LMFDB - Embedded newform 567.2.s.f.458.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			458.6
Root			$-0.617942 - 0.356769i$ of defining polynomial
Character	$\chi$	$=$	567.458
Dual form			567.2.s.f.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15715 + 1.24543i) q^{2} +(2.10220 + 3.64112i) q^{4} +1.23588 q^{5} +(2.63409 + 0.248083i) q^{7} +5.49086i q^{8} +O(q^{10})$	\(q+(2.15715 + 1.24543i) q^{2} +(2.10220 + 3.64112i) q^{4} +1.23588 q^{5} +(2.63409 + 0.248083i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} -5.49086i q^{11} +(-2.57031 - 1.48397i) q^{13} +(5.37317 + 3.81574i) q^{14} +(-2.63409 + 4.56239i) q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} +(2.59808 + 4.50000i) q^{20} +(6.83850 - 11.8446i) q^{22} -1.63148i q^{23} -3.47259 q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +(0.440925 - 0.254568i) q^{29} +(-7.04290 + 4.06622i) q^{31} +(-1.85383 + 1.07031i) q^{32} +(-9.30660 + 5.37317i) q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} -13.8248 q^{38} +6.78607i q^{40} +(-0.177017 + 0.306602i) q^{41} +(0.0318939 + 0.0552418i) q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} +(4.93224 - 8.54290i) q^{47} +(6.87691 + 1.30695i) q^{49} +(-7.49090 - 4.32488i) q^{50} -12.4784i q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(-1.36219 + 14.4635i) q^{56} +1.26819 q^{58} +(1.53921 + 2.66599i) q^{59} +(5.97259 + 3.44828i) q^{61} -20.2568 q^{62} +5.20440 q^{64} +(-3.17660 - 1.83401i) q^{65} +(6.16599 + 10.6798i) q^{67} -18.1391 q^{68} +(6.64061 + 4.71581i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +7.63148i q^{74} +(-20.2089 - 11.6676i) q^{76} +(1.36219 - 14.4635i) q^{77} +(0.165989 - 0.287501i) q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +(-3.69636 - 6.40228i) q^{83} +(-2.66599 + 4.61763i) q^{85} +0.158887i q^{86} +30.1496 q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +(5.94040 - 3.42969i) q^{92} +(21.2792 - 12.2855i) q^{94} +(-5.94040 + 3.42969i) q^{95} +(-3.85939 + 2.22822i) q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 + 4 * q^7	$ 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) $ 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.15715	+	1.24543i	1.52534	+	0.880653i	0.999549	+	0.0300373i	$0.00956260\pi$
$2$	2.15715	+	1.24543i	1.52534	+	0.880653i	0.525787	+	0.850616i	$0.323771\pi$
$3$		0			0
$3$		0			0
$4$	2.10220	+	3.64112i	1.05110	+	1.82056i
$5$	1.23588			0.552704			0.276352	−	0.961056i	$-0.410874\pi$
$5$	1.23588			0.552704			0.276352	+	0.961056i	$0.410874\pi$
$6$		0			0
$7$	2.63409	+	0.248083i	0.995594	+	0.0937667i
$7$	2.63409	+	0.248083i	0.995594	+	0.0937667i
$8$			5.49086i			1.94131i
$9$		0			0
$10$	2.66599	+	1.53921i	0.843060	+	0.486741i
$11$		−	5.49086i		−	1.65556i	−0.561055	−	0.827779i	$-0.689604\pi$
$11$		−	5.49086i		−	1.65556i	0.561055	−	0.827779i	$-0.310396\pi$
$12$		0			0
$13$	−2.57031	−	1.48397i	−0.712875	−	0.411578i	0.0992497	−	0.995063i	$-0.468356\pi$
$13$	−2.57031	−	1.48397i	−0.712875	−	0.411578i	−0.812125	+	0.583484i	$0.801689\pi$
$14$	5.37317	+	3.81574i	1.43604	+	1.01980i
$15$		0			0
$16$	−2.63409	+	4.56239i	−0.658524	+	1.14060i
$17$	−2.15715	+	3.73630i	−0.523186	+	0.906185i	0.476450	+	0.879202i	$0.341923\pi$
$17$	−2.15715	+	3.73630i	−0.523186	+	0.906185i	−0.999636	+	0.0269831i	$0.991410\pi$
$18$		0			0
$19$	−4.80660	+	2.77509i	−1.10271	+	0.636650i	−0.936932	−	0.349513i	$-0.886347\pi$
$19$	−4.80660	+	2.77509i	−1.10271	+	0.636650i	−0.165779	+	0.986163i	$0.553014\pi$
$20$	2.59808	+	4.50000i	0.580948	+	1.00623i
$21$		0			0
$22$	6.83850	−	11.8446i	1.45797	−	2.52528i
$23$		−	1.63148i		−	0.340187i	−0.985428	−	0.170093i	$-0.945593\pi$
$23$		−	1.63148i		−	0.340187i	0.985428	−	0.170093i	$-0.0544069\pi$
$24$		0			0
$25$	−3.47259			−0.694518
$26$	−3.69636	−	6.40228i	−0.724916	−	1.25559i
$27$		0			0
$28$	4.63409	+	10.1126i	0.875762	+	1.91110i
$29$	0.440925	−	0.254568i	0.0818777	−	0.0472721i	−0.458502	−	0.888693i	$-0.651614\pi$
$29$	0.440925	−	0.254568i	0.0818777	−	0.0472721i	0.540380	+	0.841421i	$0.318281\pi$
$30$		0			0
$31$	−7.04290	+	4.06622i	−1.26494	+	0.730314i	−0.974026	−	0.226434i	$-0.927293\pi$
$31$	−7.04290	+	4.06622i	−1.26494	+	0.730314i	−0.290915	+	0.956749i	$0.593960\pi$
$32$	−1.85383	+	1.07031i	−0.327713	+	0.189205i
$33$		0			0
$34$	−9.30660	+	5.37317i	−1.59607	+	0.921491i
$35$	3.25544	+	0.306602i	0.550269	+	0.0518253i
$36$		0			0
$37$	1.53189	+	2.65332i	0.251842	+	0.436203i	0.964033	−	0.265783i	$-0.0856304\pi$
$37$	1.53189	+	2.65332i	0.251842	+	0.436203i	−0.712191	+	0.701986i	$0.752297\pi$
$38$	−13.8248			−2.24267
$39$		0			0
$40$			6.78607i			1.07297i
$41$	−0.177017	+	0.306602i	−0.0276454	+	0.0478832i	−0.879517	−	0.475867i	$-0.842134\pi$
$41$	−0.177017	+	0.306602i	−0.0276454	+	0.0478832i	0.851872	+	0.523751i	$0.175468\pi$
$42$		0			0
$43$	0.0318939	+	0.0552418i	0.00486377	+	0.00842430i	0.868447	−	0.495782i	$-0.165118\pi$
$43$	0.0318939	+	0.0552418i	0.00486377	+	0.00842430i	−0.863583	+	0.504206i	$0.831785\pi$
$44$	19.9929	−	11.5429i	3.01404	−	1.74016i
$45$		0			0
$46$	2.03189	−	3.51934i	0.299586	−	0.518899i
$47$	4.93224	−	8.54290i	0.719442	−	1.24611i	−0.241779	−	0.970331i	$-0.577731\pi$
$47$	4.93224	−	8.54290i	0.719442	−	1.24611i	0.961221	−	0.275778i	$-0.0889356\pi$
$48$		0			0
$49$	6.87691	+	1.30695i	0.982416	+	0.186707i
$50$	−7.49090	−	4.32488i	−1.05937	−	0.611630i
$51$		0			0
$52$		−	12.4784i		−	1.73044i
$53$	−3.57005	−	2.06117i	−0.490384	−	0.283124i	0.234350	−	0.972152i	$-0.424704\pi$
$53$	−3.57005	−	2.06117i	−0.490384	−	0.283124i	−0.724734	+	0.689029i	$0.758037\pi$
$54$		0			0
$55$		−	6.78607i		−	0.915034i
$56$	−1.36219	+	14.4635i	−0.182031	+	1.93276i
$57$		0			0
$58$	1.26819			0.166521
$59$	1.53921	+	2.66599i	0.200388	+	0.347082i	0.948653	−	0.316317i	$-0.102446\pi$
$59$	1.53921	+	2.66599i	0.200388	+	0.347082i	−0.748266	+	0.663399i	$0.769113\pi$
$60$		0			0
$61$	5.97259	+	3.44828i	0.764712	+	0.441507i	0.830985	−	0.556295i	$-0.187778\pi$
$61$	5.97259	+	3.44828i	0.764712	+	0.441507i	−0.0662730	+	0.997802i	$0.521111\pi$
$62$	−20.2568			−2.57262
$63$		0			0
$64$	5.20440			0.650550
$65$	−3.17660	−	1.83401i	−0.394009	−	0.227481i
$66$		0			0
$67$	6.16599	+	10.6798i	0.753295	+	1.30475i	0.946217	+	0.323532i	$0.104870\pi$
$67$	6.16599	+	10.6798i	0.753295	+	1.30475i	−0.192922	+	0.981214i	$0.561796\pi$
$68$	−18.1391			−2.19968
$69$		0			0
$70$	6.64061	+	4.71581i	0.793705	+	0.563647i
$71$		−	4.63148i		−	0.549655i	−0.961494	−	0.274828i	$-0.911379\pi$
$71$		−	4.63148i		−	0.549655i	0.961494	−	0.274828i	$-0.0886208\pi$
$72$		0			0
$73$	−6.09568	−	3.51934i	−0.713446	−	0.411908i	0.0988899	−	0.995098i	$-0.468471\pi$
$73$	−6.09568	−	3.51934i	−0.713446	−	0.411908i	−0.812336	+	0.583190i	$0.801804\pi$
$74$			7.63148i			0.887141i
$75$		0			0
$76$	−20.2089	−	11.6676i	−2.31812	−	1.33837i
$77$	1.36219	−	14.4635i	0.155236	−	1.64826i
$78$		0			0
$79$	0.165989	−	0.287501i	0.0186752	−	0.0323463i	−0.856537	−	0.516086i	$-0.827388\pi$
$79$	0.165989	−	0.287501i	0.0186752	−	0.0323463i	0.875212	+	0.483740i	$0.160722\pi$
$80$	−3.25544	+	5.63858i	−0.363969	+	0.630412i
$81$		0			0
$82$	−0.763705	+	0.440925i	−0.0843371	+	0.0486920i
$83$	−3.69636	−	6.40228i	−0.405728	−	0.702742i	0.588678	−	0.808368i	$-0.299649\pi$
$83$	−3.69636	−	6.40228i	−0.405728	−	0.702742i	−0.994406	+	0.105626i	$0.966315\pi$
$84$		0			0
$85$	−2.66599	+	4.61763i	−0.289167	+	0.500852i
$86$			0.158887i			0.0171332i
$87$		0			0
$88$	30.1496			3.21396
$89$	−1.71623	−	2.97259i	−0.181920	−	0.315094i	0.760615	−	0.649204i	$-0.224898\pi$
$89$	−1.71623	−	2.97259i	−0.181920	−	0.315094i	−0.942534	+	0.334110i	$0.891564\pi$
$90$		0			0
$91$	−6.40228	−	4.54656i	−0.671142	−	0.476609i
$92$	5.94040	−	3.42969i	0.619330	−	0.357570i
$93$		0			0
$94$	21.2792	−	12.2855i	2.19478	−	1.26716i
$95$	−5.94040	+	3.42969i	−0.609472	+	0.351879i
$96$		0			0
$97$	−3.85939	+	2.22822i	−0.391861	+	0.226241i	−0.682966	−	0.730450i	$-0.739310\pi$
$97$	−3.85939	+	2.22822i	−0.391861	+	0.226241i	0.291105	+	0.956691i	$0.405977\pi$
$98$	13.2068	+	11.3840i	1.33409	+	1.14996i
$99$		0			0
$100$	−7.30008	−	12.6441i	−0.730008	−	1.26441i
$101$	9.15642			0.911098			0.455549	−	0.890211i	$-0.349443\pi$
$101$	9.15642			0.911098			0.455549	+	0.890211i	$0.349443\pi$
$102$		0			0
$103$		−	4.20382i		−	0.414215i	−0.978318	−	0.207107i	$-0.933595\pi$
$103$		−	4.20382i		−	0.414215i	0.978318	−	0.207107i	$-0.0664049\pi$
$104$	8.14826	−	14.1132i	0.799003	−	1.38391i
$105$		0			0
$106$	−5.13409	−	8.89251i	−0.498667	−	0.863717i
$107$	8.93193	−	5.15685i	0.863482	−	0.498532i	−0.00169460	−	0.999999i	$-0.500539\pi$
$107$	8.93193	−	5.15685i	0.863482	−	0.498532i	0.865177	+	0.501467i	$0.167206\pi$
$108$		0			0
$109$	−0.0637877	+	0.110484i	−0.00610976	+	0.0105824i	−0.869064	−	0.494699i	$-0.835278\pi$
$109$	−0.0637877	+	0.110484i	−0.00610976	+	0.0105824i	0.862954	+	0.505282i	$0.168611\pi$
$110$	8.45159	−	14.6386i	0.805827	−	1.39573i
$111$		0			0
$112$	−8.07031	+	11.3643i	−0.762572	+	1.07382i
$113$	1.99143	+	1.14975i	0.187338	+	0.108159i	0.590736	−	0.806865i	$-0.298838\pi$
$113$	1.99143	+	1.14975i	0.187338	+	0.108159i	−0.403398	+	0.915025i	$0.632171\pi$
$114$		0			0
$115$		−	2.01632i		−	0.188023i
$116$	1.85383	+	1.07031i	0.172123	+	0.0993755i
$117$		0			0
$118$			7.66792i			0.705889i
$119$	−6.60905	+	9.30660i	−0.605851	+	0.853135i
$120$		0			0
$121$	−19.1496			−1.74087
$122$	8.58919	+	14.8769i	0.777629	+	1.34689i
$123$		0			0
$124$	−29.6112	−	17.0960i	−2.65916	−	1.53527i
$125$	−10.4711			−0.936567
$126$		0			0
$127$	−0.386795			−0.0343225			−0.0171613	−	0.999853i	$-0.505463\pi$
$127$	−0.386795			−0.0343225			−0.0171613	+	0.999853i	$0.505463\pi$
$128$	14.9343	+	8.62234i	1.32002	+	0.762114i
$129$		0			0
$130$	−4.56827	−	7.91248i	−0.400664	−	0.693970i
$131$	20.8634			1.82285			0.911424	−	0.411469i	$-0.134984\pi$
$131$	20.8634			1.82285			0.911424	+	0.411469i	$0.134984\pi$
$132$		0			0
$133$	−13.3495	+	6.11742i	−1.15755	+	0.530448i
$134$			30.7173i			2.65357i
$135$		0			0
$136$	−20.5155	−	11.8446i	−1.75919	−	1.01567i
$137$			0.700500i			0.0598477i	0.999552	+	0.0299239i	$0.00952648\pi$
$137$			0.700500i			0.0598477i	−0.999552	+	0.0299239i	$0.990474\pi$
$138$		0			0
$139$	10.0429	+	5.79827i	0.851827	+	0.491803i	0.861267	−	0.508153i	$-0.169671\pi$
$139$	10.0429	+	5.79827i	0.851827	+	0.491803i	−0.00943957	+	0.999955i	$0.503005\pi$
$140$	5.72720	+	12.4980i	0.484037	+	1.05627i
$141$		0			0
$142$	5.76819	−	9.99080i	0.484056	−	0.838409i
$143$	−8.14826	+	14.1132i	−0.681392	+	1.18021i
$144$		0			0
$145$	0.544932	−	0.314617i	0.0452542	−	0.0261275i
$146$	−8.76620	−	15.1835i	−0.725496	−	1.25660i
$147$		0			0
$148$	−6.44070	+	11.1556i	−0.529422	+	0.916986i
$149$		−	0.350250i		−	0.0286936i	−0.999897	−	0.0143468i	$-0.995433\pi$
$149$		−	0.350250i		−	0.0286936i	0.999897	−	0.0143468i	$-0.00456688\pi$
$150$		0			0
$151$	4.65498			0.378817			0.189409	−	0.981898i	$-0.439343\pi$
$151$	4.65498			0.378817			0.189409	+	0.981898i	$0.439343\pi$
$152$	−15.2377	−	26.3924i	−1.23594	−	2.14071i
$153$		0			0
$154$	20.9517	−	29.5033i	1.68834	−	2.37745i
$155$	−8.70420	+	5.02537i	−0.699139	+	0.403648i
$156$		0			0
$157$	1.07031	−	0.617942i	0.0854198	−	0.0493171i	−0.456682	−	0.889630i	$-0.650962\pi$
$157$	1.07031	−	0.617942i	0.0854198	−	0.0493171i	0.542101	+	0.840313i	$0.317629\pi$
$158$	0.716125	−	0.413455i	0.0569718	−	0.0328927i
$159$		0			0
$160$	−2.29111	+	1.32278i	−0.181128	+	0.104575i
$161$	0.404743	−	4.29747i	0.0318982	−	0.338688i
$162$		0			0
$163$	9.80660	+	16.9855i	0.768112	+	1.33041i	0.938585	+	0.345047i	$0.112137\pi$
$163$	9.80660	+	16.9855i	0.768112	+	1.33041i	−0.170473	+	0.985362i	$0.554530\pi$
$164$	−1.48850			−0.116232
$165$		0			0
$166$		−	18.4143i		−	1.42922i
$167$	−11.8446	+	20.5155i	−0.916564	+	1.58754i	−0.111970	+	0.993712i	$0.535716\pi$
$167$	−11.8446	+	20.5155i	−0.916564	+	1.58754i	−0.804595	+	0.593825i	$0.797617\pi$
$168$		0			0
$169$	−2.09568	−	3.62983i	−0.161206	−	0.279217i
$170$	−11.5019	+	6.64061i	−0.882154	+	0.509312i
$171$		0			0
$172$	−0.134095	+	0.232259i	−0.0102246	+	0.0177096i
$173$	−5.99111	+	10.3769i	−0.455496	+	0.788942i	−0.998717	−	0.0506481i	$-0.983871\pi$
$173$	−5.99111	+	10.3769i	−0.455496	+	0.788942i	0.543221	+	0.839590i	$0.317205\pi$
$174$		0			0
$175$	−9.14713	−	0.861492i	−0.691458	−	0.0651227i
$176$	25.0514	+	14.4635i	1.88832	+	1.09022i
$177$		0			0
$178$		−	8.54977i		−	0.640832i
$179$	19.3862	+	11.1926i	1.44900	+	0.836578i	0.998422	−	0.0561615i	$-0.0178862\pi$
$179$	19.3862	+	11.1926i	1.44900	+	0.836578i	0.450574	+	0.892739i	$0.351220\pi$
$180$		0			0
$181$			8.90380i			0.661815i	0.943663	+	0.330907i	$0.107355\pi$
$181$			8.90380i			0.661815i	−0.943663	+	0.330907i	$0.892645\pi$
$182$	−8.14826	−	17.7812i	−0.603989	−	1.31803i
$183$		0			0
$184$	8.95822			0.660409
$185$	1.89324	+	3.27919i	0.139194	+	0.241091i
$186$		0			0
$187$	20.5155	+	11.8446i	1.50024	+	0.866165i
$188$	41.4743			3.02482
$189$		0			0
$190$	−17.0858			−1.23953
$191$	9.95138	+	5.74543i	0.720057	+	0.415725i	0.814774	−	0.579779i	$-0.196861\pi$
$191$	9.95138	+	5.74543i	0.720057	+	0.415725i	−0.0947169	+	0.995504i	$0.530195\pi$
$192$		0			0
$193$	−5.51100	−	9.54534i	−0.396691	−	0.687089i	0.596625	−	0.802520i	$-0.296508\pi$
$193$	−5.51100	−	9.54534i	−0.396691	−	0.687089i	−0.993315	+	0.115432i	$0.963175\pi$
$194$	−11.1004			−0.796960
$195$		0			0
$196$	9.69788	+	27.7871i	0.692706	+	1.98479i
$197$		−	19.8228i		−	1.41232i	−0.708053	−	0.706159i	$-0.750426\pi$
$197$		−	19.8228i		−	1.41232i	0.708053	−	0.706159i	$-0.249574\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$		−	19.0675i		−	1.34828i
$201$		0			0
$202$	19.7518	+	11.4037i	1.38973	+	0.802361i
$203$	1.22459	−	0.561171i	0.0859495	−	0.0393864i
$204$		0			0
$205$	−0.218772	+	0.378925i	−0.0152797	+	0.0264653i
$206$	5.23557	−	9.06827i	0.364779	−	0.631816i
$207$		0			0
$208$	13.5409	−	7.81782i	0.938890	−	0.542068i
$209$	15.2377	+	26.3924i	1.05401	+	1.82560i
$210$		0			0
$211$	−11.0813	+	19.1934i	−0.762869	+	1.32133i	0.178497	+	0.983940i	$0.442877\pi$
$211$	−11.0813	+	19.1934i	−0.762869	+	1.32133i	−0.941366	+	0.337387i	$0.890457\pi$
$212$		−	17.3320i		−	1.19037i
$213$		0			0
$214$	25.6900			1.75613
$215$	0.0394171	+	0.0682725i	0.00268823	+	0.00465614i
$216$		0			0
$217$	−19.5604	+	8.96358i	−1.32785	+	0.608487i
$218$	−0.275200	+	0.158887i	−0.0186389	+	0.0107612i
$219$		0			0
$220$	24.7089	−	14.2657i	1.66587	−	0.961792i
$221$	11.0891	−	6.40228i	0.745932	−	0.430664i
$222$		0			0
$223$	16.2343	−	9.37285i	1.08713	−	0.627653i	0.154317	−	0.988021i	$-0.450682\pi$
$223$	16.2343	−	9.37285i	1.08713	−	0.627653i	0.932810	+	0.360369i	$0.117349\pi$
$224$	−5.14868	+	2.35939i	−0.344011	+	0.157643i
$225$		0			0
$226$	2.86387	+	4.96037i	0.190502	+	0.329959i
$227$	−14.1788			−0.941079			−0.470540	−	0.882379i	$-0.655941\pi$
$227$	−14.1788			−0.941079			−0.470540	+	0.882379i	$0.655941\pi$
$228$		0			0
$229$		−	4.07075i		−	0.269003i	−0.990913	−	0.134501i	$-0.957057\pi$
$229$		−	4.07075i		−	0.269003i	0.990913	−	0.134501i	$-0.0429433\pi$
$230$	2.51119	−	4.34950i	0.165583	−	0.286798i
$231$		0			0
$232$	1.39780	+	2.42106i	0.0917700	+	0.158950i
$233$	−6.03053	+	3.48173i	−0.395073	+	0.228096i	−0.684356	−	0.729148i	$-0.739917\pi$
$233$	−6.03053	+	3.48173i	−0.395073	+	0.228096i	0.289283	+	0.957244i	$0.406583\pi$
$234$		0			0
$235$	6.09568	−	10.5580i	0.397638	−	0.688730i
$236$	−6.47145	+	11.2089i	−0.421256	+	0.729636i
$237$		0			0
$238$	−25.8475	+	11.8446i	−1.67544	+	0.767773i
$239$	−22.9844	−	13.2701i	−1.48674	−	0.858369i	−0.486852	−	0.873484i	$-0.661855\pi$
$239$	−22.9844	−	13.2701i	−1.48674	−	0.858369i	−0.999886	+	0.0151157i	$0.995188\pi$
$240$		0			0
$241$		−	13.6038i		−	0.876297i	−0.898903	−	0.438149i	$-0.855634\pi$
$241$		−	13.6038i		−	0.876297i	0.898903	−	0.438149i	$-0.144366\pi$
$242$	−41.3085	−	23.8495i	−2.65541	−	1.53310i
$243$		0			0
$244$			28.9959i			1.85627i
$245$	8.49906	+	1.61524i	0.542985	+	0.103194i
$246$		0			0
$247$	16.4726			1.04813
$248$	−22.3271	−	38.6716i	−1.41777	−	2.45565i
$249$		0			0
$250$	−22.5878	−	13.0411i	−1.42858	−	0.824791i
$251$	−2.55060			−0.160993			−0.0804963	−	0.996755i	$-0.525651\pi$
$251$	−2.55060			−0.160993			−0.0804963	+	0.996755i	$0.525651\pi$
$252$		0			0
$253$	−8.95822			−0.563198
$254$	−0.834376	−	0.481727i	−0.0523534	−	0.0302263i
$255$		0			0
$256$	16.2727	+	28.1851i	1.01704	+	1.76157i
$257$	−18.0602			−1.12657			−0.563283	−	0.826264i	$-0.690462\pi$
$257$	−18.0602			−1.12657			−0.563283	+	0.826264i	$0.690462\pi$
$258$		0			0
$259$	3.37691	+	7.36913i	0.209831	+	0.457895i
$260$		−	15.4218i		−	0.956422i
$261$		0			0
$262$	45.0056	+	25.9840i	2.78046	+	1.60530i
$263$		−	8.06902i		−	0.497557i	−0.968560	−	0.248779i	$-0.919971\pi$
$263$		−	8.06902i		−	0.497557i	0.968560	−	0.248779i	$-0.0800292\pi$
$264$		0			0
$265$	−4.41217	−	2.54737i	−0.271037	−	0.156484i
$266$	−36.4157	−	3.42969i	−2.23279	−	0.210288i
$267$		0			0
$268$	−25.9243	+	44.9022i	−1.58358	+	2.74284i
$269$	−1.04758	+	1.81445i	−0.0638718	+	0.110629i	−0.896193	−	0.443664i	$-0.853678\pi$
$269$	−1.04758	+	1.81445i	−0.0638718	+	0.110629i	0.832321	+	0.554294i	$0.187012\pi$
$270$		0			0
$271$	21.3066	−	12.3014i	1.29428	−	0.747255i	0.314873	−	0.949134i	$-0.398038\pi$
$271$	21.3066	−	12.3014i	1.29428	−	0.747255i	0.979411	+	0.201879i	$0.0647046\pi$
$272$	−11.3643	−	19.6835i	−0.689061	−	1.19349i
$273$		0			0
$274$	−0.872425	+	1.51108i	−0.0527051	+	0.0912879i
$275$			19.0675i			1.14981i
$276$		0			0
$277$	−21.6990			−1.30377			−0.651883	−	0.758319i	$-0.726021\pi$
$277$	−21.6990			−1.30377			−0.651883	+	0.758319i	$0.726021\pi$
$278$	14.4427	+	25.0155i	0.866216	+	1.50033i
$279$		0			0
$280$	−1.68351	+	17.8752i	−0.100609	+	1.06824i
$281$	−19.5994	+	11.3157i	−1.16920	+	0.675040i	−0.953493	−	0.301417i	$-0.902540\pi$
$281$	−19.5994	+	11.3157i	−1.16920	+	0.675040i	−0.215712	+	0.976457i	$0.569207\pi$
$282$		0			0
$283$	8.26370	−	4.77105i	0.491226	−	0.283610i	−0.233857	−	0.972271i	$-0.575135\pi$
$283$	8.26370	−	4.77105i	0.491226	−	0.283610i	0.725083	+	0.688661i	$0.241801\pi$
$284$	16.8638	−	9.73630i	1.00068	−	0.577743i
$285$		0			0
$286$	−35.1541	+	20.2962i	−2.07870	+	1.20014i
$287$	−0.542342	+	0.763705i	−0.0320135	+	0.0450801i
$288$		0			0
$289$	−0.806602	−	1.39708i	−0.0474472	−	0.0821810i
$290$	1.56733			0.0920371
$291$		0			0
$292$		−	29.5935i		−	1.73183i
$293$	−13.1674	+	22.8066i	−0.769248	+	1.33238i	0.168724	+	0.985663i	$0.446035\pi$
$293$	−13.1674	+	22.8066i	−0.769248	+	1.33238i	−0.937971	+	0.346713i	$0.887298\pi$
$294$		0			0
$295$	1.90228	+	3.29485i	0.110755	+	0.191834i
$296$	−14.5690	+	8.41142i	−0.846806	+	0.488904i
$297$		0			0
$298$	0.436212	−	0.755542i	0.0252691	−	0.0437674i
$299$	−2.42106	+	4.19340i	−0.140013	+	0.242510i
$300$		0			0
$301$	0.0703069	+	0.153424i	0.00405242	+	0.00884324i
$302$	10.0415	+	5.79747i	0.577824	+	0.333607i
$303$		0			0
$304$		−	29.2394i		−	1.67700i
$305$	7.38143	+	4.26167i	0.422659	+	0.244023i
$306$		0			0
$307$		−	6.81772i		−	0.389108i	−0.980892	−	0.194554i	$-0.937674\pi$
$307$		−	6.81772i		−	0.389108i	0.980892	−	0.194554i	$-0.0623259\pi$
$308$	55.5268	−	25.4452i	3.16393	−	1.44987i
$309$		0			0
$310$	−25.0350			−1.42190
$311$	−13.4707	−	23.3320i	−0.763855	−	1.32304i	−0.940850	−	0.338823i	$-0.889971\pi$
$311$	−13.4707	−	23.3320i	−0.763855	−	1.32304i	0.176995	−	0.984212i	$-0.443362\pi$
$312$		0			0
$313$	−20.0584	−	11.5807i	−1.13377	−	0.654581i	−0.188887	−	0.981999i	$-0.560488\pi$
$313$	−20.0584	−	11.5807i	−1.13377	−	0.654581i	−0.944880	+	0.327418i	$0.893821\pi$
$314$	3.07842			0.173725
$315$		0			0
$316$	1.39576			0.0785179
$317$	−21.7091	−	12.5338i	−1.21931	−	0.703966i	−0.254536	−	0.967063i	$-0.581923\pi$
$317$	−21.7091	−	12.5338i	−1.21931	−	0.703966i	−0.964769	+	0.263097i	$0.915256\pi$
$318$		0			0
$319$	−1.39780	−	2.42106i	−0.0782617	−	0.135553i
$320$	6.43204			0.359562
$321$		0			0
$322$	6.22529	−	8.76620i	0.346922	−	0.488521i
$323$		−	23.9452i		−	1.33235i
$324$		0			0
$325$	8.92562	+	5.15321i	0.495105	+	0.285849i
$326$			48.8538i			2.70576i
$327$		0			0
$328$	−1.68351	−	0.971976i	−0.0929564	−	0.0536684i
$329$	15.1113	−	21.2792i	0.833116	−	1.17316i
$330$		0			0
$331$	4.19788	−	7.27095i	0.230736	−	0.399647i	−0.727289	−	0.686332i	$-0.759220\pi$
$331$	4.19788	−	7.27095i	0.230736	−	0.399647i	0.958025	+	0.286684i	$0.0925531\pi$
$332$	15.5410	−	26.9178i	0.852922	−	1.47730i
$333$		0			0
$334$	−51.1013	+	29.5033i	−2.79614	+	1.61435i
$335$	7.62045	+	13.1990i	0.416349	+	0.721138i
$336$		0			0
$337$	14.1451	−	24.5000i	0.770533	−	1.33460i	−0.166739	−	0.986001i	$-0.553324\pi$
$337$	14.1451	−	24.5000i	0.770533	−	1.33460i	0.937271	−	0.348601i	$-0.113343\pi$
$338$		−	10.4401i		−	0.567867i
$339$		0			0
$340$	−22.4178			−1.21577
$341$	22.3271	+	38.6716i	1.20908	+	2.09418i
$342$		0			0
$343$	17.7902	+	5.14868i	0.960580	+	0.278003i
$344$	−0.303325	+	0.175125i	−0.0163542	+	0.00944210i
$345$		0			0
$346$	−25.8475	+	14.9230i	−1.38957	+	0.802268i
$347$	−8.62860	+	4.98173i	−0.463208	+	0.267433i	−0.713392	−	0.700765i	$-0.752842\pi$
$347$	−8.62860	+	4.98173i	−0.463208	+	0.267433i	0.250184	+	0.968198i	$0.419509\pi$
$348$		0			0
$349$	−19.4530	+	11.2312i	−1.04130	+	0.601193i	−0.920200	−	0.391448i	$-0.871974\pi$
$349$	−19.4530	+	11.2312i	−1.04130	+	0.601193i	−0.121097	+	0.992641i	$0.538641\pi$
$350$	−18.6588	−	13.2505i	−0.997356	−	0.708269i
$351$		0			0
$352$	5.87691	+	10.1791i	0.313240	+	0.542548i
$353$	32.0652			1.70666			0.853330	−	0.521371i	$-0.174579\pi$
$353$	32.0652			1.70666			0.853330	+	0.521371i	$0.174579\pi$
$354$		0			0
$355$		−	5.72397i		−	0.303797i
$356$	7.21570	−	12.4980i	0.382432	−	0.662391i
$357$		0			0
$358$	27.8794	+	48.2885i	1.47347	+	2.55212i
$359$	−10.2828	+	5.93680i	−0.542707	+	0.313332i	−0.746175	−	0.665749i	$-0.768112\pi$
$359$	−10.2828	+	5.93680i	−0.542707	+	0.313332i	0.203468	+	0.979082i	$0.434779\pi$
$360$		0			0
$361$	5.90228	−	10.2231i	0.310647	−	0.538056i
$362$	−11.0891	+	19.2069i	−0.582829	+	1.00949i
$363$		0			0
$364$	3.09568	−	32.8693i	0.162258	−	1.72282i
$365$	−7.53356	−	4.34950i	−0.394324	−	0.227663i
$366$		0			0
$367$			13.5721i			0.708460i	0.935158	+	0.354230i	$0.115257\pi$
$367$			13.5721i			0.708460i	−0.935158	+	0.354230i	$0.884743\pi$
$368$	7.44343	+	4.29747i	0.388016	+	0.224021i
$369$		0			0
$370$			9.43162i			0.490327i
$371$	−8.89251	−	6.31499i	−0.461676	−	0.327858i
$372$		0			0
$373$	30.1716			1.56223			0.781113	−	0.624390i	$-0.214652\pi$
$373$	30.1716			1.56223			0.781113	+	0.624390i	$0.214652\pi$
$374$	29.5033	+	51.1013i	1.52558	+	2.64238i
$375$		0			0
$376$	46.9079	+	27.0823i	2.41909	+	1.39666i
$377$	−1.51108			−0.0778248
$378$		0			0
$379$	−12.6770			−0.651173			−0.325587	−	0.945512i	$-0.605562\pi$
$379$	−12.6770			−0.651173			−0.325587	+	0.945512i	$0.605562\pi$
$380$	−24.9758	−	14.4198i	−1.28123	−	0.739720i
$381$		0			0
$382$	14.3111	+	24.7875i	0.732219	+	1.26824i
$383$	31.9864			1.63443			0.817214	−	0.576334i	$-0.195517\pi$
$383$	31.9864			1.63443			0.817214	+	0.576334i	$0.195517\pi$
$384$		0			0
$385$	1.68351	−	17.8752i	0.0857997	−	0.911002i
$386$		−	27.4543i		−	1.39739i
$387$		0			0
$388$	−16.2264	−	9.36832i	−0.823771	−	0.475604i
$389$		−	7.57666i		−	0.384152i	−0.981380	−	0.192076i	$-0.938478\pi$
$389$		−	7.57666i		−	0.384152i	0.981380	−	0.192076i	$-0.0615220\pi$
$390$		0			0
$391$	6.09568	+	3.51934i	0.308272	+	0.177981i
$392$	−7.17629	+	37.7602i	−0.362457	+	1.90718i
$393$		0			0
$394$	24.6880	−	42.7609i	1.24376	−	2.15426i
$395$	0.205143	−	0.355317i	0.0103218	−	0.0178780i
$396$		0			0
$397$	−0.824125	+	0.475809i	−0.0413617	+	0.0238802i	−0.520538	−	0.853838i	$-0.674269\pi$
$397$	−0.824125	+	0.475809i	−0.0413617	+	0.0238802i	0.479177	+	0.877719i	$0.340935\pi$
$398$	−10.7858	−	18.6815i	−0.540641	−	0.936418i
$399$		0			0
$400$	9.14713	−	15.8433i	0.457357	−	0.792165i
$401$			21.0325i			1.05031i	0.851006	+	0.525156i	$0.175993\pi$
$401$			21.0325i			1.05031i	−0.851006	+	0.525156i	$0.824007\pi$
$402$		0			0
$403$	24.1365			1.20233
$404$	19.2486	+	33.3396i	0.957655	+	1.65871i
$405$		0			0
$406$	3.34053	+	0.314617i	0.165788	+	0.0156142i
$407$	14.5690	−	8.41142i	0.722159	−	0.416939i
$408$		0			0
$409$	−17.4472	+	10.0732i	−0.862709	+	0.498085i	−0.864919	−	0.501912i	$-0.832630\pi$
$409$	−17.4472	+	10.0732i	−0.862709	+	0.498085i	0.00220932	+	0.999998i	$0.499297\pi$
$410$	−0.943850	+	0.544932i	−0.0466134	+	0.0269123i
$411$		0			0
$412$	15.3066	−	8.83727i	0.754102	−	0.435381i
$413$	3.39304	+	7.40432i	0.166960	+	0.364343i
$414$		0			0
$415$	−4.56827	−	7.91248i	−0.224248	−	0.388408i
$416$	6.35320			0.311491
$417$		0			0
$418$			75.9099i			3.71287i
$419$	−4.79464	+	8.30457i	−0.234234	+	0.405705i	−0.959050	−	0.283238i	$-0.908591\pi$
$419$	−4.79464	+	8.30457i	−0.234234	+	0.405705i	0.724816	+	0.688943i	$0.241925\pi$
$420$		0			0
$421$	−4.30660	−	7.45925i	−0.209891	−	0.363542i	0.741789	−	0.670633i	$-0.233978\pi$
$421$	−4.30660	−	7.45925i	−0.209891	−	0.363542i	−0.951680	+	0.307092i	$0.900644\pi$
$422$	−47.8081	+	27.6020i	−2.32726	+	1.34365i
$423$		0			0
$424$	11.3176	−	19.6027i	0.549632	−	0.951990i
$425$	7.49090	−	12.9746i	0.363362	−	0.629362i
$426$		0			0
$427$	14.8769	+	10.5648i	0.719944	+	0.511266i
$428$	37.5534	+	21.6815i	1.81521	+	1.04801i
$429$		0			0
$430$			0.196365i			0.00946958i
$431$	9.99885	+	5.77284i	0.481628	+	0.278068i	0.721095	−	0.692837i	$-0.243639\pi$
$431$	9.99885	+	5.77284i	0.481628	+	0.278068i	−0.239467	+	0.970905i	$0.576973\pi$
$432$		0			0
$433$		−	22.8707i		−	1.09910i	−0.835462	−	0.549548i	$-0.814800\pi$
$433$		−	22.8707i		−	1.09910i	0.835462	−	0.549548i	$-0.185200\pi$
$434$	−53.3583	−	5.02537i	−2.56128	−	0.241226i
$435$		0			0
$436$	−0.536379			−0.0256879
$437$	4.52750	+	7.84186i	0.216580	+	0.375127i
$438$		0			0
$439$	−0.218772	−	0.126308i	−0.0104414	−	0.00602837i	0.494770	−	0.869024i	$-0.335252\pi$
$439$	−0.218772	−	0.126308i	−0.0104414	−	0.00602837i	−0.505212	+	0.862995i	$0.668586\pi$
$440$	37.2614			1.77637
$441$		0			0
$442$	31.8944			1.51706
$443$	18.8552	+	10.8860i	0.895837	+	0.517212i	0.875847	−	0.482589i	$-0.160303\pi$
$443$	18.8552	+	10.8860i	0.895837	+	0.517212i	0.0199896	+	0.999800i	$0.493637\pi$
$444$		0			0
$445$	−2.12106	−	3.67378i	−0.100548	−	0.174154i
$446$	46.6930			2.21098
$447$		0			0
$448$	13.7089	+	1.29113i	0.647684	+	0.0610000i
$449$			10.7904i			0.509229i	0.967043	+	0.254614i	$0.0819485\pi$
$449$			10.7904i			0.509229i	−0.967043	+	0.254614i	$0.918051\pi$
$450$		0			0
$451$	1.68351	+	0.971976i	0.0792735	+	0.0457686i
$452$			9.66802i			0.454746i
$453$		0			0
$454$	−30.5858	−	17.6587i	−1.43546	−	0.828765i
$455$	−7.91248	−	5.61902i	−0.370943	−	0.263424i
$456$		0			0
$457$	−17.5110	+	30.3299i	−0.819130	+	1.41878i	0.0871937	+	0.996191i	$0.472210\pi$
$457$	−17.5110	+	30.3299i	−0.819130	+	1.41878i	−0.906324	+	0.422584i	$0.861123\pi$
$458$	5.06984	−	8.78123i	0.236898	−	0.410320i
$459$		0			0
$460$	7.34165	−	4.23870i	0.342306	−	0.197631i
$461$	−16.4735	−	28.5330i	−0.767249	−	1.32891i	−0.939049	−	0.343783i	$-0.888292\pi$
$461$	−16.4735	−	28.5330i	−0.767249	−	1.32891i	0.171800	−	0.985132i	$-0.445042\pi$
$462$		0			0
$463$	2.61320	−	4.52620i	0.121446	−	0.210351i	−0.798892	−	0.601474i	$-0.794580\pi$
$463$	2.61320	−	4.52620i	0.121446	−	0.210351i	0.920338	+	0.391124i	$0.127914\pi$
$464$			2.68223i			0.124519i
$465$		0			0
$466$	−17.3450			−0.803492
$467$	−10.8332	−	18.7637i	−0.501302	−	0.868281i	−0.999999	−	0.00150418i	$-0.999521\pi$
$467$	−10.8332	−	18.7637i	−0.501302	−	0.868281i	0.498697	−	0.866777i	$-0.333812\pi$
$468$		0			0
$469$	13.5923	+	29.6613i	0.627635	+	1.36963i
$470$	26.2986	−	15.1835i	1.21306	−	0.700363i
$471$		0			0
$472$	−14.6386	+	8.45159i	−0.673795	+	0.389016i
$473$	0.303325	−	0.175125i	0.0139469	−	0.00805225i
$474$		0			0
$475$	16.6914	−	9.63676i	0.765852	−	0.442165i
$476$	−47.7800	−	4.50000i	−2.18999	−	0.206257i
$477$		0			0
$478$	−33.0539	−	57.2510i	−1.51185	−	2.61860i
$479$	22.4308			1.02489			0.512444	−	0.858721i	$-0.328740\pi$
$479$	22.4308			1.02489			0.512444	+	0.858721i	$0.328740\pi$
$480$		0			0
$481$		−	9.09312i		−	0.414611i
$482$	16.9426	−	29.3454i	0.771714	−	1.33665i
$483$		0			0
$484$	−40.2563	−	69.7259i	−1.82983	−	3.16936i
$485$	−4.76975	+	2.75382i	−0.216583	+	0.125044i
$486$		0			0
$487$	−11.0813	+	19.1934i	−0.502142	+	0.869736i	0.497855	+	0.867260i	$0.334121\pi$
$487$	−11.0813	+	19.1934i	−0.502142	+	0.869736i	−0.999997	+	0.00247528i	$0.999212\pi$
$488$	−18.9340	+	32.7947i	−0.857103	+	1.48455i
$489$		0			0
$490$	16.3221	+	14.0693i	0.737357	+	0.635587i
$491$	−13.3838	−	7.72716i	−0.604004	−	0.348722i	0.166611	−	0.986023i	$-0.446718\pi$
$491$	−13.3838	−	7.72716i	−0.604004	−	0.348722i	−0.770615	+	0.637301i	$0.780051\pi$
$492$		0			0
$493$			2.19657i			0.0989285i
$494$	35.5339	+	20.5155i	1.59874	+	0.923035i
$495$		0			0
$496$		−	42.8432i		−	1.92372i
$497$	1.14899	−	12.1997i	0.0515394	−	0.547234i
$498$		0			0
$499$	−1.34502			−0.0602112			−0.0301056	−	0.999547i	$-0.509584\pi$
$499$	−1.34502			−0.0602112			−0.0301056	+	0.999547i	$0.509584\pi$
$500$	−22.0124	−	38.1267i	−0.984426	−	1.70508i
$501$		0			0
$502$	−5.50203	−	3.17660i	−0.245568	−	0.141779i
$503$	−18.1391			−0.808781			−0.404390	−	0.914586i	$-0.632516\pi$
$503$	−18.1391			−0.808781			−0.404390	+	0.914586i	$0.632516\pi$
$504$		0			0
$505$	11.3163			0.503568
$506$	−19.3242	−	11.1569i	−0.859067	−	0.495983i
$507$		0			0
$508$	−0.813121	−	1.40837i	−0.0360764	−	0.0624862i
$509$	28.1838			1.24922			0.624612	−	0.780935i	$-0.285257\pi$
$509$	28.1838			1.24922			0.624612	+	0.780935i	$0.285257\pi$
$510$		0			0
$511$	−15.1835	−	10.7825i	−0.671679	−	0.476991i
$512$			46.5767i			2.05842i
$513$		0			0
$514$	−38.9586	−	22.4928i	−1.71839	−	0.992114i
$515$		−	5.19543i		−	0.228938i
$516$		0			0
$517$	−46.9079	−	27.0823i	−2.06301	−	1.19108i
$518$	−1.89324	+	20.1020i	−0.0831843	+	0.883233i
$519$		0			0
$520$	10.0703	−	17.4423i	0.441612	−	0.764895i
$521$	17.0915	−	29.6033i	0.748792	−	1.29694i	−0.199611	−	0.979875i	$-0.563968\pi$
$521$	17.0915	−	29.6033i	0.748792	−	1.29694i	0.948402	−	0.317070i	$-0.102699\pi$
$522$		0			0
$523$	31.9157	−	18.4266i	1.39558	−	0.805737i	0.401652	−	0.915792i	$-0.368436\pi$
$523$	31.9157	−	18.4266i	1.39558	−	0.805737i	0.993925	+	0.110055i	$0.0351027\pi$
$524$	43.8591	+	75.9663i	1.91600	+	3.31860i
$525$		0			0
$526$	10.0494	−	17.4061i	0.438175	−	0.758942i
$527$		−	35.0858i		−	1.52836i
$528$		0			0
$529$	20.3383			0.884273
$530$	−6.34515	−	10.9901i	−0.275615	−	0.477380i
$531$		0			0
$532$	−50.3376	−	35.7471i	−2.18241	−	1.54983i
$533$	0.909976	−	0.525375i	0.0394154	−	0.0227565i
$534$		0			0
$535$	11.0388	−	6.37327i	0.477250	−	0.275541i
$536$	−58.6414	+	33.8566i	−2.53292	+	1.46238i
$537$		0			0
$538$	−4.51956	+	2.60937i	−0.194852	+	0.112498i
$539$	7.17629	−	37.7602i	0.309105	−	1.62645i
$540$		0			0
$541$	19.2089	+	33.2708i	0.825855	+	1.43042i	0.901264	+	0.433269i	$0.142640\pi$
$541$	19.2089	+	33.2708i	0.825855	+	1.43042i	−0.0754099	+	0.997153i	$0.524027\pi$
$542$	61.2821			2.63229
$543$		0			0
$544$		−	9.23526i		−	0.395958i
$545$	−0.0788343	+	0.136545i	−0.00337689	+	0.00584894i
$546$		0			0
$547$	−5.99797	−	10.3888i	−0.256454	−	0.444192i	0.708835	−	0.705374i	$-0.249221\pi$
$547$	−5.99797	−	10.3888i	−0.256454	−	0.444192i	−0.965290	+	0.261182i	$0.915888\pi$
$548$	−2.55060	+	1.47259i	−0.108956	+	0.0629060i
$549$		0			0
$550$	−23.7473	+	41.1315i	−1.01259	+	1.75385i
$551$	−1.41290	+	2.44722i	−0.0601916	+	0.104255i
$552$		0			0
$553$	0.508554	−	0.716125i	0.0216259	−	0.0304527i
$554$	−46.8080	−	27.0246i	−1.98868	−	1.14817i
$555$		0			0
$556$			48.7565i			2.06774i
$557$	−7.53838	−	4.35228i	−0.319411	−	0.184412i	0.331719	−	0.943378i	$-0.392371\pi$
$557$	−7.53838	−	4.35228i	−0.319411	−	0.184412i	−0.651130	+	0.758966i	$0.725705\pi$
$558$		0			0
$559$		−	0.189318i		−	0.00800729i
$560$	−9.97396	+	14.0449i	−0.421477	+	0.593507i
$561$		0			0
$562$	−56.3719			−2.37791
$563$	11.7183	+	20.2967i	0.493868	+	0.855405i	0.999975	−	0.00706612i	$-0.00224924\pi$
$563$	11.7183	+	20.2967i	0.493868	+	0.855405i	−0.506107	+	0.862471i	$0.668916\pi$
$564$		0			0
$565$	2.46117	+	1.42096i	0.103542	+	0.0597801i
$566$	23.7681			0.999047
$567$		0			0
$568$	25.4308			1.06705
$569$	−29.7165	−	17.1569i	−1.24578	−	0.719253i	−0.275517	−	0.961296i	$-0.588849\pi$
$569$	−29.7165	−	17.1569i	−1.24578	−	0.719253i	−0.970265	+	0.242044i	$0.922182\pi$
$570$		0			0
$571$	−10.7363	−	18.5958i	−0.449300	−	0.778210i	0.549041	−	0.835796i	$-0.314993\pi$
$571$	−10.7363	−	18.5958i	−0.449300	−	0.778210i	−0.998341	+	0.0575853i	$0.981660\pi$
$572$	−68.5171			−2.86485
$573$		0			0
$574$	−2.12106	+	0.971976i	−0.0885312	+	0.0405695i
$575$			5.66545i			0.236266i
$576$		0			0
$577$	−24.7850	−	14.3096i	−1.03181	−	0.595718i	−0.114310	−	0.993445i	$-0.536466\pi$
$577$	−24.7850	−	14.3096i	−1.03181	−	0.595718i	−0.917504	+	0.397727i	$0.869799\pi$
$578$		−	4.01827i		−	0.167138i
$579$		0			0
$580$	2.29111	+	1.32278i	0.0951333	+	0.0549252i
$581$	−8.14826	−	17.7812i	−0.338047	−	0.737690i
$582$		0			0
$583$	−11.3176	+	19.6027i	−0.468727	+	0.811860i
$584$	19.3242	−	33.4706i	0.799643	−	1.38502i
$585$		0			0
$586$	−56.8081	+	32.7982i	−2.34672	+	1.35488i
$587$	−9.25784	−	16.0350i	−0.382112	−	0.661837i	0.609252	−	0.792977i	$-0.291470\pi$
$587$	−9.25784	−	16.0350i	−0.382112	−	0.661837i	−0.991364	+	0.131139i	$0.958136\pi$
$588$		0			0
$589$	22.5683	−	39.0894i	0.929909	−	1.61065i
$590$			9.47666i			0.390148i
$591$		0			0
$592$	−16.1406			−0.663375
$593$	9.37285	+	16.2343i	0.384897	+	0.666661i	0.991755	−	0.128149i	$-0.0409036\pi$
$593$	9.37285	+	16.2343i	0.384897	+	0.666661i	−0.606858	+	0.794810i	$0.707570\pi$
$594$		0			0
$595$	−8.16802	+	11.5019i	−0.334856	+	0.471531i
$596$	1.27530	−	0.736295i	0.0522384	−	0.0301598i
$597$		0			0
$598$	−10.4452	+	6.03053i	−0.427135	+	0.246607i
$599$	22.4059	−	12.9360i	0.915480	−	0.528552i	0.0332896	−	0.999446i	$-0.489402\pi$
$599$	22.4059	−	12.9360i	0.915480	−	0.528552i	0.882190	+	0.470893i	$0.156068\pi$
$600$		0			0
$601$	12.6211	−	7.28677i	0.514824	−	0.297234i	−0.219991	−	0.975502i	$-0.570603\pi$
$601$	12.6211	−	7.28677i	0.514824	−	0.297234i	0.734814	+	0.678268i	$0.237269\pi$
$602$	−0.0394171	+	0.418522i	−0.00160652	+	0.0170577i
$603$		0			0
$604$	9.78571	+	16.9494i	0.398175	+	0.689659i
$605$	−23.6667			−0.962187
$606$		0			0
$607$			22.2796i			0.904300i	0.891942	+	0.452150i	$0.149343\pi$
$607$			22.2796i			0.904300i	−0.891942	+	0.452150i	$0.850657\pi$
$608$	5.94040	−	10.2891i	0.240915	−	0.417277i
$609$		0			0
$610$	10.6152	+	18.3861i	0.429798	+	0.744433i
$611$	−25.3548	+	14.6386i	−1.02574	+	0.592214i
$612$		0			0
$613$	−12.6112	+	21.8432i	−0.509360	+	0.882238i	0.490581	+	0.871396i	$0.336785\pi$
$613$	−12.6112	+	21.8432i	−0.509360	+	0.882238i	−0.999941	+	0.0108424i	$0.996549\pi$
$614$	8.49100	−	14.7069i	0.342669	−	0.593520i
$615$		0			0
$616$	79.4169	+	7.47961i	3.19980	+	0.301362i
$617$	−1.76370	−	1.01827i	−0.0710039	−	0.0409941i	0.464078	−	0.885794i	$-0.346386\pi$
$617$	−1.76370	−	1.01827i	−0.0710039	−	0.0409941i	−0.535082	+	0.844800i	$0.679719\pi$
$618$		0			0
$619$		−	38.0011i		−	1.52739i	−0.645575	−	0.763697i	$-0.723382\pi$
$619$		−	38.0011i		−	1.52739i	0.645575	−	0.763697i	$-0.276618\pi$
$620$	−36.5960	−	21.1287i	−1.46973	−	0.848549i
$621$		0			0
$622$		−	67.1075i		−	2.69076i
$623$	−3.78325	−	8.25585i	−0.151573	−	0.330764i
$624$		0			0
$625$	4.42184			0.176874
$626$	−28.8460	−	49.9627i	−1.15292	−	1.99691i
$627$		0			0
$628$	4.50000	+	2.59808i	0.179570	+	0.103675i
$629$	−13.2181			−0.527040
$630$		0			0
$631$	2.80457			0.111648			0.0558240	−	0.998441i	$-0.482221\pi$
$631$	2.80457			0.111648			0.0558240	+	0.998441i	$0.482221\pi$
$632$	1.57863	+	0.911420i	0.0627944	+	0.0362544i
$633$		0			0
$634$	−31.2199	−	54.0744i	−1.23990	−	2.14757i
$635$	−0.478034			−0.0189702
$636$		0			0
$637$	−15.7363	−	13.5644i	−0.623495	−	0.537440i
$638$		−	6.96345i		−	0.275686i
$639$		0			0
$640$	18.4571	+	10.6562i	0.729581	+	0.421224i
$641$		−	1.87766i		−	0.0741631i	−0.999312	−	0.0370815i	$-0.988194\pi$
$641$		−	1.87766i		−	0.0741631i	0.999312	−	0.0370815i	$-0.0118061\pi$
$642$		0			0
$643$	12.6211	+	7.28677i	0.497726	+	0.287362i	0.727774	−	0.685817i	$-0.240555\pi$
$643$	12.6211	+	7.28677i	0.497726	+	0.287362i	−0.230048	+	0.973179i	$0.573888\pi$
$644$	16.4984	−	7.56042i	0.650129	−	0.297922i
$645$		0			0
$646$	29.8221	−	51.6534i	1.17333	−	2.03227i
$647$	−18.2292	+	31.5739i	−0.716663	+	1.24130i	0.245651	+	0.969358i	$0.420998\pi$
$647$	−18.2292	+	31.5739i	−0.716663	+	1.24130i	−0.962315	+	0.271939i	$0.912335\pi$
$648$		0			0
$649$	14.6386	−	8.45159i	0.574615	−	0.331754i
$650$	12.8359	+	22.2325i	0.503467	+	0.872031i
$651$		0			0
$652$	−41.2309	+	71.4140i	−1.61473	+	2.79679i
$653$			15.0716i			0.589797i	0.955529	+	0.294898i	$0.0952858\pi$
$653$			15.0716i			0.589797i	−0.955529	+	0.294898i	$0.904714\pi$
$654$		0			0
$655$	25.7848			1.00750
$656$	−0.932559	−	1.61524i	−0.0364103	−	0.0630645i
$657$		0			0
$658$	59.0992	−	27.0823i	2.30393	−	1.05578i
$659$	−27.2512	+	15.7335i	−1.06156	+	0.612891i	−0.925863	−	0.377860i	$-0.876660\pi$
$659$	−27.2512	+	15.7335i	−1.06156	+	0.612891i	−0.135695	+	0.990751i	$0.543327\pi$
$660$		0			0
$661$	11.9099	−	6.87620i	0.463242	−	0.267453i	−0.250164	−	0.968203i	$-0.580485\pi$
$661$	11.9099	−	6.87620i	0.463242	−	0.267453i	0.713407	+	0.700750i	$0.247151\pi$
$662$	18.1109	−	10.4564i	0.703901	−	0.406398i
$663$		0			0
$664$	35.1541	−	20.2962i	1.36424	−	0.787646i
$665$	−16.4984	+	7.56042i	−0.639782	+	0.293181i
$666$		0			0
$667$	−0.415322	−	0.719359i	−0.0160813	−	0.0278537i
$668$	−99.5991			−3.85360
$669$		0			0
$670$			37.9630i			1.46664i
$671$	18.9340	−	32.7947i	0.730940	−	1.26602i
$672$		0			0
$673$	−5.87242	−	10.1713i	−0.226365	−	0.392076i	0.730363	−	0.683059i	$-0.239351\pi$
$673$	−5.87242	−	10.1713i	−0.226365	−	0.392076i	−0.956728	+	0.290983i	$0.906018\pi$
$674$	61.0262	−	35.2335i	2.35064	−	1.35714i
$675$		0			0
$676$	8.81109	−	15.2613i	0.338888	−	0.586971i
$677$	10.8726	−	18.8320i	0.417870	−	0.723772i	−0.577855	−	0.816139i	$-0.696110\pi$
$677$	10.8726	−	18.8320i	0.417870	−	0.723772i	0.995725	+	0.0923676i	$0.0294435\pi$
$678$		0			0
$679$	−10.7188	+	4.91189i	−0.411349	+	0.188501i
$680$	−25.3548	−	14.6386i	−0.972311	−	0.561364i
$681$		0			0
$682$			111.227i			4.25911i
$683$	−11.1647	−	6.44593i	−0.427205	−	0.246647i	0.270950	−	0.962593i	$-0.412662\pi$
$683$	−11.1647	−	6.44593i	−0.427205	−	0.246647i	−0.698155	+	0.715947i	$0.745995\pi$
$684$		0			0
$685$			0.865736i			0.0330781i
$686$	31.9638	+	33.2630i	1.22038	+	1.26999i
$687$		0			0
$688$	−0.336046			−0.0128116
$689$	6.11742	+	10.5957i	0.233055	+	0.403663i
$690$		0			0
$691$	8.95303	+	5.16904i	0.340589	+	0.196639i	0.660533	−	0.750797i	$-0.270331\pi$
$691$	8.95303	+	5.16904i	0.340589	+	0.196639i	−0.319943	+	0.947437i	$0.603664\pi$
$692$	−50.3781			−1.91509
$693$		0			0
$694$	−24.8176			−0.942063
$695$	12.4119	+	7.16599i	0.470809	+	0.271821i
$696$		0			0
$697$	−0.763705	−	1.32278i	−0.0289274	−	0.0501037i
$698$	−55.9508			−2.11777
$699$		0			0
$700$	−16.0923	−	35.1168i	−0.608232	−	1.32729i
$701$		−	41.2056i		−	1.55631i	−0.628071	−	0.778156i	$-0.716155\pi$
$701$		−	41.2056i		−	1.55631i	0.628071	−	0.778156i	$-0.283845\pi$
$702$		0			0
$703$	−14.7264	−	8.50230i	−0.555417	−	0.320670i
$704$		−	28.5767i		−	1.07702i
$705$		0			0
$706$	69.1696	+	39.9351i	2.60323	+	1.50298i
$707$	24.1189	+	2.27156i	0.907084	+	0.0854307i
$708$		0			0
$709$	−14.3001	+	24.7685i	−0.537051	+	0.930199i	0.462010	+	0.886875i	$0.347128\pi$
$709$	−14.3001	+	24.7685i	−0.537051	+	0.930199i	−0.999061	+	0.0433248i	$0.986205\pi$
$710$	7.12881	−	12.3475i	0.267540	−	0.463392i
$711$		0			0
$712$	16.3221	−	9.42356i	0.611696	−	0.353163i
$713$	6.63394	+	11.4903i	0.248443	+	0.430316i
$714$		0			0
$715$	−10.0703	+	17.4423i	−0.376608	+	0.652304i
$716$			94.1168i			3.51731i
$717$		0			0
$718$	−29.5755			−1.10375
$719$	0.881850	+	1.52741i	0.0328875	+	0.0569627i	0.882001	−	0.471248i	$-0.156196\pi$
$719$	0.881850	+	1.52741i	0.0328875	+	0.0569627i	−0.849113	+	0.528211i	$0.822863\pi$
$720$		0			0
$721$	1.04290	−	11.0733i	0.0388395	−	0.412390i
$722$	25.4642	−	14.7018i	0.947681	−	0.547144i
$723$		0			0
$724$	−32.4198	+	18.7176i	−1.20487	+	0.695634i
$725$	−1.53115	+	0.884011i	−0.0568656	+	0.0328314i
$726$		0			0
$727$	17.3515	−	10.0179i	0.643533	−	0.371544i	−0.142441	−	0.989803i	$-0.545495\pi$
$727$	17.3515	−	10.0179i	0.643533	−	0.371544i	0.785974	+	0.618259i	$0.212162\pi$
$728$	24.9645	−	35.1541i	0.925248	−	1.30290i
$729$		0			0
$730$	−10.8340	−	18.7651i	−0.400985	−	0.694526i
$731$	−0.275200			−0.0101786
$732$		0			0
$733$			15.4237i			0.569689i	0.958574	+	0.284844i	$0.0919419\pi$
$733$			15.4237i			0.569689i	−0.958574	+	0.284844i	$0.908058\pi$
$734$	−16.9032	+	29.2772i	−0.623908	+	1.08064i
$735$		0			0
$736$	1.74618	+	3.02448i	0.0643651	+	0.111484i
$737$	58.6414	−	33.8566i	2.16008	−	1.24712i
$738$		0			0
$739$	16.2284	−	28.1085i	0.596973	−	1.03399i	−0.396292	−	0.918124i	$-0.629703\pi$
$739$	16.2284	−	28.1085i	0.596973	−	1.03399i	0.993265	−	0.115863i	$-0.0369634\pi$
$740$	−7.95995	+	13.7870i	−0.292614	+	0.506822i
$741$		0			0
$742$	−11.3176	−	24.6974i	−0.415482	−	0.906670i
$743$	6.51411	+	3.76092i	0.238979	+	0.137975i	0.614708	−	0.788755i	$-0.289274\pi$
$743$	6.51411	+	3.76092i	0.238979	+	0.137975i	−0.375728	+	0.926730i	$0.622607\pi$
$744$		0			0
$745$		−	0.432868i		−	0.0158591i
$746$	65.0847	+	37.5767i	2.38292	+	1.37578i
$747$		0			0
$748$			99.5991i			3.64170i
$749$	24.8069	−	11.3678i	0.906424	−	0.415369i
$750$		0			0
$751$	25.8463			0.943147			0.471573	−	0.881827i	$-0.343686\pi$
$751$	25.8463			0.943147			0.471573	+	0.881827i	$0.343686\pi$
$752$	25.9840	+	45.0056i	0.947539	+	1.64119i
$753$		0			0
$754$	−3.25964	−	1.88195i	−0.118709	−	0.0685366i
$755$	5.75302			0.209374
$756$		0			0
$757$	33.5103			1.21795			0.608976	−	0.793188i	$-0.291580\pi$
$757$	33.5103			1.21795			0.608976	+	0.793188i	$0.291580\pi$
$758$	−27.3462	−	15.7883i	−0.993258	−	0.573458i
$759$		0			0
$760$	−18.8320	−	32.6179i	−0.683108	−	1.18318i
$761$	−8.73002			−0.316463			−0.158232	−	0.987402i	$-0.550579\pi$
$761$	−8.73002			−0.316463			−0.158232	+	0.987402i	$0.550579\pi$
$762$		0			0
$763$	−0.195432	+	0.275200i	−0.00707512	+	0.00996290i
$764$			48.3122i			1.74787i
$765$		0			0
$766$	68.9995	+	39.8369i	2.49305	+	1.43936i
$767$		−	9.13654i		−	0.329902i
$768$		0			0
$769$	4.36906	+	2.52248i	0.157552	+	0.0909628i	0.576703	−	0.816954i	$-0.304339\pi$
$769$	4.36906	+	2.52248i	0.157552	+	0.0909628i	−0.419151	+	0.907917i	$0.637672\pi$
$770$	25.8939	−	36.4627i	0.933150	−	1.31402i
$771$		0			0
$772$	23.1705	−	40.1324i	0.833924	−	1.44440i
$773$	−2.90140	+	5.02537i	−0.104356	+	0.180750i	−0.913475	−	0.406895i	$-0.866612\pi$
$773$	−2.90140	+	5.02537i	−0.104356	+	0.180750i	0.809119	+	0.587645i	$0.199945\pi$
$774$		0			0
$775$	24.4571	−	14.1203i	0.878525	−	0.507217i
$776$	−12.2348	−	21.1914i	−0.439205	−	0.760726i
$777$		0			0
$778$	9.43621	−	16.3440i	0.338305	−	0.585961i
$779$		−	1.96495i		−	0.0704018i
$780$		0			0
$781$	−25.4308			−0.909986
$782$	8.76620	+	15.1835i	0.313479	+	0.542961i
$783$		0			0
$784$	−24.0772	+	27.9325i	−0.859901	+	0.997589i
$785$	1.32278	−	0.763705i	0.0472119	−	0.0272578i
$786$		0			0
$787$	21.3944	−	12.3521i	0.762629	−	0.440304i	−0.0676098	−	0.997712i	$-0.521537\pi$
$787$	21.3944	−	12.3521i	0.762629	−	0.440304i	0.830239	+	0.557408i	$0.188204\pi$
$788$	72.1773	−	41.6716i	2.57121	−	1.48449i
$789$		0			0
$790$	0.885047	−	0.510982i	0.0314886	−	0.0181799i
$791$	4.96037	+	3.52259i	0.176370	+	0.125249i
$792$		0			0
$793$	−10.2343	−	17.7263i	−0.363429	−	0.629478i
$794$	−2.37035			−0.0841206
$795$		0			0
$796$		−	36.4112i		−	1.29056i
$797$	−2.19657	+	3.80457i	−0.0778064	+	0.134765i	−0.902303	−	0.431102i	$-0.858125\pi$
$797$	−2.19657	+	3.80457i	−0.0778064	+	0.134765i	0.824497	+	0.565867i	$0.191458\pi$
$798$		0			0
$799$	21.2792	+	36.8566i	0.752804	+	1.30389i
$800$	6.43758	−	3.71674i	0.227603	−	0.131407i
$801$		0			0
$802$	−26.1945	+	45.3702i	−0.924960	+	1.60208i
$803$	−19.3242	+	33.4706i	−0.681937	+	1.18115i
$804$		0			0
$805$	0.500215	−	5.31117i	0.0176303	−	0.187194i
$806$	52.0662	+	30.0604i	1.83395	+	1.05883i
$807$		0			0
$808$			50.2767i			1.76873i
$809$	−43.9347	−	25.3657i	−1.54466	−	0.891812i	−0.998535	−	0.0541105i	$-0.982768\pi$
$809$	−43.9347	−	25.3657i	−1.54466	−	0.891812i	−0.546129	−	0.837701i	$-0.683899\pi$
$810$		0			0
$811$			31.8126i			1.11709i	0.829474	+	0.558546i	$0.188641\pi$
$811$			31.8126i			1.11709i	−0.829474	+	0.558546i	$0.811359\pi$
$812$	4.61763	+	3.27919i	0.162047	+	0.115077i
$813$		0			0
$814$	41.9034			1.46871
$815$	12.1198	+	20.9921i	0.424539	+	0.735323i
$816$		0			0
$817$	−0.306602	−	0.177017i	−0.0107267	−	0.00619304i
$818$	−50.1817			−1.75456
$819$		0			0
$820$	−1.83961			−0.0642421
$821$	22.4679	+	12.9718i	0.784135	+	0.452720i	0.837894	−	0.545834i	$-0.183787\pi$
$821$	22.4679	+	12.9718i	0.784135	+	0.452720i	−0.0537589	+	0.998554i	$0.517120\pi$
$822$		0			0
$823$	0.0703069	+	0.121775i	0.00245074	+	0.00424481i	0.867248	−	0.497876i	$-0.165887\pi$
$823$	0.0703069	+	0.121775i	0.00245074	+	0.00424481i	−0.864797	+	0.502121i	$0.832553\pi$
$824$	23.0826			0.804120
$825$		0			0
$826$	−1.90228	+	20.1980i	−0.0661889	+	0.702779i
$827$			16.1772i			0.562535i	0.959629	+	0.281267i	$0.0907548\pi$
$827$			16.1772i			0.562535i	−0.959629	+	0.281267i	$0.909245\pi$
$828$		0			0
$829$	−28.8592	−	16.6619i	−1.00232	−	0.578690i	−0.0933864	−	0.995630i	$-0.529769\pi$
$829$	−28.8592	−	16.6619i	−1.00232	−	0.578690i	−0.908934	+	0.416940i	$0.863103\pi$
$830$		−	22.7579i		−	0.789938i
$831$		0			0
$832$	−13.3769	−	7.72316i	−0.463761	−	0.267752i
$833$	−19.7177	+	22.8749i	−0.683177	+	0.792567i
$834$		0			0
$835$	−14.6386	+	25.3548i	−0.506589	+	0.877438i
$836$	−64.0652	+	110.964i	−2.21574	+	3.83778i
$837$		0			0
$838$	−20.6855	+	11.9428i	−0.714570	+	0.412557i
$839$	10.7350	+	18.5936i	0.370615	+	0.641924i	0.989660	−	0.143431i	$-0.0458136\pi$
$839$	10.7350	+	18.5936i	0.370615	+	0.641924i	−0.619045	+	0.785355i	$0.712480\pi$
$840$		0			0
$841$	−14.3704	+	24.8902i	−0.495531	+	0.858284i
$842$		−	21.4543i		−	0.739365i
$843$		0			0
$844$	−93.1806			−3.20741
$845$	−2.59002	−	4.48605i	−0.0890994	−	0.154325i
$846$		0			0
$847$	−50.4418	−	4.75069i	−1.73320	−	0.163236i
$848$	18.8077	−	10.8586i	0.645859	−	0.372887i
$849$		0			0
$850$	32.3180	−	18.6588i	1.10850	−	0.639992i
$851$	4.32883	−	2.49925i	0.148390	−	0.0856732i
$852$		0			0
$853$	−21.8102	+	12.5921i	−0.746766	+	0.431146i	−0.824524	−	0.565827i	$-0.808557\pi$
$853$	−21.8102	+	12.5921i	−0.746766	+	0.431146i	0.0777582	+	0.996972i	$0.475224\pi$
$854$	18.9340	+	41.3180i	0.647909	+	1.41387i
$855$		0			0
$856$	28.3156	+	49.0440i	0.967806	+	1.67629i
$857$	−29.0366			−0.991871			−0.495936	−	0.868359i	$-0.665175\pi$
$857$	−29.0366			−0.991871			−0.495936	+	0.868359i	$0.665175\pi$
$858$		0			0
$859$		−	23.8314i		−	0.813116i	−0.913625	−	0.406558i	$-0.866729\pi$
$859$		−	23.8314i		−	0.813116i	0.913625	−	0.406558i	$-0.133271\pi$
$860$	−0.165725	+	0.287045i	−0.00565119	+	0.00978815i
$861$		0			0
$862$	14.3794	+	24.9058i	0.489763	+	0.848294i
$863$	−27.6069	+	15.9388i	−0.939749	+	0.542564i	−0.889881	−	0.456192i	$-0.849213\pi$
$863$	−27.6069	+	15.9388i	−0.939749	+	0.542564i	−0.0498671	+	0.998756i	$0.515880\pi$
$864$		0			0
$865$	−7.40432	+	12.8247i	−0.251754	+	0.436051i
$866$	28.4839	−	49.3355i	0.967922	−	1.67649i
$867$		0			0
$868$	−73.7574	−	52.3786i	−2.50349	−	1.77784i
$869$	−1.57863	−	0.911420i	−0.0535512	−	0.0309178i
$870$		0			0
$871$		−	36.6005i		−	1.24016i
$872$	−0.606650	−	0.350250i	−0.0205438	−	0.0118610i
$873$		0			0
$874$			22.5548i			0.762927i
$875$	−27.5820	−	2.59772i	−0.932441	−	0.0878188i
$876$		0			0
$877$	−2.28123			−0.0770316			−0.0385158	−	0.999258i	$-0.512263\pi$
$877$	−2.28123			−0.0770316			−0.0385158	+	0.999258i	$0.512263\pi$
$878$	−0.314617	−	0.544932i	−0.0106178	−	0.0183906i
$879$		0			0
$880$	30.9607	+	17.8752i	1.04368	+	0.602571i
$881$	11.8808			0.400275			0.200137	−	0.979768i	$-0.435861\pi$
$881$	11.8808			0.400275			0.200137	+	0.979768i	$0.435861\pi$
$882$		0			0
$883$	−49.7120			−1.67294			−0.836472	−	0.548010i	$-0.815385\pi$
$883$	−49.7120			−1.67294			−0.836472	+	0.548010i	$0.815385\pi$
$884$	46.6229	+	26.9178i	1.56810	+	0.905343i
$885$		0			0
$886$	27.1157	+	46.9657i	0.910968	+	1.57784i
$887$	12.3588			0.414969			0.207485	−	0.978238i	$-0.433472\pi$
$887$	12.3588			0.414969			0.207485	+	0.978238i	$0.433472\pi$
$888$		0			0
$889$	−1.01886	−	0.0959575i	−0.0341713	−	0.00321831i
$890$		−	10.5665i		−	0.354191i
$891$		0			0
$892$	68.2554	+	39.4072i	2.28536	+	1.31945i
$893$			54.7497i			1.83213i
$894$		0			0
$895$	23.9591	+	13.8328i	0.800866	+	0.462380i
$896$	37.1994	+	26.4170i	1.24274	+	0.882531i
$897$		0			0
$898$	−13.4387	+	23.2764i	−0.448454	+	0.776745i
$899$	−2.07026	+	3.58580i	−0.0690470	+	0.119593i
$900$		0			0
$901$	15.4023	−	8.89251i	0.513124	−	0.296253i
$902$	2.42106	+	4.19340i	0.0806125	+	0.139625i
$903$		0			0
$904$	−6.31312	+	10.9346i	−0.209971	+	0.363681i
$905$			11.0041i			0.365788i
$906$		0			0
$907$	−35.7628			−1.18748			−0.593742	−	0.804656i	$-0.702350\pi$
$907$	−35.7628			−1.18748			−0.593742	+	0.804656i	$0.702350\pi$
$908$	−29.8067	−	51.6267i	−0.989169	−	1.71329i
$909$		0			0
$910$	−10.0703	−	21.9755i	−0.333827	−	0.728482i
$911$	41.5024	−	23.9614i	1.37504	−	0.793877i	0.383479	−	0.923550i	$-0.374726\pi$
$911$	41.5024	−	23.9614i	1.37504	−	0.793877i	0.991557	+	0.129672i	$0.0413926\pi$
$912$		0			0
$913$	−35.1541	+	20.2962i	−1.16343	+	0.671707i
$914$	−75.5478	+	43.6175i	−2.49890	+	1.44274i
$915$		0			0
$916$	14.8221	−	8.55754i	0.489736	−	0.282749i
$917$	54.9563	+	5.17587i	1.81482	+	0.170922i
$918$		0			0
$919$	17.2408	+	29.8619i	0.568721	+	0.985053i	0.996693	+	0.0812614i	$0.0258949\pi$
$919$	17.2408	+	29.8619i	0.568721	+	0.985053i	−0.427972	+	0.903792i	$0.640772\pi$
$920$	11.0713			0.365011
$921$		0			0
$922$		−	82.0667i		−	2.70272i
$923$	−6.87296	+	11.9043i	−0.226226	+	0.391835i
$924$		0			0
$925$	−5.31964	−	9.21389i	−0.174909	−	0.302951i
$926$	11.2742	−	6.50914i	0.370492	−	0.213903i
$927$		0			0
$928$	−0.544932	+	0.943850i	−0.0178883	+	0.0309834i
$929$	29.1774	−	50.5368i	0.957280	−	1.65806i	0.228219	−	0.973610i	$-0.426710\pi$
$929$	29.1774	−	50.5368i	0.957280	−	1.65806i	0.729061	−	0.684449i	$-0.239957\pi$
$930$		0			0
$931$	−36.6815	+	12.8021i	−1.20219	+	0.419571i
$932$	−25.3548	−	14.6386i	−0.830523	−	0.479503i
$933$		0			0
$934$		−	53.9682i		−	1.76589i
$935$	25.3548	+	14.6386i	0.829189	+	0.478733i
$936$		0			0
$937$		−	29.8596i		−	0.975471i	−0.872992	−	0.487735i	$-0.837823\pi$
$937$		−	29.8596i		−	0.975471i	0.872992	−	0.487735i	$-0.162177\pi$
$938$	−7.62045	+	80.9122i	−0.248816	+	2.64188i
$939$		0			0
$940$	51.2574			1.67183
$941$	−8.10885	−	14.0449i	−0.264341	−	0.457852i	0.703050	−	0.711141i	$-0.251821\pi$
$941$	−8.10885	−	14.0449i	−0.264341	−	0.457852i	−0.967391	+	0.253289i	$0.918488\pi$
$942$		0			0
$943$	0.500215	+	0.288799i	0.0162892	+	0.00940459i
$944$	−16.2177			−0.527841
$945$		0			0
$946$	0.872425			0.0283650
$947$	24.4167	+	14.0970i	0.793435	+	0.458090i	0.841170	−	0.540770i	$-0.181867\pi$
$947$	24.4167	+	14.0970i	0.793435	+	0.458090i	−0.0477355	+	0.998860i	$0.515200\pi$
$948$		0			0
$949$	10.4452	+	18.0916i	0.339065	+	0.587278i
$950$	48.0077			1.55758
$951$		0			0
$952$	−51.1013	−	36.2894i	−1.65620	−	1.17615i
$953$			56.3488i			1.82532i	0.408725	+	0.912658i	$0.365973\pi$
$953$			56.3488i			1.82532i	−0.408725	+	0.912658i	$0.634027\pi$
$954$		0			0
$955$	12.2988	+	7.10069i	0.397978	+	0.229773i
$956$		−	111.585i		−	3.60893i
$957$		0			0
$958$	48.3866	+	27.9360i	1.56330	+	0.902571i
$959$	−0.173782	+	1.84518i	−0.00561172	+	0.0595840i
$960$		0			0
$961$	17.5683	−	30.4291i	0.566718	−	0.981585i
$962$	11.3249	−	19.6152i	0.365128	−	0.632421i
$963$		0			0
$964$	49.5330	−	28.5979i	1.59535	−	0.921076i
$965$	−6.81096	−	11.7969i	−0.219253	−	0.379757i
$966$		0			0
$967$	−17.0155	+	29.4717i	−0.547181	+	0.947746i	0.451285	+	0.892380i	$0.350966\pi$
$967$	−17.0155	+	29.4717i	−0.547181	+	0.947746i	−0.998466	+	0.0553658i	$0.982368\pi$
$968$		−	105.148i		−	3.37958i
$969$		0			0
$970$	−13.7188			−0.440483
$971$	−16.3472	−	28.3142i	−0.524608	−	0.908647i	−0.999589	−	0.0286515i	$-0.990879\pi$
$971$	−16.3472	−	28.3142i	−0.524608	−	0.908647i	0.474982	−	0.879996i	$-0.342455\pi$
$972$		0			0
$973$	25.0155	+	17.7647i	0.801960	+	0.569509i
$974$	−47.8081	+	27.6020i	−1.53187	+	0.884426i
$975$		0			0
$976$	−31.4647	+	18.1662i	−1.00716	+	0.581485i
$977$	−21.3583	+	12.3312i	−0.683313	+	0.394511i	−0.801102	−	0.598528i	$-0.795753\pi$
$977$	−21.3583	+	12.3312i	−0.683313	+	0.394511i	0.117789	+	0.993039i	$0.462419\pi$
$978$		0			0
$979$	−16.3221	+	9.42356i	−0.521656	+	0.301178i
$980$	11.9855	+	34.3416i	0.382861	+	1.09700i
$981$		0			0
$982$	−19.2473	−	33.3373i	−0.614206	−	1.06384i
$983$	−17.7915			−0.567461			−0.283730	−	0.958904i	$-0.591572\pi$
$983$	−17.7915			−0.567461			−0.283730	+	0.958904i	$0.591572\pi$
$984$		0			0
$985$		−	24.4987i		−	0.780594i
$986$	−2.73568	+	4.73833i	−0.0871217	+	0.150899i
$987$		0			0
$988$	34.6287	+	59.9787i	1.10169	+	1.90818i
$989$	0.0901258	−	0.0520341i	0.00286583	−	0.00165459i
$990$		0			0
$991$	15.9517	−	27.6292i	0.506722	−	0.877669i	−0.493247	−	0.869889i	$-0.664190\pi$
$991$	15.9517	−	27.6292i	0.506722	−	0.877669i	0.999970	−	0.00777992i	$-0.00247645\pi$
$992$	8.70420	−	15.0761i	0.276359	−	0.478667i
$993$		0			0
$994$	17.6725	−	24.8857i	0.560538	−	0.789327i
$995$	−9.26913	−	5.35153i	−0.293851	−	0.169655i
$996$		0			0
$997$			38.9553i			1.23373i	0.787070	+	0.616864i	$0.211597\pi$
$997$			38.9553i			1.23373i	−0.787070	+	0.616864i	$0.788403\pi$
$998$	−2.90140	−	1.67512i	−0.0918423	−	0.0530252i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.s.f.458.6		12
3.2	odd	2	inner	567.2.s.f.458.1		12
7.5	odd	6		567.2.i.f.215.1		12
9.2	odd	6		567.2.i.f.269.6		12
9.4	even	3		189.2.p.d.80.1	yes	12
9.5	odd	6		189.2.p.d.80.6	yes	12
9.7	even	3		567.2.i.f.269.1		12
21.5	even	6		567.2.i.f.215.6		12
63.4	even	3		1323.2.c.d.1322.2		12
63.5	even	6		189.2.p.d.26.1	✓	12
63.31	odd	6		1323.2.c.d.1322.1		12
63.32	odd	6		1323.2.c.d.1322.11		12
63.40	odd	6		189.2.p.d.26.6	yes	12
63.47	even	6	inner	567.2.s.f.26.6		12
63.59	even	6		1323.2.c.d.1322.12		12
63.61	odd	6	inner	567.2.s.f.26.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.1	✓	12	63.5	even	6
189.2.p.d.26.6	yes	12	63.40	odd	6
189.2.p.d.80.1	yes	12	9.4	even	3
189.2.p.d.80.6	yes	12	9.5	odd	6
567.2.i.f.215.1		12	7.5	odd	6
567.2.i.f.215.6		12	21.5	even	6
567.2.i.f.269.1		12	9.7	even	3
567.2.i.f.269.6		12	9.2	odd	6
567.2.s.f.26.1		12	63.61	odd	6	inner
567.2.s.f.26.6		12	63.47	even	6	inner
567.2.s.f.458.1		12	3.2	odd	2	inner
567.2.s.f.458.6		12	1.1	even	1	trivial
1323.2.c.d.1322.1		12	63.31	odd	6
1323.2.c.d.1322.2		12	63.4	even	3
1323.2.c.d.1322.11		12	63.32	odd	6
1323.2.c.d.1322.12		12	63.59	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.15715 + 1.24543i) q^{2} +(2.10220 + 3.64112i) q^{4} +1.23588 q^{5} +(2.63409 + 0.248083i) q^{7} +5.49086i q^{8} +O(q^{10})\)	\(q+(2.15715 + 1.24543i) q^{2} +(2.10220 + 3.64112i) q^{4} +1.23588 q^{5} +(2.63409 + 0.248083i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} -5.49086i q^{11} +(-2.57031 - 1.48397i) q^{13} +(5.37317 + 3.81574i) q^{14} +(-2.63409 + 4.56239i) q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} +(2.59808 + 4.50000i) q^{20} +(6.83850 - 11.8446i) q^{22} -1.63148i q^{23} -3.47259 q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +(0.440925 - 0.254568i) q^{29} +(-7.04290 + 4.06622i) q^{31} +(-1.85383 + 1.07031i) q^{32} +(-9.30660 + 5.37317i) q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} -13.8248 q^{38} +6.78607i q^{40} +(-0.177017 + 0.306602i) q^{41} +(0.0318939 + 0.0552418i) q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} +(4.93224 - 8.54290i) q^{47} +(6.87691 + 1.30695i) q^{49} +(-7.49090 - 4.32488i) q^{50} -12.4784i q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(-1.36219 + 14.4635i) q^{56} +1.26819 q^{58} +(1.53921 + 2.66599i) q^{59} +(5.97259 + 3.44828i) q^{61} -20.2568 q^{62} +5.20440 q^{64} +(-3.17660 - 1.83401i) q^{65} +(6.16599 + 10.6798i) q^{67} -18.1391 q^{68} +(6.64061 + 4.71581i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +7.63148i q^{74} +(-20.2089 - 11.6676i) q^{76} +(1.36219 - 14.4635i) q^{77} +(0.165989 - 0.287501i) q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +(-3.69636 - 6.40228i) q^{83} +(-2.66599 + 4.61763i) q^{85} +0.158887i q^{86} +30.1496 q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +(5.94040 - 3.42969i) q^{92} +(21.2792 - 12.2855i) q^{94} +(-5.94040 + 3.42969i) q^{95} +(-3.85939 + 2.22822i) q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 + 4 * q^7	\( 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) \) 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more