LMFDB - Embedded newform 700.2.r.d.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(149,700)]

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, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("700.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

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: 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
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			249.2
Root			$-1.65604 + 0.956115i$ of defining polynomial
Character	$\chi$	$=$	700.249
Dual form			700.2.r.d.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22469 - 1.28442i) q^{3} +(0.568650 + 2.58392i) q^{7} +(1.79949 + 3.11682i) q^{9} +O(q^{10})$	\(q+(-2.22469 - 1.28442i) q^{3} +(0.568650 + 2.58392i) q^{7} +(1.79949 + 3.11682i) q^{9} +(0.784425 - 1.35866i) q^{11} -5.56885i q^{13} +(-6.20753 - 3.58392i) q^{17} +(1.58392 + 2.74343i) q^{19} +(2.05378 - 6.47880i) q^{21} +(-4.96812 + 2.86834i) q^{23} -1.53871i q^{27} -1.96986 q^{29} +(-0.484931 + 0.839925i) q^{31} +(-3.49020 + 2.01507i) q^{33} +(-5.80804 + 3.35327i) q^{37} +(-7.15277 + 12.3890i) q^{39} -8.87439 q^{41} +4.59899i q^{43} +(0.347286 - 0.200506i) q^{47} +(-6.35327 + 2.93869i) q^{49} +(9.20655 + 15.9462i) q^{51} +(8.26077 + 4.76936i) q^{53} -8.13770i q^{57} +(-2.28442 + 3.95674i) q^{59} +(-7.65277 - 13.2550i) q^{61} +(-7.03032 + 6.42212i) q^{63} +(-0.746774 - 0.431150i) q^{67} +14.7367 q^{69} -12.1377 q^{71} +(3.46410 + 2.00000i) q^{73} +(3.95674 + 1.25429i) q^{77} +(-6.43719 - 11.1495i) q^{79} +(3.42212 - 5.92729i) q^{81} -17.1076i q^{83} +(4.38233 + 2.53014i) q^{87} +(-2.79949 - 4.84887i) q^{89} +(14.3895 - 3.16673i) q^{91} +(2.15764 - 1.24571i) q^{93} +0.233174i q^{97} +5.64627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{9}+O(q^{10}) $ 12 * q + 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.22469	−	1.28442i	−1.28442	−	0.741563i	−0.306771	−	0.951783i	$-0.599249\pi$
$3$	−2.22469	−	1.28442i	−1.28442	−	0.741563i	−0.977654	+	0.210220i	$0.932582\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.568650	+	2.58392i	0.214929	+	0.976630i
$7$	0.568650	+	2.58392i	0.214929	+	0.976630i
$8$		0			0
$9$	1.79949	+	3.11682i	0.599831	+	1.03894i
$10$		0			0
$11$	0.784425	−	1.35866i	0.236513	−	0.409652i	−0.723198	−	0.690640i	$-0.757329\pi$
$11$	0.784425	−	1.35866i	0.236513	−	0.409652i	0.959711	+	0.280988i	$0.0906621\pi$
$12$		0			0
$13$		−	5.56885i		−	1.54452i	−0.635306	−	0.772260i	$-0.719126\pi$
$13$		−	5.56885i		−	1.54452i	0.635306	−	0.772260i	$-0.280874\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.20753	−	3.58392i	−1.50555	−	0.869228i	−0.999979	−	0.00644117i	$-0.997950\pi$
$17$	−6.20753	−	3.58392i	−1.50555	−	0.869228i	−0.505568	−	0.862787i	$-0.668717\pi$
$18$		0			0
$19$	1.58392	+	2.74343i	0.363376	+	0.629386i	0.988514	−	0.151129i	$-0.0482907\pi$
$19$	1.58392	+	2.74343i	0.363376	+	0.629386i	−0.625138	+	0.780514i	$0.714957\pi$
$20$		0			0
$21$	2.05378	−	6.47880i	0.448172	−	1.41379i
$22$		0			0
$23$	−4.96812	+	2.86834i	−1.03592	+	0.598091i	−0.918676	−	0.395012i	$-0.870741\pi$
$23$	−4.96812	+	2.86834i	−1.03592	+	0.598091i	−0.117248	+	0.993103i	$0.537407\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.53871i		−	0.296125i
$28$		0			0
$29$	−1.96986			−0.365794			−0.182897	−	0.983132i	$-0.558547\pi$
$29$	−1.96986			−0.365794			−0.182897	+	0.983132i	$0.558547\pi$
$30$		0			0
$31$	−0.484931	+	0.839925i	−0.0870961	+	0.150855i	−0.906282	−	0.422673i	$-0.861092\pi$
$31$	−0.484931	+	0.839925i	−0.0870961	+	0.150855i	0.819186	+	0.573527i	$0.194425\pi$
$32$		0			0
$33$	−3.49020	+	2.01507i	−0.607566	+	0.350779i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.80804	+	3.35327i	−0.954836	+	0.551275i	−0.894580	−	0.446908i	$-0.852525\pi$
$37$	−5.80804	+	3.35327i	−0.954836	+	0.551275i	−0.0602563	+	0.998183i	$0.519192\pi$
$38$		0			0
$39$	−7.15277	+	12.3890i	−1.14536	+	1.98382i
$40$		0			0
$41$	−8.87439			−1.38595			−0.692973	−	0.720963i	$-0.743700\pi$
$41$	−8.87439			−1.38595			−0.692973	+	0.720963i	$0.743700\pi$
$42$		0			0
$43$			4.59899i			0.701339i	0.936499	+	0.350670i	$0.114046\pi$
$43$			4.59899i			0.701339i	−0.936499	+	0.350670i	$0.885954\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.347286	−	0.200506i	0.0506569	−	0.0292468i	−0.474458	−	0.880278i	$-0.657356\pi$
$47$	0.347286	−	0.200506i	0.0506569	−	0.0292468i	0.525115	+	0.851032i	$0.324022\pi$
$48$		0			0
$49$	−6.35327	+	2.93869i	−0.907611	+	0.419813i
$50$		0			0
$51$	9.20655	+	15.9462i	1.28917	+	2.23292i
$52$		0			0
$53$	8.26077	+	4.76936i	1.13470	+	0.655121i	0.945114	−	0.326742i	$-0.105951\pi$
$53$	8.26077	+	4.76936i	1.13470	+	0.655121i	0.189590	+	0.981863i	$0.439284\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	8.13770i		−	1.07786i
$58$		0			0
$59$	−2.28442	+	3.95674i	−0.297407	+	0.515124i	−0.975542	−	0.219814i	$-0.929455\pi$
$59$	−2.28442	+	3.95674i	−0.297407	+	0.515124i	0.678135	+	0.734937i	$0.262788\pi$
$60$		0			0
$61$	−7.65277	−	13.2550i	−0.979837	−	1.69713i	−0.662951	−	0.748663i	$-0.730696\pi$
$61$	−7.65277	−	13.2550i	−0.979837	−	1.69713i	−0.316886	−	0.948464i	$-0.602637\pi$
$62$		0			0
$63$	−7.03032	+	6.42212i	−0.885737	+	0.809112i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.746774	−	0.431150i	−0.0912330	−	0.0526734i	0.453689	−	0.891160i	$-0.350108\pi$
$67$	−0.746774	−	0.431150i	−0.0912330	−	0.0526734i	−0.544922	+	0.838486i	$0.683441\pi$
$68$		0			0
$69$	14.7367			1.77409
$70$		0			0
$71$	−12.1377			−1.44048			−0.720240	−	0.693725i	$-0.755968\pi$
$71$	−12.1377			−1.44048			−0.720240	+	0.693725i	$0.755968\pi$
$72$		0			0
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	0.688830	−	0.724923i	$-0.258125\pi$
$73$	3.46410	+	2.00000i	0.405442	+	0.234082i	−0.283387	+	0.959006i	$0.591458\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.95674	+	1.25429i	0.450912	+	0.142939i
$78$		0			0
$79$	−6.43719	−	11.1495i	−0.724241	−	1.25442i	−0.959286	−	0.282437i	$-0.908857\pi$
$79$	−6.43719	−	11.1495i	−0.724241	−	1.25442i	0.235045	−	0.971985i	$-0.424476\pi$
$80$		0			0
$81$	3.42212	−	5.92729i	0.380236	−	0.658588i
$82$		0			0
$83$		−	17.1076i		−	1.87780i	−0.344192	−	0.938899i	$-0.611847\pi$
$83$		−	17.1076i		−	1.87780i	0.344192	−	0.938899i	$-0.388153\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.38233	+	2.53014i	0.469835	+	0.271259i
$88$		0			0
$89$	−2.79949	−	4.84887i	−0.296746	−	0.513979i	0.678644	−	0.734468i	$-0.262568\pi$
$89$	−2.79949	−	4.84887i	−0.296746	−	0.513979i	−0.975389	+	0.220489i	$0.929235\pi$
$90$		0			0
$91$	14.3895	−	3.16673i	1.50842	−	0.331963i
$92$		0			0
$93$	2.15764	−	1.24571i	0.223737	−	0.129175i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			0.233174i			0.0236752i	0.999930	+	0.0118376i	$0.00376811\pi$
$97$			0.233174i			0.0236752i	−0.999930	+	0.0118376i	$0.996232\pi$
$98$		0			0
$99$	5.64627			0.567472
$100$		0			0
$101$	−6.25176	+	10.8284i	−0.622073	+	1.07746i	0.367026	+	0.930211i	$0.380376\pi$
$101$	−6.25176	+	10.8284i	−0.622073	+	1.07746i	−0.989099	+	0.147251i	$0.952957\pi$
$102$		0			0
$103$	−2.91926	+	1.68544i	−0.287643	+	0.166071i	−0.636879	−	0.770964i	$-0.719775\pi$
$103$	−2.91926	+	1.68544i	−0.287643	+	0.166071i	0.349235	+	0.937035i	$0.386441\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.3604	+	8.86834i	−1.48495	+	0.857335i	−0.999853	−	0.0171265i	$-0.994548\pi$
$107$	−15.3604	+	8.86834i	−1.48495	+	0.857335i	−0.485095	+	0.874462i	$0.661215\pi$
$108$		0			0
$109$	2.95226	−	5.11347i	0.282775	−	0.489782i	−0.689292	−	0.724484i	$-0.742078\pi$
$109$	2.95226	−	5.11347i	0.282775	−	0.489782i	0.972067	+	0.234702i	$0.0754115\pi$
$110$		0			0
$111$	17.2281			1.63522
$112$		0			0
$113$		−	15.6412i		−	1.47140i	−0.677307	−	0.735701i	$-0.736853\pi$
$113$		−	15.6412i		−	1.47140i	0.677307	−	0.735701i	$-0.263147\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	17.3571	−	10.0211i	1.60466	−	0.926452i
$118$		0			0
$119$	5.73064	−	18.0777i	0.525327	−	1.65718i
$120$		0			0
$121$	4.26936	+	7.39474i	0.388123	+	0.672249i
$122$		0			0
$123$	19.7428	+	11.3985i	1.78014	+	1.02777i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			12.8744i			1.14242i	0.820805	+	0.571209i	$0.193525\pi$
$127$			12.8744i			1.14242i	−0.820805	+	0.571209i	$0.806475\pi$
$128$		0			0
$129$	5.90705	−	10.2313i	0.520087	−	0.900817i
$130$		0			0
$131$	0.114058	+	0.197554i	0.00996526	+	0.0172603i	0.870965	−	0.491345i	$-0.163495\pi$
$131$	0.114058	+	0.197554i	0.00996526	+	0.0172603i	−0.861000	+	0.508605i	$0.830161\pi$
$132$		0			0
$133$	−6.18810	+	5.65277i	−0.536576	+	0.490157i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.38002	+	4.83821i	0.715953	+	0.413356i	0.813261	−	0.581899i	$-0.197690\pi$
$137$	8.38002	+	4.83821i	0.715953	+	0.413356i	−0.0973082	+	0.995254i	$0.531023\pi$
$138$		0			0
$139$	12.3709			1.04928			0.524642	−	0.851323i	$-0.324199\pi$
$139$	12.3709			1.04928			0.524642	+	0.851323i	$0.324199\pi$
$140$		0			0
$141$	−1.03014			−0.0867533
$142$		0			0
$143$	−7.56619	−	4.36834i	−0.632717	−	0.365299i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	17.9086	+	1.62263i	1.47708	+	0.133832i
$148$		0			0
$149$	5.95479	+	10.3140i	0.487836	+	0.844956i	0.999902	−	0.0139898i	$-0.00445323\pi$
$149$	5.95479	+	10.3140i	0.487836	+	0.844956i	−0.512067	+	0.858946i	$0.671120\pi$
$150$		0			0
$151$	−4.98493	+	8.63415i	−0.405668	+	0.702637i	−0.994399	−	0.105692i	$-0.966294\pi$
$151$	−4.98493	+	8.63415i	−0.405668	+	0.702637i	0.588731	+	0.808329i	$0.299628\pi$
$152$		0			0
$153$		−	25.7970i		−	2.08556i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.4289	+	6.02111i	0.832315	+	0.480537i	0.854645	−	0.519214i	$-0.173775\pi$
$157$	10.4289	+	6.02111i	0.832315	+	0.480537i	−0.0223299	+	0.999751i	$0.507108\pi$
$158$		0			0
$159$	−12.2518	−	21.2207i	−0.971628	−	1.68291i
$160$		0			0
$161$	−10.2367	−	11.2061i	−0.806764	−	0.883167i
$162$		0			0
$163$	14.4944	−	8.36834i	1.13529	−	0.655459i	0.190029	−	0.981778i	$-0.439142\pi$
$163$	14.4944	−	8.36834i	1.13529	−	0.655459i	0.945260	+	0.326319i	$0.105808\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	6.76683i		−	0.523633i	−0.965118	−	0.261816i	$-0.915679\pi$
$167$		−	6.76683i		−	0.523633i	0.965118	−	0.261816i	$-0.0843215\pi$
$168$		0			0
$169$	−18.0121			−1.38555
$170$		0			0
$171$	−5.70051	+	9.87357i	−0.435929	+	0.755050i
$172$		0			0
$173$	−4.06552	+	2.34723i	−0.309096	+	0.178457i	−0.646522	−	0.762895i	$-0.723777\pi$
$173$	−4.06552	+	2.34723i	−0.309096	+	0.178457i	0.337426	+	0.941352i	$0.390444\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.1643	−	5.86834i	0.763993	−	0.441092i
$178$		0			0
$179$	5.73669	−	9.93623i	0.428780	−	0.742669i	−0.567985	−	0.823039i	$-0.692277\pi$
$179$	5.73669	−	9.93623i	0.428780	−	0.742669i	0.996765	+	0.0803699i	$0.0256102\pi$
$180$		0			0
$181$	0.832162			0.0618541			0.0309271	−	0.999522i	$-0.490154\pi$
$181$	0.832162			0.0618541			0.0309271	+	0.999522i	$0.490154\pi$
$182$		0			0
$183$			39.3176i			2.90644i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.73868	+	5.62263i	−0.712163	+	0.411167i
$188$		0			0
$189$	3.97590	−	0.874988i	0.289204	−	0.0636460i
$190$		0			0
$191$	−3.46986	−	6.00998i	−0.251070	−	0.434867i	0.712750	−	0.701418i	$-0.247449\pi$
$191$	−3.46986	−	6.00998i	−0.251070	−	0.434867i	−0.963821	+	0.266551i	$0.914116\pi$
$192$		0			0
$193$	17.0403	+	9.83821i	1.22659	+	0.708169i	0.966314	−	0.257366i	$-0.0828546\pi$
$193$	17.0403	+	9.83821i	1.22659	+	0.708169i	0.260272	+	0.965535i	$0.416188\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	16.0422i		−	1.14296i	−0.820616	−	0.571481i	$-0.806369\pi$
$197$		−	16.0422i		−	1.14296i	0.820616	−	0.571481i	$-0.193631\pi$
$198$		0			0
$199$	−5.33821	+	9.24604i	−0.378415	+	0.655435i	−0.990832	−	0.135101i	$-0.956864\pi$
$199$	−5.33821	+	9.24604i	−0.378415	+	0.655435i	0.612417	+	0.790535i	$0.290198\pi$
$200$		0			0
$201$	1.10756	+	1.91835i	0.0781213	+	0.135310i
$202$		0			0
$203$	−1.12016	−	5.08996i	−0.0786199	−	0.357245i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−17.8802	−	10.3231i	−1.24276	−	0.717508i
$208$		0			0
$209$	4.96986			0.343772
$210$		0			0
$211$	11.3658			0.782455			0.391227	−	0.920294i	$-0.372051\pi$
$211$	11.3658			0.782455			0.391227	+	0.920294i	$0.372051\pi$
$212$		0			0
$213$	27.0026	+	15.5900i	1.85019	+	1.06821i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.44605	−	0.775398i	−0.166049	−	0.0526375i
$218$		0			0
$219$	−5.13770	−	8.89876i	−0.347174	−	0.601322i
$220$		0			0
$221$	−19.9583	+	34.5688i	−1.34254	+	2.32535i
$222$		0			0
$223$			6.04222i			0.404617i	0.979322	+	0.202309i	$0.0648444\pi$
$223$			6.04222i			0.404617i	−0.979322	+	0.202309i	$0.935156\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.7418	−	10.8206i	−1.24394	−	0.718189i	−0.274046	−	0.961717i	$-0.588362\pi$
$227$	−18.7418	−	10.8206i	−1.24394	−	0.718189i	−0.969894	+	0.243528i	$0.921695\pi$
$228$		0			0
$229$	−2.71558	−	4.70351i	−0.179450	−	0.310817i	0.762242	−	0.647292i	$-0.224099\pi$
$229$	−2.71558	−	4.70351i	−0.179450	−	0.310817i	−0.941692	+	0.336475i	$0.890765\pi$
$230$		0			0
$231$	−7.19148	−	7.87253i	−0.473165	−	0.517975i
$232$		0			0
$233$	6.00998	−	3.46986i	0.393727	−	0.227318i	−0.290047	−	0.957012i	$-0.593671\pi$
$233$	6.00998	−	3.46986i	0.393727	−	0.227318i	0.683774	+	0.729694i	$0.260338\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			33.0724i			2.14828i
$238$		0			0
$239$	−1.69446			−0.109606			−0.0548028	−	0.998497i	$-0.517453\pi$
$239$	−1.69446			−0.109606			−0.0548028	+	0.998497i	$0.517453\pi$
$240$		0			0
$241$	7.46733	−	12.9338i	0.481013	−	0.833139i	−0.518749	−	0.854926i	$-0.673602\pi$
$241$	7.46733	−	12.9338i	0.481013	−	0.833139i	0.999763	+	0.0217871i	$0.00693559\pi$
$242$		0			0
$243$	−19.2240	+	11.0990i	−1.23322	+	0.712000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.2777	−	8.82061i	0.972099	−	0.561242i
$248$		0			0
$249$	−21.9734	+	38.0590i	−1.39251	+	2.41189i
$250$		0			0
$251$	8.90958			0.562368			0.281184	−	0.959654i	$-0.409273\pi$
$251$	8.90958			0.562368			0.281184	+	0.959654i	$0.409273\pi$
$252$		0			0
$253$			9.00000i			0.565825i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.36955	−	4.83216i	0.522078	−	0.301422i	−0.215706	−	0.976458i	$-0.569205\pi$
$257$	8.36955	−	4.83216i	0.522078	−	0.301422i	0.737785	+	0.675036i	$0.235872\pi$
$258$		0			0
$259$	−11.9673	−	13.1007i	−0.743614	−	0.814036i
$260$		0			0
$261$	−3.54475	−	6.13969i	−0.219415	−	0.380038i
$262$		0			0
$263$	−5.28492	−	3.05125i	−0.325882	−	0.188148i	0.328129	−	0.944633i	$-0.393582\pi$
$263$	−5.28492	−	3.05125i	−0.325882	−	0.188148i	−0.654011	+	0.756485i	$0.726915\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			14.3830i			0.880223i
$268$		0			0
$269$	11.2668	−	19.5147i	0.686951	−	1.18983i	−0.285869	−	0.958269i	$-0.592282\pi$
$269$	11.2668	−	19.5147i	0.686951	−	1.18983i	0.972820	−	0.231565i	$-0.0743844\pi$
$270$		0			0
$271$	−2.23064	−	3.86359i	−0.135502	−	0.234696i	0.790287	−	0.612737i	$-0.209931\pi$
$271$	−2.23064	−	3.86359i	−0.135502	−	0.234696i	−0.925789	+	0.378040i	$0.876598\pi$
$272$		0			0
$273$	−36.0795	−	11.4372i	−2.18363	−	0.692210i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.63659	−	3.25429i	−0.338670	−	0.195531i	0.321014	−	0.947074i	$-0.395976\pi$
$277$	−5.63659	−	3.25429i	−0.338670	−	0.195531i	−0.659684	+	0.751543i	$0.729310\pi$
$278$		0			0
$279$	−3.49052			−0.208972
$280$		0			0
$281$	−11.1980			−0.668015			−0.334008	−	0.942570i	$-0.608401\pi$
$281$	−11.1980			−0.668015			−0.334008	+	0.942570i	$0.608401\pi$
$282$		0			0
$283$	−6.62187	−	3.82314i	−0.393629	−	0.227262i	0.290102	−	0.956996i	$-0.406311\pi$
$283$	−6.62187	−	3.82314i	−0.393629	−	0.227262i	−0.683731	+	0.729734i	$0.739644\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.04642	−	22.9307i	−0.297881	−	1.35356i
$288$		0			0
$289$	17.1890	+	29.7721i	1.01111	+	1.75130i
$290$		0			0
$291$	0.299494	−	0.518739i	0.0175567	−	0.0304090i
$292$		0			0
$293$		−	6.12561i		−	0.357862i	−0.983862	−	0.178931i	$-0.942736\pi$
$293$		−	6.12561i		−	0.357862i	0.983862	−	0.178931i	$-0.0572639\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.09059	−	1.20700i	−0.121308	−	0.0700374i
$298$		0			0
$299$	15.9734	+	27.6667i	0.923764	+	1.60001i
$300$		0			0
$301$	−11.8834	+	2.61521i	−0.684949	+	0.150738i
$302$		0			0
$303$	27.8164	−	16.0598i	1.59801	−	0.922613i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			26.4080i			1.50719i	0.657341	+	0.753593i	$0.271681\pi$
$307$			26.4080i			1.50719i	−0.657341	+	0.753593i	$0.728319\pi$
$308$		0			0
$309$	8.65927			0.492608
$310$		0			0
$311$	9.67641	−	16.7600i	0.548699	−	0.950374i	−0.449665	−	0.893197i	$-0.648457\pi$
$311$	9.67641	−	16.7600i	0.548699	−	0.950374i	0.998364	−	0.0571771i	$-0.0182100\pi$
$312$		0			0
$313$	−7.54009	+	4.35327i	−0.426191	+	0.246062i	−0.697723	−	0.716368i	$-0.745803\pi$
$313$	−7.54009	+	4.35327i	−0.426191	+	0.246062i	0.271531	+	0.962430i	$0.412470\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.2289	−	7.63770i	0.743008	−	0.428976i	−0.0801539	−	0.996782i	$-0.525541\pi$
$317$	13.2289	−	7.63770i	0.743008	−	0.428976i	0.823162	+	0.567807i	$0.192208\pi$
$318$		0			0
$319$	−1.54521	+	2.67638i	−0.0865150	+	0.149848i
$320$		0			0
$321$	45.5629			2.54307
$322$		0			0
$323$		−	22.7065i		−	1.26343i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.1357	+	7.58392i	−0.726408	+	0.419392i
$328$		0			0
$329$	0.715575	+	0.783342i	0.0394509	+	0.0431870i
$330$		0			0
$331$	−8.37439	−	14.5049i	−0.460298	−	0.797259i	0.538678	−	0.842512i	$-0.318924\pi$
$331$	−8.37439	−	14.5049i	−0.460298	−	0.797259i	−0.998976	+	0.0452526i	$0.985591\pi$
$332$		0			0
$333$	−20.9031	−	12.0684i	−1.14548	−	0.661344i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	31.2453i		−	1.70204i	−0.525135	−	0.851019i	$-0.675985\pi$
$337$		−	31.2453i		−	1.70204i	0.525135	−	0.851019i	$-0.324015\pi$
$338$		0			0
$339$	−20.0900	+	34.7968i	−1.09114	+	1.88990i
$340$		0			0
$341$	0.760783	+	1.31772i	0.0411987	+	0.0713583i
$342$		0			0
$343$	−11.2061	−	14.7453i	−0.605074	−	0.796169i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.4811	−	6.05125i	−0.562654	−	0.324848i	0.191556	−	0.981482i	$-0.438647\pi$
$347$	−10.4811	−	6.05125i	−0.562654	−	0.324848i	−0.754210	+	0.656633i	$0.771980\pi$
$348$		0			0
$349$	3.87439			0.207391			0.103696	−	0.994609i	$-0.466933\pi$
$349$	3.87439			0.207391			0.103696	+	0.994609i	$0.466933\pi$
$350$		0			0
$351$	−8.56885			−0.457371
$352$		0			0
$353$	−2.22031	−	1.28190i	−0.118175	−	0.0682284i	0.439747	−	0.898122i	$-0.355068\pi$
$353$	−2.22031	−	1.28190i	−0.118175	−	0.0682284i	−0.557922	+	0.829893i	$0.688401\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−35.9684	+	32.8568i	−1.90365	+	1.73897i
$358$		0			0
$359$	10.4196	+	18.0473i	0.549925	+	0.952498i	0.998279	+	0.0586422i	$0.0186771\pi$
$359$	10.4196	+	18.0473i	0.549925	+	0.952498i	−0.448354	+	0.893856i	$0.647990\pi$
$360$		0			0
$361$	4.48240	−	7.76375i	0.235916	−	0.408618i
$362$		0			0
$363$		−	21.9347i		−	1.15127i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.7111	+	7.91608i	0.715711	+	0.413216i	0.813172	−	0.582023i	$-0.197739\pi$
$367$	13.7111	+	7.91608i	0.715711	+	0.413216i	−0.0974609	+	0.995239i	$0.531072\pi$
$368$		0			0
$369$	−15.9694	−	27.6598i	−0.831334	−	1.43991i
$370$		0			0
$371$	−7.62614	+	24.0572i	−0.395930	+	1.24899i
$372$		0			0
$373$	−19.4886	+	11.2518i	−1.00908	+	0.582594i	−0.910923	−	0.412577i	$-0.864629\pi$
$373$	−19.4886	+	11.2518i	−1.00908	+	0.582594i	−0.0981594	+	0.995171i	$0.531296\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			10.9699i			0.564977i
$378$		0			0
$379$	7.36581			0.378356			0.189178	−	0.981943i	$-0.439418\pi$
$379$	7.36581			0.378356			0.189178	+	0.981943i	$0.439418\pi$
$380$		0			0
$381$	16.5362	−	28.6415i	0.847174	−	1.46735i
$382$		0			0
$383$	−29.1446	+	16.8266i	−1.48922	+	0.859802i	−0.999924	−	0.0123162i	$-0.996080\pi$
$383$	−29.1446	+	16.8266i	−1.48922	+	0.859802i	−0.489296	+	0.872118i	$0.662746\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−14.3342	+	8.27585i	−0.728648	+	0.420685i
$388$		0			0
$389$	8.74273	−	15.1429i	0.443274	−	0.767773i	−0.554656	−	0.832080i	$-0.687150\pi$
$389$	8.74273	−	15.1429i	0.443274	−	0.767773i	0.997930	+	0.0643065i	$0.0204835\pi$
$390$		0			0
$391$	41.1196			2.07951
$392$		0			0
$393$		−	0.585994i		−	0.0295595i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−6.58092	+	3.79949i	−0.330287	+	0.190691i	−0.655968	−	0.754788i	$-0.727740\pi$
$397$	−6.58092	+	3.79949i	−0.330287	+	0.190691i	0.325682	+	0.945479i	$0.394406\pi$
$398$		0			0
$399$	21.0272	−	4.62750i	1.05267	−	0.231665i
$400$		0			0
$401$	−5.42212	−	9.39139i	−0.270768	−	0.468984i	0.698291	−	0.715814i	$-0.253944\pi$
$401$	−5.42212	−	9.39139i	−0.270768	−	0.468984i	−0.969059	+	0.246830i	$0.920611\pi$
$402$		0			0
$403$	4.67741	+	2.70051i	0.232999	+	0.134522i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			10.5216i			0.521535i
$408$		0			0
$409$	−8.43466	+	14.6093i	−0.417067	+	0.722382i	−0.995643	−	0.0932469i	$-0.970275\pi$
$409$	−8.43466	+	14.6093i	−0.417067	+	0.722382i	0.578576	+	0.815629i	$0.303609\pi$
$410$		0			0
$411$	−12.4286	−	21.5270i	−0.613059	−	1.06185i
$412$		0			0
$413$	−11.5229	−	3.65277i	−0.567006	−	0.179741i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−27.5213	−	15.8895i	−1.34773	−	0.778110i
$418$		0			0
$419$	4.03014			0.196885			0.0984426	−	0.995143i	$-0.468614\pi$
$419$	4.03014			0.196885			0.0984426	+	0.995143i	$0.468614\pi$
$420$		0			0
$421$	25.1196			1.22426			0.612128	−	0.790758i	$-0.290314\pi$
$421$	25.1196			1.22426			0.612128	+	0.790758i	$0.290314\pi$
$422$		0			0
$423$	1.24988	+	0.721618i	0.0607712	+	0.0350863i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	29.8981	−	27.3116i	1.44687	−	1.32170i
$428$		0			0
$429$	11.2216	+	19.4364i	0.541785	+	0.938399i
$430$		0			0
$431$	−15.1201	+	26.1888i	−0.728310	+	1.26147i	0.229288	+	0.973359i	$0.426360\pi$
$431$	−15.1201	+	26.1888i	−0.728310	+	1.26147i	−0.957597	+	0.288111i	$0.906973\pi$
$432$		0			0
$433$			22.9769i			1.10420i	0.833778	+	0.552099i	$0.186173\pi$
$433$			22.9769i			1.10420i	−0.833778	+	0.552099i	$0.813827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.7382	−	9.08645i	−0.752860	−	0.434664i
$438$		0			0
$439$	5.97590	+	10.3506i	0.285214	+	0.494006i	0.972661	−	0.232229i	$-0.0746019\pi$
$439$	5.97590	+	10.3506i	0.285214	+	0.494006i	−0.687447	+	0.726235i	$0.741269\pi$
$440$		0			0
$441$	−20.5920	−	14.5138i	−0.980573	−	0.691135i
$442$		0			0
$443$	12.2175	−	7.05378i	0.580471	−	0.335135i	−0.180849	−	0.983511i	$-0.557885\pi$
$443$	12.2175	−	7.05378i	0.580471	−	0.335135i	0.761321	+	0.648376i	$0.224551\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	30.5939i		−	1.44704i
$448$		0			0
$449$	−37.9468			−1.79082			−0.895409	−	0.445245i	$-0.853117\pi$
$449$	−37.9468			−1.79082			−0.895409	+	0.445245i	$0.853117\pi$
$450$		0			0
$451$	−6.96129	+	12.0573i	−0.327794	+	0.567756i
$452$		0			0
$453$	22.1798	−	12.8055i	1.04210	−	0.601657i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.0611	+	9.27287i	−0.751306	+	0.433767i	−0.826165	−	0.563428i	$-0.809482\pi$
$457$	−16.0611	+	9.27287i	−0.751306	+	0.433767i	0.0748598	+	0.997194i	$0.476149\pi$
$458$		0			0
$459$	−5.51462	+	9.55159i	−0.257400	+	0.445830i
$460$		0			0
$461$	−23.2453			−1.08264			−0.541320	−	0.840817i	$-0.682075\pi$
$461$	−23.2453			−1.08264			−0.541320	+	0.840817i	$0.682075\pi$
$462$		0			0
$463$		−	7.59393i		−	0.352920i	−0.984308	−	0.176460i	$-0.943535\pi$
$463$		−	7.59393i		−	0.352920i	0.984308	−	0.176460i	$-0.0564646\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.3941	−	14.0839i	1.12882	−	0.651726i	0.185184	−	0.982704i	$-0.440712\pi$
$467$	24.3941	−	14.0839i	1.12882	−	0.651726i	0.943639	+	0.330978i	$0.107379\pi$
$468$		0			0
$469$	0.689404	−	2.17478i	0.0318337	−	0.100422i
$470$		0			0
$471$	−15.4673	−	26.7902i	−0.712697	−	1.23443i
$472$		0			0
$473$	6.24848	+	3.60756i	0.287305	+	0.165876i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			34.3297i			1.57185i
$478$		0			0
$479$	−17.0900	+	29.6007i	−0.780860	+	1.35249i	0.150581	+	0.988598i	$0.451886\pi$
$479$	−17.0900	+	29.6007i	−0.780860	+	1.35249i	−0.931441	+	0.363892i	$0.881448\pi$
$480$		0			0
$481$	18.6739	+	32.3441i	0.851456	+	1.47476i
$482$		0			0
$483$	8.38002	+	38.0784i	0.381304	+	1.73263i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.96234	+	5.75176i	0.451436	+	0.260637i	0.708437	−	0.705774i	$-0.249401\pi$
$487$	9.96234	+	5.75176i	0.451436	+	0.260637i	−0.257000	+	0.966411i	$0.582734\pi$
$488$		0			0
$489$	−42.9940			−1.94426
$490$		0			0
$491$	−25.5337			−1.15232			−0.576159	−	0.817338i	$-0.695449\pi$
$491$	−25.5337			−1.15232			−0.576159	+	0.817338i	$0.695449\pi$
$492$		0			0
$493$	12.2280	+	7.05982i	0.550720	+	0.317958i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.90210	−	31.3628i	−0.309602	−	1.40682i
$498$		0			0
$499$	−5.69798	−	9.86919i	−0.255076	−	0.441805i	0.709840	−	0.704363i	$-0.248767\pi$
$499$	−5.69798	−	9.86919i	−0.255076	−	0.441805i	−0.964916	+	0.262558i	$0.915434\pi$
$500$		0			0
$501$	−8.69148	+	15.0541i	−0.388307	+	0.672567i
$502$		0			0
$503$			2.49649i			0.111313i	0.998450	+	0.0556564i	$0.0177251\pi$
$503$			2.49649i			0.111313i	−0.998450	+	0.0556564i	$0.982275\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	40.0713	+	23.1352i	1.77963	+	1.02747i
$508$		0			0
$509$	5.77188	+	9.99720i	0.255834	+	0.443118i	0.965122	−	0.261801i	$-0.0843165\pi$
$509$	5.77188	+	9.99720i	0.255834	+	0.443118i	−0.709287	+	0.704919i	$0.750983\pi$
$510$		0			0
$511$	−3.19798	+	10.0883i	−0.141470	+	0.446278i
$512$		0			0
$513$	4.22134	−	2.43719i	0.186377	−	0.107605i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	0.629127i		−	0.0276690i
$518$		0			0
$519$	12.0594			0.529348
$520$		0			0
$521$	−11.8744	+	20.5670i	−0.520226	+	0.901058i	0.479497	+	0.877543i	$0.340819\pi$
$521$	−11.8744	+	20.5670i	−0.520226	+	0.901058i	−0.999723	+	0.0235150i	$0.992514\pi$
$522$		0			0
$523$	−13.9757	+	8.06885i	−0.611113	+	0.352826i	−0.773401	−	0.633917i	$-0.781446\pi$
$523$	−13.9757	+	8.06885i	−0.611113	+	0.352826i	0.162288	+	0.986743i	$0.448113\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.02044	−	3.47590i	0.262255	−	0.151413i
$528$		0			0
$529$	4.95479	−	8.58195i	0.215426	−	0.373128i
$530$		0			0
$531$	−16.4432			−0.713576
$532$		0			0
$533$			49.4201i			2.14062i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−25.5247	+	14.7367i	−1.10147	+	0.635935i
$538$		0			0
$539$	−0.990974	+	10.9371i	−0.0426843	+	0.471096i
$540$		0			0
$541$	0.769355	+	1.33256i	0.0330772	+	0.0572913i	0.882090	−	0.471081i	$-0.156136\pi$
$541$	0.769355	+	1.33256i	0.0330772	+	0.0572913i	−0.849013	+	0.528372i	$0.822803\pi$
$542$		0			0
$543$	−1.85130	−	1.06885i	−0.0794470	−	0.0458687i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	14.3779i		−	0.614755i	−0.951588	−	0.307377i	$-0.900549\pi$
$547$		−	14.3779i		−	0.614755i	0.951588	−	0.307377i	$-0.0994514\pi$
$548$		0			0
$549$	27.5422	−	47.7045i	1.17547	−	2.03598i
$550$		0			0
$551$	−3.12010	−	5.40417i	−0.132921	−	0.230226i
$552$		0			0
$553$	25.1490	−	22.9734i	1.06944	−	0.976927i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.6658	+	8.46733i	0.621412	+	0.358772i	0.777419	−	0.628984i	$-0.216529\pi$
$557$	14.6658	+	8.46733i	0.621412	+	0.358772i	−0.156007	+	0.987756i	$0.549862\pi$
$558$		0			0
$559$	25.6111			1.08323
$560$		0			0
$561$	28.8874			1.21963
$562$		0			0
$563$	0.575322	+	0.332162i	0.0242469	+	0.0139990i	0.512074	−	0.858941i	$-0.328877\pi$
$563$	0.575322	+	0.332162i	0.0242469	+	0.0139990i	−0.487828	+	0.872940i	$0.662211\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	17.2616	+	5.47194i	0.724921	+	0.229800i
$568$		0			0
$569$	−20.5186	−	35.5392i	−0.860184	−	1.48988i	−0.871751	−	0.489949i	$-0.837015\pi$
$569$	−20.5186	−	35.5392i	−0.860184	−	1.48988i	0.0115674	−	0.999933i	$-0.496318\pi$
$570$		0			0
$571$	14.3146	−	24.7936i	0.599046	−	1.03758i	−0.393916	−	0.919146i	$-0.628880\pi$
$571$	14.3146	−	24.7936i	0.599046	−	1.03758i	0.992962	−	0.118432i	$-0.0377866\pi$
$572$		0			0
$573$			17.8271i			0.744738i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−27.2455	−	15.7302i	−1.13424	−	0.654856i	−0.189246	−	0.981930i	$-0.560604\pi$
$577$	−27.2455	−	15.7302i	−1.13424	−	0.654856i	−0.944999	+	0.327073i	$0.893938\pi$
$578$		0			0
$579$	−25.2729	−	43.7739i	−1.05030	−	1.81918i
$580$		0			0
$581$	44.2046	−	9.72821i	1.83391	−	0.403594i
$582$		0			0
$583$	12.9599	−	7.48240i	0.536744	−	0.309889i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	9.53871i		−	0.393705i	−0.980433	−	0.196852i	$-0.936928\pi$
$587$		−	9.53871i		−	0.393705i	0.980433	−	0.196852i	$-0.0630720\pi$
$588$		0			0
$589$	−3.07236			−0.126595
$590$		0			0
$591$	−20.6050	+	35.6890i	−0.847578	+	1.46805i
$592$		0			0
$593$	−8.60805	+	4.96986i	−0.353490	+	0.204088i	−0.666221	−	0.745754i	$-0.732089\pi$
$593$	−8.60805	+	4.96986i	−0.353490	+	0.204088i	0.312731	+	0.949842i	$0.398756\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	23.7517	−	13.7130i	0.972092	−	0.561238i
$598$		0			0
$599$	4.70655	−	8.15198i	0.192304	−	0.333081i	−0.753709	−	0.657208i	$-0.771737\pi$
$599$	4.70655	−	8.15198i	0.192304	−	0.333081i	0.946014	+	0.324127i	$0.105071\pi$
$600$		0			0
$601$	−3.00506			−0.122579			−0.0612894	−	0.998120i	$-0.519521\pi$
$601$	−3.00506			−0.122579			−0.0612894	+	0.998120i	$0.519521\pi$
$602$		0			0
$603$		−	3.10341i		−	0.126381i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−16.3091	+	9.41608i	−0.661967	+	0.382187i	−0.793026	−	0.609188i	$-0.791496\pi$
$607$	−16.3091	+	9.41608i	−0.661967	+	0.382187i	0.131059	+	0.991375i	$0.458162\pi$
$608$		0			0
$609$	−4.04566	+	12.7623i	−0.163939	+	0.517156i
$610$		0			0
$611$	−1.11659	−	1.93399i	−0.0451723	−	0.0782407i
$612$		0			0
$613$	13.7171	+	7.91959i	0.554030	+	0.319869i	0.750746	−	0.660591i	$-0.229694\pi$
$613$	13.7171	+	7.91959i	0.554030	+	0.319869i	−0.196716	+	0.980461i	$0.563028\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	0.778912i		−	0.0313578i	−0.999877	−	0.0156789i	$-0.995009\pi$
$617$		−	0.778912i		−	0.0313578i	0.999877	−	0.0156789i	$-0.00499096\pi$
$618$		0			0
$619$	4.97338	−	8.61414i	0.199897	−	0.346231i	−0.748598	−	0.663024i	$-0.769273\pi$
$619$	4.97338	−	8.61414i	0.199897	−	0.346231i	0.948495	+	0.316793i	$0.102606\pi$
$620$		0			0
$621$	4.41355	+	7.64450i	0.177110	+	0.306763i
$622$		0			0
$623$	10.9371	−	9.99097i	0.438187	−	0.400280i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−11.0564	−	6.38341i	−0.441550	−	0.254929i
$628$		0			0
$629$	48.0715			1.91673
$630$		0			0
$631$	−12.5638			−0.500157			−0.250078	−	0.968226i	$-0.580456\pi$
$631$	−12.5638			−0.500157			−0.250078	+	0.968226i	$0.580456\pi$
$632$		0			0
$633$	−25.2854	−	14.5985i	−1.00500	−	0.580240i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	16.3651	+	35.3804i	0.648410	+	1.40182i
$638$		0			0
$639$	−21.8417	−	37.8310i	−0.864045	−	1.49657i
$640$		0			0
$641$	5.76033	−	9.97718i	0.227519	−	0.394075i	−0.729553	−	0.683924i	$-0.760272\pi$
$641$	5.76033	−	9.97718i	0.227519	−	0.394075i	0.957072	+	0.289849i	$0.0936052\pi$
$642$		0			0
$643$			9.74175i			0.384177i	0.981378	+	0.192088i	$0.0615261\pi$
$643$			9.74175i			0.384177i	−0.981378	+	0.192088i	$0.938474\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.3035	+	12.8769i	0.876840	+	0.506244i	0.869615	−	0.493730i	$-0.164367\pi$
$647$	22.3035	+	12.8769i	0.876840	+	0.506244i	0.00722479	+	0.999974i	$0.497700\pi$
$648$		0			0
$649$	3.58392	+	6.20753i	0.140681	+	0.243667i
$650$		0			0
$651$	4.44577	+	4.86679i	0.174243	+	0.190745i
$652$		0			0
$653$	13.1575	−	7.59646i	0.514891	−	0.297272i	−0.219951	−	0.975511i	$-0.570590\pi$
$653$	13.1575	−	7.59646i	0.514891	−	0.297272i	0.734842	+	0.678239i	$0.237256\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			14.3960i			0.561640i
$658$		0			0
$659$	14.6894			0.572218			0.286109	−	0.958197i	$-0.407638\pi$
$659$	14.6894			0.572218			0.286109	+	0.958197i	$0.407638\pi$
$660$		0			0
$661$	−2.16784	+	3.75481i	−0.0843191	+	0.146045i	−0.905101	−	0.425197i	$-0.860205\pi$
$661$	−2.16784	+	3.75481i	−0.0843191	+	0.146045i	0.820782	+	0.571242i	$0.193538\pi$
$662$		0			0
$663$	88.8020	−	51.2699i	3.44879	−	1.99116i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.78650	−	5.65024i	0.378935	−	0.218778i
$668$		0			0
$669$	7.76078	−	13.4421i	0.300049	−	0.519700i
$670$		0			0
$671$	−24.0121			−0.926976
$672$		0			0
$673$		−	34.1971i		−	1.31820i	−0.752055	−	0.659100i	$-0.770937\pi$
$673$		−	34.1971i		−	1.31820i	0.752055	−	0.659100i	$-0.229063\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.6668	−	9.04521i	0.602122	−	0.347636i	−0.167754	−	0.985829i	$-0.553651\pi$
$677$	15.6668	−	9.04521i	0.602122	−	0.347636i	0.769876	+	0.638193i	$0.220318\pi$
$678$		0			0
$679$	−0.602502	+	0.132594i	−0.0231219	+	0.00508850i
$680$		0			0
$681$	27.7965	+	48.1450i	1.06516	+	1.84492i
$682$		0			0
$683$	−20.8934	−	12.0628i	−0.799464	−	0.461570i	0.0438200	−	0.999039i	$-0.486047\pi$
$683$	−20.8934	−	12.0628i	−0.799464	−	0.461570i	−0.843284	+	0.537469i	$0.819381\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			13.9518i			0.532295i
$688$		0			0
$689$	26.5598	−	46.0030i	1.01185	−	1.75257i
$690$		0			0
$691$	−8.72415	−	15.1107i	−0.331882	−	0.574837i	0.650999	−	0.759079i	$-0.274350\pi$
$691$	−8.72415	−	15.1107i	−0.331882	−	0.574837i	−0.982881	+	0.184242i	$0.941017\pi$
$692$		0			0
$693$	3.21075	+	14.5895i	0.121966	+	0.554210i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	55.0880	+	31.8051i	2.08661	+	1.20470i
$698$		0			0
$699$	−17.8271			−0.674283
$700$		0			0
$701$	20.7015			0.781885			0.390942	−	0.920415i	$-0.372149\pi$
$701$	20.7015			0.781885			0.390942	+	0.920415i	$0.372149\pi$
$702$		0			0
$703$	−18.3989	−	10.6226i	−0.693929	−	0.400640i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−31.5347	−	9.99649i	−1.18598	−	0.375957i
$708$		0			0
$709$	3.54774	+	6.14486i	0.133238	+	0.230775i	0.924923	−	0.380154i	$-0.124129\pi$
$709$	3.54774	+	6.14486i	0.133238	+	0.230775i	−0.791685	+	0.610930i	$0.790796\pi$
$710$		0			0
$711$	23.1674	−	40.1271i	0.868845	−	1.50488i
$712$		0			0
$713$		−	5.56379i		−	0.208366i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.76965	+	2.17641i	0.140780	+	0.0812795i
$718$		0			0
$719$	26.2216	+	45.4172i	0.977901	+	1.69377i	0.670008	+	0.742354i	$0.266291\pi$
$719$	26.2216	+	45.4172i	0.977901	+	1.69377i	0.307893	+	0.951421i	$0.400376\pi$
$720$		0			0
$721$	−6.01507	−	6.58471i	−0.224013	−	0.245227i
$722$		0			0
$723$	−33.2250	+	19.1825i	−1.23565	+	0.713403i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	29.9045i		−	1.10910i	−0.832151	−	0.554549i	$-0.812891\pi$
$727$		−	29.9045i		−	1.10910i	0.832151	−	0.554549i	$-0.187109\pi$
$728$		0			0
$729$	36.4905			1.35150
$730$		0			0
$731$	16.4824	−	28.5484i	0.609624	−	1.05590i
$732$		0			0
$733$	−4.83323	+	2.79047i	−0.178519	+	0.103068i	−0.586597	−	0.809879i	$-0.699533\pi$
$733$	−4.83323	+	2.79047i	−0.178519	+	0.103068i	0.408077	+	0.912947i	$0.366199\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.17158	+	0.676410i	−0.0431556	+	0.0249159i
$738$		0			0
$739$	20.3744	−	35.2895i	0.749484	−	1.29814i	−0.198586	−	0.980083i	$-0.563635\pi$
$739$	20.3744	−	35.2895i	0.749484	−	1.29814i	0.948070	−	0.318061i	$-0.103032\pi$
$740$		0			0
$741$	−45.3176			−1.66478
$742$		0			0
$743$		−	50.5327i		−	1.85387i	−0.375226	−	0.926933i	$-0.622435\pi$
$743$		−	50.5327i		−	1.85387i	0.375226	−	0.926933i	$-0.377565\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	53.3211	−	30.7850i	1.95092	−	1.12636i
$748$		0			0
$749$	−31.6498	−	34.6471i	−1.15646	−	1.26598i
$750$		0			0
$751$	15.3568	+	26.5987i	0.560377	+	0.970602i	0.997463	+	0.0711821i	$0.0226771\pi$
$751$	15.3568	+	26.5987i	0.560377	+	0.970602i	−0.437086	+	0.899420i	$0.643990\pi$
$752$		0			0
$753$	−19.8211	−	11.4437i	−0.722319	−	0.417031i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	20.7116i		−	0.752776i	−0.926462	−	0.376388i	$-0.877166\pi$
$757$		−	20.7116i		−	0.752776i	0.926462	−	0.376388i	$-0.122834\pi$
$758$		0			0
$759$	11.5598	−	20.0222i	0.419595	−	0.726760i
$760$		0			0
$761$	17.1764	+	29.7504i	0.622644	+	1.07845i	0.988991	+	0.147973i	$0.0472750\pi$
$761$	17.1764	+	29.7504i	0.622644	+	1.07845i	−0.366347	+	0.930478i	$0.619392\pi$
$762$		0			0
$763$	14.8916	+	4.72063i	0.539112	+	0.170898i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	22.0345	+	12.7216i	0.795619	+	0.459351i
$768$		0			0
$769$	−46.8392			−1.68906			−0.844532	−	0.535505i	$-0.820121\pi$
$769$	−46.8392			−1.68906			−0.844532	+	0.535505i	$0.820121\pi$
$770$		0			0
$771$	−24.8262			−0.894094
$772$		0			0
$773$	28.8652	+	16.6653i	1.03821	+	0.599409i	0.919325	−	0.393499i	$-0.128735\pi$
$773$	28.8652	+	16.6653i	1.03821	+	0.599409i	0.118883	+	0.992908i	$0.462069\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.79677	+	44.5161i	0.351457	+	1.59700i
$778$		0			0
$779$	−14.0563	−	24.3462i	−0.503620	−	0.872295i
$780$		0			0
$781$	−9.52111	+	16.4911i	−0.340692	+	0.590096i
$782$		0			0
$783$			3.03105i			0.108321i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.28158	−	4.20402i	−0.259560	−	0.149857i	0.364574	−	0.931175i	$-0.381215\pi$
$787$	−7.28158	−	4.20402i	−0.259560	−	0.149857i	−0.624134	+	0.781317i	$0.714548\pi$
$788$		0			0
$789$	7.83821	+	13.5762i	0.279047	+	0.483324i
$790$		0			0
$791$	40.4156	−	8.89438i	1.43701	−	0.316248i
$792$		0			0
$793$	−73.8150	+	42.6171i	−2.62125	+	1.51338i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			16.2935i			0.577144i	0.957458	+	0.288572i	$0.0931804\pi$
$797$			16.2935i			0.577144i	−0.957458	+	0.288572i	$0.906820\pi$
$798$		0			0
$799$	−2.87439			−0.101688
$800$		0			0
$801$	10.0753	−	17.4510i	0.355995	−	0.616601i
$802$		0			0
$803$	5.43465	−	3.13770i	0.191785	−	0.110727i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−50.1304	+	28.9428i	−1.76467	+	1.01883i
$808$		0			0
$809$	−7.75176	+	13.4264i	−0.272537	+	0.472048i	−0.969511	−	0.245048i	$-0.921196\pi$
$809$	−7.75176	+	13.4264i	−0.272537	+	0.472048i	0.696974	+	0.717097i	$0.254529\pi$
$810$		0			0
$811$	−36.6232			−1.28601			−0.643007	−	0.765861i	$-0.722313\pi$
$811$	−36.6232			−1.28601			−0.643007	+	0.765861i	$0.722313\pi$
$812$		0			0
$813$			11.4604i			0.401933i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.6170	+	7.28442i	−0.441413	+	0.254850i
$818$		0			0
$819$	35.7638	+	39.1508i	1.24969	+	1.36804i
$820$		0			0
$821$	21.6649	+	37.5246i	0.756109	+	1.30962i	0.944821	+	0.327586i	$0.106235\pi$
$821$	21.6649	+	37.5246i	0.756109	+	1.30962i	−0.188713	+	0.982032i	$0.560431\pi$
$822$		0			0
$823$	35.5541	+	20.5272i	1.23934	+	0.715532i	0.968959	−	0.247222i	$-0.0795178\pi$
$823$	35.5541	+	20.5272i	1.23934	+	0.715532i	0.270378	+	0.962754i	$0.412851\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			30.0473i			1.04485i	0.852686	+	0.522423i	$0.174972\pi$
$827$			30.0473i			1.04485i	−0.852686	+	0.522423i	$0.825028\pi$
$828$		0			0
$829$	−21.0146	+	36.3984i	−0.729868	+	1.26417i	0.227071	+	0.973878i	$0.427085\pi$
$829$	−21.0146	+	36.3984i	−0.729868	+	1.26417i	−0.956939	+	0.290290i	$0.906248\pi$
$830$		0			0
$831$	8.35977	+	14.4795i	0.289997	+	0.502290i
$832$		0			0
$833$	49.9702	+	4.52761i	1.73136	+	0.156872i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.29240	+	0.746168i	0.0446719	+	0.0257913i
$838$		0			0
$839$	−3.38893			−0.116999			−0.0584994	−	0.998287i	$-0.518632\pi$
$839$	−3.38893			−0.116999			−0.0584994	+	0.998287i	$0.518632\pi$
$840$		0			0
$841$	−25.1196			−0.866195
$842$		0			0
$843$	24.9120	+	14.3830i	0.858015	+	0.495375i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−16.6796	+	15.2367i	−0.573119	+	0.523539i
$848$		0			0
$849$	9.82106	+	17.0106i	0.337058	+	0.583801i
$850$		0			0
$851$	19.2367	−	33.3189i	0.659425	−	1.14216i
$852$		0			0
$853$		−	25.1267i		−	0.860321i	−0.902752	−	0.430160i	$-0.858457\pi$
$853$		−	25.1267i		−	0.860321i	0.902752	−	0.430160i	$-0.141543\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.3412	−	23.8683i	−1.41219	−	0.815327i	−0.416594	−	0.909093i	$-0.636776\pi$
$857$	−41.3412	−	23.8683i	−1.41219	−	0.815327i	−0.995594	+	0.0937657i	$0.970110\pi$
$858$		0			0
$859$	−20.5211	−	35.5436i	−0.700171	−	1.21273i	−0.968406	−	0.249379i	$-0.919774\pi$
$859$	−20.5211	−	35.5436i	−0.700171	−	1.21273i	0.268235	−	0.963354i	$-0.413560\pi$
$860$		0			0
$861$	−18.2260	+	57.4954i	−0.621142	+	1.95944i
$862$		0			0
$863$	−26.9617	+	15.5663i	−0.917786	+	0.529884i	−0.882928	−	0.469509i	$-0.844431\pi$
$863$	−26.9617	+	15.5663i	−0.917786	+	0.529884i	−0.0348576	+	0.999392i	$0.511098\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	88.3117i		−	2.99922i
$868$		0			0
$869$	−20.1980			−0.685169
$870$		0			0
$871$	−2.40101	+	4.15867i	−0.0813552	+	0.140911i
$872$		0			0
$873$	−0.726760	+	0.419595i	−0.0245971	+	0.0142011i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.87600	−	3.96986i	0.232186	−	0.134053i	−0.379394	−	0.925235i	$-0.623868\pi$
$877$	6.87600	−	3.96986i	0.232186	−	0.134053i	0.611580	+	0.791182i	$0.290534\pi$
$878$		0			0
$879$	−7.86789	+	13.6276i	−0.265377	+	0.459647i
$880$		0			0
$881$	−29.3709			−0.989530			−0.494765	−	0.869027i	$-0.664746\pi$
$881$	−29.3709			−0.989530			−0.494765	+	0.869027i	$0.664746\pi$
$882$		0			0
$883$			26.9718i			0.907674i	0.891085	+	0.453837i	$0.149945\pi$
$883$			26.9718i			0.907674i	−0.891085	+	0.453837i	$0.850055\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.3390	+	11.7427i	−0.682917	+	0.394282i	−0.800953	−	0.598727i	$-0.795673\pi$
$887$	−20.3390	+	11.7427i	−0.682917	+	0.394282i	0.118036	+	0.993009i	$0.462340\pi$
$888$		0			0
$889$	−33.2664	+	7.32102i	−1.11572	+	0.245539i
$890$		0			0
$891$	−5.36880	−	9.29903i	−0.179861	−	0.311529i
$892$		0			0
$893$	1.10015	+	0.635170i	0.0368150	+	0.0212552i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	82.0664i		−	2.74012i
$898$		0			0
$899$	0.955246	−	1.65453i	0.0318592	−	0.0551818i
$900$		0			0
$901$	−34.1860	−	59.2118i	−1.13890	−	1.97263i
$902$		0			0
$903$	29.7959	+	9.44531i	0.991547	+	0.314320i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.30250	−	4.79345i	−0.275680	−	0.159164i	0.355786	−	0.934567i	$-0.384213\pi$
$907$	−8.30250	−	4.79345i	−0.275680	−	0.159164i	−0.631466	+	0.775403i	$0.717547\pi$
$908$		0			0
$909$	−45.0000			−1.49256
$910$		0			0
$911$	−3.78994			−0.125566			−0.0627831	−	0.998027i	$-0.519998\pi$
$911$	−3.78994			−0.125566			−0.0627831	+	0.998027i	$0.519998\pi$
$912$		0			0
$913$	−23.2434	−	13.4196i	−0.769245	−	0.444124i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.445604	+	0.407055i	−0.0147151	+	0.0134421i
$918$		0			0
$919$	11.6950	+	20.2563i	0.385782	+	0.668194i	0.991877	−	0.127198i	$-0.0405983\pi$
$919$	11.6950	+	20.2563i	0.385782	+	0.668194i	−0.606095	+	0.795392i	$0.707265\pi$
$920$		0			0
$921$	33.9191	−	58.7497i	1.11767	−	1.93587i
$922$		0			0
$923$			67.5930i			2.22485i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−10.5064	−	6.06587i	−0.345075	−	0.199229i
$928$		0			0
$929$	25.1287	+	43.5241i	0.824445	+	1.42798i	0.902343	+	0.431019i	$0.141846\pi$
$929$	25.1287	+	43.5241i	0.824445	+	1.42798i	−0.0778977	+	0.996961i	$0.524821\pi$
$930$		0			0
$931$	−18.1252	−	12.7751i	−0.594028	−	0.418687i
$932$		0			0
$933$	−43.0540	+	24.8572i	−1.40952	+	0.813790i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	2.43621i		−	0.0795875i	−0.999208	−	0.0397937i	$-0.987330\pi$
$937$		−	2.43621i		−	0.0795875i	0.999208	−	0.0397937i	$-0.0126701\pi$
$938$		0			0
$939$	22.3658			0.729881
$940$		0			0
$941$	11.9824	−	20.7541i	0.390615	−	0.676565i	−0.601916	−	0.798560i	$-0.705596\pi$
$941$	11.9824	−	20.7541i	0.390615	−	0.676565i	0.992531	+	0.121994i	$0.0389290\pi$
$942$		0			0
$943$	44.0890	−	25.4548i	1.43574	−	0.828922i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−44.3075	+	25.5809i	−1.43980	+	0.831269i	−0.997835	−	0.0657639i	$-0.979052\pi$
$947$	−44.3075	+	25.5809i	−1.43980	+	0.831269i	−0.441964	+	0.897033i	$0.645718\pi$
$948$		0			0
$949$	11.1377	−	19.2911i	0.361545	−	0.626214i
$950$		0			0
$951$	−39.2402			−1.27245
$952$		0			0
$953$		−	33.3306i		−	1.07968i	−0.841766	−	0.539842i	$-0.818484\pi$
$953$		−	33.3306i		−	1.07968i	0.841766	−	0.539842i	$-0.181516\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.87521	−	3.96941i	0.222244	−	0.128313i
$958$		0			0
$959$	−7.73623	+	24.4045i	−0.249816	+	0.788063i
$960$		0			0
$961$	15.0297	+	26.0322i	0.484829	+	0.839748i
$962$		0			0
$963$	−55.2820	−	31.9171i	−1.78144	−	1.02851i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	31.8392i		−	1.02388i	−0.859021	−	0.511940i	$-0.828927\pi$
$967$		−	31.8392i		−	1.02388i	0.859021	−	0.511940i	$-0.171073\pi$
$968$		0			0
$969$	−29.1649	+	50.5150i	−0.936910	+	1.62278i
$970$		0			0
$971$	−0.973375	−	1.68594i	−0.0312371	−	0.0541042i	0.849984	−	0.526808i	$-0.176611\pi$
$971$	−0.973375	−	1.68594i	−0.0312371	−	0.0541042i	−0.881221	+	0.472704i	$0.843278\pi$
$972$		0			0
$973$	7.03470	+	31.9653i	0.225522	+	1.02476i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	43.4049	+	25.0598i	1.38865	+	0.801735i	0.993163	−	0.116739i	$-0.0372440\pi$
$977$	43.4049	+	25.0598i	1.38865	+	0.801735i	0.395483	+	0.918473i	$0.370577\pi$
$978$		0			0
$979$	−8.78397			−0.280737
$980$		0			0
$981$	21.2503			0.678470
$982$		0			0
$983$	−41.5014	−	23.9608i	−1.32369	−	0.764232i	−0.339374	−	0.940652i	$-0.610215\pi$
$983$	−41.5014	−	23.9608i	−1.32369	−	0.764232i	−0.984315	+	0.176420i	$0.943548\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.585788	−	2.66179i	−0.0186458	−	0.0847259i
$988$		0			0
$989$	−13.1915	−	22.8483i	−0.419465	−	0.726534i
$990$		0			0
$991$	−4.43466	+	7.68106i	−0.140872	+	0.243997i	−0.927825	−	0.373015i	$-0.878324\pi$
$991$	−4.43466	+	7.68106i	−0.140872	+	0.243997i	0.786953	+	0.617012i	$0.211657\pi$
$992$		0			0
$993$			43.0251i			1.36536i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.5742	−	6.10503i	−0.334889	−	0.193348i	0.323121	−	0.946358i	$-0.395268\pi$
$997$	−10.5742	−	6.10503i	−0.334889	−	0.193348i	−0.658010	+	0.753010i	$0.728601\pi$
$998$		0			0
$999$	5.15972	+	8.93690i	0.163246	+	0.282751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.r.d.249.2		12
5.2	odd	4		700.2.i.e.501.1	yes	6
5.3	odd	4		700.2.i.d.501.3	yes	6
5.4	even	2	inner	700.2.r.d.249.5		12
7.2	even	3	inner	700.2.r.d.149.5		12
7.3	odd	6		4900.2.e.s.2549.2		6
7.4	even	3		4900.2.e.t.2549.5		6
35.2	odd	12		700.2.i.e.401.1	yes	6
35.3	even	12		4900.2.a.bb.1.3		3
35.4	even	6		4900.2.e.t.2549.2		6
35.9	even	6	inner	700.2.r.d.149.2		12
35.17	even	12		4900.2.a.bd.1.1		3
35.18	odd	12		4900.2.a.bc.1.1		3
35.23	odd	12		700.2.i.d.401.3	✓	6
35.24	odd	6		4900.2.e.s.2549.5		6
35.32	odd	12		4900.2.a.ba.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.3	✓	6	35.23	odd	12
700.2.i.d.501.3	yes	6	5.3	odd	4
700.2.i.e.401.1	yes	6	35.2	odd	12
700.2.i.e.501.1	yes	6	5.2	odd	4
700.2.r.d.149.2		12	35.9	even	6	inner
700.2.r.d.149.5		12	7.2	even	3	inner
700.2.r.d.249.2		12	1.1	even	1	trivial
700.2.r.d.249.5		12	5.4	even	2	inner
4900.2.a.ba.1.3		3	35.32	odd	12
4900.2.a.bb.1.3		3	35.3	even	12
4900.2.a.bc.1.1		3	35.18	odd	12
4900.2.a.bd.1.1		3	35.17	even	12
4900.2.e.s.2549.2		6	7.3	odd	6
4900.2.e.s.2549.5		6	35.24	odd	6
4900.2.e.t.2549.2		6	35.4	even	6
4900.2.e.t.2549.5		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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-2.22469 - 1.28442i) q^{3} +(0.568650 + 2.58392i) q^{7} +(1.79949 + 3.11682i) q^{9} +O(q^{10})\)	\(q+(-2.22469 - 1.28442i) q^{3} +(0.568650 + 2.58392i) q^{7} +(1.79949 + 3.11682i) q^{9} +(0.784425 - 1.35866i) q^{11} -5.56885i q^{13} +(-6.20753 - 3.58392i) q^{17} +(1.58392 + 2.74343i) q^{19} +(2.05378 - 6.47880i) q^{21} +(-4.96812 + 2.86834i) q^{23} -1.53871i q^{27} -1.96986 q^{29} +(-0.484931 + 0.839925i) q^{31} +(-3.49020 + 2.01507i) q^{33} +(-5.80804 + 3.35327i) q^{37} +(-7.15277 + 12.3890i) q^{39} -8.87439 q^{41} +4.59899i q^{43} +(0.347286 - 0.200506i) q^{47} +(-6.35327 + 2.93869i) q^{49} +(9.20655 + 15.9462i) q^{51} +(8.26077 + 4.76936i) q^{53} -8.13770i q^{57} +(-2.28442 + 3.95674i) q^{59} +(-7.65277 - 13.2550i) q^{61} +(-7.03032 + 6.42212i) q^{63} +(-0.746774 - 0.431150i) q^{67} +14.7367 q^{69} -12.1377 q^{71} +(3.46410 + 2.00000i) q^{73} +(3.95674 + 1.25429i) q^{77} +(-6.43719 - 11.1495i) q^{79} +(3.42212 - 5.92729i) q^{81} -17.1076i q^{83} +(4.38233 + 2.53014i) q^{87} +(-2.79949 - 4.84887i) q^{89} +(14.3895 - 3.16673i) q^{91} +(2.15764 - 1.24571i) q^{93} +0.233174i q^{97} +5.64627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9}+O(q^{10}) \) 12 * q + 16 * q^9	\( 12 q + 16 q^{9} - 8 q^{11} - 4 q^{19} - 22 q^{21} + 6 q^{31} - 28 q^{39} + 44 q^{41} - 24 q^{49} + 6 q^{51} - 10 q^{59} - 34 q^{61} + 96 q^{69} - 76 q^{71} - 2 q^{79} - 46 q^{81} - 28 q^{89} + 34 q^{91} - 84 q^{99}+O(q^{100}) \) 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

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