LMFDB - Embedded newform 637.2.bd.b.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, 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			97.5
Character	$\chi$	$=$	637.97
Dual form			637.2.bd.b.440.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.179714 + 0.670702i) q^{2} +(2.71085 + 1.56511i) q^{3} +(1.31451 - 0.758931i) q^{4} +(-0.0263009 - 0.0263009i) q^{5} +(-0.562545 + 2.09944i) q^{6} +(1.72723 + 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +O(q^{10})$	\(q+(0.179714 + 0.670702i) q^{2} +(2.71085 + 1.56511i) q^{3} +(1.31451 - 0.758931i) q^{4} +(-0.0263009 - 0.0263009i) 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} +(-1.09015 + 0.292106i) q^{11} +4.75124 q^{12} +(-3.58326 - 0.400306i) q^{13} +(-0.0301340 - 0.112462i) q^{15} +(0.669812 - 1.16015i) q^{16} +(-3.20096 - 5.54423i) q^{17} +(-3.33787 + 3.33787i) q^{18} +(-0.954087 + 3.56070i) q^{19} +(-0.0545333 - 0.0146122i) q^{20} +(-0.391832 - 0.678673i) q^{22} +(-2.41997 - 1.39717i) q^{23} +(1.97895 + 7.38555i) q^{24} -4.99862i q^{25} +(-0.375476 - 2.47524i) q^{26} +11.8894i q^{27} +(1.84998 - 3.20426i) q^{29} +(0.0700128 - 0.0404219i) q^{30} +(1.93054 + 1.93054i) q^{31} +(5.61737 + 1.50517i) q^{32} +(-3.41242 - 0.914355i) q^{33} +(3.14327 - 3.14327i) q^{34} +(8.93636 + 5.15941i) q^{36} +(5.39204 - 1.44479i) q^{37} -2.55963 q^{38} +(-9.08715 - 6.69336i) q^{39} -0.0908555i q^{40} +(-0.188789 + 0.0505859i) q^{41} +(1.84817 - 1.06704i) q^{43} +(-1.21133 + 1.21133i) q^{44} +(0.0654456 - 0.244246i) q^{45} +(0.502183 - 1.87417i) q^{46} +(-3.97588 + 3.97588i) q^{47} +(3.63152 - 2.09666i) q^{48} +(3.35258 - 0.898322i) q^{50} -20.0394i q^{51} +(-5.01402 + 2.19324i) q^{52} +0.591643 q^{53} +(-7.97425 + 2.13669i) q^{54} +(0.0363547 + 0.0209894i) q^{55} +(-8.15927 + 8.15927i) q^{57} +(2.48157 + 0.664935i) q^{58} +(-10.8879 - 2.91741i) q^{59} +(-0.124962 - 0.124962i) q^{60} +(1.18838 - 0.686113i) q^{61} +(-0.947871 + 1.64176i) q^{62} +1.35883i q^{64} +(0.0837147 + 0.104772i) q^{65} -2.45304i q^{66} +(1.95238 + 7.28639i) q^{67} +(-8.41537 - 4.85861i) q^{68} +(-4.37346 - 7.57505i) q^{69} +(-9.88214 - 2.64791i) q^{71} +(-4.29793 + 16.0401i) q^{72} +(1.93317 - 1.93317i) q^{73} +(1.93805 + 3.35680i) q^{74} +(7.82338 - 13.5505i) q^{75} +(1.44817 + 5.40465i) q^{76} +(2.85616 - 7.29767i) q^{78} +3.26258 q^{79} +(-0.0481297 + 0.0128963i) 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} +(1.04781 + 1.04781i) q^{86} +(10.0300 - 5.79083i) q^{87} +(-2.38748 - 1.37841i) q^{88} +(4.36016 + 16.2723i) q^{89} +0.175578 q^{90} -4.24143 q^{92} +(2.21189 + 8.25489i) q^{93} +(-3.38116 - 1.95211i) q^{94} +(0.118743 - 0.0685564i) q^{95} +(12.8721 + 12.8721i) q^{96} +(-0.663884 + 2.47765i) q^{97} +(-5.42534 - 5.42534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.179714	+	0.670702i	0.127077	+	0.474258i	0.999905	−	0.0137696i	$-0.00438313\pi$
$2$	0.179714	+	0.670702i	0.127077	+	0.474258i	−0.872828	+	0.488028i	$0.837716\pi$
$3$	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	$0.307569\pi$
$4$	1.31451	−	0.758931i	0.657253	−	0.379465i
$5$	−0.0263009	−	0.0263009i	−0.0117621	−	0.0117621i	0.701201	−	0.712963i	$-0.252647\pi$
$5$	−0.0263009	−	0.0263009i	−0.0117621	−	0.0117621i	−0.712963	+	0.701201i	$0.752647\pi$
$6$	−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
$11$	−1.09015	+	0.292106i	−0.328694	+	0.0880732i	−0.419392	−	0.907805i	$-0.637757\pi$
$11$	−1.09015	+	0.292106i	−0.328694	+	0.0880732i	0.0906984	+	0.995878i	$0.471090\pi$
$12$	4.75124			1.37156
$13$	−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
$16$	0.669812	−	1.16015i	0.167453	−	0.290037i
$17$	−3.20096	−	5.54423i	−0.776347	−	1.34467i	−0.934034	−	0.357184i	$-0.883737\pi$
$17$	−3.20096	−	5.54423i	−0.776347	−	1.34467i	0.157687	−	0.987489i	$-0.449596\pi$
$18$	−3.33787	+	3.33787i	−0.786743	+	0.786743i
$19$	−0.954087	+	3.56070i	−0.218883	+	0.816881i	0.765881	+	0.642982i	$0.222303\pi$
$19$	−0.954087	+	3.56070i	−0.218883	+	0.816881i	−0.984764	+	0.173899i	$0.944363\pi$
$20$	−0.0545333	−	0.0146122i	−0.0121940	−	0.00326738i
$21$		0			0
$22$	−0.391832	−	0.678673i	−0.0835389	−	0.144694i
$23$	−2.41997	−	1.39717i	−0.504599	−	0.291331i	0.226011	−	0.974125i	$-0.427431\pi$
$23$	−2.41997	−	1.39717i	−0.504599	−	0.291331i	−0.730611	+	0.682794i	$0.760765\pi$
$24$	1.97895	+	7.38555i	0.403952	+	1.50757i
$25$		−	4.99862i		−	0.999723i
$26$	−0.375476	−	2.47524i	−0.0736370	−	0.485435i
$27$			11.8894i			2.28811i
$28$		0			0
$29$	1.84998	−	3.20426i	0.343532	−	0.595015i	−0.641554	−	0.767078i	$-0.721710\pi$
$29$	1.84998	−	3.20426i	0.343532	−	0.595015i	0.985086	+	0.172063i	$0.0550432\pi$
$30$	0.0700128	−	0.0404219i	0.0127825	−	0.00738000i
$31$	1.93054	+	1.93054i	0.346735	+	0.346735i	0.858892	−	0.512157i	$-0.171153\pi$
$31$	1.93054	+	1.93054i	0.346735	+	0.346735i	−0.512157	+	0.858892i	$0.671153\pi$
$32$	5.61737	+	1.50517i	0.993019	+	0.266079i
$33$	−3.41242	−	0.914355i	−0.594026	−	0.159169i
$34$	3.14327	−	3.14327i	0.539066	−	0.539066i
$35$		0			0
$36$	8.93636	+	5.15941i	1.48939	+	0.859902i
$37$	5.39204	−	1.44479i	0.886445	−	0.237522i	0.213259	−	0.976996i	$-0.431592\pi$
$37$	5.39204	−	1.44479i	0.886445	−	0.237522i	0.673186	+	0.739473i	$0.264925\pi$
$38$	−2.55963			−0.415228
$39$	−9.08715	−	6.69336i	−1.45511	−	1.07180i
$40$		−	0.0908555i		−	0.0143655i
$41$	−0.188789	+	0.0505859i	−0.0294839	+	0.00790020i	−0.273531	−	0.961863i	$-0.588192\pi$
$41$	−0.188789	+	0.0505859i	−0.0294839	+	0.00790020i	0.244047	+	0.969763i	$0.421525\pi$
$42$		0			0
$43$	1.84817	−	1.06704i	0.281843	−	0.162722i	−0.352414	−	0.935844i	$-0.614639\pi$
$43$	1.84817	−	1.06704i	0.281843	−	0.162722i	0.634258	+	0.773122i	$0.281306\pi$
$44$	−1.21133	+	1.21133i	−0.182614	+	0.182614i
$45$	0.0654456	−	0.244246i	0.00975605	−	0.0364101i
$46$	0.502183	−	1.87417i	0.0740429	−	0.276332i
$47$	−3.97588	+	3.97588i	−0.579942	+	0.579942i	−0.934887	−	0.354945i	$-0.884500\pi$
$47$	−3.97588	+	3.97588i	−0.579942	+	0.579942i	0.354945	+	0.934887i	$0.384500\pi$
$48$	3.63152	−	2.09666i	0.524164	−	0.302627i
$49$		0			0
$50$	3.35258	−	0.898322i	0.474127	−	0.127042i
$51$		−	20.0394i		−	2.80608i
$52$	−5.01402	+	2.19324i	−0.695320	+	0.304148i
$53$	0.591643			0.0812684			0.0406342	−	0.999174i	$-0.487062\pi$
$53$	0.591643			0.0812684			0.0406342	+	0.999174i	$0.487062\pi$
$54$	−7.97425	+	2.13669i	−1.08516	+	0.290767i
$55$	0.0363547	+	0.0209894i	0.00490207	+	0.00283021i
$56$		0			0
$57$	−8.15927	+	8.15927i	−1.08072	+	1.08072i
$58$	2.48157	+	0.664935i	0.325846	+	0.0873102i
$59$	−10.8879	−	2.91741i	−1.41749	−	0.379814i	−0.532895	−	0.846181i	$-0.678896\pi$
$59$	−10.8879	−	2.91741i	−1.41749	−	0.379814i	−0.884591	+	0.466367i	$0.845563\pi$
$60$	−0.124962	−	0.124962i	−0.0161325	−	0.0161325i
$61$	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
$65$	0.0837147	+	0.104772i	0.0103835	+	0.0129953i
$66$		−	2.45304i		−	0.301948i
$67$	1.95238	+	7.28639i	0.238522	+	0.890174i	0.976530	+	0.215383i	$0.0690999\pi$
$67$	1.95238	+	7.28639i	0.238522	+	0.890174i	−0.738008	+	0.674792i	$0.764233\pi$
$68$	−8.41537	−	4.85861i	−1.02051	−	0.589194i
$69$	−4.37346	−	7.57505i	−0.526502	−	0.911928i
$70$		0			0
$71$	−9.88214	−	2.64791i	−1.17279	−	0.314249i	−0.380729	−	0.924686i	$-0.624327\pi$
$71$	−9.88214	−	2.64791i	−1.17279	−	0.314249i	−0.792065	+	0.610437i	$0.790994\pi$
$72$	−4.29793	+	16.0401i	−0.506516	+	1.89034i
$73$	1.93317	−	1.93317i	0.226261	−	0.226261i	−0.584868	−	0.811129i	$-0.698854\pi$
$73$	1.93317	−	1.93317i	0.226261	−	0.226261i	0.811129	+	0.584868i	$0.198854\pi$
$74$	1.93805	+	3.35680i	0.225294	+	0.390220i
$75$	7.82338	−	13.5505i	0.903366	−	1.56468i
$76$	1.44817	+	5.40465i	0.166117	+	0.619956i
$77$		0			0
$78$	2.85616	−	7.29767i	0.323397	−	0.826298i
$79$	3.26258			0.367069			0.183535	−	0.983013i	$-0.441246\pi$
$79$	3.26258			0.367069			0.183535	+	0.983013i	$0.441246\pi$
$80$	−0.0481297	+	0.0128963i	−0.00538106	+	0.00144185i
$81$	−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	$-0.374920\pi$
$83$	−4.92754	−	4.92754i	−0.540868	−	0.540868i	−0.923783	+	0.382915i	$0.874920\pi$
$84$		0			0
$85$	−0.0616301	+	0.230007i	−0.00668472	+	0.0249477i
$86$	1.04781	+	1.04781i	0.112988	+	0.112988i
$87$	10.0300	−	5.79083i	1.07533	−	0.620843i
$88$	−2.38748	−	1.37841i	−0.254506	−	0.146939i
$89$	4.36016	+	16.2723i	0.462176	+	1.72486i	0.666087	+	0.745874i	$0.267968\pi$
$89$	4.36016	+	16.2723i	0.462176	+	1.72486i	−0.203911	+	0.978989i	$0.565365\pi$
$90$	0.175578			0.0185076
$91$		0			0
$92$	−4.24143			−0.442199
$93$	2.21189	+	8.25489i	0.229363	+	0.855993i
$94$	−3.38116	−	1.95211i	−0.348740	−	0.201345i
$95$	0.118743	−	0.0685564i	0.0121828	−	0.00703374i
$96$	12.8721	+	12.8721i	1.31375	+	1.31375i
$97$	−0.663884	+	2.47765i	−0.0674072	+	0.251567i	−0.991405	−	0.130832i	$-0.958235\pi$
$97$	−0.663884	+	2.47765i	−0.0674072	+	0.251567i	0.923997	+	0.382399i	$0.124902\pi$
$98$		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	−0.728013	−	0.685564i	$-0.759556\pi$
$101$	2.30855	−	3.99852i	0.229709	−	0.397868i	0.957722	+	0.287696i	$0.0928892\pi$
$102$	13.4405	−	3.60137i	1.33081	−	0.356588i
$103$	11.7367			1.15645			0.578227	−	0.815876i	$-0.303745\pi$
$103$	11.7367			1.15645			0.578227	+	0.815876i	$0.303745\pi$
$104$	−5.49769	−	6.88053i	−0.539093	−	0.674691i
$105$		0			0
$106$	0.106327	+	0.396817i	0.0103274	+	0.0385422i
$107$	−6.53667	+	11.3218i	−0.631923	+	1.09452i	0.355235	+	0.934777i	$0.384401\pi$
$107$	−6.53667	+	11.3218i	−0.631923	+	1.09452i	−0.987158	+	0.159746i	$0.948932\pi$
$108$	9.02322	+	15.6287i	0.868260	+	1.50387i
$109$	9.22077	−	9.22077i	0.883189	−	0.883189i	−0.110668	−	0.993857i	$-0.535299\pi$
$109$	9.22077	−	9.22077i	0.883189	−	0.883189i	0.993857	+	0.110668i	$0.0352990\pi$
$110$	−0.00754419	+	0.0281553i	−0.000719310	+	0.00268450i
$111$	16.8782	+	4.52251i	1.60201	+	0.429258i
$112$		0			0
$113$	1.85773	+	3.21769i	0.174761	+	0.302694i	0.940078	−	0.340958i	$-0.110751\pi$
$113$	1.85773	+	3.21769i	0.174761	+	0.302694i	−0.765318	+	0.643653i	$0.777418\pi$
$114$	−6.93878	−	4.00611i	−0.649876	−	0.375206i
$115$	0.0269006	+	0.100395i	0.00250850	+	0.00936184i
$116$		−	5.61602i		−	0.521434i
$117$	−9.82319	−	22.4570i	−0.908154	−	2.07615i
$118$		−	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
$122$	0.673747	+	0.673747i	0.0609982	+	0.0609982i
$123$	−0.590952	−	0.158345i	−0.0532843	−	0.0142775i
$124$	4.00285	+	1.07256i	0.359466	+	0.0963187i
$125$	−0.262973	+	0.262973i	−0.0235210	+	0.0235210i
$126$		0			0
$127$	2.47692	+	1.43005i	0.219791	+	0.126897i	0.605854	−	0.795576i	$-0.292832\pi$
$127$	2.47692	+	1.43005i	0.219791	+	0.126897i	−0.386062	+	0.922473i	$0.626165\pi$
$128$	10.3234	−	2.76614i	0.912465	−	0.244494i
$129$	6.68014			0.588154
$130$	−0.0552258	+	0.0749766i	−0.00484362	+	0.00657588i
$131$			0.138319i			0.0120850i	0.999982	+	0.00604249i	$0.00192340\pi$
$131$			0.138319i			0.0120850i	−0.999982	+	0.00604249i	$0.998077\pi$
$132$	−5.17958	+	1.38786i	−0.450824	+	0.120798i
$133$		0			0
$134$	−4.53613	+	2.61894i	−0.391862	+	0.226242i
$135$	0.312702	−	0.312702i	0.0269131	−	0.0269131i
$136$	4.04736	−	15.1049i	0.347058	−	1.29524i
$137$	−4.41512	+	16.4774i	−0.377209	+	1.40776i	0.472882	+	0.881126i	$0.343214\pi$
$137$	−4.41512	+	16.4774i	−0.377209	+	1.40776i	−0.850090	+	0.526637i	$0.823453\pi$
$138$	4.29463	−	4.29463i	0.365583	−	0.365583i
$139$	−13.3885	+	7.72988i	−1.13560	+	0.655640i	−0.945338	−	0.326093i	$-0.894268\pi$
$139$	−13.3885	+	7.72988i	−1.13560	+	0.655640i	−0.190264	+	0.981733i	$0.560934\pi$
$140$		0			0
$141$	−17.0007	+	4.55532i	−1.43172	+	0.383627i
$142$		−	7.10384i		−	0.596141i
$143$	4.02324	−	0.610296i	0.336440	−	0.0510355i
$144$	9.10712			0.758927
$145$	−0.132931	+	0.0356188i	−0.0110393	+	0.00295798i
$146$	1.64400	+	0.949165i	0.136059	+	0.0785534i
$147$		0			0
$148$	5.99137	−	5.99137i	0.492487	−	0.492487i
$149$	5.50075	+	1.47392i	0.450639	+	0.120748i	0.476998	−	0.878904i	$-0.341725\pi$
$149$	5.50075	+	1.47392i	0.450639	+	0.120748i	−0.0263595	+	0.999653i	$0.508391\pi$
$150$	10.4943	+	2.81194i	0.856858	+	0.229594i
$151$	−14.6357	−	14.6357i	−1.19103	−	1.19103i	−0.976778	−	0.214256i	$-0.931267\pi$
$151$	−14.6357	−	14.6357i	−1.19103	−	1.19103i	−0.214256	−	0.976778i	$-0.568733\pi$
$152$	−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
$156$	−17.0249	−	1.90195i	−1.36308	−	0.152278i
$157$		−	9.26373i		−	0.739326i	−0.929166	−	0.369663i	$-0.879473\pi$
$157$		−	9.26373i		−	0.739326i	0.929166	−	0.369663i	$-0.120527\pi$
$158$	0.586332	+	2.18822i	0.0466461	+	0.174086i
$159$	1.60385	+	0.925986i	0.127194	+	0.0734355i
$160$	−0.108155	−	0.187329i	−0.00855037	−	0.0148097i
$161$		0			0
$162$	−11.2823	−	3.02308i	−0.886420	−	0.237516i
$163$	1.06612	−	3.97880i	0.0835047	−	0.311644i	−0.911522	−	0.411251i	$-0.865092\pi$
$163$	1.06612	−	3.97880i	0.0835047	−	0.311644i	0.995027	+	0.0996072i	$0.0317586\pi$
$164$	−0.209773	+	0.209773i	−0.0163806	+	0.0163806i
$165$	0.0657014	+	0.113798i	0.00511485	+	0.00885918i
$166$	2.41936	−	4.19046i	0.187779	−	0.325243i
$167$	−4.15955	−	15.5237i	−0.321876	−	1.20126i	−0.917415	−	0.397931i	$-0.869728\pi$
$167$	−4.15955	−	15.5237i	−0.321876	−	1.20126i	0.595540	−	0.803326i	$-0.296938\pi$
$168$		0			0
$169$	12.6795	+	2.86880i	0.975347	+	0.220677i
$170$	−0.165342			−0.0126811
$171$	−24.2066	+	6.48614i	−1.85112	+	0.496007i
$172$	1.61962	−	2.80526i	0.123495	−	0.213899i
$173$	−10.5332	−	18.2440i	−0.800821	−	1.38706i	−0.919076	−	0.394080i	$-0.871063\pi$
$173$	−10.5332	−	18.2440i	−0.800821	−	1.38706i	0.118255	−	0.992983i	$-0.462270\pi$
$174$	5.68646	+	5.68646i	0.431090	+	0.431090i
$175$		0			0
$176$	−0.391312	+	1.46040i	−0.0294963	+	0.110082i
$177$	−24.9494	−	24.9494i	−1.87531	−	1.87531i
$178$	−10.1303	+	5.84874i	−0.759299	+	0.438381i
$179$	7.89629	+	4.55893i	0.590196	+	0.340750i	0.765175	−	0.643822i	$-0.222652\pi$
$179$	7.89629	+	4.55893i	0.590196	+	0.340750i	−0.174979	+	0.984572i	$0.555986\pi$
$180$	−0.0993373	−	0.370732i	−0.00740417	−	0.0276327i
$181$	15.7169			1.16823			0.584113	−	0.811672i	$-0.301443\pi$
$181$	15.7169			1.16823			0.584113	+	0.811672i	$0.301443\pi$
$182$		0			0
$183$	4.29537			0.317523
$184$	−1.76661	−	6.59308i	−0.130236	−	0.486049i
$185$	−0.179815	−	0.103816i	−0.0132203	−	0.00763272i
$186$	−5.13907	+	2.96704i	−0.376815	+	0.217554i
$187$	5.10904	+	5.10904i	0.373610	+	0.373610i
$188$	−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
$193$	12.1595	−	3.25813i	0.875260	−	0.234525i	0.206899	−	0.978362i	$-0.433663\pi$
$193$	12.1595	−	3.25813i	0.875260	−	0.234525i	0.668361	+	0.743837i	$0.266996\pi$
$194$	−1.78107			−0.127874
$195$	0.0629589	+	0.415042i	0.00450858	+	0.0297218i
$196$		0			0
$197$	−6.43206	−	24.0048i	−0.458265	−	1.71027i	−0.678307	−	0.734778i	$-0.737286\pi$
$197$	−6.43206	−	24.0048i	−0.458265	−	1.71027i	0.220042	−	0.975490i	$-0.429381\pi$
$198$	2.66378	−	4.61380i	0.189306	−	0.327888i
$199$	5.29889	+	9.17795i	0.375629	+	0.650608i	0.990421	−	0.138081i	$-0.0440935\pi$
$199$	5.29889	+	9.17795i	0.375629	+	0.650608i	−0.614792	+	0.788689i	$0.710760\pi$
$200$	8.63375	−	8.63375i	0.610499	−	0.610499i
$201$	−6.11138	+	22.8080i	−0.431064	+	1.60875i
$202$	3.09670	+	0.829758i	0.217883	+	0.0583815i
$203$		0			0
$204$	−15.2085	−	26.3419i	−1.06481	−	1.84430i
$205$	0.00629579	+	0.00363488i	0.000439717	+	0.000253871i
$206$	2.10926	+	7.87186i	0.146959	+	0.548458i
$207$		−	18.9967i		−	1.32036i
$208$	−2.86453	+	3.88898i	−0.198619	+	0.269653i
$209$		−	4.16041i		−	0.287781i
$210$		0			0
$211$	−10.3404	+	17.9102i	−0.711865	+	1.23299i	0.252292	+	0.967651i	$0.418816\pi$
$211$	−10.3404	+	17.9102i	−0.711865	+	1.23299i	−0.964156	+	0.265335i	$0.914518\pi$
$212$	0.777719	−	0.449016i	0.0534139	−	0.0308386i
$213$	−22.6447	−	22.6447i	−1.55159	−	1.55159i
$214$	−8.76832	−	2.34946i	−0.599390	−	0.160606i
$215$	−0.0766728	−	0.0205444i	−0.00522904	−	0.00140112i
$216$	−20.5357	+	20.5357i	−1.39728	+	1.39728i
$217$		0			0
$218$	7.84149	+	4.52729i	0.531093	+	0.306627i
$219$	8.26616	−	2.21491i	0.558575	−	0.149670i
$220$	0.0637180			0.00429587
$221$	9.25049	+	21.1478i	0.622255	+	1.42255i
$222$			12.1330i			0.814316i
$223$	−3.17269	+	0.850119i	−0.212459	+	0.0569282i	−0.363479	−	0.931603i	$-0.618411\pi$
$223$	−3.17269	+	0.850119i	−0.212459	+	0.0569282i	0.151020	+	0.988531i	$0.451744\pi$
$224$		0			0
$225$	29.4292	−	16.9910i	1.96195	−	1.13273i
$226$	−1.82425	+	1.82425i	−0.121347	+	0.121347i
$227$	−4.76219	+	17.7728i	−0.316078	+	1.17962i	0.606904	+	0.794775i	$0.292411\pi$
$227$	−4.76219	+	17.7728i	−0.316078	+	1.17962i	−0.922982	+	0.384844i	$0.874255\pi$
$228$	−4.53309	+	16.9177i	−0.300211	+	1.12040i
$229$	7.75613	−	7.75613i	0.512540	−	0.512540i	−0.402764	−	0.915304i	$-0.631951\pi$
$229$	7.75613	−	7.75613i	0.512540	−	0.512540i	0.915304	+	0.402764i	$0.131951\pi$
$230$	−0.0625004	+	0.0360846i	−0.00412116	+	0.00237935i
$231$		0			0
$232$	8.72982	−	2.33915i	0.573141	−	0.153573i
$233$			8.62527i			0.565060i	0.959258	+	0.282530i	$0.0911737\pi$
$233$			8.62527i			0.565060i	−0.959258	+	0.282530i	$0.908826\pi$
$234$	13.2966	−	10.6243i	0.869227	−	0.694531i
$235$	0.209139			0.0136427
$236$	−16.5263	+	4.42822i	−1.07577	+	0.288253i
$237$	8.84437	+	5.10630i	0.574503	+	0.331690i
$238$		0			0
$239$	−5.82164	+	5.82164i	−0.376571	+	0.376571i	−0.869863	−	0.493293i	$-0.835793\pi$
$239$	−5.82164	+	5.82164i	−0.376571	+	0.376571i	0.493293	+	0.869863i	$0.335793\pi$
$240$	−0.150656	−	0.0403683i	−0.00972483	−	0.00260576i
$241$	6.06856	+	1.62607i	0.390910	+	0.104744i	0.448920	−	0.893572i	$-0.351809\pi$
$241$	6.06856	+	1.62607i	0.390910	+	0.104744i	−0.0580097	+	0.998316i	$0.518475\pi$
$242$	−4.77547	−	4.77547i	−0.306979	−	0.306979i
$243$	−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
$247$	4.84411	−	12.3770i	0.308224	−	0.787529i
$248$			6.66896i			0.423479i
$249$	−5.64568	−	21.0700i	−0.357780	−	1.33525i
$250$	−0.223637	−	0.129117i	−0.0141440	−	0.00816605i
$251$	5.23454	+	9.06650i	0.330402	+	0.572272i	0.982591	−	0.185784i	$-0.0594825\pi$
$251$	5.23454	+	9.06650i	0.330402	+	0.572272i	−0.652189	+	0.758056i	$0.726149\pi$
$252$		0			0
$253$	3.04627	+	0.816245i	0.191517	+	0.0513169i
$254$	−0.514001	+	1.91828i	−0.0322513	+	0.120364i
$255$	−0.527055	+	0.527055i	−0.0330055	+	0.0330055i
$256$	5.06934	+	8.78035i	0.316834	+	0.548772i
$257$	2.67510	−	4.63341i	0.166868	−	0.289024i	−0.770449	−	0.637502i	$-0.779968\pi$
$257$	2.67510	−	4.63341i	0.166868	−	0.289024i	0.937317	+	0.348477i	$0.113301\pi$
$258$	1.20052	+	4.48039i	0.0747409	+	0.278937i
$259$		0			0
$260$	0.189558	+	0.0741892i	0.0117559	+	0.00460102i
$261$	25.1533			1.55695
$262$	−0.0927709	+	0.0248579i	−0.00573140	+	0.00153573i
$263$	−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
$268$	8.09628	+	8.09628i	0.494559	+	0.494559i
$269$	17.7974	−	10.2754i	1.08513	−	0.626500i	0.152854	−	0.988249i	$-0.451154\pi$
$269$	17.7974	−	10.2754i	1.08513	−	0.626500i	0.932275	+	0.361749i	$0.117820\pi$
$270$	0.265927	+	0.153533i	0.0161838	+	0.00934373i
$271$	−2.62991	−	9.81495i	−0.159756	−	0.596216i	−0.998651	−	0.0519233i	$-0.983465\pi$
$271$	−2.62991	−	9.81495i	−0.159756	−	0.596216i	0.838896	−	0.544292i	$-0.183202\pi$
$272$	−8.57617			−0.520007
$273$		0			0
$274$	−11.8449			−0.715578
$275$	1.46012	+	5.44926i	0.0880488	+	0.328603i
$276$	−11.4979	−	6.63830i	−0.692090	−	0.399579i
$277$	−17.6889	+	10.2127i	−1.06283	+	0.613623i	−0.926213	−	0.377002i	$-0.876955\pi$
$277$	−17.6889	+	10.2127i	−1.06283	+	0.613623i	−0.136613	+	0.990624i	$0.543622\pi$
$278$	−7.59056	−	7.59056i	−0.455251	−	0.455251i
$279$	−4.80383	+	17.9281i	−0.287598	+	1.07333i
$280$		0			0
$281$	−13.0423	−	13.0423i	−0.778037	−	0.778037i	0.201460	−	0.979497i	$-0.435431\pi$
$281$	−13.0423	−	13.0423i	−0.778037	−	0.778037i	−0.979497	+	0.201460i	$0.935431\pi$
$282$	−6.11053	−	10.5838i	−0.363877	−	0.630253i
$283$	−1.00784	+	1.74563i	−0.0599100	+	0.103767i	−0.894425	−	0.447218i	$-0.852415\pi$
$283$	−1.00784	+	1.74563i	−0.0599100	+	0.103767i	0.834515	+	0.550986i	$0.185748\pi$
$284$	−14.9997	+	4.01916i	−0.890069	+	0.238493i
$285$	0.429193			0.0254232
$286$	1.13236	+	2.58872i	0.0669578	+	0.153074i
$287$		0			0
$288$	10.2325	+	38.1883i	0.602958	+	2.25027i
$289$	−11.9923	+	20.7713i	−0.705430	+	1.22184i
$290$	−0.0477792	−	0.0827560i	−0.00280569	−	0.00485960i
$291$	−5.67748	+	5.67748i	−0.332819	+	0.332819i
$292$	1.07402	−	4.00831i	0.0628525	−	0.234569i
$293$	−11.4688	−	3.07306i	−0.670016	−	0.179530i	−0.0922540	−	0.995736i	$-0.529407\pi$
$293$	−11.4688	−	3.07306i	−0.670016	−	0.179530i	−0.577762	+	0.816205i	$0.696074\pi$
$294$		0			0
$295$	0.209632	+	0.363093i	0.0122052	+	0.0211401i
$296$	11.8088	+	6.81779i	0.686370	+	0.396276i
$297$	−3.47296	−	12.9613i	−0.201522	−	0.752089i
$298$			3.95425i			0.229063i
$299$	8.11210	+	5.97516i	0.469135	+	0.345553i
$300$		−	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
$304$	3.49188	+	3.49188i	0.200273	+	0.200273i
$305$	−0.0493010	−	0.0132102i	−0.00282297	−	0.000756412i
$306$	29.1903	+	7.82151i	1.66870	+	0.447126i
$307$	1.46571	−	1.46571i	0.0836528	−	0.0836528i	−0.664042	−	0.747695i	$-0.731161\pi$
$307$	1.46571	−	1.46571i	0.0836528	−	0.0836528i	0.747695	+	0.664042i	$0.231161\pi$
$308$		0			0
$309$	31.8165	+	18.3693i	1.80998	+	1.04499i
$310$	0.0681097	−	0.0182500i	0.00386837	−	0.00103653i
$311$	2.74774			0.155810			0.0779051	−	0.996961i	$-0.475177\pi$
$311$	2.74774			0.155810			0.0779051	+	0.996961i	$0.475177\pi$
$312$	−4.13462	−	27.2566i	−0.234077	−	1.54310i
$313$			7.59112i			0.429075i	0.976716	+	0.214538i	$0.0688245\pi$
$313$			7.59112i			0.429075i	−0.976716	+	0.214538i	$0.931176\pi$
$314$	6.21321	−	1.66482i	0.350632	−	0.0939514i
$315$		0			0
$316$	4.28869	−	2.47607i	0.241257	−	0.139290i
$317$	−7.05236	+	7.05236i	−0.396100	+	0.396100i	−0.876855	−	0.480755i	$-0.840363\pi$
$317$	−7.05236	+	7.05236i	−0.396100	+	0.396100i	0.480755	+	0.876855i	$0.340363\pi$
$318$	−0.332826	+	1.24212i	−0.0186639	+	0.0696548i
$319$	−1.08078	+	4.03352i	−0.0605120	+	0.225834i
$320$	0.0357386	−	0.0357386i	0.00199785	−	0.00199785i
$321$	−35.4398	+	20.4612i	−1.97806	+	1.14203i
$322$		0			0
$323$	22.7953	−	6.10799i	1.26837	−	0.339858i
$324$			25.5329i			1.41849i
$325$	−2.00098	+	17.9113i	−0.110994	+	0.993543i
$326$	2.86019			0.158411
$327$	39.4276	−	10.5646i	2.18035	−	0.584223i
$328$	−0.413456	−	0.238709i	−0.0228293	−	0.0131805i
$329$		0			0
$330$	−0.0645173	+	0.0645173i	−0.00355156	+	0.00355156i
$331$	16.3370	+	4.37748i	0.897962	+	0.240608i	0.678141	−	0.734932i	$-0.262786\pi$
$331$	16.3370	+	4.37748i	0.897962	+	0.240608i	0.219821	+	0.975540i	$0.429453\pi$
$332$	−10.2169	−	2.73762i	−0.560728	−	0.150247i
$333$	26.8344	+	26.8344i	1.47052	+	1.47052i
$334$	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	$0.0692193\pi$
$337$			7.92125i			0.431498i	−0.976449	+	0.215749i	$0.930781\pi$
$338$	0.354576	+	9.01974i	0.0192864	+	0.490609i
$339$			11.6302i			0.631666i
$340$	0.0935459	+	0.349118i	0.00507324	+	0.0189336i
$341$	−2.66850	−	1.54066i	−0.144508	−	0.0834315i
$342$	−8.70054	−	15.0698i	−0.470471	−	0.814880i
$343$		0			0
$344$	5.03523	+	1.34919i	0.271482	+	0.0727433i
$345$	−0.0842049	+	0.314257i	−0.00453344	+	0.0169190i
$346$	10.3433	−	10.3433i	0.556060	−	0.556060i
$347$	−12.1691	−	21.0776i	−0.653274	−	1.13150i	−0.982324	−	0.187191i	$-0.940062\pi$
$347$	−12.1691	−	21.0776i	−0.653274	−	1.13150i	0.329050	−	0.944313i	$-0.393272\pi$
$348$	8.78968	−	15.2242i	0.471176	−	0.816101i
$349$	4.20514	+	15.6938i	0.225096	+	0.840070i	0.982366	+	0.186968i	$0.0598660\pi$
$349$	4.20514	+	15.6938i	0.225096	+	0.840070i	−0.757270	+	0.653102i	$0.773467\pi$
$350$		0			0
$351$	4.75940	−	42.6028i	0.254038	−	2.27397i
$352$	−6.56346			−0.349834
$353$	15.8182	−	4.23848i	0.841919	−	0.225591i	0.188012	−	0.982167i	$-0.439796\pi$
$353$	15.8182	−	4.23848i	0.841919	−	0.225591i	0.653907	+	0.756575i	$0.273129\pi$
$354$	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
$359$	4.88620	+	4.88620i	0.257884	+	0.257884i	0.824193	−	0.566309i	$-0.191629\pi$
$359$	4.88620	+	4.88620i	0.257884	+	0.257884i	−0.566309	+	0.824193i	$0.691629\pi$
$360$	0.534909	−	0.308830i	0.0281922	−	0.0162768i
$361$	4.68617	+	2.70556i	0.246640	+	0.142398i
$362$	2.82454	+	10.5413i	0.148455	+	0.554041i
$363$	−30.4452			−1.59796
$364$		0			0
$365$	−0.101688			−0.00532262
$366$	0.771939	+	2.88091i	0.0403499	+	0.150588i
$367$	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	$0.544940\pi$
$368$	−3.24186	+	1.87169i	−0.168993	+	0.0975684i
$369$	−0.939543	−	0.939543i	−0.0489106	−	0.0489106i
$370$	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
$375$	−1.12446	+	0.301298i	−0.0580669	+	0.0155590i
$376$	−13.7345			−0.708303
$377$	−7.91164	+	10.7411i	−0.407470	+	0.553196i
$378$		0			0
$379$	−3.37163	−	12.5831i	−0.173189	−	0.646349i	−0.996853	−	0.0792716i	$-0.974741\pi$
$379$	−3.37163	−	12.5831i	−0.173189	−	0.646349i	0.823664	−	0.567078i	$-0.191926\pi$
$380$	0.104059	−	0.180236i	0.00533812	−	0.00924589i
$381$	4.47638	+	7.75331i	0.229332	+	0.397214i
$382$	−8.49761	+	8.49761i	−0.434776	+	0.434776i
$383$	−0.594401	+	2.21834i	−0.0303725	+	0.113352i	−0.979448	−	0.201697i	$-0.935354\pi$
$383$	−0.594401	+	2.21834i	−0.0303725	+	0.113352i	0.949075	+	0.315049i	$0.102021\pi$
$384$	32.3144	+	8.65861i	1.64904	+	0.441858i
$385$		0			0
$386$	4.37047	+	7.56988i	0.222451	+	0.385297i
$387$	12.5643	+	7.25403i	0.638681	+	0.368743i
$388$	1.00768	+	3.76072i	0.0511574	+	0.190922i
$389$			12.6070i			0.639198i	0.947553	+	0.319599i	$0.103548\pi$
$389$			12.6070i			0.639198i	−0.947553	+	0.319599i	$0.896452\pi$
$390$	−0.267055	+	0.116816i	−0.0135229	+	0.00591519i
$391$			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
$395$	−0.0858090	−	0.0858090i	−0.00431752	−	0.00431752i
$396$	−11.2491	−	3.01419i	−0.565289	−	0.151469i
$397$	2.16498	+	0.580104i	0.108657	+	0.0291146i	0.312738	−	0.949839i	$-0.398754\pi$
$397$	2.16498	+	0.580104i	0.108657	+	0.0291146i	−0.204081	+	0.978954i	$0.565421\pi$
$398$	−5.20339	+	5.20339i	−0.260822	+	0.260822i
$399$		0			0
$400$	−5.79914	−	3.34813i	−0.289957	−	0.167407i
$401$	−34.8284	+	9.33225i	−1.73925	+	0.466030i	−0.982280	−	0.187421i	$-0.939987\pi$
$401$	−34.8284	+	9.33225i	−1.73925	+	0.466030i	−0.756969	+	0.653451i	$0.773320\pi$
$402$	−16.3957			−0.817742
$403$	−6.14481	−	7.69042i	−0.306095	−	0.383087i
$404$		−	7.00811i		−	0.348666i
$405$	0.604362	−	0.161938i	0.0300310	−	0.00804678i
$406$		0			0
$407$	−5.45612	+	3.15009i	−0.270450	+	0.156144i
$408$	34.6126	−	34.6126i	1.71358	−	1.71358i
$409$	−2.38876	+	8.91498i	−0.118117	+	0.440817i	−0.999501	−	0.0315823i	$-0.989945\pi$
$409$	−2.38876	+	8.91498i	−0.118117	+	0.440817i	0.881385	+	0.472400i	$0.156612\pi$
$410$	−0.00130648	+	0.00487584i	−6.45224e−5	+	0.000240801i
$411$	−37.7577	+	37.7577i	−1.86245	+	1.86245i
$412$	15.4280	−	8.90737i	0.760084	−	0.438834i
$413$		0			0
$414$	12.7411	−	3.41398i	0.626192	−	0.167788i
$415$			0.259198i			0.0127235i
$416$	−19.5260	−	7.64208i	−0.957339	−	0.374684i
$417$	−48.3924			−2.36979
$418$	2.79040	−	0.747684i	0.136483	−	0.0365704i
$419$	15.4156	+	8.90022i	0.753103	+	0.434804i	0.826814	−	0.562475i	$-0.190151\pi$
$419$	15.4156	+	8.90022i	0.753103	+	0.434804i	−0.0737108	+	0.997280i	$0.523484\pi$
$420$		0			0
$421$	−5.59661	+	5.59661i	−0.272762	+	0.272762i	−0.830211	−	0.557449i	$-0.811780\pi$
$421$	−5.59661	+	5.59661i	−0.272762	+	0.272762i	0.557449	+	0.830211i	$0.311780\pi$
$422$	−13.8707	−	3.71664i	−0.675215	−	0.180923i
$423$	−36.9224	−	9.89333i	−1.79523	−	0.481030i
$424$	1.02190	+	1.02190i	0.0496280	+	0.0496280i
$425$	−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
$429$	11.8616	+	4.64238i	0.572682	+	0.224136i
$430$		−	0.0551167i		−	0.00265796i
$431$	3.00628	+	11.2196i	0.144807	+	0.540428i	0.999764	+	0.0217286i	$0.00691696\pi$
$431$	3.00628	+	11.2196i	0.144807	+	0.540428i	−0.854957	+	0.518699i	$0.826416\pi$
$432$	13.7935	+	7.96366i	0.663638	+	0.383152i
$433$	−14.5052	−	25.1237i	−0.697073	−	1.20737i	−0.969477	−	0.245183i	$-0.921152\pi$
$433$	−14.5052	−	25.1237i	−0.697073	−	1.20737i	0.272403	−	0.962183i	$-0.412181\pi$
$434$		0			0
$435$	−0.416103	−	0.111495i	−0.0199506	−	0.00534575i
$436$	5.12283	−	19.1187i	0.245339	−	0.915619i
$437$	7.28378	−	7.28378i	0.348431	−	0.348431i
$438$	2.97109	+	5.14608i	0.141964	+	0.245889i
$439$	−8.42786	+	14.5975i	−0.402240	+	0.696700i	−0.993996	−	0.109417i	$-0.965102\pi$
$439$	−8.42786	+	14.5975i	−0.402240	+	0.696700i	0.591756	+	0.806117i	$0.298435\pi$
$440$	0.0265394	+	0.0990464i	0.00126522	+	0.00472185i
$441$		0			0
$442$	−12.5214	+	10.0049i	−0.595583	+	0.475884i
$443$	−32.2737			−1.53337			−0.766685	−	0.642023i	$-0.778095\pi$
$443$	−32.2737			−1.53337			−0.766685	+	0.642023i	$0.778095\pi$
$444$	25.6188	−	6.86455i	1.21582	−	0.325777i
$445$	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	−0.780542	−	0.625103i	$-0.785057\pi$
$449$	4.40700	−	16.4471i	0.207979	−	0.776188i	0.988521	−	0.151085i	$-0.0482766\pi$
$450$	16.6847	+	16.6847i	0.786525	+	0.786525i
$451$	0.191033	−	0.110293i	0.00899539	−	0.00519349i
$452$	4.88400	+	2.81978i	0.229724	+	0.132631i
$453$	−16.7687	−	62.5815i	−0.787860	−	2.94033i
$454$	−12.7761			−0.599610
$455$		0			0
$456$	−28.1859			−1.31992
$457$	−1.47846	−	5.51768i	−0.0691593	−	0.258106i	0.922686	−	0.385552i	$-0.125989\pi$
$457$	−1.47846	−	5.51768i	−0.0691593	−	0.258106i	−0.991846	+	0.127446i	$0.959322\pi$
$458$	6.59594	+	3.80817i	0.308208	+	0.177944i
$459$	65.9175	−	38.0575i	3.07677	−	1.77637i
$460$	0.111554	+	0.111554i	0.00520121	+	0.00520121i
$461$	−7.08521	+	26.4424i	−0.329991	+	1.23154i	0.579207	+	0.815180i	$0.303362\pi$
$461$	−7.08521	+	26.4424i	−0.329991	+	1.23154i	−0.909198	+	0.416363i	$0.863305\pi$
$462$		0			0
$463$	−13.6953	−	13.6953i	−0.636477	−	0.636477i	0.313208	−	0.949685i	$-0.398596\pi$
$463$	−13.6953	−	13.6953i	−0.636477	−	0.636477i	−0.949685	+	0.313208i	$0.898596\pi$
$464$	−2.47828	−	4.29250i	−0.115051	−	0.199274i
$465$	0.158937	−	0.275286i	0.00737051	−	0.0127661i
$466$	−5.78499	+	1.55008i	−0.267984	+	0.0718062i
$467$	−16.7364			−0.774470			−0.387235	−	0.921981i	$-0.626570\pi$
$467$	−16.7364			−0.774470			−0.387235	+	0.921981i	$0.626570\pi$
$468$	−29.9560	−	22.0648i	−1.38471	−	1.01995i
$469$		0			0
$470$	0.0375852	+	0.140270i	0.00173368	+	0.00647017i
$471$	14.4987	−	25.1126i	0.668067	−	1.15713i
$472$	−13.7669	−	23.8450i	−0.633672	−	1.09755i
$473$	−1.70310	+	1.70310i	−0.0783086	+	0.0783086i
$474$	−1.83535	+	6.84961i	−0.0843003	+	0.314613i
$475$	17.7986	+	4.76912i	0.816655	+	0.218822i
$476$		0			0
$477$	2.01107	+	3.48328i	0.0920807	+	0.159488i
$478$	−4.95082	−	2.85836i	−0.226445	−	0.130738i
$479$	5.83074	+	21.7606i	0.266413	+	0.994267i	0.961380	+	0.275225i	$0.0887525\pi$
$479$	5.83074	+	21.7606i	0.266413	+	0.994267i	−0.694967	+	0.719042i	$0.744581\pi$
$480$		−	0.677095i		−	0.0309050i
$481$	−19.8994	+	3.01860i	−0.907336	+	0.137636i
$482$			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
$486$	−8.34047	−	8.34047i	−0.378331	−	0.378331i
$487$	6.74263	+	1.80668i	0.305538	+	0.0818685i	0.408330	−	0.912834i	$-0.366111\pi$
$487$	6.74263	+	1.80668i	0.305538	+	0.0818685i	−0.102793	+	0.994703i	$0.532778\pi$
$488$	3.23768	+	0.867535i	0.146563	+	0.0392714i
$489$	9.11734	−	9.11734i	0.412300	−	0.412300i
$490$		0			0
$491$	−2.12954	−	1.22949i	−0.0961048	−	0.0554861i	0.451177	−	0.892434i	$-0.351004\pi$
$491$	−2.12954	−	1.22949i	−0.0961048	−	0.0554861i	−0.547282	+	0.836948i	$0.684338\pi$
$492$	−0.896982	+	0.240346i	−0.0404391	+	0.0108356i
$493$	−23.6868			−1.06680
$494$	9.17184	+	1.02464i	0.412660	+	0.0461006i
$495$			0.285383i			0.0128270i
$496$	3.53281	−	0.946613i	0.158628	−	0.0425042i
$497$		0			0
$498$	13.1171	−	7.57314i	0.587790	−	0.339360i
$499$	−13.1882	+	13.1882i	−0.590385	+	0.590385i	−0.937735	−	0.347350i	$-0.887082\pi$
$499$	−13.1882	+	13.1882i	−0.590385	+	0.590385i	0.347350	+	0.937735i	$0.387082\pi$
$500$	−0.146101	+	0.545258i	−0.00653385	+	0.0243847i
$501$	13.0203	−	48.5924i	0.581704	−	2.17095i
$502$	−5.14020	+	5.14020i	−0.229418	+	0.229418i
$503$	29.6335	−	17.1089i	1.32129	−	0.762849i	0.337359	−	0.941376i	$-0.390467\pi$
$503$	29.6335	−	17.1089i	1.32129	−	0.762849i	0.983935	+	0.178527i	$0.0571332\pi$
$504$		0			0
$505$	−0.165882	+	0.0444479i	−0.00738165	+	0.00197791i
$506$			2.18983i			0.0973498i
$507$	29.8822	+	27.6217i	1.32712	+	1.22672i
$508$	4.34124			0.192611
$509$	−8.28991	+	2.22128i	−0.367444	+	0.0984563i	−0.437816	−	0.899065i	$-0.644248\pi$
$509$	−8.28991	+	2.22128i	−0.367444	+	0.0984563i	0.0703723	+	0.997521i	$0.477581\pi$
$510$	−0.448217	−	0.258778i	−0.0198474	−	0.0114589i
$511$		0			0
$512$	10.1365	−	10.1365i	0.447973	−	0.447973i
$513$	−42.3346	−	11.3435i	−1.86912	−	0.500829i
$514$	3.58839	+	0.961507i	0.158277	+	0.0424103i
$515$	−0.308687	−	0.308687i	−0.0136024	−	0.0136024i
$516$	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
$520$	−0.0363700	+	0.325559i	−0.00159493	+	0.0142767i
$521$			22.9781i			1.00669i	0.864086	+	0.503344i	$0.167897\pi$
$521$			22.9781i			1.00669i	−0.864086	+	0.503344i	$0.832103\pi$
$522$	4.52040	+	16.8704i	0.197853	+	0.738396i
$523$	25.8931	+	14.9494i	1.13222	+	0.653690i	0.944493	−	0.328530i	$-0.106553\pi$
$523$	25.8931	+	14.9494i	1.13222	+	0.653690i	0.187731	+	0.982220i	$0.439887\pi$
$524$	0.104975	+	0.181821i	0.00458583	+	0.00794289i
$525$		0			0
$526$	−4.13326	−	1.10750i	−0.180218	−	0.0482894i
$527$	4.52376	−	16.8829i	0.197058	−	0.735431i
$528$	−3.34647	+	3.34647i	−0.145636	+	0.145636i
$529$	−7.59582	−	13.1563i	−0.330253	−	0.572015i
$530$	0.00764016	−	0.0132331i	0.000331867	−	0.000574811i
$531$	−19.8333	−	74.0189i	−0.860692	−	3.21215i
$532$		0			0
$533$	0.696731	−	0.105689i	0.0301788	−	0.00457790i
$534$	−36.6156			−1.58451
$535$	0.469695	−	0.125854i	0.0203067	−	0.00544116i
$536$	−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
$541$	9.06984	+	9.06984i	0.389943	+	0.389943i	0.874667	−	0.484724i	$-0.161080\pi$
$541$	9.06984	+	9.06984i	0.389943	+	0.389943i	−0.484724	+	0.874667i	$0.661080\pi$
$542$	6.11028	−	3.52777i	0.262459	−	0.151531i
$543$	42.6060	+	24.5986i	1.82840	+	1.05563i
$544$	−9.63597	−	35.9619i	−0.413139	−	1.54186i
$545$	−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	$0.245267\pi$
$548$	6.70153	+	25.0105i	0.286275	+	1.06839i
$549$	8.07894	+	4.66438i	0.344801	+	0.199071i
$550$	−3.39243	+	1.95862i	−0.144654	+	0.0835158i
$551$	9.64436	+	9.64436i	0.410864	+	0.410864i
$552$	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
$557$	−22.9234	+	6.14230i	−0.971294	+	0.260257i	−0.709374	−	0.704832i	$-0.751022\pi$
$557$	−22.9234	+	6.14230i	−0.971294	+	0.260257i	−0.261920	+	0.965090i	$0.584356\pi$
$558$	−12.8878			−0.545582
$559$	−7.04961	+	3.08365i	−0.298167	+	0.130425i
$560$		0			0
$561$	5.85363	+	21.8460i	0.247140	+	0.922340i
$562$	6.40360	−	11.0914i	0.270120	−	0.467861i
$563$	−12.3766	−	21.4369i	−0.521611	−	0.903457i	−0.999684	−	0.0251369i	$-0.991998\pi$
$563$	−12.3766	−	21.4369i	−0.521611	−	0.903457i	0.478073	−	0.878320i	$-0.341336\pi$
$564$	−18.8904	+	18.8904i	−0.795427	+	0.795427i
$565$	0.0357681	−	0.133488i	0.00150477	−	0.00561589i
$566$	−1.35193	−	0.362247i	−0.0568257	−	0.0152264i
$567$		0			0
$568$	−12.4952	−	21.6423i	−0.524285	−	0.908089i
$569$	33.4106	+	19.2896i	1.40064	+	0.808663i	0.994459	−	0.105128i	$-0.0335252\pi$
$569$	33.4106	+	19.2896i	1.40064	+	0.808663i	0.406186	+	0.913790i	$0.366859\pi$
$570$	0.0771321	+	0.287861i	0.00323071	+	0.0120572i
$571$			29.3080i			1.22650i	0.789888	+	0.613252i	$0.210139\pi$
$571$			29.3080i			1.22650i	−0.789888	+	0.613252i	$0.789861\pi$
$572$	4.82540	−	3.85559i	0.201760	−	0.161211i
$573$			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
$577$	28.2123	+	28.2123i	1.17449	+	1.17449i	0.981127	+	0.193367i	$0.0619408\pi$
$577$	28.2123	+	28.2123i	1.17449	+	1.17449i	0.193367	+	0.981127i	$0.438059\pi$
$578$	−16.0865	−	4.31037i	−0.669112	−	0.179288i
$579$	38.0619	+	10.1987i	1.58180	+	0.423842i
$580$	−0.147707	+	0.147707i	−0.00613318	+	0.00613318i
$581$		0			0
$582$	−4.82822	−	2.78757i	−0.200136	−	0.115549i
$583$	−0.644982	+	0.172822i	−0.0267124	+	0.00715757i
$584$	6.67806			0.276340
$585$	−0.332282	+	0.849000i	−0.0137382	+	0.0351018i
$586$		−	8.24444i		−	0.340575i
$587$	31.6109	−	8.47012i	1.30472	−	0.349599i	0.461489	−	0.887146i	$-0.347316\pi$
$587$	31.6109	−	8.47012i	1.30472	−	0.349599i	0.843234	+	0.537547i	$0.180649\pi$
$588$		0			0
$589$	−8.71597	+	5.03217i	−0.359135	+	0.207347i
$590$	−0.205854	+	0.205854i	−0.00847486	+	0.00847486i
$591$	20.1337	−	75.1401i	0.828191	−	3.09085i
$592$	1.93548	−	7.22330i	0.0795477	−	0.296876i
$593$	15.3805	−	15.3805i	0.631601	−	0.631601i	−0.316868	−	0.948470i	$-0.602631\pi$
$593$	15.3805	−	15.3805i	0.631601	−	0.631601i	0.948470	+	0.316868i	$0.102631\pi$
$594$	8.06901	−	4.65865i	0.331076	−	0.191147i
$595$		0			0
$596$	8.34937	−	2.23721i	0.342003	−	0.0916396i
$597$			33.1734i			1.35770i
$598$	−2.54970	+	6.51463i	−0.104265	+	0.266403i
$599$	30.1072			1.23015			0.615073	−	0.788470i	$-0.289126\pi$
$599$	30.1072			1.23015			0.615073	+	0.788470i	$0.289126\pi$
$600$	36.9176	−	9.89203i	1.50715	−	0.403840i
$601$	−16.4105	−	9.47460i	−0.669398	−	0.386477i	0.126450	−	0.991973i	$-0.459642\pi$
$601$	−16.4105	−	9.47460i	−0.669398	−	0.386477i	−0.795849	+	0.605496i	$0.792975\pi$
$602$		0			0
$603$	−36.2620	+	36.2620i	−1.47670	+	1.47670i
$604$	−30.3461	−	8.13122i	−1.23477	−	0.330855i
$605$	0.349442	+	0.0936327i	0.0142068	+	0.00380671i
$606$	7.09602	+	7.09602i	0.288256	+	0.288256i
$607$	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
$611$	15.8382	−	12.6550i	0.640745	−	0.511968i
$612$		−	66.0603i		−	2.67033i
$613$	−6.47832	−	24.1774i	−0.261657	−	0.976518i	−0.964265	−	0.264940i	$-0.914648\pi$
$613$	−6.47832	−	24.1774i	−0.261657	−	0.976518i	0.702608	−	0.711577i	$-0.252019\pi$
$614$	1.24647	+	0.719649i	0.0503034	+	0.0290427i
$615$	0.0113780	+	0.0197072i	0.000458804	+	0.000794671i
$616$		0			0
$617$	−29.1852	−	7.82015i	−1.17495	−	0.314827i	−0.382029	−	0.924150i	$-0.624775\pi$
$617$	−29.1852	−	7.82015i	−1.17495	−	0.314827i	−0.792922	+	0.609323i	$0.791441\pi$
$618$	−6.60244	+	24.6406i	−0.265589	+	0.991191i
$619$	30.0154	−	30.0154i	1.20642	−	1.20642i	0.234240	−	0.972179i	$-0.424740\pi$
$619$	30.0154	−	30.0154i	1.20642	−	1.20642i	0.972179	−	0.234240i	$-0.0752601\pi$
$620$	−0.0770693	−	0.133488i	−0.00309518	−	0.00536100i
$621$	16.6115	−	28.7720i	0.666598	−	1.15458i
$622$	0.493808	+	1.84292i	0.0197999	+	0.0738942i
$623$		0			0
$624$	−13.8520	+	6.05915i	−0.554523	+	0.242560i
$625$	−24.9792			−0.999170
$626$	−5.09138	+	1.36423i	−0.203493	+	0.0545257i
$627$	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	0.464488	+	0.885579i	$0.346238\pi$
$631$	−9.55956	+	35.6768i	−0.380560	+	1.42027i	−0.845048	+	0.534690i	$0.820428\pi$
$632$	5.63523	+	5.63523i	0.224157	+	0.224157i
$633$	−56.0627	+	32.3678i	−2.22829	+	1.28650i
$634$	−5.99744	−	3.46263i	−0.238189	−	0.137518i
$635$	−0.0275337	−	0.102757i	−0.00109264	−	0.00407779i
$636$	2.81104			0.111465
$637$		0			0
$638$	−2.89952			−0.114793
$639$	−18.0012	−	67.1814i	−0.712116	−	2.65765i
$640$	−0.344266	−	0.198762i	−0.0136083	−	0.00785676i
$641$	−7.17353	+	4.14164i	−0.283338	+	0.163585i	−0.634933	−	0.772567i	$-0.718972\pi$
$641$	−7.17353	+	4.14164i	−0.283338	+	0.163585i	0.351596	+	0.936152i	$0.385639\pi$
$642$	−20.0924	−	20.0924i	−0.792984	−	0.792984i
$643$	8.56893	−	31.9797i	0.337926	−	1.26116i	−0.562737	−	0.826636i	$-0.690252\pi$
$643$	8.56893	−	31.9797i	0.337926	−	1.26116i	0.900663	−	0.434519i	$-0.143082\pi$
$644$		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	−0.965920	−	0.258841i	$-0.916659\pi$
$647$	−6.58281	+	11.4018i	−0.258797	+	0.448250i	0.707123	+	0.707091i	$0.249993\pi$
$648$	−39.6895	+	10.6348i	−1.55915	+	0.417773i
$649$	12.7217			0.499370
$650$	−12.3728	+	1.87686i	−0.485301	+	0.0736166i
$651$		0			0
$652$	−1.61822	−	6.03927i	−0.0633743	−	0.236516i
$653$	23.6676	−	40.9935i	0.926184	−	1.60420i	0.136539	−	0.990635i	$-0.456402\pi$
$653$	23.6676	−	40.9935i	0.926184	−	1.60420i	0.789645	−	0.613564i	$-0.210265\pi$
$654$	14.1714	+	24.5456i	0.554146	+	0.959808i
$655$	0.00363792	−	0.00363792i	0.000142145	−	0.000142145i
$656$	−0.0677662	+	0.252907i	−0.00264582	+	0.00987435i
$657$	17.9526	+	4.81038i	0.700397	+	0.187671i
$658$		0			0
$659$	−2.76562	−	4.79019i	−0.107733	−	0.186599i	0.807118	−	0.590390i	$-0.201026\pi$
$659$	−2.76562	−	4.79019i	−0.107733	−	0.186599i	−0.914852	+	0.403790i	$0.867693\pi$
$660$	0.172730	+	0.0997256i	0.00672350	+	0.00388181i
$661$	−4.70431	−	17.5567i	−0.182976	−	0.682877i	−0.995055	−	0.0993289i	$-0.968330\pi$
$661$	−4.70431	−	17.5567i	−0.182976	−	0.682877i	0.812078	−	0.583549i	$-0.198336\pi$
$662$			11.7440i			0.456442i
$663$	−8.02190	+	71.8064i	−0.311545	+	2.78873i
$664$		−	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
$668$	−17.2491	−	17.2491i	−0.667389	−	0.667389i
$669$	−9.93120	−	2.66106i	−0.383962	−	0.102882i
$670$	0.188185	+	0.0504240i	0.00727022	+	0.00194805i
$671$	−1.09510	+	1.09510i	−0.0422760	+	0.0422760i
$672$		0			0
$673$	−3.86827	−	2.23334i	−0.149111	−	0.0860891i	0.423588	−	0.905855i	$-0.360770\pi$
$673$	−3.86827	−	2.23334i	−0.149111	−	0.0860891i	−0.572699	+	0.819766i	$0.694104\pi$
$674$	−5.31280	+	1.42356i	−0.204641	+	0.0548335i
$675$	59.4305			2.28748
$676$	18.8445	−	5.85181i	0.724789	−	0.225070i
$677$		−	23.2495i		−	0.893549i	−0.894647	−	0.446775i	$-0.852573\pi$
$677$		−	23.2495i		−	0.893549i	0.894647	−	0.446775i	$-0.147427\pi$
$678$	−7.80041	+	2.09011i	−0.299573	+	0.0802703i
$679$		0			0
$680$	−0.503723	+	0.290825i	−0.0193169	+	0.0111526i
$681$	−40.7259	+	40.7259i	−1.56062	+	1.56062i
$682$	0.553757	−	2.06665i	0.0212045	−	0.0791361i
$683$	2.05374	−	7.66466i	0.0785842	−	0.293280i	−0.915438	−	0.402459i	$-0.868156\pi$
$683$	2.05374	−	7.66466i	0.0785842	−	0.293280i	0.994022	+	0.109179i	$0.0348222\pi$
$684$	−26.8972	+	26.8972i	−1.02844	+	1.02844i
$685$	0.549494	−	0.317250i	0.0209951	−	0.0121215i
$686$		0			0
$687$	33.1649	−	8.88651i	1.26532	−	0.339041i
$688$		−	2.85887i		−	0.108993i
$689$	−2.12001	−	0.236838i	−0.0807660	−	0.00902282i
$690$	−0.225906			−0.00860008
$691$	11.1445	−	2.98617i	0.423958	−	0.113599i	−0.0405305	−	0.999178i	$-0.512905\pi$
$691$	11.1445	−	2.98617i	0.423958	−	0.113599i	0.464489	+	0.885579i	$0.346238\pi$
$692$	−27.6918	−	15.9879i	−1.05268	−	0.607768i
$693$		0			0
$694$	11.9498	−	11.9498i	0.453609	−	0.453609i
$695$	0.555434	+	0.148828i	0.0210688	+	0.00564537i
$696$	27.3262	+	7.32204i	1.03580	+	0.277541i
$697$	0.884767	+	0.884767i	0.0335129	+	0.0335129i
$698$	−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	$0.0666624\pi$
$701$			11.0088i			0.415797i	−0.978150	+	0.207898i	$0.933338\pi$
$702$	29.4291	−	4.46419i	1.11073	−	0.168490i
$703$			20.5779i			0.776110i
$704$	−0.396923	−	1.48134i	−0.0149596	−	0.0558299i
$705$	0.566944	+	0.327325i	0.0213523	+	0.0123278i
$706$	5.68552	+	9.84760i	0.213977	+	0.370619i
$707$		0			0
$708$	−51.7311	−	13.8613i	−1.94417	−	0.520939i
$709$	−7.69277	+	28.7098i	−0.288908	+	1.07822i	0.657028	+	0.753866i	$0.271813\pi$
$709$	−7.69277	+	28.7098i	−0.288908	+	1.07822i	−0.945936	+	0.324353i	$0.894853\pi$
$710$	−0.186838	+	0.186838i	−0.00701189	+	0.00701189i
$711$	11.0900	+	19.2084i	0.415906	+	0.720370i
$712$	−20.5750	+	35.6370i	−0.771082	+	1.33555i
$713$	−1.97456	−	7.36914i	−0.0739477	−	0.275977i
$714$		0			0
$715$	−0.121866	−	0.0897635i	−0.00455754	−	0.00335697i
$716$	13.8396			0.517211
$717$	−24.8931	+	6.67008i	−0.929649	+	0.249099i
$718$	−2.39907	+	4.15530i	−0.0895323	+	0.155075i
$719$	−12.1922	−	21.1175i	−0.454693	−	0.787552i	0.543977	−	0.839100i	$-0.316918\pi$
$719$	−12.1922	−	21.1175i	−0.454693	−	0.787552i	−0.998671	+	0.0515483i	$0.983584\pi$
$720$	−0.239526	−	0.239526i	−0.00892660	−	0.00892660i
$721$		0			0
$722$	−0.972454	+	3.62925i	−0.0361910	+	0.135067i
$723$	13.9060	+	13.9060i	0.517169	+	0.517169i
$724$	20.6599	−	11.9280i	0.767820	−	0.443301i
$725$	−16.0168	−	9.24733i	−0.594851	−	0.343437i
$726$	−5.47144	−	20.4197i	−0.203064	−	0.757846i
$727$	20.3008			0.752915			0.376458	−	0.926434i	$-0.377142\pi$
$727$	20.3008			0.752915			0.376458	+	0.926434i	$0.377142\pi$
$728$		0			0
$729$	−2.70851			−0.100315
$730$	−0.0182749	−	0.0682027i	−0.000676383	−	0.00252429i
$731$	−11.8318	−	6.83111i	−0.437616	−	0.252658i
$732$	5.64629	−	3.25989i	0.208693	−	0.120489i
$733$	−11.6143	−	11.6143i	−0.428983	−	0.428983i	0.459299	−	0.888282i	$-0.348101\pi$
$733$	−11.6143	−	11.6143i	−0.428983	−	0.428983i	−0.888282	+	0.459299i	$0.848101\pi$
$734$	−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
$739$	41.3778	−	11.0872i	1.52211	−	0.407847i	0.601672	−	0.798743i	$-0.294501\pi$
$739$	41.3778	−	11.0872i	1.52211	−	0.407847i	0.920435	+	0.390896i	$0.127835\pi$
$740$	−0.315157			−0.0115854
$741$	32.5030	−	25.9706i	1.19403	−	0.954054i
$742$		0			0
$743$	12.7481	+	47.5766i	0.467683	+	1.74542i	0.647838	+	0.761778i	$0.275673\pi$
$743$	12.7481	+	47.5766i	0.467683	+	1.74542i	−0.180155	+	0.983638i	$0.557660\pi$
$744$	−10.4376	+	18.0785i	−0.382663	+	0.662791i
$745$	−0.105909	−	0.183440i	−0.00388022	−	0.00672073i
$746$	11.1283	−	11.1283i	0.407438	−	0.407438i
$747$	12.2614	−	45.7601i	0.448621	−	1.67427i
$748$	10.5933	+	2.83846i	0.387328	+	0.103784i
$749$		0			0
$750$	−0.404163	−	0.700031i	−0.0147580	−	0.0255615i
$751$	−19.9626	−	11.5254i	−0.728444	−	0.420567i	0.0894086	−	0.995995i	$-0.471502\pi$
$751$	−19.9626	−	11.5254i	−0.728444	−	0.420567i	−0.817853	+	0.575428i	$0.804836\pi$
$752$	1.94952	+	7.27571i	0.0710917	+	0.265318i
$753$			32.7705i			1.19422i
$754$	−8.62593	−	3.37602i	−0.314138	−	0.122947i
$755$			0.769863i			0.0280182i
$756$		0			0
$757$	24.1858	−	41.8911i	0.879049	−	1.52256i	0.0266620	−	0.999645i	$-0.491512\pi$
$757$	24.1858	−	41.8911i	0.879049	−	1.52256i	0.852387	−	0.522912i	$-0.175154\pi$
$758$	7.83357	−	4.52272i	0.284528	−	0.164272i
$759$	6.98045	+	6.98045i	0.253374	+	0.253374i
$760$	0.323509	+	0.0866840i	0.0117349	+	0.00314436i
$761$	28.2385	+	7.56647i	1.02364	+	0.274284i	0.731320	−	0.682035i	$-0.238905\pi$
$761$	28.2385	+	7.56647i	1.02364	+	0.274284i	0.292324	+	0.956319i	$0.405571\pi$
$762$	−4.39570	+	4.39570i	−0.159239	+	0.159239i
$763$		0			0
$764$	22.7504	+	13.1349i	0.823079	+	0.475205i
$765$	−1.56365	+	0.418978i	−0.0565337	+	0.0151482i
$766$	−1.59467			−0.0576176
$767$	37.8464	+	14.8123i	1.36655	+	0.534842i
$768$			31.7363i			1.14518i
$769$	1.87337	−	0.501968i	0.0675554	−	0.0181014i	−0.224883	−	0.974386i	$-0.572200\pi$
$769$	1.87337	−	0.501968i	0.0675554	−	0.0181014i	0.292438	+	0.956284i	$0.405533\pi$
$770$		0			0
$771$	14.5036	−	8.37365i	0.522334	−	0.301570i
$772$	13.5111	−	13.5111i	0.486273	−	0.486273i
$773$	−1.31839	+	4.92031i	−0.0474193	+	0.176971i	−0.985574	−	0.169245i	$-0.945867\pi$
$773$	−1.31839	+	4.92031i	−0.0474193	+	0.176971i	0.938155	+	0.346216i	$0.112534\pi$
$774$	−2.60730	+	9.73059i	−0.0937176	+	0.349759i
$775$	9.65001	−	9.65001i	0.346639	−	0.346639i
$776$	−5.42614	+	3.13278i	−0.194787	+	0.112460i
$777$		0			0
$778$	−8.45552	+	2.26565i	−0.303145	+	0.0812275i
$779$		−	0.720486i		−	0.0258141i
$780$	0.397748	+	0.497794i	0.0142417	+	0.0178239i
$781$	11.5465			0.413167
$782$	−11.9983	+	3.21494i	−0.429059	+	0.114966i
$783$	38.0967	+	21.9951i	1.36146	+	0.786041i
$784$		0			0
$785$	−0.243645	+	0.243645i	−0.00869606	+	0.00869606i
$786$	−0.290393	−	0.0778106i	−0.0103580	−	0.00277541i
$787$	−29.6181	−	7.93615i	−1.05577	−	0.282893i	−0.311137	−	0.950365i	$-0.600710\pi$
$787$	−29.6181	−	7.93615i	−1.05577	−	0.282893i	−0.744635	+	0.667472i	$0.767376\pi$
$788$	−26.6729	−	26.6729i	−0.950184	−	0.950184i
$789$	−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
$793$	−4.53294	+	1.98281i	−0.160969	+	0.0704115i
$794$			1.55631i			0.0552313i
$795$	−0.0178286	−	0.0665372i	−0.000632315	−	0.00235983i
$796$	13.9309	+	8.04298i	0.493766	+	0.285076i
$797$	−15.8566	−	27.4644i	−0.561669	−	0.972839i	−0.997351	−	0.0727386i	$-0.976826\pi$
$797$	−15.8566	−	27.4644i	−0.561669	−	0.972839i	0.435682	−	0.900101i	$-0.356507\pi$
$798$		0			0
$799$	34.7698	+	9.31655i	1.23007	+	0.329596i
$800$	7.52376	−	28.0791i	0.266005	−	0.992745i
$801$	−80.9821	+	80.9821i	−2.86136	+	2.86136i
$802$	−12.5183	−	21.6824i	−0.442037	−	0.765631i
$803$	−1.54276	+	2.67214i	−0.0544429	+	0.0942979i
$804$	9.27623	+	34.6194i	0.327147	+	1.22093i
$805$		0			0
$806$	4.05368	−	5.50342i	0.142785	−	0.193850i
$807$	64.3282			2.26446
$808$	10.8938	−	2.91897i	0.383241	−	0.102689i
$809$	−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	$-0.425467\pi$
$811$	−21.0935	−	21.0935i	−0.740695	−	0.740695i	−0.972712	+	0.232017i	$0.925467\pi$
$812$		0			0
$813$	8.23219	−	30.7229i	0.288715	−	1.07750i
$814$	−3.09331	−	3.09331i	−0.108421	−	0.108421i
$815$	−0.132686	+	0.0766063i	−0.00464779	+	0.00268340i
$816$	−23.2487	−	13.4226i	−0.813867	−	0.469886i
$817$	2.03610	+	7.59883i	0.0712341	+	0.265849i
$818$	−6.40859			−0.224071
$819$		0			0
$820$	0.0110345			0.000385341
$821$	−10.1294	−	37.8035i	−0.353519	−	1.31935i	−0.882338	−	0.470615i	$-0.844032\pi$
$821$	−10.1294	−	37.8035i	−0.353519	−	1.31935i	0.528820	−	0.848734i	$-0.322635\pi$
$822$	−32.1098	−	18.5386i	−1.11996	−	0.646607i
$823$	−31.6926	+	18.2977i	−1.10473	+	0.637819i	−0.937460	−	0.348092i	$-0.886830\pi$
$823$	−31.6926	+	18.2977i	−1.10473	+	0.637819i	−0.167274	+	0.985910i	$0.553496\pi$
$824$	20.2720	+	20.2720i	0.706209	+	0.706209i
$825$	−4.57051	+	17.0574i	−0.159125	+	0.593861i
$826$		0			0
$827$	−4.61851	−	4.61851i	−0.160601	−	0.160601i	0.622232	−	0.782833i	$-0.286226\pi$
$827$	−4.61851	−	4.61851i	−0.160601	−	0.160601i	−0.782833	+	0.622232i	$0.786226\pi$
$828$	−14.4172	−	24.9713i	−0.501031	−	0.867812i
$829$	5.83825	−	10.1121i	0.202771	−	0.351209i	−0.746649	−	0.665218i	$-0.768339\pi$
$829$	5.83825	−	10.1121i	0.202771	−	0.351209i	0.949420	+	0.314009i	$0.101672\pi$
$830$	−0.173845	+	0.0465815i	−0.00603424	+	0.00161687i
$831$	−63.9361			−2.21792
$832$	0.543949	−	4.86905i	0.0188580	−	0.168804i
$833$		0			0
$834$	−8.69680	−	32.4569i	−0.301146	−	1.12389i
$835$	−0.298887	+	0.517687i	−0.0103434	+	0.0179153i
$836$	−3.15746	−	5.46888i	−0.109203	−	0.189145i
$837$	−22.9529	+	22.9529i	−0.793369	+	0.793369i
$838$	−3.19899	+	11.9388i	−0.110507	+	0.412419i
$839$	22.6006	+	6.05583i	0.780261	+	0.209070i	0.626900	−	0.779100i	$-0.284324\pi$
$839$	22.6006	+	6.05583i	0.780261	+	0.209070i	0.153361	+	0.988170i	$0.450990\pi$
$840$		0			0
$841$	7.65516	+	13.2591i	0.263971	+	0.457211i
$842$	−4.75945	−	2.74787i	−0.164021	−	0.0946978i
$843$	−14.9430	−	55.7682i	−0.514666	−	1.92076i
$844$			31.3907i			1.08051i
$845$	−0.258031	−	0.408935i	−0.00887653	−	0.0140678i
$846$		−	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
$850$	−15.7120	−	15.7120i	−0.538917	−	0.538917i
$851$	−15.0672	−	4.03725i	−0.516497	−	0.138395i
$852$	−46.9524	−	12.5808i	−1.60856	−	0.431013i
$853$	−34.6514	+	34.6514i	−1.18644	+	1.18644i	−0.208398	+	0.978044i	$0.566825\pi$
$853$	−34.6514	+	34.6514i	−1.18644	+	1.18644i	−0.978044	+	0.208398i	$0.933175\pi$
$854$		0			0
$855$	0.807248	+	0.466065i	0.0276073	+	0.0159391i
$856$	−30.8457	+	8.26508i	−1.05428	+	0.282495i
$857$	2.39334			0.0817550			0.0408775	−	0.999164i	$-0.486985\pi$
$857$	2.39334			0.0817550			0.0408775	+	0.999164i	$0.486985\pi$
$858$	−0.981967	+	8.78988i	−0.0335238	+	0.300082i
$859$			1.98266i			0.0676476i	0.999428	+	0.0338238i	$0.0107685\pi$
$859$			1.98266i			0.0676476i	−0.999428	+	0.0338238i	$0.989231\pi$
$860$	−0.116379	+	0.0311836i	−0.00396848	+	0.00106335i
$861$		0			0
$862$	−6.98473	+	4.03263i	−0.237901	+	0.137352i
$863$	10.0713	−	10.0713i	0.342832	−	0.342832i	−0.514599	−	0.857431i	$-0.672059\pi$
$863$	10.0713	−	10.0713i	0.342832	−	0.342832i	0.857431	+	0.514599i	$0.172059\pi$
$864$	−17.8955	+	66.7871i	−0.608819	+	2.27214i
$865$	−0.202802	+	0.756866i	−0.00689546	+	0.0257342i
$866$	14.2437	−	14.2437i	0.484021	−	0.484021i
$867$	−65.0186	+	37.5385i	−2.20815	+	1.27488i
$868$		0			0
$869$	−3.55672	+	0.953020i	−0.120653	+	0.0323290i
$870$		−	0.299119i		−	0.0101411i
$871$	−4.07911	−	26.8906i	−0.138215	−	0.911153i
$872$	31.8527			1.07867
$873$	−16.8437	+	4.51326i	−0.570073	+	0.152751i
$874$	6.19425	+	3.57625i	0.209524	+	0.120969i
$875$		0			0
$876$	9.18495	−	9.18495i	0.310331	−	0.310331i
$877$	47.4938	+	12.7259i	1.60375	+	0.429724i	0.946173	−	0.323660i	$-0.104914\pi$
$877$	47.4938	+	12.7259i	1.60375	+	0.429724i	0.657580	+	0.753385i	$0.271580\pi$
$878$	−11.3052	−	3.02921i	−0.381531	−	0.102231i
$879$	−26.2806	−	26.2806i	−0.886422	−	0.886422i
$880$	0.0487017	−	0.0281179i	0.00164173	−	0.000947855i
$881$	13.0843	−	22.6627i	0.440821	−	0.763525i	−0.556930	−	0.830560i	$-0.688021\pi$
$881$	13.0843	−	22.6627i	0.440821	−	0.763525i	0.997751	+	0.0670352i	$0.0213540\pi$
$882$		0			0
$883$			4.56808i			0.153728i	0.997042	+	0.0768640i	$0.0244907\pi$
$883$			4.56808i			0.153728i	−0.997042	+	0.0768640i	$0.975509\pi$
$884$	28.2095	+	20.7784i	0.948789	+	0.698853i
$885$			1.31239i			0.0441154i
$886$	−5.80004	−	21.6461i	−0.194856	−	0.727214i
$887$	−1.04425	−	0.602895i	−0.0350623	−	0.0202432i	0.482366	−	0.875970i	$-0.339777\pi$
$887$	−1.04425	−	0.602895i	−0.0350623	−	0.0202432i	−0.517429	+	0.855726i	$0.673111\pi$
$888$	21.3412	+	36.9640i	0.716163	+	1.24043i
$889$		0			0
$890$	0.420264	+	0.112609i	0.0140873	+	0.00377467i
$891$	4.91369	−	18.3381i	0.164615	−	0.614351i
$892$	−3.52534	+	3.52534i	−0.118037	+	0.118037i
$893$	−10.3636	−	17.9503i	−0.346804	−	0.600683i
$894$	−6.18883	+	10.7194i	−0.206985	+	0.358509i
$895$	−0.0877758	−	0.327584i	−0.00293402	−	0.0109499i
$896$		0			0
$897$	12.6389	+	28.8941i	0.422000	+	0.964745i
$898$	11.8231			0.394543
$899$	9.75739	−	2.61448i	0.325427	−	0.0871979i
$900$	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
$905$	−0.413368	−	0.413368i	−0.0137408	−	0.0137408i
$906$	38.9600	−	22.4936i	1.29436	−	0.747298i
$907$	30.1251	+	17.3927i	1.00029	+	0.577515i	0.908333	−	0.418248i	$-0.137356\pi$
$907$	30.1251	+	17.3927i	1.00029	+	0.577515i	0.0919531	+	0.995763i	$0.470689\pi$
$908$	7.22835	+	26.9766i	0.239881	+	0.895249i
$909$	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	$0.445530\pi$
$912$	4.00079	+	14.9311i	0.132479	+	0.494420i
$913$	6.81114	+	3.93241i	0.225416	+	0.130144i
$914$	3.43502	−	1.98321i	0.113620	−	0.0655987i
$915$	−0.112972	−	0.112972i	−0.00373475	−	0.00373475i
$916$	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
$921$	6.26733	−	1.67933i	0.206516	−	0.0553357i
$922$	−19.0083			−0.626004
$923$	34.3503	+	13.4440i	1.13065	+	0.442516i
$924$		0			0
$925$	−7.22196	−	26.9527i	−0.237457	−	0.886200i
$926$	6.72425	−	11.6467i	0.220973	−	0.382736i
$927$	39.8947	+	69.0997i	1.31031	+	2.26953i
$928$	15.2149	−	15.2149i	0.499455	−	0.499455i
$929$	0.310383	−	1.15836i	0.0101833	−	0.0380047i	−0.960647	−	0.277771i	$-0.910404\pi$
$929$	0.310383	−	1.15836i	0.0101833	−	0.0380047i	0.970831	+	0.239767i	$0.0770709\pi$
$930$	0.213198	+	0.0571263i	0.00699105	+	0.00187325i
$931$		0			0
$932$	6.54598	+	11.3380i	0.214421	+	0.371387i
$933$	7.44871	+	4.30052i	0.243860	+	0.140793i
$934$	−3.00778	−	11.2252i	−0.0984174	−	0.367299i
$935$		−	0.268745i		−	0.00878890i
$936$	21.8215	−	55.7553i	0.713259	−	1.82242i
$937$			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
$941$	26.1939	+	26.1939i	0.853896	+	0.853896i	0.990610	−	0.136715i	$-0.0436543\pi$
$941$	26.1939	+	26.1939i	0.853896	+	0.853896i	−0.136715	+	0.990610i	$0.543654\pi$
$942$	19.4487	+	5.21126i	0.633673	+	0.169792i
$943$	0.527543	+	0.141355i	0.0171791	+	0.00460314i
$944$	−10.6775	+	10.6775i	−0.347523	+	0.347523i
$945$		0			0
$946$	−1.44834	−	0.836202i	−0.0470897	−	0.0271873i
$947$	−35.9653	+	9.63686i	−1.16871	+	0.313156i	−0.790441	−	0.612538i	$-0.790149\pi$
$947$	−35.9653	+	9.63686i	−1.16871	+	0.313156i	−0.378273	+	0.925694i	$0.623482\pi$
$948$	15.5013			0.503459
$949$	−7.70092	+	6.15320i	−0.249982	+	0.199741i
$950$			12.7946i			0.415113i
$951$	−30.1556	+	8.08016i	−0.977862	+	0.262017i
$952$		0			0
$953$	−37.3599	+	21.5697i	−1.21020	+	0.698712i	−0.962804	−	0.270201i	$-0.912910\pi$
$953$	−37.3599	+	21.5697i	−1.21020	+	0.698712i	−0.247401	+	0.968913i	$0.579576\pi$
$954$	−1.97483	+	1.97483i	−0.0639374	+	0.0639374i
$955$	0.166613	−	0.621807i	0.00539146	−	0.0201212i
$956$	−3.23436	+	12.0708i	−0.104607	+	0.390398i
$957$	−9.24273	+	9.24273i	−0.298775	+	0.298775i
$958$	−13.5470	+	7.82138i	−0.437684	+	0.252697i
$959$		0			0
$960$	0.152817	−	0.0409471i	0.00493213	−	0.00132156i
$961$		−	23.5461i		−	0.759550i
$962$	−5.60079	−	12.8041i	−0.180577	−	0.412821i
$963$	−88.8760			−2.86399
$964$	9.21123	−	2.46814i	0.296674	−	0.0794935i
$965$	−0.405498	−	0.234115i	−0.0130535	−	0.00753641i
$966$		0			0
$967$	−6.54638	+	6.54638i	−0.210517	+	0.210517i	−0.804487	−	0.593970i	$-0.797560\pi$
$967$	−6.54638	+	6.54638i	−0.210517	+	0.210517i	0.593970	+	0.804487i	$0.297560\pi$
$968$	−22.9485	−	6.14902i	−0.737591	−	0.197637i
$969$	71.3544	+	19.1193i	2.29223	+	0.614202i
$970$	0.0468439	+	0.0468439i	0.00150407	+	0.00150407i
$971$	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
$975$	−33.4575	+	45.4232i	−1.07150	+	1.45471i
$976$		−	1.83827i		−	0.0588415i
$977$	−9.72109	−	36.2796i	−0.311005	−	1.16069i	−0.927651	−	0.373447i	$-0.878176\pi$
$977$	−9.72109	−	36.2796i	−0.311005	−	1.16069i	0.616646	−	0.787240i	$-0.288491\pi$
$978$	7.75354	+	4.47651i	0.247931	+	0.143143i
$979$	−9.50648	−	16.4657i	−0.303829	−	0.526246i
$980$		0			0
$981$	85.6296	+	22.9444i	2.73394	+	0.732558i
$982$	0.441914	−	1.64925i	0.0141020	−	0.0526295i
$983$	24.6592	−	24.6592i	0.786506	−	0.786506i	−0.194413	−	0.980920i	$-0.562280\pi$
$983$	24.6592	−	24.6592i	0.786506	−	0.786506i	0.980920	+	0.194413i	$0.0622803\pi$
$984$	−0.747210	−	1.29421i	−0.0238202	−	0.0412578i
$985$	−0.462179	+	0.800517i	−0.0147262	+	0.0255066i
$986$	−4.25686	−	15.8868i	−0.135566	−	0.505939i
$987$		0			0
$988$	−3.02566	−	19.9460i	−0.0962591	−	0.634566i
$989$	−5.96336			−0.189624
$990$	−0.191407	+	0.0512874i	−0.00608332	+	0.00163002i
$991$	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
$996$	−23.4119	−	23.4119i	−0.741835	−	0.741835i
$997$	−16.1229	+	9.30855i	−0.510617	+	0.294805i	−0.733087	−	0.680135i	$-0.761921\pi$
$997$	−16.1229	+	9.30855i	−0.510617	+	0.294805i	0.222470	+	0.974939i	$0.428588\pi$
$998$	−11.2155	−	6.47526i	−0.355020	−	0.204971i
$999$	17.1777	+	64.1080i	0.543478	+	2.02829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.97.5		28
7.2	even	3		91.2.ba.a.45.5	yes	28
7.3	odd	6		91.2.w.a.19.3	✓	28
7.4	even	3		637.2.x.a.19.3		28
7.5	odd	6		637.2.bb.a.227.5		28
7.6	odd	2		637.2.bd.a.97.5		28
13.11	odd	12		637.2.bd.a.440.5		28
21.2	odd	6		819.2.et.b.136.3		28
21.17	even	6		819.2.gh.b.19.5		28
91.11	odd	12		637.2.bb.a.362.5		28
91.24	even	12		91.2.ba.a.89.5	yes	28
91.37	odd	12		91.2.w.a.24.3	yes	28
91.76	even	12	inner	637.2.bd.b.440.5		28
91.89	even	12		637.2.x.a.570.3		28
273.128	even	12		819.2.gh.b.388.5		28
273.206	odd	12		819.2.et.b.271.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.3	✓	28	7.3	odd	6
91.2.w.a.24.3	yes	28	91.37	odd	12
91.2.ba.a.45.5	yes	28	7.2	even	3
91.2.ba.a.89.5	yes	28	91.24	even	12
637.2.x.a.19.3		28	7.4	even	3
637.2.x.a.570.3		28	91.89	even	12
637.2.bb.a.227.5		28	7.5	odd	6
637.2.bb.a.362.5		28	91.11	odd	12
637.2.bd.a.97.5		28	7.6	odd	2
637.2.bd.a.440.5		28	13.11	odd	12
637.2.bd.b.97.5		28	1.1	even	1	trivial
637.2.bd.b.440.5		28	91.76	even	12	inner
819.2.et.b.136.3		28	21.2	odd	6
819.2.et.b.271.3		28	273.206	odd	12
819.2.gh.b.19.5		28	21.17	even	6
819.2.gh.b.388.5		28	273.128	even	12

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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.179714 + 0.670702i) q^{2} +(2.71085 + 1.56511i) q^{3} +(1.31451 - 0.758931i) q^{4} +(-0.0263009 - 0.0263009i) q^{5} +(-0.562545 + 2.09944i) q^{6} +(1.72723 + 1.72723i) q^{8} +(3.39913 + 5.88747i) q^{9} +O(q^{10})\)	\(q+(0.179714 + 0.670702i) q^{2} +(2.71085 + 1.56511i) q^{3} +(1.31451 - 0.758931i) q^{4} +(-0.0263009 - 0.0263009i) 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} +(-1.09015 + 0.292106i) q^{11} +4.75124 q^{12} +(-3.58326 - 0.400306i) q^{13} +(-0.0301340 - 0.112462i) q^{15} +(0.669812 - 1.16015i) q^{16} +(-3.20096 - 5.54423i) q^{17} +(-3.33787 + 3.33787i) q^{18} +(-0.954087 + 3.56070i) q^{19} +(-0.0545333 - 0.0146122i) q^{20} +(-0.391832 - 0.678673i) q^{22} +(-2.41997 - 1.39717i) q^{23} +(1.97895 + 7.38555i) q^{24} -4.99862i q^{25} +(-0.375476 - 2.47524i) q^{26} +11.8894i q^{27} +(1.84998 - 3.20426i) q^{29} +(0.0700128 - 0.0404219i) q^{30} +(1.93054 + 1.93054i) q^{31} +(5.61737 + 1.50517i) q^{32} +(-3.41242 - 0.914355i) q^{33} +(3.14327 - 3.14327i) q^{34} +(8.93636 + 5.15941i) q^{36} +(5.39204 - 1.44479i) q^{37} -2.55963 q^{38} +(-9.08715 - 6.69336i) q^{39} -0.0908555i q^{40} +(-0.188789 + 0.0505859i) q^{41} +(1.84817 - 1.06704i) q^{43} +(-1.21133 + 1.21133i) q^{44} +(0.0654456 - 0.244246i) q^{45} +(0.502183 - 1.87417i) q^{46} +(-3.97588 + 3.97588i) q^{47} +(3.63152 - 2.09666i) q^{48} +(3.35258 - 0.898322i) q^{50} -20.0394i q^{51} +(-5.01402 + 2.19324i) q^{52} +0.591643 q^{53} +(-7.97425 + 2.13669i) q^{54} +(0.0363547 + 0.0209894i) q^{55} +(-8.15927 + 8.15927i) q^{57} +(2.48157 + 0.664935i) q^{58} +(-10.8879 - 2.91741i) q^{59} +(-0.124962 - 0.124962i) q^{60} +(1.18838 - 0.686113i) q^{61} +(-0.947871 + 1.64176i) q^{62} +1.35883i q^{64} +(0.0837147 + 0.104772i) q^{65} -2.45304i q^{66} +(1.95238 + 7.28639i) q^{67} +(-8.41537 - 4.85861i) q^{68} +(-4.37346 - 7.57505i) q^{69} +(-9.88214 - 2.64791i) q^{71} +(-4.29793 + 16.0401i) q^{72} +(1.93317 - 1.93317i) q^{73} +(1.93805 + 3.35680i) q^{74} +(7.82338 - 13.5505i) q^{75} +(1.44817 + 5.40465i) q^{76} +(2.85616 - 7.29767i) q^{78} +3.26258 q^{79} +(-0.0481297 + 0.0128963i) 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} +(1.04781 + 1.04781i) q^{86} +(10.0300 - 5.79083i) q^{87} +(-2.38748 - 1.37841i) q^{88} +(4.36016 + 16.2723i) q^{89} +0.175578 q^{90} -4.24143 q^{92} +(2.21189 + 8.25489i) q^{93} +(-3.38116 - 1.95211i) q^{94} +(0.118743 - 0.0685564i) q^{95} +(12.8721 + 12.8721i) q^{96} +(-0.663884 + 2.47765i) q^{97} +(-5.42534 - 5.42534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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