LMFDB - Embedded newform 243.2.e.b.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			217.2
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	243.217
Dual form			243.2.e.b.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.139184 - 0.789350i) q^{2} +(1.27568 + 0.464311i) q^{4} +(2.10650 - 1.76756i) q^{5} +(-2.23349 + 0.812925i) q^{7} +(1.34559 - 2.33062i) q^{8} +(-1.10204 - 1.90878i) q^{10} +(0.191633 + 0.160799i) q^{11} +(0.453566 + 2.57230i) q^{13} +(0.330816 + 1.87615i) q^{14} +(0.427502 + 0.358716i) q^{16} +(-0.146688 - 0.254072i) q^{17} +(1.39237 - 2.41166i) q^{19} +(3.50793 - 1.27678i) q^{20} +(0.153599 - 0.128885i) q^{22} +(-6.28639 - 2.28806i) q^{23} +(0.444822 - 2.52271i) q^{25} +2.09357 q^{26} -3.22668 q^{28} +(0.0616550 - 0.349663i) q^{29} +(-2.59869 - 0.945845i) q^{31} +(4.46577 - 3.74722i) q^{32} +(-0.220968 + 0.0804258i) q^{34} +(-3.26796 + 5.66027i) q^{35} +(3.49619 + 6.05558i) q^{37} +(-1.70985 - 1.43473i) q^{38} +(-1.28505 - 7.28786i) q^{40} +(1.68744 + 9.56997i) q^{41} +(0.199713 + 0.167579i) q^{43} +(0.169802 + 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(-10.7365 + 3.90777i) q^{47} +(-1.03467 + 0.868188i) q^{49} +(-1.92939 - 0.702240i) q^{50} +(-0.615741 + 3.49204i) q^{52} -5.43137 q^{53} +0.687897 q^{55} +(-1.11073 + 6.29929i) q^{56} +(-0.267425 - 0.0973348i) q^{58} +(-4.57859 + 3.84189i) q^{59} +(11.1323 - 4.05183i) q^{61} +(-1.10830 + 1.91963i) q^{62} +(-1.77824 - 3.08001i) q^{64} +(5.50214 + 4.61685i) q^{65} +(0.314356 + 1.78280i) q^{67} +(-0.0691597 - 0.392224i) q^{68} +(4.01309 + 3.36738i) q^{70} +(-0.185255 - 0.320871i) q^{71} +(-2.51339 + 4.35333i) q^{73} +(5.26658 - 1.91688i) q^{74} +(2.89599 - 2.43002i) q^{76} +(-0.558728 - 0.203360i) q^{77} +(0.139409 - 0.790625i) q^{79} +1.53459 q^{80} +7.78892 q^{82} +(0.478514 - 2.71379i) q^{83} +(-0.758087 - 0.275921i) q^{85} +(0.160075 - 0.134319i) q^{86} +(0.632620 - 0.230255i) q^{88} +(5.22533 - 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-6.95708 - 5.83768i) q^{92} +(1.59025 + 9.01876i) q^{94} +(-1.32973 - 7.54127i) q^{95} +(-11.3640 - 9.53550i) q^{97} +(0.541296 + 0.937552i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28}+ \cdots + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.139184	−	0.789350i	0.0984177	−	0.558155i	−0.895229	−	0.445607i	$-0.852988\pi$
$2$	0.139184	−	0.789350i	0.0984177	−	0.558155i	0.993646	−	0.112548i	$-0.0359011\pi$
$3$		0			0
$3$		0			0
$4$	1.27568	+	0.464311i	0.637842	+	0.232156i
$5$	2.10650	−	1.76756i	0.942056	−	0.790479i	−0.0358862	−	0.999356i	$-0.511425\pi$
$5$	2.10650	−	1.76756i	0.942056	−	0.790479i	0.977942	+	0.208877i	$0.0669809\pi$
$6$		0			0
$7$	−2.23349	+	0.812925i	−0.844181	+	0.307257i	−0.727666	−	0.685932i	$-0.759395\pi$
$7$	−2.23349	+	0.812925i	−0.844181	+	0.307257i	−0.116516	+	0.993189i	$0.537172\pi$
$8$	1.34559	−	2.33062i	0.475736	−	0.823999i
$9$		0			0
$10$	−1.10204	−	1.90878i	−0.348494	−	0.603610i
$11$	0.191633	+	0.160799i	0.0577795	+	0.0484827i	0.671220	−	0.741258i	$-0.265771\pi$
$11$	0.191633	+	0.160799i	0.0577795	+	0.0484827i	−0.613441	+	0.789741i	$0.710215\pi$
$12$		0			0
$13$	0.453566	+	2.57230i	0.125797	+	0.713428i	0.980832	+	0.194858i	$0.0624245\pi$
$13$	0.453566	+	2.57230i	0.125797	+	0.713428i	−0.855035	+	0.518570i	$0.826464\pi$
$14$	0.330816	+	1.87615i	0.0884144	+	0.501423i
$15$		0			0
$16$	0.427502	+	0.358716i	0.106875	+	0.0896791i
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	0.847689	−	0.530494i	$-0.177994\pi$
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	−0.883266	+	0.468873i	$0.844660\pi$
$18$		0			0
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	−0.660937	−	0.750441i	$-0.729841\pi$
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	0.980370	+	0.197168i	$0.0631745\pi$
$20$	3.50793	−	1.27678i	0.784397	−	0.285497i
$21$		0			0
$22$	0.153599	−	0.128885i	0.0327474	−	0.0274783i
$23$	−6.28639	−	2.28806i	−1.31080	−	0.477094i	−0.410304	−	0.911949i	$-0.634577\pi$
$23$	−6.28639	−	2.28806i	−1.31080	−	0.477094i	−0.900500	+	0.434855i	$0.856799\pi$
$24$		0			0
$25$	0.444822	−	2.52271i	0.0889643	−	0.504542i
$26$	2.09357			0.410584
$27$		0			0
$28$	−3.22668			−0.609786
$29$	0.0616550	−	0.349663i	0.0114490	−	0.0649308i	−0.978548	−	0.206019i	$-0.933949\pi$
$29$	0.0616550	−	0.349663i	0.0114490	−	0.0649308i	0.989997	+	0.141088i	$0.0450602\pi$
$30$		0			0
$31$	−2.59869	−	0.945845i	−0.466738	−	0.169879i	0.0979360	−	0.995193i	$-0.468776\pi$
$31$	−2.59869	−	0.945845i	−0.466738	−	0.169879i	−0.564674	+	0.825314i	$0.690998\pi$
$32$	4.46577	−	3.74722i	0.789443	−	0.662422i
$33$		0			0
$34$	−0.220968	+	0.0804258i	−0.0378957	+	0.0137929i
$35$	−3.26796	+	5.66027i	−0.552386	+	0.956760i
$36$		0			0
$37$	3.49619	+	6.05558i	0.574770	+	0.995531i	0.996067	+	0.0886080i	$0.0282418\pi$
$37$	3.49619	+	6.05558i	0.574770	+	0.995531i	−0.421297	+	0.906923i	$0.638425\pi$
$38$	−1.70985	−	1.43473i	−0.277374	−	0.232744i
$39$		0			0
$40$	−1.28505	−	7.28786i	−0.203184	−	1.15231i
$41$	1.68744	+	9.56997i	0.263535	+	1.49458i	0.773176	+	0.634192i	$0.218667\pi$
$41$	1.68744	+	9.56997i	0.263535	+	1.49458i	−0.509641	+	0.860387i	$0.670222\pi$
$42$		0			0
$43$	0.199713	+	0.167579i	0.0304559	+	0.0255555i	0.657889	−	0.753115i	$-0.271450\pi$
$43$	0.199713	+	0.167579i	0.0304559	+	0.0255555i	−0.627433	+	0.778671i	$0.715894\pi$
$44$	0.169802	+	0.294106i	0.0255986	+	0.0443381i
$45$		0			0
$46$	−2.68104	+	4.64370i	−0.395298	+	0.684677i
$47$	−10.7365	+	3.90777i	−1.56608	+	0.570007i	−0.972119	−	0.234486i	$-0.924659\pi$
$47$	−10.7365	+	3.90777i	−1.56608	+	0.570007i	−0.593962	+	0.804493i	$0.702437\pi$
$48$		0			0
$49$	−1.03467	+	0.868188i	−0.147810	+	0.124027i
$50$	−1.92939	−	0.702240i	−0.272857	−	0.0993117i
$51$		0			0
$52$	−0.615741	+	3.49204i	−0.0853879	+	0.484259i
$53$	−5.43137			−0.746056			−0.373028	−	0.927820i	$-0.621680\pi$
$53$	−5.43137			−0.746056			−0.373028	+	0.927820i	$0.621680\pi$
$54$		0			0
$55$	0.687897			0.0927560
$56$	−1.11073	+	6.29929i	−0.148428	+	0.841778i
$57$		0			0
$58$	−0.267425	−	0.0973348i	−0.0351146	−	0.0127807i
$59$	−4.57859	+	3.84189i	−0.596082	+	0.500172i	−0.890184	−	0.455602i	$-0.849424\pi$
$59$	−4.57859	+	3.84189i	−0.596082	+	0.500172i	0.294102	+	0.955774i	$0.404980\pi$
$60$		0			0
$61$	11.1323	−	4.05183i	1.42535	−	0.518784i	0.489753	−	0.871861i	$-0.337087\pi$
$61$	11.1323	−	4.05183i	1.42535	−	0.518784i	0.935594	+	0.353078i	$0.114865\pi$
$62$	−1.10830	+	1.91963i	−0.140754	+	0.243793i
$63$		0			0
$64$	−1.77824	−	3.08001i	−0.222281	−	0.385001i
$65$	5.50214	+	4.61685i	0.682457	+	0.572649i
$66$		0			0
$67$	0.314356	+	1.78280i	0.0384047	+	0.217804i	0.997970	−	0.0636814i	$-0.0202841\pi$
$67$	0.314356	+	1.78280i	0.0384047	+	0.217804i	−0.959566	+	0.281485i	$0.909173\pi$
$68$	−0.0691597	−	0.392224i	−0.00838685	−	0.0475642i
$69$		0			0
$70$	4.01309	+	3.36738i	0.479656	+	0.402479i
$71$	−0.185255	−	0.320871i	−0.0219857	−	0.0380804i	0.854823	−	0.518919i	$-0.173666\pi$
$71$	−0.185255	−	0.320871i	−0.0219857	−	0.0380804i	−0.876809	+	0.480839i	$0.840332\pi$
$72$		0			0
$73$	−2.51339	+	4.35333i	−0.294171	+	0.509518i	−0.974792	−	0.223117i	$-0.928377\pi$
$73$	−2.51339	+	4.35333i	−0.294171	+	0.509518i	0.680621	+	0.732636i	$0.261710\pi$
$74$	5.26658	−	1.91688i	0.612228	−	0.222833i
$75$		0			0
$76$	2.89599	−	2.43002i	0.332193	−	0.278743i
$77$	−0.558728	−	0.203360i	−0.0636730	−	0.0231751i
$78$		0			0
$79$	0.139409	−	0.790625i	0.0156847	−	0.0889523i	−0.975961	−	0.217947i	$-0.930064\pi$
$79$	0.139409	−	0.790625i	0.0156847	−	0.0889523i	0.991645	+	0.128995i	$0.0411751\pi$
$80$	1.53459			0.171572
$81$		0			0
$82$	7.78892			0.860143
$83$	0.478514	−	2.71379i	0.0525237	−	0.297877i	−0.947218	−	0.320589i	$-0.896119\pi$
$83$	0.478514	−	2.71379i	0.0525237	−	0.297877i	0.999742	+	0.0227124i	$0.00723021\pi$
$84$		0			0
$85$	−0.758087	−	0.275921i	−0.0822261	−	0.0299279i
$86$	0.160075	−	0.134319i	0.0172613	−	0.0144840i
$87$		0			0
$88$	0.632620	−	0.230255i	0.0674375	−	0.0245452i
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	−0.444105	−	0.895975i	$-0.646478\pi$
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	0.997989	−	0.0633809i	$-0.0201883\pi$
$90$		0			0
$91$	−3.10412	−	5.37650i	−0.325401	−	0.563611i
$92$	−6.95708	−	5.83768i	−0.725326	−	0.608621i
$93$		0			0
$94$	1.59025	+	9.01876i	0.164022	+	0.930214i
$95$	−1.32973	−	7.54127i	−0.136427	−	0.773718i
$96$		0			0
$97$	−11.3640	−	9.53550i	−1.15384	−	0.968183i	−0.154034	−	0.988066i	$-0.549226\pi$
$97$	−11.3640	−	9.53550i	−1.15384	−	0.968183i	−0.999802	+	0.0198821i	$0.993671\pi$
$98$	0.541296	+	0.937552i	0.0546791	+	0.0947070i
$99$		0			0
$100$	1.73877	−	3.01164i	0.173877	−	0.301164i
$101$	3.76378	−	1.36990i	0.374510	−	0.136310i	−0.147906	−	0.989001i	$-0.547253\pi$
$101$	3.76378	−	1.36990i	0.374510	−	0.136310i	0.522416	+	0.852691i	$0.325031\pi$
$102$		0			0
$103$	−4.53449	+	3.80489i	−0.446797	+	0.374907i	−0.838246	−	0.545293i	$-0.816418\pi$
$103$	−4.53449	+	3.80489i	−0.446797	+	0.374907i	0.391449	+	0.920200i	$0.371974\pi$
$104$	6.60537	+	2.40416i	0.647710	+	0.235747i
$105$		0			0
$106$	−0.755958	+	4.28725i	−0.0734251	+	0.416415i
$107$	0.258978			0.0250364			0.0125182	−	0.999922i	$-0.496015\pi$
$107$	0.258978			0.0250364			0.0125182	+	0.999922i	$0.496015\pi$
$108$		0			0
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$	0.0957441	−	0.542992i	0.00912884	−	0.0517722i
$111$		0			0
$112$	−1.24643	−	0.453664i	−0.117777	−	0.0428672i
$113$	2.38943	−	2.00497i	0.224779	−	0.188612i	−0.523443	−	0.852061i	$-0.675353\pi$
$113$	2.38943	−	2.00497i	0.224779	−	0.188612i	0.748221	+	0.663449i	$0.230908\pi$
$114$		0			0
$115$	−17.2866	+	6.29180i	−1.61198	+	0.586714i
$116$	0.241005	−	0.417432i	0.0223767	−	0.0387576i
$117$		0			0
$118$	2.39533	+	4.14884i	0.220508	+	0.381932i
$119$	0.534169	+	0.448221i	0.0489672	+	0.0410883i
$120$		0			0
$121$	−1.89926	−	10.7713i	−0.172660	−	0.979205i
$122$	−1.64888	−	9.35124i	−0.149282	−	0.846621i
$123$		0			0
$124$	−2.87594	−	2.41320i	−0.258267	−	0.216712i
$125$	3.35257	+	5.80682i	0.299863	+	0.519378i
$126$		0			0
$127$	9.22726	−	15.9821i	0.818787	−	1.41818i	−0.0877893	−	0.996139i	$-0.527980\pi$
$127$	9.22726	−	15.9821i	0.818787	−	1.41818i	0.906576	−	0.422042i	$-0.138686\pi$
$128$	8.27744	−	3.01274i	0.731629	−	0.266291i
$129$		0			0
$130$	4.41012	−	3.70053i	0.386793	−	0.324558i
$131$	13.3676	+	4.86540i	1.16793	+	0.425092i	0.851924	−	0.523665i	$-0.175436\pi$
$131$	13.3676	+	4.86540i	1.16793	+	0.425092i	0.316006	+	0.948757i	$0.397658\pi$
$132$		0			0
$133$	−1.14936	+	6.51832i	−0.0996618	+	0.565210i
$134$	1.45101			0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	3.41837	−	19.3865i	0.292051	−	1.65630i	−0.386903	−	0.922121i	$-0.626455\pi$
$137$	3.41837	−	19.3865i	0.292051	−	1.65630i	0.678953	−	0.734181i	$-0.262434\pi$
$138$		0			0
$139$	16.8308	+	6.12591i	1.42757	+	0.519593i	0.936234	−	0.351378i	$-0.114287\pi$
$139$	16.8308	+	6.12591i	1.42757	+	0.519593i	0.491336	+	0.870970i	$0.336509\pi$
$140$	−6.79701	+	5.70337i	−0.574452	+	0.482022i
$141$		0			0
$142$	−0.279064	+	0.101571i	−0.0234185	+	0.00852365i
$143$	−0.326705	+	0.565870i	−0.0273205	+	0.0473205i
$144$		0			0
$145$	−0.488175	−	0.845544i	−0.0405408	−	0.0702186i
$146$	3.08647	+	2.58986i	0.255438	+	0.214338i
$147$		0			0
$148$	1.64836	+	9.34832i	0.135495	+	0.768428i
$149$	−2.82863	−	16.0420i	−0.231731	−	1.31421i	−0.849390	−	0.527765i	$-0.823030\pi$
$149$	−2.82863	−	16.0420i	−0.231731	−	1.31421i	0.617660	−	0.786446i	$-0.288081\pi$
$150$		0			0
$151$	10.9352	+	9.17571i	0.889893	+	0.746709i	0.968189	−	0.250222i	$-0.0805035\pi$
$151$	10.9352	+	9.17571i	0.889893	+	0.746709i	−0.0782960	+	0.996930i	$0.524948\pi$
$152$	−3.74711	−	6.49019i	−0.303931	−	0.526424i
$153$		0			0
$154$	−0.238288	+	0.412728i	−0.0192018	+	0.0332585i
$155$	−7.14598	+	2.60092i	−0.573979	+	0.208911i
$156$		0			0
$157$	0.584763	−	0.490675i	0.0466692	−	0.0391601i	−0.619155	−	0.785269i	$-0.712525\pi$
$157$	0.584763	−	0.490675i	0.0466692	−	0.0391601i	0.665824	+	0.746109i	$0.268080\pi$
$158$	−0.604676	−	0.220084i	−0.0481055	−	0.0175090i
$159$		0			0
$160$	2.78368	−	15.7871i	0.220070	−	1.24808i
$161$	15.9006			1.25315
$162$		0			0
$163$	5.12834			0.401682			0.200841	−	0.979624i	$-0.435632\pi$
$163$	5.12834			0.401682			0.200841	+	0.979624i	$0.435632\pi$
$164$	−2.29080	+	12.9918i	−0.178881	+	1.01449i
$165$		0			0
$166$	−2.07553	−	0.755430i	−0.161092	−	0.0586327i
$167$	−6.81866	+	5.72153i	−0.527643	+	0.442745i	−0.867287	−	0.497809i	$-0.834138\pi$
$167$	−6.81866	+	5.72153i	−0.527643	+	0.442745i	0.339643	+	0.940554i	$0.389694\pi$
$168$		0			0
$169$	5.80499	−	2.11284i	0.446538	−	0.162526i
$170$	−0.323312	+	0.559992i	−0.0247969	+	0.0429495i
$171$		0			0
$172$	0.176962	+	0.306507i	0.0134932	+	0.0233709i
$173$	5.21771	+	4.37818i	0.396695	+	0.332867i	0.819215	−	0.573487i	$-0.194410\pi$
$173$	5.21771	+	4.37818i	0.396695	+	0.332867i	−0.422519	+	0.906354i	$0.638854\pi$
$174$		0			0
$175$	1.05727	+	5.99606i	0.0799219	+	0.453260i
$176$	0.0242421	+	0.137484i	0.00182732	+	0.0103632i
$177$		0			0
$178$	−6.41676	−	5.38430i	−0.480957	−	0.403571i
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	−0.973221	−	0.229870i	$-0.926170\pi$
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	0.287538	−	0.957769i	$-0.407163\pi$
$180$		0			0
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	−0.996029	−	0.0890276i	$-0.971624\pi$
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	0.575115	+	0.818073i	$0.304957\pi$
$182$	−4.67599	+	1.70192i	−0.346607	+	0.126155i
$183$		0			0
$184$	−13.7915	+	11.5724i	−1.01672	+	0.853131i
$185$	18.0683	+	6.57634i	1.32841	+	0.483502i
$186$		0			0
$187$	0.0127442	−	0.0722758i	0.000931947	−	0.00528533i
$188$	−15.5108			−1.13124
$189$		0			0
$190$	−6.13778			−0.445281
$191$	−1.19095	+	6.75422i	−0.0861742	+	0.488718i	0.910923	+	0.412577i	$0.135371\pi$
$191$	−1.19095	+	6.75422i	−0.0861742	+	0.488718i	−0.997097	+	0.0761413i	$0.975740\pi$
$192$		0			0
$193$	−19.1818	−	6.98159i	−1.38073	−	0.502546i	−0.458333	−	0.888781i	$-0.651553\pi$
$193$	−19.1818	−	6.98159i	−1.38073	−	0.502546i	−0.922400	+	0.386235i	$0.873775\pi$
$194$	−9.10853	+	7.64296i	−0.653954	+	0.548733i
$195$		0			0
$196$	−1.72302	+	0.627127i	−0.123073	+	0.0447948i
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	−0.806875	−	0.590723i	$-0.798843\pi$
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	0.915018	+	0.403413i	$0.132176\pi$
$198$		0			0
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	0.903332	−	0.428942i	$-0.141114\pi$
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	−0.823141	+	0.567837i	$0.807780\pi$
$200$	−5.28094	−	4.43123i	−0.373419	−	0.313335i
$201$		0			0
$202$	−0.557476	−	3.16160i	−0.0392239	−	0.222450i
$203$	0.146544	+	0.831091i	0.0102854	+	0.0583311i
$204$		0			0
$205$	20.4701	+	17.1765i	1.42970	+	1.19966i
$206$	2.37226	+	4.10888i	0.165283	+	0.286279i
$207$		0			0
$208$	−0.728826	+	1.26236i	−0.0505350	+	0.0875292i
$209$	0.654617	−	0.238261i	0.0452808	−	0.0164809i
$210$		0			0
$211$	19.4811	−	16.3466i	1.34114	−	1.12535i	0.359804	−	0.933028i	$-0.382844\pi$
$211$	19.4811	−	16.3466i	1.34114	−	1.12535i	0.981333	−	0.192319i	$-0.0616007\pi$
$212$	−6.92871	−	2.52184i	−0.475866	−	0.173201i
$213$		0			0
$214$	0.0360456	−	0.204425i	0.00246402	−	0.0139742i
$215$	0.716901			0.0488923
$216$		0			0
$217$	6.57305			0.446208
$218$	−1.19112	+	6.75516i	−0.0806726	+	0.457517i
$219$		0			0
$220$	0.877539	+	0.319398i	0.0591637	+	0.0215338i
$221$	0.587016	−	0.492565i	0.0394870	−	0.0331335i
$222$		0			0
$223$	3.60028	−	1.31039i	0.241093	−	0.0877505i	−0.218648	−	0.975804i	$-0.570165\pi$
$223$	3.60028	−	1.31039i	0.241093	−	0.0877505i	0.459741	+	0.888053i	$0.347942\pi$
$224$	−6.92805	+	11.9997i	−0.462900	+	0.801766i
$225$		0			0
$226$	−1.25005	−	2.16515i	−0.0831523	−	0.144024i
$227$	−1.92736	−	1.61725i	−0.127923	−	0.107341i	0.576581	−	0.817040i	$-0.304386\pi$
$227$	−1.92736	−	1.61725i	−0.127923	−	0.107341i	−0.704505	+	0.709699i	$0.748831\pi$
$228$		0			0
$229$	−2.76789	−	15.6975i	−0.182907	−	1.03732i	−0.928615	−	0.371045i	$-0.879000\pi$
$229$	−2.76789	−	15.6975i	−0.182907	−	1.03732i	0.745708	−	0.666273i	$-0.232111\pi$
$230$	2.56042	+	14.5209i	0.168829	+	0.957479i
$231$		0			0
$232$	−0.731970	−	0.614196i	−0.0480562	−	0.0403239i
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.797295	+	0.603590i	$0.206264\pi$
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.124077	+	0.992273i	$0.460403\pi$
$234$		0			0
$235$	−15.7092	+	27.2092i	−1.02476	+	1.77493i
$236$	−7.62467	+	2.77515i	−0.496324	+	0.180647i
$237$		0			0
$238$	0.428151	−	0.359261i	0.0277529	−	0.0232874i
$239$	−13.8189	−	5.02968i	−0.893872	−	0.325343i	−0.146077	−	0.989273i	$-0.546665\pi$
$239$	−13.8189	−	5.02968i	−0.893872	−	0.325343i	−0.747794	+	0.663930i	$0.768887\pi$
$240$		0			0
$241$	1.46610	−	8.31468i	0.0944400	−	0.535596i	−0.900478	−	0.434902i	$-0.856783\pi$
$241$	1.46610	−	8.31468i	0.0944400	−	0.535596i	0.994918	−	0.100693i	$-0.0321060\pi$
$242$	−8.76664			−0.563541
$243$		0			0
$244$	16.0826			1.02958
$245$	−0.644947	+	3.65768i	−0.0412042	+	0.233680i
$246$		0			0
$247$	6.83505	+	2.48775i	0.434904	+	0.158292i
$248$	−5.70116	+	4.78384i	−0.362024	+	0.303774i
$249$		0			0
$250$	5.05024	−	1.83814i	0.319405	−	0.116254i
$251$	−11.6102	+	20.1095i	−0.732832	+	1.26930i	0.222835	+	0.974856i	$0.428469\pi$
$251$	−11.6102	+	20.1095i	−0.732832	+	1.26930i	−0.955668	+	0.294447i	$0.904865\pi$
$252$		0			0
$253$	−0.836762	−	1.44931i	−0.0526067	−	0.0911176i
$254$	−11.3312	−	9.50798i	−0.710981	−	0.596584i
$255$		0			0
$256$	−2.46118	−	13.9580i	−0.153824	−	0.872377i
$257$	−1.19213	−	6.76090i	−0.0743630	−	0.421733i	−0.999149	−	0.0412458i	$-0.986867\pi$
$257$	−1.19213	−	6.76090i	−0.0743630	−	0.421733i	0.924786	−	0.380488i	$-0.124244\pi$
$258$		0			0
$259$	−12.7314	−	10.6830i	−0.791094	−	0.663806i
$260$	4.87534	+	8.44434i	0.302356	+	0.523696i
$261$		0			0
$262$	5.70105	−	9.87451i	0.352212	−	0.610049i
$263$	3.15073	−	1.14677i	0.194282	−	0.0707130i	−0.243047	−	0.970015i	$-0.578147\pi$
$263$	3.15073	−	1.14677i	0.194282	−	0.0707130i	0.437329	+	0.899302i	$0.355925\pi$
$264$		0			0
$265$	−11.4412	+	9.60029i	−0.702826	+	0.589741i
$266$	4.98526	+	1.81449i	0.305666	+	0.111253i
$267$		0			0
$268$	−0.426755	+	2.42025i	−0.0260682	+	0.147840i
$269$	−12.7416			−0.776869			−0.388434	−	0.921476i	$-0.626984\pi$
$269$	−12.7416			−0.776869			−0.388434	+	0.921476i	$0.626984\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	0.0284302	−	0.161236i	0.00172383	−	0.00977635i
$273$		0			0
$274$	−14.8270	−	5.39657i	−0.895730	−	0.326019i
$275$	0.490892	−	0.411907i	0.0296019	−	0.0248389i
$276$		0			0
$277$	−3.92906	+	1.43006i	−0.236074	+	0.0859240i	−0.457348	−	0.889288i	$-0.651201\pi$
$277$	−3.92906	+	1.43006i	−0.236074	+	0.0859240i	0.221274	+	0.975212i	$0.428978\pi$
$278$	7.17806	−	12.4328i	0.430511	−	0.745667i
$279$		0			0
$280$	8.79463	+	15.2327i	0.525580	+	0.910331i
$281$	16.5742	+	13.9074i	0.988731	+	0.829644i	0.985384	−	0.170351i	$-0.0544900\pi$
$281$	16.5742	+	13.9074i	0.988731	+	0.829644i	0.00334741	+	0.999994i	$0.498934\pi$
$282$		0			0
$283$	0.907718	+	5.14792i	0.0539582	+	0.306012i	0.999828	−	0.0185334i	$-0.00589971\pi$
$283$	0.907718	+	5.14792i	0.0539582	+	0.306012i	−0.945870	+	0.324546i	$0.894789\pi$
$284$	−0.0873428	−	0.495346i	−0.00518284	−	0.0293934i
$285$		0			0
$286$	0.401198	+	0.336645i	0.0237233	+	0.0199062i
$287$	−11.5486	−	20.0027i	−0.681690	−	1.18072i
$288$		0			0
$289$	8.45697	−	14.6479i	0.497469	−	0.861641i
$290$	−0.735376	+	0.267655i	−0.0431828	+	0.0157173i
$291$		0			0
$292$	−5.22759	+	4.38647i	−0.305922	+	0.256699i
$293$	−5.77175	−	2.10074i	−0.337189	−	0.122727i	0.167876	−	0.985808i	$-0.446309\pi$
$293$	−5.77175	−	2.10074i	−0.337189	−	0.122727i	−0.505065	+	0.863081i	$0.668531\pi$
$294$		0			0
$295$	−2.85401	+	16.1859i	−0.166167	+	0.942380i
$296$	18.8177			1.09376
$297$		0			0
$298$	−13.0564			−0.756339
$299$	3.03429	−	17.2083i	0.175477	−	0.995181i
$300$		0			0
$301$	−0.582286	−	0.211935i	−0.0335624	−	0.0122157i
$302$	8.76484	−	7.35458i	0.504360	−	0.423208i
$303$		0			0
$304$	1.46034	−	0.531522i	0.0837564	−	0.0304849i
$305$	16.2884	−	28.2123i	0.932669	−	1.61543i
$306$		0			0
$307$	−9.50194	−	16.4578i	−0.542304	−	0.939298i	−0.998771	−	0.0495580i	$-0.984219\pi$
$307$	−9.50194	−	16.4578i	−0.542304	−	0.939298i	0.456467	−	0.889740i	$-0.349115\pi$
$308$	−0.618338	−	0.518847i	−0.0352331	−	0.0295641i
$309$		0			0
$310$	1.05844	+	6.00268i	0.0601151	+	0.340930i
$311$	3.74158	+	21.2196i	0.212166	+	1.20325i	0.885758	+	0.464148i	$0.153639\pi$
$311$	3.74158	+	21.2196i	0.212166	+	1.20325i	−0.673592	+	0.739103i	$0.735250\pi$
$312$		0			0
$313$	−2.92140	−	2.45135i	−0.165127	−	0.138558i	0.556480	−	0.830861i	$-0.312152\pi$
$313$	−2.92140	−	2.45135i	−0.165127	−	0.138558i	−0.721607	+	0.692303i	$0.756596\pi$
$314$	−0.305925	−	0.529877i	−0.0172643	−	0.0299027i
$315$		0			0
$316$	0.544937	−	0.943859i	0.0306551	−	0.0530962i
$317$	3.99791	−	1.45512i	0.224545	−	0.0817277i	−0.227298	−	0.973825i	$-0.572989\pi$
$317$	3.99791	−	1.45512i	0.224545	−	0.0817277i	0.451843	+	0.892098i	$0.350767\pi$
$318$		0			0
$319$	0.0680406	−	0.0570928i	0.00380954	−	0.00319658i
$320$	−9.18999	−	3.34488i	−0.513736	−	0.186985i
$321$		0			0
$322$	2.21311	−	12.5512i	0.123332	−	0.699449i
$323$	−0.816980			−0.0454580
$324$		0			0
$325$	6.69092			0.371146
$326$	0.713781	−	4.04805i	0.0395327	−	0.224201i
$327$		0			0
$328$	24.5746	+	8.94442i	1.35690	+	0.493873i
$329$	20.8032	−	17.4560i	1.14692	−	0.962378i
$330$		0			0
$331$	13.4318	−	4.88876i	0.738277	−	0.268711i	0.0546128	−	0.998508i	$-0.482608\pi$
$331$	13.4318	−	4.88876i	0.738277	−	0.268711i	0.683664	+	0.729797i	$0.260385\pi$
$332$	1.87047	−	3.23976i	0.102656	−	0.177805i
$333$		0			0
$334$	3.56725	+	6.17865i	0.195191	+	0.338081i
$335$	3.81340	+	3.19982i	0.208348	+	0.174825i
$336$		0			0
$337$	6.20245	+	35.1759i	0.337869	+	1.91615i	0.396833	+	0.917891i	$0.370109\pi$
$337$	6.20245	+	35.1759i	0.337869	+	1.91615i	−0.0589637	+	0.998260i	$0.518780\pi$
$338$	−0.859813	−	4.87624i	−0.0467677	−	0.265233i
$339$		0			0
$340$	−0.838967	−	0.703977i	−0.0454994	−	0.0381785i
$341$	−0.345903	−	0.599121i	−0.0187317	−	0.0324442i
$342$		0			0
$343$	9.92407	−	17.1890i	0.535849	−	0.928118i
$344$	0.659294	−	0.239963i	0.0355467	−	0.0129379i
$345$		0			0
$346$	4.18214	−	3.50923i	0.224833	−	0.188657i
$347$	−18.2691	−	6.64939i	−0.980735	−	0.356958i	−0.198609	−	0.980079i	$-0.563642\pi$
$347$	−18.2691	−	6.64939i	−0.980735	−	0.356958i	−0.782126	+	0.623121i	$0.785865\pi$
$348$		0			0
$349$	−1.39278	+	7.89885i	−0.0745538	+	0.422816i	0.924572	+	0.381008i	$0.124423\pi$
$349$	−1.39278	+	7.89885i	−0.0745538	+	0.422816i	−0.999126	+	0.0418080i	$0.986688\pi$
$350$	4.88014			0.260855
$351$		0			0
$352$	1.45834			0.0777296
$353$	−1.52008	+	8.62082i	−0.0809059	+	0.458840i	0.917259	+	0.398291i	$0.130396\pi$
$353$	−1.52008	+	8.62082i	−0.0809059	+	0.458840i	−0.998165	+	0.0605496i	$0.980715\pi$
$354$		0			0
$355$	−0.957400	−	0.348465i	−0.0508135	−	0.0184946i
$356$	10.8681	−	9.11945i	0.576010	−	0.483330i
$357$		0			0
$358$	−13.8192	+	5.02979i	−0.730370	+	0.265833i
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	−0.954333	−	0.298745i	$-0.903432\pi$
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	0.735887	+	0.677104i	$0.236765\pi$
$360$		0			0
$361$	5.62260	+	9.73862i	0.295926	+	0.512559i
$362$	6.95401	+	5.83511i	0.365495	+	0.306686i
$363$		0			0
$364$	−1.46351	−	8.30000i	−0.0767089	−	0.435038i
$365$	2.40032	+	13.6129i	0.125638	+	0.712530i
$366$		0			0
$367$	−11.3373	−	9.51316i	−0.591805	−	0.496583i	0.296995	−	0.954879i	$-0.404016\pi$
$367$	−11.3373	−	9.51316i	−0.591805	−	0.496583i	−0.888800	+	0.458296i	$0.848460\pi$
$368$	−1.86668	−	3.23318i	−0.0973074	−	0.168541i
$369$		0			0
$370$	7.70585	−	13.3469i	0.400608	−	0.693874i
$371$	12.1309	−	4.41530i	0.629806	−	0.229231i
$372$		0			0
$373$	19.5597	−	16.4126i	1.01276	−	0.849810i	0.0240627	−	0.999710i	$-0.492340\pi$
$373$	19.5597	−	16.4126i	1.01276	−	0.849810i	0.988701	+	0.149901i	$0.0478954\pi$
$374$	−0.0552771	−	0.0201192i	−0.00285831	−	0.00104034i
$375$		0			0
$376$	−5.33936	+	30.2810i	−0.275356	+	1.56162i
$377$	0.927403			0.0477637
$378$		0			0
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$	1.80518	−	10.2377i	0.0926038	−	0.525182i
$381$		0			0
$382$	5.16568	+	1.88015i	0.264299	+	0.0961970i
$383$	18.2788	−	15.3377i	0.934002	−	0.783721i	−0.0425294	−	0.999095i	$-0.513542\pi$
$383$	18.2788	−	15.3377i	0.934002	−	0.783721i	0.976532	+	0.215374i	$0.0690972\pi$
$384$		0			0
$385$	−1.53641	+	0.559209i	−0.0783029	+	0.0284999i
$386$	−8.18070	+	14.1694i	−0.416387	+	0.721203i
$387$		0			0
$388$	−10.0694	−	17.4407i	−0.511196	−	0.885418i
$389$	−29.0892	−	24.4088i	−1.47488	−	1.23757i	−0.911449	−	0.411413i	$-0.865035\pi$
$389$	−29.0892	−	24.4088i	−1.47488	−	1.23757i	−0.563434	−	0.826161i	$-0.690520\pi$
$390$		0			0
$391$	0.340810	+	1.93283i	0.0172355	+	0.0977473i
$392$	0.631187	+	3.57964i	0.0318797	+	0.180799i
$393$		0			0
$394$	−1.86395	−	1.56404i	−0.0939046	−	0.0787953i
$395$	−1.10382	−	1.91187i	−0.0555390	−	0.0961964i
$396$		0			0
$397$	−10.1747	+	17.6230i	−0.510651	+	0.884474i	0.489272	+	0.872131i	$0.337262\pi$
$397$	−10.1747	+	17.6230i	−0.510651	+	0.884474i	−0.999924	+	0.0123433i	$0.996071\pi$
$398$	1.70407	−	0.620230i	0.0854173	−	0.0310893i
$399$		0			0
$400$	1.09510	−	0.918897i	0.0547550	−	0.0459449i
$401$	6.52613	+	2.37532i	0.325900	+	0.118618i	0.499788	−	0.866148i	$-0.333411\pi$
$401$	6.52613	+	2.37532i	0.325900	+	0.118618i	−0.173889	+	0.984765i	$0.555633\pi$
$402$		0			0
$403$	1.25432	−	7.11361i	0.0624822	−	0.354354i
$404$	5.43745			0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	−0.303746	+	1.72263i	−0.0150561	+	0.0853877i
$408$		0			0
$409$	10.2482	+	3.73005i	0.506743	+	0.184439i	0.582724	−	0.812670i	$-0.301987\pi$
$409$	10.2482	+	3.73005i	0.506743	+	0.184439i	−0.0759814	+	0.997109i	$0.524209\pi$
$410$	16.4074	−	13.7674i	0.810302	−	0.679924i
$411$		0			0
$412$	−7.55123	+	2.74842i	−0.372023	+	0.135405i
$413$	7.10308	−	12.3029i	0.349520	−	0.605386i
$414$		0			0
$415$	−3.78880	−	6.56240i	−0.185985	−	0.322135i
$416$	11.6645	+	9.78768i	0.571899	+	0.479881i
$417$		0			0
$418$	−0.0969594	−	0.549884i	−0.00474244	−	0.0268957i
$419$	1.74850	+	9.91621i	0.0854196	+	0.484439i	0.997265	+	0.0739054i	$0.0235463\pi$
$419$	1.74850	+	9.91621i	0.0854196	+	0.484439i	−0.911846	+	0.410533i	$0.865343\pi$
$420$		0			0
$421$	−2.38053	−	1.99750i	−0.116020	−	0.0973524i	0.582932	−	0.812521i	$-0.301905\pi$
$421$	−2.38053	−	1.99750i	−0.116020	−	0.0973524i	−0.698952	+	0.715169i	$0.746350\pi$
$422$	−10.1917	−	17.6526i	−0.496126	−	0.859315i
$423$		0			0
$424$	−7.30837	+	12.6585i	−0.354926	+	0.614750i
$425$	−0.706199	+	0.257036i	−0.0342557	+	0.0124681i
$426$		0			0
$427$	−21.5701	+	18.0995i	−1.04385	+	0.875895i
$428$	0.330375	+	0.120247i	0.0159693	+	0.00581234i
$429$		0			0
$430$	0.0997810	−	0.565886i	0.00481187	−	0.0272894i
$431$	28.0701			1.35209			0.676044	−	0.736862i	$-0.263693\pi$
$431$	28.0701			1.35209			0.676044	+	0.736862i	$0.263693\pi$
$432$		0			0
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$	0.914862	−	5.18844i	0.0439148	−	0.249053i
$435$		0			0
$436$	−10.9171	−	3.97351i	−0.522836	−	0.190297i
$437$	−14.2710	+	11.9748i	−0.682676	+	0.572833i
$438$		0			0
$439$	−13.7473	+	5.00361i	−0.656123	+	0.238809i	−0.648562	−	0.761162i	$-0.724629\pi$
$439$	−13.7473	+	5.00361i	−0.656123	+	0.238809i	−0.00756144	+	0.999971i	$0.502407\pi$
$440$	0.925624	−	1.60323i	0.0441274	−	0.0764309i
$441$		0			0
$442$	−0.307103	−	0.531918i	−0.0146074	−	0.0253008i
$443$	−14.0615	−	11.7990i	−0.668081	−	0.560586i	0.244416	−	0.969670i	$-0.421404\pi$
$443$	−14.0615	−	11.7990i	−0.668081	−	0.560586i	−0.912497	+	0.409084i	$0.865848\pi$
$444$		0			0
$445$	−4.99024	−	28.3011i	−0.236560	−	1.34160i
$446$	−0.533260	−	3.02427i	−0.0252506	−	0.143203i
$447$		0			0
$448$	6.47551	+	5.43360i	0.305939	+	0.256714i
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	0.981922	−	0.189288i	$-0.0606180\pi$
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	−0.654889	+	0.755725i	$0.727285\pi$
$450$		0			0
$451$	−1.21547	+	2.10526i	−0.0572344	+	0.0991328i
$452$	3.97909	−	1.44827i	0.187160	−	0.0681208i
$453$		0			0
$454$	−1.54483	+	1.29627i	−0.0725026	+	0.0608369i
$455$	−16.0422	−	5.83887i	−0.752068	−	0.273730i
$456$		0			0
$457$	3.06457	−	17.3800i	0.143354	−	0.813003i	−0.825319	−	0.564666i	$-0.809005\pi$
$457$	3.06457	−	17.3800i	0.143354	−	0.813003i	0.968674	−	0.248337i	$-0.0798839\pi$
$458$	−12.7760			−0.596985
$459$		0			0
$460$	−24.9736			−1.16440
$461$	−4.45200	+	25.2485i	−0.207350	+	1.17594i	0.686348	+	0.727273i	$0.259213\pi$
$461$	−4.45200	+	25.2485i	−0.207350	+	1.17594i	−0.893698	+	0.448668i	$0.851898\pi$
$462$		0			0
$463$	−17.2409	−	6.27519i	−0.801254	−	0.291633i	−0.0912482	−	0.995828i	$-0.529086\pi$
$463$	−17.2409	−	6.27519i	−0.801254	−	0.291633i	−0.710006	+	0.704195i	$0.751308\pi$
$464$	0.151787	−	0.127365i	0.00704656	−	0.00591276i
$465$		0			0
$466$	21.1859	−	7.71104i	0.981418	−	0.357207i
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	−0.990514	−	0.137412i	$-0.956121\pi$
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	0.614260	+	0.789104i	$0.289455\pi$
$468$		0			0
$469$	−2.15139	−	3.72632i	−0.0993421	−	0.172066i
$470$	19.2911	+	16.1872i	0.889832	+	0.746658i
$471$		0			0
$472$	2.79312	+	15.8406i	0.128564	+	0.729121i
$473$	0.0113250	+	0.0642272i	0.000520724	+	0.00295317i
$474$		0			0
$475$	−5.46456	−	4.58531i	−0.250731	−	0.210388i
$476$	0.473317	+	0.819809i	0.0216944	+	0.0375759i
$477$		0			0
$478$	−5.89354	+	10.2079i	−0.269564	+	0.466899i
$479$	−8.90050	+	3.23952i	−0.406674	+	0.148017i	−0.537254	−	0.843421i	$-0.680538\pi$
$479$	−8.90050	+	3.23952i	−0.406674	+	0.148017i	0.130580	+	0.991438i	$0.458316\pi$
$480$		0			0
$481$	−13.9910	+	11.7399i	−0.637936	+	0.535291i
$482$	−6.35913	−	2.31454i	−0.289651	−	0.105424i
$483$		0			0
$484$	2.57835	−	14.6226i	0.117198	−	0.664662i
$485$	−40.7928			−1.85231
$486$		0			0
$487$	−0.467564			−0.0211874			−0.0105937	−	0.999944i	$-0.503372\pi$
$487$	−0.467564			−0.0211874			−0.0105937	+	0.999944i	$0.503372\pi$
$488$	5.53619	−	31.3973i	0.250612	−	1.42129i
$489$		0			0
$490$	2.79742	+	1.01818i	0.126375	+	0.0459966i
$491$	−19.1871	+	16.0999i	−0.865902	+	0.726578i	−0.963231	−	0.268674i	$-0.913415\pi$
$491$	−19.1871	+	16.0999i	−0.865902	+	0.726578i	0.0973291	+	0.995252i	$0.468970\pi$
$492$		0			0
$493$	−0.0978836	+	0.0356267i	−0.00440845	+	0.00160455i
$494$	2.91504	−	5.04899i	0.131154	−	0.227165i
$495$		0			0
$496$	−0.771653	−	1.33654i	−0.0346482	−	0.0600125i
$497$	0.674610	+	0.566065i	0.0302604	+	0.0253915i
$498$		0			0
$499$	−2.43701	−	13.8209i	−0.109095	−	0.618711i	−0.989505	−	0.144497i	$-0.953844\pi$
$499$	−2.43701	−	13.8209i	−0.109095	−	0.618711i	0.880410	−	0.474214i	$-0.157268\pi$
$500$	1.58065	+	8.96431i	0.0706888	+	0.400896i
$501$		0			0
$502$	14.2575	+	11.9635i	0.636344	+	0.533956i
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	0.987312	+	0.158794i	$0.0507607\pi$
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	−0.356136	+	0.934434i	$0.615906\pi$
$504$		0			0
$505$	5.50701	−	9.53842i	0.245059	−	0.424454i
$506$	−1.26048	+	0.458777i	−0.0560351	+	0.0203951i
$507$		0			0
$508$	19.1917	−	16.1038i	0.851495	−	0.714489i
$509$	−26.9574	−	9.81169i	−1.19487	−	0.434895i	−0.333436	−	0.942773i	$-0.608208\pi$
$509$	−26.9574	−	9.81169i	−1.19487	−	0.434895i	−0.861429	+	0.507877i	$0.830430\pi$
$510$		0			0
$511$	2.07472	−	11.7663i	0.0917802	−	0.520512i
$512$	6.25700			0.276523
$513$		0			0
$514$	−5.50264			−0.242711
$515$	−2.82652	+	16.0300i	−0.124552	+	0.706367i
$516$		0			0
$517$	−2.68583	−	0.977564i	−0.118123	−	0.0429932i
$518$	−10.2046	+	8.56267i	−0.448364	+	0.376222i
$519$		0			0
$520$	18.1637	−	6.61106i	0.796532	−	0.289914i
$521$	−12.4548	+	21.5724i	−0.545655	+	0.945102i	0.452910	+	0.891556i	$0.350386\pi$
$521$	−12.4548	+	21.5724i	−0.545655	+	0.945102i	−0.998565	+	0.0535462i	$0.982948\pi$
$522$		0			0
$523$	12.9324	+	22.3995i	0.565494	+	0.979464i	0.997004	+	0.0773554i	$0.0246476\pi$
$523$	12.9324	+	22.3995i	0.565494	+	0.979464i	−0.431510	+	0.902108i	$0.642019\pi$
$524$	14.7937	+	12.4134i	0.646268	+	0.542283i
$525$		0			0
$526$	−0.466674	−	2.64664i	−0.0203480	−	0.115399i
$527$	0.140885	+	0.798998i	0.00613704	+	0.0348049i
$528$		0			0
$529$	16.6645	+	13.9832i	0.724544	+	0.607965i
$530$	5.98556	+	10.3673i	0.259996	+	0.450327i
$531$		0			0
$532$	−4.49274	+	7.78166i	−0.194785	+	0.337378i
$533$	−23.8515	+	8.68123i	−1.03312	+	0.376026i
$534$		0			0
$535$	0.545538	−	0.457761i	0.0235857	−	0.0197907i
$536$	4.57802	+	1.66626i	0.197741	+	0.0719717i
$537$		0			0
$538$	−1.77342	+	10.0576i	−0.0764577	+	0.433613i
$539$	−0.337880			−0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	−3.27870	+	18.5944i	−0.140832	+	0.798698i
$543$		0			0
$544$	−1.60714	−	0.584951i	−0.0689055	−	0.0250796i
$545$	−18.0272	+	15.1266i	−0.772199	+	0.647952i
$546$		0			0
$547$	9.37442	−	3.41201i	0.400821	−	0.145887i	−0.133741	−	0.991016i	$-0.542699\pi$
$547$	9.37442	−	3.41201i	0.400821	−	0.145887i	0.534562	+	0.845129i	$0.320477\pi$
$548$	13.3621	−	23.1439i	0.570802	−	0.988658i
$549$		0			0
$550$	−0.256815	−	0.444816i	−0.0109506	−	0.0189670i
$551$	−0.757421	−	0.635552i	−0.0322672	−	0.0270754i
$552$		0			0
$553$	0.331351	+	1.87918i	0.0140905	+	0.0799110i
$554$	0.581957	+	3.30044i	0.0247250	+	0.140222i
$555$		0			0
$556$	18.6264	+	15.6294i	0.789937	+	0.662836i
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	0.600162	−	0.799879i	$-0.295103\pi$
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	−0.992796	+	0.119816i	$0.961769\pi$
$558$		0			0
$559$	−0.340480	+	0.589729i	−0.0144008	+	0.0249429i
$560$	−3.42749	+	1.24750i	−0.144838	+	0.0527167i
$561$		0			0
$562$	13.2846	−	11.1471i	0.560378	−	0.470213i
$563$	41.0487	+	14.9405i	1.73000	+	0.629667i	0.998630	−	0.0523192i	$-0.0166613\pi$
$563$	41.0487	+	14.9405i	1.73000	+	0.629667i	0.731365	+	0.681986i	$0.238884\pi$
$564$		0			0
$565$	1.48942	−	8.44694i	0.0626605	−	0.355365i
$566$	4.18985			0.176113
$567$		0			0
$568$	−0.997105			−0.0418376
$569$	−2.35583	+	13.3606i	−0.0987616	+	0.560105i	0.894768	+	0.446531i	$0.147341\pi$
$569$	−2.35583	+	13.3606i	−0.0987616	+	0.560105i	−0.993530	+	0.113573i	$0.963770\pi$
$570$		0			0
$571$	−22.3165	−	8.12254i	−0.933916	−	0.339918i	−0.170155	−	0.985417i	$-0.554427\pi$
$571$	−22.3165	−	8.12254i	−0.933916	−	0.339918i	−0.763761	+	0.645500i	$0.776649\pi$
$572$	−0.679513	+	0.570179i	−0.0284119	+	0.0238404i
$573$		0			0
$574$	−17.3965	+	6.33181i	−0.726116	+	0.264285i
$575$	−8.56844	+	14.8410i	−0.357329	+	0.618911i
$576$		0			0
$577$	4.05951	+	7.03128i	0.169000	+	0.292716i	0.938068	−	0.346450i	$-0.112613\pi$
$577$	4.05951	+	7.03128i	0.169000	+	0.292716i	−0.769069	+	0.639166i	$0.779280\pi$
$578$	−10.3852	−	8.71425i	−0.431969	−	0.362465i
$579$		0			0
$580$	−0.230162	−	1.30531i	−0.00955695	−	0.0542002i
$581$	1.13735	+	6.45022i	0.0471851	+	0.267600i
$582$		0			0
$583$	−1.04083	−	0.873359i	−0.0431067	−	0.0361708i
$584$	6.76397	+	11.7155i	0.279895	+	0.484793i
$585$		0			0
$586$	−2.46156	+	4.26354i	−0.101686	+	0.176125i
$587$	−3.46934	+	1.26274i	−0.143195	+	0.0521187i	−0.412623	−	0.910902i	$-0.635387\pi$
$587$	−3.46934	+	1.26274i	−0.143195	+	0.0521187i	0.269428	+	0.963020i	$0.413165\pi$
$588$		0			0
$589$	−5.89940	+	4.95018i	−0.243081	+	0.203969i
$590$	12.3791	+	4.50563i	0.509640	+	0.185494i
$591$		0			0
$592$	−0.677609	+	3.84291i	−0.0278495	+	0.157943i
$593$	−29.4590			−1.20974			−0.604869	−	0.796325i	$-0.706774\pi$
$593$	−29.4590			−1.20974			−0.604869	+	0.796325i	$0.706774\pi$
$594$		0			0
$595$	1.91749			0.0786093
$596$	3.84003	−	21.7779i	0.157294	−	0.892056i
$597$		0			0
$598$	−13.1610	−	4.79023i	−0.538195	−	0.195887i
$599$	16.7575	−	14.0612i	0.684694	−	0.574526i	−0.232680	−	0.972553i	$-0.574749\pi$
$599$	16.7575	−	14.0612i	0.684694	−	0.574526i	0.917374	+	0.398027i	$0.130305\pi$
$600$		0			0
$601$	−34.3182	+	12.4908i	−1.39987	+	0.509510i	−0.928139	−	0.372233i	$-0.878592\pi$
$601$	−34.3182	+	12.4908i	−1.39987	+	0.509510i	−0.471729	+	0.881744i	$0.656370\pi$
$602$	−0.248335	+	0.430130i	−0.0101214	+	0.0175308i
$603$		0			0
$604$	9.68946	+	16.7826i	0.394258	+	0.682876i
$605$	−23.0397	−	19.3326i	−0.936696	−	0.785982i
$606$		0			0
$607$	−1.14275	−	6.48085i	−0.0463827	−	0.263049i	0.952794	−	0.303617i	$-0.0981944\pi$
$607$	−1.14275	−	6.48085i	−0.0463827	−	0.263049i	−0.999177	+	0.0405678i	$0.987083\pi$
$608$	−2.81902	−	15.9874i	−0.114326	−	0.648376i
$609$		0			0
$610$	−20.0023	−	16.7839i	−0.809868	−	0.679560i
$611$	−14.9217	−	25.8451i	−0.603667	−	1.04558i
$612$		0			0
$613$	3.57434	−	6.19093i	0.144366	−	0.250049i	−0.784770	−	0.619787i	$-0.787219\pi$
$613$	3.57434	−	6.19093i	0.144366	−	0.250049i	0.929136	+	0.369737i	$0.120552\pi$
$614$	−14.3135	+	5.20969i	−0.577646	+	0.210246i
$615$		0			0
$616$	−1.22577	+	1.02855i	−0.0493878	+	0.0414413i
$617$	15.5401	+	5.65615i	0.625623	+	0.227708i	0.635325	−	0.772245i	$-0.280866\pi$
$617$	15.5401	+	5.65615i	0.625623	+	0.227708i	−0.00970235	+	0.999953i	$0.503088\pi$
$618$		0			0
$619$	−0.260359	+	1.47657i	−0.0104647	+	0.0593484i	−0.989593	−	0.143895i	$-0.954037\pi$
$619$	−0.260359	+	1.47657i	−0.0104647	+	0.0593484i	0.979128	+	0.203244i	$0.0651483\pi$
$620$	−10.3236			−0.414608
$621$		0			0
$622$	17.2704			0.692481
$623$	−4.31333	+	24.4621i	−0.172810	+	0.980054i
$624$		0			0
$625$	29.3618	+	10.6868i	1.17447	+	0.427473i
$626$	−2.34158	+	1.96482i	−0.0935884	+	0.0785300i
$627$		0			0
$628$	0.973799	−	0.354434i	0.0388588	−	0.0141435i
$629$	1.02570	−	1.77657i	0.0408974	−	0.0708363i
$630$		0			0
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	0.963189	+	0.268826i	$0.0866356\pi$
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$632$	−1.65506	−	1.38876i	−0.0658348	−	0.0552420i
$633$		0			0
$634$	−0.592155	−	3.35828i	−0.0235175	−	0.133374i
$635$	−8.81213	−	49.9760i	−0.349699	−	1.98324i
$636$		0			0
$637$	−2.70253	−	2.26769i	−0.107078	−	0.0898493i
$638$	−0.0355961	−	0.0616542i	−0.00140926	−	0.00244091i
$639$		0			0
$640$	12.1112	−	20.9772i	0.478738	−	0.829198i
$641$	36.8622	−	13.4167i	1.45597	−	0.529930i	0.511718	−	0.859153i	$-0.329009\pi$
$641$	36.8622	−	13.4167i	1.45597	−	0.529930i	0.944252	+	0.329224i	$0.106787\pi$
$642$		0			0
$643$	−7.98104	+	6.69688i	−0.314741	+	0.264099i	−0.786448	−	0.617656i	$-0.788082\pi$
$643$	−7.98104	+	6.69688i	−0.314741	+	0.264099i	0.471707	+	0.881755i	$0.343638\pi$
$644$	20.2842	+	7.38284i	0.799309	+	0.290925i
$645$		0			0
$646$	−0.113710	+	0.644883i	−0.00447387	+	0.0253726i
$647$	39.1517			1.53921			0.769606	−	0.638519i	$-0.220453\pi$
$647$	39.1517			1.53921			0.769606	+	0.638519i	$0.220453\pi$
$648$		0			0
$649$	−1.49518			−0.0586910
$650$	0.931268	−	5.28148i	0.0365273	−	0.207157i
$651$		0			0
$652$	6.54214	+	2.38114i	0.256210	+	0.0932528i
$653$	−25.2104	+	21.1541i	−0.986561	+	0.827823i	−0.985066	−	0.172176i	$-0.944920\pi$
$653$	−25.2104	+	21.1541i	−0.986561	+	0.827823i	−0.00149448	+	0.999999i	$0.500476\pi$
$654$		0			0
$655$	36.7587	−	13.3791i	1.43628	−	0.522764i
$656$	−2.71152	+	4.69649i	−0.105867	+	0.183367i
$657$		0			0
$658$	−10.8834	−	18.8506i	−0.424279	−	0.734873i
$659$	16.5224	+	13.8639i	0.643620	+	0.540061i	0.905128	−	0.425140i	$-0.139775\pi$
$659$	16.5224	+	13.8639i	0.643620	+	0.540061i	−0.261508	+	0.965201i	$0.584220\pi$
$660$		0			0
$661$	4.56632	+	25.8969i	0.177609	+	1.00727i	0.935089	+	0.354413i	$0.115319\pi$
$661$	4.56632	+	25.8969i	0.177609	+	1.00727i	−0.757480	+	0.652859i	$0.773570\pi$
$662$	−1.98946	−	11.2828i	−0.0773227	−	0.438519i
$663$		0			0
$664$	−5.68093	−	4.76687i	−0.220463	−	0.184990i
$665$	9.10043	+	15.7624i	0.352900	+	0.611240i
$666$		0			0
$667$	−1.18764	+	2.05705i	−0.0459855	+	0.0796493i
$668$	−11.3550	+	4.13289i	−0.439339	+	0.159906i
$669$		0			0
$670$	3.05654	−	2.56475i	0.118085	−	0.0990848i
$671$	2.78485	+	1.01360i	0.107508	+	0.0391296i
$672$		0			0
$673$	2.00079	−	11.3471i	0.0771250	−	0.437397i	−0.921655	−	0.388011i	$-0.873162\pi$
$673$	2.00079	−	11.3471i	0.0771250	−	0.437397i	0.998780	−	0.0493865i	$-0.0157266\pi$
$674$	28.6293			1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	5.89102	−	33.4096i	0.226410	−	1.28404i	−0.633561	−	0.773693i	$-0.718407\pi$
$677$	5.89102	−	33.4096i	0.226410	−	1.28404i	0.859971	−	0.510343i	$-0.170482\pi$
$678$		0			0
$679$	33.1330	+	12.0594i	1.27153	+	0.462798i
$680$	−1.66314	+	1.39554i	−0.0637785	+	0.0535165i
$681$		0			0
$682$	−0.521061	+	0.189651i	−0.0199524	+	0.00726209i
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	−0.264135	−	0.964486i	$-0.585087\pi$
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	0.967337	−	0.253495i	$-0.0815801\pi$
$684$		0			0
$685$	−27.0661	−	46.8799i	−1.03414	−	1.79119i
$686$	−12.1869	−	10.2260i	−0.465296	−	0.390430i
$687$		0			0
$688$	0.0252642	+	0.143280i	0.000963189	+	0.00546252i
$689$	−2.46348	−	13.9711i	−0.0938513	−	0.532257i
$690$		0			0
$691$	10.2482	+	8.59929i	0.389861	+	0.327132i	0.816559	−	0.577262i	$-0.195879\pi$
$691$	10.2482	+	8.59929i	0.389861	+	0.327132i	−0.426698	+	0.904394i	$0.640323\pi$
$692$	4.62331	+	8.00781i	0.175752	+	0.304411i
$693$		0			0
$694$	−7.79146	+	13.4952i	−0.295760	+	0.512271i
$695$	46.2820	−	16.8453i	1.75558	−	0.638978i
$696$		0			0
$697$	2.18393	−	1.83254i	0.0827223	−	0.0694123i
$698$	6.04111	+	2.19878i	0.228659	+	0.0832252i
$699$		0			0
$700$	−1.43530	+	8.13998i	−0.0542492	+	0.307662i
$701$	−5.00452			−0.189018			−0.0945091	−	0.995524i	$-0.530128\pi$
$701$	−5.00452			−0.189018			−0.0945091	+	0.995524i	$0.530128\pi$
$702$		0			0
$703$	19.4720			0.734400
$704$	0.154493	−	0.876171i	0.00582266	−	0.0330219i
$705$		0			0
$706$	6.59328	+	2.39976i	0.248141	+	0.0903160i
$707$	−7.29274	+	6.11934i	−0.274272	+	0.230141i
$708$		0			0
$709$	−16.1100	+	5.86354i	−0.605022	+	0.220210i	−0.626324	−	0.779563i	$-0.715441\pi$
$709$	−16.1100	+	5.86354i	−0.605022	+	0.220210i	0.0213017	+	0.999773i	$0.493219\pi$
$710$	−0.408315	+	0.707223i	−0.0153238	+	0.0265416i
$711$		0			0
$712$	−14.0623	−	24.3566i	−0.527006	−	0.912800i
$713$	14.1722	+	11.8919i	0.530754	+	0.445356i
$714$		0			0
$715$	0.312007	+	1.76948i	0.0116684	+	0.0661747i
$716$	−4.32522	−	24.5295i	−0.161641	−	0.916711i
$717$		0			0
$718$	5.08268	+	4.26488i	0.189684	+	0.159164i
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	−0.913987	−	0.405742i	$-0.867013\pi$
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	0.105610	−	0.994408i	$-0.466320\pi$
$720$		0			0
$721$	7.03467	−	12.1844i	0.261985	−	0.453771i
$722$	8.46976	−	3.08274i	0.315212	−	0.114728i
$723$		0			0
$724$	−11.7781	+	9.88298i	−0.437729	+	0.367298i
$725$	−0.854673	−	0.311075i	−0.0317417	−	0.0115530i
$726$		0			0
$727$	−6.31105	+	35.7918i	−0.234064	+	1.32744i	0.610512	+	0.792007i	$0.290964\pi$
$727$	−6.31105	+	35.7918i	−0.234064	+	1.32744i	−0.844576	+	0.535436i	$0.820147\pi$
$728$	−16.7075			−0.619220
$729$		0			0
$730$	11.0794			0.410067
$731$	0.0132815	−	0.0753233i	0.000491235	−	0.00278593i
$732$		0			0
$733$	−3.64188	−	1.32554i	−0.134516	−	0.0489598i	0.273885	−	0.961762i	$-0.411691\pi$
$733$	−3.64188	−	1.32554i	−0.134516	−	0.0489598i	−0.408401	+	0.912803i	$0.633913\pi$
$734$	−9.08719	+	7.62506i	−0.335414	+	0.281446i
$735$		0			0
$736$	−36.6474	+	13.3386i	−1.35084	+	0.491667i
$737$	−0.226432	+	0.392191i	−0.00834071	+	0.0144465i
$738$		0			0
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	0.513422	−	0.858136i	$-0.328377\pi$
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	−0.999879	+	0.0155689i	$0.995044\pi$
$740$	19.9960	+	16.7787i	0.735069	+	0.616796i
$741$		0			0
$742$	−1.79679	−	10.1901i	−0.0659621	−	0.374090i
$743$	2.33789	+	13.2588i	0.0857688	+	0.486419i	0.997188	+	0.0749400i	$0.0238765\pi$
$743$	2.33789	+	13.2588i	0.0857688	+	0.486419i	−0.911419	+	0.411479i	$0.865012\pi$
$744$		0			0
$745$	−34.3138	−	28.7927i	−1.25716	−	1.05488i
$746$	−10.2329	−	17.7238i	−0.374651	−	0.648915i
$747$		0			0
$748$	0.0498160	−	0.0862839i	0.00182145	−	0.00315485i
$749$	−0.578427	+	0.210530i	−0.0211352	+	0.00769260i
$750$		0			0
$751$	2.88669	−	2.42222i	0.105337	−	0.0883880i	−0.588598	−	0.808426i	$-0.700320\pi$
$751$	2.88669	−	2.42222i	0.105337	−	0.0883880i	0.693935	+	0.720038i	$0.255876\pi$
$752$	−5.99166	−	2.18079i	−0.218493	−	0.0795250i
$753$		0			0
$754$	0.129079	−	0.732046i	0.00470079	−	0.0266595i
$755$	39.2536			1.42859
$756$		0			0
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$	2.80099	−	15.8852i	0.101737	−	0.576976i
$759$		0			0
$760$	−19.3651	−	7.04833i	−0.702447	−	0.255670i
$761$	7.39649	−	6.20639i	0.268122	−	0.224981i	−0.498807	−	0.866713i	$-0.666228\pi$
$761$	7.39649	−	6.20639i	0.268122	−	0.224981i	0.766929	+	0.641732i	$0.221784\pi$
$762$		0			0
$763$	19.1139	−	6.95691i	0.691971	−	0.251857i
$764$	−4.65533	+	8.06327i	−0.168424	+	0.291719i
$765$		0			0
$766$	−9.56272	−	16.5631i	−0.345515	−	0.598450i
$767$	−11.9592	−	10.0350i	−0.431822	−	0.362342i
$768$		0			0
$769$	6.72210	+	38.1229i	0.242405	+	1.37475i	0.826443	+	0.563021i	$0.190361\pi$
$769$	6.72210	+	38.1229i	0.242405	+	1.37475i	−0.584038	+	0.811726i	$0.698528\pi$
$770$	0.227568	+	1.29060i	0.00820097	+	0.0465100i
$771$		0			0
$772$	−21.2282	−	17.8126i	−0.764021	−	0.641090i
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	0.997462	−	0.0711944i	$-0.0226811\pi$
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	−0.560387	+	0.828231i	$0.689348\pi$
$774$		0			0
$775$	−3.54205	+	6.13500i	−0.127234	+	0.220376i
$776$	−37.5148	+	13.6543i	−1.34670	+	0.490160i
$777$		0			0
$778$	−23.3158	+	19.5643i	−0.835912	+	0.701414i
$779$	25.4291	+	9.25543i	0.911091	+	0.331610i
$780$		0			0
$781$	0.0160948	−	0.0912782i	0.000575918	−	0.00326619i
$782$	1.57311			0.0562544
$783$		0			0
$784$	−0.753755			−0.0269198
$785$	0.364506	−	2.06721i	0.0130098	−	0.0737820i
$786$		0			0
$787$	−19.6777	−	7.16211i	−0.701436	−	0.255302i	−0.0334119	−	0.999442i	$-0.510637\pi$
$787$	−19.6777	−	7.16211i	−0.701436	−	0.255302i	−0.668024	+	0.744140i	$0.732860\pi$
$788$	3.15700	−	2.64904i	0.112463	−	0.0943680i
$789$		0			0
$790$	−1.66276	+	0.605197i	−0.0591585	+	0.0215319i
$791$	−3.70688	+	6.42051i	−0.131802	+	0.228287i
$792$		0			0
$793$	15.4718	+	26.7979i	0.549419	+	0.951621i
$794$	12.4946	+	10.4842i	0.443416	+	0.372070i
$795$		0			0
$796$	0.533348	+	3.02477i	0.0189040	+	0.107210i
$797$	−2.07280	−	11.7554i	−0.0734222	−	0.416398i	−0.999260	−	0.0384758i	$-0.987750\pi$
$797$	−2.07280	−	11.7554i	−0.0734222	−	0.416398i	0.925837	−	0.377922i	$-0.123361\pi$
$798$		0			0
$799$	2.56778	+	2.15462i	0.0908414	+	0.0762250i
$800$	−7.46668	−	12.9327i	−0.263987	−	0.457239i
$801$		0			0
$802$	2.78329	−	4.82080i	0.0982814	−	0.170228i
$803$	−1.18166	+	0.430089i	−0.0416999	+	0.0151775i
$804$		0			0
$805$	33.4947	−	28.1054i	1.18053	−	0.990585i
$806$	−5.44055	−	1.98020i	−0.191635	−	0.0697495i
$807$		0			0
$808$	1.87176	−	10.6153i	0.0658482	−	0.373444i
$809$	−8.60808			−0.302644			−0.151322	−	0.988485i	$-0.548353\pi$
$809$	−8.60808			−0.302644			−0.151322	+	0.988485i	$0.548353\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	−0.198941	+	1.12825i	−0.00698146	+	0.0395939i
$813$		0			0
$814$	1.31748	+	0.479524i	0.0461777	+	0.0168073i
$815$	10.8028	−	9.06466i	0.378407	−	0.317521i
$816$		0			0
$817$	0.682218	−	0.248307i	0.0238678	−	0.00868716i
$818$	4.37071	−	7.57029i	0.152818	−	0.264689i
$819$		0			0
$820$	18.1382	+	31.4163i	0.633413	+	1.09710i
$821$	−22.1971	−	18.6256i	−0.774684	−	0.650037i	0.167220	−	0.985920i	$-0.446521\pi$
$821$	−22.1971	−	18.6256i	−0.774684	−	0.650037i	−0.941904	+	0.335882i	$0.890966\pi$
$822$		0			0
$823$	−1.95472	−	11.0858i	−0.0681372	−	0.386425i	−0.999737	−	0.0229391i	$-0.992698\pi$
$823$	−1.95472	−	11.0858i	−0.0681372	−	0.386425i	0.931600	−	0.363486i	$-0.118414\pi$
$824$	2.76622	+	15.6880i	0.0963657	+	0.546517i
$825$		0			0
$826$	−8.72266	−	7.31918i	−0.303500	−	0.254667i
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	0.999026	+	0.0441346i	$0.0140530\pi$
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	−0.461291	+	0.887249i	$0.652614\pi$
$828$		0			0
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	−0.767902	−	0.640567i	$-0.778699\pi$
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	0.938698	+	0.344739i	$0.112033\pi$
$830$	−5.70737	+	2.07731i	−0.198106	+	0.0721045i
$831$		0			0
$832$	7.11616	−	5.97117i	0.246709	−	0.207013i
$833$	0.372356	+	0.135526i	0.0129014	+	0.00469571i
$834$		0			0
$835$	−4.25033	+	24.1048i	−0.147089	+	0.834182i
$836$	0.945711			0.0327081
$837$		0			0
$838$	8.07072			0.278798
$839$	2.28229	−	12.9435i	0.0787935	−	0.446860i	−0.919731	−	0.392550i	$-0.871593\pi$
$839$	2.28229	−	12.9435i	0.0787935	−	0.446860i	0.998524	−	0.0543102i	$-0.0172960\pi$
$840$		0			0
$841$	27.1326	+	9.87547i	0.935608	+	0.340533i
$842$	−1.90806	+	1.60105i	−0.0657561	+	0.0551759i
$843$		0			0
$844$	32.4417	−	11.8078i	1.11669	−	0.406441i
$845$	8.49363	−	14.7114i	0.292190	−	0.506088i
$846$		0			0
$847$	12.9982	+	22.5136i	0.446624	+	0.773575i
$848$	−2.32192	−	1.94832i	−0.0797350	−	0.0669056i
$849$		0			0
$850$	0.104600	+	0.593214i	0.00358774	+	0.0203471i
$851$	−8.12290	−	46.0672i	−0.278449	−	1.57916i
$852$		0			0
$853$	11.8295	+	9.92614i	0.405035	+	0.339864i	0.822436	−	0.568858i	$-0.192615\pi$
$853$	11.8295	+	9.92614i	0.405035	+	0.339864i	−0.417401	+	0.908722i	$0.637059\pi$
$854$	11.2846	+	19.5455i	0.386151	+	0.668834i
$855$		0			0
$856$	0.348478	−	0.603581i	0.0119107	−	0.0206300i
$857$	20.6570	−	7.51854i	0.705630	−	0.256828i	0.0358174	−	0.999358i	$-0.488597\pi$
$857$	20.6570	−	7.51854i	0.705630	−	0.256828i	0.669813	+	0.742530i	$0.266374\pi$
$858$		0			0
$859$	14.9889	−	12.5772i	0.511416	−	0.429129i	−0.350211	−	0.936671i	$-0.613890\pi$
$859$	14.9889	−	12.5772i	0.511416	−	0.429129i	0.861627	+	0.507542i	$0.169446\pi$
$860$	0.914540	+	0.332865i	0.0311855	+	0.0113506i
$861$		0			0
$862$	3.90689	−	22.1571i	0.133069	−	0.754674i
$863$	−21.8676			−0.744383			−0.372191	−	0.928156i	$-0.621393\pi$
$863$	−21.8676			−0.744383			−0.372191	+	0.928156i	$0.621393\pi$
$864$		0			0
$865$	18.7298			0.636833
$866$	2.71758	−	15.4121i	0.0923470	−	0.523726i
$867$		0			0
$868$	8.38514	+	3.05194i	0.284610	+	0.103590i
$869$	0.153847	−	0.129093i	0.00521890	−	0.00437918i
$870$		0			0
$871$	−4.44332	+	1.61724i	−0.150556	+	0.0547979i
$872$	−11.5153	+	19.9452i	−0.389959	+	0.675428i
$873$		0			0
$874$	7.46602	+	12.9315i	0.252542	+	0.437416i
$875$	−12.2085	−	10.2441i	−0.412721	−	0.346314i
$876$		0			0
$877$	−6.78962	−	38.5059i	−0.229269	−	1.30025i	−0.854353	−	0.519693i	$-0.826046\pi$
$877$	−6.78962	−	38.5059i	−0.229269	−	1.30025i	0.625084	−	0.780558i	$-0.285065\pi$
$878$	2.03620	+	11.5479i	0.0687184	+	0.389721i
$879$		0			0
$880$	0.294077	+	0.246760i	0.00991334	+	0.00831828i
$881$	−3.65254	−	6.32639i	−0.123057	−	0.213141i	0.797915	−	0.602771i	$-0.205937\pi$
$881$	−3.65254	−	6.32639i	−0.123057	−	0.213141i	−0.920972	+	0.389629i	$0.872603\pi$
$882$		0			0
$883$	1.74646	−	3.02496i	0.0587732	−	0.101798i	−0.835142	−	0.550035i	$-0.814614\pi$
$883$	1.74646	−	3.02496i	0.0587732	−	0.101798i	0.893915	+	0.448237i	$0.147948\pi$
$884$	0.977551	−	0.355799i	0.0328786	−	0.0119668i
$885$		0			0
$886$	−11.2706	+	9.45720i	−0.378645	+	0.317721i
$887$	26.7073	+	9.72065i	0.896742	+	0.326388i	0.748947	−	0.662630i	$-0.230560\pi$
$887$	26.7073	+	9.72065i	0.896742	+	0.326388i	0.147796	+	0.989018i	$0.452782\pi$
$888$		0			0
$889$	−7.61679	+	43.1970i	−0.255459	+	1.44878i
$890$	−23.0340			−0.772102
$891$		0			0
$892$	5.20125			0.174151
$893$	−5.52501	+	31.3339i	−0.184887	+	1.04855i
$894$		0			0
$895$	−47.4104	−	17.2560i	−1.58476	−	0.576804i
$896$	−16.0385	+	13.4579i	−0.535808	+	0.449596i
$897$		0			0
$898$	10.4387	−	3.79939i	0.348345	−	0.126787i
$899$	−0.490949	+	0.850349i	−0.0163741	+	0.0283607i
$900$		0			0
$901$	0.796719	+	1.37996i	0.0265426	+	0.0459731i
$902$	1.49261	+	1.25245i	0.0496986	+	0.0417021i
$903$		0			0
$904$	−1.45764	−	8.26671i	−0.0484805	−	0.274947i
$905$	5.40805	+	30.6706i	0.179770	+	1.01952i
$906$		0			0
$907$	40.6897	+	34.1427i	1.35108	+	1.13369i	0.978628	+	0.205640i	$0.0659277\pi$
$907$	40.6897	+	34.1427i	1.35108	+	1.13369i	0.372453	+	0.928051i	$0.378517\pi$
$908$	−1.70780	−	2.95799i	−0.0566753	−	0.0981644i
$909$		0			0
$910$	−6.84171	+	11.8502i	−0.226801	+	0.392830i
$911$	−7.58885	+	2.76212i	−0.251430	+	0.0915130i	−0.464661	−	0.885489i	$-0.653824\pi$
$911$	−7.58885	+	2.76212i	−0.251430	+	0.0915130i	0.213231	+	0.977002i	$0.431601\pi$
$912$		0			0
$913$	0.528073	−	0.443106i	0.0174767	−	0.0146647i
$914$	−13.2924	−	4.83803i	−0.439673	−	0.160028i
$915$		0			0
$916$	3.75756	−	21.3102i	0.124153	−	0.704108i
$917$	−33.8116			−1.11656
$918$		0			0
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$	−8.59676	+	48.7547i	−0.283427	+	1.60739i
$921$		0			0
$922$	19.3103	+	7.02837i	0.635950	+	0.231467i
$923$	0.741351	−	0.622068i	0.0244019	−	0.0204756i
$924$		0			0
$925$	16.8316	−	6.12622i	0.553421	−	0.201429i
$926$	−7.35298	+	12.7357i	−0.241634	+	0.418522i
$927$		0			0
$928$	−1.03493	−	1.79255i	−0.0339732	−	0.0588433i
$929$	22.2106	+	18.6369i	0.728707	+	0.611458i	0.929779	−	0.368118i	$-0.119998\pi$
$929$	22.2106	+	18.6369i	0.728707	+	0.611458i	−0.201071	+	0.979577i	$0.564442\pi$
$930$		0			0
$931$	0.653134	+	3.70411i	0.0214056	+	0.121397i
$932$	6.63087	+	37.6055i	0.217201	+	1.23181i
$933$		0			0
$934$	9.98486	+	8.37829i	0.326715	+	0.274146i
$935$	−0.100907	−	0.174775i	−0.00330000	−	0.00571576i
$936$		0			0
$937$	−2.51425	+	4.35481i	−0.0821369	+	0.142265i	−0.904168	−	0.427178i	$-0.859508\pi$
$937$	−2.51425	+	4.35481i	−0.0821369	+	0.142265i	0.822031	+	0.569443i	$0.192841\pi$
$938$	−3.24081	+	1.17956i	−0.105816	+	0.0385140i
$939$		0			0
$940$	−32.6735	+	27.4164i	−1.06569	+	0.894223i
$941$	−52.4734	−	19.0988i	−1.71059	−	0.622602i	−0.713626	−	0.700527i	$-0.752948\pi$
$941$	−52.4734	−	19.0988i	−1.71059	−	0.622602i	−0.996959	+	0.0779249i	$0.975171\pi$
$942$		0			0
$943$	11.2887	−	64.0216i	0.367612	−	2.08483i
$944$	−3.33551			−0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	−7.38515	+	41.8833i	−0.239985	+	1.36102i	0.591872	+	0.806032i	$0.298389\pi$
$947$	−7.38515	+	41.8833i	−0.239985	+	1.36102i	−0.831857	+	0.554991i	$0.812722\pi$
$948$		0			0
$949$	−12.3381	−	4.49069i	−0.400510	−	0.145774i
$950$	−4.37999	+	3.67525i	−0.142106	+	0.119241i
$951$		0			0
$952$	1.76340	−	0.641826i	0.0571522	−	0.0208017i
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	−0.633505	−	0.773739i	$-0.718384\pi$
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	0.986830	+	0.161762i	$0.0517175\pi$
$954$		0			0
$955$	9.42977	+	16.3328i	0.305140	+	0.528518i
$956$	−15.2932	−	12.8326i	−0.494619	−	0.415035i
$957$		0			0
$958$	1.31831	+	7.47649i	0.0425926	+	0.241555i
$959$	8.12489	+	46.0785i	0.262366	+	1.48795i
$960$		0			0
$961$	−17.8888	−	15.0105i	−0.577059	−	0.484210i
$962$	7.31954	+	12.6778i	0.235991	+	0.408749i
$963$		0			0
$964$	5.73088	−	9.92618i	0.184579	−	0.319701i
$965$	−52.7468	+	19.1983i	−1.69798	+	0.618014i
$966$		0			0
$967$	3.54570	−	2.97520i	0.114022	−	0.0956759i	−0.583994	−	0.811758i	$-0.698511\pi$
$967$	3.54570	−	2.97520i	0.114022	−	0.0956759i	0.698016	+	0.716082i	$0.254066\pi$
$968$	−27.6593	−	10.0672i	−0.889005	−	0.323571i
$969$		0			0
$970$	−5.67769	+	32.1998i	−0.182300	+	1.03387i
$971$	21.6509			0.694809			0.347405	−	0.937715i	$-0.387063\pi$
$971$	21.6509			0.694809			0.347405	+	0.937715i	$0.387063\pi$
$972$		0			0
$973$	−42.5714			−1.36478
$974$	−0.0650773	+	0.369072i	−0.00208521	+	0.0118258i
$975$		0			0
$976$	6.21254	+	2.26118i	0.198859	+	0.0723786i
$977$	16.9180	−	14.1958i	0.541253	−	0.454165i	−0.330713	−	0.943731i	$-0.607289\pi$
$977$	16.9180	−	14.1958i	0.541253	−	0.454165i	0.871966	+	0.489566i	$0.162845\pi$
$978$		0			0
$979$	2.45666	−	0.894152i	0.0785153	−	0.0285772i
$980$	−2.52105	+	4.36659i	−0.0805320	+	0.139485i
$981$		0			0
$982$	10.0379	+	17.3862i	0.320323	+	0.554815i
$983$	10.6197	+	8.91100i	0.338716	+	0.284217i	0.796240	−	0.604981i	$-0.206819\pi$
$983$	10.6197	+	8.91100i	0.338716	+	0.284217i	−0.457524	+	0.889197i	$0.651264\pi$
$984$		0			0
$985$	−1.44958	−	8.22095i	−0.0461873	−	0.261941i
$986$	0.0144981	+	0.0822230i	0.000461715	+	0.00261852i
$987$		0			0
$988$	7.56427	+	6.34718i	0.240652	+	0.201931i
$989$	−0.872042	−	1.51042i	−0.0277293	−	0.0480286i
$990$		0			0
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	0.444966	+	0.895548i	$0.353216\pi$
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	−0.998050	+	0.0624224i	$0.980117\pi$
$992$	−15.1494	+	5.51394i	−0.480995	+	0.175068i
$993$		0			0
$994$	0.540718	−	0.453716i	0.0171505	−	0.0143910i
$995$	5.84624	+	2.12786i	0.185338	+	0.0674576i
$996$		0			0
$997$	−4.29775	+	24.3738i	−0.136111	+	0.771924i	0.837968	+	0.545719i	$0.183743\pi$
$997$	−4.29775	+	24.3738i	−0.136111	+	0.771924i	−0.974080	+	0.226206i	$0.927368\pi$
$998$	−11.2488			−0.356073
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.b.217.2		12
3.2	odd	2		243.2.e.c.217.1		12
9.2	odd	6		27.2.e.a.7.2	yes	12
9.4	even	3		243.2.e.a.136.2		12
9.5	odd	6		243.2.e.d.136.1		12
9.7	even	3		81.2.e.a.19.1		12
27.2	odd	18		729.2.c.e.487.4		12
27.4	even	9		243.2.e.a.109.2		12
27.5	odd	18		27.2.e.a.4.2	✓	12
27.7	even	9		729.2.c.b.244.3		12
27.11	odd	18		729.2.a.a.1.3		6
27.13	even	9	inner	243.2.e.b.28.2		12
27.14	odd	18		243.2.e.c.28.1		12
27.16	even	9		729.2.a.d.1.4		6
27.20	odd	18		729.2.c.e.244.4		12
27.22	even	9		81.2.e.a.64.1		12
27.23	odd	18		243.2.e.d.109.1		12
27.25	even	9		729.2.c.b.487.3		12
36.11	even	6		432.2.u.c.385.2		12
45.2	even	12		675.2.u.b.574.3		24
45.29	odd	6		675.2.l.c.601.1		12
45.38	even	12		675.2.u.b.574.2		24
108.59	even	18		432.2.u.c.193.2		12
135.32	even	36		675.2.u.b.274.2		24
135.59	odd	18		675.2.l.c.301.1		12
135.113	even	36		675.2.u.b.274.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	27.5	odd	18
27.2.e.a.7.2	yes	12	9.2	odd	6
81.2.e.a.19.1		12	9.7	even	3
81.2.e.a.64.1		12	27.22	even	9
243.2.e.a.109.2		12	27.4	even	9
243.2.e.a.136.2		12	9.4	even	3
243.2.e.b.28.2		12	27.13	even	9	inner
243.2.e.b.217.2		12	1.1	even	1	trivial
243.2.e.c.28.1		12	27.14	odd	18
243.2.e.c.217.1		12	3.2	odd	2
243.2.e.d.109.1		12	27.23	odd	18
243.2.e.d.136.1		12	9.5	odd	6
432.2.u.c.193.2		12	108.59	even	18
432.2.u.c.385.2		12	36.11	even	6
675.2.l.c.301.1		12	135.59	odd	18
675.2.l.c.601.1		12	45.29	odd	6
675.2.u.b.274.2		24	135.32	even	36
675.2.u.b.274.3		24	135.113	even	36
675.2.u.b.574.2		24	45.38	even	12
675.2.u.b.574.3		24	45.2	even	12
729.2.a.a.1.3		6	27.11	odd	18
729.2.a.d.1.4		6	27.16	even	9
729.2.c.b.244.3		12	27.7	even	9
729.2.c.b.487.3		12	27.25	even	9
729.2.c.e.244.4		12	27.20	odd	18
729.2.c.e.487.4		12	27.2	odd	18

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.139184 - 0.789350i) q^{2} +(1.27568 + 0.464311i) q^{4} +(2.10650 - 1.76756i) q^{5} +(-2.23349 + 0.812925i) q^{7} +(1.34559 - 2.33062i) q^{8} +(-1.10204 - 1.90878i) q^{10} +(0.191633 + 0.160799i) q^{11} +(0.453566 + 2.57230i) q^{13} +(0.330816 + 1.87615i) q^{14} +(0.427502 + 0.358716i) q^{16} +(-0.146688 - 0.254072i) q^{17} +(1.39237 - 2.41166i) q^{19} +(3.50793 - 1.27678i) q^{20} +(0.153599 - 0.128885i) q^{22} +(-6.28639 - 2.28806i) q^{23} +(0.444822 - 2.52271i) q^{25} +2.09357 q^{26} -3.22668 q^{28} +(0.0616550 - 0.349663i) q^{29} +(-2.59869 - 0.945845i) q^{31} +(4.46577 - 3.74722i) q^{32} +(-0.220968 + 0.0804258i) q^{34} +(-3.26796 + 5.66027i) q^{35} +(3.49619 + 6.05558i) q^{37} +(-1.70985 - 1.43473i) q^{38} +(-1.28505 - 7.28786i) q^{40} +(1.68744 + 9.56997i) q^{41} +(0.199713 + 0.167579i) q^{43} +(0.169802 + 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(-10.7365 + 3.90777i) q^{47} +(-1.03467 + 0.868188i) q^{49} +(-1.92939 - 0.702240i) q^{50} +(-0.615741 + 3.49204i) q^{52} -5.43137 q^{53} +0.687897 q^{55} +(-1.11073 + 6.29929i) q^{56} +(-0.267425 - 0.0973348i) q^{58} +(-4.57859 + 3.84189i) q^{59} +(11.1323 - 4.05183i) q^{61} +(-1.10830 + 1.91963i) q^{62} +(-1.77824 - 3.08001i) q^{64} +(5.50214 + 4.61685i) q^{65} +(0.314356 + 1.78280i) q^{67} +(-0.0691597 - 0.392224i) q^{68} +(4.01309 + 3.36738i) q^{70} +(-0.185255 - 0.320871i) q^{71} +(-2.51339 + 4.35333i) q^{73} +(5.26658 - 1.91688i) q^{74} +(2.89599 - 2.43002i) q^{76} +(-0.558728 - 0.203360i) q^{77} +(0.139409 - 0.790625i) q^{79} +1.53459 q^{80} +7.78892 q^{82} +(0.478514 - 2.71379i) q^{83} +(-0.758087 - 0.275921i) q^{85} +(0.160075 - 0.134319i) q^{86} +(0.632620 - 0.230255i) q^{88} +(5.22533 - 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-6.95708 - 5.83768i) q^{92} +(1.59025 + 9.01876i) q^{94} +(-1.32973 - 7.54127i) q^{95} +(-11.3640 - 9.53550i) q^{97} +(0.541296 + 0.937552i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28}+ \cdots + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Introduction

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