LMFDB - Embedded newform 414.2.j.a.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	414.53
Dual form			414.2.j.a.125.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.959224 + 2.10041i) q^{5} +(0.976881 + 3.32695i) q^{7} +(-0.540641 + 0.841254i) q^{8} +O(q^{10})$	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.959224 + 2.10041i) q^{5} +(0.976881 + 3.32695i) q^{7} +(-0.540641 + 0.841254i) q^{8} +(-0.650541 + 2.21554i) q^{10} +(-3.39535 - 3.91845i) q^{11} +(-0.768991 - 0.225796i) q^{13} +(-1.44041 + 3.15406i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(-0.138219 + 0.961332i) q^{17} +(3.59513 - 0.516901i) q^{19} +(-1.94252 + 1.24838i) q^{20} -5.18485i q^{22} +(-4.07867 + 2.52279i) q^{23} +(-0.217295 + 0.250772i) q^{25} +(-0.433300 - 0.674228i) q^{26} +(-3.15406 + 1.44041i) q^{28} +(2.90035 + 0.417007i) q^{29} +(6.19346 + 3.98030i) q^{31} +(-0.909632 - 0.415415i) q^{32} +(-0.733997 + 0.636012i) q^{34} +(-6.05091 + 5.24314i) q^{35} +(10.2963 + 4.70214i) q^{37} +(3.05551 + 1.96366i) q^{38} +(-2.28557 - 0.328615i) q^{40} +(5.56322 - 2.54064i) q^{41} +(-4.27251 - 6.64816i) q^{43} +(3.39535 - 3.91845i) q^{44} +(-4.73453 - 0.764361i) q^{46} -4.68329i q^{47} +(-4.22554 + 2.71559i) q^{49} +(-0.328442 + 0.0472228i) q^{50} +(0.114059 - 0.793298i) q^{52} +(-9.27429 + 2.72318i) q^{53} +(4.97343 - 10.8903i) q^{55} +(-3.32695 - 0.976881i) q^{56} +(1.91885 + 2.21447i) q^{58} +(3.43021 - 11.6822i) q^{59} +(2.00669 - 3.12248i) q^{61} +(2.07417 + 7.06396i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(-0.263371 - 1.83178i) q^{65} +(-9.68135 - 8.38893i) q^{67} -0.971217 q^{68} -8.00650 q^{70} +(5.02367 + 4.35304i) q^{71} +(-0.0483492 - 0.336276i) q^{73} +(4.70214 + 10.2963i) q^{74} +(1.02328 + 3.48497i) q^{76} +(9.71963 - 15.1240i) q^{77} +(-0.0511848 + 0.174319i) q^{79} +(-1.51212 - 1.74508i) q^{80} +(5.86817 + 1.72305i) q^{82} +(-1.06329 + 2.32827i) q^{83} +(-2.15177 + 0.631817i) q^{85} +(1.12467 - 7.82224i) q^{86} +(5.13207 - 0.737881i) q^{88} +(10.8328 - 6.96181i) q^{89} -2.77897i q^{91} +(-3.07757 - 3.67812i) q^{92} +(3.06690 - 3.53939i) q^{94} +(4.53423 + 7.05541i) q^{95} +(-12.6161 + 5.76160i) q^{97} +(-4.97179 - 0.714835i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.755750	+	0.654861i	0.534396	+	0.463056i
$2$	0.755750	+	0.654861i	0.534396	+	0.463056i
$3$		0			0
$3$		0			0
$4$	0.142315	+	0.989821i	0.0711574	+	0.494911i
$5$	0.959224	+	2.10041i	0.428978	+	0.939331i	0.993491	+	0.113907i	$0.0363365\pi$
$5$	0.959224	+	2.10041i	0.428978	+	0.939331i	−0.564514	+	0.825424i	$0.690936\pi$
$6$		0			0
$7$	0.976881	+	3.32695i	0.369226	+	1.25747i	0.909402	+	0.415918i	$0.136540\pi$
$7$	0.976881	+	3.32695i	0.369226	+	1.25747i	−0.540176	+	0.841552i	$0.681642\pi$
$8$	−0.540641	+	0.841254i	−0.191145	+	0.297428i
$9$		0			0
$10$	−0.650541	+	2.21554i	−0.205719	+	0.700615i
$11$	−3.39535	−	3.91845i	−1.02374	−	1.18146i	−0.983247	−	0.182276i	$-0.941654\pi$
$11$	−3.39535	−	3.91845i	−1.02374	−	1.18146i	−0.0404902	−	0.999180i	$-0.512892\pi$
$12$		0			0
$13$	−0.768991	−	0.225796i	−0.213280	−	0.0626246i	0.173347	−	0.984861i	$-0.444542\pi$
$13$	−0.768991	−	0.225796i	−0.213280	−	0.0626246i	−0.386627	+	0.922236i	$0.626360\pi$
$14$	−1.44041	+	3.15406i	−0.384967	+	0.842959i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.138219	+	0.961332i	−0.0335229	+	0.233157i	−0.999694	−	0.0247457i	$-0.992122\pi$
$17$	−0.138219	+	0.961332i	−0.0335229	+	0.233157i	0.966171	+	0.257903i	$0.0830315\pi$
$18$		0			0
$19$	3.59513	−	0.516901i	0.824779	−	0.118585i	0.283014	−	0.959116i	$-0.408666\pi$
$19$	3.59513	−	0.516901i	0.824779	−	0.118585i	0.541764	+	0.840530i	$0.317757\pi$
$20$	−1.94252	+	1.24838i	−0.434360	+	0.279146i
$21$		0			0
$22$		−	5.18485i		−	1.10541i
$23$	−4.07867	+	2.52279i	−0.850461	+	0.526038i
$23$	−4.07867	+	2.52279i	−0.850461	+	0.526038i
$24$		0			0
$25$	−0.217295	+	0.250772i	−0.0434591	+	0.0501544i
$26$	−0.433300	−	0.674228i	−0.0849771	−	0.132227i
$27$		0			0
$28$	−3.15406	+	1.44041i	−0.596062	+	0.272212i
$29$	2.90035	+	0.417007i	0.538581	+	0.0774362i	0.406237	−	0.913768i	$-0.366841\pi$
$29$	2.90035	+	0.417007i	0.538581	+	0.0774362i	0.132344	+	0.991204i	$0.457750\pi$
$30$		0			0
$31$	6.19346	+	3.98030i	1.11238	+	0.714882i	0.961810	−	0.273717i	$-0.0882532\pi$
$31$	6.19346	+	3.98030i	1.11238	+	0.714882i	0.150569	+	0.988600i	$0.451890\pi$
$32$	−0.909632	−	0.415415i	−0.160802	−	0.0734357i
$33$		0			0
$34$	−0.733997	+	0.636012i	−0.125879	+	0.109075i
$35$	−6.05091	+	5.24314i	−1.02279	+	0.886252i
$36$		0			0
$37$	10.2963	+	4.70214i	1.69269	+	0.773028i	0.998586	+	0.0531572i	$0.0169285\pi$
$37$	10.2963	+	4.70214i	1.69269	+	0.773028i	0.694108	+	0.719870i	$0.255799\pi$
$38$	3.05551	+	1.96366i	0.495670	+	0.318548i
$39$		0			0
$40$	−2.28557	−	0.328615i	−0.361380	−	0.0519587i
$41$	5.56322	−	2.54064i	0.868829	−	0.396781i	0.0694340	−	0.997587i	$-0.477881\pi$
$41$	5.56322	−	2.54064i	0.868829	−	0.396781i	0.799395	+	0.600806i	$0.205153\pi$
$42$		0			0
$43$	−4.27251	−	6.64816i	−0.651552	−	1.01383i	−0.997149	−	0.0754518i	$-0.975960\pi$
$43$	−4.27251	−	6.64816i	−0.651552	−	1.01383i	0.345597	−	0.938383i	$-0.387676\pi$
$44$	3.39535	−	3.91845i	0.511869	−	0.590728i
$45$		0			0
$46$	−4.73453	−	0.764361i	−0.698068	−	0.112699i
$47$		−	4.68329i		−	0.683128i	−0.939858	−	0.341564i	$-0.889043\pi$
$47$		−	4.68329i		−	0.683128i	0.939858	−	0.341564i	$-0.110957\pi$
$48$		0			0
$49$	−4.22554	+	2.71559i	−0.603649	+	0.387942i
$50$	−0.328442	+	0.0472228i	−0.0464487	+	0.00667831i
$51$		0			0
$52$	0.114059	−	0.793298i	0.0158171	−	0.110011i
$53$	−9.27429	+	2.72318i	−1.27392	+	0.374057i	−0.847659	−	0.530542i	$-0.821988\pi$
$53$	−9.27429	+	2.72318i	−1.27392	+	0.374057i	−0.426263	+	0.904599i	$0.640170\pi$
$54$		0			0
$55$	4.97343	−	10.8903i	0.670617	−	1.46845i
$56$	−3.32695	−	0.976881i	−0.444583	−	0.130541i
$57$		0			0
$58$	1.91885	+	2.21447i	0.251958	+	0.290775i
$59$	3.43021	−	11.6822i	0.446576	−	1.52090i	−0.361814	−	0.932250i	$-0.617842\pi$
$59$	3.43021	−	11.6822i	0.446576	−	1.52090i	0.808390	−	0.588647i	$-0.200339\pi$
$60$		0			0
$61$	2.00669	−	3.12248i	0.256931	−	0.399792i	−0.688694	−	0.725052i	$-0.741815\pi$
$61$	2.00669	−	3.12248i	0.256931	−	0.399792i	0.945625	+	0.325260i	$0.105452\pi$
$62$	2.07417	+	7.06396i	0.263419	+	0.897124i
$63$		0			0
$64$	−0.415415	−	0.909632i	−0.0519269	−	0.113704i
$65$	−0.263371	−	1.83178i	−0.0326671	−	0.227205i
$66$		0			0
$67$	−9.68135	−	8.38893i	−1.18276	−	1.02487i	−0.999123	−	0.0418783i	$-0.986666\pi$
$67$	−9.68135	−	8.38893i	−1.18276	−	1.02487i	−0.183642	−	0.982993i	$-0.558789\pi$
$68$	−0.971217			−0.117777
$69$		0			0
$70$	−8.00650			−0.956959
$71$	5.02367	+	4.35304i	0.596200	+	0.516610i	0.899865	−	0.436169i	$-0.143665\pi$
$71$	5.02367	+	4.35304i	0.596200	+	0.516610i	−0.303665	+	0.952779i	$0.598210\pi$
$72$		0			0
$73$	−0.0483492	−	0.336276i	−0.00565885	−	0.0393581i	0.986796	−	0.161966i	$-0.0517834\pi$
$73$	−0.0483492	−	0.336276i	−0.00565885	−	0.0393581i	−0.992455	+	0.122608i	$0.960874\pi$
$74$	4.70214	+	10.2963i	0.546613	+	1.19692i
$75$		0			0
$76$	1.02328	+	3.48497i	0.117378	+	0.399754i
$77$	9.71963	−	15.1240i	1.10765	−	1.72354i
$78$		0			0
$79$	−0.0511848	+	0.174319i	−0.00575874	+	0.0196125i	−0.962322	−	0.271912i	$-0.912344\pi$
$79$	−0.0511848	+	0.174319i	−0.00575874	+	0.0196125i	0.956563	+	0.291524i	$0.0941623\pi$
$80$	−1.51212	−	1.74508i	−0.169060	−	0.195106i
$81$		0			0
$82$	5.86817	+	1.72305i	0.648031	+	0.190279i
$83$	−1.06329	+	2.32827i	−0.116711	+	0.255561i	−0.958968	−	0.283515i	$-0.908499\pi$
$83$	−1.06329	+	2.32827i	−0.116711	+	0.255561i	0.842257	+	0.539077i	$0.181227\pi$
$84$		0			0
$85$	−2.15177	+	0.631817i	−0.233392	+	0.0685301i
$86$	1.12467	−	7.82224i	0.121276	−	0.843494i
$87$		0			0
$88$	5.13207	−	0.737881i	0.547081	−	0.0786584i
$89$	10.8328	−	6.96181i	1.14827	−	0.737950i	0.178979	−	0.983853i	$-0.442721\pi$
$89$	10.8328	−	6.96181i	1.14827	−	0.737950i	0.969295	+	0.245903i	$0.0790844\pi$
$90$		0			0
$91$		−	2.77897i		−	0.291316i
$92$	−3.07757	−	3.67812i	−0.320859	−	0.383471i
$93$		0			0
$94$	3.06690	−	3.53939i	0.316327	−	0.365061i
$95$	4.53423	+	7.05541i	0.465203	+	0.723869i
$96$		0			0
$97$	−12.6161	+	5.76160i	−1.28098	+	0.585002i	−0.935467	−	0.353414i	$-0.885021\pi$
$97$	−12.6161	+	5.76160i	−1.28098	+	0.585002i	−0.345508	+	0.938416i	$0.612293\pi$
$98$	−4.97179	−	0.714835i	−0.502226	−	0.0722092i
$99$		0			0
$100$	−0.279144	−	0.179395i	−0.0279144	−	0.0179395i
$101$	−5.20253	−	2.37592i	−0.517671	−	0.236412i	0.139407	−	0.990235i	$-0.455480\pi$
$101$	−5.20253	−	2.37592i	−0.517671	−	0.236412i	−0.657078	+	0.753823i	$0.728208\pi$
$102$		0			0
$103$	−10.2989	+	8.92404i	−1.01478	+	0.879311i	−0.992720	−	0.120445i	$-0.961568\pi$
$103$	−10.2989	+	8.92404i	−1.01478	+	0.879311i	−0.0220595	+	0.999757i	$0.507022\pi$
$104$	0.605700	−	0.524842i	0.0593938	−	0.0514650i
$105$		0			0
$106$	−8.79234	−	4.01533i	−0.853988	−	0.390003i
$107$	4.69910	+	3.01993i	0.454279	+	0.291948i	0.747701	−	0.664036i	$-0.231158\pi$
$107$	4.69910	+	3.01993i	0.454279	+	0.291948i	−0.293422	+	0.955983i	$0.594794\pi$
$108$		0			0
$109$	15.0054	+	2.15745i	1.43726	+	0.206646i	0.816494	−	0.577354i	$-0.195915\pi$
$109$	15.0054	+	2.15745i	1.43726	+	0.206646i	0.620761	+	0.784000i	$0.286824\pi$
$110$	10.8903	−	4.97343i	1.03835	−	0.474198i
$111$		0			0
$112$	−1.87462	−	2.91697i	−0.177135	−	0.275628i
$113$	0.0149595	−	0.0172642i	0.00140727	−	0.00162407i	−0.755046	−	0.655672i	$-0.772385\pi$
$113$	0.0149595	−	0.0172642i	0.00140727	−	0.00162407i	0.756453	+	0.654048i	$0.226931\pi$
$114$		0			0
$115$	−9.21124	−	6.14694i	−0.858953	−	0.573205i
$116$			2.93017i			0.272059i
$117$		0			0
$118$	10.2426	−	6.58253i	0.942910	−	0.605971i
$119$	−3.33333	+	0.479260i	−0.305566	+	0.0439337i
$120$		0			0
$121$	−2.26034	+	15.7210i	−0.205485	+	1.42918i
$122$	3.56135	−	1.04571i	0.322429	−	0.0946738i
$123$		0			0
$124$	−3.05836	+	6.69688i	−0.274649	+	0.601397i
$125$	10.3425	+	3.03684i	0.925065	+	0.271624i
$126$		0			0
$127$	−8.90110	−	10.2724i	−0.789845	−	0.911530i	0.207934	−	0.978143i	$-0.433326\pi$
$127$	−8.90110	−	10.2724i	−0.789845	−	0.911530i	−0.997779	+	0.0666131i	$0.978781\pi$
$128$	0.281733	−	0.959493i	0.0249019	−	0.0848080i
$129$		0			0
$130$	1.00052	−	1.55684i	0.0877515	−	0.136544i
$131$	−3.34896	−	11.4055i	−0.292600	−	0.996505i	−0.966283	−	0.257484i	$-0.917107\pi$
$131$	−3.34896	−	11.4055i	−0.292600	−	0.996505i	0.673682	−	0.739021i	$-0.264712\pi$
$132$		0			0
$133$	5.23172	+	11.4559i	0.453648	+	0.993350i
$134$	−1.82309	−	12.6799i	−0.157491	−	1.09537i
$135$		0			0
$136$	−0.733997	−	0.636012i	−0.0629397	−	0.0545376i
$137$	4.81977			0.411781			0.205890	−	0.978575i	$-0.433991\pi$
$137$	4.81977			0.411781			0.205890	+	0.978575i	$0.433991\pi$
$138$		0			0
$139$	5.66735			0.480699			0.240349	−	0.970686i	$-0.422738\pi$
$139$	5.66735			0.480699			0.240349	+	0.970686i	$0.422738\pi$
$140$	−6.05091	−	5.24314i	−0.511395	−	0.443126i
$141$		0			0
$142$	0.946005	+	6.57961i	0.0793870	+	0.552149i
$143$	1.72623	+	3.77991i	0.144354	+	0.316092i
$144$		0			0
$145$	1.90620	+	6.49191i	0.158301	+	0.539124i
$146$	0.183674	−	0.285802i	0.0152010	−	0.0236532i
$147$		0			0
$148$	−3.18897	+	10.8606i	−0.262132	+	0.892739i
$149$	11.9278	+	13.7654i	0.977163	+	1.12771i	0.991798	+	0.127813i	$0.0407959\pi$
$149$	11.9278	+	13.7654i	0.977163	+	1.12771i	−0.0146352	+	0.999893i	$0.504659\pi$
$150$		0			0
$151$	−3.44553	−	1.01170i	−0.280393	−	0.0823309i	0.138512	−	0.990361i	$-0.455768\pi$
$151$	−3.44553	−	1.01170i	−0.280393	−	0.0823309i	−0.418905	+	0.908030i	$0.637586\pi$
$152$	−1.50883	+	3.30387i	−0.122382	+	0.267979i
$153$		0			0
$154$	17.2497	−	5.06498i	1.39002	−	0.408148i
$155$	−2.41933	+	16.8268i	−0.194325	+	1.35156i
$156$		0			0
$157$	−0.764422	+	0.109907i	−0.0610075	+	0.00877156i	−0.172751	−	0.984966i	$-0.555266\pi$
$157$	−0.764422	+	0.109907i	−0.0610075	+	0.00877156i	0.111743	+	0.993737i	$0.464357\pi$
$158$	−0.152838	+	0.0982229i	−0.0121591	+	0.00781420i
$159$		0			0
$160$		−	2.30907i		−	0.182548i
$161$	−12.3776	−	11.1051i	−0.975490	−	0.875202i
$162$		0			0
$163$	12.1530	−	14.0253i	0.951897	−	1.09855i	−0.0431428	−	0.999069i	$-0.513737\pi$
$163$	12.1530	−	14.0253i	0.951897	−	1.09855i	0.995040	−	0.0994786i	$-0.0317175\pi$
$164$	3.30651	+	5.14503i	0.258195	+	0.401759i
$165$		0			0
$166$	−2.32827	+	1.06329i	−0.180709	+	0.0825271i
$167$	−13.9830	−	2.01046i	−1.08204	−	0.155574i	−0.421844	−	0.906668i	$-0.638617\pi$
$167$	−13.9830	−	2.01046i	−1.08204	−	0.155574i	−0.660195	+	0.751095i	$0.729526\pi$
$168$		0			0
$169$	−10.3959	−	6.68106i	−0.799687	−	0.513928i
$170$	−2.03995	−	0.931615i	−0.156457	−	0.0714516i
$171$		0			0
$172$	5.97245	−	5.17516i	0.455395	−	0.394602i
$173$	−13.6011	+	11.7854i	−1.03407	+	0.896030i	−0.994661	−	0.103193i	$-0.967094\pi$
$173$	−13.6011	+	11.7854i	−1.03407	+	0.896030i	−0.0394120	+	0.999223i	$0.512548\pi$
$174$		0			0
$175$	−1.04658	−	0.477957i	−0.0791139	−	0.0361301i
$176$	4.36177	+	2.80314i	0.328781	+	0.211295i
$177$		0			0
$178$	12.7459	+	1.83258i	0.955345	+	0.137358i
$179$	−15.8487	+	7.23785i	−1.18459	+	0.540982i	−0.907577	−	0.419885i	$-0.862070\pi$
$179$	−15.8487	+	7.23785i	−1.18459	+	0.540982i	−0.277008	+	0.960867i	$0.589343\pi$
$180$		0			0
$181$	−10.7664	−	16.7529i	−0.800261	−	1.24523i	−0.965867	−	0.259038i	$-0.916594\pi$
$181$	−10.7664	−	16.7529i	−0.800261	−	1.24523i	0.165606	−	0.986192i	$-0.447042\pi$
$182$	1.81984	−	2.10021i	0.134896	−	0.155678i
$183$		0			0
$184$	0.0827870	−	4.79512i	0.00610314	−	0.353501i
$185$			26.1367i			1.92161i
$186$		0			0
$187$	4.23623	−	2.72246i	0.309784	−	0.199086i
$188$	4.63562	−	0.666502i	0.338087	−	0.0486096i
$189$		0			0
$190$	−1.19356	+	8.30141i	−0.0865901	+	0.602248i
$191$	−5.61086	+	1.64750i	−0.405988	+	0.119209i	−0.478349	−	0.878170i	$-0.658765\pi$
$191$	−5.61086	+	1.64750i	−0.405988	+	0.119209i	0.0723614	+	0.997378i	$0.476947\pi$
$192$		0			0
$193$	7.63026	−	16.7079i	0.549238	−	1.20266i	−0.407899	−	0.913027i	$-0.633738\pi$
$193$	7.63026	−	16.7079i	0.549238	−	1.20266i	0.957137	−	0.289636i	$-0.0935343\pi$
$194$	−13.3077	−	3.90749i	−0.955437	−	0.280541i
$195$		0			0
$196$	−3.28931	−	3.79606i	−0.234951	−	0.271147i
$197$	−0.561313	+	1.91166i	−0.0399919	+	0.136200i	−0.977069	−	0.212922i	$-0.931702\pi$
$197$	−0.561313	+	1.91166i	−0.0399919	+	0.136200i	0.937077	+	0.349122i	$0.113520\pi$
$198$		0			0
$199$	−6.40872	+	9.97216i	−0.454302	+	0.706908i	−0.990550	−	0.137153i	$-0.956205\pi$
$199$	−6.40872	+	9.97216i	−0.454302	+	0.706908i	0.536248	+	0.844061i	$0.319841\pi$
$200$	−0.0934843	−	0.318378i	−0.00661034	−	0.0225127i
$201$		0			0
$202$	−2.37592	−	5.20253i	−0.167169	−	0.366049i
$203$	1.44593	+	10.0567i	0.101485	+	0.705840i
$204$		0			0
$205$	10.6727	+	9.24799i	0.745417	+	0.645907i
$206$	−13.6274			−0.949465
$207$		0			0
$208$	0.801456			0.0555710
$209$	−14.2322	−	12.3323i	−0.984460	−	0.853040i
$210$		0			0
$211$	−1.74553	−	12.1404i	−0.120167	−	0.835781i	−0.957365	−	0.288881i	$-0.906717\pi$
$211$	−1.74553	−	12.1404i	−0.120167	−	0.835781i	0.837198	−	0.546900i	$-0.184192\pi$
$212$	−4.01533	−	8.79234i	−0.275774	−	0.603861i
$213$		0			0
$214$	1.57371	+	5.35957i	0.107577	+	0.366372i
$215$	9.86554	−	15.3511i	0.672824	−	1.04694i
$216$		0			0
$217$	−7.19198	+	24.4936i	−0.488223	+	1.66274i
$218$	9.92749	+	11.4569i	0.672374	+	0.775961i
$219$		0			0
$220$	11.4872	+	3.37296i	0.774469	+	0.227405i
$221$	0.323354	−	0.708046i	0.0217511	−	0.0476284i
$222$		0			0
$223$	2.22938	−	0.654605i	0.149290	−	0.0438356i	−0.206234	−	0.978503i	$-0.566121\pi$
$223$	2.22938	−	0.654605i	0.149290	−	0.0438356i	0.355524	+	0.934667i	$0.384302\pi$
$224$	0.493463	−	3.43211i	0.0329709	−	0.229318i
$225$		0			0
$226$	0.0226112	−	0.00325100i	0.00150408	−	0.000216254i
$227$	−11.1803	+	7.18512i	−0.742061	+	0.476893i	−0.856247	−	0.516566i	$-0.827210\pi$
$227$	−11.1803	+	7.18512i	−0.742061	+	0.476893i	0.114187	+	0.993459i	$0.463574\pi$
$228$		0			0
$229$			25.3457i			1.67489i	0.546519	+	0.837446i	$0.315952\pi$
$229$			25.3457i			1.67489i	−0.546519	+	0.837446i	$0.684048\pi$
$230$	−2.93600	−	10.6776i	−0.193594	−	0.704062i
$231$		0			0
$232$	−1.91885	+	2.21447i	−0.125979	+	0.145387i
$233$	9.77643	+	15.2124i	0.640475	+	0.996599i	0.998032	+	0.0627077i	$0.0199736\pi$
$233$	9.77643	+	15.2124i	0.640475	+	0.996599i	−0.357557	+	0.933892i	$0.616390\pi$
$234$		0			0
$235$	9.83682	−	4.49232i	0.641683	−	0.293047i
$236$	12.0515	+	1.73274i	0.784486	+	0.112792i
$237$		0			0
$238$	−2.83301	−	1.82066i	−0.183637	−	0.118016i
$239$	−12.6002	−	5.75433i	−0.815041	−	0.372217i	−0.0361270	−	0.999347i	$-0.511502\pi$
$239$	−12.6002	−	5.75433i	−0.815041	−	0.372217i	−0.778914	+	0.627130i	$0.784229\pi$
$240$		0			0
$241$	−19.0288	+	16.4885i	−1.22575	+	1.06212i	−0.229706	+	0.973260i	$0.573777\pi$
$241$	−19.0288	+	16.4885i	−1.22575	+	1.06212i	−0.996044	+	0.0888588i	$0.971678\pi$
$242$	−12.0033	+	10.4009i	−0.771602	+	0.668597i
$243$		0			0
$244$	3.37628	+	1.54189i	0.216144	+	0.0987097i
$245$	−9.75709	−	6.27050i	−0.623357	−	0.400607i
$246$		0			0
$247$	−2.88134	−	0.414274i	−0.183335	−	0.0263596i
$248$	−6.69688	+	3.05836i	−0.425252	+	0.194206i
$249$		0			0
$250$	5.82766	+	9.06802i	0.368574	+	0.573512i
$251$	5.01620	−	5.78900i	0.316620	−	0.365398i	−0.575024	−	0.818137i	$-0.695007\pi$
$251$	5.01620	−	5.78900i	0.316620	−	0.365398i	0.891644	+	0.452738i	$0.149553\pi$
$252$		0			0
$253$	23.7339	+	7.41627i	1.49214	+	0.466257i
$254$		−	13.5924i		−	0.852860i
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	16.9636	−	2.43899i	1.05816	−	0.152140i	0.408800	−	0.912624i	$-0.365947\pi$
$257$	16.9636	−	2.43899i	1.05816	−	0.152140i	0.649357	+	0.760484i	$0.275038\pi$
$258$		0			0
$259$	−5.58559	+	38.8486i	−0.347071	+	2.41393i
$260$	1.77566	−	0.521380i	0.110122	−	0.0323346i
$261$		0			0
$262$	4.93805	−	10.8128i	0.305074	−	0.668018i
$263$	3.71751	+	1.09156i	0.229232	+	0.0673084i	0.394331	−	0.918968i	$-0.370976\pi$
$263$	3.71751	+	1.09156i	0.229232	+	0.0673084i	−0.165099	+	0.986277i	$0.552795\pi$
$264$		0			0
$265$	−14.6159	−	16.8677i	−0.897848	−	1.03617i
$266$	−3.54813	+	12.0838i	−0.217550	+	0.740906i
$267$		0			0
$268$	6.92575	−	10.7767i	0.423057	−	0.658290i
$269$	−5.40969	−	18.4237i	−0.329834	−	1.12331i	−0.942843	−	0.333237i	$-0.891859\pi$
$269$	−5.40969	−	18.4237i	−0.329834	−	1.12331i	0.613009	−	0.790076i	$-0.289959\pi$
$270$		0			0
$271$	−8.82645	−	19.3272i	−0.536169	−	1.17405i	−0.962947	−	0.269689i	$-0.913079\pi$
$271$	−8.82645	−	19.3272i	−0.536169	−	1.17405i	0.426779	−	0.904356i	$-0.359648\pi$
$272$	−0.138219	−	0.961332i	−0.00838073	−	0.0582893i
$273$		0			0
$274$	3.64254	+	3.15628i	0.220054	+	0.190678i
$275$	1.72043			0.103746
$276$		0			0
$277$	−17.8746			−1.07398			−0.536990	−	0.843589i	$-0.680439\pi$
$277$	−17.8746			−1.07398			−0.536990	+	0.843589i	$0.680439\pi$
$278$	4.28310	+	3.71133i	0.256883	+	0.222591i
$279$		0			0
$280$	−1.13944	−	7.92500i	−0.0680948	−	0.473609i
$281$	7.74803	+	16.9658i	0.462209	+	1.01210i	0.986979	+	0.160852i	$0.0514240\pi$
$281$	7.74803	+	16.9658i	0.462209	+	1.01210i	−0.524770	+	0.851244i	$0.675849\pi$
$282$		0			0
$283$	−4.13986	−	14.0991i	−0.246089	−	0.838102i	−0.986192	−	0.165608i	$-0.947041\pi$
$283$	−4.13986	−	14.0991i	−0.246089	−	0.838102i	0.740103	−	0.672494i	$-0.234777\pi$
$284$	−3.59379	+	5.59204i	−0.213252	+	0.331827i
$285$		0			0
$286$	−1.17072	+	3.98710i	−0.0692261	+	0.235762i
$287$	13.8872	+	16.0267i	0.819735	+	0.946025i
$288$		0			0
$289$	15.4063	+	4.52371i	0.906254	+	0.266100i
$290$	−2.81069	+	6.15455i	−0.165049	+	0.361408i
$291$		0			0
$292$	0.325972	−	0.0957141i	0.0190761	−	0.00560125i
$293$	−1.48847	+	10.3526i	−0.0869576	+	0.604803i	0.899018	+	0.437912i	$0.144282\pi$
$293$	−1.48847	+	10.3526i	−0.0869576	+	0.604803i	−0.985975	+	0.166891i	$0.946627\pi$
$294$		0			0
$295$	27.8278	−	4.00103i	1.62020	−	0.232949i
$296$	−9.52227	+	6.11959i	−0.553471	+	0.355694i
$297$		0			0
$298$			18.2142i			1.05512i
$299$	3.70610	−	1.01906i	0.214329	−	0.0589336i
$300$		0			0
$301$	17.9444	−	20.7089i	1.03430	−	1.19364i
$302$	−1.94144	−	3.02093i	−0.111717	−	0.173835i
$303$		0			0
$304$	−3.30387	+	1.50883i	−0.189490	+	0.0865372i
$305$	8.48334	+	1.21972i	0.485755	+	0.0698410i
$306$		0			0
$307$	25.7523	+	16.5500i	1.46976	+	0.944558i	0.998025	+	0.0628185i	$0.0200089\pi$
$307$	25.7523	+	16.5500i	1.46976	+	0.944558i	0.471736	+	0.881740i	$0.343627\pi$
$308$	16.3533	+	7.46832i	0.931818	+	0.425547i
$309$		0			0
$310$	−12.8476	+	11.1325i	−0.729695	+	0.632284i
$311$	1.38046	−	1.19618i	0.0782789	−	0.0678291i	−0.614842	−	0.788650i	$-0.710780\pi$
$311$	1.38046	−	1.19618i	0.0782789	−	0.0678291i	0.693121	+	0.720821i	$0.256235\pi$
$312$		0			0
$313$	−27.7510	−	12.6735i	−1.56858	−	0.716347i	−0.573860	−	0.818954i	$-0.694555\pi$
$313$	−27.7510	−	12.6735i	−1.56858	−	0.716347i	−0.994722	+	0.102606i	$0.967282\pi$
$314$	−0.649686	−	0.417528i	−0.0366639	−	0.0235624i
$315$		0			0
$316$	−0.179829	−	0.0258556i	−0.0101162	−	0.00145449i
$317$	0.910489	−	0.415806i	0.0511381	−	0.0233540i	−0.389682	−	0.920950i	$-0.627415\pi$
$317$	0.910489	−	0.415806i	0.0511381	−	0.0233540i	0.440820	+	0.897596i	$0.354688\pi$
$318$		0			0
$319$	−8.21368	−	12.7807i	−0.459878	−	0.715584i
$320$	1.51212	−	1.74508i	0.0845302	−	0.0975530i
$321$		0			0
$322$	−2.08208	−	16.4982i	−0.116030	−	0.919411i
$323$			3.52755i			0.196278i
$324$		0			0
$325$	0.223722	−	0.143777i	0.0124098	−	0.00797532i
$326$	18.3693	−	2.64110i	1.01738	−	0.146277i
$327$		0			0
$328$	−0.870384	+	6.05365i	−0.0480589	+	0.334257i
$329$	15.5811	−	4.57502i	0.859013	−	0.252229i
$330$		0			0
$331$	−8.86651	+	19.4150i	−0.487348	+	1.06714i	0.493030	+	0.870012i	$0.335889\pi$
$331$	−8.86651	+	19.4150i	−0.487348	+	1.06714i	−0.980377	+	0.197130i	$0.936838\pi$
$332$	−2.45590	−	0.721117i	−0.134785	−	0.0395764i
$333$		0			0
$334$	−9.25110	−	10.6763i	−0.506197	−	0.584183i
$335$	8.33360	−	28.3816i	0.455313	−	1.55065i
$336$		0			0
$337$	−8.24499	+	12.8295i	−0.449133	+	0.698865i	−0.989815	−	0.142363i	$-0.954530\pi$
$337$	−8.24499	+	12.8295i	−0.449133	+	0.698865i	0.540681	+	0.841227i	$0.318166\pi$
$338$	−3.48156	−	11.8571i	−0.189372	−	0.644941i
$339$		0			0
$340$	−0.931615	−	2.03995i	−0.0505239	−	0.110632i
$341$	−5.43241	−	37.7833i	−0.294182	−	2.04608i
$342$		0			0
$343$	5.18094	+	4.48931i	0.279745	+	0.242400i
$344$	7.90268			0.426084
$345$		0			0
$346$	−17.9968			−0.967517
$347$	1.83292	+	1.58823i	0.0983961	+	0.0852607i	0.702670	−	0.711516i	$-0.251991\pi$
$347$	1.83292	+	1.58823i	0.0983961	+	0.0852607i	−0.604274	+	0.796777i	$0.706537\pi$
$348$		0			0
$349$	−3.04521	−	21.1799i	−0.163006	−	1.13374i	−0.892926	−	0.450202i	$-0.851352\pi$
$349$	−3.04521	−	21.1799i	−0.163006	−	1.13374i	0.729920	−	0.683533i	$-0.239557\pi$
$350$	−0.477957	−	1.04658i	−0.0255479	−	0.0559420i
$351$		0			0
$352$	1.46074	+	4.97483i	0.0778577	+	0.265159i
$353$	−10.2159	+	15.8963i	−0.543740	+	0.846076i	−0.999019	−	0.0442726i	$-0.985903\pi$
$353$	−10.2159	+	15.8963i	−0.543740	+	0.846076i	0.455279	+	0.890349i	$0.349539\pi$
$354$		0			0
$355$	−4.32432	+	14.7273i	−0.229511	+	0.781643i
$356$	8.43261	+	9.73176i	0.446928	+	0.515782i
$357$		0			0
$358$	−16.7174	−	4.90867i	−0.883543	−	0.259432i
$359$	−12.0864	+	26.4656i	−0.637898	+	1.39680i	0.263861	+	0.964561i	$0.415004\pi$
$359$	−12.0864	+	26.4656i	−0.637898	+	1.39680i	−0.901758	+	0.432240i	$0.857723\pi$
$360$		0			0
$361$	−5.57262	+	1.63627i	−0.293296	+	0.0861194i
$362$	2.83408	−	19.7115i	0.148956	−	1.03601i
$363$		0			0
$364$	2.75069	−	0.395489i	0.144175	−	0.0207293i
$365$	0.659939	−	0.424117i	0.0345428	−	0.0221993i
$366$		0			0
$367$		−	36.3497i		−	1.89744i	−0.316116	−	0.948720i	$-0.602379\pi$
$367$		−	36.3497i		−	1.89744i	0.316116	−	0.948720i	$-0.397621\pi$
$368$	3.20270	−	3.56969i	0.166952	−	0.186083i
$369$		0			0
$370$	−17.1159	+	19.7528i	−0.889815	+	1.02690i
$371$	−18.1198	−	28.1949i	−0.940732	−	1.46381i
$372$		0			0
$373$	17.7350	−	8.09931i	0.918285	−	0.419367i	0.100530	−	0.994934i	$-0.467946\pi$
$373$	17.7350	−	8.09931i	0.918285	−	0.419367i	0.817754	+	0.575567i	$0.195219\pi$
$374$	4.98436	+	0.716643i	0.257735	+	0.0370567i
$375$		0			0
$376$	3.93983	+	2.53198i	0.203181	+	0.130577i
$377$	−2.13618	−	0.975562i	−0.110019	−	0.0502440i
$378$		0			0
$379$	−18.1907	+	15.7624i	−0.934396	+	0.809659i	−0.981937	−	0.189211i	$-0.939407\pi$
$379$	−18.1907	+	15.7624i	−0.934396	+	0.809659i	0.0475406	+	0.998869i	$0.484862\pi$
$380$	−6.33830	+	5.49217i	−0.325148	+	0.281742i
$381$		0			0
$382$	−5.31929	−	2.42924i	−0.272159	−	0.124291i
$383$	−5.14393	−	3.30580i	−0.262843	−	0.168919i	0.402582	−	0.915384i	$-0.368113\pi$
$383$	−5.14393	−	3.30580i	−0.262843	−	0.168919i	−0.665424	+	0.746465i	$0.731749\pi$
$384$		0			0
$385$	41.0899	+	5.90784i	2.09414	+	0.301091i
$386$	16.7079	−	7.63026i	0.850411	−	0.388370i
$387$		0			0
$388$	−7.49842	−	11.6678i	−0.380675	−	0.592341i
$389$	19.2605	−	22.2278i	0.976547	−	1.12700i	−0.0153414	−	0.999882i	$-0.504884\pi$
$389$	19.2605	−	22.2278i	0.976547	−	1.12700i	0.991888	−	0.127113i	$-0.0405710\pi$
$390$		0			0
$391$	−1.86149	−	4.26965i	−0.0941397	−	0.215925i
$392$		−	5.02291i		−	0.253695i
$393$		0			0
$394$	−1.67608	+	1.07715i	−0.0844397	+	0.0542661i
$395$	−0.415239	+	0.0597024i	−0.0208930	+	0.00300395i
$396$		0			0
$397$	3.17145	−	22.0579i	0.159170	−	1.10705i	−0.740996	−	0.671509i	$-0.765646\pi$
$397$	3.17145	−	22.0579i	0.159170	−	1.10705i	0.900167	−	0.435546i	$-0.143445\pi$
$398$	−11.3738	+	3.33964i	−0.570115	+	0.167401i
$399$		0			0
$400$	0.137843	−	0.301833i	0.00689213	−	0.0150917i
$401$	−5.29291	−	1.55414i	−0.264315	−	0.0776099i	0.146890	−	0.989153i	$-0.453074\pi$
$401$	−5.29291	−	1.55414i	−0.264315	−	0.0776099i	−0.411205	+	0.911543i	$0.634892\pi$
$402$		0			0
$403$	−3.86398	−	4.45927i	−0.192479	−	0.222132i
$404$	1.61134	−	5.48770i	0.0801669	−	0.273024i
$405$		0			0
$406$	−5.49296	+	8.54721i	−0.272611	+	0.424191i
$407$	−16.5343	−	56.3108i	−0.819577	−	2.79122i
$408$		0			0
$409$	5.08280	+	11.1298i	0.251328	+	0.550332i	0.992679	−	0.120786i	$-0.0385416\pi$
$409$	5.08280	+	11.1298i	0.251328	+	0.550332i	−0.741350	+	0.671118i	$0.765814\pi$
$410$	2.00978	+	13.9783i	0.0992560	+	0.690340i
$411$		0			0
$412$	−10.2989	−	8.92404i	−0.507390	−	0.439656i
$413$	42.2172			2.07737
$414$		0			0
$415$	−5.91025			−0.290123
$416$	0.605700	+	0.524842i	0.0296969	+	0.0257325i
$417$		0			0
$418$	−2.68005	−	18.6402i	−0.131086	−	0.911721i
$419$	12.7322	+	27.8796i	0.622008	+	1.36201i	0.914050	+	0.405602i	$0.132938\pi$
$419$	12.7322	+	27.8796i	0.622008	+	1.36201i	−0.292042	+	0.956406i	$0.594335\pi$
$420$		0			0
$421$	−0.288320	−	0.981926i	−0.0140518	−	0.0478562i	0.952169	−	0.305573i	$-0.0988480\pi$
$421$	−0.288320	−	0.981926i	−0.0140518	−	0.0478562i	−0.966220	+	0.257717i	$0.917030\pi$
$422$	6.63110	−	10.3182i	0.322797	−	0.502282i
$423$		0			0
$424$	2.72318	−	9.27429i	0.132249	−	0.450399i
$425$	−0.211041	−	0.243554i	−0.0102370	−	0.0118141i
$426$		0			0
$427$	12.3486	+	3.62589i	0.597593	+	0.175469i
$428$	−2.32044	+	5.08105i	−0.112163	+	0.245602i
$429$		0			0
$430$	17.5087	−	5.14102i	0.844345	−	0.247922i
$431$	−0.716797	+	4.98543i	−0.0345269	+	0.240140i	−0.999775	−	0.0211939i	$-0.993253\pi$
$431$	−0.716797	+	4.98543i	−0.0345269	+	0.240140i	0.965248	+	0.261334i	$0.0841623\pi$
$432$		0			0
$433$	−5.06058	+	0.727602i	−0.243196	+	0.0349663i	−0.262835	−	0.964841i	$-0.584657\pi$
$433$	−5.06058	+	0.727602i	−0.243196	+	0.0349663i	0.0196388	+	0.999807i	$0.493748\pi$
$434$	−21.4753	+	13.8013i	−1.03085	+	0.662484i
$435$		0			0
$436$			15.1597i			0.726017i
$437$	−13.3593	+	11.1780i	−0.639062	+	0.534717i
$438$		0			0
$439$	−2.40628	+	2.77700i	−0.114846	+	0.132539i	−0.810261	−	0.586069i	$-0.800675\pi$
$439$	−2.40628	+	2.77700i	−0.114846	+	0.132539i	0.695416	+	0.718608i	$0.255220\pi$
$440$	6.47266	+	10.0717i	0.308572	+	0.480147i
$441$		0			0
$442$	0.708046	−	0.323354i	0.0336783	−	0.0153804i
$443$	29.1510	+	4.19128i	1.38501	+	0.199134i	0.794189	−	0.607671i	$-0.207896\pi$
$443$	29.1510	+	4.19128i	1.38501	+	0.199134i	0.590818	+	0.806805i	$0.298805\pi$
$444$		0			0
$445$	25.0137	+	16.0753i	1.18576	+	0.762044i
$446$	2.11353	+	0.965216i	0.100078	+	0.0457043i
$447$		0			0
$448$	2.62049	−	2.27067i	0.123807	−	0.107279i
$449$	22.6640	−	19.6385i	1.06958	−	0.926798i	0.0720770	−	0.997399i	$-0.477037\pi$
$449$	22.6640	−	19.6385i	1.06958	−	0.926798i	0.997505	+	0.0706014i	$0.0224918\pi$
$450$		0			0
$451$	−28.8445	−	13.1728i	−1.35823	−	0.620284i
$452$	0.0192174	+	0.0123503i	0.000903910	+	0.000580908i
$453$		0			0
$454$	−13.1547	−	1.89137i	−0.617383	−	0.0887662i
$455$	5.83698	−	2.66566i	0.273642	−	0.124968i
$456$		0			0
$457$	−12.6797	−	19.7300i	−0.593131	−	0.922929i	−0.999956	−	0.00942302i	$-0.997001\pi$
$457$	−12.6797	−	19.7300i	−0.593131	−	0.922929i	0.406825	−	0.913506i	$-0.366636\pi$
$458$	−16.5979	+	19.1550i	−0.775570	+	0.895055i
$459$		0			0
$460$	4.77348	−	9.99229i	0.222564	−	0.465893i
$461$		−	27.0892i		−	1.26167i	−0.775917	−	0.630835i	$-0.782713\pi$
$461$		−	27.0892i		−	1.26167i	0.775917	−	0.630835i	$-0.217287\pi$
$462$		0			0
$463$	2.19966	−	1.41363i	0.102227	−	0.0656972i	−0.488529	−	0.872548i	$-0.662466\pi$
$463$	2.19966	−	1.41363i	0.102227	−	0.0656972i	0.590755	+	0.806851i	$0.298830\pi$
$464$	−2.90035	+	0.417007i	−0.134645	+	0.0193590i
$465$		0			0
$466$	−2.57349	+	17.8990i	−0.119214	+	0.829155i
$467$	14.4527	−	4.24370i	0.668792	−	0.196375i	0.0703268	−	0.997524i	$-0.477596\pi$
$467$	14.4527	−	4.24370i	0.668792	−	0.196375i	0.598465	+	0.801149i	$0.295778\pi$
$468$		0			0
$469$	18.4521	−	40.4044i	0.852037	−	1.86570i
$470$	10.3760	+	3.04667i	0.478610	+	0.140533i
$471$		0			0
$472$	7.97321	+	9.20157i	0.366997	+	0.423537i
$473$	−11.5438	+	39.3145i	−0.530783	+	1.80768i
$474$		0			0
$475$	−0.651580	+	1.01388i	−0.0298965	+	0.0465199i
$476$	−0.948764	−	3.23119i	−0.0434865	−	0.148102i
$477$		0			0
$478$	−5.75433	−	12.6002i	−0.263197	−	0.576321i
$479$	0.790818	+	5.50026i	0.0361334	+	0.251313i	0.999880	−	0.0155067i	$-0.00493613\pi$
$479$	0.790818	+	5.50026i	0.0361334	+	0.251313i	−0.963746	+	0.266820i	$0.914027\pi$
$480$		0			0
$481$	−6.85601	−	5.94076i	−0.312607	−	0.270876i
$482$	−25.1787			−1.14686
$483$		0			0
$484$	−15.8826			−0.721939
$485$	−24.2034	−	20.9724i	−1.09902	−	0.952306i
$486$		0			0
$487$	3.86962	+	26.9138i	0.175349	+	1.21958i	0.867356	+	0.497689i	$0.165818\pi$
$487$	3.86962	+	26.9138i	0.175349	+	1.21958i	−0.692007	+	0.721891i	$0.743273\pi$
$488$	1.54189	+	3.37628i	0.0697983	+	0.152837i
$489$		0			0
$490$	−3.26761	−	11.1285i	−0.147616	−	0.502733i
$491$	19.7131	−	30.6742i	0.889640	−	1.38431i	−0.0333345	−	0.999444i	$-0.510613\pi$
$491$	19.7131	−	30.6742i	0.889640	−	1.38431i	0.922974	−	0.384862i	$-0.125751\pi$
$492$		0			0
$493$	−0.801763	+	2.73056i	−0.0361096	+	0.122978i
$494$	−1.90628	−	2.19996i	−0.0857674	−	0.0989809i
$495$		0			0
$496$	−7.06396	−	2.07417i	−0.317181	−	0.0931328i
$497$	−9.57482	+	20.9659i	−0.429489	+	0.940450i
$498$		0			0
$499$	0.702685	−	0.206327i	0.0314565	−	0.00923647i	−0.265966	−	0.963982i	$-0.585691\pi$
$499$	0.702685	−	0.206327i	0.0314565	−	0.00923647i	0.297423	+	0.954746i	$0.403873\pi$
$500$	−1.53404	+	10.6695i	−0.0686042	+	0.477153i
$501$		0			0
$502$	7.58198	−	1.09012i	0.338400	−	0.0486546i
$503$	−32.7674	+	21.0583i	−1.46102	+	0.938943i	−0.462391	+	0.886676i	$0.653008\pi$
$503$	−32.7674	+	21.0583i	−1.46102	+	0.938943i	−0.998633	+	0.0522674i	$0.983355\pi$
$504$		0			0
$505$		−	13.2065i		−	0.587680i
$506$	13.0803	+	21.1473i	0.581490	+	0.940111i
$507$		0			0
$508$	8.90110	−	10.2724i	0.394923	−	0.455765i
$509$	−21.2790	−	33.1107i	−0.943174	−	1.46761i	−0.882974	−	0.469421i	$-0.844463\pi$
$509$	−21.2790	−	33.1107i	−0.943174	−	1.46761i	−0.0601997	−	0.998186i	$-0.519174\pi$
$510$		0			0
$511$	1.07154	−	0.489357i	0.0474023	−	0.0216479i
$512$	0.989821	+	0.142315i	0.0437443	+	0.00628949i
$513$		0			0
$514$	14.4174	+	9.26550i	0.635924	+	0.408684i
$515$	−28.6230	−	13.0717i	−1.26128	−	0.576008i
$516$		0			0
$517$	−18.3512	+	15.9014i	−0.807086	+	0.699344i
$518$	−29.6617	+	25.7020i	−1.30326	+	1.12928i
$519$		0			0
$520$	1.68338	+	0.768776i	0.0738213	+	0.0337130i
$521$	−21.3149	−	13.6983i	−0.933825	−	0.600133i	−0.0171871	−	0.999852i	$-0.505471\pi$
$521$	−21.3149	−	13.6983i	−0.933825	−	0.600133i	−0.916637	+	0.399720i	$0.869107\pi$
$522$		0			0
$523$	10.1375	+	1.45755i	0.443280	+	0.0637340i	0.360341	−	0.932821i	$-0.382660\pi$
$523$	10.1375	+	1.45755i	0.443280	+	0.0637340i	0.0829389	+	0.996555i	$0.473569\pi$
$524$	10.8128	−	4.93805i	0.472360	−	0.215720i
$525$		0			0
$526$	2.09469	+	3.25940i	0.0913327	+	0.142116i
$527$	−4.68244	+	5.40382i	−0.203970	+	0.235394i
$528$		0			0
$529$	10.2711	−	20.5792i	0.446567	−	0.894750i
$530$		−	22.3191i		−	0.969480i
$531$		0			0
$532$	−10.5947	+	6.80881i	−0.459339	+	0.295199i
$533$	−4.85174	+	0.697574i	−0.210152	+	0.0302153i
$534$		0			0
$535$	−1.83559	+	12.7668i	−0.0793595	+	0.551957i
$536$	12.2914	−	3.60907i	0.530906	−	0.155888i
$537$		0			0
$538$	7.97659	−	17.4663i	0.343895	−	0.753025i
$539$	24.9881	+	7.33717i	1.07631	+	0.316034i
$540$		0			0
$541$	−9.52796	−	10.9959i	−0.409639	−	0.472749i	0.513014	−	0.858380i	$-0.328529\pi$
$541$	−9.52796	−	10.9959i	−0.409639	−	0.472749i	−0.922653	+	0.385632i	$0.873984\pi$
$542$	5.98606	−	20.3866i	0.257123	−	0.875681i
$543$		0			0
$544$	0.525080	−	0.817040i	0.0225126	−	0.0350303i
$545$	9.86200	+	33.5869i	0.422442	+	1.43870i
$546$		0			0
$547$	3.96787	+	8.68843i	0.169654	+	0.371490i	0.975293	−	0.220917i	$-0.0709050\pi$
$547$	3.96787	+	8.68843i	0.169654	+	0.371490i	−0.805639	+	0.592407i	$0.798178\pi$
$548$	0.685925	+	4.77071i	0.0293013	+	0.203795i
$549$		0			0
$550$	1.30022	+	1.12664i	0.0554414	+	0.0480402i
$551$	10.6427			0.453393
$552$		0			0
$553$	−0.629954			−0.0267884
$554$	−13.5087	−	11.7054i	−0.573930	−	0.497313i
$555$		0			0
$556$	0.806548	+	5.60967i	0.0342053	+	0.237903i
$557$	4.55918	+	9.98322i	0.193179	+	0.423002i	0.981291	−	0.192529i	$-0.0616688\pi$
$557$	4.55918	+	9.98322i	0.193179	+	0.423002i	−0.788113	+	0.615531i	$0.788942\pi$
$558$		0			0
$559$	1.78440	+	6.07709i	0.0754719	+	0.257034i
$560$	4.32864	−	6.73549i	0.182918	−	0.284627i
$561$		0			0
$562$	−5.25468	+	17.8958i	−0.221655	+	0.754888i
$563$	12.9307	+	14.9228i	0.544964	+	0.628922i	0.959702	−	0.281019i	$-0.0906724\pi$
$563$	12.9307	+	14.9228i	0.544964	+	0.628922i	−0.414739	+	0.909941i	$0.636127\pi$
$564$		0			0
$565$	0.0506112	+	0.0148608i	0.00212923	+	0.000625198i
$566$	6.10422	−	13.3664i	0.256580	−	0.561831i
$567$		0			0
$568$	−6.37801	+	1.87275i	−0.267615	+	0.0785790i
$569$	−2.40323	+	16.7148i	−0.100748	+	0.700721i	0.875365	+	0.483462i	$0.160621\pi$
$569$	−2.40323	+	16.7148i	−0.100748	+	0.700721i	−0.976114	+	0.217259i	$0.930288\pi$
$570$		0			0
$571$	36.9309	−	5.30986i	1.54551	−	0.222211i	0.683822	−	0.729649i	$-0.260316\pi$
$571$	36.9309	−	5.30986i	1.54551	−	0.222211i	0.861688	+	0.507438i	$0.169407\pi$
$572$	−3.49577	+	2.24659i	−0.146165	+	0.0939348i
$573$		0			0
$574$			21.2063i			0.885135i
$575$	0.253630	−	1.57101i	0.0105771	−	0.0655155i
$576$		0			0
$577$	−21.5661	+	24.8886i	−0.897807	+	1.03613i	0.101340	+	0.994852i	$0.467687\pi$
$577$	−21.5661	+	24.8886i	−0.897807	+	1.03613i	−0.999148	+	0.0412733i	$0.986859\pi$
$578$	8.68093	+	13.5078i	0.361079	+	0.561850i
$579$		0			0
$580$	−6.15455	+	2.81069i	−0.255554	+	0.116707i
$581$	−8.78477	−	1.26306i	−0.364453	−	0.0524005i
$582$		0			0
$583$	42.1601	+	27.0947i	1.74609	+	1.12215i
$584$	0.309033	+	0.141131i	0.0127879	+	0.00584003i
$585$		0			0
$586$	−7.90440	+	6.84920i	−0.326528	+	0.282938i
$587$	−4.20569	+	3.64425i	−0.173587	+	0.150414i	−0.737322	−	0.675542i	$-0.763910\pi$
$587$	−4.20569	+	3.64425i	−0.173587	+	0.150414i	0.563734	+	0.825956i	$0.309364\pi$
$588$		0			0
$589$	24.3237	+	11.1083i	1.00224	+	0.457708i
$590$	23.6510	+	15.1996i	0.973695	+	0.625756i
$591$		0			0
$592$	−11.2039	−	1.61088i	−0.460479	−	0.0662069i
$593$	−5.03549	+	2.29963i	−0.206783	+	0.0944346i	−0.516114	−	0.856520i	$-0.672622\pi$
$593$	−5.03549	+	2.29963i	−0.206783	+	0.0944346i	0.309331	+	0.950954i	$0.399895\pi$
$594$		0			0
$595$	−4.20405	−	6.54163i	−0.172349	−	0.268181i
$596$	−11.9278	+	13.7654i	−0.488582	+	0.563853i
$597$		0			0
$598$	3.46822	+	1.65683i	0.141826	+	0.0677526i
$599$			29.9092i			1.22206i	0.791609	+	0.611028i	$0.209244\pi$
$599$			29.9092i			1.22206i	−0.791609	+	0.611028i	$0.790756\pi$
$600$		0			0
$601$	26.1425	−	16.8008i	1.06637	−	0.685317i	0.115003	−	0.993365i	$-0.463312\pi$
$601$	26.1425	−	16.8008i	1.06637	−	0.685317i	0.951371	+	0.308048i	$0.0996758\pi$
$602$	27.1229	−	3.89968i	1.10545	−	0.158939i
$603$		0			0
$604$	0.511051	−	3.55444i	0.0207944	−	0.144628i
$605$	−35.1886	+	10.3323i	−1.43062	+	0.420068i
$606$		0			0
$607$	−13.7813	+	30.1768i	−0.559365	+	1.22484i	0.392904	+	0.919580i	$0.371471\pi$
$607$	−13.7813	+	30.1768i	−0.559365	+	1.22484i	−0.952269	+	0.305260i	$0.901257\pi$
$608$	−3.48497	−	1.02328i	−0.141334	−	0.0414995i
$609$		0			0
$610$	5.61254	+	6.47721i	0.227245	+	0.262255i
$611$	−1.05747	+	3.60141i	−0.0427806	+	0.145697i
$612$		0			0
$613$	−9.80782	+	15.2613i	−0.396134	+	0.616397i	−0.980832	−	0.194854i	$-0.937577\pi$
$613$	−9.80782	+	15.2613i	−0.396134	+	0.616397i	0.584698	+	0.811251i	$0.301213\pi$
$614$	8.62434	+	29.3718i	0.348050	+	1.18535i
$615$		0			0
$616$	7.46832	+	16.3533i	0.300907	+	0.658895i
$617$	−3.10632	−	21.6049i	−0.125056	−	0.869781i	−0.951694	−	0.307047i	$-0.900659\pi$
$617$	−3.10632	−	21.6049i	−0.125056	−	0.869781i	0.826639	−	0.562733i	$-0.190250\pi$
$618$		0			0
$619$	1.11892	+	0.969548i	0.0449731	+	0.0389694i	0.677057	−	0.735930i	$-0.263255\pi$
$619$	1.11892	+	0.969548i	0.0449731	+	0.0389694i	−0.632084	+	0.774900i	$0.717800\pi$
$620$	−16.9998			−0.682729
$621$		0			0
$622$	1.82662			0.0732406
$623$	33.7440	+	29.2393i	1.35192	+	1.17145i
$624$		0			0
$625$	3.77832	+	26.2788i	0.151133	+	1.05115i
$626$	−12.6735	−	27.7510i	−0.506534	−	1.10915i
$627$		0			0
$628$	−0.217577	−	0.741000i	−0.00868227	−	0.0295691i
$629$	−5.94345	+	9.24820i	−0.236981	+	0.368750i
$630$		0			0
$631$	−7.00773	+	23.8661i	−0.278973	+	0.950096i	0.694154	+	0.719827i	$0.255779\pi$
$631$	−7.00773	+	23.8661i	−0.278973	+	0.950096i	−0.973127	+	0.230269i	$0.926039\pi$
$632$	−0.118974	−	0.137304i	−0.00473254	−	0.00546164i
$633$		0			0
$634$	0.960396	+	0.281998i	0.0381422	+	0.0111996i
$635$	13.0381	−	28.5495i	0.517402	−	1.13295i
$636$		0			0
$637$	3.86258	−	1.13415i	0.153041	−	0.0449368i
$638$	2.16212	−	15.0378i	0.0855990	−	0.595354i
$639$		0			0
$640$	2.28557	−	0.328615i	0.0903451	−	0.0129897i
$641$	−14.5271	+	9.33601i	−0.573787	+	0.368750i	−0.795124	−	0.606447i	$-0.792594\pi$
$641$	−14.5271	+	9.33601i	−0.573787	+	0.368750i	0.221337	+	0.975197i	$0.428958\pi$
$642$		0			0
$643$		−	8.82552i		−	0.348044i	−0.984742	−	0.174022i	$-0.944324\pi$
$643$		−	8.82552i		−	0.348044i	0.984742	−	0.174022i	$-0.0556764\pi$
$644$	9.23052	−	13.8320i	0.363733	−	0.545058i
$645$		0			0
$646$	−2.31006	+	2.66595i	−0.0908880	+	0.104890i
$647$	12.3604	+	19.2332i	0.485939	+	0.756135i	0.994483	−	0.104901i	$-0.0334525\pi$
$647$	12.3604	+	19.2332i	0.485939	+	0.756135i	−0.508544	+	0.861036i	$0.669816\pi$
$648$		0			0
$649$	−57.4230	+	26.2242i	−2.25405	+	1.02939i
$650$	0.263232	+	0.0378470i	0.0103248	+	0.00148448i
$651$		0			0
$652$	15.6121	+	10.0333i	0.611417	+	0.392934i
$653$	−24.8660	−	11.3559i	−0.973080	−	0.444391i	−0.135543	−	0.990771i	$-0.543278\pi$
$653$	−24.8660	−	11.3559i	−0.973080	−	0.444391i	−0.837537	+	0.546381i	$0.816005\pi$
$654$		0			0
$655$	20.7438	−	17.9746i	0.810528	−	0.702327i
$656$	−4.62209	+	4.00506i	−0.180462	+	0.156372i
$657$		0			0
$658$	14.7714	+	6.74587i	0.575849	+	0.262981i
$659$	11.3880	+	7.31864i	0.443615	+	0.285094i	0.743318	−	0.668939i	$-0.233251\pi$
$659$	11.3880	+	7.31864i	0.443615	+	0.285094i	−0.299703	+	0.954033i	$0.596888\pi$
$660$		0			0
$661$	2.21395	+	0.318317i	0.0861125	+	0.0123811i	0.185236	−	0.982694i	$-0.440695\pi$
$661$	2.21395	+	0.318317i	0.0861125	+	0.0123811i	−0.0991239	+	0.995075i	$0.531604\pi$
$662$	−19.4150	+	8.86651i	−0.754584	+	0.344607i
$663$		0			0
$664$	−1.38381	−	2.15325i	−0.0537023	−	0.0835625i
$665$	−19.0436	+	21.9775i	−0.738479	+	0.852250i
$666$		0			0
$667$	−12.8816	+	5.61613i	−0.498776	+	0.217458i
$668$		−	14.1268i		−	0.546583i
$669$		0			0
$670$	24.8841	−	15.9921i	0.961358	−	0.617827i
$671$	−19.0487	+	2.73879i	−0.735367	+	0.105730i
$672$		0			0
$673$	−0.864402	+	6.01205i	−0.0333202	+	0.231747i	−0.999676	−	0.0254626i	$-0.991894\pi$
$673$	−0.864402	+	6.01205i	−0.0333202	+	0.231747i	0.966356	+	0.257210i	$0.0828032\pi$
$674$	−14.6327	+	4.29653i	−0.563629	+	0.165496i
$675$		0			0
$676$	5.13356	−	11.2409i	0.197445	−	0.432343i
$677$	22.0412	+	6.47189i	0.847113	+	0.248735i	0.676353	−	0.736578i	$-0.263559\pi$
$677$	22.0412	+	6.47189i	0.847113	+	0.248735i	0.170760	+	0.985313i	$0.445378\pi$
$678$		0			0
$679$	−31.4930	−	36.3449i	−1.20859	−	1.39479i
$680$	0.631817	−	2.15177i	0.0242291	−	0.0825166i
$681$		0			0
$682$	20.6372	−	32.1122i	0.790241	−	1.22964i
$683$	−2.86207	−	9.74731i	−0.109514	−	0.372970i	0.886439	−	0.462845i	$-0.153171\pi$
$683$	−2.86207	−	9.74731i	−0.109514	−	0.372970i	−0.995953	+	0.0898750i	$0.971353\pi$
$684$		0			0
$685$	4.62324	+	10.1235i	0.176645	+	0.386798i
$686$	0.975621	+	6.78559i	0.0372494	+	0.259075i
$687$		0			0
$688$	5.97245	+	5.17516i	0.227697	+	0.197301i
$689$	7.74673			0.295127
$690$		0			0
$691$	10.5948			0.403046			0.201523	−	0.979484i	$-0.435411\pi$
$691$	10.5948			0.403046			0.201523	+	0.979484i	$0.435411\pi$
$692$	−13.6011	−	11.7854i	−0.517037	−	0.448015i
$693$		0			0
$694$	0.345156	+	2.40061i	0.0131019	+	0.0911259i
$695$	5.43626	+	11.9037i	0.206209	+	0.451535i
$696$		0			0
$697$	1.67345	+	5.69926i	0.0633866	+	0.215875i
$698$	11.5685	−	18.0009i	0.437873	−	0.681344i
$699$		0			0
$700$	0.324148	−	1.10395i	0.0122516	−	0.0417253i
$701$	−16.8827	−	19.4836i	−0.637649	−	0.735886i	0.341308	−	0.939951i	$-0.389130\pi$
$701$	−16.8827	−	19.4836i	−0.637649	−	0.735886i	−0.978957	+	0.204065i	$0.934585\pi$
$702$		0			0
$703$	39.4469	+	11.5827i	1.48777	+	0.436848i
$704$	−2.15386	+	4.71630i	−0.0811768	+	0.177752i
$705$		0			0
$706$	−18.1306	+	5.32362i	−0.682353	+	0.200357i
$707$	2.82230	−	19.6296i	0.106144	−	0.738246i
$708$		0			0
$709$	7.65041	−	1.09996i	0.287317	−	0.0413100i	0.00285071	−	0.999996i	$-0.499093\pi$
$709$	7.65041	−	1.09996i	0.287317	−	0.0413100i	0.284467	+	0.958686i	$0.408183\pi$
$710$	−12.9124	+	8.29831i	−0.484595	+	0.311430i
$711$		0			0
$712$			12.8770i			0.482584i
$713$	−35.3025	−	0.609493i	−1.32209	−	0.0228257i
$714$		0			0
$715$	−6.28351	+	7.25156i	−0.234990	+	0.271193i
$716$	−9.41968	−	14.6573i	−0.352030	−	0.547769i
$717$		0			0
$718$	−26.4656	+	12.0864i	−0.987688	+	0.451062i
$719$	−16.4778	−	2.36915i	−0.614517	−	0.0883542i	−0.171974	−	0.985101i	$-0.555015\pi$
$719$	−16.4778	−	2.36915i	−0.614517	−	0.0883542i	−0.442543	+	0.896747i	$0.645924\pi$
$720$		0			0
$721$	−39.7506	−	25.5462i	−1.48039	−	0.951390i
$722$	−5.28303	−	2.41268i	−0.196614	−	0.0897906i
$723$		0			0
$724$	15.0501	−	13.0410i	0.559333	−	0.484665i
$725$	−0.734805	+	0.636712i	−0.0272900	+	0.0236469i
$726$		0			0
$727$	−14.3492	−	6.55305i	−0.532182	−	0.243039i	0.131153	−	0.991362i	$-0.458132\pi$
$727$	−14.3492	−	6.55305i	−0.532182	−	0.243039i	−0.663335	+	0.748323i	$0.730859\pi$
$728$	2.33782	+	1.50243i	0.0866454	+	0.0556836i
$729$		0			0
$730$	0.776486	+	0.111642i	0.0287390	+	0.00413205i
$731$	6.98163	−	3.18840i	0.258225	−	0.117927i
$732$		0			0
$733$	−27.3958	−	42.6286i	−1.01189	−	1.57452i	−0.802465	−	0.596699i	$-0.796479\pi$
$733$	−27.3958	−	42.6286i	−1.01189	−	1.57452i	−0.209420	−	0.977826i	$-0.567158\pi$
$734$	23.8040	−	27.4713i	0.878622	−	1.01398i
$735$		0			0
$736$	4.75809	−	0.600472i	0.175386	−	0.0221337i
$737$			66.4192i			2.44658i
$738$		0			0
$739$	−9.32413	+	5.99225i	−0.342994	+	0.220429i	−0.700784	−	0.713373i	$-0.747166\pi$
$739$	−9.32413	+	5.99225i	−0.342994	+	0.220429i	0.357791	+	0.933802i	$0.383530\pi$
$740$	−25.8707	+	3.71965i	−0.951026	+	0.136737i
$741$		0			0
$742$	4.76973	−	33.1742i	0.175102	−	1.21786i
$743$	47.4535	−	13.9336i	1.74090	−	0.511175i	0.751925	−	0.659249i	$-0.229126\pi$
$743$	47.4535	−	13.9336i	1.74090	−	0.511175i	0.988976	+	0.148075i	$0.0473076\pi$
$744$		0			0
$745$	−17.4715	+	38.2573i	−0.640108	+	1.40164i
$746$	18.7072	+	5.49292i	0.684918	+	0.201110i
$747$		0			0
$748$	3.29763	+	3.80566i	0.120573	+	0.139149i
$749$	−5.45670	+	18.5838i	−0.199383	+	0.679037i
$750$		0			0
$751$	5.61691	−	8.74008i	0.204964	−	0.318930i	−0.723519	−	0.690304i	$-0.757477\pi$
$751$	5.61691	−	8.74008i	0.204964	−	0.318930i	0.928483	+	0.371374i	$0.121113\pi$
$752$	1.31944	+	4.49358i	0.0481149	+	0.163864i
$753$		0			0
$754$	−0.975562	−	2.13618i	−0.0355279	−	0.0777952i
$755$	−1.18005	−	8.20746i	−0.0429466	−	0.298700i
$756$		0			0
$757$	−10.5048	−	9.10246i	−0.381804	−	0.330835i	0.442722	−	0.896659i	$-0.354013\pi$
$757$	−10.5048	−	9.10246i	−0.381804	−	0.330835i	−0.824526	+	0.565824i	$0.808558\pi$
$758$	−24.0698			−0.874255
$759$		0			0
$760$	−8.38678			−0.304220
$761$	16.4878	+	14.2868i	0.597684	+	0.517896i	0.900331	−	0.435207i	$-0.143325\pi$
$761$	16.4878	+	14.2868i	0.597684	+	0.517896i	−0.302647	+	0.953103i	$0.597870\pi$
$762$		0			0
$763$	7.48075	+	52.0298i	0.270821	+	1.88360i
$764$	−2.42924	−	5.31929i	−0.0878867	−	0.192445i
$765$		0			0
$766$	−1.72268	−	5.86692i	−0.0622431	−	0.211980i
$767$	−5.27561	+	8.20901i	−0.190491	+	0.296410i
$768$		0			0
$769$	11.1512	−	37.9775i	0.402122	−	1.36950i	−0.471057	−	0.882103i	$-0.656127\pi$
$769$	11.1512	−	37.9775i	0.402122	−	1.36950i	0.873179	−	0.487400i	$-0.162055\pi$
$770$	27.1849	+	31.3730i	0.979675	+	1.13061i
$771$		0			0
$772$	17.6238	+	5.17481i	0.634293	+	0.186245i
$773$	4.59611	−	10.0641i	0.165311	−	0.361980i	−0.808789	−	0.588099i	$-0.799877\pi$
$773$	4.59611	−	10.0641i	0.165311	−	0.361980i	0.974100	+	0.226119i	$0.0726039\pi$
$774$		0			0
$775$	−2.34396	+	0.688248i	−0.0841975	+	0.0247226i
$776$	1.97384	−	13.7283i	0.0708566	−	0.492818i
$777$		0			0
$778$	29.1123	−	4.18571i	1.04372	−	0.150065i
$779$	18.6872	−	12.0096i	0.669539	−	0.430287i
$780$		0			0
$781$		−	34.4651i		−	1.23326i
$782$	1.38920	−	4.44580i	0.0496778	−	0.158982i
$783$		0			0
$784$	3.28931	−	3.79606i	0.117475	−	0.135574i
$785$	−0.964102	−	1.50017i	−0.0344103	−	0.0535434i
$786$		0			0
$787$	8.51811	−	3.89009i	0.303638	−	0.138667i	−0.257769	−	0.966206i	$-0.582987\pi$
$787$	8.51811	−	3.89009i	0.303638	−	0.138667i	0.561407	+	0.827540i	$0.310260\pi$
$788$	−1.97208	−	0.283542i	−0.0702525	−	0.0101008i
$789$		0			0
$790$	−0.352914	−	0.226804i	−0.0125561	−	0.00806932i
$791$	0.0720507	+	0.0329044i	0.00256183	+	0.00116995i
$792$		0			0
$793$	−2.24817	+	1.94805i	−0.0798350	+	0.0691774i
$794$	16.8417	−	14.5934i	0.597689	−	0.517900i
$795$		0			0
$796$	−10.7827	−	4.92430i	−0.382183	−	0.174537i
$797$	−28.9834	−	18.6265i	−1.02665	−	0.659785i	−0.0849962	−	0.996381i	$-0.527088\pi$
$797$	−28.9834	−	18.6265i	−1.02665	−	0.659785i	−0.941649	+	0.336596i	$0.890724\pi$
$798$		0			0
$799$	4.50220	+	0.647318i	0.159276	+	0.0229005i
$800$	0.301833	−	0.137843i	0.0106714	−	0.00487347i
$801$		0			0
$802$	−2.98237	−	4.64066i	−0.105311	−	0.163867i
$803$	−1.15352	+	1.33123i	−0.0407067	+	0.0469781i
$804$		0			0
$805$	11.4523	−	36.6502i	0.403640	−	1.29175i
$806$		−	5.90047i		−	0.207835i
$807$		0			0
$808$	4.81145	−	3.09213i	0.169266	−	0.108781i
$809$	4.82350	−	0.693515i	0.169585	−	0.0243827i	−0.0569990	−	0.998374i	$-0.518153\pi$
$809$	4.82350	−	0.693515i	0.169585	−	0.0243827i	0.226584	+	0.973992i	$0.427244\pi$
$810$		0			0
$811$	−0.0302065	+	0.210091i	−0.00106069	+	0.00737728i	−0.990345	−	0.138625i	$-0.955732\pi$
$811$	−0.0302065	+	0.210091i	−0.00106069	+	0.00737728i	0.989284	+	0.146002i	$0.0466408\pi$
$812$	−9.74854	+	2.86243i	−0.342107	+	0.100452i
$813$		0			0
$814$	24.3799	−	53.3845i	0.854515	−	1.87113i
$815$	41.1163	+	12.0728i	1.44024	+	0.422893i
$816$		0			0
$817$	−18.7967	−	21.6925i	−0.657612	−	0.758925i
$818$	−3.44713	+	11.7398i	−0.120526	+	0.410474i
$819$		0			0
$820$	−7.63497	+	11.8802i	−0.266625	+	0.414876i
$821$	5.59085	+	19.0407i	0.195122	+	0.664524i	0.997688	+	0.0679611i	$0.0216494\pi$
$821$	5.59085	+	19.0407i	0.195122	+	0.664524i	−0.802566	+	0.596563i	$0.796532\pi$
$822$		0			0
$823$	17.7788	+	38.9302i	0.619731	+	1.35702i	0.915715	+	0.401828i	$0.131625\pi$
$823$	17.7788	+	38.9302i	0.619731	+	1.35702i	−0.295984	+	0.955193i	$0.595648\pi$
$824$	−1.93938	−	13.4887i	−0.0675614	−	0.469900i
$825$		0			0
$826$	31.9056	+	27.6464i	1.11014	+	0.961940i
$827$	−16.5524			−0.575582			−0.287791	−	0.957693i	$-0.592921\pi$
$827$	−16.5524			−0.575582			−0.287791	+	0.957693i	$0.592921\pi$
$828$		0			0
$829$	16.1488			0.560870			0.280435	−	0.959873i	$-0.409521\pi$
$829$	16.1488			0.560870			0.280435	+	0.959873i	$0.409521\pi$
$830$	−4.46667	−	3.87039i	−0.155040	−	0.134343i
$831$		0			0
$832$	0.114059	+	0.793298i	0.00395429	+	0.0275027i
$833$	−2.02654	−	4.43749i	−0.0702153	−	0.153750i
$834$		0			0
$835$	−9.19007	−	31.2985i	−0.318036	−	1.08313i
$836$	10.1813	−	15.8424i	0.352127	−	0.547920i
$837$		0			0
$838$	−8.63491	+	29.4078i	−0.298288	+	1.01588i
$839$	−23.2022	−	26.7767i	−0.801028	−	0.924436i	0.197409	−	0.980321i	$-0.436747\pi$
$839$	−23.2022	−	26.7767i	−0.801028	−	0.924436i	−0.998437	+	0.0558856i	$0.982202\pi$
$840$		0			0
$841$	−19.5872	−	5.75132i	−0.675420	−	0.198321i
$842$	0.425128	−	0.930900i	0.0146509	−	0.0320809i
$843$		0			0
$844$	11.7684	−	3.45552i	0.405086	−	0.118944i
$845$	4.06092	−	28.2443i	0.139700	−	0.971634i
$846$		0			0
$847$	−54.5111	+	7.83751i	−1.87302	+	0.269300i
$848$	8.13141	−	5.22574i	0.279234	−	0.179453i
$849$		0			0
$850$		−	0.322269i		−	0.0110537i
$851$	−53.8575	+	6.79683i	−1.84621	+	0.232992i
$852$		0			0
$853$	18.2762	−	21.0918i	0.625764	−	0.722170i	−0.351027	−	0.936365i	$-0.614167\pi$
$853$	18.2762	−	21.0918i	0.625764	−	0.722170i	0.976791	+	0.214195i	$0.0687130\pi$
$854$	6.95803	+	10.8269i	0.238099	+	0.370489i
$855$		0			0
$856$	−5.08105	+	2.32044i	−0.173667	+	0.0793110i
$857$	39.0777	+	5.61852i	1.33487	+	0.191925i	0.772528	−	0.634981i	$-0.218992\pi$
$857$	39.0777	+	5.61852i	1.33487	+	0.191925i	0.562341	+	0.826906i	$0.309901\pi$
$858$		0			0
$859$	−18.7338	−	12.0395i	−0.639190	−	0.410782i	0.180512	−	0.983573i	$-0.442225\pi$
$859$	−18.7338	−	12.0395i	−0.639190	−	0.410782i	−0.819702	+	0.572790i	$0.805861\pi$
$860$	16.5988	+	7.58044i	0.566016	+	0.258491i
$861$		0			0
$862$	−3.80648	+	3.29834i	−0.129649	+	0.112342i
$863$	16.0004	−	13.8644i	0.544660	−	0.471951i	−0.338537	−	0.940953i	$-0.609932\pi$
$863$	16.0004	−	13.8644i	0.544660	−	0.471951i	0.883197	+	0.469002i	$0.155386\pi$
$864$		0			0
$865$	−37.8007	−	17.2630i	−1.28526	−	0.586960i
$866$	−4.30101	−	2.76409i	−0.146154	−	0.0939277i
$867$		0			0
$868$	−25.2679	−	3.63297i	−0.857647	−	0.123311i
$869$	0.856852	−	0.391311i	0.0290667	−	0.0132743i
$870$		0			0
$871$	5.55068	+	8.63703i	0.188078	+	0.292655i
$872$	−9.92749	+	11.4569i	−0.336187	+	0.387981i
$873$		0			0
$874$	−17.4163	−	0.300690i	−0.589116	−	0.0101710i
$875$			37.3758i			1.26353i
$876$		0			0
$877$	−27.2610	+	17.5196i	−0.920538	+	0.591594i	−0.912814	−	0.408376i	$-0.866095\pi$
$877$	−27.2610	+	17.5196i	−0.920538	+	0.591594i	−0.00772447	+	0.999970i	$0.502459\pi$
$878$	−3.63710	+	0.522936i	−0.122746	+	0.0176482i
$879$		0			0
$880$	−1.70382	+	11.8503i	−0.0574358	+	0.399475i
$881$	21.8255	−	6.40855i	0.735320	−	0.215909i	0.107431	−	0.994213i	$-0.465737\pi$
$881$	21.8255	−	6.40855i	0.735320	−	0.215909i	0.627889	+	0.778303i	$0.283919\pi$
$882$		0			0
$883$	1.47374	−	3.22705i	0.0495954	−	0.108599i	−0.883212	−	0.468974i	$-0.844624\pi$
$883$	1.47374	−	3.22705i	0.0495954	−	0.108599i	0.932808	+	0.360375i	$0.117351\pi$
$884$	0.746858	+	0.219297i	0.0251195	+	0.00737576i
$885$		0			0
$886$	19.2862	+	22.2574i	0.647931	+	0.747753i
$887$	15.5690	−	53.0230i	0.522755	−	1.78034i	−0.0967069	−	0.995313i	$-0.530831\pi$
$887$	15.5690	−	53.0230i	0.522755	−	1.78034i	0.619462	−	0.785027i	$-0.287351\pi$
$888$		0			0
$889$	25.4805	−	39.6485i	0.854590	−	1.32977i
$890$	8.37699	+	28.5294i	0.280797	+	0.956308i
$891$		0			0
$892$	0.965216	+	2.11353i	0.0323178	+	0.0707661i
$893$	−2.42080	−	16.8370i	−0.0810089	−	0.563430i
$894$		0			0
$895$	−30.4048	−	26.3460i	−1.01632	−	0.880648i
$896$	3.46741			0.115838
$897$		0			0
$898$	29.9888			1.00074
$899$	16.3034	+	14.1270i	0.543748	+	0.471160i
$900$		0			0
$901$	−1.33600	−	9.29206i	−0.0445085	−	0.309564i
$902$	−13.1728	−	28.8445i	−0.438607	−	0.960415i
$903$		0			0
$904$	0.00643583	+	0.0219184i	0.000214052	+	0.000728996i
$905$	24.8604	−	38.6836i	0.826389	−	1.28589i
$906$		0			0
$907$	−1.19992	+	4.08656i	−0.0398427	+	0.135692i	−0.977013	−	0.213181i	$-0.931617\pi$
$907$	−1.19992	+	4.08656i	−0.0398427	+	0.135692i	0.937170	+	0.348873i	$0.113436\pi$
$908$	−8.70311	−	10.0439i	−0.288823	−	0.333319i
$909$		0			0
$910$	6.15693	+	1.80784i	0.204100	+	0.0599292i
$911$	11.5364	−	25.2612i	0.382218	−	0.836940i	−0.616550	−	0.787315i	$-0.711470\pi$
$911$	11.5364	−	25.2612i	0.382218	−	0.836940i	0.998768	−	0.0496242i	$-0.0158024\pi$
$912$		0			0
$913$	12.7335	−	3.73888i	0.421416	−	0.123739i
$914$	3.33772	−	23.2143i	0.110402	−	0.767862i
$915$		0			0
$916$	−25.0877	+	3.60707i	−0.828922	+	0.119181i
$917$	34.6741	−	22.2837i	1.14504	−	0.735872i
$918$		0			0
$919$			50.2748i			1.65841i	0.558944	+	0.829206i	$0.311207\pi$
$919$			50.2748i			1.65841i	−0.558944	+	0.829206i	$0.688793\pi$
$920$	10.1511	−	4.42570i	0.334672	−	0.145911i
$921$		0			0
$922$	17.7396	−	20.4726i	0.584224	−	0.674231i
$923$	−2.88026	−	4.48177i	−0.0948049	−	0.147519i
$924$		0			0
$925$	−3.41650	+	1.56026i	−0.112334	+	0.0513011i
$926$	2.58812	+	0.372116i	0.0850510	+	0.0122285i
$927$		0			0
$928$	−2.46502	−	1.58417i	−0.0809181	−	0.0520029i
$929$	−4.76150	−	2.17450i	−0.156220	−	0.0713432i	0.335771	−	0.941944i	$-0.391003\pi$
$929$	−4.76150	−	2.17450i	−0.156220	−	0.0713432i	−0.491990	+	0.870601i	$0.663731\pi$
$930$		0			0
$931$	−13.7877	+	11.9471i	−0.451873	+	0.391550i
$932$	−13.6663	+	11.8419i	−0.447653	+	0.387894i
$933$		0			0
$934$	13.7017	+	6.25734i	0.448332	+	0.204746i
$935$	9.78176	+	6.28636i	0.319898	+	0.205586i
$936$		0			0
$937$	4.61167	+	0.663058i	0.150657	+	0.0216611i	0.217230	−	0.976120i	$-0.430298\pi$
$937$	4.61167	+	0.663058i	0.150657	+	0.0216611i	−0.0665738	+	0.997782i	$0.521207\pi$
$938$	40.4044	−	18.4521i	1.31925	−	0.602481i
$939$		0			0
$940$	5.84652	+	9.09737i	0.190693	+	0.296723i
$941$	−15.5494	+	17.9450i	−0.506897	+	0.584991i	−0.950301	−	0.311331i	$-0.899225\pi$
$941$	−15.5494	+	17.9450i	−0.506897	+	0.584991i	0.443404	+	0.896322i	$0.353771\pi$
$942$		0			0
$943$	−16.2810	+	24.3973i	−0.530183	+	0.794484i
$944$			12.1754i			0.396276i
$945$		0			0
$946$	−34.4697	+	22.1523i	−1.12071	+	0.720234i
$947$	−25.6453	+	3.68724i	−0.833360	+	0.119819i	−0.545770	−	0.837935i	$-0.683763\pi$
$947$	−25.6453	+	3.68724i	−0.833360	+	0.119819i	−0.287589	+	0.957754i	$0.592854\pi$
$948$		0			0
$949$	−0.0387498	+	0.269510i	−0.00125787	+	0.00874868i
$950$	−1.15638	+	0.339544i	−0.0375179	+	0.0110163i
$951$		0			0
$952$	1.39895	−	3.06328i	0.0453404	−	0.0992815i
$953$	−22.0533	−	6.47543i	−0.714377	−	0.209760i	−0.0957051	−	0.995410i	$-0.530511\pi$
$953$	−22.0533	−	6.47543i	−0.714377	−	0.209760i	−0.618671	+	0.785650i	$0.712329\pi$
$954$		0			0
$955$	−8.84249	−	10.2048i	−0.286136	−	0.330219i
$956$	3.90256	−	13.2909i	0.126218	−	0.429859i
$957$		0			0
$958$	−3.00425	+	4.67470i	−0.0970628	+	0.151033i
$959$	4.70835	+	16.0352i	0.152040	+	0.517802i
$960$		0			0
$961$	9.63835	+	21.1050i	0.310915	+	0.680808i
$962$	−1.29105	−	8.97946i	−0.0416252	−	0.289509i
$963$		0			0
$964$	−19.0288	−	16.4885i	−0.612875	−	0.531059i
$965$	42.4126			1.36531
$966$		0			0
$967$	33.1448			1.06587			0.532933	−	0.846157i	$-0.321090\pi$
$967$	33.1448			1.06587			0.532933	+	0.846157i	$0.321090\pi$
$968$	−12.0033	−	10.4009i	−0.385801	−	0.334298i
$969$		0			0
$970$	−4.55773	−	31.6997i	−0.146340	−	1.01782i
$971$	−14.3615	−	31.4472i	−0.460882	−	1.00919i	−0.987286	−	0.158956i	$-0.949187\pi$
$971$	−14.3615	−	31.4472i	−0.460882	−	1.00919i	0.526404	−	0.850235i	$-0.323540\pi$
$972$		0			0
$973$	5.53633	+	18.8550i	0.177487	+	0.604464i
$974$	−14.7003	+	22.8741i	−0.471028	+	0.732935i
$975$		0			0
$976$	−1.04571	+	3.56135i	−0.0334722	+	0.113996i
$977$	5.65409	+	6.52517i	0.180891	+	0.208759i	0.838952	−	0.544205i	$-0.183169\pi$
$977$	5.65409	+	6.52517i	0.180891	+	0.208759i	−0.658062	+	0.752964i	$0.728623\pi$
$978$		0			0
$979$	−64.0606	−	18.8099i	−2.04739	−	0.601167i
$980$	4.81810	−	10.5502i	0.153908	−	0.337012i
$981$		0			0
$982$	34.9855	−	10.2727i	1.11643	−	0.327814i
$983$	4.28757	−	29.8207i	0.136752	−	0.951133i	−0.799716	−	0.600379i	$-0.795016\pi$
$983$	4.28757	−	29.8207i	0.136752	−	0.951133i	0.936468	−	0.350754i	$-0.114075\pi$
$984$		0			0
$985$	−4.55368	+	0.654720i	−0.145092	+	0.0208611i
$986$	−2.39407	+	1.53857i	−0.0762426	+	0.0489981i
$987$		0			0
$988$		−	2.91097i		−	0.0926101i
$989$	34.1981	+	16.3370i	1.08744	+	0.519485i
$990$		0			0
$991$	24.7589	−	28.5733i	0.786492	−	0.907660i	−0.211068	−	0.977471i	$-0.567694\pi$
$991$	24.7589	−	28.5733i	0.786492	−	0.907660i	0.997560	+	0.0698113i	$0.0222397\pi$
$992$	−3.98030	−	6.19346i	−0.126375	−	0.196643i
$993$		0			0
$994$	−20.9659	+	9.57482i	−0.664999	+	0.303695i
$995$	−27.0930	−	3.89539i	−0.858906	−	0.123492i
$996$		0			0
$997$	26.1145	+	16.7827i	0.827053	+	0.531515i	0.884340	−	0.466843i	$-0.154609\pi$
$997$	26.1145	+	16.7827i	0.827053	+	0.531515i	−0.0572872	+	0.998358i	$0.518245\pi$
$998$	0.666170	+	0.304229i	0.0210872	+	0.00963022i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.53.8	yes	80
3.2	odd	2	inner	414.2.j.a.53.1	✓	80
23.10	odd	22	inner	414.2.j.a.125.1	yes	80
69.56	even	22	inner	414.2.j.a.125.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.53.1	✓	80	3.2	odd	2	inner
414.2.j.a.53.8	yes	80	1.1	even	1	trivial
414.2.j.a.125.1	yes	80	23.10	odd	22	inner
414.2.j.a.125.8	yes	80	69.56	even	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.959224 + 2.10041i) q^{5} +(0.976881 + 3.32695i) q^{7} +(-0.540641 + 0.841254i) q^{8} +O(q^{10})\)	\(q+(0.755750 + 0.654861i) q^{2} +(0.142315 + 0.989821i) q^{4} +(0.959224 + 2.10041i) q^{5} +(0.976881 + 3.32695i) q^{7} +(-0.540641 + 0.841254i) q^{8} +(-0.650541 + 2.21554i) q^{10} +(-3.39535 - 3.91845i) q^{11} +(-0.768991 - 0.225796i) q^{13} +(-1.44041 + 3.15406i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(-0.138219 + 0.961332i) q^{17} +(3.59513 - 0.516901i) q^{19} +(-1.94252 + 1.24838i) q^{20} -5.18485i q^{22} +(-4.07867 + 2.52279i) q^{23} +(-0.217295 + 0.250772i) q^{25} +(-0.433300 - 0.674228i) q^{26} +(-3.15406 + 1.44041i) q^{28} +(2.90035 + 0.417007i) q^{29} +(6.19346 + 3.98030i) q^{31} +(-0.909632 - 0.415415i) q^{32} +(-0.733997 + 0.636012i) q^{34} +(-6.05091 + 5.24314i) q^{35} +(10.2963 + 4.70214i) q^{37} +(3.05551 + 1.96366i) q^{38} +(-2.28557 - 0.328615i) q^{40} +(5.56322 - 2.54064i) q^{41} +(-4.27251 - 6.64816i) q^{43} +(3.39535 - 3.91845i) q^{44} +(-4.73453 - 0.764361i) q^{46} -4.68329i q^{47} +(-4.22554 + 2.71559i) q^{49} +(-0.328442 + 0.0472228i) q^{50} +(0.114059 - 0.793298i) q^{52} +(-9.27429 + 2.72318i) q^{53} +(4.97343 - 10.8903i) q^{55} +(-3.32695 - 0.976881i) q^{56} +(1.91885 + 2.21447i) q^{58} +(3.43021 - 11.6822i) q^{59} +(2.00669 - 3.12248i) q^{61} +(2.07417 + 7.06396i) q^{62} +(-0.415415 - 0.909632i) q^{64} +(-0.263371 - 1.83178i) q^{65} +(-9.68135 - 8.38893i) q^{67} -0.971217 q^{68} -8.00650 q^{70} +(5.02367 + 4.35304i) q^{71} +(-0.0483492 - 0.336276i) q^{73} +(4.70214 + 10.2963i) q^{74} +(1.02328 + 3.48497i) q^{76} +(9.71963 - 15.1240i) q^{77} +(-0.0511848 + 0.174319i) q^{79} +(-1.51212 - 1.74508i) q^{80} +(5.86817 + 1.72305i) q^{82} +(-1.06329 + 2.32827i) q^{83} +(-2.15177 + 0.631817i) q^{85} +(1.12467 - 7.82224i) q^{86} +(5.13207 - 0.737881i) q^{88} +(10.8328 - 6.96181i) q^{89} -2.77897i q^{91} +(-3.07757 - 3.67812i) q^{92} +(3.06690 - 3.53939i) q^{94} +(4.53423 + 7.05541i) q^{95} +(-12.6161 + 5.76160i) q^{97} +(-4.97179 - 0.714835i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Introduction

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