LMFDB - Embedded newform 891.2.u.c.107.4

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			107.4
Character	$\chi$	$=$	891.107
Dual form			891.2.u.c.458.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254665 + 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(3.77497 + 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(-1.45728 - 4.48505i) q^{8} +O(q^{10})$	\(q+(0.254665 + 2.42297i) q^{2} +(-3.84965 + 0.818267i) q^{4} +(3.77497 + 0.396765i) q^{5} +(0.273322 - 0.246100i) q^{7} +(-1.45728 - 4.48505i) q^{8} +9.24768i q^{10} +(2.75393 - 1.84821i) q^{11} +(-0.385693 + 0.866281i) q^{13} +(0.665900 + 0.599579i) q^{14} +(3.30524 - 1.47159i) q^{16} +(2.77873 + 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(-14.8569 + 1.56153i) q^{20} +(5.17950 + 6.20201i) q^{22} +(-4.30242 + 2.48400i) q^{23} +(9.20220 + 1.95599i) q^{25} +(-2.19720 - 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(-1.66173 - 1.84554i) q^{29} +(3.21012 + 1.42924i) q^{31} +(-0.308515 - 0.534364i) q^{32} +(-4.18401 + 7.24691i) q^{34} +(1.12943 - 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(4.22368 + 9.48654i) q^{38} +(-3.72167 - 17.5091i) q^{40} +(-1.81944 + 2.02069i) q^{41} +(-1.63461 - 0.943743i) q^{43} +(-9.08931 + 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(-0.00428458 + 0.0201574i) q^{47} +(-0.717560 + 6.82712i) q^{49} +(-2.39583 + 22.7948i) q^{50} +(0.775933 - 3.65048i) q^{52} +(-3.25941 - 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +(-1.50208 - 0.867226i) q^{56} +(4.04851 - 4.49632i) q^{58} +(-1.37725 - 6.47943i) q^{59} +(-3.96670 - 8.90935i) q^{61} +(-2.64550 + 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +(-1.79969 + 3.11715i) q^{65} +(-2.23176 - 3.86552i) q^{67} +(-12.3491 - 5.49817i) q^{68} +(2.27586 + 2.52760i) q^{70} +(6.06985 - 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(-17.1161 - 3.63814i) q^{74} +(-14.5275 + 8.38745i) q^{76} +(0.297863 - 1.18290i) q^{77} +(-10.8772 + 1.14324i) q^{79} +(13.0610 - 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(-8.38931 + 3.73516i) q^{83} +(9.68858 + 8.72364i) q^{85} +(1.87039 - 4.20095i) q^{86} +(-12.3026 - 9.65812i) q^{88} +3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(14.5302 - 13.0831i) q^{92} +(-0.0499319 - 0.00524806i) q^{94} +(15.8251 - 3.36373i) q^{95} +(1.57700 + 15.0042i) q^{97} -16.7247 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.297059\pi$
$2$	0.254665	+	2.42297i	0.180075	+	1.71330i	−0.415160	+	0.909748i	$0.636274\pi$
$3$		0			0
$3$		0			0
$4$	−3.84965	+	0.818267i	−1.92482	+	0.409134i
$5$	3.77497	+	0.396765i	1.68822	+	0.177439i	0.899381	−	0.437166i	$-0.144018\pi$
$5$	3.77497	+	0.396765i	1.68822	+	0.177439i	0.788835	+	0.614605i	$0.210685\pi$
$6$		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	0.871342	−	0.490676i	$-0.163250\pi$
$17$	2.77873	+	2.01886i	0.673940	+	0.489646i	−0.197402	+	0.980323i	$0.563250\pi$
$18$		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	−0.876263	−	0.481832i	$-0.839971\pi$
$23$	−4.30242	+	2.48400i	−0.897116	+	0.517950i	−0.0208527	+	0.999783i	$0.506638\pi$
$24$		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	0.568832	−	0.822454i	$-0.307396\pi$
$29$	−1.66173	−	1.84554i	−0.308576	−	0.342708i	−0.877408	+	0.479746i	$0.840729\pi$
$30$		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	−0.868274	−	0.496084i	$-0.834771\pi$
$41$	−1.81944	+	2.02069i	−0.284148	+	0.315578i	0.584126	+	0.811663i	$0.301437\pi$
$42$		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	−0.978459	−	0.206441i	$-0.933812\pi$
$47$	−0.00428458	+	0.0201574i	−0.000624971	+	0.00294026i	0.977834	+	0.209382i	$0.0671451\pi$
$48$		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	0.524190	−	0.851601i	$-0.324368\pi$
$53$	−3.25941	−	4.48619i	−0.447714	−	0.616226i	−0.971905	+	0.235375i	$0.924368\pi$
$54$		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	$-0.924758\pi$
$59$	−1.37725	−	6.47943i	−0.179302	−	0.843550i	0.792890	−	0.609365i	$-0.208576\pi$
$60$		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	$-0.590054\pi$
$71$	6.06985	−	8.35443i	0.720359	−	0.991489i	0.999512	−	0.0312420i	$-0.00994626\pi$
$72$		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	−0.811724	−	0.584041i	$-0.801471\pi$
$83$	−8.38931	+	3.73516i	−0.920847	+	0.409987i	−0.109122	+	0.994028i	$0.534804\pi$
$84$		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	$0.0516536\pi$
$89$			3.04837i			0.323127i	−0.986862	+	0.161563i	$0.948346\pi$
$90$		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	$-0.698317\pi$
$101$	−1.82505	−	17.3642i	−0.181599	−	1.72780i	0.401899	−	0.915684i	$-0.368350\pi$
$102$		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	$-0.832153\pi$
$107$	−4.76675	−	14.6705i	−0.460819	−	1.41825i	0.403347	−	0.915047i	$-0.367847\pi$
$108$		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	0.704917	−	0.709290i	$-0.250984\pi$
$113$	0.778087	+	0.700592i	0.0731962	+	0.0659062i	−0.631721	+	0.775196i	$0.717651\pi$
$114$		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	$0.0408582\pi$
$131$	6.94451	+	12.0282i	0.606744	+	1.05091i	−0.385029	+	0.922905i	$0.625808\pi$
$132$		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	0.894617	−	0.446834i	$-0.147449\pi$
$137$	−0.422083	−	0.948014i	−0.0360610	−	0.0809943i	−0.930678	+	0.365840i	$0.880782\pi$
$138$		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	$-0.859899\pi$
$149$	0.839990	−	7.99197i	0.0688146	−	0.654727i	0.973506	−	0.228660i	$-0.0734346\pi$
$150$		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	−0.362316	−	0.932055i	$-0.618014\pi$
$167$	−16.7662	−	7.46478i	−1.29741	−	0.577642i	−0.935089	+	0.354413i	$0.884681\pi$
$168$		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	−0.0277951	−	0.999614i	$-0.508849\pi$
$173$	−6.04729	−	1.28539i	−0.459767	−	0.0977264i	−0.431972	+	0.901887i	$0.642182\pi$
$174$		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	0.0378357	−	0.999284i	$-0.487954\pi$
$179$	8.77414	−	2.85089i	0.655810	−	0.213086i	0.617974	+	0.786198i	$0.287954\pi$
$180$		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	0.0854633	−	0.996341i	$-0.472763\pi$
$191$	14.9989	−	13.5050i	1.08528	−	0.977190i	0.999817	+	0.0191509i	$0.00609630\pi$
$192$		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	$-0.228031\pi$
$197$	21.1710			1.50837			0.754187	+	0.656659i	$0.228031\pi$
$198$		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	0.221203	−	0.975228i	$-0.429002\pi$
$227$	−11.6284	−	12.9147i	−0.771805	−	0.857176i	−0.993007	+	0.118052i	$0.962335\pi$
$228$		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	−0.997552	−	0.0699355i	$-0.977721\pi$
$233$	−18.9171	+	13.7441i	−1.23930	+	0.900404i	−0.241748	+	0.970339i	$0.577721\pi$
$234$		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	−0.134093	−	0.990969i	$-0.542812\pi$
$239$	13.3797	−	14.8597i	0.865464	−	0.961195i	0.999557	+	0.0297740i	$0.00947875\pi$
$240$		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	0.864402	−	0.502801i	$-0.167697\pi$
$251$	1.88681	+	2.59698i	0.119095	+	0.163920i	−0.745307	+	0.666721i	$0.767697\pi$
$252$		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	$0.123586\pi$
$257$	3.75130	+	17.6485i	0.234000	+	1.10088i	−0.691571	+	0.722309i	$0.743081\pi$
$258$		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	−0.896028	−	0.443997i	$-0.853560\pi$
$263$	−1.02983	+	1.78372i	−0.0635019	+	0.109989i	0.832527	+	0.553985i	$0.186894\pi$
$264$		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	−0.754287	−	0.656545i	$-0.772017\pi$
$269$	1.69280	−	2.32994i	0.103212	−	0.142059i	0.857499	+	0.514486i	$0.172017\pi$
$270$		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	−0.342954	−	0.939352i	$-0.611427\pi$
$281$	2.10612	−	0.937703i	0.125640	−	0.0559387i	0.468594	+	0.883414i	$0.344761\pi$
$282$		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	−0.502190	−	0.864757i	$-0.667472\pi$
$293$	−10.4284	+	2.21663i	−0.609236	+	0.129497i	−0.107045	+	0.994254i	$0.534139\pi$
$294$		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	0.842705	−	0.538376i	$-0.180962\pi$
$311$	6.97234	+	6.27793i	0.395365	+	0.355989i	−0.447340	+	0.894364i	$0.647628\pi$
$312$		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	−0.424853	−	0.905262i	$-0.639674\pi$
$317$	−11.6122	+	1.22050i	−0.652208	+	0.0685498i	−0.227355	+	0.973812i	$0.573008\pi$
$318$		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	$-0.764076\pi$
$347$	2.31457	−	22.0217i	0.124253	−	1.18219i	0.861928	−	0.507031i	$-0.169257\pi$
$348$		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	0.220137	−	0.975469i	$-0.429349\pi$
$353$	−9.66798	−	5.58181i	−0.514575	−	0.297090i	−0.734712	+	0.678379i	$0.762683\pi$
$354$		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	$-0.756000\pi$
$359$	5.11867	−	15.7536i	0.270153	−	0.831445i	0.990461	−	0.137791i	$-0.0440002\pi$
$360$		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	$-0.670867\pi$
$383$	9.18677	−	20.6338i	0.469422	−	1.05434i	0.980806	−	0.194987i	$-0.0624664\pi$
$384$		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	−0.796020	−	0.605270i	$-0.793065\pi$
$389$	−5.46868	+	4.92402i	−0.277273	+	0.249658i	0.518747	+	0.854928i	$0.326399\pi$
$390$		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	0.229670	−	0.973269i	$-0.426235\pi$
$401$	5.04563	+	0.530318i	0.251967	+	0.0264828i	0.0222971	+	0.999751i	$0.492902\pi$
$402$		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	−0.956180	−	0.292781i	$-0.905419\pi$
$419$	−24.1686	+	13.9538i	−1.18071	+	0.681686i	−0.224534	+	0.974466i	$0.572086\pi$
$420$		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	−0.601661	−	0.798752i	$-0.705494\pi$
$431$	−0.579760	+	0.421220i	−0.0279260	+	0.0202895i	0.573735	+	0.819041i	$0.305494\pi$
$432$		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	$0.174401\pi$
$443$	−2.90596	+	13.6715i	−0.138066	+	0.649551i	−0.991689	+	0.128659i	$0.958933\pi$
$444$		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	0.995652	−	0.0931501i	$-0.0296936\pi$
$449$	12.7008	+	17.4811i	0.599388	+	0.824986i	−0.396264	+	0.918136i	$0.629694\pi$
$450$		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	−0.685486	−	0.728085i	$-0.740410\pi$
$461$	6.17927	−	10.7028i	0.287797	−	0.498479i	0.973284	+	0.229606i	$0.0737437\pi$
$462$		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	−0.539465	−	0.842008i	$-0.681373\pi$
$467$	9.24994	−	12.7315i	0.428036	−	0.589142i	0.967501	+	0.252867i	$0.0813734\pi$
$468$		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	−0.650120	−	0.759831i	$-0.725281\pi$
$479$	−11.3911	+	5.07162i	−0.520471	+	0.231728i	0.129650	+	0.991560i	$0.458615\pi$
$480$		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	−0.214571	−	0.976708i	$-0.568835\pi$
$491$	−0.295322	+	0.0627727i	−0.0133277	+	0.00283289i	0.201243	+	0.979541i	$0.435502\pi$
$492$		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	0.854337	−	0.519719i	$-0.173963\pi$
$503$	−3.19188	−	9.82361i	−0.142319	−	0.438013i	−0.996657	+	0.0817056i	$0.973963\pi$
$504$		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	0.262656	−	0.964889i	$-0.415401\pi$
$509$	−15.1044	−	13.6001i	−0.669492	−	0.602813i	−0.932149	+	0.362076i	$0.882068\pi$
$510$		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	0.548115	−	0.836403i	$-0.315346\pi$
$521$	11.4110	+	3.70764i	0.499923	+	0.162435i	−0.0481915	+	0.998838i	$0.515346\pi$
$522$		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	−0.987968	−	0.154660i	$-0.950572\pi$
$557$	−2.30765	+	7.10223i	−0.0977784	+	0.300931i	0.890189	+	0.455591i	$0.150572\pi$
$558$		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	0.329988	−	0.943985i	$-0.392955\pi$
$563$	−3.57636	−	1.59230i	−0.150725	−	0.0671073i	−0.480713	+	0.876878i	$0.659622\pi$
$564$		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	−0.644802	−	0.764350i	$-0.723060\pi$
$569$	−36.8479	−	7.83227i	−1.54475	−	0.328346i	−0.899945	+	0.436004i	$0.856393\pi$
$570$		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	$-0.413400\pi$
$587$	30.4002	−	27.3724i	1.25475	−	1.12978i	0.986031	−	0.166562i	$-0.0532667\pi$
$588$		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	$-0.469699\pi$
$593$	4.62924			0.190100			0.0950500	+	0.995472i	$0.469699\pi$
$594$		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	0.702909	−	0.711280i	$-0.251884\pi$
$599$	30.4113	+	3.19636i	1.24257	+	0.130600i	0.539665	+	0.841880i	$0.318551\pi$
$600$		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	−0.571580	−	0.820546i	$-0.693669\pi$
$617$	−3.64536	+	2.10465i	−0.146757	+	0.0847300i	0.424824	+	0.905276i	$0.360336\pi$
$618$		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	$0.317869\pi$
$641$	−7.47236	+	35.1547i	−0.295140	+	1.38853i	−0.836607	+	0.547804i	$0.815464\pi$
$642$		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	0.926025	−	0.377461i	$-0.123203\pi$
$647$	7.14454	+	9.83361i	0.280881	+	0.386599i	−0.645145	+	0.764060i	$0.723203\pi$
$648$		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	$0.0997593\pi$
$653$	5.30599	+	24.9627i	0.207639	+	0.976866i	−0.743651	+	0.668568i	$0.766907\pi$
$654$		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	$0.349861\pi$
$659$	−13.9720	+	24.2003i	−0.544273	+	0.942708i	−0.998652	+	0.0519000i	$0.983472\pi$
$660$		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	0.355840	−	0.934547i	$-0.384195\pi$
$677$	33.5244	−	14.9260i	1.28845	−	0.573653i	0.932607	+	0.360894i	$0.117528\pi$
$678$		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	$-0.799156\pi$
$683$		−	30.8347i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$684$		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	0.834799	−	0.550555i	$-0.185584\pi$
$701$	−4.34678	−	13.3780i	−0.164176	−	0.505281i	−0.998975	+	0.0452742i	$0.985584\pi$
$702$		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	−0.362674	−	0.931916i	$-0.618136\pi$
$719$	−32.2802	−	10.4885i	−1.20385	−	0.391155i	−0.841176	+	0.540761i	$0.818136\pi$
$720$		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	$-0.887437\pi$
$743$	1.40380	−	13.3562i	0.0515003	−	0.489993i	0.989623	−	0.143689i	$-0.0458966\pi$
$744$		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	0.349494	−	0.936939i	$-0.386354\pi$
$761$	−3.11533	−	1.38703i	−0.112930	−	0.0502799i	−0.462424	+	0.886659i	$0.653020\pi$
$762$		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	−0.849836	−	0.527048i	$-0.823299\pi$
$773$	−34.1302	+	11.0896i	−1.22758	+	0.398864i	−0.377741	+	0.925911i	$0.623299\pi$
$774$		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	−0.00256245	−	0.999997i	$-0.500816\pi$
$797$	−6.01268	−	0.631958i	−0.212980	−	0.0223851i	−0.210417	+	0.977612i	$0.567482\pi$
$798$		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	0.477016	−	0.878895i	$-0.341718\pi$
$809$	−6.01444	−	4.36974i	−0.211456	−	0.153632i	−0.688472	+	0.725263i	$0.741718\pi$
$810$		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	0.730493	−	0.682920i	$-0.239290\pi$
$821$	−0.717575	−	0.796947i	−0.0250435	−	0.0278137i	−0.755536	+	0.655107i	$0.772624\pi$
$822$		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	−0.960610	−	0.277899i	$-0.910362\pi$
$827$	−28.5608	+	20.7507i	−0.993157	+	0.721571i	−0.0325471	+	0.999470i	$0.510362\pi$
$828$		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	$-0.711143\pi$
$839$	7.74116	−	36.4193i	0.267255	−	1.25733i	0.882994	−	0.469384i	$-0.155524\pi$
$840$		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	$0.337677\pi$
$857$	−14.9819	+	25.9493i	−0.511770	+	0.886412i	−0.999907	+	0.0136449i	$0.995657\pi$
$858$		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	$-0.598118\pi$
$863$	20.4637	−	28.1659i	0.696593	−	0.958778i	0.999983	−	0.00591175i	$-0.00188178\pi$
$864$		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	$0.308658\pi$
$881$			48.9571i			1.64941i	−0.565566	+	0.824703i	$0.691342\pi$
$882$		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	−0.439661	−	0.898164i	$-0.644901\pi$
$887$	−14.1763	+	3.01328i	−0.475995	+	0.101176i	−0.0363341	+	0.999340i	$0.511568\pi$
$888$		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	0.277030	−	0.960861i	$-0.410650\pi$
$911$	22.5701	−	2.37221i	0.747781	−	0.0785950i	0.470751	+	0.882266i	$0.343983\pi$
$912$		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	0.893345	−	0.449371i	$-0.148352\pi$
$929$	−1.16942	−	2.62655i	−0.0383673	−	0.0861744i	−0.931712	+	0.363197i	$0.881685\pi$
$930$		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	$-0.932666\pi$
$941$	0.683706	−	6.50503i	0.0222882	−	0.212058i	0.999998	−	0.00209621i	$-0.000667244\pi$
$942$		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	0.888687	−	0.458515i	$-0.151619\pi$
$947$	28.8021	+	16.6289i	0.935944	+	0.540368i	0.0472574	+	0.998883i	$0.484952\pi$
$948$		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	$0.449352\pi$
$953$	−16.9820	+	52.2651i	−0.550100	+	1.69303i	−0.708545	+	0.705666i	$0.750648\pi$
$954$		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	−0.825554	−	0.564323i	$-0.809137\pi$
$971$	−36.2008	+	11.7624i	−1.16174	+	0.377472i	−0.336186	+	0.941796i	$0.609137\pi$
$972$		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	$-0.695018\pi$
$977$	13.0565	−	29.3253i	0.417713	−	0.938199i	0.992764	−	0.120081i	$-0.0383156\pi$
$978$		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	−0.374861	−	0.927081i	$-0.622309\pi$
$983$	15.9259	−	14.3398i	0.507958	−	0.457368i	0.882819	+	0.469713i	$0.155643\pi$
$984$		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.107.4		32
3.2	odd	2	inner	891.2.u.c.107.1		32
9.2	odd	6		99.2.j.a.8.1	✓	16
9.4	even	3	inner	891.2.u.c.701.1		32
9.5	odd	6	inner	891.2.u.c.701.4		32
9.7	even	3		99.2.j.a.8.4	yes	16
11.7	odd	10	inner	891.2.u.c.755.4		32
33.29	even	10	inner	891.2.u.c.755.1		32
36.7	odd	6		1584.2.cd.c.305.1		16
36.11	even	6		1584.2.cd.c.305.4		16
99.2	even	30		1089.2.d.g.1088.2		16
99.7	odd	30		99.2.j.a.62.1	yes	16
99.20	odd	30		1089.2.d.g.1088.16		16
99.29	even	30		99.2.j.a.62.4	yes	16
99.40	odd	30	inner	891.2.u.c.458.1		32
99.79	odd	30		1089.2.d.g.1088.15		16
99.95	even	30	inner	891.2.u.c.458.4		32
99.97	even	15		1089.2.d.g.1088.1		16
396.7	even	30		1584.2.cd.c.161.4		16
396.227	odd	30		1584.2.cd.c.161.1		16

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