LMFDB - Embedded newform 475.2.l.a.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 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:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	475.301
Dual form			475.2.l.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93969 + 1.62760i) q^{2} +(-0.613341 + 0.223238i) q^{3} +(0.766044 + 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-1.97178 + 1.65452i) q^{9} +O(q^{10})$	\(q+(1.93969 + 1.62760i) q^{2} +(-0.613341 + 0.223238i) q^{3} +(0.766044 + 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-1.97178 + 1.65452i) q^{9} +(0.592396 - 1.02606i) q^{11} +(-1.43969 - 2.49362i) q^{12} +(2.55303 + 0.929228i) q^{13} +(-0.673648 + 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.97178 - 2.49362i) q^{17} -6.51754 q^{18} +(0.819078 - 4.28125i) q^{19} +(-0.766044 - 0.642788i) q^{21} +(2.81908 - 1.02606i) q^{22} +(0.879385 + 4.98724i) q^{23} +(0.692066 - 3.92490i) q^{24} +(3.43969 + 5.95772i) q^{26} +(1.81908 - 3.15074i) q^{27} +(-5.17752 + 4.34445i) q^{28} +(-3.56418 + 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(-0.134285 + 0.761570i) q^{33} +(-1.70574 - 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} +4.10607 q^{37} +(8.55690 - 6.97118i) q^{38} -1.77332 q^{39} +(9.38326 - 3.41523i) q^{41} +(-0.439693 - 2.49362i) q^{42} +(1.51114 - 8.57013i) q^{43} +(4.91147 + 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(-0.439693 + 0.368946i) q^{47} +(3.31908 - 2.78504i) q^{48} +(2.32635 - 4.02936i) q^{49} +(2.37939 + 0.866025i) q^{51} +(-2.08125 + 11.8034i) q^{52} +(-0.511144 - 2.89884i) q^{53} +(8.65657 - 3.15074i) q^{54} -9.35504 q^{56} +(0.453363 + 2.80872i) q^{57} -11.7811 q^{58} +(-3.01501 - 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(-3.70574 - 1.34878i) q^{63} +(0.819078 + 1.41868i) q^{64} +(-1.50000 + 1.25865i) q^{66} +(2.97771 - 2.49860i) q^{67} +(8.55690 - 14.8210i) q^{68} +(-1.65270 - 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(-2.72921 - 15.4781i) q^{72} +(5.75877 - 2.09602i) q^{73} +(7.96451 + 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} +1.81521 q^{77} +(-3.43969 - 2.88624i) q^{78} +(-9.21688 + 3.35467i) q^{79} +(0.928548 - 5.26606i) q^{81} +(23.7592 + 8.64766i) q^{82} +(6.15910 + 10.6679i) q^{83} +(2.20574 - 3.82045i) q^{84} +(16.8799 - 14.1639i) q^{86} +(1.51842 - 2.62998i) q^{87} +(3.61721 + 6.26519i) q^{88} +(2.27972 + 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(-20.9932 + 7.64090i) q^{92} +(-1.91875 - 1.61002i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(-5.64543 - 4.73708i) q^{97} +(11.0706 - 4.02936i) q^{98} +(0.529563 + 3.00330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 3 * q^29 + 9 * q^31 - 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 + 21 * q^41 + 3 * q^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * 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 $

$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.972216	+	0.234087i	$0.0752101\pi$
$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.399354	+	0.916797i	$0.369234\pi$
$3$	−0.613341	+	0.223238i	−0.354112	+	0.128886i	−0.512950	−	0.858418i	$-0.671448\pi$
$3$	−0.613341	+	0.223238i	−0.354112	+	0.128886i	0.158838	+	0.987305i	$0.449225\pi$
$4$	0.766044	+	4.34445i	0.383022	+	2.17223i
$5$		0			0
$5$		0			0
$6$	−1.55303	−	0.565258i	−0.634023	−	0.230766i
$7$	0.766044	+	1.32683i	0.289538	+	0.501494i	0.973699	−	0.227836i	$-0.0731651\pi$
$7$	0.766044	+	1.32683i	0.289538	+	0.501494i	−0.684162	+	0.729330i	$0.739832\pi$
$8$	−3.05303	+	5.28801i	−1.07941	+	1.86959i
$9$	−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	$0.109505\pi$
$12$	−1.43969	−	2.49362i	−0.415603	−	0.719846i
$13$	2.55303	+	0.929228i	0.708084	+	0.257722i	0.670859	−	0.741585i	$-0.265926\pi$
$13$	2.55303	+	0.929228i	0.708084	+	0.257722i	0.0372256	+	0.999307i	$0.488148\pi$
$14$	−0.673648	+	3.82045i	−0.180040	+	1.02106i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−2.97178	−	2.49362i	−0.720763	−	0.604792i	0.206833	−	0.978376i	$-0.433684\pi$
$17$	−2.97178	−	2.49362i	−0.720763	−	0.604792i	−0.927596	+	0.373584i	$0.878129\pi$
$18$	−6.51754			−1.53620
$19$	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
$22$	2.81908	−	1.02606i	0.601029	−	0.218757i
$23$	0.879385	+	4.98724i	0.183364	+	1.03991i	0.928039	+	0.372484i	$0.121494\pi$
$23$	0.879385	+	4.98724i	0.183364	+	1.03991i	−0.744674	+	0.667428i	$0.767395\pi$
$24$	0.692066	−	3.92490i	0.141267	−	0.801168i
$25$		0			0
$26$	3.43969	+	5.95772i	0.674579	+	1.16841i
$27$	1.81908	−	3.15074i	0.350082	−	0.606359i
$28$	−5.17752	+	4.34445i	−0.978459	+	0.821025i
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	−0.910641	−	0.413198i	$-0.864412\pi$
$29$	−3.56418	+	2.99070i	−0.661851	+	0.555359i	0.248790	+	0.968557i	$0.419967\pi$
$30$		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	$0.721342\pi$
$32$	−4.31908	−	1.57202i	−0.763512	−	0.277896i
$33$	−0.134285	+	0.761570i	−0.0233761	+	0.132572i
$34$	−1.70574	−	9.67372i	−0.292531	−	1.65903i
$35$		0			0
$36$	−8.69846	−	7.29888i	−1.44974	−	1.21648i
$37$	4.10607			0.675033			0.337517	−	0.941320i	$-0.390413\pi$
$37$	4.10607			0.675033			0.337517	+	0.941320i	$0.390413\pi$
$38$	8.55690	−	6.97118i	1.38811	−	1.13088i
$39$	−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	$0.104244\pi$
$42$	−0.439693	−	2.49362i	−0.0678460	−	0.384774i
$43$	1.51114	−	8.57013i	0.230447	−	1.30693i	−0.621545	−	0.783378i	$-0.713495\pi$
$43$	1.51114	−	8.57013i	0.230447	−	1.30693i	0.851993	−	0.523554i	$-0.175394\pi$
$44$	4.91147	+	1.78763i	0.740433	+	0.269495i
$45$		0			0
$46$	−6.41147	+	11.1050i	−0.945320	+	1.63734i
$47$	−0.439693	+	0.368946i	−0.0641358	+	0.0538163i	−0.674292	−	0.738465i	$-0.735551\pi$
$47$	−0.439693	+	0.368946i	−0.0641358	+	0.0538163i	0.610156	+	0.792281i	$0.291107\pi$
$48$	3.31908	−	2.78504i	0.479068	−	0.401985i
$49$	2.32635	−	4.02936i	0.332336	−	0.575623i
$50$		0			0
$51$	2.37939	+	0.866025i	0.333181	+	0.121268i
$52$	−2.08125	+	11.8034i	−0.288618	+	1.63683i
$53$	−0.511144	−	2.89884i	−0.0702111	−	0.398187i	−0.999579	−	0.0290308i	$-0.990758\pi$
$53$	−0.511144	−	2.89884i	−0.0702111	−	0.398187i	0.929367	−	0.369156i	$-0.120353\pi$
$54$	8.65657	−	3.15074i	1.17801	−	0.428761i
$55$		0			0
$56$	−9.35504			−1.25012
$57$	0.453363	+	2.80872i	0.0600494	+	0.372023i
$58$	−11.7811			−1.54693
$59$	−3.01501	−	2.52990i	−0.392521	−	0.329365i	0.425073	−	0.905159i	$-0.360248\pi$
$59$	−3.01501	−	2.52990i	−0.392521	−	0.329365i	−0.817595	+	0.575794i	$0.804693\pi$
$60$		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	$-0.148947\pi$
$62$	−1.68732	+	9.56926i	−0.214290	+	1.21530i
$63$	−3.70574	−	1.34878i	−0.466879	−	0.169930i
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$		0			0
$66$	−1.50000	+	1.25865i	−0.184637	+	0.154929i
$67$	2.97771	−	2.49860i	0.363785	−	0.305252i	−0.442512	−	0.896763i	$-0.645913\pi$
$67$	2.97771	−	2.49860i	0.363785	−	0.305252i	0.806297	+	0.591510i	$0.201468\pi$
$68$	8.55690	−	14.8210i	1.03768	−	1.79731i
$69$	−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	$0.920538\pi$
$72$	−2.72921	−	15.4781i	−0.321640	−	1.82411i
$73$	5.75877	−	2.09602i	0.674013	−	0.245321i	0.0177383	−	0.999843i	$-0.494353\pi$
$73$	5.75877	−	2.09602i	0.674013	−	0.245321i	0.656275	+	0.754522i	$0.272131\pi$
$74$	7.96451	+	6.68302i	0.925855	+	0.776885i
$75$		0			0
$76$	19.2271	+	0.278817i	2.20551	+	0.0319825i
$77$	1.81521			0.206862
$78$	−3.43969	−	2.88624i	−0.389468	−	0.326803i
$79$	−9.21688	+	3.35467i	−1.03698	+	0.377430i	−0.803735	−	0.594988i	$-0.797157\pi$
$79$	−9.21688	+	3.35467i	−1.03698	+	0.377430i	−0.233246	+	0.972418i	$0.574935\pi$
$80$		0			0
$81$	0.928548	−	5.26606i	0.103172	−	0.585118i
$82$	23.7592	+	8.64766i	2.62377	+	0.954974i
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	0.976161	+	0.217047i	$0.0696426\pi$
$83$	6.15910	+	10.6679i	0.676049	+	1.17095i	−0.300112	+	0.953904i	$0.597024\pi$
$84$	2.20574	−	3.82045i	0.240666	−	0.416845i
$85$		0			0
$86$	16.8799	−	14.1639i	1.82020	−	1.52733i
$87$	1.51842	−	2.62998i	0.162792	−	0.281963i
$88$	3.61721	+	6.26519i	0.385596	+	0.667872i
$89$	2.27972	+	0.829748i	0.241649	+	0.0879532i	0.460006	−	0.887916i	$-0.347847\pi$
$89$	2.27972	+	0.829748i	0.241649	+	0.0879532i	−0.218356	+	0.975869i	$0.570070\pi$
$90$		0			0
$91$	0.722811	+	4.09927i	0.0757712	+	0.429720i
$92$	−20.9932	+	7.64090i	−2.18869	+	0.796619i
$93$	−1.91875	−	1.61002i	−0.198965	−	0.166951i
$94$	−1.45336			−0.149903
$95$		0			0
$96$	3.00000			0.306186
$97$	−5.64543	−	4.73708i	−0.573207	−	0.480977i	0.309502	−	0.950899i	$-0.399838\pi$
$97$	−5.64543	−	4.73708i	−0.573207	−	0.480977i	−0.882708	+	0.469922i	$0.844282\pi$
$98$	11.0706	−	4.02936i	1.11830	−	0.407027i
$99$	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	$0.645547\pi$
$102$	3.20574	+	5.55250i	0.317415	+	0.549779i
$103$	−6.23783	+	10.8042i	−0.614631	+	1.06457i	0.375818	+	0.926694i	$0.377362\pi$
$103$	−6.23783	+	10.8042i	−0.614631	+	1.06457i	−0.990449	+	0.137879i	$0.955971\pi$
$104$	−12.7083	+	10.6635i	−1.24615	+	1.04564i
$105$		0			0
$106$	3.72668	−	6.45480i	0.361967	−	0.626946i
$107$	−3.34002	−	5.78509i	−0.322892	−	0.559266i	0.658191	−	0.752851i	$-0.271322\pi$
$107$	−3.34002	−	5.78509i	−0.322892	−	0.559266i	−0.981083	+	0.193585i	$0.937988\pi$
$108$	15.0817	+	5.48930i	1.45124	+	0.528208i
$109$	1.64156	−	9.30975i	0.157233	−	0.891712i	−0.799483	−	0.600689i	$-0.794893\pi$
$109$	1.64156	−	9.30975i	0.157233	−	0.891712i	0.956716	−	0.291023i	$-0.0939957\pi$
$110$		0			0
$111$	−2.51842	+	0.916629i	−0.239038	+	0.0870026i
$112$	−7.79086	−	6.53731i	−0.736167	−	0.617717i
$113$	−1.31046			−0.123278			−0.0616388	−	0.998099i	$-0.519633\pi$
$113$	−1.31046			−0.123278			−0.0616388	+	0.998099i	$0.519633\pi$
$114$	−3.69207	+	6.18594i	−0.345794	+	0.579366i
$115$		0			0
$116$	−15.7233	−	13.1934i	−1.45987	−	1.22498i
$117$	−6.57145	+	2.39181i	−0.607531	+	0.221123i
$118$	−1.73055	−	9.81445i	−0.159310	−	0.903493i
$119$	1.03209	−	5.85327i	0.0946114	−	0.536568i
$120$		0			0
$121$	4.79813	+	8.31061i	0.436194	+	0.755510i
$122$	5.71941	−	9.90630i	0.517811	−	0.896875i
$123$	−4.99273	+	4.18939i	−0.450179	+	0.377745i
$124$	−12.9684	+	10.8818i	−1.16459	+	0.977211i
$125$		0			0
$126$	−4.99273	−	8.64766i	−0.444787	−	0.770394i
$127$	−13.6284	−	4.96032i	−1.20932	−	0.440157i	−0.342853	−	0.939389i	$-0.611393\pi$
$127$	−13.6284	−	4.96032i	−1.20932	−	0.440157i	−0.866468	+	0.499232i	$0.833615\pi$
$128$	−2.31655	+	13.1378i	−0.204756	+	1.16123i
$129$	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	$-0.610671\pi$
$132$	−3.41147			−0.296931
$133$	6.30793	−	2.19285i	0.546967	−	0.190144i
$134$	9.84255			0.850267
$135$		0			0
$136$	22.2592	−	8.10170i	1.90871	−	0.694715i
$137$	−1.77197	−	10.0494i	−0.151390	−	0.858575i	−0.962012	−	0.273006i	$-0.911982\pi$
$137$	−1.77197	−	10.0494i	−0.151390	−	0.858575i	0.810622	−	0.585569i	$-0.199129\pi$
$138$	1.45336	−	8.24243i	0.123718	−	0.701642i
$139$	1.56031	+	0.567905i	0.132344	+	0.0481691i	0.407343	−	0.913275i	$-0.366455\pi$
$139$	1.56031	+	0.567905i	0.132344	+	0.0481691i	−0.274999	+	0.961444i	$0.588678\pi$
$140$		0			0
$141$	0.187319	−	0.324446i	0.0157751	−	0.0273232i
$142$	−13.4534	+	11.2887i	−1.12898	+	0.947328i
$143$	2.46585	−	2.06910i	0.206205	−	0.173026i
$144$	8.54323	−	14.7973i	0.711936	−	1.23311i
$145$		0			0
$146$	14.5817	+	5.30731i	1.20679	+	0.439236i
$147$	−0.527341	+	2.99070i	−0.0434944	+	0.246669i
$148$	3.14543	+	17.8386i	0.258553	+	1.46633i
$149$	−10.5312	+	3.83305i	−0.862750	+	0.314015i	−0.735228	−	0.677820i	$-0.762925\pi$
$149$	−10.5312	+	3.83305i	−0.862750	+	0.314015i	−0.127523	+	0.991836i	$0.540703\pi$
$150$		0			0
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$	20.1386	+	17.4021i	1.63346	+	1.41150i
$153$	9.98545			0.807276
$154$	3.52094	+	2.95442i	0.283726	+	0.238074i
$155$		0			0
$156$	−1.35844	−	7.70410i	−0.108762	−	0.616822i
$157$	−1.90895	+	10.8262i	−0.152351	+	0.864023i	0.808817	+	0.588060i	$0.200108\pi$
$157$	−1.90895	+	10.8262i	−0.152351	+	0.864023i	−0.961168	+	0.275964i	$0.911003\pi$
$158$	−23.3380	−	8.49432i	−1.85667	−	0.675772i
$159$	0.960637	+	1.66387i	0.0761835	+	0.131954i
$160$		0			0
$161$	−5.94356	+	4.98724i	−0.468418	+	0.393050i
$162$	10.3721	−	8.70323i	0.814910	−	0.683791i
$163$	−3.16637	+	5.48432i	−0.248010	+	0.429565i	−0.962973	−	0.269596i	$-0.913110\pi$
$163$	−3.16637	+	5.48432i	−0.248010	+	0.429565i	0.714964	+	0.699161i	$0.246443\pi$
$164$	22.0253	+	38.1489i	1.71989	+	2.97893i
$165$		0			0
$166$	−5.41622	+	30.7169i	−0.420380	+	2.38410i
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	0.925770	+	0.378087i	$0.123418\pi$
$167$	2.39259	+	13.5690i	0.185144	+	1.05000i	−0.740626	+	0.671917i	$0.765471\pi$
$168$	5.73783	−	2.08840i	0.442683	−	0.161123i
$169$	−4.30406	−	3.61154i	−0.331082	−	0.277811i
$170$		0			0
$171$	5.46838	+	9.79687i	0.418177	+	0.749186i
$172$	38.3901			2.92722
$173$	−19.3405	−	16.2286i	−1.47043	−	1.23384i	−0.915734	−	0.401784i	$-0.868390\pi$
$173$	−19.3405	−	16.2286i	−1.47043	−	1.23384i	−0.554696	−	0.832053i	$-0.687165\pi$
$174$	7.22580	−	2.62998i	0.547787	−	0.199378i
$175$		0			0
$176$	−1.36571	+	7.74535i	−0.102945	+	0.583828i
$177$	2.41400	+	0.878624i	0.181447	+	0.0660414i
$178$	3.07145	+	5.31991i	0.230215	+	0.398744i
$179$	−2.91534	+	5.04952i	−0.217903	+	0.377419i	−0.954167	−	0.299276i	$-0.903255\pi$
$179$	−2.91534	+	5.04952i	−0.217903	+	0.377419i	0.736264	+	0.676695i	$0.236588\pi$
$180$		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	$0.109627\pi$
$182$	−5.26991	+	9.12776i	−0.390632	+	0.676595i
$183$	1.47431	+	2.55358i	0.108984	+	0.188766i
$184$	−29.0574	−	10.5760i	−2.14214	−	0.779674i
$185$		0			0
$186$	−1.10132	−	6.24589i	−0.0807526	−	0.457971i
$187$	−4.31908	+	1.57202i	−0.315842	+	0.114957i
$188$	−1.93969	−	1.62760i	−0.141467	−	0.118705i
$189$	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	$0.621350\pi$
$192$	−0.819078	−	0.687288i	−0.0591119	−	0.0496007i
$193$	12.9684	−	4.72010i	0.933484	−	0.339760i	0.169895	−	0.985462i	$-0.445657\pi$
$193$	12.9684	−	4.72010i	0.933484	−	0.339760i	0.763590	+	0.645702i	$0.223435\pi$
$194$	−3.24035	−	18.3770i	−0.232644	−	1.31939i
$195$		0			0
$196$	19.2875	+	7.02006i	1.37768	+	0.501433i
$197$	−3.97044	−	6.87700i	−0.282882	−	0.489966i	0.689211	−	0.724560i	$-0.257957\pi$
$197$	−3.97044	−	6.87700i	−0.282882	−	0.489966i	−0.972093	+	0.234594i	$0.924624\pi$
$198$	−3.86097	+	6.68739i	−0.274387	+	0.475252i
$199$	20.7101	−	17.3778i	1.46810	−	1.23188i	0.550219	−	0.835020i	$-0.314544\pi$
$199$	20.7101	−	17.3778i	1.46810	−	1.23188i	0.917879	−	0.396861i	$-0.129900\pi$
$200$		0			0
$201$	−1.26857	+	2.19723i	−0.0894781	+	0.154981i
$202$	−2.74763	−	4.75903i	−0.193322	−	0.334844i
$203$	−6.69846	−	2.43804i	−0.470140	−	0.171117i
$204$	−1.93969	+	11.0005i	−0.135806	+	0.770192i
$205$		0			0
$206$	−29.6844	+	10.8042i	−2.06821	+	0.752766i
$207$	−9.98545	−	8.37879i	−0.694037	−	0.582366i
$208$	−18.0351			−1.25051
$209$	−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	$0.811843\pi$
$212$	12.2023	−	4.44129i	0.838060	−	0.305029i
$213$	−0.786112	−	4.45826i	−0.0538635	−	0.305475i
$214$	2.93717	−	16.6575i	0.200781	−	1.13868i
$215$		0			0
$216$	11.1074	+	19.2386i	0.755764	+	1.30902i
$217$	−2.93969	+	5.09170i	−0.199559	+	0.345647i
$218$	18.3366	−	15.3863i	1.24191	−	1.04209i
$219$	−3.06418	+	2.57115i	−0.207058	+	0.173742i
$220$		0			0
$221$	−5.26991	−	9.12776i	−0.354493	−	0.614000i
$222$	−6.37686	−	2.32099i	−0.427987	−	0.155774i
$223$	2.68732	−	15.2405i	0.179956	−	1.02058i	−0.752310	−	0.658809i	$-0.771060\pi$
$223$	2.68732	−	15.2405i	0.179956	−	1.02058i	0.932266	−	0.361773i	$-0.117828\pi$
$224$	−1.22281	−	6.93491i	−0.0817025	−	0.463358i
$225$		0			0
$226$	−2.54189	−	2.13290i	−0.169084	−	0.141878i
$227$	−9.87258			−0.655266			−0.327633	−	0.944805i	$-0.606251\pi$
$227$	−9.87258			−0.655266			−0.327633	+	0.944805i	$0.606251\pi$
$228$	−11.8550	+	4.12122i	−0.785119	+	0.272934i
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$		0			0
$231$	−1.11334	+	0.405223i	−0.0732524	+	0.0266617i
$232$	−4.93330	−	27.9781i	−0.323887	−	1.83685i
$233$	−0.613808	+	3.48108i	−0.0402119	+	0.228053i	−0.998290	−	0.0584538i	$-0.981383\pi$
$233$	−0.613808	+	3.48108i	−0.0402119	+	0.228053i	0.958078	+	0.286507i	$0.0924941\pi$
$234$	−16.6395	−	6.05628i	−1.08776	−	0.395912i
$235$		0			0
$236$	8.68139	−	15.0366i	0.565110	−	0.978800i
$237$	4.90420	−	4.11511i	0.318562	−	0.267305i
$238$	11.5287	−	9.67372i	0.747294	−	0.627054i
$239$	−5.98680	+	10.3694i	−0.387254	+	0.670743i	−0.992079	−	0.125615i	$-0.959910\pi$
$239$	−5.98680	+	10.3694i	−0.387254	+	0.670743i	0.604825	+	0.796358i	$0.293243\pi$
$240$		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	$0.747517\pi$
$242$	−4.21941	+	23.9294i	−0.271234	+	1.53824i
$243$	2.50134	+	14.1858i	0.160461	+	0.910021i
$244$	18.7271	−	6.81612i	1.19888	−	0.436358i
$245$		0			0
$246$	−16.5030			−1.05219
$247$	6.06939	−	10.1691i	0.386186	−	0.647042i
$248$	−23.4320			−1.48793
$249$	−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	$0.794696\pi$
$252$	3.02094	−	17.1326i	0.190302	−	1.07925i
$253$	5.63816	+	2.05212i	0.354468	+	0.129016i
$254$	−18.3614	−	31.8029i	−1.15210	−	1.99549i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	−3.81315	+	3.19961i	−0.237858	+	0.199586i	−0.753923	−	0.656963i	$-0.771841\pi$
$257$	−3.81315	+	3.19961i	−0.237858	+	0.199586i	0.516065	+	0.856549i	$0.327396\pi$
$258$	−7.19119	+	12.4555i	−0.447704	+	0.775446i
$259$	3.14543	+	5.44804i	0.195447	+	0.338525i
$260$		0			0
$261$	2.07960	−	11.7940i	0.128724	−	0.730031i
$262$	−8.70961	−	49.3946i	−0.538081	−	3.05161i
$263$	−22.5929	+	8.22313i	−1.39314	+	0.507060i	−0.926133	−	0.377196i	$-0.876888\pi$
$263$	−22.5929	+	8.22313i	−1.39314	+	0.507060i	−0.467002	+	0.884256i	$0.654666\pi$
$264$	−3.61721	−	3.03520i	−0.222624	−	0.186804i
$265$		0			0
$266$	15.8045	+	6.01330i	0.969038	+	0.368699i
$267$	−1.58347			−0.0969070
$268$	13.1361	+	11.0225i	0.802415	+	0.673306i
$269$	12.3204	−	4.48427i	0.751189	−	0.273411i	0.0620832	−	0.998071i	$-0.480226\pi$
$269$	12.3204	−	4.48427i	0.751189	−	0.273411i	0.689106	+	0.724660i	$0.258003\pi$
$270$		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	$0.756644\pi$
$272$	24.1989	+	8.80769i	1.46728	+	0.534045i
$273$	−1.35844	−	2.35289i	−0.0822166	−	0.142403i
$274$	12.9192	−	22.3767i	0.780478	−	1.35183i
$275$		0			0
$276$	11.1702	−	9.37295i	0.672370	−	0.564185i
$277$	−8.25537	+	14.2987i	−0.496017	+	0.859127i	−0.999989	−	0.00459317i	$-0.998538\pi$
$277$	−8.25537	+	14.2987i	−0.496017	+	0.859127i	0.503973	+	0.863720i	$0.331871\pi$
$278$	2.10220	+	3.64111i	0.126081	+	0.218379i
$279$	−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	$-0.251862\pi$
$282$	0.891407	−	0.324446i	0.0530825	−	0.0193205i
$283$	8.66431	+	7.27022i	0.515040	+	0.432170i	0.862899	−	0.505377i	$-0.168647\pi$
$283$	8.66431	+	7.27022i	0.515040	+	0.432170i	−0.347859	+	0.937547i	$0.613091\pi$
$284$	−30.5972			−1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	11.7194	+	9.83375i	0.691775	+	0.580468i
$288$	11.1172	−	4.04633i	0.655088	−	0.238433i
$289$	−0.338678	−	1.92074i	−0.0199222	−	0.112985i
$290$		0			0
$291$	4.52007	+	1.64517i	0.264971	+	0.0964416i
$292$	13.5175	+	23.4131i	0.791054	+	1.37015i
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	−0.803445	−	0.595379i	$-0.797002\pi$
$293$	1.94949	−	3.37662i	0.113891	−	0.197264i	0.917336	+	0.398115i	$0.130335\pi$
$294$	−5.89053	+	4.94274i	−0.343543	+	0.288267i
$295$		0			0
$296$	−12.5360	+	21.7129i	−0.728638	+	1.26204i
$297$	−2.15523	−	3.73297i	−0.125059	−	0.216609i
$298$	−26.6660	−	9.70562i	−1.54472	−	0.562231i
$299$	−2.38919	+	13.5497i	−0.138170	+	0.783602i
$300$		0			0
$301$	12.5287	−	4.56007i	0.722141	−	0.262838i
$302$	−21.4179	−	17.9717i	−1.23246	−	1.03416i
$303$	1.41653			0.0813773
$304$	4.61081	+	28.5653i	0.264448	+	1.63833i
$305$		0			0
$306$	19.3687	+	16.2523i	1.10724	+	0.929081i
$307$	21.7777	−	7.92642i	1.24292	−	0.452385i	0.364914	−	0.931041i	$-0.381098\pi$
$307$	21.7777	−	7.92642i	1.24292	−	0.452385i	0.878002	+	0.478657i	$0.158876\pi$
$308$	1.39053	+	7.88609i	0.0792328	+	0.449351i
$309$	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	$0.802047\pi$
$312$	5.41400	−	9.37732i	0.306507	−	0.530886i
$313$	17.5346	−	14.7133i	0.991115	−	0.831644i	0.00538626	−	0.999985i	$-0.498285\pi$
$313$	17.5346	−	14.7133i	0.991115	−	0.831644i	0.985729	+	0.168341i	$0.0538410\pi$
$314$	−21.3234	+	17.8925i	−1.20335	+	1.00973i
$315$		0			0
$316$	−21.6348	−	37.4725i	−1.21705	−	2.10799i
$317$	24.5453	+	8.93378i	1.37860	+	0.501771i	0.921755	−	0.387773i	$-0.126756\pi$
$317$	24.5453	+	8.93378i	1.37860	+	0.501771i	0.456849	+	0.889544i	$0.348978\pi$
$318$	−0.844770	+	4.79093i	−0.0473724	+	0.268662i
$319$	0.957234	+	5.42874i	0.0535948	+	0.303951i
$320$		0			0
$321$	3.34002	+	2.80261i	0.186422	+	0.156427i
$322$	−19.6459			−1.09482
$323$	−13.1099	+	10.6805i	−0.729456	+	0.594277i
$324$	23.5895			1.31053
$325$		0			0
$326$	−15.0680	+	5.48432i	−0.834542	+	0.303748i
$327$	1.07145	+	6.07650i	0.0592514	+	0.336031i
$328$	−10.5876	+	60.0455i	−0.584605	+	3.31546i
$329$	−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	$0.991333\pi$
$332$	−41.6279	+	34.9300i	−2.28463	+	1.91703i
$333$	−8.09627	+	6.79357i	−0.443673	+	0.372286i
$334$	−17.4440	+	30.2139i	−0.954495	+	1.65323i
$335$		0			0
$336$	6.23783	+	2.27038i	0.340301	+	0.123860i
$337$	−0.295445	+	1.67555i	−0.0160939	+	0.0912731i	−0.991797	−	0.127825i	$-0.959200\pi$
$337$	−0.295445	+	1.67555i	−0.0160939	+	0.0912731i	0.975703	+	0.219098i	$0.0703115\pi$
$338$	−2.47044	−	14.0105i	−0.134374	−	0.762073i
$339$	0.803758	−	0.292544i	0.0436542	−	0.0158888i
$340$		0			0
$341$	4.54664			0.246214
$342$	−5.33837	+	27.9032i	−0.288666	+	1.50883i
$343$	17.8530			0.963970
$344$	40.7053	+	34.1558i	2.19468	+	1.84156i
$345$		0			0
$346$	−11.1010	−	62.9570i	−0.596794	−	3.38459i
$347$	0.851167	−	4.82721i	0.0456930	−	0.259138i	−0.953400	−	0.301708i	$-0.902443\pi$
$347$	0.851167	−	4.82721i	0.0456930	−	0.259138i	0.999094	+	0.0425697i	$0.0135544\pi$
$348$	12.5890	+	4.58202i	0.674841	+	0.245622i
$349$	14.0646	+	24.3607i	0.752863	+	1.30400i	0.946430	+	0.322910i	$0.104661\pi$
$349$	14.0646	+	24.3607i	0.752863	+	1.30400i	−0.193566	+	0.981087i	$0.562006\pi$
$350$		0			0
$351$	7.57192	−	6.35359i	0.404159	−	0.339130i
$352$	−4.17159	+	3.50038i	−0.222346	+	0.186571i
$353$	−4.15998	+	7.20529i	−0.221413	+	0.383499i	−0.955237	−	0.295841i	$-0.904400\pi$
$353$	−4.15998	+	7.20529i	−0.221413	+	0.383499i	0.733824	+	0.679340i	$0.237734\pi$
$354$	3.25237	+	5.63328i	0.172862	+	0.299405i
$355$		0			0
$356$	−1.85844	+	10.5397i	−0.0984972	+	0.558605i
$357$	0.673648	+	3.82045i	0.0356532	+	0.202200i
$358$	−13.8735	+	5.04952i	−0.733235	+	0.266876i
$359$	19.0967	+	16.0241i	1.00789	+	0.845718i	0.988057	−	0.154086i	$-0.0492432\pi$
$359$	19.0967	+	16.0241i	1.00789	+	0.845718i	0.0198296	+	0.999803i	$0.493688\pi$
$360$		0			0
$361$	−17.6582	−	7.01336i	−0.929380	−	0.369124i
$362$	34.3405			1.80490
$363$	−4.79813	−	4.02611i	−0.251837	−	0.211316i
$364$	−17.2554	+	6.28044i	−0.904427	+	0.329184i
$365$		0			0
$366$	−1.29648	+	7.35273i	−0.0677683	+	0.384333i
$367$	−2.42989	−	0.884409i	−0.126839	−	0.0461657i	0.277821	−	0.960633i	$-0.410388\pi$
$367$	−2.42989	−	0.884409i	−0.126839	−	0.0461657i	−0.404660	+	0.914467i	$0.632610\pi$
$368$	−16.8084	−	29.1130i	−0.876198	−	1.51762i
$369$	−12.8512	+	22.2589i	−0.669005	+	1.15875i
$370$		0			0
$371$	3.45471	−	2.89884i	0.179359	−	0.150500i
$372$	5.52481	−	9.56926i	0.286448	−	0.496143i
$373$	−11.6917	−	20.2505i	−0.605371	−	1.04853i	−0.991993	−	0.126295i	$-0.959691\pi$
$373$	−11.6917	−	20.2505i	−0.605371	−	1.04853i	0.386622	−	0.922238i	$-0.373642\pi$
$374$	−10.9363	−	3.98048i	−0.565502	−	0.205826i
$375$		0			0
$376$	−0.608593	−	3.45150i	−0.0313858	−	0.177998i
$377$	−11.8785	+	4.32342i	−0.611774	+	0.222668i
$378$	10.8118	+	9.07218i	0.556099	+	0.466623i
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$		0			0
$381$	9.46616			0.484966
$382$	−19.9479	−	16.7383i	−1.02062	−	0.856405i
$383$	−25.8234	+	9.39895i	−1.31951	+	0.480264i	−0.903303	−	0.429003i	$-0.858865\pi$
$383$	−25.8234	+	9.39895i	−1.31951	+	0.480264i	−0.416212	+	0.909268i	$0.636643\pi$
$384$	−1.51202	−	8.57510i	−0.0771600	−	0.437596i
$385$		0			0
$386$	32.8371	+	11.9517i	1.67136	+	0.608327i
$387$	11.1998	+	19.3986i	0.569318	+	0.986088i
$388$	16.2554	−	28.1551i	0.825241	−	1.42936i
$389$	−2.56031	+	2.14835i	−0.129813	+	0.108926i	−0.705383	−	0.708827i	$-0.749225\pi$
$389$	−2.56031	+	2.14835i	−0.129813	+	0.108926i	0.575570	+	0.817753i	$0.304780\pi$
$390$		0			0
$391$	9.82295	−	17.0138i	0.496768	−	0.860427i
$392$	14.2049	+	24.6035i	0.717454	+	1.24267i
$393$	12.1493	+	4.42198i	0.612851	+	0.223060i
$394$	3.49154	−	19.8015i	0.175901	−	0.997587i
$395$		0			0
$396$	−12.6420	+	4.60132i	−0.635286	+	0.231225i
$397$	10.0530	+	8.43550i	0.504547	+	0.423365i	0.859206	−	0.511631i	$-0.170958\pi$
$397$	10.0530	+	8.43550i	0.504547	+	0.423365i	−0.354658	+	0.934996i	$0.615403\pi$
$398$	68.4552			3.43135
$399$	−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	$0.581683\pi$
$402$	−6.03684	+	2.19723i	−0.301090	+	0.109588i
$403$	1.81046	+	10.2676i	0.0901854	+	0.511467i
$404$	1.66250	−	9.42853i	0.0827127	−	0.469087i
$405$		0			0
$406$	−9.02481	−	15.6314i	−0.447894	−	0.775775i
$407$	2.43242	−	4.21307i	0.120571	−	0.208834i
$408$	−11.8439	+	9.93821i	−0.586360	+	0.492015i
$409$	−6.73964	+	5.65523i	−0.333254	+	0.279633i	−0.794024	−	0.607886i	$-0.792018\pi$
$409$	−6.73964	+	5.65523i	−0.333254	+	0.279633i	0.460770	+	0.887519i	$0.347573\pi$
$410$		0			0
$411$	3.33022	+	5.76811i	0.164268	+	0.284520i
$412$	−51.7169	−	18.8234i	−2.54791	−	0.927364i
$413$	1.04710	−	5.93842i	0.0515246	−	0.292211i
$414$	−5.73143	−	32.5046i	−0.281684	−	1.59751i
$415$		0			0
$416$	−9.56599	−	8.02682i	−0.469011	−	0.393547i
$417$	−1.08378			−0.0530728
$418$	−2.08378	−	12.9096i	−0.101921	−	0.631429i
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$		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	$0.351392\pi$
$422$	−3.54916	−	20.1283i	−0.172771	−	0.979830i
$423$	0.256549	−	1.45496i	0.0124738	−	0.0707426i
$424$	16.8897	+	6.14733i	0.820234	+	0.298541i
$425$		0			0
$426$	5.73143	−	9.92713i	0.277689	−	0.480971i
$427$	5.30200	−	4.44891i	0.256582	−	0.215298i
$428$	22.5744	−	18.9422i	1.09118	−	0.915606i
$429$	−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	$0.621107\pi$
$432$	−4.19372	+	23.7837i	−0.201770	+	1.14430i
$433$	−3.44238	−	19.5227i	−0.165430	−	0.938202i	−0.948620	−	0.316419i	$-0.897520\pi$
$433$	−3.44238	−	19.5227i	−0.165430	−	0.938202i	0.783189	−	0.621783i	$-0.213591\pi$
$434$	−13.9893	+	5.09170i	−0.671509	+	0.244409i
$435$		0			0
$436$	41.7033			1.99722
$437$	22.0719	+	0.320070i	1.05584	+	0.0153110i
$438$	−10.1284			−0.483952
$439$	−26.4800	−	22.2193i	−1.26382	−	1.06047i	−0.995264	−	0.0972078i	$-0.969009\pi$
$439$	−26.4800	−	22.2193i	−1.26382	−	1.06047i	−0.268557	−	0.963264i	$-0.586547\pi$
$440$		0			0
$441$	2.07960	+	11.7940i	0.0990287	+	0.561620i
$442$	4.63429	−	26.2823i	0.220430	−	1.25012i
$443$	15.9843	+	5.81780i	0.759436	+	0.276412i	0.692571	−	0.721350i	$-0.256478\pi$
$443$	15.9843	+	5.81780i	0.759436	+	0.276412i	0.0668650	+	0.997762i	$0.478700\pi$
$444$	−5.91147	−	10.2390i	−0.280546	−	0.485920i
$445$		0			0
$446$	30.0180	−	25.1881i	1.42139	−	1.19269i
$447$	5.60354	−	4.70193i	0.265038	−	0.222394i
$448$	−1.25490	+	2.17355i	−0.0592885	+	0.102691i
$449$	−18.7049	−	32.3978i	−0.882737	−	1.52895i	−0.848286	−	0.529539i	$-0.822365\pi$
$449$	−18.7049	−	32.3978i	−0.882737	−	1.52895i	−0.0344512	−	0.999406i	$-0.510968\pi$
$450$		0			0
$451$	2.05438	−	11.6510i	0.0967369	−	0.548622i
$452$	−1.00387	−	5.69323i	−0.0472181	−	0.267787i
$453$	6.77244	−	2.46497i	0.318197	−	0.115814i
$454$	−19.1498	−	16.0686i	−0.898743	−	0.754135i
$455$		0			0
$456$	−16.2366	−	6.17771i	−0.760351	−	0.289298i
$457$	−9.11112			−0.426200			−0.213100	−	0.977030i	$-0.568356\pi$
$457$	−9.11112			−0.426200			−0.213100	+	0.977030i	$0.568356\pi$
$458$	39.0244	+	32.7454i	1.82349	+	1.53009i
$459$	−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	$0.862756\pi$
$462$	−2.81908	−	1.02606i	−0.131155	−	0.0477367i
$463$	−0.125362	−	0.217134i	−0.00582609	−	0.0100911i	0.863098	−	0.505037i	$-0.168521\pi$
$463$	−0.125362	−	0.217134i	−0.00582609	−	0.0100911i	−0.868924	+	0.494946i	$0.835188\pi$
$464$	15.4427	−	26.7475i	0.716909	−	1.24172i
$465$		0			0
$466$	−6.85638	+	5.75319i	−0.317616	+	0.266511i
$467$	7.68092	−	13.3037i	0.355431	−	0.615624i	−0.631761	−	0.775163i	$-0.717668\pi$
$467$	7.68092	−	13.3037i	0.355431	−	0.615624i	0.987192	+	0.159539i	$0.0510009\pi$
$468$	−15.4251	−	26.7171i	−0.713028	−	1.23500i
$469$	5.59627	+	2.03687i	0.258412	+	0.0940541i
$470$		0			0
$471$	−1.24598	−	7.06629i	−0.0574116	−	0.325597i
$472$	22.5831	−	8.21956i	1.03947	−	0.378336i
$473$	−7.89827	−	6.62744i	−0.363163	−	0.304730i
$474$	16.2104			0.744567
$475$		0			0
$476$	26.2199			1.20179
$477$	5.80406	+	4.87019i	0.265750	+	0.222991i
$478$	−28.4898	+	10.3694i	−1.30309	+	0.474287i
$479$	−0.124896	−	0.708319i	−0.00570663	−	0.0323639i	0.981821	−	0.189807i	$-0.0607861\pi$
$479$	−0.124896	−	0.708319i	−0.00570663	−	0.0323639i	−0.987528	+	0.157443i	$0.949675\pi$
$480$		0			0
$481$	10.4829	+	3.81547i	0.477980	+	0.173971i
$482$	−16.3341	−	28.2915i	−0.743998	−	1.28864i
$483$	2.53209	−	4.38571i	0.115214	−	0.199557i
$484$	−32.4295	+	27.2116i	−1.47407	+	1.23689i
$485$		0			0
$486$	−18.2369	+	31.5873i	−0.827245	+	1.43283i
$487$	5.87346	+	10.1731i	0.266152	+	0.460988i	0.967865	−	0.251471i	$-0.0809145\pi$
$487$	5.87346	+	10.1731i	0.266152	+	0.460988i	−0.701713	+	0.712460i	$0.747581\pi$
$488$	25.9209	+	9.43442i	1.17338	+	0.427076i
$489$	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	$0.389527\pi$
$492$	−22.0253	−	18.4814i	−0.992976	−	0.833206i
$493$	18.0496			0.812914
$494$	28.3239	−	9.84635i	1.27435	−	0.443008i
$495$		0			0
$496$	−19.5141	−	16.3743i	−0.876211	−	0.735228i
$497$	−9.98545	+	3.63441i	−0.447909	+	0.163025i
$498$	−3.53519	−	20.0490i	−0.158416	−	0.898419i
$499$	2.55097	−	14.4673i	0.114197	−	0.647645i	−0.872947	−	0.487815i	$-0.837794\pi$
$499$	2.55097	−	14.4673i	0.114197	−	0.647645i	0.987145	−	0.159830i	$-0.0510947\pi$
$500$		0			0
$501$	−4.49660	−	7.78833i	−0.200893	−	0.347957i
$502$	−18.1839	+	31.4955i	−0.811588	+	1.40571i
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	−0.555183	−	0.831728i	$-0.687352\pi$
$503$	3.75671	−	3.15225i	0.167503	−	0.140552i	0.722686	+	0.691176i	$0.242907\pi$
$504$	18.4461	−	15.4781i	0.821654	−	0.689450i
$505$		0			0
$506$	7.59627	+	13.1571i	0.337695	+	0.584905i
$507$	3.44609	+	1.25427i	0.153046	+	0.0557043i
$508$	11.1099	−	63.0076i	0.492924	−	2.79551i
$509$	1.11375	+	6.31640i	0.0493662	+	0.279969i	0.999491	−	0.0319002i	$-0.0101559\pi$
$509$	1.11375	+	6.31640i	0.0493662	+	0.279969i	−0.950125	+	0.311870i	$0.899045\pi$
$510$		0			0
$511$	7.19253	+	6.03525i	0.318179	+	0.266984i
$512$	−50.5553			−2.23425
$513$	−11.9991	−	10.3686i	−0.529774	−	0.457786i
$514$	−12.6040			−0.555939
$515$		0			0
$516$	−23.5462	+	8.57013i	−1.03656	+	0.377279i
$517$	0.118089	+	0.669713i	0.00519353	+	0.0294540i
$518$	−2.76604	+	15.6870i	−0.121533	+	0.689248i
$519$	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	$-0.120418\pi$
$522$	23.2297	−	19.4920i	1.01674	−	0.853142i
$523$	−29.7015	+	24.9225i	−1.29875	+	1.08978i	−0.308395	+	0.951258i	$0.599792\pi$
$523$	−29.7015	+	24.9225i	−1.29875	+	1.08978i	−0.990359	+	0.138526i	$0.955764\pi$
$524$	43.6921	−	75.6770i	1.90870	−	3.30596i
$525$		0			0
$526$	−57.2071	−	20.8217i	−2.49435	−	0.907869i
$527$	2.58512	−	14.6610i	0.112610	−	0.638641i
$528$	−0.891407	−	5.05542i	−0.0387935	−	0.220009i
$529$	−2.48633	+	0.904950i	−0.108101	+	0.0393456i
$530$		0			0
$531$	10.1307			0.439636
$532$	14.3589	+	25.7247i	0.622538	+	1.11531i
$533$	27.1293			1.17510
$534$	−3.07145	−	2.57725i	−0.132915	−	0.111529i
$535$		0			0
$536$	4.12155	+	23.3745i	0.178024	+	1.00962i
$537$	0.660855	−	3.74789i	0.0285180	−	0.161734i
$538$	31.1964	+	11.3546i	1.34497	+	0.489530i
$539$	−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	$0.212381\pi$
$542$	−51.5374	+	43.2450i	−2.21372	+	1.85753i
$543$	−4.42602	+	7.66610i	−0.189939	+	0.328984i
$544$	8.91534	+	15.4418i	0.382242	+	0.662063i
$545$		0			0
$546$	1.19459	−	6.77487i	0.0511238	−	0.289938i
$547$	−2.46791	−	13.9962i	−0.105520	−	0.598435i	−0.991011	−	0.133779i	$-0.957289\pi$
$547$	−2.46791	−	13.9962i	−0.105520	−	0.598435i	0.885491	−	0.464657i	$-0.153822\pi$
$548$	42.3016	−	15.3965i	1.80703	−	0.657707i
$549$	8.90760	+	7.47437i	0.380167	+	0.318998i
$550$		0			0
$551$	9.88460	+	17.7088i	0.421098	+	0.754418i
$552$	20.1830			0.859047
$553$	−11.5116	−	9.65939i	−0.489524	−	0.410759i
$554$	−39.2854	+	14.2987i	−1.66908	+	0.607494i
$555$		0			0
$556$	−1.27197	+	7.21372i	−0.0539437	+	0.305930i
$557$	21.1805	+	7.70908i	0.897447	+	0.326644i	0.749229	−	0.662311i	$-0.230424\pi$
$557$	21.1805	+	7.70908i	0.897447	+	0.326644i	0.148218	+	0.988955i	$0.452646\pi$
$558$	−12.5055	−	21.6602i	−0.529401	−	0.916949i
$559$	11.8216	−	20.4756i	0.500001	−	0.866026i
$560$		0			0
$561$	2.29813	−	1.92836i	0.0970273	−	0.0814155i
$562$	24.5488	−	42.5197i	1.03553	−	1.79358i
$563$	−21.4859	−	37.2147i	−0.905524	−	1.56841i	−0.820213	−	0.572058i	$-0.806145\pi$
$563$	−21.4859	−	37.2147i	−0.905524	−	1.56841i	−0.0853106	−	0.996354i	$-0.527188\pi$
$564$	1.55303	+	0.565258i	0.0653945	+	0.0238017i
$565$		0			0
$566$	4.97313	+	28.2040i	0.209036	+	1.18550i
$567$	7.69846	−	2.80201i	0.323305	−	0.117673i
$568$	−32.4424	−	27.2224i	−1.36125	−	1.14223i
$569$	7.42696			0.311354			0.155677	−	0.987808i	$-0.450244\pi$
$569$	7.42696			0.311354			0.155677	+	0.987808i	$0.450244\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	10.8780	+	9.12776i	0.454834	+	0.381651i
$573$	6.30763	−	2.29579i	0.263505	−	0.0959080i
$574$	6.72668	+	38.1489i	0.280766	+	1.59230i
$575$		0			0
$576$	−3.96229	−	1.44215i	−0.165095	−	0.0600898i
$577$	1.61721	+	2.80109i	0.0673254	+	0.116611i	0.897723	−	0.440560i	$-0.145220\pi$
$577$	1.61721	+	2.80109i	0.0673254	+	0.116611i	−0.830398	+	0.557171i	$0.811887\pi$
$578$	2.46926	−	4.27688i	0.102707	−	0.177895i
$579$	−6.90033	+	5.79006i	−0.286768	+	0.240627i
$580$		0			0
$581$	−9.43629	+	16.3441i	−0.391483	+	0.678069i
$582$	6.08987	+	10.5480i	0.252433	+	0.437227i
$583$	−3.27719	−	1.19280i	−0.135727	−	0.0494007i
$584$	−6.49794	+	36.8517i	−0.268887	+	1.52493i
$585$		0			0
$586$	9.27719	−	3.37662i	0.383237	−	0.139487i
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.991738	+	0.128279i	$0.0409452\pi$
$587$	31.2610	+	26.2311i	1.29028	+	1.08267i	0.298543	+	0.954396i	$0.403499\pi$
$588$	−13.3969			−0.552480
$589$	15.7998	−	5.49254i	0.651019	−	0.226316i
$590$		0			0
$591$	3.97044	+	3.33159i	0.163322	+	0.137043i
$592$	−25.6129	+	9.32234i	−1.05268	+	0.383146i
$593$	1.92127	+	10.8961i	0.0788973	+	0.447449i	0.998507	+	0.0546164i	$0.0173936\pi$
$593$	1.92127	+	10.8961i	0.0788973	+	0.447449i	−0.919610	+	0.392832i	$0.871495\pi$
$594$	1.89528	−	10.7487i	0.0777642	−	0.441023i
$595$		0			0
$596$	−24.7199	−	42.8161i	−1.01257	−	1.75381i
$597$	−8.82295	+	15.2818i	−0.361099	+	0.625442i
$598$	−26.6878	+	22.3937i	−1.09134	+	0.915747i
$599$	−34.1332	+	28.6411i	−1.39464	+	1.17024i	−0.431224	+	0.902245i	$0.641918\pi$
$599$	−34.1332	+	28.6411i	−1.39464	+	1.17024i	−0.963419	+	0.268000i	$0.913637\pi$
$600$		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	$0.800823\pi$
$602$	31.7237	+	11.5465i	1.29296	+	0.470600i
$603$	−1.73742	+	9.85337i	−0.0707530	+	0.401260i
$604$	−8.45858	−	47.9710i	−0.344175	−	1.95191i
$605$		0			0
$606$	2.74763	+	2.30553i	0.111615	+	0.0936558i
$607$	31.1881			1.26589			0.632943	−	0.774199i	$-0.281847\pi$
$607$	31.1881			1.26589			0.632943	+	0.774199i	$0.281847\pi$
$608$	−10.2679	+	17.2035i	−0.416417	+	0.697692i
$609$	4.65270			0.188537
$610$		0			0
$611$	−1.46538	+	0.533356i	−0.0592831	+	0.0215773i
$612$	7.64930	+	43.3813i	0.309205	+	1.75359i
$613$	−2.84255	+	16.1209i	−0.114809	+	0.651117i	0.872035	+	0.489444i	$0.162800\pi$
$613$	−2.84255	+	16.1209i	−0.114809	+	0.651117i	−0.986844	+	0.161673i	$0.948311\pi$
$614$	55.1430	+	20.0704i	2.22539	+	0.809975i
$615$		0			0
$616$	−5.54189	+	9.59883i	−0.223289	+	0.386748i
$617$	−12.3014	+	10.3221i	−0.495235	+	0.415551i	−0.855898	−	0.517145i	$-0.826995\pi$
$617$	−12.3014	+	10.3221i	−0.495235	+	0.415551i	0.360663	+	0.932696i	$0.382550\pi$
$618$	15.7947	−	13.2534i	0.635357	−	0.533128i
$619$	−11.9213	+	20.6483i	−0.479156	+	0.829923i	−0.999714	−	0.0239031i	$-0.992391\pi$
$619$	−11.9213	+	20.6483i	−0.479156	+	0.829923i	0.520558	+	0.853826i	$0.325724\pi$
$620$		0			0
$621$	17.3131	+	6.30147i	0.694753	+	0.252869i
$622$	−1.52182	+	8.63068i	−0.0610195	+	0.346059i
$623$	0.645430	+	3.66041i	0.0258586	+	0.146651i
$624$	11.0617	−	4.02611i	0.442820	−	0.161173i
$625$		0			0
$626$	57.9590			2.31651
$627$	3.15048	+	1.19869i	0.125818	+	0.0478712i
$628$	−48.4962			−1.93521
$629$	−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	$0.803870\pi$
$632$	10.3999	−	58.9809i	0.413687	−	2.34613i
$633$	4.95084	+	1.80196i	0.196778	+	0.0716214i
$634$	33.0699	+	57.2787i	1.31337	+	2.27483i
$635$		0			0
$636$	−6.49273	+	5.44804i	−0.257453	+	0.216029i
$637$	9.68345	−	8.12538i	0.383672	−	0.321939i
$638$	−6.97906	+	12.0881i	−0.276303	+	0.478572i
$639$	−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	$-0.0254902\pi$
$642$	1.91710	+	10.8724i	0.0756619	+	0.429100i
$643$	26.8828	−	9.78456i	1.06016	−	0.385865i	0.247669	−	0.968845i	$-0.420335\pi$
$643$	26.8828	−	9.78456i	1.06016	−	0.385865i	0.812487	+	0.582979i	$0.198113\pi$
$644$	−26.2199	−	22.0011i	−1.03321	−	0.866964i
$645$		0			0
$646$	−42.8127	−	0.620838i	−1.68444	−	0.0244265i
$647$	−16.7128			−0.657046			−0.328523	−	0.944496i	$-0.606551\pi$
$647$	−16.7128			−0.657046			−0.328523	+	0.944496i	$0.606551\pi$
$648$	25.0121	+	20.9876i	0.982567	+	0.824472i
$649$	−4.38191	+	1.59489i	−0.172005	+	0.0626047i
$650$		0			0
$651$	0.666374	−	3.77920i	0.0261173	−	0.148118i
$652$	−26.2520	−	9.55493i	−1.02811	−	0.374200i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	−7.81180	+	13.5304i	−0.305466	+	0.529082i
$655$		0			0
$656$	−50.7772	+	42.6072i	−1.98252	+	1.66353i
$657$	−7.88713	+	13.6609i	−0.307706	+	0.532963i
$658$	−1.11334	−	1.92836i	−0.0434025	−	0.0751754i
$659$	41.2533	+	15.0150i	1.60700	+	0.584900i	0.980844	−	0.194797i	$-0.0624047\pi$
$659$	41.2533	+	15.0150i	1.60700	+	0.584900i	0.626157	+	0.779697i	$0.284627\pi$
$660$		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	$-0.122636\pi$
$662$	−45.3144	+	16.4931i	−1.76119	+	0.641022i
$663$	5.26991	+	4.42198i	0.204667	+	0.171736i
$664$	−75.2158			−2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	−18.0496	−	15.1454i	−0.698884	−	0.586434i
$668$	−57.1173	+	20.7890i	−2.20993	+	0.804350i
$669$	1.75402	+	9.94756i	0.0678144	+	0.384595i
$670$		0			0
$671$	−5.02956	−	1.83061i	−0.194164	−	0.0706700i
$672$	2.29813	+	3.98048i	0.0886524	+	0.153550i
$673$	2.32888	−	4.03374i	0.0897717	−	0.155489i	−0.817643	−	0.575726i	$-0.804720\pi$
$673$	2.32888	−	4.03374i	0.0897717	−	0.155489i	0.907415	+	0.420237i	$0.138053\pi$
$674$	−3.30019	+	2.76919i	−0.127119	+	0.106665i
$675$		0			0
$676$	12.3931	−	21.4654i	0.476656	−	0.825592i
$677$	1.63429	+	2.83067i	0.0628107	+	0.108791i	0.895721	−	0.444617i	$-0.146660\pi$
$677$	1.63429	+	2.83067i	0.0628107	+	0.108791i	−0.832910	+	0.553408i	$0.813327\pi$
$678$	2.03519	+	0.740748i	0.0781609	+	0.0284482i
$679$	1.96064	−	11.1193i	0.0752423	−	0.426721i
$680$		0			0
$681$	6.05525	−	2.20393i	0.232038	−	0.0844549i
$682$	8.81908	+	7.40008i	0.337700	+	0.283364i
$683$	−6.21894			−0.237961			−0.118981	−	0.992897i	$-0.537963\pi$
$683$	−6.21894			−0.237961			−0.118981	+	0.992897i	$0.537963\pi$
$684$	−38.3730	+	31.2620i	−1.46723	+	1.19533i
$685$		0			0
$686$	34.6293	+	29.0574i	1.32215	+	1.10942i
$687$	−12.3397	+	4.49129i	−0.470790	+	0.171353i
$688$	10.0312	+	56.8898i	0.382436	+	2.16890i
$689$	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	$0.972215\pi$
$692$	55.6887	−	96.4557i	2.11697	−	3.66670i
$693$	−3.57919	+	3.00330i	−0.135962	+	0.114086i
$694$	9.50774	−	7.97794i	0.360909	−	0.302839i
$695$		0			0
$696$	9.27156	+	16.0588i	0.351438	+	0.608708i
$697$	−36.4013	−	13.2490i	−1.37880	−	0.501841i
$698$	−12.3682	+	70.1438i	−0.468145	+	2.65498i
$699$	−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	$0.897961\pi$
$702$	25.0283			0.944631
$703$	3.36319	−	17.5791i	0.126845	−	0.663008i
$704$	1.94087			0.0731495
$705$		0			0
$706$	−19.7964	+	7.20529i	−0.745047	+	0.271175i
$707$	−0.577382	−	3.27449i	−0.0217147	−	0.123150i
$708$	−1.96791	+	11.1606i	−0.0739586	+	0.419440i
$709$	5.73947	+	2.08900i	0.215551	+	0.0784540i	0.447538	−	0.894265i	$-0.352301\pi$
$709$	5.73947	+	2.08900i	0.215551	+	0.0784540i	−0.231988	+	0.972719i	$0.574523\pi$
$710$		0			0
$711$	12.6233	−	21.8642i	0.473411	−	0.819972i
$712$	−11.3478	+	9.52190i	−0.425275	+	0.356848i
$713$	−14.8871	+	12.4918i	−0.557527	+	0.467821i
$714$	−4.91147	+	8.50692i	−0.183807	+	0.318364i
$715$		0			0
$716$	−24.1707	−	8.79742i	−0.903302	−	0.328775i
$717$	1.35710	−	7.69648i	0.0506817	−	0.287430i
$718$	10.9611	+	62.1635i	0.409065	+	2.31992i
$719$	−36.3885	+	13.2443i	−1.35706	+	0.493930i	−0.915144	−	0.403126i	$-0.867924\pi$
$719$	−36.3885	+	13.2443i	−1.35706	+	0.493930i	−0.441917	+	0.897056i	$0.645701\pi$
$720$		0			0
$721$	−19.1138			−0.711835
$722$	−22.8366	−	42.3442i	−0.849891	−	1.57589i
$723$	8.42097			0.313179
$724$	45.8316	+	38.4573i	1.70332	+	1.42925i
$725$		0			0
$726$	−2.75402	−	15.6188i	−0.102211	−	0.579669i
$727$	1.92366	−	10.9096i	0.0713445	−	0.404615i	−0.928132	−	0.372252i	$-0.878586\pi$
$727$	1.92366	−	10.9096i	0.0713445	−	0.404615i	0.999476	−	0.0323628i	$-0.0103032\pi$
$728$	−23.8837	−	8.69296i	−0.885190	−	0.322183i
$729$	3.31996	+	5.75033i	0.122961	+	0.212975i
$730$		0			0
$731$	−25.8614	+	21.7003i	−0.956520	+	0.802615i
$732$	−9.96451	+	8.36121i	−0.368299	+	0.309039i
$733$	−7.90373	+	13.6897i	−0.291931	+	0.505639i	−0.974266	−	0.225400i	$-0.927631\pi$
$733$	−7.90373	+	13.6897i	−0.291931	+	0.505639i	0.682335	+	0.731039i	$0.260964\pi$
$734$	−3.27379	−	5.67036i	−0.120838	−	0.209297i
$735$		0			0
$736$	4.04189	−	22.9227i	0.148986	−	0.844942i
$737$	−0.799726	−	4.53547i	−0.0294583	−	0.167066i
$738$	−61.1558	+	22.2589i	−2.25117	+	0.819360i
$739$	1.18685	+	0.995887i	0.0436591	+	0.0366343i	0.664356	−	0.747416i	$-0.268706\pi$
$739$	1.18685	+	0.995887i	0.0436591	+	0.0366343i	−0.620697	+	0.784050i	$0.713150\pi$
$740$		0			0
$741$	−1.45249	+	7.59202i	−0.0533584	+	0.278900i
$742$	11.4192			0.419213
$743$	−29.2349	−	24.5310i	−1.07252	−	0.899955i	−0.0772453	−	0.997012i	$-0.524612\pi$
$743$	−29.2349	−	24.5310i	−1.07252	−	0.899955i	−0.995279	+	0.0970576i	$0.969057\pi$
$744$	14.3718	−	5.23091i	0.526896	−	0.191774i
$745$		0			0
$746$	10.2815	−	58.3091i	0.376431	−	2.13485i
$747$	−29.7946	−	10.8444i	−1.09013	−	0.396774i
$748$	−10.1382	−	17.5598i	−0.370688	−	0.642050i
$749$	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	$0.430820\pi$
$752$	1.90508	−	3.29969i	0.0694710	−	0.120327i
$753$	−4.68732	−	8.11867i	−0.170815	−	0.295861i
$754$	−30.0774	−	10.9473i	−1.09536	−	0.398677i
$755$		0			0
$756$	4.26991	+	24.2159i	0.155295	+	0.880723i
$757$	39.8153	−	14.4916i	1.44711	−	0.526705i	0.505328	−	0.862927i	$-0.331372\pi$
$757$	39.8153	−	14.4916i	1.44711	−	0.526705i	0.941783	+	0.336222i	$0.109149\pi$
$758$	49.3435	+	41.4041i	1.79224	+	1.50386i
$759$	−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	$0.516491\pi$
$762$	18.3614	+	15.4071i	0.665165	+	0.558139i
$763$	13.6099	−	4.95361i	0.492713	−	0.179333i
$764$	−7.87804	−	44.6786i	−0.285018	−	1.61641i
$765$		0			0
$766$	−65.3872	−	23.7990i	−2.36253	−	0.859892i
$767$	−5.34658	−	9.26055i	−0.193054	−	0.334379i
$768$	9.95471	−	17.2421i	0.359210	−	0.622169i
$769$	14.6472	−	12.2905i	0.528193	−	0.443207i	−0.339284	−	0.940684i	$-0.610185\pi$
$769$	14.6472	−	12.2905i	0.528193	−	0.443207i	0.867477	+	0.497477i	$0.165740\pi$
$770$		0			0
$771$	1.62449	−	2.81369i	0.0585044	−	0.101333i
$772$	30.4406	+	52.7247i	1.09558	+	1.89760i
$773$	2.36319	+	0.860130i	0.0849980	+	0.0309367i	0.384169	−	0.923263i	$-0.374488\pi$
$773$	2.36319	+	0.860130i	0.0849980	+	0.0309367i	−0.299171	+	0.954199i	$0.596710\pi$
$774$	−9.84895	+	55.8561i	−0.354013	+	2.00771i
$775$		0			0
$776$	42.2854	−	15.3906i	1.51796	−	0.552491i
$777$	−3.14543	−	2.63933i	−0.112842	−	0.0946854i
$778$	−8.46286			−0.303408
$779$	−6.93582	−	42.9694i	−0.248502	−	1.53954i
$780$		0			0
$781$	6.29498	+	5.28211i	0.225252	+	0.189009i
$782$	46.7452	−	17.0138i	1.67160	−	0.608414i
$783$	2.93939	+	16.6701i	0.105045	+	0.595741i
$784$	−5.36319	+	30.4162i	−0.191542	+	1.08629i
$785$		0			0
$786$	16.3687	+	28.3514i	0.583852	+	1.01126i
$787$	1.36303	−	2.36083i	0.0485866	−	0.0841545i	−0.840709	−	0.541487i	$-0.817862\pi$
$787$	1.36303	−	2.36083i	0.0485866	−	0.0841545i	0.889296	+	0.457332i	$0.151195\pi$
$788$	26.8353	−	22.5175i	0.955967	−	0.802152i
$789$	12.0214	−	10.0872i	0.427974	−	0.359112i
$790$		0			0
$791$	−1.00387	−	1.73875i	−0.0356935	−	0.0618230i
$792$	−17.4982	−	6.36884i	−0.621773	−	0.226307i
$793$	2.13129	−	12.0872i	0.0756844	−	0.429228i
$794$	5.77022	+	32.7245i	0.204777	+	1.16135i
$795$		0			0
$796$	91.3620	+	76.6618i	3.23824	+	2.71720i
$797$	−22.0327			−0.780439			−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327			−0.780439			−0.390219	+	0.920722i	$0.627601\pi$
$798$	−11.0360	−	0.160035i	−0.390669	−	0.00566518i
$799$	2.22668			0.0787743
$800$		0			0
$801$	−5.86794	+	2.13575i	−0.207333	+	0.0754632i
$802$	7.52481	+	42.6753i	0.265710	+	1.50692i
$803$	1.26083	−	7.15052i	0.0444937	−	0.252336i
$804$	−10.5175	−	3.82807i	−0.370925	−	0.135006i
$805$		0			0
$806$	−13.1998	+	22.8627i	−0.464943	+	0.805306i
$807$	−6.55556	+	5.50077i	−0.230767	+	0.193636i
$808$	10.1514	−	8.51800i	0.357124	−	0.299662i
$809$	−27.3603	+	47.3893i	−0.961935	+	1.66612i	−0.244302	+	0.969699i	$0.578559\pi$
$809$	−27.3603	+	47.3893i	−0.961935	+	1.66612i	−0.717633	+	0.696422i	$0.754774\pi$
$810$		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	$0.598195\pi$
$812$	5.46064	−	30.9688i	0.191631	−	1.08679i
$813$	−3.01145	−	17.0788i	−0.105616	−	0.598979i
$814$	11.5753	−	4.21307i	0.405715	−	0.147668i
$815$		0			0
$816$	−16.8084			−0.588412
$817$	−35.4531	−	13.4892i	−1.24035	−	0.471927i
$818$	−22.2772			−0.778906
$819$	−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	$0.938272\pi$
$822$	−2.92855	+	16.6086i	−0.102145	+	0.579292i
$823$	19.4024	+	7.06191i	0.676327	+	0.246163i	0.657270	−	0.753656i	$-0.271711\pi$
$823$	19.4024	+	7.06191i	0.676327	+	0.246163i	0.0190572	+	0.999818i	$0.493934\pi$
$824$	−38.0886	−	65.9714i	−1.32688	−	2.29822i
$825$		0			0
$826$	11.6964	−	9.81445i	0.406970	−	0.341488i
$827$	−27.8116	+	23.3367i	−0.967103	+	0.811495i	−0.982094	−	0.188392i	$-0.939672\pi$
$827$	−27.8116	+	23.3367i	−0.967103	+	0.811495i	0.0149913	+	0.999888i	$0.495228\pi$
$828$	28.7520	−	49.7999i	0.999200	−	1.73066i
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	0.921404	−	0.388606i	$-0.127043\pi$
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	−0.797244	+	0.603657i	$0.793710\pi$
$830$		0			0
$831$	1.87134	−	10.6129i	0.0649161	−	0.368157i
$832$	0.772852	+	4.38306i	0.0267938	+	0.151955i
$833$	−16.9611	+	6.17334i	−0.587667	+	0.213893i
$834$	−2.10220	−	1.76395i	−0.0727931	−	0.0610807i
$835$		0			0
$836$	11.6762	−	19.5630i	0.403829	−	0.676602i
$837$	13.9614			0.482577
$838$	13.2679	+	11.1331i	0.458330	+	0.384585i
$839$	32.5197	−	11.8362i	1.12270	−	0.408631i	0.287065	−	0.957911i	$-0.407320\pi$
$839$	32.5197	−	11.8362i	1.12270	−	0.408631i	0.835638	+	0.549280i	$0.185098\pi$
$840$		0			0
$841$	−1.27672	+	7.24065i	−0.0440249	+	0.249678i
$842$	11.4757	+	4.17680i	0.395477	+	0.143942i
$843$	6.32800	+	10.9604i	0.217948	+	0.377497i
$844$	17.8045	−	30.8384i	0.612857	−	1.06150i
$845$		0			0
$846$	2.86571	−	2.40462i	0.0985253	−	0.0826725i
$847$	−7.35117	+	12.7326i	−0.252589	+	0.437497i
$848$	9.76991	+	16.9220i	0.335500	+	0.581103i
$849$	−6.93717	−	2.52492i	−0.238083	−	0.0866551i
$850$		0			0
$851$	3.61081	+	20.4779i	0.123777	+	0.701975i
$852$	18.7665	−	6.83045i	0.642930	−	0.234007i
$853$	−25.4716	−	21.3732i	−0.872132	−	0.731805i	0.0924142	−	0.995721i	$-0.470542\pi$
$853$	−25.4716	−	21.3732i	−0.872132	−	0.731805i	−0.964546	+	0.263915i	$0.914986\pi$
$854$	17.5253			0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	2.97700	+	2.49800i	0.101692	+	0.0853299i	0.692216	−	0.721690i	$-0.256634\pi$
$857$	2.97700	+	2.49800i	0.101692	+	0.0853299i	−0.590524	+	0.807020i	$0.701079\pi$
$858$	−4.99912	+	1.81953i	−0.170667	+	0.0621178i
$859$	0.287866	+	1.63257i	0.00982187	+	0.0557026i	0.989325	−	0.145727i	$-0.0465522\pi$
$859$	0.287866	+	1.63257i	0.00982187	+	0.0557026i	−0.979503	+	0.201430i	$0.935441\pi$
$860$		0			0
$861$	−9.38326	−	3.41523i	−0.319780	−	0.116391i
$862$	−1.65048	−	2.85872i	−0.0562156	−	0.0973684i
$863$	−26.3594	+	45.6558i	−0.897284	+	1.55414i	−0.0663308	+	0.997798i	$0.521129\pi$
$863$	−26.3594	+	45.6558i	−0.897284	+	1.55414i	−0.830953	+	0.556343i	$0.812204\pi$
$864$	−12.8097	+	10.7487i	−0.435796	+	0.365677i
$865$		0			0
$866$	25.0979	−	43.4709i	0.852862	−	1.47720i
$867$	0.636507	+	1.10246i	0.0216169	+	0.0374416i
$868$	−24.3726	−	8.87089i	−0.827259	−	0.301098i
$869$	−2.01795	+	11.4444i	−0.0684543	+	0.388224i
$870$		0			0
$871$	9.92396	−	3.61203i	0.336261	−	0.122389i
$872$	44.2183	+	37.1035i	1.49742	+	1.25648i
$873$	18.9691			0.642008
$874$	42.2918	+	36.5450i	1.43054	+	1.23615i
$875$		0			0
$876$	−13.5175	−	11.3426i	−0.456715	−	0.383230i
$877$	−19.9119	+	7.24735i	−0.672378	+	0.244726i	−0.655572	−	0.755133i	$-0.727572\pi$
$877$	−19.9119	+	7.24735i	−0.672378	+	0.244726i	−0.0168069	+	0.999859i	$0.505350\pi$
$878$	−15.1989	−	86.1974i	−0.512939	−	2.90902i
$879$	−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	$-0.348528\pi$
$882$	−15.1621	+	26.2615i	−0.510534	+	0.884271i
$883$	36.2315	−	30.4018i	1.21929	−	1.02310i	0.220425	−	0.975404i	$-0.429256\pi$
$883$	36.2315	−	30.4018i	1.21929	−	1.02310i	0.998862	−	0.0476989i	$-0.0151888\pi$
$884$	35.6181	−	29.8872i	1.19797	−	1.00521i
$885$		0			0
$886$	21.5355	+	37.3007i	0.723501	+	1.25314i
$887$	9.92602	+	3.61278i	0.333283	+	0.121305i	0.503241	−	0.864146i	$-0.332141\pi$
$887$	9.92602	+	3.61278i	0.333283	+	0.121305i	−0.169958	+	0.985451i	$0.554363\pi$
$888$	2.84167	−	16.1159i	0.0953602	−	0.540815i
$889$	−3.85844	−	21.8823i	−0.129408	−	0.733909i
$890$		0			0
$891$	−4.85323	−	4.07234i	−0.162589	−	0.136429i
$892$	68.2704			2.28586
$893$	1.21941	+	2.18463i	0.0408059	+	0.0731059i
$894$	18.5220			0.619468
$895$		0			0
$896$	−19.2062	+	6.99049i	−0.641634	+	0.233536i
$897$	−1.55943	−	8.84397i	−0.0520679	−	0.295291i
$898$	16.4488	−	93.2857i	0.548903	−	3.11298i
$899$	−16.7780	−	6.10668i	−0.559576	−	0.203669i
$900$		0			0
$901$	−5.70961	+	9.88933i	−0.190215	+	0.329461i
$902$	22.9479	−	19.2556i	0.764081	−	0.641141i
$903$	−6.66637	+	5.59375i	−0.221843	+	0.186148i
$904$	4.00088	−	6.92972i	0.133067	−	0.230479i
$905$		0			0
$906$	17.1484	+	6.24152i	0.569718	+	0.207360i
$907$	−7.45306	+	42.2684i	−0.247475	+	1.40350i	0.567200	+	0.823580i	$0.308027\pi$
$907$	−7.45306	+	42.2684i	−0.247475	+	1.40350i	−0.814674	+	0.579919i	$0.803084\pi$
$908$	−7.56283	−	42.8910i	−0.250981	−	1.42339i
$909$	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	$0.866595\pi$
$912$	−9.20486	−	16.4910i	−0.304803	−	0.546071i
$913$	14.5945			0.483008
$914$	−17.6728	−	14.8292i	−0.584563	−	0.490507i
$915$		0			0
$916$	15.4119	+	87.4055i	0.509225	+	2.88796i
$917$	5.26991	−	29.8872i	0.174028	−	0.986961i
$918$	−33.5822	−	12.2229i	−1.10838	−	0.403416i
$919$	12.2788	+	21.2676i	0.405041	+	0.701552i	0.994326	−	0.106373i	$-0.0339237\pi$
$919$	12.2788	+	21.2676i	0.405041	+	0.701552i	−0.589285	+	0.807925i	$0.700590\pi$
$920$		0			0
$921$	−11.5876	+	9.72319i	−0.381826	+	0.320390i
$922$	−47.4222	+	39.7920i	−1.56177	+	1.31048i
$923$	−9.42190	+	16.3192i	−0.310126	+	0.537154i
$924$	−2.61334	−	4.52644i	−0.0859726	−	0.148909i
$925$		0			0
$926$	0.110242	−	0.625213i	0.00362277	−	0.0205458i
$927$	−5.57620	−	31.6242i	−0.183146	−	1.03867i
$928$	20.0954	−	7.31412i	0.659663	−	0.240098i
$929$	−17.0654	−	14.3195i	−0.559896	−	0.469809i	0.318379	−	0.947963i	$-0.396861\pi$
$929$	−17.0654	−	14.3195i	−0.559896	−	0.469809i	−0.878276	+	0.478155i	$0.841306\pi$
$930$		0			0
$931$	−15.3452	−	13.2601i	−0.502920	−	0.434581i
$932$	−15.5936			−0.510785
$933$	−1.73055	−	1.45211i	−0.0566557	−	0.0475398i
$934$	36.5517	−	13.3037i	1.19601	−	0.435312i
$935$		0			0
$936$	7.41493	−	42.0522i	0.242365	−	1.37452i
$937$	−8.97565	−	3.26687i	−0.293222	−	0.106724i	0.191221	−	0.981547i	$-0.438755\pi$
$937$	−8.97565	−	3.26687i	−0.293222	−	0.106724i	−0.484443	+	0.874823i	$0.660978\pi$
$938$	7.53983	+	13.0594i	0.246184	+	0.426403i
$939$	−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	$0.915158\pi$
$942$	9.08424	−	15.7344i	0.295981	−	0.512654i
$943$	25.2841	+	43.7933i	0.823362	+	1.42610i
$944$	24.5510	+	8.93582i	0.799066	+	0.290836i
$945$		0			0
$946$	−4.53343	−	25.7104i	−0.147395	−	0.835916i
$947$	−25.4119	+	9.24919i	−0.825777	+	0.300558i	−0.720125	−	0.693845i	$-0.755915\pi$
$947$	−25.4119	+	9.24919i	−0.825777	+	0.300558i	−0.105653	+	0.994403i	$0.533693\pi$
$948$	21.6348	+	18.1537i	0.702664	+	0.589605i
$949$	16.6500			0.540482
$950$		0			0
$951$	−17.0490			−0.552852
$952$	27.8011	+	23.3279i	0.901040	+	0.756062i
$953$	21.7361	−	7.91128i	0.704100	−	0.256272i	0.0349398	−	0.999389i	$-0.488876\pi$
$953$	21.7361	−	7.91128i	0.704100	−	0.256272i	0.669161	+	0.743118i	$0.266654\pi$
$954$	3.33140	+	18.8933i	0.107858	+	0.611694i
$955$		0			0
$956$	−49.6357	−	18.0659i	−1.60533	−	0.584293i
$957$	−1.79901	−	3.11598i	−0.0581538	−	0.100725i
$958$	0.910597	−	1.57720i	0.0294200	−	0.0509570i
$959$	11.9764	−	10.0494i	0.386737	−	0.324511i
$960$		0			0
$961$	8.13681	−	14.0934i	0.262478	−	0.454625i
$962$	14.1236	+	24.4628i	0.455363	+	0.788713i
$963$	16.1573	+	5.88079i	0.520663	+	0.189506i
$964$	9.88326	−	56.0507i	0.318318	−	1.80527i
$965$		0			0
$966$	12.0496	−	4.38571i	0.387690	−	0.141108i
$967$	−29.9026	−	25.0913i	−0.961603	−	0.806881i	0.0196101	−	0.999808i	$-0.493758\pi$
$967$	−29.9026	−	25.0913i	−0.961603	−	0.806881i	−0.981213	+	0.192927i	$0.938202\pi$
$968$	−58.5954			−1.88333
$969$	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	$0.952144\pi$
$972$	−59.7135	+	21.7339i	−1.91531	+	0.697117i
$973$	0.441752	+	2.50530i	0.0141619	+	0.0803162i
$974$	−5.16503	+	29.2923i	−0.165498	+	0.938587i
$975$		0			0
$976$	14.9941	+	25.9705i	0.479948	+	0.831295i
$977$	11.2469	−	19.4802i	0.359821	−	0.623227i	−0.628110	−	0.778125i	$-0.716171\pi$
$977$	11.2469	−	19.4802i	0.359821	−	0.623227i	0.987931	+	0.154897i	$0.0495046\pi$
$978$	8.01754	−	6.72752i	0.256373	−	0.215122i
$979$	2.20187	−	1.84759i	0.0703720	−	0.0590491i
$980$		0			0
$981$	12.1664	+	21.0728i	0.388442	+	0.672802i
$982$	−0.211362	−	0.0769295i	−0.00674484	−	0.00245492i
$983$	7.73536	−	43.8694i	0.246720	−	1.39922i	−0.569746	−	0.821821i	$-0.692958\pi$
$983$	7.73536	−	43.8694i	0.246720	−	1.39922i	0.816465	−	0.577395i	$-0.195931\pi$
$984$	−6.91060	−	39.1919i	−0.220302	−	1.24939i
$985$		0			0
$986$	35.0107	+	29.3775i	1.11497	+	0.935570i
$987$	0.573978			0.0182699
$988$	48.8285	+	18.5782i	1.55344	+	0.591052i
$989$	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	$0.133044\pi$
$992$	−3.06283	−	17.3702i	−0.0972451	−	0.551504i
$993$	2.15853	−	12.2416i	0.0684988	−	0.388476i
$994$	−25.2841	−	9.20264i	−0.801961	−	0.291890i
$995$		0			0
$996$	17.7344	−	30.7169i	0.561937	−	0.973303i
$997$	8.03667	−	6.74357i	0.254524	−	0.213571i	−0.506593	−	0.862185i	$-0.669095\pi$
$997$	8.03667	−	6.74357i	0.254524	−	0.213571i	0.761117	+	0.648614i	$0.224651\pi$
$998$	28.4950	−	23.9101i	0.901994	−	0.756862i
$999$	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.l.a.301.1		6
5.2	odd	4		475.2.u.a.149.1		12
5.3	odd	4		475.2.u.a.149.2		12
5.4	even	2		19.2.e.a.16.1	yes	6
15.14	odd	2		171.2.u.c.73.1		6
19.5	even	9		9025.2.a.bd.1.3		3
19.6	even	9	inner	475.2.l.a.101.1		6
19.14	odd	18		9025.2.a.x.1.1		3
20.19	odd	2		304.2.u.b.225.1		6
35.4	even	6		931.2.x.a.814.1		6
35.9	even	6		931.2.v.b.263.1		6
35.19	odd	6		931.2.v.a.263.1		6
35.24	odd	6		931.2.x.b.814.1		6
35.34	odd	2		931.2.w.a.491.1		6
95.4	even	18		361.2.e.f.28.1		6
95.9	even	18		361.2.e.g.99.1		6
95.14	odd	18		361.2.a.h.1.3		3
95.24	even	18		361.2.a.g.1.1		3
95.29	odd	18		361.2.e.a.99.1		6
95.34	odd	18		361.2.e.b.28.1		6
95.44	even	18		19.2.e.a.6.1	✓	6
95.49	even	6		361.2.e.f.245.1		6
95.54	even	18		361.2.c.i.68.3		6
95.59	odd	18		361.2.c.h.292.1		6
95.63	odd	36		475.2.u.a.424.1		12
95.64	even	6		361.2.e.g.62.1		6
95.69	odd	6		361.2.e.a.62.1		6
95.74	even	18		361.2.c.i.292.3		6
95.79	odd	18		361.2.c.h.68.1		6
95.82	odd	36		475.2.u.a.424.2		12
95.84	odd	6		361.2.e.b.245.1		6
95.89	odd	18		361.2.e.h.234.1		6
95.94	odd	2		361.2.e.h.54.1		6
285.14	even	18		3249.2.a.s.1.1		3
285.44	odd	18		171.2.u.c.82.1		6
285.119	odd	18		3249.2.a.z.1.3		3
380.119	odd	18		5776.2.a.br.1.2		3
380.139	odd	18		304.2.u.b.177.1		6
380.299	even	18		5776.2.a.bi.1.2		3
665.44	even	18		931.2.x.a.557.1		6
665.139	odd	18		931.2.w.a.785.1		6
665.234	odd	18		931.2.v.a.177.1		6
665.424	even	18		931.2.v.b.177.1		6
665.614	odd	18		931.2.x.b.557.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	95.44	even	18
19.2.e.a.16.1	yes	6	5.4	even	2
171.2.u.c.73.1		6	15.14	odd	2
171.2.u.c.82.1		6	285.44	odd	18
304.2.u.b.177.1		6	380.139	odd	18
304.2.u.b.225.1		6	20.19	odd	2
361.2.a.g.1.1		3	95.24	even	18
361.2.a.h.1.3		3	95.14	odd	18
361.2.c.h.68.1		6	95.79	odd	18
361.2.c.h.292.1		6	95.59	odd	18
361.2.c.i.68.3		6	95.54	even	18
361.2.c.i.292.3		6	95.74	even	18
361.2.e.a.62.1		6	95.69	odd	6
361.2.e.a.99.1		6	95.29	odd	18
361.2.e.b.28.1		6	95.34	odd	18
361.2.e.b.245.1		6	95.84	odd	6
361.2.e.f.28.1		6	95.4	even	18
361.2.e.f.245.1		6	95.49	even	6
361.2.e.g.62.1		6	95.64	even	6
361.2.e.g.99.1		6	95.9	even	18
361.2.e.h.54.1		6	95.94	odd	2
361.2.e.h.234.1		6	95.89	odd	18
475.2.l.a.101.1		6	19.6	even	9	inner
475.2.l.a.301.1		6	1.1	even	1	trivial
475.2.u.a.149.1		12	5.2	odd	4
475.2.u.a.149.2		12	5.3	odd	4
475.2.u.a.424.1		12	95.63	odd	36
475.2.u.a.424.2		12	95.82	odd	36
931.2.v.a.177.1		6	665.234	odd	18
931.2.v.a.263.1		6	35.19	odd	6
931.2.v.b.177.1		6	665.424	even	18
931.2.v.b.263.1		6	35.9	even	6
931.2.w.a.491.1		6	35.34	odd	2
931.2.w.a.785.1		6	665.139	odd	18
931.2.x.a.557.1		6	665.44	even	18
931.2.x.a.814.1		6	35.4	even	6
931.2.x.b.557.1		6	665.614	odd	18
931.2.x.b.814.1		6	35.24	odd	6
3249.2.a.s.1.1		3	285.14	even	18
3249.2.a.z.1.3		3	285.119	odd	18
5776.2.a.bi.1.2		3	380.299	even	18
5776.2.a.br.1.2		3	380.119	odd	18
9025.2.a.x.1.1		3	19.14	odd	18
9025.2.a.bd.1.3		3	19.5	even	9

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93969 + 1.62760i) q^{2} +(-0.613341 + 0.223238i) q^{3} +(0.766044 + 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-1.97178 + 1.65452i) q^{9} +O(q^{10})\)	\(q+(1.93969 + 1.62760i) q^{2} +(-0.613341 + 0.223238i) q^{3} +(0.766044 + 4.34445i) q^{4} +(-1.55303 - 0.565258i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-1.97178 + 1.65452i) q^{9} +(0.592396 - 1.02606i) q^{11} +(-1.43969 - 2.49362i) q^{12} +(2.55303 + 0.929228i) q^{13} +(-0.673648 + 3.82045i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-2.97178 - 2.49362i) q^{17} -6.51754 q^{18} +(0.819078 - 4.28125i) q^{19} +(-0.766044 - 0.642788i) q^{21} +(2.81908 - 1.02606i) q^{22} +(0.879385 + 4.98724i) q^{23} +(0.692066 - 3.92490i) q^{24} +(3.43969 + 5.95772i) q^{26} +(1.81908 - 3.15074i) q^{27} +(-5.17752 + 4.34445i) q^{28} +(-3.56418 + 2.99070i) q^{29} +(1.91875 + 3.32337i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(-0.134285 + 0.761570i) q^{33} +(-1.70574 - 9.67372i) q^{34} +(-8.69846 - 7.29888i) q^{36} +4.10607 q^{37} +(8.55690 - 6.97118i) q^{38} -1.77332 q^{39} +(9.38326 - 3.41523i) q^{41} +(-0.439693 - 2.49362i) q^{42} +(1.51114 - 8.57013i) q^{43} +(4.91147 + 1.78763i) q^{44} +(-6.41147 + 11.1050i) q^{46} +(-0.439693 + 0.368946i) q^{47} +(3.31908 - 2.78504i) q^{48} +(2.32635 - 4.02936i) q^{49} +(2.37939 + 0.866025i) q^{51} +(-2.08125 + 11.8034i) q^{52} +(-0.511144 - 2.89884i) q^{53} +(8.65657 - 3.15074i) q^{54} -9.35504 q^{56} +(0.453363 + 2.80872i) q^{57} -11.7811 q^{58} +(-3.01501 - 2.52990i) q^{59} +(-0.784463 - 4.44891i) q^{61} +(-1.68732 + 9.56926i) q^{62} +(-3.70574 - 1.34878i) q^{63} +(0.819078 + 1.41868i) q^{64} +(-1.50000 + 1.25865i) q^{66} +(2.97771 - 2.49860i) q^{67} +(8.55690 - 14.8210i) q^{68} +(-1.65270 - 2.86257i) q^{69} +(-1.20439 + 6.83045i) q^{71} +(-2.72921 - 15.4781i) q^{72} +(5.75877 - 2.09602i) q^{73} +(7.96451 + 6.68302i) q^{74} +(19.2271 + 0.278817i) q^{76} +1.81521 q^{77} +(-3.43969 - 2.88624i) q^{78} +(-9.21688 + 3.35467i) q^{79} +(0.928548 - 5.26606i) q^{81} +(23.7592 + 8.64766i) q^{82} +(6.15910 + 10.6679i) q^{83} +(2.20574 - 3.82045i) q^{84} +(16.8799 - 14.1639i) q^{86} +(1.51842 - 2.62998i) q^{87} +(3.61721 + 6.26519i) q^{88} +(2.27972 + 0.829748i) q^{89} +(0.722811 + 4.09927i) q^{91} +(-20.9932 + 7.64090i) q^{92} +(-1.91875 - 1.61002i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(-5.64543 - 4.73708i) q^{97} +(11.0706 - 4.02936i) q^{98} +(0.529563 + 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 3 * q^29 + 9 * q^31 - 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 + 21 * q^41 + 3 * q^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * q^99

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