LMFDB - Embedded newform 637.2.f.j.393.6

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			393.6
Root			$-0.181721 + 0.314749i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.j.295.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19402 + 2.06810i) q^{2} +(-1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +O(q^{10})$	\(q+(1.19402 + 2.06810i) q^{2} +(-1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +(-1.17286 - 2.03145i) q^{10} +(0.293901 + 0.509052i) q^{11} +10.1880 q^{12} +(-2.39227 + 2.69760i) q^{13} +(1.35136 + 2.34063i) q^{15} +(-1.15235 - 1.99593i) q^{16} +(-3.22710 + 5.58950i) q^{17} -10.9148 q^{18} +(-1.91345 + 3.31419i) q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 + 9.68906i) q^{24} -4.03513 q^{25} +(-8.43532 - 1.72647i) q^{26} +4.32156 q^{27} +(1.98009 + 3.42962i) q^{29} +(-3.22710 + 5.58950i) q^{30} +2.98872 q^{31} +(-1.31430 + 2.27644i) q^{32} +(0.808663 - 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 - 14.6564i) q^{36} +(-0.877941 - 1.52064i) q^{37} -9.13877 q^{38} +(9.71911 + 1.98923i) q^{39} +3.99411 q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} -2.17647 q^{44} +(2.24482 - 3.88814i) q^{45} +(9.86261 - 17.0825i) q^{46} +4.34059 q^{47} +(-3.17067 + 5.49176i) q^{48} +(-4.81802 - 8.34505i) q^{50} +17.7586 q^{51} +(-4.22130 - 12.6654i) q^{52} +0.425541 q^{53} +(5.16002 + 8.93742i) q^{54} +(-0.288693 - 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} -10.0074 q^{60} +(1.10337 - 1.91109i) q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(2.34988 - 2.64980i) q^{65} +3.86223 q^{66} +(-3.50651 - 6.07346i) q^{67} +(-11.9491 - 20.6964i) q^{68} +(-11.3636 + 19.6824i) q^{69} +(-1.80127 + 3.11988i) q^{71} +(9.29247 - 16.0950i) q^{72} -4.93427 q^{73} +(2.09656 - 3.63134i) q^{74} +(5.55128 + 9.61510i) q^{75} +(-7.08496 - 12.2715i) q^{76} +(7.49088 + 22.4753i) q^{78} +2.78541 q^{79} +(1.13193 + 1.96056i) q^{80} +(0.910609 + 1.57722i) q^{81} +(-4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} -15.2377 q^{86} +(5.44818 - 9.43652i) q^{87} +(-1.19505 - 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} +10.7214 q^{90} +30.5845 q^{92} +(-4.11170 - 7.12167i) q^{93} +(5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +7.23255 q^{96} +(3.84852 - 6.66584i) q^{97} -2.68663 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}+O(q^{10}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	1.19402	+	2.06810i	0.844299	+	1.46237i	0.886229	+	0.463248i	$0.153316\pi$
$2$	1.19402	+	2.06810i	0.844299	+	1.46237i	−0.0419302	+	0.999121i	$0.513351\pi$
$3$	−1.37574	−	2.38285i	−0.794283	−	1.37574i	−0.923293	−	0.384096i	$-0.874513\pi$
$3$	−1.37574	−	2.38285i	−0.794283	−	1.37574i	0.129010	−	0.991643i	$-0.458820\pi$
$4$	−1.85136	+	3.20665i	−0.925680	+	1.60333i
$5$	−0.982280			−0.439289			−0.219644	−	0.975580i	$-0.570490\pi$
$5$	−0.982280			−0.439289			−0.219644	+	0.975580i	$0.570490\pi$
$6$	3.28532	−	5.69033i	1.34122	−	2.32307i
$7$		0			0
$7$		0			0
$8$	−4.06616			−1.43761
$9$	−2.28532	+	3.95828i	−0.761772	+	1.31943i
$10$	−1.17286	−	2.03145i	−0.370891	−	0.642402i
$11$	0.293901	+	0.509052i	0.0886146	+	0.153485i	0.906926	−	0.421291i	$-0.138423\pi$
$11$	0.293901	+	0.509052i	0.0886146	+	0.153485i	−0.818311	+	0.574775i	$0.805089\pi$
$12$	10.1880			2.94101
$13$	−2.39227	+	2.69760i	−0.663496	+	0.748179i
$13$	−2.39227	+	2.69760i	−0.663496	+	0.748179i
$14$		0			0
$15$	1.35136	+	2.34063i	0.348920	+	0.604347i
$16$	−1.15235	−	1.99593i	−0.288088	−	0.498983i
$17$	−3.22710	+	5.58950i	−0.782687	+	1.35565i	0.147685	+	0.989035i	$0.452818\pi$
$17$	−3.22710	+	5.58950i	−0.782687	+	1.35565i	−0.930371	+	0.366619i	$0.880515\pi$
$18$	−10.9148			−2.57265
$19$	−1.91345	+	3.31419i	−0.438975	+	0.760327i	−0.997611	−	0.0690863i	$-0.977992\pi$
$19$	−1.91345	+	3.31419i	−0.438975	+	0.760327i	0.558636	+	0.829413i	$0.311325\pi$
$20$	1.81855	−	3.14983i	0.406641	−	0.704323i
$21$		0			0
$22$	−0.701847	+	1.21563i	−0.149634	+	0.259174i
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	−0.870805	−	0.491629i	$-0.836402\pi$
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	0.00963902	−	0.999954i	$-0.496932\pi$
$24$	5.59398	+	9.68906i	1.14187	+	1.97777i
$25$	−4.03513			−0.807025
$26$	−8.43532	−	1.72647i	−1.65430	−	0.338589i
$27$	4.32156			0.831685
$28$		0			0
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	0.989205	−	0.146541i	$-0.0468141\pi$
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	−0.621511	+	0.783406i	$0.713481\pi$
$30$	−3.22710	+	5.58950i	−0.589185	+	1.02050i
$31$	2.98872			0.536790			0.268395	−	0.963309i	$-0.413507\pi$
$31$	2.98872			0.536790			0.268395	+	0.963309i	$0.413507\pi$
$32$	−1.31430	+	2.27644i	−0.232338	+	0.402421i
$33$	0.808663	−	1.40065i	0.140770	−	0.243821i
$34$	−15.4129			−2.64329
$35$		0			0
$36$	−8.46189	−	14.6564i	−1.41031	−	2.44274i
$37$	−0.877941	−	1.52064i	−0.144333	−	0.249991i	0.784791	−	0.619760i	$-0.212770\pi$
$37$	−0.877941	−	1.52064i	−0.144333	−	0.249991i	−0.929124	+	0.369769i	$0.879437\pi$
$38$	−9.13877			−1.48250
$39$	9.71911	+	1.98923i	1.55630	+	0.318532i
$40$	3.99411			0.631524
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	0.973023	−	0.230710i	$-0.0741049\pi$
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	−0.686312	+	0.727307i	$0.740772\pi$
$42$		0			0
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	−0.999880	−	0.0154788i	$-0.995073\pi$
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	0.513345	+	0.858182i	$0.328406\pi$
$44$	−2.17647			−0.328115
$45$	2.24482	−	3.88814i	0.334638	−	0.579610i
$46$	9.86261	−	17.0825i	1.45416	−	2.51868i
$47$	4.34059			0.633141			0.316570	−	0.948569i	$-0.397469\pi$
$47$	4.34059			0.633141			0.316570	+	0.948569i	$0.397469\pi$
$48$	−3.17067	+	5.49176i	−0.457647	+	0.792668i
$49$		0			0
$50$	−4.81802	−	8.34505i	−0.681370	−	1.18017i
$51$	17.7586			2.48670
$52$	−4.22130	−	12.6654i	−0.585389	−	1.75638i
$53$	0.425541			0.0584525			0.0292263	−	0.999573i	$-0.490696\pi$
$53$	0.425541			0.0584525			0.0292263	+	0.999573i	$0.490696\pi$
$54$	5.16002	+	8.93742i	0.702190	+	1.21623i
$55$	−0.288693	−	0.500031i	−0.0389274	−	0.0674242i
$56$		0			0
$57$	10.5296			1.39468
$58$	−4.72853	+	8.19006i	−0.620887	+	1.07541i
$59$	3.00431	−	5.20362i	0.391128	−	0.677454i	−0.601470	−	0.798895i	$-0.705418\pi$
$59$	3.00431	−	5.20362i	0.391128	−	0.677454i	0.992599	+	0.121441i	$0.0387516\pi$
$60$	−10.0074			−1.29195
$61$	1.10337	−	1.91109i	0.141272	−	0.244691i	−0.786704	−	0.617331i	$-0.788214\pi$
$61$	1.10337	−	1.91109i	0.141272	−	0.244691i	0.927976	+	0.372640i	$0.121547\pi$
$62$	3.56859	+	6.18097i	0.453211	+	0.784985i
$63$		0			0
$64$	−10.8866			−1.36083
$65$	2.34988	−	2.64980i	0.291467	−	0.328667i
$66$	3.86223			0.475408
$67$	−3.50651	−	6.07346i	−0.428389	−	0.741991i	0.568341	−	0.822793i	$-0.307585\pi$
$67$	−3.50651	−	6.07346i	−0.428389	−	0.741991i	−0.996730	+	0.0808015i	$0.974252\pi$
$68$	−11.9491	−	20.6964i	−1.44904	−	2.50980i
$69$	−11.3636	+	19.6824i	−1.36802	+	2.36948i
$70$		0			0
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	−0.952892	−	0.303311i	$-0.901908\pi$
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	0.739121	+	0.673573i	$0.235241\pi$
$72$	9.29247	−	16.0950i	1.09513	−	1.89682i
$73$	−4.93427			−0.577513			−0.288756	−	0.957403i	$-0.593242\pi$
$73$	−4.93427			−0.577513			−0.288756	+	0.957403i	$0.593242\pi$
$74$	2.09656	−	3.63134i	0.243720	−	0.422135i
$75$	5.55128	+	9.61510i	0.641007	+	1.11026i
$76$	−7.08496	−	12.2715i	−0.812701	−	1.40764i
$77$		0			0
$78$	7.49088	+	22.4753i	0.848175	+	2.54483i
$79$	2.78541			0.313383			0.156691	−	0.987648i	$-0.449917\pi$
$79$	2.78541			0.313383			0.156691	+	0.987648i	$0.449917\pi$
$80$	1.13193	+	1.96056i	0.126554	+	0.219198i
$81$	0.910609	+	1.57722i	0.101179	+	0.175247i
$82$	−4.38406	+	7.59342i	−0.484138	+	0.838552i
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$		0			0
$85$	3.16992	−	5.49045i	0.343826	−	0.595523i
$86$	−15.2377			−1.64312
$87$	5.44818	−	9.43652i	0.584106	−	1.01170i
$88$	−1.19505	−	2.06989i	−0.127393	−	0.220651i
$89$	−1.04656	−	1.81269i	−0.110935	−	0.192145i	0.805213	−	0.592986i	$-0.202051\pi$
$89$	−1.04656	−	1.81269i	−0.110935	−	0.192145i	−0.916147	+	0.400842i	$0.868718\pi$
$90$	10.7214			1.13014
$91$		0			0
$92$	30.5845			3.18866
$93$	−4.11170	−	7.12167i	−0.426363	−	0.738483i
$94$	5.18275	+	8.97679i	0.534560	+	0.925885i
$95$	1.87954	−	3.25546i	0.192837	−	0.334003i
$96$	7.23255			0.738169
$97$	3.84852	−	6.66584i	0.390758	−	0.676813i	−0.601791	−	0.798653i	$-0.705546\pi$
$97$	3.84852	−	6.66584i	0.390758	−	0.676813i	0.992550	+	0.121840i	$0.0388795\pi$
$98$		0			0
$99$	−2.68663			−0.270016
$100$	7.47047	−	12.9392i	0.747047	−	1.29392i
$101$	−1.31866	−	2.28399i	−0.131212	−	0.227265i	0.792932	−	0.609310i	$-0.208553\pi$
$101$	−1.31866	−	2.28399i	−0.131212	−	0.227265i	−0.924144	+	0.382045i	$0.875220\pi$
$102$	21.2041	+	36.7266i	2.09952	+	3.63647i
$103$	10.8619			1.07026			0.535128	−	0.844771i	$-0.320263\pi$
$103$	10.8619			1.07026			0.535128	+	0.844771i	$0.320263\pi$
$104$	9.72736	−	10.9689i	0.953846	−	1.07559i
$105$		0			0
$106$	0.508103	+	0.880061i	0.0493514	+	0.0854791i
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	0.936219	+	0.351418i	$0.114300\pi$
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	−0.163773	+	0.986498i	$0.552366\pi$
$108$	−8.00077	+	13.8577i	−0.769874	+	1.33346i
$109$	9.23477			0.884530			0.442265	−	0.896884i	$-0.354175\pi$
$109$	9.23477			0.884530			0.442265	+	0.896884i	$0.354175\pi$
$110$	0.689410	−	1.19409i	0.0657327	−	0.113852i
$111$	−2.41564	+	4.18400i	−0.229282	+	0.397128i
$112$		0			0
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	−0.999706	−	0.0242655i	$-0.992275\pi$
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	0.520867	+	0.853638i	$0.325609\pi$
$114$	12.5726	+	21.7763i	1.17753	+	2.03954i
$115$	4.05682	+	7.02662i	0.378301	+	0.655236i
$116$	−14.6635			−1.36147
$117$	−5.21077	−	15.6342i	−0.481736	−	1.44538i
$118$	14.3488			1.32092
$119$		0			0
$120$	−5.49485	−	9.51736i	−0.501609	−	0.868813i
$121$	5.32724	−	9.22706i	0.484295	−	0.838823i
$122$	5.26978			0.477104
$123$	5.05128	−	8.74908i	0.455459	−	0.788878i
$124$	−5.53320	+	9.58378i	−0.496896	+	0.860649i
$125$	8.87502			0.793806
$126$		0			0
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	0.756201	−	0.654340i	$-0.227053\pi$
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	−0.944775	+	0.327719i	$0.893720\pi$
$128$	−10.3702	−	17.9617i	−0.916606	−	1.58761i
$129$	17.5568			1.54579
$130$	8.28585	+	1.69588i	0.726717	+	0.148739i
$131$	2.16957			0.189556			0.0947779	−	0.995498i	$-0.469786\pi$
$131$	2.16957			0.189556			0.0947779	+	0.995498i	$0.469786\pi$
$132$	2.99425	+	5.18620i	0.260616	+	0.451401i
$133$		0			0
$134$	8.37369	−	14.5037i	0.723376	−	1.25292i
$135$	−4.24498			−0.365350
$136$	13.1219	−	22.7278i	1.12519	−	1.94889i
$137$	−4.18158	+	7.24271i	−0.357257	+	0.618787i	−0.987501	−	0.157610i	$-0.949621\pi$
$137$	−4.18158	+	7.24271i	−0.357257	+	0.618787i	0.630245	+	0.776396i	$0.282955\pi$
$138$	−54.2735			−4.62007
$139$	−0.288457	+	0.499622i	−0.0244666	+	0.0423774i	−0.877999	−	0.478662i	$-0.841122\pi$
$139$	−0.288457	+	0.499622i	−0.0244666	+	0.0423774i	0.853533	+	0.521039i	$0.174455\pi$
$140$		0			0
$141$	−5.97152	−	10.3430i	−0.502893	−	0.871036i
$142$	−8.60298			−0.721946
$143$	−2.07631	−	0.424962i	−0.173630	−	0.0355371i
$144$	10.5340			0.877830
$145$	−1.94500	−	3.36885i	−0.161524	−	0.279767i
$146$	−5.89161	−	10.2046i	−0.487593	−	0.844537i
$147$		0			0
$148$	6.50154			0.534423
$149$	−1.40331	+	2.43061i	−0.114964	+	0.199123i	−0.917765	−	0.397123i	$-0.870009\pi$
$149$	−1.40331	+	2.43061i	−0.114964	+	0.199123i	0.802801	+	0.596246i	$0.203342\pi$
$150$	−13.2567	+	22.9612i	−1.08240	+	1.87478i
$151$	−23.0109			−1.87260			−0.936300	−	0.351202i	$-0.885773\pi$
$151$	−23.0109			−1.87260			−0.936300	+	0.351202i	$0.885773\pi$
$152$	7.78039	−	13.4760i	0.631073	−	1.09305i
$153$	−14.7499	−	25.5476i	−1.19246	−	2.06540i
$154$		0			0
$155$	−2.93576			−0.235806
$156$	−24.3724	+	27.4830i	−1.95135	+	2.20040i
$157$	−22.5760			−1.80176			−0.900879	−	0.434071i	$-0.857077\pi$
$157$	−22.5760			−1.80176			−0.900879	+	0.434071i	$0.857077\pi$
$158$	3.32583	+	5.76050i	0.264588	+	0.458281i
$159$	−0.585433	−	1.01400i	−0.0464278	−	0.0804154i
$160$	1.29101	−	2.23610i	0.102064	−	0.176779i
$161$		0			0
$162$	−2.17457	+	3.76646i	−0.170850	+	0.295921i
$163$	−4.08857	+	7.08161i	−0.320242	+	0.554675i	−0.980538	−	0.196331i	$-0.937097\pi$
$163$	−4.08857	+	7.08161i	−0.320242	+	0.554675i	0.660296	+	0.751005i	$0.270431\pi$
$164$	−13.5952			−1.06161
$165$	−0.794333	+	1.37583i	−0.0618388	+	0.107108i
$166$	3.42467	+	5.93170i	0.265806	+	0.460389i
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	0.817475	−	0.575964i	$-0.195373\pi$
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	−0.907537	+	0.419972i	$0.862040\pi$
$168$		0			0
$169$	−1.55408	−	12.9068i	−0.119545	−	0.992829i
$170$	15.1398			1.16117
$171$	−8.74566	−	15.1479i	−0.668798	−	1.15839i
$172$	−11.8133	−	20.4611i	−0.900752	−	1.56015i
$173$	−4.06686	+	7.04401i	−0.309198	+	0.535546i	−0.978187	−	0.207726i	$-0.933394\pi$
$173$	−4.06686	+	7.04401i	−0.309198	+	0.535546i	0.668989	+	0.743272i	$0.266727\pi$
$174$	26.0209			1.97264
$175$		0			0
$176$	0.677355	−	1.17321i	0.0510576	−	0.0884343i
$177$	−16.5326			−1.24267
$178$	2.49922	−	4.32877i	0.187324	−	0.324455i
$179$	10.4963	+	18.1801i	0.784528	+	1.35884i	0.929281	+	0.369375i	$0.120428\pi$
$179$	10.4963	+	18.1801i	0.784528	+	1.35884i	−0.144752	+	0.989468i	$0.546239\pi$
$180$	8.31194	+	14.3967i	0.619536	+	1.07307i
$181$	1.60807			0.119527			0.0597635	−	0.998213i	$-0.480965\pi$
$181$	1.60807			0.119527			0.0597635	+	0.998213i	$0.480965\pi$
$182$		0			0
$183$	−6.07180			−0.448841
$184$	16.7933	+	29.0868i	1.23802	+	2.14431i
$185$	0.862384	+	1.49369i	0.0634037	+	0.109818i
$186$	9.81889	−	17.0068i	0.719956	−	1.24700i
$187$	−3.79379			−0.277430
$188$	−8.03601	+	13.9188i	−0.586086	+	1.01513i
$189$		0			0
$190$	8.97683			0.651247
$191$	5.78111	−	10.0132i	0.418307	−	0.724529i	−0.577463	−	0.816417i	$-0.695957\pi$
$191$	5.78111	−	10.0132i	0.418307	−	0.724529i	0.995769	+	0.0918886i	$0.0292904\pi$
$192$	14.9771	+	25.9412i	1.08088	+	1.87214i
$193$	−11.7894	−	20.4199i	−0.848621	−	1.46985i	−0.882439	−	0.470427i	$-0.844100\pi$
$193$	−11.7894	−	20.4199i	−0.848621	−	1.46985i	0.0338178	−	0.999428i	$-0.489233\pi$
$194$	18.3808			1.31967
$195$	−9.54689	−	1.95398i	−0.683667	−	0.139927i
$196$		0			0
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	0.891036	−	0.453933i	$-0.149980\pi$
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	−0.838636	+	0.544693i	$0.816646\pi$
$198$	−3.20788	−	5.55622i	−0.227974	−	0.394863i
$199$	4.69700	−	8.13543i	0.332961	−	0.576706i	−0.650130	−	0.759823i	$-0.725286\pi$
$199$	4.69700	−	8.13543i	0.332961	−	0.576706i	0.983091	+	0.183117i	$0.0586189\pi$
$200$	16.4075			1.16018
$201$	−9.64810	+	16.7110i	−0.680524	+	1.17870i
$202$	3.14901	−	5.45425i	0.221564	−	0.383760i
$203$		0			0
$204$	−32.8776	+	56.9456i	−2.30189	+	3.98699i
$205$	−1.80331	−	3.12343i	−0.125949	−	0.218150i
$206$	12.9693	+	22.4635i	0.903615	+	1.56511i
$207$	37.7535			2.62405
$208$	8.14096	+	1.66623i	0.564474	+	0.115532i
$209$	−2.24946			−0.155598
$210$		0			0
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	0.977881	−	0.209160i	$-0.0670730\pi$
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	−0.670079	+	0.742290i	$0.733740\pi$
$212$	−0.787829	+	1.36456i	−0.0541083	+	0.0937184i
$213$	9.91229			0.679179
$214$	−19.0810	+	33.0493i	−1.30435	+	2.25920i
$215$	3.13389	−	5.42805i	0.213729	−	0.370190i
$216$	−17.5722			−1.19563
$217$		0			0
$218$	11.0265	+	19.0984i	0.746808	+	1.29351i
$219$	6.78827	+	11.7576i	0.458709	+	0.794507i
$220$	2.13790			0.144137
$221$	−7.35814	−	22.0770i	−0.494962	−	1.48506i
$222$	−11.5373			−0.774330
$223$	10.9098	+	18.8963i	0.730574	+	1.26539i	0.956638	+	0.291279i	$0.0940809\pi$
$223$	10.9098	+	18.8963i	0.730574	+	1.26539i	−0.226064	+	0.974112i	$0.572586\pi$
$224$		0			0
$225$	9.22154	−	15.9722i	0.614769	−	1.06481i
$226$	−24.3108			−1.61713
$227$	−9.27627	+	16.0670i	−0.615687	+	1.06640i	0.374576	+	0.927196i	$0.377788\pi$
$227$	−9.27627	+	16.0670i	−0.615687	+	1.06640i	−0.990263	+	0.139206i	$0.955545\pi$
$228$	−19.4941	+	33.7648i	−1.29103	+	2.23613i
$229$	−19.3505			−1.27872			−0.639359	−	0.768909i	$-0.720800\pi$
$229$	−19.3505			−1.27872			−0.639359	+	0.768909i	$0.720800\pi$
$230$	−9.68784	+	16.7798i	−0.638797	+	1.10643i
$231$		0			0
$232$	−8.05137	−	13.9454i	−0.528599	−	0.915560i
$233$	16.1634			1.05890			0.529450	−	0.848341i	$-0.322398\pi$
$233$	16.1634			1.05890			0.529450	+	0.848341i	$0.322398\pi$
$234$	26.1113	−	29.4439i	1.70695	−	1.92481i
$235$	−4.26368			−0.278132
$236$	11.1241	+	19.2676i	0.724119	+	1.25421i
$237$	−3.83199	−	6.63720i	−0.248915	−	0.431133i
$238$		0			0
$239$	16.1037			1.04166			0.520831	−	0.853660i	$-0.325622\pi$
$239$	16.1037			1.04166			0.520831	+	0.853660i	$0.325622\pi$
$240$	3.11449	−	5.39445i	0.201039	−	0.348210i
$241$	−2.00300	+	3.46930i	−0.129025	+	0.223477i	−0.923299	−	0.384082i	$-0.874518\pi$
$241$	−2.00300	+	3.46930i	−0.129025	+	0.223477i	0.794274	+	0.607559i	$0.207851\pi$
$242$	25.4433			1.63556
$243$	8.98786	−	15.5674i	0.576572	−	0.998651i
$244$	4.08548	+	7.07625i	0.261546	+	0.453011i
$245$		0			0
$246$	24.1253			1.53817
$247$	−4.36287	−	13.0901i	−0.277603	−	0.832906i
$248$	−12.1526			−0.771692
$249$	−3.94588	−	6.83446i	−0.250060	−	0.433116i
$250$	10.5969	+	18.3544i	0.670209	+	1.16084i
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	−0.810231	−	0.586110i	$-0.800659\pi$
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	0.912702	+	0.408626i	$0.133992\pi$
$252$		0			0
$253$	2.42763	−	4.20477i	0.152624	−	0.264352i
$254$	5.07489	−	8.78996i	0.318427	−	0.551531i
$255$	−17.4439			−1.09238
$256$	13.8778	−	24.0371i	0.867365	−	1.50232i
$257$	−13.4462	−	23.2895i	−0.838751	−	1.45276i	−0.890940	−	0.454122i	$-0.849953\pi$
$257$	−13.4462	−	23.2895i	−0.838751	−	1.45276i	0.0521891	−	0.998637i	$-0.483380\pi$
$258$	20.9631	+	36.3092i	1.30511	+	2.26051i
$259$		0			0
$260$	4.14650	+	12.4410i	0.257155	+	0.771556i
$261$	−18.1005			−1.12040
$262$	2.59050	+	4.48688i	0.160042	+	0.277200i
$263$	1.90353	+	3.29701i	0.117377	+	0.203302i	0.918727	−	0.394893i	$-0.129218\pi$
$263$	1.90353	+	3.29701i	0.117377	+	0.203302i	−0.801351	+	0.598195i	$0.795885\pi$
$264$	−3.28815	+	5.69525i	−0.202372	+	0.350518i
$265$	−0.418000			−0.0256775
$266$		0			0
$267$	−2.87958	+	4.98757i	−0.176227	+	0.305235i
$268$	25.9673			1.58620
$269$	−11.9190	+	20.6444i	−0.726716	+	1.25871i	0.231548	+	0.972824i	$0.425621\pi$
$269$	−11.9190	+	20.6444i	−0.726716	+	1.25871i	−0.958264	+	0.285886i	$0.907712\pi$
$270$	−5.06859	−	8.77905i	−0.308464	−	0.534276i
$271$	4.95068	+	8.57482i	0.300732	+	0.520883i	0.976302	−	0.216413i	$-0.0694357\pi$
$271$	4.95068	+	8.57482i	0.300732	+	0.520883i	−0.675570	+	0.737296i	$0.736102\pi$
$272$	14.8750			0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	−1.18593	−	2.05409i	−0.0715142	−	0.123866i
$276$	−42.0763	−	72.8783i	−2.53270	−	4.38676i
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	−0.986958	−	0.160977i	$-0.948536\pi$
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	0.632889	+	0.774243i	$0.281869\pi$
$278$	−1.37769			−0.0826285
$279$	−6.83017	+	11.8302i	−0.408912	+	0.708256i
$280$		0			0
$281$	12.9976			0.775372			0.387686	−	0.921791i	$-0.373274\pi$
$281$	12.9976			0.775372			0.387686	+	0.921791i	$0.373274\pi$
$282$	14.2602	−	24.6994i	0.849184	−	1.47083i
$283$	−8.40249	−	14.5535i	−0.499476	−	0.865118i	0.500524	−	0.865723i	$-0.333141\pi$
$283$	−8.40249	−	14.5535i	−0.499476	−	0.865118i	−1.00000		0.000604910i	$0.999807\pi$
$284$	−6.66959	−	11.5521i	−0.395767	−	0.685489i
$285$	−10.3430			−0.612668
$286$	−1.60029	−	4.80143i	−0.0946270	−	0.283914i
$287$		0			0
$288$	−6.00719	−	10.4048i	−0.353977	−	0.613107i
$289$	−12.3283	−	21.3533i	−0.725197	−	1.25608i
$290$	4.64474	−	8.04493i	0.272749	−	0.472414i
$291$	−21.1783			−1.24149
$292$	9.13512	−	15.8225i	0.534592	−	0.925941i
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	−0.995080	−	0.0990757i	$-0.968411\pi$
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	0.583342	+	0.812227i	$0.301745\pi$
$294$		0			0
$295$	−2.95108	+	5.11141i	−0.171818	+	0.297598i
$296$	3.56985	+	6.18316i	0.207493	+	0.359389i
$297$	1.27011	+	2.19990i	0.0736994	+	0.127651i
$298$	−6.70232			−0.388255
$299$	29.1770	+	5.97172i	1.68735	+	0.345353i
$300$	−41.1097			−2.37347
$301$		0			0
$302$	−27.4754	−	47.5888i	−1.58103	−	2.73843i
$303$	−3.62827	+	6.28434i	−0.208439	+	0.361026i
$304$	8.81986			0.505854
$305$	−1.08382	+	1.87723i	−0.0620593	+	0.107490i
$306$	35.2233	−	61.0085i	2.01358	−	3.48762i
$307$	−15.8786			−0.906240			−0.453120	−	0.891450i	$-0.649689\pi$
$307$	−15.8786			−0.906240			−0.453120	+	0.891450i	$0.649689\pi$
$308$		0			0
$309$	−14.9431	−	25.8823i	−0.850086	−	1.47239i
$310$	−3.50535	−	6.07145i	−0.199091	−	0.344835i
$311$	28.6034			1.62195			0.810975	−	0.585081i	$-0.198937\pi$
$311$	28.6034			1.62195			0.810975	+	0.585081i	$0.198937\pi$
$312$	−39.5195	−	8.08853i	−2.23735	−	0.457923i
$313$	18.5792			1.05016			0.525080	−	0.851053i	$-0.324035\pi$
$313$	18.5792			1.05016			0.525080	+	0.851053i	$0.324035\pi$
$314$	−26.9561	−	46.6893i	−1.52122	−	2.63483i
$315$		0			0
$316$	−5.15679	+	8.93182i	−0.290092	+	0.502454i
$317$	30.6445			1.72117			0.860584	−	0.509309i	$-0.170099\pi$
$317$	30.6445			1.72117			0.860584	+	0.509309i	$0.170099\pi$
$318$	1.39804	−	2.42147i	0.0783979	−	0.135789i
$319$	−1.16390	+	2.01594i	−0.0651660	+	0.112871i
$320$	10.6937			0.597796
$321$	21.9850	−	38.0791i	1.22708	−	2.12537i
$322$		0			0
$323$	−12.3498	−	21.3904i	−0.687160	−	1.19020i
$324$	−6.74346			−0.374637
$325$	9.65311	−	10.8852i	0.535458	−	0.603800i
$326$	−19.5273			−1.08152
$327$	−12.7046	−	22.0051i	−0.702568	−	1.21688i
$328$	−7.46483	−	12.9295i	−0.412177	−	0.713911i
$329$		0			0
$330$	−3.79379			−0.208842
$331$	−13.6138	+	23.5799i	−0.748284	+	1.29607i	0.200360	+	0.979722i	$0.435789\pi$
$331$	−13.6138	+	23.5799i	−0.748284	+	1.29607i	−0.948644	+	0.316344i	$0.897545\pi$
$332$	−5.31005	+	9.19728i	−0.291427	+	0.504766i
$333$	8.02549			0.439794
$334$	2.77933	−	4.81395i	0.152078	−	0.263407i
$335$	3.44438	+	5.96584i	0.188187	+	0.325949i
$336$		0			0
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	24.8369	−	18.6249i	1.35095	−	1.01306i
$339$	28.0107			1.52133
$340$	11.7373	+	20.3296i	0.636545	+	1.10253i
$341$	0.878389	+	1.52141i	0.0475674	+	0.0823892i
$342$	20.8850	−	36.1738i	1.12933	−	1.95606i
$343$		0			0
$344$	12.9728	−	22.4695i	0.699445	−	1.21148i
$345$	11.1623	−	19.3336i	0.600956	−	1.04089i
$346$	−19.4236			−1.04422
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	−0.936635	−	0.350308i	$-0.886077\pi$
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	0.771693	+	0.635996i	$0.219410\pi$
$348$	20.1731	+	34.9408i	1.08139	+	1.87302i
$349$	6.51563	+	11.2854i	0.348774	+	0.604094i	0.986032	−	0.166557i	$-0.0532649\pi$
$349$	6.51563	+	11.2854i	0.348774	+	0.604094i	−0.637258	+	0.770650i	$0.719932\pi$
$350$		0			0
$351$	−10.3383	+	11.6578i	−0.551820	+	0.622249i
$352$	−1.54510			−0.0823541
$353$	15.8332	+	27.4240i	0.842718	+	1.45963i	0.887589	+	0.460637i	$0.152379\pi$
$353$	15.8332	+	27.4240i	0.842718	+	1.45963i	−0.0448710	+	0.998993i	$0.514288\pi$
$354$	−19.7402	−	34.1911i	−1.04918	−	1.81724i
$355$	1.76935	−	3.06460i	0.0939072	−	0.162652i
$356$	7.75021			0.410761
$357$		0			0
$358$	−25.0655	+	43.4147i	−1.32475	+	2.29454i
$359$	19.9322			1.05198			0.525991	−	0.850490i	$-0.323695\pi$
$359$	19.9322			1.05198			0.525991	+	0.850490i	$0.323695\pi$
$360$	−9.12780	+	15.8098i	−0.481077	+	0.833251i
$361$	2.17744	+	3.77144i	0.114602	+	0.198497i
$362$	1.92007	+	3.32566i	0.100917	+	0.174793i
$363$	−29.3156			−1.53867
$364$		0			0
$365$	4.84684			0.253695
$366$	−7.24984	−	12.5571i	−0.378955	−	0.656370i
$367$	9.85950	+	17.0772i	0.514662	+	0.891420i	0.999855	+	0.0170133i	$0.00541577\pi$
$367$	9.85950	+	17.0772i	0.514662	+	0.891420i	−0.485194	+	0.874407i	$0.661251\pi$
$368$	−9.51844	+	16.4864i	−0.496183	+	0.859414i
$369$	−16.7819			−0.873632
$370$	−2.05940	+	3.56699i	−0.107063	+	0.185439i
$371$		0			0
$372$	30.4490			1.57870
$373$	−8.77345	+	15.1961i	−0.454272	+	0.786823i	−0.998646	−	0.0520202i	$-0.983434\pi$
$373$	−8.77345	+	15.1961i	−0.454272	+	0.786823i	0.544374	+	0.838843i	$0.316767\pi$
$374$	−4.52986	−	7.84595i	−0.234234	−	0.405704i
$375$	−12.2097	−	21.1478i	−0.630507	−	1.09207i
$376$	−17.6496			−0.910207
$377$	−13.9887	−	2.86308i	−0.720452	−	0.147456i
$378$		0			0
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695034\pi$
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$380$	6.95942	+	12.0541i	0.357010	+	0.618360i
$381$	−5.84725	+	10.1277i	−0.299563	+	0.518859i
$382$	27.6110			1.41270
$383$	−10.7644	+	18.6445i	−0.550036	+	0.952690i	0.448235	+	0.893916i	$0.352053\pi$
$383$	−10.7644	+	18.6445i	−0.550036	+	0.952690i	−0.998271	+	0.0587748i	$0.981281\pi$
$384$	−28.5334	+	49.4213i	−1.45609	+	2.52202i
$385$		0			0
$386$	28.1536	−	48.7634i	1.43298	−	2.48199i
$387$	−14.5823	−	25.2572i	−0.741258	−	1.28390i
$388$	14.2500	+	24.6817i	0.723435	+	1.25303i
$389$	26.4910			1.34315			0.671574	−	0.740938i	$-0.265619\pi$
$389$	26.4910			1.34315			0.671574	+	0.740938i	$0.265619\pi$
$390$	−7.35814	−	22.0770i	−0.372594	−	1.11791i
$391$	53.3118			2.69609
$392$		0			0
$393$	−2.98476	−	5.16975i	−0.150561	−	0.260779i
$394$	−1.75633	+	3.04206i	−0.0884828	+	0.153257i
$395$	−2.73605			−0.137665
$396$	4.97392	−	8.61508i	0.249949	−	0.432924i
$397$	−16.8995	+	29.2707i	−0.848160	+	1.46906i	0.0346887	+	0.999398i	$0.488956\pi$
$397$	−16.8995	+	29.2707i	−0.848160	+	1.46906i	−0.882849	+	0.469658i	$0.844377\pi$
$398$	22.4332			1.12447
$399$		0			0
$400$	4.64989	+	8.05384i	0.232494	+	0.402692i
$401$	−10.8059	−	18.7164i	−0.539623	−	0.934655i	−0.998924	−	0.0463741i	$-0.985233\pi$
$401$	−10.8059	−	18.7164i	−0.539623	−	0.934655i	0.459301	−	0.888281i	$-0.348100\pi$
$402$	−46.0800			−2.29826
$403$	−7.14983	+	8.06237i	−0.356158	+	0.401615i
$404$	9.76527			0.485840
$405$	−0.894473	−	1.54927i	−0.0444467	−	0.0769839i
$406$		0			0
$407$	0.516056	−	0.893835i	0.0255799	−	0.0443058i
$408$	−72.2093			−3.57489
$409$	3.87109	−	6.70492i	0.191413	−	0.331537i	−0.754306	−	0.656523i	$-0.772026\pi$
$409$	3.87109	−	6.70492i	0.191413	−	0.331537i	0.945719	+	0.324986i	$0.105360\pi$
$410$	4.30637	−	7.45886i	0.212677	−	0.368367i
$411$	23.0111			1.13505
$412$	−20.1093	+	34.8303i	−0.990714	+	1.71597i
$413$		0			0
$414$	45.0783	+	78.0780i	2.21548	+	3.83732i
$415$	−2.81736			−0.138299
$416$	−2.99675	−	8.99132i	−0.146928	−	0.440836i
$417$	1.58737			0.0777337
$418$	−2.68589	−	4.65211i	−0.131371	−	0.227542i
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	0.749945	−	0.661500i	$-0.230080\pi$
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	−0.947848	+	0.318722i	$0.896746\pi$
$420$		0			0
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	−10.6771	+	18.4933i	−0.519755	+	0.900242i
$423$	−9.91963	+	17.1813i	−0.482309	+	0.835384i
$424$	−1.73032			−0.0840316
$425$	13.0218	−	22.5543i	0.631648	−	1.09405i
$426$	11.8355	+	20.4996i	0.573430	+	0.993210i
$427$		0			0
$428$	−59.1713			−2.86015
$429$	1.84384	+	5.53217i	0.0890214	+	0.267096i
$430$	14.9677			0.721806
$431$	14.7640	+	25.5721i	0.711159	+	1.23176i	0.964422	+	0.264366i	$0.0851627\pi$
$431$	14.7640	+	25.5721i	0.711159	+	1.23176i	−0.253263	+	0.967397i	$0.581504\pi$
$432$	−4.97996	−	8.62554i	−0.239598	−	0.414997i
$433$	11.0455	−	19.1314i	0.530813	−	0.919395i	−0.468540	−	0.883442i	$-0.655220\pi$
$433$	11.0455	−	19.1314i	0.530813	−	0.919395i	0.999353	−	0.0359531i	$-0.0114467\pi$
$434$		0			0
$435$	−5.35164	+	9.26931i	−0.256591	+	0.444429i
$436$	−17.0969	+	29.6127i	−0.818792	+	1.41819i
$437$	31.6102			1.51212
$438$	−16.2106	+	28.0777i	−0.774575	+	1.34160i
$439$	−3.17790	−	5.50428i	−0.151673	−	0.262705i	0.780170	−	0.625568i	$-0.215133\pi$
$439$	−3.17790	−	5.50428i	−0.151673	−	0.262705i	−0.931843	+	0.362863i	$0.881799\pi$
$440$	1.17387	+	2.03321i	0.0559622	+	0.0969294i
$441$		0			0
$442$	36.8718	−	41.5777i	1.75381	−	1.97765i
$443$	−13.5627			−0.644383			−0.322192	−	0.946675i	$-0.604420\pi$
$443$	−13.5627			−0.644383			−0.322192	+	0.946675i	$0.604420\pi$
$444$	−8.94443	−	15.4922i	−0.424484	−	0.735227i
$445$	1.02801	+	1.78057i	0.0487324	+	0.0844070i
$446$	−26.0530	+	45.1251i	−1.23365	+	2.13674i
$447$	7.72237			0.365255
$448$		0			0
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	0.482763	+	0.875751i	$0.339633\pi$
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	−0.999804	+	0.0197900i	$0.993700\pi$
$450$	44.0428			2.07620
$451$	−1.07911	+	1.86908i	−0.0508134	+	0.0880115i
$452$	−18.8473	−	32.6445i	−0.886502	−	1.53547i
$453$	31.6570	+	54.8315i	1.48737	+	2.57621i
$454$	−44.3041			−2.07930
$455$		0			0
$456$	−42.8151			−2.00500
$457$	−7.60732	−	13.1763i	−0.355855	−	0.616359i	0.631409	−	0.775450i	$-0.282477\pi$
$457$	−7.60732	−	13.1763i	−0.355855	−	0.616359i	−0.987264	+	0.159091i	$0.949144\pi$
$458$	−23.1049	−	40.0188i	−1.07962	−	1.86996i
$459$	−13.9461	+	24.1554i	−0.650949	+	1.12748i
$460$	−30.0426			−1.40074
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	−0.990717	−	0.135937i	$-0.956595\pi$
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	0.613084	+	0.790018i	$0.289929\pi$
$462$		0			0
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	4.56353	−	7.90426i	0.211856	−	0.366946i
$465$	4.03884	+	6.99547i	0.187297	+	0.324407i
$466$	19.2994	+	33.4275i	0.894027	+	1.54850i
$467$	−14.0067			−0.648155			−0.324078	−	0.946031i	$-0.605054\pi$
$467$	−14.0067			−0.648155			−0.324078	+	0.946031i	$0.605054\pi$
$468$	59.7803	+	12.2353i	2.76334	+	0.565579i
$469$		0			0
$470$	−5.09091	−	8.81772i	−0.234826	−	0.406731i
$471$	31.0586	+	53.7951i	1.43111	+	2.47875i
$472$	−12.2160	+	21.1588i	−0.562288	+	0.973912i
$473$	−3.75068			−0.172456
$474$	9.15094	−	15.8499i	0.420316	−	0.728009i
$475$	7.72100	−	13.3732i	0.354264	−	0.613603i
$476$		0			0
$477$	−0.972495	+	1.68441i	−0.0445275	+	0.0771239i
$478$	19.2281	+	33.3041i	0.879474	+	1.52329i
$479$	−15.0122	−	26.0018i	−0.685923	−	1.18805i	−0.973146	−	0.230189i	$-0.926065\pi$
$479$	−15.0122	−	26.0018i	−0.685923	−	1.18805i	0.287223	−	0.957864i	$-0.407268\pi$
$480$	−7.10439			−0.324270
$481$	6.20235	+	1.26945i	0.282803	+	0.0578817i
$482$	−9.56649			−0.435742
$483$		0			0
$484$	19.7253	+	34.1652i	0.896605	+	1.55296i
$485$	−3.78033	+	6.54772i	−0.171656	+	0.297317i
$486$	42.9267			1.94719
$487$	14.2452	−	24.6733i	0.645510	−	1.11806i	−0.338674	−	0.940904i	$-0.609978\pi$
$487$	14.2452	−	24.6733i	0.645510	−	1.11806i	0.984184	−	0.177152i	$-0.0566884\pi$
$488$	−4.48649	+	7.77082i	−0.203094	+	0.351769i
$489$	22.4992			1.01745
$490$		0			0
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	0.984903	+	0.173105i	$0.0553799\pi$
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	−0.342539	+	0.939504i	$0.611287\pi$
$492$	18.7035	+	32.3954i	0.843218	+	1.46050i
$493$	−25.5598			−1.15116
$494$	21.8624	−	24.6527i	0.983636	−	1.10918i
$495$	2.63902			0.118615
$496$	−3.44406	−	5.96528i	−0.154643	−	0.267849i
$497$		0			0
$498$	9.42290	−	16.3209i	0.422250	−	0.731359i
$499$	−26.2329			−1.17434			−0.587172	−	0.809462i	$-0.699759\pi$
$499$	−26.2329			−1.17434			−0.587172	+	0.809462i	$0.699759\pi$
$500$	−16.4309	+	28.4591i	−0.734811	+	1.27273i
$501$	−3.20233	+	5.54659i	−0.143069	+	0.247803i
$502$	7.75367			0.346063
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	−0.755112	−	0.655595i	$-0.772418\pi$
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	0.945318	+	0.326149i	$0.105751\pi$
$504$		0			0
$505$	1.29529	+	2.24352i	0.0576398	+	0.0998351i
$506$	11.5945			0.515440
$507$	−28.6169	+	21.4595i	−1.27092	+	0.953050i
$508$	15.7375			0.698240
$509$	−6.51298	−	11.2808i	−0.288683	−	0.500014i	0.684813	−	0.728719i	$-0.259884\pi$
$509$	−6.51298	−	11.2808i	−0.288683	−	0.500014i	−0.973496	+	0.228706i	$0.926551\pi$
$510$	−20.8283	−	36.0758i	−0.922295	−	1.59746i
$511$		0			0
$512$	24.8008			1.09605
$513$	−8.26908	+	14.3225i	−0.365089	+	0.632352i
$514$	32.1100	−	55.6162i	1.41631	−	2.45312i
$515$	−10.6694			−0.470151
$516$	−32.5039	+	56.2984i	−1.43090	+	2.47840i
$517$	1.27571	+	2.20959i	0.0561055	+	0.0971775i
$518$		0			0
$519$	22.3798			0.982363
$520$	−9.55499	+	10.7745i	−0.419014	+	0.472493i
$521$	−4.46570			−0.195646			−0.0978230	−	0.995204i	$-0.531188\pi$
$521$	−4.46570			−0.195646			−0.0978230	+	0.995204i	$0.531188\pi$
$522$	−21.6124	−	37.4337i	−0.945948	−	1.63843i
$523$	−1.45406	−	2.51850i	−0.0635815	−	0.110126i	0.832482	−	0.554051i	$-0.186919\pi$
$523$	−1.45406	−	2.51850i	−0.0635815	−	0.110126i	−0.896064	+	0.443925i	$0.853586\pi$
$524$	−4.01665	+	6.95704i	−0.175468	+	0.303920i
$525$		0			0
$526$	−4.54570	+	7.87339i	−0.198202	+	0.343296i
$527$	−9.64490	+	16.7055i	−0.420138	+	0.727701i
$528$	−3.72746			−0.162217
$529$	−22.6139	+	39.1684i	−0.983213	+	1.70297i
$530$	−0.499100	−	0.864466i	−0.0216795	−	0.0375500i
$531$	13.7316	+	23.7838i	0.595901	+	1.03213i
$532$		0			0
$533$	−12.9696	−	2.65451i	−0.561775	−	0.114980i
$534$	−13.7531			−0.595154
$535$	−7.84866	−	13.5943i	−0.339327	−	0.587732i
$536$	14.2581	+	24.6957i	0.615854	+	1.06669i
$537$	28.8803	−	50.0221i	1.24628	−	2.15861i
$538$	−56.9262			−2.45426
$539$		0			0
$540$	7.85899	−	13.6122i	0.338197	−	0.585775i
$541$	−18.4639			−0.793824			−0.396912	−	0.917857i	$-0.629918\pi$
$541$	−18.4639			−0.793824			−0.396912	+	0.917857i	$0.629918\pi$
$542$	−11.8224	+	20.4770i	−0.507815	+	0.879562i
$543$	−2.21229	−	3.83180i	−0.0949384	−	0.164438i
$544$	−8.48277	−	14.6926i	−0.363696	−	0.629940i
$545$	−9.07112			−0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	−15.4832	−	26.8177i	−0.661411	−	1.14560i
$549$	5.04310	+	8.73491i	0.215234	+	0.372797i
$550$	2.83204	−	4.90524i	0.120759	−	0.209160i
$551$	−15.1552			−0.645633
$552$	46.2063	−	80.0317i	1.96667	−	3.40638i
$553$		0			0
$554$	−28.1449			−1.19576
$555$	2.37283	−	4.10986i	0.100721	−	0.174454i
$556$	−1.06808	−	1.84996i	−0.0452965	−	0.0784559i
$557$	−0.0265706	−	0.0460217i	−0.00112583	−	0.00195000i	0.865462	−	0.500975i	$-0.167025\pi$
$557$	−0.0265706	−	0.0460217i	−0.00112583	−	0.00195000i	−0.866588	+	0.499025i	$0.833692\pi$
$558$	−32.6214			−1.38097
$559$	−7.27451	−	21.8261i	−0.307679	−	0.923146i
$560$		0			0
$561$	5.21927	+	9.04004i	0.220358	+	0.381671i
$562$	15.5194	+	26.8804i	0.654646	+	1.13388i
$563$	3.99253	−	6.91527i	0.168265	−	0.291444i	−0.769545	−	0.638593i	$-0.779517\pi$
$563$	3.99253	−	6.91527i	0.168265	−	0.291444i	0.937810	+	0.347149i	$0.112850\pi$
$564$	44.2218			1.86207
$565$	4.99992	−	8.66012i	0.210348	−	0.364334i
$566$	20.0655	−	34.7544i	0.843414	−	1.46084i
$567$		0			0
$568$	7.32424	−	12.6860i	0.307318	−	0.532291i
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	0.997481	+	0.0709285i	$0.0225962\pi$
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	−0.437315	+	0.899308i	$0.644070\pi$
$570$	−12.3498	−	21.3904i	−0.517275	−	0.895946i
$571$	13.4929			0.564662			0.282331	−	0.959317i	$-0.408892\pi$
$571$	13.4929			0.564662			0.282331	+	0.959317i	$0.408892\pi$
$572$	5.20670	−	5.87124i	0.217703	−	0.245489i
$573$	−31.8132			−1.32902
$574$		0			0
$575$	16.6651	+	28.8648i	0.694982	+	1.20374i
$576$	24.8794	−	43.0923i	1.03664	−	1.79551i
$577$	−12.0132			−0.500118			−0.250059	−	0.968231i	$-0.580450\pi$
$577$	−12.0132			−0.500118			−0.250059	+	0.968231i	$0.580450\pi$
$578$	29.4406	−	50.9925i	1.22457	−	2.12101i
$579$	−32.4383	+	56.1848i	−1.34809	+	2.33496i
$580$	14.4036			0.598078
$581$		0			0
$582$	−25.2872	−	43.7988i	−1.04819	−	1.81552i
$583$	0.125067	+	0.216622i	0.00517974	+	0.00897158i
$584$	20.0636			0.830236
$585$	5.11843	+	15.3571i	0.211621	+	0.634939i
$586$	−33.6609			−1.39052
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	0.953307	−	0.302002i	$-0.0976548\pi$
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	−0.738195	+	0.674588i	$0.764321\pi$
$588$		0			0
$589$	−5.71876	+	9.90518i	−0.235637	+	0.408136i
$590$	−14.0946			−0.580264
$591$	2.02364	−	3.50504i	0.0832412	−	0.144178i
$592$	−2.02339	+	3.50462i	−0.0831610	+	0.144039i
$593$	22.3501			0.917810			0.458905	−	0.888485i	$-0.348242\pi$
$593$	22.3501			0.917810			0.458905	+	0.888485i	$0.348242\pi$
$594$	−3.03307	+	5.25344i	−0.124449	+	0.215551i
$595$		0			0
$596$	−5.19607	−	8.99986i	−0.212839	−	0.368649i
$597$	−25.8474			−1.05786
$598$	22.4878	+	67.4714i	0.919595	+	2.75911i
$599$	1.15893			0.0473524			0.0236762	−	0.999720i	$-0.492463\pi$
$599$	1.15893			0.0473524			0.0236762	+	0.999720i	$0.492463\pi$
$600$	−22.5724	−	39.0966i	−0.921515	−	1.59611i
$601$	21.0907	+	36.5301i	0.860306	+	1.49009i	0.871633	+	0.490158i	$0.163061\pi$
$601$	21.0907	+	36.5301i	0.860306	+	1.49009i	−0.0113271	+	0.999936i	$0.503606\pi$
$602$		0			0
$603$	32.0540			1.30534
$604$	42.6014	−	73.7879i	1.73343	−	3.00239i
$605$	−5.23284	+	9.06355i	−0.212745	+	0.368486i
$606$	−17.3289			−0.703937
$607$	−9.07844	+	15.7243i	−0.368482	+	0.638230i	−0.989328	−	0.145702i	$-0.953456\pi$
$607$	−9.07844	+	15.7243i	−0.368482	+	0.638230i	0.620846	+	0.783932i	$0.286789\pi$
$608$	−5.02970	−	8.71169i	−0.203981	−	0.353306i
$609$		0			0
$610$	−5.17640			−0.209586
$611$	−10.3839	+	11.7092i	−0.420087	+	0.473703i
$612$	109.229			4.41534
$613$	0.451323	+	0.781714i	0.0182288	+	0.0315731i	0.874996	−	0.484130i	$-0.160864\pi$
$613$	0.451323	+	0.781714i	0.0182288	+	0.0315731i	−0.856767	+	0.515703i	$0.827531\pi$
$614$	−18.9594	−	32.8386i	−0.765137	−	1.32526i
$615$	−4.96177	+	8.59404i	−0.200078	+	0.346545i
$616$		0			0
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	−0.475363	−	0.879790i	$-0.657683\pi$
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	0.999602	−	0.0282180i	$-0.00898327\pi$
$618$	35.6848	−	61.8079i	1.43545	−	2.48628i
$619$	−26.8341			−1.07855			−0.539277	−	0.842128i	$-0.681303\pi$
$619$	−26.8341			−1.07855			−0.539277	+	0.842128i	$0.681303\pi$
$620$	5.43515	−	9.41396i	0.218281	−	0.378074i
$621$	−17.8481	−	30.9138i	−0.716218	−	1.24053i
$622$	34.1530	+	59.1547i	1.36941	+	2.37189i
$623$		0			0
$624$	−7.22948	−	21.6910i	−0.289411	−	0.868335i
$625$	11.4579			0.458315
$626$	22.1839	+	38.4237i	0.886649	+	1.53572i
$627$	3.09467	+	5.36012i	0.123589	+	0.214063i
$628$	41.7962	−	72.3932i	1.66785	−	2.88880i
$629$	11.3328			0.451869
$630$		0			0
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	−0.309135	−	0.951018i	$-0.600039\pi$
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666273\pi$
$632$	−11.3259			−0.450521
$633$	12.3021	−	21.3079i	0.488965	−	0.846913i
$634$	36.5901	+	63.3760i	1.45318	+	2.51698i
$635$	2.08747	+	3.61561i	0.0828388	+	0.143481i
$636$	4.33539			0.171909
$637$		0			0
$638$	−5.55889			−0.220078
$639$	−8.23293	−	14.2598i	−0.325690	−	0.564111i
$640$	10.1865	+	17.6435i	0.402655	+	0.697419i
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	−0.995775	−	0.0918294i	$-0.970729\pi$
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	0.577414	+	0.816452i	$0.304062\pi$
$642$	105.002			4.14410
$643$	0.330770	−	0.572910i	0.0130443	−	0.0225933i	−0.859430	−	0.511254i	$-0.829181\pi$
$643$	0.330770	−	0.572910i	0.0130443	−	0.0225933i	0.872474	+	0.488661i	$0.162514\pi$
$644$		0			0
$645$	−17.2457			−0.679047
$646$	29.4917	−	51.0811i	1.16034	−	2.00976i
$647$	−20.0162	−	34.6690i	−0.786916	−	1.36298i	−0.927848	−	0.372960i	$-0.878343\pi$
$647$	−20.0162	−	34.6690i	−0.786916	−	1.36298i	0.140931	−	0.990019i	$-0.454990\pi$
$648$	−3.70268	−	6.41323i	−0.145455	−	0.251936i
$649$	3.53188			0.138639
$650$	34.0376	+	6.96654i	1.33506	+	0.273250i
$651$		0			0
$652$	−15.1388	−	26.2212i	−0.592883	−	1.02690i
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	0.714444	−	0.699693i	$-0.246680\pi$
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	−0.963174	+	0.268880i	$0.913347\pi$
$654$	30.3391	−	52.5489i	1.18635	−	2.05482i
$655$	−2.13112			−0.0832698
$656$	4.23107	−	7.32844i	0.165196	−	0.286127i
$657$	11.2764	−	19.5313i	0.439933	−	0.761987i
$658$		0			0
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	−0.694094	−	0.719884i	$-0.744195\pi$
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	0.970485	+	0.241161i	$0.0775283\pi$
$660$	−2.94119	−	5.09430i	−0.114486	−	0.198295i
$661$	25.0890	+	43.4554i	0.975848	+	1.69022i	0.677106	+	0.735885i	$0.263234\pi$
$661$	25.0890	+	43.4554i	0.975848	+	1.69022i	0.298742	+	0.954334i	$0.403433\pi$
$662$	−65.0207			−2.52710
$663$	−42.4834	+	47.9056i	−1.64992	+	1.86050i
$664$	−11.6625			−0.452594
$665$		0			0
$666$	9.58259	+	16.5975i	0.371318	+	0.643141i
$667$	16.3556	−	28.3287i	0.633290	−	1.09689i
$668$	8.61888			0.333474
$669$	30.0181	−	51.9928i	1.16057	−	2.01016i
$670$	−8.22530	+	14.2466i	−0.317771	+	0.550396i
$671$	1.29713			0.0500751
$672$		0			0
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	0.883522	−	0.468389i	$-0.155166\pi$
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	−0.847398	+	0.530958i	$0.821832\pi$
$674$	−14.7056	−	25.4708i	−0.566438	−	0.981100i
$675$	−17.4380			−0.671191
$676$	44.2647	+	18.9117i	1.70249	+	0.727373i
$677$	2.00879			0.0772041			0.0386020	−	0.999255i	$-0.487710\pi$
$677$	2.00879			0.0772041			0.0386020	+	0.999255i	$0.487710\pi$
$678$	33.4453	+	57.9290i	1.28446	+	2.22475i
$679$		0			0
$680$	−12.8894	+	22.3251i	−0.494286	+	0.856128i
$681$	51.0469			1.95612
$682$	−2.09762	+	3.63319i	−0.0803222	+	0.139122i
$683$	7.05061	−	12.2120i	0.269784	−	0.467280i	−0.699022	−	0.715100i	$-0.746381\pi$
$683$	7.05061	−	12.2120i	0.269784	−	0.467280i	0.968806	+	0.247820i	$0.0797143\pi$
$684$	64.7655			2.47637
$685$	4.10748	−	7.11437i	0.156939	−	0.271826i
$686$		0			0
$687$	26.6212	+	46.1094i	1.01566	+	1.75918i
$688$	14.7060			0.560660
$689$	−1.01801	+	1.14794i	−0.0387830	+	0.0437330i
$690$	53.3118			2.02954
$691$	−17.8460	−	30.9102i	−0.678895	−	1.17588i	−0.975314	−	0.220822i	$-0.929126\pi$
$691$	−17.8460	−	30.9102i	−0.678895	−	1.17588i	0.296419	−	0.955058i	$-0.404207\pi$
$692$	−15.0585	−	26.0820i	−0.572437	−	0.991489i
$693$		0			0
$694$	−14.6746			−0.557041
$695$	0.283346	−	0.490769i	0.0107479	−	0.0186159i
$696$	−22.1532	+	38.3704i	−0.839714	+	1.45443i
$697$	−23.6978			−0.897618
$698$	−15.5596	+	26.9500i	−0.588938	+	1.02007i
$699$	−22.2366	−	38.5150i	−0.841066	−	1.45677i
$700$		0			0
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$	−36.4538	−	7.46106i	−1.37586	−	0.281600i
$703$	6.71957			0.253434
$704$	−3.19959	−	5.54185i	−0.120589	−	0.208866i
$705$	5.86571	+	10.1597i	0.220915	+	0.382637i
$706$	−37.8103	+	65.4894i	−1.42301	+	2.46473i
$707$		0			0
$708$	30.6078	−	53.0143i	1.15031	−	1.99240i
$709$	−17.0185	+	29.4770i	−0.639144	+	1.10703i	0.346477	+	0.938059i	$0.387378\pi$
$709$	−17.0185	+	29.4770i	−0.639144	+	1.10703i	−0.985621	+	0.168972i	$0.945955\pi$
$710$	8.45054			0.317143
$711$	−6.36553	+	11.0254i	−0.238726	+	0.413486i
$712$	4.25547	+	7.37069i	0.159480	+	0.276228i
$713$	−12.3434	−	21.3794i	−0.462265	−	0.800667i
$714$		0			0
$715$	2.03952	+	0.417432i	0.0762736	+	0.0156111i
$716$	−77.7295			−2.90489
$717$	−22.1545	−	38.3727i	−0.827375	−	1.43306i
$718$	23.7994	+	41.2218i	0.888187	+	1.53838i
$719$	−11.4824	+	19.8881i	−0.428222	+	0.741702i	−0.996715	−	0.0809859i	$-0.974193\pi$
$719$	−11.4824	+	19.8881i	−0.428222	+	0.741702i	0.568493	+	0.822688i	$0.307526\pi$
$720$	−10.3473			−0.385621
$721$		0			0
$722$	−5.19981	+	9.00633i	−0.193517	+	0.335181i
$723$	11.0224			0.409929
$724$	−2.97712	+	5.15653i	−0.110644	+	0.191641i
$725$	−7.98992	−	13.8389i	−0.296738	−	0.513966i
$726$	−35.0034	−	60.6276i	−1.29910	−	2.25010i
$727$	−1.06558			−0.0395203			−0.0197601	−	0.999805i	$-0.506290\pi$
$727$	−1.06558			−0.0395203			−0.0197601	+	0.999805i	$0.506290\pi$
$728$		0			0
$729$	−43.9962			−1.62949
$730$	5.78721	+	10.0237i	0.214194	+	0.370996i
$731$	−20.5916	−	35.6658i	−0.761609	−	1.31915i
$732$	11.2411	−	19.4702i	0.415483	−	0.719637i
$733$	26.3378			0.972808			0.486404	−	0.873734i	$-0.338308\pi$
$733$	26.3378			0.972808			0.486404	+	0.873734i	$0.338308\pi$
$734$	−23.5448	+	40.7809i	−0.869056	+	1.50525i
$735$		0			0
$736$	21.7123			0.800326
$737$	2.06114	−	3.57000i	0.0759230	−	0.131502i
$738$	−20.0379	−	34.7067i	−0.737606	−	1.27757i
$739$	−17.1075	−	29.6310i	−0.629308	−	1.08999i	−0.987691	−	0.156419i	$-0.950005\pi$
$739$	−17.1075	−	29.6310i	−0.629308	−	1.08999i	0.358383	−	0.933575i	$-0.383328\pi$
$740$	−6.38633			−0.234766
$741$	−25.1897	+	28.4047i	−0.925366	+	1.04347i
$742$		0			0
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	0.582821	−	0.812600i	$-0.301949\pi$
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	−0.995143	+	0.0984379i	$0.968615\pi$
$744$	16.7188	+	28.9579i	0.612942	+	1.06165i
$745$	1.37845	−	2.38754i	0.0505023	−	0.0874726i
$746$	−41.9027			−1.53417
$747$	−6.55472	+	11.3531i	−0.239825	+	0.415388i
$748$	7.02368	−	12.1654i	0.256811	−	0.444810i
$749$		0			0
$750$	29.1573	−	50.5018i	1.06467	−	1.84407i
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	0.934119	+	0.356961i	$0.116187\pi$
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	−0.157923	+	0.987451i	$0.550480\pi$
$752$	−5.00189	−	8.66353i	−0.182400	−	0.315927i
$753$	−8.93372			−0.325563
$754$	−10.7816	−	32.3485i	−0.392641	−	1.17806i
$755$	22.6031			0.822612
$756$		0			0
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	0.949886	−	0.312596i	$-0.101199\pi$
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	−0.745659	+	0.666327i	$0.767865\pi$
$758$	−13.9716	+	24.1996i	−0.507473	+	0.878969i
$759$	−13.3591			−0.484906
$760$	−7.64252	+	13.2372i	−0.277223	+	0.480165i
$761$	6.40422	−	11.0924i	0.232153	−	0.402101i	−0.726289	−	0.687390i	$-0.758756\pi$
$761$	6.40422	−	11.0924i	0.232153	−	0.402101i	0.958441	+	0.285289i	$0.0920897\pi$
$762$	−27.9269			−1.01168
$763$		0			0
$764$	21.4059	+	37.0760i	0.774437	+	1.34136i
$765$	14.4885	+	25.0948i	0.523833	+	0.907306i
$766$	−51.4117			−1.85758
$767$	6.85016	+	20.5529i	0.247345	+	0.742122i
$768$	−76.3692			−2.75574
$769$	−25.6759	−	44.4719i	−0.925895	−	1.60370i	−0.790115	−	0.612958i	$-0.789979\pi$
$769$	−25.6759	−	44.4719i	−0.925895	−	1.60370i	−0.135780	−	0.990739i	$-0.543354\pi$
$770$		0			0
$771$	−36.9969	+	64.0805i	−1.33241	+	2.30780i
$772$	87.3059			3.14221
$773$	10.0023	−	17.3245i	0.359759	−	0.623120i	−0.628162	−	0.778083i	$-0.716192\pi$
$773$	10.0023	−	17.3245i	0.359759	−	0.623120i	0.987920	+	0.154963i	$0.0495257\pi$
$774$	34.8230	−	60.3151i	1.25169	−	2.16798i
$775$	−12.0599			−0.433203
$776$	−15.6487	+	27.1044i	−0.561756	+	0.972990i
$777$		0			0
$778$	31.6308	+	54.7861i	1.13402	+	1.96418i
$779$	−14.0512			−0.503435
$780$	23.9405	−	26.9960i	0.857206	−	0.966613i
$781$	−2.11758			−0.0757729
$782$	63.6552	+	110.254i	2.27631	+	3.94268i
$783$	8.55708	+	14.8213i	0.305805	+	0.529670i
$784$		0			0
$785$	22.1759			0.791492
$786$	7.12771	−	12.3456i	0.254237	−	0.440351i
$787$	14.6596	−	25.3911i	0.522558	−	0.905096i	−0.477098	−	0.878850i	$-0.658311\pi$
$787$	14.6596	−	25.3911i	0.522558	−	0.905096i	0.999656	−	0.0262462i	$-0.00835537\pi$
$788$	−5.44650			−0.194023
$789$	5.23752	−	9.07166i	0.186461	−	0.322959i
$790$	−3.26689	−	5.65842i	−0.116231	−	0.201318i
$791$		0			0
$792$	10.9243			0.388177
$793$	2.51581	+	7.54831i	0.0893389	+	0.268048i
$794$	−80.7131			−2.86440
$795$	0.575059	+	0.996031i	0.0203952	+	0.0353256i
$796$	17.3917	+	30.1232i	0.616431	+	1.06769i
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	−0.837258	−	0.546809i	$-0.815842\pi$
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	0.892179	+	0.451682i	$0.149176\pi$
$798$		0			0
$799$	−14.0075	+	24.2618i	−0.495551	+	0.858319i
$800$	5.30338	−	9.18572i	0.187503	−	0.324764i
$801$	9.56685			0.338028
$802$	25.8050	−	44.6956i	0.911206	−	1.57826i
$803$	−1.45019	−	2.51180i	−0.0511761	−	0.0886395i
$804$	−35.7242	−	61.8762i	−1.25990	−	2.18220i
$805$		0			0
$806$	−25.2108	−	5.15995i	−0.888013	−	0.181751i
$807$	65.5899			2.30887
$808$	5.36189	+	9.28707i	0.188631	+	0.326718i
$809$	−3.99501	−	6.91957i	−0.140457	−	0.243279i	0.787212	−	0.616683i	$-0.211524\pi$
$809$	−3.99501	−	6.91957i	−0.140457	−	0.243279i	−0.927669	+	0.373404i	$0.878191\pi$
$810$	2.13603	−	3.69972i	0.0750526	−	0.129995i
$811$	48.2554			1.69448			0.847239	−	0.531213i	$-0.178263\pi$
$811$	48.2554			1.69448			0.847239	+	0.531213i	$0.178263\pi$
$812$		0			0
$813$	13.6217	−	23.5934i	0.477733	−	0.827458i
$814$	2.46472			0.0863884
$815$	4.01612	−	6.95612i	0.140679	−	0.243662i
$816$	−20.4642	−	35.4449i	−0.716389	−	1.24082i
$817$	−12.2094	−	21.1473i	−0.427153	−	0.739851i
$818$	18.4886			0.646439
$819$		0			0
$820$	13.3543			0.466353
$821$	13.7760	+	23.8607i	0.480785	+	0.832743i	0.999757	−	0.0220477i	$-0.00701856\pi$
$821$	13.7760	+	23.8607i	0.480785	+	0.832743i	−0.518972	+	0.854791i	$0.673685\pi$
$822$	27.4756	+	47.5892i	0.958323	+	1.65986i
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	−0.987293	−	0.158908i	$-0.949203\pi$
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	0.631265	+	0.775567i	$0.282536\pi$
$824$	−44.1663			−1.53861
$825$	−3.26306	+	5.65178i	−0.113605	+	0.196770i
$826$		0			0
$827$	−27.7142			−0.963719			−0.481859	−	0.876249i	$-0.660038\pi$
$827$	−27.7142			−0.963719			−0.481859	+	0.876249i	$0.660038\pi$
$828$	−69.8953	+	121.062i	−2.42903	+	4.20720i
$829$	4.62832	+	8.01648i	0.160748	+	0.278424i	0.935137	−	0.354286i	$-0.115276\pi$
$829$	4.62832	+	8.01648i	0.160748	+	0.278424i	−0.774389	+	0.632710i	$0.781943\pi$
$830$	−3.36398	−	5.82659i	−0.116766	−	0.202244i
$831$	32.4283			1.12493
$832$	26.0437	−	29.3677i	0.902904	−	1.01814i
$833$		0			0
$834$	1.89535	+	3.28283i	0.0656304	+	0.113675i
$835$	1.14323	+	1.98014i	0.0395632	+	0.0685255i
$836$	4.16456	−	7.21323i	0.144034	−	0.249475i
$837$	12.9159			0.446440
$838$	9.67387	−	16.7556i	0.334178	−	0.578814i
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	0.475287	+	0.879831i	$0.342344\pi$
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	−0.999599	+	0.0283045i	$0.990989\pi$
$840$		0			0
$841$	6.65848	−	11.5328i	0.229603	−	0.397683i
$842$	−38.3428	−	66.4116i	−1.32138	−	2.28869i
$843$	−17.8813	−	30.9713i	−0.615865	−	1.06671i
$844$	−33.1104			−1.13971
$845$	1.52654	+	12.6781i	0.0525147	+	0.436139i
$846$	−47.3769			−1.62885
$847$		0			0
$848$	−0.490373	−	0.849350i	−0.0168395	−	0.0291668i
$849$	−23.1193	+	40.0437i	−0.793451	+	1.37430i
$850$	62.1929			2.13320
$851$	−7.25180	+	12.5605i	−0.248589	+	0.430568i
$852$	−18.3512	+	31.7853i	−0.628703	+	1.08894i
$853$	5.30773			0.181733			0.0908666	−	0.995863i	$-0.471036\pi$
$853$	5.30773			0.181733			0.0908666	+	0.995863i	$0.471036\pi$
$854$		0			0
$855$	8.59069	+	14.8795i	0.293795	+	0.508868i
$856$	−32.4896	−	56.2737i	−1.11047	−	1.92340i
$857$	16.6371			0.568314			0.284157	−	0.958778i	$-0.408286\pi$
$857$	16.6371			0.568314			0.284157	+	0.958778i	$0.408286\pi$
$858$	−9.23951	+	10.4188i	−0.315432	+	0.355691i
$859$	10.5885			0.361276			0.180638	−	0.983550i	$-0.442184\pi$
$859$	10.5885			0.361276			0.180638	+	0.983550i	$0.442184\pi$
$860$	11.6039	+	20.0986i	0.395690	+	0.685356i
$861$		0			0
$862$	−35.2571	+	61.0671i	−1.20086	+	2.07995i
$863$	−56.0632			−1.90841			−0.954207	−	0.299148i	$-0.903298\pi$
$863$	−56.0632			−1.90841			−0.954207	+	0.299148i	$0.903298\pi$
$864$	−5.67984	+	9.83777i	−0.193232	+	0.334688i
$865$	3.99480	−	6.91919i	0.135827	−	0.235260i
$866$	52.7541			1.79266
$867$	−33.9212	+	58.7532i	−1.15202	+	1.99536i
$868$		0			0
$869$	0.818634	+	1.41792i	0.0277703	+	0.0480995i
$870$	−25.5598			−0.866559
$871$	24.7723	+	5.07019i	0.839377	+	0.171797i
$872$	−37.5501			−1.27161
$873$	17.5902	+	30.4671i	0.595337	+	1.03115i
$874$	37.7432	+	65.3731i	1.27668	+	2.21128i
$875$		0			0
$876$	−50.2702			−1.69847
$877$	1.83026	−	3.17010i	0.0618033	−	0.107047i	−0.833468	−	0.552567i	$-0.813648\pi$
$877$	1.83026	−	3.17010i	0.0618033	−	0.107047i	0.895272	+	0.445521i	$0.146982\pi$
$878$	7.58894	−	13.1444i	0.256114	−	0.443603i
$879$	38.7838			1.30815
$880$	−0.665353	+	1.15242i	−0.0224290	+	0.0388482i
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	0.939233	−	0.343281i	$-0.111538\pi$
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	−0.766906	+	0.641759i	$0.778205\pi$
$882$		0			0
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	84.4159	+	17.2776i	2.83921	+	0.581107i
$885$	16.2396			0.545890
$886$	−16.1941	−	28.0490i	−0.544052	−	0.942325i
$887$	−7.11039	−	12.3155i	−0.238743	−	0.413516i	0.721611	−	0.692299i	$-0.243402\pi$
$887$	−7.11039	−	12.3155i	−0.238743	−	0.413516i	−0.960354	+	0.278784i	$0.910069\pi$
$888$	9.82237	−	17.0128i	0.329617	−	0.570913i
$889$		0			0
$890$	−2.45493	+	4.25206i	−0.0822894	+	0.142529i
$891$	−0.535258	+	0.927094i	−0.0179318	+	0.0310588i
$892$	−80.7919			−2.70511
$893$	−8.30550	+	14.3855i	−0.277933	+	0.481394i
$894$	9.22065	+	15.9706i	0.308385	+	0.534138i
$895$	−10.3103	−	17.8579i	−0.344635	−	0.596924i
$896$		0			0
$897$	−25.9103	−	77.7400i	−0.865119	−	2.59566i
$898$	−52.3262			−1.74615
$899$	5.91794	+	10.2502i	0.197374	+	0.341862i
$900$	34.1448	+	59.1405i	1.13816	+	1.97135i
$901$	−1.37326	+	2.37856i	−0.0457500	+	0.0792413i
$902$	−5.15392			−0.171607
$903$		0			0
$904$	20.6973	−	35.8487i	0.688381	−	1.19231i
$905$	−1.57958			−0.0525069
$906$	−75.5980	+	130.940i	−2.51158	+	4.35018i
$907$	−21.7126	−	37.6074i	−0.720956	−	1.24873i	−0.960617	−	0.277876i	$-0.910370\pi$
$907$	−21.7126	−	37.6074i	−0.720956	−	1.24873i	0.239661	−	0.970857i	$-0.422964\pi$
$908$	−34.3474	−	59.4915i	−1.13986	−	1.97429i
$909$	12.0542			0.399814
$910$		0			0
$911$	24.8617			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$911$	24.8617			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$912$	−12.1338	−	21.0164i	−0.401791	−	0.695923i
$913$	0.842964	+	1.46006i	0.0278980	+	0.0483208i
$914$	18.1666	−	31.4654i	0.600896	−	1.04078i
$915$	5.96421			0.197171
$916$	35.8248	−	62.0503i	1.18368	−	2.05020i
$917$		0			0
$918$	−66.6076			−2.19838
$919$	0.831637	−	1.44044i	0.0274332	−	0.0475157i	−0.851983	−	0.523570i	$-0.824600\pi$
$919$	0.831637	−	1.44044i	0.0274332	−	0.0475157i	0.879416	+	0.476054i	$0.157933\pi$
$920$	−16.4957	−	28.5714i	−0.543847	−	0.941971i
$921$	21.8448	+	37.8363i	0.719811	+	1.24675i
$922$	−38.7250			−1.27534
$923$	−4.10708	−	12.3227i	−0.135186	−	0.405607i
$924$		0			0
$925$	3.54260	+	6.13597i	0.116480	+	0.201749i
$926$	−1.72857	−	2.99397i	−0.0568044	−	0.0983880i
$927$	−24.8229	+	42.9945i	−0.815291	+	1.41212i
$928$	−10.4098			−0.341717
$929$	4.74761	−	8.22310i	0.155764	−	0.269791i	−0.777573	−	0.628793i	$-0.783549\pi$
$929$	4.74761	−	8.22310i	0.155764	−	0.269791i	0.933337	+	0.359002i	$0.116883\pi$
$930$	−9.64490	+	16.7055i	−0.316269	+	0.547793i
$931$		0			0
$932$	−29.9243	+	51.8304i	−0.980202	+	1.69776i
$933$	−39.3508	−	68.1576i	−1.28829	−	2.23138i
$934$	−16.7243	−	28.9674i	−0.547236	−	0.947841i
$935$	3.72657			0.121872
$936$	21.1878	+	63.5710i	0.692546	+	2.07788i
$937$	6.41678			0.209627			0.104813	−	0.994492i	$-0.466575\pi$
$937$	6.41678			0.209627			0.104813	+	0.994492i	$0.466575\pi$
$938$		0			0
$939$	−25.5602	−	44.2715i	−0.834125	−	1.44475i
$940$	7.89361	−	13.6721i	0.257461	−	0.445936i
$941$	51.5186			1.67946			0.839730	−	0.543005i	$-0.182713\pi$
$941$	51.5186			1.67946			0.839730	+	0.543005i	$0.182713\pi$
$942$	−74.1691	+	128.465i	−2.41656	+	4.18561i
$943$	15.1641	−	26.2650i	0.493810	−	0.855305i
$944$	−13.8481			−0.450717
$945$		0			0
$946$	−4.47838	−	7.75678i	−0.145605	−	0.252195i
$947$	4.20109	+	7.27651i	0.136517	+	0.236455i	0.926176	−	0.377091i	$-0.123076\pi$
$947$	4.20109	+	7.27651i	0.136517	+	0.236455i	−0.789659	+	0.613546i	$0.789742\pi$
$948$	28.3776			0.921661
$949$	11.8041	−	13.3107i	0.383178	−	0.432083i
$950$	36.8761			1.19642
$951$	−42.1589	−	73.0213i	−1.36709	−	2.36788i
$952$		0			0
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	−0.410379	−	0.911915i	$-0.634604\pi$
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	0.994931	−	0.100559i	$-0.0320631\pi$
$954$	−4.64471			−0.150378
$955$	−5.67867	+	9.83575i	−0.183758	+	0.318277i
$956$	−29.8138	+	51.6390i	−0.964246	+	1.67012i
$957$	6.40491			0.207041
$958$	35.8496	−	62.0933i	1.15825	−	2.00614i
$959$		0			0
$960$	−14.7117	−	25.4815i	−0.474820	−	0.822412i
$961$	−22.0676			−0.711857
$962$	4.78037	+	14.3428i	0.154125	+	0.462431i
$963$	−73.0409			−2.35371
$964$	−7.41656	−	12.8459i	−0.238871	−	0.413737i
$965$	11.5805	+	20.0580i	0.372790	+	0.645691i
$966$		0			0
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	−21.6614	+	37.5187i	−0.696225	+	1.20590i
$969$	−33.9801	+	58.8553i	−1.09160	+	1.89070i
$970$	−18.0551			−0.579715
$971$	18.8738	−	32.6904i	0.605690	−	1.04909i	−0.386253	−	0.922393i	$-0.626231\pi$
$971$	18.8738	−	32.6904i	0.605690	−	1.04909i	0.991942	−	0.126692i	$-0.0404360\pi$
$972$	33.2795	+	57.6419i	1.06744	+	1.84886i
$973$		0			0
$974$	68.0359			2.18001
$975$	−39.2179	−	8.02679i	−1.25598	−	0.257063i
$976$	−5.08589			−0.162795
$977$	10.6538	+	18.4530i	0.340846	+	0.590363i	0.984590	−	0.174878i	$-0.0559532\pi$
$977$	10.6538	+	18.4530i	0.340846	+	0.590363i	−0.643744	+	0.765241i	$0.722620\pi$
$978$	26.8645	+	46.5307i	0.859032	+	1.48789i
$979$	0.615168	−	1.06550i	0.0196609	−	0.0340536i
$980$		0			0
$981$	−21.1044	+	36.5538i	−0.673810	+	1.16707i
$982$	−33.9910	+	58.8741i	−1.08470	+	1.87875i
$983$	22.0316			0.702700			0.351350	−	0.936244i	$-0.385723\pi$
$983$	22.0316			0.702700			0.351350	+	0.936244i	$0.385723\pi$
$984$	−20.5393	+	35.5752i	−0.654770	+	1.13409i
$985$	−0.722439	−	1.25130i	−0.0230188	−	0.0398698i
$986$	−30.5189	−	52.8603i	−0.971919	−	1.68341i
$987$		0			0
$988$	50.0528	+	10.2444i	1.59239	+	0.325918i
$989$	52.7059			1.67595
$990$	3.15104	+	5.45776i	0.100147	+	0.173459i
$991$	11.0129	+	19.0750i	0.349838	+	0.605937i	0.986220	−	0.165437i	$-0.0529033\pi$
$991$	11.0129	+	19.0750i	0.349838	+	0.605937i	−0.636383	+	0.771374i	$0.719570\pi$
$992$	−3.92808	+	6.80364i	−0.124717	+	0.216016i
$993$	74.9164			2.37740
$994$		0			0
$995$	−4.61376	+	7.99127i	−0.146266	+	0.253340i
$996$	29.2210			0.925902
$997$	5.04102	−	8.73130i	0.159651	−	0.276523i	−0.775092	−	0.631848i	$-0.782297\pi$
$997$	5.04102	−	8.73130i	0.159651	−	0.276523i	0.934743	+	0.355325i	$0.115630\pi$
$998$	−31.3225	−	54.2522i	−0.991497	−	1.71732i
$999$	−3.79408	−	6.57153i	−0.120039	−	0.207914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.j.393.6		12
7.2	even	3		637.2.g.l.263.6		12
7.3	odd	6		91.2.h.b.16.1	yes	12
7.4	even	3		637.2.h.l.471.1		12
7.5	odd	6		91.2.g.b.81.6	yes	12
7.6	odd	2		637.2.f.k.393.6		12
13.3	even	3		8281.2.a.ca.1.1		6
13.9	even	3	inner	637.2.f.j.295.6		12
13.10	even	6		8281.2.a.cf.1.6		6
21.5	even	6		819.2.n.d.172.1		12
21.17	even	6		819.2.s.d.289.6		12
91.3	odd	6		1183.2.e.h.170.6		12
91.9	even	3		637.2.h.l.165.1		12
91.10	odd	6		1183.2.e.g.170.1		12
91.48	odd	6		637.2.f.k.295.6		12
91.55	odd	6		8281.2.a.bz.1.1		6
91.61	odd	6		91.2.h.b.74.1	yes	12
91.62	odd	6		8281.2.a.ce.1.6		6
91.68	odd	6		1183.2.e.h.508.6		12
91.74	even	3		637.2.g.l.373.6		12
91.75	odd	6		1183.2.e.g.508.1		12
91.87	odd	6		91.2.g.b.9.6	✓	12
273.152	even	6		819.2.s.d.802.6		12
273.269	even	6		819.2.n.d.100.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	91.87	odd	6
91.2.g.b.81.6	yes	12	7.5	odd	6
91.2.h.b.16.1	yes	12	7.3	odd	6
91.2.h.b.74.1	yes	12	91.61	odd	6
637.2.f.j.295.6		12	13.9	even	3	inner
637.2.f.j.393.6		12	1.1	even	1	trivial
637.2.f.k.295.6		12	91.48	odd	6
637.2.f.k.393.6		12	7.6	odd	2
637.2.g.l.263.6		12	7.2	even	3
637.2.g.l.373.6		12	91.74	even	3
637.2.h.l.165.1		12	91.9	even	3
637.2.h.l.471.1		12	7.4	even	3
819.2.n.d.100.1		12	273.269	even	6
819.2.n.d.172.1		12	21.5	even	6
819.2.s.d.289.6		12	21.17	even	6
819.2.s.d.802.6		12	273.152	even	6
1183.2.e.g.170.1		12	91.10	odd	6
1183.2.e.g.508.1		12	91.75	odd	6
1183.2.e.h.170.6		12	91.3	odd	6
1183.2.e.h.508.6		12	91.68	odd	6
8281.2.a.bz.1.1		6	91.55	odd	6
8281.2.a.ca.1.1		6	13.3	even	3
8281.2.a.ce.1.6		6	91.62	odd	6
8281.2.a.cf.1.6		6	13.10	even	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)

\(f(q)\)	\(=\)	\(q+(1.19402 + 2.06810i) q^{2} +(-1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +O(q^{10})\)	\(q+(1.19402 + 2.06810i) q^{2} +(-1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 + 3.95828i) q^{9} +(-1.17286 - 2.03145i) q^{10} +(0.293901 + 0.509052i) q^{11} +10.1880 q^{12} +(-2.39227 + 2.69760i) q^{13} +(1.35136 + 2.34063i) q^{15} +(-1.15235 - 1.99593i) q^{16} +(-3.22710 + 5.58950i) q^{17} -10.9148 q^{18} +(-1.91345 + 3.31419i) q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 + 9.68906i) q^{24} -4.03513 q^{25} +(-8.43532 - 1.72647i) q^{26} +4.32156 q^{27} +(1.98009 + 3.42962i) q^{29} +(-3.22710 + 5.58950i) q^{30} +2.98872 q^{31} +(-1.31430 + 2.27644i) q^{32} +(0.808663 - 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 - 14.6564i) q^{36} +(-0.877941 - 1.52064i) q^{37} -9.13877 q^{38} +(9.71911 + 1.98923i) q^{39} +3.99411 q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} -2.17647 q^{44} +(2.24482 - 3.88814i) q^{45} +(9.86261 - 17.0825i) q^{46} +4.34059 q^{47} +(-3.17067 + 5.49176i) q^{48} +(-4.81802 - 8.34505i) q^{50} +17.7586 q^{51} +(-4.22130 - 12.6654i) q^{52} +0.425541 q^{53} +(5.16002 + 8.93742i) q^{54} +(-0.288693 - 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} -10.0074 q^{60} +(1.10337 - 1.91109i) q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(2.34988 - 2.64980i) q^{65} +3.86223 q^{66} +(-3.50651 - 6.07346i) q^{67} +(-11.9491 - 20.6964i) q^{68} +(-11.3636 + 19.6824i) q^{69} +(-1.80127 + 3.11988i) q^{71} +(9.29247 - 16.0950i) q^{72} -4.93427 q^{73} +(2.09656 - 3.63134i) q^{74} +(5.55128 + 9.61510i) q^{75} +(-7.08496 - 12.2715i) q^{76} +(7.49088 + 22.4753i) q^{78} +2.78541 q^{79} +(1.13193 + 1.96056i) q^{80} +(0.910609 + 1.57722i) q^{81} +(-4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} -15.2377 q^{86} +(5.44818 - 9.43652i) q^{87} +(-1.19505 - 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} +10.7214 q^{90} +30.5845 q^{92} +(-4.11170 - 7.12167i) q^{93} +(5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +7.23255 q^{96} +(3.84852 - 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23} + 11 q^{24} - 14 q^{25} - 11 q^{26} + 8 q^{27} + 3 q^{29} - 5 q^{30} + 32 q^{31} + 8 q^{32} - 16 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} - 34 q^{38} + 43 q^{39} - 10 q^{40} + 8 q^{41} - 11 q^{43} - 42 q^{44} + 7 q^{45} + 16 q^{46} - 2 q^{47} - 21 q^{48} + 6 q^{50} + 40 q^{51} + 16 q^{52} + 4 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} - 8 q^{58} - 13 q^{59} - 40 q^{60} + 5 q^{61} - 5 q^{62} - 30 q^{64} - 14 q^{65} + 36 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 60 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} - 14 q^{79} + 7 q^{80} - 6 q^{81} - q^{82} + 54 q^{83} - q^{85} + 14 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} - 45 q^{94} - 6 q^{95} + 38 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more