LMFDB - Embedded newform 693.2.cg.b.514.5

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			514.5
Character	$\chi$	$=$	693.514
Dual form			693.2.cg.b.271.5

$q$-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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.532540	+	1.19610i	−0.376562	+	0.845773i	0.621492	+	0.783421i	$0.286527\pi$
$2$	−0.532540	+	1.19610i	−0.376562	+	0.845773i	−0.998054	+	0.0623524i	$0.980140\pi$
$3$		0			0
$3$		0			0
$4$	0.191195	+	0.212344i	0.0955977	+	0.106172i
$5$	4.35140	+	0.457350i	1.94600	+	0.204533i	0.994629	−	0.103504i	$-0.0330054\pi$
$5$	4.35140	+	0.457350i	1.94600	+	0.204533i	0.951374	+	0.308037i	$0.0996721\pi$
$6$		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	−0.741530	−	0.670919i	$-0.765900\pi$
$13$	−1.19918	+	0.871257i	−0.332593	+	0.241643i	0.408937	+	0.912563i	$0.365900\pi$
$14$	−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	−0.930787	−	0.365562i	$-0.880877\pi$
$17$	−5.28557	+	2.35329i	−1.28194	+	0.570756i	−0.351153	+	0.936318i	$0.614210\pi$
$18$		0			0
$19$	3.23709	−	3.59515i	0.742638	−	0.824784i	−0.246902	−	0.969040i	$-0.579413\pi$
$19$	3.23709	−	3.59515i	0.742638	−	0.824784i	0.989540	+	0.144257i	$0.0460792\pi$
$20$	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	−0.997173	−	0.0751391i	$-0.976060\pi$
$23$	−2.70321	−	4.68210i	−0.563659	−	0.976286i	0.433514	−	0.901147i	$-0.357273\pi$
$24$		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	0.668793	−	0.743449i	$-0.266811\pi$
$29$	4.16203	+	1.35233i	0.772869	+	0.251121i	0.104077	+	0.994569i	$0.466811\pi$
$30$		0			0
$31$	−0.983602	+	0.103381i	−0.176660	+	0.0185677i	−0.192445	−	0.981308i	$-0.561642\pi$
$31$	−0.983602	+	0.103381i	−0.176660	+	0.0185677i	0.0157853	+	0.999875i	$0.494975\pi$
$32$	−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	0.334949	−	0.942236i	$-0.391281\pi$
$37$	6.22986	−	1.32420i	1.02418	−	0.217697i	0.689233	+	0.724539i	$0.257947\pi$
$38$	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	0.995374	−	0.0960713i	$-0.0306277\pi$
$41$	0.855652	+	2.63342i	0.133630	+	0.411272i	−0.861744	+	0.507343i	$0.830628\pi$
$42$		0			0
$43$		−	10.9025i		−	1.66261i	−0.555817	−	0.831305i	$-0.687595\pi$
$43$		−	10.9025i		−	1.66261i	0.555817	−	0.831305i	$-0.312405\pi$
$44$	−0.941184	−	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	0.470471	−	0.882415i	$-0.344084\pi$
$47$	−2.45386	−	2.20947i	−0.357933	−	0.322284i	−0.828404	+	0.560131i	$0.810751\pi$
$48$		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	−0.922912	−	0.385012i	$-0.874197\pi$
$53$	−0.729585	−	6.94154i	−0.100216	−	0.953494i	0.822695	−	0.568482i	$-0.192469\pi$
$54$		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	−0.201349	−	0.979520i	$-0.564533\pi$
$59$	5.77436	−	5.19926i	0.751758	−	0.676886i	0.953107	+	0.302634i	$0.0978659\pi$
$60$		0			0
$61$	−0.220607	+	2.09893i	−0.0282458	+	0.268741i	0.971280	+	0.237940i	$0.0764723\pi$
$61$	−0.220607	+	2.09893i	−0.0282458	+	0.268741i	−0.999526	+	0.0308005i	$0.990194\pi$
$62$	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	−0.988310	−	0.152455i	$-0.951282\pi$
$67$	−2.96412	+	5.13401i	−0.362125	+	0.627220i	0.626185	+	0.779675i	$0.284615\pi$
$68$	−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	0.890920	−	0.454160i	$-0.150061\pi$
$71$	6.18730	+	4.49534i	0.734298	+	0.533498i	−0.156622	+	0.987659i	$0.550061\pi$
$72$		0			0
$73$	−0.146924	−	0.163175i	−0.0171961	−	0.0190982i	0.734485	−	0.678624i	$-0.237424\pi$
$73$	−0.146924	−	0.163175i	−0.0171961	−	0.0190982i	−0.751682	+	0.659526i	$0.770757\pi$
$74$	−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	0.667985	+	0.744175i	$0.267157\pi$
$79$	−2.95100	+	6.62806i	−0.332014	+	0.745715i	−0.999999	+	0.00154065i	$0.999510\pi$
$80$	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	0.622335	−	0.782751i	$-0.286184\pi$
$83$	0.639620	+	0.464711i	0.0702074	+	0.0510087i	−0.552128	+	0.833759i	$0.686184\pi$
$84$		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	−0.557819	−	0.829963i	$-0.688362\pi$
$89$	−1.11283	+	0.642493i	−0.117960	+	0.0681041i	0.439859	+	0.898067i	$0.355028\pi$
$90$		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	0.997005	+	0.0773313i	$0.0246399\pi$
$97$	7.50936	+	10.3358i	0.762460	+	1.04944i	−0.234545	+	0.972105i	$0.575360\pi$
$98$	−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	0.996376	+	0.0850569i	$0.0271072\pi$
$101$	0.396543	+	3.77286i	0.0394575	+	0.375413i	−0.956919	+	0.290356i	$0.906226\pi$
$102$		0			0
$103$	−2.30869	−	10.8615i	−0.227482	−	1.07022i	−0.932540	−	0.361068i	$-0.882412\pi$
$103$	−2.30869	−	10.8615i	−0.227482	−	1.07022i	0.705058	−	0.709150i	$-0.250921\pi$
$104$	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	0.963654	−	0.267155i	$-0.0860836\pi$
$107$	8.26172	+	7.43889i	0.798691	+	0.719145i	−0.164962	+	0.986300i	$0.552750\pi$
$108$		0			0
$109$	5.45158	+	3.14747i	0.522167	+	0.301473i	0.737821	−	0.674997i	$-0.235855\pi$
$109$	5.45158	+	3.14747i	0.522167	+	0.301473i	−0.215654	+	0.976470i	$0.569188\pi$
$110$	−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	0.911870	−	0.410480i	$-0.134639\pi$
$113$	−0.713520	−	2.19599i	−0.0671223	−	0.206581i	−0.978992	+	0.203899i	$0.934639\pi$
$114$		0			0
$115$	−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	−0.771881	−	0.635767i	$-0.780684\pi$
$127$	0.803438	−	1.10584i	0.0712936	−	0.0981272i	0.843175	+	0.537640i	$0.180684\pi$
$128$	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	−0.999838	−	0.0180194i	$-0.994264\pi$
$131$	−5.90044	−	10.2199i	−0.515524	−	0.892914i	0.484314	−	0.874894i	$-0.339069\pi$
$132$		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	−0.619087	−	0.785323i	$-0.712497\pi$
$137$	−5.26394	+	2.34366i	−0.449728	+	0.200232i	0.169358	+	0.985555i	$0.445830\pi$
$138$		0			0
$139$	4.25808	−	13.1050i	0.361165	−	1.11155i	−0.591182	−	0.806538i	$-0.701339\pi$
$139$	4.25808	−	13.1050i	0.361165	−	1.11155i	0.952348	−	0.305015i	$-0.0986614\pi$
$140$	−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	0.160382	−	0.987055i	$-0.448727\pi$
$149$	1.36762	+	0.143742i	0.112040	+	0.0117758i	−0.0483427	+	0.998831i	$0.515394\pi$
$150$		0			0
$151$	−2.46608	+	11.6020i	−0.200686	+	0.944155i	0.756345	+	0.654172i	$0.226983\pi$
$151$	−2.46608	+	11.6020i	−0.200686	+	0.944155i	−0.957032	+	0.289983i	$0.906350\pi$
$152$	−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	−0.892791	−	0.450471i	$-0.851256\pi$
$157$	1.32864	−	6.25078i	0.106037	−	0.498866i	0.998828	−	0.0483952i	$-0.0154107\pi$
$158$	−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	−0.448456	−	0.893805i	$-0.648026\pi$
$163$	−18.0369	−	8.03054i	−1.41276	−	0.629001i	−0.964302	+	0.264804i	$0.914693\pi$
$164$	−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	−0.525224	−	0.850964i	$-0.676019\pi$
$167$	1.57383	−	1.14346i	0.121787	−	0.0884834i	0.647011	+	0.762480i	$0.276019\pi$
$168$		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	−0.282493	−	0.959269i	$-0.591162\pi$
$173$	9.22087	−	10.2408i	0.701050	−	0.778594i	0.983543	+	0.180675i	$0.0578282\pi$
$174$		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	0.499607	−	0.866252i	$-0.333478\pi$
$179$	8.07675	+	1.71677i	0.603685	+	0.128317i	0.104078	+	0.994569i	$0.466811\pi$
$180$		0			0
$181$	−13.2023	+	18.1714i	−0.981321	+	1.35067i	−0.0452064	+	0.998978i	$0.514395\pi$
$181$	−13.2023	+	18.1714i	−0.981321	+	1.35067i	−0.936115	+	0.351695i	$0.885605\pi$
$182$	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	0.0313799	−	0.999508i	$-0.490010\pi$
$191$	6.44831	−	1.37063i	0.466583	−	0.0991753i	0.435203	+	0.900332i	$0.356677\pi$
$192$		0			0
$193$	−6.81454	−	15.3057i	−0.490522	−	1.10173i	−0.974036	−	0.226393i	$-0.927307\pi$
$193$	−6.81454	−	15.3057i	−0.490522	−	1.10173i	0.483514	−	0.875336i	$-0.339360\pi$
$194$	−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	$0.290266\pi$
$197$			22.1951i			1.58134i	−0.612246	+	0.790668i	$0.709734\pi$
$198$		0			0
$199$	5.54103	+	3.19912i	0.392793	+	0.226779i	0.683370	−	0.730072i	$-0.260514\pi$
$199$	5.54103	+	3.19912i	0.392793	+	0.226779i	−0.290576	+	0.956852i	$0.593847\pi$
$200$	−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	0.926098	−	0.377282i	$-0.123141\pi$
$211$	4.08323	+	5.62009i	0.281101	+	0.386903i	−0.644997	+	0.764185i	$0.723141\pi$
$212$	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	−0.711054	−	0.703137i	$-0.751782\pi$
$223$	−13.0369	+	4.23595i	−0.873016	+	0.283660i	−0.161961	+	0.986797i	$0.551782\pi$
$224$	−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	0.154625	−	0.987973i	$-0.450583\pi$
$227$	−12.7176	−	14.1244i	−0.844099	−	0.937467i	−0.998724	+	0.0505062i	$0.983917\pi$
$228$		0			0
$229$	7.20381	−	16.1800i	0.476041	−	1.06921i	−0.502766	−	0.864423i	$-0.667684\pi$
$229$	7.20381	−	16.1800i	0.476041	−	1.06921i	0.978807	−	0.204784i	$-0.0656490\pi$
$230$	30.9716			2.04221
$231$		0			0
$232$	−13.0968			−0.859844
$233$	10.7984	−	24.2537i	0.707429	−	1.58891i	−0.0972894	−	0.995256i	$-0.531017\pi$
$233$	10.7984	−	24.2537i	0.707429	−	1.58891i	0.804719	−	0.593656i	$-0.202316\pi$
$234$		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	−0.842077	−	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	−0.442820	−	0.896610i	$-0.646022\pi$
$241$	8.61712	−	14.9253i	0.555077	−	0.961422i	0.997898	−	0.0648115i	$-0.0206446\pi$
$242$	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	−0.972171	−	0.234274i	$-0.924729\pi$
$251$	−14.1725	−	19.5068i	−0.894561	−	1.23126i	0.0776099	−	0.996984i	$-0.475271\pi$
$252$		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	0.891024	+	0.453956i	$0.149988\pi$
$257$	4.19495	+	19.7357i	0.261674	+	1.23108i	−0.629351	+	0.777122i	$0.716679\pi$
$258$		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	0.458872	−	0.888502i	$-0.348254\pi$
$263$	−1.31616	−	0.759883i	−0.0811576	−	0.0468564i	−0.540030	+	0.841646i	$0.681587\pi$
$264$		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	−0.998329	−	0.0577848i	$-0.981596\pi$
$269$	−6.12190	−	13.7500i	−0.373259	−	0.838353i	0.625070	−	0.780569i	$-0.285070\pi$
$270$		0			0
$271$	2.21702	−	0.471243i	0.134675	−	0.0286260i	−0.140081	−	0.990140i	$-0.544736\pi$
$271$	2.21702	−	0.471243i	0.134675	−	0.0286260i	0.274756	+	0.961514i	$0.411403\pi$
$272$	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	−0.422747	−	0.906248i	$-0.638934\pi$
$277$	−10.7821	+	1.13325i	−0.647836	+	0.0680903i	−0.225089	+	0.974338i	$0.572267\pi$
$278$	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	−0.728659	−	0.684877i	$-0.759856\pi$
$281$	2.47868	−	3.41161i	0.147866	−	0.203520i	0.876525	+	0.481357i	$0.159856\pi$
$282$		0			0
$283$	−19.6341	−	4.17335i	−1.16713	−	0.248080i	−0.416705	−	0.909042i	$-0.636815\pi$
$283$	−19.6341	−	4.17335i	−1.16713	−	0.248080i	−0.750420	+	0.660961i	$0.770149\pi$
$284$	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	−0.957004	−	0.290074i	$-0.906320\pi$
$293$	−0.210034	+	0.646419i	−0.0122703	+	0.0377642i	0.944734	+	0.327838i	$0.106320\pi$
$294$		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	−0.854548	−	0.519373i	$-0.826166\pi$
$311$	2.42252	−	11.3971i	0.137368	−	0.646268i	0.991916	−	0.126895i	$-0.0405011\pi$
$312$		0			0
$313$	−19.2508	−	2.02334i	−1.08812	−	0.114366i	−0.456561	−	0.889692i	$-0.650919\pi$
$313$	−19.2508	−	2.02334i	−1.08812	−	0.114366i	−0.631561	+	0.775326i	$0.717586\pi$
$314$	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	0.974731	−	0.223380i	$-0.0717092\pi$
$317$	26.0115	+	11.5811i	1.46095	+	0.650457i	0.486219	+	0.873837i	$0.338376\pi$
$318$		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	0.839679	−	0.543084i	$-0.182743\pi$
$331$	−0.918494	−	1.59088i	−0.0504850	−	0.0874426i	−0.890164	+	0.455641i	$0.849410\pi$
$332$	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	−0.678762	−	0.734359i	$-0.737483\pi$
$337$	−30.4650	−	9.89869i	−1.65954	−	0.539216i	−0.980775	+	0.195143i	$0.937483\pi$
$338$	−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	0.710223	−	0.703977i	$-0.248594\pi$
$347$	−5.36794	−	12.0566i	−0.288166	−	0.647231i	−0.998389	+	0.0567457i	$0.981928\pi$
$348$		0			0
$349$	−6.69435	−	20.6031i	−0.358341	−	1.10286i	−0.954047	−	0.299657i	$-0.903128\pi$
$349$	−6.69435	−	20.6031i	−0.358341	−	1.10286i	0.595707	−	0.803202i	$-0.296872\pi$
$350$	−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	0.681261	−	0.732041i	$-0.261432\pi$
$353$	7.28846	+	4.20800i	0.387926	+	0.223969i	−0.293335	+	0.956010i	$0.594765\pi$
$354$		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	0.999095	−	0.0425449i	$-0.0135465\pi$
$359$	1.30872	+	6.15705i	0.0690717	+	0.324957i	−0.930023	+	0.367502i	$0.880213\pi$
$360$		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	−0.846934	−	0.531697i	$-0.821554\pi$
$367$	−7.79084	+	7.01490i	−0.406678	+	0.366175i	0.440256	+	0.897872i	$0.354888\pi$
$368$	−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	−0.810249	−	0.586086i	$-0.800668\pi$
$373$	−13.6701	+	7.89241i	−0.707808	+	0.408653i	0.102441	+	0.994739i	$0.467335\pi$
$374$	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	0.283009	−	0.959117i	$-0.408667\pi$
$379$	−10.5460	−	7.66212i	−0.541712	−	0.393577i	−0.824720	+	0.565541i	$0.808667\pi$
$380$	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	0.231017	+	0.972950i	$0.425795\pi$
$383$	−12.6543	+	28.4221i	−0.646606	+	1.45230i	−0.877623	+	0.479352i	$0.840872\pi$
$384$		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	0.866498	−	0.499181i	$-0.166366\pi$
$389$	5.51217	+	6.12189i	0.279478	+	0.310392i	−0.587020	+	0.809573i	$0.699699\pi$
$390$		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	0.120621	−	0.992699i	$-0.461512\pi$
$397$	20.7345	−	11.9711i	1.04063	−	0.600810i	0.920013	+	0.391889i	$0.128178\pi$
$398$	−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	−0.815363	−	0.578950i	$-0.803462\pi$
$401$	2.05362	−	19.5389i	0.102553	−	0.975726i	0.917916	−	0.396775i	$-0.129871\pi$
$402$		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	0.567707	+	0.823231i	$0.307831\pi$
$409$	3.71237	+	35.3209i	0.183565	+	1.74650i	−0.384142	+	0.923274i	$0.625503\pi$
$410$	−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	$-0.823244\pi$
$419$		−	21.5828i		−	1.05439i	0.849745	−	0.527194i	$-0.176756\pi$
$420$		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	$0.807643\pi$
$422$	−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	0.289370	−	0.957217i	$-0.406554\pi$
$431$	16.0154	−	1.68328i	0.771432	−	0.0810808i	0.482063	+	0.876137i	$0.339888\pi$
$432$		0			0
$433$	−38.1354	−	12.3909i	−1.83267	−	0.595471i	−0.999071	−	0.0431017i	$-0.986276\pi$
$433$	−38.1354	−	12.3909i	−1.83267	−	0.595471i	−0.833600	−	0.552369i	$-0.813724\pi$
$434$	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	0.812938	−	0.582350i	$-0.197867\pi$
$439$	−2.05040	−	3.55140i	−0.0978604	−	0.169499i	−0.910799	+	0.412851i	$0.864533\pi$
$440$	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	−0.789183	−	0.614158i	$-0.789496\pi$
$443$	−2.01842	+	2.24168i	−0.0958979	+	0.106505i	0.693285	+	0.720663i	$0.256163\pi$
$444$		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	−0.394209	−	0.919021i	$-0.628981\pi$
$449$	7.58618	−	5.51168i	0.358014	−	0.260112i	0.752223	+	0.658908i	$0.228981\pi$
$450$		0			0
$451$	−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	0.433924	−	0.900949i	$-0.357129\pi$
$457$	14.3454	+	1.50776i	0.671049	+	0.0705300i	0.237124	+	0.971479i	$0.423795\pi$
$458$	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	−0.0277831	−	0.999614i	$-0.508845\pi$
$467$	−5.67895	−	0.596882i	−0.262791	−	0.0276204i	−0.235007	+	0.971994i	$0.575511\pi$
$468$		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	−0.826275	−	0.563267i	$-0.809544\pi$
$479$	−21.0231	+	9.36011i	−0.960572	+	0.427674i	−0.134297	+	0.990941i	$0.542878\pi$
$480$		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	0.731598	−	0.681736i	$-0.238775\pi$
$487$	24.7749	+	5.26607i	1.12266	+	0.238629i	0.391061	+	0.920365i	$0.372108\pi$
$488$	−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	0.703108	−	0.711084i	$-0.251795\pi$
$491$	18.9227	+	6.14835i	0.853969	+	0.277471i	0.150861	+	0.988555i	$0.451795\pi$
$492$		0			0
$493$	−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	−0.393844	−	0.919177i	$-0.628855\pi$
$499$	−8.48354	+	1.80323i	−0.379775	+	0.0807237i	0.0140687	+	0.999901i	$0.495522\pi$
$500$	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	0.975390	−	0.220485i	$-0.0707640\pi$
$503$	1.27132	+	3.91271i	0.0566852	+	0.174459i	−0.918705	+	0.394944i	$0.870764\pi$
$504$		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	0.878990	−	0.476841i	$-0.158218\pi$
$509$	11.2047	+	10.0888i	0.496640	+	0.447177i	−0.382349	+	0.924018i	$0.624885\pi$
$510$		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	0.445217	−	0.895423i	$-0.353127\pi$
$521$	31.5510	−	28.4086i	1.38227	−	1.24460i	0.937055	−	0.349181i	$-0.113540\pi$
$522$		0			0
$523$	1.21300	−	11.5410i	0.0530410	−	0.504651i	−0.935460	−	0.353434i	$-0.885014\pi$
$523$	1.21300	−	11.5410i	0.0530410	−	0.504651i	0.988501	−	0.151217i	$-0.0483193\pi$
$524$	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	−0.434469	−	0.900687i	$-0.643064\pi$
$541$	12.2249	−	27.4575i	0.525588	−	1.18049i	0.960057	−	0.279803i	$-0.0902693\pi$
$542$	−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	−0.273143	−	0.961974i	$-0.588063\pi$
$547$	1.66790	−	0.541933i	0.0713142	−	0.0231714i	0.344457	+	0.938802i	$0.388063\pi$
$548$	−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	−0.377963	−	0.925821i	$-0.623375\pi$
$557$	11.8778	−	10.6948i	0.503278	−	0.453153i	0.881241	+	0.472667i	$0.156709\pi$
$558$		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	−0.636771	−	0.771053i	$-0.719730\pi$
$563$	−4.13397	−	39.3321i	−0.174226	−	1.65765i	0.462545	−	0.886596i	$-0.346937\pi$
$564$		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	0.111501	−	0.993764i	$-0.464434\pi$
$569$	−20.6374	−	18.5820i	−0.865165	−	0.778998i	−0.976665	+	0.214767i	$0.931101\pi$
$570$		0			0
$571$	24.2147	+	13.9804i	1.01335	+	0.585061i	0.912172	−	0.409807i	$-0.134404\pi$
$571$	24.2147	+	13.9804i	1.01335	+	0.585061i	0.101183	+	0.994868i	$0.467737\pi$
$572$	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	0.964335	−	0.264683i	$-0.0852674\pi$
$577$	2.93946	+	6.60212i	0.122371	+	0.274850i	−0.841964	+	0.539533i	$0.818601\pi$
$578$	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	−0.222540	−	0.974924i	$-0.571435\pi$
$587$	−23.6375	−	7.68029i	−0.975624	−	0.316999i	−0.753084	+	0.657924i	$0.771435\pi$
$588$		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	0.714267	−	0.699873i	$-0.246760\pi$
$593$	−6.06292	−	10.5013i	−0.248974	−	0.431236i	−0.963241	+	0.268637i	$0.913427\pi$
$594$		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	−0.973009	−	0.230768i	$-0.925876\pi$
$599$	−35.5513	+	15.8284i	−1.45258	+	0.646732i	−0.479576	+	0.877500i	$0.659210\pi$
$600$		0			0
$601$	6.08052	−	18.7139i	0.248029	−	0.763356i	−0.747094	−	0.664718i	$-0.768552\pi$
$601$	6.08052	−	18.7139i	0.248029	−	0.763356i	0.995123	−	0.0986377i	$-0.0314485\pi$
$602$	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	0.180144	−	0.983640i	$-0.442344\pi$
$607$	−10.6015	−	4.72011i	−0.430303	−	0.191583i	−0.610447	+	0.792057i	$0.709010\pi$
$608$	−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	0.813913	+	0.580987i	$0.197333\pi$
$613$	−4.10853	+	19.3291i	−0.165942	+	0.780696i	−0.979855	+	0.199710i	$0.936000\pi$
$614$	−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	0.474165	+	0.880436i	$0.342750\pi$
$619$	−7.88965	+	37.1179i	−0.317112	+	1.49189i	−0.791277	+	0.611458i	$0.790583\pi$
$620$	−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	−0.919334	−	0.393477i	$-0.871272\pi$
$631$	1.39924	−	4.30640i	0.0557027	−	0.171435i	0.975037	+	0.222042i	$0.0712721\pi$
$632$	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	0.231413	−	0.972856i	$-0.425665\pi$
$641$	1.19306	+	0.253593i	0.0471232	+	0.0100163i	−0.184290	+	0.982872i	$0.558998\pi$
$642$		0			0
$643$	−7.60420	+	10.4663i	−0.299880	+	0.412750i	−0.932192	−	0.361964i	$-0.882106\pi$
$643$	−7.60420	+	10.4663i	−0.299880	+	0.412750i	0.632312	+	0.774714i	$0.282106\pi$
$644$	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	−0.207192	−	0.978300i	$-0.566432\pi$
$647$	−5.25145	+	0.551950i	−0.206456	+	0.0216994i	0.000735859		1.00000i	$0.499766\pi$
$648$		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	−0.546623	−	0.837379i	$-0.684087\pi$
$653$	−18.0256	+	3.83145i	−0.705395	+	0.149936i	−0.158772	+	0.987315i	$0.550753\pi$
$654$		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	$0.0283764\pi$
$659$			4.57092i			0.178058i	−0.996029	+	0.0890290i	$0.971624\pi$
$660$		0			0
$661$	−7.35634	−	4.24718i	−0.286128	−	0.165196i	0.350066	−	0.936725i	$-0.386159\pi$
$661$	−7.35634	−	4.24718i	−0.286128	−	0.165196i	−0.636195	+	0.771529i	$0.719492\pi$
$662$	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	0.999292	+	0.0376252i	$0.0119793\pi$
$673$	18.8413	+	25.9328i	0.726277	+	0.999635i	−0.273014	+	0.962010i	$0.588021\pi$
$674$	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	−0.979550	−	0.201202i	$-0.935515\pi$
$677$	0.531487	−	5.05676i	0.0204267	−	0.194347i	0.999977	+	0.00685468i	$0.00218193\pi$
$678$		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	0.472618	+	0.881267i	$0.343309\pi$
$683$	−13.7699	+	23.8502i	−0.526891	+	0.912602i	−0.999509	+	0.0313347i	$0.990024\pi$
$684$		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	0.424946	+	0.905219i	$0.360293\pi$
$691$	−13.9874	+	31.4163i	−0.532107	+	1.19513i	−0.957053	+	0.289913i	$0.906373\pi$
$692$	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	−0.493892	−	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
$704$	−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	0.970191	+	0.242340i	$0.0779151\pi$
$709$	−0.777095	+	7.39356i	−0.0291844	+	0.277671i	−0.999376	+	0.0353307i	$0.988752\pi$
$710$	−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	−0.936106	−	0.351718i	$-0.885598\pi$
$719$	−6.00604	−	28.2562i	−0.223987	−	1.05378i	0.712119	−	0.702059i	$-0.247736\pi$
$720$		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	$-0.920389\pi$
$727$		−	13.3469i		−	0.495010i	0.968887	−	0.247505i	$-0.0796106\pi$
$728$	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	−0.134968	−	0.990850i	$-0.543093\pi$
$733$	3.91890	−	0.832988i	0.144748	−	0.0307671i	0.279716	+	0.960083i	$0.409760\pi$
$734$	−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	−0.503487	−	0.864003i	$-0.667950\pi$
$739$	−22.1917	+	2.33244i	−0.816336	+	0.0858003i	−0.312848	+	0.949803i	$0.601283\pi$
$740$	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	−0.591792	−	0.806091i	$-0.701579\pi$
$743$	9.75074	−	13.4207i	0.357720	−	0.492359i	0.949512	+	0.313731i	$0.101579\pi$
$744$		0			0
$745$	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	−0.184732	+	0.982789i	$0.559142\pi$
$751$	−31.3185	+	34.7827i	−1.14283	+	1.26924i	−0.958095	+	0.286449i	$0.907525\pi$
$752$	−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	−0.989132	−	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
$761$	16.6226	+	7.40084i	0.602567	+	0.268280i	0.685264	−	0.728295i	$-0.259687\pi$
$761$	16.6226	+	7.40084i	0.602567	+	0.268280i	−0.0826970	+	0.996575i	$0.526353\pi$
$762$		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	−0.792872	−	0.609388i	$-0.791415\pi$
$773$	4.98542	−	23.4546i	0.179313	−	0.843602i	0.972185	−	0.234214i	$-0.0752516\pi$
$774$		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	−0.520818	−	0.853668i	$-0.674373\pi$
$787$	−6.59017	+	2.93413i	−0.234914	+	0.104590i	0.285904	+	0.958258i	$0.407706\pi$
$788$	−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	0.141585	+	0.989926i	$0.454780\pi$
$797$	−23.8170	+	32.7814i	−0.843643	+	1.16118i	−0.985228	+	0.171249i	$0.945220\pi$
$798$		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	0.996445	−	0.0842509i	$-0.0268497\pi$
$809$	7.59661	+	17.0623i	0.267082	+	0.599877i	−0.729362	+	0.684128i	$0.760183\pi$
$810$		0			0
$811$	11.2529	+	34.6328i	0.395142	+	1.21612i	0.928851	+	0.370454i	$0.120798\pi$
$811$	11.2529	+	34.6328i	0.395142	+	1.21612i	−0.533708	+	0.845669i	$0.679202\pi$
$812$	−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	−0.978250	−	0.207431i	$-0.933490\pi$
$821$	−4.84077	−	22.7740i	−0.168944	−	0.794819i	0.809306	−	0.587388i	$-0.199844\pi$
$822$		0			0
$823$	0.0906668	+	0.862637i	0.00316045	+	0.0300696i	0.995988	−	0.0894817i	$-0.0285211\pi$
$823$	0.0906668	+	0.862637i	0.00316045	+	0.0300696i	−0.992828	+	0.119551i	$0.961854\pi$
$824$	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
$829$	33.8967	−	30.5207i	1.17728	−	1.06003i	0.180204	−	0.983629i	$-0.442324\pi$
$829$	33.8967	−	30.5207i	1.17728	−	1.06003i	0.997077	−	0.0763994i	$-0.0243424\pi$
$830$	−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	0.515158	−	0.857095i	$-0.327733\pi$
$839$	41.5863	−	13.5122i	1.43572	−	0.466493i	0.920559	+	0.390603i	$0.127733\pi$
$840$		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	0.556666	−	0.830736i	$-0.312080\pi$
$853$	−1.79303	−	1.30271i	−0.0613922	−	0.0446041i	−0.618058	+	0.786132i	$0.712080\pi$
$854$	−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	−0.670986	−	0.741470i	$-0.734129\pi$
$857$	8.97672	−	15.5481i	0.306639	−	0.531114i	0.977625	+	0.210356i	$0.0674622\pi$
$858$		0			0
$859$	31.4261	−	18.1439i	1.07225	−	0.619061i	0.143452	−	0.989657i	$-0.454180\pi$
$859$	31.4261	−	18.1439i	1.07225	−	0.619061i	0.928794	+	0.370596i	$0.120847\pi$
$860$	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	0.953652	+	0.300912i	$0.0972910\pi$
$863$	−1.22571	+	11.6618i	−0.0417235	+	0.396972i	−0.995375	+	0.0960607i	$0.969376\pi$
$864$		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	0.857195	−	0.514993i	$-0.172205\pi$
$877$	12.8710	+	11.5891i	0.434624	+	0.391337i	−0.422570	+	0.906330i	$0.638872\pi$
$878$	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	$0.117154\pi$
$881$			21.3587i			0.719592i	−0.933031	+	0.359796i	$0.882846\pi$
$882$		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	$-0.326080\pi$
$884$	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	−0.451416	−	0.892314i	$-0.649081\pi$
$887$	−14.9171	+	3.17073i	−0.500868	+	0.106463i	−0.0494522	+	0.998776i	$0.515748\pi$
$888$		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	−0.777225	−	0.629223i	$-0.783373\pi$
$907$	−24.9872	+	11.1250i	−0.829687	+	0.369400i	−0.0524615	+	0.998623i	$0.516707\pi$
$908$	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	−0.104843	−	0.994489i	$-0.533434\pi$
$911$	24.4050	−	17.7313i	0.808574	−	0.587463i	0.913417	+	0.407026i	$0.133434\pi$
$912$		0			0
$913$	−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	0.0349991	−	0.999387i	$-0.488857\pi$
$919$	−4.20017	−	0.441456i	−0.138551	−	0.0145623i	−0.173550	+	0.984825i	$0.555524\pi$
$920$	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	−0.238583	−	0.971122i	$-0.576683\pi$
$929$	−20.5389	−	2.15873i	−0.673860	−	0.0708255i	−0.435277	+	0.900297i	$0.643350\pi$
$930$		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	−0.923770	−	0.382949i	$-0.874909\pi$
$937$	−25.8666	+	18.7932i	−0.845024	+	0.613946i	0.0787452	+	0.996895i	$0.474909\pi$
$938$	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	−0.838404	−	0.545049i	$-0.816511\pi$
$941$	−30.5026	+	13.5806i	−0.994357	+	0.442716i	−0.155952	+	0.987765i	$0.549845\pi$
$942$		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	0.991192	+	0.132434i	$0.0422791\pi$
$947$	18.7806	+	32.5289i	0.610287	+	1.05705i	−0.380905	+	0.924614i	$0.624388\pi$
$948$		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	0.961152	−	0.276021i	$-0.0890160\pi$
$953$	48.6676	+	15.8131i	1.57650	+	0.512235i	0.615347	+	0.788257i	$0.289016\pi$
$954$		0			0
$955$	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	$0.0975168\pi$
$967$			18.7568i			0.603177i	−0.953438	+	0.301588i	$0.902483\pi$
$968$	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	0.948082	−	0.318026i	$-0.103020\pi$
$971$	22.7755	+	20.5071i	0.730900	+	0.658105i	−0.217182	+	0.976131i	$0.569687\pi$
$972$		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	0.870906	+	0.491449i	$0.163533\pi$
$977$	3.78864	+	36.0465i	0.121209	+	1.15323i	−0.749697	+	0.661782i	$0.769801\pi$
$978$		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	−0.913051	−	0.407846i	$-0.866280\pi$
$983$	−18.9020	+	17.0194i	−0.602879	+	0.542835i	0.310172	+	0.950681i	$0.399613\pi$
$984$		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	−0.955316	−	0.295586i	$-0.904485\pi$
$991$	−6.97830	+	12.0868i	−0.221673	+	0.383949i	0.733643	+	0.679535i	$0.237818\pi$
$992$	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	−0.783671	−	0.621176i	$-0.786655\pi$
$997$	−41.6645	−	46.2731i	−1.31953	−	1.46548i	−0.535857	−	0.844309i	$-0.680011\pi$
$998$	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.514.5	yes	128
3.2	odd	2	inner	693.2.cg.b.514.12	yes	128
7.5	odd	6	inner	693.2.cg.b.19.12	yes	128
11.7	odd	10	inner	693.2.cg.b.73.12	yes	128
21.5	even	6	inner	693.2.cg.b.19.5	✓	128
33.29	even	10	inner	693.2.cg.b.73.5	yes	128
77.40	even	30	inner	693.2.cg.b.271.5	yes	128
231.194	odd	30	inner	693.2.cg.b.271.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.cg.b.19.5	✓	128	21.5	even	6	inner
693.2.cg.b.19.12	yes	128	7.5	odd	6	inner
693.2.cg.b.73.5	yes	128	33.29	even	10	inner
693.2.cg.b.73.12	yes	128	11.7	odd	10	inner
693.2.cg.b.271.5	yes	128	77.40	even	30	inner
693.2.cg.b.271.12	yes	128	231.194	odd	30	inner
693.2.cg.b.514.5	yes	128	1.1	even	1	trivial
693.2.cg.b.514.12	yes	128	3.2	odd	2	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

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