LMFDB - Embedded newform 700.2.i.f.401.4

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			401.4
Root			$0.656712 - 2.13746i$ of defining polynomial
Character	$\chi$	$=$	700.401
Dual form			700.2.i.f.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{3} +(-0.209313 - 2.63746i) q^{7} +(-1.13746 - 1.97014i) q^{11} +6.09095 q^{13} +(2.38876 + 4.13746i) q^{17} +(2.13746 - 3.70219i) q^{19} +(3.77492 - 2.59808i) q^{21} +(0.447399 - 0.774917i) q^{23} +5.19615 q^{27} -3.27492 q^{29} +(2.13746 + 3.70219i) q^{31} +(1.97014 - 3.41238i) q^{33} +(-2.80739 + 4.86254i) q^{37} +(5.27492 + 9.13642i) q^{39} -11.2749 q^{41} +6.50958 q^{43} +(1.07534 - 1.86254i) q^{47} +(-6.91238 + 1.10411i) q^{49} +(-4.13746 + 7.16629i) q^{51} +(3.70219 + 6.41238i) q^{53} +7.40437 q^{57} +(-2.13746 - 3.70219i) q^{59} +(-0.774917 + 1.34220i) q^{61} +(-6.95698 - 12.0498i) q^{67} +1.54983 q^{69} +10.5498 q^{71} +(1.07534 + 1.86254i) q^{73} +(-4.95807 + 3.41238i) q^{77} +(0.137459 - 0.238085i) q^{79} +(4.50000 + 7.79423i) q^{81} -5.67232 q^{83} +(-2.83616 - 4.91238i) q^{87} +(3.50000 - 6.06218i) q^{89} +(-1.27492 - 16.0646i) q^{91} +(-3.70219 + 6.41238i) q^{93} +6.92820 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

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

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	1.00000			$0$
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.209313	−	2.63746i	−0.0791130	−	0.996866i
$7$	−0.209313	−	2.63746i	−0.0791130	−	0.996866i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.13746	−	1.97014i	−0.342957	−	0.594018i	0.642024	−	0.766685i	$-0.278095\pi$
$11$	−1.13746	−	1.97014i	−0.342957	−	0.594018i	−0.984980	+	0.172666i	$0.944762\pi$
$12$		0			0
$13$	6.09095			1.68933			0.844663	−	0.535299i	$-0.179801\pi$
$13$	6.09095			1.68933			0.844663	+	0.535299i	$0.179801\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.38876	+	4.13746i	0.579360	+	1.00348i	0.995553	+	0.0942047i	$0.0300308\pi$
$17$	2.38876	+	4.13746i	0.579360	+	1.00348i	−0.416193	+	0.909276i	$0.636636\pi$
$18$		0			0
$19$	2.13746	−	3.70219i	0.490367	−	0.849340i	−0.509572	−	0.860428i	$-0.670196\pi$
$19$	2.13746	−	3.70219i	0.490367	−	0.849340i	0.999939	+	0.0110882i	$0.00352954\pi$
$20$		0			0
$21$	3.77492	−	2.59808i	0.823754	−	0.566947i
$22$		0			0
$23$	0.447399	−	0.774917i	0.0932891	−	0.161581i	−0.815604	−	0.578610i	$-0.803595\pi$
$23$	0.447399	−	0.774917i	0.0932891	−	0.161581i	0.908893	+	0.417029i	$0.136929\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.19615			1.00000
$28$		0			0
$29$	−3.27492			−0.608137			−0.304068	−	0.952650i	$-0.598345\pi$
$29$	−3.27492			−0.608137			−0.304068	+	0.952650i	$0.598345\pi$
$30$		0			0
$31$	2.13746	+	3.70219i	0.383899	+	0.664932i	0.991616	−	0.129221i	$-0.0412478\pi$
$31$	2.13746	+	3.70219i	0.383899	+	0.664932i	−0.607717	+	0.794154i	$0.707914\pi$
$32$		0			0
$33$	1.97014	−	3.41238i	0.342957	−	0.594018i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.80739	+	4.86254i	−0.461532	+	0.799397i	−0.999038	−	0.0438633i	$-0.986033\pi$
$37$	−2.80739	+	4.86254i	−0.461532	+	0.799397i	0.537506	+	0.843260i	$0.319367\pi$
$38$		0			0
$39$	5.27492	+	9.13642i	0.844663	+	1.46300i
$40$		0			0
$41$	−11.2749			−1.76085			−0.880423	−	0.474189i	$-0.842741\pi$
$41$	−11.2749			−1.76085			−0.880423	+	0.474189i	$0.842741\pi$
$42$		0			0
$43$	6.50958			0.992701			0.496351	−	0.868122i	$-0.334673\pi$
$43$	6.50958			0.992701			0.496351	+	0.868122i	$0.334673\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.07534	−	1.86254i	0.156854	−	0.271680i	−0.776878	−	0.629651i	$-0.783198\pi$
$47$	1.07534	−	1.86254i	0.156854	−	0.271680i	0.933733	+	0.357971i	$0.116531\pi$
$48$		0			0
$49$	−6.91238	+	1.10411i	−0.987482	+	0.157730i
$50$		0			0
$51$	−4.13746	+	7.16629i	−0.579360	+	1.00348i
$52$		0			0
$53$	3.70219	+	6.41238i	0.508534	+	0.880808i	0.999951	+	0.00988297i	$0.00314590\pi$
$53$	3.70219	+	6.41238i	0.508534	+	0.880808i	−0.491417	+	0.870925i	$0.663521\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.40437			0.980733
$58$		0			0
$59$	−2.13746	−	3.70219i	−0.278273	−	0.481984i	0.692682	−	0.721243i	$-0.256429\pi$
$59$	−2.13746	−	3.70219i	−0.278273	−	0.481984i	−0.970956	+	0.239259i	$0.923095\pi$
$60$		0			0
$61$	−0.774917	+	1.34220i	−0.0992180	+	0.171851i	−0.911361	−	0.411608i	$-0.864967\pi$
$61$	−0.774917	+	1.34220i	−0.0992180	+	0.171851i	0.812143	+	0.583458i	$0.198301\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.95698	−	12.0498i	−0.849930	−	1.47212i	−0.881270	−	0.472613i	$-0.843311\pi$
$67$	−6.95698	−	12.0498i	−0.849930	−	1.47212i	0.0313404	−	0.999509i	$-0.490022\pi$
$68$		0			0
$69$	1.54983			0.186578
$70$		0			0
$71$	10.5498			1.25204			0.626018	−	0.779809i	$-0.284684\pi$
$71$	10.5498			1.25204			0.626018	+	0.779809i	$0.284684\pi$
$72$		0			0
$73$	1.07534	+	1.86254i	0.125859	+	0.217994i	0.922068	−	0.387027i	$-0.126498\pi$
$73$	1.07534	+	1.86254i	0.125859	+	0.217994i	−0.796209	+	0.605021i	$0.793165\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.95807	+	3.41238i	−0.565024	+	0.388876i
$78$		0			0
$79$	0.137459	−	0.238085i	0.0154653	−	0.0267867i	−0.858189	−	0.513334i	$-0.828410\pi$
$79$	0.137459	−	0.238085i	0.0154653	−	0.0267867i	0.873654	+	0.486547i	$0.161744\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$	−5.67232			−0.622618			−0.311309	−	0.950309i	$-0.600767\pi$
$83$	−5.67232			−0.622618			−0.311309	+	0.950309i	$0.600767\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.83616	−	4.91238i	−0.304068	−	0.526662i
$88$		0			0
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$	−1.27492	−	16.0646i	−0.133648	−	1.68403i
$92$		0			0
$93$	−3.70219	+	6.41238i	−0.383899	+	0.664932i
$94$		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
$101$	−0.774917	−	1.34220i	−0.0771071	−	0.133553i	0.824894	−	0.565288i	$-0.191235\pi$
$101$	−0.774917	−	1.34220i	−0.0771071	−	0.133553i	−0.902001	+	0.431735i	$0.857902\pi$
$102$		0			0
$103$	1.28465	−	2.22508i	0.126581	−	0.219244i	−0.795769	−	0.605600i	$-0.792933\pi$
$103$	1.28465	−	2.22508i	0.126581	−	0.219244i	0.922350	+	0.386356i	$0.126266\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.95698	+	12.0498i	−0.672556	+	1.16490i	0.304621	+	0.952474i	$0.401470\pi$
$107$	−6.95698	+	12.0498i	−0.672556	+	1.16490i	−0.977177	+	0.212428i	$0.931863\pi$
$108$		0			0
$109$	−1.77492	−	3.07425i	−0.170006	−	0.294459i	0.768416	−	0.639951i	$-0.221045\pi$
$109$	−1.77492	−	3.07425i	−0.170006	−	0.294459i	−0.938422	+	0.345492i	$0.887712\pi$
$110$		0			0
$111$	−9.72508			−0.923064
$112$		0			0
$113$	−13.0192			−1.22474			−0.612369	−	0.790572i	$-0.709783\pi$
$113$	−13.0192			−1.22474			−0.612369	+	0.790572i	$0.709783\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.4124	−	7.16629i	0.954501	−	0.656933i
$120$		0			0
$121$	2.91238	−	5.04438i	0.264761	−	0.458580i
$122$		0			0
$123$	−9.76436	−	16.9124i	−0.880423	−	1.52494i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.78959			−0.158801			−0.0794004	−	0.996843i	$-0.525301\pi$
$127$	−1.78959			−0.158801			−0.0794004	+	0.996843i	$0.525301\pi$
$128$		0			0
$129$	5.63746	+	9.76436i	0.496351	+	0.859704i
$130$		0			0
$131$	9.13746	−	15.8265i	0.798343	−	1.38277i	−0.122351	−	0.992487i	$-0.539043\pi$
$131$	9.13746	−	15.8265i	0.798343	−	1.38277i	0.920694	−	0.390285i	$-0.127623\pi$
$132$		0			0
$133$	−10.2118	−	4.86254i	−0.885472	−	0.421636i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.59698	+	7.96221i	0.392747	+	0.680258i	0.992811	−	0.119695i	$-0.0381915\pi$
$137$	4.59698	+	7.96221i	0.392747	+	0.680258i	−0.600064	+	0.799952i	$0.704858\pi$
$138$		0			0
$139$	−17.0997			−1.45037			−0.725187	−	0.688551i	$-0.758247\pi$
$139$	−17.0997			−1.45037			−0.725187	+	0.688551i	$0.758247\pi$
$140$		0			0
$141$	3.72508			0.313709
$142$		0			0
$143$	−6.92820	−	12.0000i	−0.579365	−	1.00349i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.64246	−	9.41238i	−0.630339	−	0.776320i
$148$		0			0
$149$	−3.77492	+	6.53835i	−0.309253	+	0.535642i	−0.978199	−	0.207669i	$-0.933412\pi$
$149$	−3.77492	+	6.53835i	−0.309253	+	0.535642i	0.668946	+	0.743311i	$0.266746\pi$
$150$		0			0
$151$	10.1375	+	17.5586i	0.824975	+	1.42890i	0.901939	+	0.431864i	$0.142144\pi$
$151$	10.1375	+	17.5586i	0.824975	+	1.42890i	−0.0769640	+	0.997034i	$0.524523\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.43424	+	9.41238i	0.433699	+	0.751189i	0.997188	−	0.0749341i	$-0.0238747\pi$
$157$	5.43424	+	9.41238i	0.433699	+	0.751189i	−0.563489	+	0.826123i	$0.690541\pi$
$158$		0			0
$159$	−6.41238	+	11.1066i	−0.508534	+	0.880808i
$160$		0			0
$161$	−2.13746	−	1.01779i	−0.168455	−	0.0802135i
$162$		0			0
$163$	−3.70219	+	6.41238i	−0.289978	+	0.502256i	−0.973804	−	0.227389i	$-0.926981\pi$
$163$	−3.70219	+	6.41238i	−0.289978	+	0.502256i	0.683826	+	0.729645i	$0.260315\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.6005			−0.975058			−0.487529	−	0.873107i	$-0.662102\pi$
$167$	−12.6005			−0.975058			−0.487529	+	0.873107i	$0.662102\pi$
$168$		0			0
$169$	24.0997			1.85382
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.37451	+	16.2371i	−0.712731	+	1.23449i	0.251097	+	0.967962i	$0.419209\pi$
$173$	−9.37451	+	16.2371i	−0.712731	+	1.23449i	−0.963828	+	0.266524i	$0.914125\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.70219	−	6.41238i	0.278273	−	0.481984i
$178$		0			0
$179$	−0.137459	−	0.238085i	−0.0102741	−	0.0177953i	0.860843	−	0.508871i	$-0.169937\pi$
$179$	−0.137459	−	0.238085i	−0.0102741	−	0.0177953i	−0.871117	+	0.491076i	$0.836604\pi$
$180$		0			0
$181$	−16.7251			−1.24317			−0.621583	−	0.783348i	$-0.713510\pi$
$181$	−16.7251			−1.24317			−0.621583	+	0.783348i	$0.713510\pi$
$182$		0			0
$183$	−2.68439			−0.198436
$184$		0			0
$185$		0			0
$186$		0			0
$187$	5.43424	−	9.41238i	0.397391	−	0.688301i
$188$		0			0
$189$	−1.08762	−	13.7046i	−0.0791130	−	0.996866i
$190$		0			0
$191$	−11.4124	+	19.7668i	−0.825771	+	1.43028i	0.0755585	+	0.997141i	$0.475926\pi$
$191$	−11.4124	+	19.7668i	−0.825771	+	1.43028i	−0.901329	+	0.433135i	$0.857407\pi$
$192$		0			0
$193$	−4.59698	−	7.96221i	−0.330898	−	0.573132i	0.651790	−	0.758399i	$-0.274018\pi$
$193$	−4.59698	−	7.96221i	−0.330898	−	0.573132i	−0.982688	+	0.185267i	$0.940685\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−26.0383			−1.85515			−0.927576	−	0.373634i	$-0.878112\pi$
$197$	−26.0383			−1.85515			−0.927576	+	0.373634i	$0.878112\pi$
$198$		0			0
$199$	−4.86254	−	8.42217i	−0.344696	−	0.597032i	0.640602	−	0.767873i	$-0.278685\pi$
$199$	−4.86254	−	8.42217i	−0.344696	−	0.597032i	−0.985299	+	0.170841i	$0.945351\pi$
$200$		0			0
$201$	12.0498	−	20.8709i	0.849930	−	1.47212i
$202$		0			0
$203$	0.685484	+	8.63746i	0.0481115	+	0.606231i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.72508			−0.672698
$210$		0			0
$211$	−19.6495			−1.35273			−0.676364	−	0.736568i	$-0.736445\pi$
$211$	−19.6495			−1.35273			−0.676364	+	0.736568i	$0.736445\pi$
$212$		0			0
$213$	9.13642	+	15.8248i	0.626018	+	1.08429i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	9.31697	−	6.41238i	0.632477	−	0.435300i
$218$		0			0
$219$	−1.86254	+	3.22602i	−0.125859	+	0.217994i
$220$		0			0
$221$	14.5498	+	25.2011i	0.978728	+	1.69521i
$222$		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
$227$	−3.22602	−	5.58762i	−0.214118	−	0.370864i	0.738881	−	0.673836i	$-0.235354\pi$
$227$	−3.22602	−	5.58762i	−0.214118	−	0.370864i	−0.952999	+	0.302972i	$0.902021\pi$
$228$		0			0
$229$	2.13746	−	3.70219i	0.141247	−	0.244647i	−0.786719	−	0.617311i	$-0.788222\pi$
$229$	2.13746	−	3.70219i	0.141247	−	0.244647i	0.927967	+	0.372663i	$0.121555\pi$
$230$		0			0
$231$	−9.41238	−	4.48190i	−0.619289	−	0.294887i
$232$		0			0
$233$	9.31697	−	16.1375i	0.610375	−	1.05720i	−0.380802	−	0.924656i	$-0.624352\pi$
$233$	9.31697	−	16.1375i	0.610375	−	1.05720i	0.991177	−	0.132544i	$-0.0423145\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.476171			0.0309306
$238$		0			0
$239$	−14.5498			−0.941151			−0.470575	−	0.882360i	$-0.655954\pi$
$239$	−14.5498			−0.941151			−0.470575	+	0.882360i	$0.655954\pi$
$240$		0			0
$241$	6.41238	+	11.1066i	0.413057	+	0.715436i	0.995222	−	0.0976343i	$-0.0311275\pi$
$241$	6.41238	+	11.1066i	0.413057	+	0.715436i	−0.582165	+	0.813071i	$0.697794\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.0192	−	22.5498i	0.828389	−	1.43481i
$248$		0			0
$249$	−4.91238	−	8.50848i	−0.311309	−	0.539203i
$250$		0			0
$251$	−5.45017			−0.344011			−0.172006	−	0.985096i	$-0.555025\pi$
$251$	−5.45017			−0.344011			−0.172006	+	0.985096i	$0.555025\pi$
$252$		0			0
$253$	−2.03559			−0.127976
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.3624	+	21.4124i	−0.771148	+	1.33567i	0.165786	+	0.986162i	$0.446984\pi$
$257$	−12.3624	+	21.4124i	−0.771148	+	1.33567i	−0.936934	+	0.349506i	$0.886350\pi$
$258$		0			0
$259$	13.4124	+	6.38658i	0.833404	+	0.396843i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.4666	+	23.3248i	0.830383	+	1.43827i	0.897735	+	0.440536i	$0.145212\pi$
$263$	13.4666	+	23.3248i	0.830383	+	1.43827i	−0.0673516	+	0.997729i	$0.521455\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.1244			0.741999
$268$		0			0
$269$	14.7749	+	25.5909i	0.900843	+	1.56031i	0.826403	+	0.563080i	$0.190384\pi$
$269$	14.7749	+	25.5909i	0.900843	+	1.56031i	0.0744400	+	0.997225i	$0.476283\pi$
$270$		0			0
$271$	6.41238	−	11.1066i	0.389524	−	0.674676i	−0.602861	−	0.797846i	$-0.705973\pi$
$271$	6.41238	−	11.1066i	0.389524	−	0.674676i	0.992386	+	0.123170i	$0.0393062\pi$
$272$		0			0
$273$	22.9928	−	15.8248i	1.39159	−	0.957758i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.31697	+	16.1375i	0.559802	+	0.969606i	0.997512	+	0.0704898i	$0.0224562\pi$
$277$	9.31697	+	16.1375i	0.559802	+	0.969606i	−0.437710	+	0.899116i	$0.644210\pi$
$278$		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
$283$	−9.79314	−	16.9622i	−0.582142	−	1.00830i	−0.995225	−	0.0976056i	$-0.968882\pi$
$283$	−9.79314	−	16.9622i	−0.582142	−	1.00830i	0.413084	−	0.910693i	$-0.364452\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.35999	+	29.7371i	0.139306	+	1.75533i
$288$		0			0
$289$	−2.91238	+	5.04438i	−0.171316	+	0.296728i
$290$		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
$297$	−5.91041	−	10.2371i	−0.342957	−	0.594018i
$298$		0			0
$299$	2.72508	−	4.71998i	0.157596	−	0.272964i
$300$		0			0
$301$	−1.36254	−	17.1687i	−0.0785356	−	0.989590i
$302$		0			0
$303$	1.34220	−	2.32475i	0.0771071	−	0.133553i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	3.99782			0.228167			0.114084	−	0.993471i	$-0.463607\pi$
$307$	3.99782			0.228167			0.114084	+	0.993471i	$0.463607\pi$
$308$		0			0
$309$	4.45017			0.253161
$310$		0			0
$311$	−6.41238	−	11.1066i	−0.363612	−	0.629795i	0.624940	−	0.780673i	$-0.285123\pi$
$311$	−6.41238	−	11.1066i	−0.363612	−	0.629795i	−0.988552	+	0.150878i	$0.951790\pi$
$312$		0			0
$313$	7.22383	−	12.5120i	0.408315	−	0.707223i	−0.586386	−	0.810032i	$-0.699450\pi$
$313$	7.22383	−	12.5120i	0.408315	−	0.707223i	0.994701	+	0.102809i	$0.0327831\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.91259	−	3.31271i	0.107422	−	0.186060i	−0.807303	−	0.590137i	$-0.799074\pi$
$317$	1.91259	−	3.31271i	0.107422	−	0.186060i	0.914725	+	0.404077i	$0.132407\pi$
$318$		0			0
$319$	3.72508	+	6.45203i	0.208565	+	0.361244i
$320$		0			0
$321$	−24.0997			−1.34511
$322$		0			0
$323$	20.4235			1.13640
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.07425	−	5.32475i	0.170006	−	0.294459i
$328$		0			0
$329$	−5.13746	−	2.44631i	−0.283237	−	0.134869i
$330$		0			0
$331$	2.41238	−	4.17836i	0.132596	−	0.229663i	−0.792080	−	0.610417i	$-0.791002\pi$
$331$	2.41238	−	4.17836i	0.132596	−	0.229663i	0.924677	+	0.380753i	$0.124335\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	13.0192			0.709198			0.354599	−	0.935018i	$-0.384617\pi$
$337$	13.0192			0.709198			0.354599	+	0.935018i	$0.384617\pi$
$338$		0			0
$339$	−11.2749	−	19.5287i	−0.612369	−	1.06065i
$340$		0			0
$341$	4.86254	−	8.42217i	0.263321	−	0.456086i
$342$		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	$-0.0611560\pi$
$347$	6.06218	+	10.5000i	0.325435	+	0.563670i	−0.656165	+	0.754617i	$0.727823\pi$
$348$		0			0
$349$	−11.2749			−0.603532			−0.301766	−	0.953382i	$-0.597576\pi$
$349$	−11.2749			−0.603532			−0.301766	+	0.953382i	$0.597576\pi$
$350$		0			0
$351$	31.6495			1.68933
$352$		0			0
$353$	10.6304	+	18.4124i	0.565799	+	0.979992i	0.996975	+	0.0777242i	$0.0247654\pi$
$353$	10.6304	+	18.4124i	0.565799	+	0.979992i	−0.431176	+	0.902268i	$0.641901\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	19.7668	+	9.41238i	1.04617	+	0.498156i
$358$		0			0
$359$	0.687293	−	1.19043i	0.0362739	−	0.0628283i	−0.847318	−	0.531085i	$-0.821784\pi$
$359$	0.687293	−	1.19043i	0.0362739	−	0.0628283i	0.883592	+	0.468257i	$0.155118\pi$
$360$		0			0
$361$	0.362541	+	0.627940i	0.0190811	+	0.0330495i
$362$		0			0
$363$	10.0888			0.529523
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.37560	−	12.7749i	−0.385003	−	0.666845i	0.606766	−	0.794880i	$-0.292466\pi$
$367$	−7.37560	−	12.7749i	−0.385003	−	0.666845i	−0.991770	+	0.128035i	$0.959133\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.1375	−	11.1066i	0.837815	−	0.576624i
$372$		0			0
$373$	2.80739	−	4.86254i	0.145361	−	0.251773i	−0.784146	−	0.620576i	$-0.786899\pi$
$373$	2.80739	−	4.86254i	0.145361	−	0.251773i	0.929508	+	0.368803i	$0.120232\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.9474			−1.02734
$378$		0			0
$379$	23.6495			1.21479			0.607397	−	0.794399i	$-0.292214\pi$
$379$	23.6495			1.21479			0.607397	+	0.794399i	$0.292214\pi$
$380$		0			0
$381$	−1.54983	−	2.68439i	−0.0794004	−	0.137526i
$382$		0			0
$383$	10.0025	−	17.3248i	0.511101	−	0.885253i	−0.488816	−	0.872387i	$-0.662571\pi$
$383$	10.0025	−	17.3248i	0.511101	−	0.885253i	0.999917	−	0.0128665i	$-0.00409564\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.68729	+	4.65453i	0.136251	+	0.235994i	0.926075	−	0.377340i	$-0.123161\pi$
$389$	2.68729	+	4.65453i	0.136251	+	0.235994i	−0.789824	+	0.613334i	$0.789828\pi$
$390$		0			0
$391$	4.27492			0.216192
$392$		0			0
$393$	31.6531			1.59669
$394$		0			0
$395$		0			0
$396$		0			0
$397$	7.58492	−	13.1375i	0.380676	−	0.659350i	−0.610483	−	0.792029i	$-0.709025\pi$
$397$	7.58492	−	13.1375i	0.380676	−	0.659350i	0.991159	+	0.132679i	$0.0423580\pi$
$398$		0			0
$399$	−1.54983	−	19.5287i	−0.0775888	−	0.977659i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	13.0192	+	22.5498i	0.648530	+	1.12329i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.7732			0.633142
$408$		0			0
$409$	−5.04983	−	8.74657i	−0.249698	−	0.432490i	0.713744	−	0.700407i	$-0.246998\pi$
$409$	−5.04983	−	8.74657i	−0.249698	−	0.432490i	−0.963442	+	0.267917i	$0.913665\pi$
$410$		0			0
$411$	−7.96221	+	13.7910i	−0.392747	+	0.680258i
$412$		0			0
$413$	−9.31697	+	6.41238i	−0.458458	+	0.315532i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−14.8087	−	25.6495i	−0.725187	−	1.25606i
$418$		0			0
$419$	17.0997			0.835373			0.417687	−	0.908591i	$-0.362841\pi$
$419$	17.0997			0.835373			0.417687	+	0.908591i	$0.362841\pi$
$420$		0			0
$421$	3.27492			0.159610			0.0798048	−	0.996811i	$-0.474570\pi$
$421$	3.27492			0.159610			0.0798048	+	0.996811i	$0.474570\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.70219	+	1.76287i	0.179161	+	0.0853114i
$428$		0			0
$429$	12.0000	−	20.7846i	0.579365	−	1.00349i
$430$		0			0
$431$	−9.68729	−	16.7789i	−0.466620	−	0.808210i	0.532653	−	0.846334i	$-0.321195\pi$
$431$	−9.68729	−	16.7789i	−0.466620	−	0.808210i	−0.999273	+	0.0381236i	$0.987862\pi$
$432$		0			0
$433$	26.8756			1.29156			0.645778	−	0.763525i	$-0.276533\pi$
$433$	26.8756			1.29156			0.645778	+	0.763525i	$0.276533\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.91259	−	3.31271i	−0.0914917	−	0.158468i
$438$		0			0
$439$	−0.587624	+	1.01779i	−0.0280458	+	0.0485767i	−0.879708	−	0.475515i	$-0.842262\pi$
$439$	−0.587624	+	1.01779i	−0.0280458	+	0.0485767i	0.851662	+	0.524092i	$0.175595\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.06218	+	10.5000i	−0.288023	+	0.498870i	−0.973338	−	0.229377i	$-0.926331\pi$
$443$	−6.06218	+	10.5000i	−0.288023	+	0.498870i	0.685315	+	0.728247i	$0.259665\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.0767			−0.618507
$448$		0			0
$449$	−25.8248			−1.21875			−0.609373	−	0.792884i	$-0.708579\pi$
$449$	−25.8248			−1.21875			−0.609373	+	0.792884i	$0.708579\pi$
$450$		0			0
$451$	12.8248	+	22.2131i	0.603894	+	1.04598i
$452$		0			0
$453$	−17.5586	+	30.4124i	−0.824975	+	1.42890i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.2118	−	17.6873i	0.477686	−	0.827377i	−0.521987	−	0.852954i	$-0.674809\pi$
$457$	10.2118	−	17.6873i	0.477686	−	0.827377i	0.999673	+	0.0255769i	$0.00814228\pi$
$458$		0			0
$459$	12.4124	+	21.4989i	0.579360	+	1.00348i
$460$		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
$463$	−6.50958			−0.302526			−0.151263	−	0.988494i	$-0.548334\pi$
$463$	−6.50958			−0.302526			−0.151263	+	0.988494i	$0.548334\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.58382	+	16.5997i	−0.443486	+	0.768141i	−0.997945	−	0.0640700i	$-0.979592\pi$
$467$	−9.58382	+	16.5997i	−0.443486	+	0.768141i	0.554459	+	0.832211i	$0.312925\pi$
$468$		0			0
$469$	−30.3248	+	20.8709i	−1.40027	+	0.963730i
$470$		0			0
$471$	−9.41238	+	16.3027i	−0.433699	+	0.751189i
$472$		0			0
$473$	−7.40437	−	12.8248i	−0.340453	−	0.589683i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.41238	+	11.1066i	0.292989	+	0.507472i	0.974515	−	0.224322i	$-0.0720168\pi$
$479$	6.41238	+	11.1066i	0.292989	+	0.507472i	−0.681526	+	0.731794i	$0.738683\pi$
$480$		0			0
$481$	−17.0997	+	29.6175i	−0.779678	+	1.35044i
$482$		0			0
$483$	−0.324401	−	4.08762i	−0.0147608	−	0.185993i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.7213	+	28.9622i	0.757716	+	1.31240i	0.944013	+	0.329909i	$0.107018\pi$
$487$	16.7213	+	28.9622i	0.757716	+	1.31240i	−0.186296	+	0.982494i	$0.559648\pi$
$488$		0			0
$489$	−12.8248			−0.579955
$490$		0			0
$491$	−13.4502			−0.606997			−0.303499	−	0.952832i	$-0.598155\pi$
$491$	−13.4502			−0.606997			−0.303499	+	0.952832i	$0.598155\pi$
$492$		0			0
$493$	−7.82300	−	13.5498i	−0.352330	−	0.610254i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.20822	−	27.8248i	−0.0990523	−	1.24811i
$498$		0			0
$499$	−19.6873	+	34.0994i	−0.881324	+	1.52650i	−0.0314548	+	0.999505i	$0.510014\pi$
$499$	−19.6873	+	34.0994i	−0.881324	+	1.52650i	−0.849869	+	0.526993i	$0.823319\pi$
$500$		0			0
$501$	−10.9124	−	18.9008i	−0.487529	−	0.844425i
$502$		0			0
$503$	16.1797			0.721418			0.360709	−	0.932678i	$-0.382535\pi$
$503$	16.1797			0.721418			0.360709	+	0.932678i	$0.382535\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.8709	+	36.1495i	0.926910	+	1.60546i
$508$		0			0
$509$	14.7749	−	25.5909i	0.654887	−	1.13430i	−0.327036	−	0.945012i	$-0.606050\pi$
$509$	14.7749	−	25.5909i	0.654887	−	1.13430i	0.981922	−	0.189285i	$-0.0606170\pi$
$510$		0			0
$511$	4.68729	−	3.22602i	0.207354	−	0.142711i
$512$		0			0
$513$	11.1066	−	19.2371i	0.490367	−	0.849340i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−4.89261			−0.215177
$518$		0			0
$519$	−32.4743			−1.42546
$520$		0			0
$521$	6.41238	+	11.1066i	0.280931	+	0.486587i	0.971614	−	0.236570i	$-0.0760234\pi$
$521$	6.41238	+	11.1066i	0.280931	+	0.486587i	−0.690683	+	0.723158i	$0.742690\pi$
$522$		0			0
$523$	5.85286	−	10.1375i	0.255928	−	0.443280i	−0.709219	−	0.704988i	$-0.750952\pi$
$523$	5.85286	−	10.1375i	0.255928	−	0.443280i	0.965147	+	0.261708i	$0.0842857\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.2118	+	17.6873i	−0.444831	+	0.770471i
$528$		0			0
$529$	11.0997	+	19.2252i	0.482594	+	0.835878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−68.6750			−2.97464
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.238085	−	0.412376i	0.0102741	−	0.0177953i
$538$		0			0
$539$	10.0378	+	12.3624i	0.432358	+	0.532488i
$540$		0			0
$541$	1.22508	−	2.12191i	0.0526704	−	0.0912278i	−0.838488	−	0.544920i	$-0.816560\pi$
$541$	1.22508	−	2.12191i	0.0526704	−	0.0912278i	0.891159	+	0.453692i	$0.149893\pi$
$542$		0			0
$543$	−14.4843	−	25.0876i	−0.621583	−	1.07661i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−36.1271			−1.54468			−0.772341	−	0.635208i	$-0.780914\pi$
$547$	−36.1271			−1.54468			−0.772341	+	0.635208i	$0.780914\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.00000	+	12.1244i	−0.298210	+	0.516515i
$552$		0			0
$553$	−0.656712	−	0.312707i	−0.0279262	−	0.0132977i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.80739	+	4.86254i	0.118953	+	0.206032i	0.919353	−	0.393434i	$-0.128713\pi$
$557$	2.80739	+	4.86254i	0.118953	+	0.206032i	−0.800400	+	0.599466i	$0.795380\pi$
$558$		0			0
$559$	39.6495			1.67700
$560$		0			0
$561$	18.8248			0.794782
$562$		0			0
$563$	6.11972	+	10.5997i	0.257916	+	0.446723i	0.965683	−	0.259722i	$-0.0836310\pi$
$563$	6.11972	+	10.5997i	0.257916	+	0.446723i	−0.707768	+	0.706445i	$0.750298\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	19.6150	−	13.5000i	0.823754	−	0.566947i
$568$		0			0
$569$	14.6873	−	25.4391i	0.615723	−	1.06646i	−0.374534	−	0.927213i	$-0.622197\pi$
$569$	14.6873	−	25.4391i	0.615723	−	1.06646i	0.990257	−	0.139251i	$-0.0444694\pi$
$570$		0			0
$571$	0.137459	+	0.238085i	0.00575246	+	0.00996356i	0.868887	−	0.495010i	$-0.164836\pi$
$571$	0.137459	+	0.238085i	0.00575246	+	0.00996356i	−0.863135	+	0.504974i	$0.831502\pi$
$572$		0			0
$573$	−39.5336			−1.65154
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.12081	−	7.13746i	−0.171552	−	0.297136i	0.767411	−	0.641156i	$-0.221545\pi$
$577$	−4.12081	−	7.13746i	−0.171552	−	0.297136i	−0.938963	+	0.344019i	$0.888211\pi$
$578$		0			0
$579$	7.96221	−	13.7910i	0.330898	−	0.573132i
$580$		0			0
$581$	1.18729	+	14.9605i	0.0492572	+	0.620667i
$582$		0			0
$583$	8.42217	−	14.5876i	0.348811	−	0.604158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.9715			0.576665			0.288333	−	0.957530i	$-0.406899\pi$
$587$	13.9715			0.576665			0.288333	+	0.957530i	$0.406899\pi$
$588$		0			0
$589$	18.2749			0.753005
$590$		0			0
$591$	−22.5498	−	39.0575i	−0.927576	−	1.60661i
$592$		0			0
$593$	10.1542	−	17.5876i	0.416984	−	0.722237i	−0.578651	−	0.815576i	$-0.696421\pi$
$593$	10.1542	−	17.5876i	0.416984	−	0.722237i	0.995634	+	0.0933384i	$0.0297538\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.42217	−	14.5876i	0.344696	−	0.597032i
$598$		0			0
$599$	1.13746	+	1.97014i	0.0464753	+	0.0804976i	0.888327	−	0.459211i	$-0.151868\pi$
$599$	1.13746	+	1.97014i	0.0464753	+	0.0804976i	−0.841852	+	0.539709i	$0.818534\pi$
$600$		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
$607$	−16.0934	+	27.8746i	−0.653211	+	1.13139i	0.329128	+	0.944285i	$0.393245\pi$
$607$	−16.0934	+	27.8746i	−0.653211	+	1.13139i	−0.982339	+	0.187109i	$0.940088\pi$
$608$		0			0
$609$	−12.3625	+	8.50848i	−0.500955	+	0.344781i
$610$		0			0
$611$	6.54983	−	11.3446i	0.264978	−	0.458955i
$612$		0			0
$613$	18.5109	+	32.0619i	0.747650	+	1.29497i	0.948947	+	0.315437i	$0.102151\pi$
$613$	18.5109	+	32.0619i	0.747650	+	1.29497i	−0.201297	+	0.979530i	$0.564516\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.57919			−0.144093			−0.0720464	−	0.997401i	$-0.522953\pi$
$617$	−3.57919			−0.144093			−0.0720464	+	0.997401i	$0.522953\pi$
$618$		0			0
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.848287	−	0.529537i	$-0.822366\pi$
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.0344487	−	0.999406i	$-0.510968\pi$
$620$		0			0
$621$	2.32475	−	4.02659i	0.0932891	−	0.161581i
$622$		0			0
$623$	−16.7213	−	7.96221i	−0.669926	−	0.318999i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.42217	−	14.5876i	−0.336349	−	0.582574i
$628$		0			0
$629$	−26.8248			−1.06957
$630$		0			0
$631$	2.90033			0.115460			0.0577302	−	0.998332i	$-0.481614\pi$
$631$	2.90033			0.115460			0.0577302	+	0.998332i	$0.481614\pi$
$632$		0			0
$633$	−17.0170	−	29.4743i	−0.676364	−	1.17150i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−42.1029	+	6.72508i	−1.66818	+	0.266457i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.0498	−	24.3350i	−0.554935	−	0.961176i	−0.997909	−	0.0646411i	$-0.979410\pi$
$641$	−14.0498	−	24.3350i	−0.554935	−	0.961176i	0.442973	−	0.896535i	$-0.353924\pi$
$642$		0			0
$643$	−38.3353			−1.51180			−0.755898	−	0.654689i	$-0.772800\pi$
$643$	−38.3353			−1.51180			−0.755898	+	0.654689i	$0.772800\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.389855	+	0.675248i	0.0153268	+	0.0265468i	0.873587	−	0.486668i	$-0.161788\pi$
$647$	0.389855	+	0.675248i	0.0153268	+	0.0265468i	−0.858260	+	0.513215i	$0.828454\pi$
$648$		0			0
$649$	−4.86254	+	8.42217i	−0.190871	+	0.330599i
$650$		0			0
$651$	17.6873	+	8.42217i	0.693220	+	0.330091i
$652$		0			0
$653$	−18.5109	+	32.0619i	−0.724389	+	1.25468i	0.234836	+	0.972035i	$0.424545\pi$
$653$	−18.5109	+	32.0619i	−0.724389	+	1.25468i	−0.959225	+	0.282643i	$0.908789\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−25.4502			−0.991398			−0.495699	−	0.868494i	$-0.665088\pi$
$659$	−25.4502			−0.991398			−0.495699	+	0.868494i	$0.665088\pi$
$660$		0			0
$661$	7.77492	+	13.4666i	0.302409	+	0.523788i	0.976681	−	0.214695i	$-0.0688758\pi$
$661$	7.77492	+	13.4666i	0.302409	+	0.523788i	−0.674272	+	0.738483i	$0.735542\pi$
$662$		0			0
$663$	−25.2011	+	43.6495i	−0.978728	+	1.69521i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.46519	+	2.53779i	−0.0567325	+	0.0982636i
$668$		0			0
$669$	−7.54983	−	13.0767i	−0.291893	−	0.505574i
$670$		0			0
$671$	3.52575			0.136110
$672$		0			0
$673$	−3.57919			−0.137968			−0.0689838	−	0.997618i	$-0.521976\pi$
$673$	−3.57919			−0.137968			−0.0689838	+	0.997618i	$0.521976\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.3049	−	21.3127i	0.472916	−	0.819114i	−0.526604	−	0.850111i	$-0.676535\pi$
$677$	12.3049	−	21.3127i	0.472916	−	0.819114i	0.999519	+	0.0309969i	$0.00986821\pi$
$678$		0			0
$679$	−1.45017	−	18.2728i	−0.0556522	−	0.701248i
$680$		0			0
$681$	5.58762	−	9.67805i	0.214118	−	0.370864i
$682$		0			0
$683$	−7.85177	−	13.5997i	−0.300440	−	0.520377i	0.675796	−	0.737089i	$-0.263800\pi$
$683$	−7.85177	−	13.5997i	−0.300440	−	0.520377i	−0.976236	+	0.216712i	$0.930467\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	7.40437			0.282494
$688$		0			0
$689$	22.5498	+	39.0575i	0.859080	+	1.48797i
$690$		0			0
$691$	3.68729	−	6.38658i	0.140271	−	0.242957i	−0.787327	−	0.616535i	$-0.788536\pi$
$691$	3.68729	−	6.38658i	0.140271	−	0.242957i	0.927599	+	0.373578i	$0.121869\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−26.9331	−	46.6495i	−1.02016	−	1.76698i
$698$		0			0
$699$	32.2749			1.22075
$700$		0			0
$701$	−13.8248			−0.522154			−0.261077	−	0.965318i	$-0.584078\pi$
$701$	−13.8248			−0.522154			−0.261077	+	0.965318i	$0.584078\pi$
$702$		0			0
$703$	12.0014	+	20.7870i	0.452640	+	0.783995i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.37779	+	2.32475i	−0.127035	+	0.0874313i
$708$		0			0
$709$	12.7749	−	22.1268i	0.479772	−	0.830990i	−0.519959	−	0.854191i	$-0.674053\pi$
$709$	12.7749	−	22.1268i	0.479772	−	0.830990i	0.999731	+	0.0232018i	$0.00738601\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.82518			0.143254
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.6005	−	21.8248i	−0.470575	−	0.815060i
$718$		0			0
$719$	−3.68729	+	6.38658i	−0.137513	+	0.238179i	−0.926555	−	0.376160i	$-0.877244\pi$
$719$	−3.68729	+	6.38658i	−0.137513	+	0.238179i	0.789042	+	0.614340i	$0.210577\pi$
$720$		0			0
$721$	−6.13746	−	2.92248i	−0.228571	−	0.108839i
$722$		0			0
$723$	−11.1066	+	19.2371i	−0.413057	+	0.715436i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	18.6915			0.693228			0.346614	−	0.938008i	$-0.387331\pi$
$727$	18.6915			0.693228			0.346614	+	0.938008i	$0.387331\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	15.5498	+	26.9331i	0.575131	+	0.996157i
$732$		0			0
$733$	16.6638	−	28.8625i	0.615491	−	1.06606i	−0.374807	−	0.927103i	$-0.622291\pi$
$733$	16.6638	−	28.8625i	0.615491	−	1.06606i	0.990298	−	0.138959i	$-0.0443757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−15.8265	+	27.4124i	−0.582978	+	1.00975i
$738$		0			0
$739$	−15.9622	−	27.6474i	−0.587179	−	1.01702i	−0.994600	−	0.103784i	$-0.966905\pi$
$739$	−15.9622	−	27.6474i	−0.587179	−	1.01702i	0.407420	−	0.913241i	$-0.366428\pi$
$740$		0			0
$741$	45.0997			1.65678
$742$		0			0
$743$	19.5287			0.716440			0.358220	−	0.933637i	$-0.383384\pi$
$743$	19.5287			0.716440			0.358220	+	0.933637i	$0.383384\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	33.2371	+	15.8265i	1.21446	+	0.578289i
$750$		0			0
$751$	11.1375	−	19.2906i	0.406412	−	0.703926i	−0.588073	−	0.808808i	$-0.700113\pi$
$751$	11.1375	−	19.2906i	0.406412	−	0.703926i	0.994485	+	0.104882i	$0.0334466\pi$
$752$		0			0
$753$	−4.71998	−	8.17525i	−0.172006	−	0.297923i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−9.43996			−0.343101			−0.171551	−	0.985175i	$-0.554878\pi$
$757$	−9.43996			−0.343101			−0.171551	+	0.985175i	$0.554878\pi$
$758$		0			0
$759$	−1.76287	−	3.05338i	−0.0639882	−	0.110831i
$760$		0			0
$761$	14.9622	−	25.9153i	0.542380	−	0.939429i	−0.456387	−	0.889781i	$-0.650857\pi$
$761$	14.9622	−	25.9153i	0.542380	−	0.939429i	0.998767	−	0.0496479i	$-0.0158099\pi$
$762$		0			0
$763$	−7.73668	+	5.32475i	−0.280087	+	0.192769i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.0192	−	22.5498i	−0.470094	−	0.814227i
$768$		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
$771$	−42.8248			−1.54230
$772$		0			0
$773$	−13.6183	−	23.5876i	−0.489817	−	0.848388i	0.510114	−	0.860107i	$-0.329603\pi$
$773$	−13.6183	−	23.5876i	−0.489817	−	0.848388i	−0.999931	+	0.0117187i	$0.996270\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.03559	+	25.6495i	0.0730264	+	0.920171i
$778$		0			0
$779$	−24.0997	+	41.7419i	−0.863460	+	1.49556i
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$		0			0
$783$	−17.0170			−0.608137
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.866025	−	1.50000i	−0.0308705	−	0.0534692i	0.850177	−	0.526496i	$-0.176495\pi$
$787$	−0.866025	−	1.50000i	−0.0308705	−	0.0534692i	−0.881048	+	0.473027i	$0.843161\pi$
$788$		0			0
$789$	−23.3248	+	40.3997i	−0.830383	+	1.43827i
$790$		0			0
$791$	2.72508	+	34.3375i	0.0968928	+	1.22090i
$792$		0			0
$793$	−4.71998	+	8.17525i	−0.167611	+	0.290312i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.3873			1.04095			0.520476	−	0.853876i	$-0.325754\pi$
$797$	29.3873			1.04095			0.520476	+	0.853876i	$0.325754\pi$
$798$		0			0
$799$	10.2749			0.363500
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.44631	−	4.23713i	0.0863283	−	0.149525i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−25.5909	+	44.3248i	−0.900843	+	1.56031i
$808$		0			0
$809$	−21.5997	−	37.4117i	−0.759404	−	1.31533i	−0.943155	−	0.332353i	$-0.892157\pi$
$809$	−21.5997	−	37.4117i	−0.759404	−	1.31533i	0.183751	−	0.982973i	$-0.441176\pi$
$810$		0			0
$811$	22.5498			0.791832			0.395916	−	0.918287i	$-0.370427\pi$
$811$	22.5498			0.791832			0.395916	+	0.918287i	$0.370427\pi$
$812$		0			0
$813$	22.2131			0.779048
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.9140	−	24.0997i	0.486788	−	0.843141i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.68729	+	15.0468i	−0.303189	+	0.525138i	−0.976856	−	0.213896i	$-0.931385\pi$
$821$	−8.68729	+	15.0468i	−0.303189	+	0.525138i	0.673668	+	0.739034i	$0.264718\pi$
$822$		0			0
$823$	−16.1509	−	27.9743i	−0.562987	−	0.975121i	−0.997234	−	0.0743276i	$-0.976319\pi$
$823$	−16.1509	−	27.9743i	−0.562987	−	0.975121i	0.434247	−	0.900794i	$-0.357014\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	45.5670			1.58452			0.792261	−	0.610183i	$-0.208904\pi$
$827$	45.5670			1.58452			0.792261	+	0.610183i	$0.208904\pi$
$828$		0			0
$829$	−0.962210	−	1.66660i	−0.0334189	−	0.0578833i	0.848832	−	0.528662i	$-0.177306\pi$
$829$	−0.962210	−	1.66660i	−0.0334189	−	0.0578833i	−0.882251	+	0.470779i	$0.843973\pi$
$830$		0			0
$831$	−16.1375	+	27.9509i	−0.559802	+	0.969606i
$832$		0			0
$833$	−21.0802	−	25.9622i	−0.730387	−	0.899537i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	11.1066	+	19.2371i	0.383899	+	0.664932i
$838$		0			0
$839$	10.9003			0.376321			0.188161	−	0.982138i	$-0.439747\pi$
$839$	10.9003			0.376321			0.188161	+	0.982138i	$0.439747\pi$
$840$		0			0
$841$	−18.2749			−0.630170
$842$		0			0
$843$	5.19615	+	9.00000i	0.178965	+	0.309976i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−13.9140	−	6.62541i	−0.478089	−	0.227652i
$848$		0			0
$849$	16.9622	−	29.3794i	0.582142	−	1.00830i
$850$		0			0
$851$	2.51204	+	4.35099i	0.0861118	+	0.149150i
$852$		0			0
$853$	30.4547			1.04275			0.521375	−	0.853327i	$-0.325419\pi$
$853$	30.4547			1.04275			0.521375	+	0.853327i	$0.325419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.6638	+	28.8625i	0.569224	+	0.985926i	0.996643	+	0.0818717i	$0.0260898\pi$
$857$	16.6638	+	28.8625i	0.569224	+	0.985926i	−0.427418	+	0.904054i	$0.640577\pi$
$858$		0			0
$859$	−17.6873	+	30.6353i	−0.603483	+	1.04526i	0.388807	+	0.921319i	$0.372887\pi$
$859$	−17.6873	+	30.6353i	−0.603483	+	1.04526i	−0.992289	+	0.123943i	$0.960446\pi$
$860$		0			0
$861$	−42.5619	+	29.2931i	−1.45050	+	0.998306i
$862$		0			0
$863$	−12.5718	+	21.7749i	−0.427947	+	0.741227i	−0.996691	−	0.0812884i	$-0.974097\pi$
$863$	−12.5718	+	21.7749i	−0.427947	+	0.741227i	0.568743	+	0.822515i	$0.307430\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10.0888			−0.342632
$868$		0			0
$869$	−0.625414			−0.0212157
$870$		0			0
$871$	−42.3746	−	73.3949i	−1.43581	−	2.48689i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−22.3361	+	38.6873i	−0.754237	+	1.30638i	0.191516	+	0.981490i	$0.438660\pi$
$877$	−22.3361	+	38.6873i	−0.754237	+	1.30638i	−0.945753	+	0.324887i	$0.894674\pi$
$878$		0			0
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	40.0241			1.34845			0.674223	−	0.738528i	$-0.264479\pi$
$881$	40.0241			1.34845			0.674223	+	0.738528i	$0.264479\pi$
$882$		0			0
$883$	−20.6695			−0.695585			−0.347792	−	0.937572i	$-0.613069\pi$
$883$	−20.6695			−0.695585			−0.347792	+	0.937572i	$0.613069\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.6150	−	33.9743i	0.658609	−	1.14074i	−0.322367	−	0.946615i	$-0.604479\pi$
$887$	19.6150	−	33.9743i	0.658609	−	1.14074i	0.980976	−	0.194129i	$-0.0621881\pi$
$888$		0			0
$889$	0.374586	+	4.71998i	0.0125632	+	0.158303i
$890$		0			0
$891$	10.2371	−	17.7312i	0.342957	−	0.594018i
$892$		0			0
$893$	−4.59698	−	7.96221i	−0.153832	−	0.266445i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	9.43996			0.315191
$898$		0			0
$899$	−7.00000	−	12.1244i	−0.233463	−	0.404370i
$900$		0			0
$901$	−17.6873	+	30.6353i	−0.589249	+	1.02061i
$902$		0			0
$903$	24.5731	−	16.9124i	0.817742	−	0.562809i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	22.6605	+	39.2492i	0.752430	+	1.30325i	0.946642	+	0.322288i	$0.104452\pi$
$907$	22.6605	+	39.2492i	0.752430	+	1.30325i	−0.194212	+	0.980960i	$0.562215\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	5.09967			0.168960			0.0844798	−	0.996425i	$-0.473077\pi$
$911$	5.09967			0.168960			0.0844798	+	0.996425i	$0.473077\pi$
$912$		0			0
$913$	6.45203	+	11.1752i	0.213531	+	0.369847i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−43.6544	−	20.7870i	−1.44160	−	0.686446i
$918$		0			0
$919$	−2.96221	+	5.13070i	−0.0977143	+	0.169246i	−0.910738	−	0.412984i	$-0.864486\pi$
$919$	−2.96221	+	5.13070i	−0.0977143	+	0.169246i	0.813024	+	0.582230i	$0.197820\pi$
$920$		0			0
$921$	3.46221	+	5.99672i	0.114084	+	0.197599i
$922$		0			0
$923$	64.2585			2.11509
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.95017	−	15.5021i	0.293645	−	0.508609i	−0.681023	−	0.732262i	$-0.738465\pi$
$929$	8.95017	−	15.5021i	0.293645	−	0.508609i	0.974669	+	0.223653i	$0.0717982\pi$
$930$		0			0
$931$	−10.6873	+	27.9509i	−0.350262	+	0.916054i
$932$		0			0
$933$	11.1066	−	19.2371i	0.363612	−	0.629795i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	10.5074			0.343262			0.171631	−	0.985161i	$-0.445096\pi$
$937$	10.5074			0.343262			0.171631	+	0.985161i	$0.445096\pi$
$938$		0			0
$939$	25.0241			0.816630
$940$		0			0
$941$	−2.13746	−	3.70219i	−0.0696792	−	0.120688i	0.829081	−	0.559129i	$-0.188864\pi$
$941$	−2.13746	−	3.70219i	−0.0696792	−	0.120688i	−0.898760	+	0.438441i	$0.855531\pi$
$942$		0			0
$943$	−5.04438	+	8.73713i	−0.164268	+	0.284520i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.8709	−	36.1495i	0.678214	−	1.17470i	−0.297304	−	0.954783i	$-0.596088\pi$
$947$	20.8709	−	36.1495i	0.678214	−	1.17470i	0.975518	−	0.219918i	$-0.0705791\pi$
$948$		0			0
$949$	6.54983	+	11.3446i	0.212617	+	0.368263i
$950$		0			0
$951$	6.62541			0.214844
$952$		0			0
$953$	29.6175			0.959405			0.479702	−	0.877431i	$-0.340745\pi$
$953$	29.6175			0.959405			0.479702	+	0.877431i	$0.340745\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.45203	+	11.1752i	−0.208565	+	0.361244i
$958$		0			0
$959$	20.0378	−	13.7910i	0.647054	−	0.445333i
$960$		0			0
$961$	6.36254	−	11.0202i	0.205243	−	0.355492i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	6.50958			0.209334			0.104667	−	0.994507i	$-0.466622\pi$
$967$	6.50958			0.209334			0.104667	+	0.994507i	$0.466622\pi$
$968$		0			0
$969$	17.6873	+	30.6353i	0.568198	+	0.984147i
$970$		0			0
$971$	−7.96221	+	13.7910i	−0.255519	+	0.442573i	−0.965036	−	0.262116i	$-0.915580\pi$
$971$	−7.96221	+	13.7910i	−0.255519	+	0.442573i	0.709517	+	0.704688i	$0.248913\pi$
$972$		0			0
$973$	3.57919	+	45.0997i	0.114744	+	1.44583i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.42217	−	14.5876i	−0.269449	−	0.466699i	0.699271	−	0.714857i	$-0.253508\pi$
$977$	−8.42217	−	14.5876i	−0.269449	−	0.466699i	−0.968720	+	0.248158i	$0.920175\pi$
$978$		0			0
$979$	−15.9244			−0.508947
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.6052	+	32.2251i	0.593412	+	1.02782i	0.993769	+	0.111461i	$0.0355530\pi$
$983$	18.6052	+	32.2251i	0.593412	+	1.02782i	−0.400356	+	0.916360i	$0.631114\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.779710	−	9.82475i	−0.0248184	−	0.312725i
$988$		0			0
$989$	2.91238	−	5.04438i	0.0926082	−	0.160402i
$990$		0			0
$991$	17.2371	+	29.8556i	0.547555	+	0.948394i	0.998441	+	0.0558122i	$0.0177748\pi$
$991$	17.2371	+	29.8556i	0.547555	+	0.948394i	−0.450886	+	0.892582i	$0.648892\pi$
$992$		0			0
$993$	8.35671			0.265192
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.38876	+	4.13746i	0.0756529	+	0.131035i	0.901370	−	0.433050i	$-0.142563\pi$
$997$	2.38876	+	4.13746i	0.0756529	+	0.131035i	−0.825717	+	0.564084i	$0.809229\pi$
$998$		0			0
$999$	−14.5876	+	25.2665i	−0.461532	+	0.799397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.i.f.401.4		8
5.2	odd	4		140.2.q.b.9.2	yes	4
5.3	odd	4		140.2.q.a.9.1	✓	4
5.4	even	2	inner	700.2.i.f.401.1		8
7.2	even	3		4900.2.a.be.1.2		4
7.4	even	3	inner	700.2.i.f.501.4		8
7.5	odd	6		4900.2.a.bf.1.4		4
15.2	even	4		1260.2.bm.b.289.1		4
15.8	even	4		1260.2.bm.a.289.2		4
20.3	even	4		560.2.bw.e.289.1		4
20.7	even	4		560.2.bw.a.289.2		4
35.2	odd	12		980.2.e.f.589.4		4
35.3	even	12		980.2.q.b.949.2		4
35.4	even	6	inner	700.2.i.f.501.1		8
35.9	even	6		4900.2.a.be.1.4		4
35.12	even	12		980.2.e.c.589.1		4
35.13	even	4		980.2.q.g.569.2		4
35.17	even	12		980.2.q.g.949.2		4
35.18	odd	12		140.2.q.b.109.1	yes	4
35.19	odd	6		4900.2.a.bf.1.2		4
35.23	odd	12		980.2.e.f.589.2		4
35.27	even	4		980.2.q.b.569.1		4
35.32	odd	12		140.2.q.a.109.1	yes	4
35.33	even	12		980.2.e.c.589.3		4
105.32	even	12		1260.2.bm.a.109.2		4
105.53	even	12		1260.2.bm.b.109.2		4
140.67	even	12		560.2.bw.e.529.1		4
140.123	even	12		560.2.bw.a.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.1	✓	4	5.3	odd	4
140.2.q.a.109.1	yes	4	35.32	odd	12
140.2.q.b.9.2	yes	4	5.2	odd	4
140.2.q.b.109.1	yes	4	35.18	odd	12
560.2.bw.a.289.2		4	20.7	even	4
560.2.bw.a.529.1		4	140.123	even	12
560.2.bw.e.289.1		4	20.3	even	4
560.2.bw.e.529.1		4	140.67	even	12
700.2.i.f.401.1		8	5.4	even	2	inner
700.2.i.f.401.4		8	1.1	even	1	trivial
700.2.i.f.501.1		8	35.4	even	6	inner
700.2.i.f.501.4		8	7.4	even	3	inner
980.2.e.c.589.1		4	35.12	even	12
980.2.e.c.589.3		4	35.33	even	12
980.2.e.f.589.2		4	35.23	odd	12
980.2.e.f.589.4		4	35.2	odd	12
980.2.q.b.569.1		4	35.27	even	4
980.2.q.b.949.2		4	35.3	even	12
980.2.q.g.569.2		4	35.13	even	4
980.2.q.g.949.2		4	35.17	even	12
1260.2.bm.a.109.2		4	105.32	even	12
1260.2.bm.a.289.2		4	15.8	even	4
1260.2.bm.b.109.2		4	105.53	even	12
1260.2.bm.b.289.1		4	15.2	even	4
4900.2.a.be.1.2		4	7.2	even	3
4900.2.a.be.1.4		4	35.9	even	6
4900.2.a.bf.1.2		4	35.19	odd	6
4900.2.a.bf.1.4		4	7.5	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{3} +(-0.209313 - 2.63746i) q^{7} +(-1.13746 - 1.97014i) q^{11} +6.09095 q^{13} +(2.38876 + 4.13746i) q^{17} +(2.13746 - 3.70219i) q^{19} +(3.77492 - 2.59808i) q^{21} +(0.447399 - 0.774917i) q^{23} +5.19615 q^{27} -3.27492 q^{29} +(2.13746 + 3.70219i) q^{31} +(1.97014 - 3.41238i) q^{33} +(-2.80739 + 4.86254i) q^{37} +(5.27492 + 9.13642i) q^{39} -11.2749 q^{41} +6.50958 q^{43} +(1.07534 - 1.86254i) q^{47} +(-6.91238 + 1.10411i) q^{49} +(-4.13746 + 7.16629i) q^{51} +(3.70219 + 6.41238i) q^{53} +7.40437 q^{57} +(-2.13746 - 3.70219i) q^{59} +(-0.774917 + 1.34220i) q^{61} +(-6.95698 - 12.0498i) q^{67} +1.54983 q^{69} +10.5498 q^{71} +(1.07534 + 1.86254i) q^{73} +(-4.95807 + 3.41238i) q^{77} +(0.137459 - 0.238085i) q^{79} +(4.50000 + 7.79423i) q^{81} -5.67232 q^{83} +(-2.83616 - 4.91238i) q^{87} +(3.50000 - 6.06218i) q^{89} +(-1.27492 - 16.0646i) q^{91} +(-3.70219 + 6.41238i) q^{93} +6.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{11} + 2 q^{19} + 4 q^{29} + 2 q^{31} + 12 q^{39} - 60 q^{41} - 10 q^{49} - 18 q^{51} - 2 q^{59} + 24 q^{61} - 48 q^{69} + 24 q^{71} - 14 q^{79} + 36 q^{81} + 28 q^{89} + 20 q^{91}+O(q^{100}) \) 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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