LMFDB - Embedded newform 700.2.r.d.249.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(149,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,16,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.13026266817859584.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.3
Root			$-1.90412 + 1.09935i$ of defining polynomial
Character	$\chi$	$=$	700.249
Dual form			700.2.r.d.149.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.315621 - 0.182224i) q^{3} +(-1.58850 + 2.11581i) q^{7} +(-1.43359 - 2.48305i) q^{9} +(-0.682224 + 1.18165i) q^{11} +2.63555i q^{13} +(-1.93264 - 1.11581i) q^{17} +(-3.11581 - 5.39675i) q^{19} +(0.886917 - 0.378332i) q^{21} +(-5.71237 + 3.29804i) q^{23} +2.13828i q^{27} -5.50273 q^{29} +(-2.25136 + 3.89948i) q^{31} +(0.430649 - 0.248635i) q^{33} +(-1.81289 + 1.04667i) q^{37} +(0.480261 - 0.831836i) q^{39} +9.32497 q^{41} +1.86718i q^{43} +(-5.94715 + 3.43359i) q^{47} +(-1.95333 - 6.72194i) q^{49} +(0.406656 + 0.704349i) q^{51} +(-8.78001 - 5.06914i) q^{53} +2.27110i q^{57} +(-0.817776 + 1.41643i) q^{59} +(-0.0197391 - 0.0341891i) q^{61} +(7.53092 + 0.911120i) q^{63} +(5.82739 + 3.36445i) q^{67} +2.40393 q^{69} -6.27110 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-1.41643 - 3.32051i) q^{77} +(2.66248 + 4.61156i) q^{79} +(-3.91112 + 6.77426i) q^{81} +14.7738i q^{83} +(1.73678 + 1.00273i) q^{87} +(0.433589 + 0.750998i) q^{89} +(-5.57633 - 4.18658i) q^{91} +(1.42116 - 0.820506i) q^{93} -16.0988i q^{97} +3.91211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91}+ \cdots - 84 q^{99}+O(q^{100}) $ 12 * q + 16 * q^9 - 8 * q^11 - 4 * q^19 - 22 * q^21 + 6 * q^31 - 28 * q^39 + 44 * q^41 - 24 * q^49 + 6 * q^51 - 10 * q^59 - 34 * q^61 + 96 * q^69 - 76 * q^71 - 2 * q^79 - 46 * q^81 - 28 * q^89 + 34 * q^91 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.315621	−	0.182224i	−0.182224	−	0.105207i	0.406113	−	0.913823i	$-0.366884\pi$
$3$	−0.315621	−	0.182224i	−0.182224	−	0.105207i	−0.588337	+	0.808616i	$0.700217\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.58850	+	2.11581i	−0.600397	+	0.799702i
$7$	−1.58850	+	2.11581i	−0.600397	+	0.799702i
$8$		0			0
$9$	−1.43359	−	2.48305i	−0.477863	−	0.827683i
$10$		0			0
$11$	−0.682224	+	1.18165i	−0.205698	+	0.356280i	−0.950355	−	0.311168i	$-0.899280\pi$
$11$	−0.682224	+	1.18165i	−0.205698	+	0.356280i	0.744657	+	0.667448i	$0.232613\pi$
$12$		0			0
$13$			2.63555i			0.730971i	0.930817	+	0.365485i	$0.119097\pi$
$13$			2.63555i			0.730971i	−0.930817	+	0.365485i	$0.880903\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.93264	−	1.11581i	−0.468735	−	0.270624i	0.246975	−	0.969022i	$-0.420563\pi$
$17$	−1.93264	−	1.11581i	−0.468735	−	0.270624i	−0.715710	+	0.698398i	$0.753897\pi$
$18$		0			0
$19$	−3.11581	−	5.39675i	−0.714816	−	1.23810i	−0.963030	−	0.269393i	$-0.913177\pi$
$19$	−3.11581	−	5.39675i	−0.714816	−	1.23810i	0.248214	−	0.968705i	$-0.420156\pi$
$20$		0			0
$21$	0.886917	−	0.378332i	0.193541	−	0.0825589i
$22$		0			0
$23$	−5.71237	+	3.29804i	−1.19111	+	0.687688i	−0.958559	−	0.284896i	$-0.908041\pi$
$23$	−5.71237	+	3.29804i	−1.19111	+	0.687688i	−0.232552	+	0.972584i	$0.574708\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			2.13828i			0.411512i
$28$		0			0
$29$	−5.50273			−1.02183			−0.510916	−	0.859631i	$-0.670694\pi$
$29$	−5.50273			−1.02183			−0.510916	+	0.859631i	$0.670694\pi$
$30$		0			0
$31$	−2.25136	+	3.89948i	−0.404357	+	0.700367i	−0.994246	−	0.107117i	$-0.965838\pi$
$31$	−2.25136	+	3.89948i	−0.404357	+	0.700367i	0.589889	+	0.807484i	$0.299171\pi$
$32$		0			0
$33$	0.430649	−	0.248635i	0.0749663	−	0.0432818i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.81289	+	1.04667i	−0.298037	+	0.172072i	−0.641561	−	0.767072i	$-0.721713\pi$
$37$	−1.81289	+	1.04667i	−0.298037	+	0.172072i	0.343524	+	0.939144i	$0.388379\pi$
$38$		0			0
$39$	0.480261	−	0.831836i	0.0769033	−	0.133200i
$40$		0			0
$41$	9.32497			1.45632			0.728158	−	0.685410i	$-0.240377\pi$
$41$	9.32497			1.45632			0.728158	+	0.685410i	$0.240377\pi$
$42$		0			0
$43$			1.86718i			0.284742i	0.989813	+	0.142371i	$0.0454726\pi$
$43$			1.86718i			0.284742i	−0.989813	+	0.142371i	$0.954527\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.94715	+	3.43359i	−0.867481	+	0.500840i	−0.866510	−	0.499159i	$-0.833642\pi$
$47$	−5.94715	+	3.43359i	−0.867481	+	0.500840i	−0.000970685		1.00000i	$0.500309\pi$
$48$		0			0
$49$	−1.95333	−	6.72194i	−0.279047	−	0.960277i
$50$		0			0
$51$	0.406656	+	0.704349i	0.0569432	+	0.0986285i
$52$		0			0
$53$	−8.78001	−	5.06914i	−1.20603	−	0.696300i	−0.244138	−	0.969740i	$-0.578505\pi$
$53$	−8.78001	−	5.06914i	−1.20603	−	0.696300i	−0.961889	+	0.273440i	$0.911838\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			2.27110i			0.300815i
$58$		0			0
$59$	−0.817776	+	1.41643i	−0.106465	+	0.184403i	−0.914336	−	0.404956i	$-0.867287\pi$
$59$	−0.817776	+	1.41643i	−0.106465	+	0.184403i	0.807871	+	0.589360i	$0.200620\pi$
$60$		0			0
$61$	−0.0197391	−	0.0341891i	−0.00252733	−	0.00437747i	0.864759	−	0.502187i	$-0.167471\pi$
$61$	−0.0197391	−	0.0341891i	−0.00252733	−	0.00437747i	−0.867286	+	0.497810i	$0.834138\pi$
$62$		0			0
$63$	7.53092	+	0.911120i	0.948807	+	0.114790i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.82739	+	3.36445i	0.711930	+	0.411033i	0.811775	−	0.583970i	$-0.198502\pi$
$67$	5.82739	+	3.36445i	0.711930	+	0.411033i	−0.0998455	+	0.995003i	$0.531835\pi$
$68$		0			0
$69$	2.40393			0.289399
$70$		0			0
$71$	−6.27110			−0.744243			−0.372122	−	0.928184i	$-0.621370\pi$
$71$	−6.27110			−0.744243			−0.372122	+	0.928184i	$0.621370\pi$
$72$		0			0
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.41643	−	3.32051i	−0.161417	−	0.378407i
$78$		0			0
$79$	2.66248	+	4.61156i	0.299553	+	0.518841i	0.976034	−	0.217619i	$-0.0698291\pi$
$79$	2.66248	+	4.61156i	0.299553	+	0.518841i	−0.676481	+	0.736460i	$0.736496\pi$
$80$		0			0
$81$	−3.91112	+	6.77426i	−0.434569	+	0.752695i
$82$		0			0
$83$			14.7738i			1.62164i	0.585296	+	0.810819i	$0.300978\pi$
$83$			14.7738i			1.62164i	−0.585296	+	0.810819i	$0.699022\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.73678	+	1.00273i	0.186202	+	0.107504i
$88$		0			0
$89$	0.433589	+	0.750998i	0.0459603	+	0.0796056i	0.888090	−	0.459669i	$-0.152032\pi$
$89$	0.433589	+	0.750998i	0.0459603	+	0.0796056i	−0.842130	+	0.539274i	$0.818699\pi$
$90$		0			0
$91$	−5.57633	−	4.18658i	−0.584559	−	0.438873i
$92$		0			0
$93$	1.42116	−	0.820506i	0.147367	−	0.0850825i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	16.0988i		−	1.63459i	−0.576222	−	0.817293i	$-0.695474\pi$
$97$		−	16.0988i		−	1.63459i	0.576222	−	0.817293i	$-0.304526\pi$
$98$		0			0
$99$	3.91211			0.393182
$100$		0			0
$101$	7.84744	−	13.5922i	0.780849	−	1.35247i	−0.150598	−	0.988595i	$-0.548120\pi$
$101$	7.84744	−	13.5922i	0.780849	−	1.35247i	0.931448	−	0.363876i	$-0.118547\pi$
$102$		0			0
$103$	11.5787	−	6.68495i	1.14088	−	0.658688i	0.194233	−	0.980956i	$-0.437778\pi$
$103$	11.5787	−	6.68495i	1.14088	−	0.658688i	0.946649	+	0.322267i	$0.104445\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.67994	−	2.70196i	0.452427	−	0.261209i	−0.256428	−	0.966563i	$-0.582546\pi$
$107$	4.67994	−	2.70196i	0.452427	−	0.261209i	0.708854	+	0.705355i	$0.249212\pi$
$108$		0			0
$109$	−7.91385	+	13.7072i	−0.758009	+	1.31291i	0.185855	+	0.982577i	$0.440495\pi$
$109$	−7.91385	+	13.7072i	−0.758009	+	1.31291i	−0.943864	+	0.330333i	$0.892839\pi$
$110$		0			0
$111$	0.762915			0.0724127
$112$		0			0
$113$		−	18.4238i		−	1.73316i	−0.499036	−	0.866581i	$-0.666312\pi$
$113$		−	18.4238i		−	1.73316i	0.499036	−	0.866581i	$-0.333688\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.54420	−	3.77830i	0.605012	−	0.349304i
$118$		0			0
$119$	5.43086	−	2.31664i	0.497846	−	0.212366i
$120$		0			0
$121$	4.56914	+	7.91398i	0.415376	+	0.719453i
$122$		0			0
$123$	−2.94316	−	1.69923i	−0.265376	−	0.153215i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			5.32497i			0.472515i	0.971691	+	0.236257i	$0.0759208\pi$
$127$			5.32497i			0.472515i	−0.971691	+	0.236257i	$0.924079\pi$
$128$		0			0
$129$	0.340245	−	0.589321i	0.0299569	−	0.0518868i
$130$		0			0
$131$	−8.11854	−	14.0617i	−0.709320	−	1.22858i	−0.965110	−	0.261846i	$-0.915669\pi$
$131$	−8.11854	−	14.0617i	−0.709320	−	1.22858i	0.255789	−	0.966733i	$-0.417665\pi$
$132$		0			0
$133$	16.3680	+	1.98026i	1.41928	+	0.171710i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.81864	−	2.20469i	−0.326248	−	0.188360i	0.327926	−	0.944703i	$-0.393650\pi$
$137$	−3.81864	−	2.20469i	−0.326248	−	0.188360i	−0.654174	+	0.756344i	$0.726984\pi$
$138$		0			0
$139$	22.3699			1.89739			0.948695	−	0.316192i	$-0.102404\pi$
$139$	22.3699			1.89739			0.948695	+	0.316192i	$0.102404\pi$
$140$		0			0
$141$	2.50273			0.210768
$142$		0			0
$143$	−3.11429	−	1.79804i	−0.260430	−	0.150359i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.608388	+	2.47753i	−0.0501790	+	0.204343i
$148$		0			0
$149$	11.2541	+	19.4927i	0.921971	+	1.59690i	0.796361	+	0.604822i	$0.206756\pi$
$149$	11.2541	+	19.4927i	0.921971	+	1.59690i	0.125610	+	0.992080i	$0.459911\pi$
$150$		0			0
$151$	−6.75136	+	11.6937i	−0.549418	+	0.951620i	0.448896	+	0.893584i	$0.351817\pi$
$151$	−6.75136	+	11.6937i	−0.549418	+	0.951620i	−0.998314	+	0.0580365i	$0.981516\pi$
$152$		0			0
$153$			6.39847i			0.517285i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	13.4724	+	7.77830i	1.07522	+	0.620776i	0.929602	−	0.368566i	$-0.120151\pi$
$157$	13.4724	+	7.77830i	1.07522	+	0.620776i	0.145613	+	0.989342i	$0.453484\pi$
$158$		0			0
$159$	1.84744	+	3.19986i	0.146511	+	0.253765i
$160$		0			0
$161$	2.09607	−	17.3252i	0.165194	−	1.36542i
$162$		0			0
$163$	−3.81391	+	2.20196i	−0.298729	+	0.172471i	−0.641872	−	0.766812i	$-0.721842\pi$
$163$	−3.81391	+	2.20196i	−0.298729	+	0.172471i	0.343143	+	0.939283i	$0.388508\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	9.09880i		−	0.704087i	−0.935984	−	0.352043i	$-0.885487\pi$
$167$		−	9.09880i		−	0.704087i	0.935984	−	0.352043i	$-0.114513\pi$
$168$		0			0
$169$	6.05387			0.465682
$170$		0			0
$171$	−8.93359	+	15.4734i	−0.683169	+	1.18328i
$172$		0			0
$173$	17.2863	−	9.98026i	1.31425	−	0.758785i	0.331457	−	0.943470i	$-0.392460\pi$
$173$	17.2863	−	9.98026i	1.31425	−	0.758785i	0.982798	+	0.184685i	$0.0591266\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.516215	−	0.298037i	0.0388011	−	0.0224018i
$178$		0			0
$179$	−6.59607	+	11.4247i	−0.493014	+	0.853925i	−0.999968	−	0.00804839i	$-0.997438\pi$
$179$	−6.59607	+	11.4247i	−0.493014	+	0.853925i	0.506954	+	0.861973i	$0.330771\pi$
$180$		0			0
$181$	10.2316			0.760511			0.380255	−	0.924882i	$-0.375836\pi$
$181$	10.2316			0.760511			0.380255	+	0.924882i	$0.375836\pi$
$182$		0			0
$183$			0.0143878i			0.00106357i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.63699	−	1.52247i	0.192836	−	0.111334i
$188$		0			0
$189$	−4.52420	−	3.39666i	−0.329087	−	0.247071i
$190$		0			0
$191$	−7.00273	−	12.1291i	−0.506700	−	0.877630i	−0.999970	−	0.00775353i	$-0.997532\pi$
$191$	−7.00273	−	12.1291i	−0.506700	−	0.877630i	0.493270	−	0.869876i	$-0.335801\pi$
$192$		0			0
$193$	−12.4789	−	7.20469i	−0.898250	−	0.518605i	−0.0216183	−	0.999766i	$-0.506882\pi$
$193$	−12.4789	−	7.20469i	−0.898250	−	0.518605i	−0.876632	+	0.481161i	$0.840215\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	11.5566i		−	0.823373i	−0.911325	−	0.411687i	$-0.864940\pi$
$197$		−	11.5566i		−	0.823373i	0.911325	−	0.411687i	$-0.135060\pi$
$198$		0			0
$199$	−2.70469	+	4.68467i	−0.191731	+	0.332087i	−0.945824	−	0.324680i	$-0.894743\pi$
$199$	−2.70469	+	4.68467i	−0.191731	+	0.332087i	0.754093	+	0.656767i	$0.228077\pi$
$200$		0			0
$201$	−1.22617	−	2.12378i	−0.0864871	−	0.149800i
$202$		0			0
$203$	8.74109	−	11.6427i	0.613504	−	0.817161i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	16.3784	+	9.45606i	1.13838	+	0.657241i
$208$		0			0
$209$	8.50273			0.588146
$210$		0			0
$211$	−10.9660			−0.754929			−0.377465	−	0.926024i	$-0.623204\pi$
$211$	−10.9660			−0.754929			−0.377465	+	0.926024i	$0.623204\pi$
$212$		0			0
$213$	1.97929	+	1.14275i	0.135619	+	0.0782997i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.67427	−	10.9578i	−0.317310	−	0.743863i
$218$		0			0
$219$	0.728896	+	1.26249i	0.0492542	+	0.0853108i
$220$		0			0
$221$	2.94078	−	5.09359i	0.197818	−	0.342632i
$222$		0			0
$223$			21.5566i			1.44354i	0.692135	+	0.721768i	$0.256670\pi$
$223$			21.5566i			1.44354i	−0.692135	+	0.721768i	$0.743330\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.7593	−	6.21189i	−0.714120	−	0.412297i	0.0984646	−	0.995141i	$-0.468607\pi$
$227$	−10.7593	−	6.21189i	−0.714120	−	0.412297i	−0.812585	+	0.582843i	$0.801940\pi$
$228$		0			0
$229$	−4.18222	−	7.24382i	−0.276369	−	0.478685i	0.694110	−	0.719868i	$-0.255798\pi$
$229$	−4.18222	−	7.24382i	−0.276369	−	0.478685i	−0.970480	+	0.241183i	$0.922465\pi$
$230$		0			0
$231$	−0.158021	+	1.30613i	−0.0103970	+	0.0859370i
$232$		0			0
$233$	−12.1291	+	7.00273i	−0.794603	+	0.458764i	−0.841580	−	0.540132i	$-0.818374\pi$
$233$	−12.1291	+	7.00273i	−0.794603	+	0.458764i	0.0469777	+	0.998896i	$0.485041\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.94067i		−	0.126060i
$238$		0			0
$239$	−16.9605			−1.09708			−0.548542	−	0.836123i	$-0.684817\pi$
$239$	−16.9605			−1.09708			−0.548542	+	0.836123i	$0.684817\pi$
$240$		0			0
$241$	−5.16521	+	8.94641i	−0.332721	+	0.576289i	−0.983044	−	0.183368i	$-0.941300\pi$
$241$	−5.16521	+	8.94641i	−0.332721	+	0.576289i	0.650324	+	0.759657i	$0.274633\pi$
$242$		0			0
$243$	8.02428	−	4.63282i	0.514758	−	0.297196i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	14.2234	−	8.21189i	0.905014	−	0.522510i
$248$		0			0
$249$	2.69215	−	4.66294i	0.170608	−	0.295502i
$250$		0			0
$251$	19.5082			1.23135			0.615673	−	0.788002i	$-0.288884\pi$
$251$	19.5082			1.23135			0.615673	+	0.788002i	$0.288884\pi$
$252$		0			0
$253$		−	9.00000i		−	0.565825i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.6499	+	14.2316i	−1.53762	+	0.887744i	−0.538641	+	0.842535i	$0.681062\pi$
$257$	−24.6499	+	14.2316i	−1.53762	+	0.887744i	−0.998978	+	0.0452090i	$0.985605\pi$
$258$		0			0
$259$	0.665214	−	5.49837i	0.0413344	−	0.341652i
$260$		0			0
$261$	7.88865	+	13.6635i	0.488295	+	0.845752i
$262$		0			0
$263$	−24.7355	−	14.2810i	−1.52525	−	0.880606i	−0.999552	−	0.0299373i	$-0.990469\pi$
$263$	−24.7355	−	14.2810i	−1.52525	−	0.880606i	−0.525702	−	0.850669i	$-0.676197\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	0.316041i		−	0.0193414i
$268$		0			0
$269$	−4.59880	+	7.96536i	−0.280394	+	0.485657i	−0.971482	−	0.237114i	$-0.923798\pi$
$269$	−4.59880	+	7.96536i	−0.280394	+	0.485657i	0.691088	+	0.722771i	$0.257132\pi$
$270$		0			0
$271$	−1.93086	−	3.34435i	−0.117291	−	0.203155i	0.801402	−	0.598126i	$-0.204088\pi$
$271$	−1.93086	−	3.34435i	−0.117291	−	0.203155i	−0.918693	+	0.394971i	$0.870754\pi$
$272$		0			0
$273$	0.997115	+	2.33752i	0.0603481	+	0.141473i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.21539	+	5.32051i	0.553699	+	0.319678i	0.750613	−	0.660743i	$-0.229759\pi$
$277$	9.21539	+	5.32051i	0.553699	+	0.319678i	−0.196914	+	0.980421i	$0.563092\pi$
$278$		0			0
$279$	12.9101			0.772909
$280$		0			0
$281$	1.73436			0.103463			0.0517315	−	0.998661i	$-0.483526\pi$
$281$	1.73436			0.103463			0.0517315	+	0.998661i	$0.483526\pi$
$282$		0			0
$283$	5.12004	+	2.95606i	0.304355	+	0.175719i	0.644398	−	0.764691i	$-0.277108\pi$
$283$	5.12004	+	2.95606i	0.304355	+	0.175719i	−0.340043	+	0.940410i	$0.610442\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.8127	+	19.7299i	−0.874368	+	1.16462i
$288$		0			0
$289$	−6.00992	−	10.4095i	−0.353525	−	0.612323i
$290$		0			0
$291$	−2.93359	+	5.08112i	−0.171970	+	0.297861i
$292$		0			0
$293$			24.3250i			1.42108i	0.703657	+	0.710540i	$0.251549\pi$
$293$			24.3250i			1.42108i	−0.703657	+	0.710540i	$0.748451\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.52669	−	1.45879i	−0.146614	−	0.0846474i
$298$		0			0
$299$	−8.69215	−	15.0552i	−0.502680	−	0.870667i
$300$		0			0
$301$	−3.95060	−	2.96601i	−0.227709	−	0.170958i
$302$		0			0
$303$	−4.95364	+	2.85998i	−0.284579	+	0.164302i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			23.5226i			1.34250i	0.741229	+	0.671252i	$0.234243\pi$
$307$			23.5226i			1.34250i	−0.741229	+	0.671252i	$0.765757\pi$
$308$		0			0
$309$	−4.87264			−0.277195
$310$		0			0
$311$	4.40939	−	7.63728i	0.250033	−	0.433070i	−0.713501	−	0.700654i	$-0.752892\pi$
$311$	4.40939	−	7.63728i	0.250033	−	0.433070i	0.963535	+	0.267583i	$0.0862251\pi$
$312$		0			0
$313$	−0.0808384	+	0.0466721i	−0.00456926	+	0.00263806i	−0.502283	−	0.864703i	$-0.667506\pi$
$313$	−0.0808384	+	0.0466721i	−0.00456926	+	0.00263806i	0.497714	+	0.867341i	$0.334173\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.06764	+	1.77110i	−0.172296	+	0.0994751i	−0.583668	−	0.811992i	$-0.698383\pi$
$317$	−3.06764	+	1.77110i	−0.172296	+	0.0994751i	0.411372	+	0.911468i	$0.365050\pi$
$318$		0			0
$319$	3.75409	−	6.50228i	0.210189	−	0.364058i
$320$		0			0
$321$	−1.96945			−0.109924
$322$		0			0
$323$			13.9067i			0.773787i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.99556	−	2.88419i	0.276255	−	0.159496i
$328$		0			0
$329$	2.18222	−	18.0373i	0.120310	−	0.994429i
$330$		0			0
$331$	9.82497	+	17.0173i	0.540029	+	0.935358i	0.998902	+	0.0468558i	$0.0149201\pi$
$331$	9.82497	+	17.0173i	0.540029	+	0.935358i	−0.458872	+	0.888502i	$0.651747\pi$
$332$		0			0
$333$	5.19788	+	3.00099i	0.284842	+	0.164454i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			23.0449i			1.25534i	0.778480	+	0.627669i	$0.215991\pi$
$337$			23.0449i			1.25534i	−0.778480	+	0.627669i	$0.784009\pi$
$338$		0			0
$339$	−3.35725	+	5.81493i	−0.182341	+	0.315824i
$340$		0			0
$341$	−3.07187	−	5.32064i	−0.166351	−	0.288129i
$342$		0			0
$343$	17.3252	+	6.54494i	0.935475	+	0.353393i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.5393	−	11.2810i	−1.04893	−	0.605597i	−0.126577	−	0.991957i	$-0.540399\pi$
$347$	−19.5393	−	11.2810i	−1.04893	−	0.605597i	−0.922348	+	0.386360i	$0.873732\pi$
$348$		0			0
$349$	−14.3250			−0.766798			−0.383399	−	0.923583i	$-0.625247\pi$
$349$	−14.3250			−0.766798			−0.383399	+	0.923583i	$0.625247\pi$
$350$		0			0
$351$	−5.63555			−0.300804
$352$		0			0
$353$	−28.3193	−	16.3502i	−1.50729	−	0.870232i	−0.999964	−	0.00847467i	$-0.997302\pi$
$353$	−28.3193	−	16.3502i	−1.50729	−	0.870232i	−0.507321	−	0.861757i	$-0.669364\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.13624	−	0.258451i	−0.113062	−	0.0136787i
$358$		0			0
$359$	−13.0791	−	22.6536i	−0.690287	−	1.19561i	−0.971744	−	0.236038i	$-0.924151\pi$
$359$	−13.0791	−	22.6536i	−0.690287	−	1.19561i	0.281457	−	0.959574i	$-0.409182\pi$
$360$		0			0
$361$	−9.91658	+	17.1760i	−0.521925	+	0.904001i
$362$		0			0
$363$		−	3.33043i		−	0.174802i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−21.8512	−	12.6158i	−1.14062	−	0.658540i	−0.194040	−	0.980994i	$-0.562159\pi$
$367$	−21.8512	−	12.6158i	−1.14062	−	0.658540i	−0.946585	+	0.322454i	$0.895492\pi$
$368$		0			0
$369$	−13.3682	−	23.1544i	−0.695919	−	1.20537i
$370$		0			0
$371$	24.6724	−	10.5245i	1.28093	−	0.546406i
$372$		0			0
$373$	−4.93191	+	2.84744i	−0.255365	+	0.147435i	−0.622218	−	0.782844i	$-0.713768\pi$
$373$	−4.93191	+	2.84744i	−0.255365	+	0.147435i	0.366854	+	0.930279i	$0.380435\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	14.5027i		−	0.746929i
$378$		0			0
$379$	−14.9660			−0.768751			−0.384375	−	0.923177i	$-0.625583\pi$
$379$	−14.9660			−0.768751			−0.384375	+	0.923177i	$0.625583\pi$
$380$		0			0
$381$	0.970337	−	1.68067i	0.0497119	−	0.0861035i
$382$		0			0
$383$	−21.1983	+	12.2388i	−1.08318	+	0.625374i	−0.931753	−	0.363094i	$-0.881720\pi$
$383$	−21.1983	+	12.2388i	−1.08318	+	0.625374i	−0.151428	+	0.988468i	$0.548387\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.63629	−	2.67676i	0.235676	−	0.136068i
$388$		0			0
$389$	−15.6230	+	27.0598i	−0.792118	+	1.37199i	0.132535	+	0.991178i	$0.457688\pi$
$389$	−15.6230	+	27.0598i	−0.792118	+	1.37199i	−0.924653	+	0.380810i	$0.875645\pi$
$390$		0			0
$391$	14.7200			0.744421
$392$		0			0
$393$			5.91757i			0.298502i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.981053	−	0.566411i	0.0492376	−	0.0284274i	−0.475179	−	0.879889i	$-0.657617\pi$
$397$	0.981053	−	0.566411i	0.0492376	−	0.0284274i	0.524417	+	0.851462i	$0.324283\pi$
$398$		0			0
$399$	−4.80523	−	3.60765i	−0.240562	−	0.180608i
$400$		0			0
$401$	1.91112	+	3.31016i	0.0954368	+	0.165301i	0.909791	−	0.415067i	$-0.136242\pi$
$401$	1.91112	+	3.31016i	0.0954368	+	0.165301i	−0.814354	+	0.580368i	$0.802909\pi$
$402$		0			0
$403$	−10.2773	−	5.93359i	−0.511948	−	0.295573i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	2.85626i		−	0.141580i
$408$		0			0
$409$	16.8304	−	29.1512i	0.832211	−	1.44143i	−0.0640699	−	0.997945i	$-0.520408\pi$
$409$	16.8304	−	29.1512i	0.832211	−	1.44143i	0.896281	−	0.443487i	$-0.146259\pi$
$410$		0			0
$411$	0.803496	+	1.39170i	0.0396335	+	0.0686473i
$412$		0			0
$413$	−1.69786	−	3.98026i	−0.0835463	−	0.195856i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7.06042	−	4.07633i	−0.345750	−	0.199619i
$418$		0			0
$419$	0.497270			0.0242933			0.0121466	−	0.999926i	$-0.496134\pi$
$419$	0.497270			0.0242933			0.0121466	+	0.999926i	$0.496134\pi$
$420$		0			0
$421$	−1.28003			−0.0623850			−0.0311925	−	0.999513i	$-0.509930\pi$
$421$	−1.28003			−0.0623850			−0.0311925	+	0.999513i	$0.509930\pi$
$422$		0			0
$423$	17.0515	+	9.84471i	0.829074	+	0.478666i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.103693	+	0.0125452i	0.00501808	+	0.000607106i
$428$		0			0
$429$	0.655291	+	1.13500i	0.0316377	+	0.0547982i
$430$		0			0
$431$	5.14548	−	8.91222i	0.247849	−	0.429287i	−0.715080	−	0.699043i	$-0.753610\pi$
$431$	5.14548	−	8.91222i	0.247849	−	0.429287i	0.962929	+	0.269756i	$0.0869430\pi$
$432$		0			0
$433$			29.8870i			1.43628i	0.695899	+	0.718139i	$0.255006\pi$
$433$			29.8870i			1.43628i	−0.695899	+	0.718139i	$0.744994\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	35.5973	+	20.5521i	1.70285	+	0.983142i
$438$		0			0
$439$	−2.52420	−	4.37205i	−0.120474	−	0.208666i	0.799481	−	0.600692i	$-0.205108\pi$
$439$	−2.52420	−	4.37205i	−0.120474	−	0.208666i	−0.919955	+	0.392025i	$0.871775\pi$
$440$		0			0
$441$	−13.8906	+	14.4867i	−0.661459	+	0.689843i
$442$		0			0
$443$	−10.1964	+	5.88692i	−0.484447	+	0.279696i	−0.722268	−	0.691613i	$-0.756900\pi$
$443$	−10.1964	+	5.88692i	−0.484447	+	0.279696i	0.237821	+	0.971309i	$0.423567\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	8.20307i		−	0.387992i
$448$		0			0
$449$	11.3843			0.537258			0.268629	−	0.963244i	$-0.413429\pi$
$449$	11.3843			0.537258			0.268629	+	0.963244i	$0.413429\pi$
$450$		0			0
$451$	−6.36172	+	11.0188i	−0.299562	+	0.518856i
$452$		0			0
$453$	4.26175	−	2.46052i	0.200234	−	0.115605i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−32.2607	+	18.6257i	−1.50909	+	0.871275i	−0.509149	+	0.860678i	$0.670040\pi$
$457$	−32.2607	+	18.6257i	−1.50909	+	0.871275i	−0.999944	+	0.0105968i	$0.996627\pi$
$458$		0			0
$459$	2.38592	−	4.13254i	0.111365	−	0.192890i
$460$		0			0
$461$	−15.0449			−0.700713			−0.350356	−	0.936616i	$-0.613939\pi$
$461$	−15.0449			−0.700713			−0.350356	+	0.936616i	$0.613939\pi$
$462$		0			0
$463$		−	31.2031i		−	1.45013i	−0.688681	−	0.725065i	$-0.741810\pi$
$463$		−	31.2031i		−	1.45013i	0.688681	−	0.725065i	$-0.258190\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.2539	+	9.38419i	−0.752140	+	0.434248i	−0.826467	−	0.562986i	$-0.809653\pi$
$467$	−16.2539	+	9.38419i	−0.752140	+	0.434248i	0.0743264	+	0.997234i	$0.476319\pi$
$468$		0			0
$469$	−16.3754	+	6.98525i	−0.756144	+	0.322549i
$470$		0			0
$471$	−2.83479	−	4.90999i	−0.130620	−	0.226241i
$472$		0			0
$473$	−2.20634	−	1.27383i	−0.101448	−	0.0585709i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			29.0683i			1.33094i
$478$		0			0
$479$	−0.357254	+	0.618782i	−0.0163234	+	0.0282729i	−0.874072	−	0.485797i	$-0.838529\pi$
$479$	−0.357254	+	0.618782i	−0.0163234	+	0.0282729i	0.857748	+	0.514070i	$0.171863\pi$
$480$		0			0
$481$	−2.75856	−	4.77796i	−0.125779	−	0.217856i
$482$		0			0
$483$	−3.81864	+	5.08626i	−0.173754	+	0.231433i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.4582	+	8.34744i	0.655163	+	0.378259i	0.790432	−	0.612550i	$-0.209856\pi$
$487$	14.4582	+	8.34744i	0.655163	+	0.378259i	−0.135268	+	0.990809i	$0.543190\pi$
$488$		0			0
$489$	1.60500			0.0725807
$490$		0			0
$491$	6.19761			0.279694			0.139847	−	0.990173i	$-0.455339\pi$
$491$	6.19761			0.279694			0.139847	+	0.990173i	$0.455339\pi$
$492$		0			0
$493$	10.6348	+	6.14002i	0.478968	+	0.276532i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.96166	−	13.2685i	0.446841	−	0.595173i
$498$		0			0
$499$	7.23436	+	12.5303i	0.323854	+	0.560932i	0.981280	−	0.192588i	$-0.0616879\pi$
$499$	7.23436	+	12.5303i	0.323854	+	0.560932i	−0.657426	+	0.753519i	$0.728355\pi$
$500$		0			0
$501$	−1.65802	+	2.87178i	−0.0740749	+	0.128301i
$502$		0			0
$503$		−	30.6949i		−	1.36862i	−0.729193	−	0.684308i	$-0.760104\pi$
$503$		−	30.6949i		−	1.36862i	0.729193	−	0.684308i	$-0.239896\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.91073	−	1.10316i	−0.0848585	−	0.0489930i
$508$		0			0
$509$	22.2371	+	38.5158i	0.985641	+	1.70718i	0.639051	+	0.769165i	$0.279327\pi$
$509$	22.2371	+	38.5158i	0.985641	+	1.70718i	0.346591	+	0.938016i	$0.387339\pi$
$510$		0			0
$511$	9.73436	−	4.15239i	0.430623	−	0.183691i
$512$		0			0
$513$	11.5398	−	6.66248i	0.509493	−	0.294156i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	9.36991i		−	0.412088i
$518$		0			0
$519$	−7.27457			−0.319318
$520$		0			0
$521$	6.32497	−	10.9552i	0.277102	−	0.479955i	−0.693561	−	0.720398i	$-0.743959\pi$
$521$	6.32497	−	10.9552i	0.277102	−	0.479955i	0.970663	+	0.240443i	$0.0772927\pi$
$522$		0			0
$523$	8.89504	−	5.13555i	0.388953	−	0.224562i	−0.292753	−	0.956188i	$-0.594572\pi$
$523$	8.89504	−	5.13555i	0.388953	−	0.224562i	0.681706	+	0.731626i	$0.261238\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.70218	−	5.02420i	0.379073	−	0.218858i
$528$		0			0
$529$	10.2541	−	17.7606i	0.445830	−	0.772201i
$530$		0			0
$531$	4.68942			0.203503
$532$		0			0
$533$			24.5764i			1.06452i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.16372	−	2.40393i	0.179678	−	0.103737i
$538$		0			0
$539$	9.27557	+	2.27773i	0.399527	+	0.0981087i
$540$		0			0
$541$	1.06914	+	1.85181i	0.0459660	+	0.0796154i	0.888093	−	0.459664i	$-0.152030\pi$
$541$	1.06914	+	1.85181i	0.0459660	+	0.0796154i	−0.842127	+	0.539279i	$0.818697\pi$
$542$		0			0
$543$	−3.22932	−	1.86445i	−0.138583	−	0.0800111i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	32.0198i		−	1.36907i	−0.728980	−	0.684535i	$-0.760005\pi$
$547$		−	32.0198i		−	1.36907i	0.728980	−	0.684535i	$-0.239995\pi$
$548$		0			0
$549$	−0.0565955	+	0.0980263i	−0.00241544	+	0.00418366i
$550$		0			0
$551$	17.1455	+	29.6968i	0.730422	+	1.26513i
$552$		0			0
$553$	−13.9866	−	1.69215i	−0.594769	−	0.0719574i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.21436	+	4.16521i	0.305682	+	0.176486i	0.644993	−	0.764189i	$-0.276860\pi$
$557$	7.21436	+	4.16521i	0.305682	+	0.176486i	−0.339310	+	0.940674i	$0.610194\pi$
$558$		0			0
$559$	−4.92104			−0.208138
$560$		0			0
$561$	−1.10972			−0.0468525
$562$		0			0
$563$	−16.8557	−	9.73163i	−0.710382	−	0.410139i	0.100821	−	0.994905i	$-0.467853\pi$
$563$	−16.8557	−	9.73163i	−0.710382	−	0.410139i	−0.811202	+	0.584766i	$0.801187\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−8.12024	−	19.0361i	−0.341018	−	0.799442i
$568$		0			0
$569$	9.44624	+	16.3614i	0.396007	+	0.685904i	0.993229	−	0.116172i	$-0.0370622\pi$
$569$	9.44624	+	16.3614i	0.396007	+	0.685904i	−0.597222	+	0.802076i	$0.703729\pi$
$570$		0			0
$571$	9.31505	−	16.1341i	0.389823	−	0.675192i	−0.602603	−	0.798041i	$-0.705870\pi$
$571$	9.31505	−	16.1341i	0.389823	−	0.675192i	0.992425	+	0.122849i	$0.0392030\pi$
$572$		0			0
$573$			5.10426i			0.213234i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	16.1017	+	9.29630i	0.670321	+	0.387010i	0.796198	−	0.605036i	$-0.206841\pi$
$577$	16.1017	+	9.29630i	0.670321	+	0.387010i	−0.125877	+	0.992046i	$0.540175\pi$
$578$		0			0
$579$	2.62574	+	4.54791i	0.109122	+	0.189005i
$580$		0			0
$581$	−31.2587	−	23.4683i	−1.29683	−	0.973627i
$582$		0			0
$583$	11.9799	−	6.91658i	0.496155	−	0.286455i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			10.1383i			0.418452i	0.977867	+	0.209226i	$0.0670944\pi$
$587$			10.1383i			0.418452i	−0.977867	+	0.209226i	$0.932906\pi$
$588$		0			0
$589$	28.0593			1.15616
$590$		0			0
$591$	−2.10589	+	3.64751i	−0.0866247	+	0.150038i
$592$		0			0
$593$	14.7272	−	8.50273i	0.604772	−	0.349165i	−0.166145	−	0.986101i	$-0.553132\pi$
$593$	14.7272	−	8.50273i	0.604772	−	0.349165i	0.770917	+	0.636936i	$0.219799\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.70732	−	0.985720i	0.0698758	−	0.0403428i
$598$		0			0
$599$	−4.09334	+	7.08988i	−0.167250	+	0.289685i	−0.937452	−	0.348115i	$-0.886822\pi$
$599$	−4.09334	+	7.08988i	−0.167250	+	0.289685i	0.770202	+	0.637800i	$0.220155\pi$
$600$		0			0
$601$	−35.3359			−1.44138			−0.720690	−	0.693257i	$-0.756175\pi$
$601$	−35.3359			−1.44138			−0.720690	+	0.693257i	$0.756175\pi$
$602$		0			0
$603$		−	19.2929i		−	0.785669i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	24.4493	−	14.1158i	0.992367	−	0.572943i	0.0863858	−	0.996262i	$-0.472468\pi$
$607$	24.4493	−	14.1158i	0.992367	−	0.572943i	0.905981	+	0.423319i	$0.139135\pi$
$608$		0			0
$609$	−4.88046	+	2.08186i	−0.197766	+	0.0843613i
$610$		0			0
$611$	−9.04940	−	15.6740i	−0.366100	−	0.634103i
$612$		0			0
$613$	26.9837	+	15.5791i	1.08986	+	0.629232i	0.933540	−	0.358474i	$-0.116703\pi$
$613$	26.9837	+	15.5791i	1.08986	+	0.629232i	0.156323	+	0.987706i	$0.450036\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	39.1527i		−	1.57623i	−0.615530	−	0.788114i	$-0.711058\pi$
$617$		−	39.1527i		−	1.57623i	0.615530	−	0.788114i	$-0.288942\pi$
$618$		0			0
$619$	−19.6921	+	34.1078i	−0.791494	+	1.37091i	0.133547	+	0.991042i	$0.457363\pi$
$619$	−19.6921	+	34.1078i	−0.791494	+	1.37091i	−0.925042	+	0.379866i	$0.875970\pi$
$620$		0			0
$621$	−7.05213	−	12.2146i	−0.282992	−	0.490157i
$622$		0			0
$623$	−2.27773	−	0.275568i	−0.0912552	−	0.0110404i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.68364	−	1.54940i	−0.107174	−	0.0618771i
$628$		0			0
$629$	4.67156			0.186267
$630$		0			0
$631$	22.7003			0.903686			0.451843	−	0.892097i	$-0.350767\pi$
$631$	22.7003			0.903686			0.451843	+	0.892097i	$0.350767\pi$
$632$		0			0
$633$	3.46110	+	1.99827i	0.137566	+	0.0794239i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	17.7160	−	5.14810i	0.701935	−	0.203975i
$638$		0			0
$639$	8.99018	+	15.5715i	0.355646	+	0.615997i
$640$		0			0
$641$	−4.20643	+	7.28575i	−0.166144	+	0.287770i	−0.937061	−	0.349166i	$-0.886465\pi$
$641$	−4.20643	+	7.28575i	−0.166144	+	0.287770i	0.770917	+	0.636936i	$0.219798\pi$
$642$		0			0
$643$		−	29.7398i		−	1.17282i	−0.810013	−	0.586412i	$-0.800540\pi$
$643$		−	29.7398i		−	1.17282i	0.810013	−	0.586412i	$-0.199460\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.7806	−	10.8430i	−0.738341	−	0.426281i	0.0831249	−	0.996539i	$-0.473510\pi$
$647$	−18.7806	−	10.8430i	−0.738341	−	0.426281i	−0.821466	+	0.570258i	$0.806843\pi$
$648$		0			0
$649$	−1.11581	−	1.93264i	−0.0437995	−	0.0758629i
$650$		0			0
$651$	−0.521474	+	4.31028i	−0.0204382	+	0.168933i
$652$		0			0
$653$	26.0416	−	15.0351i	1.01909	−	0.588370i	0.105247	−	0.994446i	$-0.466437\pi$
$653$	26.0416	−	15.0351i	1.01909	−	0.588370i	0.913839	+	0.406076i	$0.133103\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			11.4687i			0.447437i
$658$		0			0
$659$	−2.37537			−0.0925311			−0.0462656	−	0.998929i	$-0.514732\pi$
$659$	−2.37537			−0.0925311			−0.0462656	+	0.998929i	$0.514732\pi$
$660$		0			0
$661$	7.23163	−	12.5255i	0.281278	−	0.487187i	−0.690422	−	0.723407i	$-0.742575\pi$
$661$	7.23163	−	12.5255i	0.281278	−	0.487187i	0.971700	+	0.236220i	$0.0759085\pi$
$662$		0			0
$663$	−1.85635	+	1.07176i	−0.0720946	+	0.0416238i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	31.4336	−	18.1482i	1.21711	−	0.702701i
$668$		0			0
$669$	3.92813	−	6.80372i	0.151870	−	0.263047i
$670$		0			0
$671$	0.0538660			0.00207947
$672$		0			0
$673$			8.99653i			0.346791i	0.984852	+	0.173395i	$0.0554738\pi$
$673$			8.99653i			0.346791i	−0.984852	+	0.173395i	$0.944526\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.48810	+	3.74591i	−0.249358	+	0.143967i	−0.619470	−	0.785020i	$-0.712653\pi$
$677$	−6.48810	+	3.74591i	−0.249358	+	0.143967i	0.370112	+	0.928987i	$0.379319\pi$
$678$		0			0
$679$	34.0621	+	25.5730i	1.30718	+	0.981400i
$680$		0			0
$681$	2.26391	+	3.92121i	0.0867532	+	0.150261i
$682$		0			0
$683$	36.6545	+	21.1625i	1.40255	+	0.809760i	0.994653	−	0.103270i	$-0.0329306\pi$
$683$	36.6545	+	21.1625i	1.40255	+	0.809760i	0.407892	+	0.913030i	$0.366264\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			3.04841i			0.116304i
$688$		0			0
$689$	13.3600	−	23.1402i	0.508975	−	0.881570i
$690$		0			0
$691$	−14.3232	−	24.8086i	−0.544882	−	0.943763i	−0.998614	−	0.0526247i	$-0.983241\pi$
$691$	−14.3232	−	24.8086i	−0.544882	−	0.943763i	0.453733	−	0.891138i	$-0.350092\pi$
$692$		0			0
$693$	−6.21440	+	8.27730i	−0.236066	+	0.314429i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.0219	−	10.4049i	−0.682626	−	0.394114i
$698$		0			0
$699$	5.10426			0.193061
$700$		0			0
$701$	−20.4292			−0.771601			−0.385801	−	0.922582i	$-0.626075\pi$
$701$	−20.4292			−0.771601			−0.385801	+	0.922582i	$0.626075\pi$
$702$		0			0
$703$	11.2972	+	6.52247i	0.426084	+	0.246000i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	16.2928	+	38.1949i	0.612754	+	1.43647i
$708$		0			0
$709$	14.4138	+	24.9655i	0.541323	+	0.937600i	0.998828	+	0.0483927i	$0.0154099\pi$
$709$	14.4138	+	24.9655i	0.541323	+	0.937600i	−0.457505	+	0.889207i	$0.651257\pi$
$710$		0			0
$711$	7.63382	−	13.2222i	0.286291	−	0.495870i
$712$		0			0
$713$		−	29.7003i		−	1.11229i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.35310	+	3.09061i	0.199915	+	0.115421i
$718$		0			0
$719$	15.6553	+	27.1158i	0.583844	+	1.01125i	0.995018	+	0.0996906i	$0.0317853\pi$
$719$	15.6553	+	27.1158i	0.583844	+	1.01125i	−0.411175	+	0.911557i	$0.634881\pi$
$720$		0			0
$721$	−4.24864	+	35.1174i	−0.158227	+	1.30784i
$722$		0			0
$723$	3.26050	−	1.88245i	0.121259	−	0.0700092i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			8.17230i			0.303094i	0.988450	+	0.151547i	$0.0484255\pi$
$727$			8.17230i			0.303094i	−0.988450	+	0.151547i	$0.951575\pi$
$728$		0			0
$729$	20.0899			0.744069
$730$		0			0
$731$	2.08342	−	3.60859i	0.0770581	−	0.133469i
$732$		0			0
$733$	−18.5488	+	10.7092i	−0.685116	+	0.395552i	−0.801780	−	0.597620i	$-0.796113\pi$
$733$	−18.5488	+	10.7092i	−0.685116	+	0.395552i	0.116664	+	0.993171i	$0.462780\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.95118	+	4.59061i	−0.292885	+	0.169097i
$738$		0			0
$739$	2.17503	−	3.76726i	0.0800098	−	0.138581i	−0.823244	−	0.567688i	$-0.807838\pi$
$739$	2.17503	−	3.76726i	0.0800098	−	0.138581i	0.903254	+	0.429107i	$0.141172\pi$
$740$		0			0
$741$	−5.98561			−0.219887
$742$		0			0
$743$			6.53328i			0.239683i	0.992793	+	0.119841i	$0.0382386\pi$
$743$			6.53328i			0.239683i	−0.992793	+	0.119841i	$0.961761\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	36.6841	−	21.1796i	1.34220	−	0.774921i
$748$		0			0
$749$	−1.71724	+	14.1939i	−0.0627465	+	0.518635i
$750$		0			0
$751$	−17.2415	−	29.8632i	−0.629153	−	1.08973i	−0.987722	−	0.156222i	$-0.950069\pi$
$751$	−17.2415	−	29.8632i	−0.629153	−	1.08973i	0.358569	−	0.933503i	$-0.383265\pi$
$752$		0			0
$753$	−6.15720	−	3.55486i	−0.224381	−	0.129546i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			44.2425i			1.60802i	0.594614	+	0.804011i	$0.297305\pi$
$757$			44.2425i			1.60802i	−0.594614	+	0.804011i	$0.702695\pi$
$758$		0			0
$759$	−1.64002	+	2.84059i	−0.0595288	+	0.103107i
$760$		0			0
$761$	11.9094	+	20.6277i	0.431715	+	0.747752i	0.997021	−	0.0771290i	$-0.0245753\pi$
$761$	11.9094	+	20.6277i	0.431715	+	0.747752i	−0.565306	+	0.824881i	$0.691242\pi$
$762$		0			0
$763$	−16.4307	−	38.5181i	−0.594831	−	1.39445i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.73307	−	2.15529i	−0.134793	−	0.0778230i
$768$		0			0
$769$	0.158128			0.00570225			0.00285113	−	0.999996i	$-0.499092\pi$
$769$	0.158128			0.00570225			0.00285113	+	0.999996i	$0.499092\pi$
$770$		0			0
$771$	10.3734			0.373588
$772$		0			0
$773$	15.4145	+	8.89957i	0.554421	+	0.320095i	0.750903	−	0.660412i	$-0.229618\pi$
$773$	15.4145	+	8.89957i	0.554421	+	0.320095i	−0.196482	+	0.980507i	$0.562952\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.21189	+	1.61419i	−0.0434764	+	0.0579086i
$778$		0			0
$779$	−29.0549	−	50.3245i	−1.04100	−	1.80306i
$780$		0			0
$781$	4.27830	−	7.41023i	0.153090	−	0.265159i
$782$		0			0
$783$		−	11.7664i		−	0.420496i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−35.9596	−	20.7613i	−1.28182	−	0.740060i	−0.304640	−	0.952467i	$-0.598536\pi$
$787$	−35.9596	−	20.7613i	−1.28182	−	0.740060i	−0.977181	+	0.212407i	$0.931870\pi$
$788$		0			0
$789$	5.20469	+	9.01479i	0.185292	+	0.320935i
$790$		0			0
$791$	38.9813	+	29.2662i	1.38601	+	1.04059i
$792$		0			0
$793$	0.0901072	−	0.0520234i	0.00319980	−	0.00184741i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	25.0933i		−	0.888852i	−0.895816	−	0.444426i	$-0.853408\pi$
$797$		−	25.0933i		−	0.888852i	0.895816	−	0.444426i	$-0.146592\pi$
$798$		0			0
$799$	15.3250			0.542158
$800$		0			0
$801$	1.24318	−	2.15324i	0.0439255	−	0.0760811i
$802$		0			0
$803$	4.72659	−	2.72890i	0.166798	−	0.0963007i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.90296	−	1.67602i	0.102189	−	0.0589989i
$808$		0			0
$809$	6.34744	−	10.9941i	0.223164	−	0.386531i	−0.732603	−	0.680656i	$-0.761695\pi$
$809$	6.34744	−	10.9941i	0.223164	−	0.386531i	0.955767	+	0.294125i	$0.0950281\pi$
$810$		0			0
$811$	17.9749			0.631184			0.315592	−	0.948895i	$-0.397797\pi$
$811$	17.9749			0.631184			0.315592	+	0.948895i	$0.397797\pi$
$812$		0			0
$813$			1.40740i			0.0493595i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	10.0767	−	5.81778i	0.352539	−	0.203538i
$818$		0			0
$819$	−2.40130	+	19.8481i	−0.0839084	+	0.693550i
$820$		0			0
$821$	−10.0341	−	17.3796i	−0.350193	−	0.606553i	0.636090	−	0.771615i	$-0.280551\pi$
$821$	−10.0341	−	17.3796i	−0.350193	−	0.606553i	−0.986283	+	0.165062i	$0.947217\pi$
$822$		0			0
$823$	9.18893	+	5.30523i	0.320306	+	0.184929i	0.651529	−	0.758624i	$-0.274128\pi$
$823$	9.18893	+	5.30523i	0.320306	+	0.184929i	−0.331223	+	0.943553i	$0.607461\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	34.7793i		−	1.20939i	−0.796455	−	0.604697i	$-0.793294\pi$
$827$		−	34.7793i		−	1.20939i	0.796455	−	0.604697i	$-0.206706\pi$
$828$		0			0
$829$	−13.1141	+	22.7142i	−0.455471	+	0.788898i	−0.998715	−	0.0506761i	$-0.983862\pi$
$829$	−13.1141	+	22.7142i	−0.455471	+	0.788898i	0.543244	+	0.839575i	$0.317196\pi$
$830$		0			0
$831$	−1.93905	−	3.35853i	−0.0672648	−	0.116506i
$832$		0			0
$833$	−3.72534	+	15.1707i	−0.129075	+	0.525633i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.33818	−	4.81405i	−0.288210	−	0.166398i
$838$		0			0
$839$	−33.9210			−1.17108			−0.585542	−	0.810642i	$-0.699118\pi$
$839$	−33.9210			−1.17108			−0.585542	+	0.810642i	$0.699118\pi$
$840$		0			0
$841$	1.28003			0.0441391
$842$		0			0
$843$	−0.547399	−	0.316041i	−0.0188534	−	0.0108850i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−24.0026	−	2.90393i	−0.824739	−	0.0997801i
$848$		0			0
$849$	−1.07733	−	1.86599i	−0.0369738	−	0.0640406i
$850$		0			0
$851$	6.90393	−	11.9580i	0.236664	−	0.409913i
$852$		0			0
$853$		−	57.6698i		−	1.97458i	−0.158942	−	0.987288i	$-0.550808\pi$
$853$		−	57.6698i		−	1.97458i	0.158942	−	0.987288i	$-0.449192\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.6607	+	17.7020i	1.04735	+	0.604688i	0.921906	−	0.387413i	$-0.126631\pi$
$857$	30.6607	+	17.7020i	1.04735	+	0.604688i	0.125443	+	0.992101i	$0.459965\pi$
$858$		0			0
$859$	−6.72170	−	11.6423i	−0.229342	−	0.397231i	0.728272	−	0.685289i	$-0.240324\pi$
$859$	−6.72170	−	11.6423i	−0.229342	−	0.397231i	−0.957613	+	0.288057i	$0.906991\pi$
$860$		0			0
$861$	8.27047	−	3.52794i	0.281857	−	0.120232i
$862$		0			0
$863$	−6.11828	+	3.53239i	−0.208269	+	0.120244i	−0.600507	−	0.799620i	$-0.705034\pi$
$863$	−6.11828	+	3.53239i	−0.208269	+	0.120244i	0.392238	+	0.919864i	$0.371701\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			4.38061i			0.148773i
$868$		0			0
$869$	−7.26564			−0.246470
$870$		0			0
$871$	−8.86718	+	15.3584i	−0.300453	+	0.520400i
$872$		0			0
$873$	−39.9741	+	23.0791i	−1.35292	+	0.781108i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−12.9951	+	7.50273i	−0.438814	+	0.253349i	−0.703094	−	0.711097i	$-0.748199\pi$
$877$	−12.9951	+	7.50273i	−0.438814	+	0.253349i	0.264281	+	0.964446i	$0.414865\pi$
$878$		0			0
$879$	4.43259	−	7.67748i	0.149508	−	0.258955i
$880$		0			0
$881$	−39.3699			−1.32641			−0.663203	−	0.748440i	$-0.730803\pi$
$881$	−39.3699			−1.32641			−0.663203	+	0.748440i	$0.730803\pi$
$882$		0			0
$883$			58.2229i			1.95936i	0.200574	+	0.979679i	$0.435719\pi$
$883$			58.2229i			1.95936i	−0.200574	+	0.979679i	$0.564281\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.8637	+	12.6230i	−0.734111	+	0.423839i	−0.819924	−	0.572472i	$-0.805984\pi$
$887$	−21.8637	+	12.6230i	−0.734111	+	0.423839i	0.0858133	+	0.996311i	$0.472651\pi$
$888$		0			0
$889$	−11.2666	−	8.45872i	−0.377871	−	0.283696i
$890$		0			0
$891$	−5.33652	−	9.24312i	−0.178780	−	0.309656i
$892$		0			0
$893$	37.0604	+	21.3968i	1.24018	+	0.716018i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			6.33567i			0.211542i
$898$		0			0
$899$	12.3887	−	21.4578i	0.413185	−	0.715657i
$900$		0			0
$901$	11.3124	+	19.5937i	0.376872	+	0.652761i
$902$		0			0
$903$	0.706414	+	1.65603i	0.0235080	+	0.0551093i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	23.5444	+	13.5933i	0.781778	+	0.451360i	0.837060	−	0.547111i	$-0.184273\pi$
$907$	23.5444	+	13.5933i	0.781778	+	0.451360i	−0.0552822	+	0.998471i	$0.517606\pi$
$908$		0			0
$909$	−45.0000			−1.49256
$910$		0			0
$911$	−40.7882			−1.35137			−0.675687	−	0.737189i	$-0.736153\pi$
$911$	−40.7882			−1.35137			−0.675687	+	0.737189i	$0.736153\pi$
$912$		0			0
$913$	−17.4575	−	10.0791i	−0.577757	−	0.333568i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	42.6483	+	5.15976i	1.40837	+	0.170390i
$918$		0			0
$919$	−23.5369	−	40.7670i	−0.776409	−	1.34478i	−0.933999	−	0.357276i	$-0.883706\pi$
$919$	−23.5369	−	40.7670i	−0.776409	−	1.34478i	0.157590	−	0.987505i	$-0.449628\pi$
$920$		0			0
$921$	4.28638	−	7.42423i	0.141241	−	0.244637i
$922$		0			0
$923$		−	16.5278i		−	0.544020i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−33.1981	−	19.1669i	−1.09037	−	0.629525i
$928$		0			0
$929$	8.99554	+	15.5807i	0.295134	+	0.511187i	0.975016	−	0.222134i	$-0.0713024\pi$
$929$	8.99554	+	15.5807i	0.295134	+	0.511187i	−0.679882	+	0.733321i	$0.737969\pi$
$930$		0			0
$931$	−30.1904	+	31.4859i	−0.989451	+	1.03191i
$932$		0			0
$933$	−2.78339	+	1.60699i	−0.0911242	+	0.0526106i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			37.7003i			1.23162i	0.787896	+	0.615808i	$0.211170\pi$
$937$			37.7003i			1.23162i	−0.787896	+	0.615808i	$0.788830\pi$
$938$		0			0
$939$	0.0340191			0.00111017
$940$		0			0
$941$	−2.41658	+	4.18564i	−0.0787782	+	0.136448i	−0.902723	−	0.430222i	$-0.858435\pi$
$941$	−2.41658	+	4.18564i	−0.0787782	+	0.136448i	0.823945	+	0.566670i	$0.191769\pi$
$942$		0			0
$943$	−53.2677	+	30.7541i	−1.73463	+	1.00149i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.45659	+	1.41831i	−0.0798285	+	0.0460890i	−0.539383	−	0.842061i	$-0.681342\pi$
$947$	−2.45659	+	1.41831i	−0.0798285	+	0.0460890i	0.459554	+	0.888150i	$0.348009\pi$
$948$		0			0
$949$	5.27110	−	9.12982i	0.171107	−	0.296366i
$950$		0			0
$951$	1.29095			0.0418619
$952$		0			0
$953$		−	17.7991i		−	0.576571i	−0.957545	−	0.288285i	$-0.906915\pi$
$953$		−	17.7991i		−	0.576571i	0.957545	−	0.288285i	$-0.0930852\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.36974	+	1.36817i	−0.0766029	+	0.0442267i
$958$		0			0
$959$	10.7306	−	4.57737i	0.346510	−	0.147811i
$960$		0			0
$961$	5.36271	+	9.28849i	0.172991	+	0.299629i
$962$		0			0
$963$	−13.4182	−	7.74701i	−0.432396	−	0.249644i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	15.1581i		−	0.487453i	−0.969844	−	0.243726i	$-0.921630\pi$
$967$		−	15.1581i		−	0.487453i	0.969844	−	0.243726i	$-0.0783698\pi$
$968$		0			0
$969$	2.53413	−	4.38924i	0.0814079	−	0.141003i
$970$		0			0
$971$	23.6921	+	41.0360i	0.760317	+	1.31691i	0.942687	+	0.333678i	$0.108290\pi$
$971$	23.6921	+	41.0360i	0.760317	+	1.31691i	−0.182370	+	0.983230i	$0.558377\pi$
$972$		0			0
$973$	−35.5346	+	47.3305i	−1.13919	+	1.51735i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.5421	−	11.8600i	−0.657200	−	0.379434i	0.134009	−	0.990980i	$-0.457215\pi$
$977$	−20.5421	−	11.8600i	−0.657200	−	0.379434i	−0.791209	+	0.611546i	$0.790548\pi$
$978$		0			0
$979$	−1.18322			−0.0378158
$980$		0			0
$981$	45.3808			1.44890
$982$		0			0
$983$	29.8383	+	17.2272i	0.951695	+	0.549461i	0.893607	−	0.448850i	$-0.148166\pi$
$983$	29.8383	+	17.2272i	0.951695	+	0.549461i	0.0580876	+	0.998311i	$0.481500\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.97559	+	5.29531i	−0.126544	+	0.168551i
$988$		0			0
$989$	−6.15802	−	10.6660i	−0.195814	−	0.339159i
$990$		0			0
$991$	20.8304	−	36.0794i	0.661700	−	1.14610i	−0.318468	−	0.947934i	$-0.603168\pi$
$991$	20.8304	−	36.0794i	0.661700	−	1.14610i	0.980169	−	0.198165i	$-0.0634982\pi$
$992$		0			0
$993$		−	7.16138i		−	0.227260i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−21.4672	−	12.3941i	−0.679874	−	0.392525i	0.119934	−	0.992782i	$-0.461732\pi$
$997$	−21.4672	−	12.3941i	−0.679874	−	0.392525i	−0.799808	+	0.600256i	$0.795065\pi$
$998$		0			0
$999$	−2.23808	−	3.87647i	−0.0708097	−	0.122646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.r.d.249.3		12
5.2	odd	4		700.2.i.d.501.2	yes	6
5.3	odd	4		700.2.i.e.501.2	yes	6
5.4	even	2	inner	700.2.r.d.249.4		12
7.2	even	3	inner	700.2.r.d.149.4		12
7.3	odd	6		4900.2.e.s.2549.3		6
7.4	even	3		4900.2.e.t.2549.4		6
35.2	odd	12		700.2.i.d.401.2	✓	6
35.3	even	12		4900.2.a.bd.1.2		3
35.4	even	6		4900.2.e.t.2549.3		6
35.9	even	6	inner	700.2.r.d.149.3		12
35.17	even	12		4900.2.a.bb.1.2		3
35.18	odd	12		4900.2.a.ba.1.2		3
35.23	odd	12		700.2.i.e.401.2	yes	6
35.24	odd	6		4900.2.e.s.2549.4		6
35.32	odd	12		4900.2.a.bc.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.2	✓	6	35.2	odd	12
700.2.i.d.501.2	yes	6	5.2	odd	4
700.2.i.e.401.2	yes	6	35.23	odd	12
700.2.i.e.501.2	yes	6	5.3	odd	4
700.2.r.d.149.3		12	35.9	even	6	inner
700.2.r.d.149.4		12	7.2	even	3	inner
700.2.r.d.249.3		12	1.1	even	1	trivial
700.2.r.d.249.4		12	5.4	even	2	inner
4900.2.a.ba.1.2		3	35.18	odd	12
4900.2.a.bb.1.2		3	35.17	even	12
4900.2.a.bc.1.2		3	35.32	odd	12
4900.2.a.bd.1.2		3	35.3	even	12
4900.2.e.s.2549.3		6	7.3	odd	6
4900.2.e.s.2549.4		6	35.24	odd	6
4900.2.e.t.2549.3		6	35.4	even	6
4900.2.e.t.2549.4		6	7.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.315621 - 0.182224i) q^{3} +(-1.58850 + 2.11581i) q^{7} +(-1.43359 - 2.48305i) q^{9} +(-0.682224 + 1.18165i) q^{11} +2.63555i q^{13} +(-1.93264 - 1.11581i) q^{17} +(-3.11581 - 5.39675i) q^{19} +(0.886917 - 0.378332i) q^{21} +(-5.71237 + 3.29804i) q^{23} +2.13828i q^{27} -5.50273 q^{29} +(-2.25136 + 3.89948i) q^{31} +(0.430649 - 0.248635i) q^{33} +(-1.81289 + 1.04667i) q^{37} +(0.480261 - 0.831836i) q^{39} +9.32497 q^{41} +1.86718i q^{43} +(-5.94715 + 3.43359i) q^{47} +(-1.95333 - 6.72194i) q^{49} +(0.406656 + 0.704349i) q^{51} +(-8.78001 - 5.06914i) q^{53} +2.27110i q^{57} +(-0.817776 + 1.41643i) q^{59} +(-0.0197391 - 0.0341891i) q^{61} +(7.53092 + 0.911120i) q^{63} +(5.82739 + 3.36445i) q^{67} +2.40393 q^{69} -6.27110 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-1.41643 - 3.32051i) q^{77} +(2.66248 + 4.61156i) q^{79} +(-3.91112 + 6.77426i) q^{81} +14.7738i q^{83} +(1.73678 + 1.00273i) q^{87} +(0.433589 + 0.750998i) q^{89} +(-5.57633 - 4.18658i) q^{91} +(1.42116 - 0.820506i) q^{93} -16.0988i q^{97} +3.91211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91}+ \cdots - 84 q^{99}+O(q^{100}) \) 12 * q + 16 * q^9 - 8 * q^11 - 4 * q^19 - 22 * q^21 + 6 * q^31 - 28 * q^39 + 44 * q^41 - 24 * q^49 + 6 * q^51 - 10 * q^59 - 34 * q^61 + 96 * q^69 - 76 * q^71 - 2 * q^79 - 46 * q^81 - 28 * q^89 + 34 * q^91 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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