LMFDB - Embedded newform 819.2.n.f.100.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
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			100.9
Root			$1.14017 - 1.97483i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.f.172.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14017 + 1.97483i) q^{2} +(-1.59997 + 2.77124i) q^{4} +(1.46862 - 2.54373i) q^{5} +(-2.34076 - 1.23322i) q^{7} -2.73629 q^{8} +6.69792 q^{10} +5.16954 q^{11} +(-0.364757 + 3.58705i) q^{13} +(-0.233457 - 6.02869i) q^{14} +(0.0801172 + 0.138767i) q^{16} +(2.52646 - 4.37595i) q^{17} +2.25859 q^{19} +(4.69952 + 8.13980i) q^{20} +(5.89416 + 10.2090i) q^{22} +(2.61602 + 4.53108i) q^{23} +(-1.81371 - 3.14143i) q^{25} +(-7.49971 + 3.36952i) q^{26} +(7.16271 - 4.51367i) q^{28} +(-0.216901 + 0.375683i) q^{29} +(-1.34122 - 2.32306i) q^{31} +(-2.91898 + 5.05582i) q^{32} +11.5224 q^{34} +(-6.57468 + 4.14312i) q^{35} +(2.12386 + 3.67863i) q^{37} +(2.57517 + 4.46033i) q^{38} +(-4.01857 + 6.96037i) q^{40} +(-0.269622 + 0.466999i) q^{41} +(-4.66348 - 8.07739i) q^{43} +(-8.27113 + 14.3260i) q^{44} +(-5.96541 + 10.3324i) q^{46} +(4.87054 - 8.43603i) q^{47} +(3.95832 + 5.77336i) q^{49} +(4.13587 - 7.16354i) q^{50} +(-9.35697 - 6.75002i) q^{52} +(-0.377571 - 0.653972i) q^{53} +(7.59211 - 13.1499i) q^{55} +(6.40499 + 3.37445i) q^{56} -0.989214 q^{58} +(-1.82385 + 3.15901i) q^{59} +6.95468 q^{61} +(3.05843 - 5.29736i) q^{62} -12.9921 q^{64} +(8.58881 + 6.19587i) q^{65} -13.3602 q^{67} +(8.08453 + 14.0028i) q^{68} +(-15.6782 - 8.26003i) q^{70} +(-3.90487 - 6.76343i) q^{71} +(-7.94401 - 13.7594i) q^{73} +(-4.84312 + 8.38853i) q^{74} +(-3.61368 + 6.25908i) q^{76} +(-12.1007 - 6.37520i) q^{77} +(-7.79235 + 13.4967i) q^{79} +0.470648 q^{80} -1.22966 q^{82} -13.2349 q^{83} +(-7.42083 - 12.8532i) q^{85} +(10.6343 - 18.4192i) q^{86} -14.1453 q^{88} +(-2.00143 - 3.46658i) q^{89} +(5.27744 - 7.94661i) q^{91} -16.7423 q^{92} +22.2130 q^{94} +(3.31701 - 5.74523i) q^{95} +(2.69653 + 4.67053i) q^{97} +(-6.88826 + 14.3996i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{4} - 9 q^{7} + 12 q^{8} + 8 q^{10} - 16 q^{11} - 5 q^{13} + 9 q^{14} - 20 q^{16} - 14 q^{19} - 12 q^{20} - 9 q^{22} + 14 q^{23} - 32 q^{25} - 4 q^{26} + 13 q^{28} + 9 q^{29} - 9 q^{31} - 17 q^{32}+ \cdots + 79 q^{98}+O(q^{100}) $ 20 * q - 16 * q^4 - 9 * q^7 + 12 * q^8 + 8 * q^10 - 16 * q^11 - 5 * q^13 + 9 * q^14 - 20 * q^16 - 14 * q^19 - 12 * q^20 - 9 * q^22 + 14 * q^23 - 32 * q^25 - 4 * q^26 + 13 * q^28 + 9 * q^29 - 9 * q^31 - 17 * q^32 + 12 * q^34 - 10 * q^35 + 18 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 - 10 * q^46 - 13 * q^47 - 21 * q^49 - 5 * q^50 - 2 * q^52 + 6 * q^53 - 19 * q^55 + 5 * q^56 + 15 * q^59 - 22 * q^62 + 72 * q^64 + 27 * q^65 + 44 * q^67 - 39 * q^68 + 30 * q^70 + 11 * q^71 + 3 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 + 96 * q^80 + 26 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 + 24 * q^88 - 2 * q^89 + 9 * q^91 - 66 * q^92 + 88 * q^94 + 36 * q^95 + 21 * q^97 + 79 * q^98

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.14017	+	1.97483i	0.806222	+	1.39642i	0.915463	+	0.402402i	$0.131824\pi$
$2$	1.14017	+	1.97483i	0.806222	+	1.39642i	−0.109242	+	0.994015i	$0.534842\pi$
$3$		0			0
$3$		0			0
$4$	−1.59997	+	2.77124i	−0.799987	+	1.38562i
$5$	1.46862	−	2.54373i	0.656788	−	1.13759i	−0.324654	−	0.945833i	$-0.605248\pi$
$5$	1.46862	−	2.54373i	0.656788	−	1.13759i	0.981442	−	0.191758i	$-0.0614188\pi$
$6$		0			0
$7$	−2.34076	−	1.23322i	−0.884724	−	0.466114i
$7$	−2.34076	−	1.23322i	−0.884724	−	0.466114i
$8$	−2.73629			−0.967423
$9$		0			0
$10$	6.69792			2.11807
$11$	5.16954			1.55868			0.779338	−	0.626604i	$-0.215556\pi$
$11$	5.16954			1.55868			0.779338	+	0.626604i	$0.215556\pi$
$12$		0			0
$13$	−0.364757	+	3.58705i	−0.101165	+	0.994870i
$13$	−0.364757	+	3.58705i	−0.101165	+	0.994870i
$14$	−0.233457	−	6.02869i	−0.0623939	−	1.61124i
$15$		0			0
$16$	0.0801172	+	0.138767i	0.0200293	+	0.0346918i
$17$	2.52646	−	4.37595i	0.612756	−	1.06132i	−0.378018	−	0.925798i	$-0.623394\pi$
$17$	2.52646	−	4.37595i	0.612756	−	1.06132i	0.990774	−	0.135526i	$-0.0432724\pi$
$18$		0			0
$19$	2.25859			0.518155			0.259078	−	0.965856i	$-0.416581\pi$
$19$	2.25859			0.518155			0.259078	+	0.965856i	$0.416581\pi$
$20$	4.69952	+	8.13980i	1.05084	+	1.82011i
$21$		0			0
$22$	5.89416	+	10.2090i	1.25664	+	2.17656i
$23$	2.61602	+	4.53108i	0.545478	+	0.944796i	0.998577	+	0.0533353i	$0.0169852\pi$
$23$	2.61602	+	4.53108i	0.545478	+	0.944796i	−0.453099	+	0.891460i	$0.649681\pi$
$24$		0			0
$25$	−1.81371	−	3.14143i	−0.362742	−	0.628287i
$26$	−7.49971	+	3.36952i	−1.47081	+	0.660817i
$27$		0			0
$28$	7.16271	−	4.51367i	1.35362	−	0.853004i
$29$	−0.216901	+	0.375683i	−0.0402775	+	0.0697626i	−0.885461	−	0.464713i	$-0.846158\pi$
$29$	−0.216901	+	0.375683i	−0.0402775	+	0.0697626i	0.845184	+	0.534476i	$0.179491\pi$
$30$		0			0
$31$	−1.34122	−	2.32306i	−0.240890	−	0.417234i	0.720078	−	0.693893i	$-0.244106\pi$
$31$	−1.34122	−	2.32306i	−0.240890	−	0.417234i	−0.960968	+	0.276659i	$0.910773\pi$
$32$	−2.91898	+	5.05582i	−0.516008	+	0.893751i
$33$		0			0
$34$	11.5224			1.97607
$35$	−6.57468	+	4.14312i	−1.11132	+	0.700316i
$36$		0			0
$37$	2.12386	+	3.67863i	0.349160	+	0.604764i	0.986101	−	0.166150i	$-0.0531335\pi$
$37$	2.12386	+	3.67863i	0.349160	+	0.604764i	−0.636940	+	0.770913i	$0.719800\pi$
$38$	2.57517	+	4.46033i	0.417748	+	0.723561i
$39$		0			0
$40$	−4.01857	+	6.96037i	−0.635392	+	1.10053i
$41$	−0.269622	+	0.466999i	−0.0421079	+	0.0729330i	−0.886311	−	0.463090i	$-0.846741\pi$
$41$	−0.269622	+	0.466999i	−0.0421079	+	0.0729330i	0.844203	+	0.536023i	$0.180074\pi$
$42$		0			0
$43$	−4.66348	−	8.07739i	−0.711175	−	1.23179i	−0.964416	−	0.264388i	$-0.914830\pi$
$43$	−4.66348	−	8.07739i	−0.711175	−	1.23179i	0.253242	−	0.967403i	$-0.418503\pi$
$44$	−8.27113	+	14.3260i	−1.24692	+	2.15973i
$45$		0			0
$46$	−5.96541	+	10.3324i	−0.879552	+	1.52343i
$47$	4.87054	−	8.43603i	0.710442	−	1.23052i	−0.254250	−	0.967139i	$-0.581828\pi$
$47$	4.87054	−	8.43603i	0.710442	−	1.23052i	0.964691	−	0.263383i	$-0.0848382\pi$
$48$		0			0
$49$	3.95832	+	5.77336i	0.565475	+	0.824766i
$50$	4.13587	−	7.16354i	0.584900	−	1.01308i
$51$		0			0
$52$	−9.35697	−	6.75002i	−1.29758	−	0.936059i
$53$	−0.377571	−	0.653972i	−0.0518634	−	0.0898300i	0.838928	−	0.544242i	$-0.183183\pi$
$53$	−0.377571	−	0.653972i	−0.0518634	−	0.0898300i	−0.890792	+	0.454412i	$0.849849\pi$
$54$		0			0
$55$	7.59211	−	13.1499i	1.02372	−	1.77313i
$56$	6.40499	+	3.37445i	0.855903	+	0.450930i
$57$		0			0
$58$	−0.989214			−0.129890
$59$	−1.82385	+	3.15901i	−0.237445	+	0.411267i	−0.959981	−	0.280067i	$-0.909643\pi$
$59$	−1.82385	+	3.15901i	−0.237445	+	0.411267i	0.722535	+	0.691334i	$0.242977\pi$
$60$		0			0
$61$	6.95468			0.890455			0.445228	−	0.895417i	$-0.353123\pi$
$61$	6.95468			0.890455			0.445228	+	0.895417i	$0.353123\pi$
$62$	3.05843	−	5.29736i	0.388422	−	0.672766i
$63$		0			0
$64$	−12.9921			−1.62401
$65$	8.58881	+	6.19587i	1.06531	+	0.768503i
$66$		0			0
$67$	−13.3602			−1.63221			−0.816107	−	0.577901i	$-0.803872\pi$
$67$	−13.3602			−1.63221			−0.816107	+	0.577901i	$0.803872\pi$
$68$	8.08453	+	14.0028i	0.980393	+	1.69809i
$69$		0			0
$70$	−15.6782	−	8.26003i	−1.87391	−	0.987262i
$71$	−3.90487	−	6.76343i	−0.463423	−	0.802672i	0.535706	−	0.844404i	$-0.320045\pi$
$71$	−3.90487	−	6.76343i	−0.463423	−	0.802672i	−0.999129	+	0.0417329i	$0.986712\pi$
$72$		0			0
$73$	−7.94401	−	13.7594i	−0.929776	−	1.61042i	−0.783694	−	0.621147i	$-0.786667\pi$
$73$	−7.94401	−	13.7594i	−0.929776	−	1.61042i	−0.146083	−	0.989272i	$-0.546667\pi$
$74$	−4.84312	+	8.38853i	−0.563001	+	0.975147i
$75$		0			0
$76$	−3.61368	+	6.25908i	−0.414517	+	0.717965i
$77$	−12.1007	−	6.37520i	−1.37900	−	0.726521i
$78$		0			0
$79$	−7.79235	+	13.4967i	−0.876708	+	1.51850i	−0.0217756	+	0.999763i	$0.506932\pi$
$79$	−7.79235	+	13.4967i	−0.876708	+	1.51850i	−0.854932	+	0.518740i	$0.826401\pi$
$80$	0.470648			0.0526200
$81$		0			0
$82$	−1.22966			−0.135793
$83$	−13.2349			−1.45272			−0.726360	−	0.687315i	$-0.758789\pi$
$83$	−13.2349			−1.45272			−0.726360	+	0.687315i	$0.758789\pi$
$84$		0			0
$85$	−7.42083	−	12.8532i	−0.804902	−	1.39413i
$86$	10.6343	−	18.4192i	1.14673	−	1.98619i
$87$		0			0
$88$	−14.1453			−1.50790
$89$	−2.00143	−	3.46658i	−0.212151	−	0.367457i	0.740236	−	0.672347i	$-0.234714\pi$
$89$	−2.00143	−	3.46658i	−0.212151	−	0.367457i	−0.952388	+	0.304890i	$0.901380\pi$
$90$		0			0
$91$	5.27744	−	7.94661i	0.553227	−	0.833031i
$92$	−16.7423			−1.74550
$93$		0			0
$94$	22.2130			2.29109
$95$	3.31701	−	5.74523i	0.340318	−	0.589449i
$96$		0			0
$97$	2.69653	+	4.67053i	0.273791	+	0.474220i	0.969829	−	0.243784i	$-0.0783889\pi$
$97$	2.69653	+	4.67053i	0.273791	+	0.474220i	−0.696038	+	0.718005i	$0.745056\pi$
$98$	−6.88826	+	14.3996i	−0.695819	+	1.45458i
$99$		0			0
$100$	11.6075			1.16075
$101$	3.15240			0.313676			0.156838	−	0.987624i	$-0.449870\pi$
$101$	3.15240			0.313676			0.156838	+	0.987624i	$0.449870\pi$
$102$		0			0
$103$	−6.59727	+	11.4268i	−0.650048	+	1.12592i	0.333062	+	0.942905i	$0.391918\pi$
$103$	−6.59727	+	11.4268i	−0.650048	+	1.12592i	−0.983111	+	0.183012i	$0.941415\pi$
$104$	0.998078	−	9.81520i	0.0978696	−	0.962460i
$105$		0			0
$106$	0.860990	−	1.49128i	0.0836267	−	0.144846i
$107$	2.93351	+	5.08098i	0.283593	+	0.491197i	0.972267	−	0.233874i	$-0.0751403\pi$
$107$	2.93351	+	5.08098i	0.283593	+	0.491197i	−0.688674	+	0.725071i	$0.741807\pi$
$108$		0			0
$109$	2.74399	+	4.75273i	0.262826	+	0.455229i	0.966992	−	0.254807i	$-0.0820120\pi$
$109$	2.74399	+	4.75273i	0.262826	+	0.455229i	−0.704166	+	0.710036i	$0.748679\pi$
$110$	34.6252			3.30138
$111$		0			0
$112$	−0.0164045	−	0.423623i	−0.00155008	−	0.0400286i
$113$	−0.794808	−	1.37665i	−0.0747692	−	0.129504i	0.826217	−	0.563352i	$-0.190489\pi$
$113$	−0.794808	−	1.37665i	−0.0747692	−	0.129504i	−0.900986	+	0.433848i	$0.857155\pi$
$114$		0			0
$115$	15.3678			1.43305
$116$	−0.694071	−	1.20217i	−0.0644428	−	0.111618i
$117$		0			0
$118$	−8.31800			−0.765734
$119$	−11.3104	+	7.12737i	−1.03682	+	0.653365i
$120$		0			0
$121$	15.7242			1.42947
$122$	7.92951	+	13.7343i	0.717904	+	1.24345i
$123$		0			0
$124$	8.58366			0.770835
$125$	4.03162			0.360599
$126$		0			0
$127$	0.348278	−	0.603236i	0.0309047	−	0.0535285i	−0.850159	−	0.526525i	$-0.823494\pi$
$127$	0.348278	−	0.603236i	0.0309047	−	0.0535285i	0.881064	+	0.472997i	$0.156828\pi$
$128$	−8.97519	−	15.5455i	−0.793302	−	1.37404i
$129$		0			0
$130$	−2.44311	+	24.0258i	−0.214275	+	2.10720i
$131$	−3.35469	+	5.81049i	−0.293101	+	0.507665i	−0.974541	−	0.224208i	$-0.928020\pi$
$131$	−3.35469	+	5.81049i	−0.293101	+	0.507665i	0.681441	+	0.731873i	$0.261354\pi$
$132$		0			0
$133$	−5.28681	−	2.78534i	−0.458425	−	0.241520i
$134$	−15.2329	−	26.3842i	−1.31593	−	2.27925i
$135$		0			0
$136$	−6.91311	+	11.9739i	−0.592794	+	1.02675i
$137$	6.24965	−	10.8247i	0.533944	−	0.924818i	−0.465270	−	0.885169i	$-0.654043\pi$
$137$	6.24965	−	10.8247i	0.533944	−	0.924818i	0.999214	−	0.0396491i	$-0.0126240\pi$
$138$		0			0
$139$	−0.657614	−	1.13902i	−0.0557781	−	0.0966105i	0.836788	−	0.547527i	$-0.184431\pi$
$139$	−0.657614	−	1.13902i	−0.0557781	−	0.0966105i	−0.892566	+	0.450916i	$0.851097\pi$
$140$	−0.962254	−	24.8489i	−0.0813253	−	2.10011i
$141$		0			0
$142$	8.90442	−	15.4229i	0.747243	−	1.29426i
$143$	−1.88563	+	18.5434i	−0.157684	+	1.55068i
$144$		0			0
$145$	0.637091	+	1.10347i	0.0529075	+	0.0916385i
$146$	18.1150	−	31.3762i	1.49921	−	2.59671i
$147$		0			0
$148$	−13.5925			−1.11729
$149$	−21.1927			−1.73618			−0.868088	−	0.496411i	$-0.834651\pi$
$149$	−21.1927			−1.73618			−0.868088	+	0.496411i	$0.834651\pi$
$150$		0			0
$151$	7.90358	+	13.6894i	0.643185	+	1.11403i	0.984718	+	0.174159i	$0.0557205\pi$
$151$	7.90358	+	13.6894i	0.643185	+	1.11403i	−0.341533	+	0.939870i	$0.610946\pi$
$152$	−6.18014			−0.501275
$153$		0			0
$154$	−1.20686	−	31.1656i	−0.0972518	−	2.51139i
$155$	−7.87898			−0.632855
$156$		0			0
$157$	−2.76205	−	4.78402i	−0.220436	−	0.381806i	0.734505	−	0.678604i	$-0.237415\pi$
$157$	−2.76205	−	4.78402i	−0.220436	−	0.381806i	−0.954940	+	0.296798i	$0.904081\pi$
$158$	−35.5384			−2.82728
$159$		0			0
$160$	8.57376	+	14.8502i	0.677815	+	1.17401i
$161$	−0.535646	−	13.8323i	−0.0422148	−	1.09014i
$162$		0			0
$163$	−3.14870			−0.246625			−0.123313	−	0.992368i	$-0.539352\pi$
$163$	−3.14870			−0.246625			−0.123313	+	0.992368i	$0.539352\pi$
$164$	−0.862777	−	1.49437i	−0.0673715	−	0.116691i
$165$		0			0
$166$	−15.0900	−	26.1367i	−1.17121	−	2.02860i
$167$	−6.71152	+	11.6247i	−0.519353	+	0.899546i	0.480394	+	0.877053i	$0.340494\pi$
$167$	−6.71152	+	11.6247i	−0.519353	+	0.899546i	−0.999747	+	0.0224932i	$0.992840\pi$
$168$		0			0
$169$	−12.7339	−	2.61680i	−0.979531	−	0.201293i
$170$	16.9220	−	29.3098i	1.29786	−	2.24796i
$171$		0			0
$172$	29.8458			2.27572
$173$	12.8488			0.976879			0.488439	−	0.872598i	$-0.337566\pi$
$173$	12.8488			0.976879			0.488439	+	0.872598i	$0.337566\pi$
$174$		0			0
$175$	0.371368	+	9.59005i	0.0280728	+	0.724940i
$176$	0.414169	+	0.717362i	0.0312192	+	0.0540732i
$177$		0			0
$178$	4.56394	−	7.90498i	0.342082	−	0.592503i
$179$	−18.6663			−1.39518			−0.697591	−	0.716496i	$-0.745745\pi$
$179$	−18.6663			−1.39518			−0.697591	+	0.716496i	$0.745745\pi$
$180$		0			0
$181$	0.878433			0.0652934			0.0326467	−	0.999467i	$-0.489606\pi$
$181$	0.878433			0.0652934			0.0326467	+	0.999467i	$0.489606\pi$
$182$	21.7104	+	1.36158i	1.60928	+	0.100927i
$183$		0			0
$184$	−7.15818	−	12.3983i	−0.527708	−	0.914017i
$185$	12.4766			0.917298
$186$		0			0
$187$	13.0606	−	22.6217i	0.955088	−	1.65426i
$188$	15.5855	+	26.9948i	1.13669	+	1.96880i
$189$		0			0
$190$	15.1278			1.09749
$191$	15.9513			1.15419			0.577097	−	0.816675i	$-0.304185\pi$
$191$	15.9513			1.15419			0.577097	+	0.816675i	$0.304185\pi$
$192$		0			0
$193$	3.95066			0.284375			0.142187	−	0.989840i	$-0.454586\pi$
$193$	3.95066			0.284375			0.142187	+	0.989840i	$0.454586\pi$
$194$	−6.14900	+	10.6504i	−0.441473	+	0.764653i
$195$		0			0
$196$	−22.3325	+	1.73222i	−1.59518	+	0.123730i
$197$	6.72353	−	11.6455i	0.479032	−	0.829708i	−0.520679	−	0.853753i	$-0.674321\pi$
$197$	6.72353	−	11.6455i	0.479032	−	0.829708i	0.999711	+	0.0240448i	$0.00765444\pi$
$198$		0			0
$199$	−10.4145	+	18.0385i	−0.738268	+	1.27872i	0.215007	+	0.976612i	$0.431023\pi$
$199$	−10.4145	+	18.0385i	−0.738268	+	1.27872i	−0.953275	+	0.302105i	$0.902311\pi$
$200$	4.96282	+	8.59586i	0.350925	+	0.607819i
$201$		0			0
$202$	3.59427	+	6.22546i	0.252892	+	0.438022i
$203$	0.971014	−	0.611897i	0.0681518	−	0.0429468i
$204$		0			0
$205$	0.791947	+	1.37169i	0.0553120	+	0.0958031i
$206$	−30.0880			−2.09633
$207$		0			0
$208$	−0.526988	+	0.236769i	−0.0365401	+	0.0164169i
$209$	11.6759			0.807636
$210$		0			0
$211$	7.17814	−	12.4329i	0.494164	−	0.855917i	−0.505814	−	0.862643i	$-0.668808\pi$
$211$	7.17814	−	12.4329i	0.494164	−	0.855917i	0.999977	+	0.00672604i	$0.00214098\pi$
$212$	2.41641			0.165960
$213$		0			0
$214$	−6.68939	+	11.5864i	−0.457277	+	0.792027i
$215$	−27.3956			−1.86836
$216$		0			0
$217$	0.274623	+	7.09175i	0.0186426	+	0.481419i
$218$	−6.25722	+	10.8378i	−0.423793	+	0.734030i
$219$		0			0
$220$	24.2943	+	42.0790i	1.63792	+	2.83697i
$221$	14.7752	+	10.6587i	0.993890	+	0.716981i
$222$		0			0
$223$	0.596931	−	1.03392i	0.0399735	−	0.0692361i	−0.845346	−	0.534218i	$-0.820606\pi$
$223$	0.596931	−	1.03392i	0.0399735	−	0.0692361i	0.885320	+	0.464982i	$0.153939\pi$
$224$	13.0676	−	8.23472i	0.873115	−	0.550205i
$225$		0			0
$226$	1.81243	−	3.13922i	0.120561	−	0.208818i
$227$	−7.94437	+	13.7600i	−0.527286	+	0.913286i	0.472208	+	0.881487i	$0.343457\pi$
$227$	−7.94437	+	13.7600i	−0.527286	+	0.913286i	−0.999494	+	0.0317993i	$0.989876\pi$
$228$		0			0
$229$	−4.39323	+	7.60931i	−0.290313	+	0.502837i	−0.973884	−	0.227047i	$-0.927093\pi$
$229$	−4.39323	+	7.60931i	−0.290313	+	0.502837i	0.683571	+	0.729884i	$0.260426\pi$
$230$	17.5219	+	30.3488i	1.15536	+	2.00114i
$231$		0			0
$232$	0.593502	−	1.02798i	0.0389653	−	0.0674899i
$233$	−2.86714	+	4.96604i	−0.187833	+	0.325336i	−0.944527	−	0.328432i	$-0.893480\pi$
$233$	−2.86714	+	4.96604i	−0.187833	+	0.325336i	0.756695	+	0.653769i	$0.226813\pi$
$234$		0			0
$235$	−14.3060	−	24.7787i	−0.933220	−	1.61638i
$236$	−5.83623	−	10.1086i	−0.379906	−	0.658017i
$237$		0			0
$238$	−26.9711	−	14.2096i	−1.74828	−	0.921074i
$239$	11.5411			0.746532			0.373266	−	0.927724i	$-0.378238\pi$
$239$	11.5411			0.746532			0.373266	+	0.927724i	$0.378238\pi$
$240$		0			0
$241$	2.83030	−	4.90223i	0.182316	−	0.315780i	−0.760353	−	0.649510i	$-0.774974\pi$
$241$	2.83030	−	4.90223i	0.182316	−	0.315780i	0.942669	+	0.333730i	$0.108307\pi$
$242$	17.9282	+	31.0526i	1.15247	+	1.99614i
$243$		0			0
$244$	−11.1273	+	19.2730i	−0.712352	+	1.23383i
$245$	20.4992	−	1.59001i	1.30964	−	0.101582i
$246$		0			0
$247$	−0.823835	+	8.10167i	−0.0524193	+	0.515497i
$248$	3.66996	+	6.35655i	0.233043	+	0.403642i
$249$		0			0
$250$	4.59673	+	7.96177i	0.290723	+	0.503546i
$251$	−12.1872	−	21.1088i	−0.769249	−	1.33238i	−0.937971	−	0.346715i	$-0.887297\pi$
$251$	−12.1872	−	21.1088i	−0.769249	−	1.33238i	0.168721	−	0.985664i	$-0.446036\pi$
$252$		0			0
$253$	13.5236	+	23.4236i	0.850223	+	1.47263i
$254$	1.58839			0.0996641
$255$		0			0
$256$	7.47442	−	12.9461i	0.467151	−	0.809130i
$257$	2.30268	+	3.98836i	0.143637	+	0.248787i	0.928864	−	0.370422i	$-0.120787\pi$
$257$	2.30268	+	3.98836i	0.143637	+	0.248787i	−0.785226	+	0.619209i	$0.787453\pi$
$258$		0			0
$259$	−0.434873	−	11.2300i	−0.0270217	−	0.697798i
$260$	−30.9121	+	13.8884i	−1.91709	+	0.861320i
$261$		0			0
$262$	−15.2997			−0.945216
$263$	−22.9824			−1.41715			−0.708576	−	0.705634i	$-0.750662\pi$
$263$	−22.9824			−1.41715			−0.708576	+	0.705634i	$0.750662\pi$
$264$		0			0
$265$	−2.21804			−0.136253
$266$	−0.527282	−	13.6163i	−0.0323297	−	0.834870i
$267$		0			0
$268$	21.3760	−	37.0244i	1.30575	−	2.26162i
$269$	7.00246	−	12.1286i	0.426948	−	0.739495i	−0.569652	−	0.821886i	$-0.692922\pi$
$269$	7.00246	−	12.1286i	0.426948	−	0.739495i	0.996600	+	0.0823905i	$0.0262555\pi$
$270$		0			0
$271$	9.55299	+	16.5463i	0.580303	+	1.00511i	0.995443	+	0.0953563i	$0.0303990\pi$
$271$	9.55299	+	16.5463i	0.580303	+	1.00511i	−0.415141	+	0.909757i	$0.636268\pi$
$272$	0.809651			0.0490923
$273$		0			0
$274$	28.5027			1.72191
$275$	−9.37604	−	16.2398i	−0.565397	−	0.979296i
$276$		0			0
$277$	−6.45998	+	11.1890i	−0.388142	+	0.672282i	−0.992200	−	0.124658i	$-0.960216\pi$
$277$	−6.45998	+	11.1890i	−0.388142	+	0.672282i	0.604057	+	0.796941i	$0.293550\pi$
$278$	1.49958	−	2.59735i	0.0899390	−	0.155779i
$279$		0			0
$280$	17.9902	−	11.3368i	1.07512	−	0.677502i
$281$	19.6264			1.17082			0.585408	−	0.810739i	$-0.300934\pi$
$281$	19.6264			1.17082			0.585408	+	0.810739i	$0.300934\pi$
$282$		0			0
$283$	3.26727			0.194219			0.0971095	−	0.995274i	$-0.469040\pi$
$283$	3.26727			0.194219			0.0971095	+	0.995274i	$0.469040\pi$
$284$	24.9907			1.48293
$285$		0			0
$286$	−38.7701	+	17.4189i	−2.29252	+	1.03000i
$287$	1.20704	−	0.760629i	0.0712490	−	0.0448985i
$288$		0			0
$289$	−4.26597	−	7.38888i	−0.250939	−	0.434640i
$290$	−1.45278	+	2.51629i	−0.0853104	+	0.147762i
$291$		0			0
$292$	50.8408			2.97523
$293$	−9.50947	−	16.4709i	−0.555549	−	0.962239i	−0.997861	−	0.0653778i	$-0.979175\pi$
$293$	−9.50947	−	16.4709i	−0.555549	−	0.962239i	0.442311	−	0.896862i	$-0.354159\pi$
$294$		0			0
$295$	5.35710	+	9.27878i	0.311903	+	0.540231i
$296$	−5.81149	−	10.0658i	−0.337786	−	0.585062i
$297$		0			0
$298$	−24.1633	−	41.8521i	−1.39974	−	2.42442i
$299$	−17.2074	+	7.73106i	−0.995132	+	0.447099i
$300$		0			0
$301$	0.954876	+	24.6584i	0.0550382	+	1.42128i
$302$	−18.0229	+	31.2165i	−1.03710	+	1.79631i
$303$		0			0
$304$	0.180952	+	0.313418i	0.0103783	+	0.0179757i
$305$	10.2138	−	17.6908i	0.584840	−	1.01297i
$306$		0			0
$307$	−8.30660			−0.474083			−0.237041	−	0.971500i	$-0.576178\pi$
$307$	−8.30660			−0.474083			−0.237041	+	0.971500i	$0.576178\pi$
$308$	37.0279	−	23.3336i	2.10986	−	1.32956i
$309$		0			0
$310$	−8.98338	−	15.5597i	−0.510221	−	0.883729i
$311$	−5.42853	−	9.40250i	−0.307824	−	0.533167i	0.670062	−	0.742305i	$-0.266267\pi$
$311$	−5.42853	−	9.40250i	−0.307824	−	0.533167i	−0.977886	+	0.209138i	$0.932934\pi$
$312$		0			0
$313$	0.566928	−	0.981949i	0.0320447	−	0.0555030i	−0.849558	−	0.527495i	$-0.823131\pi$
$313$	0.566928	−	0.981949i	0.0320447	−	0.0555030i	0.881603	+	0.471992i	$0.156465\pi$
$314$	6.29842	−	10.9092i	0.355440	−	0.615641i
$315$		0			0
$316$	−24.9351	−	43.1889i	−1.40271	−	2.42956i
$317$	4.98712	−	8.63795i	0.280105	−	0.485155i	−0.691306	−	0.722562i	$-0.742964\pi$
$317$	4.98712	−	8.63795i	0.280105	−	0.485155i	0.971410	+	0.237407i	$0.0762975\pi$
$318$		0			0
$319$	−1.12128	+	1.94211i	−0.0627795	+	0.108737i
$320$	−19.0804	+	33.0483i	−1.06663	+	1.84746i
$321$		0			0
$322$	26.7058	−	16.8290i	1.48825	−	0.937843i
$323$	5.70622	−	9.88347i	0.317503	−	0.549931i
$324$		0			0
$325$	11.9301	−	5.36001i	0.661760	−	0.297320i
$326$	−3.59005	−	6.21815i	−0.198835	−	0.344392i
$327$		0			0
$328$	0.737763	−	1.27784i	0.0407362	−	0.0705571i
$329$	−21.8043	+	13.7403i	−1.20211	+	0.757525i
$330$		0			0
$331$	−1.65514			−0.0909746			−0.0454873	−	0.998965i	$-0.514484\pi$
$331$	−1.65514			−0.0909746			−0.0454873	+	0.998965i	$0.514484\pi$
$332$	21.1755	−	36.6770i	1.16216	−	2.01291i
$333$		0			0
$334$	−30.6091			−1.67486
$335$	−19.6212	+	33.9849i	−1.07202	+	1.85679i
$336$		0			0
$337$	−12.4081			−0.675913			−0.337956	−	0.941162i	$-0.609736\pi$
$337$	−12.4081			−0.675913			−0.337956	+	0.941162i	$0.609736\pi$
$338$	−9.35107	−	28.1309i	−0.508631	−	1.53012i
$339$		0			0
$340$	47.4925			2.57564
$341$	−6.93349	−	12.0092i	−0.375469	−	0.650332i
$342$		0			0
$343$	−2.14565	−	18.3955i	−0.115854	−	0.993266i
$344$	12.7606	+	22.1021i	0.688007	+	1.19166i
$345$		0			0
$346$	14.6498	+	25.3743i	0.787581	+	1.36413i
$347$	6.62262	−	11.4707i	0.355521	−	0.615780i	−0.631686	−	0.775224i	$-0.717637\pi$
$347$	6.62262	−	11.4707i	0.355521	−	0.615780i	0.987207	+	0.159444i	$0.0509702\pi$
$348$		0			0
$349$	17.5068	−	30.3227i	0.937119	−	1.62314i	0.166307	−	0.986074i	$-0.446816\pi$
$349$	17.5068	−	30.3227i	0.937119	−	1.62314i	0.770812	−	0.637063i	$-0.219851\pi$
$350$	−18.5153	+	11.6677i	−0.989685	+	0.623663i
$351$		0			0
$352$	−15.0898	+	26.1363i	−0.804289	+	1.39307i
$353$	−23.1083			−1.22993			−0.614964	−	0.788555i	$-0.710829\pi$
$353$	−23.1083			−1.22993			−0.614964	+	0.788555i	$0.710829\pi$
$354$		0			0
$355$	−22.9391			−1.21748
$356$	12.8089			0.678873
$357$		0			0
$358$	−21.2827	−	36.8628i	−1.12483	−	1.94826i
$359$	6.44458	−	11.1623i	0.340132	−	0.589126i	−0.644325	−	0.764752i	$-0.722862\pi$
$359$	6.44458	−	11.1623i	0.340132	−	0.589126i	0.984457	+	0.175626i	$0.0561949\pi$
$360$		0			0
$361$	−13.8988			−0.731515
$362$	1.00156	+	1.73476i	0.0526409	+	0.0911768i
$363$		0			0
$364$	13.5781	+	27.3394i	0.711688	+	1.43297i
$365$	−46.6670			−2.44266
$366$		0			0
$367$	−26.4929			−1.38292			−0.691460	−	0.722415i	$-0.743032\pi$
$367$	−26.4929			−1.38292			−0.691460	+	0.722415i	$0.743032\pi$
$368$	−0.419177	+	0.726035i	−0.0218511	+	0.0378472i
$369$		0			0
$370$	14.2254	+	24.6392i	0.739545	+	1.28093i
$371$	0.0773099	+	1.99642i	0.00401373	+	0.103649i
$372$		0			0
$373$	−12.3710			−0.640545			−0.320273	−	0.947325i	$-0.603775\pi$
$373$	−12.3710			−0.640545			−0.320273	+	0.947325i	$0.603775\pi$
$374$	59.5653			3.08005
$375$		0			0
$376$	−13.3272	+	23.0834i	−0.687298	+	1.19043i
$377$	−1.26848	−	0.915067i	−0.0653300	−	0.0471284i
$378$		0			0
$379$	−14.0179	+	24.2797i	−0.720050	+	1.24716i	0.240929	+	0.970543i	$0.422548\pi$
$379$	−14.0179	+	24.2797i	−0.720050	+	1.24716i	−0.960979	+	0.276621i	$0.910785\pi$
$380$	10.6143	+	18.3844i	0.544500	+	0.943102i
$381$		0			0
$382$	18.1872	+	31.5011i	0.930537	+	1.61174i
$383$	26.2903			1.34337			0.671687	−	0.740835i	$-0.265570\pi$
$383$	26.2903			1.34337			0.671687	+	0.740835i	$0.265570\pi$
$384$		0			0
$385$	−33.9881	+	21.4181i	−1.73219	+	1.09157i
$386$	4.50442	+	7.80188i	0.229269	+	0.397105i
$387$		0			0
$388$	−17.2575			−0.876117
$389$	13.4205	+	23.2449i	0.680445	+	1.17856i	0.974845	+	0.222883i	$0.0715467\pi$
$389$	13.4205	+	23.2449i	0.680445	+	1.17856i	−0.294400	+	0.955682i	$0.595120\pi$
$390$		0			0
$391$	26.4371			1.33698
$392$	−10.8311	−	15.7976i	−0.547053	−	0.797897i
$393$		0			0
$394$	30.6639			1.54482
$395$	22.8881	+	39.6433i	1.15162	+	1.99467i
$396$		0			0
$397$	24.5243			1.23084			0.615419	−	0.788200i	$-0.288987\pi$
$397$	24.5243			1.23084			0.615419	+	0.788200i	$0.288987\pi$
$398$	−47.4974			−2.38083
$399$		0			0
$400$	0.290618	−	0.503366i	0.0145309	−	0.0251683i
$401$	1.58285	+	2.74158i	0.0790438	+	0.136908i	0.902838	−	0.429982i	$-0.141480\pi$
$401$	1.58285	+	2.74158i	0.0790438	+	0.136908i	−0.823794	+	0.566889i	$0.808147\pi$
$402$		0			0
$403$	8.82216	−	3.96367i	0.439463	−	0.197445i
$404$	−5.04376	+	8.73605i	−0.250936	+	0.434635i
$405$		0			0
$406$	2.31551	+	1.21992i	0.114917	+	0.0605437i
$407$	10.9794	+	19.0169i	0.544228	+	0.942630i
$408$		0			0
$409$	−9.53424	+	16.5138i	−0.471438	+	0.816555i	−0.999466	−	0.0326723i	$-0.989598\pi$
$409$	−9.53424	+	16.5138i	−0.471438	+	0.816555i	0.528028	+	0.849227i	$0.322932\pi$
$410$	−1.80591	+	3.12792i	−0.0891874	+	0.154477i
$411$		0			0
$412$	−21.1109	−	36.5652i	−1.04006	−	1.80144i
$413$	8.16496	−	5.14526i	0.401771	−	0.253182i
$414$		0			0
$415$	−19.4371	+	33.6660i	−0.954129	+	1.65260i
$416$	−17.0708	−	12.3147i	−0.836964	−	0.603777i
$417$		0			0
$418$	13.3125	+	23.0579i	0.651134	+	1.12780i
$419$	−7.80534	+	13.5192i	−0.381316	+	0.660458i	−0.991251	−	0.131993i	$-0.957862\pi$
$419$	−7.80534	+	13.5192i	−0.381316	+	0.660458i	0.609935	+	0.792452i	$0.291196\pi$
$420$		0			0
$421$	−18.0525			−0.879827			−0.439913	−	0.898040i	$-0.644991\pi$
$421$	−18.0525			−0.879827			−0.439913	+	0.898040i	$0.644991\pi$
$422$	32.7372			1.59362
$423$		0			0
$424$	1.03314	+	1.78945i	0.0501738	+	0.0869036i
$425$	−18.3290			−0.889088
$426$		0			0
$427$	−16.2792	−	8.57667i	−0.787807	−	0.415054i
$428$	−18.7741			−0.907481
$429$		0			0
$430$	−31.2356	−	54.1017i	−1.50632	−	2.60902i
$431$	17.5165			0.843741			0.421871	−	0.906656i	$-0.361374\pi$
$431$	17.5165			0.843741			0.421871	+	0.906656i	$0.361374\pi$
$432$		0			0
$433$	−3.02961	−	5.24744i	−0.145594	−	0.252176i	0.784001	−	0.620760i	$-0.213176\pi$
$433$	−3.02961	−	5.24744i	−0.145594	−	0.252176i	−0.929594	+	0.368584i	$0.879843\pi$
$434$	−13.6919	+	8.62813i	−0.657232	+	0.414163i
$435$		0			0
$436$	−17.5612			−0.841030
$437$	5.90851	+	10.2338i	0.282642	+	0.489551i
$438$		0			0
$439$	−11.6912	−	20.2497i	−0.557990	−	0.966467i	−0.997664	−	0.0683098i	$-0.978239\pi$
$439$	−11.6912	−	20.2497i	−0.557990	−	0.966467i	0.439674	−	0.898157i	$-0.355094\pi$
$440$	−20.7742	+	35.9819i	−0.990370	+	1.71537i
$441$		0			0
$442$	−4.20286	+	41.3313i	−0.199910	+	1.96593i
$443$	−4.44712	+	7.70264i	−0.211289	+	0.365963i	−0.952118	−	0.305730i	$-0.901099\pi$
$443$	−4.44712	+	7.70264i	−0.211289	+	0.365963i	0.740829	+	0.671693i	$0.234433\pi$
$444$		0			0
$445$	−11.7574			−0.557354
$446$	2.72241			0.128910
$447$		0			0
$448$	30.4113	+	16.0221i	1.43680	+	0.756973i
$449$	19.3671	+	33.5448i	0.913989	+	1.58308i	0.808375	+	0.588668i	$0.200348\pi$
$449$	19.3671	+	33.5448i	0.913989	+	1.58308i	0.105614	+	0.994407i	$0.466319\pi$
$450$		0			0
$451$	−1.39382	+	2.41417i	−0.0656326	+	0.113679i
$452$	5.08668			0.239258
$453$		0			0
$454$	−36.2317			−1.70044
$455$	−12.4634	−	25.0950i	−0.584295	−	1.17647i
$456$		0			0
$457$	−11.2001	−	19.3992i	−0.523920	−	0.907457i	−0.999612	−	0.0278448i	$-0.991136\pi$
$457$	−11.2001	−	19.3992i	−0.523920	−	0.907457i	0.475692	−	0.879612i	$-0.342198\pi$
$458$	−20.0361			−0.936227
$459$		0			0
$460$	−24.5881	+	42.5878i	−1.14642	+	1.98567i
$461$	1.40367	+	2.43123i	0.0653755	+	0.113234i	0.896860	−	0.442314i	$-0.145842\pi$
$461$	1.40367	+	2.43123i	0.0653755	+	0.113234i	−0.831485	+	0.555547i	$0.812509\pi$
$462$		0			0
$463$	37.7530			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$463$	37.7530			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$464$	−0.0695099			−0.00322692
$465$		0			0
$466$	−13.0761			−0.605740
$467$	8.04389	−	13.9324i	0.372227	−	0.644716i	−0.617681	−	0.786429i	$-0.711928\pi$
$467$	8.04389	−	13.9324i	0.372227	−	0.644716i	0.989908	+	0.141713i	$0.0452609\pi$
$468$		0			0
$469$	31.2731	+	16.4762i	1.44406	+	0.760798i
$470$	32.6225	−	56.5038i	1.50476	−	2.60633i
$471$		0			0
$472$	4.99058	−	8.64394i	0.229710	−	0.397870i
$473$	−24.1081	−	41.7564i	−1.10849	−	1.91996i
$474$		0			0
$475$	−4.09642	−	7.09520i	−0.187956	−	0.325550i
$476$	−1.65536	−	42.7473i	−0.0758731	−	1.95932i
$477$		0			0
$478$	13.1588	+	22.7917i	0.601870	+	1.04247i
$479$	−8.54850			−0.390591			−0.195295	−	0.980744i	$-0.562567\pi$
$479$	−8.54850			−0.390591			−0.195295	+	0.980744i	$0.562567\pi$
$480$		0			0
$481$	−13.9701	+	6.27659i	−0.636984	+	0.286188i
$482$	12.9081			0.587948
$483$		0			0
$484$	−25.1583	+	43.5754i	−1.14356	+	1.98070i
$485$	15.8407			0.719291
$486$		0			0
$487$	17.7881	−	30.8098i	0.806054	−	1.39613i	−0.109524	−	0.993984i	$-0.534932\pi$
$487$	17.7881	−	30.8098i	0.806054	−	1.39613i	0.915577	−	0.402142i	$-0.131734\pi$
$488$	−19.0300			−0.861447
$489$		0			0
$490$	26.5125	+	38.6695i	1.19771	+	1.74691i
$491$	−15.6990	+	27.1914i	−0.708485	+	1.22713i	0.256934	+	0.966429i	$0.417288\pi$
$491$	−15.6990	+	27.1914i	−0.708485	+	1.22713i	−0.965419	+	0.260703i	$0.916046\pi$
$492$		0			0
$493$	1.09598	+	1.89829i	0.0493605	+	0.0854949i
$494$	−16.9387	+	7.61034i	−0.762110	+	0.342406i
$495$		0			0
$496$	0.214909	−	0.372234i	0.00964972	−	0.0167138i
$497$	0.799545	+	20.6471i	0.0358645	+	0.926151i
$498$		0			0
$499$	2.14606	−	3.71708i	0.0960708	−	0.166399i	−0.813984	−	0.580887i	$-0.802706\pi$
$499$	2.14606	−	3.71708i	0.0960708	−	0.166399i	0.910055	+	0.414488i	$0.136039\pi$
$500$	−6.45048	+	11.1726i	−0.288474	+	0.499652i
$501$		0			0
$502$	27.7909	−	48.1353i	1.24037	−	2.14839i
$503$	−7.83439	−	13.5696i	−0.349318	−	0.605037i	0.636810	−	0.771021i	$-0.280253\pi$
$503$	−7.83439	−	13.5696i	−0.349318	−	0.605037i	−0.986129	+	0.165984i	$0.946920\pi$
$504$		0			0
$505$	4.62969	−	8.01886i	0.206019	−	0.356835i
$506$	−30.8385	+	53.4138i	−1.37094	+	2.37453i
$507$		0			0
$508$	1.11447	+	1.93032i	0.0494467	+	0.0856442i
$509$	0.851865	+	1.47547i	0.0377583	+	0.0653992i	0.884287	−	0.466944i	$-0.154645\pi$
$509$	0.851865	+	1.47547i	0.0377583	+	0.0653992i	−0.846529	+	0.532343i	$0.821312\pi$
$510$		0			0
$511$	1.62658	+	42.0043i	0.0719558	+	1.85816i
$512$	−1.81234			−0.0800947
$513$		0			0
$514$	−5.25089	+	9.09481i	−0.231607	+	0.401155i
$515$	19.3778	+	33.5633i	0.853888	+	1.47898i
$516$		0			0
$517$	25.1785	−	43.6104i	1.10735	−	1.91798i
$518$	21.6815	−	13.6629i	0.952631	−	0.600313i
$519$		0			0
$520$	−23.5014	−	16.9537i	−1.03061	−	0.743468i
$521$	−8.39696	−	14.5440i	−0.367878	−	0.637183i	0.621356	−	0.783528i	$-0.286582\pi$
$521$	−8.39696	−	14.5440i	−0.367878	−	0.637183i	−0.989234	+	0.146346i	$0.953249\pi$
$522$		0			0
$523$	3.74526	+	6.48697i	0.163769	+	0.283656i	0.936217	−	0.351422i	$-0.114302\pi$
$523$	3.74526	+	6.48697i	0.163769	+	0.283656i	−0.772449	+	0.635077i	$0.780968\pi$
$524$	−10.7348	−	18.5933i	−0.468953	−	0.812251i
$525$		0			0
$526$	−26.2038	−	45.3863i	−1.14254	−	1.97894i
$527$	−13.5541			−0.590427
$528$		0			0
$529$	−2.18713	+	3.78822i	−0.0950926	+	0.164705i
$530$	−2.52894	−	4.38025i	−0.109850	−	0.190266i
$531$		0			0
$532$	16.1776	−	10.1945i	0.701388	−	0.441989i
$533$	−1.57681	−	1.13749i	−0.0682990	−	0.0492702i
$534$		0			0
$535$	17.2329			0.745041
$536$	36.5574			1.57904
$537$		0			0
$538$	31.9360			1.37686
$539$	20.4627	+	29.8456i	0.881392	+	1.28554i
$540$		0			0
$541$	4.78963	−	8.29588i	0.205922	−	0.356668i	−0.744504	−	0.667618i	$-0.767314\pi$
$541$	4.78963	−	8.29588i	0.205922	−	0.356668i	0.950426	+	0.310950i	$0.100647\pi$
$542$	−21.7840	+	37.7311i	−0.935705	+	1.62069i
$543$		0			0
$544$	14.7494	+	25.5466i	0.632373	+	1.09530i
$545$	16.1195			0.690485
$546$		0			0
$547$	−30.1843			−1.29059			−0.645293	−	0.763935i	$-0.723265\pi$
$547$	−30.1843			−1.29059			−0.645293	+	0.763935i	$0.723265\pi$
$548$	19.9986	+	34.6385i	0.854296	+	1.47968i
$549$		0			0
$550$	21.3806	−	37.0322i	0.911670	−	1.57906i
$551$	−0.489889	+	0.848513i	−0.0208700	+	0.0361479i
$552$		0			0
$553$	34.8845	−	21.9829i	1.48344	−	0.934810i
$554$	−29.4619			−1.25172
$555$		0			0
$556$	4.20866			0.178487
$557$	4.67142			0.197935			0.0989673	−	0.995091i	$-0.468446\pi$
$557$	4.67142			0.197935			0.0989673	+	0.995091i	$0.468446\pi$
$558$		0			0
$559$	30.6751	−	13.7819i	1.29742	−	0.582912i
$560$	−1.10167	−	0.580414i	−0.0465542	−	0.0245270i
$561$		0			0
$562$	22.3775	+	38.7589i	0.943937	+	1.63495i
$563$	−7.19090	+	12.4550i	−0.303060	+	0.524915i	−0.976828	−	0.214028i	$-0.931342\pi$
$563$	−7.19090	+	12.4550i	−0.303060	+	0.524915i	0.673767	+	0.738943i	$0.264675\pi$
$564$		0			0
$565$	−4.66909			−0.196430
$566$	3.72524	+	6.45231i	0.156584	+	0.271211i
$567$		0			0
$568$	10.6848	+	18.5067i	0.448326	+	0.776523i
$569$	−7.28779	−	12.6228i	−0.305520	−	0.529176i	0.671857	−	0.740681i	$-0.265497\pi$
$569$	−7.28779	−	12.6228i	−0.305520	−	0.529176i	−0.977377	+	0.211505i	$0.932164\pi$
$570$		0			0
$571$	−12.9575	−	22.4430i	−0.542254	−	0.939211i	−0.998774	−	0.0494981i	$-0.984238\pi$
$571$	−12.9575	−	22.4430i	−0.542254	−	0.939211i	0.456520	−	0.889713i	$-0.349096\pi$
$572$	−48.3712	−	34.8945i	−2.02250	−	1.45901i
$573$		0			0
$574$	2.87834	+	1.51645i	0.120140	+	0.0632952i
$575$	9.48940	−	16.4361i	0.395735	−	0.685433i
$576$		0			0
$577$	11.7875	+	20.4165i	0.490719	+	0.849950i	0.999943	−	0.0106839i	$-0.00340085\pi$
$577$	11.7875	+	20.4165i	0.490719	+	0.849950i	−0.509224	+	0.860634i	$0.670068\pi$
$578$	9.72786	−	16.8491i	0.404626	−	0.700832i
$579$		0			0
$580$	−4.07731			−0.169301
$581$	30.9797	+	16.3216i	1.28526	+	0.677133i
$582$		0			0
$583$	−1.95187	−	3.38074i	−0.0808382	−	0.140016i
$584$	21.7371	+	37.6497i	0.899487	+	1.55796i
$585$		0			0
$586$	21.6848	−	37.5592i	0.895791	−	1.55156i
$587$	23.7561	−	41.1468i	0.980521	−	1.69831i	0.320160	−	0.947364i	$-0.396263\pi$
$587$	23.7561	−	41.1468i	0.980521	−	1.69831i	0.660361	−	0.750948i	$-0.270403\pi$
$588$		0			0
$589$	−3.02926	−	5.24683i	−0.124818	−	0.216192i
$590$	−12.2160	+	21.1588i	−0.502925	+	0.871092i
$591$		0			0
$592$	−0.340316	+	0.589444i	−0.0139869	+	0.0242260i
$593$	2.36887	−	4.10300i	0.0972779	−	0.168490i	−0.813279	−	0.581874i	$-0.802320\pi$
$593$	2.36887	−	4.10300i	0.0972779	−	0.168490i	0.910557	+	0.413384i	$0.135653\pi$
$594$		0			0
$595$	1.51946	+	39.2379i	0.0622917	+	1.60860i
$596$	33.9078	−	58.7300i	1.38892	−	2.40568i
$597$		0			0
$598$	−34.8870	−	25.1671i	−1.42663	−	1.02916i
$599$	−1.07453	−	1.86114i	−0.0439041	−	0.0760441i	0.843238	−	0.537540i	$-0.180646\pi$
$599$	−1.07453	−	1.86114i	−0.0439041	−	0.0760441i	−0.887142	+	0.461496i	$0.847313\pi$
$600$		0			0
$601$	0.736182	−	1.27511i	0.0300295	−	0.0520126i	−0.850620	−	0.525781i	$-0.823773\pi$
$601$	0.736182	−	1.27511i	0.0300295	−	0.0520126i	0.880650	+	0.473768i	$0.157107\pi$
$602$	−47.6074	+	30.0004i	−1.94033	+	1.22273i
$603$		0			0
$604$	−50.5821			−2.05816
$605$	23.0929	−	39.9980i	0.938859	−	1.62615i
$606$		0			0
$607$	−12.9859			−0.527082			−0.263541	−	0.964648i	$-0.584890\pi$
$607$	−12.9859			−0.527082			−0.263541	+	0.964648i	$0.584890\pi$
$608$	−6.59277	+	11.4190i	−0.267372	+	0.463102i
$609$		0			0
$610$	46.5818			1.88604
$611$	28.4839	+	20.5480i	1.15234	+	0.831283i
$612$		0			0
$613$	−40.1092			−1.61999			−0.809997	−	0.586433i	$-0.800532\pi$
$613$	−40.1092			−1.61999			−0.809997	+	0.586433i	$0.800532\pi$
$614$	−9.47093	−	16.4041i	−0.382216	−	0.662017i
$615$		0			0
$616$	33.1109	+	17.4444i	1.33407	+	0.702853i
$617$	−8.82052	−	15.2776i	−0.355101	−	0.615052i	0.632035	−	0.774940i	$-0.282220\pi$
$617$	−8.82052	−	15.2776i	−0.355101	−	0.615052i	−0.987135	+	0.159888i	$0.948887\pi$
$618$		0			0
$619$	13.3825	+	23.1792i	0.537890	+	0.931652i	0.999017	+	0.0443184i	$0.0141116\pi$
$619$	13.3825	+	23.1792i	0.537890	+	0.931652i	−0.461128	+	0.887334i	$0.652555\pi$
$620$	12.6062	−	21.8345i	0.506276	−	0.876895i
$621$		0			0
$622$	12.3789	−	21.4409i	0.496349	−	0.859701i
$623$	0.409805	+	10.5826i	0.0164185	+	0.423985i
$624$		0			0
$625$	14.9895	−	25.9625i	0.599579	−	1.03850i
$626$	2.58558			0.103340
$627$		0			0
$628$	17.6768			0.705383
$629$	21.4634			0.855800
$630$		0			0
$631$	10.1224	+	17.5324i	0.402964	+	0.697955i	0.994082	−	0.108630i	$-0.0346465\pi$
$631$	10.1224	+	17.5324i	0.402964	+	0.697955i	−0.591118	+	0.806585i	$0.701313\pi$
$632$	21.3221	−	36.9309i	0.848147	−	1.46903i
$633$		0			0
$634$	22.7447			0.903306
$635$	−1.02298	−	1.77185i	−0.0405957	−	0.0703138i
$636$		0			0
$637$	−22.1532	+	12.0928i	−0.877741	+	0.479136i
$638$	−5.11379			−0.202457
$639$		0			0
$640$	−52.7247			−2.08413
$641$	−7.38825	+	12.7968i	−0.291819	+	0.505445i	−0.974240	−	0.225515i	$-0.927594\pi$
$641$	−7.38825	+	12.7968i	−0.291819	+	0.505445i	0.682421	+	0.730959i	$0.260927\pi$
$642$		0			0
$643$	4.74073	+	8.21118i	0.186956	+	0.323817i	0.944234	−	0.329276i	$-0.106804\pi$
$643$	4.74073	+	8.21118i	0.186956	+	0.323817i	−0.757278	+	0.653093i	$0.773471\pi$
$644$	39.1896	+	20.6469i	1.54429	+	0.813603i
$645$		0			0
$646$	26.0242			1.02391
$647$	49.9026			1.96187			0.980937	−	0.194327i	$-0.0622522\pi$
$647$	49.9026			1.96187			0.980937	+	0.194327i	$0.0622522\pi$
$648$		0			0
$649$	−9.42848	+	16.3306i	−0.370100	+	0.641033i
$650$	24.1874	+	17.4485i	0.948708	+	0.684388i
$651$		0			0
$652$	5.03784	−	8.72579i	0.197297	−	0.341728i
$653$	20.7019	+	35.8568i	0.810128	+	1.40318i	0.912774	+	0.408466i	$0.133936\pi$
$653$	20.7019	+	35.8568i	0.810128	+	1.40318i	−0.102645	+	0.994718i	$0.532731\pi$
$654$		0			0
$655$	9.85355	+	17.0668i	0.385010	+	0.666857i
$656$	−0.0864055			−0.00337357
$657$		0			0
$658$	−51.9953	−	27.3936i	−2.02699	−	1.06791i
$659$	−1.08993	−	1.88781i	−0.0424576	−	0.0735387i	0.844016	−	0.536318i	$-0.180185\pi$
$659$	−1.08993	−	1.88781i	−0.0424576	−	0.0735387i	−0.886473	+	0.462780i	$0.846852\pi$
$660$		0			0
$661$	32.8566			1.27797			0.638986	−	0.769218i	$-0.279354\pi$
$661$	32.8566			1.27797			0.638986	+	0.769218i	$0.279354\pi$
$662$	−1.88714	−	3.26862i	−0.0733457	−	0.127038i
$663$		0			0
$664$	36.2145			1.40539
$665$	−14.8495	+	9.35760i	−0.575838	+	0.362872i
$666$		0			0
$667$	−2.26967			−0.0878819
$668$	−21.4765	−	37.1984i	−0.830951	−	1.43925i
$669$		0			0
$670$	−89.4858			−3.45714
$671$	35.9525			1.38793
$672$		0			0
$673$	−5.61199	+	9.72024i	−0.216326	+	0.374688i	−0.953682	−	0.300817i	$-0.902741\pi$
$673$	−5.61199	+	9.72024i	−0.216326	+	0.374688i	0.737356	+	0.675505i	$0.236074\pi$
$674$	−14.1473	−	24.5039i	−0.544936	−	0.943856i
$675$		0			0
$676$	27.6257	−	31.1018i	1.06253	−	1.19622i
$677$	−10.0207	+	17.3564i	−0.385127	+	0.667059i	−0.991787	−	0.127902i	$-0.959176\pi$
$677$	−10.0207	+	17.3564i	−0.385127	+	0.667059i	0.606660	+	0.794961i	$0.292509\pi$
$678$		0			0
$679$	−0.552131	−	14.2580i	−0.0211888	−	0.547172i
$680$	20.3055	+	35.1702i	0.778680	+	1.34871i
$681$		0			0
$682$	15.8107	−	27.3849i	0.605423	−	1.04862i
$683$	7.33004	−	12.6960i	0.280476	−	0.485799i	−0.691026	−	0.722830i	$-0.742841\pi$
$683$	7.33004	−	12.6960i	0.280476	−	0.485799i	0.971502	+	0.237031i	$0.0761743\pi$
$684$		0			0
$685$	−18.3568	−	31.7949i	−0.701376	−	1.21482i
$686$	33.8817	−	25.2113i	1.29361	−	0.962573i
$687$		0			0
$688$	0.747251	−	1.29428i	0.0284887	−	0.0493438i
$689$	2.48355	−	1.11583i	0.0946159	−	0.0425096i
$690$		0			0
$691$	−14.4726	−	25.0673i	−0.550565	−	0.953606i	−0.998234	−	0.0594069i	$-0.981079\pi$
$691$	−14.4726	−	25.0673i	−0.550565	−	0.953606i	0.447669	−	0.894199i	$-0.352254\pi$
$692$	−20.5578	+	35.6071i	−0.781490	+	1.35358i
$693$		0			0
$694$	30.2036			1.14651
$695$	−3.86315			−0.146538
$696$		0			0
$697$	1.36238	+	2.35971i	0.0516037	+	0.0893803i
$698$	79.8430			3.02210
$699$		0			0
$700$	−27.1705	−	14.3147i	−1.02695	−	0.541044i
$701$	37.6521			1.42210			0.711051	−	0.703141i	$-0.248220\pi$
$701$	37.6521			1.42210			0.711051	+	0.703141i	$0.248220\pi$
$702$		0			0
$703$	4.79692	+	8.30851i	0.180919	+	0.313362i
$704$	−67.1630			−2.53130
$705$		0			0
$706$	−26.3473	−	45.6349i	−0.991595	−	1.71749i
$707$	−7.37902	−	3.88761i	−0.277517	−	0.146209i
$708$		0			0
$709$	22.4214			0.842053			0.421026	−	0.907048i	$-0.361670\pi$
$709$	22.4214			0.842053			0.421026	+	0.907048i	$0.361670\pi$
$710$	−26.1545	−	45.3009i	−0.981560	−	1.70011i
$711$		0			0
$712$	5.47649	+	9.48555i	0.205240	+	0.355486i
$713$	7.01731	−	12.1543i	0.262800	−	0.455184i
$714$		0			0
$715$	44.4002	+	32.0298i	1.66047	+	1.19785i
$716$	29.8655	−	51.7286i	1.11613	−	1.93319i
$717$		0			0
$718$	29.3917			1.09689
$719$	−8.37217			−0.312229			−0.156115	−	0.987739i	$-0.549897\pi$
$719$	−8.37217			−0.312229			−0.156115	+	0.987739i	$0.549897\pi$
$720$		0			0
$721$	29.5344	−	18.6115i	1.09992	−	0.693129i
$722$	−15.8470	−	27.4478i	−0.589763	−	1.02150i
$723$		0			0
$724$	−1.40547	+	2.43434i	−0.0522338	+	0.0904717i
$725$	1.57358			0.0584412
$726$		0			0
$727$	20.0990			0.745432			0.372716	−	0.927945i	$-0.378427\pi$
$727$	20.0990			0.745432			0.372716	+	0.927945i	$0.378427\pi$
$728$	−14.4406	+	21.7442i	−0.535204	+	0.805893i
$729$		0			0
$730$	−53.2083	−	92.1596i	−1.96933	−	3.41098i
$731$	−47.1284			−1.74311
$732$		0			0
$733$	5.77804	−	10.0079i	0.213417	−	0.369649i	−0.739365	−	0.673305i	$-0.764874\pi$
$733$	5.77804	−	10.0079i	0.213417	−	0.369649i	0.952782	+	0.303656i	$0.0982074\pi$
$734$	−30.2064	−	52.3191i	−1.11494	−	1.93113i
$735$		0			0
$736$	−30.5444			−1.12588
$737$	−69.0664			−2.54409
$738$		0			0
$739$	24.2650			0.892601			0.446300	−	0.894883i	$-0.352741\pi$
$739$	24.2650			0.892601			0.446300	+	0.894883i	$0.352741\pi$
$740$	−19.9622	+	34.5756i	−0.733826	+	1.27102i
$741$		0			0
$742$	−3.85445	+	2.42893i	−0.141501	+	0.0891689i
$743$	−0.777681	+	1.34698i	−0.0285303	+	0.0494160i	−0.879938	−	0.475088i	$-0.842416\pi$
$743$	−0.777681	+	1.34698i	−0.0285303	+	0.0494160i	0.851408	+	0.524504i	$0.175749\pi$
$744$		0			0
$745$	−31.1241	+	53.9086i	−1.14030	+	1.97506i
$746$	−14.1050	−	24.4306i	−0.516422	−	0.894468i
$747$		0			0
$748$	41.7933	+	72.3881i	1.52811	+	2.64677i
$749$	−0.600653	−	15.5110i	−0.0219474	−	0.566761i
$750$		0			0
$751$	17.6793	+	30.6214i	0.645125	+	1.11739i	0.984273	+	0.176656i	$0.0565281\pi$
$751$	17.6793	+	30.6214i	0.645125	+	1.11739i	−0.339148	+	0.940733i	$0.610139\pi$
$752$	1.56086			0.0569186
$753$		0			0
$754$	0.360823	−	3.54836i	0.0131404	−	0.129224i
$755$	46.4295			1.68974
$756$		0			0
$757$	9.73684	−	16.8647i	0.353891	−	0.612958i	−0.633036	−	0.774122i	$-0.718192\pi$
$757$	9.73684	−	16.8647i	0.353891	−	0.612958i	0.986928	+	0.161164i	$0.0515249\pi$
$758$	−63.9310			−2.32208
$759$		0			0
$760$	−9.07629	+	15.7206i	−0.329232	+	0.570246i
$761$	−17.6396			−0.639434			−0.319717	−	0.947513i	$-0.603588\pi$
$761$	−17.6396			−0.639434			−0.319717	+	0.947513i	$0.603588\pi$
$762$		0			0
$763$	−0.561848	−	14.5089i	−0.0203403	−	0.525259i
$764$	−25.5216	+	44.2048i	−0.923341	+	1.59927i
$765$		0			0
$766$	29.9754	+	51.9190i	1.08306	+	1.87591i
$767$	−10.6663	−	7.69452i	−0.385136	−	0.277833i
$768$		0			0
$769$	−2.32077	+	4.01969i	−0.0836890	+	0.144954i	−0.904832	−	0.425769i	$-0.860004\pi$
$769$	−2.32077	+	4.01969i	−0.0836890	+	0.144954i	0.821143	+	0.570723i	$0.193337\pi$
$770$	−81.0492	−	42.7006i	−2.92081	−	1.53882i
$771$		0			0
$772$	−6.32095	+	10.9482i	−0.227496	+	0.394034i
$773$	10.0222	−	17.3590i	0.360475	−	0.624360i	−0.627564	−	0.778565i	$-0.715948\pi$
$773$	10.0222	−	17.3590i	0.360475	−	0.624360i	0.988039	+	0.154204i	$0.0492814\pi$
$774$		0			0
$775$	−4.86516	+	8.42670i	−0.174762	+	0.302696i
$776$	−7.37848	−	12.7799i	−0.264872	−	0.458772i
$777$		0			0
$778$	−30.6032	+	53.0063i	−1.09718	+	1.90037i
$779$	−0.608965	+	1.05476i	−0.0218184	+	0.0377906i
$780$		0			0
$781$	−20.1864	−	34.9638i	−0.722326	−	1.25110i
$782$	30.1427	+	52.2087i	1.07790	+	1.86698i
$783$		0			0
$784$	−0.484023	+	1.01183i	−0.0172865	+	0.0361368i
$785$	−16.2257			−0.579119
$786$		0			0
$787$	5.05832	−	8.76128i	0.180310	−	0.312306i	−0.761676	−	0.647958i	$-0.775623\pi$
$787$	5.05832	−	8.76128i	0.180310	−	0.312306i	0.941986	+	0.335652i	$0.108957\pi$
$788$	21.5150	+	37.2650i	0.766438	+	1.32751i
$789$		0			0
$790$	−52.1925	+	90.4001i	−1.85693	+	3.21629i
$791$	0.162742	+	4.20258i	0.00578643	+	0.149426i
$792$		0			0
$793$	−2.53676	+	24.9468i	−0.0900831	+	0.885887i
$794$	27.9618	+	48.4313i	0.992328	+	1.71876i
$795$		0			0
$796$	−33.3260	−	57.7223i	−1.18121	−	2.04591i
$797$	4.44188	+	7.69357i	0.157340	+	0.272520i	0.933908	−	0.357512i	$-0.116375\pi$
$797$	4.44188	+	7.69357i	0.157340	+	0.272520i	−0.776569	+	0.630032i	$0.783042\pi$
$798$		0			0
$799$	−24.6104	−	42.6265i	−0.870655	−	1.50802i
$800$	21.1767			0.748710
$801$		0			0
$802$	−3.60944	+	6.25172i	−0.127454	+	0.220756i
$803$	−41.0669	−	71.1300i	−1.44922	−	2.51012i
$804$		0			0
$805$	−35.9723	−	18.9519i	−1.26786	−	0.667967i
$806$	17.8863	+	12.9030i	0.630020	+	0.454489i
$807$		0			0
$808$	−8.62587			−0.303457
$809$	41.7569			1.46809			0.734047	−	0.679099i	$-0.237629\pi$
$809$	41.7569			1.46809			0.734047	+	0.679099i	$0.237629\pi$
$810$		0			0
$811$	−31.3690			−1.10151			−0.550757	−	0.834666i	$-0.685661\pi$
$811$	−31.3690			−1.10151			−0.550757	+	0.834666i	$0.685661\pi$
$812$	0.142115	+	3.66993i	0.00498726	+	0.128789i
$813$		0			0
$814$	−25.0367	+	43.3649i	−0.877537	+	1.51994i
$815$	−4.62425	+	8.00944i	−0.161981	+	0.280559i
$816$		0			0
$817$	−10.5329	−	18.2435i	−0.368499	−	0.638259i
$818$	−43.4826			−1.52033
$819$		0			0
$820$	−5.06838			−0.176995
$821$	15.2754	+	26.4577i	0.533114	+	0.923381i	0.999252	+	0.0386690i	$0.0123118\pi$
$821$	15.2754	+	26.4577i	0.533114	+	0.923381i	−0.466138	+	0.884712i	$0.654355\pi$
$822$		0			0
$823$	−1.67437	+	2.90010i	−0.0583650	+	0.101091i	−0.893732	−	0.448602i	$-0.851922\pi$
$823$	−1.67437	+	2.90010i	−0.0583650	+	0.101091i	0.835367	+	0.549693i	$0.185255\pi$
$824$	18.0520	−	31.2670i	0.628872	−	1.08924i
$825$		0			0
$826$	19.4705	+	10.2580i	0.677464	+	0.356920i
$827$	48.2646			1.67833			0.839163	−	0.543880i	$-0.183045\pi$
$827$	48.2646			1.67833			0.839163	+	0.543880i	$0.183045\pi$
$828$		0			0
$829$	49.8292			1.73064			0.865320	−	0.501219i	$-0.167115\pi$
$829$	49.8292			1.73064			0.865320	+	0.501219i	$0.167115\pi$
$830$	−88.6463			−3.07696
$831$		0			0
$832$	4.73894	−	46.6032i	0.164293	−	1.61568i
$833$	35.2645	−	2.73528i	1.22184	−	0.0947719i
$834$		0			0
$835$	19.7134	+	34.1446i	0.682210	+	1.18162i
$836$	−18.6811	+	32.3566i	−0.646098	+	1.11907i
$837$		0			0
$838$	−35.5976			−1.22970
$839$	−16.4441	−	28.4819i	−0.567712	−	0.983305i	−0.996792	−	0.0800390i	$-0.974496\pi$
$839$	−16.4441	−	28.4819i	−0.567712	−	0.983305i	0.429080	−	0.903266i	$-0.358838\pi$
$840$		0			0
$841$	14.4059	+	24.9518i	0.496755	+	0.860406i
$842$	−20.5830	−	35.6507i	−0.709335	−	1.22860i
$843$		0			0
$844$	22.9697	+	39.7846i	0.790649	+	1.36944i
$845$	−25.3577	+	28.5485i	−0.872333	+	0.982099i
$846$		0			0
$847$	−36.8065	−	19.3914i	−1.26469	−	0.666297i
$848$	0.0604999	−	0.104789i	0.00207757	−	0.00359846i
$849$		0			0
$850$	−20.8982	−	36.1967i	−0.716802	−	1.24154i
$851$	−11.1121	+	19.2468i	−0.380919	+	0.659771i
$852$		0			0
$853$	−17.9823			−0.615701			−0.307850	−	0.951435i	$-0.599610\pi$
$853$	−17.9823			−0.615701			−0.307850	+	0.951435i	$0.599610\pi$
$854$	−1.62361	−	41.9276i	−0.0555590	−	1.43473i
$855$		0			0
$856$	−8.02691	−	13.9030i	−0.274354	−	0.475195i
$857$	−23.5502	−	40.7901i	−0.804459	−	1.39336i	−0.916656	−	0.399678i	$-0.869122\pi$
$857$	−23.5502	−	40.7901i	−0.804459	−	1.39336i	0.112196	−	0.993686i	$-0.464211\pi$
$858$		0			0
$859$	−13.8486	+	23.9866i	−0.472510	+	0.818411i	−0.999505	−	0.0314573i	$-0.989985\pi$
$859$	−13.8486	+	23.9866i	−0.472510	+	0.818411i	0.526995	+	0.849868i	$0.323319\pi$
$860$	43.8322	−	75.9197i	1.49467	−	2.58884i
$861$		0			0
$862$	19.9718	+	34.5922i	0.680242	+	1.17821i
$863$	−18.5569	+	32.1414i	−0.631683	+	1.09411i	0.355525	+	0.934667i	$0.384302\pi$
$863$	−18.5569	+	32.1414i	−0.631683	+	1.09411i	−0.987208	+	0.159440i	$0.949031\pi$
$864$		0			0
$865$	18.8701	−	32.6840i	0.641602	−	1.11129i
$866$	6.90854	−	11.9659i	0.234762	−	0.406619i
$867$		0			0
$868$	−20.0923	−	10.5856i	−0.681977	−	0.359298i
$869$	−40.2829	+	69.7720i	−1.36650	+	2.36685i
$870$		0			0
$871$	4.87324	−	47.9239i	0.165123	−	1.62384i
$872$	−7.50833	−	13.0048i	−0.254264	−	0.440399i
$873$		0			0
$874$	−13.4734	+	23.3366i	−0.455745	+	0.789373i
$875$	−9.43705	−	4.97188i	−0.319031	−	0.168080i
$876$		0			0
$877$	28.2981			0.955559			0.477780	−	0.878480i	$-0.341442\pi$
$877$	28.2981			0.955559			0.477780	+	0.878480i	$0.341442\pi$
$878$	26.6599	−	46.1763i	0.899727	−	1.55837i
$879$		0			0
$880$	2.43303			0.0820176
$881$	9.74919	−	16.8861i	0.328458	−	0.568907i	−0.653748	−	0.756713i	$-0.726804\pi$
$881$	9.74919	−	16.8861i	0.328458	−	0.568907i	0.982206	+	0.187806i	$0.0601376\pi$
$882$		0			0
$883$	36.8164			1.23897			0.619485	−	0.785009i	$-0.287342\pi$
$883$	36.8164			1.23897			0.619485	+	0.785009i	$0.287342\pi$
$884$	−53.1777	+	23.8920i	−1.78856	+	0.803575i
$885$		0			0
$886$	−20.2819			−0.681383
$887$	−11.0920	−	19.2118i	−0.372432	−	0.645070i	0.617507	−	0.786565i	$-0.288143\pi$
$887$	−11.0920	−	19.2118i	−0.372432	−	0.645070i	−0.989939	+	0.141495i	$0.954809\pi$
$888$		0			0
$889$	−1.55916	+	0.982526i	−0.0522926	+	0.0329529i
$890$	−13.4054	−	23.2189i	−0.449351	−	0.778298i
$891$		0			0
$892$	1.91015	+	3.30847i	0.0639565	+	0.110776i
$893$	11.0005	−	19.0535i	0.368119	−	0.637601i
$894$		0			0
$895$	−27.4137	+	47.4820i	−0.916340	+	1.58715i
$896$	1.83772	+	47.4567i	0.0613941	+	1.58542i
$897$		0			0
$898$	−44.1635	+	76.4935i	−1.47376	+	2.55262i
$899$	1.16365			0.0388098
$900$		0			0
$901$	−3.81567			−0.127118
$902$	−6.35678			−0.211658
$903$		0			0
$904$	2.17482	+	3.76690i	0.0723335	+	0.125285i
$905$	1.29009	−	2.23450i	0.0428839	−	0.0742771i
$906$		0			0
$907$	−46.6084			−1.54761			−0.773803	−	0.633427i	$-0.781648\pi$
$907$	−46.6084			−1.54761			−0.773803	+	0.633427i	$0.781648\pi$
$908$	−25.4215	−	44.0314i	−0.843644	−	1.46123i
$909$		0			0
$910$	35.3479	−	53.2257i	1.17177	−	1.76442i
$911$	−0.542513			−0.0179743			−0.00898714	−	0.999960i	$-0.502861\pi$
$911$	−0.542513			−0.0179743			−0.00898714	+	0.999960i	$0.502861\pi$
$912$		0			0
$913$	−68.4184			−2.26432
$914$	25.5401	−	44.2368i	0.844792	−	1.46322i
$915$		0			0
$916$	−14.0581	−	24.3494i	−0.464493	−	0.804526i
$917$	15.0182	−	9.46389i	0.495943	−	0.312525i
$918$		0			0
$919$	33.6621			1.11041			0.555205	−	0.831713i	$-0.312640\pi$
$919$	33.6621			1.11041			0.555205	+	0.831713i	$0.312640\pi$
$920$	−42.0507			−1.38637
$921$		0			0
$922$	−3.20085	+	5.54403i	−0.105414	+	0.182583i
$923$	25.6851	−	11.5400i	0.845436	−	0.379843i
$924$		0			0
$925$	7.70412	−	13.3439i	0.253310	−	0.438746i
$926$	43.0449	+	74.5559i	1.41454	+	2.45006i
$927$		0			0
$928$	−1.26626	−	2.19322i	−0.0415669	−	0.0719961i
$929$	42.6784			1.40023			0.700116	−	0.714029i	$-0.253131\pi$
$929$	42.6784			1.40023			0.700116	+	0.714029i	$0.253131\pi$
$930$		0			0
$931$	8.94021	+	13.0396i	0.293004	+	0.427357i
$932$	−9.17471	−	15.8911i	−0.300528	−	0.520529i
$933$		0			0
$934$	36.6856			1.20039
$935$	−38.3623	−	66.4454i	−1.25458	−	2.17300i
$936$		0			0
$937$	−10.2859			−0.336026			−0.168013	−	0.985785i	$-0.553735\pi$
$937$	−10.2859			−0.336026			−0.168013	+	0.985785i	$0.553735\pi$
$938$	3.11904	+	80.5448i	0.101840	+	2.62988i
$939$		0			0
$940$	91.5568			2.98625
$941$	−5.84119	−	10.1172i	−0.190417	−	0.329813i	0.754971	−	0.655758i	$-0.227651\pi$
$941$	−5.84119	−	10.1172i	−0.190417	−	0.329813i	−0.945389	+	0.325945i	$0.894317\pi$
$942$		0			0
$943$	−2.82135			−0.0918758
$944$	−0.584488			−0.0190235
$945$		0			0
$946$	54.9746	−	95.2188i	1.78738	−	3.09583i
$947$	15.9404	+	27.6096i	0.517993	+	0.897190i	0.999782	+	0.0209026i	$0.00665399\pi$
$947$	15.9404	+	27.6096i	0.517993	+	0.897190i	−0.481789	+	0.876287i	$0.660013\pi$
$948$		0			0
$949$	52.2535	−	23.4768i	1.69622	−	0.762088i
$950$	9.34122	−	16.1795i	0.303069	−	0.524931i
$951$		0			0
$952$	30.9484	−	19.5025i	1.00304	−	0.632080i
$953$	−3.72492	−	6.45175i	−0.120662	−	0.208993i	0.799367	−	0.600843i	$-0.205168\pi$
$953$	−3.72492	−	6.45175i	−0.120662	−	0.208993i	−0.920029	+	0.391850i	$0.871835\pi$
$954$		0			0
$955$	23.4264	−	40.5758i	0.758062	−	1.31300i
$956$	−18.4655	+	31.9831i	−0.597215	+	1.03441i
$957$		0			0
$958$	−9.74674	−	16.8818i	−0.314903	−	0.545428i
$959$	−27.9782	+	17.6309i	−0.903464	+	0.569330i
$960$		0			0
$961$	11.9023	−	20.6153i	0.383944	−	0.665010i
$962$	−28.3236	−	20.4323i	−0.913188	−	0.658764i
$963$		0			0
$964$	9.05681	+	15.6869i	0.291700	+	0.505240i
$965$	5.80203	−	10.0494i	0.186774	−	0.323502i
$966$		0			0
$967$	−51.0981			−1.64320			−0.821602	−	0.570061i	$-0.806920\pi$
$967$	−51.0981			−1.64320			−0.821602	+	0.570061i	$0.806920\pi$
$968$	−43.0258			−1.38290
$969$		0			0
$970$	18.0611	+	31.2828i	0.579908	+	1.00443i
$971$	−5.01835			−0.161046			−0.0805232	−	0.996753i	$-0.525659\pi$
$971$	−5.01835			−0.161046			−0.0805232	+	0.996753i	$0.525659\pi$
$972$		0			0
$973$	0.134650	+	3.47716i	0.00431669	+	0.111473i
$974$	81.1256			2.59943
$975$		0			0
$976$	0.557189	+	0.965080i	0.0178352	+	0.0308915i
$977$	27.6611			0.884958			0.442479	−	0.896779i	$-0.354099\pi$
$977$	27.6611			0.884958			0.442479	+	0.896779i	$0.354099\pi$
$978$		0			0
$979$	−10.3465	−	17.9206i	−0.330675	−	0.572746i
$980$	−28.3918	+	59.3519i	−0.906943	+	1.89593i
$981$		0			0
$982$	−71.5980			−2.28478
$983$	−2.23464	−	3.87050i	−0.0712738	−	0.123450i	0.828186	−	0.560453i	$-0.189373\pi$
$983$	−2.23464	−	3.87050i	−0.0712738	−	0.123450i	−0.899460	+	0.437003i	$0.856040\pi$
$984$		0			0
$985$	−19.7487	−	34.2057i	−0.629245	−	1.08988i
$986$	−2.49921	+	4.32875i	−0.0795910	+	0.137856i
$987$		0			0
$988$	−21.1335	−	15.2455i	−0.672347	−	0.485024i
$989$	24.3995	−	42.2613i	0.775860	−	1.34383i
$990$		0			0
$991$	10.4243			0.331139			0.165570	−	0.986198i	$-0.447054\pi$
$991$	10.4243			0.331139			0.165570	+	0.986198i	$0.447054\pi$
$992$	15.6600			0.497204
$993$		0			0
$994$	−39.8630	+	25.1202i	−1.26438	+	0.796765i
$995$	30.5901	+	52.9836i	0.969771	+	1.67969i
$996$		0			0
$997$	7.25600	−	12.5678i	0.229800	−	0.398025i	−0.727949	−	0.685631i	$-0.759526\pi$
$997$	7.25600	−	12.5678i	0.229800	−	0.398025i	0.957749	+	0.287607i	$0.0928596\pi$
$998$	9.78748			0.309817
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.f.100.9		20
3.2	odd	2		273.2.j.c.100.2	✓	20
7.4	even	3		819.2.s.f.802.2		20
13.3	even	3		819.2.s.f.289.2		20
21.11	odd	6		273.2.l.c.256.9	yes	20
39.29	odd	6		273.2.l.c.16.9	yes	20
91.81	even	3	inner	819.2.n.f.172.9		20
273.263	odd	6		273.2.j.c.172.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.2	✓	20	3.2	odd	2
273.2.j.c.172.2	yes	20	273.263	odd	6
273.2.l.c.16.9	yes	20	39.29	odd	6
273.2.l.c.256.9	yes	20	21.11	odd	6
819.2.n.f.100.9		20	1.1	even	1	trivial
819.2.n.f.172.9		20	91.81	even	3	inner
819.2.s.f.289.2		20	13.3	even	3
819.2.s.f.802.2		20	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.14017 + 1.97483i) q^{2} +(-1.59997 + 2.77124i) q^{4} +(1.46862 - 2.54373i) q^{5} +(-2.34076 - 1.23322i) q^{7} -2.73629 q^{8} +6.69792 q^{10} +5.16954 q^{11} +(-0.364757 + 3.58705i) q^{13} +(-0.233457 - 6.02869i) q^{14} +(0.0801172 + 0.138767i) q^{16} +(2.52646 - 4.37595i) q^{17} +2.25859 q^{19} +(4.69952 + 8.13980i) q^{20} +(5.89416 + 10.2090i) q^{22} +(2.61602 + 4.53108i) q^{23} +(-1.81371 - 3.14143i) q^{25} +(-7.49971 + 3.36952i) q^{26} +(7.16271 - 4.51367i) q^{28} +(-0.216901 + 0.375683i) q^{29} +(-1.34122 - 2.32306i) q^{31} +(-2.91898 + 5.05582i) q^{32} +11.5224 q^{34} +(-6.57468 + 4.14312i) q^{35} +(2.12386 + 3.67863i) q^{37} +(2.57517 + 4.46033i) q^{38} +(-4.01857 + 6.96037i) q^{40} +(-0.269622 + 0.466999i) q^{41} +(-4.66348 - 8.07739i) q^{43} +(-8.27113 + 14.3260i) q^{44} +(-5.96541 + 10.3324i) q^{46} +(4.87054 - 8.43603i) q^{47} +(3.95832 + 5.77336i) q^{49} +(4.13587 - 7.16354i) q^{50} +(-9.35697 - 6.75002i) q^{52} +(-0.377571 - 0.653972i) q^{53} +(7.59211 - 13.1499i) q^{55} +(6.40499 + 3.37445i) q^{56} -0.989214 q^{58} +(-1.82385 + 3.15901i) q^{59} +6.95468 q^{61} +(3.05843 - 5.29736i) q^{62} -12.9921 q^{64} +(8.58881 + 6.19587i) q^{65} -13.3602 q^{67} +(8.08453 + 14.0028i) q^{68} +(-15.6782 - 8.26003i) q^{70} +(-3.90487 - 6.76343i) q^{71} +(-7.94401 - 13.7594i) q^{73} +(-4.84312 + 8.38853i) q^{74} +(-3.61368 + 6.25908i) q^{76} +(-12.1007 - 6.37520i) q^{77} +(-7.79235 + 13.4967i) q^{79} +0.470648 q^{80} -1.22966 q^{82} -13.2349 q^{83} +(-7.42083 - 12.8532i) q^{85} +(10.6343 - 18.4192i) q^{86} -14.1453 q^{88} +(-2.00143 - 3.46658i) q^{89} +(5.27744 - 7.94661i) q^{91} -16.7423 q^{92} +22.2130 q^{94} +(3.31701 - 5.74523i) q^{95} +(2.69653 + 4.67053i) q^{97} +(-6.88826 + 14.3996i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{4} - 9 q^{7} + 12 q^{8} + 8 q^{10} - 16 q^{11} - 5 q^{13} + 9 q^{14} - 20 q^{16} - 14 q^{19} - 12 q^{20} - 9 q^{22} + 14 q^{23} - 32 q^{25} - 4 q^{26} + 13 q^{28} + 9 q^{29} - 9 q^{31} - 17 q^{32}+ \cdots + 79 q^{98}+O(q^{100}) \) 20 * q - 16 * q^4 - 9 * q^7 + 12 * q^8 + 8 * q^10 - 16 * q^11 - 5 * q^13 + 9 * q^14 - 20 * q^16 - 14 * q^19 - 12 * q^20 - 9 * q^22 + 14 * q^23 - 32 * q^25 - 4 * q^26 + 13 * q^28 + 9 * q^29 - 9 * q^31 - 17 * q^32 + 12 * q^34 - 10 * q^35 + 18 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 - 10 * q^46 - 13 * q^47 - 21 * q^49 - 5 * q^50 - 2 * q^52 + 6 * q^53 - 19 * q^55 + 5 * q^56 + 15 * q^59 - 22 * q^62 + 72 * q^64 + 27 * q^65 + 44 * q^67 - 39 * q^68 + 30 * q^70 + 11 * q^71 + 3 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 + 96 * q^80 + 26 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 + 24 * q^88 - 2 * q^89 + 9 * q^91 - 66 * q^92 + 88 * q^94 + 36 * q^95 + 21 * q^97 + 79 * q^98

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