LMFDB - Embedded newform 432.2.u.c.241.2

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			241.2
Root			$0.500000 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	432.241
Dual form			432.2.u.c.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			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	−0.890828	−	0.454340i	$-0.849875\pi$
$5$	−1.33735	+	1.12217i	−0.598081	+	0.501850i	0.292747	+	0.956190i	$0.405431\pi$
$6$		0			0
$7$	2.31094	−	0.841112i	0.873452	−	0.317910i	0.133888	−	0.990997i	$-0.457254\pi$
$7$	2.31094	−	0.841112i	0.873452	−	0.317910i	0.739564	+	0.673086i	$0.235032\pi$
$8$		0			0
$9$	2.98319	−	0.317107i	0.994398	−	0.105702i
$10$		0			0
$11$	0.960783	+	0.806193i	0.289687	+	0.243076i	0.776036	−	0.630688i	$-0.217227\pi$
$11$	0.960783	+	0.806193i	0.289687	+	0.243076i	−0.486349	+	0.873764i	$0.661672\pi$
$12$		0			0
$13$	−0.789931	−	4.47992i	−0.219087	−	1.24251i	−0.873671	−	0.486517i	$-0.838267\pi$
$13$	−0.789931	−	4.47992i	−0.219087	−	1.24251i	0.654584	−	0.755989i	$-0.272844\pi$
$14$		0			0
$15$	−2.21024	+	2.06353i	−0.570683	+	0.532800i
$16$		0			0
$17$	3.32358	+	5.75662i	0.806088	+	1.39618i	0.915554	+	0.402194i	$0.131752\pi$
$17$	3.32358	+	5.75662i	0.806088	+	1.39618i	−0.109467	+	0.993990i	$0.534914\pi$
$18$		0			0
$19$	0.124578	−	0.215776i	0.0285802	−	0.0495023i	−0.851382	−	0.524547i	$-0.824235\pi$
$19$	0.124578	−	0.215776i	0.0285802	−	0.0495023i	0.879962	+	0.475045i	$0.157568\pi$
$20$		0			0
$21$	3.91994	−	1.66665i	0.855402	−	0.363693i
$22$		0			0
$23$	0.791222	+	0.287981i	0.164981	+	0.0600483i	0.423190	−	0.906041i	$-0.360910\pi$
$23$	0.791222	+	0.287981i	0.164981	+	0.0600483i	−0.258209	+	0.966089i	$0.583132\pi$
$24$		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	−0.991954	−	0.126601i	$-0.959593\pi$
$29$	−0.0889744	+	0.504599i	−0.0165221	+	0.0937016i	0.975432	+	0.220302i	$0.0707044\pi$
$30$		0			0
$31$	−0.770551	−	0.280458i	−0.138395	−	0.0503717i	0.271894	−	0.962327i	$-0.412350\pi$
$31$	−0.770551	−	0.280458i	−0.138395	−	0.0503717i	−0.410289	+	0.911956i	$0.634572\pi$
$32$		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	0.738700	−	0.674035i	$-0.235440\pi$
$37$	−1.30403	−	2.25865i	−0.214381	−	0.371319i	−0.953081	+	0.302715i	$0.902107\pi$
$38$		0			0
$39$	−1.77695	−	7.67616i	−0.284540	−	1.22917i
$40$		0			0
$41$	−1.41572	−	8.02895i	−0.221099	−	1.25391i	−0.870005	−	0.493044i	$-0.835884\pi$
$41$	−1.41572	−	8.02895i	−0.221099	−	1.25391i	0.648906	−	0.760869i	$-0.275227\pi$
$42$		0			0
$43$	−3.31478	−	2.78143i	−0.505500	−	0.424165i	0.354042	−	0.935229i	$-0.384807\pi$
$43$	−3.31478	−	2.78143i	−0.505500	−	0.424165i	−0.859542	+	0.511065i	$0.829251\pi$
$44$		0			0
$45$	−3.63373	+	3.77173i	−0.541684	+	0.562257i
$46$		0			0
$47$	−4.98256	+	1.81351i	−0.726782	+	0.264527i	−0.678802	−	0.734321i	$-0.737501\pi$
$47$	−4.98256	+	1.81351i	−0.726782	+	0.264527i	−0.0479798	+	0.998848i	$0.515278\pi$
$48$		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	−0.480455	−	0.877019i	$-0.659529\pi$
$59$	2.30289	−	1.93235i	0.299810	−	0.251571i	0.780265	+	0.625449i	$0.215084\pi$
$60$		0			0
$61$	−2.70930	+	0.986103i	−0.346890	+	0.126258i	−0.509589	−	0.860418i	$-0.670202\pi$
$61$	−2.70930	+	0.986103i	−0.346890	+	0.126258i	0.162699	+	0.986676i	$0.447980\pi$
$62$		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	−0.882676	−	0.469982i	$-0.844261\pi$
$67$	−1.75146	−	9.93303i	−0.213975	−	1.21351i	0.668701	−	0.743531i	$-0.266851\pi$
$68$		0			0
$69$	1.39492	+	0.425568i	0.167928	+	0.0512324i
$70$		0			0
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	0.868668	−	0.495395i	$-0.164977\pi$
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	−0.863358	+	0.504591i	$0.831643\pi$
$72$		0			0
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	−0.667269	−	0.744817i	$-0.732537\pi$
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	0.978665	+	0.205463i	$0.0658701\pi$
$74$		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	0.901921	+	0.431901i	$0.142157\pi$
$79$	−0.829503	+	4.70435i	−0.0933264	+	0.529280i	−0.995247	+	0.0973792i	$0.968954\pi$
$80$		0			0
$81$	8.79889	−	1.89198i	0.977654	−	0.210220i
$82$		0			0
$83$	−1.39625	+	7.91851i	−0.153258	+	0.869169i	0.807103	+	0.590410i	$0.201034\pi$
$83$	−1.39625	+	7.91851i	−0.153258	+	0.869169i	−0.960361	+	0.278759i	$0.910077\pi$
$84$		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	−0.987169	−	0.159678i	$-0.948954\pi$
$89$	−3.35189	+	5.80564i	−0.355299	+	0.615396i	0.631870	+	0.775074i	$0.282288\pi$
$90$		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	0.830840	−	0.556511i	$-0.187860\pi$
$97$	4.20603	+	3.52928i	0.427057	+	0.358344i	−0.403783	+	0.914855i	$0.632305\pi$
$98$		0			0
$99$	3.12185	+	2.10036i	0.313758	+	0.211094i
$100$		0			0
$101$	−4.70360	+	1.71197i	−0.468025	+	0.170347i	−0.565258	−	0.824914i	$-0.691223\pi$
$101$	−4.70360	+	1.71197i	−0.468025	+	0.170347i	0.0972322	+	0.995262i	$0.469001\pi$
$102$		0			0
$103$	−8.90079	+	7.46865i	−0.877021	+	0.735908i	−0.965564	−	0.260164i	$-0.916223\pi$
$103$	−8.90079	+	7.46865i	−0.877021	+	0.735908i	0.0885431	+	0.996072i	$0.471779\pi$
$104$		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	−0.857015	−	0.515292i	$-0.827684\pi$
$113$	−5.29775	+	4.44534i	−0.498371	+	0.418183i	0.358644	+	0.933474i	$0.383239\pi$
$114$		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	−0.465792	−	0.884894i	$-0.654230\pi$
$127$	6.01162	−	10.4124i	0.533445	−	0.923954i	0.999237	−	0.0390598i	$-0.0124363\pi$
$128$		0			0
$129$	−5.98830	−	4.50697i	−0.527240	−	0.396817i
$130$		0			0
$131$	−13.2354	−	4.81728i	−1.15638	−	0.420888i	−0.308577	−	0.951199i	$-0.599853\pi$
$131$	−13.2354	−	4.81728i	−1.15638	−	0.420888i	−0.847803	+	0.530311i	$0.822075\pi$
$132$		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	−0.963465	−	0.267836i	$-0.913692\pi$
$137$	0.392122	−	2.22383i	0.0335012	−	0.189995i	0.996966	+	0.0778409i	$0.0248026\pi$
$138$		0			0
$139$	−7.49414	−	2.72764i	−0.635644	−	0.231356i	0.00404179	−	0.999992i	$-0.498713\pi$
$139$	−7.49414	−	2.72764i	−0.635644	−	0.231356i	−0.639686	+	0.768636i	$0.720936\pi$
$140$		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	0.984038	−	0.177960i	$-0.0569499\pi$
$149$	−0.0185697	−	0.105314i	−0.00152129	−	0.00862764i	−0.985559	+	0.169333i	$0.945839\pi$
$150$		0			0
$151$	15.5196	+	13.0225i	1.26297	+	1.05976i	0.995359	+	0.0962282i	$0.0306779\pi$
$151$	15.5196	+	13.0225i	1.26297	+	1.05976i	0.267609	+	0.963528i	$0.413767\pi$
$152$		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	−0.273871	+	0.961767i	$0.588304\pi$
$157$	−15.8953	+	13.3377i	−1.26858	+	1.06447i	−0.994712	+	0.102701i	$0.967252\pi$
$158$		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	0.177429	−	0.984134i	$-0.443222\pi$
$167$	15.2156	−	12.7674i	1.17742	−	0.987974i	0.999993	−	0.00383999i	$-0.00122231\pi$
$168$		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	0.997573	−	0.0696342i	$-0.0221832\pi$
$173$	14.4975	+	12.1648i	1.10222	+	0.924875i	0.104650	+	0.994509i	$0.466628\pi$
$174$		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	0.994650	−	0.103302i	$-0.0329409\pi$
$179$	5.45683	+	9.45151i	0.407863	+	0.706439i	−0.586787	+	0.809741i	$0.699608\pi$
$180$		0			0
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	−0.311704	−	0.950179i	$-0.600900\pi$
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	0.978731	−	0.205146i	$-0.0657668\pi$
$182$		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	−0.0468192	−	0.998903i	$-0.514908\pi$
$191$	4.68261	−	26.5564i	0.338822	−	1.92155i	0.385641	−	0.922649i	$-0.373980\pi$
$192$		0			0
$193$	16.1202	+	5.86729i	1.16036	+	0.422337i	0.849226	−	0.528029i	$-0.177069\pi$
$193$	16.1202	+	5.86729i	1.16036	+	0.422337i	0.311135	+	0.950366i	$0.399291\pi$
$194$		0			0
$195$	10.9904	+	8.27167i	0.787037	+	0.592347i
$196$		0			0
$197$	−1.25612	+	2.17567i	−0.0894951	+	0.155010i	−0.907298	−	0.420489i	$-0.861859\pi$
$197$	−1.25612	+	2.17567i	−0.0894951	+	0.155010i	0.817803	+	0.575499i	$0.195192\pi$
$198$		0			0
$199$	9.26942	+	16.0551i	0.657092	+	1.13812i	0.981365	+	0.192153i	$0.0615470\pi$
$199$	9.26942	+	16.0551i	0.657092	+	1.13812i	−0.324273	+	0.945964i	$0.605120\pi$
$200$		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	−0.540248	−	0.841506i	$-0.681670\pi$
$211$	2.82761	−	2.37264i	0.194661	−	0.163340i	0.734908	+	0.678166i	$0.237225\pi$
$212$		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	−0.908748	−	0.417346i	$-0.862960\pi$
$223$	−19.9601	+	7.26487i	−1.33662	+	0.486491i	−0.427876	+	0.903837i	$0.640738\pi$
$224$		0			0
$225$	−0.401646	+	5.84289i	−0.0267764	+	0.389526i
$226$		0			0
$227$	10.9851	+	9.21761i	0.729108	+	0.611794i	0.929888	−	0.367842i	$-0.119903\pi$
$227$	10.9851	+	9.21761i	0.729108	+	0.611794i	−0.200781	+	0.979636i	$0.564348\pi$
$228$		0			0
$229$	2.93219	+	16.6293i	0.193765	+	1.09889i	0.914167	+	0.405337i	$0.132846\pi$
$229$	2.93219	+	16.6293i	0.193765	+	1.09889i	−0.720403	+	0.693556i	$0.756043\pi$
$230$		0			0
$231$	5.10985	+	1.55894i	0.336204	+	0.102571i
$232$		0			0
$233$	−2.79972	−	4.84926i	−0.183416	−	0.317686i	0.759626	−	0.650361i	$-0.225382\pi$
$233$	−2.79972	−	4.84926i	−0.183416	−	0.317686i	−0.943042	+	0.332675i	$0.892049\pi$
$234$		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	0.176712	−	0.984263i	$-0.443454\pi$
$239$	−4.95620	−	1.80391i	−0.320590	−	0.116685i	−0.497302	+	0.867577i	$0.665676\pi$
$240$		0			0
$241$	−1.54590	+	8.76723i	−0.0995801	+	0.564747i	0.893667	+	0.448730i	$0.148124\pi$
$241$	−1.54590	+	8.76723i	−0.0995801	+	0.564747i	−0.993247	+	0.116017i	$0.962987\pi$
$242$		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	−0.962284	−	0.272048i	$-0.912299\pi$
$251$	−3.89010	+	6.73786i	−0.245541	+	0.425290i	0.716742	+	0.697338i	$0.245632\pi$
$252$		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	−0.869511	−	0.493913i	$-0.835566\pi$
$257$	−3.54877	−	20.1261i	−0.221366	−	1.25543i	0.648145	−	0.761517i	$-0.275545\pi$
$258$		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	0.00612723	−	0.999981i	$-0.498050\pi$
$263$	10.5996	−	3.85792i	0.653596	−	0.237890i	0.647469	+	0.762092i	$0.275827\pi$
$264$		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	0.414648	−	0.909982i	$-0.363905\pi$
$277$	21.9228	−	7.97924i	1.31721	−	0.479426i	0.902564	+	0.430556i	$0.141683\pi$
$278$		0			0
$279$	−2.38764	−	0.592313i	−0.142944	−	0.0354608i
$280$		0			0
$281$	5.53502	+	4.64443i	0.330192	+	0.277064i	0.792778	−	0.609511i	$-0.208634\pi$
$281$	5.53502	+	4.64443i	0.330192	+	0.277064i	−0.462586	+	0.886574i	$0.653078\pi$
$282$		0			0
$283$	−1.23643	−	7.01212i	−0.0734979	−	0.416827i	−0.999251	−	0.0386985i	$-0.987679\pi$
$283$	−1.23643	−	7.01212i	−0.0734979	−	0.416827i	0.925753	−	0.378129i	$-0.123432\pi$
$284$		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	0.326811	−	0.945090i	$-0.394026\pi$
$293$	−0.519166	−	0.188961i	−0.0303300	−	0.0110392i	−0.357141	+	0.934051i	$0.616248\pi$
$294$		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	0.945918	−	0.324406i	$-0.105164\pi$
$307$	3.36438	+	5.82728i	0.192015	+	0.332580i	−0.753903	+	0.656986i	$0.771831\pi$
$308$		0			0
$309$	−14.7104	+	13.7339i	−0.836844	+	0.781293i
$310$		0			0
$311$	−2.67825	−	15.1891i	−0.151870	−	0.861297i	−0.961592	−	0.274483i	$-0.911493\pi$
$311$	−2.67825	−	15.1891i	−0.151870	−	0.861297i	0.809722	−	0.586814i	$-0.199618\pi$
$312$		0			0
$313$	−18.0487	−	15.1446i	−1.02017	−	0.856025i	−0.0305223	−	0.999534i	$-0.509717\pi$
$313$	−18.0487	−	15.1446i	−1.02017	−	0.856025i	−0.989649	+	0.143509i	$0.954162\pi$
$314$		0			0
$315$	−5.22486	+	11.7726i	−0.294388	+	0.663311i
$316$		0			0
$317$	−6.81469	+	2.48034i	−0.382751	+	0.139310i	−0.526228	−	0.850344i	$-0.676394\pi$
$317$	−6.81469	+	2.48034i	−0.382751	+	0.139310i	0.143477	+	0.989654i	$0.454172\pi$
$318$		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	0.543669	−	0.839300i	$-0.317035\pi$
$331$	27.2835	−	9.93037i	1.49964	−	0.545823i	0.955966	+	0.293477i	$0.0948124\pi$
$332$		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	0.978835	−	0.204652i	$-0.0656063\pi$
$337$	−0.201275	−	1.14149i	−0.0109641	−	0.0621807i	−0.989799	+	0.142471i	$0.954495\pi$
$338$		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	0.486273	−	0.873807i	$-0.338356\pi$
$347$	5.53452	+	2.01440i	0.297108	+	0.108139i	−0.189165	+	0.981945i	$0.560578\pi$
$348$		0			0
$349$	−5.31237	+	30.1279i	−0.284364	+	1.61271i	0.423183	+	0.906044i	$0.360913\pi$
$349$	−5.31237	+	30.1279i	−0.284364	+	1.61271i	−0.707547	+	0.706666i	$0.750198\pi$
$350$		0			0
$351$	−7.73516	−	22.3360i	−0.412872	−	1.19221i
$352$		0			0
$353$	6.41826	−	36.3997i	0.341609	−	1.93736i	−0.00668455	−	0.999978i	$-0.502128\pi$
$353$	6.41826	−	36.3997i	0.341609	−	1.93736i	0.348294	−	0.937385i	$-0.386761\pi$
$354$		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	0.273792	+	0.961789i	$0.411722\pi$
$359$	−13.1880	+	22.8423i	−0.696037	+	1.20557i	−0.969830	+	0.243783i	$0.921611\pi$
$360$		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	0.840318	−	0.542093i	$-0.182368\pi$
$367$	8.66636	+	7.27194i	0.452380	+	0.379592i	−0.387938	+	0.921685i	$0.626813\pi$
$368$		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	−0.519487	−	0.854478i	$-0.673877\pi$
$373$	4.47682	−	3.75650i	0.231801	−	0.194504i	0.751289	+	0.659974i	$0.229433\pi$
$374$		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	−0.565039	−	0.825064i	$-0.691139\pi$
$383$	2.92326	−	2.45291i	0.149372	−	0.125338i	0.714411	+	0.699726i	$0.246695\pi$
$384$		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	0.828580	−	0.559870i	$-0.189149\pi$
$389$	8.30534	+	6.96901i	0.421097	+	0.353343i	−0.407483	+	0.913213i	$0.633593\pi$
$390$		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	−0.703507	−	0.710689i	$-0.748383\pi$
$397$	5.25461	−	9.10124i	0.263721	−	0.456778i	0.967228	+	0.253910i	$0.0817168\pi$
$398$		0			0
$399$	0.128717	−	1.05346i	0.00644392	−	0.0527388i
$400$		0			0
$401$	−13.4992	−	4.91332i	−0.674119	−	0.245359i	−0.0177987	−	0.999842i	$-0.505666\pi$
$401$	−13.4992	−	4.91332i	−0.674119	−	0.245359i	−0.656320	+	0.754482i	$0.727888\pi$
$402$		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	−0.103195	−	0.994661i	$-0.532907\pi$
$409$	−16.6159	−	6.04769i	−0.821603	−	0.299039i	−0.718408	+	0.695622i	$0.755129\pi$
$410$		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	−0.998727	−	0.0504461i	$-0.983936\pi$
$419$	−1.58606	−	8.99500i	−0.0774842	−	0.439435i	0.921243	−	0.388988i	$-0.127175\pi$
$420$		0			0
$421$	18.5344	+	15.5522i	0.903310	+	0.757967i	0.970835	−	0.239750i	$-0.0770656\pi$
$421$	18.5344	+	15.5522i	0.903310	+	0.757967i	−0.0675243	+	0.997718i	$0.521510\pi$
$422$		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	−0.480442	−	0.877026i	$-0.659524\pi$
$439$	−5.96599	+	2.17144i	−0.284741	+	0.103637i	0.195701	+	0.980664i	$0.437302\pi$
$440$		0			0
$441$	−1.98174	+	2.05700i	−0.0943685	+	0.0979526i
$442$		0			0
$443$	−11.7618	−	9.86931i	−0.558819	−	0.468905i	0.319095	−	0.947723i	$-0.396621\pi$
$443$	−11.7618	−	9.86931i	−0.558819	−	0.468905i	−0.877914	+	0.478818i	$0.841066\pi$
$444$		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	0.944862	+	0.327468i	$0.106195\pi$
$449$	16.0199	+	27.7473i	0.756027	+	1.30948i	−0.188836	+	0.982009i	$0.560471\pi$
$450$		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	−0.802442	−	0.596730i	$-0.796466\pi$
$457$	3.32849	−	18.8768i	0.155700	−	0.883021i	0.958143	−	0.286291i	$-0.0924225\pi$
$458$		0			0
$459$	21.7840	+	26.8039i	1.01679	+	1.25110i
$460$		0			0
$461$	−0.906494	+	5.14098i	−0.0422196	+	0.239440i	−0.998614	−	0.0526405i	$-0.983236\pi$
$461$	−0.906494	+	5.14098i	−0.0422196	+	0.239440i	0.956394	+	0.292080i	$0.0943474\pi$
$462$		0			0
$463$	1.59502	+	0.580541i	0.0741271	+	0.0269800i	0.378818	−	0.925471i	$-0.376331\pi$
$463$	1.59502	+	0.580541i	0.0741271	+	0.0269800i	−0.304690	+	0.952451i	$0.598553\pi$
$464$		0			0
$465$	2.28184	−	0.970173i	0.105818	−	0.0449907i
$466$		0			0
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	−0.543307	−	0.839534i	$-0.682828\pi$
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	0.998711	+	0.0507511i	$0.0161615\pi$
$468$		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	−0.882430	−	0.470444i	$-0.844094\pi$
$479$	−27.4892	+	10.0053i	−1.25601	+	0.457152i	−0.373585	+	0.927596i	$0.621872\pi$
$480$		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	−0.893345	−	0.449372i	$-0.851648\pi$
$491$	−13.4265	+	11.2661i	−0.605927	+	0.508433i	0.287417	+	0.957805i	$0.407203\pi$
$492$		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	0.964472	+	0.264185i	$0.0851031\pi$
$499$	3.31772	+	18.8157i	0.148522	+	0.842307i	−0.815950	+	0.578122i	$0.803786\pi$
$500$		0			0
$501$	25.1469	−	23.4777i	1.12348	−	1.04890i
$502$		0			0
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	0.717483	−	0.696576i	$-0.245294\pi$
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	−0.961994	+	0.273070i	$0.911961\pi$
$504$		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	0.721379	−	0.692540i	$-0.243509\pi$
$509$	18.6993	+	6.80598i	0.828831	+	0.301670i	0.107452	+	0.994210i	$0.465731\pi$
$510$		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	0.168729	+	0.985662i	$0.446034\pi$
$521$	−17.5583	+	30.4119i	−0.769244	+	1.33237i	−0.937973	+	0.346708i	$0.887300\pi$
$522$		0			0
$523$	−7.12269	−	12.3369i	−0.311453	−	0.539453i	0.667224	−	0.744857i	$-0.267482\pi$
$523$	−7.12269	−	12.3369i	−0.311453	−	0.539453i	−0.978677	+	0.205404i	$0.934149\pi$
$524$		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	−0.648121	−	0.761537i	$-0.724445\pi$
$547$	−15.3216	+	5.57661i	−0.655105	+	0.238439i	−0.00698326	+	0.999976i	$0.502223\pi$
$548$		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	−0.982000	−	0.188883i	$-0.939513\pi$
$557$	−15.4486	−	26.7577i	−0.654577	−	1.13376i	0.327422	−	0.944878i	$-0.393820\pi$
$558$		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	0.812585	−	0.582843i	$-0.198060\pi$
$563$	25.1612	+	9.15791i	1.06042	+	0.385960i	0.247832	+	0.968803i	$0.420282\pi$
$564$		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	−0.833414	−	0.552649i	$-0.813617\pi$
$569$	3.30985	−	18.7711i	0.138756	−	0.786924i	0.972170	−	0.234275i	$-0.0752717\pi$
$570$		0			0
$571$	−17.6420	−	6.42116i	−0.738294	−	0.268717i	−0.0546227	−	0.998507i	$-0.517396\pi$
$571$	−17.6420	−	6.42116i	−0.738294	−	0.268717i	−0.683671	+	0.729790i	$0.739618\pi$
$572$		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	0.912161	−	0.409833i	$-0.134413\pi$
$577$	2.42981	+	4.20856i	0.101154	+	0.175204i	−0.811006	+	0.585038i	$0.801080\pi$
$578$		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	−0.887796	−	0.460236i	$-0.847765\pi$
$587$	−30.8194	+	11.2174i	−1.27205	+	0.462990i	−0.384257	+	0.923226i	$0.625542\pi$
$588$		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	−0.939155	−	0.343495i	$-0.888389\pi$
$599$	−18.6975	+	15.6891i	−0.763961	+	0.641039i	0.175194	+	0.984534i	$0.443945\pi$
$600$		0			0
$601$	−7.39563	+	2.69179i	−0.301674	+	0.109800i	−0.488422	−	0.872607i	$-0.662427\pi$
$601$	−7.39563	+	2.69179i	−0.301674	+	0.109800i	0.186748	+	0.982408i	$0.440205\pi$
$602$		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	0.999396	+	0.0347476i	$0.0110627\pi$
$607$	1.77772	+	10.0819i	0.0721553	+	0.409213i	−0.927241	+	0.374466i	$0.877826\pi$
$608$		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	−0.887711	−	0.460401i	$-0.847706\pi$
$613$	−1.11753	+	1.93563i	−0.0451368	+	0.0781792i	0.842574	+	0.538580i	$0.181039\pi$
$614$		0			0
$615$	19.6970	+	14.8246i	0.794262	+	0.597784i
$616$		0			0
$617$	−31.9267	−	11.6204i	−1.28532	−	0.467818i	−0.393132	−	0.919482i	$-0.628609\pi$
$617$	−31.9267	−	11.6204i	−1.28532	−	0.467818i	−0.892188	+	0.451664i	$0.850831\pi$
$618$		0			0
$619$	5.01079	−	28.4176i	0.201401	−	1.14220i	−0.701604	−	0.712567i	$-0.747532\pi$
$619$	5.01079	−	28.4176i	0.201401	−	1.14220i	0.903004	−	0.429632i	$-0.141357\pi$
$620$		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	0.833073	−	0.553163i	$-0.186579\pi$
$631$	−1.57039	−	2.71999i	−0.0625162	−	0.108281i	−0.895590	+	0.444881i	$0.853246\pi$
$632$		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	0.324518	−	0.945879i	$-0.394798\pi$
$641$	29.9034	−	10.8839i	1.18111	−	0.429890i	0.856595	+	0.515989i	$0.172576\pi$
$642$		0			0
$643$	9.84142	−	8.25794i	0.388108	−	0.325661i	−0.427768	−	0.903889i	$-0.640700\pi$
$643$	9.84142	−	8.25794i	0.388108	−	0.325661i	0.815876	+	0.578228i	$0.196255\pi$
$644$		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	−0.163897	−	0.986477i	$-0.552406\pi$
$653$	19.9099	−	16.7064i	0.779134	−	0.653771i	0.943030	+	0.332707i	$0.107962\pi$
$654$		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	0.950826	+	0.309727i	$0.100238\pi$
$659$	36.4774	+	30.6081i	1.42096	+	1.19232i	0.470131	+	0.882597i	$0.344207\pi$
$660$		0			0
$661$	−0.152204	−	0.863192i	−0.00592005	−	0.0335743i	0.981705	−	0.190410i	$-0.0609818\pi$
$661$	−0.152204	−	0.863192i	−0.00592005	−	0.0335743i	−0.987625	+	0.156836i	$0.949871\pi$
$662$		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	−0.558805	−	0.829299i	$-0.688740\pi$
$673$	6.48393	−	36.7722i	0.249937	−	1.41746i	0.808742	−	0.588164i	$-0.200149\pi$
$674$		0			0
$675$	−0.159082	+	10.1428i	−0.00612306	+	0.390397i
$676$		0			0
$677$	−2.38231	+	13.5107i	−0.0915596	+	0.519260i	0.904188	+	0.427135i	$0.140477\pi$
$677$	−2.38231	+	13.5107i	−0.0915596	+	0.519260i	−0.995747	+	0.0921251i	$0.970634\pi$
$678$		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	0.225206	−	0.974311i	$-0.427694\pi$
$683$	24.9943	−	43.2914i	0.956381	−	1.65650i	0.731175	−	0.682190i	$-0.238972\pi$
$684$		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	0.226052	−	0.974115i	$-0.427418\pi$
$691$	−18.2434	−	15.3080i	−0.694011	−	0.582345i	−0.920063	+	0.391771i	$0.871863\pi$
$692$		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	−0.601082	−	0.799187i	$-0.705264\pi$
$709$	−14.5871	+	5.30927i	−0.547830	+	0.199394i	0.0532520	+	0.998581i	$0.483041\pi$
$710$		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	0.956249	−	0.292555i	$-0.0945056\pi$
$719$	6.02686	+	10.4388i	0.224764	+	0.389303i	−0.731485	+	0.681858i	$0.761172\pi$
$720$		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	−0.695755	−	0.718279i	$-0.744930\pi$
$727$	5.49253	−	31.1497i	0.203707	−	1.15528i	0.899462	−	0.437000i	$-0.143959\pi$
$728$		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	0.650464	−	0.759537i	$-0.274575\pi$
$733$	17.8831	+	6.50891i	0.660527	+	0.240412i	0.0100630	+	0.999949i	$0.496797\pi$
$734$		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	0.977336	−	0.211696i	$-0.0678986\pi$
$739$	8.30036	+	14.3767i	0.305334	+	0.528854i	−0.672002	+	0.740550i	$0.734565\pi$
$740$		0			0
$741$	−1.87770	−	0.572858i	−0.0689789	−	0.0210445i
$742$		0			0
$743$	5.78310	+	32.7976i	0.212161	+	1.20323i	0.885765	+	0.464134i	$0.153634\pi$
$743$	5.78310	+	32.7976i	0.212161	+	1.20323i	−0.673604	+	0.739093i	$0.735255\pi$
$744$		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	−0.942387	−	0.334524i	$-0.891424\pi$
$751$	−21.2819	+	17.8577i	−0.776589	+	0.651636i	0.165798	+	0.986160i	$0.446980\pi$
$752$		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	−0.221919	+	0.975065i	$0.571232\pi$
$761$	−33.6747	+	28.2564i	−1.22071	+	1.02429i	−0.998787	+	0.0492297i	$0.984323\pi$
$762$		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	0.994223	−	0.107331i	$-0.0342305\pi$
$769$	0.644731	+	3.65645i	0.0232496	+	0.131855i	−0.970974	+	0.239186i	$0.923119\pi$
$770$		0			0
$771$	−7.98298	−	34.4852i	−0.287500	−	1.24195i
$772$		0			0
$773$	4.48452	+	7.76741i	0.161297	+	0.279374i	0.935334	−	0.353766i	$-0.115099\pi$
$773$	4.48452	+	7.76741i	0.161297	+	0.279374i	−0.774037	+	0.633140i	$0.781766\pi$
$774$		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	0.947792	−	0.318888i	$-0.103309\pi$
$787$	41.2069	+	14.9981i	1.46887	+	0.534624i	0.521074	+	0.853512i	$0.325532\pi$
$788$		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	0.999203	+	0.0399111i	$0.0127075\pi$
$797$	2.08656	+	11.8335i	0.0739097	+	0.419163i	−0.925294	+	0.379252i	$0.876181\pi$
$798$		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	0.153404	−	0.988163i	$-0.450976\pi$
$821$	−22.7250	−	19.0685i	−0.793108	−	0.665497i	−0.946513	+	0.322667i	$0.895421\pi$
$822$		0			0
$823$	−8.60266	−	48.7881i	−0.299870	−	1.70065i	−0.646722	−	0.762726i	$-0.723861\pi$
$823$	−8.60266	−	48.7881i	−0.299870	−	1.70065i	0.346852	−	0.937920i	$-0.387251\pi$
$824$		0			0
$825$	−3.09992	+	2.89415i	−0.107925	+	0.100761i
$826$		0			0
$827$	20.4215	+	35.3711i	0.710126	+	1.22997i	0.964809	+	0.262950i	$0.0846955\pi$
$827$	20.4215	+	35.3711i	0.710126	+	1.22997i	−0.254683	+	0.967025i	$0.581971\pi$
$828$		0			0
$829$	4.72638	−	8.18633i	0.164154	−	0.284323i	−0.772201	−	0.635379i	$-0.780844\pi$
$829$	4.72638	−	8.18633i	0.164154	−	0.284323i	0.936355	+	0.351056i	$0.114177\pi$
$830$		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	−0.925572	−	0.378571i	$-0.876416\pi$
$839$	2.13360	−	12.1002i	0.0736599	−	0.417746i	0.999232	−	0.0391756i	$-0.0124732\pi$
$840$		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	0.140930	−	0.990020i	$-0.454991\pi$
$853$	−23.6446	−	19.8402i	−0.809576	−	0.679315i	−0.950507	+	0.310704i	$0.899435\pi$
$854$		0			0
$855$	0.361165	+	1.25395i	0.0123516	+	0.0428840i
$856$		0			0
$857$	−10.4738	+	3.81217i	−0.357780	+	0.130221i	−0.514655	−	0.857397i	$-0.672080\pi$
$857$	−10.4738	+	3.81217i	−0.357780	+	0.130221i	0.156876	+	0.987618i	$0.449858\pi$
$858$		0			0
$859$	−3.17807	+	2.66672i	−0.108434	+	0.0909872i	−0.695393	−	0.718630i	$-0.744770\pi$
$859$	−3.17807	+	2.66672i	−0.108434	+	0.0909872i	0.586958	+	0.809617i	$0.300325\pi$
$860$		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	0.895682	+	0.444695i	$0.146688\pi$
$877$	6.10381	+	34.6164i	0.206111	+	1.16891i	−0.689571	+	0.724218i	$0.742201\pi$
$878$		0			0
$879$	−0.915284	−	0.279240i	−0.0308718	−	0.00941852i
$880$		0			0
$881$	9.67981	+	16.7659i	0.326121	+	0.564858i	0.981739	−	0.190235i	$-0.0609250\pi$
$881$	9.67981	+	16.7659i	0.326121	+	0.564858i	−0.655618	+	0.755093i	$0.727592\pi$
$882$		0			0
$883$	−6.89302	+	11.9391i	−0.231969	+	0.401781i	−0.958387	−	0.285471i	$-0.907850\pi$
$883$	−6.89302	+	11.9391i	−0.231969	+	0.401781i	0.726419	+	0.687252i	$0.241183\pi$
$884$		0			0
$885$	−1.10248	+	9.02303i	−0.0370596	+	0.303306i
$886$		0			0
$887$	−28.0192	−	10.1982i	−0.940794	−	0.342421i	−0.174315	−	0.984690i	$-0.555771\pi$
$887$	−28.0192	−	10.1982i	−0.940794	−	0.342421i	−0.766479	+	0.642269i	$0.777993\pi$
$888$		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	0.718592	−	0.695432i	$-0.244787\pi$
$907$	4.77366	+	4.00558i	0.158507	+	0.133003i	−0.560085	+	0.828435i	$0.689231\pi$
$908$		0			0
$909$	−13.4889	+	6.59868i	−0.447397	+	0.218864i
$910$		0			0
$911$	−29.7314	+	10.8213i	−0.985044	+	0.358527i	−0.783799	−	0.621014i	$-0.786721\pi$
$911$	−29.7314	+	10.8213i	−0.985044	+	0.358527i	−0.201245	+	0.979541i	$0.564499\pi$
$912$		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	0.903889	−	0.427767i	$-0.140699\pi$
$929$	19.4941	+	16.3575i	0.639580	+	0.536672i	−0.264309	+	0.964438i	$0.585144\pi$
$930$		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	−0.999077	−	0.0429549i	$-0.986323\pi$
$937$	−14.1524	+	24.5127i	−0.462338	+	0.800794i	0.536739	+	0.843749i	$0.319656\pi$
$938$		0			0
$939$	−32.6057	−	24.5400i	−1.06405	−	0.800833i
$940$		0			0
$941$	−7.79422	−	2.83687i	−0.254084	−	0.0924792i	0.211838	−	0.977305i	$-0.432055\pi$
$941$	−7.79422	−	2.83687i	−0.254084	−	0.0924792i	−0.465922	+	0.884826i	$0.654277\pi$
$942$		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	−0.555737	−	0.831358i	$-0.687564\pi$
$947$	7.71877	−	43.7753i	0.250826	−	1.42251i	0.806563	−	0.591148i	$-0.201325\pi$
$948$		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	−0.777012	−	0.629486i	$-0.783265\pi$
$953$	4.83574	−	8.37576i	0.156645	−	0.271317i	0.933657	+	0.358169i	$0.116599\pi$
$954$		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	−0.136209	−	0.990680i	$-0.543492\pi$
$967$	25.3676	−	21.2860i	0.815768	−	0.684510i	0.951977	+	0.306170i	$0.0990475\pi$
$968$		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	−0.0769792	−	0.997033i	$-0.524527\pi$
$977$	27.8668	−	23.3831i	0.891539	−	0.748090i	0.968518	+	0.248943i	$0.0800830\pi$
$978$		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	−0.0387434	−	0.999249i	$-0.512335\pi$
$983$	−32.2790	−	27.0853i	−1.02954	−	0.863886i	−0.990796	+	0.135363i	$0.956780\pi$
$984$		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	−0.588732	−	0.808328i	$-0.700373\pi$
$991$	12.7705	−	22.1191i	0.405667	−	0.702635i	0.994399	+	0.105693i	$0.0337060\pi$
$992$		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	−0.849166	−	0.528126i	$-0.822895\pi$
$997$	4.08644	−	23.1754i	0.129419	−	0.733971i	0.978585	−	0.205845i	$-0.0659942\pi$
$998$		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.241.2		12
4.3	odd	2		27.2.e.a.25.2	yes	12
12.11	even	2		81.2.e.a.73.1		12
20.3	even	4		675.2.u.b.349.2		24
20.7	even	4		675.2.u.b.349.3		24
20.19	odd	2		675.2.l.c.376.1		12
27.13	even	9	inner	432.2.u.c.337.2		12
36.7	odd	6		243.2.e.d.55.1		12
36.11	even	6		243.2.e.a.55.2		12
36.23	even	6		243.2.e.b.136.1		12
36.31	odd	6		243.2.e.c.136.2		12
108.7	odd	18		729.2.c.e.244.2		12
108.11	even	18		729.2.a.d.1.2		6
108.23	even	18		243.2.e.b.109.1		12
108.31	odd	18		243.2.e.c.109.2		12
108.43	odd	18		729.2.a.a.1.5		6
108.47	even	18		729.2.c.b.244.5		12
108.59	even	18		243.2.e.a.190.2		12
108.67	odd	18		27.2.e.a.13.2	✓	12
108.79	odd	18		729.2.c.e.487.2		12
108.83	even	18		729.2.c.b.487.5		12
108.95	even	18		81.2.e.a.10.1		12
108.103	odd	18		243.2.e.d.190.1		12
540.67	even	36		675.2.u.b.499.2		24
540.283	even	36		675.2.u.b.499.3		24
540.499	odd	18		675.2.l.c.526.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	108.67	odd	18
27.2.e.a.25.2	yes	12	4.3	odd	2
81.2.e.a.10.1		12	108.95	even	18
81.2.e.a.73.1		12	12.11	even	2
243.2.e.a.55.2		12	36.11	even	6
243.2.e.a.190.2		12	108.59	even	18
243.2.e.b.109.1		12	108.23	even	18
243.2.e.b.136.1		12	36.23	even	6
243.2.e.c.109.2		12	108.31	odd	18
243.2.e.c.136.2		12	36.31	odd	6
243.2.e.d.55.1		12	36.7	odd	6
243.2.e.d.190.1		12	108.103	odd	18
432.2.u.c.241.2		12	1.1	even	1	trivial
432.2.u.c.337.2		12	27.13	even	9	inner
675.2.l.c.376.1		12	20.19	odd	2
675.2.l.c.526.1		12	540.499	odd	18
675.2.u.b.349.2		24	20.3	even	4
675.2.u.b.349.3		24	20.7	even	4
675.2.u.b.499.2		24	540.67	even	36
675.2.u.b.499.3		24	540.283	even	36
729.2.a.a.1.5		6	108.43	odd	18
729.2.a.d.1.2		6	108.11	even	18
729.2.c.b.244.5		12	108.47	even	18
729.2.c.b.487.5		12	108.83	even	18
729.2.c.e.244.2		12	108.7	odd	18
729.2.c.e.487.2		12	108.79	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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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