LMFDB - Embedded newform 243.2.e.b.28.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(28,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [12,-3,0,3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			28.2
Root			$0.500000 - 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	243.28
Dual form			243.2.e.b.217.2

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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	0.993646	+	0.112548i	$0.0359011\pi$
$2$	0.139184	+	0.789350i	0.0984177	+	0.558155i	−0.895229	+	0.445607i	$0.852988\pi$
$3$		0			0
$3$		0			0
$4$	1.27568	−	0.464311i	0.637842	−	0.232156i
$5$	2.10650	+	1.76756i	0.942056	+	0.790479i	0.977942	−	0.208877i	$-0.0669809\pi$
$5$	2.10650	+	1.76756i	0.942056	+	0.790479i	−0.0358862	+	0.999356i	$0.511425\pi$
$6$		0			0
$7$	−2.23349	−	0.812925i	−0.844181	−	0.307257i	−0.116516	−	0.993189i	$-0.537172\pi$
$7$	−2.23349	−	0.812925i	−0.844181	−	0.307257i	−0.727666	+	0.685932i	$0.759395\pi$
$8$	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	−0.613441	−	0.789741i	$-0.710215\pi$
$11$	0.191633	−	0.160799i	0.0577795	−	0.0484827i	0.671220	+	0.741258i	$0.265771\pi$
$12$		0			0
$13$	0.453566	−	2.57230i	0.125797	−	0.713428i	−0.855035	−	0.518570i	$-0.826464\pi$
$13$	0.453566	−	2.57230i	0.125797	−	0.713428i	0.980832	−	0.194858i	$-0.0624245\pi$
$14$	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	−0.883266	−	0.468873i	$-0.844660\pi$
$17$	−0.146688	+	0.254072i	−0.0355772	+	0.0616215i	0.847689	+	0.530494i	$0.177994\pi$
$18$		0			0
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	0.980370	−	0.197168i	$-0.0631745\pi$
$19$	1.39237	+	2.41166i	0.319432	+	0.553273i	−0.660937	+	0.750441i	$0.729841\pi$
$20$	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	−0.900500	−	0.434855i	$-0.856799\pi$
$23$	−6.28639	+	2.28806i	−1.31080	+	0.477094i	−0.410304	+	0.911949i	$0.634577\pi$
$24$		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	0.989997	−	0.141088i	$-0.0450602\pi$
$29$	0.0616550	+	0.349663i	0.0114490	+	0.0649308i	−0.978548	+	0.206019i	$0.933949\pi$
$30$		0			0
$31$	−2.59869	+	0.945845i	−0.466738	+	0.169879i	−0.564674	−	0.825314i	$-0.690998\pi$
$31$	−2.59869	+	0.945845i	−0.466738	+	0.169879i	0.0979360	+	0.995193i	$0.468776\pi$
$32$	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	−0.421297	−	0.906923i	$-0.638425\pi$
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	0.996067	−	0.0886080i	$-0.0282418\pi$
$38$	−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	−0.509641	−	0.860387i	$-0.670222\pi$
$41$	1.68744	−	9.56997i	0.263535	−	1.49458i	0.773176	−	0.634192i	$-0.218667\pi$
$42$		0			0
$43$	0.199713	−	0.167579i	0.0304559	−	0.0255555i	−0.627433	−	0.778671i	$-0.715894\pi$
$43$	0.199713	−	0.167579i	0.0304559	−	0.0255555i	0.657889	+	0.753115i	$0.271450\pi$
$44$	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	−0.593962	−	0.804493i	$-0.702437\pi$
$47$	−10.7365	−	3.90777i	−1.56608	−	0.570007i	−0.972119	+	0.234486i	$0.924659\pi$
$48$		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	0.294102	−	0.955774i	$-0.404980\pi$
$59$	−4.57859	−	3.84189i	−0.596082	−	0.500172i	−0.890184	+	0.455602i	$0.849424\pi$
$60$		0			0
$61$	11.1323	+	4.05183i	1.42535	+	0.518784i	0.935594	−	0.353078i	$-0.114865\pi$
$61$	11.1323	+	4.05183i	1.42535	+	0.518784i	0.489753	+	0.871861i	$0.337087\pi$
$62$	−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	−0.959566	−	0.281485i	$-0.909173\pi$
$67$	0.314356	−	1.78280i	0.0384047	−	0.217804i	0.997970	+	0.0636814i	$0.0202841\pi$
$68$	−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	−0.876809	−	0.480839i	$-0.840332\pi$
$71$	−0.185255	+	0.320871i	−0.0219857	+	0.0380804i	0.854823	+	0.518919i	$0.173666\pi$
$72$		0			0
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	0.680621	−	0.732636i	$-0.261710\pi$
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	−0.974792	+	0.223117i	$0.928377\pi$
$74$	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	0.991645	−	0.128995i	$-0.0411751\pi$
$79$	0.139409	+	0.790625i	0.0156847	+	0.0889523i	−0.975961	+	0.217947i	$0.930064\pi$
$80$	1.53459			0.171572
$81$		0			0
$82$	7.78892			0.860143
$83$	0.478514	+	2.71379i	0.0525237	+	0.297877i	0.999742	−	0.0227124i	$-0.00723021\pi$
$83$	0.478514	+	2.71379i	0.0525237	+	0.297877i	−0.947218	+	0.320589i	$0.896119\pi$
$84$		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	0.997989	+	0.0633809i	$0.0201883\pi$
$89$	5.22533	+	9.05054i	0.553884	+	0.959356i	−0.444105	+	0.895975i	$0.646478\pi$
$90$		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	−0.999802	−	0.0198821i	$-0.993671\pi$
$97$	−11.3640	+	9.53550i	−1.15384	+	0.968183i	−0.154034	+	0.988066i	$0.549226\pi$
$98$	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	0.522416	−	0.852691i	$-0.325031\pi$
$101$	3.76378	+	1.36990i	0.374510	+	0.136310i	−0.147906	+	0.989001i	$0.547253\pi$
$102$		0			0
$103$	−4.53449	−	3.80489i	−0.446797	−	0.374907i	0.391449	−	0.920200i	$-0.371974\pi$
$103$	−4.53449	−	3.80489i	−0.446797	−	0.374907i	−0.838246	+	0.545293i	$0.816418\pi$
$104$	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	0.748221	−	0.663449i	$-0.230908\pi$
$113$	2.38943	+	2.00497i	0.224779	+	0.188612i	−0.523443	+	0.852061i	$0.675353\pi$
$114$		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	0.906576	+	0.422042i	$0.138686\pi$
$127$	9.22726	+	15.9821i	0.818787	+	1.41818i	−0.0877893	+	0.996139i	$0.527980\pi$
$128$	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	0.316006	−	0.948757i	$-0.397658\pi$
$131$	13.3676	−	4.86540i	1.16793	−	0.425092i	0.851924	+	0.523665i	$0.175436\pi$
$132$		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	0.678953	+	0.734181i	$0.262434\pi$
$137$	3.41837	+	19.3865i	0.292051	+	1.65630i	−0.386903	+	0.922121i	$0.626455\pi$
$138$		0			0
$139$	16.8308	−	6.12591i	1.42757	−	0.519593i	0.491336	−	0.870970i	$-0.336509\pi$
$139$	16.8308	−	6.12591i	1.42757	−	0.519593i	0.936234	+	0.351378i	$0.114287\pi$
$140$	−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	0.617660	+	0.786446i	$0.288081\pi$
$149$	−2.82863	+	16.0420i	−0.231731	+	1.31421i	−0.849390	+	0.527765i	$0.823030\pi$
$150$		0			0
$151$	10.9352	−	9.17571i	0.889893	−	0.746709i	−0.0782960	−	0.996930i	$-0.524948\pi$
$151$	10.9352	−	9.17571i	0.889893	−	0.746709i	0.968189	+	0.250222i	$0.0805035\pi$
$152$	−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	0.665824	−	0.746109i	$-0.268080\pi$
$157$	0.584763	+	0.490675i	0.0466692	+	0.0391601i	−0.619155	+	0.785269i	$0.712525\pi$
$158$	−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	0.339643	−	0.940554i	$-0.389694\pi$
$167$	−6.81866	−	5.72153i	−0.527643	−	0.442745i	−0.867287	+	0.497809i	$0.834138\pi$
$168$		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	−0.422519	−	0.906354i	$-0.638854\pi$
$173$	5.21771	−	4.37818i	0.396695	−	0.332867i	0.819215	+	0.573487i	$0.194410\pi$
$174$		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	0.287538	+	0.957769i	$0.407163\pi$
$179$	−9.17382	+	15.8895i	−0.685684	+	1.18764i	−0.973221	+	0.229870i	$0.926170\pi$
$180$		0			0
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	0.575115	−	0.818073i	$-0.304957\pi$
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	−0.996029	+	0.0890276i	$0.971624\pi$
$182$	−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	−0.997097	−	0.0761413i	$-0.975740\pi$
$191$	−1.19095	−	6.75422i	−0.0861742	−	0.488718i	0.910923	−	0.412577i	$-0.135371\pi$
$192$		0			0
$193$	−19.1818	+	6.98159i	−1.38073	+	0.502546i	−0.922400	−	0.386235i	$-0.873775\pi$
$193$	−19.1818	+	6.98159i	−1.38073	+	0.502546i	−0.458333	+	0.888781i	$0.651553\pi$
$194$	−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	0.915018	−	0.403413i	$-0.132176\pi$
$197$	1.51786	+	2.62902i	0.108143	+	0.187310i	−0.806875	+	0.590723i	$0.798843\pi$
$198$		0			0
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	−0.823141	−	0.567837i	$-0.807780\pi$
$199$	1.13124	−	1.95936i	0.0801912	−	0.138895i	0.903332	+	0.428942i	$0.141114\pi$
$200$	−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	0.981333	+	0.192319i	$0.0616007\pi$
$211$	19.4811	+	16.3466i	1.34114	+	1.12535i	0.359804	+	0.933028i	$0.382844\pi$
$212$	−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	0.459741	−	0.888053i	$-0.347942\pi$
$223$	3.60028	+	1.31039i	0.241093	+	0.0877505i	−0.218648	+	0.975804i	$0.570165\pi$
$224$	−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	−0.704505	−	0.709699i	$-0.748831\pi$
$227$	−1.92736	+	1.61725i	−0.127923	+	0.107341i	0.576581	+	0.817040i	$0.304386\pi$
$228$		0			0
$229$	−2.76789	+	15.6975i	−0.182907	+	1.03732i	0.745708	+	0.666273i	$0.232111\pi$
$229$	−2.76789	+	15.6975i	−0.182907	+	1.03732i	−0.928615	+	0.371045i	$0.879000\pi$
$230$	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	0.124077	−	0.992273i	$-0.460403\pi$
$233$	14.0641	−	24.3598i	0.921372	−	1.59586i	0.797295	−	0.603590i	$-0.206264\pi$
$234$		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	−0.747794	−	0.663930i	$-0.768887\pi$
$239$	−13.8189	+	5.02968i	−0.893872	+	0.325343i	−0.146077	+	0.989273i	$0.546665\pi$
$240$		0			0
$241$	1.46610	+	8.31468i	0.0944400	+	0.535596i	0.994918	+	0.100693i	$0.0321060\pi$
$241$	1.46610	+	8.31468i	0.0944400	+	0.535596i	−0.900478	+	0.434902i	$0.856783\pi$
$242$	−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	−0.955668	−	0.294447i	$-0.904865\pi$
$251$	−11.6102	−	20.1095i	−0.732832	−	1.26930i	0.222835	−	0.974856i	$-0.428469\pi$
$252$		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	0.924786	+	0.380488i	$0.124244\pi$
$257$	−1.19213	+	6.76090i	−0.0743630	+	0.421733i	−0.999149	+	0.0412458i	$0.986867\pi$
$258$		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	0.437329	−	0.899302i	$-0.355925\pi$
$263$	3.15073	+	1.14677i	0.194282	+	0.0707130i	−0.243047	+	0.970015i	$0.578147\pi$
$264$		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	0.221274	−	0.975212i	$-0.428978\pi$
$277$	−3.92906	−	1.43006i	−0.236074	−	0.0859240i	−0.457348	+	0.889288i	$0.651201\pi$
$278$	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	0.00334741	−	0.999994i	$-0.498934\pi$
$281$	16.5742	−	13.9074i	0.988731	−	0.829644i	0.985384	+	0.170351i	$0.0544900\pi$
$282$		0			0
$283$	0.907718	−	5.14792i	0.0539582	−	0.306012i	−0.945870	−	0.324546i	$-0.894789\pi$
$283$	0.907718	−	5.14792i	0.0539582	−	0.306012i	0.999828	+	0.0185334i	$0.00589971\pi$
$284$	−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	−0.505065	−	0.863081i	$-0.668531\pi$
$293$	−5.77175	+	2.10074i	−0.337189	+	0.122727i	0.167876	+	0.985808i	$0.446309\pi$
$294$		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	0.456467	+	0.889740i	$0.349115\pi$
$307$	−9.50194	+	16.4578i	−0.542304	+	0.939298i	−0.998771	+	0.0495580i	$0.984219\pi$
$308$	−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	−0.673592	−	0.739103i	$-0.735250\pi$
$311$	3.74158	−	21.2196i	0.212166	−	1.20325i	0.885758	−	0.464148i	$-0.153639\pi$
$312$		0			0
$313$	−2.92140	+	2.45135i	−0.165127	+	0.138558i	−0.721607	−	0.692303i	$-0.756596\pi$
$313$	−2.92140	+	2.45135i	−0.165127	+	0.138558i	0.556480	+	0.830861i	$0.312152\pi$
$314$	−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	0.451843	−	0.892098i	$-0.350767\pi$
$317$	3.99791	+	1.45512i	0.224545	+	0.0817277i	−0.227298	+	0.973825i	$0.572989\pi$
$318$		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	0.683664	−	0.729797i	$-0.260385\pi$
$331$	13.4318	+	4.88876i	0.738277	+	0.268711i	0.0546128	+	0.998508i	$0.482608\pi$
$332$	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	−0.0589637	−	0.998260i	$-0.518780\pi$
$337$	6.20245	−	35.1759i	0.337869	−	1.91615i	0.396833	−	0.917891i	$-0.370109\pi$
$338$	−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	−0.782126	−	0.623121i	$-0.785865\pi$
$347$	−18.2691	+	6.64939i	−0.980735	+	0.356958i	−0.198609	+	0.980079i	$0.563642\pi$
$348$		0			0
$349$	−1.39278	−	7.89885i	−0.0745538	−	0.422816i	−0.999126	−	0.0418080i	$-0.986688\pi$
$349$	−1.39278	−	7.89885i	−0.0745538	−	0.422816i	0.924572	−	0.381008i	$-0.124423\pi$
$350$	4.88014			0.260855
$351$		0			0
$352$	1.45834			0.0777296
$353$	−1.52008	−	8.62082i	−0.0809059	−	0.458840i	−0.998165	−	0.0605496i	$-0.980715\pi$
$353$	−1.52008	−	8.62082i	−0.0809059	−	0.458840i	0.917259	−	0.398291i	$-0.130396\pi$
$354$		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	0.735887	−	0.677104i	$-0.236765\pi$
$359$	−4.13896	−	7.16888i	−0.218446	−	0.378359i	−0.954333	+	0.298745i	$0.903432\pi$
$360$		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	−0.888800	−	0.458296i	$-0.848460\pi$
$367$	−11.3373	+	9.51316i	−0.591805	+	0.496583i	0.296995	+	0.954879i	$0.404016\pi$
$368$	−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	0.988701	−	0.149901i	$-0.0478954\pi$
$373$	19.5597	+	16.4126i	1.01276	+	0.849810i	0.0240627	+	0.999710i	$0.492340\pi$
$374$	−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	0.976532	−	0.215374i	$-0.0690972\pi$
$383$	18.2788	+	15.3377i	0.934002	+	0.783721i	−0.0425294	+	0.999095i	$0.513542\pi$
$384$		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	−0.563434	+	0.826161i	$0.690520\pi$
$389$	−29.0892	+	24.4088i	−1.47488	+	1.23757i	−0.911449	+	0.411413i	$0.865035\pi$
$390$		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	−0.999924	−	0.0123433i	$-0.996071\pi$
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	0.489272	−	0.872131i	$-0.337262\pi$
$398$	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	−0.173889	−	0.984765i	$-0.555633\pi$
$401$	6.52613	−	2.37532i	0.325900	−	0.118618i	0.499788	+	0.866148i	$0.333411\pi$
$402$		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	−0.0759814	−	0.997109i	$-0.524209\pi$
$409$	10.2482	−	3.73005i	0.506743	−	0.184439i	0.582724	+	0.812670i	$0.301987\pi$
$410$	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	−0.911846	−	0.410533i	$-0.865343\pi$
$419$	1.74850	−	9.91621i	0.0854196	−	0.484439i	0.997265	−	0.0739054i	$-0.0235463\pi$
$420$		0			0
$421$	−2.38053	+	1.99750i	−0.116020	+	0.0973524i	−0.698952	−	0.715169i	$-0.746350\pi$
$421$	−2.38053	+	1.99750i	−0.116020	+	0.0973524i	0.582932	+	0.812521i	$0.301905\pi$
$422$	−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	−0.00756144	−	0.999971i	$-0.502407\pi$
$439$	−13.7473	−	5.00361i	−0.656123	−	0.238809i	−0.648562	+	0.761162i	$0.724629\pi$
$440$	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	−0.912497	−	0.409084i	$-0.865848\pi$
$443$	−14.0615	+	11.7990i	−0.668081	+	0.560586i	0.244416	+	0.969670i	$0.421404\pi$
$444$		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	−0.654889	−	0.755725i	$-0.727285\pi$
$449$	6.92969	−	12.0026i	0.327032	−	0.566437i	0.981922	+	0.189288i	$0.0606180\pi$
$450$		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	0.968674	+	0.248337i	$0.0798839\pi$
$457$	3.06457	+	17.3800i	0.143354	+	0.813003i	−0.825319	+	0.564666i	$0.809005\pi$
$458$	−12.7760			−0.596985
$459$		0			0
$460$	−24.9736			−1.16440
$461$	−4.45200	−	25.2485i	−0.207350	−	1.17594i	−0.893698	−	0.448668i	$-0.851898\pi$
$461$	−4.45200	−	25.2485i	−0.207350	−	1.17594i	0.686348	−	0.727273i	$-0.259213\pi$
$462$		0			0
$463$	−17.2409	+	6.27519i	−0.801254	+	0.291633i	−0.710006	−	0.704195i	$-0.751308\pi$
$463$	−17.2409	+	6.27519i	−0.801254	+	0.291633i	−0.0912482	+	0.995828i	$0.529086\pi$
$464$	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	0.614260	−	0.789104i	$-0.289455\pi$
$467$	−8.13092	−	14.0832i	−0.376254	−	0.651692i	−0.990514	+	0.137412i	$0.956121\pi$
$468$		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	0.130580	−	0.991438i	$-0.458316\pi$
$479$	−8.90050	−	3.23952i	−0.406674	−	0.148017i	−0.537254	+	0.843421i	$0.680538\pi$
$480$		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	0.0973291	−	0.995252i	$-0.468970\pi$
$491$	−19.1871	−	16.0999i	−0.865902	−	0.726578i	−0.963231	+	0.268674i	$0.913415\pi$
$492$		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	0.880410	+	0.474214i	$0.157268\pi$
$499$	−2.43701	+	13.8209i	−0.109095	+	0.618711i	−0.989505	+	0.144497i	$0.953844\pi$
$500$	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	−0.356136	−	0.934434i	$-0.615906\pi$
$503$	14.1558	−	24.5186i	0.631176	−	1.09323i	0.987312	−	0.158794i	$-0.0507607\pi$
$504$		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	−0.861429	−	0.507877i	$-0.830430\pi$
$509$	−26.9574	+	9.81169i	−1.19487	+	0.434895i	−0.333436	+	0.942773i	$0.608208\pi$
$510$		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	−0.998565	−	0.0535462i	$-0.982948\pi$
$521$	−12.4548	−	21.5724i	−0.545655	−	0.945102i	0.452910	−	0.891556i	$-0.350386\pi$
$522$		0			0
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	−0.431510	−	0.902108i	$-0.642019\pi$
$523$	12.9324	−	22.3995i	0.565494	−	0.979464i	0.997004	−	0.0773554i	$-0.0246476\pi$
$524$	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	0.534562	−	0.845129i	$-0.320477\pi$
$547$	9.37442	+	3.41201i	0.400821	+	0.145887i	−0.133741	+	0.991016i	$0.542699\pi$
$548$	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	−0.992796	−	0.119816i	$-0.961769\pi$
$557$	−9.26650	+	16.0500i	−0.392634	+	0.680062i	0.600162	+	0.799879i	$0.295103\pi$
$558$		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	0.731365	−	0.681986i	$-0.238884\pi$
$563$	41.0487	−	14.9405i	1.73000	−	0.629667i	0.998630	+	0.0523192i	$0.0166613\pi$
$564$		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	−0.993530	−	0.113573i	$-0.963770\pi$
$569$	−2.35583	−	13.3606i	−0.0987616	−	0.560105i	0.894768	−	0.446531i	$-0.147341\pi$
$570$		0			0
$571$	−22.3165	+	8.12254i	−0.933916	+	0.339918i	−0.763761	−	0.645500i	$-0.776649\pi$
$571$	−22.3165	+	8.12254i	−0.933916	+	0.339918i	−0.170155	+	0.985417i	$0.554427\pi$
$572$	−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	−0.769069	−	0.639166i	$-0.779280\pi$
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	0.938068	+	0.346450i	$0.112613\pi$
$578$	−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	0.269428	−	0.963020i	$-0.413165\pi$
$587$	−3.46934	−	1.26274i	−0.143195	−	0.0521187i	−0.412623	+	0.910902i	$0.635387\pi$
$588$		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	0.917374	−	0.398027i	$-0.130305\pi$
$599$	16.7575	+	14.0612i	0.684694	+	0.574526i	−0.232680	+	0.972553i	$0.574749\pi$
$600$		0			0
$601$	−34.3182	−	12.4908i	−1.39987	−	0.509510i	−0.471729	−	0.881744i	$-0.656370\pi$
$601$	−34.3182	−	12.4908i	−1.39987	−	0.509510i	−0.928139	+	0.372233i	$0.878592\pi$
$602$	−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	−0.999177	−	0.0405678i	$-0.987083\pi$
$607$	−1.14275	+	6.48085i	−0.0463827	+	0.263049i	0.952794	+	0.303617i	$0.0981944\pi$
$608$	−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	0.929136	−	0.369737i	$-0.120552\pi$
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	−0.784770	+	0.619787i	$0.787219\pi$
$614$	−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	−0.00970235	−	0.999953i	$-0.503088\pi$
$617$	15.5401	−	5.65615i	0.625623	−	0.227708i	0.635325	+	0.772245i	$0.280866\pi$
$618$		0			0
$619$	−0.260359	−	1.47657i	−0.0104647	−	0.0593484i	0.979128	−	0.203244i	$-0.0651483\pi$
$619$	−0.260359	−	1.47657i	−0.0104647	−	0.0593484i	−0.989593	+	0.143895i	$0.954037\pi$
$620$	−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	−0.248785	−	0.968559i	$-0.580031\pi$
$631$	17.9456	−	31.0827i	0.714404	−	1.23738i	0.963189	−	0.268826i	$-0.0866356\pi$
$632$	−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	0.944252	−	0.329224i	$-0.106787\pi$
$641$	36.8622	+	13.4167i	1.45597	+	0.529930i	0.511718	+	0.859153i	$0.329009\pi$
$642$		0			0
$643$	−7.98104	−	6.69688i	−0.314741	−	0.264099i	0.471707	−	0.881755i	$-0.343638\pi$
$643$	−7.98104	−	6.69688i	−0.314741	−	0.264099i	−0.786448	+	0.617656i	$0.788082\pi$
$644$	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	−0.00149448	−	0.999999i	$-0.500476\pi$
$653$	−25.2104	−	21.1541i	−0.986561	−	0.827823i	−0.985066	+	0.172176i	$0.944920\pi$
$654$		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	−0.261508	−	0.965201i	$-0.584220\pi$
$659$	16.5224	−	13.8639i	0.643620	−	0.540061i	0.905128	+	0.425140i	$0.139775\pi$
$660$		0			0
$661$	4.56632	−	25.8969i	0.177609	−	1.00727i	−0.757480	−	0.652859i	$-0.773570\pi$
$661$	4.56632	−	25.8969i	0.177609	−	1.00727i	0.935089	−	0.354413i	$-0.115319\pi$
$662$	−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	0.998780	+	0.0493865i	$0.0157266\pi$
$673$	2.00079	+	11.3471i	0.0771250	+	0.437397i	−0.921655	+	0.388011i	$0.873162\pi$
$674$	28.6293			1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	5.89102	+	33.4096i	0.226410	+	1.28404i	0.859971	+	0.510343i	$0.170482\pi$
$677$	5.89102	+	33.4096i	0.226410	+	1.28404i	−0.633561	+	0.773693i	$0.718407\pi$
$678$		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	0.967337	+	0.253495i	$0.0815801\pi$
$683$	18.3777	+	31.8310i	0.703201	+	1.21798i	−0.264135	+	0.964486i	$0.585087\pi$
$684$		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	−0.426698	−	0.904394i	$-0.640323\pi$
$691$	10.2482	−	8.59929i	0.389861	−	0.327132i	0.816559	+	0.577262i	$0.195879\pi$
$692$	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	0.0213017	−	0.999773i	$-0.493219\pi$
$709$	−16.1100	−	5.86354i	−0.605022	−	0.220210i	−0.626324	+	0.779563i	$0.715441\pi$
$710$	−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	0.105610	+	0.994408i	$0.466320\pi$
$719$	−21.6760	+	37.5439i	−0.808377	+	1.40015i	−0.913987	+	0.405742i	$0.867013\pi$
$720$		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	−0.844576	−	0.535436i	$-0.820147\pi$
$727$	−6.31105	−	35.7918i	−0.234064	−	1.32744i	0.610512	−	0.792007i	$-0.290964\pi$
$728$	−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	−0.408401	−	0.912803i	$-0.633913\pi$
$733$	−3.64188	+	1.32554i	−0.134516	+	0.0489598i	0.273885	+	0.961762i	$0.411691\pi$
$734$	−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	−0.999879	−	0.0155689i	$-0.995044\pi$
$739$	−13.2241	+	22.9048i	−0.486456	+	0.842567i	0.513422	+	0.858136i	$0.328377\pi$
$740$	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	−0.911419	−	0.411479i	$-0.865012\pi$
$743$	2.33789	−	13.2588i	0.0857688	−	0.486419i	0.997188	−	0.0749400i	$-0.0238765\pi$
$744$		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	0.693935	−	0.720038i	$-0.255876\pi$
$751$	2.88669	+	2.42222i	0.105337	+	0.0883880i	−0.588598	+	0.808426i	$0.700320\pi$
$752$	−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	0.766929	−	0.641732i	$-0.221784\pi$
$761$	7.39649	+	6.20639i	0.268122	+	0.224981i	−0.498807	+	0.866713i	$0.666228\pi$
$762$		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	−0.584038	−	0.811726i	$-0.698528\pi$
$769$	6.72210	−	38.1229i	0.242405	−	1.37475i	0.826443	−	0.563021i	$-0.190361\pi$
$770$	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	−0.560387	−	0.828231i	$-0.689348\pi$
$773$	12.1519	−	21.0478i	0.437075	−	0.757036i	0.997462	+	0.0711944i	$0.0226811\pi$
$774$		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	−0.668024	−	0.744140i	$-0.732860\pi$
$787$	−19.6777	+	7.16211i	−0.701436	+	0.255302i	−0.0334119	+	0.999442i	$0.510637\pi$
$788$	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	0.925837	+	0.377922i	$0.123361\pi$
$797$	−2.07280	+	11.7554i	−0.0734222	+	0.416398i	−0.999260	+	0.0384758i	$0.987750\pi$
$798$		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	−0.941904	−	0.335882i	$-0.890966\pi$
$821$	−22.1971	+	18.6256i	−0.774684	+	0.650037i	0.167220	+	0.985920i	$0.446521\pi$
$822$		0			0
$823$	−1.95472	+	11.0858i	−0.0681372	+	0.386425i	0.931600	+	0.363486i	$0.118414\pi$
$823$	−1.95472	+	11.0858i	−0.0681372	+	0.386425i	−0.999737	+	0.0229391i	$0.992698\pi$
$824$	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	−0.461291	−	0.887249i	$-0.652614\pi$
$827$	15.4640	−	26.7844i	0.537734	−	0.931383i	0.999026	−	0.0441346i	$-0.0140530\pi$
$828$		0			0
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	0.938698	−	0.344739i	$-0.112033\pi$
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	−0.767902	+	0.640567i	$0.778699\pi$
$830$	−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	0.998524	+	0.0543102i	$0.0172960\pi$
$839$	2.28229	+	12.9435i	0.0787935	+	0.446860i	−0.919731	+	0.392550i	$0.871593\pi$
$840$		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	−0.417401	−	0.908722i	$-0.637059\pi$
$853$	11.8295	−	9.92614i	0.405035	−	0.339864i	0.822436	+	0.568858i	$0.192615\pi$
$854$	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	0.669813	−	0.742530i	$-0.266374\pi$
$857$	20.6570	+	7.51854i	0.705630	+	0.256828i	0.0358174	+	0.999358i	$0.488597\pi$
$858$		0			0
$859$	14.9889	+	12.5772i	0.511416	+	0.429129i	0.861627	−	0.507542i	$-0.169446\pi$
$859$	14.9889	+	12.5772i	0.511416	+	0.429129i	−0.350211	+	0.936671i	$0.613890\pi$
$860$	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	0.625084	+	0.780558i	$0.285065\pi$
$877$	−6.78962	+	38.5059i	−0.229269	+	1.30025i	−0.854353	+	0.519693i	$0.826046\pi$
$878$	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	−0.920972	−	0.389629i	$-0.872603\pi$
$881$	−3.65254	+	6.32639i	−0.123057	+	0.213141i	0.797915	+	0.602771i	$0.205937\pi$
$882$		0			0
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	0.893915	−	0.448237i	$-0.147948\pi$
$883$	1.74646	+	3.02496i	0.0587732	+	0.101798i	−0.835142	+	0.550035i	$0.814614\pi$
$884$	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	0.147796	−	0.989018i	$-0.452782\pi$
$887$	26.7073	−	9.72065i	0.896742	−	0.326388i	0.748947	+	0.662630i	$0.230560\pi$
$888$		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	0.372453	−	0.928051i	$-0.378517\pi$
$907$	40.6897	−	34.1427i	1.35108	−	1.13369i	0.978628	−	0.205640i	$-0.0659277\pi$
$908$	−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	0.213231	−	0.977002i	$-0.431601\pi$
$911$	−7.58885	−	2.76212i	−0.251430	−	0.0915130i	−0.464661	+	0.885489i	$0.653824\pi$
$912$		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	−0.201071	−	0.979577i	$-0.564442\pi$
$929$	22.2106	−	18.6369i	0.728707	−	0.611458i	0.929779	+	0.368118i	$0.119998\pi$
$930$		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	0.822031	−	0.569443i	$-0.192841\pi$
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	−0.904168	+	0.427178i	$0.859508\pi$
$938$	−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	−0.996959	−	0.0779249i	$-0.975171\pi$
$941$	−52.4734	+	19.0988i	−1.71059	+	0.622602i	−0.713626	+	0.700527i	$0.752948\pi$
$942$		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	−0.831857	−	0.554991i	$-0.812722\pi$
$947$	−7.38515	−	41.8833i	−0.239985	−	1.36102i	0.591872	−	0.806032i	$-0.298389\pi$
$948$		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	0.986830	−	0.161762i	$-0.0517175\pi$
$953$	10.9074	+	18.8922i	0.353325	+	0.611977i	−0.633505	+	0.773739i	$0.718384\pi$
$954$		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	0.698016	−	0.716082i	$-0.254066\pi$
$967$	3.54570	+	2.97520i	0.114022	+	0.0956759i	−0.583994	+	0.811758i	$0.698511\pi$
$968$	−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	0.871966	−	0.489566i	$-0.162845\pi$
$977$	16.9180	+	14.1958i	0.541253	+	0.454165i	−0.330713	+	0.943731i	$0.607289\pi$
$978$		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	−0.457524	−	0.889197i	$-0.651264\pi$
$983$	10.6197	−	8.91100i	0.338716	−	0.284217i	0.796240	+	0.604981i	$0.206819\pi$
$984$		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	−0.998050	−	0.0624224i	$-0.980117\pi$
$991$	−17.4112	−	30.1570i	−0.553084	−	0.957970i	0.444966	−	0.895548i	$-0.353216\pi$
$992$	−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	−0.974080	−	0.226206i	$-0.927368\pi$
$997$	−4.29775	−	24.3738i	−0.136111	−	0.771924i	0.837968	−	0.545719i	$-0.183743\pi$
$998$	−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.28.2		12
3.2	odd	2		243.2.e.c.28.1		12
9.2	odd	6		243.2.e.d.109.1		12
9.4	even	3		81.2.e.a.64.1		12
9.5	odd	6		27.2.e.a.4.2	✓	12
9.7	even	3		243.2.e.a.109.2		12
27.2	odd	18		243.2.e.c.217.1		12
27.4	even	9		729.2.c.b.487.3		12
27.5	odd	18		729.2.a.a.1.3		6
27.7	even	9		243.2.e.a.136.2		12
27.11	odd	18		27.2.e.a.7.2	yes	12
27.13	even	9		729.2.c.b.244.3		12
27.14	odd	18		729.2.c.e.244.4		12
27.16	even	9		81.2.e.a.19.1		12
27.20	odd	18		243.2.e.d.136.1		12
27.22	even	9		729.2.a.d.1.4		6
27.23	odd	18		729.2.c.e.487.4		12
27.25	even	9	inner	243.2.e.b.217.2		12
36.23	even	6		432.2.u.c.193.2		12
45.14	odd	6		675.2.l.c.301.1		12
45.23	even	12		675.2.u.b.274.3		24
45.32	even	12		675.2.u.b.274.2		24
108.11	even	18		432.2.u.c.385.2		12
135.38	even	36		675.2.u.b.574.2		24
135.92	even	36		675.2.u.b.574.3		24
135.119	odd	18		675.2.l.c.601.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	9.5	odd	6
27.2.e.a.7.2	yes	12	27.11	odd	18
81.2.e.a.19.1		12	27.16	even	9
81.2.e.a.64.1		12	9.4	even	3
243.2.e.a.109.2		12	9.7	even	3
243.2.e.a.136.2		12	27.7	even	9
243.2.e.b.28.2		12	1.1	even	1	trivial
243.2.e.b.217.2		12	27.25	even	9	inner
243.2.e.c.28.1		12	3.2	odd	2
243.2.e.c.217.1		12	27.2	odd	18
243.2.e.d.109.1		12	9.2	odd	6
243.2.e.d.136.1		12	27.20	odd	18
432.2.u.c.193.2		12	36.23	even	6
432.2.u.c.385.2		12	108.11	even	18
675.2.l.c.301.1		12	45.14	odd	6
675.2.l.c.601.1		12	135.119	odd	18
675.2.u.b.274.2		24	45.32	even	12
675.2.u.b.274.3		24	45.23	even	12
675.2.u.b.574.2		24	135.38	even	36
675.2.u.b.574.3		24	135.92	even	36
729.2.a.a.1.3		6	27.5	odd	18
729.2.a.d.1.4		6	27.22	even	9
729.2.c.b.244.3		12	27.13	even	9
729.2.c.b.487.3		12	27.4	even	9
729.2.c.e.244.4		12	27.14	odd	18
729.2.c.e.487.4		12	27.23	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 $\F_{q}$
Belyi maps

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more