LMFDB - Embedded newform 567.2.i.f.215.1

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			215.1
Root			$-0.617942 - 0.356769i$ of defining polynomial
Character	$\chi$	$=$	567.215
Dual form			567.2.i.f.269.6

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	2.49086i		−	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	$-0.0775411\pi$
$5$	0.617942	+	1.07031i	0.276352	+	0.478656i	−0.694123	+	0.719856i	$0.744208\pi$
$6$		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	$-0.0229375\pi$
$11$	4.75523	+	2.74543i	1.43376	+	0.827779i	0.436350	+	0.899777i	$0.356271\pi$
$12$		0			0
$13$	2.57031	+	1.48397i	0.712875	+	0.411578i	0.812125	−	0.583484i	$-0.198311\pi$
$13$	2.57031	+	1.48397i	0.712875	+	0.411578i	−0.0992497	+	0.995063i	$0.531644\pi$
$14$	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	0.999636	+	0.0269831i	$0.00859003\pi$
$17$	2.15715	+	3.73630i	0.523186	+	0.906185i	−0.476450	+	0.879202i	$0.658077\pi$
$18$		0			0
$19$	−4.80660	−	2.77509i	−1.10271	−	0.636650i	−0.165779	−	0.986163i	$-0.553014\pi$
$19$	−4.80660	−	2.77509i	−1.10271	−	0.636650i	−0.936932	+	0.349513i	$0.886347\pi$
$20$	−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	$-0.721074\pi$
$23$	−1.41290	+	0.815739i	−0.294610	+	0.170093i	0.345409	+	0.938452i	$0.387740\pi$
$24$		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	$-0.651614\pi$
$29$	0.440925	−	0.254568i	0.0818777	−	0.0472721i	0.540380	+	0.841421i	$0.318281\pi$
$30$		0			0
$31$			8.13244i			1.46063i	0.683111	+	0.730314i	$0.260626\pi$
$31$			8.13244i			1.46063i	−0.683111	+	0.730314i	$0.739374\pi$
$32$		−	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	−0.712191	−	0.701986i	$-0.752297\pi$
$37$	1.53189	−	2.65332i	0.251842	−	0.436203i	0.964033	+	0.265783i	$0.0856304\pi$
$38$	−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	$-0.824532\pi$
$41$	0.177017	−	0.306602i	0.0276454	−	0.0478832i	0.879517	+	0.475867i	$0.157866\pi$
$42$		0			0
$43$	0.0318939	+	0.0552418i	0.00486377	+	0.00842430i	0.868447	−	0.495782i	$-0.165118\pi$
$43$	0.0318939	+	0.0552418i	0.00486377	+	0.00842430i	−0.863583	+	0.504206i	$0.831785\pi$
$44$	−19.9929	−	11.5429i	−3.01404	−	1.74016i
$45$		0			0
$46$	2.03189	+	3.51934i	0.299586	+	0.518899i
$47$	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	−0.234350	−	0.972152i	$-0.575296\pi$
$53$	3.57005	−	2.06117i	0.490384	−	0.283124i	0.724734	+	0.689029i	$0.241963\pi$
$54$		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	$0.145556\pi$
$61$			6.89655i			0.883013i	−0.897258	+	0.441507i	$0.854444\pi$
$62$	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	−0.812336	−	0.583190i	$-0.801804\pi$
$73$	−6.09568	+	3.51934i	−0.713446	+	0.411908i	0.0988899	+	0.995098i	$0.468471\pi$
$74$	−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	$-0.0336846\pi$
$83$	3.69636	+	6.40228i	0.405728	+	0.702742i	−0.588678	+	0.808368i	$0.700351\pi$
$84$		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	$-0.775102\pi$
$89$	1.71623	−	2.97259i	0.181920	−	0.315094i	0.942534	+	0.334110i	$0.108436\pi$
$90$		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	−0.291105	−	0.956691i	$-0.594023\pi$
$97$	3.85939	−	2.22822i	0.391861	−	0.226241i	0.682966	+	0.730450i	$0.260690\pi$
$98$	−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	$-0.682776\pi$
$101$	4.57821	−	7.92969i	0.455549	−	0.789034i	0.998720	+	0.0505884i	$0.0161097\pi$
$102$		0			0
$103$	3.64061	−	2.10191i	0.358720	−	0.207107i	−0.309799	−	0.950802i	$-0.600262\pi$
$103$	3.64061	−	2.10191i	0.358720	−	0.207107i	0.668519	+	0.743695i	$0.266928\pi$
$104$	−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	$-0.499461\pi$
$107$	−8.93193	−	5.15685i	−0.863482	−	0.498532i	−0.865177	+	0.501467i	$0.832794\pi$
$108$		0			0
$109$	−0.0637877	−	0.110484i	−0.00610976	−	0.0105824i	0.862954	−	0.505282i	$-0.168611\pi$
$109$	−0.0637877	−	0.110484i	−0.00610976	−	0.0105824i	−0.869064	+	0.494699i	$0.835278\pi$
$110$	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	$-0.298838\pi$
$113$	1.99143	+	1.14975i	0.187338	+	0.108159i	−0.403398	+	0.915025i	$0.632171\pi$
$114$		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	0.812054	+	0.583582i	$0.198349\pi$
$131$	10.4317	+	18.0683i	0.911424	+	1.57863i	0.0993693	+	0.995051i	$0.468317\pi$
$132$		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	$-0.342860\pi$
$137$	−0.606650	−	0.350250i	−0.0518296	−	0.0299239i	−0.525691	+	0.850676i	$0.676193\pi$
$138$		0			0
$139$	−10.0429	−	5.79827i	−0.851827	−	0.491803i	0.00943957	−	0.999955i	$-0.496995\pi$
$139$	−10.0429	−	5.79827i	−0.851827	−	0.491803i	−0.861267	+	0.508153i	$0.830329\pi$
$140$	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	$-0.671234\pi$
$149$	−0.303325	+	0.175125i	−0.0248494	+	0.0143468i	0.487524	+	0.873110i	$0.337900\pi$
$150$		0			0
$151$	−2.32749	+	4.03133i	−0.189409	+	0.328065i	−0.945053	−	0.326916i	$-0.893990\pi$
$151$	−2.32749	+	4.03133i	−0.189409	+	0.328065i	0.755645	+	0.654982i	$0.227324\pi$
$152$	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	$-0.984295\pi$
$157$		−	1.23588i		−	0.0986343i	0.998783	−	0.0493171i	$-0.0157045\pi$
$158$			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	−0.170473	−	0.985362i	$-0.554530\pi$
$163$	9.80660	−	16.9855i	0.768112	−	1.33041i	0.938585	−	0.345047i	$-0.112137\pi$
$164$	−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	0.111970	−	0.993712i	$-0.464284\pi$
$167$	11.8446	−	20.5155i	0.916564	−	1.58754i	0.804595	−	0.593825i	$-0.202383\pi$
$168$		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	−0.998422	−	0.0561615i	$-0.982114\pi$
$179$	−19.3862	+	11.1926i	−1.44900	+	0.836578i	−0.450574	+	0.892739i	$0.648780\pi$
$180$		0			0
$181$		−	8.90380i		−	0.661815i	−0.943663	−	0.330907i	$-0.892645\pi$
$181$		−	8.90380i		−	0.661815i	0.943663	−	0.330907i	$-0.107355\pi$
$182$	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	−0.741693	−	0.670740i	$-0.765977\pi$
$199$	−7.50000	+	4.33013i	−0.531661	+	0.306955i	0.210032	+	0.977695i	$0.432643\pi$
$200$	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	0.178497	+	0.983940i	$0.442877\pi$
$211$	−11.0813	+	19.1934i	−0.762869	+	1.32133i	−0.941366	+	0.337387i	$0.890457\pi$
$212$	−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	−0.932810	−	0.360369i	$-0.882651\pi$
$223$	−16.2343	+	9.37285i	−1.08713	+	0.627653i	−0.154317	+	0.988021i	$0.549318\pi$
$224$	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	$-0.989274\pi$
$227$	−7.08940	+	12.2792i	−0.470540	+	0.814999i	0.528893	+	0.848689i	$0.322607\pi$
$228$		0			0
$229$	3.52537	−	2.03538i	0.232963	−	0.134501i	−0.378975	−	0.925407i	$-0.623723\pi$
$229$	3.52537	−	2.03538i	0.232963	−	0.134501i	0.611938	+	0.790905i	$0.290390\pi$
$230$	−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	$-0.260083\pi$
$233$	6.03053	+	3.48173i	0.395073	+	0.228096i	−0.289283	+	0.957244i	$0.593417\pi$
$234$		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	$-0.661855\pi$
$239$	−22.9844	−	13.2701i	−1.48674	−	0.858369i	−0.999886	+	0.0151157i	$0.995188\pi$
$240$		0			0
$241$	−11.7812	−	6.80189i	−0.758896	−	0.438149i	0.0700035	−	0.997547i	$-0.477699\pi$
$241$	−11.7812	−	6.80189i	−0.758896	−	0.438149i	−0.828899	+	0.559398i	$0.811032\pi$
$242$	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	−0.997207	−	0.0746853i	$-0.976205\pi$
$257$	−9.03011	−	15.6406i	−0.563283	−	0.975635i	0.433924	−	0.900949i	$-0.357129\pi$
$258$		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	$-0.253304\pi$
$263$	6.98798	+	4.03451i	0.430897	+	0.248779i	−0.268832	+	0.963187i	$0.586638\pi$
$264$		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	$-0.146322\pi$
$269$	1.04758	+	1.81445i	0.0638718	+	0.110629i	−0.832321	+	0.554294i	$0.812988\pi$
$270$		0			0
$271$	21.3066	+	12.3014i	1.29428	+	0.747255i	0.979411	−	0.201879i	$-0.0647046\pi$
$271$	21.3066	+	12.3014i	1.29428	+	0.747255i	0.314873	+	0.949134i	$0.398038\pi$
$272$	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	−0.330782	−	0.943707i	$-0.607313\pi$
$277$	10.8495	−	18.7919i	0.651883	−	1.12909i	0.982665	−	0.185388i	$-0.0593541\pi$
$278$	−14.4427	+	25.0155i	−0.866216	+	1.50033i
$279$		0			0
$280$	−1.68351	−	17.8752i	−0.100609	−	1.06824i
$281$	−19.5994	+	11.3157i	−1.16920	+	0.675040i	−0.953493	−	0.301417i	$-0.902540\pi$
$281$	−19.5994	+	11.3157i	−1.16920	+	0.675040i	−0.215712	+	0.976457i	$0.569207\pi$
$282$		0			0
$283$		−	9.54210i		−	0.567219i	−0.958940	−	0.283610i	$-0.908468\pi$
$283$		−	9.54210i		−	0.567219i	0.958940	−	0.283610i	$-0.0915320\pi$
$284$			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	−0.168724	−	0.985663i	$-0.553965\pi$
$293$	13.1674	−	22.8066i	0.769248	−	1.33238i	0.937971	−	0.346713i	$-0.112702\pi$
$294$		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	$0.0623259\pi$
$307$			6.81772i			0.389108i	−0.980892	+	0.194554i	$0.937674\pi$
$308$	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	$-0.772845\pi$
$313$		−	23.1614i		−	1.30916i	0.755992	−	0.654581i	$-0.227155\pi$
$314$	−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	−0.166739	−	0.986001i	$-0.553324\pi$
$337$	14.1451	−	24.5000i	0.770533	−	1.33460i	0.937271	−	0.348601i	$-0.113343\pi$
$338$	−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	0.121097	−	0.992641i	$-0.461359\pi$
$349$	19.4530	−	11.2312i	1.04130	−	0.601193i	0.920200	+	0.391448i	$0.128026\pi$
$350$	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	−0.0248555	−	0.999691i	$-0.507913\pi$
$353$	16.0326	−	27.7693i	0.853330	−	1.47801i	0.878186	−	0.478320i	$-0.158754\pi$
$354$		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	$-0.231888\pi$
$359$	10.2828	+	5.93680i	0.542707	+	0.313332i	−0.203468	+	0.979082i	$0.565221\pi$
$360$		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	0.774351	−	0.632756i	$-0.218076\pi$
$367$	11.7538	+	6.78607i	0.613544	+	0.354230i	−0.160807	+	0.986986i	$0.551410\pi$
$368$	−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	−0.931294	−	0.364269i	$-0.881319\pi$
$373$	−15.0858	−	26.1294i	−0.781113	−	1.35293i	0.150181	−	0.988659i	$-0.452014\pi$
$374$	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	0.907727	+	0.419561i	$0.137816\pi$
$383$	15.9932	+	27.7010i	0.817214	+	1.41546i	−0.0905126	+	0.995895i	$0.528851\pi$
$384$		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	$-0.271811\pi$
$389$	6.56158	+	3.78833i	0.332685	+	0.192076i	−0.324347	+	0.945938i	$0.605145\pi$
$390$		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	0.479177	−	0.877719i	$-0.340935\pi$
$397$	−0.824125	−	0.475809i	−0.0413617	−	0.0238802i	−0.520538	+	0.853838i	$0.674269\pi$
$398$	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	$-0.490674\pi$
$401$	18.2147	−	10.5162i	0.909597	−	0.525156i	0.880301	+	0.474415i	$0.157340\pi$
$402$		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	$0.165963\pi$
$409$			20.1463i			0.996171i	−0.867128	+	0.498085i	$0.834037\pi$
$410$		−	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	$-0.758075\pi$
$419$	4.79464	−	8.30457i	0.234234	−	0.405705i	0.959050	+	0.283238i	$0.0914086\pi$
$420$		0			0
$421$	−4.30660	−	7.45925i	−0.209891	−	0.363542i	0.741789	−	0.670633i	$-0.233978\pi$
$421$	−4.30660	−	7.45925i	−0.209891	−	0.363542i	−0.951680	+	0.307092i	$0.900644\pi$
$422$	47.8081	+	27.6020i	2.32726	+	1.34365i
$423$		0			0
$424$	11.3176	+	19.6027i	0.549632	+	0.951990i
$425$	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	$-0.756361\pi$
$431$	−9.99885	+	5.77284i	−0.481628	+	0.278068i	0.239467	+	0.970905i	$0.423027\pi$
$432$		0			0
$433$			22.8707i			1.09910i	0.835462	+	0.549548i	$0.185200\pi$
$433$			22.8707i			1.09910i	−0.835462	+	0.549548i	$0.814800\pi$
$434$	−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	$-0.998081\pi$
$439$		−	0.252617i		−	0.0120567i	0.999982	−	0.00602837i	$-0.00191890\pi$
$440$	−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	0.939049	+	0.343783i	$0.111708\pi$
$461$	16.4735	+	28.5330i	0.767249	+	1.32891i	−0.171800	+	0.985132i	$0.554958\pi$
$462$		0			0
$463$	2.61320	−	4.52620i	0.121446	−	0.210351i	−0.798892	−	0.601474i	$-0.794580\pi$
$463$	2.61320	−	4.52620i	0.121446	−	0.210351i	0.920338	+	0.391124i	$0.127914\pi$
$464$	2.32288	−	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	−0.498697	−	0.866777i	$-0.666188\pi$
$467$	10.8332	−	18.7637i	0.501302	−	0.868281i	0.999999	−	0.00150418i	$-0.000478796\pi$
$468$		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	−0.487452	−	0.873150i	$-0.662073\pi$
$479$	11.2154	−	19.4256i	0.512444	−	0.887579i	0.999896	−	0.0144295i	$-0.00459320\pi$
$480$		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	−0.999997	−	0.00247528i	$-0.999212\pi$
$487$	−11.0813	−	19.1934i	−0.502142	−	0.869736i	0.497855	−	0.867260i	$-0.334121\pi$
$488$	−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	$-0.446718\pi$
$491$	−13.3838	−	7.72716i	−0.604004	−	0.348722i	−0.770615	+	0.637301i	$0.780051\pi$
$492$		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	0.880686	−	0.473701i	$-0.157082\pi$
$499$	0.672508	+	1.16482i	0.0301056	+	0.0521444i	−0.850580	+	0.525846i	$0.823749\pi$
$500$	−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	0.988616	+	0.150463i	$0.0480764\pi$
$509$	14.0919	+	24.4079i	0.624612	+	1.08186i	−0.364003	+	0.931398i	$0.618590\pi$
$510$		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	−0.948402	−	0.317070i	$-0.897301\pi$
$521$	−17.0915	−	29.6033i	−0.748792	−	1.29694i	0.199611	−	0.979875i	$-0.436032\pi$
$522$		0			0
$523$	31.9157	+	18.4266i	1.39558	+	0.805737i	0.993925	−	0.110055i	$-0.0351027\pi$
$523$	31.9157	+	18.4266i	1.39558	+	0.805737i	0.401652	+	0.915792i	$0.368436\pi$
$524$	−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	−0.0754099	−	0.997153i	$-0.524027\pi$
$541$	19.2089	−	33.2708i	0.825855	−	1.43042i	0.901264	−	0.433269i	$-0.142640\pi$
$542$	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	0.708835	−	0.705374i	$-0.249221\pi$
$547$	−5.99797	−	10.3888i	−0.256454	−	0.444192i	−0.965290	+	0.261182i	$0.915888\pi$
$548$	2.55060	+	1.47259i	0.108956	+	0.0629060i
$549$		0			0
$550$	−23.7473	−	41.1315i	−1.01259	−	1.75385i
$551$	−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	$-0.607629\pi$
$557$	7.53838	−	4.35228i	0.319411	−	0.184412i	0.651130	+	0.758966i	$0.274295\pi$
$558$		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	$0.255516\pi$
$569$			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	−0.917504	−	0.397727i	$-0.869799\pi$
$577$	−24.7850	+	14.3096i	−1.03181	+	0.595718i	−0.114310	+	0.993445i	$0.536466\pi$
$578$	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	$-0.0418636\pi$
$587$	9.25784	+	16.0350i	0.382112	+	0.661837i	−0.609252	+	0.792977i	$0.708530\pi$
$588$		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	$-0.959096\pi$
$593$	−9.37285	+	16.2343i	−0.384897	+	0.666661i	0.606858	+	0.794810i	$0.292430\pi$
$594$		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	−0.734814	−	0.678268i	$-0.762731\pi$
$601$	−12.6211	+	7.28677i	−0.514824	+	0.297234i	0.219991	+	0.975502i	$0.429397\pi$
$602$	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	−0.837544	−	0.546369i	$-0.816010\pi$
$607$	−19.2947	+	11.1398i	−0.783147	+	0.452150i	0.0543974	+	0.998519i	$0.482676\pi$
$608$	−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	−0.999941	−	0.0108424i	$-0.996549\pi$
$613$	−12.6112	−	21.8432i	−0.509360	−	0.882238i	0.490581	−	0.871396i	$-0.336785\pi$
$614$	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	$-0.346386\pi$
$617$	−1.76370	−	1.01827i	−0.0710039	−	0.0409941i	−0.535082	+	0.844800i	$0.679719\pi$
$618$		0			0
$619$	−32.9099	−	19.0006i	−1.32276	−	0.763697i	−0.338593	−	0.940933i	$-0.609951\pi$
$619$	−32.9099	−	19.0006i	−1.32276	−	0.763697i	−0.984168	+	0.177236i	$0.943284\pi$
$620$	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	$-0.321527\pi$
$641$	1.62610	+	0.938829i	0.0642271	+	0.0370815i	−0.467543	+	0.883971i	$0.654861\pi$
$642$		0			0
$643$	−12.6211	−	7.28677i	−0.497726	−	0.287362i	0.230048	−	0.973179i	$-0.426112\pi$
$643$	−12.6211	−	7.28677i	−0.497726	−	0.287362i	−0.727774	+	0.685817i	$0.759445\pi$
$644$	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	0.962315	+	0.271939i	$0.0876648\pi$
$647$	18.2292	+	31.5739i	0.716663	+	1.24130i	−0.245651	+	0.969358i	$0.579002\pi$
$648$		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	$-0.571381\pi$
$653$	13.0524	−	7.53580i	0.510779	−	0.294898i	0.733154	+	0.680063i	$0.238048\pi$
$654$		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	$-0.876660\pi$
$659$	−27.2512	+	15.7335i	−1.06156	+	0.612891i	−0.135695	+	0.990751i	$0.543327\pi$
$660$		0			0
$661$		−	13.7524i		−	0.534906i	−0.963571	−	0.267453i	$-0.913818\pi$
$661$		−	13.7524i		−	0.534906i	0.963571	−	0.267453i	$-0.0861820\pi$
$662$			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	0.730363	−	0.683059i	$-0.239351\pi$
$673$	−5.87242	−	10.1713i	−0.226365	−	0.392076i	−0.956728	+	0.290983i	$0.906018\pi$
$674$	−61.0262	−	35.2335i	−2.35064	−	1.35714i
$675$		0			0
$676$	8.81109	+	15.2613i	0.338888	+	0.586971i
$677$	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	−0.270950	−	0.962593i	$-0.587338\pi$
$683$	11.1647	−	6.44593i	0.427205	−	0.246647i	0.698155	+	0.715947i	$0.254005\pi$
$684$		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	$0.0630028\pi$
$691$			10.3381i			0.393279i	−0.980476	+	0.196639i	$0.936997\pi$
$692$	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	$-0.843804\pi$
$719$	−0.881850	+	1.52741i	−0.0328875	+	0.0569627i	0.849113	+	0.528211i	$0.177137\pi$
$720$		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	−0.785974	−	0.618259i	$-0.787838\pi$
$727$	−17.3515	+	10.0179i	−0.643533	+	0.371544i	0.142441	+	0.989803i	$0.454505\pi$
$728$	−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	−0.725969	−	0.687727i	$-0.758609\pi$
$733$	−13.3574	+	7.71187i	−0.493365	+	0.284844i	0.232604	+	0.972571i	$0.425275\pi$
$734$	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	0.993265	+	0.115863i	$0.0369634\pi$
$739$	16.2284	+	28.1085i	0.596973	+	1.03399i	−0.396292	+	0.918124i	$0.629703\pi$
$740$	−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	$-0.289274\pi$
$743$	6.51411	+	3.76092i	0.238979	+	0.137975i	−0.375728	+	0.926730i	$0.622607\pi$
$744$		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	0.527898	−	0.849308i	$-0.322980\pi$
$751$	−12.9232	−	22.3836i	−0.471573	−	0.816789i	−0.999471	+	0.0325190i	$0.989647\pi$
$752$	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	$-0.217246\pi$
$761$	−4.36501	−	7.56042i	−0.158232	−	0.274065i	−0.934231	+	0.356668i	$0.883913\pi$
$762$		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	0.419151	−	0.907917i	$-0.362328\pi$
$769$	−4.36906	−	2.52248i	−0.157552	−	0.0909628i	−0.576703	+	0.816954i	$0.695661\pi$
$770$	−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	$-0.133388\pi$
$773$	2.90140	+	5.02537i	0.104356	+	0.180750i	−0.809119	+	0.587645i	$0.800055\pi$
$774$		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	$-0.854871\pi$
$787$		−	24.7042i		−	0.880608i	0.897849	−	0.440304i	$-0.145129\pi$
$788$			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	$-0.808542\pi$
$797$	2.19657	−	3.80457i	0.0778064	−	0.134765i	0.902303	+	0.431102i	$0.141875\pi$
$798$		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	0.546129	−	0.837701i	$-0.316101\pi$
$809$	43.9347	−	25.3657i	1.54466	−	0.891812i	0.998535	−	0.0541105i	$-0.0172323\pi$
$810$		0			0
$811$		−	31.8126i		−	1.11709i	−0.829474	−	0.558546i	$-0.811359\pi$
$811$		−	31.8126i		−	1.11709i	0.829474	−	0.558546i	$-0.188641\pi$
$812$	−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	−0.908934	−	0.416940i	$-0.863103\pi$
$829$	−28.8592	+	16.6619i	−1.00232	+	0.578690i	−0.0933864	+	0.995630i	$0.529769\pi$
$830$	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	$-0.287520\pi$
$839$	−10.7350	−	18.5936i	−0.370615	−	0.641924i	−0.989660	+	0.143431i	$0.954186\pi$
$840$		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	−0.0777582	−	0.996972i	$-0.524776\pi$
$853$	21.8102	−	12.5921i	0.746766	−	0.431146i	0.824524	+	0.565827i	$0.191443\pi$
$854$	−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	$-0.998508\pi$
$857$	−14.5183	+	25.1464i	−0.495936	+	0.858986i	0.504053	+	0.863673i	$0.331841\pi$
$858$		0			0
$859$	20.6386	−	11.9157i	0.704179	−	0.406558i	−0.104723	−	0.994501i	$-0.533396\pi$
$859$	20.6386	−	11.9157i	0.704179	−	0.406558i	0.808902	+	0.587943i	$0.200062\pi$
$860$	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	$-0.150787\pi$
$863$	27.6069	+	15.9388i	0.939749	+	0.542564i	0.0498671	+	0.998756i	$0.484120\pi$
$864$		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	0.884641	−	0.466273i	$-0.154404\pi$
$877$	1.14061	+	1.97560i	0.0385158	+	0.0667113i	−0.846125	+	0.532985i	$0.821070\pi$
$878$	−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	0.950922	−	0.309432i	$-0.100139\pi$
$887$	6.17942	+	10.7031i	0.207485	+	0.359374i	−0.743437	+	0.668806i	$0.766806\pi$
$888$		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	−0.399981	−	0.916523i	$-0.630983\pi$
$907$	17.8814	−	30.9715i	0.593742	−	1.02839i	0.993723	−	0.111868i	$-0.0356833\pi$
$908$	29.8067	−	51.6267i	0.989169	−	1.71329i
$909$		0			0
$910$	−10.0703	+	21.9755i	−0.333827	+	0.728482i
$911$	41.5024	−	23.9614i	1.37504	−	0.793877i	0.383479	−	0.923550i	$-0.374726\pi$
$911$	41.5024	−	23.9614i	1.37504	−	0.793877i	0.991557	+	0.129672i	$0.0413926\pi$
$912$		0			0
$913$			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	−0.427972	−	0.903792i	$-0.640772\pi$
$919$	17.2408	−	29.8619i	0.568721	−	0.985053i	0.996693	−	0.0812614i	$-0.0258949\pi$
$920$	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	$0.162177\pi$
$937$			29.8596i			0.975471i	−0.872992	+	0.487735i	$0.837823\pi$
$938$	−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	$-0.848534\pi$
$947$		−	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	0.451285	+	0.892380i	$0.350966\pi$
$967$	−17.0155	+	29.4717i	−0.547181	+	0.947746i	−0.998466	+	0.0553658i	$0.982368\pi$
$968$	−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	−0.474982	−	0.879996i	$-0.657545\pi$
$971$	16.3472	−	28.3142i	0.524608	−	0.908647i	0.999589	−	0.0286515i	$-0.00912132\pi$
$972$		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	$-0.924905\pi$
$983$	−8.89575	+	15.4079i	−0.283730	+	0.491435i	0.688570	+	0.725170i	$0.258239\pi$
$984$		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	0.999970	+	0.00777992i	$0.00247645\pi$
$991$	15.9517	+	27.6292i	0.506722	+	0.877669i	−0.493247	+	0.869889i	$0.664190\pi$
$992$	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	0.927755	−	0.373191i	$-0.121736\pi$
$997$	33.7363	+	19.4777i	1.06844	+	0.616864i	0.140685	+	0.990054i	$0.455070\pi$
$998$	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.215.1		12
3.2	odd	2	inner	567.2.i.f.215.6		12
7.3	odd	6		567.2.s.f.458.6		12
9.2	odd	6		567.2.s.f.26.6		12
9.4	even	3		189.2.p.d.26.6	yes	12
9.5	odd	6		189.2.p.d.26.1	✓	12
9.7	even	3		567.2.s.f.26.1		12
21.17	even	6		567.2.s.f.458.1		12
63.5	even	6		1323.2.c.d.1322.11		12
63.23	odd	6		1323.2.c.d.1322.12		12
63.31	odd	6		189.2.p.d.80.1	yes	12
63.38	even	6	inner	567.2.i.f.269.6		12
63.40	odd	6		1323.2.c.d.1322.2		12
63.52	odd	6	inner	567.2.i.f.269.1		12
63.58	even	3		1323.2.c.d.1322.1		12
63.59	even	6		189.2.p.d.80.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.1	✓	12	9.5	odd	6
189.2.p.d.26.6	yes	12	9.4	even	3
189.2.p.d.80.1	yes	12	63.31	odd	6
189.2.p.d.80.6	yes	12	63.59	even	6
567.2.i.f.215.1		12	1.1	even	1	trivial
567.2.i.f.215.6		12	3.2	odd	2	inner
567.2.i.f.269.1		12	63.52	odd	6	inner
567.2.i.f.269.6		12	63.38	even	6	inner
567.2.s.f.26.1		12	9.7	even	3
567.2.s.f.26.6		12	9.2	odd	6
567.2.s.f.458.1		12	21.17	even	6
567.2.s.f.458.6		12	7.3	odd	6
1323.2.c.d.1322.1		12	63.58	even	3
1323.2.c.d.1322.2		12	63.40	odd	6
1323.2.c.d.1322.11		12	63.5	even	6
1323.2.c.d.1322.12		12	63.23	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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