LMFDB - Embedded newform 700.2.i.f.501.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(401,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("700.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
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			501.3
Root			$-1.52274 - 1.63746i$ of defining polynomial
Character	$\chi$	$=$	700.501
Dual form			700.2.i.f.401.3

$q$-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	$-0.666667\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	1.00000			$0$
$4$		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	$-0.618684\pi$
$13$	−2.62685			−0.728557			−0.364278	+	0.931290i	$0.618684\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.209313	−	0.362541i	0.0507659	−	0.0879292i	−0.839526	−	0.543320i	$-0.817167\pi$
$17$	0.209313	−	0.362541i	0.0507659	−	0.0879292i	0.890292	+	0.455391i	$0.150500\pi$
$18$		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	$-0.863071\pi$
$23$	−3.91150	−	6.77492i	−0.815604	−	1.41267i	0.0932891	−	0.995639i	$-0.470262\pi$
$24$		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	$-0.860734\pi$
$37$	−4.98684	−	8.63746i	−0.819831	−	1.41999i	0.0859750	−	0.996297i	$-0.472599\pi$
$38$		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	$-0.447564\pi$
$43$	2.15068			0.327975			0.163988	+	0.986462i	$0.447564\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.25479	+	5.63746i	0.474760	+	0.822308i	0.999582	−	0.0289038i	$-0.00920165\pi$
$47$	3.25479	+	5.63746i	0.474760	+	0.822308i	−0.524823	+	0.851212i	$0.675868\pi$
$48$		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	−0.992393	−	0.123114i	$-0.960712\pi$
$53$	−2.83616	+	4.91238i	−0.389577	+	0.674767i	0.602816	+	0.797880i	$0.294045\pi$
$54$		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	−0.738191	−	0.674592i	$-0.764319\pi$
$67$	1.76082	−	3.04983i	0.215119	−	0.372597i	0.953309	+	0.301996i	$0.0976528\pi$
$68$		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	−0.610253	−	0.792206i	$-0.708932\pi$
$73$	3.25479	−	5.63746i	0.380944	−	0.659815i	0.991197	+	0.132392i	$0.0422657\pi$
$74$		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	$-0.366795\pi$
$83$	7.40437			0.812736			0.406368	+	0.913710i	$0.366795\pi$
$84$		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	$-0.385595\pi$
$97$	6.92820			0.703452			0.351726	+	0.936103i	$0.385595\pi$
$98$		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	$0.0210268\pi$
$103$	5.64355	+	9.77492i	0.556076	+	0.963151i	−0.441743	+	0.897141i	$0.645640\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.76082	+	3.04983i	0.170225	+	0.294839i	0.938499	−	0.345283i	$-0.112217\pi$
$107$	1.76082	+	3.04983i	0.170225	+	0.294839i	−0.768273	+	0.640122i	$0.778884\pi$
$108$		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	$-0.564848\pi$
$113$	−4.30136			−0.404637			−0.202319	+	0.979320i	$0.564848\pi$
$114$		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	$-0.255768\pi$
$127$	15.6460			1.38836			0.694179	+	0.719802i	$0.255768\pi$
$128$		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	$0.531103\pi$
$137$	−10.6592	+	18.4622i	−0.910674	+	1.57733i	−0.813115	+	0.582103i	$0.802230\pi$
$138$		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	−0.906715	−	0.421743i	$-0.861418\pi$
$157$	−1.10411	+	1.91238i	−0.0881176	+	0.152624i	0.818598	+	0.574367i	$0.194752\pi$
$158$		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	0.955459	−	0.295123i	$-0.0953607\pi$
$163$	2.83616	+	4.91238i	0.222145	+	0.384767i	−0.733314	+	0.679890i	$0.762027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.476171			0.0368472			0.0184236	−	0.999830i	$-0.494135\pi$
$167$	0.476171			0.0368472			0.0184236	+	0.999830i	$0.494135\pi$
$168$		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	$0.117390\pi$
$173$	10.2405	+	17.7371i	0.778573	+	1.34853i	−0.154190	+	0.988041i	$0.549277\pi$
$174$		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	$-0.554951\pi$
$193$	10.6592	−	18.4622i	0.767263	−	1.32894i	0.939042	−	0.343803i	$-0.111715\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.60271			−0.612918			−0.306459	−	0.951884i	$-0.599144\pi$
$197$	−8.60271			−0.612918			−0.306459	+	0.951884i	$0.599144\pi$
$198$		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	$-0.405715\pi$
$223$	8.71780			0.583787			0.291893	+	0.956451i	$0.405715\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.76436	+	16.9124i	−0.648084	+	1.12251i	0.335496	+	0.942041i	$0.391096\pi$
$227$	−9.76436	+	16.9124i	−0.648084	+	1.12251i	−0.983580	+	0.180472i	$0.942237\pi$
$228$		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	0.999314	−	0.0370231i	$-0.0117875\pi$
$233$	7.13752	+	12.3625i	0.467594	+	0.809897i	−0.531720	+	0.846920i	$0.678454\pi$
$234$		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	0.625204	−	0.780461i	$-0.285016\pi$
$257$	−5.82409	−	10.0876i	−0.363297	−	0.629249i	−0.988501	+	0.151212i	$0.951682\pi$
$258$		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	−0.853755	−	0.520674i	$-0.825681\pi$
$263$	0.389855	−	0.675248i	0.0240395	−	0.0416376i	0.877795	+	0.479037i	$0.159014\pi$
$264$		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	−0.567920	−	0.823084i	$-0.692252\pi$
$277$	7.13752	−	12.3625i	0.428852	−	0.742793i	0.996771	+	0.0802909i	$0.0255849\pi$
$278$		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	−0.656718	−	0.754136i	$-0.728056\pi$
$283$	5.46301	−	9.46221i	0.324742	−	0.562470i	0.981460	+	0.191666i	$0.0613891\pi$
$284$		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	$-0.564866\pi$
$293$	−6.92820			−0.404750			−0.202375	+	0.979308i	$0.564866\pi$
$294$		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	$-0.773156\pi$
$307$	−26.5145			−1.51326			−0.756631	+	0.653843i	$0.773156\pi$
$308$		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	$-0.770990\pi$
$313$	−16.7501	−	29.0120i	−0.946772	−	1.63986i	−0.194609	−	0.980881i	$-0.562344\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.8098	+	22.1873i	0.719472	+	1.24616i	0.961209	+	0.275821i	$0.0889496\pi$
$317$	12.8098	+	22.1873i	0.719472	+	1.24616i	−0.241737	+	0.970342i	$0.577717\pi$
$318$		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	$-0.462623\pi$
$337$	4.30136			0.234310			0.117155	+	0.993114i	$0.462623\pi$
$338$		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	−0.656165	−	0.754617i	$-0.727823\pi$
$347$	6.06218	−	10.5000i	0.325435	−	0.563670i	0.981600	+	0.190947i	$0.0611560\pi$
$348$		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	−0.736337	−	0.676615i	$-0.763446\pi$
$353$	4.09204	−	7.08762i	0.217797	−	0.377236i	0.954134	+	0.299379i	$0.0967795\pi$
$354$		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	−0.933956	−	0.357388i	$-0.883667\pi$
$367$	−3.01670	+	5.22508i	−0.157471	+	0.272747i	0.776485	+	0.630135i	$0.217001\pi$
$368$		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	0.965762	−	0.259429i	$-0.0835344\pi$
$373$	4.98684	+	8.63746i	0.258209	+	0.447231i	−0.707553	+	0.706660i	$0.750201\pi$
$374$		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	0.776730	−	0.629833i	$-0.216877\pi$
$383$	−3.07425	−	5.32475i	−0.157087	−	0.272082i	−0.933817	+	0.357751i	$0.883544\pi$
$384$		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	0.969193	−	0.246302i	$-0.0792156\pi$
$397$	5.40547	+	9.36254i	0.271293	+	0.469892i	−0.697901	+	0.716195i	$0.745882\pi$
$398$		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	$-0.356288\pi$
$433$	18.1578			0.872606			0.436303	+	0.899800i	$0.356288\pi$
$434$		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	0.685315	−	0.728247i	$-0.259665\pi$
$443$	−6.06218	−	10.5000i	−0.288023	−	0.498870i	−0.973338	+	0.229377i	$0.926331\pi$
$444$		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	0.849547	−	0.527512i	$-0.176875\pi$
$457$	−0.685484	−	1.18729i	−0.0320656	−	0.0555392i	−0.881613	+	0.471973i	$0.843542\pi$
$458$		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	$-0.515914\pi$
$463$	−2.15068			−0.0999505			−0.0499752	+	0.998750i	$0.515914\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.85177	+	13.5997i	0.363337	+	0.629318i	0.988508	−	0.151170i	$-0.0483041\pi$
$467$	7.85177	+	13.5997i	0.363337	+	0.629318i	−0.625171	+	0.780488i	$0.714971\pi$
$468$		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	−0.830917	−	0.556396i	$-0.812184\pi$
$487$	1.46519	−	2.53779i	0.0663943	−	0.114998i	0.897312	+	0.441398i	$0.145517\pi$
$488$		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	$-0.750509\pi$
$503$	−31.7682			−1.41647			−0.708236	+	0.705975i	$0.750509\pi$
$504$		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	0.935094	−	0.354400i	$-0.115315\pi$
$523$	3.67341	+	6.36254i	0.160627	+	0.278215i	−0.774467	+	0.632615i	$0.781982\pi$
$524$		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	$-0.355303\pi$
$547$	20.5386			0.878168			0.439084	+	0.898446i	$0.355303\pi$
$548$		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	−0.740822	−	0.671701i	$-0.765564\pi$
$557$	4.98684	−	8.63746i	0.211299	−	0.365981i	0.952121	+	0.305720i	$0.0988972\pi$
$558$		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	−0.999650	−	0.0264630i	$-0.991576\pi$
$563$	−11.3159	+	19.5997i	−0.476907	+	0.826028i	0.522743	+	0.852491i	$0.324909\pi$
$564$		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	−0.903602	−	0.428372i	$-0.859087\pi$
$577$	−1.94136	+	3.36254i	−0.0808200	+	0.139984i	0.822782	+	0.568357i	$0.192421\pi$
$578$		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	$-0.641949\pi$
$587$	−20.8997			−0.862623			−0.431311	+	0.902203i	$0.641949\pi$
$588$		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	$0.0737416\pi$
$593$	16.6926	+	28.9124i	0.685482	+	1.18729i	−0.287804	+	0.957689i	$0.592925\pi$
$594$		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	0.958220	−	0.286031i	$-0.0923360\pi$
$607$	5.70109	+	9.87459i	0.231400	+	0.400797i	−0.726820	+	0.686828i	$0.759003\pi$
$608$		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	$0.360793\pi$
$613$	−14.1808	+	24.5619i	−0.572757	+	0.992045i	−0.996281	+	0.0861600i	$0.972540\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.2920			1.25977			0.629884	−	0.776689i	$-0.283102\pi$
$617$	31.2920			1.25977			0.629884	+	0.776689i	$0.283102\pi$
$618$		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	$-0.287422\pi$
$643$	31.4071			1.23857			0.619287	+	0.785164i	$0.287422\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.4666	−	23.3248i	0.529425	−	0.916991i	−0.469986	−	0.882674i	$-0.655741\pi$
$647$	13.4666	−	23.3248i	0.529425	−	0.916991i	0.999411	−	0.0343169i	$-0.0109255\pi$
$648$		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	$0.0205913\pi$
$653$	14.1808	+	24.5619i	0.554938	+	0.961181i	−0.442970	+	0.896536i	$0.646075\pi$
$654$		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	$-0.293928\pi$
$673$	31.2920			1.20622			0.603109	+	0.797659i	$0.293928\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.2021	+	40.1873i	0.891731	+	1.54452i	0.837799	+	0.545979i	$0.183842\pi$
$677$	23.2021	+	40.1873i	0.891731	+	1.54452i	0.0539317	+	0.998545i	$0.482825\pi$
$678$		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	−0.622335	−	0.782751i	$-0.713816\pi$
$683$	9.58382	−	16.5997i	0.366715	−	0.635169i	0.989050	+	0.147582i	$0.0471491\pi$
$684$		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	$-0.518326\pi$
$727$	−3.10302			−0.115085			−0.0575423	+	0.998343i	$0.518326\pi$
$728$		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	$0.0783681\pi$
$733$	18.8432	+	32.6375i	0.695991	+	1.20549i	−0.273854	+	0.961771i	$0.588299\pi$
$734$		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	$-0.462239\pi$
$743$	6.45203			0.236702			0.118351	+	0.992972i	$0.462239\pi$
$744$		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	$-0.723906\pi$
$757$	−35.5934			−1.29366			−0.646831	+	0.762633i	$0.723906\pi$
$758$		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	$0.424820\pi$
$773$	−20.1567	+	34.9124i	−0.724985	+	1.25571i	−0.958980	+	0.283473i	$0.908513\pi$
$774$		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	−0.881048	−	0.473027i	$-0.843161\pi$
$787$	−0.866025	+	1.50000i	−0.0308705	+	0.0534692i	0.850177	+	0.526496i	$0.176495\pi$
$788$		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	$-0.188753\pi$
$797$	46.8229			1.65855			0.829276	+	0.558839i	$0.188753\pi$
$798$		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	$-0.535773\pi$
$823$	23.0791	−	39.9743i	0.804488	−	1.39341i	0.916636	−	0.399723i	$-0.130894\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.0547			0.523505			0.261752	−	0.965135i	$-0.415700\pi$
$827$	15.0547			0.523505			0.261752	+	0.965135i	$0.415700\pi$
$828$		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	$-0.572190\pi$
$853$	−13.1342			−0.449708			−0.224854	+	0.974392i	$0.572190\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.8432	−	32.6375i	0.643673	−	1.11487i	−0.340933	−	0.940087i	$-0.610743\pi$
$857$	18.8432	−	32.6375i	0.643673	−	1.11487i	0.984606	−	0.174787i	$-0.0559236\pi$
$858$		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	0.691709	−	0.722177i	$-0.256858\pi$
$863$	−8.21286	−	14.2251i	−0.279569	−	0.484227i	−0.971278	+	0.237949i	$0.923525\pi$
$864$		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	0.605680	−	0.795708i	$-0.292901\pi$
$877$	−11.4389	−	19.8127i	−0.386263	−	0.669028i	−0.991944	+	0.126681i	$0.959568\pi$
$878$		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	$-0.884195\pi$
$883$	−55.5407			−1.86909			−0.934547	+	0.355840i	$0.884195\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−19.6150	−	33.9743i	−0.658609	−	1.14074i	−0.980976	−	0.194129i	$-0.937812\pi$
$887$	−19.6150	−	33.9743i	−0.658609	−	1.14074i	0.322367	−	0.946615i	$-0.395521\pi$
$888$		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	$0.411226\pi$
$907$	−20.9285	+	36.2492i	−0.694918	+	1.20363i	−0.970208	+	0.242273i	$0.922107\pi$
$908$		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	$-0.630284\pi$
$937$	−24.3638			−0.795931			−0.397965	+	0.917400i	$0.630284\pi$
$938$		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	0.767342	−	0.641238i	$-0.221579\pi$
$947$	−5.28247	−	9.14950i	−0.171657	−	0.297319i	−0.938999	+	0.343919i	$0.888245\pi$
$948$		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	$-0.619782\pi$
$953$	−22.6893			−0.734978			−0.367489	+	0.930028i	$0.619782\pi$
$954$		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	$-0.488990\pi$
$967$	2.15068			0.0691611			0.0345806	+	0.999402i	$0.488990\pi$
$968$		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	−0.999700	−	0.0245034i	$-0.992200\pi$
$977$	−14.9605	+	25.9124i	−0.478629	+	0.829010i	0.521070	+	0.853514i	$0.325533\pi$
$978$		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	$-0.571715\pi$
$983$	22.9641	−	39.7749i	0.732440	−	1.26862i	0.955838	−	0.293895i	$-0.0949518\pi$
$984$		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	−0.862692	−	0.505730i	$-0.831223\pi$
$997$	0.209313	−	0.362541i	0.00662902	−	0.0114818i	0.869321	+	0.494248i	$0.164557\pi$
$998$		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.501.3		8
5.2	odd	4		140.2.q.a.109.2	yes	4
5.3	odd	4		140.2.q.b.109.2	yes	4
5.4	even	2	inner	700.2.i.f.501.2		8
7.2	even	3	inner	700.2.i.f.401.3		8
7.3	odd	6		4900.2.a.bf.1.3		4
7.4	even	3		4900.2.a.be.1.1		4
15.2	even	4		1260.2.bm.a.109.1		4
15.8	even	4		1260.2.bm.b.109.1		4
20.3	even	4		560.2.bw.a.529.2		4
20.7	even	4		560.2.bw.e.529.2		4
35.2	odd	12		140.2.q.b.9.1	yes	4
35.3	even	12		980.2.e.c.589.4		4
35.4	even	6		4900.2.a.be.1.3		4
35.9	even	6	inner	700.2.i.f.401.2		8
35.12	even	12		980.2.q.b.569.2		4
35.13	even	4		980.2.q.b.949.1		4
35.17	even	12		980.2.e.c.589.2		4
35.18	odd	12		980.2.e.f.589.1		4
35.23	odd	12		140.2.q.a.9.2	✓	4
35.24	odd	6		4900.2.a.bf.1.1		4
35.27	even	4		980.2.q.g.949.1		4
35.32	odd	12		980.2.e.f.589.3		4
35.33	even	12		980.2.q.g.569.1		4
105.2	even	12		1260.2.bm.b.289.2		4
105.23	even	12		1260.2.bm.a.289.1		4
140.23	even	12		560.2.bw.e.289.2		4
140.107	even	12		560.2.bw.a.289.1		4

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

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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