LMFDB - Embedded newform 297.2.n.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	297.91
Dual form			297.2.n.b.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.527858 - 0.235017i) q^{2} +(-1.11486 - 1.23818i) q^{4} +(-2.74468 + 1.22201i) q^{5} +(1.13888 - 0.242076i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(2.54741 + 2.12385i) q^{11} +(0.412487 + 3.92455i) q^{13} +(-0.658057 - 0.139874i) q^{14} +(-0.220374 + 2.09672i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(4.57300 + 2.03603i) q^{20} +(-0.845527 - 1.71977i) q^{22} +(-0.0427501 + 0.0740453i) q^{23} +(2.69431 - 2.99234i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(-7.53156 + 1.60088i) q^{29} +(-0.682449 - 6.49307i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(0.384637 - 3.65957i) q^{38} +(-4.25861 - 4.72966i) q^{40} +(5.68213 + 1.20777i) q^{41} +(3.39229 + 5.87562i) q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(0.219298 - 0.243555i) q^{47} +(-5.15638 + 2.29577i) q^{49} +(-2.12546 + 0.946318i) q^{50} +(4.39943 - 4.88606i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +(1.23321 + 2.13598i) q^{56} +(4.35183 + 0.925009i) q^{58} +(1.53634 + 1.70628i) q^{59} +(1.43070 - 13.6122i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.0547189 + 0.520616i) q^{68} +(1.97708 - 0.420242i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(2.41378 - 2.68077i) q^{74} +(5.30529 - 9.18904i) q^{76} +(3.41531 + 1.80213i) q^{77} +(-8.11886 - 3.61475i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(0.518229 - 4.93062i) q^{83} +(0.923335 + 0.196261i) q^{85} +(-0.409774 - 3.89874i) q^{86} +(-2.61129 + 6.52242i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(0.139342 - 0.0296180i) q^{92} +(-0.172998 + 0.0770236i) q^{94} +(-12.8027 - 14.2189i) q^{95} +(-0.0811587 - 0.0361342i) q^{97} +3.26138 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.527858	−	0.235017i	−0.373252	−	0.166182i	0.211533	−	0.977371i	$-0.432154\pi$
$2$	−0.527858	−	0.235017i	−0.373252	−	0.166182i	−0.584785	+	0.811188i	$0.698821\pi$
$3$		0			0
$3$		0			0
$4$	−1.11486	−	1.23818i	−0.557430	−	0.619089i
$5$	−2.74468	+	1.22201i	−1.22746	+	0.546500i	−0.915009	−	0.403434i	$-0.867816\pi$
$5$	−2.74468	+	1.22201i	−1.22746	+	0.546500i	−0.312450	+	0.949934i	$0.601150\pi$
$6$		0			0
$7$	1.13888	−	0.242076i	0.430455	−	0.0914960i	0.0124114	−	0.999923i	$-0.496049\pi$
$7$	1.13888	−	0.242076i	0.430455	−	0.0914960i	0.418044	+	0.908427i	$0.362716\pi$
$8$	0.654602	+	2.01466i	0.231437	+	0.712289i
$9$		0			0
$10$	1.73599			0.548970
$11$	2.54741	+	2.12385i	0.768072	+	0.640364i
$11$	2.54741	+	2.12385i	0.768072	+	0.640364i
$12$		0			0
$13$	0.412487	+	3.92455i	0.114403	+	1.08848i	0.889595	+	0.456750i	$0.150986\pi$
$13$	0.412487	+	3.92455i	0.114403	+	1.08848i	−0.775192	+	0.631726i	$0.782347\pi$
$14$	−0.658057	−	0.139874i	−0.175873	−	0.0373830i
$15$		0			0
$16$	−0.220374	+	2.09672i	−0.0550935	+	0.524179i
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	0.556534	−	0.830825i	$-0.312131\pi$
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	−0.618183	+	0.786034i	$0.712131\pi$
$18$		0			0
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	0.875222	+	0.483721i	$0.160715\pi$
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	−0.423746	+	0.905781i	$0.639285\pi$
$20$	4.57300	+	2.03603i	1.02255	+	0.455271i
$21$		0			0
$22$	−0.845527	−	1.71977i	−0.180267	−	0.366657i
$23$	−0.0427501	+	0.0740453i	−0.00891401	+	0.0154395i	−0.870448	−	0.492260i	$-0.836171\pi$
$23$	−0.0427501	+	0.0740453i	−0.00891401	+	0.0154395i	0.861534	+	0.507700i	$0.169504\pi$
$24$		0			0
$25$	2.69431	−	2.99234i	0.538862	−	0.598467i
$26$	0.704604	−	2.16855i	0.138184	−	0.425287i
$27$		0			0
$28$	−1.56942	−	1.14025i	−0.296593	−	0.215487i
$29$	−7.53156	+	1.60088i	−1.39858	+	0.297276i	−0.844663	−	0.535298i	$-0.820199\pi$
$29$	−7.53156	+	1.60088i	−1.39858	+	0.297276i	−0.553913	+	0.832575i	$0.686866\pi$
$30$		0			0
$31$	−0.682449	−	6.49307i	−0.122571	−	1.16619i	−0.866937	−	0.498418i	$-0.833915\pi$
$31$	−0.682449	−	6.49307i	−0.122571	−	1.16619i	0.744366	−	0.667772i	$-0.232752\pi$
$32$	2.72743	−	4.72404i	0.482146	−	0.835101i
$33$		0			0
$34$	0.0907715	+	0.157221i	0.0155672	+	0.0269632i
$35$	−2.83004	+	2.05614i	−0.478363	+	0.347551i
$36$		0			0
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	0.657694	+	0.753286i	$0.271532\pi$
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	−0.974855	+	0.222838i	$0.928468\pi$
$38$	0.384637	−	3.65957i	0.0623963	−	0.593661i
$39$		0			0
$40$	−4.25861	−	4.72966i	−0.673345	−	0.747825i
$41$	5.68213	+	1.20777i	0.887399	+	0.188623i	0.628990	−	0.777413i	$-0.283468\pi$
$41$	5.68213	+	1.20777i	0.887399	+	0.188623i	0.258409	+	0.966036i	$0.416802\pi$
$42$		0			0
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	0.999798	+	0.0201157i	$0.00640347\pi$
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	−0.482478	+	0.875908i	$0.660263\pi$
$44$	−0.210303	−	5.52194i	−0.0317043	−	0.832463i
$45$		0			0
$46$	0.0399679	−	0.0290384i	0.00589294	−	0.00428147i
$47$	0.219298	−	0.243555i	0.0319879	−	0.0355262i	−0.726939	−	0.686703i	$-0.759058\pi$
$47$	0.219298	−	0.243555i	0.0319879	−	0.0355262i	0.758926	+	0.651176i	$0.225724\pi$
$48$		0			0
$49$	−5.15638	+	2.29577i	−0.736625	+	0.327967i
$50$	−2.12546	+	0.946318i	−0.300586	+	0.133830i
$51$		0			0
$52$	4.39943	−	4.88606i	0.610091	−	0.677575i
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	−0.714205	−	0.699937i	$-0.753211\pi$
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	0.444978	+	0.895541i	$0.353211\pi$
$54$		0			0
$55$	−9.58718	−	2.71632i	−1.29274	−	0.366269i
$56$	1.23321	+	2.13598i	0.164795	+	0.285433i
$57$		0			0
$58$	4.35183	+	0.925009i	0.571423	+	0.121460i
$59$	1.53634	+	1.70628i	0.200015	+	0.222139i	0.834805	−	0.550545i	$-0.185580\pi$
$59$	1.53634	+	1.70628i	0.200015	+	0.222139i	−0.634790	+	0.772685i	$0.718913\pi$
$60$		0			0
$61$	1.43070	−	13.6122i	0.183183	−	1.74287i	−0.387656	−	0.921804i	$-0.626715\pi$
$61$	1.43070	−	13.6122i	0.183183	−	1.74287i	0.570839	−	0.821062i	$-0.306618\pi$
$62$	−1.16575	+	3.58780i	−0.148050	+	0.455652i
$63$		0			0
$64$	0.861321	−	0.625787i	0.107665	−	0.0782233i
$65$	−5.92799	−	10.2676i	−0.735277	−	1.27354i
$66$		0			0
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	0.250096	+	0.968221i	$0.419538\pi$
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	−0.963552	+	0.267521i	$0.913795\pi$
$68$	0.0547189	+	0.520616i	0.00663564	+	0.0631339i
$69$		0			0
$70$	1.97708	−	0.420242i	0.236307	−	0.0502286i
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	0.921532	−	0.388302i	$-0.126938\pi$
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	−0.0845279	+	0.996421i	$0.526938\pi$
$72$		0			0
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	−0.883525	−	0.468383i	$-0.844837\pi$
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	0.990096	+	0.140393i	$0.0448367\pi$
$74$	2.41378	−	2.68077i	0.280596	−	0.311633i
$75$		0			0
$76$	5.30529	−	9.18904i	0.608559	−	1.05405i
$77$	3.41531	+	1.80213i	0.389211	+	0.205372i
$78$		0			0
$79$	−8.11886	−	3.61475i	−0.913443	−	0.406691i	−0.104464	−	0.994529i	$-0.533313\pi$
$79$	−8.11886	−	3.61475i	−0.913443	−	0.406691i	−0.808979	+	0.587838i	$0.799979\pi$
$80$	−1.95735	−	6.02412i	−0.218839	−	0.673517i
$81$		0			0
$82$	−2.71551	−	1.97293i	−0.299878	−	0.217874i
$83$	0.518229	−	4.93062i	0.0568831	−	0.541206i	−0.928558	−	0.371188i	$-0.878951\pi$
$83$	0.518229	−	4.93062i	0.0568831	−	0.541206i	0.985441	−	0.170018i	$-0.0543827\pi$
$84$		0			0
$85$	0.923335	+	0.196261i	0.100150	+	0.0212875i
$86$	−0.409774	−	3.89874i	−0.0441871	−	0.420412i
$87$		0			0
$88$	−2.61129	+	6.52242i	−0.278364	+	0.695293i
$89$	−2.12862			−0.225634			−0.112817	−	0.993616i	$-0.535987\pi$
$89$	−2.12862			−0.225634			−0.112817	+	0.993616i	$0.535987\pi$
$90$		0			0
$91$	1.41981	+	4.36973i	0.148837	+	0.458072i
$92$	0.139342	−	0.0296180i	0.0145274	−	0.00308789i
$93$		0			0
$94$	−0.172998	+	0.0770236i	−0.0178434	+	0.00794437i
$95$	−12.8027	−	14.2189i	−1.31353	−	1.45882i
$96$		0			0
$97$	−0.0811587	−	0.0361342i	−0.00824041	−	0.00366887i	0.402612	−	0.915371i	$-0.368102\pi$
$97$	−0.0811587	−	0.0361342i	−0.00824041	−	0.00366887i	−0.410853	+	0.911702i	$0.634769\pi$
$98$	3.26138			0.329449
$99$		0			0
$100$	−6.70883			−0.670883
$101$	1.87869	+	0.836447i	0.186937	+	0.0832296i	0.498071	−	0.867137i	$-0.334042\pi$
$101$	1.87869	+	0.836447i	0.186937	+	0.0832296i	−0.311134	+	0.950366i	$0.600709\pi$
$102$		0			0
$103$	−2.01858	−	2.24186i	−0.198896	−	0.220897i	0.635443	−	0.772148i	$-0.280817\pi$
$103$	−2.01858	−	2.24186i	−0.198896	−	0.220897i	−0.834340	+	0.551251i	$0.814151\pi$
$104$	−7.63662	+	3.40004i	−0.748832	+	0.333401i
$105$		0			0
$106$	1.36927	−	0.291048i	0.132995	−	0.0282690i
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	−0.954088	−	0.299527i	$-0.903171\pi$
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	0.595815	−	0.803121i	$-0.296829\pi$
$108$		0			0
$109$	5.20013			0.498082			0.249041	−	0.968493i	$-0.419885\pi$
$109$	5.20013			0.498082			0.249041	+	0.968493i	$0.419885\pi$
$110$	4.42228	+	3.68699i	0.421648	+	0.351540i
$111$		0			0
$112$	0.256586	+	2.44125i	0.0242451	+	0.230676i
$113$	18.8074	+	3.99763i	1.76925	+	0.376066i	0.973343	−	0.229354i	$-0.0736612\pi$
$113$	18.8074	+	3.99763i	1.76925	+	0.376066i	0.795907	+	0.605419i	$0.206995\pi$
$114$		0			0
$115$	0.0268512	−	0.255472i	0.00250389	−	0.0238229i
$116$	10.3788	+	7.54065i	0.963649	+	0.700132i
$117$		0			0
$118$	−0.409965	−	1.26174i	−0.0377403	−	0.116153i
$119$	−0.334192	−	0.148792i	−0.0306353	−	0.0136397i
$120$		0			0
$121$	1.97856	+	10.8206i	0.179869	+	0.983691i
$122$	−3.95432	+	6.84907i	−0.358007	+	0.620086i
$123$		0			0
$124$	−7.27874	+	8.08386i	−0.653650	+	0.725952i
$125$	0.903736	−	2.78141i	0.0808326	−	0.248777i
$126$		0			0
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	0.949949	−	0.312405i	$-0.101135\pi$
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	−0.00356461	+	0.999994i	$0.501135\pi$
$128$	−11.2730	+	2.39616i	−0.996405	+	0.211792i
$129$		0			0
$130$	0.716076	+	6.81300i	0.0628040	+	0.597540i
$131$	−8.98588	+	15.5640i	−0.785100	+	1.35983i	0.143839	+	0.989601i	$0.454055\pi$
$131$	−8.98588	+	15.5640i	−0.785100	+	1.35983i	−0.928939	+	0.370233i	$0.879278\pi$
$132$		0			0
$133$	3.70742	+	6.42144i	0.321474	+	0.556810i
$134$	5.45983	−	3.96680i	0.471657	−	0.342679i
$135$		0			0
$136$	0.205670	−	0.632986i	0.0176360	−	0.0542781i
$137$	−1.71445	+	16.3119i	−0.146475	+	1.39362i	0.636361	+	0.771391i	$0.280439\pi$
$137$	−1.71445	+	16.3119i	−0.146475	+	1.39362i	−0.782836	+	0.622228i	$0.786228\pi$
$138$		0			0
$139$	−7.96373	−	8.84461i	−0.675475	−	0.750190i	0.303798	−	0.952736i	$-0.401745\pi$
$139$	−7.96373	−	8.84461i	−0.675475	−	0.750190i	−0.979273	+	0.202546i	$0.935078\pi$
$140$	5.70096	+	1.21178i	0.481819	+	0.102414i
$141$		0			0
$142$	−2.51858	−	4.36231i	−0.211355	−	0.366077i
$143$	−7.28438	+	10.8735i	−0.609150	+	0.909287i
$144$		0			0
$145$	18.7154	−	13.5976i	1.55423	−	1.12922i
$146$	−1.13923	+	1.26525i	−0.0942837	+	0.104713i
$147$		0			0
$148$	9.50253	−	4.23080i	0.781103	−	0.347770i
$149$	4.13993	−	1.84321i	0.339156	−	0.151002i	−0.230090	−	0.973169i	$-0.573902\pi$
$149$	4.13993	−	1.84321i	0.339156	−	0.151002i	0.569246	+	0.822167i	$0.307235\pi$
$150$		0			0
$151$	−1.96113	+	2.17806i	−0.159595	+	0.177248i	−0.817639	−	0.575732i	$-0.804717\pi$
$151$	−1.96113	+	2.17806i	−0.159595	+	0.177248i	0.658044	+	0.752979i	$0.271384\pi$
$152$	−10.9140	+	7.92945i	−0.885239	+	0.643164i
$153$		0			0
$154$	−1.37927	−	1.75393i	−0.111144	−	0.141336i
$155$	9.80771	+	16.9874i	0.787774	+	1.36446i
$156$		0			0
$157$	17.6591	+	3.75356i	1.40935	+	0.299567i	0.848871	−	0.528600i	$-0.177283\pi$
$157$	17.6591	+	3.75356i	1.40935	+	0.299567i	0.560481	+	0.828167i	$0.310616\pi$
$158$	3.43607	+	3.81614i	0.273359	+	0.303596i
$159$		0			0
$160$	−1.71309	+	16.2989i	−0.135431	+	1.28854i
$161$	−0.0307625	+	0.0946773i	−0.00242443	+	0.00746161i
$162$		0			0
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	−0.387786	−	0.921749i	$-0.626760\pi$
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	0.756803	+	0.653643i	$0.226760\pi$
$164$	−4.83934	−	8.38199i	−0.377889	−	0.654523i
$165$		0			0
$166$	−1.43233	+	2.48087i	−0.111171	+	0.192553i
$167$	−0.524913	−	4.99422i	−0.0406190	−	0.386464i	−0.995879	−	0.0906956i	$-0.971091\pi$
$167$	−0.524913	−	4.99422i	−0.0406190	−	0.386464i	0.955260	−	0.295769i	$-0.0955757\pi$
$168$		0			0
$169$	−2.51606	+	0.534805i	−0.193543	+	0.0411388i
$170$	−0.441265	−	0.320598i	−0.0338435	−	0.0245887i
$171$		0			0
$172$	3.49313	−	10.7508i	0.266349	−	0.819738i
$173$	10.4317	−	11.5855i	0.793104	−	0.880831i	−0.202028	−	0.979380i	$-0.564753\pi$
$173$	10.4317	−	11.5855i	0.793104	−	0.880831i	0.995132	+	0.0985486i	$0.0314200\pi$
$174$		0			0
$175$	2.34412	−	4.06013i	0.177199	−	0.306917i
$176$	−5.01449	+	4.87315i	−0.377981	+	0.367327i
$177$		0			0
$178$	1.12361	+	0.500263i	0.0842181	+	0.0374963i
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	0.836060	−	0.548638i	$-0.184853\pi$
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	−0.998868	+	0.0475668i	$0.984853\pi$
$180$		0			0
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	0.510149	−	0.860086i	$-0.329590\pi$
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	−0.660345	+	0.750962i	$0.729590\pi$
$182$	0.277504	−	2.64028i	0.0205700	−	0.195710i
$183$		0			0
$184$	−0.177160	−	0.0376566i	−0.0130604	−	0.00277608i
$185$	−1.96063	−	18.6542i	−0.144148	−	1.37148i
$186$		0			0
$187$	−0.255289	−	1.01030i	−0.0186686	−	0.0738802i
$188$	−0.546051			−0.0398249
$189$		0			0
$190$	3.41633	+	10.5144i	0.247847	+	0.762795i
$191$	−11.5646	+	2.45814i	−0.836786	+	0.177864i	−0.606325	−	0.795217i	$-0.707357\pi$
$191$	−11.5646	+	2.45814i	−0.836786	+	0.177864i	−0.230461	+	0.973081i	$0.574024\pi$
$192$		0			0
$193$	6.16338	−	2.74411i	0.443650	−	0.197526i	−0.172739	−	0.984968i	$-0.555262\pi$
$193$	6.16338	−	2.74411i	0.443650	−	0.197526i	0.616389	+	0.787442i	$0.288595\pi$
$194$	0.0343481	+	0.0381474i	0.00246605	+	0.00273882i
$195$		0			0
$196$	8.59121	+	3.82505i	0.613658	+	0.273218i
$197$	20.6474			1.47107			0.735534	−	0.677488i	$-0.236931\pi$
$197$	20.6474			1.47107			0.735534	+	0.677488i	$0.236931\pi$
$198$		0			0
$199$	−13.2862			−0.941832			−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862			−0.941832			−0.470916	+	0.882178i	$0.656077\pi$
$200$	7.79224	+	3.46933i	0.550994	+	0.245318i
$201$		0			0
$202$	−0.795102	−	0.883050i	−0.0559432	−	0.0621312i
$203$	−8.18999	+	3.64642i	−0.574824	+	0.255928i
$204$		0			0
$205$	−17.0715	+	3.62867i	−1.19233	+	0.253437i
$206$	0.538646	+	1.65778i	0.0375292	+	0.115503i
$207$		0			0
$208$	−8.31958			−0.576859
$209$	−7.85035	+	19.6085i	−0.543020	+	1.35635i
$210$		0			0
$211$	0.872292	+	8.29930i	0.0600510	+	0.571348i	0.982635	+	0.185551i	$0.0594068\pi$
$211$	0.872292	+	8.29930i	0.0600510	+	0.571348i	−0.922584	+	0.385797i	$0.873926\pi$
$212$	3.94832	+	0.839242i	0.271172	+	0.0576394i
$213$		0			0
$214$	−0.724343	+	6.89166i	−0.0495150	+	0.471104i
$215$	−16.4908	−	11.9813i	−1.12467	−	0.817117i
$216$		0			0
$217$	−2.34904	−	7.22960i	−0.159463	−	0.490778i
$218$	−2.74493	−	1.22212i	−0.185910	−	0.0827724i
$219$		0			0
$220$	7.32508	+	14.8990i	0.493857	+	1.00449i
$221$	0.619925	−	1.07374i	0.0417007	−	0.0722277i
$222$		0			0
$223$	−0.256716	+	0.285112i	−0.0171910	+	0.0190925i	−0.751679	−	0.659529i	$-0.770756\pi$
$223$	−0.256716	+	0.285112i	−0.0171910	+	0.0190925i	0.734488	+	0.678622i	$0.237422\pi$
$224$	1.96263	−	6.04035i	0.131134	−	0.403588i
$225$		0			0
$226$	−8.98811	−	6.53024i	−0.597880	−	0.434385i
$227$	17.6204	−	3.74533i	1.16951	−	0.248586i	0.418084	−	0.908408i	$-0.362702\pi$
$227$	17.6204	−	3.74533i	1.16951	−	0.248586i	0.751422	+	0.659822i	$0.229368\pi$
$228$		0			0
$229$	−1.40359	−	13.3543i	−0.0927521	−	0.882478i	−0.937657	−	0.347561i	$-0.887010\pi$
$229$	−1.40359	−	13.3543i	−0.0927521	−	0.882478i	0.844905	−	0.534916i	$-0.179657\pi$
$230$	−0.0742139	+	0.128542i	−0.00489352	+	0.00847583i
$231$		0			0
$232$	−8.15540	−	14.1256i	−0.535428	−	0.927389i
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	−0.673490	−	0.739196i	$-0.735206\pi$
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	0.494897	+	0.868952i	$0.335206\pi$
$234$		0			0
$235$	−0.304276	+	0.936466i	−0.0198488	+	0.0610883i
$236$	0.399873	−	3.80454i	0.0260295	−	0.247654i
$237$		0			0
$238$	0.141437	+	0.157082i	0.00916800	+	0.0101821i
$239$	−22.6899	−	4.82289i	−1.46769	−	0.311967i	−0.596379	−	0.802703i	$-0.703394\pi$
$239$	−22.6899	−	4.82289i	−1.46769	−	0.311967i	−0.871308	+	0.490736i	$0.836728\pi$
$240$		0			0
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	0.511507	−	0.859279i	$-0.329087\pi$
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	−0.999911	+	0.0133389i	$0.995754\pi$
$242$	1.49863	−	6.17673i	0.0963358	−	0.397055i
$243$		0			0
$244$	−18.4494	+	13.4043i	−1.18110	+	0.858120i
$245$	11.3472	−	12.6023i	0.724944	−	0.805131i
$246$		0			0
$247$	−22.9581	+	10.2216i	−1.46079	+	0.650385i
$248$	12.6346	−	5.62528i	0.802297	−	0.357205i
$249$		0			0
$250$	−1.13072	+	1.25580i	−0.0715133	+	0.0794235i
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	−0.602554	−	0.798078i	$-0.705850\pi$
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	0.572818	+	0.819682i	$0.305850\pi$
$252$		0			0
$253$	−0.266163	+	0.0978289i	−0.0167335	+	0.00615045i
$254$	−3.80863	−	6.59673i	−0.238974	−	0.413916i
$255$		0			0
$256$	4.43092	+	0.941821i	0.276933	+	0.0588638i
$257$	7.34131	+	8.15335i	0.457939	+	0.508592i	0.927251	−	0.374440i	$-0.122165\pi$
$257$	7.34131	+	8.15335i	0.457939	+	0.508592i	−0.469313	+	0.883032i	$0.655498\pi$
$258$		0			0
$259$	−0.759813	+	7.22913i	−0.0472125	+	0.449197i
$260$	−6.10421	+	18.7868i	−0.378567	+	1.16511i
$261$		0			0
$262$	8.40108	−	6.10374i	0.519020	−	0.377090i
$263$	−7.19768	−	12.4668i	−0.443828	−	0.768733i	0.554142	−	0.832422i	$-0.313047\pi$
$263$	−7.19768	−	12.4668i	−0.443828	−	0.768733i	−0.997970	+	0.0636896i	$0.979713\pi$
$264$		0			0
$265$	3.63940	−	6.30363i	0.223567	−	0.387229i
$266$	−0.447840	−	4.26092i	−0.0274589	−	0.261254i
$267$		0			0
$268$	19.0348	−	4.04598i	1.16274	−	0.247147i
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	0.599780	−	0.800165i	$-0.295255\pi$
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	−0.575660	+	0.817689i	$0.695255\pi$
$270$		0			0
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	−0.503234	−	0.864150i	$-0.667857\pi$
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	0.915060	−	0.403318i	$-0.132143\pi$
$272$	0.443230	−	0.492257i	0.0268748	−	0.0298475i
$273$		0			0
$274$	4.73856	−	8.20743i	0.286267	−	0.495829i
$275$	13.2188	−	1.90039i	0.797122	−	0.114598i
$276$		0			0
$277$	2.62144	+	1.16714i	0.157507	+	0.0701267i	0.483976	−	0.875081i	$-0.339192\pi$
$277$	2.62144	+	1.16714i	0.157507	+	0.0701267i	−0.326469	+	0.945208i	$0.605859\pi$
$278$	2.12508	+	6.54031i	0.127454	+	0.392262i
$279$		0			0
$280$	−5.99497	−	4.35560i	−0.358268	−	0.260297i
$281$	1.90013	−	18.0785i	0.113352	−	1.07847i	−0.778967	−	0.627066i	$-0.784256\pi$
$281$	1.90013	−	18.0785i	0.113352	−	1.07847i	0.892318	−	0.451406i	$-0.149078\pi$
$282$		0			0
$283$	20.0883	+	4.26991i	1.19413	+	0.253820i	0.761749	−	0.647873i	$-0.224341\pi$
$283$	20.0883	+	4.26991i	1.19413	+	0.253820i	0.432378	+	0.901692i	$0.357674\pi$
$284$	−1.51825	−	14.4452i	−0.0900916	−	0.857164i
$285$		0			0
$286$	6.40057	−	4.02770i	0.378474	−	0.238163i
$287$	6.76362			0.399244
$288$		0			0
$289$	−5.22278	−	16.0741i	−0.307223	−	0.945534i
$290$	−13.0747	+	2.77912i	−0.767776	+	0.163196i
$291$		0			0
$292$	−4.48493	+	1.99682i	−0.262461	+	0.116855i
$293$	−0.575497	−	0.639154i	−0.0336209	−	0.0373398i	0.726100	−	0.687589i	$-0.241331\pi$
$293$	−0.575497	−	0.639154i	−0.0336209	−	0.0373398i	−0.759721	+	0.650250i	$0.774664\pi$
$294$		0			0
$295$	−6.30187	−	2.80578i	−0.366909	−	0.163359i
$296$	−13.2250			−0.768685
$297$		0			0
$298$	−2.61848			−0.151684
$299$	−0.308229	−	0.137232i	−0.0178253	−	0.00793635i
$300$		0			0
$301$	5.28575	+	5.87042i	0.304665	+	0.338365i
$302$	1.54708	−	0.688804i	0.0890244	−	0.0396362i
$303$		0			0
$304$	−13.1329	+	2.79148i	−0.753221	+	0.160102i
$305$	12.7075	+	39.1095i	0.727627	+	2.23941i
$306$		0			0
$307$	3.48920			0.199139			0.0995696	−	0.995031i	$-0.468253\pi$
$307$	3.48920			0.199139			0.0995696	+	0.995031i	$0.468253\pi$
$308$	−1.57624	−	6.23790i	−0.0898144	−	0.355437i
$309$		0			0
$310$	−1.18473	−	11.2719i	−0.0672880	−	0.640203i
$311$	10.6083	+	2.25486i	0.601542	+	0.127862i	0.498610	−	0.866827i	$-0.333844\pi$
$311$	10.6083	+	2.25486i	0.601542	+	0.127862i	0.102932	+	0.994688i	$0.467178\pi$
$312$		0			0
$313$	2.95618	−	28.1261i	0.167093	−	1.58978i	−0.514133	−	0.857710i	$-0.671886\pi$
$313$	2.95618	−	28.1261i	0.167093	−	1.58978i	0.681226	−	0.732073i	$-0.261447\pi$
$314$	−8.43935	−	6.13155i	−0.476260	−	0.346023i
$315$		0			0
$316$	4.57569	+	14.0825i	0.257403	+	0.792204i
$317$	1.01634	+	0.452505i	0.0570836	+	0.0254152i	0.435080	−	0.900392i	$-0.356720\pi$
$317$	1.01634	+	0.452505i	0.0570836	+	0.0254152i	−0.377996	+	0.925807i	$0.623387\pi$
$318$		0			0
$319$	−22.5860	−	11.9178i	−1.26457	−	0.667267i
$320$	−1.59933	+	2.77013i	−0.0894055	+	0.154855i
$321$		0			0
$322$	0.0384890	−	0.0427464i	0.00214491	−	0.00238216i
$323$	0.618308	−	1.90296i	0.0344036	−	0.105883i
$324$		0			0
$325$	12.8550	+	9.33967i	0.713065	+	0.518072i
$326$	−3.29134	+	0.699597i	−0.182291	+	0.0387471i
$327$		0			0
$328$	1.28628	+	12.2382i	0.0710230	+	0.675739i
$329$	0.190795	−	0.330466i	0.0105188	−	0.0182192i
$330$		0			0
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	0.984467	−	0.175569i	$-0.0561764\pi$
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	−0.644281	+	0.764789i	$0.722843\pi$
$332$	−6.68275	+	4.85530i	−0.366763	+	0.266469i
$333$		0			0
$334$	−0.896648	+	2.75960i	−0.0490624	+	0.150999i
$335$	3.66801	−	34.8988i	0.200405	−	1.90673i
$336$		0			0
$337$	9.01561	+	10.0128i	0.491112	+	0.545435i	0.936851	−	0.349728i	$-0.113726\pi$
$337$	9.01561	+	10.0128i	0.491112	+	0.545435i	−0.445740	+	0.895163i	$0.647059\pi$
$338$	1.45381	+	0.309017i	0.0790768	+	0.0168083i
$339$		0			0
$340$	−0.786384	−	1.36206i	−0.0426477	−	0.0738679i
$341$	12.0518	−	17.9899i	0.652642	−	0.974208i
$342$		0			0
$343$	−11.9104	+	8.65342i	−0.643102	+	0.467241i
$344$	−9.61676	+	10.6805i	−0.518501	+	0.575854i
$345$		0			0
$346$	−8.22923	+	3.66389i	−0.442406	+	0.196972i
$347$	−8.89717	+	3.96128i	−0.477625	+	0.212652i	−0.631406	−	0.775453i	$-0.717522\pi$
$347$	−8.89717	+	3.96128i	−0.477625	+	0.212652i	0.153781	+	0.988105i	$0.450855\pi$
$348$		0			0
$349$	−2.97107	+	3.29971i	−0.159038	+	0.176629i	−0.817397	−	0.576074i	$-0.804584\pi$
$349$	−2.97107	+	3.29971i	−0.159038	+	0.176629i	0.658360	+	0.752703i	$0.271251\pi$
$350$	−2.19156	+	1.59226i	−0.117144	+	0.0851100i
$351$		0			0
$352$	16.9810	−	6.24142i	0.905090	−	0.332669i
$353$	16.2618	+	28.1662i	0.865527	+	1.49914i	0.866523	+	0.499137i	$0.166349\pi$
$353$	16.2618	+	28.1662i	0.865527	+	1.49914i	−0.000996749		1.00000i	$0.500317\pi$
$354$		0			0
$355$	−25.6192	−	5.44553i	−1.35973	−	0.289019i
$356$	2.37312	+	2.63561i	0.125775	+	0.139687i
$357$		0			0
$358$	−0.425736	+	4.05061i	−0.0225008	+	0.214081i
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	−0.420660	−	0.907218i	$-0.638201\pi$
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	0.873571	−	0.486697i	$-0.161799\pi$
$360$		0			0
$361$	−17.4395	+	12.6705i	−0.917868	+	0.666870i
$362$	0.721600	+	1.24985i	0.0379264	+	0.0656905i
$363$		0			0
$364$	3.82761	−	6.62962i	0.200621	−	0.347487i
$365$	0.925362	+	8.80424i	0.0484357	+	0.460835i
$366$		0			0
$367$	−1.14658	+	0.243713i	−0.0598511	+	0.0127217i	−0.237740	−	0.971329i	$-0.576407\pi$
$367$	−1.14658	+	0.243713i	−0.0598511	+	0.0127217i	0.177889	+	0.984051i	$0.443073\pi$
$368$	−0.145831	−	0.105952i	−0.00760197	−	0.00552315i
$369$		0			0
$370$	−3.34912	+	10.3075i	−0.174112	+	0.535862i
$371$	−1.88748	+	2.09626i	−0.0979929	+	0.108832i
$372$		0			0
$373$	−10.8834	+	18.8506i	−0.563520	+	0.976046i	0.433665	+	0.901074i	$0.357220\pi$
$373$	−10.8834	+	18.8506i	−0.563520	+	0.976046i	−0.997186	+	0.0749719i	$0.976113\pi$
$374$	−0.102681	+	0.593290i	−0.00530951	+	0.0306783i
$375$		0			0
$376$	0.634233	+	0.282379i	0.0327081	+	0.0145626i
$377$	−9.38942	−	28.8977i	−0.483580	−	1.48831i
$378$		0			0
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	0.871749	−	0.489953i	$-0.162986\pi$
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	−0.196588	+	0.980486i	$0.562986\pi$
$380$	−3.33224	+	31.7041i	−0.170940	+	1.62639i
$381$		0			0
$382$	6.68218	+	1.42034i	0.341890	+	0.0726709i
$383$	0.647381	+	6.15942i	0.0330796	+	0.314732i	0.998533	+	0.0541542i	$0.0172463\pi$
$383$	0.647381	+	6.15942i	0.0330796	+	0.314732i	−0.965453	+	0.260577i	$0.916087\pi$
$384$		0			0
$385$	−11.5762	−	0.772734i	−0.589977	−	0.0393821i
$386$	−3.89830			−0.198418
$387$		0			0
$388$	0.0457401	+	0.140773i	0.00232210	+	0.00714669i
$389$	−0.707409	+	0.150365i	−0.0358671	+	0.00762378i	−0.225810	−	0.974171i	$-0.572503\pi$
$389$	−0.707409	+	0.150365i	−0.0358671	+	0.00762378i	0.189943	+	0.981795i	$0.439170\pi$
$390$		0			0
$391$	0.0245409	−	0.0109263i	0.00124109	−	0.000552567i
$392$	−8.00056	−	8.88552i	−0.404089	−	0.448787i
$393$		0			0
$394$	−10.8989	−	4.85250i	−0.549079	−	0.244466i
$395$	26.7009			1.34347
$396$		0			0
$397$	4.08994			0.205268			0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994			0.205268			0.102634	+	0.994719i	$0.467273\pi$
$398$	7.01321	+	3.12248i	0.351540	+	0.156516i
$399$		0			0
$400$	5.68033	+	6.30864i	0.284016	+	0.315432i
$401$	5.15812	−	2.29654i	0.257584	−	0.114684i	−0.273882	−	0.961763i	$-0.588308\pi$
$401$	5.15812	−	2.29654i	0.257584	−	0.114684i	0.531466	+	0.847079i	$0.321641\pi$
$402$		0			0
$403$	25.2009	−	5.35662i	1.25535	−	0.266832i
$404$	−1.05881	−	3.25868i	−0.0526777	−	0.162125i
$405$		0			0
$406$	5.18012			0.257085
$407$	−17.5249	+	11.0279i	−0.868677	+	0.546634i
$408$		0			0
$409$	−0.987666	−	9.39701i	−0.0488369	−	0.464652i	−0.991423	−	0.130690i	$-0.958281\pi$
$409$	−0.987666	−	9.39701i	−0.0488369	−	0.464652i	0.942586	−	0.333962i	$-0.108386\pi$
$410$	9.86414	+	2.09669i	0.487155	+	0.103548i
$411$		0			0
$412$	−0.525386	+	4.99871i	−0.0258839	+	0.246269i
$413$	2.16276	+	1.57134i	0.106422	+	0.0773204i
$414$		0			0
$415$	4.60290	+	14.1663i	0.225948	+	0.695395i
$416$	19.6648	+	8.75533i	0.964145	+	0.429265i
$417$		0			0
$418$	8.75220	−	8.50551i	0.428084	−	0.416018i
$419$	0.0757820	−	0.131258i	0.00370219	−	0.00641238i	−0.864168	−	0.503203i	$-0.832155\pi$
$419$	0.0757820	−	0.131258i	0.00370219	−	0.00641238i	0.867871	+	0.496790i	$0.165488\pi$
$420$		0			0
$421$	11.3595	−	12.6160i	0.553630	−	0.614868i	−0.399756	−	0.916622i	$-0.630905\pi$
$421$	11.3595	−	12.6160i	0.553630	−	0.614868i	0.953386	+	0.301753i	$0.0975719\pi$
$422$	1.49003	−	4.58585i	0.0725337	−	0.223236i
$423$		0			0
$424$	−4.15194	−	3.01656i	−0.201636	−	0.146497i
$425$	−1.23747	+	0.263032i	−0.0600261	+	0.0127589i
$426$		0			0
$427$	−1.66580	−	15.8490i	−0.0806135	−	0.766986i
$428$	−9.99085	+	17.3047i	−0.482926	+	0.836453i
$429$		0			0
$430$	5.88900	+	10.2000i	0.283993	+	0.491890i
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.959618	−	0.281307i	$-0.909232\pi$
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.0289998	+	0.999579i	$0.509232\pi$
$432$		0			0
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	−0.749999	−	0.661439i	$-0.769946\pi$
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	0.995546	−	0.0942769i	$-0.0300539\pi$
$434$	−0.459123	+	4.36827i	−0.0220386	+	0.209684i
$435$		0			0
$436$	−5.79742	−	6.43868i	−0.277646	−	0.308357i
$437$	−0.532600	−	0.113208i	−0.0254777	−	0.00541545i
$438$		0			0
$439$	19.6207	+	33.9840i	0.936443	+	1.62197i	0.772040	+	0.635574i	$0.219237\pi$
$439$	19.6207	+	33.9840i	0.936443	+	1.62197i	0.164403	+	0.986393i	$0.447430\pi$
$440$	−0.803326	−	21.0930i	−0.0382971	−	1.00557i
$441$		0			0
$442$	−0.579580	+	0.421089i	−0.0275678	+	0.0200292i
$443$	−21.5389	+	23.9214i	−1.02334	+	1.13654i	−0.0327827	+	0.999463i	$0.510437\pi$
$443$	−21.5389	+	23.9214i	−1.02334	+	1.13654i	−0.990561	+	0.137075i	$0.956230\pi$
$444$		0			0
$445$	5.84239	−	2.60120i	0.276956	−	0.123309i
$446$	0.202515	−	0.0901657i	0.00958939	−	0.00426947i
$447$		0			0
$448$	0.829451	−	0.921199i	0.0391879	−	0.0435226i
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.959203	−	0.282719i	$-0.908764\pi$
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.0275281	+	0.999621i	$0.508764\pi$
$450$		0			0
$451$	11.9096	+	15.1447i	0.560799	+	0.713134i
$452$	−16.0178	−	27.7437i	−0.753415	−	1.30495i
$453$		0			0
$454$	−10.1813	−	2.16410i	−0.477831	−	0.101566i
$455$	−9.23679	−	10.2585i	−0.433027	−	0.480926i
$456$		0			0
$457$	1.32921	−	12.6466i	0.0621780	−	0.591584i	−0.918427	−	0.395590i	$-0.870540\pi$
$457$	1.32921	−	12.6466i	0.0621780	−	0.591584i	0.980605	−	0.195994i	$-0.0627932\pi$
$458$	−2.39760	+	7.37904i	−0.112032	+	0.344800i
$459$		0			0
$460$	−0.346255	+	0.251569i	−0.0161442	+	0.0117295i
$461$	−9.51087	−	16.4733i	−0.442965	−	0.767238i	0.554943	−	0.831889i	$-0.312740\pi$
$461$	−9.51087	−	16.4733i	−0.442965	−	0.767238i	−0.997908	+	0.0646502i	$0.979407\pi$
$462$		0			0
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	−0.467977	−	0.883741i	$-0.655017\pi$
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	0.999330	−	0.0365903i	$-0.0116497\pi$
$464$	−1.69684	−	16.1443i	−0.0787738	−	0.749482i
$465$		0			0
$466$	1.90448	−	0.404810i	0.0882233	−	0.0187524i
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	0.844493	−	0.535567i	$-0.179902\pi$
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	−0.248392	+	0.968660i	$0.579902\pi$
$468$		0			0
$469$	−4.20232	+	12.9334i	−0.194045	+	0.597210i
$470$	0.380700	−	0.422810i	0.0175604	−	0.0195028i
$471$		0			0
$472$	−2.43188	+	4.21215i	−0.111936	+	0.193880i
$473$	−3.83737	+	22.1723i	−0.176443	+	1.01948i
$474$		0			0
$475$	23.4259	+	10.4299i	1.07486	+	0.478556i
$476$	0.188347	+	0.579671i	0.00863285	+	0.0265692i
$477$		0			0
$478$	10.8436	+	7.87832i	0.495973	+	0.360346i
$479$	−1.71322	+	16.3002i	−0.0782789	+	0.744774i	0.883033	+	0.469311i	$0.155498\pi$
$479$	−1.71322	+	16.3002i	−0.0782789	+	0.744774i	−0.961312	+	0.275463i	$0.911169\pi$
$480$		0			0
$481$	−24.0979	−	5.12217i	−1.09877	−	0.233551i
$482$	0.915880	+	8.71402i	0.0417172	+	0.396913i
$483$		0			0
$484$	11.1920	−	14.5133i	0.508728	−	0.659694i
$485$	0.266911			0.0121198
$486$		0			0
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	0.974044	+	0.226361i	$0.0726828\pi$
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	−0.654966	+	0.755658i	$0.727317\pi$
$488$	28.3605	−	6.02821i	1.28382	−	0.272884i
$489$		0			0
$490$	−8.95145	+	3.98544i	−0.404385	+	0.180044i
$491$	29.2029	+	32.4331i	1.31791	+	1.46368i	0.788071	+	0.615584i	$0.211080\pi$
$491$	29.2029	+	32.4331i	1.31791	+	1.46368i	0.529836	+	0.848100i	$0.322253\pi$
$492$		0			0
$493$	2.21006	+	0.983982i	0.0995360	+	0.0443163i
$494$	14.5209			0.653324
$495$		0			0
$496$	13.7645			0.618045
$497$	9.27261	+	4.12843i	0.415933	+	0.185185i
$498$		0			0
$499$	−13.4519	−	14.9398i	−0.602189	−	0.668798i	0.362563	−	0.931959i	$-0.381902\pi$
$499$	−13.4519	−	14.9398i	−0.602189	−	0.668798i	−0.964752	+	0.263161i	$0.915235\pi$
$500$	−4.45142	+	1.98190i	−0.199074	+	0.0886333i
$501$		0			0
$502$	0.329111	−	0.0699546i	0.0146889	−	0.00312223i
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	0.997159	−	0.0753254i	$-0.0239995\pi$
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	−0.850994	+	0.525176i	$0.824000\pi$
$504$		0			0
$505$	−6.17856			−0.274942
$506$	0.163487	+	0.0109131i	0.00726791	+	0.000485148i
$507$		0			0
$508$	−2.29592	−	21.8442i	−0.101865	−	0.969179i
$509$	−43.4966	−	9.24549i	−1.92795	−	0.409799i	−0.999239	−	0.0390051i	$-0.987581\pi$
$509$	−43.4966	−	9.24549i	−1.92795	−	0.409799i	−0.928715	−	0.370794i	$-0.879086\pi$
$510$		0			0
$511$	0.358610	−	3.41195i	0.0158640	−	0.150936i
$512$	16.5301	+	12.0098i	0.730534	+	0.530764i
$513$		0			0
$514$	−1.95899	−	6.02915i	−0.0864073	−	0.265934i
$515$	8.27992	+	3.68646i	0.364857	+	0.162445i
$516$		0			0
$517$	1.07591	−	0.154679i	0.0473187	−	0.00680275i
$518$	2.10004	−	3.63738i	0.0922707	−	0.159817i
$519$		0			0
$520$	16.8052	−	18.6641i	0.736956	−	0.818473i
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	0.768315	+	0.640071i	$0.221095\pi$
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	−0.997805	+	0.0662243i	$0.978905\pi$
$522$		0			0
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.0931472	−	0.995652i	$-0.529693\pi$
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.975706	+	0.219085i	$0.929693\pi$
$524$	29.2890	−	6.22557i	1.27950	−	0.271965i
$525$		0			0
$526$	0.869448	+	8.27225i	0.0379098	+	0.360687i
$527$	−1.02565	+	1.77648i	−0.0446780	+	0.0773845i
$528$		0			0
$529$	11.4963	+	19.9123i	0.499841	+	0.865750i
$530$	−3.40255	+	2.47210i	−0.147797	+	0.107381i
$531$		0			0
$532$	3.81763	−	11.7495i	0.165515	−	0.509404i
$533$	−2.39617	+	22.7980i	−0.103790	+	0.987491i
$534$		0			0
$535$	24.1099	+	26.7768i	1.04236	+	1.15766i
$536$	−24.2010	−	5.14409i	−1.04533	−	0.222191i
$537$		0			0
$538$	−0.141268	−	0.244683i	−0.00609050	−	0.0105491i
$539$	−18.0112	−	5.10310i	−0.775799	−	0.219806i
$540$		0			0
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	−0.774216	−	0.632922i	$-0.781855\pi$
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	0.362699	+	0.931906i	$0.381855\pi$
$542$	−8.48229	+	9.42053i	−0.364345	+	0.404647i
$543$		0			0
$544$	−1.56569	+	0.697091i	−0.0671285	+	0.0298875i
$545$	−14.2727	+	6.35461i	−0.611375	+	0.272202i
$546$		0			0
$547$	1.70348	−	1.89190i	0.0728355	−	0.0808920i	−0.705626	−	0.708585i	$-0.749334\pi$
$547$	1.70348	−	1.89190i	0.0728355	−	0.0808920i	0.778461	+	0.627693i	$0.216001\pi$
$548$	22.1084	−	16.0627i	0.944424	−	0.686164i
$549$		0			0
$550$	−7.42425	−	2.10350i	−0.316571	−	0.0896937i
$551$	−24.5177	−	42.4659i	−1.04449	−	1.80911i
$552$		0			0
$553$	−10.1214	−	2.15137i	−0.430407	−	0.0914857i
$554$	−1.10945	−	1.23217i	−0.0471360	−	0.0523498i
$555$		0			0
$556$	−2.07276	+	19.7210i	−0.0879048	+	0.836358i
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	−0.994204	−	0.107507i	$-0.965713\pi$
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	0.867519	+	0.497404i	$0.165713\pi$
$558$		0			0
$559$	−21.6599	+	15.7368i	−0.916117	+	0.665598i
$560$	−3.68748	−	6.38690i	−0.155824	−	0.269896i
$561$		0			0
$562$	−5.25175	+	9.09630i	−0.221532	+	0.383704i
$563$	−2.50735	−	23.8558i	−0.105672	−	1.00540i	−0.910953	−	0.412510i	$-0.864652\pi$
$563$	−2.50735	−	23.8558i	−0.105672	−	1.00540i	0.805281	−	0.592893i	$-0.202014\pi$
$564$		0			0
$565$	−56.5054	+	12.0106i	−2.37720	+	0.505290i
$566$	−9.60027	−	6.97501i	−0.403530	−	0.293181i
$567$		0			0
$568$	−5.70659	+	17.5631i	−0.239443	+	0.736930i
$569$	25.1721	−	27.9565i	1.05527	−	1.17200i	0.0706111	−	0.997504i	$-0.477505\pi$
$569$	25.1721	−	27.9565i	1.05527	−	1.17200i	0.984659	−	0.174492i	$-0.0558283\pi$
$570$		0			0
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	−0.669351	−	0.742946i	$-0.733428\pi$
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	0.978086	+	0.208202i	$0.0667612\pi$
$572$	21.5844	−	3.10307i	0.902488	−	0.129746i
$573$		0			0
$574$	−3.57023	−	1.58957i	−0.149018	−	0.0663473i
$575$	0.106386	+	0.327424i	0.00443662	+	0.0136545i
$576$		0			0
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	0.896226	−	0.443598i	$-0.146298\pi$
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	−0.144937	+	0.989441i	$0.546298\pi$
$578$	−1.02080	+	9.71227i	−0.0424597	+	0.403977i
$579$		0			0
$580$	−37.7013	−	8.01366i	−1.56546	−	0.332749i
$581$	−0.603385	−	5.74083i	−0.0250326	−	0.238170i
$582$		0			0
$583$	−8.01732	−	0.535173i	−0.332044	−	0.0221646i
$584$	6.24181			0.258288
$585$		0			0
$586$	0.153568	+	0.472634i	0.00634384	+	0.0195243i
$587$	−2.44553	+	0.519814i	−0.100938	+	0.0214550i	−0.258104	−	0.966117i	$-0.583098\pi$
$587$	−2.44553	+	0.519814i	−0.100938	+	0.0214550i	0.157166	+	0.987572i	$0.449764\pi$
$588$		0			0
$589$	37.9836	−	16.9114i	1.56508	−	0.696821i
$590$	2.66709	+	2.96210i	0.109802	+	0.121948i
$591$		0			0
$592$	−12.0242	−	5.35351i	−0.494190	−	0.220028i
$593$	10.8953			0.447417			0.223708	−	0.974656i	$-0.428184\pi$
$593$	10.8953			0.447417			0.223708	+	0.974656i	$0.428184\pi$
$594$		0			0
$595$	1.09907			0.0450577
$596$	−6.89767	−	3.07104i	−0.282540	−	0.125795i
$597$		0			0
$598$	0.130449	+	0.144878i	0.00533445	+	0.00592451i
$599$	33.6533	−	14.9834i	1.37504	−	0.612205i	0.419682	−	0.907671i	$-0.362142\pi$
$599$	33.6533	−	14.9834i	1.37504	−	0.612205i	0.955353	+	0.295466i	$0.0954749\pi$
$600$		0			0
$601$	15.1166	−	3.21313i	0.616618	−	0.131066i	0.110995	−	0.993821i	$-0.464596\pi$
$601$	15.1166	−	3.21313i	0.616618	−	0.131066i	0.505623	+	0.862755i	$0.331263\pi$
$602$	−1.41047	−	4.34099i	−0.0574866	−	0.176925i
$603$		0			0
$604$	4.88321			0.198695
$605$	−18.6534	−	27.2813i	−0.758368	−	1.10914i
$606$		0			0
$607$	2.66306	+	25.3373i	0.108090	+	1.02841i	0.905319	+	0.424733i	$0.139632\pi$
$607$	2.66306	+	25.3373i	0.108090	+	1.02841i	−0.797228	+	0.603678i	$0.793701\pi$
$608$	33.9795	+	7.22257i	1.37805	+	0.292914i
$609$		0			0
$610$	2.48369	−	23.6307i	0.100562	−	0.956781i
$611$	1.04630	+	0.760183i	0.0423289	+	0.0307537i
$612$		0			0
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	−0.850672	−	0.525697i	$-0.823805\pi$
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	0.379211	−	0.925310i	$-0.376195\pi$
$614$	−1.84180	−	0.820023i	−0.0743290	−	0.0330934i
$615$		0			0
$616$	−1.39501	+	8.06037i	−0.0562066	+	0.324761i
$617$	20.9464	−	36.2802i	0.843271	−	1.46059i	−0.0438437	−	0.999038i	$-0.513960\pi$
$617$	20.9464	−	36.2802i	0.843271	−	1.46059i	0.887115	−	0.461549i	$-0.152706\pi$
$618$		0			0
$619$	−4.00783	+	4.45115i	−0.161088	+	0.178907i	−0.818286	−	0.574812i	$-0.805075\pi$
$619$	−4.00783	+	4.45115i	−0.161088	+	0.178907i	0.657197	+	0.753719i	$0.271742\pi$
$620$	10.0993	−	31.0823i	0.405596	−	1.24830i
$621$		0			0
$622$	−5.06974	−	3.68338i	−0.203278	−	0.147690i
$623$	−2.42424	+	0.515288i	−0.0971251	+	0.0206446i
$624$		0			0
$625$	3.02291	+	28.7611i	0.120917	+	1.15044i
$626$	−8.17057	+	14.1518i	−0.326562	+	0.565621i
$627$		0			0
$628$	−15.0399	−	26.0498i	−0.600157	−	1.03950i
$629$	1.58690	−	1.15295i	0.0632739	−	0.0459712i
$630$		0			0
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	0.727332	+	0.686286i	$0.240760\pi$
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	−0.991813	+	0.127702i	$0.959240\pi$
$632$	1.96786	−	18.7229i	0.0782772	−	0.744758i
$633$		0			0
$634$	−0.430138	−	0.477717i	−0.0170830	−	0.0189726i
$635$	−38.7416	−	8.23479i	−1.53741	−	0.326788i
$636$		0			0
$637$	−11.1368	−	19.2895i	−0.441256	−	0.764278i
$638$	9.12129	+	11.5990i	0.361115	+	0.459208i
$639$		0			0
$640$	28.0127	−	20.3525i	1.10730	−	0.804501i
$641$	−8.58963	+	9.53975i	−0.339270	+	0.376798i	−0.888502	−	0.458872i	$-0.848254\pi$
$641$	−8.58963	+	9.53975i	−0.339270	+	0.376798i	0.549232	+	0.835670i	$0.314920\pi$
$642$		0			0
$643$	25.9041	−	11.5332i	1.02156	−	0.454827i	0.173558	−	0.984824i	$-0.444473\pi$
$643$	25.9041	−	11.5332i	1.02156	−	0.454827i	0.848000	+	0.529997i	$0.177807\pi$
$644$	0.151523	−	0.0674625i	0.00597085	−	0.00265839i
$645$		0			0
$646$	−0.773607	+	0.859177i	−0.0304372	+	0.0338039i
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	−0.830153	−	0.557536i	$-0.811747\pi$
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	0.273717	+	0.961810i	$0.411747\pi$
$648$		0			0
$649$	0.289810	+	7.60956i	0.0113760	+	0.298701i
$650$	−4.59060	−	7.95116i	−0.180058	−	0.311870i
$651$		0			0
$652$	−9.49066	−	2.01730i	−0.371683	−	0.0790036i
$653$	19.6070	+	21.7758i	0.767282	+	0.852152i	0.992511	−	0.122153i	$-0.0389799\pi$
$653$	19.6070	+	21.7758i	0.767282	+	0.852152i	−0.225230	+	0.974306i	$0.572313\pi$
$654$		0			0
$655$	5.64400	−	53.6991i	0.220529	−	2.09820i
$656$	−3.78455	+	11.6477i	−0.147762	+	0.454764i
$657$		0			0
$658$	−0.178378	+	0.129599i	−0.00695388	+	0.00505229i
$659$	13.7935	+	23.8911i	0.537319	+	0.930664i	0.999047	+	0.0436422i	$0.0138961\pi$
$659$	13.7935	+	23.8911i	0.537319	+	0.930664i	−0.461728	+	0.887021i	$0.652771\pi$
$660$		0			0
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	0.416960	+	0.908925i	$0.363096\pi$
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	−0.995632	+	0.0933649i	$0.970238\pi$
$662$	−0.747623	−	7.11315i	−0.0290572	−	0.276461i
$663$		0			0
$664$	10.2728	−	2.18354i	0.398660	−	0.0847378i
$665$	−18.0228	−	13.0943i	−0.698893	−	0.507775i
$666$		0			0
$667$	0.203437	−	0.626115i	0.00787711	−	0.0242433i
$668$	−5.59853	+	6.21779i	−0.216613	+	0.240574i
$669$		0			0
$670$	−10.1380	+	17.5596i	−0.391666	+	0.678385i
$671$	32.5548	−	31.6373i	1.25677	−	1.22134i
$672$		0			0
$673$	8.81907	+	3.92650i	0.339950	+	0.151356i	0.569609	−	0.821916i	$-0.307094\pi$
$673$	8.81907	+	3.92650i	0.339950	+	0.151356i	−0.229659	+	0.973271i	$0.573761\pi$
$674$	−2.40577	−	7.40418i	−0.0926666	−	0.285198i
$675$		0			0
$676$	3.46724	+	2.51910i	0.133355	+	0.0968883i
$677$	−0.0102558	+	0.0975777i	−0.000394163	+	0.00375021i	−0.994717	−	0.102653i	$-0.967267\pi$
$677$	−0.0102558	+	0.0975777i	−0.000394163	+	0.00375021i	0.994323	+	0.106403i	$0.0339335\pi$
$678$		0			0
$679$	−0.101177	−	0.0215058i	−0.00388281	−	0.000825318i
$680$	0.209018	+	1.98868i	0.00801549	+	0.0762623i
$681$		0			0
$682$	−10.5896	+	6.66372i	−0.405496	+	0.255167i
$683$	−30.5246			−1.16799			−0.583996	−	0.811756i	$-0.698512\pi$
$683$	−30.5246			−1.16799			−0.583996	+	0.811756i	$0.698512\pi$
$684$		0			0
$685$	−15.2277	−	46.8660i	−0.581820	−	1.79066i
$686$	8.32071	−	1.76862i	0.317686	−	0.0675263i
$687$		0			0
$688$	−13.0671	+	5.81784i	−0.498178	+	0.221803i
$689$	−6.39713	−	7.10473i	−0.243711	−	0.270669i
$690$		0			0
$691$	29.9658	+	13.3416i	1.13995	+	0.507540i	0.887838	−	0.460157i	$-0.152207\pi$
$691$	29.9658	+	13.3416i	1.13995	+	0.507540i	0.252116	+	0.967697i	$0.418873\pi$
$692$	−25.9748			−0.987413
$693$		0			0
$694$	5.62741			0.213614
$695$	32.6661	+	14.5439i	1.23910	+	0.551681i
$696$		0			0
$697$	−1.22127	−	1.35635i	−0.0462588	−	0.0513756i
$698$	2.34379	−	1.04352i	0.0887138	−	0.0394979i
$699$		0			0
$700$	−7.64053	+	1.62405i	−0.288785	+	0.0613831i
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	0.989043	−	0.147630i	$-0.0471646\pi$
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	−0.886927	+	0.461909i	$0.847165\pi$
$702$		0			0
$703$	−39.7584			−1.49952
$704$	3.52321	+	0.235181i	0.132786	+	0.00886373i
$705$		0			0
$706$	−1.96435	−	18.6895i	−0.0739293	−	0.703390i
$707$	2.34208	+	0.497825i	0.0880831	+	0.0187226i
$708$		0			0
$709$	−2.79884	+	26.6292i	−0.105113	+	1.00008i	0.807114	+	0.590395i	$0.201028\pi$
$709$	−2.79884	+	26.6292i	−0.105113	+	1.00008i	−0.912227	+	0.409685i	$0.865639\pi$
$710$	12.2435	+	8.89542i	0.459490	+	0.333839i
$711$		0			0
$712$	−1.39340	−	4.28845i	−0.0522199	−	0.160716i
$713$	0.509956	+	0.227047i	0.0190980	+	0.00850298i
$714$		0			0
$715$	6.70577	−	38.7459i	0.250781	−	1.44901i
$716$	−5.87217	+	10.1709i	−0.219453	+	0.380105i
$717$		0			0
$718$	−10.7368	+	11.9244i	−0.400694	+	0.445016i
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	−0.826612	−	0.562772i	$-0.809735\pi$
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	0.999532	+	0.0305782i	$0.00973486\pi$
$720$		0			0
$721$	−2.84161	−	2.06455i	−0.105827	−	0.0768879i
$722$	12.1834	−	2.58965i	0.453418	−	0.0963769i
$723$		0			0
$724$	0.434995	+	4.13870i	0.0161665	+	0.153814i
$725$	−15.5020	+	26.8502i	−0.575730	+	0.997193i
$726$		0			0
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	−0.999925	−	0.0122391i	$-0.996104\pi$
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	0.489363	−	0.872080i	$-0.337229\pi$
$728$	−7.87410	+	5.72087i	−0.291834	+	0.212029i
$729$		0			0
$730$	1.58069	−	4.86486i	0.0585039	−	0.180057i
$731$	0.222818	−	2.11997i	0.00824123	−	0.0784101i
$732$		0			0
$733$	31.9441	+	35.4775i	1.17988	+	1.31039i	0.940630	+	0.339433i	$0.110235\pi$
$733$	31.9441	+	35.4775i	1.17988	+	1.31039i	0.239251	+	0.970958i	$0.423098\pi$
$734$	0.662509	+	0.140821i	0.0244536	+	0.00519778i
$735$		0			0
$736$	0.233195	+	0.403906i	0.00859570	+	0.0148882i
$737$	−36.3593	+	13.3640i	−1.33931	+	0.492267i
$738$		0			0
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	−0.609714	−	0.792622i	$-0.708716\pi$
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	0.565416	+	0.824806i	$0.308716\pi$
$740$	−20.9113	+	23.2244i	−0.768716	+	0.853746i
$741$		0			0
$742$	1.48898	−	0.662935i	0.0546620	−	0.0243371i
$743$	16.5901	−	7.38641i	0.608633	−	0.270981i	−0.0791896	−	0.996860i	$-0.525233\pi$
$743$	16.5901	−	7.38641i	0.608633	−	0.270981i	0.687823	+	0.725879i	$0.258567\pi$
$744$		0			0
$745$	−9.11035	+	10.1181i	−0.333778	+	0.370698i
$746$	10.1751	−	7.39264i	0.372537	−	0.270664i
$747$		0			0
$748$	−0.966316	+	1.44243i	−0.0353320	+	0.0527406i
$749$	−6.98177	−	12.0928i	−0.255108	−	0.441860i
$750$		0			0
$751$	4.29862	+	0.913700i	0.156859	+	0.0333414i	0.285672	−	0.958328i	$-0.407783\pi$
$751$	4.29862	+	0.913700i	0.156859	+	0.0333414i	−0.128813	+	0.991669i	$0.541117\pi$
$752$	0.462338	+	0.513479i	0.0168597	+	0.0187246i
$753$		0			0
$754$	−1.83518	+	17.4605i	−0.0668332	+	0.635875i
$755$	2.72107	−	8.37459i	0.0990299	−	0.304783i
$756$		0			0
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	−0.366708	−	0.930336i	$-0.619515\pi$
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	0.771483	+	0.636249i	$0.219515\pi$
$758$	−4.69382	−	8.12993i	−0.170487	−	0.295292i
$759$		0			0
$760$	20.2655	−	35.1008i	0.735105	−	1.27324i
$761$	−3.25147	−	30.9357i	−0.117866	−	1.12142i	−0.880321	−	0.474378i	$-0.842673\pi$
$761$	−3.25147	−	30.9357i	−0.117866	−	1.12142i	0.762456	−	0.647041i	$-0.223994\pi$
$762$		0			0
$763$	5.92230	−	1.25882i	0.214402	−	0.0455725i
$764$	15.9365	+	11.5786i	0.576564	+	0.418898i
$765$		0			0
$766$	1.10585	−	3.40344i	0.0399558	−	0.122971i
$767$	−6.06268	+	6.73329i	−0.218911	+	0.243125i
$768$		0			0
$769$	−10.9677	+	18.9966i	−0.395504	+	0.685034i	−0.993165	−	0.116715i	$-0.962764\pi$
$769$	−10.9677	+	18.9966i	−0.395504	+	0.685034i	0.597661	+	0.801749i	$0.296097\pi$
$770$	5.92897	+	3.12850i	0.213665	+	0.112743i
$771$		0			0
$772$	−10.2690	−	4.57206i	−0.369590	−	0.164552i
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	0.996522	−	0.0833281i	$-0.0265549\pi$
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	−0.855182	+	0.518327i	$0.826555\pi$
$774$		0			0
$775$	−21.2682	−	15.4522i	−0.763976	−	0.555061i
$776$	0.0196714	−	0.187160i	0.000706160	−	0.00671867i
$777$		0			0
$778$	0.408750	+	0.0868824i	0.0146544	+	0.00311489i
$779$	3.86697	+	36.7918i	0.138549	+	1.31820i
$780$		0			0
$781$	7.08334	+	28.0321i	0.253462	+	1.00307i
$782$	−0.0155220			−0.000555064
$783$		0			0
$784$	−3.67724	−	11.3174i	−0.131330	−	0.404193i
$785$	−53.0556	+	11.2773i	−1.89363	+	0.402504i
$786$		0			0
$787$	−15.7693	+	7.02095i	−0.562115	+	0.250270i	−0.668067	−	0.744102i	$-0.732878\pi$
$787$	−15.7693	+	7.02095i	−0.562115	+	0.250270i	0.105951	+	0.994371i	$0.466211\pi$
$788$	−23.0190	−	25.5652i	−0.820018	−	0.910722i
$789$		0			0
$790$	−14.0943	−	6.27518i	−0.501452	−	0.223261i
$791$	22.3870			0.795991
$792$		0			0
$793$	54.0120			1.91802
$794$	−2.15890	−	0.961206i	−0.0766166	−	0.0341119i
$795$		0			0
$796$	14.8122	+	16.4507i	0.525006	+	0.583078i
$797$	−32.1582	+	14.3177i	−1.13910	+	0.507161i	−0.887563	−	0.460687i	$-0.847603\pi$
$797$	−32.1582	+	14.3177i	−1.13910	+	0.507161i	−0.251538	+	0.967847i	$0.580936\pi$
$798$		0			0
$799$	−0.100721	+	0.0214090i	−0.00356326	+	0.000757395i
$800$	−6.78739	−	20.8894i	−0.239970	−	0.738553i
$801$		0			0
$802$	−3.26248			−0.115202
$803$	8.27126	−	5.20487i	0.291887	−	0.183676i
$804$		0			0
$805$	−0.0312634	−	0.297451i	−0.00110189	−	0.0104838i
$806$	−14.5614	−	3.09512i	−0.512903	−	0.109021i
$807$		0			0
$808$	−0.455360	+	4.33246i	−0.0160195	+	0.152415i
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	0.282371	−	0.959305i	$-0.408879\pi$
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	−0.825096	+	0.564992i	$0.808879\pi$
$810$		0			0
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	−0.965718	−	0.259593i	$-0.916412\pi$
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	0.628698	−	0.777650i	$-0.283588\pi$
$812$	13.6456	+	6.07542i	0.478867	+	0.213205i
$813$		0			0
$814$	11.8424	−	1.70252i	0.415076	−	0.0596733i
$815$	−8.74810	+	15.1522i	−0.306433	+	0.530757i
$816$		0			0
$817$	−28.9110	+	32.1090i	−1.01147	+	1.12335i
$818$	−1.68711	+	5.19240i	−0.0589885	+	0.181548i
$819$		0			0
$820$	23.5253	+	17.0922i	0.821540	+	0.596884i
$821$	33.2653	−	7.07077i	1.16097	−	0.246771i	0.413143	−	0.910666i	$-0.364431\pi$
$821$	33.2653	−	7.07077i	1.16097	−	0.246771i	0.747826	+	0.663895i	$0.231098\pi$
$822$		0			0
$823$	−1.62605	−	15.4708i	−0.0566804	−	0.539278i	−0.985612	−	0.169026i	$-0.945938\pi$
$823$	−1.62605	−	15.4708i	−0.0566804	−	0.539278i	0.928931	−	0.370252i	$-0.120729\pi$
$824$	3.19521	−	5.53426i	0.111310	−	0.192795i
$825$		0			0
$826$	−0.772337	−	1.33773i	−0.0268730	−	0.0465455i
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	−0.339054	−	0.940767i	$-0.610107\pi$
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	0.789949	+	0.613172i	$0.210107\pi$
$828$		0			0
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	−0.794727	−	0.606967i	$-0.792386\pi$
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	0.999714	−	0.0239173i	$-0.00761382\pi$
$830$	0.899644	−	8.55954i	0.0312271	−	0.297106i
$831$		0			0
$832$	2.81122	+	3.12217i	0.0974614	+	0.108242i
$833$	1.73465	+	0.368711i	0.0601021	+	0.0127751i
$834$		0			0
$835$	7.54371	+	13.0661i	0.261061	+	0.452171i
$836$	33.0308	−	12.1406i	1.14240	−	0.419891i
$837$		0			0
$838$	−0.0708501	+	0.0514756i	−0.00244747	+	0.00177819i
$839$	−0.995613	+	1.10574i	−0.0343724	+	0.0381744i	−0.760086	−	0.649823i	$-0.774843\pi$
$839$	−0.995613	+	1.10574i	−0.0343724	+	0.0381744i	0.725713	+	0.687997i	$0.241510\pi$
$840$		0			0
$841$	27.6687	−	12.3189i	0.954095	−	0.424790i
$842$	−8.96121	+	3.98979i	−0.308824	+	0.137497i
$843$		0			0
$844$	9.30353	−	10.3326i	0.320241	−	0.355663i
$845$	6.25224	−	4.54252i	0.215084	−	0.156267i
$846$		0			0
$847$	4.87274	+	11.8444i	0.167429	+	0.406977i
$848$	−2.55384	−	4.42338i	−0.0876993	−	0.151900i
$849$		0			0
$850$	0.715025	+	0.151983i	0.0245252	+	0.00521298i
$851$	−0.357172	−	0.396680i	−0.0122437	−	0.0135980i
$852$		0			0
$853$	−3.95139	+	37.5950i	−0.135293	+	1.28723i	0.690532	+	0.723302i	$0.257376\pi$
$853$	−3.95139	+	37.5950i	−0.135293	+	1.28723i	−0.825825	+	0.563926i	$0.809290\pi$
$854$	−2.84548	+	8.75750i	−0.0973704	+	0.299675i
$855$		0			0
$856$	20.5530	−	14.9326i	0.702487	−	0.510387i
$857$	9.91348	+	17.1706i	0.338638	+	0.586538i	0.984177	−	0.177189i	$-0.0567005\pi$
$857$	9.91348	+	17.1706i	0.338638	+	0.586538i	−0.645539	+	0.763727i	$0.723367\pi$
$858$		0			0
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	−0.700272	−	0.713876i	$-0.746938\pi$
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	0.968371	+	0.249515i	$0.0802711\pi$
$860$	3.55001	+	33.7761i	0.121054	+	1.15175i
$861$		0			0
$862$	14.3384	−	3.04772i	0.488368	−	0.103806i
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	0.694050	−	0.719927i	$-0.255825\pi$
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	−0.470218	+	0.882550i	$0.655825\pi$
$864$		0			0
$865$	−14.4739	+	44.5462i	−0.492128	+	1.51462i
$866$	−6.39284	+	7.09997i	−0.217237	+	0.241267i
$867$		0			0
$868$	−6.33269	+	10.9685i	−0.214945	+	0.372296i
$869$	−13.0049	−	26.4514i	−0.441159	−	0.897303i
$870$		0			0
$871$	−42.1057	−	18.7467i	−1.42670	−	0.635206i
$872$	3.40401	+	10.4765i	0.115274	+	0.354778i
$873$		0			0
$874$	0.254531	+	0.184928i	0.00860964	+	0.00625527i
$875$	0.355931	−	3.38646i	0.0120327	−	0.114483i
$876$		0			0
$877$	2.47817	+	0.526750i	0.0836817	+	0.0177871i	0.249562	−	0.968359i	$-0.419713\pi$
$877$	2.47817	+	0.526750i	0.0836817	+	0.0177871i	−0.165881	+	0.986146i	$0.553047\pi$
$878$	−2.37009	−	22.5499i	−0.0799867	−	0.761022i
$879$		0			0
$880$	7.80812	−	19.5030i	0.263212	−	0.657446i
$881$	47.4109			1.59731			0.798657	−	0.601786i	$-0.205544\pi$
$881$	47.4109			1.59731			0.798657	+	0.601786i	$0.205544\pi$
$882$		0			0
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	0.989029	+	0.147719i	$0.0471930\pi$
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	−0.713315	+	0.700844i	$0.752807\pi$
$884$	−2.02061	+	0.429495i	−0.0679606	+	0.0144455i
$885$		0			0
$886$	16.9914	−	7.56506i	0.570837	−	0.254153i
$887$	32.0041	+	35.5441i	1.07459	+	1.19345i	0.980219	+	0.197918i	$0.0634179\pi$
$887$	32.0041	+	35.5441i	1.07459	+	1.19345i	0.0943729	+	0.995537i	$0.469915\pi$
$888$		0			0
$889$	14.0221	+	6.24306i	0.470288	+	0.209386i
$890$	−3.69528			−0.123866
$891$		0			0
$892$	0.639221			0.0214027
$893$	1.90671	+	0.848920i	0.0638055	+	0.0284080i
$894$		0			0
$895$	14.1707	+	15.7382i	0.473675	+	0.526069i
$896$	−12.2585	+	5.45786i	−0.409529	+	0.182334i
$897$		0			0
$898$	14.6068	−	3.10477i	0.487435	−	0.103608i
$899$	15.5345	+	47.8104i	0.518106	+	1.59457i
$900$		0			0
$901$	0.761187			0.0253588
$902$	−2.72730	−	10.7932i	−0.0908090	−	0.359373i
$903$		0			0
$904$	4.25749	+	40.5073i	0.141602	+	1.34725i
$905$	7.34017	+	1.56020i	0.243995	+	0.0518628i
$906$		0			0
$907$	−4.96075	+	47.1984i	−0.164719	+	1.56720i	0.530052	+	0.847965i	$0.322172\pi$
$907$	−4.96075	+	47.1984i	−0.164719	+	1.56720i	−0.694771	+	0.719231i	$0.744494\pi$
$908$	−24.2817	−	17.6417i	−0.805815	−	0.585459i
$909$		0			0
$910$	2.46479	+	7.58583i	0.0817068	+	0.251468i
$911$	25.9741	+	11.5644i	0.860561	+	0.383147i	0.789076	−	0.614295i	$-0.210560\pi$
$911$	25.9741	+	11.5644i	0.860561	+	0.383147i	0.0714850	+	0.997442i	$0.477226\pi$
$912$		0			0
$913$	11.7920	−	11.4597i	0.390259	−	0.379259i
$914$	−3.67381	+	6.36322i	−0.121519	+	0.210477i
$915$		0			0
$916$	−14.9702	+	16.6261i	−0.494629	+	0.549342i
$917$	−6.46615	+	19.9008i	−0.213531	+	0.657181i
$918$		0			0
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.0569449	−	0.998377i	$-0.518136\pi$
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.967110	+	0.254358i	$0.918136\pi$
$920$	0.532265	−	0.113136i	0.0175483	−	0.00373000i
$921$		0			0
$922$	1.14887	+	10.9308i	0.0378361	+	0.359986i
$923$	−17.2007	+	29.7924i	−0.566167	+	0.980629i
$924$		0			0
$925$	12.5692	+	21.7704i	0.413272	+	0.715808i
$926$	−10.6893	+	7.76621i	−0.351271	+	0.255214i
$927$		0			0
$928$	−12.9791	+	39.9457i	−0.426061	+	1.31128i
$929$	1.39939	−	13.3143i	0.0459126	−	0.436829i	−0.947285	−	0.320391i	$-0.896186\pi$
$929$	1.39939	−	13.3143i	0.0459126	−	0.436829i	0.993198	−	0.116438i	$-0.0371476\pi$
$930$		0			0
$931$	−24.0522	−	26.7127i	−0.788280	−	0.875473i
$932$	5.49160	+	1.16728i	0.179883	+	0.0382354i
$933$		0			0
$934$	−4.60021	−	7.96779i	−0.150523	−	0.260714i
$935$	1.93528	+	2.46098i	0.0632905	+	0.0804826i
$936$		0			0
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	−0.211934	−	0.977284i	$-0.567976\pi$
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	0.863961	+	0.503559i	$0.167976\pi$
$938$	5.25781	−	5.83939i	0.171674	−	0.190663i
$939$		0			0
$940$	1.49874	−	0.667281i	0.0488834	−	0.0217643i
$941$	−7.58453	+	3.37685i	−0.247249	+	0.110082i	−0.526620	−	0.850101i	$-0.676541\pi$
$941$	−7.58453	+	3.37685i	−0.247249	+	0.110082i	0.279371	+	0.960183i	$0.409874\pi$
$942$		0			0
$943$	−0.332341	+	0.369103i	−0.0108225	+	0.0120196i
$944$	−3.91616	+	2.84526i	−0.127460	+	0.0926053i
$945$		0			0
$946$	7.23646	−	10.8020i	0.235278	−	0.351202i
$947$	18.9748	+	32.8653i	0.616598	+	1.06798i	0.990102	+	0.140351i	$0.0448231\pi$
$947$	18.9748	+	32.8653i	0.616598	+	1.06798i	−0.373503	+	0.927629i	$0.621844\pi$
$948$		0			0
$949$	11.3735	+	2.41752i	0.369201	+	0.0784761i
$950$	−9.91435	−	11.0110i	−0.321664	−	0.357244i
$951$		0			0
$952$	0.0810019	−	0.770681i	0.00262529	−	0.0249779i
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	−0.341583	−	0.939852i	$-0.610963\pi$
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	0.828778	−	0.559578i	$-0.189037\pi$
$954$		0			0
$955$	28.7373	−	20.8789i	0.929918	−	0.675625i
$956$	19.3245	+	33.4710i	0.624998	+	1.08253i
$957$		0			0
$958$	4.73516	−	8.20154i	0.152986	−	0.264980i
$959$	1.99617	+	18.9923i	0.0644596	+	0.613292i
$960$		0			0
$961$	−11.3716	+	2.41712i	−0.366827	+	0.0779716i
$962$	11.5165	+	8.36721i	0.371306	+	0.269770i
$963$		0			0
$964$	−7.80746	+	24.0289i	−0.251461	+	0.773918i
$965$	−13.5632	+	15.0634i	−0.436614	+	0.484909i
$966$		0			0
$967$	−5.48901	+	9.50724i	−0.176515	+	0.305732i	−0.940684	−	0.339283i	$-0.889816\pi$
$967$	−5.48901	+	9.50724i	−0.176515	+	0.305732i	0.764170	+	0.645015i	$0.223149\pi$
$968$	−20.5046	+	11.0693i	−0.659044	+	0.355781i
$969$		0			0
$970$	−0.140891	−	0.0627287i	−0.00452374	−	0.00201410i
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	0.865153	−	0.501508i	$-0.167221\pi$
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	−0.994702	+	0.102796i	$0.967221\pi$
$972$		0			0
$973$	−11.2108	−	8.14510i	−0.359401	−	0.261120i
$974$	1.37626	−	13.0942i	0.0440981	−	0.419565i
$975$		0			0
$976$	28.2257	+	5.99955i	0.903482	+	0.192041i
$977$	−1.15779	−	11.0156i	−0.0370410	−	0.352421i	−0.997307	−	0.0733360i	$-0.976635\pi$
$977$	−1.15779	−	11.0156i	−0.0370410	−	0.352421i	0.960266	−	0.279085i	$-0.0900312\pi$
$978$		0			0
$979$	−5.42247	−	4.52087i	−0.173303	−	0.144488i
$980$	−28.2544			−0.902554
$981$		0			0
$982$	−7.79262	−	23.9832i	−0.248673	−	0.765336i
$983$	−25.8539	+	5.49541i	−0.824611	+	0.175277i	−0.600844	−	0.799366i	$-0.705169\pi$
$983$	−25.8539	+	5.49541i	−0.824611	+	0.175277i	−0.223767	+	0.974643i	$0.571835\pi$
$984$		0			0
$985$	−56.6706	+	25.2314i	−1.80568	+	0.803938i
$986$	−0.935344	−	1.03880i	−0.0297874	−	0.0330823i
$987$		0			0
$988$	38.2512	+	17.0305i	1.21693	+	0.541814i
$989$	−0.580083			−0.0184456
$990$		0			0
$991$	−18.9911			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$992$	−32.5349	−	14.4855i	−1.03298	−	0.459914i
$993$		0			0
$994$	−3.92436	−	4.35845i	−0.124473	−	0.138242i
$995$	36.4663	−	16.2359i	1.15606	−	0.514711i
$996$		0			0
$997$	−21.6299	+	4.59758i	−0.685027	+	0.145607i	−0.537262	−	0.843416i	$-0.680541\pi$
$997$	−21.6299	+	4.59758i	−0.685027	+	0.145607i	−0.147765	+	0.989022i	$0.547208\pi$
$998$	3.58956	+	11.0475i	0.113625	+	0.349703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.91.4		72
3.2	odd	2		99.2.m.b.58.6	yes	72
9.2	odd	6		99.2.m.b.25.4	yes	72
9.4	even	3		891.2.f.e.487.6		36
9.5	odd	6		891.2.f.f.487.4		36
9.7	even	3	inner	297.2.n.b.289.6		72
11.4	even	5	inner	297.2.n.b.37.6		72
33.2	even	10		1089.2.e.o.364.11		36
33.20	odd	10		1089.2.e.p.364.8		36
33.26	odd	10		99.2.m.b.4.4	✓	72
99.2	even	30		1089.2.e.o.727.11		36
99.4	even	15		891.2.f.e.730.6		36
99.13	odd	30		9801.2.a.cn.1.11		18
99.20	odd	30		1089.2.e.p.727.8		36
99.31	even	15		9801.2.a.cp.1.8		18
99.59	odd	30		891.2.f.f.730.4		36
99.68	even	30		9801.2.a.co.1.8		18
99.70	even	15	inner	297.2.n.b.235.4		72
99.86	odd	30		9801.2.a.cm.1.11		18
99.92	odd	30		99.2.m.b.70.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	33.26	odd	10
99.2.m.b.25.4	yes	72	9.2	odd	6
99.2.m.b.58.6	yes	72	3.2	odd	2
99.2.m.b.70.6	yes	72	99.92	odd	30
297.2.n.b.37.6		72	11.4	even	5	inner
297.2.n.b.91.4		72	1.1	even	1	trivial
297.2.n.b.235.4		72	99.70	even	15	inner
297.2.n.b.289.6		72	9.7	even	3	inner
891.2.f.e.487.6		36	9.4	even	3
891.2.f.e.730.6		36	99.4	even	15
891.2.f.f.487.4		36	9.5	odd	6
891.2.f.f.730.4		36	99.59	odd	30
1089.2.e.o.364.11		36	33.2	even	10
1089.2.e.o.727.11		36	99.2	even	30
1089.2.e.p.364.8		36	33.20	odd	10
1089.2.e.p.727.8		36	99.20	odd	30
9801.2.a.cm.1.11		18	99.86	odd	30
9801.2.a.cn.1.11		18	99.13	odd	30
9801.2.a.co.1.8		18	99.68	even	30
9801.2.a.cp.1.8		18	99.31	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.527858 - 0.235017i) q^{2} +(-1.11486 - 1.23818i) q^{4} +(-2.74468 + 1.22201i) q^{5} +(1.13888 - 0.242076i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(2.54741 + 2.12385i) q^{11} +(0.412487 + 3.92455i) q^{13} +(-0.658057 - 0.139874i) q^{14} +(-0.220374 + 2.09672i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(4.57300 + 2.03603i) q^{20} +(-0.845527 - 1.71977i) q^{22} +(-0.0427501 + 0.0740453i) q^{23} +(2.69431 - 2.99234i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(-7.53156 + 1.60088i) q^{29} +(-0.682449 - 6.49307i) q^{31} +(2.72743 - 4.72404i) q^{32} +(0.0907715 + 0.157221i) q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(0.384637 - 3.65957i) q^{38} +(-4.25861 - 4.72966i) q^{40} +(5.68213 + 1.20777i) q^{41} +(3.39229 + 5.87562i) q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(0.219298 - 0.243555i) q^{47} +(-5.15638 + 2.29577i) q^{49} +(-2.12546 + 0.946318i) q^{50} +(4.39943 - 4.88606i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +(1.23321 + 2.13598i) q^{56} +(4.35183 + 0.925009i) q^{58} +(1.53634 + 1.70628i) q^{59} +(1.43070 - 13.6122i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +(-5.92799 - 10.2676i) q^{65} +(-5.83989 + 10.1150i) q^{67} +(0.0547189 + 0.520616i) q^{68} +(1.97708 - 0.420242i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(2.41378 - 2.68077i) q^{74} +(5.30529 - 9.18904i) q^{76} +(3.41531 + 1.80213i) q^{77} +(-8.11886 - 3.61475i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(0.518229 - 4.93062i) q^{83} +(0.923335 + 0.196261i) q^{85} +(-0.409774 - 3.89874i) q^{86} +(-2.61129 + 6.52242i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(0.139342 - 0.0296180i) q^{92} +(-0.172998 + 0.0770236i) q^{94} +(-12.8027 - 14.2189i) q^{95} +(-0.0811587 - 0.0361342i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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