LMFDB - Embedded newform 729.2.c.a.244.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(244,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.244"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-3,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.1
Root			$0.0878222i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.a.487.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35253 - 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(0.836192 - 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} +8.97372 q^{8} -4.52391 q^{10} +(0.958859 + 1.66079i) q^{11} +(-1.55622 + 2.69545i) q^{13} +(-0.677066 + 1.17271i) q^{14} +(-6.81987 - 11.8124i) q^{16} +2.66467 q^{17} +5.79664 q^{19} +(4.44635 + 7.70130i) q^{20} +(2.59378 - 4.49255i) q^{22} +(2.32293 - 4.02344i) q^{23} +(1.10156 + 1.90797i) q^{25} +8.41934 q^{26} +2.66183 q^{28} +(1.30754 + 2.26472i) q^{29} +(2.30730 - 3.99636i) q^{31} +(-9.47446 + 16.4103i) q^{32} +(-3.60406 - 6.24241i) q^{34} -0.837181 q^{35} -4.85867 q^{37} +(-7.84014 - 13.5795i) q^{38} +(7.50375 - 12.9969i) q^{40} +(5.77408 - 10.0010i) q^{41} +(4.50217 + 7.79798i) q^{43} -10.1972 q^{44} -12.5674 q^{46} +(-3.41612 - 5.91689i) q^{47} +(3.37470 - 5.84516i) q^{49} +(2.97980 - 5.16117i) q^{50} +(-8.27499 - 14.3327i) q^{52} -5.43322 q^{53} +3.20716 q^{55} +(-2.24608 - 3.89033i) q^{56} +(3.53697 - 6.12621i) q^{58} +(1.09566 - 1.89773i) q^{59} +(-3.42017 - 5.92391i) q^{61} -12.4828 q^{62} +23.9786 q^{64} +(2.60259 + 4.50783i) q^{65} +(-6.24180 + 10.8111i) q^{67} +(-7.08453 + 12.2708i) q^{68} +(1.13231 + 1.96123i) q^{70} -2.83568 q^{71} +9.93497 q^{73} +(6.57151 + 11.3822i) q^{74} +(-15.4114 + 26.6934i) q^{76} +(0.479996 - 0.831378i) q^{77} +(-2.65561 - 4.59964i) q^{79} -22.8109 q^{80} -31.2385 q^{82} +(1.36408 + 2.36265i) q^{83} +(2.22818 - 3.85932i) q^{85} +(12.1787 - 21.0941i) q^{86} +(8.60453 + 14.9035i) q^{88} +11.2189 q^{89} +1.55806 q^{91} +(12.3519 + 21.3941i) q^{92} +(-9.24082 + 16.0056i) q^{94} +(4.84710 - 8.39543i) q^{95} +(3.44457 + 5.96617i) q^{97} -18.2576 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28}+ \cdots + 36 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.35253	−	2.34265i	−0.956385	−	1.65651i	−0.731167	−	0.682199i	$-0.761024\pi$
$2$	−1.35253	−	2.34265i	−0.956385	−	1.65651i	−0.225218	−	0.974308i	$-0.572309\pi$
$3$		0			0
$3$		0			0
$4$	−2.65869	+	4.60498i	−1.32934	+	2.30249i
$5$	0.836192	−	1.44833i	0.373957	−	0.647712i	−0.616214	−	0.787579i	$-0.711334\pi$
$5$	0.836192	−	1.44833i	0.373957	−	0.647712i	0.990170	+	0.139867i	$0.0446676\pi$
$6$		0			0
$7$	−0.250296	−	0.433525i	−0.0946028	−	0.163857i	0.814840	−	0.579686i	$-0.196825\pi$
$7$	−0.250296	−	0.433525i	−0.0946028	−	0.163857i	−0.909443	+	0.415829i	$0.863491\pi$
$8$	8.97372			3.17269
$9$		0			0
$10$	−4.52391			−1.43059
$11$	0.958859	+	1.66079i	0.289107	+	0.500748i	0.973597	−	0.228275i	$-0.0733084\pi$
$11$	0.958859	+	1.66079i	0.289107	+	0.500748i	−0.684490	+	0.729022i	$0.739975\pi$
$12$		0			0
$13$	−1.55622	+	2.69545i	−0.431617	+	0.747583i	−0.997013	−	0.0772371i	$-0.975390\pi$
$13$	−1.55622	+	2.69545i	−0.431617	+	0.747583i	0.565396	+	0.824820i	$0.308723\pi$
$14$	−0.677066	+	1.17271i	−0.180953	+	0.313421i
$15$		0			0
$16$	−6.81987	−	11.8124i	−1.70497	−	2.95309i
$17$	2.66467			0.646278			0.323139	−	0.946352i	$-0.395262\pi$
$17$	2.66467			0.646278			0.323139	+	0.946352i	$0.395262\pi$
$18$		0			0
$19$	5.79664			1.32984			0.664920	−	0.746915i	$-0.268466\pi$
$19$	5.79664			1.32984			0.664920	+	0.746915i	$0.268466\pi$
$20$	4.44635	+	7.70130i	0.994234	+	1.72206i
$21$		0			0
$22$	2.59378	−	4.49255i	0.552995	−	0.957815i
$23$	2.32293	−	4.02344i	0.484365	−	0.838945i	−0.515473	−	0.856906i	$-0.672384\pi$
$23$	2.32293	−	4.02344i	0.484365	−	0.838945i	0.999839	+	0.0179603i	$0.00571725\pi$
$24$		0			0
$25$	1.10156	+	1.90797i	0.220313	+	0.381593i
$26$	8.41934			1.65117
$27$		0			0
$28$	2.66183			0.503039
$29$	1.30754	+	2.26472i	0.242803	+	0.420547i	0.961512	−	0.274764i	$-0.0885997\pi$
$29$	1.30754	+	2.26472i	0.242803	+	0.420547i	−0.718709	+	0.695312i	$0.755266\pi$
$30$		0			0
$31$	2.30730	−	3.99636i	0.414404	−	0.717768i	−0.580962	−	0.813931i	$-0.697324\pi$
$31$	2.30730	−	3.99636i	0.414404	−	0.717768i	0.995366	+	0.0961626i	$0.0306569\pi$
$32$	−9.47446	+	16.4103i	−1.67486	+	2.90095i
$33$		0			0
$34$	−3.60406	−	6.24241i	−0.618090	−	1.07056i
$35$	−0.837181			−0.141509
$36$		0			0
$37$	−4.85867			−0.798761			−0.399381	−	0.916785i	$-0.630775\pi$
$37$	−4.85867			−0.798761			−0.399381	+	0.916785i	$0.630775\pi$
$38$	−7.84014	−	13.5795i	−1.27184	−	2.20289i
$39$		0			0
$40$	7.50375	−	12.9969i	1.18645	−	2.05499i
$41$	5.77408	−	10.0010i	0.901760	−	1.56189i	0.0765514	−	0.997066i	$-0.475609\pi$
$41$	5.77408	−	10.0010i	0.901760	−	1.56189i	0.825208	−	0.564828i	$-0.191058\pi$
$42$		0			0
$43$	4.50217	+	7.79798i	0.686574	+	1.18918i	0.972939	+	0.231061i	$0.0742196\pi$
$43$	4.50217	+	7.79798i	0.686574	+	1.18918i	−0.286365	+	0.958121i	$0.592447\pi$
$44$	−10.1972			−1.53729
$45$		0			0
$46$	−12.5674			−1.85296
$47$	−3.41612	−	5.91689i	−0.498292	−	0.863067i	0.501706	−	0.865038i	$-0.332706\pi$
$47$	−3.41612	−	5.91689i	−0.498292	−	0.863067i	−0.999998	+	0.00197091i	$0.999373\pi$
$48$		0			0
$49$	3.37470	−	5.84516i	0.482101	−	0.835023i
$50$	2.97980	−	5.16117i	0.421408	−	0.729900i
$51$		0			0
$52$	−8.27499	−	14.3327i	−1.14754	−	1.98759i
$53$	−5.43322			−0.746309			−0.373155	−	0.927769i	$-0.621724\pi$
$53$	−5.43322			−0.746309			−0.373155	+	0.927769i	$0.621724\pi$
$54$		0			0
$55$	3.20716			0.432454
$56$	−2.24608	−	3.89033i	−0.300145	−	0.519867i
$57$		0			0
$58$	3.53697	−	6.12621i	0.464427	−	0.804410i
$59$	1.09566	−	1.89773i	0.142642	−	0.247064i	−0.785849	−	0.618419i	$-0.787773\pi$
$59$	1.09566	−	1.89773i	0.142642	−	0.247064i	0.928491	+	0.371355i	$0.121107\pi$
$60$		0			0
$61$	−3.42017	−	5.92391i	−0.437908	−	0.758478i	0.559620	−	0.828749i	$-0.310947\pi$
$61$	−3.42017	−	5.92391i	−0.437908	−	0.758478i	−0.997528	+	0.0702708i	$0.977614\pi$
$62$	−12.4828			−1.58532
$63$		0			0
$64$	23.9786			2.99733
$65$	2.60259	+	4.50783i	0.322812	+	0.559127i
$66$		0			0
$67$	−6.24180	+	10.8111i	−0.762557	+	1.32079i	0.178971	+	0.983854i	$0.442723\pi$
$67$	−6.24180	+	10.8111i	−0.762557	+	1.32079i	−0.941529	+	0.336933i	$0.890610\pi$
$68$	−7.08453	+	12.2708i	−0.859126	+	1.48805i
$69$		0			0
$70$	1.13231	+	1.96123i	0.135337	+	0.234411i
$71$	−2.83568			−0.336534			−0.168267	−	0.985741i	$-0.553817\pi$
$71$	−2.83568			−0.336534			−0.168267	+	0.985741i	$0.553817\pi$
$72$		0			0
$73$	9.93497			1.16280			0.581400	−	0.813618i	$-0.302505\pi$
$73$	9.93497			1.16280			0.581400	+	0.813618i	$0.302505\pi$
$74$	6.57151	+	11.3822i	0.763923	+	1.32315i
$75$		0			0
$76$	−15.4114	+	26.6934i	−1.76781	+	3.06194i
$77$	0.479996	−	0.831378i	0.0547007	−	0.0947443i
$78$		0			0
$79$	−2.65561	−	4.59964i	−0.298779	−	0.517500i	0.677078	−	0.735911i	$-0.263246\pi$
$79$	−2.65561	−	4.59964i	−0.298779	−	0.517500i	−0.975857	+	0.218411i	$0.929913\pi$
$80$	−22.8109			−2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	1.36408	+	2.36265i	0.149727	+	0.259334i	0.931126	−	0.364697i	$-0.118827\pi$
$83$	1.36408	+	2.36265i	0.149727	+	0.259334i	−0.781400	+	0.624031i	$0.785494\pi$
$84$		0			0
$85$	2.22818	−	3.85932i	0.241680	−	0.418602i
$86$	12.1787	−	21.0941i	1.31326	−	2.27463i
$87$		0			0
$88$	8.60453	+	14.9035i	0.917246	+	1.58872i
$89$	11.2189			1.18920			0.594600	−	0.804021i	$-0.297310\pi$
$89$	11.2189			1.18920			0.594600	+	0.804021i	$0.297310\pi$
$90$		0			0
$91$	1.55806			0.163329
$92$	12.3519	+	21.3941i	1.28778	+	2.23049i
$93$		0			0
$94$	−9.24082	+	16.0056i	−0.953118	+	1.65085i
$95$	4.84710	−	8.39543i	0.497302	−	0.861353i
$96$		0			0
$97$	3.44457	+	5.96617i	0.349743	+	0.605773i	0.986204	−	0.165536i	$-0.0529355\pi$
$97$	3.44457	+	5.96617i	0.349743	+	0.605773i	−0.636461	+	0.771309i	$0.719602\pi$
$98$	−18.2576			−1.84429
$99$		0			0
$100$	−11.7149			−1.17149
$101$	−1.86482	−	3.22997i	−0.185557	−	0.321394i	0.758207	−	0.652014i	$-0.226076\pi$
$101$	−1.86482	−	3.22997i	−0.185557	−	0.321394i	−0.943764	+	0.330620i	$0.892742\pi$
$102$		0			0
$103$	−3.84040	+	6.65177i	−0.378406	+	0.655418i	−0.990830	−	0.135111i	$-0.956861\pi$
$103$	−3.84040	+	6.65177i	−0.378406	+	0.655418i	0.612425	+	0.790529i	$0.290194\pi$
$104$	−13.9651	+	24.1882i	−1.36939	+	2.37185i
$105$		0			0
$106$	7.34860	+	12.7281i	0.713759	+	1.23627i
$107$	−10.7658			−1.04077			−0.520383	−	0.853933i	$-0.674211\pi$
$107$	−10.7658			−1.04077			−0.520383	+	0.853933i	$0.674211\pi$
$108$		0			0
$109$	12.2298			1.17141			0.585703	−	0.810526i	$-0.300819\pi$
$109$	12.2298			1.17141			0.585703	+	0.810526i	$0.300819\pi$
$110$	−4.33779	−	7.51328i	−0.413592	−	0.716363i
$111$		0			0
$112$	−3.41396	+	5.91316i	−0.322589	+	0.558741i
$113$	0.971975	−	1.68351i	0.0914357	−	0.158371i	−0.816680	−	0.577091i	$-0.804188\pi$
$113$	0.971975	−	1.68351i	0.0914357	−	0.158371i	0.908115	+	0.418720i	$0.137521\pi$
$114$		0			0
$115$	−3.88484	−	6.72874i	−0.362263	−	0.627458i
$116$	−13.9053			−1.29108
$117$		0			0
$118$	−5.92764			−0.545684
$119$	−0.666956	−	1.15520i	−0.0611397	−	0.105897i
$120$		0			0
$121$	3.66118	−	6.34135i	0.332834	−	0.576486i
$122$	−9.25178	+	16.0245i	−0.837617	+	1.45079i
$123$		0			0
$124$	12.2688	+	21.2502i	1.10177	+	1.90832i
$125$	12.0464			1.07746
$126$		0			0
$127$	2.34433			0.208026			0.104013	−	0.994576i	$-0.466832\pi$
$127$	2.34433			0.208026			0.104013	+	0.994576i	$0.466832\pi$
$128$	−13.4829	−	23.3531i	−1.19173	−	2.06414i
$129$		0			0
$130$	7.04019	−	12.1940i	0.617465	−	1.06948i
$131$	8.55119	−	14.8111i	0.747121	−	1.29405i	−0.202076	−	0.979370i	$-0.564769\pi$
$131$	8.55119	−	14.8111i	0.747121	−	1.29405i	0.949197	−	0.314682i	$-0.101898\pi$
$132$		0			0
$133$	−1.45087	−	2.51298i	−0.125807	−	0.217903i
$134$	33.7689			2.91719
$135$		0			0
$136$	23.9120			2.05044
$137$	−6.96358	−	12.0613i	−0.594939	−	1.03046i	−0.993556	−	0.113347i	$-0.963843\pi$
$137$	−6.96358	−	12.0613i	−0.594939	−	1.03046i	0.398617	−	0.917118i	$-0.369490\pi$
$138$		0			0
$139$	−3.95832	+	6.85601i	−0.335740	+	0.581519i	−0.983627	−	0.180218i	$-0.942320\pi$
$139$	−3.95832	+	6.85601i	−0.335740	+	0.581519i	0.647887	+	0.761737i	$0.275653\pi$
$140$	2.22580	−	3.85520i	0.188115	−	0.325824i
$141$		0			0
$142$	3.83536	+	6.64303i	0.321856	+	0.557471i
$143$	−5.96877			−0.499134
$144$		0			0
$145$	4.37340			0.363191
$146$	−13.4374	−	23.2742i	−1.11208	−	1.92619i
$147$		0			0
$148$	12.9177	−	22.3741i	1.06183	−	1.83914i
$149$	−0.364067	+	0.630583i	−0.0298255	+	0.0516594i	−0.880553	−	0.473948i	$-0.842829\pi$
$149$	−0.364067	+	0.630583i	−0.0298255	+	0.0516594i	0.850727	+	0.525607i	$0.176162\pi$
$150$		0			0
$151$	−2.17105	−	3.76036i	−0.176677	−	0.306014i	0.764063	−	0.645141i	$-0.223202\pi$
$151$	−2.17105	−	3.76036i	−0.176677	−	0.306014i	−0.940740	+	0.339128i	$0.889868\pi$
$152$	52.0174			4.21917
$153$		0			0
$154$	−2.59684			−0.209260
$155$	−3.85870	−	6.68346i	−0.309938	−	0.536828i
$156$		0			0
$157$	7.76163	−	13.4435i	0.619446	−	1.07291i	−0.370141	−	0.928975i	$-0.620691\pi$
$157$	7.76163	−	13.4435i	0.619446	−	1.07291i	0.989587	−	0.143936i	$-0.0459759\pi$
$158$	−7.18359	+	12.4423i	−0.571495	+	0.989859i
$159$		0			0
$160$	15.8449	+	27.4443i	1.25265	+	2.16966i
$161$	−2.32568			−0.183289
$162$		0			0
$163$	8.49738			0.665566			0.332783	−	0.943003i	$-0.392012\pi$
$163$	8.49738			0.665566			0.332783	+	0.943003i	$0.392012\pi$
$164$	30.7030	+	53.1791i	2.39750	+	4.15259i
$165$		0			0
$166$	3.68991	−	6.39111i	0.286393	−	0.496047i
$167$	−11.5710	+	20.0415i	−0.895389	+	1.55086i	−0.0620658	+	0.998072i	$0.519769\pi$
$167$	−11.5710	+	20.0415i	−0.895389	+	1.55086i	−0.833323	+	0.552787i	$0.813564\pi$
$168$		0			0
$169$	1.65637	+	2.86892i	0.127413	+	0.220686i
$170$	−12.0547			−0.924556
$171$		0			0
$172$	−47.8794			−3.65077
$173$	1.28924	+	2.23303i	0.0980190	+	0.169774i	0.910865	−	0.412705i	$-0.135416\pi$
$173$	1.28924	+	2.23303i	0.0980190	+	0.169774i	−0.812846	+	0.582479i	$0.802083\pi$
$174$		0			0
$175$	0.551433	−	0.955111i	0.0416845	−	0.0721996i
$176$	13.0786	−	22.6528i	0.985835	−	1.70752i
$177$		0			0
$178$	−15.1739	−	26.2820i	−1.13733	−	1.96992i
$179$	−8.89613			−0.664928			−0.332464	−	0.943116i	$-0.607880\pi$
$179$	−8.89613			−0.664928			−0.332464	+	0.943116i	$0.607880\pi$
$180$		0			0
$181$	7.91183			0.588082			0.294041	−	0.955793i	$-0.405000\pi$
$181$	7.91183			0.588082			0.294041	+	0.955793i	$0.405000\pi$
$182$	−2.10732	−	3.64999i	−0.156205	−	0.270555i
$183$		0			0
$184$	20.8454	−	36.1052i	1.53674	−	2.66171i
$185$	−4.06279	+	7.03695i	−0.298702	+	0.517367i
$186$		0			0
$187$	2.55504	+	4.42547i	0.186843	+	0.323622i
$188$	36.3296			2.64961
$189$		0			0
$190$	−26.2235			−1.90245
$191$	7.94867	+	13.7675i	0.575146	+	0.996182i	0.996026	+	0.0890656i	$0.0283881\pi$
$191$	7.94867	+	13.7675i	0.575146	+	0.996182i	−0.420880	+	0.907116i	$0.638279\pi$
$192$		0			0
$193$	2.29239	−	3.97054i	0.165010	−	0.285805i	−0.771649	−	0.636049i	$-0.780568\pi$
$193$	2.29239	−	3.97054i	0.165010	−	0.285805i	0.936659	+	0.350243i	$0.113901\pi$
$194$	9.31779	−	16.1389i	0.668978	−	1.15870i
$195$		0			0
$196$	17.9446	+	31.0809i	1.28176	+	2.22006i
$197$	2.99417			0.213326			0.106663	−	0.994295i	$-0.465983\pi$
$197$	2.99417			0.213326			0.106663	+	0.994295i	$0.465983\pi$
$198$		0			0
$199$	14.8885			1.05542			0.527709	−	0.849425i	$-0.323051\pi$
$199$	14.8885			1.05542			0.527709	+	0.849425i	$0.323051\pi$
$200$	9.88513	+	17.1215i	0.698984	+	1.21068i
$201$		0			0
$202$	−5.04447	+	8.73727i	−0.354928	+	0.614753i
$203$	0.654541	−	1.13370i	0.0459397	−	0.0795700i
$204$		0			0
$205$	−9.65648	−	16.7255i	−0.674438	−	1.16816i
$206$	20.7771			1.44761
$207$		0			0
$208$	42.4528			2.94357
$209$	5.55816	+	9.62701i	0.384466	+	0.665914i
$210$		0			0
$211$	−6.93948	+	12.0195i	−0.477733	+	0.827459i	−0.999674	−	0.0255232i	$-0.991875\pi$
$211$	−6.93948	+	12.0195i	−0.477733	+	0.827459i	0.521941	+	0.852982i	$0.325208\pi$
$212$	14.4452	−	25.0199i	0.992102	−	1.71837i
$213$		0			0
$214$	14.5610	+	25.2205i	0.995372	+	1.72403i
$215$	15.0587			1.02700
$216$		0			0
$217$	−2.31003			−0.156815
$218$	−16.5412	−	28.6503i	−1.12031	−	1.94044i
$219$		0			0
$220$	−8.52684	+	14.7689i	−0.574880	+	0.995721i
$221$	−4.14681	+	7.18248i	−0.278945	+	0.483146i
$222$		0			0
$223$	3.40599	+	5.89935i	0.228082	+	0.395050i	0.957240	−	0.289296i	$-0.0934213\pi$
$223$	3.40599	+	5.89935i	0.228082	+	0.395050i	−0.729158	+	0.684346i	$0.760088\pi$
$224$	9.48567			0.633788
$225$		0			0
$226$	−5.25851			−0.349791
$227$	4.87042	+	8.43582i	0.323261	+	0.559905i	0.981159	−	0.193202i	$-0.0618874\pi$
$227$	4.87042	+	8.43582i	0.323261	+	0.559905i	−0.657898	+	0.753107i	$0.728554\pi$
$228$		0			0
$229$	7.02242	−	12.1632i	0.464055	−	0.803766i	−0.535104	−	0.844786i	$-0.679727\pi$
$229$	7.02242	−	12.1632i	0.464055	−	0.803766i	0.999158	+	0.0410201i	$0.0130608\pi$
$230$	−10.5087	+	18.2017i	−0.692926	+	1.20018i
$231$		0			0
$232$	11.7334	+	20.3229i	0.770339	+	1.33427i
$233$	5.32333			0.348743			0.174372	−	0.984680i	$-0.444211\pi$
$233$	5.32333			0.348743			0.174372	+	0.984680i	$0.444211\pi$
$234$		0			0
$235$	−11.4261			−0.745359
$236$	5.82602	+	10.0910i	0.379241	+	0.656865i
$237$		0			0
$238$	−1.80416	+	3.12489i	−0.116946	+	0.202557i
$239$	−8.88675	+	15.3923i	−0.574836	+	0.995646i	0.421223	+	0.906957i	$0.361601\pi$
$239$	−8.88675	+	15.3923i	−0.574836	+	0.995646i	−0.996059	+	0.0886886i	$0.971732\pi$
$240$		0			0
$241$	1.00340	+	1.73793i	0.0646344	+	0.111950i	0.896532	−	0.442979i	$-0.146079\pi$
$241$	1.00340	+	1.73793i	0.0646344	+	0.111950i	−0.831897	+	0.554930i	$0.812745\pi$
$242$	−19.8075			−1.27327
$243$		0			0
$244$	36.3726			2.32852
$245$	−5.64380	−	9.77536i	−0.360569	−	0.624525i
$246$		0			0
$247$	−9.02083	+	15.6245i	−0.573981	+	0.994165i
$248$	20.7051	−	35.8622i	1.31477	−	2.27725i
$249$		0			0
$250$	−16.2932	−	28.2206i	−1.03047	−	1.78483i
$251$	23.5643			1.48737			0.743683	−	0.668533i	$-0.233077\pi$
$251$	23.5643			1.48737			0.743683	+	0.668533i	$0.233077\pi$
$252$		0			0
$253$	8.90947			0.560133
$254$	−3.17079	−	5.49196i	−0.198953	−	0.344596i
$255$		0			0
$256$	−12.4936	+	21.6395i	−0.780848	+	1.35247i
$257$	−2.93728	+	5.08752i	−0.183223	+	0.317351i	−0.942976	−	0.332860i	$-0.891986\pi$
$257$	−2.93728	+	5.08752i	−0.183223	+	0.317351i	0.759754	+	0.650211i	$0.225320\pi$
$258$		0			0
$259$	1.21610	+	2.10635i	0.0755651	+	0.130883i
$260$	−27.6779			−1.71651
$261$		0			0
$262$	−46.2631			−2.85814
$263$	−10.9891	−	19.0336i	−0.677615	−	1.17366i	−0.975697	−	0.219123i	$-0.929680\pi$
$263$	−10.9891	−	19.0336i	−0.677615	−	1.17366i	0.298082	−	0.954540i	$-0.403653\pi$
$264$		0			0
$265$	−4.54321	+	7.86908i	−0.279087	+	0.483393i
$266$	−3.92470	+	6.79779i	−0.240639	+	0.416799i
$267$		0			0
$268$	−33.1900	−	57.4867i	−2.02740	−	3.51156i
$269$	−30.6026			−1.86587			−0.932937	−	0.360041i	$-0.882763\pi$
$269$	−30.6026			−1.86587			−0.932937	+	0.360041i	$0.882763\pi$
$270$		0			0
$271$	−16.0823			−0.976928			−0.488464	−	0.872584i	$-0.662443\pi$
$271$	−16.0823			−0.976928			−0.488464	+	0.872584i	$0.662443\pi$
$272$	−18.1727	−	31.4761i	−1.10188	−	1.90852i
$273$		0			0
$274$	−18.8369	+	32.6265i	−1.13798	+	1.97104i
$275$	−2.11249	+	3.65894i	−0.127388	+	0.220642i
$276$		0			0
$277$	10.4068	+	18.0251i	0.625283	+	1.08302i	0.988486	+	0.151312i	$0.0483499\pi$
$277$	10.4068	+	18.0251i	0.625283	+	1.08302i	−0.363203	+	0.931710i	$0.618317\pi$
$278$	21.4150			1.28439
$279$		0			0
$280$	−7.51263			−0.448965
$281$	−6.13014	−	10.6177i	−0.365693	−	0.633400i	0.623194	−	0.782067i	$-0.285835\pi$
$281$	−6.13014	−	10.6177i	−0.365693	−	0.633400i	−0.988887	+	0.148668i	$0.952501\pi$
$282$		0			0
$283$	−2.28629	+	3.95997i	−0.135906	+	0.235396i	−0.925943	−	0.377663i	$-0.876728\pi$
$283$	−2.28629	+	3.95997i	−0.135906	+	0.235396i	0.790037	+	0.613059i	$0.210061\pi$
$284$	7.53920	−	13.0583i	0.447369	−	0.774866i
$285$		0			0
$286$	8.07296	+	13.9828i	0.477364	+	0.826819i
$287$	−5.78091			−0.341236
$288$		0			0
$289$	−9.89952			−0.582325
$290$	−5.91517	−	10.2454i	−0.347351	−	0.601629i
$291$		0			0
$292$	−26.4140	+	45.7504i	−1.54576	+	2.67734i
$293$	−13.0617	+	22.6235i	−0.763073	+	1.32168i	0.178186	+	0.983997i	$0.442977\pi$
$293$	−13.0617	+	22.6235i	−0.763073	+	1.32168i	−0.941259	+	0.337685i	$0.890356\pi$
$294$		0			0
$295$	−1.83236	−	3.17374i	−0.106684	−	0.184782i
$296$	−43.6004			−2.53422
$297$		0			0
$298$	1.96965			0.114099
$299$	7.22998	+	12.5227i	0.418121	+	0.724206i
$300$		0			0
$301$	2.25375	−	3.90360i	0.129904	−	0.225000i
$302$	−5.87282	+	10.1720i	−0.337943	+	0.585334i
$303$		0			0
$304$	−39.5323	−	68.4719i	−2.26733	−	3.92713i
$305$	−11.4397			−0.655034
$306$		0			0
$307$	3.29277			0.187928			0.0939641	−	0.995576i	$-0.470046\pi$
$307$	3.29277			0.187928			0.0939641	+	0.995576i	$0.470046\pi$
$308$	2.55232	+	4.42075i	0.145432	+	0.251896i
$309$		0			0
$310$	−10.4380	+	18.0792i	−0.592840	+	1.02683i
$311$	−17.3963	+	30.1313i	−0.986455	+	1.70859i	−0.351170	+	0.936312i	$0.614216\pi$
$311$	−17.3963	+	30.1313i	−0.986455	+	1.70859i	−0.635285	+	0.772278i	$0.719117\pi$
$312$		0			0
$313$	−5.31392	−	9.20398i	−0.300360	−	0.520239i	0.675857	−	0.737033i	$-0.263774\pi$
$313$	−5.31392	−	9.20398i	−0.300360	−	0.520239i	−0.976218	+	0.216793i	$0.930440\pi$
$314$	−41.9914			−2.36971
$315$		0			0
$316$	28.2417			1.58872
$317$	7.75011	+	13.4236i	0.435290	+	0.753944i	0.997319	−	0.0731733i	$-0.0233126\pi$
$317$	7.75011	+	13.4236i	0.435290	+	0.753944i	−0.562030	+	0.827117i	$0.689979\pi$
$318$		0			0
$319$	−2.50748	+	4.34309i	−0.140392	+	0.243166i
$320$	20.0507	−	34.7289i	1.12087	−	1.94140i
$321$		0			0
$322$	3.14556	+	5.44827i	0.175295	+	0.303620i
$323$	15.4461			0.859446
$324$		0			0
$325$	−6.85710			−0.380363
$326$	−11.4930	−	19.9064i	−0.636538	−	1.10252i
$327$		0			0
$328$	51.8150	−	89.7461i	2.86100	−	4.95540i
$329$	−1.71008	+	2.96194i	−0.0942797	+	0.163297i
$330$		0			0
$331$	7.28514	+	12.6182i	0.400427	+	0.693561i	0.993777	−	0.111384i	$-0.0355283\pi$
$331$	7.28514	+	12.6182i	0.400427	+	0.693561i	−0.593350	+	0.804945i	$0.702195\pi$
$332$	−14.5066			−0.796153
$333$		0			0
$334$	62.6005			3.42534
$335$	10.4387	+	18.0803i	0.570327	+	0.987834i
$336$		0			0
$337$	10.3074	−	17.8529i	0.561479	−	0.972511i	−0.435888	−	0.900001i	$-0.643566\pi$
$337$	10.3074	−	17.8529i	0.561479	−	0.972511i	0.997368	−	0.0725099i	$-0.0231009\pi$
$338$	4.48060	−	7.76062i	0.243712	−	0.422122i
$339$		0			0
$340$	11.8481	+	20.5214i	0.642551	+	1.11293i
$341$	8.84951			0.479228
$342$		0			0
$343$	−6.88283			−0.371638
$344$	40.4012	+	69.9769i	2.17829	+	3.77290i
$345$		0			0
$346$	3.48748	−	6.04048i	0.187488	−	0.324738i
$347$	10.5918	−	18.3455i	0.568596	−	0.984838i	−0.428109	−	0.903727i	$-0.640820\pi$
$347$	10.5918	−	18.3455i	0.568596	−	0.984838i	0.996705	−	0.0811104i	$-0.0258466\pi$
$348$		0			0
$349$	2.31299	+	4.00621i	0.123811	+	0.214447i	0.921268	−	0.388929i	$-0.127155\pi$
$349$	2.31299	+	4.00621i	0.123811	+	0.214447i	−0.797456	+	0.603377i	$0.793822\pi$
$350$	−2.98333			−0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	6.82171	+	11.8155i	0.363083	+	0.628878i	0.988467	−	0.151440i	$-0.0483909\pi$
$353$	6.82171	+	11.8155i	0.363083	+	0.628878i	−0.625384	+	0.780317i	$0.715058\pi$
$354$		0			0
$355$	−2.37118	+	4.10700i	−0.125849	+	0.217977i
$356$	−29.8275	+	51.6628i	−1.58086	+	2.73812i
$357$		0			0
$358$	12.0323	+	20.8406i	0.635927	+	1.10146i
$359$	−28.2447			−1.49070			−0.745349	−	0.666675i	$-0.767717\pi$
$359$	−28.2447			−1.49070			−0.745349	+	0.666675i	$0.767717\pi$
$360$		0			0
$361$	14.6010			0.768473
$362$	−10.7010	−	18.5347i	−0.562432	−	0.974162i
$363$		0			0
$364$	−4.14239	+	7.17483i	−0.217120	+	0.376063i
$365$	8.30755	−	14.3891i	0.434837	−	0.753160i
$366$		0			0
$367$	−17.4401	−	30.2071i	−0.910366	−	1.57680i	−0.813548	−	0.581498i	$-0.802467\pi$
$367$	−17.4401	−	30.2071i	−0.910366	−	1.57680i	−0.0968183	−	0.995302i	$-0.530867\pi$
$368$	−63.3684			−3.30331
$369$		0			0
$370$	21.9802			1.14270
$371$	1.35991	+	2.35543i	0.0706030	+	0.122288i
$372$		0			0
$373$	−1.52972	+	2.64955i	−0.0792059	+	0.137189i	−0.902908	−	0.429835i	$-0.858572\pi$
$373$	−1.52972	+	2.64955i	−0.0792059	+	0.137189i	0.823702	+	0.567023i	$0.191905\pi$
$374$	6.91156	−	11.9712i	0.357388	−	0.619015i
$375$		0			0
$376$	−30.6553	−	53.0965i	−1.58093	−	2.73824i
$377$	−8.13924			−0.419192
$378$		0			0
$379$	−7.67705			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$379$	−7.67705			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$380$	25.7739	+	44.6417i	1.32217	+	2.29007i
$381$		0			0
$382$	21.5017	−	37.2420i	1.10012	−	1.90547i
$383$	−5.18097	+	8.97370i	−0.264735	+	0.458535i	−0.967494	−	0.252893i	$-0.918618\pi$
$383$	−5.18097	+	8.97370i	−0.264735	+	0.458535i	0.702759	+	0.711428i	$0.251951\pi$
$384$		0			0
$385$	−0.802739	−	1.39038i	−0.0409113	−	0.0708605i
$386$	−12.4021			−0.631252
$387$		0			0
$388$	−36.6322			−1.85972
$389$	0.213476	+	0.369751i	0.0108236	+	0.0187471i	0.871386	−	0.490597i	$-0.163221\pi$
$389$	0.213476	+	0.369751i	0.0108236	+	0.0187471i	−0.860563	+	0.509344i	$0.829888\pi$
$390$		0			0
$391$	6.18986	−	10.7211i	0.313035	−	0.542192i
$392$	30.2836	−	52.4528i	1.52955	−	2.64927i
$393$		0			0
$394$	−4.04971	−	7.01430i	−0.204021	−	0.353376i
$395$	−8.88239			−0.446922
$396$		0			0
$397$	−27.0891			−1.35956			−0.679781	−	0.733416i	$-0.737925\pi$
$397$	−27.0891			−1.35956			−0.679781	+	0.733416i	$0.737925\pi$
$398$	−20.1372	−	34.8786i	−1.00939	−	1.74831i
$399$		0			0
$400$	15.0250	−	26.0241i	0.751252	−	1.30121i
$401$	−14.6802	+	25.4269i	−0.733096	+	1.26976i	0.222458	+	0.974942i	$0.428592\pi$
$401$	−14.6802	+	25.4269i	−0.733096	+	1.26976i	−0.955554	+	0.294817i	$0.904741\pi$
$402$		0			0
$403$	7.18133	+	12.4384i	0.357727	+	0.619602i
$404$	19.8319			0.986675
$405$		0			0
$406$	−3.54115			−0.175744
$407$	−4.65878	−	8.06925i	−0.230927	−	0.399978i
$408$		0			0
$409$	10.0920	−	17.4798i	0.499015	−	0.864320i	−0.500984	−	0.865457i	$-0.667028\pi$
$409$	10.0920	−	17.4798i	0.499015	−	0.864320i	0.999999	+	0.00113651i	$0.000361762\pi$
$410$	−26.1214	+	45.2436i	−1.29004	+	2.23442i
$411$		0			0
$412$	−20.4208	−	35.3699i	−1.00606	−	1.74255i
$413$	−1.09695			−0.0539775
$414$		0			0
$415$	4.56252			0.223965
$416$	−29.4887	−	51.0758i	−1.44580	−	2.50420i
$417$		0			0
$418$	15.0352	−	26.0417i	0.735395	−	1.27374i
$419$	−12.1852	+	21.1053i	−0.595284	+	1.03106i	0.398223	+	0.917289i	$0.369627\pi$
$419$	−12.1852	+	21.1053i	−0.595284	+	1.03106i	−0.993507	+	0.113774i	$0.963706\pi$
$420$		0			0
$421$	13.0873	+	22.6678i	0.637835	+	1.10476i	0.985907	+	0.167294i	$0.0535030\pi$
$421$	13.0873	+	22.6678i	0.637835	+	1.10476i	−0.348072	+	0.937468i	$0.613164\pi$
$422$	37.5435			1.82759
$423$		0			0
$424$	−48.7561			−2.36781
$425$	2.93531	+	5.08410i	0.142383	+	0.246615i
$426$		0			0
$427$	−1.71211	+	2.96545i	−0.0828546	+	0.143508i
$428$	28.6228	−	49.5761i	1.38353	−	2.39635i
$429$		0			0
$430$	−20.3674	−	35.2774i	−0.982203	−	1.70123i
$431$	31.9185			1.53746			0.768731	−	0.639572i	$-0.220889\pi$
$431$	31.9185			1.53746			0.768731	+	0.639572i	$0.220889\pi$
$432$		0			0
$433$	0.0123080			0.000591484			0.000295742	−	1.00000i	$-0.499906\pi$
$433$	0.0123080			0.000591484			0.000295742		1.00000i	$0.499906\pi$
$434$	3.12439	+	5.41160i	0.149976	+	0.259765i
$435$		0			0
$436$	−32.5153	+	56.3182i	−1.55720	+	2.69715i
$437$	13.4652	−	23.3224i	0.644128	−	1.11566i
$438$		0			0
$439$	−2.65240	−	4.59410i	−0.126592	−	0.219264i	0.795762	−	0.605610i	$-0.207071\pi$
$439$	−2.65240	−	4.59410i	−0.126592	−	0.219264i	−0.922354	+	0.386345i	$0.873737\pi$
$440$	28.7802			1.37204
$441$		0			0
$442$	22.4348			1.06711
$443$	−20.3482	−	35.2441i	−0.966771	−	1.67450i	−0.704781	−	0.709425i	$-0.748955\pi$
$443$	−20.3482	−	35.2441i	−0.966771	−	1.67450i	−0.261990	−	0.965071i	$-0.584379\pi$
$444$		0			0
$445$	9.38116	−	16.2486i	0.444709	−	0.770259i
$446$	9.21342	−	15.9581i	0.436268	−	0.755639i
$447$		0			0
$448$	−6.00174	−	10.3953i	−0.283556	−	0.491133i
$449$	15.4280			0.728093			0.364047	−	0.931381i	$-0.381395\pi$
$449$	15.4280			0.728093			0.364047	+	0.931381i	$0.381395\pi$
$450$		0			0
$451$	22.1461			1.04282
$452$	5.16835	+	8.95185i	0.243099	+	0.421060i
$453$		0			0
$454$	13.1748	−	22.8194i	0.618324	−	1.07097i
$455$	1.30284	−	2.25658i	0.0610779	−	0.105790i
$456$		0			0
$457$	−1.19437	−	2.06872i	−0.0558704	−	0.0967704i	0.836737	−	0.547604i	$-0.184460\pi$
$457$	−1.19437	−	2.06872i	−0.0558704	−	0.0967704i	−0.892608	+	0.450834i	$0.851127\pi$
$458$	−37.9922			−1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	−16.2419	−	28.1319i	−0.756462	−	1.31023i	−0.944644	−	0.328097i	$-0.893593\pi$
$461$	−16.2419	−	28.1319i	−0.756462	−	1.31023i	0.188182	−	0.982134i	$-0.439741\pi$
$462$		0			0
$463$	−16.9393	+	29.3397i	−0.787234	+	1.36353i	0.140421	+	0.990092i	$0.455155\pi$
$463$	−16.9393	+	29.3397i	−0.787234	+	1.36353i	−0.927655	+	0.373438i	$0.878179\pi$
$464$	17.8344	−	30.8901i	0.827943	−	1.43404i
$465$		0			0
$466$	−7.19998	−	12.4707i	−0.333533	−	0.577696i
$467$	−13.8027			−0.638711			−0.319356	−	0.947635i	$-0.603466\pi$
$467$	−13.8027			−0.638711			−0.319356	+	0.947635i	$0.603466\pi$
$468$		0			0
$469$	6.24918			0.288560
$470$	15.4542	+	26.7675i	0.712850	+	1.23469i
$471$		0			0
$472$	9.83211	−	17.0297i	0.452559	−	0.783856i
$473$	−8.63389	+	14.9543i	−0.396987	+	0.687601i
$474$		0			0
$475$	6.38537	+	11.0598i	0.292981	+	0.507458i
$476$	7.09291			0.325103
$477$		0			0
$478$	48.0785			2.19906
$479$	−2.94556	−	5.10186i	−0.134586	−	0.233110i	0.790853	−	0.612006i	$-0.209637\pi$
$479$	−2.94556	−	5.10186i	−0.134586	−	0.233110i	−0.925439	+	0.378896i	$0.876304\pi$
$480$		0			0
$481$	7.56115	−	13.0963i	0.344759	−	0.597140i
$482$	2.71425	−	4.70122i	0.123631	−	0.214135i
$483$		0			0
$484$	19.4679	+	33.7193i	0.884903	+	1.53270i
$485$	11.5213			0.523155
$486$		0			0
$487$	29.0299			1.31547			0.657736	−	0.753249i	$-0.271514\pi$
$487$	29.0299			1.31547			0.657736	+	0.753249i	$0.271514\pi$
$488$	−30.6916	−	53.1594i	−1.38934	−	2.40642i
$489$		0			0
$490$	−15.2669	+	26.4430i	−0.689686	+	1.19457i
$491$	−2.19175	+	3.79623i	−0.0989125	+	0.171321i	−0.911235	−	0.411887i	$-0.864870\pi$
$491$	−2.19175	+	3.79623i	−0.0989125	+	0.171321i	0.812322	+	0.583209i	$0.198203\pi$
$492$		0			0
$493$	3.48415	+	6.03473i	0.156918	+	0.271791i
$494$	48.8038			2.19579
$495$		0			0
$496$	−62.9420			−2.82618
$497$	0.709759	+	1.22934i	0.0318371	+	0.0551434i
$498$		0			0
$499$	−17.6718	+	30.6084i	−0.791096	+	1.37022i	0.134192	+	0.990955i	$0.457156\pi$
$499$	−17.6718	+	30.6084i	−0.791096	+	1.37022i	−0.925289	+	0.379264i	$0.876177\pi$
$500$	−32.0276	+	55.4735i	−1.43232	+	2.48085i
$501$		0			0
$502$	−31.8715	−	55.2030i	−1.42249	−	2.46383i
$503$	−8.37659			−0.373494			−0.186747	−	0.982408i	$-0.559794\pi$
$503$	−8.37659			−0.373494			−0.186747	+	0.982408i	$0.559794\pi$
$504$		0			0
$505$	−6.23740			−0.277561
$506$	−12.0503	−	20.8718i	−0.535703	−	0.927865i
$507$		0			0
$508$	−6.23285	+	10.7956i	−0.276538	+	0.478978i
$509$	1.92148	−	3.32811i	0.0851683	−	0.147516i	−0.820295	−	0.571941i	$-0.806191\pi$
$509$	1.92148	−	3.32811i	0.0851683	−	0.147516i	0.905463	+	0.424425i	$0.139524\pi$
$510$		0			0
$511$	−2.48668	−	4.30706i	−0.110004	−	0.190533i
$512$	13.6601			0.603699
$513$		0			0
$514$	15.8911			0.700925
$515$	6.42262	+	11.1243i	0.283015	+	0.490196i
$516$		0			0
$517$	6.55115	−	11.3469i	0.288119	−	0.499037i
$518$	3.28964	−	5.69783i	0.144539	−	0.250348i
$519$		0			0
$520$	23.3549	+	40.4520i	1.02418	+	1.77394i
$521$	19.6523			0.860983			0.430491	−	0.902595i	$-0.358340\pi$
$521$	19.6523			0.860983			0.430491	+	0.902595i	$0.358340\pi$
$522$		0			0
$523$	−39.6103			−1.73204			−0.866018	−	0.500012i	$-0.833329\pi$
$523$	−39.6103			−1.73204			−0.866018	+	0.500012i	$0.833329\pi$
$524$	45.4699	+	78.7562i	1.98636	+	3.44048i
$525$		0			0
$526$	−29.7261	+	51.4872i	−1.29612	+	2.24495i
$527$	6.14820	−	10.6490i	0.267820	−	0.463878i
$528$		0			0
$529$	0.707953	+	1.22621i	0.0307806	+	0.0533135i
$530$	24.5794			1.06766
$531$		0			0
$532$	15.4297			0.668961
$533$	17.9715	+	31.1275i	0.778430	+	1.34828i
$534$		0			0
$535$	−9.00224	+	15.5923i	−0.389201	+	0.674116i
$536$	−56.0121	+	97.0159i	−2.41936	+	4.19045i
$537$		0			0
$538$	41.3910	+	71.6913i	1.78449	+	3.09083i
$539$	12.9435			0.557514
$540$		0			0
$541$	−41.8257			−1.79823			−0.899115	−	0.437713i	$-0.855788\pi$
$541$	−41.8257			−1.79823			−0.899115	+	0.437713i	$0.855788\pi$
$542$	21.7518	+	37.6752i	0.934319	+	1.61829i
$543$		0			0
$544$	−25.2463	+	43.7279i	−1.08243	+	1.87482i
$545$	10.2265	−	17.7128i	0.438055	−	0.758733i
$546$		0			0
$547$	8.51716	+	14.7522i	0.364168	+	0.630757i	0.988642	−	0.150288i	$-0.0480202\pi$
$547$	8.51716	+	14.7522i	0.364168	+	0.630757i	−0.624475	+	0.781045i	$0.714687\pi$
$548$	74.0559			3.16351
$549$		0			0
$550$	11.4288			0.487328
$551$	7.57931	+	13.1277i	0.322889	+	0.559261i
$552$		0			0
$553$	−1.32937	+	2.30254i	−0.0565307	+	0.0979140i
$554$	28.1510	−	48.7590i	1.19602	−	2.07157i
$555$		0			0
$556$	−21.0479	−	36.4560i	−0.892628	−	1.54608i
$557$	−33.7680			−1.43080			−0.715398	−	0.698717i	$-0.753755\pi$
$557$	−33.7680			−1.43080			−0.715398	+	0.698717i	$0.753755\pi$
$558$		0			0
$559$	−28.0254			−1.18535
$560$	5.70946	+	9.88908i	0.241269	+	0.417890i
$561$		0			0
$562$	−16.5824	+	28.7216i	−0.699487	+	1.21155i
$563$	11.3556	−	19.6685i	0.478583	−	0.828930i	−0.521115	−	0.853486i	$-0.674484\pi$
$563$	11.3556	−	19.6685i	0.478583	−	0.828930i	0.999698	+	0.0245561i	$0.00781725\pi$
$564$		0			0
$565$	−1.62552	−	2.81548i	−0.0683860	−	0.118448i
$566$	12.3691			0.519913
$567$		0			0
$568$	−25.4466			−1.06772
$569$	−5.43572	−	9.41495i	−0.227877	−	0.394695i	0.729301	−	0.684193i	$-0.239845\pi$
$569$	−5.43572	−	9.41495i	−0.227877	−	0.394695i	−0.957179	+	0.289497i	$0.906512\pi$
$570$		0			0
$571$	−7.44185	+	12.8897i	−0.311432	+	0.539416i	−0.978673	−	0.205426i	$-0.934142\pi$
$571$	−7.44185	+	12.8897i	−0.311432	+	0.539416i	0.667241	+	0.744842i	$0.267475\pi$
$572$	15.8691	−	27.4861i	0.663521	−	1.14925i
$573$		0			0
$574$	7.81886	+	13.5427i	0.326353	+	0.565260i
$575$	10.2354			0.426848
$576$		0			0
$577$	−37.1163			−1.54517			−0.772586	−	0.634910i	$-0.781037\pi$
$577$	−37.1163			−1.54517			−0.772586	+	0.634910i	$0.781037\pi$
$578$	13.3894	+	23.1912i	0.556927	+	0.964625i
$579$		0			0
$580$	−11.6275	+	20.1394i	−0.482806	+	0.836245i
$581$	0.682844	−	1.18272i	0.0283291	−	0.0490675i
$582$		0			0
$583$	−5.20969	−	9.02344i	−0.215763	−	0.373713i
$584$	89.1536			3.68920
$585$		0			0
$586$	70.6655			2.91917
$587$	−7.32161	−	12.6814i	−0.302195	−	0.523417i	0.674438	−	0.738332i	$-0.264386\pi$
$587$	−7.32161	−	12.6814i	−0.302195	−	0.523417i	−0.976633	+	0.214914i	$0.931053\pi$
$588$		0			0
$589$	13.3746	−	23.1655i	0.551090	−	0.954516i
$590$	−4.95665	+	8.58517i	−0.204062	+	0.353446i
$591$		0			0
$592$	33.1355	+	57.3924i	1.36186	+	2.35881i
$593$	−36.4392			−1.49638			−0.748189	−	0.663485i	$-0.769076\pi$
$593$	−36.4392			−1.49638			−0.748189	+	0.663485i	$0.769076\pi$
$594$		0			0
$595$	−2.23081			−0.0914544
$596$	−1.93588	−	3.35305i	−0.0792968	−	0.137346i
$597$		0			0
$598$	19.5576	−	33.8747i	0.799769	−	1.38524i
$599$	13.7474	−	23.8113i	0.561705	−	0.972902i	−0.435642	−	0.900120i	$-0.643479\pi$
$599$	13.7474	−	23.8113i	0.561705	−	0.972902i	0.997348	−	0.0727826i	$-0.0231879\pi$
$600$		0			0
$601$	−22.5885	−	39.1244i	−0.921404	−	1.59592i	−0.797245	−	0.603656i	$-0.793710\pi$
$601$	−22.5885	−	39.1244i	−0.921404	−	1.59592i	−0.124159	−	0.992262i	$-0.539623\pi$
$602$	−12.1931			−0.496952
$603$		0			0
$604$	23.0885			0.939459
$605$	−6.12290	−	10.6052i	−0.248931	−	0.431162i
$606$		0			0
$607$	−8.56858	+	14.8412i	−0.347788	+	0.602387i	−0.985856	−	0.167593i	$-0.946400\pi$
$607$	−8.56858	+	14.8412i	−0.347788	+	0.602387i	0.638068	+	0.769980i	$0.279734\pi$
$608$	−54.9200	+	95.1243i	−2.22730	+	3.85780i
$609$		0			0
$610$	15.4725	+	26.7992i	0.626464	+	1.08507i
$611$	21.2649			0.860286
$612$		0			0
$613$	−0.468761			−0.0189331			−0.00946653	−	0.999955i	$-0.503013\pi$
$613$	−0.468761			−0.0189331			−0.00946653	+	0.999955i	$0.503013\pi$
$614$	−4.45358	−	7.71382i	−0.179732	−	0.311304i
$615$		0			0
$616$	4.30735	−	7.46055i	0.173548	−	0.300594i
$617$	−1.06742	+	1.84883i	−0.0429729	+	0.0744312i	−0.886712	−	0.462323i	$-0.847016\pi$
$617$	−1.06742	+	1.84883i	−0.0429729	+	0.0744312i	0.843739	+	0.536754i	$0.180350\pi$
$618$		0			0
$619$	−4.26880	−	7.39378i	−0.171578	−	0.297181i	0.767394	−	0.641176i	$-0.221553\pi$
$619$	−4.26880	−	7.39378i	−0.171578	−	0.297181i	−0.938972	+	0.343995i	$0.888220\pi$
$620$	41.0363			1.64806
$621$		0			0
$622$	94.1163			3.77372
$623$	−2.80804	−	4.86367i	−0.112502	−	0.194859i
$624$		0			0
$625$	4.56529	−	7.90731i	0.182612	−	0.316292i
$626$	−14.3745	+	24.8974i	−0.574520	+	0.995098i
$627$		0			0
$628$	41.2715	+	71.4844i	1.64691	+	2.85254i
$629$	−12.9468			−0.516222
$630$		0			0
$631$	−11.8708			−0.472569			−0.236284	−	0.971684i	$-0.575930\pi$
$631$	−11.8708			−0.472569			−0.236284	+	0.971684i	$0.575930\pi$
$632$	−23.8307	−	41.2759i	−0.947933	−	1.64187i
$633$		0			0
$634$	20.9646	−	36.3117i	0.832609	−	1.44212i
$635$	1.96031	−	3.39536i	0.0777926	−	0.134741i
$636$		0			0
$637$	10.5035	+	18.1927i	0.416166	+	0.720820i
$638$	13.5658			0.537076
$639$		0			0
$640$	−45.0973			−1.78263
$641$	2.65183	+	4.59310i	0.104741	+	0.181417i	0.913632	−	0.406541i	$-0.133265\pi$
$641$	2.65183	+	4.59310i	0.104741	+	0.181417i	−0.808891	+	0.587958i	$0.799932\pi$
$642$		0			0
$643$	0.411934	−	0.713491i	0.0162451	−	0.0281374i	−0.857789	−	0.514003i	$-0.828162\pi$
$643$	0.411934	−	0.713491i	0.0162451	−	0.0281374i	0.874034	+	0.485865i	$0.161495\pi$
$644$	6.18326	−	10.7097i	0.243655	−	0.422022i
$645$		0			0
$646$	−20.8914	−	36.1850i	−0.821961	−	1.42368i
$647$	40.8373			1.60548			0.802740	−	0.596329i	$-0.203374\pi$
$647$	40.8373			1.60548			0.802740	+	0.596329i	$0.203374\pi$
$648$		0			0
$649$	4.20232			0.164955
$650$	9.27445	+	16.0638i	0.363774	+	0.630074i
$651$		0			0
$652$	−22.5919	+	39.1303i	−0.884767	+	1.53246i
$653$	0.534678	−	0.926090i	0.0209236	−	0.0362407i	−0.855374	−	0.518011i	$-0.826673\pi$
$653$	0.534678	−	0.926090i	0.0209236	−	0.0362407i	0.876298	+	0.481770i	$0.160006\pi$
$654$		0			0
$655$	−14.3009	−	24.7699i	−0.558782	−	0.967838i
$656$	−157.514			−6.14988
$657$		0			0
$658$	9.25175			0.360671
$659$	−14.3321	−	24.8240i	−0.558301	−	0.967006i	−0.997638	−	0.0686837i	$-0.978120\pi$
$659$	−14.3321	−	24.8240i	−0.558301	−	0.967006i	0.439337	−	0.898322i	$-0.355213\pi$
$660$		0			0
$661$	2.24786	−	3.89341i	0.0874316	−	0.151436i	−0.818993	−	0.573803i	$-0.805467\pi$
$661$	2.24786	−	3.89341i	0.0874316	−	0.151436i	0.906425	+	0.422367i	$0.138801\pi$
$662$	19.7068	−	34.1331i	0.765925	−	1.32662i
$663$		0			0
$664$	12.2408	+	21.2017i	0.475036	+	0.822787i
$665$	−4.85283			−0.188185
$666$		0			0
$667$	12.1493			0.470422
$668$	−61.5272	−	106.568i	−2.38056	−	4.12325i
$669$		0			0
$670$	28.2373	−	48.9085i	1.09090	−	1.88950i
$671$	6.55892	−	11.3604i	0.253204	−	0.438563i
$672$		0			0
$673$	−9.02929	−	15.6392i	−0.348054	−	0.602846i	0.637850	−	0.770161i	$-0.279824\pi$
$673$	−9.02929	−	15.6392i	−0.348054	−	0.602846i	−0.985904	+	0.167314i	$0.946491\pi$
$674$	−55.7643			−2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	7.86959	+	13.6305i	0.302453	+	0.523864i	0.976691	−	0.214650i	$-0.0688612\pi$
$677$	7.86959	+	13.6305i	0.302453	+	0.523864i	−0.674238	+	0.738514i	$0.735528\pi$
$678$		0			0
$679$	1.72432	−	2.98661i	0.0661734	−	0.114616i
$680$	19.9950	−	34.6324i	0.766775	−	1.32809i
$681$		0			0
$682$	−11.9692	−	20.7313i	−0.458326	−	0.793844i
$683$	2.76118			0.105654			0.0528268	−	0.998604i	$-0.483177\pi$
$683$	2.76118			0.105654			0.0528268	+	0.998604i	$0.483177\pi$
$684$		0			0
$685$	−23.2916			−0.889925
$686$	9.30925	+	16.1241i	0.355429	+	0.615621i
$687$		0			0
$688$	61.4084	−	106.362i	2.34117	−	4.05503i
$689$	8.45526	−	14.6449i	0.322120	−	0.557928i
$690$		0			0
$691$	17.2628	+	29.9000i	0.656707	+	1.13745i	0.981463	+	0.191652i	$0.0613844\pi$
$691$	17.2628	+	29.9000i	0.656707	+	1.13745i	−0.324756	+	0.945798i	$0.605282\pi$
$692$	−13.7107			−0.521204
$693$		0			0
$694$	−57.3029			−2.17519
$695$	6.61983	+	11.4659i	0.251104	+	0.434926i
$696$		0			0
$697$	15.3860	−	26.6494i	0.582787	−	1.00942i
$698$	6.25678	−	10.8371i	0.236822	−	0.410189i
$699$		0			0
$700$	2.93218	+	5.07868i	0.110826	+	0.191956i
$701$	20.7410			0.783378			0.391689	−	0.920098i	$-0.371891\pi$
$701$	20.7410			0.783378			0.391689	+	0.920098i	$0.371891\pi$
$702$		0			0
$703$	−28.1640			−1.06222
$704$	22.9921	+	39.8235i	0.866548	+	1.50090i
$705$		0			0
$706$	18.4532	−	31.9618i	0.694494	−	1.20290i
$707$	−0.933514	+	1.61689i	−0.0351084	+	0.0608095i
$708$		0			0
$709$	−13.8536	−	23.9951i	−0.520281	−	0.901154i	−0.999722	−	0.0235795i	$-0.992494\pi$
$709$	−13.8536	−	23.9951i	−0.520281	−	0.901154i	0.479441	−	0.877574i	$-0.340840\pi$
$710$	12.8284			0.481441
$711$		0			0
$712$	100.675			3.77296
$713$	−10.7194	−	18.5666i	−0.401445	−	0.695324i
$714$		0			0
$715$	−4.99104	+	8.64474i	−0.186654	+	0.323295i
$716$	23.6520	−	40.9665i	0.883918	−	1.53099i
$717$		0			0
$718$	38.2018	+	66.1675i	1.42568	+	2.46935i
$719$	−33.1314			−1.23559			−0.617797	−	0.786337i	$-0.711975\pi$
$719$	−33.1314			−1.23559			−0.617797	+	0.786337i	$0.711975\pi$
$720$		0			0
$721$	3.84494			0.143193
$722$	−19.7483	−	34.2051i	−0.734956	−	1.27298i
$723$		0			0
$724$	−21.0351	+	36.4338i	−0.781763	+	1.35405i
$725$	−2.88067	+	4.98946i	−0.106985	+	0.185304i
$726$		0			0
$727$	0.0413027	+	0.0715384i	0.00153183	+	0.00265321i	0.866790	−	0.498673i	$-0.166179\pi$
$727$	0.0413027	+	0.0715384i	0.00153183	+	0.00265321i	−0.865258	+	0.501326i	$0.832846\pi$
$728$	13.9816			0.518191
$729$		0			0
$730$	−44.9449			−1.66349
$731$	11.9968	+	20.7791i	0.443718	+	0.768542i
$732$		0			0
$733$	15.9587	−	27.6414i	0.589450	−	1.02096i	−0.404855	−	0.914381i	$-0.632678\pi$
$733$	15.9587	−	27.6414i	0.589450	−	1.02096i	0.994305	−	0.106576i	$-0.0339887\pi$
$734$	−47.1766	+	81.7123i	−1.74132	+	3.01606i
$735$		0			0
$736$	44.0171	+	76.2399i	1.62249	+	2.81024i
$737$	−23.9400			−0.881842
$738$		0			0
$739$	−35.7919			−1.31663			−0.658314	−	0.752744i	$-0.728730\pi$
$739$	−35.7919			−1.31663			−0.658314	+	0.752744i	$0.728730\pi$
$740$	−21.6034	−	37.4181i	−0.794155	−	1.37552i
$741$		0			0
$742$	3.67864	−	6.37160i	0.135047	−	0.233909i
$743$	9.88944	−	17.1290i	0.362808	−	0.628402i	−0.625614	−	0.780133i	$-0.715151\pi$
$743$	9.88944	−	17.1290i	0.362808	−	0.628402i	0.988422	+	0.151731i	$0.0484847\pi$
$744$		0			0
$745$	0.608860	+	1.05458i	0.0223069	+	0.0386367i
$746$	8.27598			0.303005
$747$		0			0
$748$	−27.1723			−0.993517
$749$	2.69462	+	4.66722i	0.0984593	+	0.170537i
$750$		0			0
$751$	−15.2903	+	26.4835i	−0.557950	+	0.966398i	0.439717	+	0.898136i	$0.355079\pi$
$751$	−15.2903	+	26.4835i	−0.557950	+	0.966398i	−0.997667	+	0.0682617i	$0.978255\pi$
$752$	−46.5950	+	80.7048i	−1.69914	+	2.94300i
$753$		0			0
$754$	11.0086	+	19.0674i	0.400909	+	0.694395i
$755$	−7.26165			−0.264278
$756$		0			0
$757$	25.4129			0.923647			0.461824	−	0.886972i	$-0.347195\pi$
$757$	25.4129			0.923647			0.461824	+	0.886972i	$0.347195\pi$
$758$	10.3835	+	17.9847i	0.377144	+	0.653233i
$759$		0			0
$760$	43.4965	−	75.3382i	1.57778	−	2.73280i
$761$	23.4090	−	40.5456i	0.848575	−	1.46978i	−0.0339049	−	0.999425i	$-0.510794\pi$
$761$	23.4090	−	40.5456i	0.848575	−	1.46978i	0.882480	−	0.470350i	$-0.155872\pi$
$762$		0			0
$763$	−3.06107	−	5.30194i	−0.110818	−	0.191943i
$764$	−84.5322			−3.05827
$765$		0			0
$766$	28.0297			1.01275
$767$	3.41016	+	5.90657i	0.123134	+	0.213274i
$768$		0			0
$769$	−7.28271	+	12.6140i	−0.262621	+	0.454873i	−0.966938	−	0.255013i	$-0.917920\pi$
$769$	−7.28271	+	12.6140i	−0.262621	+	0.454873i	0.704316	+	0.709886i	$0.251254\pi$
$770$	−2.17146	+	3.76108i	−0.0782540	+	0.135540i
$771$		0			0
$772$	12.1895	+	21.1128i	0.438710	+	0.759867i
$773$	24.3533			0.875929			0.437964	−	0.898992i	$-0.355700\pi$
$773$	24.3533			0.875929			0.437964	+	0.898992i	$0.355700\pi$
$774$		0			0
$775$	10.1666			0.365194
$776$	30.9106	+	53.5387i	1.10963	+	1.92193i
$777$		0			0
$778$	0.577465	−	1.00020i	0.0207031	−	0.0358589i
$779$	33.4702	−	57.9722i	1.19920	−	2.07707i
$780$		0			0
$781$	−2.71902	−	4.70948i	−0.0972943	−	0.168519i
$782$	−33.4879			−1.19753
$783$		0			0
$784$	−92.0601			−3.28786
$785$	−12.9804	−	22.4828i	−0.463292	−	0.802445i
$786$		0			0
$787$	13.7836	−	23.8739i	0.491332	−	0.851012i	−0.508618	−	0.860992i	$-0.669844\pi$
$787$	13.7836	−	23.8739i	0.491332	−	0.851012i	0.999950	+	0.00998024i	$0.00317686\pi$
$788$	−7.96056	+	13.7881i	−0.283583	+	0.491181i
$789$		0			0
$790$	12.0137	+	20.8084i	0.427429	+	0.740329i
$791$	−0.973124			−0.0346003
$792$		0			0
$793$	21.2901			0.756034
$794$	36.6388	+	63.4603i	1.30026	+	2.25212i
$795$		0			0
$796$	−39.5839	+	68.5613i	−1.40301	+	2.43009i
$797$	3.30846	−	5.73042i	0.117192	−	0.202982i	−0.801462	−	0.598046i	$-0.795944\pi$
$797$	3.30846	−	5.73042i	0.117192	−	0.202982i	0.918654	+	0.395064i	$0.129278\pi$
$798$		0			0
$799$	−9.10284	−	15.7666i	−0.322035	−	0.557781i
$800$	−41.7469			−1.47598
$801$		0			0
$802$	79.4220			2.80449
$803$	9.52624	+	16.4999i	0.336174	+	0.582270i
$804$		0			0
$805$	−1.94472	+	3.36835i	−0.0685422	+	0.118719i
$806$	19.4260	−	33.6467i	0.684250	−	1.18516i
$807$		0			0
$808$	−16.7344	−	28.9848i	−0.588714	−	1.01968i
$809$	−8.61362			−0.302839			−0.151419	−	0.988470i	$-0.548384\pi$
$809$	−8.61362			−0.302839			−0.151419	+	0.988470i	$0.548384\pi$
$810$		0			0
$811$	−9.58716			−0.336651			−0.168325	−	0.985732i	$-0.553836\pi$
$811$	−9.58716			−0.336651			−0.168325	+	0.985732i	$0.553836\pi$
$812$	3.48044	+	6.02830i	0.122139	+	0.211552i
$813$		0			0
$814$	−12.6023	+	21.8278i	−0.441711	+	0.765065i
$815$	7.10545	−	12.3070i	0.248893	−	0.431095i
$816$		0			0
$817$	26.0974	+	45.2021i	0.913034	+	1.58142i
$818$	−54.5988			−1.90900
$819$		0			0
$820$	102.694			3.58624
$821$	6.93174	+	12.0061i	0.241919	+	0.419016i	0.961261	−	0.275640i	$-0.0888898\pi$
$821$	6.93174	+	12.0061i	0.241919	+	0.419016i	−0.719342	+	0.694656i	$0.755556\pi$
$822$		0			0
$823$	−23.9129	+	41.4183i	−0.833550	+	1.44375i	0.0616554	+	0.998097i	$0.480362\pi$
$823$	−23.9129	+	41.4183i	−0.833550	+	1.44375i	−0.895205	+	0.445654i	$0.852971\pi$
$824$	−34.4626	+	59.6911i	−1.20056	+	2.07944i
$825$		0			0
$826$	1.48366	+	2.56978i	0.0516232	+	0.0894141i
$827$	−42.4417			−1.47584			−0.737921	−	0.674887i	$-0.764192\pi$
$827$	−42.4417			−1.47584			−0.737921	+	0.674887i	$0.764192\pi$
$828$		0			0
$829$	26.0037			0.903146			0.451573	−	0.892234i	$-0.350863\pi$
$829$	26.0037			0.903146			0.451573	+	0.892234i	$0.350863\pi$
$830$	−6.17095	−	10.6884i	−0.214197	−	0.371000i
$831$		0			0
$832$	−37.3159	+	64.6331i	−1.29370	+	2.24075i
$833$	8.99248	−	15.5754i	0.311571	−	0.539657i
$834$		0			0
$835$	19.3511	+	33.5171i	0.669673	+	1.15991i
$836$	−59.1096			−2.04435
$837$		0			0
$838$	65.9233			2.27728
$839$	−0.628138	−	1.08797i	−0.0216857	−	0.0375608i	0.854979	−	0.518663i	$-0.173570\pi$
$839$	−0.628138	−	1.08797i	−0.0216857	−	0.0375608i	−0.876665	+	0.481102i	$0.840237\pi$
$840$		0			0
$841$	11.0807	−	19.1923i	0.382093	−	0.661805i
$842$	35.4019	−	61.3179i	1.22003	−	2.11315i
$843$		0			0
$844$	−36.8998	−	63.9124i	−1.27014	−	2.19995i
$845$	5.54019			0.190588
$846$		0			0
$847$	−3.66551			−0.125948
$848$	37.0538	+	64.1791i	1.27243	+	2.20392i
$849$		0			0
$850$	7.94020	−	13.7528i	0.272347	−	0.471718i
$851$	−11.2864	+	19.5486i	−0.386892	+	0.670117i
$852$		0			0
$853$	−0.727173	−	1.25950i	−0.0248979	−	0.0431245i	0.853308	−	0.521407i	$-0.174593\pi$
$853$	−0.727173	−	1.25950i	−0.0248979	−	0.0431245i	−0.878206	+	0.478283i	$0.841259\pi$
$854$	9.26272			0.316964
$855$		0			0
$856$	−96.6089			−3.30202
$857$	26.1548	+	45.3015i	0.893432	+	1.54747i	0.835733	+	0.549136i	$0.185043\pi$
$857$	26.1548	+	45.3015i	0.893432	+	1.54747i	0.0576998	+	0.998334i	$0.481623\pi$
$858$		0			0
$859$	10.5022	−	18.1903i	0.358329	−	0.620645i	−0.629353	−	0.777120i	$-0.716680\pi$
$859$	10.5022	−	18.1903i	0.358329	−	0.620645i	0.987682	+	0.156475i	$0.0500132\pi$
$860$	−40.0364	+	69.3451i	−1.36523	+	2.36465i
$861$		0			0
$862$	−43.1708	−	74.7741i	−1.47040	−	2.54682i
$863$	12.9813			0.441890			0.220945	−	0.975286i	$-0.429086\pi$
$863$	12.9813			0.441890			0.220945	+	0.975286i	$0.429086\pi$
$864$		0			0
$865$	4.31221			0.146619
$866$	−0.0166469	−	0.0288334i	−0.000565686	−	0.000979797i
$867$		0			0
$868$	6.14165	−	10.6376i	0.208461	−	0.361065i
$869$	5.09270	−	8.82082i	0.172758	−	0.299226i
$870$		0			0
$871$	−19.4272	−	33.6489i	−0.658265	−	1.14015i
$872$	109.747			3.71650
$873$		0			0
$874$	−72.8485			−2.46414
$875$	−3.01516	−	5.22241i	−0.101931	−	0.176550i
$876$		0			0
$877$	−15.5228	+	26.8863i	−0.524169	+	0.907887i	0.475435	+	0.879751i	$0.342291\pi$
$877$	−15.5228	+	26.8863i	−0.524169	+	0.907887i	−0.999604	+	0.0281364i	$0.991043\pi$
$878$	−7.17492	+	12.4273i	−0.242142	+	0.419402i
$879$		0			0
$880$	−21.8724	−	37.8841i	−0.737319	−	1.27707i
$881$	19.2957			0.650087			0.325044	−	0.945699i	$-0.394621\pi$
$881$	19.2957			0.650087			0.325044	+	0.945699i	$0.394621\pi$
$882$		0			0
$883$	−9.82388			−0.330600			−0.165300	−	0.986243i	$-0.552859\pi$
$883$	−9.82388			−0.330600			−0.165300	+	0.986243i	$0.552859\pi$
$884$	−22.0501	−	38.1920i	−0.741627	−	1.28453i
$885$		0			0
$886$	−55.0431	+	95.3375i	−1.84921	+	3.20293i
$887$	−22.0566	+	38.2032i	−0.740590	+	1.28274i	0.211638	+	0.977348i	$0.432120\pi$
$887$	−22.0566	+	38.2032i	−0.740590	+	1.28274i	−0.952227	+	0.305391i	$0.901213\pi$
$888$		0			0
$889$	−0.586776	−	1.01633i	−0.0196798	−	0.0340865i
$890$	−50.7533			−1.70125
$891$		0			0
$892$	−36.2219			−1.21280
$893$	−19.8020	−	34.2981i	−0.662649	−	1.14774i
$894$		0			0
$895$	−7.43888	+	12.8845i	−0.248654	+	0.430682i
$896$	−6.74943	+	11.6904i	−0.225483	+	0.390548i
$897$		0			0
$898$	−20.8669	−	36.1425i	−0.696338	−	1.20609i
$899$	12.0675			0.402474
$900$		0			0
$901$	−14.4777			−0.482323
$902$	−29.9533	−	51.8807i	−0.997337	−	1.72744i
$903$		0			0
$904$	8.72222	−	15.1073i	0.290097	−	0.502463i
$905$	6.61581	−	11.4589i	0.219917	−	0.380908i
$906$		0			0
$907$	21.2062	+	36.7302i	0.704140	+	1.21961i	0.967001	+	0.254773i	$0.0820006\pi$
$907$	21.2062	+	36.7302i	0.704140	+	1.21961i	−0.262861	+	0.964834i	$0.584666\pi$
$908$	−51.7957			−1.71890
$909$		0			0
$910$	−7.04851			−0.233656
$911$	−18.3552	−	31.7921i	−0.608134	−	1.05332i	−0.991548	−	0.129743i	$-0.958585\pi$
$911$	−18.3552	−	31.7921i	−0.608134	−	1.05332i	0.383414	−	0.923577i	$-0.374748\pi$
$912$		0			0
$913$	−2.61591	+	4.53089i	−0.0865740	+	0.149951i
$914$	−3.23086	+	5.59601i	−0.106867	+	0.185100i
$915$		0			0
$916$	37.3409	+	64.6763i	1.23378	+	2.13696i
$917$	−8.56130			−0.282719
$918$		0			0
$919$	−14.0589			−0.463761			−0.231881	−	0.972744i	$-0.574488\pi$
$919$	−14.0589			−0.463761			−0.231881	+	0.972744i	$0.574488\pi$
$920$	−34.8615	−	60.3818i	−1.14935	−	1.99073i
$921$		0			0
$922$	−43.9355	+	76.0985i	−1.44694	+	2.50617i
$923$	4.41294	−	7.64344i	0.145254	−	0.251587i
$924$		0			0
$925$	−5.35214	−	9.27018i	−0.175977	−	0.304802i
$926$	91.6436			3.01160
$927$		0			0
$928$	−49.5528			−1.62665
$929$	9.25875	+	16.0366i	0.303770	+	0.526144i	0.976987	−	0.213301i	$-0.0684213\pi$
$929$	9.25875	+	16.0366i	0.303770	+	0.526144i	−0.673217	+	0.739445i	$0.735088\pi$
$930$		0			0
$931$	19.5619	−	33.8823i	0.641116	−	1.11045i
$932$	−14.1531	+	24.5139i	−0.463600	+	0.802978i
$933$		0			0
$934$	18.6686	+	32.3349i	0.610854	+	1.05803i
$935$	8.54604			0.279485
$936$		0			0
$937$	4.46818			0.145969			0.0729845	−	0.997333i	$-0.476748\pi$
$937$	4.46818			0.145969			0.0729845	+	0.997333i	$0.476748\pi$
$938$	−8.45222	−	14.6397i	−0.275975	−	0.478002i
$939$		0			0
$940$	30.3785	−	52.6171i	0.990838	−	1.71618i
$941$	1.00193	−	1.73539i	0.0326620	−	0.0565722i	−0.849232	−	0.528019i	$-0.822935\pi$
$941$	1.00193	−	1.73539i	0.0326620	−	0.0565722i	0.881894	+	0.471447i	$0.156268\pi$
$942$		0			0
$943$	−26.8256	−	46.4633i	−0.873562	−	1.51305i
$944$	−29.8889			−0.972801
$945$		0			0
$946$	46.7105			1.51869
$947$	6.29191	+	10.8979i	0.204460	+	0.354134i	0.949960	−	0.312370i	$-0.101123\pi$
$947$	6.29191	+	10.8979i	0.204460	+	0.354134i	−0.745501	+	0.666505i	$0.767790\pi$
$948$		0			0
$949$	−15.4610	+	26.7792i	−0.501885	+	0.869290i
$950$	17.2728	−	29.9174i	0.560405	−	0.970650i
$951$		0			0
$952$	−5.98507	−	10.3664i	−0.193977	−	0.335978i
$953$	−19.9641			−0.646700			−0.323350	−	0.946279i	$-0.604809\pi$
$953$	−19.9641			−0.646700			−0.323350	+	0.946279i	$0.604809\pi$
$954$		0			0
$955$	26.5865			0.860318
$956$	−47.2542	−	81.8467i	−1.52831	−	2.64711i
$957$		0			0
$958$	−7.96793	+	13.8009i	−0.257432	+	0.445885i
$959$	−3.48591	+	6.03777i	−0.112566	+	0.194970i
$960$		0			0
$961$	4.85272	+	8.40515i	0.156539	+	0.271134i
$962$	−40.9068			−1.31889
$963$		0			0
$964$	−10.6709			−0.343686
$965$	−3.83376	−	6.64026i	−0.123413	−	0.213758i
$966$		0			0
$967$	16.1043	−	27.8934i	0.517879	−	0.896993i	−0.481905	−	0.876223i	$-0.660055\pi$
$967$	16.1043	−	27.8934i	0.517879	−	0.896993i	0.999784	−	0.0207695i	$-0.00661162\pi$
$968$	32.8544	−	56.9055i	1.05598	−	1.82901i
$969$		0			0
$970$	−15.5829	−	26.9904i	−0.500338	−	0.866610i
$971$	−6.62934			−0.212746			−0.106373	−	0.994326i	$-0.533924\pi$
$971$	−6.62934			−0.212746			−0.106373	+	0.994326i	$0.533924\pi$
$972$		0			0
$973$	3.96300			0.127048
$974$	−39.2639	−	68.0071i	−1.25810	−	2.17909i
$975$		0			0
$976$	−46.6502	+	80.8005i	−1.49324	+	2.58636i
$977$	−5.92832	+	10.2682i	−0.189664	+	0.328507i	−0.945138	−	0.326671i	$-0.894073\pi$
$977$	−5.92832	+	10.2682i	−0.189664	+	0.328507i	0.755474	+	0.655178i	$0.227406\pi$
$978$		0			0
$979$	10.7573	+	18.6323i	0.343806	+	0.595490i
$980$	60.0205			1.91728
$981$		0			0
$982$	11.8577			0.378394
$983$	26.0325	+	45.0896i	0.830308	+	1.43814i	0.897794	+	0.440415i	$0.145169\pi$
$983$	26.0325	+	45.0896i	0.830308	+	1.43814i	−0.0674866	+	0.997720i	$0.521498\pi$
$984$		0			0
$985$	2.50370	−	4.33654i	0.0797746	−	0.138174i
$986$	9.42486	−	16.3243i	0.300149	−	0.519873i
$987$		0			0
$988$	−47.9671	−	83.0815i	−1.52604	−	2.64317i
$989$	41.8330			1.33021
$990$		0			0
$991$	1.47115			0.0467326			0.0233663	−	0.999727i	$-0.492562\pi$
$991$	1.47115			0.0467326			0.0233663	+	0.999727i	$0.492562\pi$
$992$	43.7209	+	75.7268i	1.38814	+	2.40433i
$993$		0			0
$994$	1.91995	−	3.32544i	0.0608970	−	0.105477i
$995$	12.4496	−	21.5634i	0.394680	−	0.683606i
$996$		0			0
$997$	13.2106	+	22.8815i	0.418385	+	0.724665i	0.995777	−	0.0918025i	$-0.0292628\pi$
$997$	13.2106	+	22.8815i	0.418385	+	0.724665i	−0.577392	+	0.816467i	$0.695930\pi$
$998$	95.6065			3.02637
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.a.244.1		12
3.2	odd	2		729.2.c.d.244.6		12
9.2	odd	6		729.2.c.d.487.6		12
9.4	even	3		729.2.a.e.1.6	yes	6
9.5	odd	6		729.2.a.b.1.1	✓	6
9.7	even	3	inner	729.2.c.a.487.1		12
27.2	odd	18		729.2.e.s.82.1		12
27.4	even	9		729.2.e.l.649.2		12
27.5	odd	18		729.2.e.t.163.2		12
27.7	even	9		729.2.e.k.568.1		12
27.11	odd	18		729.2.e.j.325.1		12
27.13	even	9		729.2.e.u.406.2		12
27.14	odd	18		729.2.e.j.406.1		12
27.16	even	9		729.2.e.u.325.2		12
27.20	odd	18		729.2.e.t.568.2		12
27.22	even	9		729.2.e.k.163.1		12
27.23	odd	18		729.2.e.s.649.1		12
27.25	even	9		729.2.e.l.82.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.1	✓	6	9.5	odd	6
729.2.a.e.1.6	yes	6	9.4	even	3
729.2.c.a.244.1		12	1.1	even	1	trivial
729.2.c.a.487.1		12	9.7	even	3	inner
729.2.c.d.244.6		12	3.2	odd	2
729.2.c.d.487.6		12	9.2	odd	6
729.2.e.j.325.1		12	27.11	odd	18
729.2.e.j.406.1		12	27.14	odd	18
729.2.e.k.163.1		12	27.22	even	9
729.2.e.k.568.1		12	27.7	even	9
729.2.e.l.82.2		12	27.25	even	9
729.2.e.l.649.2		12	27.4	even	9
729.2.e.s.82.1		12	27.2	odd	18
729.2.e.s.649.1		12	27.23	odd	18
729.2.e.t.163.2		12	27.5	odd	18
729.2.e.t.568.2		12	27.20	odd	18
729.2.e.u.325.2		12	27.16	even	9
729.2.e.u.406.2		12	27.13	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35253 - 2.34265i) q^{2} +(-2.65869 + 4.60498i) q^{4} +(0.836192 - 1.44833i) q^{5} +(-0.250296 - 0.433525i) q^{7} +8.97372 q^{8} -4.52391 q^{10} +(0.958859 + 1.66079i) q^{11} +(-1.55622 + 2.69545i) q^{13} +(-0.677066 + 1.17271i) q^{14} +(-6.81987 - 11.8124i) q^{16} +2.66467 q^{17} +5.79664 q^{19} +(4.44635 + 7.70130i) q^{20} +(2.59378 - 4.49255i) q^{22} +(2.32293 - 4.02344i) q^{23} +(1.10156 + 1.90797i) q^{25} +8.41934 q^{26} +2.66183 q^{28} +(1.30754 + 2.26472i) q^{29} +(2.30730 - 3.99636i) q^{31} +(-9.47446 + 16.4103i) q^{32} +(-3.60406 - 6.24241i) q^{34} -0.837181 q^{35} -4.85867 q^{37} +(-7.84014 - 13.5795i) q^{38} +(7.50375 - 12.9969i) q^{40} +(5.77408 - 10.0010i) q^{41} +(4.50217 + 7.79798i) q^{43} -10.1972 q^{44} -12.5674 q^{46} +(-3.41612 - 5.91689i) q^{47} +(3.37470 - 5.84516i) q^{49} +(2.97980 - 5.16117i) q^{50} +(-8.27499 - 14.3327i) q^{52} -5.43322 q^{53} +3.20716 q^{55} +(-2.24608 - 3.89033i) q^{56} +(3.53697 - 6.12621i) q^{58} +(1.09566 - 1.89773i) q^{59} +(-3.42017 - 5.92391i) q^{61} -12.4828 q^{62} +23.9786 q^{64} +(2.60259 + 4.50783i) q^{65} +(-6.24180 + 10.8111i) q^{67} +(-7.08453 + 12.2708i) q^{68} +(1.13231 + 1.96123i) q^{70} -2.83568 q^{71} +9.93497 q^{73} +(6.57151 + 11.3822i) q^{74} +(-15.4114 + 26.6934i) q^{76} +(0.479996 - 0.831378i) q^{77} +(-2.65561 - 4.59964i) q^{79} -22.8109 q^{80} -31.2385 q^{82} +(1.36408 + 2.36265i) q^{83} +(2.22818 - 3.85932i) q^{85} +(12.1787 - 21.0941i) q^{86} +(8.60453 + 14.9035i) q^{88} +11.2189 q^{89} +1.55806 q^{91} +(12.3519 + 21.3941i) q^{92} +(-9.24082 + 16.0056i) q^{94} +(4.84710 - 8.39543i) q^{95} +(3.44457 + 5.96617i) q^{97} -18.2576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28}+ \cdots + 36 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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