LMFDB - Embedded newform 187.2.e.b.89.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(89,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.6
Character	$\chi$	$=$	187.89
Dual form			187.2.e.b.166.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.385060i q^{2} +(1.16534 - 1.16534i) q^{3} +1.85173 q^{4} +(-0.671428 + 0.671428i) q^{5} +(-0.448724 - 0.448724i) q^{6} +(1.38678 + 1.38678i) q^{7} -1.48315i q^{8} +0.283977i q^{9} +O(q^{10})$	\(q-0.385060i q^{2} +(1.16534 - 1.16534i) q^{3} +1.85173 q^{4} +(-0.671428 + 0.671428i) q^{5} +(-0.448724 - 0.448724i) q^{6} +(1.38678 + 1.38678i) q^{7} -1.48315i q^{8} +0.283977i q^{9} +(0.258540 + 0.258540i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(2.15789 - 2.15789i) q^{12} -5.16562 q^{13} +(0.533991 - 0.533991i) q^{14} +1.56488i q^{15} +3.13236 q^{16} +(-3.56033 - 2.07944i) q^{17} +0.109348 q^{18} -1.52490i q^{19} +(-1.24330 + 1.24330i) q^{20} +3.23212 q^{21} +(-0.272278 + 0.272278i) q^{22} +(-3.45377 - 3.45377i) q^{23} +(-1.72836 - 1.72836i) q^{24} +4.09837i q^{25} +1.98907i q^{26} +(3.82694 + 3.82694i) q^{27} +(2.56793 + 2.56793i) q^{28} +(0.706900 - 0.706900i) q^{29} +0.602572 q^{30} +(2.25992 - 2.25992i) q^{31} -4.17244i q^{32} -1.64804 q^{33} +(-0.800707 + 1.37094i) q^{34} -1.86224 q^{35} +0.525849i q^{36} +(-0.724470 + 0.724470i) q^{37} -0.587177 q^{38} +(-6.01969 + 6.01969i) q^{39} +(0.995825 + 0.995825i) q^{40} +(0.427468 + 0.427468i) q^{41} -1.24456i q^{42} +12.0802i q^{43} +(-1.30937 - 1.30937i) q^{44} +(-0.190670 - 0.190670i) q^{45} +(-1.32991 + 1.32991i) q^{46} -5.76631 q^{47} +(3.65026 - 3.65026i) q^{48} -3.15371i q^{49} +1.57812 q^{50} +(-6.57223 + 1.72574i) q^{51} -9.56533 q^{52} +7.56940i q^{53} +(1.47360 - 1.47360i) q^{54} +0.949542 q^{55} +(2.05679 - 2.05679i) q^{56} +(-1.77702 - 1.77702i) q^{57} +(-0.272199 - 0.272199i) q^{58} +3.89781i q^{59} +2.89773i q^{60} +(-5.57677 - 5.57677i) q^{61} +(-0.870204 - 0.870204i) q^{62} +(-0.393813 + 0.393813i) q^{63} +4.65808 q^{64} +(3.46834 - 3.46834i) q^{65} +0.634592i q^{66} +10.8269 q^{67} +(-6.59276 - 3.85055i) q^{68} -8.04962 q^{69} +0.717073i q^{70} +(5.20328 - 5.20328i) q^{71} +0.421180 q^{72} +(6.00429 - 6.00429i) q^{73} +(0.278964 + 0.278964i) q^{74} +(4.77598 + 4.77598i) q^{75} -2.82370i q^{76} -1.96120i q^{77} +(2.31794 + 2.31794i) q^{78} +(-2.85046 - 2.85046i) q^{79} +(-2.10315 + 2.10315i) q^{80} +8.06742 q^{81} +(0.164601 - 0.164601i) q^{82} +2.51642i q^{83} +5.98502 q^{84} +(3.78670 - 0.994312i) q^{85} +4.65160 q^{86} -1.64755i q^{87} +(-1.04874 + 1.04874i) q^{88} +17.8804 q^{89} +(-0.0734194 + 0.0734194i) q^{90} +(-7.16356 - 7.16356i) q^{91} +(-6.39545 - 6.39545i) q^{92} -5.26714i q^{93} +2.22037i q^{94} +(1.02386 + 1.02386i) q^{95} +(-4.86230 - 4.86230i) q^{96} +(11.0793 - 11.0793i) q^{97} -1.21437 q^{98} +(0.200802 - 0.200802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	$ 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	0.385060i		−	0.272278i	−0.990690	−	0.136139i	$-0.956531\pi$
$2$		−	0.385060i		−	0.272278i	0.990690	−	0.136139i	$-0.0434694\pi$
$3$	1.16534	−	1.16534i	0.672808	−	0.672808i	−0.285555	−	0.958362i	$-0.592178\pi$
$3$	1.16534	−	1.16534i	0.672808	−	0.672808i	0.958362	+	0.285555i	$0.0921778\pi$
$4$	1.85173			0.925865
$5$	−0.671428	+	0.671428i	−0.300272	+	0.300272i	−0.841120	−	0.540848i	$-0.818103\pi$
$5$	−0.671428	+	0.671428i	−0.300272	+	0.300272i	0.540848	+	0.841120i	$0.318103\pi$
$6$	−0.448724	−	0.448724i	−0.183191	−	0.183191i
$7$	1.38678	+	1.38678i	0.524152	+	0.524152i	0.918823	−	0.394671i	$-0.129141\pi$
$7$	1.38678	+	1.38678i	0.524152	+	0.524152i	−0.394671	+	0.918823i	$0.629141\pi$
$8$		−	1.48315i		−	0.524371i
$9$			0.283977i			0.0946591i
$10$	0.258540	+	0.258540i	0.0817574	+	0.0817574i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	2.15789	−	2.15789i	0.622929	−	0.622929i
$13$	−5.16562			−1.43269			−0.716343	−	0.697748i	$-0.754185\pi$
$13$	−5.16562			−1.43269			−0.716343	+	0.697748i	$0.754185\pi$
$14$	0.533991	−	0.533991i	0.142715	−	0.142715i
$15$			1.56488i			0.404050i
$16$	3.13236			0.783090
$17$	−3.56033	−	2.07944i	−0.863507	−	0.504338i
$17$	−3.56033	−	2.07944i	−0.863507	−	0.504338i
$18$	0.109348			0.0257736
$19$		−	1.52490i		−	0.349836i	−0.984583	−	0.174918i	$-0.944034\pi$
$19$		−	1.52490i		−	0.349836i	0.984583	−	0.174918i	$-0.0559660\pi$
$20$	−1.24330	+	1.24330i	−0.278011	+	0.278011i
$21$	3.23212			0.705307
$22$	−0.272278	+	0.272278i	−0.0580499	+	0.0580499i
$23$	−3.45377	−	3.45377i	−0.720162	−	0.720162i	0.248476	−	0.968638i	$-0.420070\pi$
$23$	−3.45377	−	3.45377i	−0.720162	−	0.720162i	−0.968638	+	0.248476i	$0.920070\pi$
$24$	−1.72836	−	1.72836i	−0.352801	−	0.352801i
$25$			4.09837i			0.819674i
$26$			1.98907i			0.390089i
$27$	3.82694	+	3.82694i	0.736495	+	0.736495i
$28$	2.56793	+	2.56793i	0.485294	+	0.485294i
$29$	0.706900	−	0.706900i	0.131268	−	0.131268i	−0.638420	−	0.769688i	$-0.720412\pi$
$29$	0.706900	−	0.706900i	0.131268	−	0.131268i	0.769688	+	0.638420i	$0.220412\pi$
$30$	0.602572			0.110014
$31$	2.25992	−	2.25992i	0.405894	−	0.405894i	−0.474410	−	0.880304i	$-0.657339\pi$
$31$	2.25992	−	2.25992i	0.405894	−	0.405894i	0.880304	+	0.474410i	$0.157339\pi$
$32$		−	4.17244i		−	0.737589i
$33$	−1.64804			−0.286886
$34$	−0.800707	+	1.37094i	−0.137320	+	0.235114i
$35$	−1.86224			−0.314776
$36$			0.525849i			0.0876415i
$37$	−0.724470	+	0.724470i	−0.119102	+	0.119102i	−0.764146	−	0.645044i	$-0.776839\pi$
$37$	−0.724470	+	0.724470i	−0.119102	+	0.119102i	0.645044	+	0.764146i	$0.276839\pi$
$38$	−0.587177			−0.0952528
$39$	−6.01969	+	6.01969i	−0.963922	+	0.963922i
$40$	0.995825	+	0.995825i	0.157454	+	0.157454i
$41$	0.427468	+	0.427468i	0.0667593	+	0.0667593i	0.739698	−	0.672939i	$-0.234968\pi$
$41$	0.427468	+	0.427468i	0.0667593	+	0.0667593i	−0.672939	+	0.739698i	$0.734968\pi$
$42$		−	1.24456i		−	0.192040i
$43$			12.0802i			1.84221i	0.389309	+	0.921107i	$0.372714\pi$
$43$			12.0802i			1.84221i	−0.389309	+	0.921107i	$0.627286\pi$
$44$	−1.30937	−	1.30937i	−0.197395	−	0.197395i
$45$	−0.190670	−	0.190670i	−0.0284234	−	0.0284234i
$46$	−1.32991	+	1.32991i	−0.196084	+	0.196084i
$47$	−5.76631			−0.841103			−0.420551	−	0.907269i	$-0.638163\pi$
$47$	−5.76631			−0.841103			−0.420551	+	0.907269i	$0.638163\pi$
$48$	3.65026	−	3.65026i	0.526869	−	0.526869i
$49$		−	3.15371i		−	0.450530i
$50$	1.57812			0.223179
$51$	−6.57223	+	1.72574i	−0.920296	+	0.241652i
$52$	−9.56533			−1.32647
$53$			7.56940i			1.03974i	0.854246	+	0.519869i	$0.174019\pi$
$53$			7.56940i			1.03974i	−0.854246	+	0.519869i	$0.825981\pi$
$54$	1.47360	−	1.47360i	0.200532	−	0.200532i
$55$	0.949542			0.128036
$56$	2.05679	−	2.05679i	0.274850	−	0.274850i
$57$	−1.77702	−	1.77702i	−0.235372	−	0.235372i
$58$	−0.272199	−	0.272199i	−0.0357414	−	0.0357414i
$59$			3.89781i			0.507452i	0.967276	+	0.253726i	$0.0816561\pi$
$59$			3.89781i			0.507452i	−0.967276	+	0.253726i	$0.918344\pi$
$60$			2.89773i			0.374096i
$61$	−5.57677	−	5.57677i	−0.714032	−	0.714032i	0.253344	−	0.967376i	$-0.418469\pi$
$61$	−5.57677	−	5.57677i	−0.714032	−	0.714032i	−0.967376	+	0.253344i	$0.918469\pi$
$62$	−0.870204	−	0.870204i	−0.110516	−	0.110516i
$63$	−0.393813	+	0.393813i	−0.0496157	+	0.0496157i
$64$	4.65808			0.582260
$65$	3.46834	−	3.46834i	0.430195	−	0.430195i
$66$			0.634592i			0.0781129i
$67$	10.8269			1.32271			0.661356	−	0.750072i	$-0.269981\pi$
$67$	10.8269			1.32271			0.661356	+	0.750072i	$0.269981\pi$
$68$	−6.59276	−	3.85055i	−0.799490	−	0.466948i
$69$	−8.04962			−0.969061
$70$			0.717073i			0.0857066i
$71$	5.20328	−	5.20328i	0.617515	−	0.617515i	−0.327378	−	0.944893i	$-0.606165\pi$
$71$	5.20328	−	5.20328i	0.617515	−	0.617515i	0.944893	+	0.327378i	$0.106165\pi$
$72$	0.421180			0.0496365
$73$	6.00429	−	6.00429i	0.702749	−	0.702749i	−0.262251	−	0.965000i	$-0.584465\pi$
$73$	6.00429	−	6.00429i	0.702749	−	0.702749i	0.965000	+	0.262251i	$0.0844648\pi$
$74$	0.278964	+	0.278964i	0.0324289	+	0.0324289i
$75$	4.77598	+	4.77598i	0.551483	+	0.551483i
$76$		−	2.82370i		−	0.323901i
$77$		−	1.96120i		−	0.223499i
$78$	2.31794	+	2.31794i	0.262455	+	0.262455i
$79$	−2.85046	−	2.85046i	−0.320702	−	0.320702i	0.528334	−	0.849036i	$-0.322817\pi$
$79$	−2.85046	−	2.85046i	−0.320702	−	0.320702i	−0.849036	+	0.528334i	$0.822817\pi$
$80$	−2.10315	+	2.10315i	−0.235140	+	0.235140i
$81$	8.06742			0.896381
$82$	0.164601	−	0.164601i	0.0181771	−	0.0181771i
$83$			2.51642i			0.276213i	0.990417	+	0.138106i	$0.0441016\pi$
$83$			2.51642i			0.276213i	−0.990417	+	0.138106i	$0.955898\pi$
$84$	5.98502			0.653019
$85$	3.78670	−	0.994312i	0.410725	−	0.107848i
$86$	4.65160			0.501595
$87$		−	1.64755i		−	0.176636i
$88$	−1.04874	+	1.04874i	−0.111796	+	0.111796i
$89$	17.8804			1.89531			0.947657	−	0.319289i	$-0.103444\pi$
$89$	17.8804			1.89531			0.947657	+	0.319289i	$0.103444\pi$
$90$	−0.0734194	+	0.0734194i	−0.00773909	+	0.00773909i
$91$	−7.16356	−	7.16356i	−0.750945	−	0.750945i
$92$	−6.39545	−	6.39545i	−0.666772	−	0.666772i
$93$		−	5.26714i		−	0.546177i
$94$			2.22037i			0.229014i
$95$	1.02386	+	1.02386i	0.105046	+	0.105046i
$96$	−4.86230	−	4.86230i	−0.496256	−	0.496256i
$97$	11.0793	−	11.0793i	1.12494	−	1.12494i	0.133948	−	0.990988i	$-0.457234\pi$
$97$	11.0793	−	11.0793i	1.12494	−	1.12494i	0.990988	−	0.133948i	$-0.0427655\pi$
$98$	−1.21437			−0.122669
$99$	0.200802	−	0.200802i	0.0201814	−	0.0201814i
$100$			7.58907i			0.758907i
$101$	−5.98632			−0.595661			−0.297831	−	0.954619i	$-0.596263\pi$
$101$	−5.98632			−0.595661			−0.297831	+	0.954619i	$0.596263\pi$
$102$	0.664512	+	2.53070i	0.0657965	+	0.250577i
$103$	−10.8134			−1.06547			−0.532737	−	0.846281i	$-0.678836\pi$
$103$	−10.8134			−1.06547			−0.532737	+	0.846281i	$0.678836\pi$
$104$			7.66137i			0.751259i
$105$	−2.17014	+	2.17014i	−0.211784	+	0.211784i
$106$	2.91467			0.283098
$107$	−4.06116	+	4.06116i	−0.392607	+	0.392607i	−0.875616	−	0.483009i	$-0.839544\pi$
$107$	−4.06116	+	4.06116i	−0.392607	+	0.392607i	0.483009	+	0.875616i	$0.339544\pi$
$108$	7.08646	+	7.08646i	0.681895	+	0.681895i
$109$	8.77223	+	8.77223i	0.840227	+	0.840227i	0.988888	−	0.148661i	$-0.0474964\pi$
$109$	8.77223	+	8.77223i	0.840227	+	0.840227i	−0.148661	+	0.988888i	$0.547496\pi$
$110$		−	0.365630i		−	0.0348615i
$111$			1.68850i			0.160266i
$112$	4.34388	+	4.34388i	0.410458	+	0.410458i
$113$	−10.4458	−	10.4458i	−0.982660	−	0.982660i	0.0171924	−	0.999852i	$-0.494527\pi$
$113$	−10.4458	−	10.4458i	−0.982660	−	0.982660i	−0.999852	+	0.0171924i	$0.994527\pi$
$114$	−0.684260	+	0.684260i	−0.0640868	+	0.0640868i
$115$	4.63792			0.432488
$116$	1.30899	−	1.30899i	0.121536	−	0.121536i
$117$		−	1.46692i		−	0.135617i
$118$	1.50089			0.138168
$119$	−2.05366	−	7.82109i	−0.188259	−	0.716958i
$120$	2.32094			0.211872
$121$			1.00000i			0.0909091i
$122$	−2.14739	+	2.14739i	−0.194415	+	0.194415i
$123$	0.996289			0.0898324
$124$	4.18476	−	4.18476i	0.375802	−	0.375802i
$125$	−6.10890	−	6.10890i	−0.546396	−	0.546396i
$126$	0.151641	+	0.151641i	0.0135093	+	0.0135093i
$127$		−	15.0032i		−	1.33131i	−0.746257	−	0.665657i	$-0.768151\pi$
$127$		−	15.0032i		−	1.33131i	0.746257	−	0.665657i	$-0.231849\pi$
$128$		−	10.1385i		−	0.896126i
$129$	14.0775	+	14.0775i	1.23946	+	1.23946i
$130$	−1.33552	−	1.33552i	−0.117133	−	0.117133i
$131$	7.28980	−	7.28980i	0.636913	−	0.636913i	−0.312880	−	0.949793i	$-0.601294\pi$
$131$	7.28980	−	7.28980i	0.636913	−	0.636913i	0.949793	+	0.312880i	$0.101294\pi$
$132$	−3.05172			−0.265618
$133$	2.11469	−	2.11469i	0.183367	−	0.183367i
$134$		−	4.16899i		−	0.360146i
$135$	−5.13903			−0.442297
$136$	−3.08411	+	5.28048i	−0.264460	+	0.452798i
$137$	−11.4100			−0.974823			−0.487411	−	0.873172i	$-0.662059\pi$
$137$	−11.4100			−0.974823			−0.487411	+	0.873172i	$0.662059\pi$
$138$			3.09958i			0.263854i
$139$	−8.79752	+	8.79752i	−0.746196	+	0.746196i	−0.973762	−	0.227567i	$-0.926923\pi$
$139$	−8.79752	+	8.79752i	−0.746196	+	0.746196i	0.227567	+	0.973762i	$0.426923\pi$
$140$	−3.44836			−0.291440
$141$	−6.71970	+	6.71970i	−0.565901	+	0.565901i
$142$	−2.00357	−	2.00357i	−0.168136	−	0.168136i
$143$	3.65265	+	3.65265i	0.305450	+	0.305450i
$144$			0.889519i			0.0741266i
$145$			0.949264i			0.0788321i
$146$	−2.31201	−	2.31201i	−0.191343	−	0.191343i
$147$	−3.67513	−	3.67513i	−0.303120	−	0.303120i
$148$	−1.34152	+	1.34152i	−0.110272	+	0.110272i
$149$	19.1436			1.56830			0.784152	−	0.620569i	$-0.213098\pi$
$149$	19.1436			1.56830			0.784152	+	0.620569i	$0.213098\pi$
$150$	1.83904	−	1.83904i	0.150157	−	0.150157i
$151$			10.1065i			0.822453i	0.911533	+	0.411226i	$0.134899\pi$
$151$			10.1065i			0.822453i	−0.911533	+	0.411226i	$0.865101\pi$
$152$	−2.26165			−0.183444
$153$	0.590513	−	1.01105i	0.0477401	−	0.0817388i
$154$	−0.755178			−0.0608539
$155$			3.03475i			0.243757i
$156$	−11.1468	+	11.1468i	−0.892462	+	0.892462i
$157$	−13.1611			−1.05037			−0.525186	−	0.850988i	$-0.676004\pi$
$157$	−13.1611			−1.05037			−0.525186	+	0.850988i	$0.676004\pi$
$158$	−1.09760	+	1.09760i	−0.0873202	+	0.0873202i
$159$	8.82091	+	8.82091i	0.699543	+	0.699543i
$160$	2.80149	+	2.80149i	0.221477	+	0.221477i
$161$		−	9.57922i		−	0.754948i
$162$		−	3.10644i		−	0.244065i
$163$	−4.95865	−	4.95865i	−0.388391	−	0.388391i	0.485722	−	0.874113i	$-0.338557\pi$
$163$	−4.95865	−	4.95865i	−0.388391	−	0.388391i	−0.874113	+	0.485722i	$0.838557\pi$
$164$	0.791555	+	0.791555i	0.0618101	+	0.0618101i
$165$	1.10654	−	1.10654i	0.0861438	−	0.0861438i
$166$	0.968971			0.0752067
$167$	−13.8527	+	13.8527i	−1.07195	+	1.07195i	−0.0747525	+	0.997202i	$0.523817\pi$
$167$	−13.8527	+	13.8527i	−1.07195	+	1.07195i	−0.997202	+	0.0747525i	$0.976183\pi$
$168$		−	4.79371i		−	0.369843i
$169$	13.6837			1.05259
$170$	−0.382869	−	1.45810i	−0.0293647	−	0.111831i
$171$	0.433037			0.0331152
$172$			22.3693i			1.70564i
$173$	10.8788	−	10.8788i	0.827101	−	0.827101i	−0.160014	−	0.987115i	$-0.551154\pi$
$173$	10.8788	−	10.8788i	0.827101	−	0.827101i	0.987115	+	0.160014i	$0.0511539\pi$
$174$	−0.634406			−0.0480942
$175$	−5.68352	+	5.68352i	−0.429634	+	0.429634i
$176$	−2.21491	−	2.21491i	−0.166955	−	0.166955i
$177$	4.54226	+	4.54226i	0.341417	+	0.341417i
$178$		−	6.88500i		−	0.516053i
$179$			16.1356i			1.20603i	0.797728	+	0.603017i	$0.206035\pi$
$179$			16.1356i			1.20603i	−0.797728	+	0.603017i	$0.793965\pi$
$180$	−0.353070	−	0.353070i	−0.0263163	−	0.0263163i
$181$	−5.80686	−	5.80686i	−0.431621	−	0.431621i	0.457559	−	0.889179i	$-0.348724\pi$
$181$	−5.80686	−	5.80686i	−0.431621	−	0.431621i	−0.889179	+	0.457559i	$0.848724\pi$
$182$	−2.75840	+	2.75840i	−0.204466	+	0.204466i
$183$	−12.9976			−0.960813
$184$	−5.12245	+	5.12245i	−0.377632	+	0.377632i
$185$		−	0.972858i		−	0.0715260i
$186$	−2.02816			−0.148712
$187$	1.04715	+	3.98792i	0.0765751	+	0.291625i
$188$	−10.6776			−0.778747
$189$			10.6142i			0.772071i
$190$	0.394247	−	0.394247i	0.0286017	−	0.0286017i
$191$	−11.7990			−0.853745			−0.426872	−	0.904312i	$-0.640385\pi$
$191$	−11.7990			−0.853745			−0.426872	+	0.904312i	$0.640385\pi$
$192$	5.42824	−	5.42824i	0.391749	−	0.391749i
$193$	−4.85324	−	4.85324i	−0.349344	−	0.349344i	0.510521	−	0.859865i	$-0.329452\pi$
$193$	−4.85324	−	4.85324i	−0.349344	−	0.349344i	−0.859865	+	0.510521i	$0.829452\pi$
$194$	−4.26621	−	4.26621i	−0.306296	−	0.306296i
$195$		−	8.08358i		−	0.578877i
$196$		−	5.83981i		−	0.417129i
$197$	9.97907	+	9.97907i	0.710979	+	0.710979i	0.966740	−	0.255761i	$-0.0823259\pi$
$197$	9.97907	+	9.97907i	0.710979	+	0.710979i	−0.255761	+	0.966740i	$0.582326\pi$
$198$	−0.0773208	−	0.0773208i	−0.00549495	−	0.00549495i
$199$	3.28927	−	3.28927i	0.233171	−	0.233171i	−0.580844	−	0.814015i	$-0.697277\pi$
$199$	3.28927	−	3.28927i	0.233171	−	0.233171i	0.814015	+	0.580844i	$0.197277\pi$
$200$	6.07848			0.429813
$201$	12.6170	−	12.6170i	0.889931	−	0.889931i
$202$			2.30509i			0.162186i
$203$	1.96062			0.137609
$204$	−12.1700	+	3.19560i	−0.852070	+	0.223737i
$205$	−0.574028			−0.0400919
$206$			4.16379i			0.290105i
$207$	0.980793	−	0.980793i	0.0681698	−	0.0681698i
$208$	−16.1806			−1.12192
$209$	−1.07827	+	1.07827i	−0.0745853	+	0.0745853i
$210$	0.835632	+	0.835632i	0.0576641	+	0.0576641i
$211$	−4.19149	−	4.19149i	−0.288554	−	0.288554i	0.547954	−	0.836508i	$-0.315407\pi$
$211$	−4.19149	−	4.19149i	−0.288554	−	0.288554i	−0.836508	+	0.547954i	$0.815407\pi$
$212$			14.0165i			0.962656i
$213$		−	12.1271i		−	0.830938i
$214$	1.56379	+	1.56379i	0.106898	+	0.106898i
$215$	−8.11099	−	8.11099i	−0.553165	−	0.553165i
$216$	5.67591	−	5.67591i	0.386197	−	0.386197i
$217$	6.26800			0.425500
$218$	3.37783	−	3.37783i	0.228776	−	0.228776i
$219$		−	13.9940i		−	0.945630i
$220$	1.75830			0.118544
$221$	18.3913	+	10.7416i	1.23713	+	0.722557i
$222$	0.650175			0.0436369
$223$			5.15267i			0.345048i	0.985005	+	0.172524i	$0.0551923\pi$
$223$			5.15267i			0.345048i	−0.985005	+	0.172524i	$0.944808\pi$
$224$	5.78623	−	5.78623i	0.386609	−	0.386609i
$225$	−1.16384			−0.0775896
$226$	−4.02226	+	4.02226i	−0.267557	+	0.267557i
$227$	8.45487	+	8.45487i	0.561169	+	0.561169i	0.929640	−	0.368470i	$-0.120118\pi$
$227$	8.45487	+	8.45487i	0.561169	+	0.561169i	−0.368470	+	0.929640i	$0.620118\pi$
$228$	−3.29057	−	3.29057i	−0.217923	−	0.217923i
$229$			10.3301i			0.682630i	0.939949	+	0.341315i	$0.110872\pi$
$229$			10.3301i			0.682630i	−0.939949	+	0.341315i	$0.889128\pi$
$230$		−	1.78588i		−	0.117757i
$231$	−2.28546	−	2.28546i	−0.150372	−	0.150372i
$232$	−1.04844	−	1.04844i	−0.0688331	−	0.0688331i
$233$	17.9877	−	17.9877i	1.17841	−	1.17841i	0.198265	−	0.980148i	$-0.436469\pi$
$233$	17.9877	−	17.9877i	1.17841	−	1.17841i	0.980148	−	0.198265i	$-0.0635306\pi$
$234$	−0.564852			−0.0369255
$235$	3.87166	−	3.87166i	0.252559	−	0.252559i
$236$			7.21769i			0.469831i
$237$	−6.64350			−0.431542
$238$	−3.01159	+	0.790783i	−0.195212	+	0.0512589i
$239$	2.97242			0.192270			0.0961349	−	0.995368i	$-0.469352\pi$
$239$	2.97242			0.192270			0.0961349	+	0.995368i	$0.469352\pi$
$240$			4.90177i			0.316408i
$241$	1.47254	−	1.47254i	0.0948546	−	0.0948546i	−0.658087	−	0.752942i	$-0.728634\pi$
$241$	1.47254	−	1.47254i	0.0948546	−	0.0948546i	0.752942	+	0.658087i	$0.228634\pi$
$242$	0.385060			0.0247526
$243$	−2.07955	+	2.07955i	−0.133403	+	0.133403i
$244$	−10.3267	−	10.3267i	−0.661097	−	0.661097i
$245$	2.11749	+	2.11749i	0.135281	+	0.135281i
$246$		−	0.383631i		−	0.0244594i
$247$			7.87706i			0.501205i
$248$	−3.35179	−	3.35179i	−0.212839	−	0.212839i
$249$	2.93248	+	2.93248i	0.185838	+	0.185838i
$250$	−2.35229	+	2.35229i	−0.148772	+	0.148772i
$251$	−15.0598			−0.950565			−0.475283	−	0.879833i	$-0.657654\pi$
$251$	−15.0598			−0.950565			−0.475283	+	0.879833i	$0.657654\pi$
$252$	−0.729235	+	0.729235i	−0.0459375	+	0.0459375i
$253$			4.88437i			0.307078i
$254$	−5.77711			−0.362488
$255$	3.25407	−	5.57149i	0.203778	−	0.348900i
$256$	5.41223			0.338265
$257$			7.70433i			0.480583i	0.970701	+	0.240291i	$0.0772430\pi$
$257$			7.70433i			0.480583i	−0.970701	+	0.240291i	$0.922757\pi$
$258$	5.42068	−	5.42068i	0.337477	−	0.337477i
$259$	−2.00935			−0.124855
$260$	6.42243	−	6.42243i	0.398302	−	0.398302i
$261$	0.200743	+	0.200743i	0.0124257	+	0.0124257i
$262$	−2.80701	−	2.80701i	−0.173418	−	0.173418i
$263$			7.82307i			0.482391i	0.970477	+	0.241196i	$0.0775395\pi$
$263$			7.82307i			0.482391i	−0.970477	+	0.241196i	$0.922460\pi$
$264$			2.44428i			0.150435i
$265$	−5.08231	−	5.08231i	−0.312204	−	0.312204i
$266$	−0.814283	−	0.814283i	−0.0499269	−	0.0499269i
$267$	20.8367	−	20.8367i	1.27518	−	1.27518i
$268$	20.0484			1.22465
$269$	4.40191	−	4.40191i	0.268389	−	0.268389i	−0.560062	−	0.828451i	$-0.689223\pi$
$269$	4.40191	−	4.40191i	0.268389	−	0.268389i	0.828451	+	0.560062i	$0.189223\pi$
$270$			1.97883i			0.120428i
$271$	9.09737			0.552626			0.276313	−	0.961068i	$-0.410887\pi$
$271$	9.09737			0.552626			0.276313	+	0.961068i	$0.410887\pi$
$272$	−11.1522	−	6.51354i	−0.676203	−	0.394942i
$273$	−16.6959			−1.01048
$274$			4.39353i			0.265423i
$275$	2.89798	−	2.89798i	0.174755	−	0.174755i
$276$	−14.9057			−0.897219
$277$	13.9746	−	13.9746i	0.839652	−	0.839652i	−0.149161	−	0.988813i	$-0.547657\pi$
$277$	13.9746	−	13.9746i	0.839652	−	0.839652i	0.988813	+	0.149161i	$0.0476572\pi$
$278$	3.38757	+	3.38757i	0.203173	+	0.203173i
$279$	0.641766	+	0.641766i	0.0384215	+	0.0384215i
$280$			2.76197i			0.165059i
$281$			0.816370i			0.0487005i	0.999703	+	0.0243503i	$0.00775170\pi$
$281$			0.816370i			0.0487005i	−0.999703	+	0.0243503i	$0.992248\pi$
$282$	2.58748	+	2.58748i	0.154082	+	0.154082i
$283$	−5.06281	−	5.06281i	−0.300953	−	0.300953i	0.540434	−	0.841387i	$-0.318260\pi$
$283$	−5.06281	−	5.06281i	−0.300953	−	0.300953i	−0.841387	+	0.540434i	$0.818260\pi$
$284$	9.63506	−	9.63506i	0.571735	−	0.571735i
$285$	2.38629			0.141351
$286$	1.40649	−	1.40649i	0.0831673	−	0.0831673i
$287$			1.18560i			0.0699840i
$288$	1.18488			0.0698195
$289$	8.35188	+	14.8070i	0.491287	+	0.870998i
$290$	0.365523			0.0214643
$291$		−	25.8223i		−	1.51373i
$292$	11.1183	−	11.1183i	0.650650	−	0.650650i
$293$	−9.52187			−0.556274			−0.278137	−	0.960541i	$-0.589717\pi$
$293$	−9.52187			−0.556274			−0.278137	+	0.960541i	$0.589717\pi$
$294$	−1.41515	+	1.41515i	−0.0825330	+	0.0825330i
$295$	−2.61710	−	2.61710i	−0.152373	−	0.152373i
$296$	1.07449	+	1.07449i	0.0624537	+	0.0624537i
$297$		−	5.41211i		−	0.314043i
$298$		−	7.37142i		−	0.427015i
$299$	17.8409	+	17.8409i	1.03177	+	1.03177i
$300$	8.84383	+	8.84383i	0.510599	+	0.510599i
$301$	−16.7525	+	16.7525i	−0.965600	+	0.965600i
$302$	3.89159			0.223936
$303$	−6.97608	+	6.97608i	−0.400766	+	0.400766i
$304$		−	4.77653i		−	0.273953i
$305$	7.48879			0.428807
$306$	−0.389316	−	0.227383i	−0.0222557	−	0.0129986i
$307$	16.0064			0.913535			0.456767	−	0.889586i	$-0.349007\pi$
$307$	16.0064			0.913535			0.456767	+	0.889586i	$0.349007\pi$
$308$		−	3.63161i		−	0.206930i
$309$	−12.6012	+	12.6012i	−0.716859	+	0.716859i
$310$	1.16856			0.0663696
$311$	−5.96095	+	5.96095i	−0.338015	+	0.338015i	−0.855620	−	0.517605i	$-0.826824\pi$
$311$	−5.96095	+	5.96095i	−0.338015	+	0.338015i	0.517605	+	0.855620i	$0.326824\pi$
$312$	8.92808	+	8.92808i	0.505453	+	0.505453i
$313$	6.50866	+	6.50866i	0.367891	+	0.367891i	0.866708	−	0.498817i	$-0.166232\pi$
$313$	6.50866	+	6.50866i	0.367891	+	0.367891i	−0.498817	+	0.866708i	$0.666232\pi$
$314$			5.06782i			0.285993i
$315$		−	0.528834i		−	0.0297964i
$316$	−5.27829	−	5.27829i	−0.296927	−	0.296927i
$317$	8.05709	+	8.05709i	0.452531	+	0.452531i	0.896194	−	0.443663i	$-0.146321\pi$
$317$	8.05709	+	8.05709i	0.452531	+	0.452531i	−0.443663	+	0.896194i	$0.646321\pi$
$318$	3.39657	−	3.39657i	0.190470	−	0.190470i
$319$	−0.999707			−0.0559729
$320$	−3.12757	+	3.12757i	−0.174836	+	0.174836i
$321$			9.46523i			0.528298i
$322$	−3.68857			−0.205556
$323$	−3.17093	+	5.42915i	−0.176435	+	0.302086i
$324$	14.9387			0.829927
$325$		−	21.1706i		−	1.17434i
$326$	−1.90937	+	1.90937i	−0.105750	+	0.105750i
$327$	20.4452			1.13062
$328$	0.633997	−	0.633997i	0.0350066	−	0.0350066i
$329$	−7.99658	−	7.99658i	−0.440866	−	0.440866i
$330$	−0.426083	−	0.426083i	−0.0234551	−	0.0234551i
$331$		−	34.2962i		−	1.88509i	−0.334083	−	0.942544i	$-0.608426\pi$
$331$		−	34.2962i		−	1.88509i	0.334083	−	0.942544i	$-0.391574\pi$
$332$			4.65972i			0.255736i
$333$	−0.205733	−	0.205733i	−0.0112741	−	0.0112741i
$334$	5.33412	+	5.33412i	0.291870	+	0.291870i
$335$	−7.26946	+	7.26946i	−0.397173	+	0.397173i
$336$	10.1242			0.552319
$337$	−16.1614	+	16.1614i	−0.880369	+	0.880369i	−0.993572	−	0.113203i	$-0.963889\pi$
$337$	−16.1614	+	16.1614i	−0.880369	+	0.880369i	0.113203	+	0.993572i	$0.463889\pi$
$338$		−	5.26902i		−	0.286597i
$339$	−24.3458			−1.32228
$340$	7.01193	−	1.84120i	0.380276	−	0.0998529i
$341$	−3.19601			−0.173074
$342$		−	0.166745i		−	0.00901654i
$343$	14.0809	−	14.0809i	0.760298	−	0.760298i
$344$	17.9167			0.966004
$345$	5.40474	−	5.40474i	0.290981	−	0.290981i
$346$	−4.18899	−	4.18899i	−0.225202	−	0.225202i
$347$	19.9872	+	19.9872i	1.07297	+	1.07297i	0.997119	+	0.0758522i	$0.0241677\pi$
$347$	19.9872	+	19.9872i	1.07297	+	1.07297i	0.0758522	+	0.997119i	$0.475832\pi$
$348$		−	3.05082i		−	0.163541i
$349$		−	1.87216i		−	0.100215i	−0.998744	−	0.0501073i	$-0.984044\pi$
$349$		−	1.87216i		−	0.100215i	0.998744	−	0.0501073i	$-0.0159563\pi$
$350$	2.18849	+	2.18849i	0.116980	+	0.116980i
$351$	−19.7685	−	19.7685i	−1.05517	−	1.05517i
$352$	−2.95036	+	2.95036i	−0.157255	+	0.157255i
$353$	−24.3640			−1.29676			−0.648382	−	0.761315i	$-0.724554\pi$
$353$	−24.3640			−1.29676			−0.648382	+	0.761315i	$0.724554\pi$
$354$	1.74904	−	1.74904i	0.0929605	−	0.0929605i
$355$			6.98725i			0.370845i
$356$	33.1096			1.75480
$357$	−11.5074	−	6.72100i	−0.609037	−	0.355713i
$358$	6.21318			0.328377
$359$			11.4432i			0.603950i	0.953316	+	0.301975i	$0.0976458\pi$
$359$			11.4432i			0.603950i	−0.953316	+	0.301975i	$0.902354\pi$
$360$	−0.282792	+	0.282792i	−0.0149044	+	0.0149044i
$361$	16.6747			0.877615
$362$	−2.23599	+	2.23599i	−0.117521	+	0.117521i
$363$	1.16534	+	1.16534i	0.0611644	+	0.0611644i
$364$	−13.2650	−	13.2650i	−0.695273	−	0.695273i
$365$			8.06289i			0.422031i
$366$			5.00486i			0.261608i
$367$	−25.0081	−	25.0081i	−1.30541	−	1.30541i	−0.924688	−	0.380727i	$-0.875674\pi$
$367$	−25.0081	−	25.0081i	−1.30541	−	1.30541i	−0.380727	−	0.924688i	$-0.624326\pi$
$368$	−10.8185	−	10.8185i	−0.563951	−	0.563951i
$369$	−0.121391	+	0.121391i	−0.00631938	+	0.00631938i
$370$	−0.374608			−0.0194750
$371$	−10.4971	+	10.4971i	−0.544980	+	0.544980i
$372$		−	9.75331i		−	0.505686i
$373$	−30.4381			−1.57603			−0.788013	−	0.615659i	$-0.788890\pi$
$373$	−30.4381			−1.57603			−0.788013	+	0.615659i	$0.788890\pi$
$374$	1.53559	−	0.403215i	0.0794032	−	0.0208497i
$375$	−14.2379			−0.735240
$376$			8.55228i			0.441050i
$377$	−3.65158	+	3.65158i	−0.188066	+	0.188066i
$378$	4.08711			0.210218
$379$	−22.9578	+	22.9578i	−1.17926	+	1.17926i	−0.199329	+	0.979933i	$0.563876\pi$
$379$	−22.9578	+	22.9578i	−1.17926	+	1.17926i	−0.979933	+	0.199329i	$0.936124\pi$
$380$	1.89591	+	1.89591i	0.0972582	+	0.0972582i
$381$	−17.4837	−	17.4837i	−0.895719	−	0.895719i
$382$			4.54331i			0.232456i
$383$			19.8664i			1.01513i	0.861614	+	0.507564i	$0.169454\pi$
$383$			19.8664i			1.01513i	−0.861614	+	0.507564i	$0.830546\pi$
$384$	−11.8148	−	11.8148i	−0.602921	−	0.602921i
$385$	1.31680	+	1.31680i	0.0671104	+	0.0671104i
$386$	−1.86879	+	1.86879i	−0.0951188	+	0.0951188i
$387$	−3.43051			−0.174382
$388$	20.5159	−	20.5159i	1.04154	−	1.04154i
$389$			35.3987i			1.79478i	0.441235	+	0.897392i	$0.354541\pi$
$389$			35.3987i			1.79478i	−0.441235	+	0.897392i	$0.645459\pi$
$390$	−3.11266			−0.157616
$391$	5.11467	+	19.4785i	0.258660	+	0.985069i
$392$	−4.67741			−0.236245
$393$		−	16.9902i		−	0.857040i
$394$	3.84254	−	3.84254i	0.193584	−	0.193584i
$395$	3.82776			0.192596
$396$	0.371831	−	0.371831i	0.0186852	−	0.0186852i
$397$	−22.7657	−	22.7657i	−1.14258	−	1.14258i	−0.987977	−	0.154600i	$-0.950591\pi$
$397$	−22.7657	−	22.7657i	−1.14258	−	1.14258i	−0.154600	−	0.987977i	$-0.549409\pi$
$398$	−1.26657	−	1.26657i	−0.0634873	−	0.0634873i
$399$		−	4.92866i		−	0.246742i
$400$			12.8376i			0.641878i
$401$	−8.83174	−	8.83174i	−0.441036	−	0.441036i	0.451324	−	0.892360i	$-0.350952\pi$
$401$	−8.83174	−	8.83174i	−0.441036	−	0.441036i	−0.892360	+	0.451324i	$0.850952\pi$
$402$	−4.85828	−	4.85828i	−0.242309	−	0.242309i
$403$	−11.6739	+	11.6739i	−0.581518	+	0.581518i
$404$	−11.0850			−0.551502
$405$	−5.41669	+	5.41669i	−0.269158	+	0.269158i
$406$		−	0.754957i		−	0.0374679i
$407$	1.02456			0.0507853
$408$	2.55952	+	9.74757i	0.126715	+	0.482577i
$409$	7.71202			0.381335			0.190668	−	0.981655i	$-0.438935\pi$
$409$	7.71202			0.381335			0.190668	+	0.981655i	$0.438935\pi$
$410$			0.221035i			0.0109161i
$411$	−13.2965	+	13.2965i	−0.655869	+	0.655869i
$412$	−20.0234			−0.986484
$413$	−5.40539	+	5.40539i	−0.265982	+	0.265982i
$414$	−0.377664	−	0.377664i	−0.0185612	−	0.0185612i
$415$	−1.68959	−	1.68959i	−0.0829389	−	0.0829389i
$416$			21.5532i			1.05673i
$417$			20.5041i			1.00409i
$418$	0.415197	+	0.415197i	0.0203080	+	0.0203080i
$419$	25.2367	+	25.2367i	1.23289	+	1.23289i	0.962847	+	0.270048i	$0.0870396\pi$
$419$	25.2367	+	25.2367i	1.23289	+	1.23289i	0.270048	+	0.962847i	$0.412960\pi$
$420$	−4.01851	+	4.01851i	−0.196083	+	0.196083i
$421$	−18.8006			−0.916285			−0.458143	−	0.888879i	$-0.651485\pi$
$421$	−18.8006			−0.916285			−0.458143	+	0.888879i	$0.651485\pi$
$422$	−1.61397	+	1.61397i	−0.0785670	+	0.0785670i
$423$		−	1.63750i		−	0.0796180i
$424$	11.2265			0.545208
$425$	8.52230	−	14.5915i	0.413392	−	0.707794i
$426$	−4.66967			−0.226246
$427$		−	15.4675i		−	0.748522i
$428$	−7.52016	+	7.52016i	−0.363501	+	0.363501i
$429$	8.51313			0.411018
$430$	−3.12321	+	3.12321i	−0.150615	+	0.150615i
$431$	22.5408	+	22.5408i	1.08575	+	1.08575i	0.995961	+	0.0897899i	$0.0286196\pi$
$431$	22.5408	+	22.5408i	1.08575	+	1.08575i	0.0897899	+	0.995961i	$0.471380\pi$
$432$	11.9874	+	11.9874i	0.576742	+	0.576742i
$433$		−	25.7742i		−	1.23863i	−0.785142	−	0.619316i	$-0.787410\pi$
$433$		−	25.7742i		−	1.23863i	0.785142	−	0.619316i	$-0.212590\pi$
$434$		−	2.41355i		−	0.115854i
$435$	1.10621	+	1.10621i	0.0530389	+	0.0530389i
$436$	16.2438	+	16.2438i	0.777936	+	0.777936i
$437$	−5.26666	+	5.26666i	−0.251938	+	0.251938i
$438$	−5.38854			−0.257474
$439$	−20.0578	+	20.0578i	−0.957308	+	0.957308i	−0.999125	−	0.0418172i	$-0.986685\pi$
$439$	−20.0578	+	20.0578i	−0.957308	+	0.957308i	0.0418172	+	0.999125i	$0.486685\pi$
$440$		−	1.40831i		−	0.0671385i
$441$	0.895581			0.0426467
$442$	4.13615	−	7.08175i	0.196737	−	0.336845i
$443$	31.7482			1.50840			0.754201	−	0.656643i	$-0.228024\pi$
$443$	31.7482			1.50840			0.754201	+	0.656643i	$0.228024\pi$
$444$			3.12665i			0.148384i
$445$	−12.0054	+	12.0054i	−0.569109	+	0.569109i
$446$	1.98408			0.0939491
$447$	22.3087	−	22.3087i	1.05517	−	1.05517i
$448$	6.45971	+	6.45971i	0.305193	+	0.305193i
$449$	−7.78489	−	7.78489i	−0.367391	−	0.367391i	0.499134	−	0.866525i	$-0.333652\pi$
$449$	−7.78489	−	7.78489i	−0.367391	−	0.367391i	−0.866525	+	0.499134i	$0.833652\pi$
$450$			0.448149i			0.0211260i
$451$		−	0.604531i		−	0.0284663i
$452$	−19.3428	−	19.3428i	−0.909810	−	0.909810i
$453$	11.7774	+	11.7774i	0.553353	+	0.553353i
$454$	3.25563	−	3.25563i	0.152794	−	0.152794i
$455$	9.61963			0.450975
$456$	−2.63558	+	2.63558i	−0.123422	+	0.123422i
$457$			1.68703i			0.0789158i	0.999221	+	0.0394579i	$0.0125631\pi$
$457$			1.68703i			0.0789158i	−0.999221	+	0.0394579i	$0.987437\pi$
$458$	3.97769			0.185865
$459$	−5.66729	−	21.5831i	−0.264526	−	1.00741i
$460$	8.58817			0.400425
$461$		−	25.6955i		−	1.19676i	−0.801213	−	0.598380i	$-0.795811\pi$
$461$		−	25.6955i		−	1.19676i	0.801213	−	0.598380i	$-0.204189\pi$
$462$	−0.880037	+	0.880037i	−0.0409430	+	0.0409430i
$463$	−3.82859			−0.177930			−0.0889648	−	0.996035i	$-0.528356\pi$
$463$	−3.82859			−0.177930			−0.0889648	+	0.996035i	$0.528356\pi$
$464$	2.21426	−	2.21426i	0.102795	−	0.102795i
$465$	3.53650	+	3.53650i	0.164001	+	0.164001i
$466$	−6.92634	−	6.92634i	−0.320856	−	0.320856i
$467$			10.3399i			0.478474i	0.970961	+	0.239237i	$0.0768973\pi$
$467$			10.3399i			0.478474i	−0.970961	+	0.239237i	$0.923103\pi$
$468$		−	2.71634i		−	0.125563i
$469$	15.0144	+	15.0144i	0.693302	+	0.693302i
$470$	−1.49082	−	1.49082i	−0.0687664	−	0.0687664i
$471$	−15.3371	+	15.3371i	−0.706698	+	0.706698i
$472$	5.78102			0.266093
$473$	8.54200	−	8.54200i	0.392761	−	0.392761i
$474$			2.55815i			0.117499i
$475$	6.24960			0.286751
$476$	−3.80283	−	14.4825i	−0.174302	−	0.663806i
$477$	−2.14954			−0.0984206
$478$		−	1.14456i		−	0.0523509i
$479$	22.2838	−	22.2838i	1.01817	−	1.01817i	0.0183415	−	0.999832i	$-0.494161\pi$
$479$	22.2838	−	22.2838i	1.01817	−	1.01817i	0.999832	−	0.0183415i	$-0.00583860\pi$
$480$	6.52936			0.298023
$481$	3.74234	−	3.74234i	0.170636	−	0.170636i
$482$	−0.567016	−	0.567016i	−0.0258269	−	0.0258269i
$483$	−11.1630	−	11.1630i	−0.507935	−	0.507935i
$484$			1.85173i			0.0841695i
$485$			14.8780i			0.675573i
$486$	0.800752	+	0.800752i	0.0363228	+	0.0363228i
$487$	11.5071	+	11.5071i	0.521438	+	0.521438i	0.918006	−	0.396567i	$-0.129799\pi$
$487$	11.5071	+	11.5071i	0.521438	+	0.521438i	−0.396567	+	0.918006i	$0.629799\pi$
$488$	−8.27116	+	8.27116i	−0.374418	+	0.374418i
$489$	−11.5570			−0.522625
$490$	0.815359	−	0.815359i	0.0368341	−	0.0368341i
$491$		−	6.27810i		−	0.283327i	−0.989915	−	0.141663i	$-0.954755\pi$
$491$		−	6.27810i		−	0.283327i	0.989915	−	0.141663i	$-0.0452450\pi$
$492$	1.84486			0.0831726
$493$	−3.98675	+	1.04684i	−0.179554	+	0.0471474i
$494$	3.03314			0.136467
$495$			0.269648i			0.0121198i
$496$	7.07888	−	7.07888i	0.317851	−	0.317851i
$497$	14.4316			0.647344
$498$	1.12918	−	1.12918i	0.0505997	−	0.0505997i
$499$	−12.8301	−	12.8301i	−0.574355	−	0.574355i	0.358987	−	0.933342i	$-0.383122\pi$
$499$	−12.8301	−	12.8301i	−0.574355	−	0.574355i	−0.933342	+	0.358987i	$0.883122\pi$
$500$	−11.3120	−	11.3120i	−0.505889	−	0.505889i
$501$			32.2862i			1.44244i
$502$			5.79892i			0.258818i
$503$	7.38760	+	7.38760i	0.329397	+	0.329397i	0.852357	−	0.522960i	$-0.175172\pi$
$503$	7.38760	+	7.38760i	0.329397	+	0.329397i	−0.522960	+	0.852357i	$0.675172\pi$
$504$	0.584082	+	0.584082i	0.0260171	+	0.0260171i
$505$	4.01938	−	4.01938i	0.178860	−	0.178860i
$506$	1.88077			0.0836106
$507$	15.9461	−	15.9461i	0.708190	−	0.708190i
$508$		−	27.7818i		−	1.23262i
$509$	−26.8687			−1.19093			−0.595467	−	0.803380i	$-0.703033\pi$
$509$	−26.8687			−1.19093			−0.595467	+	0.803380i	$0.703033\pi$
$510$	−2.14535	−	1.25301i	−0.0949979	−	0.0554842i
$511$	16.6532			0.736694
$512$		−	22.3611i		−	0.988228i
$513$	5.83570	−	5.83570i	0.257653	−	0.257653i
$514$	2.96663			0.130852
$515$	7.26040	−	7.26040i	0.319931	−	0.319931i
$516$	26.0678	+	26.0678i	1.14757	+	1.14757i
$517$	4.07740	+	4.07740i	0.179324	+	0.179324i
$518$			0.773721i			0.0339954i
$519$		−	25.3550i		−	1.11296i
$520$	−5.14406	−	5.14406i	−0.225582	−	0.225582i
$521$	7.50911	+	7.50911i	0.328980	+	0.328980i	0.852199	−	0.523219i	$-0.175269\pi$
$521$	7.50911	+	7.50911i	0.328980	+	0.328980i	−0.523219	+	0.852199i	$0.675269\pi$
$522$	0.0772982	−	0.0772982i	0.00338325	−	0.00338325i
$523$	39.7389			1.73766			0.868830	−	0.495111i	$-0.164873\pi$
$523$	39.7389			1.73766			0.868830	+	0.495111i	$0.164873\pi$
$524$	13.4987	−	13.4987i	0.589695	−	0.589695i
$525$			13.2464i			0.578122i
$526$	3.01235			0.131345
$527$	−12.7454	+	3.34670i	−0.555199	+	0.145784i
$528$	−5.16224			−0.224658
$529$			0.857100i			0.0372652i
$530$	−1.95699	+	1.95699i	−0.0850063	+	0.0850063i
$531$	−1.10689			−0.0480349
$532$	3.91584	−	3.91584i	0.169773	−	0.169773i
$533$	−2.20814	−	2.20814i	−0.0956451	−	0.0956451i
$534$	−8.02335	−	8.02335i	−0.347204	−	0.347204i
$535$		−	5.45355i		−	0.235777i
$536$		−	16.0578i		−	0.693592i
$537$	18.8035	+	18.8035i	0.811429	+	0.811429i
$538$	−1.69500	−	1.69500i	−0.0730766	−	0.0730766i
$539$	−2.23001	+	2.23001i	−0.0960532	+	0.0960532i
$540$	−9.51609			−0.409507
$541$	−11.1783	+	11.1783i	−0.480593	+	0.480593i	−0.905321	−	0.424728i	$-0.860370\pi$
$541$	−11.1783	+	11.1783i	−0.480593	+	0.480593i	0.424728	+	0.905321i	$0.360370\pi$
$542$		−	3.50303i		−	0.150468i
$543$	−13.5339			−0.580796
$544$	−8.67632	+	14.8552i	−0.371994	+	0.636913i
$545$	−11.7798			−0.504593
$546$			6.42893i			0.275133i
$547$	−17.1377	+	17.1377i	−0.732757	+	0.732757i	−0.971165	−	0.238408i	$-0.923374\pi$
$547$	−17.1377	+	17.1377i	−0.732757	+	0.732757i	0.238408	+	0.971165i	$0.423374\pi$
$548$	−21.1282			−0.902554
$549$	1.58368	−	1.58368i	0.0675896	−	0.0675896i
$550$	−1.11590	−	1.11590i	−0.0475820	−	0.0475820i
$551$	−1.07795	−	1.07795i	−0.0459223	−	0.0459223i
$552$			11.9388i			0.508147i
$553$		−	7.90591i		−	0.336193i
$554$	−5.38105	−	5.38105i	−0.228619	−	0.228619i
$555$	−1.13371	−	1.13371i	−0.0481232	−	0.0481232i
$556$	−16.2906	+	16.2906i	−0.690876	+	0.690876i
$557$	−35.8297			−1.51816			−0.759078	−	0.651000i	$-0.774350\pi$
$557$	−35.8297			−1.51816			−0.759078	+	0.651000i	$0.774350\pi$
$558$	0.247118	−	0.247118i	0.0104613	−	0.0104613i
$559$		−	62.4018i		−	2.63932i
$560$	−5.83320			−0.246498
$561$	5.86755	+	3.42699i	0.247728	+	0.144688i
$562$	0.314351			0.0132601
$563$			2.48651i			0.104794i	0.998626	+	0.0523970i	$0.0166861\pi$
$563$			2.48651i			0.104794i	−0.998626	+	0.0523970i	$0.983314\pi$
$564$	−12.4431	+	12.4431i	−0.523947	+	0.523947i
$565$	14.0272			0.590130
$566$	−1.94948	+	1.94948i	−0.0819429	+	0.0819429i
$567$	11.1877	+	11.1877i	0.469840	+	0.469840i
$568$	−7.71721	−	7.71721i	−0.323807	−	0.323807i
$569$			6.52522i			0.273551i	0.990602	+	0.136776i	$0.0436740\pi$
$569$			6.52522i			0.273551i	−0.990602	+	0.136776i	$0.956326\pi$
$570$		−	0.918862i		−	0.0384869i
$571$	3.78011	+	3.78011i	0.158193	+	0.158193i	0.781765	−	0.623573i	$-0.214319\pi$
$571$	3.78011	+	3.78011i	0.158193	+	0.158193i	−0.623573	+	0.781765i	$0.714319\pi$
$572$	6.76371	+	6.76371i	0.282805	+	0.282805i
$573$	−13.7498	+	13.7498i	−0.574406	+	0.574406i
$574$	0.456528			0.0190551
$575$	14.1548	−	14.1548i	0.590298	−	0.590298i
$576$			1.32279i			0.0551162i
$577$	20.8807			0.869276			0.434638	−	0.900605i	$-0.356876\pi$
$577$	20.8807			0.869276			0.434638	+	0.900605i	$0.356876\pi$
$578$	5.70156	−	3.21597i	0.237154	−	0.133767i
$579$	−11.3113			−0.470083
$580$			1.75778i			0.0729879i
$581$	−3.48971	+	3.48971i	−0.144777	+	0.144777i
$582$	−9.94314			−0.412156
$583$	5.35238	−	5.35238i	0.221673	−	0.221673i
$584$	−8.90523	−	8.90523i	−0.368501	−	0.368501i
$585$	0.984931	+	0.984931i	0.0407219	+	0.0407219i
$586$			3.66649i			0.151461i
$587$		−	44.9951i		−	1.85714i	−0.371151	−	0.928572i	$-0.621037\pi$
$587$		−	44.9951i		−	1.85714i	0.371151	−	0.928572i	$-0.378963\pi$
$588$	−6.80535	−	6.80535i	−0.280648	−	0.280648i
$589$	−3.44615	−	3.44615i	−0.141996	−	0.141996i
$590$	−1.00774	+	1.00774i	−0.0414879	+	0.0414879i
$591$	23.2580			0.956705
$592$	−2.26930	+	2.26930i	−0.0932676	+	0.0932676i
$593$		−	11.8389i		−	0.486165i	−0.970006	−	0.243083i	$-0.921841\pi$
$593$		−	11.8389i		−	0.486165i	0.970006	−	0.243083i	$-0.0781586\pi$
$594$	−2.08399			−0.0855070
$595$	6.63018	+	3.87241i	0.271811	+	0.158753i
$596$	35.4487			1.45204
$597$		−	7.66623i		−	0.313758i
$598$	6.86981	−	6.86981i	0.280927	−	0.280927i
$599$	35.5127			1.45101			0.725505	−	0.688217i	$-0.241606\pi$
$599$	35.5127			1.45101			0.725505	+	0.688217i	$0.241606\pi$
$600$	7.08348	−	7.08348i	0.289182	−	0.289182i
$601$	−27.2987	−	27.2987i	−1.11354	−	1.11354i	−0.992668	−	0.120869i	$-0.961432\pi$
$601$	−27.2987	−	27.2987i	−1.11354	−	1.11354i	−0.120869	−	0.992668i	$-0.538568\pi$
$602$	6.45073	+	6.45073i	0.262912	+	0.262912i
$603$			3.07458i			0.125207i
$604$			18.7144i			0.761480i
$605$	−0.671428	−	0.671428i	−0.0272974	−	0.0272974i
$606$	2.68621	+	2.68621i	0.109120	+	0.109120i
$607$	−0.702148	+	0.702148i	−0.0284993	+	0.0284993i	−0.721213	−	0.692714i	$-0.756415\pi$
$607$	−0.702148	+	0.702148i	−0.0284993	+	0.0284993i	0.692714	+	0.721213i	$0.256415\pi$
$608$	−6.36255			−0.258035
$609$	2.28479	−	2.28479i	0.0925842	−	0.0925842i
$610$		−	2.88363i		−	0.116755i
$611$	29.7866			1.20504
$612$	1.09347	−	1.87220i	0.0442009	−	0.0756790i
$613$	39.4882			1.59491			0.797457	−	0.603376i	$-0.206178\pi$
$613$	39.4882			1.59491			0.797457	+	0.603376i	$0.206178\pi$
$614$		−	6.16343i		−	0.248736i
$615$	−0.668936	+	0.668936i	−0.0269741	+	0.0269741i
$616$	−2.90874			−0.117196
$617$	21.6360	−	21.6360i	0.871032	−	0.871032i	−0.121553	−	0.992585i	$-0.538787\pi$
$617$	21.6360	−	21.6360i	0.871032	−	0.871032i	0.992585	+	0.121553i	$0.0387873\pi$
$618$	4.85222	+	4.85222i	0.195185	+	0.195185i
$619$	6.49527	+	6.49527i	0.261067	+	0.261067i	0.825487	−	0.564421i	$-0.190900\pi$
$619$	6.49527	+	6.49527i	0.261067	+	0.261067i	−0.564421	+	0.825487i	$0.690900\pi$
$620$			5.61953i			0.225686i
$621$		−	26.4348i		−	1.06079i
$622$	2.29532	+	2.29532i	0.0920340	+	0.0920340i
$623$	24.7960	+	24.7960i	0.993433	+	0.993433i
$624$	−18.8558	+	18.8558i	−0.754838	+	0.754838i
$625$	−12.2885			−0.491539
$626$	2.50622	−	2.50622i	0.100169	−	0.100169i
$627$			2.51309i			0.100363i
$628$	−24.3708			−0.972502
$629$	4.08584	−	1.07286i	0.162913	−	0.0427778i
$630$	−0.203633			−0.00811291
$631$		−	40.0856i		−	1.59578i	−0.602802	−	0.797891i	$-0.705949\pi$
$631$		−	40.0856i		−	1.59578i	0.602802	−	0.797891i	$-0.294051\pi$
$632$	−4.22765	+	4.22765i	−0.168167	+	0.168167i
$633$	−9.76899			−0.388283
$634$	3.10246	−	3.10246i	0.123214	−	0.123214i
$635$	10.0735	+	10.0735i	0.399756	+	0.399756i
$636$	16.3339	+	16.3339i	0.647682	+	0.647682i
$637$			16.2909i			0.645467i
$638$			0.384947i			0.0152402i
$639$	1.47761	+	1.47761i	0.0584534	+	0.0584534i
$640$	6.80728	+	6.80728i	0.269081	+	0.269081i
$641$	−15.1764	+	15.1764i	−0.599431	+	0.599431i	−0.940161	−	0.340730i	$-0.889326\pi$
$641$	−15.1764	+	15.1764i	−0.599431	+	0.599431i	0.340730	+	0.940161i	$0.389326\pi$
$642$	3.64468			0.143844
$643$	−20.1890	+	20.1890i	−0.796175	+	0.796175i	−0.982490	−	0.186315i	$-0.940345\pi$
$643$	−20.1890	+	20.1890i	−0.796175	+	0.796175i	0.186315	+	0.982490i	$0.440345\pi$
$644$		−	17.7381i		−	0.698980i
$645$	−18.9041			−0.744347
$646$	2.09054	+	1.22100i	0.0822514	+	0.0480395i
$647$	−20.1988			−0.794096			−0.397048	−	0.917798i	$-0.629965\pi$
$647$	−20.1988			−0.794096			−0.397048	+	0.917798i	$0.629965\pi$
$648$		−	11.9652i		−	0.470036i
$649$	2.75617	−	2.75617i	0.108189	−	0.108189i
$650$	−8.15195			−0.319746
$651$	7.30434	−	7.30434i	0.286280	−	0.286280i
$652$	−9.18207	−	9.18207i	−0.359598	−	0.359598i
$653$	1.81843	+	1.81843i	0.0711605	+	0.0711605i	0.741791	−	0.670631i	$-0.233976\pi$
$653$	1.81843	+	1.81843i	0.0711605	+	0.0711605i	−0.670631	+	0.741791i	$0.733976\pi$
$654$		−	7.87263i		−	0.307844i
$655$			9.78915i			0.382494i
$656$	1.33898	+	1.33898i	0.0522785	+	0.0522785i
$657$	1.70508	+	1.70508i	0.0665216	+	0.0665216i
$658$	−3.07916	+	3.07916i	−0.120038	+	0.120038i
$659$	−27.1974			−1.05946			−0.529730	−	0.848166i	$-0.677707\pi$
$659$	−27.1974			−1.05946			−0.529730	+	0.848166i	$0.677707\pi$
$660$	2.04901	−	2.04901i	0.0797575	−	0.0797575i
$661$			36.8469i			1.43318i	0.697496	+	0.716589i	$0.254297\pi$
$661$			36.8469i			1.43318i	−0.697496	+	0.716589i	$0.745703\pi$
$662$	−13.2061			−0.513268
$663$	33.9497	−	8.91452i	1.31850	−	0.346211i
$664$	3.73221			0.144838
$665$			2.83973i			0.110120i
$666$	−0.0792195	+	0.0792195i	−0.00306969	+	0.00306969i
$667$	−4.88294			−0.189068
$668$	−25.6515	+	25.6515i	−0.992485	+	0.992485i
$669$	6.00460	+	6.00460i	0.232151	+	0.232151i
$670$	2.79918	+	2.79918i	0.108142	+	0.108142i
$671$			7.88674i			0.304464i
$672$		−	13.4858i		−	0.520227i
$673$	17.8590	+	17.8590i	0.688415	+	0.688415i	0.961881	−	0.273467i	$-0.0881703\pi$
$673$	17.8590	+	17.8590i	0.688415	+	0.688415i	−0.273467	+	0.961881i	$0.588170\pi$
$674$	6.22311	+	6.22311i	0.239705	+	0.239705i
$675$	−15.6842	+	15.6842i	−0.603686	+	0.603686i
$676$	25.3384			0.974555
$677$	−35.6980	+	35.6980i	−1.37199	+	1.37199i	−0.514487	+	0.857498i	$0.672018\pi$
$677$	−35.6980	+	35.6980i	−1.37199	+	1.37199i	−0.857498	+	0.514487i	$0.827982\pi$
$678$			9.37458i			0.360029i
$679$	30.7291			1.17928
$680$	−1.47471	−	5.61622i	−0.0565525	−	0.215372i
$681$	19.7055			0.755118
$682$			1.23065i			0.0471242i
$683$	−2.50913	+	2.50913i	−0.0960093	+	0.0960093i	−0.753480	−	0.657471i	$-0.771626\pi$
$683$	−2.50913	+	2.50913i	−0.0960093	+	0.0960093i	0.657471	+	0.753480i	$0.271626\pi$
$684$	0.801867			0.0306602
$685$	7.66100	−	7.66100i	0.292712	−	0.292712i
$686$	−5.42199	−	5.42199i	−0.207013	−	0.207013i
$687$	12.0380	+	12.0380i	0.459279	+	0.459279i
$688$			37.8396i			1.44262i
$689$		−	39.1007i		−	1.48962i
$690$	−2.08115	−	2.08115i	−0.0792279	−	0.0792279i
$691$	−19.4235	−	19.4235i	−0.738907	−	0.738907i	0.233460	−	0.972366i	$-0.424995\pi$
$691$	−19.4235	−	19.4235i	−0.738907	−	0.738907i	−0.972366	+	0.233460i	$0.924995\pi$
$692$	20.1446	−	20.1446i	0.765783	−	0.765783i
$693$	0.556935			0.0211562
$694$	7.69628	−	7.69628i	0.292147	−	0.292147i
$695$		−	11.8138i		−	0.448123i
$696$	−2.44356			−0.0926229
$697$	−0.633034	−	2.41082i	−0.0239779	−	0.0913163i
$698$	−0.720894			−0.0272863
$699$		−	41.9235i		−	1.58569i
$700$	−10.5243	+	10.5243i	−0.397783	+	0.397783i
$701$	−21.9422			−0.828744			−0.414372	−	0.910108i	$-0.635999\pi$
$701$	−21.9422			−0.828744			−0.414372	+	0.910108i	$0.635999\pi$
$702$	−7.61207	+	7.61207i	−0.287299	+	0.287299i
$703$	1.10474	+	1.10474i	0.0416662	+	0.0416662i
$704$	−3.29376	−	3.29376i	−0.124138	−	0.124138i
$705$		−	9.02358i		−	0.339848i
$706$			9.38159i			0.353081i
$707$	−8.30168	−	8.30168i	−0.312217	−	0.312217i
$708$	8.41104	+	8.41104i	0.316106	+	0.316106i
$709$	−15.2880	+	15.2880i	−0.574153	+	0.574153i	−0.933286	−	0.359133i	$-0.883072\pi$
$709$	−15.2880	+	15.2880i	−0.574153	+	0.574153i	0.359133	+	0.933286i	$0.383072\pi$
$710$	2.69051			0.100973
$711$	0.809467	−	0.809467i	0.0303574	−	0.0303574i
$712$		−	26.5192i		−	0.993848i
$713$	−15.6105			−0.584618
$714$	−2.58798	+	4.43104i	−0.0968529	+	0.165828i
$715$	−4.90498			−0.183436
$716$			29.8788i			1.11662i
$717$	3.46387	−	3.46387i	0.129361	−	0.129361i
$718$	4.40632			0.164442
$719$	−35.2731	+	35.2731i	−1.31546	+	1.31546i	−0.398138	+	0.917326i	$0.630343\pi$
$719$	−35.2731	+	35.2731i	−1.31546	+	1.31546i	−0.917326	+	0.398138i	$0.869657\pi$
$720$	−0.597248	−	0.597248i	−0.0222581	−	0.0222581i
$721$	−14.9957	−	14.9957i	−0.558470	−	0.558470i
$722$		−	6.42075i		−	0.238955i
$723$		−	3.43201i		−	0.127638i
$724$	−10.7527	−	10.7527i	−0.399622	−	0.399622i
$725$	2.89714	+	2.89714i	0.107597	+	0.107597i
$726$	0.448724	−	0.448724i	0.0166537	−	0.0166537i
$727$	−0.801110			−0.0297115			−0.0148558	−	0.999890i	$-0.504729\pi$
$727$	−0.801110			−0.0297115			−0.0148558	+	0.999890i	$0.504729\pi$
$728$	−10.6246	+	10.6246i	−0.393774	+	0.393774i
$729$			29.0490i			1.07589i
$730$	3.10469			0.114910
$731$	25.1200	−	43.0095i	0.929098	−	1.59076i
$732$	−24.0681			−0.889582
$733$			38.9029i			1.43691i	0.695573	+	0.718456i	$0.255151\pi$
$733$			38.9029i			1.43691i	−0.695573	+	0.718456i	$0.744849\pi$
$734$	−9.62962	+	9.62962i	−0.355436	+	0.355436i
$735$	4.93517			0.182037
$736$	−14.4106	+	14.4106i	−0.531183	+	0.531183i
$737$	−7.65575	−	7.65575i	−0.282003	−	0.282003i
$738$	0.0467429	+	0.0467429i	0.00172063	+	0.00172063i
$739$		−	16.4806i		−	0.606247i	−0.952951	−	0.303124i	$-0.901971\pi$
$739$		−	16.4806i		−	0.606247i	0.952951	−	0.303124i	$-0.0980295\pi$
$740$		−	1.80147i		−	0.0662234i
$741$	9.17943	+	9.17943i	0.337215	+	0.337215i
$742$	4.04199	+	4.04199i	0.148386	+	0.148386i
$743$	−13.3464	+	13.3464i	−0.489632	+	0.489632i	−0.908190	−	0.418558i	$-0.862536\pi$
$743$	−13.3464	+	13.3464i	−0.489632	+	0.489632i	0.418558	+	0.908190i	$0.362536\pi$
$744$	−7.81193			−0.286399
$745$	−12.8535	+	12.8535i	−0.470917	+	0.470917i
$746$			11.7205i			0.429117i
$747$	−0.714606			−0.0261461
$748$	1.93904	+	7.38454i	0.0708982	+	0.270006i
$749$	−11.2638			−0.411571
$750$			5.48242i			0.200190i
$751$	−13.9611	+	13.9611i	−0.509446	+	0.509446i	−0.914357	−	0.404910i	$-0.867303\pi$
$751$	−13.9611	+	13.9611i	−0.509446	+	0.509446i	0.404910	+	0.914357i	$0.367303\pi$
$752$	−18.0622			−0.658659
$753$	−17.5497	+	17.5497i	−0.639548	+	0.639548i
$754$	1.40608	+	1.40608i	0.0512062	+	0.0512062i
$755$	−6.78576	−	6.78576i	−0.246959	−	0.246959i
$756$			19.6547i			0.714833i
$757$		−	24.6416i		−	0.895615i	−0.894130	−	0.447807i	$-0.852205\pi$
$757$		−	24.6416i		−	0.895615i	0.894130	−	0.447807i	$-0.147795\pi$
$758$	8.84011	+	8.84011i	0.321087	+	0.321087i
$759$	5.69194	+	5.69194i	0.206604	+	0.206604i
$760$	1.51853	−	1.51853i	0.0550830	−	0.0550830i
$761$	−41.0436			−1.48783			−0.743914	−	0.668275i	$-0.767033\pi$
$761$	−41.0436			−1.48783			−0.743914	+	0.668275i	$0.767033\pi$
$762$	−6.73228	+	6.73228i	−0.243885	+	0.243885i
$763$			24.3302i			0.880813i
$764$	−21.8485			−0.790452
$765$	0.282362	+	1.07534i	0.0102088	+	0.0388788i
$766$	7.64976			0.276397
$767$		−	20.1346i		−	0.727019i
$768$	6.30708	−	6.30708i	0.227587	−	0.227587i
$769$	8.03369			0.289702			0.144851	−	0.989453i	$-0.453730\pi$
$769$	8.03369			0.289702			0.144851	+	0.989453i	$0.453730\pi$
$770$	0.507047	−	0.507047i	0.0182727	−	0.0182727i
$771$	8.97814	+	8.97814i	0.323340	+	0.323340i
$772$	−8.98689	−	8.98689i	−0.323445	−	0.323445i
$773$		−	46.0482i		−	1.65624i	−0.560551	−	0.828120i	$-0.689411\pi$
$773$		−	46.0482i		−	1.65624i	0.560551	−	0.828120i	$-0.310589\pi$
$774$			1.32095i			0.0474805i
$775$	9.26199	+	9.26199i	0.332700	+	0.332700i
$776$	−16.4323	−	16.4323i	−0.589884	−	0.589884i
$777$	−2.34158	+	2.34158i	−0.0840036	+	0.0840036i
$778$	13.6306			0.488680
$779$	0.651846	−	0.651846i	0.0233548	−	0.0233548i
$780$		−	14.9686i		−	0.535962i
$781$	−7.35854			−0.263309
$782$	7.50037	−	1.96945i	0.268213	−	0.0704274i
$783$	5.41053			0.193357
$784$		−	9.87854i		−	0.352805i
$785$	8.83674	−	8.83674i	0.315397	−	0.315397i
$786$	−6.54222			−0.233353
$787$	−35.0534	+	35.0534i	−1.24952	+	1.24952i	−0.293584	+	0.955933i	$0.594848\pi$
$787$	−35.0534	+	35.0534i	−1.24952	+	1.24952i	−0.955933	+	0.293584i	$0.905152\pi$
$788$	18.4785	+	18.4785i	0.658271	+	0.658271i
$789$	9.11652	+	9.11652i	0.324557	+	0.324557i
$790$		−	1.47392i		−	0.0524396i
$791$		−	28.9720i		−	1.03013i
$792$	−0.297819	−	0.297819i	−0.0105825	−	0.0105825i
$793$	28.8075	+	28.8075i	1.02298	+	1.02298i
$794$	−8.76615	+	8.76615i	−0.311099	+	0.311099i
$795$	−11.8452			−0.420106
$796$	6.09085	−	6.09085i	0.215884	−	0.215884i
$797$		−	12.2303i		−	0.433220i	−0.976258	−	0.216610i	$-0.930500\pi$
$797$		−	12.2303i		−	0.433220i	0.976258	−	0.216610i	$-0.0694999\pi$
$798$	−1.89783			−0.0671824
$799$	20.5300	+	11.9907i	0.726298	+	0.424200i
$800$	17.1002			0.604583
$801$			5.07762i			0.179409i
$802$	−3.40075	+	3.40075i	−0.120084	+	0.120084i
$803$	−8.49135			−0.299653
$804$	23.3632	−	23.3632i	0.823956	−	0.823956i
$805$	6.43175	+	6.43175i	0.226689	+	0.226689i
$806$	4.49514	+	4.49514i	0.158335	+	0.158335i
$807$		−	10.2594i		−	0.361149i
$808$			8.87858i			0.312347i
$809$	−34.6684	−	34.6684i	−1.21887	−	1.21887i	−0.968026	−	0.250849i	$-0.919290\pi$
$809$	−34.6684	−	34.6684i	−1.21887	−	1.21887i	−0.250849	−	0.968026i	$-0.580710\pi$
$810$	2.08575	+	2.08575i	0.0732858	+	0.0732858i
$811$	14.4485	−	14.4485i	0.507357	−	0.507357i	−0.406357	−	0.913714i	$-0.633201\pi$
$811$	14.4485	−	14.4485i	0.507357	−	0.507357i	0.913714	+	0.406357i	$0.133201\pi$
$812$	3.63054			0.127407
$813$	10.6015	−	10.6015i	0.371811	−	0.371811i
$814$		−	0.394515i		−	0.0138277i
$815$	6.65875			0.233246
$816$	−20.5866	+	5.40563i	−0.720675	+	0.189235i
$817$	18.4211			0.644473
$818$		−	2.96959i		−	0.103829i
$819$	2.03429	−	2.03429i	0.0710838	−	0.0710838i
$820$	−1.06294			−0.0371196
$821$	28.2603	−	28.2603i	0.986291	−	0.986291i	−0.0136162	−	0.999907i	$-0.504334\pi$
$821$	28.2603	−	28.2603i	0.986291	−	0.986291i	0.999907	+	0.0136162i	$0.00433431\pi$
$822$	5.11995	+	5.11995i	0.178579	+	0.178579i
$823$	10.8907	+	10.8907i	0.379628	+	0.379628i	0.870968	−	0.491340i	$-0.163493\pi$
$823$	10.8907	+	10.8907i	0.379628	+	0.379628i	−0.491340	+	0.870968i	$0.663493\pi$
$824$			16.0378i			0.558703i
$825$		−	6.75426i		−	0.235153i
$826$	2.08140	+	2.08140i	0.0724210	+	0.0724210i
$827$	−0.341078	−	0.341078i	−0.0118604	−	0.0118604i	0.701152	−	0.713012i	$-0.252670\pi$
$827$	−0.341078	−	0.341078i	−0.0118604	−	0.0118604i	−0.713012	+	0.701152i	$0.752670\pi$
$828$	1.81616	−	1.81616i	0.0631160	−	0.0631160i
$829$	−7.11244			−0.247025			−0.123513	−	0.992343i	$-0.539416\pi$
$829$	−7.11244			−0.247025			−0.123513	+	0.992343i	$0.539416\pi$
$830$	−0.650594	+	0.650594i	−0.0225824	+	0.0225824i
$831$		−	32.5702i		−	1.12985i
$832$	−24.0619			−0.834196
$833$	−6.55794	+	11.2282i	−0.227219	+	0.389035i
$834$	7.89532			0.273393
$835$		−	18.6022i		−	0.643755i
$836$	−1.99666	+	1.99666i	−0.0690559	+	0.0690559i
$837$	17.2972			0.597877
$838$	9.71764	−	9.71764i	0.335690	−	0.335690i
$839$	−1.29267	−	1.29267i	−0.0446278	−	0.0446278i	0.684441	−	0.729069i	$-0.260046\pi$
$839$	−1.29267	−	1.29267i	−0.0446278	−	0.0446278i	−0.729069	+	0.684441i	$0.760046\pi$
$840$	3.21863	+	3.21863i	0.111053	+	0.111053i
$841$			28.0006i			0.965537i
$842$			7.23935i			0.249485i
$843$	0.951346	+	0.951346i	0.0327661	+	0.0327661i
$844$	−7.76150	−	7.76150i	−0.267162	−	0.267162i
$845$	−9.18759	+	9.18759i	−0.316063	+	0.316063i
$846$	−0.630536			−0.0216783
$847$	−1.38678	+	1.38678i	−0.0476502	+	0.0476502i
$848$			23.7101i			0.814208i
$849$	−11.7998			−0.404967
$850$	−5.61861	−	3.28159i	−0.192717	−	0.112558i
$851$	5.00431			0.171546
$852$		−	22.4562i		−	0.769336i
$853$	1.36027	−	1.36027i	0.0465746	−	0.0465746i	−0.683436	−	0.730011i	$-0.739515\pi$
$853$	1.36027	−	1.36027i	0.0465746	−	0.0465746i	0.730011	+	0.683436i	$0.239515\pi$
$854$	−5.95589			−0.203806
$855$	−0.290753	+	0.290753i	−0.00994355	+	0.00994355i
$856$	6.02328	+	6.02328i	0.205872	+	0.205872i
$857$	23.0670	+	23.0670i	0.787955	+	0.787955i	0.981159	−	0.193203i	$-0.0618877\pi$
$857$	23.0670	+	23.0670i	0.787955	+	0.787955i	−0.193203	+	0.981159i	$0.561888\pi$
$858$		−	3.27806i		−	0.111911i
$859$		−	28.8657i		−	0.984885i	−0.870345	−	0.492442i	$-0.836104\pi$
$859$		−	28.8657i		−	0.984885i	0.870345	−	0.492442i	$-0.163896\pi$
$860$	−15.0194	−	15.0194i	−0.512156	−	0.512156i
$861$	1.38163	+	1.38163i	0.0470858	+	0.0470858i
$862$	8.67954	−	8.67954i	0.295626	−	0.295626i
$863$	37.2076			1.26656			0.633280	−	0.773923i	$-0.281708\pi$
$863$	37.2076			1.26656			0.633280	+	0.773923i	$0.281708\pi$
$864$	15.9677	−	15.9677i	0.543231	−	0.543231i
$865$			14.6087i			0.496710i
$866$	−9.92462			−0.337252
$867$	26.9879	+	7.52234i	0.916556	+	0.255472i
$868$	11.6066			0.393955
$869$			4.03116i			0.136748i
$870$	0.425958	−	0.425958i	0.0144413	−	0.0144413i
$871$	−55.9275			−1.89503
$872$	13.0105	−	13.0105i	0.440591	−	0.440591i
$873$	3.14628	+	3.14628i	0.106485	+	0.106485i
$874$	2.02798	+	2.02798i	0.0685974	+	0.0685974i
$875$		−	16.9433i		−	0.572789i
$876$		−	25.9132i		−	0.875525i
$877$	−23.2681	−	23.2681i	−0.785707	−	0.785707i	0.195080	−	0.980787i	$-0.437503\pi$
$877$	−23.2681	−	23.2681i	−0.785707	−	0.785707i	−0.980787	+	0.195080i	$0.937503\pi$
$878$	7.72346	+	7.72346i	0.260654	+	0.260654i
$879$	−11.0962	+	11.0962i	−0.374265	+	0.374265i
$880$	2.97431			0.100264
$881$	25.3413	−	25.3413i	0.853769	−	0.853769i	−0.136826	−	0.990595i	$-0.543690\pi$
$881$	25.3413	−	25.3413i	0.853769	−	0.853769i	0.990595	+	0.136826i	$0.0436900\pi$
$882$		−	0.344852i		−	0.0116118i
$883$	−12.8641			−0.432910			−0.216455	−	0.976293i	$-0.569450\pi$
$883$	−12.8641			−0.432910			−0.216455	+	0.976293i	$0.569450\pi$
$884$	34.0557	+	19.8905i	1.14542	+	0.668990i
$885$	−6.09960			−0.205036
$886$		−	12.2249i		−	0.410705i
$887$	5.77005	−	5.77005i	0.193739	−	0.193739i	−0.603570	−	0.797310i	$-0.706256\pi$
$887$	5.77005	−	5.77005i	0.193739	−	0.193739i	0.797310	+	0.603570i	$0.206256\pi$
$888$	2.50430			0.0840387
$889$	20.8060	−	20.8060i	0.697811	−	0.697811i
$890$	4.62278	+	4.62278i	0.154956	+	0.154956i
$891$	−5.70453	−	5.70453i	−0.191109	−	0.191109i
$892$			9.54135i			0.319468i
$893$			8.79305i			0.294248i
$894$	−8.59019	−	8.59019i	−0.287299	−	0.287299i
$895$	−10.8339	−	10.8339i	−0.362138	−	0.362138i
$896$	14.0598	−	14.0598i	0.469706	−	0.469706i
$897$	41.5813			1.38836
$898$	−2.99764	+	2.99764i	−0.100033	+	0.100033i
$899$		−	3.19507i		−	0.106562i
$900$	−2.15512			−0.0718375
$901$	15.7401	−	26.9496i	0.524379	−	0.897820i
$902$	−0.232781			−0.00775074
$903$			39.0447i			1.29933i
$904$	−15.4927	+	15.4927i	−0.515278	+	0.515278i
$905$	7.79778			0.259207
$906$	4.53502	−	4.53502i	0.150666	−	0.150666i
$907$	38.7637	+	38.7637i	1.28713	+	1.28713i	0.936524	+	0.350602i	$0.114023\pi$
$907$	38.7637	+	38.7637i	1.28713	+	1.28713i	0.350602	+	0.936524i	$0.385977\pi$
$908$	15.6561	+	15.6561i	0.519567	+	0.519567i
$909$		−	1.69998i		−	0.0563848i
$910$		−	3.70413i		−	0.122791i
$911$	16.8554	+	16.8554i	0.558445	+	0.558445i	0.928865	−	0.370419i	$-0.120786\pi$
$911$	16.8554	+	16.8554i	0.558445	+	0.558445i	−0.370419	+	0.928865i	$0.620786\pi$
$912$	−5.56627	−	5.56627i	−0.184318	−	0.184318i
$913$	1.77938	−	1.77938i	0.0588888	−	0.0588888i
$914$	0.649606			0.0214870
$915$	8.72697	−	8.72697i	0.288505	−	0.288505i
$916$			19.1285i			0.632023i
$917$	20.2186			0.667678
$918$	−8.31076	+	2.18224i	−0.274296	+	0.0720248i
$919$	11.5304			0.380351			0.190176	−	0.981750i	$-0.439094\pi$
$919$	11.5304			0.380351			0.190176	+	0.981750i	$0.439094\pi$
$920$		−	6.87871i		−	0.226784i
$921$	18.6529	−	18.6529i	0.614633	−	0.614633i
$922$	−9.89430			−0.325852
$923$	−26.8782	+	26.8782i	−0.884705	+	0.884705i
$924$	−4.23205	−	4.23205i	−0.139224	−	0.139224i
$925$	−2.96914	−	2.96914i	−0.0976249	−	0.0976249i
$926$			1.47424i			0.0484464i
$927$		−	3.07075i		−	0.100857i
$928$	−2.94949	−	2.94949i	−0.0968219	−	0.0968219i
$929$	−28.8699	−	28.8699i	−0.947189	−	0.947189i	0.0514844	−	0.998674i	$-0.483605\pi$
$929$	−28.8699	−	28.8699i	−0.947189	−	0.947189i	−0.998674	+	0.0514844i	$0.983605\pi$
$930$	1.36176	−	1.36176i	0.0446540	−	0.0446540i
$931$	−4.80909			−0.157612
$932$	33.3083	−	33.3083i	1.09105	−	1.09105i
$933$			13.8930i			0.454838i
$934$	3.98148			0.130278
$935$	−3.38068	−	1.97451i	−0.110560	−	0.0645735i
$936$	−2.17565			−0.0711135
$937$		−	8.62244i		−	0.281683i	−0.990032	−	0.140841i	$-0.955019\pi$
$937$		−	8.62244i		−	0.281683i	0.990032	−	0.140841i	$-0.0449807\pi$
$938$	5.78145	−	5.78145i	0.188771	−	0.188771i
$939$	15.1696			0.495040
$940$	7.16927	−	7.16927i	0.233836	−	0.233836i
$941$	15.5921	+	15.5921i	0.508287	+	0.508287i	0.914000	−	0.405714i	$-0.132977\pi$
$941$	15.5921	+	15.5921i	0.508287	+	0.508287i	−0.405714	+	0.914000i	$0.632977\pi$
$942$	5.90572	+	5.90572i	0.192419	+	0.192419i
$943$		−	2.95276i		−	0.0961550i
$944$			12.2093i			0.397380i
$945$	−7.12668	−	7.12668i	−0.231831	−	0.231831i
$946$	−3.28918	−	3.28918i	−0.106940	−	0.106940i
$947$	−21.8552	+	21.8552i	−0.710199	+	0.710199i	−0.966577	−	0.256378i	$-0.917471\pi$
$947$	−21.8552	+	21.8552i	−0.710199	+	0.710199i	0.256378	+	0.966577i	$0.417471\pi$
$948$	−12.3020			−0.399549
$949$	−31.0159	+	31.0159i	−1.00682	+	1.00682i
$950$		−	2.40647i		−	0.0780762i
$951$	18.7785			0.608933
$952$	−11.5998	+	3.04588i	−0.375952	+	0.0987176i
$953$	−25.4479			−0.824339			−0.412170	−	0.911107i	$-0.635229\pi$
$953$	−25.4479			−0.824339			−0.412170	+	0.911107i	$0.635229\pi$
$954$			0.827700i			0.0267978i
$955$	7.92217	−	7.92217i	0.256355	−	0.256355i
$956$	5.50411			0.178016
$957$	−1.16500	+	1.16500i	−0.0376590	+	0.0376590i
$958$	−8.58059	−	8.58059i	−0.277226	−	0.277226i
$959$	−15.8231	−	15.8231i	−0.510955	−	0.510955i
$960$			7.28934i			0.235262i
$961$			20.7855i			0.670501i
$962$	−1.44102	−	1.44102i	−0.0464605	−	0.0464605i
$963$	−1.15328	−	1.15328i	−0.0371638	−	0.0371638i
$964$	2.72675	−	2.72675i	0.0878226	−	0.0878226i
$965$	6.51720			0.209796
$966$	−4.29843	+	4.29843i	−0.138300	+	0.138300i
$967$		−	9.57007i		−	0.307753i	−0.988090	−	0.153876i	$-0.950824\pi$
$967$		−	9.57007i		−	0.307753i	0.988090	−	0.153876i	$-0.0491758\pi$
$968$	1.48315			0.0476701
$969$	2.63158	+	10.0220i	0.0845385	+	0.321953i
$970$	5.72890			0.183944
$971$			31.9600i			1.02564i	0.858495	+	0.512822i	$0.171400\pi$
$971$			31.9600i			1.02564i	−0.858495	+	0.512822i	$0.828600\pi$
$972$	−3.85077	+	3.85077i	−0.123513	+	0.123513i
$973$	−24.4004			−0.782240
$974$	4.43093	−	4.43093i	0.141976	−	0.141976i
$975$	−24.6709	−	24.6709i	−0.790102	−	0.790102i
$976$	−17.4684	−	17.4684i	−0.559151	−	0.559151i
$977$			2.28452i			0.0730884i	0.999332	+	0.0365442i	$0.0116350\pi$
$977$			2.28452i			0.0730884i	−0.999332	+	0.0365442i	$0.988365\pi$
$978$			4.45013i			0.142299i
$979$	−12.6433	−	12.6433i	−0.404082	−	0.404082i
$980$	3.92101	+	3.92101i	0.125252	+	0.125252i
$981$	−2.49111	+	2.49111i	−0.0795351	+	0.0795351i
$982$	−2.41744			−0.0771436
$983$	−4.24011	+	4.24011i	−0.135238	+	0.135238i	−0.771485	−	0.636247i	$-0.780486\pi$
$983$	−4.24011	+	4.24011i	−0.135238	+	0.135238i	0.636247	+	0.771485i	$0.280486\pi$
$984$		−	1.47764i		−	0.0471055i
$985$	−13.4005			−0.426974
$986$	0.403097	+	1.53514i	0.0128372	+	0.0488887i
$987$	−18.6374			−0.593236
$988$			14.5862i			0.464048i
$989$	41.7223	−	41.7223i	1.32669	−	1.32669i
$990$	0.103831			0.00329996
$991$	37.1302	−	37.1302i	1.17948	−	1.17948i	0.199604	−	0.979877i	$-0.436035\pi$
$991$	37.1302	−	37.1302i	1.17948	−	1.17948i	0.979877	−	0.199604i	$-0.0639655\pi$
$992$	−9.42937	−	9.42937i	−0.299383	−	0.299383i
$993$	−39.9666	−	39.9666i	−1.26830	−	1.26830i
$994$		−	5.55701i		−	0.176258i
$995$			4.41702i			0.140029i
$996$	5.43015	+	5.43015i	0.172061	+	0.172061i
$997$	29.8548	+	29.8548i	0.945510	+	0.945510i	0.998590	−	0.0530803i	$-0.0169039\pi$
$997$	29.8548	+	29.8548i	0.945510	+	0.945510i	−0.0530803	+	0.998590i	$0.516904\pi$
$998$	−4.94036	+	4.94036i	−0.156384	+	0.156384i
$999$	−5.54501			−0.175436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.e.b.89.6	✓	28
17.8	even	8		3179.2.a.be.1.6		14
17.9	even	8		3179.2.a.bd.1.6		14
17.13	even	4	inner	187.2.e.b.166.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.e.b.89.6	✓	28	1.1	even	1	trivial
187.2.e.b.166.9	yes	28	17.13	even	4	inner
3179.2.a.bd.1.6		14	17.9	even	8
3179.2.a.be.1.6		14	17.8	even	8

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.385060i q^{2} +(1.16534 - 1.16534i) q^{3} +1.85173 q^{4} +(-0.671428 + 0.671428i) q^{5} +(-0.448724 - 0.448724i) q^{6} +(1.38678 + 1.38678i) q^{7} -1.48315i q^{8} +0.283977i q^{9} +O(q^{10})\)	\(q-0.385060i q^{2} +(1.16534 - 1.16534i) q^{3} +1.85173 q^{4} +(-0.671428 + 0.671428i) q^{5} +(-0.448724 - 0.448724i) q^{6} +(1.38678 + 1.38678i) q^{7} -1.48315i q^{8} +0.283977i q^{9} +(0.258540 + 0.258540i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(2.15789 - 2.15789i) q^{12} -5.16562 q^{13} +(0.533991 - 0.533991i) q^{14} +1.56488i q^{15} +3.13236 q^{16} +(-3.56033 - 2.07944i) q^{17} +0.109348 q^{18} -1.52490i q^{19} +(-1.24330 + 1.24330i) q^{20} +3.23212 q^{21} +(-0.272278 + 0.272278i) q^{22} +(-3.45377 - 3.45377i) q^{23} +(-1.72836 - 1.72836i) q^{24} +4.09837i q^{25} +1.98907i q^{26} +(3.82694 + 3.82694i) q^{27} +(2.56793 + 2.56793i) q^{28} +(0.706900 - 0.706900i) q^{29} +0.602572 q^{30} +(2.25992 - 2.25992i) q^{31} -4.17244i q^{32} -1.64804 q^{33} +(-0.800707 + 1.37094i) q^{34} -1.86224 q^{35} +0.525849i q^{36} +(-0.724470 + 0.724470i) q^{37} -0.587177 q^{38} +(-6.01969 + 6.01969i) q^{39} +(0.995825 + 0.995825i) q^{40} +(0.427468 + 0.427468i) q^{41} -1.24456i q^{42} +12.0802i q^{43} +(-1.30937 - 1.30937i) q^{44} +(-0.190670 - 0.190670i) q^{45} +(-1.32991 + 1.32991i) q^{46} -5.76631 q^{47} +(3.65026 - 3.65026i) q^{48} -3.15371i q^{49} +1.57812 q^{50} +(-6.57223 + 1.72574i) q^{51} -9.56533 q^{52} +7.56940i q^{53} +(1.47360 - 1.47360i) q^{54} +0.949542 q^{55} +(2.05679 - 2.05679i) q^{56} +(-1.77702 - 1.77702i) q^{57} +(-0.272199 - 0.272199i) q^{58} +3.89781i q^{59} +2.89773i q^{60} +(-5.57677 - 5.57677i) q^{61} +(-0.870204 - 0.870204i) q^{62} +(-0.393813 + 0.393813i) q^{63} +4.65808 q^{64} +(3.46834 - 3.46834i) q^{65} +0.634592i q^{66} +10.8269 q^{67} +(-6.59276 - 3.85055i) q^{68} -8.04962 q^{69} +0.717073i q^{70} +(5.20328 - 5.20328i) q^{71} +0.421180 q^{72} +(6.00429 - 6.00429i) q^{73} +(0.278964 + 0.278964i) q^{74} +(4.77598 + 4.77598i) q^{75} -2.82370i q^{76} -1.96120i q^{77} +(2.31794 + 2.31794i) q^{78} +(-2.85046 - 2.85046i) q^{79} +(-2.10315 + 2.10315i) q^{80} +8.06742 q^{81} +(0.164601 - 0.164601i) q^{82} +2.51642i q^{83} +5.98502 q^{84} +(3.78670 - 0.994312i) q^{85} +4.65160 q^{86} -1.64755i q^{87} +(-1.04874 + 1.04874i) q^{88} +17.8804 q^{89} +(-0.0734194 + 0.0734194i) q^{90} +(-7.16356 - 7.16356i) q^{91} +(-6.39545 - 6.39545i) q^{92} -5.26714i q^{93} +2.22037i q^{94} +(1.02386 + 1.02386i) q^{95} +(-4.86230 - 4.86230i) q^{96} +(11.0793 - 11.0793i) q^{97} -1.21437 q^{98} +(0.200802 - 0.200802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5}+O(q^{10}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5	\( 28 q + 4 q^{3} - 28 q^{4} - 16 q^{5} + 20 q^{10} - 28 q^{12} + 8 q^{13} - 12 q^{14} + 44 q^{16} - 12 q^{17} + 4 q^{18} + 28 q^{20} + 16 q^{21} - 16 q^{23} + 12 q^{24} - 20 q^{27} - 52 q^{28} + 4 q^{29} - 8 q^{30} - 16 q^{31} + 16 q^{34} - 32 q^{35} - 24 q^{37} - 8 q^{38} - 8 q^{39} - 20 q^{40} + 16 q^{41} + 8 q^{44} + 72 q^{45} + 12 q^{46} - 16 q^{47} + 44 q^{48} + 60 q^{50} + 48 q^{51} - 16 q^{52} - 64 q^{54} - 16 q^{55} + 64 q^{56} - 56 q^{57} - 48 q^{58} + 36 q^{62} + 36 q^{63} - 12 q^{64} - 32 q^{65} - 16 q^{67} - 32 q^{68} - 40 q^{69} + 44 q^{71} + 20 q^{72} + 12 q^{73} + 76 q^{74} - 12 q^{75} + 4 q^{78} + 8 q^{79} - 16 q^{80} + 12 q^{81} - 12 q^{82} - 152 q^{84} + 24 q^{85} - 24 q^{86} + 8 q^{89} - 56 q^{90} + 12 q^{91} + 92 q^{92} - 4 q^{95} - 108 q^{96} + 164 q^{98} + 16 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 28 * q^4 - 16 * q^5 + 20 * q^10 - 28 * q^12 + 8 * q^13 - 12 * q^14 + 44 * q^16 - 12 * q^17 + 4 * q^18 + 28 * q^20 + 16 * q^21 - 16 * q^23 + 12 * q^24 - 20 * q^27 - 52 * q^28 + 4 * q^29 - 8 * q^30 - 16 * q^31 + 16 * q^34 - 32 * q^35 - 24 * q^37 - 8 * q^38 - 8 * q^39 - 20 * q^40 + 16 * q^41 + 8 * q^44 + 72 * q^45 + 12 * q^46 - 16 * q^47 + 44 * q^48 + 60 * q^50 + 48 * q^51 - 16 * q^52 - 64 * q^54 - 16 * q^55 + 64 * q^56 - 56 * q^57 - 48 * q^58 + 36 * q^62 + 36 * q^63 - 12 * q^64 - 32 * q^65 - 16 * q^67 - 32 * q^68 - 40 * q^69 + 44 * q^71 + 20 * q^72 + 12 * q^73 + 76 * q^74 - 12 * q^75 + 4 * q^78 + 8 * q^79 - 16 * q^80 + 12 * q^81 - 12 * q^82 - 152 * q^84 + 24 * q^85 - 24 * q^86 + 8 * q^89 - 56 * q^90 + 12 * q^91 + 92 * q^92 - 4 * q^95 - 108 * q^96 + 164 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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