LMFDB - Embedded newform 637.2.f.k.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$-1.02197 + 1.77010i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.k.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.777343 - 1.34640i) q^{2} +(0.244626 + 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} -1.19151 q^{5} +(0.380316 - 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(0.926214 + 1.60425i) q^{10} +(-1.05807 - 1.83263i) q^{11} -0.204043 q^{12} +(2.86133 - 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} +(2.33009 + 4.03583i) q^{16} +(0.453151 - 0.784881i) q^{17} -4.29192 q^{18} +(-3.34514 + 5.79395i) q^{19} +(0.248461 - 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} +(-0.602021 - 1.04273i) q^{24} -3.58030 q^{25} +(-5.17797 - 2.14715i) q^{26} +2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 + 0.784881i) q^{30} -5.28780 q^{31} +(1.16156 - 2.01189i) q^{32} +(0.517662 - 0.896617i) q^{33} -1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} +10.4013 q^{38} +(1.62948 + 0.675696i) q^{39} +2.93230 q^{40} +(-0.768181 - 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +0.882538 q^{44} +(-1.64466 + 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} -3.18673 q^{47} +(-1.14000 + 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +0.443410 q^{51} +(0.195692 + 1.49091i) q^{52} -2.82477 q^{53} +(-2.19086 - 3.79469i) q^{54} +(1.26070 + 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 + 11.4652i) q^{58} +(5.12298 - 8.87327i) q^{59} +0.243120 q^{60} +(4.13423 - 7.16069i) q^{61} +(4.11044 + 7.11949i) q^{62} +5.70861 q^{64} +(-3.40931 + 2.61395i) q^{65} -1.60960 q^{66} +(1.87182 + 3.24208i) q^{67} +(0.188987 + 0.327336i) q^{68} +(0.880000 - 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 + 5.88368i) q^{72} -5.73044 q^{73} +(-3.88018 + 6.72066i) q^{74} +(-0.875834 - 1.51699i) q^{75} +(-1.39510 - 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +6.07240 q^{79} +(-2.77632 - 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(-1.19428 + 2.06856i) q^{82} -11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +8.44619 q^{86} +(2.08310 - 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(8.87557 + 15.3729i) q^{89} +5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +(2.47719 + 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} +1.13659 q^{96} +(-3.10217 + 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 9 q^{6} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} + 8 q^{16} + 5 q^{17} - 6 q^{18} - q^{19} - q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + q^3 - 4 * q^4 - 2 * q^5 - 9 * q^6 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 - 10 * q^12 - 2 * q^13 - 2 * q^15 + 8 * q^16 + 5 * q^17 - 6 * q^18 - q^19 - q^20 - 5 * q^22 - q^23 - 11 * q^24 - 14 * q^25 + 11 * q^26 - 8 * q^27 + 3 * q^29 - 5 * q^30 - 32 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 21 * q^36 - 13 * q^37 + 34 * q^38 + 43 * q^39 + 10 * q^40 - 8 * q^41 - 11 * q^43 - 42 * q^44 - 7 * q^45 + 16 * q^46 + 2 * q^47 + 21 * q^48 + 6 * q^50 + 40 * q^51 - 16 * q^52 + 4 * q^53 - 18 * q^54 + 9 * q^55 + 42 * q^57 - 8 * q^58 + 13 * q^59 - 40 * q^60 - 5 * q^61 + 5 * q^62 - 30 * q^64 - 14 * q^65 - 36 * q^66 - 11 * q^67 + 29 * q^68 + 23 * q^69 + 6 * q^71 + 25 * q^72 + 60 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 16 * q^78 - 14 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - q^85 + 14 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 - 38 * q^96 - 35 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.777343	−	1.34640i	−0.549665	−	0.952047i	−0.998297	−	0.0583310i	$-0.981422\pi$
$2$	−0.777343	−	1.34640i	−0.549665	−	0.952047i	0.448632	−	0.893716i	$-0.351911\pi$
$3$	0.244626	+	0.423704i	0.141235	+	0.244626i	0.927962	−	0.372675i	$-0.121559\pi$
$3$	0.244626	+	0.423704i	0.141235	+	0.244626i	−0.786727	+	0.617301i	$0.788226\pi$
$4$	−0.208526	+	0.361177i	−0.104263	+	0.180588i
$5$	−1.19151			−0.532860			−0.266430	−	0.963854i	$-0.585844\pi$
$5$	−1.19151			−0.532860			−0.266430	+	0.963854i	$0.585844\pi$
$6$	0.380316	−	0.658727i	0.155264	−	0.268924i
$7$		0			0
$7$		0			0
$8$	−2.46099			−0.870091
$9$	1.38032	−	2.39078i	0.460105	−	0.796926i
$10$	0.926214	+	1.60425i	0.292894	+	0.507308i
$11$	−1.05807	−	1.83263i	−0.319020	−	0.552559i	0.661264	−	0.750153i	$-0.270020\pi$
$11$	−1.05807	−	1.83263i	−0.319020	−	0.552559i	−0.980284	+	0.197595i	$0.936687\pi$
$12$	−0.204043			−0.0589021
$13$	2.86133	−	2.19381i	0.793590	−	0.608453i
$13$	2.86133	−	2.19381i	0.793590	−	0.608453i
$14$		0			0
$15$	−0.291474	−	0.504848i	−0.0752584	−	0.130351i
$16$	2.33009	+	4.03583i	0.582521	+	1.00896i
$17$	0.453151	−	0.784881i	0.109905	−	0.190362i	−0.805826	−	0.592152i	$-0.798279\pi$
$17$	0.453151	−	0.784881i	0.109905	−	0.190362i	0.915732	+	0.401790i	$0.131612\pi$
$18$	−4.29192			−1.01162
$19$	−3.34514	+	5.79395i	−0.767428	+	1.32922i	0.171525	+	0.985180i	$0.445130\pi$
$19$	−3.34514	+	5.79395i	−0.767428	+	1.32922i	−0.938953	+	0.344045i	$0.888203\pi$
$20$	0.248461	−	0.430346i	0.0555575	−	0.0962284i
$21$		0			0
$22$	−1.64497	+	2.84917i	−0.350708	+	0.607444i
$23$	−1.79866	−	3.11538i	−0.375048	−	0.649601i	0.615287	−	0.788303i	$-0.289040\pi$
$23$	−1.79866	−	3.11538i	−0.375048	−	0.649601i	−0.990334	+	0.138702i	$0.955707\pi$
$24$	−0.602021	−	1.04273i	−0.122887	−	0.212847i
$25$	−3.58030			−0.716060
$26$	−5.17797	−	2.14715i	−1.01548	−	0.421091i
$27$	2.81840			0.542401
$28$		0			0
$29$	−4.25772	−	7.37459i	−0.790639	−	1.36943i	−0.925572	−	0.378573i	$-0.876415\pi$
$29$	−4.25772	−	7.37459i	−0.790639	−	1.36943i	0.134932	−	0.990855i	$-0.456918\pi$
$30$	−0.453151	+	0.784881i	−0.0827337	+	0.143299i
$31$	−5.28780			−0.949717			−0.474859	−	0.880062i	$-0.657501\pi$
$31$	−5.28780			−0.949717			−0.474859	+	0.880062i	$0.657501\pi$
$32$	1.16156	−	2.01189i	0.205337	−	0.355655i
$33$	0.517662	−	0.896617i	0.0901134	−	0.156081i
$34$	−1.40902			−0.241644
$35$		0			0
$36$	0.575663	+	0.997077i	0.0959438	+	0.166180i
$37$	−2.49579	−	4.32284i	−0.410306	−	0.710670i	0.584617	−	0.811309i	$-0.301245\pi$
$37$	−2.49579	−	4.32284i	−0.410306	−	0.710670i	−0.994923	+	0.100639i	$0.967911\pi$
$38$	10.4013			1.68731
$39$	1.62948	+	0.675696i	0.260926	+	0.108198i
$40$	2.93230			0.463637
$41$	−0.768181	−	1.33053i	−0.119970	−	0.207794i	0.799786	−	0.600286i	$-0.204946\pi$
$41$	−0.768181	−	1.33053i	−0.119970	−	0.207794i	−0.919755	+	0.392492i	$0.871613\pi$
$42$		0			0
$43$	−2.71636	+	4.70488i	−0.414242	+	0.717488i	−0.995349	−	0.0963397i	$-0.969286\pi$
$43$	−2.71636	+	4.70488i	−0.414242	+	0.717488i	0.581107	+	0.813827i	$0.302620\pi$
$44$	0.882538			0.133048
$45$	−1.64466	+	2.84864i	−0.245172	+	0.424650i
$46$	−2.79636	+	4.84344i	−0.412301	+	0.714126i
$47$	−3.18673			−0.464833			−0.232416	−	0.972616i	$-0.574663\pi$
$47$	−3.18673			−0.464833			−0.232416	+	0.972616i	$0.574663\pi$
$48$	−1.14000	+	1.97453i	−0.164545	+	0.284999i
$49$		0			0
$50$	2.78312	+	4.82051i	0.393593	+	0.681723i
$51$	0.443410			0.0620898
$52$	0.195692	+	1.49091i	0.0271376	+	0.206752i
$53$	−2.82477			−0.388012			−0.194006	−	0.981000i	$-0.562148\pi$
$53$	−2.82477			−0.388012			−0.194006	+	0.981000i	$0.562148\pi$
$54$	−2.19086	−	3.79469i	−0.298139	−	0.516391i
$55$	1.26070	+	2.18360i	0.169993	+	0.294436i
$56$		0			0
$57$	−3.27323			−0.433550
$58$	−6.61943	+	11.4652i	−0.869173	+	1.50545i
$59$	5.12298	−	8.87327i	0.666956	−	1.15520i	−0.311795	−	0.950149i	$-0.600930\pi$
$59$	5.12298	−	8.87327i	0.666956	−	1.15520i	0.978751	−	0.205052i	$-0.0657363\pi$
$60$	0.243120			0.0313866
$61$	4.13423	−	7.16069i	0.529333	−	0.916832i	−0.470081	−	0.882623i	$-0.655775\pi$
$61$	4.13423	−	7.16069i	0.529333	−	0.916832i	0.999415	−	0.0342093i	$-0.0108913\pi$
$62$	4.11044	+	7.11949i	0.522026	+	0.904176i
$63$		0			0
$64$	5.70861			0.713576
$65$	−3.40931	+	2.61395i	−0.422873	+	0.324220i
$66$	−1.60960			−0.198129
$67$	1.87182	+	3.24208i	0.228679	+	0.396083i	0.957417	−	0.288709i	$-0.0932261\pi$
$67$	1.87182	+	3.24208i	0.228679	+	0.396083i	−0.728738	+	0.684793i	$0.759893\pi$
$68$	0.188987	+	0.327336i	0.0229181	+	0.0396953i
$69$	0.880000	−	1.52420i	0.105939	−	0.183493i
$70$		0			0
$71$	1.26510	−	2.19122i	0.150140	−	0.260050i	−0.781139	−	0.624357i	$-0.785361\pi$
$71$	1.26510	−	2.19122i	0.150140	−	0.260050i	0.931279	+	0.364307i	$0.118694\pi$
$72$	−3.39694	+	5.88368i	−0.400334	+	0.693398i
$73$	−5.73044			−0.670697			−0.335349	−	0.942094i	$-0.608854\pi$
$73$	−5.73044			−0.670697			−0.335349	+	0.942094i	$0.608854\pi$
$74$	−3.88018	+	6.72066i	−0.451061	+	0.781261i
$75$	−0.875834	−	1.51699i	−0.101133	−	0.175167i
$76$	−1.39510	−	2.41638i	−0.160028	−	0.277177i
$77$		0			0
$78$	−0.356910	−	2.71918i	−0.0404121	−	0.307886i
$79$	6.07240			0.683198			0.341599	−	0.939846i	$-0.389031\pi$
$79$	6.07240			0.683198			0.341599	+	0.939846i	$0.389031\pi$
$80$	−2.77632	−	4.80873i	−0.310402	−	0.537633i
$81$	−3.45150	−	5.97817i	−0.383500	−	0.664241i
$82$	−1.19428	+	2.06856i	−0.131886	+	0.228434i
$83$	−11.6309			−1.27665			−0.638327	−	0.769766i	$-0.720373\pi$
$83$	−11.6309			−1.27665			−0.638327	+	0.769766i	$0.720373\pi$
$84$		0			0
$85$	−0.539935	+	0.935195i	−0.0585642	+	0.101436i
$86$	8.44619			0.910776
$87$	2.08310	−	3.60803i	0.223331	−	0.386821i
$88$	2.60390	+	4.51008i	0.277576	+	0.480776i
$89$	8.87557	+	15.3729i	0.940808	+	1.62953i	0.763934	+	0.645295i	$0.223265\pi$
$89$	8.87557	+	15.3729i	0.940808	+	1.62953i	0.176875	+	0.984233i	$0.443401\pi$
$90$	5.11387			0.539049
$91$		0			0
$92$	1.50027			0.156414
$93$	−1.29353	−	2.24046i	−0.134133	−	0.232325i
$94$	2.47719	+	4.29061i	0.255502	+	0.442543i
$95$	3.98577	−	6.90356i	0.408932	−	0.708291i
$96$	1.13659			0.116003
$97$	−3.10217	+	5.37312i	−0.314978	+	0.545557i	−0.979433	−	0.201771i	$-0.935330\pi$
$97$	−3.10217	+	5.37312i	−0.314978	+	0.545557i	0.664455	+	0.747328i	$0.268664\pi$
$98$		0			0
$99$	−5.84188			−0.587131
$100$	0.746584	−	1.29312i	0.0746584	−	0.129312i
$101$	3.61133	+	6.25501i	0.359341	+	0.622397i	0.987851	−	0.155405i	$-0.0496682\pi$
$101$	3.61133	+	6.25501i	0.359341	+	0.622397i	−0.628510	+	0.777802i	$0.716335\pi$
$102$	−0.344682	−	0.597007i	−0.0341286	−	0.0591125i
$103$	9.92645			0.978082			0.489041	−	0.872261i	$-0.337347\pi$
$103$	9.92645			0.978082			0.489041	+	0.872261i	$0.337347\pi$
$104$	−7.04170	+	5.39894i	−0.690496	+	0.529409i
$105$		0			0
$106$	2.19582	+	3.80327i	0.213277	+	0.369406i
$107$	1.10003	+	1.90531i	0.106344	+	0.184193i	0.914287	−	0.405068i	$-0.132752\pi$
$107$	1.10003	+	1.90531i	0.106344	+	0.184193i	−0.807942	+	0.589261i	$0.799419\pi$
$108$	−0.587708	+	1.01794i	−0.0565523	+	0.0979514i
$109$	13.7458			1.31661			0.658305	−	0.752751i	$-0.271274\pi$
$109$	13.7458			1.31661			0.658305	+	0.752751i	$0.271274\pi$
$110$	1.96000	−	3.39481i	0.186878	−	0.323683i
$111$	1.22107	−	2.11496i	0.115899	−	0.200743i
$112$		0			0
$113$	8.04736	−	13.9384i	0.757032	−	1.31122i	−0.187326	−	0.982298i	$-0.559982\pi$
$113$	8.04736	−	13.9384i	0.757032	−	1.31122i	0.944358	−	0.328920i	$-0.106685\pi$
$114$	2.54442	+	4.40707i	0.238307	+	0.412760i
$115$	2.14313	+	3.71201i	0.199848	+	0.346147i
$116$	3.55138			0.329737
$117$	−1.29536	−	9.86895i	−0.119756	−	0.912385i
$118$	−15.9293			−1.46641
$119$		0			0
$120$	0.717315	+	1.24243i	0.0654816	+	0.113418i
$121$	3.26098	−	5.64818i	0.296453	−	0.513471i
$122$	−12.8549			−1.16382
$123$	0.375834	−	0.650963i	0.0338878	−	0.0586954i
$124$	1.10264	−	1.90983i	0.0990202	−	0.171508i
$125$	10.2235			0.914420
$126$		0			0
$127$	7.83921	+	13.5779i	0.695617	+	1.20484i	0.969972	+	0.243216i	$0.0782023\pi$
$127$	7.83921	+	13.5779i	0.695617	+	1.20484i	−0.274355	+	0.961628i	$0.588464\pi$
$128$	−6.76067	−	11.7098i	−0.597565	−	1.03501i
$129$	−2.65797			−0.234021
$130$	6.16962	+	2.55835i	0.541111	+	0.224382i
$131$	−9.53769			−0.833312			−0.416656	−	0.909064i	$-0.636798\pi$
$131$	−9.53769			−0.833312			−0.416656	+	0.909064i	$0.636798\pi$
$132$	0.215892	+	0.373935i	0.0187910	+	0.0325469i
$133$		0			0
$134$	2.91009	−	5.04042i	0.251393	−	0.435426i
$135$	−3.35815			−0.289024
$136$	−1.11520	+	1.93158i	−0.0956277	+	0.165632i
$137$	1.38231	−	2.39422i	0.118098	−	0.204552i	−0.800916	−	0.598777i	$-0.795654\pi$
$137$	1.38231	−	2.39422i	0.118098	−	0.204552i	0.919014	+	0.394225i	$0.128987\pi$
$138$	−2.73625			−0.232925
$139$	11.3983	−	19.7425i	0.966795	−	1.67454i	0.262081	−	0.965046i	$-0.415591\pi$
$139$	11.3983	−	19.7425i	0.966795	−	1.67454i	0.704714	−	0.709492i	$-0.251075\pi$
$140$		0			0
$141$	−0.779557	−	1.35023i	−0.0656505	−	0.113710i
$142$	−3.93368			−0.330107
$143$	−7.04792	−	2.92256i	−0.589377	−	0.244397i
$144$	12.8650			1.07209
$145$	5.07312	+	8.78691i	0.421300	+	0.729713i
$146$	4.45452	+	7.71546i	0.368659	+	0.638536i
$147$		0			0
$148$	2.08175			0.171119
$149$	7.20581	−	12.4808i	0.590323	−	1.02247i	−0.403866	−	0.914818i	$-0.632334\pi$
$149$	7.20581	−	12.4808i	0.590323	−	1.02247i	0.994189	−	0.107651i	$-0.0343329\pi$
$150$	−1.36165	+	2.35844i	−0.111178	+	0.192566i
$151$	15.2580			1.24168			0.620840	−	0.783937i	$-0.286792\pi$
$151$	15.2580			1.24168			0.620840	+	0.783937i	$0.286792\pi$
$152$	8.23236	−	14.2589i	0.667732	−	1.15655i
$153$	−1.25098	−	2.16677i	−0.101136	−	0.175173i
$154$		0			0
$155$	6.30048			0.506067
$156$	−0.583834	+	0.447631i	−0.0467442	+	0.0358392i
$157$	−11.4149			−0.911008			−0.455504	−	0.890234i	$-0.650541\pi$
$157$	−11.4149			−0.911008			−0.455504	+	0.890234i	$0.650541\pi$
$158$	−4.72034	−	8.17587i	−0.375530	−	0.650437i
$159$	−0.691012	−	1.19687i	−0.0548008	−	0.0949178i
$160$	−1.38402	+	2.39719i	−0.109416	+	0.189514i
$161$		0			0
$162$	−5.36600	+	9.29418i	−0.421592	+	0.730220i
$163$	7.20385	−	12.4774i	0.564249	−	0.977308i	−0.432870	−	0.901456i	$-0.642499\pi$
$163$	7.20385	−	12.4774i	0.564249	−	0.977308i	0.997119	−	0.0758514i	$-0.0241675\pi$
$164$	0.640742			0.0500335
$165$	−0.616800	+	1.06833i	−0.0480178	+	0.0831693i
$166$	9.04118	+	15.6598i	0.701731	+	1.21543i
$167$	−3.88595	−	6.73066i	−0.300704	−	0.520834i	0.675592	−	0.737276i	$-0.263888\pi$
$167$	−3.88595	−	6.73066i	−0.300704	−	0.520834i	−0.976296	+	0.216442i	$0.930555\pi$
$168$		0			0
$169$	3.37442	−	12.5544i	0.259571	−	0.965724i
$170$	1.67886			0.128763
$171$	9.23471	+	15.9950i	0.706196	+	1.22317i
$172$	−1.13286	−	1.96218i	−0.0863800	−	0.149615i
$173$	−3.04731	+	5.27809i	−0.231682	+	0.401286i	−0.958303	−	0.285753i	$-0.907756\pi$
$173$	−3.04731	+	5.27809i	−0.231682	+	0.401286i	0.726621	+	0.687039i	$0.241090\pi$
$174$	−6.47713			−0.491030
$175$		0			0
$176$	4.93078	−	8.54037i	0.371672	−	0.643754i
$177$	5.01286			0.376789
$178$	13.7987	−	23.9001i	1.03426	−	1.79139i
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	−0.971020	−	0.239000i	$-0.923181\pi$
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	0.278530	−	0.960428i	$-0.410153\pi$
$180$	−0.685909	−	1.18803i	−0.0511246	−	0.0885504i
$181$	−5.60520			−0.416631			−0.208316	−	0.978062i	$-0.566798\pi$
$181$	−5.60520			−0.416631			−0.208316	+	0.978062i	$0.566798\pi$
$182$		0			0
$183$	4.04535			0.299041
$184$	4.42650	+	7.66692i	0.326326	+	0.565212i
$185$	2.97377	+	5.15071i	0.218636	+	0.378688i
$186$	−2.01104	+	3.48322i	−0.147456	+	0.255402i
$187$	−1.91786			−0.140248
$188$	0.664516	−	1.15097i	0.0484648	−	0.0839435i
$189$		0			0
$190$	−12.3933			−0.899102
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	−0.874993	−	0.484135i	$-0.839134\pi$
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	0.856770	+	0.515699i	$0.172468\pi$
$192$	1.39647	+	2.41876i	0.100782	+	0.174559i
$193$	1.85622	+	3.21507i	0.133614	+	0.231426i	0.925067	−	0.379804i	$-0.124009\pi$
$193$	1.85622	+	3.21507i	0.133614	+	0.231426i	−0.791453	+	0.611230i	$0.790675\pi$
$194$	9.64581			0.692529
$195$	−1.94154	−	0.805100i	−0.139037	−	0.0576544i
$196$		0			0
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	0.967616	−	0.252427i	$-0.0812288\pi$
$197$	3.72225	+	6.44713i	0.265200	+	0.459339i	−0.702416	+	0.711766i	$0.747895\pi$
$198$	4.54115	+	7.86550i	0.322725	+	0.558977i
$199$	−3.75278	+	6.50001i	−0.266028	+	0.460773i	−0.967832	−	0.251596i	$-0.919045\pi$
$199$	−3.75278	+	6.50001i	−0.266028	+	0.460773i	0.701805	+	0.712369i	$0.252378\pi$
$200$	8.81108			0.623038
$201$	−0.915789	+	1.58619i	−0.0645948	+	0.111881i
$202$	5.61449	−	9.72458i	0.395034	−	0.684219i
$203$		0			0
$204$	−0.0924624	+	0.160149i	−0.00647366	+	0.0112127i
$205$	0.915297	+	1.58534i	0.0639271	+	0.110725i
$206$	−7.71626	−	13.3650i	−0.537617	−	0.931181i
$207$	−9.93091			−0.690246
$208$	15.5210	+	6.43608i	1.07619	+	0.446262i
$209$	14.1576			0.979299
$210$		0			0
$211$	−1.89531	−	3.28278i	−0.130479	−	0.225996i	0.793383	−	0.608723i	$-0.208318\pi$
$211$	−1.89531	−	3.28278i	−0.130479	−	0.225996i	−0.923861	+	0.382728i	$0.874985\pi$
$212$	0.589037	−	1.02024i	0.0404553	−	0.0700706i
$213$	1.23791			0.0848200
$214$	1.71020	−	2.96216i	0.116907	−	0.202489i
$215$	3.23658	−	5.60592i	0.220733	−	0.382320i
$216$	−6.93605			−0.471938
$217$		0			0
$218$	−10.6852	−	18.5073i	−0.723695	−	1.25348i
$219$	−1.40181	−	2.42801i	−0.0947258	−	0.164070i
$220$	−1.05155			−0.0708958
$221$	−0.425262	−	3.23993i	−0.0286062	−	0.217941i
$222$	−3.79676			−0.254822
$223$	−2.43440	−	4.21650i	−0.163019	−	0.282358i	0.772931	−	0.634490i	$-0.218790\pi$
$223$	−2.43440	−	4.21650i	−0.163019	−	0.282358i	−0.935950	+	0.352133i	$0.885457\pi$
$224$		0			0
$225$	−4.94195	+	8.55971i	−0.329463	+	0.570647i
$226$	−25.0223			−1.66446
$227$	−12.0884	+	20.9376i	−0.802332	+	1.38968i	0.115745	+	0.993279i	$0.463075\pi$
$227$	−12.0884	+	20.9376i	−0.802332	+	1.38968i	−0.918077	+	0.396402i	$0.870259\pi$
$228$	0.682552	−	1.18222i	0.0452031	−	0.0782941i
$229$	−21.7123			−1.43479			−0.717394	−	0.696668i	$-0.754665\pi$
$229$	−21.7123			−1.43479			−0.717394	+	0.696668i	$0.754665\pi$
$230$	3.33190	−	5.77101i	0.219699	−	0.380529i
$231$		0			0
$232$	10.4782	+	18.1488i	0.687928	+	1.19153i
$233$	3.79684			0.248739			0.124370	−	0.992236i	$-0.460309\pi$
$233$	3.79684			0.248739			0.124370	+	0.992236i	$0.460309\pi$
$234$	−12.2806	+	9.41564i	−0.802808	+	0.615520i
$235$	3.79703			0.247691
$236$	2.13655	+	3.70061i	0.139077	+	0.240889i
$237$	1.48547	+	2.57290i	0.0964914	+	0.167128i
$238$		0			0
$239$	21.9100			1.41724			0.708619	−	0.705592i	$-0.249319\pi$
$239$	21.9100			1.41724			0.708619	+	0.705592i	$0.249319\pi$
$240$	1.35832	−	2.35268i	0.0876792	−	0.151865i
$241$	10.3744	−	17.9690i	0.668273	−	1.15748i	−0.310114	−	0.950699i	$-0.600367\pi$
$241$	10.3744	−	17.9690i	0.668273	−	1.15748i	0.978387	−	0.206783i	$-0.0662994\pi$
$242$	−10.1396			−0.651798
$243$	5.91625	−	10.2472i	0.379527	−	0.657361i
$244$	1.72418	+	2.98637i	0.110380	+	0.191183i
$245$		0			0
$246$	−1.16861			−0.0745077
$247$	3.13926	+	23.9170i	0.199747	+	1.52180i
$248$	13.0132			0.826341
$249$	−2.84521	−	4.92805i	−0.180308	−	0.312302i
$250$	−7.94719	−	13.7649i	−0.502624	−	0.870571i
$251$	−6.62891	+	11.4816i	−0.418413	+	0.724713i	−0.995780	−	0.0917718i	$-0.970747\pi$
$251$	−6.62891	+	11.4816i	−0.418413	+	0.724713i	0.577367	+	0.816485i	$0.304080\pi$
$252$		0			0
$253$	−3.80622	+	6.59257i	−0.239295	+	0.414472i
$254$	12.1875	−	21.1094i	0.764713	−	1.32452i
$255$	−0.528328			−0.0330852
$256$	−4.80213	+	8.31753i	−0.300133	+	0.519845i
$257$	6.58555	+	11.4065i	0.410795	+	0.711518i	0.994977	−	0.100105i	$-0.0319178\pi$
$257$	6.58555	+	11.4065i	0.410795	+	0.711518i	−0.584182	+	0.811623i	$0.698584\pi$
$258$	2.06616	+	3.57869i	0.128633	+	0.222799i
$259$		0			0
$260$	−0.233169	−	1.77644i	−0.0144605	−	0.110170i
$261$	−23.5080			−1.45511
$262$	7.41406	+	12.8415i	0.458042	+	0.793352i
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	0.994215	+	0.107412i	$0.0342564\pi$
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	−0.404086	+	0.914721i	$0.632410\pi$
$264$	−1.27396	+	2.20657i	−0.0784069	+	0.135805i
$265$	3.36575			0.206756
$266$		0			0
$267$	−4.34239	+	7.52123i	−0.265750	+	0.460292i
$268$	−1.56129			−0.0953708
$269$	14.2411	−	24.6663i	0.868296	−	1.50393i	0.00455867	−	0.999990i	$-0.498549\pi$
$269$	14.2411	−	24.6663i	0.868296	−	1.50393i	0.863737	−	0.503943i	$-0.168118\pi$
$270$	2.61044	+	4.52141i	0.158866	+	0.275164i
$271$	−8.97371	−	15.5429i	−0.545114	−	0.944165i	−0.998600	−	0.0529014i	$-0.983153\pi$
$271$	−8.97371	−	15.5429i	−0.545114	−	0.944165i	0.453486	−	0.891263i	$-0.350180\pi$
$272$	4.22353			0.256089
$273$		0			0
$274$	−4.29811			−0.259658
$275$	3.78821	+	6.56137i	0.228437	+	0.395665i
$276$	0.367005	+	0.635671i	0.0220911	+	0.0382629i
$277$	−6.71943	+	11.6384i	−0.403732	+	0.699284i	−0.994173	−	0.107797i	$-0.965620\pi$
$277$	−6.71943	+	11.6384i	−0.403732	+	0.699284i	0.590441	+	0.807081i	$0.298954\pi$
$278$	−35.4417			−2.12565
$279$	−7.29884	+	12.6420i	−0.436970	+	0.756855i
$280$		0			0
$281$	−29.9530			−1.78685			−0.893424	−	0.449214i	$-0.851704\pi$
$281$	−29.9530			−1.78685			−0.893424	+	0.449214i	$0.851704\pi$
$282$	−1.21197	+	2.09919i	−0.0721716	+	0.125005i
$283$	4.94561	+	8.56604i	0.293986	+	0.509199i	0.974748	−	0.223306i	$-0.0716848\pi$
$283$	4.94561	+	8.56604i	0.293986	+	0.509199i	−0.680763	+	0.732504i	$0.738351\pi$
$284$	0.527613	+	0.913852i	0.0313080	+	0.0542271i
$285$	3.90009			0.231021
$286$	1.54373	+	11.7611i	0.0912824	+	0.695451i
$287$		0			0
$288$	−3.20665	−	5.55408i	−0.188954	−	0.327277i
$289$	8.08931	+	14.0111i	0.475842	+	0.824182i
$290$	7.88712	−	13.6609i	0.463148	−	0.802195i
$291$	−3.03548			−0.177943
$292$	1.19494	−	2.06970i	0.0699288	−	0.121120i
$293$	−3.95529	+	6.85076i	−0.231071	+	0.400226i	−0.958123	−	0.286356i	$-0.907556\pi$
$293$	−3.95529	+	6.85076i	−0.231071	+	0.400226i	0.727053	+	0.686581i	$0.240889\pi$
$294$		0			0
$295$	−6.10409	+	10.5726i	−0.355394	+	0.615561i
$296$	6.14212	+	10.6385i	0.357003	+	0.618348i
$297$	−2.98206	−	5.16508i	−0.173037	−	0.299708i
$298$	−22.4056			−1.29792
$299$	−11.9811	−	4.96821i	−0.692886	−	0.287319i
$300$	0.730535			0.0421775
$301$		0			0
$302$	−11.8607	−	20.5434i	−0.682508	−	1.18214i
$303$	−1.76685	+	3.06027i	−0.101503	+	0.175808i
$304$	−31.1779			−1.78817
$305$	−4.92598	+	8.53204i	−0.282061	+	0.488543i
$306$	−1.94489	+	3.36865i	−0.111182	+	0.192573i
$307$	1.27238			0.0726187			0.0363094	−	0.999341i	$-0.488440\pi$
$307$	1.27238			0.0726187			0.0363094	+	0.999341i	$0.488440\pi$
$308$		0			0
$309$	2.42827	+	4.20588i	0.138139	+	0.239264i
$310$	−4.89763	−	8.48295i	−0.278167	−	0.481799i
$311$	24.7635			1.40421			0.702103	−	0.712075i	$-0.252244\pi$
$311$	24.7635			1.40421			0.702103	+	0.712075i	$0.252244\pi$
$312$	−4.01013	−	1.66288i	−0.227029	−	0.0941421i
$313$	2.37651			0.134328			0.0671642	−	0.997742i	$-0.478605\pi$
$313$	2.37651			0.134328			0.0671642	+	0.997742i	$0.478605\pi$
$314$	8.87330	+	15.3690i	0.500749	+	0.867323i
$315$		0			0
$316$	−1.26625	+	2.19321i	−0.0712322	+	0.123378i
$317$	−19.7796			−1.11093			−0.555466	−	0.831539i	$-0.687460\pi$
$317$	−19.7796			−1.11093			−0.555466	+	0.831539i	$0.687460\pi$
$318$	−1.07431	+	1.86076i	−0.0602442	+	0.104346i
$319$	−9.00993	+	15.6057i	−0.504459	+	0.873749i
$320$	−6.80187			−0.380236
$321$	−0.538192	+	0.932176i	−0.0300390	+	0.0520290i
$322$		0			0
$323$	3.03171	+	5.25108i	0.168689	+	0.292178i
$324$	2.87890			0.159939
$325$	−10.2444	+	7.85449i	−0.568258	+	0.435689i
$326$	−22.3995			−1.24059
$327$	3.36258	+	5.82416i	0.185951	+	0.322077i
$328$	1.89049	+	3.27442i	0.104385	+	0.180799i
$329$		0			0
$330$	1.91786			0.105575
$331$	−1.96386	+	3.40151i	−0.107944	+	0.186964i	−0.914937	−	0.403596i	$-0.867760\pi$
$331$	−1.96386	+	3.40151i	−0.107944	+	0.186964i	0.806993	+	0.590561i	$0.201093\pi$
$332$	2.42533	−	4.20080i	0.133107	−	0.230549i
$333$	−13.7799			−0.755136
$334$	−6.04143	+	10.4641i	−0.330572	+	0.572568i
$335$	−2.23029	−	3.86298i	−0.121854	−	0.211057i
$336$		0			0
$337$	−7.14099			−0.388995			−0.194497	−	0.980903i	$-0.562308\pi$
$337$	−7.14099			−0.388995			−0.194497	+	0.980903i	$0.562308\pi$
$338$	−19.5263	+	5.21577i	−1.06209	+	0.283701i
$339$	7.87437			0.427677
$340$	−0.225181	−	0.390024i	−0.0122121	−	0.0211520i
$341$	5.59486	+	9.69059i	0.302979	+	0.524775i
$342$	14.3571	−	24.8672i	0.776342	−	1.34466i
$343$		0			0
$344$	6.68494	−	11.5787i	0.360428	−	0.624280i
$345$	−1.04853	+	1.81611i	−0.0564509	+	0.0977759i
$346$	9.47522			0.509391
$347$	−5.03498	+	8.72085i	−0.270292	+	0.468160i	−0.968937	−	0.247309i	$-0.920454\pi$
$347$	−5.03498	+	8.72085i	−0.270292	+	0.468160i	0.698644	+	0.715469i	$0.253787\pi$
$348$	0.868758	+	1.50473i	0.0465703	+	0.0806622i
$349$	3.14418	+	5.44588i	0.168304	+	0.291512i	0.937824	−	0.347112i	$-0.112838\pi$
$349$	3.14418	+	5.44588i	0.168304	+	0.291512i	−0.769520	+	0.638623i	$0.779504\pi$
$350$		0			0
$351$	8.06437	−	6.18302i	0.430444	−	0.330025i
$352$	−4.91606			−0.262027
$353$	−17.0836	−	29.5897i	−0.909269	−	1.57490i	−0.815083	−	0.579345i	$-0.803308\pi$
$353$	−17.0836	−	29.5897i	−0.909269	−	1.57490i	−0.0941861	−	0.995555i	$-0.530025\pi$
$354$	−3.89671	−	6.74930i	−0.207108	−	0.358721i
$355$	−1.50738	+	2.61087i	−0.0800036	+	0.138570i
$356$	−7.40313			−0.392365
$357$		0			0
$358$	−14.4040	+	24.9484i	−0.761274	+	1.31857i
$359$	18.6865			0.986238			0.493119	−	0.869962i	$-0.335857\pi$
$359$	18.6865			0.986238			0.493119	+	0.869962i	$0.335857\pi$
$360$	4.04750	−	7.01047i	0.213322	−	0.369484i
$361$	−12.8799	−	22.3087i	−0.677891	−	1.17414i
$362$	4.35716	+	7.54683i	0.229007	+	0.396653i
$363$	3.19088			0.167478
$364$		0			0
$365$	6.82788			0.357388
$366$	−3.14463	−	5.44666i	−0.164372	−	0.284701i
$367$	15.5305	+	26.8997i	0.810687	+	1.40415i	0.912384	+	0.409336i	$0.134240\pi$
$367$	15.5305	+	26.8997i	0.810687	+	1.40415i	−0.101696	+	0.994816i	$0.532427\pi$
$368$	8.38209	−	14.5182i	0.436946	−	0.756813i
$369$	−4.24133			−0.220795
$370$	4.62327	−	8.00775i	0.240353	−	0.416303i
$371$		0			0
$372$	1.07894			0.0559404
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	−0.825500	−	0.564403i	$-0.809107\pi$
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	0.901537	+	0.432702i	$0.142440\pi$
$374$	1.49084	+	2.58221i	0.0770894	+	0.133523i
$375$	2.50094	+	4.33175i	0.129148	+	0.223691i
$376$	7.84252			0.404447
$377$	−28.3612	−	11.7605i	−1.46068	−	0.605698i
$378$		0			0
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	0.706961	−	0.707252i	$-0.250066\pi$
$379$	−5.04254	−	8.73394i	−0.259018	−	0.448632i	−0.965979	+	0.258620i	$0.916732\pi$
$380$	1.66227	+	2.87914i	0.0852727	+	0.147697i
$381$	−3.83534	+	6.64301i	−0.196491	+	0.340332i
$382$	0.783100			0.0400669
$383$	−1.84466	+	3.19504i	−0.0942576	+	0.163259i	−0.909299	−	0.416144i	$-0.863381\pi$
$383$	−1.84466	+	3.19504i	−0.0942576	+	0.163259i	0.815041	+	0.579403i	$0.196714\pi$
$384$	3.30767	−	5.72905i	0.168794	−	0.292360i
$385$		0			0
$386$	2.88584	−	4.99842i	0.146885	−	0.254413i
$387$	7.49888	+	12.9884i	0.381190	+	0.660240i
$388$	−1.29376	−	2.24086i	−0.0656809	−	0.113763i
$389$	22.6667			1.14925			0.574623	−	0.818418i	$-0.305149\pi$
$389$	22.6667			1.14925			0.574623	+	0.818418i	$0.305149\pi$
$390$	0.425262	+	3.23993i	0.0215340	+	0.164060i
$391$	−3.26027			−0.164879
$392$		0			0
$393$	−2.33316	−	4.04116i	−0.117693	−	0.203849i
$394$	5.78694	−	10.0233i	0.291542	−	0.504965i
$395$	−7.23533			−0.364049
$396$	1.21818	−	2.10995i	0.0612160	−	0.106029i
$397$	14.5680	−	25.2325i	0.731146	−	1.26638i	−0.225248	−	0.974302i	$-0.572319\pi$
$397$	14.5680	−	25.2325i	0.731146	−	1.26638i	0.956394	−	0.292080i	$-0.0943475\pi$
$398$	11.6688			0.584904
$399$		0			0
$400$	−8.34241	−	14.4495i	−0.417120	−	0.722474i
$401$	−4.06026	−	7.03258i	−0.202760	−	0.351190i	0.746657	−	0.665209i	$-0.231658\pi$
$401$	−4.06026	−	7.03258i	−0.202760	−	0.351190i	−0.949417	+	0.314019i	$0.898324\pi$
$402$	2.84753			0.142022
$403$	−15.1302	+	11.6004i	−0.753687	+	0.577858i
$404$	−3.01222			−0.149864
$405$	4.11250	+	7.12305i	0.204352	+	0.353947i
$406$		0			0
$407$	−5.28144	+	9.14773i	−0.261791	+	0.453436i
$408$	−1.09123			−0.0540238
$409$	4.16131	−	7.20759i	0.205763	−	0.356393i	−0.744612	−	0.667497i	$-0.767366\pi$
$409$	4.16131	−	7.20759i	0.205763	−	0.356393i	0.950376	+	0.311105i	$0.100699\pi$
$410$	1.42300	−	2.46471i	0.0702769	−	0.121723i
$411$	1.35259			0.0667184
$412$	−2.06992	+	3.58520i	−0.101978	+	0.176630i
$413$		0			0
$414$	7.71973	+	13.3710i	0.379404	+	0.657147i
$415$	13.8583			0.680278
$416$	−1.09007	−	8.30492i	−0.0534453	−	0.407182i
$417$	11.1533			0.546180
$418$	−11.0053	−	19.0617i	−0.538286	−	0.932339i
$419$	6.50832	+	11.2727i	0.317952	+	0.550710i	0.980061	−	0.198699i	$-0.0636715\pi$
$419$	6.50832	+	11.2727i	0.317952	+	0.550710i	−0.662108	+	0.749408i	$0.730338\pi$
$420$		0			0
$421$	−8.89681			−0.433604			−0.216802	−	0.976216i	$-0.569563\pi$
$421$	−8.89681			−0.433604			−0.216802	+	0.976216i	$0.569563\pi$
$422$	−2.94662	+	5.10369i	−0.143439	+	0.248444i
$423$	−4.39870	+	7.61877i	−0.213872	+	0.370437i
$424$	6.95174			0.337606
$425$	−1.62242	+	2.81011i	−0.0786988	+	0.136310i
$426$	−0.962279	−	1.66672i	−0.0466225	−	0.0807526i
$427$		0			0
$428$	−0.917539			−0.0443509
$429$	−0.485802	−	3.70117i	−0.0234548	−	0.178694i
$430$	−10.0637			−0.485316
$431$	4.47872	+	7.75736i	0.215732	+	0.373659i	0.953499	−	0.301397i	$-0.0974529\pi$
$431$	4.47872	+	7.75736i	0.215732	+	0.373659i	−0.737767	+	0.675056i	$0.764120\pi$
$432$	6.56711	+	11.3746i	0.315960	+	0.547259i
$433$	0.0864547	−	0.149744i	0.00415475	−	0.00719624i	−0.863941	−	0.503594i	$-0.832011\pi$
$433$	0.0864547	−	0.149744i	0.00415475	−	0.00719624i	0.868095	+	0.496398i	$0.165344\pi$
$434$		0			0
$435$	−2.48203	+	4.29901i	−0.119004	+	0.206122i
$436$	−2.86636	+	4.96467i	−0.137274	+	0.237765i
$437$	24.0671			1.15129
$438$	−2.17938	+	3.77480i	−0.104135	+	0.180367i
$439$	−4.77080	−	8.26327i	−0.227698	−	0.394384i	0.729428	−	0.684058i	$-0.239787\pi$
$439$	−4.77080	−	8.26327i	−0.227698	−	0.394384i	−0.957125	+	0.289674i	$0.906453\pi$
$440$	−3.10257	−	5.37382i	−0.147909	−	0.256187i
$441$		0			0
$442$	−4.03166	+	3.09111i	−0.191767	+	0.147029i
$443$	−13.8735			−0.659151			−0.329576	−	0.944129i	$-0.606906\pi$
$443$	−13.8735			−0.659151			−0.329576	+	0.944129i	$0.606906\pi$
$444$	0.509249	+	0.882045i	0.0241679	+	0.0418600i
$445$	−10.5753	−	18.3170i	−0.501319	−	0.868310i
$446$	−3.78473	+	6.55534i	−0.179212	+	0.310404i
$447$	7.05091			0.333496
$448$		0			0
$449$	10.6456	−	18.4388i	0.502398	−	0.870180i	−0.497598	−	0.867408i	$-0.665784\pi$
$449$	10.6456	−	18.4388i	0.502398	−	0.870180i	0.999996	−	0.00277167i	$-0.000882252\pi$
$450$	15.3664			0.724377
$451$	−1.62558	+	2.81558i	−0.0765455	+	0.132581i
$452$	3.35616	+	5.81304i	0.157861	+	0.273423i
$453$	3.73251	+	6.46489i	0.175368	+	0.303747i
$454$	37.5872			1.76406
$455$		0			0
$456$	8.05539			0.377228
$457$	−4.84282	−	8.38801i	−0.226538	−	0.392375i	0.730242	−	0.683189i	$-0.239407\pi$
$457$	−4.84282	−	8.38801i	−0.226538	−	0.392375i	−0.956780	+	0.290814i	$0.906074\pi$
$458$	16.8779	+	29.2334i	0.788652	+	1.36599i
$459$	1.27716	−	2.21211i	0.0596128	−	0.103252i
$460$	−1.78759			−0.0833468
$461$	0.687178	−	1.19023i	0.0320051	−	0.0554344i	−0.849579	−	0.527461i	$-0.823144\pi$
$461$	0.687178	−	1.19023i	0.0320051	−	0.0554344i	0.881584	+	0.472027i	$0.156477\pi$
$462$		0			0
$463$	31.7710			1.47653			0.738263	−	0.674513i	$-0.235646\pi$
$463$	31.7710			1.47653			0.738263	+	0.674513i	$0.235646\pi$
$464$	19.8417	−	34.3669i	0.921128	−	1.59544i
$465$	1.54126	+	2.66954i	0.0714742	+	0.123797i
$466$	−2.95145	−	5.11206i	−0.136723	−	0.236812i
$467$	−29.1209			−1.34756			−0.673778	−	0.738934i	$-0.735330\pi$
$467$	−29.1209			−1.34756			−0.673778	+	0.738934i	$0.735330\pi$
$468$	3.83456	+	1.59007i	0.177252	+	0.0735012i
$469$		0			0
$470$	−2.95160	−	5.11231i	−0.136147	−	0.235813i
$471$	−2.79238	−	4.83654i	−0.128666	−	0.222856i
$472$	−12.6076	+	21.8370i	−0.580312	+	1.00513i
$473$	11.4964			0.528605
$474$	2.30943	−	4.00006i	0.106076	−	0.183729i
$475$	11.9766	−	20.7441i	0.549525	−	0.951804i
$476$		0			0
$477$	−3.89908	+	6.75341i	−0.178527	+	0.309217i
$478$	−17.0316	−	29.4995i	−0.779005	−	1.34928i
$479$	−4.86092	−	8.41936i	−0.222101	−	0.384690i	0.733345	−	0.679857i	$-0.237958\pi$
$479$	−4.86092	−	8.41936i	−0.222101	−	0.384690i	−0.955446	+	0.295167i	$0.904625\pi$
$480$	−1.35426			−0.0618134
$481$	−16.6248	−	6.89379i	−0.758024	−	0.314330i
$482$	−32.2578			−1.46930
$483$		0			0
$484$	1.36000	+	2.35558i	0.0618180	+	0.107072i
$485$	3.69627	−	6.40213i	0.167839	−	0.290706i
$486$	−18.3958			−0.834452
$487$	8.55666	−	14.8206i	0.387739	−	0.671584i	−0.604406	−	0.796676i	$-0.706589\pi$
$487$	8.55666	−	14.8206i	0.387739	−	0.671584i	0.992145	+	0.125093i	$0.0399228\pi$
$488$	−10.1743	+	17.6224i	−0.460568	+	0.797728i
$489$	7.04899			0.318766
$490$		0			0
$491$	12.8607	+	22.2753i	0.580394	+	1.00527i	0.995432	+	0.0954681i	$0.0304348\pi$
$491$	12.8607	+	22.2753i	0.580394	+	1.00527i	−0.415038	+	0.909804i	$0.636232\pi$
$492$	0.156742	+	0.271485i	0.00706647	+	0.0122395i
$493$	−7.71757			−0.347582
$494$	29.7615	−	22.8184i	1.33903	−	1.02665i
$495$	6.96067			0.312859
$496$	−12.3210	−	21.3407i	−0.553231	−	0.958224i
$497$		0			0
$498$	−4.42341	+	7.66157i	−0.198218	+	0.343323i
$499$	5.40396			0.241914			0.120957	−	0.992658i	$-0.461404\pi$
$499$	5.40396			0.241914			0.120957	+	0.992658i	$0.461404\pi$
$500$	−2.13187	+	3.69250i	−0.0953400	+	0.165134i
$501$	1.90121	−	3.29299i	0.0849396	−	0.147120i
$502$	20.6118			0.919948
$503$	6.30847	−	10.9266i	0.281281	−	0.487193i	−0.690420	−	0.723409i	$-0.742574\pi$
$503$	6.30847	−	10.9266i	0.281281	−	0.487193i	0.971700	+	0.236216i	$0.0759074\pi$
$504$		0			0
$505$	−4.30294	−	7.45292i	−0.191478	−	0.331650i
$506$	11.8350			0.526129
$507$	6.14483	−	1.64138i	0.272901	−	0.0728960i
$508$	−6.53870			−0.290108
$509$	0.979379	+	1.69633i	0.0434102	+	0.0751887i	0.886914	−	0.461934i	$-0.152844\pi$
$509$	0.979379	+	1.69633i	0.0434102	+	0.0751887i	−0.843504	+	0.537123i	$0.819511\pi$
$510$	0.410692	+	0.711340i	0.0181858	+	0.0314987i
$511$		0			0
$512$	−12.1111			−0.535240
$513$	−9.42794	+	16.3297i	−0.416254	+	0.720973i
$514$	10.2385	−	17.7335i	0.451599	−	0.782193i
$515$	−11.8275			−0.521181
$516$	0.554255	−	0.959998i	0.0243997	−	0.0422615i
$517$	3.37178	+	5.84010i	0.148291	+	0.256847i
$518$		0			0
$519$	−2.98180			−0.130886
$520$	8.39027	−	6.43289i	0.367938	−	0.282101i
$521$	−39.0954			−1.71280			−0.856401	−	0.516312i	$-0.827305\pi$
$521$	−39.0954			−1.71280			−0.856401	+	0.516312i	$0.827305\pi$
$522$	18.2738	+	31.6512i	0.799823	+	1.38533i
$523$	4.35634	+	7.54540i	0.190489	+	0.329937i	0.945413	−	0.325876i	$-0.105659\pi$
$523$	4.35634	+	7.54540i	0.190489	+	0.329937i	−0.754923	+	0.655813i	$0.772326\pi$
$524$	1.98885	−	3.44479i	0.0868834	−	0.150486i
$525$		0			0
$526$	14.8788	−	25.7708i	0.648746	−	1.12366i
$527$	−2.39618	+	4.15030i	−0.104379	+	0.180790i
$528$	4.82479			0.209972
$529$	5.02961	−	8.71154i	0.218679	−	0.378763i
$530$	−2.61634	−	4.53164i	−0.113647	−	0.196842i
$531$	−14.1427	−	24.4958i	−0.613740	−	1.06303i
$532$		0			0
$533$	−5.11694	−	2.12184i	−0.221639	−	0.0919072i
$534$	13.5021			0.584293
$535$	−1.31070	−	2.27020i	−0.0566665	−	0.0981493i
$536$	−4.60652	−	7.97873i	−0.198971	−	0.344629i
$537$	4.53286	−	7.85114i	0.195607	−	0.338802i
$538$	−44.2809			−1.90909
$539$		0			0
$540$	0.700261	−	1.21289i	0.0301344	−	0.0521944i
$541$	−21.4994			−0.924330			−0.462165	−	0.886794i	$-0.652927\pi$
$541$	−21.4994			−0.924330			−0.462165	+	0.886794i	$0.652927\pi$
$542$	−13.9513	+	24.1644i	−0.599260	+	1.03795i
$543$	−1.37118	−	2.37495i	−0.0588428	−	0.101919i
$544$	−1.05273	−	1.82338i	−0.0451353	−	0.0781767i
$545$	−16.3783			−0.701569
$546$		0			0
$547$	−30.2968			−1.29540			−0.647699	−	0.761896i	$-0.724269\pi$
$547$	−30.2968			−1.29540			−0.647699	+	0.761896i	$0.724269\pi$
$548$	0.576493	+	0.998514i	0.0246265	+	0.0426544i
$549$	−11.4131	−	19.7680i	−0.487098	−	0.843679i
$550$	5.88947	−	10.2009i	0.251128	−	0.434967i
$551$	56.9707			2.42703
$552$	−2.16567	+	3.75105i	−0.0921770	+	0.159655i
$553$		0			0
$554$	20.8932			0.887668
$555$	−1.45492	+	2.51999i	−0.0617579	+	0.106968i
$556$	4.75369	+	8.23364i	0.201601	+	0.349184i
$557$	8.84201	+	15.3148i	0.374648	+	0.648909i	0.990274	−	0.139129i	$-0.0444302\pi$
$557$	8.84201	+	15.3148i	0.374648	+	0.648909i	−0.615626	+	0.788038i	$0.711097\pi$
$558$	22.6948			0.960749
$559$	2.54918	+	19.4214i	0.107819	+	0.821437i
$560$		0			0
$561$	−0.469159	−	0.812606i	−0.0198079	−	0.0343083i
$562$	23.2838	+	40.3287i	0.982167	+	1.70116i
$563$	20.8695	−	36.1471i	0.879545	−	1.52342i	0.0277042	−	0.999616i	$-0.491180\pi$
$563$	20.8695	−	36.1471i	0.879545	−	1.52342i	0.851841	−	0.523801i	$-0.175486\pi$
$564$	0.650230			0.0273796
$565$	−9.58852	+	16.6078i	−0.403392	+	0.698696i
$566$	7.68887	−	13.3175i	0.323187	−	0.559777i
$567$		0			0
$568$	−3.11340	+	5.39257i	−0.130636	+	0.226267i
$569$	−2.73388	−	4.73521i	−0.114610	−	0.198510i	0.803014	−	0.595960i	$-0.203229\pi$
$569$	−2.73388	−	4.73521i	−0.114610	−	0.198510i	−0.917624	+	0.397450i	$0.869895\pi$
$570$	−3.03171	−	5.25108i	−0.126984	−	0.219943i
$571$	9.35242			0.391387			0.195693	−	0.980665i	$-0.437304\pi$
$571$	9.35242			0.391387			0.195693	+	0.980665i	$0.437304\pi$
$572$	2.52523	−	1.93612i	0.105585	−	0.0809532i
$573$	−0.246437			−0.0102951
$574$		0			0
$575$	6.43976	+	11.1540i	0.268557	+	0.465154i
$576$	7.87968	−	13.6480i	0.328320	−	0.568667i
$577$	−3.36925			−0.140264			−0.0701318	−	0.997538i	$-0.522342\pi$
$577$	−3.36925			−0.140264			−0.0701318	+	0.997538i	$0.522342\pi$
$578$	12.5763	−	21.7829i	0.523107	−	0.906048i
$579$	−0.908159	+	1.57298i	−0.0377418	+	0.0653707i
$580$	−4.23151			−0.175704
$581$		0			0
$582$	2.35961	+	4.08697i	0.0978091	+	0.169410i
$583$	2.98881	+	5.17676i	0.123784	+	0.214400i
$584$	14.1026			0.583568
$585$	1.54344	+	11.7590i	0.0638134	+	0.486174i
$586$	12.2985			0.508045
$587$	6.57639	+	11.3906i	0.271437	+	0.470142i	0.969230	−	0.246157i	$-0.0791679\pi$
$587$	6.57639	+	11.3906i	0.271437	+	0.470142i	−0.697793	+	0.716299i	$0.745835\pi$
$588$		0			0
$589$	17.6884	−	30.6373i	0.728840	−	1.26239i
$590$	18.9799			0.781390
$591$	−1.82112	+	3.15427i	−0.0749108	+	0.129749i
$592$	11.6308	−	20.1452i	0.478024	−	0.827961i
$593$	38.5916			1.58477			0.792384	−	0.610022i	$-0.208839\pi$
$593$	38.5916			1.58477			0.792384	+	0.610022i	$0.208839\pi$
$594$	−4.63617	+	8.03008i	−0.190224	+	0.329478i
$595$		0			0
$596$	3.00519	+	5.20515i	0.123097	+	0.213211i
$597$	−3.67211			−0.150289
$598$	2.62426	+	19.9934i	0.107314	+	0.817589i
$599$	18.4152			0.752426			0.376213	−	0.926533i	$-0.377226\pi$
$599$	18.4152			0.752426			0.376213	+	0.926533i	$0.377226\pi$
$600$	2.15542	+	3.73329i	0.0879946	+	0.152411i
$601$	20.7018	+	35.8566i	0.844445	+	1.46262i	0.886102	+	0.463490i	$0.153403\pi$
$601$	20.7018	+	35.8566i	0.844445	+	1.46262i	−0.0416571	+	0.999132i	$0.513264\pi$
$602$		0			0
$603$	10.3348			0.420865
$604$	−3.18169	+	5.51085i	−0.129461	+	0.224233i
$605$	−3.88549	+	6.72987i	−0.157968	+	0.273608i
$606$	5.49380			0.223170
$607$	−6.15255	+	10.6565i	−0.249724	+	0.432535i	−0.963449	−	0.267891i	$-0.913673\pi$
$607$	−6.15255	+	10.6565i	−0.249724	+	0.432535i	0.713725	+	0.700426i	$0.247007\pi$
$608$	7.77119	+	13.4601i	0.315163	+	0.545879i
$609$		0			0
$610$	15.3167			0.620155
$611$	−9.11830	+	6.99108i	−0.368887	+	0.282829i
$612$	1.04345			0.0421789
$613$	−13.1112	−	22.7093i	−0.529556	−	0.917219i	−0.999406	−	0.0344720i	$-0.989025\pi$
$613$	−13.1112	−	22.7093i	−0.529556	−	0.917219i	0.469849	−	0.882747i	$-0.344308\pi$
$614$	−0.989078	−	1.71313i	−0.0399160	−	0.0691365i
$615$	−0.447810	+	0.775630i	−0.0180575	+	0.0312764i
$616$		0			0
$617$	9.41259	−	16.3031i	0.378936	−	0.656337i	−0.611971	−	0.790880i	$-0.709623\pi$
$617$	9.41259	−	16.3031i	0.378936	−	0.656337i	0.990908	+	0.134543i	$0.0429565\pi$
$618$	3.77519	−	6.53882i	0.151860	−	0.263030i
$619$	−15.8083			−0.635389			−0.317695	−	0.948193i	$-0.602909\pi$
$619$	−15.8083			−0.635389			−0.317695	+	0.948193i	$0.602909\pi$
$620$	−1.31381	+	2.27559i	−0.0527639	+	0.0913898i
$621$	−5.06935	−	8.78038i	−0.203426	−	0.352344i
$622$	−19.2497	−	33.3415i	−0.771843	−	1.33687i
$623$		0			0
$624$	1.06984	+	8.15073i	0.0428277	+	0.326290i
$625$	5.72006			0.228802
$626$	−1.84737	−	3.19973i	−0.0738356	−	0.127887i
$627$	3.46331	+	5.99862i	0.138311	+	0.239562i
$628$	2.38030	−	4.12280i	0.0949843	−	0.164518i
$629$	−4.52389			−0.180379
$630$		0			0
$631$	8.33817	−	14.4421i	0.331937	−	0.574933i	−0.650954	−	0.759117i	$-0.725631\pi$
$631$	8.33817	−	14.4421i	0.331937	−	0.574933i	0.982892	+	0.184184i	$0.0589644\pi$
$632$	−14.9441			−0.594445
$633$	0.927285	−	1.60610i	0.0368563	−	0.0638369i
$634$	15.3755	+	26.6312i	0.610640	+	1.05766i
$635$	−9.34050	−	16.1782i	−0.370667	−	0.642013i
$636$	0.576375			0.0228548
$637$		0			0
$638$	28.0152			1.10913
$639$	−3.49248	−	6.04916i	−0.138161	−	0.239301i
$640$	8.05542	+	13.9524i	0.318418	+	0.551517i
$641$	−24.6232	+	42.6487i	−0.972559	+	1.68452i	−0.284792	+	0.958589i	$0.591925\pi$
$641$	−24.6232	+	42.6487i	−0.972559	+	1.68452i	−0.687767	+	0.725932i	$0.741409\pi$
$642$	1.67344			0.0660454
$643$	−21.4355	+	37.1275i	−0.845335	+	1.46416i	0.0399940	+	0.999200i	$0.487266\pi$
$643$	−21.4355	+	37.1275i	−0.845335	+	1.46416i	−0.885330	+	0.464964i	$0.846067\pi$
$644$		0			0
$645$	3.16700			0.124701
$646$	4.71336	−	8.16378i	0.185445	−	0.321200i
$647$	−2.12929	−	3.68804i	−0.0837112	−	0.144992i	0.821130	−	0.570741i	$-0.193344\pi$
$647$	−2.12929	−	3.68804i	−0.0837112	−	0.144992i	−0.904841	+	0.425749i	$0.860011\pi$
$648$	8.49410	+	14.7122i	0.333680	+	0.577950i
$649$	−21.6819			−0.851089
$650$	18.5387	+	7.68744i	0.727148	+	0.301526i
$651$		0			0
$652$	3.00437	+	5.20373i	0.117660	+	0.203794i
$653$	1.04776	+	1.81477i	0.0410020	+	0.0710176i	0.885798	−	0.464071i	$-0.153612\pi$
$653$	1.04776	+	1.81477i	0.0410020	+	0.0710176i	−0.844796	+	0.535088i	$0.820278\pi$
$654$	5.22776	−	9.05475i	0.204422	−	0.354069i
$655$	11.3643			0.444038
$656$	3.57986	−	6.20049i	0.139770	−	0.242089i
$657$	−7.90982	+	13.7002i	−0.308592	+	0.534496i
$658$		0			0
$659$	−12.7259	+	22.0419i	−0.495732	+	0.858632i	−0.999988	−	0.00492170i	$-0.998433\pi$
$659$	−12.7259	+	22.0419i	−0.495732	+	0.858632i	0.504256	+	0.863554i	$0.331767\pi$
$660$	−0.257237	−	0.445548i	−0.0100129	−	0.0173429i
$661$	−13.9054	−	24.0848i	−0.540857	−	0.936792i	−0.998855	−	0.0478387i	$-0.984767\pi$
$661$	−13.9054	−	24.0848i	−0.540857	−	0.936792i	0.457998	−	0.888953i	$-0.348567\pi$
$662$	6.10639			0.237332
$663$	1.26874	−	0.972756i	0.0492739	−	0.0377787i
$664$	28.6234			1.11080
$665$		0			0
$666$	10.7117	+	18.5533i	0.415072	+	0.718925i
$667$	−15.3164	+	26.5288i	−0.593055	+	1.02720i
$668$	3.24128			0.125409
$669$	1.19103	−	2.06293i	0.0460480	−	0.0797574i
$670$	−3.46740	+	6.00572i	−0.133957	+	0.232021i
$671$	−17.4972			−0.675472
$672$		0			0
$673$	−7.76033	−	13.4413i	−0.299139	−	0.518124i	0.676800	−	0.736167i	$-0.263366\pi$
$673$	−7.76033	−	13.4413i	−0.299139	−	0.518124i	−0.975939	+	0.218043i	$0.930033\pi$
$674$	5.55100	+	9.61462i	0.213817	+	0.370341i
$675$	−10.0907			−0.388392
$676$	3.83071	+	3.83668i	0.147335	+	0.147565i
$677$	34.5626			1.32835			0.664175	−	0.747577i	$-0.268783\pi$
$677$	34.5626			1.32835			0.664175	+	0.747577i	$0.268783\pi$
$678$	−6.12109	−	10.6020i	−0.235079	−	0.407169i
$679$		0			0
$680$	1.32877	−	2.30150i	0.0509562	−	0.0882587i
$681$	−11.8285			−0.453269
$682$	8.69826	−	15.0658i	0.333074	−	0.576900i
$683$	−23.5032	+	40.7087i	−0.899325	+	1.55768i	−0.0709661	+	0.997479i	$0.522608\pi$
$683$	−23.5032	+	40.7087i	−0.899325	+	1.55768i	−0.828359	+	0.560198i	$0.810725\pi$
$684$	−7.70269			−0.294520
$685$	−1.64703	+	2.85275i	−0.0629299	+	0.108998i
$686$		0			0
$687$	−5.31138	−	9.19958i	−0.202642	−	0.350986i
$688$	−25.3174			−0.965218
$689$	−8.08261	+	6.19701i	−0.307923	+	0.236087i
$690$	3.26027			0.124116
$691$	−9.50301	−	16.4597i	−0.361512	−	0.626156i	0.626698	−	0.779262i	$-0.284406\pi$
$691$	−9.50301	−	16.4597i	−0.361512	−	0.626156i	−0.988210	+	0.153106i	$0.951073\pi$
$692$	−1.27088	−	2.20123i	−0.0483117	−	0.0836784i
$693$		0			0
$694$	15.6556			0.594280
$695$	−13.5813	+	23.5234i	−0.515166	+	0.892294i
$696$	−5.12648	+	8.87933i	−0.194319	+	0.336570i
$697$	−1.39241			−0.0527413
$698$	4.88822	−	8.46665i	0.185022	−	0.320467i
$699$	0.928805	+	1.60874i	0.0351306	+	0.0608480i
$700$		0			0
$701$	−45.4648			−1.71718			−0.858591	−	0.512662i	$-0.828659\pi$
$701$	−45.4648			−1.71718			−0.858591	+	0.512662i	$0.828659\pi$
$702$	−14.5936	−	6.05152i	−0.550800	−	0.228400i
$703$	33.3951			1.25952
$704$	−6.04010	−	10.4618i	−0.227645	−	0.394293i
$705$	0.928851	+	1.60882i	0.0349826	+	0.0605916i
$706$	−26.5597	+	46.0027i	−0.999586	+	1.73133i
$707$		0			0
$708$	−1.04531	+	1.81053i	−0.0392851	+	0.0680438i
$709$	4.89390	−	8.47648i	0.183794	−	0.318341i	−0.759375	−	0.650653i	$-0.774495\pi$
$709$	4.89390	−	8.47648i	0.183794	−	0.318341i	0.943170	+	0.332312i	$0.107829\pi$
$710$	4.68702			0.175901
$711$	8.38183	−	14.5178i	0.314343	−	0.544459i
$712$	−21.8427	−	37.8326i	−0.818589	−	1.41784i
$713$	9.51099	+	16.4735i	0.356189	+	0.616938i
$714$		0			0
$715$	8.39768	+	3.48226i	0.314055	+	0.130229i
$716$	7.72786			0.288804
$717$	5.35974	+	9.28334i	0.200163	+	0.346693i
$718$	−14.5259	−	25.1595i	−0.542100	−	0.938945i
$719$	13.9201	−	24.1104i	0.519133	−	0.899165i	−0.480620	−	0.876929i	$-0.659588\pi$
$719$	13.9201	−	24.1104i	0.519133	−	0.899165i	0.999753	−	0.0222358i	$-0.00707846\pi$
$720$	−15.3288			−0.571271
$721$		0			0
$722$	−20.0243	+	34.6830i	−0.745226	+	1.29077i
$723$	10.1514			0.377533
$724$	1.16883	−	2.02447i	0.0434391	−	0.0752388i
$725$	15.2439	+	26.4033i	0.566145	+	0.980592i
$726$	−2.48041	−	4.29619i	−0.0920566	−	0.159447i
$727$	−14.5650			−0.540186			−0.270093	−	0.962834i	$-0.587055\pi$
$727$	−14.5650			−0.540186			−0.270093	+	0.962834i	$0.587055\pi$
$728$		0			0
$729$	−14.9199			−0.552589
$730$	−5.30761	−	9.19305i	−0.196444	−	0.340250i
$731$	2.46185	+	4.26405i	0.0910547	+	0.157711i
$732$	−0.843560	+	1.46109i	−0.0311789	+	0.0540034i
$733$	17.6606			0.652309			0.326155	−	0.945316i	$-0.394247\pi$
$733$	17.6606			0.652309			0.326155	+	0.945316i	$0.394247\pi$
$734$	24.1451	−	41.8206i	0.891213	−	1.54363i
$735$		0			0
$736$	−8.35705			−0.308045
$737$	3.96102	−	6.86069i	0.145906	−	0.252717i
$738$	3.29697	+	5.71052i	0.121363	+	0.210207i
$739$	−4.48279	−	7.76443i	−0.164902	−	0.285619i	0.771718	−	0.635964i	$-0.219398\pi$
$739$	−4.48279	−	7.76443i	−0.164902	−	0.285619i	−0.936621	+	0.350345i	$0.886064\pi$
$740$	−2.48042			−0.0911822
$741$	−9.36579	+	7.18084i	−0.344061	+	0.263795i
$742$		0			0
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	0.999824	−	0.0187532i	$-0.00596968\pi$
$743$	13.1839	+	22.8352i	0.483671	+	0.837743i	−0.516153	+	0.856497i	$0.672636\pi$
$744$	3.18337	+	5.51376i	0.116708	+	0.202144i
$745$	−8.58580	+	14.8710i	−0.314560	+	0.544833i
$746$	−4.56618			−0.167180
$747$	−16.0543	+	27.8068i	−0.587395	+	1.01740i
$748$	0.399923	−	0.692688i	0.0146226	−	0.0253272i
$749$		0			0
$750$	3.88818	−	6.73452i	0.141976	−	0.245910i
$751$	10.1438	+	17.5696i	0.370152	+	0.641123i	0.989589	−	0.143924i	$-0.0459721\pi$
$751$	10.1438	+	17.5696i	0.370152	+	0.641123i	−0.619436	+	0.785047i	$0.712639\pi$
$752$	−7.42536	−	12.8611i	−0.270775	−	0.468996i
$753$	−6.48641			−0.236378
$754$	6.21203	+	47.3274i	0.226229	+	1.72356i
$755$	−18.1801			−0.661642
$756$		0			0
$757$	−12.4992	−	21.6493i	−0.454292	−	0.786857i	0.544355	−	0.838855i	$-0.316774\pi$
$757$	−12.4992	−	21.6493i	−0.454292	−	0.786857i	−0.998647	+	0.0519981i	$0.983441\pi$
$758$	−7.83957	+	13.5785i	−0.284746	+	0.493195i
$759$	−3.72440			−0.135187
$760$	−9.80895	+	16.9896i	−0.355808	+	0.616277i
$761$	−10.0711	+	17.4436i	−0.365077	+	0.632332i	−0.988789	−	0.149323i	$-0.952291\pi$
$761$	−10.0711	+	17.4436i	−0.365077	+	0.632332i	0.623712	+	0.781655i	$0.285624\pi$
$762$	11.9255			0.432016
$763$		0			0
$764$	−0.105035	−	0.181926i	−0.00380003	−	0.00658184i
$765$	1.49056	+	2.58173i	0.0538914	+	0.0933426i
$766$	5.73573			0.207240
$767$	−4.80769	−	36.6282i	−0.173596	−	1.32257i
$768$	−4.69889			−0.169557
$769$	−4.33610	−	7.51034i	−0.156364	−	0.270830i	0.777191	−	0.629265i	$-0.216644\pi$
$769$	−4.33610	−	7.51034i	−0.156364	−	0.270830i	−0.933555	+	0.358435i	$0.883311\pi$
$770$		0			0
$771$	−3.22199	+	5.58065i	−0.116037	+	0.200982i
$772$	−1.54828			−0.0557237
$773$	−1.17283	+	2.03141i	−0.0421839	+	0.0730647i	−0.886346	−	0.463023i	$-0.846765\pi$
$773$	−1.17283	+	2.03141i	−0.0421839	+	0.0730647i	0.844163	+	0.536087i	$0.180098\pi$
$774$	11.6584	−	20.1930i	0.419053	−	0.725821i
$775$	18.9319			0.680055
$776$	7.63441	−	13.2232i	0.274059	−	0.474685i
$777$		0			0
$778$	−17.6198	−	30.5184i	−0.631701	−	1.09414i
$779$	10.2787			0.368273
$780$	0.695645	−	0.533357i	0.0249081	−	0.0190973i
$781$	−5.35426			−0.191591
$782$	2.53435	+	4.38962i	0.0906281	+	0.156973i
$783$	−12.0000	−	20.7845i	−0.428844	−	0.742779i
$784$		0			0
$785$	13.6010			0.485440
$786$	−3.62734	+	6.28274i	−0.129383	+	0.224098i
$787$	17.0583	−	29.5459i	0.608063	−	1.05320i	−0.383496	−	0.923543i	$-0.625280\pi$
$787$	17.0583	−	29.5459i	0.608063	−	1.05320i	0.991559	−	0.129654i	$-0.0413866\pi$
$788$	−3.10474			−0.110602
$789$	−4.68228	+	8.10994i	−0.166693	+	0.288721i
$790$	5.62434	+	9.74164i	0.200105	+	0.346592i
$791$		0			0
$792$	14.3768			0.510858
$793$	−3.87978	−	29.5588i	−0.137775	−	1.04966i
$794$	−45.2973			−1.60754
$795$	0.823349	+	1.42608i	0.0292012	+	0.0505779i
$796$	−1.56510	−	2.71084i	−0.0554736	−	0.0960830i
$797$	17.0422	−	29.5180i	0.603666	−	1.04558i	−0.388594	−	0.921409i	$-0.627039\pi$
$797$	17.0422	−	29.5180i	0.603666	−	1.04558i	0.992261	−	0.124172i	$-0.0396275\pi$
$798$		0			0
$799$	−1.44407	+	2.50121i	−0.0510876	+	0.0884863i
$800$	−4.15875	+	7.20316i	−0.147034	+	0.254670i
$801$	49.0044			1.73148
$802$	−6.31243	+	10.9335i	−0.222900	+	0.386074i
$803$	6.06320	+	10.5018i	0.213966	+	0.370600i
$804$	−0.381931	−	0.661524i	−0.0134697	−	0.0233302i
$805$		0			0
$806$	27.3801	+	11.3537i	0.964423	+	0.399917i
$807$	13.9350			0.490534
$808$	−8.88745	−	15.3935i	−0.312659	−	0.541542i
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	0.999255	−	0.0385914i	$-0.0122871\pi$
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	−0.533049	+	0.846085i	$0.678954\pi$
$810$	6.39365	−	11.0741i	0.224650	−	0.389105i
$811$	52.5463			1.84515			0.922575	−	0.385818i	$-0.126081\pi$
$811$	52.5463			1.84515			0.922575	+	0.385818i	$0.126081\pi$
$812$		0			0
$813$	4.39040	−	7.60439i	0.153978	−	0.266698i
$814$	16.4220			0.575590
$815$	−8.58347	+	14.8670i	−0.300666	+	0.520768i
$816$	1.03318	+	1.78953i	0.0361686	+	0.0626459i
$817$	−18.1732	−	31.4770i	−0.635801	−	1.10124i
$818$	−12.9391			−0.452403
$819$		0			0
$820$	−0.763451			−0.0266609
$821$	15.3773	+	26.6343i	0.536671	+	0.929542i	0.999080	+	0.0428753i	$0.0136518\pi$
$821$	15.3773	+	26.6343i	0.536671	+	0.929542i	−0.462409	+	0.886667i	$0.653015\pi$
$822$	−1.05143	−	1.82113i	−0.0366728	−	0.0635191i
$823$	14.8519	−	25.7243i	0.517705	−	0.896691i	−0.482084	−	0.876125i	$-0.660120\pi$
$823$	14.8519	−	25.7243i	0.517705	−	0.896691i	0.999789	−	0.0205659i	$-0.00654678\pi$
$824$	−24.4289			−0.851021
$825$	−1.85339	+	3.21016i	−0.0645266	+	0.111763i
$826$		0			0
$827$	14.8351			0.515866			0.257933	−	0.966163i	$-0.416959\pi$
$827$	14.8351			0.515866			0.257933	+	0.966163i	$0.416959\pi$
$828$	2.07085	−	3.58681i	0.0719670	−	0.124650i
$829$	−7.29244	−	12.6309i	−0.253277	−	0.438688i	0.711149	−	0.703041i	$-0.248175\pi$
$829$	−7.29244	−	12.6309i	−0.253277	−	0.438688i	−0.964426	+	0.264353i	$0.914842\pi$
$830$	−10.7727	−	18.6588i	−0.373925	−	0.647657i
$831$	−6.57499			−0.228084
$832$	16.3342	−	12.5236i	0.566287	−	0.434177i
$833$		0			0
$834$	−8.66995	−	15.0168i	−0.300216	−	0.519989i
$835$	4.63015	+	8.01966i	0.160233	+	0.277532i
$836$	−2.95221	+	5.11339i	−0.102104	+	0.176850i
$837$	−14.9031			−0.515128
$838$	10.1184	−	17.5256i	0.349534	−	0.605411i
$839$	−18.4043	+	31.8772i	−0.635386	+	1.10052i	0.351047	+	0.936358i	$0.385826\pi$
$839$	−18.4043	+	31.8772i	−0.635386	+	1.10052i	−0.986433	+	0.164164i	$0.947508\pi$
$840$		0			0
$841$	−21.7564	+	37.6832i	−0.750221	+	1.29942i
$842$	6.91588	+	11.9787i	0.238337	+	0.412812i
$843$	−7.32728	−	12.6912i	−0.252365	−	0.437109i
$844$	1.58088			0.0544163
$845$	−4.02066	+	14.9587i	−0.138315	+	0.514596i
$846$	13.6772			0.470232
$847$		0			0
$848$	−6.58196	−	11.4003i	−0.226025	−	0.391488i
$849$	−2.41965	+	4.19095i	−0.0830421	+	0.143833i
$850$	5.04470			0.173032
$851$	−8.97819	+	15.5507i	−0.307768	+	0.533070i
$852$	−0.258135	+	0.447103i	−0.00884357	+	0.0153175i
$853$	−4.10728			−0.140630			−0.0703152	−	0.997525i	$-0.522401\pi$
$853$	−4.10728			−0.140630			−0.0703152	+	0.997525i	$0.522401\pi$
$854$		0			0
$855$	−11.0033	−	19.0582i	−0.376303	−	0.651777i
$856$	−2.70717	−	4.68895i	−0.0925291	−	0.160265i
$857$	−38.3312			−1.30937			−0.654684	−	0.755902i	$-0.727199\pi$
$857$	−38.3312			−1.30937			−0.654684	+	0.755902i	$0.727199\pi$
$858$	−4.60561	+	3.53116i	−0.157233	+	0.120552i
$859$	−39.4369			−1.34557			−0.672785	−	0.739838i	$-0.734902\pi$
$859$	−39.4369			−1.34557			−0.672785	+	0.739838i	$0.734902\pi$
$860$	1.34982	+	2.33796i	0.0460284	+	0.0797236i
$861$		0			0
$862$	6.96300	−	12.0603i	0.237161	−	0.410775i
$863$	−38.6440			−1.31546			−0.657728	−	0.753255i	$-0.728483\pi$
$863$	−38.6440			−1.31546			−0.657728	+	0.753255i	$0.728483\pi$
$864$	3.27375	−	5.67030i	0.111375	−	0.192907i
$865$	3.63090	−	6.28891i	0.123454	−	0.213829i
$866$	−0.268820			−0.00913488
$867$	−3.95771	+	6.85495i	−0.134411	+	0.232806i
$868$		0			0
$869$	−6.42502	−	11.1285i	−0.217954	−	0.377507i
$870$	7.71757			0.261650
$871$	12.4684	+	5.17026i	0.422475	+	0.175188i
$872$	−33.8283			−1.14557
$873$	8.56395	+	14.8332i	0.289846	+	0.502028i
$874$	−18.7084	−	32.4040i	−0.632822	−	1.09608i
$875$		0			0
$876$	1.16926			0.0395055
$877$	29.0371	−	50.2937i	0.980512	−	1.69830i	0.320118	−	0.947378i	$-0.396277\pi$
$877$	29.0371	−	50.2937i	0.980512	−	1.69830i	0.660394	−	0.750919i	$-0.270389\pi$
$878$	−7.41710	+	12.8468i	−0.250315	+	0.433558i
$879$	−3.87026			−0.130541
$880$	−5.87508	+	10.1759i	−0.198049	+	0.343031i
$881$	−10.8118	−	18.7266i	−0.364259	−	0.630916i	0.624398	−	0.781107i	$-0.285345\pi$
$881$	−10.8118	−	18.7266i	−0.364259	−	0.630916i	−0.988657	+	0.150191i	$0.952011\pi$
$882$		0			0
$883$	−22.7329			−0.765022			−0.382511	−	0.923951i	$-0.624941\pi$
$883$	−22.7329			−0.765022			−0.382511	+	0.923951i	$0.624941\pi$
$884$	1.25887	+	0.522014i	0.0423403	+	0.0175572i
$885$	−5.97287			−0.200776
$886$	10.7845	+	18.6793i	0.362312	+	0.627543i
$887$	8.16585	+	14.1437i	0.274182	+	0.474898i	0.969929	−	0.243390i	$-0.0782595\pi$
$887$	8.16585	+	14.1437i	0.274182	+	0.474898i	−0.695746	+	0.718288i	$0.744926\pi$
$888$	−3.00504	+	5.20488i	−0.100843	+	0.174664i
$889$		0			0
$890$	−16.4413	+	28.4772i	−0.551115	+	0.954559i
$891$	−7.30385	+	12.6506i	−0.244688	+	0.423812i
$892$	2.03054			0.0679874
$893$	10.6601	−	18.4638i	0.356726	−	0.617867i
$894$	−5.48098	−	9.49333i	−0.183311	−	0.317504i
$895$	11.0392	+	19.1205i	0.369000	+	0.639127i
$896$		0			0
$897$	−0.825840	−	6.29180i	−0.0275740	−	0.210077i
$898$	−33.1012			−1.10460
$899$	22.5140	+	38.9954i	0.750884	+	1.30057i
$900$	−2.06105	−	3.56984i	−0.0687015	−	0.118995i
$901$	−1.28005	+	2.21711i	−0.0426446	+	0.0738627i
$902$	5.05453			0.168297
$903$		0			0
$904$	−19.8045	+	34.3023i	−0.658687	+	1.14088i
$905$	6.67866			0.222006
$906$	5.80288	−	10.0509i	0.192788	−	0.333918i
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	0.721262	−	0.692662i	$-0.243562\pi$
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	−0.960494	+	0.278301i	$0.910229\pi$
$908$	−5.04146	−	8.73207i	−0.167307	−	0.289784i
$909$	19.9391			0.661339
$910$		0			0
$911$	−1.32236			−0.0438118			−0.0219059	−	0.999760i	$-0.506973\pi$
$911$	−1.32236			−0.0438118			−0.0219059	+	0.999760i	$0.506973\pi$
$912$	−7.62691	−	13.2102i	−0.252552	−	0.437433i
$913$	12.3063	+	21.3151i	0.407278	+	0.705426i
$914$	−7.52907	+	13.0407i	−0.249039	+	0.431349i
$915$	−4.82008			−0.159347
$916$	4.52757	−	7.84197i	0.149595	−	0.259106i
$917$		0			0
$918$	−3.97117			−0.131068
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	−0.545875	−	0.837867i	$-0.683802\pi$
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	0.998551	+	0.0538078i	$0.0171358\pi$
$920$	−5.27422	−	9.13522i	−0.173886	−	0.301179i
$921$	0.311258	+	0.539114i	0.0102563	+	0.0177644i
$922$	−2.13669			−0.0703682
$923$	−1.18724	−	9.04520i	−0.0390785	−	0.297726i
$924$		0			0
$925$	8.93569	+	15.4771i	0.293804	+	0.508883i
$926$	−24.6970	−	42.7765i	−0.811594	−	1.40572i
$927$	13.7016	−	23.7319i	0.450021	−	0.779459i
$928$	−19.7825			−0.649391
$929$	14.3194	−	24.8020i	0.469805	−	0.813727i	−0.529599	−	0.848248i	$-0.677657\pi$
$929$	14.3194	−	24.8020i	0.469805	−	0.813727i	0.999404	+	0.0345217i	$0.0109908\pi$
$930$	2.39618	−	4.15030i	0.0785737	−	0.136094i
$931$		0			0
$932$	−0.791738	+	1.37133i	−0.0259343	+	0.0449194i
$933$	6.05778	+	10.4924i	0.198323	+	0.343505i
$934$	22.6370	+	39.2084i	0.740704	+	1.28294i
$935$	2.28515			0.0747326
$936$	3.18788	+	24.2874i	0.104199	+	0.793858i
$937$	27.9990			0.914688			0.457344	−	0.889290i	$-0.348801\pi$
$937$	27.9990			0.914688			0.457344	+	0.889290i	$0.348801\pi$
$938$		0			0
$939$	0.581356	+	1.00694i	0.0189718	+	0.0328602i
$940$	−0.791778	+	1.37140i	−0.0258249	+	0.0447301i
$941$	28.9003			0.942124			0.471062	−	0.882100i	$-0.343871\pi$
$941$	28.9003			0.942124			0.471062	+	0.882100i	$0.343871\pi$
$942$	−4.34127	+	7.51931i	−0.141446	+	0.244992i
$943$	−2.76340	+	4.78635i	−0.0899887	+	0.155865i
$944$	47.7480			1.55406
$945$		0			0
$946$	−8.93666	−	15.4787i	−0.290556	−	0.503257i
$947$	−15.0617	−	26.0877i	−0.489441	−	0.847736i	0.510486	−	0.859886i	$-0.329466\pi$
$947$	−15.0617	−	26.0877i	−0.489441	−	0.847736i	−0.999926	+	0.0121504i	$0.996132\pi$
$948$	−1.23903			−0.0402418
$949$	−16.3967	+	12.5715i	−0.532259	+	0.408087i
$950$	−37.2398			−1.20822
$951$	−4.83860	−	8.38070i	−0.156902	−	0.271763i
$952$		0			0
$953$	−2.46511	+	4.26969i	−0.0798527	+	0.138309i	−0.903186	−	0.429249i	$-0.858778\pi$
$953$	−2.46511	+	4.26969i	−0.0798527	+	0.138309i	0.823334	+	0.567558i	$0.192112\pi$
$954$	12.1237			0.392519
$955$	0.300084	−	0.519760i	0.00971048	−	0.0168190i
$956$	−4.56879	+	7.91337i	−0.147765	+	0.255937i
$957$	−8.81625			−0.284989
$958$	−7.55721	+	13.0895i	−0.244162	+	0.422902i
$959$		0			0
$960$	−1.66391	−	2.88198i	−0.0537025	−	0.0930155i
$961$	−3.03914			−0.0980368
$962$	3.64137	+	27.7424i	0.117402	+	0.894451i
$963$	6.07357			0.195718
$964$	4.32665	+	7.49398i	0.139352	+	0.241365i
$965$	−2.21171	−	3.83079i	−0.0711974	−	0.123317i
$966$		0			0
$967$	29.1431			0.937180			0.468590	−	0.883416i	$-0.344762\pi$
$967$	29.1431			0.937180			0.468590	+	0.883416i	$0.344762\pi$
$968$	−8.02523	+	13.9001i	−0.257941	+	0.446767i
$969$	−1.48327	+	2.56910i	−0.0476495	+	0.0825313i
$970$	−11.4931			−0.369021
$971$	−7.28843	+	12.6239i	−0.233897	+	0.405121i	−0.958952	−	0.283570i	$-0.908481\pi$
$971$	−7.28843	+	12.6239i	−0.233897	+	0.405121i	0.725055	+	0.688691i	$0.241814\pi$
$972$	2.46738	+	4.27362i	0.0791412	+	0.137077i
$973$		0			0
$974$	−26.6058			−0.852506
$975$	−5.83403	−	2.41920i	−0.186838	−	0.0774763i
$976$	38.5324			1.23339
$977$	−26.2609	−	45.4852i	−0.840161	−	1.45520i	−0.889758	−	0.456432i	$-0.849127\pi$
$977$	−26.2609	−	45.4852i	−0.840161	−	1.45520i	0.0495974	−	0.998769i	$-0.484206\pi$
$978$	−5.47948	−	9.49074i	−0.175215	−	0.303481i
$979$	18.7819	−	32.5313i	0.600273	−	1.03970i
$980$		0			0
$981$	18.9736	−	32.8632i	0.605780	−	1.04924i
$982$	19.9943	−	34.6312i	0.638044	−	1.10513i
$983$	−6.03769			−0.192572			−0.0962862	−	0.995354i	$-0.530696\pi$
$983$	−6.03769			−0.192572			−0.0962862	+	0.995354i	$0.530696\pi$
$984$	−0.924923	+	1.60201i	−0.0294855	+	0.0510703i
$985$	−4.43511	−	7.68183i	−0.141314	−	0.244764i
$986$	5.99920	+	10.3909i	0.191054	+	0.330914i
$987$		0			0
$988$	−9.29289	−	3.85348i	−0.295646	−	0.122596i
$989$	19.5433			0.621441
$990$	−5.41083	−	9.37183i	−0.171967	−	0.297856i
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	0.502090	−	0.864815i	$-0.332564\pi$
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	−0.999997	+	0.00241558i	$0.999231\pi$
$992$	−6.14212	+	10.6385i	−0.195012	+	0.337771i
$993$	−1.92165			−0.0609816
$994$		0			0
$995$	4.47148	−	7.74483i	0.141755	−	0.245528i
$996$	2.37320			0.0751976
$997$	−2.74017	+	4.74611i	−0.0867819	+	0.150311i	−0.906149	−	0.422958i	$-0.860992\pi$
$997$	−2.74017	+	4.74611i	−0.0867819	+	0.150311i	0.819367	+	0.573269i	$0.194325\pi$
$998$	−4.20073	−	7.27588i	−0.132972	−	0.230314i
$999$	−7.03414	−	12.1835i	−0.222550	−	0.385468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.k.393.2		12
7.2	even	3		91.2.g.b.81.2	yes	12
7.3	odd	6		637.2.h.l.471.5		12
7.4	even	3		91.2.h.b.16.5	yes	12
7.5	odd	6		637.2.g.l.263.2		12
7.6	odd	2		637.2.f.j.393.2		12
13.3	even	3		8281.2.a.bz.1.5		6
13.9	even	3	inner	637.2.f.k.295.2		12
13.10	even	6		8281.2.a.ce.1.2		6
21.2	odd	6		819.2.n.d.172.5		12
21.11	odd	6		819.2.s.d.289.2		12
91.9	even	3		91.2.h.b.74.5	yes	12
91.16	even	3		1183.2.e.h.508.2		12
91.23	even	6		1183.2.e.g.508.5		12
91.48	odd	6		637.2.f.j.295.2		12
91.55	odd	6		8281.2.a.ca.1.5		6
91.61	odd	6		637.2.h.l.165.5		12
91.62	odd	6		8281.2.a.cf.1.2		6
91.74	even	3		91.2.g.b.9.2	✓	12
91.81	even	3		1183.2.e.h.170.2		12
91.87	odd	6		637.2.g.l.373.2		12
91.88	even	6		1183.2.e.g.170.5		12
273.74	odd	6		819.2.n.d.100.5		12
273.191	odd	6		819.2.s.d.802.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.2	✓	12	91.74	even	3
91.2.g.b.81.2	yes	12	7.2	even	3
91.2.h.b.16.5	yes	12	7.4	even	3
91.2.h.b.74.5	yes	12	91.9	even	3
637.2.f.j.295.2		12	91.48	odd	6
637.2.f.j.393.2		12	7.6	odd	2
637.2.f.k.295.2		12	13.9	even	3	inner
637.2.f.k.393.2		12	1.1	even	1	trivial
637.2.g.l.263.2		12	7.5	odd	6
637.2.g.l.373.2		12	91.87	odd	6
637.2.h.l.165.5		12	91.61	odd	6
637.2.h.l.471.5		12	7.3	odd	6
819.2.n.d.100.5		12	273.74	odd	6
819.2.n.d.172.5		12	21.2	odd	6
819.2.s.d.289.2		12	21.11	odd	6
819.2.s.d.802.2		12	273.191	odd	6
1183.2.e.g.170.5		12	91.88	even	6
1183.2.e.g.508.5		12	91.23	even	6
1183.2.e.h.170.2		12	91.81	even	3
1183.2.e.h.508.2		12	91.16	even	3
8281.2.a.bz.1.5		6	13.3	even	3
8281.2.a.ca.1.5		6	91.55	odd	6
8281.2.a.ce.1.2		6	13.10	even	6
8281.2.a.cf.1.2		6	91.62	odd	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777343 - 1.34640i) q^{2} +(0.244626 + 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} -1.19151 q^{5} +(0.380316 - 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(0.926214 + 1.60425i) q^{10} +(-1.05807 - 1.83263i) q^{11} -0.204043 q^{12} +(2.86133 - 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} +(2.33009 + 4.03583i) q^{16} +(0.453151 - 0.784881i) q^{17} -4.29192 q^{18} +(-3.34514 + 5.79395i) q^{19} +(0.248461 - 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} +(-0.602021 - 1.04273i) q^{24} -3.58030 q^{25} +(-5.17797 - 2.14715i) q^{26} +2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 + 0.784881i) q^{30} -5.28780 q^{31} +(1.16156 - 2.01189i) q^{32} +(0.517662 - 0.896617i) q^{33} -1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} +10.4013 q^{38} +(1.62948 + 0.675696i) q^{39} +2.93230 q^{40} +(-0.768181 - 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +0.882538 q^{44} +(-1.64466 + 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} -3.18673 q^{47} +(-1.14000 + 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +0.443410 q^{51} +(0.195692 + 1.49091i) q^{52} -2.82477 q^{53} +(-2.19086 - 3.79469i) q^{54} +(1.26070 + 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 + 11.4652i) q^{58} +(5.12298 - 8.87327i) q^{59} +0.243120 q^{60} +(4.13423 - 7.16069i) q^{61} +(4.11044 + 7.11949i) q^{62} +5.70861 q^{64} +(-3.40931 + 2.61395i) q^{65} -1.60960 q^{66} +(1.87182 + 3.24208i) q^{67} +(0.188987 + 0.327336i) q^{68} +(0.880000 - 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 + 5.88368i) q^{72} -5.73044 q^{73} +(-3.88018 + 6.72066i) q^{74} +(-0.875834 - 1.51699i) q^{75} +(-1.39510 - 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +6.07240 q^{79} +(-2.77632 - 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(-1.19428 + 2.06856i) q^{82} -11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +8.44619 q^{86} +(2.08310 - 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(8.87557 + 15.3729i) q^{89} +5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +(2.47719 + 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} +1.13659 q^{96} +(-3.10217 + 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 9 q^{6} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} + 8 q^{16} + 5 q^{17} - 6 q^{18} - q^{19} - q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + q^3 - 4 * q^4 - 2 * q^5 - 9 * q^6 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 - 10 * q^12 - 2 * q^13 - 2 * q^15 + 8 * q^16 + 5 * q^17 - 6 * q^18 - q^19 - q^20 - 5 * q^22 - q^23 - 11 * q^24 - 14 * q^25 + 11 * q^26 - 8 * q^27 + 3 * q^29 - 5 * q^30 - 32 * q^31 + 8 * q^32 + 16 * q^33 + 32 * q^34 - 21 * q^36 - 13 * q^37 + 34 * q^38 + 43 * q^39 + 10 * q^40 - 8 * q^41 - 11 * q^43 - 42 * q^44 - 7 * q^45 + 16 * q^46 + 2 * q^47 + 21 * q^48 + 6 * q^50 + 40 * q^51 - 16 * q^52 + 4 * q^53 - 18 * q^54 + 9 * q^55 + 42 * q^57 - 8 * q^58 + 13 * q^59 - 40 * q^60 - 5 * q^61 + 5 * q^62 - 30 * q^64 - 14 * q^65 - 36 * q^66 - 11 * q^67 + 29 * q^68 + 23 * q^69 + 6 * q^71 + 25 * q^72 + 60 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 16 * q^78 - 14 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - q^85 + 14 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 + 54 * q^92 - 7 * q^93 + 45 * q^94 - 6 * q^95 - 38 * q^96 - 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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