LMFDB - Embedded newform 432.2.u.c.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (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:	$3.44953736732$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.2
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	432.337
Dual form			432.2.u.c.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72962 + 0.0916693i) q^{3} +(-1.33735 - 1.12217i) q^{5} +(2.31094 + 0.841112i) q^{7} +(2.98319 + 0.317107i) q^{9} +O(q^{10})$	\(q+(1.72962 + 0.0916693i) q^{3} +(-1.33735 - 1.12217i) q^{5} +(2.31094 + 0.841112i) q^{7} +(2.98319 + 0.317107i) q^{9} +(0.960783 - 0.806193i) q^{11} +(-0.789931 + 4.47992i) q^{13} +(-2.21024 - 2.06353i) q^{15} +(3.32358 - 5.75662i) q^{17} +(0.124578 + 0.215776i) q^{19} +(3.91994 + 1.66665i) q^{21} +(0.791222 - 0.287981i) q^{23} +(-0.339001 - 1.92257i) q^{25} +(5.13073 + 0.821942i) q^{27} +(-0.0889744 - 0.504599i) q^{29} +(-0.770551 + 0.280458i) q^{31} +(1.73570 - 1.30634i) q^{33} +(-2.14666 - 3.71812i) q^{35} +(-1.30403 + 2.25865i) q^{37} +(-1.77695 + 7.67616i) q^{39} +(-1.41572 + 8.02895i) q^{41} +(-3.31478 + 2.78143i) q^{43} +(-3.63373 - 3.77173i) q^{45} +(-4.98256 - 1.81351i) q^{47} +(-0.729356 - 0.612002i) q^{49} +(6.27625 - 9.65211i) q^{51} -10.4841 q^{53} -2.18959 q^{55} +(0.195693 + 0.384630i) q^{57} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(6.62725 + 3.24201i) q^{63} +(6.08365 - 5.10479i) q^{65} +(-1.75146 + 9.93303i) q^{67} +(1.39492 - 0.425568i) q^{69} +(0.0447378 - 0.0774882i) q^{71} +(2.66057 + 4.60824i) q^{73} +(-0.410103 - 3.35640i) q^{75} +(2.89841 - 1.05493i) q^{77} +(-0.829503 - 4.70435i) q^{79} +(8.79889 + 1.89198i) q^{81} +(-1.39625 - 7.91851i) q^{83} +(-10.9047 + 3.96899i) q^{85} +(-0.107636 - 0.880922i) q^{87} +(-3.35189 - 5.80564i) q^{89} +(-5.59359 + 9.68839i) q^{91} +(-1.35847 + 0.414450i) q^{93} +(0.0755324 - 0.428365i) q^{95} +(4.20603 - 3.52928i) q^{97} +(3.12185 - 2.10036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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			0
$2$		0			0
$3$	1.72962	+	0.0916693i	0.998598	+	0.0529253i
$3$	1.72962	+	0.0916693i	0.998598	+	0.0529253i
$4$		0			0
$5$	−1.33735	−	1.12217i	−0.598081	−	0.501850i	0.292747	−	0.956190i	$-0.405431\pi$
$5$	−1.33735	−	1.12217i	−0.598081	−	0.501850i	−0.890828	+	0.454340i	$0.849875\pi$
$6$		0			0
$7$	2.31094	+	0.841112i	0.873452	+	0.317910i	0.739564	−	0.673086i	$-0.235032\pi$
$7$	2.31094	+	0.841112i	0.873452	+	0.317910i	0.133888	+	0.990997i	$0.457254\pi$
$8$		0			0
$9$	2.98319	+	0.317107i	0.994398	+	0.105702i
$10$		0			0
$11$	0.960783	−	0.806193i	0.289687	−	0.243076i	−0.486349	−	0.873764i	$-0.661672\pi$
$11$	0.960783	−	0.806193i	0.289687	−	0.243076i	0.776036	+	0.630688i	$0.217227\pi$
$12$		0			0
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	0.654584	+	0.755989i	$0.272844\pi$
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	−0.873671	+	0.486517i	$0.838267\pi$
$14$		0			0
$15$	−2.21024	−	2.06353i	−0.570683	−	0.532800i
$16$		0			0
$17$	3.32358	−	5.75662i	0.806088	−	1.39618i	−0.109467	−	0.993990i	$-0.534914\pi$
$17$	3.32358	−	5.75662i	0.806088	−	1.39618i	0.915554	−	0.402194i	$-0.131752\pi$
$18$		0			0
$19$	0.124578	+	0.215776i	0.0285802	+	0.0495023i	0.879962	−	0.475045i	$-0.157568\pi$
$19$	0.124578	+	0.215776i	0.0285802	+	0.0495023i	−0.851382	+	0.524547i	$0.824235\pi$
$20$		0			0
$21$	3.91994	+	1.66665i	0.855402	+	0.363693i
$22$		0			0
$23$	0.791222	−	0.287981i	0.164981	−	0.0600483i	−0.258209	−	0.966089i	$-0.583132\pi$
$23$	0.791222	−	0.287981i	0.164981	−	0.0600483i	0.423190	+	0.906041i	$0.360910\pi$
$24$		0			0
$25$	−0.339001	−	1.92257i	−0.0678002	−	0.384514i
$26$		0			0
$27$	5.13073	+	0.821942i	0.987410	+	0.158183i
$28$		0			0
$29$	−0.0889744	−	0.504599i	−0.0165221	−	0.0937016i	0.975432	−	0.220302i	$-0.0707044\pi$
$29$	−0.0889744	−	0.504599i	−0.0165221	−	0.0937016i	−0.991954	+	0.126601i	$0.959593\pi$
$30$		0			0
$31$	−0.770551	+	0.280458i	−0.138395	+	0.0503717i	−0.410289	−	0.911956i	$-0.634572\pi$
$31$	−0.770551	+	0.280458i	−0.138395	+	0.0503717i	0.271894	+	0.962327i	$0.412350\pi$
$32$		0			0
$33$	1.73570	−	1.30634i	0.302146	−	0.227404i
$34$		0			0
$35$	−2.14666	−	3.71812i	−0.362852	−	0.628478i
$36$		0			0
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	−0.953081	−	0.302715i	$-0.902107\pi$
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	0.738700	+	0.674035i	$0.235440\pi$
$38$		0			0
$39$	−1.77695	+	7.67616i	−0.284540	+	1.22917i
$40$		0			0
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	0.648906	+	0.760869i	$0.275227\pi$
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	−0.870005	+	0.493044i	$0.835884\pi$
$42$		0			0
$43$	−3.31478	+	2.78143i	−0.505500	+	0.424165i	−0.859542	−	0.511065i	$-0.829251\pi$
$43$	−3.31478	+	2.78143i	−0.505500	+	0.424165i	0.354042	+	0.935229i	$0.384807\pi$
$44$		0			0
$45$	−3.63373	−	3.77173i	−0.541684	−	0.562257i
$46$		0			0
$47$	−4.98256	−	1.81351i	−0.726782	−	0.264527i	−0.0479798	−	0.998848i	$-0.515278\pi$
$47$	−4.98256	−	1.81351i	−0.726782	−	0.264527i	−0.678802	+	0.734321i	$0.737501\pi$
$48$		0			0
$49$	−0.729356	−	0.612002i	−0.104194	−	0.0874289i
$50$		0			0
$51$	6.27625	−	9.65211i	0.878851	−	1.35157i
$52$		0			0
$53$	−10.4841			−1.44010			−0.720052	−	0.693920i	$-0.755882\pi$
$53$	−10.4841			−1.44010			−0.720052	+	0.693920i	$0.755882\pi$
$54$		0			0
$55$	−2.18959			−0.295244
$56$		0			0
$57$	0.195693	+	0.384630i	0.0259202	+	0.0509456i
$58$		0			0
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	0.780265	−	0.625449i	$-0.215084\pi$
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	−0.480455	+	0.877019i	$0.659529\pi$
$60$		0			0
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	0.162699	−	0.986676i	$-0.447980\pi$
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	−0.509589	+	0.860418i	$0.670202\pi$
$62$		0			0
$63$	6.62725	+	3.24201i	0.834955	+	0.408455i
$64$		0			0
$65$	6.08365	−	5.10479i	0.754584	−	0.633171i
$66$		0			0
$67$	−1.75146	+	9.93303i	−0.213975	+	1.21351i	0.668701	+	0.743531i	$0.266851\pi$
$67$	−1.75146	+	9.93303i	−0.213975	+	1.21351i	−0.882676	+	0.469982i	$0.844261\pi$
$68$		0			0
$69$	1.39492	−	0.425568i	0.167928	−	0.0512324i
$70$		0			0
$71$	0.0447378	−	0.0774882i	0.00530940	−	0.00919615i	−0.863358	−	0.504591i	$-0.831643\pi$
$71$	0.0447378	−	0.0774882i	0.00530940	−	0.00919615i	0.868668	+	0.495395i	$0.164977\pi$
$72$		0			0
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	0.978665	−	0.205463i	$-0.0658701\pi$
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	−0.667269	+	0.744817i	$0.732537\pi$
$74$		0			0
$75$	−0.410103	−	3.35640i	−0.0473546	−	0.387563i
$76$		0			0
$77$	2.89841	−	1.05493i	0.330304	−	0.120221i
$78$		0			0
$79$	−0.829503	−	4.70435i	−0.0933264	−	0.529280i	−0.995247	−	0.0973792i	$-0.968954\pi$
$79$	−0.829503	−	4.70435i	−0.0933264	−	0.529280i	0.901921	−	0.431901i	$-0.142157\pi$
$80$		0			0
$81$	8.79889	+	1.89198i	0.977654	+	0.210220i
$82$		0			0
$83$	−1.39625	−	7.91851i	−0.153258	−	0.869169i	−0.960361	−	0.278759i	$-0.910077\pi$
$83$	−1.39625	−	7.91851i	−0.153258	−	0.869169i	0.807103	−	0.590410i	$-0.201034\pi$
$84$		0			0
$85$	−10.9047	+	3.96899i	−1.18278	+	0.430497i
$86$		0			0
$87$	−0.107636	−	0.880922i	−0.0115398	−	0.0944448i
$88$		0			0
$89$	−3.35189	−	5.80564i	−0.355299	−	0.615396i	0.631870	−	0.775074i	$-0.282288\pi$
$89$	−3.35189	−	5.80564i	−0.355299	−	0.615396i	−0.987169	+	0.159678i	$0.948954\pi$
$90$		0			0
$91$	−5.59359	+	9.68839i	−0.586368	+	1.01562i
$92$		0			0
$93$	−1.35847	+	0.414450i	−0.140867	+	0.0429765i
$94$		0			0
$95$	0.0755324	−	0.428365i	0.00774946	−	0.0439494i
$96$		0			0
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	−0.403783	−	0.914855i	$-0.632305\pi$
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	0.830840	+	0.556511i	$0.187860\pi$
$98$		0			0
$99$	3.12185	−	2.10036i	0.313758	−	0.211094i
$100$		0			0
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	0.0972322	−	0.995262i	$-0.469001\pi$
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	−0.565258	+	0.824914i	$0.691223\pi$
$102$		0			0
$103$	−8.90079	−	7.46865i	−0.877021	−	0.735908i	0.0885431	−	0.996072i	$-0.471779\pi$
$103$	−8.90079	−	7.46865i	−0.877021	−	0.735908i	−0.965564	+	0.260164i	$0.916223\pi$
$104$		0			0
$105$	−3.37208	−	6.62774i	−0.329081	−	0.646801i
$106$		0			0
$107$	−19.4581			−1.88109			−0.940544	−	0.339673i	$-0.889684\pi$
$107$	−19.4581			−1.88109			−0.940544	+	0.339673i	$0.889684\pi$
$108$		0			0
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$		0			0
$111$	−2.46253	+	3.78707i	−0.233733	+	0.359453i
$112$		0			0
$113$	−5.29775	−	4.44534i	−0.498371	−	0.418183i	0.358644	−	0.933474i	$-0.383239\pi$
$113$	−5.29775	−	4.44534i	−0.498371	−	0.418183i	−0.857015	+	0.515292i	$0.827684\pi$
$114$		0			0
$115$	−1.38131	−	0.502754i	−0.128807	−	0.0468821i
$116$		0			0
$117$	−3.77713	+	13.1140i	−0.349196	+	1.21239i
$118$		0			0
$119$	12.5226	−	10.5077i	1.14794	−	0.963236i
$120$		0			0
$121$	−1.63697	+	9.28373i	−0.148816	+	0.843976i
$122$		0			0
$123$	−3.18467	+	13.7573i	−0.287152	+	1.24045i
$124$		0			0
$125$	−6.06855	+	10.5110i	−0.542788	+	0.940136i
$126$		0			0
$127$	6.01162	+	10.4124i	0.533445	+	0.923954i	0.999237	+	0.0390598i	$0.0124363\pi$
$127$	6.01162	+	10.4124i	0.533445	+	0.923954i	−0.465792	+	0.884894i	$0.654230\pi$
$128$		0			0
$129$	−5.98830	+	4.50697i	−0.527240	+	0.396817i
$130$		0			0
$131$	−13.2354	+	4.81728i	−1.15638	+	0.420888i	−0.847803	−	0.530311i	$-0.822075\pi$
$131$	−13.2354	+	4.81728i	−1.15638	+	0.420888i	−0.308577	+	0.951199i	$0.599853\pi$
$132$		0			0
$133$	0.106401	+	0.603428i	0.00922610	+	0.0523238i
$134$		0			0
$135$	−5.93923	−	6.85678i	−0.511167	−	0.590138i
$136$		0			0
$137$	0.392122	+	2.22383i	0.0335012	+	0.189995i	0.996966	−	0.0778409i	$-0.0248026\pi$
$137$	0.392122	+	2.22383i	0.0335012	+	0.189995i	−0.963465	+	0.267836i	$0.913692\pi$
$138$		0			0
$139$	−7.49414	+	2.72764i	−0.635644	+	0.231356i	−0.639686	−	0.768636i	$-0.720936\pi$
$139$	−7.49414	+	2.72764i	−0.635644	+	0.231356i	0.00404179	+	0.999992i	$0.498713\pi$
$140$		0			0
$141$	−8.45172	−	3.59343i	−0.711763	−	0.302621i
$142$		0			0
$143$	2.85273	+	4.94107i	0.238557	+	0.413193i
$144$		0			0
$145$	−0.447256	+	0.774670i	−0.0371426	+	0.0643328i
$146$		0			0
$147$	−1.20541	−	1.12539i	−0.0994204	−	0.0928208i
$148$		0			0
$149$	−0.0185697	+	0.105314i	−0.00152129	+	0.00862764i	−0.985559	−	0.169333i	$-0.945839\pi$
$149$	−0.0185697	+	0.105314i	−0.00152129	+	0.00862764i	0.984038	+	0.177960i	$0.0569499\pi$
$150$		0			0
$151$	15.5196	−	13.0225i	1.26297	−	1.05976i	0.267609	−	0.963528i	$-0.413767\pi$
$151$	15.5196	−	13.0225i	1.26297	−	1.05976i	0.995359	−	0.0962282i	$-0.0306779\pi$
$152$		0			0
$153$	11.7404	−	16.1192i	0.949152	−	1.30316i
$154$		0			0
$155$	1.34522	+	0.489620i	0.108051	+	0.0393272i
$156$		0			0
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.994712	−	0.102701i	$-0.967252\pi$
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.273871	−	0.961767i	$-0.588304\pi$
$158$		0			0
$159$	−18.1336	−	0.961071i	−1.43809	−	0.0762179i
$160$		0			0
$161$	2.07069			0.163193
$162$		0			0
$163$	20.1346			1.57706			0.788531	−	0.614995i	$-0.210842\pi$
$163$	20.1346			1.57706			0.788531	+	0.614995i	$0.210842\pi$
$164$		0			0
$165$	−3.78716	−	0.200718i	−0.294830	−	0.0156259i
$166$		0			0
$167$	15.2156	+	12.7674i	1.17742	+	0.987974i	0.999993	+	0.00383999i	$0.00122231\pi$
$167$	15.2156	+	12.7674i	1.17742	+	0.987974i	0.177429	+	0.984134i	$0.443222\pi$
$168$		0			0
$169$	−7.22968	−	2.63139i	−0.556130	−	0.202415i
$170$		0			0
$171$	0.303217	+	0.683205i	0.0231876	+	0.0522460i
$172$		0			0
$173$	14.4975	−	12.1648i	1.10222	−	0.924875i	0.104650	−	0.994509i	$-0.466628\pi$
$173$	14.4975	−	12.1648i	1.10222	−	0.924875i	0.997573	+	0.0696342i	$0.0221832\pi$
$174$		0			0
$175$	0.833686	−	4.72807i	0.0630208	−	0.357409i
$176$		0			0
$177$	3.80599	+	3.55334i	0.286075	+	0.267085i
$178$		0			0
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	−0.586787	−	0.809741i	$-0.699608\pi$
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	0.994650	+	0.103302i	$0.0329409\pi$
$180$		0			0
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	0.978731	+	0.205146i	$0.0657668\pi$
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	−0.311704	+	0.950179i	$0.600900\pi$
$182$		0			0
$183$	−4.59567	−	1.95395i	−0.339721	−	0.144440i
$184$		0			0
$185$	4.27853	−	1.55726i	0.314564	−	0.114492i
$186$		0			0
$187$	−1.44770	−	8.21031i	−0.105866	−	0.600397i
$188$		0			0
$189$	11.1654	+	6.21498i	0.812167	+	0.452073i
$190$		0			0
$191$	4.68261	+	26.5564i	0.338822	+	1.92155i	0.385641	+	0.922649i	$0.373980\pi$
$191$	4.68261	+	26.5564i	0.338822	+	1.92155i	−0.0468192	+	0.998903i	$0.514908\pi$
$192$		0			0
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.311135	−	0.950366i	$-0.399291\pi$
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.849226	+	0.528029i	$0.177069\pi$
$194$		0			0
$195$	10.9904	−	8.27167i	0.787037	−	0.592347i
$196$		0			0
$197$	−1.25612	−	2.17567i	−0.0894951	−	0.155010i	0.817803	−	0.575499i	$-0.195192\pi$
$197$	−1.25612	−	2.17567i	−0.0894951	−	0.155010i	−0.907298	+	0.420489i	$0.861859\pi$
$198$		0			0
$199$	9.26942	−	16.0551i	0.657092	−	1.13812i	−0.324273	−	0.945964i	$-0.605120\pi$
$199$	9.26942	−	16.0551i	0.657092	−	1.13812i	0.981365	−	0.192153i	$-0.0615470\pi$
$200$		0			0
$201$	−3.93992	+	17.0198i	−0.277901	+	1.20049i
$202$		0			0
$203$	0.218810	−	1.24093i	0.0153574	−	0.0870964i
$204$		0			0
$205$	10.9032	−	9.14885i	0.761510	−	0.638983i
$206$		0			0
$207$	2.45169	−	0.608202i	0.170404	−	0.0422730i
$208$		0			0
$209$	0.293649	+	0.106880i	0.0203121	+	0.00739301i
$210$		0			0
$211$	2.82761	+	2.37264i	0.194661	+	0.163340i	0.734908	−	0.678166i	$-0.237225\pi$
$211$	2.82761	+	2.37264i	0.194661	+	0.163340i	−0.540248	+	0.841506i	$0.681670\pi$
$212$		0			0
$213$	0.0844829	−	0.129924i	0.00578867	−	0.00890226i
$214$		0			0
$215$	7.55427			0.515197
$216$		0			0
$217$	−2.01659			−0.136895
$218$		0			0
$219$	4.17935	+	8.21441i	0.282414	+	0.555079i
$220$		0			0
$221$	23.1638	+	19.4367i	1.55816	+	1.30746i
$222$		0			0
$223$	−19.9601	−	7.26487i	−1.33662	−	0.486491i	−0.427876	−	0.903837i	$-0.640738\pi$
$223$	−19.9601	−	7.26487i	−1.33662	−	0.486491i	−0.908748	+	0.417346i	$0.862960\pi$
$224$		0			0
$225$	−0.401646	−	5.84289i	−0.0267764	−	0.389526i
$226$		0			0
$227$	10.9851	−	9.21761i	0.729108	−	0.611794i	−0.200781	−	0.979636i	$-0.564348\pi$
$227$	10.9851	−	9.21761i	0.729108	−	0.611794i	0.929888	+	0.367842i	$0.119903\pi$
$228$		0			0
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	−0.720403	−	0.693556i	$-0.756043\pi$
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	0.914167	−	0.405337i	$-0.132846\pi$
$230$		0			0
$231$	5.10985	−	1.55894i	0.336204	−	0.102571i
$232$		0			0
$233$	−2.79972	+	4.84926i	−0.183416	+	0.317686i	−0.943042	−	0.332675i	$-0.892049\pi$
$233$	−2.79972	+	4.84926i	−0.183416	+	0.317686i	0.759626	+	0.650361i	$0.225382\pi$
$234$		0			0
$235$	4.62837	+	8.01658i	0.301922	+	0.522944i
$236$		0			0
$237$	−1.00348	−	8.21279i	−0.0651833	−	0.533478i
$238$		0			0
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	−0.497302	−	0.867577i	$-0.665676\pi$
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	0.176712	+	0.984263i	$0.443454\pi$
$240$		0			0
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	−0.993247	−	0.116017i	$-0.962987\pi$
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	0.893667	−	0.448730i	$-0.148124\pi$
$242$		0			0
$243$	15.0453	+	4.07900i	0.965158	+	0.261668i
$244$		0			0
$245$	0.288634	+	1.63692i	0.0184401	+	0.104579i
$246$		0			0
$247$	−1.06507	+	0.387652i	−0.0677685	+	0.0246657i
$248$		0			0
$249$	−1.68910	−	13.8240i	−0.107042	−	0.876062i
$250$		0			0
$251$	−3.89010	−	6.73786i	−0.245541	−	0.425290i	0.716742	−	0.697338i	$-0.245632\pi$
$251$	−3.89010	−	6.73786i	−0.245541	−	0.425290i	−0.962284	+	0.272048i	$0.912299\pi$
$252$		0			0
$253$	0.528024	−	0.914565i	0.0331966	−	0.0574982i
$254$		0			0
$255$	−19.2249	+	5.86523i	−1.20391	+	0.367295i
$256$		0			0
$257$	−3.54877	+	20.1261i	−0.221366	+	1.25543i	0.648145	+	0.761517i	$0.275545\pi$
$257$	−3.54877	+	20.1261i	−0.221366	+	1.25543i	−0.869511	+	0.493913i	$0.835566\pi$
$258$		0			0
$259$	−4.91331	+	4.12275i	−0.305298	+	0.256175i
$260$		0			0
$261$	−0.105416	−	1.53353i	−0.00652510	−	0.0949231i
$262$		0			0
$263$	10.5996	+	3.85792i	0.653596	+	0.237890i	0.647469	−	0.762092i	$-0.275827\pi$
$263$	10.5996	+	3.85792i	0.653596	+	0.237890i	0.00612723	+	0.999981i	$0.498050\pi$
$264$		0			0
$265$	14.0209	+	11.7650i	0.861299	+	0.722716i
$266$		0			0
$267$	−5.26530	−	10.3488i	−0.322231	−	0.633338i
$268$		0			0
$269$	−0.307761			−0.0187645			−0.00938226	−	0.999956i	$-0.502987\pi$
$269$	−0.307761			−0.0187645			−0.00938226	+	0.999956i	$0.502987\pi$
$270$		0			0
$271$	2.22251			0.135008			0.0675040	−	0.997719i	$-0.478496\pi$
$271$	2.22251			0.135008			0.0675040	+	0.997719i	$0.478496\pi$
$272$		0			0
$273$	−10.5629	+	16.2445i	−0.639298	+	0.983162i
$274$		0			0
$275$	−1.87567	−	1.57387i	−0.113107	−	0.0949080i
$276$		0			0
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.902564	−	0.430556i	$-0.141683\pi$
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.414648	+	0.909982i	$0.363905\pi$
$278$		0			0
$279$	−2.38764	+	0.592313i	−0.142944	+	0.0354608i
$280$		0			0
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	−0.462586	−	0.886574i	$-0.653078\pi$
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	0.792778	+	0.609511i	$0.208634\pi$
$282$		0			0
$283$	−1.23643	+	7.01212i	−0.0734979	+	0.416827i	0.925753	+	0.378129i	$0.123432\pi$
$283$	−1.23643	+	7.01212i	−0.0734979	+	0.416827i	−0.999251	+	0.0386985i	$0.987679\pi$
$284$		0			0
$285$	0.169911	−	0.733987i	0.0100646	−	0.0434776i
$286$		0			0
$287$	−10.0249	+	17.3636i	−0.591751	+	1.02494i
$288$		0			0
$289$	−13.5924	−	23.5428i	−0.799555	−	1.38487i
$290$		0			0
$291$	7.59837	−	5.71875i	0.445424	−	0.335239i
$292$		0			0
$293$	−0.519166	+	0.188961i	−0.0303300	+	0.0110392i	−0.357141	−	0.934051i	$-0.616248\pi$
$293$	−0.519166	+	0.188961i	−0.0303300	+	0.0110392i	0.326811	+	0.945090i	$0.394026\pi$
$294$		0			0
$295$	−0.911339	−	5.16846i	−0.0530602	−	0.300919i
$296$		0			0
$297$	5.59216	−	3.34665i	0.324490	−	0.194192i
$298$		0			0
$299$	0.665122	+	3.77210i	0.0384650	+	0.218146i
$300$		0			0
$301$	−9.99975	+	3.63961i	−0.576376	+	0.209784i
$302$		0			0
$303$	−7.97852	−	3.39224i	−0.458354	−	0.194879i
$304$		0			0
$305$	2.51670	+	4.35906i	0.144106	+	0.249599i
$306$		0			0
$307$	3.36438	−	5.82728i	0.192015	−	0.332580i	−0.753903	−	0.656986i	$-0.771831\pi$
$307$	3.36438	−	5.82728i	0.192015	−	0.332580i	0.945918	+	0.324406i	$0.105164\pi$
$308$		0			0
$309$	−14.7104	−	13.7339i	−0.836844	−	0.781293i
$310$		0			0
$311$	−2.67825	+	15.1891i	−0.151870	+	0.861297i	0.809722	+	0.586814i	$0.199618\pi$
$311$	−2.67825	+	15.1891i	−0.151870	+	0.861297i	−0.961592	+	0.274483i	$0.911493\pi$
$312$		0			0
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.989649	−	0.143509i	$-0.954162\pi$
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.0305223	+	0.999534i	$0.509717\pi$
$314$		0			0
$315$	−5.22486	−	11.7726i	−0.294388	−	0.663311i
$316$		0			0
$317$	−6.81469	−	2.48034i	−0.382751	−	0.139310i	0.143477	−	0.989654i	$-0.454172\pi$
$317$	−6.81469	−	2.48034i	−0.382751	−	0.139310i	−0.526228	+	0.850344i	$0.676394\pi$
$318$		0			0
$319$	−0.492289	−	0.413079i	−0.0275629	−	0.0231280i
$320$		0			0
$321$	−33.6552	−	1.78371i	−1.87845	−	0.0995571i
$322$		0			0
$323$	1.65618			0.0921525
$324$		0			0
$325$	8.88074			0.492615
$326$		0			0
$327$	10.9228	+	0.578905i	0.604034	+	0.0320135i
$328$		0			0
$329$	−9.98903	−	8.38179i	−0.550713	−	0.462103i
$330$		0			0
$331$	27.2835	+	9.93037i	1.49964	+	0.545823i	0.955966	−	0.293477i	$-0.0948124\pi$
$331$	27.2835	+	9.93037i	1.49964	+	0.545823i	0.543669	+	0.839300i	$0.317035\pi$
$332$		0			0
$333$	−4.60641	+	6.32447i	−0.252430	+	0.346579i
$334$		0			0
$335$	13.4889	−	11.3185i	0.736976	−	0.618396i
$336$		0			0
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	−0.989799	−	0.142471i	$-0.954495\pi$
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	0.978835	+	0.204652i	$0.0656063\pi$
$338$		0			0
$339$	−8.75561	−	8.17441i	−0.475540	−	0.443973i
$340$		0			0
$341$	−0.514230	+	0.890672i	−0.0278471	+	0.0482326i
$342$		0			0
$343$	−9.77810	−	16.9362i	−0.527968	−	0.914467i
$344$		0			0
$345$	−2.34305	−	0.996198i	−0.126146	−	0.0536335i
$346$		0			0
$347$	5.53452	−	2.01440i	0.297108	−	0.108139i	−0.189165	−	0.981945i	$-0.560578\pi$
$347$	5.53452	−	2.01440i	0.297108	−	0.108139i	0.486273	+	0.873807i	$0.338356\pi$
$348$		0			0
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	−0.707547	−	0.706666i	$-0.750198\pi$
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	0.423183	−	0.906044i	$-0.360913\pi$
$350$		0			0
$351$	−7.73516	+	22.3360i	−0.412872	+	1.19221i
$352$		0			0
$353$	6.41826	+	36.3997i	0.341609	+	1.93736i	0.348294	+	0.937385i	$0.386761\pi$
$353$	6.41826	+	36.3997i	0.341609	+	1.93736i	−0.00668455	+	0.999978i	$0.502128\pi$
$354$		0			0
$355$	−0.146785	+	0.0534254i	−0.00779054	+	0.00283553i
$356$		0			0
$357$	22.6225	−	17.0264i	1.19731	−	0.901131i
$358$		0			0
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	−0.969830	−	0.243783i	$-0.921611\pi$
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	0.273792	−	0.961789i	$-0.411722\pi$
$360$		0			0
$361$	9.46896	−	16.4007i	0.498366	−	0.863196i
$362$		0			0
$363$	−3.68238	+	15.9073i	−0.193275	+	0.834917i
$364$		0			0
$365$	1.61312	−	9.14845i	0.0844345	−	0.478852i
$366$		0			0
$367$	8.66636	−	7.27194i	0.452380	−	0.379592i	−0.387938	−	0.921685i	$-0.626813\pi$
$367$	8.66636	−	7.27194i	0.452380	−	0.379592i	0.840318	+	0.542093i	$0.182368\pi$
$368$		0			0
$369$	−6.76941	+	23.5030i	−0.352401	+	1.22352i
$370$		0			0
$371$	−24.2281	−	8.81831i	−1.25786	−	0.457824i
$372$		0			0
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	0.751289	−	0.659974i	$-0.229433\pi$
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	−0.519487	+	0.854478i	$0.673877\pi$
$374$		0			0
$375$	−11.4599	+	17.6238i	−0.591784	+	0.910092i
$376$		0			0
$377$	2.33085			0.120045
$378$		0			0
$379$	−24.3265			−1.24957			−0.624783	−	0.780798i	$-0.714813\pi$
$379$	−24.3265			−1.24957			−0.624783	+	0.780798i	$0.714813\pi$
$380$		0			0
$381$	9.44334	+	18.5607i	0.483797	+	0.950892i
$382$		0			0
$383$	2.92326	+	2.45291i	0.149372	+	0.125338i	0.714411	−	0.699726i	$-0.246695\pi$
$383$	2.92326	+	2.45291i	0.149372	+	0.125338i	−0.565039	+	0.825064i	$0.691139\pi$
$384$		0			0
$385$	−5.06000	−	1.84169i	−0.257881	−	0.0938612i
$386$		0			0
$387$	−10.7707	+	7.24642i	−0.547503	+	0.368356i
$388$		0			0
$389$	8.30534	−	6.96901i	0.421097	−	0.353343i	−0.407483	−	0.913213i	$-0.633593\pi$
$389$	8.30534	−	6.96901i	0.421097	−	0.353343i	0.828580	+	0.559870i	$0.189149\pi$
$390$		0			0
$391$	0.971896	−	5.51189i	0.0491509	−	0.278748i
$392$		0			0
$393$	−23.3338	+	7.11881i	−1.17704	+	0.359096i
$394$		0			0
$395$	−4.16974	+	7.22221i	−0.209802	+	0.363389i
$396$		0			0
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	0.967228	−	0.253910i	$-0.0817168\pi$
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	−0.703507	+	0.710689i	$0.748383\pi$
$398$		0			0
$399$	0.128717	+	1.05346i	0.00644392	+	0.0527388i
$400$		0			0
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.656320	−	0.754482i	$-0.727888\pi$
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.0177987	+	0.999842i	$0.505666\pi$
$402$		0			0
$403$	−0.647746	−	3.67355i	−0.0322665	−	0.182993i
$404$		0			0
$405$	−9.64407	−	12.4041i	−0.479218	−	0.616364i
$406$		0			0
$407$	0.568014	+	3.22137i	0.0281554	+	0.159677i
$408$		0			0
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.718408	−	0.695622i	$-0.755129\pi$
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.103195	+	0.994661i	$0.532907\pi$
$410$		0			0
$411$	0.474366	+	3.88234i	0.0233988	+	0.191502i
$412$		0			0
$413$	3.69650	+	6.40252i	0.181893	+	0.315047i
$414$		0			0
$415$	−7.01864	+	12.1566i	−0.344532	+	0.596746i
$416$		0			0
$417$	−13.2121	+	4.03081i	−0.646998	+	0.197390i
$418$		0			0
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	0.921243	+	0.388988i	$0.127175\pi$
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	−0.998727	+	0.0504461i	$0.983936\pi$
$420$		0			0
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	−0.0675243	−	0.997718i	$-0.521510\pi$
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	0.970835	+	0.239750i	$0.0770656\pi$
$422$		0			0
$423$	−14.2889	−	6.99004i	−0.694749	−	0.339867i
$424$		0			0
$425$	−12.1942	−	4.43832i	−0.591505	−	0.215290i
$426$		0			0
$427$	−5.43159	−	4.55764i	−0.262853	−	0.220560i
$428$		0			0
$429$	4.48120	+	8.80769i	0.216354	+	0.425239i
$430$		0			0
$431$	29.5332			1.42256			0.711282	−	0.702907i	$-0.248115\pi$
$431$	29.5332			1.42256			0.711282	+	0.702907i	$0.248115\pi$
$432$		0			0
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$		0			0
$435$	−0.844598	+	1.29889i	−0.0404954	+	0.0622769i
$436$		0			0
$437$	0.160708	+	0.134850i	0.00768772	+	0.00645076i
$438$		0			0
$439$	−5.96599	−	2.17144i	−0.284741	−	0.103637i	0.195701	−	0.980664i	$-0.437302\pi$
$439$	−5.96599	−	2.17144i	−0.284741	−	0.103637i	−0.480442	+	0.877026i	$0.659524\pi$
$440$		0			0
$441$	−1.98174	−	2.05700i	−0.0943685	−	0.0979526i
$442$		0			0
$443$	−11.7618	+	9.86931i	−0.558819	+	0.468905i	−0.877914	−	0.478818i	$-0.841066\pi$
$443$	−11.7618	+	9.86931i	−0.558819	+	0.468905i	0.319095	+	0.947723i	$0.396621\pi$
$444$		0			0
$445$	−2.03227	+	11.5256i	−0.0963387	+	0.546364i
$446$		0			0
$447$	−0.0417726	+	0.180451i	−0.00197577	+	0.00853503i
$448$		0			0
$449$	16.0199	−	27.7473i	0.756027	−	1.30948i	−0.188836	−	0.982009i	$-0.560471\pi$
$449$	16.0199	−	27.7473i	0.756027	−	1.30948i	0.944862	−	0.327468i	$-0.106195\pi$
$450$		0			0
$451$	5.11268	+	8.85543i	0.240747	+	0.416986i
$452$		0			0
$453$	28.0368	−	21.1013i	1.31729	−	0.991428i
$454$		0			0
$455$	18.3526	−	6.67980i	0.860384	−	0.313154i
$456$		0			0
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	0.958143	+	0.286291i	$0.0924225\pi$
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	−0.802442	+	0.596730i	$0.796466\pi$
$458$		0			0
$459$	21.7840	−	26.8039i	1.01679	−	1.25110i
$460$		0			0
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	0.956394	−	0.292080i	$-0.0943474\pi$
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	−0.998614	+	0.0526405i	$0.983236\pi$
$462$		0			0
$463$	1.59502	−	0.580541i	0.0741271	−	0.0269800i	−0.304690	−	0.952451i	$-0.598553\pi$
$463$	1.59502	−	0.580541i	0.0741271	−	0.0269800i	0.378818	+	0.925471i	$0.376331\pi$
$464$		0			0
$465$	2.28184	+	0.970173i	0.105818	+	0.0449907i
$466$		0			0
$467$	9.84136	+	17.0457i	0.455404	+	0.788783i	0.998711	−	0.0507511i	$-0.0161615\pi$
$467$	9.84136	+	17.0457i	0.455404	+	0.788783i	−0.543307	+	0.839534i	$0.682828\pi$
$468$		0			0
$469$	−12.4023	+	21.4814i	−0.572685	+	0.991920i
$470$		0			0
$471$	−26.2702	−	24.5264i	−1.21047	−	1.13012i
$472$		0			0
$473$	−0.942416	+	5.34471i	−0.0433324	+	0.245750i
$474$		0			0
$475$	0.372611	−	0.312658i	0.0170966	−	0.0143457i
$476$		0			0
$477$	−31.2761	−	3.32458i	−1.43204	−	0.152222i
$478$		0			0
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.373585	−	0.927596i	$-0.621872\pi$
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.882430	+	0.470444i	$0.844094\pi$
$480$		0			0
$481$	−9.08847	−	7.62613i	−0.414398	−	0.347722i
$482$		0			0
$483$	3.58151	+	0.189818i	0.162964	+	0.00863704i
$484$		0			0
$485$	−9.58538			−0.435250
$486$		0			0
$487$	20.5056			0.929199			0.464600	−	0.885521i	$-0.346198\pi$
$487$	20.5056			0.929199			0.464600	+	0.885521i	$0.346198\pi$
$488$		0			0
$489$	34.8252	+	1.84572i	1.57485	+	0.0834664i
$490$		0			0
$491$	−13.4265	−	11.2661i	−0.605927	−	0.508433i	0.287417	−	0.957805i	$-0.407203\pi$
$491$	−13.4265	−	11.2661i	−0.605927	−	0.508433i	−0.893345	+	0.449372i	$0.851648\pi$
$492$		0			0
$493$	−3.20050	−	1.16489i	−0.144143	−	0.0524638i
$494$		0			0
$495$	−6.53197	−	0.694333i	−0.293590	−	0.0312080i
$496$		0			0
$497$	0.168562	−	0.141441i	0.00756106	−	0.00634448i
$498$		0			0
$499$	3.31772	−	18.8157i	0.148522	−	0.842307i	−0.815950	−	0.578122i	$-0.803786\pi$
$499$	3.31772	−	18.8157i	0.148522	−	0.842307i	0.964472	−	0.264185i	$-0.0851031\pi$
$500$		0			0
$501$	25.1469	+	23.4777i	1.12348	+	1.04890i
$502$		0			0
$503$	−5.48381	+	9.49824i	−0.244511	+	0.423506i	−0.961994	−	0.273070i	$-0.911961\pi$
$503$	−5.48381	+	9.49824i	−0.244511	+	0.423506i	0.717483	+	0.696576i	$0.245294\pi$
$504$		0			0
$505$	4.36924	+	7.56774i	0.194429	+	0.336760i
$506$		0			0
$507$	−12.2634	−	5.21405i	−0.544637	−	0.231564i
$508$		0			0
$509$	18.6993	−	6.80598i	0.828831	−	0.301670i	0.107452	−	0.994210i	$-0.465731\pi$
$509$	18.6993	−	6.80598i	0.828831	−	0.301670i	0.721379	+	0.692540i	$0.243509\pi$
$510$		0			0
$511$	2.27236	+	12.8872i	0.100523	+	0.570096i
$512$		0			0
$513$	0.461822	+	1.20948i	0.0203899	+	0.0534000i
$514$		0			0
$515$	3.52238	+	19.9764i	0.155215	+	0.880266i
$516$		0			0
$517$	−6.24920	+	2.27452i	−0.274839	+	0.100033i
$518$		0			0
$519$	26.1903	−	19.7116i	1.14963	−	0.865243i
$520$		0			0
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	−0.937973	−	0.346708i	$-0.887300\pi$
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	0.168729	−	0.985662i	$-0.446034\pi$
$522$		0			0
$523$	−7.12269	+	12.3369i	−0.311453	+	0.539453i	−0.978677	−	0.205404i	$-0.934149\pi$
$523$	−7.12269	+	12.3369i	−0.311453	+	0.539453i	0.667224	+	0.744857i	$0.267482\pi$
$524$		0			0
$525$	1.87538	−	8.10136i	0.0818484	−	0.353572i
$526$		0			0
$527$	−0.946505	+	5.36789i	−0.0412304	+	0.233829i
$528$		0			0
$529$	−17.0759	+	14.3284i	−0.742431	+	0.622974i
$530$		0			0
$531$	6.25719	+	6.49483i	0.271539	+	0.281852i
$532$		0			0
$533$	−34.8507	−	12.6846i	−1.50955	−	0.549433i
$534$		0			0
$535$	26.0223	+	21.8353i	1.12504	+	0.944023i
$536$		0			0
$537$	10.3047	−	15.8473i	0.444679	−	0.683862i
$538$		0			0
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$		0			0
$543$	14.0967	+	27.7067i	0.604946	+	1.18901i
$544$		0			0
$545$	−8.44557	−	7.08667i	−0.361768	−	0.303560i
$546$		0			0
$547$	−15.3216	−	5.57661i	−0.655105	−	0.238439i	−0.00698326	−	0.999976i	$-0.502223\pi$
$547$	−15.3216	−	5.57661i	−0.655105	−	0.238439i	−0.648121	+	0.761537i	$0.724445\pi$
$548$		0			0
$549$	−7.76965	−	3.80087i	−0.331601	−	0.162217i
$550$		0			0
$551$	0.0977958	−	0.0820605i	0.00416624	−	0.00349589i
$552$		0			0
$553$	2.03995	−	11.5692i	0.0867476	−	0.491970i
$554$		0			0
$555$	7.54300	−	2.30126i	0.320183	−	0.0976831i
$556$		0			0
$557$	−15.4486	+	26.7577i	−0.654577	+	1.13376i	0.327422	+	0.944878i	$0.393820\pi$
$557$	−15.4486	+	26.7577i	−0.654577	+	1.13376i	−0.982000	+	0.188883i	$0.939513\pi$
$558$		0			0
$559$	−9.84215	−	17.0471i	−0.416279	−	0.721016i
$560$		0			0
$561$	−1.75134	−	14.3335i	−0.0739417	−	0.605159i
$562$		0			0
$563$	25.1612	−	9.15791i	1.06042	−	0.385960i	0.247832	−	0.968803i	$-0.420282\pi$
$563$	25.1612	−	9.15791i	1.06042	−	0.385960i	0.812585	+	0.582843i	$0.198060\pi$
$564$		0			0
$565$	2.09652	+	11.8900i	0.0882013	+	0.500214i
$566$		0			0
$567$	18.7423	+	11.7731i	0.787102	+	0.494423i
$568$		0			0
$569$	3.30985	+	18.7711i	0.138756	+	0.786924i	0.972170	+	0.234275i	$0.0752717\pi$
$569$	3.30985	+	18.7711i	0.138756	+	0.786924i	−0.833414	+	0.552649i	$0.813617\pi$
$570$		0			0
$571$	−17.6420	+	6.42116i	−0.738294	+	0.268717i	−0.683671	−	0.729790i	$-0.739618\pi$
$571$	−17.6420	+	6.42116i	−0.738294	+	0.268717i	−0.0546227	+	0.998507i	$0.517396\pi$
$572$		0			0
$573$	5.66474	+	46.3618i	0.236648	+	1.93679i
$574$		0			0
$575$	−0.821889	−	1.42355i	−0.0342751	−	0.0593663i
$576$		0			0
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	−0.811006	−	0.585038i	$-0.801080\pi$
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	0.912161	+	0.409833i	$0.134413\pi$
$578$		0			0
$579$	28.4198	−	8.67047i	1.18109	−	0.360332i
$580$		0			0
$581$	3.43371	−	19.4736i	0.142454	−	0.807899i
$582$		0			0
$583$	−10.0730	+	8.45221i	−0.417179	+	0.350055i
$584$		0			0
$585$	19.7675	−	13.2994i	0.817284	−	0.549862i
$586$		0			0
$587$	−30.8194	−	11.2174i	−1.27205	−	0.462990i	−0.384257	−	0.923226i	$-0.625542\pi$
$587$	−30.8194	−	11.2174i	−1.27205	−	0.462990i	−0.887796	+	0.460236i	$0.847765\pi$
$588$		0			0
$589$	−0.156510	−	0.131327i	−0.00644887	−	0.00541125i
$590$		0			0
$591$	−1.97318	−	3.87824i	−0.0811657	−	0.159529i
$592$		0			0
$593$	17.3446			0.712258			0.356129	−	0.934437i	$-0.384096\pi$
$593$	17.3446			0.712258			0.356129	+	0.934437i	$0.384096\pi$
$594$		0			0
$595$	−28.5384			−1.16996
$596$		0			0
$597$	17.5044	−	26.9196i	0.716406	−	1.10174i
$598$		0			0
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	0.175194	−	0.984534i	$-0.443945\pi$
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	−0.939155	+	0.343495i	$0.888389\pi$
$600$		0			0
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	0.186748	−	0.982408i	$-0.440205\pi$
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	−0.488422	+	0.872607i	$0.662427\pi$
$602$		0			0
$603$	−8.37478	+	29.0768i	−0.341047	+	1.18410i
$604$		0			0
$605$	12.6071	−	10.5786i	0.512553	−	0.430083i
$606$		0			0
$607$	1.77772	−	10.0819i	0.0721553	−	0.409213i	−0.927241	−	0.374466i	$-0.877826\pi$
$607$	1.77772	−	10.0819i	0.0721553	−	0.409213i	0.999396	−	0.0347476i	$-0.0110627\pi$
$608$		0			0
$609$	0.492214	−	2.12629i	0.0199455	−	0.0861615i
$610$		0			0
$611$	12.0602	−	20.8889i	0.487905	−	0.845076i
$612$		0			0
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	0.842574	−	0.538580i	$-0.181039\pi$
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	−0.887711	+	0.460401i	$0.847706\pi$
$614$		0			0
$615$	19.6970	−	14.8246i	0.794262	−	0.597784i
$616$		0			0
$617$	−31.9267	+	11.6204i	−1.28532	+	0.467818i	−0.892188	−	0.451664i	$-0.850831\pi$
$617$	−31.9267	+	11.6204i	−1.28532	+	0.467818i	−0.393132	+	0.919482i	$0.628609\pi$
$618$		0			0
$619$	5.01079	+	28.4176i	0.201401	+	1.14220i	0.903004	+	0.429632i	$0.141357\pi$
$619$	5.01079	+	28.4176i	0.201401	+	1.14220i	−0.701604	+	0.712567i	$0.747532\pi$
$620$		0			0
$621$	4.29625	−	0.827216i	0.172403	−	0.0331950i
$622$		0			0
$623$	−2.86280	−	16.2358i	−0.114696	−	0.650472i
$624$		0			0
$625$	10.7385	−	3.90849i	0.429540	−	0.156340i
$626$		0			0
$627$	0.498105	+	0.211780i	0.0198924	+	0.00845768i
$628$		0			0
$629$	8.66811	+	15.0136i	0.345620	+	0.598632i
$630$		0			0
$631$	−1.57039	+	2.71999i	−0.0625162	+	0.108281i	−0.895590	−	0.444881i	$-0.853246\pi$
$631$	−1.57039	+	2.71999i	−0.0625162	+	0.108281i	0.833073	+	0.553163i	$0.186579\pi$
$632$		0			0
$633$	4.67320	+	4.36299i	0.185743	+	0.173413i
$634$		0			0
$635$	3.64488	−	20.6711i	0.144643	−	0.820309i
$636$		0			0
$637$	3.31786	−	2.78402i	0.131458	−	0.110307i
$638$		0			0
$639$	0.158034	−	0.216976i	0.00625171	−	0.00858342i
$640$		0			0
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.856595	−	0.515989i	$-0.172576\pi$
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.324518	+	0.945879i	$0.394798\pi$
$642$		0			0
$643$	9.84142	+	8.25794i	0.388108	+	0.325661i	0.815876	−	0.578228i	$-0.196255\pi$
$643$	9.84142	+	8.25794i	0.388108	+	0.325661i	−0.427768	+	0.903889i	$0.640700\pi$
$644$		0			0
$645$	13.0660	+	0.692495i	0.514475	+	0.0272669i
$646$		0			0
$647$	−28.2444			−1.11040			−0.555200	−	0.831717i	$-0.687358\pi$
$647$	−28.2444			−1.11040			−0.555200	+	0.831717i	$0.687358\pi$
$648$		0			0
$649$	3.77042			0.148002
$650$		0			0
$651$	−3.48794	−	0.184859i	−0.136703	−	0.00724521i
$652$		0			0
$653$	19.9099	+	16.7064i	0.779134	+	0.653771i	0.943030	−	0.332707i	$-0.107962\pi$
$653$	19.9099	+	16.7064i	0.779134	+	0.653771i	−0.163897	+	0.986477i	$0.552406\pi$
$654$		0			0
$655$	23.1062	+	8.40995i	0.902832	+	0.328604i
$656$		0			0
$657$	6.47569	+	14.5910i	0.252641	+	0.569248i
$658$		0			0
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.470131	−	0.882597i	$-0.344207\pi$
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.950826	−	0.309727i	$-0.100238\pi$
$660$		0			0
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	−0.987625	−	0.156836i	$-0.949871\pi$
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	0.981705	+	0.190410i	$0.0609818\pi$
$662$		0			0
$663$	38.2829	+	35.7416i	1.48678	+	1.38809i
$664$		0			0
$665$	0.534854	−	0.926394i	0.0207407	−	0.0359240i
$666$		0			0
$667$	−0.215714	−	0.373627i	−0.00835246	−	0.0144669i
$668$		0			0
$669$	−33.8574	−	14.3952i	−1.30900	−	0.556551i
$670$		0			0
$671$	−3.39803	+	1.23678i	−0.131180	+	0.0477455i
$672$		0			0
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	0.808742	+	0.588164i	$0.200149\pi$
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	−0.558805	+	0.829299i	$0.688740\pi$
$674$		0			0
$675$	−0.159082	−	10.1428i	−0.00612306	−	0.390397i
$676$		0			0
$677$	−2.38231	−	13.5107i	−0.0915596	−	0.519260i	−0.995747	−	0.0921251i	$-0.970634\pi$
$677$	−2.38231	−	13.5107i	−0.0915596	−	0.519260i	0.904188	−	0.427135i	$-0.140477\pi$
$678$		0			0
$679$	12.6884	−	4.61819i	0.486935	−	0.177230i
$680$		0			0
$681$	19.8451	−	14.9360i	0.760465	−	0.572348i
$682$		0			0
$683$	24.9943	+	43.2914i	0.956381	+	1.65650i	0.731175	+	0.682190i	$0.238972\pi$
$683$	24.9943	+	43.2914i	0.956381	+	1.65650i	0.225206	+	0.974311i	$0.427694\pi$
$684$		0			0
$685$	1.97112	−	3.41407i	0.0753125	−	0.130445i
$686$		0			0
$687$	6.59598	−	28.4936i	0.251652	−	1.08710i
$688$		0			0
$689$	8.28172	−	46.9680i	0.315509	−	1.78934i
$690$		0			0
$691$	−18.2434	+	15.3080i	−0.694011	+	0.582345i	−0.920063	−	0.391771i	$-0.871863\pi$
$691$	−18.2434	+	15.3080i	−0.694011	+	0.582345i	0.226052	+	0.974115i	$0.427418\pi$
$692$		0			0
$693$	8.98103	−	2.22797i	0.341161	−	0.0846335i
$694$		0			0
$695$	13.0832	+	4.76188i	0.496273	+	0.180629i
$696$		0			0
$697$	41.5144	+	34.8347i	1.57247	+	1.31946i
$698$		0			0
$699$	−5.28700	+	8.13075i	−0.199973	+	0.307533i
$700$		0			0
$701$	34.4493			1.30113			0.650565	−	0.759450i	$-0.274532\pi$
$701$	34.4493			1.30113			0.650565	+	0.759450i	$0.274532\pi$
$702$		0			0
$703$	−0.649815			−0.0245082
$704$		0			0
$705$	7.27047	+	14.2899i	0.273822	+	0.538190i
$706$		0			0
$707$	−9.42975	−	7.91250i	−0.354642	−	0.297580i
$708$		0			0
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	0.0532520	−	0.998581i	$-0.483041\pi$
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	−0.601082	+	0.799187i	$0.705264\pi$
$710$		0			0
$711$	−0.982789	−	14.2970i	−0.0368575	−	0.536180i
$712$		0			0
$713$	−0.528911	+	0.443809i	−0.0198079	+	0.0166208i
$714$		0			0
$715$	1.72962	−	9.80918i	0.0646842	−	0.366843i
$716$		0			0
$717$	−8.73772	+	2.66575i	−0.326316	+	0.0995543i
$718$		0			0
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	−0.731485	−	0.681858i	$-0.761172\pi$
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	0.956249	+	0.292555i	$0.0945056\pi$
$720$		0			0
$721$	−14.2872	−	24.7461i	−0.532083	−	0.921594i
$722$		0			0
$723$	−1.87014	−	15.3057i	−0.0695512	−	0.569226i
$724$		0			0
$725$	−0.939963	+	0.342119i	−0.0349094	+	0.0127060i
$726$		0			0
$727$	5.49253	+	31.1497i	0.203707	+	1.15528i	0.899462	+	0.437000i	$0.143959\pi$
$727$	5.49253	+	31.1497i	0.203707	+	1.15528i	−0.695755	+	0.718279i	$0.744930\pi$
$728$		0			0
$729$	25.6488	+	8.43433i	0.949956	+	0.312383i
$730$		0			0
$731$	4.99469	+	28.3263i	0.184735	+	1.04769i
$732$		0			0
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.0100630	−	0.999949i	$-0.496797\pi$
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.650464	+	0.759537i	$0.274575\pi$
$734$		0			0
$735$	0.349172	+	2.85772i	0.0128794	+	0.105409i
$736$		0			0
$737$	6.32516	+	10.9555i	0.232990	+	0.403551i
$738$		0			0
$739$	8.30036	−	14.3767i	0.305334	−	0.528854i	−0.672002	−	0.740550i	$-0.734565\pi$
$739$	8.30036	−	14.3767i	0.305334	−	0.528854i	0.977336	+	0.211696i	$0.0678986\pi$
$740$		0			0
$741$	−1.87770	+	0.572858i	−0.0689789	+	0.0210445i
$742$		0			0
$743$	5.78310	−	32.7976i	0.212161	−	1.20323i	−0.673604	−	0.739093i	$-0.735255\pi$
$743$	5.78310	−	32.7976i	0.212161	−	1.20323i	0.885765	−	0.464134i	$-0.153634\pi$
$744$		0			0
$745$	0.143014	−	0.120003i	0.00523963	−	0.00439657i
$746$		0			0
$747$	−1.65426	−	24.0652i	−0.0605263	−	0.880499i
$748$		0			0
$749$	−44.9665	−	16.3665i	−1.64304	−	0.598017i
$750$		0			0
$751$	−21.2819	−	17.8577i	−0.776589	−	0.651636i	0.165798	−	0.986160i	$-0.446980\pi$
$751$	−21.2819	−	17.8577i	−0.776589	−	0.651636i	−0.942387	+	0.334524i	$0.891424\pi$
$752$		0			0
$753$	−6.11076	−	12.0106i	−0.222688	−	0.437689i
$754$		0			0
$755$	−35.3686			−1.28720
$756$		0			0
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$		0			0
$759$	0.997121	−	1.53345i	0.0361932	−	0.0556607i
$760$		0			0
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.998787	−	0.0492297i	$-0.984323\pi$
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.221919	−	0.975065i	$-0.571232\pi$
$762$		0			0
$763$	14.5939	+	5.31175i	0.528335	+	0.192298i
$764$		0			0
$765$	−33.7894	+	8.38230i	−1.22166	+	0.303063i
$766$		0			0
$767$	−10.4759	+	8.79032i	−0.378263	+	0.317400i
$768$		0			0
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	−0.970974	−	0.239186i	$-0.923119\pi$
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	0.994223	+	0.107331i	$0.0342305\pi$
$770$		0			0
$771$	−7.98298	+	34.4852i	−0.287500	+	1.24195i
$772$		0			0
$773$	4.48452	−	7.76741i	0.161297	−	0.279374i	−0.774037	−	0.633140i	$-0.781766\pi$
$773$	4.48452	−	7.76741i	0.161297	−	0.279374i	0.935334	+	0.353766i	$0.115099\pi$
$774$		0			0
$775$	0.800417	+	1.38636i	0.0287518	+	0.0497996i
$776$		0			0
$777$	−8.87610	+	6.68041i	−0.318428	+	0.239658i
$778$		0			0
$779$	−1.90882	+	0.694754i	−0.0683906	+	0.0248921i
$780$		0			0
$781$	−0.0194871	−	0.110517i	−0.000697302	−	0.00395459i
$782$		0			0
$783$	−0.0417527	−	2.66209i	−0.00149212	−	0.0951354i
$784$		0			0
$785$	6.29037	+	35.6745i	0.224513	+	1.27328i
$786$		0			0
$787$	41.2069	−	14.9981i	1.46887	−	0.534624i	0.521074	−	0.853512i	$-0.325532\pi$
$787$	41.2069	−	14.9981i	1.46887	−	0.534624i	0.947792	+	0.318888i	$0.103309\pi$
$788$		0			0
$789$	17.9796	+	7.64441i	0.640090	+	0.272148i
$790$		0			0
$791$	−8.50374	−	14.7289i	−0.302358	−	0.523699i
$792$		0			0
$793$	6.55782	−	11.3585i	0.232875	−	0.403351i
$794$		0			0
$795$	23.1724	+	21.6342i	0.821842	+	0.767287i
$796$		0			0
$797$	2.08656	−	11.8335i	0.0739097	−	0.419163i	−0.925294	−	0.379252i	$-0.876181\pi$
$797$	2.08656	−	11.8335i	0.0739097	−	0.419163i	0.999203	−	0.0399111i	$-0.0127075\pi$
$798$		0			0
$799$	−26.9996	+	22.6554i	−0.955178	+	0.801490i
$800$		0			0
$801$	−8.15832	−	18.3822i	−0.288260	−	0.649504i
$802$		0			0
$803$	6.27136	+	2.28259i	0.221311	+	0.0805508i
$804$		0			0
$805$	−2.76924	−	2.32366i	−0.0976027	−	0.0818984i
$806$		0			0
$807$	−0.532311	−	0.0282122i	−0.0187382	−	0.000993117i
$808$		0			0
$809$	−8.02937			−0.282298			−0.141149	−	0.989988i	$-0.545080\pi$
$809$	−8.02937			−0.282298			−0.141149	+	0.989988i	$0.545080\pi$
$810$		0			0
$811$	12.8345			0.450681			0.225341	−	0.974280i	$-0.427651\pi$
$811$	12.8345			0.450681			0.225341	+	0.974280i	$0.427651\pi$
$812$		0			0
$813$	3.84411	+	0.203736i	0.134819	+	0.00714534i
$814$		0			0
$815$	−26.9270	−	22.5944i	−0.943211	−	0.791448i
$816$		0			0
$817$	−1.01312	−	0.368744i	−0.0354444	−	0.0129007i
$818$		0			0
$819$	−19.7590	+	27.1286i	−0.690436	+	0.947949i
$820$		0			0
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	−0.946513	−	0.322667i	$-0.895421\pi$
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	0.153404	+	0.988163i	$0.450976\pi$
$822$		0			0
$823$	−8.60266	+	48.7881i	−0.299870	+	1.70065i	0.346852	+	0.937920i	$0.387251\pi$
$823$	−8.60266	+	48.7881i	−0.299870	+	1.70065i	−0.646722	+	0.762726i	$0.723861\pi$
$824$		0			0
$825$	−3.09992	−	2.89415i	−0.107925	−	0.100761i
$826$		0			0
$827$	20.4215	−	35.3711i	0.710126	−	1.22997i	−0.254683	−	0.967025i	$-0.581971\pi$
$827$	20.4215	−	35.3711i	0.710126	−	1.22997i	0.964809	−	0.262950i	$-0.0846955\pi$
$828$		0			0
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	0.936355	−	0.351056i	$-0.114177\pi$
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	−0.772201	+	0.635379i	$0.780844\pi$
$830$		0			0
$831$	37.1867	+	15.8107i	1.28999	+	0.548468i
$832$		0			0
$833$	−5.94714	+	2.16458i	−0.206056	+	0.0749983i
$834$		0			0
$835$	−6.02140	−	34.1491i	−0.208379	−	1.18178i
$836$		0			0
$837$	−4.18401	+	0.805605i	−0.144621	+	0.0278458i
$838$		0			0
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	0.999232	+	0.0391756i	$0.0124732\pi$
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	−0.925572	+	0.378571i	$0.876416\pi$
$840$		0			0
$841$	27.0044	−	9.82879i	0.931186	−	0.338924i
$842$		0			0
$843$	9.99925	−	7.52573i	0.344392	−	0.259200i
$844$		0			0
$845$	6.71575	+	11.6320i	0.231029	+	0.400154i
$846$		0			0
$847$	−11.5916	+	20.0772i	−0.398292	+	0.689862i
$848$		0			0
$849$	−2.78135	+	12.0150i	−0.0954556	+	0.412353i
$850$		0			0
$851$	−0.381330	+	2.16263i	−0.0130718	+	0.0741339i
$852$		0			0
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	−0.950507	−	0.310704i	$-0.899435\pi$
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	0.140930	+	0.990020i	$0.454991\pi$
$854$		0			0
$855$	0.361165	−	1.25395i	0.0123516	−	0.0428840i
$856$		0			0
$857$	−10.4738	−	3.81217i	−0.357780	−	0.130221i	0.156876	−	0.987618i	$-0.449858\pi$
$857$	−10.4738	−	3.81217i	−0.357780	−	0.130221i	−0.514655	+	0.857397i	$0.672080\pi$
$858$		0			0
$859$	−3.17807	−	2.66672i	−0.108434	−	0.0909872i	0.586958	−	0.809617i	$-0.300325\pi$
$859$	−3.17807	−	2.66672i	−0.108434	−	0.0909872i	−0.695393	+	0.718630i	$0.744770\pi$
$860$		0			0
$861$	−18.9310	+	29.1135i	−0.645167	+	0.992187i
$862$		0			0
$863$	47.2534			1.60852			0.804262	−	0.594275i	$-0.202561\pi$
$863$	47.2534			1.60852			0.804262	+	0.594275i	$0.202561\pi$
$864$		0			0
$865$	−33.0392			−1.12337
$866$		0			0
$867$	−21.3516	−	41.9662i	−0.725140	−	1.42525i
$868$		0			0
$869$	−4.58958	−	3.85112i	−0.155691	−	0.130640i
$870$		0			0
$871$	−43.1156	−	15.6928i	−1.46092	−	0.531731i
$872$		0			0
$873$	13.6665	−	9.19475i	0.462543	−	0.311195i
$874$		0			0
$875$	−22.8650	+	19.1860i	−0.772978	+	0.648606i
$876$		0			0
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	−0.689571	−	0.724218i	$-0.742201\pi$
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	0.895682	−	0.444695i	$-0.146688\pi$
$878$		0			0
$879$	−0.915284	+	0.279240i	−0.0308718	+	0.00941852i
$880$		0			0
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	−0.655618	−	0.755093i	$-0.727592\pi$
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	0.981739	+	0.190235i	$0.0609250\pi$
$882$		0			0
$883$	−6.89302	−	11.9391i	−0.231969	−	0.401781i	0.726419	−	0.687252i	$-0.241183\pi$
$883$	−6.89302	−	11.9391i	−0.231969	−	0.401781i	−0.958387	+	0.285471i	$0.907850\pi$
$884$		0			0
$885$	−1.10248	−	9.02303i	−0.0370596	−	0.303306i
$886$		0			0
$887$	−28.0192	+	10.1982i	−0.940794	+	0.342421i	−0.766479	−	0.642269i	$-0.777993\pi$
$887$	−28.0192	+	10.1982i	−0.940794	+	0.342421i	−0.174315	+	0.984690i	$0.555771\pi$
$888$		0			0
$889$	5.13445	+	29.1189i	0.172204	+	0.976617i
$890$		0			0
$891$	9.97912	−	5.27581i	0.334313	−	0.176746i
$892$		0			0
$893$	−0.229408	−	1.30104i	−0.00767685	−	0.0435376i
$894$		0			0
$895$	−17.9039	+	6.51649i	−0.598461	+	0.217822i
$896$		0			0
$897$	0.804626	+	6.58528i	0.0268657	+	0.219876i
$898$		0			0
$899$	0.210078	+	0.363866i	0.00700649	+	0.0121356i
$900$		0			0
$901$	−34.8448	+	60.3530i	−1.16085	+	2.01065i
$902$		0			0
$903$	−17.6294	+	5.37849i	−0.586671	+	0.178985i
$904$		0			0
$905$	5.44094	−	30.8571i	0.180863	−	1.02573i
$906$		0			0
$907$	4.77366	−	4.00558i	0.158507	−	0.133003i	−0.560085	−	0.828435i	$-0.689231\pi$
$907$	4.77366	−	4.00558i	0.158507	−	0.133003i	0.718592	+	0.695432i	$0.244787\pi$
$908$		0			0
$909$	−13.4889	−	6.59868i	−0.447397	−	0.218864i
$910$		0			0
$911$	−29.7314	−	10.8213i	−0.985044	−	0.358527i	−0.201245	−	0.979541i	$-0.564499\pi$
$911$	−29.7314	−	10.8213i	−0.985044	−	0.358527i	−0.783799	+	0.621014i	$0.786721\pi$
$912$		0			0
$913$	−7.72533	−	6.48232i	−0.255671	−	0.214534i
$914$		0			0
$915$	3.95336	+	7.77023i	0.130694	+	0.256876i
$916$		0			0
$917$	−34.6380			−1.14385
$918$		0			0
$919$	−36.0031			−1.18763			−0.593816	−	0.804601i	$-0.702379\pi$
$919$	−36.0031			−1.18763			−0.593816	+	0.804601i	$0.702379\pi$
$920$		0			0
$921$	6.35329	−	9.77058i	0.209348	−	0.321952i
$922$		0			0
$923$	0.311801	+	0.261632i	0.0102631	+	0.00861173i
$924$		0			0
$925$	4.78447	+	1.74141i	0.157313	+	0.0572571i
$926$		0			0
$927$	−24.1844	−	25.1029i	−0.794321	−	0.824489i
$928$		0			0
$929$	19.4941	−	16.3575i	0.639580	−	0.536672i	−0.264309	−	0.964438i	$-0.585144\pi$
$929$	19.4941	−	16.3575i	0.639580	−	0.536672i	0.903889	+	0.427767i	$0.140699\pi$
$930$		0			0
$931$	0.0411934	−	0.233619i	0.00135006	−	0.00765656i
$932$		0			0
$933$	−6.02475	+	26.0260i	−0.197241	+	0.852052i
$934$		0			0
$935$	−7.27728	+	12.6046i	−0.237993	+	0.412215i
$936$		0			0
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	0.536739	−	0.843749i	$-0.319656\pi$
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	−0.999077	+	0.0429549i	$0.986323\pi$
$938$		0			0
$939$	−32.6057	+	24.5400i	−1.06405	+	0.800833i
$940$		0			0
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	−0.465922	−	0.884826i	$-0.654277\pi$
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	0.211838	+	0.977305i	$0.432055\pi$
$942$		0			0
$943$	1.19204	+	6.76039i	0.0388181	+	0.220149i
$944$		0			0
$945$	−7.95786	−	20.8411i	−0.258869	−	0.677962i
$946$		0			0
$947$	7.71877	+	43.7753i	0.250826	+	1.42251i	0.806563	+	0.591148i	$0.201325\pi$
$947$	7.71877	+	43.7753i	0.250826	+	1.42251i	−0.555737	+	0.831358i	$0.687564\pi$
$948$		0			0
$949$	−22.7462	+	8.27895i	−0.738373	+	0.268746i
$950$		0			0
$951$	−11.5595	−	4.91476i	−0.374842	−	0.159372i
$952$		0			0
$953$	4.83574	+	8.37576i	0.156645	+	0.271317i	0.933657	−	0.358169i	$-0.116599\pi$
$953$	4.83574	+	8.37576i	0.156645	+	0.271317i	−0.777012	+	0.629486i	$0.783265\pi$
$954$		0			0
$955$	23.5385	−	40.7699i	0.761688	−	1.31928i
$956$		0			0
$957$	−0.813608	−	0.759599i	−0.0263002	−	0.0245544i
$958$		0			0
$959$	−0.964325	+	5.46896i	−0.0311397	+	0.176602i
$960$		0			0
$961$	−23.2323	+	19.4942i	−0.749429	+	0.628845i
$962$		0			0
$963$	−58.0473	−	6.17030i	−1.87055	−	0.198835i
$964$		0			0
$965$	−28.1425	−	10.2430i	−0.905940	−	0.329735i
$966$		0			0
$967$	25.3676	+	21.2860i	0.815768	+	0.684510i	0.951977	−	0.306170i	$-0.0990475\pi$
$967$	25.3676	+	21.2860i	0.815768	+	0.684510i	−0.136209	+	0.990680i	$0.543492\pi$
$968$		0			0
$969$	2.86457	+	0.151821i	0.0920234	+	0.00487720i
$970$		0			0
$971$	27.4309			0.880298			0.440149	−	0.897925i	$-0.354926\pi$
$971$	27.4309			0.880298			0.440149	+	0.897925i	$0.354926\pi$
$972$		0			0
$973$	−19.6127			−0.628755
$974$		0			0
$975$	15.3603	+	0.814091i	0.491924	+	0.0260718i
$976$		0			0
$977$	27.8668	+	23.3831i	0.891539	+	0.748090i	0.968518	−	0.248943i	$-0.0800830\pi$
$977$	27.8668	+	23.3831i	0.891539	+	0.748090i	−0.0769792	+	0.997033i	$0.524527\pi$
$978$		0			0
$979$	−7.90089	−	2.87569i	−0.252514	−	0.0919075i
$980$		0			0
$981$	18.8393	+	2.00258i	0.601493	+	0.0639373i
$982$		0			0
$983$	−32.2790	+	27.0853i	−1.02954	+	0.863886i	−0.990796	−	0.135363i	$-0.956780\pi$
$983$	−32.2790	+	27.0853i	−1.02954	+	0.863886i	−0.0387434	+	0.999249i	$0.512335\pi$
$984$		0			0
$985$	−0.761595	+	4.31922i	−0.0242664	+	0.137622i
$986$		0			0
$987$	−16.5089	−	15.4130i	−0.525484	−	0.490602i
$988$		0			0
$989$	−1.82173	+	3.15533i	−0.0579276	+	0.100334i
$990$		0			0
$991$	12.7705	+	22.1191i	0.405667	+	0.702635i	0.994399	−	0.105693i	$-0.0337060\pi$
$991$	12.7705	+	22.1191i	0.405667	+	0.702635i	−0.588732	+	0.808328i	$0.700373\pi$
$992$		0			0
$993$	46.2798	+	19.6769i	1.46865	+	0.624426i
$994$		0			0
$995$	−30.4130	+	11.0694i	−0.964158	+	0.350925i
$996$		0			0
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	0.978585	+	0.205845i	$0.0659942\pi$
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	−0.849166	+	0.528126i	$0.822895\pi$
$998$		0			0
$999$	−8.54711	+	10.5167i	−0.270419	+	0.332733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.c.337.2		12
4.3	odd	2		27.2.e.a.13.2	✓	12
12.11	even	2		81.2.e.a.10.1		12
20.3	even	4		675.2.u.b.499.3		24
20.7	even	4		675.2.u.b.499.2		24
20.19	odd	2		675.2.l.c.526.1		12
27.25	even	9	inner	432.2.u.c.241.2		12
36.7	odd	6		243.2.e.c.109.2		12
36.11	even	6		243.2.e.b.109.1		12
36.23	even	6		243.2.e.a.190.2		12
36.31	odd	6		243.2.e.d.190.1		12
108.7	odd	18		243.2.e.c.136.2		12
108.11	even	18		243.2.e.a.55.2		12
108.23	even	18		729.2.c.b.487.5		12
108.31	odd	18		729.2.c.e.487.2		12
108.43	odd	18		243.2.e.d.55.1		12
108.47	even	18		243.2.e.b.136.1		12
108.59	even	18		729.2.a.d.1.2		6
108.67	odd	18		729.2.c.e.244.2		12
108.79	odd	18		27.2.e.a.25.2	yes	12
108.83	even	18		81.2.e.a.73.1		12
108.95	even	18		729.2.c.b.244.5		12
108.103	odd	18		729.2.a.a.1.5		6
540.79	odd	18		675.2.l.c.376.1		12
540.187	even	36		675.2.u.b.349.3		24
540.403	even	36		675.2.u.b.349.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	4.3	odd	2
27.2.e.a.25.2	yes	12	108.79	odd	18
81.2.e.a.10.1		12	12.11	even	2
81.2.e.a.73.1		12	108.83	even	18
243.2.e.a.55.2		12	108.11	even	18
243.2.e.a.190.2		12	36.23	even	6
243.2.e.b.109.1		12	36.11	even	6
243.2.e.b.136.1		12	108.47	even	18
243.2.e.c.109.2		12	36.7	odd	6
243.2.e.c.136.2		12	108.7	odd	18
243.2.e.d.55.1		12	108.43	odd	18
243.2.e.d.190.1		12	36.31	odd	6
432.2.u.c.241.2		12	27.25	even	9	inner
432.2.u.c.337.2		12	1.1	even	1	trivial
675.2.l.c.376.1		12	540.79	odd	18
675.2.l.c.526.1		12	20.19	odd	2
675.2.u.b.349.2		24	540.403	even	36
675.2.u.b.349.3		24	540.187	even	36
675.2.u.b.499.2		24	20.7	even	4
675.2.u.b.499.3		24	20.3	even	4
729.2.a.a.1.5		6	108.103	odd	18
729.2.a.d.1.2		6	108.59	even	18
729.2.c.b.244.5		12	108.95	even	18
729.2.c.b.487.5		12	108.23	even	18
729.2.c.e.244.2		12	108.67	odd	18
729.2.c.e.487.2		12	108.31	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72962 + 0.0916693i) q^{3} +(-1.33735 - 1.12217i) q^{5} +(2.31094 + 0.841112i) q^{7} +(2.98319 + 0.317107i) q^{9} +O(q^{10})\)	\(q+(1.72962 + 0.0916693i) q^{3} +(-1.33735 - 1.12217i) q^{5} +(2.31094 + 0.841112i) q^{7} +(2.98319 + 0.317107i) q^{9} +(0.960783 - 0.806193i) q^{11} +(-0.789931 + 4.47992i) q^{13} +(-2.21024 - 2.06353i) q^{15} +(3.32358 - 5.75662i) q^{17} +(0.124578 + 0.215776i) q^{19} +(3.91994 + 1.66665i) q^{21} +(0.791222 - 0.287981i) q^{23} +(-0.339001 - 1.92257i) q^{25} +(5.13073 + 0.821942i) q^{27} +(-0.0889744 - 0.504599i) q^{29} +(-0.770551 + 0.280458i) q^{31} +(1.73570 - 1.30634i) q^{33} +(-2.14666 - 3.71812i) q^{35} +(-1.30403 + 2.25865i) q^{37} +(-1.77695 + 7.67616i) q^{39} +(-1.41572 + 8.02895i) q^{41} +(-3.31478 + 2.78143i) q^{43} +(-3.63373 - 3.77173i) q^{45} +(-4.98256 - 1.81351i) q^{47} +(-0.729356 - 0.612002i) q^{49} +(6.27625 - 9.65211i) q^{51} -10.4841 q^{53} -2.18959 q^{55} +(0.195693 + 0.384630i) q^{57} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(6.62725 + 3.24201i) q^{63} +(6.08365 - 5.10479i) q^{65} +(-1.75146 + 9.93303i) q^{67} +(1.39492 - 0.425568i) q^{69} +(0.0447378 - 0.0774882i) q^{71} +(2.66057 + 4.60824i) q^{73} +(-0.410103 - 3.35640i) q^{75} +(2.89841 - 1.05493i) q^{77} +(-0.829503 - 4.70435i) q^{79} +(8.79889 + 1.89198i) q^{81} +(-1.39625 - 7.91851i) q^{83} +(-10.9047 + 3.96899i) q^{85} +(-0.107636 - 0.880922i) q^{87} +(-3.35189 - 5.80564i) q^{89} +(-5.59359 + 9.68839i) q^{91} +(-1.35847 + 0.414450i) q^{93} +(0.0755324 - 0.428365i) q^{95} +(4.20603 - 3.52928i) q^{97} +(3.12185 - 2.10036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

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