LMFDB - Embedded newform 252.2.be.a.107.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(107,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("252.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.be (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.6
Character	$\chi$	$=$	252.107
Dual form			252.2.be.a.179.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.754782 - 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(-1.80224 - 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(2.80871 - 0.333415i) q^{8} +O(q^{10})$	\(q+(-0.754782 - 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(-1.80224 - 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(2.80871 - 0.333415i) q^{8} +(0.115881 + 2.94076i) q^{10} +(-2.13406 - 3.69630i) q^{11} -4.80655 q^{13} +(-3.63879 - 0.871343i) q^{14} +(-2.51871 - 3.10743i) q^{16} +(-2.77574 + 1.60257i) q^{17} +(-2.43886 - 1.40807i) q^{19} +(3.42954 - 2.35822i) q^{20} +(-2.80985 + 5.34213i) q^{22} +(2.33061 - 4.03674i) q^{23} +(-0.334629 - 0.579595i) q^{25} +(3.62790 + 5.74841i) q^{26} +(1.70441 + 5.00949i) q^{28} +3.87198i q^{29} +(8.90803 - 5.14305i) q^{31} +(-1.81526 + 5.35769i) q^{32} +(4.01168 + 2.11006i) q^{34} +(-5.33587 + 1.35781i) q^{35} +(-0.136891 + 0.237102i) q^{37} +(0.156815 + 3.97955i) q^{38} +(-5.40888 - 2.32163i) q^{40} +0.387186i q^{41} -0.907954i q^{43} +(8.50977 - 0.671702i) q^{44} +(-6.58686 + 0.259557i) q^{46} +(-3.92882 + 6.80492i) q^{47} +(0.176657 - 6.99777i) q^{49} +(-0.440596 + 0.837668i) q^{50} +(4.13655 - 8.67759i) q^{52} +(10.1385 - 5.85348i) q^{53} +8.88214i q^{55} +(4.70466 - 5.81947i) q^{56} +(4.63071 - 2.92250i) q^{58} +(1.85252 + 3.20865i) q^{59} +(4.01168 - 6.94844i) q^{61} +(-12.8745 - 6.77170i) q^{62} +(7.77767 - 1.87293i) q^{64} +(8.66254 + 5.00132i) q^{65} +(-1.21588 + 0.701986i) q^{67} +(-0.504416 - 6.39042i) q^{68} +(5.65130 + 5.35660i) q^{70} +11.9134 q^{71} +(6.14118 + 10.6368i) q^{73} +(0.386885 - 0.0152453i) q^{74} +(4.64099 - 3.19124i) q^{76} +(-10.8698 - 3.06010i) q^{77} +(0.715577 + 0.413138i) q^{79} +(1.30597 + 8.22109i) q^{80} +(0.463056 - 0.292241i) q^{82} -5.69055 q^{83} +6.67006 q^{85} +(-1.08587 + 0.685308i) q^{86} +(-7.22635 - 9.67029i) q^{88} +(-2.61763 - 1.51129i) q^{89} +(-9.10499 + 8.87804i) q^{91} +(5.28206 + 7.68166i) q^{92} +(11.1038 - 0.437547i) q^{94} +(2.93026 + 5.07536i) q^{95} -15.2972 q^{97} +(-8.50234 + 5.07052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) $ 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.754782	−	1.19595i	−0.533712	−	0.845666i
$2$	−0.754782	−	1.19595i	−0.533712	−	0.845666i
$3$		0			0
$3$		0			0
$4$	−0.860607	+	1.80537i	−0.430304	+	0.902684i
$5$	−1.80224	−	1.04052i	−0.805985	−	0.465335i	0.0395749	−	0.999217i	$-0.487400\pi$
$5$	−1.80224	−	1.04052i	−0.805985	−	0.465335i	−0.845560	+	0.533881i	$0.820733\pi$
$6$		0			0
$7$	1.89429	−	1.84707i	0.715974	−	0.698127i
$7$	1.89429	−	1.84707i	0.715974	−	0.698127i
$8$	2.80871	−	0.333415i	0.993028	−	0.117880i
$9$		0			0
$10$	0.115881	+	2.94076i	0.0366449	+	0.929949i
$11$	−2.13406	−	3.69630i	−0.643443	−	1.11448i	−0.984659	−	0.174491i	$-0.944172\pi$
$11$	−2.13406	−	3.69630i	−0.643443	−	1.11448i	0.341216	−	0.939985i	$-0.389161\pi$
$12$		0			0
$13$	−4.80655			−1.33310			−0.666548	−	0.745462i	$-0.732229\pi$
$13$	−4.80655			−1.33310			−0.666548	+	0.745462i	$0.732229\pi$
$14$	−3.63879	−	0.871343i	−0.972506	−	0.232876i
$15$		0			0
$16$	−2.51871	−	3.10743i	−0.629678	−	0.776856i
$17$	−2.77574	+	1.60257i	−0.673216	+	0.388681i	−0.797294	−	0.603591i	$-0.793736\pi$
$17$	−2.77574	+	1.60257i	−0.673216	+	0.388681i	0.124078	+	0.992272i	$0.460403\pi$
$18$		0			0
$19$	−2.43886	−	1.40807i	−0.559512	−	0.323034i	0.193438	−	0.981113i	$-0.438036\pi$
$19$	−2.43886	−	1.40807i	−0.559512	−	0.323034i	−0.752950	+	0.658078i	$0.771370\pi$
$20$	3.42954	−	2.35822i	0.766869	−	0.527314i
$21$		0			0
$22$	−2.80985	+	5.34213i	−0.599062	+	1.13895i
$23$	2.33061	−	4.03674i	0.485966	−	0.841718i	−0.513904	−	0.857848i	$-0.671801\pi$
$23$	2.33061	−	4.03674i	0.485966	−	0.841718i	0.999870	+	0.0161296i	$0.00513445\pi$
$24$		0			0
$25$	−0.334629	−	0.579595i	−0.0669258	−	0.115919i
$26$	3.62790	+	5.74841i	0.711489	+	1.12735i
$27$		0			0
$28$	1.70441	+	5.00949i	0.322102	+	0.946705i
$29$			3.87198i			0.719009i	0.933143	+	0.359504i	$0.117054\pi$
$29$			3.87198i			0.719009i	−0.933143	+	0.359504i	$0.882946\pi$
$30$		0			0
$31$	8.90803	−	5.14305i	1.59993	−	0.923720i	0.608431	−	0.793607i	$-0.291799\pi$
$31$	8.90803	−	5.14305i	1.59993	−	0.923720i	0.991499	−	0.130113i	$-0.0415339\pi$
$32$	−1.81526	+	5.35769i	−0.320895	+	0.947115i
$33$		0			0
$34$	4.01168	+	2.11006i	0.687998	+	0.361872i
$35$	−5.33587	+	1.35781i	−0.901927	+	0.229512i
$36$		0			0
$37$	−0.136891	+	0.237102i	−0.0225047	+	0.0389793i	−0.877058	−	0.480384i	$-0.840497\pi$
$37$	−0.136891	+	0.237102i	−0.0225047	+	0.0389793i	0.854554	+	0.519363i	$0.173831\pi$
$38$	0.156815	+	3.97955i	0.0254388	+	0.645568i
$39$		0			0
$40$	−5.40888	−	2.32163i	−0.855219	−	0.367082i
$41$			0.387186i			0.0604683i	0.999543	+	0.0302341i	$0.00962529\pi$
$41$			0.387186i			0.0604683i	−0.999543	+	0.0302341i	$0.990375\pi$
$42$		0			0
$43$		−	0.907954i		−	0.138462i	−0.997601	−	0.0692308i	$-0.977945\pi$
$43$		−	0.907954i		−	0.138462i	0.997601	−	0.0692308i	$-0.0220545\pi$
$44$	8.50977	−	0.671702i	1.28290	−	0.101263i
$45$		0			0
$46$	−6.58686	+	0.259557i	−0.971179	+	0.0382696i
$47$	−3.92882	+	6.80492i	−0.573078	+	0.992599i	0.423170	+	0.906050i	$0.360917\pi$
$47$	−3.92882	+	6.80492i	−0.573078	+	0.992599i	−0.996248	+	0.0865492i	$0.972416\pi$
$48$		0			0
$49$	0.176657	−	6.99777i	0.0252367	−	0.999682i
$50$	−0.440596	+	0.837668i	−0.0623096	+	0.118464i
$51$		0			0
$52$	4.13655	−	8.67759i	0.573636	−	1.20337i
$53$	10.1385	−	5.85348i	1.39263	−	0.804037i	0.399027	−	0.916939i	$-0.369348\pi$
$53$	10.1385	−	5.85348i	1.39263	−	0.804037i	0.993606	+	0.112902i	$0.0360147\pi$
$54$		0			0
$55$			8.88214i			1.19767i
$56$	4.70466	−	5.81947i	0.628687	−	0.777659i
$57$		0			0
$58$	4.63071	−	2.92250i	0.608041	−	0.383743i
$59$	1.85252	+	3.20865i	0.241177	+	0.417731i	0.961050	−	0.276375i	$-0.0891331\pi$
$59$	1.85252	+	3.20865i	0.241177	+	0.417731i	−0.719873	+	0.694106i	$0.755800\pi$
$60$		0			0
$61$	4.01168	−	6.94844i	0.513644	−	0.889657i	−0.486231	−	0.873830i	$-0.661629\pi$
$61$	4.01168	−	6.94844i	0.513644	−	0.889657i	0.999875	−	0.0158266i	$-0.00503796\pi$
$62$	−12.8745	−	6.77170i	−1.63506	−	0.860007i
$63$		0			0
$64$	7.77767	−	1.87293i	0.972209	−	0.234116i
$65$	8.66254	+	5.00132i	1.07446	+	0.620337i
$66$		0			0
$67$	−1.21588	+	0.701986i	−0.148543	+	0.0857613i	−0.572429	−	0.819954i	$-0.693999\pi$
$67$	−1.21588	+	0.701986i	−0.148543	+	0.0857613i	0.423886	+	0.905715i	$0.360666\pi$
$68$	−0.504416	−	6.39042i	−0.0611694	−	0.774953i
$69$		0			0
$70$	5.65130	+	5.35660i	0.675460	+	0.640236i
$71$	11.9134			1.41386			0.706931	−	0.707282i	$-0.250079\pi$
$71$	11.9134			1.41386			0.706931	+	0.707282i	$0.250079\pi$
$72$		0			0
$73$	6.14118	+	10.6368i	0.718770	+	1.24495i	0.961487	+	0.274850i	$0.0886281\pi$
$73$	6.14118	+	10.6368i	0.718770	+	1.24495i	−0.242717	+	0.970097i	$0.578039\pi$
$74$	0.386885	−	0.0152453i	0.0449745	−	0.00177223i
$75$		0			0
$76$	4.64099	−	3.19124i	0.532358	−	0.366060i
$77$	−10.8698	−	3.06010i	−1.23873	−	0.348730i
$78$		0			0
$79$	0.715577	+	0.413138i	0.0805087	+	0.0464817i	0.539714	−	0.841848i	$-0.318532\pi$
$79$	0.715577	+	0.413138i	0.0805087	+	0.0464817i	−0.459205	+	0.888330i	$0.651866\pi$
$80$	1.30597	+	8.22109i	0.146012	+	0.919146i
$81$		0			0
$82$	0.463056	−	0.292241i	0.0511360	−	0.0322726i
$83$	−5.69055			−0.624619			−0.312310	−	0.949980i	$-0.601103\pi$
$83$	−5.69055			−0.624619			−0.312310	+	0.949980i	$0.601103\pi$
$84$		0			0
$85$	6.67006			0.723469
$86$	−1.08587	+	0.685308i	−0.117092	+	0.0738986i
$87$		0			0
$88$	−7.22635	−	9.67029i	−0.770331	−	1.03086i
$89$	−2.61763	−	1.51129i	−0.277469	−	0.160197i	0.354808	−	0.934939i	$-0.384546\pi$
$89$	−2.61763	−	1.51129i	−0.277469	−	0.160197i	−0.632277	+	0.774742i	$0.717879\pi$
$90$		0			0
$91$	−9.10499	+	8.87804i	−0.954462	+	0.930671i
$92$	5.28206	+	7.68166i	0.550693	+	0.800868i
$93$		0			0
$94$	11.1038	−	0.437547i	1.14527	−	0.0451295i
$95$	2.93026	+	5.07536i	0.300639	+	0.520721i
$96$		0			0
$97$	−15.2972			−1.55319			−0.776595	−	0.630000i	$-0.783055\pi$
$97$	−15.2972			−1.55319			−0.776595	+	0.630000i	$0.783055\pi$
$98$	−8.50234	+	5.07052i	−0.858866	+	0.512200i
$99$		0			0
$100$	1.33437	−	0.105326i	0.133437	−	0.0105326i
$101$	0.335313	−	0.193593i	0.0333649	−	0.0192632i	−0.483225	−	0.875496i	$-0.660535\pi$
$101$	0.335313	−	0.193593i	0.0333649	−	0.0192632i	0.516590	+	0.856233i	$0.327201\pi$
$102$		0			0
$103$	−11.7225	−	6.76797i	−1.15505	−	0.666868i	−0.204937	−	0.978775i	$-0.565699\pi$
$103$	−11.7225	−	6.76797i	−1.15505	−	0.666868i	−0.950113	+	0.311907i	$0.899032\pi$
$104$	−13.5002	+	1.60257i	−1.32380	+	0.157145i
$105$		0			0
$106$	−14.6529	−	7.70709i	−1.42321	−	0.748579i
$107$	5.44204	−	9.42590i	0.526102	−	0.911236i	−0.473435	−	0.880829i	$-0.656986\pi$
$107$	5.44204	−	9.42590i	0.526102	−	0.911236i	0.999538	−	0.0304073i	$-0.00968045\pi$
$108$		0			0
$109$	9.35800	+	16.2085i	0.896334	+	1.55250i	0.832145	+	0.554558i	$0.187113\pi$
$109$	9.35800	+	16.2085i	0.896334	+	1.55250i	0.0641884	+	0.997938i	$0.479554\pi$
$110$	10.6226	−	6.70408i	1.01283	−	0.639209i
$111$		0			0
$112$	−10.5108	−	1.23412i	−0.993177	−	0.116614i
$113$		−	13.1377i		−	1.23589i	−0.786221	−	0.617945i	$-0.787965\pi$
$113$		−	13.1377i		−	1.23589i	0.786221	−	0.617945i	$-0.212035\pi$
$114$		0			0
$115$	−8.40063	+	4.85011i	−0.783363	+	0.452275i
$116$	−6.99035	−	3.33225i	−0.649038	−	0.309392i
$117$		0			0
$118$	2.43915	−	4.63736i	0.224542	−	0.426904i
$119$	−2.29798	+	8.16273i	−0.210656	+	0.748276i
$120$		0			0
$121$	−3.60841	+	6.24995i	−0.328037	+	0.568177i
$122$	−11.3380	+	0.446775i	−1.02649	+	0.0404491i
$123$		0			0
$124$	1.61879	+	20.5084i	0.145372	+	1.84171i
$125$			11.7980i			1.05524i
$126$		0			0
$127$		−	4.80602i		−	0.426465i	−0.977001	−	0.213233i	$-0.931601\pi$
$127$		−	4.80602i		−	0.426465i	0.977001	−	0.213233i	$-0.0683992\pi$
$128$	−8.11038	−	7.88807i	−0.716863	−	0.697214i
$129$		0			0
$130$	−0.556989	−	14.1349i	−0.0488512	−	1.23971i
$131$	7.35836	−	12.7451i	0.642903	−	1.11354i	−0.341878	−	0.939744i	$-0.611063\pi$
$131$	7.35836	−	12.7451i	0.642903	−	1.11354i	0.984782	−	0.173797i	$-0.0556036\pi$
$132$		0			0
$133$	−7.22071	+	1.83744i	−0.626115	+	0.159326i
$134$	1.75726	+	0.924284i	0.151805	+	0.0798459i
$135$		0			0
$136$	−7.26192	+	5.42664i	−0.622705	+	0.465330i
$137$	−3.43633	+	1.98397i	−0.293585	+	0.169502i	−0.639558	−	0.768743i	$-0.720882\pi$
$137$	−3.43633	+	1.98397i	−0.293585	+	0.169502i	0.345972	+	0.938245i	$0.387549\pi$
$138$		0			0
$139$			19.1682i			1.62583i	0.582383	+	0.812915i	$0.302121\pi$
$139$			19.1682i			1.62583i	−0.582383	+	0.812915i	$0.697879\pi$
$140$	2.14074	−	10.8018i	0.180926	−	0.912915i
$141$		0			0
$142$	−8.99204	−	14.2479i	−0.754595	−	1.19566i
$143$	10.2575	+	17.7664i	0.857771	+	1.48570i
$144$		0			0
$145$	4.02888	−	6.97822i	0.334580	−	0.579510i
$146$	8.08590	−	15.3731i	0.669194	−	1.27228i
$147$		0			0
$148$	−0.310247	−	0.451190i	−0.0255022	−	0.0370876i
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	0.687062	−	0.726599i	$-0.258900\pi$
$149$	4.89898	+	2.82843i	0.401340	+	0.231714i	−0.285722	+	0.958313i	$0.592233\pi$
$150$		0			0
$151$	8.38179	−	4.83923i	0.682100	−	0.393811i	−0.118546	−	0.992949i	$-0.537823\pi$
$151$	8.38179	−	4.83923i	0.682100	−	0.393811i	0.800646	+	0.599138i	$0.204490\pi$
$152$	−7.31950	−	3.14172i	−0.593690	−	0.254827i
$153$		0			0
$154$	4.54464	+	15.3095i	0.366217	+	1.23368i
$155$	−21.4058			−1.71936
$156$		0			0
$157$	−2.94304	−	5.09749i	−0.234880	−	0.406824i	0.724358	−	0.689424i	$-0.242136\pi$
$157$	−2.94304	−	5.09749i	−0.234880	−	0.406824i	−0.959238	+	0.282600i	$0.908803\pi$
$158$	−0.0460106	−	1.16763i	−0.00366041	−	0.0928913i
$159$		0			0
$160$	8.84631	−	7.76701i	0.699363	−	0.614036i
$161$	−3.04129	−	11.9516i	−0.239687	−	0.941914i
$162$		0			0
$163$	−8.40063	−	4.85011i	−0.657988	−	0.379890i	0.133522	−	0.991046i	$-0.457371\pi$
$163$	−8.40063	−	4.85011i	−0.657988	−	0.379890i	−0.791510	+	0.611156i	$0.790705\pi$
$164$	−0.699013	−	0.333215i	−0.0545837	−	0.0260197i
$165$		0			0
$166$	4.29513	+	6.80563i	0.333367	+	0.528220i
$167$	18.4218			1.42552			0.712759	−	0.701409i	$-0.247445\pi$
$167$	18.4218			1.42552			0.712759	+	0.701409i	$0.247445\pi$
$168$		0			0
$169$	10.1029			0.777146
$170$	−5.03444	−	7.97707i	−0.386124	−	0.611814i
$171$		0			0
$172$	1.63919	+	0.781392i	0.124987	+	0.0595805i
$173$	−6.13279	−	3.54077i	−0.466267	−	0.269199i	0.248409	−	0.968655i	$-0.420092\pi$
$173$	−6.13279	−	3.54077i	−0.466267	−	0.269199i	−0.714676	+	0.699456i	$0.753426\pi$
$174$		0			0
$175$	−1.70444	−	0.479836i	−0.128843	−	0.0362722i
$176$	−6.11089	+	15.9413i	−0.460626	+	1.20162i
$177$		0			0
$178$	0.168310	+	4.27126i	0.0126154	+	0.320145i
$179$	−10.5602	−	18.2908i	−0.789305	−	1.36712i	−0.926393	−	0.376557i	$-0.877108\pi$
$179$	−10.5602	−	18.2908i	−0.789305	−	1.36712i	0.137088	−	0.990559i	$-0.456226\pi$
$180$		0			0
$181$	−6.13809			−0.456240			−0.228120	−	0.973633i	$-0.573258\pi$
$181$	−6.13809			−0.456240			−0.228120	+	0.973633i	$0.573258\pi$
$182$	17.4900	+	4.18815i	1.29644	+	0.310446i
$183$		0			0
$184$	5.20010	−	12.1151i	0.383356	−	0.893135i
$185$	0.493419	−	0.284876i	0.0362769	−	0.0209445i
$186$		0			0
$187$	11.8472	+	6.83998i	0.866352	+	0.500189i
$188$	−8.90422	−	12.9493i	−0.649407	−	0.944427i
$189$		0			0
$190$	3.85819	−	7.33525i	0.279902	−	0.532155i
$191$	−5.89895	+	10.2173i	−0.426833	+	0.739297i	−0.996590	−	0.0825166i	$-0.973704\pi$
$191$	−5.89895	+	10.2173i	−0.426833	+	0.739297i	0.569756	+	0.821814i	$0.307038\pi$
$192$		0			0
$193$	7.90367	+	13.6896i	0.568919	+	0.985396i	0.996673	+	0.0815013i	$0.0259715\pi$
$193$	7.90367	+	13.6896i	0.568919	+	0.985396i	−0.427754	+	0.903895i	$0.640695\pi$
$194$	11.5460	+	18.2947i	0.828956	+	1.31348i
$195$		0			0
$196$	12.4815	+	6.34126i	0.891537	+	0.452947i
$197$			2.17812i			0.155185i	0.996985	+	0.0775924i	$0.0247233\pi$
$197$			2.17812i			0.155185i	−0.996985	+	0.0775924i	$0.975277\pi$
$198$		0			0
$199$	4.74590	−	2.74005i	0.336428	−	0.194237i	−0.322263	−	0.946650i	$-0.604444\pi$
$199$	4.74590	−	2.74005i	0.336428	−	0.194237i	0.658691	+	0.752413i	$0.271110\pi$
$200$	−1.13312	−	1.51634i	−0.0801237	−	0.107222i
$201$		0			0
$202$	−0.484616	−	0.254898i	−0.0340975	−	0.0179345i
$203$	7.15182	+	7.33465i	0.501959	+	0.514791i
$204$		0			0
$205$	0.402875	−	0.697800i	0.0281380	−	0.0487365i
$206$	0.753739	+	19.1279i	0.0525155	+	1.33270i
$207$		0			0
$208$	12.1063	+	14.9360i	0.839421	+	1.03562i
$209$			12.0196i			0.831416i
$210$		0			0
$211$		−	8.80046i		−	0.605849i	−0.953015	−	0.302924i	$-0.902037\pi$
$211$		−	8.80046i		−	0.605849i	0.953015	−	0.302924i	$-0.0979629\pi$
$212$	1.84240	+	23.3413i	0.126537	+	1.60309i
$213$		0			0
$214$	−15.3805	+	0.606073i	−1.05139	+	0.0414303i
$215$	−0.944746	+	1.63635i	−0.0644311	+	0.111598i
$216$		0			0
$217$	7.37479	−	26.1962i	0.500634	−	1.77831i
$218$	12.3214	−	23.4256i	0.834510	−	1.58658i
$219$		0			0
$220$	−16.0355	−	7.64403i	−1.08112	−	0.515360i
$221$	13.3417	−	7.70285i	0.897462	−	0.518150i
$222$		0			0
$223$		−	21.1499i		−	1.41630i	−0.706060	−	0.708152i	$-0.749529\pi$
$223$		−	21.1499i		−	1.41630i	0.706060	−	0.708152i	$-0.250471\pi$
$224$	6.45742	+	13.5019i	0.431454	+	0.902135i
$225$		0			0
$226$	−15.7121	+	9.91610i	−1.04515	+	0.659609i
$227$	−14.0475	−	24.3309i	−0.932364	−	1.61490i	−0.779269	−	0.626690i	$-0.784409\pi$
$227$	−14.0475	−	24.3309i	−0.932364	−	1.61490i	−0.153095	−	0.988211i	$-0.548924\pi$
$228$		0			0
$229$	6.81783	−	11.8088i	0.450535	−	0.780350i	−0.547884	−	0.836554i	$-0.684567\pi$
$229$	6.81783	−	11.8088i	0.450535	−	0.780350i	0.998419	+	0.0562045i	$0.0178999\pi$
$230$	12.1411	+	6.38598i	0.800563	+	0.421079i
$231$		0			0
$232$	1.29098	+	10.8753i	0.0847567	+	0.713996i
$233$	−3.73493	−	2.15637i	−0.244684	−	0.141268i	0.372644	−	0.927974i	$-0.378451\pi$
$233$	−3.73493	−	2.15637i	−0.244684	−	0.141268i	−0.617328	+	0.786706i	$0.711785\pi$
$234$		0			0
$235$	14.1613	−	8.17605i	0.923783	−	0.533347i
$236$	−7.38709	+	0.583086i	−0.480859	+	0.0379557i
$237$		0			0
$238$	11.4967	−	3.41280i	0.745222	−	0.221219i
$239$	−7.22142			−0.467115			−0.233558	−	0.972343i	$-0.575037\pi$
$239$	−7.22142			−0.467115			−0.233558	+	0.972343i	$0.575037\pi$
$240$		0			0
$241$	−2.36740	−	4.10045i	−0.152497	−	0.264133i	0.779648	−	0.626219i	$-0.215398\pi$
$241$	−2.36740	−	4.10045i	−0.152497	−	0.264133i	−0.932145	+	0.362085i	$0.882065\pi$
$242$	10.1982	−	0.401863i	0.655566	−	0.0258328i
$243$		0			0
$244$	9.09201	+	13.2224i	0.582057	+	0.846480i
$245$	−7.59971	+	12.4278i	−0.485528	+	0.793984i
$246$		0			0
$247$	11.7225	+	6.76797i	0.745883	+	0.430636i
$248$	23.3053	−	17.4154i	1.47989	−	1.10588i
$249$		0			0
$250$	14.1098	−	8.90490i	0.892383	−	0.563195i
$251$	−2.26312			−0.142847			−0.0714233	−	0.997446i	$-0.522754\pi$
$251$	−2.26312			−0.142847			−0.0714233	+	0.997446i	$0.522754\pi$
$252$		0			0
$253$	−19.8947			−1.25077
$254$	−5.74777	+	3.62750i	−0.360647	+	0.227610i
$255$		0			0
$256$	−3.31219	+	15.6534i	−0.207012	+	0.978338i
$257$	15.6241	+	9.02055i	0.974602	+	0.562687i	0.900636	−	0.434574i	$-0.143101\pi$
$257$	15.6241	+	9.02055i	0.974602	+	0.562687i	0.0739657	+	0.997261i	$0.476434\pi$
$258$		0			0
$259$	0.178633	+	0.701986i	0.0110997	+	0.0436193i
$260$	−16.4843	+	11.3349i	−1.02231	+	0.702961i
$261$		0			0
$262$	−20.7965	+	0.819490i	−1.28481	+	0.0506283i
$263$	0.335353	+	0.580849i	0.0206788	+	0.0358167i	0.876180	−	0.481985i	$-0.160084\pi$
$263$	0.335353	+	0.580849i	0.0206788	+	0.0358167i	−0.855501	+	0.517801i	$0.826751\pi$
$264$		0			0
$265$	−24.3627			−1.49659
$266$	7.64756	+	7.24876i	0.468902	+	0.444450i
$267$		0			0
$268$	−0.220953	−	2.79924i	−0.0134968	−	0.170991i
$269$	8.22457	−	4.74846i	0.501461	−	0.289518i	−0.227856	−	0.973695i	$-0.573171\pi$
$269$	8.22457	−	4.74846i	0.501461	−	0.289518i	0.729317	+	0.684176i	$0.239838\pi$
$270$		0			0
$271$	14.8698	+	8.58509i	0.903276	+	0.521507i	0.878262	−	0.478180i	$-0.158703\pi$
$271$	14.8698	+	8.58509i	0.903276	+	0.521507i	0.0250146	+	0.999687i	$0.492037\pi$
$272$	11.9712	+	4.58899i	0.725859	+	0.278248i
$273$		0			0
$274$	4.96641	+	2.61223i	0.300032	+	0.157810i
$275$	−1.42824	+	2.47378i	−0.0861259	+	0.149174i
$276$		0			0
$277$	−4.92436	−	8.52923i	−0.295876	−	0.512472i	0.679312	−	0.733849i	$-0.262278\pi$
$277$	−4.92436	−	8.52923i	−0.295876	−	0.512472i	−0.975188	+	0.221377i	$0.928945\pi$
$278$	22.9243	−	14.4679i	1.37491	−	0.867724i
$279$		0			0
$280$	−14.5342	+	5.59275i	−0.868584	+	0.334231i
$281$			7.25476i			0.432783i	0.976307	+	0.216391i	$0.0694287\pi$
$281$			7.25476i			0.432783i	−0.976307	+	0.216391i	$0.930571\pi$
$282$		0			0
$283$	−2.43886	+	1.40807i	−0.144975	+	0.0837013i	−0.570733	−	0.821136i	$-0.693341\pi$
$283$	−2.43886	+	1.40807i	−0.144975	+	0.0837013i	0.425758	+	0.904837i	$0.360007\pi$
$284$	−10.2528	+	21.5081i	−0.608390	+	1.27627i
$285$		0			0
$286$	13.5057	−	25.6772i	0.798607	−	1.51833i
$287$	0.715160	+	0.733441i	0.0422145	+	0.0432937i
$288$		0			0
$289$	−3.36351	+	5.82577i	−0.197853	+	0.342692i
$290$	−11.3866	+	0.448690i	−0.668641	+	0.0263480i
$291$		0			0
$292$	−24.4885	+	1.93296i	−1.43308	+	0.113118i
$293$			6.86151i			0.400854i	0.979709	+	0.200427i	$0.0642329\pi$
$293$			6.86151i			0.400854i	−0.979709	+	0.200427i	$0.935767\pi$
$294$		0			0
$295$		−	7.71034i		−	0.448913i
$296$	−0.305433	+	0.711591i	−0.0177529	+	0.0413604i
$297$		0			0
$298$	−0.314998	−	7.99380i	−0.0182473	−	0.463068i
$299$	−11.2022	+	19.4028i	−0.647840	+	1.12209i
$300$		0			0
$301$	−1.67706	−	1.71993i	−0.0966639	−	0.0991349i
$302$	−12.1139	−	6.37166i	−0.697077	−	0.366648i
$303$		0			0
$304$	1.76729	+	11.1251i	0.101361	+	0.638068i
$305$	−14.4600	+	8.34849i	−0.827978	+	0.478033i
$306$		0			0
$307$		−	8.29624i		−	0.473491i	−0.971572	−	0.236746i	$-0.923919\pi$
$307$		−	8.29624i		−	0.473491i	0.971572	−	0.236746i	$-0.0760808\pi$
$308$	14.8793	−	16.9905i	0.847825	−	0.968126i
$309$		0			0
$310$	16.1568	+	25.6004i	0.917642	+	1.45400i
$311$	−8.68043	−	15.0349i	−0.492222	−	0.852553i	0.507738	−	0.861512i	$-0.330482\pi$
$311$	−8.68043	−	15.0349i	−0.492222	−	0.852553i	−0.999960	+	0.00895813i	$0.997149\pi$
$312$		0			0
$313$	−3.97581	+	6.88630i	−0.224726	+	0.389237i	−0.956237	−	0.292593i	$-0.905482\pi$
$313$	−3.97581	+	6.88630i	−0.224726	+	0.389237i	0.731511	+	0.681829i	$0.238815\pi$
$314$	−3.87501	+	7.36724i	−0.218679	+	0.415757i
$315$		0			0
$316$	−1.36170	+	0.936330i	−0.0766015	+	0.0526727i
$317$	−1.89058	−	1.09153i	−0.106186	−	0.0613063i	0.445967	−	0.895050i	$-0.352860\pi$
$317$	−1.89058	−	1.09153i	−0.106186	−	0.0613063i	−0.552152	+	0.833743i	$0.686193\pi$
$318$		0			0
$319$	14.3120	−	8.26303i	0.801318	−	0.462641i
$320$	−15.9660	−	4.71737i	−0.892528	−	0.263709i
$321$		0			0
$322$	−11.9980	+	12.6581i	−0.668621	+	0.705406i
$323$	9.02618			0.502230
$324$		0			0
$325$	1.60841	+	2.78585i	0.0892186	+	0.154531i
$326$	0.540149	+	13.7075i	0.0299161	+	0.759190i
$327$		0			0
$328$	0.129094	+	1.08749i	0.00712800	+	0.0600467i
$329$	5.12685	+	20.1473i	0.282652	+	1.11076i
$330$		0			0
$331$	11.6706	+	6.73802i	0.641473	+	0.370355i	0.785182	−	0.619265i	$-0.212569\pi$
$331$	11.6706	+	6.73802i	0.641473	+	0.370355i	−0.143709	+	0.989620i	$0.545903\pi$
$332$	4.89733	−	10.2735i	0.268776	−	0.563834i
$333$		0			0
$334$	−13.9044	−	22.0316i	−0.760816	−	1.20551i
$335$	2.92173			0.159631
$336$		0			0
$337$	17.4188			0.948865			0.474432	−	0.880292i	$-0.342653\pi$
$337$	17.4188			0.948865			0.474432	+	0.880292i	$0.342653\pi$
$338$	−7.62549	−	12.0826i	−0.414772	−	0.657207i
$339$		0			0
$340$	−5.74030	+	12.0419i	−0.311311	+	0.653064i
$341$	−38.0205	−	21.9512i	−2.05893	−	1.18872i
$342$		0			0
$343$	−12.5907	−	13.5821i	−0.679836	−	0.733364i
$344$	−0.302725	−	2.55018i	−0.0163219	−	0.137496i
$345$		0			0
$346$	0.394330	+	10.0070i	0.0211993	+	0.537981i
$347$	1.10433	+	1.91275i	0.0592833	+	0.102682i	0.894144	−	0.447780i	$-0.147785\pi$
$347$	1.10433	+	1.91275i	0.0592833	+	0.102682i	−0.834861	+	0.550461i	$0.814452\pi$
$348$		0			0
$349$	31.3253			1.67681			0.838403	−	0.545051i	$-0.183490\pi$
$349$	31.3253			1.67681			0.838403	+	0.545051i	$0.183490\pi$
$350$	0.712618	+	2.40060i	0.0380910	+	0.128317i
$351$		0			0
$352$	23.6775	−	4.72390i	1.26201	−	0.251785i
$353$	5.97612	−	3.45031i	0.318077	−	0.183642i	−0.332458	−	0.943118i	$-0.607878\pi$
$353$	5.97612	−	3.45031i	0.318077	−	0.183642i	0.650535	+	0.759476i	$0.274545\pi$
$354$		0			0
$355$	−21.4708	−	12.3962i	−1.13955	−	0.657920i
$356$	4.98119	−	3.42517i	0.264003	−	0.181533i
$357$		0			0
$358$	−13.9043	+	26.4350i	−0.734863	+	1.39713i
$359$	6.57360	−	11.3858i	0.346941	−	0.600920i	−0.638763	−	0.769404i	$-0.720554\pi$
$359$	6.57360	−	11.3858i	0.346941	−	0.600920i	0.985705	+	0.168483i	$0.0538869\pi$
$360$		0			0
$361$	−5.53466	−	9.58630i	−0.291298	−	0.504542i
$362$	4.63292	+	7.34086i	0.243501	+	0.385827i
$363$		0			0
$364$	−8.19231	−	24.0784i	−0.429394	−	1.26205i
$365$		−	25.5601i		−	1.33788i
$366$		0			0
$367$	−9.79102	+	5.65285i	−0.511087	+	0.295076i	−0.733280	−	0.679926i	$-0.762012\pi$
$367$	−9.79102	+	5.65285i	−0.511087	+	0.295076i	0.222193	+	0.975003i	$0.428678\pi$
$368$	−18.4140	+	2.92518i	−0.959896	+	0.152485i
$369$		0			0
$370$	−0.713122	−	0.375087i	−0.0370735	−	0.0194998i
$371$	8.39349	−	29.8147i	0.435768	−	1.54790i
$372$		0			0
$373$	−7.07682	+	12.2574i	−0.366424	+	0.634665i	−0.989004	−	0.147892i	$-0.952751\pi$
$373$	−7.07682	+	12.2574i	−0.366424	+	0.634665i	0.622580	+	0.782556i	$0.286085\pi$
$374$	−0.761758	−	19.3314i	−0.0393896	−	0.999601i
$375$		0			0
$376$	−8.76605	+	20.4230i	−0.452074	+	1.05323i
$377$		−	18.6109i		−	0.958508i
$378$		0			0
$379$			16.2405i			0.834216i	0.908857	+	0.417108i	$0.136956\pi$
$379$			16.2405i			0.834216i	−0.908857	+	0.417108i	$0.863044\pi$
$380$	−11.6847	+	0.922311i	−0.599413	+	0.0473135i
$381$		0			0
$382$	16.6718	−	0.656958i	0.853005	−	0.0336129i
$383$	1.35904	−	2.35392i	0.0694436	−	0.120280i	−0.829213	−	0.558933i	$-0.811211\pi$
$383$	1.35904	−	2.35392i	0.0694436	−	0.120280i	0.898657	+	0.438653i	$0.144544\pi$
$384$		0			0
$385$	16.4059	+	16.8253i	0.836124	+	0.857498i
$386$	10.4065	−	19.7851i	0.529678	−	1.00703i
$387$		0			0
$388$	13.1648	−	27.6170i	0.668343	−	1.40204i
$389$	17.4029	−	10.0476i	0.882363	−	0.509432i	0.0109262	−	0.999940i	$-0.496522\pi$
$389$	17.4029	−	10.0476i	0.882363	−	0.509432i	0.871437	+	0.490508i	$0.163189\pi$
$390$		0			0
$391$			14.9399i			0.755544i
$392$	−1.83698	−	19.7136i	−0.0927817	−	0.995686i
$393$		0			0
$394$	2.60493	−	1.64401i	0.131235	−	0.0828239i
$395$	−0.859759	−	1.48915i	−0.0432592	−	0.0749271i
$396$		0			0
$397$	−7.93175	+	13.7382i	−0.398083	+	0.689501i	−0.993489	−	0.113924i	$-0.963658\pi$
$397$	−7.93175	+	13.7382i	−0.398083	+	0.689501i	0.595406	+	0.803425i	$0.296991\pi$
$398$	−6.85909	−	3.60773i	−0.343815	−	0.180839i
$399$		0			0
$400$	−0.958213	+	2.49967i	−0.0479107	+	0.124983i
$401$	−27.7148	−	16.0012i	−1.38401	−	0.799060i	−0.391381	−	0.920229i	$-0.628002\pi$
$401$	−27.7148	−	16.0012i	−1.38401	−	0.799060i	−0.992632	+	0.121169i	$0.961336\pi$
$402$		0			0
$403$	−42.8169	+	24.7203i	−2.13286	+	1.23141i
$404$	0.0609340	+	0.771970i	0.00303158	+	0.0384070i
$405$		0			0
$406$	3.37382	−	14.0893i	0.167440	−	0.699240i
$407$	1.16853			0.0579220
$408$		0			0
$409$	−2.42047	−	4.19237i	−0.119684	−	0.207300i	0.799958	−	0.600056i	$-0.204855\pi$
$409$	−2.42047	−	4.19237i	−0.119684	−	0.207300i	−0.919643	+	0.392756i	$0.871522\pi$
$410$	−1.13862	+	0.0448676i	−0.0562324	+	0.00221585i
$411$		0			0
$412$	22.3071	−	15.3388i	1.09899	−	0.755690i
$413$	9.43582	+	2.65639i	0.464306	+	0.130712i
$414$		0			0
$415$	10.2557	+	5.92114i	0.503434	+	0.290658i
$416$	8.72511	−	25.7520i	0.427784	−	1.26260i
$417$		0			0
$418$	14.3749	−	9.07222i	0.703101	−	0.443737i
$419$	9.95079			0.486128			0.243064	−	0.970010i	$-0.421848\pi$
$419$	9.95079			0.486128			0.243064	+	0.970010i	$0.421848\pi$
$420$		0			0
$421$	−2.27378			−0.110817			−0.0554087	−	0.998464i	$-0.517646\pi$
$421$	−2.27378			−0.110817			−0.0554087	+	0.998464i	$0.517646\pi$
$422$	−10.5249	+	6.64243i	−0.512346	+	0.323349i
$423$		0			0
$424$	26.5245	−	19.8210i	1.28814	−	0.962595i
$425$	1.85769	+	1.07254i	0.0901111	+	0.0520257i
$426$		0			0
$427$	−5.23498	−	20.5722i	−0.253338	−	0.995559i
$428$	12.3338	+	17.9369i	0.596175	+	0.867012i
$429$		0			0
$430$	2.67007	−	0.105215i	0.128762	−	0.00507392i
$431$	14.2652	+	24.7081i	0.687131	+	1.19015i	0.972762	+	0.231806i	$0.0744636\pi$
$431$	14.2652	+	24.7081i	0.687131	+	1.19015i	−0.285631	+	0.958340i	$0.592203\pi$
$432$		0			0
$433$	−7.86191			−0.377819			−0.188910	−	0.981994i	$-0.560495\pi$
$433$	−7.86191			−0.377819			−0.188910	+	0.981994i	$0.560495\pi$
$434$	−36.8958	+	10.9525i	−1.77105	+	0.525738i
$435$		0			0
$436$	−37.3159	+	2.94546i	−1.78711	+	0.141062i
$437$	−11.3681	+	6.56335i	−0.543808	+	0.313968i
$438$		0			0
$439$	−9.24092	−	5.33525i	−0.441045	−	0.254637i	0.262996	−	0.964797i	$-0.415289\pi$
$439$	−9.24092	−	5.33525i	−0.441045	−	0.254637i	−0.704041	+	0.710160i	$0.748623\pi$
$440$	2.96144	+	24.9473i	0.141181	+	1.18932i
$441$		0			0
$442$	−19.2824	−	10.1421i	−0.917168	−	0.482411i
$443$	−18.9902	+	32.8921i	−0.902254	+	1.56275i	−0.0776916	+	0.996977i	$0.524755\pi$
$443$	−18.9902	+	32.8921i	−0.902254	+	1.56275i	−0.824562	+	0.565772i	$0.808578\pi$
$444$		0			0
$445$	3.14506	+	5.44741i	0.149090	+	0.258232i
$446$	−25.2943	+	15.9636i	−1.19772	+	0.755898i
$447$		0			0
$448$	11.2737	−	17.9138i	0.532633	−	0.846346i
$449$			24.0046i			1.13285i	0.824114	+	0.566423i	$0.191673\pi$
$449$			24.0046i			1.13285i	−0.824114	+	0.566423i	$0.808327\pi$
$450$		0			0
$451$	1.43115	−	0.826277i	0.0673904	−	0.0389079i
$452$	23.7184	+	11.3064i	1.11562	+	0.531808i
$453$		0			0
$454$	−18.4959	+	35.1647i	−0.868054	+	1.65036i
$455$	25.6471	−	6.52638i	1.20236	−	0.305962i
$456$		0			0
$457$	−7.52257	+	13.0295i	−0.351891	+	0.609493i	−0.986581	−	0.163274i	$-0.947795\pi$
$457$	−7.52257	+	13.0295i	−0.351891	+	0.609493i	0.634690	+	0.772767i	$0.281128\pi$
$458$	−19.2688	+	0.759292i	−0.900371	+	0.0354794i
$459$		0			0
$460$	−1.52659	−	19.3403i	−0.0711775	−	0.901745i
$461$			30.3714i			1.41454i	0.706946	+	0.707268i	$0.250073\pi$
$461$			30.3714i			1.41454i	−0.706946	+	0.707268i	$0.749927\pi$
$462$		0			0
$463$			23.7810i			1.10519i	0.833448	+	0.552597i	$0.186363\pi$
$463$			23.7810i			1.10519i	−0.833448	+	0.552597i	$0.813637\pi$
$464$	12.0319	−	9.75240i	0.558566	−	0.452744i
$465$		0			0
$466$	0.240151	+	6.09439i	0.0111248	+	0.282317i
$467$	−2.35180	+	4.07343i	−0.108828	+	0.188496i	−0.915296	−	0.402782i	$-0.868043\pi$
$467$	−2.35180	+	4.07343i	−0.108828	+	0.188496i	0.806468	+	0.591278i	$0.201377\pi$
$468$		0			0
$469$	−1.00660	+	3.57557i	−0.0464805	+	0.165105i
$470$	−20.4669	−	10.7651i	−0.944067	−	0.496559i
$471$		0			0
$472$	6.27299	+	8.39451i	0.288738	+	0.386389i
$473$	−3.35607	+	1.93763i	−0.154312	+	0.0890922i
$474$		0			0
$475$			1.88473i			0.0864774i
$476$	−12.7591	−	11.1736i	−0.584811	−	0.512142i
$477$		0			0
$478$	5.45060	+	8.63648i	0.249305	+	0.395024i
$479$	−2.04513	−	3.54227i	−0.0934444	−	0.161850i	0.815514	−	0.578737i	$-0.196454\pi$
$479$	−2.04513	−	3.54227i	−0.0934444	−	0.161850i	−0.908958	+	0.416887i	$0.863121\pi$
$480$		0			0
$481$	0.657972	−	1.13964i	0.0300010	−	0.0519632i
$482$	−3.11708	+	5.92624i	−0.141979	+	0.269933i
$483$		0			0
$484$	−8.17804	−	11.8933i	−0.371729	−	0.540603i
$485$	27.5691	+	15.9170i	1.25185	+	0.722755i
$486$		0			0
$487$	−4.85177	+	2.80117i	−0.219854	+	0.126933i	−0.605883	−	0.795554i	$-0.707180\pi$
$487$	−4.85177	+	2.80117i	−0.219854	+	0.126933i	0.386028	+	0.922487i	$0.373847\pi$
$488$	8.95093	−	20.8537i	0.405190	−	0.944002i
$489$		0			0
$490$	20.5992	−	0.291406i	0.930578	−	0.0131644i
$491$	10.3094			0.465257			0.232629	−	0.972566i	$-0.425267\pi$
$491$	10.3094			0.465257			0.232629	+	0.972566i	$0.425267\pi$
$492$		0			0
$493$	−6.20514	−	10.7476i	−0.279465	−	0.484048i
$494$	−0.753739	−	19.1279i	−0.0339123	−	0.860604i
$495$		0			0
$496$	−38.4184	−	14.7272i	−1.72504	−	0.661270i
$497$	22.5674	−	22.0049i	1.01229	−	0.987056i
$498$		0			0
$499$	6.14548	+	3.54809i	0.275109	+	0.158835i	0.631207	−	0.775614i	$-0.282560\pi$
$499$	6.14548	+	3.54809i	0.275109	+	0.158835i	−0.356098	+	0.934449i	$0.615893\pi$
$500$	−21.2997	−	10.1534i	−0.952551	−	0.454075i
$501$		0			0
$502$	1.70816	+	2.70658i	0.0762389	+	0.120801i
$503$	−6.79674			−0.303052			−0.151526	−	0.988453i	$-0.548419\pi$
$503$	−6.79674			−0.303052			−0.151526	+	0.988453i	$0.548419\pi$
$504$		0			0
$505$	−0.805750			−0.0358554
$506$	15.0161	+	23.7931i	0.667549	+	1.05773i
$507$		0			0
$508$	8.67664	+	4.13609i	0.384963	+	0.183509i
$509$	16.8641	+	9.73648i	0.747487	+	0.431562i	0.824785	−	0.565446i	$-0.191296\pi$
$509$	16.8641	+	9.73648i	0.747487	+	0.431562i	−0.0772979	+	0.997008i	$0.524629\pi$
$510$		0			0
$511$	31.2801	+	8.80603i	1.38375	+	0.389556i
$512$	21.2207	−	7.85370i	0.937833	−	0.347088i
$513$		0			0
$514$	−1.00461	−	25.4942i	−0.0443113	−	1.12450i
$515$	14.0844	+	24.3950i	0.620635	+	1.07497i
$516$		0			0
$517$	33.5373			1.47497
$518$	0.704713	−	0.743484i	0.0309633	−	0.0326668i
$519$		0			0
$520$	25.9980	+	11.1590i	1.14009	+	0.489355i
$521$	29.8381	−	17.2270i	1.30723	−	0.754729i	0.325597	−	0.945509i	$-0.394435\pi$
$521$	29.8381	−	17.2270i	1.30723	−	0.754729i	0.981633	+	0.190779i	$0.0611015\pi$
$522$		0			0
$523$	−18.6920	−	10.7918i	−0.817342	−	0.471893i	0.0321570	−	0.999483i	$-0.489762\pi$
$523$	−18.6920	−	10.7918i	−0.817342	−	0.471893i	−0.849499	+	0.527590i	$0.823096\pi$
$524$	16.6769	+	24.2530i	0.728533	+	1.05950i
$525$		0			0
$526$	0.441549	−	0.839482i	0.0192525	−	0.0366031i
$527$	−16.4843	+	28.5516i	−0.718066	+	1.24373i
$528$		0			0
$529$	0.636492	+	1.10244i	0.0276736	+	0.0479320i
$530$	18.3885	+	29.1366i	0.798746	+	1.26561i
$531$		0			0
$532$	2.89693	−	14.6174i	0.125598	−	0.633743i
$533$		−	1.86103i		−	0.0806100i
$534$		0			0
$535$	−19.6157	+	11.3251i	−0.848061	+	0.489628i
$536$	−3.18099	+	2.37707i	−0.137398	+	0.102674i
$537$		0			0
$538$	−11.8867	−	6.25214i	−0.512472	−	0.269549i
$539$	−26.2428	+	14.2807i	−1.13036	+	0.615112i
$540$		0			0
$541$	21.1762	−	36.6783i	0.910437	−	1.57692i	0.0969897	−	0.995285i	$-0.469079\pi$
$541$	21.1762	−	36.6783i	0.910437	−	1.57692i	0.813448	−	0.581638i	$-0.197588\pi$
$542$	−0.956108	−	24.2635i	−0.0410684	−	1.04220i
$543$		0			0
$544$	−3.54742	−	17.7806i	−0.152094	−	0.762339i
$545$		−	38.9488i		−	1.66838i
$546$		0			0
$547$			36.9243i			1.57877i	0.613899	+	0.789385i	$0.289600\pi$
$547$			36.9243i			1.57877i	−0.613899	+	0.789385i	$0.710400\pi$
$548$	−0.624460	−	7.91125i	−0.0266756	−	0.337952i
$549$		0			0
$550$	4.03653	−	0.159061i	0.172118	−	0.00678236i
$551$	5.45203	−	9.44320i	0.232264	−	0.402294i
$552$		0			0
$553$	2.11861	−	0.539118i	0.0900922	−	0.0229256i
$554$	−6.48375	+	12.3270i	−0.275468	+	0.523725i
$555$		0			0
$556$	−34.6057	−	16.4963i	−1.46761	−	0.699600i
$557$	−13.1808	+	7.60993i	−0.558488	+	0.322443i	−0.752538	−	0.658548i	$-0.771171\pi$
$557$	−13.1808	+	7.60993i	−0.558488	+	0.322443i	0.194050	+	0.980992i	$0.437837\pi$
$558$		0			0
$559$			4.36412i			0.184583i
$560$	17.6588	+	13.1609i	0.746221	+	0.556149i
$561$		0			0
$562$	8.67635	−	5.47577i	0.365990	−	0.230981i
$563$	8.71740	+	15.0990i	0.367395	+	0.636346i	0.989157	−	0.146859i	$-0.0469165\pi$
$563$	8.71740	+	15.0990i	0.367395	+	0.636346i	−0.621763	+	0.783206i	$0.713583\pi$
$564$		0			0
$565$	−13.6701	+	23.6772i	−0.575104	+	0.996109i
$566$	3.52480	+	1.85397i	0.148158	+	0.0779281i
$567$		0			0
$568$	33.4613	−	3.97211i	1.40400	−	0.166666i
$569$	−18.0368	−	10.4136i	−0.756144	−	0.436560i	0.0717659	−	0.997422i	$-0.477137\pi$
$569$	−18.0368	−	10.4136i	−0.756144	−	0.436560i	−0.827909	+	0.560862i	$0.810470\pi$
$570$		0			0
$571$	17.8090	−	10.2820i	0.745282	−	0.430289i	−0.0787048	−	0.996898i	$-0.525078\pi$
$571$	17.8090	−	10.2820i	0.745282	−	0.430289i	0.823987	+	0.566609i	$0.191745\pi$
$572$	−40.9026	+	3.22857i	−1.71022	+	0.134993i
$573$		0			0
$574$	0.337372	−	1.40889i	0.0140816	−	0.0588058i
$575$	−3.11956			−0.130095
$576$		0			0
$577$	−1.58033	−	2.73721i	−0.0657900	−	0.113952i	0.831254	−	0.555893i	$-0.187623\pi$
$577$	−1.58033	−	2.73721i	−0.0657900	−	0.113952i	−0.897044	+	0.441941i	$0.854290\pi$
$578$	9.50606	−	0.374589i	0.395400	−	0.0155808i
$579$		0			0
$580$	9.13098	+	13.2791i	0.379143	+	0.551385i
$581$	−10.7795	+	10.5109i	−0.447211	+	0.436064i
$582$		0			0
$583$	−43.2724	−	24.9833i	−1.79216	−	1.03470i
$584$	20.7952	+	27.8282i	0.860513	+	1.15154i
$585$		0			0
$586$	8.20605	−	5.17895i	0.338989	−	0.213940i
$587$	22.1152			0.912792			0.456396	−	0.889777i	$-0.349140\pi$
$587$	22.1152			0.912792			0.456396	+	0.889777i	$0.349140\pi$
$588$		0			0
$589$	−28.9672			−1.19357
$590$	−9.22120	+	5.81963i	−0.379631	+	0.239590i
$591$		0			0
$592$	1.08156	−	0.171813i	0.0444520	−	0.00706147i
$593$	36.0411	+	20.8083i	1.48003	+	0.854496i	0.999744	−	0.0226166i	$-0.00719972\pi$
$593$	36.0411	+	20.8083i	1.48003	+	0.854496i	0.480286	+	0.877112i	$0.340533\pi$
$594$		0			0
$595$	12.6350	−	12.3201i	0.517985	−	0.505074i
$596$	−9.32245	+	6.41030i	−0.381862	+	0.262576i
$597$		0			0
$598$	31.6600	−	1.24757i	1.29468	−	0.0510170i
$599$	−19.1656	−	33.1958i	−0.783086	−	1.35634i	−0.930136	−	0.367215i	$-0.880311\pi$
$599$	−19.1656	−	33.1958i	−0.783086	−	1.35634i	0.147050	−	0.989129i	$-0.453022\pi$
$600$		0			0
$601$	29.3369			1.19668			0.598338	−	0.801244i	$-0.295828\pi$
$601$	29.3369			1.19668			0.598338	+	0.801244i	$0.295828\pi$
$602$	−0.791139	+	3.30385i	−0.0322444	+	0.134655i
$603$		0			0
$604$	1.52316	+	19.2969i	0.0619766	+	0.785179i
$605$	13.0064	−	7.50926i	0.528786	−	0.305295i
$606$		0			0
$607$	31.4700	+	18.1692i	1.27733	+	0.737465i	0.976356	−	0.216168i	$-0.0693558\pi$
$607$	31.4700	+	18.1692i	1.27733	+	0.737465i	0.300971	+	0.953633i	$0.402689\pi$
$608$	11.9712	−	10.5106i	0.485495	−	0.426262i
$609$		0			0
$610$	20.8986	+	10.9922i	0.846158	+	0.445061i
$611$	18.8841	−	32.7082i	0.763968	−	1.32323i
$612$		0			0
$613$	−13.9621	−	24.1831i	−0.563925	−	0.976746i	−0.997149	−	0.0754602i	$-0.975957\pi$
$613$	−13.9621	−	24.1831i	−0.563925	−	0.976746i	0.433224	−	0.901286i	$-0.357376\pi$
$614$	−9.92191	+	6.26185i	−0.400416	+	0.252708i
$615$		0			0
$616$	−31.5505	−	4.97074i	−1.27121	−	0.200277i
$617$			1.74855i			0.0703940i	0.999380	+	0.0351970i	$0.0112059\pi$
$617$			1.74855i			0.0703940i	−0.999380	+	0.0351970i	$0.988794\pi$
$618$		0			0
$619$	17.8090	−	10.2820i	0.715803	−	0.413269i	−0.0974033	−	0.995245i	$-0.531054\pi$
$619$	17.8090	−	10.2820i	0.715803	−	0.413269i	0.813206	+	0.581976i	$0.197720\pi$
$620$	18.4220	−	38.6454i	0.739846	−	1.55204i
$621$		0			0
$622$	−11.4293	+	21.7295i	−0.458271	+	0.871273i
$623$	−7.75002	+	1.97213i	−0.310498	+	0.0790119i
$624$		0			0
$625$	10.6029	−	18.3648i	0.424116	−	0.734591i
$626$	11.2366	−	0.442780i	0.449103	−	0.0176970i
$627$		0			0
$628$	11.7357	−	0.926332i	0.468304	−	0.0369647i
$629$		−	0.877511i		−	0.0349887i
$630$		0			0
$631$		−	14.5144i		−	0.577810i	−0.957358	−	0.288905i	$-0.906709\pi$
$631$		−	14.5144i		−	0.577810i	0.957358	−	0.288905i	$-0.0932912\pi$
$632$	2.14759	+	0.921801i	0.0854266	+	0.0366673i
$633$		0			0
$634$	0.121562	+	3.08491i	0.00482784	+	0.122518i
$635$	−5.00077	+	8.66158i	−0.198449	+	0.343724i
$636$		0			0
$637$	−0.849109	+	33.6351i	−0.0336429	+	1.33267i
$638$	−20.6846	−	10.8797i	−0.818912	−	0.430730i
$639$		0			0
$640$	6.40912	+	22.6552i	0.253343	+	0.895525i
$641$	−43.6375	+	25.1941i	−1.72358	+	0.995108i	−0.812391	+	0.583113i	$0.801835\pi$
$641$	−43.6375	+	25.1941i	−1.72358	+	0.995108i	−0.911186	+	0.411995i	$0.864832\pi$
$642$		0			0
$643$		−	40.2212i		−	1.58617i	−0.609111	−	0.793085i	$-0.708474\pi$
$643$		−	40.2212i		−	1.58617i	0.609111	−	0.793085i	$-0.291526\pi$
$644$	24.1943	+	4.79494i	0.953390	+	0.188947i
$645$		0			0
$646$	−6.81280	−	10.7949i	−0.268046	−	0.424719i
$647$	−10.1498	−	17.5800i	−0.399031	−	0.691142i	0.594576	−	0.804040i	$-0.297320\pi$
$647$	−10.1498	−	17.5800i	−0.399031	−	0.691142i	−0.993607	+	0.112898i	$0.963987\pi$
$648$		0			0
$649$	7.90676	−	13.6949i	0.310368	−	0.537572i
$650$	2.11774	−	4.02629i	0.0830648	−	0.157924i
$651$		0			0
$652$	15.9859	−	10.9922i	0.626055	−	0.430488i
$653$	−16.4671	−	9.50728i	−0.644407	−	0.372049i	0.141903	−	0.989881i	$-0.454678\pi$
$653$	−16.4671	−	9.50728i	−0.644407	−	0.372049i	−0.786310	+	0.617832i	$0.788011\pi$
$654$		0			0
$655$	−26.5230	+	15.3131i	−1.03634	+	0.598331i
$656$	1.20315	−	0.975209i	0.0469751	−	0.0380755i
$657$		0			0
$658$	20.2256	−	21.3383i	0.788474	−	0.831853i
$659$	20.4920			0.798256			0.399128	−	0.916895i	$-0.369313\pi$
$659$	20.4920			0.798256			0.399128	+	0.916895i	$0.369313\pi$
$660$		0			0
$661$	9.67706	+	16.7612i	0.376394	+	0.651933i	0.990535	−	0.137263i	$-0.0438306\pi$
$661$	9.67706	+	16.7612i	0.376394	+	0.651933i	−0.614141	+	0.789197i	$0.710497\pi$
$662$	−0.750403	−	19.0432i	−0.0291652	−	0.740135i
$663$		0			0
$664$	−15.9831	+	1.89732i	−0.620264	+	0.0736301i
$665$	14.9253	+	4.20180i	0.578779	+	0.162939i
$666$		0			0
$667$	15.6302	+	9.02408i	0.605203	+	0.349414i
$668$	−15.8539	+	33.2581i	−0.613406	+	1.28679i
$669$		0			0
$670$	−2.20527	−	3.49425i	−0.0851970	−	0.134995i
$671$	−34.2447			−1.32200
$672$		0			0
$673$	−18.9180			−0.729236			−0.364618	−	0.931157i	$-0.618800\pi$
$673$	−18.9180			−0.729236			−0.364618	+	0.931157i	$0.618800\pi$
$674$	−13.1474	−	20.8321i	−0.506420	−	0.802423i
$675$		0			0
$676$	−8.69463	+	18.2395i	−0.334409	+	0.701518i
$677$	−5.94225	−	3.43076i	−0.228379	−	0.131855i	0.381445	−	0.924392i	$-0.375427\pi$
$677$	−5.94225	−	3.43076i	−0.228379	−	0.131855i	−0.609824	+	0.792537i	$0.708760\pi$
$678$		0			0
$679$	−28.9772	+	28.2549i	−1.11204	+	1.08432i
$680$	18.7342	−	2.22390i	0.718425	−	0.0852825i
$681$		0			0
$682$	2.44467	+	62.0391i	0.0936112	+	2.37560i
$683$	11.2294	+	19.4499i	0.429682	+	0.744232i	0.996845	−	0.0793743i	$-0.0252922\pi$
$683$	11.2294	+	19.4499i	0.429682	+	0.744232i	−0.567163	+	0.823606i	$0.691959\pi$
$684$		0			0
$685$	8.25744			0.315500
$686$	−6.74027	+	25.3095i	−0.257345	+	0.966320i
$687$		0			0
$688$	−2.82140	+	2.28687i	−0.107565	+	0.0871862i
$689$	−48.7313	+	28.1350i	−1.85651	+	1.07186i
$690$		0			0
$691$	37.8628	+	21.8601i	1.44037	+	0.831598i	0.997874	−	0.0651733i	$-0.0207600\pi$
$691$	37.8628	+	21.8601i	1.44037	+	0.831598i	0.442495	+	0.896771i	$0.354093\pi$
$692$	11.6703	−	8.02473i	0.443638	−	0.305054i
$693$		0			0
$694$	1.45403	−	2.76443i	0.0551943	−	0.104936i
$695$	19.9450	−	34.5457i	0.756556	−	1.31039i
$696$		0			0
$697$	−0.620494	−	1.07473i	−0.0235029	−	0.0407082i
$698$	−23.6438	−	37.4636i	−0.894931	−	1.41802i
$699$		0			0
$700$	2.33313	−	2.66419i	0.0881840	−	0.100697i
$701$		−	5.48856i		−	0.207300i	−0.994614	−	0.103650i	$-0.966948\pi$
$701$		−	5.48856i		−	0.207300i	0.994614	−	0.103650i	$-0.0330522\pi$
$702$		0			0
$703$	0.667714	−	0.385505i	0.0251833	−	0.0145396i
$704$	−23.5209	−	24.7516i	−0.886477	−	0.932862i
$705$		0			0
$706$	−8.63708	−	4.54292i	−0.325061	−	0.170975i
$707$	0.277599	−	0.986067i	0.0104402	−	0.0370849i
$708$		0			0
$709$	5.37290	−	9.30614i	0.201784	−	0.349500i	−0.747320	−	0.664465i	$-0.768660\pi$
$709$	5.37290	−	9.30614i	0.201784	−	0.349500i	0.949103	+	0.314965i	$0.101993\pi$
$710$	1.38054	+	35.0345i	0.0518109	+	1.31482i
$711$		0			0
$712$	−7.85606	−	3.37202i	−0.294418	−	0.126372i
$713$		−	47.9459i		−	1.79559i
$714$		0			0
$715$		−	42.6924i		−	1.59661i
$716$	42.1097	−	3.32385i	1.57371	−	0.124218i
$717$		0			0
$718$	−18.5785	+	0.732092i	−0.693345	+	0.0273214i
$719$	1.88369	−	3.26265i	0.0702498	−	0.121676i	−0.828761	−	0.559603i	$-0.810954\pi$
$719$	1.88369	−	3.26265i	0.0702498	−	0.121676i	0.899011	+	0.437927i	$0.144287\pi$
$720$		0			0
$721$	−34.7067	+	8.83175i	−1.29254	+	0.328912i
$722$	−7.28731	+	13.8548i	−0.271206	+	0.515621i
$723$		0			0
$724$	5.28248	−	11.0815i	0.196322	−	0.411841i
$725$	2.24418	−	1.29568i	0.0833467	−	0.0481202i
$726$		0			0
$727$		−	50.2752i		−	1.86460i	−0.361683	−	0.932301i	$-0.617798\pi$
$727$		−	50.2752i		−	1.86460i	0.361683	−	0.932301i	$-0.382202\pi$
$728$	−22.6132	+	27.9715i	−0.838100	+	1.03669i
$729$		0			0
$730$	−30.5687	+	19.2923i	−1.13140	+	0.714041i
$731$	1.45506	+	2.52025i	0.0538175	+	0.0932146i
$732$		0			0
$733$	−4.70703	+	8.15281i	−0.173858	+	0.301131i	−0.939765	−	0.341820i	$-0.888957\pi$
$733$	−4.70703	+	8.15281i	−0.173858	+	0.301131i	0.765907	+	0.642951i	$0.222290\pi$
$734$	14.1506	+	7.44293i	0.522309	+	0.274724i
$735$		0			0
$736$	17.3969	+	19.8144i	0.641260	+	0.730369i
$737$	5.18950	+	2.99616i	0.191158	+	0.110365i
$738$		0			0
$739$	23.0267	−	13.2944i	0.847049	−	0.489044i	−0.0126048	−	0.999921i	$-0.504012\pi$
$739$	23.0267	−	13.2944i	0.847049	−	0.489044i	0.859654	+	0.510876i	$0.170679\pi$
$740$	0.0896656	+	1.13597i	0.00329617	+	0.0417591i
$741$		0			0
$742$	−41.9923	+	12.4654i	−1.54159	+	0.457620i
$743$	−52.2920			−1.91841			−0.959204	−	0.282715i	$-0.908765\pi$
$743$	−52.2920			−1.91841			−0.959204	+	0.282715i	$0.908765\pi$
$744$		0			0
$745$	−5.88608	−	10.1950i	−0.215649	−	0.373516i
$746$	20.0007	−	0.788135i	0.732279	−	0.0288557i
$747$		0			0
$748$	−22.5445	+	15.5020i	−0.824307	+	0.566810i
$749$	−7.10150	−	27.9072i	−0.259483	−	1.01971i
$750$		0			0
$751$	−3.21343	−	1.85527i	−0.117260	−	0.0676999i	0.440223	−	0.897888i	$-0.354899\pi$
$751$	−3.21343	−	1.85527i	−0.117260	−	0.0676999i	−0.557483	+	0.830189i	$0.688233\pi$
$752$	31.0413	−	4.93110i	1.13196	−	0.179819i
$753$		0			0
$754$	−22.2577	+	14.0471i	−0.810578	+	0.511567i
$755$	−20.1413			−0.733016
$756$		0			0
$757$	3.20123			0.116351			0.0581753	−	0.998306i	$-0.481472\pi$
$757$	3.20123			0.116351			0.0581753	+	0.998306i	$0.481472\pi$
$758$	19.4228	−	12.2580i	0.705469	−	0.445231i
$759$		0			0
$760$	9.92245	+	13.2782i	0.359925	+	0.481652i
$761$	30.1032	+	17.3801i	1.09124	+	0.630027i	0.933906	−	0.357519i	$-0.116377\pi$
$761$	30.1032	+	17.3801i	1.09124	+	0.630027i	0.157333	+	0.987546i	$0.449710\pi$
$762$		0			0
$763$	47.6651	+	13.4187i	1.72559	+	0.485791i
$764$	−13.3693	−	19.4429i	−0.483684	−	0.703418i
$765$		0			0
$766$	−3.84096	+	0.151354i	−0.138780	+	0.00546865i
$767$	−8.90422	−	15.4226i	−0.321513	−	0.556876i
$768$		0			0
$769$	−21.6622			−0.781160			−0.390580	−	0.920569i	$-0.627726\pi$
$769$	−21.6622			−0.781160			−0.390580	+	0.920569i	$0.627726\pi$
$770$	7.73939	−	32.3202i	0.278908	−	1.16474i
$771$		0			0
$772$	−31.5167	+	2.48771i	−1.13431	+	0.0895346i
$773$	−20.9104	+	12.0727i	−0.752096	+	0.434223i	−0.826451	−	0.563009i	$-0.809644\pi$
$773$	−20.9104	+	12.0727i	−0.752096	+	0.434223i	0.0743545	+	0.997232i	$0.476310\pi$
$774$		0			0
$775$	−5.96177	−	3.44203i	−0.214153	−	0.123641i
$776$	−42.9652	+	5.10030i	−1.54236	+	0.183090i
$777$		0			0
$778$	−25.1518	−	13.2293i	−0.901737	−	0.474295i
$779$	0.545186	−	0.944290i	0.0195333	−	0.0338327i
$780$		0			0
$781$	−25.4239	−	44.0355i	−0.909740	−	1.57572i
$782$	17.8674	−	11.2764i	0.638939	−	0.403243i
$783$		0			0
$784$	−22.1900	+	17.0764i	−0.792500	+	0.609872i
$785$			12.2492i			0.437192i
$786$		0			0
$787$	3.52292	−	2.03396i	0.125578	−	0.0725028i	−0.435895	−	0.899998i	$-0.643568\pi$
$787$	3.52292	−	2.03396i	0.125578	−	0.0725028i	0.561473	+	0.827495i	$0.310235\pi$
$788$	−3.93231	−	1.87451i	−0.140083	−	0.0667765i
$789$		0			0
$790$	−1.13202	+	2.15221i	−0.0402754	+	0.0765723i
$791$	−24.2663	−	24.8866i	−0.862809	−	0.884865i
$792$		0			0
$793$	−19.2824	+	33.3980i	−0.684736	+	1.18600i
$794$	22.4170	−	0.883348i	0.795549	−	0.0313488i
$795$		0			0
$796$	0.862439	+	10.9262i	0.0305683	+	0.387269i
$797$			19.6098i			0.694614i	0.937752	+	0.347307i	$0.112904\pi$
$797$			19.6098i			0.694614i	−0.937752	+	0.347307i	$0.887096\pi$
$798$		0			0
$799$		−	25.1849i		−	0.890979i
$800$	3.71273	−	0.740727i	0.131265	−	0.0261886i
$801$		0			0
$802$	1.78203	+	45.2230i	0.0629255	+	1.59688i
$803$	26.2113	−	45.3992i	0.924975	−	1.60210i
$804$		0			0
$805$	−6.95472	+	24.7041i	−0.245122	+	0.870704i
$806$	61.8818	+	32.5485i	2.17969	+	1.14647i
$807$		0			0
$808$	0.877248	−	0.655544i	0.0308615	−	0.0230620i
$809$	−36.1801	+	20.8886i	−1.27203	+	0.734405i	−0.975369	−	0.220580i	$-0.929205\pi$
$809$	−36.1801	+	20.8886i	−1.27203	+	0.734405i	−0.296657	+	0.954984i	$0.595872\pi$
$810$		0			0
$811$		−	4.61271i		−	0.161974i	−0.996715	−	0.0809870i	$-0.974193\pi$
$811$		−	4.61271i		−	0.161974i	0.996715	−	0.0809870i	$-0.0258072\pi$
$812$	−19.3966	+	6.59943i	−0.680689	+	0.231594i
$813$		0			0
$814$	−0.881987	−	1.39751i	−0.0309136	−	0.0489827i
$815$	10.0933	+	17.4821i	0.353552	+	0.612370i
$816$		0			0
$817$	−1.27847	+	2.21437i	−0.0447279	+	0.0774710i
$818$	−3.18695	+	6.05910i	−0.111429	+	0.211851i
$819$		0			0
$820$	0.913069	+	1.32787i	0.0318858	+	0.0463712i
$821$	14.0211	+	8.09506i	0.489339	+	0.282520i	0.724300	−	0.689485i	$-0.242163\pi$
$821$	14.0211	+	8.09506i	0.489339	+	0.282520i	−0.234961	+	0.972005i	$0.575496\pi$
$822$		0			0
$823$	−13.6183	+	7.86255i	−0.474705	+	0.274071i	−0.718207	−	0.695829i	$-0.755037\pi$
$823$	−13.6183	+	7.86255i	−0.474705	+	0.274071i	0.243502	+	0.969900i	$0.421704\pi$
$824$	−35.1815	−	15.1008i	−1.22561	−	0.526062i
$825$		0			0
$826$	−3.94508	−	13.2898i	−0.137267	−	0.462411i
$827$	13.1854			0.458500			0.229250	−	0.973368i	$-0.426373\pi$
$827$	13.1854			0.458500			0.229250	+	0.973368i	$0.426373\pi$
$828$		0			0
$829$	−17.4266	−	30.1838i	−0.605252	−	1.04833i	−0.992012	−	0.126147i	$-0.959739\pi$
$829$	−17.4266	−	30.1838i	−0.605252	−	1.04833i	0.386759	−	0.922181i	$-0.373594\pi$
$830$	−0.659429	−	16.7345i	−0.0228891	−	0.580864i
$831$		0			0
$832$	−37.3837	+	9.00233i	−1.29605	+	0.312099i
$833$	10.7241	+	19.7071i	0.371568	+	0.682811i
$834$		0			0
$835$	−33.2004	−	19.1682i	−1.14895	−	0.663345i
$836$	−21.6999	−	10.3442i	−0.750507	−	0.357761i
$837$		0			0
$838$	−7.51068	−	11.9007i	−0.259452	−	0.411102i
$839$	−10.2242			−0.352978			−0.176489	−	0.984303i	$-0.556474\pi$
$839$	−10.2242			−0.352978			−0.176489	+	0.984303i	$0.556474\pi$
$840$		0			0
$841$	14.0078			0.483027
$842$	1.71621	+	2.71934i	0.0591445	+	0.0937145i
$843$		0			0
$844$	15.8881	+	7.57374i	0.546890	+	0.260699i
$845$	−18.2078	−	10.5123i	−0.626368	−	0.361634i
$846$		0			0
$847$	4.70873	+	18.5042i	0.161794	+	0.635812i
$848$	−43.7253	−	16.7615i	−1.50153	−	0.575592i
$849$		0			0
$850$	−0.119447	−	3.03124i	−0.00409699	−	0.103971i
$851$	0.638079	+	1.10519i	0.0218731	+	0.0378853i
$852$		0			0
$853$	47.4094			1.62327			0.811634	−	0.584167i	$-0.198578\pi$
$853$	47.4094			1.62327			0.811634	+	0.584167i	$0.198578\pi$
$854$	−20.6521	+	21.7883i	−0.706702	+	0.745582i
$855$		0			0
$856$	12.1424	−	28.2890i	0.415018	−	0.966900i
$857$	−14.6387	+	8.45163i	−0.500047	+	0.288702i	−0.728733	−	0.684798i	$-0.759890\pi$
$857$	−14.6387	+	8.45163i	−0.500047	+	0.288702i	0.228686	+	0.973500i	$0.426557\pi$
$858$		0			0
$859$	9.83178	+	5.67638i	0.335456	+	0.193676i	0.658261	−	0.752790i	$-0.271292\pi$
$859$	9.83178	+	5.67638i	0.335456	+	0.193676i	−0.322805	+	0.946466i	$0.604626\pi$
$860$	−2.14116	−	3.11387i	−0.0730128	−	0.106182i
$861$		0			0
$862$	18.7826	−	35.7097i	0.639737	−	1.21628i
$863$	−15.1464	+	26.2343i	−0.515590	+	0.893027i	0.484247	+	0.874932i	$0.339094\pi$
$863$	−15.1464	+	26.2343i	−0.515590	+	0.893027i	−0.999836	+	0.0180959i	$0.994240\pi$
$864$		0			0
$865$	7.36849	+	12.7626i	0.250536	+	0.433941i
$866$	5.93403	+	9.40248i	0.201647	+	0.319509i
$867$		0			0
$868$	40.9470	+	35.8589i	1.38983	+	1.21713i
$869$		−	3.52665i		−	0.119633i
$870$		0			0
$871$	5.84417	−	3.37413i	0.198022	−	0.114328i
$872$	31.6880	+	42.4049i	1.07309	+	1.43601i
$873$		0			0
$874$	16.4299	+	8.64176i	0.555748	+	0.292312i
$875$	21.7917	+	22.3488i	0.736694	+	0.755526i
$876$		0			0
$877$	7.82172	−	13.5476i	0.264121	−	0.457471i	−0.703212	−	0.710980i	$-0.748252\pi$
$877$	7.82172	−	13.5476i	0.264121	−	0.457471i	0.967333	+	0.253510i	$0.0815849\pi$
$878$	0.594178	+	15.0787i	0.0200526	+	0.508880i
$879$		0			0
$880$	27.6006	−	22.3715i	0.930415	−	0.754144i
$881$		−	23.0836i		−	0.777705i	−0.921300	−	0.388853i	$-0.872872\pi$
$881$		−	23.0836i		−	0.777705i	0.921300	−	0.388853i	$-0.127128\pi$
$882$		0			0
$883$		−	13.4161i		−	0.451488i	−0.974187	−	0.225744i	$-0.927519\pi$
$883$		−	13.4161i		−	0.451488i	0.974187	−	0.225744i	$-0.0724813\pi$
$884$	2.42450	+	30.7159i	0.0815447	+	1.03309i
$885$		0			0
$886$	53.6709	−	2.11492i	1.80311	−	0.0710520i
$887$	23.9872	−	41.5471i	0.805412	−	1.39501i	−0.110600	−	0.993865i	$-0.535277\pi$
$887$	23.9872	−	41.5471i	0.805412	−	1.39501i	0.916012	−	0.401150i	$-0.131389\pi$
$888$		0			0
$889$	−8.87706	−	9.10399i	−0.297727	−	0.305338i
$890$	4.14101	−	7.87296i	0.138807	−	0.263902i
$891$		0			0
$892$	38.1834	+	18.2018i	1.27847	+	0.609440i
$893$	19.1637	−	11.0641i	0.641287	−	0.370247i
$894$		0			0
$895$			43.9524i			1.46917i
$896$	−29.9332	+	0.0381723i	−0.999999	+	0.00127525i
$897$		0			0
$898$	28.7084	−	18.1182i	0.958010	−	0.604614i
$899$	19.9138	+	34.4917i	0.664162	+	1.15036i
$900$		0			0
$901$	−18.7613	+	32.4955i	−0.625029	+	1.08258i
$902$	−2.06840	−	1.08793i	−0.0688701	−	0.0362242i
$903$		0			0
$904$	−4.38030	−	36.8999i	−0.145687	−	1.22727i
$905$	11.0623	+	6.38681i	0.367723	+	0.212305i
$906$		0			0
$907$	8.04388	−	4.64414i	0.267093	−	0.154206i	−0.360473	−	0.932770i	$-0.617385\pi$
$907$	8.04388	−	4.64414i	0.267093	−	0.154206i	0.627566	+	0.778564i	$0.284051\pi$
$908$	56.0157	−	4.42149i	1.85895	−	0.146732i
$909$		0			0
$910$	−27.1632	−	25.7468i	−0.900453	−	0.853497i
$911$	32.4981			1.07671			0.538354	−	0.842719i	$-0.319046\pi$
$911$	32.4981			1.07671			0.538354	+	0.842719i	$0.319046\pi$
$912$		0			0
$913$	12.1440	+	21.0340i	0.401907	+	0.696123i
$914$	21.2605	−	0.837778i	0.703236	−	0.0277112i
$915$		0			0
$916$	15.4518	+	22.4715i	0.510543	+	0.742478i
$917$	−9.60217	−	37.7342i	−0.317092	−	1.24609i
$918$		0			0
$919$	−0.384776	−	0.222151i	−0.0126926	−	0.00732808i	0.493640	−	0.869666i	$-0.335666\pi$
$919$	−0.384776	−	0.222151i	−0.0126926	−	0.00732808i	−0.506333	+	0.862338i	$0.668999\pi$
$920$	−21.9778	+	16.4234i	−0.724587	+	0.541464i
$921$		0			0
$922$	36.3227	−	22.9238i	1.19623	−	0.754955i
$923$	−57.2624			−1.88482
$924$		0			0
$925$	0.183231			0.00602459
$926$	28.4409	−	17.9494i	0.934626	−	0.589855i
$927$		0			0
$928$	−20.7449	−	7.02863i	−0.680984	−	0.230726i
$929$	−14.1031	−	8.14244i	−0.462708	−	0.267145i	0.250474	−	0.968123i	$-0.419414\pi$
$929$	−14.1031	−	8.14244i	−0.462708	−	0.267145i	−0.713182	+	0.700979i	$0.752747\pi$
$930$		0			0
$931$	−10.2842	+	16.8178i	−0.337052	+	0.551181i
$932$	7.10735	−	4.88715i	0.232809	−	0.160084i
$933$		0			0
$934$	6.64673	−	0.261916i	0.217488	−	0.00857016i
$935$	−14.2343	−	24.6545i	−0.465511	−	0.806289i
$936$		0			0
$937$	30.9796			1.01206			0.506029	−	0.862516i	$-0.331113\pi$
$937$	30.9796			1.01206			0.506029	+	0.862516i	$0.331113\pi$
$938$	5.03598	−	1.49493i	0.164431	−	0.0488113i
$939$		0			0
$940$	2.57344	+	32.6028i	0.0839364	+	1.06339i
$941$	9.45740	−	5.46023i	0.308302	−	0.177998i	−0.337864	−	0.941195i	$-0.609704\pi$
$941$	9.45740	−	5.46023i	0.308302	−	0.177998i	0.646167	+	0.763196i	$0.276371\pi$
$942$		0			0
$943$	1.56297	+	0.902380i	0.0508972	+	0.0293855i
$944$	5.30470	−	13.8382i	0.172653	−	0.450396i
$945$		0			0
$946$	4.85041	+	2.55121i	0.157700	+	0.0829471i
$947$	8.39495	−	14.5405i	0.272799	−	0.472502i	−0.696778	−	0.717286i	$-0.745384\pi$
$947$	8.39495	−	14.5405i	0.272799	−	0.472502i	0.969577	+	0.244785i	$0.0787172\pi$
$948$		0			0
$949$	−29.5179	−	51.1264i	−0.958190	−	1.65963i
$950$	2.25405	−	1.42256i	0.0731310	−	0.0461540i
$951$		0			0
$952$	−3.73279	+	23.6929i	−0.120980	+	0.767891i
$953$			39.3512i			1.27471i	0.770570	+	0.637355i	$0.219972\pi$
$953$			39.3512i			1.27471i	−0.770570	+	0.637355i	$0.780028\pi$
$954$		0			0
$955$	21.2626	−	12.2760i	0.688042	−	0.397241i
$956$	6.21481	−	13.0373i	0.201001	−	0.421657i
$957$		0			0
$958$	−2.69276	+	5.11952i	−0.0869991	+	0.165404i
$959$	−2.84487	+	10.1053i	−0.0918657	+	0.326319i
$960$		0			0
$961$	37.4020	−	64.7822i	1.20652	−	2.08975i
$962$	−1.85958	+	0.0732774i	−0.0599554	+	0.00236256i
$963$		0			0
$964$	9.44022	−	0.745146i	0.304049	−	0.0239995i
$965$		−	32.8958i		−	1.05895i
$966$		0			0
$967$			9.26652i			0.297991i	0.988838	+	0.148996i	$0.0476040\pi$
$967$			9.26652i			0.297991i	−0.988838	+	0.148996i	$0.952396\pi$
$968$	−8.05114	+	18.7574i	−0.258773	+	0.602885i
$969$		0			0
$970$	−1.77265	−	44.9852i	−0.0569165	−	1.44439i
$971$	−14.5837	+	25.2598i	−0.468014	+	0.810624i	−0.999332	−	0.0365484i	$-0.988364\pi$
$971$	−14.5837	+	25.2598i	−0.468014	+	0.810624i	0.531318	+	0.847173i	$0.321697\pi$
$972$		0			0
$973$	35.4051	+	36.3102i	1.13504	+	1.16405i
$974$	7.01209	+	3.68821i	0.224682	+	0.118178i
$975$		0			0
$976$	−31.6960	+	5.03511i	−1.01457	+	0.161170i
$977$	43.6149	−	25.1811i	1.39537	−	0.805615i	0.401463	−	0.915875i	$-0.368502\pi$
$977$	43.6149	−	25.1811i	1.39537	−	0.805615i	0.993903	+	0.110261i	$0.0351686\pi$
$978$		0			0
$979$			12.9007i			0.412309i
$980$	−15.8964	−	24.4157i	−0.507793	−	0.779932i
$981$		0			0
$982$	−7.78136	−	12.3296i	−0.248313	−	0.393452i
$983$	22.4873	+	38.9491i	0.717233	+	1.24228i	0.962092	+	0.272725i	$0.0879249\pi$
$983$	22.4873	+	38.9491i	0.717233	+	1.24228i	−0.244859	+	0.969559i	$0.578742\pi$
$984$		0			0
$985$	2.26638	−	3.92549i	0.0722130	−	0.125077i
$986$	−8.17011	+	15.5332i	−0.260189	+	0.494677i
$987$		0			0
$988$	−22.3071	+	15.3388i	−0.709684	+	0.487993i
$989$	−3.66517	−	2.11609i	−0.116546	−	0.0672877i
$990$		0			0
$991$	−28.7650	+	16.6075i	−0.913749	+	0.527553i	−0.881635	−	0.471931i	$-0.843557\pi$
$991$	−28.7650	+	16.6075i	−0.913749	+	0.527553i	−0.0321135	+	0.999484i	$0.510224\pi$
$992$	11.3845	+	57.0624i	0.361459	+	1.81173i
$993$		0			0
$994$	−43.3504	−	10.3807i	−1.37499	−	0.329255i
$995$	−11.4043			−0.361541
$996$		0			0
$997$	4.80964	+	8.33054i	0.152323	+	0.263831i	0.932081	−	0.362250i	$-0.117991\pi$
$997$	4.80964	+	8.33054i	0.152323	+	0.263831i	−0.779758	+	0.626081i	$0.784658\pi$
$998$	−0.395146	−	10.0277i	−0.0125081	−	0.317423i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.be.a.107.6	yes	32
3.2	odd	2	inner	252.2.be.a.107.11	yes	32
4.3	odd	2	inner	252.2.be.a.107.1	✓	32
7.2	even	3		1764.2.e.i.1079.6		16
7.4	even	3	inner	252.2.be.a.179.16	yes	32
7.5	odd	6		1764.2.e.h.1079.6		16
12.11	even	2	inner	252.2.be.a.107.16	yes	32
21.2	odd	6		1764.2.e.i.1079.11		16
21.5	even	6		1764.2.e.h.1079.11		16
21.11	odd	6	inner	252.2.be.a.179.1	yes	32
28.11	odd	6	inner	252.2.be.a.179.11	yes	32
28.19	even	6		1764.2.e.h.1079.12		16
28.23	odd	6		1764.2.e.i.1079.12		16
84.11	even	6	inner	252.2.be.a.179.6	yes	32
84.23	even	6		1764.2.e.i.1079.5		16
84.47	odd	6		1764.2.e.h.1079.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.1	✓	32	4.3	odd	2	inner
252.2.be.a.107.6	yes	32	1.1	even	1	trivial
252.2.be.a.107.11	yes	32	3.2	odd	2	inner
252.2.be.a.107.16	yes	32	12.11	even	2	inner
252.2.be.a.179.1	yes	32	21.11	odd	6	inner
252.2.be.a.179.6	yes	32	84.11	even	6	inner
252.2.be.a.179.11	yes	32	28.11	odd	6	inner
252.2.be.a.179.16	yes	32	7.4	even	3	inner
1764.2.e.h.1079.5		16	84.47	odd	6
1764.2.e.h.1079.6		16	7.5	odd	6
1764.2.e.h.1079.11		16	21.5	even	6
1764.2.e.h.1079.12		16	28.19	even	6
1764.2.e.i.1079.5		16	84.23	even	6
1764.2.e.i.1079.6		16	7.2	even	3
1764.2.e.i.1079.11		16	21.2	odd	6
1764.2.e.i.1079.12		16	28.23	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.754782 - 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(-1.80224 - 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(2.80871 - 0.333415i) q^{8} +O(q^{10})\)	\(q+(-0.754782 - 1.19595i) q^{2} +(-0.860607 + 1.80537i) q^{4} +(-1.80224 - 1.04052i) q^{5} +(1.89429 - 1.84707i) q^{7} +(2.80871 - 0.333415i) q^{8} +(0.115881 + 2.94076i) q^{10} +(-2.13406 - 3.69630i) q^{11} -4.80655 q^{13} +(-3.63879 - 0.871343i) q^{14} +(-2.51871 - 3.10743i) q^{16} +(-2.77574 + 1.60257i) q^{17} +(-2.43886 - 1.40807i) q^{19} +(3.42954 - 2.35822i) q^{20} +(-2.80985 + 5.34213i) q^{22} +(2.33061 - 4.03674i) q^{23} +(-0.334629 - 0.579595i) q^{25} +(3.62790 + 5.74841i) q^{26} +(1.70441 + 5.00949i) q^{28} +3.87198i q^{29} +(8.90803 - 5.14305i) q^{31} +(-1.81526 + 5.35769i) q^{32} +(4.01168 + 2.11006i) q^{34} +(-5.33587 + 1.35781i) q^{35} +(-0.136891 + 0.237102i) q^{37} +(0.156815 + 3.97955i) q^{38} +(-5.40888 - 2.32163i) q^{40} +0.387186i q^{41} -0.907954i q^{43} +(8.50977 - 0.671702i) q^{44} +(-6.58686 + 0.259557i) q^{46} +(-3.92882 + 6.80492i) q^{47} +(0.176657 - 6.99777i) q^{49} +(-0.440596 + 0.837668i) q^{50} +(4.13655 - 8.67759i) q^{52} +(10.1385 - 5.85348i) q^{53} +8.88214i q^{55} +(4.70466 - 5.81947i) q^{56} +(4.63071 - 2.92250i) q^{58} +(1.85252 + 3.20865i) q^{59} +(4.01168 - 6.94844i) q^{61} +(-12.8745 - 6.77170i) q^{62} +(7.77767 - 1.87293i) q^{64} +(8.66254 + 5.00132i) q^{65} +(-1.21588 + 0.701986i) q^{67} +(-0.504416 - 6.39042i) q^{68} +(5.65130 + 5.35660i) q^{70} +11.9134 q^{71} +(6.14118 + 10.6368i) q^{73} +(0.386885 - 0.0152453i) q^{74} +(4.64099 - 3.19124i) q^{76} +(-10.8698 - 3.06010i) q^{77} +(0.715577 + 0.413138i) q^{79} +(1.30597 + 8.22109i) q^{80} +(0.463056 - 0.292241i) q^{82} -5.69055 q^{83} +6.67006 q^{85} +(-1.08587 + 0.685308i) q^{86} +(-7.22635 - 9.67029i) q^{88} +(-2.61763 - 1.51129i) q^{89} +(-9.10499 + 8.87804i) q^{91} +(5.28206 + 7.68166i) q^{92} +(11.1038 - 0.437547i) q^{94} +(2.93026 + 5.07536i) q^{95} -15.2972 q^{97} +(-8.50234 + 5.07052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) \) 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

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