LMFDB - Embedded newform 637.2.bb.a.362.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			362.5
Character	$\chi$	$=$	637.362
Dual form			637.2.bb.a.227.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.490988 + 0.490988i) q^{2} +(2.71085 + 1.56511i) q^{3} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(0.562545 + 2.09944i) q^{6} +(1.72723 - 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +O(q^{10})$	\(q+(0.490988 + 0.490988i) q^{2} +(2.71085 + 1.56511i) q^{3} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(0.562545 + 2.09944i) q^{6} +(1.72723 - 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +(-0.0129135 + 0.0223668i) q^{10} +(0.292106 + 1.09015i) q^{11} +(2.37562 - 4.11469i) q^{12} +(3.58326 - 0.400306i) q^{13} +(-0.0301340 + 0.112462i) q^{15} -1.33962 q^{16} -6.40192 q^{17} +(-1.22174 + 4.55961i) q^{18} +(-3.56070 - 0.954087i) q^{19} +(0.0545333 - 0.0146122i) q^{20} +(-0.391832 + 0.678673i) q^{22} -2.79435i q^{23} +(7.38555 - 1.97895i) q^{24} +(4.32893 - 2.49931i) q^{25} +(1.95588 + 1.56279i) q^{26} +11.8894i q^{27} +(1.84998 + 3.20426i) q^{29} +(-0.0700128 + 0.0404219i) q^{30} +(2.63716 + 0.706626i) q^{31} +(-4.11220 - 4.11220i) q^{32} +(-0.914355 + 3.41242i) q^{33} +(-3.14327 - 3.14327i) q^{34} +(8.93636 - 5.15941i) q^{36} +(-3.94724 + 3.94724i) q^{37} +(-1.27982 - 2.21671i) q^{38} +(10.3402 + 4.52302i) q^{39} +(0.0786831 + 0.0454277i) q^{40} +(0.188789 + 0.0505859i) q^{41} +(1.84817 + 1.06704i) q^{43} +(1.65470 - 0.443376i) q^{44} +(-0.178801 + 0.178801i) q^{45} +(1.37199 - 1.37199i) q^{46} +(-5.43116 + 1.45527i) q^{47} +(-3.63152 - 2.09666i) q^{48} +(3.35258 + 0.898322i) q^{50} +(-17.3546 - 10.0197i) q^{51} +(-0.607609 - 5.43889i) q^{52} +(-0.295822 - 0.512378i) q^{53} +(-5.83755 + 5.83755i) q^{54} +(-0.0363547 + 0.0209894i) q^{55} +(-8.15927 - 8.15927i) q^{57} +(-0.664935 + 2.48157i) q^{58} +(-7.97051 - 7.97051i) q^{59} +(0.170701 + 0.0457393i) q^{60} +(1.18838 - 0.686113i) q^{61} +(0.947871 + 1.64176i) q^{62} -1.35883i q^{64} +(0.0488775 + 0.124885i) q^{65} +(-2.12439 + 1.22652i) q^{66} +(-7.28639 + 1.95238i) q^{67} +9.71723i q^{68} +(4.37346 - 7.57505i) q^{69} +(-9.88214 + 2.64791i) q^{71} +(16.0401 + 4.29793i) q^{72} +(-0.707590 + 2.64076i) q^{73} -3.87610 q^{74} +15.6468 q^{75} +(-1.44817 + 5.40465i) q^{76} +(2.85616 + 7.29767i) q^{78} +(-1.63129 + 2.82548i) q^{79} +(-0.0128963 - 0.0481297i) q^{80} +(-8.41080 + 14.5679i) q^{81} +(0.0678562 + 0.117530i) q^{82} +(4.92754 - 4.92754i) q^{83} +(-0.0616301 - 0.230007i) q^{85} +(0.383525 + 1.43133i) q^{86} +11.5817i q^{87} +(2.38748 + 1.37841i) q^{88} +(-11.9122 - 11.9122i) q^{89} -0.175578 q^{90} -4.24143 q^{92} +(6.04300 + 6.04300i) q^{93} +(-3.38116 - 1.95211i) q^{94} -0.137113i q^{95} +(-4.71151 - 17.5836i) q^{96} +(0.663884 + 2.47765i) q^{97} +(-5.42534 + 5.42534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.490988	+	0.490988i	0.347181	+	0.347181i	0.859059	−	0.511877i	$-0.171050\pi$
$2$	0.490988	+	0.490988i	0.347181	+	0.347181i	−0.511877	+	0.859059i	$0.671050\pi$
$3$	2.71085	+	1.56511i	1.56511	+	0.903616i	0.996726	+	0.0808518i	$0.0257641\pi$
$3$	2.71085	+	1.56511i	1.56511	+	0.903616i	0.568383	+	0.822764i	$0.307569\pi$
$4$		−	1.51786i		−	0.758931i
$5$	0.00962681	+	0.0359277i	0.00430524	+	0.0160674i	0.968045	−	0.250776i	$-0.0806859\pi$
$5$	0.00962681	+	0.0359277i	0.00430524	+	0.0160674i	−0.963740	+	0.266844i	$0.914019\pi$
$6$	0.562545	+	2.09944i	0.229658	+	0.857095i
$7$		0			0
$7$		0			0
$8$	1.72723	−	1.72723i	0.610667	−	0.610667i
$9$	3.39913	+	5.88747i	1.13304	+	1.96249i
$10$	−0.0129135	+	0.0223668i	−0.00408359	+	0.00707299i
$11$	0.292106	+	1.09015i	0.0880732	+	0.328694i	0.995878	−	0.0906984i	$-0.0289099\pi$
$11$	0.292106	+	1.09015i	0.0880732	+	0.328694i	−0.907805	+	0.419392i	$0.862243\pi$
$12$	2.37562	−	4.11469i	0.685782	−	1.18781i
$13$	3.58326	−	0.400306i	0.993818	−	0.111025i
$13$	3.58326	−	0.400306i	0.993818	−	0.111025i
$14$		0			0
$15$	−0.0301340	+	0.112462i	−0.00778057	+	0.0290375i
$16$	−1.33962			−0.334906
$17$	−6.40192			−1.55269			−0.776347	−	0.630306i	$-0.782930\pi$
$17$	−6.40192			−1.55269			−0.776347	+	0.630306i	$0.782930\pi$
$18$	−1.22174	+	4.55961i	−0.287968	+	1.07471i
$19$	−3.56070	−	0.954087i	−0.816881	−	0.218883i	−0.173899	−	0.984764i	$-0.555637\pi$
$19$	−3.56070	−	0.954087i	−0.816881	−	0.218883i	−0.642982	+	0.765881i	$0.722303\pi$
$20$	0.0545333	−	0.0146122i	0.0121940	−	0.00326738i
$21$		0			0
$22$	−0.391832	+	0.678673i	−0.0835389	+	0.144694i
$23$		−	2.79435i		−	0.582661i	−0.956622	−	0.291331i	$-0.905902\pi$
$23$		−	2.79435i		−	0.582661i	0.956622	−	0.291331i	$-0.0940980\pi$
$24$	7.38555	−	1.97895i	1.50757	−	0.403952i
$25$	4.32893	−	2.49931i	0.865786	−	0.499862i
$26$	1.95588	+	1.56279i	0.383580	+	0.306489i
$27$			11.8894i			2.28811i
$28$		0			0
$29$	1.84998	+	3.20426i	0.343532	+	0.595015i	0.985086	−	0.172063i	$-0.0550432\pi$
$29$	1.84998	+	3.20426i	0.343532	+	0.595015i	−0.641554	+	0.767078i	$0.721710\pi$
$30$	−0.0700128	+	0.0404219i	−0.0127825	+	0.00738000i
$31$	2.63716	+	0.706626i	0.473648	+	0.126914i	0.487744	−	0.872987i	$-0.337820\pi$
$31$	2.63716	+	0.706626i	0.473648	+	0.126914i	−0.0140952	+	0.999901i	$0.504487\pi$
$32$	−4.11220	−	4.11220i	−0.726941	−	0.726941i
$33$	−0.914355	+	3.41242i	−0.159169	+	0.594026i
$34$	−3.14327	−	3.14327i	−0.539066	−	0.539066i
$35$		0			0
$36$	8.93636	−	5.15941i	1.48939	−	0.859902i
$37$	−3.94724	+	3.94724i	−0.648923	+	0.648923i	−0.952733	−	0.303810i	$-0.901741\pi$
$37$	−3.94724	+	3.94724i	−0.648923	+	0.648923i	0.303810	+	0.952733i	$0.401741\pi$
$38$	−1.27982	−	2.21671i	−0.207614	−	0.359598i
$39$	10.3402	+	4.52302i	1.65576	+	0.724263i
$40$	0.0786831	+	0.0454277i	0.0124409	+	0.00718275i
$41$	0.188789	+	0.0505859i	0.0294839	+	0.00790020i	0.273531	−	0.961863i	$-0.411808\pi$
$41$	0.188789	+	0.0505859i	0.0294839	+	0.00790020i	−0.244047	+	0.969763i	$0.578475\pi$
$42$		0			0
$43$	1.84817	+	1.06704i	0.281843	+	0.162722i	0.634258	−	0.773122i	$-0.281306\pi$
$43$	1.84817	+	1.06704i	0.281843	+	0.162722i	−0.352414	+	0.935844i	$0.614639\pi$
$44$	1.65470	−	0.443376i	0.249456	−	0.0668414i
$45$	−0.178801	+	0.178801i	−0.0266540	+	0.0266540i
$46$	1.37199	−	1.37199i	0.202289	−	0.202289i
$47$	−5.43116	+	1.45527i	−0.792215	+	0.212273i	−0.632163	−	0.774835i	$-0.717833\pi$
$47$	−5.43116	+	1.45527i	−0.792215	+	0.212273i	−0.160052	+	0.987109i	$0.551166\pi$
$48$	−3.63152	−	2.09666i	−0.524164	−	0.302627i
$49$		0			0
$50$	3.35258	+	0.898322i	0.474127	+	0.127042i
$51$	−17.3546	−	10.0197i	−2.43014	−	1.40304i
$52$	−0.607609	−	5.43889i	−0.0842602	−	0.754239i
$53$	−0.295822	−	0.512378i	−0.0406342	−	0.0703805i	0.844993	−	0.534777i	$-0.179605\pi$
$53$	−0.295822	−	0.512378i	−0.0406342	−	0.0703805i	−0.885627	+	0.464397i	$0.846271\pi$
$54$	−5.83755	+	5.83755i	−0.794390	+	0.794390i
$55$	−0.0363547	+	0.0209894i	−0.00490207	+	0.00283021i
$56$		0			0
$57$	−8.15927	−	8.15927i	−1.08072	−	1.08072i
$58$	−0.664935	+	2.48157i	−0.0873102	+	0.325846i
$59$	−7.97051	−	7.97051i	−1.03767	−	1.03767i	−0.999262	−	0.0384097i	$-0.987771\pi$
$59$	−7.97051	−	7.97051i	−1.03767	−	1.03767i	−0.0384097	−	0.999262i	$-0.512229\pi$
$60$	0.170701	+	0.0457393i	0.0220374	+	0.00590491i
$61$	1.18838	−	0.686113i	0.152157	−	0.0878478i	−0.421989	−	0.906601i	$-0.638668\pi$
$61$	1.18838	−	0.686113i	0.152157	−	0.0878478i	0.574145	+	0.818753i	$0.305334\pi$
$62$	0.947871	+	1.64176i	0.120380	+	0.208504i
$63$		0			0
$64$		−	1.35883i		−	0.169854i
$65$	0.0488775	+	0.124885i	0.00606250	+	0.0154901i
$66$	−2.12439	+	1.22652i	−0.261495	+	0.150974i
$67$	−7.28639	+	1.95238i	−0.890174	+	0.238522i	−0.674792	−	0.738008i	$-0.735767\pi$
$67$	−7.28639	+	1.95238i	−0.890174	+	0.238522i	−0.215383	+	0.976530i	$0.569100\pi$
$68$			9.71723i			1.17839i
$69$	4.37346	−	7.57505i	0.526502	−	0.911928i
$70$		0			0
$71$	−9.88214	+	2.64791i	−1.17279	+	0.314249i	−0.792065	−	0.610437i	$-0.790994\pi$
$71$	−9.88214	+	2.64791i	−1.17279	+	0.314249i	−0.380729	+	0.924686i	$0.624327\pi$
$72$	16.0401	+	4.29793i	1.89034	+	0.506516i
$73$	−0.707590	+	2.64076i	−0.0828171	+	0.309078i	−0.994892	−	0.100946i	$-0.967813\pi$
$73$	−0.707590	+	2.64076i	−0.0828171	+	0.309078i	0.912075	+	0.410024i	$0.134480\pi$
$74$	−3.87610			−0.450588
$75$	15.6468			1.80673
$76$	−1.44817	+	5.40465i	−0.166117	+	0.619956i
$77$		0			0
$78$	2.85616	+	7.29767i	0.323397	+	0.826298i
$79$	−1.63129	+	2.82548i	−0.183535	+	0.317891i	−0.943082	−	0.332561i	$-0.892087\pi$
$79$	−1.63129	+	2.82548i	−0.183535	+	0.317891i	0.759547	+	0.650452i	$0.225421\pi$
$80$	−0.0128963	−	0.0481297i	−0.00144185	−	0.00538106i
$81$	−8.41080	+	14.5679i	−0.934533	+	1.61866i
$82$	0.0678562	+	0.117530i	0.00749347	+	0.0129791i
$83$	4.92754	−	4.92754i	0.540868	−	0.540868i	−0.382915	−	0.923783i	$-0.625080\pi$
$83$	4.92754	−	4.92754i	0.540868	−	0.540868i	0.923783	+	0.382915i	$0.125080\pi$
$84$		0			0
$85$	−0.0616301	−	0.230007i	−0.00668472	−	0.0249477i
$86$	0.383525	+	1.43133i	0.0413565	+	0.154345i
$87$			11.5817i			1.24169i
$88$	2.38748	+	1.37841i	0.254506	+	0.146939i
$89$	−11.9122	−	11.9122i	−1.26269	−	1.26269i	−0.949785	−	0.312903i	$-0.898699\pi$
$89$	−11.9122	−	11.9122i	−1.26269	−	1.26269i	−0.312903	−	0.949785i	$-0.601301\pi$
$90$	−0.175578			−0.0185076
$91$		0			0
$92$	−4.24143			−0.442199
$93$	6.04300	+	6.04300i	0.626630	+	0.626630i
$94$	−3.38116	−	1.95211i	−0.348740	−	0.201345i
$95$		−	0.137113i		−	0.0140675i
$96$	−4.71151	−	17.5836i	−0.480866	−	1.79462i
$97$	0.663884	+	2.47765i	0.0674072	+	0.251567i	0.991405	−	0.130832i	$-0.0417648\pi$
$97$	0.663884	+	2.47765i	0.0674072	+	0.251567i	−0.923997	+	0.382399i	$0.875098\pi$
$98$		0			0
$99$	−5.42534	+	5.42534i	−0.545267	+	0.545267i
$100$	−3.79360	−	6.57071i	−0.379360	−	0.657071i
$101$	−2.30855	+	3.99852i	−0.229709	+	0.397868i	−0.957722	−	0.287696i	$-0.907111\pi$
$101$	−2.30855	+	3.99852i	−0.229709	+	0.397868i	0.728013	+	0.685564i	$0.240444\pi$
$102$	−3.60137	−	13.4405i	−0.356588	−	1.33081i
$103$	5.86837	−	10.1643i	0.578227	−	1.00152i	−0.417455	−	0.908697i	$-0.637078\pi$
$103$	5.86837	−	10.1643i	0.578227	−	1.00152i	0.995683	−	0.0928218i	$-0.0295887\pi$
$104$	5.49769	−	6.88053i	0.539093	−	0.674691i
$105$		0			0
$106$	0.106327	−	0.396817i	0.0103274	−	0.0385422i
$107$	13.0733			1.26385			0.631923	−	0.775031i	$-0.282266\pi$
$107$	13.0733			1.26385			0.631923	+	0.775031i	$0.282266\pi$
$108$	18.0464			1.73652
$109$	3.37504	−	12.5958i	0.323270	−	1.20646i	−0.592770	−	0.805372i	$-0.701966\pi$
$109$	3.37504	−	12.5958i	0.323270	−	1.20646i	0.916040	−	0.401087i	$-0.131368\pi$
$110$	−0.0281553	−	0.00754419i	−0.00268450	−	0.000719310i
$111$	−16.8782	+	4.52251i	−1.60201	+	0.429258i
$112$		0			0
$113$	1.85773	−	3.21769i	0.174761	−	0.302694i	−0.765318	−	0.643653i	$-0.777418\pi$
$113$	1.85773	−	3.21769i	0.174761	−	0.302694i	0.940078	+	0.340958i	$0.110751\pi$
$114$		−	8.01221i		−	0.750413i
$115$	0.100395	−	0.0269006i	0.00936184	−	0.00250850i
$116$	4.86362	−	2.80801i	0.451575	−	0.260717i
$117$	14.5368	+	19.7356i	1.34392	+	1.82456i
$118$		−	7.82685i		−	0.720520i
$119$		0			0
$120$	0.142199	+	0.246295i	0.0129809	+	0.0224836i
$121$	8.42317	−	4.86312i	0.765743	−	0.442102i
$122$	0.920356	+	0.246609i	0.0833251	+	0.0223269i
$123$	0.432607	+	0.432607i	0.0390068	+	0.0390068i
$124$	1.07256	−	4.00285i	0.0963187	−	0.359466i
$125$	0.262973	+	0.262973i	0.0235210	+	0.0235210i
$126$		0			0
$127$	2.47692	−	1.43005i	0.219791	−	0.126897i	−0.386062	−	0.922473i	$-0.626165\pi$
$127$	2.47692	−	1.43005i	0.219791	−	0.126897i	0.605854	+	0.795576i	$0.292832\pi$
$128$	−7.55722	+	7.55722i	−0.667970	+	0.667970i
$129$	3.34007	+	5.78517i	0.294077	+	0.509356i
$130$	−0.0373187	+	0.0853152i	−0.00327307	+	0.00748264i
$131$	−0.119788	−	0.0691595i	−0.0104659	−	0.00604249i	0.494758	−	0.869031i	$-0.335257\pi$
$131$	−0.119788	−	0.0691595i	−0.0104659	−	0.00604249i	−0.505224	+	0.862988i	$0.668590\pi$
$132$	5.17958	+	1.38786i	0.450824	+	0.120798i
$133$		0			0
$134$	−4.53613	−	2.61894i	−0.391862	−	0.226242i
$135$	−0.427159	+	0.114457i	−0.0367640	+	0.00985089i
$136$	−11.0576	+	11.0576i	−0.948180	+	0.948180i
$137$	−12.0623	+	12.0623i	−1.03055	+	1.03055i	−0.0310355	+	0.999518i	$0.509880\pi$
$137$	−12.0623	+	12.0623i	−1.03055	+	1.03055i	−0.999518	+	0.0310355i	$0.990120\pi$
$138$	5.86657	−	1.57194i	0.499396	−	0.133813i
$139$	13.3885	+	7.72988i	1.13560	+	0.655640i	0.945338	−	0.326093i	$-0.105732\pi$
$139$	13.3885	+	7.72988i	1.13560	+	0.655640i	0.190264	+	0.981733i	$0.439066\pi$
$140$		0			0
$141$	−17.0007	−	4.55532i	−1.43172	−	0.383627i
$142$	−6.15211	−	3.55192i	−0.516273	−	0.298071i
$143$	1.48309	+	3.78937i	0.124022	+	0.316883i
$144$	−4.55356	−	7.88700i	−0.379463	−	0.657250i
$145$	−0.0973123	+	0.0973123i	−0.00808135	+	0.00808135i
$146$	−1.64400	+	0.949165i	−0.136059	+	0.0785534i
$147$		0			0
$148$	5.99137	+	5.99137i	0.492487	+	0.492487i
$149$	−1.47392	+	5.50075i	−0.120748	+	0.450639i	−0.999653	−	0.0263595i	$-0.991609\pi$
$149$	−1.47392	+	5.50075i	−0.120748	+	0.450639i	0.878904	+	0.476998i	$0.158275\pi$
$150$	7.68237	+	7.68237i	0.627263	+	0.627263i
$151$	19.9927	+	5.35703i	1.62698	+	0.435949i	0.953042	−	0.302838i	$-0.0979340\pi$
$151$	19.9927	+	5.35703i	1.62698	+	0.435949i	0.673940	+	0.738786i	$0.264601\pi$
$152$	−7.79807	+	4.50222i	−0.632507	+	0.365178i
$153$	−21.7610	−	37.6911i	−1.75927	−	3.04715i
$154$		0			0
$155$			0.101550i			0.00815668i
$156$	6.86532	−	15.6950i	0.549666	−	1.25660i
$157$	−8.02263	+	4.63187i	−0.640275	+	0.369663i	−0.784721	−	0.619850i	$-0.787194\pi$
$157$	−8.02263	+	4.63187i	−0.640275	+	0.369663i	0.144445	+	0.989513i	$0.453860\pi$
$158$	−2.18822	+	0.586332i	−0.174086	+	0.0466461i
$159$		−	1.85197i		−	0.146871i
$160$	0.108155	−	0.187329i	0.00855037	−	0.0148097i
$161$		0			0
$162$	−11.2823	+	3.02308i	−0.886420	+	0.237516i
$163$	−3.97880	−	1.06612i	−0.311644	−	0.0835047i	0.0996072	−	0.995027i	$-0.468241\pi$
$163$	−3.97880	−	1.06612i	−0.311644	−	0.0835047i	−0.411251	+	0.911522i	$0.634908\pi$
$164$	0.0767824	−	0.286556i	0.00599570	−	0.0223763i
$165$	−0.131403			−0.0102297
$166$	4.83873			0.375558
$167$	4.15955	−	15.5237i	0.321876	−	1.20126i	−0.595540	−	0.803326i	$-0.703062\pi$
$167$	4.15955	−	15.5237i	0.321876	−	1.20126i	0.917415	−	0.397931i	$-0.130272\pi$
$168$		0			0
$169$	12.6795	−	2.86880i	0.975347	−	0.220677i
$170$	0.0826709	−	0.143190i	0.00634057	−	0.0109822i
$171$	−6.48614	−	24.2066i	−0.496007	−	1.85112i
$172$	1.61962	−	2.80526i	0.123495	−	0.213899i
$173$	10.5332	+	18.2440i	0.800821	+	1.38706i	0.919076	+	0.394080i	$0.128937\pi$
$173$	10.5332	+	18.2440i	0.800821	+	1.38706i	−0.118255	+	0.992983i	$0.537730\pi$
$174$	−5.68646	+	5.68646i	−0.431090	+	0.431090i
$175$		0			0
$176$	−0.391312	−	1.46040i	−0.0294963	−	0.110082i
$177$	−9.13212	−	34.0816i	−0.686412	−	2.56173i
$178$		−	11.6975i		−	0.876763i
$179$	−7.89629	−	4.55893i	−0.590196	−	0.340750i	0.174979	−	0.984572i	$-0.444014\pi$
$179$	−7.89629	−	4.55893i	−0.590196	−	0.340750i	−0.765175	+	0.643822i	$0.777348\pi$
$180$	0.271395	+	0.271395i	0.0202286	+	0.0202286i
$181$	−15.7169			−1.16823			−0.584113	−	0.811672i	$-0.698557\pi$
$181$	−15.7169			−1.16823			−0.584113	+	0.811672i	$0.698557\pi$
$182$		0			0
$183$	4.29537			0.317523
$184$	−4.82647	−	4.82647i	−0.355812	−	0.355812i
$185$	−0.179815	−	0.103816i	−0.0132203	−	0.00763272i
$186$			5.93409i			0.435108i
$187$	−1.87004	−	6.97908i	−0.136751	−	0.510361i
$188$	2.20890	+	8.24374i	0.161101	+	0.601236i
$189$		0			0
$190$	0.0673208	−	0.0673208i	0.00488396	−	0.00488396i
$191$	8.65358	+	14.9884i	0.626151	+	1.08453i	0.988317	+	0.152412i	$0.0487039\pi$
$191$	8.65358	+	14.9884i	0.626151	+	1.08453i	−0.362166	+	0.932114i	$0.617963\pi$
$192$	2.12672	−	3.68359i	0.153483	−	0.265840i
$193$	−3.25813	−	12.1595i	−0.234525	−	0.875260i	−0.978362	−	0.206899i	$-0.933663\pi$
$193$	−3.25813	−	12.1595i	−0.234525	−	0.875260i	0.743837	−	0.668361i	$-0.233004\pi$
$194$	−0.890537	+	1.54245i	−0.0639368	+	0.110742i
$195$	−0.0629589	+	0.415042i	−0.00450858	+	0.0297218i
$196$		0			0
$197$	−6.43206	+	24.0048i	−0.458265	+	1.71027i	0.220042	+	0.975490i	$0.429381\pi$
$197$	−6.43206	+	24.0048i	−0.458265	+	1.71027i	−0.678307	+	0.734778i	$0.737286\pi$
$198$	−5.32756			−0.378613
$199$	10.5978			0.751257			0.375629	−	0.926770i	$-0.377427\pi$
$199$	10.5978			0.751257			0.375629	+	0.926770i	$0.377427\pi$
$200$	3.16017	−	11.7939i	0.223458	−	0.833956i
$201$	−22.8080	−	6.11138i	−1.60875	−	0.431064i
$202$	−3.09670	+	0.829758i	−0.217883	+	0.0583815i
$203$		0			0
$204$	−15.2085	+	26.3419i	−1.06481	+	1.84430i
$205$			0.00726976i			0.000507742i
$206$	7.87186	−	2.10926i	0.548458	−	0.146959i
$207$	16.4516	−	9.49835i	1.14347	−	0.660181i
$208$	−4.80022	+	0.536260i	−0.332836	+	0.0371829i
$209$		−	4.16041i		−	0.287781i
$210$		0			0
$211$	−10.3404	−	17.9102i	−0.711865	−	1.23299i	−0.964156	−	0.265335i	$-0.914518\pi$
$211$	−10.3404	−	17.9102i	−0.711865	−	1.23299i	0.252292	−	0.967651i	$-0.418816\pi$
$212$	−0.777719	+	0.449016i	−0.0534139	+	0.0308386i
$213$	−30.9332	−	8.28854i	−2.11951	−	0.567921i
$214$	6.41885	+	6.41885i	0.438784	+	0.438784i
$215$	−0.0205444	+	0.0766728i	−0.00140112	+	0.00522904i
$216$	20.5357	+	20.5357i	1.39728	+	1.39728i
$217$		0			0
$218$	7.84149	−	4.52729i	0.531093	−	0.306627i
$219$	−6.05125	+	6.05125i	−0.408905	+	0.408905i
$220$	0.0318590	+	0.0551814i	0.00214793	+	0.00372033i
$221$	−22.9398	+	2.56273i	−1.54309	+	0.172388i
$222$	−10.5075	−	6.06652i	−0.705219	−	0.407158i
$223$	3.17269	+	0.850119i	0.212459	+	0.0569282i	0.363479	−	0.931603i	$-0.381589\pi$
$223$	3.17269	+	0.850119i	0.212459	+	0.0569282i	−0.151020	+	0.988531i	$0.548256\pi$
$224$		0			0
$225$	29.4292	+	16.9910i	1.96195	+	1.13273i
$226$	2.49197	−	0.667721i	0.165763	−	0.0444162i
$227$	13.0106	−	13.0106i	0.863541	−	0.863541i	−0.128207	−	0.991747i	$-0.540922\pi$
$227$	13.0106	−	13.0106i	0.863541	−	0.863541i	0.991747	+	0.128207i	$0.0409220\pi$
$228$	−12.3846	+	12.3846i	−0.820193	+	0.820193i
$229$	10.5951	−	2.83894i	0.700142	−	0.187603i	0.108848	−	0.994058i	$-0.465284\pi$
$229$	10.5951	−	2.83894i	0.700142	−	0.187603i	0.591294	+	0.806456i	$0.298617\pi$
$230$	0.0625004	+	0.0360846i	0.00412116	+	0.00237935i
$231$		0			0
$232$	8.72982	+	2.33915i	0.573141	+	0.153573i
$233$	7.46970	+	4.31263i	0.489356	+	0.282530i	0.724307	−	0.689477i	$-0.242160\pi$
$233$	7.46970	+	4.31263i	0.489356	+	0.282530i	−0.234951	+	0.972007i	$0.575493\pi$
$234$	−2.55259	+	16.8273i	−0.166868	+	1.10004i
$235$	−0.104569	−	0.181120i	−0.00682136	−	0.0118149i
$236$	−12.0981	+	12.0981i	−0.787521	+	0.787521i
$237$	−8.84437	+	5.10630i	−0.574503	+	0.331690i
$238$		0			0
$239$	−5.82164	−	5.82164i	−0.376571	−	0.376571i	0.493293	−	0.869863i	$-0.335793\pi$
$239$	−5.82164	−	5.82164i	−0.376571	−	0.376571i	−0.869863	+	0.493293i	$0.835793\pi$
$240$	0.0403683	−	0.150656i	0.00260576	−	0.00972483i
$241$	4.44250	+	4.44250i	0.286166	+	0.286166i	0.835562	−	0.549396i	$-0.185142\pi$
$241$	4.44250	+	4.44250i	0.286166	+	0.286166i	−0.549396	+	0.835562i	$0.685142\pi$
$242$	6.52341	+	1.74794i	0.419341	+	0.112362i
$243$	−14.7113	+	8.49355i	−0.943728	+	0.544861i
$244$	−1.04142	−	1.80380i	−0.0666704	−	0.115476i
$245$		0			0
$246$			0.424810i			0.0270849i
$247$	−13.1409	−	1.99337i	−0.836132	−	0.126835i
$248$	5.77549	−	3.33448i	0.366744	−	0.211740i
$249$	21.0700	−	5.64568i	1.33525	−	0.357780i
$250$			0.258233i			0.0163321i
$251$	−5.23454	+	9.06650i	−0.330402	+	0.572272i	−0.982591	−	0.185784i	$-0.940517\pi$
$251$	−5.23454	+	9.06650i	−0.330402	+	0.572272i	0.652189	+	0.758056i	$0.273851\pi$
$252$		0			0
$253$	3.04627	−	0.816245i	0.191517	−	0.0513169i
$254$	1.91828	+	0.514001i	0.120364	+	0.0322513i
$255$	0.192916	−	0.719971i	0.0120808	−	0.0450863i
$256$	−10.1387			−0.633667
$257$	5.35020			0.333737			0.166868	−	0.985979i	$-0.446635\pi$
$257$	5.35020			0.333737			0.166868	+	0.985979i	$0.446635\pi$
$258$	−1.20052	+	4.48039i	−0.0747409	+	0.278937i
$259$		0			0
$260$	0.189558	−	0.0741892i	0.0117559	−	0.00460102i
$261$	−12.5766	+	21.7834i	−0.778474	+	1.34836i
$262$	−0.0248579	−	0.0927709i	−0.00153573	−	0.00573140i
$263$	−3.08129	+	5.33695i	−0.190000	+	0.329090i	−0.945250	−	0.326347i	$-0.894182\pi$
$263$	−3.08129	+	5.33695i	−0.190000	+	0.329090i	0.755250	+	0.655437i	$0.227516\pi$
$264$	4.31473	+	7.47333i	0.265553	+	0.459951i
$265$	0.0155608	−	0.0155608i	0.000955891	−	0.000955891i
$266$		0			0
$267$	−13.6482	−	50.9359i	−0.835259	−	3.11723i
$268$	2.96345	+	11.0597i	0.181021	+	0.675581i
$269$			20.5507i			1.25300i	0.779422	+	0.626500i	$0.215513\pi$
$269$			20.5507i			1.25300i	−0.779422	+	0.626500i	$0.784487\pi$
$270$	−0.265927	−	0.153533i	−0.0161838	−	0.00934373i
$271$	7.18504	+	7.18504i	0.436460	+	0.436460i	0.890819	−	0.454359i	$-0.150132\pi$
$271$	7.18504	+	7.18504i	0.436460	+	0.436460i	−0.454359	+	0.890819i	$0.650132\pi$
$272$	8.57617			0.520007
$273$		0			0
$274$	−11.8449			−0.715578
$275$	3.98914	+	3.98914i	0.240554	+	0.240554i
$276$	−11.4979	−	6.63830i	−0.692090	−	0.399579i
$277$			20.4254i			1.22725i	0.789599	+	0.613623i	$0.210288\pi$
$277$			20.4254i			1.22725i	−0.789599	+	0.613623i	$0.789712\pi$
$278$	2.77834	+	10.3689i	0.166634	+	0.621885i
$279$	4.80383	+	17.9281i	0.287598	+	1.07333i
$280$		0			0
$281$	−13.0423	+	13.0423i	−0.778037	+	0.778037i	−0.979497	−	0.201460i	$-0.935431\pi$
$281$	−13.0423	+	13.0423i	−0.778037	+	0.778037i	0.201460	+	0.979497i	$0.435431\pi$
$282$	−6.11053	−	10.5838i	−0.363877	−	0.630253i
$283$	1.00784	−	1.74563i	0.0599100	−	0.103767i	−0.834515	−	0.550986i	$-0.814252\pi$
$283$	1.00784	−	1.74563i	0.0599100	−	0.103767i	0.894425	+	0.447218i	$0.147585\pi$
$284$	4.01916	+	14.9997i	0.238493	+	0.890069i
$285$	0.214597	−	0.371692i	0.0127116	−	0.0220171i
$286$	−1.13236	+	2.58872i	−0.0669578	+	0.153074i
$287$		0			0
$288$	10.2325	−	38.1883i	0.602958	−	2.25027i
$289$	23.9846			1.41086
$290$	−0.0955584			−0.00561138
$291$	−2.07810	+	7.75558i	−0.121820	+	0.454640i
$292$	4.00831	+	1.07402i	0.234569	+	0.0628525i
$293$	11.4688	−	3.07306i	0.670016	−	0.179530i	0.0922540	−	0.995736i	$-0.470593\pi$
$293$	11.4688	−	3.07306i	0.670016	−	0.179530i	0.577762	+	0.816205i	$0.303926\pi$
$294$		0			0
$295$	0.209632	−	0.363093i	0.0122052	−	0.0211401i
$296$			13.6356i			0.792552i
$297$	−12.9613	+	3.47296i	−0.752089	+	0.201522i
$298$	−3.42448	+	1.97712i	−0.198375	+	0.114532i
$299$	−1.11859	−	10.0129i	−0.0646899	−	0.579059i
$300$		−	23.7496i		−	1.37118i
$301$		0			0
$302$	7.18594	+	12.4464i	0.413504	+	0.716211i
$303$	−12.5162	+	7.22626i	−0.719040	+	0.415138i
$304$	4.77000	+	1.27812i	0.273578	+	0.0733051i
$305$	0.0360908	+	0.0360908i	0.00206656	+	0.00206656i
$306$	7.82151	−	29.1903i	0.447126	−	1.66870i
$307$	−1.46571	−	1.46571i	−0.0836528	−	0.0836528i	0.664042	−	0.747695i	$-0.268839\pi$
$307$	−1.46571	−	1.46571i	−0.0836528	−	0.0836528i	−0.747695	+	0.664042i	$0.768839\pi$
$308$		0			0
$309$	31.8165	−	18.3693i	1.80998	−	1.04499i
$310$	−0.0498598	+	0.0498598i	−0.00283185	+	0.00283185i
$311$	1.37387	+	2.37961i	0.0779051	+	0.134936i	0.902346	−	0.431013i	$-0.141844\pi$
$311$	1.37387	+	2.37961i	0.0779051	+	0.134936i	−0.824441	+	0.565948i	$0.808510\pi$
$312$	25.6722	−	10.0476i	1.45340	−	0.568833i
$313$	−6.57410	−	3.79556i	−0.371590	−	0.214538i	0.302563	−	0.953129i	$-0.402158\pi$
$313$	−6.57410	−	3.79556i	−0.371590	−	0.214538i	−0.674153	+	0.738592i	$0.735491\pi$
$314$	−6.21321	−	1.66482i	−0.350632	−	0.0939514i
$315$		0			0
$316$	4.28869	+	2.47607i	0.241257	+	0.139290i
$317$	9.63370	−	2.58134i	0.541083	−	0.144983i	0.0220814	−	0.999756i	$-0.492971\pi$
$317$	9.63370	−	2.58134i	0.541083	−	0.144983i	0.519001	+	0.854774i	$0.326304\pi$
$318$	0.909297	−	0.909297i	0.0509908	−	0.0509908i
$319$	−2.95274	+	2.95274i	−0.165322	+	0.165322i
$320$	0.0488198	−	0.0130812i	0.00272911	−	0.000731262i
$321$	35.4398	+	20.4612i	1.97806	+	1.14203i
$322$		0			0
$323$	22.7953	+	6.10799i	1.26837	+	0.339858i
$324$	22.1121	+	12.7664i	1.22845	+	0.709246i
$325$	14.5112	−	10.6886i	0.804936	−	0.592895i
$326$	−1.43009	−	2.47700i	−0.0792056	−	0.137188i
$327$	28.8630	−	28.8630i	1.59613	−	1.59613i
$328$	0.413456	−	0.238709i	0.0228293	−	0.0131805i
$329$		0			0
$330$	−0.0645173	−	0.0645173i	−0.00355156	−	0.00355156i
$331$	−4.37748	+	16.3370i	−0.240608	+	0.897962i	0.734932	+	0.678141i	$0.237214\pi$
$331$	−4.37748	+	16.3370i	−0.240608	+	0.897962i	−0.975540	+	0.219821i	$0.929453\pi$
$332$	−7.47932	−	7.47932i	−0.410481	−	0.410481i
$333$	−36.6565	−	9.82208i	−2.00876	−	0.538246i
$334$	9.66423	−	5.57964i	0.528803	−	0.305305i
$335$	−0.140289	−	0.242988i	−0.00766483	−	0.0132759i
$336$		0			0
$337$		−	7.92125i		−	0.431498i	−0.976449	−	0.215749i	$-0.930781\pi$
$337$		−	7.92125i		−	0.431498i	0.976449	−	0.215749i	$-0.0692193\pi$
$338$	7.63404	+	4.81694i	0.415237	+	0.262007i
$339$	10.0721	−	5.81511i	0.547039	−	0.315833i
$340$	−0.349118	+	0.0935459i	−0.0189336	+	0.00507324i
$341$			3.08132i			0.166863i
$342$	8.70054	−	15.0698i	0.470471	−	0.814880i
$343$		0			0
$344$	5.03523	−	1.34919i	0.271482	−	0.0727433i
$345$	0.314257	+	0.0842049i	0.0169190	+	0.00453344i
$346$	−3.78592	+	14.1292i	−0.203532	+	0.759592i
$347$	24.3383			1.30655			0.653274	−	0.757122i	$-0.273395\pi$
$347$	24.3383			1.30655			0.653274	+	0.757122i	$0.273395\pi$
$348$	17.5794			0.942353
$349$	−4.20514	+	15.6938i	−0.225096	+	0.840070i	0.757270	+	0.653102i	$0.226533\pi$
$349$	−4.20514	+	15.6938i	−0.225096	+	0.840070i	−0.982366	+	0.186968i	$0.940134\pi$
$350$		0			0
$351$	4.75940	+	42.6028i	0.254038	+	2.27397i
$352$	3.28173	−	5.68412i	0.174917	−	0.302965i
$353$	4.23848	+	15.8182i	0.225591	+	0.841919i	0.982167	+	0.188012i	$0.0602044\pi$
$353$	4.23848	+	15.8182i	0.225591	+	0.841919i	−0.756575	+	0.653907i	$0.773129\pi$
$354$	12.2499	−	21.2174i	0.651074	−	1.12769i
$355$	−0.190267	−	0.329552i	−0.0100983	−	0.0174908i
$356$	−18.0810	+	18.0810i	−0.958292	+	0.958292i
$357$		0			0
$358$	−1.63861	−	6.11536i	−0.0866031	−	0.323207i
$359$	1.78847	+	6.67467i	0.0943920	+	0.352276i	0.996927	−	0.0783418i	$-0.0249625\pi$
$359$	1.78847	+	6.67467i	0.0943920	+	0.352276i	−0.902535	+	0.430617i	$0.858296\pi$
$360$			0.617659i			0.0325535i
$361$	−4.68617	−	2.70556i	−0.246640	−	0.142398i
$362$	−7.71680	−	7.71680i	−0.405586	−	0.405586i
$363$	30.4452			1.59796
$364$		0			0
$365$	−0.101688			−0.00532262
$366$	2.10898	+	2.10898i	0.110238	+	0.110238i
$367$	12.3820	+	7.14874i	0.646335	+	0.373161i	0.787050	−	0.616889i	$-0.211607\pi$
$367$	12.3820	+	7.14874i	0.646335	+	0.373161i	−0.140716	+	0.990050i	$0.544940\pi$
$368$			3.74337i			0.195137i
$369$	0.343897	+	1.28344i	0.0179025	+	0.0668132i
$370$	−0.0373145	−	0.139260i	−0.00193989	−	0.00723976i
$371$		0			0
$372$	9.17244	−	9.17244i	0.475569	−	0.475569i
$373$	−11.3326	−	19.6286i	−0.586780	−	1.01633i	−0.994651	−	0.103293i	$-0.967062\pi$
$373$	−11.3326	−	19.6286i	−0.586780	−	1.01633i	0.407871	−	0.913039i	$-0.366271\pi$
$374$	2.50848	−	4.34481i	0.129710	−	0.224665i
$375$	0.301298	+	1.12446i	0.0155590	+	0.0580669i
$376$	−6.86726	+	11.8944i	−0.354152	+	0.613409i
$377$	7.91164	+	10.7411i	0.407470	+	0.553196i
$378$		0			0
$379$	−3.37163	+	12.5831i	−0.173189	+	0.646349i	0.823664	+	0.567078i	$0.191926\pi$
$379$	−3.37163	+	12.5831i	−0.173189	+	0.646349i	−0.996853	+	0.0792716i	$0.974741\pi$
$380$	−0.208118			−0.0106762
$381$	8.95275			0.458663
$382$	−3.11034	+	11.6080i	−0.159139	+	0.593914i
$383$	−2.21834	−	0.594401i	−0.113352	−	0.0303725i	0.201697	−	0.979448i	$-0.435354\pi$
$383$	−2.21834	−	0.594401i	−0.113352	−	0.0303725i	−0.315049	+	0.949075i	$0.602021\pi$
$384$	−32.3144	+	8.65861i	−1.64904	+	0.441858i
$385$		0			0
$386$	4.37047	−	7.56988i	0.222451	−	0.385297i
$387$			14.5081i			0.737486i
$388$	3.76072	−	1.00768i	0.190922	−	0.0511574i
$389$	−10.9179	+	6.30348i	−0.553562	+	0.319599i	−0.750557	−	0.660805i	$-0.770215\pi$
$389$	−10.9179	+	6.30348i	−0.553562	+	0.319599i	0.196996	+	0.980404i	$0.436882\pi$
$390$	−0.234693	+	0.172869i	−0.0118841	+	0.00875355i
$391$			17.8892i			0.904695i
$392$		0			0
$393$	−0.216484	−	0.374962i	−0.0109202	−	0.0189143i
$394$	−14.9441	+	8.62799i	−0.752874	+	0.434672i
$395$	−0.117217	−	0.0314083i	−0.00589784	−	0.00158032i
$396$	8.23491	+	8.23491i	0.413820	+	0.413820i
$397$	0.580104	−	2.16498i	0.0291146	−	0.108657i	−0.949839	−	0.312738i	$-0.898754\pi$
$397$	0.580104	−	2.16498i	0.0291146	−	0.108657i	0.978954	+	0.204081i	$0.0654205\pi$
$398$	5.20339	+	5.20339i	0.260822	+	0.260822i
$399$		0			0
$400$	−5.79914	+	3.34813i	−0.289957	+	0.167407i
$401$	25.4962	−	25.4962i	1.27322	−	1.27322i	0.328828	−	0.944390i	$-0.393346\pi$
$401$	25.4962	−	25.4962i	1.27322	−	1.27322i	0.944390	−	0.328828i	$-0.106654\pi$
$402$	−8.19784	−	14.1991i	−0.408871	−	0.708185i
$403$	9.73251	+	1.47635i	0.484811	+	0.0735423i
$404$	6.06920	+	3.50405i	0.301954	+	0.174333i
$405$	−0.604362	−	0.161938i	−0.0300310	−	0.00804678i
$406$		0			0
$407$	−5.45612	−	3.15009i	−0.270450	−	0.156144i
$408$	−47.2817	+	12.6691i	−2.34080	+	0.627214i
$409$	6.52622	−	6.52622i	0.322701	−	0.322701i	−0.527102	−	0.849802i	$-0.676721\pi$
$409$	6.52622	−	6.52622i	0.322701	−	0.322701i	0.849802	+	0.527102i	$0.176721\pi$
$410$	−0.00356936	+	0.00356936i	−0.000176278	+	0.000176278i
$411$	−51.5780	+	13.8203i	−2.54415	+	0.681704i
$412$	−15.4280	−	8.90737i	−0.760084	−	0.438834i
$413$		0			0
$414$	12.7411	+	3.41398i	0.626192	+	0.167788i
$415$	0.224472	+	0.129599i	0.0110189	+	0.00636176i
$416$	−16.3812	−	13.0889i	−0.803155	−	0.641738i
$417$	24.1962	+	41.9090i	1.18489	+	2.05229i
$418$	2.04271	−	2.04271i	0.0999123	−	0.0999123i
$419$	−15.4156	+	8.90022i	−0.753103	+	0.434804i	−0.826814	−	0.562475i	$-0.809849\pi$
$419$	−15.4156	+	8.90022i	−0.753103	+	0.434804i	0.0737108	+	0.997280i	$0.476516\pi$
$420$		0			0
$421$	−5.59661	−	5.59661i	−0.272762	−	0.272762i	0.557449	−	0.830211i	$-0.311780\pi$
$421$	−5.59661	−	5.59661i	−0.272762	−	0.272762i	−0.830211	+	0.557449i	$0.811780\pi$
$422$	3.71664	−	13.8707i	0.180923	−	0.675215i
$423$	−27.0291	−	27.0291i	−1.31420	−	1.31420i
$424$	−1.39595	−	0.374042i	−0.0677931	−	0.0181651i
$425$	−27.7135	+	16.0004i	−1.34430	+	0.776132i
$426$	−11.1183	−	19.2574i	−0.538683	−	0.933026i
$427$		0			0
$428$		−	19.8435i		−	0.959172i
$429$	−1.91036	+	12.5936i	−0.0922330	+	0.608025i
$430$	−0.0477325	+	0.0275584i	−0.00230186	+	0.00132898i
$431$	−11.2196	+	3.00628i	−0.540428	+	0.144807i	−0.518699	−	0.854957i	$-0.673584\pi$
$431$	−11.2196	+	3.00628i	−0.540428	+	0.144807i	−0.0217286	+	0.999764i	$0.506917\pi$
$432$		−	15.9273i		−	0.766304i
$433$	14.5052	−	25.1237i	0.697073	−	1.20737i	−0.272403	−	0.962183i	$-0.587819\pi$
$433$	14.5052	−	25.1237i	0.697073	−	1.20737i	0.969477	−	0.245183i	$-0.0788481\pi$
$434$		0			0
$435$	−0.416103	+	0.111495i	−0.0199506	+	0.00534575i
$436$	−19.1187	−	5.12283i	−0.915619	−	0.245339i
$437$	−2.66605	+	9.94983i	−0.127534	+	0.475965i
$438$	−5.94218			−0.283929
$439$	−16.8557			−0.804480			−0.402240	−	0.915534i	$-0.631768\pi$
$439$	−16.8557			−0.804480			−0.402240	+	0.915534i	$0.631768\pi$
$440$	−0.0265394	+	0.0990464i	−0.00126522	+	0.00472185i
$441$		0			0
$442$	−12.5214	−	10.0049i	−0.595583	−	0.475884i
$443$	16.1369	−	27.9499i	0.766685	−	1.32794i	−0.172666	−	0.984980i	$-0.555238\pi$
$443$	16.1369	−	27.9499i	0.766685	−	1.32794i	0.939351	−	0.342957i	$-0.111429\pi$
$444$	6.86455	+	25.6188i	0.325777	+	1.21582i
$445$	0.313301	−	0.542654i	0.0148519	−	0.0257243i
$446$	1.14035	+	1.97515i	0.0539973	+	0.0935261i
$447$	−12.6048	+	12.6048i	−0.596189	+	0.596189i
$448$		0			0
$449$	4.40700	+	16.4471i	0.207979	+	0.776188i	0.988521	+	0.151085i	$0.0482766\pi$
$449$	4.40700	+	16.4471i	0.207979	+	0.776188i	−0.780542	+	0.625103i	$0.785057\pi$
$450$	6.10703	+	22.7918i	0.287888	+	1.07441i
$451$			0.220586i			0.0103870i
$452$	−4.88400	−	2.81978i	−0.229724	−	0.132631i
$453$	45.8128	+	45.8128i	2.15247	+	2.15247i
$454$	12.7761			0.599610
$455$		0			0
$456$	−28.1859			−1.31992
$457$	−4.03922	−	4.03922i	−0.188947	−	0.188947i	0.606294	−	0.795241i	$-0.292656\pi$
$457$	−4.03922	−	4.03922i	−0.188947	−	0.188947i	−0.795241	+	0.606294i	$0.792656\pi$
$458$	6.59594	+	3.80817i	0.308208	+	0.177944i
$459$		−	76.1150i		−	3.55274i
$460$	−0.0408314	−	0.152385i	−0.00190378	−	0.00710499i
$461$	7.08521	+	26.4424i	0.329991	+	1.23154i	0.909198	+	0.416363i	$0.136695\pi$
$461$	7.08521	+	26.4424i	0.329991	+	1.23154i	−0.579207	+	0.815180i	$0.696638\pi$
$462$		0			0
$463$	−13.6953	+	13.6953i	−0.636477	+	0.636477i	−0.949685	−	0.313208i	$-0.898596\pi$
$463$	−13.6953	+	13.6953i	−0.636477	+	0.636477i	0.313208	+	0.949685i	$0.398596\pi$
$464$	−2.47828	−	4.29250i	−0.115051	−	0.199274i
$465$	−0.158937	+	0.275286i	−0.00737051	+	0.0127661i
$466$	1.55008	+	5.78499i	0.0718062	+	0.267984i
$467$	−8.36822	+	14.4942i	−0.387235	+	0.670711i	−0.992077	−	0.125635i	$-0.959903\pi$
$467$	−8.36822	+	14.4942i	−0.387235	+	0.670711i	0.604841	+	0.796346i	$0.293236\pi$
$468$	29.9560	−	22.0648i	1.38471	−	1.01995i
$469$		0			0
$470$	0.0375852	−	0.140270i	0.00173368	−	0.00647017i
$471$	−28.9975			−1.33613
$472$	−27.5338			−1.26734
$473$	−0.623378	+	2.32648i	−0.0286629	+	0.106972i
$474$	−6.84961	−	1.83535i	−0.314613	−	0.0843003i
$475$	−17.7986	+	4.76912i	−0.816655	+	0.218822i
$476$		0			0
$477$	2.01107	−	3.48328i	0.0920807	−	0.159488i
$478$		−	5.71671i		−	0.261476i
$479$	21.7606	−	5.83074i	0.994267	−	0.266413i	0.275225	−	0.961380i	$-0.411248\pi$
$479$	21.7606	−	5.83074i	0.994267	−	0.266413i	0.719042	+	0.694967i	$0.244581\pi$
$480$	0.586382	−	0.338548i	0.0267645	−	0.0154525i
$481$	−12.5639	+	15.7241i	−0.572864	+	0.716958i
$482$			4.36243i			0.198703i
$483$		0			0
$484$	−7.38154	−	12.7852i	−0.335525	−	0.581146i
$485$	−0.0826252	+	0.0477037i	−0.00375182	+	0.00216611i
$486$	−11.3933	−	3.05282i	−0.516810	−	0.138479i
$487$	−4.93594	−	4.93594i	−0.223669	−	0.223669i	0.586373	−	0.810042i	$-0.300555\pi$
$487$	−4.93594	−	4.93594i	−0.223669	−	0.223669i	−0.810042	+	0.586373i	$0.800555\pi$
$488$	0.867535	−	3.23768i	0.0392714	−	0.146563i
$489$	−9.11734	−	9.11734i	−0.412300	−	0.412300i
$490$		0			0
$491$	−2.12954	+	1.22949i	−0.0961048	+	0.0554861i	−0.547282	−	0.836948i	$-0.684338\pi$
$491$	−2.12954	+	1.22949i	−0.0961048	+	0.0554861i	0.451177	+	0.892434i	$0.351004\pi$
$492$	0.656637	−	0.656637i	0.0296035	−	0.0296035i
$493$	−11.8434	−	20.5134i	−0.533401	−	0.923877i
$494$	−5.47328	−	7.43073i	−0.246255	−	0.334324i
$495$	−0.247149	−	0.142692i	−0.0111085	−	0.00641351i
$496$	−3.53281	−	0.946613i	−0.158628	−	0.0425042i
$497$		0			0
$498$	13.1171	+	7.57314i	0.587790	+	0.339360i
$499$	18.0154	−	4.82722i	0.806481	−	0.216096i	0.168054	−	0.985778i	$-0.446252\pi$
$499$	18.0154	−	4.82722i	0.806481	−	0.216096i	0.638428	+	0.769682i	$0.279585\pi$
$500$	0.399156	−	0.399156i	0.0178508	−	0.0178508i
$501$	35.5721	−	35.5721i	1.58925	−	1.58925i
$502$	−7.02164	+	1.88144i	−0.313391	+	0.0839729i
$503$	−29.6335	−	17.1089i	−1.32129	−	0.762849i	−0.337359	−	0.941376i	$-0.609533\pi$
$503$	−29.6335	−	17.1089i	−1.32129	−	0.762849i	−0.983935	+	0.178527i	$0.942867\pi$
$504$		0			0
$505$	−0.165882	−	0.0444479i	−0.00738165	−	0.00197791i
$506$	1.89645	+	1.09491i	0.0843074	+	0.0486749i
$507$	38.8622	+	12.0679i	1.72593	+	0.535956i
$508$	−2.17062	−	3.75963i	−0.0963057	−	0.166806i
$509$	−6.06864	+	6.06864i	−0.268988	+	0.268988i	−0.828692	−	0.559705i	$-0.810915\pi$
$509$	−6.06864	+	6.06864i	−0.268988	+	0.268988i	0.559705	+	0.828692i	$0.310915\pi$
$510$	0.448217	−	0.258778i	0.0198474	−	0.0114589i
$511$		0			0
$512$	10.1365	+	10.1365i	0.447973	+	0.447973i
$513$	11.3435	−	42.3346i	0.500829	−	1.86912i
$514$	2.62689	+	2.62689i	0.115867	+	0.115867i
$515$	0.421674	+	0.112987i	0.0185812	+	0.00497882i
$516$	8.78109	−	5.06976i	0.386566	−	0.223184i
$517$	−3.17294	−	5.49570i	−0.139546	−	0.241701i
$518$		0			0
$519$			65.9422i			2.89454i
$520$	0.300127	+	0.131282i	0.0131614	+	0.00575710i
$521$	19.8996	−	11.4890i	0.871817	−	0.503344i	0.00386537	−	0.999993i	$-0.498770\pi$
$521$	19.8996	−	11.4890i	0.871817	−	0.503344i	0.867952	+	0.496649i	$0.165436\pi$
$522$	−16.8704	+	4.52040i	−0.738396	+	0.197853i
$523$		−	29.8987i		−	1.30738i	−0.756762	−	0.653690i	$-0.773220\pi$
$523$		−	29.8987i		−	1.30738i	0.756762	−	0.653690i	$-0.226780\pi$
$524$	−0.104975	+	0.181821i	−0.00458583	+	0.00794289i
$525$		0			0
$526$	−4.13326	+	1.10750i	−0.180218	+	0.0482894i
$527$	−16.8829	−	4.52376i	−0.735431	−	0.197058i
$528$	1.22489	−	4.57136i	0.0533066	−	0.198943i
$529$	15.1916			0.660506
$530$	0.0152803			0.000663734
$531$	19.8333	−	74.0189i	0.860692	−	3.21215i
$532$		0			0
$533$	0.696731	+	0.105689i	0.0301788	+	0.00457790i
$534$	18.3078	−	31.7101i	0.792257	−	1.37223i
$535$	0.125854	+	0.469695i	0.00544116	+	0.0203067i
$536$	−9.21305	+	15.9575i	−0.397943	+	0.689258i
$537$	−14.2704	−	24.7171i	−0.615814	−	1.06662i
$538$	−10.0902	+	10.0902i	−0.435018	+	0.435018i
$539$		0			0
$540$	0.173730	+	0.648368i	0.00747614	+	0.0279013i
$541$	3.31979	+	12.3896i	0.142729	+	0.532672i	0.999846	+	0.0175501i	$0.00558667\pi$
$541$	3.31979	+	12.3896i	0.142729	+	0.532672i	−0.857117	+	0.515122i	$0.827747\pi$
$542$			7.05554i			0.303062i
$543$	−42.6060	−	24.5986i	−1.82840	−	1.05563i
$544$	26.3260	+	26.3260i	1.12872	+	1.12872i
$545$	0.485030			0.0207764
$546$		0			0
$547$	33.5639			1.43509			0.717543	−	0.696514i	$-0.245267\pi$
$547$	33.5639			1.43509			0.717543	+	0.696514i	$0.245267\pi$
$548$	18.3089	+	18.3089i	0.782119	+	0.782119i
$549$	8.07894	+	4.66438i	0.344801	+	0.199071i
$550$			3.91724i			0.167032i
$551$	−3.53008	−	13.1744i	−0.150387	−	0.561250i
$552$	−5.52988	−	20.6378i	−0.235367	−	0.878403i
$553$		0			0
$554$	−10.0286	+	10.0286i	−0.426076	+	0.426076i
$555$	−0.324967	−	0.562860i	−0.0137941	−	0.0238921i
$556$	11.7329	−	20.3219i	0.497585	−	0.861842i
$557$	6.14230	+	22.9234i	0.260257	+	0.971294i	0.965090	+	0.261920i	$0.0843556\pi$
$557$	6.14230	+	22.9234i	0.260257	+	0.971294i	−0.704832	+	0.709374i	$0.748978\pi$
$558$	−6.44388	+	11.1611i	−0.272791	+	0.472488i
$559$	7.04961	+	3.08365i	0.298167	+	0.130425i
$560$		0			0
$561$	5.85363	−	21.8460i	0.247140	−	0.922340i
$562$	−12.8072			−0.540239
$563$	−24.7532			−1.04322			−0.521611	−	0.853183i	$-0.674669\pi$
$563$	−24.7532			−1.04322			−0.521611	+	0.853183i	$0.674669\pi$
$564$	−6.91435	+	25.8047i	−0.291147	+	1.08657i
$565$	0.133488	+	0.0357681i	0.00561589	+	0.00150477i
$566$	1.35193	−	0.362247i	0.0568257	−	0.0152264i
$567$		0			0
$568$	−12.4952	+	21.6423i	−0.524285	+	0.908089i
$569$			38.5792i			1.61733i	0.588273	+	0.808663i	$0.299808\pi$
$569$			38.5792i			1.61733i	−0.588273	+	0.808663i	$0.700192\pi$
$570$	0.287861	−	0.0771321i	0.0120572	−	0.00323071i
$571$	−25.3815	+	14.6540i	−1.06218	+	0.613252i	−0.926035	−	0.377437i	$-0.876806\pi$
$571$	−25.3815	+	14.6540i	−1.06218	+	0.613252i	−0.136148	+	0.990689i	$0.543472\pi$
$572$	5.75174	−	2.25112i	0.240492	−	0.0941240i
$573$			54.1752i			2.26320i
$574$		0			0
$575$	−6.98393	−	12.0965i	−0.291250	−	0.504460i
$576$	8.00008	−	4.61885i	0.333337	−	0.192452i
$577$	38.5387	+	10.3264i	1.60439	+	0.429894i	0.946364	−	0.323103i	$-0.104726\pi$
$577$	38.5387	+	10.3264i	1.60439	+	0.429894i	0.658024	+	0.752997i	$0.271393\pi$
$578$	11.7762	+	11.7762i	0.489824	+	0.489824i
$579$	10.1987	−	38.0619i	0.423842	−	1.58180i
$580$	0.147707	+	0.147707i	0.00613318	+	0.00613318i
$581$		0			0
$582$	−4.82822	+	2.78757i	−0.200136	+	0.115549i
$583$	0.472160	−	0.472160i	0.0195549	−	0.0195549i
$584$	3.33903	+	5.78337i	0.138170	+	0.239317i
$585$	−0.569115	+	0.712265i	−0.0235300	+	0.0294485i
$586$	7.13990	+	4.12222i	0.294946	+	0.170287i
$587$	−31.6109	−	8.47012i	−1.30472	−	0.349599i	−0.461489	−	0.887146i	$-0.652684\pi$
$587$	−31.6109	−	8.47012i	−1.30472	−	0.349599i	−0.843234	+	0.537547i	$0.819351\pi$
$588$		0			0
$589$	−8.71597	−	5.03217i	−0.359135	−	0.207347i
$590$	0.281201	−	0.0753476i	0.0115769	−	0.00310201i
$591$	−55.0064	+	55.0064i	−2.26266	+	2.26266i
$592$	5.28782	−	5.28782i	0.217328	−	0.217328i
$593$	21.0102	−	5.62965i	0.862784	−	0.231182i	0.199819	−	0.979833i	$-0.435965\pi$
$593$	21.0102	−	5.62965i	0.862784	−	0.231182i	0.662965	+	0.748651i	$0.269298\pi$
$594$	−8.06901	−	4.65865i	−0.331076	−	0.191147i
$595$		0			0
$596$	8.34937	+	2.23721i	0.342003	+	0.0916396i
$597$	28.7290	+	16.5867i	1.17580	+	0.678848i
$598$	4.36698	−	5.46542i	0.178579	−	0.223498i
$599$	−15.0536	−	26.0736i	−0.615073	−	1.06534i	−0.990372	−	0.138434i	$-0.955793\pi$
$599$	−15.0536	−	26.0736i	−0.615073	−	1.06534i	0.375299	−	0.926904i	$-0.377540\pi$
$600$	27.0255	−	27.0255i	1.10331	−	1.10331i
$601$	16.4105	−	9.47460i	0.669398	−	0.386477i	−0.126450	−	0.991973i	$-0.540358\pi$
$601$	16.4105	−	9.47460i	0.669398	−	0.386477i	0.795849	+	0.605496i	$0.207025\pi$
$602$		0			0
$603$	−36.2620	−	36.2620i	−1.47670	−	1.47670i
$604$	8.13122	−	30.3461i	0.330855	−	1.23477i
$605$	0.255809	+	0.255809i	0.0104001	+	0.0104001i
$606$	−9.69334	−	2.59732i	−0.393765	−	0.105509i
$607$	18.4475	−	10.6507i	0.748763	−	0.432298i	−0.0764838	−	0.997071i	$-0.524369\pi$
$607$	18.4475	−	10.6507i	0.748763	−	0.432298i	0.825247	+	0.564772i	$0.191036\pi$
$608$	10.7189	+	18.5657i	0.434709	+	0.752939i
$609$		0			0
$610$			0.0354404i			0.00143494i
$611$	−18.8787	+	7.38875i	−0.763750	+	0.298917i
$612$	−57.2099	+	33.0301i	−2.31257	+	1.33516i
$613$	24.1774	−	6.47832i	0.976518	−	0.261657i	0.264940	−	0.964265i	$-0.414648\pi$
$613$	24.1774	−	6.47832i	0.976518	−	0.261657i	0.711577	+	0.702608i	$0.247981\pi$
$614$		−	1.43930i		−	0.0580853i
$615$	−0.0113780	+	0.0197072i	−0.000458804	+	0.000794671i
$616$		0			0
$617$	−29.1852	+	7.82015i	−1.17495	+	0.314827i	−0.792922	−	0.609323i	$-0.791441\pi$
$617$	−29.1852	+	7.82015i	−1.17495	+	0.314827i	−0.382029	+	0.924150i	$0.624775\pi$
$618$	24.6406	+	6.60244i	0.991191	+	0.265589i
$619$	−10.9864	+	41.0017i	−0.441580	+	1.64800i	0.283232	+	0.959052i	$0.408593\pi$
$619$	−10.9864	+	41.0017i	−0.441580	+	1.64800i	−0.724812	+	0.688947i	$0.758073\pi$
$620$	0.154139			0.00619035
$621$	33.2231			1.33320
$622$	−0.493808	+	1.84292i	−0.0197999	+	0.0738942i
$623$		0			0
$624$	−13.8520	−	6.05915i	−0.554523	−	0.242560i
$625$	12.4896	−	21.6327i	0.499585	−	0.865307i
$626$	−1.36423	−	5.09138i	−0.0545257	−	0.203493i
$627$	6.51149	−	11.2782i	0.260044	−	0.450409i
$628$	7.03053	+	12.1772i	0.280549	+	0.485924i
$629$	25.2700	−	25.2700i	1.00758	−	1.00758i
$630$		0			0
$631$	−9.55956	−	35.6768i	−0.380560	−	1.42027i	−0.845048	−	0.534690i	$-0.820428\pi$
$631$	−9.55956	−	35.6768i	−0.380560	−	1.42027i	0.464488	−	0.885579i	$-0.346238\pi$
$632$	2.06264	+	7.69786i	0.0820473	+	0.306205i
$633$		−	64.7356i		−	2.57301i
$634$	5.99744	+	3.46263i	0.238189	+	0.137518i
$635$	0.0752234	+	0.0752234i	0.00298515	+	0.00298515i
$636$	−2.81104			−0.111465
$637$		0			0
$638$	−2.89952			−0.114793
$639$	−49.1802	−	49.1802i	−1.94554	−	1.94554i
$640$	−0.344266	−	0.198762i	−0.0136083	−	0.00785676i
$641$			8.28328i			0.327170i	0.986529	+	0.163585i	$0.0523058\pi$
$641$			8.28328i			0.327170i	−0.986529	+	0.163585i	$0.947694\pi$
$642$	7.35433	+	27.4467i	0.290252	+	1.08324i
$643$	−8.56893	−	31.9797i	−0.337926	−	1.26116i	−0.900663	−	0.434519i	$-0.856918\pi$
$643$	−8.56893	−	31.9797i	−0.337926	−	1.26116i	0.562737	−	0.826636i	$-0.309748\pi$
$644$		0			0
$645$	−0.175694	+	0.175694i	−0.00691794	+	0.00691794i
$646$	8.19329	+	14.1912i	0.322361	+	0.558345i
$647$	6.58281	−	11.4018i	0.258797	−	0.448250i	−0.707123	−	0.707091i	$-0.750007\pi$
$647$	6.58281	−	11.4018i	0.258797	−	0.448250i	0.965920	+	0.258841i	$0.0833406\pi$
$648$	10.6348	+	39.6895i	0.417773	+	1.55915i
$649$	6.36085	−	11.0173i	0.249685	−	0.432467i
$650$	12.3728	+	1.87686i	0.485301	+	0.0736166i
$651$		0			0
$652$	−1.61822	+	6.03927i	−0.0633743	+	0.236516i
$653$	−47.3352			−1.85237			−0.926184	−	0.377071i	$-0.876931\pi$
$653$	−47.3352			−1.85237			−0.926184	+	0.377071i	$0.876931\pi$
$654$	28.3428			1.10829
$655$	0.00133157	−	0.00496949i	5.20288e−5	−	0.000194174i
$656$	−0.252907	−	0.0677662i	−0.00987435	−	0.00264582i
$657$	−17.9526	+	4.81038i	−0.700397	+	0.187671i
$658$		0			0
$659$	−2.76562	+	4.79019i	−0.107733	+	0.186599i	−0.914852	−	0.403790i	$-0.867693\pi$
$659$	−2.76562	+	4.79019i	−0.107733	+	0.186599i	0.807118	+	0.590390i	$0.201026\pi$
$660$			0.199451i			0.00776363i
$661$	−17.5567	+	4.70431i	−0.682877	+	0.182976i	−0.583549	−	0.812078i	$-0.698336\pi$
$661$	−17.5567	+	4.70431i	−0.682877	+	0.182976i	−0.0993289	+	0.995055i	$0.531670\pi$
$662$	−10.1706	+	5.87198i	−0.395290	+	0.228221i
$663$	−66.1971	−	28.9560i	−2.57088	−	1.12456i
$664$		−	17.0220i		−	0.660581i
$665$		0			0
$666$	−13.1754	−	22.8204i	−0.510536	−	0.884274i
$667$	8.95380	−	5.16948i	0.346692	−	0.200163i
$668$	−23.5628	−	6.31362i	−0.911671	−	0.244281i
$669$	7.27015	+	7.27015i	0.281080	+	0.281080i
$670$	0.0504240	−	0.188185i	0.00194805	−	0.00727022i
$671$	1.09510	+	1.09510i	0.0422760	+	0.0422760i
$672$		0			0
$673$	−3.86827	+	2.23334i	−0.149111	+	0.0860891i	−0.572699	−	0.819766i	$-0.694104\pi$
$673$	−3.86827	+	2.23334i	−0.149111	+	0.0860891i	0.423588	+	0.905855i	$0.360770\pi$
$674$	3.88924	−	3.88924i	0.149808	−	0.149808i
$675$	29.7153	+	51.4683i	1.14374	+	1.98102i
$676$	−4.35444	−	19.2457i	−0.167479	−	0.740221i
$677$	20.1346	+	11.6247i	0.773836	+	0.446775i	0.834241	−	0.551399i	$-0.185906\pi$
$677$	20.1346	+	11.6247i	0.773836	+	0.446775i	−0.0604051	+	0.998174i	$0.519239\pi$
$678$	7.80041	+	2.09011i	0.299573	+	0.0802703i
$679$		0			0
$680$	−0.503723	−	0.290825i	−0.0193169	−	0.0111526i
$681$	55.6326	−	14.9067i	2.13185	−	0.571226i
$682$	−1.51289	+	1.51289i	−0.0579317	+	0.0579317i
$683$	5.61092	−	5.61092i	0.214696	−	0.214696i	−0.591563	−	0.806259i	$-0.701489\pi$
$683$	5.61092	−	5.61092i	0.214696	−	0.214696i	0.806259	+	0.591563i	$0.201489\pi$
$684$	−36.7422	+	9.84506i	−1.40487	+	0.376435i
$685$	−0.549494	−	0.317250i	−0.0209951	−	0.0121215i
$686$		0			0
$687$	33.1649	+	8.88651i	1.26532	+	0.339041i
$688$	−2.47585	−	1.42943i	−0.0943910	−	0.0544967i
$689$	−1.26511	−	1.71756i	−0.0481970	−	0.0654340i
$690$	0.112953	+	0.195640i	0.00430004	+	0.00744789i
$691$	8.15837	−	8.15837i	0.310359	−	0.310359i	−0.534690	−	0.845049i	$-0.679571\pi$
$691$	8.15837	−	8.15837i	0.310359	−	0.310359i	0.845049	+	0.534690i	$0.179571\pi$
$692$	27.6918	−	15.9879i	1.05268	−	0.607768i
$693$		0			0
$694$	11.9498	+	11.9498i	0.453609	+	0.453609i
$695$	−0.148828	+	0.555434i	−0.00564537	+	0.0210688i
$696$	20.0042	+	20.0042i	0.758257	+	0.758257i
$697$	−1.20861	−	0.323847i	−0.0457795	−	0.0122666i
$698$	−9.77014	+	5.64079i	−0.369805	+	0.213507i
$699$	13.4995	+	23.3818i	0.510597	+	0.884380i
$700$		0			0
$701$		−	11.0088i		−	0.415797i	−0.978150	−	0.207898i	$-0.933338\pi$
$701$		−	11.0088i		−	0.415797i	0.978150	−	0.207898i	$-0.0666624\pi$
$702$	−18.5807	+	23.2543i	−0.701282	+	0.877676i
$703$	17.8210	−	10.2889i	0.672131	−	0.388055i
$704$	1.48134	−	0.396923i	0.0558299	−	0.0149596i
$705$		−	0.654650i		−	0.0246555i
$706$	−5.68552	+	9.84760i	−0.213977	+	0.370619i
$707$		0			0
$708$	−51.7311	+	13.8613i	−1.94417	+	0.520939i
$709$	28.7098	+	7.69277i	1.07822	+	0.288908i	0.753866	−	0.657028i	$-0.228187\pi$
$709$	28.7098	+	7.69277i	1.07822	+	0.288908i	0.324353	+	0.945936i	$0.394853\pi$
$710$	0.0683873	−	0.255225i	0.00256653	−	0.00957842i
$711$	−22.1799			−0.831811
$712$	−41.1501			−1.54216
$713$	1.97456	−	7.36914i	0.0739477	−	0.275977i
$714$		0			0
$715$	−0.121866	+	0.0897635i	−0.00455754	+	0.00335697i
$716$	−6.91982	+	11.9855i	−0.258606	+	0.447918i
$717$	−6.67008	−	24.8931i	−0.249099	−	0.929649i
$718$	−2.39907	+	4.15530i	−0.0895323	+	0.155075i
$719$	12.1922	+	21.1175i	0.454693	+	0.787552i	0.998671	−	0.0515483i	$-0.0164156\pi$
$719$	12.1922	+	21.1175i	0.454693	+	0.787552i	−0.543977	+	0.839100i	$0.683082\pi$
$720$	0.239526	−	0.239526i	0.00892660	−	0.00892660i
$721$		0			0
$722$	−0.972454	−	3.62925i	−0.0361910	−	0.135067i
$723$	5.08994	+	18.9959i	0.189297	+	0.706466i
$724$			23.8560i			0.886602i
$725$	16.0168	+	9.24733i	0.594851	+	0.343437i
$726$	14.9483	+	14.9483i	0.554782	+	0.554782i
$727$	−20.3008			−0.752915			−0.376458	−	0.926434i	$-0.622858\pi$
$727$	−20.3008			−0.752915			−0.376458	+	0.926434i	$0.622858\pi$
$728$		0			0
$729$	−2.70851			−0.100315
$730$	−0.0499278	−	0.0499278i	−0.00184791	−	0.00184791i
$731$	−11.8318	−	6.83111i	−0.437616	−	0.252658i
$732$		−	6.51977i		−	0.240978i
$733$	4.25111	+	15.8654i	0.157019	+	0.586001i	0.998924	+	0.0463761i	$0.0147673\pi$
$733$	4.25111	+	15.8654i	0.157019	+	0.586001i	−0.841906	+	0.539625i	$0.818566\pi$
$734$	2.56946	+	9.58936i	0.0948406	+	0.353950i
$735$		0			0
$736$	−11.4909	+	11.4909i	−0.423560	+	0.423560i
$737$	−4.25679	−	7.37298i	−0.156801	−	0.271587i
$738$	−0.461305	+	0.799003i	−0.0169809	+	0.0294117i
$739$	−11.0872	−	41.3778i	−0.407847	−	1.52211i	−0.798743	−	0.601672i	$-0.794501\pi$
$739$	−11.0872	−	41.3778i	−0.407847	−	1.52211i	0.390896	−	0.920435i	$-0.372165\pi$
$740$	−0.157579	+	0.272934i	−0.00579270	+	0.0100333i
$741$	−32.5030	−	25.9706i	−1.19403	−	0.954054i
$742$		0			0
$743$	12.7481	−	47.5766i	0.467683	−	1.74542i	−0.180155	−	0.983638i	$-0.557660\pi$
$743$	12.7481	−	47.5766i	0.467683	−	1.74542i	0.647838	−	0.761778i	$-0.275673\pi$
$744$	20.8753			0.765325
$745$	−0.211819			−0.00776043
$746$	4.07326	−	15.2016i	0.149133	−	0.556570i
$747$	45.7601	+	12.2614i	1.67427	+	0.448621i
$748$	−10.5933	+	2.83846i	−0.387328	+	0.103784i
$749$		0			0
$750$	−0.404163	+	0.700031i	−0.0147580	+	0.0255615i
$751$		−	23.0508i		−	0.841135i	−0.907261	−	0.420567i	$-0.861831\pi$
$751$		−	23.0508i		−	0.841135i	0.907261	−	0.420567i	$-0.138169\pi$
$752$	7.27571	−	1.94952i	0.265318	−	0.0710917i
$753$	−28.3801	+	16.3853i	−1.03423	+	0.597112i
$754$	−1.38925	+	9.15829i	−0.0505934	+	0.333525i
$755$			0.769863i			0.0280182i
$756$		0			0
$757$	24.1858	+	41.8911i	0.879049	+	1.52256i	0.852387	+	0.522912i	$0.175154\pi$
$757$	24.1858	+	41.8911i	0.879049	+	1.52256i	0.0266620	+	0.999645i	$0.491512\pi$
$758$	−7.83357	+	4.52272i	−0.284528	+	0.164272i
$759$	9.53548	+	2.55502i	0.346116	+	0.0927415i
$760$	−0.236825	−	0.236825i	−0.00859055	−	0.00859055i
$761$	7.56647	−	28.2385i	0.274284	−	1.02364i	−0.682035	−	0.731320i	$-0.738905\pi$
$761$	7.56647	−	28.2385i	0.274284	−	1.02364i	0.956319	−	0.292324i	$-0.0944285\pi$
$762$	4.39570	+	4.39570i	0.159239	+	0.159239i
$763$		0			0
$764$	22.7504	−	13.1349i	0.823079	−	0.475205i
$765$	1.14467	−	1.14467i	0.0413856	−	0.0413856i
$766$	−0.797333	−	1.38102i	−0.0288088	−	0.0498983i
$767$	−31.7510	−	25.3698i	−1.14646	−	0.916049i
$768$	−27.4844	−	15.8681i	−0.991759	−	0.572592i
$769$	−1.87337	−	0.501968i	−0.0675554	−	0.0181014i	0.224883	−	0.974386i	$-0.427800\pi$
$769$	−1.87337	−	0.501968i	−0.0675554	−	0.0181014i	−0.292438	+	0.956284i	$0.594467\pi$
$770$		0			0
$771$	14.5036	+	8.37365i	0.522334	+	0.301570i
$772$	−18.4564	+	4.94539i	−0.664262	+	0.177988i
$773$	3.60192	−	3.60192i	0.129552	−	0.129552i	−0.639358	−	0.768910i	$-0.720800\pi$
$773$	3.60192	−	3.60192i	0.129552	−	0.129552i	0.768910	+	0.639358i	$0.220800\pi$
$774$	−7.12328	+	7.12328i	−0.256041	+	0.256041i
$775$	13.1822	−	3.53215i	0.473517	−	0.126879i
$776$	5.42614	+	3.13278i	0.194787	+	0.112460i
$777$		0			0
$778$	−8.45552	−	2.26565i	−0.303145	−	0.0812275i
$779$	−0.623959	−	0.360243i	−0.0223557	−	0.0129070i
$780$	0.629977	+	0.0955629i	0.0225568	+	0.00342170i
$781$	−5.77326	−	9.99958i	−0.206583	−	0.357813i
$782$	−8.78338	+	8.78338i	−0.314093	+	0.314093i
$783$	−38.0967	+	21.9951i	−1.36146	+	0.786041i
$784$		0			0
$785$	−0.243645	−	0.243645i	−0.00869606	−	0.00869606i
$786$	0.0778106	−	0.290393i	0.00277541	−	0.0103580i
$787$	−21.6820	−	21.6820i	−0.772878	−	0.772878i	0.205730	−	0.978609i	$-0.434043\pi$
$787$	−21.6820	−	21.6820i	−0.772878	−	0.772878i	−0.978609	+	0.205730i	$0.934043\pi$
$788$	36.4359	+	9.76297i	1.29798	+	0.347791i
$789$	−16.7058	+	9.64510i	−0.594743	+	0.343375i
$790$	−0.0421312	−	0.0729734i	−0.00149896	−	0.00259628i
$791$		0			0
$792$			18.7416i			0.665954i
$793$	3.98363	−	2.93424i	0.141463	−	0.104198i
$794$	1.34780	−	0.778154i	0.0478317	−	0.0276157i
$795$	0.0665372	−	0.0178286i	0.00235983	−	0.000632315i
$796$		−	16.0860i		−	0.570152i
$797$	15.8566	−	27.4644i	0.561669	−	0.972839i	−0.435682	−	0.900101i	$-0.643493\pi$
$797$	15.8566	−	27.4644i	0.561669	−	0.972839i	0.997351	−	0.0727386i	$-0.0231739\pi$
$798$		0			0
$799$	34.7698	−	9.31655i	1.23007	−	0.329596i
$800$	−28.0791	−	7.52376i	−0.992745	−	0.266005i
$801$	29.6415	−	110.624i	1.04733	−	3.90869i
$802$	25.0366			0.884075
$803$	−3.08553			−0.108886
$804$	−9.27623	+	34.6194i	−0.327147	+	1.22093i
$805$		0			0
$806$	4.05368	+	5.50342i	0.142785	+	0.193850i
$807$	−32.1641	+	55.7099i	−1.13223	+	1.96108i
$808$	2.91897	+	10.8938i	0.102689	+	0.383241i
$809$	−4.55711	+	7.89315i	−0.160219	+	0.277508i	−0.934947	−	0.354787i	$-0.884554\pi$
$809$	−4.55711	+	7.89315i	−0.160219	+	0.277508i	0.774728	+	0.632295i	$0.217887\pi$
$810$	−0.217225	−	0.376245i	−0.00763251	−	0.0132199i
$811$	21.0935	−	21.0935i	0.740695	−	0.740695i	−0.232017	−	0.972712i	$-0.574533\pi$
$811$	21.0935	−	21.0935i	0.740695	−	0.740695i	0.972712	+	0.232017i	$0.0745325\pi$
$812$		0			0
$813$	8.23219	+	30.7229i	0.288715	+	1.07750i
$814$	−1.13223	−	4.22555i	−0.0396847	−	0.148105i
$815$		−	0.153213i		−	0.00536681i
$816$	23.2487	+	13.4226i	0.813867	+	0.469886i
$817$	−5.56273	−	5.56273i	−0.194615	−	0.194615i
$818$	6.40859			0.224071
$819$		0			0
$820$	0.0110345			0.000385341
$821$	−27.6740	−	27.6740i	−0.965831	−	0.965831i	0.0336043	−	0.999435i	$-0.489301\pi$
$821$	−27.6740	−	27.6740i	−0.965831	−	0.965831i	−0.999435	+	0.0336043i	$0.989301\pi$
$822$	−32.1098	−	18.5386i	−1.11996	−	0.646607i
$823$			36.5955i			1.27564i	0.770187	+	0.637819i	$0.220163\pi$
$823$			36.5955i			1.27564i	−0.770187	+	0.637819i	$0.779837\pi$
$824$	−7.42007	−	27.6921i	−0.258491	−	0.964700i
$825$	4.57051	+	17.0574i	0.159125	+	0.593861i
$826$		0			0
$827$	−4.61851	+	4.61851i	−0.160601	+	0.160601i	−0.782833	−	0.622232i	$-0.786226\pi$
$827$	−4.61851	+	4.61851i	−0.160601	+	0.160601i	0.622232	+	0.782833i	$0.286226\pi$
$828$	−14.4172	−	24.9713i	−0.501031	−	0.867812i
$829$	−5.83825	+	10.1121i	−0.202771	+	0.351209i	−0.949420	−	0.314009i	$-0.898328\pi$
$829$	−5.83825	+	10.1121i	−0.202771	+	0.351209i	0.746649	+	0.665218i	$0.231661\pi$
$830$	0.0465815	+	0.173845i	0.00161687	+	0.00603424i
$831$	−31.9680	+	55.3703i	−1.10896	+	1.92077i
$832$	−0.543949	−	4.86905i	−0.0188580	−	0.168804i
$833$		0			0
$834$	−8.69680	+	32.4569i	−0.301146	+	1.12389i
$835$	0.597773			0.0206868
$836$	−6.31492			−0.218406
$837$	−8.40135	+	31.3543i	−0.290393	+	1.08376i
$838$	−11.9388	−	3.19899i	−0.412419	−	0.110507i
$839$	−22.6006	+	6.05583i	−0.780261	+	0.209070i	−0.626900	−	0.779100i	$-0.715676\pi$
$839$	−22.6006	+	6.05583i	−0.780261	+	0.209070i	−0.153361	+	0.988170i	$0.549010\pi$
$840$		0			0
$841$	7.65516	−	13.2591i	0.263971	−	0.457211i
$842$		−	5.49574i		−	0.189396i
$843$	−55.7682	+	14.9430i	−1.92076	+	0.514666i
$844$	−27.1851	+	15.6953i	−0.935751	+	0.540256i
$845$	0.225133	+	0.427929i	0.00774480	+	0.0147212i
$846$		−	26.5419i		−	0.912530i
$847$		0			0
$848$	0.396290	+	0.686394i	0.0136086	+	0.0235709i
$849$	5.46422	−	3.15477i	0.187531	−	0.108271i
$850$	−21.4630	−	5.75099i	−0.736174	−	0.197257i
$851$	11.0300	+	11.0300i	0.378102	+	0.378102i
$852$	−12.5808	+	46.9524i	−0.431013	+	1.60856i
$853$	34.6514	+	34.6514i	1.18644	+	1.18644i	0.978044	+	0.208398i	$0.0668248\pi$
$853$	34.6514	+	34.6514i	1.18644	+	1.18644i	0.208398	+	0.978044i	$0.433175\pi$
$854$		0			0
$855$	0.807248	−	0.466065i	0.0276073	−	0.0159391i
$856$	22.5806	−	22.5806i	0.771790	−	0.771790i
$857$	1.19667	+	2.07269i	0.0408775	+	0.0708019i	0.885740	−	0.464181i	$-0.153651\pi$
$857$	1.19667	+	2.07269i	0.0408775	+	0.0708019i	−0.844863	+	0.534983i	$0.820318\pi$
$858$	−7.12128	+	5.24535i	−0.243116	+	0.179073i
$859$	−1.71704	−	0.991332i	−0.0585846	−	0.0338238i	0.470422	−	0.882442i	$-0.344102\pi$
$859$	−1.71704	−	0.991332i	−0.0585846	−	0.0338238i	−0.529006	+	0.848618i	$0.677435\pi$
$860$	0.116379	+	0.0311836i	0.00396848	+	0.00106335i
$861$		0			0
$862$	−6.98473	−	4.03263i	−0.237901	−	0.137352i
$863$	−13.7577	+	3.68636i	−0.468317	+	0.125485i	−0.485257	−	0.874371i	$-0.661274\pi$
$863$	−13.7577	+	3.68636i	−0.468317	+	0.125485i	0.0169406	+	0.999856i	$0.494607\pi$
$864$	48.8915	−	48.8915i	1.66332	−	1.66332i
$865$	−0.554064	+	0.554064i	−0.0188387	+	0.0188387i
$866$	19.4573	−	5.21356i	0.661186	−	0.177164i
$867$	65.0186	+	37.5385i	2.20815	+	1.27488i
$868$		0			0
$869$	−3.55672	−	0.953020i	−0.120653	−	0.0323290i
$870$	−0.259044	−	0.149559i	−0.00878243	−	0.00507054i
$871$	−25.3275	+	9.91268i	−0.858189	+	0.335878i
$872$	−15.9264	−	27.5853i	−0.539335	−	0.934156i
$873$	−12.3304	+	12.3304i	−0.417322	+	0.417322i
$874$	−6.19425	+	3.57625i	−0.209524	+	0.120969i
$875$		0			0
$876$	9.18495	+	9.18495i	0.310331	+	0.310331i
$877$	−12.7259	+	47.4938i	−0.429724	+	1.60375i	0.323660	+	0.946173i	$0.395086\pi$
$877$	−12.7259	+	47.4938i	−0.429724	+	1.60375i	−0.753385	+	0.657580i	$0.771580\pi$
$878$	−8.27596	−	8.27596i	−0.279300	−	0.279300i
$879$	35.8999	+	9.61936i	1.21087	+	0.324453i
$880$	0.0487017	−	0.0281179i	0.00164173	−	0.000947855i
$881$	−13.0843	−	22.6627i	−0.440821	−	0.763525i	0.556930	−	0.830560i	$-0.311979\pi$
$881$	−13.0843	−	22.6627i	−0.440821	−	0.763525i	−0.997751	+	0.0670352i	$0.978646\pi$
$882$		0			0
$883$		−	4.56808i		−	0.153728i	−0.997042	−	0.0768640i	$-0.975509\pi$
$883$		−	4.56808i		−	0.153728i	0.997042	−	0.0768640i	$-0.0244907\pi$
$884$	3.88987	+	34.8194i	0.130830	+	1.17110i
$885$	1.13656	−	0.656193i	0.0382051	−	0.0220577i
$886$	21.6461	−	5.80004i	0.727214	−	0.194856i
$887$			1.20579i			0.0404865i	0.999795	+	0.0202432i	$0.00644406\pi$
$887$			1.20579i			0.0404865i	−0.999795	+	0.0202432i	$0.993556\pi$
$888$	−21.3412	+	36.9640i	−0.716163	+	1.24043i
$889$		0			0
$890$	0.420264	−	0.112609i	0.0140873	−	0.00377467i
$891$	−18.3381	−	4.91369i	−0.614351	−	0.164615i
$892$	1.29036	−	4.81570i	0.0432045	−	0.161242i
$893$	20.7272			0.693609
$894$	−12.3777			−0.413971
$895$	0.0877758	−	0.327584i	0.00293402	−	0.0109499i
$896$		0			0
$897$	12.6389	−	28.8941i	0.422000	−	0.964745i
$898$	−5.91156	+	10.2391i	−0.197271	+	0.341684i
$899$	2.61448	+	9.75739i	0.0871979	+	0.325427i
$900$	25.7899	−	44.6694i	0.859664	−	1.48898i
$901$	1.89383	+	3.28020i	0.0630925	+	0.109279i
$902$	−0.108305	+	0.108305i	−0.00360616	+	0.00360616i
$903$		0			0
$904$	−2.34895	−	8.76641i	−0.0781250	−	0.291566i
$905$	−0.151303	−	0.564672i	−0.00502949	−	0.0187703i
$906$			44.9871i			1.49460i
$907$	−30.1251	−	17.3927i	−1.00029	−	0.577515i	−0.0919531	−	0.995763i	$-0.529311\pi$
$907$	−30.1251	−	17.3927i	−1.00029	−	0.577515i	−0.908333	+	0.418248i	$0.862644\pi$
$908$	−19.7482	−	19.7482i	−0.655368	−	0.655368i
$909$	−31.3882			−1.04108
$910$		0			0
$911$	10.2796			0.340579			0.170290	−	0.985394i	$-0.445530\pi$
$911$	10.2796			0.340579			0.170290	+	0.985394i	$0.445530\pi$
$912$	10.9304	+	10.9304i	0.361940	+	0.361940i
$913$	6.81114	+	3.93241i	0.225416	+	0.130144i
$914$		−	3.96642i		−	0.131197i
$915$	0.0413507	+	0.154323i	0.00136701	+	0.00510176i
$916$	−4.30912	−	16.0818i	−0.142377	−	0.531359i
$917$		0			0
$918$	37.3716	−	37.3716i	1.23345	−	1.23345i
$919$	10.5049	+	18.1950i	0.346525	+	0.600198i	0.985630	−	0.168921i	$-0.0540284\pi$
$919$	10.5049	+	18.1950i	0.346525	+	0.600198i	−0.639105	+	0.769120i	$0.720695\pi$
$920$	0.126941	−	0.219868i	0.00418511	−	0.00724883i
$921$	−1.67933	−	6.26733i	−0.0553357	−	0.206516i
$922$	−9.50413	+	16.4616i	−0.313002	+	0.542135i
$923$	−34.3503	+	13.4440i	−1.13065	+	0.442516i
$924$		0			0
$925$	−7.22196	+	26.9527i	−0.237457	+	0.886200i
$926$	−13.4485			−0.441945
$927$	79.7894			2.62063
$928$	5.56906	−	20.7840i	0.182813	−	0.682268i
$929$	1.15836	+	0.310383i	0.0380047	+	0.0101833i	0.277771	−	0.960647i	$-0.410404\pi$
$929$	1.15836	+	0.310383i	0.0380047	+	0.0101833i	−0.239767	+	0.970831i	$0.577071\pi$
$930$	−0.213198	+	0.0571263i	−0.00699105	+	0.00187325i
$931$		0			0
$932$	6.54598	−	11.3380i	0.214421	−	0.371387i
$933$			8.60103i			0.281585i
$934$	−11.2252	+	3.00778i	−0.367299	+	0.0984174i
$935$	0.232740	−	0.134373i	0.00761141	−	0.00439445i
$936$	59.1963	+	8.97965i	1.93489	+	0.293509i
$937$			21.5733i			0.704768i	0.935855	+	0.352384i	$0.114629\pi$
$937$			21.5733i			0.704768i	−0.935855	+	0.352384i	$0.885371\pi$
$938$		0			0
$939$	−11.8809	−	20.5784i	−0.387720	−	0.671550i
$940$	−0.274914	+	0.158722i	−0.00896672	+	0.00517694i
$941$	35.7815	+	9.58762i	1.16644	+	0.312548i	0.789537	−	0.613704i	$-0.210321\pi$
$941$	35.7815	+	9.58762i	1.16644	+	0.312548i	0.376907	+	0.926251i	$0.376988\pi$
$942$	−14.2374	−	14.2374i	−0.463881	−	0.463881i
$943$	0.141355	−	0.527543i	0.00460314	−	0.0171791i
$944$	10.6775	+	10.6775i	0.347523	+	0.347523i
$945$		0			0
$946$	−1.44834	+	0.836202i	−0.0470897	+	0.0271873i
$947$	26.3284	−	26.3284i	0.855558	−	0.855558i	−0.135253	−	0.990811i	$-0.543185\pi$
$947$	26.3284	−	26.3284i	0.855558	−	0.855558i	0.990811	+	0.135253i	$0.0431848\pi$
$948$	7.75065	+	13.4245i	0.251729	+	0.436008i
$949$	−1.47837	+	9.74579i	−0.0479898	+	0.316362i
$950$	−11.0805	−	6.39732i	−0.359498	−	0.207556i
$951$	30.1556	+	8.08016i	0.977862	+	0.262017i
$952$		0			0
$953$	−37.3599	−	21.5697i	−1.21020	−	0.698712i	−0.247401	−	0.968913i	$-0.579576\pi$
$953$	−37.3599	−	21.5697i	−1.21020	−	0.698712i	−0.962804	+	0.270201i	$0.912910\pi$
$954$	2.69766	−	0.722837i	0.0873401	−	0.0234027i
$955$	−0.455194	+	0.455194i	−0.0147297	+	0.0147297i
$956$	−8.83644	+	8.83644i	−0.285791	+	0.285791i
$957$	−12.6258	+	3.38307i	−0.408134	+	0.109359i
$958$	13.5470	+	7.82138i	0.437684	+	0.252697i
$959$		0			0
$960$	0.152817	+	0.0409471i	0.00493213	+	0.00132156i
$961$	−20.3915	−	11.7730i	−0.657790	−	0.379775i
$962$	−13.8891	+	1.55163i	−0.447802	+	0.0500265i
$963$	44.4380	+	76.9688i	1.43199	+	2.48029i
$964$	6.74309	−	6.74309i	0.217180	−	0.217180i
$965$	0.405498	−	0.234115i	0.0130535	−	0.00753641i
$966$		0			0
$967$	−6.54638	−	6.54638i	−0.210517	−	0.210517i	0.593970	−	0.804487i	$-0.297560\pi$
$967$	−6.54638	−	6.54638i	−0.210517	−	0.210517i	−0.804487	+	0.593970i	$0.797560\pi$
$968$	6.14902	−	22.9485i	0.197637	−	0.737591i
$969$	52.2350	+	52.2350i	1.67803	+	1.67803i
$970$	−0.0639900	−	0.0171461i	−0.00205459	−	0.000550527i
$971$	32.3192	−	18.6595i	1.03717	−	0.598812i	0.118142	−	0.992997i	$-0.462306\pi$
$971$	32.3192	−	18.6595i	1.03717	−	0.598812i	0.919031	+	0.394184i	$0.128973\pi$
$972$	12.8920	+	22.3296i	0.413512	+	0.716224i
$973$		0			0
$974$		−	4.84698i		−	0.155307i
$975$	56.0664	−	6.26349i	1.79556	−	0.200592i
$976$	−1.59199	+	0.919134i	−0.0509583	+	0.0294208i
$977$	36.2796	−	9.72109i	1.16069	−	0.311005i	0.373447	−	0.927651i	$-0.378176\pi$
$977$	36.2796	−	9.72109i	1.16069	−	0.311005i	0.787240	+	0.616646i	$0.211509\pi$
$978$		−	8.95301i		−	0.286286i
$979$	9.50648	−	16.4657i	0.303829	−	0.526246i
$980$		0			0
$981$	85.6296	−	22.9444i	2.73394	−	0.732558i
$982$	−1.64925	−	0.441914i	−0.0526295	−	0.0141020i
$983$	−9.02589	+	33.6851i	−0.287881	+	1.07439i	0.658827	+	0.752295i	$0.271053\pi$
$983$	−9.02589	+	33.6851i	−0.287881	+	1.07439i	−0.946708	+	0.322093i	$0.895614\pi$
$984$	1.49442			0.0476404
$985$	−0.924357			−0.0294525
$986$	4.25686	−	15.8868i	0.135566	−	0.505939i
$987$		0			0
$988$	−3.02566	+	19.9460i	−0.0962591	+	0.634566i
$989$	2.98168	−	5.16442i	0.0948119	−	0.164219i
$990$	−0.0512874	−	0.191407i	−0.00163002	−	0.00608332i
$991$	19.0679	−	33.0266i	0.605712	−	1.04912i	−0.386227	−	0.922404i	$-0.626222\pi$
$991$	19.0679	−	33.0266i	0.605712	−	1.04912i	0.991939	−	0.126720i	$-0.0404450\pi$
$992$	−7.93875	−	13.7503i	−0.252055	−	0.436573i
$993$	−37.4359	+	37.4359i	−1.18799	+	1.18799i
$994$		0			0
$995$	0.102023	+	0.380755i	0.00323434	+	0.0120707i
$996$	−8.56935	−	31.9813i	−0.271530	−	1.01337i
$997$		−	18.6171i		−	0.589610i	−0.955557	−	0.294805i	$-0.904745\pi$
$997$		−	18.6171i		−	0.589610i	0.955557	−	0.294805i	$-0.0952546\pi$
$998$	11.2155	+	6.47526i	0.355020	+	0.204971i
$999$	−46.9303	−	46.9303i	−1.48481	−	1.48481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.362.5		28
7.2	even	3		637.2.bd.a.440.5		28
7.3	odd	6		637.2.x.a.570.3		28
7.4	even	3		91.2.w.a.24.3	yes	28
7.5	odd	6		637.2.bd.b.440.5		28
7.6	odd	2		91.2.ba.a.89.5	yes	28
13.6	odd	12		637.2.x.a.19.3		28
21.11	odd	6		819.2.gh.b.388.5		28
21.20	even	2		819.2.et.b.271.3		28
91.6	even	12		91.2.w.a.19.3	✓	28
91.19	even	12		637.2.bd.a.97.5		28
91.32	odd	12		91.2.ba.a.45.5	yes	28
91.45	even	12	inner	637.2.bb.a.227.5		28
91.58	odd	12		637.2.bd.b.97.5		28
273.32	even	12		819.2.et.b.136.3		28
273.188	odd	12		819.2.gh.b.19.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.3	✓	28	91.6	even	12
91.2.w.a.24.3	yes	28	7.4	even	3
91.2.ba.a.45.5	yes	28	91.32	odd	12
91.2.ba.a.89.5	yes	28	7.6	odd	2
637.2.x.a.19.3		28	13.6	odd	12
637.2.x.a.570.3		28	7.3	odd	6
637.2.bb.a.227.5		28	91.45	even	12	inner
637.2.bb.a.362.5		28	1.1	even	1	trivial
637.2.bd.a.97.5		28	91.19	even	12
637.2.bd.a.440.5		28	7.2	even	3
637.2.bd.b.97.5		28	91.58	odd	12
637.2.bd.b.440.5		28	7.5	odd	6
819.2.et.b.136.3		28	273.32	even	12
819.2.et.b.271.3		28	21.20	even	2
819.2.gh.b.19.5		28	273.188	odd	12
819.2.gh.b.388.5		28	21.11	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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.490988 + 0.490988i) q^{2} +(2.71085 + 1.56511i) q^{3} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(0.562545 + 2.09944i) q^{6} +(1.72723 - 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +O(q^{10})\)	\(q+(0.490988 + 0.490988i) q^{2} +(2.71085 + 1.56511i) q^{3} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(0.562545 + 2.09944i) q^{6} +(1.72723 - 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +(-0.0129135 + 0.0223668i) q^{10} +(0.292106 + 1.09015i) q^{11} +(2.37562 - 4.11469i) q^{12} +(3.58326 - 0.400306i) q^{13} +(-0.0301340 + 0.112462i) q^{15} -1.33962 q^{16} -6.40192 q^{17} +(-1.22174 + 4.55961i) q^{18} +(-3.56070 - 0.954087i) q^{19} +(0.0545333 - 0.0146122i) q^{20} +(-0.391832 + 0.678673i) q^{22} -2.79435i q^{23} +(7.38555 - 1.97895i) q^{24} +(4.32893 - 2.49931i) q^{25} +(1.95588 + 1.56279i) q^{26} +11.8894i q^{27} +(1.84998 + 3.20426i) q^{29} +(-0.0700128 + 0.0404219i) q^{30} +(2.63716 + 0.706626i) q^{31} +(-4.11220 - 4.11220i) q^{32} +(-0.914355 + 3.41242i) q^{33} +(-3.14327 - 3.14327i) q^{34} +(8.93636 - 5.15941i) q^{36} +(-3.94724 + 3.94724i) q^{37} +(-1.27982 - 2.21671i) q^{38} +(10.3402 + 4.52302i) q^{39} +(0.0786831 + 0.0454277i) q^{40} +(0.188789 + 0.0505859i) q^{41} +(1.84817 + 1.06704i) q^{43} +(1.65470 - 0.443376i) q^{44} +(-0.178801 + 0.178801i) q^{45} +(1.37199 - 1.37199i) q^{46} +(-5.43116 + 1.45527i) q^{47} +(-3.63152 - 2.09666i) q^{48} +(3.35258 + 0.898322i) q^{50} +(-17.3546 - 10.0197i) q^{51} +(-0.607609 - 5.43889i) q^{52} +(-0.295822 - 0.512378i) q^{53} +(-5.83755 + 5.83755i) q^{54} +(-0.0363547 + 0.0209894i) q^{55} +(-8.15927 - 8.15927i) q^{57} +(-0.664935 + 2.48157i) q^{58} +(-7.97051 - 7.97051i) q^{59} +(0.170701 + 0.0457393i) q^{60} +(1.18838 - 0.686113i) q^{61} +(0.947871 + 1.64176i) q^{62} -1.35883i q^{64} +(0.0488775 + 0.124885i) q^{65} +(-2.12439 + 1.22652i) q^{66} +(-7.28639 + 1.95238i) q^{67} +9.71723i q^{68} +(4.37346 - 7.57505i) q^{69} +(-9.88214 + 2.64791i) q^{71} +(16.0401 + 4.29793i) q^{72} +(-0.707590 + 2.64076i) q^{73} -3.87610 q^{74} +15.6468 q^{75} +(-1.44817 + 5.40465i) q^{76} +(2.85616 + 7.29767i) q^{78} +(-1.63129 + 2.82548i) q^{79} +(-0.0128963 - 0.0481297i) q^{80} +(-8.41080 + 14.5679i) q^{81} +(0.0678562 + 0.117530i) q^{82} +(4.92754 - 4.92754i) q^{83} +(-0.0616301 - 0.230007i) q^{85} +(0.383525 + 1.43133i) q^{86} +11.5817i q^{87} +(2.38748 + 1.37841i) q^{88} +(-11.9122 - 11.9122i) q^{89} -0.175578 q^{90} -4.24143 q^{92} +(6.04300 + 6.04300i) q^{93} +(-3.38116 - 1.95211i) q^{94} -0.137113i q^{95} +(-4.71151 - 17.5836i) q^{96} +(0.663884 + 2.47765i) q^{97} +(-5.42534 + 5.42534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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