LMFDB - Embedded newform 1620.2.e.a.971.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.19
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.531562 - 1.31051i) q^{2} +(-1.43488 + 1.39324i) q^{4} -1.00000i q^{5} +1.38206i q^{7} +(2.58858 + 1.13984i) q^{8} +O(q^{10})$	\(q+(-0.531562 - 1.31051i) q^{2} +(-1.43488 + 1.39324i) q^{4} -1.00000i q^{5} +1.38206i q^{7} +(2.58858 + 1.13984i) q^{8} +(-1.31051 + 0.531562i) q^{10} -6.29235 q^{11} +5.01098 q^{13} +(1.81121 - 0.734652i) q^{14} +(0.117787 - 3.99827i) q^{16} -1.58487i q^{17} +0.313862i q^{19} +(1.39324 + 1.43488i) q^{20} +(3.34477 + 8.24620i) q^{22} +0.478525 q^{23} -1.00000 q^{25} +(-2.66364 - 6.56695i) q^{26} +(-1.92554 - 1.98310i) q^{28} +1.71350i q^{29} +9.47957i q^{31} +(-5.30239 + 1.97096i) q^{32} +(-2.07700 + 0.842458i) q^{34} +1.38206 q^{35} +8.55290 q^{37} +(0.411319 - 0.166837i) q^{38} +(1.13984 - 2.58858i) q^{40} -7.54314i q^{41} -6.02836i q^{43} +(9.02879 - 8.76672i) q^{44} +(-0.254365 - 0.627112i) q^{46} +10.5045 q^{47} +5.08990 q^{49} +(0.531562 + 1.31051i) q^{50} +(-7.19017 + 6.98147i) q^{52} +8.86171i q^{53} +6.29235i q^{55} +(-1.57533 + 3.57758i) q^{56} +(2.24557 - 0.910833i) q^{58} +11.9151 q^{59} -5.02092 q^{61} +(12.4231 - 5.03898i) q^{62} +(5.40152 + 5.90115i) q^{64} -5.01098i q^{65} +3.38716i q^{67} +(2.20810 + 2.27411i) q^{68} +(-0.734652 - 1.81121i) q^{70} +14.1414 q^{71} -4.55479 q^{73} +(-4.54639 - 11.2087i) q^{74} +(-0.437283 - 0.450355i) q^{76} -8.69642i q^{77} -2.85998i q^{79} +(-3.99827 - 0.117787i) q^{80} +(-9.88537 + 4.00964i) q^{82} -0.983654 q^{83} -1.58487 q^{85} +(-7.90023 + 3.20444i) q^{86} +(-16.2883 - 7.17229i) q^{88} +2.64810i q^{89} +6.92549i q^{91} +(-0.686628 + 0.666698i) q^{92} +(-5.58379 - 13.7663i) q^{94} +0.313862 q^{95} +10.1449 q^{97} +(-2.70560 - 6.67038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.531562	−	1.31051i	−0.375871	−	0.926672i
$2$	−0.531562	−	1.31051i	−0.375871	−	0.926672i
$3$		0			0
$3$		0			0
$4$	−1.43488	+	1.39324i	−0.717442	+	0.696618i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			1.38206i			0.522371i	0.965289	+	0.261185i	$0.0841134\pi$
$7$			1.38206i			0.522371i	−0.965289	+	0.261185i	$0.915887\pi$
$8$	2.58858	+	1.13984i	0.915202	+	0.402995i
$9$		0			0
$10$	−1.31051	+	0.531562i	−0.414420	+	0.168095i
$11$	−6.29235			−1.89721			−0.948607	−	0.316457i	$-0.897507\pi$
$11$	−6.29235			−1.89721			−0.948607	+	0.316457i	$0.897507\pi$
$12$		0			0
$13$	5.01098			1.38979			0.694897	−	0.719109i	$-0.255450\pi$
$13$	5.01098			1.38979			0.694897	+	0.719109i	$0.255450\pi$
$14$	1.81121	−	0.734652i	0.484066	−	0.196344i
$15$		0			0
$16$	0.117787	−	3.99827i	0.0294467	−	0.999566i
$17$		−	1.58487i		−	0.384388i	−0.981357	−	0.192194i	$-0.938440\pi$
$17$		−	1.58487i		−	0.384388i	0.981357	−	0.192194i	$-0.0615604\pi$
$18$		0			0
$19$			0.313862i			0.0720048i	0.999352	+	0.0360024i	$0.0114624\pi$
$19$			0.313862i			0.0720048i	−0.999352	+	0.0360024i	$0.988538\pi$
$20$	1.39324	+	1.43488i	0.311537	+	0.320850i
$21$		0			0
$22$	3.34477	+	8.24620i	0.713107	+	1.75810i
$23$	0.478525			0.0997793			0.0498896	−	0.998755i	$-0.484113\pi$
$23$	0.478525			0.0997793			0.0498896	+	0.998755i	$0.484113\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−2.66364	−	6.56695i	−0.522383	−	1.28788i
$27$		0			0
$28$	−1.92554	−	1.98310i	−0.363893	−	0.374771i
$29$			1.71350i			0.318190i	0.987263	+	0.159095i	$0.0508576\pi$
$29$			1.71350i			0.318190i	−0.987263	+	0.159095i	$0.949142\pi$
$30$		0			0
$31$			9.47957i			1.70258i	0.524695	+	0.851290i	$0.324179\pi$
$31$			9.47957i			1.70258i	−0.524695	+	0.851290i	$0.675821\pi$
$32$	−5.30239	+	1.97096i	−0.937338	+	0.348420i
$33$		0			0
$34$	−2.07700	+	0.842458i	−0.356202	+	0.144480i
$35$	1.38206			0.233611
$36$		0			0
$37$	8.55290			1.40609			0.703044	−	0.711146i	$-0.251824\pi$
$37$	8.55290			1.40609			0.703044	+	0.711146i	$0.251824\pi$
$38$	0.411319	−	0.166837i	0.0667248	−	0.0270645i
$39$		0			0
$40$	1.13984	−	2.58858i	0.180225	−	0.409291i
$41$		−	7.54314i		−	1.17804i	−0.808118	−	0.589020i	$-0.799514\pi$
$41$		−	7.54314i		−	1.17804i	0.808118	−	0.589020i	$-0.200486\pi$
$42$		0			0
$43$		−	6.02836i		−	0.919316i	−0.888096	−	0.459658i	$-0.847972\pi$
$43$		−	6.02836i		−	0.919316i	0.888096	−	0.459658i	$-0.152028\pi$
$44$	9.02879	−	8.76672i	1.36114	−	1.32163i
$45$		0			0
$46$	−0.254365	−	0.627112i	−0.0375041	−	0.0924627i
$47$	10.5045			1.53224			0.766120	−	0.642698i	$-0.222185\pi$
$47$	10.5045			1.53224			0.766120	+	0.642698i	$0.222185\pi$
$48$		0			0
$49$	5.08990			0.727129
$50$	0.531562	+	1.31051i	0.0751742	+	0.185334i
$51$		0			0
$52$	−7.19017	+	6.98147i	−0.997098	+	0.968156i
$53$			8.86171i			1.21725i	0.793458	+	0.608625i	$0.208278\pi$
$53$			8.86171i			1.21725i	−0.793458	+	0.608625i	$0.791722\pi$
$54$		0			0
$55$			6.29235i			0.848460i
$56$	−1.57533	+	3.57758i	−0.210513	+	0.478075i
$57$		0			0
$58$	2.24557	−	0.910833i	0.294858	−	0.119598i
$59$	11.9151			1.55122			0.775609	−	0.631213i	$-0.217443\pi$
$59$	11.9151			1.55122			0.775609	+	0.631213i	$0.217443\pi$
$60$		0			0
$61$	−5.02092			−0.642863			−0.321432	−	0.946933i	$-0.604164\pi$
$61$	−5.02092			−0.642863			−0.321432	+	0.946933i	$0.604164\pi$
$62$	12.4231	−	5.03898i	1.57773	−	0.639950i
$63$		0			0
$64$	5.40152	+	5.90115i	0.675190	+	0.737644i
$65$		−	5.01098i		−	0.621535i
$66$		0			0
$67$			3.38716i			0.413807i	0.978361	+	0.206904i	$0.0663386\pi$
$67$			3.38716i			0.413807i	−0.978361	+	0.206904i	$0.933661\pi$
$68$	2.20810	+	2.27411i	0.267772	+	0.275777i
$69$		0			0
$70$	−0.734652	−	1.81121i	−0.0878077	−	0.216481i
$71$	14.1414			1.67827			0.839136	−	0.543921i	$-0.183061\pi$
$71$	14.1414			1.67827			0.839136	+	0.543921i	$0.183061\pi$
$72$		0			0
$73$	−4.55479			−0.533098			−0.266549	−	0.963821i	$-0.585883\pi$
$73$	−4.55479			−0.533098			−0.266549	+	0.963821i	$0.585883\pi$
$74$	−4.54639	−	11.2087i	−0.528507	−	1.30298i
$75$		0			0
$76$	−0.437283	−	0.450355i	−0.0501598	−	0.0516593i
$77$		−	8.69642i		−	0.991049i
$78$		0			0
$79$		−	2.85998i		−	0.321773i	−0.986973	−	0.160886i	$-0.948565\pi$
$79$		−	2.85998i		−	0.321773i	0.986973	−	0.160886i	$-0.0514352\pi$
$80$	−3.99827	−	0.117787i	−0.447020	−	0.0131689i
$81$		0			0
$82$	−9.88537	+	4.00964i	−1.09166	+	0.442791i
$83$	−0.983654			−0.107970			−0.0539850	−	0.998542i	$-0.517192\pi$
$83$	−0.983654			−0.107970			−0.0539850	+	0.998542i	$0.517192\pi$
$84$		0			0
$85$	−1.58487			−0.171904
$86$	−7.90023	+	3.20444i	−0.851904	+	0.345544i
$87$		0			0
$88$	−16.2883	−	7.17229i	−1.73633	−	0.764568i
$89$			2.64810i			0.280699i	0.990102	+	0.140349i	$0.0448225\pi$
$89$			2.64810i			0.280699i	−0.990102	+	0.140349i	$0.955177\pi$
$90$		0			0
$91$			6.92549i			0.725988i
$92$	−0.686628	+	0.666698i	−0.0715859	+	0.0695080i
$93$		0			0
$94$	−5.58379	−	13.7663i	−0.575924	−	1.41988i
$95$	0.313862			0.0322015
$96$		0			0
$97$	10.1449			1.03006			0.515029	−	0.857173i	$-0.327781\pi$
$97$	10.1449			1.03006			0.515029	+	0.857173i	$0.327781\pi$
$98$	−2.70560	−	6.67038i	−0.273306	−	0.673810i
$99$		0			0
$100$	1.43488	−	1.39324i	0.143488	−	0.139324i
$101$		−	2.52291i		−	0.251039i	−0.992091	−	0.125519i	$-0.959940\pi$
$101$		−	2.52291i		−	0.251039i	0.992091	−	0.125519i	$-0.0400597\pi$
$102$		0			0
$103$			8.01903i			0.790138i	0.918651	+	0.395069i	$0.129279\pi$
$103$			8.01903i			0.790138i	−0.918651	+	0.395069i	$0.870721\pi$
$104$	12.9713	+	5.71173i	1.27194	+	0.560081i
$105$		0			0
$106$	11.6134	−	4.71054i	1.12799	−	0.457529i
$107$	−7.02474			−0.679107			−0.339554	−	0.940587i	$-0.610276\pi$
$107$	−7.02474			−0.679107			−0.339554	+	0.940587i	$0.610276\pi$
$108$		0			0
$109$	7.64623			0.732376			0.366188	−	0.930541i	$-0.380663\pi$
$109$	7.64623			0.732376			0.366188	+	0.930541i	$0.380663\pi$
$110$	8.24620	−	3.34477i	0.786244	−	0.318911i
$111$		0			0
$112$	5.52586	+	0.162789i	0.522144	+	0.0153821i
$113$		−	11.4061i		−	1.07300i	−0.843901	−	0.536498i	$-0.819747\pi$
$113$		−	11.4061i		−	1.07300i	0.843901	−	0.536498i	$-0.180253\pi$
$114$		0			0
$115$		−	0.478525i		−	0.0446227i
$116$	−2.38732	−	2.45868i	−0.221657	−	0.228283i
$117$		0			0
$118$	−6.33363	−	15.6149i	−0.583058	−	1.43747i
$119$	2.19040			0.200793
$120$		0			0
$121$	28.5936			2.59942
$122$	2.66893	+	6.57998i	0.241633	+	0.595723i
$123$		0			0
$124$	−13.2073	−	13.6021i	−1.18605	−	1.22150i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			0.958173i			0.0850241i	0.999096	+	0.0425121i	$0.0135361\pi$
$127$			0.958173i			0.0850241i	−0.999096	+	0.0425121i	$0.986464\pi$
$128$	4.86229	−	10.2156i	0.429770	−	0.902938i
$129$		0			0
$130$	−6.56695	+	2.66364i	−0.575959	+	0.233617i
$131$	7.55194			0.659816			0.329908	−	0.944013i	$-0.392982\pi$
$131$	7.55194			0.659816			0.329908	+	0.944013i	$0.392982\pi$
$132$		0			0
$133$	−0.433777			−0.0376132
$134$	4.43891	−	1.80048i	0.383464	−	0.155538i
$135$		0			0
$136$	1.80651	−	4.10258i	0.154907	−	0.351793i
$137$			11.6458i			0.994970i	0.867473	+	0.497485i	$0.165743\pi$
$137$			11.6458i			0.994970i	−0.867473	+	0.497485i	$0.834257\pi$
$138$		0			0
$139$		−	16.4737i		−	1.39728i	−0.715472	−	0.698641i	$-0.753788\pi$
$139$		−	16.4737i		−	1.39728i	0.715472	−	0.698641i	$-0.246212\pi$
$140$	−1.98310	+	1.92554i	−0.167603	+	0.162738i
$141$		0			0
$142$	−7.51701	−	18.5324i	−0.630814	−	1.55521i
$143$	−31.5308			−2.63674
$144$		0			0
$145$	1.71350			0.142299
$146$	2.42115	+	5.96911i	0.200376	+	0.494007i
$147$		0			0
$148$	−12.2724	+	11.9162i	−1.00879	+	0.979506i
$149$		−	16.8609i		−	1.38130i	−0.723188	−	0.690651i	$-0.757324\pi$
$149$		−	16.8609i		−	1.38130i	0.723188	−	0.690651i	$-0.242676\pi$
$150$		0			0
$151$			9.10605i			0.741040i	0.928825	+	0.370520i	$0.120820\pi$
$151$			9.10605i			0.741040i	−0.928825	+	0.370520i	$0.879180\pi$
$152$	−0.357753	+	0.812456i	−0.0290176	+	0.0658989i
$153$		0			0
$154$	−11.3968	+	4.62268i	−0.918378	+	0.372506i
$155$	9.47957			0.761417
$156$		0			0
$157$	1.28391			0.102468			0.0512338	−	0.998687i	$-0.483685\pi$
$157$	1.28391			0.102468			0.0512338	+	0.998687i	$0.483685\pi$
$158$	−3.74804	+	1.52025i	−0.298178	+	0.120945i
$159$		0			0
$160$	1.97096	+	5.30239i	0.155818	+	0.419190i
$161$			0.661351i			0.0521218i
$162$		0			0
$163$		−	22.3454i		−	1.75023i	−0.483917	−	0.875114i	$-0.660786\pi$
$163$		−	22.3454i		−	1.75023i	0.483917	−	0.875114i	$-0.339214\pi$
$164$	10.5094	+	10.8235i	0.820644	+	0.845176i
$165$		0			0
$166$	0.522873	+	1.28909i	0.0405828	+	0.100053i
$167$	−3.00412			−0.232466			−0.116233	−	0.993222i	$-0.537082\pi$
$167$	−3.00412			−0.232466			−0.116233	+	0.993222i	$0.537082\pi$
$168$		0			0
$169$	12.1099			0.931530
$170$	0.842458	+	2.07700i	0.0646136	+	0.159298i
$171$		0			0
$172$	8.39892	+	8.64999i	0.640412	+	0.659556i
$173$		−	16.4723i		−	1.25237i	−0.779675	−	0.626184i	$-0.784616\pi$
$173$		−	16.4723i		−	1.25237i	0.779675	−	0.626184i	$-0.215384\pi$
$174$		0			0
$175$		−	1.38206i		−	0.104474i
$176$	−0.741154	+	25.1585i	−0.0558666	+	1.89639i
$177$		0			0
$178$	3.47037	−	1.40763i	0.260115	−	0.105506i
$179$	3.45279			0.258073			0.129037	−	0.991640i	$-0.458811\pi$
$179$	3.45279			0.258073			0.129037	+	0.991640i	$0.458811\pi$
$180$		0			0
$181$	12.2016			0.906935			0.453468	−	0.891273i	$-0.350187\pi$
$181$	12.2016			0.906935			0.453468	+	0.891273i	$0.350187\pi$
$182$	9.07594	−	3.68132i	0.672753	−	0.272878i
$183$		0			0
$184$	1.23870	+	0.545443i	0.0913182	+	0.0402106i
$185$		−	8.55290i		−	0.628822i
$186$		0			0
$187$			9.97258i			0.729267i
$188$	−15.0728	+	14.6353i	−1.09929	+	1.06739i
$189$		0			0
$190$	−0.166837	−	0.411319i	−0.0121036	−	0.0298402i
$191$	5.33067			0.385714			0.192857	−	0.981227i	$-0.438225\pi$
$191$	5.33067			0.385714			0.192857	+	0.981227i	$0.438225\pi$
$192$		0			0
$193$	−7.46422			−0.537287			−0.268643	−	0.963240i	$-0.586575\pi$
$193$	−7.46422			−0.537287			−0.268643	+	0.963240i	$0.586575\pi$
$194$	−5.39263	−	13.2950i	−0.387168	−	0.954525i
$195$		0			0
$196$	−7.30342	+	7.09143i	−0.521673	+	0.506531i
$197$			21.2872i			1.51665i	0.651877	+	0.758324i	$0.273982\pi$
$197$			21.2872i			1.51665i	−0.651877	+	0.758324i	$0.726018\pi$
$198$		0			0
$199$			18.0533i			1.27976i	0.768474	+	0.639881i	$0.221016\pi$
$199$			18.0533i			1.27976i	−0.768474	+	0.639881i	$0.778984\pi$
$200$	−2.58858	−	1.13984i	−0.183040	−	0.0805990i
$201$		0			0
$202$	−3.30630	+	1.34108i	−0.232631	+	0.0943581i
$203$	−2.36817			−0.166213
$204$		0			0
$205$	−7.54314			−0.526836
$206$	10.5090	−	4.26261i	0.732199	−	0.296990i
$207$		0			0
$208$	0.590226	−	20.0352i	0.0409248	−	1.38919i
$209$		−	1.97493i		−	0.136608i
$210$		0			0
$211$			14.3992i			0.991283i	0.868527	+	0.495642i	$0.165067\pi$
$211$			14.3992i			0.991283i	−0.868527	+	0.495642i	$0.834933\pi$
$212$	−12.3465	−	12.7155i	−0.847958	−	0.873306i
$213$		0			0
$214$	3.73408	+	9.20601i	0.255257	+	0.629310i
$215$	−6.02836			−0.411130
$216$		0			0
$217$	−13.1014			−0.889379
$218$	−4.06444	−	10.0205i	−0.275279	−	0.678673i
$219$		0			0
$220$	−8.76672	−	9.02879i	−0.591052	−	0.608721i
$221$		−	7.94177i		−	0.534221i
$222$		0			0
$223$		−	14.8905i		−	0.997142i	−0.866849	−	0.498571i	$-0.833858\pi$
$223$		−	14.8905i		−	0.997142i	0.866849	−	0.498571i	$-0.166142\pi$
$224$	−2.72400	−	7.32823i	−0.182005	−	0.489638i
$225$		0			0
$226$	−14.9478	+	6.06305i	−0.994316	+	0.403308i
$227$	−24.2588			−1.61011			−0.805057	−	0.593197i	$-0.797866\pi$
$227$	−24.2588			−1.61011			−0.805057	+	0.593197i	$0.797866\pi$
$228$		0			0
$229$	−23.7620			−1.57024			−0.785119	−	0.619345i	$-0.787398\pi$
$229$	−23.7620			−1.57024			−0.785119	+	0.619345i	$0.787398\pi$
$230$	−0.627112	+	0.254365i	−0.0413506	+	0.0167724i
$231$		0			0
$232$	−1.95313	+	4.43555i	−0.128229	+	0.291208i
$233$			26.3838i			1.72846i	0.503096	+	0.864230i	$0.332194\pi$
$233$			26.3838i			1.72846i	−0.503096	+	0.864230i	$0.667806\pi$
$234$		0			0
$235$		−	10.5045i		−	0.685239i
$236$	−17.0968	+	16.6006i	−1.11291	+	1.08061i
$237$		0			0
$238$	−1.16433	−	2.87054i	−0.0754724	−	0.186070i
$239$	3.68242			0.238196			0.119098	−	0.992883i	$-0.462000\pi$
$239$	3.68242			0.238196			0.119098	+	0.992883i	$0.462000\pi$
$240$		0			0
$241$	−0.575465			−0.0370689			−0.0185345	−	0.999828i	$-0.505900\pi$
$241$	−0.575465			−0.0370689			−0.0185345	+	0.999828i	$0.505900\pi$
$242$	−15.1993	−	37.4723i	−0.977046	−	2.40881i
$243$		0			0
$244$	7.20444	−	6.99533i	0.461217	−	0.447830i
$245$		−	5.08990i		−	0.325182i
$246$		0			0
$247$			1.57275i			0.100072i
$248$	−10.8052	+	24.5386i	−0.686132	+	1.55821i
$249$		0			0
$250$	1.31051	−	0.531562i	0.0828841	−	0.0336189i
$251$	−15.0618			−0.950690			−0.475345	−	0.879800i	$-0.657677\pi$
$251$	−15.0618			−0.950690			−0.475345	+	0.879800i	$0.657677\pi$
$252$		0			0
$253$	−3.01104			−0.189303
$254$	1.25570	−	0.509328i	0.0787895	−	0.0319581i
$255$		0			0
$256$	−15.9723	−	0.941884i	−0.998266	−	0.0588678i
$257$			25.6283i			1.59865i	0.600897	+	0.799326i	$0.294810\pi$
$257$			25.6283i			1.59865i	−0.600897	+	0.799326i	$0.705190\pi$
$258$		0			0
$259$			11.8206i			0.734499i
$260$	6.98147	+	7.19017i	0.432973	+	0.445916i
$261$		0			0
$262$	−4.01432	−	9.89691i	−0.248006	−	0.611433i
$263$	4.25572			0.262419			0.131210	−	0.991355i	$-0.458114\pi$
$263$	4.25572			0.262419			0.131210	+	0.991355i	$0.458114\pi$
$264$		0			0
$265$	8.86171			0.544370
$266$	0.230579	+	0.568469i	0.0141377	+	0.0348551i
$267$		0			0
$268$	−4.71911	−	4.86018i	−0.288266	−	0.296883i
$269$			11.9884i			0.730945i	0.930822	+	0.365473i	$0.119093\pi$
$269$			11.9884i			0.730945i	−0.930822	+	0.365473i	$0.880907\pi$
$270$		0			0
$271$		−	26.4157i		−	1.60464i	−0.596895	−	0.802319i	$-0.703599\pi$
$271$		−	26.4157i		−	1.60464i	0.596895	−	0.802319i	$-0.296401\pi$
$272$	−6.33675	−	0.186677i	−0.384222	−	0.0113190i
$273$		0			0
$274$	15.2620	−	6.19047i	0.922011	−	0.373980i
$275$	6.29235			0.379443
$276$		0			0
$277$	30.1215			1.80982			0.904912	−	0.425598i	$-0.139936\pi$
$277$	30.1215			1.80982			0.904912	+	0.425598i	$0.139936\pi$
$278$	−21.5890	+	8.75680i	−1.29482	+	0.525198i
$279$		0			0
$280$	3.57758	+	1.57533i	0.213802	+	0.0941443i
$281$			18.1201i			1.08096i	0.841358	+	0.540478i	$0.181757\pi$
$281$			18.1201i			1.08096i	−0.841358	+	0.540478i	$0.818243\pi$
$282$		0			0
$283$		−	7.90711i		−	0.470029i	−0.971992	−	0.235015i	$-0.924486\pi$
$283$		−	7.90711i		−	0.470029i	0.971992	−	0.235015i	$-0.0755138\pi$
$284$	−20.2912	+	19.7023i	−1.20406	+	1.16912i
$285$		0			0
$286$	16.7606	+	41.3215i	0.991073	+	2.44339i
$287$	10.4251			0.615374
$288$		0			0
$289$	14.4882			0.852246
$290$	−0.910833	−	2.24557i	−0.0534860	−	0.131864i
$291$		0			0
$292$	6.53560	−	6.34590i	0.382467	−	0.371366i
$293$			2.53942i			0.148355i	0.997245	+	0.0741773i	$0.0236331\pi$
$293$			2.53942i			0.148355i	−0.997245	+	0.0741773i	$0.976367\pi$
$294$		0			0
$295$		−	11.9151i		−	0.693726i
$296$	22.1399	+	9.74896i	1.28685	+	0.566647i
$297$		0			0
$298$	−22.0965	+	8.96263i	−1.28001	+	0.519191i
$299$	2.39788			0.138673
$300$		0			0
$301$	8.33157			0.480224
$302$	11.9336	−	4.84043i	0.686701	−	0.278535i
$303$		0			0
$304$	1.25490	+	0.0369687i	0.0719736	+	0.00212030i
$305$			5.02092i			0.287497i
$306$		0			0
$307$			19.0006i			1.08442i	0.840242	+	0.542212i	$0.182413\pi$
$307$			19.0006i			1.08442i	−0.840242	+	0.542212i	$0.817587\pi$
$308$	12.1162	+	12.4784i	0.690383	+	0.711021i
$309$		0			0
$310$	−5.03898	−	12.4231i	−0.286195	−	0.705584i
$311$	4.78947			0.271586			0.135793	−	0.990737i	$-0.456642\pi$
$311$	4.78947			0.271586			0.135793	+	0.990737i	$0.456642\pi$
$312$		0			0
$313$	−4.16798			−0.235588			−0.117794	−	0.993038i	$-0.537582\pi$
$313$	−4.16798			−0.235588			−0.117794	+	0.993038i	$0.537582\pi$
$314$	−0.682480	−	1.68259i	−0.0385146	−	0.0949538i
$315$		0			0
$316$	3.98462	+	4.10374i	0.224153	+	0.230853i
$317$			15.3540i			0.862365i	0.902265	+	0.431182i	$0.141903\pi$
$317$			15.3540i			0.862365i	−0.902265	+	0.431182i	$0.858097\pi$
$318$		0			0
$319$		−	10.7820i		−	0.603674i
$320$	5.90115	−	5.40152i	0.329884	−	0.301954i
$321$		0			0
$322$	0.866709	−	0.351549i	0.0482998	−	0.0195911i
$323$	0.497431			0.0276778
$324$		0			0
$325$	−5.01098			−0.277959
$326$	−29.2839	+	11.8780i	−1.62189	+	0.657859i
$327$		0			0
$328$	8.59799	−	19.5260i	0.474745	−	1.07814i
$329$			14.5179i			0.800397i
$330$		0			0
$331$		−	18.4464i		−	1.01391i	−0.861973	−	0.506954i	$-0.830771\pi$
$331$		−	18.4464i		−	1.01391i	0.861973	−	0.506954i	$-0.169229\pi$
$332$	1.41143	−	1.37046i	0.0774623	−	0.0752139i
$333$		0			0
$334$	1.59687	+	3.93693i	0.0873770	+	0.215419i
$335$	3.38716			0.185060
$336$		0			0
$337$	−7.65381			−0.416930			−0.208465	−	0.978030i	$-0.566847\pi$
$337$	−7.65381			−0.416930			−0.208465	+	0.978030i	$0.566847\pi$
$338$	−6.43715	−	15.8702i	−0.350135	−	0.863223i
$339$		0			0
$340$	2.27411	−	2.20810i	0.123331	−	0.119751i
$341$		−	59.6487i		−	3.23016i
$342$		0			0
$343$			16.7090i			0.902202i
$344$	6.87138	−	15.6049i	0.370480	−	0.841360i
$345$		0			0
$346$	−21.5872	+	8.75606i	−1.16053	+	0.470729i
$347$	−11.9646			−0.642296			−0.321148	−	0.947029i	$-0.604069\pi$
$347$	−11.9646			−0.642296			−0.321148	+	0.947029i	$0.604069\pi$
$348$		0			0
$349$	26.4238			1.41443			0.707216	−	0.706998i	$-0.249951\pi$
$349$	26.4238			1.41443			0.707216	+	0.706998i	$0.249951\pi$
$350$	−1.81121	+	0.734652i	−0.0968133	+	0.0392688i
$351$		0			0
$352$	33.3645	−	12.4020i	1.77833	−	0.661028i
$353$			13.7478i			0.731722i	0.930669	+	0.365861i	$0.119225\pi$
$353$			13.7478i			0.731722i	−0.930669	+	0.365861i	$0.880775\pi$
$354$		0			0
$355$		−	14.1414i		−	0.750546i
$356$	−3.68943	−	3.79972i	−0.195540	−	0.201385i
$357$		0			0
$358$	−1.83537	−	4.52492i	−0.0970023	−	0.239150i
$359$	20.2229			1.06733			0.533663	−	0.845697i	$-0.320815\pi$
$359$	20.2229			1.06733			0.533663	+	0.845697i	$0.320815\pi$
$360$		0			0
$361$	18.9015			0.994815
$362$	−6.48588	−	15.9903i	−0.340891	−	0.840432i
$363$		0			0
$364$	−9.64884	−	9.93727i	−0.505737	−	0.520855i
$365$			4.55479i			0.238409i
$366$		0			0
$367$			26.2087i			1.36808i	0.729443	+	0.684041i	$0.239779\pi$
$367$			26.2087i			1.36808i	−0.729443	+	0.684041i	$0.760221\pi$
$368$	0.0563638	−	1.91327i	0.00293817	−	0.0997360i
$369$		0			0
$370$	−11.2087	+	4.54639i	−0.582711	+	0.236356i
$371$	−12.2474			−0.635856
$372$		0			0
$373$	−21.4399			−1.11012			−0.555058	−	0.831811i	$-0.687304\pi$
$373$	−21.4399			−1.11012			−0.555058	+	0.831811i	$0.687304\pi$
$374$	13.0692	−	5.30104i	0.675791	−	0.274110i
$375$		0			0
$376$	27.1918	+	11.9735i	1.40231	+	0.617485i
$377$			8.58633i			0.442219i
$378$		0			0
$379$			17.9636i			0.922728i	0.887211	+	0.461364i	$0.152640\pi$
$379$			17.9636i			0.922728i	−0.887211	+	0.461364i	$0.847360\pi$
$380$	−0.450355	+	0.437283i	−0.0231027	+	0.0224322i
$381$		0			0
$382$	−2.83358	−	6.98591i	−0.144979	−	0.357430i
$383$	−5.43719			−0.277827			−0.138914	−	0.990304i	$-0.544361\pi$
$383$	−5.43719			−0.277827			−0.138914	+	0.990304i	$0.544361\pi$
$384$		0			0
$385$	−8.69642			−0.443211
$386$	3.96770	+	9.78196i	0.201950	+	0.497889i
$387$		0			0
$388$	−14.5567	+	14.1342i	−0.739006	+	0.717556i
$389$			2.72940i			0.138386i	0.997603	+	0.0691930i	$0.0220424\pi$
$389$			2.72940i			0.138386i	−0.997603	+	0.0691930i	$0.977958\pi$
$390$		0			0
$391$		−	0.758401i		−	0.0383540i
$392$	13.1756	+	5.80169i	0.665470	+	0.293029i
$393$		0			0
$394$	27.8971	−	11.3154i	1.40544	−	0.570064i
$395$	−2.85998			−0.143901
$396$		0			0
$397$	7.21742			0.362232			0.181116	−	0.983462i	$-0.442029\pi$
$397$	7.21742			0.362232			0.181116	+	0.983462i	$0.442029\pi$
$398$	23.6590	−	9.59642i	1.18592	−	0.481025i
$399$		0			0
$400$	−0.117787	+	3.99827i	−0.00588933	+	0.199913i
$401$		−	16.0399i		−	0.800995i	−0.916298	−	0.400498i	$-0.868837\pi$
$401$		−	16.0399i		−	0.800995i	0.916298	−	0.400498i	$-0.131163\pi$
$402$		0			0
$403$			47.5019i			2.36624i
$404$	3.51501	+	3.62008i	0.174878	+	0.180106i
$405$		0			0
$406$	1.25883	+	3.10352i	0.0624747	+	0.154025i
$407$	−53.8178			−2.66765
$408$		0			0
$409$	−12.1350			−0.600035			−0.300017	−	0.953934i	$-0.596992\pi$
$409$	−12.1350			−0.600035			−0.300017	+	0.953934i	$0.596992\pi$
$410$	4.00964	+	9.88537i	0.198022	+	0.488204i
$411$		0			0
$412$	−11.1724	−	11.5064i	−0.550424	−	0.566878i
$413$			16.4675i			0.810311i
$414$		0			0
$415$			0.983654i			0.0482857i
$416$	−26.5701	+	9.87645i	−1.30271	+	0.484233i
$417$		0			0
$418$	−2.58816	+	1.04979i	−0.126591	+	0.0513471i
$419$	−34.5176			−1.68630			−0.843148	−	0.537682i	$-0.819300\pi$
$419$	−34.5176			−1.68630			−0.843148	+	0.537682i	$0.819300\pi$
$420$		0			0
$421$	−26.6082			−1.29681			−0.648403	−	0.761297i	$-0.724563\pi$
$421$	−26.6082			−1.29681			−0.648403	+	0.761297i	$0.724563\pi$
$422$	18.8704	−	7.65407i	0.918595	−	0.372595i
$423$		0			0
$424$	−10.1010	+	22.9393i	−0.490546	+	1.11403i
$425$			1.58487i			0.0768777i
$426$		0			0
$427$		−	6.93923i		−	0.335813i
$428$	10.0797	−	9.78712i	0.487220	−	0.473078i
$429$		0			0
$430$	3.20444	+	7.90023i	0.154532	+	0.380983i
$431$	13.2011			0.635875			0.317937	−	0.948112i	$-0.397010\pi$
$431$	13.2011			0.635875			0.317937	+	0.948112i	$0.397010\pi$
$432$		0			0
$433$	−28.5327			−1.37119			−0.685597	−	0.727981i	$-0.740459\pi$
$433$	−28.5327			−1.37119			−0.685597	+	0.727981i	$0.740459\pi$
$434$	6.96418	+	17.1695i	0.334291	+	0.824162i
$435$		0			0
$436$	−10.9715	+	10.6530i	−0.525438	+	0.510186i
$437$			0.150190i			0.00718458i
$438$		0			0
$439$			36.4715i			1.74069i	0.492442	+	0.870345i	$0.336104\pi$
$439$			36.4715i			1.74069i	−0.492442	+	0.870345i	$0.663896\pi$
$440$	−7.17229	+	16.2883i	−0.341925	+	0.776512i
$441$		0			0
$442$	−10.4078	+	4.22154i	−0.495048	+	0.200798i
$443$	34.9502			1.66053			0.830267	−	0.557366i	$-0.188188\pi$
$443$	34.9502			1.66053			0.830267	+	0.557366i	$0.188188\pi$
$444$		0			0
$445$	2.64810			0.125532
$446$	−19.5142	+	7.91522i	−0.924024	+	0.374797i
$447$		0			0
$448$	−8.15577	+	7.46524i	−0.385324	+	0.352699i
$449$		−	7.71112i		−	0.363910i	−0.983307	−	0.181955i	$-0.941757\pi$
$449$		−	7.71112i		−	0.363910i	0.983307	−	0.181955i	$-0.0582426\pi$
$450$		0			0
$451$			47.4640i			2.23499i
$452$	15.8914	+	16.3665i	0.747469	+	0.769813i
$453$		0			0
$454$	12.8951	+	31.7915i	0.605195	+	1.49205i
$455$	6.92549			0.324672
$456$		0			0
$457$	14.1392			0.661404			0.330702	−	0.943735i	$-0.392715\pi$
$457$	14.1392			0.661404			0.330702	+	0.943735i	$0.392715\pi$
$458$	12.6310	+	31.1404i	0.590207	+	1.45510i
$459$		0			0
$460$	0.666698	+	0.686628i	0.0310849	+	0.0320142i
$461$		−	9.80062i		−	0.456460i	−0.973607	−	0.228230i	$-0.926706\pi$
$461$		−	9.80062i		−	0.456460i	0.973607	−	0.228230i	$-0.0732939\pi$
$462$		0			0
$463$		−	26.0533i		−	1.21080i	−0.795921	−	0.605401i	$-0.793013\pi$
$463$		−	26.0533i		−	1.21080i	0.795921	−	0.605401i	$-0.206987\pi$
$464$	6.85105	+	0.201828i	0.318052	+	0.00936963i
$465$		0			0
$466$	34.5763	−	14.0246i	1.60172	−	0.649678i
$467$	14.5432			0.672978			0.336489	−	0.941687i	$-0.390761\pi$
$467$	14.5432			0.672978			0.336489	+	0.941687i	$0.390761\pi$
$468$		0			0
$469$	−4.68127			−0.216161
$470$	−13.7663	+	5.58379i	−0.634991	+	0.257561i
$471$		0			0
$472$	30.8433	+	13.5814i	1.41968	+	0.625134i
$473$			37.9325i			1.74414i
$474$		0			0
$475$		−	0.313862i		−	0.0144010i
$476$	−3.14297	+	3.05174i	−0.144058	+	0.139876i
$477$		0			0
$478$	−1.95743	−	4.82586i	−0.0895309	−	0.220729i
$479$	−13.4038			−0.612435			−0.306218	−	0.951962i	$-0.599064\pi$
$479$	−13.4038			−0.612435			−0.306218	+	0.951962i	$0.599064\pi$
$480$		0			0
$481$	42.8584			1.95417
$482$	0.305895	+	0.754154i	0.0139331	+	0.0343508i
$483$		0			0
$484$	−41.0285	+	39.8377i	−1.86493	+	1.81080i
$485$		−	10.1449i		−	0.460656i
$486$		0			0
$487$		−	35.6444i		−	1.61520i	−0.589730	−	0.807600i	$-0.700766\pi$
$487$		−	35.6444i		−	1.61520i	0.589730	−	0.807600i	$-0.299234\pi$
$488$	−12.9971	−	5.72306i	−0.588350	−	0.259071i
$489$		0			0
$490$	−6.67038	+	2.70560i	−0.301337	+	0.122226i
$491$	−31.5459			−1.42365			−0.711823	−	0.702359i	$-0.752130\pi$
$491$	−31.5459			−1.42365			−0.711823	+	0.702359i	$0.752130\pi$
$492$		0			0
$493$	2.71569			0.122309
$494$	2.06111	−	0.836015i	0.0927338	−	0.0376141i
$495$		0			0
$496$	37.9018	+	1.11657i	1.70184	+	0.0501353i
$497$			19.5443i			0.876681i
$498$		0			0
$499$			25.1993i			1.12808i	0.825748	+	0.564039i	$0.190753\pi$
$499$			25.1993i			1.12808i	−0.825748	+	0.564039i	$0.809247\pi$
$500$	−1.39324	−	1.43488i	−0.0623074	−	0.0641700i
$501$		0			0
$502$	8.00625	+	19.7386i	0.357337	+	0.880978i
$503$	−12.8113			−0.571227			−0.285613	−	0.958345i	$-0.592197\pi$
$503$	−12.8113			−0.571227			−0.285613	+	0.958345i	$0.592197\pi$
$504$		0			0
$505$	−2.52291			−0.112268
$506$	1.60055	+	3.94601i	0.0711533	+	0.175421i
$507$		0			0
$508$	−1.33496	−	1.37487i	−0.0592293	−	0.0609999i
$509$			16.6082i			0.736147i	0.929797	+	0.368073i	$0.119982\pi$
$509$			16.6082i			0.736147i	−0.929797	+	0.368073i	$0.880018\pi$
$510$		0			0
$511$		−	6.29501i		−	0.278475i
$512$	7.25589	+	21.4325i	0.320668	+	0.947192i
$513$		0			0
$514$	33.5863	−	13.6230i	1.48143	−	0.600887i
$515$	8.01903			0.353361
$516$		0			0
$517$	−66.0980			−2.90699
$518$	15.4911	−	6.28340i	0.680640	−	0.276077i
$519$		0			0
$520$	5.71173	−	12.9713i	0.250476	−	0.568830i
$521$		−	4.43554i		−	0.194324i	−0.995269	−	0.0971622i	$-0.969023\pi$
$521$		−	4.43554i		−	0.194324i	0.995269	−	0.0971622i	$-0.0309766\pi$
$522$		0			0
$523$		−	39.0882i		−	1.70921i	−0.519281	−	0.854604i	$-0.673800\pi$
$523$		−	39.0882i		−	1.70921i	0.519281	−	0.854604i	$-0.326200\pi$
$524$	−10.8362	+	10.5216i	−0.473380	+	0.459640i
$525$		0			0
$526$	−2.26218	−	5.57717i	−0.0986357	−	0.243176i
$527$	15.0239			0.654452
$528$		0			0
$529$	−22.7710			−0.990044
$530$	−4.71054	−	11.6134i	−0.204613	−	0.504453i
$531$		0			0
$532$	0.622419	−	0.604353i	0.0269853	−	0.0262020i
$533$		−	37.7985i		−	1.63723i
$534$		0			0
$535$			7.02474i			0.303706i
$536$	−3.86083	+	8.76794i	−0.166762	+	0.378717i
$537$		0			0
$538$	15.7109	−	6.37257i	0.677346	−	0.274741i
$539$	−32.0274			−1.37952
$540$		0			0
$541$	−22.5150			−0.967995			−0.483998	−	0.875069i	$-0.660816\pi$
$541$	−22.5150			−0.967995			−0.483998	+	0.875069i	$0.660816\pi$
$542$	−34.6181	+	14.0416i	−1.48697	+	0.603137i
$543$		0			0
$544$	3.12373	+	8.40362i	0.133929	+	0.360302i
$545$		−	7.64623i		−	0.327529i
$546$		0			0
$547$		−	10.4335i		−	0.446103i	−0.974807	−	0.223052i	$-0.928398\pi$
$547$		−	10.4335i		−	0.446103i	0.974807	−	0.223052i	$-0.0716019\pi$
$548$	−16.2254	−	16.7104i	−0.693114	−	0.713833i
$549$		0			0
$550$	−3.34477	−	8.24620i	−0.142621	−	0.351619i
$551$	−0.537803			−0.0229112
$552$		0			0
$553$	3.95267			0.168085
$554$	−16.0114	−	39.4746i	−0.680260	−	1.67711i
$555$		0			0
$556$	22.9518	+	23.6379i	0.973373	+	1.00247i
$557$		−	21.4327i		−	0.908133i	−0.890968	−	0.454066i	$-0.849973\pi$
$557$		−	21.4327i		−	0.908133i	0.890968	−	0.454066i	$-0.150027\pi$
$558$		0			0
$559$		−	30.2080i		−	1.27766i
$560$	0.162789	−	5.52586i	0.00687907	−	0.233510i
$561$		0			0
$562$	23.7467	−	9.63197i	1.00169	−	0.406300i
$563$	9.05262			0.381522			0.190761	−	0.981636i	$-0.438904\pi$
$563$	9.05262			0.381522			0.190761	+	0.981636i	$0.438904\pi$
$564$		0			0
$565$	−11.4061			−0.479859
$566$	−10.3624	+	4.20312i	−0.435563	+	0.176670i
$567$		0			0
$568$	36.6061	+	16.1189i	1.53596	+	0.676336i
$569$			36.7379i			1.54013i	0.637965	+	0.770065i	$0.279776\pi$
$569$			36.7379i			1.54013i	−0.637965	+	0.770065i	$0.720224\pi$
$570$		0			0
$571$			17.2985i			0.723919i	0.932194	+	0.361960i	$0.117892\pi$
$571$			17.2985i			0.723919i	−0.932194	+	0.361960i	$0.882108\pi$
$572$	45.2431	−	43.9298i	1.89171	−	1.83680i
$573$		0			0
$574$	−5.54158	−	13.6622i	−0.231301	−	0.570250i
$575$	−0.478525			−0.0199559
$576$		0			0
$577$	−1.95759			−0.0814954			−0.0407477	−	0.999169i	$-0.512974\pi$
$577$	−1.95759			−0.0814954			−0.0407477	+	0.999169i	$0.512974\pi$
$578$	−7.70136	−	18.9869i	−0.320334	−	0.789752i
$579$		0			0
$580$	−2.45868	+	2.38732i	−0.102091	+	0.0991279i
$581$		−	1.35947i		−	0.0564004i
$582$		0			0
$583$		−	55.7609i		−	2.30938i
$584$	−11.7904	−	5.19174i	−0.487892	−	0.214836i
$585$		0			0
$586$	3.32794	−	1.34986i	0.137476	−	0.0557621i
$587$	19.6489			0.810995			0.405498	−	0.914096i	$-0.367098\pi$
$587$	19.6489			0.810995			0.405498	+	0.914096i	$0.367098\pi$
$588$		0			0
$589$	−2.97527			−0.122594
$590$	−15.6149	+	6.33363i	−0.642857	+	0.260751i
$591$		0			0
$592$	1.00742	−	34.1968i	0.0414046	−	1.40548i
$593$		−	8.36132i		−	0.343358i	−0.985153	−	0.171679i	$-0.945081\pi$
$593$		−	8.36132i		−	0.343358i	0.985153	−	0.171679i	$-0.0549192\pi$
$594$		0			0
$595$		−	2.19040i		−	0.0897975i
$596$	23.4913	+	24.1935i	0.962240	+	0.991004i
$597$		0			0
$598$	−1.27462	−	3.14245i	−0.0521230	−	0.128504i
$599$	−2.89792			−0.118406			−0.0592028	−	0.998246i	$-0.518856\pi$
$599$	−2.89792			−0.118406			−0.0592028	+	0.998246i	$0.518856\pi$
$600$		0			0
$601$	−4.72085			−0.192567			−0.0962837	−	0.995354i	$-0.530696\pi$
$601$	−4.72085			−0.192567			−0.0962837	+	0.995354i	$0.530696\pi$
$602$	−4.42874	−	10.9186i	−0.180502	−	0.445010i
$603$		0			0
$604$	−12.6869	−	13.0661i	−0.516222	−	0.531653i
$605$		−	28.5936i		−	1.16250i
$606$		0			0
$607$		−	30.2927i		−	1.22954i	−0.788705	−	0.614772i	$-0.789248\pi$
$607$		−	30.2927i		−	1.22954i	0.788705	−	0.614772i	$-0.210752\pi$
$608$	−0.618610	−	1.66422i	−0.0250879	−	0.0674928i
$609$		0			0
$610$	6.57998	−	2.66893i	0.266416	−	0.108062i
$611$	52.6378			2.12950
$612$		0			0
$613$	26.0291			1.05130			0.525652	−	0.850700i	$-0.323821\pi$
$613$	26.0291			1.05130			0.525652	+	0.850700i	$0.323821\pi$
$614$	24.9006	−	10.1000i	1.00490	−	0.407603i
$615$		0			0
$616$	9.91255	−	22.5114i	0.399388	−	0.907010i
$617$			40.3932i			1.62617i	0.582147	+	0.813084i	$0.302213\pi$
$617$			40.3932i			1.62617i	−0.582147	+	0.813084i	$0.697787\pi$
$618$		0			0
$619$		−	32.3572i		−	1.30055i	−0.759700	−	0.650274i	$-0.774654\pi$
$619$		−	32.3572i		−	1.30055i	0.759700	−	0.650274i	$-0.225346\pi$
$620$	−13.6021	+	13.2073i	−0.546273	+	0.530417i
$621$		0			0
$622$	−2.54590	−	6.27666i	−0.102081	−	0.251671i
$623$	−3.65985			−0.146629
$624$		0			0
$625$	1.00000			0.0400000
$626$	2.21554	+	5.46219i	0.0885507	+	0.218313i
$627$		0			0
$628$	−1.84227	+	1.78880i	−0.0735146	+	0.0713807i
$629$		−	13.5553i		−	0.540484i
$630$		0			0
$631$			16.1040i			0.641090i	0.947233	+	0.320545i	$0.103866\pi$
$631$			16.1040i			0.641090i	−0.947233	+	0.320545i	$0.896134\pi$
$632$	3.25992	−	7.40329i	0.129673	−	0.294487i
$633$		0			0
$634$	20.1216	−	8.16158i	0.799129	−	0.324138i
$635$	0.958173			0.0380239
$636$		0			0
$637$	25.5054			1.01056
$638$	−14.1299	+	5.73128i	−0.559408	+	0.226904i
$639$		0			0
$640$	−10.2156	−	4.86229i	−0.403806	−	0.192199i
$641$		−	41.3540i		−	1.63339i	−0.577072	−	0.816693i	$-0.695805\pi$
$641$		−	41.3540i		−	1.63339i	0.577072	−	0.816693i	$-0.304195\pi$
$642$		0			0
$643$			19.3690i			0.763838i	0.924196	+	0.381919i	$0.124737\pi$
$643$			19.3690i			0.763838i	−0.924196	+	0.381919i	$0.875263\pi$
$644$	−0.921418	−	0.948963i	−0.0363090	−	0.0373944i
$645$		0			0
$646$	−0.264415	−	0.651889i	−0.0104033	−	0.0256482i
$647$	−7.26461			−0.285601			−0.142801	−	0.989751i	$-0.545611\pi$
$647$	−7.26461			−0.285601			−0.142801	+	0.989751i	$0.545611\pi$
$648$		0			0
$649$	−74.9742			−2.94299
$650$	2.66364	+	6.56695i	0.104477	+	0.257577i
$651$		0			0
$652$	31.1324	+	32.0631i	1.21924	+	1.25569i
$653$		−	22.6502i		−	0.886371i	−0.896430	−	0.443185i	$-0.853848\pi$
$653$		−	22.6502i		−	0.886371i	0.896430	−	0.443185i	$-0.146152\pi$
$654$		0			0
$655$		−	7.55194i		−	0.295079i
$656$	−30.1595	−	0.888481i	−1.17753	−	0.0346893i
$657$		0			0
$658$	19.0259	−	7.71716i	0.741706	−	0.300846i
$659$	12.0174			0.468132			0.234066	−	0.972221i	$-0.424797\pi$
$659$	12.0174			0.468132			0.234066	+	0.972221i	$0.424797\pi$
$660$		0			0
$661$	10.6253			0.413275			0.206638	−	0.978418i	$-0.433748\pi$
$661$	10.6253			0.413275			0.206638	+	0.978418i	$0.433748\pi$
$662$	−24.1743	+	9.80542i	−0.939560	+	0.381099i
$663$		0			0
$664$	−2.54627	−	1.12121i	−0.0988144	−	0.0435114i
$665$			0.433777i			0.0168211i
$666$		0			0
$667$			0.819954i			0.0317488i
$668$	4.31056	−	4.18544i	0.166781	−	0.161940i
$669$		0			0
$670$	−1.80048	−	4.43891i	−0.0695587	−	0.171490i
$671$	31.5934			1.21965
$672$		0			0
$673$	−33.1771			−1.27888			−0.639441	−	0.768840i	$-0.720834\pi$
$673$	−33.1771			−1.27888			−0.639441	+	0.768840i	$0.720834\pi$
$674$	4.06847	+	10.0304i	0.156712	+	0.386357i
$675$		0			0
$676$	−17.3763	+	16.8719i	−0.668319	+	0.648920i
$677$			10.4798i			0.402770i	0.979512	+	0.201385i	$0.0645442\pi$
$677$			10.4798i			0.402770i	−0.979512	+	0.201385i	$0.935456\pi$
$678$		0			0
$679$			14.0209i			0.538072i
$680$	−4.10258	−	1.80651i	−0.157327	−	0.0692764i
$681$		0			0
$682$	−78.1704	+	31.7070i	−2.99330	+	1.21412i
$683$	22.2498			0.851364			0.425682	−	0.904873i	$-0.360034\pi$
$683$	22.2498			0.851364			0.425682	+	0.904873i	$0.360034\pi$
$684$		0			0
$685$	11.6458			0.444964
$686$	21.8974	−	8.88187i	0.836045	−	0.339111i
$687$		0			0
$688$	−24.1030	−	0.710060i	−0.918917	−	0.0270708i
$689$			44.4058i			1.69173i
$690$		0			0
$691$		−	22.3826i		−	0.851473i	−0.904847	−	0.425736i	$-0.860015\pi$
$691$		−	22.3826i		−	0.851473i	0.904847	−	0.425736i	$-0.139985\pi$
$692$	22.9498	+	23.6359i	0.872422	+	0.898502i
$693$		0			0
$694$	6.35995	+	15.6798i	0.241420	+	0.595198i
$695$	−16.4737			−0.624884
$696$		0			0
$697$	−11.9549			−0.452825
$698$	−14.0459	−	34.6287i	−0.531644	−	1.31071i
$699$		0			0
$700$	1.92554	+	1.98310i	0.0727786	+	0.0749542i
$701$		−	38.9534i		−	1.47125i	−0.677389	−	0.735625i	$-0.736888\pi$
$701$		−	38.9534i		−	1.47125i	0.677389	−	0.735625i	$-0.263112\pi$
$702$		0			0
$703$			2.68443i			0.101245i
$704$	−33.9882	−	37.1321i	−1.28098	−	1.39947i
$705$		0			0
$706$	18.0167	−	7.30781i	0.678066	−	0.275033i
$707$	3.48682			0.131135
$708$		0			0
$709$	14.6033			0.548440			0.274220	−	0.961667i	$-0.411580\pi$
$709$	14.6033			0.548440			0.274220	+	0.961667i	$0.411580\pi$
$710$	−18.5324	+	7.51701i	−0.695510	+	0.282108i
$711$		0			0
$712$	−3.01842	+	6.85484i	−0.113120	+	0.256896i
$713$			4.53621i			0.169882i
$714$		0			0
$715$			31.5308i			1.17919i
$716$	−4.95435	+	4.81055i	−0.185153	+	0.179779i
$717$		0			0
$718$	−10.7497	−	26.5024i	−0.401177	−	0.989061i
$719$	−5.39169			−0.201076			−0.100538	−	0.994933i	$-0.532056\pi$
$719$	−5.39169			−0.201076			−0.100538	+	0.994933i	$0.532056\pi$
$720$		0			0
$721$	−11.0828			−0.412745
$722$	−10.0473	−	24.7706i	−0.373922	−	0.921868i
$723$		0			0
$724$	−17.5078	+	16.9997i	−0.650674	+	0.631787i
$725$		−	1.71350i		−	0.0636380i
$726$		0			0
$727$		−	13.5884i		−	0.503965i	−0.967732	−	0.251982i	$-0.918918\pi$
$727$		−	13.5884i		−	0.503965i	0.967732	−	0.251982i	$-0.0810825\pi$
$728$	−7.89397	+	17.9272i	−0.292570	+	0.664426i
$729$		0			0
$730$	5.96911	−	2.42115i	0.220927	−	0.0896108i
$731$	−9.55419			−0.353374
$732$		0			0
$733$	−39.4830			−1.45834			−0.729169	−	0.684334i	$-0.760093\pi$
$733$	−39.4830			−1.45834			−0.729169	+	0.684334i	$0.760093\pi$
$734$	34.3468	−	13.9315i	1.26776	−	0.514222i
$735$		0			0
$736$	−2.53732	+	0.943155i	−0.0935269	+	0.0347651i
$737$		−	21.3132i		−	0.785081i
$738$		0			0
$739$		−	43.4628i		−	1.59881i	−0.600795	−	0.799403i	$-0.705149\pi$
$739$		−	43.4628i		−	1.59881i	0.600795	−	0.799403i	$-0.294851\pi$
$740$	11.9162	+	12.2724i	0.438048	+	0.451143i
$741$		0			0
$742$	6.51027	+	16.0504i	0.239000	+	0.589230i
$743$	−33.2807			−1.22095			−0.610476	−	0.792035i	$-0.709022\pi$
$743$	−33.2807			−1.22095			−0.610476	+	0.792035i	$0.709022\pi$
$744$		0			0
$745$	−16.8609			−0.617737
$746$	11.3966	+	28.0973i	0.417261	+	1.02871i
$747$		0			0
$748$	−13.8942	−	14.3095i	−0.508021	−	0.523207i
$749$		−	9.70863i		−	0.354746i
$750$		0			0
$751$			18.1139i			0.660984i	0.943809	+	0.330492i	$0.107215\pi$
$751$			18.1139i			0.660984i	−0.943809	+	0.330492i	$0.892785\pi$
$752$	1.23729	−	41.9998i	0.0451193	−	1.53158i
$753$		0			0
$754$	11.2525	−	4.56417i	0.409792	−	0.166217i
$755$	9.10605			0.331403
$756$		0			0
$757$	4.70815			0.171121			0.0855603	−	0.996333i	$-0.472732\pi$
$757$	4.70815			0.171121			0.0855603	+	0.996333i	$0.472732\pi$
$758$	23.5415	−	9.54876i	0.855066	−	0.346826i
$759$		0			0
$760$	0.812456	+	0.357753i	0.0294709	+	0.0129771i
$761$			17.5411i			0.635866i	0.948113	+	0.317933i	$0.102989\pi$
$761$			17.5411i			0.635866i	−0.948113	+	0.317933i	$0.897011\pi$
$762$		0			0
$763$			10.5676i			0.382572i
$764$	−7.64890	+	7.42688i	−0.276727	+	0.268695i
$765$		0			0
$766$	2.89020	+	7.12550i	0.104427	+	0.257455i
$767$	59.7065			2.15588
$768$		0			0
$769$	31.2126			1.12555			0.562777	−	0.826609i	$-0.309733\pi$
$769$	31.2126			1.12555			0.562777	+	0.826609i	$0.309733\pi$
$770$	4.62268	+	11.3968i	0.166590	+	0.410711i
$771$		0			0
$772$	10.7103	−	10.3994i	0.385472	−	0.374284i
$773$		−	32.5292i		−	1.16999i	−0.811035	−	0.584997i	$-0.801096\pi$
$773$		−	32.5292i		−	1.16999i	0.811035	−	0.584997i	$-0.198904\pi$
$774$		0			0
$775$		−	9.47957i		−	0.340516i
$776$	26.2609	+	11.5636i	0.942710	+	0.415108i
$777$		0			0
$778$	3.57691	−	1.45084i	0.128238	−	0.0520152i
$779$	2.36750			0.0848245
$780$		0			0
$781$	−88.9824			−3.18404
$782$	−0.993894	+	0.403137i	−0.0355416	+	0.0144162i
$783$		0			0
$784$	0.599522	−	20.3508i	0.0214115	−	0.726813i
$785$		−	1.28391i		−	0.0458249i
$786$		0			0
$787$		−	47.5820i		−	1.69612i	−0.529903	−	0.848058i	$-0.677772\pi$
$787$		−	47.5820i		−	1.69612i	0.529903	−	0.848058i	$-0.322228\pi$
$788$	−29.6581	−	30.5446i	−1.05652	−	1.08811i
$789$		0			0
$790$	1.52025	+	3.74804i	0.0540882	+	0.133349i
$791$	15.7640			0.560502
$792$		0			0
$793$	−25.1597			−0.893448
$794$	−3.83650	−	9.45851i	−0.136152	−	0.335670i
$795$		0			0
$796$	−25.1525	−	25.9043i	−0.891505	−	0.918155i
$797$		−	3.12482i		−	0.110687i	−0.998467	−	0.0553434i	$-0.982375\pi$
$797$		−	3.12482i		−	0.110687i	0.998467	−	0.0553434i	$-0.0176254\pi$
$798$		0			0
$799$		−	16.6483i		−	0.588975i
$800$	5.30239	−	1.97096i	0.187468	−	0.0696841i
$801$		0			0
$802$	−21.0205	+	8.52620i	−0.742260	+	0.301071i
$803$	28.6603			1.01140
$804$		0			0
$805$	0.661351			0.0233096
$806$	62.2518	−	25.2502i	2.19273	−	0.889400i
$807$		0			0
$808$	2.87572	−	6.53075i	0.101167	−	0.229751i
$809$			16.8154i			0.591197i	0.955312	+	0.295599i	$0.0955191\pi$
$809$			16.8154i			0.591197i	−0.955312	+	0.295599i	$0.904481\pi$
$810$		0			0
$811$		−	2.22240i		−	0.0780389i	−0.999238	−	0.0390194i	$-0.987577\pi$
$811$		−	2.22240i		−	0.0780389i	0.999238	−	0.0390194i	$-0.0124234\pi$
$812$	3.39805	−	3.29942i	0.119248	−	0.115787i
$813$		0			0
$814$	28.6075	+	70.5289i	1.00269	+	2.47204i
$815$	−22.3454			−0.782725
$816$		0			0
$817$	1.89207			0.0661951
$818$	6.45048	+	15.9030i	0.225536	+	0.556035i
$819$		0			0
$820$	10.8235	−	10.5094i	0.377974	−	0.367003i
$821$		−	7.36036i		−	0.256878i	−0.991717	−	0.128439i	$-0.959003\pi$
$821$		−	7.36036i		−	0.256878i	0.991717	−	0.128439i	$-0.0409967\pi$
$822$		0			0
$823$		−	46.8300i		−	1.63239i	−0.577775	−	0.816196i	$-0.696079\pi$
$823$		−	46.8300i		−	1.63239i	0.577775	−	0.816196i	$-0.303921\pi$
$824$	−9.14043	+	20.7579i	−0.318422	+	0.723136i
$825$		0			0
$826$	21.5808	−	8.75348i	0.750893	−	0.304572i
$827$	−41.4266			−1.44054			−0.720272	−	0.693692i	$-0.755983\pi$
$827$	−41.4266			−1.44054			−0.720272	+	0.693692i	$0.755983\pi$
$828$		0			0
$829$	41.3350			1.43562			0.717812	−	0.696237i	$-0.245144\pi$
$829$	41.3350			1.43562			0.717812	+	0.696237i	$0.245144\pi$
$830$	1.28909	−	0.522873i	0.0447450	−	0.0181492i
$831$		0			0
$832$	27.0669	+	29.5705i	0.938375	+	1.02517i
$833$		−	8.06685i		−	0.279500i
$834$		0			0
$835$			3.00412i			0.103962i
$836$	2.75154	+	2.83379i	0.0951639	+	0.0980087i
$837$		0			0
$838$	18.3482	+	45.2357i	0.633829	+	1.56264i
$839$	−10.3285			−0.356578			−0.178289	−	0.983978i	$-0.557056\pi$
$839$	−10.3285			−0.356578			−0.178289	+	0.983978i	$0.557056\pi$
$840$		0			0
$841$	26.0639			0.898755
$842$	14.1439	+	34.8704i	0.487432	+	1.20171i
$843$		0			0
$844$	−20.0615	−	20.6612i	−0.690546	−	0.711189i
$845$		−	12.1099i		−	0.416593i
$846$		0			0
$847$			39.5182i			1.35786i
$848$	35.4315	+	1.04379i	1.21672	+	0.0358439i
$849$		0			0
$850$	2.07700	−	0.842458i	0.0712404	−	0.0288961i
$851$	4.09277			0.140298
$852$		0			0
$853$	−6.04250			−0.206891			−0.103446	−	0.994635i	$-0.532987\pi$
$853$	−6.04250			−0.206891			−0.103446	+	0.994635i	$0.532987\pi$
$854$	−9.09395	+	3.68863i	−0.311188	+	0.126222i
$855$		0			0
$856$	−18.1841	−	8.00710i	−0.621520	−	0.273677i
$857$		−	11.1082i		−	0.379448i	−0.981837	−	0.189724i	$-0.939241\pi$
$857$		−	11.1082i		−	0.379448i	0.981837	−	0.189724i	$-0.0607593\pi$
$858$		0			0
$859$		−	24.9763i		−	0.852181i	−0.904681	−	0.426090i	$-0.859891\pi$
$859$		−	24.9763i		−	0.852181i	0.904681	−	0.426090i	$-0.140109\pi$
$860$	8.64999	−	8.39892i	0.294962	−	0.286401i
$861$		0			0
$862$	−7.01720	−	17.3002i	−0.239007	−	0.589247i
$863$	−2.80028			−0.0953227			−0.0476613	−	0.998864i	$-0.515177\pi$
$863$	−2.80028			−0.0953227			−0.0476613	+	0.998864i	$0.515177\pi$
$864$		0			0
$865$	−16.4723			−0.560076
$866$	15.1669	+	37.3924i	0.515392	+	1.27065i
$867$		0			0
$868$	18.7989	−	18.2533i	0.638078	−	0.619557i
$869$			17.9960i			0.610471i
$870$		0			0
$871$			16.9730i			0.575107i
$872$	19.7929	+	8.71550i	0.670272	+	0.295144i
$873$		0			0
$874$	0.196826	−	0.0798355i	0.00665775	−	0.00270048i
$875$	−1.38206			−0.0467223
$876$		0			0
$877$	10.4748			0.353709			0.176854	−	0.984237i	$-0.443408\pi$
$877$	10.4748			0.353709			0.176854	+	0.984237i	$0.443408\pi$
$878$	47.7964	−	19.3869i	1.61305	−	0.654275i
$879$		0			0
$880$	25.1585	+	0.741154i	0.848092	+	0.0249843i
$881$		−	19.8836i		−	0.669896i	−0.942237	−	0.334948i	$-0.891281\pi$
$881$		−	19.8836i		−	0.669896i	0.942237	−	0.334948i	$-0.108719\pi$
$882$		0			0
$883$			25.0647i			0.843493i	0.906714	+	0.421747i	$0.138583\pi$
$883$			25.0647i			0.843493i	−0.906714	+	0.421747i	$0.861417\pi$
$884$	11.0648	+	11.3955i	0.372148	+	0.383273i
$885$		0			0
$886$	−18.5782	−	45.8027i	−0.624146	−	1.53877i
$887$	−26.9970			−0.906471			−0.453236	−	0.891391i	$-0.649730\pi$
$887$	−26.9970			−0.906471			−0.453236	+	0.891391i	$0.649730\pi$
$888$		0			0
$889$	−1.32426			−0.0444141
$890$	−1.40763	−	3.47037i	−0.0471839	−	0.116327i
$891$		0			0
$892$	20.7460	+	21.3662i	0.694627	+	0.715392i
$893$			3.29696i			0.110329i
$894$		0			0
$895$		−	3.45279i		−	0.115414i
$896$	14.1186	+	6.72000i	0.471669	+	0.224499i
$897$		0			0
$898$	−10.1055	+	4.09893i	−0.337225	+	0.136783i
$899$	−16.2433			−0.541744
$900$		0			0
$901$	14.0447			0.467897
$902$	62.2022	−	25.2301i	2.07111	−	0.840069i
$903$		0			0
$904$	13.0012	−	29.5257i	0.432413	−	0.982009i
$905$		−	12.2016i		−	0.405594i
$906$		0			0
$907$		−	7.52682i		−	0.249924i	−0.992162	−	0.124962i	$-0.960119\pi$
$907$		−	7.52682i		−	0.249924i	0.992162	−	0.124962i	$-0.0398809\pi$
$908$	34.8086	−	33.7983i	1.15516	−	1.12163i
$909$		0			0
$910$	−3.68132	−	9.07594i	−0.122035	−	0.300864i
$911$	23.2517			0.770363			0.385181	−	0.922841i	$-0.374139\pi$
$911$	23.2517			0.770363			0.385181	+	0.922841i	$0.374139\pi$
$912$		0			0
$913$	6.18949			0.204842
$914$	−7.51586	−	18.5296i	−0.248602	−	0.612905i
$915$		0			0
$916$	34.0957	−	33.1061i	1.12655	−	1.09386i
$917$			10.4373i			0.344669i
$918$		0			0
$919$		−	5.42134i		−	0.178833i	−0.995994	−	0.0894167i	$-0.971500\pi$
$919$		−	5.42134i		−	0.178833i	0.995994	−	0.0894167i	$-0.0285003\pi$
$920$	0.545443	−	1.23870i	0.0179827	−	0.0408387i
$921$		0			0
$922$	−12.8438	+	5.20963i	−0.422989	+	0.171570i
$923$	70.8621			2.33245
$924$		0			0
$925$	−8.55290			−0.281218
$926$	−34.1432	+	13.8490i	−1.12202	+	0.455105i
$927$		0			0
$928$	−3.37726	−	9.08566i	−0.110864	−	0.298252i
$929$		−	8.19467i		−	0.268859i	−0.990923	−	0.134429i	$-0.957080\pi$
$929$		−	8.19467i		−	0.268859i	0.990923	−	0.134429i	$-0.0429201\pi$
$930$		0			0
$931$			1.59752i			0.0523567i
$932$	−36.7589	−	37.8577i	−1.20408	−	1.24007i
$933$		0			0
$934$	−7.73059	−	19.0590i	−0.252953	−	0.623630i
$935$	9.97258			0.326138
$936$		0			0
$937$	−22.4473			−0.733322			−0.366661	−	0.930355i	$-0.619499\pi$
$937$	−22.4473			−0.733322			−0.366661	+	0.930355i	$0.619499\pi$
$938$	2.48838	+	6.13486i	0.0812485	+	0.200310i
$939$		0			0
$940$	14.6353	+	15.0728i	0.477350	+	0.491619i
$941$		−	53.0004i		−	1.72777i	−0.503693	−	0.863883i	$-0.668026\pi$
$941$		−	53.0004i		−	1.72777i	0.503693	−	0.863883i	$-0.331974\pi$
$942$		0			0
$943$		−	3.60958i		−	0.117544i
$944$	1.40344	−	47.6399i	0.0456782	−	1.55055i
$945$		0			0
$946$	49.7110	−	20.1635i	1.61624	−	0.655571i
$947$	1.89511			0.0615829			0.0307914	−	0.999526i	$-0.490197\pi$
$947$	1.89511			0.0615829			0.0307914	+	0.999526i	$0.490197\pi$
$948$		0			0
$949$	−22.8239			−0.740897
$950$	−0.411319	+	0.166837i	−0.0133450	+	0.00541290i
$951$		0			0
$952$	5.67002	+	2.49671i	0.183766	+	0.0809188i
$953$			11.0618i			0.358327i	0.983819	+	0.179163i	$0.0573391\pi$
$953$			11.0618i			0.358327i	−0.983819	+	0.179163i	$0.942661\pi$
$954$		0			0
$955$		−	5.33067i		−	0.172496i
$956$	−5.28385	+	5.13048i	−0.170892	+	0.165932i
$957$		0			0
$958$	7.12495	+	17.5658i	0.230197	+	0.567527i
$959$	−16.0953			−0.519743
$960$		0			0
$961$	−58.8622			−1.89878
$962$	−22.7819	−	56.1664i	−0.734517	−	1.81088i
$963$		0			0
$964$	0.825726	−	0.801758i	0.0265948	−	0.0258229i
$965$			7.46422i			0.240282i
$966$		0			0
$967$			32.6739i			1.05072i	0.850880	+	0.525360i	$0.176070\pi$
$967$			32.6739i			1.05072i	−0.850880	+	0.525360i	$0.823930\pi$
$968$	74.0169	+	32.5922i	2.37899	+	1.04755i
$969$		0			0
$970$	−13.2950	+	5.39263i	−0.426877	+	0.173147i
$971$	39.2972			1.26111			0.630553	−	0.776146i	$-0.282828\pi$
$971$	39.2972			1.26111			0.630553	+	0.776146i	$0.282828\pi$
$972$		0			0
$973$	22.7677			0.729900
$974$	−46.7124	+	18.9472i	−1.49676	+	0.607107i
$975$		0			0
$976$	−0.591397	+	20.0750i	−0.0189302	+	0.642584i
$977$			27.8905i			0.892295i	0.894960	+	0.446147i	$0.147204\pi$
$977$			27.8905i			0.892295i	−0.894960	+	0.446147i	$0.852796\pi$
$978$		0			0
$979$		−	16.6628i		−	0.532545i
$980$	7.09143	+	7.30342i	0.226528	+	0.233299i
$981$		0			0
$982$	16.7686	+	41.3413i	0.535107	+	1.31925i
$983$	−3.33160			−0.106262			−0.0531308	−	0.998588i	$-0.516920\pi$
$983$	−3.33160			−0.106262			−0.0531308	+	0.998588i	$0.516920\pi$
$984$		0			0
$985$	21.2872			0.678266
$986$	−1.44356	−	3.55894i	−0.0459722	−	0.113340i
$987$		0			0
$988$	−2.19122	−	2.25672i	−0.0697119	−	0.0717958i
$989$		−	2.88472i		−	0.0917287i
$990$		0			0
$991$		−	15.9832i		−	0.507725i	−0.967240	−	0.253862i	$-0.918299\pi$
$991$		−	15.9832i		−	0.507725i	0.967240	−	0.253862i	$-0.0817010\pi$
$992$	−18.6839	−	50.2643i	−0.593214	−	1.59589i
$993$		0			0
$994$	25.6130	−	10.3890i	0.812396	−	0.329519i
$995$	18.0533			0.572327
$996$		0			0
$997$	−3.91305			−0.123927			−0.0619637	−	0.998078i	$-0.519736\pi$
$997$	−3.91305			−0.123927			−0.0619637	+	0.998078i	$0.519736\pi$
$998$	33.0240	−	13.3950i	1.04536	−	0.424011i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.19	✓	48
3.2	odd	2	inner	1620.2.e.a.971.30	yes	48
4.3	odd	2	inner	1620.2.e.a.971.29	yes	48
12.11	even	2	inner	1620.2.e.a.971.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.19	✓	48	1.1	even	1	trivial
1620.2.e.a.971.20	yes	48	12.11	even	2	inner
1620.2.e.a.971.29	yes	48	4.3	odd	2	inner
1620.2.e.a.971.30	yes	48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.531562 - 1.31051i) q^{2} +(-1.43488 + 1.39324i) q^{4} -1.00000i q^{5} +1.38206i q^{7} +(2.58858 + 1.13984i) q^{8} +O(q^{10})\)	\(q+(-0.531562 - 1.31051i) q^{2} +(-1.43488 + 1.39324i) q^{4} -1.00000i q^{5} +1.38206i q^{7} +(2.58858 + 1.13984i) q^{8} +(-1.31051 + 0.531562i) q^{10} -6.29235 q^{11} +5.01098 q^{13} +(1.81121 - 0.734652i) q^{14} +(0.117787 - 3.99827i) q^{16} -1.58487i q^{17} +0.313862i q^{19} +(1.39324 + 1.43488i) q^{20} +(3.34477 + 8.24620i) q^{22} +0.478525 q^{23} -1.00000 q^{25} +(-2.66364 - 6.56695i) q^{26} +(-1.92554 - 1.98310i) q^{28} +1.71350i q^{29} +9.47957i q^{31} +(-5.30239 + 1.97096i) q^{32} +(-2.07700 + 0.842458i) q^{34} +1.38206 q^{35} +8.55290 q^{37} +(0.411319 - 0.166837i) q^{38} +(1.13984 - 2.58858i) q^{40} -7.54314i q^{41} -6.02836i q^{43} +(9.02879 - 8.76672i) q^{44} +(-0.254365 - 0.627112i) q^{46} +10.5045 q^{47} +5.08990 q^{49} +(0.531562 + 1.31051i) q^{50} +(-7.19017 + 6.98147i) q^{52} +8.86171i q^{53} +6.29235i q^{55} +(-1.57533 + 3.57758i) q^{56} +(2.24557 - 0.910833i) q^{58} +11.9151 q^{59} -5.02092 q^{61} +(12.4231 - 5.03898i) q^{62} +(5.40152 + 5.90115i) q^{64} -5.01098i q^{65} +3.38716i q^{67} +(2.20810 + 2.27411i) q^{68} +(-0.734652 - 1.81121i) q^{70} +14.1414 q^{71} -4.55479 q^{73} +(-4.54639 - 11.2087i) q^{74} +(-0.437283 - 0.450355i) q^{76} -8.69642i q^{77} -2.85998i q^{79} +(-3.99827 - 0.117787i) q^{80} +(-9.88537 + 4.00964i) q^{82} -0.983654 q^{83} -1.58487 q^{85} +(-7.90023 + 3.20444i) q^{86} +(-16.2883 - 7.17229i) q^{88} +2.64810i q^{89} +6.92549i q^{91} +(-0.686628 + 0.666698i) q^{92} +(-5.58379 - 13.7663i) q^{94} +0.313862 q^{95} +10.1449 q^{97} +(-2.70560 - 6.67038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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