LMFDB - Embedded newform 693.2.cg.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(19,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("693.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.cg (of order $30$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	693.19
Dual form			693.2.cg.b.73.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30213 - 0.136859i) q^{2} +(-0.279493 + 0.0594081i) q^{4} +(1.77962 + 3.99709i) q^{5} +(2.52240 - 0.798438i) q^{7} +(-2.84624 + 0.924799i) q^{8} +O(q^{10})$	\(q+(1.30213 - 0.136859i) q^{2} +(-0.279493 + 0.0594081i) q^{4} +(1.77962 + 3.99709i) q^{5} +(2.52240 - 0.798438i) q^{7} +(-2.84624 + 0.924799i) q^{8} +(2.86433 + 4.96116i) q^{10} +(-0.649109 - 3.25248i) q^{11} +(1.19918 - 0.871257i) q^{13} +(3.17521 - 1.38488i) q^{14} +(-3.05753 + 1.36130i) q^{16} +(-0.604779 + 5.75408i) q^{17} +(4.73203 + 1.00582i) q^{19} +(-0.734851 - 1.01144i) q^{20} +(-1.29035 - 4.14631i) q^{22} +(-2.70321 + 4.68210i) q^{23} +(-9.46406 + 10.5109i) q^{25} +(1.44225 - 1.29861i) q^{26} +(-0.657559 + 0.373009i) q^{28} +(4.16203 + 1.35233i) q^{29} +(-0.402271 + 0.903515i) q^{31} +(1.38855 - 0.801680i) q^{32} +7.57531i q^{34} +(7.68035 + 8.66135i) q^{35} +(-4.26172 - 4.73312i) q^{37} +(6.29936 + 0.662089i) q^{38} +(-8.76174 - 9.73089i) q^{40} +(-0.855652 - 2.63342i) q^{41} -10.9025i q^{43} +(0.374645 + 0.870485i) q^{44} +(-2.87914 + 6.46665i) q^{46} +(0.686524 - 3.22984i) q^{47} +(5.72499 - 4.02796i) q^{49} +(-10.8849 + 14.9818i) q^{50} +(-0.283404 + 0.314751i) q^{52} +(6.37634 + 2.83893i) q^{53} +(11.8453 - 8.38274i) q^{55} +(-6.44095 + 4.60526i) q^{56} +(5.60457 + 1.19129i) q^{58} +(-1.61551 - 7.60037i) q^{59} +(-1.92803 + 0.858416i) q^{61} +(-0.400153 + 1.23154i) q^{62} +(7.11372 - 5.16842i) q^{64} +(5.61659 + 3.24274i) q^{65} +(-2.96412 - 5.13401i) q^{67} +(-0.172808 - 1.64416i) q^{68} +(11.1862 + 10.2270i) q^{70} +(6.18730 + 4.49534i) q^{71} +(-0.214776 + 0.0456520i) q^{73} +(-6.19707 - 5.57986i) q^{74} -1.38232 q^{76} +(-4.23422 - 7.68579i) q^{77} +(7.21557 - 0.758387i) q^{79} +(-10.8825 - 9.79863i) q^{80} +(-1.47457 - 3.31195i) q^{82} +(-0.639620 - 0.464711i) q^{83} +(-24.0759 + 7.82273i) q^{85} +(-1.49210 - 14.1964i) q^{86} +(4.85541 + 8.65705i) q^{88} +(-1.11283 - 0.642493i) q^{89} +(2.32917 - 3.15513i) q^{91} +(0.477375 - 1.46921i) q^{92} +(0.451908 - 4.29962i) q^{94} +(4.40085 + 20.7044i) q^{95} +(-7.50936 - 10.3358i) q^{97} +(6.90340 - 6.02843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 20 q^{4} + 10 q^{7}+O(q^{10}) $ 128 * q - 20 * q^4 + 10 * q^7	$ 128 q - 20 q^{4} + 10 q^{7} + 76 q^{22} - 12 q^{25} + 30 q^{28} - 18 q^{31} + 16 q^{37} - 90 q^{40} - 70 q^{46} + 58 q^{49} - 20 q^{58} - 30 q^{61} - 96 q^{64} - 40 q^{67} - 118 q^{70} - 90 q^{73} - 10 q^{79} + 24 q^{82} - 180 q^{85} - 56 q^{88} - 56 q^{91} - 120 q^{94}+O(q^{100}) $ 128 * q - 20 * q^4 + 10 * q^7 + 76 * q^22 - 12 * q^25 + 30 * q^28 - 18 * q^31 + 16 * q^37 - 90 * q^40 - 70 * q^46 + 58 * q^49 - 20 * q^58 - 30 * q^61 - 96 * q^64 - 40 * q^67 - 118 * q^70 - 90 * q^73 - 10 * q^79 + 24 * q^82 - 180 * q^85 - 56 * q^88 - 56 * q^91 - 120 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.30213	−	0.136859i	0.920742	−	0.0967739i	0.367716	−	0.929938i	$-0.380140\pi$
$2$	1.30213	−	0.136859i	0.920742	−	0.0967739i	0.553026	+	0.833164i	$0.313473\pi$
$3$		0			0
$3$		0			0
$4$	−0.279493	+	0.0594081i	−0.139747	+	0.0297040i
$5$	1.77962	+	3.99709i	0.795871	+	1.78756i	0.586951	+	0.809622i	$0.300328\pi$
$5$	1.77962	+	3.99709i	0.795871	+	1.78756i	0.208919	+	0.977933i	$0.433005\pi$
$6$		0			0
$7$	2.52240	−	0.798438i	0.953377	−	0.301781i
$7$	2.52240	−	0.798438i	0.953377	−	0.301781i
$8$	−2.84624	+	0.924799i	−1.00630	+	0.326966i
$9$		0			0
$10$	2.86433	+	4.96116i	0.905781	+	1.56886i
$11$	−0.649109	−	3.25248i	−0.195714	−	0.980661i
$11$	−0.649109	−	3.25248i	−0.195714	−	0.980661i
$12$		0			0
$13$	1.19918	−	0.871257i	0.332593	−	0.241643i	−0.408937	−	0.912563i	$-0.634100\pi$
$13$	1.19918	−	0.871257i	0.332593	−	0.241643i	0.741530	+	0.670919i	$0.234100\pi$
$14$	3.17521	−	1.38488i	0.848610	−	0.370125i
$15$		0			0
$16$	−3.05753	+	1.36130i	−0.764382	+	0.340325i
$17$	−0.604779	+	5.75408i	−0.146680	+	1.39557i	0.635299	+	0.772266i	$0.280877\pi$
$17$	−0.604779	+	5.75408i	−0.146680	+	1.39557i	−0.781979	+	0.623304i	$0.785790\pi$
$18$		0			0
$19$	4.73203	+	1.00582i	1.08560	+	0.230752i	0.715763	−	0.698344i	$-0.246079\pi$
$19$	4.73203	+	1.00582i	1.08560	+	0.230752i	0.369840	+	0.929095i	$0.379413\pi$
$20$	−0.734851	−	1.01144i	−0.164318	−	0.226164i
$21$		0			0
$22$	−1.29035	−	4.14631i	−0.275104	−	0.883996i
$23$	−2.70321	+	4.68210i	−0.563659	+	0.976286i	0.433514	+	0.901147i	$0.357273\pi$
$23$	−2.70321	+	4.68210i	−0.563659	+	0.976286i	−0.997173	+	0.0751391i	$0.976060\pi$
$24$		0			0
$25$	−9.46406	+	10.5109i	−1.89281	+	2.10218i
$26$	1.44225	−	1.29861i	0.282848	−	0.254678i
$27$		0			0
$28$	−0.657559	+	0.373009i	−0.124267	+	0.0704920i
$29$	4.16203	+	1.35233i	0.772869	+	0.251121i	0.668793	−	0.743449i	$-0.266811\pi$
$29$	4.16203	+	1.35233i	0.772869	+	0.251121i	0.104077	+	0.994569i	$0.466811\pi$
$30$		0			0
$31$	−0.402271	+	0.903515i	−0.0722499	+	0.162276i	−0.946060	−	0.323991i	$-0.894975\pi$
$31$	−0.402271	+	0.903515i	−0.0722499	+	0.162276i	0.873810	+	0.486267i	$0.161642\pi$
$32$	1.38855	−	0.801680i	0.245463	−	0.141718i
$33$		0			0
$34$			7.57531i			1.29916i
$35$	7.68035	+	8.66135i	1.29822	+	1.46404i
$36$		0			0
$37$	−4.26172	−	4.73312i	−0.700622	−	0.778120i	0.282853	−	0.959163i	$-0.408719\pi$
$37$	−4.26172	−	4.73312i	−0.700622	−	0.778120i	−0.983475	+	0.181043i	$0.942053\pi$
$38$	6.29936	+	0.662089i	1.02189	+	0.107405i
$39$		0			0
$40$	−8.76174	−	9.73089i	−1.38535	−	1.53859i
$41$	−0.855652	−	2.63342i	−0.133630	−	0.411272i	0.861744	−	0.507343i	$-0.169372\pi$
$41$	−0.855652	−	2.63342i	−0.133630	−	0.411272i	−0.995374	+	0.0960713i	$0.969372\pi$
$42$		0			0
$43$		−	10.9025i		−	1.66261i	−0.555817	−	0.831305i	$-0.687595\pi$
$43$		−	10.9025i		−	1.66261i	0.555817	−	0.831305i	$-0.312405\pi$
$44$	0.374645	+	0.870485i	0.0564799	+	0.131230i
$45$		0			0
$46$	−2.87914	+	6.46665i	−0.424506	+	0.953455i
$47$	0.686524	−	3.22984i	0.100140	−	0.471121i	−0.899290	−	0.437353i	$-0.855916\pi$
$47$	0.686524	−	3.22984i	0.100140	−	0.471121i	0.999430	−	0.0337679i	$-0.0107507\pi$
$48$		0			0
$49$	5.72499	−	4.02796i	0.817856	−	0.575423i
$50$	−10.8849	+	14.9818i	−1.53936	+	2.11874i
$51$		0			0
$52$	−0.283404	+	0.314751i	−0.0393010	+	0.0436482i
$53$	6.37634	+	2.83893i	0.875858	+	0.389957i	0.794886	−	0.606759i	$-0.207531\pi$
$53$	6.37634	+	2.83893i	0.875858	+	0.389957i	0.0809724	+	0.996716i	$0.474197\pi$
$54$		0			0
$55$	11.8453	−	8.38274i	1.59722	−	1.13033i
$56$	−6.44095	+	4.60526i	−0.860709	+	0.615404i
$57$		0			0
$58$	5.60457	+	1.19129i	0.735915	+	0.156424i
$59$	−1.61551	−	7.60037i	−0.210321	−	0.989484i	−0.948963	−	0.315386i	$-0.897866\pi$
$59$	−1.61551	−	7.60037i	−0.210321	−	0.989484i	0.738642	−	0.674098i	$-0.235467\pi$
$60$		0			0
$61$	−1.92803	+	0.858416i	−0.246859	+	0.109909i	−0.526437	−	0.850214i	$-0.676472\pi$
$61$	−1.92803	+	0.858416i	−0.246859	+	0.109909i	0.279577	+	0.960123i	$0.409806\pi$
$62$	−0.400153	+	1.23154i	−0.0508195	+	0.156406i
$63$		0			0
$64$	7.11372	−	5.16842i	0.889214	−	0.646052i
$65$	5.61659	+	3.24274i	0.696652	+	0.402212i
$66$		0			0
$67$	−2.96412	−	5.13401i	−0.362125	−	0.627220i	0.626185	−	0.779675i	$-0.284615\pi$
$67$	−2.96412	−	5.13401i	−0.362125	−	0.627220i	−0.988310	+	0.152455i	$0.951282\pi$
$68$	−0.172808	−	1.64416i	−0.0209560	−	0.199383i
$69$		0			0
$70$	11.1862	+	10.2270i	1.33700	+	1.22237i
$71$	6.18730	+	4.49534i	0.734298	+	0.533498i	0.890920	−	0.454160i	$-0.150061\pi$
$71$	6.18730	+	4.49534i	0.734298	+	0.533498i	−0.156622	+	0.987659i	$0.550061\pi$
$72$		0			0
$73$	−0.214776	+	0.0456520i	−0.0251376	+	0.00534317i	−0.220463	−	0.975395i	$-0.570757\pi$
$73$	−0.214776	+	0.0456520i	−0.0251376	+	0.00534317i	0.195326	+	0.980738i	$0.437424\pi$
$74$	−6.19707	−	5.57986i	−0.720394	−	0.648646i
$75$		0			0
$76$	−1.38232			−0.158563
$77$	−4.23422	−	7.68579i	−0.482534	−	0.875877i
$78$		0			0
$79$	7.21557	−	0.758387i	0.811816	−	0.0853252i	0.310482	−	0.950579i	$-0.399510\pi$
$79$	7.21557	−	0.758387i	0.811816	−	0.0853252i	0.501334	+	0.865254i	$0.332843\pi$
$80$	−10.8825	−	9.79863i	−1.21670	−	1.09552i
$81$		0			0
$82$	−1.47457	−	3.31195i	−0.162839	−	0.365743i
$83$	−0.639620	−	0.464711i	−0.0702074	−	0.0510087i	0.552128	−	0.833759i	$-0.313816\pi$
$83$	−0.639620	−	0.464711i	−0.0702074	−	0.0510087i	−0.622335	+	0.782751i	$0.713816\pi$
$84$		0			0
$85$	−24.0759	+	7.82273i	−2.61140	+	0.848494i
$86$	−1.49210	−	14.1964i	−0.160897	−	1.53083i
$87$		0			0
$88$	4.85541	+	8.65705i	0.517589	+	0.922845i
$89$	−1.11283	−	0.642493i	−0.117960	−	0.0681041i	0.439859	−	0.898067i	$-0.355028\pi$
$89$	−1.11283	−	0.642493i	−0.117960	−	0.0681041i	−0.557819	+	0.829963i	$0.688362\pi$
$90$		0			0
$91$	2.32917	−	3.15513i	0.244164	−	0.330748i
$92$	0.477375	−	1.46921i	0.0497697	−	0.153175i
$93$		0			0
$94$	0.451908	−	4.29962i	0.0466108	−	0.443472i
$95$	4.40085	+	20.7044i	0.451518	+	2.12422i
$96$		0			0
$97$	−7.50936	−	10.3358i	−0.762460	−	1.04944i	−0.997005	−	0.0773313i	$-0.975360\pi$
$97$	−7.50936	−	10.3358i	−0.762460	−	1.04944i	0.234545	−	0.972105i	$-0.424640\pi$
$98$	6.90340	−	6.02843i	0.697349	−	0.608963i
$99$		0			0
$100$	2.02071	−	3.49997i	0.202071	−	0.349997i
$101$	3.46566	+	1.54301i	0.344846	+	0.153535i	0.571849	−	0.820359i	$-0.306226\pi$
$101$	3.46566	+	1.54301i	0.344846	+	0.153535i	−0.227003	+	0.973894i	$0.572893\pi$
$102$		0			0
$103$	8.25201	−	7.43014i	0.813094	−	0.732114i	−0.153576	−	0.988137i	$-0.549079\pi$
$103$	8.25201	−	7.43014i	0.813094	−	0.732114i	0.966671	+	0.256023i	$0.0824124\pi$
$104$	−2.60742	+	3.58881i	−0.255679	+	0.351912i
$105$		0			0
$106$	8.69134	+	2.82399i	0.844177	+	0.274290i
$107$	2.31141	−	10.8743i	0.223452	−	1.05126i	−0.713190	−	0.700971i	$-0.752750\pi$
$107$	2.31141	−	10.8743i	0.223452	−	1.05126i	0.936642	−	0.350288i	$-0.113916\pi$
$108$		0			0
$109$	−5.45158	+	3.14747i	−0.522167	+	0.301473i	−0.737821	−	0.674997i	$-0.764145\pi$
$109$	−5.45158	+	3.14747i	−0.522167	+	0.301473i	0.215654	+	0.976470i	$0.430812\pi$
$110$	14.2769	−	12.5365i	1.36124	−	1.19531i
$111$		0			0
$112$	−6.62539	+	5.87499i	−0.626040	+	0.555134i
$113$	−0.713520	−	2.19599i	−0.0671223	−	0.206581i	0.911870	−	0.410480i	$-0.134639\pi$
$113$	−0.713520	−	2.19599i	−0.0671223	−	0.206581i	−0.978992	+	0.203899i	$0.934639\pi$
$114$		0			0
$115$	−23.5255	−	2.47263i	−2.19376	−	0.230574i
$116$	−1.24360	−	0.130707i	−0.115465	−	0.0121359i
$117$		0			0
$118$	−3.14378	−	9.67555i	−0.289408	−	0.890706i
$119$	3.06879	+	14.9970i	0.281315	+	1.37477i
$120$		0			0
$121$	−10.1573	+	4.22243i	−0.923392	+	0.383857i
$122$	−2.39306	+	1.38163i	−0.216658	+	0.125087i
$123$		0			0
$124$	0.0587558	−	0.276424i	0.00527642	−	0.0248236i
$125$	−38.0494	−	12.3630i	−3.40324	−	1.10578i
$126$		0			0
$127$	0.803438	−	1.10584i	0.0712936	−	0.0981272i	−0.771881	−	0.635767i	$-0.780684\pi$
$127$	0.803438	−	1.10584i	0.0712936	−	0.0981272i	0.843175	+	0.537640i	$0.180684\pi$
$128$	6.17256	−	5.55779i	0.545582	−	0.491244i
$129$		0			0
$130$	7.75731	+	3.45377i	0.680361	+	0.302916i
$131$	5.90044	−	10.2199i	0.515524	−	0.892914i	−0.484314	−	0.874894i	$-0.660931\pi$
$131$	5.90044	−	10.2199i	0.515524	−	0.892914i	0.999838	−	0.0180194i	$-0.00573606\pi$
$132$		0			0
$133$	12.7392	−	1.24115i	1.10463	−	0.107621i
$134$	−4.56230	−	6.27947i	−0.394123	−	0.542463i
$135$		0			0
$136$	−3.60003	−	16.9368i	−0.308700	−	1.45232i
$137$	0.602303	−	5.73053i	0.0514582	−	0.489592i	−0.938194	−	0.346109i	$-0.887503\pi$
$137$	0.602303	−	5.73053i	0.0514582	−	0.489592i	0.989653	−	0.143484i	$-0.0458304\pi$
$138$		0			0
$139$	−4.25808	+	13.1050i	−0.361165	+	1.11155i	0.591182	+	0.806538i	$0.298661\pi$
$139$	−4.25808	+	13.1050i	−0.361165	+	1.11155i	−0.952348	+	0.305015i	$0.901339\pi$
$140$	−2.66116	−	1.96451i	−0.224909	−	0.166032i
$141$		0			0
$142$	8.67188	+	5.00671i	0.727728	+	0.420154i
$143$	−3.61215	−	3.33478i	−0.302063	−	0.278869i
$144$		0			0
$145$	2.00146	+	19.0427i	0.166212	+	1.58141i
$146$	−0.273417	+	0.0888387i	−0.0226282	+	0.00735234i
$147$		0			0
$148$	1.47231	+	1.06969i	0.121023	+	0.0879282i
$149$	−0.559324	−	1.25626i	−0.0458216	−	0.102917i	0.889184	−	0.457549i	$-0.151273\pi$
$149$	−0.559324	−	1.25626i	−0.0458216	−	0.102917i	−0.935006	+	0.354632i	$0.884606\pi$
$150$		0			0
$151$	−8.81457	−	7.93667i	−0.717319	−	0.645877i	0.227383	−	0.973805i	$-0.426983\pi$
$151$	−8.81457	−	7.93667i	−0.717319	−	0.645877i	−0.944703	+	0.327928i	$0.893650\pi$
$152$	−14.3987	+	1.51336i	−1.16789	+	0.122750i
$153$		0			0
$154$	−6.56536	−	9.42838i	−0.529052	−	0.759760i
$155$	−4.32732			−0.347579
$156$		0			0
$157$	−4.74901	−	4.27603i	−0.379012	−	0.341264i	0.457503	−	0.889208i	$-0.348744\pi$
$157$	−4.74901	−	4.27603i	−0.379012	−	0.341264i	−0.836515	+	0.547944i	$0.815411\pi$
$158$	9.29180	−	1.97503i	0.739216	−	0.157125i
$159$		0			0
$160$	5.67548	+	4.12348i	0.448686	+	0.325990i
$161$	−3.08021	+	13.9685i	−0.242755	+	1.10087i
$162$		0			0
$163$	2.06379	+	19.6357i	0.161649	+	1.53798i	0.711478	+	0.702708i	$0.248026\pi$
$163$	2.06379	+	19.6357i	0.161649	+	1.53798i	−0.549830	+	0.835277i	$0.685307\pi$
$164$	0.395595	+	0.685191i	0.0308908	+	0.0535044i
$165$		0			0
$166$	−0.896466	−	0.517575i	−0.0695793	−	0.0401716i
$167$	−1.57383	+	1.14346i	−0.121787	+	0.0884834i	−0.647011	−	0.762480i	$-0.723981\pi$
$167$	−1.57383	+	1.14346i	−0.121787	+	0.0884834i	0.525224	+	0.850964i	$0.323981\pi$
$168$		0			0
$169$	−3.33827	+	10.2741i	−0.256790	+	0.790319i
$170$	−30.2792	+	13.4812i	−2.32231	+	1.03396i
$171$		0			0
$172$	0.647694	+	3.04716i	0.0493862	+	0.232344i
$173$	13.4792	+	2.86510i	1.02481	+	0.217830i	0.689505	−	0.724281i	$-0.257828\pi$
$173$	13.4792	+	2.86510i	1.02481	+	0.217830i	0.335302	+	0.942111i	$0.391162\pi$
$174$		0			0
$175$	−15.4798	+	34.0692i	−1.17016	+	2.57539i
$176$	6.41227	+	9.06093i	0.483343	+	0.682993i
$177$		0			0
$178$	−1.53698	−	0.684306i	−0.115201	−	0.0512909i
$179$	−5.52514	+	6.13629i	−0.412968	+	0.458648i	−0.913361	−	0.407151i	$-0.866522\pi$
$179$	−5.52514	+	6.13629i	−0.412968	+	0.458648i	0.500393	+	0.865799i	$0.333189\pi$
$180$		0			0
$181$	13.2023	−	18.1714i	0.981321	−	1.35067i	0.0452064	−	0.998978i	$-0.485605\pi$
$181$	13.2023	−	18.1714i	0.981321	−	1.35067i	0.936115	−	0.351695i	$-0.114395\pi$
$182$	2.60107	−	4.42715i	0.192804	−	0.328162i
$183$		0			0
$184$	3.36399	−	15.8263i	0.247996	−	1.16673i
$185$	11.3345	−	25.4577i	0.833327	−	1.87168i
$186$		0			0
$187$	19.1076	−	1.76799i	1.39729	−	0.129288i
$188$			0.943504i			0.0688121i
$189$		0			0
$190$	8.56404	+	26.3574i	0.621301	+	1.91217i
$191$	−4.41115	−	4.89908i	−0.319180	−	0.354485i	0.562109	−	0.827063i	$-0.309990\pi$
$191$	−4.41115	−	4.89908i	−0.319180	−	0.354485i	−0.881289	+	0.472578i	$0.843323\pi$
$192$		0			0
$193$	16.6624	+	1.75129i	1.19939	+	0.126061i	0.683080	−	0.730343i	$-0.260640\pi$
$193$	16.6624	+	1.75129i	1.19939	+	0.126061i	0.516306	+	0.856404i	$0.327307\pi$
$194$	−11.1927	−	12.4307i	−0.803587	−	0.892474i
$195$		0			0
$196$	−1.36080	+	1.46590i	−0.0972001	+	0.104707i
$197$			22.1951i			1.58134i	0.612246	+	0.790668i	$0.290266\pi$
$197$			22.1951i			1.58134i	−0.612246	+	0.790668i	$0.709734\pi$
$198$		0			0
$199$	5.54103	−	3.19912i	0.392793	−	0.226779i	−0.290576	−	0.956852i	$-0.593847\pi$
$199$	5.54103	−	3.19912i	0.392793	−	0.226779i	0.683370	+	0.730072i	$0.260514\pi$
$200$	17.2165	−	38.6689i	1.21739	−	2.73430i
$201$		0			0
$202$	4.72390	+	1.53489i	0.332373	+	0.107994i
$203$	11.5780	+	0.0879796i	0.812620	+	0.00617495i
$204$		0			0
$205$	9.00331	−	8.10662i	0.628819	−	0.566191i
$206$	9.72827	−	10.8043i	0.677801	−	0.752774i
$207$		0			0
$208$	−2.48049	+	4.29634i	−0.171991	+	0.297898i
$209$	0.199826	−	16.0438i	0.0138223	−	1.10977i
$210$		0			0
$211$	4.08323	+	5.62009i	0.281101	+	0.386903i	0.926098	−	0.377282i	$-0.123141\pi$
$211$	4.08323	+	5.62009i	0.281101	+	0.386903i	−0.644997	+	0.764185i	$0.723141\pi$
$212$	−1.95080	−	0.414655i	−0.133981	−	0.0284786i
$213$		0			0
$214$	1.52150	−	14.4761i	0.104007	−	0.989563i
$215$	43.5781	−	19.4022i	2.97201	−	1.32322i
$216$		0			0
$217$	−0.293286	+	2.60021i	−0.0199096	+	0.176514i
$218$	−6.66789	+	4.84451i	−0.451606	+	0.328111i
$219$		0			0
$220$	−2.81268	+	3.04662i	−0.189631	+	0.205403i
$221$	4.28805	+	7.42712i	0.288445	+	0.499602i
$222$		0			0
$223$	13.0369	−	4.23595i	0.873016	−	0.283660i	0.161961	−	0.986797i	$-0.448218\pi$
$223$	13.0369	−	4.23595i	0.873016	−	0.283660i	0.711054	+	0.703137i	$0.248218\pi$
$224$	2.86238	−	3.13083i	0.191251	−	0.209187i
$225$		0			0
$226$	−1.22963	−	2.76180i	−0.0817940	−	0.183712i
$227$	−18.5909	+	3.95161i	−1.23392	+	0.262278i	−0.778298	−	0.627895i	$-0.783917\pi$
$227$	−18.5909	+	3.95161i	−1.23392	+	0.262278i	−0.455622	+	0.890173i	$0.650583\pi$
$228$		0			0
$229$	17.6142	−	1.85133i	1.16398	−	0.122339i	0.497229	−	0.867619i	$-0.334351\pi$
$229$	17.6142	−	1.85133i	1.16398	−	0.122339i	0.666751	+	0.745280i	$0.267684\pi$
$230$	−30.9716			−2.04221
$231$		0			0
$232$	−13.0968			−0.859844
$233$	−26.4035	+	2.77512i	−1.72975	+	0.181804i	−0.916481	−	0.400079i	$-0.868983\pi$
$233$	−26.4035	+	2.77512i	−1.72975	+	0.181804i	−0.813272	+	0.581883i	$0.802316\pi$
$234$		0			0
$235$	14.1317	−	3.00379i	0.921853	−	0.195946i
$236$	0.903047	+	2.02828i	0.0587834	+	0.132030i
$237$		0			0
$238$	6.04842	+	19.1080i	0.392061	+	1.23859i
$239$	−18.6490	+	6.05944i	−1.20631	+	0.391953i	−0.842077	−	0.539357i	$-0.818667\pi$
$239$	−18.6490	+	6.05944i	−1.20631	+	0.391953i	−0.364229	+	0.931310i	$0.618667\pi$
$240$		0			0
$241$	−8.61712	−	14.9253i	−0.555077	−	0.961422i	−0.997898	−	0.0648115i	$-0.979355\pi$
$241$	−8.61712	−	14.9253i	−0.555077	−	0.961422i	0.442820	−	0.896610i	$-0.353978\pi$
$242$	−12.6482	+	6.88826i	−0.813059	+	0.442794i
$243$		0			0
$244$	0.487875	−	0.354462i	0.0312330	−	0.0226921i
$245$	26.2885	+	15.7151i	1.67951	+	1.00400i
$246$		0			0
$247$	6.55090	−	2.91665i	0.416824	−	0.185582i
$248$	0.309389	−	2.94364i	0.0196462	−	0.186921i
$249$		0			0
$250$	−51.2371	−	10.8908i	−3.24052	−	0.688794i
$251$	14.1725	+	19.5068i	0.894561	+	1.23126i	0.972171	+	0.234274i	$0.0752711\pi$
$251$	14.1725	+	19.5068i	0.894561	+	1.23126i	−0.0776099	+	0.996984i	$0.524729\pi$
$252$		0			0
$253$	16.9831	+	5.75297i	1.06772	+	0.361686i
$254$	0.894834	−	1.54990i	0.0561469	−	0.0972492i
$255$		0			0
$256$	−4.49057	+	4.98728i	−0.280660	+	0.311705i
$257$	−14.9941	+	13.5008i	−0.935307	+	0.842155i	−0.987682	−	0.156473i	$-0.949988\pi$
$257$	−14.9941	+	13.5008i	−0.935307	+	0.842155i	0.0523748	+	0.998627i	$0.483321\pi$
$258$		0			0
$259$	−14.5289	−	8.53609i	−0.902779	−	0.530407i
$260$	−1.76244	−	0.572652i	−0.109302	−	0.0355144i
$261$		0			0
$262$	6.28444	−	14.1151i	0.388254	−	0.872033i
$263$	1.31616	−	0.759883i	0.0811576	−	0.0468564i	−0.458872	−	0.888502i	$-0.651746\pi$
$263$	1.31616	−	0.759883i	0.0811576	−	0.0468564i	0.540030	+	0.841646i	$0.318413\pi$
$264$		0			0
$265$			30.5391i			1.87600i
$266$	16.4181	−	3.35960i	1.00666	−	0.205990i
$267$		0			0
$268$	1.13345	+	1.25883i	0.0692367	+	0.0768952i
$269$	−14.9688	−	1.57329i	−0.912665	−	0.0959249i	−0.363457	−	0.931611i	$-0.618404\pi$
$269$	−14.9688	−	1.57329i	−0.912665	−	0.0959249i	−0.549208	+	0.835686i	$0.685070\pi$
$270$		0			0
$271$	1.51662	+	1.68438i	0.0921281	+	0.102319i	0.787446	−	0.616384i	$-0.211403\pi$
$271$	1.51662	+	1.68438i	0.0921281	+	0.102319i	−0.695318	+	0.718702i	$0.744736\pi$
$272$	−5.98390	−	18.4166i	−0.362827	−	1.11667i
$273$		0			0
$274$		−	7.54430i		−	0.455768i
$275$	40.3298	+	23.9590i	2.43198	+	1.44478i
$276$		0			0
$277$	4.40965	−	9.90423i	0.264950	−	0.595087i	−0.731257	−	0.682102i	$-0.761066\pi$
$277$	4.40965	−	9.90423i	0.264950	−	0.595087i	0.996207	+	0.0870147i	$0.0277327\pi$
$278$	−3.75101	+	17.6471i	−0.224971	+	1.05840i
$279$		0			0
$280$	−29.8701	−	17.5495i	−1.78508	−	1.04878i
$281$	2.47868	−	3.41161i	0.147866	−	0.203520i	−0.728659	−	0.684877i	$-0.759856\pi$
$281$	2.47868	−	3.41161i	0.147866	−	0.203520i	0.876525	+	0.481357i	$0.159856\pi$
$282$		0			0
$283$	−13.4313	+	14.9169i	−0.798406	+	0.886720i	−0.995606	−	0.0936434i	$-0.970149\pi$
$283$	−13.4313	+	14.9169i	−0.798406	+	0.886720i	0.197200	+	0.980363i	$0.436815\pi$
$284$	−1.99637	−	0.888840i	−0.118463	−	0.0527429i
$285$		0			0
$286$	−5.15987	−	3.84795i	−0.305110	−	0.227534i
$287$	−4.26092	−	5.95936i	−0.251514	−	0.351770i
$288$		0			0
$289$	−16.1152	−	3.42540i	−0.947954	−	0.201494i
$290$	5.21232	+	24.5220i	0.306078	+	1.43998i
$291$		0			0
$292$	0.0573163	−	0.0255188i	0.00335418	−	0.00149338i
$293$	0.210034	−	0.646419i	0.0122703	−	0.0377642i	−0.944734	−	0.327838i	$-0.893680\pi$
$293$	0.210034	−	0.646419i	0.0122703	−	0.0377642i	0.957004	+	0.290074i	$0.0936799\pi$
$294$		0			0
$295$	27.5044	−	19.9831i	1.60137	−	1.16346i
$296$	16.5071	+	9.53035i	0.959453	+	0.553940i
$297$		0			0
$298$	−0.900241	−	1.55926i	−0.0521496	−	0.0903257i
$299$	0.837669	+	7.96989i	0.0484437	+	0.460911i
$300$		0			0
$301$	−8.70494	−	27.5003i	−0.501744	−	1.58509i
$302$	−12.5639	−	9.12819i	−0.722970	−	0.525269i
$303$		0			0
$304$	−15.8375	+	3.36637i	−0.908346	+	0.193075i
$305$	−6.86234	−	6.17888i	−0.392936	−	0.353801i
$306$		0			0
$307$	−17.4703			−0.997085			−0.498543	−	0.866865i	$-0.666131\pi$
$307$	−17.4703			−0.997085			−0.498543	+	0.866865i	$0.666131\pi$
$308$	1.64003	+	1.89658i	0.0934495	+	0.108068i
$309$		0			0
$310$	−5.63472	+	0.592233i	−0.320031	+	0.0336366i
$311$	−8.65888	−	7.79649i	−0.491000	−	0.442098i	0.386064	−	0.922472i	$-0.373834\pi$
$311$	−8.65888	−	7.79649i	−0.491000	−	0.442098i	−0.877064	+	0.480374i	$0.840501\pi$
$312$		0			0
$313$	−7.87315	−	17.6834i	−0.445017	−	0.999524i	−0.987233	−	0.159285i	$-0.949081\pi$
$313$	−7.87315	−	17.6834i	−0.445017	−	0.999524i	0.542216	−	0.840239i	$-0.317586\pi$
$314$	−6.76902	−	4.91798i	−0.381998	−	0.277538i
$315$		0			0
$316$	−1.97165	+	0.640627i	−0.110914	+	0.0360381i
$317$	−2.97625	−	28.3171i	−0.167163	−	1.59045i	−0.680819	−	0.732452i	$-0.738376\pi$
$317$	−2.97625	−	28.3171i	−0.167163	−	1.59045i	0.513656	−	0.857996i	$-0.328291\pi$
$318$		0			0
$319$	1.69681	−	14.4147i	0.0950030	−	0.807071i
$320$	33.3184	+	19.2364i	1.86255	+	1.07535i
$321$		0			0
$322$	−2.09911	+	18.6103i	−0.116979	+	1.03711i
$323$	−8.64943	+	26.6202i	−0.481267	+	1.48119i
$324$		0			0
$325$	−2.19144	+	20.8501i	−0.121559	+	1.15656i
$326$	5.37464	+	25.2857i	0.297674	+	1.40044i
$327$		0			0
$328$	4.87078	+	6.70405i	0.268944	+	0.370169i
$329$	−0.847143	−	8.69510i	−0.0467045	−	0.479376i
$330$		0			0
$331$	−0.918494	+	1.59088i	−0.0504850	+	0.0874426i	−0.890164	−	0.455641i	$-0.849410\pi$
$331$	−0.918494	+	1.59088i	−0.0504850	+	0.0874426i	0.839679	+	0.543084i	$0.182743\pi$
$332$	0.206377	+	0.0918849i	0.0113264	+	0.00504284i
$333$		0			0
$334$	−1.89284	+	1.70432i	−0.103572	+	0.0932562i
$335$	15.2461	−	20.9845i	0.832985	−	1.14650i
$336$		0			0
$337$	−30.4650	−	9.89869i	−1.65954	−	0.539216i	−0.678762	−	0.734359i	$-0.737483\pi$
$337$	−30.4650	−	9.89869i	−1.65954	−	0.539216i	−0.980775	+	0.195143i	$0.937483\pi$
$338$	−2.94074	+	13.8351i	−0.159955	+	0.752530i
$339$		0			0
$340$	6.26431	−	3.61670i	0.339730	−	0.196143i
$341$	3.19979	+	0.721900i	0.173278	+	0.0390931i
$342$		0			0
$343$	11.2246	−	14.7312i	0.606073	−	0.795409i
$344$	10.0826	+	31.0310i	0.543616	+	1.67308i
$345$		0			0
$346$	17.9438	+	1.88597i	0.964664	+	0.101390i
$347$	13.1253	+	1.37952i	0.704602	+	0.0740566i	0.450051	−	0.893003i	$-0.351406\pi$
$347$	13.1253	+	1.37952i	0.704602	+	0.0740566i	0.254551	+	0.967059i	$0.418072\pi$
$348$		0			0
$349$	6.69435	+	20.6031i	0.358341	+	1.10286i	0.954047	+	0.299657i	$0.0968721\pi$
$349$	6.69435	+	20.6031i	0.358341	+	1.10286i	−0.595707	+	0.803202i	$0.703128\pi$
$350$	−15.4940	+	46.4809i	−0.828190	+	2.48451i
$351$		0			0
$352$	−3.50877	−	3.99586i	−0.187018	−	0.212980i
$353$	7.28846	−	4.20800i	0.387926	−	0.223969i	−0.293335	−	0.956010i	$-0.594765\pi$
$353$	7.28846	−	4.20800i	0.387926	−	0.223969i	0.681261	+	0.732041i	$0.261432\pi$
$354$		0			0
$355$	−6.95724	+	32.7312i	−0.369252	+	1.73719i
$356$	0.349198	+	0.113461i	0.0185074	+	0.00601343i
$357$		0			0
$358$	−6.35462	+	8.74639i	−0.335852	+	0.462261i
$359$	4.67780	−	4.21191i	0.246885	−	0.222296i	−0.536392	−	0.843969i	$-0.680213\pi$
$359$	4.67780	−	4.21191i	0.246885	−	0.222296i	0.783277	+	0.621673i	$0.213547\pi$
$360$		0			0
$361$	4.02308	+	1.79119i	0.211741	+	0.0942733i
$362$	14.7042	−	25.4684i	0.772834	−	1.33859i
$363$		0			0
$364$	−0.463547	+	1.02021i	−0.0242965	+	0.0534735i
$365$	−0.564695	−	0.777236i	−0.0295575	−	0.0406824i
$366$		0			0
$367$	2.17966	+	10.2545i	0.113778	+	0.535281i	0.997708	+	0.0676633i	$0.0215544\pi$
$367$	2.17966	+	10.2545i	0.113778	+	0.535281i	−0.883931	+	0.467618i	$0.845112\pi$
$368$	1.89141	−	17.9955i	0.0985964	−	0.938082i
$369$		0			0
$370$	11.2748	−	34.7003i	0.586150	−	1.80398i
$371$	18.3504	+	2.06980i	0.952705	+	0.107459i
$372$		0			0
$373$	13.6701	+	7.89241i	0.707808	+	0.408653i	0.810249	−	0.586086i	$-0.199332\pi$
$373$	13.6701	+	7.89241i	0.707808	+	0.408653i	−0.102441	+	0.994739i	$0.532665\pi$
$374$	24.6386	−	4.91720i	1.27403	−	0.254262i
$375$		0			0
$376$	1.03294	+	9.82780i	0.0532700	+	0.506830i
$377$	6.16926	−	2.00451i	0.317733	−	0.103238i
$378$		0			0
$379$	−10.5460	−	7.66212i	−0.541712	−	0.393577i	0.283009	−	0.959117i	$-0.408667\pi$
$379$	−10.5460	−	7.66212i	−0.541712	−	0.393577i	−0.824720	+	0.565541i	$0.808667\pi$
$380$	−2.46001	−	5.52528i	−0.126196	−	0.283441i
$381$		0			0
$382$	−6.41436	−	5.77552i	−0.328187	−	0.295501i
$383$	−30.9414	+	3.25207i	−1.58103	+	0.166173i	−0.853942	−	0.520368i	$-0.825795\pi$
$383$	−30.9414	+	3.25207i	−1.58103	+	0.166173i	−0.727091	+	0.686541i	$0.759128\pi$
$384$		0			0
$385$	23.1855	−	30.6024i	1.18164	−	1.55964i
$386$	21.9362			1.11653
$387$		0			0
$388$	2.71284	+	2.44265i	0.137724	+	0.124007i
$389$	−8.05779	+	1.71274i	−0.408546	+	0.0868392i	−0.407601	−	0.913160i	$-0.633634\pi$
$389$	−8.05779	+	1.71274i	−0.408546	+	0.0868392i	−0.000945824		1.00000i	$0.500301\pi$
$390$		0			0
$391$	−25.3064	−	18.3862i	−1.27980	−	0.929828i
$392$	−12.5696	+	16.7590i	−0.634863	+	0.846458i
$393$		0			0
$394$	3.03760	+	28.9008i	0.153032	+	1.45600i
$395$	15.8723	+	27.4917i	0.798624	+	1.38326i
$396$		0			0
$397$	20.7345	+	11.9711i	1.04063	+	0.600810i	0.920013	−	0.391889i	$-0.128178\pi$
$397$	20.7345	+	11.9711i	1.04063	+	0.600810i	0.120621	+	0.992699i	$0.461512\pi$
$398$	6.77729	−	4.92399i	0.339715	−	0.246817i
$399$		0			0
$400$	14.6281	−	45.0208i	0.731407	−	2.25104i
$401$	−17.9480	+	7.99096i	−0.896280	+	0.399049i	−0.802575	−	0.596551i	$-0.796538\pi$
$401$	−17.9480	+	7.99096i	−0.896280	+	0.399049i	−0.0937043	+	0.995600i	$0.529871\pi$
$402$		0			0
$403$	0.304798	+	1.43396i	0.0151831	+	0.0714307i
$404$	−1.06030	−	0.225373i	−0.0527517	−	0.0112127i
$405$		0			0
$406$	15.0881	−	1.47000i	0.748811	−	0.0729548i
$407$	−12.6281	+	16.9335i	−0.625951	+	0.839362i
$408$		0			0
$409$	32.4450	+	14.4454i	1.60430	+	0.714280i	0.996792	−	0.0800331i	$-0.0255026\pi$
$409$	32.4450	+	14.4454i	1.60430	+	0.714280i	0.607508	+	0.794314i	$0.292169\pi$
$410$	10.6140	−	11.7880i	0.524187	−	0.582169i
$411$		0			0
$412$	−1.86497	+	2.56691i	−0.0918804	+	0.126462i
$413$	−10.1434	−	17.8813i	−0.499124	−	0.879881i
$414$		0			0
$415$	0.719213	−	3.38363i	0.0353048	−	0.166096i
$416$	0.966656	−	2.17114i	0.0473942	−	0.106449i
$417$		0			0
$418$	−1.93553	−	20.9183i	−0.0946700	−	1.02315i
$419$			21.5828i			1.05439i	0.849745	+	0.527194i	$0.176756\pi$
$419$			21.5828i			1.05439i	−0.849745	+	0.527194i	$0.823244\pi$
$420$		0			0
$421$	3.62797	+	11.1658i	0.176817	+	0.544186i	0.999712	−	0.0240076i	$-0.00764260\pi$
$421$	3.62797	+	11.1658i	0.176817	+	0.544186i	−0.822895	+	0.568193i	$0.807643\pi$
$422$	6.08604	+	6.75924i	0.296264	+	0.329034i
$423$		0			0
$424$	−20.7740	−	2.18344i	−1.00888	−	0.106037i
$425$	−54.7570	−	60.8138i	−2.65610	−	2.94990i
$426$		0			0
$427$	−4.17788	+	3.70468i	−0.202182	+	0.179282i
$428$			3.17661i			0.153547i
$429$		0			0
$430$	54.0889	−	31.2282i	2.60840	−	1.50596i
$431$	−6.54991	+	14.7113i	−0.315498	+	0.708620i	−0.999788	−	0.0205897i	$-0.993446\pi$
$431$	−6.54991	+	14.7113i	−0.315498	+	0.708620i	0.684290	+	0.729210i	$0.260112\pi$
$432$		0			0
$433$	38.1354	+	12.3909i	1.83267	+	0.595471i	0.999071	+	0.0431017i	$0.0137239\pi$
$433$	38.1354	+	12.3909i	1.83267	+	0.595471i	0.833600	+	0.552369i	$0.186276\pi$
$434$	−0.0260332	+	3.42594i	−0.00124963	+	0.164451i
$435$		0			0
$436$	1.33669	−	1.20356i	0.0640160	−	0.0576403i
$437$	−17.5011	+	19.4369i	−0.837190	+	0.929793i
$438$		0			0
$439$	2.05040	−	3.55140i	0.0978604	−	0.169499i	−0.812938	−	0.582350i	$-0.802133\pi$
$439$	2.05040	−	3.55140i	0.0978604	−	0.169499i	0.910799	+	0.412851i	$0.135467\pi$
$440$	−25.9623	+	34.8138i	−1.23770	+	1.65968i
$441$		0			0
$442$	6.60005	+	9.08419i	0.313932	+	0.432091i
$443$	2.95056	+	0.627161i	0.140185	+	0.0297973i	0.277470	−	0.960734i	$-0.410504\pi$
$443$	2.95056	+	0.627161i	0.140185	+	0.0297973i	−0.137285	+	0.990532i	$0.543837\pi$
$444$		0			0
$445$	0.587689	−	5.59148i	0.0278591	−	0.265062i
$446$	16.3960	−	7.29995i	0.776371	−	0.345663i
$447$		0			0
$448$	13.8170	−	18.7167i	0.652790	−	0.884280i
$449$	7.58618	−	5.51168i	0.358014	−	0.260112i	−0.394209	−	0.919021i	$-0.628981\pi$
$449$	7.58618	−	5.51168i	0.358014	−	0.260112i	0.752223	+	0.658908i	$0.228981\pi$
$450$		0			0
$451$	−8.00976	+	4.49237i	−0.377165	+	0.211538i
$452$	0.329883	+	0.571374i	0.0155164	+	0.0268752i
$453$		0			0
$454$	−23.6669	+	7.68983i	−1.11074	+	0.360901i
$455$	16.7564	+	3.69498i	0.785552	+	0.173223i
$456$		0			0
$457$	−5.86693	−	13.1773i	−0.274443	−	0.616410i	0.722764	−	0.691095i	$-0.242871\pi$
$457$	−5.86693	−	13.1773i	−0.274443	−	0.616410i	−0.997207	+	0.0746851i	$0.976205\pi$
$458$	22.6826	−	4.82133i	1.05989	−	0.225286i
$459$		0			0
$460$	6.72211	−	0.706522i	0.313420	−	0.0329418i
$461$	11.6850			0.544224			0.272112	−	0.962266i	$-0.412278\pi$
$461$	11.6850			0.544224			0.272112	+	0.962266i	$0.412278\pi$
$462$		0			0
$463$	−8.02783			−0.373085			−0.186542	−	0.982447i	$-0.559728\pi$
$463$	−8.02783			−0.373085			−0.186542	+	0.982447i	$0.559728\pi$
$464$	−14.5664	+	1.53099i	−0.676230	+	0.0710746i
$465$		0			0
$466$	−34.0009	+	7.22712i	−1.57506	+	0.334790i
$467$	−2.32256	−	5.21656i	−0.107475	−	0.241393i	0.851800	−	0.523868i	$-0.175511\pi$
$467$	−2.32256	−	5.21656i	−0.107475	−	0.241393i	−0.959275	+	0.282474i	$0.908845\pi$
$468$		0			0
$469$	−11.5759	−	10.5834i	−0.534525	−	0.488694i
$470$	17.9902	−	5.84538i	0.829827	−	0.269627i
$471$		0			0
$472$	11.6269	+	20.1385i	0.535173	+	0.926948i
$473$	−35.4601	+	7.07688i	−1.63046	+	0.325395i
$474$		0			0
$475$	−55.3564	+	40.2188i	−2.53992	+	1.84536i
$476$	−1.74865	−	4.00924i	−0.0801491	−	0.183763i
$477$		0			0
$478$	−23.4541	+	10.4424i	−1.07277	+	0.477626i
$479$	−2.40548	+	22.8866i	−0.109909	+	1.04572i	0.791032	+	0.611775i	$0.209544\pi$
$479$	−2.40548	+	22.8866i	−0.109909	+	1.04572i	−0.900941	+	0.433942i	$0.857122\pi$
$480$		0			0
$481$	−9.23435	−	1.96282i	−0.421050	−	0.0894969i
$482$	−13.2632	−	18.2553i	−0.604124	−	0.831505i
$483$		0			0
$484$	2.58805	−	1.78357i	0.117639	−	0.0810712i
$485$	27.9492	−	48.4094i	1.26911	−	2.19816i
$486$		0			0
$487$	−16.9480	+	18.8227i	−0.767988	+	0.852937i	−0.992590	−	0.121514i	$-0.961225\pi$
$487$	−16.9480	+	18.8227i	−0.767988	+	0.852937i	0.224602	+	0.974451i	$0.427892\pi$
$488$	4.69378	−	4.22630i	0.212477	−	0.191316i
$489$		0			0
$490$	36.3816	+	16.8652i	1.64355	+	0.761893i
$491$	18.9227	+	6.14835i	0.853969	+	0.277471i	0.703108	−	0.711084i	$-0.251795\pi$
$491$	18.9227	+	6.14835i	0.853969	+	0.277471i	0.150861	+	0.988555i	$0.451795\pi$
$492$		0			0
$493$	−10.2985	+	23.1308i	−0.463821	+	1.04176i
$494$	8.13093	−	4.69440i	0.365828	−	0.211211i
$495$		0			0
$496$		−	3.31013i		−	0.148629i
$497$	19.1961	+	6.39886i	0.861062	+	0.287028i
$498$		0			0
$499$	5.80341	+	6.44534i	0.259796	+	0.288533i	0.858905	−	0.512134i	$-0.171145\pi$
$499$	5.80341	+	6.44534i	0.259796	+	0.288533i	−0.599109	+	0.800668i	$0.704478\pi$
$500$	11.3690	+	1.19493i	0.508438	+	0.0534389i
$501$		0			0
$502$	21.1241	+	23.4607i	0.942814	+	1.04710i
$503$	−1.27132	−	3.91271i	−0.0566852	−	0.174459i	0.918705	−	0.394944i	$-0.129236\pi$
$503$	−1.27132	−	3.91271i	−0.0566852	−	0.174459i	−0.975390	+	0.220485i	$0.929236\pi$
$504$		0			0
$505$			16.5986i			0.738626i
$506$	22.9015	+	5.16679i	1.01810	+	0.229692i
$507$		0			0
$508$	−0.158860	+	0.356804i	−0.00704825	+	0.0158306i
$509$	−3.13477	+	14.7480i	−0.138946	+	0.653692i	0.852451	+	0.522807i	$0.175115\pi$
$509$	−3.13477	+	14.7480i	−0.138946	+	0.653692i	−0.991398	+	0.130885i	$0.958218\pi$
$510$		0			0
$511$	−0.505300	+	0.286638i	−0.0223532	+	0.0126801i
$512$	−14.9290	+	20.5480i	−0.659775	+	0.908103i
$513$		0			0
$514$	−17.6765	+	19.6318i	−0.779679	+	0.865921i
$515$	44.3844	+	19.7612i	1.95581	+	0.870783i
$516$		0			0
$517$	−10.9506	−	0.136391i	−0.481609	−	0.00599847i
$518$	−20.0867	−	9.12667i	−0.882557	−	0.401003i
$519$		0			0
$520$	−18.9850	−	4.03539i	−0.832549	−	0.176964i
$521$	−8.82710	−	41.5282i	−0.386722	−	1.81938i	−0.552850	−	0.833281i	$-0.686460\pi$
$521$	−8.82710	−	41.5282i	−0.386722	−	1.81938i	0.166128	−	0.986104i	$-0.446873\pi$
$522$		0			0
$523$	10.6013	−	4.71999i	0.463561	−	0.206391i	−0.161647	−	0.986849i	$-0.551681\pi$
$523$	10.6013	−	4.71999i	0.463561	−	0.206391i	0.625208	+	0.780458i	$0.285014\pi$
$524$	−1.04199	+	3.20692i	−0.0455195	+	0.140095i
$525$		0			0
$526$	1.60980	−	1.16959i	0.0701908	−	0.0509966i
$527$	−4.95561	−	2.86113i	−0.215870	−	0.124633i
$528$		0			0
$529$	−3.11472	−	5.39486i	−0.135423	−	0.234559i
$530$	4.17955	+	39.7657i	0.181548	+	1.72731i
$531$		0			0
$532$	−3.48677	+	1.10370i	−0.151171	+	0.0478515i
$533$	−3.32047	−	2.41246i	−0.143826	−	0.104495i
$534$		0			0
$535$	47.5791	−	10.1132i	2.05702	−	0.437234i
$536$	13.1845	+	11.8714i	0.569485	+	0.512767i
$537$		0			0
$538$	−19.7066			−0.849612
$539$	−16.8170	−	16.0059i	−0.724360	−	0.689421i
$540$		0			0
$541$	−29.8913	+	3.14170i	−1.28513	+	0.135072i	−0.722346	−	0.691532i	$-0.756936\pi$
$541$	−29.8913	+	3.14170i	−1.28513	+	0.135072i	−0.562783	+	0.826605i	$0.690269\pi$
$542$	2.20535	+	1.98571i	0.0947280	+	0.0852935i
$543$		0			0
$544$	3.77317	+	8.47467i	0.161773	+	0.363349i
$545$	−22.2825	−	16.1892i	−0.954478	−	0.693469i
$546$		0			0
$547$	1.66790	−	0.541933i	0.0713142	−	0.0231714i	−0.273143	−	0.961974i	$-0.588063\pi$
$547$	1.66790	−	0.541933i	0.0713142	−	0.0231714i	0.344457	+	0.938802i	$0.388063\pi$
$548$	0.172100	+	1.63742i	0.00735176	+	0.0699473i
$549$		0			0
$550$	55.7934	+	25.6781i	2.37904	+	1.09492i
$551$	18.3347	+	10.5855i	0.781083	+	0.450958i
$552$		0			0
$553$	17.5950	−	7.67415i	0.748217	−	0.326338i
$554$	4.38643	−	13.5001i	0.186362	−	0.573562i
$555$		0			0
$556$	0.411559	−	3.91572i	0.0174540	−	0.166064i
$557$	3.32308	+	15.6339i	0.140803	+	0.662428i	0.990766	+	0.135585i	$0.0432913\pi$
$557$	3.32308	+	15.6339i	0.140803	+	0.662428i	−0.849962	+	0.526843i	$0.823375\pi$
$558$		0			0
$559$	−9.49885	−	13.0740i	−0.401758	−	0.552973i
$560$	−35.2736	−	16.0271i	−1.49058	−	0.677267i
$561$		0			0
$562$	2.76065	−	4.78158i	0.116451	−	0.201699i
$563$	−36.1296	−	16.0859i	−1.52268	−	0.677941i	−0.536542	−	0.843873i	$-0.680270\pi$
$563$	−36.1296	−	16.0859i	−1.52268	−	0.677941i	−0.986137	+	0.165933i	$0.946937\pi$
$564$		0			0
$565$	7.50778	−	6.76003i	0.315854	−	0.284397i
$566$	−15.4477	+	21.2619i	−0.649315	+	0.893705i
$567$		0			0
$568$	−21.7678	−	7.07279i	−0.913358	−	0.296768i
$569$	−5.77378	+	27.1635i	−0.242050	+	1.13875i	0.674326	+	0.738434i	$0.264434\pi$
$569$	−5.77378	+	27.1635i	−0.242050	+	1.13875i	−0.916376	+	0.400320i	$0.868899\pi$
$570$		0			0
$571$	−24.2147	+	13.9804i	−1.01335	+	0.585061i	−0.912172	−	0.409807i	$-0.865596\pi$
$571$	−24.2147	+	13.9804i	−1.01335	+	0.585061i	−0.101183	+	0.994868i	$0.532263\pi$
$572$	1.20768	+	0.717458i	0.0504958	+	0.0299984i
$573$		0			0
$574$	−6.36385	−	7.17670i	−0.265622	−	0.299550i
$575$	−23.6298	−	72.7249i	−0.985429	−	3.03284i
$576$		0			0
$577$	7.18734	+	0.755419i	0.299213	+	0.0314485i	0.252945	−	0.967481i	$-0.418601\pi$
$577$	7.18734	+	0.755419i	0.299213	+	0.0314485i	0.0462673	+	0.998929i	$0.485267\pi$
$578$	−21.4528	−	2.25478i	−0.892321	−	0.0937867i
$579$		0			0
$580$	−1.69068	−	5.20339i	−0.0702018	−	0.216059i
$581$	−1.98442	−	0.661490i	−0.0823276	−	0.0274432i
$582$		0			0
$583$	5.09464	−	22.5817i	0.210998	−	0.935240i
$584$	0.569085	−	0.328561i	0.0235489	−	0.0135960i
$585$		0			0
$586$	0.185023	−	0.870464i	0.00764323	−	0.0359586i
$587$	23.6375	+	7.68029i	0.975624	+	0.316999i	0.753084	−	0.657924i	$-0.228565\pi$
$587$	23.6375	+	7.68029i	0.975624	+	0.316999i	0.222540	+	0.974924i	$0.428565\pi$
$588$		0			0
$589$	−2.81234	+	3.87085i	−0.115880	+	0.159495i
$590$	33.0794	−	29.7848i	1.36186	−	1.22622i
$591$		0			0
$592$	19.4735	+	8.67017i	0.800356	+	0.356342i
$593$	6.06292	−	10.5013i	0.248974	−	0.431236i	−0.714267	−	0.699873i	$-0.753240\pi$
$593$	6.06292	−	10.5013i	0.248974	−	0.431236i	0.963241	+	0.268637i	$0.0865732\pi$
$594$		0			0
$595$	−54.4830	+	38.9552i	−2.23359	+	1.59701i
$596$	0.230959	+	0.317888i	0.00946046	+	0.0130212i
$597$		0			0
$598$	2.18150	+	10.2632i	0.0892083	+	0.419692i
$599$	4.06780	−	38.7025i	0.166206	−	1.58134i	−0.520150	−	0.854075i	$-0.674124\pi$
$599$	4.06780	−	38.7025i	0.166206	−	1.58134i	0.686355	−	0.727266i	$-0.259210\pi$
$600$		0			0
$601$	−6.08052	+	18.7139i	−0.248029	+	0.763356i	0.747094	+	0.664718i	$0.231448\pi$
$601$	−6.08052	+	18.7139i	−0.248029	+	0.763356i	−0.995123	+	0.0986377i	$0.968552\pi$
$602$	−15.0986	−	34.6176i	−0.615373	−	1.41091i
$603$		0			0
$604$	2.93511	+	1.69459i	0.119428	+	0.0689518i
$605$	−34.9536	−	33.0854i	−1.42107	−	1.34511i
$606$		0			0
$607$	−1.21303	−	11.5412i	−0.0492355	−	0.468445i	−0.991165	−	0.132634i	$-0.957656\pi$
$607$	−1.21303	−	11.5412i	−0.0492355	−	0.468445i	0.941930	−	0.335811i	$-0.109010\pi$
$608$	7.37701	−	2.39694i	0.299177	−	0.0972086i
$609$		0			0
$610$	−9.78126	−	7.10650i	−0.396032	−	0.287734i
$611$	−1.99076	−	4.47131i	−0.0805374	−	0.180890i
$612$		0			0
$613$	−14.6853	−	13.2227i	−0.593132	−	0.534058i	0.316974	−	0.948434i	$-0.397333\pi$
$613$	−14.6853	−	13.2227i	−0.593132	−	0.534058i	−0.910106	+	0.414376i	$0.864000\pi$
$614$	−22.7486	+	2.39097i	−0.918059	+	0.0964918i
$615$		0			0
$616$	19.1594	+	17.9598i	0.771955	+	0.723621i
$617$	−44.3298			−1.78465			−0.892325	−	0.451393i	$-0.850927\pi$
$617$	−44.3298			−1.78465			−0.892325	+	0.451393i	$0.850927\pi$
$618$		0			0
$619$	28.2002	+	25.3916i	1.13346	+	1.02057i	0.999562	+	0.0295787i	$0.00941657\pi$
$619$	28.2002	+	25.3916i	1.13346	+	1.02057i	0.133899	+	0.990995i	$0.457250\pi$
$620$	1.20946	−	0.257078i	0.0485729	−	0.0103245i
$621$		0			0
$622$	−12.3420	−	8.96697i	−0.494868	−	0.359543i
$623$	−3.31999	−	0.732097i	−0.133013	−	0.0293308i
$624$		0			0
$625$	−10.9053	−	103.757i	−0.436212	−	4.15028i
$626$	−12.6720	−	21.9485i	−0.506474	−	0.877238i
$627$		0			0
$628$	1.58135	+	0.912991i	0.0631026	+	0.0364323i
$629$	29.8122	−	21.6598i	1.18869	−	0.863633i
$630$		0			0
$631$	1.39924	−	4.30640i	0.0557027	−	0.171435i	−0.919334	−	0.393477i	$-0.871272\pi$
$631$	1.39924	−	4.30640i	0.0557027	−	0.171435i	0.975037	+	0.222042i	$0.0712721\pi$
$632$	−19.8359	+	8.83151i	−0.789029	+	0.351298i
$633$		0			0
$634$	−7.75091	−	36.4651i	−0.307828	−	1.44822i
$635$	5.84995	+	1.24345i	0.232148	+	0.0493446i
$636$		0			0
$637$	3.35592	−	9.81820i	0.132966	−	0.389011i
$638$	0.236672	−	19.0020i	0.00936992	−	0.752298i
$639$		0			0
$640$	33.1998	+	14.7815i	1.31234	+	0.584291i
$641$	−0.816150	+	0.906426i	−0.0322360	+	0.0358017i	−0.759047	−	0.651036i	$-0.774335\pi$
$641$	−0.816150	+	0.906426i	−0.0322360	+	0.0358017i	0.726811	+	0.686837i	$0.241002\pi$
$642$		0			0
$643$	7.60420	−	10.4663i	0.299880	−	0.412750i	−0.632312	−	0.774714i	$-0.717894\pi$
$643$	7.60420	−	10.4663i	0.299880	−	0.412750i	0.932192	+	0.361964i	$0.117894\pi$
$644$	0.0310570	−	4.08708i	0.00122382	−	0.161054i
$645$		0			0
$646$	−7.61944	+	35.8466i	−0.299783	+	1.41037i
$647$	−2.14772	+	4.82387i	−0.0844358	+	0.189646i	−0.950829	−	0.309717i	$-0.899766\pi$
$647$	−2.14772	+	4.82387i	−0.0844358	+	0.189646i	0.866393	+	0.499363i	$0.166432\pi$
$648$		0			0
$649$	−23.6715	+	10.1879i	−0.929186	+	0.399910i
$650$			27.4494i			1.07665i
$651$		0			0
$652$	−1.74333	−	5.36543i	−0.0682742	−	0.210126i
$653$	12.3309	+	13.6949i	0.482546	+	0.535922i	0.934426	−	0.356157i	$-0.115913\pi$
$653$	12.3309	+	13.6949i	0.482546	+	0.535922i	−0.451880	+	0.892079i	$0.649247\pi$
$654$		0			0
$655$	51.3503	+	5.39714i	2.00642	+	0.210884i
$656$	6.20106	+	6.88697i	0.242111	+	0.268891i
$657$		0			0
$658$	−2.29309	−	11.2062i	−0.0893939	−	0.436862i
$659$			4.57092i			0.178058i	0.996029	+	0.0890290i	$0.0283764\pi$
$659$			4.57092i			0.178058i	−0.996029	+	0.0890290i	$0.971624\pi$
$660$		0			0
$661$	−7.35634	+	4.24718i	−0.286128	+	0.165196i	−0.636195	−	0.771529i	$-0.719492\pi$
$661$	−7.35634	+	4.24718i	−0.286128	+	0.165196i	0.350066	+	0.936725i	$0.386159\pi$
$662$	−0.978269	+	2.19723i	−0.0380215	+	0.0853977i
$663$		0			0
$664$	2.25028	+	0.731159i	0.0873277	+	0.0283745i
$665$	27.6319	+	48.7109i	1.07152	+	1.88893i
$666$		0			0
$667$	−17.5826	+	15.8314i	−0.680800	+	0.612995i
$668$	0.371945	−	0.413087i	0.0143910	−	0.0159828i
$669$		0			0
$670$	16.9805	−	29.4110i	0.656012	−	1.13625i
$671$	4.04349	+	5.71369i	0.156097	+	0.220575i
$672$		0			0
$673$	18.8413	+	25.9328i	0.726277	+	0.999635i	0.999292	+	0.0376252i	$0.0119793\pi$
$673$	18.8413	+	25.9328i	0.726277	+	0.999635i	−0.273014	+	0.962010i	$0.588021\pi$
$674$	−41.0241	−	8.71993i	−1.58019	−	0.335879i
$675$		0			0
$676$	0.322656	−	3.06987i	0.0124099	−	0.118072i
$677$	4.64503	−	2.06810i	0.178523	−	0.0794836i	−0.315529	−	0.948916i	$-0.602182\pi$
$677$	4.64503	−	2.06810i	0.178523	−	0.0794836i	0.494052	+	0.869432i	$0.335515\pi$
$678$		0			0
$679$	−27.1941	−	20.0751i	−1.04361	−	0.770413i
$680$	61.2913	−	44.5307i	2.35041	−	1.70768i
$681$		0			0
$682$	4.26532	+	0.502086i	0.163328	+	0.0192259i
$683$	−13.7699	−	23.8502i	−0.526891	−	0.912602i	−0.999509	−	0.0313347i	$-0.990024\pi$
$683$	−13.7699	−	23.8502i	−0.526891	−	0.912602i	0.472618	−	0.881267i	$-0.343309\pi$
$684$		0			0
$685$	23.9773	−	7.79071i	0.916127	−	0.297668i
$686$	12.5998	−	20.7180i	0.481062	−	0.791019i
$687$		0			0
$688$	14.8415	+	33.3346i	0.565827	+	1.27087i
$689$	10.1198	−	2.15104i	0.385535	−	0.0819480i
$690$		0			0
$691$	−34.2010	+	3.59467i	−1.30107	+	0.136748i	−0.729599	−	0.683875i	$-0.760293\pi$
$691$	−34.2010	+	3.59467i	−1.30107	+	0.136748i	−0.571470	+	0.820623i	$0.693627\pi$
$692$	−3.93756			−0.149684
$693$		0			0
$694$	17.2796			0.655923
$695$	−59.9597	+	6.30202i	−2.27440	+	0.239049i
$696$		0			0
$697$	15.6704	−	3.33085i	0.593560	−	0.126165i
$698$	11.5366	+	25.9117i	0.436667	+	0.980771i
$699$		0			0
$700$	2.30252	−	10.4417i	0.0870271	−	0.394660i
$701$	−10.1237	+	3.28938i	−0.382366	+	0.124238i	−0.493892	−	0.869523i	$-0.664426\pi$
$701$	−10.1237	+	3.28938i	−0.382366	+	0.124238i	0.111526	+	0.993761i	$0.464426\pi$
$702$		0			0
$703$	−15.4059	−	26.6838i	−0.581045	−	1.00640i
$704$	−21.4278	−	19.7824i	−0.807590	−	0.745577i
$705$		0			0
$706$	8.91460	−	6.47683i	0.335505	−	0.243759i
$707$	9.97378	+	1.12497i	0.375103	+	0.0423090i
$708$		0			0
$709$	6.79156	−	3.02380i	0.255062	−	0.113561i	−0.275223	−	0.961381i	$-0.588752\pi$
$709$	6.79156	−	3.02380i	0.255062	−	0.113561i	0.530285	+	0.847819i	$0.322085\pi$
$710$	−4.57964	+	43.5724i	−0.171871	+	1.63524i
$711$		0			0
$712$	3.76156	+	0.799544i	0.140970	+	0.0299642i
$713$	−3.14293	−	4.32587i	−0.117703	−	0.162005i
$714$		0			0
$715$	6.90118	−	20.3728i	0.258090	−	0.761898i
$716$	1.17969	−	2.04329i	0.0440872	−	0.0763613i
$717$		0			0
$718$	5.51465	−	6.12464i	0.205805	−	0.228570i
$719$	21.4675	−	19.3295i	0.800604	−	0.720867i	−0.163456	−	0.986551i	$-0.552264\pi$
$719$	21.4675	−	19.3295i	0.800604	−	0.720867i	0.964060	+	0.265683i	$0.0855975\pi$
$720$		0			0
$721$	14.8823	−	25.3305i	0.554247	−	0.943357i
$722$	5.48370	+	1.78176i	0.204082	+	0.0663104i
$723$		0			0
$724$	−2.61043	+	5.86312i	−0.0970158	+	0.217901i
$725$	−53.6039	+	30.9482i	−1.99080	+	1.14939i
$726$		0			0
$727$			13.3469i			0.495010i	0.968887	+	0.247505i	$0.0796106\pi$
$727$			13.3469i			0.495010i	−0.968887	+	0.247505i	$0.920389\pi$
$728$	−3.71152	+	11.1343i	−0.137558	+	0.412664i
$729$		0			0
$730$	−0.841676	−	0.934776i	−0.0311518	−	0.0345976i
$731$	62.7337	+	6.59357i	2.32029	+	0.243872i
$732$		0			0
$733$	2.68084	+	2.97737i	0.0990190	+	0.109972i	0.790617	−	0.612311i	$-0.209760\pi$
$733$	2.68084	+	2.97737i	0.0990190	+	0.109972i	−0.691598	+	0.722282i	$0.743093\pi$
$734$	4.24162	+	13.0544i	0.156561	+	0.481845i
$735$		0			0
$736$			8.66844i			0.319523i
$737$	−14.7743	+	12.9733i	−0.544217	+	0.477878i
$738$		0			0
$739$	9.07590	−	20.3848i	0.333863	−	0.749867i	−0.666129	−	0.745836i	$-0.732050\pi$
$739$	9.07590	−	20.3848i	0.333863	−	0.749867i	0.999992	−	0.00403125i	$-0.00128319\pi$
$740$	−1.65552	+	7.78860i	−0.0608580	+	0.286314i
$741$		0			0
$742$	24.1778	+	0.183723i	0.887595	+	0.00674468i
$743$	9.75074	−	13.4207i	0.357720	−	0.492359i	−0.591792	−	0.806091i	$-0.701579\pi$
$743$	9.75074	−	13.4207i	0.357720	−	0.492359i	0.949512	+	0.313731i	$0.101579\pi$
$744$		0			0
$745$	4.02601	−	4.47134i	0.147502	−	0.163817i
$746$	18.8803	+	8.40604i	0.691256	+	0.307767i
$747$		0			0
$748$	−5.23542	+	1.62929i	−0.191426	+	0.0595727i
$749$	−2.85218	−	29.2749i	−0.104216	−	1.06968i
$750$		0			0
$751$	45.7819	+	9.73125i	1.67061	+	0.355098i	0.943486	−	0.331412i	$-0.107525\pi$
$751$	45.7819	+	9.73125i	1.67061	+	0.355098i	0.727120	+	0.686510i	$0.240858\pi$
$752$	2.29771	+	10.8099i	0.0837890	+	0.394196i
$753$		0			0
$754$	7.75882	−	3.45445i	0.282559	−	0.125804i
$755$	16.0370	−	49.3569i	0.583648	−	1.79628i
$756$		0			0
$757$	−31.7771	+	23.0874i	−1.15496	+	0.839127i	−0.989132	−	0.147028i	$-0.953029\pi$
$757$	−31.7771	+	23.0874i	−1.15496	+	0.839127i	−0.165826	+	0.986155i	$0.553029\pi$
$758$	−14.7809	−	8.53373i	−0.536865	−	0.309959i
$759$		0			0
$760$	−31.6732	−	54.8597i	−1.14891	−	1.98997i
$761$	1.90196	+	18.0960i	0.0689461	+	0.655979i	0.973354	+	0.229309i	$0.0736466\pi$
$761$	1.90196	+	18.0960i	0.0689461	+	0.655979i	−0.904408	+	0.426670i	$0.859687\pi$
$762$		0			0
$763$	−11.2380	+	12.2919i	−0.406843	+	0.444998i
$764$	1.52393	+	1.10720i	0.0551339	+	0.0400571i
$765$		0			0
$766$	−39.8446	+	8.46922i	−1.43964	+	0.306005i
$767$	−8.55917	−	7.70671i	−0.309054	−	0.278273i
$768$		0			0
$769$	26.1842			0.944227			0.472114	−	0.881538i	$-0.343491\pi$
$769$	26.1842			0.944227			0.472114	+	0.881538i	$0.343491\pi$
$770$	26.0023	−	43.0213i	0.937057	−	1.55038i
$771$		0			0
$772$	−4.76107	+	0.500409i	−0.171355	+	0.0180101i
$773$	−17.8195	−	16.0448i	−0.640924	−	0.577091i	0.283257	−	0.959044i	$-0.408585\pi$
$773$	−17.8195	−	16.0448i	−0.640924	−	0.577091i	−0.924182	+	0.381953i	$0.875252\pi$
$774$		0			0
$775$	−5.68964	−	12.7791i	−0.204378	−	0.459040i
$776$	30.9319	+	22.4734i	1.11039	+	0.806747i
$777$		0			0
$778$	−10.2579	+	3.33298i	−0.367762	+	0.119493i
$779$	−1.40021	−	13.3221i	−0.0501676	−	0.477313i
$780$		0			0
$781$	10.6048	−	23.0421i	0.379469	−	0.824510i
$782$	−35.4684	−	20.4777i	−1.26835	−	0.732281i
$783$		0			0
$784$	−12.0211	+	20.1090i	−0.429324	+	0.718179i
$785$	8.64025	−	26.5920i	0.308384	−	0.949108i
$786$		0			0
$787$	−0.754051	+	7.17432i	−0.0268790	+	0.255737i	0.972828	+	0.231529i	$0.0743729\pi$
$787$	−0.754051	+	7.17432i	−0.0268790	+	0.255737i	−0.999707	+	0.0242075i	$0.992294\pi$
$788$	−1.31857	−	6.20337i	−0.0469720	−	0.220986i
$789$		0			0
$790$	24.4303	+	33.6254i	0.869190	+	1.19634i
$791$	−3.55314	−	4.96946i	−0.126335	−	0.176693i
$792$		0			0
$793$	−1.56416	+	2.70921i	−0.0555451	+	0.0962069i
$794$	28.6372	+	12.7501i	1.01630	+	0.452485i
$795$		0			0
$796$	−1.35863	+	1.22331i	−0.0481552	+	0.0433592i
$797$	23.8170	−	32.7814i	0.843643	−	1.16118i	−0.141585	−	0.989926i	$-0.545220\pi$
$797$	23.8170	−	32.7814i	0.843643	−	1.16118i	0.985228	−	0.171249i	$-0.0547802\pi$
$798$		0			0
$799$	18.1696	+	5.90366i	0.642794	+	0.208856i
$800$	−4.71494	+	22.1821i	−0.166698	+	0.784254i
$801$		0			0
$802$	−22.2769	+	12.8616i	−0.786625	+	0.454158i
$803$	0.287895	+	0.668922i	0.0101596	+	0.0236058i
$804$		0			0
$805$	−61.3149	+	12.5467i	−2.16107	+	0.442213i
$806$	0.593135	+	1.82548i	0.0208923	+	0.0642999i
$807$		0			0
$808$	−11.2911	−	1.18674i	−0.397219	−	0.0417494i
$809$	−18.5746	−	1.95227i	−0.653050	−	0.0686383i	−0.227791	−	0.973710i	$-0.573150\pi$
$809$	−18.5746	−	1.95227i	−0.653050	−	0.0686383i	−0.425259	+	0.905072i	$0.639817\pi$
$810$		0			0
$811$	−11.2529	−	34.6328i	−0.395142	−	1.21612i	−0.928851	−	0.370454i	$-0.879202\pi$
$811$	−11.2529	−	34.6328i	−0.395142	−	1.21612i	0.533708	−	0.845669i	$-0.320798\pi$
$812$	−3.24121	+	0.663240i	−0.113744	+	0.0232752i
$813$		0			0
$814$	−14.1259	+	23.7778i	−0.495111	+	0.833412i
$815$	−74.8129	+	43.1932i	−2.62058	+	1.51299i
$816$		0			0
$817$	10.9660	−	51.5908i	0.383650	−	1.80493i
$818$	44.2244	+	14.3694i	1.54627	+	0.502414i
$819$		0			0
$820$	−2.03476	+	2.80061i	−0.0710570	+	0.0978016i
$821$	−17.3025	+	15.5792i	−0.603862	+	0.543719i	−0.913346	−	0.407185i	$-0.866510\pi$
$821$	−17.3025	+	15.5792i	−0.603862	+	0.543719i	0.309484	+	0.950905i	$0.399844\pi$
$822$		0			0
$823$	−0.792399	−	0.352799i	−0.0276213	−	0.0122978i	0.392880	−	0.919590i	$-0.371479\pi$
$823$	−0.792399	−	0.352799i	−0.0276213	−	0.0122978i	−0.420501	+	0.907292i	$0.638146\pi$
$824$	−16.6158	+	28.7794i	−0.578839	+	1.00258i
$825$		0			0
$826$	−15.6552	−	21.8955i	−0.544714	−	0.761841i
$827$	3.32445	+	4.57571i	0.115602	+	0.159113i	0.862897	−	0.505380i	$-0.168648\pi$
$827$	3.32445	+	4.57571i	0.115602	+	0.159113i	−0.747295	+	0.664493i	$0.768648\pi$
$828$		0			0
$829$	−9.48337	−	44.6158i	−0.329371	−	1.54957i	−0.761746	−	0.647876i	$-0.775658\pi$
$829$	−9.48337	−	44.6158i	−0.329371	−	1.54957i	0.432375	−	0.901694i	$-0.357676\pi$
$830$	0.473426	−	4.50435i	0.0164329	−	0.156348i
$831$		0			0
$832$	4.02762	−	12.3958i	0.139633	−	0.429745i
$833$	19.7149	+	35.3781i	0.683080	+	1.22578i
$834$		0			0
$835$	−7.37134	−	4.25584i	−0.255096	−	0.147280i
$836$	0.897279	+	4.49599i	0.0310330	+	0.155497i
$837$		0			0
$838$	2.95380	+	28.1035i	0.102037	+	0.970820i
$839$	−41.5863	+	13.5122i	−1.43572	+	0.466493i	−0.920559	−	0.390603i	$-0.872267\pi$
$839$	−41.5863	+	13.5122i	−1.43572	+	0.466493i	−0.515158	+	0.857095i	$0.672267\pi$
$840$		0			0
$841$	−7.96779	−	5.78894i	−0.274751	−	0.199619i
$842$	6.25221	+	14.0427i	0.215466	+	0.483943i
$843$		0			0
$844$	−1.47511	−	1.32820i	−0.0507755	−	0.0457185i
$845$	−47.0076	+	4.94069i	−1.61711	+	0.169965i
$846$		0			0
$847$	−22.2495	+	18.7606i	−0.764500	+	0.644624i
$848$	−23.3605			−0.802202
$849$		0			0
$850$	−79.6234	−	71.6932i	−2.73106	−	2.45906i
$851$	33.6813	−	7.15918i	1.15458	−	0.245413i
$852$		0			0
$853$	1.79303	+	1.30271i	0.0613922	+	0.0446041i	0.618058	−	0.786132i	$-0.287920\pi$
$853$	1.79303	+	1.30271i	0.0613922	+	0.0446041i	−0.556666	+	0.830736i	$0.687920\pi$
$854$	−4.93310	+	5.39574i	−0.168807	+	0.184639i
$855$		0			0
$856$	3.47774	+	33.0885i	0.118867	+	1.13094i
$857$	−8.97672	−	15.5481i	−0.306639	−	0.531114i	0.670986	−	0.741470i	$-0.265871\pi$
$857$	−8.97672	−	15.5481i	−0.306639	−	0.531114i	−0.977625	+	0.210356i	$0.932538\pi$
$858$		0			0
$859$	31.4261	+	18.1439i	1.07225	+	0.619061i	0.928794	−	0.370596i	$-0.120847\pi$
$859$	31.4261	+	18.1439i	1.07225	+	0.619061i	0.143452	+	0.989657i	$0.454180\pi$
$860$	−11.0271	+	8.01169i	−0.376022	+	0.273196i
$861$		0			0
$862$	−6.51543	+	20.0524i	−0.221917	+	0.682989i
$863$	10.7123	−	4.76941i	0.364650	−	0.162353i	−0.216229	−	0.976343i	$-0.569376\pi$
$863$	10.7123	−	4.76941i	0.364650	−	0.162353i	0.580879	+	0.813990i	$0.302709\pi$
$864$		0			0
$865$	12.5359	+	58.9766i	0.426232	+	2.00526i
$866$	51.3529	+	10.9154i	1.74504	+	0.370920i
$867$		0			0
$868$	−0.0725022	−	0.744165i	−0.00246088	−	0.0252586i
$869$	−7.15033	−	22.9763i	−0.242559	−	0.779417i
$870$		0			0
$871$	−8.02757	−	3.57411i	−0.272004	−	0.121104i
$872$	12.6057	−	14.0001i	0.426884	−	0.474103i
$873$		0			0
$874$	−20.1285	+	27.7045i	−0.680856	+	0.937118i
$875$	−105.847	−	0.804312i	−3.57828	−	0.0271907i
$876$		0			0
$877$	3.60097	−	16.9412i	0.121596	−	0.572064i	−0.874594	−	0.484856i	$-0.838872\pi$
$877$	3.60097	−	16.9412i	0.121596	−	0.572064i	0.996190	−	0.0872085i	$-0.0277946\pi$
$878$	2.18384	−	4.90499i	0.0737011	−	0.165535i
$879$		0			0
$880$	−24.8060	+	41.7555i	−0.836209	+	1.40758i
$881$		−	21.3587i		−	0.719592i	−0.933031	−	0.359796i	$-0.882846\pi$
$881$		−	21.3587i		−	0.719592i	0.933031	−	0.359796i	$-0.117154\pi$
$882$		0			0
$883$	−11.9745	−	36.8537i	−0.402974	−	1.24023i	−0.922575	−	0.385817i	$-0.873920\pi$
$883$	−11.9745	−	36.8537i	−0.402974	−	1.24023i	0.519602	−	0.854409i	$-0.326080\pi$
$884$	−1.63971	−	1.82108i	−0.0551494	−	0.0612496i
$885$		0			0
$886$	3.92783	+	0.412832i	0.131958	+	0.0138694i
$887$	−10.2045	−	11.3332i	−0.342633	−	0.380533i	0.547058	−	0.837094i	$-0.315748\pi$
$887$	−10.2045	−	11.3332i	−0.342633	−	0.380533i	−0.889692	+	0.456561i	$0.849081\pi$
$888$		0			0
$889$	1.14365	−	3.43086i	0.0383567	−	0.115067i
$890$		−	7.36125i		−	0.246750i
$891$		0			0
$892$	−3.39207	+	1.95841i	−0.113575	+	0.0655726i
$893$	6.49731	−	14.5932i	0.217424	−	0.488343i
$894$		0			0
$895$	−34.3600	−	11.1642i	−1.14853	−	0.373179i
$896$	11.1321	−	18.9474i	0.371897	−	0.632987i
$897$		0			0
$898$	9.12384	−	8.21514i	0.304467	−	0.274143i
$899$	−2.89611	+	3.21645i	−0.0965906	+	0.107275i
$900$		0			0
$901$	−20.1917	+	34.9731i	−0.672684	+	1.16512i
$902$	−9.81490	+	6.94584i	−0.326800	+	0.231271i
$903$		0			0
$904$	4.06169	+	5.59044i	0.135090	+	0.185935i
$905$	96.1281	+	20.4327i	3.19541	+	0.679205i
$906$		0			0
$907$	2.85905	−	27.2021i	0.0949333	−	0.903230i	−0.838602	−	0.544744i	$-0.816627\pi$
$907$	2.85905	−	27.2021i	0.0949333	−	0.903230i	0.933535	−	0.358485i	$-0.116707\pi$
$908$	4.96126	−	2.20890i	0.164645	−	0.0733048i
$909$		0			0
$910$	22.3246	+	2.51807i	0.740055	+	0.0834731i
$911$	24.4050	−	17.7313i	0.808574	−	0.587463i	−0.104843	−	0.994489i	$-0.533434\pi$
$911$	24.4050	−	17.7313i	0.808574	−	0.587463i	0.913417	+	0.407026i	$0.133434\pi$
$912$		0			0
$913$	−1.09628	+	2.38200i	−0.0362817	+	0.0788328i
$914$	−9.44292	−	16.3556i	−0.312344	−	0.540996i
$915$		0			0
$916$	−4.81307	+	1.56386i	−0.159028	+	0.0516714i
$917$	6.72334	−	30.4897i	0.222024	−	1.00686i
$918$		0			0
$919$	1.71777	+	3.85818i	0.0566641	+	0.127270i	0.939659	−	0.342114i	$-0.111143\pi$
$919$	1.71777	+	3.85818i	0.0566641	+	0.127270i	−0.882994	+	0.469384i	$0.844476\pi$
$920$	69.2459	−	14.7187i	2.28297	−	0.485260i
$921$		0			0
$922$	15.2153	−	1.59920i	0.501090	−	0.0526667i
$923$	11.3363			0.373139
$924$		0			0
$925$	90.0825			2.96190
$926$	−10.4532	+	1.09868i	−0.343515	+	0.0361049i
$927$		0			0
$928$	6.86332	−	1.45884i	0.225299	−	0.0478889i
$929$	−8.39995	−	18.8666i	−0.275593	−	0.618993i	0.721725	−	0.692180i	$-0.243350\pi$
$929$	−8.39995	−	18.8666i	−0.275593	−	0.618993i	−0.997318	+	0.0731873i	$0.976683\pi$
$930$		0			0
$931$	31.1423	−	13.3021i	1.02065	−	0.435959i
$932$	7.21474	−	2.34421i	0.236327	−	0.0767872i
$933$		0			0
$934$	−3.73820	−	6.47475i	−0.122318	−	0.211860i
$935$	41.0712	+	73.2287i	1.34317	+	2.39483i
$936$		0			0
$937$	25.8666	−	18.7932i	0.845024	−	0.613946i	−0.0787452	−	0.996895i	$-0.525091\pi$
$937$	25.8666	−	18.7932i	0.845024	−	0.613946i	0.923770	+	0.382949i	$0.125091\pi$
$938$	−16.5217	−	12.1966i	−0.539453	−	0.398233i
$939$		0			0
$940$	−3.77127	+	1.67908i	−0.123005	+	0.0547655i
$941$	−3.49013	+	33.2064i	−0.113775	+	1.08250i	0.777453	+	0.628941i	$0.216511\pi$
$941$	−3.49013	+	33.2064i	−0.113775	+	1.08250i	−0.891228	+	0.453555i	$0.850155\pi$
$942$		0			0
$943$	14.6430	+	3.11246i	0.476841	+	0.101356i
$944$	15.2858	+	21.0392i	0.497512	+	0.684766i
$945$		0			0
$946$	−45.2050	+	14.0680i	−1.46974	+	0.457391i
$947$	18.7806	−	32.5289i	0.610287	−	1.05705i	−0.380905	−	0.924614i	$-0.624388\pi$
$947$	18.7806	−	32.5289i	0.610287	−	1.05705i	0.991192	−	0.132434i	$-0.0422791\pi$
$948$		0			0
$949$	−0.217781	+	0.241870i	−0.00706947	+	0.00785144i
$950$	−66.5767	+	59.9459i	−2.16003	+	1.94490i
$951$		0			0
$952$	−22.6037	−	39.8470i	−0.732590	−	1.29145i
$953$	48.6676	+	15.8131i	1.57650	+	0.512235i	0.961152	−	0.276021i	$-0.0890160\pi$
$953$	48.6676	+	15.8131i	1.57650	+	0.512235i	0.615347	+	0.788257i	$0.289016\pi$
$954$		0			0
$955$	11.7319	−	26.3503i	0.379636	−	0.852676i
$956$	4.85230	−	2.80147i	0.156934	−	0.0906062i
$957$		0			0
$958$			30.1305i			0.973472i
$959$	−3.05623	−	14.9356i	−0.0986907	−	0.482295i
$960$		0			0
$961$	20.0885	+	22.3106i	0.648017	+	0.719696i
$962$	−12.2929	−	1.29204i	−0.396339	−	0.0416570i
$963$		0			0
$964$	3.29511	+	3.65959i	0.106128	+	0.117867i
$965$	22.6527	+	69.7179i	0.729217	+	2.24430i
$966$		0			0
$967$			18.7568i			0.603177i	0.953438	+	0.301588i	$0.0975168\pi$
$967$			18.7568i			0.603177i	−0.953438	+	0.301588i	$0.902483\pi$
$968$	25.0052	−	21.4115i	0.803699	−	0.688192i
$969$		0			0
$970$	29.7681	−	66.8602i	0.955795	−	2.14675i
$971$	−6.37196	+	29.9777i	−0.204486	+	0.962030i	0.749460	+	0.662050i	$0.230313\pi$
$971$	−6.37196	+	29.9777i	−0.204486	+	0.962030i	−0.953945	+	0.299980i	$0.903020\pi$
$972$		0			0
$973$	−0.277022	+	36.4559i	−0.00888091	+	1.16872i
$974$	−19.4924	+	26.8290i	−0.624577	+	0.859656i
$975$		0			0
$976$	4.72645	−	5.24926i	0.151290	−	0.168025i
$977$	−33.1115	−	14.7422i	−1.05933	−	0.471645i	−0.198271	−	0.980147i	$-0.563533\pi$
$977$	−33.1115	−	14.7422i	−1.05933	−	0.471645i	−0.861061	+	0.508502i	$0.830199\pi$
$978$		0			0
$979$	−1.36735	+	4.03651i	−0.0437007	+	0.129007i
$980$	−8.28104	−	2.83051i	−0.264528	−	0.0904174i
$981$		0			0
$982$	25.4812	+	5.41619i	0.813137	+	0.172838i
$983$	5.28826	+	24.8793i	0.168669	+	0.793526i	0.978399	+	0.206724i	$0.0662802\pi$
$983$	5.28826	+	24.8793i	0.168669	+	0.793526i	−0.809730	+	0.586802i	$0.800387\pi$
$984$		0			0
$985$	−88.7159	+	39.4989i	−2.82672	+	1.25854i
$986$	−10.2443	+	31.5287i	−0.326245	+	1.00408i
$987$		0			0
$988$	−1.65766	+	1.20436i	−0.0527372	+	0.0383158i
$989$	51.0464	+	29.4717i	1.62318	+	0.937144i
$990$		0			0
$991$	−6.97830	−	12.0868i	−0.221673	−	0.383949i	0.733643	−	0.679535i	$-0.237818\pi$
$991$	−6.97830	−	12.0868i	−0.221673	−	0.383949i	−0.955316	+	0.295586i	$0.904485\pi$
$992$	0.165756	+	1.57707i	0.00526277	+	0.0500719i
$993$		0			0
$994$	25.8715	+	5.70496i	0.820593	+	0.180950i
$995$	22.6481	+	16.4548i	0.717993	+	0.521653i
$996$		0			0
$997$	−60.9060	+	12.9460i	−1.92891	+	0.410003i	−0.929790	+	0.368091i	$0.880011\pi$
$997$	−60.9060	+	12.9460i	−1.92891	+	0.410003i	−0.999121	+	0.0419117i	$0.986655\pi$
$998$	8.43888	+	7.59840i	0.267128	+	0.240523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.cg.b.19.12	yes	128
3.2	odd	2	inner	693.2.cg.b.19.5	✓	128
7.3	odd	6	inner	693.2.cg.b.514.5	yes	128
11.7	odd	10	inner	693.2.cg.b.271.5	yes	128
21.17	even	6	inner	693.2.cg.b.514.12	yes	128
33.29	even	10	inner	693.2.cg.b.271.12	yes	128
77.73	even	30	inner	693.2.cg.b.73.12	yes	128
231.227	odd	30	inner	693.2.cg.b.73.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.cg.b.19.5	✓	128	3.2	odd	2	inner
693.2.cg.b.19.12	yes	128	1.1	even	1	trivial
693.2.cg.b.73.5	yes	128	231.227	odd	30	inner
693.2.cg.b.73.12	yes	128	77.73	even	30	inner
693.2.cg.b.271.5	yes	128	11.7	odd	10	inner
693.2.cg.b.271.12	yes	128	33.29	even	10	inner
693.2.cg.b.514.5	yes	128	7.3	odd	6	inner
693.2.cg.b.514.12	yes	128	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.cg (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30213 - 0.136859i) q^{2} +(-0.279493 + 0.0594081i) q^{4} +(1.77962 + 3.99709i) q^{5} +(2.52240 - 0.798438i) q^{7} +(-2.84624 + 0.924799i) q^{8} +O(q^{10})\)	\(q+(1.30213 - 0.136859i) q^{2} +(-0.279493 + 0.0594081i) q^{4} +(1.77962 + 3.99709i) q^{5} +(2.52240 - 0.798438i) q^{7} +(-2.84624 + 0.924799i) q^{8} +(2.86433 + 4.96116i) q^{10} +(-0.649109 - 3.25248i) q^{11} +(1.19918 - 0.871257i) q^{13} +(3.17521 - 1.38488i) q^{14} +(-3.05753 + 1.36130i) q^{16} +(-0.604779 + 5.75408i) q^{17} +(4.73203 + 1.00582i) q^{19} +(-0.734851 - 1.01144i) q^{20} +(-1.29035 - 4.14631i) q^{22} +(-2.70321 + 4.68210i) q^{23} +(-9.46406 + 10.5109i) q^{25} +(1.44225 - 1.29861i) q^{26} +(-0.657559 + 0.373009i) q^{28} +(4.16203 + 1.35233i) q^{29} +(-0.402271 + 0.903515i) q^{31} +(1.38855 - 0.801680i) q^{32} +7.57531i q^{34} +(7.68035 + 8.66135i) q^{35} +(-4.26172 - 4.73312i) q^{37} +(6.29936 + 0.662089i) q^{38} +(-8.76174 - 9.73089i) q^{40} +(-0.855652 - 2.63342i) q^{41} -10.9025i q^{43} +(0.374645 + 0.870485i) q^{44} +(-2.87914 + 6.46665i) q^{46} +(0.686524 - 3.22984i) q^{47} +(5.72499 - 4.02796i) q^{49} +(-10.8849 + 14.9818i) q^{50} +(-0.283404 + 0.314751i) q^{52} +(6.37634 + 2.83893i) q^{53} +(11.8453 - 8.38274i) q^{55} +(-6.44095 + 4.60526i) q^{56} +(5.60457 + 1.19129i) q^{58} +(-1.61551 - 7.60037i) q^{59} +(-1.92803 + 0.858416i) q^{61} +(-0.400153 + 1.23154i) q^{62} +(7.11372 - 5.16842i) q^{64} +(5.61659 + 3.24274i) q^{65} +(-2.96412 - 5.13401i) q^{67} +(-0.172808 - 1.64416i) q^{68} +(11.1862 + 10.2270i) q^{70} +(6.18730 + 4.49534i) q^{71} +(-0.214776 + 0.0456520i) q^{73} +(-6.19707 - 5.57986i) q^{74} -1.38232 q^{76} +(-4.23422 - 7.68579i) q^{77} +(7.21557 - 0.758387i) q^{79} +(-10.8825 - 9.79863i) q^{80} +(-1.47457 - 3.31195i) q^{82} +(-0.639620 - 0.464711i) q^{83} +(-24.0759 + 7.82273i) q^{85} +(-1.49210 - 14.1964i) q^{86} +(4.85541 + 8.65705i) q^{88} +(-1.11283 - 0.642493i) q^{89} +(2.32917 - 3.15513i) q^{91} +(0.477375 - 1.46921i) q^{92} +(0.451908 - 4.29962i) q^{94} +(4.40085 + 20.7044i) q^{95} +(-7.50936 - 10.3358i) q^{97} +(6.90340 - 6.02843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 20 q^{4} + 10 q^{7}+O(q^{10}) \) 128 * q - 20 * q^4 + 10 * q^7	\( 128 q - 20 q^{4} + 10 q^{7} + 76 q^{22} - 12 q^{25} + 30 q^{28} - 18 q^{31} + 16 q^{37} - 90 q^{40} - 70 q^{46} + 58 q^{49} - 20 q^{58} - 30 q^{61} - 96 q^{64} - 40 q^{67} - 118 q^{70} - 90 q^{73} - 10 q^{79} + 24 q^{82} - 180 q^{85} - 56 q^{88} - 56 q^{91} - 120 q^{94}+O(q^{100}) \) 128 * q - 20 * q^4 + 10 * q^7 + 76 * q^22 - 12 * q^25 + 30 * q^28 - 18 * q^31 + 16 * q^37 - 90 * q^40 - 70 * q^46 + 58 * q^49 - 20 * q^58 - 30 * q^61 - 96 * q^64 - 40 * q^67 - 118 * q^70 - 90 * q^73 - 10 * q^79 + 24 * q^82 - 180 * q^85 - 56 * q^88 - 56 * q^91 - 120 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more