LMFDB - Embedded newform 700.2.i.e.501.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(401,700)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			501.2
Root			$1.09935 + 1.90412i$ of defining polynomial
Character	$\chi$	$=$	700.501
Dual form			700.2.i.e.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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
$3$	0.182224	−	0.315621i	0.105207	−	0.182224i	−0.808616	−	0.588337i	$-0.799783\pi$
$3$	0.182224	−	0.315621i	0.105207	−	0.182224i	0.913823	+	0.406113i	$0.133116\pi$
$4$		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	−0.950355	−	0.311168i	$-0.899280\pi$
$11$	−0.682224	+	1.18165i	−0.205698	+	0.356280i	0.744657	+	0.667448i	$0.232613\pi$
$12$		0			0
$13$	−2.63555			−0.730971			−0.365485	−	0.930817i	$-0.619097\pi$
$13$	−2.63555			−0.730971			−0.365485	+	0.930817i	$0.619097\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.11581	+	1.93264i	−0.270624	+	0.468735i	−0.969022	−	0.246975i	$-0.920563\pi$
$17$	−1.11581	+	1.93264i	−0.270624	+	0.468735i	0.698398	+	0.715710i	$0.253897\pi$
$18$		0			0
$19$	3.11581	+	5.39675i	0.714816	+	1.23810i	0.963030	+	0.269393i	$0.0868231\pi$
$19$	3.11581	+	5.39675i	0.714816	+	1.23810i	−0.248214	+	0.968705i	$0.579844\pi$
$20$		0			0
$21$	0.886917	−	0.378332i	0.193541	−	0.0825589i
$22$		0			0
$23$	−3.29804	−	5.71237i	−0.687688	−	1.19111i	−0.972584	−	0.232552i	$-0.925292\pi$
$23$	−3.29804	−	5.71237i	−0.687688	−	1.19111i	0.284896	−	0.958559i	$-0.408041\pi$
$24$		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	−0.994246	−	0.107117i	$-0.965838\pi$
$31$	−2.25136	+	3.89948i	−0.404357	+	0.700367i	0.589889	+	0.807484i	$0.299171\pi$
$32$		0			0
$33$	0.248635	+	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	$-0.111621\pi$
$37$	1.04667	+	1.81289i	0.172072	+	0.298037i	−0.767072	+	0.641561i	$0.778287\pi$
$38$		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	$-0.545473\pi$
$43$	−1.86718			−0.284742			−0.142371	+	0.989813i	$0.545473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.43359	+	5.94715i	0.500840	+	0.867481i	1.00000		0.000970685i	$0.000308979\pi$
$47$	3.43359	+	5.94715i	0.500840	+	0.867481i	−0.499159	+	0.866510i	$0.666358\pi$
$48$		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	−0.273440	−	0.961889i	$-0.588162\pi$
$53$	5.06914	−	8.78001i	0.696300	−	1.20603i	0.969740	−	0.244138i	$-0.0785050\pi$
$54$		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	−0.807871	−	0.589360i	$-0.799380\pi$
$59$	0.817776	−	1.41643i	0.106465	−	0.184403i	0.914336	+	0.404956i	$0.132713\pi$
$60$		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
$63$	−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	$-0.698502\pi$
$67$	3.36445	−	5.82739i	0.411033	−	0.711930i	0.995003	+	0.0998455i	$0.0318348\pi$
$68$		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	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		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	0.676481	−	0.736460i	$-0.263504\pi$
$79$	−2.66248	−	4.61156i	−0.299553	−	0.518841i	−0.976034	+	0.217619i	$0.930171\pi$
$80$		0			0
$81$	−3.91112	+	6.77426i	−0.434569	+	0.752695i
$82$		0			0
$83$	−14.7738			−1.62164			−0.810819	−	0.585296i	$-0.800978\pi$
$83$	−14.7738			−1.62164			−0.810819	+	0.585296i	$0.800978\pi$
$84$		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	0.842130	−	0.539274i	$-0.181301\pi$
$89$	−0.433589	−	0.750998i	−0.0459603	−	0.0796056i	−0.888090	+	0.459669i	$0.847968\pi$
$90$		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	$-0.804526\pi$
$97$	−16.0988			−1.63459			−0.817293	+	0.576222i	$0.804526\pi$
$98$		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
$103$	6.68495	+	11.5787i	0.658688	+	1.14088i	0.980956	+	0.194233i	$0.0622216\pi$
$103$	6.68495	+	11.5787i	0.658688	+	1.14088i	−0.322267	+	0.946649i	$0.604445\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.70196	−	4.67994i	−0.261209	−	0.452427i	0.705355	−	0.708854i	$-0.250788\pi$
$107$	−2.70196	−	4.67994i	−0.261209	−	0.452427i	−0.966563	+	0.256428i	$0.917454\pi$
$108$		0			0
$109$	7.91385	−	13.7072i	0.758009	−	1.31291i	−0.185855	−	0.982577i	$-0.559505\pi$
$109$	7.91385	−	13.7072i	0.758009	−	1.31291i	0.943864	−	0.330333i	$-0.107161\pi$
$110$		0			0
$111$	0.762915			0.0724127
$112$		0			0
$113$	18.4238			1.73316			0.866581	−	0.499036i	$-0.166312\pi$
$113$	18.4238			1.73316			0.866581	+	0.499036i	$0.166312\pi$
$114$		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	$-0.424079\pi$
$127$	5.32497			0.472515			0.236257	+	0.971691i	$0.424079\pi$
$128$		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
$133$	−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	$-0.893650\pi$
$137$	−2.20469	+	3.81864i	−0.188360	+	0.326248i	0.756344	+	0.654174i	$0.226984\pi$
$138$		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	−0.796361	−	0.604822i	$-0.793244\pi$
$149$	−11.2541	−	19.4927i	−0.921971	−	1.59690i	−0.125610	−	0.992080i	$-0.540089\pi$
$150$		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
$153$	−6.39847			−0.517285
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.77830	−	13.4724i	0.620776	−	1.07522i	−0.368566	−	0.929602i	$-0.620151\pi$
$157$	7.77830	−	13.4724i	0.620776	−	1.07522i	0.989342	−	0.145613i	$-0.0465156\pi$
$158$		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	$-0.221842\pi$
$163$	−2.20196	−	3.81391i	−0.172471	−	0.298729i	−0.939283	+	0.343143i	$0.888508\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.09880			−0.704087			−0.352043	−	0.935984i	$-0.614513\pi$
$167$	−9.09880			−0.704087			−0.352043	+	0.935984i	$0.614513\pi$
$168$		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	0.943470	+	0.331457i	$0.107540\pi$
$173$	9.98026	+	17.2863i	0.758785	+	1.31425i	−0.184685	+	0.982798i	$0.559127\pi$
$174$		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	−0.506954	−	0.861973i	$-0.669229\pi$
$179$	6.59607	−	11.4247i	0.493014	−	0.853925i	0.999968	+	0.00804839i	$0.00256191\pi$
$180$		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	−0.999970	−	0.00775353i	$-0.997532\pi$
$191$	−7.00273	−	12.1291i	−0.506700	−	0.877630i	0.493270	−	0.869876i	$-0.335801\pi$
$192$		0			0
$193$	7.20469	−	12.4789i	0.518605	−	0.898250i	−0.481161	−	0.876632i	$-0.659785\pi$
$193$	7.20469	−	12.4789i	0.518605	−	0.898250i	0.999766	−	0.0216183i	$-0.00688185\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.5566			−0.823373			−0.411687	−	0.911325i	$-0.635060\pi$
$197$	−11.5566			−0.823373			−0.411687	+	0.911325i	$0.635060\pi$
$198$		0			0
$199$	2.70469	−	4.68467i	0.191731	−	0.332087i	−0.754093	−	0.656767i	$-0.771923\pi$
$199$	2.70469	−	4.68467i	0.191731	−	0.332087i	0.945824	+	0.324680i	$0.105257\pi$
$200$		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	$-0.756670\pi$
$223$	−21.5566			−1.44354			−0.721768	+	0.692135i	$0.756670\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.21189	+	10.7593i	−0.412297	+	0.714120i	−0.995141	−	0.0984646i	$-0.968607\pi$
$227$	−6.21189	+	10.7593i	−0.412297	+	0.714120i	0.582843	+	0.812585i	$0.301940\pi$
$228$		0			0
$229$	4.18222	+	7.24382i	0.276369	+	0.478685i	0.970480	−	0.241183i	$-0.0775354\pi$
$229$	4.18222	+	7.24382i	0.276369	+	0.478685i	−0.694110	+	0.719868i	$0.744202\pi$
$230$		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	$-0.318374\pi$
$233$	−7.00273	−	12.1291i	−0.458764	−	0.794603i	−0.998896	+	0.0469777i	$0.985041\pi$
$234$		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	−0.983044	−	0.183368i	$-0.941300\pi$
$241$	−5.16521	+	8.94641i	−0.332721	+	0.576289i	0.650324	+	0.759657i	$0.274633\pi$
$242$		0			0
$243$	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	0.842535	+	0.538641i	$0.181062\pi$
$257$	14.2316	+	24.6499i	0.887744	+	1.53762i	0.0452090	+	0.998978i	$0.485605\pi$
$258$		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	0.0299373	−	0.999552i	$-0.490469\pi$
$263$	14.2810	−	24.7355i	0.880606	−	1.52525i	0.850669	−	0.525702i	$-0.176197\pi$
$264$		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	−0.691088	−	0.722771i	$-0.742868\pi$
$269$	4.59880	−	7.96536i	0.280394	−	0.485657i	0.971482	+	0.237114i	$0.0762016\pi$
$270$		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
$273$	−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	$-0.729759\pi$
$277$	5.32051	−	9.21539i	0.319678	−	0.553699i	0.980421	+	0.196914i	$0.0630919\pi$
$278$		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	$-0.889558\pi$
$283$	−2.95606	+	5.12004i	−0.175719	+	0.304355i	0.764691	+	0.644398i	$0.222892\pi$
$284$		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	$-0.751549\pi$
$293$	−24.3250			−1.42108			−0.710540	+	0.703657i	$0.751549\pi$
$294$		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	$-0.265757\pi$
$307$	23.5226			1.34250			0.671252	+	0.741229i	$0.265757\pi$
$308$		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
$313$	−0.0466721	−	0.0808384i	−0.00263806	−	0.00456926i	0.864703	−	0.502283i	$-0.167506\pi$
$313$	−0.0466721	−	0.0808384i	−0.00263806	−	0.00456926i	−0.867341	+	0.497714i	$0.834173\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.77110	+	3.06764i	0.0994751	+	0.172296i	0.911468	−	0.411372i	$-0.134950\pi$
$317$	1.77110	+	3.06764i	0.0994751	+	0.172296i	−0.811992	+	0.583668i	$0.801617\pi$
$318$		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	0.998902	+	0.0468558i	$0.0149201\pi$
$331$	9.82497	+	17.0173i	0.540029	+	0.935358i	−0.458872	+	0.888502i	$0.651747\pi$
$332$		0			0
$333$	−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	$-0.284009\pi$
$337$	23.0449			1.25534			0.627669	+	0.778480i	$0.284009\pi$
$338$		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	0.386360	+	0.922348i	$0.373732\pi$
$347$	−11.2810	+	19.5393i	−0.605597	+	1.04893i	−0.991957	+	0.126577i	$0.959601\pi$
$348$		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	0.00847467	−	0.999964i	$-0.497302\pi$
$353$	16.3502	−	28.3193i	0.870232	−	1.50729i	0.861757	−	0.507321i	$-0.169364\pi$
$354$		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	0.971744	+	0.236038i	$0.0758489\pi$
$359$	13.0791	+	22.6536i	0.690287	+	1.19561i	−0.281457	+	0.959574i	$0.590818\pi$
$360$		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	0.322454	+	0.946585i	$0.395492\pi$
$367$	−12.6158	+	21.8512i	−0.658540	+	1.14062i	−0.980994	+	0.194040i	$0.937841\pi$
$368$		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	$-0.213768\pi$
$373$	−2.84744	−	4.93191i	−0.147435	−	0.255365i	−0.930279	+	0.366854i	$0.880435\pi$
$374$		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	−0.988468	−	0.151428i	$-0.951613\pi$
$383$	−12.2388	−	21.1983i	−0.625374	−	1.08318i	0.363094	−	0.931753i	$-0.381720\pi$
$384$		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	−0.132535	−	0.991178i	$-0.542312\pi$
$389$	15.6230	−	27.0598i	0.792118	−	1.37199i	0.924653	−	0.380810i	$-0.124355\pi$
$390$		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	$-0.175717\pi$
$397$	−0.566411	−	0.981053i	−0.0284274	−	0.0492376i	−0.879889	+	0.475179i	$0.842383\pi$
$398$		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
$403$	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	0.0640699	+	0.997945i	$0.479592\pi$
$409$	−16.8304	+	29.1512i	−0.832211	+	1.44143i	−0.896281	+	0.443487i	$0.853741\pi$
$410$		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	−0.715080	−	0.699043i	$-0.753610\pi$
$431$	5.14548	−	8.91222i	0.247849	−	0.429287i	0.962929	+	0.269756i	$0.0869430\pi$
$432$		0			0
$433$	−29.8870			−1.43628			−0.718139	−	0.695899i	$-0.755006\pi$
$433$	−29.8870			−1.43628			−0.718139	+	0.695899i	$0.755006\pi$
$434$		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	0.919955	−	0.392025i	$-0.128225\pi$
$439$	2.52420	+	4.37205i	0.120474	+	0.208666i	−0.799481	+	0.600692i	$0.794892\pi$
$440$		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	$-0.256900\pi$
$443$	−5.88692	−	10.1964i	−0.279696	−	0.484447i	−0.971309	+	0.237821i	$0.923567\pi$
$444$		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	0.860678	+	0.509149i	$0.170040\pi$
$457$	18.6257	+	32.2607i	0.871275	+	1.50909i	0.0105968	+	0.999944i	$0.496627\pi$
$458$		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	$-0.241810\pi$
$463$	31.2031			1.45013			0.725065	+	0.688681i	$0.241810\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.38419	+	16.2539i	0.434248	+	0.752140i	0.997234	−	0.0743264i	$-0.0236807\pi$
$467$	9.38419	+	16.2539i	0.434248	+	0.752140i	−0.562986	+	0.826467i	$0.690347\pi$
$468$		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	−0.857748	−	0.514070i	$-0.828137\pi$
$479$	0.357254	−	0.618782i	0.0163234	−	0.0282729i	0.874072	+	0.485797i	$0.161471\pi$
$480$		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	$-0.709856\pi$
$487$	8.34744	−	14.4582i	0.378259	−	0.655163i	0.990809	+	0.135268i	$0.0431897\pi$
$488$		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	0.657426	−	0.753519i	$-0.271645\pi$
$499$	−7.23436	−	12.5303i	−0.323854	−	0.560932i	−0.981280	+	0.192588i	$0.938312\pi$
$500$		0			0
$501$	−1.65802	+	2.87178i	−0.0740749	+	0.128301i
$502$		0			0
$503$	30.6949			1.36862			0.684308	−	0.729193i	$-0.260104\pi$
$503$	30.6949			1.36862			0.684308	+	0.729193i	$0.260104\pi$
$504$		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	−0.639051	−	0.769165i	$-0.720673\pi$
$509$	−22.2371	−	38.5158i	−0.985641	−	1.70718i	−0.346591	−	0.938016i	$-0.612661\pi$
$510$		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	−0.693561	−	0.720398i	$-0.743959\pi$
$521$	6.32497	−	10.9552i	0.277102	−	0.479955i	0.970663	+	0.240443i	$0.0772927\pi$
$522$		0			0
$523$	5.13555	+	8.89504i	0.224562	+	0.388953i	0.956188	−	0.292753i	$-0.0945715\pi$
$523$	5.13555	+	8.89504i	0.224562	+	0.388953i	−0.731626	+	0.681706i	$0.761238\pi$
$524$		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	0.888093	−	0.459664i	$-0.152030\pi$
$541$	1.06914	+	1.85181i	0.0459660	+	0.0796154i	−0.842127	+	0.539279i	$0.818697\pi$
$542$		0			0
$543$	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	$-0.739995\pi$
$547$	−32.0198			−1.36907			−0.684535	+	0.728980i	$0.739995\pi$
$548$		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	$-0.776860\pi$
$557$	4.16521	−	7.21436i	0.176486	−	0.305682i	0.940674	+	0.339310i	$0.110194\pi$
$558$		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	$-0.698813\pi$
$563$	9.73163	−	16.8557i	0.410139	−	0.710382i	0.994905	+	0.100821i	$0.0321468\pi$
$564$		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	0.597222	−	0.802076i	$-0.296271\pi$
$569$	−9.44624	−	16.3614i	−0.396007	−	0.685904i	−0.993229	+	0.116172i	$0.962938\pi$
$570$		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
$573$	−5.10426			−0.213234
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.29630	−	16.1017i	0.387010	−	0.670321i	−0.605036	−	0.796198i	$-0.706841\pi$
$577$	9.29630	−	16.1017i	0.387010	−	0.670321i	0.992046	+	0.125877i	$0.0401745\pi$
$578$		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	$-0.432906\pi$
$587$	10.1383			0.418452			0.209226	+	0.977867i	$0.432906\pi$
$588$		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	$-0.0531319\pi$
$593$	8.50273	+	14.7272i	0.349165	+	0.604772i	−0.636936	+	0.770917i	$0.719799\pi$
$594$		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	−0.770202	−	0.637800i	$-0.779845\pi$
$599$	4.09334	−	7.08988i	0.167250	−	0.289685i	0.937452	+	0.348115i	$0.113178\pi$
$600$		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	−0.996262	−	0.0863858i	$-0.972468\pi$
$607$	−14.1158	−	24.4493i	−0.572943	−	0.992367i	0.423319	−	0.905981i	$-0.360865\pi$
$608$		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	0.358474	+	0.933540i	$0.383297\pi$
$613$	−15.5791	+	26.9837i	−0.629232	+	1.08986i	−0.987706	+	0.156323i	$0.950036\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−39.1527			−1.57623			−0.788114	−	0.615530i	$-0.788942\pi$
$617$	−39.1527			−1.57623			−0.788114	+	0.615530i	$0.788942\pi$
$618$		0			0
$619$	19.6921	−	34.1078i	0.791494	−	1.37091i	−0.133547	−	0.991042i	$-0.542637\pi$
$619$	19.6921	−	34.1078i	0.791494	−	1.37091i	0.925042	−	0.379866i	$-0.124030\pi$
$620$		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	−0.937061	−	0.349166i	$-0.886465\pi$
$641$	−4.20643	+	7.28575i	−0.166144	+	0.287770i	0.770917	+	0.636936i	$0.219798\pi$
$642$		0			0
$643$	29.7398			1.17282			0.586412	−	0.810013i	$-0.300540\pi$
$643$	29.7398			1.17282			0.586412	+	0.810013i	$0.300540\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.8430	+	18.7806i	−0.426281	+	0.738341i	−0.996539	−	0.0831249i	$-0.973510\pi$
$647$	−10.8430	+	18.7806i	−0.426281	+	0.738341i	0.570258	+	0.821466i	$0.306843\pi$
$648$		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	0.994446	+	0.105247i	$0.0335634\pi$
$653$	15.0351	+	26.0416i	0.588370	+	1.01909i	−0.406076	+	0.913839i	$0.633103\pi$
$654$		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	−0.690422	−	0.723407i	$-0.742575\pi$
$661$	7.23163	−	12.5255i	0.281278	−	0.487187i	0.971700	+	0.236220i	$0.0759085\pi$
$662$		0			0
$663$	−1.07176	−	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	$-0.555474\pi$
$673$	−8.99653			−0.346791			−0.173395	+	0.984852i	$0.555474\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.74591	+	6.48810i	0.143967	+	0.249358i	0.928987	−	0.370112i	$-0.120681\pi$
$677$	3.74591	+	6.48810i	0.143967	+	0.249358i	−0.785020	+	0.619470i	$0.787347\pi$
$678$		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	0.103270	+	0.994653i	$0.467069\pi$
$683$	−21.1625	+	36.6545i	−0.809760	+	1.40255i	−0.913030	+	0.407892i	$0.866264\pi$
$684$		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	−0.998614	−	0.0526247i	$-0.983241\pi$
$691$	−14.3232	−	24.8086i	−0.544882	−	0.943763i	0.453733	−	0.891138i	$-0.350092\pi$
$692$		0			0
$693$	−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	−0.998828	−	0.0483927i	$-0.984590\pi$
$709$	−14.4138	−	24.9655i	−0.541323	−	0.937600i	0.457505	−	0.889207i	$-0.348743\pi$
$710$		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	−0.995018	−	0.0996906i	$-0.968215\pi$
$719$	−15.6553	−	27.1158i	−0.583844	−	1.01125i	0.411175	−	0.911557i	$-0.365119\pi$
$720$		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	$-0.451575\pi$
$727$	8.17230			0.303094			0.151547	+	0.988450i	$0.451575\pi$
$728$		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	$-0.296113\pi$
$733$	−10.7092	−	18.5488i	−0.395552	−	0.685116i	−0.993171	+	0.116664i	$0.962780\pi$
$734$		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	−0.903254	−	0.429107i	$-0.858828\pi$
$739$	−2.17503	+	3.76726i	−0.0800098	+	0.138581i	0.823244	+	0.567688i	$0.192162\pi$
$740$		0			0
$741$	−5.98561			−0.219887
$742$		0			0
$743$	−6.53328			−0.239683			−0.119841	−	0.992793i	$-0.538239\pi$
$743$	−6.53328			−0.239683			−0.119841	+	0.992793i	$0.538239\pi$
$744$		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	−0.987722	−	0.156222i	$-0.950069\pi$
$751$	−17.2415	−	29.8632i	−0.629153	−	1.08973i	0.358569	−	0.933503i	$-0.383265\pi$
$752$		0			0
$753$	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	$-0.202695\pi$
$757$	44.2425			1.60802			0.804011	+	0.594614i	$0.202695\pi$
$758$		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
$763$	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	$-0.937048\pi$
$773$	−8.89957	+	15.4145i	−0.320095	+	0.554421i	0.660412	+	0.750903i	$0.270382\pi$
$774$		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	0.212407	+	0.977181i	$0.431870\pi$
$787$	−20.7613	+	35.9596i	−0.740060	+	1.28182i	−0.952467	+	0.304640i	$0.901464\pi$
$788$		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	$-0.646592\pi$
$797$	−25.0933			−0.888852			−0.444426	+	0.895816i	$0.646592\pi$
$798$		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	−0.955767	−	0.294125i	$-0.904972\pi$
$809$	−6.34744	+	10.9941i	−0.223164	+	0.386531i	0.732603	+	0.680656i	$0.238305\pi$
$810$		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	0.636090	−	0.771615i	$-0.280551\pi$
$821$	−10.0341	−	17.3796i	−0.350193	−	0.606553i	−0.986283	+	0.165062i	$0.947217\pi$
$822$		0			0
$823$	−5.30523	+	9.18893i	−0.184929	+	0.320306i	−0.943553	−	0.331223i	$-0.892539\pi$
$823$	−5.30523	+	9.18893i	−0.184929	+	0.320306i	0.758624	+	0.651529i	$0.225872\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.7793			−1.20939			−0.604697	−	0.796455i	$-0.706706\pi$
$827$	−34.7793			−1.20939			−0.604697	+	0.796455i	$0.706706\pi$
$828$		0			0
$829$	13.1141	−	22.7142i	0.455471	−	0.788898i	−0.543244	−	0.839575i	$-0.682804\pi$
$829$	13.1141	−	22.7142i	0.455471	−	0.788898i	0.998715	+	0.0506761i	$0.0161376\pi$
$830$		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	$-0.0508082\pi$
$853$	57.6698			1.97458			0.987288	+	0.158942i	$0.0508082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.7020	−	30.6607i	0.604688	−	1.04735i	−0.387413	−	0.921906i	$-0.626631\pi$
$857$	17.7020	−	30.6607i	0.604688	−	1.04735i	0.992101	−	0.125443i	$-0.0400353\pi$
$858$		0			0
$859$	6.72170	+	11.6423i	0.229342	+	0.397231i	0.957613	−	0.288057i	$-0.0930094\pi$
$859$	6.72170	+	11.6423i	0.229342	+	0.397231i	−0.728272	+	0.685289i	$0.759676\pi$
$860$		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	$-0.205034\pi$
$863$	−3.53239	−	6.11828i	−0.120244	−	0.208269i	−0.919864	+	0.392238i	$0.871701\pi$
$864$		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	$-0.0851345\pi$
$877$	7.50273	+	12.9951i	0.253349	+	0.438814i	−0.711097	+	0.703094i	$0.751801\pi$
$878$		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	$-0.935719\pi$
$883$	−58.2229			−1.95936			−0.979679	+	0.200574i	$0.935719\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.6230	+	21.8637i	0.423839	+	0.734111i	0.996311	−	0.0858133i	$-0.0273489\pi$
$887$	12.6230	+	21.8637i	0.423839	+	0.734111i	−0.572472	+	0.819924i	$0.694016\pi$
$888$		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	$-0.684273\pi$
$907$	13.5933	−	23.5444i	0.451360	−	0.781778i	0.998471	+	0.0552822i	$0.0176058\pi$
$908$		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	0.933999	+	0.357276i	$0.116294\pi$
$919$	23.5369	+	40.7670i	0.776409	+	1.34478i	−0.157590	+	0.987505i	$0.550372\pi$
$920$		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	0.679882	−	0.733321i	$-0.262031\pi$
$929$	−8.99554	−	15.5807i	−0.295134	−	0.511187i	−0.975016	+	0.222134i	$0.928698\pi$
$930$		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	$-0.288830\pi$
$937$	37.7003			1.23162			0.615808	+	0.787896i	$0.288830\pi$
$938$		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
$943$	−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	$-0.151991\pi$
$947$	1.41831	+	2.45659i	0.0460890	+	0.0798285i	−0.842061	+	0.539383i	$0.818658\pi$
$948$		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	$-0.406915\pi$
$953$	17.7991			0.576571			0.288285	+	0.957545i	$0.406915\pi$
$954$		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	$-0.578370\pi$
$967$	−15.1581			−0.487453			−0.243726	+	0.969844i	$0.578370\pi$
$968$		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
$973$	−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	$-0.957215\pi$
$977$	−11.8600	+	20.5421i	−0.379434	+	0.657200i	0.611546	+	0.791209i	$0.290548\pi$
$978$		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	0.448850	+	0.893607i	$0.351834\pi$
$983$	−17.2272	+	29.8383i	−0.549461	+	0.951695i	−0.998311	+	0.0580876i	$0.981500\pi$
$984$		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	−0.318468	−	0.947934i	$-0.603168\pi$
$991$	20.8304	−	36.0794i	0.661700	−	1.14610i	0.980169	−	0.198165i	$-0.0634982\pi$
$992$		0			0
$993$	7.16138			0.227260
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.3941	+	21.4672i	−0.392525	+	0.679874i	−0.992782	−	0.119934i	$-0.961732\pi$
$997$	−12.3941	+	21.4672i	−0.392525	+	0.679874i	0.600256	+	0.799808i	$0.295065\pi$
$998$		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.e.501.2	yes	6
5.2	odd	4		700.2.r.d.249.3		12
5.3	odd	4		700.2.r.d.249.4		12
5.4	even	2		700.2.i.d.501.2	yes	6
7.2	even	3	inner	700.2.i.e.401.2	yes	6
7.3	odd	6		4900.2.a.bd.1.2		3
7.4	even	3		4900.2.a.ba.1.2		3
35.2	odd	12		700.2.r.d.149.4		12
35.3	even	12		4900.2.e.s.2549.4		6
35.4	even	6		4900.2.a.bc.1.2		3
35.9	even	6		700.2.i.d.401.2	✓	6
35.17	even	12		4900.2.e.s.2549.3		6
35.18	odd	12		4900.2.e.t.2549.3		6
35.23	odd	12		700.2.r.d.149.3		12
35.24	odd	6		4900.2.a.bb.1.2		3
35.32	odd	12		4900.2.e.t.2549.4		6

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

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more