LMFDB - Embedded newform 567.2.i.f.269.6

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			269.6
Root			$-0.617942 + 0.356769i$ of defining polynomial
Character	$\chi$	$=$	567.269
Dual form			567.2.i.f.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.49086i q^{2} -4.20440 q^{4} +(0.617942 - 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} -5.49086i q^{8} +O(q^{10})$	\(q+2.49086i q^{2} -4.20440 q^{4} +(0.617942 - 1.07031i) q^{5} +(-1.10220 - 2.40523i) q^{7} -5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} +(4.75523 - 2.74543i) q^{11} +(2.57031 - 1.48397i) q^{13} +(5.99111 - 2.74543i) q^{14} +5.26819 q^{16} +(2.15715 - 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} +(-2.59808 + 4.50000i) q^{20} +(6.83850 + 11.8446i) q^{22} +(-1.41290 - 0.815739i) q^{23} +(1.73630 + 3.00735i) q^{25} +(3.69636 + 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +(0.440925 + 0.254568i) q^{29} -8.13244i q^{31} +2.14061i q^{32} +(9.30660 + 5.37317i) q^{34} +(-3.25544 - 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} +(-6.91238 - 11.9726i) q^{38} +(-5.87691 - 3.39304i) q^{40} +(0.177017 + 0.306602i) q^{41} +(0.0318939 - 0.0552418i) q^{43} +(-19.9929 + 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} +9.86449 q^{47} +(-4.57031 + 5.30210i) q^{49} +(-7.49090 + 4.32488i) q^{50} +(-10.8066 + 6.23919i) q^{52} +(3.57005 + 2.06117i) q^{53} -6.78607i q^{55} +(-13.2068 + 6.05203i) q^{56} +(-0.634095 + 1.09828i) q^{58} +3.07842 q^{59} -6.89655i q^{61} +20.2568 q^{62} +5.20440 q^{64} -3.66802i q^{65} -12.3320 q^{67} +(-9.06953 + 15.7089i) q^{68} +(0.763705 - 8.10885i) q^{70} +4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +(-6.60905 + 3.81574i) q^{74} +(20.2089 - 11.6676i) q^{76} +(-11.8446 - 8.41142i) q^{77} -0.331977 q^{79} +(3.25544 - 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +(3.69636 - 6.40228i) q^{83} +(-2.66599 - 4.61763i) q^{85} +(0.137600 + 0.0794433i) q^{86} +(-15.0748 - 26.1103i) q^{88} +(1.71623 + 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +(5.94040 + 3.42969i) q^{92} +24.5711i q^{94} +6.85939i q^{95} +(3.85939 + 2.22822i) q^{97} +(-13.2068 - 11.3840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.342896\pi$
$2$			2.49086i			1.76131i	−0.473761	+	0.880653i	$0.657104\pi$
$3$		0			0
$3$		0			0
$4$	−4.20440			−2.10220
$5$	0.617942	−	1.07031i	0.276352	−	0.478656i	−0.694123	−	0.719856i	$-0.744208\pi$
$5$	0.617942	−	1.07031i	0.276352	−	0.478656i	0.970475	+	0.241200i	$0.0775411\pi$
$6$		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	0.436350	−	0.899777i	$-0.356271\pi$
$11$	4.75523	−	2.74543i	1.43376	−	0.827779i	0.997405	+	0.0719981i	$0.0229375\pi$
$12$		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	$-0.658077\pi$
$17$	2.15715	−	3.73630i	0.523186	−	0.906185i	0.999636	−	0.0269831i	$-0.00859003\pi$
$18$		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	0.345409	−	0.938452i	$-0.387740\pi$
$23$	−1.41290	−	0.815739i	−0.294610	−	0.170093i	−0.640019	+	0.768359i	$0.721074\pi$
$24$		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	0.540380	−	0.841421i	$-0.318281\pi$
$29$	0.440925	+	0.254568i	0.0818777	+	0.0472721i	−0.458502	+	0.888693i	$0.651614\pi$
$30$		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	0.879517	−	0.475867i	$-0.157866\pi$
$41$	0.177017	+	0.306602i	0.0276454	+	0.0478832i	−0.851872	+	0.523751i	$0.824532\pi$
$42$		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	$-0.244398\pi$
$47$	9.86449			1.43888			0.719442	+	0.694553i	$0.244398\pi$
$48$		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	0.724734	−	0.689029i	$-0.241963\pi$
$53$	3.57005	+	2.06117i	0.490384	+	0.283124i	−0.234350	+	0.972152i	$0.575296\pi$
$54$		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	$-0.435780\pi$
$59$	3.07842			0.400776			0.200388	+	0.979717i	$0.435780\pi$
$60$		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	$0.0886208\pi$
$71$			4.63148i			0.549655i	−0.961494	+	0.274828i	$0.911379\pi$
$72$		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	−0.588678	−	0.808368i	$-0.700351\pi$
$83$	3.69636	−	6.40228i	0.405728	−	0.702742i	0.994406	+	0.105626i	$0.0336846\pi$
$84$		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	0.942534	−	0.334110i	$-0.108436\pi$
$89$	1.71623	+	2.97259i	0.181920	+	0.315094i	−0.760615	+	0.649204i	$0.775102\pi$
$90$		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	0.998720	−	0.0505884i	$-0.0161097\pi$
$101$	4.57821	+	7.92969i	0.455549	+	0.789034i	−0.543171	+	0.839622i	$0.682776\pi$
$102$		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	−0.865177	−	0.501467i	$-0.832794\pi$
$107$	−8.93193	+	5.15685i	−0.863482	+	0.498532i	0.00169460	+	0.999999i	$0.499461\pi$
$108$		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	−0.403398	−	0.915025i	$-0.632171\pi$
$113$	1.99143	−	1.14975i	0.187338	−	0.108159i	0.590736	+	0.806865i	$0.298838\pi$
$114$		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	$-0.468317\pi$
$131$	10.4317	−	18.0683i	0.911424	−	1.57863i	0.812054	−	0.583582i	$-0.198349\pi$
$132$		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	−0.525691	−	0.850676i	$-0.676193\pi$
$137$	−0.606650	+	0.350250i	−0.0518296	+	0.0299239i	0.473861	+	0.880600i	$0.342860\pi$
$138$		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	0.487524	−	0.873110i	$-0.337900\pi$
$149$	−0.303325	−	0.175125i	−0.0248494	−	0.0143468i	−0.512373	+	0.858763i	$0.671234\pi$
$150$		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	$0.202383\pi$
$167$	11.8446	+	20.5155i	0.916564	+	1.58754i	0.111970	+	0.993712i	$0.464284\pi$
$168$		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	$-0.650538\pi$
$173$	−11.9822			−0.910992			−0.455496	+	0.890238i	$0.650538\pi$
$174$		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	−0.450574	−	0.892739i	$-0.648780\pi$
$179$	−19.3862	−	11.1926i	−1.44900	−	0.836578i	−0.998422	+	0.0561615i	$0.982114\pi$
$180$		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	$0.136472\pi$
$191$			11.4909i			0.831450i	−0.909490	+	0.415725i	$0.863528\pi$
$192$		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	$0.249574\pi$
$197$			19.8228i			1.41232i	−0.708053	+	0.706159i	$0.750426\pi$
$198$		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	0.528893	−	0.848689i	$-0.322607\pi$
$227$	−7.08940	−	12.2792i	−0.470540	−	0.814999i	−0.999432	+	0.0336901i	$0.989274\pi$
$228$		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	−0.289283	−	0.957244i	$-0.593417\pi$
$233$	6.03053	−	3.48173i	0.395073	−	0.228096i	0.684356	+	0.729148i	$0.260083\pi$
$234$		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	−0.999886	−	0.0151157i	$-0.995188\pi$
$239$	−22.9844	+	13.2701i	−1.48674	+	0.858369i	−0.486852	+	0.873484i	$0.661855\pi$
$240$		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	$-0.474349\pi$
$251$	2.55060			0.160993			0.0804963	+	0.996755i	$0.474349\pi$
$252$		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	$0.357129\pi$
$257$	−9.03011	+	15.6406i	−0.563283	+	0.975635i	−0.997207	+	0.0746853i	$0.976205\pi$
$258$		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	−0.268832	−	0.963187i	$-0.586638\pi$
$263$	6.98798	−	4.03451i	0.430897	−	0.248779i	0.699729	+	0.714409i	$0.253304\pi$
$264$		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	−0.832321	−	0.554294i	$-0.812988\pi$
$269$	1.04758	−	1.81445i	0.0638718	−	0.110629i	0.896193	+	0.443664i	$0.146322\pi$
$270$		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	−0.215712	−	0.976457i	$-0.569207\pi$
$281$	−19.5994	−	11.3157i	−1.16920	−	0.675040i	−0.953493	+	0.301417i	$0.902540\pi$
$282$		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	$0.112702\pi$
$293$	13.1674	+	22.8066i	0.769248	+	1.33238i	−0.168724	+	0.985663i	$0.553965\pi$
$294$		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	$-0.776696\pi$
$311$	−26.9414			−1.52771			−0.763855	+	0.645388i	$0.776696\pi$
$312$		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	$-0.751411\pi$
$317$		−	25.0675i		−	1.40793i	0.710234	−	0.703966i	$-0.248589\pi$
$318$		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	$0.0861754\pi$
$347$			9.96345i			0.534866i	−0.963576	+	0.267433i	$0.913825\pi$
$348$		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	$0.158754\pi$
$353$	16.0326	+	27.7693i	0.853330	+	1.47801i	−0.0248555	+	0.999691i	$0.507913\pi$
$354$		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	−0.203468	−	0.979082i	$-0.565221\pi$
$359$	10.2828	−	5.93680i	0.542707	−	0.313332i	0.746175	+	0.665749i	$0.231888\pi$
$360$		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	$-0.528851\pi$
$383$	15.9932	−	27.7010i	0.817214	−	1.41546i	0.907727	−	0.419561i	$-0.137816\pi$
$384$		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	−0.324347	−	0.945938i	$-0.605145\pi$
$389$	6.56158	−	3.78833i	0.332685	−	0.192076i	0.657033	+	0.753862i	$0.271811\pi$
$390$		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	0.880301	−	0.474415i	$-0.157340\pi$
$401$	18.2147	+	10.5162i	0.909597	+	0.525156i	0.0292953	+	0.999571i	$0.490674\pi$
$402$		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	0.959050	−	0.283238i	$-0.0914086\pi$
$419$	4.79464	+	8.30457i	0.234234	+	0.405705i	−0.724816	+	0.688943i	$0.758075\pi$
$420$		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	0.239467	−	0.970905i	$-0.423027\pi$
$431$	−9.99885	−	5.77284i	−0.481628	−	0.278068i	−0.721095	+	0.692837i	$0.756361\pi$
$432$		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	$0.173030\pi$
$443$			21.7721i			1.03442i	−0.855858	+	0.517212i	$0.826970\pi$
$444$		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	$-0.918051\pi$
$449$		−	10.7904i		−	0.509229i	0.967043	−	0.254614i	$-0.0819485\pi$
$450$		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	$-0.554958\pi$
$461$	16.4735	−	28.5330i	0.767249	−	1.32891i	0.939049	−	0.343783i	$-0.111708\pi$
$462$		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	$0.000478796\pi$
$467$	10.8332	+	18.7637i	0.501302	+	0.868281i	−0.498697	+	0.866777i	$0.666188\pi$
$468$		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	$0.00459320\pi$
$479$	11.2154	+	19.4256i	0.512444	+	0.887579i	−0.487452	+	0.873150i	$0.662073\pi$
$480$		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	−0.770615	−	0.637301i	$-0.780051\pi$
$491$	−13.3838	+	7.72716i	−0.604004	+	0.348722i	0.166611	+	0.986023i	$0.446718\pi$
$492$		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	$-0.367484\pi$
$503$	18.1391			0.808781			0.404390	+	0.914586i	$0.367484\pi$
$504$		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	$-0.618590\pi$
$509$	14.0919	−	24.4079i	0.624612	−	1.08186i	0.988616	−	0.150463i	$-0.0480764\pi$
$510$		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	$0.436032\pi$
$521$	−17.0915	+	29.6033i	−0.748792	+	1.29694i	−0.948402	+	0.317070i	$0.897301\pi$
$522$		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	0.651130	−	0.758966i	$-0.274295\pi$
$557$	7.53838	+	4.35228i	0.319411	+	0.184412i	−0.331719	+	0.943378i	$0.607629\pi$
$558$		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	$-0.335583\pi$
$563$	23.4366			0.987736			0.493868	+	0.869537i	$0.335583\pi$
$564$		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	$-0.744484\pi$
$569$		−	34.3137i		−	1.43851i	0.694749	−	0.719253i	$-0.255516\pi$
$570$		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	−0.609252	−	0.792977i	$-0.708530\pi$
$587$	9.25784	−	16.0350i	0.382112	−	0.661837i	0.991364	+	0.131139i	$0.0418636\pi$
$588$		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	0.606858	−	0.794810i	$-0.292430\pi$
$593$	−9.37285	−	16.2343i	−0.384897	−	0.666661i	−0.991755	+	0.128149i	$0.959096\pi$
$594$		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	$-0.822735\pi$
$599$		−	25.8721i		−	1.05710i	0.848901	−	0.528552i	$-0.177265\pi$
$600$		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	−0.535082	−	0.844800i	$-0.679719\pi$
$617$	−1.76370	+	1.01827i	−0.0710039	+	0.0409941i	0.464078	+	0.885794i	$0.346386\pi$
$618$		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	−0.467543	−	0.883971i	$-0.654861\pi$
$641$	1.62610	−	0.938829i	0.0642271	−	0.0370815i	0.531770	+	0.846889i	$0.321527\pi$
$642$		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	$-0.579002\pi$
$647$	18.2292	−	31.5739i	0.716663	−	1.24130i	0.962315	−	0.271939i	$-0.0876648\pi$
$648$		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	0.733154	−	0.680063i	$-0.238048\pi$
$653$	13.0524	+	7.53580i	0.510779	+	0.294898i	−0.222375	+	0.974961i	$0.571381\pi$
$654$		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	−0.135695	−	0.990751i	$-0.543327\pi$
$659$	−27.2512	−	15.7335i	−1.06156	−	0.612891i	−0.925863	+	0.377860i	$0.876660\pi$
$660$		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	$-0.362777\pi$
$677$	21.7453			0.835740			0.417870	+	0.908507i	$0.362777\pi$
$678$		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	0.698155	−	0.715947i	$-0.254005\pi$
$683$	11.1647	+	6.44593i	0.427205	+	0.246647i	−0.270950	+	0.962593i	$0.587338\pi$
$684$		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	$0.283845\pi$
$701$			41.2056i			1.55631i	−0.628071	+	0.778156i	$0.716155\pi$
$702$		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	0.849113	−	0.528211i	$-0.177137\pi$
$719$	−0.881850	−	1.52741i	−0.0328875	−	0.0569627i	−0.882001	+	0.471248i	$0.843804\pi$
$720$		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	−0.375728	−	0.926730i	$-0.622607\pi$
$743$	6.51411	−	3.76092i	0.238979	−	0.137975i	0.614708	+	0.788755i	$0.289274\pi$
$744$		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	−0.934231	−	0.356668i	$-0.883913\pi$
$761$	−4.36501	+	7.56042i	−0.158232	+	0.274065i	0.775999	+	0.630734i	$0.217246\pi$
$762$		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	−0.809119	−	0.587645i	$-0.800055\pi$
$773$	2.90140	−	5.02537i	0.104356	−	0.180750i	0.913475	+	0.406895i	$0.133388\pi$
$774$		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	0.902303	−	0.431102i	$-0.141875\pi$
$797$	2.19657	+	3.80457i	0.0778064	+	0.134765i	−0.824497	+	0.565867i	$0.808542\pi$
$798$		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	$0.0172323\pi$
$809$	43.9347	+	25.3657i	1.54466	+	0.891812i	0.546129	+	0.837701i	$0.316101\pi$
$810$		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	$0.149546\pi$
$821$			25.9437i			0.905441i	−0.891653	+	0.452720i	$0.850454\pi$
$822$		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	$-0.909245\pi$
$827$		−	16.1772i		−	0.562535i	0.959629	−	0.281267i	$-0.0907548\pi$
$828$		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	−0.989660	−	0.143431i	$-0.954186\pi$
$839$	−10.7350	+	18.5936i	−0.370615	+	0.641924i	0.619045	+	0.785355i	$0.287520\pi$
$840$		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	0.504053	−	0.863673i	$-0.331841\pi$
$857$	−14.5183	−	25.1464i	−0.495936	−	0.858986i	−0.999989	+	0.00468678i	$0.998508\pi$
$858$		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	0.0498671	−	0.998756i	$-0.484120\pi$
$863$	27.6069	−	15.9388i	0.939749	−	0.542564i	0.889881	+	0.456192i	$0.150787\pi$
$864$		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	$-0.564139\pi$
$881$	−11.8808			−0.400275			−0.200137	+	0.979768i	$0.564139\pi$
$882$		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	−0.743437	−	0.668806i	$-0.766806\pi$
$887$	6.17942	−	10.7031i	0.207485	−	0.359374i	0.950922	+	0.309432i	$0.100139\pi$
$888$		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	0.991557	−	0.129672i	$-0.0413926\pi$
$911$	41.5024	+	23.9614i	1.37504	+	0.793877i	0.383479	+	0.923550i	$0.374726\pi$
$912$		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	$-0.0933763\pi$
$929$	58.3549			1.91456			0.957280	+	0.289161i	$0.0933763\pi$
$930$		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	$-0.585154\pi$
$941$	−16.2177			−0.528682			−0.264341	+	0.964429i	$0.585154\pi$
$942$		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	$0.151466\pi$
$947$			28.1939i			0.916180i	−0.888906	+	0.458090i	$0.848534\pi$
$948$		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	$-0.634027\pi$
$953$		−	56.3488i		−	1.82532i	0.408725	−	0.912658i	$-0.365973\pi$
$954$		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	$0.00912132\pi$
$971$	16.3472	+	28.3142i	0.524608	+	0.908647i	−0.474982	+	0.879996i	$0.657545\pi$
$972$		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	$0.129086\pi$
$977$			24.6625i			0.789022i	−0.918891	+	0.394511i	$0.870914\pi$
$978$		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	0.688570	−	0.725170i	$-0.258239\pi$
$983$	−8.89575	−	15.4079i	−0.283730	−	0.491435i	−0.972300	+	0.233734i	$0.924905\pi$
$984$		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.269.6		12
3.2	odd	2	inner	567.2.i.f.269.1		12
7.5	odd	6		567.2.s.f.26.6		12
9.2	odd	6		189.2.p.d.80.1	yes	12
9.4	even	3		567.2.s.f.458.1		12
9.5	odd	6		567.2.s.f.458.6		12
9.7	even	3		189.2.p.d.80.6	yes	12
21.5	even	6		567.2.s.f.26.1		12
63.5	even	6	inner	567.2.i.f.215.1		12
63.11	odd	6		1323.2.c.d.1322.2		12
63.25	even	3		1323.2.c.d.1322.11		12
63.38	even	6		1323.2.c.d.1322.1		12
63.40	odd	6	inner	567.2.i.f.215.6		12
63.47	even	6		189.2.p.d.26.6	yes	12
63.52	odd	6		1323.2.c.d.1322.12		12
63.61	odd	6		189.2.p.d.26.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.1	✓	12	63.61	odd	6
189.2.p.d.26.6	yes	12	63.47	even	6
189.2.p.d.80.1	yes	12	9.2	odd	6
189.2.p.d.80.6	yes	12	9.7	even	3
567.2.i.f.215.1		12	63.5	even	6	inner
567.2.i.f.215.6		12	63.40	odd	6	inner
567.2.i.f.269.1		12	3.2	odd	2	inner
567.2.i.f.269.6		12	1.1	even	1	trivial
567.2.s.f.26.1		12	21.5	even	6
567.2.s.f.26.6		12	7.5	odd	6
567.2.s.f.458.1		12	9.4	even	3
567.2.s.f.458.6		12	9.5	odd	6
1323.2.c.d.1322.1		12	63.38	even	6
1323.2.c.d.1322.2		12	63.11	odd	6
1323.2.c.d.1322.11		12	63.25	even	3
1323.2.c.d.1322.12		12	63.52	odd	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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