LMFDB - Embedded newform 338.2.c.i.315.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,2,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.69894358832$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.2.c.i.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.34601 - 2.33136i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.49396 q^{5} +(1.34601 - 2.33136i) q^{6} +(0.801938 - 1.38900i) q^{7} -1.00000 q^{8} +(-2.12349 + 3.67799i) q^{9} +(1.24698 + 2.15983i) q^{10} +(-1.02446 - 1.77441i) q^{11} +2.69202 q^{12} +1.60388 q^{14} +(-3.35690 - 5.81431i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.27144 - 3.93425i) q^{17} -4.24698 q^{18} +(2.42543 - 4.20096i) q^{19} +(-1.24698 + 2.15983i) q^{20} -4.31767 q^{21} +(1.02446 - 1.77441i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(1.34601 + 2.33136i) q^{24} +1.21983 q^{25} +3.35690 q^{27} +(0.801938 + 1.38900i) q^{28} +(4.60388 + 7.97415i) q^{29} +(3.35690 - 5.81431i) q^{30} +5.10992 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.75786 + 4.77676i) q^{33} +4.54288 q^{34} +(2.00000 - 3.46410i) q^{35} +(-2.12349 - 3.67799i) q^{36} +(-3.80194 - 6.58515i) q^{37} +4.85086 q^{38} -2.49396 q^{40} +(1.73341 + 3.00235i) q^{41} +(-2.15883 - 3.73921i) q^{42} +(-5.67241 + 9.82490i) q^{43} +2.04892 q^{44} +(-5.29590 + 9.17276i) q^{45} +(1.35690 - 2.35021i) q^{46} +0.219833 q^{47} +(-1.34601 + 2.33136i) q^{48} +(2.21379 + 3.83440i) q^{49} +(0.609916 + 1.05641i) q^{50} -12.2295 q^{51} -2.71379 q^{53} +(1.67845 + 2.90716i) q^{54} +(-2.55496 - 4.42532i) q^{55} +(-0.801938 + 1.38900i) q^{56} -13.0586 q^{57} +(-4.60388 + 7.97415i) q^{58} +(2.03803 - 3.52998i) q^{59} +6.71379 q^{60} +(-5.20775 + 9.02009i) q^{61} +(2.55496 + 4.42532i) q^{62} +(3.40581 + 5.89904i) q^{63} +1.00000 q^{64} -5.51573 q^{66} +(6.03803 + 10.4582i) q^{67} +(2.27144 + 3.93425i) q^{68} +(-3.65279 + 6.32682i) q^{69} +4.00000 q^{70} +(-0.643104 + 1.11389i) q^{71} +(2.12349 - 3.67799i) q^{72} +3.62565 q^{73} +(3.80194 - 6.58515i) q^{74} +(-1.64191 - 2.84387i) q^{75} +(2.42543 + 4.20096i) q^{76} -3.28621 q^{77} -5.32975 q^{79} +(-1.24698 - 2.15983i) q^{80} +(1.85205 + 3.20785i) q^{81} +(-1.73341 + 3.00235i) q^{82} +4.85086 q^{83} +(2.15883 - 3.73921i) q^{84} +(5.66487 - 9.81185i) q^{85} -11.3448 q^{86} +(12.3937 - 21.4666i) q^{87} +(1.02446 + 1.77441i) q^{88} +(8.28501 + 14.3501i) q^{89} -10.5918 q^{90} +2.71379 q^{92} +(-6.87800 - 11.9130i) q^{93} +(0.109916 + 0.190381i) q^{94} +(6.04892 - 10.4770i) q^{95} -2.69202 q^{96} +(-2.32036 + 4.01897i) q^{97} +(-2.21379 + 3.83440i) q^{98} +8.70171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} - 8 q^{9} - 2 q^{10} + 3 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} - 3 q^{16} - 5 q^{17} - 16 q^{18} + q^{19} + 2 q^{20} + 8 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 - 8 * q^9 - 2 * q^10 + 3 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 - 3 * q^16 - 5 * q^17 - 16 * q^18 + q^19 + 2 * q^20 + 8 * q^21 - 3 * q^22 + 3 * q^24 + 10 * q^25 + 12 * q^27 - 4 * q^28 + 10 * q^29 + 12 * q^30 + 32 * q^31 + 3 * q^32 - 4 * q^33 - 10 * q^34 + 12 * q^35 - 8 * q^36 - 14 * q^37 + 2 * q^38 + 4 * q^40 + 7 * q^41 + 4 * q^42 - 11 * q^43 - 6 * q^44 - 4 * q^45 + 4 * q^47 - 3 * q^48 - 3 * q^49 + 5 * q^50 - 32 * q^51 + 6 * q^54 - 16 * q^55 + 4 * q^56 - 16 * q^57 - 10 * q^58 - 3 * q^59 + 24 * q^60 + 4 * q^61 + 16 * q^62 - 6 * q^63 + 6 * q^64 - 8 * q^66 + 21 * q^67 - 5 * q^68 + 14 * q^69 + 24 * q^70 - 12 * q^71 + 8 * q^72 - 2 * q^73 + 14 * q^74 + 23 * q^75 + q^76 - 36 * q^77 - 36 * q^79 + 2 * q^80 + 25 * q^81 - 7 * q^82 + 2 * q^83 - 4 * q^84 + 36 * q^85 - 22 * q^86 + 10 * q^87 - 3 * q^88 + 25 * q^89 - 8 * q^90 - 2 * q^93 + 2 * q^94 + 18 * q^95 - 6 * q^96 + 23 * q^97 + 3 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.34601	−	2.33136i	−0.777120	−	1.34601i	−0.933595	−	0.358329i	$-0.883347\pi$
$3$	−1.34601	−	2.33136i	−0.777120	−	1.34601i	0.156476	−	0.987682i	$-0.449987\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.49396			1.11533			0.557666	−	0.830065i	$-0.311697\pi$
$5$	2.49396			1.11533			0.557666	+	0.830065i	$0.311697\pi$
$6$	1.34601	−	2.33136i	0.549507	−	0.951773i
$7$	0.801938	−	1.38900i	0.303104	−	0.524991i	−0.673733	−	0.738974i	$-0.735310\pi$
$7$	0.801938	−	1.38900i	0.303104	−	0.524991i	0.976837	+	0.213983i	$0.0686437\pi$
$8$	−1.00000			−0.353553
$9$	−2.12349	+	3.67799i	−0.707830	+	1.22600i
$10$	1.24698	+	2.15983i	0.394330	+	0.682999i
$11$	−1.02446	−	1.77441i	−0.308886	−	0.535006i	0.669233	−	0.743053i	$-0.266623\pi$
$11$	−1.02446	−	1.77441i	−0.308886	−	0.535006i	−0.978119	+	0.208047i	$0.933289\pi$
$12$	2.69202			0.777120
$13$		0			0
$13$		0			0
$14$	1.60388			0.428654
$15$	−3.35690	−	5.81431i	−0.866747	−	1.50125i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.27144	−	3.93425i	0.550905	−	0.954195i	−0.447305	−	0.894382i	$-0.647616\pi$
$17$	2.27144	−	3.93425i	0.550905	−	0.954195i	0.998210	−	0.0598134i	$-0.0190506\pi$
$18$	−4.24698			−1.00102
$19$	2.42543	−	4.20096i	0.556431	−	0.963767i	−0.441359	−	0.897330i	$-0.645504\pi$
$19$	2.42543	−	4.20096i	0.556431	−	0.963767i	0.997791	−	0.0664368i	$-0.0211631\pi$
$20$	−1.24698	+	2.15983i	−0.278833	+	0.482953i
$21$	−4.31767			−0.942192
$22$	1.02446	−	1.77441i	0.218415	−	0.378306i
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	0.689173	−	0.724597i	$-0.257974\pi$
$23$	−1.35690	−	2.35021i	−0.282932	−	0.490053i	−0.972106	+	0.234543i	$0.924641\pi$
$24$	1.34601	+	2.33136i	0.274753	+	0.475887i
$25$	1.21983			0.243967
$26$		0			0
$27$	3.35690			0.646035
$28$	0.801938	+	1.38900i	0.151552	+	0.262496i
$29$	4.60388	+	7.97415i	0.854918	+	1.48076i	0.876721	+	0.480999i	$0.159726\pi$
$29$	4.60388	+	7.97415i	0.854918	+	1.48076i	−0.0218027	+	0.999762i	$0.506941\pi$
$30$	3.35690	−	5.81431i	0.612883	−	1.06154i
$31$	5.10992			0.917768			0.458884	−	0.888496i	$-0.348249\pi$
$31$	5.10992			0.917768			0.458884	+	0.888496i	$0.348249\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.75786	+	4.77676i	−0.480083	+	0.831528i
$34$	4.54288			0.779097
$35$	2.00000	−	3.46410i	0.338062	−	0.585540i
$36$	−2.12349	−	3.67799i	−0.353915	−	0.612999i
$37$	−3.80194	−	6.58515i	−0.625035	−	1.08259i	−0.988534	−	0.150997i	$-0.951751\pi$
$37$	−3.80194	−	6.58515i	−0.625035	−	1.08259i	0.363499	−	0.931594i	$-0.381582\pi$
$38$	4.85086			0.786913
$39$		0			0
$40$	−2.49396			−0.394330
$41$	1.73341	+	3.00235i	0.270713	+	0.468888i	0.969044	−	0.246886i	$-0.0794074\pi$
$41$	1.73341	+	3.00235i	0.270713	+	0.468888i	−0.698332	+	0.715774i	$0.746074\pi$
$42$	−2.15883	−	3.73921i	−0.333115	−	0.576973i
$43$	−5.67241	+	9.82490i	−0.865034	+	1.49828i	0.00197946	+	0.999998i	$0.499370\pi$
$43$	−5.67241	+	9.82490i	−0.865034	+	1.49828i	−0.867013	+	0.498285i	$0.833963\pi$
$44$	2.04892			0.308886
$45$	−5.29590	+	9.17276i	−0.789466	+	1.36739i
$46$	1.35690	−	2.35021i	0.200063	−	0.346520i
$47$	0.219833			0.0320659			0.0160329	−	0.999871i	$-0.494896\pi$
$47$	0.219833			0.0320659			0.0160329	+	0.999871i	$0.494896\pi$
$48$	−1.34601	+	2.33136i	−0.194280	+	0.336503i
$49$	2.21379	+	3.83440i	0.316256	+	0.547771i
$50$	0.609916	+	1.05641i	0.0862552	+	0.149398i
$51$	−12.2295			−1.71248
$52$		0			0
$53$	−2.71379			−0.372768			−0.186384	−	0.982477i	$-0.559677\pi$
$53$	−2.71379			−0.372768			−0.186384	+	0.982477i	$0.559677\pi$
$54$	1.67845	+	2.90716i	0.228408	+	0.395614i
$55$	−2.55496	−	4.42532i	−0.344510	−	0.596710i
$56$	−0.801938	+	1.38900i	−0.107163	+	0.185613i
$57$	−13.0586			−1.72965
$58$	−4.60388	+	7.97415i	−0.604518	+	1.04706i
$59$	2.03803	−	3.52998i	0.265329	−	0.459564i	−0.702321	−	0.711861i	$-0.747853\pi$
$59$	2.03803	−	3.52998i	0.265329	−	0.459564i	0.967650	+	0.252297i	$0.0811860\pi$
$60$	6.71379			0.866747
$61$	−5.20775	+	9.02009i	−0.666784	+	1.15490i	0.312014	+	0.950077i	$0.398996\pi$
$61$	−5.20775	+	9.02009i	−0.666784	+	1.15490i	−0.978798	+	0.204827i	$0.934337\pi$
$62$	2.55496	+	4.42532i	0.324480	+	0.562016i
$63$	3.40581	+	5.89904i	0.429092	+	0.743209i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.51573			−0.678939
$67$	6.03803	+	10.4582i	0.737663	+	1.27767i	0.953545	+	0.301250i	$0.0974040\pi$
$67$	6.03803	+	10.4582i	0.737663	+	1.27767i	−0.215882	+	0.976419i	$0.569263\pi$
$68$	2.27144	+	3.93425i	0.275452	+	0.477097i
$69$	−3.65279	+	6.32682i	−0.439745	+	0.761660i
$70$	4.00000			0.478091
$71$	−0.643104	+	1.11389i	−0.0763224	+	0.132194i	−0.901661	−	0.432444i	$-0.857651\pi$
$71$	−0.643104	+	1.11389i	−0.0763224	+	0.132194i	0.825338	+	0.564639i	$0.190984\pi$
$72$	2.12349	−	3.67799i	0.250256	−	0.433456i
$73$	3.62565			0.424350			0.212175	−	0.977232i	$-0.431945\pi$
$73$	3.62565			0.424350			0.212175	+	0.977232i	$0.431945\pi$
$74$	3.80194	−	6.58515i	0.441966	−	0.765508i
$75$	−1.64191	−	2.84387i	−0.189591	−	0.328382i
$76$	2.42543	+	4.20096i	0.278216	+	0.481884i
$77$	−3.28621			−0.374498
$78$		0			0
$79$	−5.32975			−0.599644			−0.299822	−	0.953995i	$-0.596927\pi$
$79$	−5.32975			−0.599644			−0.299822	+	0.953995i	$0.596927\pi$
$80$	−1.24698	−	2.15983i	−0.139417	−	0.241477i
$81$	1.85205	+	3.20785i	0.205784	+	0.356427i
$82$	−1.73341	+	3.00235i	−0.191423	+	0.331554i
$83$	4.85086			0.532451			0.266225	−	0.963911i	$-0.414223\pi$
$83$	4.85086			0.532451			0.266225	+	0.963911i	$0.414223\pi$
$84$	2.15883	−	3.73921i	0.235548	−	0.407981i
$85$	5.66487	−	9.81185i	0.614442	−	1.06424i
$86$	−11.3448			−1.22334
$87$	12.3937	−	21.4666i	1.32875	−	2.30146i
$88$	1.02446	+	1.77441i	0.109208	+	0.189153i
$89$	8.28501	+	14.3501i	0.878209	+	1.52110i	0.853304	+	0.521414i	$0.174595\pi$
$89$	8.28501	+	14.3501i	0.878209	+	1.52110i	0.0249054	+	0.999690i	$0.492072\pi$
$90$	−10.5918			−1.11647
$91$		0			0
$92$	2.71379			0.282932
$93$	−6.87800	−	11.9130i	−0.713216	−	1.23533i
$94$	0.109916	+	0.190381i	0.0113370	+	0.0196363i
$95$	6.04892	−	10.4770i	0.620606	−	1.07492i
$96$	−2.69202			−0.274753
$97$	−2.32036	+	4.01897i	−0.235596	+	0.408065i	−0.959446	−	0.281893i	$-0.909038\pi$
$97$	−2.32036	+	4.01897i	−0.235596	+	0.408065i	0.723849	+	0.689958i	$0.242371\pi$
$98$	−2.21379	+	3.83440i	−0.223627	+	0.387333i
$99$	8.70171			0.874555
$100$	−0.609916	+	1.05641i	−0.0609916	+	0.105641i
$101$	−3.71379	−	6.43248i	−0.369536	−	0.640055i	0.619957	−	0.784636i	$-0.287150\pi$
$101$	−3.71379	−	6.43248i	−0.369536	−	0.640055i	−0.989493	+	0.144581i	$0.953817\pi$
$102$	−6.11476	−	10.5911i	−0.605452	−	1.04867i
$103$	0.518122			0.0510521			0.0255261	−	0.999674i	$-0.491874\pi$
$103$	0.518122			0.0510521			0.0255261	+	0.999674i	$0.491874\pi$
$104$		0			0
$105$	−10.7681			−1.05086
$106$	−1.35690	−	2.35021i	−0.131793	−	0.228273i
$107$	−1.75518	−	3.04005i	−0.169679	−	0.293893i	0.768628	−	0.639696i	$-0.220940\pi$
$107$	−1.75518	−	3.04005i	−0.169679	−	0.293893i	−0.938307	+	0.345803i	$0.887607\pi$
$108$	−1.67845	+	2.90716i	−0.161509	+	0.279741i
$109$	−3.38404			−0.324133			−0.162066	−	0.986780i	$-0.551816\pi$
$109$	−3.38404			−0.324133			−0.162066	+	0.986780i	$0.551816\pi$
$110$	2.55496	−	4.42532i	0.243606	−	0.421937i
$111$	−10.2349	+	17.7274i	−0.971454	+	1.68261i
$112$	−1.60388			−0.151552
$113$	2.72468	−	4.71928i	0.256316	−	0.443952i	−0.708936	−	0.705273i	$-0.750825\pi$
$113$	2.72468	−	4.71928i	0.256316	−	0.443952i	0.965252	+	0.261320i	$0.0841579\pi$
$114$	−6.52930	−	11.3091i	−0.611525	−	1.05919i
$115$	−3.38404	−	5.86133i	−0.315564	−	0.546572i
$116$	−9.20775			−0.854918
$117$		0			0
$118$	4.07606			0.375232
$119$	−3.64310	−	6.31004i	−0.333963	−	0.578441i
$120$	3.35690	+	5.81431i	0.306441	+	0.530772i
$121$	3.40097	−	5.89065i	0.309179	−	0.535514i
$122$	−10.4155			−0.942975
$123$	4.66637	−	8.08238i	0.420752	−	0.728764i
$124$	−2.55496	+	4.42532i	−0.229442	+	0.397405i
$125$	−9.42758			−0.843229
$126$	−3.40581	+	5.89904i	−0.303414	+	0.525528i
$127$	3.09783	+	5.36561i	0.274888	+	0.476121i	0.970107	−	0.242678i	$-0.0780258\pi$
$127$	3.09783	+	5.36561i	0.274888	+	0.476121i	−0.695219	+	0.718798i	$0.744692\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	30.5405			2.68894
$130$		0			0
$131$	−4.13706			−0.361457			−0.180728	−	0.983533i	$-0.557846\pi$
$131$	−4.13706			−0.361457			−0.180728	+	0.983533i	$0.557846\pi$
$132$	−2.75786	−	4.77676i	−0.240041	−	0.415764i
$133$	−3.89008	−	6.73782i	−0.337313	−	0.584243i
$134$	−6.03803	+	10.4582i	−0.521607	+	0.903449i
$135$	8.37196			0.720544
$136$	−2.27144	+	3.93425i	−0.194774	+	0.337359i
$137$	9.69083	−	16.7850i	0.827943	−	1.43404i	−0.0717061	−	0.997426i	$-0.522844\pi$
$137$	9.69083	−	16.7850i	0.827943	−	1.43404i	0.899649	−	0.436614i	$-0.143822\pi$
$138$	−7.30559			−0.621893
$139$	−9.29321	+	16.0963i	−0.788240	+	1.36527i	0.138805	+	0.990320i	$0.455674\pi$
$139$	−9.29321	+	16.0963i	−0.788240	+	1.36527i	−0.927044	+	0.374951i	$0.877659\pi$
$140$	2.00000	+	3.46410i	0.169031	+	0.292770i
$141$	−0.295897	−	0.512509i	−0.0249190	−	0.0431610i
$142$	−1.28621			−0.107936
$143$		0			0
$144$	4.24698			0.353915
$145$	11.4819	+	19.8872i	0.953518	+	1.65154i
$146$	1.81282	+	3.13990i	0.150030	+	0.259860i
$147$	5.95957	−	10.3223i	0.491537	−	0.851368i
$148$	7.60388			0.625035
$149$	1.82908	−	3.16807i	0.149844	−	0.259538i	−0.781325	−	0.624124i	$-0.785456\pi$
$149$	1.82908	−	3.16807i	0.149844	−	0.259538i	0.931170	+	0.364586i	$0.118789\pi$
$150$	1.64191	−	2.84387i	0.134061	−	0.232201i
$151$	14.5918			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$151$	14.5918			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$152$	−2.42543	+	4.20096i	−0.196728	+	0.340743i
$153$	9.64675	+	16.7087i	0.779894	+	1.35082i
$154$	−1.64310	−	2.84594i	−0.132405	−	0.229332i
$155$	12.7439			1.02362
$156$		0			0
$157$	21.6039			1.72418			0.862088	−	0.506758i	$-0.169156\pi$
$157$	21.6039			1.72418			0.862088	+	0.506758i	$0.169156\pi$
$158$	−2.66487	−	4.61570i	−0.212006	−	0.367205i
$159$	3.65279	+	6.32682i	0.289685	+	0.501750i
$160$	1.24698	−	2.15983i	0.0985824	−	0.170750i
$161$	−4.35258			−0.343032
$162$	−1.85205	+	3.20785i	−0.145511	+	0.252032i
$163$	−6.80463	+	11.7860i	−0.532979	+	0.923147i	0.466279	+	0.884638i	$0.345594\pi$
$163$	−6.80463	+	11.7860i	−0.532979	+	0.923147i	−0.999258	+	0.0385097i	$0.987739\pi$
$164$	−3.46681			−0.270713
$165$	−6.87800	+	11.9130i	−0.535452	+	0.927430i
$166$	2.42543	+	4.20096i	0.188250	+	0.326058i
$167$	−7.00000	−	12.1244i	−0.541676	−	0.938211i	−0.998808	−	0.0488118i	$-0.984457\pi$
$167$	−7.00000	−	12.1244i	−0.541676	−	0.938211i	0.457132	−	0.889399i	$-0.348877\pi$
$168$	4.31767			0.333115
$169$		0			0
$170$	11.3297			0.868952
$171$	10.3007	+	17.8414i	0.787717	+	1.36437i
$172$	−5.67241	−	9.82490i	−0.432517	−	0.749141i
$173$	2.10992	−	3.65448i	0.160414	−	0.277845i	−0.774603	−	0.632447i	$-0.782050\pi$
$173$	2.10992	−	3.65448i	0.160414	−	0.277845i	0.935017	+	0.354602i	$0.115384\pi$
$174$	24.7875			1.87913
$175$	0.978230	−	1.69434i	0.0739472	−	0.128080i
$176$	−1.02446	+	1.77441i	−0.0772215	+	0.133752i
$177$	−10.9729			−0.824770
$178$	−8.28501	+	14.3501i	−0.620988	+	1.07558i
$179$	−7.91454	−	13.7084i	−0.591561	−	1.02461i	−0.994022	−	0.109176i	$-0.965179\pi$
$179$	−7.91454	−	13.7084i	−0.591561	−	1.02461i	0.402462	−	0.915437i	$-0.368155\pi$
$180$	−5.29590	−	9.17276i	−0.394733	−	0.683697i
$181$	−15.3056			−1.13766			−0.568828	−	0.822457i	$-0.692603\pi$
$181$	−15.3056			−1.13766			−0.568828	+	0.822457i	$0.692603\pi$
$182$		0			0
$183$	28.0388			2.07268
$184$	1.35690	+	2.35021i	0.100032	+	0.173260i
$185$	−9.48188	−	16.4231i	−0.697122	−	1.20745i
$186$	6.87800	−	11.9130i	0.504320	−	0.873507i
$187$	−9.30798			−0.680667
$188$	−0.109916	+	0.190381i	−0.00801647	+	0.0138849i
$189$	2.69202	−	4.66272i	0.195816	−	0.339163i
$190$	12.0978			0.877669
$191$	−1.80194	+	3.12105i	−0.130384	+	0.225831i	−0.923824	−	0.382816i	$-0.874954\pi$
$191$	−1.80194	+	3.12105i	−0.130384	+	0.225831i	0.793441	+	0.608647i	$0.208288\pi$
$192$	−1.34601	−	2.33136i	−0.0971400	−	0.168251i
$193$	5.61141	+	9.71924i	0.403918	+	0.699607i	0.994195	−	0.107594i	$-0.0343148\pi$
$193$	5.61141	+	9.71924i	0.403918	+	0.699607i	−0.590277	+	0.807201i	$0.700981\pi$
$194$	−4.64071			−0.333184
$195$		0			0
$196$	−4.42758			−0.316256
$197$	−11.5526	−	20.0096i	−0.823086	−	1.42563i	−0.903373	−	0.428855i	$-0.858917\pi$
$197$	−11.5526	−	20.0096i	−0.823086	−	1.42563i	0.0802870	−	0.996772i	$-0.474416\pi$
$198$	4.35086	+	7.53590i	0.309202	+	0.535553i
$199$	−10.6310	+	18.4135i	−0.753613	+	1.30530i	0.192448	+	0.981307i	$0.438357\pi$
$199$	−10.6310	+	18.4135i	−0.753613	+	1.30530i	−0.946061	+	0.323989i	$0.894976\pi$
$200$	−1.21983			−0.0862552
$201$	16.2545	−	28.1536i	1.14650	−	1.98580i
$202$	3.71379	−	6.43248i	0.261301	−	0.452587i
$203$	14.7681			1.03652
$204$	6.11476	−	10.5911i	0.428119	−	0.741524i
$205$	4.32304	+	7.48773i	0.301934	+	0.522966i
$206$	0.259061	+	0.448707i	0.0180496	+	0.0312629i
$207$	11.5254			0.801072
$208$		0			0
$209$	−9.93900			−0.687495
$210$	−5.38404	−	9.32544i	−0.371534	−	0.643516i
$211$	−0.853543	−	1.47838i	−0.0587604	−	0.101776i	0.835149	−	0.550024i	$-0.185381\pi$
$211$	−0.853543	−	1.47838i	−0.0587604	−	0.101776i	−0.893909	+	0.448248i	$0.852048\pi$
$212$	1.35690	−	2.35021i	0.0931920	−	0.161413i
$213$	3.46250			0.237247
$214$	1.75518	−	3.04005i	0.119981	−	0.207814i
$215$	−14.1468	+	24.5029i	−0.964800	+	1.67108i
$216$	−3.35690			−0.228408
$217$	4.09783	−	7.09766i	0.278179	−	0.481820i
$218$	−1.69202	−	2.93067i	−0.114598	−	0.198490i
$219$	−4.88016	−	8.45268i	−0.329771	−	0.571179i
$220$	5.10992			0.344510
$221$		0			0
$222$	−20.4698			−1.37384
$223$	−3.10992	−	5.38653i	−0.208255	−	0.360709i	0.742910	−	0.669392i	$-0.233445\pi$
$223$	−3.10992	−	5.38653i	−0.208255	−	0.360709i	−0.951165	+	0.308683i	$0.900112\pi$
$224$	−0.801938	−	1.38900i	−0.0535817	−	0.0928063i
$225$	−2.59030	+	4.48653i	−0.172687	+	0.299102i
$226$	5.44935			0.362486
$227$	0.477697	−	0.827396i	0.0317059	−	0.0549162i	−0.849737	−	0.527207i	$-0.823239\pi$
$227$	0.477697	−	0.827396i	0.0317059	−	0.0549162i	0.881443	+	0.472291i	$0.156573\pi$
$228$	6.52930	−	11.3091i	0.432414	−	0.748962i
$229$	−22.4155			−1.48126			−0.740629	−	0.671914i	$-0.765472\pi$
$229$	−22.4155			−1.48126			−0.740629	+	0.671914i	$0.765472\pi$
$230$	3.38404	−	5.86133i	0.223137	−	0.386485i
$231$	4.42327	+	7.66133i	0.291030	+	0.504079i
$232$	−4.60388	−	7.97415i	−0.302259	−	0.523528i
$233$	2.99031			0.195902			0.0979509	−	0.995191i	$-0.468771\pi$
$233$	2.99031			0.195902			0.0979509	+	0.995191i	$0.468771\pi$
$234$		0			0
$235$	0.548253			0.0357641
$236$	2.03803	+	3.52998i	0.132665	+	0.229782i
$237$	7.17390	+	12.4256i	0.465995	+	0.807127i
$238$	3.64310	−	6.31004i	0.236147	−	0.409019i
$239$	−11.1293			−0.719894			−0.359947	−	0.932973i	$-0.617205\pi$
$239$	−11.1293			−0.719894			−0.359947	+	0.932973i	$0.617205\pi$
$240$	−3.35690	+	5.81431i	−0.216687	+	0.375312i
$241$	−2.60388	+	4.51004i	−0.167730	+	0.290518i	−0.937622	−	0.347658i	$-0.886977\pi$
$241$	−2.60388	+	4.51004i	−0.167730	+	0.290518i	0.769891	+	0.638175i	$0.220310\pi$
$242$	6.80194			0.437245
$243$	10.0211	−	17.3571i	0.642854	−	1.11346i
$244$	−5.20775	−	9.02009i	−0.333392	−	0.577452i
$245$	5.52111	+	9.56284i	0.352731	+	0.610947i
$246$	9.33273			0.595033
$247$		0			0
$248$	−5.10992			−0.324480
$249$	−6.52930	−	11.3091i	−0.413778	−	0.716684i
$250$	−4.71379	−	8.16453i	−0.298126	−	0.516370i
$251$	11.3475	−	19.6545i	0.716248	−	1.24058i	−0.246228	−	0.969212i	$-0.579191\pi$
$251$	11.3475	−	19.6545i	0.716248	−	1.24058i	0.962476	−	0.271366i	$-0.0874754\pi$
$252$	−6.81163			−0.429092
$253$	−2.78017	+	4.81539i	−0.174788	+	0.302741i
$254$	−3.09783	+	5.36561i	−0.194375	+	0.336668i
$255$	−30.4999			−1.90998
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.21528	−	9.03314i	−0.325320	−	0.563472i	0.656257	−	0.754538i	$-0.272139\pi$
$257$	−5.21528	−	9.03314i	−0.325320	−	0.563472i	−0.981577	+	0.191066i	$0.938806\pi$
$258$	15.2702	+	26.4488i	0.950684	+	1.64663i
$259$	−12.1957			−0.757802
$260$		0			0
$261$	−39.1051			−2.42055
$262$	−2.06853	−	3.58280i	−0.127794	−	0.221346i
$263$	3.55496	+	6.15737i	0.219208	+	0.379680i	0.954566	−	0.297999i	$-0.0963193\pi$
$263$	3.55496	+	6.15737i	0.219208	+	0.379680i	−0.735358	+	0.677679i	$0.762986\pi$
$264$	2.75786	−	4.77676i	0.169735	−	0.293989i
$265$	−6.76809			−0.415760
$266$	3.89008	−	6.73782i	0.238516	−	0.413122i
$267$	22.3034	−	38.6307i	1.36495	−	2.36416i
$268$	−12.0761			−0.737663
$269$	−1.01208	+	1.75298i	−0.0617077	+	0.106881i	−0.895229	−	0.445607i	$-0.852988\pi$
$269$	−1.01208	+	1.75298i	−0.0617077	+	0.106881i	0.833521	+	0.552488i	$0.186321\pi$
$270$	4.18598	+	7.25033i	0.254751	+	0.441241i
$271$	7.98254	+	13.8262i	0.484905	+	0.839880i	0.999850	−	0.0173435i	$-0.00552089\pi$
$271$	7.98254	+	13.8262i	0.484905	+	0.839880i	−0.514945	+	0.857223i	$0.672188\pi$
$272$	−4.54288			−0.275452
$273$		0			0
$274$	19.3817			1.17089
$275$	−1.24967	−	2.16449i	−0.0753578	−	0.130524i
$276$	−3.65279	−	6.32682i	−0.219872	−	0.380830i
$277$	−6.85086	+	11.8660i	−0.411628	+	0.712961i	−0.995068	−	0.0991957i	$-0.968373\pi$
$277$	−6.85086	+	11.8660i	−0.411628	+	0.712961i	0.583440	+	0.812156i	$0.301706\pi$
$278$	−18.5864			−1.11474
$279$	−10.8509	+	18.7942i	−0.649624	+	1.12518i
$280$	−2.00000	+	3.46410i	−0.119523	+	0.207020i
$281$	15.2024			0.906898			0.453449	−	0.891282i	$-0.350193\pi$
$281$	15.2024			0.906898			0.453449	+	0.891282i	$0.350193\pi$
$282$	0.295897	−	0.512509i	0.0176204	−	0.0305194i
$283$	−10.3034	−	17.8461i	−0.612475	−	1.06084i	−0.990822	−	0.135174i	$-0.956841\pi$
$283$	−10.3034	−	17.8461i	−0.612475	−	1.06084i	0.378347	−	0.925664i	$-0.376493\pi$
$284$	−0.643104	−	1.11389i	−0.0381612	−	0.0660972i
$285$	−32.5676			−1.92914
$286$		0			0
$287$	5.56033			0.328216
$288$	2.12349	+	3.67799i	0.125128	+	0.216728i
$289$	−1.81886	−	3.15036i	−0.106992	−	0.185316i
$290$	−11.4819	+	19.8872i	−0.674239	+	1.16782i
$291$	12.4929			0.732346
$292$	−1.81282	+	3.13990i	−0.106087	+	0.183749i
$293$	−1.08815	+	1.88472i	−0.0635702	+	0.110107i	−0.896059	−	0.443935i	$-0.853582\pi$
$293$	−1.08815	+	1.88472i	−0.0635702	+	0.110107i	0.832489	+	0.554042i	$0.186915\pi$
$294$	11.9191			0.695139
$295$	5.08277	−	8.80361i	0.295930	−	0.512566i
$296$	3.80194	+	6.58515i	0.220983	+	0.382754i
$297$	−3.43900	−	5.95652i	−0.199551	−	0.345633i
$298$	3.65817			0.211912
$299$		0			0
$300$	3.28382			0.189591
$301$	9.09783	+	15.7579i	0.524390	+	0.908271i
$302$	7.29590	+	12.6369i	0.419832	+	0.727170i
$303$	−9.99761	+	17.3164i	−0.574348	+	0.994799i
$304$	−4.85086			−0.278216
$305$	−12.9879	+	22.4957i	−0.743686	+	1.28810i
$306$	−9.64675	+	16.7087i	−0.551468	+	0.955171i
$307$	17.0127			0.970965			0.485482	−	0.874247i	$-0.338644\pi$
$307$	17.0127			0.970965			0.485482	+	0.874247i	$0.338644\pi$
$308$	1.64310	−	2.84594i	0.0936245	−	0.162162i
$309$	−0.697398	−	1.20793i	−0.0396736	−	0.0687167i
$310$	6.37196	+	11.0366i	0.361903	+	0.626835i
$311$	−4.71379			−0.267295			−0.133647	−	0.991029i	$-0.542669\pi$
$311$	−4.71379			−0.267295			−0.133647	+	0.991029i	$0.542669\pi$
$312$		0			0
$313$	1.67696			0.0947872			0.0473936	−	0.998876i	$-0.484909\pi$
$313$	1.67696			0.0947872			0.0473936	+	0.998876i	$0.484909\pi$
$314$	10.8019	+	18.7095i	0.609589	+	1.05584i
$315$	8.49396	+	14.7120i	0.478580	+	0.828926i
$316$	2.66487	−	4.61570i	0.149911	−	0.259653i
$317$	29.1400			1.63667			0.818334	−	0.574743i	$-0.194898\pi$
$317$	29.1400			1.63667			0.818334	+	0.574743i	$0.194898\pi$
$318$	−3.65279	+	6.32682i	−0.204838	+	0.354791i
$319$	9.43296	−	16.3384i	0.528144	−	0.914773i
$320$	2.49396			0.139417
$321$	−4.72497	+	8.18389i	−0.263722	+	0.456780i
$322$	−2.17629	−	3.76945i	−0.121280	−	0.210063i
$323$	−11.0184	−	19.0845i	−0.613081	−	1.06189i
$324$	−3.70410			−0.205784
$325$		0			0
$326$	−13.6093			−0.753747
$327$	4.55496	+	7.88942i	0.251890	+	0.436286i
$328$	−1.73341	−	3.00235i	−0.0957113	−	0.165777i
$329$	0.176292	−	0.305347i	0.00971929	−	0.0168343i
$330$	−13.7560			−0.757243
$331$	−4.37196	+	7.57246i	−0.240305	+	0.416220i	−0.960801	−	0.277239i	$-0.910581\pi$
$331$	−4.37196	+	7.57246i	−0.240305	+	0.416220i	0.720496	+	0.693459i	$0.243914\pi$
$332$	−2.42543	+	4.20096i	−0.133113	+	0.230558i
$333$	32.2935			1.76967
$334$	7.00000	−	12.1244i	0.383023	−	0.663415i
$335$	15.0586	+	26.0823i	0.822740	+	1.42503i
$336$	2.15883	+	3.73921i	0.117774	+	0.203991i
$337$	−3.10560			−0.169173			−0.0845865	−	0.996416i	$-0.526957\pi$
$337$	−3.10560			−0.169173			−0.0845865	+	0.996416i	$0.526957\pi$
$338$		0			0
$339$	−14.6698			−0.796753
$340$	5.66487	+	9.81185i	0.307221	+	0.532122i
$341$	−5.23490	−	9.06711i	−0.283486	−	0.491011i
$342$	−10.3007	+	17.8414i	−0.557000	+	0.964753i
$343$	18.3284			0.989642
$344$	5.67241	−	9.82490i	0.305836	−	0.529723i
$345$	−9.10992	+	15.7788i	−0.490461	+	0.849504i
$346$	4.21983			0.226860
$347$	−8.98792	+	15.5675i	−0.482497	+	0.835709i	−0.999798	−	0.0200944i	$-0.993603\pi$
$347$	−8.98792	+	15.5675i	−0.482497	+	0.835709i	0.517301	+	0.855803i	$0.326937\pi$
$348$	12.3937	+	21.4666i	0.664374	+	1.15073i
$349$	−7.58211	−	13.1326i	−0.405861	−	0.702972i	0.588560	−	0.808453i	$-0.299695\pi$
$349$	−7.58211	−	13.1326i	−0.405861	−	0.702972i	−0.994421	+	0.105482i	$0.966362\pi$
$350$	1.95646			0.104577
$351$		0			0
$352$	−2.04892			−0.109208
$353$	1.65010	+	2.85806i	0.0878262	+	0.152119i	0.906592	−	0.422008i	$-0.138675\pi$
$353$	1.65010	+	2.85806i	0.0878262	+	0.152119i	−0.818766	+	0.574128i	$0.805341\pi$
$354$	−5.48643	−	9.50277i	−0.291600	−	0.505066i
$355$	−1.60388	+	2.77799i	−0.0851249	+	0.147441i
$356$	−16.5700			−0.878209
$357$	−9.80731	+	16.9868i	−0.519058	+	0.899035i
$358$	7.91454	−	13.7084i	0.418297	−	0.724511i
$359$	18.8901			0.996980			0.498490	−	0.866895i	$-0.333888\pi$
$359$	18.8901			0.996980			0.498490	+	0.866895i	$0.333888\pi$
$360$	5.29590	−	9.17276i	0.279118	−	0.483447i
$361$	−2.26540	−	3.92378i	−0.119231	−	0.206515i
$362$	−7.65279	−	13.2550i	−0.402222	−	0.696669i
$363$	−18.3110			−0.961076
$364$		0			0
$365$	9.04221			0.473291
$366$	14.0194	+	24.2823i	0.732805	+	1.26925i
$367$	0.0978347	+	0.169455i	0.00510693	+	0.00884546i	0.868568	−	0.495571i	$-0.165041\pi$
$367$	0.0978347	+	0.169455i	0.00510693	+	0.00884546i	−0.863461	+	0.504416i	$0.831708\pi$
$368$	−1.35690	+	2.35021i	−0.0707331	+	0.122513i
$369$	−14.7235			−0.766474
$370$	9.48188	−	16.4231i	0.492939	−	0.853796i
$371$	−2.17629	+	3.76945i	−0.112987	+	0.195700i
$372$	13.7560			0.713216
$373$	5.38404	−	9.32544i	0.278775	−	0.482853i	−0.692305	−	0.721605i	$-0.743405\pi$
$373$	5.38404	−	9.32544i	0.278775	−	0.482853i	0.971081	+	0.238752i	$0.0767382\pi$
$374$	−4.65399	−	8.06095i	−0.240652	−	0.416822i
$375$	12.6896	+	21.9791i	0.655290	+	1.13499i
$376$	−0.219833			−0.0113370
$377$		0			0
$378$	5.38404			0.276925
$379$	−13.9813	−	24.2164i	−0.718173	−	1.24391i	−0.961723	−	0.274024i	$-0.911645\pi$
$379$	−13.9813	−	24.2164i	−0.718173	−	1.24391i	0.243549	−	0.969889i	$-0.421688\pi$
$380$	6.04892	+	10.4770i	0.310303	+	0.537460i
$381$	8.33944	−	14.4443i	0.427242	−	0.740005i
$382$	−3.60388			−0.184390
$383$	−16.4155	+	28.4325i	−0.838793	+	1.45283i	0.0521115	+	0.998641i	$0.483405\pi$
$383$	−16.4155	+	28.4325i	−0.838793	+	1.45283i	−0.890904	+	0.454191i	$0.849928\pi$
$384$	1.34601	−	2.33136i	0.0686883	−	0.118972i
$385$	−8.19567			−0.417690
$386$	−5.61141	+	9.71924i	−0.285613	+	0.494697i
$387$	−24.0906	−	41.7261i	−1.22459	−	2.12106i
$388$	−2.32036	−	4.01897i	−0.117798	−	0.204032i
$389$	8.90946			0.451728			0.225864	−	0.974159i	$-0.427480\pi$
$389$	8.90946			0.451728			0.225864	+	0.974159i	$0.427480\pi$
$390$		0			0
$391$	−12.3284			−0.623475
$392$	−2.21379	−	3.83440i	−0.111813	−	0.193666i
$393$	5.56853	+	9.64498i	0.280895	+	0.486525i
$394$	11.5526	−	20.0096i	0.582010	−	1.00807i
$395$	−13.2922			−0.668802
$396$	−4.35086	+	7.53590i	−0.218639	+	0.378693i
$397$	−5.89440	+	10.2094i	−0.295831	+	0.512395i	−0.975178	−	0.221423i	$-0.928930\pi$
$397$	−5.89440	+	10.2094i	−0.295831	+	0.512395i	0.679347	+	0.733817i	$0.262263\pi$
$398$	−21.2620			−1.06577
$399$	−10.4722	+	18.1384i	−0.524265	+	0.908054i
$400$	−0.609916	−	1.05641i	−0.0304958	−	0.0528203i
$401$	−1.60656	−	2.78265i	−0.0802280	−	0.138959i	0.823120	−	0.567868i	$-0.192231\pi$
$401$	−1.60656	−	2.78265i	−0.0802280	−	0.138959i	−0.903348	+	0.428909i	$0.858898\pi$
$402$	32.5090			1.62140
$403$		0			0
$404$	7.42758			0.369536
$405$	4.61894	+	8.00024i	0.229517	+	0.397535i
$406$	7.38404	+	12.7895i	0.366464	+	0.634734i
$407$	−7.78986	+	13.4924i	−0.386129	+	0.668795i
$408$	12.2295			0.605452
$409$	−6.01089	+	10.4112i	−0.297219	+	0.514799i	−0.975499	−	0.220005i	$-0.929393\pi$
$409$	−6.01089	+	10.4112i	−0.297219	+	0.514799i	0.678280	+	0.734804i	$0.262726\pi$
$410$	−4.32304	+	7.48773i	−0.213500	+	0.369793i
$411$	−52.1758			−2.57364
$412$	−0.259061	+	0.448707i	−0.0127630	+	0.0221062i
$413$	−3.26875	−	5.66164i	−0.160845	−	0.278591i
$414$	5.76271	+	9.98130i	0.283222	+	0.490554i
$415$	12.0978			0.593859
$416$		0			0
$417$	50.0350			2.45023
$418$	−4.96950	−	8.60743i	−0.243066	−	0.421003i
$419$	1.78017	+	3.08334i	0.0869669	+	0.150631i	0.906228	−	0.422790i	$-0.138949\pi$
$419$	1.78017	+	3.08334i	0.0869669	+	0.150631i	−0.819261	+	0.573421i	$0.805616\pi$
$420$	5.38404	−	9.32544i	0.262714	−	0.455035i
$421$	−1.28621			−0.0626860			−0.0313430	−	0.999509i	$-0.509978\pi$
$421$	−1.28621			−0.0626860			−0.0313430	+	0.999509i	$0.509978\pi$
$422$	0.853543	−	1.47838i	0.0415498	−	0.0719664i
$423$	−0.466812	+	0.808542i	−0.0226972	+	0.0393127i
$424$	2.71379			0.131793
$425$	2.77077	−	4.79912i	0.134402	−	0.232792i
$426$	1.73125	+	2.99861i	0.0838793	+	0.145283i
$427$	8.35258	+	14.4671i	0.404210	+	0.700112i
$428$	3.51035			0.169679
$429$		0			0
$430$	−28.2935			−1.36443
$431$	−13.4940	−	23.3722i	−0.649981	−	1.12580i	−0.983127	−	0.182925i	$-0.941443\pi$
$431$	−13.4940	−	23.3722i	−0.649981	−	1.12580i	0.333146	−	0.942875i	$-0.391890\pi$
$432$	−1.67845	−	2.90716i	−0.0807544	−	0.139871i
$433$	8.00849	−	13.8711i	0.384864	−	0.666603i	−0.606887	−	0.794788i	$-0.707582\pi$
$433$	8.00849	−	13.8711i	0.384864	−	0.666603i	0.991750	+	0.128185i	$0.0409152\pi$
$434$	8.19567			0.393405
$435$	30.9095	−	53.5368i	1.48200	−	2.56689i
$436$	1.69202	−	2.93067i	0.0810331	−	0.140354i
$437$	−13.1642			−0.629730
$438$	4.88016	−	8.45268i	0.233183	−	0.403885i
$439$	18.5700	+	32.1642i	0.886299	+	1.53511i	0.844218	+	0.536000i	$0.180065\pi$
$439$	18.5700	+	32.1642i	0.886299	+	1.53511i	0.0420812	+	0.999114i	$0.486601\pi$
$440$	2.55496	+	4.42532i	0.121803	+	0.210969i
$441$	−18.8039			−0.895422
$442$		0			0
$443$	−41.2083			−1.95787			−0.978934	−	0.204178i	$-0.934548\pi$
$443$	−41.2083			−1.95787			−0.978934	+	0.204178i	$0.934548\pi$
$444$	−10.2349	−	17.7274i	−0.485727	−	0.841303i
$445$	20.6625	+	35.7885i	0.979496	+	1.69654i
$446$	3.10992	−	5.38653i	0.147259	−	0.255060i
$447$	−9.84787			−0.465788
$448$	0.801938	−	1.38900i	0.0378880	−	0.0656239i
$449$	5.06315	−	8.76964i	0.238945	−	0.413865i	−0.721467	−	0.692449i	$-0.756532\pi$
$449$	5.06315	−	8.76964i	0.238945	−	0.413865i	0.960412	+	0.278584i	$0.0898651\pi$
$450$	−5.18060			−0.244216
$451$	3.55161	−	6.15156i	0.167239	−	0.289666i
$452$	2.72468	+	4.71928i	0.128158	+	0.221976i
$453$	−19.6407	−	34.0187i	−0.922801	−	1.59834i
$454$	0.955395			0.0448389
$455$		0			0
$456$	13.0586			0.611525
$457$	−10.8780	−	18.8413i	−0.508851	−	0.881357i	−0.999947	−	0.0102511i	$-0.996737\pi$
$457$	−10.8780	−	18.8413i	−0.508851	−	0.881357i	0.491096	−	0.871105i	$-0.336596\pi$
$458$	−11.2078	−	19.4124i	−0.523704	−	0.907082i
$459$	7.62498	−	13.2069i	0.355904	−	0.616443i
$460$	6.76809			0.315564
$461$	19.2838	−	33.4005i	0.898137	−	1.55562i	0.0682631	−	0.997667i	$-0.478254\pi$
$461$	19.2838	−	33.4005i	0.898137	−	1.55562i	0.829874	−	0.557951i	$-0.188412\pi$
$462$	−4.42327	+	7.66133i	−0.205789	+	0.356437i
$463$	−33.0073			−1.53398			−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073			−1.53398			−0.766990	+	0.641660i	$0.778246\pi$
$464$	4.60388	−	7.97415i	0.213730	−	0.370190i
$465$	−17.1535	−	29.7107i	−0.795473	−	1.37780i
$466$	1.49516	+	2.58969i	0.0692617	+	0.119965i
$467$	6.53989			0.302630			0.151315	−	0.988486i	$-0.451649\pi$
$467$	6.53989			0.302630			0.151315	+	0.988486i	$0.451649\pi$
$468$		0			0
$469$	19.3685			0.894354
$470$	0.274127	+	0.474801i	0.0126445	+	0.0219010i
$471$	−29.0790	−	50.3664i	−1.33989	−	2.32076i
$472$	−2.03803	+	3.52998i	−0.0938080	+	0.162480i
$473$	23.2446			1.06879
$474$	−7.17390	+	12.4256i	−0.329508	+	0.570725i
$475$	2.95862	−	5.12447i	0.135751	−	0.235127i
$476$	7.28621			0.333963
$477$	5.76271	−	9.98130i	0.263856	−	0.457013i
$478$	−5.56465	−	9.63825i	−0.254521	−	0.440843i
$479$	−4.15346	−	7.19400i	−0.189776	−	0.328702i	0.755399	−	0.655265i	$-0.227443\pi$
$479$	−4.15346	−	7.19400i	−0.189776	−	0.328702i	−0.945176	+	0.326563i	$0.894110\pi$
$480$	−6.71379			−0.306441
$481$		0			0
$482$	−5.20775			−0.237207
$483$	5.85862	+	10.1474i	0.266577	+	0.461724i
$484$	3.40097	+	5.89065i	0.154589	+	0.267757i
$485$	−5.78687	+	10.0232i	−0.262768	+	0.455128i
$486$	20.0422			0.909133
$487$	15.8267	−	27.4126i	0.717176	−	1.24219i	−0.244938	−	0.969539i	$-0.578768\pi$
$487$	15.8267	−	27.4126i	0.717176	−	1.24219i	0.962114	−	0.272646i	$-0.0878989\pi$
$488$	5.20775	−	9.02009i	0.235744	−	0.408320i
$489$	36.6364			1.65676
$490$	−5.52111	+	9.56284i	−0.249418	+	0.432005i
$491$	18.3315	+	31.7512i	0.827291	+	1.43291i	0.900156	+	0.435568i	$0.143452\pi$
$491$	18.3315	+	31.7512i	0.827291	+	1.43291i	−0.0728653	+	0.997342i	$0.523214\pi$
$492$	4.66637	+	8.08238i	0.210376	+	0.364382i
$493$	41.8297			1.88391
$494$		0			0
$495$	21.7017			0.975419
$496$	−2.55496	−	4.42532i	−0.114721	−	0.198703i
$497$	1.03146	+	1.78654i	0.0462673	+	0.0801372i
$498$	6.52930	−	11.3091i	0.292585	−	0.506772i
$499$	−29.8920			−1.33815			−0.669075	−	0.743195i	$-0.733309\pi$
$499$	−29.8920			−1.33815			−0.669075	+	0.743195i	$0.733309\pi$
$500$	4.71379	−	8.16453i	0.210807	−	0.365129i
$501$	−18.8442	+	32.6390i	−0.841895	+	1.45820i
$502$	22.6950			1.01293
$503$	−7.79523	+	13.5017i	−0.347572	+	0.602013i	−0.985818	−	0.167820i	$-0.946327\pi$
$503$	−7.79523	+	13.5017i	−0.347572	+	0.602013i	0.638245	+	0.769833i	$0.279661\pi$
$504$	−3.40581	−	5.89904i	−0.151707	−	0.262764i
$505$	−9.26205	−	16.0423i	−0.412156	−	0.713874i
$506$	−5.56033			−0.247187
$507$		0			0
$508$	−6.19567			−0.274888
$509$	8.58211	+	14.8646i	0.380395	+	0.658864i	0.991119	−	0.132980i	$-0.0424547\pi$
$509$	8.58211	+	14.8646i	0.380395	+	0.658864i	−0.610724	+	0.791844i	$0.709121\pi$
$510$	−15.2500	−	26.4137i	−0.675280	−	1.16962i
$511$	2.90754	−	5.03601i	0.128622	−	0.222780i
$512$	−1.00000			−0.0441942
$513$	8.14191	−	14.1022i	0.359474	−	0.622627i
$514$	5.21528	−	9.03314i	0.230036	−	0.398435i
$515$	1.29218			0.0569401
$516$	−15.2702	+	26.4488i	−0.672235	+	1.16435i
$517$	−0.225209	−	0.390074i	−0.00990470	−	0.0171554i
$518$	−6.09783	−	10.5618i	−0.267923	−	0.464057i
$519$	−11.3599			−0.498643
$520$		0			0
$521$	6.15452			0.269634			0.134817	−	0.990870i	$-0.456955\pi$
$521$	6.15452			0.269634			0.134817	+	0.990870i	$0.456955\pi$
$522$	−19.5526	−	33.8660i	−0.855793	−	1.48228i
$523$	−3.46950	−	6.00935i	−0.151711	−	0.262771i	0.780146	−	0.625598i	$-0.215145\pi$
$523$	−3.46950	−	6.00935i	−0.151711	−	0.262771i	−0.931856	+	0.362827i	$0.881812\pi$
$524$	2.06853	−	3.58280i	0.0903642	−	0.156515i
$525$	−5.26683			−0.229863
$526$	−3.55496	+	6.15737i	−0.155004	+	0.268474i
$527$	11.6069	−	20.1037i	0.505603	−	0.875730i
$528$	5.51573			0.240041
$529$	7.81767	−	13.5406i	0.339899	−	0.588722i
$530$	−3.38404	−	5.86133i	−0.146993	−	0.254600i
$531$	8.65548	+	14.9917i	0.375616	+	0.650586i
$532$	7.78017			0.337313
$533$		0			0
$534$	44.6069			1.93033
$535$	−4.37734	−	7.58177i	−0.189249	−	0.327789i
$536$	−6.03803	−	10.4582i	−0.260803	−	0.451725i
$537$	−21.3061	+	36.9033i	−0.919427	+	1.59249i
$538$	−2.02416			−0.0872679
$539$	4.53588	−	7.85637i	0.195374	−	0.338398i
$540$	−4.18598	+	7.25033i	−0.180136	+	0.312005i
$541$	−0.426256			−0.0183262			−0.00916308	−	0.999958i	$-0.502917\pi$
$541$	−0.426256			−0.0183262			−0.00916308	+	0.999958i	$0.502917\pi$
$542$	−7.98254	+	13.8262i	−0.342880	+	0.593885i
$543$	20.6015	+	35.6828i	0.884094	+	1.53130i
$544$	−2.27144	−	3.93425i	−0.0973871	−	0.168679i
$545$	−8.43967			−0.361516
$546$		0			0
$547$	3.72348			0.159205			0.0796023	−	0.996827i	$-0.474635\pi$
$547$	3.72348			0.159205			0.0796023	+	0.996827i	$0.474635\pi$
$548$	9.69083	+	16.7850i	0.413972	+	0.717020i
$549$	−22.1172	−	38.3081i	−0.943940	−	1.63495i
$550$	1.24967	−	2.16449i	0.0532860	−	0.0922941i
$551$	44.6655			1.90281
$552$	3.65279	−	6.32682i	0.155473	−	0.269287i
$553$	−4.27413	+	7.40300i	−0.181754	+	0.314808i
$554$	−13.7017			−0.582130
$555$	−25.5254	+	44.2113i	−1.08349	+	1.87667i
$556$	−9.29321	−	16.0963i	−0.394120	−	0.682636i
$557$	21.3980	+	37.0625i	0.906664	+	1.57039i	0.818668	+	0.574268i	$0.194713\pi$
$557$	21.3980	+	37.0625i	0.906664	+	1.57039i	0.0879966	+	0.996121i	$0.471954\pi$
$558$	−21.7017			−0.918707
$559$		0			0
$560$	−4.00000			−0.169031
$561$	12.5286	+	21.7002i	0.528960	+	0.916185i
$562$	7.60119	+	13.1656i	0.320637	+	0.555359i
$563$	−1.46250	+	2.53312i	−0.0616370	+	0.106758i	−0.895197	−	0.445670i	$-0.852965\pi$
$563$	−1.46250	+	2.53312i	−0.0616370	+	0.106758i	0.833560	+	0.552429i	$0.186299\pi$
$564$	0.591794			0.0249190
$565$	6.79523	−	11.7697i	0.285878	−	0.495155i
$566$	10.3034	−	17.8461i	0.433085	−	0.750126i
$567$	5.94092			0.249495
$568$	0.643104	−	1.11389i	0.0269840	−	0.0467377i
$569$	13.2947	+	23.0271i	0.557343	+	0.965346i	0.997717	+	0.0675318i	$0.0215124\pi$
$569$	13.2947	+	23.0271i	0.557343	+	0.965346i	−0.440374	+	0.897814i	$0.645154\pi$
$570$	−16.2838	−	28.2044i	−0.682054	−	1.18135i
$571$	−2.34422			−0.0981027			−0.0490513	−	0.998796i	$-0.515620\pi$
$571$	−2.34422			−0.0981027			−0.0490513	+	0.998796i	$0.515620\pi$
$572$		0			0
$573$	9.70171			0.405295
$574$	2.78017	+	4.81539i	0.116042	+	0.200991i
$575$	−1.65519	−	2.86687i	−0.0690260	−	0.119557i
$576$	−2.12349	+	3.67799i	−0.0884787	+	0.153250i
$577$	40.4064			1.68214			0.841070	−	0.540926i	$-0.181926\pi$
$577$	40.4064			1.68214			0.841070	+	0.540926i	$0.181926\pi$
$578$	1.81886	−	3.15036i	0.0756548	−	0.131038i
$579$	15.1060	−	26.1644i	0.627785	−	1.08736i
$580$	−22.9638			−0.953518
$581$	3.89008	−	6.73782i	0.161388	−	0.279532i
$582$	6.24645	+	10.8192i	0.258924	+	0.448469i
$583$	2.78017	+	4.81539i	0.115143	+	0.199433i
$584$	−3.62565			−0.150030
$585$		0			0
$586$	−2.17629			−0.0899018
$587$	21.6090	+	37.4279i	0.891900	+	1.54482i	0.837596	+	0.546291i	$0.183961\pi$
$587$	21.6090	+	37.4279i	0.891900	+	1.54482i	0.0543039	+	0.998524i	$0.482706\pi$
$588$	5.95957	+	10.3223i	0.245769	+	0.425684i
$589$	12.3937	−	21.4666i	0.510675	−	0.884515i
$590$	10.1655			0.418509
$591$	−31.0998	+	53.8664i	−1.27927	+	2.21577i
$592$	−3.80194	+	6.58515i	−0.156259	+	0.270648i
$593$	−7.01746			−0.288172			−0.144086	−	0.989565i	$-0.546024\pi$
$593$	−7.01746			−0.288172			−0.144086	+	0.989565i	$0.546024\pi$
$594$	3.43900	−	5.95652i	0.141104	−	0.244399i
$595$	−9.08575	−	15.7370i	−0.372480	−	0.645154i
$596$	1.82908	+	3.16807i	0.0749222	+	0.129769i
$597$	57.2379			2.34259
$598$		0			0
$599$	14.9772			0.611950			0.305975	−	0.952039i	$-0.401018\pi$
$599$	14.9772			0.611950			0.305975	+	0.952039i	$0.401018\pi$
$600$	1.64191	+	2.84387i	0.0670306	+	0.116100i
$601$	18.6386	+	32.2829i	0.760283	+	1.31685i	0.942705	+	0.333628i	$0.108273\pi$
$601$	18.6386	+	32.2829i	0.760283	+	1.31685i	−0.182422	+	0.983220i	$0.558394\pi$
$602$	−9.09783	+	15.7579i	−0.370800	+	0.642245i
$603$	−51.2868			−2.08856
$604$	−7.29590	+	12.6369i	−0.296866	+	0.514187i
$605$	8.48188	−	14.6910i	0.344837	−	0.597276i
$606$	−19.9952			−0.812250
$607$	−0.401501	+	0.695421i	−0.0162964	+	0.0282263i	−0.874059	−	0.485820i	$-0.838521\pi$
$607$	−0.401501	+	0.695421i	−0.0162964	+	0.0282263i	0.857762	+	0.514047i	$0.171854\pi$
$608$	−2.42543	−	4.20096i	−0.0983641	−	0.170372i
$609$	−19.8780	−	34.4297i	−0.805497	−	1.39516i
$610$	−25.9758			−1.05173
$611$		0			0
$612$	−19.2935			−0.779894
$613$	−2.43535	−	4.21816i	−0.0983630	−	0.170370i	0.812644	−	0.582760i	$-0.198027\pi$
$613$	−2.43535	−	4.21816i	−0.0983630	−	0.170370i	−0.911007	+	0.412390i	$0.864694\pi$
$614$	8.50634	+	14.7334i	0.343288	+	0.594592i
$615$	11.6377	−	20.1571i	0.469278	−	0.812814i
$616$	3.28621			0.132405
$617$	−1.67145	+	2.89503i	−0.0672899	+	0.116550i	−0.897707	−	0.440592i	$-0.854769\pi$
$617$	−1.67145	+	2.89503i	−0.0672899	+	0.116550i	0.830418	+	0.557142i	$0.188102\pi$
$618$	0.697398	−	1.20793i	0.0280535	−	0.0485900i
$619$	−34.1715			−1.37347			−0.686734	−	0.726908i	$-0.740956\pi$
$619$	−34.1715			−1.37347			−0.686734	+	0.726908i	$0.740956\pi$
$620$	−6.37196	+	11.0366i	−0.255904	+	0.443239i
$621$	−4.55496	−	7.88942i	−0.182784	−	0.316591i
$622$	−2.35690	−	4.08226i	−0.0945029	−	0.163684i
$623$	26.5763			1.06476
$624$		0			0
$625$	−29.6112			−1.18445
$626$	0.838478	+	1.45229i	0.0335123	+	0.0580450i
$627$	13.3780	+	23.1714i	0.534266	+	0.925376i
$628$	−10.8019	+	18.7095i	−0.431044	+	0.746591i
$629$	−34.5435			−1.37734
$630$	−8.49396	+	14.7120i	−0.338407	+	0.586139i
$631$	−19.9148	+	34.4935i	−0.792797	+	1.37316i	0.131431	+	0.991325i	$0.458043\pi$
$631$	−19.9148	+	34.4935i	−0.792797	+	1.37316i	−0.924229	+	0.381840i	$0.875291\pi$
$632$	5.32975			0.212006
$633$	−2.29776	+	3.97983i	−0.0913277	+	0.158184i
$634$	14.5700	+	25.2360i	0.578650	+	1.00225i
$635$	7.72587	+	13.3816i	0.306592	+	0.531033i
$636$	−7.30559			−0.289685
$637$		0			0
$638$	18.8659			0.746909
$639$	−2.73125	−	4.73066i	−0.108047	−	0.187142i
$640$	1.24698	+	2.15983i	0.0492912	+	0.0853749i
$641$	6.74549	−	11.6835i	0.266431	−	0.461472i	−0.701507	−	0.712663i	$-0.747489\pi$
$641$	6.74549	−	11.6835i	0.266431	−	0.461472i	0.967937	+	0.251191i	$0.0808223\pi$
$642$	−9.44994			−0.372960
$643$	8.33190	−	14.4313i	0.328578	−	0.569114i	−0.653652	−	0.756795i	$-0.726764\pi$
$643$	8.33190	−	14.4313i	0.328578	−	0.569114i	0.982230	+	0.187681i	$0.0600972\pi$
$644$	2.17629	−	3.76945i	0.0857579	−	0.148537i
$645$	76.1667			2.99906
$646$	11.0184	−	19.0845i	0.433514	−	0.750868i
$647$	−24.3666	−	42.2042i	−0.957949	−	1.65922i	−0.727470	−	0.686140i	$-0.759304\pi$
$647$	−24.3666	−	42.2042i	−0.957949	−	1.65922i	−0.230479	−	0.973077i	$-0.574029\pi$
$648$	−1.85205	−	3.20785i	−0.0727555	−	0.126016i
$649$	−8.35152			−0.327826
$650$		0			0
$651$	−22.0629			−0.864714
$652$	−6.80463	−	11.7860i	−0.266490	−	0.461574i
$653$	−23.5351	−	40.7640i	−0.921000	−	1.59522i	−0.797871	−	0.602828i	$-0.794041\pi$
$653$	−23.5351	−	40.7640i	−0.921000	−	1.59522i	−0.123129	−	0.992391i	$-0.539293\pi$
$654$	−4.55496	+	7.88942i	−0.178113	+	0.308501i
$655$	−10.3177			−0.403145
$656$	1.73341	−	3.00235i	0.0676781	−	0.117222i
$657$	−7.69902	+	13.3351i	−0.300367	+	0.520252i
$658$	0.352584			0.0137452
$659$	11.1262	−	19.2711i	0.433414	−	0.750696i	−0.563750	−	0.825945i	$-0.690642\pi$
$659$	11.1262	−	19.2711i	0.433414	−	0.750696i	0.997165	+	0.0752495i	$0.0239753\pi$
$660$	−6.87800	−	11.9130i	−0.267726	−	0.463715i
$661$	1.28621	+	2.22778i	0.0500277	+	0.0866505i	0.889955	−	0.456049i	$-0.150736\pi$
$661$	1.28621	+	2.22778i	0.0500277	+	0.0866505i	−0.839927	+	0.542699i	$0.817402\pi$
$662$	−8.74392			−0.339842
$663$		0			0
$664$	−4.85086			−0.188250
$665$	−9.70171	−	16.8039i	−0.376216	−	0.651626i
$666$	16.1468	+	27.9670i	0.625674	+	1.08370i
$667$	12.4940	−	21.6402i	0.483768	−	0.837911i
$668$	14.0000			0.541676
$669$	−8.37196	+	14.5007i	−0.323679	+	0.560628i
$670$	−15.0586	+	26.0823i	−0.581765	+	1.00765i
$671$	21.3405			0.823841
$672$	−2.15883	+	3.73921i	−0.0832788	+	0.144243i
$673$	−12.0846	−	20.9311i	−0.465825	−	0.806833i	0.533413	−	0.845855i	$-0.320909\pi$
$673$	−12.0846	−	20.9311i	−0.465825	−	0.806833i	−0.999238	+	0.0390217i	$0.987576\pi$
$674$	−1.55280	−	2.68953i	−0.0598117	−	0.103597i
$675$	4.09485			0.157611
$676$		0			0
$677$	−4.91425			−0.188870			−0.0944349	−	0.995531i	$-0.530104\pi$
$677$	−4.91425			−0.188870			−0.0944349	+	0.995531i	$0.530104\pi$
$678$	−7.33489	−	12.7044i	−0.281695	−	0.487910i
$679$	3.72156	+	6.44593i	0.142820	+	0.247372i
$680$	−5.66487	+	9.81185i	−0.217238	+	0.376267i
$681$	−2.57194			−0.0985571
$682$	5.23490	−	9.06711i	0.200455	−	0.347198i
$683$	0.982779	−	1.70222i	0.0376050	−	0.0651337i	−0.846610	−	0.532213i	$-0.821360\pi$
$683$	0.982779	−	1.70222i	0.0376050	−	0.0651337i	0.884215	+	0.467079i	$0.154694\pi$
$684$	−20.6015			−0.787717
$685$	24.1685	−	41.8611i	0.923432	−	1.59943i
$686$	9.16421	+	15.8729i	0.349891	+	0.606029i
$687$	30.1715	+	52.2586i	1.15111	+	1.99379i
$688$	11.3448			0.432517
$689$		0			0
$690$	−18.2198			−0.693617
$691$	−12.7538	−	22.0903i	−0.485179	−	0.840355i	0.514676	−	0.857385i	$-0.327912\pi$
$691$	−12.7538	−	22.0903i	−0.485179	−	0.840355i	−0.999855	+	0.0170298i	$0.994579\pi$
$692$	2.10992	+	3.65448i	0.0802070	+	0.138923i
$693$	6.97823	−	12.0866i	0.265081	−	0.459134i
$694$	−17.9758			−0.682353
$695$	−23.1769	+	40.1435i	−0.879149	+	1.52273i
$696$	−12.3937	+	21.4666i	−0.469783	+	0.813688i
$697$	15.7493			0.596547
$698$	7.58211	−	13.1326i	0.286987	−	0.497076i
$699$	−4.02499	−	6.97149i	−0.152239	−	0.263686i
$700$	0.978230	+	1.69434i	0.0369736	+	0.0640402i
$701$	−41.8491			−1.58062			−0.790308	−	0.612709i	$-0.790080\pi$
$701$	−41.8491			−1.58062			−0.790308	+	0.612709i	$0.790080\pi$
$702$		0			0
$703$	−36.8853			−1.39116
$704$	−1.02446	−	1.77441i	−0.0386107	−	0.0668758i
$705$	−0.737955	−	1.27818i	−0.0277930	−	0.0481389i
$706$	−1.65010	+	2.85806i	−0.0621025	+	0.107565i
$707$	−11.9129			−0.448031
$708$	5.48643	−	9.50277i	0.206193	−	0.357136i
$709$	−16.6528	+	28.8435i	−0.625409	+	1.08324i	0.363053	+	0.931769i	$0.381734\pi$
$709$	−16.6528	+	28.8435i	−0.625409	+	1.08324i	−0.988462	+	0.151471i	$0.951599\pi$
$710$	−3.20775			−0.120385
$711$	11.3177	−	19.6028i	0.424446	−	0.735161i
$712$	−8.28501	−	14.3501i	−0.310494	−	0.537791i
$713$	−6.93362	−	12.0094i	−0.259666	−	0.449755i
$714$	−19.6146			−0.734059
$715$		0			0
$716$	15.8291			0.591561
$717$	14.9801	+	25.9464i	0.559444	+	0.968985i
$718$	9.44504	+	16.3593i	0.352486	+	0.610523i
$719$	−3.18598	+	5.51828i	−0.118817	+	0.205797i	−0.919299	−	0.393560i	$-0.871244\pi$
$719$	−3.18598	+	5.51828i	−0.118817	+	0.205797i	0.800482	+	0.599357i	$0.204577\pi$
$720$	10.5918			0.394733
$721$	0.415502	−	0.719670i	0.0154741	−	0.0268019i
$722$	2.26540	−	3.92378i	0.0843094	−	0.146028i
$723$	14.0194			0.521386
$724$	7.65279	−	13.2550i	0.284414	−	0.492619i
$725$	5.61596	+	9.72712i	0.208571	+	0.361256i
$726$	−9.15548	−	15.8578i	−0.339792	−	0.588537i
$727$	23.7995			0.882676			0.441338	−	0.897341i	$-0.354504\pi$
$727$	23.7995			0.882676			0.441338	+	0.897341i	$0.354504\pi$
$728$		0			0
$729$	−42.8418			−1.58673
$730$	4.52111	+	7.83079i	0.167334	+	0.289830i
$731$	25.7690	+	44.6333i	0.953103	+	1.65082i
$732$	−14.0194	+	24.2823i	−0.518171	+	0.897499i
$733$	−27.4142			−1.01257			−0.506283	−	0.862368i	$-0.668981\pi$
$733$	−27.4142			−1.01257			−0.506283	+	0.862368i	$0.668981\pi$
$734$	−0.0978347	+	0.169455i	−0.00361114	+	0.00625468i
$735$	14.8629	−	25.7434i	0.548228	−	0.949558i
$736$	−2.71379			−0.100032
$737$	12.3714	−	21.4279i	0.455707	−	0.789308i
$738$	−7.36174	−	12.7509i	−0.270989	−	0.469367i
$739$	−17.6637	−	30.5944i	−0.649769	−	1.12543i	−0.983178	−	0.182650i	$-0.941532\pi$
$739$	−17.6637	−	30.5944i	−0.649769	−	1.12543i	0.333409	−	0.942782i	$-0.391801\pi$
$740$	18.9638			0.697122
$741$		0			0
$742$	−4.35258			−0.159788
$743$	11.9879	+	20.7637i	0.439794	+	0.761746i	0.997673	−	0.0681765i	$-0.0217181\pi$
$743$	11.9879	+	20.7637i	0.439794	+	0.761746i	−0.557879	+	0.829922i	$0.688385\pi$
$744$	6.87800	+	11.9130i	0.252160	+	0.436754i
$745$	4.56166	−	7.90103i	0.167126	−	0.289471i
$746$	10.7681			0.394248
$747$	−10.3007	+	17.8414i	−0.376884	+	0.652783i
$748$	4.65399	−	8.06095i	0.170167	−	0.294737i
$749$	−5.63017			−0.205722
$750$	−12.6896	+	21.9791i	−0.463360	+	0.802563i
$751$	12.4330	+	21.5345i	0.453685	+	0.785806i	0.998612	−	0.0526781i	$-0.0167757\pi$
$751$	12.4330	+	21.5345i	0.453685	+	0.785806i	−0.544926	+	0.838484i	$0.683442\pi$
$752$	−0.109916	−	0.190381i	−0.00400823	−	0.00694246i
$753$	−61.0954			−2.22644
$754$		0			0
$755$	36.3913			1.32442
$756$	2.69202	+	4.66272i	0.0979079	+	0.169581i
$757$	−2.46681	−	4.27264i	−0.0896578	−	0.155292i	0.817709	−	0.575632i	$-0.195244\pi$
$757$	−2.46681	−	4.27264i	−0.0896578	−	0.155292i	−0.907367	+	0.420340i	$0.861911\pi$
$758$	13.9813	−	24.2164i	0.507825	−	0.879579i
$759$	14.9685			0.543324
$760$	−6.04892	+	10.4770i	−0.219417	+	0.380042i
$761$	7.50335	−	12.9962i	0.271996	−	0.471111i	−0.697377	−	0.716705i	$-0.745649\pi$
$761$	7.50335	−	12.9962i	0.271996	−	0.471111i	0.969373	+	0.245593i	$0.0789828\pi$
$762$	16.6789			0.604212
$763$	−2.71379	+	4.70043i	−0.0982459	+	0.170167i
$764$	−1.80194	−	3.12105i	−0.0651918	−	0.112916i
$765$	24.0586	+	41.6707i	0.869841	+	1.50661i
$766$	−32.8310			−1.18623
$767$		0			0
$768$	2.69202			0.0971400
$769$	−11.1320	−	19.2812i	−0.401430	−	0.695296i	0.592469	−	0.805593i	$-0.298153\pi$
$769$	−11.1320	−	19.2812i	−0.401430	−	0.695296i	−0.993899	+	0.110297i	$0.964820\pi$
$770$	−4.09783	−	7.09766i	−0.147676	−	0.255782i
$771$	−14.0397	+	24.3174i	−0.505626	+	0.875770i
$772$	−11.2228			−0.403918
$773$	5.86831	−	10.1642i	0.211069	−	0.365581i	−0.740981	−	0.671526i	$-0.765639\pi$
$773$	5.86831	−	10.1642i	0.211069	−	0.365581i	0.952049	+	0.305945i	$0.0989723\pi$
$774$	24.0906	−	41.7261i	0.865919	−	1.49982i
$775$	6.23324			0.223905
$776$	2.32036	−	4.01897i	0.0832959	−	0.144273i
$777$	16.4155	+	28.4325i	0.588903	+	1.02001i
$778$	4.45473	+	7.71582i	0.159710	+	0.276626i
$779$	16.8170			0.602532
$780$		0			0
$781$	2.63533			0.0942997
$782$	−6.16421	−	10.6767i	−0.220432	−	0.381799i
$783$	15.4547	+	26.7684i	0.552307	+	0.956624i
$784$	2.21379	−	3.83440i	0.0790640	−	0.136943i
$785$	53.8792			1.92303
$786$	−5.56853	+	9.64498i	−0.198623	+	0.344025i
$787$	7.47488	−	12.9469i	0.266451	−	0.461506i	−0.701492	−	0.712677i	$-0.747482\pi$
$787$	7.47488	−	12.9469i	0.266451	−	0.461506i	0.967943	+	0.251171i	$0.0808157\pi$
$788$	23.1051			0.823086
$789$	9.57002	−	16.5758i	0.340702	−	0.590113i
$790$	−6.64609	−	11.5114i	−0.236457	−	0.409556i
$791$	−4.37004	−	7.56914i	−0.155381	−	0.269127i
$792$	−8.70171			−0.309202
$793$		0			0
$794$	−11.7888			−0.418369
$795$	9.10992	+	15.7788i	0.323095	+	0.559618i
$796$	−10.6310	−	18.4135i	−0.376807	−	0.652648i
$797$	−17.5864	+	30.4606i	−0.622943	+	1.07897i	0.365992	+	0.930618i	$0.380730\pi$
$797$	−17.5864	+	30.4606i	−0.622943	+	1.07897i	−0.988935	+	0.148351i	$0.952604\pi$
$798$	−20.9444			−0.741423
$799$	0.499336	−	0.864875i	0.0176652	−	0.0305971i
$800$	0.609916	−	1.05641i	0.0215638	−	0.0373496i
$801$	−70.3726			−2.48649
$802$	1.60656	−	2.78265i	0.0567297	−	0.0982588i
$803$	−3.71432	−	6.43340i	−0.131076	−	0.227030i
$804$	16.2545	+	28.1536i	0.573252	+	0.992902i
$805$	−10.8552			−0.382594
$806$		0			0
$807$	5.44909			0.191817
$808$	3.71379	+	6.43248i	0.130651	+	0.226294i
$809$	−21.4743	−	37.1947i	−0.754998	−	1.30769i	−0.945375	−	0.325984i	$-0.894305\pi$
$809$	−21.4743	−	37.1947i	−0.754998	−	1.30769i	0.190378	−	0.981711i	$-0.439029\pi$
$810$	−4.61894	+	8.00024i	−0.162293	+	0.281100i
$811$	−20.4644			−0.718603			−0.359301	−	0.933222i	$-0.616985\pi$
$811$	−20.4644			−0.718603			−0.359301	+	0.933222i	$0.616985\pi$
$812$	−7.38404	+	12.7895i	−0.259129	+	0.448825i
$813$	21.4892	−	37.2203i	0.753658	−	1.30537i
$814$	−15.5797			−0.546069
$815$	−16.9705	+	29.3937i	−0.594449	+	1.02962i
$816$	6.11476	+	10.5911i	0.214059	+	0.370762i
$817$	27.5160	+	47.6592i	0.962664	+	1.66738i
$818$	−12.0218			−0.420331
$819$		0			0
$820$	−8.64609			−0.301934
$821$	18.4993	+	32.0418i	0.645631	+	1.11827i	0.984155	+	0.177308i	$0.0567390\pi$
$821$	18.4993	+	32.0418i	0.645631	+	1.11827i	−0.338524	+	0.940958i	$0.609928\pi$
$822$	−26.0879	−	45.1856i	−0.909920	−	1.57603i
$823$	−4.63773	+	8.03278i	−0.161661	+	0.280005i	−0.935465	−	0.353421i	$-0.885018\pi$
$823$	−4.63773	+	8.03278i	−0.161661	+	0.280005i	0.773804	+	0.633426i	$0.218352\pi$
$824$	−0.518122			−0.0180496
$825$	−3.36413	+	5.82685i	−0.117124	+	0.202865i
$826$	3.26875	−	5.66164i	0.113734	−	0.196994i
$827$	6.05669			0.210612			0.105306	−	0.994440i	$-0.466418\pi$
$827$	6.05669			0.210612			0.105306	+	0.994440i	$0.466418\pi$
$828$	−5.76271	+	9.98130i	−0.200268	+	0.346874i
$829$	−4.97046	−	8.60909i	−0.172631	−	0.299006i	0.766708	−	0.641996i	$-0.221894\pi$
$829$	−4.97046	−	8.60909i	−0.172631	−	0.299006i	−0.939339	+	0.342990i	$0.888560\pi$
$830$	6.04892	+	10.4770i	0.209961	+	0.363663i
$831$	36.8853			1.27954
$832$		0			0
$833$	20.1140			0.696908
$834$	25.0175	+	43.3316i	0.866286	+	1.50045i
$835$	−17.4577	−	30.2376i	−0.604149	−	1.04642i
$836$	4.96950	−	8.60743i	0.171874	−	0.297694i
$837$	17.1535			0.592910
$838$	−1.78017	+	3.08334i	−0.0614949	+	0.106512i
$839$	−17.2349	+	29.8517i	−0.595015	+	1.03060i	0.398530	+	0.917155i	$0.369520\pi$
$839$	−17.2349	+	29.8517i	−0.595015	+	1.03060i	−0.993545	+	0.113441i	$0.963813\pi$
$840$	10.7681			0.371534
$841$	−27.8913	+	48.3092i	−0.961770	+	1.66584i
$842$	−0.643104	−	1.11389i	−0.0221628	−	0.0383872i
$843$	−20.4626	−	35.4422i	−0.704768	−	1.22069i
$844$	1.70709			0.0587604
$845$		0			0
$846$	−0.933624			−0.0320987
$847$	−5.45473	−	9.44787i	−0.187427	−	0.324633i
$848$	1.35690	+	2.35021i	0.0465960	+	0.0807066i
$849$	−27.7371	+	48.0420i	−0.951933	+	1.64880i
$850$	5.54155			0.190074
$851$	−10.3177	+	17.8707i	−0.353685	+	0.612601i
$852$	−1.73125	+	2.99861i	−0.0593117	+	0.102731i
$853$	22.1521			0.758474			0.379237	−	0.925299i	$-0.376186\pi$
$853$	22.1521			0.758474			0.379237	+	0.925299i	$0.376186\pi$
$854$	−8.35258	+	14.4671i	−0.285820	+	0.495054i
$855$	25.6896	+	44.4957i	0.878567	+	1.52172i
$856$	1.75518	+	3.04005i	0.0599907	+	0.103907i
$857$	−30.5187			−1.04250			−0.521250	−	0.853404i	$-0.674534\pi$
$857$	−30.5187			−1.04250			−0.521250	+	0.853404i	$0.674534\pi$
$858$		0			0
$859$	−20.9071			−0.713340			−0.356670	−	0.934230i	$-0.616088\pi$
$859$	−20.9071			−0.713340			−0.356670	+	0.934230i	$0.616088\pi$
$860$	−14.1468	−	24.5029i	−0.482400	−	0.835542i
$861$	−7.48427	−	12.9631i	−0.255063	−	0.441783i
$862$	13.4940	−	23.3722i	0.459606	−	0.796061i
$863$	−55.6969			−1.89595			−0.947973	−	0.318352i	$-0.896871\pi$
$863$	−55.6969			−1.89595			−0.947973	+	0.318352i	$0.896871\pi$
$864$	1.67845	−	2.90716i	0.0571020	−	0.0989035i
$865$	5.26205	−	9.11413i	0.178915	−	0.309890i
$866$	16.0170			0.544279
$867$	−4.89642	+	8.48085i	−0.166291	+	0.288025i
$868$	4.09783	+	7.09766i	0.139090	+	0.240910i
$869$	5.46011	+	9.45718i	0.185221	+	0.320813i
$870$	61.8189			2.09586
$871$		0			0
$872$	3.38404			0.114598
$873$	−9.85450	−	17.0685i	−0.333524	−	0.577681i
$874$	−6.58211	−	11.4005i	−0.222643	−	0.385629i
$875$	−7.56033	+	13.0949i	−0.255586	+	0.442688i
$876$	9.76032			0.329771
$877$	16.3961	−	28.3989i	0.553658	−	0.958963i	−0.444349	−	0.895854i	$-0.646565\pi$
$877$	16.3961	−	28.3989i	0.553658	−	0.958963i	0.998007	−	0.0631096i	$-0.0201018\pi$
$878$	−18.5700	+	32.1642i	−0.626708	+	1.08549i
$879$	5.85862			0.197607
$880$	−2.55496	+	4.42532i	−0.0861276	+	0.149177i
$881$	−11.2051	−	19.4077i	−0.377508	−	0.653863i	0.613191	−	0.789935i	$-0.289886\pi$
$881$	−11.2051	−	19.4077i	−0.377508	−	0.653863i	−0.990699	+	0.136071i	$0.956552\pi$
$882$	−9.40193	−	16.2846i	−0.316579	−	0.548332i
$883$	−38.9670			−1.31134			−0.655672	−	0.755046i	$-0.727615\pi$
$883$	−38.9670			−1.31134			−0.655672	+	0.755046i	$0.727615\pi$
$884$		0			0
$885$	−27.3658			−0.919893
$886$	−20.6042	−	35.6875i	−0.692211	−	1.19894i
$887$	17.4373	+	30.2022i	0.585486	+	1.01409i	0.994815	+	0.101705i	$0.0324297\pi$
$887$	17.4373	+	30.2022i	0.585486	+	1.01409i	−0.409328	+	0.912387i	$0.634237\pi$
$888$	10.2349	−	17.7274i	0.343461	−	0.594891i
$889$	9.93708			0.333279
$890$	−20.6625	+	35.7885i	−0.692608	+	1.19963i
$891$	3.79470	−	6.57261i	0.127127	−	0.220191i
$892$	6.21983			0.208255
$893$	0.533188	−	0.923508i	0.0178425	−	0.0309040i
$894$	−4.92394	−	8.52851i	−0.164681	−	0.285236i
$895$	−19.7385	−	34.1882i	−0.659787	−	1.14278i
$896$	1.60388			0.0535817
$897$		0			0
$898$	10.1263			0.337919
$899$	23.5254	+	40.7472i	0.784617	+	1.35900i
$900$	−2.59030	−	4.48653i	−0.0863434	−	0.149551i
$901$	−6.16421	+	10.6767i	−0.205360	+	0.355693i
$902$	7.10321			0.236511
$903$	24.4916	−	42.4206i	0.815028	−	1.41167i
$904$	−2.72468	+	4.71928i	−0.0906214	+	0.156961i
$905$	−38.1715			−1.26886
$906$	19.6407	−	34.0187i	0.652519	−	1.13020i
$907$	−7.56584	−	13.1044i	−0.251220	−	0.435125i	0.712642	−	0.701528i	$-0.247498\pi$
$907$	−7.56584	−	13.1044i	−0.251220	−	0.435125i	−0.963862	+	0.266402i	$0.914165\pi$
$908$	0.477697	+	0.827396i	0.0158529	+	0.0274581i
$909$	31.5448			1.04627
$910$		0			0
$911$	23.0810			0.764707			0.382353	−	0.924016i	$-0.375114\pi$
$911$	23.0810			0.764707			0.382353	+	0.924016i	$0.375114\pi$
$912$	6.52930	+	11.3091i	0.216207	+	0.374481i
$913$	−4.96950	−	8.60743i	−0.164466	−	0.284864i
$914$	10.8780	−	18.8413i	0.359812	−	0.623213i
$915$	69.9275			2.31173
$916$	11.2078	−	19.4124i	0.370315	−	0.641404i
$917$	−3.31767	+	5.74637i	−0.109559	+	0.189762i
$918$	15.2500			0.503324
$919$	19.9638	−	34.5782i	0.658544	−	1.14063i	−0.322449	−	0.946587i	$-0.604506\pi$
$919$	19.9638	−	34.5782i	0.658544	−	1.14063i	0.980993	−	0.194044i	$-0.0621605\pi$
$920$	3.38404	+	5.86133i	0.111569	+	0.193242i
$921$	−22.8992	−	39.6626i	−0.754556	−	1.30693i
$922$	38.5676			1.27016
$923$		0			0
$924$	−8.84654			−0.291030
$925$	−4.63773	−	8.03278i	−0.152488	−	0.264116i
$926$	−16.5036	−	28.5852i	−0.542344	−	0.939367i
$927$	−1.10023	+	1.90565i	−0.0361362	+	0.0625898i
$928$	9.20775			0.302259
$929$	22.5886	−	39.1246i	0.741107	−	1.28364i	−0.210885	−	0.977511i	$-0.567634\pi$
$929$	22.5886	−	39.1246i	0.741107	−	1.28364i	0.951992	−	0.306124i	$-0.0990322\pi$
$930$	17.1535	−	29.7107i	0.562484	−	0.974251i
$931$	21.4776			0.703899
$932$	−1.49516	+	2.58969i	−0.0489755	+	0.0848280i
$933$	6.34481	+	10.9895i	0.207720	+	0.359781i
$934$	3.26995	+	5.66371i	0.106996	+	0.185322i
$935$	−23.2137			−0.759170
$936$		0			0
$937$	29.0901			0.950331			0.475165	−	0.879896i	$-0.342388\pi$
$937$	29.0901			0.950331			0.475165	+	0.879896i	$0.342388\pi$
$938$	9.68425	+	16.7736i	0.316202	+	0.547678i
$939$	−2.25720	−	3.90959i	−0.0736610	−	0.127585i
$940$	−0.274127	+	0.474801i	−0.00894103	+	0.0154863i
$941$	−26.1220			−0.851553			−0.425776	−	0.904828i	$-0.639999\pi$
$941$	−26.1220			−0.851553			−0.425776	+	0.904828i	$0.639999\pi$
$942$	29.0790	−	50.3664i	0.947447	−	1.64103i
$943$	4.70410	−	8.14775i	0.153187	−	0.265327i
$944$	−4.07606			−0.132665
$945$	6.71379	−	11.6286i	0.218400	−	0.378279i
$946$	11.6223	+	20.1304i	0.377873	+	0.654496i
$947$	−21.3349	−	36.9531i	−0.693291	−	1.20081i	−0.970754	−	0.240078i	$-0.922827\pi$
$947$	−21.3349	−	36.9531i	−0.693291	−	1.20081i	0.277463	−	0.960736i	$-0.410506\pi$
$948$	−14.3478			−0.465995
$949$		0			0
$950$	5.91723			0.191980
$951$	−39.2228	−	67.9359i	−1.27189	−	2.20297i
$952$	3.64310	+	6.31004i	0.118074	+	0.204510i
$953$	14.9519	−	25.8975i	0.484340	−	0.838901i	−0.515498	−	0.856891i	$-0.672393\pi$
$953$	14.9519	−	25.8975i	0.484340	−	0.838901i	0.999838	+	0.0179893i	$0.00572648\pi$
$954$	11.5254			0.373149
$955$	−4.49396	+	7.78377i	−0.145421	+	0.251877i
$956$	5.56465	−	9.63825i	0.179974	−	0.311723i
$957$	−50.7875			−1.64173
$958$	4.15346	−	7.19400i	0.134192	−	0.232428i
$959$	−15.5429	−	26.9211i	−0.501906	−	0.869326i
$960$	−3.35690	−	5.81431i	−0.108343	−	0.187656i
$961$	−4.88876			−0.157702
$962$		0			0
$963$	14.9084			0.480416
$964$	−2.60388	−	4.51004i	−0.0838652	−	0.145259i
$965$	13.9946	+	24.2394i	0.450503	+	0.780294i
$966$	−5.85862	+	10.1474i	−0.188498	+	0.326488i
$967$	−5.16900			−0.166224			−0.0831119	−	0.996540i	$-0.526486\pi$
$967$	−5.16900			−0.166224			−0.0831119	+	0.996540i	$0.526486\pi$
$968$	−3.40097	+	5.89065i	−0.109311	+	0.189333i
$969$	−29.6618	+	51.3758i	−0.952875	+	1.65043i
$970$	−11.5737			−0.371611
$971$	−17.9858	+	31.1523i	−0.577191	+	0.999723i	0.418609	+	0.908166i	$0.362518\pi$
$971$	−17.9858	+	31.1523i	−0.577191	+	0.999723i	−0.995800	+	0.0915570i	$0.970816\pi$
$972$	10.0211	+	17.3571i	0.321427	+	0.556728i
$973$	14.9051	+	25.8165i	0.477837	+	0.827638i
$974$	31.6534			1.01424
$975$		0			0
$976$	10.4155			0.333392
$977$	−17.1218	−	29.6558i	−0.547774	−	0.948772i	−0.998427	−	0.0560726i	$-0.982142\pi$
$977$	−17.1218	−	29.6558i	−0.547774	−	0.948772i	0.450653	−	0.892699i	$-0.351191\pi$
$978$	18.3182	+	31.7281i	0.585751	+	1.01455i
$979$	16.9753	−	29.4021i	0.542533	−	0.939695i
$980$	−11.0422			−0.352731
$981$	7.18598	−	12.4465i	0.229431	−	0.397386i
$982$	−18.3315	+	31.7512i	−0.584983	+	1.01322i
$983$	−54.8939			−1.75084			−0.875422	−	0.483359i	$-0.839416\pi$
$983$	−54.8939			−1.75084			−0.875422	+	0.483359i	$0.839416\pi$
$984$	−4.66637	+	8.08238i	−0.148758	+	0.257657i
$985$	−28.8116	−	49.9032i	−0.918015	−	1.59005i
$986$	20.9148	+	36.2256i	0.666064	+	1.15366i
$987$	−0.949164			−0.0302122
$988$		0			0
$989$	30.7875			0.978984
$990$	10.8509	+	18.7942i	0.344863	+	0.597320i
$991$	8.33273	+	14.4327i	0.264698	+	0.458470i	0.967484	−	0.252931i	$-0.0813944\pi$
$991$	8.33273	+	14.4327i	0.264698	+	0.458470i	−0.702786	+	0.711401i	$0.748061\pi$
$992$	2.55496	−	4.42532i	0.0811200	−	0.140504i
$993$	23.5388			0.746982
$994$	−1.03146	+	1.78654i	−0.0327159	+	0.0566656i
$995$	−26.5133	+	45.9224i	−0.840529	+	1.45584i
$996$	13.0586			0.413778
$997$	−8.19806	+	14.1995i	−0.259635	+	0.449701i	−0.966144	−	0.258003i	$-0.916936\pi$
$997$	−8.19806	+	14.1995i	−0.259635	+	0.449701i	0.706509	+	0.707704i	$0.250269\pi$
$998$	−14.9460	−	25.8872i	−0.473107	−	0.819446i
$999$	−12.7627	−	22.1057i	−0.403794	−	0.699392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.c.i.315.1		6
13.2	odd	12		338.2.b.d.337.6		6
13.3	even	3		338.2.a.g.1.3	✓	3
13.4	even	6		338.2.c.h.191.1		6
13.5	odd	4		338.2.e.e.23.4		12
13.6	odd	12		338.2.e.e.147.1		12
13.7	odd	12		338.2.e.e.147.4		12
13.8	odd	4		338.2.e.e.23.1		12
13.9	even	3	inner	338.2.c.i.191.1		6
13.10	even	6		338.2.a.h.1.3	yes	3
13.11	odd	12		338.2.b.d.337.3		6
13.12	even	2		338.2.c.h.315.1		6
39.2	even	12		3042.2.b.n.1351.3		6
39.11	even	12		3042.2.b.n.1351.4		6
39.23	odd	6		3042.2.a.z.1.3		3
39.29	odd	6		3042.2.a.bi.1.1		3
52.3	odd	6		2704.2.a.v.1.1		3
52.11	even	12		2704.2.f.m.337.2		6
52.15	even	12		2704.2.f.m.337.1		6
52.23	odd	6		2704.2.a.w.1.1		3
65.29	even	6		8450.2.a.bx.1.1		3
65.49	even	6		8450.2.a.bn.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.2.a.g.1.3	✓	3	13.3	even	3
338.2.a.h.1.3	yes	3	13.10	even	6
338.2.b.d.337.3		6	13.11	odd	12
338.2.b.d.337.6		6	13.2	odd	12
338.2.c.h.191.1		6	13.4	even	6
338.2.c.h.315.1		6	13.12	even	2
338.2.c.i.191.1		6	13.9	even	3	inner
338.2.c.i.315.1		6	1.1	even	1	trivial
338.2.e.e.23.1		12	13.8	odd	4
338.2.e.e.23.4		12	13.5	odd	4
338.2.e.e.147.1		12	13.6	odd	12
338.2.e.e.147.4		12	13.7	odd	12
2704.2.a.v.1.1		3	52.3	odd	6
2704.2.a.w.1.1		3	52.23	odd	6
2704.2.f.m.337.1		6	52.15	even	12
2704.2.f.m.337.2		6	52.11	even	12
3042.2.a.z.1.3		3	39.23	odd	6
3042.2.a.bi.1.1		3	39.29	odd	6
3042.2.b.n.1351.3		6	39.2	even	12
3042.2.b.n.1351.4		6	39.11	even	12
8450.2.a.bn.1.1		3	65.49	even	6
8450.2.a.bx.1.1		3	65.29	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.34601 - 2.33136i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.49396 q^{5} +(1.34601 - 2.33136i) q^{6} +(0.801938 - 1.38900i) q^{7} -1.00000 q^{8} +(-2.12349 + 3.67799i) q^{9} +(1.24698 + 2.15983i) q^{10} +(-1.02446 - 1.77441i) q^{11} +2.69202 q^{12} +1.60388 q^{14} +(-3.35690 - 5.81431i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.27144 - 3.93425i) q^{17} -4.24698 q^{18} +(2.42543 - 4.20096i) q^{19} +(-1.24698 + 2.15983i) q^{20} -4.31767 q^{21} +(1.02446 - 1.77441i) q^{22} +(-1.35690 - 2.35021i) q^{23} +(1.34601 + 2.33136i) q^{24} +1.21983 q^{25} +3.35690 q^{27} +(0.801938 + 1.38900i) q^{28} +(4.60388 + 7.97415i) q^{29} +(3.35690 - 5.81431i) q^{30} +5.10992 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.75786 + 4.77676i) q^{33} +4.54288 q^{34} +(2.00000 - 3.46410i) q^{35} +(-2.12349 - 3.67799i) q^{36} +(-3.80194 - 6.58515i) q^{37} +4.85086 q^{38} -2.49396 q^{40} +(1.73341 + 3.00235i) q^{41} +(-2.15883 - 3.73921i) q^{42} +(-5.67241 + 9.82490i) q^{43} +2.04892 q^{44} +(-5.29590 + 9.17276i) q^{45} +(1.35690 - 2.35021i) q^{46} +0.219833 q^{47} +(-1.34601 + 2.33136i) q^{48} +(2.21379 + 3.83440i) q^{49} +(0.609916 + 1.05641i) q^{50} -12.2295 q^{51} -2.71379 q^{53} +(1.67845 + 2.90716i) q^{54} +(-2.55496 - 4.42532i) q^{55} +(-0.801938 + 1.38900i) q^{56} -13.0586 q^{57} +(-4.60388 + 7.97415i) q^{58} +(2.03803 - 3.52998i) q^{59} +6.71379 q^{60} +(-5.20775 + 9.02009i) q^{61} +(2.55496 + 4.42532i) q^{62} +(3.40581 + 5.89904i) q^{63} +1.00000 q^{64} -5.51573 q^{66} +(6.03803 + 10.4582i) q^{67} +(2.27144 + 3.93425i) q^{68} +(-3.65279 + 6.32682i) q^{69} +4.00000 q^{70} +(-0.643104 + 1.11389i) q^{71} +(2.12349 - 3.67799i) q^{72} +3.62565 q^{73} +(3.80194 - 6.58515i) q^{74} +(-1.64191 - 2.84387i) q^{75} +(2.42543 + 4.20096i) q^{76} -3.28621 q^{77} -5.32975 q^{79} +(-1.24698 - 2.15983i) q^{80} +(1.85205 + 3.20785i) q^{81} +(-1.73341 + 3.00235i) q^{82} +4.85086 q^{83} +(2.15883 - 3.73921i) q^{84} +(5.66487 - 9.81185i) q^{85} -11.3448 q^{86} +(12.3937 - 21.4666i) q^{87} +(1.02446 + 1.77441i) q^{88} +(8.28501 + 14.3501i) q^{89} -10.5918 q^{90} +2.71379 q^{92} +(-6.87800 - 11.9130i) q^{93} +(0.109916 + 0.190381i) q^{94} +(6.04892 - 10.4770i) q^{95} -2.69202 q^{96} +(-2.32036 + 4.01897i) q^{97} +(-2.21379 + 3.83440i) q^{98} +8.70171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 4 q^{5} + 3 q^{6} - 4 q^{7} - 6 q^{8} - 8 q^{9} - 2 q^{10} + 3 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} - 3 q^{16} - 5 q^{17} - 16 q^{18} + q^{19} + 2 q^{20} + 8 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 4 * q^5 + 3 * q^6 - 4 * q^7 - 6 * q^8 - 8 * q^9 - 2 * q^10 + 3 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 - 3 * q^16 - 5 * q^17 - 16 * q^18 + q^19 + 2 * q^20 + 8 * q^21 - 3 * q^22 + 3 * q^24 + 10 * q^25 + 12 * q^27 - 4 * q^28 + 10 * q^29 + 12 * q^30 + 32 * q^31 + 3 * q^32 - 4 * q^33 - 10 * q^34 + 12 * q^35 - 8 * q^36 - 14 * q^37 + 2 * q^38 + 4 * q^40 + 7 * q^41 + 4 * q^42 - 11 * q^43 - 6 * q^44 - 4 * q^45 + 4 * q^47 - 3 * q^48 - 3 * q^49 + 5 * q^50 - 32 * q^51 + 6 * q^54 - 16 * q^55 + 4 * q^56 - 16 * q^57 - 10 * q^58 - 3 * q^59 + 24 * q^60 + 4 * q^61 + 16 * q^62 - 6 * q^63 + 6 * q^64 - 8 * q^66 + 21 * q^67 - 5 * q^68 + 14 * q^69 + 24 * q^70 - 12 * q^71 + 8 * q^72 - 2 * q^73 + 14 * q^74 + 23 * q^75 + q^76 - 36 * q^77 - 36 * q^79 + 2 * q^80 + 25 * q^81 - 7 * q^82 + 2 * q^83 - 4 * q^84 + 36 * q^85 - 22 * q^86 + 10 * q^87 - 3 * q^88 + 25 * q^89 - 8 * q^90 - 2 * q^93 + 2 * q^94 + 18 * q^95 - 6 * q^96 + 23 * q^97 + 3 * q^98 - 2 * q^99

Introduction

L-functions

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