LMFDB - Embedded newform 684.2.r.a.559.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(487,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("684.487");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 6 x^{14} - 9 x^{13} + 12 x^{12} - 9 x^{11} + 3 x^{10} + 6 x^{9} - 10 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 6x^14 - 9x^13 + 12x^12 - 9x^11 + 3x^10 + 6x^9 - 10x^8 + 12x^7 + 12x^6 - 72x^5 + 192x^4 - 288x^3 + 384x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.7
Root			$1.16486 + 0.801943i$ of defining polynomial
Character	$\chi$	$=$	684.559
Dual form			684.2.r.a.487.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16486 - 0.801943i) q^{2} +(0.713775 - 1.86829i) q^{4} +(-1.59295 + 2.75907i) q^{5} +2.36291i q^{7} +(-0.666820 - 2.74870i) q^{8} +(0.357061 + 4.49138i) q^{10} +5.46750i q^{11} +(-2.31924 + 1.33901i) q^{13} +(1.89492 + 2.75245i) q^{14} +(-2.98105 - 2.66709i) q^{16} +(0.552780 - 0.957443i) q^{17} +(-1.37952 + 4.13484i) q^{19} +(4.01775 + 4.94546i) q^{20} +(4.38462 + 6.36885i) q^{22} +(2.46168 - 1.42125i) q^{23} +(-2.57499 - 4.46001i) q^{25} +(-1.62777 + 3.41965i) q^{26} +(4.41462 + 1.68659i) q^{28} +(5.63736 - 3.25473i) q^{29} -1.01504 q^{31} +(-5.61134 - 0.716137i) q^{32} +(-0.123906 - 1.55858i) q^{34} +(-6.51945 - 3.76400i) q^{35} +0.450315i q^{37} +(1.70896 + 5.92279i) q^{38} +(8.64607 + 2.53874i) q^{40} +(-0.336089 - 0.194041i) q^{41} +(4.96197 + 2.86479i) q^{43} +(10.2149 + 3.90257i) q^{44} +(1.72774 - 3.62968i) q^{46} +(2.91563 - 1.68334i) q^{47} +1.41665 q^{49} +(-6.57616 - 3.13027i) q^{50} +(0.846255 + 5.28878i) q^{52} +(3.53036 - 2.03825i) q^{53} +(-15.0852 - 8.70946i) q^{55} +(6.49494 - 1.57564i) q^{56} +(3.95660 - 8.31213i) q^{58} +(-6.82450 + 11.8204i) q^{59} +(-6.77885 - 11.7413i) q^{61} +(-1.18237 + 0.814002i) q^{62} +(-7.11070 + 3.66578i) q^{64} -8.53193i q^{65} +(4.27064 + 7.39696i) q^{67} +(-1.39422 - 1.71616i) q^{68} +(-10.6127 + 0.843703i) q^{70} +(1.07447 - 1.86103i) q^{71} +(3.91944 - 6.78867i) q^{73} +(0.361127 + 0.524552i) q^{74} +(6.74043 + 5.52870i) q^{76} -12.9192 q^{77} +(5.57208 - 9.65112i) q^{79} +(12.1073 - 3.97639i) q^{80} +(-0.547104 + 0.0434943i) q^{82} +4.14868i q^{83} +(1.76110 + 3.05032i) q^{85} +(8.07738 - 0.642145i) q^{86} +(15.0285 - 3.64584i) q^{88} +(-4.19126 + 2.41982i) q^{89} +(-3.16397 - 5.48016i) q^{91} +(-0.898230 - 5.61360i) q^{92} +(2.04634 - 4.29901i) q^{94} +(-9.21082 - 10.3928i) q^{95} +(-0.641491 - 0.370365i) q^{97} +(1.65019 - 1.13607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 3 q^{4} + 2 q^{5} - 6 q^{10} - 18 q^{13} + 6 q^{14} - 3 q^{16} - 2 q^{17} - 4 q^{20} + 3 q^{22} - 2 q^{25} + 24 q^{26} - 4 q^{28} + 6 q^{29} - 27 q^{32} + 36 q^{34} + 24 q^{38} + 48 q^{40}+ \cdots - 51 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 3 * q^4 + 2 * q^5 - 6 * q^10 - 18 * q^13 + 6 * q^14 - 3 * q^16 - 2 * q^17 - 4 * q^20 + 3 * q^22 - 2 * q^25 + 24 * q^26 - 4 * q^28 + 6 * q^29 - 27 * q^32 + 36 * q^34 + 24 * q^38 + 48 * q^40 + 48 * q^41 + 25 * q^44 + 16 * q^49 + 6 * q^52 - 6 * q^53 - 40 * q^58 - 26 * q^61 - 32 * q^62 - 18 * q^64 + 36 * q^68 - 54 * q^70 + 16 * q^73 + 2 * q^74 + 43 * q^76 - 80 * q^77 + 30 * q^80 + 11 * q^82 + 14 * q^85 + 48 * q^86 - 18 * q^89 + 52 * q^92 - 12 * q^97 - 51 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	1.16486	−	0.801943i	0.823677	−	0.567059i
$2$	1.16486	−	0.801943i	0.823677	−	0.567059i
$3$		0			0
$3$		0			0
$4$	0.713775	−	1.86829i	0.356888	−	0.934147i
$5$	−1.59295	+	2.75907i	−0.712389	+	1.23389i	0.251569	+	0.967839i	$0.419054\pi$
$5$	−1.59295	+	2.75907i	−0.712389	+	1.23389i	−0.963958	+	0.266055i	$0.914280\pi$
$6$		0			0
$7$			2.36291i			0.893097i	0.894759	+	0.446548i	$0.147347\pi$
$7$			2.36291i			0.893097i	−0.894759	+	0.446548i	$0.852653\pi$
$8$	−0.666820	−	2.74870i	−0.235757	−	0.971812i
$9$		0			0
$10$	0.357061	+	4.49138i	0.112913	+	1.42030i
$11$			5.46750i			1.64851i	0.566216	+	0.824257i	$0.308407\pi$
$11$			5.46750i			1.64851i	−0.566216	+	0.824257i	$0.691593\pi$
$12$		0			0
$13$	−2.31924	+	1.33901i	−0.643241	+	0.371375i	−0.785862	−	0.618402i	$-0.787780\pi$
$13$	−2.31924	+	1.33901i	−0.643241	+	0.371375i	0.142621	+	0.989777i	$0.454447\pi$
$14$	1.89492	+	2.75245i	0.506439	+	0.735623i
$15$		0			0
$16$	−2.98105	−	2.66709i	−0.745262	−	0.666771i
$17$	0.552780	−	0.957443i	0.134069	−	0.232214i	−0.791173	−	0.611593i	$-0.790529\pi$
$17$	0.552780	−	0.957443i	0.134069	−	0.232214i	0.925241	+	0.379379i	$0.123862\pi$
$18$		0			0
$19$	−1.37952	+	4.13484i	−0.316484	+	0.948598i
$19$	−1.37952	+	4.13484i	−0.316484	+	0.948598i
$20$	4.01775	+	4.94546i	0.898396	+	1.10584i
$21$		0			0
$22$	4.38462	+	6.36885i	0.934805	+	1.35784i
$23$	2.46168	−	1.42125i	0.513296	−	0.296352i	−0.220891	−	0.975298i	$-0.570897\pi$
$23$	2.46168	−	1.42125i	0.513296	−	0.296352i	0.734187	+	0.678947i	$0.237563\pi$
$24$		0			0
$25$	−2.57499	−	4.46001i	−0.514997	−	0.892001i
$26$	−1.62777	+	3.41965i	−0.319231	+	0.670649i
$27$		0			0
$28$	4.41462	+	1.68659i	0.834284	+	0.318735i
$29$	5.63736	−	3.25473i	1.04683	−	0.604389i	0.125071	−	0.992148i	$-0.460084\pi$
$29$	5.63736	−	3.25473i	1.04683	−	0.604389i	0.921761	+	0.387759i	$0.126751\pi$
$30$		0			0
$31$	−1.01504			−0.182306			−0.0911531	−	0.995837i	$-0.529055\pi$
$31$	−1.01504			−0.182306			−0.0911531	+	0.995837i	$0.529055\pi$
$32$	−5.61134	−	0.716137i	−0.991954	−	0.126596i
$33$		0			0
$34$	−0.123906	−	1.55858i	−0.0212497	−	0.267294i
$35$	−6.51945	−	3.76400i	−1.10199	−	0.636233i
$36$		0			0
$37$			0.450315i			0.0740314i	0.999315	+	0.0370157i	$0.0117851\pi$
$37$			0.450315i			0.0740314i	−0.999315	+	0.0370157i	$0.988215\pi$
$38$	1.70896	+	5.92279i	0.277231	+	0.960803i
$39$		0			0
$40$	8.64607	+	2.53874i	1.36706	+	0.401410i
$41$	−0.336089	−	0.194041i	−0.0524882	−	0.0303041i	0.473526	−	0.880780i	$-0.342981\pi$
$41$	−0.336089	−	0.194041i	−0.0524882	−	0.0303041i	−0.526014	+	0.850476i	$0.676314\pi$
$42$		0			0
$43$	4.96197	+	2.86479i	0.756693	+	0.436877i	0.828107	−	0.560570i	$-0.189418\pi$
$43$	4.96197	+	2.86479i	0.756693	+	0.436877i	−0.0714141	+	0.997447i	$0.522751\pi$
$44$	10.2149	+	3.90257i	1.53995	+	0.588334i
$45$		0			0
$46$	1.72774	−	3.62968i	0.254741	−	0.535167i
$47$	2.91563	−	1.68334i	0.425288	−	0.245540i	−0.272049	−	0.962283i	$-0.587701\pi$
$47$	2.91563	−	1.68334i	0.425288	−	0.245540i	0.697337	+	0.716743i	$0.254368\pi$
$48$		0			0
$49$	1.41665			0.202378
$50$	−6.57616	−	3.13027i	−0.930009	−	0.442687i
$51$		0			0
$52$	0.846255	+	5.28878i	0.117355	+	0.733421i
$53$	3.53036	−	2.03825i	0.484932	−	0.279976i	−0.237537	−	0.971378i	$-0.576340\pi$
$53$	3.53036	−	2.03825i	0.484932	−	0.279976i	0.722470	+	0.691403i	$0.243007\pi$
$54$		0			0
$55$	−15.0852	−	8.70946i	−2.03409	−	1.17438i
$56$	6.49494	−	1.57564i	0.867922	−	0.210553i
$57$		0			0
$58$	3.95660	−	8.31213i	0.519527	−	1.09144i
$59$	−6.82450	+	11.8204i	−0.888474	+	1.53888i	−0.0467951	+	0.998905i	$0.514901\pi$
$59$	−6.82450	+	11.8204i	−0.888474	+	1.53888i	−0.841679	+	0.539978i	$0.818433\pi$
$60$		0			0
$61$	−6.77885	−	11.7413i	−0.867943	−	1.50332i	−0.864095	−	0.503329i	$-0.832108\pi$
$61$	−6.77885	−	11.7413i	−0.867943	−	1.50332i	−0.00384839	−	0.999993i	$-0.501225\pi$
$62$	−1.18237	+	0.814002i	−0.150161	+	0.103378i
$63$		0			0
$64$	−7.11070	+	3.66578i	−0.888838	+	0.458222i
$65$		−	8.53193i		−	1.05826i
$66$		0			0
$67$	4.27064	+	7.39696i	0.521742	+	0.903683i	0.999680	+	0.0252897i	$0.00805083\pi$
$67$	4.27064	+	7.39696i	0.521742	+	0.903683i	−0.477939	+	0.878393i	$0.658616\pi$
$68$	−1.39422	−	1.71616i	−0.169075	−	0.208114i
$69$		0			0
$70$	−10.6127	+	0.843703i	−1.26846	+	0.100842i
$71$	1.07447	−	1.86103i	0.127516	−	0.220864i	−0.795198	−	0.606350i	$-0.792633\pi$
$71$	1.07447	−	1.86103i	0.127516	−	0.220864i	0.922714	+	0.385486i	$0.125966\pi$
$72$		0			0
$73$	3.91944	−	6.78867i	0.458736	−	0.794554i	−0.540158	−	0.841563i	$-0.681636\pi$
$73$	3.91944	−	6.78867i	0.458736	−	0.794554i	0.998894	+	0.0470092i	$0.0149690\pi$
$74$	0.361127	+	0.524552i	0.0419802	+	0.0609779i
$75$		0			0
$76$	6.74043	+	5.52870i	0.773181	+	0.634186i
$77$	−12.9192			−1.47228
$78$		0			0
$79$	5.57208	−	9.65112i	0.626908	−	1.08584i	−0.361261	−	0.932465i	$-0.617654\pi$
$79$	5.57208	−	9.65112i	0.626908	−	1.08584i	0.988169	−	0.153371i	$-0.0490131\pi$
$80$	12.1073	−	3.97639i	1.35364	−	0.444574i
$81$		0			0
$82$	−0.547104	+	0.0434943i	−0.0604176	+	0.00480315i
$83$			4.14868i			0.455376i	0.973734	+	0.227688i	$0.0731167\pi$
$83$			4.14868i			0.455376i	−0.973734	+	0.227688i	$0.926883\pi$
$84$		0			0
$85$	1.76110	+	3.05032i	0.191018	+	0.330854i
$86$	8.07738	−	0.642145i	0.871006	−	0.0692443i
$87$		0			0
$88$	15.0285	−	3.64584i	1.60205	−	0.388648i
$89$	−4.19126	+	2.41982i	−0.444272	+	0.256501i	−0.705408	−	0.708801i	$-0.749236\pi$
$89$	−4.19126	+	2.41982i	−0.444272	+	0.256501i	0.261136	+	0.965302i	$0.415903\pi$
$90$		0			0
$91$	−3.16397	−	5.48016i	−0.331674	−	0.574477i
$92$	−0.898230	−	5.61360i	−0.0936470	−	0.585258i
$93$		0			0
$94$	2.04634	−	4.29901i	0.211064	−	0.443409i
$95$	−9.21082	−	10.3928i	−0.945010	−	1.06628i
$96$		0			0
$97$	−0.641491	−	0.370365i	−0.0651335	−	0.0376048i	0.467080	−	0.884215i	$-0.345306\pi$
$97$	−0.641491	−	0.370365i	−0.0651335	−	0.0376048i	−0.532213	+	0.846610i	$0.678639\pi$
$98$	1.65019	−	1.13607i	0.166694	−	0.114760i
$99$		0			0
$100$	−10.1706	+	1.62739i	−1.01706	+	0.162739i
$101$	−2.69851	−	4.67396i	−0.268512	−	0.465076i	0.699966	−	0.714176i	$-0.253199\pi$
$101$	−2.69851	−	4.67396i	−0.268512	−	0.465076i	−0.968478	+	0.249100i	$0.919865\pi$
$102$		0			0
$103$	−7.54816			−0.743743			−0.371871	−	0.928284i	$-0.621284\pi$
$103$	−7.54816			−0.743743			−0.371871	+	0.928284i	$0.621284\pi$
$104$	5.22706	+	5.48201i	0.512556	+	0.537555i
$105$		0			0
$106$	2.47779	−	5.20542i	0.240665	−	0.505595i
$107$	18.4008			1.77887			0.889437	−	0.457058i	$-0.151097\pi$
$107$	18.4008			1.77887			0.889437	+	0.457058i	$0.151097\pi$
$108$		0			0
$109$	4.23847	+	2.44708i	0.405971	+	0.234388i	0.689057	−	0.724707i	$-0.258025\pi$
$109$	4.23847	+	2.44708i	0.405971	+	0.234388i	−0.283086	+	0.959095i	$0.591358\pi$
$110$	−24.5566	+	1.95223i	−2.34138	+	0.186138i
$111$		0			0
$112$	6.30209	−	7.04396i	0.595491	−	0.665591i
$113$			17.8362i			1.67789i	0.544220	+	0.838943i	$0.316826\pi$
$113$			17.8362i			1.67789i	−0.544220	+	0.838943i	$0.683174\pi$
$114$		0			0
$115$			9.05594i			0.844471i
$116$	−2.05699	−	12.8554i	−0.190987	−	1.19359i
$117$		0			0
$118$	1.52972	+	19.2419i	0.140822	+	1.77136i
$119$	2.26235	+	1.30617i	0.207390	+	0.119736i
$120$		0			0
$121$	−18.8936			−1.71760
$122$	−17.3122	−	8.24068i	−1.56738	−	0.746076i
$123$		0			0
$124$	−0.724509	+	1.89639i	−0.0650628	+	0.170301i
$125$	0.477794			0.0427352
$126$		0			0
$127$	4.84855	+	8.39793i	0.430239	+	0.745196i	0.996894	−	0.0787596i	$-0.0250959\pi$
$127$	4.84855	+	8.39793i	0.430239	+	0.745196i	−0.566655	+	0.823955i	$0.691763\pi$
$128$	−5.34319	+	9.97248i	−0.472276	+	0.881451i
$129$		0			0
$130$	−6.84212	−	9.93846i	−0.600094	−	0.871661i
$131$	−6.81626	−	3.93537i	−0.595539	−	0.343835i	0.171745	−	0.985141i	$-0.445059\pi$
$131$	−6.81626	−	3.93537i	−0.595539	−	0.343835i	−0.767285	+	0.641307i	$0.778393\pi$
$132$		0			0
$133$	−9.77027	−	3.25969i	−0.847190	−	0.282651i
$134$	10.9066	+	5.19158i	0.942188	+	0.448485i
$135$		0			0
$136$	−3.00033	−	0.880984i	−0.257276	−	0.0755437i
$137$	−5.32438	−	9.22210i	−0.454893	−	0.787897i	0.543790	−	0.839222i	$-0.316989\pi$
$137$	−5.32438	−	9.22210i	−0.454893	−	0.787897i	−0.998682	+	0.0513247i	$0.983656\pi$
$138$		0			0
$139$	−3.86571	+	2.23187i	−0.327885	+	0.189305i	−0.654902	−	0.755714i	$-0.727290\pi$
$139$	−3.86571	+	2.23187i	−0.327885	+	0.189305i	0.327017	+	0.945019i	$0.393957\pi$
$140$	−11.6857	+	9.49359i	−0.987621	+	0.802355i
$141$		0			0
$142$	−0.240842	−	3.02949i	−0.0202110	−	0.254229i
$143$	−7.32106	−	12.6804i	−0.612218	−	1.06039i
$144$		0			0
$145$			20.7385i			1.72224i
$146$	−0.878545	−	11.0510i	−0.0727089	−	0.914587i
$147$		0			0
$148$	0.841321	+	0.321424i	0.0691562	+	0.0264209i
$149$	4.00960	−	6.94483i	0.328479	−	0.568942i	−0.653731	−	0.756727i	$-0.726797\pi$
$149$	4.00960	−	6.94483i	0.328479	−	0.568942i	0.982210	+	0.187785i	$0.0601307\pi$
$150$		0			0
$151$	5.53975			0.450818			0.225409	−	0.974264i	$-0.427628\pi$
$151$	5.53975			0.450818			0.225409	+	0.974264i	$0.427628\pi$
$152$	12.2853	+	1.03469i	0.996472	+	0.0839247i
$153$		0			0
$154$	−15.0490	+	10.3605i	−1.21269	+	0.834871i
$155$	1.61691	−	2.80056i	0.129873	−	0.224947i
$156$		0			0
$157$	1.42480	−	2.46782i	0.113711	−	0.196954i	−0.803553	−	0.595234i	$-0.797059\pi$
$157$	1.42480	−	2.46782i	0.113711	−	0.196954i	0.917264	+	0.398280i	$0.130393\pi$
$158$	−1.24898	−	15.7106i	−0.0993638	−	1.24987i
$159$		0			0
$160$	10.9145	−	14.3413i	0.862864	−	1.13378i
$161$	3.35829	+	5.81674i	0.264671	+	0.458423i
$162$		0			0
$163$		−	8.60401i		−	0.673918i	−0.941519	−	0.336959i	$-0.890602\pi$
$163$		−	8.60401i		−	0.673918i	0.941519	−	0.336959i	$-0.109398\pi$
$164$	−0.602417	+	0.489411i	−0.0470409	+	0.0382166i
$165$		0			0
$166$	3.32700	+	4.83261i	0.258225	+	0.375083i
$167$	9.00563	+	15.5982i	0.696877	+	1.20703i	0.969544	+	0.244918i	$0.0787610\pi$
$167$	9.00563	+	15.5982i	0.696877	+	1.20703i	−0.272667	+	0.962108i	$0.587906\pi$
$168$		0			0
$169$	−2.91409	+	5.04735i	−0.224161	+	0.388257i
$170$	4.49761	+	2.14088i	0.344951	+	0.164198i
$171$		0			0
$172$	8.89401	−	7.22560i	0.678162	−	0.550947i
$173$	15.3081	+	8.83813i	1.16385	+	0.671951i	0.952224	−	0.305399i	$-0.0987899\pi$
$173$	15.3081	+	8.83813i	1.16385	+	0.671951i	0.211629	+	0.977350i	$0.432123\pi$
$174$		0			0
$175$	10.5386	−	6.08447i	0.796644	−	0.459942i
$176$	14.5823	−	16.2989i	1.09918	−	1.22858i
$177$		0			0
$178$	−2.94165	+	6.17989i	−0.220486	+	0.463203i
$179$	14.9607			1.11822			0.559108	−	0.829095i	$-0.311144\pi$
$179$	14.9607			1.11822			0.559108	+	0.829095i	$0.311144\pi$
$180$		0			0
$181$	15.1591	−	8.75213i	1.12677	−	0.650541i	0.183649	−	0.982992i	$-0.441209\pi$
$181$	15.1591	−	8.75213i	1.12677	−	0.650541i	0.943121	+	0.332451i	$0.107876\pi$
$182$	−8.08034	−	3.84627i	−0.598955	−	0.285104i
$183$		0			0
$184$	−5.54809	−	5.81870i	−0.409011	−	0.428960i
$185$	−1.24245	−	0.717330i	−0.0913469	−	0.0527392i
$186$		0			0
$187$	5.23482	+	3.02233i	0.382808	+	0.221014i
$188$	−1.06387	−	6.64877i	−0.0775906	−	0.484912i
$189$		0			0
$190$	−19.0637	−	4.71956i	−1.38303	−	0.342393i
$191$		−	18.6529i		−	1.34967i	−0.737967	−	0.674837i	$-0.764214\pi$
$191$		−	18.6529i		−	1.34967i	0.737967	−	0.674837i	$-0.235786\pi$
$192$		0			0
$193$	−6.44722	−	3.72230i	−0.464081	−	0.267937i	0.249678	−	0.968329i	$-0.419675\pi$
$193$	−6.44722	−	3.72230i	−0.464081	−	0.267937i	−0.713759	+	0.700392i	$0.753009\pi$
$194$	−1.04425	+	0.0830174i	−0.0749731	+	0.00596030i
$195$		0			0
$196$	1.01117	−	2.64671i	0.0722262	−	0.189051i
$197$	−14.1748			−1.00991			−0.504955	−	0.863146i	$-0.668491\pi$
$197$	−14.1748			−1.00991			−0.504955	+	0.863146i	$0.668491\pi$
$198$		0			0
$199$	5.81457	−	3.35704i	0.412184	−	0.237974i	−0.279544	−	0.960133i	$-0.590183\pi$
$199$	5.81457	−	3.35704i	0.412184	−	0.237974i	0.691728	+	0.722159i	$0.256850\pi$
$200$	−10.5422	+	10.0519i	−0.745444	+	0.710776i
$201$		0			0
$202$	−6.89162	−	3.28043i	−0.484893	−	0.230810i
$203$	7.69065	+	13.3206i	0.539778	+	0.934922i
$204$		0			0
$205$	1.07075	−	0.618195i	0.0747841	−	0.0431766i
$206$	−8.79252	+	6.05319i	−0.612604	+	0.421746i
$207$		0			0
$208$	10.4850	+	2.19394i	0.727006	+	0.152123i
$209$	−22.6073	−	7.54254i	−1.56378	−	0.521728i
$210$		0			0
$211$	−3.81983	+	6.61614i	−0.262968	+	0.455474i	−0.967029	−	0.254665i	$-0.918035\pi$
$211$	−3.81983	+	6.61614i	−0.262968	+	0.455474i	0.704061	+	0.710139i	$0.251368\pi$
$212$	−1.28817	−	8.05061i	−0.0884722	−	0.552918i
$213$		0			0
$214$	21.4343	−	14.7564i	1.46522	−	1.00873i
$215$	−15.8083	+	9.12695i	−1.07812	+	0.622453i
$216$		0			0
$217$		−	2.39845i		−	0.162817i
$218$	6.89962	−	0.548514i	0.467301	−	0.0371501i
$219$		0			0
$220$	−27.0393	+	21.9671i	−1.82299	+	1.48102i
$221$			2.96072i			0.199160i
$222$		0			0
$223$	0.858455	−	1.48689i	0.0574864	−	0.0995693i	−0.835850	−	0.548958i	$-0.815025\pi$
$223$	0.858455	−	1.48689i	0.0574864	−	0.0995693i	0.893336	+	0.449388i	$0.148358\pi$
$224$	1.69217	−	13.2591i	0.113063	−	0.885911i
$225$		0			0
$226$	14.3036	+	20.7766i	0.951460	+	1.38204i
$227$	−17.2724			−1.14641			−0.573203	−	0.819413i	$-0.694299\pi$
$227$	−17.2724			−1.14641			−0.573203	+	0.819413i	$0.694299\pi$
$228$		0			0
$229$	16.7940			1.10978			0.554891	−	0.831923i	$-0.312760\pi$
$229$	16.7940			1.10978			0.554891	+	0.831923i	$0.312760\pi$
$230$	7.26235	+	10.5489i	0.478865	+	0.695571i
$231$		0			0
$232$	−12.7054	−	13.3251i	−0.834150	−	0.874835i
$233$	1.66348	−	2.88123i	0.108978	−	0.188756i	−0.806378	−	0.591400i	$-0.798575\pi$
$233$	1.66348	−	2.88123i	0.108978	−	0.188756i	0.915357	+	0.402644i	$0.131909\pi$
$234$		0			0
$235$			10.7259i			0.699680i
$236$	17.2128	+	21.1873i	1.12046	+	1.37917i
$237$		0			0
$238$	3.68279	−	0.292779i	0.238720	−	0.0189780i
$239$			4.83178i			0.312542i	0.987714	+	0.156271i	$0.0499473\pi$
$239$			4.83178i			0.312542i	−0.987714	+	0.156271i	$0.950053\pi$
$240$		0			0
$241$	23.1768	−	13.3811i	1.49295	−	0.861954i	0.492980	−	0.870041i	$-0.335908\pi$
$241$	23.1768	−	13.3811i	1.49295	−	0.861954i	0.999967	+	0.00808705i	$0.00257422\pi$
$242$	−22.0083	+	15.1516i	−1.41475	+	0.973980i
$243$		0			0
$244$	−26.7748	+	4.28423i	−1.71408	+	0.274270i
$245$	−2.25665	+	3.90863i	−0.144172	+	0.249713i
$246$		0			0
$247$	−2.33717	−	11.4369i	−0.148710	−	0.727712i
$248$	0.676848	+	2.79003i	0.0429799	+	0.177167i
$249$		0			0
$250$	0.556561	−	0.383164i	0.0352000	−	0.0242334i
$251$	12.7393	−	7.35502i	0.804096	−	0.464245i	−0.0408056	−	0.999167i	$-0.512992\pi$
$251$	12.7393	−	7.35502i	0.804096	−	0.464245i	0.844901	+	0.534922i	$0.179659\pi$
$252$		0			0
$253$	7.77070	+	13.4592i	0.488540	+	0.846176i
$254$	12.3825	+	5.89412i	0.776948	+	0.369830i
$255$		0			0
$256$	1.77331	+	15.9014i	0.110832	+	0.993839i
$257$	8.75454	−	5.05443i	0.546093	−	0.315287i	−0.201452	−	0.979498i	$-0.564566\pi$
$257$	8.75454	−	5.05443i	0.546093	−	0.315287i	0.747545	+	0.664212i	$0.231233\pi$
$258$		0			0
$259$	−1.06406			−0.0661172
$260$	−15.9402	−	6.08988i	−0.988567	−	0.377678i
$261$		0			0
$262$	−11.0959	+	0.882115i	−0.685507	+	0.0544972i
$263$	−13.6702	−	7.89252i	−0.842943	−	0.486673i	0.0153204	−	0.999883i	$-0.495123\pi$
$263$	−13.6702	−	7.89252i	−0.842943	−	0.486673i	−0.858264	+	0.513209i	$0.828457\pi$
$264$		0			0
$265$			12.9874i			0.797807i
$266$	−13.9950	+	4.03813i	−0.858091	+	0.247594i
$267$		0			0
$268$	16.8680	−	2.69904i	1.03038	−	0.164870i
$269$	0.0632774	+	0.0365332i	0.00385809	+	0.00222747i	0.501928	−	0.864910i	$-0.332624\pi$
$269$	0.0632774	+	0.0365332i	0.00385809	+	0.00222747i	−0.498070	+	0.867137i	$0.665958\pi$
$270$		0			0
$271$	6.48453	+	3.74384i	0.393907	+	0.227422i	0.683852	−	0.729621i	$-0.260304\pi$
$271$	6.48453	+	3.74384i	0.393907	+	0.227422i	−0.289945	+	0.957043i	$0.593637\pi$
$272$	−4.20145	+	1.37987i	−0.254750	+	0.0836671i
$273$		0			0
$274$	−13.5977	−	6.47256i	−0.821469	−	0.391022i
$275$	24.3851	−	14.0787i	1.47048	−	0.848980i
$276$		0			0
$277$	−19.0585			−1.14511			−0.572557	−	0.819865i	$-0.694048\pi$
$277$	−19.0585			−1.14511			−0.572557	+	0.819865i	$0.694048\pi$
$278$	−2.71316	+	5.69988i	−0.162725	+	0.341856i
$279$		0			0
$280$	−5.99882	+	20.4299i	−0.358498	+	1.22092i
$281$	7.58314	−	4.37813i	0.452372	−	0.261177i	−0.256459	−	0.966555i	$-0.582556\pi$
$281$	7.58314	−	4.37813i	0.452372	−	0.261177i	0.708832	+	0.705378i	$0.249223\pi$
$282$		0			0
$283$	−17.9331	−	10.3537i	−1.06601	−	0.615461i	−0.138921	−	0.990303i	$-0.544363\pi$
$283$	−17.9331	−	10.3537i	−1.06601	−	0.615461i	−0.927088	+	0.374843i	$0.877697\pi$
$284$	−2.71003	−	3.33578i	−0.160810	−	0.197942i
$285$		0			0
$286$	−18.6970	−	8.89981i	−1.10557	−	0.526257i
$287$	0.458501	−	0.794148i	0.0270645	−	0.0468771i
$288$		0			0
$289$	7.88887	+	13.6639i	0.464051	+	0.803760i
$290$	16.6311	+	24.1574i	0.976612	+	1.41857i
$291$		0			0
$292$	−9.88564	−	12.1683i	−0.578513	−	0.712094i
$293$			19.7950i			1.15643i	0.815883	+	0.578217i	$0.196251\pi$
$293$			19.7950i			1.15643i	−0.815883	+	0.578217i	$0.803749\pi$
$294$		0			0
$295$	−21.7422	−	37.6586i	−1.26588	−	2.19257i
$296$	1.23778	−	0.300279i	0.0719446	−	0.0174534i
$297$		0			0
$298$	−0.898753	−	11.3052i	−0.0520634	−	0.654892i
$299$	−3.80615	+	6.59245i	−0.220115	+	0.381251i
$300$		0			0
$301$	−6.76926	+	11.7247i	−0.390173	+	0.675800i
$302$	6.45300	−	4.44256i	0.371329	−	0.255641i
$303$		0			0
$304$	15.1404	−	8.64687i	0.868361	−	0.495932i
$305$	43.1935			2.47325
$306$		0			0
$307$	4.47582	−	7.75235i	0.255449	−	0.442450i	−0.709569	−	0.704636i	$-0.751110\pi$
$307$	4.47582	−	7.75235i	0.255449	−	0.442450i	0.965017	+	0.262186i	$0.0844435\pi$
$308$	−9.22143	+	24.1369i	−0.525440	+	1.37533i
$309$		0			0
$310$	−0.362430	−	4.55892i	−0.0205846	−	0.258929i
$311$		−	0.249429i		−	0.0141438i	−0.999975	−	0.00707191i	$-0.997749\pi$
$311$		−	0.249429i		−	0.0141438i	0.999975	−	0.00707191i	$-0.00225108\pi$
$312$		0			0
$313$	11.8686	+	20.5570i	0.670852	+	1.16195i	0.977663	+	0.210179i	$0.0674046\pi$
$313$	11.8686	+	20.5570i	0.670852	+	1.16195i	−0.306811	+	0.951770i	$0.599262\pi$
$314$	−0.319369	−	4.01727i	−0.0180231	−	0.226707i
$315$		0			0
$316$	−14.0539	−	17.2990i	−0.790595	−	0.973146i
$317$	14.6359	−	8.45005i	0.822035	−	0.474602i	−0.0290826	−	0.999577i	$-0.509259\pi$
$317$	14.6359	−	8.45005i	0.822035	−	0.474602i	0.851118	+	0.524975i	$0.175925\pi$
$318$		0			0
$319$	17.7953	+	30.8223i	0.996343	+	1.72572i
$320$	1.21285	−	25.4583i	0.0678005	−	1.42316i
$321$		0			0
$322$	8.57662	+	4.08250i	0.477956	+	0.227509i
$323$	3.19630	+	3.60647i	0.177847	+	0.200669i
$324$		0			0
$325$	11.9440	+	6.89588i	0.662535	+	0.382515i
$326$	−6.89993	−	10.0224i	−0.382152	−	0.555091i
$327$		0			0
$328$	−0.309249	+	1.05320i	−0.0170754	+	0.0581531i
$329$	3.97758	+	6.88937i	0.219291	+	0.379823i
$330$		0			0
$331$	9.72419			0.534490			0.267245	−	0.963629i	$-0.413887\pi$
$331$	9.72419			0.534490			0.267245	+	0.963629i	$0.413887\pi$
$332$	7.75095	+	2.96122i	0.425388	+	0.162518i
$333$		0			0
$334$	22.9991	+	10.9477i	1.25846	+	0.599029i
$335$	−27.2117			−1.48673
$336$		0			0
$337$	8.24404	+	4.75970i	0.449081	+	0.259277i	0.707442	−	0.706771i	$-0.249849\pi$
$337$	8.24404	+	4.75970i	0.449081	+	0.259277i	−0.258361	+	0.966049i	$0.583182\pi$
$338$	0.653194	+	8.21636i	0.0355291	+	0.446911i
$339$		0			0
$340$	6.95593	−	1.11302i	0.377238	−	0.0603618i
$341$		−	5.54972i		−	0.300534i
$342$		0			0
$343$			19.8878i			1.07384i
$344$	4.56572	−	15.5493i	0.246167	−	0.838360i
$345$		0			0
$346$	24.9194	−	1.98107i	1.33967	−	0.106503i
$347$	15.9269	+	9.19538i	0.854999	+	0.493634i	0.862334	−	0.506339i	$-0.169002\pi$
$347$	15.9269	+	9.19538i	0.854999	+	0.493634i	−0.00733524	+	0.999973i	$0.502335\pi$
$348$		0			0
$349$	5.86074			0.313718			0.156859	−	0.987621i	$-0.449863\pi$
$349$	5.86074			0.313718			0.156859	+	0.987621i	$0.449863\pi$
$350$	7.39655	−	15.5389i	0.395362	−	0.830588i
$351$		0			0
$352$	3.91548	−	30.6800i	0.208696	−	1.63525i
$353$	12.9828			0.691006			0.345503	−	0.938418i	$-0.387708\pi$
$353$	12.9828			0.691006			0.345503	+	0.938418i	$0.387708\pi$
$354$		0			0
$355$	3.42315	+	5.92906i	0.181682	+	0.314682i
$356$	1.52933	+	9.55772i	0.0810542	+	0.506558i
$357$		0			0
$358$	17.4271	−	11.9976i	0.921049	−	0.634095i
$359$	−29.5172	−	17.0418i	−1.55786	−	0.899430i	−0.997462	−	0.0712049i	$-0.977316\pi$
$359$	−29.5172	−	17.0418i	−1.55786	−	0.899430i	−0.560396	−	0.828225i	$-0.689351\pi$
$360$		0			0
$361$	−15.1938	−	11.4082i	−0.799676	−	0.600432i
$362$	10.6395	−	22.3517i	0.559199	−	1.17478i
$363$		0			0
$364$	−12.4969	+	1.99963i	−0.655016	+	0.104809i
$365$	12.4870	+	21.6281i	0.653597	+	1.13206i
$366$		0			0
$367$	11.3161	−	6.53337i	0.590697	−	0.341039i	−0.174676	−	0.984626i	$-0.555888\pi$
$367$	11.3161	−	6.53337i	0.590697	−	0.341039i	0.765373	+	0.643587i	$0.222554\pi$
$368$	−11.1290	−	2.32869i	−0.580139	−	0.121391i
$369$		0			0
$370$	−2.02253	+	0.160790i	−0.105147	+	0.00835907i
$371$	4.81621	+	8.34193i	0.250045	+	0.433091i
$372$		0			0
$373$		−	11.8954i		−	0.615922i	−0.951399	−	0.307961i	$-0.900353\pi$
$373$		−	11.8954i		−	0.615922i	0.951399	−	0.307961i	$-0.0996466\pi$
$374$	8.52154	−	0.677456i	0.440638	−	0.0350304i
$375$		0			0
$376$	−6.57119	−	6.89170i	−0.338883	−	0.355412i
$377$	−8.71626	+	15.0970i	−0.448910	+	0.777535i
$378$		0			0
$379$	−8.93709			−0.459068			−0.229534	−	0.973301i	$-0.573720\pi$
$379$	−8.93709			−0.459068			−0.229534	+	0.973301i	$0.573720\pi$
$380$	−25.9913	+	9.79039i	−1.33332	+	0.502237i
$381$		0			0
$382$	−14.9585	−	21.7279i	−0.765345	−	1.11169i
$383$	6.14400	−	10.6417i	0.313944	−	0.543767i	−0.665269	−	0.746604i	$-0.731683\pi$
$383$	6.14400	−	10.6417i	0.313944	−	0.543767i	0.979212	+	0.202838i	$0.0650163\pi$
$384$		0			0
$385$	20.5797	−	35.6451i	1.04884	−	1.81664i
$386$	−10.4952	+	0.834356i	−0.534189	+	0.0424676i
$387$		0			0
$388$	−1.14983	+	0.934136i	−0.0583738	+	0.0474236i
$389$	3.61961	+	6.26935i	0.183522	+	0.317869i	0.943077	−	0.332573i	$-0.107917\pi$
$389$	3.61961	+	6.26935i	0.183522	+	0.317869i	−0.759556	+	0.650442i	$0.774584\pi$
$390$		0			0
$391$		−	3.14256i		−	0.158926i
$392$	−0.944648	−	3.89393i	−0.0477119	−	0.196673i
$393$		0			0
$394$	−16.5115	+	11.3673i	−0.831839	+	0.572679i
$395$	17.7521	+	30.7475i	0.893205	+	1.54708i
$396$		0			0
$397$	−14.7425	+	25.5347i	−0.739904	+	1.28155i	0.212633	+	0.977132i	$0.431796\pi$
$397$	−14.7425	+	25.5347i	−0.739904	+	1.28155i	−0.952538	+	0.304420i	$0.901537\pi$
$398$	4.08097	−	8.57342i	0.204561	−	0.429747i
$399$		0			0
$400$	−4.21906	+	20.1632i	−0.210953	+	1.00816i
$401$	−3.17820	−	1.83494i	−0.158712	−	0.0916323i	0.418541	−	0.908198i	$-0.362542\pi$
$401$	−3.17820	−	1.83494i	−0.158712	−	0.0916323i	−0.577252	+	0.816566i	$0.695875\pi$
$402$		0			0
$403$	2.35412	−	1.35915i	0.117267	−	0.0677040i
$404$	−10.6585	+	1.70546i	−0.530278	+	0.0848497i
$405$		0			0
$406$	19.6408	+	9.34910i	0.974759	+	0.463988i
$407$	−2.46210			−0.122042
$408$		0			0
$409$	0.913849	−	0.527611i	0.0451869	−	0.0260887i	−0.477236	−	0.878775i	$-0.658361\pi$
$409$	0.913849	−	0.527611i	0.0451869	−	0.0260887i	0.522423	+	0.852686i	$0.325028\pi$
$410$	0.751506	−	1.57878i	0.0371142	−	0.0779706i
$411$		0			0
$412$	−5.38769	+	14.1022i	−0.265433	+	0.694765i
$413$	−27.9305	−	16.1257i	−1.37437	−	0.793494i
$414$		0			0
$415$	−11.4465	−	6.60864i	−0.561886	−	0.324405i
$416$	13.9730	−	5.85277i	0.685081	−	0.286955i
$417$		0			0
$418$	−32.3829	+	9.34376i	−1.58390	+	0.457018i
$419$			12.9932i			0.634757i	0.948299	+	0.317379i	$0.102803\pi$
$419$			12.9932i			0.634757i	−0.948299	+	0.317379i	$0.897197\pi$
$420$		0			0
$421$	28.8014	+	16.6285i	1.40369	+	0.810424i	0.994770	−	0.102144i	$-0.0325704\pi$
$421$	28.8014	+	16.6285i	1.40369	+	0.810424i	0.408925	+	0.912568i	$0.365904\pi$
$422$	0.856217	+	10.7701i	0.0416800	+	0.524282i
$423$		0			0
$424$	−7.95666	−	8.34475i	−0.386410	−	0.405257i
$425$	−5.69360			−0.276180
$426$		0			0
$427$	27.7437	−	16.0178i	1.34261	−	0.775157i
$428$	13.1340	−	34.3781i	0.634858	−	1.66173i
$429$		0			0
$430$	−11.0951	+	23.3090i	−0.535055	+	1.12406i
$431$	4.67046	+	8.08948i	0.224968	+	0.389656i	0.956310	−	0.292355i	$-0.0944388\pi$
$431$	4.67046	+	8.08948i	0.224968	+	0.389656i	−0.731342	+	0.682011i	$0.761106\pi$
$432$		0			0
$433$	−11.4412	+	6.60558i	−0.549829	+	0.317444i	−0.749053	−	0.662510i	$-0.769491\pi$
$433$	−11.4412	+	6.60558i	−0.549829	+	0.317444i	0.199224	+	0.979954i	$0.436158\pi$
$434$	−1.92342	−	2.79384i	−0.0923269	−	0.134109i
$435$		0			0
$436$	7.59718	−	6.17204i	0.363839	−	0.295587i
$437$	2.48071	+	12.1393i	0.118669	+	0.580702i
$438$		0			0
$439$	−9.90270	+	17.1520i	−0.472630	+	0.818619i	−0.999509	−	0.0313210i	$-0.990029\pi$
$439$	−9.90270	+	17.1520i	−0.472630	+	0.818619i	0.526879	+	0.849940i	$0.323362\pi$
$440$	−13.8806	+	47.2724i	−0.661730	+	2.25362i
$441$		0			0
$442$	2.37433	+	3.44881i	0.112935	+	0.164043i
$443$	−8.86172	+	5.11632i	−0.421033	+	0.243084i	−0.695519	−	0.718508i	$-0.744826\pi$
$443$	−8.86172	+	5.11632i	−0.421033	+	0.243084i	0.274486	+	0.961591i	$0.411492\pi$
$444$		0			0
$445$		−	15.4186i		−	0.730914i
$446$	−0.192423	−	2.42044i	−0.00911150	−	0.114611i
$447$		0			0
$448$	−8.66191	−	16.8020i	−0.409237	−	0.793818i
$449$		−	9.69618i		−	0.457591i	−0.973475	−	0.228795i	$-0.926521\pi$
$449$		−	9.69618i		−	0.457591i	0.973475	−	0.228795i	$-0.0734787\pi$
$450$		0			0
$451$	1.06092	−	1.83757i	0.0499567	−	0.0865276i
$452$	33.3232	+	12.7310i	1.56739	+	0.598817i
$453$		0			0
$454$	−20.1198	+	13.8514i	−0.944269	+	0.650080i
$455$	20.1602			0.945125
$456$		0			0
$457$	−8.85003			−0.413987			−0.206993	−	0.978342i	$-0.566368\pi$
$457$	−8.85003			−0.413987			−0.206993	+	0.978342i	$0.566368\pi$
$458$	19.5626	−	13.4679i	0.914102	−	0.629312i
$459$		0			0
$460$	16.9192	+	6.46391i	0.788860	+	0.301381i
$461$	4.85595	−	8.41075i	0.226164	−	0.391728i	−0.730504	−	0.682909i	$-0.760715\pi$
$461$	4.85595	−	8.41075i	0.226164	−	0.391728i	0.956668	+	0.291181i	$0.0940481\pi$
$462$		0			0
$463$		−	38.4094i		−	1.78504i	−0.451013	−	0.892518i	$-0.648937\pi$
$463$		−	38.4094i		−	1.78504i	0.451013	−	0.892518i	$-0.351063\pi$
$464$	−25.4859	−	5.33281i	−1.18315	−	0.247569i
$465$		0			0
$466$	−0.372870	−	4.69024i	−0.0172729	−	0.217271i
$467$		−	21.7838i		−	1.00803i	−0.863694	−	0.504016i	$-0.831855\pi$
$467$		−	21.7838i		−	1.00803i	0.863694	−	0.504016i	$-0.168145\pi$
$468$		0			0
$469$	−17.4784	+	10.0911i	−0.807076	+	0.465966i
$470$	8.60156	+	12.4941i	0.396760	+	0.576311i
$471$		0			0
$472$	37.0414	+	10.8764i	1.70497	+	0.500628i
$473$	−15.6633	+	27.1296i	−0.720198	+	1.24742i
$474$		0			0
$475$	21.9937	−	4.49448i	1.00914	−	0.206221i
$476$	4.05512	−	3.29443i	0.185866	−	0.151000i
$477$		0			0
$478$	3.87481	+	5.62833i	0.177230	+	0.257434i
$479$	10.5544	−	6.09359i	0.482243	−	0.278423i	−0.239108	−	0.970993i	$-0.576855\pi$
$479$	10.5544	−	6.09359i	0.482243	−	0.278423i	0.721351	+	0.692570i	$0.243522\pi$
$480$		0			0
$481$	−0.602978	−	1.04439i	−0.0274934	−	0.0476200i
$482$	16.2667	−	34.1735i	0.740928	−	1.55656i
$483$		0			0
$484$	−13.4858	+	35.2988i	−0.612990	+	1.60449i
$485$	2.04373	−	1.17995i	0.0928008	−	0.0535786i
$486$		0			0
$487$	−27.8697			−1.26290			−0.631448	−	0.775418i	$-0.717539\pi$
$487$	−27.8697			−1.26290			−0.631448	+	0.775418i	$0.717539\pi$
$488$	−27.7531	+	26.4624i	−1.25632	+	1.19790i
$489$		0			0
$490$	0.505829	+	6.36269i	0.0228510	+	0.287437i
$491$	14.9996	+	8.66002i	0.676922	+	0.390821i	0.798694	−	0.601737i	$-0.205524\pi$
$491$	14.9996	+	8.66002i	0.676922	+	0.390821i	−0.121772	+	0.992558i	$0.538858\pi$
$492$		0			0
$493$		−	7.19660i		−	0.324119i
$494$	−11.8942	−	11.4480i	−0.535145	−	0.515072i
$495$		0			0
$496$	3.02588	+	2.70719i	0.135866	+	0.121557i
$497$	4.39745	+	2.53887i	0.197253	+	0.113884i
$498$		0			0
$499$	−1.00693	−	0.581349i	−0.0450762	−	0.0260248i	0.477293	−	0.878744i	$-0.341618\pi$
$499$	−1.00693	−	0.581349i	−0.0450762	−	0.0260248i	−0.522369	+	0.852720i	$0.674952\pi$
$500$	0.341038	−	0.892660i	0.0152517	−	0.0399210i
$501$		0			0
$502$	8.94110	−	18.7837i	0.399061	−	0.838358i
$503$	−11.1928	+	6.46214i	−0.499060	+	0.288133i	−0.728325	−	0.685231i	$-0.759701\pi$
$503$	−11.1928	+	6.46214i	−0.499060	+	0.288133i	0.229265	+	0.973364i	$0.426368\pi$
$504$		0			0
$505$	17.1944			0.765140
$506$	19.8453	+	9.44642i	0.882231	+	0.419944i
$507$		0			0
$508$	19.1506	−	3.06428i	0.849670	−	0.135955i
$509$	−25.6884	+	14.8312i	−1.13862	+	0.657381i	−0.946088	−	0.323910i	$-0.895002\pi$
$509$	−25.6884	+	14.8312i	−1.13862	+	0.657381i	−0.192530	+	0.981291i	$0.561669\pi$
$510$		0			0
$511$	16.0410	+	9.26130i	0.709614	+	0.409696i
$512$	14.8177	+	17.1008i	0.654855	+	0.755754i
$513$		0			0
$514$	6.14440	−	12.9083i	0.271018	−	0.569362i
$515$	12.0239	−	20.8259i	0.529834	−	0.917700i
$516$		0			0
$517$	9.20365	+	15.9412i	0.404776	+	0.701093i
$518$	−1.23947	+	0.853312i	−0.0544592	+	0.0374924i
$519$		0			0
$520$	−23.4517	+	5.68927i	−1.02843	+	0.249491i
$521$		−	35.2430i		−	1.54402i	−0.635608	−	0.772012i	$-0.719251\pi$
$521$		−	35.2430i		−	1.54402i	0.635608	−	0.772012i	$-0.280749\pi$
$522$		0			0
$523$	11.4242	+	19.7872i	0.499543	+	0.865234i	1.00000		0.000527203i	$-0.000167814\pi$
$523$	11.4242	+	19.7872i	0.499543	+	0.865234i	−0.500457	+	0.865762i	$0.666834\pi$
$524$	−12.2177	+	9.92581i	−0.533733	+	0.433611i
$525$		0			0
$526$	−22.2532	+	1.76911i	−0.970286	+	0.0771369i
$527$	−0.561093	+	0.971841i	−0.0244416	+	0.0423341i
$528$		0			0
$529$	−7.46008	+	12.9212i	−0.324351	+	0.561793i
$530$	10.4151	+	15.1284i	0.452404	+	0.657135i
$531$		0			0
$532$	−13.0638	+	15.9271i	−0.566389	+	0.690525i
$533$	1.03929			0.0450168
$534$		0			0
$535$	−29.3116	+	50.7692i	−1.26725	+	2.19494i
$536$	17.4843	−	16.6712i	0.755206	−	0.720084i
$537$		0			0
$538$	0.103007	−	0.00818894i	0.00444093	−	0.000353050i
$539$			7.74551i			0.333623i
$540$		0			0
$541$	−18.2188	−	31.5560i	−0.783289	−	1.35670i	−0.930016	−	0.367520i	$-0.880207\pi$
$541$	−18.2188	−	31.5560i	−0.783289	−	1.35670i	0.146727	−	0.989177i	$-0.453126\pi$
$542$	10.5559	−	0.839184i	0.453414	−	0.0360460i
$543$		0			0
$544$	−3.78750	+	4.97667i	−0.162388	+	0.213373i
$545$	−13.5033	+	7.79616i	−0.578420	+	0.333951i
$546$		0			0
$547$	14.8588	+	25.7362i	0.635317	+	1.10040i	0.986448	+	0.164075i	$0.0524638\pi$
$547$	14.8588	+	25.7362i	0.635317	+	1.10040i	−0.351131	+	0.936326i	$0.614203\pi$
$548$	−21.0300	+	3.36500i	−0.898357	+	0.143746i
$549$		0			0
$550$	17.1148	−	35.9551i	0.729776	−	1.53313i
$551$	5.68094	+	27.7996i	0.242016	+	1.18430i
$552$		0			0
$553$	22.8048	+	13.1663i	0.969757	+	0.559889i
$554$	−22.2004	+	15.2838i	−0.943204	+	0.649347i
$555$		0			0
$556$	1.41054	+	8.81534i	0.0598202	+	0.373854i
$557$	2.98070	+	5.16273i	0.126296	+	0.218752i	0.922239	−	0.386620i	$-0.126358\pi$
$557$	2.98070	+	5.16273i	0.126296	+	0.218752i	−0.795943	+	0.605372i	$0.793024\pi$
$558$		0			0
$559$	−15.3440			−0.648982
$560$	9.39587	+	28.6086i	0.397048	+	1.20893i
$561$		0			0
$562$	5.32225	−	11.1811i	0.224506	−	0.471647i
$563$	−35.3916			−1.49158			−0.745789	−	0.666182i	$-0.767927\pi$
$563$	−35.3916			−1.49158			−0.745789	+	0.666182i	$0.767927\pi$
$564$		0			0
$565$	−49.2113	−	28.4121i	−2.07033	−	1.19531i
$566$	−29.1925	+	2.32078i	−1.22705	+	0.0975495i
$567$		0			0
$568$	−5.83189	−	1.71241i	−0.244701	−	0.0718512i
$569$		−	30.2541i		−	1.26832i	−0.773203	−	0.634158i	$-0.781347\pi$
$569$		−	30.2541i		−	1.26832i	0.773203	−	0.634158i	$-0.218653\pi$
$570$		0			0
$571$		−	25.4945i		−	1.06691i	−0.845828	−	0.533456i	$-0.820893\pi$
$571$		−	25.4945i		−	1.06691i	0.845828	−	0.533456i	$-0.179107\pi$
$572$	−28.9164	+	4.62690i	−1.20906	+	0.193461i
$573$		0			0
$574$	−0.102773	−	1.29276i	−0.00428968	−	0.0539587i
$575$	−12.6776	−	7.31941i	−0.528692	−	0.305240i
$576$		0			0
$577$	−12.0785			−0.502836			−0.251418	−	0.967879i	$-0.580897\pi$
$577$	−12.0785			−0.502836			−0.251418	+	0.967879i	$0.580897\pi$
$578$	20.1471	+	9.59007i	0.838008	+	0.398894i
$579$		0			0
$580$	38.7457	+	14.8026i	1.60883	+	0.614646i
$581$	−9.80296			−0.406695
$582$		0			0
$583$	11.1442	+	19.3022i	0.461544	+	0.799417i
$584$	−21.2736	−	6.24655i	−0.880307	−	0.258484i
$585$		0			0
$586$	15.8744	+	23.0583i	0.655766	+	0.952528i
$587$	−18.8754	−	10.8977i	−0.779070	−	0.449796i	0.0570304	−	0.998372i	$-0.481837\pi$
$587$	−18.8754	−	10.8977i	−0.779070	−	0.449796i	−0.836101	+	0.548576i	$0.815170\pi$
$588$		0			0
$589$	1.40027	−	4.19702i	0.0576970	−	0.172935i
$590$	−55.5265	−	26.4308i	−2.28599	−	1.08814i
$591$		0			0
$592$	1.20103	−	1.34241i	0.0493620	−	0.0551728i
$593$	10.3212	+	17.8768i	0.423839	+	0.734111i	0.996311	−	0.0858135i	$-0.0273489\pi$
$593$	10.3212	+	17.8768i	0.423839	+	0.734111i	−0.572472	+	0.819924i	$0.694016\pi$
$594$		0			0
$595$	−7.20764	+	4.16133i	−0.295484	+	0.170598i
$596$	−10.1130	−	12.4482i	−0.414246	−	0.509896i
$597$		0			0
$598$	0.853151	+	10.7316i	0.0348879	+	0.438846i
$599$	−18.6426	−	32.2900i	−0.761717	−	1.31933i	−0.941965	−	0.335711i	$-0.891023\pi$
$599$	−18.6426	−	32.2900i	−0.761717	−	1.31933i	0.180248	−	0.983621i	$-0.442310\pi$
$600$		0			0
$601$		−	32.9087i		−	1.34238i	−0.741287	−	0.671188i	$-0.765784\pi$
$601$		−	32.9087i		−	1.34238i	0.741287	−	0.671188i	$-0.234216\pi$
$602$	1.51733	+	19.0861i	0.0618418	+	0.777893i
$603$		0			0
$604$	3.95413	−	10.3499i	0.160891	−	0.421131i
$605$	30.0965	−	52.1287i	1.22360	−	2.11933i
$606$		0			0
$607$	−43.4094			−1.76193			−0.880966	−	0.473180i	$-0.843106\pi$
$607$	−43.4094			−1.76193			−0.880966	+	0.473180i	$0.843106\pi$
$608$	10.7021	−	22.2141i	0.434027	−	0.900900i
$609$		0			0
$610$	50.3142	−	34.6387i	2.03716	−	1.40248i
$611$	−4.50802	+	7.80813i	−0.182375	+	0.315883i
$612$		0			0
$613$	−23.0269	+	39.8838i	−0.930048	+	1.61089i	−0.146814	+	0.989164i	$0.546902\pi$
$613$	−23.0269	+	39.8838i	−0.930048	+	1.61089i	−0.783234	+	0.621727i	$0.786431\pi$
$614$	−1.00326	−	12.6197i	−0.0404882	−	0.509290i
$615$		0			0
$616$	8.61480	+	35.5111i	0.347100	+	1.43078i
$617$	4.97177	+	8.61136i	0.200156	+	0.346680i	0.948579	−	0.316542i	$-0.102522\pi$
$617$	4.97177	+	8.61136i	0.200156	+	0.346680i	−0.748423	+	0.663222i	$0.769188\pi$
$618$		0			0
$619$		−	4.75114i		−	0.190964i	−0.995431	−	0.0954822i	$-0.969561\pi$
$619$		−	4.75114i		−	0.190964i	0.995431	−	0.0954822i	$-0.0304393\pi$
$620$	−4.07817	−	5.01983i	−0.163783	−	0.201601i
$621$		0			0
$622$	−0.200028	−	0.290549i	−0.00802038	−	0.0116499i
$623$	−5.71783	−	9.90358i	−0.229080	−	0.396778i
$624$		0			0
$625$	12.1138	−	20.9818i	0.484553	−	0.839270i
$626$	30.3107	+	14.4280i	1.21146	+	0.576658i
$627$		0			0
$628$	−3.59364	−	4.42342i	−0.143402	−	0.176514i
$629$	0.431151	+	0.248925i	0.0171911	+	0.00992530i
$630$		0			0
$631$	−17.8068	+	10.2807i	−0.708876	+	0.409270i	−0.810645	−	0.585538i	$-0.800883\pi$
$631$	−17.8068	+	10.2807i	−0.708876	+	0.409270i	0.101769	+	0.994808i	$0.467550\pi$
$632$	−30.2436	−	8.88041i	−1.20303	−	0.353244i
$633$		0			0
$634$	10.2723	−	21.5803i	0.407964	−	0.857062i
$635$	−30.8940			−1.22599
$636$		0			0
$637$	−3.28554	+	1.89691i	−0.130178	+	0.0751582i
$638$	45.4466	+	21.6327i	1.79925	+	0.856448i
$639$		0			0
$640$	−19.0033	−	30.6279i	−0.751173	−	1.21067i
$641$	−33.0540	−	19.0838i	−1.30556	−	0.753763i	−0.324205	−	0.945987i	$-0.605097\pi$
$641$	−33.0540	−	19.0838i	−1.30556	−	0.753763i	−0.981351	+	0.192223i	$0.938430\pi$
$642$		0			0
$643$	−18.5705	−	10.7217i	−0.732350	−	0.422822i	0.0869313	−	0.996214i	$-0.472294\pi$
$643$	−18.5705	−	10.7217i	−0.732350	−	0.422822i	−0.819281	+	0.573392i	$0.805627\pi$
$644$	13.2644	−	2.12244i	0.522692	−	0.0836358i
$645$		0			0
$646$	6.61542	+	1.63776i	0.260280	+	0.0644370i
$647$			23.8222i			0.936547i	0.883583	+	0.468274i	$0.155124\pi$
$647$			23.8222i			0.936547i	−0.883583	+	0.468274i	$0.844876\pi$
$648$		0			0
$649$	−64.6280	−	37.3130i	−2.53687	−	1.46466i
$650$	19.4432	−	1.54571i	0.762623	−	0.0606279i
$651$		0			0
$652$	−16.0748	−	6.14133i	−0.629539	−	0.240513i
$653$	−16.6726			−0.652450			−0.326225	−	0.945292i	$-0.605777\pi$
$653$	−16.6726			−0.652450			−0.326225	+	0.945292i	$0.605777\pi$
$654$		0			0
$655$	21.7159	−	12.5377i	0.848512	−	0.489888i
$656$	0.484373	+	1.47482i	0.0189116	+	0.0575821i
$657$		0			0
$658$	10.1582	+	4.83533i	0.396007	+	0.188501i
$659$	7.26163	+	12.5775i	0.282873	+	0.489950i	0.972091	−	0.234604i	$-0.0753792\pi$
$659$	7.26163	+	12.5775i	0.282873	+	0.489950i	−0.689218	+	0.724554i	$0.742046\pi$
$660$		0			0
$661$	19.7070	−	11.3778i	0.766513	−	0.442547i	−0.0651162	−	0.997878i	$-0.520742\pi$
$661$	19.7070	−	11.3778i	0.766513	−	0.442547i	0.831629	+	0.555331i	$0.187408\pi$
$662$	11.3273	−	7.79825i	0.440247	−	0.303087i
$663$		0			0
$664$	11.4035	−	2.76642i	0.442540	−	0.107358i
$665$	24.5573	−	21.7644i	0.952290	−	0.843985i
$666$		0			0
$667$	9.25159	−	16.0242i	0.358223	−	0.620461i
$668$	35.5701	−	5.69155i	1.37625	−	0.220213i
$669$		0			0
$670$	−31.6977	+	21.8222i	−1.22459	+	0.843065i
$671$	64.1957	−	37.0634i	2.47825	−	1.43082i
$672$		0			0
$673$			11.1598i			0.430180i	0.976594	+	0.215090i	$0.0690044\pi$
$673$			11.1598i			0.430180i	−0.976594	+	0.215090i	$0.930996\pi$
$674$	13.4201	−	1.06689i	0.516924	−	0.0410950i
$675$		0			0
$676$	7.34993	+	9.04704i	0.282689	+	0.347963i
$677$		−	36.0612i		−	1.38594i	−0.720965	−	0.692972i	$-0.756301\pi$
$677$		−	36.0612i		−	1.38594i	0.720965	−	0.692972i	$-0.243699\pi$
$678$		0			0
$679$	0.875139	−	1.51579i	0.0335848	−	0.0581705i
$680$	7.21007	−	6.87476i	0.276494	−	0.263635i
$681$		0			0
$682$	−4.45056	−	6.46462i	−0.170421	−	0.247543i
$683$	15.5917			0.596598			0.298299	−	0.954472i	$-0.403581\pi$
$683$	15.5917			0.596598			0.298299	+	0.954472i	$0.403581\pi$
$684$		0			0
$685$	33.9259			1.29624
$686$	15.9489	+	23.1664i	0.608931	+	0.884497i
$687$		0			0
$688$	−7.15122	−	21.7741i	−0.272638	−	0.830129i
$689$	−5.45850	+	9.45440i	−0.207952	+	0.360184i
$690$		0			0
$691$		−	22.9437i		−	0.872818i	−0.899748	−	0.436409i	$-0.856250\pi$
$691$		−	22.9437i		−	0.872818i	0.899748	−	0.436409i	$-0.143750\pi$
$692$	27.4388	−	22.2916i	1.04307	−	0.847399i
$693$		0			0
$694$	25.9267	−	2.06115i	0.984163	−	0.0782402i
$695$		−	14.2210i		−	0.539435i
$696$		0			0
$697$	−0.371566	+	0.214524i	−0.0140741	+	0.00812567i
$698$	6.82691	−	4.69998i	0.258403	−	0.177897i
$699$		0			0
$700$	−3.84538	−	24.0322i	−0.145342	−	0.908330i
$701$	9.13435	−	15.8212i	0.345000	−	0.597557i	−0.640354	−	0.768080i	$-0.721212\pi$
$701$	9.13435	−	15.8212i	0.345000	−	0.597557i	0.985354	+	0.170523i	$0.0545457\pi$
$702$		0			0
$703$	−1.86198	−	0.621220i	−0.0702260	−	0.0234297i
$704$	−20.0427	−	38.8778i	−0.755386	−	1.46526i
$705$		0			0
$706$	15.1231	−	10.4115i	0.569166	−	0.391842i
$707$	11.0442	−	6.37634i	0.415358	−	0.239807i
$708$		0			0
$709$	−17.4758	−	30.2690i	−0.656318	−	1.13678i	−0.981562	−	0.191146i	$-0.938780\pi$
$709$	−17.4758	−	30.2690i	−0.656318	−	1.13678i	0.325244	−	0.945630i	$-0.394554\pi$
$710$	8.74224	+	4.16133i	0.328090	+	0.156172i
$711$		0			0
$712$	9.44619	+	9.90692i	0.354011	+	0.371278i
$713$	−2.49870	+	1.44262i	−0.0935770	+	0.0540267i
$714$		0			0
$715$	46.6483			1.74455
$716$	10.6786	−	27.9510i	0.399078	−	1.04458i
$717$		0			0
$718$	−48.0498	+	3.81992i	−1.79320	+	0.142558i
$719$	−3.07635	−	1.77613i	−0.114728	−	0.0662385i	0.441538	−	0.897243i	$-0.354433\pi$
$719$	−3.07635	−	1.77613i	−0.114728	−	0.0662385i	−0.556266	+	0.831004i	$0.687766\pi$
$720$		0			0
$721$		−	17.8356i		−	0.664234i
$722$	−26.8474	−	1.10432i	−0.999155	−	0.0410985i
$723$		0			0
$724$	−5.53134	−	34.5688i	−0.205571	−	1.28474i
$725$	−29.0323	−	16.7618i	−1.07823	−	0.622517i
$726$		0			0
$727$	−6.15483	−	3.55349i	−0.228270	−	0.131792i	0.381504	−	0.924367i	$-0.375406\pi$
$727$	−6.15483	−	3.55349i	−0.228270	−	0.131792i	−0.609774	+	0.792576i	$0.708740\pi$
$728$	−12.9535	+	12.3511i	−0.480089	+	0.457762i
$729$		0			0
$730$	31.8900	+	15.1797i	1.18030	+	0.561827i
$731$	5.48575	−	3.16720i	0.202898	−	0.117143i
$732$		0			0
$733$	−15.8748			−0.586350			−0.293175	−	0.956059i	$-0.594712\pi$
$733$	−15.8748			−0.586350			−0.293175	+	0.956059i	$0.594712\pi$
$734$	7.94226	−	16.6853i	0.293154	−	0.615866i
$735$		0			0
$736$	−14.8311	+	6.21223i	−0.546683	+	0.228986i
$737$	−40.4429	+	23.3497i	−1.48973	+	0.860098i
$738$		0			0
$739$	−16.0186	−	9.24836i	−0.589255	−	0.340206i	0.175548	−	0.984471i	$-0.443830\pi$
$739$	−16.0186	−	9.24836i	−0.589255	−	0.340206i	−0.764803	+	0.644264i	$0.777164\pi$
$740$	−2.22702	+	1.80925i	−0.0818667	+	0.0665095i
$741$		0			0
$742$	12.2999	+	5.85481i	0.451545	+	0.214937i
$743$	7.00831	−	12.1387i	0.257110	−	0.445328i	−0.708357	−	0.705855i	$-0.750563\pi$
$743$	7.00831	−	12.1387i	0.257110	−	0.445328i	0.965466	+	0.260527i	$0.0838964\pi$
$744$		0			0
$745$	12.7742	+	22.1255i	0.468010	+	0.810617i
$746$	−9.53945	−	13.8565i	−0.349264	−	0.507321i
$747$		0			0
$748$	9.38308	−	7.62293i	0.343079	−	0.278722i
$749$			43.4795i			1.58871i
$750$		0			0
$751$	−10.3122	−	17.8612i	−0.376297	−	0.651765i	0.614223	−	0.789132i	$-0.289469\pi$
$751$	−10.3122	−	17.8612i	−0.376297	−	0.651765i	−0.990520	+	0.137367i	$0.956136\pi$
$752$	−13.1812	−	2.75811i	−0.480670	−	0.100578i
$753$		0			0
$754$	1.95375	+	24.5758i	0.0711515	+	0.894997i
$755$	−8.82454	+	15.2846i	−0.321158	+	0.556262i
$756$		0			0
$757$	12.5598	−	21.7543i	0.456495	−	0.790672i	−0.542278	−	0.840199i	$-0.682438\pi$
$757$	12.5598	−	21.7543i	0.456495	−	0.790672i	0.998773	+	0.0495268i	$0.0157713\pi$
$758$	−10.4104	+	7.16704i	−0.378123	+	0.260319i
$759$		0			0
$760$	−22.4247	+	32.2479i	−0.813430	+	1.16975i
$761$	−7.58718			−0.275035			−0.137518	−	0.990499i	$-0.543912\pi$
$761$	−7.58718			−0.275035			−0.137518	+	0.990499i	$0.543912\pi$
$762$		0			0
$763$	−5.78224	+	10.0151i	−0.209331	+	0.362572i
$764$	−34.8490	−	13.3139i	−1.26079	−	0.481682i
$765$		0			0
$766$	−1.37718	−	17.3232i	−0.0497596	−	0.625913i
$767$		−	36.5524i		−	1.31983i
$768$		0			0
$769$	−10.2413	−	17.7384i	−0.369309	−	0.639663i	0.620148	−	0.784485i	$-0.287072\pi$
$769$	−10.2413	−	17.7384i	−0.369309	−	0.639663i	−0.989458	+	0.144822i	$0.953739\pi$
$770$	−4.61295	−	58.0251i	−0.166239	−	2.09108i
$771$		0			0
$772$	−11.5562	+	9.38842i	−0.415918	+	0.337897i
$773$	−16.5528	+	9.55676i	−0.595363	+	0.343733i	−0.767215	−	0.641390i	$-0.778358\pi$
$773$	−16.5528	+	9.55676i	−0.595363	+	0.343733i	0.171852	+	0.985123i	$0.445025\pi$
$774$		0			0
$775$	2.61371	+	4.52707i	0.0938872	+	0.162617i
$776$	−0.590262	+	2.01023i	−0.0211892	+	0.0721631i
$777$		0			0
$778$	9.24399	+	4.40017i	0.331413	+	0.157754i
$779$	1.26597	−	1.12199i	0.0453581	−	0.0401995i
$780$		0			0
$781$	10.1752	+	5.87465i	0.364097	+	0.210211i
$782$	−2.52015	−	3.66063i	−0.0901205	−	0.130904i
$783$		0			0
$784$	−4.22309	−	3.77832i	−0.150825	−	0.134940i
$785$	4.53927	+	7.86225i	0.162014	+	0.280616i
$786$		0			0
$787$	15.1750			0.540931			0.270465	−	0.962730i	$-0.412822\pi$
$787$	15.1750			0.540931			0.270465	+	0.962730i	$0.412822\pi$
$788$	−10.1176	+	26.4826i	−0.360424	+	0.943404i
$789$		0			0
$790$	45.3364	+	21.5803i	1.61300	+	0.767791i
$791$	−42.1453			−1.49851
$792$		0			0
$793$	31.4436	+	18.1539i	1.11659	+	0.644666i
$794$	3.30454	+	41.5669i	0.117274	+	1.47515i
$795$		0			0
$796$	−2.12165	−	13.2595i	−0.0751998	−	0.469971i
$797$			46.7518i			1.65603i	0.560704	+	0.828017i	$0.310531\pi$
$797$			46.7518i			1.65603i	−0.560704	+	0.828017i	$0.689469\pi$
$798$		0			0
$799$		−	3.72206i		−	0.131677i
$800$	11.2551	+	26.8707i	0.397929	+	0.950021i
$801$		0			0
$802$	−5.17366	+	0.411302i	−0.182688	+	0.0145236i
$803$	37.1171	+	21.4296i	1.30983	+	0.756233i
$804$		0			0
$805$	−21.3984			−0.754194
$806$	1.65224	−	3.47108i	0.0581978	−	0.122264i
$807$		0			0
$808$	−11.0479	+	10.5341i	−0.388663	+	0.370588i
$809$	−29.0772			−1.02230			−0.511151	−	0.859491i	$-0.670781\pi$
$809$	−29.0772			−1.02230			−0.511151	+	0.859491i	$0.670781\pi$
$810$		0			0
$811$	23.7677	+	41.1669i	0.834597	+	1.44556i	0.894358	+	0.447352i	$0.147633\pi$
$811$	23.7677	+	41.1669i	0.834597	+	1.44556i	−0.0597609	+	0.998213i	$0.519034\pi$
$812$	30.3762	−	4.86048i	1.06600	−	0.170570i
$813$		0			0
$814$	−2.86799	+	1.97446i	−0.100523	+	0.0692049i
$815$	23.7391	+	13.7058i	0.831544	+	0.480092i
$816$		0			0
$817$	−18.6906	+	16.5649i	−0.653902	+	0.579533i
$818$	0.641388	−	1.34744i	0.0224256	−	0.0471123i
$819$		0			0
$820$	−0.390699	−	2.44172i	−0.0136438	−	0.0852686i
$821$	−18.3351	−	31.7574i	−0.639900	−	1.10834i	−0.985454	−	0.169940i	$-0.945642\pi$
$821$	−18.3351	−	31.7574i	−0.639900	−	1.10834i	0.345554	−	0.938399i	$-0.387691\pi$
$822$		0			0
$823$	39.9324	−	23.0550i	1.39196	−	0.803647i	0.398425	−	0.917201i	$-0.369557\pi$
$823$	39.9324	−	23.0550i	1.39196	−	0.803647i	0.993532	+	0.113554i	$0.0362236\pi$
$824$	5.03327	+	20.7476i	0.175342	+	0.722778i
$825$		0			0
$826$	−45.4669	+	3.61458i	−1.58200	+	0.125767i
$827$	−3.93836	−	6.82143i	−0.136950	−	0.237205i	0.789391	−	0.613891i	$-0.210397\pi$
$827$	−3.93836	−	6.82143i	−0.136950	−	0.237205i	−0.926341	+	0.376687i	$0.877063\pi$
$828$		0			0
$829$		−	2.15631i		−	0.0748918i	−0.999299	−	0.0374459i	$-0.988078\pi$
$829$		−	2.15631i		−	0.0748918i	0.999299	−	0.0374459i	$-0.0119222\pi$
$830$	−18.6333	+	1.48133i	−0.646770	+	0.0514177i
$831$		0			0
$832$	11.5829	−	18.0231i	0.401564	−	0.624840i
$833$	0.783093	−	1.35636i	0.0271326	−	0.0469950i
$834$		0			0
$835$	−57.3821			−1.98579
$836$	−30.2282	+	36.8533i	−1.04546	+	1.27460i
$837$		0			0
$838$	10.4198	+	15.1351i	0.359945	+	0.522835i
$839$	−16.4564	+	28.5033i	−0.568137	+	0.984043i	0.428613	+	0.903488i	$0.359002\pi$
$839$	−16.4564	+	28.5033i	−0.568137	+	0.984043i	−0.996750	+	0.0805545i	$0.974331\pi$
$840$		0			0
$841$	6.68657	−	11.5815i	0.230571	−	0.399361i
$842$	46.8846	−	3.72729i	1.61575	−	0.128451i
$843$		0			0
$844$	9.63440	+	11.8590i	0.331630	+	0.408204i
$845$	−9.28399	−	16.0803i	−0.319379	−	0.553181i
$846$		0			0
$847$		−	44.6439i		−	1.53398i
$848$	−15.9604	−	3.33963i	−0.548081	−	0.114684i
$849$		0			0
$850$	−6.63222	+	4.56594i	−0.227483	+	0.156611i
$851$	0.640011	+	1.10853i	0.0219393	+	0.0380000i
$852$		0			0
$853$	2.93070	−	5.07612i	0.100345	−	0.173803i	−0.811482	−	0.584378i	$-0.801339\pi$
$853$	2.93070	−	5.07612i	0.100345	−	0.173803i	0.911827	+	0.410575i	$0.134672\pi$
$854$	19.4720	−	40.9073i	0.666318	−	1.39982i
$855$		0			0
$856$	−12.2700	−	50.5783i	−0.419381	−	1.72873i
$857$	−1.57854	−	0.911371i	−0.0539219	−	0.0311318i	0.472797	−	0.881172i	$-0.343245\pi$
$857$	−1.57854	−	0.911371i	−0.0539219	−	0.0311318i	−0.526719	+	0.850040i	$0.676578\pi$
$858$		0			0
$859$	−36.6465	+	21.1578i	−1.25036	+	0.721896i	−0.971181	−	0.238342i	$-0.923396\pi$
$859$	−36.6465	+	21.1578i	−1.25036	+	0.721896i	−0.279180	+	0.960239i	$0.590063\pi$
$860$	5.76823	+	36.0492i	0.196695	+	1.22927i
$861$		0			0
$862$	11.9277	+	5.67763i	0.406259	+	0.193381i
$863$	−32.8925			−1.11967			−0.559836	−	0.828603i	$-0.689136\pi$
$863$	−32.8925			−1.11967			−0.559836	+	0.828603i	$0.689136\pi$
$864$		0			0
$865$	−48.7701	+	28.1574i	−1.65823	+	0.957381i
$866$	−8.03004	+	16.8697i	−0.272872	+	0.573257i
$867$		0			0
$868$	−4.48100	−	1.71195i	−0.152095	−	0.0581074i
$869$	52.7675	+	30.4654i	1.79002	+	1.03347i
$870$		0			0
$871$	−19.8093	−	11.4369i	−0.671211	−	0.387524i
$872$	3.89999	−	13.2820i	0.132070	−	0.449786i
$873$		0			0
$874$	12.6247	+	12.1512i	0.427037	+	0.411019i
$875$			1.12899i			0.0381667i
$876$		0			0
$877$	37.4930	+	21.6466i	1.26605	+	0.730954i	0.974238	−	0.225522i	$-0.0724088\pi$
$877$	37.4930	+	21.6466i	1.26605	+	0.730954i	0.291811	+	0.956476i	$0.405742\pi$
$878$	2.21969	+	27.9210i	0.0749110	+	0.942287i
$879$		0			0
$880$	21.7409	+	66.1969i	0.732887	+	2.23150i
$881$	10.1569			0.342193			0.171097	−	0.985254i	$-0.445269\pi$
$881$	10.1569			0.342193			0.171097	+	0.985254i	$0.445269\pi$
$882$		0			0
$883$	31.8465	−	18.3866i	1.07172	−	0.618757i	0.143068	−	0.989713i	$-0.454303\pi$
$883$	31.8465	−	18.3866i	1.07172	−	0.618757i	0.928651	+	0.370956i	$0.120970\pi$
$884$	5.53150	+	2.11329i	0.186044	+	0.0710776i
$885$		0			0
$886$	−6.21963	+	13.0664i	−0.208952	+	0.438973i
$887$	19.3619	+	33.5357i	0.650108	+	1.12602i	0.983096	+	0.183089i	$0.0586095\pi$
$887$	19.3619	+	33.5357i	0.650108	+	1.12602i	−0.332989	+	0.942931i	$0.608057\pi$
$888$		0			0
$889$	−19.8436	+	11.4567i	−0.665532	+	0.384245i
$890$	−12.3649	−	17.9605i	−0.414471	−	0.602037i
$891$		0			0
$892$	−2.16520	−	2.66515i	−0.0724962	−	0.0892358i
$893$	2.93817	+	14.3779i	0.0983220	+	0.481137i
$894$		0			0
$895$	−23.8317	+	41.2777i	−0.796606	+	1.37976i
$896$	−23.5641	−	12.6255i	−0.787221	−	0.421788i
$897$		0			0
$898$	−7.77578	−	11.2946i	−0.259481	−	0.376907i
$899$	−5.72214	+	3.30368i	−0.190844	+	0.110184i
$900$		0			0
$901$		−	4.50682i		−	0.150144i
$902$	−0.237805	−	2.99129i	−0.00791805	−	0.0995992i
$903$		0			0
$904$	49.0263	−	11.8935i	1.63059	−	0.395573i
$905$			55.7669i			1.85375i
$906$		0			0
$907$	−27.5458	+	47.7107i	−0.914643	+	1.58421i	−0.107220	+	0.994235i	$0.534195\pi$
$907$	−27.5458	+	47.7107i	−0.914643	+	1.58421i	−0.807423	+	0.589973i	$0.799138\pi$
$908$	−12.3286	+	32.2698i	−0.409138	+	1.07091i
$909$		0			0
$910$	23.4837	−	16.1673i	0.778478	−	0.535942i
$911$	−3.72616			−0.123453			−0.0617266	−	0.998093i	$-0.519661\pi$
$911$	−3.72616			−0.123453			−0.0617266	+	0.998093i	$0.519661\pi$
$912$		0			0
$913$	−22.6829			−0.750694
$914$	−10.3090	+	7.09722i	−0.340991	+	0.234755i
$915$		0			0
$916$	11.9872	−	31.3762i	0.396067	−	1.03670i
$917$	9.29893	−	16.1062i	0.307078	−	0.531874i
$918$		0			0
$919$			17.4986i			0.577224i	0.957446	+	0.288612i	$0.0931938\pi$
$919$			17.4986i			0.577224i	−0.957446	+	0.288612i	$0.906806\pi$
$920$	24.8921	−	6.03869i	0.820667	−	0.199090i
$921$		0			0
$922$	−1.08846	−	13.6915i	−0.0358466	−	0.450906i
$923$			5.75490i			0.189425i
$924$		0			0
$925$	2.00841	−	1.15956i	0.0660361	−	0.0381259i
$926$	−30.8021	−	44.7414i	−1.01222	−	1.47029i
$927$		0			0
$928$	−33.9640	+	14.2263i	−1.11492	+	0.467001i
$929$	7.98584	−	13.8319i	0.262007	−	0.453810i	−0.704768	−	0.709438i	$-0.748949\pi$
$929$	7.98584	−	13.8319i	0.262007	−	0.453810i	0.966775	+	0.255628i	$0.0822823\pi$
$930$		0			0
$931$	−1.95429	+	5.85761i	−0.0640494	+	0.191975i
$932$	−4.19564	−	5.16443i	−0.137433	−	0.169166i
$933$		0			0
$934$	−17.4693	−	25.3749i	−0.571614	−	0.830293i
$935$	−16.6776	+	9.62883i	−0.545417	+	0.314897i
$936$		0			0
$937$	0.674194	+	1.16774i	0.0220249	+	0.0381483i	0.876828	−	0.480805i	$-0.159655\pi$
$937$	0.674194	+	1.16774i	0.0220249	+	0.0381483i	−0.854803	+	0.518953i	$0.826322\pi$
$938$	−12.2673	+	25.7714i	−0.400540	+	0.841465i
$939$		0			0
$940$	20.0391	+	7.65588i	0.653605	+	0.249707i
$941$	41.2979	−	23.8434i	1.34627	−	0.777271i	0.358553	−	0.933509i	$-0.383270\pi$
$941$	41.2979	−	23.8434i	1.34627	−	0.777271i	0.987719	+	0.156238i	$0.0499367\pi$
$942$		0			0
$943$	−1.10312			−0.0359227
$944$	51.8701	−	17.0356i	1.68823	−	0.554462i
$945$		0			0
$946$	3.51093	+	44.1631i	0.114150	+	1.43587i
$947$	−22.7091	−	13.1111i	−0.737946	−	0.426053i	0.0833759	−	0.996518i	$-0.473430\pi$
$947$	−22.7091	−	13.1111i	−0.737946	−	0.426053i	−0.821322	+	0.570465i	$0.806763\pi$
$948$		0			0
$949$			20.9927i			0.681453i
$950$	22.0151	−	22.8731i	0.714265	−	0.742101i
$951$		0			0
$952$	2.08169	−	7.08951i	0.0674679	−	0.229772i
$953$	23.7784	+	13.7285i	0.770257	+	0.444708i	0.832966	−	0.553324i	$-0.186641\pi$
$953$	23.7784	+	13.7285i	0.770257	+	0.444708i	−0.0627090	+	0.998032i	$0.519974\pi$
$954$		0			0
$955$	51.4646	+	29.7131i	1.66535	+	0.961493i
$956$	9.02719	+	3.44881i	0.291960	+	0.111542i
$957$		0			0
$958$	7.40765	−	15.5622i	0.239330	−	0.502791i
$959$	21.7910	−	12.5810i	0.703668	−	0.406263i
$960$		0			0
$961$	−29.9697			−0.966764
$962$	−1.53992	−	0.733008i	−0.0496491	−	0.0236331i
$963$		0			0
$964$	−8.45686	−	52.8522i	−0.272377	−	1.70225i
$965$	20.5402	−	11.8589i	0.661213	−	0.381751i
$966$		0			0
$967$	14.9005	+	8.60278i	0.479166	+	0.276647i	0.720069	−	0.693902i	$-0.244110\pi$
$967$	14.9005	+	8.60278i	0.479166	+	0.276647i	−0.240903	+	0.970549i	$0.577443\pi$
$968$	12.5986	+	51.9328i	0.404935	+	1.66918i
$969$		0			0
$970$	1.43440	−	3.01342i	0.0460557	−	0.0967550i
$971$	−6.50590	+	11.2685i	−0.208784	+	0.361625i	−0.951332	−	0.308168i	$-0.900284\pi$
$971$	−6.50590	+	11.2685i	−0.208784	+	0.361625i	0.742548	+	0.669793i	$0.233617\pi$
$972$		0			0
$973$	−5.27371	−	9.13434i	−0.169067	−	0.292833i
$974$	−32.4642	+	22.3499i	−1.04022	+	0.716137i
$975$		0			0
$976$	−11.1070	+	53.0812i	−0.355527	+	1.69909i
$977$		−	38.1644i		−	1.22099i	−0.792021	−	0.610494i	$-0.790971\pi$
$977$		−	38.1644i		−	1.22099i	0.792021	−	0.610494i	$-0.209029\pi$
$978$		0			0
$979$	−13.2304	−	22.9157i	−0.422845	−	0.732389i
$980$	5.69173	+	7.00596i	0.181816	+	0.223797i
$981$		0			0
$982$	24.4172	−	1.94115i	0.779184	−	0.0619445i
$983$	−11.7428	+	20.3391i	−0.374536	+	0.648715i	−0.990257	−	0.139249i	$-0.955531\pi$
$983$	−11.7428	+	20.3391i	−0.374536	+	0.648715i	0.615722	+	0.787964i	$0.288865\pi$
$984$		0			0
$985$	22.5797	−	39.1092i	0.719449	−	1.24612i
$986$	−5.77127	−	8.38300i	−0.183795	−	0.266969i
$987$		0			0
$988$	−23.0357	−	3.79685i	−0.732863	−	0.120794i
$989$	16.2864			0.517877
$990$		0			0
$991$	13.8156	−	23.9293i	0.438866	−	0.760139i	−0.558736	−	0.829346i	$-0.688714\pi$
$991$	13.8156	−	23.9293i	0.438866	−	0.760139i	0.997602	+	0.0692069i	$0.0220469\pi$
$992$	5.69572	+	0.726907i	0.180839	+	0.0230793i
$993$		0			0
$994$	7.15842	−	0.569089i	0.227051	−	0.0180504i
$995$			21.3904i			0.678122i
$996$		0			0
$997$	11.8340	+	20.4970i	0.374786	+	0.649148i	0.990295	−	0.138982i	$-0.0443829\pi$
$997$	11.8340	+	20.4970i	0.374786	+	0.649148i	−0.615509	+	0.788130i	$0.711050\pi$
$998$	−1.63913	+	0.130310i	−0.0518858	+	0.00412488i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.r.a.559.7		16
3.2	odd	2		76.2.f.a.27.2	✓	16
4.3	odd	2	inner	684.2.r.a.559.4		16
12.11	even	2		76.2.f.a.27.5	yes	16
19.12	odd	6	inner	684.2.r.a.487.4		16
24.5	odd	2		1216.2.n.f.255.4		16
24.11	even	2		1216.2.n.f.255.5		16
57.50	even	6		76.2.f.a.31.5	yes	16
76.31	even	6	inner	684.2.r.a.487.7		16
228.107	odd	6		76.2.f.a.31.2	yes	16
456.107	odd	6		1216.2.n.f.639.4		16
456.221	even	6		1216.2.n.f.639.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.f.a.27.2	✓	16	3.2	odd	2
76.2.f.a.27.5	yes	16	12.11	even	2
76.2.f.a.31.2	yes	16	228.107	odd	6
76.2.f.a.31.5	yes	16	57.50	even	6
684.2.r.a.487.4		16	19.12	odd	6	inner
684.2.r.a.487.7		16	76.31	even	6	inner
684.2.r.a.559.4		16	4.3	odd	2	inner
684.2.r.a.559.7		16	1.1	even	1	trivial
1216.2.n.f.255.4		16	24.5	odd	2
1216.2.n.f.255.5		16	24.11	even	2
1216.2.n.f.639.4		16	456.107	odd	6
1216.2.n.f.639.5		16	456.221	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16486 - 0.801943i) q^{2} +(0.713775 - 1.86829i) q^{4} +(-1.59295 + 2.75907i) q^{5} +2.36291i q^{7} +(-0.666820 - 2.74870i) q^{8} +(0.357061 + 4.49138i) q^{10} +5.46750i q^{11} +(-2.31924 + 1.33901i) q^{13} +(1.89492 + 2.75245i) q^{14} +(-2.98105 - 2.66709i) q^{16} +(0.552780 - 0.957443i) q^{17} +(-1.37952 + 4.13484i) q^{19} +(4.01775 + 4.94546i) q^{20} +(4.38462 + 6.36885i) q^{22} +(2.46168 - 1.42125i) q^{23} +(-2.57499 - 4.46001i) q^{25} +(-1.62777 + 3.41965i) q^{26} +(4.41462 + 1.68659i) q^{28} +(5.63736 - 3.25473i) q^{29} -1.01504 q^{31} +(-5.61134 - 0.716137i) q^{32} +(-0.123906 - 1.55858i) q^{34} +(-6.51945 - 3.76400i) q^{35} +0.450315i q^{37} +(1.70896 + 5.92279i) q^{38} +(8.64607 + 2.53874i) q^{40} +(-0.336089 - 0.194041i) q^{41} +(4.96197 + 2.86479i) q^{43} +(10.2149 + 3.90257i) q^{44} +(1.72774 - 3.62968i) q^{46} +(2.91563 - 1.68334i) q^{47} +1.41665 q^{49} +(-6.57616 - 3.13027i) q^{50} +(0.846255 + 5.28878i) q^{52} +(3.53036 - 2.03825i) q^{53} +(-15.0852 - 8.70946i) q^{55} +(6.49494 - 1.57564i) q^{56} +(3.95660 - 8.31213i) q^{58} +(-6.82450 + 11.8204i) q^{59} +(-6.77885 - 11.7413i) q^{61} +(-1.18237 + 0.814002i) q^{62} +(-7.11070 + 3.66578i) q^{64} -8.53193i q^{65} +(4.27064 + 7.39696i) q^{67} +(-1.39422 - 1.71616i) q^{68} +(-10.6127 + 0.843703i) q^{70} +(1.07447 - 1.86103i) q^{71} +(3.91944 - 6.78867i) q^{73} +(0.361127 + 0.524552i) q^{74} +(6.74043 + 5.52870i) q^{76} -12.9192 q^{77} +(5.57208 - 9.65112i) q^{79} +(12.1073 - 3.97639i) q^{80} +(-0.547104 + 0.0434943i) q^{82} +4.14868i q^{83} +(1.76110 + 3.05032i) q^{85} +(8.07738 - 0.642145i) q^{86} +(15.0285 - 3.64584i) q^{88} +(-4.19126 + 2.41982i) q^{89} +(-3.16397 - 5.48016i) q^{91} +(-0.898230 - 5.61360i) q^{92} +(2.04634 - 4.29901i) q^{94} +(-9.21082 - 10.3928i) q^{95} +(-0.641491 - 0.370365i) q^{97} +(1.65019 - 1.13607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 3 q^{4} + 2 q^{5} - 6 q^{10} - 18 q^{13} + 6 q^{14} - 3 q^{16} - 2 q^{17} - 4 q^{20} + 3 q^{22} - 2 q^{25} + 24 q^{26} - 4 q^{28} + 6 q^{29} - 27 q^{32} + 36 q^{34} + 24 q^{38} + 48 q^{40}+ \cdots - 51 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 3 * q^4 + 2 * q^5 - 6 * q^10 - 18 * q^13 + 6 * q^14 - 3 * q^16 - 2 * q^17 - 4 * q^20 + 3 * q^22 - 2 * q^25 + 24 * q^26 - 4 * q^28 + 6 * q^29 - 27 * q^32 + 36 * q^34 + 24 * q^38 + 48 * q^40 + 48 * q^41 + 25 * q^44 + 16 * q^49 + 6 * q^52 - 6 * q^53 - 40 * q^58 - 26 * q^61 - 32 * q^62 - 18 * q^64 + 36 * q^68 - 54 * q^70 + 16 * q^73 + 2 * q^74 + 43 * q^76 - 80 * q^77 + 30 * q^80 + 11 * q^82 + 14 * q^85 + 48 * q^86 - 18 * q^89 + 52 * q^92 - 12 * q^97 - 51 * q^98

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