LMFDB - Embedded newform 567.2.i.f.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(215,567)]

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([5, 5]))

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

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

chi := DirichletCharacter("567.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.i (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:	$\Z[a_1, \ldots, a_{7}]$
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			269.1
Root			$0.617942 - 0.356769i$ of defining polynomial
Character	$\chi$	$=$	567.269
Dual form			567.2.i.f.215.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49086i q^{2} -4.20440 q^{4} +(-0.617942 + 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} +5.49086i q^{8} +O(q^{10})$	\(q-2.49086i q^{2} -4.20440 q^{4} +(-0.617942 + 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} +(-4.75523 + 2.74543i) q^{11} +(2.57031 - 1.48397i) q^{13} +(-5.99111 + 2.74543i) q^{14} +5.26819 q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} +(2.59808 - 4.50000i) q^{20} +(6.83850 + 11.8446i) q^{22} +(1.41290 + 0.815739i) q^{23} +(1.73630 + 3.00735i) q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +(-0.440925 - 0.254568i) q^{29} -8.13244i q^{31} -2.14061i q^{32} +(9.30660 + 5.37317i) q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} +(6.91238 + 11.9726i) q^{38} +(-5.87691 - 3.39304i) q^{40} +(-0.177017 - 0.306602i) q^{41} +(0.0318939 - 0.0552418i) q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} -9.86449 q^{47} +(-4.57031 + 5.30210i) q^{49} +(7.49090 - 4.32488i) q^{50} +(-10.8066 + 6.23919i) q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(13.2068 - 6.05203i) q^{56} +(-0.634095 + 1.09828i) q^{58} -3.07842 q^{59} -6.89655i q^{61} -20.2568 q^{62} +5.20440 q^{64} +3.66802i q^{65} -12.3320 q^{67} +(9.06953 - 15.7089i) q^{68} +(0.763705 - 8.10885i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +(6.60905 - 3.81574i) q^{74} +(20.2089 - 11.6676i) q^{76} +(11.8446 + 8.41142i) q^{77} -0.331977 q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +(-3.69636 + 6.40228i) q^{83} +(-2.66599 - 4.61763i) q^{85} +(-0.137600 - 0.0794433i) q^{86} +(-15.0748 - 26.1103i) q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +(-5.94040 - 3.42969i) q^{92} +24.5711i q^{94} -6.85939i q^{95} +(3.85939 + 2.22822i) q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q - 16 * q^4 + 4 * q^7	$ 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) $ 12 * q - 16 * q^4 + 4 * q^7 - 6 * q^10 + 24 * q^13 + 8 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 28 * q^28 + 60 * q^34 + 8 * q^37 - 12 * q^40 - 10 * q^43 + 14 * q^46 - 48 * q^49 - 78 * q^52 + 20 * q^58 + 28 * q^64 - 72 * q^67 + 54 * q^70 - 42 * q^73 + 108 * q^76 + 72 * q^79 - 54 * q^82 + 6 * q^85 - 74 * q^88 + 6 * q^91 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	2.49086i		−	1.76131i	−0.473761	−	0.880653i	$-0.657104\pi$
$2$		−	2.49086i		−	1.76131i	0.473761	−	0.880653i	$-0.342896\pi$
$3$		0			0
$3$		0			0
$4$	−4.20440			−2.10220
$5$	−0.617942	+	1.07031i	−0.276352	+	0.478656i	−0.970475	−	0.241200i	$-0.922459\pi$
$5$	−0.617942	+	1.07031i	−0.276352	+	0.478656i	0.694123	+	0.719856i	$0.255792\pi$
$6$		0			0
$7$	−1.10220	−	2.40523i	−0.416593	−	0.909093i
$7$	−1.10220	−	2.40523i	−0.416593	−	0.909093i
$8$			5.49086i			1.94131i
$9$		0			0
$10$	2.66599	+	1.53921i	0.843060	+	0.486741i
$11$	−4.75523	+	2.74543i	−1.43376	+	0.827779i	−0.997405	−	0.0719981i	$-0.977062\pi$
$11$	−4.75523	+	2.74543i	−1.43376	+	0.827779i	−0.436350	+	0.899777i	$0.643729\pi$
$12$		0			0
$13$	2.57031	−	1.48397i	0.712875	−	0.411578i	−0.0992497	−	0.995063i	$-0.531644\pi$
$13$	2.57031	−	1.48397i	0.712875	−	0.411578i	0.812125	+	0.583484i	$0.198311\pi$
$14$	−5.99111	+	2.74543i	−1.60119	+	0.733748i
$15$		0			0
$16$	5.26819			1.31705
$17$	−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
$23$	1.41290	+	0.815739i	0.294610	+	0.170093i	0.640019	−	0.768359i	$-0.278926\pi$
$23$	1.41290	+	0.815739i	0.294610	+	0.170093i	−0.345409	+	0.938452i	$0.612260\pi$
$24$		0			0
$25$	1.73630	+	3.00735i	0.347259	+	0.601470i
$26$	−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	$-0.348386\pi$
$29$	−0.440925	−	0.254568i	−0.0818777	−	0.0472721i	−0.540380	+	0.841421i	$0.681719\pi$
$30$		0			0
$31$		−	8.13244i		−	1.46063i	−0.683111	−	0.730314i	$-0.739374\pi$
$31$		−	8.13244i		−	1.46063i	0.683111	−	0.730314i	$-0.260626\pi$
$32$		−	2.14061i		−	0.378411i
$33$		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	$0.752297\pi$
$38$	6.91238	+	11.9726i	1.12134	+	1.94221i
$39$		0			0
$40$	−5.87691	−	3.39304i	−0.929221	−	0.536486i
$41$	−0.177017	−	0.306602i	−0.0276454	−	0.0478832i	0.851872	−	0.523751i	$-0.175468\pi$
$41$	−0.177017	−	0.306602i	−0.0276454	−	0.0478832i	−0.879517	+	0.475867i	$0.842134\pi$
$42$		0			0
$43$	0.0318939	−	0.0552418i	0.00486377	−	0.00842430i	−0.863583	−	0.504206i	$-0.831785\pi$
$43$	0.0318939	−	0.0552418i	0.00486377	−	0.00842430i	0.868447	+	0.495782i	$0.165118\pi$
$44$	19.9929	−	11.5429i	3.01404	−	1.74016i
$45$		0			0
$46$	2.03189	−	3.51934i	0.299586	−	0.518899i
$47$	−9.86449			−1.43888			−0.719442	−	0.694553i	$-0.755602\pi$
$47$	−9.86449			−1.43888			−0.719442	+	0.694553i	$0.755602\pi$
$48$		0			0
$49$	−4.57031	+	5.30210i	−0.652901	+	0.757443i
$50$	7.49090	−	4.32488i	1.05937	−	0.611630i
$51$		0			0
$52$	−10.8066	+	6.23919i	−1.49861	+	0.865221i
$53$	−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
$56$	13.2068	−	6.05203i	1.76483	−	0.808737i
$57$		0			0
$58$	−0.634095	+	1.09828i	−0.0832607	+	0.144212i
$59$	−3.07842			−0.400776			−0.200388	−	0.979717i	$-0.564220\pi$
$59$	−3.07842			−0.400776			−0.200388	+	0.979717i	$0.564220\pi$
$60$		0			0
$61$		−	6.89655i		−	0.883013i	−0.897258	−	0.441507i	$-0.854444\pi$
$61$		−	6.89655i		−	0.883013i	0.897258	−	0.441507i	$-0.145556\pi$
$62$	−20.2568			−2.57262
$63$		0			0
$64$	5.20440			0.650550
$65$			3.66802i			0.454962i
$66$		0			0
$67$	−12.3320			−1.50659			−0.753295	−	0.657682i	$-0.771537\pi$
$67$	−12.3320			−1.50659			−0.753295	+	0.657682i	$0.771537\pi$
$68$	9.06953	−	15.7089i	1.09984	−	1.90498i
$69$		0			0
$70$	0.763705	−	8.10885i	0.0912802	−	0.969192i
$71$		−	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	$0.801804\pi$
$74$	6.60905	−	3.81574i	0.768287	−	0.443571i
$75$		0			0
$76$	20.2089	−	11.6676i	2.31812	−	1.33837i
$77$	11.8446	+	8.41142i	1.34982	+	0.958570i
$78$		0			0
$79$	−0.331977			−0.0373503			−0.0186752	−	0.999826i	$-0.505945\pi$
$79$	−0.331977			−0.0373503			−0.0186752	+	0.999826i	$0.505945\pi$
$80$	−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	−0.994406	−	0.105626i	$-0.966315\pi$
$83$	−3.69636	+	6.40228i	−0.405728	+	0.702742i	0.588678	+	0.808368i	$0.299649\pi$
$84$		0			0
$85$	−2.66599	−	4.61763i	−0.289167	−	0.500852i
$86$	−0.137600	−	0.0794433i	−0.0148378	−	0.00856659i
$87$		0			0
$88$	−15.0748	−	26.1103i	−1.60698	−	2.78337i
$89$	−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
$94$			24.5711i			2.53432i
$95$		−	6.85939i		−	0.703758i
$96$		0			0
$97$	3.85939	+	2.22822i	0.391861	+	0.226241i	0.682966	−	0.730450i	$-0.260690\pi$
$97$	3.85939	+	2.22822i	0.391861	+	0.226241i	−0.291105	+	0.956691i	$0.594023\pi$
$98$	13.2068	+	11.3840i	1.33409	+	1.14996i
$99$		0			0
$100$	−7.30008	−	12.6441i	−0.730008	−	1.26441i
$101$	−4.57821	−	7.92969i	−0.455549	−	0.789034i	0.543171	−	0.839622i	$-0.317224\pi$
$101$	−4.57821	−	7.92969i	−0.455549	−	0.789034i	−0.998720	+	0.0505884i	$0.983890\pi$
$102$		0			0
$103$	3.64061	+	2.10191i	0.358720	+	0.207107i	0.668519	−	0.743695i	$-0.266928\pi$
$103$	3.64061	+	2.10191i	0.358720	+	0.207107i	−0.309799	+	0.950802i	$0.600262\pi$
$104$	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	$0.168611\pi$
$110$	−16.9032			−1.61165
$111$		0			0
$112$	−5.80660	−	12.6712i	−0.548672	−	1.19732i
$113$	−1.99143	+	1.14975i	−0.187338	+	0.108159i	−0.590736	−	0.806865i	$-0.701162\pi$
$113$	−1.99143	+	1.14975i	−0.187338	+	0.108159i	0.403398	+	0.915025i	$0.367829\pi$
$114$		0			0
$115$	−1.74618	+	1.00816i	−0.162832	+	0.0940113i
$116$	1.85383	+	1.07031i	0.172123	+	0.0993755i
$117$		0			0
$118$			7.66792i			0.705889i
$119$	11.3643	+	1.07031i	1.04176	+	0.0981149i
$120$		0			0
$121$	9.57479	−	16.5840i	0.870436	−	1.50764i
$122$	−17.1784			−1.55526
$123$		0			0
$124$			34.1920i			3.07054i
$125$	−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	$0.505463\pi$
$128$		−	17.2447i		−	1.52423i
$129$		0			0
$130$	9.13654			0.801328
$131$	−10.4317	+	18.0683i	−0.911424	+	1.57863i	−0.0993693	+	0.995051i	$0.531683\pi$
$131$	−10.4317	+	18.0683i	−0.911424	+	1.57863i	−0.812054	+	0.583582i	$0.801651\pi$
$132$		0			0
$133$	11.9726	+	8.50230i	1.03816	+	0.737243i
$134$			30.7173i			2.65357i
$135$		0			0
$136$	−20.5155	−	11.8446i	−1.75919	−	1.01567i
$137$	0.606650	−	0.350250i	0.0518296	−	0.0299239i	−0.473861	−	0.880600i	$-0.657140\pi$
$137$	0.606650	−	0.350250i	0.0518296	−	0.0299239i	0.525691	+	0.850676i	$0.323807\pi$
$138$		0			0
$139$	−10.0429	+	5.79827i	−0.851827	+	0.491803i	−0.861267	−	0.508153i	$-0.830329\pi$
$139$	−10.0429	+	5.79827i	−0.851827	+	0.491803i	0.00943957	+	0.999955i	$0.496995\pi$
$140$	−13.6872	−	1.28908i	−1.15678	−	0.108947i
$141$		0			0
$142$	−11.5364			−0.968111
$143$	−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
$149$	0.303325	+	0.175125i	0.0248494	+	0.0143468i	0.512373	−	0.858763i	$-0.328766\pi$
$149$	0.303325	+	0.175125i	0.0248494	+	0.0143468i	−0.487524	+	0.873110i	$0.662100\pi$
$150$		0			0
$151$	−2.32749	−	4.03133i	−0.189409	−	0.328065i	0.755645	−	0.654982i	$-0.227324\pi$
$151$	−2.32749	−	4.03133i	−0.189409	−	0.328065i	−0.945053	+	0.326916i	$0.893990\pi$
$152$	−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
$157$			1.23588i			0.0986343i	0.998783	+	0.0493171i	$0.0157045\pi$
$157$			1.23588i			0.0986343i	−0.998783	+	0.0493171i	$0.984295\pi$
$158$			0.826910i			0.0657854i
$159$		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	$0.554530\pi$
$164$	0.744250	+	1.28908i	0.0581162	+	0.100660i
$165$		0			0
$166$	15.9472	+	9.20713i	1.23774	+	0.714612i
$167$	−11.8446	−	20.5155i	−0.916564	−	1.58754i	−0.804595	−	0.593825i	$-0.797617\pi$
$167$	−11.8446	−	20.5155i	−0.916564	−	1.58754i	−0.111970	−	0.993712i	$-0.535716\pi$
$168$		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
$173$	11.9822			0.910992			0.455496	−	0.890238i	$-0.349462\pi$
$173$	11.9822			0.910992			0.455496	+	0.890238i	$0.349462\pi$
$174$		0			0
$175$	5.31964	−	7.49090i	0.402127	−	0.566259i
$176$	−25.0514	+	14.4635i	−1.88832	+	1.09022i
$177$		0			0
$178$	−7.40432	+	4.27489i	−0.554977	+	0.320416i
$179$	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	$0.892645\pi$
$182$	−11.3249	+	15.9472i	−0.839455	+	1.18209i
$183$		0			0
$184$	−4.47911	+	7.75805i	−0.330204	+	0.571931i
$185$	−3.78649			−0.278388
$186$		0			0
$187$		−	23.6892i		−	1.73233i
$188$	41.4743			3.02482
$189$		0			0
$190$	−17.0858			−1.23953
$191$		−	11.4909i		−	0.831450i	−0.909490	−	0.415725i	$-0.863528\pi$
$191$		−	11.4909i		−	0.831450i	0.909490	−	0.415725i	$-0.136472\pi$
$192$		0			0
$193$	11.0220			0.793381			0.396691	−	0.917952i	$-0.370159\pi$
$193$	11.0220			0.793381			0.396691	+	0.917952i	$0.370159\pi$
$194$	5.55019	−	9.61320i	0.398480	−	0.690188i
$195$		0			0
$196$	19.2154	−	22.2922i	1.37253	−	1.59230i
$197$		−	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	$0.765977\pi$
$200$	−16.5130	+	9.53376i	−1.16764	+	0.674139i
$201$		0			0
$202$	−19.7518	+	11.4037i	−1.38973	+	0.802361i
$203$	−0.126308	+	1.34111i	−0.00886510	+	0.0941277i
$204$		0			0
$205$	0.437545			0.0305595
$206$	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	−0.941366	−	0.337387i	$-0.890457\pi$
$211$	−11.0813	−	19.1934i	−0.762869	−	1.32133i	0.178497	−	0.983940i	$-0.442877\pi$
$212$	15.0099	+	8.66599i	1.03089	+	0.595183i
$213$		0			0
$214$	−12.8450	−	22.2482i	−0.878067	−	1.52086i
$215$	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
$220$			28.5314i			1.92358i
$221$			12.8046i			0.861328i
$222$		0			0
$223$	−16.2343	−	9.37285i	−1.08713	−	0.627653i	−0.154317	−	0.988021i	$-0.549318\pi$
$223$	−16.2343	−	9.37285i	−1.08713	−	0.627653i	−0.932810	+	0.360369i	$0.882651\pi$
$224$	−5.14868	+	2.35939i	−0.344011	+	0.157643i
$225$		0			0
$226$	2.86387	+	4.96037i	0.190502	+	0.329959i
$227$	7.08940	+	12.2792i	0.470540	+	0.814999i	0.999432	−	0.0336901i	$-0.0107259\pi$
$227$	7.08940	+	12.2792i	0.470540	+	0.814999i	−0.528893	+	0.848689i	$0.677393\pi$
$228$		0			0
$229$	3.52537	+	2.03538i	0.232963	+	0.134501i	0.611938	−	0.790905i	$-0.290390\pi$
$229$	3.52537	+	2.03538i	0.232963	+	0.134501i	−0.378975	+	0.925407i	$0.623723\pi$
$230$	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
$236$	12.9429			0.842511
$237$		0			0
$238$	2.66599	−	28.3069i	0.172810	−	1.83486i
$239$	22.9844	−	13.2701i	1.48674	−	0.858369i	0.486852	−	0.873484i	$-0.338145\pi$
$239$	22.9844	−	13.2701i	1.48674	−	0.858369i	0.999886	+	0.0151157i	$0.00481166\pi$
$240$		0			0
$241$	−11.7812	+	6.80189i	−0.758896	+	0.438149i	−0.828899	−	0.559398i	$-0.811032\pi$
$241$	−11.7812	+	6.80189i	−0.758896	+	0.438149i	0.0700035	+	0.997547i	$0.477699\pi$
$242$	−41.3085	−	23.8495i	−2.65541	−	1.53310i
$243$		0			0
$244$			28.9959i			1.85627i
$245$	−2.85069	−	8.16802i	−0.182124	−	0.521836i
$246$		0			0
$247$	−8.23630	+	14.2657i	−0.524063	+	0.907704i
$248$	44.6541			2.83554
$249$		0			0
$250$			26.0822i			1.64958i
$251$	−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
$254$			0.963454i			0.0604525i
$255$		0			0
$256$	−32.5453			−2.03408
$257$	9.03011	−	15.6406i	0.563283	−	0.975635i	−0.433924	−	0.900949i	$-0.642871\pi$
$257$	9.03011	−	15.6406i	0.563283	−	0.975635i	0.997207	−	0.0746853i	$-0.0237952\pi$
$258$		0			0
$259$	4.69340	−	6.60905i	0.291634	−	0.410667i
$260$		−	15.4218i		−	0.956422i
$261$		0			0
$262$	45.0056	+	25.9840i	2.78046	+	1.60530i
$263$	−6.98798	+	4.03451i	−0.430897	+	0.248779i	−0.699729	−	0.714409i	$-0.746696\pi$
$263$	−6.98798	+	4.03451i	−0.430897	+	0.248779i	0.268832	+	0.963187i	$0.413362\pi$
$264$		0			0
$265$	4.41217	−	2.54737i	0.271037	−	0.156484i
$266$	21.1781	−	29.8221i	1.29851	−	1.82851i
$267$		0			0
$268$	51.8486			3.16716
$269$	−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
$275$	−16.5130	−	9.53376i	−0.995769	−	0.574907i
$276$		0			0
$277$	10.8495	+	18.7919i	0.651883	+	1.12909i	0.982665	+	0.185388i	$0.0593541\pi$
$277$	10.8495	+	18.7919i	0.651883	+	1.12909i	−0.330782	+	0.943707i	$0.607313\pi$
$278$	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	$-0.0974595\pi$
$281$	19.5994	+	11.3157i	1.16920	+	0.675040i	0.215712	+	0.976457i	$0.430793\pi$
$282$		0			0
$283$			9.54210i			0.567219i	0.958940	+	0.283610i	$0.0915320\pi$
$283$			9.54210i			0.567219i	−0.958940	+	0.283610i	$0.908468\pi$
$284$			19.4726i			1.15549i
$285$		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
$290$	−0.783667	−	1.35735i	−0.0460185	−	0.0797064i
$291$		0			0
$292$	25.6287	+	14.7967i	1.49981	+	0.865913i
$293$	−13.1674	−	22.8066i	−0.769248	−	1.33238i	−0.937971	−	0.346713i	$-0.887298\pi$
$293$	−13.1674	−	22.8066i	−0.769248	−	1.33238i	0.168724	−	0.985663i	$-0.446035\pi$
$294$		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
$299$	4.84212			0.280027
$300$		0			0
$301$	−0.168023	−	0.0158247i	−0.00968468	−	0.000912120i
$302$	−10.0415	+	5.79747i	−0.577824	+	0.333607i
$303$		0			0
$304$	−25.3221	+	14.6197i	−1.45232	+	0.838498i
$305$	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	$-0.0623259\pi$
$308$	−49.7996	−	35.3650i	−2.83759	−	2.01511i
$309$		0			0
$310$	12.5175	−	21.6810i	0.710948	−	1.23140i
$311$	26.9414			1.52771			0.763855	−	0.645388i	$-0.223304\pi$
$311$	26.9414			1.52771			0.763855	+	0.645388i	$0.223304\pi$
$312$		0			0
$313$			23.1614i			1.30916i	0.755992	+	0.654581i	$0.227155\pi$
$313$			23.1614i			1.30916i	−0.755992	+	0.654581i	$0.772845\pi$
$314$	3.07842			0.173725
$315$		0			0
$316$	1.39576			0.0785179
$317$			25.0675i			1.40793i	0.710234	+	0.703966i	$0.248589\pi$
$317$			25.0675i			1.40793i	−0.710234	+	0.703966i	$0.751411\pi$
$318$		0			0
$319$	2.79560			0.156523
$320$	−3.21602	+	5.57031i	−0.179781	+	0.311390i
$321$		0			0
$322$	−10.7044	−	1.00816i	−0.596533	−	0.0561825i
$323$		−	23.9452i		−	1.33235i
$324$		0			0
$325$	8.92562	+	5.15321i	0.495105	+	0.285849i
$326$	42.3086	−	24.4269i	2.34326	−	1.35288i
$327$		0			0
$328$	1.68351	−	0.971976i	0.0929564	−	0.0536684i
$329$	10.8726	+	23.7264i	0.599428	+	1.30808i
$330$		0			0
$331$	−8.39576			−0.461473			−0.230736	−	0.973016i	$-0.574114\pi$
$331$	−8.39576			−0.461473			−0.230736	+	0.973016i	$0.574114\pi$
$332$	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	0.937271	+	0.348601i	$0.113343\pi$
$337$	14.1451	+	24.5000i	0.770533	+	1.33460i	−0.166739	+	0.986001i	$0.553324\pi$
$338$	9.04140	+	5.22006i	0.491788	+	0.283934i
$339$		0			0
$340$	11.2089	+	19.4144i	0.607887	+	1.05289i
$341$	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
$346$		−	29.8461i		−	1.60454i
$347$		−	9.96345i		−	0.534866i	−0.963576	−	0.267433i	$-0.913825\pi$
$347$		−	9.96345i		−	0.534866i	0.963576	−	0.267433i	$-0.0861754\pi$
$348$		0			0
$349$	19.4530	+	11.2312i	1.04130	+	0.601193i	0.920200	−	0.391448i	$-0.128026\pi$
$349$	19.4530	+	11.2312i	1.04130	+	0.601193i	0.121097	+	0.992641i	$0.461359\pi$
$350$	−18.6588	−	13.2505i	−0.997356	−	0.708269i
$351$		0			0
$352$	5.87691	+	10.1791i	0.313240	+	0.542548i
$353$	−16.0326	−	27.7693i	−0.853330	−	1.47801i	−0.878186	−	0.478320i	$-0.841246\pi$
$353$	−16.0326	−	27.7693i	−0.853330	−	1.47801i	0.0248555	−	0.999691i	$-0.492087\pi$
$354$		0			0
$355$	4.95710	+	2.86198i	0.263096	+	0.151898i
$356$	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
$362$	22.1782			1.16566
$363$		0			0
$364$	26.9178	+	19.1156i	1.41087	+	1.00193i
$365$	7.53356	−	4.34950i	0.394324	−	0.227663i
$366$		0			0
$367$	11.7538	−	6.78607i	0.613544	−	0.354230i	−0.160807	−	0.986986i	$-0.551410\pi$
$367$	11.7538	−	6.78607i	0.613544	−	0.354230i	0.774351	+	0.632756i	$0.218076\pi$
$368$	7.44343	+	4.29747i	0.388016	+	0.224021i
$369$		0			0
$370$			9.43162i			0.490327i
$371$	−1.02268	+	10.8586i	−0.0530951	+	0.563752i
$372$		0			0
$373$	−15.0858	+	26.1294i	−0.781113	+	1.35293i	0.150181	+	0.988659i	$0.452014\pi$
$373$	−15.0858	+	26.1294i	−0.781113	+	1.35293i	−0.931294	+	0.364269i	$0.881319\pi$
$374$	−59.0067			−3.05116
$375$		0			0
$376$		−	54.1646i		−	2.79332i
$377$	−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	$0.605562\pi$
$380$			28.8396i			1.47944i
$381$		0			0
$382$	−28.6222			−1.46444
$383$	−15.9932	+	27.7010i	−0.817214	+	1.41546i	0.0905126	+	0.995895i	$0.471149\pi$
$383$	−15.9932	+	27.7010i	−0.817214	+	1.41546i	−0.907727	+	0.419561i	$0.862184\pi$
$384$		0			0
$385$	−16.3221	+	7.47961i	−0.831851	+	0.381196i
$386$		−	27.4543i		−	1.39739i
$387$		0			0
$388$	−16.2264	−	9.36832i	−0.823771	−	0.475604i
$389$	−6.56158	+	3.78833i	−0.332685	+	0.192076i	−0.657033	−	0.753862i	$-0.728189\pi$
$389$	−6.56158	+	3.78833i	−0.332685	+	0.192076i	0.324347	+	0.945938i	$0.394855\pi$
$390$		0			0
$391$	−6.09568	+	3.51934i	−0.308272	+	0.177981i
$392$	−29.1131	−	25.0949i	−1.47043	−	1.26749i
$393$		0			0
$394$	−49.3760			−2.48753
$395$	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
$401$	−18.2147	−	10.5162i	−0.909597	−	0.525156i	−0.0292953	−	0.999571i	$-0.509326\pi$
$401$	−18.2147	−	10.5162i	−0.909597	−	0.525156i	−0.880301	+	0.474415i	$0.842660\pi$
$402$		0			0
$403$	−12.0683	−	20.9029i	−0.601163	−	1.04125i
$404$	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
$409$		−	20.1463i		−	0.996171i	−0.867128	−	0.498085i	$-0.834037\pi$
$409$		−	20.1463i		−	0.996171i	0.867128	−	0.498085i	$-0.165963\pi$
$410$		−	1.08986i		−	0.0538246i
$411$		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
$416$	−3.17660	−	5.50203i	−0.155746	−	0.269759i
$417$		0			0
$418$	−65.7399	−	37.9549i	−3.21544	−	1.85644i
$419$	−4.79464	−	8.30457i	−0.234234	−	0.405705i	0.724816	−	0.688943i	$-0.241925\pi$
$419$	−4.79464	−	8.30457i	−0.234234	−	0.405705i	−0.959050	+	0.283238i	$0.908591\pi$
$420$		0			0
$421$	−4.30660	+	7.45925i	−0.209891	+	0.363542i	−0.951680	−	0.307092i	$-0.900644\pi$
$421$	−4.30660	+	7.45925i	−0.209891	+	0.363542i	0.741789	+	0.670633i	$0.233978\pi$
$422$	−47.8081	+	27.6020i	−2.32726	+	1.34365i
$423$		0			0
$424$	11.3176	−	19.6027i	0.549632	−	0.951990i
$425$	−14.9818			−0.726724
$426$		0			0
$427$	−16.5878	+	7.60139i	−0.802741	+	0.367857i
$428$	−37.5534	+	21.6815i	−1.81521	+	1.04801i
$429$		0			0
$430$	0.170057	−	0.0981827i	0.00820090	−	0.00473479i
$431$	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	$-0.185200\pi$
$434$	22.3271	+	48.7223i	1.07173	+	2.33875i
$435$		0			0
$436$	0.268189	−	0.464517i	0.0128439	−	0.0222464i
$437$	−9.05500			−0.433160
$438$		0			0
$439$			0.252617i			0.0120567i	0.999982	+	0.00602837i	$0.00191890\pi$
$439$			0.252617i			0.0120567i	−0.999982	+	0.00602837i	$0.998081\pi$
$440$	37.2614			1.77637
$441$		0			0
$442$	31.8944			1.51706
$443$		−	21.7721i		−	1.03442i	−0.855858	−	0.517212i	$-0.826970\pi$
$443$		−	21.7721i		−	1.03442i	0.855858	−	0.517212i	$-0.173030\pi$
$444$		0			0
$445$	4.24211			0.201095
$446$	−23.3465	+	40.4373i	−1.10549	+	1.91476i
$447$		0			0
$448$	−5.73630	−	12.5178i	−0.271014	−	0.591411i
$449$			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
$452$	8.37275	−	4.83401i	0.393821	−	0.227373i
$453$		0			0
$454$	30.5858	−	17.6587i	1.43546	−	0.828765i
$455$	8.82246	−	4.04290i	0.413603	−	0.189534i
$456$		0			0
$457$	35.0220			1.63826			0.819130	−	0.573608i	$-0.194457\pi$
$457$	35.0220			1.63826			0.819130	+	0.573608i	$0.194457\pi$
$458$	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	0.171800	+	0.985132i	$0.445042\pi$
$461$	−16.4735	+	28.5330i	−0.767249	+	1.32891i	−0.939049	+	0.343783i	$0.888292\pi$
$462$		0			0
$463$	2.61320	+	4.52620i	0.121446	+	0.210351i	0.920338	−	0.391124i	$-0.127914\pi$
$463$	2.61320	+	4.52620i	0.121446	+	0.210351i	−0.798892	+	0.601474i	$0.794580\pi$
$464$	−2.32288	−	1.34111i	−0.107837	−	0.0622596i
$465$		0			0
$466$	8.67251	+	15.0212i	0.401746	+	0.695845i
$467$	−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
$472$		−	16.9032i		−	0.778032i
$473$			0.350250i			0.0161045i
$474$		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
$479$	−11.2154	−	19.4256i	−0.512444	−	0.887579i	−0.999896	−	0.0144295i	$-0.995407\pi$
$479$	−11.2154	−	19.4256i	−0.512444	−	0.887579i	0.487452	−	0.873150i	$-0.337927\pi$
$480$		0			0
$481$	7.87487	+	4.54656i	0.359063	+	0.207305i
$482$	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	$0.999212\pi$
$488$	37.8680			1.71421
$489$		0			0
$490$	−20.3454	+	7.10069i	−0.919113	+	0.320776i
$491$	13.3838	−	7.72716i	0.604004	−	0.348722i	−0.166611	−	0.986023i	$-0.553282\pi$
$491$	13.3838	−	7.72716i	0.604004	−	0.348722i	0.770615	+	0.637301i	$0.219949\pi$
$492$		0			0
$493$	1.90228	−	1.09828i	0.0856746	−	0.0494642i
$494$	35.5339	+	20.5155i	1.59874	+	0.923035i
$495$		0			0
$496$		−	42.8432i		−	1.92372i
$497$	−11.1398	+	5.10482i	−0.499688	+	0.228982i
$498$		0			0
$499$	0.672508	−	1.16482i	0.0301056	−	0.0521444i	−0.850580	−	0.525846i	$-0.823749\pi$
$499$	0.672508	−	1.16482i	0.0301056	−	0.0521444i	0.880686	+	0.473701i	$0.157082\pi$
$500$	44.0249			1.96885
$501$		0			0
$502$			6.35320i			0.283557i
$503$	−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
$506$			22.3137i			0.991965i
$507$		0			0
$508$	1.62624			0.0721529
$509$	−14.0919	+	24.4079i	−0.624612	+	1.08186i	0.364003	+	0.931398i	$0.381410\pi$
$509$	−14.0919	+	24.4079i	−0.624612	+	1.08186i	−0.988616	+	0.150463i	$0.951924\pi$
$510$		0			0
$511$	−1.74618	+	18.5406i	−0.0772465	+	0.820186i
$512$			46.5767i			2.05842i
$513$		0			0
$514$	−38.9586	−	22.4928i	−1.71839	−	0.992114i
$515$	−4.49938	+	2.59772i	−0.198266	+	0.114469i
$516$		0			0
$517$	46.9079	−	27.0823i	2.06301	−	1.19108i
$518$	−16.4623	−	11.6906i	−0.723310	−	0.513656i
$519$		0			0
$520$	−20.1406			−0.883224
$521$	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
$527$	30.3852	+	17.5429i	1.32360	+	0.764181i
$528$		0			0
$529$	−10.1691	−	17.6135i	−0.442137	−	0.765803i
$530$	−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
$535$			12.7465i			0.551081i
$536$		−	67.7132i		−	2.92476i
$537$		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	$0.524027\pi$
$542$	−30.6410	−	53.0718i	−1.31615	−	2.27963i
$543$		0			0
$544$	7.99797	+	4.61763i	0.342910	+	0.197979i
$545$	−0.0788343	−	0.136545i	−0.00337689	−	0.00584894i
$546$		0			0
$547$	−5.99797	+	10.3888i	−0.256454	+	0.444192i	−0.965290	−	0.261182i	$-0.915888\pi$
$547$	−5.99797	+	10.3888i	−0.256454	+	0.444192i	0.708835	+	0.705374i	$0.249221\pi$
$548$	−2.55060	+	1.47259i	−0.108956	+	0.0629060i
$549$		0			0
$550$	−23.7473	+	41.1315i	−1.01259	+	1.75385i
$551$	2.82580			0.120383
$552$		0			0
$553$	0.365905	+	0.798483i	0.0155599	+	0.0339549i
$554$	46.8080	−	27.0246i	1.98868	−	1.14817i
$555$		0			0
$556$	42.2244	−	24.3783i	1.79071	−	1.03387i
$557$	−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
$560$	17.1502	+	1.61524i	0.724730	+	0.0682563i
$561$		0			0
$562$	28.1860	−	48.8195i	1.18895	−	2.05933i
$563$	−23.4366			−0.987736			−0.493868	−	0.869537i	$-0.664417\pi$
$563$	−23.4366			−0.987736			−0.493868	+	0.869537i	$0.664417\pi$
$564$		0			0
$565$		−	2.84192i		−	0.119560i
$566$	23.7681			0.999047
$567$		0			0
$568$	25.4308			1.06705
$569$			34.3137i			1.43851i	0.694749	+	0.719253i	$0.255516\pi$
$569$			34.3137i			1.43851i	−0.694749	+	0.719253i	$0.744484\pi$
$570$		0			0
$571$	21.4726			0.898600			0.449300	−	0.893381i	$-0.351673\pi$
$571$	21.4726			0.898600			0.449300	+	0.893381i	$0.351673\pi$
$572$	34.2586	−	59.3376i	1.43242	−	2.48103i
$573$		0			0
$574$	1.90228	+	1.35090i	0.0793998	+	0.0563855i
$575$			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	$0.869799\pi$
$578$	−3.47993	+	2.00914i	−0.144746	+	0.0835691i
$579$		0			0
$580$	−2.29111	+	1.32278i	−0.0951333	+	0.0549252i
$581$	19.4731	+	1.83401i	0.807881	+	0.0760876i
$582$		0			0
$583$	22.6352			0.937455
$584$	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	−0.991364	−	0.131139i	$-0.958136\pi$
$587$	−9.25784	+	16.0350i	−0.382112	+	0.661837i	0.609252	+	0.792977i	$0.291470\pi$
$588$		0			0
$589$	22.5683	+	39.0894i	0.929909	+	1.61065i
$590$	−8.20703	−	4.73833i	−0.337878	−	0.195074i
$591$		0			0
$592$	8.07031	+	13.9782i	0.331688	+	0.574500i
$593$	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
$598$		−	12.0611i		−	0.493213i
$599$			25.8721i			1.05710i	0.848901	+	0.528552i	$0.177265\pi$
$599$			25.8721i			1.05710i	−0.848901	+	0.528552i	$0.822735\pi$
$600$		0			0
$601$	−12.6211	−	7.28677i	−0.514824	−	0.297234i	0.219991	−	0.975502i	$-0.429397\pi$
$601$	−12.6211	−	7.28677i	−0.514824	−	0.297234i	−0.734814	+	0.678268i	$0.762731\pi$
$602$	−0.0394171	+	0.418522i	−0.00160652	+	0.0170577i
$603$		0			0
$604$	9.78571	+	16.9494i	0.398175	+	0.689659i
$605$	11.8333	+	20.4959i	0.481093	+	0.833278i
$606$		0			0
$607$	−19.2947	−	11.1398i	−0.783147	−	0.452150i	0.0543974	−	0.998519i	$-0.482676\pi$
$607$	−19.2947	−	11.1398i	−0.783147	−	0.452150i	−0.837544	+	0.546369i	$0.816010\pi$
$608$	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	$0.996549\pi$
$614$	−16.9820			−0.685338
$615$		0			0
$616$	−46.1860	+	65.0372i	−1.86089	+	2.62042i
$617$	1.76370	−	1.01827i	0.0710039	−	0.0409941i	−0.464078	−	0.885794i	$-0.653614\pi$
$617$	1.76370	−	1.01827i	0.0710039	−	0.0409941i	0.535082	+	0.844800i	$0.320281\pi$
$618$		0			0
$619$	−32.9099	+	19.0006i	−1.32276	+	0.763697i	−0.984168	−	0.177236i	$-0.943284\pi$
$619$	−32.9099	+	19.0006i	−1.32276	+	0.763697i	−0.338593	+	0.940933i	$0.609951\pi$
$620$	−36.5960	−	21.1287i	−1.46973	−	0.848549i
$621$		0			0
$622$		−	67.1075i		−	2.69076i
$623$	−5.25815	+	7.40432i	−0.210663	+	0.296648i
$624$		0			0
$625$	−2.21092	+	3.82943i	−0.0884368	+	0.153177i
$626$	57.6920			2.30583
$627$		0			0
$628$		−	5.19615i		−	0.207349i
$629$	−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	$0.482221\pi$
$632$		−	1.82284i		−	0.0725087i
$633$		0			0
$634$	62.4398			2.47980
$635$	0.239017	−	0.413990i	0.00948510	−	0.0164287i
$636$		0			0
$637$	−3.87894	+	20.4102i	−0.153689	+	0.808682i
$638$		−	6.96345i		−	0.275686i
$639$		0			0
$640$	18.4571	+	10.6562i	0.729581	+	0.421224i
$641$	−1.62610	+	0.938829i	−0.0642271	+	0.0370815i	−0.531770	−	0.846889i	$-0.678473\pi$
$641$	−1.62610	+	0.938829i	−0.0642271	+	0.0370815i	0.467543	+	0.883971i	$0.345139\pi$
$642$		0			0
$643$	−12.6211	+	7.28677i	−0.497726	+	0.287362i	−0.727774	−	0.685817i	$-0.759445\pi$
$643$	−12.6211	+	7.28677i	−0.497726	+	0.287362i	0.230048	+	0.973179i	$0.426112\pi$
$644$	−1.70170	+	18.0683i	−0.0670564	+	0.711990i
$645$		0			0
$646$	−59.6442			−2.34667
$647$	−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
$653$	−13.0524	−	7.53580i	−0.510779	−	0.294898i	0.222375	−	0.974961i	$-0.428619\pi$
$653$	−13.0524	−	7.53580i	−0.510779	−	0.294898i	−0.733154	+	0.680063i	$0.761952\pi$
$654$		0			0
$655$	−12.8924	−	22.3303i	−0.503748	−	0.872517i
$656$	−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	$-0.123340\pi$
$659$	27.2512	+	15.7335i	1.06156	+	0.612891i	0.135695	+	0.990751i	$0.456673\pi$
$660$		0			0
$661$			13.7524i			0.534906i	0.963571	+	0.267453i	$0.0861820\pi$
$661$			13.7524i			0.534906i	−0.963571	+	0.267453i	$0.913818\pi$
$662$			20.9127i			0.812795i
$663$		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
$668$	49.7996	+	86.2554i	1.92680	+	3.33732i
$669$		0			0
$670$	−32.8769	−	18.9815i	−1.27015	−	0.733319i
$671$	18.9340	+	32.7947i	0.730940	+	1.26602i
$672$		0			0
$673$	−5.87242	+	10.1713i	−0.226365	+	0.392076i	−0.956728	−	0.290983i	$-0.906018\pi$
$673$	−5.87242	+	10.1713i	−0.226365	+	0.392076i	0.730363	+	0.683059i	$0.239351\pi$
$674$	61.0262	−	35.2335i	2.35064	−	1.35714i
$675$		0			0
$676$	8.81109	−	15.2613i	0.338888	−	0.586971i
$677$	−21.7453			−0.835740			−0.417870	−	0.908507i	$-0.637223\pi$
$677$	−21.7453			−0.835740			−0.417870	+	0.908507i	$0.637223\pi$
$678$		0			0
$679$	1.10557	−	11.7387i	0.0424278	−	0.450489i
$680$	25.3548	−	14.6386i	0.972311	−	0.561364i
$681$		0			0
$682$	96.3257	−	55.6136i	3.68850	−	2.12956i
$683$	−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
$686$	12.8247	−	44.3130i	0.489648	−	1.69188i
$687$		0			0
$688$	0.168023	−	0.291024i	0.00640582	−	0.0110952i
$689$	−12.2348			−0.466110
$690$		0			0
$691$		−	10.3381i		−	0.393279i	−0.980476	−	0.196639i	$-0.936997\pi$
$691$		−	10.3381i		−	0.393279i	0.980476	−	0.196639i	$-0.0630028\pi$
$692$	−50.3781			−1.91509
$693$		0			0
$694$	−24.8176			−0.942063
$695$		−	14.3320i		−	0.543643i
$696$		0			0
$697$	1.52741			0.0578547
$698$	27.9754	−	48.4549i	1.05889	−	1.83404i
$699$		0			0
$700$	−22.3659	+	31.4948i	−0.845352	+	1.19039i
$701$		−	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
$704$	−24.7481	+	14.2883i	−0.932730	+	0.538512i
$705$		0			0
$706$	−69.1696	+	39.9351i	−2.60323	+	1.50298i
$707$	−14.0267	+	19.7518i	−0.527527	+	0.742842i
$708$		0			0
$709$	28.6002			1.07410			0.537051	−	0.843550i	$-0.319538\pi$
$709$	28.6002			1.07410			0.537051	+	0.843550i	$0.319538\pi$
$710$	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
$716$	−81.5075	−	47.0584i	−3.04608	−	1.75865i
$717$		0			0
$718$	14.7877	+	25.6131i	0.551874	+	0.955873i
$719$	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
$724$		−	37.4352i		−	1.39127i
$725$		−	1.76802i		−	0.0656627i
$726$		0			0
$727$	−17.3515	−	10.0179i	−0.643533	−	0.371544i	0.142441	−	0.989803i	$-0.454505\pi$
$727$	−17.3515	−	10.0179i	−0.643533	−	0.371544i	−0.785974	+	0.618259i	$0.787838\pi$
$728$	24.9645	−	35.1541i	0.925248	−	1.30290i
$729$		0			0
$730$	−10.8340	−	18.7651i	−0.400985	−	0.694526i
$731$	0.137600	+	0.238330i	0.00508931	+	0.00881495i
$732$		0			0
$733$	−13.3574	−	7.71187i	−0.493365	−	0.284844i	0.232604	−	0.972571i	$-0.425275\pi$
$733$	−13.3574	−	7.71187i	−0.493365	−	0.284844i	−0.725969	+	0.687727i	$0.758609\pi$
$734$	−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	$-0.0369634\pi$
$740$	15.9199			0.585227
$741$		0			0
$742$	27.0474	+	2.54737i	0.992941	+	0.0935168i
$743$	−6.51411	+	3.76092i	−0.238979	+	0.137975i	−0.614708	−	0.788755i	$-0.710726\pi$
$743$	−6.51411	+	3.76092i	−0.238979	+	0.137975i	0.375728	+	0.926730i	$0.377393\pi$
$744$		0			0
$745$	−0.374875	+	0.216434i	−0.0137343	+	0.00792953i
$746$	65.0847	+	37.5767i	2.38292	+	1.37578i
$747$		0			0
$748$			99.5991i			3.64170i
$749$	−22.2482	−	15.7995i	−0.812932	−	0.577301i
$750$		0			0
$751$	−12.9232	+	22.3836i	−0.471573	+	0.816789i	−0.999471	−	0.0325190i	$-0.989647\pi$
$751$	−12.9232	+	22.3836i	−0.471573	+	0.816789i	0.527898	+	0.849308i	$0.322980\pi$
$752$	−51.9680			−1.89508
$753$		0			0
$754$			3.76390i			0.137073i
$755$	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	$0.291580\pi$
$758$			31.5767i			1.14692i
$759$		0			0
$760$	37.6640			1.36622
$761$	4.36501	−	7.56042i	0.158232	−	0.274065i	−0.775999	−	0.630734i	$-0.782754\pi$
$761$	4.36501	−	7.56042i	0.158232	−	0.274065i	0.934231	+	0.356668i	$0.116087\pi$
$762$		0			0
$763$	0.336046	+	0.0316494i	0.0121657	+	0.00114578i
$764$			48.3122i			1.74787i
$765$		0			0
$766$	68.9995	+	39.8369i	2.49305	+	1.43936i
$767$	−7.91248	+	4.56827i	−0.285703	+	0.164951i
$768$		0			0
$769$	−4.36906	+	2.52248i	−0.157552	+	0.0909628i	−0.576703	−	0.816954i	$-0.695661\pi$
$769$	−4.36906	+	2.52248i	−0.157552	+	0.0909628i	0.419151	+	0.907917i	$0.362328\pi$
$770$	18.6307	+	40.6561i	0.671404	+	1.46514i
$771$		0			0
$772$	−46.3409			−1.66785
$773$	−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
$779$	1.70170	+	0.982477i	0.0609697	+	0.0352009i
$780$		0			0
$781$	12.7154	+	22.0237i	0.454993	+	0.788071i
$782$	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
$787$			24.7042i			0.880608i	0.897849	+	0.440304i	$0.145129\pi$
$787$			24.7042i			0.880608i	−0.897849	+	0.440304i	$0.854871\pi$
$788$			83.3432i			2.96898i
$789$		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
$794$	1.18518	+	2.05278i	0.0420603	+	0.0728506i
$795$		0			0
$796$	31.5330	+	18.2056i	1.11766	+	0.645280i
$797$	−2.19657	−	3.80457i	−0.0778064	−	0.134765i	0.824497	−	0.565867i	$-0.191458\pi$
$797$	−2.19657	−	3.80457i	−0.0778064	−	0.134765i	−0.902303	+	0.431102i	$0.858125\pi$
$798$		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
$803$	38.6485			1.36387
$804$		0			0
$805$	4.34950	+	3.08878i	0.153300	+	0.108865i
$806$	−52.0662	+	30.0604i	−1.83395	+	1.05883i
$807$		0			0
$808$	43.5409	−	25.1383i	1.53176	−	0.884363i
$809$	−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	$0.811359\pi$
$812$	0.531051	−	5.63858i	0.0186362	−	0.197875i
$813$		0			0
$814$	−20.9517	+	36.2894i	−0.734357	+	1.27194i
$815$	−24.2396			−0.849078
$816$		0			0
$817$			0.354034i			0.0123861i
$818$	−50.1817			−1.75456
$819$		0			0
$820$	−1.83961			−0.0642421
$821$		−	25.9437i		−	0.905441i	−0.891653	−	0.452720i	$-0.850454\pi$
$821$		−	25.9437i		−	0.905441i	0.891653	−	0.452720i	$-0.149546\pi$
$822$		0			0
$823$	−0.140614			−0.00490149			−0.00245074	−	0.999997i	$-0.500780\pi$
$823$	−0.140614			−0.00490149			−0.00245074	+	0.999997i	$0.500780\pi$
$824$	−11.5413	+	19.9901i	−0.402060	+	0.696389i
$825$		0			0
$826$	18.4431	−	8.45159i	0.641719	−	0.294068i
$827$			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	$0.863103\pi$
$830$	−19.7089	+	11.3789i	−0.684106	+	0.394969i
$831$		0			0
$832$	13.3769	−	7.72316i	0.463761	−	0.267752i
$833$	−9.95138	−	28.5135i	−0.344795	−	0.987933i
$834$		0			0
$835$	29.2772			1.01318
$836$	−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	−0.619045	−	0.785355i	$-0.712480\pi$
$839$	10.7350	−	18.5936i	0.370615	−	0.641924i	0.989660	+	0.143431i	$0.0458136\pi$
$840$		0			0
$841$	−14.3704	−	24.8902i	−0.495531	−	0.858284i
$842$	18.5800	+	10.7272i	0.640309	+	0.369682i
$843$		0			0
$844$	46.5903	+	80.6967i	1.60370	+	2.77770i
$845$	−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
$850$			37.3176i			1.27998i
$851$			4.99850i			0.171346i
$852$		0			0
$853$	21.8102	+	12.5921i	0.746766	+	0.431146i	0.824524	−	0.565827i	$-0.191443\pi$
$853$	21.8102	+	12.5921i	0.746766	+	0.431146i	−0.0777582	+	0.996972i	$0.524776\pi$
$854$	18.9340	+	41.3180i	0.647909	+	1.41387i
$855$		0			0
$856$	28.3156	+	49.0440i	0.967806	+	1.67629i
$857$	14.5183	+	25.1464i	0.495936	+	0.858986i	0.999989	−	0.00468678i	$-0.00149185\pi$
$857$	14.5183	+	25.1464i	0.495936	+	0.858986i	−0.504053	+	0.863673i	$0.668159\pi$
$858$		0			0
$859$	20.6386	+	11.9157i	0.704179	+	0.406558i	0.808902	−	0.587943i	$-0.200062\pi$
$859$	20.6386	+	11.9157i	0.704179	+	0.406558i	−0.104723	+	0.994501i	$0.533396\pi$
$860$	−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
$866$	−56.9678			−1.93584
$867$		0			0
$868$	82.2399	−	37.6865i	2.79140	−	1.27916i
$869$	1.57863	−	0.911420i	0.0535512	−	0.0309178i
$870$		0			0
$871$	−31.6970	+	18.3003i	−1.07401	+	0.620080i
$872$	−0.606650	−	0.350250i	−0.0205438	−	0.0118610i
$873$		0			0
$874$			22.5548i			0.762927i
$875$	11.5413	+	25.1855i	0.390167	+	0.851427i
$876$		0			0
$877$	1.14061	−	1.97560i	0.0385158	−	0.0667113i	−0.846125	−	0.532985i	$-0.821070\pi$
$877$	1.14061	−	1.97560i	0.0385158	−	0.0667113i	0.884641	+	0.466273i	$0.154404\pi$
$878$	0.629233			0.0212356
$879$		0			0
$880$		−	35.7503i		−	1.20514i
$881$	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	$0.815385\pi$
$884$		−	53.8355i		−	1.81069i
$885$		0			0
$886$	−54.2313			−1.82194
$887$	−6.17942	+	10.7031i	−0.207485	+	0.359374i	−0.950922	−	0.309432i	$-0.899861\pi$
$887$	−6.17942	+	10.7031i	−0.207485	+	0.359374i	0.743437	+	0.668806i	$0.233194\pi$
$888$		0			0
$889$	0.426326	+	0.930334i	0.0142985	+	0.0312024i
$890$		−	10.5665i		−	0.354191i
$891$		0			0
$892$	68.2554	+	39.4072i	2.28536	+	1.31945i
$893$	47.4147	−	27.3749i	1.58667	−	0.916065i
$894$		0			0
$895$	−23.9591	+	13.8328i	−0.800866	+	0.462380i
$896$	−41.4775	+	19.0071i	−1.38567	+	0.634983i
$897$		0			0
$898$	26.8773			0.896908
$899$	−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
$905$	−9.52980	−	5.50203i	−0.316781	−	0.182894i
$906$		0			0
$907$	17.8814	+	30.9715i	0.593742	+	1.02839i	0.993723	+	0.111868i	$0.0356833\pi$
$907$	17.8814	+	30.9715i	0.593742	+	1.02839i	−0.399981	+	0.916523i	$0.630983\pi$
$908$	−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	$-0.625274\pi$
$911$	−41.5024	−	23.9614i	−1.37504	−	0.793877i	−0.991557	+	0.129672i	$0.958607\pi$
$912$		0			0
$913$		−	40.5924i		−	1.34341i
$914$		−	87.2350i		−	2.88548i
$915$		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	$0.640772\pi$
$920$	−5.53566	−	9.58804i	−0.182505	−	0.316108i
$921$		0			0
$922$	71.0718	+	41.0333i	2.34063	+	1.35136i
$923$	−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
$929$	−58.3549			−1.91456			−0.957280	−	0.289161i	$-0.906624\pi$
$929$	−58.3549			−1.91456			−0.957280	+	0.289161i	$0.906624\pi$
$930$		0			0
$931$	7.25382	−	38.1681i	0.237734	−	1.25091i
$932$	25.3548	−	14.6386i	0.830523	−	0.479503i
$933$		0			0
$934$	−46.7378	+	26.9841i	−1.52931	+	0.882947i
$935$	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	$-0.162177\pi$
$938$	73.8822	−	33.8566i	2.41234	−	1.10546i
$939$		0			0
$940$	−25.6287	+	44.3902i	−0.835916	+	1.44785i
$941$	16.2177			0.528682			0.264341	−	0.964429i	$-0.414846\pi$
$941$	16.2177			0.528682			0.264341	+	0.964429i	$0.414846\pi$
$942$		0			0
$943$		−	0.577598i		−	0.0188092i
$944$	−16.2177			−0.527841
$945$		0			0
$946$	0.872425			0.0283650
$947$		−	28.1939i		−	0.916180i	−0.888906	−	0.458090i	$-0.848534\pi$
$947$		−	28.1939i		−	0.916180i	0.888906	−	0.458090i	$-0.151466\pi$
$948$		0			0
$949$	−20.8904			−0.678130
$950$	−24.0039	+	41.5759i	−0.778788	+	1.34890i
$951$		0			0
$952$	−5.87691	+	62.3997i	−0.190472	+	2.02239i
$953$			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
$956$	−96.6357	+	55.7926i	−3.12542	+	1.80446i
$957$		0			0
$958$	−48.3866	+	27.9360i	−1.56330	+	0.902571i
$959$	−1.51108	−	1.07309i	−0.0487954	−	0.0346519i
$960$		0			0
$961$	−35.1365			−1.13344
$962$	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	−0.998466	−	0.0553658i	$-0.982368\pi$
$967$	−17.0155	−	29.4717i	−0.547181	−	0.947746i	0.451285	−	0.892380i	$-0.350966\pi$
$968$	91.0606	+	52.5739i	2.92680	+	1.68979i
$969$		0			0
$970$	6.85939	+	11.8808i	0.220242	+	0.381470i
$971$	−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
$976$		−	36.3324i		−	1.16297i
$977$		−	24.6625i		−	0.789022i	−0.918891	−	0.394511i	$-0.870914\pi$
$977$		−	24.6625i		−	0.789022i	0.918891	−	0.394511i	$-0.129086\pi$
$978$		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
$983$	8.89575	+	15.4079i	0.283730	+	0.491435i	0.972300	−	0.233734i	$-0.0750946\pi$
$983$	8.89575	+	15.4079i	0.283730	+	0.491435i	−0.688570	+	0.725170i	$0.741761\pi$
$984$		0			0
$985$	21.2165	+	12.2494i	0.676015	+	0.390297i
$986$	−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	$-0.00247645\pi$
$992$	−17.4084			−0.552718
$993$		0			0
$994$	12.7154	+	27.7477i	0.403308	+	0.880104i
$995$	9.26913	−	5.35153i	0.293851	−	0.169655i
$996$		0			0
$997$	33.7363	−	19.4777i	1.06844	−	0.616864i	0.140685	−	0.990054i	$-0.455070\pi$
$997$	33.7363	−	19.4777i	1.06844	−	0.616864i	0.927755	+	0.373191i	$0.121736\pi$
$998$	−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.i.f.269.1		12
3.2	odd	2	inner	567.2.i.f.269.6		12
7.5	odd	6		567.2.s.f.26.1		12
9.2	odd	6		189.2.p.d.80.6	yes	12
9.4	even	3		567.2.s.f.458.6		12
9.5	odd	6		567.2.s.f.458.1		12
9.7	even	3		189.2.p.d.80.1	yes	12
21.5	even	6		567.2.s.f.26.6		12
63.5	even	6	inner	567.2.i.f.215.6		12
63.11	odd	6		1323.2.c.d.1322.11		12
63.25	even	3		1323.2.c.d.1322.2		12
63.38	even	6		1323.2.c.d.1322.12		12
63.40	odd	6	inner	567.2.i.f.215.1		12
63.47	even	6		189.2.p.d.26.1	✓	12
63.52	odd	6		1323.2.c.d.1322.1		12
63.61	odd	6		189.2.p.d.26.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.1	✓	12	63.47	even	6
189.2.p.d.26.6	yes	12	63.61	odd	6
189.2.p.d.80.1	yes	12	9.7	even	3
189.2.p.d.80.6	yes	12	9.2	odd	6
567.2.i.f.215.1		12	63.40	odd	6	inner
567.2.i.f.215.6		12	63.5	even	6	inner
567.2.i.f.269.1		12	1.1	even	1	trivial
567.2.i.f.269.6		12	3.2	odd	2	inner
567.2.s.f.26.1		12	7.5	odd	6
567.2.s.f.26.6		12	21.5	even	6
567.2.s.f.458.1		12	9.5	odd	6
567.2.s.f.458.6		12	9.4	even	3
1323.2.c.d.1322.1		12	63.52	odd	6
1323.2.c.d.1322.2		12	63.25	even	3
1323.2.c.d.1322.11		12	63.11	odd	6
1323.2.c.d.1322.12		12	63.38	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.49086i q^{2} -4.20440 q^{4} +(-0.617942 + 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} +5.49086i q^{8} +O(q^{10})\)	\(q-2.49086i q^{2} -4.20440 q^{4} +(-0.617942 + 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} +(-4.75523 + 2.74543i) q^{11} +(2.57031 - 1.48397i) q^{13} +(-5.99111 + 2.74543i) q^{14} +5.26819 q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} +(2.59808 - 4.50000i) q^{20} +(6.83850 + 11.8446i) q^{22} +(1.41290 + 0.815739i) q^{23} +(1.73630 + 3.00735i) q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +(-0.440925 - 0.254568i) q^{29} -8.13244i q^{31} -2.14061i q^{32} +(9.30660 + 5.37317i) q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} +(6.91238 + 11.9726i) q^{38} +(-5.87691 - 3.39304i) q^{40} +(-0.177017 - 0.306602i) q^{41} +(0.0318939 - 0.0552418i) q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} -9.86449 q^{47} +(-4.57031 + 5.30210i) q^{49} +(7.49090 - 4.32488i) q^{50} +(-10.8066 + 6.23919i) q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(13.2068 - 6.05203i) q^{56} +(-0.634095 + 1.09828i) q^{58} -3.07842 q^{59} -6.89655i q^{61} -20.2568 q^{62} +5.20440 q^{64} +3.66802i q^{65} -12.3320 q^{67} +(9.06953 - 15.7089i) q^{68} +(0.763705 - 8.10885i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +(6.60905 - 3.81574i) q^{74} +(20.2089 - 11.6676i) q^{76} +(11.8446 + 8.41142i) q^{77} -0.331977 q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +(-3.69636 + 6.40228i) q^{83} +(-2.66599 - 4.61763i) q^{85} +(-0.137600 - 0.0794433i) q^{86} +(-15.0748 - 26.1103i) q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +(-5.94040 - 3.42969i) q^{92} +24.5711i q^{94} -6.85939i q^{95} +(3.85939 + 2.22822i) q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q - 16 * q^4 + 4 * q^7	\( 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) \) 12 * q - 16 * q^4 + 4 * q^7 - 6 * q^10 + 24 * q^13 + 8 * q^16 - 6 * q^19 + 20 * q^22 - 24 * q^25 + 28 * q^28 + 60 * q^34 + 8 * q^37 - 12 * q^40 - 10 * q^43 + 14 * q^46 - 48 * q^49 - 78 * q^52 + 20 * q^58 + 28 * q^64 - 72 * q^67 + 54 * q^70 - 42 * q^73 + 108 * q^76 + 72 * q^79 - 54 * q^82 + 6 * q^85 - 74 * q^88 + 6 * q^91 + 60 * q^97

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