LMFDB - Embedded newform 891.2.u.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	891.107
Dual form			891.2.u.c.458.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254665 - 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(-3.77497 - 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(1.45728 + 4.48505i) q^{8} +O(q^{10})$	\(q+(-0.254665 - 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(-3.77497 - 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(1.45728 + 4.48505i) q^{8} +9.24768i q^{10} +(-2.75393 + 1.84821i) q^{11} +(-0.385693 + 0.866281i) q^{13} +(-0.665900 - 0.599579i) q^{14} +(3.30524 - 1.47159i) q^{16} +(-2.77873 - 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(14.8569 - 1.56153i) q^{20} +(5.17950 + 6.20201i) q^{22} +(4.30242 - 2.48400i) q^{23} +(9.20220 + 1.95599i) q^{25} +(2.19720 + 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(1.66173 + 1.84554i) q^{29} +(3.21012 + 1.42924i) q^{31} +(0.308515 + 0.534364i) q^{32} +(-4.18401 + 7.24691i) q^{34} +(-1.12943 + 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(-4.22368 - 9.48654i) q^{38} +(-3.72167 - 17.5091i) q^{40} +(1.81944 - 2.02069i) q^{41} +(-1.63461 - 0.943743i) q^{43} +(9.08931 - 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(0.00428458 - 0.0201574i) q^{47} +(-0.717560 + 6.82712i) q^{49} +(2.39583 - 22.7948i) q^{50} +(0.775933 - 3.65048i) q^{52} +(3.25941 + 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +(1.50208 + 0.867226i) q^{56} +(4.04851 - 4.49632i) q^{58} +(1.37725 + 6.47943i) q^{59} +(-3.96670 - 8.90935i) q^{61} +(2.64550 - 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +(1.79969 - 3.11715i) q^{65} +(-2.23176 - 3.86552i) q^{67} +(12.3491 + 5.49817i) q^{68} +(2.27586 + 2.52760i) q^{70} +(-6.06985 + 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(17.1161 + 3.63814i) q^{74} +(-14.5275 + 8.38745i) q^{76} +(-0.297863 + 1.18290i) q^{77} +(-10.8772 + 1.14324i) q^{79} +(-13.0610 + 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(8.38931 - 3.73516i) q^{83} +(9.68858 + 8.72364i) q^{85} +(-1.87039 + 4.20095i) q^{86} +(-12.3026 - 9.65812i) q^{88} -3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(-14.5302 + 13.0831i) q^{92} +(-0.0499319 - 0.00524806i) q^{94} +(-15.8251 + 3.36373i) q^{95} +(1.57700 + 15.0042i) q^{97} +16.7247 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4}+O(q^{10}) $ 32 * q + 4 * q^4	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.254665	−	2.42297i	−0.180075	−	1.71330i	−0.595235	−	0.803552i	$-0.702941\pi$
$2$	−0.254665	−	2.42297i	−0.180075	−	1.71330i	0.415160	−	0.909748i	$-0.363726\pi$
$3$		0			0
$3$		0			0
$4$	−3.84965	+	0.818267i	−1.92482	+	0.409134i
$5$	−3.77497	−	0.396765i	−1.68822	−	0.177439i	−0.788835	−	0.614605i	$-0.789315\pi$
$5$	−3.77497	−	0.396765i	−1.68822	−	0.177439i	−0.899381	+	0.437166i	$0.855982\pi$
$6$		0			0
$7$	0.273322	−	0.246100i	0.103306	−	0.0930172i	−0.615859	−	0.787856i	$-0.711191\pi$
$7$	0.273322	−	0.246100i	0.103306	−	0.0930172i	0.719165	+	0.694839i	$0.244524\pi$
$8$	1.45728	+	4.48505i	0.515226	+	1.58570i
$9$		0			0
$10$			9.24768i			2.92437i
$11$	−2.75393	+	1.84821i	−0.830340	+	0.557257i
$11$	−2.75393	+	1.84821i	−0.830340	+	0.557257i
$12$		0			0
$13$	−0.385693	+	0.866281i	−0.106972	+	0.240263i	−0.959098	−	0.283073i	$-0.908646\pi$
$13$	−0.385693	+	0.866281i	−0.106972	+	0.240263i	0.852126	+	0.523336i	$0.175313\pi$
$14$	−0.665900	−	0.599579i	−0.177969	−	0.160244i
$15$		0			0
$16$	3.30524	−	1.47159i	0.826310	−	0.367897i
$17$	−2.77873	−	2.01886i	−0.673940	−	0.489646i	0.197402	−	0.980323i	$-0.436750\pi$
$17$	−2.77873	−	2.01886i	−0.673940	−	0.489646i	−0.871342	+	0.490676i	$0.836750\pi$
$18$		0			0
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.195425	−	0.980719i	$-0.437391\pi$
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.734554	+	0.678550i	$0.237391\pi$
$20$	14.8569	−	1.56153i	3.32211	−	0.349168i
$21$		0			0
$22$	5.17950	+	6.20201i	1.10427	+	1.32227i
$23$	4.30242	−	2.48400i	0.897116	−	0.517950i	0.0208527	−	0.999783i	$-0.493362\pi$
$23$	4.30242	−	2.48400i	0.897116	−	0.517950i	0.876263	+	0.481832i	$0.160029\pi$
$24$		0			0
$25$	9.20220	+	1.95599i	1.84044	+	0.391198i
$26$	2.19720	+	0.713913i	0.430906	+	0.140010i
$27$		0			0
$28$	−0.850818	+	1.17105i	−0.160789	+	0.221308i
$29$	1.66173	+	1.84554i	0.308576	+	0.342708i	0.877408	−	0.479746i	$-0.159271\pi$
$29$	1.66173	+	1.84554i	0.308576	+	0.342708i	−0.568832	+	0.822454i	$0.692604\pi$
$30$		0			0
$31$	3.21012	+	1.42924i	0.576554	+	0.256698i	0.674232	−	0.738520i	$-0.264475\pi$
$31$	3.21012	+	1.42924i	0.576554	+	0.256698i	−0.0976778	+	0.995218i	$0.531141\pi$
$32$	0.308515	+	0.534364i	0.0545383	+	0.0944632i
$33$		0			0
$34$	−4.18401	+	7.24691i	−0.717551	+	1.24284i
$35$	−1.12943	+	0.820576i	−0.190908	+	0.138703i
$36$		0			0
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	0.585179	+	0.810904i	$0.301024\pi$
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	−0.950057	+	0.312075i	$0.898976\pi$
$38$	−4.22368	−	9.48654i	−0.685171	−	1.53892i
$39$		0			0
$40$	−3.72167	−	17.5091i	−0.588448	−	2.76843i
$41$	1.81944	−	2.02069i	0.284148	−	0.315578i	−0.584126	−	0.811663i	$-0.698563\pi$
$41$	1.81944	−	2.02069i	0.284148	−	0.315578i	0.868274	+	0.496084i	$0.165229\pi$
$42$		0			0
$43$	−1.63461	−	0.943743i	−0.249276	−	0.143919i	0.370157	−	0.928969i	$-0.379304\pi$
$43$	−1.63461	−	0.943743i	−0.249276	−	0.143919i	−0.619433	+	0.785050i	$0.712637\pi$
$44$	9.08931	−	9.36841i	1.37026	−	1.41234i
$45$		0			0
$46$	−7.11434	−	9.79205i	−1.04895	−	1.44376i
$47$	0.00428458	−	0.0201574i	0.000624971	−	0.00294026i	−0.977834	−	0.209382i	$-0.932855\pi$
$47$	0.00428458	−	0.0201574i	0.000624971	−	0.00294026i	0.978459	+	0.206441i	$0.0661883\pi$
$48$		0			0
$49$	−0.717560	+	6.82712i	−0.102509	+	0.975303i
$50$	2.39583	−	22.7948i	0.338822	−	3.22367i
$51$		0			0
$52$	0.775933	−	3.65048i	0.107602	−	0.506230i
$53$	3.25941	+	4.48619i	0.447714	+	0.616226i	0.971905	−	0.235375i	$-0.0756319\pi$
$53$	3.25941	+	4.48619i	0.447714	+	0.616226i	−0.524190	+	0.851601i	$0.675632\pi$
$54$		0			0
$55$	11.1293	−	5.88428i	1.50067	−	0.793436i
$56$	1.50208	+	0.867226i	0.200724	+	0.115888i
$57$		0			0
$58$	4.04851	−	4.49632i	0.531595	−	0.590396i
$59$	1.37725	+	6.47943i	0.179302	+	0.843550i	0.972192	+	0.234185i	$0.0752422\pi$
$59$	1.37725	+	6.47943i	0.179302	+	0.843550i	−0.792890	+	0.609365i	$0.791424\pi$
$60$		0			0
$61$	−3.96670	−	8.90935i	−0.507884	−	1.14073i	−0.967561	−	0.252639i	$-0.918701\pi$
$61$	−3.96670	−	8.90935i	−0.507884	−	1.14073i	0.459677	−	0.888086i	$-0.347965\pi$
$62$	2.64550	−	8.14200i	0.335978	−	1.03404i
$63$		0			0
$64$	7.07028	−	5.13686i	0.883786	−	0.642108i
$65$	1.79969	−	3.11715i	0.223224	−	0.386635i
$66$		0			0
$67$	−2.23176	−	3.86552i	−0.272652	−	0.472248i	0.696888	−	0.717180i	$-0.254568\pi$
$67$	−2.23176	−	3.86552i	−0.272652	−	0.472248i	−0.969540	+	0.244932i	$0.921234\pi$
$68$	12.3491	+	5.49817i	1.49755	+	0.666751i
$69$		0			0
$70$	2.27586	+	2.52760i	0.272017	+	0.302106i
$71$	−6.06985	+	8.35443i	−0.720359	+	0.991489i	0.279153	+	0.960247i	$0.409946\pi$
$71$	−6.06985	+	8.35443i	−0.720359	+	0.991489i	−0.999512	+	0.0312420i	$0.990054\pi$
$72$		0			0
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	0.0539588	−	0.998543i	$-0.482816\pi$
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	−0.543275	+	0.839555i	$0.682816\pi$
$74$	17.1161	+	3.63814i	1.98971	+	0.422925i
$75$		0			0
$76$	−14.5275	+	8.38745i	−1.66642	+	0.962106i
$77$	−0.297863	+	1.18290i	−0.0339447	+	0.134804i
$78$		0			0
$79$	−10.8772	+	1.14324i	−1.22378	+	0.128624i	−0.694292	−	0.719693i	$-0.744283\pi$
$79$	−10.8772	+	1.14324i	−1.22378	+	0.128624i	−0.529488	+	0.848318i	$0.677616\pi$
$80$	−13.0610	+	4.24379i	−1.46027	+	0.474470i
$81$		0			0
$82$	−5.35942	−	3.89384i	−0.591848	−	0.430003i
$83$	8.38931	−	3.73516i	0.920847	−	0.409987i	0.109122	−	0.994028i	$-0.465196\pi$
$83$	8.38931	−	3.73516i	0.920847	−	0.409987i	0.811724	+	0.584041i	$0.198529\pi$
$84$		0			0
$85$	9.68858	+	8.72364i	1.05087	+	0.946212i
$86$	−1.87039	+	4.20095i	−0.201689	+	0.453000i
$87$		0			0
$88$	−12.3026	−	9.65812i	−1.31146	−	1.02956i
$89$		−	3.04837i		−	0.323127i	−0.986862	−	0.161563i	$-0.948346\pi$
$89$		−	3.04837i		−	0.323127i	0.986862	−	0.161563i	$-0.0516536\pi$
$90$		0			0
$91$	0.107774	+	0.331693i	0.0112978	+	0.0347709i
$92$	−14.5302	+	13.0831i	−1.51488	+	1.36400i
$93$		0			0
$94$	−0.0499319	−	0.00524806i	−0.00515008	−	0.000541296i
$95$	−15.8251	+	3.36373i	−1.62362	+	0.345111i
$96$		0			0
$97$	1.57700	+	15.0042i	0.160121	+	1.52345i	0.719476	+	0.694517i	$0.244382\pi$
$97$	1.57700	+	15.0042i	0.160121	+	1.52345i	−0.559355	+	0.828928i	$0.688951\pi$
$98$	16.7247			1.68945
$99$		0			0
$100$	−37.0257			−3.70257
$101$	1.82505	+	17.3642i	0.181599	+	1.72780i	0.583498	+	0.812114i	$0.301683\pi$
$101$	1.82505	+	17.3642i	0.181599	+	1.72780i	−0.401899	+	0.915684i	$0.631650\pi$
$102$		0			0
$103$	9.11204	−	1.93682i	0.897836	−	0.190841i	0.264196	−	0.964469i	$-0.414893\pi$
$103$	9.11204	−	1.93682i	0.897836	−	0.190841i	0.633640	+	0.773628i	$0.281560\pi$
$104$	−4.44738	−	0.467438i	−0.436101	−	0.0458361i
$105$		0			0
$106$	10.0399	−	9.03994i	0.975158	−	0.878036i
$107$	4.76675	+	14.6705i	0.460819	+	1.41825i	0.864166	+	0.503207i	$0.167847\pi$
$107$	4.76675	+	14.6705i	0.460819	+	1.41825i	−0.403347	+	0.915047i	$0.632153\pi$
$108$		0			0
$109$			10.6286i			1.01803i	0.860757	+	0.509016i	$0.169991\pi$
$109$			10.6286i			1.01803i	−0.860757	+	0.509016i	$0.830009\pi$
$110$	−17.0917	−	25.4674i	−1.62963	−	2.42822i
$111$		0			0
$112$	0.541237	−	1.21564i	0.0511421	−	0.114867i
$113$	−0.778087	−	0.700592i	−0.0731962	−	0.0659062i	0.631721	−	0.775196i	$-0.282349\pi$
$113$	−0.778087	−	0.700592i	−0.0731962	−	0.0659062i	−0.704917	+	0.709290i	$0.749016\pi$
$114$		0			0
$115$	−17.2270	+	7.66997i	−1.60643	+	0.715229i
$116$	−7.90722	−	5.74493i	−0.734167	−	0.533404i
$117$		0			0
$118$	15.3487	−	4.98711i	1.41297	−	0.459101i
$119$	−1.25633	+	0.132046i	−0.115168	+	0.0121046i
$120$		0			0
$121$	4.16822	−	10.1797i	0.378929	−	0.925426i
$122$	−20.5769	+	11.8801i	−1.86295	+	1.07557i
$123$		0			0
$124$	−13.5273	−	2.87532i	−1.21479	−	0.258211i
$125$	−15.9120	−	5.17013i	−1.42321	−	0.462430i
$126$		0			0
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	−0.0502930	−	0.998735i	$-0.516016\pi$
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	0.965394	−	0.260794i	$-0.0839845\pi$
$128$	−13.4213	−	14.9058i	−1.18628	−	1.31750i
$129$		0			0
$130$	−8.01109	−	3.56677i	−0.702619	−	0.312826i
$131$	−6.94451	−	12.0282i	−0.606744	−	1.05091i	−0.991773	−	0.128008i	$-0.959142\pi$
$131$	−6.94451	−	12.0282i	−0.606744	−	1.05091i	0.385029	−	0.922905i	$-0.374192\pi$
$132$		0			0
$133$	0.783818	−	1.35761i	0.0679656	−	0.117720i
$134$	−8.79769	+	6.39189i	−0.760004	+	0.552176i
$135$		0			0
$136$	5.00531	−	15.4048i	0.429202	−	1.32095i
$137$	0.422083	+	0.948014i	0.0360610	+	0.0809943i	0.930678	−	0.365840i	$-0.119218\pi$
$137$	0.422083	+	0.948014i	0.0360610	+	0.0809943i	−0.894617	+	0.446834i	$0.852551\pi$
$138$		0			0
$139$	4.12394	+	19.4016i	0.349788	+	1.64563i	0.703810	+	0.710388i	$0.251481\pi$
$139$	4.12394	+	19.4016i	0.349788	+	1.64563i	−0.354022	+	0.935237i	$0.615186\pi$
$140$	3.67644	−	4.08310i	0.310716	−	0.345085i
$141$		0			0
$142$	21.7883	+	12.5795i	1.82844	+	1.05565i
$143$	−0.538902	−	3.09852i	−0.0450652	−	0.259111i
$144$		0			0
$145$	−5.54073	−	7.62616i	−0.460133	−	0.633318i
$146$	−2.22668	+	10.4757i	−0.184281	+	0.866976i
$147$		0			0
$148$	2.95473	−	28.1123i	0.242877	−	2.31082i
$149$	−0.839990	+	7.99197i	−0.0688146	+	0.654727i	0.904692	+	0.426067i	$0.140101\pi$
$149$	−0.839990	+	7.99197i	−0.0688146	+	0.654727i	−0.973506	+	0.228660i	$0.926565\pi$
$150$		0			0
$151$	2.09441	−	9.85341i	0.170440	−	0.801859i	−0.806984	−	0.590573i	$-0.798902\pi$
$151$	2.09441	−	9.85341i	0.170440	−	0.801859i	0.977424	−	0.211286i	$-0.0677650\pi$
$152$	11.8147	+	16.2615i	0.958299	+	1.31899i
$153$		0			0
$154$	2.94199	+	0.420471i	0.237072	+	0.0338826i
$155$	−11.5510	−	6.66898i	−0.927800	−	0.535665i
$156$		0			0
$157$	−10.8281	+	12.0258i	−0.864177	+	0.959765i	−0.999518	−	0.0310336i	$-0.990120\pi$
$157$	−10.8281	+	12.0258i	−0.864177	+	0.959765i	0.135342	+	0.990799i	$0.456787\pi$
$158$	5.54007	+	26.0640i	0.440745	+	2.07354i
$159$		0			0
$160$	−0.952618	−	2.13962i	−0.0753111	−	0.169151i
$161$	0.564633	−	1.73776i	0.0444993	−	0.136955i
$162$		0			0
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	−0.714959	−	0.699166i	$-0.753555\pi$
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	0.444012	+	0.896021i	$0.353555\pi$
$164$	−5.35072	+	9.26772i	−0.417821	+	0.723687i
$165$		0			0
$166$	−11.1867	−	19.3759i	−0.868253	−	1.50386i
$167$	16.7662	+	7.46478i	1.29741	+	0.577642i	0.935089	−	0.354413i	$-0.115319\pi$
$167$	16.7662	+	7.46478i	1.29741	+	0.577642i	0.362316	+	0.932055i	$0.381986\pi$
$168$		0			0
$169$	8.09701	+	8.99265i	0.622847	+	0.691742i
$170$	18.6698	−	25.6968i	1.43191	−	1.97085i
$171$		0			0
$172$	7.06490	+	2.29553i	0.538694	+	0.175032i
$173$	6.04729	+	1.28539i	0.459767	+	0.0977264i	0.431972	−	0.901887i	$-0.357818\pi$
$173$	6.04729	+	1.28539i	0.459767	+	0.0977264i	0.0277951	+	0.999614i	$0.491151\pi$
$174$		0			0
$175$	2.99654	−	1.73005i	0.226517	−	0.130780i
$176$	−6.38258	+	10.1614i	−0.481105	+	0.765946i
$177$		0			0
$178$	−7.38612	+	0.776312i	−0.553613	+	0.0581871i
$179$	−8.77414	+	2.85089i	−0.655810	+	0.213086i	−0.617974	−	0.786198i	$-0.712046\pi$
$179$	−8.77414	+	2.85089i	−0.655810	+	0.213086i	−0.0378357	+	0.999284i	$0.512046\pi$
$180$		0			0
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	0.706533	−	0.707680i	$-0.250258\pi$
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	−0.454713	+	0.890638i	$0.650258\pi$
$182$	0.776237	−	0.345603i	0.0575386	−	0.0256178i
$183$		0			0
$184$	17.4107	+	15.6767i	1.28353	+	1.15570i
$185$	11.0886	−	24.9055i	0.815253	−	1.83109i
$186$		0			0
$187$	11.3837	+	0.424121i	0.832459	+	0.0310148i
$188$			0.0811047i			0.00591517i
$189$		0			0
$190$	12.1803	+	37.4872i	0.883653	+	2.71960i
$191$	−14.9989	+	13.5050i	−1.08528	+	0.977190i	−0.999817	−	0.0191509i	$-0.993904\pi$
$191$	−14.9989	+	13.5050i	−1.08528	+	0.977190i	−0.0854633	+	0.996341i	$0.527237\pi$
$192$		0			0
$193$	−7.97006	−	0.837687i	−0.573697	−	0.0602980i	−0.186762	−	0.982405i	$-0.559799\pi$
$193$	−7.97006	−	0.837687i	−0.573697	−	0.0602980i	−0.386935	+	0.922107i	$0.626466\pi$
$194$	35.9531	−	7.64208i	2.58129	−	0.548669i
$195$		0			0
$196$	−2.82406	−	26.8692i	−0.201719	−	1.91923i
$197$	−21.1710			−1.50837			−0.754187	−	0.656659i	$-0.771969\pi$
$197$	−21.1710			−1.50837			−0.754187	+	0.656659i	$0.771969\pi$
$198$		0			0
$199$	−10.5160			−0.745457			−0.372729	−	0.927940i	$-0.621578\pi$
$199$	−10.5160			−0.745457			−0.372729	+	0.927940i	$0.621578\pi$
$200$	4.63749	+	44.1227i	0.327920	+	3.11995i
$201$		0			0
$202$	41.6081	−	8.84407i	2.92754	−	0.622267i
$203$	0.908376	+	0.0954742i	0.0637555	+	0.00670098i
$204$		0			0
$205$	−7.67004	+	6.90614i	−0.535699	+	0.482346i
$206$	−7.01339	−	21.5850i	−0.488646	−	1.50390i
$207$		0			0
$208$			3.43085i			0.237886i
$209$	−8.72922	+	11.1193i	−0.603813	+	0.769140i
$210$		0			0
$211$	−1.50420	+	3.37850i	−0.103554	+	0.232585i	−0.957890	−	0.287135i	$-0.907297\pi$
$211$	−1.50420	+	3.37850i	−0.103554	+	0.232585i	0.854336	+	0.519720i	$0.173964\pi$
$212$	−16.2185	−	14.6032i	−1.11389	−	1.00295i
$213$		0			0
$214$	34.3324	−	15.2858i	2.34691	−	1.04491i
$215$	5.79615	+	4.21115i	0.395294	+	0.287198i
$216$		0			0
$217$	1.22913	−	0.399369i	0.0834390	−	0.0271110i
$218$	25.7527	−	2.70672i	1.74419	−	0.183322i
$219$		0			0
$220$	−38.0289	+	31.7591i	−2.56391	+	2.14120i
$221$	2.82064	−	1.62850i	0.189737	−	0.109545i
$222$		0			0
$223$	17.5060	+	3.72102i	1.17229	+	0.249178i	0.752593	−	0.658486i	$-0.228803\pi$
$223$	17.5060	+	3.72102i	1.17229	+	0.249178i	0.419697	+	0.907664i	$0.362136\pi$
$224$	0.215832	+	0.0701279i	0.0144209	+	0.00468562i
$225$		0			0
$226$	−1.49936	+	2.06370i	−0.0997363	+	0.137275i
$227$	11.6284	+	12.9147i	0.771805	+	0.857176i	0.993007	−	0.118052i	$-0.0376649\pi$
$227$	11.6284	+	12.9147i	0.771805	+	0.857176i	−0.221203	+	0.975228i	$0.570998\pi$
$228$		0			0
$229$	3.90692	+	1.73947i	0.258176	+	0.114948i	0.531744	−	0.846905i	$-0.321537\pi$
$229$	3.90692	+	1.73947i	0.258176	+	0.114948i	−0.273567	+	0.961853i	$0.588204\pi$
$230$	22.9713	+	39.7874i	1.51468	+	2.62350i
$231$		0			0
$232$	−5.85572	+	10.1424i	−0.384447	+	0.665882i
$233$	18.9171	−	13.7441i	1.23930	−	0.900404i	0.241748	−	0.970339i	$-0.422279\pi$
$233$	18.9171	−	13.7441i	1.23930	−	0.900404i	0.997552	+	0.0699355i	$0.0222793\pi$
$234$		0			0
$235$	−0.0241719	+	0.0743935i	−0.00157680	+	0.00485289i
$236$	−10.6038	−	23.8166i	−0.690250	−	1.55033i
$237$		0			0
$238$	0.639886	+	3.01043i	0.0414777	+	0.195137i
$239$	−13.3797	+	14.8597i	−0.865464	+	0.961195i	−0.999557	−	0.0297740i	$-0.990521\pi$
$239$	−13.3797	+	14.8597i	−0.865464	+	0.961195i	0.134093	+	0.990969i	$0.457188\pi$
$240$		0			0
$241$	−2.01411	−	1.16285i	−0.129740	−	0.0749057i	0.433725	−	0.901045i	$-0.357199\pi$
$241$	−2.01411	−	1.16285i	−0.129740	−	0.0749057i	−0.563466	+	0.826140i	$0.690532\pi$
$242$	−25.7266	−	7.50707i	−1.65377	−	0.482573i
$243$		0			0
$244$	22.5606	+	31.0520i	1.44430	+	1.98790i
$245$	5.41753	−	25.4875i	0.346113	−	1.62833i
$246$		0			0
$247$	−0.422481	+	4.01963i	−0.0268818	+	0.255763i
$248$	−1.73215	+	16.4803i	−0.109992	+	1.04650i
$249$		0			0
$250$	−8.47485	+	39.8710i	−0.535997	+	2.52167i
$251$	−1.88681	−	2.59698i	−0.119095	−	0.163920i	0.745307	−	0.666721i	$-0.232303\pi$
$251$	−1.88681	−	2.59698i	−0.119095	−	0.163920i	−0.864402	+	0.502801i	$0.832303\pi$
$252$		0			0
$253$	−7.25758	+	14.7925i	−0.456280	+	0.929999i
$254$	−37.0184	−	21.3726i	−2.32274	−	1.34103i
$255$		0			0
$256$	−21.0030	+	23.3262i	−1.31269	+	1.45789i
$257$	−3.75130	−	17.6485i	−0.234000	−	1.10088i	−0.925571	−	0.378574i	$-0.876414\pi$
$257$	−3.75130	−	17.6485i	−0.234000	−	1.10088i	0.691571	−	0.722309i	$-0.256919\pi$
$258$		0			0
$259$	1.07444	+	2.41323i	0.0667623	+	0.149951i
$260$	−4.37750	+	13.4726i	−0.271481	+	0.835533i
$261$		0			0
$262$	−27.3756	+	19.8895i	−1.69127	+	1.22878i
$263$	1.02983	−	1.78372i	0.0635019	−	0.109989i	−0.832527	−	0.553985i	$-0.813106\pi$
$263$	1.02983	−	1.78372i	0.0635019	−	0.109989i	0.896028	+	0.443997i	$0.146440\pi$
$264$		0			0
$265$	−10.5242	−	18.2284i	−0.646496	−	1.11976i
$266$	−3.48907	−	1.55343i	−0.213928	−	0.0952471i
$267$		0			0
$268$	11.7545	+	13.0547i	0.718020	+	0.797442i
$269$	−1.69280	+	2.32994i	−0.103212	+	0.142059i	−0.857499	−	0.514486i	$-0.827983\pi$
$269$	−1.69280	+	2.32994i	−0.103212	+	0.142059i	0.754287	+	0.656545i	$0.227983\pi$
$270$		0			0
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	0.587692	−	0.809085i	$-0.300037\pi$
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	−0.000115761		1.00000i	$0.500037\pi$
$272$	−12.1553	−	2.58369i	−0.737023	−	0.156659i
$273$		0			0
$274$	2.18952	−	1.26412i	0.132274	−	0.0763683i
$275$	−28.9573	+	11.6210i	−1.74619	+	0.700772i
$276$		0			0
$277$	−7.27067	+	0.764179i	−0.436852	+	0.0459150i	−0.320402	−	0.947282i	$-0.603818\pi$
$277$	−7.27067	+	0.764179i	−0.436852	+	0.0459150i	−0.116450	+	0.993197i	$0.537151\pi$
$278$	45.9594	−	14.9331i	2.75646	−	0.895629i
$279$		0			0
$280$	−5.32621	−	3.86972i	−0.318302	−	0.231260i
$281$	−2.10612	+	0.937703i	−0.125640	+	0.0559387i	−0.468594	−	0.883414i	$-0.655239\pi$
$281$	−2.10612	+	0.937703i	−0.125640	+	0.0559387i	0.342954	+	0.939352i	$0.388573\pi$
$282$		0			0
$283$	−18.1571	−	16.3487i	−1.07933	−	0.971832i	−0.0796411	−	0.996824i	$-0.525377\pi$
$283$	−18.1571	−	16.3487i	−1.07933	−	0.971832i	−0.999688	+	0.0249916i	$0.992044\pi$
$284$	16.5306	−	37.1284i	0.980911	−	2.20316i
$285$		0			0
$286$	−7.37038	+	2.09483i	−0.435820	+	0.123870i
$287$		−	1.00006i		−	0.0590318i
$288$		0			0
$289$	−1.60777	−	4.94822i	−0.0945749	−	0.291072i
$290$	−17.0670	+	15.3672i	−1.00221	+	0.902390i
$291$		0			0
$292$	17.2058	+	1.80841i	1.00690	+	0.105829i
$293$	10.4284	−	2.21663i	0.609236	−	0.129497i	0.107045	−	0.994254i	$-0.465861\pi$
$293$	10.4284	−	2.21663i	0.609236	−	0.129497i	0.502190	+	0.864757i	$0.332528\pi$
$294$		0			0
$295$	−2.62824	−	25.0061i	−0.153022	−	1.45591i
$296$	−33.8709			−1.96871
$297$		0			0
$298$	19.5782			1.13414
$299$	0.492431	+	4.68517i	0.0284780	+	0.270950i
$300$		0			0
$301$	−0.679031	+	0.144332i	−0.0391387	+	0.00831919i
$302$	−24.4079	−	2.56537i	−1.40452	−	0.147621i
$303$		0			0
$304$	11.4601	−	10.3187i	0.657284	−	0.591821i
$305$	11.4392	+	35.2063i	0.655009	+	2.01591i
$306$		0			0
$307$			4.56848i			0.260737i	0.991466	+	0.130369i	$0.0416160\pi$
$307$			4.56848i			0.260737i	−0.991466	+	0.130369i	$0.958384\pi$
$308$	0.178739	−	4.79748i	0.0101846	−	0.273362i
$309$		0			0
$310$	−13.2171	+	29.6861i	−0.750682	+	1.68606i
$311$	−6.97234	−	6.27793i	−0.395365	−	0.355989i	0.447340	−	0.894364i	$-0.352372\pi$
$311$	−6.97234	−	6.27793i	−0.395365	−	0.355989i	−0.842705	+	0.538376i	$0.819038\pi$
$312$		0			0
$313$	−4.58235	+	2.04019i	−0.259010	+	0.115319i	−0.532134	−	0.846660i	$-0.678610\pi$
$313$	−4.58235	+	2.04019i	−0.259010	+	0.115319i	0.273124	+	0.961979i	$0.411943\pi$
$314$	31.8958	+	23.1736i	1.79998	+	1.30776i
$315$		0			0
$316$	40.9379	−	13.3015i	2.30294	−	0.748269i
$317$	11.6122	−	1.22050i	0.652208	−	0.0685498i	0.227355	−	0.973812i	$-0.426992\pi$
$317$	11.6122	−	1.22050i	0.652208	−	0.0685498i	0.424853	+	0.905262i	$0.360326\pi$
$318$		0			0
$319$	−7.98724	−	2.01125i	−0.447199	−	0.112608i
$320$	−28.7282	+	16.5862i	−1.60596	+	0.927199i
$321$		0			0
$322$	−4.35434	−	0.925543i	−0.242658	−	0.0515785i
$323$	−13.9232	−	4.52391i	−0.774706	−	0.251717i
$324$		0			0
$325$	−5.24366	+	7.21728i	−0.290866	+	0.400343i
$326$	6.97054	+	7.74157i	0.386062	+	0.428766i
$327$		0			0
$328$	11.7143	+	5.21554i	0.646814	+	0.287980i
$329$	−0.00378967	−	0.00656390i	−0.000208931	−	0.000361880i
$330$		0			0
$331$	14.5258	−	25.1595i	0.798411	−	1.38289i	−0.122239	−	0.992501i	$-0.539007\pi$
$331$	14.5258	−	25.1595i	0.798411	−	1.38289i	0.920650	−	0.390388i	$-0.127659\pi$
$332$	−29.2395	+	21.2438i	−1.60473	+	1.16590i
$333$		0			0
$334$	13.8172	−	42.5250i	0.756044	−	2.32686i
$335$	6.89110	+	15.4777i	0.376501	+	0.845635i
$336$		0			0
$337$	−6.00455	−	28.2492i	−0.327089	−	1.53883i	−0.767508	−	0.641040i	$-0.778503\pi$
$337$	−6.00455	−	28.2492i	−0.327089	−	1.53883i	0.440419	−	0.897792i	$-0.354830\pi$
$338$	19.7269	−	21.9089i	1.07300	−	1.19169i
$339$		0			0
$340$	−44.4359	−	25.6551i	−2.40987	−	1.39134i
$341$	−11.4820	+	1.99697i	−0.621783	+	0.108142i
$342$		0			0
$343$	2.99731	+	4.12544i	0.161840	+	0.222753i
$344$	1.85065	−	8.70660i	0.0997801	−	0.469429i
$345$		0			0
$346$	1.57444	−	14.9798i	0.0846422	−	0.805316i
$347$	−2.31457	+	22.0217i	−0.124253	+	1.18219i	0.737675	+	0.675156i	$0.235924\pi$
$347$	−2.31457	+	22.0217i	−0.124253	+	1.18219i	−0.861928	+	0.507031i	$0.830743\pi$
$348$		0			0
$349$	3.25641	−	15.3202i	0.174312	−	0.820072i	−0.800900	−	0.598798i	$-0.795645\pi$
$349$	3.25641	−	15.3202i	0.174312	−	0.820072i	0.975212	−	0.221274i	$-0.0710215\pi$
$350$	−4.95498	−	6.81994i	−0.264855	−	0.364541i
$351$		0			0
$352$	−1.83725	−	0.901398i	−0.0979257	−	0.0480447i
$353$	9.66798	+	5.58181i	0.514575	+	0.297090i	0.734712	−	0.678379i	$-0.237317\pi$
$353$	9.66798	+	5.58181i	0.514575	+	0.297090i	−0.220137	+	0.975469i	$0.570651\pi$
$354$		0			0
$355$	26.2282	−	29.1294i	1.39205	−	1.54603i
$356$	2.49438	+	11.7351i	0.132202	+	0.621961i
$357$		0			0
$358$	9.14209	+	20.5335i	0.483175	+	1.08523i
$359$	−5.11867	+	15.7536i	−0.270153	+	0.831445i	0.720308	+	0.693654i	$0.244000\pi$
$359$	−5.11867	+	15.7536i	−0.270153	+	0.831445i	−0.990461	+	0.137791i	$0.956000\pi$
$360$		0			0
$361$	−0.673787	+	0.489535i	−0.0354625	+	0.0257650i
$362$	5.10125	−	8.83563i	0.268116	−	0.464390i
$363$		0			0
$364$	−0.686304	−	1.18871i	−0.0359721	−	0.0623055i
$365$	15.2431	+	6.78667i	0.797861	+	0.355231i
$366$		0			0
$367$	6.56435	+	7.29045i	0.342656	+	0.380559i	0.889700	−	0.456546i	$-0.150913\pi$
$367$	6.56435	+	7.29045i	0.342656	+	0.380559i	−0.547044	+	0.837104i	$0.684247\pi$
$368$	10.5651	−	14.5416i	0.550743	−	0.758033i
$369$		0			0
$370$	−63.1692	−	20.5249i	−3.28401	−	1.06704i
$371$	1.99492	+	0.424034i	0.103571	+	0.0220148i
$372$		0			0
$373$	−10.9422	+	6.31750i	−0.566567	+	0.327108i	−0.755777	−	0.654829i	$-0.772741\pi$
$373$	−10.9422	+	6.31750i	−0.566567	+	0.327108i	0.189210	+	0.981937i	$0.439407\pi$
$374$	−1.87139	−	27.6904i	−0.0967674	−	1.43184i
$375$		0			0
$376$	0.0966507	−	0.0101584i	0.00498438	−	0.000523879i
$377$	−2.23967	+	0.727714i	−0.115349	+	0.0374792i
$378$		0			0
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.983695	−	0.179843i	$-0.942441\pi$
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.475019	−	0.879975i	$-0.657559\pi$
$380$	58.1686	−	25.8983i	2.98399	−	1.32856i
$381$		0			0
$382$	36.5420	+	32.9026i	1.86965	+	1.68344i
$383$	−9.18677	+	20.6338i	−0.469422	+	1.05434i	0.511384	+	0.859352i	$0.329133\pi$
$383$	−9.18677	+	20.6338i	−0.469422	+	1.05434i	−0.980806	+	0.194987i	$0.937534\pi$
$384$		0			0
$385$	1.59376	−	4.34723i	0.0812254	−	0.221555i
$386$			19.5246i			0.993774i
$387$		0			0
$388$	−18.3484	−	56.4704i	−0.931497	−	2.86685i
$389$	5.46868	−	4.92402i	0.277273	−	0.249658i	−0.518747	−	0.854928i	$-0.673601\pi$
$389$	5.46868	−	4.92402i	0.277273	−	0.249658i	0.796020	+	0.605270i	$0.206935\pi$
$390$		0			0
$391$	−16.9701	−	1.78363i	−0.858215	−	0.0902020i
$392$	−31.6657	+	6.73074i	−1.59936	+	0.339954i
$393$		0			0
$394$	5.39152	+	51.2969i	0.271621	+	2.58430i
$395$	41.5146			2.08883
$396$		0			0
$397$	16.7327			0.839790			0.419895	−	0.907573i	$-0.362067\pi$
$397$	16.7327			0.839790			0.419895	+	0.907573i	$0.362067\pi$
$398$	2.67804	+	25.4799i	0.134238	+	1.27719i
$399$		0			0
$400$	33.2939	−	7.07683i	1.66469	−	0.353842i
$401$	−5.04563	−	0.530318i	−0.251967	−	0.0264828i	−0.0222971	−	0.999751i	$-0.507098\pi$
$401$	−5.04563	−	0.530318i	−0.251967	−	0.0264828i	−0.229670	+	0.973269i	$0.573765\pi$
$402$		0			0
$403$	−2.47624	+	2.22962i	−0.123350	+	0.111065i
$404$	−21.2343	−	65.3525i	−1.05645	−	3.25141i
$405$		0			0
$406$		−	2.22528i		−	0.110439i
$407$	−6.51256	−	22.9136i	−0.322815	−	1.13579i
$408$		0			0
$409$	13.1570	−	29.5511i	0.650571	−	1.46121i	−0.223152	−	0.974784i	$-0.571635\pi$
$409$	13.1570	−	29.5511i	0.650571	−	1.46121i	0.873723	−	0.486423i	$-0.161699\pi$
$410$	18.6867	+	16.8256i	0.922869	+	0.830955i
$411$		0			0
$412$	−33.4933	+	14.9122i	−1.65010	+	0.734670i
$413$	1.97102	+	1.43203i	0.0969877	+	0.0704657i
$414$		0			0
$415$	−33.1513	+	10.7715i	−1.62734	+	0.528753i
$416$	−0.581902	+	0.0611604i	−0.0285301	+	0.00299864i
$417$		0			0
$418$	29.1648	+	18.3190i	1.42650	+	0.896010i
$419$	24.1686	−	13.9538i	1.18071	−	0.681686i	0.224534	−	0.974466i	$-0.427914\pi$
$419$	24.1686	−	13.9538i	1.18071	−	0.681686i	0.956180	+	0.292781i	$0.0945806\pi$
$420$		0			0
$421$	−26.1446	−	5.55720i	−1.27421	−	0.270841i	−0.479343	−	0.877628i	$-0.659125\pi$
$421$	−26.1446	−	5.55720i	−1.27421	−	0.270841i	−0.794865	+	0.606786i	$0.792458\pi$
$422$	8.56907	+	2.78426i	0.417136	+	0.135536i
$423$		0			0
$424$	−15.3709	+	21.1562i	−0.746478	+	1.02744i
$425$	−21.6215	−	24.0131i	−1.04880	−	1.16481i
$426$		0			0
$427$	−3.27678	−	1.45892i	−0.158575	−	0.0706020i
$428$	−30.3547	−	52.5759i	−1.46725	−	2.54135i
$429$		0			0
$430$	8.72743	−	15.1164i	0.420874	−	0.728975i
$431$	0.579760	−	0.421220i	0.0279260	−	0.0202895i	−0.573735	−	0.819041i	$-0.694506\pi$
$431$	0.579760	−	0.421220i	0.0279260	−	0.0202895i	0.601661	+	0.798752i	$0.294506\pi$
$432$		0			0
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	−0.829580	−	0.558387i	$-0.811420\pi$
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	0.999356	+	0.0358703i	$0.0114203\pi$
$434$	−1.28068	−	2.87645i	−0.0614745	−	0.138074i
$435$		0			0
$436$	−8.69701	−	40.9162i	−0.416511	−	1.95953i
$437$	14.1689	−	15.7362i	0.677791	−	0.752763i
$438$		0			0
$439$	−7.42639	−	4.28763i	−0.354442	−	0.204637i	0.312198	−	0.950017i	$-0.398935\pi$
$439$	−7.42639	−	4.28763i	−0.354442	−	0.204637i	−0.666640	+	0.745380i	$0.732268\pi$
$440$	42.6097	+	41.3403i	2.03134	+	1.97082i
$441$		0			0
$442$	−4.66412	−	6.41961i	−0.221850	−	0.305350i
$443$	2.90596	−	13.6715i	0.138066	−	0.649551i	−0.853622	−	0.520892i	$-0.825599\pi$
$443$	2.90596	−	13.6715i	0.138066	−	0.649551i	0.991689	−	0.128659i	$-0.0410673\pi$
$444$		0			0
$445$	−1.20949	+	11.5075i	−0.0573351	+	0.545507i
$446$	4.55776	−	43.3642i	0.215816	−	2.05336i
$447$		0			0
$448$	0.668282	−	3.14402i	0.0315734	−	0.148541i
$449$	−12.7008	−	17.4811i	−0.599388	−	0.824986i	0.396264	−	0.918136i	$-0.370306\pi$
$449$	−12.7008	−	17.4811i	−0.599388	−	0.824986i	−0.995652	+	0.0931501i	$0.970306\pi$
$450$		0			0
$451$	−1.27593	+	8.92753i	−0.0600811	+	0.420381i
$452$	3.56863	+	2.06035i	0.167854	+	0.0969107i
$453$		0			0
$454$	28.3305	−	31.4642i	1.32962	−	1.47669i
$455$	−0.275238	−	1.29489i	−0.0129033	−	0.0607054i
$456$		0			0
$457$	3.98808	+	8.95737i	0.186554	+	0.419008i	0.982475	−	0.186392i	$-0.0596796\pi$
$457$	3.98808	+	8.95737i	0.186554	+	0.419008i	−0.795921	+	0.605401i	$0.793013\pi$
$458$	3.21974	−	9.90934i	0.150449	−	0.463033i
$459$		0			0
$460$	60.0419	−	43.6230i	2.79947	−	2.03393i
$461$	−6.17927	+	10.7028i	−0.287797	+	0.498479i	−0.973284	−	0.229606i	$-0.926256\pi$
$461$	−6.17927	+	10.7028i	−0.287797	+	0.498479i	0.685486	+	0.728085i	$0.259590\pi$
$462$		0			0
$463$	16.9359	+	29.3338i	0.787076	+	1.36326i	0.927751	+	0.373200i	$0.121739\pi$
$463$	16.9359	+	29.3338i	0.787076	+	1.36326i	−0.140675	+	0.990056i	$0.544927\pi$
$464$	8.20829	+	3.65457i	0.381060	+	0.169659i
$465$		0			0
$466$	−38.1190	−	42.3354i	−1.76583	−	1.96115i
$467$	−9.24994	+	12.7315i	−0.428036	+	0.589142i	−0.967501	−	0.252867i	$-0.918627\pi$
$467$	−9.24994	+	12.7315i	−0.428036	+	0.589142i	0.539465	+	0.842008i	$0.318627\pi$
$468$		0			0
$469$	−1.56129	−	0.507295i	−0.0720939	−	0.0234247i
$470$	0.186409	+	0.0396225i	0.00859841	+	0.00182765i
$471$		0			0
$472$	−27.0535	+	15.6194i	−1.24524	+	0.718939i
$473$	6.24583	−	0.422111i	0.287184	−	0.0194087i
$474$		0			0
$475$	39.8791	−	4.19146i	1.82978	−	0.192317i
$476$	4.72838	−	1.53634i	0.216725	−	0.0704182i
$477$		0			0
$478$	39.4120	+	28.6345i	1.80266	+	1.30971i
$479$	11.3911	−	5.07162i	0.520471	−	0.231728i	−0.129650	−	0.991560i	$-0.541385\pi$
$479$	11.3911	−	5.07162i	0.520471	−	0.231728i	0.650120	+	0.759831i	$0.274719\pi$
$480$		0			0
$481$	−5.06137	−	4.55728i	−0.230779	−	0.207794i
$482$	−2.30463	+	5.17628i	−0.104973	+	0.235773i
$483$		0			0
$484$	−7.71645	+	42.5989i	−0.350748	+	1.93631i
$485$		−	57.2660i		−	2.60032i
$486$		0			0
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	0.890468	−	0.455046i	$-0.150377\pi$
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	−0.987873	+	0.155263i	$0.950377\pi$
$488$	34.1783	−	30.7743i	1.54718	−	1.39309i
$489$		0			0
$490$	−63.1350	−	6.63576i	−2.85215	−	0.299773i
$491$	0.295322	−	0.0627727i	0.0133277	−	0.00283289i	−0.201243	−	0.979541i	$-0.564498\pi$
$491$	0.295322	−	0.0627727i	0.0133277	−	0.00283289i	0.214571	+	0.976708i	$0.431165\pi$
$492$		0			0
$493$	−0.891605	−	8.48306i	−0.0401559	−	0.382058i
$494$	9.84705			0.443040
$495$		0			0
$496$	12.7135			0.570851
$497$	0.397004	+	3.77725i	0.0178081	+	0.169433i
$498$		0			0
$499$	−6.47212	+	1.37569i	−0.289732	+	0.0615844i	−0.350485	−	0.936568i	$-0.613983\pi$
$499$	−6.47212	+	1.37569i	−0.289732	+	0.0615844i	0.0607529	+	0.998153i	$0.480650\pi$
$500$	65.4862	+	6.88288i	2.92863	+	0.307812i
$501$		0			0
$502$	−5.81190	+	5.23305i	−0.259398	+	0.233563i
$503$	3.19188	+	9.82361i	0.142319	+	0.438013i	0.996657	−	0.0817056i	$-0.0260367\pi$
$503$	3.19188	+	9.82361i	0.142319	+	0.438013i	−0.854337	+	0.519719i	$0.826037\pi$
$504$		0			0
$505$		−	66.2732i		−	2.94912i
$506$	37.6902	+	13.8178i	1.67553	+	0.614275i
$507$		0			0
$508$	−28.0855	+	63.0810i	−1.24609	+	2.79877i
$509$	15.1044	+	13.6001i	0.669492	+	0.602813i	0.932149	−	0.362076i	$-0.117932\pi$
$509$	15.1044	+	13.6001i	0.669492	+	0.602813i	−0.262656	+	0.964889i	$0.584599\pi$
$510$		0			0
$511$	−1.47699	+	0.657597i	−0.0653381	+	0.0290904i
$512$	29.4132	+	21.3699i	1.29989	+	0.944427i
$513$		0			0
$514$	−41.8065	+	13.5838i	−1.84401	+	0.599154i
$515$	−35.1661	+	3.69611i	−1.54960	+	0.162870i
$516$		0			0
$517$	0.0254557	+	0.0634308i	0.00111954	+	0.00278968i
$518$	5.57356	−	3.21790i	0.244888	−	0.141386i
$519$		0			0
$520$	16.6032	+	3.52912i	0.728100	+	0.154762i
$521$	−11.4110	−	3.70764i	−0.499923	−	0.162435i	0.0481915	−	0.998838i	$-0.484654\pi$
$521$	−11.4110	−	3.70764i	−0.499923	−	0.162435i	−0.548115	+	0.836403i	$0.684654\pi$
$522$		0			0
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.0316743	+	0.999498i	$0.510084\pi$
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.940791	+	0.338986i	$0.889916\pi$
$524$	36.5762	+	40.6220i	1.59784	+	1.77458i
$525$		0			0
$526$	−4.58415	−	2.04100i	−0.199879	−	0.0889917i
$527$	−6.03461	−	10.4522i	−0.262872	−	0.455307i
$528$		0			0
$529$	0.840532	−	1.45584i	0.0365449	−	0.0632976i
$530$	−41.4869	+	30.1420i	−1.80207	+	1.30928i
$531$		0			0
$532$	−1.90653	+	5.86770i	−0.0826586	+	0.254397i
$533$	1.04874	+	2.35551i	0.0454260	+	0.102028i
$534$		0			0
$535$	−12.1735	−	57.2720i	−0.526308	−	2.47609i
$536$	14.0847	−	15.6427i	0.608367	−	0.675660i
$537$		0			0
$538$	6.07649	+	3.50826i	0.261976	+	0.151252i
$539$	−10.6419	−	20.1276i	−0.458378	−	0.866957i
$540$		0			0
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	0.959559	+	0.281508i	$0.0908345\pi$
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	−0.0287904	+	0.999585i	$0.509166\pi$
$542$	5.15176	−	24.2371i	0.221287	−	1.04107i
$543$		0			0
$544$	0.221529	−	2.10770i	0.00949796	−	0.0903671i
$545$	4.21704	−	40.1225i	0.180638	−	1.71866i
$546$		0			0
$547$	−7.62505	+	35.8730i	−0.326023	+	1.53382i	0.444131	+	0.895962i	$0.353513\pi$
$547$	−7.62505	+	35.8730i	−0.326023	+	1.53382i	−0.770154	+	0.637858i	$0.779821\pi$
$548$	−2.40060	−	3.30414i	−0.102548	−	0.141146i
$549$		0			0
$550$	35.5317	+	67.2032i	1.51508	+	2.86555i
$551$	9.16693	+	5.29253i	0.390524	+	0.225469i
$552$		0			0
$553$	−2.69163	+	2.98936i	−0.114460	+	0.127120i
$554$	3.70317	+	17.4220i	0.157333	+	0.740191i
$555$		0			0
$556$	−31.7514	−	71.3149i	−1.34656	−	3.02443i
$557$	2.30765	−	7.10223i	0.0977784	−	0.300931i	−0.890189	−	0.455591i	$-0.849428\pi$
$557$	2.30765	−	7.10223i	0.0977784	−	0.300931i	0.987968	+	0.154660i	$0.0494281\pi$
$558$		0			0
$559$	1.44800	−	1.05204i	0.0612441	−	0.0444964i
$560$	−2.52547	+	4.37425i	−0.106721	+	0.184846i
$561$		0			0
$562$	2.80838	+	4.86426i	0.118464	+	0.205186i
$563$	3.57636	+	1.59230i	0.150725	+	0.0671073i	0.480713	−	0.876878i	$-0.340378\pi$
$563$	3.57636	+	1.59230i	0.150725	+	0.0671073i	−0.329988	+	0.943985i	$0.607045\pi$
$564$		0			0
$565$	2.65928	+	2.95343i	0.111877	+	0.124252i
$566$	−34.9886	+	48.1576i	−1.47068	+	2.02422i
$567$		0			0
$568$	−46.3155	−	15.0488i	−1.94335	−	0.631434i
$569$	36.8479	+	7.83227i	1.54475	+	0.328346i	0.899945	−	0.436004i	$-0.143607\pi$
$569$	36.8479	+	7.83227i	1.54475	+	0.328346i	0.644802	+	0.764350i	$0.276940\pi$
$570$		0			0
$571$	−26.2762	+	15.1706i	−1.09962	+	0.634868i	−0.936122	−	0.351675i	$-0.885612\pi$
$571$	−26.2762	+	15.1706i	−1.09962	+	0.634868i	−0.163502	+	0.986543i	$0.552279\pi$
$572$	4.61000	+	11.4872i	0.192754	+	0.480305i
$573$		0			0
$574$	−2.42312	+	0.254681i	−0.101139	+	0.0106302i
$575$	44.4504	−	14.4428i	1.85371	−	0.602307i
$576$		0			0
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	0.642282	−	0.766468i	$-0.277988\pi$
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	−0.530478	+	0.847699i	$0.677988\pi$
$578$	−11.5800	+	5.15573i	−0.481663	+	0.214450i
$579$		0			0
$580$	27.5701	+	24.8242i	1.14479	+	1.03077i
$581$	1.37376	−	3.08552i	0.0569932	−	0.128009i
$582$		0			0
$583$	−17.2676	−	6.33056i	−0.715152	−	0.262185i
$584$		−	20.7303i		−	0.857826i
$585$		0			0
$586$	−8.02659	−	24.7033i	−0.331576	−	1.02048i
$587$	−30.4002	+	27.3724i	−1.25475	+	1.12978i	−0.268718	+	0.963219i	$0.586600\pi$
$587$	−30.4002	+	27.3724i	−1.25475	+	1.12978i	−0.986031	+	0.166562i	$0.946733\pi$
$588$		0			0
$589$	14.8953	+	1.56556i	0.613749	+	0.0645076i
$590$	−59.9197	+	12.7363i	−2.46685	+	0.524346i
$591$		0			0
$592$	2.71627	+	25.8436i	0.111638	+	1.06217i
$593$	−4.62924			−0.190100			−0.0950500	−	0.995472i	$-0.530301\pi$
$593$	−4.62924			−0.190100			−0.0950500	+	0.995472i	$0.530301\pi$
$594$		0			0
$595$	4.79500			0.196576
$596$	−3.30590	−	31.4536i	−0.135415	−	1.28839i
$597$		0			0
$598$	11.2266	−	2.38629i	0.459091	−	0.0975828i
$599$	−30.4113	−	3.19636i	−1.24257	−	0.130600i	−0.539665	−	0.841880i	$-0.681449\pi$
$599$	−30.4113	−	3.19636i	−1.24257	−	0.130600i	−0.702909	+	0.711280i	$0.748116\pi$
$600$		0			0
$601$	23.2084	−	20.8970i	0.946692	−	0.852405i	−0.0424903	−	0.999097i	$-0.513529\pi$
$601$	23.2084	−	20.8970i	0.946692	−	0.852405i	0.989182	+	0.146692i	$0.0468625\pi$
$602$	0.522639	+	1.60852i	0.0213012	+	0.0655583i
$603$		0			0
$604$			39.6459i			1.61317i
$605$	−19.7738	+	36.7742i	−0.803920	+	1.49508i
$606$		0			0
$607$	−12.5139	+	28.1068i	−0.507925	+	1.14082i	0.459619	+	0.888116i	$0.347986\pi$
$607$	−12.5139	+	28.1068i	−0.507925	+	1.14082i	−0.967544	+	0.252703i	$0.918681\pi$
$608$	1.95445	+	1.75979i	0.0792633	+	0.0713690i
$609$		0			0
$610$	82.3908	−	36.6828i	3.33591	−	1.48524i
$611$	0.0158094	+	0.0114862i	0.000639581	+	0.000464683i
$612$		0			0
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.224205	−	0.974542i	$-0.428021\pi$
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.754207	+	0.656636i	$0.228021\pi$
$614$	11.0693	−	1.16343i	0.446721	−	0.0469523i
$615$		0			0
$616$	−5.73943	+	0.387887i	−0.231248	+	0.0156284i
$617$	3.64536	−	2.10465i	0.146757	−	0.0847300i	−0.424824	−	0.905276i	$-0.639664\pi$
$617$	3.64536	−	2.10465i	0.146757	−	0.0847300i	0.571580	+	0.820546i	$0.306331\pi$
$618$		0			0
$619$	−37.6618	−	8.00527i	−1.51376	−	0.321759i	−0.625177	−	0.780483i	$-0.714973\pi$
$619$	−37.6618	−	8.00527i	−1.51376	−	0.321759i	−0.888579	+	0.458724i	$0.848307\pi$
$620$	49.9243	+	16.2214i	2.00501	+	0.651467i
$621$		0			0
$622$	−13.4356	+	18.4926i	−0.538720	+	0.741484i
$623$	−0.750205	−	0.833188i	−0.0300563	−	0.0333810i
$624$		0			0
$625$	15.0438	+	6.69793i	0.601752	+	0.267917i
$626$	6.11030	+	10.5833i	0.244217	+	0.422995i
$627$		0			0
$628$	31.8440	−	55.1554i	1.27071	−	2.20094i
$629$	19.9578	−	14.5002i	0.795769	−	0.578160i
$630$		0			0
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	−0.997083	−	0.0763220i	$-0.975682\pi$
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	0.851518	+	0.524325i	$0.175682\pi$
$632$	−20.9786	−	47.1187i	−0.834484	−	1.87428i
$633$		0			0
$634$	−5.91445	−	27.8253i	−0.234893	−	1.10508i
$635$	−44.5617	+	49.4908i	−1.76838	+	1.96398i
$636$		0			0
$637$	−5.63745	−	3.25478i	−0.223364	−	0.128959i
$638$	−2.83913	+	19.8650i	−0.112402	+	0.786465i
$639$		0			0
$640$	44.7507	+	61.5941i	1.76893	+	2.43472i
$641$	7.47236	−	35.1547i	0.295140	−	1.38853i	−0.541466	−	0.840723i	$-0.682131\pi$
$641$	7.47236	−	35.1547i	0.295140	−	1.38853i	0.836607	−	0.547804i	$-0.184536\pi$
$642$		0			0
$643$	−0.340268	+	3.23744i	−0.0134189	+	0.127672i	−0.999180	−	0.0404769i	$-0.987112\pi$
$643$	−0.340268	+	3.23744i	−0.0134189	+	0.127672i	0.985762	+	0.168149i	$0.0537789\pi$
$644$	−0.751682	+	7.15178i	−0.0296204	+	0.281820i
$645$		0			0
$646$	−7.41557	+	34.8875i	−0.291762	+	1.37263i
$647$	−7.14454	−	9.83361i	−0.280881	−	0.386599i	0.645145	−	0.764060i	$-0.276797\pi$
$647$	−7.14454	−	9.83361i	−0.280881	−	0.386599i	−0.926025	+	0.377461i	$0.876797\pi$
$648$		0			0
$649$	−15.7682	−	15.2984i	−0.618956	−	0.600516i
$650$	18.8227	+	10.8673i	0.738285	+	0.426249i
$651$		0			0
$652$	11.2603	−	12.5058i	0.440986	−	0.489765i
$653$	−5.30599	−	24.9627i	−0.207639	−	0.976866i	−0.951290	−	0.308298i	$-0.900241\pi$
$653$	−5.30599	−	24.9627i	−0.207639	−	0.976866i	0.743651	−	0.668568i	$-0.233093\pi$
$654$		0			0
$655$	21.4429	+	48.1615i	0.837843	+	1.88183i
$656$	3.04005	−	9.35631i	0.118694	−	0.365303i
$657$		0			0
$658$	−0.0149391	+	0.0108539i	−0.000582385	+	0.000423127i
$659$	13.9720	−	24.2003i	0.544273	−	0.942708i	−0.454379	−	0.890808i	$-0.650139\pi$
$659$	13.9720	−	24.2003i	0.544273	−	0.942708i	0.998652	−	0.0519000i	$-0.0165277\pi$
$660$		0			0
$661$	13.6899	+	23.7116i	0.532475	+	0.922274i	0.999281	+	0.0379144i	$0.0120714\pi$
$661$	13.6899	+	23.7116i	0.532475	+	0.922274i	−0.466806	+	0.884360i	$0.654595\pi$
$662$	−64.6599	−	28.7884i	−2.51308	−	1.11889i
$663$		0			0
$664$	28.9780	+	32.1833i	1.12456	+	1.24895i
$665$	−3.49754	+	4.81395i	−0.135629	+	0.186677i
$666$		0			0
$667$	11.7338	+	3.81254i	0.454334	+	0.147622i
$668$	−70.6520	−	15.0175i	−2.73361	−	0.581046i
$669$		0			0
$670$	35.7470	−	20.6386i	1.38103	−	0.797337i
$671$	27.3904	+	17.2044i	1.05739	+	0.664168i
$672$		0			0
$673$	13.4746	−	1.41623i	0.519406	−	0.0545918i	0.158801	−	0.987311i	$-0.449237\pi$
$673$	13.4746	−	1.41623i	0.519406	−	0.0545918i	0.360605	+	0.932719i	$0.382570\pi$
$674$	−66.9179	+	21.7429i	−2.57758	+	0.837507i
$675$		0			0
$676$	−38.5290	−	27.9930i	−1.48189	−	1.07665i
$677$	−33.5244	+	14.9260i	−1.28845	+	0.573653i	−0.932607	−	0.360894i	$-0.882472\pi$
$677$	−33.5244	+	14.9260i	−1.28845	+	0.573653i	−0.355840	+	0.934547i	$0.615805\pi$
$678$		0			0
$679$	4.12357	+	3.71288i	0.158248	+	0.142487i
$680$	−25.0070	+	56.1665i	−0.958973	+	2.15389i
$681$		0			0
$682$	7.76265	+	27.3119i	0.297247	+	1.04583i
$683$			30.8347i			1.17986i	0.807455	+	0.589929i	$0.200844\pi$
$683$			30.8347i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$684$		0			0
$685$	−1.21721	−	3.74619i	−0.0465072	−	0.143134i
$686$	9.23253	−	8.31300i	0.352499	−	0.317392i
$687$		0			0
$688$	−6.79158	−	0.713823i	−0.258926	−	0.0272143i
$689$	−5.14344	+	1.09327i	−0.195949	+	0.0416503i
$690$		0			0
$691$	4.98809	+	47.4585i	0.189756	+	1.80541i	0.512251	+	0.858836i	$0.328812\pi$
$691$	4.98809	+	47.4585i	0.189756	+	1.80541i	−0.322495	+	0.946571i	$0.604521\pi$
$692$	−24.3317			−0.924953
$693$		0			0
$694$	53.9474			2.04782
$695$	−7.86986	−	74.8767i	−0.298521	−	2.84024i
$696$		0			0
$697$	−9.13521	+	1.94175i	−0.346021	+	0.0735490i
$698$	−37.9498	−	3.98868i	−1.43642	−	0.150974i
$699$		0			0
$700$	−10.1200	+	9.11205i	−0.382499	+	0.344403i
$701$	4.34678	+	13.3780i	0.164176	+	0.505281i	0.998975	−	0.0452742i	$-0.0144162\pi$
$701$	4.34678	+	13.3780i	0.164176	+	0.505281i	−0.834799	+	0.550555i	$0.814416\pi$
$702$		0			0
$703$			30.6133i			1.15460i
$704$	−9.97702	+	27.2139i	−0.376023	+	1.02566i
$705$		0			0
$706$	11.0625	−	24.8467i	0.416342	−	0.935119i
$707$	4.77215	+	4.29687i	0.179475	+	0.161600i
$708$		0			0
$709$	−8.28966	+	3.69079i	−0.311325	+	0.138611i	−0.556451	−	0.830880i	$-0.687837\pi$
$709$	−8.28966	+	3.69079i	−0.311325	+	0.138611i	0.245126	+	0.969491i	$0.421171\pi$
$710$	−77.2591	−	56.1320i	−2.89948	−	2.10660i
$711$		0			0
$712$	13.6721	−	4.44233i	0.512383	−	0.166483i
$713$	17.3615	−	1.82477i	0.650193	−	0.0683380i
$714$		0			0
$715$	0.804952	+	11.9106i	0.0301035	+	0.445432i
$716$	31.4445	−	18.1545i	1.17514	−	0.678466i
$717$		0			0
$718$	39.4742	+	8.39049i	1.47316	+	0.313130i
$719$	32.2802	+	10.4885i	1.20385	+	0.391155i	0.841176	−	0.540761i	$-0.181864\pi$
$719$	32.2802	+	10.4885i	1.20385	+	0.391155i	0.362674	+	0.931916i	$0.381864\pi$
$720$		0			0
$721$	2.01387	−	2.77186i	0.0750005	−	0.103229i
$722$	1.35772	+	1.50790i	0.0505291	+	0.0561183i
$723$		0			0
$724$	−15.0563	−	6.70351i	−0.559564	−	0.249134i
$725$	11.6817	+	20.2334i	0.433849	+	0.751448i
$726$		0			0
$727$	−15.4496	+	26.7595i	−0.572993	+	0.992454i	0.423263	+	0.906007i	$0.360885\pi$
$727$	−15.4496	+	26.7595i	−0.572993	+	0.992454i	−0.996256	+	0.0864469i	$0.972449\pi$
$728$	−1.33060	+	0.966740i	−0.0493154	+	0.0358298i
$729$		0			0
$730$	12.5620	−	38.6620i	0.464942	−	1.43094i
$731$	2.63685	+	5.92246i	0.0975274	+	0.219050i
$732$		0			0
$733$	8.64932	+	40.6919i	0.319470	+	1.50299i	0.785857	+	0.618408i	$0.212222\pi$
$733$	8.64932	+	40.6919i	0.319470	+	1.50299i	−0.466387	+	0.884581i	$0.654445\pi$
$734$	15.9929	−	17.7619i	0.590307	−	0.655602i
$735$		0			0
$736$	2.65472	+	1.53271i	0.0978545	+	0.0564963i
$737$	13.2904	+	6.52058i	0.489558	+	0.240189i
$738$		0			0
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	0.624883	−	0.780718i	$-0.285146\pi$
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	−0.935607	+	0.353044i	$0.885146\pi$
$740$	−22.3080	+	104.951i	−0.820057	+	3.85807i
$741$		0			0
$742$	0.519386	−	4.94163i	0.0190673	−	0.181413i
$743$	−1.40380	+	13.3562i	−0.0515003	+	0.489993i	0.938123	+	0.346303i	$0.112563\pi$
$743$	−1.40380	+	13.3562i	−0.0515003	+	0.489993i	−0.989623	+	0.143689i	$0.954103\pi$
$744$		0			0
$745$	6.34186	−	29.8361i	0.232348	−	1.09311i
$746$	18.0937	+	24.9039i	0.662459	+	0.911796i
$747$		0			0
$748$	−44.1703	+	7.68220i	−1.61502	+	0.280889i
$749$	4.91328	+	2.83669i	0.179528	+	0.103650i
$750$		0			0
$751$	−24.3326	+	27.0241i	−0.887911	+	0.986125i	−0.999971	−	0.00757678i	$-0.997588\pi$
$751$	−24.3326	+	27.0241i	−0.887911	+	0.986125i	0.112061	+	0.993701i	$0.464255\pi$
$752$	−0.0155018	−	0.0729301i	−0.000565291	−	0.00265949i
$753$		0			0
$754$	2.33360	+	5.24135i	0.0849846	+	0.190879i
$755$	−11.8158	+	36.3653i	−0.430021	+	1.32347i
$756$		0			0
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.991397	−	0.130887i	$-0.958218\pi$
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.181878	+	0.983321i	$0.558218\pi$
$758$	−42.7599	+	74.0623i	−1.55311	+	2.69006i
$759$		0			0
$760$	−38.1481	−	66.0744i	−1.38378	−	2.39677i
$761$	3.11533	+	1.38703i	0.112930	+	0.0502799i	0.462424	−	0.886659i	$-0.346980\pi$
$761$	3.11533	+	1.38703i	0.112930	+	0.0502799i	−0.349494	+	0.936939i	$0.613646\pi$
$762$		0			0
$763$	2.61570	+	2.90502i	0.0946945	+	0.105169i
$764$	46.6896	−	64.2627i	1.68917	−	2.32494i
$765$		0			0
$766$	52.3347	+	17.0046i	1.89093	+	0.614401i
$767$	−6.14420	−	1.30599i	−0.221854	−	0.0471566i
$768$		0			0
$769$	18.5463	−	10.7077i	0.668796	−	0.386130i	−0.126824	−	0.991925i	$-0.540478\pi$
$769$	18.5463	−	10.7077i	0.668796	−	0.386130i	0.795620	+	0.605795i	$0.207145\pi$
$770$	−10.9391	−	2.75454i	−0.394217	−	0.0992668i
$771$		0			0
$772$	31.3673	−	3.29684i	1.12894	−	0.118656i
$773$	34.1302	−	11.0896i	1.22758	−	0.398864i	0.377741	−	0.925911i	$-0.376701\pi$
$773$	34.1302	−	11.0896i	1.22758	−	0.398864i	0.849836	+	0.527048i	$0.176701\pi$
$774$		0			0
$775$	26.7446	+	19.4311i	0.960694	+	0.697985i
$776$	−64.9964	+	28.9383i	−2.33323	+	1.03882i
$777$		0			0
$778$	−13.3235	−	11.9965i	−0.477669	−	0.430095i
$779$	4.71392	−	10.5876i	0.168894	−	0.379342i
$780$		0			0
$781$	1.27515	−	34.2259i	0.0456284	−	1.22470i
$782$			41.5723i			1.48662i
$783$		0			0
$784$	7.67500	+	23.6212i	0.274107	+	0.843615i
$785$	45.6471	−	41.1009i	1.62922	−	1.46695i
$786$		0			0
$787$	47.8002	+	5.02400i	1.70389	+	0.179086i	0.905874	−	0.423548i	$-0.139215\pi$
$787$	47.8002	+	5.02400i	1.70389	+	0.179086i	0.798018	+	0.602634i	$0.205882\pi$
$788$	81.5010	−	17.3236i	2.90335	−	0.617127i
$789$		0			0
$790$	−10.5723	−	100.589i	−0.376146	−	3.57879i
$791$	−0.385085			−0.0136920
$792$		0			0
$793$	9.24793			0.328404
$794$	−4.26123	−	40.5429i	−0.151225	−	1.43881i
$795$		0			0
$796$	40.4827	−	8.60487i	1.43487	−	0.304992i
$797$	6.01268	+	0.631958i	0.212980	+	0.0223851i	0.210417	−	0.977612i	$-0.432518\pi$
$797$	6.01268	+	0.631958i	0.212980	+	0.0223851i	0.00256245	+	0.999997i	$0.499184\pi$
$798$		0			0
$799$	−0.0526007	+	0.0473619i	−0.00186088	+	0.00167554i
$800$	1.79381	+	5.52078i	0.0634208	+	0.195189i
$801$		0			0
$802$			12.3605i			0.436464i
$803$	14.0240	−	3.98594i	0.494897	−	0.140661i
$804$		0			0
$805$	−2.82095	+	6.33596i	−0.0994254	+	0.223313i
$806$	6.03291	+	5.43206i	0.212500	+	0.191336i
$807$		0			0
$808$	−75.2195	+	33.4899i	−2.64621	+	1.17817i
$809$	6.01444	+	4.36974i	0.211456	+	0.153632i	0.688472	−	0.725263i	$-0.258282\pi$
$809$	6.01444	+	4.36974i	0.211456	+	0.153632i	−0.477016	+	0.878895i	$0.658282\pi$
$810$		0			0
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.221530	−	0.975154i	$-0.428895\pi$
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.752402	+	0.658704i	$0.228895\pi$
$812$	−3.57505	+	0.375753i	−0.125460	+	0.0131863i
$813$		0			0
$814$	−53.8605	+	21.6150i	−1.88781	+	0.757606i
$815$	14.0556	−	8.11503i	0.492348	−	0.284257i
$816$		0			0
$817$	−7.86922	−	1.67265i	−0.275309	−	0.0585187i
$818$	−74.9521	−	24.3534i	−2.62064	−	0.851497i
$819$		0			0
$820$	23.8759	−	32.8623i	0.833782	−	1.14760i
$821$	0.717575	+	0.796947i	0.0250435	+	0.0278137i	0.755536	−	0.655107i	$-0.227376\pi$
$821$	0.717575	+	0.796947i	0.0250435	+	0.0278137i	−0.730493	+	0.682920i	$0.760710\pi$
$822$		0			0
$823$	−8.17276	−	3.63875i	−0.284884	−	0.126839i	0.259320	−	0.965792i	$-0.416502\pi$
$823$	−8.17276	−	3.63875i	−0.284884	−	0.126839i	−0.544204	+	0.838953i	$0.683168\pi$
$824$	21.9655	+	38.0454i	0.765206	+	1.32538i
$825$		0			0
$826$	2.96782	−	5.14042i	0.103264	−	0.178858i
$827$	28.5608	−	20.7507i	0.993157	−	0.721571i	0.0325471	−	0.999470i	$-0.489638\pi$
$827$	28.5608	−	20.7507i	0.993157	−	0.721571i	0.960610	+	0.277899i	$0.0896381\pi$
$828$		0			0
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	−0.694106	−	0.719873i	$-0.744200\pi$
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	0.984674	−	0.174404i	$-0.0557998\pi$
$830$	34.5416	+	77.5817i	1.19896	+	2.69290i
$831$		0			0
$832$	1.72301	+	8.10611i	0.0597345	+	0.281029i
$833$	15.7769	−	17.5221i	0.546638	−	0.607103i
$834$		0			0
$835$	−60.3300	−	34.8315i	−2.08780	−	1.20539i
$836$	24.5058	−	49.9483i	0.847552	−	1.72750i
$837$		0			0
$838$	−39.9645	−	55.0064i	−1.38055	−	1.90016i
$839$	−7.74116	+	36.4193i	−0.267255	+	1.25733i	0.615739	+	0.787950i	$0.288857\pi$
$839$	−7.74116	+	36.4193i	−0.267255	+	1.25733i	−0.882994	+	0.469384i	$0.844476\pi$
$840$		0			0
$841$	2.38666	−	22.7076i	0.0822986	−	0.783019i
$842$	−6.80684	+	64.7628i	−0.234579	+	2.23187i
$843$		0			0
$844$	3.02614	−	14.2369i	0.104164	−	0.490053i
$845$	−26.9980	−	37.1595i	−0.928759	−	1.27833i
$846$		0			0
$847$	−1.36596	−	3.80813i	−0.0469349	−	0.130849i
$848$	17.3750	+	10.0314i	0.596658	+	0.344481i
$849$		0			0
$850$	−52.6770	+	58.5037i	−1.80680	+	2.00666i
$851$	7.41869	+	34.9022i	0.254309	+	1.19643i
$852$		0			0
$853$	14.2842	+	32.0828i	0.489080	+	1.09849i	0.974536	+	0.224231i	$0.0719871\pi$
$853$	14.2842	+	32.0828i	0.489080	+	1.09849i	−0.485455	+	0.874261i	$0.661346\pi$
$854$	−2.70044	+	8.31109i	−0.0924070	+	0.284400i
$855$		0			0
$856$	−58.8516	+	42.7582i	−2.01151	+	1.46144i
$857$	14.9819	−	25.9493i	0.511770	−	0.886412i	−0.488137	−	0.872767i	$-0.662323\pi$
$857$	14.9819	−	25.9493i	0.511770	−	0.886412i	0.999907	−	0.0136449i	$-0.00434344\pi$
$858$		0			0
$859$	−8.63419	−	14.9548i	−0.294595	−	0.510253i	0.680296	−	0.732938i	$-0.261851\pi$
$859$	−8.63419	−	14.9548i	−0.294595	−	0.510253i	−0.974891	+	0.222685i	$0.928518\pi$
$860$	−25.7590	−	11.4686i	−0.878374	−	0.391077i
$861$		0			0
$862$	−1.16825	−	1.29747i	−0.0397907	−	0.0441921i
$863$	−20.4637	+	28.1659i	−0.696593	+	0.958778i	0.303389	+	0.952867i	$0.401882\pi$
$863$	−20.4637	+	28.1659i	−0.696593	+	0.958778i	−0.999983	+	0.00591175i	$0.998118\pi$
$864$		0			0
$865$	−22.3183	−	7.25166i	−0.758845	−	0.246564i
$866$	−27.2444	−	5.79097i	−0.925801	−	0.196785i
$867$		0			0
$868$	−4.40493	+	2.54319i	−0.149513	+	0.0863215i
$869$	27.8420	−	23.2518i	0.944477	−	0.788762i
$870$		0			0
$871$	4.20940	−	0.442425i	0.142630	−	0.0149910i
$872$	−47.6696	+	15.4888i	−1.61430	+	0.524517i
$873$		0			0
$874$	−41.7366	−	30.3234i	−1.41176	−	1.02570i
$875$	−5.62148	+	2.50284i	−0.190041	+	0.0846116i
$876$		0			0
$877$	1.47358	+	1.32682i	0.0497592	+	0.0448034i	0.693635	−	0.720327i	$-0.256008\pi$
$877$	1.47358	+	1.32682i	0.0497592	+	0.0448034i	−0.643876	+	0.765130i	$0.722675\pi$
$878$	−8.49756	+	19.0858i	−0.286779	+	0.644116i
$879$		0			0
$880$	28.1257	−	35.8267i	0.948117	−	1.20772i
$881$		−	48.9571i		−	1.64941i	−0.565566	−	0.824703i	$-0.691342\pi$
$881$		−	48.9571i		−	1.64941i	0.565566	−	0.824703i	$-0.308658\pi$
$882$		0			0
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	0.952187	+	0.305515i	$0.0988286\pi$
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	−0.590758	+	0.806848i	$0.701171\pi$
$884$	−9.52592	+	8.57718i	−0.320391	+	0.288482i
$885$		0			0
$886$	−33.8657	−	3.55942i	−1.13774	−	0.119581i
$887$	14.1763	−	3.01328i	0.475995	−	0.101176i	0.0363341	−	0.999340i	$-0.488432\pi$
$887$	14.1763	−	3.01328i	0.475995	−	0.101176i	0.439661	+	0.898164i	$0.355099\pi$
$888$		0			0
$889$	−0.674510	−	6.41754i	−0.0226223	−	0.215237i
$890$	28.1903			0.944943
$891$		0			0
$892$	−70.4368			−2.35840
$893$	−0.00918138	−	0.0873550i	−0.000307243	−	0.00292322i
$894$		0			0
$895$	34.2532	−	7.28074i	1.14496	−	0.243368i
$896$	−7.33667	−	0.771115i	−0.245101	−	0.0257611i
$897$		0			0
$898$	−39.1219	+	35.2255i	−1.30551	+	1.17549i
$899$	2.69664	+	8.29941i	0.0899380	+	0.276801i
$900$		0			0
$901$		−	19.0462i		−	0.634521i
$902$	21.9561	+	0.818015i	0.731058	+	0.0272369i
$903$		0			0
$904$	2.00830	−	4.51072i	0.0667951	−	0.150024i
$905$	−11.8126	−	10.6361i	−0.392664	−	0.353556i
$906$		0			0
$907$	20.8007	−	9.26105i	0.690674	−	0.307508i	−0.0312188	−	0.999513i	$-0.509939\pi$
$907$	20.8007	−	9.26105i	0.690674	−	0.307508i	0.721893	+	0.692005i	$0.243272\pi$
$908$	−55.3329	−	40.2017i	−1.83629	−	1.33414i
$909$		0			0
$910$	−3.06739	+	0.996656i	−0.101683	+	0.0330388i
$911$	−22.5701	+	2.37221i	−0.747781	+	0.0785950i	−0.470751	−	0.882266i	$-0.656017\pi$
$911$	−22.5701	+	2.37221i	−0.747781	+	0.0785950i	−0.277030	+	0.960861i	$0.589350\pi$
$912$		0			0
$913$	−16.2002	+	25.7916i	−0.536147	+	0.853577i
$914$	20.6878	−	11.9441i	0.684293	−	0.395077i
$915$		0			0
$916$	−16.4636	−	3.49945i	−0.543973	−	0.115625i
$917$	−4.85824	−	1.57854i	−0.160433	−	0.0521280i
$918$		0			0
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	−0.821012	−	0.570911i	$-0.806590\pi$
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	0.796676	+	0.604407i	$0.206590\pi$
$920$	−59.5048	−	66.0868i	−1.96182	−	2.17882i
$921$		0			0
$922$	27.5062	+	12.2466i	0.905870	+	0.403319i
$923$	−4.89619	−	8.48045i	−0.161160	−	0.279137i
$924$		0			0
$925$	−33.7850	+	58.5173i	−1.11084	+	1.92404i
$926$	66.7619	−	48.5054i	2.19393	−	1.59399i
$927$		0			0
$928$	−0.473521	+	1.45735i	−0.0155441	+	0.0478398i
$929$	1.16942	+	2.62655i	0.0383673	+	0.0861744i	0.931712	−	0.363197i	$-0.118315\pi$
$929$	1.16942	+	2.62655i	0.0383673	+	0.0861744i	−0.893345	+	0.449371i	$0.851648\pi$
$930$		0			0
$931$	6.08339	+	28.6201i	0.199375	+	0.937986i
$932$	−61.5777	+	68.3890i	−2.01705	+	2.24016i
$933$		0			0
$934$	33.2036	+	19.1701i	1.08645	+	0.627265i
$935$	−42.8048	−	6.11769i	−1.39987	−	0.200070i
$936$		0			0
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	0.994975	−	0.100120i	$-0.0319227\pi$
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	−0.402684	+	0.915339i	$0.631923\pi$
$938$	−0.831556	+	3.91216i	−0.0271513	+	0.127737i
$939$		0			0
$940$	0.0321795	−	0.306168i	0.00104958	−	0.00998608i
$941$	−0.683706	+	6.50503i	−0.0222882	+	0.212058i	0.977710	+	0.209962i	$0.0673339\pi$
$941$	−0.683706	+	6.50503i	−0.0222882	+	0.212058i	−0.999998	+	0.00209621i	$0.999333\pi$
$942$		0			0
$943$	2.80858	−	13.2133i	0.0914599	−	0.430285i
$944$	14.0872	+	19.3893i	0.458498	+	0.631069i
$945$		0			0
$946$	−2.61336	−	15.0260i	−0.0849675	−	0.488537i
$947$	−28.8021	−	16.6289i	−0.935944	−	0.540368i	−0.0472574	−	0.998883i	$-0.515048\pi$
$947$	−28.8021	−	16.6289i	−0.935944	−	0.540368i	−0.888687	+	0.458515i	$0.848381\pi$
$948$		0			0
$949$	2.78923	−	3.09776i	0.0905423	−	0.100557i
$950$	−20.3116	−	95.5585i	−0.658995	−	3.10033i
$951$		0			0
$952$	−2.42306	−	5.44228i	−0.0785318	−	0.176385i
$953$	16.9820	−	52.2651i	0.550100	−	1.69303i	−0.158445	−	0.987368i	$-0.550648\pi$
$953$	16.9820	−	52.2651i	0.550100	−	1.69303i	0.708545	−	0.705666i	$-0.249352\pi$
$954$		0			0
$955$	61.9785	−	45.0300i	2.00558	−	1.45714i
$956$	39.3481	−	68.1528i	1.27261	−	2.20422i
$957$		0			0
$958$	−15.1893	−	26.3086i	−0.490744	−	0.849994i
$959$	0.348671	+	0.155238i	0.0112592	+	0.00501291i
$960$		0			0
$961$	−12.4809	−	13.8615i	−0.402610	−	0.447144i
$962$	−9.75321	+	13.4241i	−0.314456	+	0.432812i
$963$		0			0
$964$	8.70515	+	2.82847i	0.280374	+	0.0910990i
$965$	29.7543	+	6.32448i	0.957825	+	0.203592i
$966$		0			0
$967$	29.4790	−	17.0197i	0.947982	−	0.547318i	0.0555286	−	0.998457i	$-0.482316\pi$
$967$	29.4790	−	17.0197i	0.947982	−	0.547318i	0.892454	+	0.451139i	$0.148982\pi$
$968$	51.7306	+	3.86000i	1.66269	+	0.124065i
$969$		0			0
$970$	−138.754	+	14.5836i	−4.45512	+	0.468252i
$971$	36.2008	−	11.7624i	1.16174	−	0.377472i	0.336186	−	0.941796i	$-0.390863\pi$
$971$	36.2008	−	11.7624i	1.16174	−	0.377472i	0.825554	+	0.564323i	$0.190863\pi$
$972$		0			0
$973$	5.90192	+	4.28799i	0.189207	+	0.137467i
$974$	−15.4821	+	6.89307i	−0.496078	+	0.220868i
$975$		0			0
$976$	−26.2218	−	23.6102i	−0.839339	−	0.755744i
$977$	−13.0565	+	29.3253i	−0.417713	+	0.938199i	0.575051	+	0.818118i	$0.304982\pi$
$977$	−13.0565	+	29.3253i	−0.417713	+	0.938199i	−0.992764	+	0.120081i	$0.961684\pi$
$978$		0			0
$979$	5.63404	+	8.39499i	0.180065	+	0.268305i
$980$			102.551i			3.27586i
$981$		0			0
$982$	−0.227305	−	0.699572i	−0.00725358	−	0.0223242i
$983$	−15.9259	+	14.3398i	−0.507958	+	0.457368i	−0.882819	−	0.469713i	$-0.844357\pi$
$983$	−15.9259	+	14.3398i	−0.507958	+	0.457368i	0.374861	+	0.927081i	$0.377691\pi$
$984$		0			0
$985$	79.9200	+	8.39993i	2.54646	+	0.267644i
$986$	−20.3272	+	4.32067i	−0.647349	+	0.137598i
$987$		0			0
$988$	−1.66274	−	15.8199i	−0.0528987	−	0.503297i
$989$	−9.37704			−0.298172
$990$		0			0
$991$	−29.3068			−0.930962			−0.465481	−	0.885058i	$-0.654119\pi$
$991$	−29.3068			−0.930962			−0.465481	+	0.885058i	$0.654119\pi$
$992$	0.226638	+	2.15631i	0.00719576	+	0.0684631i
$993$		0			0
$994$	9.05106	−	1.92386i	0.287082	−	0.0610212i
$995$	39.6974	+	4.17237i	1.25849	+	0.132273i
$996$		0			0
$997$	24.3471	−	21.9222i	0.771080	−	0.694283i	−0.186499	−	0.982455i	$-0.559714\pi$
$997$	24.3471	−	21.9222i	0.771080	−	0.694283i	0.957579	+	0.288172i	$0.0930475\pi$
$998$	4.98148	+	15.3314i	0.157686	+	0.485308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.107.1		32
3.2	odd	2	inner	891.2.u.c.107.4		32
9.2	odd	6		99.2.j.a.8.4	yes	16
9.4	even	3	inner	891.2.u.c.701.4		32
9.5	odd	6	inner	891.2.u.c.701.1		32
9.7	even	3		99.2.j.a.8.1	✓	16
11.7	odd	10	inner	891.2.u.c.755.1		32
33.29	even	10	inner	891.2.u.c.755.4		32
36.7	odd	6		1584.2.cd.c.305.4		16
36.11	even	6		1584.2.cd.c.305.1		16
99.2	even	30		1089.2.d.g.1088.15		16
99.7	odd	30		99.2.j.a.62.4	yes	16
99.20	odd	30		1089.2.d.g.1088.1		16
99.29	even	30		99.2.j.a.62.1	yes	16
99.40	odd	30	inner	891.2.u.c.458.4		32
99.79	odd	30		1089.2.d.g.1088.2		16
99.95	even	30	inner	891.2.u.c.458.1		32
99.97	even	15		1089.2.d.g.1088.16		16
396.7	even	30		1584.2.cd.c.161.1		16
396.227	odd	30		1584.2.cd.c.161.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.1	✓	16	9.7	even	3
99.2.j.a.8.4	yes	16	9.2	odd	6
99.2.j.a.62.1	yes	16	99.29	even	30
99.2.j.a.62.4	yes	16	99.7	odd	30
891.2.u.c.107.1		32	1.1	even	1	trivial
891.2.u.c.107.4		32	3.2	odd	2	inner
891.2.u.c.458.1		32	99.95	even	30	inner
891.2.u.c.458.4		32	99.40	odd	30	inner
891.2.u.c.701.1		32	9.5	odd	6	inner
891.2.u.c.701.4		32	9.4	even	3	inner
891.2.u.c.755.1		32	11.7	odd	10	inner
891.2.u.c.755.4		32	33.29	even	10	inner
1089.2.d.g.1088.1		16	99.20	odd	30
1089.2.d.g.1088.2		16	99.79	odd	30
1089.2.d.g.1088.15		16	99.2	even	30
1089.2.d.g.1088.16		16	99.97	even	15
1584.2.cd.c.161.1		16	396.7	even	30
1584.2.cd.c.161.4		16	396.227	odd	30
1584.2.cd.c.305.1		16	36.11	even	6
1584.2.cd.c.305.4		16	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254665 - 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(-3.77497 - 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(1.45728 + 4.48505i) q^{8} +O(q^{10})\)	\(q+(-0.254665 - 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(-3.77497 - 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(1.45728 + 4.48505i) q^{8} +9.24768i q^{10} +(-2.75393 + 1.84821i) q^{11} +(-0.385693 + 0.866281i) q^{13} +(-0.665900 - 0.599579i) q^{14} +(3.30524 - 1.47159i) q^{16} +(-2.77873 - 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(14.8569 - 1.56153i) q^{20} +(5.17950 + 6.20201i) q^{22} +(4.30242 - 2.48400i) q^{23} +(9.20220 + 1.95599i) q^{25} +(2.19720 + 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(1.66173 + 1.84554i) q^{29} +(3.21012 + 1.42924i) q^{31} +(0.308515 + 0.534364i) q^{32} +(-4.18401 + 7.24691i) q^{34} +(-1.12943 + 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(-4.22368 - 9.48654i) q^{38} +(-3.72167 - 17.5091i) q^{40} +(1.81944 - 2.02069i) q^{41} +(-1.63461 - 0.943743i) q^{43} +(9.08931 - 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(0.00428458 - 0.0201574i) q^{47} +(-0.717560 + 6.82712i) q^{49} +(2.39583 - 22.7948i) q^{50} +(0.775933 - 3.65048i) q^{52} +(3.25941 + 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +(1.50208 + 0.867226i) q^{56} +(4.04851 - 4.49632i) q^{58} +(1.37725 + 6.47943i) q^{59} +(-3.96670 - 8.90935i) q^{61} +(2.64550 - 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +(1.79969 - 3.11715i) q^{65} +(-2.23176 - 3.86552i) q^{67} +(12.3491 + 5.49817i) q^{68} +(2.27586 + 2.52760i) q^{70} +(-6.06985 + 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(17.1161 + 3.63814i) q^{74} +(-14.5275 + 8.38745i) q^{76} +(-0.297863 + 1.18290i) q^{77} +(-10.8772 + 1.14324i) q^{79} +(-13.0610 + 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(8.38931 - 3.73516i) q^{83} +(9.68858 + 8.72364i) q^{85} +(-1.87039 + 4.20095i) q^{86} +(-12.3026 - 9.65812i) q^{88} -3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(-14.5302 + 13.0831i) q^{92} +(-0.0499319 - 0.00524806i) q^{94} +(-15.8251 + 3.36373i) q^{95} +(1.57700 + 15.0042i) q^{97} +16.7247 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4}+O(q^{10}) \) 32 * q + 4 * q^4	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

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