LMFDB - Embedded newform 700.2.i.d.401.1

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			401.1
Root			$0.356769 - 0.617942i$ of defining polynomial
Character	$\chi$	$=$	700.401
Dual form			700.2.i.d.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60220 - 2.77509i) q^{3} +(1.53189 - 2.15715i) q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})$	\(q+(-1.60220 - 2.77509i) q^{3} +(1.53189 - 2.15715i) q^{7} +(-3.63409 + 6.29444i) q^{9} +(-2.10220 - 3.64112i) q^{11} -0.204402 q^{13} +(-2.53189 - 4.38537i) q^{17} +(-0.531894 + 0.921267i) q^{19} +(-8.44070 - 0.794959i) q^{21} +(1.07031 - 1.85383i) q^{23} +13.6770 q^{27} -7.47259 q^{29} +(4.23630 + 7.33748i) q^{31} +(-6.73630 + 11.6676i) q^{33} +(-5.30660 + 9.19130i) q^{37} +(0.327492 + 0.567233i) q^{39} +10.5494 q^{41} -8.26819 q^{43} +(1.63409 - 2.83033i) q^{47} +(-2.30660 - 6.60905i) q^{49} +(-8.11320 + 14.0525i) q^{51} +(2.83850 + 4.91642i) q^{53} +3.40880 q^{57} +(-0.602201 - 1.04304i) q^{59} +(-0.827492 + 1.43326i) q^{61} +(8.01100 + 17.4817i) q^{63} +(-6.20440 - 10.7463i) q^{67} -6.85939 q^{69} -0.591197 q^{71} +(-2.00000 - 3.46410i) q^{73} +(-11.0748 - 1.04304i) q^{77} +(-3.27471 + 5.67196i) q^{79} +(-11.0110 - 19.0716i) q^{81} -3.88139 q^{83} +(11.9726 + 20.7371i) q^{87} +(4.63409 - 8.02649i) q^{89} +(-0.313121 + 0.440925i) q^{91} +(13.5748 - 23.5122i) q^{93} -1.33198 q^{97} +30.5584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

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

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
$3$	−1.60220	−	2.77509i	−0.925031	−	1.60220i	−0.791511	−	0.611155i	$-0.790705\pi$
$3$	−1.60220	−	2.77509i	−0.925031	−	1.60220i	−0.133520	−	0.991046i	$-0.542628\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.53189	−	2.15715i	0.579001	−	0.815327i
$7$	1.53189	−	2.15715i	0.579001	−	0.815327i
$8$		0			0
$9$	−3.63409	+	6.29444i	−1.21136	+	2.09815i
$10$		0			0
$11$	−2.10220	−	3.64112i	−0.633837	−	1.09784i	−0.986760	−	0.162186i	$-0.948146\pi$
$11$	−2.10220	−	3.64112i	−0.633837	−	1.09784i	0.352923	−	0.935652i	$-0.385188\pi$
$12$		0			0
$13$	−0.204402			−0.0566908			−0.0283454	−	0.999598i	$-0.509024\pi$
$13$	−0.204402			−0.0566908			−0.0283454	+	0.999598i	$0.509024\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.53189	−	4.38537i	−0.614074	−	1.06361i	−0.990546	−	0.137180i	$-0.956196\pi$
$17$	−2.53189	−	4.38537i	−0.614074	−	1.06361i	0.376472	−	0.926428i	$-0.377137\pi$
$18$		0			0
$19$	−0.531894	+	0.921267i	−0.122025	+	0.211353i	−0.920566	−	0.390587i	$-0.872272\pi$
$19$	−0.531894	+	0.921267i	−0.122025	+	0.211353i	0.798541	+	0.601940i	$0.205605\pi$
$20$		0			0
$21$	−8.44070	−	0.794959i	−1.84191	−	0.173474i
$22$		0			0
$23$	1.07031	−	1.85383i	0.223174	−	0.386549i	−0.732596	−	0.680664i	$-0.761691\pi$
$23$	1.07031	−	1.85383i	0.223174	−	0.386549i	0.955770	+	0.294115i	$0.0950247\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	13.6770			2.63214
$28$		0			0
$29$	−7.47259			−1.38763			−0.693813	−	0.720156i	$-0.744070\pi$
$29$	−7.47259			−1.38763			−0.693813	+	0.720156i	$0.744070\pi$
$30$		0			0
$31$	4.23630	+	7.33748i	0.760861	+	1.31785i	0.942407	+	0.334468i	$0.108557\pi$
$31$	4.23630	+	7.33748i	0.760861	+	1.31785i	−0.181546	+	0.983382i	$0.558110\pi$
$32$		0			0
$33$	−6.73630	+	11.6676i	−1.17264	+	2.03107i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.30660	+	9.19130i	−0.872400	+	1.51104i	−0.0128933	+	0.999917i	$0.504104\pi$
$37$	−5.30660	+	9.19130i	−0.872400	+	1.51104i	−0.859507	+	0.511124i	$0.829229\pi$
$38$		0			0
$39$	0.327492	+	0.567233i	0.0524407	+	0.0908300i
$40$		0			0
$41$	10.5494			1.64754			0.823771	−	0.566923i	$-0.191866\pi$
$41$	10.5494			1.64754			0.823771	+	0.566923i	$0.191866\pi$
$42$		0			0
$43$	−8.26819			−1.26089			−0.630444	−	0.776235i	$-0.717127\pi$
$43$	−8.26819			−1.26089			−0.630444	+	0.776235i	$0.717127\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.63409	−	2.83033i	0.238357	−	0.412847i	−0.721886	−	0.692012i	$-0.756724\pi$
$47$	1.63409	−	2.83033i	0.238357	−	0.412847i	0.960243	+	0.279165i	$0.0900578\pi$
$48$		0			0
$49$	−2.30660	−	6.60905i	−0.329515	−	0.944150i
$50$		0			0
$51$	−8.11320	+	14.0525i	−1.13608	+	1.96774i
$52$		0			0
$53$	2.83850	+	4.91642i	0.389897	+	0.675322i	0.992435	−	0.122768i	$-0.0391771\pi$
$53$	2.83850	+	4.91642i	0.389897	+	0.675322i	−0.602538	+	0.798090i	$0.705844\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.40880			0.451507
$58$		0			0
$59$	−0.602201	−	1.04304i	−0.0783999	−	0.135793i	0.824160	−	0.566357i	$-0.191648\pi$
$59$	−0.602201	−	1.04304i	−0.0783999	−	0.135793i	−0.902560	+	0.430565i	$0.858314\pi$
$60$		0			0
$61$	−0.827492	+	1.43326i	−0.105950	+	0.183510i	−0.914126	−	0.405431i	$-0.867122\pi$
$61$	−0.827492	+	1.43326i	−0.105950	+	0.183510i	0.808176	+	0.588941i	$0.200455\pi$
$62$		0			0
$63$	8.01100	+	17.4817i	1.00929	+	2.20249i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.20440	−	10.7463i	−0.757988	−	1.31287i	−0.943875	−	0.330303i	$-0.892849\pi$
$67$	−6.20440	−	10.7463i	−0.757988	−	1.31287i	0.185887	−	0.982571i	$-0.440484\pi$
$68$		0			0
$69$	−6.85939			−0.825773
$70$		0			0
$71$	−0.591197			−0.0701622			−0.0350811	−	0.999384i	$-0.511169\pi$
$71$	−0.591197			−0.0701622			−0.0350811	+	0.999384i	$0.511169\pi$
$72$		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
$77$	−11.0748	−	1.04304i	−1.26209	−	0.118866i
$78$		0			0
$79$	−3.27471	+	5.67196i	−0.368433	+	0.638146i	−0.989321	−	0.145754i	$-0.953439\pi$
$79$	−3.27471	+	5.67196i	−0.368433	+	0.638146i	0.620887	+	0.783900i	$0.286772\pi$
$80$		0			0
$81$	−11.0110	−	19.0716i	−1.22344	−	2.11907i
$82$		0			0
$83$	−3.88139			−0.426038			−0.213019	−	0.977048i	$-0.568330\pi$
$83$	−3.88139			−0.426038			−0.213019	+	0.977048i	$0.568330\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	11.9726	+	20.7371i	1.28360	+	2.22325i
$88$		0			0
$89$	4.63409	−	8.02649i	0.491213	−	0.850806i	−0.508736	−	0.860923i	$-0.669887\pi$
$89$	4.63409	−	8.02649i	0.491213	−	0.850806i	0.999949	+	0.0101167i	$0.00322032\pi$
$90$		0			0
$91$	−0.313121	+	0.440925i	−0.0328241	+	0.0462215i
$92$		0			0
$93$	13.5748	−	23.5122i	1.40764	−	2.43810i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.33198			−0.135242			−0.0676209	−	0.997711i	$-0.521541\pi$
$97$	−1.33198			−0.135242			−0.0676209	+	0.997711i	$0.521541\pi$
$98$		0			0
$99$	30.5584			3.07123
$100$		0			0
$101$	−3.09568	−	5.36188i	−0.308032	−	0.533527i	0.669900	−	0.742451i	$-0.266337\pi$
$101$	−3.09568	−	5.36188i	−0.308032	−	0.533527i	−0.977932	+	0.208925i	$0.933004\pi$
$102$		0			0
$103$	4.87039	−	8.43576i	0.479894	−	0.831200i	−0.519840	−	0.854264i	$-0.674009\pi$
$103$	4.87039	−	8.43576i	0.479894	−	0.831200i	0.999734	+	0.0230631i	$0.00734186\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.92969	−	8.53848i	0.476571	−	0.825446i	−0.523068	−	0.852291i	$-0.675213\pi$
$107$	4.92969	−	8.53848i	0.476571	−	0.825446i	0.999640	+	0.0268449i	$0.00854603\pi$
$108$		0			0
$109$	2.03841	+	3.53063i	0.195245	+	0.338173i	0.946981	−	0.321291i	$-0.104117\pi$
$109$	2.03841	+	3.53063i	0.195245	+	0.338173i	−0.751736	+	0.659464i	$0.770783\pi$
$110$		0			0
$111$	34.0090			3.22799
$112$		0			0
$113$	−2.21744			−0.208599			−0.104300	−	0.994546i	$-0.533260\pi$
$113$	−2.21744			−0.208599			−0.104300	+	0.994546i	$0.533260\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.742815	−	1.28659i	0.0686732	−	0.118946i
$118$		0			0
$119$	−13.3385	−	1.25624i	−1.22274	−	0.115159i
$120$		0			0
$121$	−3.33850	+	5.78245i	−0.303500	+	0.525677i
$122$		0			0
$123$	−16.9023	−	29.2756i	−1.52403	−	2.63969i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.54942			−0.581167			−0.290583	−	0.956850i	$-0.593849\pi$
$127$	−6.54942			−0.581167			−0.290583	+	0.956850i	$0.593849\pi$
$128$		0			0
$129$	13.2473	+	22.9450i	1.16636	+	2.02019i
$130$		0			0
$131$	8.50448	−	14.7302i	0.743040	−	1.28698i	−0.208065	−	0.978115i	$-0.566716\pi$
$131$	8.50448	−	14.7302i	0.743040	−	1.28698i	0.951105	−	0.308868i	$-0.0999503\pi$
$132$		0			0
$133$	1.17251	+	2.55866i	0.101669	+	0.221864i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.54290	−	14.7967i	−0.729869	−	1.26417i	−0.956938	−	0.290292i	$-0.906248\pi$
$137$	−8.54290	−	14.7967i	−0.729869	−	1.26417i	0.227069	−	0.973879i	$-0.427086\pi$
$138$		0			0
$139$	0.740780			0.0628322			0.0314161	−	0.999506i	$-0.489998\pi$
$139$	0.740780			0.0628322			0.0314161	+	0.999506i	$0.489998\pi$
$140$		0			0
$141$	−10.4726			−0.881951
$142$		0			0
$143$	0.429693	+	0.744250i	0.0359327	+	0.0622373i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−14.6451	+	16.9901i	−1.20791	+	1.40132i
$148$		0			0
$149$	8.20889	−	14.2182i	0.672498	−	1.16480i	−0.304695	−	0.952450i	$-0.598555\pi$
$149$	8.20889	−	14.2182i	0.672498	−	1.16480i	0.977193	−	0.212351i	$-0.0681120\pi$
$150$		0			0
$151$	−0.263705	−	0.456750i	−0.0214600	−	0.0371698i	0.855096	−	0.518470i	$-0.173498\pi$
$151$	−0.263705	−	0.456750i	−0.0214600	−	0.0371698i	−0.876556	+	0.481300i	$0.840165\pi$
$152$		0			0
$153$	36.8046			2.97547
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.74281	−	8.21480i	−0.378518	−	0.655612i	0.612329	−	0.790603i	$-0.290233\pi$
$157$	−4.74281	−	8.21480i	−0.378518	−	0.655612i	−0.990847	+	0.134991i	$0.956899\pi$
$158$		0			0
$159$	9.09568	−	15.7542i	0.721334	−	1.24939i
$160$		0			0
$161$	−2.35939	−	5.14868i	−0.185946	−	0.405773i
$162$		0			0
$163$	4.42969	−	7.67245i	0.346960	−	0.600953i	−0.638748	−	0.769416i	$-0.720547\pi$
$163$	4.42969	−	7.67245i	0.346960	−	0.600953i	0.985708	+	0.168463i	$0.0538805\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.33198			−0.644748			−0.322374	−	0.946612i	$-0.604481\pi$
$167$	−8.33198			−0.644748			−0.322374	+	0.946612i	$0.604481\pi$
$168$		0			0
$169$	−12.9582			−0.996786
$170$		0			0
$171$	−3.86591	−	6.69594i	−0.295633	−	0.512052i
$172$		0			0
$173$	−9.17251	+	15.8872i	−0.697373	+	1.20789i	0.272001	+	0.962297i	$0.412314\pi$
$173$	−9.17251	+	15.8872i	−0.697373	+	1.20789i	−0.969374	+	0.245588i	$0.921019\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.92969	+	3.34233i	−0.145045	+	0.251225i
$178$		0			0
$179$	2.14061	+	3.70765i	0.159997	+	0.277123i	0.934867	−	0.354997i	$-0.115518\pi$
$179$	2.14061	+	3.70765i	0.159997	+	0.277123i	−0.774870	+	0.632120i	$0.782185\pi$
$180$		0			0
$181$	2.93621			0.218247			0.109123	−	0.994028i	$-0.465196\pi$
$181$	2.93621			0.218247			0.109123	+	0.994028i	$0.465196\pi$
$182$		0			0
$183$	5.30324			0.392026
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.6451	+	18.4379i	−0.778447	+	1.34831i
$188$		0			0
$189$	20.9517	−	29.5033i	1.52401	−	2.14605i
$190$		0			0
$191$	5.97259	−	10.3448i	0.432162	−	0.748526i	−0.564898	−	0.825161i	$-0.691084\pi$
$191$	5.97259	−	10.3448i	0.432162	−	0.748526i	0.997059	+	0.0766353i	$0.0244177\pi$
$192$		0			0
$193$	3.54290	+	6.13648i	0.255023	+	0.441713i	0.964902	−	0.262611i	$-0.0845835\pi$
$193$	3.54290	+	6.13648i	0.255023	+	0.441713i	−0.709879	+	0.704324i	$0.751250\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.48563			0.390835			0.195417	−	0.980720i	$-0.437394\pi$
$197$	5.48563			0.390835			0.195417	+	0.980720i	$0.437394\pi$
$198$		0			0
$199$	−8.04290	−	13.9307i	−0.570146	−	0.987522i	−0.996550	−	0.0829891i	$-0.973553\pi$
$199$	−8.04290	−	13.9307i	−0.570146	−	0.987522i	0.426405	−	0.904533i	$-0.359780\pi$
$200$		0			0
$201$	−19.8814	+	34.4356i	−1.40233	+	2.42890i
$202$		0			0
$203$	−11.4472	+	16.1195i	−0.803437	+	1.13137i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.77919	+	13.4740i	0.540691	+	0.936505i
$208$		0			0
$209$	4.47259			0.309376
$210$		0			0
$211$	16.6002			1.14280			0.571401	−	0.820671i	$-0.306400\pi$
$211$	16.6002			1.14280			0.571401	+	0.820671i	$0.306400\pi$
$212$		0			0
$213$	0.947216	+	1.64063i	0.0649022	+	0.112414i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	22.3176	+	2.10191i	1.51502	+	0.142687i
$218$		0			0
$219$	−6.40880	+	11.1004i	−0.433067	+	0.750094i
$220$		0			0
$221$	0.517523	+	0.896376i	0.0348124	+	0.0602968i
$222$		0			0
$223$	15.4856			1.03699			0.518497	−	0.855079i	$-0.326492\pi$
$223$	15.4856			1.03699			0.518497	+	0.855079i	$0.326492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.89128	−	3.27579i	−0.125529	−	0.217422i	0.796411	−	0.604756i	$-0.206729\pi$
$227$	−1.89128	−	3.27579i	−0.125529	−	0.217422i	−0.921939	+	0.387334i	$0.873396\pi$
$228$		0			0
$229$	5.60220	−	9.70330i	0.370204	−	0.641212i	−0.619393	−	0.785081i	$-0.712621\pi$
$229$	5.60220	−	9.70330i	0.370204	−	0.641212i	0.989597	+	0.143869i	$0.0459545\pi$
$230$		0			0
$231$	14.8495	+	32.4047i	0.977025	+	2.13208i
$232$		0			0
$233$	−5.97259	+	10.3448i	−0.391277	+	0.677712i	−0.992618	−	0.121280i	$-0.961300\pi$
$233$	−5.97259	+	10.3448i	−0.391277	+	0.677712i	0.601341	+	0.798993i	$0.294633\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	20.9870			1.36325
$238$		0			0
$239$	15.3450			0.992587			0.496293	−	0.868155i	$-0.334694\pi$
$239$	15.3450			0.992587			0.496293	+	0.868155i	$0.334694\pi$
$240$		0			0
$241$	7.19788	+	12.4671i	0.463656	+	0.803076i	0.999140	−	0.0414694i	$-0.0132039\pi$
$241$	7.19788	+	12.4671i	0.463656	+	0.803076i	−0.535483	+	0.844546i	$0.679871\pi$
$242$		0			0
$243$	−14.7682	+	25.5793i	−0.947380	+	1.64091i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.108720	−	0.188308i	0.00691768	−	0.0119818i
$248$		0			0
$249$	6.21877	+	10.7712i	0.394099	+	0.682599i
$250$		0			0
$251$	−19.4178			−1.22564			−0.612819	−	0.790223i	$-0.709965\pi$
$251$	−19.4178			−1.22564			−0.612819	+	0.790223i	$0.709965\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.93621	+	12.0139i	−0.432669	+	0.749405i	−0.997102	−	0.0760740i	$-0.975761\pi$
$257$	−6.93621	+	12.0139i	−0.432669	+	0.749405i	0.564433	+	0.825479i	$0.309095\pi$
$258$		0			0
$259$	11.6979	+	25.5272i	0.726871	+	1.58619i
$260$		0			0
$261$	27.1561	−	47.0357i	1.68092	−	2.91144i
$262$		0			0
$263$	1.72978	+	2.99606i	0.106663	+	0.184745i	0.914416	−	0.404775i	$-0.132650\pi$
$263$	1.72978	+	2.99606i	0.106663	+	0.184745i	−0.807754	+	0.589520i	$0.799317\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−29.6990			−1.81755
$268$		0			0
$269$	−12.8320	−	22.2256i	−0.782379	−	1.35512i	−0.930552	−	0.366159i	$-0.880672\pi$
$269$	−12.8320	−	22.2256i	−0.782379	−	1.35512i	0.148173	−	0.988962i	$-0.452661\pi$
$270$		0			0
$271$	−9.83850	+	17.0408i	−0.597646	+	1.03515i	0.395522	+	0.918457i	$0.370564\pi$
$271$	−9.83850	+	17.0408i	−0.597646	+	1.03515i	−0.993168	+	0.116697i	$0.962769\pi$
$272$		0			0
$273$	1.72529	+	0.162491i	0.104419	+	0.00983439i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.07479	+	15.7180i	0.545251	+	0.944403i	0.998591	+	0.0530653i	$0.0168991\pi$
$277$	9.07479	+	15.7180i	0.545251	+	0.944403i	−0.453340	+	0.891338i	$0.649768\pi$
$278$		0			0
$279$	−61.5804			−3.68672
$280$		0			0
$281$	−18.5364			−1.10579			−0.552894	−	0.833252i	$-0.686476\pi$
$281$	−18.5364			−1.10579			−0.552894	+	0.833252i	$0.686476\pi$
$282$		0			0
$283$	−14.2792	−	24.7323i	−0.848810	−	1.47018i	−0.882271	−	0.470742i	$-0.843986\pi$
$283$	−14.2792	−	24.7323i	−0.848810	−	1.47018i	0.0334610	−	0.999440i	$-0.489347\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.1606	−	22.7567i	0.953929	−	1.34328i
$288$		0			0
$289$	−4.32097	+	7.48415i	−0.254175	+	0.440244i
$290$		0			0
$291$	2.13409	+	3.69636i	0.125103	+	0.216684i
$292$		0			0
$293$	25.5494			1.49261			0.746306	−	0.665603i	$-0.231825\pi$
$293$	25.5494			1.49261			0.746306	+	0.665603i	$0.231825\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−28.7518	−	49.7996i	−1.66835	−	2.88966i
$298$		0			0
$299$	−0.218772	+	0.378925i	−0.0126519	+	0.0219138i
$300$		0			0
$301$	−12.6660	+	17.8357i	−0.730055	+	1.02803i
$302$		0			0
$303$	−9.91981	+	17.1816i	−0.569878	+	0.987058i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	10.1145			0.577267			0.288634	−	0.957440i	$-0.406799\pi$
$307$	10.1145			0.577267			0.288634	+	0.957440i	$0.406799\pi$
$308$		0			0
$309$	−31.2134			−1.77567
$310$		0			0
$311$	−17.0858	−	29.5935i	−0.968847	−	1.67809i	−0.698905	−	0.715215i	$-0.746329\pi$
$311$	−17.0858	−	29.5935i	−0.968847	−	1.67809i	−0.269942	−	0.962877i	$-0.587005\pi$
$312$		0			0
$313$	4.30660	−	7.45925i	0.243424	−	0.421622i	−0.718264	−	0.695771i	$-0.755063\pi$
$313$	4.30660	−	7.45925i	0.243424	−	0.421622i	0.961687	+	0.274149i	$0.0883962\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.90880	−	6.77025i	0.219540	−	0.380255i	−0.735127	−	0.677929i	$-0.762878\pi$
$317$	3.90880	−	6.77025i	0.219540	−	0.380255i	0.954667	+	0.297674i	$0.0962109\pi$
$318$		0			0
$319$	15.7089	+	27.2086i	0.879529	+	1.52339i
$320$		0			0
$321$	−31.5934			−1.76337
$322$		0			0
$323$	5.38680			0.299729
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.53189	−	11.3136i	0.361215	−	0.625642i
$328$		0			0
$329$	−3.60220	−	7.86076i	−0.198596	−	0.433378i
$330$		0			0
$331$	11.0494	−	19.1382i	0.607331	−	1.05193i	−0.384348	−	0.923188i	$-0.625574\pi$
$331$	11.0494	−	19.1382i	0.607331	−	1.05193i	0.991678	−	0.128739i	$-0.0410931\pi$
$332$		0			0
$333$	−38.5694	−	66.8041i	−2.11359	−	3.66084i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.29020			0.0702815			0.0351408	−	0.999382i	$-0.488812\pi$
$337$	1.29020			0.0702815			0.0351408	+	0.999382i	$0.488812\pi$
$338$		0			0
$339$	3.55278	+	6.15360i	0.192961	+	0.334218i
$340$		0			0
$341$	17.8111	−	30.8497i	0.964524	−	1.67061i
$342$		0			0
$343$	−17.7902	−	5.14868i	−0.960580	−	0.278003i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.72978	−	8.19221i	−0.253908	−	0.439781i	0.710691	−	0.703505i	$-0.248383\pi$
$347$	−4.72978	−	8.19221i	−0.253908	−	0.439781i	−0.964598	+	0.263724i	$0.915049\pi$
$348$		0			0
$349$	15.5494			0.832341			0.416171	−	0.909287i	$-0.363372\pi$
$349$	15.5494			0.832341			0.416171	+	0.909287i	$0.363372\pi$
$350$		0			0
$351$	−2.79560			−0.149218
$352$		0			0
$353$	7.56827	+	13.1086i	0.402818	+	0.697702i	0.994065	−	0.108789i	$-0.0346972\pi$
$353$	7.56827	+	13.1086i	0.402818	+	0.697702i	−0.591246	+	0.806491i	$0.701364\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	17.8848	+	39.0283i	0.946562	+	2.06560i
$358$		0			0
$359$	−5.15947	+	8.93646i	−0.272306	+	0.471648i	−0.969452	−	0.245281i	$-0.921120\pi$
$359$	−5.15947	+	8.93646i	−0.272306	+	0.471648i	0.697146	+	0.716930i	$0.254453\pi$
$360$		0			0
$361$	8.93418	+	15.4744i	0.470220	+	0.814445i
$362$		0			0
$363$	21.3958			1.12299
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.96811	+	15.5332i	0.468131	+	0.810827i	0.999337	−	0.0364158i	$-0.0115941\pi$
$367$	8.96811	+	15.5332i	0.468131	+	0.810827i	−0.531205	+	0.847243i	$0.678261\pi$
$368$		0			0
$369$	−38.3376	+	66.4026i	−1.99577	+	3.45678i
$370$		0			0
$371$	14.9537	+	1.40837i	0.776359	+	0.0731188i
$372$		0			0
$373$	−8.09568	+	14.0221i	−0.419179	+	0.726038i	−0.995857	−	0.0909327i	$-0.971015\pi$
$373$	−8.09568	+	14.0221i	−0.419179	+	0.726038i	0.576679	+	0.816971i	$0.304349\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.52741			0.0786656
$378$		0			0
$379$	−12.6002			−0.647227			−0.323614	−	0.946189i	$-0.604898\pi$
$379$	−12.6002			−0.647227			−0.323614	+	0.946189i	$0.604898\pi$
$380$		0			0
$381$	10.4935	+	18.1752i	0.537597	+	0.931146i
$382$		0			0
$383$	7.58783	−	13.1425i	0.387720	−	0.671551i	−0.604422	−	0.796664i	$-0.706596\pi$
$383$	7.58783	−	13.1425i	0.387720	−	0.671551i	0.992142	+	0.125113i	$0.0399294\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	30.0474	−	52.0436i	1.52739	−	2.64552i
$388$		0			0
$389$	14.6197	+	25.3221i	0.741249	+	1.28388i	0.951927	+	0.306326i	$0.0990998\pi$
$389$	14.6197	+	25.3221i	0.741249	+	1.28388i	−0.210677	+	0.977556i	$0.567567\pi$
$390$		0			0
$391$	−10.8396			−0.548183
$392$		0			0
$393$	−54.5036			−2.74934
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.63409	−	9.75854i	0.282767	−	0.489767i	−0.689298	−	0.724478i	$-0.742081\pi$
$397$	5.63409	−	9.75854i	0.282767	−	0.489767i	0.972065	+	0.234711i	$0.0754143\pi$
$398$		0			0
$399$	5.22192	−	7.35330i	0.261423	−	0.368126i
$400$		0			0
$401$	9.01100	−	15.6075i	0.449988	−	0.779402i	−0.548397	−	0.836218i	$-0.684762\pi$
$401$	9.01100	−	15.6075i	0.449988	−	0.779402i	0.998385	+	0.0568162i	$0.0180949\pi$
$402$		0			0
$403$	−0.865905	−	1.49979i	−0.0431338	−	0.0747100i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	44.6222			2.21184
$408$		0			0
$409$	7.89576	+	13.6759i	0.390420	+	0.676228i	0.992505	−	0.122204i	$-0.0389963\pi$
$409$	7.89576	+	13.6759i	0.390420	+	0.676228i	−0.602085	+	0.798432i	$0.705663\pi$
$410$		0			0
$411$	−27.3749	+	47.4147i	−1.35030	+	2.33879i
$412$		0			0
$413$	−3.17251	−	0.298792i	−0.156109	−	0.0147026i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.18688	−	2.05573i	−0.0581217	−	0.100670i
$418$		0			0
$419$	−13.4726			−0.658179			−0.329090	−	0.944299i	$-0.606742\pi$
$419$	−13.4726			−0.658179			−0.329090	+	0.944299i	$0.606742\pi$
$420$		0			0
$421$	−26.8396			−1.30808			−0.654041	−	0.756459i	$-0.726928\pi$
$421$	−26.8396			−1.30808			−0.654041	+	0.756459i	$0.726928\pi$
$422$		0			0
$423$	11.8769	+	20.5714i	0.577475	+	1.00022i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.82413	+	3.98063i	0.0882756	+	0.192636i
$428$		0			0
$429$	1.37691	−	2.38488i	0.0664778	−	0.115143i
$430$		0			0
$431$	−8.02537	−	13.9004i	−0.386569	−	0.669557i	0.605417	−	0.795909i	$-0.293006\pi$
$431$	−8.02537	−	13.9004i	−0.386569	−	0.669557i	−0.991985	+	0.126352i	$0.959673\pi$
$432$		0			0
$433$	−0.910136			−0.0437383			−0.0218692	−	0.999761i	$-0.506962\pi$
$433$	−0.910136			−0.0437383			−0.0218692	+	0.999761i	$0.506962\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.13858	+	1.97208i	0.0544656	+	0.0943373i
$438$		0			0
$439$	18.9517	−	32.8253i	0.904515	−	1.56667i	0.0829488	−	0.996554i	$-0.473566\pi$
$439$	18.9517	−	32.8253i	0.904515	−	1.56667i	0.821566	−	0.570113i	$-0.193100\pi$
$440$		0			0
$441$	49.9827	+	9.49916i	2.38013	+	0.452341i
$442$		0			0
$443$	−3.44070	+	5.95946i	−0.163472	+	0.283143i	−0.936112	−	0.351703i	$-0.885603\pi$
$443$	−3.44070	+	5.95946i	−0.163472	+	0.283143i	0.772639	+	0.634845i	$0.218936\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−52.6091			−2.48833
$448$		0			0
$449$	6.43754			0.303807			0.151903	−	0.988395i	$-0.451460\pi$
$449$	6.43754			0.303807			0.151903	+	0.988395i	$0.451460\pi$
$450$		0			0
$451$	−22.1770	−	38.4117i	−1.04427	−	1.80874i
$452$		0			0
$453$	−0.845015	+	1.46361i	−0.0397023	+	0.0687664i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.64713	+	8.04907i	−0.217384	+	0.376520i	−0.954007	−	0.299783i	$-0.903086\pi$
$457$	−4.64713	+	8.04907i	−0.217384	+	0.376520i	0.736624	+	0.676303i	$0.236419\pi$
$458$		0			0
$459$	−34.6287	−	59.9787i	−1.61633	−	2.79956i
$460$		0			0
$461$	9.29020			0.432688			0.216344	−	0.976317i	$-0.430587\pi$
$461$	9.29020			0.432688			0.216344	+	0.976317i	$0.430587\pi$
$462$		0			0
$463$	29.6091			1.37605			0.688027	−	0.725685i	$-0.258477\pi$
$463$	29.6091			1.37605			0.688027	+	0.725685i	$0.258477\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.0319	+	22.5719i	−0.603044	+	1.04450i	0.389313	+	0.921105i	$0.372712\pi$
$467$	−13.0319	+	22.5719i	−0.603044	+	1.04450i	−0.992357	+	0.123398i	$0.960621\pi$
$468$		0			0
$469$	−32.6860	−	3.07842i	−1.50930	−	0.142148i
$470$		0			0
$471$	−15.1979	+	26.3235i	−0.700281	+	1.21292i
$472$		0			0
$473$	17.3814	+	30.1055i	0.799197	+	1.38425i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−41.2615			−1.88923
$478$		0			0
$479$	0.552784	+	0.957450i	0.0252573	+	0.0437470i	0.878378	−	0.477967i	$-0.158626\pi$
$479$	0.552784	+	0.957450i	0.0252573	+	0.0437470i	−0.853120	+	0.521714i	$0.825293\pi$
$480$		0			0
$481$	1.08468	−	1.87872i	0.0494570	−	0.0856621i
$482$		0			0
$483$	−10.5079	+	14.7967i	−0.478124	+	0.673275i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	2.59568	+	4.49585i	0.117622	+	0.203727i	0.918825	−	0.394666i	$-0.129140\pi$
$487$	2.59568	+	4.49585i	0.117622	+	0.203727i	−0.801203	+	0.598393i	$0.795806\pi$
$488$		0			0
$489$	−28.3890			−1.28380
$490$		0			0
$491$	−28.6640			−1.29359			−0.646793	−	0.762666i	$-0.723890\pi$
$491$	−28.6640			−1.29359			−0.646793	+	0.762666i	$0.723890\pi$
$492$		0			0
$493$	18.9198	+	32.7701i	0.852105	+	1.47589i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.905651	+	1.27530i	−0.0406240	+	0.0572051i
$498$		0			0
$499$	13.0364	−	22.5797i	0.583588	−	1.01080i	−0.411461	−	0.911427i	$-0.634981\pi$
$499$	13.0364	−	22.5797i	0.583588	−	1.01080i	0.995050	−	0.0993776i	$-0.0316852\pi$
$500$		0			0
$501$	13.3495	+	23.1220i	0.596412	+	1.03302i
$502$		0			0
$503$	−8.80864			−0.392758			−0.196379	−	0.980528i	$-0.562918\pi$
$503$	−8.80864			−0.392758			−0.196379	+	0.980528i	$0.562918\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.7617	+	35.9603i	0.922058	+	1.59705i
$508$		0			0
$509$	11.0090	−	19.0681i	0.487964	−	0.845178i	−0.511940	−	0.859021i	$-0.671073\pi$
$509$	11.0090	−	19.0681i	0.487964	−	0.845178i	0.999904	+	0.0138427i	$0.00440640\pi$
$510$		0			0
$511$	−10.5364	−	0.992334i	−0.466102	−	0.0438983i
$512$		0			0
$513$	−7.27471	+	12.6002i	−0.321186	+	0.556311i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−13.7408			−0.604319
$518$		0			0
$519$	58.7848			2.58037
$520$		0			0
$521$	7.54942	+	13.0760i	0.330746	+	0.572869i	0.982658	−	0.185426i	$-0.0593663\pi$
$521$	7.54942	+	13.0760i	0.330746	+	0.572869i	−0.651912	+	0.758294i	$0.726033\pi$
$522$		0			0
$523$	−2.29560	+	3.97609i	−0.100380	+	0.173862i	−0.911841	−	0.410543i	$-0.865339\pi$
$523$	−2.29560	+	3.97609i	−0.100380	+	0.173862i	0.811462	+	0.584406i	$0.198672\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.4517	−	37.1554i	0.934451	−	1.61852i
$528$		0			0
$529$	9.20889	+	15.9503i	0.400386	+	0.693490i
$530$		0			0
$531$	8.75382			0.379883
$532$		0			0
$533$	−2.15632			−0.0934005
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.85939	−	11.8808i	0.296004	−	0.512695i
$538$		0			0
$539$	−19.2154	+	22.2922i	−0.827666	+	0.960192i
$540$		0			0
$541$	−6.83850	+	11.8446i	−0.294010	+	0.509240i	−0.974754	−	0.223281i	$-0.928323\pi$
$541$	−6.83850	+	11.8446i	−0.294010	+	0.509240i	0.680744	+	0.732521i	$0.261657\pi$
$542$		0			0
$543$	−4.70440	−	8.14826i	−0.201885	−	0.349675i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.3581			0.485635			0.242818	−	0.970072i	$-0.421928\pi$
$547$	11.3581			0.485635			0.242818	+	0.970072i	$0.421928\pi$
$548$		0			0
$549$	−6.01437	−	10.4172i	−0.256687	−	0.444595i
$550$		0			0
$551$	3.97463	−	6.88425i	0.169325	−	0.293279i
$552$		0			0
$553$	7.21877	+	15.7529i	0.306973	+	0.669881i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.19788	+	14.1991i	0.347355	+	0.601637i	0.985779	−	0.168048i	$-0.0537464\pi$
$557$	8.19788	+	14.1991i	0.347355	+	0.601637i	−0.638423	+	0.769685i	$0.720413\pi$
$558$		0			0
$559$	1.69003			0.0714807
$560$		0			0
$561$	68.2223			2.88035
$562$		0			0
$563$	−2.43621	−	4.21964i	−0.102674	−	0.177837i	0.810111	−	0.586276i	$-0.199407\pi$
$563$	−2.43621	−	4.21964i	−0.102674	−	0.177837i	−0.912786	+	0.408439i	$0.866073\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−58.0081	−	5.46330i	−2.43611	−	0.229437i
$568$		0			0
$569$	18.9277	−	32.7837i	0.793489	−	1.37436i	−0.130306	−	0.991474i	$-0.541596\pi$
$569$	18.9277	−	32.7837i	0.793489	−	1.37436i	0.923794	−	0.382889i	$-0.125071\pi$
$570$		0			0
$571$	20.8704	+	36.1486i	0.873399	+	1.51277i	0.858459	+	0.512882i	$0.171422\pi$
$571$	20.8704	+	36.1486i	0.873399	+	1.51277i	0.0149398	+	0.999888i	$0.495244\pi$
$572$		0			0
$573$	−38.2772			−1.59905
$574$		0			0
$575$		0			0
$576$		0			0
$577$	21.5265	+	37.2850i	0.896160	+	1.55219i	0.832363	+	0.554231i	$0.186988\pi$
$577$	21.5265	+	37.2850i	0.896160	+	1.55219i	0.0637967	+	0.997963i	$0.479679\pi$
$578$		0			0
$579$	11.3529	−	19.6637i	0.471809	−	0.817197i
$580$		0			0
$581$	−5.94588	+	8.37275i	−0.246677	+	0.347360i
$582$		0			0
$583$	11.9342	−	20.6706i	0.494263	−	0.856089i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.67699			0.234315			0.117157	−	0.993113i	$-0.462622\pi$
$587$	5.67699			0.234315			0.117157	+	0.993113i	$0.462622\pi$
$588$		0			0
$589$	−9.01304			−0.371376
$590$		0			0
$591$	−8.78908	−	15.2231i	−0.361534	−	0.626196i
$592$		0			0
$593$	4.47259	−	7.74675i	0.183667	−	0.318121i	−0.759459	−	0.650555i	$-0.774536\pi$
$593$	4.47259	−	7.74675i	0.183667	−	0.318121i	0.943127	+	0.332434i	$0.107870\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−25.7727	+	44.6396i	−1.05481	+	1.82698i
$598$		0			0
$599$	12.6132	+	21.8467i	0.515362	+	0.892632i	0.999841	+	0.0178298i	$0.00567570\pi$
$599$	12.6132	+	21.8467i	0.515362	+	0.892632i	−0.484479	+	0.874803i	$0.660991\pi$
$600$		0			0
$601$	15.3409			0.625770			0.312885	−	0.949791i	$-0.398705\pi$
$601$	15.3409			0.625770			0.312885	+	0.949791i	$0.398705\pi$
$602$		0			0
$603$	90.1895			3.67280
$604$		0			0
$605$		0			0
$606$		0			0
$607$	10.4681	−	18.1313i	0.424887	−	0.735926i	−0.571523	−	0.820586i	$-0.693647\pi$
$607$	10.4681	−	18.1313i	0.424887	−	0.735926i	0.996410	+	0.0846599i	$0.0269804\pi$
$608$		0			0
$609$	63.0739	+	5.94040i	2.55588	+	0.240717i
$610$		0			0
$611$	−0.334011	+	0.578525i	−0.0135127	+	0.0234046i
$612$		0			0
$613$	−2.65947	−	4.60634i	−0.107415	−	0.186048i	0.807307	−	0.590131i	$-0.200924\pi$
$613$	−2.65947	−	4.60634i	−0.107415	−	0.186048i	−0.914722	+	0.404083i	$0.867591\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.6262			1.15245			0.576225	−	0.817291i	$-0.304525\pi$
$617$	28.6262			1.15245			0.576225	+	0.817291i	$0.304525\pi$
$618$		0			0
$619$	10.7812	+	18.6736i	0.433334	+	0.750557i	0.997158	−	0.0753383i	$-0.0240037\pi$
$619$	10.7812	+	18.6736i	0.433334	+	0.750557i	−0.563824	+	0.825895i	$0.690670\pi$
$620$		0			0
$621$	14.6386	−	25.3548i	0.587426	−	1.01745i
$622$		0			0
$623$	−10.2154	−	22.2922i	−0.409272	−	0.893117i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.16599	−	12.4119i	−0.286182	−	0.495682i
$628$		0			0
$629$	53.7430			2.14287
$630$		0			0
$631$	−25.1365			−1.00067			−0.500335	−	0.865832i	$-0.666790\pi$
$631$	−25.1365			−1.00067			−0.500335	+	0.865832i	$0.666790\pi$
$632$		0			0
$633$	−26.5968	−	46.0670i	−1.05713	−	1.83100i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.471473	+	1.35090i	0.0186804	+	0.0535246i
$638$		0			0
$639$	2.14847	−	3.72125i	0.0849920	−	0.147210i
$640$		0			0
$641$	−22.0539	−	38.1985i	−0.871077	−	1.50875i	−0.860884	−	0.508801i	$-0.830089\pi$
$641$	−22.0539	−	38.1985i	−0.871077	−	1.50875i	−0.0101927	−	0.999948i	$-0.503244\pi$
$642$		0			0
$643$	16.4816			0.649969			0.324985	−	0.945719i	$-0.394641\pi$
$643$	16.4816			0.649969			0.324985	+	0.945719i	$0.394641\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.7199	−	27.2276i	−0.618013	−	1.07043i	−0.989848	−	0.142131i	$-0.954605\pi$
$647$	−15.7199	−	27.2276i	−0.618013	−	1.07043i	0.371835	−	0.928299i	$-0.378729\pi$
$648$		0			0
$649$	−2.53189	+	4.38537i	−0.0993855	+	0.172141i
$650$		0			0
$651$	−29.9243	−	65.3011i	−1.17283	−	2.55935i
$652$		0			0
$653$	20.4387	−	35.4008i	0.799827	−	1.38534i	−0.119902	−	0.992786i	$-0.538258\pi$
$653$	20.4387	−	35.4008i	0.799827	−	1.38534i	0.919729	−	0.392555i	$-0.128409\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	29.0728			1.13424
$658$		0			0
$659$	−46.6860			−1.81863			−0.909313	−	0.416112i	$-0.863392\pi$
$659$	−46.6860			−1.81863			−0.909313	+	0.416112i	$0.863392\pi$
$660$		0			0
$661$	−0.0637877	−	0.110484i	−0.00248106	−	0.00429731i	0.864782	−	0.502147i	$-0.167456\pi$
$661$	−0.0637877	−	0.110484i	−0.00248106	−	0.00429731i	−0.867263	+	0.497850i	$0.834123\pi$
$662$		0			0
$663$	1.65835	−	2.87235i	0.0644050	−	0.111553i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.99797	+	13.8529i	−0.309682	+	0.536386i
$668$		0			0
$669$	−24.8111	−	42.9741i	−0.959252	−	1.66147i
$670$		0			0
$671$	6.95822			0.268619
$672$		0			0
$673$	−48.1936			−1.85773			−0.928863	−	0.370423i	$-0.879213\pi$
$673$	−48.1936			−1.85773			−0.928863	+	0.370423i	$0.879213\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.2089	+	40.1990i	−0.891990	+	1.54497i	−0.0545037	+	0.998514i	$0.517358\pi$
$677$	−23.2089	+	40.1990i	−0.891990	+	1.54497i	−0.837486	+	0.546458i	$0.815976\pi$
$678$		0			0
$679$	−2.04045	+	2.87328i	−0.0783052	+	0.110266i
$680$		0			0
$681$	−6.06042	+	10.4970i	−0.232236	+	0.402244i
$682$		0			0
$683$	21.7747	+	37.7149i	0.833186	+	1.44312i	0.895499	+	0.445064i	$0.146819\pi$
$683$	21.7747	+	37.7149i	0.833186	+	1.44312i	−0.0623127	+	0.998057i	$0.519848\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−35.9034			−1.36980
$688$		0			0
$689$	−0.580193	−	1.00492i	−0.0221036	−	0.0382845i
$690$		0			0
$691$	13.0474	−	22.5987i	0.496346	−	0.859696i	−0.503645	−	0.863911i	$-0.668008\pi$
$691$	13.0474	−	22.5987i	0.496346	−	0.859696i	0.999991	+	0.00421436i	$0.00134147\pi$
$692$		0			0
$693$	46.8122	−	65.9191i	1.77825	−	2.50406i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−26.7100	−	46.2631i	−1.01171	−	1.75234i
$698$		0			0
$699$	38.2772			1.44778
$700$		0			0
$701$	21.7277			0.820645			0.410323	−	0.911940i	$-0.365416\pi$
$701$	21.7277			0.820645			0.410323	+	0.911940i	$0.365416\pi$
$702$		0			0
$703$	−5.64510	−	9.77760i	−0.212909	−	0.368769i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−16.3086	−	1.53597i	−0.613349	−	0.0577663i
$708$		0			0
$709$	−8.53841	+	14.7890i	−0.320667	+	0.555411i	−0.980626	−	0.195890i	$-0.937240\pi$
$709$	−8.53841	+	14.7890i	−0.320667	+	0.555411i	0.659959	+	0.751302i	$0.270574\pi$
$710$		0			0
$711$	−23.8012	−	41.2249i	−0.892615	−	1.54605i
$712$		0			0
$713$	18.1365			0.679219
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.5858	−	42.5838i	−0.918173	−	1.59032i
$718$		0			0
$719$	−13.6231	+	23.5959i	−0.508056	+	0.879978i	0.491901	+	0.870651i	$0.336302\pi$
$719$	−13.6231	+	23.5959i	−0.508056	+	0.879978i	−0.999957	+	0.00932687i	$0.997031\pi$
$720$		0			0
$721$	−10.7363	−	23.4289i	−0.399841	−	0.872536i
$722$		0			0
$723$	23.0649	−	39.9496i	0.857793	−	1.48574i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−19.9232			−0.738910			−0.369455	−	0.929249i	$-0.620456\pi$
$727$	−19.9232			−0.738910			−0.369455	+	0.929249i	$0.620456\pi$
$728$		0			0
$729$	28.5804			1.05853
$730$		0			0
$731$	20.9342	+	36.2591i	0.774279	+	1.34109i
$732$		0			0
$733$	15.5813	−	26.9876i	0.575509	−	0.996811i	−0.420477	−	0.907303i	$-0.638137\pi$
$733$	15.5813	−	26.9876i	0.575509	−	0.996811i	0.995986	−	0.0895075i	$-0.0285293\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26.0858	+	45.1819i	−0.960883	+	1.66430i
$738$		0			0
$739$	−0.950583	−	1.64646i	−0.0349678	−	0.0605659i	0.848012	−	0.529977i	$-0.177800\pi$
$739$	−0.950583	−	1.64646i	−0.0349678	−	0.0605659i	−0.882980	+	0.469411i	$0.844466\pi$
$740$		0			0
$741$	−0.696765			−0.0255963
$742$		0			0
$743$	−36.0660			−1.32313			−0.661567	−	0.749886i	$-0.730108\pi$
$743$	−36.0660			−1.32313			−0.661567	+	0.749886i	$0.730108\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	14.1054	−	24.4312i	0.516088	−	0.893890i
$748$		0			0
$749$	−10.8670	−	23.7141i	−0.397072	−	0.866496i
$750$		0			0
$751$	0.384761	−	0.666425i	0.0140401	−	0.0243182i	−0.858920	−	0.512110i	$-0.828864\pi$
$751$	0.384761	−	0.666425i	0.0140401	−	0.0243182i	0.872960	+	0.487792i	$0.162197\pi$
$752$		0			0
$753$	31.1112	+	53.8861i	1.13375	+	1.96372i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	14.9542			0.543518			0.271759	−	0.962365i	$-0.412395\pi$
$757$	14.9542			0.543518			0.271759	+	0.962365i	$0.412395\pi$
$758$		0			0
$759$	14.4198	+	24.9758i	0.523406	+	0.906565i
$760$		0			0
$761$	−9.58580	+	16.6031i	−0.347485	+	0.601861i	−0.985802	−	0.167912i	$-0.946298\pi$
$761$	−9.58580	+	16.6031i	−0.347485	+	0.601861i	0.638317	+	0.769773i	$0.279631\pi$
$762$		0			0
$763$	10.7387	+	1.01139i	0.388769	+	0.0366149i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.123091	+	0.213199i	0.00444455	+	0.00769819i
$768$		0			0
$769$	36.3189			1.30969			0.654847	−	0.755761i	$-0.272733\pi$
$769$	36.3189			1.30969			0.654847	+	0.755761i	$0.272733\pi$
$770$		0			0
$771$	44.4528			1.60093
$772$		0			0
$773$	−23.7343	−	41.1089i	−0.853662	−	1.47859i	−0.877881	−	0.478879i	$-0.841043\pi$
$773$	−23.7343	−	41.1089i	−0.853662	−	1.47859i	0.0242187	−	0.999707i	$-0.492290\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	52.0981	−	73.3625i	1.86901	−	2.63186i
$778$		0			0
$779$	−5.61117	+	9.71883i	−0.201041	+	0.348213i
$780$		0			0
$781$	1.24281	+	2.15262i	0.0444714	+	0.0770267i
$782$		0			0
$783$	−102.203			−3.65242
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.94273	+	6.82901i	0.140543	+	0.243428i	0.927701	−	0.373323i	$-0.121782\pi$
$787$	3.94273	+	6.82901i	0.140543	+	0.243428i	−0.787158	+	0.616751i	$0.788448\pi$
$788$		0			0
$789$	5.54290	−	9.60058i	0.197332	−	0.341790i
$790$		0			0
$791$	−3.39688	+	4.78335i	−0.120779	+	0.170076i
$792$		0			0
$793$	0.169141	−	0.292960i	0.00600636	−	0.0104033i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	33.6132			1.19064			0.595320	−	0.803488i	$-0.297025\pi$
$797$	33.6132			1.19064			0.595320	+	0.803488i	$0.297025\pi$
$798$		0			0
$799$	−16.5494			−0.585476
$800$		0			0
$801$	33.6815	+	58.3380i	1.19008	+	2.06127i
$802$		0			0
$803$	−8.40880	+	14.5645i	−0.296740	+	0.513969i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−41.1188	+	71.2199i	−1.44745	+	2.50706i
$808$		0			0
$809$	4.59568	+	7.95995i	0.161576	+	0.279857i	0.935434	−	0.353502i	$-0.115009\pi$
$809$	4.59568	+	7.95995i	0.161576	+	0.279857i	−0.773858	+	0.633359i	$0.781676\pi$
$810$		0			0
$811$	21.6483			0.760173			0.380086	−	0.924951i	$-0.375894\pi$
$811$	21.6483			0.760173			0.380086	+	0.924951i	$0.375894\pi$
$812$		0			0
$813$	63.0530			2.21136
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.39780	−	7.61721i	0.153860	−	0.266493i
$818$		0			0
$819$	−1.63746	−	3.57329i	−0.0572175	−	0.124861i
$820$		0			0
$821$	−16.1307	+	27.9392i	−0.562966	+	0.975086i	0.434269	+	0.900783i	$0.357007\pi$
$821$	−16.1307	+	27.9392i	−0.562966	+	0.975086i	−0.997236	+	0.0743032i	$0.976327\pi$
$822$		0			0
$823$	5.72192	+	9.91066i	0.199454	+	0.345464i	0.948351	−	0.317222i	$-0.102750\pi$
$823$	5.72192	+	9.91066i	0.199454	+	0.345464i	−0.748898	+	0.662686i	$0.769417\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.82658			−0.341704			−0.170852	−	0.985297i	$-0.554652\pi$
$827$	−9.82658			−0.341704			−0.170852	+	0.985297i	$0.554652\pi$
$828$		0			0
$829$	−19.1287	−	33.1319i	−0.664367	−	1.15072i	−0.979457	−	0.201655i	$-0.935368\pi$
$829$	−19.1287	−	33.1319i	−0.664367	−	1.15072i	0.315090	−	0.949062i	$-0.397965\pi$
$830$		0			0
$831$	29.0793	−	50.3668i	1.00875	−	1.74720i
$832$		0			0
$833$	−23.1431	+	26.8487i	−0.801860	+	0.930253i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	57.9398	+	100.355i	2.00269	+	3.46876i
$838$		0			0
$839$	30.6900			1.05954			0.529769	−	0.848142i	$-0.322279\pi$
$839$	30.6900			1.05954			0.529769	+	0.848142i	$0.322279\pi$
$840$		0			0
$841$	26.8396			0.925504
$842$		0			0
$843$	29.6990	+	51.4402i	1.02289	+	1.77169i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.35939	+	16.0597i	0.252872	+	0.551819i
$848$		0			0
$849$	−45.7563	+	79.2522i	−1.57035	+	2.71993i
$850$		0			0
$851$	11.3594	+	19.6750i	0.389395	+	0.674451i
$852$		0			0
$853$	−39.4569			−1.35098			−0.675489	−	0.737370i	$-0.736067\pi$
$853$	−39.4569			−1.35098			−0.675489	+	0.737370i	$0.736067\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.9297	−	34.5192i	−0.680785	−	1.17915i	−0.974742	−	0.223336i	$-0.928305\pi$
$857$	−19.9297	−	34.5192i	−0.680785	−	1.17915i	0.293956	−	0.955819i	$-0.405028\pi$
$858$		0			0
$859$	9.75719	−	16.8999i	0.332911	−	0.576619i	−0.650170	−	0.759788i	$-0.725303\pi$
$859$	9.75719	−	16.8999i	0.332911	−	0.576619i	0.983081	+	0.183170i	$0.0586358\pi$
$860$		0			0
$861$	−89.0444	−	8.38635i	−3.03463	−	0.285806i
$862$		0			0
$863$	−18.9661	+	32.8502i	−0.645613	+	1.11823i	0.338547	+	0.940949i	$0.390065\pi$
$863$	−18.9661	+	32.8502i	−0.645613	+	1.11823i	−0.984160	+	0.177284i	$0.943269\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	27.6923			0.940479
$868$		0			0
$869$	27.5364			0.934108
$870$		0			0
$871$	1.26819	+	2.19657i	0.0429710	+	0.0744279i
$872$		0			0
$873$	4.84053	−	8.38404i	0.163827	−	0.283757i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.47259	−	9.47881i	0.184796	−	0.320077i	−0.758712	−	0.651427i	$-0.774171\pi$
$877$	5.47259	−	9.47881i	0.184796	−	0.320077i	0.943508	+	0.331350i	$0.107504\pi$
$878$		0			0
$879$	−40.9353	−	70.9020i	−1.38071	−	2.39147i
$880$		0			0
$881$	−16.2592			−0.547787			−0.273894	−	0.961760i	$-0.588312\pi$
$881$	−16.2592			−0.547787			−0.273894	+	0.961760i	$0.588312\pi$
$882$		0			0
$883$	−23.2511			−0.782461			−0.391231	−	0.920293i	$-0.627951\pi$
$883$	−23.2511			−0.782461			−0.391231	+	0.920293i	$0.627951\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.6197	+	20.1260i	−0.390152	+	0.675763i	−0.992469	−	0.122494i	$-0.960911\pi$
$887$	−11.6197	+	20.1260i	−0.390152	+	0.675763i	0.602317	+	0.798257i	$0.294244\pi$
$888$		0			0
$889$	−10.0330	+	14.1281i	−0.336496	+	0.473841i
$890$		0			0
$891$	−46.2947	+	80.1847i	−1.55093	+	2.68629i
$892$		0			0
$893$	1.73833	+	3.01088i	0.0581710	+	0.100755i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.40207			0.0468137
$898$		0			0
$899$	−31.6561	−	54.8300i	−1.05579	−	1.82868i
$900$		0			0
$901$	14.3735	−	24.8957i	0.478852	−	0.829396i
$902$		0			0
$903$	69.7893	+	6.57287i	2.32244	+	0.218731i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−22.1132	−	38.3012i	−0.734257	−	1.27177i	−0.955049	−	0.296449i	$-0.904197\pi$
$907$	−22.1132	−	38.3012i	−0.734257	−	1.27177i	0.220792	−	0.975321i	$-0.429136\pi$
$908$		0			0
$909$	45.0000			1.49256
$910$		0			0
$911$	−27.4218			−0.908526			−0.454263	−	0.890868i	$-0.650097\pi$
$911$	−27.4218			−0.908526			−0.454263	+	0.890868i	$0.650097\pi$
$912$		0			0
$913$	8.15947	+	14.1326i	0.270039	+	0.467721i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−18.7473	−	40.9106i	−0.619090	−	1.35099i
$918$		0			0
$919$	16.6581	−	28.8527i	0.549501	−	0.951764i	−0.448807	−	0.893628i	$-0.648151\pi$
$919$	16.6581	−	28.8527i	0.549501	−	0.951764i	0.998309	−	0.0581356i	$-0.0185156\pi$
$920$		0			0
$921$	−16.2055	−	28.0688i	−0.533990	−	0.924898i
$922$		0			0
$923$	0.120842			0.00397755
$924$		0			0
$925$		0			0
$926$		0			0
$927$	35.3989	+	61.3127i	1.16265	+	2.01377i
$928$		0			0
$929$	6.62421	−	11.4735i	0.217333	−	0.376432i	−0.736659	−	0.676265i	$-0.763598\pi$
$929$	6.62421	−	11.4735i	0.217333	−	0.376432i	0.953992	+	0.299833i	$0.0969308\pi$
$930$		0			0
$931$	7.31557	+	1.39032i	0.239758	+	0.0455658i
$932$		0			0
$933$	−54.7497	+	94.8293i	−1.79243	+	3.10457i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	10.1365			0.331146			0.165573	−	0.986197i	$-0.447053\pi$
$937$	10.1365			0.331146			0.165573	+	0.986197i	$0.447053\pi$
$938$		0			0
$939$	−27.6002			−0.900697
$940$		0			0
$941$	16.4342	+	28.4648i	0.535739	+	0.927927i	0.999127	+	0.0417716i	$0.0133002\pi$
$941$	16.4342	+	28.4648i	0.535739	+	0.927927i	−0.463388	+	0.886155i	$0.653366\pi$
$942$		0			0
$943$	11.2911	−	19.5568i	0.367689	−	0.636856i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.1626	+	19.3342i	−0.362736	+	0.628278i	−0.988410	−	0.151807i	$-0.951491\pi$
$947$	−11.1626	+	19.3342i	−0.362736	+	0.628278i	0.625674	+	0.780085i	$0.284824\pi$
$948$		0			0
$949$	0.408803	+	0.708068i	0.0132703	+	0.0229849i
$950$		0			0
$951$	−25.0507			−0.812326
$952$		0			0
$953$	47.4685			1.53766			0.768828	−	0.639455i	$-0.220840\pi$
$953$	47.4685			1.53766			0.768828	+	0.639455i	$0.220840\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	50.3376	−	87.1872i	1.62718	−	2.81836i
$958$		0			0
$959$	−45.0056	−	4.23870i	−1.45331	−	0.136875i
$960$		0			0
$961$	−20.3924	+	35.3207i	−0.657819	+	1.13938i
$962$		0			0
$963$	35.8299	+	62.0593i	1.15460	+	1.99983i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−21.3189			−0.685571			−0.342785	−	0.939414i	$-0.611370\pi$
$967$	−21.3189			−0.685571			−0.342785	+	0.939414i	$0.611370\pi$
$968$		0			0
$969$	−8.63073	−	14.9489i	−0.277259	−	0.480227i
$970$		0			0
$971$	14.7812	−	25.6018i	0.474352	−	0.821602i	−0.525217	−	0.850969i	$-0.676016\pi$
$971$	14.7812	−	25.6018i	0.474352	−	0.821602i	0.999569	+	0.0293666i	$0.00934901\pi$
$972$		0			0
$973$	1.13480	−	1.59797i	0.0363799	−	0.0512287i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.919807	−	1.59315i	−0.0294272	−	0.0509695i	0.850937	−	0.525268i	$-0.176035\pi$
$977$	−0.919807	−	1.59315i	−0.0294272	−	0.0509695i	−0.880364	+	0.474299i	$0.842702\pi$
$978$		0			0
$979$	−38.9672			−1.24540
$980$		0			0
$981$	−29.6311			−0.946050
$982$		0			0
$983$	−5.68800	−	9.85190i	−0.181419	−	0.314227i	0.760945	−	0.648816i	$-0.224736\pi$
$983$	−5.68800	−	9.85190i	−0.181419	−	0.314227i	−0.942364	+	0.334590i	$0.891402\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−16.0429	+	22.5910i	−0.510651	+	0.719078i
$988$		0			0
$989$	−8.84950	+	15.3278i	−0.281398	+	0.487395i
$990$		0			0
$991$	−3.89576	−	6.74766i	−0.123753	−	0.214347i	0.797492	−	0.603330i	$-0.206160\pi$
$991$	−3.89576	−	6.74766i	−0.123753	−	0.214347i	−0.921245	+	0.388983i	$0.872826\pi$
$992$		0			0
$993$	−70.8135			−2.24720
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.71092	+	9.89160i	0.180867	+	0.313270i	0.942176	−	0.335119i	$-0.108776\pi$
$997$	5.71092	+	9.89160i	0.180867	+	0.313270i	−0.761309	+	0.648389i	$0.775443\pi$
$998$		0			0
$999$	−72.5784	+	125.709i	−2.29628	+	3.97727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.i.d.401.1	✓	6
5.2	odd	4		700.2.r.d.149.1		12
5.3	odd	4		700.2.r.d.149.6		12
5.4	even	2		700.2.i.e.401.3	yes	6
7.2	even	3		4900.2.a.bc.1.3		3
7.4	even	3	inner	700.2.i.d.501.1	yes	6
7.5	odd	6		4900.2.a.bb.1.1		3
35.2	odd	12		4900.2.e.t.2549.1		6
35.4	even	6		700.2.i.e.501.3	yes	6
35.9	even	6		4900.2.a.ba.1.1		3
35.12	even	12		4900.2.e.s.2549.6		6
35.18	odd	12		700.2.r.d.249.1		12
35.19	odd	6		4900.2.a.bd.1.3		3
35.23	odd	12		4900.2.e.t.2549.6		6
35.32	odd	12		700.2.r.d.249.6		12
35.33	even	12		4900.2.e.s.2549.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.1	✓	6	1.1	even	1	trivial
700.2.i.d.501.1	yes	6	7.4	even	3	inner
700.2.i.e.401.3	yes	6	5.4	even	2
700.2.i.e.501.3	yes	6	35.4	even	6
700.2.r.d.149.1		12	5.2	odd	4
700.2.r.d.149.6		12	5.3	odd	4
700.2.r.d.249.1		12	35.18	odd	12
700.2.r.d.249.6		12	35.32	odd	12
4900.2.a.ba.1.1		3	35.9	even	6
4900.2.a.bb.1.1		3	7.5	odd	6
4900.2.a.bc.1.3		3	7.2	even	3
4900.2.a.bd.1.3		3	35.19	odd	6
4900.2.e.s.2549.1		6	35.33	even	12
4900.2.e.s.2549.6		6	35.12	even	12
4900.2.e.t.2549.1		6	35.2	odd	12
4900.2.e.t.2549.6		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.60220 - 2.77509i) q^{3} +(1.53189 - 2.15715i) q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})\)	\(q+(-1.60220 - 2.77509i) q^{3} +(1.53189 - 2.15715i) q^{7} +(-3.63409 + 6.29444i) q^{9} +(-2.10220 - 3.64112i) q^{11} -0.204402 q^{13} +(-2.53189 - 4.38537i) q^{17} +(-0.531894 + 0.921267i) q^{19} +(-8.44070 - 0.794959i) q^{21} +(1.07031 - 1.85383i) q^{23} +13.6770 q^{27} -7.47259 q^{29} +(4.23630 + 7.33748i) q^{31} +(-6.73630 + 11.6676i) q^{33} +(-5.30660 + 9.19130i) q^{37} +(0.327492 + 0.567233i) q^{39} +10.5494 q^{41} -8.26819 q^{43} +(1.63409 - 2.83033i) q^{47} +(-2.30660 - 6.60905i) q^{49} +(-8.11320 + 14.0525i) q^{51} +(2.83850 + 4.91642i) q^{53} +3.40880 q^{57} +(-0.602201 - 1.04304i) q^{59} +(-0.827492 + 1.43326i) q^{61} +(8.01100 + 17.4817i) q^{63} +(-6.20440 - 10.7463i) q^{67} -6.85939 q^{69} -0.591197 q^{71} +(-2.00000 - 3.46410i) q^{73} +(-11.0748 - 1.04304i) q^{77} +(-3.27471 + 5.67196i) q^{79} +(-11.0110 - 19.0716i) q^{81} -3.88139 q^{83} +(11.9726 + 20.7371i) q^{87} +(4.63409 - 8.02649i) q^{89} +(-0.313121 + 0.440925i) q^{91} +(13.5748 - 23.5122i) q^{93} -1.33198 q^{97} +30.5584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 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