LMFDB - Embedded newform 297.2.n.b.64.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(37,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			64.9
Character	$\chi$	$=$	297.64
Dual form			297.2.n.b.181.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.27811 - 0.484227i) q^{2} +(3.12821 - 1.39277i) q^{4} +(-0.310092 - 0.0659121i) q^{5} +(0.148273 - 1.41072i) q^{7} +(2.68358 - 1.94973i) q^{8} -0.738340 q^{10} +(-1.02493 - 3.15429i) q^{11} +(2.80837 + 3.11901i) q^{13} +(-0.345328 - 3.28557i) q^{14} +(0.586822 - 0.651731i) q^{16} +(1.92957 + 5.93860i) q^{17} +(-2.50622 + 1.82087i) q^{19} +(-1.06183 + 0.225700i) q^{20} +(-3.86228 - 6.68951i) q^{22} +(-2.26025 + 3.91487i) q^{23} +(-4.47591 - 1.99281i) q^{25} +(7.90807 + 5.74555i) q^{26} +(-1.50098 - 4.61954i) q^{28} +(0.306106 - 2.91240i) q^{29} +(-6.38469 - 7.09091i) q^{31} +(-2.29583 + 3.97649i) q^{32} +(7.27140 + 12.5944i) q^{34} +(-0.138962 + 0.427681i) q^{35} +(-0.685637 - 0.498145i) q^{37} +(-4.82772 + 5.36173i) q^{38} +(-0.960667 + 0.427717i) q^{40} +(-0.404484 - 3.84841i) q^{41} +(-1.77651 - 3.07700i) q^{43} +(-7.59937 - 8.43978i) q^{44} +(-3.25341 + 10.0130i) q^{46} +(6.80683 + 3.03059i) q^{47} +(4.87888 + 1.03704i) q^{49} +(-11.1616 - 2.37247i) q^{50} +(13.1292 + 5.84550i) q^{52} +(-2.06517 + 6.35595i) q^{53} +(0.109916 + 1.04568i) q^{55} +(-2.35263 - 4.07487i) q^{56} +(-0.712921 - 6.78299i) q^{58} +(11.0309 - 4.91125i) q^{59} +(3.09160 - 3.43357i) q^{61} +(-17.9786 - 13.0622i) q^{62} +(-3.84663 + 11.8387i) q^{64} +(-0.665272 - 1.15229i) q^{65} +(-4.98385 + 8.63229i) q^{67} +(14.3072 + 15.8897i) q^{68} +(-0.109476 + 1.04159i) q^{70} +(-0.905630 - 2.78724i) q^{71} +(-3.43158 - 2.49319i) q^{73} +(-1.80317 - 0.802823i) q^{74} +(-5.30392 + 9.18665i) q^{76} +(-4.60179 + 0.978190i) q^{77} +(3.30808 - 0.703155i) q^{79} +(-0.224926 + 0.163418i) q^{80} +(-2.78496 - 8.57123i) q^{82} +(9.02488 - 10.0231i) q^{83} +(-0.206918 - 1.96870i) q^{85} +(-5.53705 - 6.14951i) q^{86} +(-8.90048 - 6.46644i) q^{88} -2.69745 q^{89} +(4.81645 - 3.49936i) q^{91} +(-1.61803 + 15.3945i) q^{92} +(16.9742 + 3.60797i) q^{94} +(0.897177 - 0.399449i) q^{95} +(5.14256 - 1.09308i) q^{97} +11.6168 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.27811	−	0.484227i	1.61087	−	0.342400i	0.687459	−	0.726223i	$-0.258726\pi$
$2$	2.27811	−	0.484227i	1.61087	−	0.342400i	0.923407	+	0.383823i	$0.125393\pi$
$3$		0			0
$3$		0			0
$4$	3.12821	−	1.39277i	1.56410	−	0.696384i
$5$	−0.310092	−	0.0659121i	−0.138677	−	0.0294768i	0.138050	−	0.990425i	$-0.455917\pi$
$5$	−0.310092	−	0.0659121i	−0.138677	−	0.0294768i	−0.276727	+	0.960948i	$0.589250\pi$
$6$		0			0
$7$	0.148273	−	1.41072i	0.0560419	−	0.533203i	−0.930101	−	0.367304i	$-0.880281\pi$
$7$	0.148273	−	1.41072i	0.0560419	−	0.533203i	0.986143	−	0.165899i	$-0.0530525\pi$
$8$	2.68358	−	1.94973i	0.948787	−	0.689334i
$9$		0			0
$10$	−0.738340			−0.233484
$11$	−1.02493	−	3.15429i	−0.309027	−	0.951053i
$11$	−1.02493	−	3.15429i	−0.309027	−	0.951053i
$12$		0			0
$13$	2.80837	+	3.11901i	0.778901	+	0.865057i	0.993754	−	0.111590i	$-0.0355942\pi$
$13$	2.80837	+	3.11901i	0.778901	+	0.865057i	−0.214854	+	0.976646i	$0.568928\pi$
$14$	−0.345328	−	3.28557i	−0.0922927	−	0.878107i
$15$		0			0
$16$	0.586822	−	0.651731i	0.146705	−	0.162933i
$17$	1.92957	+	5.93860i	0.467989	+	1.44032i	0.855184	+	0.518325i	$0.173444\pi$
$17$	1.92957	+	5.93860i	0.467989	+	1.44032i	−0.387195	+	0.921998i	$0.626556\pi$
$18$		0			0
$19$	−2.50622	+	1.82087i	−0.574966	+	0.417737i	−0.836906	−	0.547347i	$-0.815638\pi$
$19$	−2.50622	+	1.82087i	−0.574966	+	0.417737i	0.261940	+	0.965084i	$0.415638\pi$
$20$	−1.06183	+	0.225700i	−0.237433	+	0.0504680i
$21$		0			0
$22$	−3.86228	−	6.68951i	−0.823441	−	1.42621i
$23$	−2.26025	+	3.91487i	−0.471295	+	0.816306i	−0.999461	−	0.0328349i	$-0.989546\pi$
$23$	−2.26025	+	3.91487i	−0.471295	+	0.816306i	0.528166	+	0.849141i	$0.322880\pi$
$24$		0			0
$25$	−4.47591	−	1.99281i	−0.895183	−	0.398561i
$26$	7.90807	+	5.74555i	1.55090	+	1.12679i
$27$		0			0
$28$	−1.50098	−	4.61954i	−0.283659	−	0.873011i
$29$	0.306106	−	2.91240i	0.0568424	−	0.540820i	−0.928633	−	0.371000i	$-0.879015\pi$
$29$	0.306106	−	2.91240i	0.0568424	−	0.540820i	0.985475	−	0.169819i	$-0.0543184\pi$
$30$		0			0
$31$	−6.38469	−	7.09091i	−1.14672	−	1.27357i	−0.956470	−	0.291830i	$-0.905736\pi$
$31$	−6.38469	−	7.09091i	−1.14672	−	1.27357i	−0.190253	−	0.981735i	$-0.560931\pi$
$32$	−2.29583	+	3.97649i	−0.405848	+	0.702950i
$33$		0			0
$34$	7.27140	+	12.5944i	1.24703	+	2.15993i
$35$	−0.138962	+	0.427681i	−0.0234889	+	0.0722913i
$36$		0			0
$37$	−0.685637	−	0.498145i	−0.112718	−	0.0818945i	0.529998	−	0.847999i	$-0.322193\pi$
$37$	−0.685637	−	0.498145i	−0.112718	−	0.0818945i	−0.642716	+	0.766104i	$0.722193\pi$
$38$	−4.82772	+	5.36173i	−0.783159	+	0.869787i
$39$		0			0
$40$	−0.960667	+	0.427717i	−0.151895	+	0.0676279i
$41$	−0.404484	−	3.84841i	−0.0631698	−	0.601021i	−0.979618	−	0.200868i	$-0.935624\pi$
$41$	−0.404484	−	3.84841i	−0.0631698	−	0.601021i	0.916448	−	0.400153i	$-0.131043\pi$
$42$		0			0
$43$	−1.77651	−	3.07700i	−0.270915	−	0.469239i	0.698181	−	0.715921i	$-0.253993\pi$
$43$	−1.77651	−	3.07700i	−0.270915	−	0.469239i	−0.969096	+	0.246682i	$0.920660\pi$
$44$	−7.59937	−	8.43978i	−1.14565	−	1.27235i
$45$		0			0
$46$	−3.25341	+	10.0130i	−0.479689	+	1.47633i
$47$	6.80683	+	3.03059i	0.992878	+	0.442058i	0.837878	−	0.545857i	$-0.183796\pi$
$47$	6.80683	+	3.03059i	0.992878	+	0.442058i	0.154999	+	0.987915i	$0.450462\pi$
$48$		0			0
$49$	4.87888	+	1.03704i	0.696983	+	0.148148i
$50$	−11.1616	−	2.37247i	−1.57849	−	0.335518i
$51$		0			0
$52$	13.1292	+	5.84550i	1.82069	+	0.810625i
$53$	−2.06517	+	6.35595i	−0.283673	+	0.873057i	0.703120	+	0.711071i	$0.251790\pi$
$53$	−2.06517	+	6.35595i	−0.283673	+	0.873057i	−0.986793	+	0.161986i	$0.948210\pi$
$54$		0			0
$55$	0.109916	+	1.04568i	0.0148210	+	0.140999i
$56$	−2.35263	−	4.07487i	−0.314383	−	0.544528i
$57$		0			0
$58$	−0.712921	−	6.78299i	−0.0936111	−	0.890650i
$59$	11.0309	−	4.91125i	1.43609	−	0.639391i	0.466592	−	0.884473i	$-0.345482\pi$
$59$	11.0309	−	4.91125i	1.43609	−	0.639391i	0.969502	+	0.245082i	$0.0788149\pi$
$60$		0			0
$61$	3.09160	−	3.43357i	0.395838	−	0.439623i	−0.511973	−	0.859001i	$-0.671085\pi$
$61$	3.09160	−	3.43357i	0.395838	−	0.439623i	0.907812	+	0.419378i	$0.137752\pi$
$62$	−17.9786	−	13.0622i	−2.28329	−	1.65890i
$63$		0			0
$64$	−3.84663	+	11.8387i	−0.480828	+	1.47984i
$65$	−0.665272	−	1.15229i	−0.0825169	−	0.142923i
$66$		0			0
$67$	−4.98385	+	8.63229i	−0.608875	+	1.05460i	0.382552	+	0.923934i	$0.375045\pi$
$67$	−4.98385	+	8.63229i	−0.608875	+	1.05460i	−0.991426	+	0.130668i	$0.958288\pi$
$68$	14.3072	+	15.8897i	1.73500	+	1.92691i
$69$		0			0
$70$	−0.109476	+	1.04159i	−0.0130849	+	0.124494i
$71$	−0.905630	−	2.78724i	−0.107479	−	0.330785i	0.882826	−	0.469701i	$-0.155638\pi$
$71$	−0.905630	−	2.78724i	−0.107479	−	0.330785i	−0.990304	+	0.138916i	$0.955638\pi$
$72$		0			0
$73$	−3.43158	−	2.49319i	−0.401636	−	0.291806i	0.368571	−	0.929600i	$-0.379847\pi$
$73$	−3.43158	−	2.49319i	−0.401636	−	0.291806i	−0.770207	+	0.637794i	$0.779847\pi$
$74$	−1.80317	−	0.802823i	−0.209614	−	0.0933263i
$75$		0			0
$76$	−5.30392	+	9.18665i	−0.608401	+	1.05378i
$77$	−4.60179	+	0.978190i	−0.524423	+	0.111475i
$78$		0			0
$79$	3.30808	−	0.703155i	0.372188	−	0.0791111i	−0.0180200	−	0.999838i	$-0.505736\pi$
$79$	3.30808	−	0.703155i	0.372188	−	0.0791111i	0.390208	+	0.920727i	$0.372403\pi$
$80$	−0.224926	+	0.163418i	−0.0251475	+	0.0182707i
$81$		0			0
$82$	−2.78496	−	8.57123i	−0.307548	−	0.946534i
$83$	9.02488	−	10.0231i	0.990609	−	1.10018i	−0.00435860	−	0.999991i	$-0.501387\pi$
$83$	9.02488	−	10.0231i	0.990609	−	1.10018i	0.994968	−	0.100193i	$-0.0319459\pi$
$84$		0			0
$85$	−0.206918	−	1.96870i	−0.0224435	−	0.213535i
$86$	−5.53705	−	6.14951i	−0.597075	−	0.663119i
$87$		0			0
$88$	−8.90048	−	6.46644i	−0.948795	−	0.689325i
$89$	−2.69745			−0.285929			−0.142965	−	0.989728i	$-0.545664\pi$
$89$	−2.69745			−0.285929			−0.142965	+	0.989728i	$0.545664\pi$
$90$		0			0
$91$	4.81645	−	3.49936i	0.504902	−	0.366833i
$92$	−1.61803	+	15.3945i	−0.168691	+	1.60499i
$93$		0			0
$94$	16.9742	+	3.60797i	1.75075	+	0.372134i
$95$	0.897177	−	0.399449i	0.0920484	−	0.0409826i
$96$		0			0
$97$	5.14256	−	1.09308i	0.522147	−	0.110986i	0.0607045	−	0.998156i	$-0.480665\pi$
$97$	5.14256	−	1.09308i	0.522147	−	0.110986i	0.461443	+	0.887170i	$0.347332\pi$
$98$	11.6168			1.17347
$99$		0			0
$100$	−16.7771			−1.67771
$101$	−9.32150	+	1.98135i	−0.927524	+	0.197151i	−0.646819	−	0.762643i	$-0.723901\pi$
$101$	−9.32150	+	1.98135i	−0.927524	+	0.197151i	−0.280704	+	0.959794i	$0.590568\pi$
$102$		0			0
$103$	8.71123	−	3.87849i	0.858343	−	0.382159i	0.0701126	−	0.997539i	$-0.477664\pi$
$103$	8.71123	−	3.87849i	0.858343	−	0.382159i	0.788231	+	0.615380i	$0.210997\pi$
$104$	13.6177	+	2.89453i	1.33532	+	0.283832i
$105$		0			0
$106$	−1.62697	+	15.4796i	−0.158025	+	1.50351i
$107$	4.18472	−	3.04038i	0.404552	−	0.293924i	−0.366840	−	0.930284i	$-0.619560\pi$
$107$	4.18472	−	3.04038i	0.404552	−	0.293924i	0.771393	+	0.636359i	$0.219560\pi$
$108$		0			0
$109$	14.4767			1.38661			0.693307	−	0.720643i	$-0.256153\pi$
$109$	14.4767			1.38661			0.693307	+	0.720643i	$0.256153\pi$
$110$	0.756744	+	2.32894i	0.0721527	+	0.222055i
$111$		0			0
$112$	−0.832402	−	0.924476i	−0.0786546	−	0.0873548i
$113$	−0.776815	−	7.39090i	−0.0730766	−	0.695277i	−0.968322	−	0.249704i	$-0.919667\pi$
$113$	−0.776815	−	7.39090i	−0.0730766	−	0.695277i	0.895246	−	0.445573i	$-0.147000\pi$
$114$		0			0
$115$	0.958923	−	1.06499i	0.0894200	−	0.0993110i
$116$	−3.09874	−	9.53694i	−0.287711	−	0.885482i
$117$		0			0
$118$	22.7513	−	16.5298i	2.09443	−	1.52169i
$119$	8.66382	−	1.84155i	0.794211	−	0.168815i
$120$		0			0
$121$	−8.89905	+	6.46582i	−0.809005	+	0.587802i
$122$	5.38037	−	9.31907i	0.487116	−	0.843709i
$123$		0			0
$124$	−29.8486	−	13.2895i	−2.68049	−	1.19343i
$125$	2.53897	+	1.84467i	0.227092	+	0.164992i
$126$		0			0
$127$	−4.08040	−	12.5582i	−0.362077	−	1.11436i	−0.951791	−	0.306746i	$-0.900760\pi$
$127$	−4.08040	−	12.5582i	−0.362077	−	1.11436i	0.589715	−	0.807612i	$-0.299240\pi$
$128$	−2.07050	+	19.6995i	−0.183008	+	1.74120i
$129$		0			0
$130$	−2.07353	−	2.30289i	−0.181861	−	0.201977i
$131$	−3.65021	+	6.32236i	−0.318921	+	0.552387i	−0.980263	−	0.197697i	$-0.936654\pi$
$131$	−3.65021	+	6.32236i	−0.318921	+	0.552387i	0.661342	+	0.750084i	$0.269987\pi$
$132$		0			0
$133$	2.19714	+	3.80556i	0.190516	+	0.329984i
$134$	−7.17377	+	22.0786i	−0.619719	+	1.90730i
$135$		0			0
$136$	16.7568	+	12.1746i	1.43689	+	1.04396i
$137$	−6.56239	+	7.28827i	−0.560662	+	0.622679i	−0.955114	−	0.296238i	$-0.904268\pi$
$137$	−6.56239	+	7.28827i	−0.560662	+	0.622679i	0.394452	+	0.918917i	$0.370935\pi$
$138$		0			0
$139$	−8.65757	+	3.85460i	−0.734326	+	0.326943i	−0.739603	−	0.673043i	$-0.764987\pi$
$139$	−8.65757	+	3.85460i	−0.734326	+	0.326943i	0.00527735	+	0.999986i	$0.498320\pi$
$140$	0.160958	+	1.53142i	0.0136035	+	0.129428i
$141$		0			0
$142$	−3.41278	−	5.91111i	−0.286394	−	0.496049i
$143$	6.95987	−	12.0551i	0.582014	−	1.00810i
$144$		0			0
$145$	−0.286884	+	0.882938i	−0.0238244	+	0.0733240i
$146$	−9.02479	−	4.01809i	−0.746897	−	0.332540i
$147$		0			0
$148$	−2.83862	−	0.603367i	−0.233333	−	0.0495964i
$149$	−4.03725	−	0.858145i	−0.330745	−	0.0703020i	0.0395464	−	0.999218i	$-0.487409\pi$
$149$	−4.03725	−	0.858145i	−0.330745	−	0.0703020i	−0.370291	+	0.928916i	$0.620742\pi$
$150$		0			0
$151$	−16.2385	−	7.22985i	−1.32147	−	0.588357i	−0.379855	−	0.925046i	$-0.624026\pi$
$151$	−16.2385	−	7.22985i	−1.32147	−	0.588357i	−0.941616	+	0.336689i	$0.890693\pi$
$152$	−3.17541	+	9.77291i	−0.257560	+	0.792688i
$153$		0			0
$154$	−10.0097	+	4.45673i	−0.806605	+	0.359134i
$155$	1.51246	+	2.61967i	0.121484	+	0.210417i
$156$		0			0
$157$	0.210861	+	2.00621i	0.0168285	+	0.160113i	0.999709	−	0.0241329i	$-0.00768247\pi$
$157$	0.210861	+	2.00621i	0.0168285	+	0.160113i	−0.982880	+	0.184246i	$0.941016\pi$
$158$	7.19568	−	3.20372i	0.572458	−	0.254875i
$159$		0			0
$160$	0.974017	−	1.08175i	0.0770028	−	0.0855202i
$161$	5.18765	+	3.76905i	0.408844	+	0.297043i
$162$		0			0
$163$	−0.488377	+	1.50307i	−0.0382526	+	0.117729i	−0.968359	−	0.249560i	$-0.919714\pi$
$163$	−0.488377	+	1.50307i	−0.0382526	+	0.117729i	0.930107	+	0.367289i	$0.119714\pi$
$164$	−6.62526	−	11.4753i	−0.517346	−	0.896069i
$165$		0			0
$166$	15.7062	−	27.2039i	1.21904	−	2.11143i
$167$	−10.2522	−	11.3862i	−0.793337	−	0.881090i	0.201817	−	0.979423i	$-0.435315\pi$
$167$	−10.2522	−	11.3862i	−0.793337	−	0.881090i	−0.995154	+	0.0983335i	$0.968649\pi$
$168$		0			0
$169$	−0.482411	+	4.58984i	−0.0371085	+	0.353064i
$170$	−1.42468	−	4.38471i	−0.109268	−	0.336292i
$171$		0			0
$172$	−9.84284	−	7.15124i	−0.750510	−	0.545277i
$173$	0.900792	+	0.401058i	0.0684859	+	0.0304919i	0.440694	−	0.897658i	$-0.354732\pi$
$173$	0.900792	+	0.401058i	0.0684859	+	0.0304919i	−0.372208	+	0.928149i	$0.621399\pi$
$174$		0			0
$175$	−3.47495	+	6.01879i	−0.262682	+	0.454978i
$176$	−2.65720	−	1.18303i	−0.200294	−	0.0891740i
$177$		0			0
$178$	−6.14509	+	1.30618i	−0.460594	+	0.0979023i
$179$	−9.08186	+	6.59836i	−0.678810	+	0.493185i	−0.872963	−	0.487787i	$-0.837804\pi$
$179$	−9.08186	+	6.59836i	−0.678810	+	0.493185i	0.194153	+	0.980971i	$0.437804\pi$
$180$		0			0
$181$	5.53932	+	17.0483i	0.411735	+	1.26719i	0.915139	+	0.403138i	$0.132081\pi$
$181$	5.53932	+	17.0483i	0.411735	+	1.26719i	−0.503405	+	0.864051i	$0.667919\pi$
$182$	9.27792	−	10.3042i	0.687725	−	0.763796i
$183$		0			0
$184$	1.56739	+	14.9127i	0.115550	+	1.09938i
$185$	0.179777	+	0.199663i	0.0132175	+	0.0146795i
$186$		0			0
$187$	16.7544	−	12.1730i	1.22520	−	0.890181i
$188$	25.5141			1.86081
$189$		0			0
$190$	1.85044	−	1.34442i	0.134245	−	0.0975348i
$191$	1.34716	−	12.8173i	0.0974768	−	0.927430i	−0.831058	−	0.556185i	$-0.812264\pi$
$191$	1.34716	−	12.8173i	0.0974768	−	0.927430i	0.928535	−	0.371245i	$-0.121069\pi$
$192$		0			0
$193$	22.6451	+	4.81337i	1.63003	+	0.346474i	0.929978	−	0.367616i	$-0.119826\pi$
$193$	22.6451	+	4.81337i	1.63003	+	0.346474i	0.700054	+	0.714090i	$0.253159\pi$
$194$	11.1860	−	4.98033i	0.803108	−	0.357567i
$195$		0			0
$196$	16.7065	−	3.55108i	1.19332	−	0.253649i
$197$	−1.07766			−0.0767801			−0.0383900	−	0.999263i	$-0.512223\pi$
$197$	−1.07766			−0.0767801			−0.0383900	+	0.999263i	$0.512223\pi$
$198$		0			0
$199$	16.4307			1.16474			0.582371	−	0.812923i	$-0.302125\pi$
$199$	16.4307			1.16474			0.582371	+	0.812923i	$0.302125\pi$
$200$	−15.8969	+	3.37899i	−1.12408	+	0.238931i
$201$		0			0
$202$	−20.2760	+	9.02744i	−1.42661	+	0.635168i
$203$	−4.06320	−	0.863660i	−0.285181	−	0.0606171i
$204$		0			0
$205$	−0.128230	+	1.22002i	−0.00895594	+	0.0852101i
$206$	17.9671	−	13.0538i	1.25182	−	0.909503i
$207$		0			0
$208$	3.68076			0.255215
$209$	8.31225	+	6.03907i	0.574970	+	0.417731i
$210$		0			0
$211$	−10.0034	−	11.1099i	−0.688660	−	0.764834i	0.292868	−	0.956153i	$-0.405390\pi$
$211$	−10.0034	−	11.1099i	−0.688660	−	0.764834i	−0.981528	+	0.191319i	$0.938724\pi$
$212$	2.39207	+	22.7590i	0.164288	+	1.56310i
$213$		0			0
$214$	8.06101	−	8.95266i	0.551040	−	0.611991i
$215$	0.348070	+	1.07125i	0.0237382	+	0.0730585i
$216$		0			0
$217$	−10.9500	+	7.95563i	−0.743333	+	0.540063i
$218$	32.9794	−	7.00999i	2.23365	−	0.474776i
$219$		0			0
$220$	1.80022	+	3.11800i	0.121371	+	0.210216i
$221$	−13.1036	+	22.6961i	−0.881444	+	1.52671i
$222$		0			0
$223$	1.75974	+	0.783488i	0.117841	+	0.0524662i	0.464810	−	0.885410i	$-0.346123\pi$
$223$	1.75974	+	0.783488i	0.117841	+	0.0524662i	−0.346969	+	0.937877i	$0.612789\pi$
$224$	5.26931	+	3.82838i	0.352070	+	0.255794i
$225$		0			0
$226$	−5.34854	−	16.4611i	−0.355779	−	1.09498i
$227$	−1.67361	+	15.9234i	−0.111082	+	1.05687i	0.786973	+	0.616988i	$0.211647\pi$
$227$	−1.67361	+	15.9234i	−0.111082	+	1.05687i	−0.898055	+	0.439884i	$0.855020\pi$
$228$		0			0
$229$	−0.349905	−	0.388609i	−0.0231224	−	0.0256800i	0.731473	−	0.681871i	$-0.238833\pi$
$229$	−0.349905	−	0.388609i	−0.0231224	−	0.0256800i	−0.754595	+	0.656191i	$0.772167\pi$
$230$	1.66883	−	2.89050i	0.110040	−	0.190594i
$231$		0			0
$232$	−4.85695	−	8.41248i	−0.318874	−	0.552306i
$233$	3.16820	−	9.75073i	0.207556	−	0.638792i	−0.792043	−	0.610466i	$-0.790982\pi$
$233$	3.16820	−	9.75073i	0.207556	−	0.638792i	0.999599	−	0.0283260i	$-0.00901764\pi$
$234$		0			0
$235$	−1.91099	−	1.38842i	−0.124659	−	0.0905703i
$236$	27.6666	−	30.7268i	1.80094	−	2.00015i
$237$		0			0
$238$	18.8454	−	8.39051i	1.22157	−	0.543876i
$239$	−1.00776	−	9.58823i	−0.0651868	−	0.620211i	−0.977532	−	0.210788i	$-0.932397\pi$
$239$	−1.00776	−	9.58823i	−0.0651868	−	0.620211i	0.912345	−	0.409423i	$-0.134270\pi$
$240$		0			0
$241$	0.139366	+	0.241388i	0.00897733	+	0.0155492i	0.870479	−	0.492205i	$-0.163809\pi$
$241$	0.139366	+	0.241388i	0.00897733	+	0.0155492i	−0.861502	+	0.507754i	$0.830476\pi$
$242$	−17.1421	+	19.0390i	−1.10193	+	1.22387i
$243$		0			0
$244$	4.88900	−	15.0468i	0.312986	−	0.963272i
$245$	−1.44455	−	0.643155i	−0.0922889	−	0.0410897i
$246$		0			0
$247$	−12.7177	−	2.70323i	−0.809207	−	0.172002i
$248$	−30.9592	−	6.58057i	−1.96591	−	0.417867i
$249$		0			0
$250$	6.67728	+	2.97292i	0.422308	+	0.188024i
$251$	−1.36753	+	4.20881i	−0.0863175	+	0.265658i	−0.984894	−	0.173159i	$-0.944602\pi$
$251$	−1.36753	+	4.20881i	−0.0863175	+	0.265658i	0.898576	+	0.438817i	$0.144602\pi$
$252$		0			0
$253$	14.6652	+	3.11703i	0.921993	+	0.195966i
$254$	−15.3766	−	26.6330i	−0.964813	−	1.67111i
$255$		0			0
$256$	2.21987	+	21.1206i	0.138742	+	1.32004i
$257$	−3.33857	+	1.48643i	−0.208254	+	0.0927209i	−0.508213	−	0.861231i	$-0.669694\pi$
$257$	−3.33857	+	1.48643i	−0.208254	+	0.0927209i	0.299959	+	0.953952i	$0.403027\pi$
$258$		0			0
$259$	−0.804405	+	0.893382i	−0.0499833	+	0.0555121i
$260$	−3.68598	−	2.67802i	−0.228595	−	0.166084i
$261$		0			0
$262$	−5.25413	+	16.1705i	−0.324601	+	0.999019i
$263$	−7.22621	−	12.5162i	−0.445587	−	0.771780i	0.552506	−	0.833509i	$-0.313672\pi$
$263$	−7.22621	−	12.5162i	−0.445587	−	0.771780i	−0.998093	+	0.0617294i	$0.980338\pi$
$264$		0			0
$265$	1.05933	−	1.83481i	0.0650741	−	0.112712i
$266$	6.84808	+	7.60557i	0.419883	+	0.466327i
$267$		0			0
$268$	−3.56776	+	33.9450i	−0.217936	+	2.07352i
$269$	−0.283600	−	0.872830i	−0.0172914	−	0.0532174i	0.942039	−	0.335505i	$-0.108907\pi$
$269$	−0.283600	−	0.872830i	−0.0172914	−	0.0532174i	−0.959330	+	0.282287i	$0.908907\pi$
$270$		0			0
$271$	2.13921	+	1.55422i	0.129948	+	0.0944124i	0.650860	−	0.759197i	$-0.274408\pi$
$271$	2.13921	+	1.55422i	0.129948	+	0.0944124i	−0.520913	+	0.853610i	$0.674408\pi$
$272$	5.00269	+	2.22734i	0.303332	+	0.135052i
$273$		0			0
$274$	−11.4206	+	19.7811i	−0.689947	+	1.19502i
$275$	−1.69840	+	16.1608i	−0.102417	+	0.974533i
$276$		0			0
$277$	−28.2729	+	6.00958i	−1.69875	+	0.361081i	−0.952490	−	0.304571i	$-0.901487\pi$
$277$	−28.2729	+	6.00958i	−1.69875	+	0.361081i	−0.746262	+	0.665652i	$0.768153\pi$
$278$	−17.8564	+	12.9734i	−1.07095	+	0.778094i
$279$		0			0
$280$	0.460948	+	1.41865i	0.0275469	+	0.0847807i
$281$	−5.84992	+	6.49700i	−0.348977	+	0.387578i	−0.891921	−	0.452190i	$-0.850643\pi$
$281$	−5.84992	+	6.49700i	−0.348977	+	0.387578i	0.542944	+	0.839769i	$0.317309\pi$
$282$		0			0
$283$	2.42686	+	23.0901i	0.144262	+	1.37256i	0.791917	+	0.610629i	$0.209083\pi$
$283$	2.42686	+	23.0901i	0.144262	+	1.37256i	−0.647655	+	0.761934i	$0.724250\pi$
$284$	−6.71498	−	7.45775i	−0.398461	−	0.442536i
$285$		0			0
$286$	10.0179	−	30.8331i	0.592372	−	1.82320i
$287$	−5.48901			−0.324006
$288$		0			0
$289$	−17.7905	+	12.9255i	−1.04650	+	0.760326i
$290$	−0.226010	+	2.15034i	−0.0132718	+	0.126273i
$291$		0			0
$292$	−14.2071	−	3.01982i	−0.831410	−	0.176722i
$293$	19.1620	−	8.53146i	1.11945	−	0.498413i	0.238276	−	0.971197i	$-0.423418\pi$
$293$	19.1620	−	8.53146i	1.11945	−	0.498413i	0.881178	+	0.472784i	$0.156751\pi$
$294$		0			0
$295$	−3.74429	+	0.795874i	−0.218001	+	0.0463376i
$296$	−2.81121			−0.163398
$297$		0			0
$298$	−9.61284			−0.556857
$299$	−18.5581	+	3.94465i	−1.07324	+	0.228125i
$300$		0			0
$301$	−4.60420	+	2.04992i	−0.265382	+	0.118156i
$302$	−40.4940	−	8.60726i	−2.33017	−	0.495292i
$303$		0			0
$304$	−0.283982	+	2.70191i	−0.0162875	+	0.154965i
$305$	−1.18499	+	0.860949i	−0.0678526	+	0.0492978i
$306$		0			0
$307$	23.1324			1.32024			0.660118	−	0.751162i	$-0.270506\pi$
$307$	23.1324			1.32024			0.660118	+	0.751162i	$0.270506\pi$
$308$	−13.0330	+	9.46921i	−0.742622	+	0.539558i
$309$		0			0
$310$	4.71407	+	5.23550i	0.267741	+	0.297357i
$311$	2.13393	+	20.3030i	0.121004	+	1.15128i	0.871498	+	0.490399i	$0.163149\pi$
$311$	2.13393	+	20.3030i	0.121004	+	1.15128i	−0.750494	+	0.660877i	$0.770184\pi$
$312$		0			0
$313$	−22.7768	+	25.2962i	−1.28742	+	1.42982i	−0.440816	+	0.897597i	$0.645311\pi$
$313$	−22.7768	+	25.2962i	−1.28742	+	1.42982i	−0.846602	+	0.532226i	$0.821356\pi$
$314$	1.45182	+	4.46825i	0.0819311	+	0.252158i
$315$		0			0
$316$	9.36904	−	6.80701i	0.527050	−	0.382924i
$317$	−26.8212	+	5.70102i	−1.50643	+	0.320201i	−0.885861	−	0.463951i	$-0.846431\pi$
$317$	−26.8212	+	5.70102i	−1.50643	+	0.320201i	−0.620568	+	0.784152i	$0.713098\pi$
$318$		0			0
$319$	−9.50029	+	2.01945i	−0.531914	+	0.113068i
$320$	1.97312	−	3.41755i	0.110301	−	0.191047i
$321$		0			0
$322$	13.6431	+	6.07430i	0.760301	+	0.338508i
$323$	−15.6494	−	11.3699i	−0.870754	−	0.632640i
$324$		0			0
$325$	−6.35443	−	19.5569i	−0.352480	−	1.08482i
$326$	−0.384748	+	3.66064i	−0.0213092	+	0.202744i
$327$		0			0
$328$	−8.58884	−	9.53887i	−0.474239	−	0.526696i
$329$	5.28459	−	9.15318i	0.291349	−	0.504631i
$330$		0			0
$331$	8.98622	+	15.5646i	0.493927	+	0.855507i	0.999976	−	0.00699827i	$-0.00222764\pi$
$331$	8.98622	+	15.5646i	0.493927	+	0.855507i	−0.506048	+	0.862505i	$0.668894\pi$
$332$	14.2718	−	43.9241i	0.783266	−	2.41065i
$333$		0			0
$334$	−28.8690	−	20.9746i	−1.57964	−	1.14768i
$335$	2.11443	−	2.34831i	0.115524	−	0.128302i
$336$		0			0
$337$	10.0236	−	4.46277i	0.546018	−	0.243103i	−0.115141	−	0.993349i	$-0.536732\pi$
$337$	10.0236	−	4.46277i	0.546018	−	0.243103i	0.661158	+	0.750246i	$0.270065\pi$
$338$	1.12354	+	10.6897i	0.0611123	+	0.581445i
$339$		0			0
$340$	−3.38922	−	5.87031i	−0.183806	−	0.318362i
$341$	−15.8229	+	27.4068i	−0.856860	+	1.48416i
$342$		0			0
$343$	5.25475	−	16.1724i	0.283730	−	0.873230i
$344$	−10.7667	−	4.79366i	−0.580503	−	0.258457i
$345$		0			0
$346$	2.24630	+	0.477467i	0.120762	+	0.0256688i
$347$	21.6159	+	4.59460i	1.16040	+	0.246651i	0.747587	−	0.664164i	$-0.231212\pi$
$347$	21.6159	+	4.59460i	1.16040	+	0.246651i	0.412815	+	0.910815i	$0.364546\pi$
$348$		0			0
$349$	−16.8126	−	7.48547i	−0.899960	−	0.400688i	−0.0960068	−	0.995381i	$-0.530607\pi$
$349$	−16.8126	−	7.48547i	−0.899960	−	0.400688i	−0.803953	+	0.594693i	$0.797274\pi$
$350$	−5.00185	+	15.3941i	−0.267360	+	0.822850i
$351$		0			0
$352$	14.8960	+	3.16609i	0.793961	+	0.168753i
$353$	16.5354	+	28.6401i	0.880089	+	1.52436i	0.851241	+	0.524776i	$0.175851\pi$
$353$	16.5354	+	28.6401i	0.880089	+	1.52436i	0.0288486	+	0.999584i	$0.490816\pi$
$354$		0			0
$355$	0.0971158	+	0.923995i	0.00515437	+	0.0490405i
$356$	−8.43820	+	3.75693i	−0.447224	+	0.199117i
$357$		0			0
$358$	−17.4944	+	19.4295i	−0.924606	+	1.02688i
$359$	2.42595	+	1.76256i	0.128037	+	0.0930242i	0.649960	−	0.759968i	$-0.274785\pi$
$359$	2.42595	+	1.76256i	0.128037	+	0.0930242i	−0.521924	+	0.852992i	$0.674785\pi$
$360$		0			0
$361$	−2.90578	+	8.94306i	−0.152936	+	0.470687i
$362$	20.8744	+	36.1555i	1.09713	+	1.90029i
$363$		0			0
$364$	10.1931	−	17.6549i	0.534262	−	0.925370i
$365$	0.899776	+	0.999302i	0.0470964	+	0.0523059i
$366$		0			0
$367$	−0.173774	+	1.65335i	−0.00907095	+	0.0863043i	−0.998121	−	0.0612779i	$-0.980482\pi$
$367$	−0.173774	+	1.65335i	−0.00907095	+	0.0863043i	0.989050	+	0.147582i	$0.0471491\pi$
$368$	1.22508	+	3.77040i	0.0638616	+	0.196546i
$369$		0			0
$370$	0.506234	+	0.367800i	0.0263178	+	0.0191210i
$371$	8.66027	+	3.85580i	0.449619	+	0.200183i
$372$		0			0
$373$	10.7543	−	18.6271i	0.556839	−	0.964473i	−0.440919	−	0.897547i	$-0.645348\pi$
$373$	10.7543	−	18.6271i	0.556839	−	0.964473i	0.997758	−	0.0669259i	$-0.0213191\pi$
$374$	32.2738	−	35.8444i	1.66884	−	1.85347i
$375$		0			0
$376$	24.1755	−	5.13866i	1.24676	−	0.265006i
$377$	9.94346	−	7.22435i	0.512114	−	0.372073i
$378$		0			0
$379$	3.83779	+	11.8115i	0.197134	+	0.606715i	0.999945	+	0.0104822i	$0.00333665\pi$
$379$	3.83779	+	11.8115i	0.197134	+	0.606715i	−0.802811	+	0.596233i	$0.796663\pi$
$380$	2.25022	−	2.49912i	0.115434	−	0.128202i
$381$		0			0
$382$	−3.13753	−	29.8516i	−0.160530	−	1.52734i
$383$	−0.535088	−	0.594276i	−0.0273417	−	0.0303661i	0.729319	−	0.684174i	$-0.239837\pi$
$383$	−0.535088	−	0.594276i	−0.0273417	−	0.0303661i	−0.756661	+	0.653808i	$0.773170\pi$
$384$		0			0
$385$	1.49145		1.54122e-5i	0.0760116		7.85476e-7i
$386$	53.9188			2.74439
$387$		0			0
$388$	14.5646	−	10.5818i	0.739404	−	0.537209i
$389$	−0.181533	+	1.72717i	−0.00920409	+	0.0875711i	−0.998160	−	0.0606416i	$-0.980685\pi$
$389$	−0.181533	+	1.72717i	−0.00920409	+	0.0875711i	0.988956	+	0.148213i	$0.0473520\pi$
$390$		0			0
$391$	−27.6101	−	5.86872i	−1.39631	−	0.296794i
$392$	15.1148	−	6.72954i	0.763413	−	0.339893i
$393$		0			0
$394$	−2.45502	+	0.521832i	−0.123682	+	0.0262895i
$395$	−1.07216			−0.0539461
$396$		0			0
$397$	−24.7599			−1.24267			−0.621333	−	0.783547i	$-0.713409\pi$
$397$	−24.7599			−1.24267			−0.621333	+	0.783547i	$0.713409\pi$
$398$	37.4309	−	7.95619i	1.87624	−	0.398808i
$399$		0			0
$400$	−3.92534	+	1.74767i	−0.196267	+	0.0873836i
$401$	21.3748	+	4.54336i	1.06741	+	0.226884i	0.707939	−	0.706273i	$-0.249625\pi$
$401$	21.3748	+	4.54336i	1.06741	+	0.226884i	0.359468	+	0.933158i	$0.382958\pi$
$402$		0			0
$403$	4.18606	−	39.8277i	0.208523	−	1.98396i
$404$	−26.4000	+	19.1807i	−1.31345	+	0.954278i
$405$		0			0
$406$	−9.67462			−0.480143
$407$	−0.868564	+	2.67326i	−0.0430531	+	0.132509i
$408$		0			0
$409$	5.37631	+	5.97100i	0.265842	+	0.295247i	0.861256	−	0.508172i	$-0.169679\pi$
$409$	5.37631	+	5.97100i	0.265842	+	0.295247i	−0.595414	+	0.803419i	$0.703012\pi$
$410$	0.298647	+	2.84144i	0.0147491	+	0.140329i
$411$		0			0
$412$	21.8487	−	24.2655i	1.07641	−	1.19547i
$413$	−5.29283	−	16.2897i	−0.260443	−	0.801562i
$414$		0			0
$415$	−3.45919	+	2.51325i	−0.169805	+	0.123371i
$416$	−18.8502	+	4.00673i	−0.924207	+	0.196446i
$417$		0			0
$418$	21.8605	+	9.73264i	1.06923	+	0.476039i
$419$	−2.79840	+	4.84698i	−0.136711	+	0.236790i	−0.926250	−	0.376910i	$-0.876986\pi$
$419$	−2.79840	+	4.84698i	−0.136711	+	0.236790i	0.789539	+	0.613701i	$0.210320\pi$
$420$		0			0
$421$	34.5817	+	15.3968i	1.68541	+	0.750392i	0.999747	+	0.0224717i	$0.00715355\pi$
$421$	34.5817	+	15.3968i	1.68541	+	0.750392i	0.685661	+	0.727921i	$0.259513\pi$
$422$	−28.1684	−	20.4656i	−1.37122	−	0.996248i
$423$		0			0
$424$	6.85035	+	21.0832i	0.332682	+	1.02389i
$425$	3.19789	−	30.4259i	0.155121	−	1.47587i
$426$		0			0
$427$	−4.38541	−	4.87049i	−0.212225	−	0.235699i
$428$	8.85614	−	15.3393i	0.428078	−	0.741452i
$429$		0			0
$430$	1.31167	+	2.27187i	0.0632542	+	0.109560i
$431$	9.20389	−	28.3267i	0.443336	−	1.36445i	−0.440963	−	0.897525i	$-0.645363\pi$
$431$	9.20389	−	28.3267i	0.443336	−	1.36445i	0.884299	−	0.466922i	$-0.154637\pi$
$432$		0			0
$433$	0.225935	+	0.164152i	0.0108578	+	0.00788862i	0.593201	−	0.805054i	$-0.297864\pi$
$433$	0.225935	+	0.164152i	0.0108578	+	0.00788862i	−0.582343	+	0.812943i	$0.697864\pi$
$434$	−21.0929	+	23.4260i	−1.01249	+	1.12449i
$435$		0			0
$436$	45.2860	−	20.1626i	2.16881	−	0.965615i
$437$	−1.46380	−	13.9271i	−0.0700231	−	0.666225i
$438$		0			0
$439$	−7.49827	−	12.9874i	−0.357873	−	0.619854i	0.629732	−	0.776812i	$-0.283165\pi$
$439$	−7.49827	−	12.9874i	−0.357873	−	0.619854i	−0.987605	+	0.156958i	$0.949831\pi$
$440$	2.33375	+	2.59184i	0.111257	+	0.123561i
$441$		0			0
$442$	−18.8614	+	58.0493i	−0.897143	+	2.76112i
$443$	−13.2462	−	5.89760i	−0.629348	−	0.280204i	0.0671719	−	0.997741i	$-0.478602\pi$
$443$	−13.2462	−	5.89760i	−0.629348	−	0.280204i	−0.696520	+	0.717538i	$0.745269\pi$
$444$		0			0
$445$	0.836459	+	0.177795i	0.0396520	+	0.00842829i
$446$	4.38827	+	0.932755i	0.207791	+	0.0441672i
$447$		0			0
$448$	16.1308	+	7.18188i	0.762107	+	0.339312i
$449$	6.55787	−	20.1830i	0.309485	−	0.952497i	−0.668481	−	0.743730i	$-0.733055\pi$
$449$	6.55787	−	20.1830i	0.309485	−	0.952497i	0.977965	−	0.208767i	$-0.0669450\pi$
$450$		0			0
$451$	−11.7244	+	5.22020i	−0.552082	+	0.245809i
$452$	−12.7238	−	22.0383i	−0.598479	−	1.03660i
$453$		0			0
$454$	3.89785	+	37.0856i	0.182935	+	1.74051i
$455$	−1.72420	+	0.767661i	−0.0808315	+	0.0359885i
$456$		0			0
$457$	−2.14758	+	2.38512i	−0.100459	+	0.111571i	−0.791278	−	0.611457i	$-0.790584\pi$
$457$	−2.14758	+	2.38512i	−0.100459	+	0.111571i	0.690818	+	0.723028i	$0.257250\pi$
$458$	−0.985297	−	0.715860i	−0.0460399	−	0.0334499i
$459$		0			0
$460$	1.51642	−	4.66707i	0.0707037	−	0.217603i
$461$	13.1628	+	22.7986i	0.613052	+	1.06184i	0.990723	+	0.135897i	$0.0433918\pi$
$461$	13.1628	+	22.7986i	0.613052	+	1.06184i	−0.377671	+	0.925940i	$0.623275\pi$
$462$		0			0
$463$	−1.81412	+	3.14215i	−0.0843093	+	0.146028i	−0.905097	−	0.425206i	$-0.860202\pi$
$463$	−1.81412	+	3.14215i	−0.0843093	+	0.146028i	0.820787	+	0.571234i	$0.193535\pi$
$464$	−1.71847	−	1.90856i	−0.0797782	−	0.0886027i
$465$		0			0
$466$	2.49595	−	23.7473i	0.115622	−	1.10007i
$467$	5.71532	+	17.5899i	0.264473	+	0.813965i	0.991814	+	0.127689i	$0.0407559\pi$
$467$	5.71532	+	17.5899i	0.264473	+	0.813965i	−0.727341	+	0.686276i	$0.759244\pi$
$468$		0			0
$469$	11.4388	+	8.31077i	0.528194	+	0.383756i
$470$	−5.02575	−	2.23761i	−0.231821	−	0.103213i
$471$		0			0
$472$	20.0265	−	34.6869i	0.921795	−	1.59660i
$473$	−7.88496	+	8.75732i	−0.362551	+	0.402662i
$474$		0			0
$475$	14.8463	−	3.15567i	0.681193	−	0.144792i
$476$	24.5374	−	17.8275i	1.12467	−	0.817120i
$477$		0			0
$478$	−6.93867	−	21.3550i	−0.317367	−	0.976756i
$479$	0.105052	−	0.116672i	0.00479996	−	0.00533090i	−0.740740	−	0.671792i	$-0.765525\pi$
$479$	0.105052	−	0.116672i	0.00479996	−	0.00533090i	0.745540	+	0.666461i	$0.232192\pi$
$480$		0			0
$481$	−0.371804	−	3.53748i	−0.0169528	−	0.161295i
$482$	0.434376	+	0.482424i	0.0197853	+	0.0219738i
$483$		0			0
$484$	−18.8327	+	32.6208i	−0.856032	+	1.48276i
$485$	−1.66671			−0.0756816
$486$		0			0
$487$	−14.5028	+	10.5369i	−0.657187	+	0.477474i	−0.865712	−	0.500543i	$-0.833134\pi$
$487$	−14.5028	+	10.5369i	−0.657187	+	0.477474i	0.208525	+	0.978017i	$0.433134\pi$
$488$	1.60200	−	15.2420i	0.0725192	−	0.689974i
$489$		0			0
$490$	−3.60227	−	0.765687i	−0.162734	−	0.0345902i
$491$	6.07322	−	2.70397i	0.274081	−	0.122029i	−0.265094	−	0.964223i	$-0.585403\pi$
$491$	6.07322	−	2.70397i	0.274081	−	0.122029i	0.539175	+	0.842194i	$0.318736\pi$
$492$		0			0
$493$	17.8863	−	3.80184i	0.805557	−	0.171226i
$494$	−30.2813			−1.36242
$495$		0			0
$496$	−8.36804			−0.375736
$497$	−4.06631	+	0.864320i	−0.182399	+	0.0387701i
$498$		0			0
$499$	31.0124	−	13.8076i	1.38831	−	0.618114i	0.429733	−	0.902956i	$-0.358608\pi$
$499$	31.0124	−	13.8076i	1.38831	−	0.618114i	0.958575	+	0.284842i	$0.0919411\pi$
$500$	10.5116	+	2.23431i	0.470094	+	0.0999216i
$501$		0			0
$502$	−1.07735	+	10.2503i	−0.0480846	+	0.457494i
$503$	2.53812	−	1.84405i	0.113169	−	0.0822222i	−0.529761	−	0.848147i	$-0.677718\pi$
$503$	2.53812	−	1.84405i	0.113169	−	0.0822222i	0.642930	+	0.765925i	$0.277718\pi$
$504$		0			0
$505$	3.02112			0.134438
$506$	34.9183		0.000360833i	1.55231		1.60410e-5i
$507$		0			0
$508$	−30.2550	−	33.6015i	−1.34235	−	1.49083i
$509$	2.38361	+	22.6786i	0.105652	+	1.00521i	0.910999	+	0.412407i	$0.135312\pi$
$509$	2.38361	+	22.6786i	0.105652	+	1.00521i	−0.805348	+	0.592803i	$0.798021\pi$
$510$		0			0
$511$	−4.02601	+	4.47134i	−0.178100	+	0.197800i
$512$	3.04225	+	9.36310i	0.134450	+	0.413794i
$513$		0			0
$514$	−6.88586	+	5.00287i	−0.303722	+	0.220667i
$515$	−2.95693	+	0.628514i	−0.130298	+	0.0276956i
$516$		0			0
$517$	2.58287	−	24.5768i	0.113595	−	1.08089i
$518$	−1.39992	+	2.42474i	−0.0615090	+	0.106537i
$519$		0			0
$520$	−4.03196	−	1.79514i	−0.176813	−	0.0787222i
$521$	4.26200	+	3.09653i	0.186722	+	0.135661i	0.677219	−	0.735781i	$-0.263185\pi$
$521$	4.26200	+	3.09653i	0.186722	+	0.135661i	−0.490497	+	0.871443i	$0.663185\pi$
$522$		0			0
$523$	3.67595	+	11.3134i	0.160738	+	0.494701i	0.998697	−	0.0510325i	$-0.0162512\pi$
$523$	3.67595	+	11.3134i	0.160738	+	0.494701i	−0.837959	+	0.545733i	$0.816251\pi$
$524$	−2.61305	+	24.8616i	−0.114152	+	1.08608i
$525$		0			0
$526$	−22.5227	−	25.0140i	−0.982038	−	1.09066i
$527$	29.7904	−	51.5985i	1.29769	−	2.24767i
$528$		0			0
$529$	1.28255	+	2.22144i	0.0557629	+	0.0965843i
$530$	1.52480	−	4.69285i	0.0662331	−	0.203845i
$531$		0			0
$532$	12.1734	+	8.84448i	0.527783	+	0.383457i
$533$	10.8673	−	12.0693i	0.470714	−	0.522781i
$534$		0			0
$535$	−1.49805	+	0.666974i	−0.0647663	+	0.0288358i
$536$	3.45610	+	32.8826i	0.149281	+	1.42031i
$537$		0			0
$538$	−1.06872	−	1.85108i	−0.0460757	−	0.0798055i
$539$	−1.72938	−	16.4523i	−0.0744895	−	0.708650i
$540$		0			0
$541$	12.5401	−	38.5945i	0.539142	−	1.65931i	−0.195383	−	0.980727i	$-0.562595\pi$
$541$	12.5401	−	38.5945i	0.539142	−	1.65931i	0.734525	−	0.678581i	$-0.237405\pi$
$542$	5.62594	+	2.50483i	0.241655	+	0.107592i
$543$		0			0
$544$	−28.0447	−	5.96109i	−1.20241	−	0.255580i
$545$	−4.48910	−	0.954188i	−0.192292	−	0.0408729i
$546$		0			0
$547$	21.4997	+	9.57226i	0.919259	+	0.409280i	0.811136	−	0.584857i	$-0.198849\pi$
$547$	21.4997	+	9.57226i	0.919259	+	0.409280i	0.108123	+	0.994138i	$0.465516\pi$
$548$	−10.3776	+	31.9391i	−0.443311	+	1.36437i
$549$		0			0
$550$	3.95635	+	37.6384i	0.168699	+	1.60491i
$551$	4.53595	+	7.85650i	0.193238	+	0.334698i
$552$		0			0
$553$	−0.501457	−	4.77104i	−0.0213241	−	0.202885i
$554$	−61.4986	+	27.3810i	−2.61283	+	1.16331i
$555$		0			0
$556$	−21.7141	+	24.1160i	−0.920884	+	1.02275i
$557$	−5.08590	−	3.69513i	−0.215497	−	0.156568i	0.474800	−	0.880093i	$-0.342520\pi$
$557$	−5.08590	−	3.69513i	−0.215497	−	0.156568i	−0.690297	+	0.723526i	$0.742520\pi$
$558$		0			0
$559$	4.60811	−	14.1823i	0.194902	−	0.599847i
$560$	0.197187	+	0.341538i	0.00833268	+	0.0144326i
$561$		0			0
$562$	−10.1807	+	17.6335i	−0.429448	+	0.743826i
$563$	11.3527	+	12.6085i	0.478461	+	0.531385i	0.933256	−	0.359211i	$-0.116954\pi$
$563$	11.3527	+	12.6085i	0.478461	+	0.531385i	−0.454795	+	0.890596i	$0.650288\pi$
$564$		0			0
$565$	−0.246266	+	2.34306i	−0.0103605	+	0.0985734i
$566$	16.7095	+	51.4265i	0.702352	+	2.16162i
$567$		0			0
$568$	−7.86471	−	5.71404i	−0.329996	−	0.239756i
$569$	−20.3268	−	9.05009i	−0.852146	−	0.379400i	−0.0662831	−	0.997801i	$-0.521114\pi$
$569$	−20.3268	−	9.05009i	−0.852146	−	0.379400i	−0.785863	+	0.618401i	$0.787781\pi$
$570$		0			0
$571$	−17.6576	+	30.5838i	−0.738947	+	1.27989i	0.214023	+	0.976829i	$0.431343\pi$
$571$	−17.6576	+	30.5838i	−0.738947	+	1.27989i	−0.952970	+	0.303065i	$0.901990\pi$
$572$	4.98192	−	47.4045i	0.208304	−	1.98208i
$573$		0			0
$574$	−12.5046	+	2.65793i	−0.521930	+	0.110940i
$575$	17.9182	−	13.0184i	0.747243	−	0.542904i
$576$		0			0
$577$	−11.8156	−	36.3646i	−0.491889	−	1.51388i	−0.821749	−	0.569850i	$-0.807001\pi$
$577$	−11.8156	−	36.3646i	−0.491889	−	1.51388i	0.329859	−	0.944030i	$-0.392999\pi$
$578$	−34.2697	+	38.0604i	−1.42543	+	1.58310i
$579$		0			0
$580$	0.332295	+	3.16158i	0.0137978	+	0.131277i
$581$	−12.8017	−	14.2178i	−0.531105	−	0.589852i
$582$		0			0
$583$	22.1651		0.000229047i	0.917986		9.48614e-6i
$584$	−14.0700			−0.582219
$585$		0			0
$586$	39.5219	−	28.7143i	1.63263	−	1.18618i
$587$	−1.29507	+	12.3218i	−0.0534533	+	0.508574i	0.934737	+	0.355341i	$0.115635\pi$
$587$	−1.29507	+	12.3218i	−0.0534533	+	0.508574i	−0.988190	+	0.153233i	$0.951031\pi$
$588$		0			0
$589$	28.9131	+	6.14566i	1.19134	+	0.253228i
$590$	−8.14452	+	3.62617i	−0.335305	+	0.149287i
$591$		0			0
$592$	−0.727003	+	0.154529i	−0.0298797	+	0.00635112i
$593$	−4.18039			−0.171668			−0.0858340	−	0.996309i	$-0.527355\pi$
$593$	−4.18039			−0.171668			−0.0858340	+	0.996309i	$0.527355\pi$
$594$		0			0
$595$	−2.80796			−0.115115
$596$	−13.8246	+	2.93850i	−0.566276	+	0.120366i
$597$		0			0
$598$	−40.3672	+	17.9727i	−1.65074	+	0.734957i
$599$	−43.1155	−	9.16449i	−1.76165	−	0.374451i	−0.790417	−	0.612570i	$-0.790136\pi$
$599$	−43.1155	−	9.16449i	−1.76165	−	0.374451i	−0.971236	+	0.238119i	$0.923469\pi$
$600$		0			0
$601$	0.183062	−	1.74172i	0.00746727	−	0.0710463i	−0.990154	−	0.139985i	$-0.955295\pi$
$601$	0.183062	−	1.74172i	0.00746727	−	0.0710463i	0.997621	+	0.0689386i	$0.0219613\pi$
$602$	−9.49624	+	6.89943i	−0.387038	+	0.281200i
$603$		0			0
$604$	−60.8670			−2.47664
$605$	3.18570	−	1.41845i	0.129517	−	0.0576680i
$606$		0			0
$607$	−7.27288	−	8.07735i	−0.295197	−	0.327850i	0.577241	−	0.816574i	$-0.304129\pi$
$607$	−7.27288	−	8.07735i	−0.295197	−	0.327850i	−0.872438	+	0.488724i	$0.837462\pi$
$608$	−1.48684	−	14.1464i	−0.0602994	−	0.573710i
$609$		0			0
$610$	−2.28265	+	2.53514i	−0.0924218	+	0.102645i
$611$	9.66362	+	29.7416i	0.390948	+	1.20321i
$612$		0			0
$613$	−14.3951	+	10.4586i	−0.581412	+	0.422421i	−0.839233	−	0.543772i	$-0.816996\pi$
$613$	−14.3951	+	10.4586i	−0.581412	+	0.422421i	0.257821	+	0.966193i	$0.416996\pi$
$614$	52.6981	−	11.2013i	2.12672	−	0.452049i
$615$		0			0
$616$	−10.4420	+	11.5973i	−0.420722	+	0.467269i
$617$	1.99805	−	3.46073i	0.0804386	−	0.139324i	−0.823000	−	0.568042i	$-0.807701\pi$
$617$	1.99805	−	3.46073i	0.0804386	−	0.139324i	0.903438	+	0.428718i	$0.141035\pi$
$618$		0			0
$619$	−10.0265	−	4.46409i	−0.403000	−	0.179427i	0.195220	−	0.980760i	$-0.437458\pi$
$619$	−10.0265	−	4.46409i	−0.403000	−	0.179427i	−0.598219	+	0.801333i	$0.704125\pi$
$620$	8.37989	+	6.08835i	0.336544	+	0.244514i
$621$		0			0
$622$	14.6926	+	45.2191i	0.589118	+	1.81312i
$623$	−0.399959	+	3.80536i	−0.0160240	+	0.152458i
$624$		0			0
$625$	15.7263	+	17.4658i	0.629052	+	0.698633i
$626$	−39.6388	+	68.6565i	−1.58429	+	2.74407i
$627$		0			0
$628$	3.45380	+	5.98216i	0.137822	+	0.238714i
$629$	1.63530	−	5.03293i	0.0652037	−	0.200676i
$630$		0			0
$631$	−6.99735	−	5.08388i	−0.278560	−	0.202386i	0.439729	−	0.898131i	$-0.355075\pi$
$631$	−6.99735	−	5.08388i	−0.278560	−	0.202386i	−0.718289	+	0.695745i	$0.755075\pi$
$632$	7.50653	−	8.33685i	0.298594	−	0.331622i
$633$		0			0
$634$	−58.3410	+	25.9751i	−2.31702	+	1.03160i
$635$	0.437564	+	4.16314i	0.0173642	+	0.165209i
$636$		0			0
$637$	10.4672	+	18.1296i	0.414724	+	0.718323i
$638$	−20.6648	+	9.20082i	−0.818128	+	0.364264i
$639$		0			0
$640$	1.94048	−	5.97219i	0.0767042	−	0.236071i
$641$	−33.8812	−	15.0849i	−1.33823	−	0.595817i	−0.392193	−	0.919883i	$-0.628283\pi$
$641$	−33.8812	−	15.0849i	−1.33823	−	0.595817i	−0.946035	+	0.324066i	$0.894950\pi$
$642$		0			0
$643$	39.8425	+	8.46878i	1.57123	+	0.333976i	0.909481	−	0.415746i	$-0.136479\pi$
$643$	39.8425	+	8.46878i	1.57123	+	0.333976i	0.661753	+	0.749722i	$0.269813\pi$
$644$	21.4775	+	4.56518i	0.846331	+	0.179893i
$645$		0			0
$646$	−41.1566	−	18.3241i	−1.61928	−	0.720952i
$647$	0.175813	−	0.541098i	0.00691193	−	0.0212727i	−0.947541	−	0.319634i	$-0.896440\pi$
$647$	0.175813	−	0.541098i	0.00691193	−	0.0212727i	0.954453	+	0.298361i	$0.0964400\pi$
$648$		0			0
$649$	−26.7973	−	29.7608i	−1.05189	−	1.16821i
$650$	−23.9461	−	41.4758i	−0.939242	−	1.62682i
$651$		0			0
$652$	0.565682	+	5.38211i	0.0221538	+	0.210780i
$653$	33.3696	−	14.8571i	1.30585	−	0.581404i	0.368450	−	0.929648i	$-0.379889\pi$
$653$	33.3696	−	14.8571i	1.30585	−	0.581404i	0.937404	+	0.348244i	$0.113222\pi$
$654$		0			0
$655$	1.54862	−	1.71992i	0.0605097	−	0.0672029i
$656$	−2.74549	−	1.99472i	−0.107193	−	0.0778806i
$657$		0			0
$658$	7.60666	−	23.4109i	0.296538	−	0.912651i
$659$	−12.0035	−	20.7907i	−0.467590	−	0.809889i	0.531725	−	0.846917i	$-0.321544\pi$
$659$	−12.0035	−	20.7907i	−0.467590	−	0.809889i	−0.999314	+	0.0370284i	$0.988211\pi$
$660$		0			0
$661$	−6.49165	+	11.2439i	−0.252496	+	0.437336i	−0.964212	−	0.265131i	$-0.914585\pi$
$661$	−6.49165	+	11.2439i	−0.252496	+	0.437336i	0.711717	+	0.702467i	$0.247918\pi$
$662$	28.0084	+	31.1064i	1.08858	+	1.20899i
$663$		0			0
$664$	4.67651	−	44.4940i	0.181484	−	1.72670i
$665$	−0.430484	−	1.32489i	−0.0166935	−	0.0513772i
$666$		0			0
$667$	10.7098	+	7.78112i	0.414685	+	0.301286i
$668$	−47.9293	−	21.3395i	−1.85444	−	0.825649i
$669$		0			0
$670$	3.67978	−	6.37356i	0.142162	−	0.246232i
$671$	−13.9991	−	6.23263i	−0.540430	−	0.240608i
$672$		0			0
$673$	−16.6536	+	3.53983i	−0.641949	+	0.136451i	−0.517374	−	0.855760i	$-0.673090\pi$
$673$	−16.6536	+	3.53983i	−0.641949	+	0.136451i	−0.124576	+	0.992210i	$0.539757\pi$
$674$	20.6737	−	15.0204i	0.796323	−	0.578562i
$675$		0			0
$676$	4.88349	+	15.0298i	0.187827	+	0.578071i
$677$	23.7084	−	26.3308i	0.911187	−	1.01198i	−0.0886859	−	0.996060i	$-0.528267\pi$
$677$	23.7084	−	26.3308i	0.911187	−	1.01198i	0.999873	−	0.0159165i	$-0.00506658\pi$
$678$		0			0
$679$	−0.779536	−	7.41679i	−0.0299158	−	0.284630i
$680$	−4.39371	−	4.87971i	−0.168491	−	0.187128i
$681$		0			0
$682$	−22.7753	+	70.0975i	−0.872110	+	2.68417i
$683$	−23.8967			−0.914381			−0.457191	−	0.889369i	$-0.651144\pi$
$683$	−23.8967			−0.914381			−0.457191	+	0.889369i	$0.651144\pi$
$684$		0			0
$685$	2.51533	−	1.82749i	0.0961058	−	0.0698250i
$686$	4.13975	−	39.3871i	0.158056	−	1.50381i
$687$		0			0
$688$	−3.04787	−	0.647845i	−0.116199	−	0.0246989i
$689$	−25.6240	+	11.4085i	−0.976197	+	0.434631i
$690$		0			0
$691$	0.579665	−	0.123212i	0.0220515	−	0.00468719i	−0.196873	−	0.980429i	$-0.563079\pi$
$691$	0.579665	−	0.123212i	0.0220515	−	0.00468719i	0.218924	+	0.975742i	$0.429745\pi$
$692$	3.37645			0.128353
$693$		0			0
$694$	51.4682			1.95371
$695$	2.93871	−	0.624643i	0.111472	−	0.0236940i
$696$		0			0
$697$	22.0737	−	9.82785i	0.836101	−	0.372256i
$698$	−41.9257	−	8.91158i	−1.58691	−	0.337308i
$699$		0			0
$700$	−2.48759	+	23.6678i	−0.0940221	+	0.894560i
$701$	−20.5701	+	14.9451i	−0.776922	+	0.564467i	−0.904054	−	0.427419i	$-0.859423\pi$
$701$	−20.5701	+	14.9451i	−0.776922	+	0.564467i	0.127131	+	0.991886i	$0.459423\pi$
$702$		0			0
$703$	2.62542			0.0990194
$704$	41.2852		0.000426626i	1.55599		1.60791e-5i
$705$		0			0
$706$	51.5377	+	57.2384i	1.93965	+	2.15420i
$707$	1.41300	+	13.4438i	0.0531414	+	0.505607i
$708$		0			0
$709$	10.1070	−	11.2250i	0.379576	−	0.421562i	−0.522838	−	0.852432i	$-0.675127\pi$
$709$	10.1070	−	11.2250i	0.379576	−	0.421562i	0.902414	+	0.430870i	$0.141793\pi$
$710$	0.668663	+	2.05793i	0.0250945	+	0.0772329i
$711$		0			0
$712$	−7.23882	+	5.25931i	−0.271286	+	0.197101i
$713$	42.1909	−	8.96796i	1.58006	−	0.335853i
$714$		0			0
$715$	−2.95278	+	3.27947i	−0.110428	+	0.122645i
$716$	−19.2200	+	33.2900i	−0.718284	+	1.24410i
$717$		0			0
$718$	6.38005	+	2.84058i	0.238101	+	0.106010i
$719$	9.74281	+	7.07857i	0.363345	+	0.263986i	0.754446	−	0.656362i	$-0.227906\pi$
$719$	9.74281	+	7.07857i	0.363345	+	0.263986i	−0.391101	+	0.920348i	$0.627906\pi$
$720$		0			0
$721$	−4.17983	−	12.8642i	−0.155665	−	0.479088i
$722$	−2.28920	+	21.7803i	−0.0851953	+	0.810579i
$723$		0			0
$724$	41.0725	+	45.6156i	1.52645	+	1.69529i
$725$	−7.17396	+	12.4257i	−0.266434	+	0.461477i
$726$		0			0
$727$	−24.7966	−	42.9489i	−0.919654	−	1.59289i	−0.799940	−	0.600079i	$-0.795136\pi$
$727$	−24.7966	−	42.9489i	−0.919654	−	1.59289i	−0.119714	−	0.992808i	$-0.538198\pi$
$728$	6.10251	−	18.7816i	0.226174	−	0.696092i
$729$		0			0
$730$	2.53368	+	1.84082i	0.0937755	+	0.0681319i
$731$	14.8452	−	16.4873i	0.549070	−	0.609804i
$732$		0			0
$733$	−29.4759	+	13.1235i	−1.08872	+	0.484728i	−0.871000	−	0.491284i	$-0.836528\pi$
$733$	−29.4759	+	13.1235i	−1.08872	+	0.484728i	−0.217717	+	0.976012i	$0.569861\pi$
$734$	0.404721	+	3.85066i	0.0149385	+	0.142131i
$735$		0			0
$736$	−10.3783	−	17.9757i	−0.382548	−	0.662593i
$737$	32.3368	+	6.87305i	1.19114	+	0.253172i
$738$		0			0
$739$	−0.968005	+	2.97921i	−0.0356086	+	0.109592i	−0.967281	−	0.253708i	$-0.918350\pi$
$739$	−0.968005	+	2.97921i	−0.0356086	+	0.109592i	0.931672	+	0.363300i	$0.118350\pi$
$740$	0.840464	+	0.374199i	0.0308961	+	0.0137558i
$741$		0			0
$742$	21.5961	+	4.59040i	0.792818	+	0.168519i
$743$	7.61856	+	1.61938i	0.279498	+	0.0594091i	0.345528	−	0.938409i	$-0.387700\pi$
$743$	7.61856	+	1.61938i	0.279498	+	0.0594091i	−0.0660298	+	0.997818i	$0.521033\pi$
$744$		0			0
$745$	1.19536	+	0.532208i	0.0437946	+	0.0194986i
$746$	15.4798	−	47.6420i	0.566756	−	1.74430i
$747$		0			0
$748$	35.4570	−	61.4148i	1.29644	−	2.24555i
$749$	−3.66865	−	6.35428i	−0.134049	−	0.232180i
$750$		0			0
$751$	−5.19392	−	49.4168i	−0.189529	−	1.80325i	−0.514467	−	0.857510i	$-0.672010\pi$
$751$	−5.19392	−	49.4168i	−0.189529	−	1.80325i	0.324938	−	0.945735i	$-0.394656\pi$
$752$	5.96953	−	2.65780i	0.217686	−	0.0969201i
$753$		0			0
$754$	19.1541	−	21.2727i	0.697549	−	0.774707i
$755$	4.55890	+	3.31224i	0.165915	+	0.120545i
$756$		0			0
$757$	−8.35296	+	25.7078i	−0.303594	+	0.934365i	0.676605	+	0.736346i	$0.263451\pi$
$757$	−8.35296	+	25.7078i	−0.303594	+	0.934365i	−0.980198	+	0.198018i	$0.936549\pi$
$758$	14.4623	+	25.0495i	0.525295	+	0.909838i
$759$		0			0
$760$	1.62882	−	2.82121i	0.0590836	−	0.102336i
$761$	−29.7834	−	33.0778i	−1.07965	−	1.19907i	−0.978939	−	0.204153i	$-0.934556\pi$
$761$	−29.7834	−	33.0778i	−1.07965	−	1.19907i	−0.100707	−	0.994916i	$-0.532111\pi$
$762$		0			0
$763$	2.14650	−	20.4226i	0.0777084	−	0.739346i
$764$	−13.6374	−	41.9716i	−0.493384	−	1.51848i
$765$		0			0
$766$	−1.50675	−	1.09472i	−0.0544412	−	0.0395538i
$767$	46.2969	+	20.6127i	1.67168	+	0.744282i
$768$		0			0
$769$	1.65952	−	2.87438i	0.0598440	−	0.103653i	−0.834551	−	0.550930i	$-0.814273\pi$
$769$	1.65952	−	2.87438i	0.0598440	−	0.103653i	0.894395	+	0.447277i	$0.147606\pi$
$770$	3.39769	−	0.722237i	0.122444	−	0.0260276i
$771$		0			0
$772$	77.5426	−	16.4822i	2.79082	−	0.593207i
$773$	23.0471	−	16.7447i	0.828946	−	0.602264i	−0.0903152	−	0.995913i	$-0.528787\pi$
$773$	23.0471	−	16.7447i	0.828946	−	0.602264i	0.919261	+	0.393649i	$0.128787\pi$
$774$		0			0
$775$	14.4465	+	44.4617i	0.518934	+	1.59711i
$776$	11.6692	−	12.9600i	0.418901	−	0.465236i
$777$		0			0
$778$	0.422791	+	4.02259i	0.0151578	+	0.144217i
$779$	8.02120	+	8.90844i	0.287389	+	0.319178i
$780$		0			0
$781$	−7.86356	+	5.71334i	−0.281380	+	0.204439i
$782$	−65.7407			−2.35088
$783$		0			0
$784$	3.53890	−	2.57116i	0.126389	−	0.0918273i
$785$	0.0668471	−	0.636008i	0.00238588	−	0.0227001i
$786$		0			0
$787$	−12.7636	−	2.71298i	−0.454972	−	0.0967072i	−0.0252751	−	0.999681i	$-0.508046\pi$
$787$	−12.7636	−	2.71298i	−0.454972	−	0.0967072i	−0.429697	+	0.902973i	$0.641379\pi$
$788$	−3.37114	+	1.50093i	−0.120092	+	0.0534684i
$789$		0			0
$790$	−2.44249	+	0.519167i	−0.0868999	+	0.0184711i
$791$	−10.5417			−0.374819
$792$		0			0
$793$	19.3917			0.688618
$794$	−56.4058	+	11.9894i	−2.00177	+	0.425489i
$795$		0			0
$796$	51.3987	−	22.8842i	1.82178	−	0.811108i
$797$	49.0769	+	10.4316i	1.73839	+	0.369507i	0.964556	−	0.263877i	$-0.0850012\pi$
$797$	49.0769	+	10.4316i	1.73839	+	0.369507i	0.773838	+	0.633384i	$0.218334\pi$
$798$		0			0
$799$	−4.86326	+	46.2708i	−0.172050	+	1.63694i
$800$	18.2003	−	13.2233i	0.643477	−	0.467514i
$801$		0			0
$802$	50.8941			1.79713
$803$	−4.34712	+	13.3795i	−0.153407	+	0.472154i
$804$		0			0
$805$	−1.36023	−	1.51068i	−0.0479416	−	0.0532446i
$806$	−9.74935	−	92.7589i	−0.343406	−	3.26729i
$807$		0			0
$808$	−21.1519	+	23.4915i	−0.744120	+	0.826429i
$809$	10.8621	+	33.4301i	0.381892	+	1.17534i	0.938710	+	0.344707i	$0.112022\pi$
$809$	10.8621	+	33.4301i	0.381892	+	1.17534i	−0.556819	+	0.830634i	$0.687978\pi$
$810$		0			0
$811$	−17.8837	+	12.9933i	−0.627981	+	0.456255i	−0.855700	−	0.517472i	$-0.826873\pi$
$811$	−17.8837	+	12.9933i	−0.627981	+	0.456255i	0.227719	+	0.973727i	$0.426873\pi$
$812$	−13.9134	+	2.95739i	−0.488266	+	0.103784i
$813$		0			0
$814$	−0.684219	+	6.51055i	−0.0239819	+	0.228195i
$815$	0.250512	−	0.433900i	0.00877506	−	0.0151989i
$816$		0			0
$817$	10.0552	+	4.47684i	0.351785	+	0.156625i
$818$	15.1391	+	10.9992i	0.529327	+	0.384579i
$819$		0			0
$820$	1.29808	+	3.99508i	0.0453309	+	0.139514i
$821$	0.265209	−	2.52330i	0.00925587	−	0.0880637i	−0.988919	−	0.148458i	$-0.952569\pi$
$821$	0.265209	−	2.52330i	0.00925587	−	0.0880637i	0.998175	+	0.0603941i	$0.0192357\pi$
$822$		0			0
$823$	−6.94069	−	7.70841i	−0.241937	−	0.268698i	0.609931	−	0.792454i	$-0.291197\pi$
$823$	−6.94069	−	7.70841i	−0.241937	−	0.268698i	−0.851868	+	0.523756i	$0.824530\pi$
$824$	15.8152	−	27.3928i	0.550950	−	0.954273i
$825$		0			0
$826$	−19.9455	−	34.5467i	−0.693994	−	1.20203i
$827$	−16.2925	+	50.1431i	−0.566546	+	1.74365i	0.0967683	+	0.995307i	$0.469149\pi$
$827$	−16.2925	+	50.1431i	−0.566546	+	1.74365i	−0.663314	+	0.748341i	$0.730851\pi$
$828$		0			0
$829$	−30.6163	−	22.2440i	−1.06335	−	0.772566i	−0.0886419	−	0.996064i	$-0.528253\pi$
$829$	−30.6163	−	22.2440i	−1.06335	−	0.772566i	−0.974705	+	0.223497i	$0.928253\pi$
$830$	−6.66343	+	7.40049i	−0.231291	+	0.256875i
$831$		0			0
$832$	−47.7277	+	21.2497i	−1.65466	+	0.736703i
$833$	3.25558	+	30.9748i	0.112799	+	1.07321i
$834$		0			0
$835$	2.42863	+	4.20651i	0.0840462	+	0.145572i
$836$	34.4135	+	7.31444i	1.19021	+	0.252975i
$837$		0			0
$838$	−4.02803	+	12.3970i	−0.139146	+	0.428247i
$839$	18.3765	+	8.18173i	0.634426	+	0.282465i	0.698642	−	0.715471i	$-0.253788\pi$
$839$	18.3765	+	8.18173i	0.634426	+	0.282465i	−0.0642158	+	0.997936i	$0.520455\pi$
$840$		0			0
$841$	19.9779	+	4.24643i	0.688893	+	0.146429i
$842$	86.2364	+	18.3301i	2.97190	+	0.631697i
$843$		0			0
$844$	−46.7660	−	20.8216i	−1.60975	−	0.716709i
$845$	0.452118	−	1.39148i	0.0155533	−	0.0478682i
$846$		0			0
$847$	7.80199	+	13.5128i	0.268079	+	0.464305i
$848$	2.93048	+	5.07575i	0.100633	+	0.174302i
$849$		0			0
$850$	−7.44790	−	70.8621i	−0.255461	−	2.43055i
$851$	3.49988	−	1.55825i	0.119974	−	0.0534160i
$852$		0			0
$853$	6.10260	−	6.77762i	0.208949	−	0.232061i	−0.629556	−	0.776955i	$-0.716763\pi$
$853$	6.10260	−	6.77762i	0.208949	−	0.232061i	0.838505	+	0.544894i	$0.183430\pi$
$854$	−12.3489	−	8.97197i	−0.422569	−	0.307014i
$855$		0			0
$856$	5.30210	−	16.3182i	0.181222	−	0.557744i
$857$	−0.922678	−	1.59813i	−0.0315181	−	0.0545909i	0.849836	−	0.527047i	$-0.176701\pi$
$857$	−0.922678	−	1.59813i	−0.0315181	−	0.0545909i	−0.881354	+	0.472456i	$0.843368\pi$
$858$		0			0
$859$	−14.2555	+	24.6913i	−0.486392	+	0.842456i	−0.999878	−	0.0156422i	$-0.995021\pi$
$859$	−14.2555	+	24.6913i	−0.486392	+	0.842456i	0.513485	+	0.858098i	$0.328354\pi$
$860$	2.58084	+	2.86631i	0.0880058	+	0.0977403i
$861$		0			0
$862$	7.25093	−	68.9880i	0.246968	−	2.34974i
$863$	3.30628	+	10.1757i	0.112547	+	0.346385i	0.991428	−	0.130658i	$-0.0417089\pi$
$863$	3.30628	+	10.1757i	0.112547	+	0.346385i	−0.878880	+	0.477042i	$0.841709\pi$
$864$		0			0
$865$	−0.252894	−	0.183738i	−0.00859865	−	0.00624729i
$866$	0.594192	+	0.264551i	0.0201915	+	0.00898981i
$867$		0			0
$868$	−23.1735	+	40.1376i	−0.786559	+	1.36236i
$869$	−5.60849	−	9.71396i	−0.190255	−	0.329524i
$870$		0			0
$871$	−40.9206	+	8.69795i	−1.38654	+	0.294719i
$872$	38.8492	−	28.2256i	1.31560	−	0.955840i
$873$		0			0
$874$	−10.0786	−	31.0187i	−0.340913	−	1.04922i
$875$	2.97878	−	3.30826i	0.100701	−	0.111840i
$876$		0			0
$877$	−4.26813	−	40.6086i	−0.144125	−	1.37125i	−0.792472	−	0.609909i	$-0.791206\pi$
$877$	−4.26813	−	40.6086i	−0.144125	−	1.37125i	0.648347	−	0.761345i	$-0.275461\pi$
$878$	−23.3707	−	25.9558i	−0.788723	−	0.875966i
$879$		0			0
$880$	0.746000	+	0.541989i	0.0251477	+	0.0182705i
$881$	−21.0458			−0.709050			−0.354525	−	0.935047i	$-0.615357\pi$
$881$	−21.0458			−0.709050			−0.354525	+	0.935047i	$0.615357\pi$
$882$		0			0
$883$	−10.2973	+	7.48145i	−0.346533	+	0.251771i	−0.747413	−	0.664360i	$-0.768704\pi$
$883$	−10.2973	+	7.48145i	−0.346533	+	0.251771i	0.400880	+	0.916130i	$0.368704\pi$
$884$	−9.38039	+	89.2484i	−0.315497	+	3.00175i
$885$		0			0
$886$	−33.0321	−	7.02120i	−1.10974	−	0.235882i
$887$	−9.79776	+	4.36224i	−0.328977	+	0.146470i	−0.564578	−	0.825380i	$-0.690961\pi$
$887$	−9.79776	+	4.36224i	−0.328977	+	0.146470i	0.235601	+	0.971850i	$0.424294\pi$
$888$		0			0
$889$	−18.3211	+	3.89427i	−0.614470	+	0.130610i
$890$	1.99164			0.0667599
$891$		0			0
$892$	6.59606			0.220852
$893$	−22.5777	+	4.79904i	−0.755535	+	0.160594i
$894$		0			0
$895$	3.25113	−	1.44750i	0.108673	−	0.0483844i
$896$	27.4835	+	5.84180i	0.918159	+	0.195161i
$897$		0			0
$898$	5.16636	−	49.1546i	0.172404	−	1.64031i
$899$	−22.6060	+	16.4242i	−0.753952	+	0.547778i
$900$		0			0
$901$	−41.7304			−1.39024
$902$	−24.1817	+	17.5695i	−0.805164	+	0.584999i
$903$		0			0
$904$	−16.4949	−	18.3195i	−0.548613	−	0.609296i
$905$	−0.594012	−	5.65165i	−0.0197456	−	0.187867i
$906$		0			0
$907$	−8.86302	+	9.84338i	−0.294292	+	0.326844i	−0.872099	−	0.489329i	$-0.837242\pi$
$907$	−8.86302	+	9.84338i	−0.294292	+	0.326844i	0.577807	+	0.816173i	$0.303908\pi$
$908$	16.9422	+	52.1426i	0.562245	+	1.73041i
$909$		0			0
$910$	−3.55618	+	2.58372i	−0.117886	+	0.0856494i
$911$	−55.8762	+	11.8768i	−1.85126	+	0.393497i	−0.992840	−	0.119451i	$-0.961887\pi$
$911$	−55.8762	+	11.8768i	−1.85126	+	0.393497i	−0.858420	+	0.512948i	$0.828553\pi$
$912$		0			0
$913$	−40.8657	−	18.1941i	−1.35246	−	0.602136i
$914$	−3.73747	+	6.47348i	−0.123624	+	0.214124i
$915$		0			0
$916$	−1.63582	−	0.728314i	−0.0540490	−	0.0240642i
$917$	8.37786	+	6.08687i	0.276661	+	0.201006i
$918$		0			0
$919$	5.12287	+	15.7666i	0.168988	+	0.520091i	0.999308	−	0.0371955i	$-0.0118424\pi$
$919$	5.12287	+	15.7666i	0.168988	+	0.520091i	−0.830320	+	0.557287i	$0.811842\pi$
$920$	0.496894	−	4.72763i	0.0163821	−	0.155865i
$921$		0			0
$922$	41.0259	+	45.5639i	1.35112	+	1.50057i
$923$	6.15009	−	10.6523i	0.202433	−	0.350624i
$924$		0			0
$925$	2.07615	+	3.59600i	0.0682634	+	0.118236i
$926$	−2.61125	+	8.03660i	−0.0858109	+	0.264099i
$927$		0			0
$928$	10.8784	+	7.90359i	0.357100	+	0.259448i
$929$	4.92734	−	5.47236i	0.161661	−	0.179542i	−0.656872	−	0.754002i	$-0.728121\pi$
$929$	4.92734	−	5.47236i	0.161661	−	0.179542i	0.818533	+	0.574459i	$0.194788\pi$
$930$		0			0
$931$	−14.1159	+	6.28478i	−0.462629	+	0.205976i
$932$	−3.66970	−	34.9149i	−0.120205	−	1.14368i
$933$		0			0
$934$	21.5376	+	37.3043i	0.704733	+	1.22063i
$935$	−5.99776	+	2.67045i	−0.196148	+	0.0873330i
$936$		0			0
$937$	14.6033	−	44.9444i	0.477069	−	1.46827i	−0.366077	−	0.930584i	$-0.619299\pi$
$937$	14.6033	−	44.9444i	0.477069	−	1.46827i	0.843147	−	0.537684i	$-0.180701\pi$
$938$	30.0831	+	13.3939i	0.982248	+	0.437325i
$939$		0			0
$940$	−7.91172	−	1.68169i	−0.258052	−	0.0548506i
$941$	−54.9022	−	11.6698i	−1.78976	−	0.380425i	−0.810937	−	0.585134i	$-0.801042\pi$
$941$	−54.9022	−	11.6698i	−1.78976	−	0.380425i	−0.978823	+	0.204709i	$0.934375\pi$
$942$		0			0
$943$	15.9803	+	7.11487i	0.520389	+	0.231692i
$944$	3.27233	−	10.0712i	0.106505	−	0.327789i
$945$		0			0
$946$	−13.7223	+	23.7682i	−0.446149	+	0.772772i
$947$	−6.39323	−	11.0734i	−0.207752	−	0.359837i	0.743254	−	0.669009i	$-0.233281\pi$
$947$	−6.39323	−	11.0734i	−0.207752	−	0.359837i	−0.951006	+	0.309172i	$0.899948\pi$
$948$		0			0
$949$	−1.86086	−	17.7049i	−0.0604061	−	0.574726i
$950$	32.2933	−	14.3779i	1.04773	−	0.466481i
$951$		0			0
$952$	19.6595	−	21.8341i	0.637168	−	0.707646i
$953$	−18.8480	−	13.6939i	−0.610547	−	0.443588i	0.239060	−	0.971005i	$-0.423161\pi$
$953$	−18.8480	−	13.6939i	−0.610547	−	0.443588i	−0.849607	+	0.527417i	$0.823161\pi$
$954$		0			0
$955$	−1.26256	+	3.88576i	−0.0408555	+	0.125740i
$956$	−16.5067	−	28.5904i	−0.533864	−	0.924680i
$957$		0			0
$958$	0.182825	−	0.316662i	0.00590680	−	0.0102309i
$959$	9.30870	+	10.3384i	0.300593	+	0.333843i
$960$		0			0
$961$	−6.27644	+	59.7163i	−0.202466	+	1.92633i
$962$	−2.55995	−	7.87872i	−0.0825362	−	0.254020i
$963$		0			0
$964$	0.772163	+	0.561009i	0.0248697	+	0.0180689i
$965$	−6.70482	−	2.98518i	−0.215836	−	0.0960962i
$966$		0			0
$967$	27.7586	−	48.0794i	0.892657	−	1.54613i	0.0559798	−	0.998432i	$-0.482172\pi$
$967$	27.7586	−	48.0794i	0.892657	−	1.54613i	0.836677	−	0.547696i	$-0.184495\pi$
$968$	−11.2747	+	34.7023i	−0.362382	+	1.11537i
$969$		0			0
$970$	−3.79695	+	0.807068i	−0.121913	+	0.0259134i
$971$	−3.65698	+	2.65695i	−0.117358	+	0.0852656i	−0.644916	−	0.764253i	$-0.723108\pi$
$971$	−3.65698	+	2.65695i	−0.117358	+	0.0852656i	0.527558	+	0.849519i	$0.323108\pi$
$972$		0			0
$973$	4.15409	+	12.7850i	0.133174	+	0.409867i
$974$	−27.9368	+	31.0269i	−0.895152	+	0.994167i
$975$		0			0
$976$	−0.423547	−	4.02978i	−0.0135574	−	0.128990i
$977$	18.0928	+	20.0941i	0.578840	+	0.642867i	0.959453	−	0.281867i	$-0.0909537\pi$
$977$	18.0928	+	20.0941i	0.578840	+	0.642867i	−0.380613	+	0.924734i	$0.624287\pi$
$978$		0			0
$979$	2.76469	+	8.50854i	0.0883599	+	0.271934i
$980$	−5.41462			−0.172964
$981$		0			0
$982$	12.5261	−	9.10076i	0.399725	−	0.290417i
$983$	1.11193	−	10.5793i	0.0354651	−	0.337428i	−0.962374	−	0.271727i	$-0.912405\pi$
$983$	1.11193	−	10.5793i	0.0354651	−	0.337428i	0.997839	−	0.0657006i	$-0.0209282\pi$
$984$		0			0
$985$	0.334174	+	0.0710309i	0.0106477	+	0.00226323i
$986$	38.9059	−	17.3220i	1.23902	−	0.551645i
$987$		0			0
$988$	−43.5486	+	9.25653i	−1.38546	+	0.294490i
$989$	16.0614			0.510723
$990$		0			0
$991$	−18.7938			−0.597005			−0.298502	−	0.954409i	$-0.596487\pi$
$991$	−18.7938			−0.597005			−0.298502	+	0.954409i	$0.596487\pi$
$992$	42.8550	−	9.10912i	1.36065	−	0.289215i
$993$		0			0
$994$	−8.84496	+	3.93803i	−0.280545	+	0.124907i
$995$	−5.09504	−	1.08298i	−0.161524	−	0.0343329i
$996$		0			0
$997$	2.73106	−	25.9843i	0.0864935	−	0.822931i	−0.862165	−	0.506628i	$-0.830892\pi$
$997$	2.73106	−	25.9843i	0.0864935	−	0.822931i	0.948658	−	0.316303i	$-0.102442\pi$
$998$	63.9637	−	46.4723i	2.02473	−	1.47106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.64.9		72
3.2	odd	2		99.2.m.b.31.1	yes	72
9.2	odd	6		99.2.m.b.97.9	yes	72
9.4	even	3		891.2.f.e.163.1		36
9.5	odd	6		891.2.f.f.163.9		36
9.7	even	3	inner	297.2.n.b.262.1		72
11.5	even	5	inner	297.2.n.b.280.1		72
33.5	odd	10		99.2.m.b.49.9	yes	72
33.26	odd	10		1089.2.e.p.364.1		36
33.29	even	10		1089.2.e.o.364.18		36
99.4	even	15		9801.2.a.cp.1.1		18
99.5	odd	30		891.2.f.f.82.9		36
99.16	even	15	inner	297.2.n.b.181.9		72
99.29	even	30		1089.2.e.o.727.18		36
99.38	odd	30		99.2.m.b.16.1	✓	72
99.40	odd	30		9801.2.a.cn.1.18		18
99.49	even	15		891.2.f.e.82.1		36
99.59	odd	30		9801.2.a.cm.1.18		18
99.92	odd	30		1089.2.e.p.727.1		36
99.95	even	30		9801.2.a.co.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	99.38	odd	30
99.2.m.b.31.1	yes	72	3.2	odd	2
99.2.m.b.49.9	yes	72	33.5	odd	10
99.2.m.b.97.9	yes	72	9.2	odd	6
297.2.n.b.64.9		72	1.1	even	1	trivial
297.2.n.b.181.9		72	99.16	even	15	inner
297.2.n.b.262.1		72	9.7	even	3	inner
297.2.n.b.280.1		72	11.5	even	5	inner
891.2.f.e.82.1		36	99.49	even	15
891.2.f.e.163.1		36	9.4	even	3
891.2.f.f.82.9		36	99.5	odd	30
891.2.f.f.163.9		36	9.5	odd	6
1089.2.e.o.364.18		36	33.29	even	10
1089.2.e.o.727.18		36	99.29	even	30
1089.2.e.p.364.1		36	33.26	odd	10
1089.2.e.p.727.1		36	99.92	odd	30
9801.2.a.cm.1.18		18	99.59	odd	30
9801.2.a.cn.1.18		18	99.40	odd	30
9801.2.a.co.1.1		18	99.95	even	30
9801.2.a.cp.1.1		18	99.4	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)

\(f(q)\)	\(=\)	\(q+(2.27811 - 0.484227i) q^{2} +(3.12821 - 1.39277i) q^{4} +(-0.310092 - 0.0659121i) q^{5} +(0.148273 - 1.41072i) q^{7} +(2.68358 - 1.94973i) q^{8} -0.738340 q^{10} +(-1.02493 - 3.15429i) q^{11} +(2.80837 + 3.11901i) q^{13} +(-0.345328 - 3.28557i) q^{14} +(0.586822 - 0.651731i) q^{16} +(1.92957 + 5.93860i) q^{17} +(-2.50622 + 1.82087i) q^{19} +(-1.06183 + 0.225700i) q^{20} +(-3.86228 - 6.68951i) q^{22} +(-2.26025 + 3.91487i) q^{23} +(-4.47591 - 1.99281i) q^{25} +(7.90807 + 5.74555i) q^{26} +(-1.50098 - 4.61954i) q^{28} +(0.306106 - 2.91240i) q^{29} +(-6.38469 - 7.09091i) q^{31} +(-2.29583 + 3.97649i) q^{32} +(7.27140 + 12.5944i) q^{34} +(-0.138962 + 0.427681i) q^{35} +(-0.685637 - 0.498145i) q^{37} +(-4.82772 + 5.36173i) q^{38} +(-0.960667 + 0.427717i) q^{40} +(-0.404484 - 3.84841i) q^{41} +(-1.77651 - 3.07700i) q^{43} +(-7.59937 - 8.43978i) q^{44} +(-3.25341 + 10.0130i) q^{46} +(6.80683 + 3.03059i) q^{47} +(4.87888 + 1.03704i) q^{49} +(-11.1616 - 2.37247i) q^{50} +(13.1292 + 5.84550i) q^{52} +(-2.06517 + 6.35595i) q^{53} +(0.109916 + 1.04568i) q^{55} +(-2.35263 - 4.07487i) q^{56} +(-0.712921 - 6.78299i) q^{58} +(11.0309 - 4.91125i) q^{59} +(3.09160 - 3.43357i) q^{61} +(-17.9786 - 13.0622i) q^{62} +(-3.84663 + 11.8387i) q^{64} +(-0.665272 - 1.15229i) q^{65} +(-4.98385 + 8.63229i) q^{67} +(14.3072 + 15.8897i) q^{68} +(-0.109476 + 1.04159i) q^{70} +(-0.905630 - 2.78724i) q^{71} +(-3.43158 - 2.49319i) q^{73} +(-1.80317 - 0.802823i) q^{74} +(-5.30392 + 9.18665i) q^{76} +(-4.60179 + 0.978190i) q^{77} +(3.30808 - 0.703155i) q^{79} +(-0.224926 + 0.163418i) q^{80} +(-2.78496 - 8.57123i) q^{82} +(9.02488 - 10.0231i) q^{83} +(-0.206918 - 1.96870i) q^{85} +(-5.53705 - 6.14951i) q^{86} +(-8.90048 - 6.46644i) q^{88} -2.69745 q^{89} +(4.81645 - 3.49936i) q^{91} +(-1.61803 + 15.3945i) q^{92} +(16.9742 + 3.60797i) q^{94} +(0.897177 - 0.399449i) q^{95} +(5.14256 - 1.09308i) q^{97} +11.6168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 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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