LMFDB - Embedded newform 1400.2.bh.e.849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(249,1400)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.e.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(1.73205 - 1.00000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.00000i q^{13} +(-1.73205 + 1.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-1.00000 + 5.19615i) q^{21} +(6.06218 + 3.50000i) q^{23} +4.00000i q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.73205 + 1.00000i) q^{33} +(4.33013 + 2.50000i) q^{37} +(3.00000 + 5.19615i) q^{39} -5.00000 q^{41} -6.00000i q^{43} +(7.79423 + 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-9.52628 + 5.50000i) q^{53} +10.0000i q^{57} +(4.00000 + 6.92820i) q^{59} +(6.00000 - 10.3923i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-3.46410 + 2.00000i) q^{67} +14.0000 q^{69} -4.00000 q^{71} +(-10.3923 + 6.00000i) q^{73} +(-2.59808 - 0.500000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000i q^{83} +(10.3923 - 6.00000i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-6.00000 - 5.19615i) q^{91} +(-6.92820 - 4.00000i) q^{93} +6.00000i q^{97} +1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} + 2 q^{11} - 10 q^{19} - 4 q^{21} + 24 q^{29} - 8 q^{31} + 12 q^{39} - 20 q^{41} - 4 q^{49} - 8 q^{51} + 16 q^{59} + 24 q^{61} + 56 q^{69} - 16 q^{71} + 28 q^{79} + 22 q^{81} + 12 q^{89} - 24 q^{91} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 + 2 * q^11 - 10 * q^19 - 4 * q^21 + 24 * q^29 - 8 * q^31 + 12 * q^39 - 20 * q^41 - 4 * q^49 - 8 * q^51 + 16 * q^59 + 24 * q^61 + 56 * q^69 - 16 * q^71 + 28 * q^79 + 22 * q^81 + 12 * q^89 - 24 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.0917517	−	0.995782i	$-0.470753\pi$
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.908248	+	0.418432i	$0.137420\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$			3.00000i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$13$			3.00000i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	−1.00000	+	5.19615i	−0.218218	+	1.13389i
$22$		0			0
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.973856	−	0.227167i	$-0.0729463\pi$
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.290196	+	0.956967i	$0.406280\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			4.00000i			0.769800i
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	0.811752	−	0.584002i	$-0.198514\pi$
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	−0.0998840	+	0.994999i	$0.531847\pi$
$38$		0			0
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$		0			0
$41$	−5.00000			−0.780869			−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000			−0.780869			−0.390434	+	0.920631i	$0.627675\pi$
$42$		0			0
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.945662	−	0.325150i	$-0.105415\pi$
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.191243	+	0.981543i	$0.438748\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	−9.52628	+	5.50000i	−1.30854	+	0.755483i	−0.981852	−	0.189651i	$-0.939264\pi$
$53$	−9.52628	+	5.50000i	−1.30854	+	0.755483i	−0.326683	+	0.945134i	$0.605931\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			10.0000i			1.32453i
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	−0.170305	−	0.985391i	$-0.554475\pi$
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	0.938527	−	0.345207i	$-0.112191\pi$
$62$		0			0
$63$	0.866025	+	2.50000i	0.109109	+	0.314970i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$		0			0
$69$	14.0000			1.68540
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	−10.3923	+	6.00000i	−1.21633	+	0.702247i	−0.964130	−	0.265429i	$-0.914486\pi$
$73$	−10.3923	+	6.00000i	−1.21633	+	0.702247i	−0.252197	+	0.967676i	$0.581153\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.59808	−	0.500000i	−0.296078	−	0.0569803i
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.3923	−	6.00000i	1.11417	−	0.643268i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−6.00000	−	5.19615i	−0.628971	−	0.544705i
$92$		0			0
$93$	−6.92820	−	4.00000i	−0.718421	−	0.414781i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	17.3205	+	10.0000i	1.70664	+	0.985329i	0.938652	+	0.344865i	$0.112075\pi$
$103$	17.3205	+	10.0000i	1.70664	+	0.985329i	0.767988	+	0.640464i	$0.221258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$		0			0
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$		0			0
$111$	10.0000			0.949158
$112$		0			0
$113$		−	20.0000i		−	1.88144i	−0.339182	−	0.940721i	$-0.610150\pi$
$113$		−	20.0000i		−	1.88144i	0.339182	−	0.940721i	$-0.389850\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.59808	+	1.50000i	0.240192	+	0.138675i
$118$		0			0
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−8.66025	+	5.00000i	−0.780869	+	0.450835i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			17.0000i			1.50851i	0.656584	+	0.754253i	$0.272001\pi$
$127$			17.0000i			1.50851i	−0.656584	+	0.754253i	$0.727999\pi$
$128$		0			0
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$		0			0
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$		0			0
$133$	−4.33013	−	12.5000i	−0.375470	−	1.08389i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	−2.59808	+	1.50000i	−0.217262	+	0.125436i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.66025	−	11.0000i	−0.714286	−	0.907265i
$148$		0			0
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$			2.00000i			0.161690i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.33013	−	2.50000i	0.345582	−	0.199522i	−0.317156	−	0.948373i	$-0.602728\pi$
$157$	4.33013	−	2.50000i	0.345582	−	0.199522i	0.662738	+	0.748852i	$0.269394\pi$
$158$		0			0
$159$	−11.0000	+	19.0526i	−0.872357	+	1.51097i
$160$		0			0
$161$	−17.5000	+	6.06218i	−1.37919	+	0.477767i
$162$		0			0
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			5.00000i			0.386912i	0.981109	+	0.193456i	$0.0619696\pi$
$167$			5.00000i			0.386912i	−0.981109	+	0.193456i	$0.938030\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$		0			0
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$		0			0
$173$	16.4545	+	9.50000i	1.25101	+	0.722272i	0.971310	−	0.237816i	$-0.0764314\pi$
$173$	16.4545	+	9.50000i	1.25101	+	0.722272i	0.279701	+	0.960087i	$0.409765\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	13.8564	+	8.00000i	1.04151	+	0.601317i
$178$		0			0
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	24.0000i		−	1.77413i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.73205	−	1.00000i	−0.126660	−	0.0731272i
$188$		0			0
$189$	−8.00000	−	6.92820i	−0.581914	−	0.503953i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.276296	−	0.961073i	$-0.410893\pi$
$193$	17.3205	−	10.0000i	1.24676	−	0.719816i	0.970461	+	0.241257i	$0.0775596\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	27.0000i		−	1.92367i	−0.273629	−	0.961835i	$-0.588224\pi$
$197$		−	27.0000i		−	1.92367i	0.273629	−	0.961835i	$-0.411776\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$		0			0
$203$	−10.3923	+	12.0000i	−0.729397	+	0.842235i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.06218	−	3.50000i	0.421350	−	0.243267i
$208$		0			0
$209$	−5.00000			−0.345857
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		0			0
$213$	−6.92820	+	4.00000i	−0.474713	+	0.274075i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.3923	+	2.00000i	0.705476	+	0.135769i
$218$		0			0
$219$	−12.0000	+	20.7846i	−0.810885	+	1.40449i
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	−0.711977	−	0.702202i	$-0.752200\pi$
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	0.252136	+	0.967692i	$0.418867\pi$
$228$		0			0
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.133820	+	0.991006i	$0.542724\pi$
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.791326	+	0.611394i	$0.790609\pi$
$230$		0			0
$231$	−5.00000	+	1.73205i	−0.328976	+	0.113961i
$232$		0			0
$233$	1.73205	+	1.00000i	0.113470	+	0.0655122i	0.555661	−	0.831409i	$-0.312465\pi$
$233$	1.73205	+	1.00000i	0.113470	+	0.0655122i	−0.442191	+	0.896921i	$0.645799\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	28.0000i		−	1.81880i
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$	8.66025	+	5.00000i	0.555556	+	0.320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.9904	−	7.50000i	−0.826558	−	0.477214i
$248$		0			0
$249$	4.00000	+	6.92820i	0.253490	+	0.439057i
$250$		0			0
$251$	29.0000			1.83046			0.915232	−	0.402928i	$-0.132007\pi$
$251$	29.0000			1.83046			0.915232	+	0.402928i	$0.132007\pi$
$252$		0			0
$253$			7.00000i			0.440086i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	−12.5000	+	4.33013i	−0.776712	+	0.269061i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	−6.92820	+	4.00000i	−0.427211	+	0.246651i	−0.698158	−	0.715944i	$-0.745997\pi$
$263$	−6.92820	+	4.00000i	−0.427211	+	0.246651i	0.270947	+	0.962594i	$0.412663\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	12.0000i		−	0.734388i
$268$		0			0
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$		0			0
$273$	−15.5885	−	3.00000i	−0.943456	−	0.181568i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	−0.447062	−	0.894503i	$-0.647530\pi$
$277$	1.73205	−	1.00000i	0.104069	−	0.0600842i	0.551131	+	0.834419i	$0.314196\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.187980	−	0.982173i	$-0.439806\pi$
$283$	19.0526	−	11.0000i	1.13256	−	0.653882i	0.944577	+	0.328291i	$0.106473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.66025	−	10.0000i	0.511199	−	0.590281i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	6.00000	+	10.3923i	0.351726	+	0.609208i
$292$		0			0
$293$		−	21.0000i		−	1.22683i	−0.789760	−	0.613417i	$-0.789795\pi$
$293$		−	21.0000i		−	1.22683i	0.789760	−	0.613417i	$-0.210205\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.46410	+	2.00000i	−0.201008	+	0.116052i
$298$		0			0
$299$	−10.5000	+	18.1865i	−0.607231	+	1.05175i
$300$		0			0
$301$	12.0000	+	10.3923i	0.691669	+	0.599002i
$302$		0			0
$303$	−20.7846	−	12.0000i	−1.19404	−	0.689382i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	6.00000i		−	0.342438i	−0.985233	−	0.171219i	$-0.945229\pi$
$307$		−	6.00000i		−	0.342438i	0.985233	−	0.171219i	$-0.0547706\pi$
$308$		0			0
$309$	40.0000			2.27552
$310$		0			0
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	0.917143	−	0.398559i	$-0.130489\pi$
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	−0.803733	+	0.594990i	$0.797156\pi$
$312$		0			0
$313$	13.8564	+	8.00000i	0.783210	+	0.452187i	0.837567	−	0.546335i	$-0.183977\pi$
$313$	13.8564	+	8.00000i	0.783210	+	0.452187i	−0.0543564	+	0.998522i	$0.517311\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	−24.0000			−1.33955
$322$		0			0
$323$		−	10.0000i		−	0.556415i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.92820	−	4.00000i	−0.383131	−	0.221201i
$328$		0			0
$329$	−22.5000	+	7.79423i	−1.24047	+	0.429710i
$330$		0			0
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	−0.209544	−	0.977799i	$-0.567198\pi$
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	0.951571	−	0.307429i	$-0.0994688\pi$
$332$		0			0
$333$	4.33013	−	2.50000i	0.237289	−	0.136999i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	26.0000i		−	1.41631i	−0.706057	−	0.708155i	$-0.749528\pi$
$337$		−	26.0000i		−	1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$338$		0			0
$339$	−20.0000	−	34.6410i	−1.08625	−	1.88144i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	−0.302374	−	0.953189i	$-0.597779\pi$
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	0.674299	+	0.738458i	$0.264446\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−12.0000			−0.640513
$352$		0			0
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.884234	−	0.467045i	$-0.845319\pi$
$353$	−17.3205	+	10.0000i	−0.921878	+	0.532246i	−0.0376440	+	0.999291i	$0.511985\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.46410	−	10.0000i	−0.183340	−	0.529256i
$358$		0			0
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	−0.133263	−	0.991081i	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$		−	20.0000i		−	1.04973i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	−0.00473247	−	0.999989i	$-0.501506\pi$
$367$	16.4545	−	9.50000i	0.858917	−	0.495896i	0.863649	+	0.504093i	$0.168173\pi$
$368$		0			0
$369$	−2.50000	+	4.33013i	−0.130145	+	0.225417i
$370$		0			0
$371$	5.50000	−	28.5788i	0.285546	−	1.48374i
$372$		0			0
$373$	12.1244	+	7.00000i	0.627775	+	0.362446i	0.779890	−	0.625917i	$-0.215275\pi$
$373$	12.1244	+	7.00000i	0.627775	+	0.362446i	−0.152115	+	0.988363i	$0.548608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			18.0000i			0.927047i
$378$		0			0
$379$	21.0000			1.07870			0.539349	−	0.842082i	$-0.318670\pi$
$379$	21.0000			1.07870			0.539349	+	0.842082i	$0.318670\pi$
$380$		0			0
$381$	17.0000	+	29.4449i	0.870936	+	1.50851i
$382$		0			0
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.0427020	−	0.999088i	$-0.513597\pi$
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.19615	−	3.00000i	−0.264135	−	0.152499i
$388$		0			0
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	0.588777	−	0.808296i	$-0.299610\pi$
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	−0.994393	+	0.105748i	$0.966276\pi$
$390$		0			0
$391$	−14.0000			−0.708010
$392$		0			0
$393$			14.0000i			0.706207i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	0.0549046	−	0.998492i	$-0.482515\pi$
$397$	−15.5885	−	9.00000i	−0.782362	−	0.451697i	−0.837267	+	0.546795i	$0.815848\pi$
$398$		0			0
$399$	−20.0000	−	17.3205i	−1.00125	−	0.867110i
$400$		0			0
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	−0.981430	−	0.191820i	$-0.938561\pi$
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	0.656836	+	0.754034i	$0.271895\pi$
$402$		0			0
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.00000i			0.247841i
$408$		0			0
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$		0			0
$411$	−12.0000	+	20.7846i	−0.591916	+	1.02523i
$412$		0			0
$413$	−20.7846	−	4.00000i	−1.02274	−	0.196827i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.92820	+	4.00000i	−0.339276	+	0.195881i
$418$		0			0
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$		0			0
$423$	7.79423	−	4.50000i	0.378968	−	0.218797i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.3923	+	30.0000i	0.502919	+	1.45180i
$428$		0			0
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$		0			0
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$		0			0
$433$		−	24.0000i		−	1.15337i	−0.816968	−	0.576683i	$-0.804347\pi$
$433$		−	24.0000i		−	1.15337i	0.816968	−	0.576683i	$-0.195653\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.3109	+	17.5000i	−1.44997	+	0.837139i
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−27.7128	−	16.0000i	−1.31668	−	0.760183i	−0.333483	−	0.942756i	$-0.608224\pi$
$443$	−27.7128	−	16.0000i	−1.31668	−	0.760183i	−0.983192	+	0.182573i	$0.941557\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	20.0000i		−	0.945968i
$448$		0			0
$449$	−13.0000			−0.613508			−0.306754	−	0.951789i	$-0.599243\pi$
$449$	−13.0000			−0.613508			−0.306754	+	0.951789i	$0.599243\pi$
$450$		0			0
$451$	−2.50000	−	4.33013i	−0.117720	−	0.203898i
$452$		0			0
$453$	17.3205	+	10.0000i	0.813788	+	0.469841i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.0526	+	11.0000i	0.891241	+	0.514558i	0.874348	−	0.485299i	$-0.161289\pi$
$457$	19.0526	+	11.0000i	0.891241	+	0.514558i	0.0168929	+	0.999857i	$0.494623\pi$
$458$		0			0
$459$	−4.00000	−	6.92820i	−0.186704	−	0.323381i
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$		−	9.00000i		−	0.418265i	−0.977887	−	0.209133i	$-0.932936\pi$
$463$		−	9.00000i		−	0.418265i	0.977887	−	0.209133i	$-0.0670641\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.66025	+	5.00000i	0.400749	+	0.231372i	0.686807	−	0.726840i	$-0.259012\pi$
$467$	8.66025	+	5.00000i	0.400749	+	0.231372i	−0.286058	+	0.958212i	$0.592345\pi$
$468$		0			0
$469$	2.00000	−	10.3923i	0.0923514	−	0.479872i
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$	5.19615	−	3.00000i	0.238919	−	0.137940i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			11.0000i			0.503655i
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$		0			0
$483$	−24.2487	+	28.0000i	−1.10335	+	1.27404i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	−0.648691	−	0.761052i	$-0.724683\pi$
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	0.334744	+	0.942309i	$0.391350\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$	−10.3923	+	6.00000i	−0.468046	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.92820	−	8.00000i	0.310772	−	0.358849i
$498$		0			0
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$		0			0
$503$		−	16.0000i		−	0.713405i	−0.934218	−	0.356702i	$-0.883901\pi$
$503$		−	16.0000i		−	0.713405i	0.934218	−	0.356702i	$-0.116099\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.92820	−	4.00000i	0.307692	−	0.177646i
$508$		0			0
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$	6.00000	−	31.1769i	0.265424	−	1.37919i
$512$		0			0
$513$	−17.3205	−	10.0000i	−0.764719	−	0.441511i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			9.00000i			0.395820i
$518$		0			0
$519$	38.0000			1.66801
$520$		0			0
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$		0			0
$523$	24.2487	+	14.0000i	1.06032	+	0.612177i	0.925521	−	0.378695i	$-0.123627\pi$
$523$	24.2487	+	14.0000i	1.06032	+	0.612177i	0.134801	+	0.990873i	$0.456961\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.92820	+	4.00000i	0.301797	+	0.174243i
$528$		0			0
$529$	13.0000	+	22.5167i	0.565217	+	0.978985i
$530$		0			0
$531$	8.00000			0.347170
$532$		0			0
$533$		−	15.0000i		−	0.649722i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	15.5885	+	9.00000i	0.672692	+	0.388379i
$538$		0			0
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$		0			0
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	−0.0121878	−	0.999926i	$-0.503880\pi$
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	0.872055	−	0.489408i	$-0.162787\pi$
$542$		0			0
$543$	3.46410	−	2.00000i	0.148659	−	0.0858282i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$		0			0
$549$	−6.00000	−	10.3923i	−0.256074	−	0.443533i
$550$		0			0
$551$	−15.0000	+	25.9808i	−0.639021	+	1.10682i
$552$		0			0
$553$	12.1244	+	35.0000i	0.515580	+	1.48835i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	−0.0624962	−	0.998045i	$-0.519906\pi$
$557$	18.1865	−	10.5000i	0.770588	−	0.444899i	0.833084	+	0.553146i	$0.186573\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$	−4.00000			−0.168880
$562$		0			0
$563$	−5.19615	+	3.00000i	−0.218992	+	0.126435i	−0.605483	−	0.795858i	$-0.707020\pi$
$563$	−5.19615	+	3.00000i	−0.218992	+	0.126435i	0.386492	+	0.922293i	$0.373687\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−28.5788	−	5.50000i	−1.20020	−	0.230978i
$568$		0			0
$569$	−5.50000	+	9.52628i	−0.230572	+	0.399362i	−0.957977	−	0.286846i	$-0.907393\pi$
$569$	−5.50000	+	9.52628i	−0.230572	+	0.399362i	0.727405	+	0.686209i	$0.240726\pi$
$570$		0			0
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	0.408883	−	0.912587i	$-0.365918\pi$
$572$		0			0
$573$			24.0000i			1.00261i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	−0.570370	−	0.821388i	$-0.693200\pi$
$577$	−3.46410	+	2.00000i	−0.144212	+	0.0832611i	0.426158	+	0.904649i	$0.359867\pi$
$578$		0			0
$579$	20.0000	−	34.6410i	0.831172	−	1.43963i
$580$		0			0
$581$	−8.00000	−	6.92820i	−0.331896	−	0.287430i
$582$		0			0
$583$	−9.52628	−	5.50000i	−0.394538	−	0.227787i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$		0			0
$591$	−27.0000	−	46.7654i	−1.11063	−	1.92367i
$592$		0			0
$593$	−10.3923	−	6.00000i	−0.426761	−	0.246390i	0.271205	−	0.962522i	$-0.412578\pi$
$593$	−10.3923	−	6.00000i	−0.426761	−	0.246390i	−0.697966	+	0.716131i	$0.745911\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.92820	−	4.00000i	−0.283552	−	0.163709i
$598$		0			0
$599$	17.0000	+	29.4449i	0.694601	+	1.20308i	0.970315	+	0.241845i	$0.0777525\pi$
$599$	17.0000	+	29.4449i	0.694601	+	1.20308i	−0.275714	+	0.961240i	$0.588914\pi$
$600$		0			0
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−28.5788	−	16.5000i	−1.15998	−	0.669714i	−0.208680	−	0.977984i	$-0.566917\pi$
$607$	−28.5788	−	16.5000i	−1.15998	−	0.669714i	−0.951299	+	0.308270i	$0.900250\pi$
$608$		0			0
$609$	−6.00000	+	31.1769i	−0.243132	+	1.26335i
$610$		0			0
$611$	−13.5000	+	23.3827i	−0.546152	+	0.945962i
$612$		0			0
$613$	35.5070	−	20.5000i	1.43412	−	0.827987i	0.436684	−	0.899615i	$-0.356153\pi$
$613$	35.5070	−	20.5000i	1.43412	−	0.827987i	0.997431	+	0.0716275i	$0.0228193\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			42.0000i			1.69086i	0.534089	+	0.845428i	$0.320655\pi$
$617$			42.0000i			1.69086i	−0.534089	+	0.845428i	$0.679345\pi$
$618$		0			0
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	0.967271	+	0.253744i	$0.0816620\pi$
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	−0.263887	+	0.964554i	$0.585005\pi$
$620$		0			0
$621$	−14.0000	+	24.2487i	−0.561801	+	0.973067i
$622$		0			0
$623$	5.19615	+	15.0000i	0.208179	+	0.600962i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.66025	+	5.00000i	−0.345857	+	0.199681i
$628$		0			0
$629$	−10.0000			−0.398726
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$	−22.5167	+	13.0000i	−0.894957	+	0.516704i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	20.7846	−	3.00000i	0.823516	−	0.118864i
$638$		0			0
$639$	−2.00000	+	3.46410i	−0.0791188	+	0.137038i
$640$		0			0
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	−0.971442	−	0.237276i	$-0.923745\pi$
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	0.280234	−	0.959932i	$-0.409588\pi$
$642$		0			0
$643$			34.0000i			1.34083i	0.741987	+	0.670415i	$0.233884\pi$
$643$			34.0000i			1.34083i	−0.741987	+	0.670415i	$0.766116\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.9186	−	11.5000i	0.783080	−	0.452112i	−0.0544405	−	0.998517i	$-0.517338\pi$
$647$	19.9186	−	11.5000i	0.783080	−	0.452112i	0.837521	+	0.546405i	$0.184004\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$		0			0
$651$	20.0000	−	6.92820i	0.783862	−	0.271538i
$652$		0			0
$653$	38.9711	+	22.5000i	1.52506	+	0.880493i	0.999559	+	0.0296993i	$0.00945498\pi$
$653$	38.9711	+	22.5000i	1.52506	+	0.880493i	0.525500	+	0.850794i	$0.323878\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			12.0000i			0.468165i
$658$		0			0
$659$	16.0000			0.623272			0.311636	−	0.950202i	$-0.399123\pi$
$659$	16.0000			0.623272			0.311636	+	0.950202i	$0.399123\pi$
$660$		0			0
$661$	18.0000	+	31.1769i	0.700119	+	1.21264i	0.968424	+	0.249308i	$0.0802030\pi$
$661$	18.0000	+	31.1769i	0.700119	+	1.21264i	−0.268306	+	0.963334i	$0.586464\pi$
$662$		0			0
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	36.3731	+	21.0000i	1.40837	+	0.813123i
$668$		0			0
$669$	16.0000	+	27.7128i	0.618596	+	1.07144i
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$			42.0000i			1.61898i	0.587133	+	0.809491i	$0.300257\pi$
$673$			42.0000i			1.61898i	−0.587133	+	0.809491i	$0.699743\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.1865	−	10.5000i	−0.698965	−	0.403548i	0.107997	−	0.994151i	$-0.465556\pi$
$677$	−18.1865	−	10.5000i	−0.698965	−	0.403548i	−0.806962	+	0.590603i	$0.798890\pi$
$678$		0			0
$679$	−12.0000	−	10.3923i	−0.460518	−	0.398820i
$680$		0			0
$681$	−8.00000	+	13.8564i	−0.306561	+	0.530979i
$682$		0			0
$683$	31.1769	−	18.0000i	1.19295	−	0.688751i	0.233977	−	0.972242i	$-0.424826\pi$
$683$	31.1769	−	18.0000i	1.19295	−	0.688751i	0.958975	+	0.283491i	$0.0914927\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			56.0000i			2.13653i
$688$		0			0
$689$	−16.5000	−	28.5788i	−0.628600	−	1.08877i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$		0			0
$693$	−1.73205	+	2.00000i	−0.0657952	+	0.0759737i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	8.66025	−	5.00000i	0.328031	−	0.189389i
$698$		0			0
$699$	4.00000			0.151294
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−21.6506	+	12.5000i	−0.816569	+	0.471446i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	31.1769	+	6.00000i	1.17253	+	0.225653i
$708$		0			0
$709$	−9.00000	+	15.5885i	−0.338002	+	0.585437i	−0.984057	−	0.177854i	$-0.943084\pi$
$709$	−9.00000	+	15.5885i	−0.338002	+	0.585437i	0.646055	+	0.763291i	$0.276418\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$		0			0
$713$		−	28.0000i		−	1.04861i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−10.3923	+	6.00000i	−0.388108	+	0.224074i
$718$		0			0
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	−50.0000	+	17.3205i	−1.86210	+	0.645049i
$722$		0			0
$723$	−39.8372	−	23.0000i	−1.48156	−	0.855379i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			41.0000i			1.52061i	0.649569	+	0.760303i	$0.274949\pi$
$727$			41.0000i			1.52061i	−0.649569	+	0.760303i	$0.725051\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	26.8468	+	15.5000i	0.991609	+	0.572506i	0.905755	−	0.423802i	$-0.139305\pi$
$733$	26.8468	+	15.5000i	0.991609	+	0.572506i	0.0858539	+	0.996308i	$0.472638\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.46410	−	2.00000i	−0.127602	−	0.0736709i
$738$		0			0
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$		0			0
$741$	−30.0000			−1.10208
$742$		0			0
$743$			3.00000i			0.110059i	0.998485	+	0.0550297i	$0.0175253\pi$
$743$			3.00000i			0.110059i	−0.998485	+	0.0550297i	$0.982475\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.46410	+	2.00000i	0.126745	+	0.0731762i
$748$		0			0
$749$	30.0000	−	10.3923i	1.09618	−	0.379727i
$750$		0			0
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	−0.982197	−	0.187851i	$-0.939848\pi$
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	0.653783	+	0.756682i	$0.273181\pi$
$752$		0			0
$753$	50.2295	−	29.0000i	1.83046	−	1.05682i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$		0			0
$759$	7.00000	+	12.1244i	0.254084	+	0.440086i
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$	10.3923	+	2.00000i	0.376227	+	0.0724049i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.7846	+	12.0000i	−0.750489	+	0.433295i
$768$		0			0
$769$	41.0000			1.47850			0.739249	−	0.673432i	$-0.235181\pi$
$769$	41.0000			1.47850			0.739249	+	0.673432i	$0.235181\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	−12.9904	+	7.50000i	−0.467232	+	0.269756i	−0.715080	−	0.699043i	$-0.753610\pi$
$773$	−12.9904	+	7.50000i	−0.467232	+	0.269756i	0.247849	+	0.968799i	$0.420276\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−17.3205	+	20.0000i	−0.621370	+	0.717496i
$778$		0			0
$779$	12.5000	−	21.6506i	0.447859	−	0.775715i
$780$		0			0
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$		0			0
$783$			24.0000i			0.857690i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−15.5885	+	9.00000i	−0.555668	+	0.320815i	−0.751405	−	0.659841i	$-0.770624\pi$
$787$	−15.5885	+	9.00000i	−0.555668	+	0.320815i	0.195737	+	0.980656i	$0.437290\pi$
$788$		0			0
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$		0			0
$791$	40.0000	+	34.6410i	1.42224	+	1.23169i
$792$		0			0
$793$	31.1769	+	18.0000i	1.10712	+	0.639199i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$	−10.3923	−	6.00000i	−0.366736	−	0.211735i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−20.7846	−	12.0000i	−0.731653	−	0.422420i
$808$		0			0
$809$	27.5000	+	47.6314i	0.966849	+	1.67463i	0.704564	+	0.709640i	$0.251142\pi$
$809$	27.5000	+	47.6314i	0.966849	+	1.67463i	0.262284	+	0.964991i	$0.415524\pi$
$810$		0			0
$811$	−5.00000			−0.175574			−0.0877869	−	0.996139i	$-0.527979\pi$
$811$	−5.00000			−0.175574			−0.0877869	+	0.996139i	$0.527979\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	25.9808	+	15.0000i	0.908952	+	0.524784i
$818$		0			0
$819$	−7.50000	+	2.59808i	−0.262071	+	0.0907841i
$820$		0			0
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$		0			0
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	−0.559159	−	0.829060i	$-0.688876\pi$
$823$	−3.46410	+	2.00000i	−0.120751	+	0.0697156i	0.438408	+	0.898776i	$0.355543\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	14.0000i		−	0.486828i	−0.969923	−	0.243414i	$-0.921733\pi$
$827$		−	14.0000i		−	0.486828i	0.969923	−	0.243414i	$-0.0782673\pi$
$828$		0			0
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	0.980642	+	0.195810i	$0.0627335\pi$
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	−0.320745	+	0.947166i	$0.603933\pi$
$830$		0			0
$831$	2.00000	−	3.46410i	0.0693792	−	0.120168i
$832$		0			0
$833$	8.66025	+	11.0000i	0.300060	+	0.381127i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.8564	−	8.00000i	0.478947	−	0.276520i
$838$		0			0
$839$	14.0000			0.483334			0.241667	−	0.970359i	$-0.422306\pi$
$839$	14.0000			0.483334			0.241667	+	0.970359i	$0.422306\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−5.19615	+	3.00000i	−0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	8.66025	+	25.0000i	0.297570	+	0.859010i
$848$		0			0
$849$	22.0000	−	38.1051i	0.755038	−	1.30776i
$850$		0			0
$851$	17.5000	+	30.3109i	0.599892	+	1.03904i
$852$		0			0
$853$		−	23.0000i		−	0.787505i	−0.919216	−	0.393753i	$-0.871177\pi$
$853$		−	23.0000i		−	0.787505i	0.919216	−	0.393753i	$-0.128823\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.969599	−	0.244701i	$-0.921310\pi$
$857$	−36.3731	+	21.0000i	−1.24248	+	0.717346i	−0.272882	+	0.962048i	$0.587977\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$		0			0
$861$	5.00000	−	25.9808i	0.170400	−	0.885422i
$862$		0			0
$863$	−11.2583	−	6.50000i	−0.383238	−	0.221263i	0.295988	−	0.955192i	$-0.404351\pi$
$863$	−11.2583	−	6.50000i	−0.383238	−	0.221263i	−0.679226	+	0.733929i	$0.737684\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			26.0000i			0.883006i
$868$		0			0
$869$	14.0000			0.474917
$870$		0			0
$871$	−6.00000	−	10.3923i	−0.203302	−	0.352130i
$872$		0			0
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.79423	−	4.50000i	−0.263192	−	0.151954i	0.362598	−	0.931946i	$-0.381890\pi$
$877$	−7.79423	−	4.50000i	−0.263192	−	0.151954i	−0.625790	+	0.779992i	$0.715223\pi$
$878$		0			0
$879$	−21.0000	−	36.3731i	−0.708312	−	1.22683i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$		0			0
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	−34.0000	−	29.4449i	−1.14032	−	0.987549i
$890$		0			0
$891$	−5.50000	+	9.52628i	−0.184257	+	0.319142i
$892$		0			0
$893$	−38.9711	+	22.5000i	−1.30412	+	0.752934i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			42.0000i			1.40234i
$898$		0			0
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$	11.0000	−	19.0526i	0.366463	−	0.634733i
$902$		0			0
$903$	31.1769	+	6.00000i	1.03750	+	0.199667i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	19.0526	−	11.0000i	0.632630	−	0.365249i	−0.149140	−	0.988816i	$-0.547651\pi$
$907$	19.0526	−	11.0000i	0.632630	−	0.365249i	0.781770	+	0.623567i	$0.214317\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$		0			0
$913$	−3.46410	+	2.00000i	−0.114645	+	0.0661903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.06218	−	17.5000i	−0.200191	−	0.577901i
$918$		0			0
$919$	−9.00000	+	15.5885i	−0.296883	+	0.514216i	−0.975421	−	0.220349i	$-0.929280\pi$
$919$	−9.00000	+	15.5885i	−0.296883	+	0.514216i	0.678538	+	0.734565i	$0.262614\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$		0			0
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	17.3205	−	10.0000i	0.568880	−	0.328443i
$928$		0			0
$929$	−15.5000	+	26.8468i	−0.508539	+	0.880815i	0.491413	+	0.870927i	$0.336481\pi$
$929$	−15.5000	+	26.8468i	−0.508539	+	0.880815i	−0.999951	+	0.00988764i	$0.996853\pi$
$930$		0			0
$931$	32.5000	+	12.9904i	1.06514	+	0.425743i
$932$		0			0
$933$	6.92820	+	4.00000i	0.226819	+	0.130954i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	38.0000i		−	1.24141i	−0.784046	−	0.620703i	$-0.786847\pi$
$937$		−	38.0000i		−	1.24141i	0.784046	−	0.620703i	$-0.213153\pi$
$938$		0			0
$939$	32.0000			1.04428
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$		0			0
$943$	−30.3109	−	17.5000i	−0.987058	−	0.569878i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.1244	−	7.00000i	−0.393989	−	0.227469i	0.289898	−	0.957057i	$-0.406379\pi$
$947$	−12.1244	−	7.00000i	−0.393989	−	0.227469i	−0.683887	+	0.729588i	$0.739712\pi$
$948$		0			0
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$		0			0
$951$	−4.00000			−0.129709
$952$		0			0
$953$			20.0000i			0.647864i	0.946080	+	0.323932i	$0.105005\pi$
$953$			20.0000i			0.647864i	−0.946080	+	0.323932i	$0.894995\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	10.3923	+	6.00000i	0.335936	+	0.193952i
$958$		0			0
$959$	6.00000	−	31.1769i	0.193750	−	1.00676i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$		0			0
$969$	−10.0000	−	17.3205i	−0.321246	−	0.556415i
$970$		0			0
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	−0.916705	−	0.399564i	$-0.869162\pi$
$971$	−3.50000	+	6.06218i	−0.112320	+	0.194545i	0.804385	+	0.594108i	$0.202495\pi$
$972$		0			0
$973$	6.92820	−	8.00000i	0.222108	−	0.256468i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−4.00000			−0.127710
$982$		0			0
$983$	2.59808	−	1.50000i	0.0828658	−	0.0478426i	−0.457995	−	0.888955i	$-0.651432\pi$
$983$	2.59808	−	1.50000i	0.0828658	−	0.0478426i	0.540860	+	0.841112i	$0.318099\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−31.1769	+	36.0000i	−0.992372	+	1.14589i
$988$		0			0
$989$	21.0000	−	36.3731i	0.667761	−	1.15660i
$990$		0			0
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$		0			0
$993$		−	54.0000i		−	1.71364i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	39.8372	−	23.0000i	1.26166	−	0.728417i	0.288261	−	0.957552i	$-0.406923\pi$
$997$	39.8372	−	23.0000i	1.26166	−	0.728417i	0.973395	+	0.229135i	$0.0735896\pi$
$998$		0			0
$999$	−10.0000	+	17.3205i	−0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.e.849.2		4
5.2	odd	4		1400.2.q.a.401.1		2
5.3	odd	4		280.2.q.c.121.1	yes	2
5.4	even	2	inner	1400.2.bh.e.849.1		4
7.4	even	3	inner	1400.2.bh.e.249.1		4
15.8	even	4		2520.2.bi.e.1801.1		2
20.3	even	4		560.2.q.c.401.1		2
35.2	odd	12		9800.2.a.bi.1.1		1
35.3	even	12		1960.2.q.c.361.1		2
35.4	even	6	inner	1400.2.bh.e.249.2		4
35.12	even	12		9800.2.a.g.1.1		1
35.13	even	4		1960.2.q.c.961.1		2
35.18	odd	12		280.2.q.c.81.1	✓	2
35.23	odd	12		1960.2.a.a.1.1		1
35.32	odd	12		1400.2.q.a.1201.1		2
35.33	even	12		1960.2.a.m.1.1		1
105.53	even	12		2520.2.bi.e.361.1		2
140.23	even	12		3920.2.a.bf.1.1		1
140.103	odd	12		3920.2.a.i.1.1		1
140.123	even	12		560.2.q.c.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.c.81.1	✓	2	35.18	odd	12
280.2.q.c.121.1	yes	2	5.3	odd	4
560.2.q.c.81.1		2	140.123	even	12
560.2.q.c.401.1		2	20.3	even	4
1400.2.q.a.401.1		2	5.2	odd	4
1400.2.q.a.1201.1		2	35.32	odd	12
1400.2.bh.e.249.1		4	7.4	even	3	inner
1400.2.bh.e.249.2		4	35.4	even	6	inner
1400.2.bh.e.849.1		4	5.4	even	2	inner
1400.2.bh.e.849.2		4	1.1	even	1	trivial
1960.2.a.a.1.1		1	35.23	odd	12
1960.2.a.m.1.1		1	35.33	even	12
1960.2.q.c.361.1		2	35.3	even	12
1960.2.q.c.961.1		2	35.13	even	4
2520.2.bi.e.361.1		2	105.53	even	12
2520.2.bi.e.1801.1		2	15.8	even	4
3920.2.a.i.1.1		1	140.103	odd	12
3920.2.a.bf.1.1		1	140.23	even	12
9800.2.a.g.1.1		1	35.12	even	12
9800.2.a.bi.1.1		1	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.00000i q^{13} +(-1.73205 + 1.00000i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-1.00000 + 5.19615i) q^{21} +(6.06218 + 3.50000i) q^{23} +4.00000i q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.73205 + 1.00000i) q^{33} +(4.33013 + 2.50000i) q^{37} +(3.00000 + 5.19615i) q^{39} -5.00000 q^{41} -6.00000i q^{43} +(7.79423 + 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-9.52628 + 5.50000i) q^{53} +10.0000i q^{57} +(4.00000 + 6.92820i) q^{59} +(6.00000 - 10.3923i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-3.46410 + 2.00000i) q^{67} +14.0000 q^{69} -4.00000 q^{71} +(-10.3923 + 6.00000i) q^{73} +(-2.59808 - 0.500000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000i q^{83} +(10.3923 - 6.00000i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-6.00000 - 5.19615i) q^{91} +(-6.92820 - 4.00000i) q^{93} +6.00000i q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} + 2 q^{11} - 10 q^{19} - 4 q^{21} + 24 q^{29} - 8 q^{31} + 12 q^{39} - 20 q^{41} - 4 q^{49} - 8 q^{51} + 16 q^{59} + 24 q^{61} + 56 q^{69} - 16 q^{71} + 28 q^{79} + 22 q^{81} + 12 q^{89} - 24 q^{91} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 + 2 * q^11 - 10 * q^19 - 4 * q^21 + 24 * q^29 - 8 * q^31 + 12 * q^39 - 20 * q^41 - 4 * q^49 - 8 * q^51 + 16 * q^59 + 24 * q^61 + 56 * q^69 - 16 * q^71 + 28 * q^79 + 22 * q^81 + 12 * q^89 - 24 * q^91 + 4 * q^99

Introduction

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