LMFDB - Embedded newform 700.2.i.f.501.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(401,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.401"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2702336256.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 $ x^8 + 9x^6 + 56x^4 + 225*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.2
Root			$1.52274 + 1.63746i$ of defining polynomial
Character	$\chi$	$=$	700.501
Dual form			700.2.i.f.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.50000i) q^{3} +(2.38876 + 1.13746i) q^{7} +(2.63746 - 4.56821i) q^{11} +2.62685 q^{13} +(-0.209313 + 0.362541i) q^{17} +(-1.63746 - 2.83616i) q^{19} +(-3.77492 + 2.59808i) q^{21} +(3.91150 + 6.77492i) q^{23} -5.19615 q^{27} +4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(4.56821 + 7.91238i) q^{33} +(4.98684 + 8.63746i) q^{37} +(-2.27492 + 3.94027i) q^{39} -3.72508 q^{41} -2.15068 q^{43} +(-3.25479 - 5.63746i) q^{47} +(4.41238 + 5.43424i) q^{49} +(-0.362541 - 0.627940i) q^{51} +(2.83616 - 4.91238i) q^{53} +5.67232 q^{57} +(1.63746 - 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-1.76082 + 3.04983i) q^{67} -13.5498 q^{69} -4.54983 q^{71} +(-3.25479 + 5.63746i) q^{73} +(11.4964 - 7.91238i) q^{77} +(-3.63746 - 6.30026i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.40437 q^{83} +(-3.70219 + 6.41238i) q^{87} +(3.50000 + 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(-2.83616 - 4.91238i) q^{93} -6.92820 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{11} + 2 q^{19} + 4 q^{29} + 2 q^{31} + 12 q^{39} - 60 q^{41} - 10 q^{49} - 18 q^{51} - 2 q^{59} + 24 q^{61} - 48 q^{69} + 24 q^{71} - 14 q^{79} + 36 q^{81} + 28 q^{89} + 20 q^{91}+O(q^{100}) $ 8 * q + 6 * q^11 + 2 * q^19 + 4 * q^29 + 2 * q^31 + 12 * q^39 - 60 * q^41 - 10 * q^49 - 18 * q^51 - 2 * q^59 + 24 * q^61 - 48 * q^69 + 24 * q^71 - 14 * q^79 + 36 * q^81 + 28 * q^89 + 20 * q^91

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.38876	+	1.13746i	0.902867	+	0.429919i
$7$	2.38876	+	1.13746i	0.902867	+	0.429919i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	−0.127473	−	0.991842i	$-0.540687\pi$
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	0.922697	−	0.385526i	$-0.125980\pi$
$12$		0			0
$13$	2.62685			0.728557			0.364278	−	0.931290i	$-0.381316\pi$
$13$	2.62685			0.728557			0.364278	+	0.931290i	$0.381316\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.209313	+	0.362541i	−0.0507659	+	0.0879292i	−0.890292	−	0.455391i	$-0.849500\pi$
$17$	−0.209313	+	0.362541i	−0.0507659	+	0.0879292i	0.839526	+	0.543320i	$0.182833\pi$
$18$		0			0
$19$	−1.63746	−	2.83616i	−0.375659	−	0.650660i	0.614767	−	0.788709i	$-0.289250\pi$
$19$	−1.63746	−	2.83616i	−0.375659	−	0.650660i	−0.990425	+	0.138049i	$0.955917\pi$
$20$		0			0
$21$	−3.77492	+	2.59808i	−0.823754	+	0.566947i
$22$		0			0
$23$	3.91150	+	6.77492i	0.815604	+	1.41267i	0.908893	+	0.417029i	$0.136929\pi$
$23$	3.91150	+	6.77492i	0.815604	+	1.41267i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	4.27492			0.793832			0.396916	−	0.917855i	$-0.370080\pi$
$29$	4.27492			0.793832			0.396916	+	0.917855i	$0.370080\pi$
$30$		0			0
$31$	−1.63746	+	2.83616i	−0.294096	+	0.509390i	−0.974774	−	0.223193i	$-0.928352\pi$
$31$	−1.63746	+	2.83616i	−0.294096	+	0.509390i	0.680678	+	0.732583i	$0.261685\pi$
$32$		0			0
$33$	4.56821	+	7.91238i	0.795224	+	1.37737i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.98684	+	8.63746i	0.819831	+	1.41999i	0.905806	+	0.423692i	$0.139266\pi$
$37$	4.98684	+	8.63746i	0.819831	+	1.41999i	−0.0859750	+	0.996297i	$0.527401\pi$
$38$		0			0
$39$	−2.27492	+	3.94027i	−0.364278	+	0.630949i
$40$		0			0
$41$	−3.72508			−0.581760			−0.290880	−	0.956760i	$-0.593948\pi$
$41$	−3.72508			−0.581760			−0.290880	+	0.956760i	$0.593948\pi$
$42$		0			0
$43$	−2.15068			−0.327975			−0.163988	−	0.986462i	$-0.552436\pi$
$43$	−2.15068			−0.327975			−0.163988	+	0.986462i	$0.552436\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.25479	−	5.63746i	−0.474760	−	0.822308i	0.524823	−	0.851212i	$-0.324132\pi$
$47$	−3.25479	−	5.63746i	−0.474760	−	0.822308i	−0.999582	+	0.0289038i	$0.990798\pi$
$48$		0			0
$49$	4.41238	+	5.43424i	0.630339	+	0.776320i
$50$		0			0
$51$	−0.362541	−	0.627940i	−0.0507659	−	0.0879292i
$52$		0			0
$53$	2.83616	−	4.91238i	0.389577	−	0.674767i	−0.602816	−	0.797880i	$-0.705955\pi$
$53$	2.83616	−	4.91238i	0.389577	−	0.674767i	0.992393	+	0.123114i	$0.0392880\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.67232			0.751318
$58$		0			0
$59$	1.63746	−	2.83616i	0.213179	−	0.369237i	−0.739529	−	0.673125i	$-0.764952\pi$
$59$	1.63746	−	2.83616i	0.213179	−	0.369237i	0.952708	+	0.303888i	$0.0982849\pi$
$60$		0			0
$61$	6.77492	+	11.7345i	0.867439	+	1.50245i	0.864605	+	0.502453i	$0.167569\pi$
$61$	6.77492	+	11.7345i	0.867439	+	1.50245i	0.00283468	+	0.999996i	$0.499098\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.76082	+	3.04983i	−0.215119	+	0.372597i	−0.953309	−	0.301996i	$-0.902347\pi$
$67$	−1.76082	+	3.04983i	−0.215119	+	0.372597i	0.738191	+	0.674592i	$0.235681\pi$
$68$		0			0
$69$	−13.5498			−1.63121
$70$		0			0
$71$	−4.54983			−0.539966			−0.269983	−	0.962865i	$-0.587018\pi$
$71$	−4.54983			−0.539966			−0.269983	+	0.962865i	$0.587018\pi$
$72$		0			0
$73$	−3.25479	+	5.63746i	−0.380944	+	0.659815i	−0.991197	−	0.132392i	$-0.957734\pi$
$73$	−3.25479	+	5.63746i	−0.380944	+	0.659815i	0.610253	+	0.792206i	$0.291068\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.4964	−	7.91238i	1.31014	−	0.901699i
$78$		0			0
$79$	−3.63746	−	6.30026i	−0.409246	−	0.708835i	0.585559	−	0.810630i	$-0.300875\pi$
$79$	−3.63746	−	6.30026i	−0.409246	−	0.708835i	−0.994805	+	0.101795i	$0.967542\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$	−7.40437			−0.812736			−0.406368	−	0.913710i	$-0.633205\pi$
$83$	−7.40437			−0.812736			−0.406368	+	0.913710i	$0.633205\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.70219	+	6.41238i	−0.396916	+	0.687479i
$88$		0			0
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	6.27492	+	2.98793i	0.657790	+	0.313220i
$92$		0			0
$93$	−2.83616	−	4.91238i	−0.294096	−	0.509390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.92820			−0.703452			−0.351726	−	0.936103i	$-0.614405\pi$
$97$	−6.92820			−0.703452			−0.351726	+	0.936103i	$0.614405\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.77492	−	11.7345i	0.674129	−	1.16763i	−0.302593	−	0.953120i	$-0.597852\pi$
$101$	6.77492	−	11.7345i	0.674129	−	1.16763i	0.976723	−	0.214507i	$-0.0688144\pi$
$102$		0			0
$103$	−5.64355	−	9.77492i	−0.556076	−	0.963151i	−0.997819	−	0.0660098i	$-0.978973\pi$
$103$	−5.64355	−	9.77492i	−0.556076	−	0.963151i	0.441743	−	0.897141i	$-0.354360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.76082	−	3.04983i	−0.170225	−	0.294839i	0.768273	−	0.640122i	$-0.221116\pi$
$107$	−1.76082	−	3.04983i	−0.170225	−	0.294839i	−0.938499	+	0.345283i	$0.887783\pi$
$108$		0			0
$109$	5.77492	−	10.0025i	0.553137	−	0.958061i	−0.444909	−	0.895576i	$-0.646764\pi$
$109$	5.77492	−	10.0025i	0.553137	−	0.958061i	0.998046	−	0.0624852i	$-0.0199026\pi$
$110$		0			0
$111$	−17.2749			−1.63966
$112$		0			0
$113$	4.30136			0.404637			0.202319	−	0.979320i	$-0.435152\pi$
$113$	4.30136			0.404637			0.202319	+	0.979320i	$0.435152\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.912376	+	0.627940i	−0.0836374	+	0.0575632i
$120$		0			0
$121$	−8.41238	−	14.5707i	−0.764761	−	1.32461i
$122$		0			0
$123$	3.22602	−	5.58762i	0.290880	−	0.503819i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.6460			−1.38836			−0.694179	−	0.719802i	$-0.744232\pi$
$127$	−15.6460			−1.38836			−0.694179	+	0.719802i	$0.744232\pi$
$128$		0			0
$129$	1.86254	−	3.22602i	0.163988	−	0.284035i
$130$		0			0
$131$	5.36254	+	9.28819i	0.468527	+	0.811513i	0.999353	−	0.0359678i	$-0.0114514\pi$
$131$	5.36254	+	9.28819i	0.468527	+	0.811513i	−0.530826	+	0.847481i	$0.678118\pi$
$132$		0			0
$133$	−0.685484	−	8.63746i	−0.0594390	−	0.748963i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.6592	−	18.4622i	0.910674	−	1.57733i	0.0975588	−	0.995230i	$-0.468897\pi$
$137$	10.6592	−	18.4622i	0.910674	−	1.57733i	0.813115	−	0.582103i	$-0.197770\pi$
$138$		0			0
$139$	13.0997			1.11110			0.555550	−	0.831483i	$-0.312508\pi$
$139$	13.0997			1.11110			0.555550	+	0.831483i	$0.312508\pi$
$140$		0			0
$141$	11.2749			0.949519
$142$		0			0
$143$	6.92820	−	12.0000i	0.579365	−	1.00349i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.9726	+	1.91238i	−0.987482	+	0.157730i
$148$		0			0
$149$	3.77492	+	6.53835i	0.309253	+	0.535642i	0.978199	−	0.207669i	$-0.0665876\pi$
$149$	3.77492	+	6.53835i	0.309253	+	0.535642i	−0.668946	+	0.743311i	$0.733254\pi$
$150$		0			0
$151$	6.36254	−	11.0202i	0.517776	−	0.896815i	−0.482011	−	0.876165i	$-0.660093\pi$
$151$	6.36254	−	11.0202i	0.517776	−	0.896815i	0.999787	−	0.0206494i	$-0.00657337\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.10411	−	1.91238i	0.0881176	−	0.152624i	−0.818598	−	0.574367i	$-0.805248\pi$
$157$	1.10411	−	1.91238i	0.0881176	−	0.152624i	0.906715	+	0.421743i	$0.138582\pi$
$158$		0			0
$159$	4.91238	+	8.50848i	0.389577	+	0.674767i
$160$		0			0
$161$	1.63746	+	20.6328i	0.129050	+	1.62610i
$162$		0			0
$163$	−2.83616	−	4.91238i	−0.222145	−	0.384767i	0.733314	−	0.679890i	$-0.237973\pi$
$163$	−2.83616	−	4.91238i	−0.222145	−	0.384767i	−0.955459	+	0.295123i	$0.904639\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.476171			−0.0368472			−0.0184236	−	0.999830i	$-0.505865\pi$
$167$	−0.476171			−0.0368472			−0.0184236	+	0.999830i	$0.505865\pi$
$168$		0			0
$169$	−6.09967			−0.469205
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.2405	−	17.7371i	−0.778573	−	1.34853i	−0.932764	−	0.360488i	$-0.882610\pi$
$173$	−10.2405	−	17.7371i	−0.778573	−	1.34853i	0.154190	−	0.988041i	$-0.450723\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.83616	+	4.91238i	0.213179	+	0.369237i
$178$		0			0
$179$	3.63746	−	6.30026i	0.271876	−	0.470904i	−0.697466	−	0.716618i	$-0.745689\pi$
$179$	3.63746	−	6.30026i	0.271876	−	0.470904i	0.969342	+	0.245714i	$0.0790225\pi$
$180$		0			0
$181$	−24.2749			−1.80434			−0.902170	−	0.431380i	$-0.858027\pi$
$181$	−24.2749			−1.80434			−0.902170	+	0.431380i	$0.858027\pi$
$182$		0			0
$183$	−23.4690			−1.73488
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.10411	+	1.91238i	0.0807406	+	0.139847i
$188$		0			0
$189$	−12.4124	−	5.91041i	−0.902867	−	0.429919i
$190$		0			0
$191$	−0.0876242	−	0.151770i	−0.00634026	−	0.0109817i	0.862838	−	0.505481i	$-0.168685\pi$
$191$	−0.0876242	−	0.151770i	−0.00634026	−	0.0109817i	−0.869178	+	0.494499i	$0.835352\pi$
$192$		0			0
$193$	−10.6592	+	18.4622i	−0.767263	+	1.32894i	0.171778	+	0.985136i	$0.445049\pi$
$193$	−10.6592	+	18.4622i	−0.767263	+	1.32894i	−0.939042	+	0.343803i	$0.888285\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.60271			0.612918			0.306459	−	0.951884i	$-0.400856\pi$
$197$	8.60271			0.612918			0.306459	+	0.951884i	$0.400856\pi$
$198$		0			0
$199$	−8.63746	+	14.9605i	−0.612293	+	1.06052i	0.378560	+	0.925577i	$0.376419\pi$
$199$	−8.63746	+	14.9605i	−0.612293	+	1.06052i	−0.990853	+	0.134946i	$0.956914\pi$
$200$		0			0
$201$	−3.04983	−	5.28247i	−0.215119	−	0.372597i
$202$		0			0
$203$	10.2118	+	4.86254i	0.716725	+	0.341284i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−17.2749			−1.19493
$210$		0			0
$211$	25.6495			1.76578			0.882892	−	0.469576i	$-0.155593\pi$
$211$	25.6495			1.76578			0.882892	+	0.469576i	$0.155593\pi$
$212$		0			0
$213$	3.94027	−	6.82475i	0.269983	−	0.467624i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−7.13752	+	4.91238i	−0.484526	+	0.333474i
$218$		0			0
$219$	−5.63746	−	9.76436i	−0.380944	−	0.659815i
$220$		0			0
$221$	−0.549834	+	0.952341i	−0.0369859	+	0.0640614i
$222$		0			0
$223$	−8.71780			−0.583787			−0.291893	−	0.956451i	$-0.594285\pi$
$223$	−8.71780			−0.583787			−0.291893	+	0.956451i	$0.594285\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.76436	−	16.9124i	0.648084	−	1.12251i	−0.335496	−	0.942041i	$-0.608904\pi$
$227$	9.76436	−	16.9124i	0.648084	−	1.12251i	0.983580	−	0.180472i	$-0.0577626\pi$
$228$		0			0
$229$	−1.63746	−	2.83616i	−0.108206	−	0.187419i	0.806837	−	0.590774i	$-0.201177\pi$
$229$	−1.63746	−	2.83616i	−0.108206	−	0.187419i	−0.915044	+	0.403355i	$0.867844\pi$
$230$		0			0
$231$	1.91238	+	24.0969i	0.125825	+	1.58546i
$232$		0			0
$233$	−7.13752	−	12.3625i	−0.467594	−	0.809897i	0.531720	−	0.846920i	$-0.321546\pi$
$233$	−7.13752	−	12.3625i	−0.467594	−	0.809897i	−0.999314	+	0.0370231i	$0.988212\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	12.6005			0.818492
$238$		0			0
$239$	0.549834			0.0355658			0.0177829	−	0.999842i	$-0.494339\pi$
$239$	0.549834			0.0355658			0.0177829	+	0.999842i	$0.494339\pi$
$240$		0			0
$241$	−4.91238	+	8.50848i	−0.316434	+	0.548080i	−0.979741	−	0.200267i	$-0.935819\pi$
$241$	−4.91238	+	8.50848i	−0.316434	+	0.548080i	0.663307	+	0.748347i	$0.269152\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.30136	−	7.45017i	−0.273689	−	0.474043i
$248$		0			0
$249$	6.41238	−	11.1066i	0.406368	−	0.703850i
$250$		0			0
$251$	−20.5498			−1.29709			−0.648547	−	0.761175i	$-0.724623\pi$
$251$	−20.5498			−1.29709			−0.648547	+	0.761175i	$0.724623\pi$
$252$		0			0
$253$	41.2657			2.59435
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.82409	+	10.0876i	0.363297	+	0.629249i	0.988501	−	0.151212i	$-0.0483177\pi$
$257$	5.82409	+	10.0876i	0.363297	+	0.629249i	−0.625204	+	0.780461i	$0.714984\pi$
$258$		0			0
$259$	2.08762	+	26.3052i	0.129719	+	1.63452i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.389855	+	0.675248i	−0.0240395	+	0.0416376i	−0.877795	−	0.479037i	$-0.840986\pi$
$263$	−0.389855	+	0.675248i	−0.0240395	+	0.0416376i	0.853755	+	0.520674i	$0.174319\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−12.1244			−0.741999
$268$		0			0
$269$	7.22508	−	12.5142i	0.440521	−	0.763005i	−0.557207	−	0.830374i	$-0.688127\pi$
$269$	7.22508	−	12.5142i	0.440521	−	0.763005i	0.997728	+	0.0673687i	$0.0214604\pi$
$270$		0			0
$271$	−4.91238	−	8.50848i	−0.298406	−	0.516854i	0.677366	−	0.735646i	$-0.263121\pi$
$271$	−4.91238	−	8.50848i	−0.298406	−	0.516854i	−0.975771	+	0.218793i	$0.929788\pi$
$272$		0			0
$273$	−9.91613	+	6.82475i	−0.600152	+	0.413053i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.13752	+	12.3625i	−0.428852	+	0.742793i	−0.996771	−	0.0802909i	$-0.974415\pi$
$277$	−7.13752	+	12.3625i	−0.428852	+	0.742793i	0.567920	+	0.823084i	$0.307748\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−5.46301	+	9.46221i	−0.324742	+	0.562470i	−0.981460	−	0.191666i	$-0.938611\pi$
$283$	−5.46301	+	9.46221i	−0.324742	+	0.562470i	0.656718	+	0.754136i	$0.271944\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.89834	−	4.23713i	−0.525252	−	0.250110i
$288$		0			0
$289$	8.41238	+	14.5707i	0.494846	+	0.857098i
$290$		0			0
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$		0			0
$293$	6.92820			0.404750			0.202375	−	0.979308i	$-0.435134\pi$
$293$	6.92820			0.404750			0.202375	+	0.979308i	$0.435134\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−13.7046	+	23.7371i	−0.795224	+	1.37737i
$298$		0			0
$299$	10.2749	+	17.7967i	0.594214	+	1.02921i
$300$		0			0
$301$	−5.13746	−	2.44631i	−0.296118	−	0.141003i
$302$		0			0
$303$	11.7345	+	20.3248i	0.674129	+	1.16763i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	26.5145			1.51326			0.756631	−	0.653843i	$-0.226844\pi$
$307$	26.5145			1.51326			0.756631	+	0.653843i	$0.226844\pi$
$308$		0			0
$309$	19.5498			1.11215
$310$		0			0
$311$	4.91238	−	8.50848i	0.278555	−	0.482472i	−0.692471	−	0.721446i	$-0.743478\pi$
$311$	4.91238	−	8.50848i	0.278555	−	0.482472i	0.971026	+	0.238974i	$0.0768111\pi$
$312$		0			0
$313$	16.7501	+	29.0120i	0.946772	+	1.63986i	0.752163	+	0.658977i	$0.229010\pi$
$313$	16.7501	+	29.0120i	0.946772	+	1.63986i	0.194609	+	0.980881i	$0.437656\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.8098	−	22.1873i	−0.719472	−	1.24616i	−0.961209	−	0.275821i	$-0.911050\pi$
$317$	−12.8098	−	22.1873i	−0.719472	−	1.24616i	0.241737	−	0.970342i	$-0.422283\pi$
$318$		0			0
$319$	11.2749	−	19.5287i	0.631274	−	1.09340i
$320$		0			0
$321$	6.09967			0.340450
$322$		0			0
$323$	1.37097			0.0762827
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10.0025	+	17.3248i	0.553137	+	0.958061i
$328$		0			0
$329$	−1.36254	−	17.1687i	−0.0751193	−	0.946543i
$330$		0			0
$331$	−8.91238	−	15.4367i	−0.489868	−	0.848477i	0.510064	−	0.860137i	$-0.329622\pi$
$331$	−8.91238	−	15.4367i	−0.489868	−	0.848477i	−0.999932	+	0.0116596i	$0.996289\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−4.30136			−0.234310			−0.117155	−	0.993114i	$-0.537377\pi$
$337$	−4.30136			−0.234310			−0.117155	+	0.993114i	$0.537377\pi$
$338$		0			0
$339$	−3.72508	+	6.45203i	−0.202319	+	0.350426i
$340$		0			0
$341$	8.63746	+	14.9605i	0.467745	+	0.810157i
$342$		0			0
$343$	4.35890	+	18.0000i	0.235358	+	0.971909i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.06218	+	10.5000i	−0.325435	+	0.563670i	−0.981600	−	0.190947i	$-0.938844\pi$
$347$	−6.06218	+	10.5000i	−0.325435	+	0.563670i	0.656165	+	0.754617i	$0.272177\pi$
$348$		0			0
$349$	−3.72508			−0.199399			−0.0996996	−	0.995018i	$-0.531788\pi$
$349$	−3.72508			−0.199399			−0.0996996	+	0.995018i	$0.531788\pi$
$350$		0			0
$351$	−13.6495			−0.728557
$352$		0			0
$353$	−4.09204	+	7.08762i	−0.217797	+	0.377236i	−0.954134	−	0.299379i	$-0.903221\pi$
$353$	−4.09204	+	7.08762i	−0.217797	+	0.377236i	0.736337	+	0.676615i	$0.236554\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.151770	−	1.91238i	−0.00803249	−	0.101214i
$358$		0			0
$359$	−18.1873	−	31.5013i	−0.959889	−	1.66258i	−0.722762	−	0.691097i	$-0.757128\pi$
$359$	−18.1873	−	31.5013i	−0.959889	−	1.66258i	−0.237127	−	0.971479i	$-0.576206\pi$
$360$		0			0
$361$	4.13746	−	7.16629i	0.217761	−	0.377173i
$362$		0			0
$363$	29.1413			1.52952
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.01670	−	5.22508i	0.157471	−	0.272747i	−0.776485	−	0.630135i	$-0.782999\pi$
$367$	3.01670	−	5.22508i	0.157471	−	0.272747i	0.933956	+	0.357388i	$0.116333\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.3625	−	8.50848i	0.641831	−	0.441739i
$372$		0			0
$373$	−4.98684	−	8.63746i	−0.258209	−	0.447231i	0.707553	−	0.706660i	$-0.249799\pi$
$373$	−4.98684	−	8.63746i	−0.258209	−	0.447231i	−0.965762	+	0.259429i	$0.916466\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.2296			0.578352
$378$		0			0
$379$	−21.6495			−1.11206			−0.556030	−	0.831162i	$-0.687676\pi$
$379$	−21.6495			−1.11206			−0.556030	+	0.831162i	$0.687676\pi$
$380$		0			0
$381$	13.5498	−	23.4690i	0.694179	−	1.20235i
$382$		0			0
$383$	3.07425	+	5.32475i	0.157087	+	0.272082i	0.933817	−	0.357751i	$-0.116456\pi$
$383$	3.07425	+	5.32475i	0.157087	+	0.272082i	−0.776730	+	0.629833i	$0.783123\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.1873	+	28.0372i	−0.820728	+	1.42154i	0.0844123	+	0.996431i	$0.473099\pi$
$389$	−16.1873	+	28.0372i	−0.820728	+	1.42154i	−0.905141	+	0.425112i	$0.860235\pi$
$390$		0			0
$391$	−3.27492			−0.165620
$392$		0			0
$393$	−18.5764			−0.937055
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.40547	−	9.36254i	−0.271293	−	0.469892i	0.697901	−	0.716195i	$-0.254118\pi$
$397$	−5.40547	−	9.36254i	−0.271293	−	0.469892i	−0.969193	+	0.246302i	$0.920784\pi$
$398$		0			0
$399$	13.5498	+	6.45203i	0.678340	+	0.323006i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−4.30136	+	7.45017i	−0.214266	+	0.371119i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	52.6103			2.60780
$408$		0			0
$409$	10.0498	−	17.4068i	0.496932	−	0.860712i	−0.503061	−	0.864251i	$-0.667793\pi$
$409$	10.0498	−	17.4068i	0.496932	−	0.860712i	0.999994	+	0.00353862i	$0.00112638\pi$
$410$		0			0
$411$	18.4622	+	31.9775i	0.910674	+	1.57733i
$412$		0			0
$413$	7.13752	−	4.91238i	0.351214	−	0.241722i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.3446	+	19.6495i	−0.555550	+	0.962240i
$418$		0			0
$419$	−13.0997			−0.639961			−0.319980	−	0.947424i	$-0.603676\pi$
$419$	−13.0997			−0.639961			−0.319980	+	0.947424i	$0.603676\pi$
$420$		0			0
$421$	−4.27492			−0.208347			−0.104173	−	0.994559i	$-0.533220\pi$
$421$	−4.27492			−0.208347			−0.104173	+	0.994559i	$0.533220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.83616	+	35.7371i	0.137251	+	1.72944i
$428$		0			0
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$	9.18729	−	15.9129i	0.442536	−	0.766495i	−0.555341	−	0.831623i	$-0.687412\pi$
$431$	9.18729	−	15.9129i	0.442536	−	0.766495i	0.997877	+	0.0651276i	$0.0207454\pi$
$432$		0			0
$433$	−18.1578			−0.872606			−0.436303	−	0.899800i	$-0.643712\pi$
$433$	−18.1578			−0.872606			−0.436303	+	0.899800i	$0.643712\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.8098	−	22.1873i	0.612778	−	1.06136i
$438$		0			0
$439$	−11.9124	−	20.6328i	−0.568547	−	0.984752i	−0.996710	−	0.0810504i	$-0.974173\pi$
$439$	−11.9124	−	20.6328i	−0.568547	−	0.984752i	0.428163	−	0.903701i	$-0.359161\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.06218	+	10.5000i	0.288023	+	0.498870i	0.973338	−	0.229377i	$-0.0736688\pi$
$443$	6.06218	+	10.5000i	0.288023	+	0.498870i	−0.685315	+	0.728247i	$0.740335\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.0767			−0.618507
$448$		0			0
$449$	−3.17525			−0.149849			−0.0749246	−	0.997189i	$-0.523872\pi$
$449$	−3.17525			−0.149849			−0.0749246	+	0.997189i	$0.523872\pi$
$450$		0			0
$451$	−9.82475	+	17.0170i	−0.462629	+	0.801298i
$452$		0			0
$453$	11.0202	+	19.0876i	0.517776	+	0.896815i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.685484	+	1.18729i	0.0320656	+	0.0555392i	0.881613	−	0.471973i	$-0.156458\pi$
$457$	0.685484	+	1.18729i	0.0320656	+	0.0555392i	−0.849547	+	0.527512i	$0.823125\pi$
$458$		0			0
$459$	1.08762	−	1.88382i	0.0507659	−	0.0879292i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	2.15068			0.0999505			0.0499752	−	0.998750i	$-0.484086\pi$
$463$	2.15068			0.0999505			0.0499752	+	0.998750i	$0.484086\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.85177	−	13.5997i	−0.363337	−	0.629318i	0.625171	−	0.780488i	$-0.285029\pi$
$467$	−7.85177	−	13.5997i	−0.363337	−	0.629318i	−0.988508	+	0.151170i	$0.951696\pi$
$468$		0			0
$469$	−7.67525	+	5.28247i	−0.354410	+	0.243922i
$470$		0			0
$471$	1.91238	+	3.31233i	0.0881176	+	0.152624i
$472$		0			0
$473$	−5.67232	+	9.82475i	−0.260814	+	0.451743i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.91238	+	8.50848i	−0.224452	+	0.388763i	−0.956155	−	0.292861i	$-0.905393\pi$
$479$	−4.91238	+	8.50848i	−0.224452	+	0.388763i	0.731703	+	0.681624i	$0.238726\pi$
$480$		0			0
$481$	13.0997	+	22.6893i	0.597293	+	1.03454i
$482$		0			0
$483$	−32.3673	−	15.4124i	−1.47277	−	0.701287i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.46519	+	2.53779i	−0.0663943	+	0.114998i	−0.897312	−	0.441398i	$-0.854483\pi$
$487$	−1.46519	+	2.53779i	−0.0663943	+	0.114998i	0.830917	+	0.556396i	$0.187816\pi$
$488$		0			0
$489$	9.82475			0.444291
$490$		0			0
$491$	−28.5498			−1.28844			−0.644218	−	0.764842i	$-0.722817\pi$
$491$	−28.5498			−1.28844			−0.644218	+	0.764842i	$0.722817\pi$
$492$		0			0
$493$	−0.894797	+	1.54983i	−0.0402996	+	0.0698010i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.8685	−	5.17525i	−0.487518	−	0.232142i
$498$		0			0
$499$	−0.812707	−	1.40765i	−0.0363818	−	0.0630151i	0.847261	−	0.531177i	$-0.178250\pi$
$499$	−0.812707	−	1.40765i	−0.0363818	−	0.0630151i	−0.883643	+	0.468161i	$0.844917\pi$
$500$		0			0
$501$	0.412376	−	0.714256i	0.0184236	−	0.0319106i
$502$		0			0
$503$	31.7682			1.41647			0.708236	−	0.705975i	$-0.249491\pi$
$503$	31.7682			1.41647			0.708236	+	0.705975i	$0.249491\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.28247	−	9.14950i	0.234603	−	0.406344i
$508$		0			0
$509$	7.22508	+	12.5142i	0.320246	+	0.554683i	0.980539	−	0.196326i	$-0.0629010\pi$
$509$	7.22508	+	12.5142i	0.320246	+	0.554683i	−0.660293	+	0.751008i	$0.729568\pi$
$510$		0			0
$511$	−14.1873	+	9.76436i	−0.627609	+	0.431950i
$512$		0			0
$513$	8.50848	+	14.7371i	0.375659	+	0.650660i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−34.3375			−1.51016
$518$		0			0
$519$	35.4743			1.55715
$520$		0			0
$521$	−4.91238	+	8.50848i	−0.215215	+	0.372763i	−0.953339	−	0.301902i	$-0.902379\pi$
$521$	−4.91238	+	8.50848i	−0.215215	+	0.372763i	0.738124	+	0.674665i	$0.235712\pi$
$522$		0			0
$523$	−3.67341	−	6.36254i	−0.160627	−	0.278215i	0.774467	−	0.632615i	$-0.218018\pi$
$523$	−3.67341	−	6.36254i	−0.160627	−	0.278215i	−0.935094	+	0.354400i	$0.884685\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.685484	−	1.18729i	−0.0298602	−	0.0517193i
$528$		0			0
$529$	−19.0997	+	33.0816i	−0.830420	+	1.43833i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.78523			−0.423845
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.30026	+	10.9124i	0.271876	+	0.470904i
$538$		0			0
$539$	36.4622	−	5.82409i	1.57054	−	0.250861i
$540$		0			0
$541$	8.77492	+	15.1986i	0.377263	+	0.653439i	0.990663	−	0.136334i	$-0.0435319\pi$
$541$	8.77492	+	15.1986i	0.377263	+	0.653439i	−0.613400	+	0.789773i	$0.710199\pi$
$542$		0			0
$543$	21.0227	−	36.4124i	0.902170	−	1.56260i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.5386			−0.878168			−0.439084	−	0.898446i	$-0.644697\pi$
$547$	−20.5386			−0.878168			−0.439084	+	0.898446i	$0.644697\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.00000	−	12.1244i	−0.298210	−	0.516515i
$552$		0			0
$553$	−1.52274	−	19.1873i	−0.0647534	−	0.815927i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.98684	+	8.63746i	−0.211299	+	0.365981i	−0.952121	−	0.305720i	$-0.901103\pi$
$557$	−4.98684	+	8.63746i	−0.211299	+	0.365981i	0.740822	+	0.671701i	$0.234436\pi$
$558$		0			0
$559$	−5.64950			−0.238949
$560$		0			0
$561$	−3.82475			−0.161481
$562$		0			0
$563$	11.3159	−	19.5997i	0.476907	−	0.826028i	−0.522743	−	0.852491i	$-0.675091\pi$
$563$	11.3159	−	19.5997i	0.476907	−	0.826028i	0.999650	+	0.0264630i	$0.00842443\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	19.6150	−	13.5000i	0.823754	−	0.566947i
$568$		0			0
$569$	−4.18729	−	7.25260i	−0.175540	−	0.304045i	0.764808	−	0.644259i	$-0.222834\pi$
$569$	−4.18729	−	7.25260i	−0.175540	−	0.304045i	−0.940348	+	0.340214i	$0.889501\pi$
$570$		0			0
$571$	−3.63746	+	6.30026i	−0.152223	+	0.263658i	−0.932044	−	0.362344i	$-0.881976\pi$
$571$	−3.63746	+	6.30026i	−0.152223	+	0.263658i	0.779821	+	0.626002i	$0.215310\pi$
$572$		0			0
$573$	0.303539			0.0126805
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.94136	−	3.36254i	0.0808200	−	0.139984i	−0.822782	−	0.568357i	$-0.807579\pi$
$577$	1.94136	−	3.36254i	0.0808200	−	0.139984i	0.903602	+	0.428372i	$0.140913\pi$
$578$		0			0
$579$	−18.4622	−	31.9775i	−0.767263	−	1.32894i
$580$		0			0
$581$	−17.6873	−	8.42217i	−0.733793	−	0.349410i
$582$		0			0
$583$	−14.9605	−	25.9124i	−0.619601	−	1.07318i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.8997			0.862623			0.431311	−	0.902203i	$-0.358051\pi$
$587$	20.8997			0.862623			0.431311	+	0.902203i	$0.358051\pi$
$588$		0			0
$589$	10.7251			0.441919
$590$		0			0
$591$	−7.45017	+	12.9041i	−0.306459	+	0.530802i
$592$		0			0
$593$	−16.6926	−	28.9124i	−0.685482	−	1.18729i	−0.973285	−	0.229600i	$-0.926258\pi$
$593$	−16.6926	−	28.9124i	−0.685482	−	1.18729i	0.287804	−	0.957689i	$-0.407075\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−14.9605	−	25.9124i	−0.612293	−	1.06052i
$598$		0			0
$599$	−2.63746	+	4.56821i	−0.107764	+	0.186652i	−0.914864	−	0.403762i	$-0.867702\pi$
$599$	−2.63746	+	4.56821i	−0.107764	+	0.186652i	0.807100	+	0.590414i	$0.201036\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−5.70109	−	9.87459i	−0.231400	−	0.400797i	0.726820	−	0.686828i	$-0.240997\pi$
$607$	−5.70109	−	9.87459i	−0.231400	−	0.400797i	−0.958220	+	0.286031i	$0.907664\pi$
$608$		0			0
$609$	−16.1375	+	11.1066i	−0.653923	+	0.450061i
$610$		0			0
$611$	−8.54983	−	14.8087i	−0.345889	−	0.599098i
$612$		0			0
$613$	14.1808	−	24.5619i	0.572757	−	0.992045i	−0.423524	−	0.905885i	$-0.639207\pi$
$613$	14.1808	−	24.5619i	0.572757	−	0.992045i	0.996281	−	0.0861600i	$-0.0274596\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.2920			−1.25977			−0.629884	−	0.776689i	$-0.716898\pi$
$617$	−31.2920			−1.25977			−0.629884	+	0.776689i	$0.716898\pi$
$618$		0			0
$619$	4.46221	−	7.72877i	0.179351	−	0.310646i	−0.762307	−	0.647215i	$-0.775933\pi$
$619$	4.46221	−	7.72877i	0.179351	−	0.310646i	0.941659	+	0.336570i	$0.109267\pi$
$620$		0			0
$621$	−20.3248	−	35.2035i	−0.815604	−	1.41267i
$622$		0			0
$623$	1.46519	+	18.4622i	0.0587017	+	0.739673i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	14.9605	−	25.9124i	0.597466	−	1.03484i
$628$		0			0
$629$	−4.17525			−0.166478
$630$		0			0
$631$	33.0997			1.31768			0.658839	−	0.752284i	$-0.271048\pi$
$631$	33.0997			1.31768			0.658839	+	0.752284i	$0.271048\pi$
$632$		0			0
$633$	−22.2131	+	38.4743i	−0.882892	+	1.52921i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.5906	+	14.2749i	0.459238	+	0.565593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.04983	−	1.81837i	0.0414660	−	0.0718212i	−0.844548	−	0.535481i	$-0.820131\pi$
$641$	1.04983	−	1.81837i	0.0414660	−	0.0718212i	0.886014	+	0.463659i	$0.153464\pi$
$642$		0			0
$643$	−31.4071			−1.23857			−0.619287	−	0.785164i	$-0.712578\pi$
$643$	−31.4071			−1.23857			−0.619287	+	0.785164i	$0.712578\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.4666	+	23.3248i	−0.529425	+	0.916991i	0.469986	+	0.882674i	$0.344259\pi$
$647$	−13.4666	+	23.3248i	−0.529425	+	0.916991i	−0.999411	+	0.0343169i	$0.989074\pi$
$648$		0			0
$649$	−8.63746	−	14.9605i	−0.339050	−	0.587252i
$650$		0			0
$651$	−1.18729	−	14.9605i	−0.0465337	−	0.586349i
$652$		0			0
$653$	−14.1808	−	24.5619i	−0.554938	−	0.961181i	−0.997908	−	0.0646444i	$-0.979409\pi$
$653$	−14.1808	−	24.5619i	−0.554938	−	0.961181i	0.442970	−	0.896536i	$-0.353925\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−40.5498			−1.57960			−0.789799	−	0.613366i	$-0.789815\pi$
$659$	−40.5498			−1.57960			−0.789799	+	0.613366i	$0.789815\pi$
$660$		0			0
$661$	0.225083	−	0.389855i	0.00875471	−	0.0151636i	−0.861615	−	0.507563i	$-0.830547\pi$
$661$	0.225083	−	0.389855i	0.00875471	−	0.0151636i	0.870370	+	0.492399i	$0.163880\pi$
$662$		0			0
$663$	−0.952341	−	1.64950i	−0.0369859	−	0.0640614i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	16.7213	+	28.9622i	0.647453	+	1.12142i
$668$		0			0
$669$	7.54983	−	13.0767i	0.291893	−	0.505574i
$670$		0			0
$671$	71.4743			2.75923
$672$		0			0
$673$	−31.2920			−1.20622			−0.603109	−	0.797659i	$-0.706072\pi$
$673$	−31.2920			−1.20622			−0.603109	+	0.797659i	$0.706072\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.2021	−	40.1873i	−0.891731	−	1.54452i	−0.837799	−	0.545979i	$-0.816158\pi$
$677$	−23.2021	−	40.1873i	−0.891731	−	1.54452i	−0.0539317	−	0.998545i	$-0.517175\pi$
$678$		0			0
$679$	−16.5498	−	7.88054i	−0.635124	−	0.302428i
$680$		0			0
$681$	16.9124	+	29.2931i	0.648084	+	1.12251i
$682$		0			0
$683$	−9.58382	+	16.5997i	−0.366715	+	0.635169i	−0.989050	−	0.147582i	$-0.952851\pi$
$683$	−9.58382	+	16.5997i	−0.366715	+	0.635169i	0.622335	+	0.782751i	$0.286184\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.67232			0.216413
$688$		0			0
$689$	7.45017	−	12.9041i	0.283829	−	0.491606i
$690$		0			0
$691$	−15.1873	−	26.3052i	−0.577752	−	1.00070i	−0.995737	−	0.0922416i	$-0.970597\pi$
$691$	−15.1873	−	26.3052i	−0.577752	−	1.00070i	0.417985	−	0.908454i	$-0.362737\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.779710	−	1.35050i	0.0295336	−	0.0511537i
$698$		0			0
$699$	24.7251			0.935189
$700$		0			0
$701$	8.82475			0.333306			0.166653	−	0.986016i	$-0.446704\pi$
$701$	8.82475			0.333306			0.166653	+	0.986016i	$0.446704\pi$
$702$		0			0
$703$	16.3315	−	28.2870i	0.615954	−	1.06686i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	29.5312	−	20.3248i	1.11063	−	0.764391i
$708$		0			0
$709$	5.22508	+	9.05011i	0.196232	+	0.339884i	0.947304	−	0.320337i	$-0.103796\pi$
$709$	5.22508	+	9.05011i	0.196232	+	0.339884i	−0.751072	+	0.660221i	$0.770463\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−25.6197			−0.959465
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.476171	+	0.824752i	−0.0177829	+	0.0308009i
$718$		0			0
$719$	15.1873	+	26.3052i	0.566390	+	0.981017i	0.996919	+	0.0784400i	$0.0249939\pi$
$719$	15.1873	+	26.3052i	0.566390	+	0.981017i	−0.430528	+	0.902577i	$0.641673\pi$
$720$		0			0
$721$	−2.36254	−	29.7693i	−0.0879856	−	1.10867i
$722$		0			0
$723$	−8.50848	−	14.7371i	−0.316434	−	0.548080i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.10302			0.115085			0.0575423	−	0.998343i	$-0.481674\pi$
$727$	3.10302			0.115085			0.0575423	+	0.998343i	$0.481674\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	0.450166	−	0.779710i	0.0166500	−	0.0288386i
$732$		0			0
$733$	−18.8432	−	32.6375i	−0.695991	−	1.20549i	−0.969845	−	0.243721i	$-0.921632\pi$
$733$	−18.8432	−	32.6375i	−0.695991	−	1.20549i	0.273854	−	0.961771i	$-0.411701\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.28819	+	16.0876i	0.342135	+	0.592595i
$738$		0			0
$739$	10.4622	−	18.1211i	0.384859	−	0.666595i	−0.606891	−	0.794785i	$-0.707584\pi$
$739$	10.4622	−	18.1211i	0.384859	−	0.666595i	0.991750	+	0.128190i	$0.0409169\pi$
$740$		0			0
$741$	14.9003			0.547377
$742$		0			0
$743$	−6.45203			−0.236702			−0.118351	−	0.992972i	$-0.537761\pi$
$743$	−6.45203			−0.236702			−0.118351	+	0.992972i	$0.537761\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.737127	−	9.28819i	−0.0269341	−	0.339383i
$750$		0			0
$751$	7.36254	+	12.7523i	0.268663	+	0.465338i	0.968517	−	0.248948i	$-0.0800849\pi$
$751$	7.36254	+	12.7523i	0.268663	+	0.465338i	−0.699854	+	0.714286i	$0.746752\pi$
$752$		0			0
$753$	17.7967	−	30.8248i	0.648547	−	1.12332i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	35.5934			1.29366			0.646831	−	0.762633i	$-0.276094\pi$
$757$	35.5934			1.29366			0.646831	+	0.762633i	$0.276094\pi$
$758$		0			0
$759$	−35.7371	+	61.8985i	−1.29718	+	2.24677i
$760$		0			0
$761$	−11.4622	−	19.8531i	−0.415505	−	0.719675i	0.579977	−	0.814633i	$-0.303062\pi$
$761$	−11.4622	−	19.8531i	−0.415505	−	0.719675i	−0.995481	+	0.0949578i	$0.969728\pi$
$762$		0			0
$763$	25.1723	−	17.3248i	0.911298	−	0.627198i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.30136	−	7.45017i	0.155313	−	0.269010i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−20.1752			−0.726594
$772$		0			0
$773$	20.1567	−	34.9124i	0.724985	−	1.25571i	−0.233995	−	0.972238i	$-0.575180\pi$
$773$	20.1567	−	34.9124i	0.724985	−	1.25571i	0.958980	−	0.283473i	$-0.0914867\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−41.2657	−	19.6495i	−1.48040	−	0.704922i
$778$		0			0
$779$	6.09967	+	10.5649i	0.218543	+	0.378528i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$		0			0
$783$	−22.2131			−0.793832
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.866025	−	1.50000i	0.0308705	−	0.0534692i	−0.850177	−	0.526496i	$-0.823505\pi$
$787$	0.866025	−	1.50000i	0.0308705	−	0.0534692i	0.881048	+	0.473027i	$0.156839\pi$
$788$		0			0
$789$	−0.675248	−	1.16956i	−0.0240395	−	0.0416376i
$790$		0			0
$791$	10.2749	+	4.89261i	0.365334	+	0.173961i
$792$		0			0
$793$	17.7967	+	30.8248i	0.631979	+	1.09462i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−46.8229			−1.65855			−0.829276	−	0.558839i	$-0.811247\pi$
$797$	−46.8229			−1.65855			−0.829276	+	0.558839i	$0.811247\pi$
$798$		0			0
$799$	2.72508			0.0964065
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.1687	+	29.7371i	0.605872	+	1.04940i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.5142	+	21.6752i	0.440521	+	0.763005i
$808$		0			0
$809$	8.59967	−	14.8951i	0.302348	−	0.523683i	−0.674319	−	0.738440i	$-0.735563\pi$
$809$	8.59967	−	14.8951i	0.302348	−	0.523683i	0.976667	+	0.214757i	$0.0688961\pi$
$810$		0			0
$811$	7.45017			0.261611			0.130805	−	0.991408i	$-0.458244\pi$
$811$	7.45017			0.261611			0.130805	+	0.991408i	$0.458244\pi$
$812$		0			0
$813$	17.0170			0.596811
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.52165	+	6.09967i	0.123207	+	0.213400i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.1873	+	17.6449i	0.355539	+	0.615812i	0.987210	−	0.159425i	$-0.0509640\pi$
$821$	10.1873	+	17.6449i	0.355539	+	0.615812i	−0.631671	+	0.775237i	$0.717631\pi$
$822$		0			0
$823$	−23.0791	+	39.9743i	−0.804488	+	1.39341i	0.112147	+	0.993692i	$0.464227\pi$
$823$	−23.0791	+	39.9743i	−0.804488	+	1.39341i	−0.916636	+	0.399723i	$0.869106\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.0547			−0.523505			−0.261752	−	0.965135i	$-0.584300\pi$
$827$	−15.0547			−0.523505			−0.261752	+	0.965135i	$0.584300\pi$
$828$		0			0
$829$	25.4622	−	44.1018i	0.884339	−	1.53172i	0.0378699	−	0.999283i	$-0.487943\pi$
$829$	25.4622	−	44.1018i	0.884339	−	1.53172i	0.846469	−	0.532438i	$-0.178724\pi$
$830$		0			0
$831$	−12.3625	−	21.4125i	−0.428852	−	0.742793i
$832$		0			0
$833$	−2.89371	+	0.462210i	−0.100261	+	0.0160146i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.50848	−	14.7371i	0.294096	−	0.509390i
$838$		0			0
$839$	41.0997			1.41892			0.709459	−	0.704747i	$-0.248939\pi$
$839$	41.0997			1.41892			0.709459	+	0.704747i	$0.248939\pi$
$840$		0			0
$841$	−10.7251			−0.369830
$842$		0			0
$843$	−5.19615	+	9.00000i	−0.178965	+	0.309976i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.52165	−	44.3746i	−0.121005	−	1.52473i
$848$		0			0
$849$	−9.46221	−	16.3890i	−0.324742	−	0.562470i
$850$		0			0
$851$	−39.0120	+	67.5708i	−1.33732	+	2.31630i
$852$		0			0
$853$	13.1342			0.449708			0.224854	−	0.974392i	$-0.427810\pi$
$853$	13.1342			0.449708			0.224854	+	0.974392i	$0.427810\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.8432	+	32.6375i	−0.643673	+	1.11487i	0.340933	+	0.940087i	$0.389257\pi$
$857$	−18.8432	+	32.6375i	−0.643673	+	1.11487i	−0.984606	+	0.174787i	$0.944076\pi$
$858$		0			0
$859$	1.18729	+	2.05645i	0.0405099	+	0.0701652i	0.885569	−	0.464507i	$-0.153768\pi$
$859$	1.18729	+	2.05645i	0.0405099	+	0.0701652i	−0.845060	+	0.534672i	$0.820435\pi$
$860$		0			0
$861$	14.0619	−	9.67805i	0.479228	−	0.329827i
$862$		0			0
$863$	8.21286	+	14.2251i	0.279569	+	0.484227i	0.971278	−	0.237949i	$-0.0764751\pi$
$863$	8.21286	+	14.2251i	0.279569	+	0.484227i	−0.691709	+	0.722177i	$0.743142\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−29.1413			−0.989691
$868$		0			0
$869$	−38.3746			−1.30177
$870$		0			0
$871$	−4.62541	+	8.01145i	−0.156726	+	0.271458i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.4389	+	19.8127i	0.386263	+	0.669028i	0.991944	−	0.126681i	$-0.0404323\pi$
$877$	11.4389	+	19.8127i	0.386263	+	0.669028i	−0.605680	+	0.795708i	$0.707099\pi$
$878$		0			0
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$		0			0
$881$	−43.0241			−1.44952			−0.724759	−	0.689002i	$-0.758049\pi$
$881$	−43.0241			−1.44952			−0.724759	+	0.689002i	$0.758049\pi$
$882$		0			0
$883$	55.5407			1.86909			0.934547	−	0.355840i	$-0.115805\pi$
$883$	55.5407			1.86909			0.934547	+	0.355840i	$0.115805\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.6150	+	33.9743i	0.658609	+	1.14074i	0.980976	+	0.194129i	$0.0621881\pi$
$887$	19.6150	+	33.9743i	0.658609	+	1.14074i	−0.322367	+	0.946615i	$0.604479\pi$
$888$		0			0
$889$	−37.3746	−	17.7967i	−1.25350	−	0.596881i
$890$		0			0
$891$	−23.7371	−	41.1139i	−0.795224	−	1.37737i
$892$		0			0
$893$	−10.6592	+	18.4622i	−0.356695	+	0.617814i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−35.5934			−1.18843
$898$		0			0
$899$	−7.00000	+	12.1244i	−0.233463	+	0.404370i
$900$		0			0
$901$	1.18729	+	2.05645i	0.0395545	+	0.0685103i
$902$		0			0
$903$	8.11863	−	5.58762i	0.270171	−	0.185944i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	20.9285	−	36.2492i	0.694918	−	1.20363i	−0.275290	−	0.961361i	$-0.588774\pi$
$907$	20.9285	−	36.2492i	0.694918	−	1.20363i	0.970208	−	0.242273i	$-0.0778929\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.0997			−0.831589			−0.415795	−	0.909459i	$-0.636496\pi$
$911$	−25.0997			−0.831589			−0.415795	+	0.909459i	$0.636496\pi$
$912$		0			0
$913$	−19.5287	+	33.8248i	−0.646307	+	1.11944i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.24490	+	28.2870i	0.0741332	+	0.934118i
$918$		0			0
$919$	23.4622	+	40.6377i	0.773947	+	1.34052i	0.935384	+	0.353632i	$0.115054\pi$
$919$	23.4622	+	40.6377i	0.773947	+	1.34052i	−0.161438	+	0.986883i	$0.551613\pi$
$920$		0			0
$921$	−22.9622	+	39.7717i	−0.756631	+	1.31052i
$922$		0			0
$923$	−11.9517			−0.393396
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.0498	+	41.6555i	0.789049	+	1.36667i	0.926550	+	0.376172i	$0.122760\pi$
$929$	24.0498	+	41.6555i	0.789049	+	1.36667i	−0.137500	+	0.990502i	$0.543907\pi$
$930$		0			0
$931$	8.18729	−	21.4125i	0.268328	−	0.701768i
$932$		0			0
$933$	8.50848	+	14.7371i	0.278555	+	0.482472i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	24.3638			0.795931			0.397965	−	0.917400i	$-0.369716\pi$
$937$	24.3638			0.795931			0.397965	+	0.917400i	$0.369716\pi$
$938$		0			0
$939$	−58.0241			−1.89354
$940$		0			0
$941$	1.63746	−	2.83616i	0.0533796	−	0.0924562i	−0.838101	−	0.545515i	$-0.816334\pi$
$941$	1.63746	−	2.83616i	0.0533796	−	0.0924562i	0.891481	+	0.453059i	$0.149667\pi$
$942$		0			0
$943$	−14.5707	−	25.2371i	−0.474486	−	0.821834i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.28247	+	9.14950i	0.171657	+	0.297319i	0.938999	−	0.343919i	$-0.111755\pi$
$947$	5.28247	+	9.14950i	0.171657	+	0.297319i	−0.767342	+	0.641238i	$0.778421\pi$
$948$		0			0
$949$	−8.54983	+	14.8087i	−0.277539	+	0.480712i
$950$		0			0
$951$	44.3746			1.43894
$952$		0			0
$953$	22.6893			0.734978			0.367489	−	0.930028i	$-0.380218\pi$
$953$	22.6893			0.734978			0.367489	+	0.930028i	$0.380218\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	19.5287	+	33.8248i	0.631274	+	1.09340i
$958$		0			0
$959$	46.4622	−	31.9775i	1.50034	−	1.03261i
$960$		0			0
$961$	10.1375	+	17.5586i	0.327015	+	0.566406i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.15068			−0.0691611			−0.0345806	−	0.999402i	$-0.511010\pi$
$967$	−2.15068			−0.0691611			−0.0345806	+	0.999402i	$0.511010\pi$
$968$		0			0
$969$	−1.18729	+	2.05645i	−0.0381413	+	0.0660628i
$970$		0			0
$971$	18.4622	+	31.9775i	0.592481	+	1.02621i	0.993897	+	0.110311i	$0.0351846\pi$
$971$	18.4622	+	31.9775i	0.592481	+	1.02621i	−0.401417	+	0.915896i	$0.631482\pi$
$972$		0			0
$973$	31.2920	+	14.9003i	1.00318	+	0.477683i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.9605	−	25.9124i	0.478629	−	0.829010i	−0.521070	−	0.853514i	$-0.674467\pi$
$977$	14.9605	−	25.9124i	0.478629	−	0.829010i	0.999700	+	0.0245034i	$0.00780044\pi$
$978$		0			0
$979$	36.9244			1.18011
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.9641	+	39.7749i	−0.732440	+	1.26862i	0.223398	+	0.974727i	$0.428285\pi$
$983$	−22.9641	+	39.7749i	−0.732440	+	1.26862i	−0.955838	+	0.293895i	$0.905048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	26.9331	+	12.8248i	0.857290	+	0.408216i
$988$		0			0
$989$	−8.41238	−	14.5707i	−0.267498	−	0.463320i
$990$		0			0
$991$	−16.7371	+	28.9896i	−0.531672	+	0.920884i	0.467644	+	0.883917i	$0.345103\pi$
$991$	−16.7371	+	28.9896i	−0.531672	+	0.920884i	−0.999316	+	0.0369667i	$0.988230\pi$
$992$		0			0
$993$	30.8734			0.979737
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.209313	+	0.362541i	−0.00662902	+	0.0114818i	−0.869321	−	0.494248i	$-0.835443\pi$
$997$	−0.209313	+	0.362541i	−0.00662902	+	0.0114818i	0.862692	+	0.505730i	$0.168777\pi$
$998$		0			0
$999$	−25.9124	−	44.8816i	−0.819831	−	1.41999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.i.f.501.2		8
5.2	odd	4		140.2.q.b.109.2	yes	4
5.3	odd	4		140.2.q.a.109.2	yes	4
5.4	even	2	inner	700.2.i.f.501.3		8
7.2	even	3	inner	700.2.i.f.401.2		8
7.3	odd	6		4900.2.a.bf.1.1		4
7.4	even	3		4900.2.a.be.1.3		4
15.2	even	4		1260.2.bm.b.109.1		4
15.8	even	4		1260.2.bm.a.109.1		4
20.3	even	4		560.2.bw.e.529.2		4
20.7	even	4		560.2.bw.a.529.2		4
35.2	odd	12		140.2.q.a.9.2	✓	4
35.3	even	12		980.2.e.c.589.2		4
35.4	even	6		4900.2.a.be.1.1		4
35.9	even	6	inner	700.2.i.f.401.3		8
35.12	even	12		980.2.q.g.569.1		4
35.13	even	4		980.2.q.g.949.1		4
35.17	even	12		980.2.e.c.589.4		4
35.18	odd	12		980.2.e.f.589.3		4
35.23	odd	12		140.2.q.b.9.1	yes	4
35.24	odd	6		4900.2.a.bf.1.3		4
35.27	even	4		980.2.q.b.949.1		4
35.32	odd	12		980.2.e.f.589.1		4
35.33	even	12		980.2.q.b.569.2		4
105.2	even	12		1260.2.bm.a.289.1		4
105.23	even	12		1260.2.bm.b.289.2		4
140.23	even	12		560.2.bw.a.289.1		4
140.107	even	12		560.2.bw.e.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.2	✓	4	35.2	odd	12
140.2.q.a.109.2	yes	4	5.3	odd	4
140.2.q.b.9.1	yes	4	35.23	odd	12
140.2.q.b.109.2	yes	4	5.2	odd	4
560.2.bw.a.289.1		4	140.23	even	12
560.2.bw.a.529.2		4	20.7	even	4
560.2.bw.e.289.2		4	140.107	even	12
560.2.bw.e.529.2		4	20.3	even	4
700.2.i.f.401.2		8	7.2	even	3	inner
700.2.i.f.401.3		8	35.9	even	6	inner
700.2.i.f.501.2		8	1.1	even	1	trivial
700.2.i.f.501.3		8	5.4	even	2	inner
980.2.e.c.589.2		4	35.3	even	12
980.2.e.c.589.4		4	35.17	even	12
980.2.e.f.589.1		4	35.32	odd	12
980.2.e.f.589.3		4	35.18	odd	12
980.2.q.b.569.2		4	35.33	even	12
980.2.q.b.949.1		4	35.27	even	4
980.2.q.g.569.1		4	35.12	even	12
980.2.q.g.949.1		4	35.13	even	4
1260.2.bm.a.109.1		4	15.8	even	4
1260.2.bm.a.289.1		4	105.2	even	12
1260.2.bm.b.109.1		4	15.2	even	4
1260.2.bm.b.289.2		4	105.23	even	12
4900.2.a.be.1.1		4	35.4	even	6
4900.2.a.be.1.3		4	7.4	even	3
4900.2.a.bf.1.1		4	7.3	odd	6
4900.2.a.bf.1.3		4	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{3} +(2.38876 + 1.13746i) q^{7} +(2.63746 - 4.56821i) q^{11} +2.62685 q^{13} +(-0.209313 + 0.362541i) q^{17} +(-1.63746 - 2.83616i) q^{19} +(-3.77492 + 2.59808i) q^{21} +(3.91150 + 6.77492i) q^{23} -5.19615 q^{27} +4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(4.56821 + 7.91238i) q^{33} +(4.98684 + 8.63746i) q^{37} +(-2.27492 + 3.94027i) q^{39} -3.72508 q^{41} -2.15068 q^{43} +(-3.25479 - 5.63746i) q^{47} +(4.41238 + 5.43424i) q^{49} +(-0.362541 - 0.627940i) q^{51} +(2.83616 - 4.91238i) q^{53} +5.67232 q^{57} +(1.63746 - 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-1.76082 + 3.04983i) q^{67} -13.5498 q^{69} -4.54983 q^{71} +(-3.25479 + 5.63746i) q^{73} +(11.4964 - 7.91238i) q^{77} +(-3.63746 - 6.30026i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.40437 q^{83} +(-3.70219 + 6.41238i) q^{87} +(3.50000 + 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(-2.83616 - 4.91238i) q^{93} -6.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{11} + 2 q^{19} + 4 q^{29} + 2 q^{31} + 12 q^{39} - 60 q^{41} - 10 q^{49} - 18 q^{51} - 2 q^{59} + 24 q^{61} - 48 q^{69} + 24 q^{71} - 14 q^{79} + 36 q^{81} + 28 q^{89} + 20 q^{91}+O(q^{100}) \) 8 * q + 6 * q^11 + 2 * q^19 + 4 * q^29 + 2 * q^31 + 12 * q^39 - 60 * q^41 - 10 * q^49 - 18 * q^51 - 2 * q^59 + 24 * q^61 - 48 * q^69 + 24 * q^71 - 14 * q^79 + 36 * q^81 + 28 * q^89 + 20 * q^91

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