LMFDB - Embedded newform 729.2.e.l.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.2
Root			$1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.l.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.469730 + 2.66397i) q^{2} +(-4.99670 + 1.81865i) q^{4} +(-1.28112 - 1.07499i) q^{5} +(-0.470402 - 0.171212i) q^{7} +(-4.48686 - 7.77147i) q^{8} +(2.26195 - 3.91782i) q^{10} +(-1.46906 + 1.23269i) q^{11} +(0.540469 - 3.06515i) q^{13} +(0.235142 - 1.33356i) q^{14} +(10.4486 - 8.76745i) q^{16} +(-1.33234 + 2.30767i) q^{17} +(-2.89832 - 5.02003i) q^{19} +(8.35640 + 3.04148i) q^{20} +(-3.97390 - 3.33449i) q^{22} +(4.36569 - 1.58898i) q^{23} +(-0.382569 - 2.16966i) q^{25} +8.41934 q^{26} +2.66183 q^{28} +(-0.454102 - 2.57534i) q^{29} +(4.33631 - 1.57829i) q^{31} +(14.5157 + 12.1801i) q^{32} +(-6.77341 - 2.46532i) q^{34} +(0.418591 + 0.725020i) q^{35} +(2.42934 - 4.20773i) q^{37} +(12.0118 - 10.0791i) q^{38} +(-2.60603 + 14.7795i) q^{40} +(-2.00532 + 11.3727i) q^{41} +(-6.89772 + 5.78788i) q^{43} +(5.09861 - 8.83106i) q^{44} +(6.28369 + 10.8837i) q^{46} +(-6.42020 - 2.33676i) q^{47} +(-5.17035 - 4.33844i) q^{49} +(5.60020 - 2.03831i) q^{50} +(2.87388 + 16.2986i) q^{52} -5.43322 q^{53} +3.20716 q^{55} +(0.780056 + 4.42392i) q^{56} +(6.64732 - 2.41943i) q^{58} +(-1.67864 - 1.40855i) q^{59} +(-6.42781 - 2.33953i) q^{61} +(6.24140 + 10.8104i) q^{62} +(-11.9893 + 20.7661i) q^{64} +(-3.98741 + 3.34583i) q^{65} +(2.16775 - 12.2939i) q^{67} +(2.46043 - 13.9538i) q^{68} +(-1.73481 + 1.45568i) q^{70} +(1.41784 - 2.45578i) q^{71} +(-4.96749 - 8.60394i) q^{73} +(12.3504 + 4.49518i) q^{74} +(23.6117 + 19.8126i) q^{76} +(0.902098 - 0.328337i) q^{77} +(0.922282 + 5.23052i) q^{79} -22.8109 q^{80} -31.2385 q^{82} +(-0.473738 - 2.68670i) q^{83} +(4.18761 - 1.52416i) q^{85} +(-18.6588 - 15.6566i) q^{86} +(16.1712 + 5.88584i) q^{88} +(-5.60945 - 9.71585i) q^{89} +(-0.779029 + 1.34932i) q^{91} +(-18.9242 + 15.8793i) q^{92} +(3.20930 - 18.2009i) q^{94} +(-1.68338 + 9.54693i) q^{95} +(-5.27739 + 4.42826i) q^{97} +(9.12879 - 15.8115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 + 27 * q^16 + 9 * q^17 - 12 * q^19 + 39 * q^20 - 39 * q^22 + 21 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 + 6 * q^31 + 27 * q^32 - 18 * q^34 - 30 * q^35 - 3 * q^37 + 3 * q^38 + 33 * q^40 - 15 * q^41 - 30 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 - 3 * q^49 + 6 * q^50 - 18 * q^53 + 30 * q^55 + 15 * q^56 - 3 * q^58 + 30 * q^59 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 12 * q^65 - 39 * q^67 + 18 * q^68 + 51 * q^70 - 12 * q^73 + 57 * q^74 + 57 * q^76 - 24 * q^77 + 15 * q^79 - 42 * q^80 - 42 * q^82 - 21 * q^83 + 54 * q^85 - 60 * q^86 + 12 * q^88 + 9 * q^89 - 18 * q^91 - 15 * q^92 + 33 * q^94 + 42 * q^95 - 12 * q^97 - 18 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.469730	+	2.66397i	0.332149	+	1.88371i	0.453746	+	0.891131i	$0.350087\pi$
$2$	0.469730	+	2.66397i	0.332149	+	1.88371i	−0.121597	+	0.992580i	$0.538802\pi$
$3$		0			0
$3$		0			0
$4$	−4.99670	+	1.81865i	−2.49835	+	0.909325i
$5$	−1.28112	−	1.07499i	−0.572935	−	0.480749i	0.309684	−	0.950840i	$-0.399777\pi$
$5$	−1.28112	−	1.07499i	−0.572935	−	0.480749i	−0.882618	+	0.470090i	$0.844221\pi$
$6$		0			0
$7$	−0.470402	−	0.171212i	−0.177795	−	0.0647122i	0.251589	−	0.967834i	$-0.419047\pi$
$7$	−0.470402	−	0.171212i	−0.177795	−	0.0647122i	−0.429384	+	0.903122i	$0.641269\pi$
$8$	−4.48686	−	7.77147i	−1.58634	−	2.74763i
$9$		0			0
$10$	2.26195	−	3.91782i	0.715293	−	1.23892i
$11$	−1.46906	+	1.23269i	−0.442937	+	0.371669i	−0.836807	−	0.547498i	$-0.815581\pi$
$11$	−1.46906	+	1.23269i	−0.442937	+	0.371669i	0.393870	+	0.919166i	$0.371136\pi$
$12$		0			0
$13$	0.540469	−	3.06515i	0.149899	−	0.850120i	−0.813403	−	0.581700i	$-0.802388\pi$
$13$	0.540469	−	3.06515i	0.149899	−	0.850120i	0.963302	−	0.268419i	$-0.0865013\pi$
$14$	0.235142	−	1.33356i	0.0628445	−	0.356409i
$15$		0			0
$16$	10.4486	−	8.76745i	2.61216	−	2.19186i
$17$	−1.33234	+	2.30767i	−0.323139	+	0.559693i	−0.981134	−	0.193329i	$-0.938071\pi$
$17$	−1.33234	+	2.30767i	−0.323139	+	0.559693i	0.657995	+	0.753022i	$0.271405\pi$
$18$		0			0
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	−0.979307	−	0.202380i	$-0.935132\pi$
$19$	−2.89832	−	5.02003i	−0.664920	−	1.15167i	0.314387	−	0.949295i	$-0.398201\pi$
$20$	8.35640	+	3.04148i	1.86855	+	0.680096i
$21$		0			0
$22$	−3.97390	−	3.33449i	−0.847237	−	0.710917i
$23$	4.36569	−	1.58898i	0.910309	−	0.331325i	0.155933	−	0.987768i	$-0.450162\pi$
$23$	4.36569	−	1.58898i	0.910309	−	0.331325i	0.754376	+	0.656442i	$0.227939\pi$
$24$		0			0
$25$	−0.382569	−	2.16966i	−0.0765139	−	0.433932i
$26$	8.41934			1.65117
$27$		0			0
$28$	2.66183			0.503039
$29$	−0.454102	−	2.57534i	−0.0843247	−	0.478229i	−0.997500	−	0.0706626i	$-0.977489\pi$
$29$	−0.454102	−	2.57534i	−0.0843247	−	0.478229i	0.913176	−	0.407566i	$-0.133622\pi$
$30$		0			0
$31$	4.33631	−	1.57829i	0.778824	−	0.283469i	0.0781418	−	0.996942i	$-0.475101\pi$
$31$	4.33631	−	1.57829i	0.778824	−	0.283469i	0.700682	+	0.713473i	$0.252879\pi$
$32$	14.5157	+	12.1801i	2.56604	+	2.15316i
$33$		0			0
$34$	−6.77341	−	2.46532i	−1.16163	−	0.422799i
$35$	0.418591	+	0.725020i	0.0707547	+	0.122551i
$36$		0			0
$37$	2.42934	−	4.20773i	0.399381	−	0.691747i	−0.594269	−	0.804266i	$-0.702559\pi$
$37$	2.42934	−	4.20773i	0.399381	−	0.691747i	0.993650	+	0.112519i	$0.0358919\pi$
$38$	12.0118	−	10.0791i	1.94857	−	1.63504i
$39$		0			0
$40$	−2.60603	+	14.7795i	−0.412049	+	2.33685i
$41$	−2.00532	+	11.3727i	−0.313178	+	1.77612i	0.269082	+	0.963117i	$0.413280\pi$
$41$	−2.00532	+	11.3727i	−0.313178	+	1.77612i	−0.582260	+	0.813003i	$0.697831\pi$
$42$		0			0
$43$	−6.89772	+	5.78788i	−1.05189	+	0.882643i	−0.993291	−	0.115639i	$-0.963109\pi$
$43$	−6.89772	+	5.78788i	−1.05189	+	0.882643i	−0.0586014	+	0.998281i	$0.518664\pi$
$44$	5.09861	−	8.83106i	0.768645	−	1.33133i
$45$		0			0
$46$	6.28369	+	10.8837i	0.926479	+	1.60471i
$47$	−6.42020	−	2.33676i	−0.936483	−	0.340852i	−0.171707	−	0.985148i	$-0.554928\pi$
$47$	−6.42020	−	2.33676i	−0.936483	−	0.340852i	−0.764776	+	0.644296i	$0.777150\pi$
$48$		0			0
$49$	−5.17035	−	4.33844i	−0.738621	−	0.619777i
$50$	5.60020	−	2.03831i	0.791988	−	0.288260i
$51$		0			0
$52$	2.87388	+	16.2986i	0.398535	+	2.26020i
$53$	−5.43322			−0.746309			−0.373155	−	0.927769i	$-0.621724\pi$
$53$	−5.43322			−0.746309			−0.373155	+	0.927769i	$0.621724\pi$
$54$		0			0
$55$	3.20716			0.432454
$56$	0.780056	+	4.42392i	0.104239	+	0.591171i
$57$		0			0
$58$	6.64732	−	2.41943i	0.872836	−	0.317686i
$59$	−1.67864	−	1.40855i	−0.218541	−	0.183377i	0.526944	−	0.849900i	$-0.323338\pi$
$59$	−1.67864	−	1.40855i	−0.218541	−	0.183377i	−0.745485	+	0.666522i	$0.767782\pi$
$60$		0			0
$61$	−6.42781	−	2.33953i	−0.822997	−	0.299547i	−0.104016	−	0.994576i	$-0.533169\pi$
$61$	−6.42781	−	2.33953i	−0.822997	−	0.299547i	−0.718982	+	0.695029i	$0.755391\pi$
$62$	6.24140	+	10.8104i	0.792659	+	1.37293i
$63$		0			0
$64$	−11.9893	+	20.7661i	−1.49866	+	2.59576i
$65$	−3.98741	+	3.34583i	−0.494577	+	0.414999i
$66$		0			0
$67$	2.16775	−	12.2939i	0.264833	−	1.50194i	−0.504676	−	0.863309i	$-0.668388\pi$
$67$	2.16775	−	12.2939i	0.264833	−	1.50194i	0.769509	−	0.638635i	$-0.220501\pi$
$68$	2.46043	−	13.9538i	0.298371	−	1.69215i
$69$		0			0
$70$	−1.73481	+	1.45568i	−0.207349	+	0.173986i
$71$	1.41784	−	2.45578i	0.168267	−	0.291447i	−0.769544	−	0.638594i	$-0.779516\pi$
$71$	1.41784	−	2.45578i	0.168267	−	0.291447i	0.937811	+	0.347147i	$0.112850\pi$
$72$		0			0
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	−0.995314	−	0.0966986i	$-0.969172\pi$
$73$	−4.96749	−	8.60394i	−0.581400	−	1.00701i	0.413913	−	0.910316i	$-0.364162\pi$
$74$	12.3504	+	4.49518i	1.43571	+	0.522554i
$75$		0			0
$76$	23.6117	+	19.8126i	2.70845	+	2.27266i
$77$	0.902098	−	0.328337i	0.102804	−	0.0374175i
$78$		0			0
$79$	0.922282	+	5.23052i	0.103765	+	0.588480i	0.991706	+	0.128524i	$0.0410238\pi$
$79$	0.922282	+	5.23052i	0.103765	+	0.588480i	−0.887942	+	0.459956i	$0.847865\pi$
$80$	−22.8109			−2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	−0.473738	−	2.68670i	−0.0519995	−	0.294904i	0.947707	−	0.319143i	$-0.103395\pi$
$83$	−0.473738	−	2.68670i	−0.0519995	−	0.294904i	−0.999706	+	0.0242387i	$0.992284\pi$
$84$		0			0
$85$	4.18761	−	1.52416i	0.454210	−	0.165319i
$86$	−18.6588	−	15.6566i	−2.01203	−	1.68829i
$87$		0			0
$88$	16.1712	+	5.88584i	1.72386	+	0.627433i
$89$	−5.60945	−	9.71585i	−0.594600	−	1.02988i	−0.993603	−	0.112928i	$-0.963977\pi$
$89$	−5.60945	−	9.71585i	−0.594600	−	1.02988i	0.399003	−	0.916950i	$-0.369356\pi$
$90$		0			0
$91$	−0.779029	+	1.34932i	−0.0816644	+	0.141447i
$92$	−18.9242	+	15.8793i	−1.97299	+	1.65553i
$93$		0			0
$94$	3.20930	−	18.2009i	0.331014	−	1.87728i
$95$	−1.68338	+	9.54693i	−0.172711	+	0.979494i
$96$		0			0
$97$	−5.27739	+	4.42826i	−0.535838	+	0.449621i	−0.870112	−	0.492855i	$-0.835953\pi$
$97$	−5.27739	+	4.42826i	−0.535838	+	0.449621i	0.334274	+	0.942476i	$0.391509\pi$
$98$	9.12879	−	15.8115i	0.922147	−	1.59721i
$99$		0			0
$100$	5.85743	+	10.1454i	0.585743	+	1.01454i
$101$	−3.50472	−	1.27561i	−0.348733	−	0.126928i	0.161714	−	0.986838i	$-0.448298\pi$
$101$	−3.50472	−	1.27561i	−0.348733	−	0.126928i	−0.510447	+	0.859909i	$0.670520\pi$
$102$		0			0
$103$	5.88383	+	4.93712i	0.579751	+	0.486469i	0.884865	−	0.465847i	$-0.154250\pi$
$103$	5.88383	+	4.93712i	0.579751	+	0.486469i	−0.305114	+	0.952316i	$0.598695\pi$
$104$	−26.2457	+	9.55266i	−2.57360	+	0.936715i
$105$		0			0
$106$	−2.55214	−	14.4739i	−0.247886	−	1.40583i
$107$	−10.7658			−1.04077			−0.520383	−	0.853933i	$-0.674211\pi$
$107$	−10.7658			−1.04077			−0.520383	+	0.853933i	$0.674211\pi$
$108$		0			0
$109$	12.2298			1.17141			0.585703	−	0.810526i	$-0.300819\pi$
$109$	12.2298			1.17141			0.585703	+	0.810526i	$0.300819\pi$
$110$	1.50650	+	8.54378i	0.143639	+	0.814618i
$111$		0			0
$112$	−6.41616	+	2.33529i	−0.606270	+	0.220664i
$113$	−1.48915	−	1.24955i	−0.140088	−	0.117547i	0.570051	−	0.821609i	$-0.306923\pi$
$113$	−1.48915	−	1.24955i	−0.140088	−	0.117547i	−0.710139	+	0.704062i	$0.751368\pi$
$114$		0			0
$115$	−7.30111	−	2.65739i	−0.680832	−	0.247803i
$116$	6.95266	+	12.0424i	0.645538	+	1.11810i
$117$		0			0
$118$	2.96382	−	5.13349i	0.272842	−	0.472576i
$119$	1.02184	−	0.857422i	0.0936715	−	0.0785997i
$120$		0			0
$121$	−1.27151	+	7.21111i	−0.115592	+	0.655556i
$122$	3.21311	−	18.2224i	0.290901	−	1.64978i
$123$		0			0
$124$	−18.7969	+	15.7725i	−1.68801	+	1.41641i
$125$	−6.02320	+	10.4325i	−0.538732	+	0.933110i
$126$		0			0
$127$	−1.17217	−	2.03025i	−0.104013	−	0.180156i	0.809322	−	0.587366i	$-0.199835\pi$
$127$	−1.17217	−	2.03025i	−0.104013	−	0.180156i	−0.913335	+	0.407210i	$0.866502\pi$
$128$	−25.3396	−	9.22286i	−2.23973	−	0.815194i
$129$		0			0
$130$	−10.7862	−	9.05069i	−0.946012	−	0.793798i
$131$	16.0710	−	5.84936i	1.40413	−	0.511061i	0.474728	−	0.880133i	$-0.342547\pi$
$131$	16.0710	−	5.84936i	1.40413	−	0.511061i	0.929401	+	0.369072i	$0.120324\pi$
$132$		0			0
$133$	0.503883	+	2.85766i	0.0436922	+	0.247791i
$134$	33.7689			2.91719
$135$		0			0
$136$	23.9120			2.05044
$137$	2.41843	+	13.7156i	0.206620	+	1.17180i	0.894870	+	0.446327i	$0.147268\pi$
$137$	2.41843	+	13.7156i	0.206620	+	1.17180i	−0.688250	+	0.725474i	$0.741621\pi$
$138$		0			0
$139$	−7.43920	+	2.70765i	−0.630985	+	0.229660i	−0.637660	−	0.770318i	$-0.720098\pi$
$139$	−7.43920	+	2.70765i	−0.630985	+	0.229660i	0.00667492	+	0.999978i	$0.497875\pi$
$140$	−3.41013	−	2.86144i	−0.288208	−	0.241836i
$141$		0			0
$142$	7.20811	+	2.62354i	0.604891	+	0.220162i
$143$	2.98439	+	5.16911i	0.249567	+	0.432263i
$144$		0			0
$145$	−2.18670	+	3.78748i	−0.181596	+	0.314533i
$146$	20.5872	−	17.2748i	1.70381	−	1.42967i
$147$		0			0
$148$	−4.48627	+	25.4429i	−0.368769	+	2.09139i
$149$	0.126439	−	0.717072i	0.0103583	−	0.0587449i	−0.979190	−	0.202943i	$-0.934949\pi$
$149$	0.126439	−	0.717072i	0.0103583	−	0.0587449i	0.989549	+	0.144198i	$0.0460604\pi$
$150$		0			0
$151$	3.32623	−	2.79104i	0.270685	−	0.227132i	−0.497333	−	0.867560i	$-0.665687\pi$
$151$	3.32623	−	2.79104i	0.270685	−	0.227132i	0.768018	+	0.640428i	$0.221243\pi$
$152$	−26.0087	+	45.0484i	−2.10958	+	3.65390i
$153$		0			0
$154$	1.29842	+	2.24893i	0.104630	+	0.181224i
$155$	−7.25198	−	2.63950i	−0.582493	−	0.212010i
$156$		0			0
$157$	−11.8915	−	9.97816i	−0.949046	−	0.796344i	0.0300908	−	0.999547i	$-0.490420\pi$
$157$	−11.8915	−	9.97816i	−0.949046	−	0.796344i	−0.979137	+	0.203203i	$0.934865\pi$
$158$	−13.5007	+	4.91386i	−1.07406	+	0.390926i
$159$		0			0
$160$	−5.50289	−	31.2085i	−0.435042	−	2.46725i
$161$	−2.32568			−0.183289
$162$		0			0
$163$	8.49738			0.665566			0.332783	−	0.943003i	$-0.392012\pi$
$163$	8.49738			0.665566			0.332783	+	0.943003i	$0.392012\pi$
$164$	−10.6630	−	60.4730i	−0.832642	−	4.72215i
$165$		0			0
$166$	6.93477	−	2.52405i	0.538242	−	0.195904i
$167$	17.7278	+	14.8754i	1.37182	+	1.15109i	0.972131	+	0.234436i	$0.0753244\pi$
$167$	17.7278	+	14.8754i	1.37182	+	1.15109i	0.399684	+	0.916653i	$0.369120\pi$
$168$		0			0
$169$	3.11296	+	1.13303i	0.239459	+	0.0871559i
$170$	6.02737	+	10.4397i	0.462278	+	0.800689i
$171$		0			0
$172$	23.9397	−	41.4648i	1.82539	−	3.16166i
$173$	−1.97523	+	1.65741i	−0.150174	+	0.126011i	−0.714779	−	0.699350i	$-0.753473\pi$
$173$	−1.97523	+	1.65741i	−0.150174	+	0.126011i	0.564605	+	0.825361i	$0.309028\pi$
$174$		0			0
$175$	−0.191511	+	1.08611i	−0.0144769	+	0.0821023i
$176$	−4.54214	+	25.7598i	−0.342377	+	1.94172i
$177$		0			0
$178$	23.2478	−	19.5072i	1.74250	−	1.46213i
$179$	4.44806	−	7.70427i	0.332464	−	0.575844i	−0.650530	−	0.759480i	$-0.725453\pi$
$179$	4.44806	−	7.70427i	0.332464	−	0.575844i	0.982994	+	0.183636i	$0.0587867\pi$
$180$		0			0
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	0.680720	−	0.732543i	$-0.261667\pi$
$181$	−3.95592	−	6.85185i	−0.294041	−	0.509294i	−0.974761	+	0.223250i	$0.928334\pi$
$182$	−3.96047	−	1.44149i	−0.293570	−	0.106851i
$183$		0			0
$184$	−31.9369	−	26.7983i	−2.35442	−	1.97559i
$185$	−7.63554	+	2.77911i	−0.561376	+	0.204324i
$186$		0			0
$187$	−0.887358	−	5.03246i	−0.0648900	−	0.368010i
$188$	36.3296			2.64961
$189$		0			0
$190$	−26.2235			−1.90245
$191$	−2.76055	−	15.6558i	−0.199746	−	1.13282i	−0.905496	−	0.424355i	$-0.860501\pi$
$191$	−2.76055	−	15.6558i	−0.199746	−	1.13282i	0.705750	−	0.708461i	$-0.250610\pi$
$192$		0			0
$193$	4.30828	−	1.56809i	0.310117	−	0.112873i	−0.182273	−	0.983248i	$-0.558346\pi$
$193$	4.30828	−	1.56809i	0.310117	−	0.112873i	0.492390	+	0.870375i	$0.336123\pi$
$194$	−14.2757	−	11.9787i	−1.02493	−	0.860022i
$195$		0			0
$196$	33.7248	+	12.2748i	2.40891	+	0.876772i
$197$	−1.49708	−	2.59303i	−0.106663	−	0.184745i	0.807754	−	0.589520i	$-0.200683\pi$
$197$	−1.49708	−	2.59303i	−0.106663	−	0.184745i	−0.914416	+	0.404775i	$0.867350\pi$
$198$		0			0
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	0.471770	+	0.881722i	$0.343615\pi$
$199$	−7.44425	+	12.8938i	−0.527709	+	0.914018i	−0.999478	+	0.0322965i	$0.989718\pi$
$200$	−15.1449	+	12.7081i	−1.07091	+	0.898597i
$201$		0			0
$202$	1.75193	−	9.93566i	0.123265	−	0.699071i
$203$	−0.227320	+	1.28919i	−0.0159547	+	0.0904836i
$204$		0			0
$205$	14.7946	−	12.4141i	1.03330	−	0.867041i
$206$	−10.3885	+	17.9935i	−0.723803	+	1.25366i
$207$		0			0
$208$	−21.2264	−	36.7652i	−1.47179	−	2.54921i
$209$	10.4459	+	3.80200i	0.722559	+	0.262990i
$210$		0			0
$211$	10.6319	+	8.92122i	0.731930	+	0.614162i	0.930657	−	0.365893i	$-0.119236\pi$
$211$	10.6319	+	8.92122i	0.731930	+	0.614162i	−0.198727	+	0.980055i	$0.563681\pi$
$212$	27.1481	−	9.88111i	1.86454	−	0.678638i
$213$		0			0
$214$	−5.05699	−	28.6796i	−0.345689	−	1.96050i
$215$	15.0587			1.02700
$216$		0			0
$217$	−2.31003			−0.156815
$218$	5.74472	+	32.5799i	0.389081	+	2.20659i
$219$		0			0
$220$	−16.0252	+	5.83271i	−1.08042	+	0.393241i
$221$	6.35328	+	5.33104i	0.427368	+	0.358604i
$222$		0			0
$223$	6.40117	+	2.32983i	0.428654	+	0.156017i	0.547332	−	0.836916i	$-0.315643\pi$
$223$	6.40117	+	2.32983i	0.428654	+	0.156017i	−0.118678	+	0.992933i	$0.537866\pi$
$224$	−4.74283	−	8.21483i	−0.316894	−	0.548876i
$225$		0			0
$226$	2.62925	−	4.55400i	0.174895	−	0.302928i
$227$	−7.46192	+	6.26129i	−0.495265	+	0.415577i	−0.855909	−	0.517127i	$-0.827001\pi$
$227$	−7.46192	+	6.26129i	−0.495265	+	0.415577i	0.360644	+	0.932704i	$0.382557\pi$
$228$		0			0
$229$	−2.43886	+	13.8315i	−0.161165	+	0.914009i	0.791767	+	0.610823i	$0.209161\pi$
$229$	−2.43886	+	13.8315i	−0.161165	+	0.914009i	−0.952931	+	0.303186i	$0.901950\pi$
$230$	3.64965	−	20.6982i	0.240651	−	1.36480i
$231$		0			0
$232$	−17.9767	+	15.0842i	−1.18023	+	0.990328i
$233$	−2.66167	+	4.61014i	−0.174372	+	0.302020i	−0.939944	−	0.341330i	$-0.889123\pi$
$233$	−2.66167	+	4.61014i	−0.174372	+	0.302020i	0.765572	+	0.643350i	$0.222456\pi$
$234$		0			0
$235$	5.71307	+	9.89532i	0.372679	+	0.645499i
$236$	10.9493	+	3.98523i	0.712741	+	0.259416i
$237$		0			0
$238$	2.76413	+	2.31938i	0.179172	+	0.150343i
$239$	−16.7016	+	6.07890i	−1.08034	+	0.393211i	−0.820034	−	0.572315i	$-0.806045\pi$
$239$	−16.7016	+	6.07890i	−1.08034	+	0.393211i	−0.260305	+	0.965526i	$0.583823\pi$
$240$		0			0
$241$	−0.348476	−	1.97631i	−0.0224473	−	0.127305i	0.971525	−	0.236938i	$-0.0761437\pi$
$241$	−0.348476	−	1.97631i	−0.0224473	−	0.127305i	−0.993972	+	0.109633i	$0.965033\pi$
$242$	−19.8075			−1.27327
$243$		0			0
$244$	36.3726			2.32852
$245$	1.96007	+	11.1161i	0.125224	+	0.710183i
$246$		0			0
$247$	−16.9536	+	6.17061i	−1.07873	+	0.392626i
$248$	−31.7220	−	26.6179i	−2.01435	−	1.69024i
$249$		0			0
$250$	−30.6211	−	11.1452i	−1.93665	−	0.704883i
$251$	−11.7822	−	20.4073i	−0.743683	−	1.28810i	−0.950808	−	0.309782i	$-0.899744\pi$
$251$	−11.7822	−	20.4073i	−0.743683	−	1.28810i	0.207125	−	0.978314i	$-0.433589\pi$
$252$		0			0
$253$	−4.45473	+	7.71582i	−0.280067	+	0.485090i
$254$	4.85793	−	4.07628i	0.304813	−	0.255769i
$255$		0			0
$256$	4.33897	−	24.6075i	0.271186	−	1.53797i
$257$	1.02011	−	5.78532i	0.0636326	−	0.360878i	−0.936320	−	0.351148i	$-0.885792\pi$
$257$	1.02011	−	5.78532i	0.0636326	−	0.360878i	0.999953	−	0.00973053i	$-0.00309737\pi$
$258$		0			0
$259$	−1.86318	+	1.56339i	−0.115772	+	0.0971446i
$260$	13.8390	−	23.9698i	0.858257	−	1.48654i
$261$		0			0
$262$	23.1315	+	40.0650i	1.42907	+	2.47522i
$263$	−20.6527	−	7.51696i	−1.27350	−	0.463516i	−0.385222	−	0.922824i	$-0.625875\pi$
$263$	−20.6527	−	7.51696i	−1.27350	−	0.463516i	−0.888277	+	0.459308i	$0.848097\pi$
$264$		0			0
$265$	6.96061	+	5.84064i	0.427587	+	0.358788i
$266$	−7.37603	+	2.68466i	−0.452253	+	0.164607i
$267$		0			0
$268$	11.5268	+	65.3715i	0.704109	+	3.99320i
$269$	−30.6026			−1.86587			−0.932937	−	0.360041i	$-0.882763\pi$
$269$	−30.6026			−1.86587			−0.932937	+	0.360041i	$0.882763\pi$
$270$		0			0
$271$	−16.0823			−0.976928			−0.488464	−	0.872584i	$-0.662443\pi$
$271$	−16.0823			−0.976928			−0.488464	+	0.872584i	$0.662443\pi$
$272$	6.31131	+	35.7932i	0.382680	+	2.17028i
$273$		0			0
$274$	−35.4019	+	12.8852i	−2.13870	+	0.778425i
$275$	3.23652	+	2.71577i	0.195170	+	0.163767i
$276$		0			0
$277$	19.5584	+	7.11866i	1.17515	+	0.427719i	0.854486	−	0.519475i	$-0.173872\pi$
$277$	19.5584	+	7.11866i	1.17515	+	0.427719i	0.320662	+	0.947194i	$0.396095\pi$
$278$	−10.7075	−	18.5459i	−0.642194	−	1.11231i
$279$		0			0
$280$	3.75631	−	6.50612i	0.224483	−	0.388815i
$281$	9.39192	−	7.88075i	0.560275	−	0.470126i	−0.318128	−	0.948048i	$-0.603054\pi$
$281$	9.39192	−	7.88075i	0.560275	−	0.470126i	0.878403	+	0.477921i	$0.158610\pi$
$282$		0			0
$283$	0.794020	−	4.50311i	0.0471996	−	0.267682i	−0.952071	−	0.305878i	$-0.901050\pi$
$283$	0.794020	−	4.50311i	0.0471996	−	0.267682i	0.999270	+	0.0381959i	$0.0121611\pi$
$284$	−2.61834	+	14.8493i	−0.155370	+	0.881145i
$285$		0			0
$286$	−12.3685	+	10.3784i	−0.731364	+	0.613687i
$287$	2.89045	−	5.00641i	0.170618	−	0.295519i
$288$		0			0
$289$	4.94976	+	8.57324i	0.291162	+	0.504308i
$290$	−11.1169	−	4.04621i	−0.652806	−	0.237602i
$291$		0			0
$292$	40.4686	+	33.9572i	2.36824	+	1.98719i
$293$	−24.5480	+	8.93473i	−1.43411	+	0.521973i	−0.938106	−	0.346348i	$-0.887421\pi$
$293$	−24.5480	+	8.93473i	−1.43411	+	0.521973i	−0.496002	+	0.868321i	$0.665199\pi$
$294$		0			0
$295$	0.636372	+	3.60904i	0.0370510	+	0.210127i
$296$	−43.6004			−2.53422
$297$		0			0
$298$	1.96965			0.114099
$299$	−2.51095	−	14.2403i	−0.145212	−	0.823537i
$300$		0			0
$301$	4.23566	−	1.54165i	0.244139	−	0.0888594i
$302$	8.99768	+	7.54995i	0.517758	+	0.434451i
$303$		0			0
$304$	−74.2964	−	27.0417i	−4.26119	−	1.55095i
$305$	5.71984	+	9.90705i	0.327517	+	0.567276i
$306$		0			0
$307$	−1.64638	+	2.85162i	−0.0939641	+	0.162751i	−0.909176	−	0.416412i	$-0.863287\pi$
$307$	−1.64638	+	2.85162i	−0.0939641	+	0.162751i	0.815212	+	0.579163i	$0.196621\pi$
$308$	−3.91038	+	3.28120i	−0.222815	+	0.186964i
$309$		0			0
$310$	3.62509	−	20.5589i	0.205891	−	1.16767i
$311$	6.04168	−	34.2641i	0.342592	−	1.94294i	0.00975457	−	0.999952i	$-0.496895\pi$
$311$	6.04168	−	34.2641i	0.342592	−	1.94294i	0.332838	−	0.942984i	$-0.391994\pi$
$312$		0			0
$313$	8.14139	−	6.83144i	0.460179	−	0.386136i	−0.383018	−	0.923741i	$-0.625115\pi$
$313$	8.14139	−	6.83144i	0.460179	−	0.386136i	0.843197	+	0.537605i	$0.180671\pi$
$314$	20.9957	−	36.3657i	1.18486	−	2.05223i
$315$		0			0
$316$	−14.1209	−	24.4580i	−0.794360	−	1.37587i
$317$	14.5654	+	5.30139i	0.818077	+	0.297756i	0.716956	−	0.697118i	$-0.245535\pi$
$317$	14.5654	+	5.30139i	0.818077	+	0.297756i	0.101121	+	0.994874i	$0.467757\pi$
$318$		0			0
$319$	3.84169	+	3.22356i	0.215093	+	0.180485i
$320$	37.6831	−	13.7155i	2.10655	−	0.766720i
$321$		0			0
$322$	−1.09244	−	6.19554i	−0.0608794	−	0.345264i
$323$	15.4461			0.859446
$324$		0			0
$325$	−6.85710			−0.380363
$326$	3.99147	+	22.6368i	0.221067	+	1.25373i
$327$		0			0
$328$	97.3803	−	35.4435i	5.37693	−	1.95704i
$329$	2.61999	+	2.19844i	0.144445	+	0.121204i
$330$		0			0
$331$	13.6916	+	4.98333i	0.752557	+	0.273908i	0.689682	−	0.724113i	$-0.257751\pi$
$331$	13.6916	+	4.98333i	0.752557	+	0.273908i	0.0628759	+	0.998021i	$0.479973\pi$
$332$	7.25330	+	12.5631i	0.398077	+	0.689489i
$333$		0			0
$334$	−31.3002	+	54.2136i	−1.71267	+	2.96644i
$335$	−15.9930	+	13.4197i	−0.873791	+	0.733198i
$336$		0			0
$337$	−3.57972	+	20.3016i	−0.195000	+	1.10590i	0.717419	+	0.696641i	$0.245323\pi$
$337$	−3.57972	+	20.3016i	−0.195000	+	1.10590i	−0.912419	+	0.409257i	$0.865788\pi$
$338$	−1.55610	+	8.82506i	−0.0846404	+	0.480020i
$339$		0			0
$340$	−18.1523	+	15.2316i	−0.984446	+	0.826048i
$341$	−4.42475	+	7.66390i	−0.239614	+	0.415023i
$342$		0			0
$343$	3.44142	+	5.96071i	0.185819	+	0.321848i
$344$	75.9294	+	27.6360i	4.09384	+	1.49004i
$345$		0			0
$346$	−5.34312	−	4.48341i	−0.287248	−	0.241030i
$347$	19.9060	−	7.24520i	1.06861	−	0.388943i	0.252954	−	0.967478i	$-0.418598\pi$
$347$	19.9060	−	7.24520i	1.06861	−	0.388943i	0.815657	+	0.578536i	$0.196376\pi$
$348$		0			0
$349$	−0.803291	−	4.55569i	−0.0429992	−	0.243861i	0.955731	−	0.294242i	$-0.0950673\pi$
$349$	−0.803291	−	4.55569i	−0.0429992	−	0.243861i	−0.998730	+	0.0503818i	$0.983956\pi$
$350$	−2.98333			−0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	−2.36915	−	13.4361i	−0.126097	−	0.715133i	−0.980650	−	0.195769i	$-0.937280\pi$
$353$	−2.36915	−	13.4361i	−0.126097	−	0.715133i	0.854553	−	0.519365i	$-0.173831\pi$
$354$		0			0
$355$	−4.45636	+	1.62198i	−0.236519	+	0.0860858i
$356$	45.6984	+	38.3456i	2.42201	+	2.03231i
$357$		0			0
$358$	22.6133	+	8.23058i	1.19515	+	0.435000i
$359$	14.1223	+	24.4606i	0.745349	+	1.29098i	0.950032	+	0.312153i	$0.101050\pi$
$359$	14.1223	+	24.4606i	0.745349	+	1.29098i	−0.204683	+	0.978828i	$0.565616\pi$
$360$		0			0
$361$	−7.30050	+	12.6448i	−0.384237	+	0.665517i
$362$	16.3949	−	13.7570i	0.861697	−	0.723049i
$363$		0			0
$364$	1.43864	−	8.15891i	0.0754050	−	0.427643i
$365$	−2.88518	+	16.3627i	−0.151017	+	0.856462i
$366$		0			0
$367$	26.7198	−	22.4206i	1.39476	−	1.17034i	0.431393	−	0.902164i	$-0.358022\pi$
$367$	26.7198	−	22.4206i	1.39476	−	1.17034i	0.963369	−	0.268180i	$-0.0864221\pi$
$368$	31.6842	−	54.8786i	1.65165	−	2.86075i
$369$		0			0
$370$	−10.9901	−	19.0354i	−0.571348	−	0.989604i
$371$	2.55579	+	0.930233i	0.132690	+	0.0482953i
$372$		0			0
$373$	2.34367	+	1.96657i	0.121350	+	0.101825i	0.701443	−	0.712725i	$-0.252539\pi$
$373$	2.34367	+	1.96657i	0.121350	+	0.101825i	−0.580093	+	0.814550i	$0.696984\pi$
$374$	12.9895	−	4.72779i	0.671670	−	0.244468i
$375$		0			0
$376$	10.6465	+	60.3791i	0.549050	+	3.11382i
$377$	−8.13924			−0.419192
$378$		0			0
$379$	−7.67705			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$379$	−7.67705			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$380$	−8.95117	−	50.7646i	−0.459185	−	2.60417i
$381$		0			0
$382$	40.4099	−	14.7080i	2.06755	−	0.752528i
$383$	7.93771	+	6.66053i	0.405598	+	0.340337i	0.822653	−	0.568544i	$-0.192493\pi$
$383$	7.93771	+	6.66053i	0.405598	+	0.340337i	−0.417055	+	0.908881i	$0.636938\pi$
$384$		0			0
$385$	−1.50866	−	0.549106i	−0.0768882	−	0.0279850i
$386$	6.20106	+	10.7406i	0.315626	+	0.546680i
$387$		0			0
$388$	18.3161	−	31.7244i	0.929858	−	1.61056i
$389$	−0.327064	+	0.274439i	−0.0165828	+	0.0139146i	−0.651041	−	0.759042i	$-0.725668\pi$
$389$	−0.327064	+	0.274439i	−0.0165828	+	0.0139146i	0.634459	+	0.772957i	$0.281223\pi$
$390$		0			0
$391$	−2.14972	+	12.1916i	−0.108716	+	0.616558i
$392$	−10.5174	+	59.6471i	−0.531209	+	3.01263i
$393$		0			0
$394$	6.20452	−	5.20621i	0.312579	−	0.262285i
$395$	4.44119	−	7.69238i	0.223461	−	0.387045i
$396$		0			0
$397$	13.5445	+	23.4598i	0.679781	+	1.17741i	0.975047	+	0.221999i	$0.0712583\pi$
$397$	13.5445	+	23.4598i	0.679781	+	1.17741i	−0.295266	+	0.955415i	$0.595408\pi$
$398$	−37.8455	−	13.7746i	−1.89702	−	0.690460i
$399$		0			0
$400$	−23.0197	−	19.3158i	−1.15099	−	0.965791i
$401$	−27.5898	+	10.0419i	−1.37777	+	0.501467i	−0.921501	−	0.388375i	$-0.873037\pi$
$401$	−27.5898	+	10.0419i	−1.37777	+	0.501467i	−0.456268	+	0.889842i	$0.650814\pi$
$402$		0			0
$403$	−2.49405	−	14.1445i	−0.124237	−	0.704585i
$404$	19.8319			0.986675
$405$		0			0
$406$	−3.54115			−0.175744
$407$	1.61798	+	9.17601i	0.0802002	+	0.454838i
$408$		0			0
$409$	18.9667	−	6.90331i	0.937842	−	0.341347i	0.172529	−	0.985004i	$-0.444806\pi$
$409$	18.9667	−	6.90331i	0.937842	−	0.341347i	0.765313	+	0.643658i	$0.222584\pi$
$410$	40.0203	+	33.5810i	1.97646	+	1.65845i
$411$		0			0
$412$	−38.3786	−	13.9687i	−1.89078	−	0.688187i
$413$	0.548476	+	0.949988i	0.0269887	+	0.0467459i
$414$		0			0
$415$	−2.28126	+	3.95126i	−0.111983	+	0.193960i
$416$	45.1792	−	37.9099i	2.21509	−	1.85869i
$417$		0			0
$418$	−5.22166	+	29.6135i	−0.255400	+	1.44844i
$419$	4.23186	−	24.0001i	0.206740	−	1.17248i	−0.687938	−	0.725769i	$-0.741484\pi$
$419$	4.23186	−	24.0001i	0.206740	−	1.17248i	0.894678	−	0.446711i	$-0.147405\pi$
$420$		0			0
$421$	−20.0509	+	16.8247i	−0.977219	+	0.819984i	−0.983668	−	0.179995i	$-0.942392\pi$
$421$	−20.0509	+	16.8247i	−0.977219	+	0.819984i	0.00644834	+	0.999979i	$0.497947\pi$
$422$	−18.7717	+	32.5136i	−0.913794	+	1.58274i
$423$		0			0
$424$	24.3781	+	42.2240i	1.18390	+	2.05058i
$425$	5.51658	+	2.00787i	0.267593	+	0.0973960i
$426$		0			0
$427$	2.62310	+	2.20104i	0.126941	+	0.106516i
$428$	53.7932	−	19.5791i	2.60019	−	0.946393i
$429$		0			0
$430$	7.07352	+	40.1159i	0.341116	+	1.93456i
$431$	31.9185			1.53746			0.768731	−	0.639572i	$-0.220889\pi$
$431$	31.9185			1.53746			0.768731	+	0.639572i	$0.220889\pi$
$432$		0			0
$433$	0.0123080			0.000591484			0.000295742	−	1.00000i	$-0.499906\pi$
$433$	0.0123080			0.000591484			0.000295742		1.00000i	$0.499906\pi$
$434$	−1.08509	−	6.15385i	−0.0520860	−	0.295394i
$435$		0			0
$436$	−61.1088	+	22.2418i	−2.92658	+	1.06519i
$437$	−20.6299	−	17.3105i	−0.986862	−	0.828075i
$438$		0			0
$439$	−4.98489	−	1.81435i	−0.237916	−	0.0865942i	0.220311	−	0.975430i	$-0.429293\pi$
$439$	−4.98489	−	1.81435i	−0.237916	−	0.0865942i	−0.458226	+	0.888836i	$0.651515\pi$
$440$	−14.3901	−	24.9244i	−0.686020	−	1.18822i
$441$		0			0
$442$	−11.2174	+	19.4291i	−0.533557	+	0.924147i
$443$	31.1752	−	26.1591i	1.48118	−	1.24286i	0.576264	−	0.817264i	$-0.304510\pi$
$443$	31.1752	−	26.1591i	1.48118	−	1.24286i	0.904915	−	0.425593i	$-0.139934\pi$
$444$		0			0
$445$	−3.25804	+	18.4773i	−0.154446	+	0.875907i
$446$	−3.19979	+	18.1469i	−0.151514	+	0.859281i
$447$		0			0
$448$	9.19520	−	7.71569i	0.434432	−	0.364532i
$449$	−7.71401	+	13.3611i	−0.364047	+	0.630547i	−0.988623	−	0.150417i	$-0.951938\pi$
$449$	−7.71401	+	13.3611i	−0.364047	+	0.630547i	0.624576	+	0.780964i	$0.285272\pi$
$450$		0			0
$451$	−11.0731	−	19.1791i	−0.521410	−	0.903109i
$452$	9.71333	+	3.53536i	0.456877	+	0.166289i
$453$		0			0
$454$	−20.1850	−	16.9372i	−0.947328	−	0.794902i
$455$	2.44853	−	0.891192i	0.114789	−	0.0417797i
$456$		0			0
$457$	0.414801	+	2.35246i	0.0194036	+	0.110043i	0.992971	−	0.118355i	$-0.0377622\pi$
$457$	0.414801	+	2.35246i	0.0194036	+	0.110043i	−0.973568	+	0.228399i	$0.926651\pi$
$458$	−37.9922			−1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	5.64076	+	31.9904i	0.262717	+	1.48994i	0.775459	+	0.631397i	$0.217518\pi$
$461$	5.64076	+	31.9904i	0.262717	+	1.48994i	−0.512743	+	0.858542i	$0.671371\pi$
$462$		0			0
$463$	−31.8354	+	11.5871i	−1.47952	+	0.538500i	−0.950666	−	0.310215i	$-0.899599\pi$
$463$	−31.8354	+	11.5871i	−1.47952	+	0.538500i	−0.528850	+	0.848715i	$0.677377\pi$
$464$	−27.3239	−	22.9275i	−1.26848	−	1.06438i
$465$		0			0
$466$	−13.5315	−	4.92508i	−0.626836	−	0.228150i
$467$	6.90133	+	11.9535i	0.319356	+	0.553140i	0.980354	−	0.197247i	$-0.0632002\pi$
$467$	6.90133	+	11.9535i	0.319356	+	0.553140i	−0.660998	+	0.750388i	$0.729867\pi$
$468$		0			0
$469$	−3.12459	+	5.41195i	−0.144280	+	0.249901i
$470$	−23.6772	+	19.8676i	−1.09215	+	0.916422i
$471$		0			0
$472$	−3.41466	+	19.3655i	−0.157172	+	0.891368i
$473$	2.99852	−	17.0054i	0.137872	−	0.781911i
$474$		0			0
$475$	−9.78295	+	8.20887i	−0.448873	+	0.376649i
$476$	−3.54645	+	6.14264i	−0.162551	+	0.281547i
$477$		0			0
$478$	−24.0392	−	41.6372i	−1.09953	−	1.90444i
$479$	−5.53584	−	2.01488i	−0.252939	−	0.0920623i	0.212439	−	0.977174i	$-0.431859\pi$
$479$	−5.53584	−	2.01488i	−0.252939	−	0.0920623i	−0.465378	+	0.885112i	$0.654082\pi$
$480$		0			0
$481$	−11.5844	−	9.72043i	−0.528201	−	0.443214i
$482$	5.10113	−	1.85666i	0.232350	−	0.0845685i
$483$		0			0
$484$	−6.76112	−	38.3442i	−0.307324	−	1.74292i
$485$	11.5213			0.523155
$486$		0			0
$487$	29.0299			1.31547			0.657736	−	0.753249i	$-0.271514\pi$
$487$	29.0299			1.31547			0.657736	+	0.753249i	$0.271514\pi$
$488$	10.6591	+	60.4507i	0.482514	+	2.73647i
$489$		0			0
$490$	−28.6923	+	10.4431i	−1.29619	+	0.471773i
$491$	3.35796	+	2.81766i	0.151543	+	0.127159i	0.715407	−	0.698708i	$-0.246241\pi$
$491$	3.35796	+	2.81766i	0.151543	+	0.127159i	−0.563864	+	0.825868i	$0.690686\pi$
$492$		0			0
$493$	6.54806	+	2.38330i	0.294910	+	0.107338i
$494$	−24.4019	−	42.2654i	−1.09789	−	1.90161i
$495$		0			0
$496$	31.4710	−	54.5093i	1.41309	−	2.44754i
$497$	−1.08741	+	0.912449i	−0.0487772	+	0.0409289i
$498$		0			0
$499$	6.13734	−	34.8066i	0.274745	−	1.55816i	−0.465026	−	0.885297i	$-0.653955\pi$
$499$	6.13734	−	34.8066i	0.274745	−	1.55816i	0.739771	−	0.672859i	$-0.234934\pi$
$500$	11.1231	−	63.0821i	0.497439	−	2.82112i
$501$		0			0
$502$	48.8299	−	40.9732i	2.17939	−	1.82872i
$503$	4.18829	−	7.25434i	0.186747	−	0.323455i	−0.757417	−	0.652932i	$-0.773539\pi$
$503$	4.18829	−	7.25434i	0.186747	−	0.323455i	0.944164	+	0.329477i	$0.106872\pi$
$504$		0			0
$505$	3.11870	+	5.40175i	0.138780	+	0.240375i
$506$	−22.6472	−	8.24292i	−1.00679	−	0.366442i
$507$		0			0
$508$	9.54928	+	8.01280i	0.423681	+	0.355510i
$509$	3.61121	−	1.31437i	0.160064	−	0.0582586i	−0.260745	−	0.965408i	$-0.583968\pi$
$509$	3.61121	−	1.31437i	0.160064	−	0.0582586i	0.420809	+	0.907149i	$0.361746\pi$
$510$		0			0
$511$	0.863615	+	4.89780i	0.0382041	+	0.216666i
$512$	13.6601			0.603699
$513$		0			0
$514$	15.8911			0.700925
$515$	−2.23055	−	12.6501i	−0.0982899	−	0.557430i
$516$		0			0
$517$	12.3121	−	4.48125i	0.541487	−	0.197085i
$518$	−5.04002	−	4.22908i	−0.221446	−	0.185815i
$519$		0			0
$520$	43.8929	+	15.9757i	1.92483	+	0.700582i
$521$	−9.82615	−	17.0194i	−0.430491	−	0.745633i	0.566424	−	0.824114i	$-0.308326\pi$
$521$	−9.82615	−	17.0194i	−0.430491	−	0.745633i	−0.996916	+	0.0784810i	$0.974993\pi$
$522$		0			0
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	−1.41543e−5	−	1.00000i	$-0.500005\pi$
$523$	19.8051	−	34.3035i	0.866018	−	1.49999i	0.866032	−	0.499988i	$-0.166662\pi$
$524$	−69.6639	+	58.4550i	−3.04328	+	2.55362i
$525$		0			0
$526$	10.3238	−	58.5491i	0.450138	−	2.55286i
$527$	−2.13525	+	12.1096i	−0.0930129	+	0.527502i
$528$		0			0
$529$	−1.08465	+	0.910127i	−0.0471586	+	0.0395707i
$530$	−12.2897	+	21.2864i	−0.533830	+	0.924620i
$531$		0			0
$532$	−7.71483	−	13.3625i	−0.334480	−	0.579337i
$533$	33.7753	+	12.2932i	1.46297	+	0.532477i
$534$		0			0
$535$	13.7922	+	11.5731i	0.596290	+	0.500347i
$536$	−105.268	+	38.3146i	−4.54690	+	1.65494i
$537$		0			0
$538$	−14.3749	−	81.5244i	−0.619748	−	3.51476i
$539$	12.9435			0.557514
$540$		0			0
$541$	−41.8257			−1.79823			−0.899115	−	0.437713i	$-0.855788\pi$
$541$	−41.8257			−1.79823			−0.899115	+	0.437713i	$0.855788\pi$
$542$	−7.55432	−	42.8427i	−0.324486	−	1.84025i
$543$		0			0
$544$	−47.4476	+	17.2695i	−2.03430	+	0.740424i
$545$	−15.6679	−	13.1469i	−0.671139	−	0.563153i
$546$		0			0
$547$	16.0070	+	5.82608i	0.684411	+	0.249105i	0.660740	−	0.750615i	$-0.270242\pi$
$547$	16.0070	+	5.82608i	0.684411	+	0.249105i	0.0236708	+	0.999720i	$0.492465\pi$
$548$	−37.0280	−	64.1343i	−1.58176	−	2.73968i
$549$		0			0
$550$	−5.71442	+	9.89767i	−0.243664	+	0.422038i
$551$	−11.6122	+	9.74377i	−0.494695	+	0.415098i
$552$		0			0
$553$	0.461686	−	2.61835i	0.0196329	−	0.111344i
$554$	−9.77675	+	55.4467i	−0.415374	+	2.35571i
$555$		0			0
$556$	32.2472	−	27.0586i	1.36759	−	1.14754i
$557$	16.8840	−	29.2439i	0.715398	−	1.23911i	−0.247408	−	0.968911i	$-0.579579\pi$
$557$	16.8840	−	29.2439i	0.715398	−	1.23911i	0.962806	−	0.270194i	$-0.0870880\pi$
$558$		0			0
$559$	14.0127	+	24.2707i	0.592674	+	1.02654i
$560$	10.7303	+	3.90550i	0.453437	+	0.165038i
$561$		0			0
$562$	25.4057	+	21.3180i	1.07168	+	0.899244i
$563$	21.3416	−	7.76771i	0.899442	−	0.327370i	0.149413	−	0.988775i	$-0.452262\pi$
$563$	21.3416	−	7.76771i	0.899442	−	0.327370i	0.750029	+	0.661405i	$0.230039\pi$
$564$		0			0
$565$	0.564536	+	3.20164i	0.0237502	+	0.134694i
$566$	12.3691			0.519913
$567$		0			0
$568$	−25.4466			−1.06772
$569$	1.88781	+	10.7063i	0.0791410	+	0.448831i	0.998468	+	0.0553359i	$0.0176230\pi$
$569$	1.88781	+	10.7063i	0.0791410	+	0.448831i	−0.919327	+	0.393495i	$0.871266\pi$
$570$		0			0
$571$	−13.9861	+	5.09053i	−0.585300	+	0.213032i	−0.617661	−	0.786444i	$-0.711920\pi$
$571$	−13.9861	+	5.09053i	−0.585300	+	0.213032i	0.0323607	+	0.999476i	$0.489697\pi$
$572$	−24.3129	−	20.4009i	−1.01657	−	0.853006i
$573$		0			0
$574$	14.6947	+	5.34842i	0.613343	+	0.223239i
$575$	−5.11772	−	8.86416i	−0.213424	−	0.369661i
$576$		0			0
$577$	18.5582	−	32.1437i	0.772586	−	1.33816i	−0.163555	−	0.986534i	$-0.552296\pi$
$577$	18.5582	−	32.1437i	0.772586	−	1.33816i	0.936141	−	0.351624i	$-0.114371\pi$
$578$	−20.5138	+	17.2131i	−0.853261	+	0.715971i
$579$		0			0
$580$	4.03819	−	22.9017i	0.167677	−	0.950943i
$581$	−0.237149	+	1.34494i	−0.00983861	+	0.0557975i
$582$		0			0
$583$	7.98170	−	6.69745i	0.330568	−	0.277380i
$584$	−44.5768	+	77.2093i	−1.84460	+	3.19494i
$585$		0			0
$586$	−35.3328	−	61.1981i	−1.45958	−	2.52807i
$587$	−13.7601	−	5.00828i	−0.567941	−	0.206714i	0.0420588	−	0.999115i	$-0.486608\pi$
$587$	−13.7601	−	5.00828i	−0.567941	−	0.206714i	−0.610000	+	0.792401i	$0.708831\pi$
$588$		0			0
$589$	−20.4911	−	17.1940i	−0.844319	−	0.708468i
$590$	−9.31545	+	3.39055i	−0.383511	+	0.139587i
$591$		0			0
$592$	−11.5078	−	65.2642i	−0.472969	−	2.68234i
$593$	−36.4392			−1.49638			−0.748189	−	0.663485i	$-0.769076\pi$
$593$	−36.4392			−1.49638			−0.748189	+	0.663485i	$0.769076\pi$
$594$		0			0
$595$	−2.23081			−0.0914544
$596$	0.672325	+	3.81294i	0.0275395	+	0.156184i
$597$		0			0
$598$	36.7562	−	13.3782i	1.50307	−	0.547074i
$599$	−21.0623	−	17.6734i	−0.860583	−	0.722115i	0.101511	−	0.994834i	$-0.467632\pi$
$599$	−21.0623	−	17.6734i	−0.860583	−	0.722115i	−0.962094	+	0.272720i	$0.912077\pi$
$600$		0			0
$601$	−42.4525	−	15.4514i	−1.73167	−	0.630277i	−0.732925	−	0.680309i	$-0.761846\pi$
$601$	−42.4525	−	15.4514i	−1.73167	−	0.630277i	−0.998748	+	0.0500315i	$0.984068\pi$
$602$	6.09653	+	10.5595i	0.248476	+	0.430373i
$603$		0			0
$604$	−11.5443	+	19.9953i	−0.469729	+	0.813595i
$605$	9.38083	−	7.87145i	0.381385	−	0.320020i
$606$		0			0
$607$	2.97584	−	16.8768i	0.120786	−	0.685009i	−0.862937	−	0.505312i	$-0.831377\pi$
$607$	2.97584	−	16.8768i	0.120786	−	0.685009i	0.983722	−	0.179697i	$-0.0575116\pi$
$608$	19.0735	−	108.171i	0.773534	−	4.38693i
$609$		0			0
$610$	−23.7053	+	19.8911i	−0.959799	+	0.805367i
$611$	−10.6324	+	18.4159i	−0.430143	+	0.745029i
$612$		0			0
$613$	0.234380	+	0.405959i	0.00946653	+	0.0163965i	0.870720	−	0.491779i	$-0.163653\pi$
$613$	0.234380	+	0.405959i	0.00946653	+	0.0163965i	−0.861253	+	0.508176i	$0.830320\pi$
$614$	−8.36998	−	3.04643i	−0.337785	−	0.122944i
$615$		0			0
$616$	−6.59925	−	5.53742i	−0.265891	−	0.223109i
$617$	−2.00610	+	0.730161i	−0.0807626	+	0.0293952i	−0.382086	−	0.924127i	$-0.624794\pi$
$617$	−2.00610	+	0.730161i	−0.0807626	+	0.0293952i	0.301323	+	0.953522i	$0.402572\pi$
$618$		0			0
$619$	1.48254	+	8.40790i	0.0595883	+	0.337942i	0.999998	−	0.00210213i	$-0.000669129\pi$
$619$	1.48254	+	8.40790i	0.0595883	+	0.337942i	−0.940410	+	0.340044i	$0.889558\pi$
$620$	41.0363			1.64806
$621$		0			0
$622$	94.1163			3.77372
$623$	0.975222	+	5.53076i	0.0390715	+	0.221585i
$624$		0			0
$625$	8.57993	−	3.12284i	0.343197	−	0.124914i
$626$	22.0230	+	18.4795i	0.880216	+	0.738589i
$627$		0			0
$628$	77.5651	+	28.2314i	3.09518	+	1.12655i
$629$	6.47339	+	11.2122i	0.258111	+	0.447061i
$630$		0			0
$631$	5.93539	−	10.2804i	0.236284	−	0.409256i	−0.723361	−	0.690470i	$-0.757404\pi$
$631$	5.93539	−	10.2804i	0.236284	−	0.409256i	0.959645	+	0.281214i	$0.0907370\pi$
$632$	36.5107	−	30.6361i	1.45232	−	1.21864i
$633$		0			0
$634$	−7.28091	+	41.2921i	−0.289162	+	1.63992i
$635$	−0.680810	+	3.86106i	−0.0270171	+	0.153222i
$636$		0			0
$637$	−16.0924	+	13.5031i	−0.637603	+	0.535012i
$638$	−6.78291	+	11.7483i	−0.268538	+	0.465121i
$639$		0			0
$640$	22.5486	+	39.0554i	0.891313	+	1.54380i
$641$	4.98381	+	1.81396i	0.196849	+	0.0716470i	0.438563	−	0.898700i	$-0.355488\pi$
$641$	4.98381	+	1.81396i	0.196849	+	0.0716470i	−0.241715	+	0.970347i	$0.577710\pi$
$642$		0			0
$643$	−0.631120	−	0.529573i	−0.0248889	−	0.0208843i	0.630258	−	0.776386i	$-0.282949\pi$
$643$	−0.631120	−	0.529573i	−0.0248889	−	0.0208843i	−0.655147	+	0.755501i	$0.727393\pi$
$644$	11.6207	−	4.22960i	0.457921	−	0.166670i
$645$		0			0
$646$	7.25551	+	41.1480i	0.285464	+	1.61895i
$647$	40.8373			1.60548			0.802740	−	0.596329i	$-0.203374\pi$
$647$	40.8373			1.60548			0.802740	+	0.596329i	$0.203374\pi$
$648$		0			0
$649$	4.20232			0.164955
$650$	−3.22098	−	18.2671i	−0.126337	−	0.716494i
$651$		0			0
$652$	−42.4589	+	15.4538i	−1.66282	+	0.605216i
$653$	−0.819175	−	0.687369i	−0.0320568	−	0.0268988i	0.626618	−	0.779326i	$-0.284438\pi$
$653$	−0.819175	−	0.687369i	−0.0320568	−	0.0268988i	−0.658675	+	0.752427i	$0.728883\pi$
$654$		0			0
$655$	−26.8769	−	9.78238i	−1.05017	−	0.382229i
$656$	78.7569	+	136.411i	3.07494	+	5.32595i
$657$		0			0
$658$	−4.62587	+	8.01225i	−0.180335	+	0.312350i
$659$	21.9581	−	18.4250i	0.855367	−	0.717738i	−0.105598	−	0.994409i	$-0.533676\pi$
$659$	21.9581	−	18.4250i	0.855367	−	0.717738i	0.960965	+	0.276671i	$0.0892312\pi$
$660$		0			0
$661$	−0.780673	+	4.42742i	−0.0303647	+	0.172207i	−0.996219	−	0.0868799i	$-0.972310\pi$
$661$	−0.780673	+	4.42742i	−0.0303647	+	0.172207i	0.965854	+	0.259086i	$0.0834215\pi$
$662$	−6.84409	+	38.8148i	−0.266003	+	1.50858i
$663$		0			0
$664$	−18.7540	+	15.7365i	−0.727797	+	0.610695i
$665$	2.42642	−	4.20268i	0.0940924	−	0.162973i
$666$		0			0
$667$	−6.07464	−	10.5216i	−0.235211	−	0.407397i
$668$	−115.633	−	42.0871i	−4.47399	−	1.62840i
$669$		0			0
$670$	−43.2621	−	36.3012i	−1.67136	−	1.40244i
$671$	12.3267	−	4.48656i	0.475868	−	0.173202i
$672$		0			0
$673$	3.13584	+	17.7842i	0.120878	+	0.685532i	0.983671	+	0.179975i	$0.0576017\pi$
$673$	3.13584	+	17.7842i	0.120878	+	0.685532i	−0.862793	+	0.505557i	$0.831287\pi$
$674$	−55.7643			−2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	−2.73308	−	15.5001i	−0.105041	−	0.595716i	−0.991204	−	0.132343i	$-0.957750\pi$
$677$	−2.73308	−	15.5001i	−0.105041	−	0.595716i	0.886163	−	0.463373i	$-0.153361\pi$
$678$		0			0
$679$	3.24066	−	1.17951i	0.124365	−	0.0452653i
$680$	−30.6342	−	25.7051i	−1.17477	−	0.985747i
$681$		0			0
$682$	−22.4948	−	8.18745i	−0.861371	−	0.313514i
$683$	−1.38059	−	2.39125i	−0.0528268	−	0.0914987i	0.838403	−	0.545051i	$-0.183490\pi$
$683$	−1.38059	−	2.39125i	−0.0528268	−	0.0914987i	−0.891230	+	0.453552i	$0.850156\pi$
$684$		0			0
$685$	11.6458	−	20.1711i	0.444963	−	0.770698i
$686$	−14.2626	+	11.9677i	−0.544549	+	0.456931i
$687$		0			0
$688$	−21.3269	+	120.951i	−0.813081	+	4.61121i
$689$	−2.93648	+	16.6536i	−0.111871	+	0.634452i
$690$		0			0
$691$	−26.4481	+	22.1926i	−1.00613	+	0.844246i	−0.987822	−	0.155586i	$-0.950273\pi$
$691$	−26.4481	+	22.1926i	−1.00613	+	0.844246i	−0.0183109	+	0.999832i	$0.505829\pi$
$692$	6.85537	−	11.8738i	0.260602	−	0.451376i
$693$		0			0
$694$	28.6514	+	49.6257i	1.08759	+	1.88377i
$695$	12.4412	+	4.52823i	0.471922	+	0.171766i
$696$		0			0
$697$	−23.5728	−	19.7799i	−0.892882	−	0.749217i
$698$	11.7589	−	4.27989i	0.445081	−	0.161996i
$699$		0			0
$700$	−1.01834	−	5.77527i	−0.0384894	−	0.218285i
$701$	20.7410			0.783378			0.391689	−	0.920098i	$-0.371891\pi$
$701$	20.7410			0.783378			0.391689	+	0.920098i	$0.371891\pi$
$702$		0			0
$703$	−28.1640			−1.06222
$704$	−7.98508	−	45.2856i	−0.300949	−	1.70677i
$705$		0			0
$706$	34.6806	−	12.6227i	1.30522	−	0.475062i
$707$	1.43023	+	1.20010i	0.0537892	+	0.0451345i
$708$		0			0
$709$	−26.0362	−	9.47639i	−0.977809	−	0.355893i	−0.196821	−	0.980439i	$-0.563062\pi$
$709$	−26.0362	−	9.47639i	−0.977809	−	0.355893i	−0.780988	+	0.624546i	$0.785284\pi$
$710$	−6.41419	−	11.1097i	−0.240720	−	0.416940i
$711$		0			0
$712$	−50.3376	+	87.1873i	−1.88648	+	3.26748i
$713$	16.4231	−	13.7806i	0.615050	−	0.516088i
$714$		0			0
$715$	1.73337	−	9.83044i	0.0648244	−	0.367637i
$716$	−8.21426	+	46.5854i	−0.306981	+	1.74098i
$717$		0			0
$718$	−58.5286	+	49.1113i	−2.18427	+	1.83282i
$719$	16.5657	−	28.6927i	0.617797	−	1.07006i	−0.372090	−	0.928197i	$-0.621359\pi$
$719$	16.5657	−	28.6927i	0.617797	−	1.07006i	0.989887	−	0.141859i	$-0.0453081\pi$
$720$		0			0
$721$	−1.92247	−	3.32981i	−0.0715965	−	0.124009i
$722$	−37.1147	−	13.5086i	−1.38127	−	0.502740i
$723$		0			0
$724$	32.2276	+	27.0422i	1.19773	+	1.00502i
$725$	−5.41389	+	1.97049i	−0.201067	+	0.0731823i
$726$		0			0
$727$	−0.0143443	−	0.0813505i	−0.000532000	−	0.00301712i	0.984541	−	0.175157i	$-0.0560432\pi$
$727$	−0.0143443	−	0.0813505i	−0.000532000	−	0.00301712i	−0.985073	+	0.172139i	$0.944932\pi$
$728$	13.9816			0.518191
$729$		0			0
$730$	−44.9449			−1.66349
$731$	−4.16645	−	23.6291i	−0.154102	−	0.873953i
$732$		0			0
$733$	29.9926	−	10.9164i	1.10780	−	0.403207i	0.277616	−	0.960692i	$-0.410456\pi$
$733$	29.9926	−	10.9164i	1.10780	−	0.403207i	0.830187	+	0.557485i	$0.188234\pi$
$734$	72.2788	+	60.6491i	2.66786	+	2.23860i
$735$		0			0
$736$	82.7251	+	30.1095i	3.04929	+	1.10985i
$737$	11.9700	+	20.7327i	0.440921	+	0.763698i
$738$		0			0
$739$	17.8960	−	30.9967i	0.658314	−	1.14023i	−0.322738	−	0.946488i	$-0.604603\pi$
$739$	17.8960	−	30.9967i	0.658314	−	1.14023i	0.981052	−	0.193745i	$-0.0620634\pi$
$740$	33.0983	−	27.7727i	1.21672	−	1.02095i
$741$		0			0
$742$	−1.27758	+	7.24551i	−0.0469014	+	0.265991i
$743$	−3.43457	+	19.4784i	−0.126002	+	0.714593i	0.854706	+	0.519113i	$0.173738\pi$
$743$	−3.43457	+	19.4784i	−0.126002	+	0.714593i	−0.980708	+	0.195480i	$0.937374\pi$
$744$		0			0
$745$	−0.932828	+	0.782736i	−0.0341762	+	0.0286772i
$746$	−4.13799	+	7.16721i	−0.151503	+	0.262410i
$747$		0			0
$748$	13.5861	+	23.5319i	0.496758	+	0.860411i
$749$	5.06423	+	1.84323i	0.185043	+	0.0673501i
$750$		0			0
$751$	23.4261	+	19.6568i	0.854829	+	0.717287i	0.960848	−	0.277077i	$-0.0893658\pi$
$751$	23.4261	+	19.6568i	0.854829	+	0.717287i	−0.106018	+	0.994364i	$0.533810\pi$
$752$	−87.5699	+	31.8728i	−3.19334	+	1.16228i
$753$		0			0
$754$	−3.82324	−	21.6827i	−0.139234	−	0.789636i
$755$	−7.26165			−0.264278
$756$		0			0
$757$	25.4129			0.923647			0.461824	−	0.886972i	$-0.347195\pi$
$757$	25.4129			0.923647			0.461824	+	0.886972i	$0.347195\pi$
$758$	−3.60614	−	20.4514i	−0.130981	−	0.742829i
$759$		0			0
$760$	81.7467	−	29.7534i	2.96527	−	1.07927i
$761$	−35.8646	−	30.0940i	−1.30009	−	1.09091i	−0.990129	−	0.140159i	$-0.955239\pi$
$761$	−35.8646	−	30.0940i	−1.30009	−	1.09091i	−0.309963	−	0.950749i	$-0.600317\pi$
$762$		0			0
$763$	−5.75294	−	2.09390i	−0.208270	−	0.0758042i
$764$	42.2661	+	73.2070i	1.52913	+	2.64854i
$765$		0			0
$766$	−14.0149	+	24.2744i	−0.506377	+	0.877071i
$767$	−5.22467	+	4.38402i	−0.188652	+	0.158298i
$768$		0			0
$769$	2.52926	−	14.3441i	0.0912074	−	0.517263i	−0.904636	−	0.426184i	$-0.859857\pi$
$769$	2.52926	−	14.3441i	0.0912074	−	0.517263i	0.995844	−	0.0910785i	$-0.0290314\pi$
$770$	0.754140	−	4.27694i	0.0271773	−	0.154130i
$771$		0			0
$772$	−18.6754	+	15.6705i	−0.672142	+	0.563994i
$773$	−12.1767	+	21.0906i	−0.437964	+	0.758576i	−0.997532	−	0.0702080i	$-0.977634\pi$
$773$	−12.1767	+	21.0906i	−0.437964	+	0.758576i	0.559568	+	0.828784i	$0.310967\pi$
$774$		0			0
$775$	−5.08328	−	8.80451i	−0.182597	−	0.316267i
$776$	58.0929	+	21.1441i	2.08541	+	0.759029i
$777$		0			0
$778$	−0.884728	−	0.742375i	−0.0317190	−	0.0266154i
$779$	62.9035	−	22.8950i	2.25375	−	0.820298i
$780$		0			0
$781$

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.469730 + 2.66397i) q^{2} +(-4.99670 + 1.81865i) q^{4} +(-1.28112 - 1.07499i) q^{5} +(-0.470402 - 0.171212i) q^{7} +(-4.48686 - 7.77147i) q^{8} +(2.26195 - 3.91782i) q^{10} +(-1.46906 + 1.23269i) q^{11} +(0.540469 - 3.06515i) q^{13} +(0.235142 - 1.33356i) q^{14} +(10.4486 - 8.76745i) q^{16} +(-1.33234 + 2.30767i) q^{17} +(-2.89832 - 5.02003i) q^{19} +(8.35640 + 3.04148i) q^{20} +(-3.97390 - 3.33449i) q^{22} +(4.36569 - 1.58898i) q^{23} +(-0.382569 - 2.16966i) q^{25} +8.41934 q^{26} +2.66183 q^{28} +(-0.454102 - 2.57534i) q^{29} +(4.33631 - 1.57829i) q^{31} +(14.5157 + 12.1801i) q^{32} +(-6.77341 - 2.46532i) q^{34} +(0.418591 + 0.725020i) q^{35} +(2.42934 - 4.20773i) q^{37} +(12.0118 - 10.0791i) q^{38} +(-2.60603 + 14.7795i) q^{40} +(-2.00532 + 11.3727i) q^{41} +(-6.89772 + 5.78788i) q^{43} +(5.09861 - 8.83106i) q^{44} +(6.28369 + 10.8837i) q^{46} +(-6.42020 - 2.33676i) q^{47} +(-5.17035 - 4.33844i) q^{49} +(5.60020 - 2.03831i) q^{50} +(2.87388 + 16.2986i) q^{52} -5.43322 q^{53} +3.20716 q^{55} +(0.780056 + 4.42392i) q^{56} +(6.64732 - 2.41943i) q^{58} +(-1.67864 - 1.40855i) q^{59} +(-6.42781 - 2.33953i) q^{61} +(6.24140 + 10.8104i) q^{62} +(-11.9893 + 20.7661i) q^{64} +(-3.98741 + 3.34583i) q^{65} +(2.16775 - 12.2939i) q^{67} +(2.46043 - 13.9538i) q^{68} +(-1.73481 + 1.45568i) q^{70} +(1.41784 - 2.45578i) q^{71} +(-4.96749 - 8.60394i) q^{73} +(12.3504 + 4.49518i) q^{74} +(23.6117 + 19.8126i) q^{76} +(0.902098 - 0.328337i) q^{77} +(0.922282 + 5.23052i) q^{79} -22.8109 q^{80} -31.2385 q^{82} +(-0.473738 - 2.68670i) q^{83} +(4.18761 - 1.52416i) q^{85} +(-18.6588 - 15.6566i) q^{86} +(16.1712 + 5.88584i) q^{88} +(-5.60945 - 9.71585i) q^{89} +(-0.779029 + 1.34932i) q^{91} +(-18.9242 + 15.8793i) q^{92} +(3.20930 - 18.2009i) q^{94} +(-1.68338 + 9.54693i) q^{95} +(-5.27739 + 4.42826i) q^{97} +(9.12879 - 15.8115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 + 27 * q^16 + 9 * q^17 - 12 * q^19 + 39 * q^20 - 39 * q^22 + 21 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 + 6 * q^31 + 27 * q^32 - 18 * q^34 - 30 * q^35 - 3 * q^37 + 3 * q^38 + 33 * q^40 - 15 * q^41 - 30 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 - 3 * q^49 + 6 * q^50 - 18 * q^53 + 30 * q^55 + 15 * q^56 - 3 * q^58 + 30 * q^59 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 12 * q^65 - 39 * q^67 + 18 * q^68 + 51 * q^70 - 12 * q^73 + 57 * q^74 + 57 * q^76 - 24 * q^77 + 15 * q^79 - 42 * q^80 - 42 * q^82 - 21 * q^83 + 54 * q^85 - 60 * q^86 + 12 * q^88 + 9 * q^89 - 18 * q^91 - 15 * q^92 + 33 * q^94 + 42 * q^95 - 12 * q^97 - 18 * q^98

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