LMFDB - Embedded newform 637.2.bc.a.411.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			411.5
Character	$\chi$	$=$	637.411
Dual form			637.2.bc.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98293 - 0.531325i) q^{2} +(-1.57586 + 0.909822i) q^{3} +(1.91766 - 1.10716i) q^{4} +(0.737409 + 2.75205i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 - 0.269427i) q^{9} +O(q^{10})$	\(q+(1.98293 - 0.531325i) q^{2} +(-1.57586 + 0.909822i) q^{3} +(1.91766 - 1.10716i) q^{4} +(0.737409 + 2.75205i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 - 0.269427i) q^{9} +(2.92446 + 5.06531i) q^{10} +(-0.616905 - 0.165299i) q^{11} +(-2.01464 + 3.48946i) q^{12} +(-3.40251 + 1.19288i) q^{13} +(-3.66593 - 3.66593i) q^{15} +(-1.76271 + 3.05311i) q^{16} +(-2.16336 - 3.74705i) q^{17} +(0.165299 - 0.616905i) q^{18} +(1.24540 + 4.64791i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +(0.808282 + 0.466662i) q^{23} +(-0.207209 + 0.773315i) q^{24} +(-2.69986 + 1.55877i) q^{25} +(-6.11313 + 4.17322i) q^{26} -4.89283i q^{27} +6.33185 q^{29} +(-9.21707 - 5.32148i) q^{30} +(7.48282 + 2.00502i) q^{31} +(-2.10089 + 7.84064i) q^{32} +(1.12255 - 0.300786i) q^{33} +(-6.28070 - 6.28070i) q^{34} -0.688892i q^{36} +(0.783477 + 2.92397i) q^{37} +(4.93910 + 8.55477i) q^{38} +(4.27656 - 4.97548i) q^{39} +(1.08560 + 0.626770i) q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(-1.36603 + 0.366025i) q^{44} +(0.856183 + 0.229414i) q^{45} +(1.85072 + 0.495898i) q^{46} +(8.07264 - 2.16306i) q^{47} -6.41503i q^{48} +(-4.52543 + 4.52543i) q^{50} +(6.81830 + 3.93655i) q^{51} +(-5.20414 + 6.05464i) q^{52} +(-1.68098 - 2.91155i) q^{53} +(-2.59968 - 9.70214i) q^{54} -1.81964i q^{55} +(-6.19135 - 6.19135i) q^{57} +(12.5556 - 3.36427i) q^{58} +(0.0935769 - 0.349234i) q^{59} +(-11.0888 - 2.97122i) q^{60} +(-6.74625 - 3.89495i) q^{61} +15.9032 q^{62} +9.61285i q^{64} +(-5.79189 - 8.48422i) q^{65} +(2.06612 - 1.19288i) q^{66} +(2.66503 - 9.94603i) q^{67} +(-8.29717 - 4.79037i) q^{68} -1.69832 q^{69} +(5.56914 + 5.56914i) q^{71} +(-0.0354269 - 0.132215i) q^{72} +(3.24351 - 12.1050i) q^{73} +(3.10716 + 5.38176i) q^{74} +(2.83640 - 4.91279i) q^{75} +(7.53424 + 7.53424i) q^{76} +(5.83654 - 12.1383i) q^{78} +(6.89853 - 11.9486i) q^{79} +(-9.70214 - 2.59968i) q^{80} +(4.91827 + 8.51869i) q^{81} +(-2.64141 + 4.57505i) q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(5.56801 + 20.7801i) q^{86} +(-9.97810 + 5.76086i) q^{87} +(-0.243350 + 0.140498i) q^{88} +(7.66632 - 2.05418i) q^{89} +1.81964 q^{90} +2.06668 q^{92} +(-13.6161 + 3.64842i) q^{93} +(14.8582 - 8.57839i) q^{94} +(-11.8729 + 6.85482i) q^{95} +(-3.82288 - 14.2672i) q^{96} +(0.236784 - 0.236784i) q^{97} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.98293	−	0.531325i	1.40214	−	0.375703i	0.523030	−	0.852315i	$-0.324802\pi$
$2$	1.98293	−	0.531325i	1.40214	−	0.375703i	0.879114	+	0.476611i	$0.158135\pi$
$3$	−1.57586	+	0.909822i	−0.909822	+	0.525286i	−0.880374	−	0.474280i	$-0.842708\pi$
$3$	−1.57586	+	0.909822i	−0.909822	+	0.525286i	−0.0294485	+	0.999566i	$0.509375\pi$
$4$	1.91766	−	1.10716i	0.958829	−	0.553580i
$5$	0.737409	+	2.75205i	0.329779	+	1.23075i	0.909419	+	0.415880i	$0.136526\pi$
$5$	0.737409	+	2.75205i	0.329779	+	1.23075i	−0.579640	+	0.814872i	$0.696807\pi$
$6$	−2.64141	+	2.64141i	−1.07835	+	1.07835i
$7$		0			0
$7$		0			0
$8$	0.311108	−	0.311108i	0.109993	−	0.109993i
$9$	0.155554	−	0.269427i	0.0518513	−	0.0898091i
$10$	2.92446	+	5.06531i	0.924796	+	1.60179i
$11$	−0.616905	−	0.165299i	−0.186004	−	0.0498396i	0.164615	−	0.986358i	$-0.447362\pi$
$11$	−0.616905	−	0.165299i	−0.186004	−	0.0498396i	−0.350619	+	0.936518i	$0.614029\pi$
$12$	−2.01464	+	3.48946i	−0.581576	+	1.00732i
$13$	−3.40251	+	1.19288i	−0.943685	+	0.330844i
$13$	−3.40251	+	1.19288i	−0.943685	+	0.330844i
$14$		0			0
$15$	−3.66593	−	3.66593i	−0.946538	−	0.946538i
$16$	−1.76271	+	3.05311i	−0.440678	+	0.763277i
$17$	−2.16336	−	3.74705i	−0.524692	−	0.908794i	−0.999587	−	0.0287509i	$-0.990847\pi$
$17$	−2.16336	−	3.74705i	−0.524692	−	0.908794i	0.474894	−	0.880043i	$-0.342486\pi$
$18$	0.165299	−	0.616905i	0.0389614	−	0.145406i
$19$	1.24540	+	4.64791i	0.285715	+	1.06630i	0.948315	+	0.317330i	$0.102786\pi$
$19$	1.24540	+	4.64791i	0.285715	+	1.06630i	−0.662600	+	0.748974i	$0.730547\pi$
$20$	4.46105	+	4.46105i	0.997522	+	0.997522i
$21$		0			0
$22$	−1.31111			−0.279529
$23$	0.808282	+	0.466662i	0.168538	+	0.0973057i	0.581896	−	0.813263i	$-0.302311\pi$
$23$	0.808282	+	0.466662i	0.168538	+	0.0973057i	−0.413358	+	0.910569i	$0.635644\pi$
$24$	−0.207209	+	0.773315i	−0.0422964	+	0.157852i
$25$	−2.69986	+	1.55877i	−0.539972	+	0.311753i
$26$	−6.11313	+	4.17322i	−1.19888	+	0.818437i
$27$		−	4.89283i		−	0.941625i
$28$		0			0
$29$	6.33185			1.17580			0.587898	−	0.808935i	$-0.299956\pi$
$29$	6.33185			1.17580			0.587898	+	0.808935i	$0.299956\pi$
$30$	−9.21707	−	5.32148i	−1.68280	−	0.971565i
$31$	7.48282	+	2.00502i	1.34395	+	0.360112i	0.857900	−	0.513817i	$-0.171769\pi$
$31$	7.48282	+	2.00502i	1.34395	+	0.360112i	0.486055	+	0.873928i	$0.338435\pi$
$32$	−2.10089	+	7.84064i	−0.371389	+	1.38604i
$33$	1.12255	−	0.300786i	0.195411	−	0.0523601i
$34$	−6.28070	−	6.28070i	−1.07713	−	1.07713i
$35$		0			0
$36$		−	0.688892i		−	0.114815i
$37$	0.783477	+	2.92397i	0.128803	+	0.480699i	0.999947	−	0.0103293i	$-0.00328799\pi$
$37$	0.783477	+	2.92397i	0.128803	+	0.480699i	−0.871144	+	0.491028i	$0.836621\pi$
$38$	4.93910	+	8.55477i	0.801228	+	1.38777i
$39$	4.27656	−	4.97548i	0.684798	−	0.796714i
$40$	1.08560	+	0.626770i	0.171648	+	0.0991010i
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	−0.834774	−	0.550593i	$-0.814402\pi$
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	0.550593	+	0.834774i	$0.314402\pi$
$42$		0			0
$43$			10.4795i			1.59811i	0.601259	+	0.799054i	$0.294666\pi$
$43$			10.4795i			1.59811i	−0.601259	+	0.799054i	$0.705334\pi$
$44$	−1.36603	+	0.366025i	−0.205936	+	0.0551804i
$45$	0.856183	+	0.229414i	0.127632	+	0.0341990i
$46$	1.85072	+	0.495898i	0.272873	+	0.0731161i
$47$	8.07264	−	2.16306i	1.17752	−	0.315514i	0.383575	−	0.923510i	$-0.374693\pi$
$47$	8.07264	−	2.16306i	1.17752	−	0.315514i	0.793941	+	0.607995i	$0.208026\pi$
$48$		−	6.41503i		−	0.925929i
$49$		0			0
$50$	−4.52543	+	4.52543i	−0.639992	+	0.639992i
$51$	6.81830	+	3.93655i	0.954754	+	0.551227i
$52$	−5.20414	+	6.05464i	−0.721684	+	0.839628i
$53$	−1.68098	−	2.91155i	−0.230901	−	0.399932i	0.727173	−	0.686454i	$-0.240834\pi$
$53$	−1.68098	−	2.91155i	−0.230901	−	0.399932i	−0.958073	+	0.286523i	$0.907501\pi$
$54$	−2.59968	−	9.70214i	−0.353772	−	1.32029i
$55$		−	1.81964i		−	0.245361i
$56$		0			0
$57$	−6.19135	−	6.19135i	−0.820065	−	0.820065i
$58$	12.5556	−	3.36427i	1.64863	−	0.441750i
$59$	0.0935769	−	0.349234i	0.0121827	−	0.0454663i	−0.959567	−	0.281481i	$-0.909175\pi$
$59$	0.0935769	−	0.349234i	0.0121827	−	0.0454663i	0.971750	+	0.236014i	$0.0758412\pi$
$60$	−11.0888	−	2.97122i	−1.43155	−	0.383583i
$61$	−6.74625	−	3.89495i	−0.863768	−	0.498697i	0.00150413	−	0.999999i	$-0.499521\pi$
$61$	−6.74625	−	3.89495i	−0.863768	−	0.498697i	−0.865272	+	0.501302i	$0.832855\pi$
$62$	15.9032			2.01971
$63$		0			0
$64$			9.61285i			1.20161i
$65$	−5.79189	−	8.48422i	−0.718395	−	1.05234i
$66$	2.06612	−	1.19288i	0.254322	−	0.146833i
$67$	2.66503	−	9.94603i	0.325585	−	1.21510i	−0.588137	−	0.808761i	$-0.700138\pi$
$67$	2.66503	−	9.94603i	0.325585	−	1.21510i	0.913722	−	0.406339i	$-0.133195\pi$
$68$	−8.29717	−	4.79037i	−1.00618	−	0.580918i
$69$	−1.69832			−0.204453
$70$		0			0
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	0.955600	−	0.294665i	$-0.0952082\pi$
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	−0.294665	+	0.955600i	$0.595208\pi$
$72$	−0.0354269	−	0.132215i	−0.00417510	−	0.0155817i
$73$	3.24351	−	12.1050i	0.379624	−	1.41678i	−0.466844	−	0.884339i	$-0.654609\pi$
$73$	3.24351	−	12.1050i	0.379624	−	1.41678i	0.846469	−	0.532438i	$-0.178724\pi$
$74$	3.10716	+	5.38176i	0.361200	+	0.625617i
$75$	2.83640	−	4.91279i	0.327519	−	0.567280i
$76$	7.53424	+	7.53424i	0.864236	+	0.864236i
$77$		0			0
$78$	5.83654	−	12.1383i	0.660857	−	1.37439i
$79$	6.89853	−	11.9486i	0.776145	−	1.34432i	−0.158004	−	0.987439i	$-0.550506\pi$
$79$	6.89853	−	11.9486i	0.776145	−	1.34432i	0.934149	−	0.356884i	$-0.116161\pi$
$80$	−9.70214	−	2.59968i	−1.08473	−	0.290653i
$81$	4.91827	+	8.51869i	0.546474	+	0.946521i
$82$	−2.64141	+	4.57505i	−0.291695	+	0.505230i
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	−0.902835	−	0.429987i	$-0.858518\pi$
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	0.429987	+	0.902835i	$0.358518\pi$
$84$		0			0
$85$	8.71678	−	8.71678i	0.945468	−	0.945468i
$86$	5.56801	+	20.7801i	0.600414	+	2.24078i
$87$	−9.97810	+	5.76086i	−1.06976	+	0.617629i
$88$	−0.243350	+	0.140498i	−0.0259412	+	0.0149772i
$89$	7.66632	−	2.05418i	0.812628	−	0.217743i	0.171507	−	0.985183i	$-0.445136\pi$
$89$	7.66632	−	2.05418i	0.812628	−	0.217743i	0.641121	+	0.767440i	$0.278470\pi$
$90$	1.81964			0.191807
$91$		0			0
$92$	2.06668			0.215466
$93$	−13.6161	+	3.64842i	−1.41192	+	0.378323i
$94$	14.8582	−	8.57839i	1.53251	−	0.884793i
$95$	−11.8729	+	6.85482i	−1.21813	+	0.703289i
$96$	−3.82288	−	14.2672i	−0.390171	−	1.45614i
$97$	0.236784	−	0.236784i	0.0240417	−	0.0240417i	−0.694984	−	0.719025i	$-0.744588\pi$
$97$	0.236784	−	0.236784i	0.0240417	−	0.0240417i	0.719025	+	0.694984i	$0.244588\pi$
$98$		0			0
$99$	−0.140498	+	0.140498i	−0.0141206	+	0.0141206i
$100$	−3.45161	+	5.97836i	−0.345161	+	0.597836i
$101$	4.60978	+	7.98437i	0.458690	+	0.794474i	0.998892	−	0.0470611i	$-0.0149856\pi$
$101$	4.60978	+	7.98437i	0.458690	+	0.794474i	−0.540202	+	0.841535i	$0.681652\pi$
$102$	15.6118	+	4.18317i	1.54580	+	0.414196i
$103$	−1.25354	+	2.17119i	−0.123515	+	0.213934i	−0.921151	−	0.389204i	$-0.872750\pi$
$103$	−1.25354	+	2.17119i	−0.123515	+	0.213934i	0.797637	+	0.603138i	$0.206083\pi$
$104$	−0.687433	+	1.42966i	−0.0674084	+	0.140190i
$105$		0			0
$106$	−4.88025	−	4.88025i	−0.474011	−	0.474011i
$107$	−1.44123	+	2.49629i	−0.139329	+	0.241326i	−0.927243	−	0.374460i	$-0.877828\pi$
$107$	−1.44123	+	2.49629i	−0.139329	+	0.241326i	0.787914	+	0.615786i	$0.211161\pi$
$108$	−5.41714	−	9.38277i	−0.521265	−	0.902857i
$109$	−1.29880	+	4.84720i	−0.124403	+	0.464277i	−0.999818	−	0.0190949i	$-0.993922\pi$
$109$	−1.29880	+	4.84720i	−0.124403	+	0.464277i	0.875415	+	0.483372i	$0.160588\pi$
$110$	−0.966822	−	3.60823i	−0.0921829	−	0.344031i
$111$	−3.89495	−	3.89495i	−0.369692	−	0.369692i
$112$		0			0
$113$	−16.3526			−1.53832			−0.769161	−	0.639055i	$-0.779326\pi$
$113$	−16.3526			−1.53832			−0.769161	+	0.639055i	$0.779326\pi$
$114$	−15.5666	−	8.98741i	−1.45795	−	0.841748i
$115$	−0.688241	+	2.56855i	−0.0641788	+	0.239518i
$116$	12.1423	−	7.01037i	1.12739	−	0.650897i
$117$	−0.207880	+	1.10228i	−0.0192185	+	0.101906i
$118$		−	0.742226i		−	0.0683274i
$119$		0			0
$120$	−2.28100			−0.208226
$121$	−9.17303	−	5.29605i	−0.833912	−	0.481459i
$122$	−15.4468	−	4.13896i	−1.39849	−	0.374724i
$123$	1.21195	−	4.52306i	0.109278	−	0.407830i
$124$	16.5694	−	4.43975i	1.48797	−	0.398701i
$125$	3.79249	+	3.79249i	0.339211	+	0.339211i
$126$		0			0
$127$		−	13.8272i		−	1.22696i	−0.789709	−	0.613481i	$-0.789769\pi$
$127$		−	13.8272i		−	1.22696i	0.789709	−	0.613481i	$-0.210231\pi$
$128$	0.905756	+	3.38033i	0.0800583	+	0.298782i
$129$	−9.53448	−	16.5142i	−0.839464	−	1.45399i
$130$	−15.9928	−	13.7462i	−1.40266	−	1.20563i
$131$	11.1112	+	6.41503i	0.970786	+	0.560483i	0.899476	−	0.436971i	$-0.143949\pi$
$131$	11.1112	+	6.41503i	0.970786	+	0.560483i	0.0713101	+	0.997454i	$0.477282\pi$
$132$	1.81964	−	1.81964i	0.158380	−	0.158380i
$133$		0			0
$134$		−	21.1383i		−	1.82607i
$135$	13.4653	−	3.60801i	1.15891	−	0.310528i
$136$	−1.83878	−	0.492699i	−0.157674	−	0.0422486i
$137$	−3.27949	−	0.878736i	−0.280185	−	0.0750755i	0.115990	−	0.993250i	$-0.462996\pi$
$137$	−3.27949	−	0.878736i	−0.280185	−	0.0750755i	−0.396175	+	0.918175i	$0.629663\pi$
$138$	−3.36765	+	0.902358i	−0.286673	+	0.0768138i
$139$			3.34184i			0.283451i	0.989906	+	0.141726i	$0.0452651\pi$
$139$			3.34184i			0.283451i	−0.989906	+	0.141726i	$0.954735\pi$
$140$		0			0
$141$	−10.7533	+	10.7533i	−0.905595	+	0.905595i
$142$	14.0022	+	8.08419i	1.17504	+	0.678410i
$143$	2.29621	−	0.173459i	0.192018	−	0.0145054i
$144$	0.548394	+	0.949846i	0.0456995	+	0.0791539i
$145$	4.66916	+	17.4255i	0.387753	+	1.44711i
$146$		−	25.7266i		−	2.12915i
$147$		0			0
$148$	4.73975	+	4.73975i	0.389605	+	0.389605i
$149$	−3.59177	+	0.962413i	−0.294250	+	0.0788439i	−0.402924	−	0.915233i	$-0.632006\pi$
$149$	−3.59177	+	0.962413i	−0.294250	+	0.0788439i	0.108674	+	0.994077i	$0.465339\pi$
$150$	3.01410	−	11.2488i	0.246100	−	0.918458i
$151$	6.53432	+	1.75087i	0.531756	+	0.142484i	0.514699	−	0.857371i	$-0.327904\pi$
$151$	6.53432	+	1.75087i	0.531756	+	0.142484i	0.0170568	+	0.999855i	$0.494570\pi$
$152$	1.83346	+	1.05855i	0.148713	+	0.0858594i
$153$	−1.34608			−0.108824
$154$		0			0
$155$			22.0716i			1.77283i
$156$	2.69233	−	14.2761i	0.215559	−	1.14300i
$157$	2.96650	−	1.71271i	0.236753	−	0.136689i	−0.376931	−	0.926242i	$-0.623020\pi$
$157$	2.96650	−	1.71271i	0.236753	−	0.136689i	0.613683	+	0.789552i	$0.289687\pi$
$158$	7.33072	−	27.3586i	0.583200	−	2.17653i
$159$	5.29798	+	3.05879i	0.420157	+	0.242578i
$160$	−23.1270			−1.82835
$161$		0			0
$162$	14.2788	+	14.2788i	1.12185	+	1.12185i
$163$	3.82474	+	14.2741i	0.299577	+	1.11804i	0.937514	+	0.347947i	$0.113121\pi$
$163$	3.82474	+	14.2741i	0.299577	+	1.11804i	−0.637937	+	0.770088i	$0.720212\pi$
$164$	−1.47482	+	5.50409i	−0.115164	+	0.429797i
$165$	1.65555	+	2.86750i	0.128885	+	0.223235i
$166$	−6.25330	+	10.8310i	−0.485350	+	0.840651i
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.952933	+	0.303180i	$0.0980483\pi$
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.303180	+	0.952933i	$0.401952\pi$
$168$		0			0
$169$	10.1541	−	8.11753i	0.781084	−	0.624426i
$170$	12.6533	−	21.9162i	0.970466	−	1.68090i
$171$	1.44600	+	0.387455i	0.110578	+	0.0296294i
$172$	11.6025	+	20.0961i	0.884680	+	1.53231i
$173$	7.19052	−	12.4543i	0.546685	−	0.946886i	−0.451814	−	0.892112i	$-0.649223\pi$
$173$	7.19052	−	12.4543i	0.546685	−	0.946886i	0.998499	−	0.0547740i	$-0.0174439\pi$
$174$	−16.7250	+	16.7250i	−1.26792	+	1.26792i
$175$		0			0
$176$	1.59210	−	1.59210i	0.120009	−	0.120009i
$177$	0.170277	+	0.635481i	0.0127988	+	0.0477657i
$178$	14.1103	−	8.14661i	1.05762	−	0.610614i
$179$	−3.56030	+	2.05554i	−0.266109	+	0.153638i	−0.627118	−	0.778924i	$-0.715766\pi$
$179$	−3.56030	+	2.05554i	−0.266109	+	0.153638i	0.361009	+	0.932562i	$0.382432\pi$
$180$	1.89586	−	0.507995i	0.141309	−	0.0378637i
$181$	−21.5760			−1.60373			−0.801867	−	0.597502i	$-0.796160\pi$
$181$	−21.5760			−1.60373			−0.801867	+	0.597502i	$0.796160\pi$
$182$		0			0
$183$	14.1748			1.04783
$184$	0.396645	−	0.106281i	0.0292411	−	0.00783512i
$185$	−7.46917	+	4.31233i	−0.549144	+	0.317049i
$186$	−25.0613	+	14.4691i	−1.83758	+	1.06093i
$187$	0.715204	+	2.66918i	0.0523009	+	0.195190i
$188$	13.0857	−	13.0857i	0.954373	−	0.954373i
$189$		0			0
$190$	−19.9010	+	19.9010i	−1.44377	+	1.44377i
$191$	−5.15087	+	8.92157i	−0.372704	+	0.645542i	−0.989980	−	0.141204i	$-0.954903\pi$
$191$	−5.15087	+	8.92157i	−0.372704	+	0.645542i	0.617277	+	0.786746i	$0.288236\pi$
$192$	−8.74598	−	15.1485i	−0.631187	−	1.09325i
$193$	−8.58672	−	2.30081i	−0.618086	−	0.165616i	−0.0638284	−	0.997961i	$-0.520331\pi$
$193$	−8.58672	−	2.30081i	−0.618086	−	0.165616i	−0.554257	+	0.832345i	$0.686998\pi$
$194$	0.343717	−	0.595335i	0.0246774	−	0.0427425i
$195$	16.8463	+	8.10034i	1.20639	+	0.580078i
$196$		0			0
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	0.581751	−	0.813367i	$-0.302368\pi$
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	−0.813367	+	0.581751i	$0.802368\pi$
$198$	−0.203948	+	0.353248i	−0.0144939	+	0.0251043i
$199$	−3.10058	−	5.37036i	−0.219794	−	0.380695i	0.734951	−	0.678121i	$-0.237205\pi$
$199$	−3.10058	−	5.37036i	−0.219794	−	0.380695i	−0.954745	+	0.297426i	$0.903872\pi$
$200$	−0.355004	+	1.32489i	−0.0251026	+	0.0936840i
$201$	4.84941	+	18.0982i	0.342051	+	1.27655i
$202$	13.3832	+	13.3832i	0.941636	+	0.941636i
$203$		0			0
$204$	17.4336			1.22059
$205$	−6.34957	−	3.66593i	−0.443473	−	0.256039i
$206$	−1.33207	+	4.97136i	−0.0928099	+	0.346371i
$207$	0.251463	−	0.145182i	0.0174779	−	0.0100909i
$208$	2.35567	−	12.4909i	0.163336	−	0.866090i
$209$		−	3.07318i		−	0.212577i
$210$		0			0
$211$	−9.55554			−0.657830			−0.328915	−	0.944359i	$-0.606683\pi$
$211$	−9.55554			−0.657830			−0.328915	+	0.944359i	$0.606683\pi$
$212$	−6.44709	−	3.72223i	−0.442788	−	0.255644i
$213$	−13.8431	−	3.70925i	−0.948514	−	0.254153i
$214$	−1.53153	+	5.71573i	−0.104693	+	0.390720i
$215$	−28.8401	+	7.72767i	−1.96688	+	0.527023i
$216$	−1.52220	−	1.52220i	−0.103572	−	0.103572i
$217$		0			0
$218$			10.3017i			0.697722i
$219$	5.90204	+	22.0267i	0.398823	+	1.48843i
$220$	−2.01464	−	3.48946i	−0.135827	−	0.235259i
$221$	11.8306	+	10.1687i	0.795813	+	0.684024i
$222$	−9.79289	−	5.65393i	−0.657256	−	0.379467i
$223$	2.58074	−	2.58074i	0.172819	−	0.172819i	−0.615398	−	0.788217i	$-0.711005\pi$
$223$	2.58074	−	2.58074i	0.172819	−	0.172819i	0.788217	+	0.615398i	$0.211005\pi$
$224$		0			0
$225$			0.969888i			0.0646592i
$226$	−32.4261	+	8.68854i	−2.15695	+	0.577953i
$227$	7.17713	+	1.92311i	0.476363	+	0.127641i	0.489009	−	0.872279i	$-0.337359\pi$
$227$	7.17713	+	1.92311i	0.476363	+	0.127641i	−0.0126456	+	0.999920i	$0.504025\pi$
$228$	−18.7277	−	5.01807i	−1.24027	−	0.332330i
$229$	−0.996139	+	0.266915i	−0.0658267	+	0.0176382i	−0.291582	−	0.956546i	$-0.594182\pi$
$229$	−0.996139	+	0.266915i	−0.0658267	+	0.0176382i	0.225755	+	0.974184i	$0.427515\pi$
$230$			5.45893i			0.359952i
$231$		0			0
$232$	1.96989	−	1.96989i	0.129330	−	0.129330i
$233$	21.3154	+	12.3064i	1.39642	+	0.806221i	0.994015	−	0.109243i	$-0.0348428\pi$
$233$	21.3154	+	12.3064i	1.39642	+	0.806221i	0.402400	+	0.915464i	$0.368176\pi$
$234$	0.173459	+	2.29621i	0.0113394	+	0.150108i
$235$	11.9057	+	20.6212i	0.776640	+	1.34518i
$236$	−0.207209	−	0.773315i	−0.0134882	−	0.0503385i
$237$			25.1057i			1.63079i
$238$		0			0
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	0.463830	−	0.885924i	$-0.346475\pi$
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	−0.885924	+	0.463830i	$0.846475\pi$
$240$	17.6545	−	4.73050i	1.13959	−	0.305352i
$241$	−7.37772	+	27.5340i	−0.475240	+	1.77362i	0.145237	+	0.989397i	$0.453606\pi$
$241$	−7.37772	+	27.5340i	−0.475240	+	1.77362i	−0.620477	+	0.784225i	$0.713061\pi$
$242$	−21.0034	−	5.62785i	−1.35015	−	0.361772i
$243$	−2.78905	−	1.61026i	−0.178917	−	0.103298i
$244$	−17.2493			−1.10427
$245$		0			0
$246$		−	9.61285i		−	0.612893i
$247$	−9.78187	−	14.3289i	−0.622406	−	0.911728i
$248$	2.95174	−	1.70419i	0.187436	−	0.108216i
$249$	2.86918	−	10.7079i	0.181827	−	0.678588i
$250$	9.53529	+	5.50520i	0.603065	+	0.348180i
$251$	14.4448			0.911747			0.455873	−	0.890045i	$-0.349327\pi$
$251$	14.4448			0.911747			0.455873	+	0.890045i	$0.349327\pi$
$252$		0			0
$253$	−0.421494	−	0.421494i	−0.0264991	−	0.0264991i
$254$	−7.34672	−	27.4183i	−0.460974	−	1.72038i
$255$	−5.80569	+	21.6671i	−0.363567	+	1.35685i
$256$	−6.02074	−	10.4282i	−0.376296	−	0.651765i
$257$	7.31185	−	12.6645i	0.456101	−	0.789989i	−0.542650	−	0.839959i	$-0.682579\pi$
$257$	7.31185	−	12.6645i	0.456101	−	0.789989i	0.998751	+	0.0499695i	$0.0159124\pi$
$258$	−27.6806	−	27.6806i	−1.72332	−	1.72332i
$259$		0			0
$260$	−20.5002	−	9.85728i	−1.27137	−	0.611322i
$261$	0.984944	−	1.70597i	0.0609665	−	0.105597i
$262$	25.4411	+	6.81692i	1.57176	+	0.421151i
$263$	1.30865	+	2.26664i	0.0806946	+	0.139767i	0.903548	−	0.428486i	$-0.140953\pi$
$263$	1.30865	+	2.26664i	0.0806946	+	0.139767i	−0.822854	+	0.568253i	$0.807619\pi$
$264$	0.255657	−	0.442810i	0.0157346	−	0.0272531i
$265$	6.77314	−	6.77314i	0.416071	−	0.416071i
$266$		0			0
$267$	−10.2121	+	10.2121i	−0.624970	+	0.624970i
$268$	−5.90123	−	22.0237i	−0.360475	−	1.34531i
$269$	8.50732	−	4.91170i	0.518700	−	0.299472i	−0.217702	−	0.976015i	$-0.569856\pi$
$269$	8.50732	−	4.91170i	0.518700	−	0.299472i	0.736403	+	0.676543i	$0.236523\pi$
$270$	24.7837	−	14.3089i	1.50829	−	0.870811i
$271$	−4.69145	+	1.25707i	−0.284985	+	0.0763616i	−0.398480	−	0.917177i	$-0.630462\pi$
$271$	−4.69145	+	1.25707i	−0.284985	+	0.0763616i	0.113495	+	0.993539i	$0.463796\pi$
$272$	15.2535			0.924882
$273$		0			0
$274$	−6.96989			−0.421066
$275$	1.92322	−	0.515326i	0.115975	−	0.0310753i
$276$	−3.25679	+	1.88031i	−0.196036	+	0.113181i
$277$	5.10848	−	2.94938i	0.306939	−	0.177211i	−0.338617	−	0.940924i	$-0.609959\pi$
$277$	5.10848	−	2.94938i	0.306939	−	0.177211i	0.645556	+	0.763713i	$0.276626\pi$
$278$	1.77560	+	6.62664i	0.106494	+	0.397440i
$279$	1.70419	−	1.70419i	0.102027	−	0.102027i
$280$		0			0
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	−0.375694	−	0.926744i	$-0.622595\pi$
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	0.926744	+	0.375694i	$0.122595\pi$
$282$	−15.6096	+	27.0367i	−0.929539	+	1.61001i
$283$	4.16360	+	7.21158i	0.247501	+	0.428684i	0.962832	−	0.270102i	$-0.0870574\pi$
$283$	4.16360	+	7.21158i	0.247501	+	0.428684i	−0.715331	+	0.698786i	$0.753724\pi$
$284$	16.8456	+	4.51377i	0.999604	+	0.267843i
$285$	12.4733	−	21.6044i	0.738857	−	1.27974i
$286$	4.46105	−	1.56399i	0.263788	−	0.0924806i
$287$		0			0
$288$	1.78568	+	1.78568i	0.105222	+	0.105222i
$289$	−0.860268	+	1.49003i	−0.0506040	+	0.0876486i
$290$	18.5172	+	32.0728i	1.08737	+	1.88338i
$291$	−0.157707	+	0.588569i	−0.00924492	+	0.0345025i
$292$	−7.18217	−	26.8042i	−0.420305	−	1.56860i
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	0.0909047	−	0.995860i	$-0.471024\pi$
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	−0.995860	+	0.0909047i	$0.971024\pi$
$294$		0			0
$295$	1.03011			0.0599754
$296$	1.15342	+	0.665926i	0.0670410	+	0.0387061i
$297$	−0.808781	+	3.01841i	−0.0469302	+	0.175146i
$298$	−6.61088	+	3.81680i	−0.382958	+	0.221101i
$299$	−3.30685	−	0.623640i	−0.191240	−	0.0360660i
$300$		−	12.5614i		−	0.725232i
$301$		0			0
$302$	13.8874			0.799130
$303$	−14.5287	−	8.38816i	−0.834653	−	0.481887i
$304$	−16.3859	−	4.39058i	−0.939794	−	0.251817i
$305$	5.74433	−	21.4381i	0.328920	−	1.22754i
$306$	−2.66918	+	0.715204i	−0.152587	+	0.0408855i
$307$	5.77526	+	5.77526i	0.329611	+	0.329611i	0.852439	−	0.522827i	$-0.175123\pi$
$307$	5.77526	+	5.77526i	0.329611	+	0.329611i	−0.522827	+	0.852439i	$0.675123\pi$
$308$		0			0
$309$		−	4.56199i		−	0.259523i
$310$	11.7272	+	43.7664i	0.666059	+	2.48577i
$311$	1.31281	+	2.27385i	0.0744426	+	0.128938i	0.900844	−	0.434143i	$-0.142949\pi$
$311$	1.31281	+	2.27385i	0.0744426	+	0.128938i	−0.826401	+	0.563082i	$0.809616\pi$
$312$	−0.217438	−	2.87838i	−0.0123100	−	0.162956i
$313$	−17.1897	−	9.92447i	−0.971618	−	0.560964i	−0.0718889	−	0.997413i	$-0.522903\pi$
$313$	−17.1897	−	9.92447i	−0.971618	−	0.560964i	−0.899729	+	0.436449i	$0.856236\pi$
$314$	4.97237	−	4.97237i	0.280607	−	0.280607i
$315$		0			0
$316$		−	30.5511i		−	1.71863i
$317$	−1.56771	+	0.420067i	−0.0880514	+	0.0235933i	−0.302576	−	0.953125i	$-0.597847\pi$
$317$	−1.56771	+	0.420067i	−0.0880514	+	0.0235933i	0.214524	+	0.976719i	$0.431180\pi$
$318$	12.1307	+	3.25042i	0.680258	+	0.182275i
$319$	−3.90615	−	1.04665i	−0.218703	−	0.0586012i
$320$	−26.4550	+	7.08860i	−1.47888	+	0.396265i
$321$		−	5.24507i		−	0.292751i
$322$		0			0
$323$	14.7217	−	14.7217i	0.819137	−	0.819137i
$324$	18.8631	+	10.8906i	1.04795	+	0.605034i
$325$	7.32688	−	8.52431i	0.406422	−	0.472844i
$326$	15.1684	+	26.2724i	0.840099	+	1.45509i
$327$	−2.36336	−	8.82018i	−0.130694	−	0.487757i
$328$			1.13221i			0.0625159i
$329$		0			0
$330$	4.80642	+	4.80642i	0.264585	+	0.264585i
$331$	3.96586	−	1.06265i	0.217983	−	0.0584085i	−0.148174	−	0.988961i	$-0.547340\pi$
$331$	3.96586	−	1.06265i	0.217983	−	0.0584085i	0.366158	+	0.930553i	$0.380673\pi$
$332$	−3.49150	+	13.0305i	−0.191621	+	0.715139i
$333$	0.909671	+	0.243746i	0.0498497	+	0.0133572i
$334$	40.8128	+	23.5633i	2.23318	+	1.28933i
$335$	29.3371			1.60286
$336$		0			0
$337$		−	4.47304i		−	0.243662i	−0.992551	−	0.121831i	$-0.961123\pi$
$337$		−	4.47304i		−	0.243662i	0.992551	−	0.121831i	$-0.0388766\pi$
$338$	15.8218	−	21.4916i	0.860594	−	1.16899i
$339$	25.7694	−	14.8780i	1.39960	−	0.808060i
$340$	7.06493	−	26.3667i	0.383149	−	1.42993i
$341$	−4.28477	−	2.47381i	−0.232033	−	0.133964i
$342$	3.07318			0.166179
$343$		0			0
$344$	3.26025	+	3.26025i	0.175781	+	0.175781i
$345$	−1.25235	−	4.67385i	−0.0674245	−	0.251632i
$346$	7.64100	−	28.5166i	0.410783	−	1.53306i
$347$	−4.40567	−	7.63085i	−0.236509	−	0.409645i	0.723201	−	0.690637i	$-0.242670\pi$
$347$	−4.40567	−	7.63085i	−0.236509	−	0.409645i	−0.959710	+	0.280992i	$0.909337\pi$
$348$	−12.7564	+	22.0947i	−0.683814	+	1.18440i
$349$	−11.8133	−	11.8133i	−0.632351	−	0.632351i	0.316306	−	0.948657i	$-0.397557\pi$
$349$	−11.8133	−	11.8133i	−0.632351	−	0.632351i	−0.948657	+	0.316306i	$0.897557\pi$
$350$		0			0
$351$	5.83654	+	16.6479i	0.311531	+	0.888598i
$352$	2.59210	−	4.48966i	0.138160	−	0.239299i
$353$	3.97522	+	1.06516i	0.211580	+	0.0566926i	0.363052	−	0.931769i	$-0.381735\pi$
$353$	3.97522	+	1.06516i	0.211580	+	0.0566926i	−0.151472	+	0.988462i	$0.548401\pi$
$354$	0.675294	+	1.16964i	0.0358915	+	0.0621658i
$355$	−11.2198	+	19.4333i	−0.595485	+	1.03141i
$356$	12.4271	−	12.4271i	0.658633	−	0.658633i
$357$		0			0
$358$	−5.96767	+	5.96767i	−0.315401	+	0.315401i
$359$	1.28958	+	4.81279i	0.0680616	+	0.254009i	0.991571	−	0.129567i	$-0.0413589\pi$
$359$	1.28958	+	4.81279i	0.0680616	+	0.254009i	−0.923509	+	0.383577i	$0.874692\pi$
$360$	0.337738	−	0.194993i	0.0178003	−	0.0102770i
$361$	−3.59755	+	2.07705i	−0.189345	+	0.109318i
$362$	−42.7838	+	11.4639i	−2.24867	+	0.602528i
$363$	19.2739			1.01162
$364$		0			0
$365$	35.7052			1.86890
$366$	28.1077	−	7.53144i	1.46921	−	0.393675i
$367$	−17.1570	+	9.90559i	−0.895588	+	0.517068i	−0.875766	−	0.482736i	$-0.839643\pi$
$367$	−17.1570	+	9.90559i	−0.895588	+	0.517068i	−0.0198215	+	0.999804i	$0.506310\pi$
$368$	−2.84954	+	1.64518i	−0.148542	+	0.0857610i
$369$	0.207209	+	0.773315i	0.0107869	+	0.0402572i
$370$	−12.5196	+	12.5196i	−0.650863	+	0.650863i
$371$		0			0
$372$	−22.0716	+	22.0716i	−1.14436	+	1.14436i
$373$	12.2684	−	21.2495i	0.635234	−	1.10026i	−0.351232	−	0.936289i	$-0.614237\pi$
$373$	12.2684	−	21.2495i	0.635234	−	1.10026i	0.986466	−	0.163969i	$-0.0524296\pi$
$374$	2.83640	+	4.91279i	0.146667	+	0.254034i
$375$	−9.42693	−	2.52594i	−0.486804	−	0.130439i
$376$	1.83852	−	3.18441i	0.0948143	−	0.164223i
$377$	−21.5442	+	7.55311i	−1.10958	+	0.389005i
$378$		0			0
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	0.444569	−	0.895745i	$-0.353357\pi$
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	−0.895745	+	0.444569i	$0.853357\pi$
$380$	−15.1788	+	26.2904i	−0.778654	+	1.34867i
$381$	12.5803	+	21.7897i	0.644507	+	1.11632i
$382$	−5.47357	+	20.4276i	−0.280052	+	1.04517i
$383$	−6.55149	−	24.4505i	−0.334765	−	1.24936i	−0.904123	−	0.427272i	$-0.859475\pi$
$383$	−6.55149	−	24.4505i	−0.334765	−	1.24936i	0.569358	−	0.822090i	$-0.307192\pi$
$384$	−4.50284	−	4.50284i	−0.229785	−	0.229785i
$385$		0			0
$386$	−18.2494			−0.928868
$387$	2.82346	+	1.63013i	0.143525	+	0.0828640i
$388$	0.191913	−	0.716228i	0.00974289	−	0.0363609i
$389$	10.4500	−	6.03334i	0.529838	−	0.305902i	−0.211112	−	0.977462i	$-0.567709\pi$
$389$	10.4500	−	6.03334i	0.529838	−	0.305902i	0.740951	+	0.671559i	$0.234375\pi$
$390$	37.7090	+	7.11155i	1.90947	+	0.360107i
$391$		−	4.03823i		−	0.204222i
$392$		0			0
$393$	−23.3461			−1.17766
$394$	−8.17355	−	4.71900i	−0.411778	−	0.237740i
$395$	37.9701	+	10.1741i	1.91049	+	0.511913i
$396$	−0.113873	+	0.424981i	−0.00572235	+	0.0213561i
$397$	−10.6847	+	2.86297i	−0.536251	+	0.143688i	−0.516774	−	0.856122i	$-0.672867\pi$
$397$	−10.6847	+	2.86297i	−0.536251	+	0.143688i	−0.0194779	+	0.999810i	$0.506200\pi$
$398$	−9.00164	−	9.00164i	−0.451212	−	0.451212i
$399$		0			0
$400$		−	10.9906i		−	0.549532i
$401$	−6.44855	−	24.0663i	−0.322025	−	1.20181i	−0.917269	−	0.398269i	$-0.869611\pi$
$401$	−6.44855	−	24.0663i	−0.322025	−	1.20181i	0.595243	−	0.803546i	$-0.297056\pi$
$402$	19.2321	+	33.3109i	0.959209	+	1.66140i
$403$	−27.8521	+	2.10400i	−1.38741	+	0.104807i
$404$	17.6799	+	10.2075i	0.879610	+	0.507843i
$405$	−19.8171	+	19.8171i	−0.984717	+	0.984717i
$406$		0			0
$407$		−	1.93332i		−	0.0958313i
$408$	3.34592	−	0.896536i	0.165648	−	0.0443852i
$409$	−32.8153	−	8.79283i	−1.62261	−	0.434777i	−0.670844	−	0.741598i	$-0.734068\pi$
$409$	−32.8153	−	8.79283i	−1.62261	−	0.434777i	−0.951767	+	0.306821i	$0.900735\pi$
$410$	−14.5386	−	3.89559i	−0.718008	−	0.192390i
$411$	5.96750	−	1.59899i	0.294355	−	0.0788722i
$412$			5.55147i			0.273501i
$413$		0			0
$414$	0.421494	−	0.421494i	0.0207153	−	0.0207153i
$415$	−15.0321	−	8.67876i	−0.737894	−	0.426024i
$416$	−2.20460	−	29.1839i	−0.108090	−	1.43086i
$417$	−3.04048	−	5.26627i	−0.148893	−	0.257890i
$418$	−1.63286	−	6.09391i	−0.0798657	−	0.298063i
$419$			19.6899i			0.961912i	0.876745	+	0.480956i	$0.159710\pi$
$419$			19.6899i			0.961912i	−0.876745	+	0.480956i	$0.840290\pi$
$420$		0			0
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.930619	+	0.365989i	$0.119269\pi$
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.365989	+	0.930619i	$0.380731\pi$
$422$	−18.9480	+	5.07709i	−0.922373	+	0.247149i
$423$	0.672944	−	2.51146i	0.0327197	−	0.122111i
$424$	−1.42877	−	0.382838i	−0.0693873	−	0.0185923i
$425$	11.6816	+	6.74435i	0.566639	+	0.327149i
$426$	−29.4207			−1.42544
$427$		0			0
$428$			6.38271i			0.308520i
$429$	−3.46068	+	2.36249i	−0.167083	+	0.114062i
$430$	−53.0819	+	30.6469i	−2.55984	+	1.47792i
$431$	−1.76107	+	6.57242i	−0.0848280	+	0.316582i	−0.995282	−	0.0970289i	$-0.969066\pi$
$431$	−1.76107	+	6.57242i	−0.0848280	+	0.316582i	0.910454	+	0.413611i	$0.135733\pi$
$432$	14.9383	+	8.62466i	0.718721	+	0.414954i
$433$	8.34704			0.401133			0.200567	−	0.979680i	$-0.435722\pi$
$433$	8.34704			0.401133			0.200567	+	0.979680i	$0.435722\pi$
$434$		0			0
$435$	−23.2121	−	23.2121i	−1.11293	−	1.11293i
$436$	2.87596	+	10.7332i	0.137734	+	0.514029i
$437$	−1.16236	+	4.33800i	−0.0556034	+	0.207515i
$438$	23.4067	+	40.5416i	1.11841	+	1.93715i
$439$	−1.21175	+	2.09881i	−0.0578336	+	0.100171i	−0.893493	−	0.449078i	$-0.851753\pi$
$439$	−1.21175	+	2.09881i	−0.0578336	+	0.100171i	0.835659	+	0.549248i	$0.185086\pi$
$440$	−0.566106	−	0.566106i	−0.0269880	−	0.0269880i
$441$		0			0
$442$	28.8622	+	13.8780i	1.37283	+	0.660110i
$443$	−6.88816	+	11.9306i	−0.327266	+	0.566842i	−0.981968	−	0.189045i	$-0.939461\pi$
$443$	−6.88816	+	11.9306i	−0.327266	+	0.566842i	0.654702	+	0.755887i	$0.272794\pi$
$444$	−11.7815	−	3.15684i	−0.559125	−	0.149817i
$445$	11.3064	+	19.5833i	0.535976	+	0.928337i
$446$	3.74622	−	6.48865i	0.177389	−	0.307246i
$447$	4.78450	−	4.78450i	0.226299	−	0.226299i
$448$		0			0
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.185043	+	0.982730i	$0.559242\pi$
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.982730	+	0.185043i	$0.940758\pi$
$450$	0.515326	+	1.92322i	0.0242927	+	0.0906615i
$451$	1.42333	−	0.821763i	0.0670222	−	0.0386953i
$452$	−31.3587	+	18.1049i	−1.47499	+	0.851585i
$453$	−11.8902	+	3.18596i	−0.558648	+	0.149689i
$454$	15.2535			0.715885
$455$		0			0
$456$	−3.85236			−0.180403
$457$	3.88663	−	1.04142i	0.181809	−	0.0487156i	−0.166766	−	0.985997i	$-0.553332\pi$
$457$	3.88663	−	1.04142i	0.181809	−	0.0487156i	0.348575	+	0.937281i	$0.386666\pi$
$458$	−1.83346	+	1.05855i	−0.0856718	+	0.0494626i
$459$	−18.3337	+	10.5850i	−0.855743	+	0.494064i
$460$	1.52399	+	5.68759i	0.0710562	+	0.265185i
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	−0.649363	−	0.760479i	$-0.724964\pi$
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	0.760479	+	0.649363i	$0.224964\pi$
$462$		0			0
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	−0.168270	−	0.985741i	$-0.553818\pi$
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	0.985741	+	0.168270i	$0.0538180\pi$
$464$	−11.1612	+	19.3318i	−0.518148	+	0.897458i
$465$	−20.0812	−	34.7817i	−0.931245	−	1.61296i
$466$	48.8056	+	13.0774i	2.26087	+	0.605799i
$467$	−10.7144	+	18.5578i	−0.495801	+	0.858753i	−0.999988	−	0.00484163i	$-0.998459\pi$
$467$	−10.7144	+	18.5578i	−0.495801	+	0.858753i	0.504187	+	0.863594i	$0.331792\pi$
$468$	0.821763	+	2.34396i	0.0379860	+	0.108350i
$469$		0			0
$470$	34.5647	+	34.5647i	1.59435	+	1.59435i
$471$	−3.11653	+	5.39798i	−0.143602	+	0.248726i
$472$	−0.0795368	−	0.137762i	−0.00366098	−	0.00634100i
$473$	1.73225	−	6.46485i	0.0796491	−	0.297254i
$474$	13.3393	+	49.7829i	0.612694	+	2.28661i
$475$	−10.6074	−	10.6074i	−0.486702	−	0.486702i
$476$		0			0
$477$	−1.04593			−0.0478900
$478$	−16.4066	−	9.47235i	−0.750420	−	0.433255i
$479$	−1.68893	+	6.30319i	−0.0771694	+	0.288000i	−0.993716	−	0.111927i	$-0.964298\pi$
$479$	−1.68893	+	6.30319i	−0.0771694	+	0.288000i	0.916547	+	0.399927i	$0.130964\pi$
$480$	36.4449	−	21.0415i	1.66348	−	0.960408i
$481$	−6.15372	−	9.01425i	−0.280586	−	0.411015i
$482$			58.5180i			2.66542i
$483$		0			0
$484$	−23.4543			−1.06610
$485$	0.826246	+	0.477034i	0.0375179	+	0.0216610i
$486$	−6.38606	−	1.71114i	−0.289677	−	0.0776188i
$487$	3.52434	−	13.1530i	0.159703	−	0.596020i	−0.838954	−	0.544203i	$-0.816832\pi$
$487$	3.52434	−	13.1530i	0.159703	−	0.596020i	0.998657	−	0.0518167i	$-0.0165012\pi$
$488$	−3.31056	+	0.887061i	−0.149862	+	0.0401554i
$489$	−19.0142	−	19.0142i	−0.859850	−	0.859850i
$490$		0			0
$491$		−	9.21924i		−	0.416059i	−0.978123	−	0.208029i	$-0.933295\pi$
$491$		−	9.21924i		−	0.416059i	0.978123	−	0.208029i	$-0.0667049\pi$
$492$	−2.68364	−	10.0155i	−0.120988	−	0.451533i
$493$	−13.6981	−	23.7258i	−0.616931	−	1.06856i
$494$	−27.0101	−	23.2159i	−1.21524	−	1.04453i
$495$	−0.490262	−	0.283053i	−0.0220356	−	0.0127223i
$496$	−19.3116	+	19.3116i	−0.867117	+	0.867117i
$497$		0			0
$498$		−	22.7576i		−	1.01979i
$499$	9.09701	−	2.43754i	0.407238	−	0.109119i	−0.0493841	−	0.998780i	$-0.515726\pi$
$499$	9.09701	−	2.43754i	0.407238	−	0.109119i	0.456622	+	0.889661i	$0.349059\pi$
$500$	11.4716	+	3.07380i	0.513025	+	0.137465i
$501$	−40.3490	−	10.8115i	−1.80266	−	0.483021i
$502$	28.6430	−	7.67487i	1.27840	−	0.342546i
$503$			1.81069i			0.0807346i	0.999185	+	0.0403673i	$0.0128528\pi$
$503$			1.81069i			0.0807346i	−0.999185	+	0.0403673i	$0.987147\pi$
$504$		0			0
$505$	−18.5741	+	18.5741i	−0.826535	+	0.826535i
$506$	−1.05974	−	0.611844i	−0.0471114	−	0.0271998i
$507$	−8.61591	+	22.0305i	−0.382646	+	0.978409i
$508$	−15.3089	−	26.5158i	−0.679222	−	1.17645i
$509$	8.15738	+	30.4438i	0.361570	+	1.34940i	0.872012	+	0.489485i	$0.162815\pi$
$509$	8.15738	+	30.4438i	0.361570	+	1.34940i	−0.510442	+	0.859912i	$0.670518\pi$
$510$			46.0491i			2.03909i
$511$		0			0
$512$	−22.4286	−	22.4286i	−0.991215	−	0.991215i
$513$	22.7414	−	6.09355i	1.00406	−	0.269037i
$514$	7.76993	−	28.9978i	0.342717	−	1.27904i
$515$	−6.89960	−	1.84874i	−0.304033	−	0.0814653i
$516$	−36.5677	−	21.1124i	−1.60980	−	0.929421i
$517$	−5.33761			−0.234748
$518$		0			0
$519$			26.1684i			1.14866i
$520$	−4.44141	−	0.837606i	−0.194769	−	0.0367314i
$521$	13.7477	−	7.93722i	0.602297	−	0.347736i	−0.167648	−	0.985847i	$-0.553617\pi$
$521$	13.7477	−	7.93722i	0.602297	−	0.347736i	0.769945	+	0.638111i	$0.220284\pi$
$522$	1.04665	−	3.90615i	0.0458106	−	0.170968i
$523$	−3.38438	−	1.95397i	−0.147989	−	0.0854413i	0.424177	−	0.905579i	$-0.360563\pi$
$523$	−3.38438	−	1.95397i	−0.147989	−	0.0854413i	−0.572166	+	0.820138i	$0.693897\pi$
$524$	28.4098			1.24109
$525$		0			0
$526$	3.79928	+	3.79928i	0.165656	+	0.165656i
$527$	−8.67515	−	32.3761i	−0.377896	−	1.41033i
$528$	−1.06040	+	3.95746i	−0.0461479	+	0.172226i
$529$	−11.0645	−	19.1642i	−0.481063	−	0.833226i
$530$	9.83193	−	17.0294i	0.427072	−	0.739710i
$531$	−0.0795368	−	0.0795368i	−0.00345160	−	0.00345160i
$532$		0			0
$533$	4.02074	−	8.36196i	0.174158	−	0.362197i
$534$	−14.8239	+	25.6758i	−0.641495	+	1.11110i
$535$	−7.93269	−	2.12556i	−0.342960	−	0.0918958i
$536$	−2.26517	−	3.92340i	−0.0978407	−	0.169465i
$537$	3.74035	−	6.47848i	0.161408	−	0.279567i
$538$	14.2597	−	14.2597i	0.614780	−	0.614780i
$539$		0			0
$540$	21.8272	−	21.8272i	0.939292	−	0.939292i
$541$	3.13832	+	11.7124i	0.134927	+	0.503555i	0.999998	+	0.00190544i	$0.000606522\pi$
$541$	3.13832	+	11.7124i	0.134927	+	0.503555i	−0.865071	+	0.501649i	$0.832727\pi$
$542$	−8.63491	+	4.98537i	−0.370901	+	0.214140i
$543$	34.0008	−	19.6304i	1.45911	−	0.842420i
$544$	33.9243	−	9.08998i	1.45449	−	0.389730i
$545$	−14.2975			−0.612436
$546$		0			0
$547$	−4.72546			−0.202046			−0.101023	−	0.994884i	$-0.532212\pi$
$547$	−4.72546			−0.202046			−0.101023	+	0.994884i	$0.532212\pi$
$548$	−7.26183	+	1.94580i	−0.310210	+	0.0831205i
$549$	−2.09881	+	1.21175i	−0.0895750	+	0.0517162i
$550$	3.53981	−	2.04371i	0.150938	−	0.0871441i
$551$	7.88571	+	29.4299i	0.335943	+	1.25375i
$552$	−0.528360	+	0.528360i	−0.0224885	+	0.0224885i
$553$		0			0
$554$	8.56268	−	8.56268i	0.363794	−	0.363794i
$555$	7.84691	−	13.5912i	0.333083	−	0.576916i
$556$	3.69995	+	6.40851i	0.156913	+	0.271781i
$557$	32.5680	+	8.72658i	1.37995	+	0.369757i	0.871104	−	0.491099i	$-0.163405\pi$
$557$	32.5680	+	8.72658i	1.37995	+	0.369757i	0.508848	+	0.860856i	$0.330071\pi$
$558$	2.47381	−	4.28477i	0.104725	−	0.181389i
$559$	−12.5007	−	35.6565i	−0.528725	−	1.50811i
$560$		0			0
$561$	−3.55554	−	3.55554i	−0.150115	−	0.150115i
$562$	13.4089	−	23.2249i	0.565620	−	0.979683i
$563$	−20.6388	−	35.7475i	−0.869823	−	1.50658i	−0.862178	−	0.506606i	$-0.830900\pi$
$563$	−20.6388	−	35.7475i	−0.869823	−	1.50658i	−0.00764487	−	0.999971i	$-0.502433\pi$
$564$	−8.71556	+	32.5269i	−0.366991	+	1.36963i
$565$	−12.0585	−	45.0031i	−0.507307	−	1.89329i
$566$	12.0878	+	12.0878i	0.508089	+	0.508089i
$567$		0			0
$568$	3.46520			0.145397
$569$	37.7069	+	21.7701i	1.58076	+	0.912650i	0.994749	+	0.102344i	$0.0326342\pi$
$569$	37.7069	+	21.7701i	1.58076	+	0.912650i	0.586007	+	0.810306i	$0.300699\pi$
$570$	13.2548	−	49.4675i	0.555182	−	2.07197i
$571$	18.4204	−	10.6350i	0.770872	−	0.445063i	−0.0623138	−	0.998057i	$-0.519848\pi$
$571$	18.4204	−	10.6350i	0.770872	−	0.445063i	0.833185	+	0.552994i	$0.186515\pi$
$572$	4.21129	−	2.87490i	0.176083	−	0.120206i
$573$		−	18.7455i		−	0.783105i
$574$		0			0
$575$	−2.90967			−0.121341
$576$	2.58996	+	1.49532i	0.107915	+	0.0623048i
$577$	11.9350	+	3.19797i	0.496861	+	0.133133i	0.498543	−	0.866865i	$-0.333869\pi$
$577$	11.9350	+	3.19797i	0.496861	+	0.133133i	−0.00168199	+	0.999999i	$0.500535\pi$
$578$	−0.914163	+	3.41170i	−0.0380242	+	0.141908i
$579$	15.6248	−	4.18665i	0.649344	−	0.173991i
$580$	28.2467	+	28.2467i	1.17288	+	1.17288i
$581$		0			0
$582$			1.25088i			0.0518508i
$583$	0.555730	+	2.07401i	0.0230160	+	0.0858968i
$584$	−2.75686	−	4.77503i	−0.114080	−	0.197592i
$585$	−3.18683	+	0.240739i	−0.131759	+	0.00995332i
$586$	−38.9467	−	22.4859i	−1.60887	−	0.928882i
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.319131	−	0.947711i	$-0.396609\pi$
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.947711	−	0.319131i	$-0.103391\pi$
$588$		0			0
$589$			37.2766i			1.53595i
$590$	2.04264	−	0.547324i	0.0840941	−	0.0225330i
$591$	8.08066	+	2.16521i	0.332394	+	0.0890647i
$592$	−10.3083	−	2.76209i	−0.423667	−	0.113521i
$593$	−7.07650	+	1.89614i	−0.290597	+	0.0778653i	−0.401173	−	0.916002i	$-0.631397\pi$
$593$	−7.07650	+	1.89614i	−0.290597	+	0.0778653i	0.110575	+	0.993868i	$0.464731\pi$
$594$			6.41503i			0.263212i
$595$		0			0
$596$	−5.82225	+	5.82225i	−0.238488	+	0.238488i
$597$	9.77215	+	5.64196i	0.399948	+	0.230910i
$598$	−6.88862	+	0.520378i	−0.281696	+	0.0212798i
$599$	9.26271	+	16.0435i	0.378464	+	0.655519i	0.990839	−	0.135048i	$-0.0431190\pi$
$599$	9.26271	+	16.0435i	0.378464	+	0.655519i	−0.612375	+	0.790568i	$0.709786\pi$
$600$	−0.645981	−	2.41083i	−0.0263721	−	0.0984219i
$601$		−	30.9807i		−	1.26373i	−0.775079	−	0.631864i	$-0.782290\pi$
$601$		−	30.9807i		−	1.26373i	0.775079	−	0.631864i	$-0.217710\pi$
$602$		0			0
$603$	−2.26517	−	2.26517i	−0.0922451	−	0.0922451i
$604$	14.4691	−	3.87698i	0.588739	−	0.157752i
$605$	7.81071	−	29.1500i	0.317550	−	1.18511i
$606$	−33.2663	−	8.91367i	−1.35135	−	0.362093i
$607$	−25.5195	−	14.7337i	−1.03581	−	0.598023i	−0.117164	−	0.993113i	$-0.537380\pi$
$607$	−25.5195	−	14.7337i	−1.03581	−	0.598023i	−0.918643	+	0.395090i	$0.870714\pi$
$608$	−39.0591			−1.58405
$609$		0			0
$610$		−	45.5625i		−	1.84477i
$611$	−24.8870	+	16.9895i	−1.00682	+	0.687321i
$612$	−2.58132	+	1.49032i	−0.104343	+	0.0602427i
$613$	5.10231	−	19.0421i	0.206080	−	0.769103i	−0.783037	−	0.621975i	$-0.786331\pi$
$613$	5.10231	−	19.0421i	0.206080	−	0.769103i	0.989118	−	0.147128i	$-0.0470028\pi$
$614$	14.5205	+	8.38340i	0.585998	+	0.338326i
$615$	13.3414			0.537976
$616$		0			0
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.992412	−	0.122957i	$-0.960762\pi$
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.122957	−	0.992412i	$-0.539238\pi$
$618$	−2.42390	−	9.04611i	−0.0975035	−	0.363888i
$619$	−1.67875	+	6.26517i	−0.0674746	+	0.251819i	−0.991422	−	0.130701i	$-0.958277\pi$
$619$	−1.67875	+	6.26517i	−0.0674746	+	0.251819i	0.923947	+	0.382520i	$0.124944\pi$
$620$	24.4368	+	42.3258i	0.981405	+	1.69984i
$621$	2.28330	−	3.95478i	0.0916255	−	0.158700i
$622$	3.81137	+	3.81137i	0.152822	+	0.152822i
$623$		0			0
$624$	7.65233	+	21.8272i	0.306338	+	0.873786i
$625$	−15.4343	+	26.7330i	−0.617373	+	1.06932i
$626$	−39.3591	−	10.5462i	−1.57310	−	0.421512i
$627$	2.79605	+	4.84290i	0.111664	+	0.193407i
$628$	3.79249	−	6.56879i	0.151337	−	0.262123i
$629$	9.26134	−	9.26134i	0.369274	−	0.369274i
$630$		0			0
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$632$	−1.57112	−	5.86349i	−0.0624957	−	0.233237i
$633$	15.0582	−	8.69384i	0.598509	−	0.345549i
$634$	−2.88547	+	1.66593i	−0.114597	+	0.0661624i
$635$	38.0530	−	10.1963i	1.51009	−	0.404627i
$636$	13.5463			0.537145
$637$		0			0
$638$	−8.30174			−0.328669
$639$	2.36678	−	0.634176i	0.0936283	−	0.0250876i
$640$	−8.63491	+	4.98537i	−0.341325	+	0.197064i
$641$	−19.3635	+	11.1795i	−0.764812	+	0.441565i	−0.831021	−	0.556241i	$-0.812243\pi$
$641$	−19.3635	+	11.1795i	−0.764812	+	0.441565i	0.0662085	+	0.997806i	$0.478910\pi$
$642$	−2.78683	−	10.4006i	−0.109988	−	0.410479i
$643$	5.69880	−	5.69880i	0.224739	−	0.224739i	−0.585752	−	0.810491i	$-0.699201\pi$
$643$	5.69880	−	5.69880i	0.224739	−	0.224739i	0.810491	+	0.585752i	$0.199201\pi$
$644$		0			0
$645$	38.4170	−	38.4170i	1.51267	−	1.51267i
$646$	21.3701	−	37.0141i	0.840796	−	1.45630i
$647$	3.86755	+	6.69879i	0.152049	+	0.263357i	0.931981	−	0.362508i	$-0.118079\pi$
$647$	3.86755	+	6.69879i	0.152049	+	0.263357i	−0.779932	+	0.625865i	$0.784746\pi$
$648$	4.18034	+	1.12012i	0.164219	+	0.0440024i
$649$	−0.115456	+	0.199976i	−0.00453205	+	0.00784974i
$650$	9.99952	−	20.7961i	0.392214	−	0.815689i
$651$		0			0
$652$	23.1383	+	23.1383i	0.906165	+	0.906165i
$653$	−10.6960	+	18.5261i	−0.418568	+	0.724982i	−0.995796	−	0.0916019i	$-0.970801\pi$
$653$	−10.6960	+	18.5261i	−0.418568	+	0.724982i	0.577227	+	0.816583i	$0.304135\pi$
$654$	−9.37275	−	16.2341i	−0.366504	−	0.634803i
$655$	−9.46099	+	35.3089i	−0.369672	+	1.37963i
$656$	−2.34806	−	8.76309i	−0.0916764	−	0.342141i
$657$	−2.75686	−	2.75686i	−0.107555	−	0.107555i
$658$		0			0
$659$	−1.68445			−0.0656167			−0.0328084	−	0.999462i	$-0.510445\pi$
$659$	−1.68445			−0.0656167			−0.0328084	+	0.999462i	$0.510445\pi$
$660$	6.34957	+	3.66593i	0.247157	+	0.142696i
$661$	8.56704	−	31.9726i	0.333219	−	1.24359i	−0.572567	−	0.819858i	$-0.694052\pi$
$661$	8.56704	−	31.9726i	0.333219	−	1.24359i	0.905787	−	0.423734i	$-0.139281\pi$
$662$	7.29942	−	4.21432i	0.283700	−	0.163794i
$663$	−27.8951	−	5.26075i	−1.08336	−	0.204311i
$664$			2.68041i			0.104020i
$665$		0			0
$666$	1.93332			0.0749148
$667$	5.11792	+	2.95483i	0.198167	+	0.114412i
$668$	49.1005	+	13.1564i	1.89976	+	0.509038i
$669$	−1.71887	+	6.41491i	−0.0664553	+	0.248015i
$670$	58.1735	−	15.5875i	2.24744	−	0.602199i
$671$	3.51796	+	3.51796i	0.135809	+	0.135809i
$672$		0			0
$673$			26.2464i			1.01173i	0.862614	+	0.505863i	$0.168826\pi$
$673$			26.2464i			1.01173i	−0.862614	+	0.505863i	$0.831174\pi$
$674$	−2.37664	−	8.86973i	−0.0915446	−	0.341649i
$675$	7.62677	+	13.2100i	0.293555	+	0.508452i
$676$	10.4847	−	26.8089i	0.403257	−	1.03111i
$677$	31.8402	+	18.3829i	1.22372	+	0.706513i	0.965708	−	0.259630i	$-0.0836005\pi$
$677$	31.8402	+	18.3829i	1.22372	+	0.706513i	0.258008	+	0.966143i	$0.416934\pi$
$678$	43.1939	−	43.1939i	1.65885	−	1.65885i
$679$		0			0
$680$		−	5.42372i		−	0.207990i
$681$	−13.0598	+	3.49937i	−0.500454	+	0.134096i
$682$	−9.81079	−	2.62879i	−0.375675	−	0.100662i
$683$	19.9183	+	5.33709i	0.762152	+	0.204218i	0.618902	−	0.785468i	$-0.287578\pi$
$683$	19.9183	+	5.33709i	0.762152	+	0.204218i	0.143251	+	0.989686i	$0.454245\pi$
$684$	3.20191	−	0.857949i	0.122428	−	0.0328045i
$685$		−	9.67329i		−	0.369597i
$686$		0			0
$687$	1.32693	−	1.32693i	0.0506255	−	0.0506255i
$688$	−31.9950	−	18.4723i	−1.21980	−	0.704252i
$689$	9.19266	+	7.90135i	0.350212	+	0.301017i
$690$	−4.96666	−	8.60251i	−0.189078	−	0.327492i
$691$	−11.1514	−	41.6177i	−0.424220	−	1.58321i	−0.765620	−	0.643293i	$-0.777568\pi$
$691$	−11.1514	−	41.6177i	−0.424220	−	1.58321i	0.341399	−	0.939918i	$-0.389099\pi$
$692$		−	31.8442i		−	1.21054i
$693$		0			0
$694$	−12.7906	−	12.7906i	−0.485525	−	0.485525i
$695$	−9.19691	+	2.46430i	−0.348859	+	0.0934764i
$696$	−1.31202	+	4.89651i	−0.0497319	+	0.185602i
$697$	10.7549	+	2.88175i	0.407369	+	0.109154i
$698$	−29.7016	−	17.1483i	−1.12422	−	0.649071i
$699$	−44.7866			−1.69399
$700$		0			0
$701$		−	17.7368i		−	0.669911i	−0.942234	−	0.334955i	$-0.891279\pi$
$701$		−	17.7368i		−	0.669911i	0.942234	−	0.334955i	$-0.108721\pi$
$702$	20.4189	+	29.9105i	0.770661	+	1.12890i
$703$	−12.6146	+	7.28306i	−0.475770	+	0.274686i
$704$	1.58900	−	5.93022i	0.0598876	−	0.223503i
$705$	−37.5233	−	21.6641i	−1.41321	−	0.815917i
$706$	8.44854			0.317965
$707$		0			0
$708$	1.03011	+	1.03011i	0.0387140	+	0.0387140i
$709$	7.04314	+	26.2853i	0.264511	+	0.987167i	0.962549	+	0.271107i	$0.0873897\pi$
$709$	7.04314	+	26.2853i	0.264511	+	0.987167i	−0.698039	+	0.716060i	$0.745944\pi$
$710$	−11.9227	+	44.4962i	−0.447451	+	1.66991i
$711$	−2.14619	−	3.71730i	−0.0804883	−	0.139410i
$712$	1.74598	−	3.02413i	0.0654334	−	0.113334i
$713$	5.11257	+	5.11257i	0.191467	+	0.191467i
$714$		0			0
$715$	2.17061	+	6.19135i	0.0811762	+	0.231543i
$716$	−4.55162	+	7.88364i	−0.170102	+	0.294625i
$717$	16.2201	+	4.34617i	0.605752	+	0.162311i
$718$	5.11430	+	8.85824i	0.190864	+	0.330586i
$719$	21.1775	−	36.6806i	0.789789	−	1.36795i	−0.136308	−	0.990667i	$-0.543524\pi$
$719$	21.1775	−	36.6806i	0.789789	−	1.36795i	0.926096	−	0.377287i	$-0.123143\pi$
$720$	−2.20963	+	2.20963i	−0.0823481	+	0.0823481i
$721$		0			0
$722$	−6.03011	+	6.03011i	−0.224418	+	0.224418i
$723$	−13.4248	−	50.1021i	−0.499275	−	1.86332i
$724$	−41.3754	+	23.8881i	−1.53771	+	0.887795i
$725$	−17.0951	+	9.86987i	−0.634897	+	0.366558i
$726$	38.2187	−	10.2407i	1.41843	−	0.380067i
$727$	−23.2484			−0.862234			−0.431117	−	0.902296i	$-0.641880\pi$
$727$	−23.2484			−0.862234			−0.431117	+	0.902296i	$0.641880\pi$
$728$		0			0
$729$	−23.6494			−0.875904
$730$	70.8009	−	18.9710i	2.62046	−	0.702150i
$731$	39.2672	−	22.6709i	1.45235	−	0.838515i
$732$	27.1825	−	15.6938i	1.00469	−	0.580060i
$733$	−8.83146	−	32.9595i	−0.326197	−	1.21739i	−0.913103	−	0.407730i	$-0.866321\pi$
$733$	−8.83146	−	32.9595i	−0.326197	−	1.21739i	0.586905	−	0.809656i	$-0.300346\pi$
$734$	−28.7580	+	28.7580i	−1.06148	+	1.06148i
$735$		0			0
$736$	−5.35704	+	5.35704i	−0.197463	+	0.197463i
$737$	−3.28814	+	5.69523i	−0.121120	+	0.209786i
$738$	0.821763	+	1.42333i	0.0302495	+	0.0523937i
$739$	−6.10053	−	1.63463i	−0.224412	−	0.0601309i	0.144861	−	0.989452i	$-0.453726\pi$
$739$	−6.10053	−	1.63463i	−0.224412	−	0.0601309i	−0.369273	+	0.929321i	$0.620393\pi$
$740$	−9.54887	+	16.5391i	−0.351024	+	0.607991i
$741$	28.4516	+	13.6806i	1.04520	+	0.502570i
$742$		0			0
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	0.866485	−	0.499203i	$-0.166374\pi$
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	−0.499203	+	0.866485i	$0.666374\pi$
$744$	−3.10102	+	5.37112i	−0.113689	+	0.196915i
$745$	−5.29721	−	9.17504i	−0.194075	−	0.336147i
$746$	13.0370	−	48.6548i	0.477319	−	1.78138i
$747$	0.490549	+	1.83076i	0.0179483	+	0.0669838i
$748$	4.32672	+	4.32672i	0.158201	+	0.158201i
$749$		0			0
$750$	−20.0350			−0.731576
$751$	−7.07270	−	4.08343i	−0.258087	−	0.149006i	0.365375	−	0.930860i	$-0.380941\pi$
$751$	−7.07270	−	4.08343i	−0.258087	−	0.149006i	−0.623461	+	0.781854i	$0.714274\pi$
$752$	−7.62570	+	28.4595i	−0.278081	+	1.03781i
$753$	−22.7629	+	13.1422i	−0.829528	+	0.478928i
$754$	−38.7074	+	26.4242i	−1.40964	+	0.962314i
$755$			19.2739i			0.701448i
$756$		0			0
$757$	10.5210			0.382392			0.191196	−	0.981552i	$-0.438763\pi$
$757$	10.5210			0.382392			0.191196	+	0.981552i	$0.438763\pi$
$758$	−22.0839	−	12.7501i	−0.802122	−	0.463105i
$759$	1.04770	+	0.280731i	0.0380291	+	0.0101899i
$760$	−1.56116	+	5.82634i	−0.0566293	+	0.211343i
$761$	8.12973	−	2.17835i	0.294702	−	0.0789653i	−0.108439	−	0.994103i	$-0.534585\pi$
$761$	8.12973	−	2.17835i	0.294702	−	0.0789653i	0.403141	+	0.915138i	$0.367918\pi$
$762$	36.5232	+	36.5232i	1.32310	+	1.32310i
$763$		0			0
$764$			22.8113i			0.825286i
$765$	−0.992609	−	3.70447i	−0.0358879	−	0.133935i
$766$	−25.9823	−	45.0027i	−0.938779	−	1.62601i
$767$	0.0981963	+	1.29990i	0.00354566	+	0.0469365i
$768$	18.9757	+	10.9556i	0.684726	+	0.395327i
$769$	−9.73800	+	9.73800i	−0.351161	+	0.351161i	−0.860541	−	0.509380i	$-0.829875\pi$
$769$	−9.73800	+	9.73800i	−0.351161	+	0.351161i	0.509380	+	0.860541i	$0.329875\pi$
$770$		0			0
$771$			26.6099i			0.958333i
$772$	−19.0138	+	5.09472i	−0.684320	+	0.183363i
$773$	−21.8900	−	5.86540i	−0.787327	−	0.210964i	−0.157315	−	0.987549i	$-0.550284\pi$
$773$	−21.8900	−	5.86540i	−0.787327	−	0.210964i	−0.630013	+	0.776585i	$0.716950\pi$
$774$	6.46485	+	1.73225i	0.232374	+	0.0622645i
$775$	−23.3279	+	6.25070i	−0.837964	+	0.224532i
$776$		−	0.147331i		−	0.00528886i
$777$		0			0
$778$	17.5161	−	17.5161i	0.627981	−	0.627981i
$779$	−10.7237	−	6.19135i	−0.384218	−	0.221828i
$780$	41.2739	−	3.11790i	1.47784	−	0.111639i
$781$	−2.51506	−	4.35620i	−0.0899958	−	0.155877i
$782$	−2.14561	−	8.00753i	−0.0767269	−	0.286349i
$783$		−	30.9807i		−	1.10716i
$784$		0			0
$785$	6.90099	+	6.90099i	0.246307	+	0.246307i
$786$	−46.2938	+	12.4044i	−1.65124	+	0.442450i
$787$	6.58275	−	24.5672i	0.234650	−	0.875725i	−0.743657	−	0.668562i	$-0.766910\pi$
$787$	6.58275	−	24.5672i	0.234650	−	0.875725i	0.978306	−	0.207163i	$-0.0664231\pi$
$788$	−9.83333	−	2.63483i	−0.350298	−	0.0938620i
$789$	−4.12448	−	2.38127i	−0.146836	−	0.0847755i
$790$	80.6979			2.87110
$791$		0			0
$792$			0.0874201i			0.00310634i
$793$	27.6003	+	5.20515i	0.980116	+	0.184840i
$794$	−19.6659	+	11.3541i	−0.697917	+	0.402943i
$795$	−4.51116	+	16.8359i	−0.159994	+	0.597106i
$796$	−11.8917	−	6.86568i	−0.421490	−	0.243347i
$797$	−43.9698			−1.55749			−0.778745	−	0.627341i	$-0.784143\pi$
$797$	−43.9698			−1.55749			−0.778745	+	0.627341i	$0.784143\pi$
$798$		0			0
$799$	−25.5691	−	25.5691i	−0.904571	−	0.904571i
$800$	−6.54960	−	24.4434i	−0.231563	−	0.864206i
$801$	0.639073	−	2.38505i	0.0225805	−	0.0842717i
$802$	−25.5741	−	44.2956i	−0.903051	−	1.56413i
$803$	−4.00188	+	6.93146i	−0.141223	+	0.244606i
$804$	29.3371	+	29.3371i	1.03464	+	1.03464i
$805$		0			0
$806$	−54.1109	+	18.9706i	−1.90597	+	0.668210i
$807$	−8.93755	+	15.4803i	−0.314617	+	0.544932i
$808$	3.91814	+	1.04986i	0.137840	+	0.0369340i
$809$	−6.02543	−	10.4363i	−0.211843	−	0.366922i	0.740449	−	0.672113i	$-0.234613\pi$
$809$	−6.02543	−	10.4363i	−0.211843	−	0.366922i	−0.952291	+	0.305191i	$0.901280\pi$
$810$	−28.7666	+	49.8251i	−1.01075	+	1.75068i
$811$	1.07742	−	1.07742i	0.0378333	−	0.0378333i	−0.687937	−	0.725770i	$-0.741483\pi$
$811$	1.07742	−	1.07742i	0.0378333	−	0.0378333i	0.725770	+	0.687937i	$0.241483\pi$
$812$		0			0
$813$	6.24935	−	6.24935i	0.219174	−	0.219174i
$814$	−1.02722	−	3.83365i	−0.0360041	−	0.134369i
$815$	−36.4627	+	21.0517i	−1.27723	+	0.737410i
$816$	−24.0374	+	13.8780i	−0.841479	+	0.485828i
$817$	−48.7077	+	13.0512i	−1.70407	+	0.456604i
$818$	−69.7423			−2.43848
$819$		0			0
$820$	−16.2351			−0.566953
$821$	46.6971	−	12.5125i	1.62974	−	0.436688i	0.675899	−	0.736994i	$-0.263756\pi$
$821$	46.6971	−	12.5125i	1.62974	−	0.436688i	0.953843	+	0.300306i	$0.0970889\pi$
$822$	10.9836	−	6.34136i	0.383096	−	0.221180i
$823$	4.08425	−	2.35804i	0.142368	−	0.0821963i	−0.427124	−	0.904193i	$-0.640473\pi$
$823$	4.08425	−	2.35804i	0.142368	−	0.0821963i	0.569492	+	0.821997i	$0.307140\pi$
$824$	0.285489	+	1.06546i	0.00994550	+	0.0371171i
$825$	−2.56187	+	2.56187i	−0.0891929	+	0.0891929i
$826$		0			0
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	−0.150746	−	0.988572i	$-0.548168\pi$
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	0.988572	+	0.150746i	$0.0481677\pi$
$828$	0.321480	−	0.556819i	0.0111722	−	0.0193508i
$829$	−6.23443	−	10.7983i	−0.216531	−	0.375042i	0.737214	−	0.675659i	$-0.236141\pi$
$829$	−6.23443	−	10.7983i	−0.216531	−	0.375042i	−0.953745	+	0.300617i	$0.902807\pi$
$830$	−34.4188	−	9.22248i	−1.19469	−	0.320117i
$831$	−5.36683	+	9.29562i	−0.186173	+	0.322462i
$832$	−11.4669	−	32.7078i	−0.397544	−	1.13394i
$833$		0			0
$834$	−8.82717	−	8.82717i	−0.305660	−	0.305660i
$835$	−32.7027	+	56.6428i	−1.13172	+	1.96020i
$836$	−3.40251	−	5.89331i	−0.117678	−	0.203825i
$837$	9.81020	−	36.6122i	0.339090	−	1.26550i
$838$	10.4617	+	39.0436i	0.361394	+	1.34874i
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	0.995664	−	0.0930239i	$-0.0296533\pi$
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	−0.0930239	+	0.995664i	$0.529653\pi$
$840$		0			0
$841$	11.0923			0.382495
$842$	66.8897	+	38.6188i	2.30517	+	1.33089i
$843$	−6.15237	+	22.9609i	−0.211899	+	0.790817i
$844$	−18.3242	+	10.5795i	−0.630747	+	0.364162i
$845$	29.8275	+	21.9586i	1.02610	+	0.755399i
$846$		−	5.33761i		−	0.183511i
$847$		0			0
$848$	11.8524			0.407012
$849$	−13.1225	−	7.57628i	−0.450363	−	0.260017i
$850$	26.7472	+	7.16688i	0.917420	+	0.245822i
$851$	−0.731237	+	2.72901i	−0.0250665	+	0.0935494i
$852$	−30.6531	+	8.21346i	−1.05016	+	0.281389i
$853$	15.4396	+	15.4396i	0.528641	+	0.528641i	0.920167	−	0.391526i	$-0.128053\pi$
$853$	15.4396	+	15.4396i	0.528641	+	0.528641i	−0.391526	+	0.920167i	$0.628053\pi$
$854$		0			0
$855$			4.26517i			0.145866i
$856$	0.328236	+	1.22499i	0.0112189	+	0.0418695i
$857$	17.9655	+	31.1172i	0.613691	+	1.06294i	0.990613	+	0.136699i	$0.0436493\pi$
$857$	17.9655	+	31.1172i	0.613691	+	1.06294i	−0.376922	+	0.926245i	$0.623017\pi$
$858$	−5.60704	+	6.52339i	−0.191421	+	0.222705i
$859$	5.24036	+	3.02552i	0.178799	+	0.103229i	0.586728	−	0.809784i	$-0.300416\pi$
$859$	5.24036	+	3.02552i	0.178799	+	0.103229i	−0.407929	+	0.913013i	$0.633749\pi$
$860$	−46.7496	+	46.7496i	−1.59415	+	1.59415i
$861$		0			0
$862$			13.9684i			0.475764i
$863$	16.1906	−	4.33826i	0.551135	−	0.147676i	0.0275046	−	0.999622i	$-0.491244\pi$
$863$	16.1906	−	4.33826i	0.551135	−	0.147676i	0.523631	+	0.851945i	$0.324577\pi$
$864$	38.3629	+	10.2793i	1.30513	+	0.349709i
$865$	39.5773	+	10.6047i	1.34567	+	0.360571i
$866$	16.5516	−	4.43499i	0.562446	−	0.150707i
$867$		−	3.13076i		−	0.106326i
$868$		0			0
$869$	−6.23083	+	6.23083i	−0.211367	+	0.211367i
$870$	−58.3611	−	33.6948i	−1.97863	−	1.14236i
$871$	2.79659	+	37.0205i	0.0947588	+	1.25439i
$872$	1.10393	+	1.91207i	0.0373839	+	0.0647508i
$873$	−0.0269634	−	0.100629i	−0.000912572	−	0.00340576i
$874$			9.21955i			0.311856i
$875$		0			0
$876$	35.7052	+	35.7052i	1.20637	+	1.20637i
$877$	−40.6722	+	10.8981i	−1.37340	+	0.368002i	−0.868720	−	0.495304i	$-0.835057\pi$
$877$	−40.6722	+	10.8981i	−1.37340	+	0.368002i	−0.504682	+	0.863306i	$0.668390\pi$
$878$	−1.28766	+	4.80563i	−0.0434565	+	0.162182i
$879$	38.5040	+	10.3171i	1.29871	+	0.347988i
$880$	5.55558	+	3.20751i	0.187278	+	0.108125i
$881$	−18.8928			−0.636516			−0.318258	−	0.948004i	$-0.603098\pi$
$881$	−18.8928			−0.636516			−0.318258	+	0.948004i	$0.603098\pi$
$882$		0			0
$883$			7.28391i			0.245123i	0.992461	+	0.122562i	$0.0391109\pi$
$883$			7.28391i			0.245123i	−0.992461	+	0.122562i	$0.960889\pi$
$884$	33.9455	+	6.40179i	1.14171	+	0.215315i
$885$	−1.62331	+	0.937219i	−0.0545670	+	0.0315043i
$886$	−7.31969	+	27.3175i	−0.245910	+	0.917748i
$887$	31.6549	+	18.2760i	1.06287	+	0.613648i	0.926224	−	0.376973i	$-0.123035\pi$
$887$	31.6549	+	18.2760i	1.06287	+	0.613648i	0.136644	+	0.990620i	$0.456368\pi$
$888$	−2.42350			−0.0813272
$889$		0			0
$890$	32.8249	+	32.8249i	1.10029	+	1.10029i
$891$	−1.62597	−	6.06821i	−0.0544721	−	0.203293i
$892$	2.09169	−	7.80628i	0.0700348	−	0.261373i
$893$	20.1074	+	34.8270i	0.672868	+	1.16544i
$894$	6.94521	−	12.0295i	0.232283	−	0.402325i
$895$	−8.28233	−	8.28233i	−0.276848	−	0.276848i
$896$		0			0
$897$	5.77854	−	2.02588i	0.192940	−	0.0676422i
$898$	−35.9195	+	62.2144i	−1.19865	+	2.07612i
$899$	47.3801	+	12.6955i	1.58022	+	0.423418i
$900$	1.07382	+	1.85991i	0.0357941	+	0.0619971i
$901$	−7.27314	+	12.5975i	−0.242303	+	0.419682i
$902$	2.38575	−	2.38575i	0.0794368	−	0.0794368i
$903$		0			0
$904$	−5.08742	+	5.08742i	−0.169205	+	0.169205i
$905$	−15.9104	−	59.3783i	−0.528878	−	1.97380i
$906$	−21.8846	+	12.6351i	−0.727066	+	0.419772i
$907$	7.32549	−	4.22938i	0.243239	−	0.140434i	−0.373426	−	0.927660i	$-0.621817\pi$
$907$	7.32549	−	4.22938i	0.243239	−	0.140434i	0.616665	+	0.787226i	$0.288484\pi$
$908$	15.8925	−	4.25837i	0.527410	−	0.141319i
$909$	2.86827			0.0951347
$910$		0			0
$911$	−11.0973			−0.367669			−0.183834	−	0.982957i	$-0.558851\pi$
$911$	−11.0973			−0.367669			−0.183834	+	0.982957i	$0.558851\pi$
$912$	29.8165	−	7.98930i	0.987322	−	0.264552i
$913$	3.36962	−	1.94545i	0.111518	−	0.0643850i
$914$	7.15359	−	4.13013i	0.236620	−	0.136612i
$915$	10.4526	+	39.0098i	0.345554	+	1.28962i
$916$	−1.61474	+	1.61474i	−0.0533524	+	0.0533524i
$917$		0			0
$918$	−30.7304	+	30.7304i	−1.01425	+	1.01425i
$919$	15.3613	−	26.6065i	0.506722	−	0.877668i	−0.493248	−	0.869889i	$-0.664191\pi$
$919$	15.3613	−	26.6065i	0.506722	−	0.877668i	0.999970	−	0.00777889i	$-0.00247612\pi$
$920$	0.584979	+	1.01321i	0.0192862	+	0.0334046i
$921$	−14.3554	−	3.84653i	−0.473028	−	0.126747i
$922$	3.46317	−	5.99839i	0.114053	−	0.197546i
$923$	−25.5923	−	12.3057i	−0.842381	−	0.405048i
$924$		0			0
$925$	−6.67307	−	6.67307i	−0.219409	−	0.219409i
$926$	25.5336	−	44.2255i	0.839085	−	1.45334i
$927$	0.389986	+	0.675475i	0.0128088	+	0.0221855i
$928$	−13.3025	+	49.6458i	−0.436677	+	1.62970i
$929$	9.06302	+	33.8237i	0.297348	+	1.10972i	0.939335	+	0.343002i	$0.111444\pi$
$929$	9.06302	+	33.8237i	0.297348	+	1.10972i	−0.641987	+	0.766716i	$0.721890\pi$
$930$	−58.3001	−	58.3001i	−1.91174	−	1.91174i
$931$		0			0
$932$	54.5007			1.78523
$933$	−4.13761	−	2.38885i	−0.135459	−	0.0782074i
$934$	−11.3856	+	42.4916i	−0.372548	+	1.39037i
$935$	−6.81830	+	3.93655i	−0.222982	+	0.128739i
$936$	0.278256	+	0.407602i	0.00909509	+	0.0133229i
$937$			18.9594i			0.619376i	0.950838	+	0.309688i	$0.100225\pi$
$937$			18.9594i			0.619376i	−0.950838	+	0.309688i	$0.899775\pi$
$938$		0			0
$939$	36.1180			1.17867
$940$	45.6620	+	26.3630i	1.48933	+	0.859865i
$941$	−44.7841	−	11.9999i	−1.45992	−	0.391184i	−0.560457	−	0.828183i	$-0.689375\pi$
$941$	−44.7841	−	11.9999i	−1.45992	−	0.391184i	−0.899462	+	0.436999i	$0.856041\pi$
$942$	−3.31178	+	12.3597i	−0.107903	+	0.402701i
$943$	−2.31994	+	0.621627i	−0.0755478	+	0.0202430i
$944$	0.901299	+	0.901299i	0.0293348	+	0.0293348i
$945$		0			0
$946$		−	13.7397i		−	0.446718i
$947$	−10.9715	−	40.9464i	−0.356527	−	1.33058i	−0.878552	−	0.477647i	$-0.841490\pi$
$947$	−10.9715	−	40.9464i	−0.356527	−	1.33058i	0.522025	−	0.852930i	$-0.325177\pi$
$948$	27.7961	+	48.1442i	0.902774	+	1.56365i
$949$	3.40363	+	45.0563i	0.110486	+	1.46259i
$950$	−26.6698	−	15.3978i	−0.865281	−	0.499570i
$951$	2.08830	−	2.08830i	0.0677179	−	0.0677179i
$952$		0			0
$953$			41.0785i			1.33066i	0.746548	+	0.665332i	$0.231710\pi$
$953$			41.0785i			1.33066i	−0.746548	+	0.665332i	$0.768290\pi$
$954$	−2.07401	+	0.555730i	−0.0671486	+	0.0179924i
$955$	−28.3509	−	7.59659i	−0.917413	−	0.245820i
$956$	−19.7382	−	5.28884i	−0.638380	−	0.171053i
$957$	7.10781	−	1.90453i	0.229763	−	0.0615648i
$958$			13.3962i			0.432810i
$959$		0			0
$960$	35.2400	−	35.2400i	1.13737	−	1.13737i
$961$	25.1258	+	14.5064i	0.810509	+	0.467948i
$962$	−16.9919	−	14.6050i	−0.547841	−	0.470885i
$963$	0.448379	+	0.776616i	0.0144488	+	0.0250261i
$964$	16.3366	+	60.9691i	0.526167	+	1.96368i
$965$		−	25.3277i		−	0.815327i
$966$		0			0
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.760492	−	0.649347i	$-0.775042\pi$
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.649347	−	0.760492i	$-0.724958\pi$
$968$	−4.50144	+	1.20616i	−0.144682	+	0.0387674i
$969$	−9.80519	+	36.5935i	−0.314988	+	1.17555i
$970$	1.89185	+	0.506919i	0.0607436	+	0.0162762i
$971$	38.3513	+	22.1421i	1.23075	+	0.710575i	0.967187	−	0.254066i	$-0.0817681\pi$
$971$	38.3513	+	22.1421i	1.23075	+	0.710575i	0.263566	+	0.964641i	$0.415101\pi$
$972$	−7.13125			−0.228735
$973$		0			0
$974$		−	27.9541i		−	0.895706i
$975$	−3.79052	+	20.0993i	−0.121394	+	0.643692i
$976$	23.7834	−	13.7314i	0.761288	−	0.439530i
$977$	2.56659	−	9.57866i	0.0821126	−	0.306449i	−0.912639	−	0.408766i	$-0.865959\pi$
$977$	2.56659	−	9.57866i	0.0821126	−	0.306449i	0.994752	+	0.102318i	$0.0326258\pi$
$978$	−47.8065	−	27.6011i	−1.52868	−	0.882585i
$979$	−5.06895			−0.162004
$980$		0			0
$981$	1.10393	+	1.10393i	0.0352459	+	0.0352459i
$982$	−4.89841	−	18.2811i	−0.156315	−	0.583374i
$983$	11.6408	−	43.4442i	0.371285	−	1.38566i	−0.487412	−	0.873172i	$-0.662059\pi$
$983$	11.6408	−	43.4442i	0.371285	−	1.38566i	0.858697	−	0.512484i	$-0.171274\pi$
$984$	−1.03011	−	1.78421i	−0.0328388	−	0.0568784i
$985$	6.54936	−	11.3438i	0.208680	−	0.361444i
$986$	−39.7684	−	39.7684i	−1.26649	−	1.26649i
$987$		0			0
$988$	−34.6227	−	16.6479i	−1.10149	−	0.529640i
$989$	−4.89038	+	8.47038i	−0.155505	+	0.269343i
$990$	−1.12255	−	0.300786i	−0.0356769	−	0.00955961i
$991$	−21.0684	−	36.4915i	−0.669259	−	1.15919i	−0.978112	−	0.208081i	$-0.933278\pi$
$991$	−21.0684	−	36.4915i	−0.669259	−	1.15919i	0.308853	−	0.951110i	$-0.400055\pi$
$992$	−31.4412	+	54.4578i	−0.998260	+	1.72904i
$993$	−5.28281	+	5.28281i	−0.167645	+	0.167645i
$994$		0			0
$995$	12.4931	−	12.4931i	0.396058	−	0.396058i
$996$	−6.35329	−	23.7108i	−0.201312	−	0.751306i
$997$	24.0161	−	13.8657i	0.760596	−	0.439131i	−0.0689134	−	0.997623i	$-0.521953\pi$
$997$	24.0161	−	13.8657i	0.760596	−	0.439131i	0.829510	+	0.558492i	$0.188620\pi$
$998$	16.7436	−	9.66693i	0.530010	−	0.306001i
$999$	14.3065	−	3.83342i	0.452638	−	0.121284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.411.5		24
7.2	even	3		91.2.i.a.34.1	✓	12
7.3	odd	6	inner	637.2.bc.a.619.1		24
7.4	even	3	inner	637.2.bc.a.619.2		24
7.5	odd	6		91.2.i.a.34.2	yes	12
7.6	odd	2	inner	637.2.bc.a.411.6		24
13.5	odd	4	inner	637.2.bc.a.460.1		24
21.2	odd	6		819.2.y.h.307.5		12
21.5	even	6		819.2.y.h.307.6		12
91.5	even	12		91.2.i.a.83.2	yes	12
91.18	odd	12	inner	637.2.bc.a.31.6		24
91.31	even	12	inner	637.2.bc.a.31.5		24
91.44	odd	12		91.2.i.a.83.1	yes	12
91.83	even	4	inner	637.2.bc.a.460.2		24
273.5	odd	12		819.2.y.h.811.5		12
273.44	even	12		819.2.y.h.811.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.1	✓	12	7.2	even	3
91.2.i.a.34.2	yes	12	7.5	odd	6
91.2.i.a.83.1	yes	12	91.44	odd	12
91.2.i.a.83.2	yes	12	91.5	even	12
637.2.bc.a.31.5		24	91.31	even	12	inner
637.2.bc.a.31.6		24	91.18	odd	12	inner
637.2.bc.a.411.5		24	1.1	even	1	trivial
637.2.bc.a.411.6		24	7.6	odd	2	inner
637.2.bc.a.460.1		24	13.5	odd	4	inner
637.2.bc.a.460.2		24	91.83	even	4	inner
637.2.bc.a.619.1		24	7.3	odd	6	inner
637.2.bc.a.619.2		24	7.4	even	3	inner
819.2.y.h.307.5		12	21.2	odd	6
819.2.y.h.307.6		12	21.5	even	6
819.2.y.h.811.5		12	273.5	odd	12
819.2.y.h.811.6		12	273.44	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.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.98293 - 0.531325i) q^{2} +(-1.57586 + 0.909822i) q^{3} +(1.91766 - 1.10716i) q^{4} +(0.737409 + 2.75205i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 - 0.269427i) q^{9} +O(q^{10})\)	\(q+(1.98293 - 0.531325i) q^{2} +(-1.57586 + 0.909822i) q^{3} +(1.91766 - 1.10716i) q^{4} +(0.737409 + 2.75205i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 - 0.269427i) q^{9} +(2.92446 + 5.06531i) q^{10} +(-0.616905 - 0.165299i) q^{11} +(-2.01464 + 3.48946i) q^{12} +(-3.40251 + 1.19288i) q^{13} +(-3.66593 - 3.66593i) q^{15} +(-1.76271 + 3.05311i) q^{16} +(-2.16336 - 3.74705i) q^{17} +(0.165299 - 0.616905i) q^{18} +(1.24540 + 4.64791i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +(0.808282 + 0.466662i) q^{23} +(-0.207209 + 0.773315i) q^{24} +(-2.69986 + 1.55877i) q^{25} +(-6.11313 + 4.17322i) q^{26} -4.89283i q^{27} +6.33185 q^{29} +(-9.21707 - 5.32148i) q^{30} +(7.48282 + 2.00502i) q^{31} +(-2.10089 + 7.84064i) q^{32} +(1.12255 - 0.300786i) q^{33} +(-6.28070 - 6.28070i) q^{34} -0.688892i q^{36} +(0.783477 + 2.92397i) q^{37} +(4.93910 + 8.55477i) q^{38} +(4.27656 - 4.97548i) q^{39} +(1.08560 + 0.626770i) q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(-1.36603 + 0.366025i) q^{44} +(0.856183 + 0.229414i) q^{45} +(1.85072 + 0.495898i) q^{46} +(8.07264 - 2.16306i) q^{47} -6.41503i q^{48} +(-4.52543 + 4.52543i) q^{50} +(6.81830 + 3.93655i) q^{51} +(-5.20414 + 6.05464i) q^{52} +(-1.68098 - 2.91155i) q^{53} +(-2.59968 - 9.70214i) q^{54} -1.81964i q^{55} +(-6.19135 - 6.19135i) q^{57} +(12.5556 - 3.36427i) q^{58} +(0.0935769 - 0.349234i) q^{59} +(-11.0888 - 2.97122i) q^{60} +(-6.74625 - 3.89495i) q^{61} +15.9032 q^{62} +9.61285i q^{64} +(-5.79189 - 8.48422i) q^{65} +(2.06612 - 1.19288i) q^{66} +(2.66503 - 9.94603i) q^{67} +(-8.29717 - 4.79037i) q^{68} -1.69832 q^{69} +(5.56914 + 5.56914i) q^{71} +(-0.0354269 - 0.132215i) q^{72} +(3.24351 - 12.1050i) q^{73} +(3.10716 + 5.38176i) q^{74} +(2.83640 - 4.91279i) q^{75} +(7.53424 + 7.53424i) q^{76} +(5.83654 - 12.1383i) q^{78} +(6.89853 - 11.9486i) q^{79} +(-9.70214 - 2.59968i) q^{80} +(4.91827 + 8.51869i) q^{81} +(-2.64141 + 4.57505i) q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(5.56801 + 20.7801i) q^{86} +(-9.97810 + 5.76086i) q^{87} +(-0.243350 + 0.140498i) q^{88} +(7.66632 - 2.05418i) q^{89} +1.81964 q^{90} +2.06668 q^{92} +(-13.6161 + 3.64842i) q^{93} +(14.8582 - 8.57839i) q^{94} +(-11.8729 + 6.85482i) q^{95} +(-3.82288 - 14.2672i) q^{96} +(0.236784 - 0.236784i) q^{97} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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