LMFDB - Embedded newform 819.2.s.f.289.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] 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("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,32,0,0,3,12,0,-4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.7
Root			$-0.707433 - 1.22531i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.f.802.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41487 q^{2} +0.00184802 q^{4} +(1.42962 - 2.47618i) q^{5} +(2.56093 + 0.664549i) q^{7} -2.82712 q^{8} +(2.02273 - 3.50347i) q^{10} +(1.15352 - 1.99796i) q^{11} +(-3.12586 - 1.79694i) q^{13} +(3.62338 + 0.940248i) q^{14} -4.00369 q^{16} +7.45162 q^{17} +(-0.282836 - 0.489887i) q^{19} +(0.00264197 - 0.00457603i) q^{20} +(1.63208 - 2.82685i) q^{22} +0.797888 q^{23} +(-1.58765 - 2.74989i) q^{25} +(-4.42268 - 2.54243i) q^{26} +(0.00473265 + 0.00122810i) q^{28} +(-3.00672 - 5.20778i) q^{29} +(-3.80370 - 6.58820i) q^{31} -0.0104540 q^{32} +10.5431 q^{34} +(5.30672 - 5.39128i) q^{35} +2.30147 q^{37} +(-0.400176 - 0.693125i) q^{38} +(-4.04172 + 7.00046i) q^{40} +(5.68100 + 9.83978i) q^{41} +(-3.76945 + 6.52888i) q^{43} +(0.00213173 - 0.00369227i) q^{44} +1.12890 q^{46} +(-0.134822 + 0.233518i) q^{47} +(6.11675 + 3.40373i) q^{49} +(-2.24632 - 3.89073i) q^{50} +(-0.00577664 - 0.00332077i) q^{52} +(-2.35993 - 4.08751i) q^{53} +(-3.29821 - 5.71267i) q^{55} +(-7.24006 - 1.87876i) q^{56} +(-4.25410 - 7.36832i) q^{58} +5.82180 q^{59} +(1.46702 + 2.54094i) q^{61} +(-5.38172 - 9.32142i) q^{62} +7.99259 q^{64} +(-8.91836 + 5.17125i) q^{65} +(-1.58734 + 2.74935i) q^{67} +0.0137707 q^{68} +(7.50830 - 7.62794i) q^{70} +(3.01045 - 5.21425i) q^{71} +(5.31799 + 9.21103i) q^{73} +3.25627 q^{74} +(-0.000522686 - 0.000905319i) q^{76} +(4.28184 - 4.35007i) q^{77} +(-2.01404 + 3.48841i) q^{79} +(-5.72378 + 9.91387i) q^{80} +(8.03786 + 13.9220i) q^{82} -16.2573 q^{83} +(10.6530 - 18.4516i) q^{85} +(-5.33327 + 9.23749i) q^{86} +(-3.26115 + 5.64848i) q^{88} +1.41839 q^{89} +(-6.81097 - 6.67913i) q^{91} +0.00147451 q^{92} +(-0.190755 + 0.330397i) q^{94} -1.61740 q^{95} +(-5.23049 + 9.05948i) q^{97} +(8.65439 + 4.81582i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32}+ \cdots + 76 q^{98}+O(q^{100}) $ 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.41487			1.00046			0.500231	−	0.865892i	$-0.333248\pi$
$2$	1.41487			1.00046			0.500231	+	0.865892i	$0.333248\pi$
$3$		0			0
$3$		0			0
$4$	0.00184802			0.000924008
$5$	1.42962	−	2.47618i	0.639347	−	1.10738i	−0.346229	−	0.938150i	$-0.612538\pi$
$5$	1.42962	−	2.47618i	0.639347	−	1.10738i	0.985576	−	0.169232i	$-0.0541288\pi$
$6$		0			0
$7$	2.56093	+	0.664549i	0.967941	+	0.251176i
$7$	2.56093	+	0.664549i	0.967941	+	0.251176i
$8$	−2.82712			−0.999537
$9$		0			0
$10$	2.02273	−	3.50347i	0.639643	−	1.10789i
$11$	1.15352	−	1.99796i	0.347801	−	0.602408i	−0.638058	−	0.769988i	$-0.720262\pi$
$11$	1.15352	−	1.99796i	0.347801	−	0.602408i	0.985858	+	0.167580i	$0.0535953\pi$
$12$		0			0
$13$	−3.12586	−	1.79694i	−0.866958	−	0.498381i
$13$	−3.12586	−	1.79694i	−0.866958	−	0.498381i
$14$	3.62338	+	0.940248i	0.968389	+	0.251292i
$15$		0			0
$16$	−4.00369			−1.00092
$17$	7.45162			1.80728			0.903642	−	0.428289i	$-0.140883\pi$
$17$	7.45162			1.80728			0.903642	+	0.428289i	$0.140883\pi$
$18$		0			0
$19$	−0.282836	−	0.489887i	−0.0648871	−	0.112388i	0.831757	−	0.555140i	$-0.187335\pi$
$19$	−0.282836	−	0.489887i	−0.0648871	−	0.112388i	−0.896644	+	0.442752i	$0.854002\pi$
$20$	0.00264197	−	0.00457603i	0.000590762	−	0.00102323i
$21$		0			0
$22$	1.63208	−	2.82685i	0.347961	−	0.602686i
$23$	0.797888			0.166371			0.0831855	−	0.996534i	$-0.473491\pi$
$23$	0.797888			0.166371			0.0831855	+	0.996534i	$0.473491\pi$
$24$		0			0
$25$	−1.58765	−	2.74989i	−0.317530	−	0.549979i
$26$	−4.42268	−	2.54243i	−0.867358	−	0.498611i
$27$		0			0
$28$	0.00473265	+	0.00122810i	0.000894386	+	0.000232089i
$29$	−3.00672	−	5.20778i	−0.558333	−	0.967061i	−0.997636	−	0.0687221i	$-0.978108\pi$
$29$	−3.00672	−	5.20778i	−0.558333	−	0.967061i	0.439303	−	0.898339i	$-0.355225\pi$
$30$		0			0
$31$	−3.80370	−	6.58820i	−0.683164	−	1.18328i	−0.974010	−	0.226505i	$-0.927270\pi$
$31$	−3.80370	−	6.58820i	−0.683164	−	1.18328i	0.290846	−	0.956770i	$-0.406063\pi$
$32$	−0.0104540			−0.00184802
$33$		0			0
$34$	10.5431			1.80812
$35$	5.30672	−	5.39128i	0.896999	−	0.911293i
$36$		0			0
$37$	2.30147			0.378359			0.189179	−	0.981943i	$-0.439417\pi$
$37$	2.30147			0.378359			0.189179	+	0.981943i	$0.439417\pi$
$38$	−0.400176	−	0.693125i	−0.0649171	−	0.112440i
$39$		0			0
$40$	−4.04172	+	7.00046i	−0.639052	+	1.10687i
$41$	5.68100	+	9.83978i	0.887223	+	1.53672i	0.843144	+	0.537688i	$0.180702\pi$
$41$	5.68100	+	9.83978i	0.887223	+	1.53672i	0.0440794	+	0.999028i	$0.485965\pi$
$42$		0			0
$43$	−3.76945	+	6.52888i	−0.574835	+	0.995644i	0.421224	+	0.906957i	$0.361601\pi$
$43$	−3.76945	+	6.52888i	−0.574835	+	0.995644i	−0.996059	+	0.0886876i	$0.971733\pi$
$44$	0.00213173	−	0.00369227i	0.000321371	−	0.000556630i
$45$		0			0
$46$	1.12890			0.166448
$47$	−0.134822	+	0.233518i	−0.0196658	+	0.0340621i	−0.875691	−	0.482872i	$-0.839594\pi$
$47$	−0.134822	+	0.233518i	−0.0196658	+	0.0340621i	0.856025	+	0.516934i	$0.172927\pi$
$48$		0			0
$49$	6.11675	+	3.40373i	0.873821	+	0.486247i
$50$	−2.24632	−	3.89073i	−0.317677	−	0.550233i
$51$		0			0
$52$	−0.00577664	−	0.00332077i	−0.000801076	−	0.000460508i
$53$	−2.35993	−	4.08751i	−0.324161	−	0.561463i	0.657181	−	0.753733i	$-0.271749\pi$
$53$	−2.35993	−	4.08751i	−0.324161	−	0.561463i	−0.981342	+	0.192269i	$0.938415\pi$
$54$		0			0
$55$	−3.29821	−	5.71267i	−0.444731	−	0.770296i
$56$	−7.24006	−	1.87876i	−0.967494	−	0.251060i
$57$		0			0
$58$	−4.25410	−	7.36832i	−0.558591	−	0.967508i
$59$	5.82180			0.757934			0.378967	−	0.925410i	$-0.376279\pi$
$59$	5.82180			0.757934			0.378967	+	0.925410i	$0.376279\pi$
$60$		0			0
$61$	1.46702	+	2.54094i	0.187832	+	0.325335i	0.944527	−	0.328433i	$-0.106521\pi$
$61$	1.46702	+	2.54094i	0.187832	+	0.325335i	−0.756695	+	0.653768i	$0.773187\pi$
$62$	−5.38172	−	9.32142i	−0.683480	−	1.18382i
$63$		0			0
$64$	7.99259			0.999074
$65$	−8.91836	+	5.17125i	−1.10619	+	0.641415i
$66$		0			0
$67$	−1.58734	+	2.74935i	−0.193924	+	0.335887i	−0.946547	−	0.322565i	$-0.895455\pi$
$67$	−1.58734	+	2.74935i	−0.193924	+	0.335887i	0.752623	+	0.658452i	$0.228788\pi$
$68$	0.0137707			0.00166995
$69$		0			0
$70$	7.50830	−	7.62794i	0.897413	−	0.911714i
$71$	3.01045	−	5.21425i	0.357275	−	0.618818i	−0.630230	−	0.776409i	$-0.717039\pi$
$71$	3.01045	−	5.21425i	0.357275	−	0.618818i	0.987505	+	0.157591i	$0.0503727\pi$
$72$		0			0
$73$	5.31799	+	9.21103i	0.622424	+	1.07807i	0.989033	+	0.147694i	$0.0471852\pi$
$73$	5.31799	+	9.21103i	0.622424	+	1.07807i	−0.366609	+	0.930375i	$0.619481\pi$
$74$	3.25627			0.378533
$75$		0			0
$76$	−0.000522686	0	0.000905319i	−5.99562e−5	0	0.000103847i
$77$	4.28184	−	4.35007i	0.487961	−	0.495737i
$78$		0			0
$79$	−2.01404	+	3.48841i	−0.226597	+	0.392477i	−0.956797	−	0.290756i	$-0.906093\pi$
$79$	−2.01404	+	3.48841i	−0.226597	+	0.392477i	0.730201	+	0.683233i	$0.239427\pi$
$80$	−5.72378	+	9.91387i	−0.639938	+	1.10840i
$81$		0			0
$82$	8.03786	+	13.9220i	0.887633	+	1.53743i
$83$	−16.2573			−1.78447			−0.892237	−	0.451567i	$-0.850865\pi$
$83$	−16.2573			−1.78447			−0.892237	+	0.451567i	$0.850865\pi$
$84$		0			0
$85$	10.6530	−	18.4516i	1.15548	−	2.00135i
$86$	−5.33327	+	9.23749i	−0.575101	+	0.996104i
$87$		0			0
$88$	−3.26115	+	5.64848i	−0.347640	+	0.602130i
$89$	1.41839			0.150349			0.0751745	−	0.997170i	$-0.476049\pi$
$89$	1.41839			0.150349			0.0751745	+	0.997170i	$0.476049\pi$
$90$		0			0
$91$	−6.81097	−	6.67913i	−0.713983	−	0.700163i
$92$	0.00147451			0.000153728
$93$		0			0
$94$	−0.190755	+	0.330397i	−0.0196748	+	0.0340778i
$95$	−1.61740			−0.165942
$96$		0			0
$97$	−5.23049	+	9.05948i	−0.531076	+	0.919851i	0.468266	+	0.883588i	$0.344879\pi$
$97$	−5.23049	+	9.05948i	−0.531076	+	0.919851i	−0.999342	+	0.0362635i	$0.988454\pi$
$98$	8.65439	+	4.81582i	0.874225	+	0.486472i
$99$		0			0
$100$	−0.00293401	−	0.00508185i	−0.000293401	−	0.000508185i
$101$	−4.73742	+	8.20545i	−0.471391	+	0.816473i	−0.999464	−	0.0327260i	$-0.989581\pi$
$101$	−4.73742	+	8.20545i	−0.471391	+	0.816473i	0.528074	+	0.849199i	$0.322914\pi$
$102$		0			0
$103$	−10.1433	+	17.5686i	−0.999444	+	1.73109i	−0.470857	+	0.882210i	$0.656055\pi$
$103$	−10.1433	+	17.5686i	−0.999444	+	1.73109i	−0.528588	+	0.848879i	$0.677278\pi$
$104$	8.83718	+	5.08016i	0.866557	+	0.498151i
$105$		0			0
$106$	−3.33898	−	5.78329i	−0.324311	−	0.561723i
$107$	13.3661			1.29215			0.646075	−	0.763274i	$-0.276409\pi$
$107$	13.3661			1.29215			0.646075	+	0.763274i	$0.276409\pi$
$108$		0			0
$109$	−0.471097	−	0.815964i	−0.0451229	−	0.0781551i	0.842582	−	0.538568i	$-0.181035\pi$
$109$	−0.471097	−	0.815964i	−0.0451229	−	0.0781551i	−0.887705	+	0.460413i	$0.847701\pi$
$110$	−4.66653	−	8.08267i	−0.444936	−	0.770652i
$111$		0			0
$112$	−10.2532	−	2.66065i	−0.968835	−	0.251408i
$113$	1.28957	−	2.23360i	0.121313	−	0.210120i	−0.798973	−	0.601367i	$-0.794623\pi$
$113$	1.28957	−	2.23360i	0.121313	−	0.210120i	0.920286	+	0.391247i	$0.127956\pi$
$114$		0			0
$115$	1.14068	−	1.97572i	0.106369	−	0.184236i
$116$	−0.00555646	−	0.00962407i	−0.000515904	−	0.000893572i
$117$		0			0
$118$	8.23707			0.758284
$119$	19.0831	+	4.95197i	1.74934	+	0.453946i
$120$		0			0
$121$	2.83876	+	4.91689i	0.258070	+	0.446990i
$122$	2.07563	+	3.59510i	0.187919	+	0.325485i
$123$		0			0
$124$	−0.00702930	−	0.0121751i	−0.000631249	−	0.00109336i
$125$	5.21726			0.466646
$126$		0			0
$127$	−2.06314	−	3.57347i	−0.183074	−	0.317094i	0.759852	−	0.650097i	$-0.225272\pi$
$127$	−2.06314	−	3.57347i	−0.183074	−	0.317094i	−0.942926	+	0.333003i	$0.891938\pi$
$128$	11.3294			1.00138
$129$		0			0
$130$	−12.6183	+	7.31664i	−1.10670	+	0.641711i
$131$	−3.77229	+	6.53379i	−0.329586	+	0.570860i	−0.982430	−	0.186633i	$-0.940243\pi$
$131$	−3.77229	+	6.53379i	−0.329586	+	0.570860i	0.652844	+	0.757493i	$0.273576\pi$
$132$		0			0
$133$	−0.398771	−	1.44253i	−0.0345778	−	0.125083i
$134$	−2.24588	+	3.88997i	−0.194014	+	0.336042i
$135$		0			0
$136$	−21.0666			−1.80645
$137$	−16.6998			−1.42676			−0.713381	−	0.700776i	$-0.752837\pi$
$137$	−16.6998			−1.42676			−0.713381	+	0.700776i	$0.752837\pi$
$138$		0			0
$139$	−5.17295	+	8.95981i	−0.438764	+	0.759961i	−0.997594	−	0.0693207i	$-0.977917\pi$
$139$	−5.17295	+	8.95981i	−0.438764	+	0.759961i	0.558831	+	0.829282i	$0.311250\pi$
$140$	0.00980690	−	0.00996317i	0.000828834	−	0.000842042i
$141$		0			0
$142$	4.25939	−	7.37747i	0.357440	−	0.619104i
$143$	−7.19597	+	4.17254i	−0.601757	+	0.348925i
$144$		0			0
$145$	−17.1939			−1.42788
$146$	7.52425	+	13.0324i	0.622711	+	1.07857i
$147$		0			0
$148$	0.00425315			0.000349606
$149$	−6.12229	−	10.6041i	−0.501558	−	0.868724i	−0.999998	−	0.00179987i	$-0.999427\pi$
$149$	−6.12229	−	10.6041i	−0.501558	−	0.868724i	0.498440	−	0.866924i	$-0.333906\pi$
$150$		0			0
$151$	−9.04334	−	15.6635i	−0.735936	−	1.27468i	−0.954311	−	0.298814i	$-0.903409\pi$
$151$	−9.04334	−	15.6635i	−0.735936	−	1.27468i	0.218375	−	0.975865i	$-0.429924\pi$
$152$	0.799612	+	1.38497i	0.0648571	+	0.112336i
$153$		0			0
$154$	6.05823	−	6.15477i	0.488186	−	0.495966i
$155$	−21.7514			−1.74712
$156$		0			0
$157$	10.9151	+	18.9055i	0.871120	+	1.50882i	0.860839	+	0.508877i	$0.169939\pi$
$157$	10.9151	+	18.9055i	0.871120	+	1.50882i	0.0102810	+	0.999947i	$0.496727\pi$
$158$	−2.84959	+	4.93564i	−0.226701	+	0.392658i
$159$		0			0
$160$	−0.0149452	+	0.0258859i	−0.00118152	+	0.00204646i
$161$	2.04334	+	0.530235i	0.161037	+	0.0417884i
$162$		0			0
$163$	5.68715	+	9.85044i	0.445452	+	0.771546i	0.998084	−	0.0618799i	$-0.0197096\pi$
$163$	5.68715	+	9.85044i	0.445452	+	0.771546i	−0.552631	+	0.833426i	$0.686376\pi$
$164$	0.0104986	+	0.0181841i	0.000819802	+	0.00141994i
$165$		0			0
$166$	−23.0020			−1.78530
$167$	−0.262814	−	0.455207i	−0.0203372	−	0.0352250i	0.855678	−	0.517509i	$-0.173141\pi$
$167$	−0.262814	−	0.455207i	−0.0203372	−	0.0352250i	−0.876015	+	0.482284i	$0.839807\pi$
$168$		0			0
$169$	6.54202	+	11.2340i	0.503232	+	0.864151i
$170$	15.0726	−	26.1065i	1.15602	−	2.00228i
$171$		0			0
$172$	−0.00696600	+	0.0120655i	−0.000531153	+	0.000919984i
$173$	−4.57259	−	7.91995i	−0.347647	−	0.602143i	0.638184	−	0.769884i	$-0.279686\pi$
$173$	−4.57259	−	7.91995i	−0.347647	−	0.602143i	−0.985831	+	0.167741i	$0.946353\pi$
$174$		0			0
$175$	−2.23843	−	8.09736i	−0.169209	−	0.612103i
$176$	−4.61836	+	7.99923i	−0.348122	+	0.602964i
$177$		0			0
$178$	2.00683			0.150418
$179$	−0.861430	+	1.49204i	−0.0643863	+	0.111520i	−0.896422	−	0.443202i	$-0.853842\pi$
$179$	−0.861430	+	1.49204i	−0.0643863	+	0.111520i	0.832035	+	0.554723i	$0.187176\pi$
$180$		0			0
$181$	−3.97723			−0.295625			−0.147813	−	0.989015i	$-0.547223\pi$
$181$	−3.97723			−0.295625			−0.147813	+	0.989015i	$0.547223\pi$
$182$	−9.63661	−	9.45007i	−0.714313	−	0.700486i
$183$		0			0
$184$	−2.25572			−0.166294
$185$	3.29023	−	5.69885i	0.241903	−	0.418988i
$186$		0			0
$187$	8.59562	−	14.8881i	0.628574	−	1.08872i
$188$	−0.000249153	0	0.000431545i	−1.81713e−5	0	3.14737e-5i
$189$		0			0
$190$	−2.28840			−0.166018
$191$	12.5767	+	21.7835i	0.910019	+	1.57620i	0.814034	+	0.580817i	$0.197267\pi$
$191$	12.5767	+	21.7835i	0.910019	+	1.57620i	0.0959855	+	0.995383i	$0.469400\pi$
$192$		0			0
$193$	9.07766	−	15.7230i	0.653425	−	1.13176i	−0.328862	−	0.944378i	$-0.606665\pi$
$193$	9.07766	−	15.7230i	0.653425	−	1.13176i	0.982286	−	0.187386i	$-0.0600017\pi$
$194$	−7.40045	+	12.8180i	−0.531322	+	0.920276i
$195$		0			0
$196$	0.0113039	+	0.00629015i	0.000807418	+	0.000449296i
$197$	−0.782504	−	1.35534i	−0.0557511	−	0.0965638i	0.836803	−	0.547504i	$-0.184422\pi$
$197$	−0.782504	−	1.35534i	−0.0557511	−	0.0965638i	−0.892554	+	0.450940i	$0.851089\pi$
$198$		0			0
$199$	−15.1161			−1.07155			−0.535776	−	0.844360i	$-0.679981\pi$
$199$	−15.1161			−1.07155			−0.535776	+	0.844360i	$0.679981\pi$
$200$	4.48848	+	7.77427i	0.317383	+	0.549724i
$201$		0			0
$202$	−6.70281	+	11.6096i	−0.471608	+	0.816850i
$203$	−4.23917	−	15.3349i	−0.297531	−	1.07630i
$204$		0			0
$205$	32.4868			2.26898
$206$	−14.3514	+	24.8573i	−0.999906	+	1.73189i
$207$		0			0
$208$	12.5150	+	7.19439i	0.867758	+	0.498841i
$209$	−1.30503			−0.0902711
$210$		0			0
$211$	−8.28852	−	14.3561i	−0.570606	−	0.988318i	−0.996504	−	0.0835467i	$-0.973375\pi$
$211$	−8.28852	−	14.3561i	−0.570606	−	0.988318i	0.425898	−	0.904771i	$-0.359958\pi$
$212$	−0.00436118	−	0.00755379i	−0.000299527	−	0.000518797i
$213$		0			0
$214$	18.9112			1.29275
$215$	10.7778	+	18.6677i	0.735039	+	1.27313i
$216$		0			0
$217$	−5.36283	−	19.3997i	−0.364053	−	1.31694i
$218$	−0.666539	−	1.15448i	−0.0451437	−	0.0781912i
$219$		0			0
$220$	−0.00609515	−	0.0105571i	−0.000410935	−	0.000711760i
$221$	−23.2927	−	13.3901i	−1.56684	−	0.900716i
$222$		0			0
$223$	3.10234	+	5.37341i	0.207748	+	0.359830i	0.951005	−	0.309176i	$-0.100053\pi$
$223$	3.10234	+	5.37341i	0.207748	+	0.359830i	−0.743257	+	0.669006i	$0.766720\pi$
$224$	−0.0267719	−	0.00694716i	−0.00178877	−	0.000464177i
$225$		0			0
$226$	1.82457	−	3.16025i	0.121369	−	0.210217i
$227$	1.54064			0.102256			0.0511278	−	0.998692i	$-0.483718\pi$
$227$	1.54064			0.102256			0.0511278	+	0.998692i	$0.483718\pi$
$228$		0			0
$229$	10.6720	−	18.4845i	0.705227	−	1.22149i	−0.261383	−	0.965235i	$-0.584179\pi$
$229$	10.6720	−	18.4845i	0.705227	−	1.22149i	0.966610	−	0.256253i	$-0.0824880\pi$
$230$	1.61391	−	2.79537i	0.106418	−	0.184321i
$231$		0			0
$232$	8.50034	+	14.7230i	0.558075	+	0.966614i
$233$	4.31457	−	7.47305i	0.282657	−	0.489576i	−0.689381	−	0.724399i	$-0.742118\pi$
$233$	4.31457	−	7.47305i	0.282657	−	0.489576i	0.972038	+	0.234823i	$0.0754509\pi$
$234$		0			0
$235$	0.385489	+	0.667686i	0.0251465	+	0.0435550i
$236$	0.0107588			0.000700337
$237$		0			0
$238$	27.0000	+	7.00637i	1.75015	+	0.454156i
$239$	−20.3222			−1.31454			−0.657268	−	0.753657i	$-0.728288\pi$
$239$	−20.3222			−1.31454			−0.657268	+	0.753657i	$0.728288\pi$
$240$		0			0
$241$	26.1153			1.68224			0.841119	−	0.540851i	$-0.181898\pi$
$241$	26.1153			1.68224			0.841119	+	0.540851i	$0.181898\pi$
$242$	4.01647	+	6.95674i	0.258189	+	0.447196i
$243$		0			0
$244$	0.00271107	+	0.00469571i	0.000173558	+	0.000300612i
$245$	17.1729	−	10.2801i	1.09714	−	0.656773i
$246$		0			0
$247$	0.00381039	+	2.03956i	0.000242449	+	0.129774i
$248$	10.7535	+	18.6256i	0.682848	+	1.18273i
$249$		0			0
$250$	7.38173			0.466862
$251$	11.2757	−	19.5301i	0.711718	−	1.23273i	−0.252494	−	0.967599i	$-0.581251\pi$
$251$	11.2757	−	19.5301i	0.711718	−	1.23273i	0.964212	−	0.265133i	$-0.0854160\pi$
$252$		0			0
$253$	0.920383	−	1.59415i	0.0578640	−	0.100223i
$254$	−2.91907	−	5.05598i	−0.183159	−	0.317240i
$255$		0			0
$256$	0.0443524			0.00277202
$257$	1.07243			0.0668965			0.0334483	−	0.999440i	$-0.489351\pi$
$257$	1.07243			0.0668965			0.0334483	+	0.999440i	$0.489351\pi$
$258$		0			0
$259$	5.89390	+	1.52944i	0.366229	+	0.0950345i
$260$	−0.0164813	+	0.00955656i	−0.00102212	+	0.000592673i
$261$		0			0
$262$	−5.33728	+	9.24445i	−0.329738	+	0.571124i
$263$	7.73455	−	13.3966i	0.476933	−	0.826072i	−0.522718	−	0.852506i	$-0.675082\pi$
$263$	7.73455	−	13.3966i	0.476933	−	0.826072i	0.999651	+	0.0264339i	$0.00841516\pi$
$264$		0			0
$265$	−13.4952			−0.829006
$266$	−0.564208	−	2.04098i	−0.0345938	−	0.125141i
$267$		0			0
$268$	−0.00293343	+	0.00508085i	−0.000179188	+	0.000310362i
$269$	−2.23782			−0.136442			−0.0682212	−	0.997670i	$-0.521732\pi$
$269$	−2.23782			−0.136442			−0.0682212	+	0.997670i	$0.521732\pi$
$270$		0			0
$271$	6.14439			0.373245			0.186623	−	0.982432i	$-0.440246\pi$
$271$	6.14439			0.373245			0.186623	+	0.982432i	$0.440246\pi$
$272$	−29.8340			−1.80895
$273$		0			0
$274$	−23.6280			−1.42742
$275$	−7.32558			−0.441749
$276$		0			0
$277$	−3.34827			−0.201178			−0.100589	−	0.994928i	$-0.532073\pi$
$277$	−3.34827			−0.201178			−0.100589	+	0.994928i	$0.532073\pi$
$278$	−7.31903	+	12.6769i	−0.438966	+	0.760312i
$279$		0			0
$280$	−15.0027	+	15.2418i	−0.896584	+	0.910871i
$281$	14.2117			0.847800			0.423900	−	0.905709i	$-0.360661\pi$
$281$	14.2117			0.847800			0.423900	+	0.905709i	$0.360661\pi$
$282$		0			0
$283$	−7.31417	+	12.6685i	−0.434782	+	0.753065i	−0.997278	−	0.0737351i	$-0.976508\pi$
$283$	−7.31417	+	12.6685i	−0.434782	+	0.753065i	0.562495	+	0.826800i	$0.309841\pi$
$284$	0.00556336	−	0.00963602i	0.000330125	−	0.000571793i
$285$		0			0
$286$	−10.1813	+	5.90359i	−0.602035	+	0.349087i
$287$	8.00964	+	28.9743i	0.472794	+	1.71030i
$288$		0			0
$289$	38.5267			2.26627
$290$	−24.3271			−1.42853
$291$		0			0
$292$	0.00982773	+	0.0170221i	0.000575125	+	0.000996145i
$293$	10.7723	−	18.6582i	0.629324	−	1.09002i	−0.358363	−	0.933582i	$-0.616665\pi$
$293$	10.7723	−	18.6582i	0.629324	−	1.09002i	0.987688	−	0.156439i	$-0.0500016\pi$
$294$		0			0
$295$	8.32299	−	14.4158i	0.484583	−	0.839323i
$296$	−6.50652			−0.378184
$297$		0			0
$298$	−8.66223	−	15.0034i	−0.501790	−	0.869125i
$299$	−2.49409	−	1.43376i	−0.144237	−	0.0829162i
$300$		0			0
$301$	−13.9921	+	14.2150i	−0.806489	+	0.819341i
$302$	−12.7951	−	22.1618i	−0.736276	−	1.27527i
$303$		0			0
$304$	1.13239	+	1.96136i	0.0649470	+	0.112492i
$305$	8.38912			0.480360
$306$		0			0
$307$	18.6457			1.06416			0.532082	−	0.846693i	$-0.321410\pi$
$307$	18.6457			1.06416			0.532082	+	0.846693i	$0.321410\pi$
$308$	0.00791291	−	0.00803901i	0.000450880	−	0.000458065i
$309$		0			0
$310$	−30.7754			−1.74792
$311$	0.578424	+	1.00186i	0.0327994	+	0.0568103i	0.881959	−	0.471326i	$-0.156224\pi$
$311$	0.578424	+	1.00186i	0.0327994	+	0.0568103i	−0.849160	+	0.528136i	$0.822891\pi$
$312$		0			0
$313$	−6.86004	+	11.8819i	−0.387752	+	0.671607i	−0.992147	−	0.125078i	$-0.960082\pi$
$313$	−6.86004	+	11.8819i	−0.387752	+	0.671607i	0.604394	+	0.796685i	$0.293415\pi$
$314$	15.4434	+	26.7488i	0.871523	+	1.50952i
$315$		0			0
$316$	−0.00372197	+	0.00644664i	−0.000209377	+	0.000362652i
$317$	2.13847	−	3.70393i	0.120108	−	0.208034i	−0.799702	−	0.600397i	$-0.795009\pi$
$317$	2.13847	−	3.70393i	0.120108	−	0.208034i	0.919810	+	0.392364i	$0.128342\pi$
$318$		0			0
$319$	−13.8733			−0.776754
$320$	11.4264	−	19.7911i	0.638756	−	1.10636i
$321$		0			0
$322$	2.89105	+	0.750212i	0.161112	+	0.0418077i
$323$	−2.10759	−	3.65045i	−0.117269	−	0.203117i
$324$		0			0
$325$	0.0213889	+	11.4487i	0.00118644	+	0.635060i
$326$	8.04657	+	13.9371i	0.445658	+	0.771902i
$327$		0			0
$328$	−16.0609	−	27.8182i	−0.886813	−	1.53601i
$329$	−0.500453	+	0.508428i	−0.0275909	+	0.0280306i
$330$		0			0
$331$	−5.83057	−	10.0988i	−0.320477	−	0.555083i	0.660109	−	0.751170i	$-0.270510\pi$
$331$	−5.83057	−	10.0988i	−0.320477	−	0.555083i	−0.980587	+	0.196087i	$0.937177\pi$
$332$	−0.0300438			−0.00164887
$333$		0			0
$334$	−0.371847	−	0.644057i	−0.0203465	−	0.0352412i
$335$	4.53860	+	7.86109i	0.247970	+	0.429497i
$336$		0			0
$337$	−16.2903			−0.887387			−0.443693	−	0.896179i	$-0.646332\pi$
$337$	−16.2903			−0.887387			−0.443693	+	0.896179i	$0.646332\pi$
$338$	9.25609	+	15.8946i	0.503465	+	0.864550i
$339$		0			0
$340$	0.0196870	−	0.0340988i	0.00106768	−	0.00184927i
$341$	−17.5506			−0.950420
$342$		0			0
$343$	13.4026	+	12.7816i	0.723674	+	0.690142i
$344$	10.6567	−	18.4579i	0.574570	−	0.995184i
$345$		0			0
$346$	−6.46960	−	11.2057i	−0.347808	−	0.602421i
$347$	−25.7112			−1.38025			−0.690126	−	0.723689i	$-0.742445\pi$
$347$	−25.7112			−1.38025			−0.690126	+	0.723689i	$0.742445\pi$
$348$		0			0
$349$	−0.908371	−	1.57334i	−0.0486240	−	0.0842192i	0.840689	−	0.541518i	$-0.182150\pi$
$349$	−0.908371	−	1.57334i	−0.0486240	−	0.0842192i	−0.889313	+	0.457299i	$0.848817\pi$
$350$	−3.16708	−	11.4567i	−0.169288	−	0.612386i
$351$		0			0
$352$	−0.0120589	+	0.0208866i	−0.000642741	+	0.00111326i
$353$	−0.0312072	+	0.0540524i	−0.00166099	+	0.00287692i	−0.866855	−	0.498561i	$-0.833862\pi$
$353$	−0.0312072	+	0.0540524i	−0.00166099	+	0.00287692i	0.865194	+	0.501438i	$0.167195\pi$
$354$		0			0
$355$	−8.60762	−	14.9088i	−0.456845	−	0.791279i
$356$	0.00262121			0.000138924
$357$		0			0
$358$	−1.21881	+	2.11104i	−0.0644160	+	0.111572i
$359$	6.71414	−	11.6292i	0.354359	−	0.613767i	−0.632649	−	0.774438i	$-0.718033\pi$
$359$	6.71414	−	11.6292i	0.354359	−	0.613767i	0.987008	+	0.160671i	$0.0513659\pi$
$360$		0			0
$361$	9.34001	−	16.1774i	0.491579	−	0.851440i
$362$	−5.62725			−0.295762
$363$		0			0
$364$	−0.0125868	−	0.0123431i	−0.000659726	−	0.000646956i
$365$	30.4109			1.59178
$366$		0			0
$367$	−10.6716	+	18.4837i	−0.557052	+	0.964843i	0.440688	+	0.897660i	$0.354734\pi$
$367$	−10.6716	+	18.4837i	−0.557052	+	0.964843i	−0.997741	+	0.0671828i	$0.978599\pi$
$368$	−3.19450			−0.166525
$369$		0			0
$370$	4.65524	−	8.06311i	0.242014	−	0.419181i
$371$	−3.32726	−	12.0361i	−0.172743	−	0.624885i
$372$		0			0
$373$	−14.3838	−	24.9135i	−0.744767	−	1.28997i	−0.950304	−	0.311325i	$-0.899227\pi$
$373$	−14.3838	−	24.9135i	−0.744767	−	1.28997i	0.205537	−	0.978649i	$-0.434106\pi$
$374$	12.1617	−	21.0646i	0.628865	−	1.08923i
$375$		0			0
$376$	0.381157	−	0.660183i	0.0196567	−	0.0340463i
$377$	0.0405066	+	21.6817i	0.00208620	+	1.11666i
$378$		0			0
$379$	9.71923	+	16.8342i	0.499244	+	0.864715i	1.00000		0.000873266i	$-0.000277969\pi$
$379$	9.71923	+	16.8342i	0.499244	+	0.864715i	−0.500756	+	0.865588i	$0.666945\pi$
$380$	−0.00298898			−0.000153331
$381$		0			0
$382$	17.7944	+	30.8208i	0.910440	+	1.57693i
$383$	15.1306	+	26.2069i	0.773137	+	1.33911i	0.935836	+	0.352437i	$0.114647\pi$
$383$	15.1306	+	26.2069i	0.773137	+	1.33911i	−0.162699	+	0.986676i	$0.552020\pi$
$384$		0			0
$385$	−4.65015	−	16.8216i	−0.236994	−	0.857307i
$386$	12.8437	−	22.2459i	0.653726	−	1.13229i
$387$		0			0
$388$	−0.00966604	+	0.0167421i	−0.000490719	+	0.000849950i
$389$	−0.308324	−	0.534034i	−0.0156327	−	0.0270766i	0.858103	−	0.513477i	$-0.171643\pi$
$389$	−0.308324	−	0.534034i	−0.0156327	−	0.0270766i	−0.873736	+	0.486401i	$0.838310\pi$
$390$		0			0
$391$	5.94556			0.300680
$392$	−17.2928	−	9.62275i	−0.873417	−	0.486022i
$393$		0			0
$394$	−1.10714	−	1.91762i	−0.0557769	−	0.0966084i
$395$	5.75863	+	9.97424i	0.289748	+	0.501858i
$396$		0			0
$397$	−14.7888	−	25.6149i	−0.742227	−	1.28557i	−0.951479	−	0.307713i	$-0.900436\pi$
$397$	−14.7888	−	25.6149i	−0.742227	−	1.28557i	0.209252	−	0.977862i	$-0.432897\pi$
$398$	−21.3873			−1.07205
$399$		0			0
$400$	6.35647	+	11.0097i	0.317823	+	0.550486i
$401$	19.8474			0.991130			0.495565	−	0.868571i	$-0.334961\pi$
$401$	19.8474			0.991130			0.495565	+	0.868571i	$0.334961\pi$
$402$		0			0
$403$	0.0512436	+	27.4288i	0.00255263	+	1.36633i
$404$	−0.00875483	+	0.0151638i	−0.000435569	+	0.000754427i
$405$		0			0
$406$	−5.99786	−	21.6968i	−0.297669	−	1.07680i
$407$	2.65480	−	4.59824i	0.131593	−	0.227926i
$408$		0			0
$409$	23.5323			1.16360			0.581800	−	0.813332i	$-0.302349\pi$
$409$	23.5323			1.16360			0.581800	+	0.813332i	$0.302349\pi$
$410$	45.9645			2.27002
$411$		0			0
$412$	−0.0187449	+	0.0324671i	−0.000923495	+	0.00159954i
$413$	14.9092	+	3.86887i	0.733636	+	0.190375i
$414$		0			0
$415$	−23.2419	+	40.2561i	−1.14090	+	1.97610i
$416$	0.0326776	+	0.0187851i	0.00160215	+	0.000921016i
$417$		0			0
$418$	−1.84645			−0.0903128
$419$	−17.6833	−	30.6285i	−0.863888	−	1.49630i	−0.868147	−	0.496307i	$-0.834689\pi$
$419$	−17.6833	−	30.6285i	−0.863888	−	1.49630i	0.00425910	−	0.999991i	$-0.498644\pi$
$420$		0			0
$421$	−10.1261			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$421$	−10.1261			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$422$	−11.7272	−	20.3120i	−0.570869	−	0.988774i
$423$		0			0
$424$	6.67179	+	11.5559i	0.324011	+	0.561203i
$425$	−11.8306	−	20.4912i	−0.573867	−	0.993967i
$426$		0			0
$427$	2.06834	+	7.48209i	0.100094	+	0.362084i
$428$	0.0247008			0.00119396
$429$		0			0
$430$	15.2491	+	26.4123i	0.735379	+	1.27371i
$431$	−3.12150	+	5.40659i	−0.150357	+	0.260426i	−0.931359	−	0.364103i	$-0.881376\pi$
$431$	−3.12150	+	5.40659i	−0.150357	+	0.260426i	0.781002	+	0.624529i	$0.214709\pi$
$432$		0			0
$433$	16.9222	−	29.3101i	0.813229	−	1.40855i	−0.0973634	−	0.995249i	$-0.531041\pi$
$433$	16.9222	−	29.3101i	0.813229	−	1.40855i	0.910593	−	0.413305i	$-0.135626\pi$
$434$	−7.58769	−	27.4479i	−0.364221	−	1.31754i
$435$		0			0
$436$	−0.000870595	−	0.00150791i	−4.16939e−5	−	7.22160e-5i
$437$	−0.225672	−	0.390875i	−0.0107953	−	0.0186981i
$438$		0			0
$439$	8.87482			0.423572			0.211786	−	0.977316i	$-0.432072\pi$
$439$	8.87482			0.423572			0.211786	+	0.977316i	$0.432072\pi$
$440$	9.32444	+	16.1504i	0.444525	+	0.769940i
$441$		0			0
$442$	−32.9561	−	18.9452i	−1.56756	−	0.901132i
$443$	−5.95160	+	10.3085i	−0.282769	+	0.489770i	−0.972066	−	0.234709i	$-0.924586\pi$
$443$	−5.95160	+	10.3085i	−0.282769	+	0.489770i	0.689297	+	0.724479i	$0.257920\pi$
$444$		0			0
$445$	2.02776	−	3.51219i	0.0961252	−	0.166494i
$446$	4.38940	+	7.60266i	0.207844	+	0.359996i
$447$		0			0
$448$	20.4685	+	5.31147i	0.967045	+	0.250943i
$449$	−2.97292	+	5.14925i	−0.140301	+	0.243008i	−0.927610	−	0.373550i	$-0.878140\pi$
$449$	−2.97292	+	5.14925i	−0.140301	+	0.243008i	0.787309	+	0.616558i	$0.211474\pi$
$450$		0			0
$451$	26.2127			1.23431
$452$	0.00238315	−	0.00412774i	0.000112094	−	0.000194153i
$453$		0			0
$454$	2.17980			0.102303
$455$	−26.2759	+	7.31655i	−1.23183	+	0.343005i
$456$		0			0
$457$	12.1123			0.566588			0.283294	−	0.959033i	$-0.408573\pi$
$457$	12.1123			0.566588			0.283294	+	0.959033i	$0.408573\pi$
$458$	15.0995	−	26.1531i	0.705552	−	1.22205i
$459$		0			0
$460$	0.00210800	−	0.00365115i	9.82858e−5	−	0.000170236i
$461$	2.55673	−	4.42839i	0.119079	−	0.206251i	−0.800324	−	0.599568i	$-0.795339\pi$
$461$	2.55673	−	4.42839i	0.119079	−	0.206251i	0.919403	+	0.393317i	$0.128673\pi$
$462$		0			0
$463$	−38.9344			−1.80944			−0.904718	−	0.426010i	$-0.859919\pi$
$463$	−38.9344			−1.80944			−0.904718	+	0.426010i	$0.859919\pi$
$464$	12.0380	+	20.8504i	0.558848	+	0.967954i
$465$		0			0
$466$	6.10454	−	10.5734i	0.282787	−	0.489802i
$467$	−7.02626	+	12.1698i	−0.325136	+	0.563153i	−0.981540	−	0.191257i	$-0.938744\pi$
$467$	−7.02626	+	12.1698i	−0.325136	+	0.563153i	0.656404	+	0.754410i	$0.272077\pi$
$468$		0			0
$469$	−5.89215	+	5.98604i	−0.272074	+	0.276410i
$470$	0.545415	+	0.944687i	0.0251581	+	0.0435752i
$471$		0			0
$472$	−16.4589			−0.757584
$473$	8.69630	+	15.0624i	0.399856	+	0.692571i
$474$		0			0
$475$	−0.898091	+	1.55554i	−0.0412073	+	0.0713731i
$476$	0.0352659	+	0.00915132i	0.00161641	+	0.000419450i
$477$		0			0
$478$	−28.7533			−1.31514
$479$	−16.1368	+	27.9497i	−0.737308	+	1.27705i	0.216395	+	0.976306i	$0.430570\pi$
$479$	−16.1368	+	27.9497i	−0.737308	+	1.27705i	−0.953703	+	0.300749i	$0.902763\pi$
$480$		0			0
$481$	−7.19406	−	4.13559i	−0.328021	−	0.188567i
$482$	36.9497			1.68301
$483$		0			0
$484$	0.00524608	+	0.00908648i	0.000238458	+	0.000413022i
$485$	14.9553	+	25.9033i	0.679084	+	1.17621i
$486$		0			0
$487$	−12.2816			−0.556533			−0.278266	−	0.960504i	$-0.589760\pi$
$487$	−12.2816			−0.556533			−0.278266	+	0.960504i	$0.589760\pi$
$488$	−4.14743	−	7.18355i	−0.187745	−	0.325184i
$489$		0			0
$490$	24.2974	−	14.5450i	1.09764	−	0.657077i
$491$	10.8531	+	18.7981i	0.489792	+	0.848345i	0.999931	−	0.0117472i	$-0.00373933\pi$
$491$	10.8531	+	18.7981i	0.489792	+	0.848345i	−0.510139	+	0.860092i	$0.670406\pi$
$492$		0			0
$493$	−22.4049	−	38.8064i	−1.00907	−	1.74775i
$494$	0.00539119	+	2.88570i	0.000242561	+	0.129834i
$495$		0			0
$496$	15.2288	+	26.3771i	0.683795	+	1.18437i
$497$	11.1747	−	11.3528i	0.501253	−	0.509241i
$498$		0			0
$499$	−4.93997	+	8.55628i	−0.221143	+	0.383032i	−0.955155	−	0.296105i	$-0.904312\pi$
$499$	−4.93997	+	8.55628i	−0.221143	+	0.383032i	0.734012	+	0.679136i	$0.237646\pi$
$500$	0.00964159			0.000431185
$501$		0			0
$502$	15.9537	−	27.6326i	0.712047	−	1.23330i
$503$	17.2279	−	29.8396i	0.768155	−	1.33048i	−0.170407	−	0.985374i	$-0.554508\pi$
$503$	17.2279	−	29.8396i	0.768155	−	1.33048i	0.938562	−	0.345110i	$-0.112158\pi$
$504$		0			0
$505$	13.5455	+	23.4614i	0.602765	+	1.04402i
$506$	1.30222	−	2.25551i	0.0578907	−	0.100270i
$507$		0			0
$508$	−0.00381272	−	0.00660383i	−0.000169162	−	0.000292998i
$509$	−10.8665			−0.481648			−0.240824	−	0.970569i	$-0.577418\pi$
$509$	−10.8665			−0.481648			−0.240824	+	0.970569i	$0.577418\pi$
$510$		0			0
$511$	7.49784	+	27.1229i	0.331685	+	1.19985i
$512$	−22.5960			−0.998610
$513$		0			0
$514$	1.51735			0.0669274
$515$	29.0021	+	50.2331i	1.27798	+	2.21353i
$516$		0			0
$517$	0.311040	+	0.538737i	0.0136795	+	0.0236936i
$518$	8.33908	+	2.16395i	0.366398	+	0.0950784i
$519$		0			0
$520$	25.2133	−	14.6198i	1.10567	−	0.641119i
$521$	−19.0141	−	32.9334i	−0.833024	−	1.44284i	−0.895630	−	0.444801i	$-0.853274\pi$
$521$	−19.0141	−	32.9334i	−0.833024	−	1.44284i	0.0626059	−	0.998038i	$-0.480059\pi$
$522$		0			0
$523$	27.2284			1.19061			0.595307	−	0.803498i	$-0.297030\pi$
$523$	27.2284			1.19061			0.595307	+	0.803498i	$0.297030\pi$
$524$	−0.00697125	+	0.0120746i	−0.000304540	+	0.000527479i
$525$		0			0
$526$	10.9434	−	18.9545i	0.477153	−	0.826453i
$527$	−28.3437	−	49.0927i	−1.23467	−	2.13851i
$528$		0			0
$529$	−22.3634			−0.972321
$530$	−19.0940			−0.829389
$531$		0			0
$532$	−0.000736936	−	0.00266581i	−3.19502e−5	−	0.000115578i
$533$	−0.0765348	−	40.9662i	−0.00331509	−	1.77444i
$534$		0			0
$535$	19.1085	−	33.0969i	0.826132	−	1.43090i
$536$	4.48760	−	7.77275i	0.193835	−	0.335732i
$537$		0			0
$538$	−3.16622			−0.136505
$539$	13.8563	−	8.29475i	0.596835	−	0.357280i
$540$		0			0
$541$	−19.4083	+	33.6162i	−0.834430	+	1.44528i	0.0600635	+	0.998195i	$0.480870\pi$
$541$	−19.4083	+	33.6162i	−0.834430	+	1.44528i	−0.894494	+	0.447081i	$0.852464\pi$
$542$	8.69350			0.373418
$543$		0			0
$544$	−0.0778989			−0.00333989
$545$	−2.69397			−0.115397
$546$		0			0
$547$	−8.34899			−0.356977			−0.178489	−	0.983942i	$-0.557121\pi$
$547$	−8.34899			−0.356977			−0.178489	+	0.983942i	$0.557121\pi$
$548$	−0.0308616			−0.00131834
$549$		0			0
$550$	−10.3647			−0.441953
$551$	−1.70082	+	2.94590i	−0.0724572	+	0.125500i
$552$		0			0
$553$	−7.47603	+	7.59516i	−0.317913	+	0.322979i
$554$	−4.73736			−0.201271
$555$		0			0
$556$	−0.00955969	+	0.0165579i	−0.000405421	+	0.000702210i
$557$	10.1701	−	17.6151i	0.430921	−	0.746377i	−0.566032	−	0.824383i	$-0.691522\pi$
$557$	10.1701	−	17.6151i	0.430921	−	0.746377i	0.996953	+	0.0780065i	$0.0248555\pi$
$558$		0			0
$559$	23.5148	−	13.6349i	0.994569	−	0.576695i
$560$	−21.2465	+	21.5850i	−0.897827	+	0.912134i
$561$		0			0
$562$	20.1077			0.848191
$563$	3.65384			0.153991			0.0769955	−	0.997031i	$-0.475467\pi$
$563$	3.65384			0.153991			0.0769955	+	0.997031i	$0.475467\pi$
$564$		0			0
$565$	−3.68721	−	6.38643i	−0.155122	−	0.268679i
$566$	−10.3486	+	17.9243i	−0.434983	+	0.753413i
$567$		0			0
$568$	−8.51090	+	14.7413i	−0.357109	+	0.618532i
$569$	−5.38814			−0.225883			−0.112941	−	0.993602i	$-0.536027\pi$
$569$	−5.38814			−0.225883			−0.112941	+	0.993602i	$0.536027\pi$
$570$		0			0
$571$	−3.46902	−	6.00851i	−0.145174	−	0.251448i	0.784264	−	0.620427i	$-0.213041\pi$
$571$	−3.46902	−	6.00851i	−0.145174	−	0.251448i	−0.929438	+	0.368979i	$0.879707\pi$
$572$	−0.0132983	+	0.00771092i	−0.000556029	+	0.000322410i
$573$		0			0
$574$	11.3326	+	40.9948i	0.473013	+	1.71109i
$575$	−1.26677	−	2.19411i	−0.0528279	−	0.0915005i
$576$		0			0
$577$	−4.66974	−	8.08823i	−0.194404	−	0.336718i	0.752301	−	0.658820i	$-0.228944\pi$
$577$	−4.66974	−	8.08823i	−0.194404	−	0.336718i	−0.946705	+	0.322102i	$0.895611\pi$
$578$	54.5101			2.26732
$579$		0			0
$580$	−0.0317746			−0.00131937
$581$	−41.6339	−	10.8038i	−1.72727	−	0.448217i
$582$		0			0
$583$	−10.8889			−0.450973
$584$	−15.0346	−	26.0407i	−0.622136	−	1.07757i
$585$		0			0
$586$	15.2414	−	26.3988i	0.629615	−	1.09053i
$587$	11.8226	+	20.4774i	0.487972	+	0.845192i	0.999904	−	0.0138340i	$-0.00440363\pi$
$587$	11.8226	+	20.4774i	0.487972	+	0.845192i	−0.511933	+	0.859026i	$0.671070\pi$
$588$		0			0
$589$	−2.15165	+	3.72676i	−0.0886571	+	0.153559i
$590$	11.7759	−	20.3965i	0.484807	−	0.839710i
$591$		0			0
$592$	−9.21436			−0.378708
$593$	−6.02330	+	10.4327i	−0.247347	+	0.428418i	−0.962789	−	0.270254i	$-0.912892\pi$
$593$	−6.02330	+	10.4327i	−0.247347	+	0.428418i	0.715442	+	0.698673i	$0.246226\pi$
$594$		0			0
$595$	39.5436	−	40.1738i	1.62113	−	1.64696i
$596$	−0.0113141	−	0.0195966i	−0.000463444	−	0.000802708i
$597$		0			0
$598$	−3.52880	−	2.02857i	−0.144303	−	0.0829545i
$599$	−3.07545	−	5.32684i	−0.125660	−	0.217649i	0.796331	−	0.604861i	$-0.206771\pi$
$599$	−3.07545	−	5.32684i	−0.125660	−	0.217649i	−0.921991	+	0.387212i	$0.873438\pi$
$600$		0			0
$601$	2.33860	+	4.05057i	0.0953934	+	0.165226i	0.909773	−	0.415107i	$-0.136256\pi$
$601$	2.33860	+	4.05057i	0.0953934	+	0.165226i	−0.814379	+	0.580333i	$0.802922\pi$
$602$	−19.7969	+	20.1124i	−0.806861	+	0.819719i
$603$		0			0
$604$	−0.0167122	−	0.0289464i	−0.000680011	−	0.00117781i
$605$	16.2335			0.659984
$606$		0			0
$607$	7.65004	+	13.2502i	0.310505	+	0.537811i	0.978472	−	0.206380i	$-0.0661684\pi$
$607$	7.65004	+	13.2502i	0.310505	+	0.537811i	−0.667967	+	0.744191i	$0.732835\pi$
$608$	0.00295676	+	0.00512126i	0.000119912	+	0.000207694i
$609$		0			0
$610$	11.8695			0.480582
$611$	0.841051	−	0.487679i	0.0340253	−	0.0197294i
$612$		0			0
$613$	−5.76413	+	9.98376i	−0.232811	+	0.403240i	−0.958634	−	0.284641i	$-0.908126\pi$
$613$	−5.76413	+	9.98376i	−0.232811	+	0.403240i	0.725823	+	0.687881i	$0.241459\pi$
$614$	26.3811			1.06466
$615$		0			0
$616$	−12.1053	+	12.2982i	−0.487735	+	0.495508i
$617$	−10.2940	+	17.8298i	−0.414423	+	0.717801i	−0.995368	−	0.0961418i	$-0.969350\pi$
$617$	−10.2940	+	17.8298i	−0.414423	+	0.717801i	0.580945	+	0.813943i	$0.302683\pi$
$618$		0			0
$619$	−9.83404	−	17.0331i	−0.395263	−	0.684616i	0.597871	−	0.801592i	$-0.296013\pi$
$619$	−9.83404	−	17.0331i	−0.395263	−	0.684616i	−0.993135	+	0.116976i	$0.962680\pi$
$620$	−0.0401970			−0.00161435
$621$		0			0
$622$	0.818393	+	1.41750i	0.0328146	+	0.0568365i
$623$	3.63240	+	0.942589i	0.145529	+	0.0377640i
$624$		0			0
$625$	15.3970	−	26.6684i	0.615879	−	1.06673i
$626$	−9.70605	+	16.8114i	−0.387932	+	0.671917i
$627$		0			0
$628$	0.0201713	+	0.0349377i	0.000804922	+	0.00139417i
$629$	17.1496			0.683801
$630$		0			0
$631$	21.7095	−	37.6019i	0.864241	−	1.49691i	−0.00355775	−	0.999994i	$-0.501132\pi$
$631$	21.7095	−	37.6019i	0.864241	−	1.49691i	0.867799	−	0.496916i	$-0.165534\pi$
$632$	5.69392	−	9.86215i	0.226492	−	0.392295i
$633$		0			0
$634$	3.02565	−	5.24057i	0.120164	−	0.208130i
$635$	−11.7981			−0.468192
$636$		0			0
$637$	−13.0038	−	21.6310i	−0.515230	−	0.857052i
$638$	−19.6288			−0.777113
$639$		0			0
$640$	16.1967	−	28.0536i	0.640232	−	1.10891i
$641$	−26.9811			−1.06569			−0.532844	−	0.846214i	$-0.678877\pi$
$641$	−26.9811			−1.06569			−0.532844	+	0.846214i	$0.678877\pi$
$642$		0			0
$643$	−2.55705	+	4.42895i	−0.100840	+	0.174661i	−0.912031	−	0.410121i	$-0.865486\pi$
$643$	−2.55705	+	4.42895i	−0.100840	+	0.174661i	0.811191	+	0.584782i	$0.198820\pi$
$644$	0.00377612		0.000979884i	0.000148800		3.86128e-5i
$645$		0			0
$646$	−2.98196	−	5.16490i	−0.117324	−	0.203210i
$647$	9.77239	−	16.9263i	0.384192	−	0.665440i	−0.607465	−	0.794347i	$-0.707813\pi$
$647$	9.77239	−	16.9263i	0.384192	−	0.665440i	0.991657	+	0.128906i	$0.0411467\pi$
$648$		0			0
$649$	6.71559	−	11.6317i	0.263610	−	0.456586i
$650$	0.0302625	+	16.1984i	0.00118699	+	0.635353i
$651$		0			0
$652$	0.0105100	+	0.0182038i	0.000411602	+	0.000712915i
$653$	−15.3626			−0.601186			−0.300593	−	0.953753i	$-0.597185\pi$
$653$	−15.3626			−0.601186			−0.300593	+	0.953753i	$0.597185\pi$
$654$		0			0
$655$	10.7859	+	18.6817i	0.421440	+	0.729956i
$656$	−22.7450	−	39.3955i	−0.888042	−	1.53813i
$657$		0			0
$658$	−0.708075	+	0.719358i	−0.0276036	+	0.0280435i
$659$	8.71206	−	15.0897i	0.339374	−	0.587813i	−0.644941	−	0.764232i	$-0.723118\pi$
$659$	8.71206	−	15.0897i	0.339374	−	0.587813i	0.984315	+	0.176420i	$0.0564515\pi$
$660$		0			0
$661$	−8.35831	+	14.4770i	−0.325101	+	0.563091i	−0.981533	−	0.191294i	$-0.938732\pi$
$661$	−8.35831	+	14.4770i	−0.325101	+	0.563091i	0.656432	+	0.754385i	$0.272065\pi$
$662$	−8.24948	−	14.2885i	−0.320625	−	0.555339i
$663$		0			0
$664$	45.9614			1.78365
$665$	−4.14205	−	1.07484i	−0.160622	−	0.0416805i
$666$		0			0
$667$	−2.39902	−	4.15523i	−0.0928905	−	0.160891i
$668$	−0.000485684	0	0.000841230i	−1.87917e−5	0	3.25482e-5i
$669$		0			0
$670$	6.42152	+	11.1224i	0.248085	+	0.429695i
$671$	6.76895			0.261312
$672$		0			0
$673$	−15.0178	−	26.0116i	−0.578894	−	1.00267i	−0.995607	−	0.0936354i	$-0.970151\pi$
$673$	−15.0178	−	26.0116i	−0.578894	−	1.00267i	0.416713	−	0.909038i	$-0.363182\pi$
$674$	−23.0485			−0.887797
$675$		0			0
$676$	0.0120898	+	0.0207606i	0.000464991	+	0.000798483i
$677$	−1.91898	+	3.32377i	−0.0737525	+	0.127743i	−0.900543	−	0.434767i	$-0.856831\pi$
$677$	−1.91898	+	3.32377i	−0.0737525	+	0.127743i	0.826791	+	0.562510i	$0.190164\pi$
$678$		0			0
$679$	−19.4154	+	19.7248i	−0.745095	+	0.756968i
$680$	−30.1174	+	52.1648i	−1.15495	+	2.00043i
$681$		0			0
$682$	−24.8318			−0.950859
$683$	−27.9568			−1.06974			−0.534868	−	0.844935i	$-0.679639\pi$
$683$	−27.9568			−1.06974			−0.534868	+	0.844935i	$0.679639\pi$
$684$		0			0
$685$	−23.8745	+	41.3518i	−0.912197	+	1.57997i
$686$	18.9629	+	18.0843i	0.724009	+	0.690460i
$687$		0			0
$688$	15.0917	−	26.1396i	0.575366	−	0.996563i
$689$	0.0317931	+	17.0176i	0.00121122	+	0.648321i
$690$		0			0
$691$	−17.9471			−0.682738			−0.341369	−	0.939929i	$-0.610891\pi$
$691$	−17.9471			−0.682738			−0.341369	+	0.939929i	$0.610891\pi$
$692$	−0.00845022	−	0.0146362i	−0.000321229	−	0.000556385i
$693$		0			0
$694$	−36.3780			−1.38089
$695$	14.7907	+	25.6183i	0.561045	+	0.971758i
$696$		0			0
$697$	42.3327	+	73.3223i	1.60346	+	2.77728i
$698$	−1.28522	−	2.22607i	−0.0486464	−	0.0842581i
$699$		0			0
$700$	−0.00413666	−	0.0149641i	−0.000156351	−	0.000565588i
$701$	−35.0636			−1.32433			−0.662167	−	0.749356i	$-0.730363\pi$
$701$	−35.0636			−1.32433			−0.662167	+	0.749356i	$0.730363\pi$
$702$		0			0
$703$	−0.650938	−	1.12746i	−0.0245506	−	0.0425229i
$704$	9.21965	−	15.9689i	0.347479	−	0.601851i
$705$		0			0
$706$	−0.0441540	+	0.0764769i	−0.00166176	+	0.00287825i
$707$	−17.5851	+	17.8654i	−0.661357	+	0.671896i
$708$		0			0
$709$	3.82252	+	6.62079i	0.143558	+	0.248649i	0.928834	−	0.370496i	$-0.120812\pi$
$709$	3.82252	+	6.62079i	0.143558	+	0.248649i	−0.785276	+	0.619146i	$0.787479\pi$
$710$	−12.1786	−	21.0940i	−0.457056	−	0.791645i
$711$		0			0
$712$	−4.00995			−0.150279
$713$	−3.03492	−	5.25664i	−0.113659	−	0.196863i
$714$		0			0
$715$	0.0444337	+	23.7837i	0.00166173	+	0.889460i
$716$	−0.00159194	+	0.00275732i	−5.94935e−5	+	0.000103046i
$717$		0			0
$718$	9.49961	−	16.4538i	0.354522	−	0.614051i
$719$	13.9765	+	24.2081i	0.521237	+	0.902809i	0.999695	+	0.0246986i	$0.00786261\pi$
$719$	13.9765	+	24.2081i	0.521237	+	0.902809i	−0.478458	+	0.878111i	$0.658804\pi$
$720$		0			0
$721$	−37.6514	+	38.2514i	−1.40221	+	1.42456i
$722$	13.2149	−	22.8888i	0.491806	−	0.851834i
$723$		0			0
$724$	−0.00734999			−0.000273160
$725$	−9.54723	+	16.5363i	−0.354575	+	0.614142i
$726$		0			0
$727$	−9.94798			−0.368950			−0.184475	−	0.982837i	$-0.559058\pi$
$727$	−9.94798			−0.368950			−0.184475	+	0.982837i	$0.559058\pi$
$728$	19.2554	+	18.8827i	0.713653	+	0.699839i
$729$		0			0
$730$	43.0274			1.59252
$731$	−28.0885	+	48.6507i	−1.03889	+	1.79941i
$732$		0			0
$733$	−15.9308	+	27.5929i	−0.588416	+	1.01917i	0.406024	+	0.913863i	$0.366915\pi$
$733$	−15.9308	+	27.5929i	−0.588416	+	1.01917i	−0.994440	+	0.105304i	$0.966418\pi$
$734$	−15.0989	+	26.1520i	−0.557310	+	0.965289i
$735$		0			0
$736$	−0.00834108			−0.000307456
$737$	3.66207	+	6.34289i	0.134894	+	0.233643i
$738$		0			0
$739$	9.07418	−	15.7169i	0.333799	−	0.578157i	−0.649454	−	0.760401i	$-0.725003\pi$
$739$	9.07418	−	15.7169i	0.333799	−	0.578157i	0.983253	+	0.182244i	$0.0583359\pi$
$740$	0.00608040	−	0.0105316i	0.000223520	−	0.000387148i
$741$		0			0
$742$	−4.70763	−	17.0295i	−0.172823	−	0.625174i
$743$	12.8238	+	22.2115i	0.470460	+	0.814861i	0.999429	−	0.0337802i	$-0.0107546\pi$
$743$	12.8238	+	22.2115i	0.470460	+	0.814861i	−0.528969	+	0.848641i	$0.677421\pi$
$744$		0			0
$745$	−35.0103			−1.28268
$746$	−20.3512	−	35.2493i	−0.745111	−	1.29057i
$747$		0			0
$748$	0.0158849	−	0.0275134i	0.000580808	−	0.00100599i
$749$	34.2297	+	8.88242i	1.25072	+	0.324557i
$750$		0			0
$751$	−50.5739			−1.84547			−0.922734	−	0.385438i	$-0.874050\pi$
$751$	−50.5739			−1.84547			−0.922734	+	0.385438i	$0.874050\pi$
$752$	0.539785	−	0.934934i	0.0196839	−	0.0340935i
$753$		0			0
$754$	0.0573115	+	30.6767i	0.00208716	+	1.11718i
$755$	−51.7143			−1.88208
$756$		0			0
$757$	0.651718	+	1.12881i	0.0236871	+	0.0410272i	0.877626	−	0.479346i	$-0.159126\pi$
$757$	0.651718	+	1.12881i	0.0236871	+	0.0410272i	−0.853939	+	0.520373i	$0.825793\pi$
$758$	13.7514	+	23.8182i	0.499474	+	0.865115i
$759$		0			0
$760$	4.57258			0.165865
$761$	7.67600	+	13.2952i	0.278255	+	0.481952i	0.970951	−	0.239278i	$-0.0769107\pi$
$761$	7.67600	+	13.2952i	0.278255	+	0.481952i	−0.692696	+	0.721229i	$0.743577\pi$
$762$		0			0
$763$	−0.664199	−	2.40269i	−0.0240456	−	0.0869834i
$764$	0.0232420	+	0.0402563i	0.000840866	+	0.00145642i
$765$		0			0
$766$	21.4078	+	37.0793i	0.773494	+	1.33973i
$767$	−18.1981	−	10.4614i	−0.657097	−	0.377740i
$768$		0			0
$769$	−9.84042	−	17.0441i	−0.354855	−	0.614626i	0.632239	−	0.774774i	$-0.282136\pi$
$769$	−9.84042	−	17.0441i	−0.354855	−	0.614626i	−0.987093	+	0.160148i	$0.948803\pi$
$770$	−6.57934	−	23.8003i	−0.237103	−	0.857703i
$771$		0			0
$772$	0.0167757	−	0.0290563i	0.000603770	−	0.00104576i
$773$	18.3611			0.660402			0.330201	−	0.943911i	$-0.392883\pi$
$773$	18.3611			0.660402			0.330201	+	0.943911i	$0.392883\pi$
$774$		0			0
$775$	−12.0779	+	20.9195i	−0.433851	+	0.751451i
$776$	14.7872	−	25.6122i	0.530831	−	0.919426i
$777$		0			0
$778$	−0.436238	−	0.755586i	−0.0156399	−	0.0270891i
$779$	3.21359	−	5.56610i	0.115139	−	0.199426i
$780$		0			0
$781$	−6.94525	−	12.0295i	−0.248521	−	0.430450i
$782$	8.41217			0.300819
$783$		0			0
$784$	−24.4896	−	13.6275i	−0.874628	−	0.486696i
$785$	62.4180			2.22779
$786$		0			0
$787$	−3.22399			−0.114923			−0.0574615	−	0.998348i	$-0.518301\pi$
$787$	−3.22399			−0.114923			−0.0574615	+	0.998348i	$0.518301\pi$
$788$	−0.00144608	−	0.00250469i	−5.15145e−5	−	8.92257e-5i
$789$		0			0
$790$	8.14769	+	14.1122i	0.289882	+	0.502090i
$791$	4.78685	−	4.86313i	0.170201	−	0.172913i
$792$		0			0
$793$	−0.0197637	−	10.5788i	−0.000701830	−	0.375663i
$794$	−20.9241	−	36.2417i	−0.742570	−	1.28617i
$795$		0			0
$796$	−0.0279348			−0.000990123
$797$	7.59673	−	13.1579i	0.269090	−	0.466078i	−0.699537	−	0.714596i	$-0.746610\pi$
$797$	7.59673	−	13.1579i	0.269090	−	0.466078i	0.968627	+	0.248519i	$0.0799438\pi$
$798$		0			0
$799$	−1.00464	+	1.74009i	−0.0355416	+	0.0615599i
$800$	0.0165972	+	0.0287473i	0.000586801	+	0.00101637i
$801$		0			0
$802$	28.0814			0.991588
$803$	24.5377			0.865917
$804$		0			0
$805$	4.23416	−	4.30164i	0.149235	−	0.151613i
$806$	0.0725029	+	38.8081i	0.00255381	+	1.36696i
$807$		0			0
$808$	13.3932	−	23.1978i	0.471173	−	0.816095i
$809$	−14.5054	+	25.1242i	−0.509984	+	0.883319i	0.489949	+	0.871751i	$0.337015\pi$
$809$	−14.5054	+	25.1242i	−0.509984	+	0.883319i	−0.999933	+	0.0115675i	$0.996318\pi$
$810$		0			0
$811$	−20.5902			−0.723020			−0.361510	−	0.932368i	$-0.617739\pi$
$811$	−20.5902			−0.723020			−0.361510	+	0.932368i	$0.617739\pi$
$812$	−0.00783405	−	0.0283391i	−0.000274921	−	0.000994508i
$813$		0			0
$814$	3.75618	−	6.50590i	0.131654	−	0.228032i
$815$	32.5220			1.13920
$816$		0			0
$817$	4.26455			0.149198
$818$	33.2951			1.16414
$819$		0			0
$820$	0.0600361			0.00209655
$821$	−0.286058			−0.00998349			−0.00499174	−	0.999988i	$-0.501589\pi$
$821$	−0.286058			−0.00998349			−0.00499174	+	0.999988i	$0.501589\pi$
$822$		0			0
$823$	22.5814			0.787137			0.393568	−	0.919295i	$-0.371240\pi$
$823$	22.5814			0.787137			0.393568	+	0.919295i	$0.371240\pi$
$824$	28.6762	−	49.6686i	0.998982	−	1.73029i
$825$		0			0
$826$	21.0946	+	5.47394i	0.733975	+	0.190463i
$827$	−27.6090			−0.960060			−0.480030	−	0.877252i	$-0.659374\pi$
$827$	−27.6090			−0.960060			−0.480030	+	0.877252i	$0.659374\pi$
$828$		0			0
$829$	−15.0977	+	26.1500i	−0.524366	+	0.908228i	0.475232	+	0.879861i	$0.342364\pi$
$829$	−15.0977	+	26.1500i	−0.524366	+	0.908228i	−0.999598	+	0.0283673i	$0.990969\pi$
$830$	−32.8842	+	56.9570i	−1.14143	+	1.97701i
$831$		0			0
$832$	−24.9837	−	14.3622i	−0.866155	−	0.497920i
$833$	45.5797	+	25.3633i	1.57924	+	0.878786i
$834$		0			0
$835$	−1.50290			−0.0520100
$836$	−0.00241172			−8.34113e−5
$837$		0			0
$838$	−25.0196	−	43.3352i	−0.864287	−	1.49699i
$839$	−25.9928	+	45.0209i	−0.897372	+	1.55429i	−0.0665306	+	0.997784i	$0.521193\pi$
$839$	−25.9928	+	45.0209i	−0.897372	+	1.55429i	−0.830841	+	0.556509i	$0.812140\pi$
$840$		0			0
$841$	−3.58067	+	6.20190i	−0.123471	+	0.213859i
$842$	−14.3270			−0.493742
$843$		0			0
$844$	−0.0153173	−	0.0265304i	−0.000527244	−	0.000913214i
$845$	37.1700	−	0.138885i	1.27869	−	0.00477781i
$846$		0			0
$847$	4.00237	+	14.4783i	0.137523	+	0.497481i
$848$	9.44842	+	16.3651i	0.324460	+	0.561981i
$849$		0			0
$850$	−16.7387	−	28.9923i	−0.574132	−	0.994427i
$851$	1.83631			0.0629479
$852$		0			0
$853$	11.5389			0.395085			0.197542	−	0.980294i	$-0.436704\pi$
$853$	11.5389			0.395085			0.197542	+	0.980294i	$0.436704\pi$
$854$	2.92643	+	10.5862i	0.100140	+	0.362251i
$855$		0			0
$856$	−37.7875			−1.29155
$857$	−3.43142	−	5.94339i	−0.117215	−	0.203022i	0.801448	−	0.598064i	$-0.204063\pi$
$857$	−3.43142	−	5.94339i	−0.117215	−	0.203022i	−0.918663	+	0.395042i	$0.870730\pi$
$858$		0			0
$859$	−6.60534	+	11.4408i	−0.225371	+	0.390355i	−0.956431	−	0.291959i	$-0.905693\pi$
$859$	−6.60534	+	11.4408i	−0.225371	+	0.390355i	0.731059	+	0.682314i	$0.239026\pi$
$860$	0.0199175	+	0.0344982i	0.000679182	+	0.00117638i
$861$		0			0
$862$	−4.41650	+	7.64961i	−0.150427	+	0.260547i
$863$	−11.4551	+	19.8408i	−0.389937	+	0.675390i	−0.992441	−	0.122726i	$-0.960836\pi$
$863$	−11.4551	+	19.8408i	−0.389937	+	0.675390i	0.602504	+	0.798116i	$0.294170\pi$
$864$		0			0
$865$	−26.1483			−0.889070
$866$	23.9427	−	41.4699i	0.813605	−	1.40920i
$867$		0			0
$868$	−0.00991060	−	0.0358509i	−0.000336388	−	0.00121686i
$869$	4.64648	+	8.04793i	0.157621	+	0.273007i
$870$		0			0
$871$	9.90223	−	5.74175i	0.335524	−	0.194552i
$872$	1.33185	+	2.30683i	0.0451020	+	0.0781190i
$873$		0			0
$874$	−0.319295	−	0.553036i	−0.0108003	−	0.0187067i
$875$	13.3611	+	3.46713i	0.451686	+	0.117210i
$876$		0			0
$877$	14.2509	+	24.6834i	0.481220	+	0.833498i	0.999768	−	0.0215511i	$-0.00686045\pi$
$877$	14.2509	+	24.6834i	0.481220	+	0.833498i	−0.518548	+	0.855049i	$0.673527\pi$
$878$	12.5567			0.423767
$879$		0			0
$880$	13.2050	+	22.8718i	0.445141	+	0.771007i
$881$	−15.9035	−	27.5457i	−0.535804	−	0.928039i	−0.999124	−	0.0418483i	$-0.986675\pi$
$881$	−15.9035	−	27.5457i	−0.535804	−	0.928039i	0.463320	−	0.886191i	$-0.346658\pi$
$882$		0			0
$883$	11.0073			0.370427			0.185213	−	0.982698i	$-0.440702\pi$
$883$	11.0073			0.370427			0.185213	+	0.982698i	$0.440702\pi$
$884$	−0.0430454	−	0.0247451i	−0.00144777	−	0.000832269i
$885$		0			0
$886$	−8.42072	+	14.5851i	−0.282900	+	0.489997i
$887$	22.2051			0.745574			0.372787	−	0.927917i	$-0.378402\pi$
$887$	22.2051			0.745574			0.372787	+	0.927917i	$0.378402\pi$
$888$		0			0
$889$	−2.90883	−	10.5225i	−0.0975589	−	0.352912i
$890$	2.86901	−	4.96928i	0.0961696	−	0.166571i
$891$		0			0
$892$	0.00573317	+	0.00993015i	0.000191961	+	0.000332486i
$893$	0.152530			0.00510422
$894$		0			0
$895$	2.46304	+	4.26611i	0.0823304	+	0.142600i
$896$	29.0137	+	7.52892i	0.969281	+	0.251523i
$897$		0			0
$898$	−4.20628	+	7.28550i	−0.140366	+	0.243120i
$899$	−22.8733	+	39.6177i	−0.762866	+	1.32132i
$900$		0			0
$901$	−17.5853	−	30.4586i	−0.585851	−	1.01472i
$902$	37.0875			1.23488
$903$		0			0
$904$	−3.64577	+	6.31467i	−0.121257	+	0.210023i
$905$	−5.68595	+	9.84835i	−0.189007	+	0.327370i
$906$		0			0
$907$	−0.795213	+	1.37735i	−0.0264046	+	0.0457341i	−0.878926	−	0.476959i	$-0.841739\pi$
$907$	−0.795213	+	1.37735i	−0.0264046	+	0.0457341i	0.852521	+	0.522693i	$0.175072\pi$
$908$	0.00284712			9.44850e−5
$909$		0			0
$910$	−37.1768	+	10.3519i	−1.23240	+	0.343164i
$911$	2.61896			0.0867699			0.0433849	−	0.999058i	$-0.486186\pi$
$911$	2.61896			0.0867699			0.0433849	+	0.999058i	$0.486186\pi$
$912$		0			0
$913$	−18.7532	+	32.4815i	−0.620641	+	1.07498i
$914$	17.1372			0.566849
$915$		0			0
$916$	0.0197221	−	0.0341596i	0.000651635	−	0.00112867i
$917$	−14.0026	+	14.2257i	−0.462406	+	0.469775i
$918$		0			0
$919$	−10.0892	−	17.4750i	−0.332811	−	0.576446i	0.650251	−	0.759720i	$-0.274664\pi$
$919$	−10.0892	−	17.4750i	−0.332811	−	0.576446i	−0.983062	+	0.183274i	$0.941331\pi$
$920$	−3.22484	+	5.58558i	−0.106320	+	0.184151i
$921$		0			0
$922$	3.61743	−	6.26558i	0.119134	−	0.206346i
$923$	−18.7799	+	10.8894i	−0.618149	+	0.358430i
$924$		0			0
$925$	−3.65392	−	6.32878i	−0.120140	−	0.208089i
$926$	−55.0870			−1.81027
$927$		0			0
$928$	0.0314321	+	0.0544419i	0.00103181	+	0.00178714i
$929$	−16.4051	−	28.4145i	−0.538234	−	0.932248i	−0.998999	−	0.0447264i	$-0.985758\pi$
$929$	−16.4051	−	28.4145i	−0.538234	−	0.932248i	0.460765	−	0.887522i	$-0.347575\pi$
$930$		0			0
$931$	−0.0625967	−	3.95921i	−0.00205152	−	0.129758i
$932$	0.00797339	−	0.0138103i	0.000261177	−	0.000452372i
$933$		0			0
$934$	−9.94122	+	17.2187i	−0.325287	+	0.563413i
$935$	−24.5770	−	42.5687i	−0.803755	−	1.39214i
$936$		0			0
$937$	48.1088			1.57165			0.785823	−	0.618452i	$-0.212240\pi$
$937$	48.1088			1.57165			0.785823	+	0.618452i	$0.212240\pi$
$938$	−8.33661	+	8.46946i	−0.272200	+	0.276538i
$939$		0			0
$940$	0.000712390		0.00123389i	2.32356e−5		4.02452e-5i
$941$	−5.25163	−	9.09609i	−0.171198	−	0.296524i	0.767641	−	0.640880i	$-0.221431\pi$
$941$	−5.25163	−	9.09609i	−0.171198	−	0.296524i	−0.938839	+	0.344356i	$0.888097\pi$
$942$		0			0
$943$	4.53280	+	7.85104i	0.147608	+	0.255665i
$944$	−23.3087			−0.758634
$945$		0			0
$946$	12.3041	+	21.3113i	0.400041	+	0.692891i
$947$	0.629609			0.0204595			0.0102298	−	0.999948i	$-0.496744\pi$
$947$	0.629609			0.0204595			0.0102298	+	0.999948i	$0.496744\pi$
$948$		0			0
$949$	−0.0716443	−	38.3485i	−0.00232567	−	1.24485i
$950$	−1.27068	+	2.20088i	−0.0412263	+	0.0714060i
$951$		0			0
$952$	−53.9502	−	13.9998i	−1.74854	−	0.453736i
$953$	−10.6206	+	18.3954i	−0.344034	+	0.595885i	−0.985178	−	0.171536i	$-0.945127\pi$
$953$	−10.6206	+	18.3954i	−0.344034	+	0.595885i	0.641144	+	0.767421i	$0.278460\pi$
$954$		0			0
$955$	71.9199			2.32727
$956$	−0.0375558			−0.00121464
$957$		0			0
$958$	−22.8314	+	39.5451i	−0.737648	+	1.27764i
$959$	−42.7671	−	11.0979i	−1.38102	−	0.358368i
$960$		0			0
$961$	−13.4362	+	23.2722i	−0.433427	+	0.750717i
$962$	−10.1786	−	5.85131i	−0.328173	−	0.188654i
$963$		0			0
$964$	0.0482616			0.00155440
$965$	−25.9553	−	44.9559i	−0.835531	−	1.44718i
$966$		0			0
$967$	15.0353			0.483502			0.241751	−	0.970338i	$-0.422278\pi$
$967$	15.0353			0.483502			0.241751	+	0.970338i	$0.422278\pi$
$968$	−8.02553	−	13.9006i	−0.257950	−	0.446783i
$969$		0			0
$970$	21.1597	+	36.6497i	0.679398	+	1.17675i
$971$	−3.94070	−	6.82549i	−0.126463	−	0.219040i	0.795841	−	0.605506i	$-0.207029\pi$
$971$	−3.94070	−	6.82549i	−0.126463	−	0.219040i	−0.922304	+	0.386465i	$0.873696\pi$
$972$		0			0
$973$	−19.2018	+	19.5078i	−0.615582	+	0.625391i
$974$	−17.3768			−0.556790
$975$		0			0
$976$	−5.87348	−	10.1732i	−0.188005	−	0.325635i
$977$	8.97409	−	15.5436i	0.287107	−	0.497283i	−0.686011	−	0.727591i	$-0.740640\pi$
$977$	8.97409	−	15.5436i	0.287107	−	0.497283i	0.973118	+	0.230308i	$0.0739733\pi$
$978$		0			0
$979$	1.63615	−	2.83389i	0.0522914	−	0.0905714i
$980$	0.0317358	−	0.0189979i	0.00101376	−	0.000606864i
$981$		0			0
$982$	15.3556	+	26.5968i	0.490018	+	0.848737i
$983$	−2.92791	−	5.07129i	−0.0933858	−	0.161749i	0.815548	−	0.578689i	$-0.196436\pi$
$983$	−2.92791	−	5.07129i	−0.0933858	−	0.161749i	−0.908934	+	0.416941i	$0.863102\pi$
$984$		0			0
$985$	−4.47475			−0.142577
$986$	−31.7000	−	54.9059i	−1.00953	−	1.74856i
$987$		0			0
$988$	7.04166e−6		0.00376914i	2.24025e−7		0.000119912i
$989$	−3.00760	+	5.20931i	−0.0956360	+	0.165646i
$990$		0			0
$991$	−25.6014	+	44.3429i	−0.813255	+	1.40860i	0.0973198	+	0.995253i	$0.468973\pi$
$991$	−25.6014	+	44.3429i	−0.813255	+	1.40860i	−0.910574	+	0.413345i	$0.864360\pi$
$992$	0.0397637	+	0.0688727i	0.00126250	+	0.00218671i
$993$		0			0
$994$	15.8107	−	16.0626i	0.501485	−	0.509476i
$995$	−21.6104	+	37.4302i	−0.685094	+	1.18662i
$996$		0			0
$997$	5.05724			0.160164			0.0800822	−	0.996788i	$-0.474482\pi$
$997$	5.05724			0.160164			0.0800822	+	0.996788i	$0.474482\pi$
$998$	−6.98940	+	12.1060i	−0.221246	+	0.383208i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.f.289.7		20
3.2	odd	2		273.2.l.c.16.4	yes	20
7.4	even	3		819.2.n.f.172.4		20
13.9	even	3		819.2.n.f.100.4		20
21.11	odd	6		273.2.j.c.172.7	yes	20
39.35	odd	6		273.2.j.c.100.7	✓	20
91.74	even	3	inner	819.2.s.f.802.7		20
273.74	odd	6		273.2.l.c.256.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.7	✓	20	39.35	odd	6
273.2.j.c.172.7	yes	20	21.11	odd	6
273.2.l.c.16.4	yes	20	3.2	odd	2
273.2.l.c.256.4	yes	20	273.74	odd	6
819.2.n.f.100.4		20	13.9	even	3
819.2.n.f.172.4		20	7.4	even	3
819.2.s.f.289.7		20	1.1	even	1	trivial
819.2.s.f.802.7		20	91.74	even	3	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41487 q^{2} +0.00184802 q^{4} +(1.42962 - 2.47618i) q^{5} +(2.56093 + 0.664549i) q^{7} -2.82712 q^{8} +(2.02273 - 3.50347i) q^{10} +(1.15352 - 1.99796i) q^{11} +(-3.12586 - 1.79694i) q^{13} +(3.62338 + 0.940248i) q^{14} -4.00369 q^{16} +7.45162 q^{17} +(-0.282836 - 0.489887i) q^{19} +(0.00264197 - 0.00457603i) q^{20} +(1.63208 - 2.82685i) q^{22} +0.797888 q^{23} +(-1.58765 - 2.74989i) q^{25} +(-4.42268 - 2.54243i) q^{26} +(0.00473265 + 0.00122810i) q^{28} +(-3.00672 - 5.20778i) q^{29} +(-3.80370 - 6.58820i) q^{31} -0.0104540 q^{32} +10.5431 q^{34} +(5.30672 - 5.39128i) q^{35} +2.30147 q^{37} +(-0.400176 - 0.693125i) q^{38} +(-4.04172 + 7.00046i) q^{40} +(5.68100 + 9.83978i) q^{41} +(-3.76945 + 6.52888i) q^{43} +(0.00213173 - 0.00369227i) q^{44} +1.12890 q^{46} +(-0.134822 + 0.233518i) q^{47} +(6.11675 + 3.40373i) q^{49} +(-2.24632 - 3.89073i) q^{50} +(-0.00577664 - 0.00332077i) q^{52} +(-2.35993 - 4.08751i) q^{53} +(-3.29821 - 5.71267i) q^{55} +(-7.24006 - 1.87876i) q^{56} +(-4.25410 - 7.36832i) q^{58} +5.82180 q^{59} +(1.46702 + 2.54094i) q^{61} +(-5.38172 - 9.32142i) q^{62} +7.99259 q^{64} +(-8.91836 + 5.17125i) q^{65} +(-1.58734 + 2.74935i) q^{67} +0.0137707 q^{68} +(7.50830 - 7.62794i) q^{70} +(3.01045 - 5.21425i) q^{71} +(5.31799 + 9.21103i) q^{73} +3.25627 q^{74} +(-0.000522686 - 0.000905319i) q^{76} +(4.28184 - 4.35007i) q^{77} +(-2.01404 + 3.48841i) q^{79} +(-5.72378 + 9.91387i) q^{80} +(8.03786 + 13.9220i) q^{82} -16.2573 q^{83} +(10.6530 - 18.4516i) q^{85} +(-5.33327 + 9.23749i) q^{86} +(-3.26115 + 5.64848i) q^{88} +1.41839 q^{89} +(-6.81097 - 6.67913i) q^{91} +0.00147451 q^{92} +(-0.190755 + 0.330397i) q^{94} -1.61740 q^{95} +(-5.23049 + 9.05948i) q^{97} +(8.65439 + 4.81582i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32}+ \cdots + 76 q^{98}+O(q^{100}) \) 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

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