LMFDB - Embedded newform 700.2.r.d.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			249.1
Root			$-0.617942 + 0.356769i$ of defining polynomial
Character	$\chi$	$=$	700.249
Dual form			700.2.r.d.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.77509 - 1.60220i) q^{3} +(2.15715 - 1.53189i) q^{7} +(3.63409 + 6.29444i) q^{9} +(-2.10220 + 3.64112i) q^{11} -0.204402i q^{13} +(4.38537 + 2.53189i) q^{17} +(0.531894 + 0.921267i) q^{19} +(-8.44070 + 0.794959i) q^{21} +(-1.85383 + 1.07031i) q^{23} -13.6770i q^{27} +7.47259 q^{29} +(4.23630 - 7.33748i) q^{31} +(11.6676 - 6.73630i) q^{33} +(-9.19130 + 5.30660i) q^{37} +(-0.327492 + 0.567233i) q^{39} +10.5494 q^{41} -8.26819i q^{43} +(2.83033 - 1.63409i) q^{47} +(2.30660 - 6.60905i) q^{49} +(-8.11320 - 14.0525i) q^{51} +(4.91642 + 2.83850i) q^{53} -3.40880i q^{57} +(0.602201 - 1.04304i) q^{59} +(-0.827492 - 1.43326i) q^{61} +(17.4817 + 8.01100i) q^{63} +(10.7463 + 6.20440i) q^{67} +6.85939 q^{69} -0.591197 q^{71} +(-3.46410 - 2.00000i) q^{73} +(1.04304 + 11.0748i) q^{77} +(3.27471 + 5.67196i) q^{79} +(-11.0110 + 19.0716i) q^{81} -3.88139i q^{83} +(-20.7371 - 11.9726i) q^{87} +(-4.63409 - 8.02649i) q^{89} +(-0.313121 - 0.440925i) q^{91} +(-23.5122 + 13.5748i) q^{93} +1.33198i q^{97} -30.5584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91}+ \cdots - 84 q^{99}+O(q^{100}) $ 12 * q + 16 * q^9 - 8 * q^11 - 4 * q^19 - 22 * q^21 + 6 * q^31 - 28 * q^39 + 44 * q^41 - 24 * q^49 + 6 * q^51 - 10 * q^59 - 34 * q^61 + 96 * q^69 - 76 * q^71 - 2 * q^79 - 46 * q^81 - 28 * q^89 + 34 * q^91 - 84 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.77509	−	1.60220i	−1.60220	−	0.925031i	−0.991046	−	0.133520i	$-0.957372\pi$
$3$	−2.77509	−	1.60220i	−1.60220	−	0.925031i	−0.611155	−	0.791511i	$-0.709295\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.15715	−	1.53189i	0.815327	−	0.579001i
$7$	2.15715	−	1.53189i	0.815327	−	0.579001i
$8$		0			0
$9$	3.63409	+	6.29444i	1.21136	+	2.09815i
$10$		0			0
$11$	−2.10220	+	3.64112i	−0.633837	+	1.09784i	0.352923	+	0.935652i	$0.385188\pi$
$11$	−2.10220	+	3.64112i	−0.633837	+	1.09784i	−0.986760	+	0.162186i	$0.948146\pi$
$12$		0			0
$13$		−	0.204402i		−	0.0566908i	−0.999598	−	0.0283454i	$-0.990976\pi$
$13$		−	0.204402i		−	0.0566908i	0.999598	−	0.0283454i	$-0.00902383\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.38537	+	2.53189i	1.06361	+	0.614074i	0.926428	−	0.376472i	$-0.122863\pi$
$17$	4.38537	+	2.53189i	1.06361	+	0.614074i	0.137180	+	0.990546i	$0.456196\pi$
$18$		0			0
$19$	0.531894	+	0.921267i	0.122025	+	0.211353i	0.920566	−	0.390587i	$-0.127728\pi$
$19$	0.531894	+	0.921267i	0.122025	+	0.211353i	−0.798541	+	0.601940i	$0.794395\pi$
$20$		0			0
$21$	−8.44070	+	0.794959i	−1.84191	+	0.173474i
$22$		0			0
$23$	−1.85383	+	1.07031i	−0.386549	+	0.223174i	−0.680664	−	0.732596i	$-0.738309\pi$
$23$	−1.85383	+	1.07031i	−0.386549	+	0.223174i	0.294115	+	0.955770i	$0.404975\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	13.6770i		−	2.63214i
$28$		0			0
$29$	7.47259			1.38763			0.693813	−	0.720156i	$-0.255930\pi$
$29$	7.47259			1.38763			0.693813	+	0.720156i	$0.255930\pi$
$30$		0			0
$31$	4.23630	−	7.33748i	0.760861	−	1.31785i	−0.181546	−	0.983382i	$-0.558110\pi$
$31$	4.23630	−	7.33748i	0.760861	−	1.31785i	0.942407	−	0.334468i	$-0.108557\pi$
$32$		0			0
$33$	11.6676	−	6.73630i	2.03107	−	1.17264i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−9.19130	+	5.30660i	−1.51104	+	0.872400i	−0.511124	+	0.859507i	$0.670771\pi$
$37$	−9.19130	+	5.30660i	−1.51104	+	0.872400i	−0.999917	+	0.0128933i	$0.995896\pi$
$38$		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
$43$		−	8.26819i		−	1.26089i	−0.776235	−	0.630444i	$-0.782873\pi$
$43$		−	8.26819i		−	1.26089i	0.776235	−	0.630444i	$-0.217127\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.83033	−	1.63409i	0.412847	−	0.238357i	−0.279165	−	0.960243i	$-0.590058\pi$
$47$	2.83033	−	1.63409i	0.412847	−	0.238357i	0.692012	+	0.721886i	$0.256724\pi$
$48$		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
$53$	4.91642	+	2.83850i	0.675322	+	0.389897i	0.798090	−	0.602538i	$-0.205844\pi$
$53$	4.91642	+	2.83850i	0.675322	+	0.389897i	−0.122768	+	0.992435i	$0.539177\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	3.40880i		−	0.451507i
$58$		0			0
$59$	0.602201	−	1.04304i	0.0783999	−	0.135793i	−0.824160	−	0.566357i	$-0.808352\pi$
$59$	0.602201	−	1.04304i	0.0783999	−	0.135793i	0.902560	+	0.430565i	$0.141686\pi$
$60$		0			0
$61$	−0.827492	−	1.43326i	−0.105950	−	0.183510i	0.808176	−	0.588941i	$-0.200455\pi$
$61$	−0.827492	−	1.43326i	−0.105950	−	0.183510i	−0.914126	+	0.405431i	$0.867122\pi$
$62$		0			0
$63$	17.4817	+	8.01100i	2.20249	+	1.00929i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.7463	+	6.20440i	1.31287	+	0.757988i	0.982571	−	0.185887i	$-0.0595157\pi$
$67$	10.7463	+	6.20440i	1.31287	+	0.757988i	0.330303	+	0.943875i	$0.392849\pi$
$68$		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
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.04304	+	11.0748i	0.118866	+	1.26209i
$78$		0			0
$79$	3.27471	+	5.67196i	0.368433	+	0.638146i	0.989321	−	0.145754i	$-0.0465609\pi$
$79$	3.27471	+	5.67196i	0.368433	+	0.638146i	−0.620887	+	0.783900i	$0.713228\pi$
$80$		0			0
$81$	−11.0110	+	19.0716i	−1.22344	+	2.11907i
$82$		0			0
$83$		−	3.88139i		−	0.426038i	−0.977048	−	0.213019i	$-0.931670\pi$
$83$		−	3.88139i		−	0.426038i	0.977048	−	0.213019i	$-0.0683297\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−20.7371	−	11.9726i	−2.22325	−	1.28360i
$88$		0			0
$89$	−4.63409	−	8.02649i	−0.491213	−	0.850806i	0.508736	−	0.860923i	$-0.330113\pi$
$89$	−4.63409	−	8.02649i	−0.491213	−	0.850806i	−0.999949	+	0.0101167i	$0.996780\pi$
$90$		0			0
$91$	−0.313121	−	0.440925i	−0.0328241	−	0.0462215i
$92$		0			0
$93$	−23.5122	+	13.5748i	−2.43810	+	1.40764i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			1.33198i			0.135242i	0.997711	+	0.0676209i	$0.0215408\pi$
$97$			1.33198i			0.135242i	−0.997711	+	0.0676209i	$0.978459\pi$
$98$		0			0
$99$	−30.5584			−3.07123
$100$		0			0
$101$	−3.09568	+	5.36188i	−0.308032	+	0.533527i	−0.977932	−	0.208925i	$-0.933004\pi$
$101$	−3.09568	+	5.36188i	−0.308032	+	0.533527i	0.669900	+	0.742451i	$0.266337\pi$
$102$		0			0
$103$	−8.43576	+	4.87039i	−0.831200	+	0.479894i	−0.854264	−	0.519840i	$-0.825991\pi$
$103$	−8.43576	+	4.87039i	−0.831200	+	0.479894i	0.0230631	+	0.999734i	$0.492658\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.53848	−	4.92969i	0.825446	−	0.476571i	−0.0268449	−	0.999640i	$-0.508546\pi$
$107$	8.53848	−	4.92969i	0.825446	−	0.476571i	0.852291	+	0.523068i	$0.175213\pi$
$108$		0			0
$109$	−2.03841	+	3.53063i	−0.195245	+	0.338173i	−0.946981	−	0.321291i	$-0.895883\pi$
$109$	−2.03841	+	3.53063i	−0.195245	+	0.338173i	0.751736	+	0.659464i	$0.229217\pi$
$110$		0			0
$111$	34.0090			3.22799
$112$		0			0
$113$		−	2.21744i		−	0.208599i	−0.994546	−	0.104300i	$-0.966740\pi$
$113$		−	2.21744i		−	0.208599i	0.994546	−	0.104300i	$-0.0332601\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.28659	−	0.742815i	0.118946	−	0.0686732i
$118$		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
$123$	−29.2756	−	16.9023i	−2.63969	−	1.52403i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			6.54942i			0.581167i	0.956850	+	0.290583i	$0.0938494\pi$
$127$			6.54942i			0.581167i	−0.956850	+	0.290583i	$0.906151\pi$
$128$		0			0
$129$	−13.2473	+	22.9450i	−1.16636	+	2.02019i
$130$		0			0
$131$	8.50448	+	14.7302i	0.743040	+	1.28698i	0.951105	+	0.308868i	$0.0999503\pi$
$131$	8.50448	+	14.7302i	0.743040	+	1.28698i	−0.208065	+	0.978115i	$0.566716\pi$
$132$		0			0
$133$	2.55866	+	1.17251i	0.221864	+	0.101669i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.7967	+	8.54290i	1.26417	+	0.729869i	0.973879	−	0.227069i	$-0.0729144\pi$
$137$	14.7967	+	8.54290i	1.26417	+	0.729869i	0.290292	+	0.956938i	$0.406248\pi$
$138$		0			0
$139$	−0.740780			−0.0628322			−0.0314161	−	0.999506i	$-0.510002\pi$
$139$	−0.740780			−0.0628322			−0.0314161	+	0.999506i	$0.510002\pi$
$140$		0			0
$141$	−10.4726			−0.881951
$142$		0			0
$143$	0.744250	+	0.429693i	0.0622373	+	0.0359327i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−16.9901	+	14.6451i	−1.40132	+	1.20791i
$148$		0			0
$149$	−8.20889	−	14.2182i	−0.672498	−	1.16480i	−0.977193	−	0.212351i	$-0.931888\pi$
$149$	−8.20889	−	14.2182i	−0.672498	−	1.16480i	0.304695	−	0.952450i	$-0.401445\pi$
$150$		0			0
$151$	−0.263705	+	0.456750i	−0.0214600	+	0.0371698i	−0.876556	−	0.481300i	$-0.840165\pi$
$151$	−0.263705	+	0.456750i	−0.0214600	+	0.0371698i	0.855096	+	0.518470i	$0.173498\pi$
$152$		0			0
$153$			36.8046i			2.97547i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.21480	+	4.74281i	0.655612	+	0.378518i	0.790603	−	0.612329i	$-0.209767\pi$
$157$	8.21480	+	4.74281i	0.655612	+	0.378518i	−0.134991	+	0.990847i	$0.543101\pi$
$158$		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
$163$	−7.67245	+	4.42969i	−0.600953	+	0.346960i	−0.769416	−	0.638748i	$-0.779453\pi$
$163$	−7.67245	+	4.42969i	−0.600953	+	0.346960i	0.168463	+	0.985708i	$0.446119\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			8.33198i			0.644748i	0.946612	+	0.322374i	$0.104481\pi$
$167$			8.33198i			0.644748i	−0.946612	+	0.322374i	$0.895519\pi$
$168$		0			0
$169$	12.9582			0.996786
$170$		0			0
$171$	−3.86591	+	6.69594i	−0.295633	+	0.512052i
$172$		0			0
$173$	15.8872	−	9.17251i	1.20789	−	0.697373i	0.245588	−	0.969374i	$-0.421019\pi$
$173$	15.8872	−	9.17251i	1.20789	−	0.697373i	0.962297	+	0.272001i	$0.0876855\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.34233	+	1.92969i	−0.251225	+	0.145045i
$178$		0			0
$179$	−2.14061	+	3.70765i	−0.159997	+	0.277123i	−0.934867	−	0.354997i	$-0.884482\pi$
$179$	−2.14061	+	3.70765i	−0.159997	+	0.277123i	0.774870	+	0.632120i	$0.217815\pi$
$180$		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
$183$			5.30324i			0.392026i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−18.4379	+	10.6451i	−1.34831	+	0.778447i
$188$		0			0
$189$	−20.9517	−	29.5033i	−1.52401	−	2.14605i
$190$		0			0
$191$	5.97259	+	10.3448i	0.432162	+	0.748526i	0.997059	−	0.0766353i	$-0.0244177\pi$
$191$	5.97259	+	10.3448i	0.432162	+	0.748526i	−0.564898	+	0.825161i	$0.691084\pi$
$192$		0			0
$193$	6.13648	+	3.54290i	0.441713	+	0.255023i	0.704324	−	0.709879i	$-0.251250\pi$
$193$	6.13648	+	3.54290i	0.441713	+	0.255023i	−0.262611	+	0.964902i	$0.584584\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.48563i		−	0.390835i	−0.980720	−	0.195417i	$-0.937394\pi$
$197$		−	5.48563i		−	0.390835i	0.980720	−	0.195417i	$-0.0626062\pi$
$198$		0			0
$199$	8.04290	−	13.9307i	0.570146	−	0.987522i	−0.426405	−	0.904533i	$-0.640220\pi$
$199$	8.04290	−	13.9307i	0.570146	−	0.987522i	0.996550	−	0.0829891i	$-0.0264467\pi$
$200$		0			0
$201$	−19.8814	−	34.4356i	−1.40233	−	2.42890i
$202$		0			0
$203$	16.1195	−	11.4472i	1.13137	−	0.803437i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.4740	−	7.77919i	−0.936505	−	0.540691i
$208$		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
$213$	1.64063	+	0.947216i	0.112414	+	0.0649022i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.10191	−	22.3176i	−0.142687	−	1.51502i
$218$		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
$223$			15.4856i			1.03699i	0.855079	+	0.518497i	$0.173508\pi$
$223$			15.4856i			1.03699i	−0.855079	+	0.518497i	$0.826492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.27579	+	1.89128i	0.217422	+	0.125529i	0.604756	−	0.796411i	$-0.293271\pi$
$227$	3.27579	+	1.89128i	0.217422	+	0.125529i	−0.387334	+	0.921939i	$0.626604\pi$
$228$		0			0
$229$	−5.60220	−	9.70330i	−0.370204	−	0.641212i	0.619393	−	0.785081i	$-0.287379\pi$
$229$	−5.60220	−	9.70330i	−0.370204	−	0.641212i	−0.989597	+	0.143869i	$0.954045\pi$
$230$		0			0
$231$	14.8495	−	32.4047i	0.977025	−	2.13208i
$232$		0			0
$233$	10.3448	−	5.97259i	0.677712	−	0.391277i	−0.121280	−	0.992618i	$-0.538700\pi$
$233$	10.3448	−	5.97259i	0.677712	−	0.391277i	0.798993	+	0.601341i	$0.205367\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	20.9870i		−	1.36325i
$238$		0			0
$239$	−15.3450			−0.992587			−0.496293	−	0.868155i	$-0.665306\pi$
$239$	−15.3450			−0.992587			−0.496293	+	0.868155i	$0.665306\pi$
$240$		0			0
$241$	7.19788	−	12.4671i	0.463656	−	0.803076i	−0.535483	−	0.844546i	$-0.679871\pi$
$241$	7.19788	−	12.4671i	0.463656	−	0.803076i	0.999140	+	0.0414694i	$0.0132039\pi$
$242$		0			0
$243$	25.5793	−	14.7682i	1.64091	−	0.947380i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.188308	−	0.108720i	0.0119818	−	0.00691768i
$248$		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
$253$		−	9.00000i		−	0.565825i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.0139	+	6.93621i	−0.749405	+	0.432669i	−0.825479	−	0.564433i	$-0.809095\pi$
$257$	−12.0139	+	6.93621i	−0.749405	+	0.432669i	0.0760740	+	0.997102i	$0.475761\pi$
$258$		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
$263$	2.99606	+	1.72978i	0.184745	+	0.106663i	0.589520	−	0.807754i	$-0.299317\pi$
$263$	2.99606	+	1.72978i	0.184745	+	0.106663i	−0.404775	+	0.914416i	$0.632650\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			29.6990i			1.81755i
$268$		0			0
$269$	12.8320	−	22.2256i	0.782379	−	1.35512i	−0.148173	−	0.988962i	$-0.547339\pi$
$269$	12.8320	−	22.2256i	0.782379	−	1.35512i	0.930552	−	0.366159i	$-0.119328\pi$
$270$		0			0
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	−0.993168	−	0.116697i	$-0.962769\pi$
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	0.395522	−	0.918457i	$-0.370564\pi$
$272$		0			0
$273$	0.162491	+	1.72529i	0.00983439	+	0.104419i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.7180	−	9.07479i	−0.944403	−	0.545251i	−0.0530653	−	0.998591i	$-0.516899\pi$
$277$	−15.7180	−	9.07479i	−0.944403	−	0.545251i	−0.891338	+	0.453340i	$0.850232\pi$
$278$		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
$283$	−24.7323	−	14.2792i	−1.47018	−	0.848810i	−0.470742	−	0.882271i	$-0.656014\pi$
$283$	−24.7323	−	14.2792i	−1.47018	−	0.848810i	−0.999440	+	0.0334610i	$0.989347\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.7567	−	16.1606i	1.34328	−	0.953929i
$288$		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
$293$			25.5494i			1.49261i	0.665603	+	0.746306i	$0.268175\pi$
$293$			25.5494i			1.49261i	−0.665603	+	0.746306i	$0.731825\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	49.7996	+	28.7518i	2.88966	+	1.66835i
$298$		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
$303$	17.1816	−	9.91981i	0.987058	−	0.569878i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	10.1145i		−	0.577267i	−0.957440	−	0.288634i	$-0.906799\pi$
$307$		−	10.1145i		−	0.577267i	0.957440	−	0.288634i	$-0.0932009\pi$
$308$		0			0
$309$	31.2134			1.77567
$310$		0			0
$311$	−17.0858	+	29.5935i	−0.968847	+	1.67809i	−0.269942	+	0.962877i	$0.587005\pi$
$311$	−17.0858	+	29.5935i	−0.968847	+	1.67809i	−0.698905	+	0.715215i	$0.746329\pi$
$312$		0			0
$313$	−7.45925	+	4.30660i	−0.421622	+	0.243424i	−0.695771	−	0.718264i	$-0.744937\pi$
$313$	−7.45925	+	4.30660i	−0.421622	+	0.243424i	0.274149	+	0.961687i	$0.411604\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.77025	−	3.90880i	0.380255	−	0.219540i	−0.297674	−	0.954667i	$-0.596211\pi$
$317$	6.77025	−	3.90880i	0.380255	−	0.219540i	0.677929	+	0.735127i	$0.262878\pi$
$318$		0			0
$319$	−15.7089	+	27.2086i	−0.879529	+	1.52339i
$320$		0			0
$321$	−31.5934			−1.76337
$322$		0			0
$323$			5.38680i			0.299729i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	11.3136	−	6.53189i	0.625642	−	0.361215i
$328$		0			0
$329$	3.60220	−	7.86076i	0.198596	−	0.433378i
$330$		0			0
$331$	11.0494	+	19.1382i	0.607331	+	1.05193i	0.991678	+	0.128739i	$0.0410931\pi$
$331$	11.0494	+	19.1382i	0.607331	+	1.05193i	−0.384348	+	0.923188i	$0.625574\pi$
$332$		0			0
$333$	−66.8041	−	38.5694i	−3.66084	−	2.11359i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	1.29020i		−	0.0702815i	−0.999382	−	0.0351408i	$-0.988812\pi$
$337$		−	1.29020i		−	0.0702815i	0.999382	−	0.0351408i	$-0.0111880\pi$
$338$		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
$343$	−5.14868	−	17.7902i	−0.278003	−	0.960580i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.19221	+	4.72978i	0.439781	+	0.253908i	0.703505	−	0.710691i	$-0.251617\pi$
$347$	8.19221	+	4.72978i	0.439781	+	0.253908i	−0.263724	+	0.964598i	$0.584951\pi$
$348$		0			0
$349$	−15.5494			−0.832341			−0.416171	−	0.909287i	$-0.636628\pi$
$349$	−15.5494			−0.832341			−0.416171	+	0.909287i	$0.636628\pi$
$350$		0			0
$351$	−2.79560			−0.149218
$352$		0			0
$353$	13.1086	+	7.56827i	0.697702	+	0.402818i	0.806491	−	0.591246i	$-0.201364\pi$
$353$	13.1086	+	7.56827i	0.697702	+	0.402818i	−0.108789	+	0.994065i	$0.534697\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−39.0283	−	17.8848i	−2.06560	−	0.946562i
$358$		0			0
$359$	5.15947	+	8.93646i	0.272306	+	0.471648i	0.969452	−	0.245281i	$-0.0788802\pi$
$359$	5.15947	+	8.93646i	0.272306	+	0.471648i	−0.697146	+	0.716930i	$0.745547\pi$
$360$		0			0
$361$	8.93418	−	15.4744i	0.470220	−	0.814445i
$362$		0			0
$363$			21.3958i			1.12299i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−15.5332	−	8.96811i	−0.810827	−	0.468131i	0.0364158	−	0.999337i	$-0.488406\pi$
$367$	−15.5332	−	8.96811i	−0.810827	−	0.468131i	−0.847243	+	0.531205i	$0.821739\pi$
$368$		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
$373$	14.0221	−	8.09568i	0.726038	−	0.419179i	−0.0909327	−	0.995857i	$-0.528985\pi$
$373$	14.0221	−	8.09568i	0.726038	−	0.419179i	0.816971	+	0.576679i	$0.195651\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.52741i		−	0.0786656i
$378$		0			0
$379$	12.6002			0.647227			0.323614	−	0.946189i	$-0.395102\pi$
$379$	12.6002			0.647227			0.323614	+	0.946189i	$0.395102\pi$
$380$		0			0
$381$	10.4935	−	18.1752i	0.537597	−	0.931146i
$382$		0			0
$383$	−13.1425	+	7.58783i	−0.671551	+	0.387720i	−0.796664	−	0.604422i	$-0.793404\pi$
$383$	−13.1425	+	7.58783i	−0.671551	+	0.387720i	0.125113	+	0.992142i	$0.460071\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	52.0436	−	30.0474i	2.64552	−	1.52739i
$388$		0			0
$389$	−14.6197	+	25.3221i	−0.741249	+	1.28388i	0.210677	+	0.977556i	$0.432433\pi$
$389$	−14.6197	+	25.3221i	−0.741249	+	1.28388i	−0.951927	+	0.306326i	$0.900900\pi$
$390$		0			0
$391$	−10.8396			−0.548183
$392$		0			0
$393$		−	54.5036i		−	2.74934i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.75854	−	5.63409i	0.489767	−	0.282767i	−0.234711	−	0.972065i	$-0.575414\pi$
$397$	9.75854	−	5.63409i	0.489767	−	0.282767i	0.724478	+	0.689298i	$0.242081\pi$
$398$		0			0
$399$	−5.22192	−	7.35330i	−0.261423	−	0.368126i
$400$		0			0
$401$	9.01100	+	15.6075i	0.449988	+	0.779402i	0.998385	−	0.0568162i	$-0.0180949\pi$
$401$	9.01100	+	15.6075i	0.449988	+	0.779402i	−0.548397	+	0.836218i	$0.684762\pi$
$402$		0			0
$403$	−1.49979	−	0.865905i	−0.0747100	−	0.0431338i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	44.6222i		−	2.21184i
$408$		0			0
$409$	−7.89576	+	13.6759i	−0.390420	+	0.676228i	−0.992505	−	0.122204i	$-0.961004\pi$
$409$	−7.89576	+	13.6759i	−0.390420	+	0.676228i	0.602085	+	0.798432i	$0.294337\pi$
$410$		0			0
$411$	−27.3749	−	47.4147i	−1.35030	−	2.33879i
$412$		0			0
$413$	−0.298792	−	3.17251i	−0.0147026	−	0.156109i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.05573	+	1.18688i	0.100670	+	0.0581217i
$418$		0			0
$419$	13.4726			0.658179			0.329090	−	0.944299i	$-0.393258\pi$
$419$	13.4726			0.658179			0.329090	+	0.944299i	$0.393258\pi$
$420$		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
$423$	20.5714	+	11.8769i	1.00022	+	0.577475i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.98063	−	1.82413i	−0.192636	−	0.0882756i
$428$		0			0
$429$	−1.37691	−	2.38488i	−0.0664778	−	0.115143i
$430$		0			0
$431$	−8.02537	+	13.9004i	−0.386569	+	0.669557i	−0.991985	−	0.126352i	$-0.959673\pi$
$431$	−8.02537	+	13.9004i	−0.386569	+	0.669557i	0.605417	+	0.795909i	$0.293006\pi$
$432$		0			0
$433$		−	0.910136i		−	0.0437383i	−0.999761	−	0.0218692i	$-0.993038\pi$
$433$		−	0.910136i		−	0.0437383i	0.999761	−	0.0218692i	$-0.00696173\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.97208	−	1.13858i	−0.0943373	−	0.0544656i
$438$		0			0
$439$	−18.9517	−	32.8253i	−0.904515	−	1.56667i	−0.821566	−	0.570113i	$-0.806900\pi$
$439$	−18.9517	−	32.8253i	−0.904515	−	1.56667i	−0.0829488	−	0.996554i	$-0.526434\pi$
$440$		0			0
$441$	49.9827	−	9.49916i	2.38013	−	0.452341i
$442$		0			0
$443$	5.95946	−	3.44070i	0.283143	−	0.163472i	−0.351703	−	0.936112i	$-0.614397\pi$
$443$	5.95946	−	3.44070i	0.283143	−	0.163472i	0.634845	+	0.772639i	$0.281064\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			52.6091i			2.48833i
$448$		0			0
$449$	−6.43754			−0.303807			−0.151903	−	0.988395i	$-0.548540\pi$
$449$	−6.43754			−0.303807			−0.151903	+	0.988395i	$0.548540\pi$
$450$		0			0
$451$	−22.1770	+	38.4117i	−1.04427	+	1.80874i
$452$		0			0
$453$	1.46361	−	0.845015i	0.0687664	−	0.0397023i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.04907	+	4.64713i	−0.376520	+	0.217384i	−0.676303	−	0.736624i	$-0.736419\pi$
$457$	−8.04907	+	4.64713i	−0.376520	+	0.217384i	0.299783	+	0.954007i	$0.403086\pi$
$458$		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
$463$			29.6091i			1.37605i	0.725685	+	0.688027i	$0.241523\pi$
$463$			29.6091i			1.37605i	−0.725685	+	0.688027i	$0.758477\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.5719	+	13.0319i	−1.04450	+	0.603044i	−0.921105	−	0.389313i	$-0.872712\pi$
$467$	−22.5719	+	13.0319i	−1.04450	+	0.603044i	−0.123398	+	0.992357i	$0.539379\pi$
$468$		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
$473$	30.1055	+	17.3814i	1.38425	+	0.799197i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			41.2615i			1.88923i
$478$		0			0
$479$	−0.552784	+	0.957450i	−0.0252573	+	0.0437470i	−0.878378	−	0.477967i	$-0.841374\pi$
$479$	−0.552784	+	0.957450i	−0.0252573	+	0.0437470i	0.853120	+	0.521714i	$0.174707\pi$
$480$		0			0
$481$	1.08468	+	1.87872i	0.0494570	+	0.0856621i
$482$		0			0
$483$	14.7967	−	10.5079i	0.673275	−	0.478124i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.49585	−	2.59568i	−0.203727	−	0.117622i	0.394666	−	0.918825i	$-0.370860\pi$
$487$	−4.49585	−	2.59568i	−0.203727	−	0.117622i	−0.598393	+	0.801203i	$0.704194\pi$
$488$		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
$493$	32.7701	+	18.9198i	1.47589	+	0.852105i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.27530	+	0.905651i	−0.0572051	+	0.0406240i
$498$		0			0
$499$	−13.0364	−	22.5797i	−0.583588	−	1.01080i	−0.995050	−	0.0993776i	$-0.968315\pi$
$499$	−13.0364	−	22.5797i	−0.583588	−	1.01080i	0.411461	−	0.911427i	$-0.365019\pi$
$500$		0			0
$501$	13.3495	−	23.1220i	0.596412	−	1.03302i
$502$		0			0
$503$		−	8.80864i		−	0.392758i	−0.980528	−	0.196379i	$-0.937082\pi$
$503$		−	8.80864i		−	0.392758i	0.980528	−	0.196379i	$-0.0629182\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−35.9603	−	20.7617i	−1.59705	−	0.922058i
$508$		0			0
$509$	−11.0090	−	19.0681i	−0.487964	−	0.845178i	0.511940	−	0.859021i	$-0.328927\pi$
$509$	−11.0090	−	19.0681i	−0.487964	−	0.845178i	−0.999904	+	0.0138427i	$0.995594\pi$
$510$		0			0
$511$	−10.5364	+	0.992334i	−0.466102	+	0.0438983i
$512$		0			0
$513$	12.6002	−	7.27471i	0.556311	−	0.321186i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			13.7408i			0.604319i
$518$		0			0
$519$	−58.7848			−2.58037
$520$		0			0
$521$	7.54942	−	13.0760i	0.330746	−	0.572869i	−0.651912	−	0.758294i	$-0.726033\pi$
$521$	7.54942	−	13.0760i	0.330746	−	0.572869i	0.982658	+	0.185426i	$0.0593663\pi$
$522$		0			0
$523$	3.97609	−	2.29560i	0.173862	−	0.100380i	−0.410543	−	0.911841i	$-0.634661\pi$
$523$	3.97609	−	2.29560i	0.173862	−	0.100380i	0.584406	+	0.811462i	$0.301328\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	37.1554	−	21.4517i	1.61852	−	0.934451i
$528$		0			0
$529$	−9.20889	+	15.9503i	−0.400386	+	0.693490i
$530$		0			0
$531$	8.75382			0.379883
$532$		0			0
$533$		−	2.15632i		−	0.0934005i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.8808	−	6.85939i	0.512695	−	0.296004i
$538$		0			0
$539$	19.2154	+	22.2922i	0.827666	+	0.960192i
$540$		0			0
$541$	−6.83850	−	11.8446i	−0.294010	−	0.509240i	0.680744	−	0.732521i	$-0.261657\pi$
$541$	−6.83850	−	11.8446i	−0.294010	−	0.509240i	−0.974754	+	0.223281i	$0.928323\pi$
$542$		0			0
$543$	−8.14826	−	4.70440i	−0.349675	−	0.201885i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	11.3581i		−	0.485635i	−0.970072	−	0.242818i	$-0.921928\pi$
$547$		−	11.3581i		−	0.485635i	0.970072	−	0.242818i	$-0.0780717\pi$
$548$		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
$553$	15.7529	+	7.21877i	0.669881	+	0.306973i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.1991	−	8.19788i	−0.601637	−	0.347355i	0.168048	−	0.985779i	$-0.446254\pi$
$557$	−14.1991	−	8.19788i	−0.601637	−	0.347355i	−0.769685	+	0.638423i	$0.779587\pi$
$558$		0			0
$559$	−1.69003			−0.0714807
$560$		0			0
$561$	68.2223			2.88035
$562$		0			0
$563$	−4.21964	−	2.43621i	−0.177837	−	0.102674i	0.408439	−	0.912786i	$-0.366073\pi$
$563$	−4.21964	−	2.43621i	−0.177837	−	0.102674i	−0.586276	+	0.810111i	$0.699407\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	5.46330	+	58.0081i	0.229437	+	2.43611i
$568$		0			0
$569$	−18.9277	−	32.7837i	−0.793489	−	1.37436i	−0.923794	−	0.382889i	$-0.874929\pi$
$569$	−18.9277	−	32.7837i	−0.793489	−	1.37436i	0.130306	−	0.991474i	$-0.458404\pi$
$570$		0			0
$571$	20.8704	−	36.1486i	0.873399	−	1.51277i	0.0149398	−	0.999888i	$-0.495244\pi$
$571$	20.8704	−	36.1486i	0.873399	−	1.51277i	0.858459	−	0.512882i	$-0.171422\pi$
$572$		0			0
$573$		−	38.2772i		−	1.59905i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−37.2850	−	21.5265i	−1.55219	−	0.896160i	−0.997963	−	0.0637967i	$-0.979679\pi$
$577$	−37.2850	−	21.5265i	−1.55219	−	0.896160i	−0.554231	−	0.832363i	$-0.686988\pi$
$578$		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
$583$	−20.6706	+	11.9342i	−0.856089	+	0.494263i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	5.67699i		−	0.234315i	−0.993113	−	0.117157i	$-0.962622\pi$
$587$		−	5.67699i		−	0.234315i	0.993113	−	0.117157i	$-0.0373782\pi$
$588$		0			0
$589$	9.01304			0.371376
$590$		0			0
$591$	−8.78908	+	15.2231i	−0.361534	+	0.626196i
$592$		0			0
$593$	−7.74675	+	4.47259i	−0.318121	+	0.183667i	−0.650555	−	0.759459i	$-0.725464\pi$
$593$	−7.74675	+	4.47259i	−0.318121	+	0.183667i	0.332434	+	0.943127i	$0.392130\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−44.6396	+	25.7727i	−1.82698	+	1.05481i
$598$		0			0
$599$	−12.6132	+	21.8467i	−0.515362	+	0.892632i	0.484479	+	0.874803i	$0.339009\pi$
$599$	−12.6132	+	21.8467i	−0.515362	+	0.892632i	−0.999841	+	0.0178298i	$0.994324\pi$
$600$		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
$603$			90.1895i			3.67280i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.1313	−	10.4681i	0.735926	−	0.424887i	−0.0846599	−	0.996410i	$-0.526980\pi$
$607$	18.1313	−	10.4681i	0.735926	−	0.424887i	0.820586	+	0.571523i	$0.193647\pi$
$608$		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
$613$	−4.60634	−	2.65947i	−0.186048	−	0.107415i	0.404083	−	0.914722i	$-0.367591\pi$
$613$	−4.60634	−	2.65947i	−0.186048	−	0.107415i	−0.590131	+	0.807307i	$0.700924\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	28.6262i		−	1.15245i	−0.817291	−	0.576225i	$-0.804525\pi$
$617$		−	28.6262i		−	1.15245i	0.817291	−	0.576225i	$-0.195475\pi$
$618$		0			0
$619$	−10.7812	+	18.6736i	−0.433334	+	0.750557i	−0.997158	−	0.0753383i	$-0.975996\pi$
$619$	−10.7812	+	18.6736i	−0.433334	+	0.750557i	0.563824	+	0.825895i	$0.309330\pi$
$620$		0			0
$621$	14.6386	+	25.3548i	0.587426	+	1.01745i
$622$		0			0
$623$	−22.2922	−	10.2154i	−0.893117	−	0.409272i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	12.4119	+	7.16599i	0.495682	+	0.286182i
$628$		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
$633$	−46.0670	−	26.5968i	−1.83100	−	1.05713i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.35090	−	0.471473i	−0.0535246	−	0.0186804i
$638$		0			0
$639$	−2.14847	−	3.72125i	−0.0849920	−	0.147210i
$640$		0			0
$641$	−22.0539	+	38.1985i	−0.871077	+	1.50875i	−0.0101927	+	0.999948i	$0.503244\pi$
$641$	−22.0539	+	38.1985i	−0.871077	+	1.50875i	−0.860884	+	0.508801i	$0.830089\pi$
$642$		0			0
$643$			16.4816i			0.649969i	0.945719	+	0.324985i	$0.105359\pi$
$643$			16.4816i			0.649969i	−0.945719	+	0.324985i	$0.894641\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	27.2276	+	15.7199i	1.07043	+	0.618013i	0.928299	−	0.371835i	$-0.121271\pi$
$647$	27.2276	+	15.7199i	1.07043	+	0.618013i	0.142131	+	0.989848i	$0.454605\pi$
$648$		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
$653$	−35.4008	+	20.4387i	−1.38534	+	0.799827i	−0.992786	−	0.119902i	$-0.961742\pi$
$653$	−35.4008	+	20.4387i	−1.38534	+	0.799827i	−0.392555	+	0.919729i	$0.628409\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	29.0728i		−	1.13424i
$658$		0			0
$659$	46.6860			1.81863			0.909313	−	0.416112i	$-0.136608\pi$
$659$	46.6860			1.81863			0.909313	+	0.416112i	$0.136608\pi$
$660$		0			0
$661$	−0.0637877	+	0.110484i	−0.00248106	+	0.00429731i	−0.867263	−	0.497850i	$-0.834123\pi$
$661$	−0.0637877	+	0.110484i	−0.00248106	+	0.00429731i	0.864782	+	0.502147i	$0.167456\pi$
$662$		0			0
$663$	−2.87235	+	1.65835i	−0.111553	+	0.0644050i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.8529	+	7.99797i	−0.536386	+	0.309682i
$668$		0			0
$669$	24.8111	−	42.9741i	0.959252	−	1.66147i
$670$		0			0
$671$	6.95822			0.268619
$672$		0			0
$673$		−	48.1936i		−	1.85773i	−0.370423	−	0.928863i	$-0.620787\pi$
$673$		−	48.1936i		−	1.85773i	0.370423	−	0.928863i	$-0.379213\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−40.1990	+	23.2089i	−1.54497	+	0.891990i	−0.546458	+	0.837486i	$0.684024\pi$
$677$	−40.1990	+	23.2089i	−1.54497	+	0.891990i	−0.998514	+	0.0545037i	$0.982642\pi$
$678$		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
$683$	37.7149	+	21.7747i	1.44312	+	0.833186i	0.998057	−	0.0623127i	$-0.0198476\pi$
$683$	37.7149	+	21.7747i	1.44312	+	0.833186i	0.445064	+	0.895499i	$0.353181\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			35.9034i			1.36980i
$688$		0			0
$689$	0.580193	−	1.00492i	0.0221036	−	0.0382845i
$690$		0			0
$691$	13.0474	+	22.5987i	0.496346	+	0.859696i	0.999991	−	0.00421436i	$-0.00134147\pi$
$691$	13.0474	+	22.5987i	0.496346	+	0.859696i	−0.503645	+	0.863911i	$0.668008\pi$
$692$		0			0
$693$	−65.9191	+	46.8122i	−2.50406	+	1.77825i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	46.2631	+	26.7100i	1.75234	+	1.01171i
$698$		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
$703$	−9.77760	−	5.64510i	−0.368769	−	0.212909i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.53597	+	16.3086i	0.0577663	+	0.613349i
$708$		0			0
$709$	8.53841	+	14.7890i	0.320667	+	0.555411i	0.980626	−	0.195890i	$-0.0627597\pi$
$709$	8.53841	+	14.7890i	0.320667	+	0.555411i	−0.659959	+	0.751302i	$0.729426\pi$
$710$		0			0
$711$	−23.8012	+	41.2249i	−0.892615	+	1.54605i
$712$		0			0
$713$			18.1365i			0.679219i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	42.5838	+	24.5858i	1.59032	+	0.918173i
$718$		0			0
$719$	13.6231	+	23.5959i	0.508056	+	0.879978i	0.999957	+	0.00932687i	$0.00296888\pi$
$719$	13.6231	+	23.5959i	0.508056	+	0.879978i	−0.491901	+	0.870651i	$0.663698\pi$
$720$		0			0
$721$	−10.7363	+	23.4289i	−0.399841	+	0.872536i
$722$		0			0
$723$	−39.9496	+	23.0649i	−1.48574	+	0.857793i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			19.9232i			0.738910i	0.929249	+	0.369455i	$0.120456\pi$
$727$			19.9232i			0.738910i	−0.929249	+	0.369455i	$0.879544\pi$
$728$		0			0
$729$	−28.5804			−1.05853
$730$		0			0
$731$	20.9342	−	36.2591i	0.774279	−	1.34109i
$732$		0			0
$733$	−26.9876	+	15.5813i	−0.996811	+	0.575509i	−0.907303	−	0.420477i	$-0.861863\pi$
$733$	−26.9876	+	15.5813i	−0.996811	+	0.575509i	−0.0895075	+	0.995986i	$0.528529\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−45.1819	+	26.0858i	−1.66430	+	0.960883i
$738$		0			0
$739$	0.950583	−	1.64646i	0.0349678	−	0.0605659i	−0.848012	−	0.529977i	$-0.822200\pi$
$739$	0.950583	−	1.64646i	0.0349678	−	0.0605659i	0.882980	+	0.469411i	$0.155534\pi$
$740$		0			0
$741$	−0.696765			−0.0255963
$742$		0			0
$743$		−	36.0660i		−	1.32313i	−0.749886	−	0.661567i	$-0.769892\pi$
$743$		−	36.0660i		−	1.32313i	0.749886	−	0.661567i	$-0.230108\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	24.4312	−	14.1054i	0.893890	−	0.516088i
$748$		0			0
$749$	10.8670	−	23.7141i	0.397072	−	0.866496i
$750$		0			0
$751$	0.384761	+	0.666425i	0.0140401	+	0.0243182i	0.872960	−	0.487792i	$-0.162197\pi$
$751$	0.384761	+	0.666425i	0.0140401	+	0.0243182i	−0.858920	+	0.512110i	$0.828864\pi$
$752$		0			0
$753$	53.8861	+	31.1112i	1.96372	+	1.13375i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	14.9542i		−	0.543518i	−0.962365	−	0.271759i	$-0.912395\pi$
$757$		−	14.9542i		−	0.543518i	0.962365	−	0.271759i	$-0.0876053\pi$
$758$		0			0
$759$	−14.4198	+	24.9758i	−0.523406	+	0.906565i
$760$		0			0
$761$	−9.58580	−	16.6031i	−0.347485	−	0.601861i	0.638317	−	0.769773i	$-0.279631\pi$
$761$	−9.58580	−	16.6031i	−0.347485	−	0.601861i	−0.985802	+	0.167912i	$0.946298\pi$
$762$		0			0
$763$	1.01139	+	10.7387i	0.0366149	+	0.388769i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.213199	−	0.123091i	−0.00769819	−	0.00444455i
$768$		0			0
$769$	−36.3189			−1.30969			−0.654847	−	0.755761i	$-0.727267\pi$
$769$	−36.3189			−1.30969			−0.654847	+	0.755761i	$0.727267\pi$
$770$		0			0
$771$	44.4528			1.60093
$772$		0			0
$773$	−41.1089	−	23.7343i	−1.47859	−	0.853662i	−0.478879	−	0.877881i	$-0.658957\pi$
$773$	−41.1089	−	23.7343i	−1.47859	−	0.853662i	−0.999707	+	0.0242187i	$0.992290\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	73.3625	−	52.0981i	2.63186	−	1.86901i
$778$		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
$783$		−	102.203i		−	3.65242i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−6.82901	−	3.94273i	−0.243428	−	0.140543i	0.373323	−	0.927701i	$-0.378218\pi$
$787$	−6.82901	−	3.94273i	−0.243428	−	0.140543i	−0.616751	+	0.787158i	$0.711552\pi$
$788$		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
$793$	−0.292960	+	0.169141i	−0.0104033	+	0.00600636i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	33.6132i		−	1.19064i	−0.803488	−	0.595320i	$-0.797025\pi$
$797$		−	33.6132i		−	1.19064i	0.803488	−	0.595320i	$-0.202975\pi$
$798$		0			0
$799$	16.5494			0.585476
$800$		0			0
$801$	33.6815	−	58.3380i	1.19008	−	2.06127i
$802$		0			0
$803$	14.5645	−	8.40880i	0.513969	−	0.296740i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−71.2199	+	41.1188i	−2.50706	+	1.44745i
$808$		0			0
$809$	−4.59568	+	7.95995i	−0.161576	+	0.279857i	−0.935434	−	0.353502i	$-0.884991\pi$
$809$	−4.59568	+	7.95995i	−0.161576	+	0.279857i	0.773858	+	0.633359i	$0.218324\pi$
$810$		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
$813$			63.0530i			2.21136i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.61721	−	4.39780i	0.266493	−	0.153860i
$818$		0			0
$819$	1.63746	−	3.57329i	0.0572175	−	0.124861i
$820$		0			0
$821$	−16.1307	−	27.9392i	−0.562966	−	0.975086i	−0.997236	−	0.0743032i	$-0.976327\pi$
$821$	−16.1307	−	27.9392i	−0.562966	−	0.975086i	0.434269	−	0.900783i	$-0.357007\pi$
$822$		0			0
$823$	9.91066	+	5.72192i	0.345464	+	0.199454i	0.662686	−	0.748898i	$-0.269417\pi$
$823$	9.91066	+	5.72192i	0.345464	+	0.199454i	−0.317222	+	0.948351i	$0.602750\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			9.82658i			0.341704i	0.985297	+	0.170852i	$0.0546519\pi$
$827$			9.82658i			0.341704i	−0.985297	+	0.170852i	$0.945348\pi$
$828$		0			0
$829$	19.1287	−	33.1319i	0.664367	−	1.15072i	−0.315090	−	0.949062i	$-0.602035\pi$
$829$	19.1287	−	33.1319i	0.664367	−	1.15072i	0.979457	−	0.201655i	$-0.0646321\pi$
$830$		0			0
$831$	29.0793	+	50.3668i	1.00875	+	1.74720i
$832$		0			0
$833$	26.8487	−	23.1431i	0.930253	−	0.801860i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−100.355	−	57.9398i	−3.46876	−	2.00269i
$838$		0			0
$839$	−30.6900			−1.05954			−0.529769	−	0.848142i	$-0.677721\pi$
$839$	−30.6900			−1.05954			−0.529769	+	0.848142i	$0.677721\pi$
$840$		0			0
$841$	26.8396			0.925504
$842$		0			0
$843$	51.4402	+	29.6990i	1.77169	+	1.02289i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−16.0597	−	7.35939i	−0.551819	−	0.252872i
$848$		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
$853$		−	39.4569i		−	1.35098i	−0.737370	−	0.675489i	$-0.763933\pi$
$853$		−	39.4569i		−	1.35098i	0.737370	−	0.675489i	$-0.236067\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	34.5192	+	19.9297i	1.17915	+	0.680785i	0.955819	−	0.293956i	$-0.0949720\pi$
$857$	34.5192	+	19.9297i	1.17915	+	0.680785i	0.223336	+	0.974742i	$0.428305\pi$
$858$		0			0
$859$	−9.75719	−	16.8999i	−0.332911	−	0.576619i	0.650170	−	0.759788i	$-0.274697\pi$
$859$	−9.75719	−	16.8999i	−0.332911	−	0.576619i	−0.983081	+	0.183170i	$0.941364\pi$
$860$		0			0
$861$	−89.0444	+	8.38635i	−3.03463	+	0.285806i
$862$		0			0
$863$	32.8502	−	18.9661i	1.11823	−	0.645613i	0.177284	−	0.984160i	$-0.443269\pi$
$863$	32.8502	−	18.9661i	1.11823	−	0.645613i	0.940949	+	0.338547i	$0.109935\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	27.6923i		−	0.940479i
$868$		0			0
$869$	−27.5364			−0.934108
$870$		0			0
$871$	1.26819	−	2.19657i	0.0429710	−	0.0744279i
$872$		0			0
$873$	−8.38404	+	4.84053i	−0.283757	+	0.163827i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.47881	−	5.47259i	0.320077	−	0.184796i	−0.331350	−	0.943508i	$-0.607504\pi$
$877$	9.47881	−	5.47259i	0.320077	−	0.184796i	0.651427	+	0.758712i	$0.274171\pi$
$878$		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
$883$		−	23.2511i		−	0.782461i	−0.920293	−	0.391231i	$-0.872049\pi$
$883$		−	23.2511i		−	0.782461i	0.920293	−	0.391231i	$-0.127951\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.1260	+	11.6197i	−0.675763	+	0.390152i	−0.798257	−	0.602317i	$-0.794244\pi$
$887$	−20.1260	+	11.6197i	−0.675763	+	0.390152i	0.122494	+	0.992469i	$0.460911\pi$
$888$		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
$893$	3.01088	+	1.73833i	0.100755	+	0.0581710i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	1.40207i		−	0.0468137i
$898$		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
$903$	6.57287	+	69.7893i	0.218731	+	2.32244i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	38.3012	+	22.1132i	1.27177	+	0.734257i	0.975321	−	0.220792i	$-0.0708641\pi$
$907$	38.3012	+	22.1132i	1.27177	+	0.734257i	0.296449	+	0.955049i	$0.404197\pi$
$908$		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
$913$	14.1326	+	8.15947i	0.467721	+	0.270039i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	40.9106	+	18.7473i	1.35099	+	0.619090i
$918$		0			0
$919$	−16.6581	−	28.8527i	−0.549501	−	0.951764i	−0.998309	−	0.0581356i	$-0.981484\pi$
$919$	−16.6581	−	28.8527i	−0.549501	−	0.951764i	0.448807	−	0.893628i	$-0.351849\pi$
$920$		0			0
$921$	−16.2055	+	28.0688i	−0.533990	+	0.924898i
$922$		0			0
$923$			0.120842i			0.00397755i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−61.3127	−	35.3989i	−2.01377	−	1.16265i
$928$		0			0
$929$	−6.62421	−	11.4735i	−0.217333	−	0.376432i	0.736659	−	0.676265i	$-0.236402\pi$
$929$	−6.62421	−	11.4735i	−0.217333	−	0.376432i	−0.953992	+	0.299833i	$0.903069\pi$
$930$		0			0
$931$	7.31557	−	1.39032i	0.239758	−	0.0455658i
$932$		0			0
$933$	94.8293	−	54.7497i	3.10457	−	1.79243i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	10.1365i		−	0.331146i	−0.986197	−	0.165573i	$-0.947053\pi$
$937$		−	10.1365i		−	0.331146i	0.986197	−	0.165573i	$-0.0529474\pi$
$938$		0			0
$939$	27.6002			0.900697
$940$		0			0
$941$	16.4342	−	28.4648i	0.535739	−	0.927927i	−0.463388	−	0.886155i	$-0.653366\pi$
$941$	16.4342	−	28.4648i	0.535739	−	0.927927i	0.999127	−	0.0417716i	$-0.0133002\pi$
$942$		0			0
$943$	−19.5568	+	11.2911i	−0.636856	+	0.367689i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.3342	+	11.1626i	−0.628278	+	0.362736i	−0.780085	−	0.625674i	$-0.784824\pi$
$947$	−19.3342	+	11.1626i	−0.628278	+	0.362736i	0.151807	+	0.988410i	$0.451491\pi$
$948$		0			0
$949$	−0.408803	+	0.708068i	−0.0132703	+	0.0229849i
$950$		0			0
$951$	−25.0507			−0.812326
$952$		0			0
$953$			47.4685i			1.53766i	0.639455	+	0.768828i	$0.279160\pi$
$953$			47.4685i			1.53766i	−0.639455	+	0.768828i	$0.720840\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	87.1872	−	50.3376i	2.81836	−	1.62718i
$958$		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
$963$	62.0593	+	35.8299i	1.99983	+	1.15460i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			21.3189i			0.685571i	0.939414	+	0.342785i	$0.111370\pi$
$967$			21.3189i			0.685571i	−0.939414	+	0.342785i	$0.888630\pi$
$968$		0			0
$969$	8.63073	−	14.9489i	0.277259	−	0.480227i
$970$		0			0
$971$	14.7812	+	25.6018i	0.474352	+	0.821602i	0.999569	−	0.0293666i	$-0.00934901\pi$
$971$	14.7812	+	25.6018i	0.474352	+	0.821602i	−0.525217	+	0.850969i	$0.676016\pi$
$972$		0			0
$973$	−1.59797	+	1.13480i	−0.0512287	+	0.0363799i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.59315	+	0.919807i	0.0509695	+	0.0294272i	0.525268	−	0.850937i	$-0.323965\pi$
$977$	1.59315	+	0.919807i	0.0509695	+	0.0294272i	−0.474299	+	0.880364i	$0.657298\pi$
$978$		0			0
$979$	38.9672			1.24540
$980$		0			0
$981$	−29.6311			−0.946050
$982$		0			0
$983$	−9.85190	−	5.68800i	−0.314227	−	0.181419i	0.334590	−	0.942364i	$-0.391402\pi$
$983$	−9.85190	−	5.68800i	−0.314227	−	0.181419i	−0.648816	+	0.760945i	$0.724736\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−22.5910	+	16.0429i	−0.719078	+	0.510651i
$988$		0			0
$989$	8.84950	+	15.3278i	0.281398	+	0.487395i
$990$		0			0
$991$	−3.89576	+	6.74766i	−0.123753	+	0.214347i	−0.921245	−	0.388983i	$-0.872826\pi$
$991$	−3.89576	+	6.74766i	−0.123753	+	0.214347i	0.797492	+	0.603330i	$0.206160\pi$
$992$		0			0
$993$		−	70.8135i		−	2.24720i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.89160	−	5.71092i	−0.313270	−	0.180867i	0.335119	−	0.942176i	$-0.391224\pi$
$997$	−9.89160	−	5.71092i	−0.313270	−	0.180867i	−0.648389	+	0.761309i	$0.724557\pi$
$998$		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.r.d.249.1		12
5.2	odd	4		700.2.i.d.501.1	yes	6
5.3	odd	4		700.2.i.e.501.3	yes	6
5.4	even	2	inner	700.2.r.d.249.6		12
7.2	even	3	inner	700.2.r.d.149.6		12
7.3	odd	6		4900.2.e.s.2549.1		6
7.4	even	3		4900.2.e.t.2549.6		6
35.2	odd	12		700.2.i.d.401.1	✓	6
35.3	even	12		4900.2.a.bd.1.3		3
35.4	even	6		4900.2.e.t.2549.1		6
35.9	even	6	inner	700.2.r.d.149.1		12
35.17	even	12		4900.2.a.bb.1.1		3
35.18	odd	12		4900.2.a.ba.1.1		3
35.23	odd	12		700.2.i.e.401.3	yes	6
35.24	odd	6		4900.2.e.s.2549.6		6
35.32	odd	12		4900.2.a.bc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.1	✓	6	35.2	odd	12
700.2.i.d.501.1	yes	6	5.2	odd	4
700.2.i.e.401.3	yes	6	35.23	odd	12
700.2.i.e.501.3	yes	6	5.3	odd	4
700.2.r.d.149.1		12	35.9	even	6	inner
700.2.r.d.149.6		12	7.2	even	3	inner
700.2.r.d.249.1		12	1.1	even	1	trivial
700.2.r.d.249.6		12	5.4	even	2	inner
4900.2.a.ba.1.1		3	35.18	odd	12
4900.2.a.bb.1.1		3	35.17	even	12
4900.2.a.bc.1.3		3	35.32	odd	12
4900.2.a.bd.1.3		3	35.3	even	12
4900.2.e.s.2549.1		6	7.3	odd	6
4900.2.e.s.2549.6		6	35.24	odd	6
4900.2.e.t.2549.1		6	35.4	even	6
4900.2.e.t.2549.6		6	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.77509 - 1.60220i) q^{3} +(2.15715 - 1.53189i) q^{7} +(3.63409 + 6.29444i) q^{9} +(-2.10220 + 3.64112i) q^{11} -0.204402i q^{13} +(4.38537 + 2.53189i) q^{17} +(0.531894 + 0.921267i) q^{19} +(-8.44070 + 0.794959i) q^{21} +(-1.85383 + 1.07031i) q^{23} -13.6770i q^{27} +7.47259 q^{29} +(4.23630 - 7.33748i) q^{31} +(11.6676 - 6.73630i) q^{33} +(-9.19130 + 5.30660i) q^{37} +(-0.327492 + 0.567233i) q^{39} +10.5494 q^{41} -8.26819i q^{43} +(2.83033 - 1.63409i) q^{47} +(2.30660 - 6.60905i) q^{49} +(-8.11320 - 14.0525i) q^{51} +(4.91642 + 2.83850i) q^{53} -3.40880i q^{57} +(0.602201 - 1.04304i) q^{59} +(-0.827492 - 1.43326i) q^{61} +(17.4817 + 8.01100i) q^{63} +(10.7463 + 6.20440i) q^{67} +6.85939 q^{69} -0.591197 q^{71} +(-3.46410 - 2.00000i) q^{73} +(1.04304 + 11.0748i) q^{77} +(3.27471 + 5.67196i) q^{79} +(-11.0110 + 19.0716i) q^{81} -3.88139i q^{83} +(-20.7371 - 11.9726i) q^{87} +(-4.63409 - 8.02649i) q^{89} +(-0.313121 - 0.440925i) q^{91} +(-23.5122 + 13.5748i) q^{93} +1.33198i q^{97} -30.5584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91}+ \cdots - 84 q^{99}+O(q^{100}) \) 12 * q + 16 * q^9 - 8 * q^11 - 4 * q^19 - 22 * q^21 + 6 * q^31 - 28 * q^39 + 44 * q^41 - 24 * q^49 + 6 * q^51 - 10 * q^59 - 34 * q^61 + 96 * q^69 - 76 * q^71 - 2 * q^79 - 46 * q^81 - 28 * q^89 + 34 * q^91 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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