LMFDB - Embedded newform 729.2.e.l.649.2

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			649.2
Root			$-1.37340i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.l.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.469730	−	2.66397i	0.332149	−	1.88371i	−0.121597	−	0.992580i	$-0.538802\pi$
$2$	0.469730	−	2.66397i	0.332149	−	1.88371i	0.453746	−	0.891131i	$-0.350087\pi$
$3$		0			0
$3$		0			0
$4$	−4.99670	−	1.81865i	−2.49835	−	0.909325i
$5$	−1.28112	+	1.07499i	−0.572935	+	0.480749i	−0.882618	−	0.470090i	$-0.844221\pi$
$5$	−1.28112	+	1.07499i	−0.572935	+	0.480749i	0.309684	+	0.950840i	$0.399777\pi$
$6$		0			0
$7$	−0.470402	+	0.171212i	−0.177795	+	0.0647122i	−0.429384	−	0.903122i	$-0.641269\pi$
$7$	−0.470402	+	0.171212i	−0.177795	+	0.0647122i	0.251589	+	0.967834i	$0.419047\pi$
$8$	−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	0.393870	−	0.919166i	$-0.371136\pi$
$11$	−1.46906	−	1.23269i	−0.442937	−	0.371669i	−0.836807	+	0.547498i	$0.815581\pi$
$12$		0			0
$13$	0.540469	+	3.06515i	0.149899	+	0.850120i	0.963302	+	0.268419i	$0.0865013\pi$
$13$	0.540469	+	3.06515i	0.149899	+	0.850120i	−0.813403	+	0.581700i	$0.802388\pi$
$14$	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	0.657995	−	0.753022i	$-0.271405\pi$
$17$	−1.33234	−	2.30767i	−0.323139	−	0.559693i	−0.981134	+	0.193329i	$0.938071\pi$
$18$		0			0
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	0.314387	+	0.949295i	$0.398201\pi$
$19$	−2.89832	+	5.02003i	−0.664920	+	1.15167i	−0.979307	+	0.202380i	$0.935132\pi$
$20$	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	0.754376	−	0.656442i	$-0.227939\pi$
$23$	4.36569	+	1.58898i	0.910309	+	0.331325i	0.155933	+	0.987768i	$0.450162\pi$
$24$		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	0.913176	+	0.407566i	$0.133622\pi$
$29$	−0.454102	+	2.57534i	−0.0843247	+	0.478229i	−0.997500	+	0.0706626i	$0.977489\pi$
$30$		0			0
$31$	4.33631	+	1.57829i	0.778824	+	0.283469i	0.700682	−	0.713473i	$-0.252879\pi$
$31$	4.33631	+	1.57829i	0.778824	+	0.283469i	0.0781418	+	0.996942i	$0.475101\pi$
$32$	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	0.993650	−	0.112519i	$-0.0358919\pi$
$37$	2.42934	+	4.20773i	0.399381	+	0.691747i	−0.594269	+	0.804266i	$0.702559\pi$
$38$	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	−0.582260	−	0.813003i	$-0.697831\pi$
$41$	−2.00532	−	11.3727i	−0.313178	−	1.77612i	0.269082	−	0.963117i	$-0.413280\pi$
$42$		0			0
$43$	−6.89772	−	5.78788i	−1.05189	−	0.882643i	−0.0586014	−	0.998281i	$-0.518664\pi$
$43$	−6.89772	−	5.78788i	−1.05189	−	0.882643i	−0.993291	+	0.115639i	$0.963109\pi$
$44$	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	−0.764776	−	0.644296i	$-0.777150\pi$
$47$	−6.42020	+	2.33676i	−0.936483	+	0.340852i	−0.171707	+	0.985148i	$0.554928\pi$
$48$		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	−0.745485	−	0.666522i	$-0.767782\pi$
$59$	−1.67864	+	1.40855i	−0.218541	+	0.183377i	0.526944	+	0.849900i	$0.323338\pi$
$60$		0			0
$61$	−6.42781	+	2.33953i	−0.822997	+	0.299547i	−0.718982	−	0.695029i	$-0.755391\pi$
$61$	−6.42781	+	2.33953i	−0.822997	+	0.299547i	−0.104016	+	0.994576i	$0.533169\pi$
$62$	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	0.769509	+	0.638635i	$0.220501\pi$
$67$	2.16775	+	12.2939i	0.264833	+	1.50194i	−0.504676	+	0.863309i	$0.668388\pi$
$68$	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	0.937811	−	0.347147i	$-0.112850\pi$
$71$	1.41784	+	2.45578i	0.168267	+	0.291447i	−0.769544	+	0.638594i	$0.779516\pi$
$72$		0			0
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	0.413913	+	0.910316i	$0.364162\pi$
$73$	−4.96749	+	8.60394i	−0.581400	+	1.00701i	−0.995314	+	0.0966986i	$0.969172\pi$
$74$	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	−0.887942	−	0.459956i	$-0.847865\pi$
$79$	0.922282	−	5.23052i	0.103765	−	0.588480i	0.991706	−	0.128524i	$-0.0410238\pi$
$80$	−22.8109			−2.55033
$81$		0			0
$82$	−31.2385			−3.44972
$83$	−0.473738	+	2.68670i	−0.0519995	+	0.294904i	−0.999706	−	0.0242387i	$-0.992284\pi$
$83$	−0.473738	+	2.68670i	−0.0519995	+	0.294904i	0.947707	+	0.319143i	$0.103395\pi$
$84$		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	0.399003	+	0.916950i	$0.369356\pi$
$89$	−5.60945	+	9.71585i	−0.594600	+	1.02988i	−0.993603	+	0.112928i	$0.963977\pi$
$90$		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	0.334274	−	0.942476i	$-0.391509\pi$
$97$	−5.27739	−	4.42826i	−0.535838	−	0.449621i	−0.870112	+	0.492855i	$0.835953\pi$
$98$	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	−0.510447	−	0.859909i	$-0.670520\pi$
$101$	−3.50472	+	1.27561i	−0.348733	+	0.126928i	0.161714	+	0.986838i	$0.448298\pi$
$102$		0			0
$103$	5.88383	−	4.93712i	0.579751	−	0.486469i	−0.305114	−	0.952316i	$-0.598695\pi$
$103$	5.88383	−	4.93712i	0.579751	−	0.486469i	0.884865	+	0.465847i	$0.154250\pi$
$104$	−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	−0.710139	−	0.704062i	$-0.751368\pi$
$113$	−1.48915	+	1.24955i	−0.140088	+	0.117547i	0.570051	+	0.821609i	$0.306923\pi$
$114$		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	−0.913335	−	0.407210i	$-0.866502\pi$
$127$	−1.17217	+	2.03025i	−0.104013	+	0.180156i	0.809322	+	0.587366i	$0.199835\pi$
$128$	−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	0.929401	−	0.369072i	$-0.120324\pi$
$131$	16.0710	+	5.84936i	1.40413	+	0.511061i	0.474728	+	0.880133i	$0.342547\pi$
$132$		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	−0.688250	−	0.725474i	$-0.741621\pi$
$137$	2.41843	−	13.7156i	0.206620	−	1.17180i	0.894870	−	0.446327i	$-0.147268\pi$
$138$		0			0
$139$	−7.43920	−	2.70765i	−0.630985	−	0.229660i	0.00667492	−	0.999978i	$-0.497875\pi$
$139$	−7.43920	−	2.70765i	−0.630985	−	0.229660i	−0.637660	+	0.770318i	$0.720098\pi$
$140$	−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	0.989549	−	0.144198i	$-0.0460604\pi$
$149$	0.126439	+	0.717072i	0.0103583	+	0.0587449i	−0.979190	+	0.202943i	$0.934949\pi$
$150$		0			0
$151$	3.32623	+	2.79104i	0.270685	+	0.227132i	0.768018	−	0.640428i	$-0.221243\pi$
$151$	3.32623	+	2.79104i	0.270685	+	0.227132i	−0.497333	+	0.867560i	$0.665687\pi$
$152$	−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	−0.979137	−	0.203203i	$-0.934865\pi$
$157$	−11.8915	+	9.97816i	−0.949046	+	0.796344i	0.0300908	+	0.999547i	$0.490420\pi$
$158$	−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	0.399684	−	0.916653i	$-0.369120\pi$
$167$	17.7278	−	14.8754i	1.37182	−	1.15109i	0.972131	−	0.234436i	$-0.0753244\pi$
$168$		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	0.564605	−	0.825361i	$-0.309028\pi$
$173$	−1.97523	−	1.65741i	−0.150174	−	0.126011i	−0.714779	+	0.699350i	$0.753473\pi$
$174$		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	0.982994	−	0.183636i	$-0.0587867\pi$
$179$	4.44806	+	7.70427i	0.332464	+	0.575844i	−0.650530	+	0.759480i	$0.725453\pi$
$180$		0			0
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	−0.974761	−	0.223250i	$-0.928334\pi$
$181$	−3.95592	+	6.85185i	−0.294041	+	0.509294i	0.680720	+	0.732543i	$0.261667\pi$
$182$	−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	0.705750	+	0.708461i	$0.250610\pi$
$191$	−2.76055	+	15.6558i	−0.199746	+	1.13282i	−0.905496	+	0.424355i	$0.860501\pi$
$192$		0			0
$193$	4.30828	+	1.56809i	0.310117	+	0.112873i	0.492390	−	0.870375i	$-0.336123\pi$
$193$	4.30828	+	1.56809i	0.310117	+	0.112873i	−0.182273	+	0.983248i	$0.558346\pi$
$194$	−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	−0.914416	−	0.404775i	$-0.867350\pi$
$197$	−1.49708	+	2.59303i	−0.106663	+	0.184745i	0.807754	+	0.589520i	$0.200683\pi$
$198$		0			0
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	−0.999478	−	0.0322965i	$-0.989718\pi$
$199$	−7.44425	−	12.8938i	−0.527709	−	0.914018i	0.471770	−	0.881722i	$-0.343615\pi$
$200$	−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	−0.198727	−	0.980055i	$-0.563681\pi$
$211$	10.6319	−	8.92122i	0.731930	−	0.614162i	0.930657	+	0.365893i	$0.119236\pi$
$212$	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	−0.118678	−	0.992933i	$-0.537866\pi$
$223$	6.40117	−	2.32983i	0.428654	−	0.156017i	0.547332	+	0.836916i	$0.315643\pi$
$224$	−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	0.360644	−	0.932704i	$-0.382557\pi$
$227$	−7.46192	−	6.26129i	−0.495265	−	0.415577i	−0.855909	+	0.517127i	$0.827001\pi$
$228$		0			0
$229$	−2.43886	−	13.8315i	−0.161165	−	0.914009i	−0.952931	−	0.303186i	$-0.901950\pi$
$229$	−2.43886	−	13.8315i	−0.161165	−	0.914009i	0.791767	−	0.610823i	$-0.209161\pi$
$230$	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	0.765572	−	0.643350i	$-0.222456\pi$
$233$	−2.66167	−	4.61014i	−0.174372	−	0.302020i	−0.939944	+	0.341330i	$0.889123\pi$
$234$		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	−0.260305	−	0.965526i	$-0.583823\pi$
$239$	−16.7016	−	6.07890i	−1.08034	−	0.393211i	−0.820034	+	0.572315i	$0.806045\pi$
$240$		0			0
$241$	−0.348476	+	1.97631i	−0.0224473	+	0.127305i	−0.993972	−	0.109633i	$-0.965033\pi$
$241$	−0.348476	+	1.97631i	−0.0224473	+	0.127305i	0.971525	+	0.236938i	$0.0761437\pi$
$242$	−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	0.207125	+	0.978314i	$0.433589\pi$
$251$	−11.7822	+	20.4073i	−0.743683	+	1.28810i	−0.950808	+	0.309782i	$0.899744\pi$
$252$		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	0.999953	+	0.00973053i	$0.00309737\pi$
$257$	1.02011	+	5.78532i	0.0636326	+	0.360878i	−0.936320	+	0.351148i	$0.885792\pi$
$258$		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	−0.888277	−	0.459308i	$-0.848097\pi$
$263$	−20.6527	+	7.51696i	−1.27350	+	0.463516i	−0.385222	+	0.922824i	$0.625875\pi$
$264$		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	0.320662	−	0.947194i	$-0.396095\pi$
$277$	19.5584	−	7.11866i	1.17515	−	0.427719i	0.854486	+	0.519475i	$0.173872\pi$
$278$	−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	0.878403	−	0.477921i	$-0.158610\pi$
$281$	9.39192	+	7.88075i	0.560275	+	0.470126i	−0.318128	+	0.948048i	$0.603054\pi$
$282$		0			0
$283$	0.794020	+	4.50311i	0.0471996	+	0.267682i	0.999270	−	0.0381959i	$-0.0121611\pi$
$283$	0.794020	+	4.50311i	0.0471996	+	0.267682i	−0.952071	+	0.305878i	$0.901050\pi$
$284$	−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	−0.496002	−	0.868321i	$-0.665199\pi$
$293$	−24.5480	−	8.93473i	−1.43411	−	0.521973i	−0.938106	+	0.346348i	$0.887421\pi$
$294$		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	0.815212	−	0.579163i	$-0.196621\pi$
$307$	−1.64638	−	2.85162i	−0.0939641	−	0.162751i	−0.909176	+	0.416412i	$0.863287\pi$
$308$	−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	0.332838	+	0.942984i	$0.391994\pi$
$311$	6.04168	+	34.2641i	0.342592	+	1.94294i	0.00975457	+	0.999952i	$0.496895\pi$
$312$		0			0
$313$	8.14139	+	6.83144i	0.460179	+	0.386136i	0.843197	−	0.537605i	$-0.180671\pi$
$313$	8.14139	+	6.83144i	0.460179	+	0.386136i	−0.383018	+	0.923741i	$0.625115\pi$
$314$	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	0.101121	−	0.994874i	$-0.467757\pi$
$317$	14.5654	−	5.30139i	0.818077	−	0.297756i	0.716956	+	0.697118i	$0.245535\pi$
$318$		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	0.0628759	−	0.998021i	$-0.479973\pi$
$331$	13.6916	−	4.98333i	0.752557	−	0.273908i	0.689682	+	0.724113i	$0.257751\pi$
$332$	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	−0.912419	−	0.409257i	$-0.865788\pi$
$337$	−3.57972	−	20.3016i	−0.195000	−	1.10590i	0.717419	−	0.696641i	$-0.245323\pi$
$338$	−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	0.815657	−	0.578536i	$-0.196376\pi$
$347$	19.9060	+	7.24520i	1.06861	+	0.388943i	0.252954	+	0.967478i	$0.418598\pi$
$348$		0			0
$349$	−0.803291	+	4.55569i	−0.0429992	+	0.243861i	−0.998730	−	0.0503818i	$-0.983956\pi$
$349$	−0.803291	+	4.55569i	−0.0429992	+	0.243861i	0.955731	+	0.294242i	$0.0950673\pi$
$350$	−2.98333			−0.159466
$351$		0			0
$352$	−36.3387			−1.93686
$353$	−2.36915	+	13.4361i	−0.126097	+	0.715133i	0.854553	+	0.519365i	$0.173831\pi$
$353$	−2.36915	+	13.4361i	−0.126097	+	0.715133i	−0.980650	+	0.195769i	$0.937280\pi$
$354$		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	−0.204683	−	0.978828i	$-0.565616\pi$
$359$	14.1223	−	24.4606i	0.745349	−	1.29098i	0.950032	−	0.312153i	$-0.101050\pi$
$360$		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	0.963369	+	0.268180i	$0.0864221\pi$
$367$	26.7198	+	22.4206i	1.39476	+	1.17034i	0.431393	+	0.902164i	$0.358022\pi$
$368$	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	−0.580093	−	0.814550i	$-0.696984\pi$
$373$	2.34367	−	1.96657i	0.121350	−	0.101825i	0.701443	+	0.712725i	$0.252539\pi$
$374$	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	−0.417055	−	0.908881i	$-0.636938\pi$
$383$	7.93771	−	6.66053i	0.405598	−	0.340337i	0.822653	+	0.568544i	$0.192493\pi$
$384$		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	0.634459	−	0.772957i	$-0.281223\pi$
$389$	−0.327064	−	0.274439i	−0.0165828	−	0.0139146i	−0.651041	+	0.759042i	$0.725668\pi$
$390$		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	−0.295266	−	0.955415i	$-0.595408\pi$
$397$	13.5445	−	23.4598i	0.679781	−	1.17741i	0.975047	−	0.221999i	$-0.0712583\pi$
$398$	−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	−0.456268	−	0.889842i	$-0.650814\pi$
$401$	−27.5898	−	10.0419i	−1.37777	−	0.501467i	−0.921501	+	0.388375i	$0.873037\pi$
$402$		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	0.765313	−	0.643658i	$-0.222584\pi$
$409$	18.9667	+	6.90331i	0.937842	+	0.341347i	0.172529	+	0.985004i	$0.444806\pi$
$410$	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	0.894678	+	0.446711i	$0.147405\pi$
$419$	4.23186	+	24.0001i	0.206740	+	1.17248i	−0.687938	+	0.725769i	$0.741484\pi$
$420$		0			0
$421$	−20.0509	−	16.8247i	−0.977219	−	0.819984i	0.00644834	−	0.999979i	$-0.497947\pi$
$421$	−20.0509	−	16.8247i	−0.977219	−	0.819984i	−0.983668	+	0.179995i	$0.942392\pi$
$422$	−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	−0.458226	−	0.888836i	$-0.651515\pi$
$439$	−4.98489	+	1.81435i	−0.237916	+	0.0865942i	0.220311	+	0.975430i	$0.429293\pi$
$440$	−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	0.904915	+	0.425593i	$0.139934\pi$
$443$	31.1752	+	26.1591i	1.48118	+	1.24286i	0.576264	+	0.817264i	$0.304510\pi$
$444$		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	0.624576	−	0.780964i	$-0.285272\pi$
$449$	−7.71401	−	13.3611i	−0.364047	−	0.630547i	−0.988623	+	0.150417i	$0.951938\pi$
$450$		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	−0.973568	−	0.228399i	$-0.926651\pi$
$457$	0.414801	−	2.35246i	0.0194036	−	0.110043i	0.992971	+	0.118355i	$0.0377622\pi$
$458$	−37.9922			−1.77526
$459$		0			0
$460$	41.3143			1.92629
$461$	5.64076	−	31.9904i	0.262717	−	1.48994i	−0.512743	−	0.858542i	$-0.671371\pi$
$461$	5.64076	−	31.9904i	0.262717	−	1.48994i	0.775459	−	0.631397i	$-0.217518\pi$
$462$		0			0
$463$	−31.8354	−	11.5871i	−1.47952	−	0.538500i	−0.528850	−	0.848715i	$-0.677377\pi$
$463$	−31.8354	−	11.5871i	−1.47952	−	0.538500i	−0.950666	+	0.310215i	$0.899599\pi$
$464$	−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	−0.660998	−	0.750388i	$-0.729867\pi$
$467$	6.90133	−	11.9535i	0.319356	−	0.553140i	0.980354	+	0.197247i	$0.0632002\pi$
$468$		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	−0.465378	−	0.885112i	$-0.654082\pi$
$479$	−5.53584	+	2.01488i	−0.252939	+	0.0920623i	0.212439	+	0.977174i	$0.431859\pi$
$480$		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	−0.563864	−	0.825868i	$-0.690686\pi$
$491$	3.35796	−	2.81766i	0.151543	−	0.127159i	0.715407	+	0.698708i	$0.246241\pi$
$492$		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	0.739771	+	0.672859i	$0.234934\pi$
$499$	6.13734	+	34.8066i	0.274745	+	1.55816i	−0.465026	+	0.885297i	$0.653955\pi$
$500$	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	0.944164	−	0.329477i	$-0.106872\pi$
$503$	4.18829	+	7.25434i	0.186747	+	0.323455i	−0.757417	+	0.652932i	$0.773539\pi$
$504$		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	0.420809	−	0.907149i	$-0.361746\pi$
$509$	3.61121	+	1.31437i	0.160064	+	0.0582586i	−0.260745	+	0.965408i	$0.583968\pi$
$510$		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	−0.996916	−	0.0784810i	$-0.974993\pi$
$521$	−9.82615	+	17.0194i	−0.430491	+	0.745633i	0.566424	+	0.824114i	$0.308326\pi$
$522$		0			0
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	0.866032	+	0.499988i	$0.166662\pi$
$523$	19.8051	+	34.3035i	0.866018	+	1.49999i	−1.41543e−5		1.00000i	$0.500005\pi$
$524$	−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	0.0236708	−	0.999720i	$-0.492465\pi$
$547$	16.0070	−	5.82608i	0.684411	−	0.249105i	0.660740	+	0.750615i	$0.270242\pi$
$548$	−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	0.962806	+	0.270194i	$0.0870880\pi$
$557$	16.8840	+	29.2439i	0.715398	+	1.23911i	−0.247408	+	0.968911i	$0.579579\pi$
$558$		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	0.750029	−	0.661405i	$-0.230039\pi$
$563$	21.3416	+	7.76771i	0.899442	+	0.327370i	0.149413	+	0.988775i	$0.452262\pi$
$564$		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	−0.919327	−	0.393495i	$-0.871266\pi$
$569$	1.88781	−	10.7063i	0.0791410	−	0.448831i	0.998468	−	0.0553359i	$-0.0176230\pi$
$570$		0			0
$571$	−13.9861	−	5.09053i	−0.585300	−	0.213032i	0.0323607	−	0.999476i	$-0.489697\pi$
$571$	−13.9861	−	5.09053i	−0.585300	−	0.213032i	−0.617661	+	0.786444i	$0.711920\pi$
$572$	−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	0.936141	+	0.351624i	$0.114371\pi$
$577$	18.5582	+	32.1437i	0.772586	+	1.33816i	−0.163555	+	0.986534i	$0.552296\pi$
$578$	−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	−0.610000	−	0.792401i	$-0.708831\pi$
$587$	−13.7601	+	5.00828i	−0.567941	+	0.206714i	0.0420588	+	0.999115i	$0.486608\pi$
$588$		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	−0.962094	−	0.272720i	$-0.912077\pi$
$599$	−21.0623	+	17.6734i	−0.860583	+	0.722115i	0.101511	+	0.994834i	$0.467632\pi$
$600$		0			0
$601$	−42.4525	+	15.4514i	−1.73167	+	0.630277i	−0.998748	−	0.0500315i	$-0.984068\pi$
$601$	−42.4525	+	15.4514i	−1.73167	+	0.630277i	−0.732925	+	0.680309i	$0.761846\pi$
$602$	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	0.983722	+	0.179697i	$0.0575116\pi$
$607$	2.97584	+	16.8768i	0.120786	+	0.685009i	−0.862937	+	0.505312i	$0.831377\pi$
$608$	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	−0.861253	−	0.508176i	$-0.830320\pi$
$613$	0.234380	−	0.405959i	0.00946653	−	0.0163965i	0.870720	+	0.491779i	$0.163653\pi$
$614$	−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	0.301323	−	0.953522i	$-0.402572\pi$
$617$	−2.00610	−	0.730161i	−0.0807626	−	0.0293952i	−0.382086	+	0.924127i	$0.624794\pi$
$618$		0			0
$619$	1.48254	−	8.40790i	0.0595883	−	0.337942i	−0.940410	−	0.340044i	$-0.889558\pi$
$619$	1.48254	−	8.40790i	0.0595883	−	0.337942i	0.999998	+	0.00210213i	$0.000669129\pi$
$620$	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	0.959645	−	0.281214i	$-0.0907370\pi$
$631$	5.93539	+	10.2804i	0.236284	+	0.409256i	−0.723361	+	0.690470i	$0.757404\pi$
$632$	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	−0.241715	−	0.970347i	$-0.577710\pi$
$641$	4.98381	−	1.81396i	0.196849	−	0.0716470i	0.438563	+	0.898700i	$0.355488\pi$
$642$		0			0
$643$	−0.631120	+	0.529573i	−0.0248889	+	0.0208843i	−0.655147	−	0.755501i	$-0.727393\pi$
$643$	−0.631120	+	0.529573i	−0.0248889	+	0.0208843i	0.630258	+	0.776386i	$0.282949\pi$
$644$	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	−0.658675	−	0.752427i	$-0.728883\pi$
$653$	−0.819175	+	0.687369i	−0.0320568	+	0.0268988i	0.626618	+	0.779326i	$0.284438\pi$
$654$		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	0.960965	−	0.276671i	$-0.0892312\pi$
$659$	21.9581	+	18.4250i	0.855367	+	0.717738i	−0.105598	+	0.994409i	$0.533676\pi$
$660$		0			0
$661$	−0.780673	−	4.42742i	−0.0303647	−	0.172207i	0.965854	−	0.259086i	$-0.0834215\pi$
$661$	−0.780673	−	4.42742i	−0.0303647	−	0.172207i	−0.996219	+	0.0868799i	$0.972310\pi$
$662$	−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	−0.862793	−	0.505557i	$-0.831287\pi$
$673$	3.13584	−	17.7842i	0.120878	−	0.685532i	0.983671	−	0.179975i	$-0.0576017\pi$
$674$	−55.7643			−2.14796
$675$		0			0
$676$	−17.6151			−0.677505
$677$	−2.73308	+	15.5001i	−0.105041	+	0.595716i	0.886163	+	0.463373i	$0.153361\pi$
$677$	−2.73308	+	15.5001i	−0.105041	+	0.595716i	−0.991204	+	0.132343i	$0.957750\pi$
$678$		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	−0.891230	−	0.453552i	$-0.850156\pi$
$683$	−1.38059	+	2.39125i	−0.0528268	+	0.0914987i	0.838403	+	0.545051i	$0.183490\pi$
$684$		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	−0.0183109	−	0.999832i	$-0.505829\pi$
$691$	−26.4481	−	22.1926i	−1.00613	−	0.844246i	−0.987822	+	0.155586i	$0.950273\pi$
$692$	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	−0.780988	−	0.624546i	$-0.785284\pi$
$709$	−26.0362	+	9.47639i	−0.977809	+	0.355893i	−0.196821	+	0.980439i	$0.563062\pi$
$710$	−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	0.989887	+	0.141859i	$0.0453081\pi$
$719$	16.5657	+	28.6927i	0.617797	+	1.07006i	−0.372090	+	0.928197i	$0.621359\pi$
$720$		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	−0.985073	−	0.172139i	$-0.944932\pi$
$727$	−0.0143443	+	0.0813505i	−0.000532000	+	0.00301712i	0.984541	+	0.175157i	$0.0560432\pi$
$728$	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	0.830187	−	0.557485i	$-0.188234\pi$
$733$	29.9926	+	10.9164i	1.10780	+	0.403207i	0.277616	+	0.960692i	$0.410456\pi$
$734$	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	0.981052	+	0.193745i	$0.0620634\pi$
$739$	17.8960	+	30.9967i	0.658314	+	1.14023i	−0.322738	+	0.946488i	$0.604603\pi$
$740$	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	−0.980708	−	0.195480i	$-0.937374\pi$
$743$	−3.43457	−	19.4784i	−0.126002	−	0.714593i	0.854706	−	0.519113i	$-0.173738\pi$
$744$		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	−0.106018	−	0.994364i	$-0.533810\pi$
$751$	23.4261	−	19.6568i	0.854829	−	0.717287i	0.960848	+	0.277077i	$0.0893658\pi$
$752$	−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	−0.309963	+	0.950749i	$0.600317\pi$
$761$	−35.8646	+	30.0940i	−1.30009	+	1.09091i	−0.990129	+	0.140159i	$0.955239\pi$
$762$		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	0.995844	+	0.0910785i	$0.0290314\pi$
$769$	2.52926	+	14.3441i	0.0912074	+	0.517263i	−0.904636	+	0.426184i	$0.859857\pi$
$770$	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	0.559568	−	0.828784i	$-0.310967\pi$
$773$	−12.1767	−	21.0906i	−0.437964	−	0.758576i	−0.997532	+	0.0702080i	$0.977634\pi$
$774$		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
$781$	0.944306	−	5.35543i	0.0337899	−	0.191632i
$782$	−33.4879			−1.19753
$783$		0			0
$784$	−92.0601			−3.28786
$785$	4.50806	−	25.5665i	0.160899	−	0.912506i
$786$		0			0
$787$	25.9047	+	9.42853i	0.923402	+	0.336091i	0.759591	−	0.650401i	$-0.225399\pi$
$787$	25.9047	+	9.42853i	0.923402	+	0.336091i	0.163811	+	0.986492i	$0.447621\pi$
$788$	12.1963	−	10.2339i	0.434475	−	0.364568i
$789$		0			0
$790$	22.5784	−	8.21787i	0.803304	−	0.292379i
$791$	0.486562	−	0.842750i	0.0173001	−	0.0299647i
$792$		0			0
$793$	−10.6451	−	18.4378i	−0.378017	−	0.654744i
$794$	−56.1340	−	47.1020i	−1.99212	−	1.67159i
$795$		0			0
$796$	13.7473	+	77.9650i	0.487261	+	2.76340i
$797$	−1.14902	−	6.51639i	−0.0407002	−	0.230822i	0.957672	−	0.287863i	$-0.0929447\pi$
$797$	−1.14902	−	6.51639i	−0.0407002	−	0.230822i	−0.998372	+	0.0570404i	$0.981834\pi$
$798$		0			0
$799$	13.9464	+	11.7024i	0.493387	+	0.414000i
$800$	20.8735	+	36.1539i	0.737989	+	1.27823i
$801$		0			0
$802$	−39.7110	+	68.7815i	−1.40224	+	2.42876i
$803$	17.9035	−	6.51633i	0.631800	−	0.229956i
$804$		0			0
$805$	2.97948	−	2.50008i	0.105013	−	0.0881162i
$806$	36.5089	+	13.2881i	1.28597	+	0.468055i
$807$		0			0
$808$	5.81179	−	32.9603i	0.204458	−	1.15954i
$809$	−8.61362			−0.302839			−0.151419	−	0.988470i	$-0.548384\pi$
$809$	−8.61362			−0.302839			−0.151419	+	0.988470i	$0.548384\pi$
$810$		0			0
$811$	−9.58716			−0.336651			−0.168325	−	0.985732i	$-0.553836\pi$
$811$	−9.58716			−0.336651			−0.168325	+	0.985732i	$0.553836\pi$
$812$	−1.20874	+	6.85512i	−0.0424186	+	0.240568i
$813$		0			0
$814$	−23.6846	−	8.62049i	−0.830145	−	0.302148i
$815$	−10.8862	+	9.13459i	−0.381326	+	0.319971i
$816$		0			0
$817$	49.0471	−	17.8517i	1.71594	−	0.624552i
$818$	27.2994	−	47.2840i	0.954502	−	1.65325i
$819$		0			0
$820$	−51.3472	−	88.9359i	−1.79312	−	3.10578i
$821$	−10.6200	−	8.91127i	−0.370642	−	0.311005i	0.438374	−	0.898793i	$-0.355555\pi$
$821$	−10.6200	−	8.91127i	−0.370642	−	0.311005i	−0.809015	+	0.587787i	$0.799999\pi$
$822$		0			0
$823$	8.30485	+	47.0992i	0.289489	+	1.64177i	0.688795	+	0.724956i	$0.258140\pi$
$823$	8.30485	+	47.0992i	0.289489	+	1.64177i	−0.399307	+	0.916817i	$0.630749\pi$
$824$	11.9688	+	67.8782i	0.416951	+	2.36465i
$825$		0			0
$826$	−2.27310	−	1.90736i	−0.0790914	−	0.0663655i
$827$	21.2209	+	36.7556i	0.737921	+	1.27812i	0.953430	+	0.301615i	$0.0975258\pi$
$827$	21.2209	+	36.7556i	0.737921	+	1.27812i	−0.215508	+	0.976502i	$0.569141\pi$
$828$		0			0
$829$	−13.0018	+	22.5199i	−0.451573	+	0.782147i	−0.998484	−	0.0550437i	$-0.982470\pi$
$829$	−13.0018	+	22.5199i	−0.451573	+	0.782147i	0.546911	+	0.837191i	$0.315804\pi$
$830$	−11.5976	+	4.22118i	−0.402558	+	0.146519i
$831$		0			0
$832$	57.1713	−	47.9724i	1.98206	−	1.66315i
$833$	16.9003	+	6.15122i	0.585562	+	0.213127i
$834$		0			0
$835$	−6.72057	+	38.1143i	−0.232575	+	1.31900i
$836$	−59.1096			−2.04435
$837$		0			0
$838$	65.9233			2.27728
$839$	0.218150	−	1.23719i	0.00753138	−	0.0427126i	−0.980810	−	0.194964i	$-0.937541\pi$
$839$	0.218150	−	1.23719i	0.00753138	−	0.0427126i	0.988342	+	0.152251i	$0.0486522\pi$
$840$		0			0
$841$	20.8249	+	7.57965i	0.718100	+	0.261367i
$842$	−54.2389	+	45.5118i	−1.86920	+	1.56844i
$843$		0			0
$844$	−69.3490	+	25.2410i	−2.38709	+	0.868830i
$845$	−2.77009	+	4.79794i	−0.0952941	+	0.165054i
$846$		0			0
$847$	1.83275	+	3.17442i	0.0629742	+	0.109074i
$848$	−56.7697	−	47.6354i	−1.94948	−	1.63581i
$849$		0			0
$850$	−2.75760	−	15.6391i	−0.0945850	−	0.536418i
$851$	3.91972	+	22.2298i	0.134366	+	0.762029i
$852$		0			0
$853$	1.11409	+	0.934836i	0.0381459	+	0.0320082i	0.661661	−	0.749803i	$-0.269852\pi$
$853$	1.11409	+	0.934836i	0.0381459	+	0.0320082i	−0.623515	+	0.781811i	$0.714296\pi$
$854$	−4.63136	−	8.02175i	−0.158482	−	0.274499i
$855$		0			0
$856$	48.3044	−	83.6657i	1.65101	−	2.85964i
$857$	49.1550	−	17.8910i	1.67910	−	0.611144i	0.685917	−	0.727680i	$-0.259401\pi$
$857$	49.1550	−	17.8910i	1.67910	−	0.611144i	0.993187	+	0.116536i	$0.0371789\pi$
$858$		0			0
$859$	−16.0903	+	13.5013i	−0.548992	+	0.460659i	−0.874600	−	0.484846i	$-0.838876\pi$
$859$	−16.0903	+	13.5013i	−0.548992	+	0.460659i	0.325607	+	0.945505i	$0.394431\pi$
$860$	−75.2439	−	27.3865i	−2.56579	−	0.933873i
$861$		0			0
$862$	14.9931	−	85.0300i	0.510666	−	2.89613i
$863$	12.9813			0.441890			0.220945	−	0.975286i	$-0.429086\pi$
$863$	12.9813			0.441890			0.220945	+	0.975286i	$0.429086\pi$
$864$		0			0
$865$	4.31221			0.146619
$866$	0.00578142	−	0.0327881i	0.000196461	−	0.00111418i
$867$		0			0
$868$	11.5425	+	4.20113i	0.391779	+	0.142596i
$869$	−7.80247	+	6.54705i	−0.264681	+	0.222094i
$870$		0			0
$871$	−36.5112	+	13.2890i	−1.23713	+	0.450280i
$872$	−54.8735	+	95.0438i	−1.85825	+	3.21859i
$873$		0			0
$874$	36.4243	+	63.0887i	1.23207	+	2.13401i
$875$	4.61950	+	3.87622i	0.156167	+	0.131040i
$876$		0			0
$877$	5.39102	+	30.5740i	0.182042	+	1.03241i	0.929697	+	0.368324i	$0.120068\pi$
$877$	5.39102	+	30.5740i	0.182042	+	1.03241i	−0.747655	+	0.664087i	$0.768821\pi$
$878$	2.49182	+	14.1318i	0.0840950	+	0.476926i
$879$		0			0
$880$	33.5105	+	28.1186i	1.12964	+	0.947879i
$881$	−9.64783	−	16.7105i	−0.325044	−	0.562992i	0.656478	−	0.754346i	$-0.272046\pi$
$881$	−9.64783	−	16.7105i	−0.325044	−	0.562992i	−0.981521	+	0.191353i	$0.938712\pi$
$882$		0			0
$883$	4.91194	−	8.50773i	0.165300	−	0.286308i	−0.771462	−	0.636276i	$-0.780474\pi$
$883$	4.91194	−	8.50773i	0.165300	−	0.286308i	0.936762	+	0.349968i	$0.113807\pi$
$884$	−41.4407	+	15.0832i	−1.39380	+	0.507302i
$885$		0			0
$886$	84.3309	−	70.7621i	2.83315	−	2.37730i
$887$	−41.4529	−	15.0876i	−1.39185	−	0.506593i	−0.466104	−	0.884730i	$-0.654343\pi$
$887$	−41.4529	−	15.0876i	−1.39185	−	0.506593i	−0.925750	+	0.378137i	$0.876565\pi$
$888$		0			0
$889$	0.203785	−	1.15572i	0.00683474	−	0.0387617i
$890$	−50.7533			−1.70125
$891$		0			0
$892$	−36.2219			−1.21280
$893$	6.87716	−	39.0023i	0.230135	−	1.30516i
$894$		0			0
$895$	−13.9805	−	5.08849i	−0.467317	−	0.170089i
$896$	10.3407	−	8.67690i	0.345460	−	0.289875i
$897$		0			0
$898$	−39.2169	+	14.2738i	−1.30869	+	0.476323i
$899$	−6.03376	+	10.4508i	−0.201237	+	0.348553i
$900$		0			0
$901$	7.23887	+	12.5381i	0.241162	+	0.417704i
$902$	45.8912	+	38.5073i	1.52801	+	1.28215i
$903$		0			0
$904$	−3.02920	−	17.1794i	−0.100750	−	0.571379i
$905$	−2.29765	−	13.0306i	−0.0763764	−	0.433152i
$906$		0			0
$907$	−32.4898	−	27.2622i	−1.07881	−	0.905225i	−0.0829841	−	0.996551i	$-0.526445\pi$
$907$	−32.4898	−	27.2622i	−1.07881	−	0.905225i	−0.995821	+	0.0913259i	$0.970890\pi$
$908$	25.8979	+	44.8564i	0.859451	+	1.48861i
$909$		0			0
$910$	3.52426	−	6.10419i	0.116828	−	0.202352i
$911$	−34.4965	+	12.5557i	−1.14292	+	0.415988i	−0.842967	−	0.537966i	$-0.819193\pi$
$911$	−34.4965	+	12.5557i	−1.14292	+	0.415988i	−0.299952	+	0.953954i	$0.596971\pi$
$912$		0			0
$913$	4.00781	−	3.36295i	0.132639	−	0.111297i
$914$	−6.07203	−	2.21004i	−0.200845	−	0.0731015i
$915$		0			0
$916$	−12.9683	+	73.5471i	−0.428486	+	2.43007i
$917$	−8.56130			−0.282719
$918$		0			0
$919$	−14.0589			−0.463761			−0.231881	−	0.972744i	$-0.574488\pi$
$919$	−14.0589			−0.463761			−0.231881	+	0.972744i	$0.574488\pi$
$920$	12.1073	−	68.6637i	0.399164	−	2.26377i
$921$		0			0
$922$	−82.5717	−	30.0536i	−2.71935	−	0.989764i
$923$	−6.76102	+	5.67317i	−0.222542	+	0.186735i
$924$		0			0
$925$	−10.0587	+	3.66108i	−0.330729	+	0.120376i
$926$	−45.8218	+	79.3657i	−1.50580	+	2.60812i
$927$		0			0
$928$	24.7764	+	42.9140i	0.813325	+	1.40872i
$929$	−14.1852	−	11.9028i	−0.465402	−	0.390519i	0.379712	−	0.925105i	$-0.376023\pi$
$929$	−14.1852	−	11.9028i	−0.465402	−	0.390519i	−0.845114	+	0.534586i	$0.820468\pi$
$930$		0			0
$931$	−6.79379	−	38.5295i	−0.222657	−	1.26275i
$932$	4.91531	+	27.8761i	0.161006	+	0.913113i
$933$		0			0
$934$	−28.6019	−	23.9998i	−0.935882	−	0.785298i
$935$	−4.27302	−	7.40108i	−0.139743	−	0.242041i
$936$		0			0
$937$	−2.23409	+	3.86955i	−0.0729845	+	0.126413i	−0.900208	−	0.435460i	$-0.856586\pi$
$937$	−2.23409	+	3.86955i	−0.0729845	+	0.126413i	0.827224	+	0.561873i	$0.189919\pi$
$938$	−15.8850	+	5.78166i	−0.518663	+	0.188778i
$939$		0			0
$940$	−46.5426	+	39.0539i	−1.51805	+	1.27380i
$941$	1.88301	+	0.685360i	0.0613844	+	0.0223421i	0.372530	−	0.928020i	$-0.378490\pi$
$941$	1.88301	+	0.685360i	0.0613844	+	0.0223421i	−0.311145	+	0.950362i	$0.600713\pi$
$942$		0			0
$943$	9.31644	−	52.8362i	0.303385	−	1.72058i
$944$	−29.8889			−0.972801
$945$		0			0
$946$	46.7105			1.51869
$947$	−2.18516	+	12.3926i	−0.0710081	+	0.402707i	0.928500	+	0.371333i	$0.121099\pi$
$947$	−2.18516	+	12.3926i	−0.0710081	+	0.402707i	−0.999508	+	0.0313735i	$0.990012\pi$
$948$		0			0
$949$	−29.0571	−	10.5759i	−0.943235	−	0.343309i
$950$	−26.4635	+	22.2055i	−0.858590	+	0.720443i
$951$		0			0
$952$	−11.2483	+	4.09403i	−0.364558	+	0.132688i
$953$	9.98205	−	17.2894i	0.323350	−	0.560059i	−0.657827	−	0.753169i	$-0.728524\pi$
$953$	9.98205	−	17.2894i	0.323350	−	0.560059i	0.981177	+	0.193110i	$0.0618575\pi$
$954$		0			0
$955$	−13.2932	−	23.0246i	−0.430159	−	0.745058i
$956$	72.3976	+	60.7488i	2.34151	+	1.96476i
$957$		0			0
$958$	2.76723	+	15.6938i	0.0894052	+	0.507042i
$959$	1.21064	+	6.86590i	0.0390937	+	0.221711i
$960$		0			0
$961$	−7.43480	−	6.23853i	−0.239832	−	0.201243i
$962$	20.4534	+	35.4263i	0.659444	+	1.14219i
$963$		0			0
$964$	5.33544	−	9.24125i	0.171843	−	0.297640i
$965$	−7.20511	+	2.62244i	−0.231941	+	0.0844195i
$966$		0			0
$967$	−24.6732	+	20.7033i	−0.793437	+	0.665773i	−0.946594	−	0.322429i	$-0.895501\pi$
$967$	−24.6732	+	20.7033i	−0.793437	+	0.665773i	0.153157	+	0.988202i	$0.451056\pi$
$968$	61.7460	+	22.4737i	1.98459	+	0.722333i
$969$		0			0
$970$	5.41189	−	30.6924i	0.173765	−	0.985473i
$971$	−6.62934			−0.212746			−0.106373	−	0.994326i	$-0.533924\pi$
$971$	−6.62934			−0.212746			−0.106373	+	0.994326i	$0.533924\pi$
$972$		0			0
$973$	3.96300			0.127048
$974$	13.6362	−	77.3348i	0.436932	−	2.47797i
$975$		0			0
$976$	−87.6737	−	31.9106i	−2.80637	−	1.02143i
$977$	9.08272	−	7.62130i	0.290582	−	0.243827i	−0.485830	−	0.874054i	$-0.661482\pi$
$977$	9.08272	−	7.62130i	0.290582	−	0.243827i	0.776411	+	0.630226i	$0.217038\pi$
$978$		0			0
$979$	20.2172	−	7.35845i	0.646144	−	0.235177i
$980$	−30.0102	+	51.9792i	−0.958642	+	1.66042i
$981$		0			0
$982$	−5.92884	−	10.2690i	−0.189197	−	0.327698i
$983$	−39.8841	−	33.4667i	−1.27211	−	1.06742i	−0.994281	−	0.106791i	$-0.965942\pi$
$983$	−39.8841	−	33.4667i	−1.27211	−	1.06742i	−0.277824	−	0.960632i	$-0.589613\pi$
$984$		0			0
$985$	−0.869526	−	4.93133i	−0.0277054	−	0.157125i
$986$	−3.27322	−	18.5633i	−0.104241	−	0.591177i
$987$		0			0
$988$	73.4899	+	61.6654i	2.33803	+	1.96184i
$989$	−20.9165	−	36.2284i	−0.665105	−	1.15200i
$990$		0			0
$991$	−0.735575	+	1.27405i	−0.0233663	+	0.0404716i	−0.877472	−	0.479628i	$-0.840772\pi$
$991$	−0.735575	+	1.27405i	−0.0233663	+	0.0404716i	0.854106	+	0.520099i	$0.174105\pi$
$992$	82.1684	−	29.9069i	2.60885	−	0.949544i
$993$		0			0
$994$	−2.94153	+	2.46823i	−0.0932996	+	0.0782876i
$995$	23.3977	+	8.51606i	0.741756	+	0.269977i
$996$		0			0
$997$	−4.58801	+	26.0199i	−0.145304	+	0.824058i	0.821819	+	0.569748i	$0.192959\pi$
$997$	−4.58801	+	26.0199i	−0.145304	+	0.824058i	−0.967123	+	0.254310i	$0.918152\pi$
$998$	95.6065			3.02637
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.1	✓	6	27.11	odd	18
729.2.a.e.1.6	yes	6	27.16	even	9
729.2.c.a.244.1		12	27.7	even	9
729.2.c.a.487.1		12	27.25	even	9
729.2.c.d.244.6		12	27.20	odd	18
729.2.c.d.487.6		12	27.2	odd	18
729.2.e.j.325.1		12	27.23	odd	18
729.2.e.j.406.1		12	9.5	odd	6
729.2.e.k.163.1		12	9.7	even	3
729.2.e.k.568.1		12	27.22	even	9
729.2.e.l.82.2		12	27.13	even	9	inner
729.2.e.l.649.2		12	1.1	even	1	trivial
729.2.e.s.82.1		12	27.14	odd	18
729.2.e.s.649.1		12	3.2	odd	2
729.2.e.t.163.2		12	9.2	odd	6
729.2.e.t.568.2		12	27.5	odd	18
729.2.e.u.325.2		12	27.4	even	9
729.2.e.u.406.2		12	9.4	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

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