LMFDB - Embedded newform 513.2.t.a.179.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(179,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.179"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.10
Character	$\chi$	$=$	513.179
Dual form			513.2.t.a.278.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.676405 q^{2} -1.54248 q^{4} +(0.120039 - 0.0693047i) q^{5} +(0.877021 + 1.51904i) q^{7} -2.39615 q^{8} +(0.0811952 - 0.0468781i) q^{10} +(4.04328 - 2.33439i) q^{11} +6.55555i q^{13} +(0.593221 + 1.02749i) q^{14} +1.46419 q^{16} +(4.06437 + 2.34656i) q^{17} +(4.35516 - 0.180615i) q^{19} +(-0.185158 + 0.106901i) q^{20} +(2.73489 - 1.57899i) q^{22} +1.08841i q^{23} +(-2.49039 + 4.31349i) q^{25} +4.43421i q^{26} +(-1.35278 - 2.34309i) q^{28} +(0.477136 - 0.826424i) q^{29} +(-5.38094 - 3.10669i) q^{31} +5.78268 q^{32} +(2.74916 + 1.58723i) q^{34} +(0.210554 + 0.121563i) q^{35} +4.68926i q^{37} +(2.94585 - 0.122169i) q^{38} +(-0.287632 + 0.166064i) q^{40} +(-3.88755 - 6.73343i) q^{41} -1.08373 q^{43} +(-6.23666 + 3.60074i) q^{44} +0.736205i q^{46} +(10.8483 + 6.26324i) q^{47} +(1.96167 - 3.39771i) q^{49} +(-1.68451 + 2.91767i) q^{50} -10.1118i q^{52} +(-1.27386 - 2.20639i) q^{53} +(0.323568 - 0.560437i) q^{55} +(-2.10147 - 3.63986i) q^{56} +(0.322737 - 0.558997i) q^{58} +(-5.51548 - 9.55309i) q^{59} +(-0.556799 + 0.964404i) q^{61} +(-3.63969 - 2.10138i) q^{62} +0.983063 q^{64} +(0.454331 + 0.786924i) q^{65} +4.42825i q^{67} +(-6.26919 - 3.61952i) q^{68} +(0.142420 + 0.0822261i) q^{70} +(-3.99931 + 6.92701i) q^{71} +(-0.561346 + 0.972280i) q^{73} +3.17184i q^{74} +(-6.71772 + 0.278594i) q^{76} +(7.09208 + 4.09461i) q^{77} -3.40591i q^{79} +(0.175760 - 0.101475i) q^{80} +(-2.62956 - 4.55452i) q^{82} +(-3.07334 + 1.77440i) q^{83} +0.650512 q^{85} -0.733037 q^{86} +(-9.68830 + 5.59354i) q^{88} +(-7.79231 - 13.4967i) q^{89} +(-9.95817 + 5.74935i) q^{91} -1.67885i q^{92} +(7.33782 + 4.23649i) q^{94} +(0.510272 - 0.323514i) q^{95} -14.5597i q^{97} +(1.32688 - 2.29823i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.676405			0.478291			0.239145	−	0.970984i	$-0.423133\pi$
$2$	0.676405			0.478291			0.239145	+	0.970984i	$0.423133\pi$
$3$		0			0
$3$		0			0
$4$	−1.54248			−0.771238
$5$	0.120039	−	0.0693047i	0.0536832	−	0.0309940i	−0.472918	−	0.881106i	$-0.656799\pi$
$5$	0.120039	−	0.0693047i	0.0536832	−	0.0309940i	0.526601	+	0.850112i	$0.323466\pi$
$6$		0			0
$7$	0.877021	+	1.51904i	0.331483	+	0.574145i	0.982803	−	0.184658i	$-0.0591178\pi$
$7$	0.877021	+	1.51904i	0.331483	+	0.574145i	−0.651320	+	0.758803i	$0.725784\pi$
$8$	−2.39615			−0.847167
$9$		0			0
$10$	0.0811952	−	0.0468781i	0.0256762	−	0.0148241i
$11$	4.04328	−	2.33439i	1.21909	−	0.703845i	0.254370	−	0.967107i	$-0.418132\pi$
$11$	4.04328	−	2.33439i	1.21909	−	0.703845i	0.964724	+	0.263262i	$0.0847985\pi$
$12$		0			0
$13$			6.55555i			1.81818i	0.416597	+	0.909091i	$0.363223\pi$
$13$			6.55555i			1.81818i	−0.416597	+	0.909091i	$0.636777\pi$
$14$	0.593221	+	1.02749i	0.158545	+	0.274608i
$15$		0			0
$16$	1.46419			0.366046
$17$	4.06437	+	2.34656i	0.985754	+	0.569125i	0.904002	−	0.427528i	$-0.140615\pi$
$17$	4.06437	+	2.34656i	0.985754	+	0.569125i	0.0817513	+	0.996653i	$0.473949\pi$
$18$		0			0
$19$	4.35516	−	0.180615i	0.999141	−	0.0414359i
$19$	4.35516	−	0.180615i	0.999141	−	0.0414359i
$20$	−0.185158	+	0.106901i	−0.0414025	+	0.0239038i
$21$		0			0
$22$	2.73489	−	1.57899i	0.583081	−	0.336642i
$23$			1.08841i			0.226949i	0.993541	+	0.113474i	$0.0361980\pi$
$23$			1.08841i			0.226949i	−0.993541	+	0.113474i	$0.963802\pi$
$24$		0			0
$25$	−2.49039	+	4.31349i	−0.498079	+	0.862698i
$26$			4.43421i			0.869620i
$27$		0			0
$28$	−1.35278	−	2.34309i	−0.255652	−	0.442802i
$29$	0.477136	−	0.826424i	0.0886019	−	0.153463i	−0.818318	−	0.574765i	$-0.805093\pi$
$29$	0.477136	−	0.826424i	0.0886019	−	0.153463i	0.906920	+	0.421302i	$0.138427\pi$
$30$		0			0
$31$	−5.38094	−	3.10669i	−0.966445	−	0.557977i	−0.0682946	−	0.997665i	$-0.521756\pi$
$31$	−5.38094	−	3.10669i	−0.966445	−	0.557977i	−0.898151	+	0.439688i	$0.855089\pi$
$32$	5.78268			1.02224
$33$		0			0
$34$	2.74916	+	1.58723i	0.471477	+	0.272207i
$35$	0.210554	+	0.121563i	0.0355901	+	0.0205480i
$36$		0			0
$37$			4.68926i			0.770909i	0.922727	+	0.385455i	$0.125955\pi$
$37$			4.68926i			0.770909i	−0.922727	+	0.385455i	$0.874045\pi$
$38$	2.94585	−	0.122169i	0.477880	−	0.0198184i
$39$		0			0
$40$	−0.287632	+	0.166064i	−0.0454786	+	0.0262571i
$41$	−3.88755	−	6.73343i	−0.607133	−	1.05158i	−0.991711	−	0.128492i	$-0.958986\pi$
$41$	−3.88755	−	6.73343i	−0.607133	−	1.05158i	0.384578	−	0.923092i	$-0.374347\pi$
$42$		0			0
$43$	−1.08373			−0.165267			−0.0826333	−	0.996580i	$-0.526333\pi$
$43$	−1.08373			−0.165267			−0.0826333	+	0.996580i	$0.526333\pi$
$44$	−6.23666	+	3.60074i	−0.940212	+	0.542832i
$45$		0			0
$46$			0.736205i			0.108548i
$47$	10.8483	+	6.26324i	1.58238	+	0.913588i	0.994511	+	0.104633i	$0.0333667\pi$
$47$	10.8483	+	6.26324i	1.58238	+	0.913588i	0.587870	+	0.808955i	$0.299967\pi$
$48$		0			0
$49$	1.96167	−	3.39771i	0.280238	−	0.485387i
$50$	−1.68451	+	2.91767i	−0.238226	+	0.412620i
$51$		0			0
$52$		−	10.1118i		−	1.40225i
$53$	−1.27386	−	2.20639i	−0.174978	−	0.303071i	0.765176	−	0.643822i	$-0.222652\pi$
$53$	−1.27386	−	2.20639i	−0.174978	−	0.303071i	−0.940154	+	0.340751i	$0.889319\pi$
$54$		0			0
$55$	0.323568	−	0.560437i	0.0436299	−	0.0755693i
$56$	−2.10147	−	3.63986i	−0.280821	−	0.486396i
$57$		0			0
$58$	0.322737	−	0.558997i	0.0423775	−	0.0733999i
$59$	−5.51548	−	9.55309i	−0.718054	−	1.24371i	−0.961770	−	0.273860i	$-0.911700\pi$
$59$	−5.51548	−	9.55309i	−0.718054	−	1.24371i	0.243715	−	0.969847i	$-0.421634\pi$
$60$		0			0
$61$	−0.556799	+	0.964404i	−0.0712908	+	0.123479i	−0.899467	−	0.436988i	$-0.856045\pi$
$61$	−0.556799	+	0.964404i	−0.0712908	+	0.123479i	0.828176	+	0.560467i	$0.189378\pi$
$62$	−3.63969	−	2.10138i	−0.462242	−	0.266875i
$63$		0			0
$64$	0.983063			0.122883
$65$	0.454331	+	0.786924i	0.0563528	+	0.0976059i
$66$		0			0
$67$			4.42825i			0.540996i	0.962721	+	0.270498i	$0.0871884\pi$
$67$			4.42825i			0.540996i	−0.962721	+	0.270498i	$0.912812\pi$
$68$	−6.26919	−	3.61952i	−0.760251	−	0.438931i
$69$		0			0
$70$	0.142420	+	0.0822261i	0.0170224	+	0.00982790i
$71$	−3.99931	+	6.92701i	−0.474631	+	0.822085i	−0.999578	−	0.0290503i	$-0.990752\pi$
$71$	−3.99931	+	6.92701i	−0.474631	+	0.822085i	0.524947	+	0.851135i	$0.324085\pi$
$72$		0			0
$73$	−0.561346	+	0.972280i	−0.0657006	+	0.113797i	−0.897005	−	0.442021i	$-0.854262\pi$
$73$	−0.561346	+	0.972280i	−0.0657006	+	0.113797i	0.831304	+	0.555818i	$0.187595\pi$
$74$			3.17184i			0.368719i
$75$		0			0
$76$	−6.71772	+	0.278594i	−0.770576	+	0.0319569i
$77$	7.09208	+	4.09461i	0.808217	+	0.466625i
$78$		0			0
$79$		−	3.40591i		−	0.383195i	−0.981474	−	0.191597i	$-0.938633\pi$
$79$		−	3.40591i		−	0.383195i	0.981474	−	0.191597i	$-0.0613668\pi$
$80$	0.175760	−	0.101475i	0.0196505	−	0.0113452i
$81$		0			0
$82$	−2.62956	−	4.55452i	−0.290386	−	0.502963i
$83$	−3.07334	+	1.77440i	−0.337343	+	0.194765i	−0.659097	−	0.752058i	$-0.729061\pi$
$83$	−3.07334	+	1.77440i	−0.337343	+	0.194765i	0.321753	+	0.946824i	$0.395728\pi$
$84$		0			0
$85$	0.650512			0.0705579
$86$	−0.733037			−0.0790454
$87$		0			0
$88$	−9.68830	+	5.59354i	−1.03278	+	0.596273i
$89$	−7.79231	−	13.4967i	−0.825983	−	1.43065i	−0.901165	−	0.433476i	$-0.857287\pi$
$89$	−7.79231	−	13.4967i	−0.825983	−	1.43065i	0.0751819	−	0.997170i	$-0.476046\pi$
$90$		0			0
$91$	−9.95817	+	5.74935i	−1.04390	+	0.602696i
$92$		−	1.67885i		−	0.175032i
$93$		0			0
$94$	7.33782	+	4.23649i	0.756838	+	0.436961i
$95$	0.510272	−	0.323514i	0.0523528	−	0.0331918i
$96$		0			0
$97$		−	14.5597i		−	1.47832i	−0.673532	−	0.739158i	$-0.735224\pi$
$97$		−	14.5597i		−	1.47832i	0.673532	−	0.739158i	$-0.264776\pi$
$98$	1.32688	−	2.29823i	0.134035	−	0.232156i
$99$		0			0
$100$	3.84137	−	6.65345i	0.384137	−	0.665345i
$101$	−6.51866	−	3.76355i	−0.648631	−	0.374487i	0.139300	−	0.990250i	$-0.455515\pi$
$101$	−6.51866	−	3.76355i	−0.648631	−	0.374487i	−0.787932	+	0.615763i	$0.788848\pi$
$102$		0			0
$103$	−0.293683	−	0.169558i	−0.0289375	−	0.0167071i	0.485461	−	0.874258i	$-0.338652\pi$
$103$	−0.293683	−	0.169558i	−0.0289375	−	0.0167071i	−0.514399	+	0.857551i	$0.671985\pi$
$104$		−	15.7081i		−	1.54030i
$105$		0			0
$106$	−0.861646	−	1.49241i	−0.0836904	−	0.144956i
$107$	11.8620			1.14674			0.573369	−	0.819297i	$-0.305636\pi$
$107$	11.8620			1.14674			0.573369	+	0.819297i	$0.305636\pi$
$108$		0			0
$109$	8.94952	+	5.16701i	0.857209	+	0.494910i	0.863077	−	0.505073i	$-0.168534\pi$
$109$	8.94952	+	5.16701i	0.857209	+	0.494910i	−0.00586793	+	0.999983i	$0.501868\pi$
$110$	0.218863	−	0.379082i	0.0208678	−	0.0361441i
$111$		0			0
$112$	1.28412	+	2.22416i	0.121338	+	0.210164i
$113$	−1.09234	+	1.89199i	−0.102759	+	0.177983i	−0.912820	−	0.408361i	$-0.866100\pi$
$113$	−1.09234	+	1.89199i	−0.102759	+	0.177983i	0.810062	+	0.586345i	$0.199434\pi$
$114$		0			0
$115$	0.0754319	+	0.130652i	0.00703406	+	0.0121834i
$116$	−0.735971	+	1.27474i	−0.0683332	+	0.118357i
$117$		0			0
$118$	−3.73070	−	6.46176i	−0.343439	−	0.594853i
$119$			8.23194i			0.754621i
$120$		0			0
$121$	5.39874	−	9.35088i	0.490794	−	0.850080i
$122$	−0.376622	+	0.652328i	−0.0340977	+	0.0590590i
$123$		0			0
$124$	8.29997	+	4.79199i	0.745360	+	0.430334i
$125$			1.38343i			0.123738i
$126$		0			0
$127$	−4.44199	+	2.56458i	−0.394163	+	0.227570i	−0.683962	−	0.729517i	$-0.739745\pi$
$127$	−4.44199	+	2.56458i	−0.394163	+	0.227570i	0.289799	+	0.957087i	$0.406411\pi$
$128$	−10.9004			−0.963469
$129$		0			0
$130$	0.307312	+	0.532279i	0.0269530	+	0.0466840i
$131$	−13.6250	+	7.86640i	−1.19042	+	0.687290i	−0.958402	−	0.285421i	$-0.907867\pi$
$131$	−13.6250	+	7.86640i	−1.19042	+	0.687290i	−0.232019	+	0.972711i	$0.574533\pi$
$132$		0			0
$133$	4.09392	+	6.45727i	0.354988	+	0.559917i
$134$			2.99529i			0.258753i
$135$		0			0
$136$	−9.73883	−	5.62271i	−0.835097	−	0.482144i
$137$	2.84441	+	1.64222i	0.243014	+	0.140304i	0.616561	−	0.787307i	$-0.288525\pi$
$137$	2.84441	+	1.64222i	0.243014	+	0.140304i	−0.373547	+	0.927611i	$0.621859\pi$
$138$		0			0
$139$	16.1681			1.37136			0.685681	−	0.727902i	$-0.259505\pi$
$139$	16.1681			1.37136			0.685681	+	0.727902i	$0.259505\pi$
$140$	−0.324774	−	0.187509i	−0.0274485	−	0.0158474i
$141$		0			0
$142$	−2.70515	+	4.68546i	−0.227011	+	0.393195i
$143$	15.3032	+	26.5059i	1.27972	+	2.21654i
$144$		0			0
$145$		−	0.132271i		−	0.0109845i
$146$	−0.379698	+	0.657655i	−0.0314240	+	0.0544279i
$147$		0			0
$148$		−	7.23307i		−	0.594555i
$149$	5.19597	−	2.99989i	0.425670	−	0.245761i	−0.271830	−	0.962345i	$-0.587629\pi$
$149$	5.19597	−	2.99989i	0.425670	−	0.245761i	0.697500	+	0.716584i	$0.254296\pi$
$150$		0			0
$151$	10.8923	−	6.28866i	0.886401	−	0.511764i	0.0136375	−	0.999907i	$-0.495659\pi$
$151$	10.8923	−	6.28866i	0.886401	−	0.511764i	0.872764	+	0.488143i	$0.162326\pi$
$152$	−10.4356	+	0.432780i	−0.846439	+	0.0351031i
$153$		0			0
$154$	4.79712	+	2.76962i	0.386563	+	0.223182i
$155$	−0.861232			−0.0691759
$156$		0			0
$157$	−7.88036	−	13.6492i	−0.628922	−	1.08932i	−0.987768	−	0.155928i	$-0.950163\pi$
$157$	−7.88036	−	13.6492i	−0.628922	−	1.08932i	0.358847	−	0.933396i	$-0.383170\pi$
$158$		−	2.30377i		−	0.183278i
$159$		0			0
$160$	0.694149	−	0.400767i	0.0548773	−	0.0316834i
$161$	−1.65334	+	0.954557i	−0.130302	+	0.0752297i
$162$		0			0
$163$	−6.65366			−0.521155			−0.260578	−	0.965453i	$-0.583913\pi$
$163$	−6.65366			−0.521155			−0.260578	+	0.965453i	$0.583913\pi$
$164$	5.99645	+	10.3861i	0.468244	+	0.811022i
$165$		0			0
$166$	−2.07882	+	1.20021i	−0.161348	+	0.0931544i
$167$	−4.21808			−0.326404			−0.163202	−	0.986593i	$-0.552182\pi$
$167$	−4.21808			−0.326404			−0.163202	+	0.986593i	$0.552182\pi$
$168$		0			0
$169$	−29.9752			−2.30579
$170$	0.440009			0.0337472
$171$		0			0
$172$	1.67162			0.127460
$173$	−10.8955			−0.828372			−0.414186	−	0.910192i	$-0.635934\pi$
$173$	−10.8955			−0.828372			−0.414186	+	0.910192i	$0.635934\pi$
$174$		0			0
$175$	−8.73651			−0.660418
$176$	5.92011	−	3.41798i	0.446245	−	0.257640i
$177$		0			0
$178$	−5.27076	−	9.12922i	−0.395060	−	0.684264i
$179$	5.16954			0.386390			0.193195	−	0.981160i	$-0.438115\pi$
$179$	5.16954			0.386390			0.193195	+	0.981160i	$0.438115\pi$
$180$		0			0
$181$	4.70681	−	2.71748i	0.349855	−	0.201989i	−0.314767	−	0.949169i	$-0.601926\pi$
$181$	4.70681	−	2.71748i	0.349855	−	0.201989i	0.664621	+	0.747180i	$0.268593\pi$
$182$	−6.73576	+	3.88889i	−0.499288	+	0.288264i
$183$		0			0
$184$		−	2.60799i		−	0.192264i
$185$	0.324988	+	0.562895i	0.0238936	+	0.0413849i
$186$		0			0
$187$	21.9112			1.60230
$188$	−16.7332	−	9.66091i	−1.22039	−	0.704594i
$189$		0			0
$190$	0.345151	−	0.218826i	0.0250399	−	0.0158753i
$191$	10.8662	−	6.27361i	0.786251	−	0.453942i	−0.0523898	−	0.998627i	$-0.516684\pi$
$191$	10.8662	−	6.27361i	0.786251	−	0.453942i	0.838641	+	0.544684i	$0.183350\pi$
$192$		0			0
$193$	−0.103288	+	0.0596333i	−0.00743482	+	0.00429250i	−0.503713	−	0.863871i	$-0.668033\pi$
$193$	−0.103288	+	0.0596333i	−0.00743482	+	0.00429250i	0.496278	+	0.868164i	$0.334700\pi$
$194$		−	9.84827i		−	0.707065i
$195$		0			0
$196$	−3.02583	+	5.24089i	−0.216131	+	0.374349i
$197$		−	14.8993i		−	1.06153i	−0.847519	−	0.530765i	$-0.821905\pi$
$197$		−	14.8993i		−	1.06153i	0.847519	−	0.530765i	$-0.178095\pi$
$198$		0			0
$199$	3.99752	+	6.92391i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752120\pi$
$199$	3.99752	+	6.92391i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$200$	5.96735	−	10.3358i	0.421956	−	0.730849i
$201$		0			0
$202$	−4.40926	−	2.54568i	−0.310234	−	0.179114i
$203$	1.67383			0.117480
$204$		0			0
$205$	−0.933316	−	0.538851i	−0.0651856	−	0.0376350i
$206$	−0.198649	−	0.114690i	−0.0138405	−	0.00799083i
$207$		0			0
$208$			9.59854i			0.665539i
$209$	17.1875	−	10.8969i	1.18888	−	0.753754i
$210$		0			0
$211$	10.1008	−	5.83168i	0.695366	−	0.401470i	−0.110253	−	0.993904i	$-0.535166\pi$
$211$	10.1008	−	5.83168i	0.695366	−	0.401470i	0.805619	+	0.592434i	$0.201833\pi$
$212$	1.96490	+	3.40331i	0.134950	+	0.233740i
$213$		0			0
$214$	8.02348			0.548474
$215$	−0.130090	+	0.0751073i	−0.00887204	+	0.00512227i
$216$		0			0
$217$		−	10.8985i		−	0.739840i
$218$	6.05350	+	3.49499i	0.409995	+	0.236711i
$219$		0			0
$220$	−0.499096	+	0.864460i	−0.0336491	+	0.0582819i
$221$	−15.3830	+	26.6442i	−1.03477	+	1.79228i
$222$		0			0
$223$			20.8438i			1.39581i	0.716192	+	0.697903i	$0.245884\pi$
$223$			20.8438i			1.39581i	−0.716192	+	0.697903i	$0.754116\pi$
$224$	5.07153	+	8.78415i	0.338856	+	0.586916i
$225$		0			0
$226$	−0.738865	+	1.27975i	−0.0491486	+	0.0851278i
$227$	−11.9369	−	20.6753i	−0.792279	−	1.37227i	−0.924553	−	0.381054i	$-0.875561\pi$
$227$	−11.9369	−	20.6753i	−0.792279	−	1.37227i	0.132274	−	0.991213i	$-0.457772\pi$
$228$		0			0
$229$	−8.94882	+	15.4998i	−0.591355	+	1.02426i	0.402695	+	0.915334i	$0.368073\pi$
$229$	−8.94882	+	15.4998i	−0.591355	+	1.02426i	−0.994050	+	0.108923i	$0.965260\pi$
$230$	0.0510225	+	0.0883736i	0.00336432	+	0.00582718i
$231$		0			0
$232$	−1.14329	+	1.98023i	−0.0750606	+	0.130009i
$233$	1.17373	+	0.677654i	0.0768936	+	0.0443946i	0.537954	−	0.842974i	$-0.319197\pi$
$233$	1.17373	+	0.677654i	0.0768936	+	0.0443946i	−0.461060	+	0.887369i	$0.652531\pi$
$234$		0			0
$235$	1.73629			0.113263
$236$	8.50750	+	14.7354i	0.553791	+	0.959194i
$237$		0			0
$238$			5.56812i			0.360928i
$239$	6.15584	+	3.55408i	0.398188	+	0.229894i	0.685702	−	0.727882i	$-0.259495\pi$
$239$	6.15584	+	3.55408i	0.398188	+	0.229894i	−0.287514	+	0.957777i	$0.592829\pi$
$240$		0			0
$241$	14.3678	+	8.29527i	0.925513	+	0.534345i	0.885390	−	0.464849i	$-0.153892\pi$
$241$	14.3678	+	8.29527i	0.925513	+	0.534345i	0.0401234	+	0.999195i	$0.487225\pi$
$242$	3.65173	−	6.32499i	0.234742	−	0.406585i
$243$		0			0
$244$	0.858849	−	1.48757i	0.0549822	−	0.0952319i
$245$		−	0.543812i		−	0.0347429i
$246$		0			0
$247$	1.18403	+	28.5504i	0.0753380	+	1.81662i
$248$	12.8935	+	7.44408i	0.818740	+	0.472700i
$249$		0			0
$250$			0.935760i			0.0591827i
$251$	4.43373	−	2.55982i	0.279855	−	0.161574i	−0.353503	−	0.935433i	$-0.615010\pi$
$251$	4.43373	−	2.55982i	0.279855	−	0.161574i	0.633358	+	0.773859i	$0.281676\pi$
$252$		0			0
$253$	2.54077	+	4.40074i	0.159737	+	0.276672i
$254$	−3.00458	+	1.73470i	−0.188524	+	0.108845i
$255$		0			0
$256$	−9.33922			−0.583701
$257$	3.35771			0.209448			0.104724	−	0.994501i	$-0.466604\pi$
$257$	3.35771			0.209448			0.104724	+	0.994501i	$0.466604\pi$
$258$		0			0
$259$	−7.12319	+	4.11258i	−0.442614	+	0.255543i
$260$	−0.700794	−	1.21381i	−0.0434614	−	0.0752774i
$261$		0			0
$262$	−9.21602	+	5.32087i	−0.569367	+	0.328724i
$263$		−	28.1184i		−	1.73385i	−0.498437	−	0.866926i	$-0.666092\pi$
$263$		−	28.1184i		−	1.73385i	0.498437	−	0.866926i	$-0.333908\pi$
$264$		0			0
$265$	−0.305827	−	0.176569i	−0.0187868	−	0.0108466i
$266$	2.76915	+	4.36773i	0.169788	+	0.267803i
$267$		0			0
$268$		−	6.83046i		−	0.417237i
$269$	4.97903	−	8.62394i	0.303577	−	0.525811i	−0.673366	−	0.739309i	$-0.735152\pi$
$269$	4.97903	−	8.62394i	0.303577	−	0.525811i	0.976944	+	0.213498i	$0.0684857\pi$
$270$		0			0
$271$	2.04225	−	3.53729i	0.124058	−	0.214875i	−0.797306	−	0.603575i	$-0.793742\pi$
$271$	2.04225	−	3.53729i	0.124058	−	0.214875i	0.921364	+	0.388700i	$0.127076\pi$
$272$	5.95099	+	3.43580i	0.360832	+	0.208326i
$273$		0			0
$274$	1.92397	+	1.11081i	0.116232	+	0.0671063i
$275$			23.2542i			1.40228i
$276$		0			0
$277$	−7.84697	−	13.5914i	−0.471479	−	0.816626i	0.527989	−	0.849251i	$-0.322946\pi$
$277$	−7.84697	−	13.5914i	−0.471479	−	0.816626i	−0.999468	+	0.0326258i	$0.989613\pi$
$278$	10.9362			0.655909
$279$		0			0
$280$	−0.504519	−	0.291284i	−0.0301508	−	0.0174075i
$281$	−3.42719	+	5.93607i	−0.204449	+	0.354117i	−0.949957	−	0.312380i	$-0.898874\pi$
$281$	−3.42719	+	5.93607i	−0.204449	+	0.354117i	0.745508	+	0.666497i	$0.232207\pi$
$282$		0			0
$283$	−0.278438	−	0.482268i	−0.0165514	−	0.0286679i	0.857631	−	0.514265i	$-0.171935\pi$
$283$	−0.278438	−	0.482268i	−0.0165514	−	0.0286679i	−0.874182	+	0.485598i	$0.838602\pi$
$284$	6.16884	−	10.6847i	0.366053	−	0.634023i
$285$		0			0
$286$	10.3512	+	17.9287i	0.612077	+	1.06015i
$287$	6.81892	−	11.8107i	0.402508	−	0.697164i
$288$		0			0
$289$	2.51272	+	4.35215i	0.147807	+	0.256009i
$290$		−	0.0894689i		−	0.00525379i
$291$		0			0
$292$	0.865863	−	1.49972i	0.0506708	−	0.0877644i
$293$	2.27576	−	3.94172i	0.132951	−	0.230278i	−0.791862	−	0.610700i	$-0.790888\pi$
$293$	2.27576	−	3.94172i	0.132951	−	0.230278i	0.924813	+	0.380422i	$0.124221\pi$
$294$		0			0
$295$	−1.32415	−	0.764498i	−0.0770949	−	0.0445108i
$296$		−	11.2362i		−	0.653088i
$297$		0			0
$298$	3.51458	−	2.02914i	0.203594	−	0.117545i
$299$	−7.13512			−0.412635
$300$		0			0
$301$	−0.950449	−	1.64623i	−0.0547830	−	0.0948869i
$302$	7.36759	−	4.25368i	0.423957	−	0.244772i
$303$		0			0
$304$	6.37676	−	0.264454i	0.365732	−	0.0151675i
$305$			0.154355i			0.00883835i
$306$		0			0
$307$	6.39989	+	3.69498i	0.365261	+	0.210883i	0.671386	−	0.741108i	$-0.265699\pi$
$307$	6.39989	+	3.69498i	0.365261	+	0.210883i	−0.306125	+	0.951991i	$0.599033\pi$
$308$	−10.9394	−	6.31584i	−0.623328	−	0.359879i
$309$		0			0
$310$	−0.582542			−0.0330862
$311$	26.1635	+	15.1055i	1.48360	+	0.856556i	0.999826	−	0.0186380i	$-0.00593299\pi$
$311$	26.1635	+	15.1055i	1.48360	+	0.856556i	0.483772	+	0.875194i	$0.339266\pi$
$312$		0			0
$313$	−0.632333	+	1.09523i	−0.0357416	+	0.0619062i	−0.883343	−	0.468727i	$-0.844713\pi$
$313$	−0.632333	+	1.09523i	−0.0357416	+	0.0619062i	0.847601	+	0.530634i	$0.178046\pi$
$314$	−5.33032	−	9.23238i	−0.300807	−	0.521013i
$315$		0			0
$316$			5.25353i			0.295534i
$317$	−7.05696	+	12.2230i	−0.396358	+	0.686513i	−0.993274	−	0.115792i	$-0.963060\pi$
$317$	−7.05696	+	12.2230i	−0.396358	+	0.686513i	0.596915	+	0.802304i	$0.296393\pi$
$318$		0			0
$319$		−	4.45528i		−	0.249448i
$320$	0.118006	−	0.0681309i	0.00659675	−	0.00380863i
$321$		0			0
$322$	−1.11833	+	0.645667i	−0.0623220	+	0.0359816i
$323$	18.1248	+	9.48556i	1.00849	+	0.527791i
$324$		0			0
$325$	−28.2773	−	16.3259i	−1.56854	−	0.905598i
$326$	−4.50057			−0.249264
$327$		0			0
$328$	9.31514	+	16.1343i	0.514342	+	0.890867i
$329$			21.9720i			1.21135i
$330$		0			0
$331$	−15.7116	+	9.07108i	−0.863586	+	0.498592i	−0.865212	−	0.501407i	$-0.832816\pi$
$331$	−15.7116	+	9.07108i	−0.863586	+	0.498592i	0.00162545	+	0.999999i	$0.499483\pi$
$332$	4.74056	−	2.73696i	0.260172	−	0.150210i
$333$		0			0
$334$	−2.85313			−0.156116
$335$	0.306898	+	0.531563i	0.0167676	+	0.0290424i
$336$		0			0
$337$	5.33828	−	3.08206i	0.290795	−	0.167890i	−0.347505	−	0.937678i	$-0.612971\pi$
$337$	5.33828	−	3.08206i	0.290795	−	0.167890i	0.638300	+	0.769788i	$0.279638\pi$
$338$	−20.2754			−1.10284
$339$		0			0
$340$	−1.00340			−0.0544169
$341$	−29.0089			−1.57092
$342$		0			0
$343$	19.1600			1.03454
$344$	2.59677			0.140008
$345$		0			0
$346$	−7.36979			−0.396202
$347$	13.9949	−	8.07999i	0.751288	−	0.433756i	−0.0748709	−	0.997193i	$-0.523854\pi$
$347$	13.9949	−	8.07999i	0.751288	−	0.433756i	0.826159	+	0.563437i	$0.190521\pi$
$348$		0			0
$349$	11.5382	+	19.9847i	0.617624	+	1.06976i	0.989918	+	0.141641i	$0.0452379\pi$
$349$	11.5382	+	19.9847i	0.617624	+	1.06976i	−0.372294	+	0.928115i	$0.621429\pi$
$350$	−5.90942			−0.315872
$351$		0			0
$352$	23.3810	−	13.4990i	1.24621	−	0.719500i
$353$	−26.3912	+	15.2370i	−1.40466	+	0.810982i	−0.994867	−	0.101196i	$-0.967733\pi$
$353$	−26.3912	+	15.2370i	−1.40466	+	0.810982i	−0.409795	+	0.912178i	$0.634400\pi$
$354$		0			0
$355$			1.10868i			0.0588428i
$356$	12.0195	+	20.8183i	0.637030	+	1.10337i
$357$		0			0
$358$	3.49670			0.184806
$359$	1.17054	+	0.675809i	0.0617785	+	0.0356679i	0.530571	−	0.847640i	$-0.321977\pi$
$359$	1.17054	+	0.675809i	0.0617785	+	0.0356679i	−0.468793	+	0.883308i	$0.655311\pi$
$360$		0			0
$361$	18.9348	−	1.57321i	0.996566	−	0.0828006i
$362$	3.18371	−	1.83812i	0.167332	−	0.0966093i
$363$		0			0
$364$	15.3602	−	8.86824i	0.805096	−	0.464822i
$365$			0.155616i			0.00814530i
$366$		0			0
$367$	−0.793706	+	1.37474i	−0.0414311	+	0.0717608i	−0.885997	−	0.463690i	$-0.846525\pi$
$367$	−0.793706	+	1.37474i	−0.0414311	+	0.0717608i	0.844566	+	0.535451i	$0.179858\pi$
$368$			1.59363i			0.0830739i
$369$		0			0
$370$	0.219823	+	0.380745i	0.0114281	+	0.0197940i
$371$	2.23440	−	3.87010i	0.116004	−	0.200926i
$372$		0			0
$373$	−26.0140	−	15.0192i	−1.34695	−	0.777663i	−0.359135	−	0.933285i	$-0.616928\pi$
$373$	−26.0140	−	15.0192i	−1.34695	−	0.777663i	−0.987817	+	0.155622i	$0.950262\pi$
$374$	14.8208			0.766366
$375$		0			0
$376$	−25.9940	−	15.0077i	−1.34054	−	0.773961i
$377$	5.41766	+	3.12789i	0.279024	+	0.161095i
$378$		0			0
$379$		−	20.4900i		−	1.05250i	−0.850330	−	0.526250i	$-0.823598\pi$
$379$		−	20.4900i		−	1.05250i	0.850330	−	0.526250i	$-0.176402\pi$
$380$	−0.787083	+	0.499012i	−0.0403765	+	0.0255988i
$381$		0			0
$382$	7.34996	−	4.24350i	0.376057	−	0.217116i
$383$	−14.8650	−	25.7469i	−0.759565	−	1.31561i	−0.943073	−	0.332587i	$-0.892078\pi$
$383$	−14.8650	−	25.7469i	−0.759565	−	1.31561i	0.183507	−	0.983018i	$-0.441255\pi$
$384$		0			0
$385$	1.13510			0.0578503
$386$	−0.0698644	+	0.0403362i	−0.00355600	+	0.00205306i
$387$		0			0
$388$			22.4580i			1.14013i
$389$	−14.8922	−	8.59803i	−0.755066	−	0.435938i	0.0724554	−	0.997372i	$-0.476916\pi$
$389$	−14.8922	−	8.59803i	−0.755066	−	0.435938i	−0.827521	+	0.561434i	$0.810250\pi$
$390$		0			0
$391$	−2.55402	+	4.42369i	−0.129162	+	0.223716i
$392$	−4.70045	+	8.14142i	−0.237409	+	0.411204i
$393$		0			0
$394$		−	10.0779i		−	0.507720i
$395$	−0.236046	−	0.408843i	−0.0118767	−	0.0205711i
$396$		0			0
$397$	−12.1112	+	20.9772i	−0.607844	+	1.05282i	0.383751	+	0.923437i	$0.374632\pi$
$397$	−12.1112	+	20.9772i	−0.607844	+	1.05282i	−0.991595	+	0.129380i	$0.958701\pi$
$398$	2.70394	+	4.68337i	0.135536	+	0.234756i
$399$		0			0
$400$	−3.64640	+	6.31575i	−0.182320	+	0.315787i
$401$	−8.70752	−	15.0819i	−0.434833	−	0.753153i	0.562449	−	0.826832i	$-0.309859\pi$
$401$	−8.70752	−	15.0819i	−0.434833	−	0.753153i	−0.997282	+	0.0736792i	$0.976526\pi$
$402$		0			0
$403$	20.3660	−	35.2750i	1.01450	−	1.75717i
$404$	10.0549	+	5.80519i	0.500249	+	0.288819i
$405$		0			0
$406$	1.13219			0.0561896
$407$	10.9465	+	18.9600i	0.542600	+	0.939811i
$408$		0			0
$409$		−	23.3316i		−	1.15367i	−0.816859	−	0.576837i	$-0.804287\pi$
$409$		−	23.3316i		−	1.15367i	0.816859	−	0.576837i	$-0.195713\pi$
$410$	−0.631300	−	0.364481i	−0.0311777	−	0.0180004i
$411$		0			0
$412$	0.453000	+	0.261539i	0.0223177	+	0.0128851i
$413$	9.67438	−	16.7565i	0.476045	−	0.824535i
$414$		0			0
$415$	−0.245948	+	0.425994i	−0.0120731	+	0.0209112i
$416$			37.9086i			1.85862i
$417$		0			0
$418$	11.6257	−	7.37072i	0.568632	−	0.360514i
$419$	−6.86848	−	3.96552i	−0.335547	−	0.193728i	0.322754	−	0.946483i	$-0.395391\pi$
$419$	−6.86848	−	3.96552i	−0.335547	−	0.193728i	−0.658301	+	0.752755i	$0.728725\pi$
$420$		0			0
$421$		−	28.2153i		−	1.37513i	−0.726123	−	0.687565i	$-0.758680\pi$
$421$		−	28.2153i		−	1.37513i	0.726123	−	0.687565i	$-0.241320\pi$
$422$	6.83221	−	3.94458i	0.332587	−	0.192019i
$423$		0			0
$424$	3.05236	+	5.28684i	0.148236	+	0.256752i
$425$	−20.2437	+	11.6877i	−0.981966	+	0.566938i
$426$		0			0
$427$	−1.95330			−0.0945267
$428$	−18.2968			−0.884408
$429$		0			0
$430$	−0.0879933	+	0.0508029i	−0.00424341	+	0.00244994i
$431$	3.39423	+	5.87899i	0.163494	+	0.283181i	0.936120	−	0.351682i	$-0.114390\pi$
$431$	3.39423	+	5.87899i	0.163494	+	0.283181i	−0.772625	+	0.634863i	$0.781057\pi$
$432$		0			0
$433$	29.7286	−	17.1638i	1.42866	−	0.824839i	0.431648	−	0.902042i	$-0.357932\pi$
$433$	29.7286	−	17.1638i	1.42866	−	0.824839i	0.997015	+	0.0772030i	$0.0245990\pi$
$434$		−	7.37181i		−	0.353858i
$435$		0			0
$436$	−13.8044	−	7.96999i	−0.661112	−	0.381693i
$437$	0.196583	+	4.74019i	0.00940384	+	0.226754i
$438$		0			0
$439$		−	13.8023i		−	0.658747i	−0.944200	−	0.329373i	$-0.893163\pi$
$439$		−	13.8023i		−	0.658747i	0.944200	−	0.329373i	$-0.106837\pi$
$440$	−0.775318	+	1.34289i	−0.0369618	+	0.0640198i
$441$		0			0
$442$	−10.4051	+	18.0222i	−0.494922	+	0.857231i
$443$	−23.3421	−	13.4766i	−1.10902	−	0.640292i	−0.170444	−	0.985367i	$-0.554520\pi$
$443$	−23.3421	−	13.4766i	−1.10902	−	0.640292i	−0.938575	+	0.345075i	$0.887853\pi$
$444$		0			0
$445$	−1.87077	−	1.08009i	−0.0886829	−	0.0512011i
$446$			14.0989i			0.667601i
$447$		0			0
$448$	0.862167	+	1.49332i	0.0407335	+	0.0705526i
$449$	1.78199			0.0840972			0.0420486	−	0.999116i	$-0.486612\pi$
$449$	1.78199			0.0840972			0.0420486	+	0.999116i	$0.486612\pi$
$450$		0			0
$451$	−31.4369	−	18.1501i	−1.48030	−	0.854654i
$452$	1.68491	−	2.91835i	0.0792515	−	0.137268i
$453$		0			0
$454$	−8.07417	−	13.9849i	−0.378940	−	0.656343i
$455$	−0.796915	+	1.38030i	−0.0373599	+	0.0647093i
$456$		0			0
$457$	−5.41688	−	9.38231i	−0.253391	−	0.438886i	0.711066	−	0.703125i	$-0.248213\pi$
$457$	−5.41688	−	9.38231i	−0.253391	−	0.438886i	−0.964457	+	0.264239i	$0.914879\pi$
$458$	−6.05303	+	10.4842i	−0.282839	+	0.489892i
$459$		0			0
$460$	−0.116352	−	0.201527i	−0.00542494	−	0.00939626i
$461$		−	20.7337i		−	0.965665i	−0.875713	−	0.482833i	$-0.839608\pi$
$461$		−	20.7337i		−	0.965665i	0.875713	−	0.482833i	$-0.160392\pi$
$462$		0			0
$463$	−13.1769	+	22.8231i	−0.612384	+	1.06068i	0.378453	+	0.925620i	$0.376456\pi$
$463$	−13.1769	+	22.8231i	−0.612384	+	1.06068i	−0.990837	+	0.135060i	$0.956877\pi$
$464$	0.698616	−	1.21004i	0.0324324	−	0.0561746i
$465$		0			0
$466$	0.793917	+	0.458368i	0.0367775	+	0.0212335i
$467$		−	12.0210i		−	0.556265i	−0.960543	−	0.278133i	$-0.910285\pi$
$467$		−	12.0210i		−	0.556265i	0.960543	−	0.278133i	$-0.0897155\pi$
$468$		0			0
$469$	−6.72670	+	3.88366i	−0.310610	+	0.179331i
$470$	1.17444			0.0541727
$471$		0			0
$472$	13.2159	+	22.8906i	0.608312	+	1.05363i
$473$	−4.38180	+	2.52983i	−0.201475	+	0.116322i
$474$		0			0
$475$	−10.0670	+	19.2357i	−0.461904	+	0.882595i
$476$		−	12.6976i		−	0.581992i
$477$		0			0
$478$	4.16384	+	2.40400i	0.190450	+	0.109956i
$479$	−30.4077	−	17.5559i	−1.38936	−	0.802149i	−0.396119	−	0.918199i	$-0.629643\pi$
$479$	−30.4077	−	17.5559i	−1.38936	−	0.802149i	−0.993243	+	0.116051i	$0.962977\pi$
$480$		0			0
$481$	−30.7407			−1.40165
$482$	9.71847	+	5.61096i	0.442664	+	0.255572i
$483$		0			0
$484$	−8.32742	+	14.4235i	−0.378519	+	0.655614i
$485$	−1.00906	−	1.74774i	−0.0458189	−	0.0793607i
$486$		0			0
$487$			14.1105i			0.639409i	0.947517	+	0.319705i	$0.103584\pi$
$487$			14.1105i			0.639409i	−0.947517	+	0.319705i	$0.896416\pi$
$488$	1.33417	−	2.31086i	0.0603952	−	0.104608i
$489$		0			0
$490$		−	0.367837i		−	0.0166172i
$491$	25.6095	−	14.7857i	1.15574	−	0.667267i	0.205461	−	0.978665i	$-0.434130\pi$
$491$	25.6095	−	14.7857i	1.15574	−	0.667267i	0.950280	+	0.311398i	$0.100797\pi$
$492$		0			0
$493$	3.87851	−	2.23926i	0.174679	−	0.100851i
$494$	0.800884	+	19.3117i	0.0360335	+	0.868873i
$495$		0			0
$496$	−7.87869	−	4.54877i	−0.353764	−	0.204246i
$497$	−14.0299			−0.629327
$498$		0			0
$499$	17.8745	+	30.9595i	0.800172	+	1.38594i	0.919502	+	0.393084i	$0.128592\pi$
$499$	17.8745	+	30.9595i	0.800172	+	1.38594i	−0.119330	+	0.992855i	$0.538075\pi$
$500$		−	2.13391i		−	0.0954314i
$501$		0			0
$502$	2.99900	−	1.73147i	0.133852	−	0.0772794i
$503$	3.21576	−	1.85662i	0.143384	−	0.0827826i	−0.426592	−	0.904444i	$-0.640286\pi$
$503$	3.21576	−	1.85662i	0.143384	−	0.0827826i	0.569976	+	0.821662i	$0.306953\pi$
$504$		0			0
$505$	−1.04333			−0.0464275
$506$	1.71859	+	2.97668i	0.0764006	+	0.132330i
$507$		0			0
$508$	6.85166	−	3.95581i	0.303993	−	0.175511i
$509$	−34.9419			−1.54877			−0.774386	−	0.632714i	$-0.781941\pi$
$509$	−34.9419			−1.54877			−0.774386	+	0.632714i	$0.781941\pi$
$510$		0			0
$511$	−1.96925			−0.0871145
$512$	15.4837			0.684291
$513$		0			0
$514$	2.27117			0.100177
$515$	−0.0470047			−0.00207128
$516$		0			0
$517$	58.4834			2.57210
$518$	−4.81816	+	2.78177i	−0.211698	+	0.122224i
$519$		0			0
$520$	−1.08864	−	1.88559i	−0.0477402	−	0.0826884i
$521$	−39.1773			−1.71639			−0.858195	−	0.513324i	$-0.828414\pi$
$521$	−39.1773			−1.71639			−0.858195	+	0.513324i	$0.828414\pi$
$522$		0			0
$523$	−35.3599	+	20.4151i	−1.54618	+	0.892689i	−0.547754	+	0.836639i	$0.684517\pi$
$523$	−35.3599	+	20.4151i	−1.54618	+	0.892689i	−0.998428	+	0.0560491i	$0.982150\pi$
$524$	21.0162	−	12.1337i	0.918099	−	0.530064i
$525$		0			0
$526$		−	19.0194i		−	0.829285i
$527$	−14.5801	−	25.2534i	−0.635118	−	1.10006i
$528$		0			0
$529$	21.8154			0.948494
$530$	−0.206863	−	0.119432i	−0.00898554	−	0.00518780i
$531$		0			0
$532$	−6.31478	−	9.96019i	−0.273780	−	0.431829i
$533$	44.1413	−	25.4850i	1.91197	−	1.10388i
$534$		0			0
$535$	1.42390	−	0.822089i	0.0615606	−	0.0355420i
$536$		−	10.6107i		−	0.458314i
$537$		0			0
$538$	3.36784	−	5.83328i	0.145198	−	0.251490i
$539$		−	18.3172i		−	0.788977i
$540$		0			0
$541$	−14.5634	−	25.2245i	−0.626129	−	1.08449i	−0.988321	−	0.152384i	$-0.951305\pi$
$541$	−14.5634	−	25.2245i	−0.626129	−	1.08449i	0.362192	−	0.932104i	$-0.382028\pi$
$542$	1.38139	−	2.39264i	0.0593358	−	0.102773i
$543$		0			0
$544$	23.5029	+	13.5694i	1.00768	+	0.581784i
$545$	1.43239			0.0613569
$546$		0			0
$547$	−15.7898	−	9.11626i	−0.675124	−	0.389783i	0.122891	−	0.992420i	$-0.460783\pi$
$547$	−15.7898	−	9.11626i	−0.675124	−	0.389783i	−0.798015	+	0.602637i	$0.794117\pi$
$548$	−4.38744	−	2.53309i	−0.187422	−	0.108208i
$549$		0			0
$550$			15.7292i			0.670697i
$551$	1.92874	−	3.68538i	0.0821670	−	0.157003i
$552$		0			0
$553$	5.17373	−	2.98705i	0.220009	−	0.127022i
$554$	−5.30773	−	9.19326i	−0.225504	−	0.390584i
$555$		0			0
$556$	−24.9389			−1.05765
$557$	30.1772	−	17.4228i	1.27865	−	0.738230i	0.302051	−	0.953292i	$-0.402329\pi$
$557$	30.1772	−	17.4228i	1.27865	−	0.738230i	0.976600	+	0.215062i	$0.0689955\pi$
$558$		0			0
$559$		−	7.10441i		−	0.300485i
$560$	0.308290	+	0.177991i	0.0130276	+	0.00752151i
$561$		0			0
$562$	−2.31817	+	4.01519i	−0.0977862	+	0.169371i
$563$	−13.2981	+	23.0329i	−0.560446	+	0.970722i	0.437011	+	0.899456i	$0.356037\pi$
$563$	−13.2981	+	23.0329i	−0.560446	+	0.970722i	−0.997457	+	0.0712655i	$0.977296\pi$
$564$		0			0
$565$			0.302818i			0.0127396i
$566$	−0.188337	−	0.326209i	−0.00791638	−	0.0137116i
$567$		0			0
$568$	9.58294	−	16.5981i	0.402091	−	0.696442i
$569$	14.6846	+	25.4344i	0.615610	+	1.06627i	0.990277	+	0.139108i	$0.0444235\pi$
$569$	14.6846	+	25.4344i	0.615610	+	1.06627i	−0.374668	+	0.927159i	$0.622243\pi$
$570$		0			0
$571$	0.947842	−	1.64171i	0.0396660	−	0.0687035i	−0.845511	−	0.533958i	$-0.820704\pi$
$571$	0.947842	−	1.64171i	0.0396660	−	0.0687035i	0.885177	+	0.465255i	$0.154037\pi$
$572$	−23.6048	−	40.8847i	−0.986967	−	1.70948i
$573$		0			0
$574$	4.61235	−	7.98882i	0.192516	−	0.333447i
$575$	−4.69484	−	2.71057i	−0.195788	−	0.113038i
$576$		0			0
$577$	15.2421			0.634537			0.317268	−	0.948336i	$-0.397234\pi$
$577$	15.2421			0.634537			0.317268	+	0.948336i	$0.397234\pi$
$578$	1.69961	+	2.94382i	0.0706946	+	0.122447i
$579$		0			0
$580$			0.204025i			0.00847168i
$581$	−5.39077	−	3.11236i	−0.223647	−	0.129123i
$582$		0			0
$583$	−10.3011	−	5.94737i	−0.426630	−	0.246315i
$584$	1.34507	−	2.32973i	0.0556594	−	0.0964049i
$585$		0			0
$586$	1.53933	−	2.66620i	0.0635892	−	0.110140i
$587$			41.8816i			1.72864i	0.502943	+	0.864319i	$0.332250\pi$
$587$			41.8816i			1.72864i	−0.502943	+	0.864319i	$0.667750\pi$
$588$		0			0
$589$	−23.9959	−	12.5582i	−0.988736	−	0.517453i
$590$	−0.895661	−	0.517110i	−0.0368738	−	0.0212891i
$591$		0			0
$592$			6.86594i			0.282189i
$593$	−6.19893	+	3.57896i	−0.254560	+	0.146970i	−0.621850	−	0.783136i	$-0.713619\pi$
$593$	−6.19893	+	3.57896i	−0.254560	+	0.146970i	0.367291	+	0.930106i	$0.380285\pi$
$594$		0			0
$595$	0.570512	+	0.988156i	0.0233887	+	0.0405105i
$596$	−8.01465	+	4.62726i	−0.328293	+	0.189540i
$597$		0			0
$598$	−4.82623			−0.197359
$599$	6.23274			0.254663			0.127331	−	0.991860i	$-0.459359\pi$
$599$	6.23274			0.254663			0.127331	+	0.991860i	$0.459359\pi$
$600$		0			0
$601$	−19.8585	+	11.4653i	−0.810044	+	0.467679i	−0.846971	−	0.531639i	$-0.821576\pi$
$601$	−19.8585	+	11.4653i	−0.810044	+	0.467679i	0.0369272	+	0.999318i	$0.488243\pi$
$602$	−0.642889	−	1.11352i	−0.0262022	−	0.0453835i
$603$		0			0
$604$	−16.8011	+	9.70011i	−0.683626	+	0.394692i
$605$		−	1.49663i		−	0.0608467i
$606$		0			0
$607$	−1.44140	−	0.832190i	−0.0585044	−	0.0337775i	0.470462	−	0.882420i	$-0.344087\pi$
$607$	−1.44140	−	0.832190i	−0.0585044	−	0.0337775i	−0.528967	+	0.848642i	$0.677420\pi$
$608$	25.1845	−	1.04444i	1.02137	−	0.0423576i
$609$		0			0
$610$			0.104407i			0.00422730i
$611$	−41.0590	+	71.1163i	−1.66107	+	2.87706i
$612$		0			0
$613$	18.5832	−	32.1871i	0.750570	−	1.30003i	−0.196977	−	0.980408i	$-0.563112\pi$
$613$	18.5832	−	32.1871i	0.750570	−	1.30003i	0.947547	−	0.319617i	$-0.103554\pi$
$614$	4.32891	+	2.49930i	0.174701	+	0.100864i
$615$		0			0
$616$	−16.9937	−	9.81130i	−0.684695	−	0.395309i
$617$			15.6197i			0.628824i	0.949287	+	0.314412i	$0.101807\pi$
$617$			15.6197i			0.628824i	−0.949287	+	0.314412i	$0.898193\pi$
$618$		0			0
$619$	−17.0708	−	29.5674i	−0.686132	−	1.18842i	−0.973080	−	0.230469i	$-0.925974\pi$
$619$	−17.0708	−	29.5674i	−0.686132	−	1.18842i	0.286948	−	0.957946i	$-0.407359\pi$
$620$	1.32843			0.0533511
$621$		0			0
$622$	17.6972	+	10.2175i	0.709591	+	0.409683i
$623$	13.6680	−	23.6737i	0.547598	−	0.948468i
$624$		0			0
$625$	−12.3561	−	21.4014i	−0.494244	−	0.856055i
$626$	−0.427713	+	0.740821i	−0.0170948	+	0.0296091i
$627$		0			0
$628$	12.1553	+	21.0536i	0.485048	+	0.840128i
$629$	−11.0036	+	19.0589i	−0.438744	+	0.759927i
$630$		0			0
$631$	9.09528	+	15.7535i	0.362077	+	0.627136i	0.988303	−	0.152506i	$-0.0487343\pi$
$631$	9.09528	+	15.7535i	0.362077	+	0.627136i	−0.626225	+	0.779642i	$0.715401\pi$
$632$			8.16107i			0.324630i
$633$		0			0
$634$	−4.77336	+	8.26771i	−0.189574	+	0.328353i
$635$	−0.355476	+	0.615702i	−0.0141066	+	0.0244334i
$636$		0			0
$637$	22.2739	+	12.8598i	0.882522	+	0.509525i
$638$		−	3.01358i		−	0.119309i
$639$		0			0
$640$	−1.30848	+	0.755450i	−0.0517221	+	0.0298618i
$641$	12.6220			0.498539			0.249269	−	0.968434i	$-0.419810\pi$
$641$	12.6220			0.498539			0.249269	+	0.968434i	$0.419810\pi$
$642$		0			0
$643$	−13.2003	−	22.8636i	−0.520568	−	0.901651i	−0.999714	−	0.0239155i	$-0.992387\pi$
$643$	−13.2003	−	22.8636i	−0.520568	−	0.901651i	0.479146	−	0.877735i	$-0.340947\pi$
$644$	2.55024	−	1.47238i	0.100494	−	0.0580200i
$645$		0			0
$646$	12.2597	+	6.41608i	0.482351	+	0.252437i
$647$			17.9111i			0.704159i	0.935970	+	0.352079i	$0.114525\pi$
$647$			17.9111i			0.704159i	−0.935970	+	0.352079i	$0.885475\pi$
$648$		0			0
$649$	−44.6013	−	25.7505i	−1.75075	−	1.01080i
$650$	−19.1269	−	11.0429i	−0.750219	−	0.433139i
$651$		0			0
$652$	10.2631			0.401935
$653$	−3.92191	−	2.26431i	−0.153476	−	0.0886094i	0.421295	−	0.906924i	$-0.361576\pi$
$653$	−3.92191	−	2.26431i	−0.153476	−	0.0886094i	−0.574771	+	0.818314i	$0.694909\pi$
$654$		0			0
$655$	−1.09036	+	1.88855i	−0.0426038	+	0.0737919i
$656$	−5.69209	−	9.85898i	−0.222239	−	0.384929i
$657$		0			0
$658$			14.8620i			0.579380i
$659$	−10.4986	+	18.1841i	−0.408968	+	0.708353i	−0.994774	−	0.102098i	$-0.967445\pi$
$659$	−10.4986	+	18.1841i	−0.408968	+	0.708353i	0.585806	+	0.810451i	$0.300778\pi$
$660$		0			0
$661$			19.1203i			0.743693i	0.928294	+	0.371847i	$0.121275\pi$
$661$			19.1203i			0.743693i	−0.928294	+	0.371847i	$0.878725\pi$
$662$	−10.6274	+	6.13572i	−0.413045	+	0.238472i
$663$		0			0
$664$	7.36419	−	4.25172i	0.285786	−	0.164999i
$665$	0.938951	+	0.491398i	0.0364110	+	0.0190556i
$666$		0			0
$667$	0.899487	+	0.519319i	0.0348283	+	0.0201081i
$668$	6.50628			0.251736
$669$		0			0
$670$	0.207588	+	0.359552i	0.00801981	+	0.0138907i
$671$			5.19914i			0.200711i
$672$		0			0
$673$	−8.12324	+	4.68995i	−0.313128	+	0.180784i	−0.648325	−	0.761363i	$-0.724530\pi$
$673$	−8.12324	+	4.68995i	−0.313128	+	0.180784i	0.335197	+	0.942148i	$0.391197\pi$
$674$	3.61084	−	2.08472i	0.139084	−	0.0803004i
$675$		0			0
$676$	46.2361			1.77831
$677$	−15.3198	−	26.5347i	−0.588787	−	1.01981i	−0.994392	−	0.105761i	$-0.966272\pi$
$677$	−15.3198	−	26.5347i	−0.588787	−	1.01981i	0.405604	−	0.914049i	$-0.367061\pi$
$678$		0			0
$679$	22.1169	−	12.7692i	0.848767	−	0.490036i
$680$	−1.55872			−0.0597743
$681$		0			0
$682$	−19.6217			−0.751355
$683$	30.9867			1.18567			0.592837	−	0.805323i	$-0.298008\pi$
$683$	30.9867			1.18567			0.592837	+	0.805323i	$0.298008\pi$
$684$		0			0
$685$	0.455255			0.0173944
$686$	12.9599			0.494812
$687$		0			0
$688$	−1.58677			−0.0604952
$689$	14.4641	−	8.35086i	0.551039	−	0.318142i
$690$		0			0
$691$	8.00656	+	13.8678i	0.304584	+	0.527555i	0.977169	−	0.212465i	$-0.0681493\pi$
$691$	8.00656	+	13.8678i	0.304584	+	0.527555i	−0.672585	+	0.740020i	$0.734816\pi$
$692$	16.8061			0.638872
$693$		0			0
$694$	9.46625	−	5.46534i	0.359334	−	0.207462i
$695$	1.94081	−	1.12053i	0.0736191	−	0.0425040i
$696$		0			0
$697$		−	36.4895i		−	1.38214i
$698$	7.80447	+	13.5177i	0.295404	+	0.511654i
$699$		0			0
$700$	13.4759			0.509340
$701$	−29.7676	−	17.1863i	−1.12431	−	0.649119i	−0.181810	−	0.983334i	$-0.558196\pi$
$701$	−29.7676	−	17.1863i	−1.12431	−	0.649119i	−0.942497	+	0.334215i	$0.891529\pi$
$702$		0			0
$703$	0.846950	+	20.4224i	0.0319433	+	0.770247i
$704$	3.97480	−	2.29485i	0.149806	−	0.0864904i
$705$		0			0
$706$	−17.8511	+	10.3064i	−0.671836	+	0.387885i
$707$		−	13.2029i		−	0.496544i
$708$		0			0
$709$	1.67597	−	2.90287i	0.0629425	−	0.109020i	−0.832837	−	0.553518i	$-0.813285\pi$
$709$	1.67597	−	2.90287i	0.0629425	−	0.109020i	0.895779	+	0.444499i	$0.146618\pi$
$710$			0.749920i			0.0281440i
$711$		0			0
$712$	18.6715	+	32.3401i	0.699746	+	1.21199i
$713$	3.38135	−	5.85666i	0.126632	−	0.219334i
$714$		0			0
$715$	3.67397	+	2.12117i	0.137399	+	0.0793272i
$716$	−7.97389			−0.297998
$717$		0			0
$718$	0.791756	+	0.457121i	0.0295481	+	0.0170596i
$719$	21.7299	+	12.5458i	0.810389	+	0.467878i	0.847091	−	0.531448i	$-0.178352\pi$
$719$	21.7299	+	12.5458i	0.810389	+	0.467878i	−0.0367021	+	0.999326i	$0.511685\pi$
$720$		0			0
$721$		−	0.594824i		−	0.0221524i
$722$	12.8076	−	1.06413i	0.476648	−	0.0396028i
$723$		0			0
$724$	−7.26015	+	4.19165i	−0.269821	+	0.155781i
$725$	2.37651	+	4.11624i	0.0882615	+	0.152873i
$726$		0			0
$727$	46.8522			1.73765			0.868825	−	0.495119i	$-0.164875\pi$
$727$	46.8522			1.73765			0.868825	+	0.495119i	$0.164875\pi$
$728$	23.8613	−	13.7763i	0.884357	−	0.510584i
$729$		0			0
$730$			0.105259i			0.00389582i
$731$	−4.40466	−	2.54303i	−0.162912	−	0.0940573i
$732$		0			0
$733$	−11.0279	+	19.1009i	−0.407325	+	0.705508i	−0.994589	−	0.103888i	$-0.966872\pi$
$733$	−11.0279	+	19.1009i	−0.407325	+	0.705508i	0.587264	+	0.809396i	$0.300205\pi$
$734$	−0.536867	+	0.929880i	−0.0198161	+	0.0343225i
$735$		0			0
$736$			6.29392i			0.231997i
$737$	10.3372	+	17.9046i	0.380777	+	0.659526i
$738$		0			0
$739$	−6.35102	+	11.0003i	−0.233626	+	0.404652i	−0.958872	−	0.283837i	$-0.908392\pi$
$739$	−6.35102	+	11.0003i	−0.233626	+	0.404652i	0.725247	+	0.688489i	$0.241726\pi$
$740$	−0.501286	−	0.868253i	−0.0184276	−	0.0319176i
$741$		0			0
$742$	1.51136	−	2.61776i	0.0554839	−	0.0961009i
$743$	13.6353	+	23.6170i	0.500230	+	0.866423i	1.00000		0.000265368i	$8.44691e-5\pi$
$743$	13.6353	+	23.6170i	0.500230	+	0.866423i	−0.499770	+	0.866158i	$0.666582\pi$
$744$		0			0
$745$	0.415813	−	0.720210i	0.0152342	−	0.0263865i
$746$	−17.5960	−	10.1590i	−0.644235	−	0.371949i
$747$		0			0
$748$	−33.7974			−1.23576
$749$	10.4032	+	18.0188i	0.380124	+	0.658394i
$750$		0			0
$751$			41.1874i			1.50295i	0.659762	+	0.751475i	$0.270657\pi$
$751$			41.1874i			1.50295i	−0.659762	+	0.751475i	$0.729343\pi$
$752$	15.8839	+	9.17055i	0.579225	+	0.334416i
$753$		0			0
$754$	3.66453	+	2.11572i	0.133454	+	0.0770500i
$755$	0.871668	−	1.50977i	0.0317232	−	0.0549463i
$756$		0			0
$757$	0.190902	−	0.330651i	0.00693844	−	0.0120177i	−0.862535	−	0.505997i	$-0.831125\pi$
$757$	0.190902	−	0.330651i	0.00693844	−	0.0120177i	0.869474	+	0.493979i	$0.164458\pi$
$758$		−	13.8595i		−	0.503401i
$759$		0			0
$760$	−1.22269	+	0.775187i	−0.0443516	+	0.0281190i
$761$	35.7329	+	20.6304i	1.29532	+	0.747852i	0.979592	−	0.200998i	$-0.0644185\pi$
$761$	35.7329	+	20.6304i	1.29532	+	0.747852i	0.315726	+	0.948850i	$0.397752\pi$
$762$		0			0
$763$			18.1263i			0.656216i
$764$	−16.7609	+	9.67689i	−0.606387	+	0.350098i
$765$		0			0
$766$	−10.0547	−	17.4153i	−0.363293	−	0.629242i
$767$	62.6258	−	36.1570i	2.26129	−	1.30555i
$768$		0			0
$769$	17.0881			0.616214			0.308107	−	0.951352i	$-0.400305\pi$
$769$	17.0881			0.616214			0.308107	+	0.951352i	$0.400305\pi$
$770$	0.767790			0.0276692
$771$		0			0
$772$	0.159319	−	0.0919829i	0.00573402	−	0.00331054i
$773$	−2.79674	−	4.84409i	−0.100592	−	0.174230i	0.811337	−	0.584579i	$-0.198740\pi$
$773$	−2.79674	−	4.84409i	−0.100592	−	0.174230i	−0.911929	+	0.410349i	$0.865407\pi$
$774$		0			0
$775$	26.8013	−	15.4737i	0.962732	−	0.555833i
$776$			34.8873i			1.25238i
$777$		0			0
$778$	−10.0732	−	5.81575i	−0.361141	−	0.208505i
$779$	−18.1470	−	28.6230i	−0.650184	−	1.02552i
$780$		0			0
$781$			37.3438i			1.33626i
$782$	−1.72755	+	2.99221i	−0.0617771	+	0.107001i
$783$		0			0
$784$	2.87225	−	4.97488i	0.102580	−	0.177674i
$785$	−1.89191	−	1.09229i	−0.0675251	−	0.0389856i
$786$		0			0
$787$	5.68500	+	3.28224i	0.202648	+	0.116999i	0.597890	−	0.801578i	$-0.296006\pi$
$787$	5.68500	+	3.28224i	0.202648	+	0.116999i	−0.395242	+	0.918577i	$0.629339\pi$
$788$			22.9818i			0.818692i
$789$		0			0
$790$	−0.159662	−	0.276543i	−0.00568053	−	0.00983898i
$791$	−3.83202			−0.136251
$792$		0			0
$793$	−6.32220	−	3.65012i	−0.224508	−	0.129620i
$794$	−8.19208	+	14.1891i	−0.290726	+	0.503552i
$795$		0			0
$796$	−6.16608	−	10.6800i	−0.218551	−	0.378541i
$797$	14.0122	−	24.2699i	0.496339	−	0.859684i	−0.503652	−	0.863906i	$-0.668011\pi$
$797$	14.0122	−	24.2699i	0.496339	−	0.859684i	0.999991	+	0.00422263i	$0.00134411\pi$
$798$		0			0
$799$	29.3942	+	50.9122i	1.03989	+	1.80115i
$800$	−14.4011	+	24.9435i	−0.509158	+	0.881887i
$801$		0			0
$802$	−5.88981	−	10.2015i	−0.207976	−	0.360226i
$803$			5.24160i			0.184972i
$804$		0			0
$805$	−0.132311	+	0.229169i	−0.00466334	+	0.00807714i
$806$	13.7757	−	23.8602i	0.485228	−	0.840440i
$807$		0			0
$808$	15.6197	+	9.01803i	0.549499	+	0.317253i
$809$			32.3776i			1.13834i	0.822221	+	0.569168i	$0.192734\pi$
$809$			32.3776i			1.13834i	−0.822221	+	0.569168i	$0.807266\pi$
$810$		0			0
$811$	6.65521	−	3.84239i	0.233696	−	0.134924i	−0.378580	−	0.925569i	$-0.623588\pi$
$811$	6.65521	−	3.84239i	0.233696	−	0.134924i	0.612276	+	0.790644i	$0.290254\pi$
$812$	−2.58185			−0.0906051
$813$		0			0
$814$	7.40430	+	12.8246i	0.259521	+	0.449503i
$815$	−0.798701	+	0.461130i	−0.0279773	+	0.0161527i
$816$		0			0
$817$	−4.71979	+	0.195737i	−0.165125	+	0.00684797i
$818$		−	15.7816i		−	0.551791i
$819$		0			0
$820$	1.43962	+	0.831164i	0.0502737	+	0.0290255i
$821$	47.8717	+	27.6387i	1.67073	+	0.964598i	0.967228	+	0.253908i	$0.0817159\pi$
$821$	47.8717	+	27.6387i	1.67073	+	0.964598i	0.703505	+	0.710691i	$0.251617\pi$
$822$		0			0
$823$	15.9381			0.555566			0.277783	−	0.960644i	$-0.410400\pi$
$823$	15.9381			0.555566			0.277783	+	0.960644i	$0.410400\pi$
$824$	0.703709	+	0.406287i	0.0245149	+	0.0141537i
$825$		0			0
$826$	6.54380	−	11.3342i	0.227688	−	0.394367i
$827$	5.61139	+	9.71922i	0.195127	+	0.337970i	0.946942	−	0.321404i	$-0.104155\pi$
$827$	5.61139	+	9.71922i	0.195127	+	0.337970i	−0.751815	+	0.659374i	$0.770821\pi$
$828$		0			0
$829$			27.7051i			0.962238i	0.876655	+	0.481119i	$0.159769\pi$
$829$			27.7051i			0.962238i	−0.876655	+	0.481119i	$0.840231\pi$
$830$	−0.166360	+	0.288145i	−0.00577446	+	0.0100017i
$831$		0			0
$832$			6.44452i			0.223423i
$833$	15.9459	−	9.20636i	0.552492	−	0.318981i
$834$		0			0
$835$	−0.506335	+	0.292333i	−0.0175224	+	0.0101166i
$836$	−26.5113	+	16.8082i	−0.916912	+	0.581324i
$837$		0			0
$838$	−4.64587	−	2.68229i	−0.160489	−	0.0926583i
$839$	39.0956			1.34973			0.674865	−	0.737941i	$-0.264202\pi$
$839$	39.0956			1.34973			0.674865	+	0.737941i	$0.264202\pi$
$840$		0			0
$841$	14.0447	+	24.3261i	0.484299	+	0.838831i
$842$		−	19.0850i		−	0.657712i
$843$		0			0
$844$	−15.5802	+	8.99523i	−0.536293	+	0.309629i
$845$	−3.59821	+	2.07743i	−0.123782	+	0.0714656i
$846$		0			0
$847$	18.9392			0.650759
$848$	−1.86517	−	3.23057i	−0.0640501	−	0.110938i
$849$		0			0
$850$	−13.6930	+	7.90564i	−0.469665	+	0.271161i
$851$	−5.10383			−0.174957
$852$		0			0
$853$	5.97157			0.204463			0.102231	−	0.994761i	$-0.467402\pi$
$853$	5.97157			0.204463			0.102231	+	0.994761i	$0.467402\pi$
$854$	−1.32122			−0.0452112
$855$		0			0
$856$	−28.4230			−0.971478
$857$	−50.4729			−1.72412			−0.862061	−	0.506804i	$-0.830827\pi$
$857$	−50.4729			−1.72412			−0.862061	+	0.506804i	$0.830827\pi$
$858$		0			0
$859$	−12.8388			−0.438053			−0.219026	−	0.975719i	$-0.570288\pi$
$859$	−12.8388			−0.438053			−0.219026	+	0.975719i	$0.570288\pi$
$860$	0.200660	−	0.115851i	0.00684245	−	0.00395049i
$861$		0			0
$862$	2.29588	+	3.97658i	0.0781979	+	0.135443i
$863$	−23.6047			−0.803512			−0.401756	−	0.915747i	$-0.631600\pi$
$863$	−23.6047			−0.803512			−0.401756	+	0.915747i	$0.631600\pi$
$864$		0			0
$865$	−1.30789	+	0.755112i	−0.0444697	+	0.0256746i
$866$	20.1085	−	11.6097i	0.683316	−	0.394513i
$867$		0			0
$868$			16.8107i			0.570592i
$869$	−7.95071	−	13.7710i	−0.269710	−	0.467151i
$870$		0			0
$871$	−29.0296			−0.983630
$872$	−21.4444	−	12.3809i	−0.726198	−	0.419271i
$873$		0			0
$874$	0.132970	+	3.20629i	0.00449777	+	0.108454i
$875$	−2.10149	+	1.21330i	−0.0710435	+	0.0410170i
$876$		0			0
$877$	27.8434	−	16.0754i	0.940206	−	0.542828i	0.0501813	−	0.998740i	$-0.484020\pi$
$877$	27.8434	−	16.0754i	0.940206	−	0.542828i	0.890025	+	0.455912i	$0.150687\pi$
$878$		−	9.33593i		−	0.315072i
$879$		0			0
$880$	0.473764	−	0.820583i	0.0159706	−	0.0276619i
$881$		−	51.5651i		−	1.73727i	−0.495449	−	0.868637i	$-0.664997\pi$
$881$		−	51.5651i		−	1.73727i	0.495449	−	0.868637i	$-0.335003\pi$
$882$		0			0
$883$	11.6957	+	20.2576i	0.393592	+	0.681722i	0.992920	−	0.118781i	$-0.0378988\pi$
$883$	11.6957	+	20.2576i	0.393592	+	0.681722i	−0.599328	+	0.800504i	$0.704565\pi$
$884$	23.7279	−	41.0980i	0.798057	−	1.38227i
$885$		0			0
$886$	−15.7887	−	9.11564i	−0.530433	−	0.306246i
$887$	21.4014			0.718587			0.359294	−	0.933225i	$-0.383018\pi$
$887$	21.4014			0.718587			0.359294	+	0.933225i	$0.383018\pi$
$888$		0			0
$889$	−7.79143	−	4.49839i	−0.261316	−	0.150871i
$890$	−1.26540	−	0.730577i	−0.0424162	−	0.0244890i
$891$		0			0
$892$		−	32.1511i		−	1.07650i
$893$	48.3771	+	25.3180i	1.61888	+	0.847236i
$894$		0			0
$895$	0.620548	−	0.358274i	0.0207426	−	0.0119758i
$896$	−9.55989	−	16.5582i	−0.319373	−	0.553171i
$897$		0			0
$898$	1.20535			0.0402229
$899$	−5.13488	+	2.96463i	−0.171258	+	0.0988758i
$900$		0			0
$901$		−	11.9568i		−	0.398338i
$902$	−21.2640	−	12.2768i	−0.708015	−	0.408773i
$903$		0			0
$904$	2.61741	−	4.53349i	0.0870538	−	0.150782i
$905$	0.376668	−	0.652409i	0.0125209	−	0.0216868i
$906$		0			0
$907$			35.2140i			1.16926i	0.811299	+	0.584631i	$0.198761\pi$
$907$			35.2140i			1.16926i	−0.811299	+	0.584631i	$0.801239\pi$
$908$	18.4124	+	31.8911i	0.611036	+	1.05834i
$909$		0			0
$910$	−0.539037	+	0.933640i	−0.0178689	+	0.0309499i
$911$	−5.48367	−	9.49800i	−0.181682	−	0.314683i	0.760771	−	0.649020i	$-0.224821\pi$
$911$	−5.48367	−	9.49800i	−0.181682	−	0.314683i	−0.942454	+	0.334337i	$0.891488\pi$
$912$		0			0
$913$	−8.28426	+	14.3488i	−0.274169	+	0.474874i
$914$	−3.66401	−	6.34624i	−0.121195	−	0.209915i
$915$		0			0
$916$	13.8033	−	23.9081i	0.456075	−	0.789946i
$917$	−23.8988	−	13.7980i	−0.789208	−	0.455650i
$918$		0			0
$919$	−34.7810			−1.14732			−0.573659	−	0.819094i	$-0.694477\pi$
$919$	−34.7810			−1.14732			−0.573659	+	0.819094i	$0.694477\pi$
$920$	−0.180746	−	0.313061i	−0.00595902	−	0.0103213i
$921$		0			0
$922$		−	14.0244i		−	0.461869i
$923$	−45.4103	−	26.2177i	−1.49470	−	0.862965i
$924$		0			0
$925$	−20.2271	−	11.6781i	−0.665062	−	0.383973i
$926$	−8.91295	+	15.4377i	−0.292898	+	0.507314i
$927$		0			0
$928$	2.75913	−	4.77895i	0.0905727	−	0.156877i
$929$			36.6293i			1.20177i	0.799336	+	0.600885i	$0.205185\pi$
$929$			36.6293i			1.20177i	−0.799336	+	0.600885i	$0.794815\pi$
$930$		0			0
$931$	7.92970	−	15.1519i	0.259885	−	0.496582i
$932$	−1.81045	−	1.04526i	−0.0593033	−	0.0342388i
$933$		0			0
$934$		−	8.13106i		−	0.266056i
$935$	2.63020	−	1.51855i	0.0860167	−	0.0496618i
$936$		0			0
$937$	−7.00421	−	12.1317i	−0.228818	−	0.396324i	0.728640	−	0.684897i	$-0.240153\pi$
$937$	−7.00421	−	12.1317i	−0.228818	−	0.396324i	−0.957458	+	0.288573i	$0.906819\pi$
$938$	−4.54998	+	2.62693i	−0.148562	+	0.0857723i
$939$		0			0
$940$	−2.67819			−0.0873528
$941$	−14.6106			−0.476292			−0.238146	−	0.971229i	$-0.576540\pi$
$941$	−14.6106			−0.476292			−0.238146	+	0.971229i	$0.576540\pi$
$942$		0			0
$943$	7.32872	−	4.23124i	0.238656	−	0.137788i
$944$	−8.07569	−	13.9875i	−0.262841	−	0.455254i
$945$		0			0
$946$	−2.96387	+	1.71119i	−0.0963638	+	0.0556357i
$947$		−	19.6671i		−	0.639094i	−0.947570	−	0.319547i	$-0.896469\pi$
$947$		−	19.6671i		−	0.639094i	0.947570	−	0.319547i	$-0.103531\pi$
$948$		0			0
$949$	−6.37383	−	3.67993i	−0.206903	−	0.119456i
$950$	−6.80935	+	13.0111i	−0.220924	+	0.422137i
$951$		0			0
$952$		−	19.7249i		−	0.639289i
$953$	5.16671	−	8.94901i	0.167366	−	0.289887i	−0.770127	−	0.637891i	$-0.779807\pi$
$953$	5.16671	−	8.94901i	0.167366	−	0.289887i	0.937493	+	0.348004i	$0.113140\pi$
$954$		0			0
$955$	0.869582	−	1.50616i	0.0281390	−	0.0487382i
$956$	−9.49524	−	5.48208i	−0.307098	−	0.177303i
$957$		0			0
$958$	−20.5679	−	11.8749i	−0.664519	−	0.383660i
$959$			5.76105i			0.186034i
$960$		0			0
$961$	3.80301	+	6.58701i	0.122678	+	0.212484i
$962$	−20.7931			−0.670398
$963$		0			0
$964$	−22.1620	−	12.7953i	−0.713791	−	0.412107i
$965$	−0.00826573	+	0.0143167i	−0.000266083	+	0.000460870i
$966$		0			0
$967$	9.82237	+	17.0128i	0.315866	+	0.547096i	0.979621	−	0.200854i	$-0.0643716\pi$
$967$	9.82237	+	17.0128i	0.315866	+	0.547096i	−0.663755	+	0.747950i	$0.731038\pi$
$968$	−12.9362	+	22.4061i	−0.415784	+	0.720160i
$969$		0			0
$970$	−0.682532	−	1.18218i	−0.0219148	−	0.0379575i
$971$	11.8669	−	20.5541i	0.380828	−	0.659614i	−0.610353	−	0.792130i	$-0.708972\pi$
$971$	11.8669	−	20.5541i	0.380828	−	0.659614i	0.991181	+	0.132516i	$0.0423056\pi$
$972$		0			0
$973$	14.1798	+	24.5601i	0.454583	+	0.787360i
$974$			9.54444i			0.305823i
$975$		0			0
$976$	−0.815257	+	1.41207i	−0.0260957	+	0.0451991i
$977$	−8.38318	+	14.5201i	−0.268202	+	0.464539i	−0.968397	−	0.249412i	$-0.919763\pi$
$977$	−8.38318	+	14.5201i	−0.268202	+	0.464539i	0.700196	+	0.713951i	$0.253096\pi$
$978$		0			0
$979$	−63.0130	−	36.3806i	−2.01390	−	1.16273i
$980$			0.838817i			0.0267950i
$981$		0			0
$982$	17.3224	−	10.0011i	0.552780	−	0.319148i
$983$	8.58590			0.273848			0.136924	−	0.990582i	$-0.456278\pi$
$983$	8.58590			0.273848			0.136924	+	0.990582i	$0.456278\pi$
$984$		0			0
$985$	−1.03259	−	1.78850i	−0.0329011	−	0.0569863i
$986$	2.62344	−	1.51465i	0.0835475	−	0.0482362i
$987$		0			0
$988$	−1.82634	−	44.0384i	−0.0581036	−	1.40105i
$989$		−	1.17954i		−	0.0375071i
$990$		0			0
$991$	10.7837	+	6.22600i	0.342557	+	0.197775i	0.661402	−	0.750031i	$-0.269962\pi$
$991$	10.7837	+	6.22600i	0.342557	+	0.197775i	−0.318845	+	0.947807i	$0.603295\pi$
$992$	−31.1163	−	17.9650i	−0.987942	−	0.570389i
$993$		0			0
$994$	−9.48990			−0.301001
$995$	0.959719	+	0.554094i	0.0304251	+	0.0175660i
$996$		0			0
$997$	1.75449	−	3.03886i	0.0555652	−	0.0962417i	−0.836905	−	0.547348i	$-0.815637\pi$
$997$	1.75449	−	3.03886i	0.0555652	−	0.0962417i	0.892470	+	0.451107i	$0.148971\pi$
$998$	12.0904	+	20.9412i	0.382715	+	0.662881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.t.a.179.10		36
3.2	odd	2		171.2.t.a.122.9	yes	36
9.2	odd	6		513.2.k.a.8.10		36
9.7	even	3		171.2.k.a.65.9	yes	36
19.12	odd	6		513.2.k.a.449.10		36
57.50	even	6		171.2.k.a.50.9	✓	36
171.88	odd	6		171.2.t.a.164.9	yes	36
171.164	even	6	inner	513.2.t.a.278.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.9	✓	36	57.50	even	6
171.2.k.a.65.9	yes	36	9.7	even	3
171.2.t.a.122.9	yes	36	3.2	odd	2
171.2.t.a.164.9	yes	36	171.88	odd	6
513.2.k.a.8.10		36	9.2	odd	6
513.2.k.a.449.10		36	19.12	odd	6
513.2.t.a.179.10		36	1.1	even	1	trivial
513.2.t.a.278.10		36	171.164	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.676405 q^{2} -1.54248 q^{4} +(0.120039 - 0.0693047i) q^{5} +(0.877021 + 1.51904i) q^{7} -2.39615 q^{8} +(0.0811952 - 0.0468781i) q^{10} +(4.04328 - 2.33439i) q^{11} +6.55555i q^{13} +(0.593221 + 1.02749i) q^{14} +1.46419 q^{16} +(4.06437 + 2.34656i) q^{17} +(4.35516 - 0.180615i) q^{19} +(-0.185158 + 0.106901i) q^{20} +(2.73489 - 1.57899i) q^{22} +1.08841i q^{23} +(-2.49039 + 4.31349i) q^{25} +4.43421i q^{26} +(-1.35278 - 2.34309i) q^{28} +(0.477136 - 0.826424i) q^{29} +(-5.38094 - 3.10669i) q^{31} +5.78268 q^{32} +(2.74916 + 1.58723i) q^{34} +(0.210554 + 0.121563i) q^{35} +4.68926i q^{37} +(2.94585 - 0.122169i) q^{38} +(-0.287632 + 0.166064i) q^{40} +(-3.88755 - 6.73343i) q^{41} -1.08373 q^{43} +(-6.23666 + 3.60074i) q^{44} +0.736205i q^{46} +(10.8483 + 6.26324i) q^{47} +(1.96167 - 3.39771i) q^{49} +(-1.68451 + 2.91767i) q^{50} -10.1118i q^{52} +(-1.27386 - 2.20639i) q^{53} +(0.323568 - 0.560437i) q^{55} +(-2.10147 - 3.63986i) q^{56} +(0.322737 - 0.558997i) q^{58} +(-5.51548 - 9.55309i) q^{59} +(-0.556799 + 0.964404i) q^{61} +(-3.63969 - 2.10138i) q^{62} +0.983063 q^{64} +(0.454331 + 0.786924i) q^{65} +4.42825i q^{67} +(-6.26919 - 3.61952i) q^{68} +(0.142420 + 0.0822261i) q^{70} +(-3.99931 + 6.92701i) q^{71} +(-0.561346 + 0.972280i) q^{73} +3.17184i q^{74} +(-6.71772 + 0.278594i) q^{76} +(7.09208 + 4.09461i) q^{77} -3.40591i q^{79} +(0.175760 - 0.101475i) q^{80} +(-2.62956 - 4.55452i) q^{82} +(-3.07334 + 1.77440i) q^{83} +0.650512 q^{85} -0.733037 q^{86} +(-9.68830 + 5.59354i) q^{88} +(-7.79231 - 13.4967i) q^{89} +(-9.95817 + 5.74935i) q^{91} -1.67885i q^{92} +(7.33782 + 4.23649i) q^{94} +(0.510272 - 0.323514i) q^{95} -14.5597i q^{97} +(1.32688 - 2.29823i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} + 30 q^{4} + 3 q^{5} - q^{7} + 12 q^{8} - 6 q^{10} + 9 q^{11} + 3 q^{14} + 18 q^{16} - 27 q^{17} + q^{19} - 9 q^{20} - 6 q^{22} + 11 q^{25} + 2 q^{28} + 12 q^{29} - 12 q^{31} + 30 q^{32}+ \cdots - 84 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 + 30 * q^4 + 3 * q^5 - q^7 + 12 * q^8 - 6 * q^10 + 9 * q^11 + 3 * q^14 + 18 * q^16 - 27 * q^17 + q^19 - 9 * q^20 - 6 * q^22 + 11 * q^25 + 2 * q^28 + 12 * q^29 - 12 * q^31 + 30 * q^32 - 21 * q^34 + 15 * q^35 + 36 * q^38 - 30 * q^40 - 18 * q^41 - 6 * q^43 + 66 * q^44 - 45 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^53 - 7 * q^55 + 6 * q^56 - 6 * q^58 + 9 * q^59 + 8 * q^61 - 12 * q^62 + 12 * q^64 - 18 * q^65 - 60 * q^68 - 24 * q^70 + 9 * q^71 - 18 * q^73 + 10 * q^76 + 6 * q^77 - 12 * q^80 - 9 * q^82 + 9 * q^83 - 22 * q^85 - 102 * q^86 - 3 * q^88 - 18 * q^89 + 27 * q^91 - 12 * q^94 + 21 * q^95 - 84 * q^98

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