LMFDB - Embedded newform 1400.2.bh.i.249.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1400,2,Mod(249,1400)] 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("1400.249"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1400, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,18,0,-6] 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.32905425960566784.37
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 $ x^12 + 36x^10 + 432x^8 + 2040x^6 + 3780x^4 + 2592*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.6
Root			$2.22358i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.i.849.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.84918 + 1.64497i) q^{3} +(-0.0641892 - 2.64497i) q^{7} +(3.91187 + 6.77556i) q^{9} +(-2.91187 + 5.04351i) q^{11} +2.75615i q^{13} +(1.73205 + 1.00000i) q^{17} +(-0.378076 - 0.654846i) q^{19} +(4.16802 - 7.64158i) q^{21} +(-0.462279 + 0.266897i) q^{23} +15.8698i q^{27} +0.823739 q^{29} +(1.28995 - 2.23425i) q^{31} +(-16.5929 + 9.57989i) q^{33} +(-4.11895 + 2.37808i) q^{37} +(-4.53379 + 7.85276i) q^{39} +6.06759 q^{41} +0.710055i q^{43} +(11.1642 - 6.44566i) q^{47} +(-6.99176 + 0.339557i) q^{49} +(3.28995 + 5.69835i) q^{51} +(7.27776 + 4.20181i) q^{53} -2.48770i q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.70181 - 8.14378i) q^{61} +(17.6701 - 10.7817i) q^{63} +(10.2796 + 5.93492i) q^{67} -1.75615 q^{69} +(-3.04174 - 1.75615i) q^{73} +(13.5268 + 7.37808i) q^{77} +(-4.75615 - 8.23790i) q^{79} +(-14.3698 + 24.8893i) q^{81} -6.71005i q^{83} +(2.34698 + 1.35503i) q^{87} +(0.878076 + 1.52087i) q^{89} +(7.28995 - 0.176915i) q^{91} +(7.35056 - 4.24385i) q^{93} +2.00000i q^{97} -45.5634 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) $ 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	2.84918	+	1.64497i	1.64497	+	0.949725i	0.979028	+	0.203724i	$0.0653044\pi$
$3$	2.84918	+	1.64497i	1.64497	+	0.949725i	0.665944	+	0.746002i	$0.268029\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.0641892	−	2.64497i	−0.0242612	−	0.999706i
$7$	−0.0641892	−	2.64497i	−0.0242612	−	0.999706i
$8$		0			0
$9$	3.91187	+	6.77556i	1.30396	+	2.25852i
$10$		0			0
$11$	−2.91187	+	5.04351i	−0.877962	+	1.52067i	−0.0243876	+	0.999703i	$0.507764\pi$
$11$	−2.91187	+	5.04351i	−0.877962	+	1.52067i	−0.853574	+	0.520972i	$0.825570\pi$
$12$		0			0
$13$			2.75615i			0.764419i	0.924076	+	0.382209i	$0.124837\pi$
$13$			2.75615i			0.764419i	−0.924076	+	0.382209i	$0.875163\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	−0.378076	−	0.654846i	−0.0867365	−	0.150232i	0.819393	−	0.573232i	$-0.194310\pi$
$19$	−0.378076	−	0.654846i	−0.0867365	−	0.150232i	−0.906130	+	0.423000i	$0.860977\pi$
$20$		0			0
$21$	4.16802	−	7.64158i	0.909537	−	1.66753i
$22$		0			0
$23$	−0.462279	+	0.266897i	−0.0963918	+	0.0556518i	−0.547421	−	0.836857i	$-0.684390\pi$
$23$	−0.462279	+	0.266897i	−0.0963918	+	0.0556518i	0.451029	+	0.892509i	$0.351057\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			15.8698i			3.05415i
$28$		0			0
$29$	0.823739			0.152964			0.0764822	−	0.997071i	$-0.475631\pi$
$29$	0.823739			0.152964			0.0764822	+	0.997071i	$0.475631\pi$
$30$		0			0
$31$	1.28995	−	2.23425i	0.231681	−	0.401283i	−0.726622	−	0.687038i	$-0.758911\pi$
$31$	1.28995	−	2.23425i	0.231681	−	0.401283i	0.958303	+	0.285754i	$0.0922441\pi$
$32$		0			0
$33$	−16.5929	+	9.57989i	−2.88845	+	1.66764i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.11895	+	2.37808i	−0.677151	+	0.390953i	−0.798781	−	0.601622i	$-0.794521\pi$
$37$	−4.11895	+	2.37808i	−0.677151	+	0.390953i	0.121630	+	0.992576i	$0.461188\pi$
$38$		0			0
$39$	−4.53379	+	7.85276i	−0.725988	+	1.25745i
$40$		0			0
$41$	6.06759			0.947598			0.473799	−	0.880633i	$-0.342882\pi$
$41$	6.06759			0.947598			0.473799	+	0.880633i	$0.342882\pi$
$42$		0			0
$43$			0.710055i			0.108282i	0.998533	+	0.0541412i	$0.0172421\pi$
$43$			0.710055i			0.108282i	−0.998533	+	0.0541412i	$0.982758\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	11.1642	−	6.44566i	1.62847	−	0.940197i	0.643918	−	0.765095i	$-0.277308\pi$
$47$	11.1642	−	6.44566i	1.62847	−	0.940197i	0.984550	−	0.175102i	$-0.0560255\pi$
$48$		0			0
$49$	−6.99176	+	0.339557i	−0.998823	+	0.0485082i
$50$		0			0
$51$	3.28995	+	5.69835i	0.460684	+	0.797929i
$52$		0			0
$53$	7.27776	+	4.20181i	0.999677	+	0.577164i	0.908153	−	0.418639i	$-0.137493\pi$
$53$	7.27776	+	4.20181i	0.999677	+	0.577164i	0.0915241	+	0.995803i	$0.470826\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.48770i		−	0.329504i
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−4.70181	−	8.14378i	−0.602006	−	1.04270i	−0.992517	−	0.122106i	$-0.961035\pi$
$61$	−4.70181	−	8.14378i	−0.602006	−	1.04270i	0.390511	−	0.920598i	$-0.372298\pi$
$62$		0			0
$63$	17.6701	−	10.7817i	2.22622	−	1.35837i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.2796	+	5.93492i	1.25585	+	0.725066i	0.972265	−	0.233881i	$-0.0751428\pi$
$67$	10.2796	+	5.93492i	1.25585	+	0.725066i	0.283585	+	0.958947i	$0.408476\pi$
$68$		0			0
$69$	−1.75615			−0.211416
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−3.04174	−	1.75615i	−0.356009	−	0.205542i	0.311320	−	0.950305i	$-0.399229\pi$
$73$	−3.04174	−	1.75615i	−0.356009	−	0.205542i	−0.667329	+	0.744763i	$0.732562\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.5268	+	7.37808i	1.54153	+	0.840810i
$78$		0			0
$79$	−4.75615	−	8.23790i	−0.535109	−	0.926836i	−0.999158	−	0.0410263i	$-0.986937\pi$
$79$	−4.75615	−	8.23790i	−0.535109	−	0.926836i	0.464049	−	0.885809i	$-0.346396\pi$
$80$		0			0
$81$	−14.3698	+	24.8893i	−1.59665	+	2.76548i
$82$		0			0
$83$		−	6.71005i		−	0.736524i	−0.929722	−	0.368262i	$-0.879953\pi$
$83$		−	6.71005i		−	0.736524i	0.929722	−	0.368262i	$-0.120047\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.34698	+	1.35503i	0.251622	+	0.145274i
$88$		0			0
$89$	0.878076	+	1.52087i	0.0930758	+	0.161212i	0.908804	−	0.417223i	$-0.136997\pi$
$89$	0.878076	+	1.52087i	0.0930758	+	0.161212i	−0.815728	+	0.578436i	$0.803663\pi$
$90$		0			0
$91$	7.28995	−	0.176915i	0.764194	−	0.0185458i
$92$		0			0
$93$	7.35056	−	4.24385i	0.762218	−	0.440067i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		0			0
$99$	−45.5634			−4.57929
$100$		0			0
$101$	−1.16802	+	2.02307i	−0.116222	+	0.201303i	−0.918268	−	0.395960i	$-0.870412\pi$
$101$	−1.16802	+	2.02307i	−0.116222	+	0.201303i	0.802045	+	0.597263i	$0.203745\pi$
$102$		0			0
$103$	−1.92462	+	1.11118i	−0.189638	+	0.109488i	−0.591813	−	0.806075i	$-0.701588\pi$
$103$	−1.92462	+	1.11118i	−0.189638	+	0.109488i	0.402175	+	0.915563i	$0.368254\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.7437	+	7.93492i	−1.32865	+	0.767097i	−0.985091	−	0.172033i	$-0.944966\pi$
$107$	−13.7437	+	7.93492i	−1.32865	+	0.767097i	−0.343561	+	0.939131i	$0.611633\pi$
$108$		0			0
$109$	−1.63423	+	2.83056i	−0.156531	+	0.271119i	−0.933615	−	0.358277i	$-0.883364\pi$
$109$	−1.63423	+	2.83056i	−0.156531	+	0.271119i	0.777085	+	0.629396i	$0.216698\pi$
$110$		0			0
$111$	−15.6475			−1.48519
$112$		0			0
$113$		−	13.1598i		−	1.23797i	−0.785404	−	0.618984i	$-0.787545\pi$
$113$		−	13.1598i		−	1.23797i	0.785404	−	0.618984i	$-0.212455\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−18.6745	+	10.7817i	−1.72645	+	0.996769i
$118$		0			0
$119$	2.53379	−	4.64542i	0.232272	−	0.425845i
$120$		0			0
$121$	−11.4580	−	19.8458i	−1.04163	−	1.80416i
$122$		0			0
$123$	17.2876	+	9.98101i	1.55877	+	0.899958i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	11.9159i		−	1.05737i	−0.848819	−	0.528684i	$-0.822686\pi$
$127$		−	11.9159i		−	1.05737i	0.848819	−	0.528684i	$-0.177314\pi$
$128$		0			0
$129$	−1.16802	+	2.02307i	−0.102839	+	0.178122i
$130$		0			0
$131$	−10.7817	−	18.6745i	−0.942002	−	1.63160i	−0.761646	−	0.647994i	$-0.775608\pi$
$131$	−10.7817	−	18.6745i	−0.942002	−	1.63160i	−0.180356	−	0.983601i	$-0.557725\pi$
$132$		0			0
$133$	−1.70778	+	1.04203i	−0.148084	+	0.0903558i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	0.640626	−	0.767853i	$-0.278675\pi$
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	−0.344668	+	0.938725i	$0.612008\pi$
$138$		0			0
$139$	−6.57989			−0.558099			−0.279049	−	0.960277i	$-0.590019\pi$
$139$	−6.57989			−0.558099			−0.279049	+	0.960277i	$0.590019\pi$
$140$		0			0
$141$	42.4118			3.57171
$142$		0			0
$143$	−13.9007	−	8.02555i	−1.16243	−	0.671130i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−20.4793	−	10.5338i	−1.68911	−	0.868813i
$148$		0			0
$149$	0.0543371	+	0.0941146i	0.00445147	+	0.00771017i	0.868243	−	0.496140i	$-0.165250\pi$
$149$	0.0543371	+	0.0941146i	0.00445147	+	0.00771017i	−0.863791	+	0.503850i	$0.831916\pi$
$150$		0			0
$151$	6.53379	−	11.3169i	0.531713	−	0.920953i	−0.467602	−	0.883939i	$-0.654882\pi$
$151$	6.53379	−	11.3169i	0.531713	−	0.920953i	0.999315	−	0.0370142i	$-0.0117847\pi$
$152$		0			0
$153$			15.6475i			1.26502i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.70011	+	4.44566i	0.614536	+	0.354803i	0.774739	−	0.632282i	$-0.217881\pi$
$157$	7.70011	+	4.44566i	0.614536	+	0.354803i	−0.160203	+	0.987084i	$0.551215\pi$
$158$		0			0
$159$	13.8237	+	23.9434i	1.09629	+	1.89884i
$160$		0			0
$161$	0.735608	+	1.20558i	0.0579740	+	0.0950132i
$162$		0			0
$163$	−9.96995	+	5.75615i	−0.780907	+	0.450857i	−0.836751	−	0.547583i	$-0.815548\pi$
$163$	−9.96995	+	5.75615i	−0.780907	+	0.450857i	0.0558449	+	0.998439i	$0.482215\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	1.46621i		−	0.113458i	−0.998390	−	0.0567292i	$-0.981933\pi$
$167$		−	1.46621i		−	0.113458i	0.998390	−	0.0567292i	$-0.0180672\pi$
$168$		0			0
$169$	5.40363			0.415664
$170$		0			0
$171$	2.95797	−	5.12335i	0.226201	−	0.391792i
$172$		0			0
$173$	−9.73746	+	5.62192i	−0.740325	+	0.427427i	−0.822188	−	0.569217i	$-0.807247\pi$
$173$	−9.73746	+	5.62192i	−0.740325	+	0.427427i	0.0818623	+	0.996644i	$0.473913\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	22.7934	−	13.1598i	1.71326	−	0.989150i
$178$		0			0
$179$	3.66802	−	6.35320i	0.274161	−	0.474860i	−0.695762	−	0.718272i	$-0.744933\pi$
$179$	3.66802	−	6.35320i	0.274161	−	0.474860i	0.969923	+	0.243412i	$0.0782666\pi$
$180$		0			0
$181$	−18.4712			−1.37295			−0.686477	−	0.727151i	$-0.740844\pi$
$181$	−18.4712			−1.37295			−0.686477	+	0.727151i	$0.740844\pi$
$182$		0			0
$183$		−	30.9374i		−	2.28696i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.0870	+	5.82374i	−0.737635	+	0.425874i
$188$		0			0
$189$	41.9753	−	1.01867i	3.05325	−	0.0740975i
$190$		0			0
$191$	−7.28995	−	12.6266i	−0.527482	−	0.913625i	−0.999487	−	0.0320296i	$-0.989803\pi$
$191$	−7.28995	−	12.6266i	−0.527482	−	0.913625i	0.472005	−	0.881596i	$-0.343530\pi$
$192$		0			0
$193$	16.2876	+	9.40363i	1.17240	+	0.676888i	0.954245	−	0.299025i	$-0.0966615\pi$
$193$	16.2876	+	9.40363i	1.17240	+	0.676888i	0.218159	+	0.975913i	$0.429995\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.75615i		−	0.196368i	−0.995168	−	0.0981838i	$-0.968697\pi$
$197$		−	2.75615i		−	0.196368i	0.995168	−	0.0981838i	$-0.0313033\pi$
$198$		0			0
$199$	7.51230	−	13.0117i	0.532533	−	0.922374i	−0.466745	−	0.884392i	$-0.654574\pi$
$199$	7.51230	−	13.0117i	0.532533	−	0.922374i	0.999278	−	0.0379825i	$-0.0120931\pi$
$200$		0			0
$201$	19.5256	+	33.8192i	1.37723	+	2.38543i
$202$		0			0
$203$	−0.0528751	−	2.17877i	−0.00371111	−	0.152919i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.61675	−	2.08813i	−0.251381	−	0.145135i
$208$		0			0
$209$	4.40363			0.304605
$210$		0			0
$211$	−21.9159			−1.50875			−0.754377	−	0.656441i	$-0.772061\pi$
$211$	−21.9159			−1.50875			−0.754377	+	0.656441i	$0.772061\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.99233	−	3.26845i	−0.406786	−	0.221877i
$218$		0			0
$219$	−5.77764	−	10.0072i	−0.390417	−	0.676222i
$220$		0			0
$221$	−2.75615	+	4.77379i	−0.185399	+	0.321120i
$222$		0			0
$223$			18.8073i			1.25943i	0.776827	+	0.629714i	$0.216828\pi$
$223$			18.8073i			1.25943i	−0.776827	+	0.629714i	$0.783172\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.4384	+	8.33604i	0.958313	+	0.553283i	0.895654	−	0.444752i	$-0.146708\pi$
$227$	14.4384	+	8.33604i	0.958313	+	0.553283i	0.0626599	+	0.998035i	$0.480042\pi$
$228$		0			0
$229$	9.75615	+	16.8982i	0.644705	+	1.11666i	0.984370	+	0.176115i	$0.0563530\pi$
$229$	9.75615	+	16.8982i	0.644705	+	1.11666i	−0.339665	+	0.940546i	$0.610314\pi$
$230$		0			0
$231$	26.4036	+	43.2727i	1.73723	+	2.84714i
$232$		0			0
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.106773	−	0.994283i	$-0.465948\pi$
$233$	15.5885	−	9.00000i	1.02123	−	0.589610i	0.914461	+	0.404674i	$0.132615\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	31.2950i		−	2.03283i
$238$		0			0
$239$	16.0922			1.04092			0.520459	−	0.853887i	$-0.325761\pi$
$239$	16.0922			1.04092			0.520459	+	0.853887i	$0.325761\pi$
$240$		0			0
$241$	−0.445663	+	0.771911i	−0.0287077	+	0.0497231i	−0.880022	−	0.474932i	$-0.842473\pi$
$241$	−0.445663	+	0.771911i	−0.0287077	+	0.0497231i	0.851315	+	0.524655i	$0.175806\pi$
$242$		0			0
$243$	−40.6533	+	23.4712i	−2.60791	+	1.50568i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.80486	−	1.04203i	0.114840	−	0.0663030i
$248$		0			0
$249$	11.0379	−	19.1181i	0.699496	−	1.21156i
$250$		0			0
$251$	17.4712			1.10277			0.551387	−	0.834250i	$-0.314099\pi$
$251$	17.4712			1.10277			0.551387	+	0.834250i	$0.314099\pi$
$252$		0			0
$253$		−	3.10867i		−	0.195441i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.08349	−	3.51230i	0.379478	−	0.219091i	−0.298113	−	0.954530i	$-0.596357\pi$
$257$	6.08349	−	3.51230i	0.379478	−	0.219091i	0.677591	+	0.735439i	$0.263024\pi$
$258$		0			0
$259$	6.55434	+	10.7419i	0.407267	+	0.667467i
$260$		0			0
$261$	3.22236	+	5.58129i	0.199459	+	0.345473i
$262$		0			0
$263$	−15.3959	−	8.88882i	−0.949351	−	0.548108i	−0.0564719	−	0.998404i	$-0.517985\pi$
$263$	−15.3959	−	8.88882i	−0.949351	−	0.548108i	−0.892879	+	0.450296i	$0.851318\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			5.77764i			0.353586i
$268$		0			0
$269$	−4.70181	+	8.14378i	−0.286675	+	0.496535i	−0.973014	−	0.230746i	$-0.925883\pi$
$269$	−4.70181	+	8.14378i	−0.286675	+	0.496535i	0.686339	+	0.727282i	$0.259217\pi$
$270$		0			0
$271$	−3.51230	−	6.08349i	−0.213357	−	0.369546i	0.739406	−	0.673260i	$-0.235106\pi$
$271$	−3.51230	−	6.08349i	−0.213357	−	0.369546i	−0.952763	+	0.303714i	$0.901773\pi$
$272$		0			0
$273$	21.0614	+	11.4877i	1.27469	+	0.695267i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	23.5211	+	13.5799i	1.41324	+	0.815937i	0.995693	−	0.0927170i	$-0.0295552\pi$
$277$	23.5211	+	13.5799i	1.41324	+	0.815937i	0.417551	+	0.908653i	$0.362889\pi$
$278$		0			0
$279$	20.1844			1.20841
$280$		0			0
$281$	−0.620977			−0.0370444			−0.0185222	−	0.999828i	$-0.505896\pi$
$281$	−0.620977			−0.0370444			−0.0185222	+	0.999828i	$0.505896\pi$
$282$		0			0
$283$	−2.73645	−	1.57989i	−0.162665	−	0.0939147i	0.416458	−	0.909155i	$-0.363271\pi$
$283$	−2.73645	−	1.57989i	−0.162665	−	0.0939147i	−0.579123	+	0.815240i	$0.696605\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.389474	−	16.0486i	−0.0229899	−	0.947319i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−3.28995	+	5.69835i	−0.192860	+	0.334043i
$292$		0			0
$293$			11.2438i			0.656873i	0.944526	+	0.328436i	$0.106522\pi$
$293$			11.2438i			0.656873i	−0.944526	+	0.328436i	$0.893478\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−80.0396	−	46.2109i	−4.64437	−	2.68143i
$298$		0			0
$299$	−0.735608	−	1.27411i	−0.0425413	−	0.0736837i
$300$		0			0
$301$	1.87808	−	0.0455779i	0.108250	−	0.00262706i
$302$		0			0
$303$	−6.65579	+	3.84272i	−0.382365	+	0.220759i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	23.5173i		−	1.34220i	−0.741365	−	0.671102i	$-0.765821\pi$
$307$		−	23.5173i		−	1.34220i	0.741365	−	0.671102i	$-0.234179\pi$
$308$		0			0
$309$	−7.31144			−0.415933
$310$		0			0
$311$	14.5799	−	25.2531i	0.826750	−	1.43197i	−0.0738250	−	0.997271i	$-0.523521\pi$
$311$	14.5799	−	25.2531i	0.826750	−	1.43197i	0.900575	−	0.434701i	$-0.143146\pi$
$312$		0			0
$313$	−20.9443	+	12.0922i	−1.18384	+	0.683491i	−0.956900	−	0.290417i	$-0.906206\pi$
$313$	−20.9443	+	12.0922i	−1.18384	+	0.683491i	−0.226941	+	0.973908i	$0.572873\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.5094	+	6.06759i	−0.590265	+	0.340790i	−0.765202	−	0.643790i	$-0.777361\pi$
$317$	−10.5094	+	6.06759i	−0.590265	+	0.340790i	0.174937	+	0.984580i	$0.444028\pi$
$318$		0			0
$319$	−2.39862	+	4.15453i	−0.134297	+	0.232609i
$320$		0			0
$321$	−52.2109			−2.91413
$322$		0			0
$323$		−	1.51230i		−	0.0841468i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−9.31240	+	5.37652i	−0.514977	+	0.297322i
$328$		0			0
$329$	−17.7652	−	29.1153i	−0.979428	−	1.60518i
$330$		0			0
$331$	0.911869	+	1.57940i	0.0501209	+	0.0868119i	0.889997	−	0.455966i	$-0.150706\pi$
$331$	0.911869	+	1.57940i	0.0501209	+	0.0868119i	−0.839877	+	0.542778i	$0.817373\pi$
$332$		0			0
$333$	−32.2256	−	18.6054i	−1.76595	−	1.01957i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			17.7827i			0.968683i	0.874879	+	0.484341i	$0.160941\pi$
$337$			17.7827i			0.968683i	−0.874879	+	0.484341i	$0.839059\pi$
$338$		0			0
$339$	21.6475	−	37.4945i	1.17573	−	2.03642i
$340$		0			0
$341$	7.51230	+	13.0117i	0.406814	+	0.704623i
$342$		0			0
$343$	1.34692	+	18.4712i	0.0727266	+	0.997352i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.11713	−	0.644973i	−0.0599704	−	0.0346239i	0.469715	−	0.882818i	$-0.344357\pi$
$347$	−1.11713	−	0.644973i	−0.0599704	−	0.0346239i	−0.529685	+	0.848194i	$0.677690\pi$
$348$		0			0
$349$	−1.31144			−0.0701995			−0.0350998	−	0.999384i	$-0.511175\pi$
$349$	−1.31144			−0.0701995			−0.0350998	+	0.999384i	$0.511175\pi$
$350$		0			0
$351$	−43.7397			−2.33465
$352$		0			0
$353$	9.54759	+	5.51230i	0.508167	+	0.293390i	0.732080	−	0.681219i	$-0.238550\pi$
$353$	9.54759	+	5.51230i	0.508167	+	0.293390i	−0.223913	+	0.974609i	$0.571883\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	14.8608	−	9.06759i	0.786517	−	0.479908i
$358$		0			0
$359$	5.11368	+	8.85716i	0.269890	+	0.467463i	0.968833	−	0.247714i	$-0.0796794\pi$
$359$	5.11368	+	8.85716i	0.269890	+	0.467463i	−0.698943	+	0.715177i	$0.746346\pi$
$360$		0			0
$361$	9.21412	−	15.9593i	0.484954	−	0.839964i
$362$		0			0
$363$		−	75.3922i		−	3.95706i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	15.0178	+	8.67053i	0.783922	+	0.452598i	0.837819	−	0.545949i	$-0.183831\pi$
$367$	15.0178	+	8.67053i	0.783922	+	0.452598i	−0.0538962	+	0.998547i	$0.517164\pi$
$368$		0			0
$369$	23.7356	+	41.1113i	1.23563	+	2.14017i
$370$		0			0
$371$	10.6465	−	19.5192i	0.552740	−	1.01339i
$372$		0			0
$373$	−15.4002	+	8.89133i	−0.797394	+	0.460375i	−0.842559	−	0.538604i	$-0.818952\pi$
$373$	−15.4002	+	8.89133i	−0.797394	+	0.460375i	0.0451654	+	0.998980i	$0.485619\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.27035i			0.116929i
$378$		0			0
$379$	33.2109			1.70593			0.852964	−	0.521969i	$-0.174802\pi$
$379$	33.2109			1.70593			0.852964	+	0.521969i	$0.174802\pi$
$380$		0			0
$381$	19.6014	−	33.9506i	1.00421	−	1.73934i
$382$		0			0
$383$	12.7835	−	7.38058i	0.653208	−	0.377130i	−0.136476	−	0.990643i	$-0.543578\pi$
$383$	12.7835	−	7.38058i	0.653208	−	0.377130i	0.789684	+	0.613513i	$0.210244\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.81102	+	2.77764i	−0.244558	+	0.141195i
$388$		0			0
$389$	−11.4036	+	19.7517i	−0.578187	+	1.00145i	0.417500	+	0.908677i	$0.362906\pi$
$389$	−11.4036	+	19.7517i	−0.578187	+	1.00145i	−0.995687	+	0.0927724i	$0.970427\pi$
$390$		0			0
$391$	−1.06759			−0.0539902
$392$		0			0
$393$		−	70.9424i		−	3.57857i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	12.3585	−	7.13517i	0.620255	−	0.358104i	−0.156714	−	0.987644i	$-0.550090\pi$
$397$	12.3585	−	7.13517i	0.620255	−	0.358104i	0.776968	+	0.629540i	$0.216757\pi$
$398$		0			0
$399$	−6.57989	+	0.159683i	−0.329407	+	0.00799416i
$400$		0			0
$401$	5.74385	+	9.94864i	0.286834	+	0.496811i	0.973052	−	0.230585i	$-0.0740638\pi$
$401$	5.74385	+	9.94864i	0.286834	+	0.496811i	−0.686218	+	0.727396i	$0.740730\pi$
$402$		0			0
$403$	6.15793	+	3.55528i	0.306748	+	0.177101i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	27.6986i		−	1.37297i
$408$		0			0
$409$	0.899566	−	1.55809i	0.0444807	−	0.0770428i	−0.842928	−	0.538027i	$-0.819170\pi$
$409$	0.899566	−	1.55809i	0.0444807	−	0.0770428i	0.887409	+	0.460984i	$0.152503\pi$
$410$		0			0
$411$	6.57989	+	11.3967i	0.324562	+	0.562158i
$412$		0			0
$413$	−18.5817	−	10.1352i	−0.914344	−	0.498719i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−18.7473	−	10.8237i	−0.918058	−	0.530041i
$418$		0			0
$419$	−27.4282			−1.33996			−0.669978	−	0.742381i	$-0.733697\pi$
$419$	−27.4282			−1.33996			−0.669978	+	0.742381i	$0.733697\pi$
$420$		0			0
$421$	2.91593			0.142114			0.0710569	−	0.997472i	$-0.477363\pi$
$421$	2.91593			0.142114			0.0710569	+	0.997472i	$0.477363\pi$
$422$		0			0
$423$	87.3459	+	50.4292i	4.24690	+	2.45195i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−21.2383	+	12.9589i	−1.02779	+	0.627126i
$428$		0			0
$429$	−26.4036	−	45.7324i	−1.27478	−	2.20798i
$430$		0			0
$431$	−7.28995	+	12.6266i	−0.351144	+	0.608200i	−0.986450	−	0.164061i	$-0.947541\pi$
$431$	−7.28995	+	12.6266i	−0.351144	+	0.608200i	0.635306	+	0.772261i	$0.280874\pi$
$432$		0			0
$433$			21.1598i			1.01687i	0.861099	+	0.508437i	$0.169777\pi$
$433$			21.1598i			1.01687i	−0.861099	+	0.508437i	$0.830223\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.349553	+	0.201814i	0.0167214	+	0.00965409i
$438$		0			0
$439$	−15.4712	−	26.7969i	−0.738401	−	1.27895i	−0.953215	−	0.302293i	$-0.902248\pi$
$439$	−15.4712	−	26.7969i	−0.738401	−	1.27895i	0.214814	−	0.976655i	$-0.431085\pi$
$440$		0			0
$441$	−29.6515	−	46.0448i	−1.41198	−	2.19261i
$442$		0			0
$443$	32.4909	−	18.7587i	1.54369	−	0.891251i	0.545090	−	0.838377i	$-0.316495\pi$
$443$	32.4909	−	18.7587i	1.54369	−	0.891251i	0.998601	−	0.0528732i	$-0.0168379\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			0.357532i			0.0169107i
$448$		0			0
$449$	−31.0922			−1.46733			−0.733666	−	0.679511i	$-0.762192\pi$
$449$	−31.0922			−1.46733			−0.733666	+	0.679511i	$0.762192\pi$
$450$		0			0
$451$	−17.6680	+	30.6019i	−0.831955	+	1.44099i
$452$		0			0
$453$	37.2319	−	21.4958i	1.74931	−	1.00996i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.76940	−	2.17626i	0.176325	−	0.101801i	−0.409240	−	0.912427i	$-0.634206\pi$
$457$	3.76940	−	2.17626i	0.176325	−	0.101801i	0.585565	+	0.810626i	$0.300873\pi$
$458$		0			0
$459$	−15.8698	+	27.4874i	−0.740740	+	1.28300i
$460$		0			0
$461$	37.2950			1.73700			0.868500	−	0.495690i	$-0.165085\pi$
$461$	37.2950			1.73700			0.868500	+	0.495690i	$0.165085\pi$
$462$		0			0
$463$		−	9.81873i		−	0.456315i	−0.973624	−	0.228158i	$-0.926730\pi$
$463$		−	9.81873i		−	0.456315i	0.973624	−	0.228158i	$-0.0732701\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.7473	−	11.4011i	0.913797	−	0.527581i	0.0321463	−	0.999483i	$-0.489766\pi$
$467$	19.7473	−	11.4011i	0.913797	−	0.527581i	0.881651	+	0.471902i	$0.156432\pi$
$468$		0			0
$469$	15.0379	−	27.5702i	0.694384	−	1.27307i
$470$		0			0
$471$	14.6260	+	25.3330i	0.673930	+	1.16728i
$472$		0			0
$473$	−3.58117	−	2.06759i	−0.164662	−	0.0950678i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			65.7478i			3.01038i
$478$		0			0
$479$	−10.2224	+	17.7056i	−0.467071	+	0.808991i	−0.999292	−	0.0376140i	$-0.988024\pi$
$479$	−10.2224	+	17.7056i	−0.467071	+	0.808991i	0.532221	+	0.846606i	$0.321358\pi$
$480$		0			0
$481$	−6.55434	−	11.3524i	−0.298852	−	0.517627i
$482$		0			0
$483$	0.112726	+	4.64497i	0.00512921	+	0.211354i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−37.0722	−	21.4036i	−1.67990	−	0.969891i	−0.961720	−	0.274034i	$-0.911642\pi$
$487$	−37.0722	−	21.4036i	−1.67990	−	0.969891i	−0.718181	−	0.695857i	$-0.755025\pi$
$488$		0			0
$489$	−37.8748			−1.71276
$490$		0			0
$491$	−18.8502			−0.850699			−0.425350	−	0.905029i	$-0.639849\pi$
$491$	−18.8502			−0.850699			−0.425350	+	0.905029i	$0.639849\pi$
$492$		0			0
$493$	1.42676	+	0.823739i	0.0642579	+	0.0370993i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	13.8698	+	24.0233i	0.620899	+	1.07543i	0.989319	+	0.145769i	$0.0465657\pi$
$499$	13.8698	+	24.0233i	0.620899	+	1.07543i	−0.368420	+	0.929660i	$0.620101\pi$
$500$		0			0
$501$	2.41187	−	4.17748i	0.107754	−	0.186636i
$502$		0			0
$503$			14.7101i			0.655889i	0.944697	+	0.327944i	$0.106356\pi$
$503$			14.7101i			0.655889i	−0.944697	+	0.327944i	$0.893644\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	15.3959	+	8.88882i	0.683755	+	0.394766i
$508$		0			0
$509$	−6.99176	−	12.1101i	−0.309904	−	0.536770i	0.668437	−	0.743769i	$-0.266964\pi$
$509$	−6.99176	−	12.1101i	−0.309904	−	0.536770i	−0.978341	+	0.206999i	$0.933630\pi$
$510$		0			0
$511$	−4.44973	+	8.15805i	−0.196844	+	0.360891i
$512$		0			0
$513$	10.3923	−	6.00000i	0.458831	−	0.264906i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			75.0757i			3.30183i
$518$		0			0
$519$	−36.9916			−1.62375
$520$		0			0
$521$	−10.3616	+	17.9468i	−0.453950	+	0.786264i	−0.998627	−	0.0523817i	$-0.983319\pi$
$521$	−10.3616	+	17.9468i	−0.453950	+	0.786264i	0.544677	+	0.838646i	$0.316652\pi$
$522$		0			0
$523$	−19.3579	+	11.1763i	−0.846460	+	0.488704i	−0.859455	−	0.511212i	$-0.829197\pi$
$523$	−19.3579	+	11.1763i	−0.846460	+	0.488704i	0.0129950	+	0.999916i	$0.495863\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.46850	−	2.57989i	0.194651	−	0.112382i
$528$		0			0
$529$	−11.3575	+	19.6718i	−0.493806	+	0.855297i
$530$		0			0
$531$	62.5899			2.71617
$532$		0			0
$533$			16.7232i			0.724362i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	20.9017	−	12.0676i	0.901974	−	0.520755i
$538$		0			0
$539$	18.6465	−	36.2517i	0.803163	−	1.56147i
$540$		0			0
$541$	−16.3278	−	28.2806i	−0.701987	−	1.21588i	−0.967768	−	0.251844i	$-0.918963\pi$
$541$	−16.3278	−	28.2806i	−0.701987	−	1.21588i	0.265781	−	0.964033i	$-0.414370\pi$
$542$		0			0
$543$	−52.6277	−	30.3846i	−2.25847	−	1.30393i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	31.1648i		−	1.33251i	−0.745724	−	0.666255i	$-0.767896\pi$
$547$		−	31.1648i		−	1.33251i	0.745724	−	0.666255i	$-0.232104\pi$
$548$		0			0
$549$	36.7858	−	63.7148i	1.56998	−	2.71928i
$550$		0			0
$551$	−0.311436	−	0.539422i	−0.0132676	−	0.0229802i
$552$		0			0
$553$	−21.4837	+	13.1087i	−0.913581	+	0.557438i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−38.7314	−	22.3616i	−1.64110	−	0.947491i	−0.980442	−	0.196806i	$-0.936943\pi$
$557$	−38.7314	−	22.3616i	−1.64110	−	0.947491i	−0.660660	−	0.750685i	$-0.729724\pi$
$558$		0			0
$559$	−1.95702			−0.0827731
$560$		0			0
$561$	−38.3196			−1.61785
$562$		0			0
$563$	28.1395	+	16.2464i	1.18594	+	0.684702i	0.957381	−	0.288828i	$-0.0932656\pi$
$563$	28.1395	+	16.2464i	1.18594	+	0.684702i	0.228558	+	0.973530i	$0.426599\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	66.7539	+	36.4102i	2.80340	+	1.52908i
$568$		0			0
$569$	17.3370	+	30.0285i	0.726804	+	1.25886i	0.958227	+	0.286009i	$0.0923287\pi$
$569$	17.3370	+	30.0285i	0.726804	+	1.25886i	−0.231423	+	0.972853i	$0.574338\pi$
$570$		0			0
$571$	−1.55528	+	2.69383i	−0.0650866	+	0.112733i	−0.896732	−	0.442573i	$-0.854066\pi$
$571$	−1.55528	+	2.69383i	−0.0650866	+	0.112733i	0.831646	+	0.555306i	$0.187399\pi$
$572$		0			0
$573$		−	47.9670i		−	2.00385i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.582041	+	0.336042i	0.0242307	+	0.0139896i	0.512066	−	0.858946i	$-0.328880\pi$
$577$	0.582041	+	0.336042i	0.0242307	+	0.0139896i	−0.487836	+	0.872935i	$0.662213\pi$
$578$		0			0
$579$	30.9374	+	53.5852i	1.28572	+	2.22692i
$580$		0			0
$581$	−17.7479	+	0.430713i	−0.736307	+	0.0178690i
$582$		0			0
$583$	−42.3837	+	24.4703i	−1.75536	+	1.01345i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			4.67208i			0.192838i	0.995341	+	0.0964188i	$0.0307388\pi$
$587$			4.67208i			0.192838i	−0.995341	+	0.0964188i	$0.969261\pi$
$588$		0			0
$589$	−1.95079			−0.0803808
$590$		0			0
$591$	4.53379	−	7.85276i	0.186495	−	0.323019i
$592$		0			0
$593$	17.4802	−	10.0922i	0.717825	−	0.414437i	−0.0961264	−	0.995369i	$-0.530645\pi$
$593$	17.4802	−	10.0922i	0.717825	−	0.414437i	0.813952	+	0.580932i	$0.197312\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	42.8077	−	24.7151i	1.75200	−	1.01152i
$598$		0			0
$599$	10.7562	−	18.6302i	0.439484	−	0.761209i	−0.558165	−	0.829730i	$-0.688494\pi$
$599$	10.7562	−	18.6302i	0.439484	−	0.761209i	0.997650	+	0.0685204i	$0.0218278\pi$
$600$		0			0
$601$	5.29495			0.215986			0.107993	−	0.994152i	$-0.465558\pi$
$601$	5.29495			0.215986			0.107993	+	0.994152i	$0.465558\pi$
$602$		0			0
$603$			92.8665i			3.78182i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−31.7989	+	18.3591i	−1.29068	+	0.745172i	−0.978774	−	0.204942i	$-0.934300\pi$
$607$	−31.7989	+	18.3591i	−1.29068	+	0.745172i	−0.311902	+	0.950114i	$0.600966\pi$
$608$		0			0
$609$	3.43336	−	6.29467i	0.139127	−	0.255073i
$610$		0			0
$611$	17.7652	+	30.7703i	0.718704	+	1.24483i
$612$		0			0
$613$	−35.2673	−	20.3616i	−1.42443	−	0.822397i	−0.427760	−	0.903892i	$-0.640697\pi$
$613$	−35.2673	−	20.3616i	−1.42443	−	0.822397i	−0.996674	+	0.0814954i	$0.974030\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	16.8073i		−	0.676635i	−0.941032	−	0.338317i	$-0.890142\pi$
$617$		−	16.8073i		−	0.676635i	0.941032	−	0.338317i	$-0.109858\pi$
$618$		0			0
$619$	−17.8954	+	30.9957i	−0.719276	+	1.24582i	0.242010	+	0.970274i	$0.422193\pi$
$619$	−17.8954	+	30.9957i	−0.719276	+	1.24582i	−0.961287	+	0.275550i	$0.911140\pi$
$620$		0			0
$621$	−4.23561	−	7.33629i	−0.169969	−	0.294395i
$622$		0			0
$623$	3.96630	−	2.42011i	0.158907	−	0.0969597i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	12.5467	+	7.24385i	0.501067	+	0.289291i
$628$		0			0
$629$	−9.51230			−0.379280
$630$		0			0
$631$	−32.4447			−1.29160			−0.645802	−	0.763505i	$-0.723477\pi$
$631$	−32.4447			−1.29160			−0.645802	+	0.763505i	$0.723477\pi$
$632$		0			0
$633$	−62.4423	−	36.0511i	−2.48186	−	1.43290i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.935872	−	19.2703i	−0.0370806	−	0.763519i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.45390	+	14.6426i	−0.333909	+	0.578348i	−0.983275	−	0.182129i	$-0.941701\pi$
$641$	−8.45390	+	14.6426i	−0.333909	+	0.578348i	0.649366	+	0.760476i	$0.275035\pi$
$642$		0			0
$643$			0.135174i			0.00533075i	0.999996	+	0.00266538i	$0.000848417\pi$
$643$			0.135174i			0.00533075i	−0.999996	+	0.00266538i	$0.999152\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.54125	−	2.04454i	−0.139221	−	0.0803791i	0.428772	−	0.903413i	$-0.358946\pi$
$647$	−3.54125	−	2.04454i	−0.139221	−	0.0803791i	−0.567993	+	0.823034i	$0.692280\pi$
$648$		0			0
$649$	23.2950	+	40.3480i	0.914407	+	1.58380i
$650$		0			0
$651$	−11.6967	−	19.1696i	−0.458429	−	0.751317i
$652$		0			0
$653$	27.6400	−	15.9580i	1.08164	−	0.624483i	0.150300	−	0.988641i	$-0.451976\pi$
$653$	27.6400	−	15.9580i	1.08164	−	0.624483i	0.931338	+	0.364157i	$0.118643\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	27.4793i		−	1.07207i
$658$		0			0
$659$	−4.70505			−0.183283			−0.0916413	−	0.995792i	$-0.529211\pi$
$659$	−4.70505			−0.183283			−0.0916413	+	0.995792i	$0.529211\pi$
$660$		0			0
$661$	−2.25710	+	3.90941i	−0.0877910	+	0.152058i	−0.906577	−	0.422040i	$-0.861314\pi$
$661$	−2.25710	+	3.90941i	−0.0877910	+	0.152058i	0.818786	+	0.574099i	$0.194647\pi$
$662$		0			0
$663$	−15.7055	+	9.06759i	−0.609952	+	0.352156i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.380797	+	0.219853i	−0.0147445	+	0.00851275i
$668$		0			0
$669$	−30.9374	+	53.5852i	−1.19611	+	2.07172i
$670$		0			0
$671$	54.7643			2.11415
$672$		0			0
$673$			46.9424i			1.80950i	0.425945	+	0.904749i	$0.359942\pi$
$673$			46.9424i			1.80950i	−0.425945	+	0.904749i	$0.640058\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.00981	−	5.20181i	0.346275	−	0.199922i	−0.316768	−	0.948503i	$-0.602598\pi$
$677$	9.00981	−	5.20181i	0.346275	−	0.199922i	0.663043	+	0.748581i	$0.269264\pi$
$678$		0			0
$679$	5.28995	−	0.128378i	0.203009	−	0.00492671i
$680$		0			0
$681$	27.4251	+	47.5017i	1.05093	+	1.82027i
$682$		0			0
$683$	−4.38432	−	2.53129i	−0.167761	−	0.0968571i	0.413768	−	0.910382i	$-0.364212\pi$
$683$	−4.38432	−	2.53129i	−0.167761	−	0.0968571i	−0.581530	+	0.813525i	$0.697546\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			64.1944i			2.44917i
$688$		0			0
$689$	−11.5808	+	20.0586i	−0.441195	+	0.764172i
$690$		0			0
$691$	2.22236	+	3.84924i	0.0845425	+	0.146432i	0.905196	−	0.424994i	$-0.139724\pi$
$691$	2.22236	+	3.84924i	0.0845425	+	0.146432i	−0.820654	+	0.571426i	$0.806390\pi$
$692$		0			0
$693$	2.92468	+	120.514i	0.111099	+	4.57795i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.5094	+	6.06759i	0.398071	+	0.229826i
$698$		0			0
$699$	59.2190			2.23987
$700$		0			0
$701$	21.7562			0.821719			0.410859	−	0.911699i	$-0.365229\pi$
$701$	21.7562			0.821719			0.410859	+	0.911699i	$0.365229\pi$
$702$		0			0
$703$	3.11455	+	1.79819i	0.117467	+	0.0678199i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.42594	+	2.95952i	0.204064	+	0.111304i
$708$		0			0
$709$	−20.5041	−	35.5141i	−0.770046	−	1.33376i	−0.937537	−	0.347886i	$-0.886900\pi$
$709$	−20.5041	−	35.5141i	−0.770046	−	1.33376i	0.167491	−	0.985874i	$-0.446434\pi$
$710$		0			0
$711$	37.2109	−	64.4511i	1.39552	−	2.41711i
$712$		0			0
$713$			1.37713i			0.0515739i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	45.8495	+	26.4712i	1.71228	+	0.988586i
$718$		0			0
$719$	11.8698	+	20.5592i	0.442670	+	0.766727i	0.997887	−	0.0649787i	$-0.0206979\pi$
$719$	11.8698	+	20.5592i	0.442670	+	0.766727i	−0.555216	+	0.831706i	$0.687365\pi$
$720$		0			0
$721$	3.06258	+	5.01924i	0.114056	+	0.186926i
$722$		0			0
$723$	−2.53954	+	1.46621i	−0.0944467	+	0.0545288i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			28.8534i			1.07011i	0.844817	+	0.535056i	$0.179709\pi$
$727$			28.8534i			1.07011i	−0.844817	+	0.535056i	$0.820291\pi$
$728$		0			0
$729$	−68.2190			−2.52663
$730$		0			0
$731$	−0.710055	+	1.22985i	−0.0262623	+	0.0454877i
$732$		0			0
$733$	40.5805	−	23.4292i	1.49888	−	0.865377i	0.498877	−	0.866673i	$-0.333746\pi$
$733$	40.5805	−	23.4292i	1.49888	−	0.865377i	0.999999	+	0.00129620i	$0.000412593\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−59.8656	+	34.5634i	−2.20518	+	1.27316i
$738$		0			0
$739$	8.07165	−	13.9805i	0.296920	−	0.514281i	−0.678509	−	0.734592i	$-0.737374\pi$
$739$	8.07165	−	13.9805i	0.296920	−	0.514281i	0.975430	+	0.220310i	$0.0707071\pi$
$740$		0			0
$741$	6.85647			0.251879
$742$		0			0
$743$		−	16.2243i		−	0.595210i	−0.954689	−	0.297605i	$-0.903812\pi$
$743$		−	16.2243i		−	0.595210i	0.954689	−	0.297605i	$-0.0961878\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	45.4644	−	26.2489i	1.66345	−	0.960395i
$748$		0			0
$749$	21.8698	+	35.8423i	0.799106	+	1.30965i
$750$		0			0
$751$	−10.7562	−	18.6302i	−0.392498	−	0.679826i	0.600281	−	0.799789i	$-0.295056\pi$
$751$	−10.7562	−	18.6302i	−0.392498	−	0.679826i	−0.992778	+	0.119964i	$0.961722\pi$
$752$		0			0
$753$	49.7786	+	28.7397i	1.81403	+	1.04733i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	0.840220i		−	0.0305383i	−0.999883	−	0.0152692i	$-0.995139\pi$
$757$		−	0.840220i		−	0.0305383i	0.999883	−	0.0152692i	$-0.00486051\pi$
$758$		0			0
$759$	5.11368	−	8.85716i	0.185615	−	0.321495i
$760$		0			0
$761$	14.4457	+	25.0206i	0.523655	+	0.906997i	0.999621	+	0.0275332i	$0.00876519\pi$
$761$	14.4457	+	25.0206i	0.523655	+	0.906997i	−0.475966	+	0.879464i	$0.657901\pi$
$762$		0			0
$763$	7.59167	+	4.14079i	0.274837	+	0.149907i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.0952	+	11.0246i	0.689487	+	0.398075i
$768$		0			0
$769$	27.3790			0.987313			0.493656	−	0.869657i	$-0.335660\pi$
$769$	27.3790			0.987313			0.493656	+	0.869657i	$0.335660\pi$
$770$		0			0
$771$	23.1106			0.832307
$772$		0			0
$773$	33.1129	+	19.1177i	1.19099	+	0.687618i	0.958531	−	0.284989i	$-0.0919899\pi$
$773$	33.1129	+	19.1177i	1.19099	+	0.687618i	0.232458	+	0.972607i	$0.425323\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.00440	+	41.3871i	0.0360326	+	1.48476i
$778$		0			0
$779$	−2.29401	−	3.97334i	−0.0821914	−	0.142360i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			13.0726i			0.467176i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	6.35050	+	3.66646i	0.226371	+	0.130695i	0.608897	−	0.793249i	$-0.291612\pi$
$787$	6.35050	+	3.66646i	0.226371	+	0.130695i	−0.382526	+	0.923945i	$0.624946\pi$
$788$		0			0
$789$	−29.2437	−	50.6516i	−1.04110	−	1.80325i
$790$		0			0
$791$	−34.8073	+	0.844716i	−1.23760	+	0.0300346i
$792$		0			0
$793$	22.4455	−	12.9589i	0.797063	−	0.460184i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	14.4877i		−	0.513181i	−0.966520	−	0.256590i	$-0.917401\pi$
$797$		−	14.4877i		−	0.513181i	0.966520	−	0.256590i	$-0.0825991\pi$
$798$		0			0
$799$	25.7827			0.912125
$800$		0			0
$801$	−6.86984	+	11.8989i	−0.242734	+	0.420427i
$802$		0			0
$803$	17.7143	−	10.2274i	0.625125	−	0.360916i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−26.7926	+	15.4687i	−0.943144	+	0.544524i
$808$		0			0
$809$	−5.67626	+	9.83157i	−0.199567	+	0.345660i	−0.948388	−	0.317112i	$-0.897287\pi$
$809$	−5.67626	+	9.83157i	−0.199567	+	0.345660i	0.748821	+	0.662772i	$0.230620\pi$
$810$		0			0
$811$	−28.7662			−1.01012			−0.505058	−	0.863085i	$-0.668529\pi$
$811$	−28.7662			−1.01012			−0.505058	+	0.863085i	$0.668529\pi$
$812$		0			0
$813$		−	23.1106i		−	0.810523i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.464977	−	0.268455i	0.0162675	−	0.00939204i
$818$		0			0
$819$	29.7160	+	48.7014i	1.03836	+	1.70176i
$820$		0			0
$821$	8.02461	+	13.8990i	0.280061	+	0.485079i	0.971399	−	0.237451i	$-0.0763121\pi$
$821$	8.02461	+	13.8990i	0.280061	+	0.485079i	−0.691339	+	0.722531i	$0.742979\pi$
$822$		0			0
$823$	−12.1287	−	7.00250i	−0.422780	−	0.244092i	0.273486	−	0.961876i	$-0.411823\pi$
$823$	−12.1287	−	7.00250i	−0.422780	−	0.244092i	−0.696266	+	0.717784i	$0.745157\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	15.2899i		−	0.531683i	−0.964017	−	0.265842i	$-0.914350\pi$
$827$		−	15.2899i		−	0.531683i	0.964017	−	0.265842i	$-0.0856499\pi$
$828$		0			0
$829$	−10.6475	+	18.4420i	−0.369802	+	0.640516i	−0.989534	−	0.144297i	$-0.953908\pi$
$829$	−10.6475	+	18.4420i	−0.369802	+	0.640516i	0.619732	+	0.784813i	$0.287241\pi$
$830$		0			0
$831$	44.6771	+	77.3830i	1.54983	+	2.68439i
$832$		0			0
$833$	−12.4496	−	6.40363i	−0.431354	−	0.221873i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	35.4572	+	20.4712i	1.22558	+	0.707589i
$838$		0			0
$839$	−42.2274			−1.45785			−0.728925	−	0.684593i	$-0.759980\pi$
$839$	−42.2274			−1.45785			−0.728925	+	0.684593i	$0.759980\pi$
$840$		0			0
$841$	−28.3215			−0.976602
$842$		0			0
$843$	−1.76927	−	1.02149i	−0.0609370	−	0.0351820i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−51.7561	+	31.5799i	−1.77836	+	1.08510i
$848$		0			0
$849$	−5.19775	−	9.00277i	−0.178386	−	0.308974i
$850$		0			0
$851$	1.26940	−	2.19867i	0.0435145	−	0.0753694i
$852$		0			0
$853$		−	13.2931i		−	0.455146i	−0.973761	−	0.227573i	$-0.926921\pi$
$853$		−	13.2931i		−	0.455146i	0.973761	−	0.227573i	$-0.0730790\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.3028	+	19.2274i	1.13760	+	0.656794i	0.945835	−	0.324646i	$-0.105245\pi$
$857$	33.3028	+	19.2274i	1.13760	+	0.656794i	0.191766	+	0.981441i	$0.438579\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	25.2898	−	46.3660i	0.861875	−	1.58015i
$862$		0			0
$863$	−40.7731	+	23.5404i	−1.38793	+	0.801323i	−0.993082	−	0.117422i	$-0.962537\pi$
$863$	−40.7731	+	23.5404i	−1.38793	+	0.801323i	−0.394850	+	0.918745i	$0.629204\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	42.7693i		−	1.45252i
$868$		0			0
$869$	55.3972			1.87922
$870$		0			0
$871$	−16.3575	+	28.3321i	−0.554254	+	0.959996i
$872$		0			0
$873$	−13.5511	+	7.82374i	−0.458636	+	0.264793i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.95926	−	2.28588i	0.133695	−	0.0771888i	−0.431661	−	0.902036i	$-0.642072\pi$
$877$	3.95926	−	2.28588i	0.133695	−	0.0771888i	0.565356	+	0.824847i	$0.308739\pi$
$878$		0			0
$879$	−18.4958	+	32.0357i	−0.623849	+	1.08054i
$880$		0			0
$881$	−14.2849			−0.481272			−0.240636	−	0.970615i	$-0.577356\pi$
$881$	−14.2849			−0.481272			−0.240636	+	0.970615i	$0.577356\pi$
$882$		0			0
$883$		−	15.9670i		−	0.537334i	−0.963233	−	0.268667i	$-0.913417\pi$
$883$		−	15.9670i		−	0.537334i	0.963233	−	0.268667i	$-0.0865831\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.20489	−	3.58239i	0.208340	−	0.120285i	−0.392200	−	0.919880i	$-0.628286\pi$
$887$	6.20489	−	3.58239i	0.208340	−	0.120285i	0.600540	+	0.799595i	$0.294952\pi$
$888$		0			0
$889$	−31.5173	+	0.764874i	−1.05706	+	0.0256531i
$890$		0			0
$891$	−83.6862	−	144.949i	−2.80359	−	4.85596i
$892$		0			0
$893$	−8.44184	−	4.87390i	−0.282495	−	0.163099i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	4.84022i		−	0.161610i
$898$		0			0
$899$	1.06258	−	1.84044i	0.0354389	−	0.0613821i
$900$		0			0
$901$	8.40363	+	14.5555i	0.279965	+	0.484914i
$902$		0			0
$903$	5.42594	+	2.95952i	0.180564	+	0.0984868i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	7.15799	+	4.13267i	0.237677	+	0.137223i	0.614109	−	0.789221i	$-0.289516\pi$
$907$	7.15799	+	4.13267i	0.237677	+	0.137223i	−0.376431	+	0.926444i	$0.622849\pi$
$908$		0			0
$909$	−18.2766			−0.606196
$910$		0			0
$911$	26.2274			0.868951			0.434476	−	0.900684i	$-0.356934\pi$
$911$	26.2274			0.868951			0.434476	+	0.900684i	$0.356934\pi$
$912$		0			0
$913$	33.8422	+	19.5388i	1.12001	+	0.646640i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−48.7014	+	29.7160i	−1.60826	+	0.981309i
$918$		0			0
$919$	−9.37902	−	16.2449i	−0.309385	−	0.535871i	0.668843	−	0.743404i	$-0.266790\pi$
$919$	−9.37902	−	16.2449i	−0.309385	−	0.535871i	−0.978228	+	0.207533i	$0.933457\pi$
$920$		0			0
$921$	38.6853	−	67.0050i	1.27473	−	2.20789i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.0577	−	8.69357i	−0.494560	−	0.285534i
$928$		0			0
$929$	−6.45390	−	11.1785i	−0.211746	−	0.366754i	0.740515	−	0.672040i	$-0.234582\pi$
$929$	−6.45390	−	11.1785i	−0.211746	−	0.366754i	−0.952261	+	0.305285i	$0.901248\pi$
$930$		0			0
$931$	2.86577	+	4.45015i	0.0939219	+	0.145848i
$932$		0			0
$933$	83.0813	−	47.9670i	2.71996	−	1.57037i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1.78265i		−	0.0582367i	−0.999576	−	0.0291183i	$-0.990730\pi$
$937$		−	1.78265i		−	0.0582367i	0.999576	−	0.0291183i	$-0.00926997\pi$
$938$		0			0
$939$	−79.5653			−2.59652
$940$		0			0
$941$	22.5634	−	39.0810i	0.735546	−	1.27400i	−0.218937	−	0.975739i	$-0.570259\pi$
$941$	22.5634	−	39.0810i	0.735546	−	1.27400i	0.954483	−	0.298264i	$-0.0964077\pi$
$942$		0			0
$943$	−2.80492	+	1.61942i	−0.0913407	+	0.0527356i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.1281	+	11.0436i	−0.621579	+	0.358869i	−0.777483	−	0.628904i	$-0.783504\pi$
$947$	−19.1281	+	11.0436i	−0.621579	+	0.358869i	0.155905	+	0.987772i	$0.450171\pi$
$948$		0			0
$949$	4.84022	−	8.38351i	0.157120	−	0.272140i
$950$		0			0
$951$	−39.9241			−1.29463
$952$		0			0
$953$		−	45.3442i		−	1.46884i	−0.678694	−	0.734421i	$-0.737454\pi$
$953$		−	45.3442i		−	1.46884i	0.678694	−	0.734421i	$-0.262546\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−13.6682	+	7.89133i	−0.441829	+	0.255090i
$958$		0			0
$959$	5.06759	−	9.29083i	0.163641	−	0.300017i
$960$		0			0
$961$	12.1721	+	21.0827i	0.392648	+	0.680086i
$962$		0			0
$963$	−107.527	−	62.0807i	−3.46501	−	2.00052i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			17.0296i			0.547636i	0.961782	+	0.273818i	$0.0882865\pi$
$967$			17.0296i			0.547636i	−0.961782	+	0.273818i	$0.911713\pi$
$968$		0			0
$969$	2.48770	−	4.30882i	0.0799163	−	0.138419i
$970$		0			0
$971$	14.6054	+	25.2974i	0.468711	+	0.811831i	0.999360	−	0.0357602i	$-0.0113852\pi$
$971$	14.6054	+	25.2974i	0.468711	+	0.811831i	−0.530649	+	0.847591i	$0.678052\pi$
$972$		0			0
$973$	0.422358	+	17.4036i	0.0135402	+	0.557935i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.727652	+	0.420110i	0.0232796	+	0.0134405i	0.511595	−	0.859227i	$-0.329055\pi$
$977$	0.727652	+	0.420110i	0.0232796	+	0.0134405i	−0.488315	+	0.872667i	$0.662388\pi$
$978$		0			0
$979$	−10.2274			−0.326868
$980$		0			0
$981$	−25.5715			−0.816436
$982$		0			0
$983$	−7.20225	−	4.15822i	−0.229716	−	0.132627i	0.380725	−	0.924688i	$-0.375674\pi$
$983$	−7.20225	−	4.15822i	−0.229716	−	0.132627i	−0.610441	+	0.792062i	$0.709008\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.72238	−	112.178i	−0.0866542	−	3.57066i
$988$		0			0
$989$	−0.189511	−	0.328243i	−0.00602611	−	0.0104375i
$990$		0			0
$991$	10.1302	−	17.5460i	0.321795	−	0.557366i	−0.659063	−	0.752088i	$-0.729047\pi$
$991$	10.1302	−	17.5460i	0.321795	−	0.557366i	0.980859	+	0.194722i	$0.0623804\pi$
$992$		0			0
$993$			6.00000i			0.190404i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−45.9666	−	26.5388i	−1.45578	−	0.840492i	−0.456976	−	0.889479i	$-0.651067\pi$
$997$	−45.9666	−	26.5388i	−1.45578	−	0.840492i	−0.998799	+	0.0489867i	$0.984401\pi$
$998$		0			0
$999$	−37.7397	−	65.3670i	−1.19403	−	2.06812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.i.249.6		12
5.2	odd	4		280.2.q.e.81.3	✓	6
5.3	odd	4		1400.2.q.j.1201.1		6
5.4	even	2	inner	1400.2.bh.i.249.1		12
7.2	even	3	inner	1400.2.bh.i.849.1		12
15.2	even	4		2520.2.bi.q.361.3		6
20.7	even	4		560.2.q.l.81.1		6
35.2	odd	12		280.2.q.e.121.3	yes	6
35.3	even	12		9800.2.a.cf.1.1		3
35.9	even	6	inner	1400.2.bh.i.849.6		12
35.12	even	12		1960.2.q.w.961.1		6
35.17	even	12		1960.2.a.v.1.3		3
35.18	odd	12		9800.2.a.ce.1.3		3
35.23	odd	12		1400.2.q.j.401.1		6
35.27	even	4		1960.2.q.w.361.1		6
35.32	odd	12		1960.2.a.w.1.1		3
105.2	even	12		2520.2.bi.q.1801.3		6
140.67	even	12		3920.2.a.cc.1.3		3
140.87	odd	12		3920.2.a.cb.1.1		3
140.107	even	12		560.2.q.l.401.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.3	✓	6	5.2	odd	4
280.2.q.e.121.3	yes	6	35.2	odd	12
560.2.q.l.81.1		6	20.7	even	4
560.2.q.l.401.1		6	140.107	even	12
1400.2.q.j.401.1		6	35.23	odd	12
1400.2.q.j.1201.1		6	5.3	odd	4
1400.2.bh.i.249.1		12	5.4	even	2	inner
1400.2.bh.i.249.6		12	1.1	even	1	trivial
1400.2.bh.i.849.1		12	7.2	even	3	inner
1400.2.bh.i.849.6		12	35.9	even	6	inner
1960.2.a.v.1.3		3	35.17	even	12
1960.2.a.w.1.1		3	35.32	odd	12
1960.2.q.w.361.1		6	35.27	even	4
1960.2.q.w.961.1		6	35.12	even	12
2520.2.bi.q.361.3		6	15.2	even	4
2520.2.bi.q.1801.3		6	105.2	even	12
3920.2.a.cb.1.1		3	140.87	odd	12
3920.2.a.cc.1.3		3	140.67	even	12
9800.2.a.ce.1.3		3	35.18	odd	12
9800.2.a.cf.1.1		3	35.3	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.84918 + 1.64497i) q^{3} +(-0.0641892 - 2.64497i) q^{7} +(3.91187 + 6.77556i) q^{9} +(-2.91187 + 5.04351i) q^{11} +2.75615i q^{13} +(1.73205 + 1.00000i) q^{17} +(-0.378076 - 0.654846i) q^{19} +(4.16802 - 7.64158i) q^{21} +(-0.462279 + 0.266897i) q^{23} +15.8698i q^{27} +0.823739 q^{29} +(1.28995 - 2.23425i) q^{31} +(-16.5929 + 9.57989i) q^{33} +(-4.11895 + 2.37808i) q^{37} +(-4.53379 + 7.85276i) q^{39} +6.06759 q^{41} +0.710055i q^{43} +(11.1642 - 6.44566i) q^{47} +(-6.99176 + 0.339557i) q^{49} +(3.28995 + 5.69835i) q^{51} +(7.27776 + 4.20181i) q^{53} -2.48770i q^{57} +(4.00000 - 6.92820i) q^{59} +(-4.70181 - 8.14378i) q^{61} +(17.6701 - 10.7817i) q^{63} +(10.2796 + 5.93492i) q^{67} -1.75615 q^{69} +(-3.04174 - 1.75615i) q^{73} +(13.5268 + 7.37808i) q^{77} +(-4.75615 - 8.23790i) q^{79} +(-14.3698 + 24.8893i) q^{81} -6.71005i q^{83} +(2.34698 + 1.35503i) q^{87} +(0.878076 + 1.52087i) q^{89} +(7.28995 - 0.176915i) q^{91} +(7.35056 - 4.24385i) q^{93} +2.00000i q^{97} -45.5634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) \) 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Introduction

L-functions

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