LMFDB - Embedded newform 704.2.j.a.177.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(177,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("704.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.j (of order $4$, degree $2$, not 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:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			177.5
Character	$\chi$	$=$	704.177
Dual form			704.2.j.a.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34498 + 1.34498i) q^{3} +(2.40794 + 2.40794i) q^{5} +4.88654i q^{7} -0.617917i q^{9} +O(q^{10})$	\(q+(-1.34498 + 1.34498i) q^{3} +(2.40794 + 2.40794i) q^{5} +4.88654i q^{7} -0.617917i q^{9} +(0.707107 + 0.707107i) q^{11} +(-0.532694 + 0.532694i) q^{13} -6.47725 q^{15} -1.53906 q^{17} +(5.98507 - 5.98507i) q^{19} +(-6.57227 - 6.57227i) q^{21} -0.294585i q^{23} +6.59638i q^{25} +(-3.20384 - 3.20384i) q^{27} +(4.94569 - 4.94569i) q^{29} +1.43981 q^{31} -1.90208 q^{33} +(-11.7665 + 11.7665i) q^{35} +(1.66532 + 1.66532i) q^{37} -1.43292i q^{39} +4.09275i q^{41} +(-4.95316 - 4.95316i) q^{43} +(1.48791 - 1.48791i) q^{45} +0.856661 q^{47} -16.8783 q^{49} +(2.07000 - 2.07000i) q^{51} +(-0.0858734 - 0.0858734i) q^{53} +3.40535i q^{55} +16.0995i q^{57} +(3.37953 + 3.37953i) q^{59} +(0.868220 - 0.868220i) q^{61} +3.01948 q^{63} -2.56539 q^{65} +(1.38054 - 1.38054i) q^{67} +(0.396210 + 0.396210i) q^{69} -2.83422i q^{71} +5.62070i q^{73} +(-8.87197 - 8.87197i) q^{75} +(-3.45530 + 3.45530i) q^{77} +10.1538 q^{79} +10.4719 q^{81} +(-5.47789 + 5.47789i) q^{83} +(-3.70597 - 3.70597i) q^{85} +13.3037i q^{87} -8.20417i q^{89} +(-2.60303 - 2.60303i) q^{91} +(-1.93651 + 1.93651i) q^{93} +28.8234 q^{95} -7.42322 q^{97} +(0.436933 - 0.436933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 16 q^{15} + 16 q^{19} - 24 q^{27} - 24 q^{31} - 24 q^{35} + 40 q^{47} - 40 q^{49} + 24 q^{51} + 8 q^{59} + 32 q^{61} - 16 q^{65} + 24 q^{67} + 32 q^{69} + 56 q^{75} - 32 q^{79} - 40 q^{81} - 40 q^{83} - 32 q^{85} + 16 q^{91} - 48 q^{93} + 48 q^{95}+O(q^{100}) $ 40 * q + 16 * q^15 + 16 * q^19 - 24 * q^27 - 24 * q^31 - 24 * q^35 + 40 * q^47 - 40 * q^49 + 24 * q^51 + 8 * q^59 + 32 * q^61 - 16 * q^65 + 24 * q^67 + 32 * q^69 + 56 * q^75 - 32 * q^79 - 40 * q^81 - 40 * q^83 - 32 * q^85 + 16 * q^91 - 48 * q^93 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	−1.34498	+	1.34498i	−0.776522	+	0.776522i	−0.979238	−	0.202716i	$-0.935023\pi$
$3$	−1.34498	+	1.34498i	−0.776522	+	0.776522i	0.202716	+	0.979238i	$0.435023\pi$
$4$		0			0
$5$	2.40794	+	2.40794i	1.07687	+	1.07687i	0.996789	+	0.0800763i	$0.0255164\pi$
$5$	2.40794	+	2.40794i	1.07687	+	1.07687i	0.0800763	+	0.996789i	$0.474484\pi$
$6$		0			0
$7$			4.88654i			1.84694i	0.383673	+	0.923469i	$0.374659\pi$
$7$			4.88654i			1.84694i	−0.383673	+	0.923469i	$0.625341\pi$
$8$		0			0
$9$		−	0.617917i		−	0.205972i
$10$		0			0
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$		0			0
$13$	−0.532694	+	0.532694i	−0.147743	+	0.147743i	−0.777109	−	0.629366i	$-0.783315\pi$
$13$	−0.532694	+	0.532694i	−0.147743	+	0.147743i	0.629366	+	0.777109i	$0.283315\pi$
$14$		0			0
$15$	−6.47725			−1.67242
$16$		0			0
$17$	−1.53906			−0.373277			−0.186639	−	0.982429i	$-0.559759\pi$
$17$	−1.53906			−0.373277			−0.186639	+	0.982429i	$0.559759\pi$
$18$		0			0
$19$	5.98507	−	5.98507i	1.37307	−	1.37307i	0.517213	−	0.855857i	$-0.326970\pi$
$19$	5.98507	−	5.98507i	1.37307	−	1.37307i	0.855857	−	0.517213i	$-0.173030\pi$
$20$		0			0
$21$	−6.57227	−	6.57227i	−1.43419	−	1.43419i
$22$		0			0
$23$		−	0.294585i		−	0.0614252i	−0.999528	−	0.0307126i	$-0.990222\pi$
$23$		−	0.294585i		−	0.0614252i	0.999528	−	0.0307126i	$-0.00977767\pi$
$24$		0			0
$25$			6.59638i			1.31928i
$26$		0			0
$27$	−3.20384	−	3.20384i	−0.616580	−	0.616580i
$28$		0			0
$29$	4.94569	−	4.94569i	0.918391	−	0.918391i	−0.0785216	−	0.996912i	$-0.525020\pi$
$29$	4.94569	−	4.94569i	0.918391	−	0.918391i	0.996912	+	0.0785216i	$0.0250200\pi$
$30$		0			0
$31$	1.43981			0.258598			0.129299	−	0.991606i	$-0.458727\pi$
$31$	1.43981			0.258598			0.129299	+	0.991606i	$0.458727\pi$
$32$		0			0
$33$	−1.90208			−0.331110
$34$		0			0
$35$	−11.7665	+	11.7665i	−1.98890	+	1.98890i
$36$		0			0
$37$	1.66532	+	1.66532i	0.273777	+	0.273777i	0.830619	−	0.556842i	$-0.187987\pi$
$37$	1.66532	+	1.66532i	0.273777	+	0.273777i	−0.556842	+	0.830619i	$0.687987\pi$
$38$		0			0
$39$		−	1.43292i		−	0.229451i
$40$		0			0
$41$			4.09275i			0.639179i	0.947556	+	0.319590i	$0.103545\pi$
$41$			4.09275i			0.639179i	−0.947556	+	0.319590i	$0.896455\pi$
$42$		0			0
$43$	−4.95316	−	4.95316i	−0.755350	−	0.755350i	0.220122	−	0.975472i	$-0.429354\pi$
$43$	−4.95316	−	4.95316i	−0.755350	−	0.755350i	−0.975472	+	0.220122i	$0.929354\pi$
$44$		0			0
$45$	1.48791	−	1.48791i	0.221804	−	0.221804i
$46$		0			0
$47$	0.856661			0.124957			0.0624784	−	0.998046i	$-0.480100\pi$
$47$	0.856661			0.124957			0.0624784	+	0.998046i	$0.480100\pi$
$48$		0			0
$49$	−16.8783			−2.41118
$50$		0			0
$51$	2.07000	−	2.07000i	0.289858	−	0.289858i
$52$		0			0
$53$	−0.0858734	−	0.0858734i	−0.0117956	−	0.0117956i	0.701184	−	0.712980i	$-0.252655\pi$
$53$	−0.0858734	−	0.0858734i	−0.0117956	−	0.0117956i	−0.712980	+	0.701184i	$0.752655\pi$
$54$		0			0
$55$			3.40535i			0.459177i
$56$		0			0
$57$			16.0995i			2.13244i
$58$		0			0
$59$	3.37953	+	3.37953i	0.439978	+	0.439978i	0.892004	−	0.452027i	$-0.149299\pi$
$59$	3.37953	+	3.37953i	0.439978	+	0.439978i	−0.452027	+	0.892004i	$0.649299\pi$
$60$		0			0
$61$	0.868220	−	0.868220i	0.111164	−	0.111164i	−0.649337	−	0.760501i	$-0.724953\pi$
$61$	0.868220	−	0.868220i	0.111164	−	0.111164i	0.760501	+	0.649337i	$0.224953\pi$
$62$		0			0
$63$	3.01948			0.380418
$64$		0			0
$65$	−2.56539			−0.318198
$66$		0			0
$67$	1.38054	−	1.38054i	0.168660	−	0.168660i	−0.617730	−	0.786390i	$-0.711948\pi$
$67$	1.38054	−	1.38054i	0.168660	−	0.168660i	0.786390	+	0.617730i	$0.211948\pi$
$68$		0			0
$69$	0.396210	+	0.396210i	0.0476980	+	0.0476980i
$70$		0			0
$71$		−	2.83422i		−	0.336360i	−0.985756	−	0.168180i	$-0.946211\pi$
$71$		−	2.83422i		−	0.336360i	0.985756	−	0.168180i	$-0.0537890\pi$
$72$		0			0
$73$			5.62070i			0.657854i	0.944355	+	0.328927i	$0.106687\pi$
$73$			5.62070i			0.657854i	−0.944355	+	0.328927i	$0.893313\pi$
$74$		0			0
$75$	−8.87197	−	8.87197i	−1.02445	−	1.02445i
$76$		0			0
$77$	−3.45530	+	3.45530i	−0.393769	+	0.393769i
$78$		0			0
$79$	10.1538			1.14240			0.571198	−	0.820812i	$-0.306479\pi$
$79$	10.1538			1.14240			0.571198	+	0.820812i	$0.306479\pi$
$80$		0			0
$81$	10.4719			1.16355
$82$		0			0
$83$	−5.47789	+	5.47789i	−0.601276	+	0.601276i	−0.940651	−	0.339375i	$-0.889784\pi$
$83$	−5.47789	+	5.47789i	−0.601276	+	0.601276i	0.339375	+	0.940651i	$0.389784\pi$
$84$		0			0
$85$	−3.70597	−	3.70597i	−0.401969	−	0.401969i
$86$		0			0
$87$			13.3037i			1.42630i
$88$		0			0
$89$		−	8.20417i		−	0.869641i	−0.900517	−	0.434820i	$-0.856812\pi$
$89$		−	8.20417i		−	0.869641i	0.900517	−	0.434820i	$-0.143188\pi$
$90$		0			0
$91$	−2.60303	−	2.60303i	−0.272872	−	0.272872i
$92$		0			0
$93$	−1.93651	+	1.93651i	−0.200807	+	0.200807i
$94$		0			0
$95$	28.8234			2.95722
$96$		0			0
$97$	−7.42322			−0.753714			−0.376857	−	0.926272i	$-0.622995\pi$
$97$	−7.42322			−0.753714			−0.376857	+	0.926272i	$0.622995\pi$
$98$		0			0
$99$	0.436933	−	0.436933i	0.0439135	−	0.0439135i
$100$		0			0
$101$	−6.39297	−	6.39297i	−0.636125	−	0.636125i	0.313473	−	0.949597i	$-0.398508\pi$
$101$	−6.39297	−	6.39297i	−0.636125	−	0.636125i	−0.949597	+	0.313473i	$0.898508\pi$
$102$		0			0
$103$			9.42991i			0.929157i	0.885532	+	0.464578i	$0.153794\pi$
$103$			9.42991i			0.929157i	−0.885532	+	0.464578i	$0.846206\pi$
$104$		0			0
$105$		−	31.6513i		−	3.08885i
$106$		0			0
$107$	−2.34961	−	2.34961i	−0.227145	−	0.227145i	0.584354	−	0.811499i	$-0.301348\pi$
$107$	−2.34961	−	2.34961i	−0.227145	−	0.227145i	−0.811499	+	0.584354i	$0.801348\pi$
$108$		0			0
$109$	9.17318	−	9.17318i	0.878631	−	0.878631i	−0.114762	−	0.993393i	$-0.536610\pi$
$109$	9.17318	−	9.17318i	0.878631	−	0.878631i	0.993393	+	0.114762i	$0.0366105\pi$
$110$		0			0
$111$	−4.47963			−0.425187
$112$		0			0
$113$	−2.88288			−0.271198			−0.135599	−	0.990764i	$-0.543296\pi$
$113$	−2.88288			−0.271198			−0.135599	+	0.990764i	$0.543296\pi$
$114$		0			0
$115$	0.709344	−	0.709344i	0.0661467	−	0.0661467i
$116$		0			0
$117$	0.329161	+	0.329161i	0.0304309	+	0.0304309i
$118$		0			0
$119$		−	7.52068i		−	0.689420i
$120$		0			0
$121$			1.00000i			0.0909091i
$122$		0			0
$123$	−5.50464	−	5.50464i	−0.496337	−	0.496337i
$124$		0			0
$125$	−3.84400	+	3.84400i	−0.343818	+	0.343818i
$126$		0			0
$127$	6.43582			0.571087			0.285544	−	0.958366i	$-0.407826\pi$
$127$	6.43582			0.571087			0.285544	+	0.958366i	$0.407826\pi$
$128$		0			0
$129$	13.3238			1.17309
$130$		0			0
$131$	8.02413	−	8.02413i	0.701072	−	0.701072i	−0.263569	−	0.964641i	$-0.584900\pi$
$131$	8.02413	−	8.02413i	0.701072	−	0.701072i	0.964641	+	0.263569i	$0.0848997\pi$
$132$		0			0
$133$	29.2463	+	29.2463i	2.53597	+	2.53597i
$134$		0			0
$135$		−	15.4293i		−	1.32795i
$136$		0			0
$137$		−	10.5001i		−	0.897081i	−0.893762	−	0.448541i	$-0.851944\pi$
$137$		−	10.5001i		−	0.897081i	0.893762	−	0.448541i	$-0.148056\pi$
$138$		0			0
$139$	14.1139	+	14.1139i	1.19712	+	1.19712i	0.975024	+	0.222100i	$0.0712913\pi$
$139$	14.1139	+	14.1139i	1.19712	+	1.19712i	0.222100	+	0.975024i	$0.428709\pi$
$140$		0			0
$141$	−1.15219	+	1.15219i	−0.0970317	+	0.0970317i
$142$		0			0
$143$	−0.753343			−0.0629977
$144$		0			0
$145$	23.8179			1.97797
$146$		0			0
$147$	22.7008	−	22.7008i	1.87233	−	1.87233i
$148$		0			0
$149$	8.66331	+	8.66331i	0.709726	+	0.709726i	0.966477	−	0.256752i	$-0.0826522\pi$
$149$	8.66331	+	8.66331i	0.709726	+	0.709726i	−0.256752	+	0.966477i	$0.582652\pi$
$150$		0			0
$151$		−	8.43652i		−	0.686554i	−0.939234	−	0.343277i	$-0.888463\pi$
$151$		−	8.43652i		−	0.686554i	0.939234	−	0.343277i	$-0.111537\pi$
$152$		0			0
$153$			0.951012i			0.0768847i
$154$		0			0
$155$	3.46698	+	3.46698i	0.278475	+	0.278475i
$156$		0			0
$157$	0.353693	−	0.353693i	0.0282278	−	0.0282278i	−0.692852	−	0.721080i	$-0.743646\pi$
$157$	0.353693	−	0.353693i	0.0282278	−	0.0282278i	0.721080	+	0.692852i	$0.243646\pi$
$158$		0			0
$159$	0.230995			0.0183191
$160$		0			0
$161$	1.43950			0.113449
$162$		0			0
$163$	−7.03184	+	7.03184i	−0.550777	+	0.550777i	−0.926665	−	0.375888i	$-0.877338\pi$
$163$	−7.03184	+	7.03184i	−0.550777	+	0.550777i	0.375888	+	0.926665i	$0.377338\pi$
$164$		0			0
$165$	−4.58011	−	4.58011i	−0.356561	−	0.356561i
$166$		0			0
$167$		−	4.68704i		−	0.362694i	−0.983419	−	0.181347i	$-0.941954\pi$
$167$		−	4.68704i		−	0.362694i	0.983419	−	0.181347i	$-0.0580457\pi$
$168$		0			0
$169$			12.4325i			0.956344i
$170$		0			0
$171$	−3.69828	−	3.69828i	−0.282814	−	0.282814i
$172$		0			0
$173$	11.9586	−	11.9586i	0.909193	−	0.909193i	−0.0870143	−	0.996207i	$-0.527733\pi$
$173$	11.9586	−	11.9586i	0.909193	−	0.909193i	0.996207	+	0.0870143i	$0.0277326\pi$
$174$		0			0
$175$	−32.2335			−2.43662
$176$		0			0
$177$	−9.09078			−0.683305
$178$		0			0
$179$	−14.7068	+	14.7068i	−1.09924	+	1.09924i	−0.104739	+	0.994500i	$0.533401\pi$
$179$	−14.7068	+	14.7068i	−1.09924	+	1.09924i	−0.994500	+	0.104739i	$0.966599\pi$
$180$		0			0
$181$	−7.86290	−	7.86290i	−0.584445	−	0.584445i	0.351677	−	0.936121i	$-0.385612\pi$
$181$	−7.86290	−	7.86290i	−0.584445	−	0.584445i	−0.936121	+	0.351677i	$0.885612\pi$
$182$		0			0
$183$			2.33547i			0.172643i
$184$		0			0
$185$			8.01999i			0.589641i
$186$		0			0
$187$	−1.08828	−	1.08828i	−0.0795829	−	0.0795829i
$188$		0			0
$189$	15.6557	−	15.6557i	1.13878	−	1.13878i
$190$		0			0
$191$	−19.6689			−1.42319			−0.711596	−	0.702589i	$-0.752027\pi$
$191$	−19.6689			−1.42319			−0.711596	+	0.702589i	$0.752027\pi$
$192$		0			0
$193$	−8.82705			−0.635385			−0.317692	−	0.948194i	$-0.602908\pi$
$193$	−8.82705			−0.635385			−0.317692	+	0.948194i	$0.602908\pi$
$194$		0			0
$195$	3.45039	−	3.45039i	0.247088	−	0.247088i
$196$		0			0
$197$	−15.7396	−	15.7396i	−1.12140	−	1.12140i	−0.991531	−	0.129869i	$-0.958544\pi$
$197$	−15.7396	−	15.7396i	−1.12140	−	1.12140i	−0.129869	−	0.991531i	$-0.541456\pi$
$198$		0			0
$199$			21.9510i			1.55606i	0.628225	+	0.778032i	$0.283782\pi$
$199$			21.9510i			1.55606i	−0.628225	+	0.778032i	$0.716218\pi$
$200$		0			0
$201$			3.71359i			0.261936i
$202$		0			0
$203$	24.1673	+	24.1673i	1.69621	+	1.69621i
$204$		0			0
$205$	−9.85510	+	9.85510i	−0.688310	+	0.688310i
$206$		0			0
$207$	−0.182029			−0.0126519
$208$		0			0
$209$	8.46417			0.585479
$210$		0			0
$211$	5.76721	−	5.76721i	0.397031	−	0.397031i	−0.480154	−	0.877184i	$-0.659419\pi$
$211$	5.76721	−	5.76721i	0.397031	−	0.397031i	0.877184	+	0.480154i	$0.159419\pi$
$212$		0			0
$213$	3.81196	+	3.81196i	0.261191	+	0.261191i
$214$		0			0
$215$		−	23.8539i		−	1.62682i
$216$		0			0
$217$			7.03569i			0.477614i
$218$		0			0
$219$	−7.55971	−	7.55971i	−0.510838	−	0.510838i
$220$		0			0
$221$	0.819848	−	0.819848i	0.0551489	−	0.0551489i
$222$		0			0
$223$	−5.37001			−0.359602			−0.179801	−	0.983703i	$-0.557545\pi$
$223$	−5.37001			−0.359602			−0.179801	+	0.983703i	$0.557545\pi$
$224$		0			0
$225$	4.07602			0.271734
$226$		0			0
$227$	1.10438	−	1.10438i	0.0733002	−	0.0733002i	−0.669506	−	0.742806i	$-0.733494\pi$
$227$	1.10438	−	1.10438i	0.0733002	−	0.0733002i	0.742806	+	0.669506i	$0.233494\pi$
$228$		0			0
$229$	17.0029	+	17.0029i	1.12359	+	1.12359i	0.991198	+	0.132388i	$0.0422645\pi$
$229$	17.0029	+	17.0029i	1.12359	+	1.12359i	0.132388	+	0.991198i	$0.457735\pi$
$230$		0			0
$231$		−	9.29460i		−	0.611540i
$232$		0			0
$233$		−	14.8204i		−	0.970914i	−0.874261	−	0.485457i	$-0.838653\pi$
$233$		−	14.8204i		−	0.970914i	0.874261	−	0.485457i	$-0.161347\pi$
$234$		0			0
$235$	2.06279	+	2.06279i	0.134562	+	0.134562i
$236$		0			0
$237$	−13.6567	+	13.6567i	−0.887096	+	0.887096i
$238$		0			0
$239$	−9.10228			−0.588778			−0.294389	−	0.955686i	$-0.595116\pi$
$239$	−9.10228			−0.588778			−0.294389	+	0.955686i	$0.595116\pi$
$240$		0			0
$241$	−9.08731			−0.585365			−0.292683	−	0.956210i	$-0.594548\pi$
$241$	−9.08731			−0.585365			−0.292683	+	0.956210i	$0.594548\pi$
$242$		0			0
$243$	−4.47296	+	4.47296i	−0.286940	+	0.286940i
$244$		0			0
$245$	−40.6419	−	40.6419i	−2.59652	−	2.59652i
$246$		0			0
$247$			6.37642i			0.405722i
$248$		0			0
$249$		−	14.7352i		−	0.933808i
$250$		0			0
$251$	−16.1734	−	16.1734i	−1.02086	−	1.02086i	−0.999778	−	0.0210806i	$-0.993289\pi$
$251$	−16.1734	−	16.1734i	−1.02086	−	1.02086i	−0.0210806	−	0.999778i	$-0.506711\pi$
$252$		0			0
$253$	0.208303	−	0.208303i	0.0130959	−	0.0130959i
$254$		0			0
$255$	9.96888			0.624275
$256$		0			0
$257$	12.6407			0.788507			0.394254	−	0.919002i	$-0.371003\pi$
$257$	12.6407			0.788507			0.394254	+	0.919002i	$0.371003\pi$
$258$		0			0
$259$	−8.13765	+	8.13765i	−0.505649	+	0.505649i
$260$		0			0
$261$	−3.05602	−	3.05602i	−0.189163	−	0.189163i
$262$		0			0
$263$		−	3.27578i		−	0.201993i	−0.994887	−	0.100997i	$-0.967797\pi$
$263$		−	3.27578i		−	0.201993i	0.994887	−	0.100997i	$-0.0322031\pi$
$264$		0			0
$265$		−	0.413557i		−	0.0254046i
$266$		0			0
$267$	11.0344	+	11.0344i	0.675295	+	0.675295i
$268$		0			0
$269$	6.23599	−	6.23599i	0.380215	−	0.380215i	−0.490965	−	0.871179i	$-0.663356\pi$
$269$	6.23599	−	6.23599i	0.380215	−	0.380215i	0.871179	+	0.490965i	$0.163356\pi$
$270$		0			0
$271$	5.85546			0.355694			0.177847	−	0.984058i	$-0.443087\pi$
$271$	5.85546			0.355694			0.177847	+	0.984058i	$0.443087\pi$
$272$		0			0
$273$	7.00202			0.423781
$274$		0			0
$275$	−4.66435	+	4.66435i	−0.281271	+	0.281271i
$276$		0			0
$277$	7.26327	+	7.26327i	0.436407	+	0.436407i	0.890801	−	0.454394i	$-0.150144\pi$
$277$	7.26327	+	7.26327i	0.436407	+	0.436407i	−0.454394	+	0.890801i	$0.650144\pi$
$278$		0			0
$279$		−	0.889684i		−	0.0532640i
$280$		0			0
$281$			19.4088i			1.15783i	0.815386	+	0.578917i	$0.196525\pi$
$281$			19.4088i			1.15783i	−0.815386	+	0.578917i	$0.803475\pi$
$282$		0			0
$283$	19.3205	+	19.3205i	1.14848	+	1.14848i	0.986851	+	0.161633i	$0.0516760\pi$
$283$	19.3205	+	19.3205i	1.14848	+	1.14848i	0.161633	+	0.986851i	$0.448324\pi$
$284$		0			0
$285$	−38.7668	+	38.7668i	−2.29635	+	2.29635i
$286$		0			0
$287$	−19.9994			−1.18052
$288$		0			0
$289$	−14.6313			−0.860664
$290$		0			0
$291$	9.98404	−	9.98404i	0.585275	−	0.585275i
$292$		0			0
$293$	12.2444	+	12.2444i	0.715327	+	0.715327i	0.967644	−	0.252318i	$-0.0811928\pi$
$293$	12.2444	+	12.2444i	0.715327	+	0.715327i	−0.252318	+	0.967644i	$0.581193\pi$
$294$		0			0
$295$			16.2755i			0.947594i
$296$		0			0
$297$		−	4.53092i		−	0.262911i
$298$		0			0
$299$	0.156924	+	0.156924i	0.00907513	+	0.00907513i
$300$		0			0
$301$	24.2038	−	24.2038i	1.39508	−	1.39508i
$302$		0			0
$303$	17.1968			0.987929
$304$		0			0
$305$	4.18125			0.239417
$306$		0			0
$307$	3.81602	−	3.81602i	0.217792	−	0.217792i	−0.589775	−	0.807567i	$-0.700784\pi$
$307$	3.81602	−	3.81602i	0.217792	−	0.217792i	0.807567	+	0.589775i	$0.200784\pi$
$308$		0			0
$309$	−12.6830	−	12.6830i	−0.721510	−	0.721510i
$310$		0			0
$311$		−	2.88098i		−	0.163365i	−0.996658	−	0.0816826i	$-0.973971\pi$
$311$		−	2.88098i		−	0.163365i	0.996658	−	0.0816826i	$-0.0260294\pi$
$312$		0			0
$313$			5.85067i			0.330700i	0.986235	+	0.165350i	$0.0528753\pi$
$313$			5.85067i			0.330700i	−0.986235	+	0.165350i	$0.947125\pi$
$314$		0			0
$315$	7.27073	+	7.27073i	0.409659	+	0.409659i
$316$		0			0
$317$	−13.0696	+	13.0696i	−0.734062	+	0.734062i	−0.971422	−	0.237360i	$-0.923718\pi$
$317$	−13.0696	+	13.0696i	−0.734062	+	0.734062i	0.237360	+	0.971422i	$0.423718\pi$
$318$		0			0
$319$	6.99426			0.391603
$320$		0			0
$321$	6.32032			0.352766
$322$		0			0
$323$	−9.21139	+	9.21139i	−0.512535	+	0.512535i
$324$		0			0
$325$	−3.51385	−	3.51385i	−0.194913	−	0.194913i
$326$		0			0
$327$			24.6754i			1.36455i
$328$		0			0
$329$			4.18611i			0.230788i
$330$		0			0
$331$	−6.01896	−	6.01896i	−0.330832	−	0.330832i	0.522071	−	0.852902i	$-0.325160\pi$
$331$	−6.01896	−	6.01896i	−0.330832	−	0.330832i	−0.852902	+	0.522071i	$0.825160\pi$
$332$		0			0
$333$	1.02903	−	1.02903i	0.0563905	−	0.0563905i
$334$		0			0
$335$	6.64853			0.363248
$336$		0			0
$337$	29.3513			1.59887			0.799434	−	0.600754i	$-0.205133\pi$
$337$	29.3513			1.59887			0.799434	+	0.600754i	$0.205133\pi$
$338$		0			0
$339$	3.87740	−	3.87740i	0.210591	−	0.210591i
$340$		0			0
$341$	1.01810	+	1.01810i	0.0551332	+	0.0551332i
$342$		0			0
$343$		−	48.2705i		−	2.60636i
$344$		0			0
$345$			1.90810i			0.102729i
$346$		0			0
$347$	−12.6001	−	12.6001i	−0.676410	−	0.676410i	0.282776	−	0.959186i	$-0.408745\pi$
$347$	−12.6001	−	12.6001i	−0.676410	−	0.676410i	−0.959186	+	0.282776i	$0.908745\pi$
$348$		0			0
$349$	−19.3967	+	19.3967i	−1.03828	+	1.03828i	−0.0390466	+	0.999237i	$0.512432\pi$
$349$	−19.3967	+	19.3967i	−1.03828	+	1.03828i	−0.999237	+	0.0390466i	$0.987568\pi$
$350$		0			0
$351$	3.41333			0.182190
$352$		0			0
$353$	−20.5371			−1.09308			−0.546541	−	0.837433i	$-0.684056\pi$
$353$	−20.5371			−1.09308			−0.546541	+	0.837433i	$0.684056\pi$
$354$		0			0
$355$	6.82465	−	6.82465i	0.362215	−	0.362215i
$356$		0			0
$357$	10.1151	+	10.1151i	0.535349	+	0.535349i
$358$		0			0
$359$			8.90052i			0.469751i	0.972025	+	0.234876i	$0.0754683\pi$
$359$			8.90052i			0.469751i	−0.972025	+	0.234876i	$0.924532\pi$
$360$		0			0
$361$		−	52.6422i		−	2.77064i
$362$		0			0
$363$	−1.34498	−	1.34498i	−0.0705929	−	0.0705929i
$364$		0			0
$365$	−13.5343	+	13.5343i	−0.708420	+	0.708420i
$366$		0			0
$367$	32.2561			1.68375			0.841877	−	0.539669i	$-0.181451\pi$
$367$	32.2561			1.68375			0.841877	+	0.539669i	$0.181451\pi$
$368$		0			0
$369$	2.52898			0.131653
$370$		0			0
$371$	0.419624	−	0.419624i	0.0217858	−	0.0217858i
$372$		0			0
$373$	16.1348	+	16.1348i	0.835426	+	0.835426i	0.988253	−	0.152827i	$-0.0488376\pi$
$373$	16.1348	+	16.1348i	0.835426	+	0.835426i	−0.152827	+	0.988253i	$0.548838\pi$
$374$		0			0
$375$		−	10.3402i		−	0.533964i
$376$		0			0
$377$			5.26907i			0.271371i
$378$		0			0
$379$	−2.56853	−	2.56853i	−0.131936	−	0.131936i	0.638055	−	0.769991i	$-0.279739\pi$
$379$	−2.56853	−	2.56853i	−0.131936	−	0.131936i	−0.769991	+	0.638055i	$0.779739\pi$
$380$		0			0
$381$	−8.65603	+	8.65603i	−0.443462	+	0.443462i
$382$		0			0
$383$	−28.0600			−1.43380			−0.716900	−	0.697176i	$-0.754440\pi$
$383$	−28.0600			−1.43380			−0.716900	+	0.697176i	$0.754440\pi$
$384$		0			0
$385$	−16.6404			−0.848071
$386$		0			0
$387$	−3.06064	+	3.06064i	−0.155581	+	0.155581i
$388$		0			0
$389$	−12.5053	−	12.5053i	−0.634044	−	0.634044i	0.315036	−	0.949080i	$-0.397984\pi$
$389$	−12.5053	−	12.5053i	−0.634044	−	0.634044i	−0.949080	+	0.315036i	$0.897984\pi$
$390$		0			0
$391$			0.453384i			0.0229286i
$392$		0			0
$393$			21.5845i			1.08879i
$394$		0			0
$395$	24.4499	+	24.4499i	1.23021	+	1.23021i
$396$		0			0
$397$	−19.7711	+	19.7711i	−0.992283	+	0.992283i	−0.999970	−	0.00768742i	$-0.997553\pi$
$397$	−19.7711	+	19.7711i	−0.992283	+	0.992283i	0.00768742	+	0.999970i	$0.497553\pi$
$398$		0			0
$399$	−78.6711			−3.93848
$400$		0			0
$401$	2.05935			0.102839			0.0514195	−	0.998677i	$-0.483625\pi$
$401$	2.05935			0.102839			0.0514195	+	0.998677i	$0.483625\pi$
$402$		0			0
$403$	−0.766978	+	0.766978i	−0.0382059	+	0.0382059i
$404$		0			0
$405$	25.2158	+	25.2158i	1.25298	+	1.25298i
$406$		0			0
$407$			2.35512i			0.116739i
$408$		0			0
$409$			1.04009i			0.0514289i	0.999669	+	0.0257145i	$0.00818607\pi$
$409$			1.04009i			0.0514289i	−0.999669	+	0.0257145i	$0.991814\pi$
$410$		0			0
$411$	14.1223	+	14.1223i	0.696603	+	0.696603i
$412$		0			0
$413$	−16.5142	+	16.5142i	−0.812612	+	0.812612i
$414$		0			0
$415$	−26.3809			−1.29499
$416$		0			0
$417$	−37.9657			−1.85919
$418$		0			0
$419$	12.1644	−	12.1644i	0.594271	−	0.594271i	−0.344511	−	0.938782i	$-0.611955\pi$
$419$	12.1644	−	12.1644i	0.594271	−	0.594271i	0.938782	+	0.344511i	$0.111955\pi$
$420$		0			0
$421$	0.787881	+	0.787881i	0.0383990	+	0.0383990i	0.726046	−	0.687647i	$-0.241356\pi$
$421$	0.787881	+	0.787881i	0.0383990	+	0.0383990i	−0.687647	+	0.726046i	$0.741356\pi$
$422$		0			0
$423$		−	0.529345i		−	0.0257376i
$424$		0			0
$425$		−	10.1522i		−	0.492456i
$426$		0			0
$427$	4.24259	+	4.24259i	0.205313	+	0.205313i
$428$		0			0
$429$	1.01323	−	1.01323i	0.0489191	−	0.0489191i
$430$		0			0
$431$	20.8973			1.00659			0.503293	−	0.864116i	$-0.332122\pi$
$431$	20.8973			1.00659			0.503293	+	0.864116i	$0.332122\pi$
$432$		0			0
$433$	31.9139			1.53368			0.766842	−	0.641836i	$-0.221827\pi$
$433$	31.9139			1.53368			0.766842	+	0.641836i	$0.221827\pi$
$434$		0			0
$435$	−32.0344	+	32.0344i	−1.53593	+	1.53593i
$436$		0			0
$437$	−1.76311	−	1.76311i	−0.0843411	−	0.0843411i
$438$		0			0
$439$			0.0658140i			0.00314113i	0.999999	+	0.00157056i	$0.000499926\pi$
$439$			0.0658140i			0.00314113i	−0.999999	+	0.00157056i	$0.999500\pi$
$440$		0			0
$441$			10.4294i			0.496637i
$442$		0			0
$443$	−17.0350	−	17.0350i	−0.809357	−	0.809357i	0.175180	−	0.984536i	$-0.443949\pi$
$443$	−17.0350	−	17.0350i	−0.809357	−	0.809357i	−0.984536	+	0.175180i	$0.943949\pi$
$444$		0			0
$445$	19.7552	−	19.7552i	0.936485	−	0.936485i
$446$		0			0
$447$	−23.3039			−1.10224
$448$		0			0
$449$	−24.1440			−1.13943			−0.569714	−	0.821843i	$-0.692946\pi$
$449$	−24.1440			−1.13943			−0.569714	+	0.821843i	$0.692946\pi$
$450$		0			0
$451$	−2.89401	+	2.89401i	−0.136274	+	0.136274i
$452$		0			0
$453$	11.3469	+	11.3469i	0.533124	+	0.533124i
$454$		0			0
$455$		−	12.5359i		−	0.587692i
$456$		0			0
$457$		−	5.17834i		−	0.242233i	−0.992638	−	0.121116i	$-0.961353\pi$
$457$		−	5.17834i		−	0.242233i	0.992638	−	0.121116i	$-0.0386474\pi$
$458$		0			0
$459$	4.93091	+	4.93091i	0.230155	+	0.230155i
$460$		0			0
$461$	21.5047	−	21.5047i	1.00157	−	1.00157i	0.00157450	−	0.999999i	$-0.499499\pi$
$461$	21.5047	−	21.5047i	1.00157	−	1.00157i	0.999999	−	0.00157450i	$-0.000501180\pi$
$462$		0			0
$463$	23.4294			1.08886			0.544428	−	0.838808i	$-0.316747\pi$
$463$	23.4294			1.08886			0.544428	+	0.838808i	$0.316747\pi$
$464$		0			0
$465$	−9.32601			−0.432484
$466$		0			0
$467$	13.2909	−	13.2909i	0.615030	−	0.615030i	−0.329222	−	0.944252i	$-0.606787\pi$
$467$	13.2909	−	13.2909i	0.615030	−	0.615030i	0.944252	+	0.329222i	$0.106787\pi$
$468$		0			0
$469$	6.74607	+	6.74607i	0.311505	+	0.311505i
$470$		0			0
$471$			0.951418i			0.0438390i
$472$		0			0
$473$		−	7.00483i		−	0.322082i
$474$		0			0
$475$	39.4798	+	39.4798i	1.81146	+	1.81146i
$476$		0			0
$477$	−0.0530626	+	0.0530626i	−0.00242957	+	0.00242957i
$478$		0			0
$479$	43.4425			1.98494			0.992469	−	0.122495i	$-0.0390896\pi$
$479$	43.4425			1.98494			0.992469	+	0.122495i	$0.0390896\pi$
$480$		0			0
$481$	−1.77421			−0.0808970
$482$		0			0
$483$	−1.93609	+	1.93609i	−0.0880953	+	0.0880953i
$484$		0			0
$485$	−17.8747	−	17.8747i	−0.811648	−	0.811648i
$486$		0			0
$487$			20.5820i			0.932661i	0.884610	+	0.466331i	$0.154424\pi$
$487$			20.5820i			0.932661i	−0.884610	+	0.466331i	$0.845576\pi$
$488$		0			0
$489$		−	18.9153i		−	0.855380i
$490$		0			0
$491$	−19.5086	−	19.5086i	−0.880412	−	0.880412i	0.113164	−	0.993576i	$-0.463901\pi$
$491$	−19.5086	−	19.5086i	−0.880412	−	0.880412i	−0.993576	+	0.113164i	$0.963901\pi$
$492$		0			0
$493$	−7.61171	+	7.61171i	−0.342814	+	0.342814i
$494$		0			0
$495$	2.10422			0.0945777
$496$		0			0
$497$	13.8495			0.621237
$498$		0			0
$499$	−20.3380	+	20.3380i	−0.910456	+	0.910456i	−0.996308	−	0.0858519i	$-0.972639\pi$
$499$	−20.3380	+	20.3380i	−0.910456	+	0.910456i	0.0858519	+	0.996308i	$0.472639\pi$
$500$		0			0
$501$	6.30395	+	6.30395i	0.281640	+	0.281640i
$502$		0			0
$503$			12.2713i			0.547152i	0.961850	+	0.273576i	$0.0882065\pi$
$503$			12.2713i			0.547152i	−0.961850	+	0.273576i	$0.911793\pi$
$504$		0			0
$505$		−	30.7878i		−	1.37004i
$506$		0			0
$507$	−16.7214	−	16.7214i	−0.742622	−	0.742622i
$508$		0			0
$509$	−17.5441	+	17.5441i	−0.777629	+	0.777629i	−0.979427	−	0.201798i	$-0.935322\pi$
$509$	−17.5441	+	17.5441i	−0.777629	+	0.777629i	0.201798	+	0.979427i	$0.435322\pi$
$510$		0			0
$511$	−27.4658			−1.21502
$512$		0			0
$513$	−38.3505			−1.69321
$514$		0			0
$515$	−22.7067	+	22.7067i	−1.00058	+	1.00058i
$516$		0			0
$517$	0.605751	+	0.605751i	0.0266409	+	0.0266409i
$518$		0			0
$519$			32.1679i			1.41202i
$520$		0			0
$521$			35.7622i			1.56677i	0.621538	+	0.783384i	$0.286508\pi$
$521$			35.7622i			1.56677i	−0.621538	+	0.783384i	$0.713492\pi$
$522$		0			0
$523$	−16.2700	−	16.2700i	−0.711437	−	0.711437i	0.255399	−	0.966836i	$-0.417793\pi$
$523$	−16.2700	−	16.2700i	−0.711437	−	0.711437i	−0.966836	+	0.255399i	$0.917793\pi$
$524$		0			0
$525$	43.3532	−	43.3532i	1.89209	−	1.89209i
$526$		0			0
$527$	−2.21596			−0.0965286
$528$		0			0
$529$	22.9132			0.996227
$530$		0			0
$531$	2.08827	−	2.08827i	0.0906233	−	0.0906233i
$532$		0			0
$533$	−2.18018	−	2.18018i	−0.0944341	−	0.0944341i
$534$		0			0
$535$		−	11.3154i		−	0.489209i
$536$		0			0
$537$		−	39.5606i		−	1.70717i
$538$		0			0
$539$	−11.9347	−	11.9347i	−0.514065	−	0.514065i
$540$		0			0
$541$	−25.1002	+	25.1002i	−1.07914	+	1.07914i	−0.0825554	+	0.996586i	$0.526308\pi$
$541$	−25.1002	+	25.1002i	−1.07914	+	1.07914i	−0.996586	+	0.0825554i	$0.973692\pi$
$542$		0			0
$543$	21.1508			0.907668
$544$		0			0
$545$	44.1770			1.89233
$546$		0			0
$547$	−3.89719	+	3.89719i	−0.166632	+	0.166632i	−0.785497	−	0.618865i	$-0.787593\pi$
$547$	−3.89719	+	3.89719i	−0.166632	+	0.166632i	0.618865	+	0.785497i	$0.287593\pi$
$548$		0			0
$549$	−0.536488	−	0.536488i	−0.0228967	−	0.0228967i
$550$		0			0
$551$		−	59.2006i		−	2.52203i
$552$		0			0
$553$			49.6172i			2.10994i
$554$		0			0
$555$	−10.7867	−	10.7867i	−0.457869	−	0.457869i
$556$		0			0
$557$	25.1453	−	25.1453i	1.06544	−	1.06544i	0.0677385	−	0.997703i	$-0.478422\pi$
$557$	25.1453	−	25.1453i	1.06544	−	1.06544i	0.997703	−	0.0677385i	$-0.0215784\pi$
$558$		0			0
$559$	5.27704			0.223195
$560$		0			0
$561$	2.92742			0.123596
$562$		0			0
$563$	14.1939	−	14.1939i	0.598200	−	0.598200i	−0.341633	−	0.939833i	$-0.610980\pi$
$563$	14.1939	−	14.1939i	0.598200	−	0.598200i	0.939833	+	0.341633i	$0.110980\pi$
$564$		0			0
$565$	−6.94180	−	6.94180i	−0.292044	−	0.292044i
$566$		0			0
$567$			51.1715i			2.14900i
$568$		0			0
$569$		−	18.7864i		−	0.787567i	−0.919203	−	0.393784i	$-0.871166\pi$
$569$		−	18.7864i		−	0.787567i	0.919203	−	0.393784i	$-0.128834\pi$
$570$		0			0
$571$	−28.1583	−	28.1583i	−1.17839	−	1.17839i	−0.980155	−	0.198234i	$-0.936480\pi$
$571$	−28.1583	−	28.1583i	−1.17839	−	1.17839i	−0.198234	−	0.980155i	$-0.563520\pi$
$572$		0			0
$573$	26.4542	−	26.4542i	1.10514	−	1.10514i
$574$		0			0
$575$	1.94320			0.0810369
$576$		0			0
$577$	29.0480			1.20928			0.604642	−	0.796498i	$-0.293316\pi$
$577$	29.0480			1.20928			0.604642	+	0.796498i	$0.293316\pi$
$578$		0			0
$579$	11.8722	−	11.8722i	0.493390	−	0.493390i
$580$		0			0
$581$	−26.7679	−	26.7679i	−1.11052	−	1.11052i
$582$		0			0
$583$		−	0.121443i		−	0.00502967i
$584$		0			0
$585$			1.58520i			0.0655399i
$586$		0			0
$587$	−23.1186	−	23.1186i	−0.954206	−	0.954206i	0.0447900	−	0.998996i	$-0.485738\pi$
$587$	−23.1186	−	23.1186i	−0.954206	−	0.954206i	−0.998996	+	0.0447900i	$0.985738\pi$
$588$		0			0
$589$	8.61737	−	8.61737i	0.355073	−	0.355073i
$590$		0			0
$591$	42.3388			1.74158
$592$		0			0
$593$	18.0038			0.739326			0.369663	−	0.929166i	$-0.379473\pi$
$593$	18.0038			0.739326			0.369663	+	0.929166i	$0.379473\pi$
$594$		0			0
$595$	18.1094	−	18.1094i	0.742412	−	0.742412i
$596$		0			0
$597$	−29.5235	−	29.5235i	−1.20832	−	1.20832i
$598$		0			0
$599$			31.9869i			1.30695i	0.756948	+	0.653475i	$0.226690\pi$
$599$			31.9869i			1.30695i	−0.756948	+	0.653475i	$0.773310\pi$
$600$		0			0
$601$		−	23.8213i		−	0.971689i	−0.874045	−	0.485845i	$-0.838512\pi$
$601$		−	23.8213i		−	0.971689i	0.874045	−	0.485845i	$-0.161488\pi$
$602$		0			0
$603$	−0.853060	−	0.853060i	−0.0347393	−	0.0347393i
$604$		0			0
$605$	−2.40794	+	2.40794i	−0.0978968	+	0.0978968i
$606$		0			0
$607$	−28.0295			−1.13768			−0.568842	−	0.822447i	$-0.692608\pi$
$607$	−28.0295			−1.13768			−0.568842	+	0.822447i	$0.692608\pi$
$608$		0			0
$609$	−65.0088			−2.63429
$610$		0			0
$611$	−0.456338	+	0.456338i	−0.0184615	+	0.0184615i
$612$		0			0
$613$	18.5453	+	18.5453i	0.749038	+	0.749038i	0.974299	−	0.225260i	$-0.0723232\pi$
$613$	18.5453	+	18.5453i	0.749038	+	0.749038i	−0.225260	+	0.974299i	$0.572323\pi$
$614$		0			0
$615$		−	26.5097i		−	1.06898i
$616$		0			0
$617$		−	13.6782i		−	0.550664i	−0.961349	−	0.275332i	$-0.911212\pi$
$617$		−	13.6782i		−	0.550664i	0.961349	−	0.275332i	$-0.0887877\pi$
$618$		0			0
$619$	3.06112	+	3.06112i	0.123037	+	0.123037i	0.765944	−	0.642907i	$-0.222272\pi$
$619$	3.06112	+	3.06112i	0.123037	+	0.123037i	−0.642907	+	0.765944i	$0.722272\pi$
$620$		0			0
$621$	−0.943804	+	0.943804i	−0.0378736	+	0.0378736i
$622$		0			0
$623$	40.0900			1.60617
$624$		0			0
$625$	14.4696			0.578786
$626$		0			0
$627$	−11.3841	+	11.3841i	−0.454637	+	0.454637i
$628$		0			0
$629$	−2.56303	−	2.56303i	−0.102195	−	0.102195i
$630$		0			0
$631$		−	16.5679i		−	0.659556i	−0.944059	−	0.329778i	$-0.893026\pi$
$631$		−	16.5679i		−	0.659556i	0.944059	−	0.329778i	$-0.106974\pi$
$632$		0			0
$633$			15.5135i			0.616606i
$634$		0			0
$635$	15.4971	+	15.4971i	0.614984	+	0.614984i
$636$		0			0
$637$	8.99095	−	8.99095i	0.356234	−	0.356234i
$638$		0			0
$639$	−1.75131			−0.0692809
$640$		0			0
$641$	42.4474			1.67657			0.838285	−	0.545232i	$-0.183558\pi$
$641$	42.4474			1.67657			0.838285	+	0.545232i	$0.183558\pi$
$642$		0			0
$643$	24.6339	−	24.6339i	0.971464	−	0.971464i	−0.0281396	−	0.999604i	$-0.508958\pi$
$643$	24.6339	−	24.6339i	0.971464	−	0.971464i	0.999604	+	0.0281396i	$0.00895829\pi$
$644$		0			0
$645$	32.0829	+	32.0829i	1.26326	+	1.26326i
$646$		0			0
$647$		−	25.5797i		−	1.00564i	−0.864391	−	0.502820i	$-0.832296\pi$
$647$		−	25.5797i		−	1.00564i	0.864391	−	0.502820i	$-0.167704\pi$
$648$		0			0
$649$			4.77938i			0.187607i
$650$		0			0
$651$	−9.46283	−	9.46283i	−0.370878	−	0.370878i
$652$		0			0
$653$	12.5576	−	12.5576i	0.491416	−	0.491416i	−0.417336	−	0.908752i	$-0.637036\pi$
$653$	12.5576	−	12.5576i	0.491416	−	0.491416i	0.908752	+	0.417336i	$0.137036\pi$
$654$		0			0
$655$	38.6433			1.50992
$656$		0			0
$657$	3.47313			0.135500
$658$		0			0
$659$	−29.3389	+	29.3389i	−1.14288	+	1.14288i	−0.154958	+	0.987921i	$0.549524\pi$
$659$	−29.3389	+	29.3389i	−1.14288	+	1.14288i	−0.987921	+	0.154958i	$0.950476\pi$
$660$		0			0
$661$	−31.6490	−	31.6490i	−1.23100	−	1.23100i	−0.963579	−	0.267426i	$-0.913827\pi$
$661$	−31.6490	−	31.6490i	−1.23100	−	1.23100i	−0.267426	−	0.963579i	$-0.586173\pi$
$662$		0			0
$663$			2.20535i			0.0856487i
$664$		0			0
$665$			140.847i			5.46180i
$666$		0			0
$667$	−1.45693	−	1.45693i	−0.0564124	−	0.0564124i
$668$		0			0
$669$	7.22253	−	7.22253i	0.279239	−	0.279239i
$670$		0			0
$671$	1.22785			0.0474005
$672$		0			0
$673$	−18.3424			−0.707048			−0.353524	−	0.935425i	$-0.615017\pi$
$673$	−18.3424			−0.707048			−0.353524	+	0.935425i	$0.615017\pi$
$674$		0			0
$675$	21.1338	−	21.1338i	0.813439	−	0.813439i
$676$		0			0
$677$	29.5579	+	29.5579i	1.13600	+	1.13600i	0.989160	+	0.146843i	$0.0469113\pi$
$677$	29.5579	+	29.5579i	1.13600	+	1.13600i	0.146843	+	0.989160i	$0.453089\pi$
$678$		0			0
$679$		−	36.2738i		−	1.39206i
$680$		0			0
$681$			2.97073i			0.113838i
$682$		0			0
$683$	−7.57608	−	7.57608i	−0.289891	−	0.289891i	0.547146	−	0.837037i	$-0.315714\pi$
$683$	−7.57608	−	7.57608i	−0.289891	−	0.289891i	−0.837037	+	0.547146i	$0.815714\pi$
$684$		0			0
$685$	25.2836	−	25.2836i	0.966035	−	0.966035i
$686$		0			0
$687$	−45.7371			−1.74498
$688$		0			0
$689$	0.0914884			0.00348543
$690$		0			0
$691$	−12.8736	+	12.8736i	−0.489736	+	0.489736i	−0.908223	−	0.418487i	$-0.862561\pi$
$691$	−12.8736	+	12.8736i	−0.489736	+	0.489736i	0.418487	+	0.908223i	$0.362561\pi$
$692$		0			0
$693$	2.13509	+	2.13509i	0.0811054	+	0.0811054i
$694$		0			0
$695$			67.9709i			2.57828i
$696$		0			0
$697$		−	6.29898i		−	0.238591i
$698$		0			0
$699$	19.9330	+	19.9330i	0.753936	+	0.753936i
$700$		0			0
$701$	−5.49286	+	5.49286i	−0.207463	+	0.207463i	−0.803188	−	0.595726i	$-0.796865\pi$
$701$	−5.49286	+	5.49286i	−0.207463	+	0.207463i	0.595726	+	0.803188i	$0.296865\pi$
$702$		0			0
$703$	19.9341			0.751829
$704$		0			0
$705$	−5.54880			−0.208980
$706$		0			0
$707$	31.2395	−	31.2395i	1.17488	−	1.17488i
$708$		0			0
$709$	−30.5453	−	30.5453i	−1.14715	−	1.14715i	−0.987110	−	0.160041i	$-0.948837\pi$
$709$	−30.5453	−	30.5453i	−1.14715	−	1.14715i	−0.160041	−	0.987110i	$-0.551163\pi$
$710$		0			0
$711$		−	6.27423i		−	0.235302i
$712$		0			0
$713$		−	0.424147i		−	0.0158844i
$714$		0			0
$715$	−1.81401	−	1.81401i	−0.0678400	−	0.0678400i
$716$		0			0
$717$	12.2423	−	12.2423i	0.457199	−	0.457199i
$718$		0			0
$719$	17.7339			0.661364			0.330682	−	0.943742i	$-0.392721\pi$
$719$	17.7339			0.661364			0.330682	+	0.943742i	$0.392721\pi$
$720$		0			0
$721$	−46.0796			−1.71609
$722$		0			0
$723$	12.2222	−	12.2222i	0.454549	−	0.454549i
$724$		0			0
$725$	32.6236	+	32.6236i	1.21161	+	1.21161i
$726$		0			0
$727$			39.2767i			1.45669i	0.685210	+	0.728345i	$0.259710\pi$
$727$			39.2767i			1.45669i	−0.685210	+	0.728345i	$0.740290\pi$
$728$		0			0
$729$			19.3838i			0.717917i
$730$		0			0
$731$	7.62321	+	7.62321i	0.281955	+	0.281955i
$732$		0			0
$733$	0.305033	−	0.305033i	0.0112667	−	0.0112667i	−0.701451	−	0.712718i	$-0.747464\pi$
$733$	0.305033	−	0.305033i	0.0112667	−	0.0112667i	0.712718	+	0.701451i	$0.247464\pi$
$734$		0			0
$735$	109.325			4.03250
$736$		0			0
$737$	1.95238			0.0719168
$738$		0			0
$739$	8.16495	−	8.16495i	0.300353	−	0.300353i	−0.540799	−	0.841152i	$-0.681878\pi$
$739$	8.16495	−	8.16495i	0.300353	−	0.300353i	0.841152	+	0.540799i	$0.181878\pi$
$740$		0			0
$741$	−8.57613	−	8.57613i	−0.315052	−	0.315052i
$742$		0			0
$743$		−	13.2880i		−	0.487488i	−0.969840	−	0.243744i	$-0.921624\pi$
$743$		−	13.2880i		−	0.487488i	0.969840	−	0.243744i	$-0.0783757\pi$
$744$		0			0
$745$			41.7215i			1.52856i
$746$		0			0
$747$	3.38488	+	3.38488i	0.123846	+	0.123846i
$748$		0			0
$749$	11.4814	−	11.4814i	0.419523	−	0.419523i
$750$		0			0
$751$	−19.9332			−0.727372			−0.363686	−	0.931522i	$-0.618482\pi$
$751$	−19.9332			−0.727372			−0.363686	+	0.931522i	$0.618482\pi$
$752$		0			0
$753$	43.5057			1.58544
$754$		0			0
$755$	20.3147	−	20.3147i	0.739326	−	0.739326i
$756$		0			0
$757$	−10.4321	−	10.4321i	−0.379160	−	0.379160i	0.491639	−	0.870799i	$-0.336398\pi$
$757$	−10.4321	−	10.4321i	−0.379160	−	0.379160i	−0.870799	+	0.491639i	$0.836398\pi$
$758$		0			0
$759$			0.560325i			0.0203385i
$760$		0			0
$761$		−	8.05745i		−	0.292082i	−0.989279	−	0.146041i	$-0.953347\pi$
$761$		−	8.05745i		−	0.292082i	0.989279	−	0.146041i	$-0.0466532\pi$
$762$		0			0
$763$	44.8251	+	44.8251i	1.62278	+	1.62278i
$764$		0			0
$765$	−2.28998	+	2.28998i	−0.0827945	+	0.0827945i
$766$		0			0
$767$	−3.60051			−0.130007
$768$		0			0
$769$	−47.7768			−1.72287			−0.861437	−	0.507864i	$-0.830435\pi$
$769$	−47.7768			−1.72287			−0.861437	+	0.507864i	$0.830435\pi$
$770$		0			0
$771$	−17.0015	+	17.0015i	−0.612293	+	0.612293i
$772$		0			0
$773$	13.4035	+	13.4035i	0.482091	+	0.482091i	0.905799	−	0.423708i	$-0.139272\pi$
$773$	13.4035	+	13.4035i	0.482091	+	0.482091i	−0.423708	+	0.905799i	$0.639272\pi$
$774$		0			0
$775$			9.49754i			0.341162i
$776$		0			0
$777$		−	21.8899i		−	0.785295i
$778$		0			0
$779$	24.4954	+	24.4954i	0.877638	+	0.877638i
$780$		0			0
$781$	2.00410	−	2.00410i	0.0717123	−	0.0717123i
$782$		0			0
$783$	−31.6904			−1.13252
$784$		0			0
$785$	1.70335			0.0607951
$786$		0			0
$787$	19.6451	−	19.6451i	0.700271	−	0.700271i	−0.264198	−	0.964468i	$-0.585107\pi$
$787$	19.6451	−	19.6451i	0.700271	−	0.700271i	0.964468	+	0.264198i	$0.0851072\pi$
$788$		0			0
$789$	4.40584	+	4.40584i	0.156852	+	0.156852i
$790$		0			0
$791$		−	14.0873i		−	0.500886i
$792$		0			0
$793$			0.924990i			0.0328474i
$794$		0			0
$795$	0.556223	+	0.556223i	0.0197272	+	0.0197272i
$796$		0			0
$797$	16.4970	−	16.4970i	0.584352	−	0.584352i	−0.351744	−	0.936096i	$-0.614411\pi$
$797$	16.4970	−	16.4970i	0.584352	−	0.584352i	0.936096	+	0.351744i	$0.114411\pi$
$798$		0			0
$799$	−1.31845			−0.0466435
$800$		0			0
$801$	−5.06950			−0.179122
$802$		0			0
$803$	−3.97444	+	3.97444i	−0.140255	+	0.140255i
$804$		0			0
$805$	3.46624	+	3.46624i	0.122169	+	0.122169i
$806$		0			0
$807$			16.7745i			0.590490i
$808$		0			0
$809$		−	54.1309i		−	1.90314i	−0.307430	−	0.951571i	$-0.599469\pi$
$809$		−	54.1309i		−	1.90314i	0.307430	−	0.951571i	$-0.400531\pi$
$810$		0			0
$811$	−4.58286	−	4.58286i	−0.160926	−	0.160926i	0.622051	−	0.782977i	$-0.286300\pi$
$811$	−4.58286	−	4.58286i	−0.160926	−	0.160926i	−0.782977	+	0.622051i	$0.786300\pi$
$812$		0			0
$813$	−7.87545	+	7.87545i	−0.276204	+	0.276204i
$814$		0			0
$815$	−33.8646			−1.18622
$816$		0			0
$817$	−59.2900			−2.07430
$818$		0			0
$819$	−1.60846	+	1.60846i	−0.0562040	+	0.0562040i
$820$		0			0
$821$	−13.8584	−	13.8584i	−0.483663	−	0.483663i	0.422636	−	0.906299i	$-0.361105\pi$
$821$	−13.8584	−	13.8584i	−0.483663	−	0.483663i	−0.906299	+	0.422636i	$0.861105\pi$
$822$		0			0
$823$			25.4191i			0.886052i	0.896509	+	0.443026i	$0.146095\pi$
$823$			25.4191i			0.886052i	−0.896509	+	0.443026i	$0.853905\pi$
$824$		0			0
$825$		−	12.5469i		−	0.436826i
$826$		0			0
$827$	−29.0520	−	29.0520i	−1.01024	−	1.01024i	−0.999947	−	0.0102897i	$-0.996725\pi$
$827$	−29.0520	−	29.0520i	−1.01024	−	1.01024i	−0.0102897	−	0.999947i	$-0.503275\pi$
$828$		0			0
$829$	−2.05453	+	2.05453i	−0.0713568	+	0.0713568i	−0.741884	−	0.670528i	$-0.766068\pi$
$829$	−2.05453	+	2.05453i	−0.0713568	+	0.0713568i	0.670528	+	0.741884i	$0.266068\pi$
$830$		0			0
$831$	−19.5378			−0.677760
$832$		0			0
$833$	25.9767			0.900038
$834$		0			0
$835$	11.2861	−	11.2861i	0.390573	−	0.390573i
$836$		0			0
$837$	−4.61293	−	4.61293i	−0.159446	−	0.159446i
$838$		0			0
$839$		−	47.0571i		−	1.62459i	−0.583246	−	0.812295i	$-0.698218\pi$
$839$		−	47.0571i		−	1.62459i	0.583246	−	0.812295i	$-0.301782\pi$
$840$		0			0
$841$		−	19.9196i		−	0.686883i
$842$		0			0
$843$	−26.1044	−	26.1044i	−0.899084	−	0.899084i
$844$		0			0
$845$	−29.9367	+	29.9367i	−1.02985	+	1.02985i
$846$		0			0
$847$	−4.88654			−0.167903
$848$		0			0
$849$	−51.9712			−1.78365
$850$		0			0
$851$	0.490578	−	0.490578i	0.0168168	−	0.0168168i
$852$		0			0
$853$	−25.7103	−	25.7103i	−0.880302	−	0.880302i	0.113263	−	0.993565i	$-0.463870\pi$
$853$	−25.7103	−	25.7103i	−0.880302	−	0.880302i	−0.993565	+	0.113263i	$0.963870\pi$
$854$		0			0
$855$		−	17.8105i		−	0.609106i
$856$		0			0
$857$			20.1931i			0.689784i	0.938642	+	0.344892i	$0.112084\pi$
$857$			20.1931i			0.689784i	−0.938642	+	0.344892i	$0.887916\pi$
$858$		0			0
$859$	14.7908	+	14.7908i	0.504656	+	0.504656i	0.912881	−	0.408225i	$-0.133852\pi$
$859$	14.7908	+	14.7908i	0.504656	+	0.504656i	−0.408225	+	0.912881i	$0.633852\pi$
$860$		0			0
$861$	26.8986	−	26.8986i	0.916703	−	0.916703i
$862$		0			0
$863$	−8.04857			−0.273976			−0.136988	−	0.990573i	$-0.543742\pi$
$863$	−8.04857			−0.273976			−0.136988	+	0.990573i	$0.543742\pi$
$864$		0			0
$865$	57.5911			1.95816
$866$		0			0
$867$	19.6787	−	19.6787i	0.668325	−	0.668325i
$868$		0			0
$869$	7.17985	+	7.17985i	0.243560	+	0.243560i
$870$		0			0
$871$			1.47081i			0.0498365i
$872$		0			0
$873$			4.58693i			0.155244i
$874$		0			0
$875$	−18.7839	−	18.7839i	−0.635010	−	0.635010i
$876$		0			0
$877$	9.03375	−	9.03375i	0.305048	−	0.305048i	−0.537937	−	0.842985i	$-0.680796\pi$
$877$	9.03375	−	9.03375i	0.305048	−	0.305048i	0.842985	+	0.537937i	$0.180796\pi$
$878$		0			0
$879$	−32.9369			−1.11093
$880$		0			0
$881$	−6.16395			−0.207669			−0.103834	−	0.994595i	$-0.533111\pi$
$881$	−6.16395			−0.207669			−0.103834	+	0.994595i	$0.533111\pi$
$882$		0			0
$883$	35.1572	−	35.1572i	1.18313	−	1.18313i	0.204206	−	0.978928i	$-0.434539\pi$
$883$	35.1572	−	35.1572i	1.18313	−	1.18313i	0.978928	−	0.204206i	$-0.0654612\pi$
$884$		0			0
$885$	−21.8901	−	21.8901i	−0.735827	−	0.735827i
$886$		0			0
$887$		−	50.5055i		−	1.69581i	−0.530150	−	0.847904i	$-0.677864\pi$
$887$		−	50.5055i		−	1.69581i	0.530150	−	0.847904i	$-0.322136\pi$
$888$		0			0
$889$			31.4489i			1.05476i
$890$		0			0
$891$	7.40477	+	7.40477i	0.248069	+	0.248069i
$892$		0			0
$893$	5.12718	−	5.12718i	0.171574	−	0.171574i
$894$		0			0
$895$	−70.8264			−2.36746
$896$		0			0
$897$	−0.422117			−0.0140941
$898$		0			0
$899$	7.12085	−	7.12085i	0.237494	−	0.237494i
$900$		0			0
$901$	0.132164	+	0.132164i	0.00440303	+	0.00440303i
$902$		0			0
$903$			65.1071i			2.16663i
$904$		0			0
$905$		−	37.8668i		−	1.25874i
$906$		0			0
$907$	−38.2155	−	38.2155i	−1.26893	−	1.26893i	−0.946643	−	0.322283i	$-0.895550\pi$
$907$	−38.2155	−	38.2155i	−1.26893	−	1.26893i	−0.322283	−	0.946643i	$-0.604450\pi$
$908$		0			0
$909$	−3.95033	+	3.95033i	−0.131024	+	0.131024i
$910$		0			0
$911$	24.8890			0.824609			0.412304	−	0.911046i	$-0.364724\pi$
$911$	24.8890			0.824609			0.412304	+	0.911046i	$0.364724\pi$
$912$		0			0
$913$	−7.74690			−0.256385
$914$		0			0
$915$	−5.62367	+	5.62367i	−0.185913	+	0.185913i
$916$		0			0
$917$	39.2102	+	39.2102i	1.29484	+	1.29484i
$918$		0			0
$919$			18.2745i			0.602819i	0.953495	+	0.301410i	$0.0974571\pi$
$919$			18.2745i			0.602819i	−0.953495	+	0.301410i	$0.902543\pi$
$920$		0			0
$921$			10.2649i			0.338240i
$922$		0			0
$923$	1.50977	+	1.50977i	0.0496948	+	0.0496948i
$924$		0			0
$925$	−10.9851	+	10.9851i	−0.361187	+	0.361187i
$926$		0			0
$927$	5.82690			0.191381
$928$		0			0
$929$	−29.4590			−0.966520			−0.483260	−	0.875477i	$-0.660547\pi$
$929$	−29.4590			−0.966520			−0.483260	+	0.875477i	$0.660547\pi$
$930$		0			0
$931$	−101.018	+	101.018i	−3.31072	+	3.31072i
$932$		0			0
$933$	3.87484	+	3.87484i	0.126857	+	0.126857i
$934$		0			0
$935$		−	5.24103i		−	0.171400i
$936$		0			0
$937$		−	24.0064i		−	0.784254i	−0.919911	−	0.392127i	$-0.871739\pi$
$937$		−	24.0064i		−	0.784254i	0.919911	−	0.392127i	$-0.128261\pi$
$938$		0			0
$939$	−7.86901	−	7.86901i	−0.256796	−	0.256796i
$940$		0			0
$941$	9.66150	−	9.66150i	0.314956	−	0.314956i	−0.531870	−	0.846826i	$-0.678511\pi$
$941$	9.66150	−	9.66150i	0.314956	−	0.314956i	0.846826	+	0.531870i	$0.178511\pi$
$942$		0			0
$943$	1.20566			0.0392617
$944$		0			0
$945$	75.3961			2.45264
$946$		0			0
$947$	−30.5375	+	30.5375i	−0.992335	+	0.992335i	−0.999971	−	0.00763605i	$-0.997569\pi$
$947$	−30.5375	+	30.5375i	−0.992335	+	0.992335i	0.00763605	+	0.999971i	$0.497569\pi$
$948$		0			0
$949$	−2.99411	−	2.99411i	−0.0971930	−	0.0971930i
$950$		0			0
$951$		−	35.1566i		−	1.14003i
$952$		0			0
$953$			32.6689i			1.05825i	0.848544	+	0.529124i	$0.177480\pi$
$953$			32.6689i			1.05825i	−0.848544	+	0.529124i	$0.822520\pi$
$954$		0			0
$955$	−47.3616	−	47.3616i	−1.53258	−	1.53258i
$956$		0			0
$957$	−9.40710	+	9.40710i	−0.304088	+	0.304088i
$958$		0			0
$959$	51.3090			1.65685
$960$		0			0
$961$	−28.9269			−0.933127
$962$		0			0
$963$	−1.45186	+	1.45186i	−0.0467856	+	0.0467856i
$964$		0			0
$965$	−21.2550	−	21.2550i	−0.684223	−	0.684223i
$966$		0			0
$967$			14.5873i			0.469097i	0.972104	+	0.234549i	$0.0753612\pi$
$967$			14.5873i			0.469097i	−0.972104	+	0.234549i	$0.924639\pi$
$968$		0			0
$969$		−	24.7782i		−	0.795990i
$970$		0			0
$971$	23.5279	+	23.5279i	0.755045	+	0.755045i	0.975416	−	0.220371i	$-0.0707267\pi$
$971$	23.5279	+	23.5279i	0.755045	+	0.755045i	−0.220371	+	0.975416i	$0.570727\pi$
$972$		0			0
$973$	−68.9681	+	68.9681i	−2.21101	+	2.21101i
$974$		0			0
$975$	9.45209			0.302709
$976$		0			0
$977$	−54.7989			−1.75317			−0.876586	−	0.481246i	$-0.840184\pi$
$977$	−54.7989			−1.75317			−0.876586	+	0.481246i	$0.840184\pi$
$978$		0			0
$979$	5.80123	−	5.80123i	0.185408	−	0.185408i
$980$		0			0
$981$	−5.66826	−	5.66826i	−0.180974	−	0.180974i
$982$		0			0
$983$			9.00546i			0.287229i	0.989634	+	0.143615i	$0.0458726\pi$
$983$			9.00546i			0.287229i	−0.989634	+	0.143615i	$0.954127\pi$
$984$		0			0
$985$		−	75.8001i		−	2.41519i
$986$		0			0
$987$	−5.63021	−	5.63021i	−0.179212	−	0.179212i
$988$		0			0
$989$	−1.45913	+	1.45913i	−0.0463976	+	0.0463976i
$990$		0			0
$991$	52.9389			1.68166			0.840831	−	0.541298i	$-0.182067\pi$
$991$	52.9389			1.68166			0.840831	+	0.541298i	$0.182067\pi$
$992$		0			0
$993$	16.1907			0.513796
$994$		0			0
$995$	−52.8567	+	52.8567i	−1.67567	+	1.67567i
$996$		0			0
$997$	3.97532	+	3.97532i	0.125900	+	0.125900i	0.767249	−	0.641349i	$-0.221625\pi$
$997$	3.97532	+	3.97532i	0.125900	+	0.125900i	−0.641349	+	0.767249i	$0.721625\pi$
$998$		0			0
$999$		−	10.6708i		−	0.337611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.j.a.177.5		40
4.3	odd	2		176.2.j.a.133.9	yes	40
8.3	odd	2		1408.2.j.a.353.5		40
8.5	even	2		1408.2.j.b.353.16		40
16.3	odd	4		176.2.j.a.45.9	✓	40
16.5	even	4		1408.2.j.b.1057.16		40
16.11	odd	4		1408.2.j.a.1057.5		40
16.13	even	4	inner	704.2.j.a.529.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.j.a.45.9	✓	40	16.3	odd	4
176.2.j.a.133.9	yes	40	4.3	odd	2
704.2.j.a.177.5		40	1.1	even	1	trivial
704.2.j.a.529.5		40	16.13	even	4	inner
1408.2.j.a.353.5		40	8.3	odd	2
1408.2.j.a.1057.5		40	16.11	odd	4
1408.2.j.b.353.16		40	8.5	even	2
1408.2.j.b.1057.16		40	16.5	even	4

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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34498 + 1.34498i) q^{3} +(2.40794 + 2.40794i) q^{5} +4.88654i q^{7} -0.617917i q^{9} +O(q^{10})\)	\(q+(-1.34498 + 1.34498i) q^{3} +(2.40794 + 2.40794i) q^{5} +4.88654i q^{7} -0.617917i q^{9} +(0.707107 + 0.707107i) q^{11} +(-0.532694 + 0.532694i) q^{13} -6.47725 q^{15} -1.53906 q^{17} +(5.98507 - 5.98507i) q^{19} +(-6.57227 - 6.57227i) q^{21} -0.294585i q^{23} +6.59638i q^{25} +(-3.20384 - 3.20384i) q^{27} +(4.94569 - 4.94569i) q^{29} +1.43981 q^{31} -1.90208 q^{33} +(-11.7665 + 11.7665i) q^{35} +(1.66532 + 1.66532i) q^{37} -1.43292i q^{39} +4.09275i q^{41} +(-4.95316 - 4.95316i) q^{43} +(1.48791 - 1.48791i) q^{45} +0.856661 q^{47} -16.8783 q^{49} +(2.07000 - 2.07000i) q^{51} +(-0.0858734 - 0.0858734i) q^{53} +3.40535i q^{55} +16.0995i q^{57} +(3.37953 + 3.37953i) q^{59} +(0.868220 - 0.868220i) q^{61} +3.01948 q^{63} -2.56539 q^{65} +(1.38054 - 1.38054i) q^{67} +(0.396210 + 0.396210i) q^{69} -2.83422i q^{71} +5.62070i q^{73} +(-8.87197 - 8.87197i) q^{75} +(-3.45530 + 3.45530i) q^{77} +10.1538 q^{79} +10.4719 q^{81} +(-5.47789 + 5.47789i) q^{83} +(-3.70597 - 3.70597i) q^{85} +13.3037i q^{87} -8.20417i q^{89} +(-2.60303 - 2.60303i) q^{91} +(-1.93651 + 1.93651i) q^{93} +28.8234 q^{95} -7.42322 q^{97} +(0.436933 - 0.436933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 16 q^{15} + 16 q^{19} - 24 q^{27} - 24 q^{31} - 24 q^{35} + 40 q^{47} - 40 q^{49} + 24 q^{51} + 8 q^{59} + 32 q^{61} - 16 q^{65} + 24 q^{67} + 32 q^{69} + 56 q^{75} - 32 q^{79} - 40 q^{81} - 40 q^{83} - 32 q^{85} + 16 q^{91} - 48 q^{93} + 48 q^{95}+O(q^{100}) \) 40 * q + 16 * q^15 + 16 * q^19 - 24 * q^27 - 24 * q^31 - 24 * q^35 + 40 * q^47 - 40 * q^49 + 24 * q^51 + 8 * q^59 + 32 * q^61 - 16 * q^65 + 24 * q^67 + 32 * q^69 + 56 * q^75 - 32 * q^79 - 40 * q^81 - 40 * q^83 - 32 * q^85 + 16 * q^91 - 48 * q^93 + 48 * q^95

Introduction

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