LMFDB - Embedded newform 760.2.bx.a.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(59,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 9, 1]))

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

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

chi := DirichletCharacter("760.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.bx (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{18}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	760.59
Dual form			760.2.bx.a.219.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(2.10122 - 0.764780i) q^{5} +(1.61753 + 2.80164i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})$	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(2.10122 - 0.764780i) q^{5} +(1.61753 + 2.80164i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.520945 - 2.95442i) q^{9} +(3.11424 - 0.549124i) q^{10} +(-3.28788 + 5.69478i) q^{11} +(-0.671428 - 0.800176i) q^{13} +(1.56476 + 4.29915i) q^{14} +(3.06418 + 2.57115i) q^{16} -4.24264i q^{18} +(3.63518 - 2.40530i) q^{19} +4.47214 q^{20} +(-5.97763 + 7.12386i) q^{22} +(-8.34455 - 3.03717i) q^{23} +(3.83022 - 3.21394i) q^{25} +(-0.738613 - 1.27931i) q^{26} +(1.12352 + 6.37181i) q^{28} +(3.63616 + 4.33340i) q^{32} +(5.54141 + 4.64980i) q^{35} +(1.04189 - 5.90885i) q^{36} -11.5414i q^{37} +(5.65350 - 2.45722i) q^{38} +(6.22847 + 1.09825i) q^{40} +(-2.67792 + 3.19143i) q^{41} +(-10.0747 + 8.45364i) q^{44} +(-3.35410 - 5.80948i) q^{45} +(-10.8758 - 6.27917i) q^{46} +(-1.59022 - 9.01857i) q^{47} +(-1.73279 + 3.00128i) q^{49} +(6.12372 - 3.53553i) q^{50} +(-0.714519 - 1.96312i) q^{52} +(-3.38750 + 9.30708i) q^{53} +(-2.55330 + 14.4805i) q^{55} +9.15011i q^{56} +(15.0544 + 2.65450i) q^{59} +(7.43459 - 6.23836i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-2.02277 - 1.16785i) q^{65} +(6.57581 + 7.83674i) q^{70} +(2.90214 - 7.97356i) q^{72} +(2.83430 - 16.0741i) q^{74} +(8.47723 - 2.03387i) q^{76} -21.2730 q^{77} +(8.40487 + 3.05912i) q^{80} +(-8.45723 + 3.07818i) q^{81} +(-4.51336 + 3.78716i) q^{82} +(-16.1073 + 9.29954i) q^{88} +(-0.444008 - 0.529149i) q^{89} +(-3.24469 - 8.91471i) q^{90} +(1.15575 - 3.17541i) q^{91} +(-13.6051 - 11.4160i) q^{92} -12.9509i q^{94} +(5.79878 - 7.83417i) q^{95} +(-3.15034 + 3.75443i) q^{98} +(18.5376 + 6.74713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 48 q^{14} + 48 q^{26} + 60 q^{35} - 12 q^{41} + 24 q^{44} - 84 q^{49} + 96 q^{64} - 180 q^{65} - 96 q^{74} + 72 q^{76} + 168 q^{89} + 96 q^{91} + 36 q^{99}+O(q^{100}) $ 24 * q - 48 * q^14 + 48 * q^26 + 60 * q^35 - 12 * q^41 + 24 * q^44 - 84 * q^49 + 96 * q^64 - 180 * q^65 - 96 * q^74 + 72 * q^76 + 168 * q^89 + 96 * q^91 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.39273	+	0.245576i	0.984808	+	0.173648i
$2$	1.39273	+	0.245576i	0.984808	+	0.173648i
$3$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$3$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$4$	1.87939	+	0.684040i	0.939693	+	0.342020i
$5$	2.10122	−	0.764780i	0.939693	−	0.342020i
$5$	2.10122	−	0.764780i	0.939693	−	0.342020i
$6$		0			0
$7$	1.61753	+	2.80164i	0.611368	+	1.05892i	0.991010	+	0.133787i	$0.0427137\pi$
$7$	1.61753	+	2.80164i	0.611368	+	1.05892i	−0.379642	+	0.925133i	$0.623953\pi$
$8$	2.44949	+	1.41421i	0.866025	+	0.500000i
$9$	−0.520945	−	2.95442i	−0.173648	−	0.984808i
$10$	3.11424	−	0.549124i	0.984808	−	0.173648i
$11$	−3.28788	+	5.69478i	−0.991334	+	1.71704i	−0.381903	+	0.924202i	$0.624731\pi$
$11$	−3.28788	+	5.69478i	−0.991334	+	1.71704i	−0.609431	+	0.792839i	$0.708602\pi$
$12$		0			0
$13$	−0.671428	−	0.800176i	−0.186221	−	0.221929i	0.664855	−	0.746973i	$-0.268493\pi$
$13$	−0.671428	−	0.800176i	−0.186221	−	0.221929i	−0.851075	+	0.525044i	$0.824049\pi$
$14$	1.56476	+	4.29915i	0.418200	+	1.14900i
$15$		0			0
$16$	3.06418	+	2.57115i	0.766044	+	0.642788i
$17$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$17$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$18$		−	4.24264i		−	1.00000i
$19$	3.63518	−	2.40530i	0.833968	−	0.551814i
$19$	3.63518	−	2.40530i	0.833968	−	0.551814i
$20$	4.47214			1.00000
$21$		0			0
$22$	−5.97763	+	7.12386i	−1.27443	+	1.51881i
$23$	−8.34455	−	3.03717i	−1.73996	−	0.633294i	−0.740703	−	0.671833i	$-0.765507\pi$
$23$	−8.34455	−	3.03717i	−1.73996	−	0.633294i	−0.999257	+	0.0385394i	$0.987729\pi$
$24$		0			0
$25$	3.83022	−	3.21394i	0.766044	−	0.642788i
$26$	−0.738613	−	1.27931i	−0.144854	−	0.250894i
$27$		0			0
$28$	1.12352	+	6.37181i	0.212326	+	1.20416i
$29$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$29$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	3.63616	+	4.33340i	0.642788	+	0.766044i
$33$		0			0
$34$		0			0
$35$	5.54141	+	4.64980i	0.936670	+	0.785959i
$36$	1.04189	−	5.90885i	0.173648	−	0.984808i
$37$		−	11.5414i		−	1.89740i	−0.316177	−	0.948700i	$-0.602399\pi$
$37$		−	11.5414i		−	1.89740i	0.316177	−	0.948700i	$-0.397601\pi$
$38$	5.65350	−	2.45722i	0.917119	−	0.398613i
$39$		0			0
$40$	6.22847	+	1.09825i	0.984808	+	0.173648i
$41$	−2.67792	+	3.19143i	−0.418221	+	0.498417i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−2.67792	+	3.19143i	−0.418221	+	0.498417i	0.515264	+	0.857031i	$0.327694\pi$
$42$		0			0
$43$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$43$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$44$	−10.0747	+	8.45364i	−1.51881	+	1.27443i
$45$	−3.35410	−	5.80948i	−0.500000	−	0.866025i
$46$	−10.8758	−	6.27917i	−1.60356	−	0.925813i
$47$	−1.59022	−	9.01857i	−0.231957	−	1.31549i	−0.848928	−	0.528508i	$-0.822752\pi$
$47$	−1.59022	−	9.01857i	−0.231957	−	1.31549i	0.616971	−	0.786986i	$-0.288359\pi$
$48$		0			0
$49$	−1.73279	+	3.00128i	−0.247541	+	0.428754i
$50$	6.12372	−	3.53553i	0.866025	−	0.500000i
$51$		0			0
$52$	−0.714519	−	1.96312i	−0.0990859	−	0.272236i
$53$	−3.38750	+	9.30708i	−0.465309	+	1.27843i	0.456134	+	0.889911i	$0.349234\pi$
$53$	−3.38750	+	9.30708i	−0.465309	+	1.27843i	−0.921443	+	0.388514i	$0.872988\pi$
$54$		0			0
$55$	−2.55330	+	14.4805i	−0.344287	+	1.95255i
$56$			9.15011i			1.22274i
$57$		0			0
$58$		0			0
$59$	15.0544	+	2.65450i	1.95992	+	0.345586i	0.997170	+	0.0751747i	$0.0239515\pi$
$59$	15.0544	+	2.65450i	1.95992	+	0.345586i	0.962745	+	0.270411i	$0.0871597\pi$
$60$		0			0
$61$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$61$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$62$		0			0
$63$	7.43459	−	6.23836i	0.936670	−	0.785959i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	−2.02277	−	1.16785i	−0.250894	−	0.144854i
$66$		0			0
$67$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$67$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$68$		0			0
$69$		0			0
$70$	6.57581	+	7.83674i	0.785959	+	0.936670i
$71$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$71$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$72$	2.90214	−	7.97356i	0.342020	−	0.939693i
$73$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$73$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$74$	2.83430	−	16.0741i	0.329480	−	1.86857i
$75$		0			0
$76$	8.47723	−	2.03387i	0.972404	−	0.233301i
$77$	−21.2730			−2.42428
$78$		0			0
$79$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$79$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$80$	8.40487	+	3.05912i	0.939693	+	0.342020i
$81$	−8.45723	+	3.07818i	−0.939693	+	0.342020i
$82$	−4.51336	+	3.78716i	−0.498417	+	0.418221i
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−16.1073	+	9.29954i	−1.71704	+	0.991334i
$89$	−0.444008	−	0.529149i	−0.0470648	−	0.0560896i	0.741999	−	0.670402i	$-0.233878\pi$
$89$	−0.444008	−	0.529149i	−0.0470648	−	0.0560896i	−0.789063	+	0.614312i	$0.789434\pi$
$90$	−3.24469	−	8.91471i	−0.342020	−	0.939693i
$91$	1.15575	−	3.17541i	0.121156	−	0.332873i
$92$	−13.6051	−	11.4160i	−1.41843	−	1.19020i
$93$		0			0
$94$		−	12.9509i		−	1.33579i
$95$	5.79878	−	7.83417i	0.594942	−	0.803769i
$96$		0			0
$97$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$97$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$98$	−3.15034	+	3.75443i	−0.318233	+	0.379255i
$99$	18.5376	+	6.74713i	1.86310	+	0.678113i
$100$	9.39693	−	3.42020i	0.939693	−	0.342020i
$101$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$101$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$102$		0			0
$103$	−17.4370	−	10.0673i	−1.71812	−	0.991957i	−0.922348	−	0.386360i	$-0.873732\pi$
$103$	−17.4370	−	10.0673i	−1.71812	−	0.991957i	−0.795772	−	0.605597i	$-0.792934\pi$
$104$	−0.513035	−	2.90957i	−0.0503072	−	0.285306i
$105$		0			0
$106$	−7.00346	+	12.1303i	−0.680236	+	1.17820i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$109$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$110$	−7.11210	+	19.5403i	−0.678113	+	1.86310i
$111$		0			0
$112$	−2.24705	+	12.7436i	−0.212326	+	1.20416i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−19.8565			−1.85163
$116$		0			0
$117$	−2.01428	+	2.40053i	−0.186221	+	0.221929i
$118$	20.3148	+	7.39398i	1.87013	+	0.680671i
$119$		0			0
$120$		0			0
$121$	−16.1204	−	27.9213i	−1.46549	−	2.53830i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.59017	−	9.68246i	0.500000	−	0.866025i
$126$	11.8863	−	6.86259i	1.05892	−	0.611368i
$127$	−10.6316	−	12.6703i	−0.943404	−	1.12431i	−0.992095	−	0.125491i	$-0.959949\pi$
$127$	−10.6316	−	12.6703i	−0.943404	−	1.12431i	0.0486908	−	0.998814i	$-0.484495\pi$
$128$	3.86952	+	10.6314i	0.342020	+	0.939693i
$129$		0			0
$130$	−2.53038	−	2.12324i	−0.221929	−	0.186221i
$131$	−2.22055	+	12.5934i	−0.194010	+	1.10029i	0.719811	+	0.694170i	$0.244228\pi$
$131$	−2.22055	+	12.5934i	−0.194010	+	1.10029i	−0.913821	+	0.406117i	$0.866883\pi$
$132$		0			0
$133$	12.6188	+	6.29383i	1.09419	+	0.545744i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$137$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$138$		0			0
$139$	−17.9497	+	15.0616i	−1.52247	+	1.27751i	−0.689338	+	0.724440i	$0.742098\pi$
$139$	−17.9497	+	15.0616i	−1.52247	+	1.27751i	−0.833137	+	0.553067i	$0.813457\pi$
$140$	7.23380	+	12.5293i	0.611368	+	1.05892i
$141$		0			0
$142$		0			0
$143$	6.76441	−	1.19275i	0.565668	−	0.0997426i
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	7.89481	−	21.6908i	0.648949	−	1.78297i
$149$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$149$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	12.3059	−	0.750835i	0.998144	−	0.0609008i
$153$		0			0
$154$	−29.6275	−	5.22412i	−2.38745	−	0.420972i
$155$		0			0
$156$		0			0
$157$	−9.26252	+	3.37128i	−0.739229	+	0.269057i	−0.684066	−	0.729420i	$-0.739790\pi$
$157$	−9.26252	+	3.37128i	−0.739229	+	0.269057i	−0.0551630	+	0.998477i	$0.517568\pi$
$158$		0			0
$159$		0			0
$160$	10.9545	+	6.32456i	0.866025	+	0.500000i
$161$	−4.98849	−	28.2911i	−0.393148	−	2.22965i
$162$	−12.5346	+	2.21018i	−0.984808	+	0.173648i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	−7.21592	+	4.16611i	−0.563468	+	0.325319i
$165$		0			0
$166$		0			0
$167$	0.00552937	−	0.0151918i	0.000427875	−	0.00117558i	−0.939478	−	0.342608i	$-0.888690\pi$
$167$	0.00552937	−	0.0151918i	0.000427875	−	0.00117558i	0.939906	+	0.341432i	$0.110912\pi$
$168$		0			0
$169$	2.06796	−	11.7280i	0.159074	−	0.902152i
$170$		0			0
$171$	−9.00000	−	9.48683i	−0.688247	−	0.725476i
$172$		0			0
$173$	9.14234	+	1.61204i	0.695079	+	0.122561i	0.510015	−	0.860165i	$-0.329640\pi$
$173$	9.14234	+	1.61204i	0.695079	+	0.122561i	0.185064	+	0.982727i	$0.440751\pi$
$174$		0			0
$175$	15.1998	+	5.53227i	1.14900	+	0.418200i
$176$	−24.7168	+	8.99618i	−1.86310	+	0.678113i
$177$		0			0
$178$	−0.488437	−	0.845998i	−0.0366099	−	0.0634102i
$179$	10.2776	+	5.93379i	0.768186	+	0.443513i	0.832227	−	0.554435i	$-0.187065\pi$
$179$	10.2776	+	5.93379i	0.768186	+	0.443513i	−0.0640409	+	0.997947i	$0.520399\pi$
$180$	−2.32973	−	13.2126i	−0.173648	−	0.984808i
$181$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$181$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$182$	2.38945	−	4.13865i	0.177118	−	0.306777i
$183$		0			0
$184$	−16.1447	−	19.2405i	−1.19020	−	1.41843i
$185$	−8.82666	−	24.2511i	−0.648949	−	1.78297i
$186$		0			0
$187$		0			0
$188$	3.18043	−	18.0371i	0.231957	−	1.31549i
$189$		0			0
$190$	10.0000	−	9.48683i	0.725476	−	0.688247i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$193$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$194$		0			0
$195$		0			0
$196$	−5.30957	+	4.45526i	−0.379255	+	0.318233i
$197$	10.2978	+	17.8363i	0.733689	+	1.27079i	0.955296	+	0.295651i	$0.0955364\pi$
$197$	10.2978	+	17.8363i	0.733689	+	1.27079i	−0.221607	+	0.975136i	$0.571130\pi$
$198$	24.1609	+	13.9493i	1.71704	+	0.991334i
$199$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$199$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$200$	13.9273	−	2.45576i	0.984808	−	0.173648i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.18616	+	8.75390i	−0.222531	+	0.611399i
$206$	−21.8127	−	18.3031i	−1.51977	−	1.27524i
$207$	−4.62603	+	26.2355i	−0.321532	+	1.82350i
$208$		−	4.17822i		−	0.289708i
$209$	1.74561	+	28.6099i	0.120746	+	1.97899i
$210$		0			0
$211$	24.5813	+	4.33435i	1.69225	+	0.298389i	0.934976	−	0.354712i	$-0.115421\pi$
$211$	24.5813	+	4.33435i	1.69225	+	0.298389i	0.757271	+	0.653101i	$0.226532\pi$
$212$	−12.7328	+	15.1744i	−0.874495	+	1.04218i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−14.7039	+	25.4678i	−0.991334	+	1.71704i
$221$		0			0
$222$		0			0
$223$	6.35573	+	17.4622i	0.425611	+	1.16936i	0.948450	+	0.316926i	$0.102651\pi$
$223$	6.35573	+	17.4622i	0.425611	+	1.16936i	−0.522839	+	0.852431i	$0.675127\pi$
$224$	−6.25905	+	17.1966i	−0.418200	+	1.14900i
$225$	−11.4907	−	9.64181i	−0.766044	−	0.642788i
$226$		0			0
$227$		0			0			−	1.00000i	$-0.5\pi$
$227$		0			0				1.00000i	$0.5\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−27.6547	−	4.87627i	−1.82350	−	0.321532i
$231$		0			0
$232$		0			0
$233$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$233$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$234$	−3.39486	+	2.84863i	−0.221929	+	0.186221i
$235$	−10.2386	−	17.7338i	−0.667893	−	1.15683i
$236$	26.4772	+	15.2866i	1.72352	+	0.995075i
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$		0			0
$241$	18.1508	+	21.6312i	1.16919	+	1.39339i	0.903093	+	0.429445i	$0.141291\pi$
$241$	18.1508	+	21.6312i	1.16919	+	1.39339i	0.266100	+	0.963945i	$0.414265\pi$
$242$	−15.5945	−	42.8455i	−1.00245	−	2.75421i
$243$		0			0
$244$		0			0
$245$	−1.34565	+	7.63153i	−0.0859701	+	0.487561i
$246$		0			0
$247$	−4.36543	−	1.29380i	−0.277765	−	0.0823226i
$248$		0			0
$249$		0			0
$250$	10.1634	−	12.1122i	0.642788	−	0.766044i
$251$	−24.7948	−	9.02459i	−1.56504	−	0.569627i	−0.593154	−	0.805089i	$-0.702117\pi$
$251$	−24.7948	−	9.02459i	−1.56504	−	0.569627i	−0.971883	+	0.235462i	$0.924340\pi$
$252$	18.2397	−	6.63872i	1.14900	−	0.418200i
$253$	44.7319	−	37.5346i	2.81227	−	2.35978i
$254$	−11.6955	−	20.2571i	−0.733838	−	1.27104i
$255$		0			0
$256$	2.77837	+	15.7569i	0.173648	+	0.984808i
$257$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$257$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$258$		0			0
$259$	32.3349	−	18.6686i	2.00920	−	1.16001i
$260$	−3.00272	−	3.57850i	−0.186221	−	0.221929i
$261$		0			0
$262$	−6.18524	+	16.9938i	−0.382126	+	1.04988i
$263$	2.23710	+	1.87715i	0.137945	+	0.115750i	0.709150	−	0.705058i	$-0.249079\pi$
$263$	2.23710	+	1.87715i	0.137945	+	0.115750i	−0.571204	+	0.820808i	$0.693524\pi$
$264$		0			0
$265$			22.1469i			1.36047i
$266$	16.0289	+	11.8645i	0.982797	+	0.727456i
$267$		0			0
$268$		0			0
$269$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$269$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$270$		0			0
$271$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$271$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.70935	+	32.3793i	0.344287	+	1.95255i
$276$		0			0
$277$	−2.92726	+	5.07016i	−0.175882	+	0.304636i	−0.940466	−	0.339887i	$-0.889611\pi$
$277$	−2.92726	+	5.07016i	−0.175882	+	0.304636i	0.764584	+	0.644524i	$0.222944\pi$
$278$	−28.6978	+	16.5687i	−1.72118	+	0.993724i
$279$		0			0
$280$	6.99783	+	19.2264i	0.418200	+	1.14900i
$281$	−10.7042	+	29.4096i	−0.638559	+	1.75443i	0.0176458	+	0.999844i	$0.494383\pi$
$281$	−10.7042	+	29.4096i	−0.638559	+	1.75443i	−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$283$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$284$		0			0
$285$		0			0
$286$	9.71389			0.574394
$287$	−13.2728	−	2.34036i	−0.783471	−	0.138147i
$288$	10.9085	−	13.0002i	0.642788	−	0.766044i
$289$	−15.9748	−	5.81434i	−0.939693	−	0.342020i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	26.2966	+	15.1823i	1.53626	+	0.886961i	0.999053	+	0.0435123i	$0.0138548\pi$
$293$	26.2966	+	15.1823i	1.53626	+	0.886961i	0.537209	+	0.843449i	$0.319479\pi$
$294$		0			0
$295$	33.6627	−	5.93563i	1.95992	−	0.345586i
$296$	16.3221	−	28.2706i	0.948700	−	1.64320i
$297$		0			0
$298$		0			0
$299$	3.17249	+	8.71636i	0.183470	+	0.504080i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	17.3232	+	1.97633i	0.993555	+	0.113350i
$305$		0			0
$306$		0			0
$307$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$307$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$308$	−39.9801	−	14.5516i	−2.27808	−	0.829152i
$309$		0			0
$310$		0			0
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		0			0
$313$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$313$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$314$	−13.7281	+	2.42063i	−0.774720	+	0.136604i
$315$	10.8507	−	18.7940i	0.611368	−	1.05892i
$316$		0			0
$317$	−17.9225	−	21.3592i	−1.00663	−	1.19965i	−0.979793	−	0.200012i	$-0.935902\pi$
$317$	−17.9225	−	21.3592i	−1.00663	−	1.19965i	−0.0268342	−	0.999640i	$-0.508543\pi$
$318$		0			0
$319$		0			0
$320$	13.7034	+	11.4985i	0.766044	+	0.642788i
$321$		0			0
$322$		−	40.6269i		−	2.26405i
$323$		0			0
$324$	−18.0000			−1.00000
$325$	−5.14344	−	0.906926i	−0.285306	−	0.0503072i
$326$		0			0
$327$		0			0
$328$	−11.0729	+	4.03021i	−0.611399	+	0.222531i
$329$	22.6946	−	19.0430i	1.25119	−	1.04987i
$330$		0			0
$331$	31.0661	+	17.9360i	1.70755	+	0.985853i	0.937580	+	0.347771i	$0.113061\pi$
$331$	31.0661	+	17.9360i	1.70755	+	0.985853i	0.769968	+	0.638082i	$0.220272\pi$
$332$		0			0
$333$	−34.0983	+	6.01245i	−1.86857	+	0.329480i
$334$	0.0114316	−	0.0198002i	0.000625512	−	0.00108342i
$335$		0			0
$336$		0			0
$337$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$337$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$338$	5.76021	−	15.8261i	0.313314	−	0.860824i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−10.2048	−	15.4228i	−0.551814	−	0.833968i
$343$	11.4341			0.617381
$344$		0			0
$345$		0			0
$346$	12.3369	+	4.49027i	0.663237	+	0.241398i
$347$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$347$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$348$		0			0
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$	19.8106	+	11.4376i	1.05892	+	0.611368i
$351$		0			0
$352$	−36.6330	+	6.45939i	−1.95255	+	0.344287i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$	−0.472504	−	1.29819i	−0.0250427	−	0.0688041i
$357$		0			0
$358$	12.8568	+	10.7881i	0.679501	+	0.570169i
$359$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$359$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$360$		−	18.9737i		−	1.00000i
$361$	7.42907	−	17.4874i	0.391004	−	0.920389i
$362$		0			0
$363$		0			0
$364$	4.34421	−	5.17723i	0.227698	−	0.271361i
$365$		0			0
$366$		0			0
$367$	−12.0760	+	10.1329i	−0.630360	+	0.528935i	−0.901041	−	0.433734i	$-0.857196\pi$
$367$	−12.0760	+	10.1329i	−0.630360	+	0.528935i	0.270681	+	0.962669i	$0.412751\pi$
$368$	−17.7602	−	30.7615i	−0.925813	−	1.60356i
$369$	10.8239	+	6.24917i	0.563468	+	0.325319i
$370$	−6.33768	−	35.9428i	−0.329480	−	1.86857i
$371$	−31.5544	+	5.56390i	−1.63823	+	0.288863i
$372$		0			0
$373$	−9.14167	+	5.27795i	−0.473338	+	0.273282i	−0.717636	−	0.696418i	$-0.754776\pi$
$373$	−9.14167	+	5.27795i	−0.473338	+	0.273282i	0.244298	+	0.969700i	$0.421442\pi$
$374$		0			0
$375$		0			0
$376$	8.85896	−	24.3398i	0.456866	−	1.25523i
$377$		0			0
$378$		0			0
$379$			19.9580i			1.02518i	0.858635	+	0.512588i	$0.171313\pi$
$379$			19.9580i			1.02518i	−0.858635	+	0.512588i	$0.828687\pi$
$380$	16.2570	−	10.7568i	0.833968	−	0.551814i
$381$		0			0
$382$		0			0
$383$	−19.2860	+	22.9842i	−0.985470	+	1.17444i	−0.000801512		1.00000i	$0.500255\pi$
$383$	−19.2860	+	22.9842i	−0.985470	+	1.17444i	−0.984668	+	0.174437i	$0.944189\pi$
$384$		0			0
$385$	−44.6991	+	16.2691i	−2.27808	+	0.829152i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$389$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$390$		0			0
$391$		0			0
$392$	−8.48889	+	4.90106i	−0.428754	+	0.247541i
$393$		0			0
$394$	9.96189	+	27.3701i	0.501873	+	1.37888i
$395$		0			0
$396$	30.2240	+	25.3609i	1.51881	+	1.27443i
$397$	6.63680	−	37.6392i	0.333092	−	1.88906i	−0.112225	−	0.993683i	$-0.535798\pi$
$397$	6.63680	−	37.6392i	0.333092	−	1.88906i	0.445317	−	0.895373i	$-0.353091\pi$
$398$		0			0
$399$		0			0
$400$	20.0000			1.00000
$401$	12.4569	+	2.19650i	0.622070	+	0.109688i	0.475795	−	0.879556i	$-0.342160\pi$
$401$	12.4569	+	2.19650i	0.622070	+	0.109688i	0.146275	+	0.989244i	$0.453272\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−15.4163	+	12.9359i	−0.766044	+	0.642788i
$406$		0			0
$407$	65.7260	+	37.9469i	3.25792	+	1.88096i
$408$		0			0
$409$	39.8326	−	7.02357i	1.96960	−	0.347293i	0.984039	−	0.177955i	$-0.0569481\pi$
$409$	39.8326	−	7.02357i	1.96960	−	0.347293i	0.985558	−	0.169338i	$-0.0541630\pi$
$410$	−6.58720	+	11.4094i	−0.325319	+	0.563468i
$411$		0			0
$412$	−25.8844	−	30.8479i	−1.27524	−	1.51977i
$413$	16.9140	+	46.4707i	0.832281	+	2.28667i
$414$	−12.8856	+	35.4029i	−0.633294	+	1.73996i
$415$		0			0
$416$	1.02607	−	5.81913i	0.0503072	−	0.285306i
$417$		0			0
$418$	−4.59474	+	40.2745i	−0.224736	+	1.96989i
$419$	−35.2476			−1.72196			−0.860980	−	0.508639i	$-0.830149\pi$
$419$	−35.2476			−1.72196			−0.860980	+	0.508639i	$0.830149\pi$
$420$		0			0
$421$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$421$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$422$	33.1707	+	12.0731i	1.61472	+	0.587711i
$423$	−25.8163	+	9.39635i	−1.25523	+	0.456866i
$424$	−21.4598	+	18.0069i	−1.04218	+	0.874495i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$431$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$432$		0			0
$433$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$433$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−37.6393	+	9.03049i	−1.80053	+	0.431987i
$438$		0			0
$439$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$439$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$440$	−26.7328	+	31.8589i	−1.27443	+	1.51881i
$441$	9.76973	+	3.55589i	0.465225	+	0.169328i
$442$		0			0
$443$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$443$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$444$		0			0
$445$	−1.33764	−	0.772287i	−0.0634102	−	0.0366099i
$446$	4.56351	+	25.8810i	0.216088	+	1.22550i
$447$		0			0
$448$	−12.9402	+	22.4131i	−0.611368	+	1.05892i
$449$	25.1931	−	14.5452i	1.18894	−	0.686432i	0.230871	−	0.972984i	$-0.425843\pi$
$449$	25.1931	−	14.5452i	1.18894	−	0.686432i	0.958065	+	0.286552i	$0.0925092\pi$
$450$	−13.6356	−	16.2503i	−0.642788	−	0.766044i
$451$	−9.36977	−	25.7432i	−0.441205	−	1.21220i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	7.55611i		−	0.354236i
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$	−37.3180	−	13.5826i	−1.73996	−	0.633294i
$461$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$461$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$	−16.1640	−	27.9969i	−0.751206	−	1.30113i	−0.947239	−	0.320529i	$-0.896139\pi$
$463$	−16.1640	−	27.9969i	−0.751206	−	1.30113i	0.196033	−	0.980597i	$-0.437194\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$	−5.42767	+	3.13367i	−0.250894	+	0.144854i
$469$		0			0
$470$	−9.90462	−	27.2127i	−0.456866	−	1.25523i
$471$		0			0
$472$	33.1216	+	27.7923i	1.52454	+	1.27924i
$473$		0			0
$474$		0			0
$475$	6.19306	−	20.8961i	0.284157	−	0.958778i
$476$		0			0
$477$	29.2617	+	5.15964i	1.33980	+	0.236243i
$478$		0			0
$479$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$479$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$480$		0			0
$481$	−9.23519	+	7.74924i	−0.421088	+	0.353335i
$482$	19.9670	+	34.5838i	0.909471	+	1.57525i
$483$		0			0
$484$	−11.1971	−	63.5018i	−0.508958	−	2.88645i
$485$		0			0
$486$		0			0
$487$	34.5919	−	19.9716i	1.56751	−	0.905002i	0.571051	−	0.820915i	$-0.306536\pi$
$487$	34.5919	−	19.9716i	1.56751	−	0.905002i	0.996458	−	0.0840870i	$-0.0267974\pi$
$488$		0			0
$489$		0			0
$490$	−3.74824	+	10.2982i	−0.169328	+	0.465225i
$491$	20.6260	+	17.3073i	0.930838	+	0.781066i	0.975968	−	0.217915i	$-0.0699256\pi$
$491$	20.6260	+	17.3073i	0.930838	+	0.781066i	−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$		0			0
$494$	−5.76213	−	2.87395i	−0.259250	−	0.129305i
$495$	44.1116			1.98267
$496$		0			0
$497$		0			0
$498$		0			0
$499$	19.5268	−	7.10719i	0.874142	−	0.318162i	0.134298	−	0.990941i	$-0.457122\pi$
$499$	19.5268	−	7.10719i	0.874142	−	0.318162i	0.739843	+	0.672779i	$0.234900\pi$
$500$	17.1293	−	14.3732i	0.766044	−	0.642788i
$501$		0			0
$502$	−32.3163	−	18.6578i	−1.44235	−	0.832739i
$503$	−4.59949	−	26.0850i	−0.205081	−	1.16307i	−0.897312	−	0.441397i	$-0.854483\pi$
$503$	−4.59949	−	26.0850i	−0.205081	−	1.16307i	0.692231	−	0.721676i	$-0.256628\pi$
$504$	27.0333	−	4.76670i	1.20416	−	0.212326i
$505$		0			0
$506$	71.5170	−	41.2904i	3.17932	−	1.83558i
$507$		0			0
$508$	−11.3139	−	31.0848i	−0.501975	−	1.37916i
$509$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$509$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$		0			0
$514$		0			0
$515$	−44.3382	−	7.81802i	−1.95377	−	0.344503i
$516$		0			0
$517$	56.5872	+	20.5961i	2.48870	+	0.905814i
$518$	49.6183	−	18.0596i	2.18010	−	0.793493i
$519$		0			0
$520$	−3.30318	−	5.72127i	−0.144854	−	0.250894i
$521$	21.9089	+	12.6491i	0.959846	+	0.554168i	0.896126	−	0.443800i	$-0.146370\pi$
$521$	21.9089	+	12.6491i	0.959846	+	0.554168i	0.0637207	+	0.997968i	$0.479703\pi$
$522$		0			0
$523$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$523$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$524$	−12.7876	+	22.1488i	−0.558630	+	0.967576i
$525$		0			0
$526$	2.65469	+	3.16373i	0.115750	+	0.137945i
$527$		0			0
$528$		0			0
$529$	42.7882	+	35.9035i	1.86035	+	1.56102i
$530$	−5.43873	+	30.8446i	−0.236243	+	1.33980i
$531$		−	45.8599i		−	1.99015i
$532$	19.4103	+	20.4603i	0.841544	+	0.887066i
$533$	4.35174			0.188495
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.3944	−	19.7357i	−0.490792	−	0.850076i
$540$		0			0
$541$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$541$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$547$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$548$		0			0
$549$		0			0
$550$			46.4977i			1.98267i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−5.32198	+	6.34249i	−0.226109	+	0.269467i
$555$		0			0
$556$	−44.0371	+	16.0282i	−1.86759	+	0.679748i
$557$	21.5146	−	18.0529i	0.911604	−	0.764927i	−0.0608191	−	0.998149i	$-0.519371\pi$
$557$	21.5146	−	18.0529i	0.911604	−	0.764927i	0.972424	+	0.233222i	$0.0749268\pi$
$558$		0			0
$559$		0			0
$560$	5.02455	+	28.4956i	0.212326	+	1.20416i
$561$		0			0
$562$	−22.1303	+	38.3308i	−0.933511	+	1.61689i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.3038	−	18.7151i	−0.936670	−	0.785959i
$568$		0			0
$569$		−	3.84665i		−	0.161260i	−0.996744	−	0.0806300i	$-0.974307\pi$
$569$		−	3.84665i		−	0.161260i	0.996744	−	0.0806300i	$-0.0256932\pi$
$570$		0			0
$571$	29.3406			1.22787			0.613933	−	0.789359i	$-0.289587\pi$
$571$	29.3406			1.22787			0.613933	+	0.789359i	$0.289587\pi$
$572$	13.5288	+	2.38549i	0.565668	+	0.0997426i
$573$		0			0
$574$	−17.9107	−	6.51897i	−0.747579	−	0.272097i
$575$	−41.7228	+	15.1858i	−1.73996	+	0.633294i
$576$	18.3851	−	15.4269i	0.766044	−	0.642788i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−20.8207	−	12.0208i	−0.866025	−	0.500000i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−41.8641	−	49.8917i	−1.73383	−	2.06630i
$584$		0			0
$585$	−2.39657	+	6.58452i	−0.0990859	+	0.272236i
$586$	32.8956	+	27.6027i	1.35890	+	1.14026i
$587$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$587$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$588$		0			0
$589$		0			0
$590$	48.3406			1.99015
$591$		0			0
$592$	29.6748	−	35.3650i	1.21963	−	1.45349i
$593$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$593$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	2.27790	+	12.9186i	0.0931502	+	0.528281i
$599$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$599$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$600$		0			0
$601$	−39.6249	+	22.8775i	−1.61633	+	0.933191i	−0.628477	+	0.777828i	$0.716321\pi$
$601$	−39.6249	+	22.8775i	−1.61633	+	0.933191i	−0.987858	+	0.155363i	$0.950345\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−55.2260	−	46.3401i	−2.24526	−	1.88399i
$606$		0			0
$607$			19.4830i			0.790791i	0.918511	+	0.395396i	$0.129393\pi$
$607$			19.4830i			0.790791i	−0.918511	+	0.395396i	$0.870607\pi$
$608$	23.6412	+	7.00665i	0.958778	+	0.284157i
$609$		0			0
$610$		0			0
$611$	−6.14873	+	7.32777i	−0.248751	+	0.296450i
$612$		0			0
$613$	2.79225	−	1.01629i	0.112778	−	0.0410478i	−0.285015	−	0.958523i	$-0.591999\pi$
$613$	2.79225	−	1.01629i	0.112778	−	0.0410478i	0.397793	+	0.917475i	$0.369776\pi$
$614$		0			0
$615$		0			0
$616$	−52.1079	−	30.0845i	−2.09949	−	1.21214i
$617$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$617$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$618$		0			0
$619$	−24.8576	+	43.0547i	−0.999112	+	1.73051i	−0.463068	+	0.886323i	$0.653252\pi$
$619$	−24.8576	+	43.0547i	−0.999112	+	1.73051i	−0.536044	+	0.844190i	$0.680082\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.764288	−	2.09986i	0.0306205	−	0.0841292i
$624$		0			0
$625$	4.34120	−	24.6202i	0.173648	−	0.984808i
$626$		0			0
$627$		0			0
$628$	−19.7139			−0.786671
$629$		0			0
$630$	19.7274	−	23.5102i	0.785959	−	0.936670i
$631$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$631$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$632$		0			0
$633$		0			0
$634$	−19.7159	−	34.1489i	−0.783017	−	1.35623i
$635$	−32.0293	−	18.4921i	−1.27104	−	0.733838i
$636$		0			0
$637$	3.56499	−	0.628604i	0.141250	−	0.0249062i
$638$		0			0
$639$		0			0
$640$	16.2614	+	19.3796i	0.642788	+	0.766044i
$641$	8.06011	+	22.1450i	0.318355	+	0.874673i	0.990898	+	0.134615i	$0.0429798\pi$
$641$	8.06011	+	22.1450i	0.318355	+	0.874673i	−0.672543	+	0.740058i	$0.734798\pi$
$642$		0			0
$643$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$643$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$644$	9.97698	−	56.5823i	0.393148	−	2.22965i
$645$		0			0
$646$		0			0
$647$	10.8338			0.425922			0.212961	−	0.977061i	$-0.431689\pi$
$647$	10.8338			0.425922			0.212961	+	0.977061i	$0.431689\pi$
$648$	−25.0691	−	4.42036i	−0.984808	−	0.173648i
$649$	−64.6139	+	77.0038i	−2.53632	+	3.02266i
$650$	−6.94069	−	2.52620i	−0.272236	−	0.0990859i
$651$		0			0
$652$		0			0
$653$	10.8076	+	18.7194i	0.422935	+	0.732545i	0.996225	−	0.0868074i	$-0.0276665\pi$
$653$	10.8076	+	18.7194i	0.422935	+	0.732545i	−0.573290	+	0.819353i	$0.694333\pi$
$654$		0			0
$655$	4.96530	+	28.1596i	0.194010	+	1.10029i
$656$	−16.4113	+	2.89375i	−0.640753	+	0.112982i
$657$		0			0
$658$	36.2838	−	20.9485i	1.41449	−	0.816657i
$659$	−21.4002	−	25.5037i	−0.833632	−	0.993484i	−0.999973	−	0.00741531i	$-0.997640\pi$
$659$	−21.4002	−	25.5037i	−0.833632	−	0.993484i	0.166341	−	0.986068i	$-0.446805\pi$
$660$		0			0
$661$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$661$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$662$	38.8620	+	32.6091i	1.51041	+	1.26739i
$663$		0			0
$664$		0			0
$665$	31.3282	+	3.57409i	1.21486	+	0.138597i
$666$	−48.9662			−1.89740
$667$		0			0
$668$	0.0207836	−	0.0247689i	0.000804142	−	0.000958339i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$673$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$674$		0			0
$675$		0			0
$676$	11.9089	−	20.6268i	0.458035	−	0.793339i
$677$	−38.6431	+	22.3106i	−1.48517	+	0.857466i	−0.999858	−	0.0168732i	$-0.994629\pi$
$677$	−38.6431	+	22.3106i	−1.48517	+	0.857466i	−0.485316	+	0.874339i	$0.661296\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	−10.4251	−	23.9858i	−0.398613	−	0.917119i
$685$		0			0
$686$	15.9245	+	2.80793i	0.608002	+	0.107207i
$687$		0			0
$688$		0			0
$689$	9.72177	−	3.53843i	0.370370	−	0.134804i
$690$		0			0
$691$	−26.2503	−	45.4668i	−0.998608	−	1.72964i	−0.544977	−	0.838451i	$-0.683461\pi$
$691$	−26.2503	−	45.4668i	−0.998608	−	1.72964i	−0.453632	−	0.891189i	$-0.649872\pi$
$692$	16.0793	+	9.28337i	0.611242	+	0.352901i
$693$	11.0820	+	62.8493i	0.420972	+	2.38745i
$694$		0			0
$695$	−26.1974	+	45.3752i	−0.993724	+	1.72118i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	24.7820	+	20.7945i	0.936670	+	0.785959i
$701$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$701$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$702$		0			0
$703$	−27.7606	−	41.9552i	−1.04701	−	1.58237i
$704$	−52.6061			−1.98267
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$709$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$710$		0			0
$711$		0			0
$712$	−0.339265	−	1.92407i	−0.0127145	−	0.0721074i
$713$		0			0
$714$		0			0
$715$	13.3013	−	7.67951i	0.497440	−	0.287197i
$716$	15.2567	+	18.1822i	0.570169	+	0.679501i
$717$		0			0
$718$		0			0
$719$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$719$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$720$	4.65947	−	26.4252i	0.173648	−	0.984808i
$721$		−	65.1363i		−	2.42580i
$722$	14.6412	−	22.5308i	0.544887	−	0.838509i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.20243	−	1.52956i	0.155860	−	0.0567283i	−0.262912	−	0.964820i	$-0.584683\pi$
$727$	4.20243	−	1.52956i	0.155860	−	0.0567283i	0.418772	+	0.908092i	$0.362461\pi$
$728$	7.32171	−	6.14364i	0.271361	−	0.227698i
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	26.9829	−	46.7358i	0.996636	−	1.72622i	0.427344	−	0.904089i	$-0.359449\pi$
$733$	26.9829	−	46.7358i	0.996636	−	1.72622i	0.569292	−	0.822135i	$-0.307217\pi$
$734$	−19.3069	+	11.1469i	−0.712632	+	0.411438i
$735$		0			0
$736$	−17.1808	−	47.2039i	−0.633294	−	1.73996i
$737$		0			0
$738$	13.5401	+	11.3615i	0.498417	+	0.418221i
$739$	7.88914	−	44.7415i	0.290207	−	1.64584i	−0.395864	−	0.918309i	$-0.629555\pi$
$739$	7.88914	−	44.7415i	0.290207	−	1.64584i	0.686071	−	0.727535i	$-0.259334\pi$
$740$		−	51.6149i		−	1.89740i
$741$		0			0
$742$	−45.3131			−1.66350
$743$	−20.4702	−	3.60946i	−0.750980	−	0.132418i	−0.214960	−	0.976623i	$-0.568962\pi$
$743$	−20.4702	−	3.60946i	−0.750980	−	0.132418i	−0.536021	+	0.844205i	$0.680073\pi$
$744$		0			0
$745$		0			0
$746$	−14.0280	+	5.10577i	−0.513602	+	0.186936i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$751$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$752$	18.3154	−	31.7232i	0.667893	−	1.15683i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−38.3048	−	32.1415i	−1.39221	−	1.16820i	−0.964435	−	0.264319i	$-0.914853\pi$
$757$	−38.3048	−	32.1415i	−1.39221	−	1.16820i	−0.427776	−	0.903885i	$-0.640703\pi$
$758$	−4.90121	+	27.7961i	−0.178020	+	1.00960i
$759$		0			0
$760$	25.2832	−	10.9890i	0.917119	−	0.398613i
$761$	−46.0075			−1.66777			−0.833885	−	0.551938i	$-0.813889\pi$
$761$	−46.0075			−1.66777			−0.833885	+	0.551938i	$0.813889\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−32.5046	+	27.2746i	−1.17444	+	0.985470i
$767$	−7.98387	−	13.8285i	−0.288281	−	0.499317i
$768$		0			0
$769$	2.78628	+	15.8018i	0.100476	+	0.569827i	0.992931	+	0.118691i	$0.0378698\pi$
$769$	2.78628	+	15.8018i	0.100476	+	0.569827i	−0.892455	+	0.451136i	$0.851019\pi$
$770$	−66.2490	+	11.6815i	−2.38745	+	0.420972i
$771$		0			0
$772$		0			0
$773$	15.8302	+	18.8657i	0.569373	+	0.678553i	0.971502	−	0.237030i	$-0.0761741\pi$
$773$	15.8302	+	18.8657i	0.569373	+	0.678553i	−0.402129	+	0.915583i	$0.631730\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.05840	+	18.0426i	−0.0737499	+	0.646444i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−13.0263	+	4.74119i	−0.465225	+	0.169328i
$785$	−16.8843	+	14.1676i	−0.602625	+	0.505663i
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	7.15279	+	40.5655i	0.254808	+	1.44509i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	35.8658	+	42.7432i	1.27443	+	1.51881i
$793$		0			0
$794$	18.4865	−	50.7913i	0.656062	−	1.80252i
$795$		0			0
$796$		0			0
$797$		−	46.5139i		−	1.64761i	−0.566876	−	0.823803i	$-0.691848\pi$
$797$		−	46.5139i		−	1.64761i	0.566876	−	0.823803i	$-0.308152\pi$
$798$		0			0
$799$		0			0
$800$	27.8546	+	4.91151i	0.984808	+	0.173648i
$801$	−1.33203	+	1.58745i	−0.0470648	+	0.0560896i
$802$	16.8097	+	6.11824i	0.593572	+	0.216043i
$803$		0			0
$804$		0			0
$805$	−32.1184	−	55.6307i	−1.13202	−	1.96072i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	15.4089	−	26.6890i	0.541748	−	0.938335i	−0.457056	−	0.889438i	$-0.651096\pi$
$809$	15.4089	−	26.6890i	0.541748	−	0.938335i	0.998804	−	0.0488972i	$-0.0155707\pi$
$810$	−24.6475	+	14.2302i	−0.866025	+	0.500000i
$811$	−34.8213	−	41.4984i	−1.22274	−	1.45721i	−0.847934	−	0.530102i	$-0.822154\pi$
$811$	−34.8213	−	41.4984i	−1.22274	−	1.45721i	−0.374806	−	0.927103i	$-0.622291\pi$
$812$		0			0
$813$		0			0
$814$	82.2196	+	68.9904i	2.88180	+	2.41811i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	57.2009			1.99998
$819$	−9.98357	−	1.76037i	−0.348854	−	0.0615124i
$820$	−11.9760	+	14.2725i	−0.418221	+	0.498417i
$821$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$821$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$822$		0			0
$823$	−5.30588	+	4.45217i	−0.184952	+	0.155193i	−0.730563	−	0.682846i	$-0.760742\pi$
$823$	−5.30588	+	4.45217i	−0.184952	+	0.155193i	0.545611	+	0.838039i	$0.316298\pi$
$824$	−28.4745	−	49.3193i	−0.991957	−	1.71812i
$825$		0			0
$826$	12.1445	+	68.8747i	0.422560	+	2.39646i
$827$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$827$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$828$	−26.6403	+	46.1423i	−0.925813	+	1.60356i
$829$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$829$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$830$		0			0
$831$		0			0
$832$	2.85807	−	7.85249i	0.0990859	−	0.272236i
$833$		0			0
$834$		0			0
$835$		−	0.0361500i		−	0.00125102i
$836$	−16.2897	+	54.9631i	−0.563390	+	1.90094i
$837$		0			0
$838$	−49.0904	−	8.65596i	−1.69580	−	0.299015i
$839$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$839$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$840$		0			0
$841$	27.2511	−	9.91858i	0.939693	−	0.342020i
$842$		0			0
$843$		0			0
$844$	43.2329	+	24.9605i	1.48814	+	0.859176i
$845$	−4.62410	−	26.2246i	−0.159074	−	0.902152i
$846$	−38.2625	+	6.74672i	−1.31549	+	0.231957i
$847$	52.1502	−	90.3269i	1.79190	−	3.10367i
$848$	−34.3098	+	19.8088i	−1.17820	+	0.680236i
$849$		0			0
$850$		0			0
$851$	−35.0533	+	96.3081i	−1.20161	+	3.30140i
$852$		0			0
$853$	−4.19706	+	23.8027i	−0.143705	+	0.814989i	0.824694	+	0.565580i	$0.191348\pi$
$853$	−4.19706	+	23.8027i	−0.143705	+	0.814989i	−0.968398	+	0.249409i	$0.919764\pi$
$854$		0			0
$855$	−26.1663	−	13.0509i	−0.894868	−	0.446330i
$856$		0			0
$857$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$857$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$858$		0			0
$859$	5.93174	+	2.15898i	0.202389	+	0.0736634i	0.441225	−	0.897396i	$-0.354544\pi$
$859$	5.93174	+	2.15898i	0.202389	+	0.0736634i	−0.238837	+	0.971060i	$0.576766\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−48.3078	−	27.8905i	−1.64442	−	0.949405i	−0.979236	−	0.202723i	$-0.935021\pi$
$863$	−48.3078	−	27.8905i	−1.64442	−	0.949405i	−0.665181	−	0.746682i	$-0.731646\pi$
$864$		0			0
$865$	20.4429	−	3.60463i	0.695079	−	0.122561i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−54.6389	+	3.33374i	−1.84819	+	0.112766i
$875$	36.1690			1.22274
$876$		0			0
$877$	5.94764	−	7.08812i	0.200837	−	0.239349i	−0.656220	−	0.754570i	$-0.727846\pi$
$877$	5.94764	−	7.08812i	0.200837	−	0.239349i	0.857057	+	0.515221i	$0.172290\pi$
$878$		0			0
$879$		0			0
$880$	−45.0553	+	37.8058i	−1.51881	+	1.27443i
$881$	25.0880	+	43.4536i	0.845235	+	1.46399i	0.885417	+	0.464797i	$0.153873\pi$
$881$	25.0880	+	43.4536i	0.845235	+	1.46399i	−0.0401822	+	0.999192i	$0.512794\pi$
$882$	12.7333	+	7.35159i	0.428754	+	0.247541i
$883$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$883$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.6003	+	19.7835i	0.557384	+	0.664264i	0.968991	−	0.247097i	$-0.0794767\pi$
$887$	16.6003	+	19.7835i	0.557384	+	0.664264i	−0.411607	+	0.911362i	$0.635032\pi$
$888$		0			0
$889$	18.3006	−	50.2805i	0.613782	−	1.68635i
$890$	−1.67331	−	1.40408i	−0.0560896	−	0.0470648i
$891$	10.2768	−	58.2828i	0.344287	−	1.95255i
$892$			37.1658i			1.24440i
$893$	−27.4731	−	28.9592i	−0.919352	−	0.969082i
$894$		0			0
$895$	26.1336	+	4.60806i	0.873549	+	0.154030i
$896$	−23.5263	+	28.0376i	−0.785959	+	0.936670i
$897$		0			0
$898$	38.6591	−	14.0708i	1.29007	−	0.469547i
$899$		0			0
$900$	−15.0000	−	25.9808i	−0.500000	−	0.866025i
$901$		0			0
$902$	−6.72764	−	38.1543i	−0.224006	−	1.27040i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$907$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$908$		0			0
$909$		0			0
$910$	1.85560	−	10.5236i	0.0615124	−	0.348854i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−38.8738	+	14.1489i	−1.28373	+	0.467239i
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$	−48.6382	−	28.0813i	−1.60356	−	0.925813i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−37.0935	−	44.2063i	−1.21963	−	1.45349i
$926$	−15.6367	−	42.9616i	−0.513855	−	1.41181i
$927$	−20.6592	+	56.7608i	−0.678538	+	1.86427i
$928$		0			0
$929$	8.55296	−	48.5063i	0.280614	−	1.59144i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	8.55296	−	48.5063i	0.280614	−	1.59144i	0.720545	−	0.693408i	$-0.243891\pi$
$930$		0			0
$931$	0.919973	+	15.0781i	0.0301509	+	0.494163i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−8.32883	+	3.03145i	−0.272236	+	0.0990859i
$937$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$937$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$938$		0			0
$939$		0			0
$940$	−7.11167	−	40.3323i	−0.231957	−	1.31549i
$941$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$941$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$942$		0			0
$943$	32.0390	−	18.4977i	1.04333	−	0.602368i
$944$	39.3042	+	46.8410i	1.27924	+	1.52454i
$945$		0			0
$946$		0			0
$947$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$947$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$948$		0			0
$949$		0			0
$950$	13.7568	−	27.5817i	0.446330	−	0.894868i
$951$		0			0
$952$		0			0
$953$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$953$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$954$	39.4866	+	14.3719i	1.27843	+	0.465309i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−14.7651	+	8.52465i	−0.476047	+	0.274846i
$963$		0			0
$964$	19.3156	+	53.0693i	0.622115	+	1.70925i
$965$		0			0
$966$		0			0
$967$	−5.43605	+	30.8294i	−0.174812	+	0.991405i	0.763550	+	0.645749i	$0.223455\pi$
$967$	−5.43605	+	30.8294i	−0.174812	+	0.991405i	−0.938361	+	0.345656i	$0.887656\pi$
$968$		−	91.1905i		−	2.93097i
$969$		0			0
$970$		0			0
$971$	−49.7636	−	8.77467i	−1.59699	−	0.281592i	−0.696858	−	0.717209i	$-0.745419\pi$
$971$	−49.7636	−	8.77467i	−1.59699	−	0.281592i	−0.900132	+	0.435617i	$0.856530\pi$
$972$		0			0
$973$	−71.2313	−	25.9261i	−2.28357	−	0.831151i
$974$	53.0817	−	19.3202i	1.70085	−	0.619058i
$975$		0			0
$976$		0			0
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$	4.47323	−	0.788752i	0.142965	−	0.0252086i
$980$	−7.74926	+	13.4221i	−0.247541	+	0.428754i
$981$		0			0
$982$	24.4762	+	29.1696i	0.781066	+	0.930838i
$983$	21.4466	+	58.9240i	0.684040	+	1.87938i	0.343138	+	0.939285i	$0.388510\pi$
$983$	21.4466	+	58.9240i	0.684040	+	1.87938i	0.340902	+	0.940099i	$0.389268\pi$
$984$		0			0
$985$	35.2788	+	29.6024i	1.12408	+	0.943212i
$986$		0			0
$987$		0			0
$988$	−7.31930	−	5.41768i	−0.232858	−	0.172359i
$989$		0			0
$990$	61.4355	+	10.8327i	1.95255	+	0.344287i
$991$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$991$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	10.9637	+	62.1783i	0.347224	+	1.96921i	0.193685	+	0.981064i	$0.437956\pi$
$997$	10.9637	+	62.1783i	0.347224	+	1.96921i	0.153539	+	0.988143i	$0.450933\pi$
$998$	28.9409	−	5.10307i	0.916110	−	0.161535i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.bx.a.59.4	yes	24
5.4	even	2	inner	760.2.bx.a.59.1	✓	24
8.3	odd	2	inner	760.2.bx.a.59.1	✓	24
19.10	odd	18	inner	760.2.bx.a.219.4	yes	24
40.19	odd	2	CM	760.2.bx.a.59.4	yes	24
95.29	odd	18	inner	760.2.bx.a.219.1	yes	24
152.67	even	18	inner	760.2.bx.a.219.1	yes	24
760.219	even	18	inner	760.2.bx.a.219.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.bx.a.59.1	✓	24	5.4	even	2	inner
760.2.bx.a.59.1	✓	24	8.3	odd	2	inner
760.2.bx.a.59.4	yes	24	1.1	even	1	trivial
760.2.bx.a.59.4	yes	24	40.19	odd	2	CM
760.2.bx.a.219.1	yes	24	95.29	odd	18	inner
760.2.bx.a.219.1	yes	24	152.67	even	18	inner
760.2.bx.a.219.4	yes	24	19.10	odd	18	inner
760.2.bx.a.219.4	yes	24	760.219	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(2.10122 - 0.764780i) q^{5} +(1.61753 + 2.80164i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})\)	\(q+(1.39273 + 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(2.10122 - 0.764780i) q^{5} +(1.61753 + 2.80164i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.520945 - 2.95442i) q^{9} +(3.11424 - 0.549124i) q^{10} +(-3.28788 + 5.69478i) q^{11} +(-0.671428 - 0.800176i) q^{13} +(1.56476 + 4.29915i) q^{14} +(3.06418 + 2.57115i) q^{16} -4.24264i q^{18} +(3.63518 - 2.40530i) q^{19} +4.47214 q^{20} +(-5.97763 + 7.12386i) q^{22} +(-8.34455 - 3.03717i) q^{23} +(3.83022 - 3.21394i) q^{25} +(-0.738613 - 1.27931i) q^{26} +(1.12352 + 6.37181i) q^{28} +(3.63616 + 4.33340i) q^{32} +(5.54141 + 4.64980i) q^{35} +(1.04189 - 5.90885i) q^{36} -11.5414i q^{37} +(5.65350 - 2.45722i) q^{38} +(6.22847 + 1.09825i) q^{40} +(-2.67792 + 3.19143i) q^{41} +(-10.0747 + 8.45364i) q^{44} +(-3.35410 - 5.80948i) q^{45} +(-10.8758 - 6.27917i) q^{46} +(-1.59022 - 9.01857i) q^{47} +(-1.73279 + 3.00128i) q^{49} +(6.12372 - 3.53553i) q^{50} +(-0.714519 - 1.96312i) q^{52} +(-3.38750 + 9.30708i) q^{53} +(-2.55330 + 14.4805i) q^{55} +9.15011i q^{56} +(15.0544 + 2.65450i) q^{59} +(7.43459 - 6.23836i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-2.02277 - 1.16785i) q^{65} +(6.57581 + 7.83674i) q^{70} +(2.90214 - 7.97356i) q^{72} +(2.83430 - 16.0741i) q^{74} +(8.47723 - 2.03387i) q^{76} -21.2730 q^{77} +(8.40487 + 3.05912i) q^{80} +(-8.45723 + 3.07818i) q^{81} +(-4.51336 + 3.78716i) q^{82} +(-16.1073 + 9.29954i) q^{88} +(-0.444008 - 0.529149i) q^{89} +(-3.24469 - 8.91471i) q^{90} +(1.15575 - 3.17541i) q^{91} +(-13.6051 - 11.4160i) q^{92} -12.9509i q^{94} +(5.79878 - 7.83417i) q^{95} +(-3.15034 + 3.75443i) q^{98} +(18.5376 + 6.74713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 48 q^{14} + 48 q^{26} + 60 q^{35} - 12 q^{41} + 24 q^{44} - 84 q^{49} + 96 q^{64} - 180 q^{65} - 96 q^{74} + 72 q^{76} + 168 q^{89} + 96 q^{91} + 36 q^{99}+O(q^{100}) \) 24 * q - 48 * q^14 + 48 * q^26 + 60 * q^35 - 12 * q^41 + 24 * q^44 - 84 * q^49 + 96 * q^64 - 180 * q^65 - 96 * q^74 + 72 * q^76 + 168 * q^89 + 96 * q^91 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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