LMFDB - Embedded newform 693.2.cg.b.271.5

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			271.5
Character	$\chi$	$=$	693.271
Dual form			693.2.cg.b.514.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.532540 - 1.19610i) q^{2} +(0.191195 - 0.212344i) q^{4} +(4.35140 - 0.457350i) q^{5} +(1.57135 - 2.12858i) q^{7} +(-2.84624 - 0.924799i) q^{8} +O(q^{10})$	\(q+(-0.532540 - 1.19610i) q^{2} +(0.191195 - 0.212344i) q^{4} +(4.35140 - 0.457350i) q^{5} +(1.57135 - 2.12858i) q^{7} +(-2.84624 - 0.924799i) q^{8} +(-2.86433 - 4.96116i) q^{10} +(-2.49218 - 2.18839i) q^{11} +(-1.19918 - 0.871257i) q^{13} +(-3.38281 - 0.745949i) q^{14} +(0.349844 + 3.32855i) q^{16} +(-5.28557 - 2.35329i) q^{17} +(3.23709 + 3.59515i) q^{19} +(0.734851 - 1.01144i) q^{20} +(-1.29035 + 4.14631i) q^{22} +(-2.70321 + 4.68210i) q^{23} +(13.8347 - 2.94066i) q^{25} +(-0.403502 + 1.89833i) q^{26} +(-0.151556 - 0.740642i) q^{28} +(4.16203 - 1.35233i) q^{29} +(-0.983602 - 0.103381i) q^{31} +(-1.38855 + 0.801680i) q^{32} +7.57531i q^{34} +(5.86407 - 9.98095i) q^{35} +(6.22986 + 1.32420i) q^{37} +(2.57629 - 5.78645i) q^{38} +(-12.8081 - 2.72244i) q^{40} +(0.855652 - 2.63342i) q^{41} +10.9025i q^{43} +(-0.941184 + 0.110790i) q^{44} +(7.03985 + 0.739918i) q^{46} +(-2.45386 + 2.20947i) q^{47} +(-2.06170 - 6.68950i) q^{49} +(-10.8849 - 14.9818i) q^{50} +(-0.414285 + 0.0880589i) q^{52} +(-0.729585 + 6.94154i) q^{53} +(-11.8453 - 8.38274i) q^{55} +(-6.44095 + 4.60526i) q^{56} +(-3.83397 - 4.25805i) q^{58} +(5.77436 + 5.19926i) q^{59} +(-0.220607 - 2.09893i) q^{61} +(0.400153 + 1.23154i) q^{62} +(7.11372 + 5.16842i) q^{64} +(-5.61659 - 3.24274i) q^{65} +(-2.96412 - 5.13401i) q^{67} +(-1.51028 + 0.672422i) q^{68} +(-15.0611 - 1.69879i) q^{70} +(6.18730 - 4.49534i) q^{71} +(-0.146924 + 0.163175i) q^{73} +(-1.73377 - 8.15675i) q^{74} +1.38232 q^{76} +(-8.57425 + 1.86607i) q^{77} +(-2.95100 - 6.62806i) q^{79} +(3.04462 + 14.3238i) q^{80} +(-3.60552 + 0.378955i) q^{82} +(0.639620 - 0.464711i) q^{83} +(-24.0759 - 7.82273i) q^{85} +(13.0405 - 5.80599i) q^{86} +(5.06952 + 8.53344i) q^{88} +(-1.11283 - 0.642493i) q^{89} +(-3.73888 + 1.18350i) q^{91} +(0.477375 + 1.46921i) q^{92} +(3.94953 + 1.75845i) q^{94} +(15.7301 + 14.1634i) q^{95} +(7.50936 - 10.3358i) q^{97} +(-6.90340 + 6.02843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.532540	−	1.19610i	−0.376562	−	0.845773i	−0.998054	−	0.0623524i	$-0.980140\pi$
$2$	−0.532540	−	1.19610i	−0.376562	−	0.845773i	0.621492	−	0.783421i	$-0.286527\pi$
$3$		0			0
$3$		0			0
$4$	0.191195	−	0.212344i	0.0955977	−	0.106172i
$5$	4.35140	−	0.457350i	1.94600	−	0.204533i	0.951374	−	0.308037i	$-0.0996721\pi$
$5$	4.35140	−	0.457350i	1.94600	−	0.204533i	0.994629	+	0.103504i	$0.0330054\pi$
$6$		0			0
$7$	1.57135	−	2.12858i	0.593916	−	0.804527i
$7$	1.57135	−	2.12858i	0.593916	−	0.804527i
$8$	−2.84624	−	0.924799i	−1.00630	−	0.326966i
$9$		0			0
$10$	−2.86433	−	4.96116i	−0.905781	−	1.56886i
$11$	−2.49218	−	2.18839i	−0.751421	−	0.659824i
$11$	−2.49218	−	2.18839i	−0.751421	−	0.659824i
$12$		0			0
$13$	−1.19918	−	0.871257i	−0.332593	−	0.241643i	0.408937	−	0.912563i	$-0.365900\pi$
$13$	−1.19918	−	0.871257i	−0.332593	−	0.241643i	−0.741530	+	0.670919i	$0.765900\pi$
$14$	−3.38281	−	0.745949i	−0.904094	−	0.199363i
$15$		0			0
$16$	0.349844	+	3.32855i	0.0874611	+	0.832136i
$17$	−5.28557	−	2.35329i	−1.28194	−	0.570756i	−0.351153	−	0.936318i	$-0.614210\pi$
$17$	−5.28557	−	2.35329i	−1.28194	−	0.570756i	−0.930787	+	0.365562i	$0.880877\pi$
$18$		0			0
$19$	3.23709	+	3.59515i	0.742638	+	0.824784i	0.989540	−	0.144257i	$-0.0460792\pi$
$19$	3.23709	+	3.59515i	0.742638	+	0.824784i	−0.246902	+	0.969040i	$0.579413\pi$
$20$	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
$25$	13.8347	−	2.94066i	2.76695	−	0.588133i
$26$	−0.403502	+	1.89833i	−0.0791332	+	0.372292i
$27$		0			0
$28$	−0.151556	−	0.740642i	−0.0286413	−	0.139968i
$29$	4.16203	−	1.35233i	0.772869	−	0.251121i	0.104077	−	0.994569i	$-0.466811\pi$
$29$	4.16203	−	1.35233i	0.772869	−	0.251121i	0.668793	+	0.743449i	$0.266811\pi$
$30$		0			0
$31$	−0.983602	−	0.103381i	−0.176660	−	0.0185677i	0.0157853	−	0.999875i	$-0.494975\pi$
$31$	−0.983602	−	0.103381i	−0.176660	−	0.0185677i	−0.192445	+	0.981308i	$0.561642\pi$
$32$	−1.38855	+	0.801680i	−0.245463	+	0.141718i
$33$		0			0
$34$			7.57531i			1.29916i
$35$	5.86407	−	9.98095i	0.991209	−	1.68709i
$36$		0			0
$37$	6.22986	+	1.32420i	1.02418	+	0.217697i	0.689233	−	0.724539i	$-0.257947\pi$
$37$	6.22986	+	1.32420i	1.02418	+	0.217697i	0.334949	+	0.942236i	$0.391281\pi$
$38$	2.57629	−	5.78645i	0.417930	−	0.938686i
$39$		0			0
$40$	−12.8081	−	2.72244i	−2.02513	−	0.430455i
$41$	0.855652	−	2.63342i	0.133630	−	0.411272i	−0.861744	−	0.507343i	$-0.830628\pi$
$41$	0.855652	−	2.63342i	0.133630	−	0.411272i	0.995374	+	0.0960713i	$0.0306277\pi$
$42$		0			0
$43$			10.9025i			1.66261i	0.555817	+	0.831305i	$0.312405\pi$
$43$			10.9025i			1.66261i	−0.555817	+	0.831305i	$0.687595\pi$
$44$	−0.941184	+	0.110790i	−0.141889	+	0.0167022i
$45$		0			0
$46$	7.03985	+	0.739918i	1.03797	+	0.109095i
$47$	−2.45386	+	2.20947i	−0.357933	+	0.322284i	−0.828404	−	0.560131i	$-0.810751\pi$
$47$	−2.45386	+	2.20947i	−0.357933	+	0.322284i	0.470471	+	0.882415i	$0.344084\pi$
$48$		0			0
$49$	−2.06170	−	6.68950i	−0.294528	−	0.955643i
$50$	−10.8849	−	14.9818i	−1.53936	−	2.11874i
$51$		0			0
$52$	−0.414285	+	0.0880589i	−0.0574509	+	0.0122116i
$53$	−0.729585	+	6.94154i	−0.100216	+	0.953494i	0.822695	+	0.568482i	$0.192469\pi$
$53$	−0.729585	+	6.94154i	−0.100216	+	0.953494i	−0.922912	+	0.385012i	$0.874197\pi$
$54$		0			0
$55$	−11.8453	−	8.38274i	−1.59722	−	1.13033i
$56$	−6.44095	+	4.60526i	−0.860709	+	0.615404i
$57$		0			0
$58$	−3.83397	−	4.25805i	−0.503425	−	0.559110i
$59$	5.77436	+	5.19926i	0.751758	+	0.676886i	0.953107	−	0.302634i	$-0.0978659\pi$
$59$	5.77436	+	5.19926i	0.751758	+	0.676886i	−0.201349	+	0.979520i	$0.564533\pi$
$60$		0			0
$61$	−0.220607	−	2.09893i	−0.0282458	−	0.268741i	−0.999526	−	0.0308005i	$-0.990194\pi$
$61$	−0.220607	−	2.09893i	−0.0282458	−	0.268741i	0.971280	−	0.237940i	$-0.0764723\pi$
$62$	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	$0.951282\pi$
$68$	−1.51028	+	0.672422i	−0.183149	+	0.0815431i
$69$		0			0
$70$	−15.0611	−	1.69879i	−1.80015	−	0.203044i
$71$	6.18730	−	4.49534i	0.734298	−	0.533498i	−0.156622	−	0.987659i	$-0.550061\pi$
$71$	6.18730	−	4.49534i	0.734298	−	0.533498i	0.890920	+	0.454160i	$0.150061\pi$
$72$		0			0
$73$	−0.146924	+	0.163175i	−0.0171961	+	0.0190982i	−0.751682	−	0.659526i	$-0.770757\pi$
$73$	−0.146924	+	0.163175i	−0.0171961	+	0.0190982i	0.734485	+	0.678624i	$0.237424\pi$
$74$	−1.73377	−	8.15675i	−0.201547	−	0.948203i
$75$		0			0
$76$	1.38232			0.158563
$77$	−8.57425	+	1.86607i	−0.977127	+	0.212659i
$78$		0			0
$79$	−2.95100	−	6.62806i	−0.332014	−	0.745715i	−0.999999	−	0.00154065i	$-0.999510\pi$
$79$	−2.95100	−	6.62806i	−0.332014	−	0.745715i	0.667985	−	0.744175i	$-0.267157\pi$
$80$	3.04462	+	14.3238i	0.340399	+	1.60145i
$81$		0			0
$82$	−3.60552	+	0.378955i	−0.398163	+	0.0418486i
$83$	0.639620	−	0.464711i	0.0702074	−	0.0510087i	−0.552128	−	0.833759i	$-0.686184\pi$
$83$	0.639620	−	0.464711i	0.0702074	−	0.0510087i	0.622335	+	0.782751i	$0.286184\pi$
$84$		0			0
$85$	−24.0759	−	7.82273i	−2.61140	−	0.848494i
$86$	13.0405	−	5.80599i	1.40619	−	0.626076i
$87$		0			0
$88$	5.06952	+	8.53344i	0.540413	+	0.909667i
$89$	−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
$91$	−3.73888	+	1.18350i	−0.391941	+	0.124065i
$92$	0.477375	+	1.46921i	0.0497697	+	0.153175i
$93$		0			0
$94$	3.94953	+	1.75845i	0.407363	+	0.181370i
$95$	15.7301	+	14.1634i	1.61387	+	1.45314i
$96$		0			0
$97$	7.50936	−	10.3358i	0.762460	−	1.04944i	−0.234545	−	0.972105i	$-0.575360\pi$
$97$	7.50936	−	10.3358i	0.762460	−	1.04944i	0.997005	−	0.0773313i	$-0.0246399\pi$
$98$	−6.90340	+	6.02843i	−0.697349	+	0.608963i
$99$		0			0
$100$	2.02071	−	3.49997i	0.202071	−	0.349997i
$101$	0.396543	−	3.77286i	0.0394575	−	0.375413i	−0.956919	−	0.290356i	$-0.906226\pi$
$101$	0.396543	−	3.77286i	0.0394575	−	0.375413i	0.996376	−	0.0850569i	$-0.0271072\pi$
$102$		0			0
$103$	−2.30869	+	10.8615i	−0.227482	+	1.07022i	0.705058	+	0.709150i	$0.250921\pi$
$103$	−2.30869	+	10.8615i	−0.227482	+	1.07022i	−0.932540	+	0.361068i	$0.882412\pi$
$104$	2.60742	+	3.58881i	0.255679	+	0.351912i
$105$		0			0
$106$	8.69134	−	2.82399i	0.844177	−	0.274290i
$107$	8.26172	−	7.43889i	0.798691	−	0.719145i	−0.164962	−	0.986300i	$-0.552750\pi$
$107$	8.26172	−	7.43889i	0.798691	−	0.719145i	0.963654	+	0.267155i	$0.0860836\pi$
$108$		0			0
$109$	5.45158	−	3.14747i	0.522167	−	0.301473i	−0.215654	−	0.976470i	$-0.569188\pi$
$109$	5.45158	−	3.14747i	0.522167	−	0.301473i	0.737821	+	0.674997i	$0.235855\pi$
$110$	−3.71852	+	18.6324i	−0.354547	+	1.77653i
$111$		0			0
$112$	7.63480	+	4.48565i	0.721421	+	0.423854i
$113$	−0.713520	+	2.19599i	−0.0671223	+	0.206581i	−0.978992	−	0.203899i	$-0.934639\pi$
$113$	−0.713520	+	2.19599i	−0.0671223	+	0.206581i	0.911870	+	0.410480i	$0.134639\pi$
$114$		0			0
$115$	−9.62139	+	21.6100i	−0.897199	+	2.01514i
$116$	0.508603	−	1.14234i	0.0472226	−	0.106064i
$117$		0			0
$118$	3.14378	−	9.67555i	0.289408	−	0.890706i
$119$	−13.3147	+	7.55291i	−1.22055	+	0.692374i
$120$		0			0
$121$	1.42192	+	10.9077i	0.129266	+	0.991610i
$122$	−2.39306	+	1.38163i	−0.216658	+	0.125087i
$123$		0			0
$124$	−0.210012	+	0.189096i	−0.0188597	+	0.0169813i
$125$	38.0494	−	12.3630i	3.40324	−	1.10578i
$126$		0			0
$127$	0.803438	+	1.10584i	0.0712936	+	0.0981272i	0.843175	−	0.537640i	$-0.180684\pi$
$127$	0.803438	+	1.10584i	0.0712936	+	0.0981272i	−0.771881	+	0.635767i	$0.780684\pi$
$128$	1.72691	−	8.12449i	0.152639	−	0.718110i
$129$		0			0
$130$	−0.887596	+	8.44491i	−0.0778473	+	0.740668i
$131$	−5.90044	+	10.2199i	−0.515524	+	0.892914i	0.484314	+	0.874894i	$0.339069\pi$
$131$	−5.90044	+	10.2199i	−0.515524	+	0.892914i	−0.999838	+	0.0180194i	$0.994264\pi$
$132$		0			0
$133$	12.7392	−	1.24115i	1.10463	−	0.107621i
$134$	−4.56230	+	6.27947i	−0.394123	+	0.542463i
$135$		0			0
$136$	12.8677	+	11.5861i	1.10339	+	0.993501i
$137$	−5.26394	−	2.34366i	−0.449728	−	0.200232i	0.169358	−	0.985555i	$-0.445830\pi$
$137$	−5.26394	−	2.34366i	−0.449728	−	0.200232i	−0.619087	+	0.785323i	$0.712497\pi$
$138$		0			0
$139$	4.25808	+	13.1050i	0.361165	+	1.11155i	0.952348	+	0.305015i	$0.0986614\pi$
$139$	4.25808	+	13.1050i	0.361165	+	1.11155i	−0.591182	+	0.806538i	$0.701339\pi$
$140$	−0.998211	−	3.15351i	−0.0843642	−	0.266520i
$141$		0			0
$142$	−8.67188	−	5.00671i	−0.727728	−	0.420154i
$143$	1.08193	+	4.79561i	0.0904757	+	0.401029i
$144$		0			0
$145$	17.4922	−	7.78801i	1.45264	−	0.646759i
$146$	0.273417	+	0.0888387i	0.0226282	+	0.00735234i
$147$		0			0
$148$	1.47231	−	1.06969i	0.121023	−	0.0879282i
$149$	1.36762	−	0.143742i	0.112040	−	0.0117758i	−0.0483427	−	0.998831i	$-0.515394\pi$
$149$	1.36762	−	0.143742i	0.112040	−	0.0117758i	0.160382	+	0.987055i	$0.448727\pi$
$150$		0			0
$151$	−2.46608	−	11.6020i	−0.200686	−	0.944155i	−0.957032	−	0.289983i	$-0.906350\pi$
$151$	−2.46608	−	11.6020i	−0.200686	−	0.944155i	0.756345	−	0.654172i	$-0.226983\pi$
$152$	−5.88873	−	13.2263i	−0.477639	−	1.07279i
$153$		0			0
$154$	6.79815	+	9.26194i	0.547810	+	0.746348i
$155$	−4.32732			−0.347579
$156$		0			0
$157$	1.32864	+	6.25078i	0.106037	+	0.498866i	0.998828	+	0.0483952i	$0.0154107\pi$
$157$	1.32864	+	6.25078i	0.106037	+	0.498866i	−0.892791	+	0.450471i	$0.851256\pi$
$158$	−6.35633	+	7.05942i	−0.505682	+	0.561617i
$159$		0			0
$160$	−5.67548	+	4.12348i	−0.448686	+	0.325990i
$161$	5.71852	+	13.1112i	0.450683	+	1.03331i
$162$		0			0
$163$	−18.0369	+	8.03054i	−1.41276	+	0.629001i	−0.964302	−	0.264804i	$-0.914693\pi$
$163$	−18.0369	+	8.03054i	−1.41276	+	0.629001i	−0.448456	+	0.893805i	$0.648026\pi$
$164$	−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	$-0.276019\pi$
$167$	1.57383	+	1.14346i	0.121787	+	0.0884834i	−0.525224	+	0.850964i	$0.676019\pi$
$168$		0			0
$169$	−3.33827	−	10.2741i	−0.256790	−	0.790319i
$170$	3.46457	+	32.9632i	0.265720	+	2.52816i
$171$		0			0
$172$	2.31507	+	2.08450i	0.176523	+	0.158942i
$173$	9.22087	+	10.2408i	0.701050	+	0.778594i	0.983543	−	0.180675i	$-0.0578282\pi$
$173$	9.22087	+	10.2408i	0.701050	+	0.778594i	−0.282493	+	0.959269i	$0.591162\pi$
$174$		0			0
$175$	15.4798	−	34.0692i	1.17016	−	2.57539i
$176$	6.41227	−	9.06093i	0.483343	−	0.682993i
$177$		0			0
$178$	−0.175862	+	1.67321i	−0.0131814	+	0.125413i
$179$	8.07675	−	1.71677i	0.603685	−	0.128317i	0.104078	−	0.994569i	$-0.466811\pi$
$179$	8.07675	−	1.71677i	0.603685	−	0.128317i	0.499607	+	0.866252i	$0.333478\pi$
$180$		0			0
$181$	−13.2023	−	18.1714i	−0.981321	−	1.35067i	−0.936115	−	0.351695i	$-0.885605\pi$
$181$	−13.2023	−	18.1714i	−0.981321	−	1.35067i	−0.0452064	−	0.998978i	$-0.514395\pi$
$182$	3.40669	+	3.84183i	0.252521	+	0.284775i
$183$		0			0
$184$	12.0240	−	10.8265i	0.886421	−	0.798137i
$185$	27.7142	+	2.91288i	2.03759	+	0.214159i
$186$		0			0
$187$	8.02269	+	17.4317i	0.586677	+	1.27473i
$188$			0.943504i			0.0688121i
$189$		0			0
$190$	8.56404	−	26.3574i	0.621301	−	1.91217i
$191$	6.44831	+	1.37063i	0.466583	+	0.0991753i	0.435203	−	0.900332i	$-0.356677\pi$
$191$	6.44831	+	1.37063i	0.466583	+	0.0991753i	0.0313799	+	0.999508i	$0.490010\pi$
$192$		0			0
$193$	−6.81454	+	15.3057i	−0.490522	+	1.10173i	0.483514	+	0.875336i	$0.339360\pi$
$193$	−6.81454	+	15.3057i	−0.490522	+	1.10173i	−0.974036	+	0.226393i	$0.927307\pi$
$194$	−16.3617	−	3.47778i	−1.17470	−	0.249690i
$195$		0			0
$196$	−1.81466	−	0.841212i	−0.129619	−	0.0600866i
$197$		−	22.1951i		−	1.58134i	−0.612246	−	0.790668i	$-0.709734\pi$
$197$		−	22.1951i		−	1.58134i	0.612246	−	0.790668i	$-0.290266\pi$
$198$		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	$0.260514\pi$
$200$	−42.0965	−	4.42452i	−2.97667	−	0.312861i
$201$		0			0
$202$	−4.72390	+	1.53489i	−0.332373	+	0.107994i
$203$	3.66149	−	10.9842i	0.256986	−	0.770939i
$204$		0			0
$205$	2.51888	−	11.8504i	0.175926	−	0.827668i
$206$	14.2210	−	3.02276i	0.990822	−	0.210606i
$207$		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	−0.644997	−	0.764185i	$-0.723141\pi$
$211$	4.08323	−	5.62009i	0.281101	−	0.386903i	0.926098	+	0.377282i	$0.123141\pi$
$212$	1.33450	+	1.48211i	0.0916539	+	0.101792i
$213$		0			0
$214$	−13.2974	−	5.92038i	−0.908990	−	0.404709i
$215$	4.98624	+	47.4409i	0.340059	+	3.23544i
$216$		0			0
$217$	−1.76564	+	1.93123i	−0.119859	+	0.131100i
$218$	−6.66789	−	4.84451i	−0.451606	−	0.328111i
$219$		0			0
$220$	−4.04480	+	0.912542i	−0.272700	+	0.0615236i
$221$	4.28805	+	7.42712i	0.288445	+	0.499602i
$222$		0			0
$223$	−13.0369	−	4.23595i	−0.873016	−	0.283660i	−0.161961	−	0.986797i	$-0.551782\pi$
$223$	−13.0369	−	4.23595i	−0.873016	−	0.283660i	−0.711054	+	0.703137i	$0.751782\pi$
$224$	−0.475464	+	4.21536i	−0.0317683	+	0.281651i
$225$		0			0
$226$	3.00661	−	0.316007i	0.199997	−	0.0210205i
$227$	−12.7176	+	14.1244i	−0.844099	+	0.937467i	−0.998724	−	0.0505062i	$-0.983917\pi$
$227$	−12.7176	+	14.1244i	−0.844099	+	0.937467i	0.154625	+	0.987973i	$0.450583\pi$
$228$		0			0
$229$	7.20381	+	16.1800i	0.476041	+	1.06921i	0.978807	+	0.204784i	$0.0656490\pi$
$229$	7.20381	+	16.1800i	0.476041	+	1.06921i	−0.502766	+	0.864423i	$0.667684\pi$
$230$	30.9716			2.04221
$231$		0			0
$232$	−13.0968			−0.859844
$233$	10.7984	+	24.2537i	0.707429	+	1.58891i	0.804719	+	0.593656i	$0.202316\pi$
$233$	10.7984	+	24.2537i	0.707429	+	1.58891i	−0.0972894	+	0.995256i	$0.531017\pi$
$234$		0			0
$235$	−9.66723	+	10.7366i	−0.630621	+	0.700375i
$236$	2.20806	−	0.232077i	0.143733	−	0.0151069i
$237$		0			0
$238$	16.1247	+	11.9035i	1.04521	+	0.771589i
$239$	−18.6490	−	6.05944i	−1.20631	−	0.391953i	−0.364229	−	0.931310i	$-0.618667\pi$
$239$	−18.6490	−	6.05944i	−1.20631	−	0.391953i	−0.842077	+	0.539357i	$0.818667\pi$
$240$		0			0
$241$	8.61712	+	14.9253i	0.555077	+	0.961422i	0.997898	+	0.0648115i	$0.0206446\pi$
$241$	8.61712	+	14.9253i	0.555077	+	0.961422i	−0.442820	+	0.896610i	$0.646022\pi$
$242$	12.2895	−	7.50956i	0.790000	−	0.482733i
$243$		0			0
$244$	−0.487875	−	0.354462i	−0.0312330	−	0.0226921i
$245$	−12.0307	−	28.1657i	−0.768614	−	1.79944i
$246$		0			0
$247$	−0.749559	−	7.13157i	−0.0476933	−	0.453771i
$248$	2.70396	+	1.20388i	0.171702	+	0.0764465i
$249$		0			0
$250$	−35.0503	−	38.9273i	−2.21677	−	2.46198i
$251$	−14.1725	+	19.5068i	−0.894561	+	1.23126i	0.0776099	+	0.996984i	$0.475271\pi$
$251$	−14.1725	+	19.5068i	−0.894561	+	1.23126i	−0.972171	+	0.234274i	$0.924729\pi$
$252$		0			0
$253$	16.9831	−	5.75297i	1.06772	−	0.361686i
$254$	0.894834	−	1.54990i	0.0561469	−	0.0972492i
$255$		0			0
$256$	6.56440	−	1.39531i	0.410275	−	0.0872066i
$257$	4.19495	−	19.7357i	0.261674	−	1.23108i	−0.629351	−	0.777122i	$-0.716679\pi$
$257$	4.19495	−	19.7357i	0.261674	−	1.23108i	0.891024	−	0.453956i	$-0.149988\pi$
$258$		0			0
$259$	12.6080	−	11.1800i	0.783421	−	0.694690i
$260$	−1.76244	+	0.572652i	−0.109302	+	0.0355144i
$261$		0			0
$262$	15.3662	+	1.61506i	0.949330	+	0.0997786i
$263$	−1.31616	+	0.759883i	−0.0811576	+	0.0468564i	−0.540030	−	0.841646i	$-0.681587\pi$
$263$	−1.31616	+	0.759883i	−0.0811576	+	0.0468564i	0.458872	+	0.888502i	$0.348254\pi$
$264$		0			0
$265$			30.5391i			1.87600i
$266$	−8.26865	−	14.5764i	−0.506983	−	0.893737i
$267$		0			0
$268$	−1.65690	−	0.352186i	−0.101212	−	0.0215132i
$269$	−6.12190	+	13.7500i	−0.373259	+	0.838353i	0.625070	+	0.780569i	$0.285070\pi$
$269$	−6.12190	+	13.7500i	−0.373259	+	0.838353i	−0.998329	+	0.0577848i	$0.981596\pi$
$270$		0			0
$271$	2.21702	+	0.471243i	0.134675	+	0.0286260i	0.274756	−	0.961514i	$-0.411403\pi$
$271$	2.21702	+	0.471243i	0.134675	+	0.0286260i	−0.140081	+	0.990140i	$0.544736\pi$
$272$	5.98390	−	18.4166i	0.362827	−	1.11667i
$273$		0			0
$274$			7.54430i			0.455768i
$275$	−40.9140	−	22.9471i	−2.46721	−	1.38376i
$276$		0			0
$277$	−10.7821	−	1.13325i	−0.647836	−	0.0680903i	−0.225089	−	0.974338i	$-0.572267\pi$
$277$	−10.7821	−	1.13325i	−0.647836	−	0.0680903i	−0.422747	+	0.906248i	$0.638934\pi$
$278$	13.4074	−	12.0720i	0.804120	−	0.724033i
$279$		0			0
$280$	−25.9209	+	22.9851i	−1.54907	+	1.37362i
$281$	2.47868	+	3.41161i	0.147866	+	0.203520i	0.876525	−	0.481357i	$-0.159856\pi$
$281$	2.47868	+	3.41161i	0.147866	+	0.203520i	−0.728659	+	0.684877i	$0.759856\pi$
$282$		0			0
$283$	−19.6341	+	4.17335i	−1.16713	+	0.248080i	−0.750420	−	0.660961i	$-0.770149\pi$
$283$	−19.6341	+	4.17335i	−1.16713	+	0.248080i	−0.416705	+	0.909042i	$0.636815\pi$
$284$	0.228426	−	2.17332i	0.0135546	−	0.128963i
$285$		0			0
$286$	5.15987	−	3.84795i	0.305110	−	0.227534i
$287$	−4.26092	−	5.95936i	−0.251514	−	0.351770i
$288$		0			0
$289$	11.0241	+	12.2435i	0.648476	+	0.720205i
$290$	−18.6305	−	16.7750i	−1.09402	−	0.985062i
$291$		0			0
$292$	0.00655817	+	0.0623968i	0.000383788	+	0.00365149i
$293$	−0.210034	−	0.646419i	−0.0122703	−	0.0377642i	0.944734	−	0.327838i	$-0.106320\pi$
$293$	−0.210034	−	0.646419i	−0.0122703	−	0.0377642i	−0.957004	+	0.290074i	$0.906320\pi$
$294$		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
$299$	7.32096	−	3.25950i	0.423382	−	0.188502i
$300$		0			0
$301$	23.2067	+	17.1316i	1.33761	+	0.987450i
$302$	−12.5639	+	9.12819i	−0.722970	+	0.525269i
$303$		0			0
$304$	−10.8341	+	12.0325i	−0.621380	+	0.690113i
$305$	−1.91990	−	9.03240i	−0.109933	−	0.517194i
$306$		0			0
$307$	17.4703			0.997085			0.498543	−	0.866865i	$-0.333869\pi$
$307$	17.4703			0.997085			0.498543	+	0.866865i	$0.333869\pi$
$308$	−1.24311	+	2.17748i	−0.0708326	+	0.124073i
$309$		0			0
$310$	2.30447	+	5.17593i	0.130885	+	0.293973i
$311$	2.42252	+	11.3971i	0.137368	+	0.646268i	0.991916	+	0.126895i	$0.0405011\pi$
$311$	2.42252	+	11.3971i	0.137368	+	0.646268i	−0.854548	+	0.519373i	$0.826166\pi$
$312$		0			0
$313$	−19.2508	+	2.02334i	−1.08812	+	0.114366i	−0.631561	−	0.775326i	$-0.717586\pi$
$313$	−19.2508	+	2.02334i	−1.08812	+	0.114366i	−0.456561	+	0.889692i	$0.650919\pi$
$314$	6.76902	−	4.91798i	0.381998	−	0.277538i
$315$		0			0
$316$	−1.97165	−	0.640627i	−0.110914	−	0.0360381i
$317$	26.0115	−	11.5811i	1.46095	−	0.650457i	0.486219	−	0.873837i	$-0.338376\pi$
$317$	26.0115	−	11.5811i	1.46095	−	0.650457i	0.974731	+	0.223380i	$0.0717092\pi$
$318$		0			0
$319$	−13.3319	−	5.73789i	−0.746445	−	0.321260i
$320$	33.3184	+	19.2364i	1.86255	+	1.07535i
$321$		0			0
$322$	12.6371	−	13.8222i	0.704236	−	0.770281i
$323$	−8.64943	−	26.6202i	−0.481267	−	1.48119i
$324$		0			0
$325$	−19.1525	−	8.52722i	−1.06239	−	0.473005i
$326$	19.2107	+	17.2974i	1.06398	+	0.958015i
$327$		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	$0.182743\pi$
$332$	0.0236138	−	0.224670i	0.00129597	−	0.0123304i
$333$		0			0
$334$	0.529565	−	2.49141i	0.0289765	−	0.136324i
$335$	−15.2461	−	20.9845i	−0.832985	−	1.14650i
$336$		0			0
$337$	−30.4650	+	9.89869i	−1.65954	+	0.539216i	−0.980775	−	0.195143i	$-0.937483\pi$
$337$	−30.4650	+	9.89869i	−1.65954	+	0.539216i	−0.678762	+	0.734359i	$0.737483\pi$
$338$	−10.5112	+	9.46431i	−0.571733	+	0.514790i
$339$		0			0
$340$	−6.26431	+	3.61670i	−0.339730	+	0.196143i
$341$	2.22508	+	2.41015i	0.120495	+	0.130517i
$342$		0			0
$343$	−17.4788	−	6.12308i	−0.943766	−	0.330615i
$344$	10.0826	−	31.0310i	0.543616	−	1.67308i
$345$		0			0
$346$	7.33859	−	16.4828i	0.394525	−	0.886118i
$347$	−5.36794	+	12.0566i	−0.288166	+	0.647231i	−0.998389	−	0.0567457i	$-0.981928\pi$
$347$	−5.36794	+	12.0566i	−0.288166	+	0.647231i	0.710223	+	0.703977i	$0.248594\pi$
$348$		0			0
$349$	−6.69435	+	20.6031i	−0.358341	+	1.10286i	0.595707	+	0.803202i	$0.296872\pi$
$349$	−6.69435	+	20.6031i	−0.358341	+	1.10286i	−0.954047	+	0.299657i	$0.903128\pi$
$350$	−48.9939	−	0.372296i	−2.61883	−	0.0199001i
$351$		0			0
$352$	5.21490	+	1.04075i	0.277955	+	0.0554724i
$353$	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
$355$	24.8675	−	22.3908i	1.31983	−	1.18838i
$356$	−0.349198	+	0.113461i	−0.0185074	+	0.00601343i
$357$		0			0
$358$	−6.35462	−	8.74639i	−0.335852	−	0.462261i
$359$	1.30872	−	6.15705i	0.0690717	−	0.324957i	−0.930023	−	0.367502i	$-0.880213\pi$
$359$	1.30872	−	6.15705i	0.0690717	−	0.324957i	0.999095	+	0.0425449i	$0.0135465\pi$
$360$		0			0
$361$	−0.460324	+	4.37969i	−0.0242276	+	0.230510i
$362$	−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
$367$	−7.79084	−	7.01490i	−0.406678	−	0.366175i	0.440256	−	0.897872i	$-0.354888\pi$
$367$	−7.79084	−	7.01490i	−0.406678	−	0.366175i	−0.846934	+	0.531697i	$0.821554\pi$
$368$	−16.5303	−	7.35976i	−0.861701	−	0.383654i
$369$		0			0
$370$	−11.2748	−	34.7003i	−0.586150	−	1.80398i
$371$	13.6292	+	12.4606i	0.707592	+	0.646922i
$372$		0			0
$373$	−13.6701	−	7.89241i	−0.707808	−	0.408653i	0.102441	−	0.994739i	$-0.467335\pi$
$373$	−13.6701	−	7.89241i	−0.707808	−	0.408653i	−0.810249	+	0.586086i	$0.800668\pi$
$374$	16.5777	−	18.8790i	0.857213	−	0.976212i
$375$		0			0
$376$	9.02760	−	4.01935i	0.465563	−	0.207282i
$377$	−6.16926	−	2.00451i	−0.317733	−	0.103238i
$378$		0			0
$379$	−10.5460	+	7.66212i	−0.541712	+	0.393577i	−0.824720	−	0.565541i	$-0.808667\pi$
$379$	−10.5460	+	7.66212i	−0.541712	+	0.393577i	0.283009	+	0.959117i	$0.408667\pi$
$380$	6.01504	−	0.632206i	0.308565	−	0.0324315i
$381$		0			0
$382$	−1.79456	−	8.44276i	−0.0918179	−	0.431969i
$383$	−12.6543	−	28.4221i	−0.646606	−	1.45230i	−0.877623	−	0.479352i	$-0.840872\pi$
$383$	−12.6543	−	28.4221i	−0.646606	−	1.45230i	0.231017	−	0.972950i	$-0.425795\pi$
$384$		0			0
$385$	−36.4565	+	12.0415i	−1.85800	+	0.613690i
$386$	21.9362			1.11653
$387$		0			0
$388$	−0.758979	−	3.57072i	−0.0385313	−	0.181276i
$389$	5.51217	−	6.12189i	0.279478	−	0.310392i	−0.587020	−	0.809573i	$-0.699699\pi$
$389$	5.51217	−	6.12189i	0.279478	−	0.310392i	0.866498	+	0.499181i	$0.166366\pi$
$390$		0			0
$391$	25.3064	−	18.3862i	1.27980	−	0.929828i
$392$	−0.318357	+	20.9466i	−0.0160795	+	1.05796i
$393$		0			0
$394$	−26.5476	+	11.8198i	−1.33745	+	0.595471i
$395$	−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
$401$	2.05362	+	19.5389i	0.102553	+	0.975726i	0.917916	+	0.396775i	$0.129871\pi$
$401$	2.05362	+	19.5389i	0.102553	+	0.975726i	−0.815363	+	0.578950i	$0.803462\pi$
$402$		0			0
$403$	1.08945	+	0.980943i	0.0542692	+	0.0488642i
$404$	−0.725326	−	0.805557i	−0.0360863	−	0.0400779i
$405$		0			0
$406$	−15.0881	+	1.47000i	−0.748811	+	0.0729548i
$407$	−12.6281	−	16.9335i	−0.625951	−	0.839362i
$408$		0			0
$409$	3.71237	−	35.3209i	0.183565	−	1.74650i	−0.384142	−	0.923274i	$-0.625503\pi$
$409$	3.71237	−	35.3209i	0.183565	−	1.74650i	0.567707	−	0.823231i	$-0.307831\pi$
$410$	−15.5157	+	3.29797i	−0.766267	+	0.162875i
$411$		0			0
$412$	1.86497	+	2.56691i	0.0918804	+	0.126462i
$413$	20.1406	−	4.12131i	0.991054	−	0.202797i
$414$		0			0
$415$	2.57070	−	2.31467i	0.126191	−	0.113623i
$416$	2.36359	+	0.248424i	0.115885	+	0.0121800i
$417$		0			0
$418$	−19.0836	+	8.78295i	−0.933408	+	0.429588i
$419$			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	−0.822895	−	0.568193i	$-0.807643\pi$
$421$	3.62797	−	11.1658i	0.176817	−	0.544186i	0.999712	+	0.0240076i	$0.00764260\pi$
$422$	−8.89669	−	1.89105i	−0.433084	−	0.0920549i
$423$		0			0
$424$	8.49610	−	19.0826i	0.412607	−	0.926731i
$425$	−80.0448	−	17.0140i	−3.88274	−	0.825302i
$426$		0			0
$427$	−4.81440	−	2.82859i	−0.232985	−	0.136885i
$428$		−	3.17661i		−	0.153547i
$429$		0			0
$430$	54.0889	−	31.2282i	2.60840	−	1.50596i
$431$	16.0154	+	1.68328i	0.771432	+	0.0810808i	0.482063	−	0.876137i	$-0.339888\pi$
$431$	16.0154	+	1.68328i	0.771432	+	0.0810808i	0.289370	+	0.957217i	$0.406554\pi$
$432$		0			0
$433$	−38.1354	+	12.3909i	−1.83267	+	0.595471i	−0.833600	+	0.552369i	$0.813724\pi$
$433$	−38.1354	+	12.3909i	−1.83267	+	0.595471i	−0.999071	+	0.0431017i	$0.986276\pi$
$434$	3.25022	+	1.08343i	0.156016	+	0.0520065i
$435$		0			0
$436$	0.373971	−	1.75939i	0.0179099	−	0.0842597i
$437$	−25.5834	+	5.43792i	−1.22382	+	0.260131i
$438$		0			0
$439$	−2.05040	+	3.55140i	−0.0978604	+	0.169499i	−0.910799	−	0.412851i	$-0.864533\pi$
$439$	−2.05040	+	3.55140i	−0.0978604	+	0.169499i	0.812938	+	0.582350i	$0.197867\pi$
$440$	25.9623	+	34.8138i	1.23770	+	1.65968i
$441$		0			0
$442$	6.60005	−	9.08419i	0.313932	−	0.432091i
$443$	−2.01842	−	2.24168i	−0.0958979	−	0.106505i	0.693285	−	0.720663i	$-0.256163\pi$
$443$	−2.01842	−	2.24168i	−0.0958979	−	0.106505i	−0.789183	+	0.614158i	$0.789496\pi$
$444$		0			0
$445$	−5.13621	−	2.28679i	−0.243480	−	0.108404i
$446$	1.87604	+	17.8493i	0.0888329	+	0.845189i
$447$		0			0
$448$	22.1795	−	7.02070i	1.04789	−	0.331697i
$449$	7.58618	+	5.51168i	0.358014	+	0.260112i	0.752223	−	0.658908i	$-0.228981\pi$
$449$	7.58618	+	5.51168i	0.358014	+	0.260112i	−0.394209	+	0.919021i	$0.628981\pi$
$450$		0			0
$451$	−7.89539	+	4.69047i	−0.371779	+	0.220866i
$452$	0.329883	+	0.571374i	0.0155164	+	0.0268752i
$453$		0			0
$454$	23.6669	+	7.68983i	1.11074	+	0.360901i
$455$	−15.7281	+	6.85987i	−0.737343	+	0.321595i
$456$		0			0
$457$	14.3454	−	1.50776i	0.671049	−	0.0705300i	0.237124	−	0.971479i	$-0.423795\pi$
$457$	14.3454	−	1.50776i	0.671049	−	0.0705300i	0.433924	+	0.900949i	$0.357129\pi$
$458$	15.5167	−	17.2330i	0.725046	−	0.805246i
$459$		0			0
$460$	2.74919	+	6.17478i	0.128182	+	0.287900i
$461$	−11.6850			−0.544224			−0.272112	−	0.962266i	$-0.587722\pi$
$461$	−11.6850			−0.544224			−0.272112	+	0.962266i	$0.587722\pi$
$462$		0			0
$463$	−8.02783			−0.373085			−0.186542	−	0.982447i	$-0.559728\pi$
$463$	−8.02783			−0.373085			−0.186542	+	0.982447i	$0.559728\pi$
$464$	5.95734	+	13.3804i	0.276563	+	0.621170i
$465$		0			0
$466$	23.2593	−	25.8321i	1.07747	−	1.19665i
$467$	−5.67895	+	0.596882i	−0.262791	+	0.0276204i	−0.235007	−	0.971994i	$-0.575511\pi$
$467$	−5.67895	+	0.596882i	−0.262791	+	0.0276204i	−0.0277831	+	0.999614i	$0.508845\pi$
$468$		0			0
$469$	−15.5858	−	1.75798i	−0.719687	−	0.0811758i
$470$	17.9902	+	5.84538i	0.829827	+	0.269627i
$471$		0			0
$472$	−11.6269	−	20.1385i	−0.535173	−	0.926948i
$473$	23.8588	−	27.1709i	1.09703	−	1.24932i
$474$		0			0
$475$	55.3564	+	40.2188i	2.53992	+	1.84536i
$476$	−0.941887	+	4.27137i	−0.0431713	+	0.195778i
$477$		0			0
$478$	2.68363	+	25.5331i	0.122747	+	1.16786i
$479$	−21.0231	−	9.36011i	−0.960572	−	0.427674i	−0.134297	−	0.990941i	$-0.542878\pi$
$479$	−21.0231	−	9.36011i	−0.960572	−	0.427674i	−0.826275	+	0.563267i	$0.809544\pi$
$480$		0			0
$481$	−6.31703	−	7.01577i	−0.288032	−	0.319891i
$482$	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
$487$	24.7749	−	5.26607i	1.12266	−	0.238629i	0.391061	−	0.920365i	$-0.372108\pi$
$487$	24.7749	−	5.26607i	1.12266	−	0.238629i	0.731598	+	0.681736i	$0.238775\pi$
$488$	−1.31319	+	6.17808i	−0.0594454	+	0.279669i
$489$		0			0
$490$	−27.2823	+	29.3894i	−1.23249	+	1.32768i
$491$	18.9227	−	6.14835i	0.853969	−	0.277471i	0.150861	−	0.988555i	$-0.451795\pi$
$491$	18.9227	−	6.14835i	0.853969	−	0.277471i	0.703108	+	0.711084i	$0.251795\pi$
$492$		0			0
$493$	−25.1811	−	2.64664i	−1.13410	−	0.119199i
$494$	−8.13093	+	4.69440i	−0.365828	+	0.211211i
$495$		0			0
$496$		−	3.31013i		−	0.148629i
$497$	0.153754	−	20.2339i	0.00689681	−	0.907616i
$498$		0			0
$499$	−8.48354	−	1.80323i	−0.379775	−	0.0807237i	0.0140687	−	0.999901i	$-0.495522\pi$
$499$	−8.48354	−	1.80323i	−0.379775	−	0.0807237i	−0.393844	+	0.919177i	$0.628855\pi$
$500$	4.64966	−	10.4433i	0.207939	−	0.467039i
$501$		0			0
$502$	30.8796	+	6.56365i	1.37822	+	0.292950i
$503$	1.27132	−	3.91271i	0.0566852	−	0.174459i	−0.918705	−	0.394944i	$-0.870764\pi$
$503$	1.27132	−	3.91271i	0.0566852	−	0.174459i	0.975390	+	0.220485i	$0.0707640\pi$
$504$		0			0
$505$		−	16.5986i		−	0.738626i
$506$	−15.9253	−	17.2499i	−0.707968	−	0.766853i
$507$		0			0
$508$	0.388432	+	0.0408258i	0.0172339	+	0.00181135i
$509$	11.2047	−	10.0888i	0.496640	−	0.447177i	−0.382349	−	0.924018i	$-0.624885\pi$
$509$	11.2047	−	10.0888i	0.496640	−	0.447177i	0.878990	+	0.476841i	$0.158218\pi$
$510$		0			0
$511$	0.116463	+	0.569145i	0.00515200	+	0.0251775i
$512$	−14.9290	−	20.5480i	−0.659775	−	0.908103i
$513$		0			0
$514$	−25.8399	+	5.49244i	−1.13975	+	0.242261i
$515$	−5.07849	+	48.3186i	−0.223785	+	2.12917i
$516$		0			0
$517$	10.9506	−	0.136391i	0.481609	−	0.00599847i
$518$	−20.0867	−	9.12667i	−0.882557	−	0.401003i
$519$		0			0
$520$	12.9873	+	14.4238i	0.569530	+	0.632527i
$521$	31.5510	+	28.4086i	1.38227	+	1.24460i	0.937055	+	0.349181i	$0.113540\pi$
$521$	31.5510	+	28.4086i	1.38227	+	1.24460i	0.445217	+	0.895423i	$0.353127\pi$
$522$		0			0
$523$	1.21300	+	11.5410i	0.0530410	+	0.504651i	0.988501	+	0.151217i	$0.0483193\pi$
$523$	1.21300	+	11.5410i	0.0530410	+	0.504651i	−0.935460	+	0.353434i	$0.885014\pi$
$524$	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
$530$	36.5279	−	16.2633i	1.58667	−	0.706431i
$531$		0			0
$532$	2.17212	−	2.94239i	0.0941733	−	0.127569i
$533$	−3.32047	+	2.41246i	−0.143826	+	0.104495i
$534$		0			0
$535$	32.5479	−	36.1481i	1.40717	−	1.56282i
$536$	3.68867	+	17.3538i	0.159326	+	0.749572i
$537$		0			0
$538$	19.7066			0.849612
$539$	−9.50109	+	21.1832i	−0.409241	+	0.912426i
$540$		0			0
$541$	12.2249	+	27.4575i	0.525588	+	1.18049i	0.960057	+	0.279803i	$0.0902693\pi$
$541$	12.2249	+	27.4575i	0.525588	+	1.18049i	−0.434469	+	0.900687i	$0.643064\pi$
$542$	−0.616998	−	2.90275i	−0.0265023	−	0.124684i
$543$		0			0
$544$	9.22586	−	0.969677i	0.395556	−	0.0415746i
$545$	22.2825	−	16.1892i	0.954478	−	0.693469i
$546$		0			0
$547$	1.66790	+	0.541933i	0.0713142	+	0.0231714i	0.344457	−	0.938802i	$-0.388063\pi$
$547$	1.66790	+	0.541933i	0.0713142	+	0.0231714i	−0.273143	+	0.961974i	$0.588063\pi$
$548$	−1.50410	+	0.669669i	−0.0642520	+	0.0286068i
$549$		0			0
$550$	−5.65879	+	61.1576i	−0.241292	+	2.60777i
$551$	18.3347	+	10.5855i	0.781083	+	0.450958i
$552$		0			0
$553$	−18.7454	−	4.13358i	−0.797137	−	0.175778i
$554$	4.38643	+	13.5001i	0.186362	+	0.573562i
$555$		0			0
$556$	3.59690	+	1.60144i	0.152542	+	0.0679162i
$557$	11.8778	+	10.6948i	0.503278	+	0.453153i	0.881241	−	0.472667i	$-0.156709\pi$
$557$	11.8778	+	10.6948i	0.503278	+	0.453153i	−0.377963	+	0.925821i	$0.623375\pi$
$558$		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
$563$	−4.13397	+	39.3321i	−0.174226	+	1.65765i	0.462545	+	0.886596i	$0.346937\pi$
$563$	−4.13397	+	39.3321i	−0.174226	+	1.65765i	−0.636771	+	0.771053i	$0.719730\pi$
$564$		0			0
$565$	−2.10047	+	9.88194i	−0.0883675	+	0.415736i
$566$	15.4477	+	21.2619i	0.649315	+	0.893705i
$567$		0			0
$568$	−21.7678	+	7.07279i	−0.913358	+	0.296768i
$569$	−20.6374	+	18.5820i	−0.865165	+	0.778998i	−0.976665	−	0.214767i	$-0.931101\pi$
$569$	−20.6374	+	18.5820i	−0.865165	+	0.778998i	0.111501	+	0.993764i	$0.464434\pi$
$570$		0			0
$571$	24.2147	−	13.9804i	1.01335	−	0.585061i	0.101183	−	0.994868i	$-0.467737\pi$
$571$	24.2147	−	13.9804i	1.01335	−	0.585061i	0.912172	+	0.409807i	$0.134404\pi$
$572$	1.22518	+	0.687156i	0.0512273	+	0.0287314i
$573$		0			0
$574$	−4.85891	+	8.27010i	−0.202807	+	0.345187i
$575$	−23.6298	+	72.7249i	−0.985429	+	3.03284i
$576$		0			0
$577$	2.93946	−	6.60212i	0.122371	−	0.274850i	−0.841964	−	0.539533i	$-0.818601\pi$
$577$	2.93946	−	6.60212i	0.122371	−	0.274850i	0.964335	+	0.264683i	$0.0852674\pi$
$578$	8.77372	−	19.7061i	0.364939	−	0.819666i
$579$		0			0
$580$	1.69068	−	5.20339i	0.0702018	−	0.216059i
$581$	0.0158945	−	2.09171i	0.000659416	−	0.0867787i
$582$		0			0
$583$	17.0090	−	15.7030i	0.704442	−	0.650350i
$584$	0.569085	−	0.328561i	0.0235489	−	0.0135960i
$585$		0			0
$586$	−0.661333	+	0.595467i	−0.0273194	+	0.0245985i
$587$	−23.6375	+	7.68029i	−0.975624	+	0.316999i	−0.753084	−	0.657924i	$-0.771435\pi$
$587$	−23.6375	+	7.68029i	−0.975624	+	0.316999i	−0.222540	+	0.974924i	$0.571435\pi$
$588$		0			0
$589$	−2.81234	−	3.87085i	−0.115880	−	0.159495i
$590$	9.25470	−	43.5399i	0.381010	−	1.79251i
$591$		0			0
$592$	−2.22817	+	21.1996i	−0.0915773	+	0.871300i
$593$	−6.06292	+	10.5013i	−0.248974	+	0.431236i	−0.963241	−	0.268637i	$-0.913427\pi$
$593$	−6.06292	+	10.5013i	−0.248974	+	0.431236i	0.714267	+	0.699873i	$0.246760\pi$
$594$		0			0
$595$	−54.4830	+	38.9552i	−2.23359	+	1.59701i
$596$	0.230959	−	0.317888i	0.00946046	−	0.0130212i
$597$		0			0
$598$	−7.79741	−	7.02082i	−0.318860	−	0.287103i
$599$	−35.5513	−	15.8284i	−1.45258	−	0.646732i	−0.479576	−	0.877500i	$-0.659210\pi$
$599$	−35.5513	−	15.8284i	−1.45258	−	0.646732i	−0.973009	+	0.230768i	$0.925876\pi$
$600$		0			0
$601$	6.08052	+	18.7139i	0.248029	+	0.763356i	0.995123	+	0.0986377i	$0.0314485\pi$
$601$	6.08052	+	18.7139i	0.248029	+	0.763356i	−0.747094	+	0.664718i	$0.768552\pi$
$602$	8.13267	−	36.8809i	0.331463	−	1.50315i
$603$		0			0
$604$	−2.93511	−	1.69459i	−0.119428	−	0.0689518i
$605$	11.1760	+	46.8134i	0.454369	+	1.90324i
$606$		0			0
$607$	−10.6015	+	4.72011i	−0.430303	+	0.191583i	−0.610447	−	0.792057i	$-0.709010\pi$
$607$	−10.6015	+	4.72011i	−0.430303	+	0.191583i	0.180144	+	0.983640i	$0.442344\pi$
$608$	−7.37701	−	2.39694i	−0.299177	−	0.0972086i
$609$		0			0
$610$	−9.78126	+	7.10650i	−0.396032	+	0.287734i
$611$	4.86765	−	0.511610i	0.196924	−	0.0206975i
$612$		0			0
$613$	−4.10853	−	19.3291i	−0.165942	−	0.780696i	−0.979855	−	0.199710i	$-0.936000\pi$
$613$	−4.10853	−	19.3291i	−0.165942	−	0.780696i	0.813913	−	0.580987i	$-0.197333\pi$
$614$	−9.30365	−	20.8963i	−0.375465	−	0.843308i
$615$		0			0
$616$	26.1301	+	2.61817i	1.05281	+	0.105489i
$617$	−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
$619$	−7.88965	−	37.1179i	−0.317112	−	1.49189i	−0.791277	−	0.611458i	$-0.790583\pi$
$619$	−7.88965	−	37.1179i	−0.317112	−	1.49189i	0.474165	−	0.880436i	$-0.342750\pi$
$620$	−0.827364	+	0.918881i	−0.0332277	+	0.0369032i
$621$		0			0
$622$	12.3420	−	8.96697i	0.494868	−	0.359543i
$623$	−3.11625	+	1.35916i	−0.124850	+	0.0544538i
$624$		0			0
$625$	95.3088	−	42.4342i	3.81235	−	1.69737i
$626$	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	0.975037	−	0.222042i	$-0.0712721\pi$
$631$	1.39924	+	4.30640i	0.0557027	+	0.171435i	−0.919334	+	0.393477i	$0.871272\pi$
$632$	2.26964	+	21.5941i	0.0902812	+	0.858969i
$633$		0			0
$634$	−27.7043	−	24.9451i	−1.10028	−	0.990695i
$635$	4.00183	+	4.44448i	0.158808	+	0.176374i
$636$		0			0
$637$	−3.35592	+	9.81820i	−0.132966	+	0.389011i
$638$	0.236672	+	19.0020i	0.00936992	+	0.752298i
$639$		0			0
$640$	3.79875	−	36.1427i	0.150159	−	1.42866i
$641$	1.19306	−	0.253593i	0.0471232	−	0.0100163i	−0.184290	−	0.982872i	$-0.558998\pi$
$641$	1.19306	−	0.253593i	0.0471232	−	0.0100163i	0.231413	+	0.972856i	$0.425665\pi$
$642$		0			0
$643$	−7.60420	−	10.4663i	−0.299880	−	0.412750i	0.632312	−	0.774714i	$-0.282106\pi$
$643$	−7.60420	−	10.4663i	−0.299880	−	0.412750i	−0.932192	+	0.361964i	$0.882106\pi$
$644$	3.87745	+	1.29251i	0.152793	+	0.0509322i
$645$		0			0
$646$	−27.2344	+	24.5219i	−1.07152	+	0.964803i
$647$	−5.25145	−	0.551950i	−0.206456	−	0.0216994i	0.000735859	−	1.00000i	$-0.499766\pi$
$647$	−5.25145	−	0.551950i	−0.206456	−	0.0216994i	−0.207192	+	0.978300i	$0.566432\pi$
$648$		0			0
$649$	−3.01276	−	25.5940i	−0.118261	−	1.00465i
$650$			27.4494i			1.07665i
$651$		0			0
$652$	−1.74333	+	5.36543i	−0.0682742	+	0.210126i
$653$	−18.0256	−	3.83145i	−0.705395	−	0.149936i	−0.158772	−	0.987315i	$-0.550753\pi$
$653$	−18.0256	−	3.83145i	−0.705395	−	0.149936i	−0.546623	+	0.837379i	$0.684087\pi$
$654$		0			0
$655$	−21.0011	+	47.1693i	−0.820581	+	1.84306i
$656$	9.06482	+	1.92679i	0.353922	+	0.0752284i
$657$		0			0
$658$	9.94911	−	5.64376i	0.387857	−	0.220017i
$659$		−	4.57092i		−	0.178058i	−0.996029	−	0.0890290i	$-0.971624\pi$
$659$		−	4.57092i		−	0.178058i	0.996029	−	0.0890290i	$-0.0283764\pi$
$660$		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	$0.386159\pi$
$662$	2.39199	+	0.251408i	0.0929673	+	0.00977126i
$663$		0			0
$664$	−2.25028	+	0.731159i	−0.0873277	+	0.0283745i
$665$	54.8655	−	11.2270i	2.12759	−	0.435363i
$666$		0			0
$667$	−4.91913	+	23.1427i	−0.190469	+	0.896088i
$668$	0.543716	−	0.115571i	0.0210370	−	0.00447156i
$669$		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	−0.273014	−	0.962010i	$-0.588021\pi$
$673$	18.8413	−	25.9328i	0.726277	−	0.999635i	0.999292	−	0.0376252i	$-0.0119793\pi$
$674$	28.0637	+	31.1679i	1.08097	+	1.20054i
$675$		0			0
$676$	−2.81991	−	1.25551i	−0.108458	−	0.0482887i
$677$	0.531487	+	5.05676i	0.0204267	+	0.194347i	0.999977	−	0.00685468i	$-0.00218193\pi$
$677$	0.531487	+	5.05676i	0.0204267	+	0.194347i	−0.979550	+	0.201202i	$0.935515\pi$
$678$		0			0
$679$	−10.2006	−	32.2254i	−0.391463	−	1.23670i
$680$	61.2913	+	44.5307i	2.35041	+	1.70768i
$681$		0			0
$682$	1.69784	−	3.94492i	0.0650137	−	0.151059i
$683$	−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
$686$	1.98431	+	24.1672i	0.0757613	+	0.922709i
$687$		0			0
$688$	−36.2893	+	3.81416i	−1.38352	+	0.145414i
$689$	6.92277	−	7.68852i	0.263737	−	0.292909i
$690$		0			0
$691$	−13.9874	−	31.4163i	−0.532107	−	1.19513i	−0.957053	−	0.289913i	$-0.906373\pi$
$691$	−13.9874	−	31.4163i	−0.532107	−	1.19513i	0.424946	−	0.905219i	$-0.360293\pi$
$692$	3.93756			0.149684
$693$		0			0
$694$	17.2796			0.655923
$695$	24.5222	+	55.0777i	0.930178	+	2.08922i
$696$		0			0
$697$	−10.7198	+	11.9056i	−0.406042	+	0.450955i
$698$	28.2085	−	2.96483i	1.06771	−	0.112220i
$699$		0			0
$700$	−4.27471	−	9.80092i	−0.161569	−	0.370440i
$701$	−10.1237	−	3.28938i	−0.382366	−	0.124238i	0.111526	−	0.993761i	$-0.464426\pi$
$701$	−10.1237	−	3.28938i	−0.382366	−	0.124238i	−0.493892	+	0.869523i	$0.664426\pi$
$702$		0			0
$703$	15.4059	+	26.6838i	0.581045	+	1.00640i
$704$	−6.41817	−	28.4482i	−0.241894	−	1.07218i
$705$		0			0
$706$	−8.91460	−	6.47683i	−0.335505	−	0.243759i
$707$	−7.40772	−	6.77257i	−0.278596	−	0.254709i
$708$		0			0
$709$	−0.777095	−	7.39356i	−0.0291844	−	0.277671i	−0.999376	−	0.0353307i	$-0.988752\pi$
$709$	−0.777095	−	7.39356i	−0.0291844	−	0.277671i	0.970191	−	0.242340i	$-0.0779151\pi$
$710$	−40.0246	−	17.8201i	−1.50210	−	0.668776i
$711$		0			0
$712$	2.57320	+	2.85783i	0.0964349	+	0.107102i
$713$	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
$718$	−8.06142	+	1.71351i	−0.300850	+	0.0639475i
$719$	−6.00604	+	28.2562i	−0.223987	+	1.05378i	0.712119	+	0.702059i	$0.247736\pi$
$719$	−6.00604	+	28.2562i	−0.223987	+	1.05378i	−0.936106	+	0.351718i	$0.885598\pi$
$720$		0			0
$721$	19.4918	+	21.9815i	0.725914	+	0.818634i
$722$	5.48370	−	1.78176i	0.204082	−	0.0663104i
$723$		0			0
$724$	−6.38282	−	0.670861i	−0.237216	−	0.0249324i
$725$	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	$0.920389\pi$
$728$	11.7362	+	0.0891817i	0.434974	+	0.00330529i
$729$		0			0
$730$	1.23038	+	0.261525i	0.0455383	+	0.00967947i
$731$	25.6566	−	57.6257i	0.948945	−	2.13136i
$732$		0			0
$733$	3.91890	+	0.832988i	0.144748	+	0.0307671i	0.279716	−	0.960083i	$-0.409760\pi$
$733$	3.91890	+	0.832988i	0.144748	+	0.0307671i	−0.134968	+	0.990850i	$0.543093\pi$
$734$	−4.24162	+	13.0544i	−0.156561	+	0.481845i
$735$		0			0
$736$		−	8.66844i		−	0.319523i
$737$	−3.84808	+	19.2815i	−0.141746	+	0.710245i
$738$		0			0
$739$	−22.1917	−	2.33244i	−0.816336	−	0.0858003i	−0.312848	−	0.949803i	$-0.601283\pi$
$739$	−22.1917	−	2.33244i	−0.816336	−	0.0858003i	−0.503487	+	0.864003i	$0.667950\pi$
$740$	5.91736	−	5.32802i	0.217527	−	0.195862i
$741$		0			0
$742$	7.64608	−	22.9377i	0.280696	−	0.842069i
$743$	9.75074	+	13.4207i	0.357720	+	0.492359i	0.949512	−	0.313731i	$-0.101579\pi$
$743$	9.75074	+	13.4207i	0.357720	+	0.492359i	−0.591792	+	0.806091i	$0.701579\pi$
$744$		0			0
$745$	5.88530	−	1.25096i	0.215621	−	0.0458316i
$746$	−2.16029	+	20.5538i	−0.0790940	+	0.752529i
$747$		0			0
$748$	5.23542	+	1.62929i	0.191426	+	0.0595727i
$749$	−2.85218	−	29.2749i	−0.104216	−	1.06968i
$750$		0			0
$751$	−31.3185	−	34.7827i	−1.14283	−	1.26924i	−0.958095	−	0.286449i	$-0.907525\pi$
$751$	−31.3185	−	34.7827i	−1.14283	−	1.26924i	−0.184732	−	0.982789i	$-0.559142\pi$
$752$	−8.21279	−	7.39483i	−0.299490	−	0.269662i
$753$		0			0
$754$	0.887769	+	8.44656i	0.0323306	+	0.307605i
$755$	−16.0370	−	49.3569i	−0.583648	−	1.79628i
$756$		0			0
$757$	−31.7771	−	23.0874i	−1.15496	−	0.839127i	−0.165826	−	0.986155i	$-0.553029\pi$
$757$	−31.7771	−	23.0874i	−1.15496	−	0.839127i	−0.989132	+	0.147028i	$0.953029\pi$
$758$	14.7809	+	8.53373i	0.536865	+	0.309959i
$759$		0			0
$760$	−31.6732	−	54.8597i	−1.14891	−	1.98997i
$761$	16.6226	−	7.40084i	0.602567	−	0.268280i	−0.0826970	−	0.996575i	$-0.526353\pi$
$761$	16.6226	−	7.40084i	0.602567	−	0.268280i	0.685264	+	0.728295i	$0.259687\pi$
$762$		0			0
$763$	1.86672	−	16.5499i	0.0675797	−	0.599147i
$764$	1.52393	−	1.10720i	0.0551339	−	0.0400571i
$765$		0			0
$766$	−27.2568	+	30.2718i	−0.984830	+	1.09376i
$767$	−2.39462	−	11.2658i	−0.0864648	−	0.406785i
$768$		0			0
$769$	−26.1842			−0.944227			−0.472114	−	0.881538i	$-0.656509\pi$
$769$	−26.1842			−0.944227			−0.472114	+	0.881538i	$0.656509\pi$
$770$	33.8174	+	37.1932i	1.21869	+	1.34035i
$771$		0			0
$772$	1.94717	+	4.37341i	0.0700801	+	0.157403i
$773$	4.98542	+	23.4546i	0.179313	+	0.843602i	0.972185	+	0.234214i	$0.0752516\pi$
$773$	4.98542	+	23.4546i	0.179313	+	0.843602i	−0.792872	+	0.609388i	$0.791415\pi$
$774$		0			0
$775$	−13.9119	+	1.46220i	−0.499730	+	0.0525237i
$776$	−30.9319	+	22.4734i	−1.11039	+	0.806747i
$777$		0			0
$778$	−10.2579	−	3.33298i	−0.367762	−	0.119493i
$779$	12.2374	−	5.44843i	0.438449	−	0.195210i
$780$		0			0
$781$	−25.2574	−	2.33702i	−0.903781	−	0.0836251i
$782$	−35.4684	−	20.4777i	−1.26835	−	0.732281i
$783$		0			0
$784$	21.5450	−	9.20274i	0.769465	−	0.328669i
$785$	8.64025	+	26.5920i	0.308384	+	0.949108i
$786$		0			0
$787$	−6.59017	−	2.93413i	−0.234914	−	0.104590i	0.285904	−	0.958258i	$-0.407706\pi$
$787$	−6.59017	−	2.93413i	−0.234914	−	0.104590i	−0.520818	+	0.853668i	$0.674373\pi$
$788$	−4.71300	−	4.24360i	−0.167894	−	0.151172i
$789$		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
$794$	3.27669	−	31.1756i	0.116285	−	1.10638i
$795$		0			0
$796$	0.380107	−	1.78826i	0.0134725	−	0.0633832i
$797$	−23.8170	−	32.7814i	−0.843643	−	1.16118i	−0.985228	−	0.171249i	$-0.945220\pi$
$797$	−23.8170	−	32.7814i	−0.843643	−	1.16118i	0.141585	−	0.989926i	$-0.454780\pi$
$798$		0			0
$799$	18.1696	−	5.90366i	0.642794	−	0.208856i
$800$	−16.8528	+	15.1743i	−0.595835	+	0.536492i
$801$		0			0
$802$	22.2769	−	12.8616i	0.786625	−	0.454158i
$803$	0.723251	−	0.0851364i	0.0255230	−	0.00300440i
$804$		0			0
$805$	30.8800	+	54.4368i	1.08838	+	1.91865i
$806$	0.593135	−	1.82548i	0.0208923	−	0.0642999i
$807$		0			0
$808$	−4.61779	+	10.3717i	−0.162453	+	0.364876i
$809$	7.59661	−	17.0623i	0.267082	−	0.599877i	−0.729362	−	0.684128i	$-0.760183\pi$
$809$	7.59661	−	17.0623i	0.267082	−	0.599877i	0.996445	+	0.0842509i	$0.0268497\pi$
$810$		0			0
$811$	11.2529	−	34.6328i	0.395142	−	1.21612i	−0.533708	−	0.845669i	$-0.679202\pi$
$811$	11.2529	−	34.6328i	0.395142	−	1.21612i	0.928851	−	0.370454i	$-0.120798\pi$
$812$	−1.63237	−	2.87762i	−0.0572849	−	0.100985i
$813$		0			0
$814$	−13.5293	+	24.1222i	−0.474200	+	0.845484i
$815$	−74.8129	+	43.1932i	−2.62058	+	1.51299i
$816$		0			0
$817$	−39.1959	+	35.2922i	−1.37129	+	1.23472i
$818$	−44.2244	+	14.3694i	−1.54627	+	0.502414i
$819$		0			0
$820$	−2.03476	−	2.80061i	−0.0710570	−	0.0978016i
$821$	−4.84077	+	22.7740i	−0.168944	+	0.794819i	0.809306	+	0.587388i	$0.199844\pi$
$821$	−4.84077	+	22.7740i	−0.168944	+	0.794819i	−0.978250	+	0.207431i	$0.933490\pi$
$822$		0			0
$823$	0.0906668	−	0.862637i	0.00316045	−	0.0300696i	−0.992828	−	0.119551i	$-0.961854\pi$
$823$	0.0906668	−	0.862637i	0.00316045	−	0.0300696i	0.995988	+	0.0894817i	$0.0285211\pi$
$824$	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	−0.747295	−	0.664493i	$-0.768648\pi$
$827$	3.32445	−	4.57571i	0.115602	−	0.159113i	0.862897	+	0.505380i	$0.168648\pi$
$828$		0			0
$829$	33.8967	+	30.5207i	1.17728	+	1.06003i	0.997077	+	0.0763994i	$0.0243424\pi$
$829$	33.8967	+	30.5207i	1.17728	+	1.06003i	0.180204	+	0.983629i	$0.442324\pi$
$830$	−4.13759	−	1.84217i	−0.143618	−	0.0639428i
$831$		0			0
$832$	−4.02762	−	12.3958i	−0.139633	−	0.429745i
$833$	−4.84507	+	40.2096i	−0.167872	+	1.39318i
$834$		0			0
$835$	7.37134	+	4.25584i	0.255096	+	0.147280i
$836$	−3.44500	−	3.02506i	−0.119148	−	0.104624i
$837$		0			0
$838$	25.8153	−	11.4937i	0.891774	−	0.397043i
$839$	41.5863	+	13.5122i	1.43572	+	0.466493i	0.920559	−	0.390603i	$-0.127733\pi$
$839$	41.5863	+	13.5122i	1.43572	+	0.466493i	0.515158	+	0.857095i	$0.327733\pi$
$840$		0			0
$841$	−7.96779	+	5.78894i	−0.274751	+	0.199619i
$842$	−15.2874	+	1.60678i	−0.526840	+	0.0553731i
$843$		0			0
$844$	−0.412697	−	1.94158i	−0.0142056	−	0.0668321i
$845$	−19.2250	−	43.1801i	−0.661361	−	1.48544i
$846$		0			0
$847$	25.4523	+	14.1132i	0.874550	+	0.484935i
$848$	−23.3605			−0.802202
$849$		0			0
$850$	22.2765	+	104.802i	0.764076	+	3.59470i
$851$	−23.0407	+	25.5893i	−0.789824	+	0.877189i
$852$		0			0
$853$	−1.79303	+	1.30271i	−0.0613922	+	0.0446041i	−0.618058	−	0.786132i	$-0.712080\pi$
$853$	−1.79303	+	1.30271i	−0.0613922	+	0.0446041i	0.556666	+	0.830736i	$0.312080\pi$
$854$	−0.819426	+	7.26485i	−0.0280402	+	0.248598i
$855$		0			0
$856$	−30.3943	+	13.5324i	−1.03886	+	0.462529i
$857$	8.97672	+	15.5481i	0.306639	+	0.531114i	0.977625	−	0.210356i	$-0.0674622\pi$
$857$	8.97672	+	15.5481i	0.306639	+	0.531114i	−0.670986	+	0.741470i	$0.734129\pi$
$858$		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
$863$	−1.22571	−	11.6618i	−0.0417235	−	0.396972i	−0.995375	−	0.0960607i	$-0.969376\pi$
$863$	−1.22571	−	11.6618i	−0.0417235	−	0.396972i	0.953652	−	0.300912i	$-0.0972910\pi$
$864$		0			0
$865$	44.8073	+	40.3447i	1.52349	+	1.37176i
$866$	35.1295	+	39.0152i	1.19375	+	1.32579i
$867$		0			0
$868$	0.0725022	+	0.744165i	0.00246088	+	0.0252586i
$869$	−7.15033	+	22.9763i	−0.242559	+	0.779417i
$870$		0			0
$871$	−0.918520	+	8.73914i	−0.0311229	+	0.296114i
$872$	−18.4273	+	3.91684i	−0.624027	+	0.132641i
$873$		0			0
$874$	20.1285	+	27.7045i	0.680856	+	0.937118i
$875$	33.4734	−	100.418i	1.13161	−	3.39474i
$876$		0			0
$877$	12.8710	−	11.5891i	0.434624	−	0.391337i	−0.422570	−	0.906330i	$-0.638872\pi$
$877$	12.8710	−	11.5891i	0.434624	−	0.391337i	0.857195	+	0.514993i	$0.172205\pi$
$878$	5.33976	+	0.561232i	0.180208	+	0.0189407i
$879$		0			0
$880$	23.7583	−	42.3603i	0.800893	−	1.42797i
$881$		−	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	0.519602	+	0.854409i	$0.326080\pi$
$883$	−11.9745	+	36.8537i	−0.402974	+	1.24023i	−0.922575	+	0.385817i	$0.873920\pi$
$884$	2.39696	+	0.509489i	0.0806184	+	0.0171360i
$885$		0			0
$886$	−1.60639	+	3.60802i	−0.0539679	+	0.121214i
$887$	−14.9171	−	3.17073i	−0.500868	−	0.106463i	−0.0494522	−	0.998776i	$-0.515748\pi$
$887$	−14.9171	−	3.17073i	−0.500868	−	0.106463i	−0.451416	+	0.892314i	$0.649081\pi$
$888$		0			0
$889$	3.61635	+	0.0274800i	0.121288	+	0.000921649i
$890$			7.36125i			0.246750i
$891$		0			0
$892$	−3.39207	+	1.95841i	−0.113575	+	0.0655726i
$893$	−15.8867	−	1.66976i	−0.531629	−	0.0558765i
$894$		0			0
$895$	34.3600	−	11.1642i	1.14853	−	0.373179i
$896$	−14.5800	−	16.4423i	−0.487084	−	0.549299i
$897$		0			0
$898$	2.55260	−	12.0090i	0.0851814	−	0.400747i
$899$	−4.23358	+	0.899876i	−0.141198	+	0.0300126i
$900$		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
$905$	−65.7593	−	73.0331i	−2.18591	−	2.42770i
$906$		0			0
$907$	−24.9872	−	11.1250i	−0.829687	−	0.369400i	−0.0524615	−	0.998623i	$-0.516707\pi$
$907$	−24.9872	−	11.1250i	−0.829687	−	0.369400i	−0.777225	+	0.629223i	$0.783373\pi$
$908$	0.567671	+	5.40103i	0.0188388	+	0.179239i
$909$		0			0
$910$	16.5809	+	15.1593i	0.549653	+	0.502524i
$911$	24.4050	+	17.7313i	0.808574	+	0.587463i	0.913417	−	0.407026i	$-0.133434\pi$
$911$	24.4050	+	17.7313i	0.808574	+	0.587463i	−0.104843	+	0.994489i	$0.533434\pi$
$912$		0			0
$913$	−2.61102	−	0.241592i	−0.0864120	−	0.00799554i
$914$	−9.44292	−	16.3556i	−0.312344	−	0.540996i
$915$		0			0
$916$	4.81307	+	1.56386i	0.159028	+	0.0516714i
$917$	12.4821	+	28.6186i	0.412196	+	0.945069i
$918$		0			0
$919$	−4.20017	+	0.441456i	−0.138551	+	0.0145623i	−0.173550	−	0.984825i	$-0.555524\pi$
$919$	−4.20017	+	0.441456i	−0.138551	+	0.0145623i	0.0349991	+	0.999387i	$0.488857\pi$
$920$	47.3697	−	52.6094i	1.56173	−	1.73448i
$921$		0			0
$922$	6.22272	+	13.9765i	0.204934	+	0.460290i
$923$	−11.3363			−0.373139
$924$		0			0
$925$	90.0825			2.96190
$926$	4.27514	+	9.60211i	0.140490	+	0.315545i
$927$		0			0
$928$	−4.69505	+	5.21438i	−0.154123	+	0.171171i
$929$	−20.5389	+	2.15873i	−0.673860	+	0.0708255i	−0.435277	−	0.900297i	$-0.643350\pi$
$929$	−20.5389	+	2.15873i	−0.673860	+	0.0708255i	−0.238583	+	0.971122i	$0.576683\pi$
$930$		0			0
$931$	17.3758	−	29.0666i	0.569470	−	0.952619i
$932$	7.21474	+	2.34421i	0.236327	+	0.0767872i
$933$		0			0
$934$	3.73820	+	6.47475i	0.122318	+	0.211860i
$935$	42.8823	+	72.1830i	1.40240	+	2.36064i
$936$		0			0
$937$	−25.8666	−	18.7932i	−0.845024	−	0.613946i	0.0787452	−	0.996895i	$-0.474909\pi$
$937$	−25.8666	−	18.7932i	−0.845024	−	0.613946i	−0.923770	+	0.382949i	$0.874909\pi$
$938$	6.19736	+	19.5785i	0.202351	+	0.639260i
$939$		0			0
$940$	0.431512	+	4.10556i	0.0140744	+	0.133909i
$941$	−30.5026	−	13.5806i	−0.994357	−	0.442716i	−0.155952	−	0.987765i	$-0.549845\pi$
$941$	−30.5026	−	13.5806i	−0.994357	−	0.442716i	−0.838404	+	0.545049i	$0.816511\pi$
$942$		0			0
$943$	10.0170	+	11.1250i	0.326197	+	0.362278i
$944$	−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
$949$	0.318356	−	0.0676687i	0.0103343	−	0.00219662i
$950$	18.6263	−	87.6300i	0.604318	−	2.84309i
$951$		0			0
$952$	44.8816	−	9.18400i	1.45462	−	0.297655i
$953$	48.6676	−	15.8131i	1.57650	−	0.512235i	0.615347	−	0.788257i	$-0.289016\pi$
$953$	48.6676	−	15.8131i	1.57650	−	0.512235i	0.961152	+	0.276021i	$0.0890160\pi$
$954$		0			0
$955$	28.6860	+	3.01502i	0.928257	+	0.0975637i
$956$	−4.85230	+	2.80147i	−0.156934	+	0.0906062i
$957$		0			0
$958$			30.1305i			0.973472i
$959$	−13.2602	+	7.52199i	−0.428193	+	0.242898i
$960$		0			0
$961$	−29.3658	−	6.24189i	−0.947284	−	0.201351i
$962$	−5.02752	+	11.2920i	−0.162094	+	0.364068i
$963$		0			0
$964$	4.81685	+	1.02385i	0.155140	+	0.0329761i
$965$	−22.6527	+	69.7179i	−0.729217	+	2.24430i
$966$		0			0
$967$		−	18.7568i		−	0.603177i	−0.953438	−	0.301588i	$-0.902483\pi$
$967$		−	18.7568i		−	0.603177i	0.953438	−	0.301588i	$-0.0975168\pi$
$968$	6.04030	−	32.3609i	0.194143	−	1.04012i
$969$		0			0
$970$	−72.7866	−	7.65019i	−2.33704	−	0.245633i
$971$	22.7755	−	20.5071i	0.730900	−	0.658105i	−0.217182	−	0.976131i	$-0.569687\pi$
$971$	22.7755	−	20.5071i	0.730900	−	0.658105i	0.948082	+	0.318026i	$0.103020\pi$
$972$		0			0
$973$	34.5860	+	11.5290i	1.10878	+	0.369601i
$974$	−19.4924	−	26.8290i	−0.624577	−	0.859656i
$975$		0			0
$976$	6.90922	−	1.46860i	0.221159	−	0.0470087i
$977$	3.78864	−	36.0465i	0.121209	−	1.15323i	−0.749697	−	0.661782i	$-0.769801\pi$
$977$	3.78864	−	36.0465i	0.121209	−	1.15323i	0.870906	−	0.491449i	$-0.163533\pi$
$978$		0			0
$979$	1.36735	+	4.03651i	0.0437007	+	0.129007i
$980$	−8.28104	−	2.83051i	−0.264528	−	0.0904174i
$981$		0			0
$982$	−17.4312	−	19.3593i	−0.556250	−	0.617779i
$983$	−18.9020	−	17.0194i	−0.602879	−	0.542835i	0.310172	−	0.950681i	$-0.399613\pi$
$983$	−18.9020	−	17.0194i	−0.602879	−	0.542835i	−0.913051	+	0.407846i	$0.866280\pi$
$984$		0			0
$985$	−10.1509	−	96.5797i	−0.323436	−	3.07728i
$986$	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	$0.904485\pi$
$992$	1.44866	−	0.644984i	0.0459950	−	0.0204783i
$993$		0			0
$994$	−24.2838	+	10.5915i	−0.770234	+	0.335941i
$995$	22.6481	−	16.4548i	0.717993	−	0.521653i
$996$		0			0
$997$	−41.6645	+	46.2731i	−1.31953	+	1.46548i	−0.535857	+	0.844309i	$0.680011\pi$
$997$	−41.6645	+	46.2731i	−1.31953	+	1.46548i	−0.783671	+	0.621176i	$0.786655\pi$
$998$	2.36097	+	11.1075i	0.0747352	+	0.351601i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.cg.b.19.5	✓	128	33.8	even	10	inner
693.2.cg.b.19.12	yes	128	11.8	odd	10	inner
693.2.cg.b.73.5	yes	128	21.17	even	6	inner
693.2.cg.b.73.12	yes	128	7.3	odd	6	inner
693.2.cg.b.271.5	yes	128	1.1	even	1	trivial
693.2.cg.b.271.12	yes	128	3.2	odd	2	inner
693.2.cg.b.514.5	yes	128	77.52	even	30	inner
693.2.cg.b.514.12	yes	128	231.206	odd	30	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)

\(f(q)\)	\(=\)	\(q+(-0.532540 - 1.19610i) q^{2} +(0.191195 - 0.212344i) q^{4} +(4.35140 - 0.457350i) q^{5} +(1.57135 - 2.12858i) q^{7} +(-2.84624 - 0.924799i) q^{8} +O(q^{10})\)	\(q+(-0.532540 - 1.19610i) q^{2} +(0.191195 - 0.212344i) q^{4} +(4.35140 - 0.457350i) q^{5} +(1.57135 - 2.12858i) q^{7} +(-2.84624 - 0.924799i) q^{8} +(-2.86433 - 4.96116i) q^{10} +(-2.49218 - 2.18839i) q^{11} +(-1.19918 - 0.871257i) q^{13} +(-3.38281 - 0.745949i) q^{14} +(0.349844 + 3.32855i) q^{16} +(-5.28557 - 2.35329i) q^{17} +(3.23709 + 3.59515i) q^{19} +(0.734851 - 1.01144i) q^{20} +(-1.29035 + 4.14631i) q^{22} +(-2.70321 + 4.68210i) q^{23} +(13.8347 - 2.94066i) q^{25} +(-0.403502 + 1.89833i) q^{26} +(-0.151556 - 0.740642i) q^{28} +(4.16203 - 1.35233i) q^{29} +(-0.983602 - 0.103381i) q^{31} +(-1.38855 + 0.801680i) q^{32} +7.57531i q^{34} +(5.86407 - 9.98095i) q^{35} +(6.22986 + 1.32420i) q^{37} +(2.57629 - 5.78645i) q^{38} +(-12.8081 - 2.72244i) q^{40} +(0.855652 - 2.63342i) q^{41} +10.9025i q^{43} +(-0.941184 + 0.110790i) q^{44} +(7.03985 + 0.739918i) q^{46} +(-2.45386 + 2.20947i) q^{47} +(-2.06170 - 6.68950i) q^{49} +(-10.8849 - 14.9818i) q^{50} +(-0.414285 + 0.0880589i) q^{52} +(-0.729585 + 6.94154i) q^{53} +(-11.8453 - 8.38274i) q^{55} +(-6.44095 + 4.60526i) q^{56} +(-3.83397 - 4.25805i) q^{58} +(5.77436 + 5.19926i) q^{59} +(-0.220607 - 2.09893i) q^{61} +(0.400153 + 1.23154i) q^{62} +(7.11372 + 5.16842i) q^{64} +(-5.61659 - 3.24274i) q^{65} +(-2.96412 - 5.13401i) q^{67} +(-1.51028 + 0.672422i) q^{68} +(-15.0611 - 1.69879i) q^{70} +(6.18730 - 4.49534i) q^{71} +(-0.146924 + 0.163175i) q^{73} +(-1.73377 - 8.15675i) q^{74} +1.38232 q^{76} +(-8.57425 + 1.86607i) q^{77} +(-2.95100 - 6.62806i) q^{79} +(3.04462 + 14.3238i) q^{80} +(-3.60552 + 0.378955i) q^{82} +(0.639620 - 0.464711i) q^{83} +(-24.0759 - 7.82273i) q^{85} +(13.0405 - 5.80599i) q^{86} +(5.06952 + 8.53344i) q^{88} +(-1.11283 - 0.642493i) q^{89} +(-3.73888 + 1.18350i) q^{91} +(0.477375 + 1.46921i) q^{92} +(3.94953 + 1.75845i) q^{94} +(15.7301 + 14.1634i) q^{95} +(7.50936 - 10.3358i) q^{97} +(-6.90340 + 6.02843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 20 q^{4} + 10 q^{7}+O(q^{10}) \) 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

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