LMFDB - Embedded newform 639.2.z.a.485.5

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			485.5
Character	$\chi$	$=$	639.485
Dual form			639.2.z.a.278.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30887 + 1.25141i) q^{2} +(0.0573898 - 1.27788i) q^{4} +(1.91833 - 2.64036i) q^{5} +(-0.412177 - 0.0558332i) q^{7} +(-0.858815 - 0.982992i) q^{8} +O(q^{10})$	\(q+(-1.30887 + 1.25141i) q^{2} +(0.0573898 - 1.27788i) q^{4} +(1.91833 - 2.64036i) q^{5} +(-0.412177 - 0.0558332i) q^{7} +(-0.858815 - 0.982992i) q^{8} +(0.793318 + 5.85651i) q^{10} +(0.629778 - 0.376275i) q^{11} +(-3.07808 + 5.15183i) q^{13} +(0.609357 - 0.442724i) q^{14} +(4.90225 + 0.441210i) q^{16} +(1.57553 - 4.84897i) q^{17} +(2.05429 - 3.11211i) q^{19} +(-3.26398 - 2.60293i) q^{20} +(-0.353425 + 1.28061i) q^{22} +(-1.29670 - 0.624458i) q^{23} +(-1.74640 - 5.37488i) q^{25} +(-2.41825 - 10.5950i) q^{26} +(-0.0950031 + 0.523510i) q^{28} +(-1.40488 - 5.09046i) q^{29} +(-0.903222 - 10.0356i) q^{31} +(-4.92748 + 3.92954i) q^{32} +(4.00589 + 8.31831i) q^{34} +(-0.938112 + 0.981188i) q^{35} +(1.28654 - 0.619567i) q^{37} +(1.20573 + 6.64411i) q^{38} +(-4.24294 + 0.381872i) q^{40} +(0.613695 - 2.68877i) q^{41} +(11.8795 + 2.15581i) q^{43} +(-0.444693 - 0.826377i) q^{44} +(2.47867 - 0.805368i) q^{46} +(1.96057 - 0.735815i) q^{47} +(-6.58097 - 1.81623i) q^{49} +(9.01200 + 4.84956i) q^{50} +(6.40679 + 4.22909i) q^{52} +(-0.154248 - 3.43459i) q^{53} +(0.214623 - 2.38466i) q^{55} +(0.299100 + 0.453117i) q^{56} +(8.20906 + 4.90468i) q^{58} +(1.16596 - 2.72790i) q^{59} +(8.61432 - 1.16689i) q^{61} +(13.7409 + 12.0050i) q^{62} +(0.210575 - 1.55453i) q^{64} +(7.69791 + 18.0102i) q^{65} +(-7.09298 - 0.318546i) q^{67} +(-6.10600 - 2.29162i) q^{68} -2.45821i q^{70} +(-1.87943 + 8.21388i) q^{71} +(-0.921673 - 0.963994i) q^{73} +(-0.908590 + 2.42093i) q^{74} +(-3.85902 - 2.80374i) q^{76} +(-0.280589 + 0.119929i) q^{77} +(8.42260 - 7.35861i) q^{79} +(10.5691 - 12.0973i) q^{80} +(2.56151 + 4.28724i) q^{82} +(14.4993 + 6.19729i) q^{83} +(-9.78064 - 13.4619i) q^{85} +(-18.2466 + 12.0445i) q^{86} +(-0.910738 - 0.295917i) q^{88} +(-10.1302 + 0.454946i) q^{89} +(1.55636 - 1.95161i) q^{91} +(-0.872402 + 1.62119i) q^{92} +(-1.64533 + 3.41657i) q^{94} +(-4.27628 - 11.3941i) q^{95} +(-16.5330 + 3.77356i) q^{97} +(10.8865 - 5.85827i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{3}{70}\right)$	$-1$

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 $

$2$	−1.30887	+	1.25141i	−0.925512	+	0.884880i	−0.993618	−	0.112798i	$-0.964019\pi$
$2$	−1.30887	+	1.25141i	−0.925512	+	0.884880i	0.0681058	+	0.997678i	$0.478304\pi$
$3$		0			0
$3$		0			0
$4$	0.0573898	−	1.27788i	0.0286949	−	0.638942i
$5$	1.91833	−	2.64036i	0.857904	−	1.18080i	−0.124161	−	0.992262i	$-0.539624\pi$
$5$	1.91833	−	2.64036i	0.857904	−	1.18080i	0.982065	−	0.188542i	$-0.0603760\pi$
$6$		0			0
$7$	−0.412177	−	0.0558332i	−0.155788	−	0.0211030i	0.0559238	−	0.998435i	$-0.482190\pi$
$7$	−0.412177	−	0.0558332i	−0.155788	−	0.0211030i	−0.211712	+	0.977332i	$0.567904\pi$
$8$	−0.858815	−	0.982992i	−0.303637	−	0.347540i
$9$		0			0
$10$	0.793318	+	5.85651i	0.250869	+	1.85199i
$11$	0.629778	−	0.376275i	0.189885	−	0.113451i	−0.414810	−	0.909908i	$-0.636152\pi$
$11$	0.629778	−	0.376275i	0.189885	−	0.113451i	0.604695	+	0.796457i	$0.293295\pi$
$12$		0			0
$13$	−3.07808	+	5.15183i	−0.853705	+	1.42886i	0.0490915	+	0.998794i	$0.484367\pi$
$13$	−3.07808	+	5.15183i	−0.853705	+	1.42886i	−0.902797	+	0.430068i	$0.858490\pi$
$14$	0.609357	−	0.442724i	0.162858	−	0.118323i
$15$		0			0
$16$	4.90225	+	0.441210i	1.22556	+	0.110303i
$17$	1.57553	−	4.84897i	0.382121	−	1.17605i	−0.556426	−	0.830897i	$-0.687828\pi$
$17$	1.57553	−	4.84897i	0.382121	−	1.17605i	0.938547	−	0.345151i	$-0.112172\pi$
$18$		0			0
$19$	2.05429	−	3.11211i	0.471286	−	0.713967i	−0.518728	−	0.854939i	$-0.673594\pi$
$19$	2.05429	−	3.11211i	0.471286	−	0.713967i	0.990014	+	0.140972i	$0.0450228\pi$
$20$	−3.26398	−	2.60293i	−0.729847	−	0.582034i
$21$		0			0
$22$	−0.353425	+	1.28061i	−0.0753504	+	0.273026i
$23$	−1.29670	−	0.624458i	−0.270381	−	0.130208i	0.293781	−	0.955873i	$-0.405086\pi$
$23$	−1.29670	−	0.624458i	−0.270381	−	0.130208i	−0.564162	+	0.825664i	$0.690801\pi$
$24$		0			0
$25$	−1.74640	−	5.37488i	−0.349281	−	1.07498i
$26$	−2.41825	−	10.5950i	−0.474257	−	2.07786i
$27$		0			0
$28$	−0.0950031	+	0.523510i	−0.0179539	+	0.0989341i
$29$	−1.40488	−	5.09046i	−0.260879	−	0.945275i	−0.970581	−	0.240773i	$-0.922599\pi$
$29$	−1.40488	−	5.09046i	−0.260879	−	0.945275i	0.709702	−	0.704502i	$-0.248830\pi$
$30$		0			0
$31$	−0.903222	−	10.0356i	−0.162224	−	1.80245i	−0.505090	−	0.863067i	$-0.668541\pi$
$31$	−0.903222	−	10.0356i	−0.162224	−	1.80245i	0.342866	−	0.939384i	$-0.388602\pi$
$32$	−4.92748	+	3.92954i	−0.871064	+	0.694651i
$33$		0			0
$34$	4.00589	+	8.31831i	0.687004	+	1.42658i
$35$	−0.938112	+	0.981188i	−0.158570	+	0.165851i
$36$		0			0
$37$	1.28654	−	0.619567i	0.211507	−	0.101856i	−0.325131	−	0.945669i	$-0.605408\pi$
$37$	1.28654	−	0.619567i	0.211507	−	0.101856i	0.536638	+	0.843813i	$0.319694\pi$
$38$	1.20573	+	6.64411i	0.195595	+	1.07782i
$39$		0			0
$40$	−4.24294	+	0.381872i	−0.670868	+	0.0603792i
$41$	0.613695	−	2.68877i	0.0958430	−	0.419916i	−0.904130	−	0.427257i	$-0.859480\pi$
$41$	0.613695	−	2.68877i	0.0958430	−	0.419916i	0.999973	+	0.00734179i	$0.00233699\pi$
$42$		0			0
$43$	11.8795	+	2.15581i	1.81161	+	0.328759i	0.975533	−	0.219854i	$-0.0705580\pi$
$43$	11.8795	+	2.15581i	1.81161	+	0.328759i	0.836077	+	0.548612i	$0.184844\pi$
$44$	−0.444693	−	0.826377i	−0.0670399	−	0.124581i
$45$		0			0
$46$	2.47867	−	0.805368i	0.365460	−	0.118745i
$47$	1.96057	−	0.735815i	0.285979	−	0.107330i	−0.204263	−	0.978916i	$-0.565480\pi$
$47$	1.96057	−	0.735815i	0.285979	−	0.107330i	0.490242	+	0.871586i	$0.336908\pi$
$48$		0			0
$49$	−6.58097	−	1.81623i	−0.940138	−	0.259462i
$50$	9.01200	+	4.84956i	1.27449	+	0.685832i
$51$		0			0
$52$	6.40679	+	4.22909i	0.888463	+	0.586469i
$53$	−0.154248	−	3.43459i	−0.0211875	−	0.471777i	−0.981338	−	0.192292i	$-0.938408\pi$
$53$	−0.154248	−	3.43459i	−0.0211875	−	0.471777i	0.960150	−	0.279485i	$-0.0901636\pi$
$54$		0			0
$55$	0.214623	−	2.38466i	0.0289398	−	0.321547i
$56$	0.299100	+	0.453117i	0.0399689	+	0.0605503i
$57$		0			0
$58$	8.20906	+	4.90468i	1.07790	+	0.644017i
$59$	1.16596	−	2.72790i	0.151795	−	0.355142i	−0.826322	−	0.563198i	$-0.809571\pi$
$59$	1.16596	−	2.72790i	0.151795	−	0.355142i	0.978117	+	0.208056i	$0.0667136\pi$
$60$		0			0
$61$	8.61432	−	1.16689i	1.10295	−	0.149405i	0.439949	−	0.898023i	$-0.354997\pi$
$61$	8.61432	−	1.16689i	1.10295	−	0.149405i	0.663001	+	0.748618i	$0.269282\pi$
$62$	13.7409	+	12.0050i	1.74509	+	1.52464i
$63$		0			0
$64$	0.210575	−	1.55453i	0.0263219	−	0.194316i
$65$	7.69791	+	18.0102i	0.954808	+	2.23388i
$66$		0			0
$67$	−7.09298	−	0.318546i	−0.866545	−	0.0389166i	−0.392847	−	0.919604i	$-0.628510\pi$
$67$	−7.09298	−	0.318546i	−0.866545	−	0.0389166i	−0.473698	+	0.880687i	$0.657081\pi$
$68$	−6.10600	−	2.29162i	−0.740462	−	0.277900i
$69$		0			0
$70$		−	2.45821i		−	0.293813i
$71$	−1.87943	+	8.21388i	−0.223047	+	0.974808i
$71$	−1.87943	+	8.21388i	−0.223047	+	0.974808i
$72$		0			0
$73$	−0.921673	−	0.963994i	−0.107874	−	0.112827i	0.666653	−	0.745368i	$-0.267726\pi$
$73$	−0.921673	−	0.963994i	−0.107874	−	0.112827i	−0.774527	+	0.632541i	$0.782012\pi$
$74$	−0.908590	+	2.42093i	−0.105621	+	0.281427i
$75$		0			0
$76$	−3.85902	−	2.80374i	−0.442660	−	0.321611i
$77$	−0.280589	+	0.119929i	−0.0319760	+	0.0136672i
$78$		0			0
$79$	8.42260	−	7.35861i	0.947617	−	0.827908i	−0.0375871	−	0.999293i	$-0.511967\pi$
$79$	8.42260	−	7.35861i	0.947617	−	0.827908i	0.985204	+	0.171385i	$0.0548243\pi$
$80$	10.5691	−	12.0973i	1.18166	−	1.35252i
$81$		0			0
$82$	2.56151	+	4.28724i	0.282871	+	0.473446i
$83$	14.4993	+	6.19729i	1.59150	+	0.680241i	0.992695	−	0.120651i	$-0.0384982\pi$
$83$	14.4993	+	6.19729i	1.59150	+	0.680241i	0.598809	+	0.800892i	$0.295641\pi$
$84$		0			0
$85$	−9.78064	−	13.4619i	−1.06086	−	1.46015i
$86$	−18.2466	+	12.0445i	−1.96758	+	1.29879i
$87$		0			0
$88$	−0.910738	−	0.295917i	−0.0970850	−	0.0315448i
$89$	−10.1302	+	0.454946i	−1.07380	+	0.0482242i	−0.574732	−	0.818341i	$-0.694894\pi$
$89$	−10.1302	+	0.454946i	−1.07380	+	0.0482242i	−0.499063	+	0.866566i	$0.666322\pi$
$90$		0			0
$91$	1.55636	−	1.95161i	0.163150	−	0.204584i
$92$	−0.872402	+	1.62119i	−0.0909542	+	0.169021i
$93$		0			0
$94$	−1.64533	+	3.41657i	−0.169703	+	0.352392i
$95$	−4.27628	−	11.3941i	−0.438737	−	1.16901i
$96$		0			0
$97$	−16.5330	+	3.77356i	−1.67868	+	0.383147i	−0.952542	−	0.304407i	$-0.901542\pi$
$97$	−16.5330	+	3.77356i	−1.67868	+	0.383147i	−0.726134	+	0.687553i	$0.758685\pi$
$98$	10.8865	−	5.85827i	1.09970	−	0.591775i
$99$		0			0
$100$	−6.96870	+	1.92324i	−0.696870	+	0.192324i
$101$	−8.49761	−	1.93952i	−0.845544	−	0.192990i	−0.222262	−	0.974987i	$-0.571344\pi$
$101$	−8.49761	−	1.93952i	−0.845544	−	0.192990i	−0.623282	+	0.781997i	$0.714201\pi$
$102$		0			0
$103$	4.86024	+	6.09455i	0.478894	+	0.600514i	0.961324	−	0.275421i	$-0.0888171\pi$
$103$	4.86024	+	6.09455i	0.478894	+	0.600514i	−0.482430	+	0.875935i	$0.660246\pi$
$104$	7.70771	−	1.39874i	0.755803	−	0.137158i
$105$		0			0
$106$	4.49997	+	4.30241i	0.437076	+	0.417887i
$107$	3.82563	+	3.65768i	0.369838	+	0.353601i	0.852983	−	0.521939i	$-0.174791\pi$
$107$	3.82563	+	3.65768i	0.369838	+	0.353601i	−0.483145	+	0.875541i	$0.660505\pi$
$108$		0			0
$109$	15.4810	−	2.80939i	1.48281	−	0.269091i	0.624017	−	0.781411i	$-0.285500\pi$
$109$	15.4810	−	2.80939i	1.48281	−	0.269091i	0.858795	+	0.512320i	$0.171214\pi$
$110$	2.70327	+	3.38979i	0.257747	+	0.323204i
$111$		0			0
$112$	−1.99596	−	0.455565i	−0.188601	−	0.0430468i
$113$	−3.26365	+	0.900710i	−0.307018	+	0.0847316i	−0.416151	−	0.909296i	$-0.636621\pi$
$113$	−3.26365	+	0.900710i	−0.307018	+	0.0847316i	0.109133	+	0.994027i	$0.465193\pi$
$114$		0			0
$115$	−4.13629	+	2.22583i	−0.385711	+	0.207560i
$116$	−6.58564	+	1.50313i	−0.611462	+	0.139562i
$117$		0			0
$118$	1.88763	+	5.02956i	0.173770	+	0.463009i
$119$	−0.920130	+	1.91067i	−0.0843482	+	0.175151i
$120$		0			0
$121$	−4.95752	+	9.21261i	−0.450683	+	0.837510i
$122$	−9.81478	+	12.3073i	−0.888588	+	1.11425i
$123$		0			0
$124$	−12.8762	+	0.578270i	−1.15632	+	0.0519302i
$125$	−2.02216	−	0.657039i	−0.180867	−	0.0587673i
$126$		0			0
$127$	2.92188	−	1.92872i	0.259275	−	0.171146i	−0.414573	−	0.910016i	$-0.636069\pi$
$127$	2.92188	−	1.92872i	0.259275	−	0.171146i	0.673848	+	0.738870i	$0.264640\pi$
$128$	−5.73929	−	7.89945i	−0.507286	−	0.698219i
$129$		0			0
$130$	−32.6137	−	13.9397i	−2.86041	−	1.22260i
$131$	−4.68176	−	7.83594i	−0.409047	−	0.684630i	0.582722	−	0.812672i	$-0.301988\pi$
$131$	−4.68176	−	7.83594i	−0.409047	−	0.684630i	−0.991769	+	0.128042i	$0.959131\pi$
$132$		0			0
$133$	−1.02049	+	1.16804i	−0.0884876	+	0.101282i
$134$	9.68243	−	8.45928i	0.836434	−	0.730771i
$135$		0			0
$136$	−6.11959	+	2.61564i	−0.524750	+	0.224289i
$137$	−6.82606	−	4.95942i	−0.583190	−	0.423712i	0.256683	−	0.966496i	$-0.417370\pi$
$137$	−6.82606	−	4.95942i	−0.583190	−	0.423712i	−0.839873	+	0.542784i	$0.817370\pi$
$138$		0			0
$139$	−3.15364	+	8.40285i	−0.267489	+	0.712721i	0.732017	+	0.681286i	$0.238579\pi$
$139$	−3.15364	+	8.40285i	−0.267489	+	0.712721i	−0.999506	+	0.0314346i	$0.989992\pi$
$140$	1.20001	+	1.25511i	0.101419	+	0.106076i
$141$		0			0
$142$	−7.81899	−	13.1028i	−0.656155	−	1.09957i
$143$			4.40272i			0.368174i
$144$		0			0
$145$	−16.1357	−	6.05582i	−1.33999	−	0.502908i
$146$	2.41270	+	0.108355i	0.199677	+	0.00896749i
$147$		0			0
$148$	−0.717900	−	1.67961i	−0.0590110	−	0.138063i
$149$	0.531526	−	3.92388i	0.0435443	−	0.321457i	−0.956056	−	0.293184i	$-0.905285\pi$
$149$	0.531526	−	3.92388i	0.0435443	−	0.321457i	0.999600	−	0.0282726i	$-0.00900064\pi$
$150$		0			0
$151$	3.96128	+	3.46087i	0.322365	+	0.281641i	0.803874	−	0.594799i	$-0.202768\pi$
$151$	3.96128	+	3.46087i	0.322365	+	0.281641i	−0.481510	+	0.876441i	$0.659911\pi$
$152$	−4.82343	+	0.653378i	−0.391232	+	0.0529960i
$153$		0			0
$154$	0.217174	−	0.508104i	0.0175004	−	0.0409442i
$155$	−28.2303	−	16.8668i	−2.26751	−	1.35478i
$156$		0			0
$157$	0.472286	+	0.715483i	0.0376925	+	0.0571018i	0.852931	−	0.522024i	$-0.174823\pi$
$157$	0.472286	+	0.715483i	0.0376925	+	0.0571018i	−0.815238	+	0.579125i	$0.803394\pi$
$158$	−1.81548	+	20.1716i	−0.144432	+	1.60477i
$159$		0			0
$160$	0.922833	+	20.5485i	0.0729564	+	1.62450i
$161$	0.499605	+	0.329786i	0.0393744	+	0.0259908i
$162$		0			0
$163$	8.88996	+	4.78389i	0.696316	+	0.374703i	0.783417	−	0.621496i	$-0.213475\pi$
$163$	8.88996	+	4.78389i	0.696316	+	0.374703i	−0.0871017	+	0.996199i	$0.527761\pi$
$164$	−3.40072	−	0.938538i	−0.265551	−	0.0732875i
$165$		0			0
$166$	−26.7331	+	10.0331i	−2.07489	+	0.778718i
$167$	−2.38887	+	0.776191i	−0.184856	+	0.0600634i	−0.399982	−	0.916523i	$-0.630984\pi$
$167$	−2.38887	+	0.776191i	−0.184856	+	0.0600634i	0.215126	+	0.976586i	$0.430984\pi$
$168$		0			0
$169$	−10.9065	−	20.2678i	−0.838965	−	1.55906i
$170$	29.6479	+	5.38031i	2.27389	+	0.412651i
$171$		0			0
$172$	3.43664	−	15.0569i	0.262042	−	1.14808i
$173$	−15.3013	+	1.37714i	−1.16334	+	0.104702i	−0.654432	−	0.756121i	$-0.727092\pi$
$173$	−15.3013	+	1.37714i	−1.16334	+	0.104702i	−0.508904	+	0.860823i	$0.669949\pi$
$174$		0			0
$175$	0.419731	+	2.31291i	0.0317287	+	0.174840i
$176$	3.25334	−	1.56673i	0.245230	−	0.118097i
$177$		0			0
$178$	12.6898	−	13.2725i	0.951138	−	0.994813i
$179$	7.97934	+	16.5693i	0.596404	+	1.23845i	0.952654	+	0.304055i	$0.0983407\pi$
$179$	7.97934	+	16.5693i	0.596404	+	1.23845i	−0.356250	+	0.934390i	$0.615945\pi$
$180$		0			0
$181$	8.63546	−	6.88655i	0.641869	−	0.511873i	−0.247604	−	0.968861i	$-0.579643\pi$
$181$	8.63546	−	6.88655i	0.641869	−	0.511873i	0.889473	+	0.456988i	$0.151072\pi$
$182$	0.405191	+	4.50205i	0.0300348	+	0.333714i
$183$		0			0
$184$	0.499788	+	1.81094i	0.0368448	+	0.133504i
$185$	0.832141	−	4.58547i	0.0611802	−	0.337131i
$186$		0			0
$187$	−0.832315	−	3.64661i	−0.0608649	−	0.266666i
$188$	−0.827770	−	2.54761i	−0.0603713	−	0.185804i
$189$		0			0
$190$	19.8558	+	9.56205i	1.44049	+	0.693704i
$191$	−1.23605	+	4.47873i	−0.0894375	+	0.324070i	−0.994966	−	0.100217i	$-0.968046\pi$
$191$	−1.23605	+	4.47873i	−0.0894375	+	0.324070i	0.905528	+	0.424286i	$0.139475\pi$
$192$		0			0
$193$	6.60789	+	5.26962i	0.475646	+	0.379315i	0.831767	−	0.555125i	$-0.187329\pi$
$193$	6.60789	+	5.26962i	0.475646	+	0.379315i	−0.356121	+	0.934440i	$0.615901\pi$
$194$	16.9174	−	25.6287i	1.21460	−	1.84003i
$195$		0			0
$196$	−2.69861	+	8.30548i	−0.192758	+	0.593248i
$197$	−21.2853	−	1.91571i	−1.51652	−	0.136489i	−0.700138	−	0.714007i	$-0.746878\pi$
$197$	−21.2853	−	1.91571i	−1.51652	−	0.136489i	−0.816378	+	0.577518i	$0.804021\pi$
$198$		0			0
$199$	0.441062	−	0.320450i	0.0312660	−	0.0227161i	−0.572042	−	0.820224i	$-0.693849\pi$
$199$	0.441062	−	0.320450i	0.0312660	−	0.0227161i	0.603309	+	0.797508i	$0.293849\pi$
$200$	−3.78363	+	6.33273i	−0.267543	+	0.447791i
$201$		0			0
$202$	13.5494	−	8.09540i	0.953334	−	0.569591i
$203$	0.294842	+	2.17661i	0.0206939	+	0.152768i
$204$		0			0
$205$	−5.92205	−	6.77833i	−0.413614	−	0.473419i
$206$	−13.9882	−	1.89483i	−0.974605	−	0.132019i
$207$		0			0
$208$	−17.3625	+	23.8975i	−1.20388	+	1.65699i
$209$	0.122735	−	2.73291i	0.00848978	−	0.189040i
$210$		0			0
$211$	18.0220	−	17.2308i	1.24069	−	1.18622i	0.265676	−	0.964062i	$-0.414405\pi$
$211$	18.0220	−	17.2308i	1.24069	−	1.18622i	0.975011	−	0.222156i	$-0.0713095\pi$
$212$	−4.39786			−0.302046
$213$		0			0
$214$	−9.58452			−0.655185
$215$	28.4810	−	27.2306i	1.94239	−	1.85711i
$216$		0			0
$217$	−0.188033	+	4.18688i	−0.0127645	+	0.284224i
$218$	−16.7470	+	23.0502i	−1.13425	+	1.56116i
$219$		0			0
$220$	−3.03500	−	0.411119i	−0.204620	−	0.0277176i
$221$	20.1315	+	23.0424i	1.35419	+	1.55000i
$222$		0			0
$223$	1.44290	+	10.6519i	0.0966235	+	0.713304i	0.972855	+	0.231414i	$0.0743352\pi$
$223$	1.44290	+	10.6519i	0.0966235	+	0.713304i	−0.876232	+	0.481890i	$0.839951\pi$
$224$	2.25039	−	1.34455i	0.150361	−	0.0898364i
$225$		0			0
$226$	3.14454	−	5.26307i	0.209172	−	0.350094i
$227$	3.37369	−	2.45113i	0.223919	−	0.162687i	−0.470170	−	0.882576i	$-0.655807\pi$
$227$	3.37369	−	2.45113i	0.223919	−	0.162687i	0.694089	+	0.719889i	$0.255807\pi$
$228$		0			0
$229$	−21.2426	−	1.91187i	−1.40375	−	0.126340i	−0.638276	−	0.769808i	$-0.720352\pi$
$229$	−21.2426	−	1.91187i	−1.40375	−	0.126340i	−0.765473	+	0.643468i	$0.777495\pi$
$230$	2.62845	−	8.08953i	0.173315	−	0.533408i
$231$		0			0
$232$	−3.79736	+	5.75275i	−0.249309	+	0.377686i
$233$	9.58483	+	7.64364i	0.627923	+	0.500752i	0.884971	−	0.465647i	$-0.154178\pi$
$233$	9.58483	+	7.64364i	0.627923	+	0.500752i	−0.257048	+	0.966399i	$0.582750\pi$
$234$		0			0
$235$	1.81821	−	6.58815i	0.118607	−	0.429764i
$236$	−3.41902	−	1.64651i	−0.222559	−	0.107179i
$237$		0			0
$238$	−1.18670	−	3.65228i	−0.0769222	−	0.236742i
$239$	−4.20779	−	18.4355i	−0.272180	−	1.19250i	−0.907434	−	0.420194i	$-0.861962\pi$
$239$	−4.20779	−	18.4355i	−0.272180	−	1.19250i	0.635255	−	0.772303i	$-0.280895\pi$
$240$		0			0
$241$	−3.99940	+	22.0385i	−0.257624	+	1.41963i	0.552571	+	0.833466i	$0.313647\pi$
$241$	−3.99940	+	22.0385i	−0.257624	+	1.41963i	−0.810195	+	0.586160i	$0.800639\pi$
$242$	−5.04000	−	18.2620i	−0.323983	−	1.17393i
$243$		0			0
$244$	−0.996773	−	11.0751i	−0.0638119	−	0.709008i
$245$	−17.4200	+	13.8920i	−1.11292	+	0.887525i
$246$		0			0
$247$	9.70982	+	20.1627i	0.617821	+	1.28292i
$248$	−9.08924	+	9.50660i	−0.577167	+	0.603670i
$249$		0			0
$250$	3.46897	−	1.67057i	0.219397	−	0.105656i
$251$	4.77484	+	26.3115i	0.301385	+	1.66077i	0.678498	+	0.734602i	$0.262631\pi$
$251$	4.77484	+	26.3115i	0.301385	+	1.66077i	−0.377113	+	0.926167i	$0.623083\pi$
$252$		0			0
$253$	−1.05160	+	0.0946458i	−0.0661136	+	0.00595033i
$254$	−1.41075	+	6.18091i	−0.0885185	+	0.387825i
$255$		0			0
$256$	20.4845	+	3.71738i	1.28028	+	0.232336i
$257$	8.83650	+	16.4210i	0.551206	+	1.02431i	0.991944	+	0.126677i	$0.0404310\pi$
$257$	8.83650	+	16.4210i	0.551206	+	1.02431i	−0.440738	+	0.897636i	$0.645283\pi$
$258$		0			0
$259$	−0.564877	+	0.183540i	−0.0350997	+	0.0114046i
$260$	23.4567	−	8.80343i	1.45472	−	0.545966i
$261$		0			0
$262$	15.9338	+	4.39745i	0.984393	+	0.271675i
$263$	2.62653	+	1.41340i	0.161959	+	0.0871538i	0.552840	−	0.833287i	$-0.313544\pi$
$263$	2.62653	+	1.41340i	0.161959	+	0.0871538i	−0.390881	+	0.920441i	$0.627830\pi$
$264$		0			0
$265$	−9.36444	−	6.18141i	−0.575253	−	0.379721i
$266$	−0.126012	−	2.80587i	−0.00772627	−	0.172039i
$267$		0			0
$268$	−0.814129	+	9.04572i	−0.0497309	+	0.552555i
$269$	−10.8914	−	16.4998i	−0.664062	−	1.00601i	−0.997987	−	0.0634119i	$-0.979802\pi$
$269$	−10.8914	−	16.4998i	−0.664062	−	1.00601i	0.333925	−	0.942600i	$-0.391627\pi$
$270$		0			0
$271$	6.15923	+	3.67997i	0.374147	+	0.223542i	0.687646	−	0.726046i	$-0.258644\pi$
$271$	6.15923	+	3.67997i	0.374147	+	0.223542i	−0.313499	+	0.949588i	$0.601501\pi$
$272$	9.86304	−	23.0757i	0.598035	−	1.39917i
$273$		0			0
$274$	15.1407	−	2.05095i	0.914683	−	0.123902i
$275$	−3.12228	−	2.72785i	−0.188281	−	0.164496i
$276$		0			0
$277$	0.624527	−	4.61044i	0.0375242	−	0.277015i	−0.962460	−	0.271423i	$-0.912506\pi$
$277$	0.624527	−	4.61044i	0.0375242	−	0.277015i	0.999984	−	0.00559170i	$-0.00177990\pi$
$278$	−6.38770	−	14.9448i	−0.383109	−	0.896327i
$279$		0			0
$280$	1.77016	+	0.0794982i	0.105788	+	0.00475093i
$281$	20.0760	+	7.53465i	1.19763	+	0.449480i	0.868921	−	0.494950i	$-0.164814\pi$
$281$	20.0760	+	7.53465i	1.19763	+	0.449480i	0.328713	+	0.944430i	$0.393385\pi$
$282$		0			0
$283$			11.0496i			0.656828i	0.944534	+	0.328414i	$0.106514\pi$
$283$			11.0496i			0.656828i	−0.944534	+	0.328414i	$0.893486\pi$
$284$	10.3885	+	2.87308i	0.616445	+	0.170486i
$285$		0			0
$286$	−5.50960	−	5.76259i	−0.325790	−	0.340749i
$287$	−0.403073	+	1.07399i	−0.0237927	+	0.0633954i
$288$		0			0
$289$	−7.27697	−	5.28703i	−0.428057	−	0.311002i
$290$	28.6978	−	12.2660i	1.68519	−	0.720287i
$291$		0			0
$292$	−1.28477	+	1.12247i	−0.0751853	+	0.0656874i
$293$	−18.7596	+	21.4721i	−1.09595	+	1.25441i	−0.131165	+	0.991361i	$0.541872\pi$
$293$	−18.7596	+	21.4721i	−1.09595	+	1.25441i	−0.964782	+	0.263052i	$0.915271\pi$
$294$		0			0
$295$	−4.96593	−	8.31156i	−0.289128	−	0.483918i
$296$	−1.71393	−	0.732570i	−0.0996204	−	0.0425798i
$297$		0			0
$298$	4.21468	+	5.80101i	0.244150	+	0.336044i
$299$	7.20845	−	4.75826i	0.416875	−	0.275177i
$300$		0			0
$301$	−4.77610	−	1.55185i	−0.275290	−	0.0894471i
$302$	−9.51578	+	0.427354i	−0.547571	+	0.0245915i
$303$		0			0
$304$	11.4437	−	14.3500i	0.656342	−	0.823027i
$305$	13.4441	−	24.9833i	0.769808	−	1.43054i
$306$		0			0
$307$	−1.81420	+	3.76722i	−0.103542	+	0.215006i	−0.946303	−	0.323281i	$-0.895214\pi$
$307$	−1.81420	+	3.76722i	−0.103542	+	0.215006i	0.842761	+	0.538287i	$0.180928\pi$
$308$	0.137153	+	0.365442i	0.00781501	+	0.0208230i
$309$		0			0
$310$	58.0572	−	13.2512i	3.29743	−	0.752616i
$311$	−4.86567	+	2.61833i	−0.275907	+	0.148472i	−0.605971	−	0.795487i	$-0.707215\pi$
$311$	−4.86567	+	2.61833i	−0.275907	+	0.148472i	0.330064	+	0.943958i	$0.392930\pi$
$312$		0			0
$313$	28.0055	−	7.72903i	1.58297	−	0.436871i	0.639622	−	0.768689i	$-0.279091\pi$
$313$	28.0055	−	7.72903i	1.58297	−	0.436871i	0.943343	+	0.331819i	$0.107662\pi$
$314$	−1.51352	−	0.345452i	−0.0854131	−	0.0194950i
$315$		0			0
$316$	−8.92007	−	11.1854i	−0.501793	−	0.629229i
$317$	−8.98776	+	1.63104i	−0.504803	+	0.0916082i	−0.424983	−	0.905201i	$-0.639720\pi$
$317$	−8.98776	+	1.63104i	−0.504803	+	0.0916082i	−0.0798193	+	0.996809i	$0.525434\pi$
$318$		0			0
$319$	−2.80017	−	2.67724i	−0.156780	−	0.149897i
$320$	−3.70055	−	3.53809i	−0.206867	−	0.197785i
$321$		0			0
$322$	−1.06662	+	0.193562i	−0.0594402	+	0.0107868i
$323$	−11.8540	−	14.8644i	−0.659572	−	0.827077i
$324$		0			0
$325$	33.0661	+	7.54711i	1.83418	+	0.418639i
$326$	−17.6224	+	4.86348i	−0.976016	+	0.269363i
$327$		0			0
$328$	−3.17009	+	1.70590i	−0.175039	+	0.0941925i
$329$	−0.849186	+	0.193821i	−0.0468172	+	0.0106857i
$330$		0			0
$331$	−10.6525	−	28.3834i	−0.585513	−	1.56009i	−0.810504	−	0.585733i	$-0.800807\pi$
$331$	−10.6525	−	28.3834i	−0.585513	−	1.56009i	0.224991	−	0.974361i	$-0.427765\pi$
$332$	8.75153	−	18.1727i	0.480303	−	0.997359i
$333$		0			0
$334$	2.15539	−	4.00539i	0.117938	−	0.219165i
$335$	−14.4478	+	18.1169i	−0.789365	+	0.989833i
$336$		0			0
$337$	8.69419	−	0.390456i	0.473602	−	0.0212695i	0.193215	−	0.981156i	$-0.438108\pi$
$337$	8.69419	−	0.390456i	0.473602	−	0.0212695i	0.280387	+	0.959887i	$0.409537\pi$
$338$	39.6385	+	12.8793i	2.15605	+	0.700544i
$339$		0			0
$340$	−17.7640	+	11.7259i	−0.963390	+	0.635928i
$341$	−4.34498	−	5.98035i	−0.235294	−	0.323854i
$342$		0			0
$343$	5.28841	+	2.26037i	0.285547	+	0.122049i
$344$	−8.08315	−	13.5289i	−0.435815	−	0.729431i
$345$		0			0
$346$	18.3041	−	20.9507i	0.984033	−	1.12632i
$347$	−13.5074	+	11.8011i	−0.725115	+	0.633514i	−0.939228	−	0.343295i	$-0.888457\pi$
$347$	−13.5074	+	11.8011i	−0.725115	+	0.633514i	0.214113	+	0.976809i	$0.431314\pi$
$348$		0			0
$349$	13.0161	−	5.56336i	0.696737	−	0.297800i	−0.0153586	−	0.999882i	$-0.504889\pi$
$349$	13.0161	−	5.56336i	0.696737	−	0.297800i	0.712096	+	0.702082i	$0.247746\pi$
$350$	−3.44377	−	2.50205i	−0.184077	−	0.133740i
$351$		0			0
$352$	−1.62463	+	4.32882i	−0.0865933	+	0.230727i
$353$	13.0027	+	13.5998i	0.692065	+	0.723843i	0.971688	−	0.236267i	$-0.0759238\pi$
$353$	13.0027	+	13.5998i	0.692065	+	0.723843i	−0.279623	+	0.960110i	$0.590210\pi$
$354$		0			0
$355$	18.0822	+	20.7193i	0.959704	+	1.09967i
$356$			12.9713i			0.687477i
$357$		0			0
$358$	−31.1789	−	11.7016i	−1.64786	−	0.618450i
$359$	25.5180	+	1.14601i	1.34679	+	0.0604843i	0.706534	−	0.707679i	$-0.250258\pi$
$359$	25.5180	+	1.14601i	1.34679	+	0.0604843i	0.640254	+	0.768164i	$0.278829\pi$
$360$		0			0
$361$	2.00234	+	4.68470i	0.105386	+	0.246563i
$362$	−2.68482	+	19.8201i	−0.141111	+	1.04172i
$363$		0			0
$364$	−2.40461	−	2.10084i	−0.126036	−	0.110114i
$365$	−4.31336	+	0.584285i	−0.225772	+	0.0305829i
$366$		0			0
$367$	5.39473	−	12.6216i	0.281602	−	0.658841i	−0.717694	−	0.696359i	$-0.754802\pi$
$367$	5.39473	−	12.6216i	0.281602	−	0.658841i	0.999296	+	0.0375175i	$0.0119450\pi$
$368$	−6.08123	−	3.63337i	−0.317006	−	0.189402i
$369$		0			0
$370$	4.64914	+	7.04315i	0.241697	+	0.366156i
$371$	−0.128187	+	1.42427i	−0.00665512	+	0.0739445i
$372$		0			0
$373$	1.47971	+	32.9484i	0.0766166	+	1.70600i	0.558286	+	0.829648i	$0.311459\pi$
$373$	1.47971	+	32.9484i	0.0766166	+	1.70600i	−0.481670	+	0.876353i	$0.659970\pi$
$374$	5.65279	+	3.73138i	0.292299	+	0.192945i
$375$		0			0
$376$	−2.40707	−	1.29530i	−0.124135	−	0.0668000i
$377$	30.5495	+	8.43114i	1.57338	+	0.434226i
$378$		0			0
$379$	−32.6565	+	12.2562i	−1.67745	+	0.629559i	−0.994862	−	0.101242i	$-0.967718\pi$
$379$	−32.6565	+	12.2562i	−1.67745	+	0.629559i	−0.682591	+	0.730800i	$0.739147\pi$
$380$	−14.8058	+	4.81068i	−0.759519	+	0.246783i
$381$		0			0
$382$	−3.98689	−	7.40889i	−0.203987	−	0.379072i
$383$	−12.9566	−	2.35127i	−0.662049	−	0.120144i	−0.162876	−	0.986647i	$-0.552077\pi$
$383$	−12.9566	−	2.35127i	−0.662049	−	0.120144i	−0.499173	+	0.866502i	$0.666363\pi$
$384$		0			0
$385$	−0.221606	+	0.970919i	−0.0112941	+	0.0494826i
$386$	−15.2433	+	1.37192i	−0.775865	+	0.0698291i
$387$		0			0
$388$	3.87334	+	21.3439i	0.196639	+	1.08357i
$389$	32.7036	−	15.7492i	1.65814	−	0.798518i	0.659226	−	0.751945i	$-0.270884\pi$
$389$	32.7036	−	15.7492i	1.65814	−	0.798518i	0.998915	−	0.0465734i	$-0.0148302\pi$
$390$		0			0
$391$	−5.07097	+	5.30382i	−0.256450	+	0.268225i
$392$	3.86649	+	8.02885i	0.195287	+	0.405518i
$393$		0			0
$394$	30.2571	−	24.1292i	1.52433	−	1.21561i
$395$	−3.27200	−	36.3549i	−0.164632	−	1.82922i
$396$		0			0
$397$	−4.00461	−	14.5104i	−0.200986	−	0.728256i	−0.993037	−	0.117801i	$-0.962415\pi$
$397$	−4.00461	−	14.5104i	−0.200986	−	0.728256i	0.792051	−	0.610454i	$-0.209013\pi$
$398$	−0.176279	+	0.971377i	−0.00883607	+	0.0486907i
$399$		0			0
$400$	−6.18986	−	27.1195i	−0.309493	−	1.35598i
$401$	0.896981	+	2.76062i	0.0447931	+	0.137859i	0.970952	−	0.239275i	$-0.0769097\pi$
$401$	0.896981	+	2.76062i	0.0447931	+	0.137859i	−0.926159	+	0.377134i	$0.876910\pi$
$402$		0			0
$403$	54.4821	+	26.2372i	2.71394	+	1.30697i
$404$	−2.96616	+	10.7476i	−0.147572	+	0.534716i
$405$		0			0
$406$	−3.10974	−	2.47994i	−0.154334	−	0.123077i
$407$	0.577110	−	0.874284i	0.0286063	−	0.0433367i
$408$		0			0
$409$	1.58866	−	4.88939i	0.0785541	−	0.241765i	−0.904066	−	0.427393i	$-0.859432\pi$
$409$	1.58866	−	4.88939i	0.0785541	−	0.241765i	0.982620	+	0.185628i	$0.0594321\pi$
$410$	16.2337	+	1.46106i	0.801724	+	0.0721564i
$411$		0			0
$412$	8.06706	−	5.86106i	0.397435	−	0.288754i
$413$	−0.632889	+	1.05928i	−0.0311424	+	0.0521237i
$414$		0			0
$415$	44.1775	−	26.3948i	2.16859	−	1.29567i
$416$	−5.07715	−	37.4810i	−0.248928	−	1.83766i
$417$		0			0
$418$	3.25935	+	3.73063i	0.159420	+	0.182471i
$419$	−22.3901	−	3.03295i	−1.09383	−	0.148169i	−0.434977	−	0.900441i	$-0.643244\pi$
$419$	−22.3901	−	3.03295i	−1.09383	−	0.148169i	−0.658852	+	0.752272i	$0.728958\pi$
$420$		0			0
$421$	−14.1255	+	19.4420i	−0.688433	+	0.947546i	−0.999996	−	0.00267899i	$-0.999147\pi$
$421$	−14.1255	+	19.4420i	−0.688433	+	0.947546i	0.311564	+	0.950225i	$0.399147\pi$
$422$	−2.02571	+	45.1059i	−0.0986099	+	2.19572i
$423$		0			0
$424$	−3.24371	+	3.10130i	−0.157528	+	0.150612i
$425$	−28.8142			−1.39769
$426$		0			0
$427$	−3.61577			−0.174980
$428$	4.89364	−	4.67880i	0.236543	−	0.226158i
$429$		0			0
$430$	−3.20131	+	71.2828i	−0.154381	+	3.43756i
$431$	1.38046	−	1.90004i	0.0664943	−	0.0915215i	−0.774475	−	0.632605i	$-0.781986\pi$
$431$	1.38046	−	1.90004i	0.0664943	−	0.0915215i	0.840969	+	0.541083i	$0.181986\pi$
$432$		0			0
$433$	−19.1801	−	2.59811i	−0.921735	−	0.124857i	−0.342035	−	0.939687i	$-0.611116\pi$
$433$	−19.1801	−	2.59811i	−0.921735	−	0.124857i	−0.579700	+	0.814830i	$0.696830\pi$
$434$	−4.99339	−	5.71540i	−0.239691	−	0.274348i
$435$		0			0
$436$	−2.70162	−	19.9442i	−0.129384	−	0.955152i
$437$	−4.60718	+	2.75266i	−0.220391	+	0.131678i
$438$		0			0
$439$	−7.75062	+	12.9724i	−0.369917	+	0.619137i	−0.985647	−	0.168821i	$-0.946004\pi$
$439$	−7.75062	+	12.9724i	−0.369917	+	0.619137i	0.615730	+	0.787957i	$0.288861\pi$
$440$	−2.52842	+	1.83701i	−0.120538	+	0.0875759i
$441$		0			0
$442$	−55.1850	−	4.96674i	−2.62488	−	0.236244i
$443$	10.1430	−	31.2169i	0.481908	−	1.48316i	−0.354502	−	0.935055i	$-0.615350\pi$
$443$	10.1430	−	31.2169i	0.481908	−	1.48316i	0.836410	−	0.548105i	$-0.184650\pi$
$444$		0			0
$445$	−18.2318	+	27.6200i	−0.864270	+	1.30931i
$446$	−15.2185	−	12.1363i	−0.720615	−	0.574671i
$447$		0			0
$448$	−0.173588	+	0.628983i	−0.00820128	+	0.0297167i
$449$	22.9770	+	11.0652i	1.08435	+	0.522197i	0.888706	−	0.458477i	$-0.151605\pi$
$449$	22.9770	+	11.0652i	1.08435	+	0.522197i	0.195647	+	0.980674i	$0.437319\pi$
$450$		0			0
$451$	−0.625226	−	1.92425i	−0.0294407	−	0.0906092i
$452$	0.963702	+	4.22225i	0.0453287	+	0.198598i
$453$		0			0
$454$	−1.34836	+	7.43007i	−0.0632817	+	0.348711i
$455$	−2.16734	−	7.85317i	−0.101606	−	0.368162i
$456$		0			0
$457$	−0.0898625	−	0.998454i	−0.00420359	−	0.0467057i	0.993599	−	0.112968i	$-0.0360356\pi$
$457$	−0.0898625	−	0.998454i	−0.00420359	−	0.0467057i	−0.997802	+	0.0662618i	$0.978893\pi$
$458$	30.1963	−	24.0808i	1.41098	−	1.12522i
$459$		0			0
$460$	2.60698	+	5.41344i	0.121551	+	0.252403i
$461$	−23.6094	+	24.6935i	−1.09960	+	1.15009i	−0.111899	+	0.993720i	$0.535693\pi$
$461$	−23.6094	+	24.6935i	−1.09960	+	1.15009i	−0.987699	+	0.156370i	$0.950021\pi$
$462$		0			0
$463$	−13.7067	+	6.60080i	−0.637005	+	0.306765i	−0.724370	−	0.689411i	$-0.757869\pi$
$463$	−13.7067	+	6.60080i	−0.637005	+	0.306765i	0.0873657	+	0.996176i	$0.472155\pi$
$464$	−4.64110	−	25.5746i	−0.215458	−	1.18727i
$465$		0			0
$466$	−22.1106	+	1.98999i	−1.02426	+	0.0921847i
$467$	9.05673	−	39.6801i	0.419095	−	1.83618i	−0.118474	−	0.992957i	$-0.537800\pi$
$467$	9.05673	−	39.6801i	0.419095	−	1.83618i	0.537570	−	0.843219i	$-0.319343\pi$
$468$		0			0
$469$	2.90578	+	0.527321i	0.134176	+	0.0243494i
$470$	5.86467	+	10.8984i	0.270517	+	0.502705i
$471$		0			0
$472$	−3.68285	+	1.19663i	−0.169517	+	0.0550793i
$473$	8.29264	−	3.11228i	0.381296	−	0.143103i
$474$		0			0
$475$	−20.3148	−	5.60654i	−0.932109	−	0.257246i
$476$	2.38881	+	1.28547i	0.109491	+	0.0589195i
$477$		0			0
$478$	28.5779	+	18.8641i	1.30712	+	0.862824i
$479$	−0.564680	−	12.5736i	−0.0258009	−	0.574501i	−0.969705	−	0.244280i	$-0.921448\pi$
$479$	−0.564680	−	12.5736i	−0.0258009	−	0.574501i	0.943904	−	0.330221i	$-0.107123\pi$
$480$		0			0
$481$	−0.768177	+	8.53514i	−0.0350258	+	0.389169i
$482$	−22.3445	−	33.8505i	−1.01776	−	1.54185i
$483$		0			0
$484$	11.4881	+	6.86384i	0.522188	+	0.311993i
$485$	−21.7523	+	50.8921i	−0.987722	+	2.31089i
$486$		0			0
$487$	−10.9531	+	1.48369i	−0.496331	+	0.0672326i	−0.378121	−	0.925756i	$-0.623430\pi$
$487$	−10.9531	+	1.48369i	−0.496331	+	0.0672326i	−0.118210	+	0.992989i	$0.537716\pi$
$488$	−8.54514	−	7.46567i	−0.386820	−	0.337955i
$489$		0			0
$490$	5.41598	−	39.9823i	0.244669	−	1.80622i
$491$	−1.70908	−	3.99860i	−0.0771298	−	0.180454i	0.876525	−	0.481355i	$-0.159855\pi$
$491$	−1.70908	−	3.99860i	−0.0771298	−	0.180454i	−0.953655	+	0.300901i	$0.902713\pi$
$492$		0			0
$493$	−26.8969	−	1.20794i	−1.21138	−	0.0544030i
$494$	−37.9407	−	14.2394i	−1.70703	−	0.640659i
$495$		0			0
$496$		−	49.5956i		−	2.22691i
$497$	1.23326	−	3.28064i	0.0553194	−	0.147157i
$498$		0			0
$499$	11.0110	+	11.5166i	0.492921	+	0.515555i	0.921726	−	0.387842i	$-0.126779\pi$
$499$	11.0110	+	11.5166i	0.492921	+	0.515555i	−0.428805	+	0.903397i	$0.641065\pi$
$500$	−0.955670	+	2.54637i	−0.0427389	+	0.113877i
$501$		0			0
$502$	−39.1762	−	28.4631i	−1.74852	−	1.27037i
$503$	7.33310	−	3.13432i	0.326967	−	0.139752i	−0.223280	−	0.974754i	$-0.571676\pi$
$503$	7.33310	−	3.13432i	0.326967	−	0.139752i	0.550247	+	0.835002i	$0.314534\pi$
$504$		0			0
$505$	−21.4223	+	18.7161i	−0.953279	+	0.832855i
$506$	1.25797	−	1.43986i	0.0559236	−	0.0640097i
$507$		0			0
$508$	−2.29699	−	3.84451i	−0.101912	−	0.170573i
$509$	−27.1425	−	11.6013i	−1.20307	−	0.514217i	−0.304275	−	0.952584i	$-0.598414\pi$
$509$	−27.1425	−	11.6013i	−1.20307	−	0.514217i	−0.898796	+	0.438367i	$0.855557\pi$
$510$		0			0
$511$	0.326069	+	0.448796i	0.0144245	+	0.0198536i
$512$	−15.1655	+	10.0107i	−0.670228	+	0.442414i
$513$		0			0
$514$	−32.1152	−	10.4349i	−1.41654	−	0.460262i
$515$	25.4154	−	1.14140i	1.11993	−	0.0502963i
$516$		0			0
$517$	0.957857	−	1.20111i	0.0421265	−	0.0528250i
$518$	0.509668	−	0.947122i	0.0223935	−	0.0416141i
$519$		0			0
$520$	11.0928	−	23.0344i	0.486450	−	1.01012i
$521$	10.0131	+	26.6797i	0.438681	+	1.16886i	0.950762	+	0.309923i	$0.100303\pi$
$521$	10.0131	+	26.6797i	0.438681	+	1.16886i	−0.512081	+	0.858937i	$0.671125\pi$
$522$		0			0
$523$	−36.5156	+	8.33445i	−1.59672	+	0.364440i	−0.926075	−	0.377340i	$-0.876839\pi$
$523$	−36.5156	+	8.33445i	−1.59672	+	0.364440i	−0.670642	+	0.741781i	$0.733982\pi$
$524$	−10.2821	+	5.53304i	−0.449176	+	0.241712i
$525$		0			0
$526$	−5.20653	+	1.43691i	−0.227016	+	0.0626523i
$527$	−50.0855	−	11.4317i	−2.18176	−	0.497972i
$528$		0			0
$529$	−13.0488	−	16.3627i	−0.567338	−	0.711420i
$530$	19.9923	−	3.62807i	0.868411	−	0.157593i
$531$		0			0
$532$	1.43406	+	1.37110i	0.0621743	+	0.0594447i
$533$	11.9631	+	11.4379i	0.518180	+	0.495430i
$534$		0			0
$535$	16.9964	−	3.08440i	0.734819	−	0.133350i
$536$	5.77842	+	7.24591i	0.249590	+	0.312976i
$537$		0			0
$538$	34.9035	+	7.96650i	1.50480	+	0.343460i
$539$	−4.82795	+	1.33243i	−0.207955	+	0.0573918i
$540$		0			0
$541$	−3.13355	+	1.68624i	−0.134722	+	0.0724970i	−0.539841	−	0.841767i	$-0.681516\pi$
$541$	−3.13355	+	1.68624i	−0.134722	+	0.0724970i	0.405119	+	0.914264i	$0.367230\pi$
$542$	−12.6668	+	2.89111i	−0.544086	+	0.124184i
$543$		0			0
$544$	11.2908	+	30.0843i	0.484091	+	1.28985i
$545$	22.2799	−	46.2647i	0.954367	−	1.98176i
$546$		0			0
$547$	−6.39789	+	11.8893i	−0.273554	+	0.508348i	−0.979893	−	0.199526i	$-0.936060\pi$
$547$	−6.39789	+	11.8893i	−0.273554	+	0.508348i	0.706339	+	0.707874i	$0.250346\pi$
$548$	−6.72931	+	8.43829i	−0.287462	+	0.360466i
$549$		0			0
$550$	7.50033	−	0.336840i	0.319815	−	0.0143629i
$551$	−18.7281	−	6.08513i	−0.797844	−	0.259235i
$552$		0			0
$553$	−3.88246	+	2.56279i	−0.165099	+	0.108981i
$554$	4.95213	+	6.81602i	0.210396	+	0.289585i
$555$		0			0
$556$	10.5569	+	4.51223i	0.447711	+	0.191361i
$557$	19.5867	+	32.7826i	0.829916	+	1.38904i	0.919510	+	0.393066i	$0.128586\pi$
$557$	19.5867	+	32.7826i	0.829916	+	1.38904i	−0.0895946	+	0.995978i	$0.528557\pi$
$558$		0			0
$559$	−47.6725	+	54.5656i	−2.01633	+	2.30788i
$560$	−5.03177	+	4.39612i	−0.212631	+	0.185770i
$561$		0			0
$562$	−35.7059	+	15.2614i	−1.50616	+	0.643764i
$563$	33.3954	+	24.2632i	1.40745	+	1.02257i	0.993687	+	0.112185i	$0.0357849\pi$
$563$	33.3954	+	24.2632i	1.40745	+	1.02257i	0.413761	+	0.910386i	$0.364215\pi$
$564$		0			0
$565$	−3.88256	+	10.3451i	−0.163341	+	0.435220i
$566$	−13.8275	−	14.4625i	−0.581214	−	0.607902i
$567$		0			0
$568$	9.68826	−	5.20673i	0.406510	−	0.218470i
$569$			21.2848i			0.892303i	0.894957	+	0.446152i	$0.147206\pi$
$569$			21.2848i			0.892303i	−0.894957	+	0.446152i	$0.852794\pi$
$570$		0			0
$571$	32.4818	+	12.1906i	1.35932	+	0.510161i	0.921317	−	0.388813i	$-0.127115\pi$
$571$	32.4818	+	12.1906i	1.35932	+	0.510161i	0.438002	+	0.898974i	$0.355686\pi$
$572$	5.62616	+	0.252671i	0.235241	+	0.0105647i
$573$		0			0
$574$	−0.816424	−	1.91012i	−0.0340769	−	0.0797268i
$575$	−1.09182	+	8.06017i	−0.0455322	+	0.336132i
$576$		0			0
$577$	27.2729	+	23.8276i	1.13538	+	0.991955i	0.999999	+	0.00116243i	$0.000370013\pi$
$577$	27.2729	+	23.8276i	1.13538	+	0.991955i	0.135385	+	0.990793i	$0.456773\pi$
$578$	16.1409	−	2.18643i	0.671371	−	0.0909434i
$579$		0			0
$580$	−8.66465	+	20.2720i	−0.359780	+	0.841747i
$581$	−5.63026	−	3.36392i	−0.233583	−	0.139559i
$582$		0			0
$583$	−1.38949	−	2.10499i	−0.0575469	−	0.0871798i
$584$	−0.156053	+	1.73389i	−0.00645751	+	0.0717488i
$585$		0			0
$586$	−2.31647	−	51.5801i	−0.0956923	−	2.13076i
$587$	1.16159	+	0.766762i	0.0479441	+	0.0316477i	0.574642	−	0.818405i	$-0.305141\pi$
$587$	1.16159	+	0.766762i	0.0479441	+	0.0316477i	−0.526698	+	0.850053i	$0.676570\pi$
$588$		0			0
$589$	−33.0874	−	17.8051i	−1.36334	−	0.733647i
$590$	16.9009	+	4.66436i	0.695801	+	0.192029i
$591$		0			0
$592$	6.58032	−	2.46964i	0.270450	−	0.101501i
$593$	9.72992	−	3.16144i	0.399560	−	0.129825i	−0.102342	−	0.994749i	$-0.532634\pi$
$593$	9.72992	−	3.16144i	0.399560	−	0.129825i	0.501902	+	0.864924i	$0.332634\pi$
$594$		0			0
$595$	3.27973	+	6.09477i	0.134456	+	0.249861i
$596$	−4.98376	−	0.904419i	−0.204143	−	0.0370464i
$597$		0			0
$598$	−3.48041	+	15.2487i	−0.142325	+	0.623564i
$599$	20.1688	−	1.81523i	0.824076	−	0.0741682i	0.330429	−	0.943831i	$-0.392807\pi$
$599$	20.1688	−	1.81523i	0.824076	−	0.0741682i	0.493647	+	0.869663i	$0.335664\pi$
$600$		0			0
$601$	−7.12820	−	39.2796i	−0.290765	−	1.60225i	−0.716624	−	0.697459i	$-0.754314\pi$
$601$	−7.12820	−	39.2796i	−0.290765	−	1.60225i	0.425859	−	0.904789i	$-0.359972\pi$
$602$	8.19330	−	3.94569i	0.333934	−	0.160814i
$603$		0			0
$604$	4.64992	−	4.86344i	0.189203	−	0.197891i
$605$	14.8144	+	30.7625i	0.602292	+	1.25067i
$606$		0			0
$607$	14.7148	−	11.7346i	0.597255	−	0.476295i	−0.277589	−	0.960700i	$-0.589535\pi$
$607$	14.7148	−	11.7346i	0.597255	−	0.476295i	0.874844	+	0.484405i	$0.160964\pi$
$608$	2.10669	+	23.4073i	0.0854376	+	0.949290i
$609$		0			0
$610$	13.6678	+	49.5241i	0.553392	+	2.00517i
$611$	−2.24400	+	12.3654i	−0.0907824	+	0.500252i
$612$		0			0
$613$	−6.65468	−	29.1561i	−0.268780	−	1.17760i	−0.911434	−	0.411446i	$-0.865024\pi$
$613$	−6.65468	−	29.1561i	−0.268780	−	1.17760i	0.642654	−	0.766156i	$-0.277833\pi$
$614$	−2.33978	−	7.20111i	−0.0944259	−	0.290613i
$615$		0			0
$616$	0.358863	+	0.172819i	0.0144590	+	0.00696309i
$617$	−0.323399	+	1.17181i	−0.0130195	+	0.0471753i	−0.970184	−	0.242370i	$-0.922075\pi$
$617$	−0.323399	+	1.17181i	−0.0130195	+	0.0471753i	0.957164	+	0.289545i	$0.0935039\pi$
$618$		0			0
$619$	−23.8613	−	19.0287i	−0.959066	−	0.764829i	0.0129086	−	0.999917i	$-0.495891\pi$
$619$	−23.8613	−	19.0287i	−0.959066	−	0.764829i	−0.971974	+	0.235087i	$0.924462\pi$
$620$	−23.1740	+	35.1071i	−0.930689	+	1.40993i
$621$		0			0
$622$	3.09193	−	9.51600i	0.123975	−	0.381557i
$623$	4.20082	+	0.378081i	0.168302	+	0.0151475i
$624$		0			0
$625$	17.2467	−	12.5305i	0.689870	−	0.501220i
$626$	−26.9834	+	45.1627i	−1.07848	+	1.80506i
$627$		0			0
$628$	0.941408	−	0.562465i	0.0375663	−	0.0224448i
$629$	−0.977279	−	7.21457i	−0.0389667	−	0.287664i
$630$		0			0
$631$	−15.0121	−	17.1827i	−0.597623	−	0.684034i	0.372114	−	0.928187i	$-0.378633\pi$
$631$	−15.0121	−	17.1827i	−0.597623	−	0.684034i	−0.969737	+	0.244153i	$0.921490\pi$
$632$	−14.4669	−	1.95968i	−0.575463	−	0.0779517i
$633$		0			0
$634$	9.72273	−	13.3822i	0.386139	−	0.531474i
$635$	0.512636	−	11.4147i	0.0203433	−	0.452980i
$636$		0			0
$637$	29.6137	−	28.3136i	1.17334	−	1.12182i
$638$	7.01540			0.277742
$639$		0			0
$640$	−31.8672			−1.25966
$641$	2.89199	−	2.76503i	0.114227	−	0.109212i	−0.631788	−	0.775141i	$-0.717679\pi$
$641$	2.89199	−	2.76503i	0.114227	−	0.109212i	0.746015	+	0.665929i	$0.231965\pi$
$642$		0			0
$643$	1.09985	−	24.4901i	0.0433740	−	0.965796i	−0.852839	−	0.522173i	$-0.825121\pi$
$643$	1.09985	−	24.4901i	0.0433740	−	0.965796i	0.896213	−	0.443623i	$-0.146307\pi$
$644$	0.450101	−	0.619510i	0.0177364	−	0.0244121i
$645$		0			0
$646$	34.1168	+	4.62143i	1.34231	+	0.181828i
$647$	2.70605	+	3.09733i	0.106386	+	0.121769i	0.803799	−	0.594901i	$-0.202809\pi$
$647$	2.70605	+	3.09733i	0.106386	+	0.121769i	−0.697413	+	0.716669i	$0.745666\pi$
$648$		0			0
$649$	−0.292144	−	2.15669i	−0.0114676	−	0.0846576i
$650$	−52.7238	+	31.5010i	−2.06800	+	1.23557i
$651$		0			0
$652$	6.62345	−	11.0858i	0.259394	−	0.434153i
$653$	−9.89550	+	7.18950i	−0.387241	+	0.281347i	−0.764324	−	0.644832i	$-0.776927\pi$
$653$	−9.89550	+	7.18950i	−0.387241	+	0.281347i	0.377083	+	0.926179i	$0.376927\pi$
$654$		0			0
$655$	−29.6709	−	2.67043i	−1.15934	−	0.104342i
$656$	4.19480	−	12.9103i	0.163779	−	0.504061i
$657$		0			0
$658$	0.868926	−	1.31637i	0.0338743	−	0.0513173i
$659$	32.6081	+	26.0041i	1.27023	+	1.01298i	0.998722	+	0.0505417i	$0.0160948\pi$
$659$	32.6081	+	26.0041i	1.27023	+	1.01298i	0.271511	+	0.962435i	$0.412477\pi$
$660$		0			0
$661$	11.0146	−	39.9104i	0.428417	−	1.55233i	−0.357446	−	0.933934i	$-0.616352\pi$
$661$	11.0146	−	39.9104i	0.428417	−	1.55233i	0.785863	−	0.618401i	$-0.212219\pi$
$662$	49.4620	+	23.8197i	1.92240	+	0.925777i
$663$		0			0
$664$	−6.36031	−	19.5750i	−0.246828	−	0.759658i
$665$	1.12642	+	4.93515i	0.0436805	+	0.191377i
$666$		0			0
$667$	−1.35707	+	7.47809i	−0.0525461	+	0.289553i
$668$	0.854784	+	3.09724i	0.0330726	+	0.119836i
$669$		0			0
$670$	−3.76142	−	41.7928i	−0.145316	−	1.61460i
$671$	4.98604	−	3.97623i	0.192484	−	0.153501i
$672$		0			0
$673$	5.69756	+	11.8311i	0.219625	+	0.456056i	0.981448	−	0.191730i	$-0.0614097\pi$
$673$	5.69756	+	11.8311i	0.219625	+	0.456056i	−0.761823	+	0.647785i	$0.775695\pi$
$674$	−10.8910	+	11.3910i	−0.419504	+	0.438767i
$675$		0			0
$676$	−26.5258	+	12.7741i	−1.02022	+	0.491313i
$677$	−8.38534	−	46.2070i	−0.322275	−	1.77588i	−0.585023	−	0.811017i	$-0.698915\pi$
$677$	−8.38534	−	46.2070i	−0.322275	−	1.77588i	0.262748	−	0.964864i	$-0.415371\pi$
$678$		0			0
$679$	7.02523	−	0.632282i	0.269604	−	0.0242648i
$680$	−4.83318	+	21.1756i	−0.185344	+	0.812046i
$681$		0			0
$682$	13.1709	+	2.39017i	0.504340	+	0.0915242i
$683$	8.31845	+	15.4583i	0.318297	+	0.591494i	0.988595	−	0.150597i	$-0.0481197\pi$
$683$	8.31845	+	15.4583i	0.318297	+	0.591494i	−0.670299	+	0.742092i	$0.733834\pi$
$684$		0			0
$685$	−26.1893	+	8.50942i	−1.00064	+	0.325128i
$686$	−9.75050	+	3.65942i	−0.372276	+	0.139717i
$687$		0			0
$688$	57.2852	+	15.8097i	2.18398	+	0.602739i
$689$	18.1692	+	9.77728i	0.692192	+	0.372485i
$690$		0			0
$691$	29.4993	+	19.4723i	1.12221	+	0.740762i	0.968909	−	0.247418i	$-0.0795822\pi$
$691$	29.4993	+	19.4723i	1.12221	+	0.740762i	0.153297	+	0.988180i	$0.451011\pi$
$692$	0.881688	+	19.6323i	0.0335167	+	0.746308i
$693$		0			0
$694$	2.91149	−	32.3493i	0.110519	−	1.22796i
$695$	16.1368	+	24.4462i	0.612104	+	0.927297i
$696$		0			0
$697$	−12.0709	−	7.21202i	−0.457217	−	0.273175i
$698$	−10.0744	+	23.5702i	−0.381322	+	0.892146i
$699$		0			0
$700$	2.97972	−	0.403630i	0.112623	−	0.0152558i
$701$	1.48897	+	1.30087i	0.0562376	+	0.0491334i	0.685599	−	0.727980i	$-0.259540\pi$
$701$	1.48897	+	1.30087i	0.0562376	+	0.0491334i	−0.629361	+	0.777113i	$0.716683\pi$
$702$		0			0
$703$	0.714769	−	5.27664i	0.0269580	−	0.199012i
$704$	−0.452314	−	1.05824i	−0.0170472	−	0.0398839i
$705$		0			0
$706$	−34.0378	−	1.52864i	−1.28103	−	0.0575311i
$707$	3.39423	+	1.27388i	0.127653	+	0.0479090i
$708$		0			0
$709$			2.08770i			0.0784052i	0.999231	+	0.0392026i	$0.0124818\pi$
$709$			2.08770i			0.0784052i	−0.999231	+	0.0392026i	$0.987518\pi$
$710$	−49.5956	−	4.49067i	−1.86129	−	0.168532i
$711$		0			0
$712$	9.14714	+	9.56716i	0.342804	+	0.358545i
$713$	−5.09562	+	13.5772i	−0.190832	+	0.508471i
$714$		0			0
$715$	11.6247	+	8.44587i	0.434741	+	0.315858i
$716$	21.6315	−	9.24576i	0.808408	−	0.345530i
$717$		0			0
$718$	−34.8339	+	30.4335i	−1.29999	+	1.13577i
$719$	22.1288	−	25.3285i	0.825266	−	0.944593i	−0.173927	−	0.984758i	$-0.555646\pi$
$719$	22.1288	−	25.3285i	0.825266	−	0.944593i	0.999193	+	0.0401658i	$0.0127886\pi$
$720$		0			0
$721$	−1.66300	−	2.78340i	−0.0619335	−	0.103659i
$722$	−8.48328	−	3.62593i	−0.315715	−	0.134943i
$723$		0			0
$724$	−8.30462	−	11.4303i	−0.308639	−	0.424805i
$725$	−24.9071	+	16.4411i	−0.925028	+	0.610606i
$726$		0			0
$727$	17.6768	+	5.74353i	0.655595	+	0.213016i	0.617880	−	0.786273i	$-0.287992\pi$
$727$	17.6768	+	5.74353i	0.655595	+	0.213016i	0.0377158	+	0.999289i	$0.487992\pi$
$728$	−3.25504	+	0.146184i	−0.120640	+	0.00541794i
$729$		0			0
$730$	4.91446	−	6.16254i	0.181892	−	0.228086i
$731$	29.1700	−	54.2069i	1.07889	−	2.00492i
$732$		0			0
$733$	2.18065	−	4.52818i	0.0805443	−	0.167252i	−0.856807	−	0.515637i	$-0.827555\pi$
$733$	2.18065	−	4.52818i	0.0805443	−	0.167252i	0.937352	+	0.348385i	$0.113270\pi$
$734$	8.73377	+	23.2711i	0.322369	+	0.858950i
$735$		0			0
$736$	8.84330	−	2.01843i	0.325968	−	0.0744002i
$737$	−4.58686	+	2.46830i	−0.168959	+	0.0909208i
$738$		0			0
$739$	36.5887	−	10.0978i	1.34594	−	0.371455i	0.482494	−	0.875899i	$-0.339731\pi$
$739$	36.5887	−	10.0978i	1.34594	−	0.371455i	0.863444	+	0.504444i	$0.168303\pi$
$740$	−5.81195	−	1.32654i	−0.213651	−	0.0487645i
$741$		0			0
$742$	−1.61457	−	2.02460i	−0.0592726	−	0.0743255i
$743$	27.3891	−	4.97038i	1.00481	−	0.182346i	0.348878	−	0.937168i	$-0.386563\pi$
$743$	27.3891	−	4.97038i	1.00481	−	0.182346i	0.655929	+	0.754822i	$0.272277\pi$
$744$		0			0
$745$	−9.34080	−	8.93072i	−0.342221	−	0.327196i
$746$	−43.1686	−	41.2734i	−1.58052	−	1.51113i
$747$		0			0
$748$	−4.70771	+	0.854323i	−0.172131	+	0.0312371i
$749$	−1.37262	−	1.72121i	−0.0501544	−	0.0628916i
$750$		0			0
$751$	18.9887	+	4.33406i	0.692909	+	0.158152i	0.554451	−	0.832216i	$-0.312928\pi$
$751$	18.9887	+	4.33406i	0.692909	+	0.158152i	0.138458	+	0.990368i	$0.455785\pi$
$752$	9.93587	−	2.74212i	0.362324	−	0.0999950i
$753$		0			0
$754$	−50.5363	+	27.1947i	−1.84042	+	0.990373i
$755$	16.7370	−	3.82011i	0.609121	−	0.139028i
$756$		0			0
$757$	9.70380	+	25.8557i	0.352691	+	0.939741i	0.986134	+	0.165952i	$0.0530695\pi$
$757$	9.70380	+	25.8557i	0.352691	+	0.939741i	−0.633443	+	0.773789i	$0.718359\pi$
$758$	27.4057	−	56.9085i	0.995419	−	2.06701i
$759$		0			0
$760$	−7.52779	+	13.9890i	−0.273062	+	0.507434i
$761$	33.3441	−	41.8121i	1.20872	−	1.51569i	0.412183	−	0.911101i	$-0.364767\pi$
$761$	33.3441	−	41.8121i	1.20872	−	1.51569i	0.796539	−	0.604587i	$-0.206662\pi$
$762$		0			0
$763$	−6.53777	+	0.293612i	−0.236683	+	0.0106295i
$764$	5.65236	+	1.83656i	0.204495	+	0.0664445i
$765$		0			0
$766$	19.9009	−	13.1364i	0.719048	−	0.474639i
$767$	10.4648	+	14.4035i	0.377861	+	0.520081i
$768$		0			0
$769$	−13.3239	−	5.69490i	−0.480471	−	0.205363i	0.139139	−	0.990273i	$-0.455567\pi$
$769$	−13.3239	−	5.69490i	−0.480471	−	0.205363i	−0.619610	+	0.784910i	$0.712709\pi$
$770$	−0.924963	−	1.54813i	−0.0333334	−	0.0557907i
$771$		0			0
$772$	7.11318	−	8.14169i	0.256009	−	0.293026i
$773$	−0.0520122	+	0.0454416i	−0.00187075	+	0.00163442i	−0.658874	−	0.752254i	$-0.728967\pi$
$773$	−0.0520122	+	0.0454416i	−0.00187075	+	0.00163442i	0.657003	+	0.753888i	$0.271824\pi$
$774$		0			0
$775$	−52.3629	+	22.3810i	−1.88093	+	0.803948i
$776$	17.9082	+	13.0111i	0.642867	+	0.467070i
$777$		0			0
$778$	−23.0961	+	61.5394i	−0.828036	+	2.20629i
$779$	−7.10705	−	7.43339i	−0.254636	−	0.266329i
$780$		0			0
$781$	1.90705	+	5.88010i	0.0682397	+	0.210407i
$782$		−	13.2879i		−	0.475173i
$783$		0			0
$784$	−31.4602	−	11.8072i	−1.12358	−	0.421686i
$785$	2.79513	+	0.125530i	0.0997626	+	0.00448034i
$786$		0			0
$787$	16.7590	+	39.2097i	0.597395	+	1.39768i	0.896324	+	0.443400i	$0.146228\pi$
$787$	16.7590	+	39.2097i	0.597395	+	1.39768i	−0.298929	+	0.954275i	$0.596629\pi$
$788$	−3.66962	+	27.0902i	−0.130725	+	0.965049i
$789$		0			0
$790$	49.7776	+	43.4893i	1.77101	+	1.54728i
$791$	1.39549	−	0.189032i	0.0496179	−	0.00672120i
$792$		0			0
$793$	−20.5039	+	47.9713i	−0.728115	+	1.70351i
$794$	23.4000	+	13.9808i	0.830434	+	0.496161i
$795$		0			0
$796$	−0.384186	−	0.582016i	−0.0136171	−	0.0206290i
$797$	3.77551	−	41.9493i	0.133735	−	1.48592i	−0.596437	−	0.802660i	$-0.703418\pi$
$797$	3.77551	−	41.9493i	0.133735	−	1.48592i	0.730173	−	0.683262i	$-0.239440\pi$
$798$		0			0
$799$	−0.479014	−	10.6661i	−0.0169463	−	0.377338i
$800$	29.7262	+	19.6221i	1.05098	+	0.693745i
$801$		0			0
$802$	−4.62871	−	2.49081i	−0.163445	−	0.0879536i
$803$	−0.943176	−	0.260300i	−0.0332840	−	0.00918579i
$804$		0			0
$805$	1.82916	−	0.686496i	0.0644695	−	0.0241958i
$806$	−104.143	+	33.8383i	−3.66830	+	1.19190i
$807$		0			0
$808$	5.39133	+	10.0188i	0.189667	+	0.352459i
$809$	42.2193	+	7.66168i	1.48435	+	0.269370i	0.859404	−	0.511296i	$-0.170835\pi$
$809$	42.2193	+	7.66168i	1.48435	+	0.269370i	0.624948	+	0.780667i	$0.285120\pi$
$810$		0			0
$811$	11.6891	−	51.2132i	0.410459	−	1.79834i	−0.171571	−	0.985172i	$-0.554884\pi$
$811$	11.6891	−	51.2132i	0.410459	−	1.79834i	0.582030	−	0.813167i	$-0.302259\pi$
$812$	2.79838	−	0.251858i	0.0982038	−	0.00883850i
$813$		0			0
$814$	0.338725	+	1.86653i	0.0118723	+	0.0654217i
$815$	29.6851	−	14.2956i	1.03982	−	0.500752i
$816$		0			0
$817$	31.1131	−	32.5417i	1.08851	−	1.13849i
$818$	4.03928	+	8.38764i	0.141230	+	0.293267i
$819$		0			0
$820$	−9.00178	+	7.17868i	−0.314356	+	0.250690i
$821$	1.15595	+	12.8437i	0.0403429	+	0.448247i	0.990601	+	0.136783i	$0.0436764\pi$
$821$	1.15595	+	12.8437i	0.0403429	+	0.448247i	−0.950258	+	0.311464i	$0.899181\pi$
$822$		0			0
$823$	9.32150	+	33.7757i	0.324927	+	1.17735i	0.925804	+	0.378005i	$0.123390\pi$
$823$	9.32150	+	33.7757i	0.324927	+	1.17735i	−0.600877	+	0.799342i	$0.705182\pi$
$824$	1.81685	−	10.0117i	0.0632930	−	0.348773i
$825$		0			0
$826$	−0.497220	−	2.17846i	−0.0173005	−	0.0757984i
$827$	−7.19931	−	22.1572i	−0.250345	−	0.770481i	−0.994711	−	0.102710i	$-0.967249\pi$
$827$	−7.19931	−	22.1572i	−0.250345	−	0.770481i	0.744367	−	0.667771i	$-0.232751\pi$
$828$		0			0
$829$	9.58217	+	4.61453i	0.332803	+	0.160269i	0.592821	−	0.805334i	$-0.298014\pi$
$829$	9.58217	+	4.61453i	0.332803	+	0.160269i	−0.260018	+	0.965604i	$0.583729\pi$
$830$	−24.7920	+	89.8316i	−0.860541	+	3.11810i
$831$		0			0
$832$	7.36050	+	5.86980i	0.255179	+	0.203499i
$833$	−19.1754	+	29.0494i	−0.664387	+	1.00650i
$834$		0			0
$835$	−2.53322	+	7.79646i	−0.0876658	+	0.269808i
$836$	−3.48530	−	0.313683i	−0.120542	−	0.0108490i
$837$		0			0
$838$	33.1013	−	24.0495i	1.14346	−	0.830776i
$839$	15.7602	−	26.3782i	0.544104	−	0.910677i	−0.455685	−	0.890141i	$-0.650606\pi$
$839$	15.7602	−	26.3782i	0.544104	−	0.910677i	0.999789	−	0.0205358i	$-0.00653719\pi$
$840$		0			0
$841$	0.955888	−	0.571116i	0.0329616	−	0.0196937i
$842$	−5.84152	−	43.1239i	−0.201312	−	1.48615i
$843$		0			0
$844$	−20.9847	−	24.0189i	−0.722323	−	0.826765i
$845$	−74.4365	−	10.0831i	−2.56069	−	0.346869i
$846$		0			0
$847$	2.55774	−	3.52043i	0.0878851	−	0.120964i
$848$	0.759216	−	16.9053i	0.0260716	−	0.580529i
$849$		0			0
$850$	37.7140	−	36.0583i	1.29358	−	1.23679i
$851$	−2.05516			−0.0704499
$852$		0			0
$853$	−37.2260			−1.27459			−0.637297	−	0.770618i	$-0.719948\pi$
$853$	−37.2260			−1.27459			−0.637297	+	0.770618i	$0.719948\pi$
$854$	4.73259	−	4.52481i	0.161946	−	0.154836i
$855$		0			0
$856$	0.309962	−	6.90184i	0.0105943	−	0.235900i
$857$	6.12025	−	8.42380i	0.209064	−	0.287752i	−0.691589	−	0.722291i	$-0.743089\pi$
$857$	6.12025	−	8.42380i	0.209064	−	0.287752i	0.900653	+	0.434540i	$0.143089\pi$
$858$		0			0
$859$	16.1010	+	2.18103i	0.549359	+	0.0744157i	0.403653	−	0.914912i	$-0.367740\pi$
$859$	16.1010	+	2.18103i	0.549359	+	0.0744157i	0.145706	+	0.989328i	$0.453455\pi$
$860$	−33.1630	−	37.9581i	−1.13085	−	1.29436i
$861$		0			0
$862$	0.570882	+	4.21442i	0.0194443	+	0.143544i
$863$	−7.82419	+	4.67474i	−0.266339	+	0.159130i	−0.639860	−	0.768492i	$-0.721008\pi$
$863$	−7.82419	+	4.67474i	−0.266339	+	0.159130i	0.373521	+	0.927622i	$0.378150\pi$
$864$		0			0
$865$	−25.7168	+	43.0427i	−0.874398	+	1.46350i
$866$	28.3555	−	20.6015i	0.963560	−	0.700068i
$867$		0			0
$868$	5.33956	+	0.480569i	0.181236	+	0.0163116i
$869$	2.53551	−	7.80350i	0.0860114	−	0.264716i
$870$		0			0
$871$	23.4738	−	35.5613i	0.795380	−	1.20495i
$872$	−16.0569	−	12.8050i	−0.543756	−	0.433631i
$873$		0			0
$874$	2.58550	−	9.36834i	0.0874558	−	0.316889i
$875$	0.796802	+	0.383720i	0.0269368	+	0.0129721i
$876$		0			0
$877$	−10.7696	−	33.1453i	−0.363663	−	1.11924i	−0.950814	−	0.309762i	$-0.899751\pi$
$877$	−10.7696	−	33.1453i	−0.363663	−	1.11924i	0.587152	−	0.809477i	$-0.300249\pi$
$878$	−6.08916	−	26.6784i	−0.205499	−	0.900351i
$879$		0			0
$880$	2.10427	−	11.5955i	0.0709350	−	0.390884i
$881$	2.28328	+	8.27329i	0.0769257	+	0.278734i	0.992298	−	0.123875i	$-0.0395321\pi$
$881$	2.28328	+	8.27329i	0.0769257	+	0.278734i	−0.915372	+	0.402609i	$0.868104\pi$
$882$		0			0
$883$	−5.08093	−	56.4537i	−0.170987	−	1.89982i	−0.384887	−	0.922964i	$-0.625760\pi$
$883$	−5.08093	−	56.4537i	−0.170987	−	1.89982i	0.213900	−	0.976856i	$-0.431383\pi$
$884$	30.6008	−	24.4033i	1.02922	−	0.820773i
$885$		0			0
$886$	25.7893	+	53.5520i	0.866407	+	1.79911i
$887$	−18.8402	+	19.7053i	−0.632591	+	0.661638i	−0.958939	−	0.283611i	$-0.908467\pi$
$887$	−18.8402	+	19.7053i	−0.632591	+	0.661638i	0.326348	+	0.945250i	$0.394182\pi$
$888$		0			0
$889$	−1.31202	+	0.631835i	−0.0440037	+	0.0211911i
$890$	−10.7008	−	58.9665i	−0.358693	−	1.97656i
$891$		0			0
$892$	13.6947	−	1.23254i	0.458532	−	0.0412686i
$893$	1.73764	−	7.61310i	0.0581479	−	0.254763i
$894$		0			0
$895$	59.0558	+	10.7171i	1.97402	+	0.358232i
$896$	1.92455	+	3.57641i	0.0642947	+	0.119480i
$897$		0			0
$898$	−43.9210	+	14.2708i	−1.46566	+	0.476223i
$899$	−49.8170	+	18.6966i	−1.66149	+	0.623568i
$900$		0			0
$901$	−16.8973	−	4.66335i	−0.562929	−	0.155359i
$902$	3.22636	+	1.73618i	0.107426	+	0.0578084i
$903$		0			0
$904$	3.68826	+	2.43460i	0.122670	+	0.0809735i
$905$	−1.61727	−	36.0114i	−0.0537600	−	1.19706i
$906$		0			0
$907$	1.34743	−	14.9712i	0.0447408	−	0.497111i	−0.942091	−	0.335359i	$-0.891143\pi$
$907$	1.34743	−	14.9712i	0.0447408	−	0.497111i	0.986831	−	0.161752i	$-0.0517146\pi$
$908$	−2.93864	−	4.45185i	−0.0975222	−	0.147740i
$909$		0			0
$910$	12.6643	+	7.56657i	0.419818	+	0.250829i
$911$	−16.1042	+	37.6776i	−0.533556	+	1.24832i	0.408469	+	0.912772i	$0.366063\pi$
$911$	−16.1042	+	37.6776i	−0.533556	+	1.24832i	−0.942025	+	0.335543i	$0.891080\pi$
$912$		0			0
$913$	11.4632	−	1.55280i	0.379377	−	0.0513901i
$914$	1.36709	+	1.19439i	0.0452194	+	0.0395070i
$915$		0			0
$916$	−3.66225	+	27.0358i	−0.121004	+	0.893288i
$917$	1.49221	+	3.49119i	0.0492770	+	0.115289i
$918$		0			0
$919$	15.8422	+	0.711473i	0.522586	+	0.0234693i	0.304596	−	0.952482i	$-0.401479\pi$
$919$	15.8422	+	0.711473i	0.522586	+	0.0234693i	0.217990	+	0.975951i	$0.430050\pi$
$920$	5.74029	+	2.15437i	0.189252	+	0.0710274i
$921$		0			0
$922$		−	61.8656i		−	2.03743i
$923$	−36.5315	−	34.9654i	−1.20245	−	1.15090i
$924$		0			0
$925$	−5.57693	−	5.83301i	−0.183368	−	0.191788i
$926$	9.68001	−	25.7923i	0.318105	−	0.847588i
$927$		0			0
$928$	26.9257	+	19.5626i	0.883879	+	0.642175i
$929$	3.35734	−	1.43500i	0.110151	−	0.0470807i	−0.337244	−	0.941417i	$-0.609495\pi$
$929$	3.35734	−	1.43500i	0.110151	−	0.0470807i	0.447395	+	0.894337i	$0.352352\pi$
$930$		0			0
$931$	−19.1715	+	16.7496i	−0.628321	+	0.548947i
$932$	10.3178	−	11.8096i	0.337969	−	0.386837i
$933$		0			0
$934$	37.8020	+	63.2699i	1.23692	+	2.07025i
$935$	−11.2250	−	4.79780i	−0.367097	−	0.156905i
$936$		0			0
$937$	−4.46277	−	6.14247i	−0.145792	−	0.200666i	0.729875	−	0.683580i	$-0.239578\pi$
$937$	−4.46277	−	6.14247i	−0.145792	−	0.200666i	−0.875667	+	0.482915i	$0.839578\pi$
$938$	−4.46318	+	2.94612i	−0.145728	+	0.0961943i
$939$		0			0
$940$	−8.31454	−	2.70156i	−0.271191	−	0.0881151i
$941$	29.6562	−	1.33186i	0.966765	−	0.0434174i	0.444119	−	0.895968i	$-0.353517\pi$
$941$	29.6562	−	1.33186i	0.966765	−	0.0434174i	0.522645	+	0.852550i	$0.324945\pi$
$942$		0			0
$943$	−2.47480	+	3.10330i	−0.0805907	+	0.101057i
$944$	6.91940	−	12.8584i	0.225207	−	0.418505i
$945$		0			0
$946$	−6.95927	+	14.4511i	−0.226265	+	0.469845i
$947$	9.02813	+	24.0554i	0.293375	+	0.781694i	0.997437	+	0.0715555i	$0.0227963\pi$
$947$	9.02813	+	24.0554i	0.293375	+	0.781694i	−0.704062	+	0.710139i	$0.748632\pi$
$948$		0			0
$949$	7.80332	−	1.78106i	0.253306	−	0.0578155i
$950$	33.6056	−	18.0839i	1.09031	−	0.586720i
$951$		0			0
$952$	2.66839	−	0.736430i	0.0864831	−	0.0238678i
$953$	−1.94155	−	0.443145i	−0.0628928	−	0.0143549i	0.190959	−	0.981598i	$-0.438840\pi$
$953$	−1.94155	−	0.443145i	−0.0628928	−	0.0143549i	−0.253852	+	0.967243i	$0.581697\pi$
$954$		0			0
$955$	9.45429	+	11.8553i	0.305934	+	0.383629i
$956$	−23.8000	+	4.31906i	−0.769746	+	0.139688i
$957$		0			0
$958$	16.4738	+	15.7506i	0.532244	+	0.508877i
$959$	2.53664	+	2.42528i	0.0819125	+	0.0783164i
$960$		0			0
$961$	−69.3961	+	12.5935i	−2.23858	+	0.406243i
$962$	−9.67551	−	12.1327i	−0.311951	−	0.391174i
$963$		0			0
$964$	27.9331	+	6.37556i	0.899666	+	0.205343i
$965$	26.5898	−	7.33832i	0.855956	−	0.236229i
$966$		0			0
$967$	11.3705	−	6.11871i	0.365650	−	0.196764i	−0.280719	−	0.959790i	$-0.590573\pi$
$967$	11.3705	−	6.11871i	0.365650	−	0.196764i	0.646368	+	0.763026i	$0.276287\pi$
$968$	13.3135	−	3.03872i	0.427913	−	0.0976683i
$969$		0			0
$970$	−35.2158	−	93.8323i	−1.13071	−	3.01277i
$971$	−20.5708	+	42.7156i	−0.660147	+	1.37081i	0.254704	+	0.967019i	$0.418022\pi$
$971$	−20.5708	+	42.7156i	−0.660147	+	1.37081i	−0.914851	+	0.403790i	$0.867692\pi$
$972$		0			0
$973$	1.76902	−	3.28739i	0.0567121	−	0.105389i
$974$	12.4795	−	15.6487i	0.399868	−	0.501418i
$975$		0			0
$976$	42.7444	−	1.91965i	1.36821	−	0.0614465i
$977$	−28.6466	−	9.30784i	−0.916486	−	0.297784i	−0.187461	−	0.982272i	$-0.560026\pi$
$977$	−28.6466	−	9.30784i	−0.916486	−	0.297784i	−0.729024	+	0.684488i	$0.760026\pi$
$978$		0			0
$979$	−6.20857	+	4.09824i	−0.198427	+	0.130980i
$980$	16.7526	+	23.0580i	0.535142	+	0.736560i
$981$		0			0
$982$	7.24085	+	3.09489i	0.231065	+	0.0987619i
$983$	26.1031	+	43.6893i	0.832560	+	1.39347i	0.917772	+	0.397108i	$0.129986\pi$
$983$	26.1031	+	43.6893i	0.832560	+	1.39347i	−0.0852113	+	0.996363i	$0.527157\pi$
$984$		0			0
$985$	−45.8905	+	52.5259i	−1.46219	+	1.67361i
$986$	36.7163	−	32.0780i	1.16928	−	1.02157i
$987$		0			0
$988$	26.3228	−	11.2509i	0.837439	−	0.357939i
$989$	−14.0580	−	10.2137i	−0.447017	−	0.324777i
$990$		0			0
$991$	7.97510	−	21.2496i	0.253337	−	0.675015i	−0.746615	−	0.665256i	$-0.768322\pi$
$991$	7.97510	−	21.2496i	0.253337	−	0.675015i	0.999952	−	0.00975855i	$-0.00310629\pi$
$992$	43.8860	+	45.9011i	1.39338	+	1.45736i
$993$		0			0
$994$	2.49124	+	5.83725i	0.0790172	+	0.185146i
$995$		−	1.77929i		−	0.0564073i
$996$		0			0
$997$	−2.34449	−	0.879900i	−0.0742506	−	0.0278667i	0.313973	−	0.949432i	$-0.398340\pi$
$997$	−2.34449	−	0.879900i	−0.0742506	−	0.0278667i	−0.388224	+	0.921565i	$0.626911\pi$
$998$	−28.8240	−	1.29449i	−0.912409	−	0.0409763i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.485.5	yes	576
3.2	odd	2	inner	639.2.z.a.485.20	yes	576
71.65	odd	70	inner	639.2.z.a.278.20	yes	576
213.65	even	70	inner	639.2.z.a.278.5	✓	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.278.5	✓	576	213.65	even	70	inner
639.2.z.a.278.20	yes	576	71.65	odd	70	inner
639.2.z.a.485.5	yes	576	1.1	even	1	trivial
639.2.z.a.485.20	yes	576	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.30887 + 1.25141i) q^{2} +(0.0573898 - 1.27788i) q^{4} +(1.91833 - 2.64036i) q^{5} +(-0.412177 - 0.0558332i) q^{7} +(-0.858815 - 0.982992i) q^{8} +O(q^{10})\)	\(q+(-1.30887 + 1.25141i) q^{2} +(0.0573898 - 1.27788i) q^{4} +(1.91833 - 2.64036i) q^{5} +(-0.412177 - 0.0558332i) q^{7} +(-0.858815 - 0.982992i) q^{8} +(0.793318 + 5.85651i) q^{10} +(0.629778 - 0.376275i) q^{11} +(-3.07808 + 5.15183i) q^{13} +(0.609357 - 0.442724i) q^{14} +(4.90225 + 0.441210i) q^{16} +(1.57553 - 4.84897i) q^{17} +(2.05429 - 3.11211i) q^{19} +(-3.26398 - 2.60293i) q^{20} +(-0.353425 + 1.28061i) q^{22} +(-1.29670 - 0.624458i) q^{23} +(-1.74640 - 5.37488i) q^{25} +(-2.41825 - 10.5950i) q^{26} +(-0.0950031 + 0.523510i) q^{28} +(-1.40488 - 5.09046i) q^{29} +(-0.903222 - 10.0356i) q^{31} +(-4.92748 + 3.92954i) q^{32} +(4.00589 + 8.31831i) q^{34} +(-0.938112 + 0.981188i) q^{35} +(1.28654 - 0.619567i) q^{37} +(1.20573 + 6.64411i) q^{38} +(-4.24294 + 0.381872i) q^{40} +(0.613695 - 2.68877i) q^{41} +(11.8795 + 2.15581i) q^{43} +(-0.444693 - 0.826377i) q^{44} +(2.47867 - 0.805368i) q^{46} +(1.96057 - 0.735815i) q^{47} +(-6.58097 - 1.81623i) q^{49} +(9.01200 + 4.84956i) q^{50} +(6.40679 + 4.22909i) q^{52} +(-0.154248 - 3.43459i) q^{53} +(0.214623 - 2.38466i) q^{55} +(0.299100 + 0.453117i) q^{56} +(8.20906 + 4.90468i) q^{58} +(1.16596 - 2.72790i) q^{59} +(8.61432 - 1.16689i) q^{61} +(13.7409 + 12.0050i) q^{62} +(0.210575 - 1.55453i) q^{64} +(7.69791 + 18.0102i) q^{65} +(-7.09298 - 0.318546i) q^{67} +(-6.10600 - 2.29162i) q^{68} -2.45821i q^{70} +(-1.87943 + 8.21388i) q^{71} +(-0.921673 - 0.963994i) q^{73} +(-0.908590 + 2.42093i) q^{74} +(-3.85902 - 2.80374i) q^{76} +(-0.280589 + 0.119929i) q^{77} +(8.42260 - 7.35861i) q^{79} +(10.5691 - 12.0973i) q^{80} +(2.56151 + 4.28724i) q^{82} +(14.4993 + 6.19729i) q^{83} +(-9.78064 - 13.4619i) q^{85} +(-18.2466 + 12.0445i) q^{86} +(-0.910738 - 0.295917i) q^{88} +(-10.1302 + 0.454946i) q^{89} +(1.55636 - 1.95161i) q^{91} +(-0.872402 + 1.62119i) q^{92} +(-1.64533 + 3.41657i) q^{94} +(-4.27628 - 11.3941i) q^{95} +(-16.5330 + 3.77356i) q^{97} +(10.8865 - 5.85827i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 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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