−	12.7326i	−1.32577	−	1.11245i	−0.340722	−	0.940164i	$-0.610671\pi$
$132$			3.41147i			0.296931i
$133$	2.19285	+	6.30793i	0.190144	+	0.546967i
$134$	−9.84255			−0.850267
$135$		0			0
$136$	22.2592	−	8.10170i	1.90871	−	0.694715i
$137$	−10.0494	+	1.77197i	−0.858575	+	0.151390i	−0.585569	−	0.810622i	$-0.699129\pi$
$137$	−10.0494	+	1.77197i	−0.858575	+	0.151390i	−0.273006	+	0.962012i	$0.588018\pi$
$138$	8.24243	+	1.45336i	0.701642	+	0.123718i
$139$	−1.56031	−	0.567905i	−0.132344	−	0.0481691i	0.274999	−	0.961444i	$-0.411322\pi$
$139$	−1.56031	−	0.567905i	−0.132344	−	0.0481691i	−0.407343	+	0.913275i	$0.633545\pi$
$140$		0			0
$141$	0.187319	−	0.324446i	0.0157751	−	0.0273232i
$142$	11.2887	+	13.4534i	0.947328	+	1.12898i
$143$	2.06910	+	2.46585i	0.173026	+	0.206205i
$144$	−8.54323	+	14.7973i	−0.711936	+	1.23311i
$145$		0			0
$146$	14.5817	+	5.30731i	1.20679	+	0.439236i
$147$	2.99070	+	0.527341i	0.246669	+	0.0434944i
$148$	−17.8386	+	3.14543i	−1.46633	+	0.258553i
$149$	10.5312	−	3.83305i	0.862750	−	0.314015i	0.127523	−	0.991836i	$-0.459297\pi$
$149$	10.5312	−	3.83305i	0.862750	−	0.314015i	0.735228	+	0.677820i	$0.237075\pi$
$150$		0			0
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$	17.4021	−	20.1386i	1.41150	−	1.63346i
$153$			9.98545i			0.807276i
$154$	−3.52094	−	2.95442i	−0.283726	−	0.238074i
$155$		0			0
$156$	−1.35844	−	7.70410i	−0.108762	−	0.616822i
$157$	10.8262	+	1.90895i	0.864023	+	0.152351i	0.588060	−	0.808817i	$-0.299892\pi$
$157$	10.8262	+	1.90895i	0.864023	+	0.152351i	0.275964	+	0.961168i	$0.411003\pi$
$158$	8.49432	−	23.3380i	0.675772	−	1.85667i
$159$	−0.960637	−	1.66387i	−0.0761835	−	0.131954i
$160$		0			0
$161$	−5.94356	+	4.98724i	−0.468418	+	0.393050i
$162$	−8.70323	−	10.3721i	−0.683791	−	0.814910i
$163$	−5.48432	−	3.16637i	−0.429565	−	0.248010i	0.269596	−	0.962973i	$-0.413110\pi$
$163$	−5.48432	−	3.16637i	−0.429565	−	0.248010i	−0.699161	+	0.714964i	$0.746443\pi$
$164$	−22.0253	−	38.1489i	−1.71989	−	2.97893i
$165$		0			0
$166$	−5.41622	+	30.7169i	−0.420380	+	2.38410i
$167$	13.5690	−	2.39259i	1.05000	−	0.185144i	0.378087	−	0.925770i	$-0.376582\pi$
$167$	13.5690	−	2.39259i	1.05000	−	0.185144i	0.671917	+	0.740626i	$0.265471\pi$
$168$	2.08840	+	5.73783i	0.161123	+	0.442683i
$169$	4.30406	+	3.61154i	0.331082	+	0.277811i
$170$		0			0
$171$	5.46838	+	9.79687i	0.418177	+	0.749186i
$172$		−	38.3901i		−	2.92722i
$173$	16.2286	−	19.3405i	1.23384	−	1.47043i	0.401784	−	0.915734i	$-0.368390\pi$
$173$	16.2286	−	19.3405i	1.23384	−	1.47043i	0.832053	−	0.554696i	$-0.187165\pi$
$174$	−7.22580	+	2.62998i	−0.547787	+	0.199378i
$175$		0			0
$176$	−1.36571	+	7.74535i	−0.102945	+	0.583828i
$177$	0.878624	−	2.41400i	0.0660414	−	0.181447i
$178$	−5.31991	+	3.07145i	−0.398744	+	0.230215i
$179$	2.91534	−	5.04952i	0.217903	−	0.377419i	−0.736264	−	0.676695i	$-0.763412\pi$
$179$	2.91534	−	5.04952i	0.217903	−	0.377419i	0.954167	+	0.299276i	$0.0967450\pi$
$180$		0			0
$181$	10.3892	−	8.71756i	0.772222	−	0.647971i	−0.169055	−	0.985607i	$-0.554072\pi$
$181$	10.3892	−	8.71756i	0.772222	−	0.647971i	0.941277	+	0.337635i	$0.109627\pi$
$182$	9.12776	+	5.26991i	0.676595	+	0.390632i
$183$	−2.55358	+	1.47431i	−0.188766	+	0.108984i
$184$	29.0574	+	10.5760i	2.14214	+	0.779674i
$185$		0			0
$186$	−1.10132	−	6.24589i	−0.0807526	−	0.457971i
$187$	1.57202	+	4.31908i	0.114957	+	0.315842i
$188$	1.62760	−	1.93969i	0.118705	−	0.141467i
$189$	−5.57398			−0.405447
$190$		0			0
$191$	−10.2841			−0.744128			−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841			−0.744128			−0.372064	+	0.928207i	$0.621350\pi$
$192$	−0.687288	+	0.819078i	−0.0496007	+	0.0591119i
$193$	4.72010	+	12.9684i	0.339760	+	0.933484i	0.985462	+	0.169895i	$0.0543427\pi$
$193$	4.72010	+	12.9684i	0.339760	+	0.933484i	−0.645702	+	0.763590i	$0.723435\pi$
$194$	3.24035	+	18.3770i	0.232644	+	1.31939i
$195$		0			0
$196$	19.2875	+	7.02006i	1.37768	+	0.501433i
$197$	−6.87700	+	3.97044i	−0.489966	+	0.282882i	−0.724560	−	0.689211i	$-0.757957\pi$
$197$	−6.87700	+	3.97044i	−0.489966	+	0.282882i	0.234594	+	0.972093i	$0.424624\pi$
$198$	−6.68739	−	3.86097i	−0.475252	−	0.274387i
$199$	−20.7101	+	17.3778i	−1.46810	+	1.23188i	−0.550219	+	0.835020i	$0.685456\pi$
$199$	−20.7101	+	17.3778i	−1.46810	+	1.23188i	−0.917879	+	0.396861i	$0.870100\pi$
$200$		0			0
$201$	−1.26857	+	2.19723i	−0.0894781	+	0.154981i
$202$	−4.75903	+	2.74763i	−0.334844	+	0.193322i
$203$	2.43804	−	6.69846i	0.171117	−	0.470140i
$204$	1.93969	−	11.0005i	0.135806	−	0.770192i
$205$		0			0
$206$	−29.6844	+	10.8042i	−2.06821	+	0.752766i
$207$	−8.37879	+	9.98545i	−0.582366	+	0.694037i
$208$		−	18.0351i		−	1.25051i
$209$	3.90760	+	3.37662i	0.270295	+	0.233566i
$210$		0			0
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	0.404635	−	0.914478i	$-0.367399\pi$
$211$	−6.18345	−	5.18853i	−0.425686	−	0.357193i	−0.830321	+	0.557285i	$0.811843\pi$
$212$	−4.44129	−	12.2023i	−0.305029	−	0.838060i
$213$	4.45826	−	0.786112i	0.305475	−	0.0538635i
$214$	−2.93717	+	16.6575i	−0.200781	+	1.13868i
$215$		0			0
$216$	11.1074	+	19.2386i	0.755764	+	1.30902i
$217$	5.09170	+	2.93969i	0.345647	+	0.199559i
$218$	15.3863	+	18.3366i	1.04209	+	1.24191i
$219$	3.06418	−	2.57115i	0.207058	−	0.173742i
$220$		0			0
$221$	−5.26991	−	9.12776i	−0.354493	−	0.614000i
$222$	−2.32099	+	6.37686i	−0.155774	+	0.427987i
$223$	15.2405	+	2.68732i	1.02058	+	0.179956i	0.658809	−	0.752310i	$-0.271060\pi$
$223$	15.2405	+	2.68732i	1.02058	+	0.179956i	0.361773	+	0.932266i	$0.382172\pi$
$224$	1.22281	+	6.93491i	0.0817025	+	0.463358i
$225$		0			0
$226$	−2.54189	−	2.13290i	−0.169084	−	0.141878i
$227$			9.87258i			0.655266i	0.944805	+	0.327633i	$0.106251\pi$
$227$			9.87258i			0.655266i	−0.944805	+	0.327633i	$0.893749\pi$
$228$	−4.12122	−	11.8550i	−0.272934	−	0.785119i
$229$	−20.1189			−1.32949			−0.664746	−	0.747070i	$-0.731460\pi$
$229$	−20.1189			−1.32949			−0.664746	+	0.747070i	$0.731460\pi$
$230$		0			0
$231$	−1.11334	+	0.405223i	−0.0732524	+	0.0266617i
$232$	−27.9781	+	4.93330i	−1.83685	+	0.323887i
$233$	−3.48108	−	0.613808i	−0.228053	−	0.0402119i	0.0584538	−	0.998290i	$-0.481383\pi$
$233$	−3.48108	−	0.613808i	−0.228053	−	0.0402119i	−0.286507	+	0.958078i	$0.592494\pi$
$234$	16.6395	+	6.05628i	1.08776	+	0.395912i
$235$		0			0
$236$	8.68139	−	15.0366i	0.565110	−	0.978800i
$237$	−4.11511	−	4.90420i	−0.267305	−	0.318562i
$238$	9.67372	+	11.5287i	0.627054	+	0.747294i
$239$	5.98680	−	10.3694i	0.387254	−	0.670743i	−0.604825	−	0.796358i	$-0.706757\pi$
$239$	5.98680	−	10.3694i	0.387254	−	0.670743i	0.992079	+	0.125615i	$0.0400904\pi$
$240$		0			0
$241$	−12.1236	−	4.41263i	−0.780950	−	0.284243i	−0.0793814	−	0.996844i	$-0.525294\pi$
$241$	−12.1236	−	4.41263i	−0.780950	−	0.284243i	−0.701569	+	0.712602i	$0.747517\pi$
$242$	23.9294	+	4.21941i	1.53824	+	0.271234i
$243$	−14.1858	+	2.50134i	−0.910021	+	0.160461i
$244$	−18.7271	+	6.81612i	−1.19888	+	0.436358i
$245$		0			0
$246$	−16.5030			−1.05219
$247$	−10.1691	−	6.06939i	−0.647042	−	0.386186i
$248$		−	23.4320i		−	1.48793i
$249$	6.15910	+	5.16810i	0.390317	+	0.327515i
$250$		0			0
$251$	2.49407	+	14.1446i	0.157424	+	0.892798i	0.956536	+	0.291615i	$0.0941925\pi$
$251$	2.49407	+	14.1446i	0.157424	+	0.892798i	−0.799112	+	0.601183i	$0.794696\pi$
$252$	−17.1326	−	3.02094i	−1.07925	−	0.190302i
$253$	−2.05212	+	5.63816i	−0.129016	+	0.354468i
$254$	18.3614	+	31.8029i	1.15210	+	1.99549i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	3.19961	+	3.81315i	0.199586	+	0.237858i	0.856549	−	0.516065i	$-0.172604\pi$
$257$	3.19961	+	3.81315i	0.199586	+	0.237858i	−0.656963	+	0.753923i	$0.728159\pi$
$258$	−12.4555	−	7.19119i	−0.775446	−	0.447704i
$259$	−3.14543	−	5.44804i	−0.195447	−	0.338525i
$260$		0			0
$261$	2.07960	−	11.7940i	0.128724	−	0.730031i
$262$	−49.3946	+	8.70961i	−3.05161	+	0.538081i
$263$	−8.22313	−	22.5929i	−0.507060	−	1.39314i	−0.884256	−	0.467002i	$-0.845334\pi$
$263$	−8.22313	−	22.5929i	−0.507060	−	1.39314i	0.377196	−	0.926133i	$-0.376888\pi$
$264$	3.61721	+	3.03520i	0.222624	+	0.186804i
$265$		0			0
$266$	15.8045	+	6.01330i	0.969038	+	0.368699i
$267$			1.58347i			0.0969070i
$268$	−11.0225	+	13.1361i	−0.673306	+	0.802415i
$269$	−12.3204	+	4.48427i	−0.751189	+	0.273411i	−0.689106	−	0.724660i	$-0.741997\pi$
$269$	−12.3204	+	4.48427i	−0.751189	+	0.273411i	−0.0620832	+	0.998071i	$0.519774\pi$
$270$		0			0
$271$	−4.61381	+	26.1662i	−0.280269	+	1.58948i	0.441443	+	0.897290i	$0.354467\pi$
$271$	−4.61381	+	26.1662i	−0.280269	+	1.58948i	−0.721711	+	0.692194i	$0.756644\pi$
$272$	8.80769	−	24.1989i	0.534045	−	1.46728i
$273$	2.35289	−	1.35844i	0.142403	−	0.0822166i
$274$	−12.9192	+	22.3767i	−0.780478	+	1.35183i
$275$		0			0
$276$	11.1702	−	9.37295i	0.672370	−	0.564185i
$277$	14.2987	+	8.25537i	0.859127	+	0.496017i	0.863720	−	0.503973i	$-0.168129\pi$
$277$	14.2987	+	8.25537i	0.859127	+	0.496017i	−0.00459317	+	0.999989i	$0.501462\pi$
$278$	−3.64111	+	2.10220i	−0.218379	+	0.126081i
$279$	9.28194	+	3.37835i	0.555695	+	0.202256i
$280$		0			0
$281$	−3.36706	−	19.0955i	−0.200862	−	1.13914i	−0.903820	−	0.427913i	$-0.859249\pi$
$281$	−3.36706	−	19.0955i	−0.200862	−	1.13914i	0.702958	−	0.711231i	$-0.251862\pi$
$282$	−0.324446	−	0.891407i	−0.0193205	−	0.0530825i
$283$	−7.27022	+	8.66431i	−0.432170	+	0.515040i	−0.937547	−	0.347859i	$-0.886909\pi$
$283$	−7.27022	+	8.66431i	−0.432170	+	0.515040i	0.505377	+	0.862899i	$0.331353\pi$
$284$	30.5972			1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	9.83375	−	11.7194i	0.580468	−	0.691775i
$288$	4.04633	+	11.1172i	0.238433	+	0.655088i
$289$	0.338678	+	1.92074i	0.0199222	+	0.112985i
$290$		0			0
$291$	4.52007	+	1.64517i	0.264971	+	0.0964416i
$292$	23.4131	−	13.5175i	1.37015	−	0.791054i
$293$	3.37662	+	1.94949i	0.197264	+	0.113891i	0.595379	−	0.803445i	$-0.297002\pi$
$293$	3.37662	+	1.94949i	0.197264	+	0.113891i	−0.398115	+	0.917336i	$0.630335\pi$
$294$	5.89053	−	4.94274i	0.343543	−	0.288267i
$295$		0			0
$296$	−12.5360	+	21.7129i	−0.728638	+	1.26204i
$297$	−3.73297	+	2.15523i	−0.216609	+	0.125059i
$298$	9.70562	−	26.6660i	0.562231	−	1.54472i
$299$	2.38919	−	13.5497i	0.138170	−	0.783602i
$300$		0			0
$301$	12.5287	−	4.56007i	0.722141	−	0.262838i
$302$	−17.9717	+	21.4179i	−1.03416	+	1.23246i
$303$			1.41653i			0.0813773i
$304$	−4.61081	−	28.5653i	−0.264448	−	1.63833i
$305$		0			0
$306$	19.3687	+	16.2523i	1.10724	+	0.929081i
$307$	−7.92642	−	21.7777i	−0.452385	−	1.24292i	−0.931041	−	0.364914i	$-0.881098\pi$
$307$	−7.92642	−	21.7777i	−0.452385	−	1.24292i	0.478657	−	0.878002i	$-0.341124\pi$
$308$	−7.88609	+	1.39053i	−0.449351	+	0.0792328i
$309$	−1.41400	+	8.01919i	−0.0804397	+	0.456196i
$310$		0			0
$311$	1.73055	+	2.99740i	0.0981306	+	0.169967i	0.910911	−	0.412603i	$-0.135380\pi$
$311$	1.73055	+	2.99740i	0.0981306	+	0.169967i	−0.812780	+	0.582570i	$0.802047\pi$
$312$	−9.37732	−	5.41400i	−0.530886	−	0.306507i
$313$	14.7133	+	17.5346i	0.831644	+	0.991115i	0.999985	+	0.00538626i	$0.00171451\pi$
$313$	14.7133	+	17.5346i	0.831644	+	0.991115i	−0.168341	+	0.985729i	$0.553841\pi$
$314$	21.3234	−	17.8925i	1.20335	−	1.00973i
$315$		0			0
$316$	−21.6348	−	37.4725i	−1.21705	−	2.10799i
$317$	8.93378	−	24.5453i	0.501771	−	1.37860i	−0.387773	−	0.921755i	$-0.626756\pi$
$317$	8.93378	−	24.5453i	0.501771	−	1.37860i	0.889544	−	0.456849i	$-0.151022\pi$
$318$	−4.79093	−	0.844770i	−0.268662	−	0.0473724i
$319$	−0.957234	−	5.42874i	−0.0535948	−	0.303951i
$320$		0			0
$321$	3.34002	+	2.80261i	0.186422	+	0.156427i
$322$			19.6459i			1.09482i
$323$	−10.6805	−	13.1099i	−0.594277	−	0.729456i
$324$	−23.5895			−1.31053
$325$		0			0
$326$	−15.0680	+	5.48432i	−0.834542	+	0.303748i
$327$	6.07650	−	1.07145i	0.336031	−	0.0592514i
$328$	−60.0455	−	10.5876i	−3.31546	−	0.584605i
$329$	0.826352	+	0.300767i	0.0455583	+	0.0165818i
$330$		0			0
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	0.476237	+	0.879317i	$0.342000\pi$
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	−0.999629	+	0.0272251i	$0.991333\pi$
$332$	34.9300	+	41.6279i	1.91703	+	2.28463i
$333$	−6.79357	−	8.09627i	−0.372286	−	0.443673i
$334$	17.4440	−	30.2139i	0.954495	−	1.65323i
$335$		0			0
$336$	6.23783	+	2.27038i	0.340301	+	0.123860i
$337$	1.67555	+	0.295445i	0.0912731	+	0.0160939i	0.219098	−	0.975703i	$-0.429688\pi$
$337$	1.67555	+	0.295445i	0.0912731	+	0.0160939i	−0.127825	+	0.991797i	$0.540800\pi$
$338$	14.0105	−	2.47044i	0.762073	−	0.134374i
$339$	−0.803758	+	0.292544i	−0.0436542	+	0.0158888i
$340$		0			0
$341$	4.54664			0.246214
$342$	27.9032	+	5.33837i	1.50883	+	0.288666i
$343$			17.8530i			0.963970i
$344$	−40.7053	−	34.1558i	−2.19468	−	1.84156i
$345$		0			0
$346$	−11.1010	−	62.9570i	−0.596794	−	3.38459i
$347$	−4.82721	−	0.851167i	−0.259138	−	0.0456930i	0.0425697	−	0.999094i	$-0.486446\pi$
$347$	−4.82721	−	0.851167i	−0.259138	−	0.0456930i	−0.301708	+	0.953400i	$0.597557\pi$
$348$	−4.58202	+	12.5890i	−0.245622	+	0.674841i
$349$	−14.0646	−	24.3607i	−0.752863	−	1.30400i	−0.946430	−	0.322910i	$-0.895339\pi$
$349$	−14.0646	−	24.3607i	−0.752863	−	1.30400i	0.193566	−	0.981087i	$-0.437994\pi$
$350$		0			0
$351$	7.57192	−	6.35359i	0.404159	−	0.339130i
$352$	3.50038	+	4.17159i	0.186571	+	0.222346i
$353$	−7.20529	−	4.15998i	−0.383499	−	0.221413i	0.295841	−	0.955237i	$-0.404400\pi$
$353$	−7.20529	−	4.15998i	−0.383499	−	0.221413i	−0.679340	+	0.733824i	$0.737734\pi$
$354$	−3.25237	−	5.63328i	−0.172862	−	0.299405i
$355$		0			0
$356$	−1.85844	+	10.5397i	−0.0984972	+	0.558605i
$357$	3.82045	−	0.673648i	0.202200	−	0.0356532i
$358$	−5.04952	−	13.8735i	−0.266876	−	0.733235i
$359$	−19.0967	−	16.0241i	−1.00789	−	0.845718i	−0.0198296	−	0.999803i	$-0.506312\pi$
$359$	−19.0967	−	16.0241i	−1.00789	−	0.845718i	−0.988057	+	0.154086i	$0.950757\pi$
$360$		0			0
$361$	−17.6582	−	7.01336i	−0.929380	−	0.369124i
$362$		−	34.3405i		−	1.80490i
$363$	4.02611	−	4.79813i	0.211316	−	0.251837i
$364$	17.2554	−	6.28044i	0.904427	−	0.329184i
$365$		0			0
$366$	−1.29648	+	7.35273i	−0.0677683	+	0.384333i
$367$	−0.884409	+	2.42989i	−0.0461657	+	0.126839i	−0.960633	−	0.277821i	$-0.910388\pi$
$367$	−0.884409	+	2.42989i	−0.0461657	+	0.126839i	0.914467	+	0.404660i	$0.132610\pi$
$368$	29.1130	−	16.8084i	1.51762	−	0.876198i
$369$	12.8512	−	22.2589i	0.669005	−	1.15875i
$370$		0			0
$371$	3.45471	−	2.89884i	0.179359	−	0.150500i
$372$	−9.56926	−	5.52481i	−0.496143	−	0.286448i
$373$	20.2505	−	11.6917i	1.04853	−	0.605371i	0.126295	−	0.991993i	$-0.459691\pi$
$373$	20.2505	−	11.6917i	1.04853	−	0.605371i	0.922238	+	0.386622i	$0.126358\pi$
$374$	10.9363	+	3.98048i	0.565502	+	0.205826i
$375$		0			0
$376$	−0.608593	−	3.45150i	−0.0313858	−	0.177998i
$377$	4.32342	+	11.8785i	0.222668	+	0.611774i
$378$	−9.07218	+	10.8118i	−0.466623	+	0.556099i
$379$	−25.4388			−1.30670			−0.653352	−	0.757054i	$-0.726638\pi$
$379$	−25.4388			−1.30670			−0.653352	+	0.757054i	$0.726638\pi$
$380$		0			0
$381$	9.46616			0.484966
$382$	−16.7383	+	19.9479i	−0.856405	+	1.02062i
$383$	−9.39895	−	25.8234i	−0.480264	−	1.31951i	−0.909268	−	0.416212i	$-0.863357\pi$
$383$	−9.39895	−	25.8234i	−0.480264	−	1.31951i	0.429003	−	0.903303i	$-0.358865\pi$
$384$	1.51202	+	8.57510i	0.0771600	+	0.437596i
$385$		0			0
$386$	32.8371	+	11.9517i	1.67136	+	0.608327i
$387$	19.3986	−	11.1998i	0.986088	−	0.569318i
$388$	28.1551	+	16.2554i	1.42936	+	0.825241i
$389$	2.56031	−	2.14835i	0.129813	−	0.108926i	−0.575570	−	0.817753i	$-0.695220\pi$
$389$	2.56031	−	2.14835i	0.129813	−	0.108926i	0.705383	+	0.708827i	$0.250775\pi$
$390$		0			0
$391$	9.82295	−	17.0138i	0.496768	−	0.860427i
$392$	24.6035	−	14.2049i	1.24267	−	0.717454i
$393$	−4.42198	+	12.1493i	−0.223060	+	0.612851i
$394$	−3.49154	+	19.8015i	−0.175901	+	0.997587i
$395$		0			0
$396$	−12.6420	+	4.60132i	−0.635286	+	0.231225i
$397$	8.43550	−	10.0530i	0.423365	−	0.504547i	−0.511631	−	0.859206i	$-0.670958\pi$
$397$	8.43550	−	10.0530i	0.423365	−	0.504547i	0.934996	+	0.354658i	$0.115403\pi$
$398$			68.4552i			3.43135i
$399$	3.37939	−	2.75314i	0.169181	−	0.137829i
$400$		0			0
$401$	13.1099	+	11.0005i	0.654679	+	0.549341i	0.908487	−	0.417914i	$-0.137239\pi$
$401$	13.1099	+	11.0005i	0.654679	+	0.549341i	−0.253808	+	0.967255i	$0.581683\pi$
$402$	2.19723	+	6.03684i	0.109588	+	0.301090i
$403$	−10.2676	+	1.81046i	−0.511467	+	0.0901854i
$404$	−1.66250	+	9.42853i	−0.0827127	+	0.469087i
$405$		0			0
$406$	−9.02481	−	15.6314i	−0.447894	−	0.775775i
$407$	−4.21307	−	2.43242i	−0.208834	−	0.120571i
$408$	−9.93821	−	11.8439i	−0.492015	−	0.586360i
$409$	6.73964	−	5.65523i	0.333254	−	0.279633i	−0.460770	−	0.887519i	$-0.652427\pi$
$409$	6.73964	−	5.65523i	0.333254	−	0.279633i	0.794024	+	0.607886i	$0.207982\pi$
$410$		0			0
$411$	3.33022	+	5.76811i	0.164268	+	0.284520i
$412$	−18.8234	+	51.7169i	−0.927364	+	2.54791i
$413$	5.93842	+	1.04710i	0.292211	+	0.0515246i
$414$	5.73143	+	32.5046i	0.281684	+	1.59751i
$415$		0			0
$416$	−9.56599	−	8.02682i	−0.469011	−	0.393547i
$417$			1.08378i			0.0530728i
$418$	12.9096	−	2.08378i	0.631429	−	0.101921i
$419$	−6.84018			−0.334165			−0.167082	−	0.985943i	$-0.553435\pi$
$419$	−6.84018			−0.334165			−0.167082	+	0.985943i	$0.553435\pi$
$420$		0			0
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	−0.229210	−	0.973377i	$-0.573614\pi$
$421$	4.53209	−	1.64955i	0.220880	−	0.0803939i	0.450090	+	0.892983i	$0.351392\pi$
$422$	−20.1283	+	3.54916i	−0.979830	+	0.172771i
$423$	1.45496	+	0.256549i	0.0707426	+	0.0124738i
$424$	−16.8897	−	6.14733i	−0.820234	−	0.298541i
$425$		0			0
$426$	5.73143	−	9.92713i	0.277689	−	0.480971i
$427$	−4.44891	−	5.30200i	−0.215298	−	0.256582i
$428$	18.9422	+	22.5744i	0.915606	+	1.09118i
$429$	1.05051	−	1.81953i	0.0507190	−	0.0878478i
$430$		0			0
$431$	−1.22503	−	0.445875i	−0.0590077	−	0.0214771i	0.312348	−	0.949968i	$-0.398885\pi$
$431$	−1.22503	−	0.445875i	−0.0590077	−	0.0214771i	−0.371355	+	0.928491i	$0.621107\pi$
$432$	23.7837	+	4.19372i	1.14430	+	0.201770i
$433$	19.5227	−	3.44238i	0.938202	−	0.165430i	0.316419	−	0.948620i	$-0.397520\pi$
$433$	19.5227	−	3.44238i	0.938202	−	0.165430i	0.621783	+	0.783189i	$0.286409\pi$
$434$	13.9893	−	5.09170i	0.671509	−	0.244409i
$435$		0			0
$436$	41.7033			1.99722
$437$	0.320070	−	22.0719i	0.0153110	−	1.05584i
$438$		−	10.1284i		−	0.483952i
$439$	26.4800	+	22.2193i	1.26382	+	1.06047i	0.995264	+	0.0972078i	$0.0309912\pi$
$439$	26.4800	+	22.2193i	1.26382	+	1.06047i	0.268557	+	0.963264i	$0.413453\pi$
$440$		0			0
$441$	2.07960	+	11.7940i	0.0990287	+	0.561620i
$442$	−26.2823	−	4.63429i	−1.25012	−	0.220430i
$443$	−5.81780	+	15.9843i	−0.276412	+	0.759436i	0.721350	+	0.692571i	$0.243522\pi$
$443$	−5.81780	+	15.9843i	−0.276412	+	0.759436i	−0.997762	+	0.0668650i	$0.978700\pi$
$444$	5.91147	+	10.2390i	0.280546	+	0.485920i
$445$		0			0
$446$	30.0180	−	25.1881i	1.42139	−	1.19269i
$447$	−4.70193	−	5.60354i	−0.222394	−	0.265038i
$448$	−2.17355	−	1.25490i	−0.102691	−	0.0592885i
$449$	18.7049	+	32.3978i	0.882737	+	1.52895i	0.848286	+	0.529539i	$0.177635\pi$
$449$	18.7049	+	32.3978i	0.882737	+	1.52895i	0.0344512	+	0.999406i	$0.489032\pi$
$450$		0			0
$451$	2.05438	−	11.6510i	0.0967369	−	0.548622i
$452$	−5.69323	+	1.00387i	−0.267787	+	0.0472181i
$453$	2.46497	+	6.77244i	0.115814	+	0.318197i
$454$	19.1498	+	16.0686i	0.898743	+	0.754135i
$455$		0			0
$456$	−16.2366	−	6.17771i	−0.760351	−	0.289298i
$457$			9.11112i			0.426200i	0.977030	+	0.213100i	$0.0683560\pi$
$457$			9.11112i			0.426200i	−0.977030	+	0.213100i	$0.931644\pi$
$458$	−32.7454	+	39.0244i	−1.53009	+	1.82349i
$459$	13.2626	−	4.82721i	0.619047	−	0.225315i
$460$		0			0
$461$	−4.24540	+	24.0769i	−0.197728	+	1.12137i	0.710751	+	0.703443i	$0.248355\pi$
$461$	−4.24540	+	24.0769i	−0.197728	+	1.12137i	−0.908480	+	0.417929i	$0.862756\pi$
$462$	−1.02606	+	2.81908i	−0.0477367	+	0.131155i
$463$	0.217134	−	0.125362i	0.0100911	−	0.00582609i	−0.494946	−	0.868924i	$-0.664812\pi$
$463$	0.217134	−	0.125362i	0.0100911	−	0.00582609i	0.505037	+	0.863098i	$0.331479\pi$
$464$	−15.4427	+	26.7475i	−0.716909	+	1.24172i
$465$		0			0
$466$	−6.85638	+	5.75319i	−0.317616	+	0.266511i
$467$	−13.3037	−	7.68092i	−0.615624	−	0.355431i	0.159539	−	0.987192i	$-0.448999\pi$
$467$	−13.3037	−	7.68092i	−0.615624	−	0.355431i	−0.775163	+	0.631761i	$0.782332\pi$
$468$	26.7171	−	15.4251i	1.23500	−	0.713028i
$469$	−5.59627	−	2.03687i	−0.258412	−	0.0940541i
$470$		0			0
$471$	−1.24598	−	7.06629i	−0.0574116	−	0.325597i
$472$	−8.21956	−	22.5831i	−0.378336	−	1.03947i
$473$	6.62744	−	7.89827i	0.304730	−	0.363163i
$474$	−16.2104			−0.744567
$475$		0			0
$476$	26.2199			1.20179
$477$	4.87019	−	5.80406i	0.222991	−	0.265750i
$478$	−10.3694	−	28.4898i	−0.474287	−	1.30309i
$479$	0.124896	+	0.708319i	0.00570663	+	0.0323639i	0.987528	−	0.157443i	$-0.0503250\pi$
$479$	0.124896	+	0.708319i	0.00570663	+	0.0323639i	−0.981821	+	0.189807i	$0.939214\pi$
$480$		0			0
$481$	10.4829	+	3.81547i	0.477980	+	0.173971i
$482$	−28.2915	+	16.3341i	−1.28864	+	0.743998i
$483$	4.38571	+	2.53209i	0.199557	+	0.115214i
$484$	32.4295	−	27.2116i	1.47407	−	1.23689i
$485$		0			0
$486$	−18.2369	+	31.5873i	−0.827245	+	1.43283i
$487$	10.1731	−	5.87346i	0.460988	−	0.266152i	−0.251471	−	0.967865i	$-0.580914\pi$
$487$	10.1731	−	5.87346i	0.460988	−	0.266152i	0.712460	+	0.701713i	$0.247581\pi$
$488$	−9.43442	+	25.9209i	−0.427076	+	1.17338i
$489$	−0.717759	+	4.07061i	−0.0324582	+	0.184079i
$490$		0			0
$491$	−0.0834734	+	0.0303818i	−0.00376710	+	0.00137111i	−0.343903	−	0.939005i	$-0.611749\pi$
$491$	−0.0834734	+	0.0303818i	−0.00376710	+	0.00137111i	0.340136	+	0.940376i	$0.389527\pi$
$492$	−18.4814	+	22.0253i	−0.833206	+	0.992976i
$493$			18.0496i			0.812914i
$494$	−28.3239	+	9.84635i	−1.27435	+	0.443008i
$495$		0			0
$496$	−19.5141	−	16.3743i	−0.876211	−	0.735228i
$497$	3.63441	+	9.98545i	0.163025	+	0.447909i
$498$	20.0490	−	3.53519i	0.898419	−	0.158416i
$499$	−2.55097	+	14.4673i	−0.114197	+	0.647645i	0.872947	+	0.487815i	$0.162206\pi$
$499$	−2.55097	+	14.4673i	−0.114197	+	0.647645i	−0.987145	+	0.159830i	$0.948905\pi$
$500$		0			0
$501$	−4.49660	−	7.78833i	−0.200893	−	0.347957i
$502$	31.4955	+	18.1839i	1.40571	+	0.811588i
$503$	3.15225	+	3.75671i	0.140552	+	0.167503i	0.831728	−	0.555183i	$-0.187352\pi$
$503$	3.15225	+	3.75671i	0.140552	+	0.167503i	−0.691176	+	0.722686i	$0.742907\pi$
$504$	−18.4461	+	15.4781i	−0.821654	+	0.689450i
$505$		0			0
$506$	7.59627	+	13.1571i	0.337695	+	0.584905i
$507$	1.25427	−	3.44609i	0.0557043	−	0.153046i
$508$	63.0076	+	11.1099i	2.79551	+	0.492924i
$509$	−1.11375	−	6.31640i	−0.0493662	−	0.279969i	0.950125	−	0.311870i	$-0.100955\pi$
$509$	−1.11375	−	6.31640i	−0.0493662	−	0.279969i	−0.999491	+	0.0319002i	$0.989844\pi$
$510$		0			0
$511$	7.19253	+	6.03525i	0.318179	+	0.266984i
$512$			50.5553i			2.23425i
$513$	10.3686	−	11.9991i	0.457786	−	0.529774i
$514$	12.6040			0.555939
$515$		0			0
$516$	−23.5462	+	8.57013i	−1.03656	+	0.377279i
$517$	0.669713	−	0.118089i	0.0294540	−	0.00519353i
$518$	−15.6870	−	2.76604i	−0.689248	−	0.121533i
$519$	−15.4851	−	5.63613i	−0.679723	−	0.247399i
$520$		0			0
$521$	17.9067	−	31.0154i	0.784508	−	1.35881i	−0.144785	−	0.989463i	$-0.546249\pi$
$521$	17.9067	−	31.0154i	0.784508	−	1.35881i	0.929293	−	0.369344i	$-0.120418\pi$
$522$	−19.4920	−	23.2297i	−0.853142	−	1.01674i
$523$	−24.9225	−	29.7015i	−1.08978	−	1.29875i	−0.951258	−	0.308395i	$-0.900208\pi$
$523$	−24.9225	−	29.7015i	−1.08978	−	1.29875i	−0.138526	−	0.990359i	$-0.544236\pi$
$524$	−43.6921	+	75.6770i	−1.90870	+	3.30596i
$525$		0			0
$526$	−57.2071	−	20.8217i	−2.49435	−	0.907869i
$527$	−14.6610	−	2.58512i	−0.638641	−	0.112610i
$528$	5.05542	−	0.891407i	0.220009	−	0.0387935i
$529$	2.48633	−	0.904950i	0.108101	−	0.0393456i
$530$		0			0
$531$	10.1307			0.439636
$532$	25.7247	−	14.3589i	1.11531	−	0.622538i
$533$			27.1293i			1.17510i
$534$	3.07145	+	2.57725i	0.132915	+	0.111529i
$535$		0			0
$536$	4.12155	+	23.3745i	0.178024	+	1.00962i
$537$	−3.74789	−	0.660855i	−0.161734	−	0.0285180i
$538$	−11.3546	+	31.1964i	−0.489530	+	1.34497i
$539$	2.75624	+	4.77396i	0.118720	+	0.205629i
$540$		0			0
$541$	7.26991	−	6.10018i	0.312558	−	0.262267i	−0.472990	−	0.881068i	$-0.656825\pi$
$541$	7.26991	−	6.10018i	0.312558	−	0.262267i	0.785548	+	0.618800i	$0.212381\pi$
$542$	43.2450	+	51.5374i	1.85753	+	2.21372i
$543$	−7.66610	−	4.42602i	−0.328984	−	0.189939i
$544$	−8.91534	−	15.4418i	−0.382242	−	0.662063i
$545$		0			0
$546$	1.19459	−	6.77487i	0.0511238	−	0.289938i
$547$	−13.9962	+	2.46791i	−0.598435	+	0.105520i	−0.464657	−	0.885491i	$-0.653822\pi$
$547$	−13.9962	+	2.46791i	−0.598435	+	0.105520i	−0.133779	+	0.991011i	$0.542711\pi$
$548$	15.3965	+	42.3016i	0.657707	+	1.80703i
$549$	−8.90760	−	7.47437i	−0.380167	−	0.318998i
$550$		0			0
$551$	9.88460	+	17.7088i	0.421098	+	0.754418i
$552$		−	20.1830i		−	0.859047i
$553$	9.65939	−	11.5116i	0.410759	−	0.489524i
$554$	39.2854	−	14.2987i	1.66908	−	0.607494i
$555$		0			0
$556$	−1.27197	+	7.21372i	−0.0539437	+	0.305930i
$557$	7.70908	−	21.1805i	0.326644	−	0.897447i	−0.662311	−	0.749229i	$-0.730424\pi$
$557$	7.70908	−	21.1805i	0.326644	−	0.897447i	0.988955	−	0.148218i	$-0.0473537\pi$
$558$	21.6602	−	12.5055i	0.916949	−	0.529401i
$559$	−11.8216	+	20.4756i	−0.500001	+	0.866026i
$560$		0			0
$561$	2.29813	−	1.92836i	0.0970273	−	0.0814155i
$562$	−42.5197	−	24.5488i	−1.79358	−	1.03553i
$563$	37.2147	−	21.4859i	1.56841	−	0.905524i	0.572058	−	0.820213i	$-0.306145\pi$
$563$	37.2147	−	21.4859i	1.56841	−	0.905524i	0.996354	−	0.0853106i	$-0.0271882\pi$
$564$	−1.55303	−	0.565258i	−0.0653945	−	0.0238017i
$565$		0			0
$566$	4.97313	+	28.2040i	0.209036	+	1.18550i
$567$	−2.80201	−	7.69846i	−0.117673	−	0.323305i
$568$	27.2224	−	32.4424i	1.14223	−	1.36125i
$569$	−7.42696			−0.311354			−0.155677	−	0.987808i	$-0.549756\pi$
$569$	−7.42696			−0.311354			−0.155677	+	0.987808i	$0.549756\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	9.12776	−	10.8780i	0.381651	−	0.454834i
$573$	2.29579	+	6.30763i	0.0959080	+	0.263505i
$574$	−6.72668	−	38.1489i	−0.280766	−	1.59230i
$575$		0			0
$576$	−3.96229	−	1.44215i	−0.165095	−	0.0600898i
$577$	2.80109	−	1.61721i	0.116611	−	0.0673254i	−0.440560	−	0.897723i	$-0.645220\pi$
$577$	2.80109	−	1.61721i	0.116611	−	0.0673254i	0.557171	+	0.830398i	$0.311887\pi$
$578$	4.27688	+	2.46926i	0.177895	+	0.102707i
$579$	6.90033	−	5.79006i	0.286768	−	0.240627i
$580$		0			0
$581$	−9.43629	+	16.3441i	−0.391483	+	0.678069i
$582$	10.5480	−	6.08987i	0.437227	−	0.252433i
$583$	1.19280	−	3.27719i	0.0494007	−	0.135727i
$584$	6.49794	−	36.8517i	0.268887	−	1.52493i
$585$		0			0
$586$	9.27719	−	3.37662i	0.383237	−	0.139487i
$587$	26.2311	−	31.2610i	1.08267	−	1.29028i	0.128279	−	0.991738i	$-0.459055\pi$
$587$	26.2311	−	31.2610i	1.08267	−	1.29028i	0.954396	−	0.298543i	$-0.0965008\pi$
$588$		−	13.3969i		−	0.552480i
$589$	−15.7998	+	5.49254i	−0.651019	+	0.226316i
$590$		0			0
$591$	3.97044	+	3.33159i	0.163322	+	0.137043i
$592$	9.32234	+	25.6129i	0.383146	+	1.05268i
$593$	−10.8961	+	1.92127i	−0.447449	+	0.0788973i	−0.392832	−	0.919610i	$-0.628505\pi$
$593$	−10.8961	+	1.92127i	−0.447449	+	0.0788973i	−0.0546164	+	0.998507i	$0.517394\pi$
$594$	−1.89528	+	10.7487i	−0.0777642	+	0.441023i
$595$		0			0
$596$	−24.7199	−	42.8161i	−1.01257	−	1.75381i
$597$	15.2818	+	8.82295i	0.625442	+	0.361099i
$598$	−22.3937	−	26.6878i	−0.915747	−	1.09134i
$599$	34.1332	−	28.6411i	1.39464	−	1.17024i	0.431224	−	0.902245i	$-0.358082\pi$
$599$	34.1332	−	28.6411i	1.39464	−	1.17024i	0.963419	−	0.268000i	$-0.0863626\pi$
$600$		0			0
$601$	2.49953	+	4.32932i	0.101958	+	0.176597i	0.912491	−	0.409096i	$-0.134156\pi$
$601$	2.49953	+	4.32932i	0.101958	+	0.176597i	−0.810533	+	0.585693i	$0.800823\pi$
$602$	11.5465	−	31.7237i	0.470600	−	1.29296i
$603$	−9.85337	−	1.73742i	−0.401260	−	0.0707530i
$604$	8.45858	+	47.9710i	0.344175	+	1.95191i
$605$		0			0
$606$	2.74763	+	2.30553i	0.111615	+	0.0936558i
$607$		−	31.1881i		−	1.26589i	−0.774199	−	0.632943i	$-0.781847\pi$
$607$		−	31.1881i		−	1.26589i	0.774199	−	0.632943i	$-0.218153\pi$
$608$	−17.2035	−	10.2679i	−0.697692	−	0.416417i
$609$	−4.65270			−0.188537
$610$		0			0
$611$	−1.46538	+	0.533356i	−0.0592831	+	0.0215773i
$612$	43.3813	−	7.64930i	1.75359	−	0.309205i
$613$	−16.1209	−	2.84255i	−0.651117	−	0.114809i	−0.161673	−	0.986844i	$-0.551689\pi$
$613$	−16.1209	−	2.84255i	−0.651117	−	0.114809i	−0.489444	+	0.872035i	$0.662800\pi$
$614$	−55.1430	−	20.0704i	−2.22539	−	0.809975i
$615$		0			0
$616$	−5.54189	+	9.59883i	−0.223289	+	0.386748i
$617$	10.3221	+	12.3014i	0.415551	+	0.495235i	0.932696	−	0.360663i	$-0.117450\pi$
$617$	10.3221	+	12.3014i	0.415551	+	0.495235i	−0.517145	+	0.855898i	$0.673005\pi$
$618$	13.2534	+	15.7947i	0.533128	+	0.635357i
$619$	11.9213	−	20.6483i	0.479156	−	0.829923i	−0.520558	−	0.853826i	$-0.674276\pi$
$619$	11.9213	−	20.6483i	0.479156	−	0.829923i	0.999714	+	0.0239031i	$0.00760931\pi$
$620$		0			0
$621$	17.3131	+	6.30147i	0.694753	+	0.252869i
$622$	8.63068	+	1.52182i	0.346059	+	0.0610195i
$623$	−3.66041	+	0.645430i	−0.146651	+	0.0258586i
$624$	−11.0617	+	4.02611i	−0.442820	+	0.161173i
$625$		0			0
$626$	57.9590			2.31651
$627$	1.19869	−	3.15048i	0.0478712	−	0.125818i
$628$		−	48.4962i		−	1.93521i
$629$	12.2023	+	10.2390i	0.486539	+	0.408255i
$630$		0			0
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	0.964541	+	0.263931i	$0.0850193\pi$
$631$	3.72874	+	21.1467i	0.148439	+	0.841838i	−0.816103	+	0.577907i	$0.803870\pi$
$632$	−58.9809	−	10.3999i	−2.34613	−	0.413687i
$633$	−1.80196	+	4.95084i	−0.0716214	+	0.196778i
$634$	−33.0699	−	57.2787i	−1.31337	−	2.27483i
$635$		0			0
$636$	−6.49273	+	5.44804i	−0.257453	+	0.216029i
$637$	−8.12538	−	9.68345i	−0.321939	−	0.383672i
$638$	−12.0881	−	6.97906i	−0.478572	−	0.276303i
$639$	8.92633	+	15.4609i	0.353120	+	0.611622i
$640$		0			0
$641$	2.21466	−	12.5600i	0.0874738	−	0.496089i	−0.909322	−	0.416094i	$-0.863399\pi$
$641$	2.21466	−	12.5600i	0.0874738	−	0.496089i	0.996795	−	0.0799944i	$-0.0254902\pi$
$642$	10.8724	−	1.91710i	0.429100	−	0.0756619i
$643$	9.78456	+	26.8828i	0.385865	+	1.06016i	0.968845	+	0.247669i	$0.0796646\pi$
$643$	9.78456	+	26.8828i	0.385865	+	1.06016i	−0.582979	+	0.812487i	$0.698113\pi$
$644$	26.2199	+	22.0011i	1.03321	+	0.866964i
$645$		0			0
$646$	−42.8127	−	0.620838i	−1.68444	−	0.0244265i
$647$			16.7128i			0.657046i	0.944496	+	0.328523i	$0.106551\pi$
$647$			16.7128i			0.657046i	−0.944496	+	0.328523i	$0.893449\pi$
$648$	−20.9876	+	25.0121i	−0.824472	+	0.982567i
$649$	4.38191	−	1.59489i	0.172005	−	0.0626047i
$650$		0			0
$651$	0.666374	−	3.77920i	0.0261173	−	0.148118i
$652$	−9.55493	+	26.2520i	−0.374200	+	1.02811i
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.882048	−	0.471160i	$-0.843835\pi$
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.0329874	+	0.999456i	$0.510502\pi$
$654$	7.81180	−	13.5304i	0.305466	−	0.529082i
$655$		0			0
$656$	−50.7772	+	42.6072i	−1.98252	+	1.66353i
$657$	13.6609	+	7.88713i	0.532963	+	0.307706i
$658$	1.92836	−	1.11334i	0.0751754	−	0.0434025i
$659$	−41.2533	−	15.0150i	−1.60700	−	0.584900i	−0.626157	−	0.779697i	$-0.715373\pi$
$659$	−41.2533	−	15.0150i	−1.60700	−	0.584900i	−0.980844	+	0.194797i	$0.937595\pi$
$660$		0			0
$661$	−1.86777	−	10.5927i	−0.0726480	−	0.412007i	−0.999345	−	0.0361971i	$-0.988476\pi$
$661$	−1.86777	−	10.5927i	−0.0726480	−	0.412007i	0.926697	−	0.375810i	$-0.122636\pi$
$662$	16.4931	+	45.3144i	0.641022	+	1.76119i
$663$	−4.42198	+	5.26991i	−0.171736	+	0.204667i
$664$	75.2158			2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	−15.1454	+	18.0496i	−0.586434	+	0.698884i
$668$	−20.7890	−	57.1173i	−0.804350	−	2.20993i
$669$	−1.75402	−	9.94756i	−0.0678144	−	0.384595i
$670$		0			0
$671$	−5.02956	−	1.83061i	−0.194164	−	0.0706700i
$672$	3.98048	−	2.29813i	0.153550	−	0.0886524i
$673$	4.03374	+	2.32888i	0.155489	+	0.0897717i	0.575726	−	0.817643i	$-0.304720\pi$
$673$	4.03374	+	2.32888i	0.155489	+	0.0897717i	−0.420237	+	0.907415i	$0.638053\pi$
$674$	3.30019	−	2.76919i	0.127119	−	0.106665i
$675$		0			0
$676$	12.3931	−	21.4654i	0.476656	−	0.825592i
$677$	2.83067	−	1.63429i	0.108791	−	0.0628107i	−0.444617	−	0.895721i	$-0.646660\pi$
$677$	2.83067	−	1.63429i	0.108791	−	0.0628107i	0.553408	+	0.832910i	$0.313327\pi$
$678$	−0.740748	+	2.03519i	−0.0284482	+	0.0781609i
$679$	−1.96064	+	11.1193i	−0.0752423	+	0.426721i
$680$		0			0
$681$	6.05525	−	2.20393i	0.232038	−	0.0844549i
$682$	7.40008	−	8.81908i	0.283364	−	0.337700i
$683$		−	6.21894i		−	0.237961i	−0.992897	−	0.118981i	$-0.962037\pi$
$683$		−	6.21894i		−	0.237961i	0.992897	−	0.118981i	$-0.0379626\pi$
$684$	38.3730	−	31.2620i	1.46723	−	1.19533i
$685$		0			0
$686$	34.6293	+	29.0574i	1.32215	+	1.10942i
$687$	4.49129	+	12.3397i	0.171353	+	0.470790i
$688$	−56.8898	+	10.0312i	−2.16890	+	0.382436i
$689$	−1.38872	+	7.87581i	−0.0529060	+	0.300045i
$690$		0			0
$691$	−11.1088	−	19.2409i	−0.422597	−	0.731959i	0.573596	−	0.819139i	$-0.305548\pi$
$691$	−11.1088	−	19.2409i	−0.422597	−	0.731959i	−0.996193	+	0.0871792i	$0.972215\pi$
$692$	−96.4557	−	55.6887i	−3.66670	−	2.11697i
$693$	−3.00330	−	3.57919i	−0.114086	−	0.135962i
$694$	−9.50774	+	7.97794i	−0.360909	+	0.302839i
$695$		0			0
$696$	9.27156	+	16.0588i	0.351438	+	0.608708i
$697$	−13.2490	+	36.4013i	−0.501841	+	1.37880i
$698$	−70.1438	−	12.3682i	−2.65498	−	0.468145i
$699$	0.400634	+	2.27211i	0.0151534	+	0.0859391i
$700$		0			0
$701$	−21.2750	−	17.8518i	−0.803544	−	0.674254i	0.145513	−	0.989356i	$-0.453517\pi$
$701$	−21.2750	−	17.8518i	−0.803544	−	0.674254i	−0.949058	+	0.315102i	$0.897961\pi$
$702$		−	25.0283i		−	0.944631i
$703$	17.5791	+	3.36319i	0.663008	+	0.126845i
$704$	−1.94087			−0.0731495
$705$		0			0
$706$	−19.7964	+	7.20529i	−0.745047	+	0.271175i
$707$	−3.27449	+	0.577382i	−0.123150	+	0.0217147i
$708$	−11.1606	−	1.96791i	−0.419440	−	0.0739586i
$709$	−5.73947	−	2.08900i	−0.215551	−	0.0784540i	0.231988	−	0.972719i	$-0.425477\pi$
$709$	−5.73947	−	2.08900i	−0.215551	−	0.0784540i	−0.447538	+	0.894265i	$0.647699\pi$
$710$		0			0
$711$	12.6233	−	21.8642i	0.473411	−	0.819972i
$712$	9.52190	+	11.3478i	0.356848	+	0.425275i
$713$	−12.4918	−	14.8871i	−0.467821	−	0.557527i
$714$	4.91147	−	8.50692i	0.183807	−	0.318364i
$715$		0			0
$716$	−24.1707	−	8.79742i	−0.903302	−	0.328775i
$717$	−7.69648	−	1.35710i	−0.287430	−	0.0506817i
$718$	−62.1635	+	10.9611i	−2.31992	+	0.409065i
$719$	36.3885	−	13.2443i	1.35706	−	0.493930i	0.441917	−	0.897056i	$-0.354299\pi$
$719$	36.3885	−	13.2443i	1.35706	−	0.493930i	0.915144	+	0.403126i	$0.132076\pi$
$720$		0			0
$721$	−19.1138			−0.711835
$722$	−42.3442	+	22.8366i	−1.57589	+	0.849891i
$723$			8.42097i			0.313179i
$724$	−45.8316	−	38.4573i	−1.70332	−	1.42925i
$725$		0			0
$726$	−2.75402	−	15.6188i	−0.102211	−	0.579669i
$727$	−10.9096	−	1.92366i	−0.404615	−	0.0713445i	−0.0323628	−	0.999476i	$-0.510303\pi$
$727$	−10.9096	−	1.92366i	−0.404615	−	0.0713445i	−0.372252	+	0.928132i	$0.621414\pi$
$728$	8.69296	−	23.8837i	0.322183	−	0.885190i
$729$	−3.31996	−	5.75033i	−0.122961	−	0.212975i
$730$		0			0
$731$	−25.8614	+	21.7003i	−0.956520	+	0.802615i
$732$	8.36121	+	9.96451i	0.309039	+	0.368299i
$733$	−13.6897	−	7.90373i	−0.505639	−	0.291931i	0.225400	−	0.974266i	$-0.427631\pi$
$733$	−13.6897	−	7.90373i	−0.505639	−	0.291931i	−0.731039	+	0.682335i	$0.760964\pi$
$734$	3.27379	+	5.67036i	0.120838	+	0.209297i
$735$		0			0
$736$	4.04189	−	22.9227i	0.148986	−	0.844942i
$737$	−4.53547	+	0.799726i	−0.167066	+	0.0294583i
$738$	−22.2589	−	61.1558i	−0.819360	−	2.25117i
$739$	−1.18685	−	0.995887i	−0.0436591	−	0.0366343i	0.620697	−	0.784050i	$-0.286850\pi$
$739$	−1.18685	−	0.995887i	−0.0436591	−	0.0366343i	−0.664356	+	0.747416i	$0.731294\pi$
$740$		0			0
$741$	−1.45249	+	7.59202i	−0.0533584	+	0.278900i
$742$		−	11.4192i		−	0.419213i
$743$	24.5310	−	29.2349i	0.899955	−	1.07252i	−0.0970576	−	0.995279i	$-0.530943\pi$
$743$	24.5310	−	29.2349i	0.899955	−	1.07252i	0.997012	−	0.0772453i	$-0.0246125\pi$
$744$	−14.3718	+	5.23091i	−0.526896	+	0.191774i
$745$		0			0
$746$	10.2815	−	58.3091i	0.376431	−	2.13485i
$747$	−10.8444	+	29.7946i	−0.396774	+	1.09013i
$748$	17.5598	−	10.1382i	0.642050	−	0.370688i
$749$	−5.11721	+	8.86327i	−0.186979	+	0.323857i
$750$		0			0
$751$	−19.4179	+	16.2935i	−0.708568	+	0.594559i	−0.924197	−	0.381916i	$-0.875264\pi$
$751$	−19.4179	+	16.2935i	−0.708568	+	0.594559i	0.215629	+	0.976475i	$0.430820\pi$
$752$	−3.29969	−	1.90508i	−0.120327	−	0.0694710i
$753$	8.11867	−	4.68732i	0.295861	−	0.170815i
$754$	30.0774	+	10.9473i	1.09536	+	0.398677i
$755$		0			0
$756$	4.26991	+	24.2159i	0.155295	+	0.880723i
$757$	−14.4916	−	39.8153i	−0.526705	−	1.44711i	−0.862927	−	0.505328i	$-0.831372\pi$
$757$	−14.4916	−	39.8153i	−0.526705	−	1.44711i	0.336222	−	0.941783i	$-0.390851\pi$
$758$	−41.4041	+	49.3435i	−1.50386	+	1.79224i
$759$	3.91622			0.142150
$760$		0			0
$761$	−2.85710			−0.103570			−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710			−0.103570			−0.0517848	+	0.998658i	$0.516491\pi$
$762$	15.4071	−	18.3614i	0.558139	−	0.665165i
$763$	4.95361	+	13.6099i	0.179333	+	0.492713i
$764$	7.87804	+	44.6786i	0.285018	+	1.61641i
$765$		0			0
$766$	−65.3872	−	23.7990i	−2.36253	−	0.859892i
$767$	−9.26055	+	5.34658i	−0.334379	+	0.193054i
$768$	17.2421	+	9.95471i	0.622169	+	0.359210i
$769$	−14.6472	+	12.2905i	−0.528193	+	0.443207i	−0.867477	−	0.497477i	$-0.834260\pi$
$769$	−14.6472	+	12.2905i	−0.528193	+	0.443207i	0.339284	+	0.940684i	$0.389815\pi$
$770$		0			0
$771$	1.62449	−	2.81369i	0.0585044	−	0.101333i
$772$	52.7247	−	30.4406i	1.89760	−	1.09558i
$773$	−0.860130	+	2.36319i	−0.0309367	+	0.0849980i	−0.954199	−	0.299171i	$-0.903290\pi$
$773$	−0.860130	+	2.36319i	−0.0309367	+	0.0849980i	0.923263	+	0.384169i	$0.125512\pi$
$774$	9.84895	−	55.8561i	0.354013	−	2.00771i
$775$		0			0
$776$	42.2854	−	15.3906i	1.51796	−	0.552491i
$777$	−2.63933	+	3.14543i	−0.0946854	+	0.112842i
$778$		−	8.46286i		−	0.303408i
$779$	6.93582	+	42.9694i	0.248502	+	1.53954i
$780$		0			0
$781$	6.29498	+	5.28211i	0.225252	+	0.189009i
$782$	−17.0138	−	46.7452i	−0.608414	−	1.67160i
$783$	−16.6701	+	2.93939i	−0.595741	+	0.105045i
$784$	5.36319	−	30.4162i	0.191542	−	1.08629i
$785$		0			0
$786$	16.3687	+	28.3514i	0.583852	+	1.01126i
$787$	−2.36083	−	1.36303i	−0.0841545	−	0.0485866i	0.457332	−	0.889296i	$-0.348805\pi$
$787$	−2.36083	−	1.36303i	−0.0841545	−	0.0485866i	−0.541487	+	0.840709i	$0.682138\pi$
$788$	22.5175	+	26.8353i	0.802152	+	0.955967i
$789$	−12.0214	+	10.0872i	−0.427974	+	0.359112i
$790$		0			0
$791$	−1.00387	−	1.73875i	−0.0356935	−	0.0618230i
$792$	−6.36884	+	17.4982i	−0.226307	+	0.621773i
$793$	12.0872	+	2.13129i	0.429228	+	0.0756844i
$794$	−5.77022	−	32.7245i	−0.204777	−	1.16135i
$795$		0			0
$796$	91.3620	+	76.6618i	3.23824	+	2.71720i
$797$			22.0327i			0.780439i	0.920722	+	0.390219i	$0.127601\pi$
$797$			22.0327i			0.780439i	−0.920722	+	0.390219i	$0.872399\pi$
$798$	0.160035	−	11.0360i	0.00566518	−	0.390669i
$799$	−2.22668			−0.0787743
$800$		0			0
$801$	−5.86794	+	2.13575i	−0.207333	+	0.0754632i
$802$	42.6753	−	7.52481i	1.50692	−	0.265710i
$803$	7.15052	+	1.26083i	0.252336	+	0.0444937i
$804$	10.5175	+	3.82807i	0.370925	+	0.135006i
$805$		0			0
$806$	−13.1998	+	22.8627i	−0.464943	+	0.805306i
$807$	5.50077	+	6.55556i	0.193636	+	0.230767i
$808$	8.51800	+	10.1514i	0.299662	+	0.357124i
$809$	27.3603	−	47.3893i	0.961935	−	1.66612i	0.244302	−	0.969699i	$-0.421441\pi$
$809$	27.3603	−	47.3893i	0.961935	−	1.66612i	0.717633	−	0.696422i	$-0.245226\pi$
$810$		0			0
$811$	2.17112	+	0.790224i	0.0762384	+	0.0277485i	0.379858	−	0.925045i	$-0.375973\pi$
$811$	2.17112	+	0.790224i	0.0762384	+	0.0277485i	−0.303619	+	0.952793i	$0.598195\pi$
$812$	−30.9688	−	5.46064i	−1.08679	−	0.191631i
$813$	17.0788	−	3.01145i	0.598979	−	0.105616i
$814$	−11.5753	+	4.21307i	−0.405715	+	0.147668i
$815$		0			0
$816$	−16.8084			−0.588412
$817$	−13.4892	+	35.4531i	−0.471927	+	1.24035i
$818$		−	22.2772i		−	0.778906i
$819$	8.20755	+	6.88695i	0.286795	+	0.240650i
$820$		0			0
$821$	0.192944	+	1.09424i	0.00673379	+	0.0381892i	0.987990	−	0.154521i	$-0.0493834\pi$
$821$	0.192944	+	1.09424i	0.00673379	+	0.0381892i	−0.981256	+	0.192710i	$0.938272\pi$
$822$	16.6086	+	2.92855i	0.579292	+	0.102145i
$823$	−7.06191	+	19.4024i	−0.246163	+	0.676327i	0.753656	+	0.657270i	$0.228289\pi$
$823$	−7.06191	+	19.4024i	−0.246163	+	0.676327i	−0.999818	+	0.0190572i	$0.993934\pi$
$824$	38.0886	+	65.9714i	1.32688	+	2.29822i
$825$		0			0
$826$	11.6964	−	9.81445i	0.406970	−	0.341488i
$827$	23.3367	+	27.8116i	0.811495	+	0.967103i	0.999888	−	0.0149913i	$-0.00477207\pi$
$827$	23.3367	+	27.8116i	0.811495	+	0.967103i	−0.188392	+	0.982094i	$0.560328\pi$
$828$	49.7999	+	28.7520i	1.73066	+	0.999200i
$829$	−3.57486	−	6.19183i	−0.124160	−	0.215051i	0.797244	−	0.603657i	$-0.206290\pi$
$829$	−3.57486	−	6.19183i	−0.124160	−	0.215051i	−0.921404	+	0.388606i	$0.872957\pi$
$830$		0			0
$831$	1.87134	−	10.6129i	0.0649161	−	0.368157i
$832$	4.38306	−	0.772852i	0.151955	−	0.0267938i
$833$	−6.17334	−	16.9611i	−0.213893	−	0.587667i
$834$	2.10220	+	1.76395i	0.0727931	+	0.0610807i
$835$		0			0
$836$	11.6762	−	19.5630i	0.403829	−	0.676602i
$837$		−	13.9614i		−	0.482577i
$838$	−11.1331	+	13.2679i	−0.384585	+	0.458330i
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.835638	−	0.549280i	$-0.814902\pi$
$839$	−32.5197	+	11.8362i	−1.12270	+	0.408631i	−0.287065	+	0.957911i	$0.592680\pi$
$840$		0			0
$841$	−1.27672	+	7.24065i	−0.0440249	+	0.249678i
$842$	4.17680	−	11.4757i	0.143942	−	0.395477i
$843$	−10.9604	+	6.32800i	−0.377497	+	0.217948i
$844$	−17.8045	+	30.8384i	−0.612857	+	1.06150i
$845$		0			0
$846$	2.86571	−	2.40462i	0.0985253	−	0.0826725i
$847$	12.7326	+	7.35117i	0.437497	+	0.252589i
$848$	−16.9220	+	9.76991i	−0.581103	+	0.335500i
$849$	6.93717	+	2.52492i	0.238083	+	0.0866551i
$850$		0			0
$851$	3.61081	+	20.4779i	0.123777	+	0.701975i
$852$	−6.83045	−	18.7665i	−0.234007	−	0.642930i
$853$	21.3732	−	25.4716i	0.731805	−	0.872132i	−0.263915	−	0.964546i	$-0.585014\pi$
$853$	21.3732	−	25.4716i	0.731805	−	0.872132i	0.995721	+	0.0924142i	$0.0294584\pi$
$854$	−17.5253			−0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	2.49800	−	2.97700i	0.0853299	−	0.101692i	−0.721690	−	0.692216i	$-0.756634\pi$
$857$	2.49800	−	2.97700i	0.0853299	−	0.101692i	0.807020	+	0.590524i	$0.201079\pi$
$858$	−1.81953	−	4.99912i	−0.0621178	−	0.170667i
$859$	−0.287866	−	1.63257i	−0.00982187	−	0.0557026i	0.979503	−	0.201430i	$-0.0645589\pi$
$859$	−0.287866	−	1.63257i	−0.00982187	−	0.0557026i	−0.989325	+	0.145727i	$0.953448\pi$
$860$		0			0
$861$	−9.38326	−	3.41523i	−0.319780	−	0.116391i
$862$	−2.85872	+	1.65048i	−0.0973684	+	0.0562156i
$863$	−45.6558	−	26.3594i	−1.55414	−	0.897284i	−0.997798	−	0.0663308i	$-0.978871\pi$
$863$	−45.6558	−	26.3594i	−1.55414	−	0.897284i	−0.556343	−	0.830953i	$-0.687796\pi$
$864$	12.8097	−	10.7487i	0.435796	−	0.365677i
$865$		0			0
$866$	25.0979	−	43.4709i	0.852862	−	1.47720i
$867$	1.10246	−	0.636507i	0.0374416	−	0.0216169i
$868$	8.87089	−	24.3726i	0.301098	−	0.827259i
$869$	2.01795	−	11.4444i	0.0684543	−	0.388224i
$870$		0			0
$871$	9.92396	−	3.61203i	0.336261	−	0.122389i
$872$	37.1035	−	44.2183i	1.25648	−	1.49742i
$873$			18.9691i			0.642008i
$874$	−42.2918	−	36.5450i	−1.43054	−	1.23615i
$875$		0			0
$876$	−13.5175	−	11.3426i	−0.456715	−	0.383230i
$877$	7.24735	+	19.9119i	0.244726	+	0.672378i	0.999859	+	0.0168069i	$0.00535004\pi$
$877$	7.24735	+	19.9119i	0.244726	+	0.672378i	−0.755133	+	0.655572i	$0.772428\pi$
$878$	86.1974	−	15.1989i	2.90902	−	0.512939i
$879$	0.441914	−	2.50622i	0.0149054	−	0.0845327i
$880$		0			0
$881$	−16.0505	−	27.8003i	−0.540755	−	0.936616i	−0.998861	−	0.0477179i	$-0.984805\pi$
$881$	−16.0505	−	27.8003i	−0.540755	−	0.936616i	0.458106	−	0.888898i	$-0.348528\pi$
$882$	26.2615	+	15.1621i	0.884271	+	0.510534i
$883$	30.4018	+	36.2315i	1.02310	+	1.21929i	0.975404	+	0.220425i	$0.0707444\pi$
$883$	30.4018	+	36.2315i	1.02310	+	1.21929i	0.0476989	+	0.998862i	$0.484811\pi$
$884$	−35.6181	+	29.8872i	−1.19797	+	1.00521i
$885$		0			0
$886$	21.5355	+	37.3007i	0.723501	+	1.25314i
$887$	3.61278	−	9.92602i	0.121305	−	0.333283i	−0.864146	−	0.503241i	$-0.832141\pi$
$887$	3.61278	−	9.92602i	0.121305	−	0.333283i	0.985451	+	0.169958i	$0.0543631\pi$
$888$	16.1159	+	2.84167i	0.540815	+	0.0953602i
$889$	3.85844	+	21.8823i	0.129408	+	0.733909i
$890$		0			0
$891$	−4.85323	−	4.07234i	−0.162589	−	0.136429i
$892$		−	68.2704i		−	2.28586i
$893$	−2.18463	+	1.21941i	−0.0731059	+	0.0408059i
$894$	−18.5220			−0.619468
$895$		0			0
$896$	−19.2062	+	6.99049i	−0.641634	+	0.233536i
$897$	−8.84397	+	1.55943i	−0.295291	+	0.0520679i
$898$	93.2857	+	16.4488i	3.11298	+	0.548903i
$899$	16.7780	+	6.10668i	0.559576	+	0.203669i
$900$		0			0
$901$	−5.70961	+	9.88933i	−0.190215	+	0.329461i
$902$	−19.2556	−	22.9479i	−0.641141	−	0.764081i
$903$	−5.59375	−	6.66637i	−0.186148	−	0.221843i
$904$	−4.00088	+	6.92972i	−0.133067	+	0.230479i
$905$		0			0
$906$	17.1484	+	6.24152i	0.569718	+	0.207360i
$907$	42.2684	+	7.45306i	1.40350	+	0.247475i	0.823580	−	0.567200i	$-0.191973\pi$
$907$	42.2684	+	7.45306i	1.40350	+	0.247475i	0.579919	+	0.814674i	$0.303084\pi$
$908$	42.8910	−	7.56283i	1.42339	−	0.250981i
$909$	−5.24928	+	1.91058i	−0.174107	+	0.0633699i
$910$		0			0
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$	−16.4910	+	9.20486i	−0.546071	+	0.304803i
$913$			14.5945i			0.483008i
$914$	17.6728	+	14.8292i	0.584563	+	0.490507i
$915$		0			0
$916$	15.4119	+	87.4055i	0.509225	+	2.88796i
$917$	−29.8872	−	5.26991i	−0.986961	−	0.174028i
$918$	12.2229	−	33.5822i	0.403416	−	1.10838i
$919$	−12.2788	−	21.2676i	−0.405041	−	0.701552i	0.589285	−	0.807925i	$-0.299410\pi$
$919$	−12.2788	−	21.2676i	−0.405041	−	0.701552i	−0.994326	+	0.106373i	$0.966076\pi$
$920$		0			0
$921$	−11.5876	+	9.72319i	−0.381826	+	0.320390i
$922$	39.7920	+	47.4222i	1.31048	+	1.56177i
$923$	−16.3192	−	9.42190i	−0.537154	−	0.310126i
$924$	2.61334	+	4.52644i	0.0859726	+	0.148909i
$925$		0			0
$926$	0.110242	−	0.625213i	0.00362277	−	0.0205458i
$927$	−31.6242	+	5.57620i	−1.03867	+	0.183146i
$928$	7.31412	+	20.0954i	0.240098	+	0.659663i
$929$	17.0654	+	14.3195i	0.559896	+	0.469809i	0.878276	−	0.478155i	$-0.158694\pi$
$929$	17.0654	+	14.3195i	0.559896	+	0.469809i	−0.318379	+	0.947963i	$0.603139\pi$
$930$		0			0
$931$	−15.3452	−	13.2601i	−0.502920	−	0.434581i
$932$			15.5936i			0.510785i
$933$	1.45211	−	1.73055i	0.0475398	−	0.0566557i
$934$	−36.5517	+	13.3037i	−1.19601	+	0.435312i
$935$		0			0
$936$	7.41493	−	42.0522i	0.242365	−	1.37452i
$937$	−3.26687	+	8.97565i	−0.106724	+	0.293222i	−0.981547	−	0.191221i	$-0.938755\pi$
$937$	−3.26687	+	8.97565i	−0.106724	+	0.293222i	0.874823	+	0.484443i	$0.160978\pi$
$938$	−13.0594	+	7.53983i	−0.426403	+	0.246184i
$939$	7.47013	−	12.9386i	0.243779	−	0.422237i
$940$		0			0
$941$	−42.6883	+	35.8197i	−1.39160	+	1.16769i	−0.426909	+	0.904295i	$0.640398\pi$
$941$	−42.6883	+	35.8197i	−1.39160	+	1.16769i	−0.964688	+	0.263394i	$0.915158\pi$
$942$	−15.7344	−	9.08424i	−0.512654	−	0.295981i
$943$	−43.7933	+	25.2841i	−1.42610	+	0.823362i
$944$	−24.5510	−	8.93582i	−0.799066	−	0.290836i
$945$		0			0
$946$	−4.53343	−	25.7104i	−0.147395	−	0.835916i
$947$	9.24919	+	25.4119i	0.300558	+	0.825777i	0.994403	+	0.105653i	$0.0336931\pi$
$947$	9.24919	+	25.4119i	0.300558	+	0.825777i	−0.693845	+	0.720125i	$0.744085\pi$
$948$	−18.1537	+	21.6348i	−0.589605	+	0.702664i
$949$	−16.6500			−0.540482
$950$		0			0
$951$	−17.0490			−0.552852
$952$	23.3279	−	27.8011i	0.756062	−	0.901040i
$953$	7.91128	+	21.7361i	0.256272	+	0.704100i	0.999389	+	0.0349398i	$0.0111240\pi$
$953$	7.91128	+	21.7361i	0.256272	+	0.704100i	−0.743118	+	0.669161i	$0.766654\pi$
$954$	−3.33140	−	18.8933i	−0.107858	−	0.611694i
$955$		0			0
$956$	−49.6357	−	18.0659i	−1.60533	−	0.584293i
$957$	−3.11598	+	1.79901i	−0.100725	+	0.0581538i
$958$	1.57720	+	0.910597i	0.0509570	+	0.0294200i
$959$	−11.9764	+	10.0494i	−0.386737	+	0.324511i
$960$		0			0
$961$	8.13681	−	14.0934i	0.262478	−	0.454625i
$962$	24.4628	−	14.1236i	0.788713	−	0.455363i
$963$	−5.88079	+	16.1573i	−0.189506	+	0.520663i
$964$	−9.88326	+	56.0507i	−0.318318	+	1.80527i
$965$		0			0
$966$	12.0496	−	4.38571i	0.387690	−	0.141108i
$967$	−25.0913	+	29.9026i	−0.806881	+	0.961603i	−0.999808	−	0.0196101i	$-0.993758\pi$
$967$	−25.0913	+	29.9026i	−0.806881	+	0.961603i	0.192927	+	0.981213i	$0.438202\pi$
$968$		−	58.5954i		−	1.88333i
$969$	−5.65657	+	9.47740i	−0.181715	+	0.304458i
$970$		0			0
$971$	−31.5631	−	26.4845i	−1.01291	−	0.849930i	−0.0241869	−	0.999707i	$-0.507700\pi$
$971$	−31.5631	−	26.4845i	−1.01291	−	0.849930i	−0.988720	+	0.149778i	$0.952144\pi$
$972$	21.7339	+	59.7135i	0.697117	+	1.91531i
$973$	−2.50530	+	0.441752i	−0.0803162	+	0.0141619i
$974$	5.16503	−	29.2923i	0.165498	−	0.938587i
$975$		0			0
$976$	14.9941	+	25.9705i	0.479948	+	0.831295i
$977$	−19.4802	−	11.2469i	−0.623227	−	0.359821i	0.154897	−	0.987931i	$-0.450495\pi$
$977$	−19.4802	−	11.2469i	−0.623227	−	0.359821i	−0.778125	+	0.628110i	$0.783829\pi$
$978$	6.72752	+	8.01754i	0.215122	+	0.256373i
$979$	−2.20187	+	1.84759i	−0.0703720	+	0.0590491i
$980$		0			0
$981$	12.1664	+	21.0728i	0.388442	+	0.672802i
$982$	−0.0769295	+	0.211362i	−0.00245492	+	0.00674484i
$983$	43.8694	+	7.73536i	1.39922	+	0.246720i	0.821821	−	0.569746i	$-0.192958\pi$
$983$	43.8694	+	7.73536i	1.39922	+	0.246720i	0.577395	+	0.816465i	$0.304069\pi$
$984$	6.91060	+	39.1919i	0.220302	+	1.24939i
$985$		0			0
$986$	35.0107	+	29.3775i	1.11497	+	0.935570i
$987$		−	0.573978i		−	0.0182699i
$988$	−18.5782	+	48.8285i	−0.591052	+	1.55344i
$989$	−44.0702			−1.40135
$990$		0			0
$991$	42.5959	−	15.5036i	1.35310	−	0.492489i	0.439187	−	0.898395i	$-0.355266\pi$
$991$	42.5959	−	15.5036i	1.35310	−	0.492489i	0.913915	+	0.405907i	$0.133044\pi$
$992$	−17.3702	+	3.06283i	−0.551504	+	0.0972451i
$993$	12.2416	+	2.15853i	0.388476	+	0.0684988i
$994$	25.2841	+	9.20264i	0.801961	+	0.291890i
$995$		0			0
$996$	17.7344	−	30.7169i	0.561937	−	0.973303i
$997$	−6.74357	−	8.03667i	−0.213571	−	0.254524i	0.648614	−	0.761117i	$-0.275349\pi$
$997$	−6.74357	−	8.03667i	−0.213571	−	0.254524i	−0.862185	+	0.506593i	$0.830905\pi$
$998$	23.9101	+	28.4950i	0.756862	+	0.901994i
$999$	−7.46926	+	12.9371i	−0.236317	+	0.409313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.a.149.2		12
5.2	odd	4		475.2.l.a.301.1		6
5.3	odd	4		19.2.e.a.16.1	yes	6
5.4	even	2	inner	475.2.u.a.149.1		12
15.8	even	4		171.2.u.c.73.1		6
19.6	even	9	inner	475.2.u.a.424.1		12
20.3	even	4		304.2.u.b.225.1		6
35.3	even	12		931.2.x.b.814.1		6
35.13	even	4		931.2.w.a.491.1		6
35.18	odd	12		931.2.x.a.814.1		6
35.23	odd	12		931.2.v.b.263.1		6
35.33	even	12		931.2.v.a.263.1		6
95.3	even	36		361.2.c.h.68.1		6
95.8	even	12		361.2.e.b.245.1		6
95.13	even	36		361.2.e.h.234.1		6
95.18	even	4		361.2.e.h.54.1		6
95.23	odd	36		361.2.e.f.28.1		6
95.28	odd	36		361.2.e.g.99.1		6
95.33	even	36		361.2.a.h.1.3		3
95.43	odd	36		361.2.a.g.1.1		3
95.44	even	18	inner	475.2.u.a.424.2		12
95.48	even	36		361.2.e.a.99.1		6
95.52	even	36		9025.2.a.x.1.1		3
95.53	even	36		361.2.e.b.28.1		6
95.62	odd	36		9025.2.a.bd.1.3		3
95.63	odd	36		19.2.e.a.6.1	✓	6
95.68	odd	12		361.2.e.f.245.1		6
95.73	odd	36		361.2.c.i.68.3		6
95.78	even	36		361.2.c.h.292.1		6
95.82	odd	36		475.2.l.a.101.1		6
95.83	odd	12		361.2.e.g.62.1		6
95.88	even	12		361.2.e.a.62.1		6
95.93	odd	36		361.2.c.i.292.3		6
285.128	odd	36		3249.2.a.s.1.1		3
285.158	even	36		171.2.u.c.82.1		6
285.233	even	36		3249.2.a.z.1.3		3
380.43	even	36		5776.2.a.br.1.2		3
380.63	even	36		304.2.u.b.177.1		6
380.223	odd	36		5776.2.a.bi.1.2		3
665.158	odd	36		931.2.v.b.177.1		6
665.348	even	36		931.2.x.b.557.1		6
665.443	odd	36		931.2.x.a.557.1		6
665.538	even	36		931.2.w.a.785.1		6
665.633	even	36		931.2.v.a.177.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	95.63	odd	36
19.2.e.a.16.1	yes	6	5.3	odd	4
171.2.u.c.73.1		6	15.8	even	4
171.2.u.c.82.1		6	285.158	even	36
304.2.u.b.177.1		6	380.63	even	36
304.2.u.b.225.1		6	20.3	even	4
361.2.a.g.1.1		3	95.43	odd	36
361.2.a.h.1.3		3	95.33	even	36
361.2.c.h.68.1		6	95.3	even	36
361.2.c.h.292.1		6	95.78	even	36
361.2.c.i.68.3		6	95.73	odd	36
361.2.c.i.292.3		6	95.93	odd	36
361.2.e.a.62.1		6	95.88	even	12
361.2.e.a.99.1		6	95.48	even	36
361.2.e.b.28.1		6	95.53	even	36
361.2.e.b.245.1		6	95.8	even	12
361.2.e.f.28.1		6	95.23	odd	36
361.2.e.f.245.1		6	95.68	odd	12
361.2.e.g.62.1		6	95.83	odd	12
361.2.e.g.99.1		6	95.28	odd	36
361.2.e.h.54.1		6	95.18	even	4
361.2.e.h.234.1		6	95.13	even	36
475.2.l.a.101.1		6	95.82	odd	36
475.2.l.a.301.1		6	5.2	odd	4
475.2.u.a.149.1		12	5.4	even	2	inner
475.2.u.a.149.2		12	1.1	even	1	trivial
475.2.u.a.424.1		12	19.6	even	9	inner
475.2.u.a.424.2		12	95.44	even	18	inner
931.2.v.a.177.1		6	665.633	even	36
931.2.v.a.263.1		6	35.33	even	12
931.2.v.b.177.1		6	665.158	odd	36
931.2.v.b.263.1		6	35.23	odd	12
931.2.w.a.491.1		6	35.13	even	4
931.2.w.a.785.1		6	665.538	even	36
931.2.x.a.557.1		6	665.443	odd	36
931.2.x.a.814.1		6	35.18	odd	12
931.2.x.b.557.1		6	665.348	even	36
931.2.x.b.814.1		6	35.3	even	12
3249.2.a.s.1.1		3	285.128	odd	36
3249.2.a.z.1.3		3	285.233	even	36
5776.2.a.bi.1.2		3	380.223	odd	36
5776.2.a.br.1.2		3	380.43	even	36
9025.2.a.x.1.1		3	95.52	even	36
9025.2.a.bd.1.3		3	95.62	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62760 - 1.93969i) q^{2} +(-0.223238 - 0.613341i) q^{3} +(-0.766044 - 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(1.32683 - 0.766044i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(1.97178 - 1.65452i) q^{9} +O(q^{10})\)	\(q+(1.62760 - 1.93969i) q^{2} +(-0.223238 - 0.613341i) q^{3} +(-0.766044 - 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(1.32683 - 0.766044i) q^{7} +(-5.28801 - 3.05303i) q^{8} +(1.97178 - 1.65452i) q^{9} +(0.592396 - 1.02606i) q^{11} +(-2.49362 + 1.43969i) q^{12} +(-0.929228 + 2.55303i) q^{13} +(0.673648 - 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.49362 + 2.97178i) q^{17} -6.51754i q^{18} +(-0.819078 + 4.28125i) q^{19} +(-0.766044 - 0.642788i) q^{21} +(-1.02606 - 2.81908i) q^{22} +(-4.98724 + 0.879385i) q^{23} +(-0.692066 + 3.92490i) q^{24} +(3.43969 + 5.95772i) q^{26} +(-3.15074 - 1.81908i) q^{27} +(-4.34445 - 5.17752i) q^{28} +(3.56418 - 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-1.57202 + 4.31908i) q^{32} +(-0.761570 - 0.134285i) q^{33} +(1.70574 + 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} -4.10607i q^{37} +(6.97118 + 8.55690i) q^{38} +1.77332 q^{39} +(9.38326 - 3.41523i) q^{41} +(-2.49362 + 0.439693i) q^{42} +(8.57013 + 1.51114i) q^{43} +(-4.91147 - 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(0.368946 + 0.439693i) q^{47} +(2.78504 + 3.31908i) q^{48} +(-2.32635 + 4.02936i) q^{49} +(2.37939 + 0.866025i) q^{51} +(11.8034 + 2.08125i) q^{52} +(2.89884 - 0.511144i) q^{53} +(-8.65657 + 3.15074i) q^{54} -9.35504 q^{56} +(2.80872 - 0.453363i) q^{57} -11.7811i q^{58} +(3.01501 + 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(9.56926 + 1.68732i) q^{62} +(1.34878 - 3.70574i) q^{63} +(-0.819078 - 1.41868i) q^{64} +(-1.50000 + 1.25865i) q^{66} +(-2.49860 - 2.97771i) q^{67} +(14.8210 + 8.55690i) q^{68} +(1.65270 + 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(-15.4781 + 2.72921i) q^{72} +(2.09602 + 5.75877i) q^{73} +(-7.96451 - 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} -1.81521i q^{77} +(2.88624 - 3.43969i) q^{78} +(9.21688 - 3.35467i) q^{79} +(0.928548 - 5.26606i) q^{81} +(8.64766 - 23.7592i) q^{82} +(-10.6679 + 6.15910i) q^{83} +(-2.20574 + 3.82045i) q^{84} +(16.8799 - 14.1639i) q^{86} +(-2.62998 - 1.51842i) q^{87} +(-6.26519 + 3.61721i) q^{88} +(-2.27972 - 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(7.64090 + 20.9932i) q^{92} +(1.61002 - 1.91875i) q^{93} +1.45336 q^{94} +3.00000 q^{96} +(-4.73708 + 5.64543i) q^{97} +(4.02936 + 11.0706i) q^{98} +(-0.529563 - 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 - 6 * q^9	\( 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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