LMFDB - Embedded newform 700.2.i.d.401.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(401,700)] 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("700.401"); 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, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-1,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.2
Root			$1.09935 - 1.90412i$ of defining polynomial
Character	$\chi$	$=$	700.401
Dual form			700.2.i.d.501.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.182224 - 0.315621i) q^{3} +(-2.11581 + 1.58850i) q^{7} +(1.43359 - 2.48305i) q^{9} +(-0.682224 - 1.18165i) q^{11} +2.63555 q^{13} +(1.11581 + 1.93264i) q^{17} +(3.11581 - 5.39675i) q^{19} +(0.886917 + 0.378332i) q^{21} +(3.29804 - 5.71237i) q^{23} -2.13828 q^{27} +5.50273 q^{29} +(-2.25136 - 3.89948i) q^{31} +(-0.248635 + 0.430649i) q^{33} +(-1.04667 + 1.81289i) q^{37} +(-0.480261 - 0.831836i) q^{39} +9.32497 q^{41} +1.86718 q^{43} +(-3.43359 + 5.94715i) q^{47} +(1.95333 - 6.72194i) q^{49} +(0.406656 - 0.704349i) q^{51} +(-5.06914 - 8.78001i) q^{53} -2.27110 q^{57} +(0.817776 + 1.41643i) q^{59} +(-0.0197391 + 0.0341891i) q^{61} +(0.911120 + 7.53092i) q^{63} +(-3.36445 - 5.82739i) q^{67} -2.40393 q^{69} -6.27110 q^{71} +(-2.00000 - 3.46410i) q^{73} +(3.32051 + 1.41643i) q^{77} +(-2.66248 + 4.61156i) q^{79} +(-3.91112 - 6.77426i) q^{81} +14.7738 q^{83} +(-1.00273 - 1.73678i) q^{87} +(-0.433589 + 0.750998i) q^{89} +(-5.57633 + 4.18658i) q^{91} +(-0.820506 + 1.42116i) q^{93} +16.0988 q^{97} -3.91211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 4 q^{7} - 8 q^{9} - 4 q^{11} + 16 q^{13} - 10 q^{17} + 2 q^{19} - 11 q^{21} + 3 q^{23} + 20 q^{27} + 3 q^{31} - 18 q^{33} - 6 q^{37} + 14 q^{39} + 22 q^{41} - 22 q^{43} - 4 q^{47} + 12 q^{49}+ \cdots + 42 q^{99}+O(q^{100}) $ 6 * q - q^3 + 4 * q^7 - 8 * q^9 - 4 * q^11 + 16 * q^13 - 10 * q^17 + 2 * q^19 - 11 * q^21 + 3 * q^23 + 20 * q^27 + 3 * q^31 - 18 * q^33 - 6 * q^37 + 14 * q^39 + 22 * q^41 - 22 * q^43 - 4 * q^47 + 12 * q^49 + 3 * q^51 - 14 * q^53 - 14 * q^57 + 5 * q^59 - 17 * q^61 + 5 * q^63 - 20 * q^67 - 48 * q^69 - 38 * q^71 - 12 * q^73 - 13 * q^77 + q^79 - 23 * q^81 + 56 * q^83 + 27 * q^87 + 14 * q^89 + 17 * q^91 + 28 * q^93 + 30 * q^97 + 42 * q^99

Character values

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

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

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
$3$	−0.182224	−	0.315621i	−0.105207	−	0.182224i	0.808616	−	0.588337i	$-0.200217\pi$
$3$	−0.182224	−	0.315621i	−0.105207	−	0.182224i	−0.913823	+	0.406113i	$0.866884\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.11581	+	1.58850i	−0.799702	+	0.600397i
$7$	−2.11581	+	1.58850i	−0.799702	+	0.600397i
$8$		0			0
$9$	1.43359	−	2.48305i	0.477863	−	0.827683i
$10$		0			0
$11$	−0.682224	−	1.18165i	−0.205698	−	0.356280i	0.744657	−	0.667448i	$-0.232613\pi$
$11$	−0.682224	−	1.18165i	−0.205698	−	0.356280i	−0.950355	+	0.311168i	$0.899280\pi$
$12$		0			0
$13$	2.63555			0.730971			0.365485	−	0.930817i	$-0.380903\pi$
$13$	2.63555			0.730971			0.365485	+	0.930817i	$0.380903\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.11581	+	1.93264i	0.270624	+	0.468735i	0.969022	−	0.246975i	$-0.0794365\pi$
$17$	1.11581	+	1.93264i	0.270624	+	0.468735i	−0.698398	+	0.715710i	$0.746103\pi$
$18$		0			0
$19$	3.11581	−	5.39675i	0.714816	−	1.23810i	−0.248214	−	0.968705i	$-0.579844\pi$
$19$	3.11581	−	5.39675i	0.714816	−	1.23810i	0.963030	−	0.269393i	$-0.0868231\pi$
$20$		0			0
$21$	0.886917	+	0.378332i	0.193541	+	0.0825589i
$22$		0			0
$23$	3.29804	−	5.71237i	0.687688	−	1.19111i	−0.284896	−	0.958559i	$-0.591959\pi$
$23$	3.29804	−	5.71237i	0.687688	−	1.19111i	0.972584	−	0.232552i	$-0.0747077\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.13828			−0.411512
$28$		0			0
$29$	5.50273			1.02183			0.510916	−	0.859631i	$-0.329306\pi$
$29$	5.50273			1.02183			0.510916	+	0.859631i	$0.329306\pi$
$30$		0			0
$31$	−2.25136	−	3.89948i	−0.404357	−	0.700367i	0.589889	−	0.807484i	$-0.299171\pi$
$31$	−2.25136	−	3.89948i	−0.404357	−	0.700367i	−0.994246	+	0.107117i	$0.965838\pi$
$32$		0			0
$33$	−0.248635	+	0.430649i	−0.0432818	+	0.0749663i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.04667	+	1.81289i	−0.172072	+	0.298037i	−0.939144	−	0.343524i	$-0.888379\pi$
$37$	−1.04667	+	1.81289i	−0.172072	+	0.298037i	0.767072	+	0.641561i	$0.221713\pi$
$38$		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
$43$	1.86718			0.284742			0.142371	−	0.989813i	$-0.454527\pi$
$43$	1.86718			0.284742			0.142371	+	0.989813i	$0.454527\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.43359	+	5.94715i	−0.500840	+	0.867481i	0.499159	+	0.866510i	$0.333642\pi$
$47$	−3.43359	+	5.94715i	−0.500840	+	0.867481i	−1.00000		0.000970685i	$0.999691\pi$
$48$		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
$53$	−5.06914	−	8.78001i	−0.696300	−	1.20603i	−0.969740	−	0.244138i	$-0.921495\pi$
$53$	−5.06914	−	8.78001i	−0.696300	−	1.20603i	0.273440	−	0.961889i	$-0.411838\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.27110			−0.300815
$58$		0			0
$59$	0.817776	+	1.41643i	0.106465	+	0.184403i	0.914336	−	0.404956i	$-0.132713\pi$
$59$	0.817776	+	1.41643i	0.106465	+	0.184403i	−0.807871	+	0.589360i	$0.799380\pi$
$60$		0			0
$61$	−0.0197391	+	0.0341891i	−0.00252733	+	0.00437747i	−0.867286	−	0.497810i	$-0.834138\pi$
$61$	−0.0197391	+	0.0341891i	−0.00252733	+	0.00437747i	0.864759	+	0.502187i	$0.167471\pi$
$62$		0			0
$63$	0.911120	+	7.53092i	0.114790	+	0.948807i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.36445	−	5.82739i	−0.411033	−	0.711930i	0.583970	−	0.811775i	$-0.301498\pi$
$67$	−3.36445	−	5.82739i	−0.411033	−	0.711930i	−0.995003	+	0.0998455i	$0.968165\pi$
$68$		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
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.32051	+	1.41643i	0.378407	+	0.161417i
$78$		0			0
$79$	−2.66248	+	4.61156i	−0.299553	+	0.518841i	−0.976034	−	0.217619i	$-0.930171\pi$
$79$	−2.66248	+	4.61156i	−0.299553	+	0.518841i	0.676481	+	0.736460i	$0.263504\pi$
$80$		0			0
$81$	−3.91112	−	6.77426i	−0.434569	−	0.752695i
$82$		0			0
$83$	14.7738			1.62164			0.810819	−	0.585296i	$-0.199022\pi$
$83$	14.7738			1.62164			0.810819	+	0.585296i	$0.199022\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.00273	−	1.73678i	−0.107504	−	0.186202i
$88$		0			0
$89$	−0.433589	+	0.750998i	−0.0459603	+	0.0796056i	−0.888090	−	0.459669i	$-0.847968\pi$
$89$	−0.433589	+	0.750998i	−0.0459603	+	0.0796056i	0.842130	+	0.539274i	$0.181301\pi$
$90$		0			0
$91$	−5.57633	+	4.18658i	−0.584559	+	0.438873i
$92$		0			0
$93$	−0.820506	+	1.42116i	−0.0850825	+	0.147367i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	16.0988			1.63459			0.817293	−	0.576222i	$-0.195474\pi$
$97$	16.0988			1.63459			0.817293	+	0.576222i	$0.195474\pi$
$98$		0			0
$99$	−3.91211			−0.393182
$100$		0			0
$101$	7.84744	+	13.5922i	0.780849	+	1.35247i	0.931448	+	0.363876i	$0.118547\pi$
$101$	7.84744	+	13.5922i	0.780849	+	1.35247i	−0.150598	+	0.988595i	$0.548120\pi$
$102$		0			0
$103$	−6.68495	+	11.5787i	−0.658688	+	1.14088i	0.322267	+	0.946649i	$0.395555\pi$
$103$	−6.68495	+	11.5787i	−0.658688	+	1.14088i	−0.980956	+	0.194233i	$0.937778\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.70196	−	4.67994i	0.261209	−	0.452427i	−0.705355	−	0.708854i	$-0.749212\pi$
$107$	2.70196	−	4.67994i	0.261209	−	0.452427i	0.966563	+	0.256428i	$0.0825456\pi$
$108$		0			0
$109$	7.91385	+	13.7072i	0.758009	+	1.31291i	0.943864	+	0.330333i	$0.107161\pi$
$109$	7.91385	+	13.7072i	0.758009	+	1.31291i	−0.185855	+	0.982577i	$0.559505\pi$
$110$		0			0
$111$	0.762915			0.0724127
$112$		0			0
$113$	−18.4238			−1.73316			−0.866581	−	0.499036i	$-0.833688\pi$
$113$	−18.4238			−1.73316			−0.866581	+	0.499036i	$0.833688\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.77830	−	6.54420i	0.349304	−	0.605012i
$118$		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
$123$	−1.69923	−	2.94316i	−0.153215	−	0.265376i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.32497			−0.472515			−0.236257	−	0.971691i	$-0.575921\pi$
$127$	−5.32497			−0.472515			−0.236257	+	0.971691i	$0.575921\pi$
$128$		0			0
$129$	−0.340245	−	0.589321i	−0.0299569	−	0.0518868i
$130$		0			0
$131$	−8.11854	+	14.0617i	−0.709320	+	1.22858i	0.255789	+	0.966733i	$0.417665\pi$
$131$	−8.11854	+	14.0617i	−0.709320	+	1.22858i	−0.965110	+	0.261846i	$0.915669\pi$
$132$		0			0
$133$	1.98026	+	16.3680i	0.171710	+	1.41928i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.20469	+	3.81864i	0.188360	+	0.326248i	0.944703	−	0.327926i	$-0.106350\pi$
$137$	2.20469	+	3.81864i	0.188360	+	0.326248i	−0.756344	+	0.654174i	$0.773016\pi$
$138$		0			0
$139$	−22.3699			−1.89739			−0.948695	−	0.316192i	$-0.897596\pi$
$139$	−22.3699			−1.89739			−0.948695	+	0.316192i	$0.897596\pi$
$140$		0			0
$141$	2.50273			0.210768
$142$		0			0
$143$	−1.79804	−	3.11429i	−0.150359	−	0.260430i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.47753	+	0.608388i	−0.204343	+	0.0501790i
$148$		0			0
$149$	−11.2541	+	19.4927i	−0.921971	+	1.59690i	−0.125610	+	0.992080i	$0.540089\pi$
$149$	−11.2541	+	19.4927i	−0.921971	+	1.59690i	−0.796361	+	0.604822i	$0.793244\pi$
$150$		0			0
$151$	−6.75136	−	11.6937i	−0.549418	−	0.951620i	−0.998314	−	0.0580365i	$-0.981516\pi$
$151$	−6.75136	−	11.6937i	−0.549418	−	0.951620i	0.448896	−	0.893584i	$-0.351817\pi$
$152$		0			0
$153$	6.39847			0.517285
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.77830	−	13.4724i	−0.620776	−	1.07522i	−0.989342	−	0.145613i	$-0.953484\pi$
$157$	−7.77830	−	13.4724i	−0.620776	−	1.07522i	0.368566	−	0.929602i	$-0.379849\pi$
$158$		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
$163$	2.20196	−	3.81391i	0.172471	−	0.298729i	−0.766812	−	0.641872i	$-0.778158\pi$
$163$	2.20196	−	3.81391i	0.172471	−	0.298729i	0.939283	+	0.343143i	$0.111492\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.09880			0.704087			0.352043	−	0.935984i	$-0.385487\pi$
$167$	9.09880			0.704087			0.352043	+	0.935984i	$0.385487\pi$
$168$		0			0
$169$	−6.05387			−0.465682
$170$		0			0
$171$	−8.93359	−	15.4734i	−0.683169	−	1.18328i
$172$		0			0
$173$	−9.98026	+	17.2863i	−0.758785	+	1.31425i	0.184685	+	0.982798i	$0.440873\pi$
$173$	−9.98026	+	17.2863i	−0.758785	+	1.31425i	−0.943470	+	0.331457i	$0.892460\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.298037	−	0.516215i	0.0224018	−	0.0388011i
$178$		0			0
$179$	6.59607	+	11.4247i	0.493014	+	0.853925i	0.999968	−	0.00804839i	$-0.00256191\pi$
$179$	6.59607	+	11.4247i	0.493014	+	0.853925i	−0.506954	+	0.861973i	$0.669229\pi$
$180$		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
$183$	0.0143878			0.00106357
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.52247	−	2.63699i	0.111334	−	0.192836i
$188$		0			0
$189$	4.52420	−	3.39666i	0.329087	−	0.247071i
$190$		0			0
$191$	−7.00273	+	12.1291i	−0.506700	+	0.877630i	0.493270	+	0.869876i	$0.335801\pi$
$191$	−7.00273	+	12.1291i	−0.506700	+	0.877630i	−0.999970	+	0.00775353i	$0.997532\pi$
$192$		0			0
$193$	−7.20469	−	12.4789i	−0.518605	−	0.898250i	−0.999766	−	0.0216183i	$-0.993118\pi$
$193$	−7.20469	−	12.4789i	−0.518605	−	0.898250i	0.481161	−	0.876632i	$-0.340215\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.5566			0.823373			0.411687	−	0.911325i	$-0.364940\pi$
$197$	11.5566			0.823373			0.411687	+	0.911325i	$0.364940\pi$
$198$		0			0
$199$	2.70469	+	4.68467i	0.191731	+	0.332087i	0.945824	−	0.324680i	$-0.105257\pi$
$199$	2.70469	+	4.68467i	0.191731	+	0.332087i	−0.754093	+	0.656767i	$0.771923\pi$
$200$		0			0
$201$	−1.22617	+	2.12378i	−0.0864871	+	0.149800i
$202$		0			0
$203$	−11.6427	+	8.74109i	−0.817161	+	0.613504i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−9.45606	−	16.3784i	−0.657241	−	1.13838i
$208$		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
$213$	1.14275	+	1.97929i	0.0782997	+	0.135619i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.9578	+	4.67427i	0.743863	+	0.317310i
$218$		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
$223$	21.5566			1.44354			0.721768	−	0.692135i	$-0.243330\pi$
$223$	21.5566			1.44354			0.721768	+	0.692135i	$0.243330\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.21189	+	10.7593i	0.412297	+	0.714120i	0.995141	−	0.0984646i	$-0.0313931\pi$
$227$	6.21189	+	10.7593i	0.412297	+	0.714120i	−0.582843	+	0.812585i	$0.698060\pi$
$228$		0			0
$229$	4.18222	−	7.24382i	0.276369	−	0.478685i	−0.694110	−	0.719868i	$-0.744202\pi$
$229$	4.18222	−	7.24382i	0.276369	−	0.478685i	0.970480	+	0.241183i	$0.0775354\pi$
$230$		0			0
$231$	−0.158021	−	1.30613i	−0.0103970	−	0.0859370i
$232$		0			0
$233$	7.00273	−	12.1291i	0.458764	−	0.794603i	−0.540132	−	0.841580i	$-0.681626\pi$
$233$	7.00273	−	12.1291i	0.458764	−	0.794603i	0.998896	+	0.0469777i	$0.0149590\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.94067			0.126060
$238$		0			0
$239$	16.9605			1.09708			0.548542	−	0.836123i	$-0.315183\pi$
$239$	16.9605			1.09708			0.548542	+	0.836123i	$0.315183\pi$
$240$		0			0
$241$	−5.16521	−	8.94641i	−0.332721	−	0.576289i	0.650324	−	0.759657i	$-0.274633\pi$
$241$	−5.16521	−	8.94641i	−0.332721	−	0.576289i	−0.983044	+	0.183368i	$0.941300\pi$
$242$		0			0
$243$	−4.63282	+	8.02428i	−0.297196	+	0.514758i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.21189	−	14.2234i	0.522510	−	0.905014i
$248$		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
$253$	−9.00000			−0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.2316	+	24.6499i	−0.887744	+	1.53762i	−0.0452090	+	0.998978i	$0.514395\pi$
$257$	−14.2316	+	24.6499i	−0.887744	+	1.53762i	−0.842535	+	0.538641i	$0.818938\pi$
$258$		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
$263$	−14.2810	−	24.7355i	−0.880606	−	1.52525i	−0.850669	−	0.525702i	$-0.823803\pi$
$263$	−14.2810	−	24.7355i	−0.880606	−	1.52525i	−0.0299373	−	0.999552i	$-0.509531\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.316041			0.0193414
$268$		0			0
$269$	4.59880	+	7.96536i	0.280394	+	0.485657i	0.971482	−	0.237114i	$-0.0762016\pi$
$269$	4.59880	+	7.96536i	0.280394	+	0.485657i	−0.691088	+	0.722771i	$0.742868\pi$
$270$		0			0
$271$	−1.93086	+	3.34435i	−0.117291	+	0.203155i	−0.918693	−	0.394971i	$-0.870754\pi$
$271$	−1.93086	+	3.34435i	−0.117291	+	0.203155i	0.801402	+	0.598126i	$0.204088\pi$
$272$		0			0
$273$	2.33752	+	0.997115i	0.141473	+	0.0603481i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.32051	−	9.21539i	−0.319678	−	0.553699i	0.660743	−	0.750613i	$-0.270241\pi$
$277$	−5.32051	−	9.21539i	−0.319678	−	0.553699i	−0.980421	+	0.196914i	$0.936908\pi$
$278$		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
$283$	2.95606	+	5.12004i	0.175719	+	0.304355i	0.940410	−	0.340043i	$-0.110442\pi$
$283$	2.95606	+	5.12004i	0.175719	+	0.304355i	−0.764691	+	0.644398i	$0.777108\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−19.7299	+	14.8127i	−1.16462	+	0.874368i
$288$		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
$293$	24.3250			1.42108			0.710540	−	0.703657i	$-0.248451\pi$
$293$	24.3250			1.42108			0.710540	+	0.703657i	$0.248451\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.45879	+	2.52669i	0.0846474	+	0.146614i
$298$		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
$303$	2.85998	−	4.95364i	0.164302	−	0.284579i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−23.5226			−1.34250			−0.671252	−	0.741229i	$-0.734243\pi$
$307$	−23.5226			−1.34250			−0.671252	+	0.741229i	$0.734243\pi$
$308$		0			0
$309$	4.87264			0.277195
$310$		0			0
$311$	4.40939	+	7.63728i	0.250033	+	0.433070i	0.963535	−	0.267583i	$-0.0862251\pi$
$311$	4.40939	+	7.63728i	0.250033	+	0.433070i	−0.713501	+	0.700654i	$0.752892\pi$
$312$		0			0
$313$	0.0466721	−	0.0808384i	0.00263806	−	0.00456926i	−0.864703	−	0.502283i	$-0.832494\pi$
$313$	0.0466721	−	0.0808384i	0.00263806	−	0.00456926i	0.867341	+	0.497714i	$0.165827\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.77110	+	3.06764i	−0.0994751	+	0.172296i	−0.911468	−	0.411372i	$-0.865050\pi$
$317$	−1.77110	+	3.06764i	−0.0994751	+	0.172296i	0.811992	+	0.583668i	$0.198383\pi$
$318$		0			0
$319$	−3.75409	−	6.50228i	−0.210189	−	0.364058i
$320$		0			0
$321$	−1.96945			−0.109924
$322$		0			0
$323$	13.9067			0.773787
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.88419	−	4.99556i	0.159496	−	0.276255i
$328$		0			0
$329$	−2.18222	−	18.0373i	−0.120310	−	0.994429i
$330$		0			0
$331$	9.82497	−	17.0173i	0.540029	−	0.935358i	−0.458872	−	0.888502i	$-0.651747\pi$
$331$	9.82497	−	17.0173i	0.540029	−	0.935358i	0.998902	−	0.0468558i	$-0.0149201\pi$
$332$		0			0
$333$	3.00099	+	5.19788i	0.164454	+	0.284842i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−23.0449			−1.25534			−0.627669	−	0.778480i	$-0.715991\pi$
$337$	−23.0449			−1.25534			−0.627669	+	0.778480i	$0.715991\pi$
$338$		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
$343$	6.54494	+	17.3252i	0.353393	+	0.935475i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.2810	+	19.5393i	0.605597	+	1.04893i	0.991957	+	0.126577i	$0.0403991\pi$
$347$	11.2810	+	19.5393i	0.605597	+	1.04893i	−0.386360	+	0.922348i	$0.626268\pi$
$348$		0			0
$349$	14.3250			0.766798			0.383399	−	0.923583i	$-0.374753\pi$
$349$	14.3250			0.766798			0.383399	+	0.923583i	$0.374753\pi$
$350$		0			0
$351$	−5.63555			−0.300804
$352$		0			0
$353$	−16.3502	−	28.3193i	−0.870232	−	1.50729i	−0.861757	−	0.507321i	$-0.830636\pi$
$353$	−16.3502	−	28.3193i	−0.870232	−	1.50729i	−0.00847467	−	0.999964i	$-0.502698\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.258451	+	2.13624i	0.0136787	+	0.113062i
$358$		0			0
$359$	13.0791	−	22.6536i	0.690287	−	1.19561i	−0.281457	−	0.959574i	$-0.590818\pi$
$359$	13.0791	−	22.6536i	0.690287	−	1.19561i	0.971744	−	0.236038i	$-0.0758489\pi$
$360$		0			0
$361$	−9.91658	−	17.1760i	−0.521925	−	0.904001i
$362$		0			0
$363$	−3.33043			−0.174802
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.6158	+	21.8512i	0.658540	+	1.14062i	0.980994	+	0.194040i	$0.0621590\pi$
$367$	12.6158	+	21.8512i	0.658540	+	1.14062i	−0.322454	+	0.946585i	$0.604508\pi$
$368$		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
$373$	2.84744	−	4.93191i	0.147435	−	0.255365i	−0.782844	−	0.622218i	$-0.786232\pi$
$373$	2.84744	−	4.93191i	0.147435	−	0.255365i	0.930279	+	0.366854i	$0.119565\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.5027			0.746929
$378$		0			0
$379$	14.9660			0.768751			0.384375	−	0.923177i	$-0.374417\pi$
$379$	14.9660			0.768751			0.384375	+	0.923177i	$0.374417\pi$
$380$		0			0
$381$	0.970337	+	1.68067i	0.0497119	+	0.0861035i
$382$		0			0
$383$	12.2388	−	21.1983i	0.625374	−	1.08318i	−0.363094	−	0.931753i	$-0.618280\pi$
$383$	12.2388	−	21.1983i	0.625374	−	1.08318i	0.988468	−	0.151428i	$-0.0483871\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.67676	−	4.63629i	0.136068	−	0.235676i
$388$		0			0
$389$	15.6230	+	27.0598i	0.792118	+	1.37199i	0.924653	+	0.380810i	$0.124355\pi$
$389$	15.6230	+	27.0598i	0.792118	+	1.37199i	−0.132535	+	0.991178i	$0.542312\pi$
$390$		0			0
$391$	14.7200			0.744421
$392$		0			0
$393$	5.91757			0.298502
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.566411	−	0.981053i	0.0284274	−	0.0492376i	−0.851462	−	0.524417i	$-0.824283\pi$
$397$	0.566411	−	0.981053i	0.0284274	−	0.0492376i	0.879889	+	0.475179i	$0.157617\pi$
$398$		0			0
$399$	4.80523	−	3.60765i	0.240562	−	0.180608i
$400$		0			0
$401$	1.91112	−	3.31016i	0.0954368	−	0.165301i	−0.814354	−	0.580368i	$-0.802909\pi$
$401$	1.91112	−	3.31016i	0.0954368	−	0.165301i	0.909791	+	0.415067i	$0.136242\pi$
$402$		0			0
$403$	−5.93359	−	10.2773i	−0.295573	−	0.511948i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.85626			0.141580
$408$		0			0
$409$	−16.8304	−	29.1512i	−0.832211	−	1.44143i	−0.896281	−	0.443487i	$-0.853741\pi$
$409$	−16.8304	−	29.1512i	−0.832211	−	1.44143i	0.0640699	−	0.997945i	$-0.479592\pi$
$410$		0			0
$411$	0.803496	−	1.39170i	0.0396335	−	0.0686473i
$412$		0			0
$413$	−3.98026	−	1.69786i	−0.195856	−	0.0835463i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.07633	+	7.06042i	0.199619	+	0.345750i
$418$		0			0
$419$	−0.497270			−0.0242933			−0.0121466	−	0.999926i	$-0.503866\pi$
$419$	−0.497270			−0.0242933			−0.0121466	+	0.999926i	$0.503866\pi$
$420$		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
$423$	9.84471	+	17.0515i	0.478666	+	0.829074i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.0125452	−	0.103693i	−0.000607106	−	0.00501808i
$428$		0			0
$429$	−0.655291	+	1.13500i	−0.0316377	+	0.0547982i
$430$		0			0
$431$	5.14548	+	8.91222i	0.247849	+	0.429287i	0.962929	−	0.269756i	$-0.0869430\pi$
$431$	5.14548	+	8.91222i	0.247849	+	0.429287i	−0.715080	+	0.699043i	$0.753610\pi$
$432$		0			0
$433$	29.8870			1.43628			0.718139	−	0.695899i	$-0.244994\pi$
$433$	29.8870			1.43628			0.718139	+	0.695899i	$0.244994\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−20.5521	−	35.5973i	−0.983142	−	1.70285i
$438$		0			0
$439$	2.52420	−	4.37205i	0.120474	−	0.208666i	−0.799481	−	0.600692i	$-0.794892\pi$
$439$	2.52420	−	4.37205i	0.120474	−	0.208666i	0.919955	+	0.392025i	$0.128225\pi$
$440$		0			0
$441$	−13.8906	−	14.4867i	−0.661459	−	0.689843i
$442$		0			0
$443$	5.88692	−	10.1964i	0.279696	−	0.484447i	−0.691613	−	0.722268i	$-0.743100\pi$
$443$	5.88692	−	10.1964i	0.279696	−	0.484447i	0.971309	+	0.237821i	$0.0764330\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.20307			0.387992
$448$		0			0
$449$	−11.3843			−0.537258			−0.268629	−	0.963244i	$-0.586571\pi$
$449$	−11.3843			−0.537258			−0.268629	+	0.963244i	$0.586571\pi$
$450$		0			0
$451$	−6.36172	−	11.0188i	−0.299562	−	0.518856i
$452$		0			0
$453$	−2.46052	+	4.26175i	−0.115605	+	0.200234i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.6257	+	32.2607i	−0.871275	+	1.50909i	−0.0105968	+	0.999944i	$0.503373\pi$
$457$	−18.6257	+	32.2607i	−0.871275	+	1.50909i	−0.860678	+	0.509149i	$0.829960\pi$
$458$		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
$463$	−31.2031			−1.45013			−0.725065	−	0.688681i	$-0.758190\pi$
$463$	−31.2031			−1.45013			−0.725065	+	0.688681i	$0.758190\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.38419	+	16.2539i	−0.434248	+	0.752140i	−0.997234	−	0.0743264i	$-0.976319\pi$
$467$	−9.38419	+	16.2539i	−0.434248	+	0.752140i	0.562986	+	0.826467i	$0.309653\pi$
$468$		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
$473$	−1.27383	−	2.20634i	−0.0585709	−	0.101448i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−29.0683			−1.33094
$478$		0			0
$479$	0.357254	+	0.618782i	0.0163234	+	0.0282729i	0.874072	−	0.485797i	$-0.161471\pi$
$479$	0.357254	+	0.618782i	0.0163234	+	0.0282729i	−0.857748	+	0.514070i	$0.828137\pi$
$480$		0			0
$481$	−2.75856	+	4.77796i	−0.125779	+	0.217856i
$482$		0			0
$483$	5.08626	−	3.81864i	0.231433	−	0.173754i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.34744	−	14.4582i	−0.378259	−	0.655163i	0.612550	−	0.790432i	$-0.290144\pi$
$487$	−8.34744	−	14.4582i	−0.378259	−	0.655163i	−0.990809	+	0.135268i	$0.956810\pi$
$488$		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
$493$	6.14002	+	10.6348i	0.276532	+	0.478968i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.2685	−	9.96166i	0.595173	−	0.446841i
$498$		0			0
$499$	−7.23436	+	12.5303i	−0.323854	+	0.560932i	−0.981280	−	0.192588i	$-0.938312\pi$
$499$	−7.23436	+	12.5303i	−0.323854	+	0.560932i	0.657426	+	0.753519i	$0.271645\pi$
$500$		0			0
$501$	−1.65802	−	2.87178i	−0.0740749	−	0.128301i
$502$		0			0
$503$	−30.6949			−1.36862			−0.684308	−	0.729193i	$-0.739896\pi$
$503$	−30.6949			−1.36862			−0.684308	+	0.729193i	$0.739896\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.10316	+	1.91073i	0.0489930	+	0.0848585i
$508$		0			0
$509$	−22.2371	+	38.5158i	−0.985641	+	1.70718i	−0.346591	+	0.938016i	$0.612661\pi$
$509$	−22.2371	+	38.5158i	−0.985641	+	1.70718i	−0.639051	+	0.769165i	$0.720673\pi$
$510$		0			0
$511$	9.73436	+	4.15239i	0.430623	+	0.183691i
$512$		0			0
$513$	−6.66248	+	11.5398i	−0.294156	+	0.509493i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	9.36991			0.412088
$518$		0			0
$519$	7.27457			0.319318
$520$		0			0
$521$	6.32497	+	10.9552i	0.277102	+	0.479955i	0.970663	−	0.240443i	$-0.0772927\pi$
$521$	6.32497	+	10.9552i	0.277102	+	0.479955i	−0.693561	+	0.720398i	$0.743959\pi$
$522$		0			0
$523$	−5.13555	+	8.89504i	−0.224562	+	0.388953i	−0.956188	−	0.292753i	$-0.905428\pi$
$523$	−5.13555	+	8.89504i	−0.224562	+	0.388953i	0.731626	+	0.681706i	$0.238762\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.02420	−	8.70218i	0.218858	−	0.379073i
$528$		0			0
$529$	−10.2541	−	17.7606i	−0.445830	−	0.772201i
$530$		0			0
$531$	4.68942			0.203503
$532$		0			0
$533$	24.5764			1.06452
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.40393	−	4.16372i	0.103737	−	0.179678i
$538$		0			0
$539$	−9.27557	+	2.27773i	−0.399527	+	0.0981087i
$540$		0			0
$541$	1.06914	−	1.85181i	0.0459660	−	0.0796154i	−0.842127	−	0.539279i	$-0.818697\pi$
$541$	1.06914	−	1.85181i	0.0459660	−	0.0796154i	0.888093	+	0.459664i	$0.152030\pi$
$542$		0			0
$543$	−1.86445	−	3.22932i	−0.0800111	−	0.138583i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	32.0198			1.36907			0.684535	−	0.728980i	$-0.260005\pi$
$547$	32.0198			1.36907			0.684535	+	0.728980i	$0.260005\pi$
$548$		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
$553$	−1.69215	−	13.9866i	−0.0719574	−	0.594769i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.16521	−	7.21436i	−0.176486	−	0.305682i	0.764189	−	0.644993i	$-0.223140\pi$
$557$	−4.16521	−	7.21436i	−0.176486	−	0.305682i	−0.940674	+	0.339310i	$0.889806\pi$
$558$		0			0
$559$	4.92104			0.208138
$560$		0			0
$561$	−1.10972			−0.0468525
$562$		0			0
$563$	−9.73163	−	16.8557i	−0.410139	−	0.710382i	0.584766	−	0.811202i	$-0.301187\pi$
$563$	−9.73163	−	16.8557i	−0.410139	−	0.710382i	−0.994905	+	0.100821i	$0.967853\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	19.0361	+	8.12024i	0.799442	+	0.341018i
$568$		0			0
$569$	−9.44624	+	16.3614i	−0.396007	+	0.685904i	−0.993229	−	0.116172i	$-0.962938\pi$
$569$	−9.44624	+	16.3614i	−0.396007	+	0.685904i	0.597222	+	0.802076i	$0.296271\pi$
$570$		0			0
$571$	9.31505	+	16.1341i	0.389823	+	0.675192i	0.992425	−	0.122849i	$-0.0392030\pi$
$571$	9.31505	+	16.1341i	0.389823	+	0.675192i	−0.602603	+	0.798041i	$0.705870\pi$
$572$		0			0
$573$	5.10426			0.213234
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−9.29630	−	16.1017i	−0.387010	−	0.670321i	0.605036	−	0.796198i	$-0.293159\pi$
$577$	−9.29630	−	16.1017i	−0.387010	−	0.670321i	−0.992046	+	0.125877i	$0.959825\pi$
$578$		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
$583$	−6.91658	+	11.9799i	−0.286455	+	0.496155i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1383			−0.418452			−0.209226	−	0.977867i	$-0.567094\pi$
$587$	−10.1383			−0.418452			−0.209226	+	0.977867i	$0.567094\pi$
$588$		0			0
$589$	−28.0593			−1.15616
$590$		0			0
$591$	−2.10589	−	3.64751i	−0.0866247	−	0.150038i
$592$		0			0
$593$	−8.50273	+	14.7272i	−0.349165	+	0.604772i	−0.986101	−	0.166145i	$-0.946868\pi$
$593$	−8.50273	+	14.7272i	−0.349165	+	0.604772i	0.636936	+	0.770917i	$0.280201\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.985720	−	1.70732i	0.0403428	−	0.0698758i
$598$		0			0
$599$	4.09334	+	7.08988i	0.167250	+	0.289685i	0.937452	−	0.348115i	$-0.113178\pi$
$599$	4.09334	+	7.08988i	0.167250	+	0.289685i	−0.770202	+	0.637800i	$0.779845\pi$
$600$		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
$603$	−19.2929			−0.785669
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.1158	−	24.4493i	0.572943	−	0.992367i	−0.423319	−	0.905981i	$-0.639135\pi$
$607$	14.1158	−	24.4493i	0.572943	−	0.992367i	0.996262	−	0.0863858i	$-0.0275318\pi$
$608$		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
$613$	15.5791	+	26.9837i	0.629232	+	1.08986i	0.987706	+	0.156323i	$0.0499640\pi$
$613$	15.5791	+	26.9837i	0.629232	+	1.08986i	−0.358474	+	0.933540i	$0.616703\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.1527			1.57623			0.788114	−	0.615530i	$-0.211058\pi$
$617$	39.1527			1.57623			0.788114	+	0.615530i	$0.211058\pi$
$618$		0			0
$619$	19.6921	+	34.1078i	0.791494	+	1.37091i	0.925042	+	0.379866i	$0.124030\pi$
$619$	19.6921	+	34.1078i	0.791494	+	1.37091i	−0.133547	+	0.991042i	$0.542637\pi$
$620$		0			0
$621$	−7.05213	+	12.2146i	−0.282992	+	0.490157i
$622$		0			0
$623$	−0.275568	−	2.27773i	−0.0110404	−	0.0912552i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.54940	+	2.68364i	0.0618771	+	0.107174i
$628$		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
$633$	1.99827	+	3.46110i	0.0794239	+	0.137566i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.14810	−	17.7160i	0.203975	−	0.701935i
$638$		0			0
$639$	−8.99018	+	15.5715i	−0.355646	+	0.615997i
$640$		0			0
$641$	−4.20643	−	7.28575i	−0.166144	−	0.287770i	0.770917	−	0.636936i	$-0.219798\pi$
$641$	−4.20643	−	7.28575i	−0.166144	−	0.287770i	−0.937061	+	0.349166i	$0.886465\pi$
$642$		0			0
$643$	−29.7398			−1.17282			−0.586412	−	0.810013i	$-0.699460\pi$
$643$	−29.7398			−1.17282			−0.586412	+	0.810013i	$0.699460\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.8430	+	18.7806i	0.426281	+	0.738341i	0.996539	−	0.0831249i	$-0.0264900\pi$
$647$	10.8430	+	18.7806i	0.426281	+	0.738341i	−0.570258	+	0.821466i	$0.693157\pi$
$648$		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
$653$	−15.0351	+	26.0416i	−0.588370	+	1.01909i	0.406076	+	0.913839i	$0.366897\pi$
$653$	−15.0351	+	26.0416i	−0.588370	+	1.01909i	−0.994446	+	0.105247i	$0.966437\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−11.4687			−0.447437
$658$		0			0
$659$	2.37537			0.0925311			0.0462656	−	0.998929i	$-0.485268\pi$
$659$	2.37537			0.0925311			0.0462656	+	0.998929i	$0.485268\pi$
$660$		0			0
$661$	7.23163	+	12.5255i	0.281278	+	0.487187i	0.971700	−	0.236220i	$-0.0759085\pi$
$661$	7.23163	+	12.5255i	0.281278	+	0.487187i	−0.690422	+	0.723407i	$0.742575\pi$
$662$		0			0
$663$	1.07176	−	1.85635i	0.0416238	−	0.0720946i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	18.1482	−	31.4336i	0.702701	−	1.21711i
$668$		0			0
$669$	−3.92813	−	6.80372i	−0.151870	−	0.263047i
$670$		0			0
$671$	0.0538660			0.00207947
$672$		0			0
$673$	8.99653			0.346791			0.173395	−	0.984852i	$-0.444526\pi$
$673$	8.99653			0.346791			0.173395	+	0.984852i	$0.444526\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.74591	+	6.48810i	−0.143967	+	0.249358i	−0.928987	−	0.370112i	$-0.879319\pi$
$677$	−3.74591	+	6.48810i	−0.143967	+	0.249358i	0.785020	+	0.619470i	$0.212653\pi$
$678$		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
$683$	21.1625	+	36.6545i	0.809760	+	1.40255i	0.913030	+	0.407892i	$0.133736\pi$
$683$	21.1625	+	36.6545i	0.809760	+	1.40255i	−0.103270	+	0.994653i	$0.532931\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.04841			−0.116304
$688$		0			0
$689$	−13.3600	−	23.1402i	−0.508975	−	0.881570i
$690$		0			0
$691$	−14.3232	+	24.8086i	−0.544882	+	0.943763i	0.453733	+	0.891138i	$0.350092\pi$
$691$	−14.3232	+	24.8086i	−0.544882	+	0.943763i	−0.998614	+	0.0526247i	$0.983241\pi$
$692$		0			0
$693$	8.27730	−	6.21440i	0.314429	−	0.236066i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.4049	+	18.0219i	0.394114	+	0.682626i
$698$		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
$703$	6.52247	+	11.2972i	0.246000	+	0.426084i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−38.1949	−	16.2928i	−1.43647	−	0.612754i
$708$		0			0
$709$	−14.4138	+	24.9655i	−0.541323	+	0.937600i	0.457505	+	0.889207i	$0.348743\pi$
$709$	−14.4138	+	24.9655i	−0.541323	+	0.937600i	−0.998828	+	0.0483927i	$0.984590\pi$
$710$		0			0
$711$	7.63382	+	13.2222i	0.286291	+	0.495870i
$712$		0			0
$713$	−29.7003			−1.11229
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.09061	−	5.35310i	−0.115421	−	0.199915i
$718$		0			0
$719$	−15.6553	+	27.1158i	−0.583844	+	1.01125i	0.411175	+	0.911557i	$0.365119\pi$
$719$	−15.6553	+	27.1158i	−0.583844	+	1.01125i	−0.995018	+	0.0996906i	$0.968215\pi$
$720$		0			0
$721$	−4.24864	−	35.1174i	−0.158227	−	1.30784i
$722$		0			0
$723$	−1.88245	+	3.26050i	−0.0700092	+	0.121259i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.17230			−0.303094			−0.151547	−	0.988450i	$-0.548425\pi$
$727$	−8.17230			−0.303094			−0.151547	+	0.988450i	$0.548425\pi$
$728$		0			0
$729$	−20.0899			−0.744069
$730$		0			0
$731$	2.08342	+	3.60859i	0.0770581	+	0.133469i
$732$		0			0
$733$	10.7092	−	18.5488i	0.395552	−	0.685116i	−0.597620	−	0.801780i	$-0.703887\pi$
$733$	10.7092	−	18.5488i	0.395552	−	0.685116i	0.993171	+	0.116664i	$0.0372201\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.59061	+	7.95118i	−0.169097	+	0.292885i
$738$		0			0
$739$	−2.17503	−	3.76726i	−0.0800098	−	0.138581i	0.823244	−	0.567688i	$-0.192162\pi$
$739$	−2.17503	−	3.76726i	−0.0800098	−	0.138581i	−0.903254	+	0.429107i	$0.858828\pi$
$740$		0			0
$741$	−5.98561			−0.219887
$742$		0			0
$743$	6.53328			0.239683			0.119841	−	0.992793i	$-0.461761\pi$
$743$	6.53328			0.239683			0.119841	+	0.992793i	$0.461761\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	21.1796	−	36.6841i	0.774921	−	1.34220i
$748$		0			0
$749$	1.71724	+	14.1939i	0.0627465	+	0.518635i
$750$		0			0
$751$	−17.2415	+	29.8632i	−0.629153	+	1.08973i	0.358569	+	0.933503i	$0.383265\pi$
$751$	−17.2415	+	29.8632i	−0.629153	+	1.08973i	−0.987722	+	0.156222i	$0.950069\pi$
$752$		0			0
$753$	−3.55486	−	6.15720i	−0.129546	−	0.224381i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−44.2425			−1.60802			−0.804011	−	0.594614i	$-0.797305\pi$
$757$	−44.2425			−1.60802			−0.804011	+	0.594614i	$0.797305\pi$
$758$		0			0
$759$	1.64002	+	2.84059i	0.0595288	+	0.103107i
$760$		0			0
$761$	11.9094	−	20.6277i	0.431715	−	0.747752i	−0.565306	−	0.824881i	$-0.691242\pi$
$761$	11.9094	−	20.6277i	0.431715	−	0.747752i	0.997021	+	0.0771290i	$0.0245753\pi$
$762$		0			0
$763$	−38.5181	−	16.4307i	−1.39445	−	0.594831i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.15529	+	3.73307i	0.0778230	+	0.134793i
$768$		0			0
$769$	−0.158128			−0.00570225			−0.00285113	−	0.999996i	$-0.500908\pi$
$769$	−0.158128			−0.00570225			−0.00285113	+	0.999996i	$0.500908\pi$
$770$		0			0
$771$	10.3734			0.373588
$772$		0			0
$773$	8.89957	+	15.4145i	0.320095	+	0.554421i	0.980507	−	0.196482i	$-0.0629517\pi$
$773$	8.89957	+	15.4145i	0.320095	+	0.554421i	−0.660412	+	0.750903i	$0.729618\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.61419	+	1.21189i	−0.0579086	+	0.0434764i
$778$		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
$783$	−11.7664			−0.420496
$784$		0			0
$785$		0			0
$786$		0			0
$787$	20.7613	+	35.9596i	0.740060	+	1.28182i	0.952467	+	0.304640i	$0.0985363\pi$
$787$	20.7613	+	35.9596i	0.740060	+	1.28182i	−0.212407	+	0.977181i	$0.568130\pi$
$788$		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
$793$	−0.0520234	+	0.0901072i	−0.00184741	+	0.00319980i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	25.0933			0.888852			0.444426	−	0.895816i	$-0.353408\pi$
$797$	25.0933			0.888852			0.444426	+	0.895816i	$0.353408\pi$
$798$		0			0
$799$	−15.3250			−0.542158
$800$		0			0
$801$	1.24318	+	2.15324i	0.0439255	+	0.0760811i
$802$		0			0
$803$	−2.72890	+	4.72659i	−0.0963007	+	0.166798i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.67602	−	2.90296i	0.0589989	−	0.102189i
$808$		0			0
$809$	−6.34744	−	10.9941i	−0.223164	−	0.386531i	0.732603	−	0.680656i	$-0.238305\pi$
$809$	−6.34744	−	10.9941i	−0.223164	−	0.386531i	−0.955767	+	0.294125i	$0.904972\pi$
$810$		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
$813$	1.40740			0.0493595
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.81778	−	10.0767i	0.203538	−	0.352539i
$818$		0			0
$819$	2.40130	+	19.8481i	0.0839084	+	0.693550i
$820$		0			0
$821$	−10.0341	+	17.3796i	−0.350193	+	0.606553i	−0.986283	−	0.165062i	$-0.947217\pi$
$821$	−10.0341	+	17.3796i	−0.350193	+	0.606553i	0.636090	+	0.771615i	$0.280551\pi$
$822$		0			0
$823$	5.30523	+	9.18893i	0.184929	+	0.320306i	0.943553	−	0.331223i	$-0.107461\pi$
$823$	5.30523	+	9.18893i	0.184929	+	0.320306i	−0.758624	+	0.651529i	$0.774128\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	34.7793			1.20939			0.604697	−	0.796455i	$-0.293294\pi$
$827$	34.7793			1.20939			0.604697	+	0.796455i	$0.293294\pi$
$828$		0			0
$829$	13.1141	+	22.7142i	0.455471	+	0.788898i	0.998715	−	0.0506761i	$-0.0161376\pi$
$829$	13.1141	+	22.7142i	0.455471	+	0.788898i	−0.543244	+	0.839575i	$0.682804\pi$
$830$		0			0
$831$	−1.93905	+	3.35853i	−0.0672648	+	0.116506i
$832$		0			0
$833$	15.1707	−	3.72534i	0.525633	−	0.129075i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.81405	+	8.33818i	0.166398	+	0.288210i
$838$		0			0
$839$	33.9210			1.17108			0.585542	−	0.810642i	$-0.300882\pi$
$839$	33.9210			1.17108			0.585542	+	0.810642i	$0.300882\pi$
$840$		0			0
$841$	1.28003			0.0441391
$842$		0			0
$843$	−0.316041	−	0.547399i	−0.0108850	−	0.0188534i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.90393	+	24.0026i	0.0997801	+	0.824739i
$848$		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
$853$	−57.6698			−1.97458			−0.987288	−	0.158942i	$-0.949192\pi$
$853$	−57.6698			−1.97458			−0.987288	+	0.158942i	$0.949192\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.7020	−	30.6607i	−0.604688	−	1.04735i	−0.992101	−	0.125443i	$-0.959965\pi$
$857$	−17.7020	−	30.6607i	−0.604688	−	1.04735i	0.387413	−	0.921906i	$-0.373369\pi$
$858$		0			0
$859$	6.72170	−	11.6423i	0.229342	−	0.397231i	−0.728272	−	0.685289i	$-0.759676\pi$
$859$	6.72170	−	11.6423i	0.229342	−	0.397231i	0.957613	+	0.288057i	$0.0930094\pi$
$860$		0			0
$861$	8.27047	+	3.52794i	0.281857	+	0.120232i
$862$		0			0
$863$	3.53239	−	6.11828i	0.120244	−	0.208269i	−0.799620	−	0.600507i	$-0.794966\pi$
$863$	3.53239	−	6.11828i	0.120244	−	0.208269i	0.919864	+	0.392238i	$0.128299\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.38061			−0.148773
$868$		0			0
$869$	7.26564			0.246470
$870$		0			0
$871$	−8.86718	−	15.3584i	−0.300453	−	0.520400i
$872$		0			0
$873$	23.0791	−	39.9741i	0.781108	−	1.35292i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.50273	+	12.9951i	−0.253349	+	0.438814i	−0.964446	−	0.264281i	$-0.914865\pi$
$877$	−7.50273	+	12.9951i	−0.253349	+	0.438814i	0.711097	+	0.703094i	$0.248199\pi$
$878$		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
$883$	58.2229			1.95936			0.979679	−	0.200574i	$-0.0642808\pi$
$883$	58.2229			1.95936			0.979679	+	0.200574i	$0.0642808\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.6230	+	21.8637i	−0.423839	+	0.734111i	−0.996311	−	0.0858133i	$-0.972651\pi$
$887$	−12.6230	+	21.8637i	−0.423839	+	0.734111i	0.572472	+	0.819924i	$0.305984\pi$
$888$		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
$893$	21.3968	+	37.0604i	0.716018	+	1.24018i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.33567			−0.211542
$898$		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
$903$	1.65603	+	0.706414i	0.0551093	+	0.0235080i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−13.5933	−	23.5444i	−0.451360	−	0.781778i	0.547111	−	0.837060i	$-0.315727\pi$
$907$	−13.5933	−	23.5444i	−0.451360	−	0.781778i	−0.998471	+	0.0552822i	$0.982394\pi$
$908$		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
$913$	−10.0791	−	17.4575i	−0.333568	−	0.577757i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.15976	−	42.6483i	−0.170390	−	1.40837i
$918$		0			0
$919$	23.5369	−	40.7670i	0.776409	−	1.34478i	−0.157590	−	0.987505i	$-0.550372\pi$
$919$	23.5369	−	40.7670i	0.776409	−	1.34478i	0.933999	−	0.357276i	$-0.116294\pi$
$920$		0			0
$921$	4.28638	+	7.42423i	0.141241	+	0.244637i
$922$		0			0
$923$	−16.5278			−0.544020
$924$		0			0
$925$		0			0
$926$		0			0
$927$	19.1669	+	33.1981i	0.629525	+	1.09037i
$928$		0			0
$929$	−8.99554	+	15.5807i	−0.295134	+	0.511187i	−0.975016	−	0.222134i	$-0.928698\pi$
$929$	−8.99554	+	15.5807i	−0.295134	+	0.511187i	0.679882	+	0.733321i	$0.262031\pi$
$930$		0			0
$931$	−30.1904	−	31.4859i	−0.989451	−	1.03191i
$932$		0			0
$933$	1.60699	−	2.78339i	0.0526106	−	0.0911242i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−37.7003			−1.23162			−0.615808	−	0.787896i	$-0.711170\pi$
$937$	−37.7003			−1.23162			−0.615808	+	0.787896i	$0.711170\pi$
$938$		0			0
$939$	−0.0340191			−0.00111017
$940$		0			0
$941$	−2.41658	−	4.18564i	−0.0787782	−	0.136448i	0.823945	−	0.566670i	$-0.191769\pi$
$941$	−2.41658	−	4.18564i	−0.0787782	−	0.136448i	−0.902723	+	0.430222i	$0.858435\pi$
$942$		0			0
$943$	30.7541	−	53.2677i	1.00149	−	1.73463i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.41831	+	2.45659i	−0.0460890	+	0.0798285i	−0.888150	−	0.459554i	$-0.848009\pi$
$947$	−1.41831	+	2.45659i	−0.0460890	+	0.0798285i	0.842061	+	0.539383i	$0.181342\pi$
$948$		0			0
$949$	−5.27110	−	9.12982i	−0.171107	−	0.296366i
$950$		0			0
$951$	1.29095			0.0418619
$952$		0			0
$953$	−17.7991			−0.576571			−0.288285	−	0.957545i	$-0.593085\pi$
$953$	−17.7991			−0.576571			−0.288285	+	0.957545i	$0.593085\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.36817	+	2.36974i	−0.0442267	+	0.0766029i
$958$		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
$963$	−7.74701	−	13.4182i	−0.249644	−	0.432396i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.1581			0.487453			0.243726	−	0.969844i	$-0.421630\pi$
$967$	15.1581			0.487453			0.243726	+	0.969844i	$0.421630\pi$
$968$		0			0
$969$	−2.53413	−	4.38924i	−0.0814079	−	0.141003i
$970$		0			0
$971$	23.6921	−	41.0360i	0.760317	−	1.31691i	−0.182370	−	0.983230i	$-0.558377\pi$
$971$	23.6921	−	41.0360i	0.760317	−	1.31691i	0.942687	−	0.333678i	$-0.108290\pi$
$972$		0			0
$973$	47.3305	−	35.5346i	1.51735	−	1.13919i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.8600	+	20.5421i	0.379434	+	0.657200i	0.990980	−	0.134009i	$-0.0427852\pi$
$977$	11.8600	+	20.5421i	0.379434	+	0.657200i	−0.611546	+	0.791209i	$0.709452\pi$
$978$		0			0
$979$	1.18322			0.0378158
$980$		0			0
$981$	45.3808			1.44890
$982$		0			0
$983$	17.2272	+	29.8383i	0.549461	+	0.951695i	0.998311	+	0.0580876i	$0.0185003\pi$
$983$	17.2272	+	29.8383i	0.549461	+	0.951695i	−0.448850	+	0.893607i	$0.648166\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−5.29531	+	3.97559i	−0.168551	+	0.126544i
$988$		0			0
$989$	6.15802	−	10.6660i	0.195814	−	0.339159i
$990$		0			0
$991$	20.8304	+	36.0794i	0.661700	+	1.14610i	0.980169	+	0.198165i	$0.0634982\pi$
$991$	20.8304	+	36.0794i	0.661700	+	1.14610i	−0.318468	+	0.947934i	$0.603168\pi$
$992$		0			0
$993$	−7.16138			−0.227260
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.3941	+	21.4672i	0.392525	+	0.679874i	0.992782	−	0.119934i	$-0.0382682\pi$
$997$	12.3941	+	21.4672i	0.392525	+	0.679874i	−0.600256	+	0.799808i	$0.704935\pi$
$998$		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.i.d.401.2	✓	6
5.2	odd	4		700.2.r.d.149.3		12
5.3	odd	4		700.2.r.d.149.4		12
5.4	even	2		700.2.i.e.401.2	yes	6
7.2	even	3		4900.2.a.bc.1.2		3
7.4	even	3	inner	700.2.i.d.501.2	yes	6
7.5	odd	6		4900.2.a.bb.1.2		3
35.2	odd	12		4900.2.e.t.2549.3		6
35.4	even	6		700.2.i.e.501.2	yes	6
35.9	even	6		4900.2.a.ba.1.2		3
35.12	even	12		4900.2.e.s.2549.4		6
35.18	odd	12		700.2.r.d.249.3		12
35.19	odd	6		4900.2.a.bd.1.2		3
35.23	odd	12		4900.2.e.t.2549.4		6
35.32	odd	12		700.2.r.d.249.4		12
35.33	even	12		4900.2.e.s.2549.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.2	✓	6	1.1	even	1	trivial
700.2.i.d.501.2	yes	6	7.4	even	3	inner
700.2.i.e.401.2	yes	6	5.4	even	2
700.2.i.e.501.2	yes	6	35.4	even	6
700.2.r.d.149.3		12	5.2	odd	4
700.2.r.d.149.4		12	5.3	odd	4
700.2.r.d.249.3		12	35.18	odd	12
700.2.r.d.249.4		12	35.32	odd	12
4900.2.a.ba.1.2		3	35.9	even	6
4900.2.a.bb.1.2		3	7.5	odd	6
4900.2.a.bc.1.2		3	7.2	even	3
4900.2.a.bd.1.2		3	35.19	odd	6
4900.2.e.s.2549.3		6	35.33	even	12
4900.2.e.s.2549.4		6	35.12	even	12
4900.2.e.t.2549.3		6	35.2	odd	12
4900.2.e.t.2549.4		6	35.23	odd	12

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.182224 - 0.315621i) q^{3} +(-2.11581 + 1.58850i) q^{7} +(1.43359 - 2.48305i) q^{9} +(-0.682224 - 1.18165i) q^{11} +2.63555 q^{13} +(1.11581 + 1.93264i) q^{17} +(3.11581 - 5.39675i) q^{19} +(0.886917 + 0.378332i) q^{21} +(3.29804 - 5.71237i) q^{23} -2.13828 q^{27} +5.50273 q^{29} +(-2.25136 - 3.89948i) q^{31} +(-0.248635 + 0.430649i) q^{33} +(-1.04667 + 1.81289i) q^{37} +(-0.480261 - 0.831836i) q^{39} +9.32497 q^{41} +1.86718 q^{43} +(-3.43359 + 5.94715i) q^{47} +(1.95333 - 6.72194i) q^{49} +(0.406656 - 0.704349i) q^{51} +(-5.06914 - 8.78001i) q^{53} -2.27110 q^{57} +(0.817776 + 1.41643i) q^{59} +(-0.0197391 + 0.0341891i) q^{61} +(0.911120 + 7.53092i) q^{63} +(-3.36445 - 5.82739i) q^{67} -2.40393 q^{69} -6.27110 q^{71} +(-2.00000 - 3.46410i) q^{73} +(3.32051 + 1.41643i) q^{77} +(-2.66248 + 4.61156i) q^{79} +(-3.91112 - 6.77426i) q^{81} +14.7738 q^{83} +(-1.00273 - 1.73678i) q^{87} +(-0.433589 + 0.750998i) q^{89} +(-5.57633 + 4.18658i) q^{91} +(-0.820506 + 1.42116i) q^{93} +16.0988 q^{97} -3.91211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 4 q^{7} - 8 q^{9} - 4 q^{11} + 16 q^{13} - 10 q^{17} + 2 q^{19} - 11 q^{21} + 3 q^{23} + 20 q^{27} + 3 q^{31} - 18 q^{33} - 6 q^{37} + 14 q^{39} + 22 q^{41} - 22 q^{43} - 4 q^{47} + 12 q^{49}+ \cdots + 42 q^{99}+O(q^{100}) \) 6 * q - q^3 + 4 * q^7 - 8 * q^9 - 4 * q^11 + 16 * q^13 - 10 * q^17 + 2 * q^19 - 11 * q^21 + 3 * q^23 + 20 * q^27 + 3 * q^31 - 18 * q^33 - 6 * q^37 + 14 * q^39 + 22 * q^41 - 22 * q^43 - 4 * q^47 + 12 * q^49 + 3 * q^51 - 14 * q^53 - 14 * q^57 + 5 * q^59 - 17 * q^61 + 5 * q^63 - 20 * q^67 - 48 * q^69 - 38 * q^71 - 12 * q^73 - 13 * q^77 + q^79 - 23 * q^81 + 56 * q^83 + 27 * q^87 + 14 * q^89 + 17 * q^91 + 28 * q^93 + 30 * q^97 + 42 * q^99

Introduction

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