LMFDB - Embedded newform 1620.2.e.b.971.44

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:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.44
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32567 + 0.492552i) q^{2} +(1.51479 + 1.30592i) q^{4} -1.00000i q^{5} +3.84799i q^{7} +(1.36487 + 2.47732i) q^{8} +O(q^{10})$	\(q+(1.32567 + 0.492552i) q^{2} +(1.51479 + 1.30592i) q^{4} -1.00000i q^{5} +3.84799i q^{7} +(1.36487 + 2.47732i) q^{8} +(0.492552 - 1.32567i) q^{10} -2.81913 q^{11} -5.79080 q^{13} +(-1.89534 + 5.10116i) q^{14} +(0.589153 + 3.95637i) q^{16} +2.42512i q^{17} +4.07233i q^{19} +(1.30592 - 1.51479i) q^{20} +(-3.73723 - 1.38857i) q^{22} -4.34759 q^{23} -1.00000 q^{25} +(-7.67667 - 2.85227i) q^{26} +(-5.02517 + 5.82889i) q^{28} -7.01227i q^{29} +2.25002i q^{31} +(-1.16770 + 5.53502i) q^{32} +(-1.19450 + 3.21490i) q^{34} +3.84799 q^{35} +4.29414 q^{37} +(-2.00583 + 5.39855i) q^{38} +(2.47732 - 1.36487i) q^{40} -0.109580i q^{41} -0.205995i q^{43} +(-4.27038 - 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +10.7759 q^{47} -7.80706 q^{49} +(-1.32567 - 0.492552i) q^{50} +(-8.77182 - 7.56231i) q^{52} +7.55580i q^{53} +2.81913i q^{55} +(-9.53273 + 5.25201i) q^{56} +(3.45390 - 9.29593i) q^{58} +8.33488 q^{59} +6.12960 q^{61} +(-1.10825 + 2.98277i) q^{62} +(-4.27426 + 6.76245i) q^{64} +5.79080i q^{65} +5.18422i q^{67} +(-3.16701 + 3.67354i) q^{68} +(5.10116 + 1.89534i) q^{70} +5.46464 q^{71} -12.9936 q^{73} +(5.69261 + 2.11509i) q^{74} +(-5.31813 + 6.16871i) q^{76} -10.8480i q^{77} -4.99379i q^{79} +(3.95637 - 0.589153i) q^{80} +(0.0539740 - 0.145267i) q^{82} +7.71433 q^{83} +2.42512 q^{85} +(0.101463 - 0.273080i) q^{86} +(-3.84774 - 6.98389i) q^{88} -0.134752i q^{89} -22.2830i q^{91} +(-6.58567 - 5.67760i) q^{92} +(14.2852 + 5.30767i) q^{94} +4.07233 q^{95} -12.9967 q^{97} +(-10.3496 - 3.84538i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

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 $

$2$	1.32567	+	0.492552i	0.937388	+	0.348287i
$2$	1.32567	+	0.492552i	0.937388	+	0.348287i
$3$		0			0
$3$		0			0
$4$	1.51479	+	1.30592i	0.757393	+	0.652959i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			3.84799i			1.45441i	0.686423	+	0.727203i	$0.259180\pi$
$7$			3.84799i			1.45441i	−0.686423	+	0.727203i	$0.740820\pi$
$8$	1.36487	+	2.47732i	0.482554	+	0.875866i
$9$		0			0
$10$	0.492552	−	1.32567i	0.155758	−	0.419213i
$11$	−2.81913			−0.849999			−0.425000	−	0.905194i	$-0.639726\pi$
$11$	−2.81913			−0.849999			−0.425000	+	0.905194i	$0.639726\pi$
$12$		0			0
$13$	−5.79080			−1.60608			−0.803039	−	0.595926i	$-0.796785\pi$
$13$	−5.79080			−1.60608			−0.803039	+	0.595926i	$0.796785\pi$
$14$	−1.89534	+	5.10116i	−0.506550	+	1.36334i
$15$		0			0
$16$	0.589153	+	3.95637i	0.147288	+	0.989094i
$17$			2.42512i			0.588178i	0.955778	+	0.294089i	$0.0950162\pi$
$17$			2.42512i			0.588178i	−0.955778	+	0.294089i	$0.904984\pi$
$18$		0			0
$19$			4.07233i			0.934256i	0.884190	+	0.467128i	$0.154711\pi$
$19$			4.07233i			0.934256i	−0.884190	+	0.467128i	$0.845289\pi$
$20$	1.30592	−	1.51479i	0.292012	−	0.338716i
$21$		0			0
$22$	−3.73723	−	1.38857i	−0.796779	−	0.296043i
$23$	−4.34759			−0.906535			−0.453267	−	0.891375i	$-0.649742\pi$
$23$	−4.34759			−0.906535			−0.453267	+	0.891375i	$0.649742\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−7.67667	−	2.85227i	−1.50552	−	0.559376i
$27$		0			0
$28$	−5.02517	+	5.82889i	−0.949667	+	1.10156i
$29$		−	7.01227i		−	1.30215i	−0.759015	−	0.651073i	$-0.774319\pi$
$29$		−	7.01227i		−	1.30215i	0.759015	−	0.651073i	$-0.225681\pi$
$30$		0			0
$31$			2.25002i			0.404115i	0.979374	+	0.202058i	$0.0647628\pi$
$31$			2.25002i			0.404115i	−0.979374	+	0.202058i	$0.935237\pi$
$32$	−1.16770	+	5.53502i	−0.206422	+	0.978463i
$33$		0			0
$34$	−1.19450	+	3.21490i	−0.204855	+	0.551351i
$35$	3.84799			0.650430
$36$		0			0
$37$	4.29414			0.705953			0.352976	−	0.935632i	$-0.385170\pi$
$37$	4.29414			0.705953			0.352976	+	0.935632i	$0.385170\pi$
$38$	−2.00583	+	5.39855i	−0.325389	+	0.875761i
$39$		0			0
$40$	2.47732	−	1.36487i	0.391699	−	0.215805i
$41$		−	0.109580i		−	0.0171136i	−0.999963	−	0.00855679i	$-0.997276\pi$
$41$		−	0.109580i		−	0.0171136i	0.999963	−	0.00855679i	$-0.00272374\pi$
$42$		0			0
$43$		−	0.205995i		−	0.0314139i	−0.999877	−	0.0157069i	$-0.995000\pi$
$43$		−	0.205995i		−	0.0314139i	0.999877	−	0.0157069i	$-0.00499988\pi$
$44$	−4.27038	−	3.68155i	−0.643783	−	0.555015i
$45$		0			0
$46$	−5.76345	−	2.14141i	−0.849775	−	0.315734i
$47$	10.7759			1.57182			0.785910	−	0.618340i	$-0.212195\pi$
$47$	10.7759			1.57182			0.785910	+	0.618340i	$0.212195\pi$
$48$		0			0
$49$	−7.80706			−1.11529
$50$	−1.32567	−	0.492552i	−0.187478	−	0.0696573i
$51$		0			0
$52$	−8.77182	−	7.56231i	−1.21643	−	1.04870i
$53$			7.55580i			1.03787i	0.854814	+	0.518934i	$0.173671\pi$
$53$			7.55580i			1.03787i	−0.854814	+	0.518934i	$0.826329\pi$
$54$		0			0
$55$			2.81913i			0.380131i
$56$	−9.53273	+	5.25201i	−1.27386	+	0.701830i
$57$		0			0
$58$	3.45390	−	9.29593i	0.453520	−	1.22062i
$59$	8.33488			1.08511			0.542554	−	0.840021i	$-0.317457\pi$
$59$	8.33488			1.08511			0.542554	+	0.840021i	$0.317457\pi$
$60$		0			0
$61$	6.12960			0.784815			0.392407	−	0.919792i	$-0.371642\pi$
$61$	6.12960			0.784815			0.392407	+	0.919792i	$0.371642\pi$
$62$	−1.10825	+	2.98277i	−0.140748	+	0.378813i
$63$		0			0
$64$	−4.27426	+	6.76245i	−0.534283	+	0.845306i
$65$			5.79080i			0.718260i
$66$		0			0
$67$			5.18422i			0.633353i	0.948534	+	0.316677i	$0.102567\pi$
$67$			5.18422i			0.633353i	−0.948534	+	0.316677i	$0.897433\pi$
$68$	−3.16701	+	3.67354i	−0.384056	+	0.445482i
$69$		0			0
$70$	5.10116	+	1.89534i	0.609705	+	0.226536i
$71$	5.46464			0.648533			0.324267	−	0.945966i	$-0.394882\pi$
$71$	5.46464			0.648533			0.324267	+	0.945966i	$0.394882\pi$
$72$		0			0
$73$	−12.9936			−1.52078			−0.760390	−	0.649466i	$-0.774992\pi$
$73$	−12.9936			−1.52078			−0.760390	+	0.649466i	$0.774992\pi$
$74$	5.69261	+	2.11509i	0.661752	+	0.245874i
$75$		0			0
$76$	−5.31813	+	6.16871i	−0.610031	+	0.707599i
$77$		−	10.8480i		−	1.23624i
$78$		0			0
$79$		−	4.99379i		−	0.561845i	−0.959730	−	0.280923i	$-0.909360\pi$
$79$		−	4.99379i		−	0.561845i	0.959730	−	0.280923i	$-0.0906404\pi$
$80$	3.95637	−	0.589153i	0.442336	−	0.0658694i
$81$		0			0
$82$	0.0539740	−	0.145267i	0.00596043	−	0.0160421i
$83$	7.71433			0.846758			0.423379	−	0.905953i	$-0.360844\pi$
$83$	7.71433			0.846758			0.423379	+	0.905953i	$0.360844\pi$
$84$		0			0
$85$	2.42512			0.263041
$86$	0.101463	−	0.273080i	0.0109410	−	0.0294470i
$87$		0			0
$88$	−3.84774	−	6.98389i	−0.410171	−	0.744485i
$89$		−	0.134752i		−	0.0142837i	−0.999974	−	0.00714184i	$-0.997727\pi$
$89$		−	0.134752i		−	0.0142837i	0.999974	−	0.00714184i	$-0.00227334\pi$
$90$		0			0
$91$		−	22.2830i		−	2.33589i
$92$	−6.58567	−	5.67760i	−0.686603	−	0.591930i
$93$		0			0
$94$	14.2852	+	5.30767i	1.47341	+	0.547444i
$95$	4.07233			0.417812
$96$		0			0
$97$	−12.9967			−1.31961			−0.659806	−	0.751436i	$-0.729362\pi$
$97$	−12.9967			−1.31961			−0.659806	+	0.751436i	$0.729362\pi$
$98$	−10.3496	−	3.84538i	−1.04546	−	0.388442i
$99$		0			0
$100$	−1.51479	−	1.30592i	−0.151479	−	0.130592i
$101$			3.35857i			0.334190i	0.985941	+	0.167095i	$0.0534386\pi$
$101$			3.35857i			0.334190i	−0.985941	+	0.167095i	$0.946561\pi$
$102$		0			0
$103$			3.83768i			0.378138i	0.981964	+	0.189069i	$0.0605469\pi$
$103$			3.83768i			0.378138i	−0.981964	+	0.189069i	$0.939453\pi$
$104$	−7.90369	−	14.3457i	−0.775020	−	1.40671i
$105$		0			0
$106$	−3.72162	+	10.0165i	−0.361476	+	0.972886i
$107$	0.556704			0.0538186			0.0269093	−	0.999638i	$-0.491433\pi$
$107$	0.556704			0.0538186			0.0269093	+	0.999638i	$0.491433\pi$
$108$		0			0
$109$	15.5306			1.48756			0.743779	−	0.668425i	$-0.233031\pi$
$109$	15.5306			1.48756			0.743779	+	0.668425i	$0.233031\pi$
$110$	−1.38857	+	3.73723i	−0.132395	+	0.356330i
$111$		0			0
$112$	−15.2241	+	2.26706i	−1.43854	+	0.214217i
$113$			7.58559i			0.713593i	0.934182	+	0.356796i	$0.116131\pi$
$113$			7.58559i			0.713593i	−0.934182	+	0.356796i	$0.883869\pi$
$114$		0			0
$115$			4.34759i			0.405415i
$116$	9.15745	−	10.6221i	0.850248	−	0.986236i
$117$		0			0
$118$	11.0493	+	4.10536i	1.01717	+	0.377929i
$119$	−9.33185			−0.855449
$120$		0			0
$121$	−3.05252			−0.277501
$122$	8.12581	+	3.01914i	0.735676	+	0.273340i
$123$		0			0
$124$	−2.93834	+	3.40830i	−0.263871	+	0.306074i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			18.5602i			1.64695i	0.567352	+	0.823476i	$0.307968\pi$
$127$			18.5602i			1.64695i	−0.567352	+	0.823476i	$0.692032\pi$
$128$	−8.99710	+	6.85946i	−0.795239	+	0.606296i
$129$		0			0
$130$	−2.85227	+	7.67667i	−0.250160	+	0.673289i
$131$	9.50661			0.830596			0.415298	−	0.909685i	$-0.363677\pi$
$131$	9.50661			0.830596			0.415298	+	0.909685i	$0.363677\pi$
$132$		0			0
$133$	−15.6703			−1.35879
$134$	−2.55350	+	6.87255i	−0.220588	+	0.593698i
$135$		0			0
$136$	−6.00781	+	3.30997i	−0.515165	+	0.283828i
$137$			0.800850i			0.0684212i	0.999415	+	0.0342106i	$0.0108917\pi$
$137$			0.800850i			0.0684212i	−0.999415	+	0.0342106i	$0.989108\pi$
$138$		0			0
$139$			7.30260i			0.619398i	0.950835	+	0.309699i	$0.100228\pi$
$139$			7.30260i			0.619398i	−0.950835	+	0.309699i	$0.899772\pi$
$140$	5.82889	+	5.02517i	0.492631	+	0.424704i
$141$		0			0
$142$	7.24429	+	2.69162i	0.607928	+	0.225875i
$143$	16.3250			1.36517
$144$		0			0
$145$	−7.01227			−0.582337
$146$	−17.2251	−	6.40000i	−1.42556	−	0.529667i
$147$		0			0
$148$	6.50471	+	5.60780i	0.534684	+	0.460959i
$149$		−	0.113818i		−	0.00932437i	−0.999989	−	0.00466219i	$-0.998516\pi$
$149$		−	0.113818i		−	0.00932437i	0.999989	−	0.00466219i	$-0.00148403\pi$
$150$		0			0
$151$			1.69619i			0.138034i	0.997615	+	0.0690169i	$0.0219862\pi$
$151$			1.69619i			0.138034i	−0.997615	+	0.0690169i	$0.978014\pi$
$152$	−10.0885	+	5.55820i	−0.818283	+	0.450829i
$153$		0			0
$154$	5.34319	−	14.3808i	0.430567	−	1.15884i
$155$	2.25002			0.180726
$156$		0			0
$157$	22.4941			1.79522			0.897612	−	0.440787i	$-0.145301\pi$
$157$	22.4941			1.79522			0.897612	+	0.440787i	$0.145301\pi$
$158$	2.45970	−	6.62010i	0.195683	−	0.526667i
$159$		0			0
$160$	5.53502	+	1.16770i	0.437582	+	0.0923146i
$161$		−	16.7295i		−	1.31847i
$162$		0			0
$163$		−	1.64377i		−	0.128750i	−0.997926	−	0.0643749i	$-0.979495\pi$
$163$		−	1.64377i		−	0.128750i	0.997926	−	0.0643749i	$-0.0205054\pi$
$164$	0.143103	−	0.165991i	0.0111745	−	0.0129617i
$165$		0			0
$166$	10.2266	+	3.79970i	0.793741	+	0.294914i
$167$	2.43870			0.188712			0.0943561	−	0.995539i	$-0.469921\pi$
$167$	2.43870			0.188712			0.0943561	+	0.995539i	$0.469921\pi$
$168$		0			0
$169$	20.5334			1.57949
$170$	3.21490	+	1.19450i	0.246572	+	0.0916137i
$171$		0			0
$172$	0.269012	−	0.312038i	0.0205120	−	0.0237927i
$173$		−	10.5585i		−	0.802747i	−0.915914	−	0.401374i	$-0.868533\pi$
$173$		−	10.5585i		−	0.802747i	0.915914	−	0.401374i	$-0.131467\pi$
$174$		0			0
$175$		−	3.84799i		−	0.290881i
$176$	−1.66090	−	11.1535i	−0.125195	−	0.840729i
$177$		0			0
$178$	0.0663723	−	0.178636i	0.00497481	−	0.0133894i
$179$	3.01061			0.225023			0.112512	−	0.993650i	$-0.464110\pi$
$179$	3.01061			0.225023			0.112512	+	0.993650i	$0.464110\pi$
$180$		0			0
$181$	−19.5270			−1.45143			−0.725715	−	0.687996i	$-0.758491\pi$
$181$	−19.5270			−1.45143			−0.725715	+	0.687996i	$0.758491\pi$
$182$	10.9755	−	29.5398i	0.813559	−	2.18964i
$183$		0			0
$184$	−5.93389	−	10.7704i	−0.437452	−	0.794003i
$185$		−	4.29414i		−	0.315712i
$186$		0			0
$187$		−	6.83673i		−	0.499951i
$188$	16.3231	+	14.0724i	1.19049	+	1.02633i
$189$		0			0
$190$	5.39855	+	2.00583i	0.391652	+	0.145518i
$191$	0.964171			0.0697650			0.0348825	−	0.999391i	$-0.488894\pi$
$191$	0.964171			0.0697650			0.0348825	+	0.999391i	$0.488894\pi$
$192$		0			0
$193$	−15.9934			−1.15123			−0.575615	−	0.817721i	$-0.695237\pi$
$193$	−15.9934			−1.15123			−0.575615	+	0.817721i	$0.695237\pi$
$194$	−17.2293	−	6.40153i	−1.23699	−	0.459603i
$195$		0			0
$196$	−11.8260	−	10.1954i	−0.844716	−	0.728242i
$197$		−	26.0766i		−	1.85788i	−0.370233	−	0.928939i	$-0.620722\pi$
$197$		−	26.0766i		−	1.85788i	0.370233	−	0.928939i	$-0.379278\pi$
$198$		0			0
$199$			16.6714i			1.18181i	0.806743	+	0.590903i	$0.201228\pi$
$199$			16.6714i			1.18181i	−0.806743	+	0.590903i	$0.798772\pi$
$200$	−1.36487	−	2.47732i	−0.0965109	−	0.175173i
$201$		0			0
$202$	−1.65427	+	4.45234i	−0.116394	+	0.313266i
$203$	26.9832			1.89385
$204$		0			0
$205$	−0.109580			−0.00765342
$206$	−1.89025	+	5.08748i	−0.131700	+	0.354462i
$207$		0			0
$208$	−3.41167	−	22.9106i	−0.236557	−	1.58856i
$209$		−	11.4804i		−	0.794117i
$210$		0			0
$211$		−	21.8675i		−	1.50542i	−0.658353	−	0.752709i	$-0.728747\pi$
$211$		−	21.8675i		−	1.50542i	0.658353	−	0.752709i	$-0.271253\pi$
$212$	−9.86726	+	11.4454i	−0.677686	+	0.786075i
$213$		0			0
$214$	0.738004	+	0.274205i	0.0504489	+	0.0187443i
$215$	−0.205995			−0.0140487
$216$		0			0
$217$	−8.65806			−0.587747
$218$	20.5884	+	7.64960i	1.39442	+	0.518097i
$219$		0			0
$220$	−3.68155	+	4.27038i	−0.248210	+	0.287909i
$221$		−	14.0434i		−	0.944660i
$222$		0			0
$223$			2.46864i			0.165313i	0.996578	+	0.0826563i	$0.0263404\pi$
$223$			2.46864i			0.165313i	−0.996578	+	0.0826563i	$0.973660\pi$
$224$	−21.2987	−	4.49329i	−1.42308	−	0.300221i
$225$		0			0
$226$	−3.73630	+	10.0560i	−0.248535	+	0.668913i
$227$	9.02512			0.599018			0.299509	−	0.954093i	$-0.403177\pi$
$227$	9.02512			0.599018			0.299509	+	0.954093i	$0.403177\pi$
$228$		0			0
$229$	12.1010			0.799655			0.399827	−	0.916590i	$-0.369070\pi$
$229$	12.1010			0.799655			0.399827	+	0.916590i	$0.369070\pi$
$230$	−2.14141	+	5.76345i	−0.141200	+	0.380031i
$231$		0			0
$232$	17.3717	−	9.57083i	1.14051	−	0.628356i
$233$		−	12.9280i		−	0.846943i	−0.905909	−	0.423471i	$-0.860811\pi$
$233$		−	12.9280i		−	0.846943i	0.905909	−	0.423471i	$-0.139189\pi$
$234$		0			0
$235$		−	10.7759i		−	0.702940i
$236$	12.6256	+	10.8847i	0.821854	+	0.708532i
$237$		0			0
$238$	−12.3709	−	4.59642i	−0.801888	−	0.297941i
$239$	−9.16203			−0.592642			−0.296321	−	0.955088i	$-0.595760\pi$
$239$	−9.16203			−0.592642			−0.296321	+	0.955088i	$0.595760\pi$
$240$		0			0
$241$	−10.5996			−0.682783			−0.341391	−	0.939921i	$-0.610898\pi$
$241$	−10.5996			−0.682783			−0.341391	+	0.939921i	$0.610898\pi$
$242$	−4.04662	−	1.50352i	−0.260127	−	0.0966500i
$243$		0			0
$244$	9.28503	+	8.00476i	0.594413	+	0.512452i
$245$			7.80706i			0.498775i
$246$		0			0
$247$		−	23.5820i		−	1.50049i
$248$	−5.57402	+	3.07098i	−0.353951	+	0.195008i
$249$		0			0
$250$	−0.492552	+	1.32567i	−0.0311517	+	0.0838425i
$251$	−10.2219			−0.645198			−0.322599	−	0.946536i	$-0.604557\pi$
$251$	−10.2219			−0.645198			−0.322599	+	0.946536i	$0.604557\pi$
$252$		0			0
$253$	12.2564			0.770554
$254$	−9.14185	+	24.6046i	−0.573611	+	1.54383i
$255$		0			0
$256$	−15.3058	+	4.66182i	−0.956612	+	0.291364i
$257$		−	6.44695i		−	0.402150i	−0.979576	−	0.201075i	$-0.935557\pi$
$257$		−	6.44695i		−	0.402150i	0.979576	−	0.201075i	$-0.0644435\pi$
$258$		0			0
$259$			16.5238i			1.02674i
$260$	−7.56231	+	8.77182i	−0.468995	+	0.544005i
$261$		0			0
$262$	12.6026	+	4.68249i	0.778591	+	0.289285i
$263$	18.1345			1.11822			0.559112	−	0.829092i	$-0.311142\pi$
$263$	18.1345			1.11822			0.559112	+	0.829092i	$0.311142\pi$
$264$		0			0
$265$	7.55580			0.464149
$266$	−20.7736	−	7.71843i	−1.27371	−	0.473247i
$267$		0			0
$268$	−6.77017	+	7.85298i	−0.413554	+	0.479697i
$269$			3.40907i			0.207854i	0.994585	+	0.103927i	$0.0331409\pi$
$269$			3.40907i			0.207854i	−0.994585	+	0.103927i	$0.966859\pi$
$270$		0			0
$271$			8.61740i			0.523470i	0.965140	+	0.261735i	$0.0842946\pi$
$271$			8.61740i			0.523470i	−0.965140	+	0.261735i	$0.915705\pi$
$272$	−9.59469	+	1.42877i	−0.581763	+	0.0866318i
$273$		0			0
$274$	−0.394460	+	1.06166i	−0.0238302	+	0.0641372i
$275$	2.81913			0.170000
$276$		0			0
$277$	7.22084			0.433858			0.216929	−	0.976187i	$-0.430396\pi$
$277$	7.22084			0.433858			0.216929	+	0.976187i	$0.430396\pi$
$278$	−3.59691	+	9.68081i	−0.215728	+	0.580617i
$279$		0			0
$280$	5.25201	+	9.53273i	0.313868	+	0.569689i
$281$		−	27.3561i		−	1.63193i	−0.578102	−	0.815964i	$-0.696207\pi$
$281$		−	27.3561i		−	1.63193i	0.578102	−	0.815964i	$-0.303793\pi$
$282$		0			0
$283$			5.39257i			0.320555i	0.987072	+	0.160277i	$0.0512389\pi$
$283$			5.39257i			0.320555i	−0.987072	+	0.160277i	$0.948761\pi$
$284$	8.27776	+	7.13638i	0.491195	+	0.423466i
$285$		0			0
$286$	21.6415	+	8.04091i	1.27969	+	0.475469i
$287$	0.421665			0.0248901
$288$		0			0
$289$	11.1188			0.654046
$290$	−9.29593	−	3.45390i	−0.545876	−	0.202820i
$291$		0			0
$292$	−19.6825	−	16.9685i	−1.15183	−	0.993008i
$293$			17.8671i			1.04381i	0.853004	+	0.521904i	$0.174778\pi$
$293$			17.8671i			1.04381i	−0.853004	+	0.521904i	$0.825222\pi$
$294$		0			0
$295$		−	8.33488i		−	0.485275i
$296$	5.86095	+	10.6380i	0.340661	+	0.618320i
$297$		0			0
$298$	0.0560615	−	0.150885i	0.00324755	−	0.00874056i
$299$	25.1760			1.45597
$300$		0			0
$301$	0.792666			0.0456885
$302$	−0.835459	+	2.24858i	−0.0480753	+	0.129391i
$303$		0			0
$304$	−16.1117	+	2.39923i	−0.924067	+	0.137605i
$305$		−	6.12960i		−	0.350980i
$306$		0			0
$307$		−	5.37209i		−	0.306601i	−0.988180	−	0.153301i	$-0.951010\pi$
$307$		−	5.37209i		−	0.306601i	0.988180	−	0.153301i	$-0.0489903\pi$
$308$	14.1666	−	16.4324i	0.807217	−	0.936322i
$309$		0			0
$310$	2.98277	+	1.10825i	0.169410	+	0.0629444i
$311$	−30.3174			−1.71914			−0.859572	−	0.511015i	$-0.829270\pi$
$311$	−30.3174			−1.71914			−0.859572	+	0.511015i	$0.829270\pi$
$312$		0			0
$313$	24.7176			1.39712			0.698561	−	0.715551i	$-0.253824\pi$
$313$	24.7176			1.39712			0.698561	+	0.715551i	$0.253824\pi$
$314$	29.8197	+	11.0795i	1.68282	+	0.625252i
$315$		0			0
$316$	6.52148	−	7.56452i	0.366862	−	0.425537i
$317$			24.3998i			1.37043i	0.728341	+	0.685215i	$0.240292\pi$
$317$			24.3998i			1.37043i	−0.728341	+	0.685215i	$0.759708\pi$
$318$		0			0
$319$			19.7685i			1.10682i
$320$	6.76245	+	4.27426i	0.378032	+	0.238938i
$321$		0			0
$322$	8.24014	−	22.1777i	0.459205	−	1.23592i
$323$	−9.87589			−0.549509
$324$		0			0
$325$	5.79080			0.321216
$326$	0.809640	−	2.17909i	0.0448418	−	0.120689i
$327$		0			0
$328$	0.271466	−	0.149563i	0.0149892	−	0.00825823i
$329$			41.4655i			2.28606i
$330$		0			0
$331$		−	28.2153i		−	1.55085i	−0.631439	−	0.775426i	$-0.717535\pi$
$331$		−	28.2153i		−	1.55085i	0.631439	−	0.775426i	$-0.282465\pi$
$332$	11.6856	+	10.0743i	0.641328	+	0.552898i
$333$		0			0
$334$	3.23290	+	1.20119i	0.176897	+	0.0657259i
$335$	5.18422			0.283244
$336$		0			0
$337$	28.6415			1.56020			0.780101	−	0.625653i	$-0.215167\pi$
$337$	28.6415			1.56020			0.780101	+	0.625653i	$0.215167\pi$
$338$	27.2204	+	10.1137i	1.48059	+	0.550115i
$339$		0			0
$340$	3.67354	+	3.16701i	0.199226	+	0.171755i
$341$		−	6.34309i		−	0.343498i
$342$		0			0
$343$		−	3.10557i		−	0.167685i
$344$	0.510315	−	0.281156i	0.0275144	−	0.0151589i
$345$		0			0
$346$	5.20060	−	13.9970i	0.279586	−	0.752486i
$347$	−20.8971			−1.12181			−0.560907	−	0.827879i	$-0.689548\pi$
$347$	−20.8971			−1.12181			−0.560907	+	0.827879i	$0.689548\pi$
$348$		0			0
$349$	13.0124			0.696537			0.348269	−	0.937395i	$-0.386770\pi$
$349$	13.0124			0.696537			0.348269	+	0.937395i	$0.386770\pi$
$350$	1.89534	−	5.10116i	0.101310	−	0.272668i
$351$		0			0
$352$	3.29189	−	15.6039i	0.175458	−	0.831693i
$353$			28.4548i			1.51450i	0.653126	+	0.757249i	$0.273457\pi$
$353$			28.4548i			1.51450i	−0.653126	+	0.757249i	$0.726543\pi$
$354$		0			0
$355$		−	5.46464i		−	0.290033i
$356$	0.175975	−	0.204120i	0.00932666	−	0.0108184i
$357$		0			0
$358$	3.99106	+	1.48288i	0.210934	+	0.0783726i
$359$	−5.90878			−0.311854			−0.155927	−	0.987769i	$-0.549836\pi$
$359$	−5.90878			−0.311854			−0.155927	+	0.987769i	$0.549836\pi$
$360$		0			0
$361$	2.41614			0.127165
$362$	−25.8863	−	9.61805i	−1.36055	−	0.505513i
$363$		0			0
$364$	29.0997	−	33.7539i	1.52524	−	1.76919i
$365$			12.9936i			0.680114i
$366$		0			0
$367$			24.2273i			1.26465i	0.774701	+	0.632327i	$0.217900\pi$
$367$			24.2273i			1.26465i	−0.774701	+	0.632327i	$0.782100\pi$
$368$	−2.56140	−	17.2007i	−0.133522	−	0.896648i
$369$		0			0
$370$	2.11509	−	5.69261i	0.109958	−	0.295944i
$371$	−29.0747			−1.50948
$372$		0			0
$373$	7.57980			0.392467			0.196234	−	0.980557i	$-0.437129\pi$
$373$	7.57980			0.392467			0.196234	+	0.980557i	$0.437129\pi$
$374$	3.36744	−	9.06322i	0.174126	−	0.468648i
$375$		0			0
$376$	14.7076	+	26.6953i	0.758489	+	1.37670i
$377$			40.6066i			2.09135i
$378$		0			0
$379$		−	27.0962i		−	1.39184i	−0.718120	−	0.695919i	$-0.754997\pi$
$379$		−	27.0962i		−	1.39184i	0.718120	−	0.695919i	$-0.245003\pi$
$380$	6.16871	+	5.31813i	0.316448	+	0.272814i
$381$		0			0
$382$	1.27817	+	0.474904i	0.0653969	+	0.0242982i
$383$	26.4267			1.35034			0.675171	−	0.737661i	$-0.264070\pi$
$383$	26.4267			1.35034			0.675171	+	0.737661i	$0.264070\pi$
$384$		0			0
$385$	−10.8480			−0.552865
$386$	−21.2019	−	7.87758i	−1.07915	−	0.400958i
$387$		0			0
$388$	−19.6872	−	16.9726i	−0.999465	−	0.861653i
$389$		−	20.4623i		−	1.03748i	−0.854933	−	0.518739i	$-0.826402\pi$
$389$		−	20.4623i		−	1.03748i	0.854933	−	0.518739i	$-0.173598\pi$
$390$		0			0
$391$		−	10.5434i		−	0.533204i
$392$	−10.6556	−	19.3406i	−0.538190	−	0.976849i
$393$		0			0
$394$	12.8440	−	34.5688i	0.647074	−	1.74155i
$395$	−4.99379			−0.251265
$396$		0			0
$397$	−0.127520			−0.00640003			−0.00320001	−	0.999995i	$-0.501019\pi$
$397$	−0.127520			−0.00640003			−0.00320001	+	0.999995i	$0.501019\pi$
$398$	−8.21153	+	22.1007i	−0.411607	+	1.10781i
$399$		0			0
$400$	−0.589153	−	3.95637i	−0.0294577	−	0.197819i
$401$		−	14.8379i		−	0.740969i	−0.928839	−	0.370484i	$-0.879192\pi$
$401$		−	14.8379i		−	0.740969i	0.928839	−	0.370484i	$-0.120808\pi$
$402$		0			0
$403$		−	13.0294i		−	0.649041i
$404$	−4.38601	+	5.08751i	−0.218212	+	0.253113i
$405$		0			0
$406$	35.7707	+	13.2906i	1.77527	+	0.659602i
$407$	−12.1057			−0.600059
$408$		0			0
$409$	−14.7314			−0.728421			−0.364210	−	0.931317i	$-0.618661\pi$
$409$	−14.7314			−0.728421			−0.364210	+	0.931317i	$0.618661\pi$
$410$	−0.145267	−	0.0539740i	−0.00717423	−	0.00266558i
$411$		0			0
$412$	−5.01169	+	5.81326i	−0.246908	+	0.286399i
$413$			32.0726i			1.57819i
$414$		0			0
$415$		−	7.71433i		−	0.378682i
$416$	6.76190	−	32.0522i	0.331529	−	1.57149i
$417$		0			0
$418$	5.65470	−	15.2192i	0.276580	−	0.744396i
$419$	11.2753			0.550834			0.275417	−	0.961325i	$-0.411184\pi$
$419$	11.2753			0.550834			0.275417	+	0.961325i	$0.411184\pi$
$420$		0			0
$421$	−0.0355167			−0.00173098			−0.000865488	−	1.00000i	$-0.500275\pi$
$421$	−0.0355167			−0.00173098			−0.000865488		1.00000i	$0.500275\pi$
$422$	10.7709	−	28.9890i	0.524317	−	1.41116i
$423$		0			0
$424$	−18.7182	+	10.3127i	−0.909034	+	0.500828i
$425$		−	2.42512i		−	0.117636i
$426$		0			0
$427$			23.5867i			1.14144i
$428$	0.843287	+	0.727010i	0.0407618	+	0.0351414i
$429$		0			0
$430$	−0.273080	−	0.101463i	−0.0131691	−	0.00489298i
$431$	17.3085			0.833722			0.416861	−	0.908970i	$-0.363130\pi$
$431$	17.3085			0.833722			0.416861	+	0.908970i	$0.363130\pi$
$432$		0			0
$433$	16.3482			0.785642			0.392821	−	0.919615i	$-0.371499\pi$
$433$	16.3482			0.785642			0.392821	+	0.919615i	$0.371499\pi$
$434$	−11.4777	−	4.26454i	−0.550947	−	0.204704i
$435$		0			0
$436$	23.5255	+	20.2817i	1.12667	+	0.971315i
$437$		−	17.7048i		−	0.846936i
$438$		0			0
$439$			11.3220i			0.540369i	0.962809	+	0.270184i	$0.0870846\pi$
$439$			11.3220i			0.540369i	−0.962809	+	0.270184i	$0.912915\pi$
$440$	−6.98389	+	3.84774i	−0.332944	+	0.183434i
$441$		0			0
$442$	6.91709	−	18.6169i	0.329013	−	0.885514i
$443$	−36.0068			−1.71074			−0.855368	−	0.518021i	$-0.826669\pi$
$443$	−36.0068			−1.71074			−0.855368	+	0.518021i	$0.826669\pi$
$444$		0			0
$445$	−0.134752			−0.00638786
$446$	−1.21593	+	3.27260i	−0.0575761	+	0.154962i
$447$		0			0
$448$	−26.0219	−	16.4473i	−1.22942	−	0.777064i
$449$		−	0.577403i		−	0.0272493i	−0.999907	−	0.0136247i	$-0.995663\pi$
$449$		−	0.577403i		−	0.0272493i	0.999907	−	0.0136247i	$-0.00433700\pi$
$450$		0			0
$451$			0.308921i			0.0145465i
$452$	−9.90617	+	11.4906i	−0.465947	+	0.540470i
$453$		0			0
$454$	11.9643	+	4.44534i	0.561513	+	0.208630i
$455$	−22.2830			−1.04464
$456$		0			0
$457$	−23.2709			−1.08857			−0.544283	−	0.838901i	$-0.683198\pi$
$457$	−23.2709			−1.08857			−0.544283	+	0.838901i	$0.683198\pi$
$458$	16.0419	+	5.96035i	0.749587	+	0.278509i
$459$		0			0
$460$	−5.67760	+	6.58567i	−0.264719	+	0.307058i
$461$			7.93306i			0.369480i	0.982787	+	0.184740i	$0.0591442\pi$
$461$			7.93306i			0.369480i	−0.982787	+	0.184740i	$0.940856\pi$
$462$		0			0
$463$		−	31.1666i		−	1.44843i	−0.689573	−	0.724216i	$-0.742202\pi$
$463$		−	31.1666i		−	1.44843i	0.689573	−	0.724216i	$-0.257798\pi$
$464$	27.7432	−	4.13130i	1.28794	−	0.191791i
$465$		0			0
$466$	6.36772	−	17.1383i	0.294979	−	0.793914i
$467$	−28.3340			−1.31114			−0.655571	−	0.755133i	$-0.727572\pi$
$467$	−28.3340			−1.31114			−0.655571	+	0.755133i	$0.727572\pi$
$468$		0			0
$469$	−19.9488			−0.921152
$470$	5.30767	−	14.2852i	0.244824	−	0.658927i
$471$		0			0
$472$	11.3760	+	20.6482i	0.523624	+	0.950410i
$473$			0.580725i			0.0267018i
$474$		0			0
$475$		−	4.07233i		−	0.186851i
$476$	−14.1358	−	12.1866i	−0.647911	−	0.558574i
$477$		0			0
$478$	−12.1458	−	4.51277i	−0.555536	−	0.206409i
$479$	−24.4644			−1.11781			−0.558904	−	0.829233i	$-0.688778\pi$
$479$	−24.4644			−1.11781			−0.558904	+	0.829233i	$0.688778\pi$
$480$		0			0
$481$	−24.8665			−1.13382
$482$	−14.0516	−	5.22087i	−0.640032	−	0.237804i
$483$		0			0
$484$	−4.62391	−	3.98634i	−0.210178	−	0.181197i
$485$			12.9967i			0.590149i
$486$		0			0
$487$			4.05853i			0.183909i	0.995763	+	0.0919547i	$0.0293115\pi$
$487$			4.05853i			0.183909i	−0.995763	+	0.0919547i	$0.970688\pi$
$488$	8.36610	+	15.1850i	0.378716	+	0.687393i
$489$		0			0
$490$	−3.84538	+	10.3496i	−0.173717	+	0.467546i
$491$	16.5608			0.747379			0.373689	−	0.927554i	$-0.378093\pi$
$491$	16.5608			0.747379			0.373689	+	0.927554i	$0.378093\pi$
$492$		0			0
$493$	17.0056			0.765894
$494$	11.6154	−	31.2619i	0.522600	−	1.40654i
$495$		0			0
$496$	−8.90191	+	1.32561i	−0.399708	+	0.0595215i
$497$			21.0279i			0.943231i
$498$		0			0
$499$			20.1173i			0.900573i	0.892884	+	0.450287i	$0.148678\pi$
$499$			20.1173i			0.900573i	−0.892884	+	0.450287i	$0.851322\pi$
$500$	−1.30592	+	1.51479i	−0.0584025	+	0.0677433i
$501$		0			0
$502$	−13.5508	−	5.03480i	−0.604801	−	0.224714i
$503$	21.9942			0.980674			0.490337	−	0.871533i	$-0.336874\pi$
$503$	21.9942			0.980674			0.490337	+	0.871533i	$0.336874\pi$
$504$		0			0
$505$	3.35857			0.149454
$506$	16.2479	+	6.03691i	0.722308	+	0.268373i
$507$		0			0
$508$	−24.2381	+	28.1147i	−1.07539	+	1.24739i
$509$		−	22.2512i		−	0.986269i	−0.869953	−	0.493134i	$-0.835851\pi$
$509$		−	22.2512i		−	0.986269i	0.869953	−	0.493134i	$-0.164149\pi$
$510$		0			0
$511$		−	49.9991i		−	2.21183i
$512$	−22.5866	−	1.35887i	−0.998195	−	0.0600541i
$513$		0			0
$514$	3.17546	−	8.54651i	0.140063	−	0.376970i
$515$	3.83768			0.169108
$516$		0			0
$517$	−30.3785			−1.33605
$518$	−8.13884	+	21.9051i	−0.357600	+	0.962456i
$519$		0			0
$520$	−14.3457	+	7.90369i	−0.629100	+	0.346600i
$521$			18.5073i			0.810820i	0.914135	+	0.405410i	$0.132871\pi$
$521$			18.5073i			0.810820i	−0.914135	+	0.405410i	$0.867129\pi$
$522$		0			0
$523$			0.982630i			0.0429674i	0.999769	+	0.0214837i	$0.00683900\pi$
$523$			0.982630i			0.0429674i	−0.999769	+	0.0214837i	$0.993161\pi$
$524$	14.4005	+	12.4149i	0.629088	+	0.542345i
$525$		0			0
$526$	24.0403	+	8.93219i	1.04821	+	0.389462i
$527$	−5.45657			−0.237692
$528$		0			0
$529$	−4.09848			−0.178195
$530$	10.0165	+	3.72162i	0.435088	+	0.161657i
$531$		0			0
$532$	−23.7371	−	20.4641i	−1.02914	−	0.887233i
$533$			0.634558i			0.0274857i
$534$		0			0
$535$		−	0.556704i		−	0.0240684i
$536$	−12.8430	+	7.07578i	−0.554733	+	0.305627i
$537$		0			0
$538$	−1.67914	+	4.51929i	−0.0723929	+	0.194840i
$539$	22.0091			0.948000
$540$		0			0
$541$	27.5892			1.18615			0.593077	−	0.805146i	$-0.297913\pi$
$541$	27.5892			1.18615			0.593077	+	0.805146i	$0.297913\pi$
$542$	−4.24451	+	11.4238i	−0.182317	+	0.490694i
$543$		0			0
$544$	−13.4231	−	2.83181i	−0.575511	−	0.121413i
$545$		−	15.5306i		−	0.665256i
$546$		0			0
$547$			46.1910i			1.97498i	0.157671	+	0.987492i	$0.449601\pi$
$547$			46.1910i			1.97498i	−0.157671	+	0.987492i	$0.550399\pi$
$548$	−1.04584	+	1.21312i	−0.0446763	+	0.0518218i
$549$		0			0
$550$	3.73723	+	1.38857i	0.159356	+	0.0592086i
$551$	28.5563			1.21654
$552$		0			0
$553$	19.2161			0.817150
$554$	9.57243	+	3.55664i	0.406694	+	0.151107i
$555$		0			0
$556$	−9.53660	+	11.0619i	−0.404442	+	0.469128i
$557$		−	44.3389i		−	1.87870i	−0.342960	−	0.939350i	$-0.611429\pi$
$557$		−	44.3389i		−	1.87870i	0.342960	−	0.939350i	$-0.388571\pi$
$558$		0			0
$559$			1.19287i			0.0504532i
$560$	2.26706	+	15.2241i	0.0958007	+	0.643336i
$561$		0			0
$562$	13.4743	−	36.2651i	0.568379	−	1.52975i
$563$	−28.2699			−1.19143			−0.595717	−	0.803195i	$-0.703132\pi$
$563$	−28.2699			−1.19143			−0.595717	+	0.803195i	$0.703132\pi$
$564$		0			0
$565$	7.58559			0.319128
$566$	−2.65612	+	7.14875i	−0.111645	+	0.300484i
$567$		0			0
$568$	7.45852	+	13.5377i	0.312953	+	0.568028i
$569$			26.4300i			1.10801i	0.832515	+	0.554003i	$0.186900\pi$
$569$			26.4300i			1.10801i	−0.832515	+	0.554003i	$0.813100\pi$
$570$		0			0
$571$		−	16.9338i		−	0.708657i	−0.935121	−	0.354329i	$-0.884709\pi$
$571$		−	16.9338i		−	0.708657i	0.935121	−	0.354329i	$-0.115291\pi$
$572$	24.7289	+	21.3191i	1.03397	+	0.891398i
$573$		0			0
$574$	0.558987	+	0.207692i	0.0233317	+	0.00866888i
$575$	4.34759			0.181307
$576$		0			0
$577$	7.68326			0.319858			0.159929	−	0.987129i	$-0.448873\pi$
$577$	7.68326			0.319858			0.159929	+	0.987129i	$0.448873\pi$
$578$	14.7398	+	5.47658i	0.613095	+	0.227796i
$579$		0			0
$580$	−10.6221	−	9.15745i	−0.441058	−	0.380243i
$581$			29.6847i			1.23153i
$582$		0			0
$583$		−	21.3008i		−	0.882188i
$584$	−17.7345	−	32.1892i	−0.733859	−	1.33200i
$585$		0			0
$586$	−8.80047	+	23.6858i	−0.363544	+	0.978452i
$587$	−36.3907			−1.50201			−0.751003	−	0.660299i	$-0.770430\pi$
$587$	−36.3907			−1.50201			−0.751003	+	0.660299i	$0.770430\pi$
$588$		0			0
$589$	−9.16281			−0.377547
$590$	4.10536	−	11.0493i	0.169015	−	0.454891i
$591$		0			0
$592$	2.52991	+	16.9892i	0.103979	+	0.698254i
$593$			21.9804i			0.902628i	0.892365	+	0.451314i	$0.149045\pi$
$593$			21.9804i			0.902628i	−0.892365	+	0.451314i	$0.850955\pi$
$594$		0			0
$595$			9.33185i			0.382569i
$596$	0.148638	−	0.172411i	0.00608844	−	0.00706222i
$597$		0			0
$598$	33.3750	+	12.4005i	1.36481	+	0.507093i
$599$	−13.4376			−0.549044			−0.274522	−	0.961581i	$-0.588520\pi$
$599$	−13.4376			−0.549044			−0.274522	+	0.961581i	$0.588520\pi$
$600$		0			0
$601$	−37.3846			−1.52495			−0.762475	−	0.647018i	$-0.776016\pi$
$601$	−37.3846			−1.52495			−0.762475	+	0.647018i	$0.776016\pi$
$602$	1.05081	+	0.390429i	0.0428279	+	0.0159127i
$603$		0			0
$604$	−2.21508	+	2.56936i	−0.0901304	+	0.104546i
$605$			3.05252i			0.124102i
$606$		0			0
$607$			47.6499i			1.93405i	0.254680	+	0.967025i	$0.418030\pi$
$607$			47.6499i			1.93405i	−0.254680	+	0.967025i	$0.581970\pi$
$608$	−22.5404	−	4.75525i	−0.914135	−	0.192851i
$609$		0			0
$610$	3.01914	−	8.12581i	0.122242	−	0.329004i
$611$	−62.4008			−2.52447
$612$		0			0
$613$	23.4840			0.948509			0.474254	−	0.880388i	$-0.342718\pi$
$613$	23.4840			0.948509			0.474254	+	0.880388i	$0.342718\pi$
$614$	2.64603	−	7.12160i	0.106785	−	0.287404i
$615$		0			0
$616$	26.8740	−	14.8061i	1.08278	−	0.596555i
$617$		−	22.9327i		−	0.923237i	−0.887078	−	0.461619i	$-0.847269\pi$
$617$		−	22.9327i		−	0.923237i	0.887078	−	0.461619i	$-0.152731\pi$
$618$		0			0
$619$		−	26.1177i		−	1.04976i	−0.851177	−	0.524878i	$-0.824111\pi$
$619$		−	26.1177i		−	1.04976i	0.851177	−	0.524878i	$-0.175889\pi$
$620$	3.40830	+	2.93834i	0.136880	+	0.118007i
$621$		0			0
$622$	−40.1908	−	14.9329i	−1.61150	−	0.598754i
$623$	0.518525			0.0207743
$624$		0			0
$625$	1.00000			0.0400000
$626$	32.7673	+	12.1747i	1.30965	+	0.486599i
$627$		0			0
$628$	34.0737	+	29.3754i	1.35969	+	1.17221i
$629$			10.4138i			0.415226i
$630$		0			0
$631$		−	16.5066i		−	0.657117i	−0.944484	−	0.328558i	$-0.893437\pi$
$631$		−	16.5066i		−	0.657117i	0.944484	−	0.328558i	$-0.106563\pi$
$632$	12.3712	−	6.81587i	0.492101	−	0.271121i
$633$		0			0
$634$	−12.0182	+	32.3460i	−0.477302	+	1.28462i
$635$	18.5602			0.736539
$636$		0			0
$637$	45.2091			1.79125
$638$	−9.73700	+	26.2064i	−0.385491	+	1.03752i
$639$		0			0
$640$	6.85946	+	8.99710i	0.271144	+	0.355642i
$641$		−	11.4842i		−	0.453600i	−0.973941	−	0.226800i	$-0.927174\pi$
$641$		−	11.4842i		−	0.453600i	0.973941	−	0.226800i	$-0.0728263\pi$
$642$		0			0
$643$			39.3054i			1.55005i	0.631928	+	0.775027i	$0.282264\pi$
$643$			39.3054i			1.55005i	−0.631928	+	0.775027i	$0.717736\pi$
$644$	21.8474	−	25.3416i	0.860907	−	0.998599i
$645$		0			0
$646$	−13.0921	−	4.86438i	−0.515103	−	0.191387i
$647$	25.1943			0.990489			0.495244	−	0.868754i	$-0.335079\pi$
$647$	25.1943			0.990489			0.495244	+	0.868754i	$0.335079\pi$
$648$		0			0
$649$	−23.4971			−0.922341
$650$	7.67667	+	2.85227i	0.301104	+	0.111875i
$651$		0			0
$652$	2.14663	−	2.48996i	0.0840684	−	0.0975142i
$653$			13.7872i			0.539533i	0.962926	+	0.269766i	$0.0869465\pi$
$653$			13.7872i			0.539533i	−0.962926	+	0.269766i	$0.913054\pi$
$654$		0			0
$655$		−	9.50661i		−	0.371454i
$656$	0.433541	−	0.0645596i	0.0169269	−	0.00252063i
$657$		0			0
$658$	−20.4239	+	54.9694i	−0.796205	+	2.14293i
$659$	−4.51795			−0.175994			−0.0879972	−	0.996121i	$-0.528047\pi$
$659$	−4.51795			−0.175994			−0.0879972	+	0.996121i	$0.528047\pi$
$660$		0			0
$661$	−16.7102			−0.649953			−0.324977	−	0.945722i	$-0.605356\pi$
$661$	−16.7102			−0.649953			−0.324977	+	0.945722i	$0.605356\pi$
$662$	13.8975	−	37.4041i	0.540141	−	1.45375i
$663$		0			0
$664$	10.5291	+	19.1109i	0.408607	+	0.741646i
$665$			15.6703i			0.607668i
$666$		0			0
$667$			30.4865i			1.18044i
$668$	3.69411	+	3.18474i	0.142929	+	0.123221i
$669$		0			0
$670$	6.87255	+	2.55350i	0.265510	+	0.0986501i
$671$	−17.2801			−0.667092
$672$		0			0
$673$	−10.2684			−0.395818			−0.197909	−	0.980220i	$-0.563415\pi$
$673$	−10.2684			−0.395818			−0.197909	+	0.980220i	$0.563415\pi$
$674$	37.9691	+	14.1074i	1.46252	+	0.543398i
$675$		0			0
$676$	31.1036	+	26.8149i	1.19629	+	1.03134i
$677$		−	42.3682i		−	1.62834i	−0.580624	−	0.814172i	$-0.697191\pi$
$677$		−	42.3682i		−	1.62834i	0.580624	−	0.814172i	$-0.302809\pi$
$678$		0			0
$679$		−	50.0111i		−	1.91925i
$680$	3.30997	+	6.00781i	0.126932	+	0.230389i
$681$		0			0
$682$	3.12430	−	8.40882i	0.119636	−	0.321991i
$683$	−7.70020			−0.294640			−0.147320	−	0.989089i	$-0.547065\pi$
$683$	−7.70020			−0.294640			−0.147320	+	0.989089i	$0.547065\pi$
$684$		0			0
$685$	0.800850			0.0305989
$686$	1.52966	−	4.11696i	0.0584025	−	0.157186i
$687$		0			0
$688$	0.814992	−	0.121362i	0.0310713	−	0.00462690i
$689$		−	43.7541i		−	1.66690i
$690$		0			0
$691$			41.3746i			1.57397i	0.616975	+	0.786983i	$0.288358\pi$
$691$			41.3746i			1.57397i	−0.616975	+	0.786983i	$0.711642\pi$
$692$	13.7885	−	15.9939i	0.524161	−	0.607995i
$693$		0			0
$694$	−27.7026	−	10.2929i	−1.05158	−	0.390713i
$695$	7.30260			0.277003
$696$		0			0
$697$	0.265746			0.0100658
$698$	17.2501	+	6.40927i	0.652926	+	0.242595i
$699$		0			0
$700$	5.02517	−	5.82889i	0.189933	−	0.220311i
$701$			12.5415i			0.473685i	0.971548	+	0.236842i	$0.0761125\pi$
$701$			12.5415i			0.473685i	−0.971548	+	0.236842i	$0.923887\pi$
$702$		0			0
$703$			17.4872i			0.659541i
$704$	12.0497	−	19.0642i	0.454140	−	0.718509i
$705$		0			0
$706$	−14.0155	+	37.7216i	−0.527479	+	1.41967i
$707$	−12.9237			−0.486048
$708$		0			0
$709$	1.94674			0.0731113			0.0365557	−	0.999332i	$-0.488361\pi$
$709$	1.94674			0.0731113			0.0365557	+	0.999332i	$0.488361\pi$
$710$	2.69162	−	7.24429i	0.101015	−	0.271873i
$711$		0			0
$712$	0.333824	−	0.183919i	0.0125106	−	0.00689265i
$713$		−	9.78215i		−	0.366344i
$714$		0			0
$715$		−	16.3250i		−	0.610521i
$716$	4.56042	+	3.93161i	0.170431	+	0.146931i
$717$		0			0
$718$	−7.83308	−	2.91038i	−0.292328	−	0.108614i
$719$	−25.7606			−0.960708			−0.480354	−	0.877075i	$-0.659492\pi$
$719$	−25.7606			−0.960708			−0.480354	+	0.877075i	$0.659492\pi$
$720$		0			0
$721$	−14.7674			−0.549965
$722$	3.20300	+	1.19007i	0.119203	+	0.0442899i
$723$		0			0
$724$	−29.5792	−	25.5007i	−1.09930	−	0.947724i
$725$			7.01227i			0.260429i
$726$		0			0
$727$			8.20253i			0.304215i	0.988364	+	0.152107i	$0.0486060\pi$
$727$			8.20253i			0.304215i	−0.988364	+	0.152107i	$0.951394\pi$
$728$	55.2021	−	30.4133i	2.04593	−	1.12719i
$729$		0			0
$730$	−6.40000	+	17.2251i	−0.236874	+	0.637531i
$731$	0.499562			0.0184770
$732$		0			0
$733$	21.1447			0.780998			0.390499	−	0.920603i	$-0.372303\pi$
$733$	21.1447			0.780998			0.390499	+	0.920603i	$0.372303\pi$
$734$	−11.9332	+	32.1173i	−0.440462	+	1.18547i
$735$		0			0
$736$	5.07667	−	24.0640i	0.187128	−	0.887011i
$737$		−	14.6150i		−	0.538350i
$738$		0			0
$739$			0.668371i			0.0245864i	0.999924	+	0.0122932i	$0.00391315\pi$
$739$			0.668371i			0.0245864i	−0.999924	+	0.0122932i	$0.996087\pi$
$740$	5.60780	−	6.50471i	0.206147	−	0.239118i
$741$		0			0
$742$	−38.5433	−	14.3208i	−1.41497	−	0.525732i
$743$	−33.8831			−1.24305			−0.621526	−	0.783394i	$-0.713487\pi$
$743$	−33.8831			−1.24305			−0.621526	+	0.783394i	$0.713487\pi$
$744$		0			0
$745$	−0.113818			−0.00416999
$746$	10.0483	+	3.73344i	0.367894	+	0.136691i
$747$		0			0
$748$	8.92821	−	10.3562i	0.326448	−	0.378659i
$749$			2.14219i			0.0782740i
$750$		0			0
$751$			10.6489i			0.388584i	0.980944	+	0.194292i	$0.0622409\pi$
$751$			10.6489i			0.388584i	−0.980944	+	0.194292i	$0.937759\pi$
$752$	6.34863	+	42.6333i	0.231511	+	1.55468i
$753$		0			0
$754$	−20.0009	+	53.8309i	−0.728389	+	1.96041i
$755$	1.69619			0.0617306
$756$		0			0
$757$	−11.8276			−0.429880			−0.214940	−	0.976627i	$-0.568956\pi$
$757$	−11.8276			−0.429880			−0.214940	+	0.976627i	$0.568956\pi$
$758$	13.3463	−	35.9205i	0.484758	−	1.30469i
$759$		0			0
$760$	5.55820	+	10.0885i	0.201617	+	0.365947i
$761$		−	0.0518467i		−	0.00187944i	−1.00000		0.000939722i	$-0.999701\pi$
$761$		−	0.0518467i		−	0.00187944i	1.00000		0.000939722i	$-0.000299123\pi$
$762$		0			0
$763$			59.7615i			2.16351i
$764$	1.46051	+	1.25913i	0.0528395	+	0.0455537i
$765$		0			0
$766$	35.0330	+	13.0165i	1.26580	+	0.470306i
$767$	−48.2656			−1.74277
$768$		0			0
$769$	−26.0961			−0.941049			−0.470524	−	0.882387i	$-0.655935\pi$
$769$	−26.0961			−0.941049			−0.470524	+	0.882387i	$0.655935\pi$
$770$	−14.3808	−	5.34319i	−0.518249	−	0.192555i
$771$		0			0
$772$	−24.2266	−	20.8861i	−0.871934	−	0.751707i
$773$		−	11.4187i		−	0.410702i	−0.978688	−	0.205351i	$-0.934166\pi$
$773$		−	11.4187i		−	0.410702i	0.978688	−	0.205351i	$-0.0658336\pi$
$774$		0			0
$775$		−	2.25002i		−	0.0808230i
$776$	−17.7388	−	32.1970i	−0.636785	−	1.15580i
$777$		0			0
$778$	10.0787	−	27.1261i	0.361339	−	0.972519i
$779$	0.446247			0.0159885
$780$		0			0
$781$	−15.4055			−0.551253
$782$	5.19318	−	13.9771i	0.185708	−	0.499819i
$783$		0			0
$784$	−4.59956	−	30.8877i	−0.164270	−	1.10313i
$785$		−	22.4941i		−	0.802848i
$786$		0			0
$787$			30.8141i			1.09840i	0.835690	+	0.549202i	$0.185068\pi$
$787$			30.8141i			1.09840i	−0.835690	+	0.549202i	$0.814932\pi$
$788$	34.0539	−	39.5004i	1.21312	−	1.40714i
$789$		0			0
$790$	−6.62010	−	2.45970i	−0.235533	−	0.0875121i
$791$	−29.1893			−1.03785
$792$		0			0
$793$	−35.4953			−1.26047
$794$	−0.169049	−	0.0628100i	−0.00599931	−	0.00222904i
$795$		0			0
$796$	−21.7715	+	25.2536i	−0.771671	+	0.895091i
$797$			49.9771i			1.77028i	0.465327	+	0.885139i	$0.345937\pi$
$797$			49.9771i			1.77028i	−0.465327	+	0.885139i	$0.654063\pi$
$798$		0			0
$799$			26.1328i			0.924511i
$800$	1.16770	−	5.53502i	0.0412843	−	0.195693i
$801$		0			0
$802$	7.30842	−	19.6701i	0.258069	−	0.694575i
$803$	36.6305			1.29266
$804$		0			0
$805$	−16.7295			−0.589637
$806$	6.41765	−	17.2726i	0.226052	−	0.608403i
$807$		0			0
$808$	−8.32026	+	4.58401i	−0.292706	+	0.161265i
$809$		−	31.1937i		−	1.09671i	−0.836245	−	0.548356i	$-0.815254\pi$
$809$		−	31.1937i		−	1.09671i	0.836245	−	0.548356i	$-0.184746\pi$
$810$		0			0
$811$		−	47.9220i		−	1.68277i	−0.540436	−	0.841385i	$-0.681741\pi$
$811$		−	47.9220i		−	1.68277i	0.540436	−	0.841385i	$-0.318259\pi$
$812$	40.8737	+	35.2378i	1.43439	+	1.23661i
$813$		0			0
$814$	−16.0482	−	5.96270i	−0.562489	−	0.208993i
$815$	−1.64377			−0.0575787
$816$		0			0
$817$	0.838878			0.0293486
$818$	−19.5289	−	7.25597i	−0.682813	−	0.253699i
$819$		0			0
$820$	−0.165991	−	0.143103i	−0.00579665	−	0.00499737i
$821$		−	35.8042i		−	1.24958i	−0.780794	−	0.624788i	$-0.785185\pi$
$821$		−	35.8042i		−	1.24958i	0.780794	−	0.624788i	$-0.214815\pi$
$822$		0			0
$823$		−	25.0600i		−	0.873535i	−0.899574	−	0.436768i	$-0.856123\pi$
$823$		−	25.0600i		−	0.873535i	0.899574	−	0.436768i	$-0.143877\pi$
$824$	−9.50717	+	5.23793i	−0.331198	+	0.182472i
$825$		0			0
$826$	−15.7974	+	42.5175i	−0.549661	+	1.47937i
$827$	−0.111136			−0.00386458			−0.00193229	−	0.999998i	$-0.500615\pi$
$827$	−0.111136			−0.00386458			−0.00193229	+	0.999998i	$0.500615\pi$
$828$		0			0
$829$	35.8024			1.24347			0.621735	−	0.783228i	$-0.286428\pi$
$829$	35.8024			1.24347			0.621735	+	0.783228i	$0.286428\pi$
$830$	3.79970	−	10.2266i	0.131890	−	0.354972i
$831$		0			0
$832$	24.7514	−	39.1600i	0.858100	−	1.35763i
$833$		−	18.9331i		−	0.655992i
$834$		0			0
$835$		−	2.43870i		−	0.0843947i
$836$	14.9925	−	17.3904i	0.518526	−	0.601459i
$837$		0			0
$838$	14.9473	+	5.55366i	0.516346	+	0.191848i
$839$	3.43743			0.118673			0.0593367	−	0.998238i	$-0.481101\pi$
$839$	3.43743			0.118673			0.0593367	+	0.998238i	$0.481101\pi$
$840$		0			0
$841$	−20.1719			−0.695584
$842$	−0.0470833	−	0.0174938i	−0.00162260	−	0.000602876i
$843$		0			0
$844$	28.5571	−	33.1245i	0.982977	−	1.14019i
$845$		−	20.5334i		−	0.706369i
$846$		0			0
$847$		−	11.7461i		−	0.403600i
$848$	−29.8936	+	4.45152i	−1.02655	+	0.152866i
$849$		0			0
$850$	1.19450	−	3.21490i	0.0409709	−	0.110270i
$851$	−18.6692			−0.639971
$852$		0			0
$853$	13.1391			0.449876			0.224938	−	0.974373i	$-0.427782\pi$
$853$	13.1391			0.449876			0.224938	+	0.974373i	$0.427782\pi$
$854$	−11.6176	+	31.2681i	−0.397548	+	1.06997i
$855$		0			0
$856$	0.759828	+	1.37914i	0.0259704	+	0.0471379i
$857$		−	20.9666i		−	0.716206i	−0.933682	−	0.358103i	$-0.883424\pi$
$857$		−	20.9666i		−	0.716206i	0.933682	−	0.358103i	$-0.116576\pi$
$858$		0			0
$859$			25.5455i			0.871601i	0.900043	+	0.435801i	$0.143535\pi$
$859$			25.5455i			0.871601i	−0.900043	+	0.435801i	$0.856465\pi$
$860$	−0.312038	−	0.269012i	−0.0106404	−	0.00917324i
$861$		0			0
$862$	22.9453	+	8.52534i	0.781521	+	0.290374i
$863$	−12.4343			−0.423267			−0.211633	−	0.977349i	$-0.567878\pi$
$863$	−12.4343			−0.423267			−0.211633	+	0.977349i	$0.567878\pi$
$864$		0			0
$865$	−10.5585			−0.359000
$866$	21.6722	+	8.05231i	0.736452	+	0.273629i
$867$		0			0
$868$	−13.1151	−	11.3067i	−0.445156	−	0.383775i
$869$			14.0781i			0.477568i
$870$		0			0
$871$		−	30.0208i		−	1.01722i
$872$	21.1972	+	38.4742i	0.717828	+	1.30290i
$873$		0			0
$874$	8.72053	−	23.4707i	0.294976	−	0.793908i
$875$	−3.84799			−0.130086
$876$		0			0
$877$	−6.84231			−0.231048			−0.115524	−	0.993305i	$-0.536855\pi$
$877$	−6.84231			−0.231048			−0.115524	+	0.993305i	$0.536855\pi$
$878$	−5.57666	+	15.0092i	−0.188203	+	0.506535i
$879$		0			0
$880$	−11.1535	+	1.66090i	−0.375985	+	0.0559889i
$881$			11.7126i			0.394606i	0.980343	+	0.197303i	$0.0632183\pi$
$881$			11.7126i			0.394606i	−0.980343	+	0.197303i	$0.936782\pi$
$882$		0			0
$883$			15.1968i			0.511413i	0.966754	+	0.255707i	$0.0823082\pi$
$883$			15.1968i			0.511413i	−0.966754	+	0.255707i	$0.917692\pi$
$884$	18.3395	−	21.2727i	0.616825	−	0.715479i
$885$		0			0
$886$	−47.7331	−	17.7352i	−1.60362	−	0.595826i
$887$	33.7627			1.13364			0.566820	−	0.823841i	$-0.308173\pi$
$887$	33.7627			1.13364			0.566820	+	0.823841i	$0.308173\pi$
$888$		0			0
$889$	−71.4195			−2.39533
$890$	−0.178636	−	0.0663723i	−0.00598790	−	0.00222480i
$891$		0			0
$892$	−3.22385	+	3.73947i	−0.107942	+	0.125207i
$893$			43.8828i			1.46848i
$894$		0			0
$895$		−	3.01061i		−	0.100633i
$896$	−26.3952	−	34.6208i	−0.881800	−	1.15660i
$897$		0			0
$898$	0.284401	−	0.765444i	0.00949057	−	0.0255432i
$899$	15.7777			0.526217
$900$		0			0
$901$	−18.3237			−0.610452
$902$	−0.152160	+	0.409526i	−0.00506636	+	0.0136357i
$903$		0			0
$904$	−18.7920	+	10.3533i	−0.625012	+	0.344347i
$905$			19.5270i			0.649099i
$906$		0			0
$907$		−	34.2862i		−	1.13846i	−0.822180	−	0.569228i	$-0.807242\pi$
$907$		−	34.2862i		−	1.13846i	0.822180	−	0.569228i	$-0.192758\pi$
$908$	13.6711	+	11.7861i	0.453692	+	0.391135i
$909$		0			0
$910$	−29.5398	−	10.9755i	−0.979235	−	0.363835i
$911$	6.48282			0.214785			0.107393	−	0.994217i	$-0.465750\pi$
$911$	6.48282			0.214785			0.107393	+	0.994217i	$0.465750\pi$
$912$		0			0
$913$	−21.7477			−0.719743
$914$	−30.8495	−	11.4621i	−1.02041	−	0.379133i
$915$		0			0
$916$	18.3304	+	15.8029i	0.605653	+	0.522142i
$917$			36.5814i			1.20802i
$918$		0			0
$919$			18.1763i			0.599580i	0.954005	+	0.299790i	$0.0969166\pi$
$919$			18.1763i			0.599580i	−0.954005	+	0.299790i	$0.903083\pi$
$920$	−10.7704	+	5.93389i	−0.355089	+	0.195635i
$921$		0			0
$922$	−3.90744	+	10.5166i	−0.128685	+	0.346346i
$923$	−31.6446			−1.04160
$924$		0			0
$925$	−4.29414			−0.141191
$926$	15.3511	−	41.3165i	0.504470	−	1.35774i
$927$		0			0
$928$	38.8131	+	8.18821i	1.27410	+	0.268791i
$929$			23.8075i			0.781100i	0.920582	+	0.390550i	$0.127715\pi$
$929$			23.8075i			0.781100i	−0.920582	+	0.390550i	$0.872285\pi$
$930$		0			0
$931$		−	31.7929i		−	1.04197i
$932$	16.8829	−	19.5832i	0.553019	−	0.641469i
$933$		0			0
$934$	−37.5615	−	13.9560i	−1.22905	−	0.456653i
$935$	−6.83673			−0.223585
$936$		0			0
$937$	16.4490			0.537366			0.268683	−	0.963229i	$-0.413412\pi$
$937$	16.4490			0.537366			0.268683	+	0.963229i	$0.413412\pi$
$938$	−26.4455	−	9.82584i	−0.863477	−	0.320825i
$939$		0			0
$940$	14.0724	−	16.3231i	0.458991	−	0.532402i
$941$		−	7.92385i		−	0.258310i	−0.991624	−	0.129155i	$-0.958773\pi$
$941$		−	7.92385i		−	0.258310i	0.991624	−	0.129155i	$-0.0412265\pi$
$942$		0			0
$943$			0.476410i			0.0155141i
$944$	4.91052	+	32.9759i	0.159824	+	1.07327i
$945$		0			0
$946$	−0.286037	+	0.769848i	−0.00929987	+	0.0250299i
$947$	50.2804			1.63389			0.816947	−	0.576713i	$-0.195665\pi$
$947$	50.2804			1.63389			0.816947	+	0.576713i	$0.195665\pi$
$948$		0			0
$949$	75.2431			2.44249
$950$	2.00583	−	5.39855i	0.0650778	−	0.175152i
$951$		0			0
$952$	−12.7368	−	23.1180i	−0.412801	−	0.749259i
$953$		−	32.4601i		−	1.05149i	−0.850644	−	0.525743i	$-0.823787\pi$
$953$		−	32.4601i		−	1.05149i	0.850644	−	0.525743i	$-0.176213\pi$
$954$		0			0
$955$		−	0.964171i		−	0.0311999i
$956$	−13.8785	−	11.9649i	−0.448863	−	0.386971i
$957$		0			0
$958$	−32.4317	−	12.0500i	−1.04782	−	0.389317i
$959$	−3.08167			−0.0995122
$960$		0			0
$961$	25.9374			0.836691
$962$	−32.9647	−	12.2480i	−1.06283	−	0.394893i
$963$		0			0
$964$	−16.0562	−	13.8423i	−0.517135	−	0.445829i
$965$			15.9934i			0.514846i
$966$		0			0
$967$		−	25.4806i		−	0.819402i	−0.912220	−	0.409701i	$-0.865633\pi$
$967$		−	25.4806i		−	0.819402i	0.912220	−	0.409701i	$-0.134367\pi$
$968$	−4.16629	−	7.56207i	−0.133910	−	0.243054i
$969$		0			0
$970$	−6.40153	+	17.2293i	−0.205541	+	0.553198i
$971$	40.6423			1.30427			0.652137	−	0.758101i	$-0.273873\pi$
$971$	40.6423			1.30427			0.652137	+	0.758101i	$0.273873\pi$
$972$		0			0
$973$	−28.1004			−0.900856
$974$	−1.99903	+	5.38026i	−0.0640532	+	0.172395i
$975$		0			0
$976$	3.61127	+	24.2510i	0.115594	+	0.776255i
$977$			56.6360i			1.81195i	0.423335	+	0.905973i	$0.360859\pi$
$977$			56.6360i			1.81195i	−0.423335	+	0.905973i	$0.639141\pi$
$978$		0			0
$979$			0.379883i			0.0121411i
$980$	−10.1954	+	11.8260i	−0.325680	+	0.377769i
$981$		0			0
$982$	21.9541	+	8.15705i	0.700584	+	0.260302i
$983$	10.5127			0.335302			0.167651	−	0.985846i	$-0.446382\pi$
$983$	10.5127			0.335302			0.167651	+	0.985846i	$0.446382\pi$
$984$		0			0
$985$	−26.0766			−0.830868
$986$	22.5438	+	8.37613i	0.717940	+	0.266750i
$987$		0			0
$988$	30.7962	−	35.7217i	0.979758	−	1.13646i
$989$			0.895580i			0.0284778i
$990$		0			0
$991$			31.2300i			0.992053i	0.868307	+	0.496027i	$0.165208\pi$
$991$			31.2300i			0.992053i	−0.868307	+	0.496027i	$0.834792\pi$
$992$	−12.4539	−	2.62734i	−0.395412	−	0.0834181i
$993$		0			0
$994$	−10.3573	+	27.8760i	−0.328514	+	0.884173i
$995$	16.6714			0.528519
$996$		0			0
$997$	53.8356			1.70499			0.852495	−	0.522735i	$-0.175088\pi$
$997$	53.8356			1.70499			0.852495	+	0.522735i	$0.175088\pi$
$998$	−9.90880	+	26.6688i	−0.313658	+	0.844187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.44		48
3.2	odd	2	inner	1620.2.e.b.971.5		48
4.3	odd	2	inner	1620.2.e.b.971.6		48
9.2	odd	6		540.2.q.a.71.14		48
9.4	even	3		540.2.q.a.251.6		48
9.5	odd	6		180.2.q.a.11.19	yes	48
9.7	even	3		180.2.q.a.131.11	yes	48
12.11	even	2	inner	1620.2.e.b.971.43		48
36.7	odd	6		180.2.q.a.131.19	yes	48
36.11	even	6		540.2.q.a.71.6		48
36.23	even	6		180.2.q.a.11.11	✓	48
36.31	odd	6		540.2.q.a.251.14		48
45.7	odd	12		900.2.o.c.599.24		48
45.14	odd	6		900.2.r.f.551.6		48
45.23	even	12		900.2.o.c.299.7		48
45.32	even	12		900.2.o.b.299.18		48
45.34	even	6		900.2.r.f.851.14		48
45.43	odd	12		900.2.o.b.599.1		48
180.7	even	12		900.2.o.c.599.7		48
180.23	odd	12		900.2.o.c.299.24		48
180.43	even	12		900.2.o.b.599.18		48
180.59	even	6		900.2.r.f.551.14		48
180.79	odd	6		900.2.r.f.851.6		48
180.167	odd	12		900.2.o.b.299.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.11	✓	48	36.23	even	6
180.2.q.a.11.19	yes	48	9.5	odd	6
180.2.q.a.131.11	yes	48	9.7	even	3
180.2.q.a.131.19	yes	48	36.7	odd	6
540.2.q.a.71.6		48	36.11	even	6
540.2.q.a.71.14		48	9.2	odd	6
540.2.q.a.251.6		48	9.4	even	3
540.2.q.a.251.14		48	36.31	odd	6
900.2.o.b.299.1		48	180.167	odd	12
900.2.o.b.299.18		48	45.32	even	12
900.2.o.b.599.1		48	45.43	odd	12
900.2.o.b.599.18		48	180.43	even	12
900.2.o.c.299.7		48	45.23	even	12
900.2.o.c.299.24		48	180.23	odd	12
900.2.o.c.599.7		48	180.7	even	12
900.2.o.c.599.24		48	45.7	odd	12
900.2.r.f.551.6		48	45.14	odd	6
900.2.r.f.551.14		48	180.59	even	6
900.2.r.f.851.6		48	180.79	odd	6
900.2.r.f.851.14		48	45.34	even	6
1620.2.e.b.971.5		48	3.2	odd	2	inner
1620.2.e.b.971.6		48	4.3	odd	2	inner
1620.2.e.b.971.43		48	12.11	even	2	inner
1620.2.e.b.971.44		48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.32567 + 0.492552i) q^{2} +(1.51479 + 1.30592i) q^{4} -1.00000i q^{5} +3.84799i q^{7} +(1.36487 + 2.47732i) q^{8} +O(q^{10})\)	\(q+(1.32567 + 0.492552i) q^{2} +(1.51479 + 1.30592i) q^{4} -1.00000i q^{5} +3.84799i q^{7} +(1.36487 + 2.47732i) q^{8} +(0.492552 - 1.32567i) q^{10} -2.81913 q^{11} -5.79080 q^{13} +(-1.89534 + 5.10116i) q^{14} +(0.589153 + 3.95637i) q^{16} +2.42512i q^{17} +4.07233i q^{19} +(1.30592 - 1.51479i) q^{20} +(-3.73723 - 1.38857i) q^{22} -4.34759 q^{23} -1.00000 q^{25} +(-7.67667 - 2.85227i) q^{26} +(-5.02517 + 5.82889i) q^{28} -7.01227i q^{29} +2.25002i q^{31} +(-1.16770 + 5.53502i) q^{32} +(-1.19450 + 3.21490i) q^{34} +3.84799 q^{35} +4.29414 q^{37} +(-2.00583 + 5.39855i) q^{38} +(2.47732 - 1.36487i) q^{40} -0.109580i q^{41} -0.205995i q^{43} +(-4.27038 - 3.68155i) q^{44} +(-5.76345 - 2.14141i) q^{46} +10.7759 q^{47} -7.80706 q^{49} +(-1.32567 - 0.492552i) q^{50} +(-8.77182 - 7.56231i) q^{52} +7.55580i q^{53} +2.81913i q^{55} +(-9.53273 + 5.25201i) q^{56} +(3.45390 - 9.29593i) q^{58} +8.33488 q^{59} +6.12960 q^{61} +(-1.10825 + 2.98277i) q^{62} +(-4.27426 + 6.76245i) q^{64} +5.79080i q^{65} +5.18422i q^{67} +(-3.16701 + 3.67354i) q^{68} +(5.10116 + 1.89534i) q^{70} +5.46464 q^{71} -12.9936 q^{73} +(5.69261 + 2.11509i) q^{74} +(-5.31813 + 6.16871i) q^{76} -10.8480i q^{77} -4.99379i q^{79} +(3.95637 - 0.589153i) q^{80} +(0.0539740 - 0.145267i) q^{82} +7.71433 q^{83} +2.42512 q^{85} +(0.101463 - 0.273080i) q^{86} +(-3.84774 - 6.98389i) q^{88} -0.134752i q^{89} -22.2830i q^{91} +(-6.58567 - 5.67760i) q^{92} +(14.2852 + 5.30767i) q^{94} +4.07233 q^{95} -12.9967 q^{97} +(-10.3496 - 3.84538i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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