LMFDB - Embedded newform 1260.2.bm.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(109,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("1260.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.bm (of order $6$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.2
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	1260.109
Dual form			1260.2.bm.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 2.17945i) q^{5} +(2.63746 + 0.209313i) q^{7} +(1.13746 - 1.97014i) q^{11} +6.09095i q^{13} +(4.13746 + 2.38876i) q^{17} +(-2.13746 - 3.70219i) q^{19} +(0.774917 - 0.447399i) q^{23} +(-4.50000 + 2.17945i) q^{25} -3.27492 q^{29} +(2.13746 - 3.70219i) q^{31} +(0.862541 + 5.85286i) q^{35} +(-4.86254 + 2.80739i) q^{37} +11.2749 q^{41} +6.50958i q^{43} +(-1.86254 + 1.07534i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-6.41238 - 3.70219i) q^{53} +(4.86254 + 1.49397i) q^{55} +(-2.13746 + 3.70219i) q^{59} +(-0.774917 - 1.34220i) q^{61} +(-13.2749 + 3.04547i) q^{65} +(12.0498 + 6.95698i) q^{67} -10.5498 q^{71} +(1.86254 + 1.07534i) q^{73} +(3.41238 - 4.95807i) q^{77} +(-0.137459 - 0.238085i) q^{79} +5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} +(3.50000 + 6.06218i) q^{89} +(-1.27492 + 16.0646i) q^{91} +(7.00000 - 6.50958i) q^{95} -6.92820i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} + 3 q^{7} - 3 q^{11} + 9 q^{17} - q^{19} - 12 q^{23} - 18 q^{25} + 2 q^{29} + q^{31} + 11 q^{35} - 27 q^{37} + 30 q^{41} - 15 q^{47} + 5 q^{49} - 3 q^{53} + 27 q^{55} - q^{59} + 12 q^{61}+ \cdots + 28 q^{95}+O(q^{100}) $ 4 * q + 2 * q^5 + 3 * q^7 - 3 * q^11 + 9 * q^17 - q^19 - 12 * q^23 - 18 * q^25 + 2 * q^29 + q^31 + 11 * q^35 - 27 * q^37 + 30 * q^41 - 15 * q^47 + 5 * q^49 - 3 * q^53 + 27 * q^55 - q^59 + 12 * q^61 - 38 * q^65 + 18 * q^67 - 12 * q^71 + 15 * q^73 - 9 * q^77 + 7 * q^79 - 5 * q^85 + 14 * q^89 + 10 * q^91 + 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	0.500000	+	2.17945i	0.223607	+	0.974679i
$5$	0.500000	+	2.17945i	0.223607	+	0.974679i
$6$		0			0
$7$	2.63746	+	0.209313i	0.996866	+	0.0791130i
$7$	2.63746	+	0.209313i	0.996866	+	0.0791130i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.13746	−	1.97014i	0.342957	−	0.594018i	−0.642024	−	0.766685i	$-0.721905\pi$
$11$	1.13746	−	1.97014i	0.342957	−	0.594018i	0.984980	+	0.172666i	$0.0552383\pi$
$12$		0			0
$13$			6.09095i			1.68933i	0.535299	+	0.844663i	$0.320199\pi$
$13$			6.09095i			1.68933i	−0.535299	+	0.844663i	$0.679801\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.13746	+	2.38876i	1.00348	+	0.579360i	0.909276	−	0.416193i	$-0.136636\pi$
$17$	4.13746	+	2.38876i	1.00348	+	0.579360i	0.0942047	+	0.995553i	$0.469969\pi$
$18$		0			0
$19$	−2.13746	−	3.70219i	−0.490367	−	0.849340i	0.509572	−	0.860428i	$-0.329804\pi$
$19$	−2.13746	−	3.70219i	−0.490367	−	0.849340i	−0.999939	+	0.0110882i	$0.996470\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.774917	−	0.447399i	0.161581	−	0.0932891i	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	0.774917	−	0.447399i	0.161581	−	0.0932891i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−4.50000	+	2.17945i	−0.900000	+	0.435890i
$26$		0			0
$27$		0			0
$28$		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
$33$		0			0
$34$		0			0
$35$	0.862541	+	5.85286i	0.145796	+	0.989315i
$36$		0			0
$37$	−4.86254	+	2.80739i	−0.799397	+	0.461532i	−0.843260	−	0.537506i	$-0.819367\pi$
$37$	−4.86254	+	2.80739i	−0.799397	+	0.461532i	0.0438633	+	0.999038i	$0.486033\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	11.2749			1.76085			0.880423	−	0.474189i	$-0.157259\pi$
$41$	11.2749			1.76085			0.880423	+	0.474189i	$0.157259\pi$
$42$		0			0
$43$			6.50958i			0.992701i	0.868122	+	0.496351i	$0.165327\pi$
$43$			6.50958i			0.992701i	−0.868122	+	0.496351i	$0.834673\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.86254	+	1.07534i	−0.271680	+	0.156854i	−0.629651	−	0.776878i	$-0.716802\pi$
$47$	−1.86254	+	1.07534i	−0.271680	+	0.156854i	0.357971	+	0.933733i	$0.383469\pi$
$48$		0			0
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.41238	−	3.70219i	−0.880808	−	0.508534i	−0.00988297	−	0.999951i	$-0.503146\pi$
$53$	−6.41238	−	3.70219i	−0.880808	−	0.508534i	−0.870925	+	0.491417i	$0.836479\pi$
$54$		0			0
$55$	4.86254	+	1.49397i	0.655665	+	0.201446i
$56$		0			0
$57$		0			0
$58$		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
$65$	−13.2749	+	3.04547i	−1.64655	+	0.377745i
$66$		0			0
$67$	12.0498	+	6.95698i	1.47212	+	0.849930i	0.999509	−	0.0313404i	$-0.00997759\pi$
$67$	12.0498	+	6.95698i	1.47212	+	0.849930i	0.472613	+	0.881270i	$0.343311\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.5498			−1.25204			−0.626018	−	0.779809i	$-0.715316\pi$
$71$	−10.5498			−1.25204			−0.626018	+	0.779809i	$0.715316\pi$
$72$		0			0
$73$	1.86254	+	1.07534i	0.217994	+	0.125859i	0.605021	−	0.796209i	$-0.293165\pi$
$73$	1.86254	+	1.07534i	0.217994	+	0.125859i	−0.387027	+	0.922068i	$0.626498\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.41238	−	4.95807i	0.388876	−	0.565024i
$78$		0			0
$79$	−0.137459	−	0.238085i	−0.0154653	−	0.0267867i	0.858189	−	0.513334i	$-0.171590\pi$
$79$	−0.137459	−	0.238085i	−0.0154653	−	0.0267867i	−0.873654	+	0.486547i	$0.838256\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			5.67232i			0.622618i	0.950309	+	0.311309i	$0.100767\pi$
$83$			5.67232i			0.622618i	−0.950309	+	0.311309i	$0.899233\pi$
$84$		0			0
$85$	−3.13746	+	10.2118i	−0.340305	+	1.10762i
$86$		0			0
$87$		0			0
$88$		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
$93$		0			0
$94$		0			0
$95$	7.00000	−	6.50958i	0.718185	−	0.667868i
$96$		0			0
$97$		−	6.92820i		−	0.703452i	−0.936103	−	0.351726i	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.774917	−	1.34220i	0.0771071	−	0.133553i	−0.824894	−	0.565288i	$-0.808765\pi$
$101$	0.774917	−	1.34220i	0.0771071	−	0.133553i	0.902001	+	0.431735i	$0.142098\pi$
$102$		0			0
$103$	−2.22508	+	1.28465i	−0.219244	+	0.126581i	−0.605600	−	0.795769i	$-0.707067\pi$
$103$	−2.22508	+	1.28465i	−0.219244	+	0.126581i	0.386356	+	0.922350i	$0.373734\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.0498	−	6.95698i	1.16490	−	0.672556i	0.212428	−	0.977177i	$-0.431863\pi$
$107$	12.0498	−	6.95698i	1.16490	−	0.672556i	0.952474	+	0.304621i	$0.0985297\pi$
$108$		0			0
$109$	1.77492	−	3.07425i	0.170006	−	0.294459i	−0.768416	−	0.639951i	$-0.778955\pi$
$109$	1.77492	−	3.07425i	0.170006	−	0.294459i	0.938422	+	0.345492i	$0.112288\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			13.0192i			1.22474i	0.790572	+	0.612369i	$0.209783\pi$
$113$			13.0192i			1.22474i	−0.790572	+	0.612369i	$0.790217\pi$
$114$		0			0
$115$	1.36254	+	1.46519i	0.127058	+	0.136630i
$116$		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
$123$		0			0
$124$		0			0
$125$	−7.00000	−	8.71780i	−0.626099	−	0.779744i
$126$		0			0
$127$			1.78959i			0.158801i	0.996843	+	0.0794004i	$0.0253006\pi$
$127$			1.78959i			0.158801i	−0.996843	+	0.0794004i	$0.974699\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.13746	−	15.8265i	−0.798343	−	1.38277i	−0.920694	−	0.390285i	$-0.872377\pi$
$131$	−9.13746	−	15.8265i	−0.798343	−	1.38277i	0.122351	−	0.992487i	$-0.460957\pi$
$132$		0			0
$133$	−4.86254	−	10.2118i	−0.421636	−	0.885472i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.96221	+	4.59698i	0.680258	+	0.392747i	0.799952	−	0.600064i	$-0.204858\pi$
$137$	7.96221	+	4.59698i	0.680258	+	0.392747i	−0.119695	+	0.992811i	$0.538192\pi$
$138$		0			0
$139$	17.0997			1.45037			0.725187	−	0.688551i	$-0.241753\pi$
$139$	17.0997			1.45037			0.725187	+	0.688551i	$0.241753\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.0000	+	6.92820i	1.00349	+	0.579365i
$144$		0			0
$145$	−1.63746	−	7.13752i	−0.135984	−	0.592738i
$146$		0			0
$147$		0			0
$148$		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
$155$	9.13746	+	2.80739i	0.733938	+	0.225495i
$156$		0			0
$157$	−9.41238	−	5.43424i	−0.751189	−	0.433699i	0.0749341	−	0.997188i	$-0.476125\pi$
$157$	−9.41238	−	5.43424i	−0.751189	−	0.433699i	−0.826123	+	0.563489i	$0.809459\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.13746	−	1.01779i	0.168455	−	0.0802135i
$162$		0			0
$163$	6.41238	−	3.70219i	0.502256	−	0.289978i	−0.227389	−	0.973804i	$-0.573019\pi$
$163$	6.41238	−	3.70219i	0.502256	−	0.289978i	0.729645	+	0.683826i	$0.239685\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	12.6005i		−	0.975058i	−0.873107	−	0.487529i	$-0.837898\pi$
$167$		−	12.6005i		−	0.975058i	0.873107	−	0.487529i	$-0.162102\pi$
$168$		0			0
$169$	−24.0997			−1.85382
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.2371	+	9.37451i	−1.23449	+	0.712731i	−0.967962	−	0.251097i	$-0.919209\pi$
$173$	−16.2371	+	9.37451i	−1.23449	+	0.712731i	−0.266524	+	0.963828i	$0.585875\pi$
$174$		0			0
$175$	−12.3248	+	4.80630i	−0.931664	+	0.363322i
$176$		0			0
$177$		0			0
$178$		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
$183$		0			0
$184$		0			0
$185$	−8.54983	−	9.19397i	−0.628596	−	0.675954i
$186$		0			0
$187$	9.41238	−	5.43424i	0.688301	−	0.397391i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.4124	+	19.7668i	0.825771	+	1.43028i	0.901329	+	0.433135i	$0.142593\pi$
$191$	11.4124	+	19.7668i	0.825771	+	1.43028i	−0.0755585	+	0.997141i	$0.524074\pi$
$192$		0			0
$193$	−7.96221	−	4.59698i	−0.573132	−	0.330898i	0.185267	−	0.982688i	$-0.440685\pi$
$193$	−7.96221	−	4.59698i	−0.573132	−	0.330898i	−0.758399	+	0.651790i	$0.774018\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	26.0383i		−	1.85515i	−0.373634	−	0.927576i	$-0.621888\pi$
$197$		−	26.0383i		−	1.85515i	0.373634	−	0.927576i	$-0.378112\pi$
$198$		0			0
$199$	4.86254	−	8.42217i	0.344696	−	0.597032i	−0.640602	−	0.767873i	$-0.721315\pi$
$199$	4.86254	−	8.42217i	0.344696	−	0.597032i	0.985299	+	0.170841i	$0.0546485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.63746	−	0.685484i	−0.606231	−	0.0481115i
$204$		0			0
$205$	5.63746	+	24.5731i	0.393737	+	1.71626i
$206$		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
$213$		0			0
$214$		0			0
$215$	−14.1873	+	3.25479i	−0.967565	+	0.221975i
$216$		0			0
$217$	6.41238	−	9.31697i	0.435300	−	0.632477i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−14.5498	+	25.2011i	−0.978728	+	1.69521i
$222$		0			0
$223$		−	8.71780i		−	0.583787i	−0.956451	−	0.291893i	$-0.905715\pi$
$223$		−	8.71780i		−	0.583787i	0.956451	−	0.291893i	$-0.0942853\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.58762	−	3.22602i	−0.370864	−	0.214118i	0.302972	−	0.952999i	$-0.402021\pi$
$227$	−5.58762	−	3.22602i	−0.370864	−	0.214118i	−0.673836	+	0.738881i	$0.735354\pi$
$228$		0			0
$229$	−2.13746	−	3.70219i	−0.141247	−	0.244647i	0.786719	−	0.617311i	$-0.211778\pi$
$229$	−2.13746	−	3.70219i	−0.141247	−	0.244647i	−0.927967	+	0.372663i	$0.878445\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	16.1375	−	9.31697i	1.05720	−	0.610375i	0.132544	−	0.991177i	$-0.457686\pi$
$233$	16.1375	−	9.31697i	1.05720	−	0.610375i	0.924656	+	0.380802i	$0.124352\pi$
$234$		0			0
$235$	−3.27492	−	3.52165i	−0.213632	−	0.229727i
$236$		0			0
$237$		0			0
$238$		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
$245$	1.04983	+	15.6172i	0.0670715	+	0.997748i
$246$		0			0
$247$	22.5498	−	13.0192i	1.43481	−	0.828389i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.45017			0.344011			0.172006	−	0.985096i	$-0.444975\pi$
$251$	5.45017			0.344011			0.172006	+	0.985096i	$0.444975\pi$
$252$		0			0
$253$		−	2.03559i		−	0.127976i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	21.4124	−	12.3624i	1.33567	−	0.771148i	0.349506	−	0.936934i	$-0.386350\pi$
$257$	21.4124	−	12.3624i	1.33567	−	0.771148i	0.986162	+	0.165786i	$0.0530162\pi$
$258$		0			0
$259$	−13.4124	+	6.38658i	−0.833404	+	0.396843i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−23.3248	−	13.4666i	−1.43827	−	0.830383i	−0.440536	−	0.897735i	$-0.645212\pi$
$263$	−23.3248	−	13.4666i	−1.43827	−	0.830383i	−0.997729	+	0.0673516i	$0.978545\pi$
$264$		0			0
$265$	4.86254	−	15.8265i	0.298704	−	0.972217i
$266$		0			0
$267$		0			0
$268$		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
$273$		0			0
$274$		0			0
$275$	−0.824752	+	11.3446i	−0.0497344	+	0.684108i
$276$		0			0
$277$	−16.1375	−	9.31697i	−0.969606	−	0.559802i	−0.0704898	−	0.997512i	$-0.522456\pi$
$277$	−16.1375	−	9.31697i	−0.969606	−	0.559802i	−0.899116	+	0.437710i	$0.855790\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−16.9622	−	9.79314i	−1.00830	−	0.582142i	−0.0976056	−	0.995225i	$-0.531118\pi$
$283$	−16.9622	−	9.79314i	−1.00830	−	0.582142i	−0.910693	+	0.413084i	$0.864452\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	29.7371	+	2.35999i	1.75533	+	0.139306i
$288$		0			0
$289$	2.91238	+	5.04438i	0.171316	+	0.296728i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			6.92820i			0.404750i	0.979308	+	0.202375i	$0.0648660\pi$
$293$			6.92820i			0.404750i	−0.979308	+	0.202375i	$0.935134\pi$
$294$		0			0
$295$	−9.13746	−	2.80739i	−0.532003	−	0.163453i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	2.53779	−	2.35999i	0.145313	−	0.135133i
$306$		0			0
$307$		−	3.99782i		−	0.228167i	−0.993471	−	0.114084i	$-0.963607\pi$
$307$		−	3.99782i		−	0.228167i	0.993471	−	0.114084i	$-0.0363932\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.41238	−	11.1066i	0.363612	−	0.629795i	−0.624940	−	0.780673i	$-0.714877\pi$
$311$	6.41238	−	11.1066i	0.363612	−	0.629795i	0.988552	+	0.150878i	$0.0482099\pi$
$312$		0			0
$313$	−12.5120	+	7.22383i	−0.707223	+	0.408315i	−0.810032	−	0.586386i	$-0.800550\pi$
$313$	−12.5120	+	7.22383i	−0.707223	+	0.408315i	0.102809	+	0.994701i	$0.467217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.31271	+	1.91259i	−0.186060	+	0.107422i	−0.590137	−	0.807303i	$-0.700926\pi$
$317$	−3.31271	+	1.91259i	−0.186060	+	0.107422i	0.404077	+	0.914725i	$0.367593\pi$
$318$		0			0
$319$	−3.72508	+	6.45203i	−0.208565	+	0.361244i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	20.4235i		−	1.13640i
$324$		0			0
$325$	−13.2749	−	27.4093i	−0.736360	−	1.52039i
$326$		0			0
$327$		0			0
$328$		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
$335$	−9.13746	+	29.7405i	−0.499233	+	1.62490i
$336$		0			0
$337$		−	13.0192i		−	0.709198i	−0.935018	−	0.354599i	$-0.884617\pi$
$337$		−	13.0192i		−	0.709198i	0.935018	−	0.354599i	$-0.115383\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.86254	−	8.42217i	−0.263321	−	0.456086i
$342$		0			0
$343$	18.0000	+	4.35890i	0.971909	+	0.235358i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	0.754617	−	0.656165i	$-0.227823\pi$
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	−0.190947	+	0.981600i	$0.561156\pi$
$348$		0			0
$349$	11.2749			0.603532			0.301766	−	0.953382i	$-0.402424\pi$
$349$	11.2749			0.603532			0.301766	+	0.953382i	$0.402424\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.4124	−	10.6304i	−0.979992	−	0.565799i	−0.0777242	−	0.996975i	$-0.524765\pi$
$353$	−18.4124	−	10.6304i	−0.979992	−	0.565799i	−0.902268	+	0.431176i	$0.858099\pi$
$354$		0			0
$355$	−5.27492	−	22.9928i	−0.279964	−	1.22033i
$356$		0			0
$357$		0			0
$358$		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
$363$		0			0
$364$		0			0
$365$	−1.41238	+	4.59698i	−0.0739271	+	0.240617i
$366$		0			0
$367$	12.7749	+	7.37560i	0.666845	+	0.385003i	0.794880	−	0.606766i	$-0.207534\pi$
$367$	12.7749	+	7.37560i	0.666845	+	0.385003i	−0.128035	+	0.991770i	$0.540867\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.1375	−	11.1066i	−0.837815	−	0.576624i
$372$		0			0
$373$	−4.86254	+	2.80739i	−0.251773	+	0.145361i	−0.620576	−	0.784146i	$-0.713101\pi$
$373$	−4.86254	+	2.80739i	−0.251773	+	0.145361i	0.368803	+	0.929508i	$0.379768\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	19.9474i		−	1.02734i
$378$		0			0
$379$	−23.6495			−1.21479			−0.607397	−	0.794399i	$-0.707786\pi$
$379$	−23.6495			−1.21479			−0.607397	+	0.794399i	$0.707786\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.3248	−	10.0025i	0.885253	−	0.511101i	0.0128665	−	0.999917i	$-0.495904\pi$
$383$	17.3248	−	10.0025i	0.885253	−	0.511101i	0.872387	+	0.488816i	$0.162571\pi$
$384$		0			0
$385$	12.5120	+	4.95807i	0.637673	+	0.252686i
$386$		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
$393$		0			0
$394$		0			0
$395$	0.450166	−	0.418627i	0.0226503	−	0.0210634i
$396$		0			0
$397$	13.1375	−	7.58492i	0.659350	−	0.380676i	−0.132679	−	0.991159i	$-0.542358\pi$
$397$	13.1375	−	7.58492i	0.659350	−	0.380676i	0.792029	+	0.610483i	$0.209025\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	22.5498	+	13.0192i	1.12329	+	0.648530i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.7732i			0.633142i
$408$		0			0
$409$	5.04983	−	8.74657i	0.249698	−	0.432490i	−0.713744	−	0.700407i	$-0.753002\pi$
$409$	5.04983	−	8.74657i	0.249698	−	0.432490i	0.963442	+	0.267917i	$0.0863352\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.41238	+	9.31697i	−0.315532	+	0.458458i
$414$		0			0
$415$	−12.3625	+	2.83616i	−0.606853	+	0.139222i
$416$		0			0
$417$		0			0
$418$		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
$425$	−23.8248	−	1.73205i	−1.15567	−	0.0840168i
$426$		0			0
$427$	−1.76287	−	3.70219i	−0.0853114	−	0.179161i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.68729	−	16.7789i	0.466620	−	0.808210i	−0.532653	−	0.846334i	$-0.678805\pi$
$431$	9.68729	−	16.7789i	0.466620	−	0.808210i	0.999273	+	0.0381236i	$0.0121381\pi$
$432$		0			0
$433$			26.8756i			1.29156i	0.763525	+	0.645778i	$0.223467\pi$
$433$			26.8756i			1.29156i	−0.763525	+	0.645778i	$0.776533\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.31271	−	1.91259i	−0.158468	−	0.0914917i
$438$		0			0
$439$	0.587624	+	1.01779i	0.0280458	+	0.0485767i	0.879708	−	0.475515i	$-0.157738\pi$
$439$	0.587624	+	1.01779i	0.0280458	+	0.0485767i	−0.851662	+	0.524092i	$0.824405\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	−0.728247	−	0.685315i	$-0.759665\pi$
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	0.229377	+	0.973338i	$0.426331\pi$
$444$		0			0
$445$	−11.4622	+	10.6592i	−0.543361	+	0.505293i
$446$		0			0
$447$		0			0
$448$		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
$453$		0			0
$454$		0			0
$455$	−35.6495	+	5.25370i	−1.67127	+	0.246297i
$456$		0			0
$457$	17.6873	−	10.2118i	0.827377	−	0.477686i	−0.0255769	−	0.999673i	$-0.508142\pi$
$457$	17.6873	−	10.2118i	0.827377	−	0.477686i	0.852954	+	0.521987i	$0.174809\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$		−	6.50958i		−	0.302526i	−0.988494	−	0.151263i	$-0.951666\pi$
$463$		−	6.50958i		−	0.302526i	0.988494	−	0.151263i	$-0.0483340\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.5997	−	9.58382i	0.768141	−	0.443486i	−0.0640700	−	0.997945i	$-0.520408\pi$
$467$	16.5997	−	9.58382i	0.768141	−	0.443486i	0.832211	+	0.554459i	$0.187075\pi$
$468$		0			0
$469$	30.3248	+	20.8709i	1.40027	+	0.963730i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.8248	+	7.40437i	0.589683	+	0.340453i
$474$		0			0
$475$	17.6873	+	12.0014i	0.811549	+	0.550660i
$476$		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			0
$484$		0			0
$485$	15.0997	−	3.46410i	0.685641	−	0.157297i
$486$		0			0
$487$	−28.9622	−	16.7213i	−1.31240	−	0.757716i	−0.329909	−	0.944013i	$-0.607018\pi$
$487$	−28.9622	−	16.7213i	−1.31240	−	0.757716i	−0.982494	+	0.186296i	$0.940352\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.4502			0.606997			0.303499	−	0.952832i	$-0.401845\pi$
$491$	13.4502			0.606997			0.303499	+	0.952832i	$0.401845\pi$
$492$		0			0
$493$	−13.5498	−	7.82300i	−0.610254	−	0.352330i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.8248	−	2.20822i	−1.24811	−	0.0990523i
$498$		0			0
$499$	19.6873	+	34.0994i	0.881324	+	1.52650i	0.849869	+	0.526993i	$0.176681\pi$
$499$	19.6873	+	34.0994i	0.881324	+	1.52650i	0.0314548	+	0.999505i	$0.489986\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	16.1797i		−	0.721418i	−0.932678	−	0.360709i	$-0.882535\pi$
$503$		−	16.1797i		−	0.721418i	0.932678	−	0.360709i	$-0.117465\pi$
$504$		0			0
$505$	3.31271	+	1.01779i	0.147414	+	0.0452913i
$506$		0			0
$507$		0			0
$508$		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
$513$		0			0
$514$		0			0
$515$	−3.91238	−	4.20713i	−0.172400	−	0.185388i
$516$		0			0
$517$			4.89261i			0.215177i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.41238	+	11.1066i	−0.280931	+	0.486587i	−0.971614	−	0.236570i	$-0.923977\pi$
$521$	−6.41238	+	11.1066i	−0.280931	+	0.486587i	0.690683	+	0.723158i	$0.257310\pi$
$522$		0			0
$523$	−10.1375	+	5.85286i	−0.443280	+	0.255928i	−0.704988	−	0.709219i	$-0.749048\pi$
$523$	−10.1375	+	5.85286i	−0.443280	+	0.255928i	0.261708	+	0.965147i	$0.415714\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.6873	−	10.2118i	0.770471	−	0.444831i
$528$		0			0
$529$	−11.0997	+	19.2252i	−0.482594	+	0.835878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			68.6750i			2.97464i
$534$		0			0
$535$	21.1873	+	22.7835i	0.916007	+	0.985017i
$536$		0			0
$537$		0			0
$538$		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
$543$		0			0
$544$		0			0
$545$	7.58762	+	2.33122i	0.325018	+	0.0998585i
$546$		0			0
$547$			36.1271i			1.54468i	0.635208	+	0.772341i	$0.280914\pi$
$547$			36.1271i			1.54468i	−0.635208	+	0.772341i	$0.719086\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$		0			0
$553$	−0.312707	−	0.656712i	−0.0132977	−	0.0279262i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.86254	+	2.80739i	0.206032	+	0.118953i	0.599466	−	0.800400i	$-0.295380\pi$
$557$	4.86254	+	2.80739i	0.206032	+	0.118953i	−0.393434	+	0.919353i	$0.628713\pi$
$558$		0			0
$559$	−39.6495			−1.67700
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.5997	−	6.11972i	−0.446723	−	0.257916i	0.259722	−	0.965683i	$-0.416369\pi$
$563$	−10.5997	−	6.11972i	−0.446723	−	0.257916i	−0.706445	+	0.707768i	$0.749702\pi$
$564$		0			0
$565$	−28.3746	+	6.50958i	−1.19373	+	0.273860i
$566$		0			0
$567$		0			0
$568$		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
$573$		0			0
$574$		0			0
$575$	−2.51204	+	3.70219i	−0.104760	+	0.154392i
$576$		0			0
$577$	7.13746	+	4.12081i	0.297136	+	0.171552i	0.641156	−	0.767411i	$-0.278455\pi$
$577$	7.13746	+	4.12081i	0.297136	+	0.171552i	−0.344019	+	0.938963i	$0.611789\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.18729	+	14.9605i	−0.0492572	+	0.620667i
$582$		0			0
$583$	−14.5876	+	8.42217i	−0.604158	+	0.348811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			13.9715i			0.576665i	0.957530	+	0.288333i	$0.0931009\pi$
$587$			13.9715i			0.576665i	−0.957530	+	0.288333i	$0.906899\pi$
$588$		0			0
$589$	−18.2749			−0.753005
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.5876	−	10.1542i	0.722237	−	0.416984i	−0.0933384	−	0.995634i	$-0.529754\pi$
$593$	17.5876	−	10.1542i	0.722237	−	0.416984i	0.815576	+	0.578651i	$0.196421\pi$
$594$		0			0
$595$	−10.4124	+	26.2764i	−0.426866	+	1.07723i
$596$		0			0
$597$		0			0
$598$		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
$605$	−9.53779	+	8.86957i	−0.387766	+	0.360599i
$606$		0			0
$607$	−27.8746	+	16.0934i	−1.13139	+	0.653211i	−0.944285	−	0.329128i	$-0.893245\pi$
$607$	−27.8746	+	16.0934i	−1.13139	+	0.653211i	−0.187109	+	0.982339i	$0.559912\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.54983	−	11.3446i	−0.264978	−	0.458955i
$612$		0			0
$613$	32.0619	+	18.5109i	1.29497	+	0.747650i	0.979530	−	0.201297i	$-0.0645156\pi$
$613$	32.0619	+	18.5109i	1.29497	+	0.747650i	0.315437	+	0.948947i	$0.397849\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.57919i		−	0.144093i	−0.997401	−	0.0720464i	$-0.977047\pi$
$617$		−	3.57919i		−	0.144093i	0.997401	−	0.0720464i	$-0.0229530\pi$
$618$		0			0
$619$	21.9622	−	38.0397i	0.882736	−	1.52894i	0.0344487	−	0.999406i	$-0.489032\pi$
$619$	21.9622	−	38.0397i	0.882736	−	1.52894i	0.848287	−	0.529537i	$-0.177634\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.96221	+	16.7213i	0.318999	+	0.669926i
$624$		0			0
$625$	15.5000	−	19.6150i	0.620000	−	0.784602i
$626$		0			0
$627$		0			0
$628$		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
$633$		0			0
$634$		0			0
$635$	−3.90033	+	0.894797i	−0.154780	+	0.0355089i
$636$		0			0
$637$	−6.72508	+	42.1029i	−0.266457	+	1.66818i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14.0498	−	24.3350i	0.554935	−	0.961176i	−0.442973	−	0.896535i	$-0.646076\pi$
$641$	14.0498	−	24.3350i	0.554935	−	0.961176i	0.997909	−	0.0646411i	$-0.0205902\pi$
$642$		0			0
$643$		−	38.3353i		−	1.51180i	−0.654689	−	0.755898i	$-0.727200\pi$
$643$		−	38.3353i		−	1.51180i	0.654689	−	0.755898i	$-0.272800\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.675248	+	0.389855i	0.0265468	+	0.0153268i	0.513215	−	0.858260i	$-0.328454\pi$
$647$	0.675248	+	0.389855i	0.0265468	+	0.0153268i	−0.486668	+	0.873587i	$0.661788\pi$
$648$		0			0
$649$	4.86254	+	8.42217i	0.190871	+	0.330599i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−32.0619	+	18.5109i	−1.25468	+	0.724389i	−0.972035	−	0.234836i	$-0.924545\pi$
$653$	−32.0619	+	18.5109i	−1.25468	+	0.724389i	−0.282643	+	0.959225i	$0.591211\pi$
$654$		0			0
$655$	29.9244	−	27.8279i	1.16924	−	1.08733i
$656$		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
$663$		0			0
$664$		0			0
$665$	19.8248	−	15.7035i	0.768771	−	0.608957i
$666$		0			0
$667$	−2.53779	+	1.46519i	−0.0982636	+	0.0567325i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.52575			−0.136110
$672$		0			0
$673$		−	3.57919i		−	0.137968i	−0.997618	−	0.0689838i	$-0.978024\pi$
$673$		−	3.57919i		−	0.137968i	0.997618	−	0.0689838i	$-0.0219757\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.3127	+	12.3049i	−0.819114	+	0.472916i	−0.850111	−	0.526604i	$-0.823465\pi$
$677$	−21.3127	+	12.3049i	−0.819114	+	0.472916i	0.0309969	+	0.999519i	$0.490132\pi$
$678$		0			0
$679$	1.45017	−	18.2728i	0.0556522	−	0.701248i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.5997	+	7.85177i	0.520377	+	0.300440i	0.737089	−	0.675796i	$-0.236200\pi$
$683$	13.5997	+	7.85177i	0.520377	+	0.300440i	−0.216712	+	0.976236i	$0.569533\pi$
$684$		0			0
$685$	−6.03779	+	19.6517i	−0.230692	+	0.750854i
$686$		0			0
$687$		0			0
$688$		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
$695$	8.54983	+	37.2679i	0.324314	+	1.41365i
$696$		0			0
$697$	46.6495	+	26.9331i	1.76698	+	1.02016i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	13.8248			0.522154			0.261077	−	0.965318i	$-0.415922\pi$
$701$	13.8248			0.522154			0.261077	+	0.965318i	$0.415922\pi$
$702$		0			0
$703$	20.7870	+	12.0014i	0.783995	+	0.452640i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.32475	−	3.37779i	0.0874313	−	0.127035i
$708$		0			0
$709$	−12.7749	−	22.1268i	−0.479772	−	0.830990i	0.519959	−	0.854191i	$-0.325947\pi$
$709$	−12.7749	−	22.1268i	−0.479772	−	0.830990i	−0.999731	+	0.0232018i	$0.992614\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	3.82518i		−	0.143254i
$714$		0			0
$715$	−9.09967	+	29.6175i	−0.340308	+	1.10763i
$716$		0			0
$717$		0			0
$718$		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
$723$		0			0
$724$		0			0
$725$	14.7371	−	7.13752i	0.547323	−	0.265081i
$726$		0			0
$727$		−	18.6915i		−	0.693228i	−0.938008	−	0.346614i	$-0.887331\pi$
$727$		−	18.6915i		−	0.693228i	0.938008	−	0.346614i	$-0.112669\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.5498	+	26.9331i	−0.575131	+	0.996157i
$732$		0			0
$733$	−28.8625	+	16.6638i	−1.06606	+	0.615491i	−0.927103	−	0.374807i	$-0.877709\pi$
$733$	−28.8625	+	16.6638i	−1.06606	+	0.615491i	−0.138959	+	0.990298i	$0.544376\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	27.4124	−	15.8265i	1.00975	−	0.582978i
$738$		0			0
$739$	15.9622	−	27.6474i	0.587179	−	1.01702i	−0.407420	−	0.913241i	$-0.633572\pi$
$739$	15.9622	−	27.6474i	0.587179	−	1.01702i	0.994600	−	0.103784i	$-0.0330950\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	19.5287i		−	0.716440i	−0.933637	−	0.358220i	$-0.883384\pi$
$743$		−	19.5287i		−	0.716440i	0.933637	−	0.358220i	$-0.116616\pi$
$744$		0			0
$745$	12.3625	−	11.4964i	0.452928	−	0.421196i
$746$		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
$753$		0			0
$754$		0			0
$755$	43.3368	+	13.3148i	1.57719	+	0.484575i
$756$		0			0
$757$			9.43996i			0.343101i	0.985175	+	0.171551i	$0.0548777\pi$
$757$			9.43996i			0.343101i	−0.985175	+	0.171551i	$0.945122\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.9622	−	25.9153i	−0.542380	−	0.939429i	−0.998767	−	0.0496479i	$-0.984190\pi$
$761$	−14.9622	−	25.9153i	−0.542380	−	0.939429i	0.456387	−	0.889781i	$-0.349143\pi$
$762$		0			0
$763$	5.32475	−	7.73668i	0.192769	−	0.280087i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.5498	−	13.0192i	−0.814227	−	0.470094i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.5876	+	13.6183i	0.848388	+	0.489817i	0.860107	−	0.510114i	$-0.170397\pi$
$773$	23.5876	+	13.6183i	0.848388	+	0.489817i	−0.0117187	+	0.999931i	$0.503730\pi$
$774$		0			0
$775$	−1.54983	+	21.3183i	−0.0556717	+	0.765777i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		0			0
$785$	7.13746	−	23.2309i	0.254747	−	0.829147i
$786$		0			0
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	0.526496	−	0.850177i	$-0.323505\pi$
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	−0.473027	+	0.881048i	$0.656839\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.72508	+	34.3375i	−0.0968928	+	1.22090i
$792$		0			0
$793$	8.17525	−	4.71998i	0.290312	−	0.167611i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			29.3873i			1.04095i	0.853876	+	0.520476i	$0.174246\pi$
$797$			29.3873i			1.04095i	−0.853876	+	0.520476i	$0.825754\pi$
$798$		0			0
$799$	−10.2749			−0.363500
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.23713	−	2.44631i	0.149525	−	0.0863283i
$804$		0			0
$805$	3.28696	+	4.14959i	0.115850	+	0.146254i
$806$		0			0
$807$		0			0
$808$		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
$813$		0			0
$814$		0			0
$815$	11.2749	+	12.1244i	0.394943	+	0.424698i
$816$		0			0
$817$	24.0997	−	13.9140i	0.843141	−	0.486788i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.68729	+	15.0468i	0.303189	+	0.525138i	0.976856	−	0.213896i	$-0.0686154\pi$
$821$	8.68729	+	15.0468i	0.303189	+	0.525138i	−0.673668	+	0.739034i	$0.735282\pi$
$822$		0			0
$823$	−27.9743	−	16.1509i	−0.975121	−	0.562987i	−0.0743276	−	0.997234i	$-0.523681\pi$
$823$	−27.9743	−	16.1509i	−0.975121	−	0.562987i	−0.900794	+	0.434247i	$0.857014\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			45.5670i			1.58452i	0.610183	+	0.792261i	$0.291096\pi$
$827$			45.5670i			1.58452i	−0.610183	+	0.792261i	$0.708904\pi$
$828$		0			0
$829$	0.962210	−	1.66660i	0.0334189	−	0.0578833i	−0.848832	−	0.528662i	$-0.822694\pi$
$829$	0.962210	−	1.66660i	0.0334189	−	0.0578833i	0.882251	+	0.470779i	$0.156027\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.9622	+	21.0802i	0.899537	+	0.730387i
$834$		0			0
$835$	27.4622	−	6.30026i	0.950369	−	0.218030i
$836$		0			0
$837$		0			0
$838$		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
$843$		0			0
$844$		0			0
$845$	−12.0498	−	52.5240i	−0.414527	−	1.80688i
$846$		0			0
$847$	6.62541	+	13.9140i	0.227652	+	0.478089i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.51204	+	4.35099i	−0.0861118	+	0.149150i
$852$		0			0
$853$			30.4547i			1.04275i	0.853327	+	0.521375i	$0.174581\pi$
$853$			30.4547i			1.04275i	−0.853327	+	0.521375i	$0.825419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.8625	+	16.6638i	0.985926	+	0.569224i	0.904054	−	0.427418i	$-0.140577\pi$
$857$	28.8625	+	16.6638i	0.985926	+	0.569224i	0.0818717	+	0.996643i	$0.473910\pi$
$858$		0			0
$859$	17.6873	+	30.6353i	0.603483	+	1.04526i	0.992289	+	0.123943i	$0.0395541\pi$
$859$	17.6873	+	30.6353i	0.603483	+	1.04526i	−0.388807	+	0.921319i	$0.627113\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−21.7749	+	12.5718i	−0.741227	+	0.427947i	−0.822515	−	0.568743i	$-0.807430\pi$
$863$	−21.7749	+	12.5718i	−0.741227	+	0.427947i	0.0812884	+	0.996691i	$0.474097\pi$
$864$		0			0
$865$	−28.5498	−	30.7007i	−0.970723	−	1.04386i
$866$		0			0
$867$		0			0
$868$		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
$875$	−16.6375	−	24.4580i	−0.562449	−	0.826832i
$876$		0			0
$877$	−38.6873	+	22.3361i	−1.30638	+	0.754237i	−0.981490	−	0.191516i	$-0.938660\pi$
$877$	−38.6873	+	22.3361i	−1.30638	+	0.754237i	−0.324887	+	0.945753i	$0.605326\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−40.0241			−1.34845			−0.674223	−	0.738528i	$-0.735521\pi$
$881$	−40.0241			−1.34845			−0.674223	+	0.738528i	$0.735521\pi$
$882$		0			0
$883$		−	20.6695i		−	0.695585i	−0.937572	−	0.347792i	$-0.886931\pi$
$883$		−	20.6695i		−	0.695585i	0.937572	−	0.347792i	$-0.113069\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.9743	+	19.6150i	−1.14074	+	0.658609i	−0.946615	−	0.322367i	$-0.895521\pi$
$887$	−33.9743	+	19.6150i	−1.14074	+	0.658609i	−0.194129	+	0.980976i	$0.562188\pi$
$888$		0			0
$889$	−0.374586	+	4.71998i	−0.0125632	+	0.158303i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.96221	+	4.59698i	0.266445	+	0.153832i
$894$		0			0
$895$	−0.587624	−	0.180541i	−0.0196421	−	0.00603483i
$896$		0			0
$897$		0			0
$898$		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
$903$		0			0
$904$		0			0
$905$	−8.36254	−	36.4515i	−0.277980	−	1.21169i
$906$		0			0
$907$	−39.2492	−	22.6605i	−1.30325	−	0.752430i	−0.322288	−	0.946642i	$-0.604452\pi$
$907$	−39.2492	−	22.6605i	−1.30325	−	0.752430i	−0.980960	+	0.194212i	$0.937785\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.09967			−0.168960			−0.0844798	−	0.996425i	$-0.526923\pi$
$911$	−5.09967			−0.168960			−0.0844798	+	0.996425i	$0.526923\pi$
$912$		0			0
$913$	11.1752	+	6.45203i	0.369847	+	0.213531i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.7870	−	43.6544i	−0.686446	−	1.44160i
$918$		0			0
$919$	2.96221	+	5.13070i	0.0977143	+	0.169246i	0.910738	−	0.412984i	$-0.135514\pi$
$919$	2.96221	+	5.13070i	0.0977143	+	0.169246i	−0.813024	+	0.582230i	$0.802180\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	64.2585i		−	2.11509i
$924$		0			0
$925$	15.7629	−	23.2309i	0.518280	−	0.763828i
$926$		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
$933$		0			0
$934$		0			0
$935$	16.5498	+	17.7967i	0.541237	+	0.582014i
$936$		0			0
$937$		−	10.5074i		−	0.343262i	−0.985161	−	0.171631i	$-0.945096\pi$
$937$		−	10.5074i		−	0.343262i	0.985161	−	0.171631i	$-0.0549036\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.13746	−	3.70219i	0.0696792	−	0.120688i	−0.829081	−	0.559129i	$-0.811136\pi$
$941$	2.13746	−	3.70219i	0.0696792	−	0.120688i	0.898760	+	0.438441i	$0.144469\pi$
$942$		0			0
$943$	8.73713	−	5.04438i	0.284520	−	0.164268i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.1495	+	20.8709i	−1.17470	+	0.678214i	−0.954783	−	0.297304i	$-0.903912\pi$
$947$	−36.1495	+	20.8709i	−1.17470	+	0.678214i	−0.219918	+	0.975518i	$0.570579\pi$
$948$		0			0
$949$	−6.54983	+	11.3446i	−0.212617	+	0.368263i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	29.6175i		−	0.959405i	−0.877431	−	0.479702i	$-0.840745\pi$
$953$		−	29.6175i		−	0.959405i	0.877431	−	0.479702i	$-0.159255\pi$
$954$		0			0
$955$	−37.3746	+	34.7561i	−1.20941	+	1.12468i
$956$		0			0
$957$		0			0
$958$		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
$965$	6.03779	−	19.6517i	0.194363	−	0.632611i
$966$		0			0
$967$		−	6.50958i		−	0.209334i	−0.994507	−	0.104667i	$-0.966622\pi$
$967$		−	6.50958i		−	0.209334i	0.994507	−	0.104667i	$-0.0333777\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.96221	+	13.7910i	0.255519	+	0.442573i	0.965036	−	0.262116i	$-0.0844202\pi$
$971$	7.96221	+	13.7910i	0.255519	+	0.442573i	−0.709517	+	0.704688i	$0.751087\pi$
$972$		0			0
$973$	45.0997	+	3.57919i	1.44583	+	0.114744i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.5876	−	8.42217i	−0.466699	−	0.269449i	0.248158	−	0.968720i	$-0.420175\pi$
$977$	−14.5876	−	8.42217i	−0.466699	−	0.269449i	−0.714857	+	0.699271i	$0.753508\pi$
$978$		0			0
$979$	15.9244			0.508947
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−32.2251	−	18.6052i	−1.02782	−	0.593412i	−0.111461	−	0.993769i	$-0.535553\pi$
$983$	−32.2251	−	18.6052i	−1.02782	−	0.593412i	−0.916360	+	0.400356i	$0.868886\pi$
$984$		0			0
$985$	56.7492	−	13.0192i	1.80818	−	0.414825i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		0			0
$995$	20.7870	+	6.38658i	0.658991	+	0.202468i
$996$		0			0
$997$	−4.13746	−	2.38876i	−0.131035	−	0.0756529i	0.433050	−	0.901370i	$-0.357437\pi$
$997$	−4.13746	−	2.38876i	−0.131035	−	0.0756529i	−0.564084	+	0.825717i	$0.690771\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.bm.b.109.2		4
3.2	odd	2		140.2.q.b.109.1	yes	4
5.4	even	2		1260.2.bm.a.109.2		4
7.2	even	3		1260.2.bm.a.289.2		4
12.11	even	2		560.2.bw.a.529.1		4
15.2	even	4		700.2.i.f.501.4		8
15.8	even	4		700.2.i.f.501.1		8
15.14	odd	2		140.2.q.a.109.1	yes	4
21.2	odd	6		140.2.q.a.9.1	✓	4
21.5	even	6		980.2.q.g.569.2		4
21.11	odd	6		980.2.e.f.589.2		4
21.17	even	6		980.2.e.c.589.3		4
21.20	even	2		980.2.q.b.949.2		4
35.9	even	6	inner	1260.2.bm.b.289.1		4
60.59	even	2		560.2.bw.e.529.1		4
84.23	even	6		560.2.bw.e.289.1		4
105.2	even	12		700.2.i.f.401.4		8
105.17	odd	12		4900.2.a.bf.1.4		4
105.23	even	12		700.2.i.f.401.1		8
105.32	even	12		4900.2.a.be.1.2		4
105.38	odd	12		4900.2.a.bf.1.2		4
105.44	odd	6		140.2.q.b.9.2	yes	4
105.53	even	12		4900.2.a.be.1.4		4
105.59	even	6		980.2.e.c.589.1		4
105.74	odd	6		980.2.e.f.589.4		4
105.89	even	6		980.2.q.b.569.1		4
105.104	even	2		980.2.q.g.949.2		4
420.359	even	6		560.2.bw.a.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.1	✓	4	21.2	odd	6
140.2.q.a.109.1	yes	4	15.14	odd	2
140.2.q.b.9.2	yes	4	105.44	odd	6
140.2.q.b.109.1	yes	4	3.2	odd	2
560.2.bw.a.289.2		4	420.359	even	6
560.2.bw.a.529.1		4	12.11	even	2
560.2.bw.e.289.1		4	84.23	even	6
560.2.bw.e.529.1		4	60.59	even	2
700.2.i.f.401.1		8	105.23	even	12
700.2.i.f.401.4		8	105.2	even	12
700.2.i.f.501.1		8	15.8	even	4
700.2.i.f.501.4		8	15.2	even	4
980.2.e.c.589.1		4	105.59	even	6
980.2.e.c.589.3		4	21.17	even	6
980.2.e.f.589.2		4	21.11	odd	6
980.2.e.f.589.4		4	105.74	odd	6
980.2.q.b.569.1		4	105.89	even	6
980.2.q.b.949.2		4	21.20	even	2
980.2.q.g.569.2		4	21.5	even	6
980.2.q.g.949.2		4	105.104	even	2
1260.2.bm.a.109.2		4	5.4	even	2
1260.2.bm.a.289.2		4	7.2	even	3
1260.2.bm.b.109.2		4	1.1	even	1	trivial
1260.2.bm.b.289.1		4	35.9	even	6	inner
4900.2.a.be.1.2		4	105.32	even	12
4900.2.a.be.1.4		4	105.53	even	12
4900.2.a.bf.1.2		4	105.38	odd	12
4900.2.a.bf.1.4		4	105.17	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 2.17945i) q^{5} +(2.63746 + 0.209313i) q^{7} +(1.13746 - 1.97014i) q^{11} +6.09095i q^{13} +(4.13746 + 2.38876i) q^{17} +(-2.13746 - 3.70219i) q^{19} +(0.774917 - 0.447399i) q^{23} +(-4.50000 + 2.17945i) q^{25} -3.27492 q^{29} +(2.13746 - 3.70219i) q^{31} +(0.862541 + 5.85286i) q^{35} +(-4.86254 + 2.80739i) q^{37} +11.2749 q^{41} +6.50958i q^{43} +(-1.86254 + 1.07534i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-6.41238 - 3.70219i) q^{53} +(4.86254 + 1.49397i) q^{55} +(-2.13746 + 3.70219i) q^{59} +(-0.774917 - 1.34220i) q^{61} +(-13.2749 + 3.04547i) q^{65} +(12.0498 + 6.95698i) q^{67} -10.5498 q^{71} +(1.86254 + 1.07534i) q^{73} +(3.41238 - 4.95807i) q^{77} +(-0.137459 - 0.238085i) q^{79} +5.67232i q^{83} +(-3.13746 + 10.2118i) q^{85} +(3.50000 + 6.06218i) q^{89} +(-1.27492 + 16.0646i) q^{91} +(7.00000 - 6.50958i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} + 3 q^{7} - 3 q^{11} + 9 q^{17} - q^{19} - 12 q^{23} - 18 q^{25} + 2 q^{29} + q^{31} + 11 q^{35} - 27 q^{37} + 30 q^{41} - 15 q^{47} + 5 q^{49} - 3 q^{53} + 27 q^{55} - q^{59} + 12 q^{61}+ \cdots + 28 q^{95}+O(q^{100}) \) 4 * q + 2 * q^5 + 3 * q^7 - 3 * q^11 + 9 * q^17 - q^19 - 12 * q^23 - 18 * q^25 + 2 * q^29 + q^31 + 11 * q^35 - 27 * q^37 + 30 * q^41 - 15 * q^47 + 5 * q^49 - 3 * q^53 + 27 * q^55 - q^59 + 12 * q^61 - 38 * q^65 + 18 * q^67 - 12 * q^71 + 15 * q^73 - 9 * q^77 + 7 * q^79 - 5 * q^85 + 14 * q^89 + 10 * q^91 + 28 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more