LMFDB - Embedded newform 639.2.z.a.269.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			269.23
Character	$\chi$	$=$	639.269
Dual form			639.2.z.a.620.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23678 + 0.956046i) q^{2} +(2.70704 + 2.83134i) q^{4} +(-1.60507 - 0.521518i) q^{5} +(3.14948 + 3.60487i) q^{7} +(1.63870 + 4.36630i) q^{8} +O(q^{10})$	\(q+(2.23678 + 0.956046i) q^{2} +(2.70704 + 2.83134i) q^{4} +(-1.60507 - 0.521518i) q^{5} +(3.14948 + 3.60487i) q^{7} +(1.63870 + 4.36630i) q^{8} +(-3.09159 - 2.70104i) q^{10} +(-3.16381 + 0.873156i) q^{11} +(0.682481 - 2.47292i) q^{13} +(3.59827 + 11.0744i) q^{14} +(-0.157481 + 3.50660i) q^{16} +(0.780535 - 0.567092i) q^{17} +(3.71439 + 6.90249i) q^{19} +(-2.86838 - 5.95626i) q^{20} +(-7.91152 - 1.07169i) q^{22} +(0.573174 - 2.51124i) q^{23} +(-1.74083 - 1.26479i) q^{25} +(3.89078 - 4.87889i) q^{26} +(-1.68085 + 18.6758i) q^{28} +(4.96732 - 0.672869i) q^{29} +(-2.19385 + 0.0985259i) q^{31} +(0.342271 - 0.710734i) q^{32} +(2.28805 - 0.522233i) q^{34} +(-3.17512 - 7.42856i) q^{35} +(-2.06376 - 9.04194i) q^{37} +(1.70917 + 18.9905i) q^{38} +(-0.353119 - 7.86282i) q^{40} +(-3.14308 - 3.94130i) q^{41} +(-1.39530 - 0.125579i) q^{43} +(-11.0368 - 6.59415i) q^{44} +(3.68293 - 5.06911i) q^{46} +(-6.57665 + 1.19349i) q^{47} +(-2.13623 + 15.7703i) q^{49} +(-2.68466 - 4.49336i) q^{50} +(8.84917 - 4.76194i) q^{52} +(9.06761 - 9.48398i) q^{53} +(5.53349 + 0.248509i) q^{55} +(-10.5789 + 19.6589i) q^{56} +(11.7541 + 3.24393i) q^{58} +(4.93677 + 7.47888i) q^{59} +(7.45302 - 8.53067i) q^{61} +(-5.00136 - 1.87704i) q^{62} +(6.73184 - 5.88143i) q^{64} +(-2.38510 + 3.61327i) q^{65} +(-3.23291 + 3.09097i) q^{67} +(3.71857 + 0.674821i) q^{68} -19.6516i q^{70} +(-7.48114 + 3.87718i) q^{71} +(2.59092 - 6.06175i) q^{73} +(4.02832 - 22.1979i) q^{74} +(-9.48831 + 29.2020i) q^{76} +(-13.1120 - 8.65513i) q^{77} +(0.412503 - 0.154815i) q^{79} +(2.08152 - 5.54619i) q^{80} +(-3.26232 - 11.8208i) q^{82} +(-8.23805 + 5.43789i) q^{83} +(-1.54856 + 0.503157i) q^{85} +(-3.00092 - 1.61486i) q^{86} +(-8.99700 - 12.3833i) q^{88} +(-8.89902 - 8.50833i) q^{89} +(11.0640 - 5.32814i) q^{91} +(8.66179 - 5.17518i) q^{92} +(-15.8515 - 3.61801i) q^{94} +(-2.36207 - 13.0161i) q^{95} +(0.579325 + 0.461996i) q^{97} +(-19.8554 + 33.2323i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{19}{70}\right)$	$-1$

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 $

$2$	2.23678	+	0.956046i	1.58164	+	0.676027i	0.991360	−	0.131170i	$-0.0418733\pi$
$2$	2.23678	+	0.956046i	1.58164	+	0.676027i	0.590283	+	0.807196i	$0.299016\pi$
$3$		0			0
$3$		0			0
$4$	2.70704	+	2.83134i	1.35352	+	1.41567i
$5$	−1.60507	−	0.521518i	−0.717807	−	0.233230i	−0.0727351	−	0.997351i	$-0.523173\pi$
$5$	−1.60507	−	0.521518i	−0.717807	−	0.233230i	−0.645072	+	0.764122i	$0.723173\pi$
$6$		0			0
$7$	3.14948	+	3.60487i	1.19039	+	1.36251i	0.916142	+	0.400854i	$0.131287\pi$
$7$	3.14948	+	3.60487i	1.19039	+	1.36251i	0.274249	+	0.961659i	$0.411571\pi$
$8$	1.63870	+	4.36630i	0.579368	+	1.54372i
$9$		0			0
$10$	−3.09159	−	2.70104i	−0.977645	−	0.854143i
$11$	−3.16381	+	0.873156i	−0.953924	+	0.263266i	−0.708151	−	0.706061i	$-0.750470\pi$
$11$	−3.16381	+	0.873156i	−0.953924	+	0.263266i	−0.245773	+	0.969327i	$0.579042\pi$
$12$		0			0
$13$	0.682481	−	2.47292i	0.189286	−	0.685863i	−0.806258	−	0.591564i	$-0.798511\pi$
$13$	0.682481	−	2.47292i	0.189286	−	0.685863i	0.995544	−	0.0942988i	$-0.0300609\pi$
$14$	3.59827	+	11.0744i	0.961679	+	2.95974i
$15$		0			0
$16$	−0.157481	+	3.50660i	−0.0393704	+	0.876649i
$17$	0.780535	−	0.567092i	0.189308	−	0.137540i	−0.489095	−	0.872231i	$-0.662673\pi$
$17$	0.780535	−	0.567092i	0.189308	−	0.137540i	0.678402	+	0.734691i	$0.262673\pi$
$18$		0			0
$19$	3.71439	+	6.90249i	0.852139	+	1.58354i	0.811490	+	0.584366i	$0.198657\pi$
$19$	3.71439	+	6.90249i	0.852139	+	1.58354i	0.0406486	+	0.999174i	$0.487058\pi$
$20$	−2.86838	−	5.95626i	−0.641390	−	1.33186i
$21$		0			0
$22$	−7.91152	−	1.07169i	−1.68674	−	0.228485i
$23$	0.573174	−	2.51124i	0.119515	−	0.523630i	−0.879358	−	0.476162i	$-0.842028\pi$
$23$	0.573174	−	2.51124i	0.119515	−	0.523630i	0.998873	−	0.0474680i	$-0.0151152\pi$
$24$		0			0
$25$	−1.74083	−	1.26479i	−0.348166	−	0.252957i
$26$	3.89078	−	4.87889i	0.763045	−	0.956828i
$27$		0			0
$28$	−1.68085	+	18.6758i	−0.317651	+	3.52939i
$29$	4.96732	−	0.672869i	0.922408	−	0.124949i	0.342395	−	0.939556i	$-0.388762\pi$
$29$	4.96732	−	0.672869i	0.922408	−	0.124949i	0.580013	+	0.814607i	$0.303048\pi$
$30$		0			0
$31$	−2.19385	+	0.0985259i	−0.394027	+	0.0176958i	−0.240997	−	0.970526i	$-0.577474\pi$
$31$	−2.19385	+	0.0985259i	−0.394027	+	0.0176958i	−0.153030	+	0.988222i	$0.548903\pi$
$32$	0.342271	−	0.710734i	0.0605056	−	0.125641i
$33$		0			0
$34$	2.28805	−	0.522233i	0.392398	−	0.0895622i
$35$	−3.17512	−	7.42856i	−0.536693	−	1.25566i
$36$		0			0
$37$	−2.06376	−	9.04194i	−0.339281	−	1.48649i	−0.800572	−	0.599237i	$-0.795471\pi$
$37$	−2.06376	−	9.04194i	−0.339281	−	1.48649i	0.461291	−	0.887249i	$-0.347386\pi$
$38$	1.70917	+	18.9905i	0.277265	+	3.08066i
$39$		0			0
$40$	−0.353119	−	7.86282i	−0.0558331	−	1.24322i
$41$	−3.14308	−	3.94130i	−0.490867	−	0.615528i	0.473275	−	0.880915i	$-0.343072\pi$
$41$	−3.14308	−	3.94130i	−0.490867	−	0.615528i	−0.964142	+	0.265387i	$0.914500\pi$
$42$		0			0
$43$	−1.39530	−	0.125579i	−0.212781	−	0.0191507i	−0.0172642	−	0.999851i	$-0.505496\pi$
$43$	−1.39530	−	0.125579i	−0.212781	−	0.0191507i	−0.195517	+	0.980700i	$0.562639\pi$
$44$	−11.0368	−	6.59415i	−1.66385	−	0.994106i
$45$		0			0
$46$	3.68293	−	5.06911i	0.543018	−	0.747400i
$47$	−6.57665	+	1.19349i	−0.959302	+	0.174088i	−0.635555	−	0.772056i	$-0.719229\pi$
$47$	−6.57665	+	1.19349i	−0.959302	+	0.174088i	−0.323748	+	0.946143i	$0.604943\pi$
$48$		0			0
$49$	−2.13623	+	15.7703i	−0.305176	+	2.25290i
$50$	−2.68466	−	4.49336i	−0.379668	−	0.635457i
$51$		0			0
$52$	8.84917	−	4.76194i	1.22716	−	0.660363i
$53$	9.06761	−	9.48398i	1.24553	−	1.30272i	0.309462	−	0.950912i	$-0.399851\pi$
$53$	9.06761	−	9.48398i	1.24553	−	1.30272i	0.936070	−	0.351813i	$-0.114435\pi$
$54$		0			0
$55$	5.53349	+	0.248509i	0.746135	+	0.0335090i
$56$	−10.5789	+	19.6589i	−1.41366	+	2.62703i
$57$		0			0
$58$	11.7541	+	3.24393i	1.54339	+	0.425948i
$59$	4.93677	+	7.47888i	0.642712	+	0.973667i	0.999224	+	0.0393766i	$0.0125372\pi$
$59$	4.93677	+	7.47888i	0.642712	+	0.973667i	−0.356512	+	0.934291i	$0.616034\pi$
$60$		0			0
$61$	7.45302	−	8.53067i	0.954262	−	1.09224i	−0.0413952	−	0.999143i	$-0.513180\pi$
$61$	7.45302	−	8.53067i	0.954262	−	1.09224i	0.995657	−	0.0930976i	$-0.0296769\pi$
$62$	−5.00136	−	1.87704i	−0.635173	−	0.238384i
$63$		0			0
$64$	6.73184	−	5.88143i	0.841480	−	0.735179i
$65$	−2.38510	+	3.61327i	−0.295835	+	0.448171i
$66$		0			0
$67$	−3.23291	+	3.09097i	−0.394962	+	0.377623i	−0.862250	−	0.506483i	$-0.830945\pi$
$67$	−3.23291	+	3.09097i	−0.394962	+	0.377623i	0.467288	+	0.884105i	$0.345231\pi$
$68$	3.71857	+	0.674821i	0.450943	+	0.0818341i
$69$		0			0
$70$		−	19.6516i		−	2.34882i
$71$	−7.48114	+	3.87718i	−0.887848	+	0.460137i
$71$	−7.48114	+	3.87718i	−0.887848	+	0.460137i
$72$		0			0
$73$	2.59092	−	6.06175i	0.303244	−	0.709474i	−0.696725	−	0.717338i	$-0.745360\pi$
$73$	2.59092	−	6.06175i	0.303244	−	0.709474i	0.999969	+	0.00786379i	$0.00250315\pi$
$74$	4.02832	−	22.1979i	0.468283	−	2.58045i
$75$		0			0
$76$	−9.48831	+	29.2020i	−1.08838	+	3.34970i
$77$	−13.1120	−	8.65513i	−1.49425	−	0.986344i
$78$		0			0
$79$	0.412503	−	0.154815i	0.0464102	−	0.0174180i	−0.328062	−	0.944656i	$-0.606395\pi$
$79$	0.412503	−	0.154815i	0.0464102	−	0.0174180i	0.374472	+	0.927238i	$0.377824\pi$
$80$	2.08152	−	5.54619i	0.232721	−	0.620083i
$81$		0			0
$82$	−3.26232	−	11.8208i	−0.360263	−	1.30538i
$83$	−8.23805	+	5.43789i	−0.904243	+	0.596886i	−0.915176	−	0.403055i	$-0.867948\pi$
$83$	−8.23805	+	5.43789i	−0.904243	+	0.596886i	0.0109329	+	0.999940i	$0.496520\pi$
$84$		0			0
$85$	−1.54856	+	0.503157i	−0.167965	+	0.0545751i
$86$	−3.00092	−	1.61486i	−0.323598	−	0.174135i
$87$		0			0
$88$	−8.99700	−	12.3833i	−0.959083	−	1.32006i
$89$	−8.89902	−	8.50833i	−0.943294	−	0.901881i	0.0520133	−	0.998646i	$-0.483436\pi$
$89$	−8.89902	−	8.50833i	−0.943294	−	0.901881i	−0.995307	+	0.0967651i	$0.969150\pi$
$90$		0			0
$91$	11.0640	−	5.32814i	1.15982	−	0.558541i
$92$	8.66179	−	5.17518i	0.903054	−	0.539549i
$93$		0			0
$94$	−15.8515	−	3.61801i	−1.63496	−	0.373169i
$95$	−2.36207	−	13.0161i	−0.242343	−	1.33542i
$96$		0			0
$97$	0.579325	+	0.461996i	0.0588215	+	0.0469086i	0.652459	−	0.757824i	$-0.273737\pi$
$97$	0.579325	+	0.461996i	0.0588215	+	0.0469086i	−0.593638	+	0.804732i	$0.702309\pi$
$98$	−19.8554	+	33.2323i	−2.00570	+	3.35697i
$99$		0			0
$100$	−1.13145	−	8.35271i	−0.113145	−	0.835271i
$101$	−3.38845	+	2.70220i	−0.337164	+	0.268879i	−0.777405	−	0.629000i	$-0.783464\pi$
$101$	−3.38845	+	2.70220i	−0.337164	+	0.268879i	0.440241	+	0.897880i	$0.354893\pi$
$102$		0			0
$103$	−12.6606	−	6.09702i	−1.24749	−	0.600758i	−0.310649	−	0.950525i	$-0.600547\pi$
$103$	−12.6606	−	6.09702i	−1.24749	−	0.600758i	−0.936837	+	0.349767i	$0.886261\pi$
$104$	11.9159	−	1.07245i	1.16845	−	0.105162i
$105$		0			0
$106$	29.3494	−	12.5445i	2.85066	−	1.21843i
$107$	12.0756	−	5.16137i	1.16740	−	0.498969i	0.280010	−	0.959997i	$-0.409662\pi$
$107$	12.0756	−	5.16137i	1.16740	−	0.498969i	0.887386	+	0.461028i	$0.152519\pi$
$108$		0			0
$109$	11.0298	−	0.992704i	1.05647	−	0.0950838i	0.452241	−	0.891896i	$-0.350625\pi$
$109$	11.0298	−	0.992704i	1.05647	−	0.0950838i	0.604227	+	0.796812i	$0.293482\pi$
$110$	12.1396	+	5.84613i	1.15747	+	0.557407i
$111$		0			0
$112$	−13.1368	+	10.4763i	−1.24131	+	0.989913i
$113$	−0.625240	−	4.61571i	−0.0588176	−	0.434209i	−0.996284	−	0.0861325i	$-0.972549\pi$
$113$	−0.625240	−	4.61571i	−0.0588176	−	0.434209i	0.937466	−	0.348077i	$-0.113165\pi$
$114$		0			0
$115$	−2.22964	+	3.73179i	−0.207915	+	0.347991i
$116$	15.3519	+	12.2427i	1.42538	+	1.13671i
$117$		0			0
$118$	3.89231	+	21.4484i	0.358316	+	1.97448i
$119$	4.50257	+	1.02768i	0.412750	+	0.0942075i
$120$		0			0
$121$	−0.195654	+	0.116898i	−0.0177868	+	0.0106271i
$122$	24.8265	−	11.9558i	2.24769	−	1.08243i
$123$		0			0
$124$	−6.21780	−	5.94482i	−0.558375	−	0.533861i
$125$	7.09446	+	9.76469i	0.634548	+	0.873381i
$126$		0			0
$127$	−9.28324	−	4.99552i	−0.823754	−	0.443281i	0.00696287	−	0.999976i	$-0.497784\pi$
$127$	−9.28324	−	4.99552i	−0.823754	−	0.443281i	−0.830717	+	0.556695i	$0.812069\pi$
$128$	19.1801	−	6.23199i	1.69530	−	0.550835i
$129$		0			0
$130$	−8.78939	+	5.80182i	−0.770880	+	0.508854i
$131$	1.03849	+	3.76289i	0.0907334	+	0.328765i	0.995210	−	0.0977576i	$-0.0311670\pi$
$131$	1.03849	+	3.76289i	0.0907334	+	0.328765i	−0.904477	+	0.426523i	$0.859738\pi$
$132$		0			0
$133$	−13.1842	+	35.1291i	−1.14321	+	3.04608i
$134$	−10.1864	+	3.82303i	−0.879972	+	0.330259i
$135$		0			0
$136$	3.75516	+	2.47876i	0.322002	+	0.212552i
$137$	2.41900	−	7.44492i	0.206669	−	0.636063i	−0.792971	−	0.609259i	$-0.791467\pi$
$137$	2.41900	−	7.44492i	0.206669	−	0.636063i	0.999641	−	0.0268039i	$-0.00853297\pi$
$138$		0			0
$139$	−0.225464	+	1.24241i	−0.0191236	+	0.105380i	−0.992080	−	0.125611i	$-0.959911\pi$
$139$	−0.225464	+	1.24241i	−0.0191236	+	0.105380i	0.972956	+	0.230991i	$0.0741966\pi$
$140$	12.4376	−	29.0993i	1.05117	−	2.45934i
$141$		0			0
$142$	−20.4404	+	1.52010i	−1.71532	+	0.127564i
$143$			8.41974i			0.704094i
$144$		0			0
$145$	−8.32379	−	1.51055i	−0.691253	−	0.125444i
$146$	11.5906	−	11.0818i	0.959247	−	0.917134i
$147$		0			0
$148$	20.0141	−	30.3201i	1.64515	−	2.49230i
$149$	−1.07647	+	0.940481i	−0.0881876	+	0.0770472i	−0.700904	−	0.713256i	$-0.747220\pi$
$149$	−1.07647	+	0.940481i	−0.0881876	+	0.0770472i	0.612716	+	0.790303i	$0.290077\pi$
$150$		0			0
$151$	18.2206	+	6.83830i	1.48277	+	0.556493i	0.955962	−	0.293490i	$-0.0948168\pi$
$151$	18.2206	+	6.83830i	1.48277	+	0.556493i	0.526809	+	0.849984i	$0.323388\pi$
$152$	−24.0516	+	27.5293i	−1.95084	+	2.23292i
$153$		0			0
$154$	−21.0539	−	31.8953i	−1.69657	−	2.57019i
$155$	3.57266	+	0.985991i	0.286963	+	0.0791967i
$156$		0			0
$157$	−11.6850	+	21.7143i	−0.932562	+	1.73299i	−0.309325	+	0.950956i	$0.600103\pi$
$157$	−11.6850	+	21.7143i	−0.932562	+	1.73299i	−0.623237	+	0.782033i	$0.714183\pi$
$158$	1.07069	+	0.0480847i	0.0851794	+	0.00382541i
$159$		0			0
$160$	−0.920029	+	0.962274i	−0.0727346	+	0.0760745i
$161$	10.8579	−	5.84288i	0.855722	−	0.460484i
$162$		0			0
$163$	3.72690	+	6.23778i	0.291913	+	0.488581i	0.968913	−	0.247403i	$-0.0795772\pi$
$163$	3.72690	+	6.23778i	0.291913	+	0.488581i	−0.676999	+	0.735984i	$0.736720\pi$
$164$	2.65072	−	19.5684i	0.206986	−	1.52803i
$165$		0			0
$166$	−23.6256	+	4.28741i	−1.83370	+	0.332768i
$167$	−5.20100	+	7.15856i	−0.402466	+	0.553946i	−0.961361	−	0.275292i	$-0.911225\pi$
$167$	−5.20100	+	7.15856i	−0.402466	+	0.553946i	0.558895	+	0.829238i	$0.311225\pi$
$168$		0			0
$169$	5.51030	+	3.29225i	0.423870	+	0.253250i
$170$	−3.94483	−	0.355041i	−0.302555	−	0.0272304i
$171$		0			0
$172$	−3.42158	−	4.29052i	−0.260893	−	0.327149i
$173$	0.969659	+	21.5911i	0.0737218	+	1.64154i	0.606353	+	0.795196i	$0.292632\pi$
$173$	0.969659	+	21.5911i	0.0737218	+	1.64154i	−0.532631	+	0.846347i	$0.678797\pi$
$174$		0			0
$175$	−0.923316	−	10.2589i	−0.0697961	−	0.775498i
$176$	−2.56356	−	11.2317i	−0.193236	−	0.846622i
$177$		0			0
$178$	−11.7708	−	27.5391i	−0.882258	−	2.06415i
$179$	−4.71802	+	1.07686i	−0.352642	+	0.0804882i	−0.395172	−	0.918607i	$-0.629315\pi$
$179$	−4.71802	+	1.07686i	−0.352642	+	0.0804882i	0.0425307	+	0.999095i	$0.486458\pi$
$180$		0			0
$181$	−0.405725	+	0.842496i	−0.0301573	+	0.0626222i	−0.915503	−	0.402311i	$-0.868207\pi$
$181$	−0.405725	+	0.842496i	−0.0301573	+	0.0626222i	0.885346	+	0.464933i	$0.153922\pi$
$182$	29.8417	−	1.34019i	2.21201	−	0.0993416i
$183$		0			0
$184$	11.9041	−	1.61252i	0.877582	−	0.118877i
$185$	−1.40305	+	15.5892i	−0.103155	+	1.14614i
$186$		0			0
$187$	−1.97430	+	2.47570i	−0.144375	+	0.181041i
$188$	−21.1824	−	15.3899i	−1.54489	−	1.12243i
$189$		0			0
$190$	7.16053	−	31.3723i	0.519480	−	2.27599i
$191$	−22.3592	−	3.02876i	−1.61786	−	0.219154i	−0.731394	−	0.681955i	$-0.761130\pi$
$191$	−22.3592	−	3.02876i	−1.61786	−	0.219154i	−0.886462	+	0.462801i	$0.846844\pi$
$192$		0			0
$193$	−0.403936	−	0.838783i	−0.0290760	−	0.0603769i	0.885925	−	0.463829i	$-0.153525\pi$
$193$	−0.403936	−	0.838783i	−0.0290760	−	0.0603769i	−0.915001	+	0.403452i	$0.867810\pi$
$194$	0.854133	+	1.58724i	0.0613232	+	0.113958i
$195$		0			0
$196$	−50.4339	+	36.6424i	−3.60242	+	2.61731i
$197$	0.169152	−	3.76646i	0.0120516	−	0.268349i	−0.983916	−	0.178633i	$-0.942833\pi$
$197$	0.169152	−	3.76646i	0.0120516	−	0.268349i	0.995967	−	0.0897164i	$-0.0285961\pi$
$198$		0			0
$199$	2.61924	+	8.06120i	0.185673	+	0.571443i	0.999959	−	0.00902055i	$-0.00287137\pi$
$199$	2.61924	+	8.06120i	0.185673	+	0.571443i	−0.814286	+	0.580464i	$0.802871\pi$
$200$	2.66974	−	9.67359i	0.188779	−	0.684026i
$201$		0			0
$202$	−10.1627	+	2.80471i	−0.715042	+	0.197339i
$203$	18.0701	+	15.7874i	1.26827	+	1.10805i
$204$		0			0
$205$	2.98940	+	7.96522i	0.208789	+	0.556315i
$206$	−22.4900	−	25.7418i	−1.56695	−	1.79352i
$207$		0			0
$208$	8.56404	+	2.78263i	0.593809	+	0.192940i
$209$	−17.7786	−	18.5949i	−1.22977	−	1.28624i
$210$		0			0
$211$	−22.0761	−	9.43577i	−1.51978	−	0.649585i	−0.538579	−	0.842575i	$-0.681039\pi$
$211$	−22.0761	−	9.43577i	−1.51978	−	0.649585i	−0.981201	+	0.192990i	$0.938182\pi$
$212$	51.3988			3.53008
$213$		0			0
$214$	31.9451			2.18372
$215$	2.17406	+	0.929237i	0.148269	+	0.0633734i
$216$		0			0
$217$	−7.26466	−	7.59824i	−0.493157	−	0.515802i
$218$	25.6204	+	8.32458i	1.73523	+	0.563812i
$219$		0			0
$220$	14.2758	+	16.3399i	0.962471	+	1.10164i
$221$	−0.869670	−	2.31723i	−0.0585003	−	0.155874i
$222$		0			0
$223$	9.14086	+	7.98612i	0.612117	+	0.534790i	0.907210	−	0.420678i	$-0.138208\pi$
$223$	9.14086	+	7.98612i	0.612117	+	0.534790i	−0.295093	+	0.955469i	$0.595351\pi$
$224$	3.64008	−	1.00460i	0.243213	−	0.0671225i
$225$		0			0
$226$	3.01430	−	10.9221i	0.200508	−	0.726526i
$227$	4.91319	+	15.1212i	0.326100	+	1.00363i	0.970942	+	0.239316i	$0.0769232\pi$
$227$	4.91319	+	15.1212i	0.326100	+	1.00363i	−0.644842	+	0.764316i	$0.723077\pi$
$228$		0			0
$229$	−0.219203	+	4.88094i	−0.0144853	+	0.322541i	0.978647	+	0.205547i	$0.0658973\pi$
$229$	−0.219203	+	4.88094i	−0.0144853	+	0.322541i	−0.993133	+	0.116994i	$0.962674\pi$
$230$	−8.55497	+	6.21555i	−0.564098	+	0.409841i
$231$		0			0
$232$	11.0779	+	20.5862i	0.727300	+	1.35155i
$233$	11.3557	+	23.5804i	0.743939	+	1.54481i	0.835800	+	0.549034i	$0.185004\pi$
$233$	11.3557	+	23.5804i	0.743939	+	1.54481i	−0.0918609	+	0.995772i	$0.529282\pi$
$234$		0			0
$235$	11.1784	+	1.51421i	0.729197	+	0.0987764i
$236$	−7.81124	+	34.2233i	−0.508469	+	2.22775i
$237$		0			0
$238$	9.08876	+	6.60337i	0.589137	+	0.428033i
$239$	0.449079	−	0.563127i	0.0290485	−	0.0364257i	−0.767095	−	0.641533i	$-0.778299\pi$
$239$	0.449079	−	0.563127i	0.0290485	−	0.0364257i	0.796144	+	0.605108i	$0.206870\pi$
$240$		0			0
$241$	0.504679	−	5.60744i	0.0325092	−	0.361207i	−0.963208	−	0.268757i	$-0.913387\pi$
$241$	0.504679	−	5.60744i	0.0325092	−	0.361207i	0.995717	−	0.0924504i	$-0.0294700\pi$
$242$	−0.549396	+	0.0744207i	−0.0353165	+	0.00478394i
$243$		0			0
$244$	44.3289	−	1.99081i	2.83787	−	0.127449i
$245$	11.6533	−	24.1983i	0.744500	−	1.54597i
$246$		0			0
$247$	19.6043	−	4.47455i	1.24739	−	0.284709i
$248$	−4.02526	−	9.41756i	−0.255604	−	0.598015i
$249$		0			0
$250$	6.53327	+	28.6241i	0.413200	+	1.81035i
$251$	1.60815	+	17.8680i	0.101506	+	1.12782i	0.871709	+	0.490023i	$0.163012\pi$
$251$	1.60815	+	17.8680i	0.101506	+	1.12782i	−0.770204	+	0.637798i	$0.779846\pi$
$252$		0			0
$253$	0.379290	+	8.44555i	0.0238458	+	0.530967i
$254$	−15.9886	−	20.0491i	−1.00322	−	1.25799i
$255$		0			0
$256$	31.0533	+	2.79485i	1.94083	+	0.174678i
$257$	−10.4915	−	6.26837i	−0.654441	−	0.391010i	0.146956	−	0.989143i	$-0.453052\pi$
$257$	−10.4915	−	6.26837i	−0.654441	−	0.391010i	−0.801397	+	0.598133i	$0.795910\pi$
$258$		0			0
$259$	26.0952	−	35.9170i	1.62148	−	2.23177i
$260$	−16.6869	+	3.02823i	−1.03488	+	0.187803i
$261$		0			0
$262$	−1.27462	+	9.40960i	−0.0787461	+	0.581327i
$263$	4.49490	+	7.52320i	0.277168	+	0.463900i	0.965103	−	0.261872i	$-0.0843398\pi$
$263$	4.49490	+	7.52320i	0.277168	+	0.463900i	−0.687935	+	0.725772i	$0.741483\pi$
$264$		0			0
$265$	−19.5002	+	10.4935i	−1.19789	+	0.644610i
$266$	−63.0752	+	65.9715i	−3.86739	+	4.04497i
$267$		0			0
$268$	−17.5032	−	0.786070i	−1.06918	−	0.0480169i
$269$	−11.0839	+	20.5973i	−0.675795	+	1.25584i	0.279489	+	0.960149i	$0.409835\pi$
$269$	−11.0839	+	20.5973i	−0.675795	+	1.25584i	−0.955284	+	0.295689i	$0.904451\pi$
$270$		0			0
$271$	−25.4348	−	7.01957i	−1.54506	−	0.426408i	−0.613407	−	0.789767i	$-0.710201\pi$
$271$	−25.4348	−	7.01957i	−1.54506	−	0.426408i	−0.931649	+	0.363359i	$0.881630\pi$
$272$	1.86564	+	2.82633i	0.113121	+	0.171371i
$273$		0			0
$274$	12.5285	−	14.3400i	0.756872	−	0.866310i
$275$	6.61200	+	2.48153i	0.398719	+	0.149642i
$276$		0			0
$277$	2.46795	−	2.15618i	0.148285	−	0.129552i	−0.580600	−	0.814189i	$-0.697182\pi$
$277$	2.46795	−	2.15618i	0.148285	−	0.129552i	0.728885	+	0.684637i	$0.240039\pi$
$278$	−1.69211	+	2.56344i	−0.101486	+	0.153745i
$279$		0			0
$280$	27.2323	−	26.0367i	1.62744	−	1.55599i
$281$	−14.5843	−	2.64665i	−0.870025	−	0.157886i	−0.274854	−	0.961486i	$-0.588630\pi$
$281$	−14.5843	−	2.64665i	−0.870025	−	0.157886i	−0.595170	+	0.803600i	$0.702915\pi$
$282$		0			0
$283$		−	5.32783i		−	0.316707i	−0.987383	−	0.158353i	$-0.949382\pi$
$283$		−	5.32783i		−	0.316707i	0.987383	−	0.158353i	$-0.0506185\pi$
$284$	−31.2294	−	10.6860i	−1.85312	−	0.634095i
$285$		0			0
$286$	−8.04966	+	18.8331i	−0.475986	+	1.11363i
$287$	4.30880	−	23.7434i	0.254340	−	1.40153i
$288$		0			0
$289$	−4.96565	+	15.2827i	−0.292097	+	0.898982i
$290$	−17.1743	−	11.3367i	−1.00851	−	0.665713i
$291$		0			0
$292$	24.1766	−	9.07363i	1.41483	−	0.530994i
$293$	7.45859	−	19.8733i	0.435735	−	1.16101i	−0.516672	−	0.856184i	$-0.672829\pi$
$293$	7.45859	−	19.8733i	0.435735	−	1.16101i	0.952407	−	0.304829i	$-0.0985994\pi$
$294$		0			0
$295$	−4.02347	−	14.5787i	−0.234255	−	0.848805i
$296$	36.0979	−	23.8280i	2.09815	−	1.38498i
$297$		0			0
$298$	−3.30696	+	1.07450i	−0.191567	+	0.0622440i
$299$	−5.81890	−	3.13129i	−0.336516	−	0.181087i
$300$		0			0
$301$	−3.94177	−	5.42538i	−0.227200	−	0.312714i
$302$	34.2178	+	32.7155i	1.96901	+	1.88257i
$303$		0			0
$304$	−24.7892	+	11.9378i	−1.42176	+	0.684683i
$305$	−16.4115	+	9.80541i	−0.939719	+	0.561456i
$306$		0			0
$307$	0.633056	+	0.144491i	0.0361304	+	0.00824654i	0.240548	−	0.970637i	$-0.422673\pi$
$307$	0.633056	+	0.144491i	0.0361304	+	0.00824654i	−0.204418	+	0.978884i	$0.565530\pi$
$308$	−10.9890	−	60.5542i	−0.626155	−	3.45040i
$309$		0			0
$310$	7.04860	+	5.62107i	0.400333	+	0.319255i
$311$	13.2900	−	22.2436i	0.753604	−	1.26132i	−0.205608	−	0.978634i	$-0.565917\pi$
$311$	13.2900	−	22.2436i	0.753604	−	1.26132i	0.959212	−	0.282687i	$-0.0912258\pi$
$312$		0			0
$313$	−4.31617	−	31.8633i	−0.243964	−	1.80102i	−0.535582	−	0.844483i	$-0.679908\pi$
$313$	−4.31617	−	31.8633i	−0.243964	−	1.80102i	0.291618	−	0.956535i	$-0.405806\pi$
$314$	−46.8966	+	37.3988i	−2.64653	+	2.11053i
$315$		0			0
$316$	1.55500	+	0.748846i	0.0874753	+	0.0421259i
$317$	6.57257	−	0.591542i	0.369152	−	0.0332243i	0.0964897	−	0.995334i	$-0.469239\pi$
$317$	6.57257	−	0.591542i	0.369152	−	0.0332243i	0.272663	+	0.962110i	$0.412096\pi$
$318$		0			0
$319$	−15.1281	+	6.46607i	−0.847013	+	0.362031i
$320$	−13.8723	+	5.92931i	−0.775486	+	0.331459i
$321$		0			0
$322$	29.8728	−	2.68860i	1.66475	−	0.149830i
$323$	6.81356	+	3.28124i	0.379116	+	0.182573i
$324$		0			0
$325$	−4.31579	+	3.44173i	−0.239397	+	0.190913i
$326$	2.37265	+	17.5156i	0.131409	+	0.970101i
$327$		0			0
$328$	12.0583	−	20.1823i	0.665810	−	1.11438i
$329$	−25.0154	−	19.9491i	−1.37914	−	1.09983i
$330$		0			0
$331$	−5.65426	−	31.1575i	−0.310786	−	1.71257i	−0.640049	−	0.768334i	$-0.721086\pi$
$331$	−5.65426	−	31.1575i	−0.310786	−	1.71257i	0.329263	−	0.944238i	$-0.393200\pi$
$332$	−37.6972	−	8.60415i	−2.06890	−	0.472214i
$333$		0			0
$334$	−18.4774	+	11.0397i	−1.01104	+	0.604068i
$335$	6.80103	−	3.27520i	0.371580	−	0.178943i
$336$		0			0
$337$	−17.1272	−	16.3753i	−0.932980	−	0.892020i	0.0613761	−	0.998115i	$-0.480451\pi$
$337$	−17.1272	−	16.3753i	−0.932980	−	0.892020i	−0.994356	+	0.106095i	$0.966165\pi$
$338$	9.17780	+	12.6322i	0.499206	+	0.687099i
$339$		0			0
$340$	−5.61662	−	3.02243i	−0.304604	−	0.163914i
$341$	6.85489	−	2.22729i	0.371213	−	0.120614i
$342$		0			0
$343$	−35.6127	+	23.5078i	−1.92291	+	1.26930i
$344$	−1.73816	−	6.29809i	−0.0937154	−	0.339570i
$345$		0			0
$346$	−18.4732	+	49.2217i	−0.993125	+	2.64617i
$347$	−28.1603	+	10.5687i	−1.51172	+	0.567359i	−0.963202	−	0.268777i	$-0.913380\pi$
$347$	−28.1603	+	10.5687i	−1.51172	+	0.567359i	−0.548521	+	0.836137i	$0.684809\pi$
$348$		0			0
$349$	15.1590	+	10.0064i	0.811445	+	0.535630i	0.887140	−	0.461501i	$-0.152689\pi$
$349$	15.1590	+	10.0064i	0.811445	+	0.535630i	−0.0756949	+	0.997131i	$0.524117\pi$
$350$	7.74270	−	23.8296i	0.413865	−	1.27375i
$351$		0			0
$352$	−0.462300	+	2.54748i	−0.0246407	+	0.135781i
$353$	−2.38473	+	5.57936i	−0.126927	+	0.296959i	−0.970924	−	0.239388i	$-0.923053\pi$
$353$	−2.38473	+	5.57936i	−0.126927	+	0.296959i	0.843998	+	0.536347i	$0.180196\pi$
$354$		0			0
$355$	14.0297	−	2.32159i	0.744621	−	0.123217i
$356$		−	48.2285i		−	2.55611i
$357$		0			0
$358$	−11.5827	−	2.10195i	−0.612165	−	0.111092i
$359$	−3.00143	+	2.86966i	−0.158410	+	0.151455i	−0.766106	−	0.642715i	$-0.777808\pi$
$359$	−3.00143	+	2.86966i	−0.158410	+	0.151455i	0.607696	+	0.794170i	$0.292094\pi$
$360$		0			0
$361$	−23.3806	+	35.4201i	−1.23056	+	1.86422i
$362$	−1.71298	+	1.49659i	−0.0900323	+	0.0786589i
$363$		0			0
$364$	45.0365	+	16.9025i	2.36055	+	0.885930i
$365$	−7.31990	+	8.37830i	−0.383141	+	0.438540i
$366$		0			0
$367$	5.03854	+	7.63307i	0.263010	+	0.398443i	0.941951	−	0.335750i	$-0.108990\pi$
$367$	5.03854	+	7.63307i	0.263010	+	0.398443i	−0.678941	+	0.734192i	$0.737561\pi$
$368$	8.71565	+	2.40537i	0.454334	+	0.125388i
$369$		0			0
$370$	−18.0423	+	33.5282i	−0.937975	+	1.74305i
$371$	62.7468	+	2.81796i	3.25765	+	0.146301i
$372$		0			0
$373$	8.06889	−	8.43940i	0.417791	−	0.436976i	−0.480086	−	0.877222i	$-0.659394\pi$
$373$	8.06889	−	8.43940i	0.417791	−	0.436976i	0.897877	+	0.440246i	$0.145109\pi$
$374$	−6.78297	+	3.65007i	−0.350739	+	0.188741i
$375$		0			0
$376$	−15.9883	−	26.7599i	−0.824532	−	1.38003i
$377$	1.72615	−	12.7430i	0.0889015	−	0.656297i
$378$		0			0
$379$	29.1990	−	5.29884i	1.49985	−	0.272183i	0.634334	−	0.773059i	$-0.281274\pi$
$379$	29.1990	−	5.29884i	1.49985	−	0.272183i	0.865519	+	0.500876i	$0.166989\pi$
$380$	30.4587	−	41.9228i	1.56250	−	2.15060i
$381$		0			0
$382$	−47.1170	−	28.1511i	−2.41072	−	1.44034i
$383$	−1.93589	−	0.174233i	−0.0989193	−	0.00890289i	0.0400691	−	0.999197i	$-0.487242\pi$
$383$	−1.93589	−	0.174233i	−0.0989193	−	0.00890289i	−0.138988	+	0.990294i	$0.544385\pi$
$384$		0			0
$385$	16.5318	+	20.7302i	0.842537	+	1.05651i
$386$	−0.101602	−	2.26236i	−0.00517143	−	0.115151i
$387$		0			0
$388$	0.260186	+	2.89091i	0.0132090	+	0.146764i
$389$	−3.80357	−	16.6645i	−0.192848	−	0.844924i	−0.975065	−	0.221918i	$-0.928768\pi$
$389$	−3.80357	−	16.6645i	−0.192848	−	0.844924i	0.782217	−	0.623006i	$-0.214089\pi$
$390$		0			0
$391$	−0.976722	−	2.28515i	−0.0493950	−	0.115565i
$392$	−72.3584	+	16.5153i	−3.65465	+	0.834151i
$393$		0			0
$394$	3.97927	−	8.26304i	0.200473	−	0.416286i
$395$	−0.742833	+	0.0333607i	−0.0373760	+	0.00167856i
$396$		0			0
$397$	−0.784136	+	0.106218i	−0.0393546	+	0.00533095i	−0.153884	−	0.988089i	$-0.549178\pi$
$397$	−0.784136	+	0.106218i	−0.0393546	+	0.00533095i	0.114529	+	0.993420i	$0.463464\pi$
$398$	−1.84821	+	20.5352i	−0.0926422	+	1.02934i
$399$		0			0
$400$	4.70924	−	5.90521i	0.235462	−	0.295260i
$401$	30.6833	+	22.2927i	1.53225	+	1.11325i	0.954970	+	0.296701i	$0.0958866\pi$
$401$	30.6833	+	22.2927i	1.53225	+	1.11325i	0.577282	+	0.816545i	$0.304113\pi$
$402$		0			0
$403$	−1.25362	+	5.49245i	−0.0624470	+	0.273598i
$404$	−16.8235	−	2.27890i	−0.837002	−	0.113380i
$405$		0			0
$406$	25.3254	+	52.5887i	1.25688	+	2.60993i
$407$	14.4244	+	26.8050i	0.714989	+	1.32867i
$408$		0			0
$409$	−12.7005	+	9.22745i	−0.627999	+	0.456268i	−0.855706	−	0.517462i	$-0.826877\pi$
$409$	−12.7005	+	9.22745i	−0.627999	+	0.456268i	0.227707	+	0.973730i	$0.426877\pi$
$410$	−0.928491	+	20.6745i	−0.0458549	+	1.02104i
$411$		0			0
$412$	−17.0100	−	52.3514i	−0.838022	−	2.57917i
$413$	−11.4121	+	41.3510i	−0.561555	+	2.03475i
$414$		0			0
$415$	16.0586	−	4.43188i	0.788284	−	0.217553i
$416$	−1.52399	−	1.33147i	−0.0747198	−	0.0652807i
$417$		0			0
$418$	−21.9891	−	58.5899i	−1.07552	−	2.86572i
$419$	20.5323	+	23.5011i	1.00307	+	1.14810i	0.988957	+	0.148202i	$0.0473487\pi$
$419$	20.5323	+	23.5011i	1.00307	+	1.14810i	0.0141103	+	0.999900i	$0.495508\pi$
$420$		0			0
$421$	−29.1049	−	9.45675i	−1.41849	−	0.460894i	−0.503365	−	0.864074i	$-0.667905\pi$
$421$	−29.1049	−	9.45675i	−1.41849	−	0.460894i	−0.915121	+	0.403180i	$0.867905\pi$
$422$	−40.3583	−	42.2115i	−1.96461	−	2.05482i
$423$		0			0
$424$	56.2690	+	24.0505i	2.73267	+	1.16800i
$425$	−2.07603			−0.100702
$426$		0			0
$427$	54.2251			2.62414
$428$	47.3028	+	20.2182i	2.28647	+	0.977284i
$429$		0			0
$430$	3.97450	+	4.15700i	0.191667	+	0.200468i
$431$	23.3139	+	7.57513i	1.12299	+	0.364881i	0.810908	−	0.585174i	$-0.198974\pi$
$431$	23.3139	+	7.57513i	1.12299	+	0.364881i	0.312082	+	0.950055i	$0.398974\pi$
$432$		0			0
$433$	−16.7364	−	19.1564i	−0.804301	−	0.920596i	0.193872	−	0.981027i	$-0.437895\pi$
$433$	−16.7364	−	19.1564i	−0.804301	−	0.920596i	−0.998172	+	0.0604308i	$0.980753\pi$
$434$	−8.98518	−	23.9409i	−0.431303	−	1.14920i
$435$		0			0
$436$	32.6689	+	28.5420i	1.56456	+	1.36691i
$437$	19.4628	−	5.37139i	0.931032	−	0.256949i
$438$		0			0
$439$	4.18288	−	15.1563i	0.199638	−	0.723372i	−0.793718	−	0.608286i	$-0.791857\pi$
$439$	4.18288	−	15.1563i	0.199638	−	0.723372i	0.993356	−	0.115086i	$-0.0367142\pi$
$440$	7.98266	+	24.5681i	0.380559	+	1.17124i
$441$		0			0
$442$	0.270115	−	6.01458i	0.0128481	−	0.286084i
$443$	3.10866	−	2.25857i	0.147697	−	0.107308i	−0.511483	−	0.859293i	$-0.670904\pi$
$443$	3.10866	−	2.25857i	0.147697	−	0.107308i	0.659180	+	0.751985i	$0.270904\pi$
$444$		0			0
$445$	9.84627	+	18.2974i	0.466758	+	0.867381i
$446$	12.8110	+	26.6023i	0.606618	+	1.25965i
$447$		0			0
$448$	42.4036	+	5.74396i	2.00338	+	0.271376i
$449$	2.44702	−	10.7211i	0.115482	−	0.505960i	−0.883793	−	0.467879i	$-0.845018\pi$
$449$	2.44702	−	10.7211i	0.115482	−	0.505960i	0.999275	−	0.0380813i	$-0.0121246\pi$
$450$		0			0
$451$	13.3855	+	9.72512i	0.630298	+	0.457938i
$452$	11.3761	−	14.2652i	0.535086	−	0.670977i
$453$		0			0
$454$	−3.46688	+	38.5201i	−0.162709	+	1.80784i
$455$	−20.5372	+	2.78195i	−0.962797	+	0.130420i
$456$		0			0
$457$	−26.3941	+	1.18536i	−1.23466	+	0.0554488i	−0.652605	−	0.757698i	$-0.726324\pi$
$457$	−26.3941	+	1.18536i	−1.23466	+	0.0554488i	−0.582059	+	0.813147i	$0.697753\pi$
$458$	−5.15671	+	10.7080i	−0.240957	+	0.500353i
$459$		0			0
$460$	−16.6017	+	3.78923i	−0.774057	+	0.176674i
$461$	−1.17433	−	2.74747i	−0.0546938	−	0.127962i	0.889952	−	0.456054i	$-0.150738\pi$
$461$	−1.17433	−	2.74747i	−0.0546938	−	0.127962i	−0.944646	+	0.328091i	$0.893595\pi$
$462$		0			0
$463$	2.04393	+	8.95503i	0.0949893	+	0.416175i	0.999957	−	0.00930556i	$-0.00296210\pi$
$463$	2.04393	+	8.95503i	0.0949893	+	0.416175i	−0.904967	+	0.425481i	$0.860105\pi$
$464$	1.57722	+	17.5244i	0.0732206	+	0.813548i
$465$		0			0
$466$	2.85632	+	63.6009i	0.132316	+	2.94625i
$467$	−6.40008	−	8.02544i	−0.296160	−	0.371373i	0.611381	−	0.791336i	$-0.290614\pi$
$467$	−6.40008	−	8.02544i	−0.296160	−	0.371373i	−0.907541	+	0.419963i	$0.862043\pi$
$468$		0			0
$469$	−21.3245	−	1.91924i	−0.984675	−	0.0886224i
$470$	23.5559	+	14.0740i	1.08655	+	0.649185i
$471$		0			0
$472$	−24.5652	+	33.8111i	−1.13070	+	1.55628i
$473$	4.52411	−	0.821005i	0.208019	−	0.0377499i
$474$		0			0
$475$	2.26406	−	16.7140i	0.103882	−	0.766889i
$476$	9.27892	+	15.5303i	0.425299	+	0.711830i
$477$		0			0
$478$	1.54287	−	0.830252i	0.0705691	−	0.0379748i
$479$	7.66066	−	8.01242i	0.350025	−	0.366097i	−0.524220	−	0.851583i	$-0.675643\pi$
$479$	7.66066	−	8.01242i	0.350025	−	0.366097i	0.874244	+	0.485486i	$0.161357\pi$
$480$		0			0
$481$	−23.7684	−	1.06744i	−1.08375	−	0.0486711i
$482$	6.48983	−	12.0601i	0.295604	−	0.549324i
$483$		0			0
$484$	−0.860622	−	0.237517i	−0.0391192	−	0.0107962i
$485$	−0.688915	−	1.04366i	−0.0312820	−	0.0473902i
$486$		0			0
$487$	−4.69779	+	5.37705i	−0.212877	+	0.243658i	−0.849590	−	0.527443i	$-0.823151\pi$
$487$	−4.69779	+	5.37705i	−0.212877	+	0.243658i	0.636713	+	0.771101i	$0.280294\pi$
$488$	49.4608	+	18.5629i	2.23898	+	0.840305i
$489$		0			0
$490$	49.2004	−	42.9851i	2.22265	−	1.94187i
$491$	−10.5710	+	16.0144i	−0.477063	+	0.722719i	−0.990816	−	0.135219i	$-0.956826\pi$
$491$	−10.5710	+	16.0144i	−0.477063	+	0.722719i	0.513753	+	0.857938i	$0.328255\pi$
$492$		0			0
$493$	3.49559	−	3.34213i	0.157433	−	0.150522i
$494$	48.1283	+	8.73400i	2.16540	+	0.392961i
$495$		0			0
$496$		−	7.70846i		−	0.346120i
$497$	−37.5384	−	14.7574i	−1.68383	−	0.661961i
$498$		0			0
$499$	10.0719	−	23.5643i	0.450878	−	1.05488i	−0.527779	−	0.849382i	$-0.676975\pi$
$499$	10.0719	−	23.5643i	0.450878	−	1.05488i	0.978657	−	0.205501i	$-0.0658822\pi$
$500$	−8.44218	+	46.5203i	−0.377546	+	2.08045i
$501$		0			0
$502$	−13.4856	+	41.5044i	−0.601891	+	1.85243i
$503$	−5.40427	−	3.56733i	−0.240965	−	0.159059i	0.424644	−	0.905360i	$-0.360399\pi$
$503$	−5.40427	−	3.56733i	−0.240965	−	0.159059i	−0.665608	+	0.746301i	$0.731828\pi$
$504$		0			0
$505$	6.84794	−	2.57007i	0.304729	−	0.114367i
$506$	−7.22595	+	19.2535i	−0.321233	+	0.855921i
$507$		0			0
$508$	−10.9861	−	39.8071i	−0.487428	−	1.76615i
$509$	−2.13097	+	1.40664i	−0.0944537	+	0.0623483i	−0.597241	−	0.802062i	$-0.703736\pi$
$509$	−2.13097	+	1.40664i	−0.0944537	+	0.0623483i	0.502787	+	0.864410i	$0.332308\pi$
$510$		0			0
$511$	30.0119	−	9.75145i	1.32765	−	0.431379i
$512$	31.2693	+	16.8267i	1.38192	+	0.743644i
$513$		0			0
$514$	−17.4743	−	24.0513i	−0.770759	−	1.06086i
$515$	17.1414	+	16.3889i	0.755340	+	0.722179i
$516$		0			0
$517$	19.7651	−	9.51839i	0.869270	−	0.418619i
$518$	92.7076	−	55.3902i	4.07334	−	2.43371i
$519$		0			0
$520$	−19.6851	−	4.49299i	−0.863248	−	0.197031i
$521$	1.13399	+	6.24882i	0.0496812	+	0.273766i	0.999202	−	0.0399377i	$-0.0127159\pi$
$521$	1.13399	+	6.24882i	0.0496812	+	0.273766i	−0.949521	+	0.313703i	$0.898430\pi$
$522$		0			0
$523$	−21.0872	−	16.8165i	−0.922077	−	0.735332i	0.0425100	−	0.999096i	$-0.486465\pi$
$523$	−21.0872	−	16.8165i	−0.922077	−	0.735332i	−0.964587	+	0.263764i	$0.915036\pi$
$524$	−7.84279	+	13.1266i	−0.342614	+	0.573439i
$525$		0			0
$526$	2.86159	+	21.1251i	0.124771	+	0.921098i
$527$	−1.65650	+	1.32102i	−0.0721584	+	0.0575444i
$528$		0			0
$529$	14.7445	+	7.10057i	0.641064	+	0.308720i
$530$	−53.6499	+	4.82858i	−2.33040	+	0.209740i
$531$		0			0
$532$	−135.153	+	57.7670i	−5.85961	+	2.50452i
$533$	−11.8916	+	5.08271i	−0.515082	+	0.220157i
$534$		0			0
$535$	−22.0739	+	1.98669i	−0.954340	+	0.0858921i
$536$	−18.7939	−	9.05066i	−0.811773	−	0.390929i
$537$		0			0
$538$	−44.4841	+	35.4749i	−1.91785	+	1.52943i
$539$	−7.01129	−	51.7594i	−0.301997	−	2.22943i
$540$		0			0
$541$	21.5998	−	36.1519i	0.928647	−	1.55429i	0.0996629	−	0.995021i	$-0.468224\pi$
$541$	21.5998	−	36.1519i	0.928647	−	1.55429i	0.828984	−	0.559272i	$-0.188919\pi$
$542$	−50.1811	−	40.0181i	−2.15546	−	1.71892i
$543$		0			0
$544$	−0.135897	−	0.748852i	−0.00582652	−	0.0321068i
$545$	−18.2213	−	4.15890i	−0.780517	−	0.178148i
$546$		0			0
$547$	29.6507	−	17.7155i	1.26777	−	0.757460i	0.288012	−	0.957627i	$-0.407006\pi$
$547$	29.6507	−	17.7155i	1.26777	−	0.757460i	0.979762	+	0.200167i	$0.0641486\pi$
$548$	27.6275	−	13.3047i	1.18019	−	0.568348i
$549$		0			0
$550$	12.4171	+	11.8720i	0.529469	+	0.506224i
$551$	23.0950	+	31.7876i	0.983881	+	1.35420i
$552$		0			0
$553$	1.85726	+	0.999432i	0.0789786	+	0.0425002i
$554$	7.58167	−	2.46343i	0.322114	−	0.104661i
$555$		0			0
$556$	−4.12802	+	2.72488i	−0.175067	+	0.115561i
$557$	7.24362	+	26.2467i	0.306922	+	1.11211i	0.940880	+	0.338739i	$0.110000\pi$
$557$	7.24362	+	26.2467i	0.306922	+	1.11211i	−0.633958	+	0.773367i	$0.718571\pi$
$558$		0			0
$559$	−1.26281	+	3.36475i	−0.0534113	+	0.142314i
$560$	26.5490	−	9.96401i	1.12190	−	0.421056i
$561$		0			0
$562$	−30.0915	−	19.8632i	−1.26933	−	0.837879i
$563$	12.3629	−	38.0490i	0.521032	−	1.60357i	−0.250998	−	0.967988i	$-0.580759\pi$
$563$	12.3629	−	38.0490i	0.521032	−	1.60357i	0.772031	−	0.635585i	$-0.219241\pi$
$564$		0			0
$565$	−1.40362	+	7.73459i	−0.0590508	+	0.325397i
$566$	5.09365	−	11.9172i	0.214102	−	0.500917i
$567$		0			0
$568$	−29.1883	−	26.3114i	−1.22471	−	1.10400i
$569$		−	6.33974i		−	0.265776i	−0.991131	−	0.132888i	$-0.957575\pi$
$569$		−	6.33974i		−	0.265776i	0.991131	−	0.132888i	$-0.0424250\pi$
$570$		0			0
$571$	−16.3136	−	2.96048i	−0.682701	−	0.123892i	−0.173884	−	0.984766i	$-0.555632\pi$
$571$	−16.3136	−	2.96048i	−0.682701	−	0.123892i	−0.508818	+	0.860874i	$0.669917\pi$
$572$	−23.8392	+	22.7926i	−0.996766	+	0.953006i
$573$		0			0
$574$	32.3377	−	48.9895i	1.34975	−	2.04478i
$575$	−4.17398	+	3.64670i	−0.174067	+	0.152078i
$576$		0			0
$577$	10.6237	+	3.98715i	0.442271	+	0.165987i	0.562568	−	0.826751i	$-0.309813\pi$
$577$	10.6237	+	3.98715i	0.442271	+	0.165987i	−0.120297	+	0.992738i	$0.538385\pi$
$578$	−25.7180	+	29.4366i	−1.06973	+	1.22440i
$579$		0			0
$580$	−18.2560	−	27.6566i	−0.758037	−	1.14838i
$581$	−45.5484	−	12.5706i	−1.88967	−	0.521515i
$582$		0			0
$583$	−20.4072	+	37.9229i	−0.845180	+	1.57061i
$584$	30.7132	+	1.37933i	1.27092	+	0.0570771i
$585$		0			0
$586$	35.6831	−	37.3215i	1.47405	−	1.54174i
$587$	22.2545	−	11.9757i	0.918541	−	0.494288i	0.0549549	−	0.998489i	$-0.482498\pi$
$587$	22.2545	−	11.9757i	0.918541	−	0.494288i	0.863587	+	0.504201i	$0.168213\pi$
$588$		0			0
$589$	−8.82888	−	14.7771i	−0.363788	−	0.608878i
$590$	4.93830	−	36.4560i	0.203307	−	1.50087i
$591$		0			0
$592$	32.0314	−	5.81285i	1.31648	−	0.238907i
$593$	6.19124	−	8.52151i	0.254244	−	0.349936i	−0.662748	−	0.748842i	$-0.730610\pi$
$593$	6.19124	−	8.52151i	0.254244	−	0.349936i	0.916992	+	0.398906i	$0.130610\pi$
$594$		0			0
$595$	−6.69097	−	3.99767i	−0.274303	−	0.163888i
$596$	−5.57686	−	0.501927i	−0.228437	−	0.0205597i
$597$		0			0
$598$	−10.0220	−	12.5671i	−0.409828	−	0.513909i
$599$	−1.97090	−	43.8855i	−0.0805288	−	1.79311i	−0.480916	−	0.876767i	$-0.659696\pi$
$599$	−1.97090	−	43.8855i	−0.0805288	−	1.79311i	0.400387	−	0.916346i	$-0.368876\pi$
$600$		0			0
$601$	1.25013	+	13.8900i	0.0509937	+	0.566587i	0.980332	+	0.197357i	$0.0632357\pi$
$601$	1.25013	+	13.8900i	0.0509937	+	0.566587i	−0.929338	+	0.369230i	$0.879621\pi$
$602$	−3.62996	−	15.9039i	−0.147946	−	0.648195i
$603$		0			0
$604$	29.9623	+	70.1003i	1.21915	+	2.85234i
$605$	0.375003	−	0.0855919i	0.0152460	−	0.00347980i
$606$		0			0
$607$	14.7196	−	30.5656i	0.597450	−	1.24062i	−0.354698	−	0.934981i	$-0.615416\pi$
$607$	14.7196	−	30.5656i	0.597450	−	1.24062i	0.952148	−	0.305637i	$-0.0988693\pi$
$608$	6.17716	−	0.277417i	0.250517	−	0.0112507i
$609$		0			0
$610$	−46.0833	+	6.24241i	−1.86586	+	0.252748i
$611$	−1.53705	+	17.0780i	−0.0621824	+	0.690903i
$612$		0			0
$613$	−5.68304	+	7.12630i	−0.229536	+	0.287829i	−0.883240	−	0.468922i	$-0.844643\pi$
$613$	−5.68304	+	7.12630i	−0.229536	+	0.287829i	0.653704	+	0.756750i	$0.273214\pi$
$614$	1.27787	+	0.928426i	0.0515706	+	0.0374682i
$615$		0			0
$616$	16.3043	−	71.4340i	0.656920	−	2.87816i
$617$	16.1350	+	2.18563i	0.649571	+	0.0879903i	0.451604	−	0.892218i	$-0.350852\pi$
$617$	16.1350	+	2.18563i	0.649571	+	0.0879903i	0.197967	+	0.980209i	$0.436566\pi$
$618$		0			0
$619$	11.6149	+	24.1185i	0.466840	+	0.969404i	0.992900	+	0.118956i	$0.0379547\pi$
$619$	11.6149	+	24.1185i	0.466840	+	0.969404i	−0.526059	+	0.850448i	$0.676331\pi$
$620$	6.87965	+	12.7845i	0.276293	+	0.513439i
$621$		0			0
$622$	50.9927	−	37.0483i	2.04462	−	1.48550i
$623$	2.64415	−	58.8766i	0.105936	−	2.35884i
$624$		0			0
$625$	−2.96994	−	9.14053i	−0.118798	−	0.365621i
$626$	20.8084	−	75.3976i	0.831671	−	3.01349i
$627$		0			0
$628$	−93.1123	+	25.6973i	−3.71558	+	1.02544i
$629$	−6.73845	−	5.88721i	−0.268680	−	0.234738i
$630$		0			0
$631$	5.45707	+	14.5403i	0.217243	+	0.578841i	0.998998	−	0.0447437i	$-0.0142471\pi$
$631$	5.45707	+	14.5403i	0.217243	+	0.578841i	−0.781756	+	0.623585i	$0.785676\pi$
$632$	1.35194	+	1.54742i	0.0537772	+	0.0615529i
$633$		0			0
$634$	15.2669	+	4.96053i	0.606328	+	0.197008i
$635$	12.2950	+	12.8595i	0.487911	+	0.510314i
$636$		0			0
$637$	37.5406	+	16.0456i	1.48741	+	0.635751i
$638$	−40.0202			−1.58441
$639$		0			0
$640$	−34.0354			−1.34537
$641$	−8.44790	−	3.61081i	−0.333672	−	0.142618i	0.219666	−	0.975575i	$-0.429503\pi$
$641$	−8.44790	−	3.61081i	−0.333672	−	0.142618i	−0.553338	+	0.832957i	$0.686646\pi$
$642$		0			0
$643$	−11.1988	−	11.7131i	−0.441639	−	0.461918i	0.464082	−	0.885792i	$-0.346384\pi$
$643$	−11.1988	−	11.7131i	−0.441639	−	0.461918i	−0.905721	+	0.423874i	$0.860670\pi$
$644$	45.9359	+	14.9255i	1.81013	+	0.588147i
$645$		0			0
$646$	12.1034	+	13.8535i	0.476203	+	0.545058i
$647$	10.8094	+	28.8015i	0.424961	+	1.13230i	0.958139	+	0.286302i	$0.0924261\pi$
$647$	10.8094	+	28.8015i	0.424961	+	1.13230i	−0.533178	+	0.846003i	$0.679002\pi$
$648$		0			0
$649$	−22.1492	−	19.3512i	−0.869432	−	0.759600i
$650$	−12.9439	+	3.57230i	−0.507703	+	0.140117i
$651$		0			0
$652$	−7.57242	+	27.4380i	−0.296559	+	1.07456i
$653$	1.77862	+	5.47403i	0.0696028	+	0.214215i	0.979807	−	0.199943i	$-0.0640758\pi$
$653$	1.77862	+	5.47403i	0.0696028	+	0.214215i	−0.910205	+	0.414159i	$0.864076\pi$
$654$		0			0
$655$	0.295565	−	6.58128i	0.0115487	−	0.257152i
$656$	14.3155	−	10.4008i	0.558928	−	0.406085i
$657$		0			0
$658$	−36.8817	−	68.5376i	−1.43780	−	2.67187i
$659$	−1.08248	−	2.24780i	−0.0421676	−	0.0875619i	0.878821	−	0.477152i	$-0.158331\pi$
$659$	−1.08248	−	2.24780i	−0.0421676	−	0.0875619i	−0.920988	+	0.389590i	$0.872617\pi$
$660$		0			0
$661$	5.31347	+	0.719758i	0.206670	+	0.0279953i	0.236836	−	0.971550i	$-0.423889\pi$
$661$	5.31347	+	0.719758i	0.206670	+	0.0279953i	−0.0301665	+	0.999545i	$0.509604\pi$
$662$	17.1407	−	75.0983i	0.666192	−	2.91878i
$663$		0			0
$664$	−37.2431	−	27.0587i	−1.44531	−	1.05008i
$665$	39.4819	−	49.5088i	1.53104	−	1.91987i
$666$		0			0
$667$	1.15740	−	12.8598i	0.0448148	−	0.497934i
$668$	−34.3477	+	4.65271i	−1.32895	+	0.180019i
$669$		0			0
$670$	18.3436	−	0.823814i	0.708677	−	0.0318267i
$671$	−16.1313	+	33.4971i	−0.622743	+	1.29314i
$672$		0			0
$673$	25.6189	−	5.84735i	0.987537	−	0.225399i	0.301898	−	0.953340i	$-0.402380\pi$
$673$	25.6189	−	5.84735i	0.987537	−	0.225399i	0.685639	+	0.727941i	$0.259523\pi$
$674$	−22.6543	−	53.0024i	−0.872612	−	2.04158i
$675$		0			0
$676$	5.59512	+	24.5138i	0.215197	+	0.942839i
$677$	−0.591231	−	6.56912i	−0.0227229	−	0.252472i	−0.999303	−	0.0373195i	$-0.988118\pi$
$677$	−0.591231	−	6.56912i	−0.0227229	−	0.252472i	0.976581	−	0.215152i	$-0.0690248\pi$
$678$		0			0
$679$	0.159136	+	3.54344i	0.00610707	+	0.135985i
$680$	−4.73456	−	5.93695i	−0.181562	−	0.227672i
$681$		0			0
$682$	17.4623	+	1.57163i	0.668665	+	0.0601810i
$683$	−32.0223	−	19.1324i	−1.22530	−	0.732081i	−0.253372	−	0.967369i	$-0.581540\pi$
$683$	−32.0223	−	19.1324i	−1.22530	−	0.732081i	−0.971926	+	0.235288i	$0.924397\pi$
$684$		0			0
$685$	−7.76532	+	10.6880i	−0.296698	+	0.408369i
$686$	−102.132	+	18.5343i	−3.89943	+	0.707643i
$687$		0			0
$688$	0.660090	−	4.87298i	0.0251657	−	0.185781i
$689$	−17.2646	−	28.8961i	−0.657729	−	1.10085i
$690$		0			0
$691$	−40.8164	+	21.9642i	−1.55273	+	0.835559i	−0.552731	+	0.833360i	$0.686414\pi$
$691$	−40.8164	+	21.9642i	−1.55273	+	0.835559i	−0.999998	+	0.00219903i	$0.999300\pi$
$692$	−58.5069	+	61.1935i	−2.22410	+	2.32623i
$693$		0			0
$694$	−73.0926	−	3.28259i	−2.77456	−	0.124605i
$695$	1.00982	−	1.87656i	0.0383048	−	0.0711822i
$696$		0			0
$697$	−4.68837	−	1.29391i	−0.177585	−	0.0490102i
$698$	24.3409	+	36.8749i	0.921316	+	1.39573i
$699$		0			0
$700$	26.5469	−	30.3854i	1.00338	−	1.14846i
$701$	5.32469	+	1.99839i	0.201111	+	0.0754782i	0.449898	−	0.893080i	$-0.351460\pi$
$701$	5.32469	+	1.99839i	0.201111	+	0.0754782i	−0.248787	+	0.968558i	$0.580032\pi$
$702$		0			0
$703$	54.7462	−	47.8304i	2.06479	−	1.80396i
$704$	−16.1629	+	24.4857i	−0.609160	+	0.922839i
$705$		0			0
$706$	−10.6683	+	10.1999i	−0.401505	+	0.383878i
$707$	−20.4129	−	3.70440i	−0.767708	−	0.139318i
$708$		0			0
$709$		−	30.7125i		−	1.15343i	−0.816945	−	0.576715i	$-0.804334\pi$
$709$		−	30.7125i		−	1.15343i	0.816945	−	0.576715i	$-0.195666\pi$
$710$	33.6010	+	8.22019i	1.26102	+	0.308498i
$711$		0			0
$712$	22.5671	−	52.7984i	0.845739	−	1.97870i
$713$	−1.01004	+	5.56576i	−0.0378261	+	0.208439i
$714$		0			0
$715$	4.39104	−	13.5142i	0.164216	−	0.505404i
$716$	−15.8208	−	10.4432i	−0.591252	−	0.390282i
$717$		0			0
$718$	−9.45708	+	3.54930i	−0.352935	+	0.132459i
$719$	−16.4406	+	43.8057i	−0.613129	+	1.63368i	0.150941	+	0.988543i	$0.451770\pi$
$719$	−16.4406	+	43.8057i	−0.613129	+	1.63368i	−0.764070	+	0.645134i	$0.776802\pi$
$720$		0			0
$721$	−17.8953	−	64.8423i	−0.666457	−	2.41485i
$722$	−86.1606	+	56.8741i	−3.20657	+	2.11664i
$723$		0			0
$724$	−3.48371	+	1.13192i	−0.129471	+	0.0420676i
$725$	−9.49829	−	5.11125i	−0.352758	−	0.189827i
$726$		0			0
$727$	10.9709	+	15.1002i	0.406889	+	0.560035i	0.962456	−	0.271437i	$-0.0874987\pi$
$727$	10.9709	+	15.1002i	0.406889	+	0.560035i	−0.555567	+	0.831472i	$0.687499\pi$
$728$	41.3949	+	39.5775i	1.53420	+	1.46684i
$729$		0			0
$730$	−24.3831	+	11.7423i	−0.902458	+	0.434601i
$731$	−1.16030	+	0.693245i	−0.0429151	+	0.0256406i
$732$		0			0
$733$	37.6937	+	8.60334i	1.39225	+	0.317772i	0.851915	−	0.523680i	$-0.175441\pi$
$733$	37.6937	+	8.60334i	1.39225	+	0.317772i	0.540333	+	0.841451i	$0.318298\pi$
$734$	3.97255	+	21.8906i	0.146630	+	0.807996i
$735$		0			0
$736$	−1.58864	−	1.26690i	−0.0585582	−	0.0466986i
$737$	7.52939	−	12.6021i	0.277349	−	0.464204i
$738$		0			0
$739$	1.08784	+	8.03078i	0.0400169	+	0.295417i	0.999888	+	0.0149748i	$0.00476679\pi$
$739$	1.08784	+	8.03078i	0.0400169	+	0.295417i	−0.959871	+	0.280442i	$0.909519\pi$
$740$	−47.9365	+	38.2280i	−1.76218	+	1.40529i
$741$		0			0
$742$	137.657	+	66.2920i	5.05353	+	2.43365i
$743$	−45.0142	+	4.05135i	−1.65141	+	0.148630i	−0.875831	−	0.482618i	$-0.839686\pi$
$743$	−45.0142	+	4.05135i	−1.65141	+	0.148630i	−0.775581	+	0.631248i	$0.782543\pi$
$744$		0			0
$745$	2.21828	−	0.948137i	0.0812714	−	0.0347371i
$746$	26.1168	−	11.1629i	0.956204	−	0.408701i
$747$		0			0
$748$	−12.3541	+	1.11189i	−0.451710	+	0.0406546i
$749$	56.6380	+	27.2754i	2.06951	+	0.996623i
$750$		0			0
$751$	15.2981	−	12.1998i	0.558236	−	0.445178i	−0.303285	−	0.952900i	$-0.598084\pi$
$751$	15.2981	−	12.1998i	0.558236	−	0.445178i	0.861521	+	0.507722i	$0.169512\pi$
$752$	−3.14937	−	23.2496i	−0.114846	−	0.847826i
$753$		0			0
$754$	16.0439	−	26.8530i	0.584285	−	0.977928i
$755$	−25.6790	−	20.4783i	−0.934553	−	0.745281i
$756$		0			0
$757$	7.14408	+	39.3671i	0.259656	+	1.43082i	0.805331	+	0.592825i	$0.201988\pi$
$757$	7.14408	+	39.3671i	0.259656	+	1.43082i	−0.545675	+	0.837997i	$0.683727\pi$
$758$	70.3777	+	16.0633i	2.55623	+	0.583444i
$759$		0			0
$760$	52.9614	−	31.6429i	1.92111	−	1.14781i
$761$	−1.00278	+	0.482914i	−0.0363508	+	0.0175056i	−0.451971	−	0.892033i	$-0.649279\pi$
$761$	−1.00278	+	0.482914i	−0.0363508	+	0.0175056i	0.415620	+	0.909538i	$0.363565\pi$
$762$		0			0
$763$	38.3169	+	36.6347i	1.38716	+	1.32626i
$764$	−51.9518	−	71.5056i	−1.87955	−	2.58698i
$765$		0			0
$766$	−4.16358	−	2.24052i	−0.150436	−	0.0809533i
$767$	21.8639	−	7.10401i	0.789459	−	0.256511i
$768$		0			0
$769$	−15.9486	+	10.5276i	−0.575122	+	0.379635i	−0.804723	−	0.593650i	$-0.797686\pi$
$769$	−15.9486	+	10.5276i	−0.575122	+	0.379635i	0.229601	+	0.973285i	$0.426258\pi$
$770$	17.1589	+	62.1740i	0.618365	+	2.24059i
$771$		0			0
$772$	1.28141	−	3.41430i	0.0461189	−	0.122883i
$773$	41.7933	−	15.6853i	1.50320	−	0.564160i	0.542088	−	0.840321i	$-0.317634\pi$
$773$	41.7933	−	15.6853i	1.50320	−	0.564160i	0.961111	+	0.276161i	$0.0890623\pi$
$774$		0			0
$775$	3.94373	+	2.60323i	0.141663	+	0.0935109i
$776$	−1.06787	+	3.28658i	−0.0383345	+	0.117981i
$777$		0			0
$778$	7.42430	−	40.9112i	0.266174	−	1.46674i
$779$	15.5302	−	36.3346i	0.556426	−	1.30182i
$780$		0			0
$781$	20.2835	−	18.7989i	0.725801	−	0.672676i
$782$		−	6.04518i		−	0.216175i
$783$		0			0
$784$	−54.9636	−	9.97442i	−1.96299	−	0.356229i
$785$	30.0795	−	28.7590i	1.07358	−	1.02645i
$786$		0			0
$787$	7.15683	−	10.8421i	0.255113	−	0.386480i	−0.684337	−	0.729166i	$-0.739908\pi$
$787$	7.15683	−	10.8421i	0.255113	−	0.386480i	0.939450	+	0.342686i	$0.111337\pi$
$788$	11.1220	−	9.71704i	0.396206	−	0.346155i
$789$		0			0
$790$	−1.69345	−	0.635562i	−0.0602502	−	0.0226123i
$791$	14.6698	−	16.7910i	0.521599	−	0.597019i
$792$		0			0
$793$	−16.0091	−	24.2527i	−0.568499	−	0.861239i
$794$	−1.85549	−	0.512083i	−0.0658489	−	0.0181731i
$795$		0			0
$796$	−15.7336	+	29.2379i	−0.557663	+	1.03631i
$797$	23.9283	+	1.07462i	0.847582	+	0.0380650i	0.464419	−	0.885616i	$-0.346263\pi$
$797$	23.9283	+	1.07462i	0.847582	+	0.0380650i	0.383163	+	0.923681i	$0.374835\pi$
$798$		0			0
$799$	−4.45649	+	4.66112i	−0.157659	+	0.164899i
$800$	−1.49476	+	0.804366i	−0.0528478	+	0.0284386i
$801$		0			0
$802$	47.3190	+	79.1986i	1.67089	+	2.79660i
$803$	−2.90431	+	21.4405i	−0.102491	+	0.756619i
$804$		0			0
$805$	−20.4748	+	3.71563i	−0.721642	+	0.130959i
$806$	−8.05509	+	11.0869i	−0.283729	+	0.390519i
$807$		0			0
$808$	−17.3513	−	10.3669i	−0.610416	−	0.364707i
$809$	37.6755	+	3.39086i	1.32460	+	0.119216i	0.729249	−	0.684248i	$-0.239870\pi$
$809$	37.6755	+	3.39086i	1.32460	+	0.119216i	0.595352	+	0.803465i	$0.297012\pi$
$810$		0			0
$811$	12.7181	+	15.9479i	0.446592	+	0.560008i	0.953267	−	0.302129i	$-0.0976972\pi$
$811$	12.7181	+	15.9479i	0.446592	+	0.560008i	−0.506676	+	0.862137i	$0.669126\pi$
$812$	4.21703	+	93.8995i	0.147989	+	3.29523i
$813$		0			0
$814$	6.63737	+	73.7472i	0.232640	+	2.58484i
$815$	−2.72881	−	11.9557i	−0.0955860	−	0.418790i
$816$		0			0
$817$	−4.31588	−	10.0975i	−0.150993	−	0.353267i
$818$	−37.2301	+	8.49753i	−1.30172	+	0.297109i
$819$		0			0
$820$	−14.4598	+	30.0262i	−0.504960	+	1.04856i
$821$	−35.2341	+	1.58237i	−1.22968	+	0.0552249i	−0.650201	−	0.759763i	$-0.725315\pi$
$821$	−35.2341	+	1.58237i	−1.22968	+	0.0552249i	−0.579478	+	0.814988i	$0.696744\pi$
$822$		0			0
$823$	−20.3932	+	2.76245i	−0.710862	+	0.0962928i	−0.480733	−	0.876867i	$-0.659629\pi$
$823$	−20.3932	+	2.76245i	−0.710862	+	0.0962928i	−0.230129	+	0.973160i	$0.573915\pi$
$824$	5.87452	−	65.2712i	0.204648	−	2.27383i
$825$		0			0
$826$	−65.0599	+	81.5825i	−2.26372	+	2.83862i
$827$	−16.1629	−	11.7430i	−0.562039	−	0.408345i	0.270166	−	0.962814i	$-0.412922\pi$
$827$	−16.1629	−	11.7430i	−0.562039	−	0.408345i	−0.832205	+	0.554469i	$0.812922\pi$
$828$		0			0
$829$	−9.46737	+	41.4793i	−0.328815	+	1.44063i	0.492576	+	0.870270i	$0.336055\pi$
$829$	−9.46737	+	41.4793i	−0.328815	+	1.44063i	−0.821391	+	0.570365i	$0.806802\pi$
$830$	40.1566	+	5.43958i	1.39385	+	0.188810i
$831$		0			0
$832$	−9.94993	−	20.6612i	−0.344952	−	0.716300i
$833$	7.27580	+	13.5207i	0.252091	+	0.468464i
$834$		0			0
$835$	12.0813	−	8.77756i	0.418090	−	0.303760i
$836$	4.52129	−	100.674i	0.156372	−	3.48189i
$837$		0			0
$838$	23.4581	+	72.1966i	0.810346	+	2.49399i
$839$	−12.9070	+	46.7674i	−0.445599	+	1.61459i	0.303983	+	0.952678i	$0.401684\pi$
$839$	−12.9070	+	46.7674i	−0.445599	+	1.61459i	−0.749581	+	0.661912i	$0.769745\pi$
$840$		0			0
$841$	−3.73341	+	1.03036i	−0.128738	+	0.0355295i
$842$	−56.0602	−	48.9783i	−1.93196	−	1.68790i
$843$		0			0
$844$	−33.0449	−	88.0479i	−1.13745	−	3.03073i
$845$	−7.12743	−	8.15800i	−0.245191	−	0.280644i
$846$		0			0
$847$	−1.03761	−	0.337140i	−0.0356528	−	0.0115843i
$848$	31.8285	+	33.2900i	1.09300	+	1.14318i
$849$		0			0
$850$	−4.64362	−	1.98478i	−0.159275	−	0.0680773i
$851$	−23.8894			−0.818917
$852$		0			0
$853$	6.60176			0.226040			0.113020	−	0.993593i	$-0.463948\pi$
$853$	6.60176			0.226040			0.113020	+	0.993593i	$0.463948\pi$
$854$	121.290	+	51.8417i	4.15045	+	1.77399i
$855$		0			0
$856$	42.3245	+	44.2679i	1.44662	+	1.51305i
$857$	−1.45891	−	0.474027i	−0.0498353	−	0.0161925i	0.283993	−	0.958826i	$-0.408341\pi$
$857$	−1.45891	−	0.474027i	−0.0498353	−	0.0161925i	−0.333829	+	0.942634i	$0.608341\pi$
$858$		0			0
$859$	−8.18375	−	9.36706i	−0.279226	−	0.319600i	0.596309	−	0.802755i	$-0.296633\pi$
$859$	−8.18375	−	9.36706i	−0.279226	−	0.319600i	−0.875535	+	0.483155i	$0.839491\pi$
$860$	3.25427	+	8.67098i	0.110970	+	0.295678i
$861$		0			0
$862$	44.9058	+	39.2330i	1.52950	+	1.33628i
$863$	−23.7674	+	6.55937i	−0.809050	+	0.223284i	−0.646003	−	0.763335i	$-0.723561\pi$
$863$	−23.7674	+	6.55937i	−0.809050	+	0.223284i	−0.163047	+	0.986618i	$0.552132\pi$
$864$		0			0
$865$	9.70379	−	35.1609i	0.329939	−	1.19551i
$866$	−19.1213	−	58.8494i	−0.649769	−	1.99978i
$867$		0			0
$868$	1.84749	−	41.1375i	0.0627077	−	1.39630i
$869$	−1.16990	+	0.849984i	−0.0396862	+	0.0288337i
$870$		0			0
$871$	5.43732	+	10.1042i	0.184237	+	0.342369i
$872$	22.4091	+	46.5329i	0.758867	+	1.57580i
$873$		0			0
$874$	48.6693	+	6.59271i	1.64626	+	0.223002i
$875$	−12.8566	+	56.3283i	−0.434631	+	1.90424i
$876$		0			0
$877$	26.5025	+	19.2552i	0.894926	+	0.650202i	0.937158	−	0.348906i	$-0.113447\pi$
$877$	26.5025	+	19.2552i	0.894926	+	0.650202i	−0.0422315	+	0.999108i	$0.513447\pi$
$878$	23.8463	−	29.9024i	0.804775	−	1.00916i
$879$		0			0
$880$	−1.74284	+	19.3646i	−0.0587513	+	0.652780i
$881$	4.46382	−	0.604666i	0.150390	−	0.0203717i	−0.0586512	−	0.998279i	$-0.518680\pi$
$881$	4.46382	−	0.604666i	0.150390	−	0.0203717i	0.209041	+	0.977907i	$0.432966\pi$
$882$		0			0
$883$	−13.3730	+	0.600583i	−0.450038	+	0.0202112i	−0.268731	−	0.963215i	$-0.586604\pi$
$883$	−13.3730	+	0.600583i	−0.450038	+	0.0202112i	−0.181307	+	0.983427i	$0.558033\pi$
$884$	4.20663	−	8.73516i	0.141484	−	0.293795i
$885$		0			0
$886$	9.11268	−	2.07991i	0.306147	−	0.0698759i
$887$	−15.9150	−	37.2351i	−0.534375	−	1.25023i	−0.941547	−	0.336881i	$-0.890628\pi$
$887$	−15.9150	−	37.2351i	−0.534375	−	1.25023i	0.407172	−	0.913351i	$-0.366515\pi$
$888$		0			0
$889$	−11.2292	−	49.1982i	−0.376614	−	1.65005i
$890$	4.53076	+	50.3408i	0.151871	+	1.68743i
$891$		0			0
$892$	2.13321	+	47.4996i	0.0714252	+	1.59041i
$893$	−32.6662	−	40.9622i	−1.09313	−	1.37075i
$894$		0			0
$895$	8.13434	+	0.732104i	0.271901	+	0.0244715i
$896$	82.8728	+	49.5142i	2.76859	+	1.65415i
$897$		0			0
$898$	15.7233	−	21.6413i	0.524694	−	0.722180i
$899$	−10.8313	+	1.96558i	−0.361243	+	0.0655559i
$900$		0			0
$901$	1.69930	−	12.5448i	0.0566120	−	0.417926i
$902$	20.6427	+	34.5501i	0.687327	+	1.15039i
$903$		0			0
$904$	19.1290	−	10.2937i	0.636221	−	0.342365i
$905$	1.09059	−	1.14067i	0.0362525	−	0.0379171i
$906$		0			0
$907$	−32.7868	−	1.47246i	−1.08867	−	0.0488921i	−0.506714	−	0.862114i	$-0.669140\pi$
$907$	−32.7868	−	1.47246i	−1.08867	−	0.0488921i	−0.581954	+	0.813222i	$0.697711\pi$
$908$	−29.5132	+	54.8447i	−0.979430	+	1.82009i
$909$		0			0
$910$	−48.5968	−	13.4119i	−1.61097	−	0.444599i
$911$	8.91278	+	13.5023i	0.295294	+	0.447351i	0.951688	−	0.307067i	$-0.0993477\pi$
$911$	8.91278	+	13.5023i	0.295294	+	0.447351i	−0.656394	+	0.754418i	$0.727919\pi$
$912$		0			0
$913$	21.3155	−	24.3975i	0.705439	−	0.807440i
$914$	−60.1711	−	22.5826i	−1.99028	−	0.746965i
$915$		0			0
$916$	−14.4130	+	12.5922i	−0.476218	+	0.416060i
$917$	−10.2940	+	15.5948i	−0.339938	+	0.514985i
$918$		0			0
$919$	0.520901	−	0.498033i	0.0171829	−	0.0164286i	−0.682422	−	0.730958i	$-0.739073\pi$
$919$	0.520901	−	0.498033i	0.0171829	−	0.0164286i	0.699605	+	0.714530i	$0.253359\pi$
$920$	−19.9478	−	3.62000i	−0.657660	−	0.119348i
$921$		0			0
$922$		−	7.26820i		−	0.239365i
$923$	4.48221	+	21.1463i	0.147534	+	0.696040i
$924$		0			0
$925$	−7.84346	+	18.3507i	−0.257891	+	0.603367i
$926$	−3.98960	+	21.9845i	−0.131106	+	0.722456i
$927$		0			0
$928$	1.22194	−	3.76075i	0.0401122	−	0.123453i
$929$	11.0792	+	7.31335i	0.363498	+	0.239943i	0.719424	−	0.694571i	$-0.244406\pi$
$929$	11.0792	+	7.31335i	0.363498	+	0.239943i	−0.355926	+	0.934514i	$0.615834\pi$
$930$		0			0
$931$	−116.789	+	43.8316i	−3.82760	+	1.43652i
$932$	−36.0238	+	95.9851i	−1.18000	+	3.14410i
$933$		0			0
$934$	−6.64288	−	24.0699i	−0.217362	−	0.787592i
$935$	4.46001	−	2.94403i	0.145858	−	0.0962800i
$936$		0			0
$937$	−29.1564	+	9.47350i	−0.952499	+	0.309486i	−0.743731	−	0.668479i	$-0.766946\pi$
$937$	−29.1564	+	9.47350i	−0.952499	+	0.309486i	−0.208769	+	0.977965i	$0.566946\pi$
$938$	−45.8634	−	24.6802i	−1.49749	−	0.805836i
$939$		0			0
$940$	25.9730	+	35.7488i	0.847147	+	1.16600i
$941$	−23.6410	−	22.6031i	−0.770674	−	0.736840i	0.199329	−	0.979933i	$-0.436124\pi$
$941$	−23.6410	−	22.6031i	−0.770674	−	0.736840i	−0.970003	+	0.243093i	$0.921838\pi$
$942$		0			0
$943$	−11.6991	+	5.63398i	−0.380975	+	0.183468i
$944$	−27.0029	+	16.1335i	−0.878869	+	0.525100i
$945$		0			0
$946$	10.9044	+	2.48885i	0.354532	+	0.0809195i
$947$	−0.606999	−	3.34484i	−0.0197248	−	0.108693i	0.972565	−	0.232631i	$-0.0747333\pi$
$947$	−0.606999	−	3.34484i	−0.0197248	−	0.108693i	−0.992290	+	0.123938i	$0.960448\pi$
$948$		0			0
$949$	−13.2219	−	10.5442i	−0.429203	−	0.342278i
$950$	21.0435	−	35.2209i	0.682742	−	1.14272i
$951$		0			0
$952$	2.89120	+	21.3437i	0.0937042	+	0.691752i
$953$	25.0015	−	19.9380i	0.809877	−	0.645855i	−0.128407	−	0.991722i	$-0.540986\pi$
$953$	25.0015	−	19.9380i	0.809877	−	0.645855i	0.938284	+	0.345866i	$0.112415\pi$
$954$		0			0
$955$	34.3085	+	16.5221i	1.11020	+	0.534642i
$956$	2.81008	−	0.252912i	0.0908845	−	0.00817975i
$957$		0			0
$958$	24.7955	−	10.5981i	0.801105	−	0.342409i
$959$	34.4566	−	14.7274i	1.11266	−	0.475574i
$960$		0			0
$961$	−26.0719	+	2.34652i	−0.841030	+	0.0756941i
$962$	−52.1442	−	25.1113i	−1.68120	−	0.809622i
$963$		0			0
$964$	17.2428	−	13.7507i	0.555352	−	0.442879i
$965$	0.210905	+	1.55696i	0.00678927	+	0.0501204i
$966$		0			0
$967$	7.68624	−	12.8646i	0.247173	−	0.413698i	−0.709569	−	0.704636i	$-0.751110\pi$
$967$	7.68624	−	12.8646i	0.247173	−	0.413698i	0.956742	+	0.290938i	$0.0939674\pi$
$968$	−0.831031	−	0.662725i	−0.0267103	−	0.0213008i
$969$		0			0
$970$	−0.543164	−	2.99308i	−0.0174399	−	0.0961019i
$971$	−37.1348	−	8.47577i	−1.19171	−	0.272001i	−0.419733	−	0.907648i	$-0.637876\pi$
$971$	−37.1348	−	8.47577i	−1.19171	−	0.272001i	−0.771980	+	0.635647i	$0.780733\pi$
$972$		0			0
$973$	−5.18882	+	3.10017i	−0.166346	+	0.0993870i
$974$	−15.6486	+	7.53599i	−0.501415	+	0.241469i
$975$		0			0
$976$	28.7399	+	27.4782i	0.919942	+	0.879555i
$977$	20.9531	+	28.8395i	0.670350	+	0.922657i	0.999768	−	0.0215267i	$-0.00685268\pi$
$977$	20.9531	+	28.8395i	0.670350	+	0.922657i	−0.329418	+	0.944184i	$0.606853\pi$
$978$		0			0
$979$	35.5839	+	19.1485i	1.13727	+	0.611989i
$980$	100.059	−	32.5113i	3.19628	−	1.03853i
$981$		0			0
$982$	−38.9555	+	25.7143i	−1.24312	+	0.820577i
$983$	0.856431	+	3.10321i	0.0273159	+	0.0989770i	0.976350	−	0.216198i	$-0.0693655\pi$
$983$	0.856431	+	3.10321i	0.0273159	+	0.0989770i	−0.949034	+	0.315175i	$0.897937\pi$
$984$		0			0
$985$	−2.23578	+	5.95721i	−0.0712378	+	0.189812i
$986$	11.0141	−	4.13366i	0.350760	−	0.131643i
$987$		0			0
$988$	65.7385	+	43.3936i	2.09142	+	1.38053i
$989$	−1.11511	+	3.43196i	−0.0354584	+	0.109130i
$990$		0			0
$991$	4.24269	−	23.3791i	0.134773	−	0.742663i	−0.843783	−	0.536684i	$-0.819677\pi$
$991$	4.24269	−	23.3791i	0.134773	−	0.742663i	0.978557	−	0.205978i	$-0.0660377\pi$
$992$	−0.680866	+	1.59297i	−0.0216175	+	0.0505767i
$993$		0			0
$994$	−69.8565	−	68.8976i	−2.21571	−	2.18530i
$995$		−	14.3047i		−	0.453490i
$996$		0			0
$997$	9.25953	+	1.68036i	0.293252	+	0.0532175i	0.323189	−	0.946334i	$-0.395245\pi$
$997$	9.25953	+	1.68036i	0.293252	+	0.0532175i	−0.0299369	+	0.999552i	$0.509531\pi$
$998$	45.0571	−	43.0790i	1.42626	−	1.36364i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.269.23	yes	576
3.2	odd	2	inner	639.2.z.a.269.2	✓	576
71.52	odd	70	inner	639.2.z.a.620.2	yes	576
213.194	even	70	inner	639.2.z.a.620.23	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.269.2	✓	576	3.2	odd	2	inner
639.2.z.a.269.23	yes	576	1.1	even	1	trivial
639.2.z.a.620.2	yes	576	71.52	odd	70	inner
639.2.z.a.620.23	yes	576	213.194	even	70	inner

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.23678 + 0.956046i) q^{2} +(2.70704 + 2.83134i) q^{4} +(-1.60507 - 0.521518i) q^{5} +(3.14948 + 3.60487i) q^{7} +(1.63870 + 4.36630i) q^{8} +O(q^{10})\)	\(q+(2.23678 + 0.956046i) q^{2} +(2.70704 + 2.83134i) q^{4} +(-1.60507 - 0.521518i) q^{5} +(3.14948 + 3.60487i) q^{7} +(1.63870 + 4.36630i) q^{8} +(-3.09159 - 2.70104i) q^{10} +(-3.16381 + 0.873156i) q^{11} +(0.682481 - 2.47292i) q^{13} +(3.59827 + 11.0744i) q^{14} +(-0.157481 + 3.50660i) q^{16} +(0.780535 - 0.567092i) q^{17} +(3.71439 + 6.90249i) q^{19} +(-2.86838 - 5.95626i) q^{20} +(-7.91152 - 1.07169i) q^{22} +(0.573174 - 2.51124i) q^{23} +(-1.74083 - 1.26479i) q^{25} +(3.89078 - 4.87889i) q^{26} +(-1.68085 + 18.6758i) q^{28} +(4.96732 - 0.672869i) q^{29} +(-2.19385 + 0.0985259i) q^{31} +(0.342271 - 0.710734i) q^{32} +(2.28805 - 0.522233i) q^{34} +(-3.17512 - 7.42856i) q^{35} +(-2.06376 - 9.04194i) q^{37} +(1.70917 + 18.9905i) q^{38} +(-0.353119 - 7.86282i) q^{40} +(-3.14308 - 3.94130i) q^{41} +(-1.39530 - 0.125579i) q^{43} +(-11.0368 - 6.59415i) q^{44} +(3.68293 - 5.06911i) q^{46} +(-6.57665 + 1.19349i) q^{47} +(-2.13623 + 15.7703i) q^{49} +(-2.68466 - 4.49336i) q^{50} +(8.84917 - 4.76194i) q^{52} +(9.06761 - 9.48398i) q^{53} +(5.53349 + 0.248509i) q^{55} +(-10.5789 + 19.6589i) q^{56} +(11.7541 + 3.24393i) q^{58} +(4.93677 + 7.47888i) q^{59} +(7.45302 - 8.53067i) q^{61} +(-5.00136 - 1.87704i) q^{62} +(6.73184 - 5.88143i) q^{64} +(-2.38510 + 3.61327i) q^{65} +(-3.23291 + 3.09097i) q^{67} +(3.71857 + 0.674821i) q^{68} -19.6516i q^{70} +(-7.48114 + 3.87718i) q^{71} +(2.59092 - 6.06175i) q^{73} +(4.02832 - 22.1979i) q^{74} +(-9.48831 + 29.2020i) q^{76} +(-13.1120 - 8.65513i) q^{77} +(0.412503 - 0.154815i) q^{79} +(2.08152 - 5.54619i) q^{80} +(-3.26232 - 11.8208i) q^{82} +(-8.23805 + 5.43789i) q^{83} +(-1.54856 + 0.503157i) q^{85} +(-3.00092 - 1.61486i) q^{86} +(-8.99700 - 12.3833i) q^{88} +(-8.89902 - 8.50833i) q^{89} +(11.0640 - 5.32814i) q^{91} +(8.66179 - 5.17518i) q^{92} +(-15.8515 - 3.61801i) q^{94} +(-2.36207 - 13.0161i) q^{95} +(0.579325 + 0.461996i) q^{97} +(-19.8554 + 33.2323i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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