LMFDB - Embedded newform 700.2.i.f.501.1

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			501.1
Root			$-0.656712 - 2.13746i$ of defining polynomial
Character	$\chi$	$=$	700.501
Dual form			700.2.i.f.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	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	−0.984980	−	0.172666i	$-0.944762\pi$
$11$	−1.13746	+	1.97014i	−0.342957	+	0.594018i	0.642024	+	0.766685i	$0.278095\pi$
$12$		0			0
$13$	−6.09095			−1.68933			−0.844663	−	0.535299i	$-0.820199\pi$
$13$	−6.09095			−1.68933			−0.844663	+	0.535299i	$0.820199\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.38876	+	4.13746i	−0.579360	+	1.00348i	0.416193	+	0.909276i	$0.363364\pi$
$17$	−2.38876	+	4.13746i	−0.579360	+	1.00348i	−0.995553	+	0.0942047i	$0.969969\pi$
$18$		0			0
$19$	2.13746	+	3.70219i	0.490367	+	0.849340i	0.999939	−	0.0110882i	$-0.00352954\pi$
$19$	2.13746	+	3.70219i	0.490367	+	0.849340i	−0.509572	+	0.860428i	$0.670196\pi$
$20$		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	$-0.196405\pi$
$23$	−0.447399	−	0.774917i	−0.0932891	−	0.161581i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		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	−0.607717	−	0.794154i	$-0.707914\pi$
$31$	2.13746	−	3.70219i	0.383899	−	0.664932i	0.991616	+	0.129221i	$0.0412478\pi$
$32$		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	$-0.0139666\pi$
$37$	2.80739	+	4.86254i	0.461532	+	0.799397i	−0.537506	+	0.843260i	$0.680633\pi$
$38$		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	$-0.665327\pi$
$43$	−6.50958			−0.992701			−0.496351	+	0.868122i	$0.665327\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.07534	−	1.86254i	−0.156854	−	0.271680i	0.776878	−	0.629651i	$-0.216802\pi$
$47$	−1.07534	−	1.86254i	−0.156854	−	0.271680i	−0.933733	+	0.357971i	$0.883469\pi$
$48$		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	0.491417	+	0.870925i	$0.336479\pi$
$53$	−3.70219	+	6.41238i	−0.508534	+	0.880808i	−0.999951	+	0.00988297i	$0.996854\pi$
$54$		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	−0.970956	−	0.239259i	$-0.923095\pi$
$59$	−2.13746	+	3.70219i	−0.278273	+	0.481984i	0.692682	+	0.721243i	$0.256429\pi$
$60$		0			0
$61$	−0.774917	−	1.34220i	−0.0992180	−	0.171851i	0.812143	−	0.583458i	$-0.198301\pi$
$61$	−0.774917	−	1.34220i	−0.0992180	−	0.171851i	−0.911361	+	0.411608i	$0.864967\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.95698	−	12.0498i	0.849930	−	1.47212i	−0.0313404	−	0.999509i	$-0.509978\pi$
$67$	6.95698	−	12.0498i	0.849930	−	1.47212i	0.881270	−	0.472613i	$-0.156689\pi$
$68$		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	$-0.873502\pi$
$73$	−1.07534	+	1.86254i	−0.125859	+	0.217994i	0.796209	+	0.605021i	$0.206835\pi$
$74$		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	0.873654	−	0.486547i	$-0.161744\pi$
$79$	0.137459	+	0.238085i	0.0154653	+	0.0267867i	−0.858189	+	0.513334i	$0.828410\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$	5.67232			0.622618			0.311309	−	0.950309i	$-0.399233\pi$
$83$	5.67232			0.622618			0.311309	+	0.950309i	$0.399233\pi$
$84$		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	0.989720	−	0.143022i	$-0.0456819\pi$
$89$	3.50000	+	6.06218i	0.370999	+	0.642590i	−0.618720	+	0.785611i	$0.712349\pi$
$90$		0			0
$91$	−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	$-0.614405\pi$
$97$	−6.92820			−0.703452			−0.351726	+	0.936103i	$0.614405\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.774917	+	1.34220i	−0.0771071	+	0.133553i	−0.902001	−	0.431735i	$-0.857902\pi$
$101$	−0.774917	+	1.34220i	−0.0771071	+	0.133553i	0.824894	+	0.565288i	$0.191235\pi$
$102$		0			0
$103$	−1.28465	−	2.22508i	−0.126581	−	0.219244i	0.795769	−	0.605600i	$-0.207067\pi$
$103$	−1.28465	−	2.22508i	−0.126581	−	0.219244i	−0.922350	+	0.386356i	$0.873734\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.95698	+	12.0498i	0.672556	+	1.16490i	0.977177	+	0.212428i	$0.0681370\pi$
$107$	6.95698	+	12.0498i	0.672556	+	1.16490i	−0.304621	+	0.952474i	$0.598530\pi$
$108$		0			0
$109$	−1.77492	+	3.07425i	−0.170006	+	0.294459i	−0.938422	−	0.345492i	$-0.887712\pi$
$109$	−1.77492	+	3.07425i	−0.170006	+	0.294459i	0.768416	+	0.639951i	$0.221045\pi$
$110$		0			0
$111$	−9.72508			−0.923064
$112$		0			0
$113$	13.0192			1.22474			0.612369	−	0.790572i	$-0.290217\pi$
$113$	13.0192			1.22474			0.612369	+	0.790572i	$0.290217\pi$
$114$		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	$-0.474699\pi$
$127$	1.78959			0.158801			0.0794004	+	0.996843i	$0.474699\pi$
$128$		0			0
$129$	5.63746	−	9.76436i	0.496351	−	0.859704i
$130$		0			0
$131$	9.13746	+	15.8265i	0.798343	+	1.38277i	0.920694	+	0.390285i	$0.127623\pi$
$131$	9.13746	+	15.8265i	0.798343	+	1.38277i	−0.122351	+	0.992487i	$0.539043\pi$
$132$		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	$-0.961808\pi$
$137$	−4.59698	+	7.96221i	−0.392747	+	0.680258i	0.600064	+	0.799952i	$0.295142\pi$
$138$		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	0.668946	−	0.743311i	$-0.266746\pi$
$149$	−3.77492	−	6.53835i	−0.309253	−	0.535642i	−0.978199	+	0.207669i	$0.933412\pi$
$150$		0			0
$151$	10.1375	−	17.5586i	0.824975	−	1.42890i	−0.0769640	−	0.997034i	$-0.524523\pi$
$151$	10.1375	−	17.5586i	0.824975	−	1.42890i	0.901939	−	0.431864i	$-0.142144\pi$
$152$		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	$-0.976125\pi$
$157$	−5.43424	+	9.41238i	−0.433699	+	0.751189i	0.563489	+	0.826123i	$0.309459\pi$
$158$		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	$-0.0730188\pi$
$163$	3.70219	+	6.41238i	0.289978	+	0.502256i	−0.683826	+	0.729645i	$0.739685\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.6005			0.975058			0.487529	−	0.873107i	$-0.337898\pi$
$167$	12.6005			0.975058			0.487529	+	0.873107i	$0.337898\pi$
$168$		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	0.963828	+	0.266524i	$0.0858752\pi$
$173$	9.37451	+	16.2371i	0.712731	+	1.23449i	−0.251097	+	0.967962i	$0.580791\pi$
$174$		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	−0.871117	−	0.491076i	$-0.836604\pi$
$179$	−0.137459	+	0.238085i	−0.0102741	+	0.0177953i	0.860843	+	0.508871i	$0.169937\pi$
$180$		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	−0.901329	−	0.433135i	$-0.857407\pi$
$191$	−11.4124	−	19.7668i	−0.825771	−	1.43028i	0.0755585	−	0.997141i	$-0.475926\pi$
$192$		0			0
$193$	4.59698	−	7.96221i	0.330898	−	0.573132i	−0.651790	−	0.758399i	$-0.725982\pi$
$193$	4.59698	−	7.96221i	0.330898	−	0.573132i	0.982688	+	0.185267i	$0.0593150\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	26.0383			1.85515			0.927576	−	0.373634i	$-0.121888\pi$
$197$	26.0383			1.85515			0.927576	+	0.373634i	$0.121888\pi$
$198$		0			0
$199$	−4.86254	+	8.42217i	−0.344696	+	0.597032i	−0.985299	−	0.170841i	$-0.945351\pi$
$199$	−4.86254	+	8.42217i	−0.344696	+	0.597032i	0.640602	+	0.767873i	$0.278685\pi$
$200$		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	$-0.405715\pi$
$223$	8.71780			0.583787			0.291893	+	0.956451i	$0.405715\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.22602	−	5.58762i	0.214118	−	0.370864i	−0.738881	−	0.673836i	$-0.764646\pi$
$227$	3.22602	−	5.58762i	0.214118	−	0.370864i	0.952999	+	0.302972i	$0.0979789\pi$
$228$		0			0
$229$	2.13746	+	3.70219i	0.141247	+	0.244647i	0.927967	−	0.372663i	$-0.121555\pi$
$229$	2.13746	+	3.70219i	0.141247	+	0.244647i	−0.786719	+	0.617311i	$0.788222\pi$
$230$		0			0
$231$	−9.41238	+	4.48190i	−0.619289	+	0.294887i
$232$		0			0
$233$	−9.31697	−	16.1375i	−0.610375	−	1.05720i	−0.991177	−	0.132544i	$-0.957686\pi$
$233$	−9.31697	−	16.1375i	−0.610375	−	1.05720i	0.380802	−	0.924656i	$-0.375648\pi$
$234$		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	−0.582165	−	0.813071i	$-0.697794\pi$
$241$	6.41238	−	11.1066i	0.413057	−	0.715436i	0.995222	+	0.0976343i	$0.0311275\pi$
$242$		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	0.936934	+	0.349506i	$0.113650\pi$
$257$	12.3624	+	21.4124i	0.771148	+	1.33567i	−0.165786	+	0.986162i	$0.553016\pi$
$258$		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	0.0673516	+	0.997729i	$0.478545\pi$
$263$	−13.4666	+	23.3248i	−0.830383	+	1.43827i	−0.897735	+	0.440536i	$0.854788\pi$
$264$		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	0.0744400	−	0.997225i	$-0.476283\pi$
$269$	14.7749	−	25.5909i	0.900843	−	1.56031i	0.826403	−	0.563080i	$-0.190384\pi$
$270$		0			0
$271$	6.41238	+	11.1066i	0.389524	+	0.674676i	0.992386	−	0.123170i	$-0.0393062\pi$
$271$	6.41238	+	11.1066i	0.389524	+	0.674676i	−0.602861	+	0.797846i	$0.705973\pi$
$272$		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	0.437710	+	0.899116i	$0.355790\pi$
$277$	−9.31697	+	16.1375i	−0.559802	+	0.969606i	−0.997512	+	0.0704898i	$0.977544\pi$
$278$		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	−0.413084	−	0.910693i	$-0.635548\pi$
$283$	9.79314	−	16.9622i	0.582142	−	1.00830i	0.995225	−	0.0976056i	$-0.0311184\pi$
$284$		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	$-0.435134\pi$
$293$	6.92820			0.404750			0.202375	+	0.979308i	$0.435134\pi$
$294$		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	$-0.536393\pi$
$307$	−3.99782			−0.228167			−0.114084	+	0.993471i	$0.536393\pi$
$308$		0			0
$309$	4.45017			0.253161
$310$		0			0
$311$	−6.41238	+	11.1066i	−0.363612	+	0.629795i	−0.988552	−	0.150878i	$-0.951790\pi$
$311$	−6.41238	+	11.1066i	−0.363612	+	0.629795i	0.624940	+	0.780673i	$0.285123\pi$
$312$		0			0
$313$	−7.22383	−	12.5120i	−0.408315	−	0.707223i	0.586386	−	0.810032i	$-0.300550\pi$
$313$	−7.22383	−	12.5120i	−0.408315	−	0.707223i	−0.994701	+	0.102809i	$0.967217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.91259	−	3.31271i	−0.107422	−	0.186060i	0.807303	−	0.590137i	$-0.200926\pi$
$317$	−1.91259	−	3.31271i	−0.107422	−	0.186060i	−0.914725	+	0.404077i	$0.867593\pi$
$318$		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	0.924677	−	0.380753i	$-0.124335\pi$
$331$	2.41238	+	4.17836i	0.132596	+	0.229663i	−0.792080	+	0.610417i	$0.791002\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−13.0192			−0.709198			−0.354599	−	0.935018i	$-0.615383\pi$
$337$	−13.0192			−0.709198			−0.354599	+	0.935018i	$0.615383\pi$
$338$		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	$-0.938844\pi$
$347$	−6.06218	+	10.5000i	−0.325435	+	0.563670i	0.656165	+	0.754617i	$0.272177\pi$
$348$		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	0.431176	+	0.902268i	$0.358099\pi$
$353$	−10.6304	+	18.4124i	−0.565799	+	0.979992i	−0.996975	+	0.0777242i	$0.975235\pi$
$354$		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	0.883592	−	0.468257i	$-0.155118\pi$
$359$	0.687293	+	1.19043i	0.0362739	+	0.0628283i	−0.847318	+	0.531085i	$0.821784\pi$
$360$		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	$-0.707534\pi$
$367$	7.37560	−	12.7749i	0.385003	−	0.666845i	0.991770	+	0.128035i	$0.0408670\pi$
$368$		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	$-0.213101\pi$
$373$	−2.80739	−	4.86254i	−0.145361	−	0.251773i	−0.929508	+	0.368803i	$0.879768\pi$
$374$		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	−0.999917	−	0.0128665i	$-0.995904\pi$
$383$	−10.0025	−	17.3248i	−0.511101	−	0.885253i	0.488816	−	0.872387i	$-0.337429\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.68729	−	4.65453i	0.136251	−	0.235994i	−0.789824	−	0.613334i	$-0.789828\pi$
$389$	2.68729	−	4.65453i	0.136251	−	0.235994i	0.926075	+	0.377340i	$0.123161\pi$
$390$		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	$-0.290975\pi$
$397$	−7.58492	−	13.1375i	−0.380676	−	0.659350i	−0.991159	+	0.132679i	$0.957642\pi$
$398$		0			0
$399$	−1.54983	+	19.5287i	−0.0775888	+	0.977659i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−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	−0.963442	−	0.267917i	$-0.913665\pi$
$409$	−5.04983	+	8.74657i	−0.249698	+	0.432490i	0.713744	+	0.700407i	$0.246998\pi$
$410$		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	−0.999273	−	0.0381236i	$-0.987862\pi$
$431$	−9.68729	+	16.7789i	−0.466620	+	0.808210i	0.532653	+	0.846334i	$0.321195\pi$
$432$		0			0
$433$	−26.8756			−1.29156			−0.645778	−	0.763525i	$-0.723467\pi$
$433$	−26.8756			−1.29156			−0.645778	+	0.763525i	$0.723467\pi$
$434$		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	0.851662	−	0.524092i	$-0.175595\pi$
$439$	−0.587624	−	1.01779i	−0.0280458	−	0.0485767i	−0.879708	+	0.475515i	$0.842262\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.06218	+	10.5000i	0.288023	+	0.498870i	0.973338	−	0.229377i	$-0.0736688\pi$
$443$	6.06218	+	10.5000i	0.288023	+	0.498870i	−0.685315	+	0.728247i	$0.740335\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	13.0767			0.618507
$448$		0			0
$449$	−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	$-0.325191\pi$
$457$	−10.2118	−	17.6873i	−0.477686	−	0.827377i	−0.999673	+	0.0255769i	$0.991858\pi$
$458$		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	$-0.451666\pi$
$463$	6.50958			0.302526			0.151263	+	0.988494i	$0.451666\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.58382	+	16.5997i	0.443486	+	0.768141i	0.997945	−	0.0640700i	$-0.0204081\pi$
$467$	9.58382	+	16.5997i	0.443486	+	0.768141i	−0.554459	+	0.832211i	$0.687075\pi$
$468$		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	−0.681526	−	0.731794i	$-0.738683\pi$
$479$	6.41238	−	11.1066i	0.292989	−	0.507472i	0.974515	+	0.224322i	$0.0720168\pi$
$480$		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	0.186296	+	0.982494i	$0.440352\pi$
$487$	−16.7213	+	28.9622i	−0.757716	+	1.31240i	−0.944013	+	0.329909i	$0.892982\pi$
$488$		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	−0.849869	−	0.526993i	$-0.823319\pi$
$499$	−19.6873	−	34.0994i	−0.881324	−	1.52650i	−0.0314548	−	0.999505i	$-0.510014\pi$
$500$		0			0
$501$	−10.9124	+	18.9008i	−0.487529	+	0.844425i
$502$		0			0
$503$	−16.1797			−0.721418			−0.360709	−	0.932678i	$-0.617465\pi$
$503$	−16.1797			−0.721418			−0.360709	+	0.932678i	$0.617465\pi$
$504$		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	0.981922	+	0.189285i	$0.0606170\pi$
$509$	14.7749	+	25.5909i	0.654887	+	1.13430i	−0.327036	+	0.945012i	$0.606050\pi$
$510$		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	−0.690683	−	0.723158i	$-0.742690\pi$
$521$	6.41238	−	11.1066i	0.280931	−	0.486587i	0.971614	+	0.236570i	$0.0760234\pi$
$522$		0			0
$523$	−5.85286	−	10.1375i	−0.255928	−	0.443280i	0.709219	−	0.704988i	$-0.249048\pi$
$523$	−5.85286	−	10.1375i	−0.255928	−	0.443280i	−0.965147	+	0.261708i	$0.915714\pi$
$524$		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	0.891159	−	0.453692i	$-0.149893\pi$
$541$	1.22508	+	2.12191i	0.0526704	+	0.0912278i	−0.838488	+	0.544920i	$0.816560\pi$
$542$		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	$-0.219086\pi$
$547$	36.1271			1.54468			0.772341	+	0.635208i	$0.219086\pi$
$548$		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	$-0.871287\pi$
$557$	−2.80739	+	4.86254i	−0.118953	+	0.206032i	0.800400	+	0.599466i	$0.204620\pi$
$558$		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	$-0.916369\pi$
$563$	−6.11972	+	10.5997i	−0.257916	+	0.446723i	0.707768	+	0.706445i	$0.249702\pi$
$564$		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	0.990257	+	0.139251i	$0.0444694\pi$
$569$	14.6873	+	25.4391i	0.615723	+	1.06646i	−0.374534	+	0.927213i	$0.622197\pi$
$570$		0			0
$571$	0.137459	−	0.238085i	0.00575246	−	0.00996356i	−0.863135	−	0.504974i	$-0.831502\pi$
$571$	0.137459	−	0.238085i	0.00575246	−	0.00996356i	0.868887	+	0.495010i	$0.164836\pi$
$572$		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	$-0.778455\pi$
$577$	4.12081	−	7.13746i	0.171552	−	0.297136i	0.938963	+	0.344019i	$0.111789\pi$
$578$		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	$-0.593101\pi$
$587$	−13.9715			−0.576665			−0.288333	+	0.957530i	$0.593101\pi$
$588$		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	$-0.303579\pi$
$593$	−10.1542	−	17.5876i	−0.416984	−	0.722237i	−0.995634	+	0.0933384i	$0.970246\pi$
$594$		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	−0.841852	−	0.539709i	$-0.818534\pi$
$599$	1.13746	−	1.97014i	0.0464753	−	0.0804976i	0.888327	+	0.459211i	$0.151868\pi$
$600$		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	0.982339	+	0.187109i	$0.0599119\pi$
$607$	16.0934	+	27.8746i	0.653211	+	1.13139i	−0.329128	+	0.944285i	$0.606755\pi$
$608$		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	0.201297	+	0.979530i	$0.435484\pi$
$613$	−18.5109	+	32.0619i	−0.747650	+	1.29497i	−0.948947	+	0.315437i	$0.897849\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.57919			0.144093			0.0720464	−	0.997401i	$-0.477047\pi$
$617$	3.57919			0.144093			0.0720464	+	0.997401i	$0.477047\pi$
$618$		0			0
$619$	−21.9622	+	38.0397i	−0.882736	+	1.52894i	−0.0344487	+	0.999406i	$0.510968\pi$
$619$	−21.9622	+	38.0397i	−0.882736	+	1.52894i	−0.848287	+	0.529537i	$0.822366\pi$
$620$		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	0.442973	+	0.896535i	$0.353924\pi$
$641$	−14.0498	+	24.3350i	−0.554935	+	0.961176i	−0.997909	+	0.0646411i	$0.979410\pi$
$642$		0			0
$643$	38.3353			1.51180			0.755898	−	0.654689i	$-0.227200\pi$
$643$	38.3353			1.51180			0.755898	+	0.654689i	$0.227200\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.389855	+	0.675248i	−0.0153268	+	0.0265468i	−0.873587	−	0.486668i	$-0.838212\pi$
$647$	−0.389855	+	0.675248i	−0.0153268	+	0.0265468i	0.858260	+	0.513215i	$0.171546\pi$
$648$		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	0.959225	+	0.282643i	$0.0912113\pi$
$653$	18.5109	+	32.0619i	0.724389	+	1.25468i	−0.234836	+	0.972035i	$0.575455\pi$
$654$		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	−0.674272	−	0.738483i	$-0.735542\pi$
$661$	7.77492	−	13.4666i	0.302409	−	0.523788i	0.976681	+	0.214695i	$0.0688758\pi$
$662$		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	$-0.478024\pi$
$673$	3.57919			0.137968			0.0689838	+	0.997618i	$0.478024\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.3049	−	21.3127i	−0.472916	−	0.819114i	0.526604	−	0.850111i	$-0.323465\pi$
$677$	−12.3049	−	21.3127i	−0.472916	−	0.819114i	−0.999519	+	0.0309969i	$0.990132\pi$
$678$		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	$-0.736200\pi$
$683$	7.85177	−	13.5997i	0.300440	−	0.520377i	0.976236	+	0.216712i	$0.0695332\pi$
$684$		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	0.927599	−	0.373578i	$-0.121869\pi$
$691$	3.68729	+	6.38658i	0.140271	+	0.242957i	−0.787327	+	0.616535i	$0.788536\pi$
$692$		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	0.999731	−	0.0232018i	$-0.00738601\pi$
$709$	12.7749	+	22.1268i	0.479772	+	0.830990i	−0.519959	+	0.854191i	$0.674053\pi$
$710$		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	0.789042	−	0.614340i	$-0.210577\pi$
$719$	−3.68729	−	6.38658i	−0.137513	−	0.238179i	−0.926555	+	0.376160i	$0.877244\pi$
$720$		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	$-0.612669\pi$
$727$	−18.6915			−0.693228			−0.346614	+	0.938008i	$0.612669\pi$
$728$		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	−0.990298	−	0.138959i	$-0.955624\pi$
$733$	−16.6638	−	28.8625i	−0.615491	−	1.06606i	0.374807	−	0.927103i	$-0.377709\pi$
$734$		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	0.407420	+	0.913241i	$0.366428\pi$
$739$	−15.9622	+	27.6474i	−0.587179	+	1.01702i	−0.994600	+	0.103784i	$0.966905\pi$
$740$		0			0
$741$	45.0997			1.65678
$742$		0			0
$743$	−19.5287			−0.716440			−0.358220	−	0.933637i	$-0.616616\pi$
$743$	−19.5287			−0.716440			−0.358220	+	0.933637i	$0.616616\pi$
$744$		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	0.994485	−	0.104882i	$-0.0334466\pi$
$751$	11.1375	+	19.2906i	0.406412	+	0.703926i	−0.588073	+	0.808808i	$0.700113\pi$
$752$		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	$-0.445122\pi$
$757$	9.43996			0.343101			0.171551	+	0.985175i	$0.445122\pi$
$758$		0			0
$759$	−1.76287	+	3.05338i	−0.0639882	+	0.110831i
$760$		0			0
$761$	14.9622	+	25.9153i	0.542380	+	0.939429i	0.998767	+	0.0496479i	$0.0158099\pi$
$761$	14.9622	+	25.9153i	0.542380	+	0.939429i	−0.456387	+	0.889781i	$0.650857\pi$
$762$		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	$-0.670397\pi$
$773$	13.6183	−	23.5876i	0.489817	−	0.848388i	0.999931	+	0.0117187i	$0.00373027\pi$
$774$		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	$-0.823505\pi$
$787$	0.866025	−	1.50000i	0.0308705	−	0.0534692i	0.881048	+	0.473027i	$0.156839\pi$
$788$		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	$-0.674246\pi$
$797$	−29.3873			−1.04095			−0.520476	+	0.853876i	$0.674246\pi$
$798$		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	0.183751	+	0.982973i	$0.441176\pi$
$809$	−21.5997	+	37.4117i	−0.759404	+	1.31533i	−0.943155	+	0.332353i	$0.892157\pi$
$810$		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	0.673668	−	0.739034i	$-0.264718\pi$
$821$	−8.68729	−	15.0468i	−0.303189	−	0.525138i	−0.976856	+	0.213896i	$0.931385\pi$
$822$		0			0
$823$	16.1509	−	27.9743i	0.562987	−	0.975121i	−0.434247	−	0.900794i	$-0.642986\pi$
$823$	16.1509	−	27.9743i	0.562987	−	0.975121i	0.997234	−	0.0743276i	$-0.0236810\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.5670			−1.58452			−0.792261	−	0.610183i	$-0.791096\pi$
$827$	−45.5670			−1.58452			−0.792261	+	0.610183i	$0.791096\pi$
$828$		0			0
$829$	−0.962210	+	1.66660i	−0.0334189	+	0.0578833i	−0.882251	−	0.470779i	$-0.843973\pi$
$829$	−0.962210	+	1.66660i	−0.0334189	+	0.0578833i	0.848832	+	0.528662i	$0.177306\pi$
$830$		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	$-0.674581\pi$
$853$	−30.4547			−1.04275			−0.521375	+	0.853327i	$0.674581\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.6638	+	28.8625i	−0.569224	+	0.985926i	0.427418	+	0.904054i	$0.359423\pi$
$857$	−16.6638	+	28.8625i	−0.569224	+	0.985926i	−0.996643	+	0.0818717i	$0.973910\pi$
$858$		0			0
$859$	−17.6873	−	30.6353i	−0.603483	−	1.04526i	−0.992289	−	0.123943i	$-0.960446\pi$
$859$	−17.6873	−	30.6353i	−0.603483	−	1.04526i	0.388807	−	0.921319i	$-0.372887\pi$
$860$		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	$-0.0259035\pi$
$863$	12.5718	+	21.7749i	0.427947	+	0.741227i	−0.568743	+	0.822515i	$0.692570\pi$
$864$		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	0.945753	+	0.324887i	$0.105326\pi$
$877$	22.3361	+	38.6873i	0.754237	+	1.30638i	−0.191516	+	0.981490i	$0.561340\pi$
$878$		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	$-0.386931\pi$
$883$	20.6695			0.695585			0.347792	+	0.937572i	$0.386931\pi$
$884$		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
$889$	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	0.194212	+	0.980960i	$0.437785\pi$
$907$	−22.6605	+	39.2492i	−0.752430	+	1.30325i	−0.946642	+	0.322288i	$0.895548\pi$
$908$		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	0.813024	−	0.582230i	$-0.197820\pi$
$919$	−2.96221	−	5.13070i	−0.0977143	−	0.169246i	−0.910738	+	0.412984i	$0.864486\pi$
$920$		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	0.974669	−	0.223653i	$-0.0717982\pi$
$929$	8.95017	+	15.5021i	0.293645	+	0.508609i	−0.681023	+	0.732262i	$0.738465\pi$
$930$		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	$-0.554904\pi$
$937$	−10.5074			−0.343262			−0.171631	+	0.985161i	$0.554904\pi$
$938$		0			0
$939$	25.0241			0.816630
$940$		0			0
$941$	−2.13746	+	3.70219i	−0.0696792	+	0.120688i	−0.898760	−	0.438441i	$-0.855531\pi$
$941$	−2.13746	+	3.70219i	−0.0696792	+	0.120688i	0.829081	+	0.559129i	$0.188864\pi$
$942$		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	−0.975518	−	0.219918i	$-0.929421\pi$
$947$	−20.8709	−	36.1495i	−0.678214	−	1.17470i	0.297304	−	0.954783i	$-0.403912\pi$
$948$		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	$-0.659255\pi$
$953$	−29.6175			−0.959405			−0.479702	+	0.877431i	$0.659255\pi$
$954$		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	$-0.533378\pi$
$967$	−6.50958			−0.209334			−0.104667	+	0.994507i	$0.533378\pi$
$968$		0			0
$969$	17.6873	−	30.6353i	0.568198	−	0.984147i
$970$		0			0
$971$	−7.96221	−	13.7910i	−0.255519	−	0.442573i	0.709517	−	0.704688i	$-0.248913\pi$
$971$	−7.96221	−	13.7910i	−0.255519	−	0.442573i	−0.965036	+	0.262116i	$0.915580\pi$
$972$		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	$-0.746492\pi$
$977$	8.42217	−	14.5876i	0.269449	−	0.466699i	0.968720	+	0.248158i	$0.0798251\pi$
$978$		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	0.400356	+	0.916360i	$0.368886\pi$
$983$	−18.6052	+	32.2251i	−0.593412	+	1.02782i	−0.993769	+	0.111461i	$0.964447\pi$
$984$		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	−0.450886	−	0.892582i	$-0.648892\pi$
$991$	17.2371	−	29.8556i	0.547555	−	0.948394i	0.998441	−	0.0558122i	$-0.0177748\pi$
$992$		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	$-0.857437\pi$
$997$	−2.38876	+	4.13746i	−0.0756529	+	0.131035i	0.825717	+	0.564084i	$0.190771\pi$
$998$		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.501.1		8
5.2	odd	4		140.2.q.b.109.1	yes	4
5.3	odd	4		140.2.q.a.109.1	yes	4
5.4	even	2	inner	700.2.i.f.501.4		8
7.2	even	3	inner	700.2.i.f.401.1		8
7.3	odd	6		4900.2.a.bf.1.2		4
7.4	even	3		4900.2.a.be.1.4		4
15.2	even	4		1260.2.bm.b.109.2		4
15.8	even	4		1260.2.bm.a.109.2		4
20.3	even	4		560.2.bw.e.529.1		4
20.7	even	4		560.2.bw.a.529.1		4
35.2	odd	12		140.2.q.a.9.1	✓	4
35.3	even	12		980.2.e.c.589.1		4
35.4	even	6		4900.2.a.be.1.2		4
35.9	even	6	inner	700.2.i.f.401.4		8
35.12	even	12		980.2.q.g.569.2		4
35.13	even	4		980.2.q.g.949.2		4
35.17	even	12		980.2.e.c.589.3		4
35.18	odd	12		980.2.e.f.589.4		4
35.23	odd	12		140.2.q.b.9.2	yes	4
35.24	odd	6		4900.2.a.bf.1.4		4
35.27	even	4		980.2.q.b.949.2		4
35.32	odd	12		980.2.e.f.589.2		4
35.33	even	12		980.2.q.b.569.1		4
105.2	even	12		1260.2.bm.a.289.2		4
105.23	even	12		1260.2.bm.b.289.1		4
140.23	even	12		560.2.bw.a.289.2		4
140.107	even	12		560.2.bw.e.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.1	✓	4	35.2	odd	12
140.2.q.a.109.1	yes	4	5.3	odd	4
140.2.q.b.9.2	yes	4	35.23	odd	12
140.2.q.b.109.1	yes	4	5.2	odd	4
560.2.bw.a.289.2		4	140.23	even	12
560.2.bw.a.529.1		4	20.7	even	4
560.2.bw.e.289.1		4	140.107	even	12
560.2.bw.e.529.1		4	20.3	even	4
700.2.i.f.401.1		8	7.2	even	3	inner
700.2.i.f.401.4		8	35.9	even	6	inner
700.2.i.f.501.1		8	1.1	even	1	trivial
700.2.i.f.501.4		8	5.4	even	2	inner
980.2.e.c.589.1		4	35.3	even	12
980.2.e.c.589.3		4	35.17	even	12
980.2.e.f.589.2		4	35.32	odd	12
980.2.e.f.589.4		4	35.18	odd	12
980.2.q.b.569.1		4	35.33	even	12
980.2.q.b.949.2		4	35.27	even	4
980.2.q.g.569.2		4	35.12	even	12
980.2.q.g.949.2		4	35.13	even	4
1260.2.bm.a.109.2		4	15.8	even	4
1260.2.bm.a.289.2		4	105.2	even	12
1260.2.bm.b.109.2		4	15.2	even	4
1260.2.bm.b.289.1		4	105.23	even	12
4900.2.a.be.1.2		4	35.4	even	6
4900.2.a.be.1.4		4	7.4	even	3
4900.2.a.bf.1.2		4	7.3	odd	6
4900.2.a.bf.1.4		4	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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