LMFDB - Embedded newform 275.2.e.d.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(32,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("275.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.e (of order $4$, degree $2$, 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6879707136000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{12} + 86x^{8} + 36x^{4} + 1 $ x^16 + 21x^12 + 86x^8 + 36*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-0.294032 - 0.294032i$ of defining polynomial
Character	$\chi$	$=$	275.43
Dual form			275.2.e.d.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 - 1.34500i) q^{2} +(-1.98168 - 1.98168i) q^{3} +1.61803i q^{4} +5.33070i q^{6} +(3.00750 + 3.00750i) q^{7} +(-0.513743 + 0.513743i) q^{8} +4.85410i q^{9} +O(q^{10})$	\(q+(-1.34500 - 1.34500i) q^{2} +(-1.98168 - 1.98168i) q^{3} +1.61803i q^{4} +5.33070i q^{6} +(3.00750 + 3.00750i) q^{7} +(-0.513743 + 0.513743i) q^{8} +4.85410i q^{9} +(-2.61803 + 2.03615i) q^{11} +(3.20642 - 3.20642i) q^{12} +(-2.17625 + 2.17625i) q^{13} -8.09017i q^{14} +4.61803 q^{16} +(0.831254 + 0.831254i) q^{17} +(6.52875 - 6.52875i) q^{18} +1.25841 q^{19} -11.9198i q^{21} +(6.25986 + 0.782635i) q^{22} +(0.756934 + 0.756934i) q^{23} +2.03615 q^{24} +5.85410 q^{26} +(3.67423 - 3.67423i) q^{27} +(-4.86624 + 4.86624i) q^{28} -8.62526 q^{29} +1.47214 q^{31} +(-5.18376 - 5.18376i) q^{32} +(9.22309 + 1.15311i) q^{33} -2.23607i q^{34} -7.85410 q^{36} +(-6.70197 + 6.70197i) q^{37} +(-1.69256 - 1.69256i) q^{38} +8.62526 q^{39} +7.84752i q^{41} +(-16.0321 + 16.0321i) q^{42} +(3.71748 - 3.71748i) q^{43} +(-3.29456 - 4.23607i) q^{44} -2.03615i q^{46} +(4.25248 - 4.25248i) q^{47} +(-9.15146 - 9.15146i) q^{48} +11.0902i q^{49} -3.29456i q^{51} +(-3.52125 - 3.52125i) q^{52} +(4.14205 + 4.14205i) q^{53} -9.88367 q^{54} -3.09017 q^{56} +(-2.49376 - 2.49376i) q^{57} +(11.6009 + 11.6009i) q^{58} +1.00000i q^{59} +5.81137i q^{61} +(-1.98002 - 1.98002i) q^{62} +(-14.5987 + 14.5987i) q^{63} +4.70820i q^{64} +(-10.8541 - 13.9560i) q^{66} +(4.89898 - 4.89898i) q^{67} +(-1.34500 + 1.34500i) q^{68} -3.00000i q^{69} +0.291796 q^{71} +(-2.49376 - 2.49376i) q^{72} +(-7.99503 + 7.99503i) q^{73} +18.0283 q^{74} +2.03615i q^{76} +(-13.9975 - 1.75003i) q^{77} +(-11.6009 - 11.6009i) q^{78} +0.480669 q^{79} +(10.5549 - 10.5549i) q^{82} +(-0.196232 + 0.196232i) q^{83} +19.2867 q^{84} -10.0000 q^{86} +(17.0925 + 17.0925i) q^{87} +(0.298940 - 2.39105i) q^{88} -9.32624i q^{89} -13.0902 q^{91} +(-1.22474 + 1.22474i) q^{92} +(-2.91730 - 2.91730i) q^{93} -11.4391 q^{94} +20.5451i q^{96} +(-0.178688 + 0.178688i) q^{97} +(14.9162 - 14.9162i) q^{98} +(-9.88367 - 12.7082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 24 q^{11} + 56 q^{16} + 40 q^{26} - 48 q^{31} - 72 q^{36} + 40 q^{56} - 120 q^{66} + 112 q^{71} - 160 q^{86} - 120 q^{91}+O(q^{100}) $ 16 * q - 24 * q^11 + 56 * q^16 + 40 * q^26 - 48 * q^31 - 72 * q^36 + 40 * q^56 - 120 * q^66 + 112 * q^71 - 160 * q^86 - 120 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.34500	−	1.34500i	−0.951057	−	0.951057i	0.0478004	−	0.998857i	$-0.484779\pi$
$2$	−1.34500	−	1.34500i	−0.951057	−	0.951057i	−0.998857	+	0.0478004i	$0.984779\pi$
$3$	−1.98168	−	1.98168i	−1.14412	−	1.14412i	−0.987688	−	0.156434i	$-0.950000\pi$
$3$	−1.98168	−	1.98168i	−1.14412	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$4$			1.61803i			0.809017i
$5$		0			0
$5$		0			0
$6$			5.33070i			2.17625i
$7$	3.00750	+	3.00750i	1.13673	+	1.13673i	0.989033	+	0.147697i	$0.0471862\pi$
$7$	3.00750	+	3.00750i	1.13673	+	1.13673i	0.147697	+	0.989033i	$0.452814\pi$
$8$	−0.513743	+	0.513743i	−0.181636	+	0.181636i
$9$			4.85410i			1.61803i
$10$		0			0
$11$	−2.61803	+	2.03615i	−0.789367	+	0.613922i
$11$	−2.61803	+	2.03615i	−0.789367	+	0.613922i
$12$	3.20642	−	3.20642i	0.925615	−	0.925615i
$13$	−2.17625	+	2.17625i	−0.603583	+	0.603583i	−0.941262	−	0.337678i	$-0.890358\pi$
$13$	−2.17625	+	2.17625i	−0.603583	+	0.603583i	0.337678	+	0.941262i	$0.390358\pi$
$14$		−	8.09017i		−	2.16219i
$15$		0			0
$16$	4.61803			1.15451
$17$	0.831254	+	0.831254i	0.201609	+	0.201609i	0.800689	−	0.599080i	$-0.204467\pi$
$17$	0.831254	+	0.831254i	0.201609	+	0.201609i	−0.599080	+	0.800689i	$0.704467\pi$
$18$	6.52875	−	6.52875i	1.53884	−	1.53884i
$19$	1.25841			0.288699			0.144349	−	0.989527i	$-0.453891\pi$
$19$	1.25841			0.288699			0.144349	+	0.989527i	$0.453891\pi$
$20$		0			0
$21$		−	11.9198i		−	2.60112i
$22$	6.25986	+	0.782635i	1.33461	+	0.166858i
$23$	0.756934	+	0.756934i	0.157832	+	0.157832i	0.781605	−	0.623774i	$-0.214401\pi$
$23$	0.756934	+	0.756934i	0.157832	+	0.157832i	−0.623774	+	0.781605i	$0.714401\pi$
$24$	2.03615			0.415627
$25$		0			0
$26$	5.85410			1.14808
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$	−4.86624	+	4.86624i	−0.919634	+	0.919634i
$29$	−8.62526			−1.60167			−0.800835	−	0.598885i	$-0.795611\pi$
$29$	−8.62526			−1.60167			−0.800835	+	0.598885i	$0.795611\pi$
$30$		0			0
$31$	1.47214			0.264403			0.132202	−	0.991223i	$-0.457795\pi$
$31$	1.47214			0.264403			0.132202	+	0.991223i	$0.457795\pi$
$32$	−5.18376	−	5.18376i	−0.916367	−	0.916367i
$33$	9.22309	+	1.15311i	1.60553	+	0.200731i
$34$		−	2.23607i		−	0.383482i
$35$		0			0
$36$	−7.85410			−1.30902
$37$	−6.70197	+	6.70197i	−1.10180	+	1.10180i	−0.107603	+	0.994194i	$0.534318\pi$
$37$	−6.70197	+	6.70197i	−1.10180	+	1.10180i	−0.994194	+	0.107603i	$0.965682\pi$
$38$	−1.69256	−	1.69256i	−0.274569	−	0.274569i
$39$	8.62526			1.38115
$40$		0			0
$41$			7.84752i			1.22558i	0.790247	+	0.612788i	$0.209952\pi$
$41$			7.84752i			1.22558i	−0.790247	+	0.612788i	$0.790048\pi$
$42$	−16.0321	+	16.0321i	−2.47381	+	2.47381i
$43$	3.71748	−	3.71748i	0.566910	−	0.566910i	−0.364351	−	0.931262i	$-0.618709\pi$
$43$	3.71748	−	3.71748i	0.566910	−	0.566910i	0.931262	+	0.364351i	$0.118709\pi$
$44$	−3.29456	−	4.23607i	−0.496673	−	0.638611i
$45$		0			0
$46$		−	2.03615i		−	0.300214i
$47$	4.25248	−	4.25248i	0.620288	−	0.620288i	−0.325317	−	0.945605i	$-0.605471\pi$
$47$	4.25248	−	4.25248i	0.620288	−	0.620288i	0.945605	+	0.325317i	$0.105471\pi$
$48$	−9.15146	−	9.15146i	−1.32090	−	1.32090i
$49$			11.0902i			1.58431i
$50$		0			0
$51$		−	3.29456i		−	0.461330i
$52$	−3.52125	−	3.52125i	−0.488309	−	0.488309i
$53$	4.14205	+	4.14205i	0.568954	+	0.568954i	0.931835	−	0.362882i	$-0.118207\pi$
$53$	4.14205	+	4.14205i	0.568954	+	0.568954i	−0.362882	+	0.931835i	$0.618207\pi$
$54$	−9.88367			−1.34500
$55$		0			0
$56$	−3.09017			−0.412941
$57$	−2.49376	−	2.49376i	−0.330307	−	0.330307i
$58$	11.6009	+	11.6009i	1.52328	+	1.52328i
$59$			1.00000i			0.130189i	0.997879	+	0.0650945i	$0.0207349\pi$
$59$			1.00000i			0.130189i	−0.997879	+	0.0650945i	$0.979265\pi$
$60$		0			0
$61$			5.81137i			0.744070i	0.928219	+	0.372035i	$0.121340\pi$
$61$			5.81137i			0.744070i	−0.928219	+	0.372035i	$0.878660\pi$
$62$	−1.98002	−	1.98002i	−0.251463	−	0.251463i
$63$	−14.5987	+	14.5987i	−1.83927	+	1.83927i
$64$			4.70820i			0.588525i
$65$		0			0
$66$	−10.8541	−	13.9560i	−1.33605	−	1.71786i
$67$	4.89898	−	4.89898i	0.598506	−	0.598506i	−0.341409	−	0.939915i	$-0.610904\pi$
$67$	4.89898	−	4.89898i	0.598506	−	0.598506i	0.939915	+	0.341409i	$0.110904\pi$
$68$	−1.34500	+	1.34500i	−0.163105	+	0.163105i
$69$		−	3.00000i		−	0.361158i
$70$		0			0
$71$	0.291796			0.0346298			0.0173149	−	0.999850i	$-0.494488\pi$
$71$	0.291796			0.0346298			0.0173149	+	0.999850i	$0.494488\pi$
$72$	−2.49376	−	2.49376i	−0.293893	−	0.293893i
$73$	−7.99503	+	7.99503i	−0.935747	+	0.935747i	−0.998057	−	0.0623096i	$-0.980153\pi$
$73$	−7.99503	+	7.99503i	−0.935747	+	0.935747i	0.0623096	+	0.998057i	$0.480153\pi$
$74$	18.0283			2.09574
$75$		0			0
$76$			2.03615i			0.233562i
$77$	−13.9975	−	1.75003i	−1.59516	−	0.199434i
$78$	−11.6009	−	11.6009i	−1.31355	−	1.31355i
$79$	0.480669			0.0540795			0.0270398	−	0.999634i	$-0.491392\pi$
$79$	0.480669			0.0540795			0.0270398	+	0.999634i	$0.491392\pi$
$80$		0			0
$81$		0			0
$82$	10.5549	−	10.5549i	1.16559	−	1.16559i
$83$	−0.196232	+	0.196232i	−0.0215393	+	0.0215393i	−0.717794	−	0.696255i	$-0.754848\pi$
$83$	−0.196232	+	0.196232i	−0.0215393	+	0.0215393i	0.696255	+	0.717794i	$0.254848\pi$
$84$	19.2867			2.10435
$85$		0			0
$86$	−10.0000			−1.07833
$87$	17.0925	+	17.0925i	1.83251	+	1.83251i
$88$	0.298940	−	2.39105i	0.0318671	−	0.254887i
$89$		−	9.32624i		−	0.988579i	−0.869297	−	0.494290i	$-0.835428\pi$
$89$		−	9.32624i		−	0.988579i	0.869297	−	0.494290i	$-0.164572\pi$
$90$		0			0
$91$	−13.0902			−1.37222
$92$	−1.22474	+	1.22474i	−0.127688	+	0.127688i
$93$	−2.91730	−	2.91730i	−0.302510	−	0.302510i
$94$	−11.4391			−1.17986
$95$		0			0
$96$			20.5451i			2.09687i
$97$	−0.178688	+	0.178688i	−0.0181430	+	0.0181430i	−0.716120	−	0.697977i	$-0.754084\pi$
$97$	−0.178688	+	0.178688i	−0.0181430	+	0.0181430i	0.697977	+	0.716120i	$0.254084\pi$
$98$	14.9162	−	14.9162i	1.50677	−	1.50677i
$99$	−9.88367	−	12.7082i	−0.993346	−	1.27722i
$100$		0			0
$101$			7.36685i			0.733029i	0.930412	+	0.366515i	$0.119449\pi$
$101$			7.36685i			0.733029i	−0.930412	+	0.366515i	$0.880551\pi$
$102$	−4.43117	+	4.43117i	−0.438751	+	0.438751i
$103$	12.3579	+	12.3579i	1.21766	+	1.21766i	0.968450	+	0.249209i	$0.0801705\pi$
$103$	12.3579	+	12.3579i	1.21766	+	1.21766i	0.249209	+	0.968450i	$0.419829\pi$
$104$		−	2.23607i		−	0.219265i
$105$		0			0
$106$		−	11.1421i		−	1.08221i
$107$	1.14876	+	1.14876i	0.111055	+	0.111055i	0.760451	−	0.649396i	$-0.224978\pi$
$107$	1.14876	+	1.14876i	0.111055	+	0.111055i	−0.649396	+	0.760451i	$0.724978\pi$
$108$	5.94504	+	5.94504i	0.572061	+	0.572061i
$109$	2.03615			0.195028			0.0975138	−	0.995234i	$-0.468911\pi$
$109$	2.03615			0.195028			0.0975138	+	0.995234i	$0.468911\pi$
$110$		0			0
$111$	26.5623			2.52118
$112$	13.8888	+	13.8888i	1.31236	+	1.31236i
$113$	−9.15146	−	9.15146i	−0.860897	−	0.860897i	0.130545	−	0.991442i	$-0.458327\pi$
$113$	−9.15146	−	9.15146i	−0.860897	−	0.860897i	−0.991442	+	0.130545i	$0.958327\pi$
$114$			6.70820i			0.628281i
$115$		0			0
$116$		−	13.9560i		−	1.29578i
$117$	−10.5637	−	10.5637i	−0.976618	−	0.976618i
$118$	1.34500	−	1.34500i	0.123817	−	0.123817i
$119$			5.00000i			0.458349i
$120$		0			0
$121$	2.70820	−	10.6614i	0.246200	−	0.969219i
$122$	7.81628	−	7.81628i	0.707653	−	0.707653i
$123$	15.5513	−	15.5513i	1.40221	−	1.40221i
$124$			2.38197i			0.213907i
$125$		0			0
$126$	39.2705			3.49850
$127$	−9.92872	−	9.92872i	−0.881032	−	0.881032i	0.112608	−	0.993640i	$-0.464080\pi$
$127$	−9.92872	−	9.92872i	−0.881032	−	0.881032i	−0.993640	+	0.112608i	$0.964080\pi$
$128$	−4.03499	+	4.03499i	−0.356646	+	0.356646i
$129$	−14.7337			−1.29723
$130$		0			0
$131$			4.85003i			0.423750i	0.977297	+	0.211875i	$0.0679569\pi$
$131$			4.85003i			0.423750i	−0.977297	+	0.211875i	$0.932043\pi$
$132$	−1.86577	+	14.9233i	−0.162395	+	1.29890i
$133$	3.78467	+	3.78467i	0.328172	+	0.328172i
$134$	−13.1782			−1.13843
$135$		0			0
$136$	−0.854102			−0.0732386
$137$	3.85292	−	3.85292i	0.329177	−	0.329177i	−0.523096	−	0.852274i	$-0.675223\pi$
$137$	3.85292	−	3.85292i	0.329177	−	0.329177i	0.852274	+	0.523096i	$0.175223\pi$
$138$	−4.03499	+	4.03499i	−0.343481	+	0.343481i
$139$	−18.5089			−1.56991			−0.784953	−	0.619555i	$-0.787313\pi$
$139$	−18.5089			−1.56991			−0.784953	+	0.619555i	$0.787313\pi$
$140$		0			0
$141$	−16.8541			−1.41937
$142$	−0.392465	−	0.392465i	−0.0329349	−	0.0329349i
$143$	1.26633	−	10.1287i	0.105896	−	0.847002i
$144$			22.4164i			1.86803i
$145$		0			0
$146$	21.5066			1.77990
$147$	21.9772	−	21.9772i	1.81265	−	1.81265i
$148$	−10.8440	−	10.8440i	−0.891373	−	0.891373i
$149$	14.7337			1.20703			0.603516	−	0.797351i	$-0.293766\pi$
$149$	14.7337			1.20703			0.603516	+	0.797351i	$0.293766\pi$
$150$		0			0
$151$			2.81389i			0.228991i	0.993424	+	0.114495i	$0.0365251\pi$
$151$			2.81389i			0.228991i	−0.993424	+	0.114495i	$0.963475\pi$
$152$	−0.646499	+	0.646499i	−0.0524380	+	0.0524380i
$153$	−4.03499	+	4.03499i	−0.326210	+	0.326210i
$154$	16.4728	+	21.1803i	1.32741	+	1.70676i
$155$		0			0
$156$			13.9560i			1.11737i
$157$	−12.8257	+	12.8257i	−1.02360	+	1.02360i	−0.0238872	+	0.999715i	$0.507604\pi$
$157$	−12.8257	+	12.8257i	−1.02360	+	1.02360i	−0.999715	+	0.0238872i	$0.992396\pi$
$158$	−0.646499	−	0.646499i	−0.0514327	−	0.0514327i
$159$		−	16.4164i		−	1.30191i
$160$		0			0
$161$			4.55296i			0.358824i
$162$		0			0
$163$	−1.33518	−	1.33518i	−0.104579	−	0.104579i	0.652881	−	0.757460i	$-0.273560\pi$
$163$	−1.33518	−	1.33518i	−0.104579	−	0.104579i	−0.757460	+	0.652881i	$0.773560\pi$
$164$	−12.6976			−0.991513
$165$		0			0
$166$	0.527864			0.0409702
$167$	3.83876	+	3.83876i	0.297052	+	0.297052i	0.839858	−	0.542806i	$-0.182638\pi$
$167$	3.83876	+	3.83876i	0.297052	+	0.297052i	−0.542806	+	0.839858i	$0.682638\pi$
$168$	6.12372	+	6.12372i	0.472456	+	0.472456i
$169$			3.52786i			0.271374i
$170$		0			0
$171$			6.10844i			0.467124i
$172$	6.01501	+	6.01501i	0.458640	+	0.458640i
$173$	8.19126	−	8.19126i	0.622770	−	0.622770i	−0.323469	−	0.946239i	$-0.604849\pi$
$173$	8.19126	−	8.19126i	0.622770	−	0.622770i	0.946239	+	0.323469i	$0.104849\pi$
$174$		−	45.9787i		−	3.48564i
$175$		0			0
$176$	−12.0902	+	9.40300i	−0.911331	+	0.708778i
$177$	1.98168	−	1.98168i	0.148952	−	0.148952i
$178$	−12.5438	+	12.5438i	−0.940195	+	0.940195i
$179$			15.2705i			1.14137i	0.821169	+	0.570686i	$0.193323\pi$
$179$			15.2705i			1.14137i	−0.821169	+	0.570686i	$0.806677\pi$
$180$		0			0
$181$	−10.0344			−0.745854			−0.372927	−	0.927861i	$-0.621646\pi$
$181$	−10.0344			−0.745854			−0.372927	+	0.927861i	$0.621646\pi$
$182$	17.6062	+	17.6062i	1.30506	+	1.30506i
$183$	11.5163	−	11.5163i	0.851308	−	0.851308i
$184$	−0.777739			−0.0573357
$185$		0			0
$186$			7.84752i			0.575408i
$187$	−3.86881	−	0.483695i	−0.282915	−	0.0353713i
$188$	6.88066	+	6.88066i	0.501824	+	0.501824i
$189$	22.1006			1.60758
$190$		0			0
$191$	5.61803			0.406507			0.203253	−	0.979126i	$-0.434848\pi$
$191$	5.61803			0.406507			0.203253	+	0.979126i	$0.434848\pi$
$192$	9.33015	−	9.33015i	0.673345	−	0.673345i
$193$	3.71748	−	3.71748i	0.267590	−	0.267590i	−0.560538	−	0.828128i	$-0.689406\pi$
$193$	3.71748	−	3.71748i	0.267590	−	0.267590i	0.828128	+	0.560538i	$0.189406\pi$
$194$	0.480669			0.0345100
$195$		0			0
$196$	−17.9443			−1.28173
$197$	−4.27755	−	4.27755i	−0.304763	−	0.304763i	0.538111	−	0.842874i	$-0.319138\pi$
$197$	−4.27755	−	4.27755i	−0.304763	−	0.304763i	−0.842874	+	0.538111i	$0.819138\pi$
$198$	−3.79899	+	30.3860i	−0.269983	+	2.15944i
$199$			8.56231i			0.606966i	0.952837	+	0.303483i	$0.0981495\pi$
$199$			8.56231i			0.606966i	−0.952837	+	0.303483i	$0.901850\pi$
$200$		0			0
$201$	−19.4164			−1.36953
$202$	9.90839	−	9.90839i	0.697152	−	0.697152i
$203$	−25.9405	−	25.9405i	−1.82067	−	1.82067i
$204$	5.33070			0.373224
$205$		0			0
$206$		−	33.2426i		−	2.31612i
$207$	−3.67423	+	3.67423i	−0.255377	+	0.255377i
$208$	−10.0500	+	10.0500i	−0.696842	+	0.696842i
$209$	−3.29456	+	2.56231i	−0.227889	+	0.177238i
$210$		0			0
$211$		−	22.5812i		−	1.55456i	−0.629157	−	0.777278i	$-0.716600\pi$
$211$		−	22.5812i		−	1.55456i	0.629157	−	0.777278i	$-0.283400\pi$
$212$	−6.70197	+	6.70197i	−0.460293	+	0.460293i
$213$	−0.578246	−	0.578246i	−0.0396208	−	0.0396208i
$214$		−	3.09017i		−	0.211240i
$215$		0			0
$216$			3.77523i			0.256872i
$217$	4.42746	+	4.42746i	0.300555	+	0.300555i
$218$	−2.73861	−	2.73861i	−0.185482	−	0.185482i
$219$	31.6872			2.14122
$220$		0			0
$221$	−3.61803			−0.243375
$222$	−35.7262	−	35.7262i	−2.39779	−	2.39779i
$223$	−3.67423	−	3.67423i	−0.246045	−	0.246045i	0.573300	−	0.819345i	$-0.305663\pi$
$223$	−3.67423	−	3.67423i	−0.246045	−	0.246045i	−0.819345	+	0.573300i	$0.805663\pi$
$224$		−	31.1803i		−	2.08332i
$225$		0			0
$226$			24.6174i			1.63752i
$227$	5.81878	+	5.81878i	0.386206	+	0.386206i	0.873332	−	0.487126i	$-0.161955\pi$
$227$	5.81878	+	5.81878i	0.386206	+	0.386206i	−0.487126	+	0.873332i	$0.661955\pi$
$228$	4.03499	−	4.03499i	0.267224	−	0.267224i
$229$		−	18.2705i		−	1.20735i	−0.797231	−	0.603675i	$-0.793703\pi$
$229$		−	18.2705i		−	1.20735i	0.797231	−	0.603675i	$-0.206297\pi$
$230$		0			0
$231$	24.2705	+	31.2065i	1.59688	+	2.05324i
$232$	4.43117	−	4.43117i	0.290920	−	0.290920i
$233$	−19.3900	+	19.3900i	−1.27028	+	1.27028i	−0.324343	+	0.945939i	$0.605143\pi$
$233$	−19.3900	+	19.3900i	−1.27028	+	1.27028i	−0.945939	+	0.324343i	$0.894857\pi$
$234$			28.4164i			1.85764i
$235$		0			0
$236$	−1.61803			−0.105325
$237$	−0.952532	−	0.952532i	−0.0618736	−	0.0618736i
$238$	6.72499	−	6.72499i	0.435916	−	0.435916i
$239$	15.5114			1.00335			0.501676	−	0.865056i	$-0.332717\pi$
$239$	15.5114			1.00335			0.501676	+	0.865056i	$0.332717\pi$
$240$		0			0
$241$		−	14.2530i		−	0.918119i	−0.888406	−	0.459059i	$-0.848187\pi$
$241$		−	14.2530i		−	0.918119i	0.888406	−	0.459059i	$-0.151813\pi$
$242$	−17.9821	+	10.6970i	−1.15593	+	0.687632i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$	−9.40300			−0.601965
$245$		0			0
$246$	−41.8328			−2.66716
$247$	−2.73861	+	2.73861i	−0.174254	+	0.174254i
$248$	−0.756300	+	0.756300i	−0.0480251	+	0.0480251i
$249$	0.777739			0.0492872
$250$		0			0
$251$	−8.85410			−0.558866			−0.279433	−	0.960165i	$-0.590146\pi$
$251$	−8.85410			−0.558866			−0.279433	+	0.960165i	$0.590146\pi$
$252$	−23.6212	−	23.6212i	−1.48800	−	1.48800i
$253$	−3.52291	−	0.440449i	−0.221483	−	0.0276908i
$254$			26.7082i			1.67582i
$255$		0			0
$256$	20.2705			1.26691
$257$	−12.8257	+	12.8257i	−0.800045	+	0.800045i	−0.983102	−	0.183057i	$-0.941401\pi$
$257$	−12.8257	+	12.8257i	−0.800045	+	0.800045i	0.183057	+	0.983102i	$0.441401\pi$
$258$	19.8168	+	19.8168i	1.23374	+	1.23374i
$259$	−40.3124			−2.50489
$260$		0			0
$261$		−	41.8679i		−	2.59156i
$262$	6.52328	−	6.52328i	0.403010	−	0.403010i
$263$	−19.3437	+	19.3437i	−1.19278	+	1.19278i	−0.216501	+	0.976282i	$0.569465\pi$
$263$	−19.3437	+	19.3437i	−1.19278	+	1.19278i	−0.976282	+	0.216501i	$0.930535\pi$
$264$	−5.33070	+	4.14590i	−0.328082	+	0.255162i
$265$		0			0
$266$		−	10.1807i		−	0.624221i
$267$	−18.4816	+	18.4816i	−1.13106	+	1.13106i
$268$	7.92672	+	7.92672i	0.484201	+	0.484201i
$269$			20.2705i			1.23591i	0.786212	+	0.617957i	$0.212040\pi$
$269$			20.2705i			1.23591i	−0.786212	+	0.617957i	$0.787960\pi$
$270$		0			0
$271$			14.4366i			0.876963i	0.898740	+	0.438482i	$0.144484\pi$
$271$			14.4366i			0.876963i	−0.898740	+	0.438482i	$0.855516\pi$
$272$	3.83876	+	3.83876i	0.232759	+	0.232759i
$273$	25.9405	+	25.9405i	1.56999	+	1.56999i
$274$	−10.3643			−0.626133
$275$		0			0
$276$	4.85410			0.292183
$277$	11.6662	+	11.6662i	0.700953	+	0.700953i	0.964615	−	0.263662i	$-0.0849304\pi$
$277$	11.6662	+	11.6662i	0.700953	+	0.700953i	−0.263662	+	0.964615i	$0.584930\pi$
$278$	24.8945	+	24.8945i	1.49307	+	1.49307i
$279$			7.14590i			0.427814i
$280$		0			0
$281$		−	14.4366i		−	0.861217i	−0.902539	−	0.430609i	$-0.858299\pi$
$281$		−	14.4366i		−	0.861217i	0.902539	−	0.430609i	$-0.141701\pi$
$282$	22.6687	+	22.6687i	1.34990	+	1.34990i
$283$	20.6887	−	20.6887i	1.22982	−	1.22982i	0.265782	−	0.964033i	$-0.414370\pi$
$283$	20.6887	−	20.6887i	1.22982	−	1.22982i	0.964033	−	0.265782i	$-0.0856303\pi$
$284$			0.472136i			0.0280161i
$285$		0			0
$286$	−15.3262	+	11.9198i	−0.906259	+	0.704834i
$287$	−23.6015	+	23.6015i	−1.39315	+	1.39315i
$288$	25.1625	−	25.1625i	1.48271	−	1.48271i
$289$		−	15.6180i		−	0.918708i
$290$		0			0
$291$	0.708204			0.0415156
$292$	−12.9362	−	12.9362i	−0.757035	−	0.757035i
$293$	2.29753	−	2.29753i	0.134223	−	0.134223i	−0.636803	−	0.771026i	$-0.719744\pi$
$293$	2.29753	−	2.29753i	0.134223	−	0.134223i	0.771026	+	0.636803i	$0.219744\pi$
$294$	−59.1184			−3.44786
$295$		0			0
$296$		−	6.88618i		−	0.400251i
$297$	−2.13799	+	17.1006i	−0.124059	+	0.992275i
$298$	−19.8168	−	19.8168i	−1.14796	−	1.14796i
$299$	−3.29456			−0.190529
$300$		0			0
$301$	22.3607			1.28885
$302$	3.78467	−	3.78467i	0.217783	−	0.217783i
$303$	14.5987	−	14.5987i	0.838675	−	0.838675i
$304$	5.81137			0.333305
$305$		0			0
$306$	10.8541			0.620488
$307$	−17.6062	−	17.6062i	−1.00484	−	1.00484i	−0.999988	−	0.00485295i	$-0.998455\pi$
$307$	−17.6062	−	17.6062i	−1.00484	−	1.00484i	−0.00485295	−	0.999988i	$-0.501545\pi$
$308$	2.83160	−	22.6484i	0.161345	−	1.29051i
$309$		−	48.9787i		−	2.78630i
$310$		0			0
$311$	8.70820			0.493797			0.246898	−	0.969041i	$-0.420589\pi$
$311$	8.70820			0.493797			0.246898	+	0.969041i	$0.420589\pi$
$312$	−4.43117	+	4.43117i	−0.250866	+	0.250866i
$313$	16.7891	+	16.7891i	0.948973	+	0.948973i	0.998760	−	0.0497865i	$-0.0158541\pi$
$313$	16.7891	+	16.7891i	0.948973	+	0.948973i	−0.0497865	+	0.998760i	$0.515854\pi$
$314$	34.5010			1.94701
$315$		0			0
$316$			0.777739i			0.0437513i
$317$	18.1925	−	18.1925i	1.02179	−	1.02179i	0.0220346	−	0.999757i	$-0.492986\pi$
$317$	18.1925	−	18.1925i	1.02179	−	1.02179i	0.999757	−	0.0220346i	$-0.00701439\pi$
$318$	−22.0800	+	22.0800i	−1.23819	+	1.23819i
$319$	22.5812	−	17.5623i	1.26431	−	0.983300i
$320$		0			0
$321$		−	4.55296i		−	0.254122i
$322$	6.12372	−	6.12372i	0.341262	−	0.341262i
$323$	1.04606	+	1.04606i	0.0582042	+	0.0582042i
$324$		0			0
$325$		0			0
$326$			3.59163i			0.198922i
$327$	−4.03499	−	4.03499i	−0.223136	−	0.223136i
$328$	−4.03161	−	4.03161i	−0.222608	−	0.222608i
$329$	25.5787			1.41020
$330$		0			0
$331$	23.1803			1.27411			0.637053	−	0.770820i	$-0.280153\pi$
$331$	23.1803			1.27411			0.637053	+	0.770820i	$0.280153\pi$
$332$	−0.317511	−	0.317511i	−0.0174257	−	0.0174257i
$333$	−32.5320	−	32.5320i	−1.78275	−	1.78275i
$334$		−	10.3262i		−	0.565027i
$335$		0			0
$336$		−	55.0461i		−	3.00301i
$337$	−17.4100	−	17.4100i	−0.948384	−	0.948384i	0.0503482	−	0.998732i	$-0.483967\pi$
$337$	−17.4100	−	17.4100i	−0.948384	−	0.948384i	−0.998732	+	0.0503482i	$0.983967\pi$
$338$	4.74497	−	4.74497i	0.258092	−	0.258092i
$339$			36.2705i			1.96994i
$340$		0			0
$341$	−3.85410	+	2.99749i	−0.208711	+	0.162323i
$342$	8.21584	−	8.21584i	0.444262	−	0.444262i
$343$	−12.3012	+	12.3012i	−0.664203	+	0.664203i
$344$			3.81966i			0.205942i
$345$		0			0
$346$	−22.0344			−1.18458
$347$	13.7675	+	13.7675i	0.739077	+	0.739077i	0.972399	−	0.233322i	$-0.0749597\pi$
$347$	13.7675	+	13.7675i	0.739077	+	0.739077i	−0.233322	+	0.972399i	$0.574960\pi$
$348$	−27.6562	+	27.6562i	−1.48253	+	1.48253i
$349$	17.5476			0.939301			0.469651	−	0.882852i	$-0.344380\pi$
$349$	17.5476			0.939301			0.469651	+	0.882852i	$0.344380\pi$
$350$		0			0
$351$			15.9921i			0.853596i
$352$	24.1261	+	3.01636i	1.28593	+	0.160772i
$353$	17.4356	+	17.4356i	0.928001	+	0.928001i	0.997577	−	0.0695759i	$-0.0221646\pi$
$353$	17.4356	+	17.4356i	0.928001	+	0.928001i	−0.0695759	+	0.997577i	$0.522165\pi$
$354$	−5.33070			−0.283324
$355$		0			0
$356$	15.0902			0.799777
$357$	9.90839	−	9.90839i	0.524408	−	0.524408i
$358$	20.5388	−	20.5388i	1.08551	−	1.08551i
$359$	6.58911			0.347760			0.173880	−	0.984767i	$-0.444370\pi$
$359$	6.58911			0.347760			0.173880	+	0.984767i	$0.444370\pi$
$360$		0			0
$361$	−17.4164			−0.916653
$362$	13.4963	+	13.4963i	0.709349	+	0.709349i
$363$	−26.4943	+	15.7607i	−1.39059	+	0.827222i
$364$		−	21.1803i		−	1.11015i
$365$		0			0
$366$	−30.9787			−1.61928
$367$	20.9311	−	20.9311i	1.09259	−	1.09259i	0.0973436	−	0.995251i	$-0.468965\pi$
$367$	20.9311	−	20.9311i	1.09259	−	1.09259i	0.995251	−	0.0973436i	$-0.0310346\pi$
$368$	3.49555	+	3.49555i	0.182218	+	0.182218i
$369$	−38.0927			−1.98303
$370$		0			0
$371$			24.9144i			1.29349i
$372$	4.72029	−	4.72029i	0.244736	−	0.244736i
$373$	10.4888	−	10.4888i	0.543089	−	0.543089i	−0.381344	−	0.924433i	$-0.624539\pi$
$373$	10.4888	−	10.4888i	0.543089	−	0.543089i	0.924433	+	0.381344i	$0.124539\pi$
$374$	4.55296	+	5.85410i	0.235428	+	0.302708i
$375$		0			0
$376$			4.36937i			0.225333i
$377$	18.7707	−	18.7707i	0.966742	−	0.966742i
$378$	−29.7252	−	29.7252i	−1.52890	−	1.52890i
$379$			12.7082i			0.652777i	0.945236	+	0.326388i	$0.105832\pi$
$379$			12.7082i			0.652777i	−0.945236	+	0.326388i	$0.894168\pi$
$380$		0			0
$381$			39.3511i			2.01602i
$382$	−7.55624	−	7.55624i	−0.386611	−	0.386611i
$383$	0.357376	+	0.357376i	0.0182610	+	0.0182610i	0.716178	−	0.697917i	$-0.245890\pi$
$383$	0.357376	+	0.357376i	0.0182610	+	0.0182610i	−0.697917	+	0.716178i	$0.745890\pi$
$384$	15.9921			0.816094
$385$		0			0
$386$	−10.0000			−0.508987
$387$	18.0450	+	18.0450i	0.917280	+	0.917280i
$388$	−0.289123	−	0.289123i	−0.0146780	−	0.0146780i
$389$		−	14.0000i		−	0.709828i	−0.934899	−	0.354914i	$-0.884510\pi$
$389$		−	14.0000i		−	0.709828i	0.934899	−	0.354914i	$-0.115490\pi$
$390$		0			0
$391$			1.25841i			0.0636405i
$392$	−5.69750	−	5.69750i	−0.287767	−	0.287767i
$393$	9.61121	−	9.61121i	0.484821	−	0.484821i
$394$			11.5066i			0.579693i
$395$		0			0
$396$	20.5623	−	15.9921i	1.03329	−	0.803634i
$397$	−9.68752	+	9.68752i	−0.486203	+	0.486203i	−0.907106	−	0.420903i	$-0.861713\pi$
$397$	−9.68752	+	9.68752i	−0.486203	+	0.486203i	0.420903	+	0.907106i	$0.361713\pi$
$398$	11.5163	−	11.5163i	0.577259	−	0.577259i
$399$		−	15.0000i		−	0.750939i
$400$		0			0
$401$	25.4164			1.26923			0.634617	−	0.772826i	$-0.281158\pi$
$401$	25.4164			1.26923			0.634617	+	0.772826i	$0.281158\pi$
$402$	26.1150	+	26.1150i	1.30250	+	1.30250i
$403$	−3.20374	+	3.20374i	−0.159590	+	0.159590i
$404$	−11.9198			−0.593033
$405$		0			0
$406$			69.7798i			3.46311i
$407$	3.89978	−	31.1922i	0.193305	−	1.54614i
$408$	1.69256	+	1.69256i	0.0837940	+	0.0837940i
$409$	27.6149			1.36547			0.682733	−	0.730668i	$-0.260791\pi$
$409$	27.6149			1.36547			0.682733	+	0.730668i	$0.260791\pi$
$410$		0			0
$411$	−15.2705			−0.753239
$412$	−19.9955	+	19.9955i	−0.985106	+	0.985106i
$413$	−3.00750	+	3.00750i	−0.147990	+	0.147990i
$414$	9.88367			0.485756
$415$		0			0
$416$	22.5623			1.10621
$417$	36.6788	+	36.6788i	1.79617	+	1.79617i
$418$	7.87746	+	0.984875i	0.385299	+	0.0481718i
$419$			34.4164i			1.68135i	0.541539	+	0.840676i	$0.317842\pi$
$419$			34.4164i			1.68135i	−0.541539	+	0.840676i	$0.682158\pi$
$420$		0			0
$421$	25.0902			1.22282			0.611410	−	0.791314i	$-0.290603\pi$
$421$	25.0902			1.22282			0.611410	+	0.791314i	$0.290603\pi$
$422$	−30.3717	+	30.3717i	−1.47847	+	1.47847i
$423$	20.6420	+	20.6420i	1.00365	+	1.00365i
$424$	−4.25590			−0.206685
$425$		0			0
$426$			1.55548i			0.0753632i
$427$	−17.4777	+	17.4777i	−0.845807	+	0.845807i
$428$	−1.85874	+	1.85874i	−0.0898456	+	0.0898456i
$429$	−22.5812	+	17.5623i	−1.09023	+	0.847916i
$430$		0			0
$431$		−	5.33070i		−	0.256771i	−0.991724	−	0.128385i	$-0.959021\pi$
$431$		−	5.33070i		−	0.256771i	0.991724	−	0.128385i	$-0.0409795\pi$
$432$	16.9677	−	16.9677i	0.816361	−	0.816361i
$433$	−2.38124	−	2.38124i	−0.114435	−	0.114435i	0.647571	−	0.762006i	$-0.275785\pi$
$433$	−2.38124	−	2.38124i	−0.114435	−	0.114435i	−0.762006	+	0.647571i	$0.775785\pi$
$434$		−	11.9098i		−	0.571690i
$435$		0			0
$436$			3.29456i			0.157781i
$437$	0.952532	+	0.952532i	0.0455658	+	0.0455658i
$438$	−42.6191	−	42.6191i	−2.03642	−	2.03642i
$439$	−25.8758			−1.23498			−0.617492	−	0.786577i	$-0.711851\pi$
$439$	−25.8758			−1.23498			−0.617492	+	0.786577i	$0.711851\pi$
$440$		0			0
$441$	−53.8328			−2.56347
$442$	4.86624	+	4.86624i	0.231464	+	0.231464i
$443$	−0.935622	−	0.935622i	−0.0444527	−	0.0444527i	0.684531	−	0.728984i	$-0.260007\pi$
$443$	−0.935622	−	0.935622i	−0.0444527	−	0.0444527i	−0.728984	+	0.684531i	$0.760007\pi$
$444$			42.9787i			2.03968i
$445$		0			0
$446$			9.88367i			0.468005i
$447$	−29.1975	−	29.1975i	−1.38099	−	1.38099i
$448$	−14.1599	+	14.1599i	−0.668995	+	0.668995i
$449$			27.3820i			1.29223i	0.763238	+	0.646117i	$0.223608\pi$
$449$			27.3820i			1.29223i	−0.763238	+	0.646117i	$0.776392\pi$
$450$		0			0
$451$	−15.9787	−	20.5451i	−0.752408	−	0.967430i
$452$	14.8074	−	14.8074i	0.696480	−	0.696480i
$453$	5.57622	−	5.57622i	0.261994	−	0.261994i
$454$		−	15.6525i		−	0.734607i
$455$		0			0
$456$	2.56231			0.119991
$457$	−26.1900	−	26.1900i	−1.22511	−	1.22511i	−0.965790	−	0.259325i	$-0.916500\pi$
$457$	−26.1900	−	26.1900i	−1.22511	−	1.22511i	−0.259325	−	0.965790i	$-0.583500\pi$
$458$	−24.5738	+	24.5738i	−1.14826	+	1.14826i
$459$	6.10844			0.285118
$460$		0			0
$461$			30.7258i			1.43104i	0.698590	+	0.715522i	$0.253811\pi$
$461$			30.7258i			1.43104i	−0.698590	+	0.715522i	$0.746189\pi$
$462$	9.32887	−	74.6164i	0.434018	−	3.47147i
$463$	−1.58212	−	1.58212i	−0.0735274	−	0.0735274i	0.669387	−	0.742914i	$-0.266557\pi$
$463$	−1.58212	−	1.58212i	−0.0735274	−	0.0735274i	−0.742914	+	0.669387i	$0.766557\pi$
$464$	−39.8317			−1.84914
$465$		0			0
$466$	52.1591			2.41622
$467$	11.8218	−	11.8218i	0.547049	−	0.547049i	−0.378537	−	0.925586i	$-0.623573\pi$
$467$	11.8218	−	11.8218i	0.547049	−	0.547049i	0.925586	+	0.378537i	$0.123573\pi$
$468$	17.0925	−	17.0925i	0.790101	−	0.790101i
$469$	29.4674			1.36068
$470$		0			0
$471$	50.8328			2.34225
$472$	−0.513743	−	0.513743i	−0.0236469	−	0.0236469i
$473$	−2.16315	+	17.3018i	−0.0994618	+	0.795539i
$474$			2.56231i			0.117691i
$475$		0			0
$476$	−8.09017			−0.370812
$477$	−20.1059	+	20.1059i	−0.920586	+	0.920586i
$478$	−20.8628	−	20.8628i	−0.954244	−	0.954244i
$479$	−21.6199			−0.987838			−0.493919	−	0.869508i	$-0.664436\pi$
$479$	−21.6199			−0.987838			−0.493919	+	0.869508i	$0.664436\pi$
$480$		0			0
$481$		−	29.1703i		−	1.33005i
$482$	−19.1703	+	19.1703i	−0.873183	+	0.873183i
$483$	9.02251	−	9.02251i	0.410539	−	0.410539i
$484$	17.2505	+	4.38197i	0.784115	+	0.199180i
$485$		0			0
$486$			29.6510i			1.34500i
$487$	0.867369	−	0.867369i	0.0393042	−	0.0393042i	−0.687182	−	0.726486i	$-0.741152\pi$
$487$	0.867369	−	0.867369i	0.0393042	−	0.0393042i	0.726486	+	0.687182i	$0.241152\pi$
$488$	−2.98555	−	2.98555i	−0.135150	−	0.135150i
$489$			5.29180i			0.239303i
$490$		0			0
$491$		−	30.7258i		−	1.38664i	−0.720631	−	0.693318i	$-0.756148\pi$
$491$		−	30.7258i		−	1.38664i	0.720631	−	0.693318i	$-0.243852\pi$
$492$	25.1625	+	25.1625i	1.13441	+	1.13441i
$493$	−7.16978	−	7.16978i	−0.322911	−	0.322911i
$494$	7.36685			0.331450
$495$		0			0
$496$	6.79837			0.305256
$497$	0.877578	+	0.877578i	0.0393648	+	0.0393648i
$498$	−1.04606	−	1.04606i	−0.0468749	−	0.0468749i
$499$		−	1.56231i		−	0.0699384i	−0.999388	−	0.0349692i	$-0.988867\pi$
$499$		−	1.56231i		−	0.0699384i	0.999388	−	0.0349692i	$-0.0111333\pi$
$500$		0			0
$501$		−	15.2144i		−	0.679728i
$502$	11.9087	+	11.9087i	0.531513	+	0.531513i
$503$	−1.66251	+	1.66251i	−0.0741276	+	0.0741276i	−0.743199	−	0.669071i	$-0.766692\pi$
$503$	−1.66251	+	1.66251i	−0.0741276	+	0.0741276i	0.669071	+	0.743199i	$0.266692\pi$
$504$		−	15.0000i		−	0.668153i
$505$		0			0
$506$	4.14590	+	5.33070i	0.184308	+	0.236979i
$507$	6.99109	−	6.99109i	0.310485	−	0.310485i
$508$	16.0650	−	16.0650i	0.712770	−	0.712770i
$509$		−	36.6869i		−	1.62612i	−0.582181	−	0.813060i	$-0.697800\pi$
$509$		−	36.6869i		−	1.62612i	0.582181	−	0.813060i	$-0.302200\pi$
$510$		0			0
$511$	−48.0902			−2.12738
$512$	−19.1938	−	19.1938i	−0.848254	−	0.848254i
$513$	4.62369	−	4.62369i	0.204141	−	0.204141i
$514$	34.5010			1.52178
$515$		0			0
$516$		−	23.8396i		−	1.04948i
$517$	−2.47446	+	19.7918i	−0.108827	+	0.870443i
$518$	54.2201	+	54.2201i	2.38229	+	2.38229i
$519$	−32.4649			−1.42505
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	−56.3122	+	56.3122i	−2.46472	+	2.46472i
$523$	−17.0175	+	17.0175i	−0.744125	+	0.744125i	−0.973369	−	0.229244i	$-0.926375\pi$
$523$	−17.0175	+	17.0175i	−0.744125	+	0.744125i	0.229244	+	0.973369i	$0.426375\pi$
$524$	−7.84752			−0.342821
$525$		0			0
$526$	52.0344			2.26881
$527$	1.22372	+	1.22372i	0.0533060	+	0.0533060i
$528$	42.5926	+	5.32511i	1.85360	+	0.231746i
$529$		−	21.8541i		−	0.950178i
$530$		0			0
$531$	−4.85410			−0.210650
$532$	−6.12372	+	6.12372i	−0.265497	+	0.265497i
$533$	−17.0782	−	17.0782i	−0.739738	−	0.739738i
$534$	49.7154			2.15140
$535$		0			0
$536$			5.03363i			0.217420i
$537$	30.2612	−	30.2612i	1.30587	−	1.30587i
$538$	27.2638	−	27.2638i	1.17542	−	1.17542i
$539$	−22.5812	−	29.0344i	−0.972642	−	1.25060i
$540$		0			0
$541$			3.29456i			0.141644i	0.997489	+	0.0708220i	$0.0225622\pi$
$541$			3.29456i			0.141644i	−0.997489	+	0.0708220i	$0.977438\pi$
$542$	19.4172	−	19.4172i	0.834041	−	0.834041i
$543$	19.8850	+	19.8850i	0.853349	+	0.853349i
$544$		−	8.61803i		−	0.369495i
$545$		0			0
$546$		−	69.7798i		−	2.98630i
$547$	21.2024	+	21.2024i	0.906551	+	0.906551i	0.995992	−	0.0894412i	$-0.0285081\pi$
$547$	21.2024	+	21.2024i	0.906551	+	0.906551i	−0.0894412	+	0.995992i	$0.528508\pi$
$548$	6.23416	+	6.23416i	0.266310	+	0.266310i
$549$	−28.2090			−1.20393
$550$		0			0
$551$	−10.8541			−0.462400
$552$	1.54123	+	1.54123i	0.0655991	+	0.0655991i
$553$	1.44562	+	1.44562i	0.0614738	+	0.0614738i
$554$		−	31.3820i		−	1.33329i
$555$		0			0
$556$		−	29.9481i		−	1.27008i
$557$	−1.14876	−	1.14876i	−0.0486747	−	0.0486747i	0.682350	−	0.731025i	$-0.260958\pi$
$557$	−1.14876	−	1.14876i	−0.0486747	−	0.0486747i	−0.731025	+	0.682350i	$0.760958\pi$
$558$	9.61121	−	9.61121i	0.406875	−	0.406875i
$559$			16.1803i			0.684355i
$560$		0			0
$561$	6.70820	+	8.62526i	0.283221	+	0.364159i
$562$	−19.4172	+	19.4172i	−0.819066	+	0.819066i
$563$	22.8649	−	22.8649i	0.963643	−	0.963643i	−0.0357191	−	0.999362i	$-0.511372\pi$
$563$	22.8649	−	22.8649i	0.963643	−	0.963643i	0.999362	+	0.0357191i	$0.0113722\pi$
$564$		−	27.2705i		−	1.14830i
$565$		0			0
$566$	−55.6525			−2.33925
$567$		0			0
$568$	−0.149908	+	0.149908i	−0.00629001	+	0.00629001i
$569$	−38.3897			−1.60938			−0.804691	−	0.593694i	$-0.797669\pi$
$569$	−38.3897			−1.60938			−0.804691	+	0.593694i	$0.797669\pi$
$570$		0			0
$571$		−	28.6897i		−	1.20063i	−0.799765	−	0.600313i	$-0.795043\pi$
$571$		−	28.6897i		−	1.20063i	0.799765	−	0.600313i	$-0.204957\pi$
$572$	16.3885	+	2.04897i	0.685239	+	0.0856715i
$573$	−11.1331	−	11.1331i	−0.465094	−	0.465094i
$574$	63.4878			2.64993
$575$		0			0
$576$	−22.8541			−0.952254
$577$	−17.2569	+	17.2569i	−0.718413	+	0.718413i	−0.968280	−	0.249867i	$-0.919613\pi$
$577$	−17.2569	+	17.2569i	−0.718413	+	0.718413i	0.249867	+	0.968280i	$0.419613\pi$
$578$	−21.0062	+	21.0062i	−0.873743	+	0.873743i
$579$	−14.7337			−0.612312
$580$		0			0
$581$	−1.18034			−0.0489687
$582$	−0.952532	−	0.952532i	−0.0394837	−	0.0394837i
$583$	−19.2778	−	2.41020i	−0.798406	−	0.0998202i
$584$		−	8.21478i		−	0.339930i
$585$		0			0
$586$	−6.18034			−0.255307
$587$	2.55992	−	2.55992i	0.105659	−	0.105659i	−0.652301	−	0.757960i	$-0.726196\pi$
$587$	2.55992	−	2.55992i	0.105659	−	0.105659i	0.757960	+	0.652301i	$0.226196\pi$
$588$	35.5598	+	35.5598i	1.46646	+	1.46646i
$589$	1.85255			0.0763329
$590$		0			0
$591$			16.9535i			0.697372i
$592$	−30.9499	+	30.9499i	−1.27203	+	1.27203i
$593$	−8.04135	+	8.04135i	−0.330219	+	0.330219i	−0.852669	−	0.522451i	$-0.825018\pi$
$593$	−8.04135	+	8.04135i	−0.330219	+	0.330219i	0.522451	+	0.852669i	$0.325018\pi$
$594$	25.8758	−	20.1246i	1.06170	−	0.825723i
$595$		0			0
$596$			23.8396i			0.976509i
$597$	16.9677	−	16.9677i	0.694443	−	0.694443i
$598$	4.43117	+	4.43117i	0.181204	+	0.181204i
$599$		−	26.5623i		−	1.08531i	−0.839957	−	0.542653i	$-0.817420\pi$
$599$		−	26.5623i		−	1.08531i	0.839957	−	0.542653i	$-0.182580\pi$
$600$		0			0
$601$			1.73908i			0.0709385i	0.999371	+	0.0354692i	$0.0112926\pi$
$601$			1.73908i			0.0709385i	−0.999371	+	0.0354692i	$0.988707\pi$
$602$	−30.0750	−	30.0750i	−1.22577	−	1.22577i
$603$	23.7801	+	23.7801i	0.968402	+	0.968402i
$604$	−4.55296			−0.185258
$605$		0			0
$606$	−39.2705			−1.59526
$607$	14.8699	+	14.8699i	0.603551	+	0.603551i	0.941253	−	0.337702i	$-0.109650\pi$
$607$	14.8699	+	14.8699i	0.603551	+	0.603551i	−0.337702	+	0.941253i	$0.609650\pi$
$608$	−6.52328	−	6.52328i	−0.264554	−	0.264554i
$609$			102.812i			4.16613i
$610$		0			0
$611$			18.5089i			0.748791i
$612$	−6.52875	−	6.52875i	−0.263909	−	0.263909i
$613$	−8.02366	+	8.02366i	−0.324072	+	0.324072i	−0.850327	−	0.526255i	$-0.823596\pi$
$613$	−8.02366	+	8.02366i	−0.324072	+	0.324072i	0.526255	+	0.850327i	$0.323596\pi$
$614$			47.3607i			1.91132i
$615$		0			0
$616$	8.09017	−	6.29204i	0.325962	−	0.253514i
$617$	23.4228	−	23.4228i	0.942965	−	0.942965i	−0.0554938	−	0.998459i	$-0.517673\pi$
$617$	23.4228	−	23.4228i	0.942965	−	0.942965i	0.998459	+	0.0554938i	$0.0176733\pi$
$618$	−65.8762	+	65.8762i	−2.64993	+	2.64993i
$619$		−	17.9443i		−	0.721241i	−0.932713	−	0.360621i	$-0.882565\pi$
$619$		−	17.9443i		−	0.721241i	0.932713	−	0.360621i	$-0.117435\pi$
$620$		0			0
$621$	5.56231			0.223208
$622$	−11.7125	−	11.7125i	−0.469629	−	0.469629i
$623$	28.0487	−	28.0487i	1.12375	−	1.12375i
$624$	39.8317			1.59455
$625$		0			0
$626$		−	45.1625i		−	1.80505i
$627$	11.6064	+	1.45109i	0.463516	+	0.0579508i
$628$	−20.7524	−	20.7524i	−0.828111	−	0.828111i
$629$	−11.1421			−0.444264
$630$		0			0
$631$	−27.2705			−1.08562			−0.542811	−	0.839855i	$-0.682640\pi$
$631$	−27.2705			−1.08562			−0.542811	+	0.839855i	$0.682640\pi$
$632$	−0.246941	+	0.246941i	−0.00982277	+	0.00982277i
$633$	−44.7487	+	44.7487i	−1.77860	+	1.77860i
$634$	−48.9377			−1.94356
$635$		0			0
$636$	26.5623			1.05326
$637$	−24.1350	−	24.1350i	−0.956263	−	0.956263i
$638$	−53.9929	−	6.75043i	−2.13760	−	0.267252i
$639$			1.41641i			0.0560322i
$640$		0			0
$641$	27.0000			1.06644			0.533218	−	0.845978i	$-0.320983\pi$
$641$	27.0000			1.06644			0.533218	+	0.845978i	$0.320983\pi$
$642$	−6.12372	+	6.12372i	−0.241684	+	0.241684i
$643$	23.5593	+	23.5593i	0.929087	+	0.929087i	0.997647	−	0.0685599i	$-0.0218404\pi$
$643$	23.5593	+	23.5593i	0.929087	+	0.929087i	−0.0685599	+	0.997647i	$0.521840\pi$
$644$	−7.36685			−0.290295
$645$		0			0
$646$		−	2.81389i		−	0.110711i
$647$	23.2702	−	23.2702i	0.914844	−	0.914844i	−0.0818043	−	0.996648i	$-0.526068\pi$
$647$	23.2702	−	23.2702i	0.914844	−	0.914844i	0.996648	+	0.0818043i	$0.0260683\pi$
$648$		0			0
$649$	−2.03615	−	2.61803i	−0.0799258	−	0.102767i
$650$		0			0
$651$		−	17.5476i		−	0.687744i
$652$	2.16037	−	2.16037i	0.0846065	−	0.0846065i
$653$	17.8351	+	17.8351i	0.697942	+	0.697942i	0.963966	−	0.266025i	$-0.0857102\pi$
$653$	17.8351	+	17.8351i	0.697942	+	0.697942i	−0.266025	+	0.963966i	$0.585710\pi$
$654$			10.8541i			0.424429i
$655$		0			0
$656$			36.2401i			1.41494i
$657$	−38.8087	−	38.8087i	−1.51407	−	1.51407i
$658$	−34.4033	−	34.4033i	−1.34118	−	1.34118i
$659$	31.5036			1.22720			0.613602	−	0.789615i	$-0.289720\pi$
$659$	31.5036			1.22720			0.613602	+	0.789615i	$0.289720\pi$
$660$		0			0
$661$	−11.2918			−0.439200			−0.219600	−	0.975590i	$-0.570475\pi$
$661$	−11.2918			−0.439200			−0.219600	+	0.975590i	$0.570475\pi$
$662$	−31.1775	−	31.1775i	−1.21175	−	1.21175i
$663$	7.16978	+	7.16978i	0.278451	+	0.278451i
$664$		−	0.201626i		−	0.00782461i
$665$		0			0
$666$			87.5110i			3.39098i
$667$	−6.52875	−	6.52875i	−0.252794	−	0.252794i
$668$	−6.21124	+	6.21124i	−0.240320	+	0.240320i
$669$			14.5623i			0.563011i
$670$		0			0
$671$	−11.8328	−	15.2144i	−0.456801	−	0.587344i
$672$	−61.7894	+	61.7894i	−2.38358	+	2.38358i
$673$	−7.55624	+	7.55624i	−0.291272	+	0.291272i	−0.837582	−	0.546311i	$-0.816032\pi$
$673$	−7.55624	+	7.55624i	−0.291272	+	0.291272i	0.546311	+	0.837582i	$0.316032\pi$
$674$			46.8328i			1.80393i
$675$		0			0
$676$	−5.70820			−0.219546
$677$	23.4250	+	23.4250i	0.900297	+	0.900297i	0.995462	−	0.0951650i	$-0.0303379\pi$
$677$	23.4250	+	23.4250i	0.900297	+	0.900297i	−0.0951650	+	0.995462i	$0.530338\pi$
$678$	48.7837	−	48.7837i	1.87353	−	1.87353i
$679$	−1.07481			−0.0412474
$680$		0			0
$681$		−	23.0619i		−	0.883734i
$682$	9.21537	+	1.15215i	0.352875	+	0.0441179i
$683$	−18.8129	−	18.8129i	−0.719856	−	0.719856i	0.248719	−	0.968576i	$-0.419990\pi$
$683$	−18.8129	−	18.8129i	−0.719856	−	0.719856i	−0.968576	+	0.248719i	$0.919990\pi$
$684$	−9.88367			−0.377912
$685$		0			0
$686$	33.0902			1.26339
$687$	−36.2063	+	36.2063i	−1.38136	+	1.38136i
$688$	17.1675	−	17.1675i	0.654503	−	0.654503i
$689$	−18.0283			−0.686822
$690$		0			0
$691$	−15.5623			−0.592018			−0.296009	−	0.955185i	$-0.595656\pi$
$691$	−15.5623			−0.592018			−0.296009	+	0.955185i	$0.595656\pi$
$692$	13.2537	+	13.2537i	0.503832	+	0.503832i
$693$	8.49480	−	67.9452i	0.322691	−	2.58102i
$694$		−	37.0344i		−	1.40581i
$695$		0			0
$696$	−17.5623			−0.665697
$697$	−6.52328	+	6.52328i	−0.247087	+	0.247087i
$698$	−23.6015	−	23.6015i	−0.893328	−	0.893328i
$699$	76.8496			2.90672
$700$		0			0
$701$			32.9456i			1.24434i	0.782883	+	0.622168i	$0.213748\pi$
$701$			32.9456i			1.24434i	−0.782883	+	0.622168i	$0.786252\pi$
$702$	21.5093	−	21.5093i	0.811818	−	0.811818i
$703$	−8.43382	+	8.43382i	−0.318087	+	0.318087i
$704$	−9.58660	−	12.3262i	−0.361309	−	0.464563i
$705$		0			0
$706$		−	46.9015i		−	1.76516i
$707$	−22.1558	+	22.1558i	−0.833256	+	0.833256i
$708$	3.20642	+	3.20642i	0.120505	+	0.120505i
$709$			2.18034i			0.0818844i	0.999162	+	0.0409422i	$0.0130359\pi$
$709$			2.18034i			0.0818844i	−0.999162	+	0.0409422i	$0.986964\pi$
$710$		0			0
$711$			2.33322i			0.0875025i
$712$	4.79129	+	4.79129i	0.179561	+	0.179561i
$713$	1.11431	+	1.11431i	0.0417312	+	0.0417312i
$714$	−26.6535			−0.997483
$715$		0			0
$716$	−24.7082			−0.923389
$717$	−30.7387	−	30.7387i	−1.14796	−	1.14796i
$718$	−8.86234	−	8.86234i	−0.330739	−	0.330739i
$719$		−	31.3607i		−	1.16956i	−0.811193	−	0.584778i	$-0.801182\pi$
$719$		−	31.3607i		−	1.16956i	0.811193	−	0.584778i	$-0.198818\pi$
$720$		0			0
$721$			74.3328i			2.76830i
$722$	23.4250	+	23.4250i	0.871789	+	0.871789i
$723$	−28.2449	+	28.2449i	−1.05044	+	1.05044i
$724$		−	16.2361i		−	0.603409i
$725$		0			0
$726$	56.8328	+	14.4366i	2.10926	+	0.535794i
$727$	−17.2569	+	17.2569i	−0.640022	+	0.640022i	−0.950561	−	0.310539i	$-0.899490\pi$
$727$	−17.2569	+	17.2569i	−0.640022	+	0.640022i	0.310539	+	0.950561i	$0.399490\pi$
$728$	6.72499	−	6.72499i	0.249245	−	0.249245i
$729$			43.6869i			1.61803i
$730$		0			0
$731$	6.18034			0.228588
$732$	18.6337	+	18.6337i	0.688722	+	0.688722i
$733$	1.39132	−	1.39132i	0.0513896	−	0.0513896i	−0.680945	−	0.732335i	$-0.738431\pi$
$733$	1.39132	−	1.39132i	0.0513896	−	0.0513896i	0.732335	+	0.680945i	$0.238431\pi$
$734$	−56.3045			−2.07824
$735$		0			0
$736$		−	7.84752i		−	0.289263i
$737$	−2.85065	+	22.8007i	−0.105005	+	0.839876i
$738$	51.2345	+	51.2345i	1.88597	+	1.88597i
$739$	42.8292			1.57550			0.787749	−	0.615996i	$-0.211246\pi$
$739$	42.8292			1.57550			0.787749	+	0.615996i	$0.211246\pi$
$740$		0			0
$741$	10.8541			0.398735
$742$	33.5099	−	33.5099i	1.23019	−	1.23019i
$743$	7.60256	−	7.60256i	0.278911	−	0.278911i	−0.553763	−	0.832674i	$-0.686809\pi$
$743$	7.60256	−	7.60256i	0.278911	−	0.278911i	0.832674	+	0.553763i	$0.186809\pi$
$744$	2.99749			0.109893
$745$		0			0
$746$	−28.2148			−1.03302
$747$	−0.952532	−	0.952532i	−0.0348513	−	0.0348513i
$748$	0.782635	−	6.25986i	0.0286160	−	0.228883i
$749$			6.90983i			0.252480i
$750$		0			0
$751$	−17.1459			−0.625663			−0.312831	−	0.949809i	$-0.601277\pi$
$751$	−17.1459			−0.625663			−0.312831	+	0.949809i	$0.601277\pi$
$752$	19.6381	−	19.6381i	0.716128	−	0.716128i
$753$	17.5460	+	17.5460i	0.639411	+	0.639411i
$754$	−50.4932			−1.83885
$755$		0			0
$756$			35.7595i			1.30056i
$757$	16.4999	−	16.4999i	0.599700	−	0.599700i	−0.340533	−	0.940233i	$-0.610607\pi$
$757$	16.4999	−	16.4999i	0.599700	−	0.599700i	0.940233	+	0.340533i	$0.110607\pi$
$758$	17.0925	−	17.0925i	0.620827	−	0.620827i
$759$	6.10844	+	7.85410i	0.221722	+	0.285086i
$760$		0			0
$761$			18.8060i			0.681717i	0.940115	+	0.340858i	$0.110718\pi$
$761$			18.8060i			0.681717i	−0.940115	+	0.340858i	$0.889282\pi$
$762$	52.9271	−	52.9271i	1.91735	−	1.91735i
$763$	6.12372	+	6.12372i	0.221694	+	0.221694i
$764$			9.09017i			0.328871i
$765$		0			0
$766$		−	0.961339i		−	0.0347346i
$767$	−2.17625	−	2.17625i	−0.0785799	−	0.0785799i
$768$	−40.1696	−	40.1696i	−1.44950	−	1.44950i
$769$	−11.3257			−0.408414			−0.204207	−	0.978928i	$-0.565462\pi$
$769$	−11.3257			−0.408414			−0.204207	+	0.978928i	$0.565462\pi$
$770$		0			0
$771$	50.8328			1.83070
$772$	6.01501	+	6.01501i	0.216485	+	0.216485i
$773$	33.6203	+	33.6203i	1.20924	+	1.20924i	0.971274	+	0.237964i	$0.0764799\pi$
$773$	33.6203	+	33.6203i	1.20924	+	1.20924i	0.237964	+	0.971274i	$0.423520\pi$
$774$		−	48.5410i		−	1.74477i
$775$		0			0
$776$		−	0.183599i		−	0.00659083i
$777$	79.8863	+	79.8863i	2.86590	+	2.86590i
$778$	−18.8300	+	18.8300i	−0.675087	+	0.675087i
$779$			9.87539i			0.353823i
$780$		0			0
$781$	−0.763932	+	0.594140i	−0.0273356	+	0.0212600i
$782$	1.69256	−	1.69256i	0.0605257	−	0.0605257i
$783$	−31.6912	+	31.6912i	−1.13255	+	1.13255i
$784$			51.2148i			1.82910i
$785$		0			0
$786$	−25.8541			−0.922185
$787$	7.79880	+	7.79880i	0.277997	+	0.277997i	0.832309	−	0.554312i	$-0.187019\pi$
$787$	7.79880	+	7.79880i	0.277997	+	0.277997i	−0.554312	+	0.832309i	$0.687019\pi$
$788$	6.92122	−	6.92122i	0.246558	−	0.246558i
$789$	76.6660			2.72938
$790$		0			0
$791$		−	55.0461i		−	1.95721i
$792$	11.6064	+	1.45109i	0.412416	+	0.0515621i
$793$	−12.6470	−	12.6470i	−0.449108	−	0.449108i
$794$	26.0594			0.924813
$795$		0			0
$796$	−13.8541			−0.491046
$797$	−24.8262	+	24.8262i	−0.879389	+	0.879389i	−0.993471	−	0.114082i	$-0.963607\pi$
$797$	−24.8262	+	24.8262i	−0.879389	+	0.879389i	0.114082	+	0.993471i	$0.463607\pi$
$798$	−20.1750	+	20.1750i	−0.714186	+	0.714186i
$799$	7.06978			0.250111
$800$		0			0
$801$	45.2705			1.59955
$802$	−34.1850	−	34.1850i	−1.20711	−	1.20711i
$803$	4.65220	−	37.2103i	0.164172	−	1.31312i
$804$		−	31.4164i		−	1.10797i
$805$		0			0
$806$	8.61803			0.303557
$807$	40.1696	−	40.1696i	1.41404	−	1.41404i
$808$	−3.78467	−	3.78467i	−0.133144	−	0.133144i
$809$	10.0673			0.353946			0.176973	−	0.984216i	$-0.443369\pi$
$809$	10.0673			0.353946			0.176973	+	0.984216i	$0.443369\pi$
$810$		0			0
$811$		−	4.36937i		−	0.153429i	−0.997053	−	0.0767146i	$-0.975557\pi$
$811$		−	4.36937i		−	0.153429i	0.997053	−	0.0767146i	$-0.0244430\pi$
$812$	41.9726	−	41.9726i	1.47295	−	1.47295i
$813$	28.6088	−	28.6088i	1.00335	−	1.00335i
$814$	−47.1986	+	36.7082i	−1.65431	+	1.28662i
$815$		0			0
$816$		−	15.2144i		−	0.532610i
$817$	4.67811	−	4.67811i	0.163666	−	0.163666i
$818$	−37.1419	−	37.1419i	−1.29864	−	1.29864i
$819$		−	63.5410i		−	2.22030i
$820$		0			0
$821$		−	33.9069i		−	1.18336i	−0.806173	−	0.591680i	$-0.798465\pi$
$821$		−	33.9069i		−	1.18336i	0.806173	−	0.591680i	$-0.201535\pi$
$822$	20.5388	+	20.5388i	0.716373	+	0.716373i
$823$	−9.79796	−	9.79796i	−0.341535	−	0.341535i	0.515409	−	0.856944i	$-0.327640\pi$
$823$	−9.79796	−	9.79796i	−0.341535	−	0.341535i	−0.856944	+	0.515409i	$0.827640\pi$
$824$	−12.6976			−0.442340
$825$		0			0
$826$	8.09017			0.281493
$827$	−34.4275	−	34.4275i	−1.19716	−	1.19716i	−0.975012	−	0.222151i	$-0.928692\pi$
$827$	−34.4275	−	34.4275i	−1.19716	−	1.19716i	−0.222151	−	0.975012i	$-0.571308\pi$
$828$	−5.94504	−	5.94504i	−0.206604	−	0.206604i
$829$			21.3262i			0.740691i	0.928894	+	0.370345i	$0.120761\pi$
$829$			21.3262i			0.740691i	−0.928894	+	0.370345i	$0.879239\pi$
$830$		0			0
$831$		−	46.2373i		−	1.60395i
$832$	−10.2462	−	10.2462i	−0.355224	−	0.355224i
$833$	−9.21875	+	9.21875i	−0.319411	+	0.319411i
$834$		−	98.6656i		−	3.41651i
$835$		0			0
$836$	−4.14590	−	5.33070i	−0.143389	−	0.184366i
$837$	5.40897	−	5.40897i	0.186961	−	0.186961i
$838$	46.2900	−	46.2900i	1.59906	−	1.59906i
$839$		−	18.1459i		−	0.626466i	−0.949676	−	0.313233i	$-0.898588\pi$
$839$		−	18.1459i		−	0.626466i	0.949676	−	0.313233i	$-0.101412\pi$
$840$		0			0
$841$	45.3951			1.56535
$842$	−33.7462	−	33.7462i	−1.16297	−	1.16297i
$843$	−28.6088	+	28.6088i	−0.985338	+	0.985338i
$844$	36.5372			1.25766
$845$		0			0
$846$		−	55.5268i		−	1.90905i
$847$	40.2092	−	23.9193i	1.38160	−	0.821877i
$848$	19.1281	+	19.1281i	0.656862	+	0.656862i
$849$	−81.9967			−2.81412
$850$		0			0
$851$	−10.1459			−0.347797
$852$	0.935622	−	0.935622i	0.0320539	−	0.0320539i
$853$	32.5688	−	32.5688i	1.11513	−	1.11513i	0.122690	−	0.992445i	$-0.460848\pi$
$853$	32.5688	−	32.5688i	1.11513	−	1.11513i	0.992445	−	0.122690i	$-0.0391520\pi$
$854$	47.0150			1.60882
$855$		0			0
$856$	−1.18034			−0.0403432
$857$	8.04135	+	8.04135i	0.274687	+	0.274687i	0.830984	−	0.556297i	$-0.187778\pi$
$857$	8.04135	+	8.04135i	0.274687	+	0.274687i	−0.556297	+	0.830984i	$0.687778\pi$
$858$	53.9929	+	6.75043i	1.84329	+	0.230456i
$859$			50.7214i			1.73059i	0.501263	+	0.865295i	$0.332869\pi$
$859$			50.7214i			1.73059i	−0.501263	+	0.865295i	$0.667131\pi$
$860$		0			0
$861$	93.5410			3.18787
$862$	−7.16978	+	7.16978i	−0.244204	+	0.244204i
$863$	35.9593	+	35.9593i	1.22407	+	1.22407i	0.966172	+	0.257898i	$0.0830299\pi$
$863$	35.9593	+	35.9593i	1.22407	+	1.22407i	0.257898	+	0.966172i	$0.416970\pi$
$864$	−38.0927			−1.29594
$865$		0			0
$866$			6.40551i			0.217668i
$867$	−30.9499	+	30.9499i	−1.05111	+	1.05111i
$868$	−7.16377	+	7.16377i	−0.243154	+	0.243154i
$869$	−1.25841	+	0.978714i	−0.0426886	+	0.0332006i
$870$		0			0
$871$			21.3228i			0.722496i
$872$	−1.04606	+	1.04606i	−0.0354240	+	0.0354240i
$873$	−0.867369	−	0.867369i	−0.0293560	−	0.0293560i
$874$		−	2.56231i		−	0.0866713i
$875$		0			0
$876$			51.2709i			1.73228i
$877$	35.4550	+	35.4550i	1.19723	+	1.19723i	0.974992	+	0.222239i	$0.0713366\pi$
$877$	35.4550	+	35.4550i	1.19723	+	1.19723i	0.222239	+	0.974992i	$0.428663\pi$
$878$	34.8028	+	34.8028i	1.17454	+	1.17454i
$879$	−9.10593			−0.307135
$880$		0			0
$881$	−10.4377			−0.351655			−0.175827	−	0.984421i	$-0.556260\pi$
$881$	−10.4377			−0.351655			−0.175827	+	0.984421i	$0.556260\pi$
$882$	72.4050	+	72.4050i	2.43800	+	2.43800i
$883$	14.0504	+	14.0504i	0.472835	+	0.472835i	0.902831	−	0.429996i	$-0.141485\pi$
$883$	14.0504	+	14.0504i	0.472835	+	0.472835i	−0.429996	+	0.902831i	$0.641485\pi$
$884$		−	5.85410i		−	0.196895i
$885$		0			0
$886$			2.51682i			0.0845541i
$887$	14.3562	+	14.3562i	0.482033	+	0.482033i	0.905780	−	0.423747i	$-0.139286\pi$
$887$	14.3562	+	14.3562i	0.482033	+	0.482033i	−0.423747	+	0.905780i	$0.639286\pi$
$888$	−13.6462	+	13.6462i	−0.457937	+	0.457937i
$889$		−	59.7214i		−	2.00299i
$890$		0			0
$891$		0			0
$892$	5.94504	−	5.94504i	0.199055	−	0.199055i
$893$	5.35136	−	5.35136i	0.179076	−	0.179076i
$894$			78.5410i			2.62680i
$895$		0			0
$896$	−24.2705			−0.810821
$897$	6.52875	+	6.52875i	0.217989	+	0.217989i
$898$	36.8287	−	36.8287i	1.22899	−	1.22899i
$899$	−12.6976			−0.423487
$900$		0			0
$901$			6.88618i			0.229412i
$902$	−6.14175	+	49.1244i	−0.204498	+	1.63566i
$903$	−44.3117	−	44.3117i	−1.47460	−	1.47460i
$904$	9.40300			0.312739
$905$		0			0
$906$	−15.0000			−0.498342
$907$	0.220870	−	0.220870i	0.00733388	−	0.00733388i	−0.703430	−	0.710764i	$-0.748349\pi$
$907$	0.220870	−	0.220870i	0.00733388	−	0.00733388i	0.710764	+	0.703430i	$0.248349\pi$
$908$	−9.41498	+	9.41498i	−0.312447	+	0.312447i
$909$	−35.7595			−1.18607
$910$		0			0
$911$	3.70820			0.122858			0.0614291	−	0.998111i	$-0.480434\pi$
$911$	3.70820			0.122858			0.0614291	+	0.998111i	$0.480434\pi$
$912$	−11.5163	−	11.5163i	−0.381342	−	0.381342i
$913$	0.114185	−	0.913301i	0.00377897	−	0.0302259i
$914$			70.4508i			2.33031i
$915$		0			0
$916$	29.5623			0.976766
$917$	−14.5865	+	14.5865i	−0.481689	+	0.481689i
$918$	−8.21584	−	8.21584i	−0.271163	−	0.271163i
$919$	24.4338			0.805996			0.402998	−	0.915201i	$-0.367968\pi$
$919$	24.4338			0.805996			0.402998	+	0.915201i	$0.367968\pi$
$920$		0			0
$921$			69.7798i			2.29932i
$922$	41.3261	−	41.3261i	1.36100	−	1.36100i
$923$	−0.635021	+	0.635021i	−0.0209020	+	0.0209020i
$924$	−50.4932	+	39.2705i	−1.66110	+	1.29190i
$925$		0			0
$926$			4.25590i			0.139857i
$927$	−59.9864	+	59.9864i	−1.97021	+	1.97021i
$928$	44.7112	+	44.7112i	1.46772	+	1.46772i
$929$			11.0000i			0.360898i	0.983584	+	0.180449i	$0.0577551\pi$
$929$			11.0000i			0.360898i	−0.983584	+	0.180449i	$0.942245\pi$
$930$		0			0
$931$			13.9560i			0.457388i
$932$	−31.3737	−	31.3737i	−1.02768	−	1.02768i
$933$	−17.2569	−	17.2569i	−0.564964	−	0.564964i
$934$	−31.8006			−1.04055
$935$		0			0
$936$	10.8541			0.354777
$937$	11.7875	+	11.7875i	0.385080	+	0.385080i	0.872928	−	0.487849i	$-0.162218\pi$
$937$	11.7875	+	11.7875i	0.385080	+	0.385080i	−0.487849	+	0.872928i	$0.662218\pi$
$938$	−39.6336	−	39.6336i	−1.29408	−	1.29408i
$939$		−	66.5410i		−	2.17148i
$940$		0			0
$941$		−	30.7258i		−	1.00163i	−0.865553	−	0.500817i	$-0.833033\pi$
$941$		−	30.7258i		−	1.00163i	0.865553	−	0.500817i	$-0.166967\pi$
$942$	−68.3700	−	68.3700i	−2.22761	−	2.22761i
$943$	−5.94006	+	5.94006i	−0.193435	+	0.193435i
$944$			4.61803i			0.150304i
$945$		0			0
$946$	26.1803	−	20.3615i	0.851196	−	0.662009i
$947$	6.83848	−	6.83848i	0.222221	−	0.222221i	−0.587212	−	0.809433i	$-0.699775\pi$
$947$	6.83848	−	6.83848i	0.222221	−	0.222221i	0.809433	+	0.587212i	$0.199775\pi$
$948$	1.54123	−	1.54123i	0.0500568	−	0.0500568i
$949$		−	34.7984i		−	1.12960i
$950$		0			0
$951$	−72.1033			−2.33811
$952$	−2.56872	−	2.56872i	−0.0832526	−	0.0832526i
$953$	−11.3950	+	11.3950i	−0.369120	+	0.369120i	−0.867156	−	0.498036i	$-0.834055\pi$
$953$	−11.3950	+	11.3950i	−0.369120	+	0.369120i	0.498036	+	0.867156i	$0.334055\pi$
$954$	54.0848			1.75106
$955$		0			0
$956$			25.0980i			0.811729i
$957$	−79.5516	−	9.94589i	−2.57154	−	0.321505i
$958$	29.0787	+	29.0787i	0.939490	+	0.939490i
$959$	23.1754			0.748372
$960$		0			0
$961$	−28.8328			−0.930091
$962$	−39.2340	+	39.2340i	−1.26496	+	1.26496i
$963$	−5.57622	+	5.57622i	−0.179691	+	0.179691i
$964$	23.0619			0.742774
$965$		0			0
$966$	−24.2705			−0.780891
$967$	6.84626	+	6.84626i	0.220161	+	0.220161i	0.808566	−	0.588405i	$-0.200244\pi$
$967$	6.84626	+	6.84626i	0.220161	+	0.220161i	−0.588405	+	0.808566i	$0.700244\pi$
$968$	4.08590	+	6.86855i	0.131326	+	0.220763i
$969$		−	4.14590i		−	0.133185i
$970$		0			0
$971$	−30.4377			−0.976792			−0.488396	−	0.872622i	$-0.662418\pi$
$971$	−30.4377			−0.976792			−0.488396	+	0.872622i	$0.662418\pi$
$972$	17.8351	−	17.8351i	0.572061	−	0.572061i
$973$	−55.6657	−	55.6657i	−1.78456	−	1.78456i
$974$	−2.33322			−0.0747611
$975$		0			0
$976$			26.8371i			0.859035i
$977$	25.3623	−	25.3623i	0.811411	−	0.811411i	−0.173435	−	0.984845i	$-0.555487\pi$
$977$	25.3623	−	25.3623i	0.811411	−	0.811411i	0.984845	+	0.173435i	$0.0554865\pi$
$978$	7.11745	−	7.11745i	0.227591	−	0.227591i
$979$	18.9896	+	24.4164i	0.606910	+	0.780352i
$980$		0			0
$981$			9.88367i			0.315561i
$982$	−41.3261	+	41.3261i	−1.31877	+	1.31877i
$983$	−29.6147	−	29.6147i	−0.944564	−	0.944564i	0.0539784	−	0.998542i	$-0.482810\pi$
$983$	−29.6147	−	29.6147i	−0.944564	−	0.944564i	−0.998542	+	0.0539784i	$0.982810\pi$
$984$			15.9787i			0.509383i
$985$		0			0
$986$			19.2867i			0.614213i
$987$	−50.6888	−	50.6888i	−1.61344	−	1.61344i
$988$	−4.43117	−	4.43117i	−0.140974	−	0.140974i
$989$	5.62777			0.178953
$990$		0			0
$991$	−34.6312			−1.10010			−0.550048	−	0.835133i	$-0.685391\pi$
$991$	−34.6312			−1.10010			−0.550048	+	0.835133i	$0.685391\pi$
$992$	−7.63119	−	7.63119i	−0.242291	−	0.242291i
$993$	−45.9360	−	45.9360i	−1.45773	−	1.45773i
$994$		−	2.36068i		−	0.0748762i
$995$		0			0
$996$			1.25841i			0.0398742i
$997$	−36.0437	−	36.0437i	−1.14152	−	1.14152i	−0.988173	−	0.153344i	$-0.950996\pi$
$997$	−36.0437	−	36.0437i	−1.14152	−	1.14152i	−0.153344	−	0.988173i	$-0.549004\pi$
$998$	−2.10130	+	2.10130i	−0.0665154	+	0.0665154i
$999$			49.2492i			1.55818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.e.d.43.1	yes	16
5.2	odd	4	inner	275.2.e.d.32.7	yes	16
5.3	odd	4	inner	275.2.e.d.32.2	yes	16
5.4	even	2	inner	275.2.e.d.43.8	yes	16
11.10	odd	2	inner	275.2.e.d.43.7	yes	16
55.32	even	4	inner	275.2.e.d.32.1	✓	16
55.43	even	4	inner	275.2.e.d.32.8	yes	16
55.54	odd	2	inner	275.2.e.d.43.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.e.d.32.1	✓	16	55.32	even	4	inner
275.2.e.d.32.2	yes	16	5.3	odd	4	inner
275.2.e.d.32.7	yes	16	5.2	odd	4	inner
275.2.e.d.32.8	yes	16	55.43	even	4	inner
275.2.e.d.43.1	yes	16	1.1	even	1	trivial
275.2.e.d.43.2	yes	16	55.54	odd	2	inner
275.2.e.d.43.7	yes	16	11.10	odd	2	inner
275.2.e.d.43.8	yes	16	5.4	even	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 1.34500i) q^{2} +(-1.98168 - 1.98168i) q^{3} +1.61803i q^{4} +5.33070i q^{6} +(3.00750 + 3.00750i) q^{7} +(-0.513743 + 0.513743i) q^{8} +4.85410i q^{9} +O(q^{10})\)	\(q+(-1.34500 - 1.34500i) q^{2} +(-1.98168 - 1.98168i) q^{3} +1.61803i q^{4} +5.33070i q^{6} +(3.00750 + 3.00750i) q^{7} +(-0.513743 + 0.513743i) q^{8} +4.85410i q^{9} +(-2.61803 + 2.03615i) q^{11} +(3.20642 - 3.20642i) q^{12} +(-2.17625 + 2.17625i) q^{13} -8.09017i q^{14} +4.61803 q^{16} +(0.831254 + 0.831254i) q^{17} +(6.52875 - 6.52875i) q^{18} +1.25841 q^{19} -11.9198i q^{21} +(6.25986 + 0.782635i) q^{22} +(0.756934 + 0.756934i) q^{23} +2.03615 q^{24} +5.85410 q^{26} +(3.67423 - 3.67423i) q^{27} +(-4.86624 + 4.86624i) q^{28} -8.62526 q^{29} +1.47214 q^{31} +(-5.18376 - 5.18376i) q^{32} +(9.22309 + 1.15311i) q^{33} -2.23607i q^{34} -7.85410 q^{36} +(-6.70197 + 6.70197i) q^{37} +(-1.69256 - 1.69256i) q^{38} +8.62526 q^{39} +7.84752i q^{41} +(-16.0321 + 16.0321i) q^{42} +(3.71748 - 3.71748i) q^{43} +(-3.29456 - 4.23607i) q^{44} -2.03615i q^{46} +(4.25248 - 4.25248i) q^{47} +(-9.15146 - 9.15146i) q^{48} +11.0902i q^{49} -3.29456i q^{51} +(-3.52125 - 3.52125i) q^{52} +(4.14205 + 4.14205i) q^{53} -9.88367 q^{54} -3.09017 q^{56} +(-2.49376 - 2.49376i) q^{57} +(11.6009 + 11.6009i) q^{58} +1.00000i q^{59} +5.81137i q^{61} +(-1.98002 - 1.98002i) q^{62} +(-14.5987 + 14.5987i) q^{63} +4.70820i q^{64} +(-10.8541 - 13.9560i) q^{66} +(4.89898 - 4.89898i) q^{67} +(-1.34500 + 1.34500i) q^{68} -3.00000i q^{69} +0.291796 q^{71} +(-2.49376 - 2.49376i) q^{72} +(-7.99503 + 7.99503i) q^{73} +18.0283 q^{74} +2.03615i q^{76} +(-13.9975 - 1.75003i) q^{77} +(-11.6009 - 11.6009i) q^{78} +0.480669 q^{79} +(10.5549 - 10.5549i) q^{82} +(-0.196232 + 0.196232i) q^{83} +19.2867 q^{84} -10.0000 q^{86} +(17.0925 + 17.0925i) q^{87} +(0.298940 - 2.39105i) q^{88} -9.32624i q^{89} -13.0902 q^{91} +(-1.22474 + 1.22474i) q^{92} +(-2.91730 - 2.91730i) q^{93} -11.4391 q^{94} +20.5451i q^{96} +(-0.178688 + 0.178688i) q^{97} +(14.9162 - 14.9162i) q^{98} +(-9.88367 - 12.7082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 24 q^{11} + 56 q^{16} + 40 q^{26} - 48 q^{31} - 72 q^{36} + 40 q^{56} - 120 q^{66} + 112 q^{71} - 160 q^{86} - 120 q^{91}+O(q^{100}) \) 16 * q - 24 * q^11 + 56 * q^16 + 40 * q^26 - 48 * q^31 - 72 * q^36 + 40 * q^56 - 120 * q^66 + 112 * q^71 - 160 * q^86 - 120 * q^91

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