LMFDB - Embedded newform 252.2.be.a.179.1

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			179.1
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41312 + 0.0556843i) q^{2} +(1.99380 - 0.157377i) q^{4} +(-1.80224 + 1.04052i) q^{5} +(-1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +O(q^{10})$	\(q+(-1.41312 + 0.0556843i) q^{2} +(1.99380 - 0.157377i) q^{4} +(-1.80224 + 1.04052i) q^{5} +(-1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +(2.48883 - 1.57073i) q^{10} +(2.13406 - 3.69630i) q^{11} -4.80655 q^{13} +(2.77970 + 2.50465i) q^{14} +(3.95047 - 0.627555i) q^{16} +(-2.77574 - 1.60257i) q^{17} +(2.43886 - 1.40807i) q^{19} +(-3.42954 + 2.35822i) q^{20} +(-2.80985 + 5.34213i) q^{22} +(-2.33061 - 4.03674i) q^{23} +(-0.334629 + 0.579595i) q^{25} +(6.79221 - 0.267649i) q^{26} +(-4.06752 - 3.38457i) q^{28} -3.87198i q^{29} +(-8.90803 - 5.14305i) q^{31} +(-5.54752 + 1.10679i) q^{32} +(4.01168 + 2.11006i) q^{34} +(5.33587 + 1.35781i) q^{35} +(-0.136891 - 0.237102i) q^{37} +(-3.36798 + 2.12558i) q^{38} +(4.71503 - 3.52341i) q^{40} -0.387186i q^{41} -0.907954i q^{43} +(3.67317 - 7.70552i) q^{44} +(3.51821 + 5.57461i) q^{46} +(3.92882 + 6.80492i) q^{47} +(0.176657 + 6.99777i) q^{49} +(0.440596 - 0.837668i) q^{50} +(-9.58329 + 0.756439i) q^{52} +(10.1385 + 5.85348i) q^{53} +8.88214i q^{55} +(5.93634 + 4.55630i) q^{56} +(0.215608 + 5.47156i) q^{58} +(-1.85252 + 3.20865i) q^{59} +(4.01168 + 6.94844i) q^{61} +(12.8745 + 6.77170i) q^{62} +(7.77767 - 1.87293i) q^{64} +(8.66254 - 5.00132i) q^{65} +(1.21588 + 0.701986i) q^{67} +(-5.78648 - 2.75837i) q^{68} +(-7.61582 - 1.62162i) q^{70} -11.9134 q^{71} +(6.14118 - 10.6368i) q^{73} +(0.206646 + 0.327430i) q^{74} +(4.64099 - 3.19124i) q^{76} +(-10.8698 + 3.06010i) q^{77} +(-0.715577 + 0.413138i) q^{79} +(-6.46669 + 5.24155i) q^{80} +(0.0215602 + 0.547139i) q^{82} +5.69055 q^{83} +6.67006 q^{85} +(0.0505587 + 1.28305i) q^{86} +(-4.76154 + 11.0933i) q^{88} +(-2.61763 + 1.51129i) q^{89} +(9.10499 + 8.87804i) q^{91} +(-5.28206 - 7.68166i) q^{92} +(-5.93081 - 9.39737i) q^{94} +(-2.93026 + 5.07536i) q^{95} -15.2972 q^{97} +(-0.639302 - 9.87883i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.41312	+	0.0556843i	−0.999225	+	0.0393747i
$2$	−1.41312	+	0.0556843i	−0.999225	+	0.0393747i
$3$		0			0
$3$		0			0
$4$	1.99380	−	0.157377i	0.996899	−	0.0786884i
$5$	−1.80224	+	1.04052i	−0.805985	+	0.465335i	−0.845560	−	0.533881i	$-0.820733\pi$
$5$	−1.80224	+	1.04052i	−0.805985	+	0.465335i	0.0395749	+	0.999217i	$0.487400\pi$
$6$		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
$10$	2.48883	−	1.57073i	0.787037	−	0.496710i
$11$	2.13406	−	3.69630i	0.643443	−	1.11448i	−0.341216	−	0.939985i	$-0.610839\pi$
$11$	2.13406	−	3.69630i	0.643443	−	1.11448i	0.984659	−	0.174491i	$-0.0558279\pi$
$12$		0			0
$13$	−4.80655			−1.33310			−0.666548	−	0.745462i	$-0.732229\pi$
$13$	−4.80655			−1.33310			−0.666548	+	0.745462i	$0.732229\pi$
$14$	2.77970	+	2.50465i	0.742907	+	0.669395i
$15$		0			0
$16$	3.95047	−	0.627555i	0.987616	−	0.156889i
$17$	−2.77574	−	1.60257i	−0.673216	−	0.388681i	0.124078	−	0.992272i	$-0.460403\pi$
$17$	−2.77574	−	1.60257i	−0.673216	−	0.388681i	−0.797294	+	0.603591i	$0.793736\pi$
$18$		0			0
$19$	2.43886	−	1.40807i	0.559512	−	0.323034i	−0.193438	−	0.981113i	$-0.561964\pi$
$19$	2.43886	−	1.40807i	0.559512	−	0.323034i	0.752950	+	0.658078i	$0.228630\pi$
$20$	−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	$-0.328199\pi$
$23$	−2.33061	−	4.03674i	−0.485966	−	0.841718i	−0.999870	+	0.0161296i	$0.994866\pi$
$24$		0			0
$25$	−0.334629	+	0.579595i	−0.0669258	+	0.115919i
$26$	6.79221	−	0.267649i	1.33206	−	0.0524903i
$27$		0			0
$28$	−4.06752	−	3.38457i	−0.768688	−	0.639624i
$29$		−	3.87198i		−	0.719009i	−0.933143	−	0.359504i	$-0.882946\pi$
$29$		−	3.87198i		−	0.719009i	0.933143	−	0.359504i	$-0.117054\pi$
$30$		0			0
$31$	−8.90803	−	5.14305i	−1.59993	−	0.923720i	−0.991499	−	0.130113i	$-0.958466\pi$
$31$	−8.90803	−	5.14305i	−1.59993	−	0.923720i	−0.608431	−	0.793607i	$-0.708201\pi$
$32$	−5.54752	+	1.10679i	−0.980673	+	0.195654i
$33$		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	0.854554	−	0.519363i	$-0.173831\pi$
$37$	−0.136891	−	0.237102i	−0.0225047	−	0.0389793i	−0.877058	+	0.480384i	$0.840497\pi$
$38$	−3.36798	+	2.12558i	−0.546359	+	0.344814i
$39$		0			0
$40$	4.71503	−	3.52341i	0.745511	−	0.557101i
$41$		−	0.387186i		−	0.0604683i	−0.999543	−	0.0302341i	$-0.990375\pi$
$41$		−	0.387186i		−	0.0604683i	0.999543	−	0.0302341i	$-0.00962529\pi$
$42$		0			0
$43$		−	0.907954i		−	0.138462i	−0.997601	−	0.0692308i	$-0.977945\pi$
$43$		−	0.907954i		−	0.138462i	0.997601	−	0.0692308i	$-0.0220545\pi$
$44$	3.67317	−	7.70552i	0.553751	−	1.16165i
$45$		0			0
$46$	3.51821	+	5.57461i	0.518732	+	0.821931i
$47$	3.92882	+	6.80492i	0.573078	+	0.992599i	0.996248	+	0.0865492i	$0.0275840\pi$
$47$	3.92882	+	6.80492i	0.573078	+	0.992599i	−0.423170	+	0.906050i	$0.639083\pi$
$48$		0			0
$49$	0.176657	+	6.99777i	0.0252367	+	0.999682i
$50$	0.440596	−	0.837668i	0.0623096	−	0.118464i
$51$		0			0
$52$	−9.58329	+	0.756439i	−1.32896	+	0.104899i
$53$	10.1385	+	5.85348i	1.39263	+	0.804037i	0.993606	−	0.112902i	$-0.0360147\pi$
$53$	10.1385	+	5.85348i	1.39263	+	0.804037i	0.399027	+	0.916939i	$0.369348\pi$
$54$		0			0
$55$			8.88214i			1.19767i
$56$	5.93634	+	4.55630i	0.793277	+	0.608861i
$57$		0			0
$58$	0.215608	+	5.47156i	0.0283108	+	0.718451i
$59$	−1.85252	+	3.20865i	−0.241177	+	0.417731i	−0.961050	−	0.276375i	$-0.910867\pi$
$59$	−1.85252	+	3.20865i	−0.241177	+	0.417731i	0.719873	+	0.694106i	$0.244200\pi$
$60$		0			0
$61$	4.01168	+	6.94844i	0.513644	+	0.889657i	0.999875	+	0.0158266i	$0.00503796\pi$
$61$	4.01168	+	6.94844i	0.513644	+	0.889657i	−0.486231	+	0.873830i	$0.661629\pi$
$62$	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	$-0.306001\pi$
$67$	1.21588	+	0.701986i	0.148543	+	0.0857613i	−0.423886	+	0.905715i	$0.639334\pi$
$68$	−5.78648	−	2.75837i	−0.701713	−	0.334502i
$69$		0			0
$70$	−7.61582	−	1.62162i	−0.910265	−	0.193821i
$71$	−11.9134			−1.41386			−0.706931	−	0.707282i	$-0.749921\pi$
$71$	−11.9134			−1.41386			−0.706931	+	0.707282i	$0.749921\pi$
$72$		0			0
$73$	6.14118	−	10.6368i	0.718770	−	1.24495i	−0.242717	−	0.970097i	$-0.578039\pi$
$73$	6.14118	−	10.6368i	0.718770	−	1.24495i	0.961487	−	0.274850i	$-0.0886281\pi$
$74$	0.206646	+	0.327430i	0.0240221	+	0.0380630i
$75$		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	$-0.681468\pi$
$79$	−0.715577	+	0.413138i	−0.0805087	+	0.0464817i	0.459205	+	0.888330i	$0.348134\pi$
$80$	−6.46669	+	5.24155i	−0.722998	+	0.586023i
$81$		0			0
$82$	0.0215602	+	0.547139i	0.00238092	+	0.0604214i
$83$	5.69055			0.624619			0.312310	−	0.949980i	$-0.398897\pi$
$83$	5.69055			0.624619			0.312310	+	0.949980i	$0.398897\pi$
$84$		0			0
$85$	6.67006			0.723469
$86$	0.0505587	+	1.28305i	0.00545189	+	0.138354i
$87$		0			0
$88$	−4.76154	+	11.0933i	−0.507582	+	1.18255i
$89$	−2.61763	+	1.51129i	−0.277469	+	0.160197i	−0.632277	−	0.774742i	$-0.717879\pi$
$89$	−2.61763	+	1.51129i	−0.277469	+	0.160197i	0.354808	+	0.934939i	$0.384546\pi$
$90$		0			0
$91$	9.10499	+	8.87804i	0.954462	+	0.930671i
$92$	−5.28206	−	7.68166i	−0.550693	−	0.800868i
$93$		0			0
$94$	−5.93081	−	9.39737i	−0.611716	−	0.969265i
$95$	−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	$0.783055\pi$
$98$	−0.639302	−	9.87883i	−0.0645793	−	0.997913i
$99$		0			0
$100$	−0.575968	+	1.20826i	−0.0575968	+	0.120826i
$101$	0.335313	+	0.193593i	0.0333649	+	0.0192632i	0.516590	−	0.856233i	$-0.327201\pi$
$101$	0.335313	+	0.193593i	0.0333649	+	0.0192632i	−0.483225	+	0.875496i	$0.660535\pi$
$102$		0			0
$103$	11.7225	−	6.76797i	1.15505	−	0.666868i	0.204937	−	0.978775i	$-0.434301\pi$
$103$	11.7225	−	6.76797i	1.15505	−	0.666868i	0.950113	+	0.311907i	$0.100968\pi$
$104$	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	−0.999538	−	0.0304073i	$-0.990320\pi$
$107$	−5.44204	−	9.42590i	−0.526102	−	0.911236i	0.473435	−	0.880829i	$-0.343014\pi$
$108$		0			0
$109$	9.35800	−	16.2085i	0.896334	−	1.55250i	0.0641884	−	0.997938i	$-0.479554\pi$
$109$	9.35800	−	16.2085i	0.896334	−	1.55250i	0.832145	−	0.554558i	$-0.187113\pi$
$110$	−0.494595	−	12.5515i	−0.0471578	−	1.19674i
$111$		0			0
$112$	−8.64246	−	6.10802i	−0.816636	−	0.577154i
$113$			13.1377i			1.23589i	0.786221	+	0.617945i	$0.212035\pi$
$113$			13.1377i			1.23589i	−0.786221	+	0.617945i	$0.787965\pi$
$114$		0			0
$115$	8.40063	+	4.85011i	0.783363	+	0.452275i
$116$	−0.609360	−	7.71995i	−0.0565776	−	0.716779i
$117$		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
$122$	−6.05590	−	9.59557i	−0.548275	−	0.868742i
$123$		0			0
$124$	−18.5702	−	8.85230i	−1.66765	−	0.794960i
$125$		−	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	$-0.0683992\pi$
$128$	−10.8865	+	3.07976i	−0.962236	+	0.272215i
$129$		0			0
$130$	−11.9627	+	7.54981i	−1.04920	+	0.662162i
$131$	−7.35836	−	12.7451i	−0.642903	−	1.11354i	−0.984782	−	0.173797i	$-0.944396\pi$
$131$	−7.35836	−	12.7451i	−0.642903	−	1.11354i	0.341878	−	0.939744i	$-0.388937\pi$
$132$		0			0
$133$	−7.22071	−	1.83744i	−0.626115	−	0.159326i
$134$	−1.75726	−	0.924284i	−0.151805	−	0.0798459i
$135$		0			0
$136$	8.33057	+	3.57569i	0.714340	+	0.306613i
$137$	−3.43633	−	1.98397i	−0.293585	−	0.169502i	0.345972	−	0.938245i	$-0.387549\pi$
$137$	−3.43633	−	1.98397i	−0.293585	−	0.169502i	−0.639558	+	0.768743i	$0.720882\pi$
$138$		0			0
$139$			19.1682i			1.62583i	0.582383	+	0.812915i	$0.302121\pi$
$139$			19.1682i			1.62583i	−0.582383	+	0.812915i	$0.697879\pi$
$140$	10.8523	+	1.86746i	0.917190	+	0.157829i
$141$		0			0
$142$	16.8351	−	0.663390i	1.41277	−	0.0556704i
$143$	−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	−0.285722	−	0.958313i	$-0.592233\pi$
$149$	4.89898	−	2.82843i	0.401340	−	0.231714i	0.687062	+	0.726599i	$0.258900\pi$
$150$		0			0
$151$	−8.38179	−	4.83923i	−0.682100	−	0.393811i	0.118546	−	0.992949i	$-0.462177\pi$
$151$	−8.38179	−	4.83923i	−0.682100	−	0.393811i	−0.800646	+	0.599138i	$0.795510\pi$
$152$	−6.38056	+	4.76802i	−0.517532	+	0.386737i
$153$		0			0
$154$	15.1900	−	4.92955i	1.22404	−	0.397235i
$155$	21.4058			1.71936
$156$		0			0
$157$	−2.94304	+	5.09749i	−0.234880	+	0.406824i	−0.959238	−	0.282600i	$-0.908803\pi$
$157$	−2.94304	+	5.09749i	−0.234880	+	0.406824i	0.724358	+	0.689424i	$0.242136\pi$
$158$	0.988188	−	0.623659i	0.0786160	−	0.0496157i
$159$		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	$-0.542629\pi$
$163$	8.40063	−	4.85011i	0.657988	−	0.379890i	0.791510	+	0.611156i	$0.209295\pi$
$164$	−0.0609340	−	0.771970i	−0.00475815	−	0.0602808i
$165$		0			0
$166$	−8.04142	+	0.316874i	−0.624135	+	0.0245942i
$167$	−18.4218			−1.42552			−0.712759	−	0.701409i	$-0.752555\pi$
$167$	−18.4218			−1.42552			−0.712759	+	0.701409i	$0.752555\pi$
$168$		0			0
$169$	10.1029			0.777146
$170$	−9.42557	+	0.371417i	−0.722908	+	0.0284864i
$171$		0			0
$172$	−0.142891	−	1.81028i	−0.0108953	−	0.138032i
$173$	−6.13279	+	3.54077i	−0.466267	+	0.269199i	−0.714676	−	0.699456i	$-0.753426\pi$
$173$	−6.13279	+	3.54077i	−0.466267	+	0.269199i	0.248409	+	0.968655i	$0.420092\pi$
$174$		0			0
$175$	1.70444	−	0.479836i	0.128843	−	0.0362722i
$176$	6.11089	−	15.9413i	0.460626	−	1.20162i
$177$		0			0
$178$	3.61487	−	2.28139i	0.270946	−	0.170998i
$179$	10.5602	−	18.2908i	0.789305	−	1.36712i	−0.137088	−	0.990559i	$-0.543774\pi$
$179$	10.5602	−	18.2908i	0.789305	−	1.36712i	0.926393	−	0.376557i	$-0.122892\pi$
$180$		0			0
$181$	−6.13809			−0.456240			−0.228120	−	0.973633i	$-0.573258\pi$
$181$	−6.13809			−0.456240			−0.228120	+	0.973633i	$0.573258\pi$
$182$	−13.3608	−	12.0387i	−0.990367	−	0.892368i
$183$		0			0
$184$	7.89192	+	10.5610i	0.581800	+	0.778564i
$185$	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	$-0.0262958\pi$
$191$	5.89895	+	10.2173i	0.426833	+	0.739297i	−0.569756	+	0.821814i	$0.692962\pi$
$192$		0			0
$193$	7.90367	−	13.6896i	0.568919	−	0.985396i	−0.427754	−	0.903895i	$-0.640695\pi$
$193$	7.90367	−	13.6896i	0.568919	−	0.985396i	0.996673	−	0.0815013i	$-0.0259715\pi$
$194$	21.6167	−	0.851811i	1.55199	−	0.0611564i
$195$		0			0
$196$	1.45350	+	13.9243i	0.103822	+	0.994596i
$197$		−	2.17812i		−	0.155185i	−0.996985	−	0.0775924i	$-0.975277\pi$
$197$		−	2.17812i		−	0.155185i	0.996985	−	0.0775924i	$-0.0247233\pi$
$198$		0			0
$199$	−4.74590	−	2.74005i	−0.336428	−	0.194237i	0.322263	−	0.946650i	$-0.395556\pi$
$199$	−4.74590	−	2.74005i	−0.336428	−	0.194237i	−0.658691	+	0.752413i	$0.728890\pi$
$200$	0.746630	−	1.73948i	0.0527947	−	0.123000i
$201$		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
$206$	−16.1884	+	10.2167i	−1.12790	+	0.711831i
$207$		0			0
$208$	−18.9881	+	3.01637i	−1.31659	+	0.209148i
$209$		−	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	$-0.0979629\pi$
$212$	21.1354	+	10.0751i	1.45158	+	0.691960i
$213$		0			0
$214$	8.21512	+	13.0169i	0.561574	+	0.889814i
$215$	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
$220$	1.39784	+	17.7092i	0.0942425	+	1.19395i
$221$	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	$-0.250471\pi$
$224$	12.5529	+	8.15010i	0.838728	+	0.544551i
$225$		0			0
$226$	−0.731563	−	18.5651i	−0.0486628	−	1.23493i
$227$	14.0475	−	24.3309i	0.932364	−	1.61490i	0.153095	−	0.988211i	$-0.451076\pi$
$227$	14.0475	−	24.3309i	0.932364	−	1.61490i	0.779269	−	0.626690i	$-0.215591\pi$
$228$		0			0
$229$	6.81783	+	11.8088i	0.450535	+	0.780350i	0.998419	−	0.0562045i	$-0.0178999\pi$
$229$	6.81783	+	11.8088i	0.450535	+	0.780350i	−0.547884	+	0.836554i	$0.684567\pi$
$230$	−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	−0.617328	−	0.786706i	$-0.711785\pi$
$233$	−3.73493	+	2.15637i	−0.244684	+	0.141268i	0.372644	+	0.927974i	$0.378451\pi$
$234$		0			0
$235$	−14.1613	−	8.17605i	−0.923783	−	0.533347i
$236$	−3.18858	+	6.68895i	−0.207559	+	0.435414i
$237$		0			0
$238$	−3.70186	−	11.4069i	−0.239956	−	0.739401i
$239$	7.22142			0.467115			0.233558	−	0.972343i	$-0.424963\pi$
$239$	7.22142			0.467115			0.233558	+	0.972343i	$0.424963\pi$
$240$		0			0
$241$	−2.36740	+	4.10045i	−0.152497	+	0.264133i	−0.932145	−	0.362085i	$-0.882065\pi$
$241$	−2.36740	+	4.10045i	−0.152497	+	0.264133i	0.779648	+	0.626219i	$0.215398\pi$
$242$	5.44713	+	8.63098i	0.350155	+	0.554820i
$243$		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
$248$	26.7348	+	11.4753i	1.69766	+	0.728680i
$249$		0			0
$250$	0.656961	+	16.6719i	0.0415499	+	1.05442i
$251$	2.26312			0.142847			0.0714233	−	0.997446i	$-0.477246\pi$
$251$	2.26312			0.142847			0.0714233	+	0.997446i	$0.477246\pi$
$252$		0			0
$253$	−19.8947			−1.25077
$254$	0.267620	+	6.79147i	0.0167919	+	0.426135i
$255$		0			0
$256$	15.2123	−	4.95827i	0.950772	−	0.309892i
$257$	15.6241	−	9.02055i	0.974602	−	0.562687i	0.0739657	−	0.997261i	$-0.476434\pi$
$257$	15.6241	−	9.02055i	0.974602	−	0.562687i	0.900636	+	0.434574i	$0.143101\pi$
$258$		0			0
$259$	−0.178633	+	0.701986i	−0.0110997	+	0.0436193i
$260$	16.4843	−	11.3349i	1.02231	−	0.702961i
$261$		0			0
$262$	11.1079	+	17.6005i	0.686250	+	1.08736i
$263$	−0.335353	+	0.580849i	−0.0206788	+	0.0358167i	−0.876180	−	0.481985i	$-0.839916\pi$
$263$	−0.335353	+	0.580849i	−0.0206788	+	0.0358167i	0.855501	+	0.517801i	$0.173249\pi$
$264$		0			0
$265$	−24.3627			−1.49659
$266$	10.3060	+	2.19444i	0.631903	+	0.134550i
$267$		0			0
$268$	2.53469	+	1.20827i	0.154831	+	0.0738068i
$269$	8.22457	+	4.74846i	0.501461	+	0.289518i	0.729317	−	0.684176i	$-0.239838\pi$
$269$	8.22457	+	4.74846i	0.501461	+	0.289518i	−0.227856	+	0.973695i	$0.573171\pi$
$270$		0			0
$271$	−14.8698	+	8.58509i	−0.903276	+	0.521507i	−0.878262	−	0.478180i	$-0.841297\pi$
$271$	−14.8698	+	8.58509i	−0.903276	+	0.521507i	−0.0250146	+	0.999687i	$0.507963\pi$
$272$	−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	−0.975188	−	0.221377i	$-0.928945\pi$
$277$	−4.92436	+	8.52923i	−0.295876	+	0.512472i	0.679312	+	0.733849i	$0.262278\pi$
$278$	−1.06737	−	27.0870i	−0.0640166	−	1.62457i
$279$		0			0
$280$	−15.4396	−	2.03463i	−0.922694	−	0.121593i
$281$		−	7.25476i		−	0.432783i	−0.976307	−	0.216391i	$-0.930571\pi$
$281$		−	7.25476i		−	0.432783i	0.976307	−	0.216391i	$-0.0694287\pi$
$282$		0			0
$283$	2.43886	+	1.40807i	0.144975	+	0.0837013i	0.570733	−	0.821136i	$-0.306659\pi$
$283$	2.43886	+	1.40807i	0.144975	+	0.0837013i	−0.425758	+	0.904837i	$0.639993\pi$
$284$	−23.7530	+	1.87489i	−1.40948	+	0.111255i
$285$		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
$290$	−6.08185	−	9.63670i	−0.357139	−	0.565886i
$291$		0			0
$292$	10.5703	−	22.1742i	0.618579	−	1.29765i
$293$		−	6.86151i		−	0.400854i	−0.979709	−	0.200427i	$-0.935767\pi$
$293$		−	6.86151i		−	0.400854i	0.979709	−	0.200427i	$-0.0642329\pi$
$294$		0			0
$295$		−	7.71034i		−	0.448913i
$296$	0.463540	+	0.620308i	0.0269427	+	0.0360547i
$297$		0			0
$298$	−6.76533	+	4.26969i	−0.391905	+	0.247337i
$299$	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
$304$	8.75097	−	7.09306i	0.501903	−	0.406815i
$305$	−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	$-0.0760808\pi$
$308$	−21.1907	+	7.81188i	−1.20745	+	0.445123i
$309$		0			0
$310$	−30.2490	+	1.19197i	−1.71803	+	0.0676993i
$311$	8.68043	−	15.0349i	0.492222	−	0.852553i	−0.507738	−	0.861512i	$-0.669518\pi$
$311$	8.68043	−	15.0349i	0.492222	−	0.852553i	0.999960	+	0.00895813i	$0.00285150\pi$
$312$		0			0
$313$	−3.97581	−	6.88630i	−0.224726	−	0.389237i	0.731511	−	0.681829i	$-0.238815\pi$
$313$	−3.97581	−	6.88630i	−0.224726	−	0.389237i	−0.956237	+	0.292593i	$0.905482\pi$
$314$	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	−0.552152	−	0.833743i	$-0.686193\pi$
$317$	−1.89058	+	1.09153i	−0.106186	+	0.0613063i	0.445967	+	0.895050i	$0.352860\pi$
$318$		0			0
$319$	−14.3120	−	8.26303i	−0.801318	−	0.462641i
$320$	−12.0684	+	11.4683i	−0.674643	+	0.641097i
$321$		0			0
$322$	3.63219	−	17.0583i	0.202414	−	0.950622i
$323$	−9.02618			−0.502230
$324$		0			0
$325$	1.60841	−	2.78585i	0.0892186	−	0.154531i
$326$	−11.6010	+	7.32155i	−0.642520	+	0.405503i
$327$		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	$-0.787431\pi$
$331$	−11.6706	+	6.73802i	−0.641473	+	0.370355i	0.143709	+	0.989620i	$0.454097\pi$
$332$	11.3458	−	0.895561i	0.622683	−	0.0491503i
$333$		0			0
$334$	26.0321	−	1.02580i	1.42441	−	0.0561294i
$335$	−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	$0.342653\pi$
$338$	−14.2766	+	0.562573i	−0.776544	+	0.0305999i
$339$		0			0
$340$	13.2987	−	1.04971i	0.721226	−	0.0569286i
$341$	−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
$346$	8.46918	−	5.34502i	0.455306	−	0.287350i
$347$	−1.10433	+	1.91275i	−0.0592833	+	0.102682i	−0.894144	−	0.447780i	$-0.852215\pi$
$347$	−1.10433	+	1.91275i	−0.0592833	+	0.102682i	0.834861	+	0.550461i	$0.185548\pi$
$348$		0			0
$349$	31.3253			1.67681			0.838403	−	0.545051i	$-0.183490\pi$
$349$	31.3253			1.67681			0.838403	+	0.545051i	$0.183490\pi$
$350$	−2.38185	+	0.772974i	−0.127315	+	0.0413172i
$351$		0			0
$352$	−7.74772	+	22.8672i	−0.412955	+	1.21883i
$353$	5.97612	+	3.45031i	0.318077	+	0.183642i	0.650535	−	0.759476i	$-0.274545\pi$
$353$	5.97612	+	3.45031i	0.318077	+	0.183642i	−0.332458	+	0.943118i	$0.607878\pi$
$354$		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	$-0.279446\pi$
$359$	−6.57360	−	11.3858i	−0.346941	−	0.600920i	−0.985705	+	0.168483i	$0.946113\pi$
$360$		0			0
$361$	−5.53466	+	9.58630i	−0.291298	+	0.504542i
$362$	8.67383	−	0.341795i	0.455887	−	0.0179643i
$363$		0			0
$364$	19.5507	+	16.2681i	1.02474	+	0.852680i
$365$			25.5601i			1.33788i
$366$		0			0
$367$	9.79102	+	5.65285i	0.511087	+	0.295076i	0.733280	−	0.679926i	$-0.237988\pi$
$367$	9.79102	+	5.65285i	0.511087	+	0.295076i	−0.222193	+	0.975003i	$0.571322\pi$
$368$	−11.7403	−	14.4844i	−0.612004	−	0.755052i
$369$		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	0.622580	−	0.782556i	$-0.286085\pi$
$373$	−7.07682	−	12.2574i	−0.366424	−	0.634665i	−0.989004	+	0.147892i	$0.952751\pi$
$374$	16.3606	−	10.3254i	0.845985	−	0.533913i
$375$		0			0
$376$	−13.3038	−	17.8031i	−0.686090	−	0.918125i
$377$			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	$0.863044\pi$
$380$	−5.04361	+	10.5804i	−0.258732	+	0.542764i
$381$		0			0
$382$	−8.90485	−	14.1097i	−0.455612	−	0.721917i
$383$	−1.35904	−	2.35392i	−0.0694436	−	0.120280i	0.829213	−	0.558933i	$-0.188789\pi$
$383$	−1.35904	−	2.35392i	−0.0694436	−	0.120280i	−0.898657	+	0.438653i	$0.855456\pi$
$384$		0			0
$385$	16.4059	−	16.8253i	0.836124	−	0.857498i
$386$	−10.4065	+	19.7851i	−0.529678	+	1.00703i
$387$		0			0
$388$	−30.4994	+	2.40742i	−1.54837	+	0.122218i
$389$	17.4029	+	10.0476i	0.882363	+	0.509432i	0.871437	−	0.490508i	$-0.163189\pi$
$389$	17.4029	+	10.0476i	0.882363	+	0.509432i	0.0109262	+	0.999940i	$0.496522\pi$
$390$		0			0
$391$			14.9399i			0.755544i
$392$	−2.82934	−	19.5958i	−0.142903	−	0.989737i
$393$		0			0
$394$	0.121287	+	3.07794i	0.00611036	+	0.155064i
$395$	0.859759	−	1.48915i	0.0432592	−	0.0749271i
$396$		0			0
$397$	−7.93175	−	13.7382i	−0.398083	−	0.689501i	0.595406	−	0.803425i	$-0.296991\pi$
$397$	−7.93175	−	13.7382i	−0.398083	−	0.689501i	−0.993489	+	0.113924i	$0.963658\pi$
$398$	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	−0.992632	−	0.121169i	$-0.961336\pi$
$401$	−27.7148	+	16.0012i	−1.38401	+	0.799060i	−0.391381	+	0.920229i	$0.628002\pi$
$402$		0			0
$403$	42.8169	+	24.7203i	2.13286	+	1.23141i
$404$	0.699013	+	0.333215i	0.0347772	+	0.0165781i
$405$		0			0
$406$	9.69794	−	10.7630i	0.481300	−	0.534157i
$407$	−1.16853			−0.0579220
$408$		0			0
$409$	−2.42047	+	4.19237i	−0.119684	+	0.207300i	−0.919643	−	0.392756i	$-0.871522\pi$
$409$	−2.42047	+	4.19237i	−0.119684	+	0.207300i	0.799958	+	0.600056i	$0.204855\pi$
$410$	−0.608166	−	0.963639i	−0.0300352	−	0.0475908i
$411$		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
$416$	26.6644	−	5.31983i	1.30733	−	0.260826i
$417$		0			0
$418$	0.669305	+	16.9852i	0.0327368	+	0.830772i
$419$	−9.95079			−0.486128			−0.243064	−	0.970010i	$-0.578152\pi$
$419$	−9.95079			−0.486128			−0.243064	+	0.970010i	$0.578152\pi$
$420$		0			0
$421$	−2.27378			−0.110817			−0.0554087	−	0.998464i	$-0.517646\pi$
$421$	−2.27378			−0.110817			−0.0554087	+	0.998464i	$0.517646\pi$
$422$	0.490047	+	12.4361i	0.0238551	+	0.605379i
$423$		0			0
$424$	−30.4278	−	13.0604i	−1.47770	−	0.634268i
$425$	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
$430$	−1.42616	−	2.25974i	−0.0687753	−	0.108974i
$431$	−14.2652	+	24.7081i	−0.687131	+	1.19015i	0.285631	+	0.958340i	$0.407797\pi$
$431$	−14.2652	+	24.7081i	−0.687131	+	1.19015i	−0.972762	+	0.231806i	$0.925536\pi$
$432$		0			0
$433$	−7.86191			−0.377819			−0.188910	−	0.981994i	$-0.560495\pi$
$433$	−7.86191			−0.377819			−0.188910	+	0.981994i	$0.560495\pi$
$434$	−11.8802	−	36.6076i	−0.570266	−	1.75722i
$435$		0			0
$436$	16.1071	−	33.7893i	0.771391	−	1.61821i
$437$	−11.3681	−	6.56335i	−0.543808	−	0.313968i
$438$		0			0
$439$	9.24092	−	5.33525i	0.441045	−	0.254637i	−0.262996	−	0.964797i	$-0.584711\pi$
$439$	9.24092	−	5.33525i	0.441045	−	0.254637i	0.704041	+	0.710160i	$0.251377\pi$
$440$	−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	0.824562	+	0.565772i	$0.191422\pi$
$443$	18.9902	+	32.8921i	0.902254	+	1.56275i	0.0776916	+	0.996977i	$0.475245\pi$
$444$		0			0
$445$	3.14506	−	5.44741i	0.149090	−	0.258232i
$446$	1.17772	+	29.8873i	0.0557665	+	1.41520i
$447$		0			0
$448$	−18.1926	−	10.8180i	−0.859519	−	0.511104i
$449$		−	24.0046i		−	1.13285i	−0.824114	−	0.566423i	$-0.808327\pi$
$449$		−	24.0046i		−	1.13285i	0.824114	−	0.566423i	$-0.191673\pi$
$450$		0			0
$451$	−1.43115	−	0.826277i	−0.0673904	−	0.0389079i
$452$	2.06757	+	26.1939i	0.0972502	+	1.23206i
$453$		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	0.634690	−	0.772767i	$-0.281128\pi$
$457$	−7.52257	−	13.0295i	−0.351891	−	0.609493i	−0.986581	+	0.163274i	$0.947795\pi$
$458$	−10.2920	−	16.3076i	−0.480912	−	0.762005i
$459$		0			0
$460$	17.5125	+	8.34807i	0.816522	+	0.389231i
$461$		−	30.3714i		−	1.41454i	−0.706946	−	0.707268i	$-0.749927\pi$
$461$		−	30.3714i		−	1.41454i	0.706946	−	0.707268i	$-0.250073\pi$
$462$		0			0
$463$			23.7810i			1.10519i	0.833448	+	0.552597i	$0.186363\pi$
$463$			23.7810i			1.10519i	−0.833448	+	0.552597i	$0.813637\pi$
$464$	−2.42988	−	15.2961i	−0.112804	−	0.710105i
$465$		0			0
$466$	5.15782	−	3.25517i	0.238932	−	0.150793i
$467$	2.35180	+	4.07343i	0.108828	+	0.188496i	0.915296	−	0.402782i	$-0.131957\pi$
$467$	2.35180	+	4.07343i	0.108828	+	0.188496i	−0.806468	+	0.591278i	$0.798623\pi$
$468$		0			0
$469$	−1.00660	−	3.57557i	−0.0464805	−	0.165105i
$470$	20.4669	+	10.7651i	0.944067	+	0.496559i
$471$		0			0
$472$	4.13337	−	9.62983i	0.190254	−	0.443249i
$473$	−3.35607	−	1.93763i	−0.154312	−	0.0890922i
$474$		0			0
$475$			1.88473i			0.0864774i
$476$	5.86634	+	15.9132i	0.268883	+	0.729380i
$477$		0			0
$478$	−10.2047	+	0.402120i	−0.466753	+	0.0183925i
$479$	2.04513	−	3.54227i	0.0934444	−	0.161850i	−0.815514	−	0.578737i	$-0.803546\pi$
$479$	2.04513	−	3.54227i	0.0934444	−	0.161850i	0.908958	+	0.416887i	$0.136879\pi$
$480$		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	$-0.292820\pi$
$487$	4.85177	+	2.80117i	0.219854	+	0.126933i	−0.386028	+	0.922487i	$0.626153\pi$
$488$	−13.5844	−	18.1786i	−0.614935	−	0.822906i
$489$		0			0
$490$	11.4313	+	17.1388i	0.516414	+	0.774251i
$491$	−10.3094			−0.465257			−0.232629	−	0.972566i	$-0.574733\pi$
$491$	−10.3094			−0.465257			−0.232629	+	0.972566i	$0.574733\pi$
$492$		0			0
$493$	−6.20514	+	10.7476i	−0.279465	+	0.484048i
$494$	16.1884	−	10.2167i	0.728349	−	0.459671i
$495$		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	$-0.717440\pi$
$499$	−6.14548	+	3.54809i	−0.275109	+	0.158835i	0.356098	+	0.934449i	$0.384107\pi$
$500$	−1.85673	−	23.5228i	−0.0830353	−	1.05197i
$501$		0			0
$502$	−3.19805	+	0.126020i	−0.142736	+	0.00562455i
$503$	6.79674			0.303052			0.151526	−	0.988453i	$-0.451581\pi$
$503$	6.79674			0.303052			0.151526	+	0.988453i	$0.451581\pi$
$504$		0			0
$505$	−0.805750			−0.0358554
$506$	28.1135	−	1.10782i	1.24980	−	0.0492486i
$507$		0			0
$508$	−0.756356	−	9.58223i	−0.0335579	−	0.425143i
$509$	16.8641	−	9.73648i	0.747487	−	0.431562i	−0.0772979	−	0.997008i	$-0.524629\pi$
$509$	16.8641	−	9.73648i	0.747487	−	0.431562i	0.824785	+	0.565446i	$0.191296\pi$
$510$		0			0
$511$	−31.2801	+	8.80603i	−1.38375	+	0.389556i
$512$	−21.2207	+	7.85370i	−0.937833	+	0.347088i
$513$		0			0
$514$	−21.5763	+	13.6171i	−0.951690	+	0.600625i
$515$	−14.0844	+	24.3950i	−0.620635	+	1.07497i
$516$		0			0
$517$	33.5373			1.47497
$518$	0.213340	−	1.00194i	0.00937363	−	0.0440225i
$519$		0			0
$520$	−22.6630	+	16.9355i	−0.993839	+	0.742669i
$521$	29.8381	+	17.2270i	1.30723	+	0.754729i	0.981633	−	0.190779i	$-0.0611015\pi$
$521$	29.8381	+	17.2270i	1.30723	+	0.754729i	0.325597	+	0.945509i	$0.394435\pi$
$522$		0			0
$523$	18.6920	−	10.7918i	0.817342	−	0.471893i	−0.0321570	−	0.999483i	$-0.510238\pi$
$523$	18.6920	−	10.7918i	0.817342	−	0.471893i	0.849499	+	0.527590i	$0.176904\pi$
$524$	−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
$530$	34.4273	−	1.35662i	1.49543	−	0.0589277i
$531$		0			0
$532$	−14.6858	−	2.52712i	−0.636711	−	0.109564i
$533$			1.86103i			0.0806100i
$534$		0			0
$535$	19.6157	+	11.3251i	0.848061	+	0.489628i
$536$	−3.64909	−	1.56628i	−0.157617	−	0.0676531i
$537$		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	0.813448	+	0.581638i	$0.197588\pi$
$541$	21.1762	+	36.6783i	0.910437	+	1.57692i	0.0969897	+	0.995285i	$0.469079\pi$
$542$	20.5347	−	12.9597i	0.882042	−	0.556669i
$543$		0			0
$544$	17.1722	+	5.81817i	0.736252	+	0.249452i
$545$			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	$0.710400\pi$
$548$	−7.16358	−	3.41483i	−0.306013	−	0.145874i
$549$		0			0
$550$	−2.15602	−	3.41621i	−0.0919328	−	0.145668i
$551$	−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
$556$	3.01664	+	38.2176i	0.127934	+	1.62079i
$557$	−13.1808	−	7.60993i	−0.558488	−	0.322443i	0.194050	−	0.980992i	$-0.437837\pi$
$557$	−13.1808	−	7.60993i	−0.558488	−	0.322443i	−0.752538	+	0.658548i	$0.771171\pi$
$558$		0			0
$559$			4.36412i			0.184583i
$560$	21.9313	+	2.01543i	0.926766	+	0.0851674i
$561$		0			0
$562$	0.403976	+	10.2518i	0.0170407	+	0.432447i
$563$	−8.71740	+	15.0990i	−0.367395	+	0.636346i	−0.989157	−	0.146859i	$-0.953084\pi$
$563$	−8.71740	+	15.0990i	−0.367395	+	0.636346i	0.621763	+	0.783206i	$0.286417\pi$
$564$		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	−0.827909	−	0.560862i	$-0.810470\pi$
$569$	−18.0368	+	10.4136i	−0.756144	+	0.436560i	0.0717659	+	0.997422i	$0.477137\pi$
$570$		0			0
$571$	−17.8090	−	10.2820i	−0.745282	−	0.430289i	0.0787048	−	0.996898i	$-0.474922\pi$
$571$	−17.8090	−	10.2820i	−0.745282	−	0.430289i	−0.823987	+	0.566609i	$0.808255\pi$
$572$	−17.6553	+	37.0370i	−0.738204	+	1.54859i
$573$		0			0
$574$	0.969763	−	1.07626i	0.0404771	−	0.0449223i
$575$	3.11956			0.130095
$576$		0			0
$577$	−1.58033	+	2.73721i	−0.0657900	+	0.113952i	−0.897044	−	0.441941i	$-0.854290\pi$
$577$	−1.58033	+	2.73721i	−0.0657900	+	0.113952i	0.831254	+	0.555893i	$0.187623\pi$
$578$	5.07743	+	8.04519i	0.211193	+	0.334636i
$579$		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
$584$	−13.7023	+	31.9233i	−0.567005	+	1.32100i
$585$		0			0
$586$	0.382078	+	9.69612i	0.0157835	+	0.400543i
$587$	−22.1152			−0.912792			−0.456396	−	0.889777i	$-0.650860\pi$
$587$	−22.1152			−0.912792			−0.456396	+	0.889777i	$0.650860\pi$
$588$		0			0
$589$	−28.9672			−1.19357
$590$	0.429345	+	10.8956i	0.0176758	+	0.448565i
$591$		0			0
$592$	−0.689577	−	0.850756i	−0.0283414	−	0.0349659i
$593$	36.0411	−	20.8083i	1.48003	−	0.854496i	0.480286	−	0.877112i	$-0.340533\pi$
$593$	36.0411	−	20.8083i	1.48003	−	0.854496i	0.999744	+	0.0226166i	$0.00719972\pi$
$594$		0			0
$595$	−12.6350	−	12.3201i	−0.517985	−	0.505074i
$596$	9.32245	−	6.41030i	0.381862	−	0.262576i
$597$		0			0
$598$	−16.9104	−	26.7946i	−0.691520	−	1.09571i
$599$	19.1656	−	33.1958i	0.783086	−	1.35634i	−0.147050	−	0.989129i	$-0.546978\pi$
$599$	19.1656	−	33.1958i	0.783086	−	1.35634i	0.930136	−	0.367215i	$-0.119689\pi$
$600$		0			0
$601$	29.3369			1.19668			0.598338	−	0.801244i	$-0.295828\pi$
$601$	29.3369			1.19668			0.598338	+	0.801244i	$0.295828\pi$
$602$	2.27410	−	2.52384i	0.0926855	−	0.102864i
$603$		0			0
$604$	−17.4732	−	8.32935i	−0.710973	−	0.338916i
$605$	13.0064	+	7.50926i	0.528786	+	0.305295i
$606$		0			0
$607$	−31.4700	+	18.1692i	−1.27733	+	0.737465i	−0.976356	−	0.216168i	$-0.930644\pi$
$607$	−31.4700	+	18.1692i	−1.27733	+	0.737465i	−0.300971	+	0.953633i	$0.597311\pi$
$608$	−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	0.433224	+	0.901286i	$0.357376\pi$
$613$	−13.9621	+	24.1831i	−0.563925	+	0.976746i	−0.997149	+	0.0754602i	$0.975957\pi$
$614$	0.461970	+	11.7236i	0.0186436	+	0.473124i
$615$		0			0
$616$	29.5099	−	12.2191i	1.18899	−	0.492321i
$617$		−	1.74855i		−	0.0703940i	−0.999380	−	0.0351970i	$-0.988794\pi$
$617$		−	1.74855i		−	0.0703940i	0.999380	−	0.0351970i	$-0.0112059\pi$
$618$		0			0
$619$	−17.8090	−	10.2820i	−0.715803	−	0.413269i	0.0974033	−	0.995245i	$-0.468946\pi$
$619$	−17.8090	−	10.2820i	−0.715803	−	0.413269i	−0.813206	+	0.581976i	$0.802280\pi$
$620$	42.6789	−	3.36878i	1.71403	−	0.135294i
$621$		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
$626$	6.00174	+	9.50975i	0.239878	+	0.380086i
$627$		0			0
$628$	−5.06560	+	10.6265i	−0.202140	+	0.424045i
$629$			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	$-0.0932912\pi$
$632$	1.87210	−	1.39897i	0.0744681	−	0.0556480i
$633$		0			0
$634$	2.61083	−	1.64773i	0.103689	−	0.0654398i
$635$	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
$640$	16.4154	−	16.8781i	0.648876	−	0.667164i
$641$	−43.6375	−	25.1941i	−1.72358	−	0.995108i	−0.911186	−	0.411995i	$-0.864832\pi$
$641$	−43.6375	−	25.1941i	−1.72358	−	0.995108i	−0.812391	−	0.583113i	$-0.801835\pi$
$642$		0			0
$643$		−	40.2212i		−	1.58617i	−0.609111	−	0.793085i	$-0.708474\pi$
$643$		−	40.2212i		−	1.58617i	0.609111	−	0.793085i	$-0.291526\pi$
$644$	−4.18283	+	24.3076i	−0.164826	+	0.957854i
$645$		0			0
$646$	12.7550	−	0.502616i	0.501840	−	0.0197752i
$647$	10.1498	−	17.5800i	0.399031	−	0.691142i	−0.594576	−	0.804040i	$-0.702680\pi$
$647$	10.1498	−	17.5800i	0.399031	−	0.691142i	0.993607	+	0.112898i	$0.0360133\pi$
$648$		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	−0.786310	−	0.617832i	$-0.788011\pi$
$653$	−16.4671	+	9.50728i	−0.644407	+	0.372049i	0.141903	+	0.989881i	$0.454678\pi$
$654$		0			0
$655$	26.5230	+	15.3131i	1.03634	+	0.598331i
$656$	−0.242980	−	1.52956i	−0.00948679	−	0.0597194i
$657$		0			0
$658$	−6.12295	+	28.7560i	−0.238697	+	1.12102i
$659$	−20.4920			−0.798256			−0.399128	−	0.916895i	$-0.630687\pi$
$659$	−20.4920			−0.798256			−0.399128	+	0.916895i	$0.630687\pi$
$660$		0			0
$661$	9.67706	−	16.7612i	0.376394	−	0.651933i	−0.614141	−	0.789197i	$-0.710497\pi$
$661$	9.67706	−	16.7612i	0.376394	−	0.651933i	0.990535	+	0.137263i	$0.0438306\pi$
$662$	16.1167	−	10.1715i	0.626393	−	0.395325i
$663$		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
$668$	−36.7293	+	2.89916i	−1.42110	+	0.112172i
$669$		0			0
$670$	4.12874	−	0.162694i	0.159507	−	0.00628543i
$671$	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	$0.618800\pi$
$674$	−24.6149	+	0.969956i	−0.948129	+	0.0373613i
$675$		0			0
$676$	20.1431	−	1.58996i	0.774737	−	0.0611524i
$677$	−5.94225	+	3.43076i	−0.228379	+	0.131855i	−0.609824	−	0.792537i	$-0.708760\pi$
$677$	−5.94225	+	3.43076i	−0.228379	+	0.131855i	0.381445	+	0.924392i	$0.375427\pi$
$678$		0			0
$679$	28.9772	+	28.2549i	1.11204	+	1.08432i
$680$	−18.7342	+	2.22390i	−0.718425	+	0.0852825i
$681$		0			0
$682$	52.5051	−	33.1367i	2.01052	−	1.26887i
$683$	−11.2294	+	19.4499i	−0.429682	+	0.744232i	−0.996845	−	0.0793743i	$-0.974708\pi$
$683$	−11.2294	+	19.4499i	−0.429682	+	0.744232i	0.567163	+	0.823606i	$0.308041\pi$
$684$		0			0
$685$	8.25744			0.315500
$686$	−17.0359	+	19.8942i	−0.650433	+	0.759564i
$687$		0			0
$688$	−0.569791	−	3.58684i	−0.0217231	−	0.136747i
$689$	−48.7313	−	28.1350i	−1.85651	−	1.07186i
$690$		0			0
$691$	−37.8628	+	21.8601i	−1.44037	+	0.831598i	−0.997874	−	0.0651733i	$-0.979240\pi$
$691$	−37.8628	+	21.8601i	−1.44037	+	0.831598i	−0.442495	+	0.896771i	$0.645907\pi$
$692$	−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
$698$	−44.2663	+	1.74433i	−1.67551	+	0.0660238i
$699$		0			0
$700$	3.32279	−	1.22493i	0.125590	−	0.0462982i
$701$			5.48856i			0.207300i	0.994614	+	0.103650i	$0.0330522\pi$
$701$			5.48856i			0.207300i	−0.994614	+	0.103650i	$0.966948\pi$
$702$		0			0
$703$	−0.667714	−	0.385505i	−0.0251833	−	0.0145396i
$704$	9.67509	−	32.7455i	0.364644	−	1.23414i
$705$		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	0.949103	−	0.314965i	$-0.101993\pi$
$709$	5.37290	+	9.30614i	0.201784	+	0.349500i	−0.747320	+	0.664465i	$0.768660\pi$
$710$	−29.6505	+	18.7128i	−1.11276	+	0.702280i
$711$		0			0
$712$	6.84828	−	5.11753i	0.256650	−	0.191788i
$713$			47.9459i			1.79559i
$714$		0			0
$715$		−	42.6924i		−	1.59661i
$716$	18.1763	−	38.1300i	0.679281	−	1.42499i
$717$		0			0
$718$	9.92328	+	15.7234i	0.370334	+	0.586794i
$719$	−1.88369	−	3.26265i	−0.0702498	−	0.121676i	0.828761	−	0.559603i	$-0.189046\pi$
$719$	−1.88369	−	3.26265i	−0.0702498	−	0.121676i	−0.899011	+	0.437927i	$0.855713\pi$
$720$		0			0
$721$	−34.7067	−	8.83175i	−1.29254	−	0.328912i
$722$	7.28731	−	13.8548i	0.271206	−	0.515621i
$723$		0			0
$724$	−12.2381	+	0.965992i	−0.454826	+	0.0359008i
$725$	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	$-0.382202\pi$
$728$	−28.5333	−	21.9001i	−1.05751	−	0.811670i
$729$		0			0
$730$	−1.42330	−	36.1194i	−0.0526785	−	1.33684i
$731$	−1.45506	+	2.52025i	−0.0538175	+	0.0932146i
$732$		0			0
$733$	−4.70703	−	8.15281i	−0.173858	−	0.301131i	0.765907	−	0.642951i	$-0.222290\pi$
$733$	−4.70703	−	8.15281i	−0.173858	−	0.301131i	−0.939765	+	0.341820i	$0.888957\pi$
$734$	−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	$-0.495988\pi$
$739$	−23.0267	−	13.2944i	−0.847049	−	0.489044i	−0.859654	+	0.510876i	$0.829321\pi$
$740$	1.02861	+	0.490332i	0.0378125	+	0.0180250i
$741$		0			0
$742$	13.5212	+	41.6643i	0.496379	+	1.52955i
$743$	52.2920			1.91841			0.959204	−	0.282715i	$-0.0912352\pi$
$743$	52.2920			1.91841			0.959204	+	0.282715i	$0.0912352\pi$
$744$		0			0
$745$	−5.88608	+	10.1950i	−0.215649	+	0.373516i
$746$	10.6829	+	16.9271i	0.391129	+	0.619745i
$747$		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	$-0.645101\pi$
$751$	3.21343	−	1.85527i	0.117260	−	0.0676999i	0.557483	+	0.830189i	$0.311767\pi$
$752$	19.7911	+	24.4170i	0.721708	+	0.890398i
$753$		0			0
$754$	−1.03633	−	26.2993i	−0.0377410	−	0.957764i
$755$	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	$0.481472\pi$
$758$	−0.904338	−	22.9497i	−0.0328470	−	0.833570i
$759$		0			0
$760$	6.53805	−	15.2322i	0.237160	−	0.552530i
$761$	30.1032	−	17.3801i	1.09124	−	0.630027i	0.157333	−	0.987546i	$-0.449710\pi$
$761$	30.1032	−	17.3801i	1.09124	−	0.630027i	0.933906	+	0.357519i	$0.116377\pi$
$762$		0			0
$763$	−47.6651	+	13.4187i	−1.72559	+	0.485791i
$764$	13.3693	+	19.4429i	0.483684	+	0.703418i
$765$		0			0
$766$	2.05156	+	3.25069i	0.0741258	+	0.117452i
$767$	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	$0.627726\pi$
$770$	−22.2466	+	24.6897i	−0.801712	+	0.889755i
$771$		0			0
$772$	13.6039	−	28.5381i	0.489616	−	1.02711i
$773$	−20.9104	−	12.0727i	−0.752096	−	0.434223i	0.0743545	−	0.997232i	$-0.476310\pi$
$773$	−20.9104	−	12.0727i	−0.752096	−	0.434223i	−0.826451	+	0.563009i	$0.809644\pi$
$774$		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
$782$	−0.831919	−	21.1119i	−0.0297493	−	0.754958i
$783$		0			0
$784$	5.08936	+	27.5336i	0.181763	+	0.983342i
$785$		−	12.2492i		−	0.437192i
$786$		0			0
$787$	−3.52292	−	2.03396i	−0.125578	−	0.0725028i	0.435895	−	0.899998i	$-0.356432\pi$
$787$	−3.52292	−	2.03396i	−0.125578	−	0.0725028i	−0.561473	+	0.827495i	$0.689765\pi$
$788$	−0.342786	−	4.34274i	−0.0122112	−	0.154704i
$789$		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
$794$	11.9735	+	18.9720i	0.424924	+	0.673291i
$795$		0			0
$796$	−9.89358	−	4.71620i	−0.350669	−	0.167161i
$797$		−	19.6098i		−	0.694614i	−0.937752	−	0.347307i	$-0.887096\pi$
$797$		−	19.6098i		−	0.694614i	0.937752	−	0.347307i	$-0.112904\pi$
$798$		0			0
$799$		−	25.1849i		−	0.890979i
$800$	1.21487	−	3.58568i	0.0429523	−	0.126773i
$801$		0			0
$802$	38.2733	−	24.1548i	1.35148	−	0.852936i
$803$	−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
$808$	−1.00634	−	0.431947i	−0.0354030	−	0.0151959i
$809$	−36.1801	−	20.8886i	−1.27203	−	0.734405i	−0.296657	−	0.954984i	$-0.595872\pi$
$809$	−36.1801	−	20.8886i	−1.27203	−	0.734405i	−0.975369	+	0.220580i	$0.929205\pi$
$810$		0			0
$811$		−	4.61271i		−	0.161974i	−0.996715	−	0.0809870i	$-0.974193\pi$
$811$		−	4.61271i		−	0.161974i	0.996715	−	0.0809870i	$-0.0258072\pi$
$812$	−13.1050	+	15.7493i	−0.459895	+	0.552693i
$813$		0			0
$814$	1.65127	−	0.0650688i	0.0578771	−	0.00228066i
$815$	−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	−0.234961	−	0.972005i	$-0.575496\pi$
$821$	14.0211	−	8.09506i	0.489339	−	0.282520i	0.724300	+	0.689485i	$0.242163\pi$
$822$		0			0
$823$	13.6183	+	7.86255i	0.474705	+	0.274071i	0.718207	−	0.695829i	$-0.244963\pi$
$823$	13.6183	+	7.86255i	0.474705	+	0.274071i	−0.243502	+	0.969900i	$0.578296\pi$
$824$	−30.6685	+	22.9177i	−1.06839	+	0.798376i
$825$		0			0
$826$	−13.1860	+	4.27921i	−0.458799	+	0.148893i
$827$	−13.1854			−0.458500			−0.229250	−	0.973368i	$-0.573627\pi$
$827$	−13.1854			−0.458500			−0.229250	+	0.973368i	$0.573627\pi$
$828$		0			0
$829$	−17.4266	+	30.1838i	−0.605252	+	1.04833i	0.386759	+	0.922181i	$0.373594\pi$
$829$	−17.4266	+	30.1838i	−0.605252	+	1.04833i	−0.992012	+	0.126147i	$0.959739\pi$
$830$	14.1628	−	8.93835i	0.491599	−	0.310255i
$831$		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
$836$	−1.89161	−	23.9648i	−0.0654228	−	0.828838i
$837$		0			0
$838$	14.0616	−	0.554102i	0.485751	−	0.0191411i
$839$	10.2242			0.352978			0.176489	−	0.984303i	$-0.443526\pi$
$839$	10.2242			0.352978			0.176489	+	0.984303i	$0.443526\pi$
$840$		0			0
$841$	14.0078			0.483027
$842$	3.21312	−	0.126614i	0.110731	−	0.00436340i
$843$		0			0
$844$	−1.38499	−	17.5463i	−0.0476732	−	0.603970i
$845$	−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
$850$	−2.56541	+	1.61906i	−0.0879927	+	0.0555334i
$851$	−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	$0.198578\pi$
$854$	−6.25209	+	29.3625i	−0.213942	+	1.00476i
$855$		0			0
$856$	18.4278	+	24.6601i	0.629851	+	0.842866i
$857$	−14.6387	−	8.45163i	−0.500047	−	0.288702i	0.228686	−	0.973500i	$-0.426557\pi$
$857$	−14.6387	−	8.45163i	−0.500047	−	0.288702i	−0.728733	+	0.684798i	$0.759890\pi$
$858$		0			0
$859$	−9.83178	+	5.67638i	−0.335456	+	0.193676i	−0.658261	−	0.752790i	$-0.728708\pi$
$859$	−9.83178	+	5.67638i	−0.335456	+	0.193676i	0.322805	+	0.946466i	$0.395374\pi$
$860$	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	0.999836	+	0.0180959i	$0.00576043\pi$
$863$	15.1464	+	26.2343i	0.515590	+	0.893027i	−0.484247	+	0.874932i	$0.660906\pi$
$864$		0			0
$865$	7.36849	−	12.7626i	0.250536	−	0.433941i
$866$	11.1098	−	0.437785i	0.377526	−	0.0148765i
$867$		0			0
$868$	18.8265	+	51.0693i	0.639014	+	1.73341i
$869$			3.52665i			0.119633i
$870$		0			0
$871$	−5.84417	−	3.37413i	−0.198022	−	0.114328i
$872$	−20.8797	+	48.6451i	−0.707076	+	1.64733i
$873$		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	0.967333	−	0.253510i	$-0.0815849\pi$
$877$	7.82172	+	13.5476i	0.264121	+	0.457471i	−0.703212	+	0.710980i	$0.748252\pi$
$878$	−12.7614	+	8.05390i	−0.430677	+	0.271806i
$879$		0			0
$880$	5.57403	+	35.0886i	0.187901	+	1.18284i
$881$			23.0836i			0.777705i	0.921300	+	0.388853i	$0.127128\pi$
$881$			23.0836i			0.777705i	−0.921300	+	0.388853i	$0.872872\pi$
$882$		0			0
$883$		−	13.4161i		−	0.451488i	−0.974187	−	0.225744i	$-0.927519\pi$
$883$		−	13.4161i		−	0.451488i	0.974187	−	0.225744i	$-0.0724813\pi$
$884$	27.8130	+	13.2583i	0.935452	+	0.445923i
$885$		0			0
$886$	−28.6670	−	45.4229i	−0.963087	−	1.52601i
$887$	−23.9872	−	41.5471i	−0.805412	−	1.39501i	−0.916012	−	0.401150i	$-0.868611\pi$
$887$	−23.9872	−	41.5471i	−0.805412	−	1.39501i	0.110600	−	0.993865i	$-0.464723\pi$
$888$		0			0
$889$	−8.87706	+	9.10399i	−0.297727	+	0.305338i
$890$	−4.14101	+	7.87296i	−0.138807	+	0.263902i
$891$		0			0
$892$	−3.32850	−	42.1687i	−0.111447	−	1.41191i
$893$	19.1637	+	11.0641i	0.641287	+	0.370247i
$894$		0			0
$895$			43.9524i			1.46917i
$896$	26.3106	+	14.2741i	0.878977	+	0.476865i
$897$		0			0
$898$	1.33668	+	33.9213i	0.0446055	+	1.13197i
$899$	−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	$-0.382615\pi$
$907$	−8.04388	−	4.64414i	−0.267093	−	0.154206i	−0.627566	+	0.778564i	$0.715949\pi$
$908$	24.1787	−	50.7217i	0.802399	−	1.68326i
$909$		0			0
$910$	36.6058	+	7.79440i	1.21347	+	0.258382i
$911$	−32.4981			−1.07671			−0.538354	−	0.842719i	$-0.680954\pi$
$911$	−32.4981			−1.07671			−0.538354	+	0.842719i	$0.680954\pi$
$912$		0			0
$913$	12.1440	−	21.0340i	0.401907	−	0.696123i
$914$	11.3558	+	17.9933i	0.375617	+	0.595165i
$915$		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	$-0.664334\pi$
$919$	0.384776	−	0.222151i	0.0126926	−	0.00732808i	0.506333	+	0.862338i	$0.331001\pi$
$920$	−25.2120	−	10.8216i	−0.831215	−	0.356779i
$921$		0			0
$922$	1.69121	+	42.9183i	0.0556970	+	1.41344i
$923$	57.2624			1.88482
$924$		0			0
$925$	0.183231			0.00602459
$926$	−1.32422	−	33.6053i	−0.0435167	−	1.10434i
$927$		0			0
$928$	4.28546	+	21.4799i	0.140677	+	0.705112i
$929$	−14.1031	+	8.14244i	−0.462708	+	0.267145i	−0.713182	−	0.700979i	$-0.752747\pi$
$929$	−14.1031	+	8.14244i	−0.462708	+	0.267145i	0.250474	+	0.968123i	$0.419414\pi$
$930$		0			0
$931$	10.2842	+	16.8178i	0.337052	+	0.551181i
$932$	−7.10735	+	4.88715i	−0.232809	+	0.160084i
$933$		0			0
$934$	−3.55019	−	5.62528i	−0.116166	−	0.184065i
$935$	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	$0.331113\pi$
$938$	1.62155	+	4.99665i	0.0529454	+	0.163146i
$939$		0			0
$940$	−29.5216	−	14.0727i	−0.962887	−	0.459002i
$941$	9.45740	+	5.46023i	0.308302	+	0.177998i	0.646167	−	0.763196i	$-0.276371\pi$
$941$	9.45740	+	5.46023i	0.308302	+	0.177998i	−0.337864	+	0.941195i	$0.609704\pi$
$942$		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	$-0.254616\pi$
$947$	−8.39495	−	14.5405i	−0.272799	−	0.472502i	−0.969577	+	0.244785i	$0.921283\pi$
$948$		0			0
$949$	−29.5179	+	51.1264i	−0.958190	+	1.65963i
$950$	−0.104950	−	2.66334i	−0.00340502	−	0.0864103i
$951$		0			0
$952$	−9.17594	−	22.1605i	−0.297394	−	0.718227i
$953$		−	39.3512i		−	1.27471i	−0.770570	−	0.637355i	$-0.780028\pi$
$953$		−	39.3512i		−	1.27471i	0.770570	−	0.637355i	$-0.219972\pi$
$954$		0			0
$955$	−21.2626	−	12.2760i	−0.688042	−	0.397241i
$956$	14.3981	−	1.13648i	0.465667	−	0.0367565i
$957$		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
$962$	−0.993252	−	1.57381i	−0.0320237	−	0.0507416i
$963$		0			0
$964$	−4.07479	+	8.54804i	−0.131240	+	0.275314i
$965$			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	$0.952396\pi$
$968$	12.2188	+	16.3512i	0.392727	+	0.525547i
$969$		0			0
$970$	−38.0720	+	24.0278i	−1.22242	+	0.771485i
$971$	14.5837	+	25.2598i	0.468014	+	0.810624i	0.999332	−	0.0365484i	$-0.0116363\pi$
$971$	14.5837	+	25.2598i	0.468014	+	0.810624i	−0.531318	+	0.847173i	$0.678303\pi$
$972$		0			0
$973$	35.4051	−	36.3102i	1.13504	−	1.16405i
$974$	−7.01209	−	3.68821i	−0.224682	−	0.118178i
$975$		0			0
$976$	20.2085	+	24.9320i	0.646860	+	0.798055i
$977$	43.6149	+	25.1811i	1.39537	+	0.805615i	0.993903	−	0.110261i	$-0.0351686\pi$
$977$	43.6149	+	25.1811i	1.39537	+	0.805615i	0.401463	+	0.915875i	$0.368502\pi$
$978$		0			0
$979$			12.9007i			0.412309i
$980$	−17.1081	−	23.5826i	−0.546499	−	0.753317i
$981$		0			0
$982$	14.5684	−	0.574072i	0.464896	−	0.0183194i
$983$	−22.4873	+	38.9491i	−0.717233	+	1.24228i	0.244859	+	0.969559i	$0.421258\pi$
$983$	−22.4873	+	38.9491i	−0.717233	+	1.24228i	−0.962092	+	0.272725i	$0.912075\pi$
$984$		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	$-0.156443\pi$
$991$	28.7650	+	16.6075i	0.913749	+	0.527553i	0.0321135	+	0.999484i	$0.489776\pi$
$992$	55.1098	+	18.6719i	1.74974	+	0.592834i
$993$		0			0
$994$	−33.1158	−	29.8389i	−1.05037	−	0.946432i
$995$	11.4043			0.361541
$996$		0			0
$997$	4.80964	−	8.33054i	0.152323	−	0.263831i	−0.779758	−	0.626081i	$-0.784658\pi$
$997$	4.80964	−	8.33054i	0.152323	−	0.263831i	0.932081	+	0.362250i	$0.117991\pi$
$998$	8.48671	−	5.35608i	0.268642	−	0.169544i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.1	✓	32	84.23	even	6	inner
252.2.be.a.107.6	yes	32	21.2	odd	6	inner
252.2.be.a.107.11	yes	32	7.2	even	3	inner
252.2.be.a.107.16	yes	32	28.23	odd	6	inner
252.2.be.a.179.1	yes	32	1.1	even	1	trivial
252.2.be.a.179.6	yes	32	4.3	odd	2	inner
252.2.be.a.179.11	yes	32	12.11	even	2	inner
252.2.be.a.179.16	yes	32	3.2	odd	2	inner
1764.2.e.h.1079.5		16	28.3	even	6
1764.2.e.h.1079.6		16	21.17	even	6
1764.2.e.h.1079.11		16	7.3	odd	6
1764.2.e.h.1079.12		16	84.59	odd	6
1764.2.e.i.1079.5		16	28.11	odd	6
1764.2.e.i.1079.6		16	21.11	odd	6
1764.2.e.i.1079.11		16	7.4	even	3
1764.2.e.i.1079.12		16	84.11	even	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)

\(f(q)\)	\(=\)	\(q+(-1.41312 + 0.0556843i) q^{2} +(1.99380 - 0.157377i) q^{4} +(-1.80224 + 1.04052i) q^{5} +(-1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +O(q^{10})\)	\(q+(-1.41312 + 0.0556843i) q^{2} +(1.99380 - 0.157377i) q^{4} +(-1.80224 + 1.04052i) q^{5} +(-1.89429 - 1.84707i) q^{7} +(-2.80871 + 0.333415i) q^{8} +(2.48883 - 1.57073i) q^{10} +(2.13406 - 3.69630i) q^{11} -4.80655 q^{13} +(2.77970 + 2.50465i) q^{14} +(3.95047 - 0.627555i) q^{16} +(-2.77574 - 1.60257i) q^{17} +(2.43886 - 1.40807i) q^{19} +(-3.42954 + 2.35822i) q^{20} +(-2.80985 + 5.34213i) q^{22} +(-2.33061 - 4.03674i) q^{23} +(-0.334629 + 0.579595i) q^{25} +(6.79221 - 0.267649i) q^{26} +(-4.06752 - 3.38457i) q^{28} -3.87198i q^{29} +(-8.90803 - 5.14305i) q^{31} +(-5.54752 + 1.10679i) q^{32} +(4.01168 + 2.11006i) q^{34} +(5.33587 + 1.35781i) q^{35} +(-0.136891 - 0.237102i) q^{37} +(-3.36798 + 2.12558i) q^{38} +(4.71503 - 3.52341i) q^{40} -0.387186i q^{41} -0.907954i q^{43} +(3.67317 - 7.70552i) q^{44} +(3.51821 + 5.57461i) q^{46} +(3.92882 + 6.80492i) q^{47} +(0.176657 + 6.99777i) q^{49} +(0.440596 - 0.837668i) q^{50} +(-9.58329 + 0.756439i) q^{52} +(10.1385 + 5.85348i) q^{53} +8.88214i q^{55} +(5.93634 + 4.55630i) q^{56} +(0.215608 + 5.47156i) q^{58} +(-1.85252 + 3.20865i) q^{59} +(4.01168 + 6.94844i) q^{61} +(12.8745 + 6.77170i) q^{62} +(7.77767 - 1.87293i) q^{64} +(8.66254 - 5.00132i) q^{65} +(1.21588 + 0.701986i) q^{67} +(-5.78648 - 2.75837i) q^{68} +(-7.61582 - 1.62162i) q^{70} -11.9134 q^{71} +(6.14118 - 10.6368i) q^{73} +(0.206646 + 0.327430i) q^{74} +(4.64099 - 3.19124i) q^{76} +(-10.8698 + 3.06010i) q^{77} +(-0.715577 + 0.413138i) q^{79} +(-6.46669 + 5.24155i) q^{80} +(0.0215602 + 0.547139i) q^{82} +5.69055 q^{83} +6.67006 q^{85} +(0.0505587 + 1.28305i) q^{86} +(-4.76154 + 11.0933i) q^{88} +(-2.61763 + 1.51129i) q^{89} +(9.10499 + 8.87804i) q^{91} +(-5.28206 - 7.68166i) q^{92} +(-5.93081 - 9.39737i) q^{94} +(-2.93026 + 5.07536i) q^{95} -15.2972 q^{97} +(-0.639302 - 9.87883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more