LMFDB - Embedded newform 364.2.bq.a.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [364,2,Mod(121,364)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(364, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("364.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 364 = 2^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	364.bq (of order $6$, degree $2$, 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:	$2.90655463357$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 188 x^{14} - 49 x^{13} + 1116 x^{12} - x^{11} + 4649 x^{10} + \cdots + 16 $ x^18 - x^17 + 17x^16 - 6x^15 + 188x^14 - 49x^13 + 1116x^12 - x^11 + 4649x^10 + 106x^9 + 9589x^8 + 3532x^7 + 12349x^6 + 753x^5 + 2622x^4 - 883x^3 + 541x^2 - 92*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.6
Root			$-0.302937 - 0.524702i$ of defining polynomial
Character	$\chi$	$=$	364.361
Dual form			364.2.bq.a.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.605874 q^{3} +(3.48722 - 2.01335i) q^{5} +(2.30111 + 1.30571i) q^{7} -2.63292 q^{9} -3.01596i q^{11} +(-1.03064 + 3.45511i) q^{13} +(2.11282 - 1.21984i) q^{15} +(-2.53164 - 4.38494i) q^{17} +3.31908i q^{19} +(1.39418 + 0.791096i) q^{21} +(-2.45461 + 4.25150i) q^{23} +(5.60715 - 9.71187i) q^{25} -3.41284 q^{27} +(-1.30988 - 2.26878i) q^{29} +(8.86474 + 5.11806i) q^{31} -1.82729i q^{33} +(10.6533 - 0.0796422i) q^{35} +(-1.76903 - 1.02135i) q^{37} +(-0.624435 + 2.09336i) q^{39} +(0.252355 - 0.145697i) q^{41} +(-0.581173 + 1.00662i) q^{43} +(-9.18157 + 5.30098i) q^{45} +(3.64039 - 2.10178i) q^{47} +(3.59024 + 6.00917i) q^{49} +(-1.53386 - 2.65672i) q^{51} +(-1.74405 + 3.02079i) q^{53} +(-6.07218 - 10.5173i) q^{55} +2.01094i q^{57} +(-5.84388 + 3.37397i) q^{59} -13.2920 q^{61} +(-6.05864 - 3.43783i) q^{63} +(3.36229 + 14.1238i) q^{65} +4.13667i q^{67} +(-1.48718 + 2.57588i) q^{69} +(-1.10708 - 0.639174i) q^{71} +(-12.9146 - 7.45626i) q^{73} +(3.39722 - 5.88417i) q^{75} +(3.93797 - 6.94006i) q^{77} +(3.45991 + 5.99274i) q^{79} +5.83100 q^{81} -10.4993i q^{83} +(-17.6568 - 10.1942i) q^{85} +(-0.793622 - 1.37459i) q^{87} +(0.511598 + 0.295371i) q^{89} +(-6.88298 + 6.60489i) q^{91} +(5.37092 + 3.10090i) q^{93} +(6.68246 + 11.5744i) q^{95} +(-4.94617 - 2.85568i) q^{97} +7.94077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} + q^{7} + 12 q^{9} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 7 q^{21} - 6 q^{23} + 5 q^{25} - 20 q^{27} + 2 q^{29} + 9 q^{31} + 3 q^{35} + 18 q^{37} + 11 q^{39} - 9 q^{41} - 14 q^{43} + 30 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) $ 18 * q - 2 * q^3 + q^7 + 12 * q^9 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 7 * q^21 - 6 * q^23 + 5 * q^25 - 20 * q^27 + 2 * q^29 + 9 * q^31 + 3 * q^35 + 18 * q^37 + 11 * q^39 - 9 * q^41 - 14 * q^43 + 30 * q^45 + 36 * q^47 - 11 * q^49 + 2 * q^51 - 13 * q^53 - q^55 - 42 * q^61 - 32 * q^63 + 30 * q^65 - q^69 - 45 * q^71 - 33 * q^73 + 25 * q^75 - 9 * q^77 - 14 * q^79 + 2 * q^81 - 30 * q^85 + 2 * q^87 - 9 * q^89 + 21 * q^93 + 30 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/364\mathbb{Z}\right)^\times$.

$n$	$157$	$183$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.605874			0.349801			0.174901	−	0.984586i	$-0.444040\pi$
$3$	0.605874			0.349801			0.174901	+	0.984586i	$0.444040\pi$
$4$		0			0
$5$	3.48722	−	2.01335i	1.55953	−	0.900397i	0.562232	−	0.826979i	$-0.309943\pi$
$5$	3.48722	−	2.01335i	1.55953	−	0.900397i	0.997301	−	0.0734176i	$-0.0233906\pi$
$6$		0			0
$7$	2.30111	+	1.30571i	0.869739	+	0.493512i
$7$	2.30111	+	1.30571i	0.869739	+	0.493512i
$8$		0			0
$9$	−2.63292			−0.877639
$10$		0			0
$11$		−	3.01596i		−	0.909346i	−0.890658	−	0.454673i	$-0.849756\pi$
$11$		−	3.01596i		−	0.909346i	0.890658	−	0.454673i	$-0.150244\pi$
$12$		0			0
$13$	−1.03064	+	3.45511i	−0.285847	+	0.958275i
$13$	−1.03064	+	3.45511i	−0.285847	+	0.958275i
$14$		0			0
$15$	2.11282	−	1.21984i	0.545527	−	0.314960i
$16$		0			0
$17$	−2.53164	−	4.38494i	−0.614014	−	1.06350i	−0.990557	−	0.137104i	$-0.956221\pi$
$17$	−2.53164	−	4.38494i	−0.614014	−	1.06350i	0.376543	−	0.926399i	$-0.377113\pi$
$18$		0			0
$19$			3.31908i			0.761449i	0.924689	+	0.380724i	$0.124325\pi$
$19$			3.31908i			0.761449i	−0.924689	+	0.380724i	$0.875675\pi$
$20$		0			0
$21$	1.39418	+	0.791096i	0.304236	+	0.172631i
$22$		0			0
$23$	−2.45461	+	4.25150i	−0.511821	+	0.886500i	0.488085	+	0.872796i	$0.337696\pi$
$23$	−2.45461	+	4.25150i	−0.511821	+	0.886500i	−0.999906	+	0.0137038i	$0.995638\pi$
$24$		0			0
$25$	5.60715	−	9.71187i	1.12143	−	1.94237i
$26$		0			0
$27$	−3.41284			−0.656801
$28$		0			0
$29$	−1.30988	−	2.26878i	−0.243239	−	0.421302i	0.718396	−	0.695634i	$-0.244876\pi$
$29$	−1.30988	−	2.26878i	−0.243239	−	0.421302i	−0.961635	+	0.274332i	$0.911543\pi$
$30$		0			0
$31$	8.86474	+	5.11806i	1.59216	+	0.919231i	0.992937	+	0.118646i	$0.0378552\pi$
$31$	8.86474	+	5.11806i	1.59216	+	0.919231i	0.599218	+	0.800586i	$0.295478\pi$
$32$		0			0
$33$		−	1.82729i		−	0.318090i
$34$		0			0
$35$	10.6533	−	0.0796422i	1.80074	−	0.0134620i
$36$		0			0
$37$	−1.76903	−	1.02135i	−0.290826	−	0.167909i	0.347488	−	0.937684i	$-0.387035\pi$
$37$	−1.76903	−	1.02135i	−0.290826	−	0.167909i	−0.638314	+	0.769776i	$0.720368\pi$
$38$		0			0
$39$	−0.624435	+	2.09336i	−0.0999897	+	0.335206i
$40$		0			0
$41$	0.252355	−	0.145697i	0.0394112	−	0.0227540i	−0.480165	−	0.877178i	$-0.659423\pi$
$41$	0.252355	−	0.145697i	0.0394112	−	0.0227540i	0.519576	+	0.854424i	$0.326090\pi$
$42$		0			0
$43$	−0.581173	+	1.00662i	−0.0886281	+	0.153508i	−0.906931	−	0.421278i	$-0.861582\pi$
$43$	−0.581173	+	1.00662i	−0.0886281	+	0.153508i	0.818303	+	0.574787i	$0.194915\pi$
$44$		0			0
$45$	−9.18157	+	5.30098i	−1.36871	+	0.790224i
$46$		0			0
$47$	3.64039	−	2.10178i	0.531006	−	0.306576i	−0.210420	−	0.977611i	$-0.567483\pi$
$47$	3.64039	−	2.10178i	0.531006	−	0.306576i	0.741426	+	0.671035i	$0.234150\pi$
$48$		0			0
$49$	3.59024	+	6.00917i	0.512892	+	0.858453i
$50$		0			0
$51$	−1.53386	−	2.65672i	−0.214783	−	0.372015i
$52$		0			0
$53$	−1.74405	+	3.02079i	−0.239564	+	0.414937i	−0.960589	−	0.277972i	$-0.910338\pi$
$53$	−1.74405	+	3.02079i	−0.239564	+	0.414937i	0.721025	+	0.692909i	$0.243671\pi$
$54$		0			0
$55$	−6.07218	−	10.5173i	−0.818772	−	1.41816i
$56$		0			0
$57$			2.01094i			0.266356i
$58$		0			0
$59$	−5.84388	+	3.37397i	−0.760809	+	0.439253i	−0.829586	−	0.558379i	$-0.811424\pi$
$59$	−5.84388	+	3.37397i	−0.760809	+	0.439253i	0.0687772	+	0.997632i	$0.478090\pi$
$60$		0			0
$61$	−13.2920			−1.70187			−0.850936	−	0.525270i	$-0.823964\pi$
$61$	−13.2920			−1.70187			−0.850936	+	0.525270i	$0.823964\pi$
$62$		0			0
$63$	−6.05864	−	3.43783i	−0.763317	−	0.433125i
$64$		0			0
$65$	3.36229	+	14.1238i	0.417040	+	1.75184i
$66$		0			0
$67$			4.13667i			0.505375i	0.967548	+	0.252687i	$0.0813144\pi$
$67$			4.13667i			0.505375i	−0.967548	+	0.252687i	$0.918686\pi$
$68$		0			0
$69$	−1.48718	+	2.57588i	−0.179036	+	0.310099i
$70$		0			0
$71$	−1.10708	−	0.639174i	−0.131387	−	0.0758560i	0.432866	−	0.901458i	$-0.357502\pi$
$71$	−1.10708	−	0.639174i	−0.131387	−	0.0758560i	−0.564253	+	0.825602i	$0.690836\pi$
$72$		0			0
$73$	−12.9146	−	7.45626i	−1.51154	−	0.872690i	−0.999909	−	0.0134859i	$-0.995707\pi$
$73$	−12.9146	−	7.45626i	−1.51154	−	0.872690i	−0.511634	−	0.859204i	$-0.670959\pi$
$74$		0			0
$75$	3.39722	−	5.88417i	0.392278	−	0.679445i
$76$		0			0
$77$	3.93797	−	6.94006i	0.448773	−	0.790894i
$78$		0			0
$79$	3.45991	+	5.99274i	0.389270	+	0.674236i	0.992352	−	0.123444i	$-0.0393938\pi$
$79$	3.45991	+	5.99274i	0.389270	+	0.674236i	−0.603081	+	0.797680i	$0.706060\pi$
$80$		0			0
$81$	5.83100			0.647889
$82$		0			0
$83$		−	10.4993i		−	1.15245i	−0.817292	−	0.576224i	$-0.804526\pi$
$83$		−	10.4993i		−	1.15245i	0.817292	−	0.576224i	$-0.195474\pi$
$84$		0			0
$85$	−17.6568	−	10.1942i	−1.91515	−	1.10571i
$86$		0			0
$87$	−0.793622	−	1.37459i	−0.0850852	−	0.147372i
$88$		0			0
$89$	0.511598	+	0.295371i	0.0542293	+	0.0313093i	0.526870	−	0.849946i	$-0.323366\pi$
$89$	0.511598	+	0.295371i	0.0542293	+	0.0313093i	−0.472640	+	0.881255i	$0.656699\pi$
$90$		0			0
$91$	−6.88298	+	6.60489i	−0.721533	+	0.692380i
$92$		0			0
$93$	5.37092	+	3.10090i	0.556938	+	0.321548i
$94$		0			0
$95$	6.68246	+	11.5744i	0.685606	+	1.18750i
$96$		0			0
$97$	−4.94617	−	2.85568i	−0.502208	−	0.289950i	0.227417	−	0.973797i	$-0.426972\pi$
$97$	−4.94617	−	2.85568i	−0.502208	−	0.289950i	−0.729625	+	0.683848i	$0.760305\pi$
$98$		0			0
$99$			7.94077i			0.798077i
$100$		0			0
$101$	1.62019			0.161215			0.0806075	−	0.996746i	$-0.474314\pi$
$101$	1.62019			0.161215			0.0806075	+	0.996746i	$0.474314\pi$
$102$		0			0
$103$	3.68130	+	6.37620i	0.362729	+	0.628265i	0.988409	−	0.151815i	$-0.0485117\pi$
$103$	3.68130	+	6.37620i	0.362729	+	0.628265i	−0.625680	+	0.780080i	$0.715178\pi$
$104$		0			0
$105$	6.45458	−	0.0482531i	0.629903	−	0.00470902i
$106$		0			0
$107$	−4.62841	+	8.01664i	−0.447445	+	0.774998i	−0.998219	−	0.0596565i	$-0.980999\pi$
$107$	−4.62841	+	8.01664i	−0.447445	+	0.774998i	0.550774	+	0.834655i	$0.314333\pi$
$108$		0			0
$109$	9.86259	+	5.69417i	0.944665	+	0.545402i	0.891420	−	0.453179i	$-0.149710\pi$
$109$	9.86259	+	5.69417i	0.944665	+	0.545402i	0.0532452	+	0.998581i	$0.483044\pi$
$110$		0			0
$111$	−1.07181	−	0.618808i	−0.101731	−	0.0587347i
$112$		0			0
$113$	−7.06719	+	12.2407i	−0.664826	+	1.15151i	0.314507	+	0.949255i	$0.398161\pi$
$113$	−7.06719	+	12.2407i	−0.664826	+	1.15151i	−0.979333	+	0.202257i	$0.935172\pi$
$114$		0			0
$115$			19.7679i			1.84337i
$116$		0			0
$117$	2.71358	−	9.09702i	0.250870	−	0.841020i
$118$		0			0
$119$	−0.100144	−	13.3958i	−0.00918022	−	1.22799i
$120$		0			0
$121$	1.90399			0.173090
$122$		0			0
$123$	0.152895	−	0.0882740i	0.0137861	−	0.00795940i
$124$		0			0
$125$		−	25.0231i		−	2.23813i
$126$		0			0
$127$	−1.67517	−	2.90149i	−0.148648	−	0.257465i	0.782080	−	0.623178i	$-0.214159\pi$
$127$	−1.67517	−	2.90149i	−0.148648	−	0.257465i	−0.930728	+	0.365712i	$0.880825\pi$
$128$		0			0
$129$	−0.352118	+	0.609886i	−0.0310022	+	0.0536974i
$130$		0			0
$131$	−6.08531	−	10.5401i	−0.531676	−	0.920890i	−0.999316	−	0.0369713i	$-0.988229\pi$
$131$	−6.08531	−	10.5401i	−0.531676	−	0.920890i	0.467640	−	0.883919i	$-0.345104\pi$
$132$		0			0
$133$	−4.33375	+	7.63757i	−0.375784	+	0.662262i
$134$		0			0
$135$	−11.9013	+	6.87123i	−1.02430	+	0.591381i
$136$		0			0
$137$	2.99901	−	1.73148i	0.256223	−	0.147930i	−0.366388	−	0.930462i	$-0.619406\pi$
$137$	2.99901	−	1.73148i	0.256223	−	0.147930i	0.622610	+	0.782532i	$0.286072\pi$
$138$		0			0
$139$	4.58975	−	7.94968i	0.389297	−	0.674283i	−0.603058	−	0.797697i	$-0.706051\pi$
$139$	4.58975	−	7.94968i	0.389297	−	0.674283i	0.992355	+	0.123415i	$0.0393846\pi$
$140$		0			0
$141$	2.20562	−	1.27341i	0.185747	−	0.107241i
$142$		0			0
$143$	10.4205	+	3.10836i	0.871404	+	0.259934i
$144$		0			0
$145$	−9.13569	−	5.27449i	−0.758678	−	0.438023i
$146$		0			0
$147$	2.17523	+	3.64080i	0.179410	+	0.300288i
$148$		0			0
$149$		−	6.18683i		−	0.506845i	−0.967356	−	0.253422i	$-0.918444\pi$
$149$		−	6.18683i		−	0.506845i	0.967356	−	0.253422i	$-0.0815563\pi$
$150$		0			0
$151$	−17.0651	−	9.85256i	−1.38874	−	0.801790i	−0.395568	−	0.918437i	$-0.629452\pi$
$151$	−17.0651	−	9.85256i	−1.38874	−	0.801790i	−0.993174	+	0.116646i	$0.962786\pi$
$152$		0			0
$153$	6.66561	+	11.5452i	0.538882	+	0.933372i
$154$		0			0
$155$	41.2178			3.31069
$156$		0			0
$157$	9.33447	−	16.1678i	0.744972	−	1.29033i	−0.205236	−	0.978713i	$-0.565796\pi$
$157$	9.33447	−	16.1678i	0.744972	−	1.29033i	0.950208	−	0.311617i	$-0.100871\pi$
$158$		0			0
$159$	−1.05668	+	1.83022i	−0.0837998	+	0.145146i
$160$		0			0
$161$	−11.1996	+	6.57819i	−0.882649	+	0.518434i
$162$		0			0
$163$			18.8843i			1.47913i	0.673083	+	0.739567i	$0.264970\pi$
$163$			18.8843i			1.47913i	−0.673083	+	0.739567i	$0.735030\pi$
$164$		0			0
$165$	−3.67897	−	6.37217i	−0.286408	−	0.496073i
$166$		0			0
$167$	−12.3365	+	7.12250i	−0.954630	+	0.551156i	−0.894516	−	0.447036i	$-0.852480\pi$
$167$	−12.3365	+	7.12250i	−0.954630	+	0.551156i	−0.0601137	+	0.998192i	$0.519146\pi$
$168$		0			0
$169$	−10.8756	−	7.12192i	−0.836583	−	0.547840i
$170$		0			0
$171$		−	8.73886i		−	0.668277i
$172$		0			0
$173$	19.9996			1.52054			0.760272	−	0.649605i	$-0.225066\pi$
$173$	19.9996			1.52054			0.760272	+	0.649605i	$0.225066\pi$
$174$		0			0
$175$	25.5836	−	15.0268i	1.93394	−	1.13592i
$176$		0			0
$177$	−3.54066	+	2.04420i	−0.266132	+	0.153651i
$178$		0			0
$179$	23.4022			1.74916			0.874580	−	0.484881i	$-0.161137\pi$
$179$	23.4022			1.74916			0.874580	+	0.484881i	$0.161137\pi$
$180$		0			0
$181$	−5.15299			−0.383019			−0.191509	−	0.981491i	$-0.561338\pi$
$181$	−5.15299			−0.383019			−0.191509	+	0.981491i	$0.561338\pi$
$182$		0			0
$183$	−8.05330			−0.595317
$184$		0			0
$185$	−8.22532			−0.604738
$186$		0			0
$187$	−13.2248	+	7.63534i	−0.967092	+	0.558351i
$188$		0			0
$189$	−7.85332	−	4.45618i	−0.571245	−	0.324139i
$190$		0			0
$191$	22.3386			1.61636			0.808182	−	0.588933i	$-0.200452\pi$
$191$	22.3386			1.61636			0.808182	+	0.588933i	$0.200452\pi$
$192$		0			0
$193$			10.3162i			0.742577i	0.928518	+	0.371288i	$0.121084\pi$
$193$			10.3162i			0.742577i	−0.928518	+	0.371288i	$0.878916\pi$
$194$		0			0
$195$	2.03712	+	8.55722i	0.145881	+	0.612795i
$196$		0			0
$197$	23.1481	−	13.3646i	1.64923	−	0.952186i	0.671857	−	0.740681i	$-0.265497\pi$
$197$	23.1481	−	13.3646i	1.64923	−	0.952186i	0.977377	−	0.211505i	$-0.0678364\pi$
$198$		0			0
$199$	0.0439516	+	0.0761264i	0.00311565	+	0.00539646i	0.867579	−	0.497299i	$-0.165675\pi$
$199$	0.0439516	+	0.0761264i	0.00311565	+	0.00539646i	−0.864463	+	0.502696i	$0.832342\pi$
$200$		0			0
$201$			2.50630i			0.176781i
$202$		0			0
$203$	−0.0518150	−	6.93104i	−0.00363670	−	0.486464i
$204$		0			0
$205$	0.586678	−	1.01616i	0.0409753	−	0.0709714i
$206$		0			0
$207$	6.46278	−	11.1939i	0.449194	−	0.778027i
$208$		0			0
$209$	10.0102			0.692420
$210$		0			0
$211$	−12.1986	−	21.1285i	−0.839783	−	1.45455i	−0.890076	−	0.455813i	$-0.849349\pi$
$211$	−12.1986	−	21.1285i	−0.839783	−	1.45455i	0.0502926	−	0.998735i	$-0.483985\pi$
$212$		0			0
$213$	−0.670752	−	0.387259i	−0.0459592	−	0.0265345i
$214$		0			0
$215$			4.68042i			0.319202i
$216$		0			0
$217$	13.7161	+	23.3520i	0.931108	+	1.58524i
$218$		0			0
$219$	−7.82463	−	4.51755i	−0.528740	−	0.305268i
$220$		0			0
$221$	17.7596	−	4.22784i	1.19464	−	0.284395i
$222$		0			0
$223$	−2.25338	+	1.30099i	−0.150897	+	0.0871206i	−0.573548	−	0.819172i	$-0.694433\pi$
$223$	−2.25338	+	1.30099i	−0.150897	+	0.0871206i	0.422650	+	0.906293i	$0.361100\pi$
$224$		0			0
$225$	−14.7632	+	25.5705i	−0.984210	+	1.70470i
$226$		0			0
$227$	−12.8164	+	7.39957i	−0.850657	+	0.491127i	−0.860872	−	0.508821i	$-0.830081\pi$
$227$	−12.8164	+	7.39957i	−0.850657	+	0.491127i	0.0102158	+	0.999948i	$0.496748\pi$
$228$		0			0
$229$	−2.79819	+	1.61554i	−0.184910	+	0.106758i	−0.589597	−	0.807697i	$-0.700714\pi$
$229$	−2.79819	+	1.61554i	−0.184910	+	0.106758i	0.404688	+	0.914455i	$0.367380\pi$
$230$		0			0
$231$	2.38591	−	4.20480i	0.156981	−	0.276656i
$232$		0			0
$233$	5.44152	+	9.42499i	0.356486	+	0.617452i	0.987371	−	0.158424i	$-0.0506414\pi$
$233$	5.44152	+	9.42499i	0.356486	+	0.617452i	−0.630885	+	0.775876i	$0.717308\pi$
$234$		0			0
$235$	8.46324	−	14.6588i	0.552081	−	0.956232i
$236$		0			0
$237$	2.09627	+	3.63085i	0.136167	+	0.235849i
$238$		0			0
$239$		−	14.2791i		−	0.923639i	−0.886974	−	0.461819i	$-0.847197\pi$
$239$		−	14.2791i		−	0.923639i	0.886974	−	0.461819i	$-0.152803\pi$
$240$		0			0
$241$	21.9539	−	12.6751i	1.41417	−	0.816473i	0.418394	−	0.908266i	$-0.362593\pi$
$241$	21.9539	−	12.6751i	1.41417	−	0.816473i	0.995778	+	0.0917927i	$0.0292597\pi$
$242$		0			0
$243$	13.7714			0.883433
$244$		0			0
$245$	24.6185	+	13.7269i	1.57282	+	0.876980i
$246$		0			0
$247$	−11.4678	−	3.42076i	−0.729677	−	0.217658i
$248$		0			0
$249$		−	6.36125i		−	0.403128i
$250$		0			0
$251$	−10.6797	+	18.4977i	−0.674094	+	1.16756i	0.302639	+	0.953105i	$0.402132\pi$
$251$	−10.6797	+	18.4977i	−0.674094	+	1.16756i	−0.976733	+	0.214460i	$0.931201\pi$
$252$		0			0
$253$	12.8224	+	7.40299i	0.806135	+	0.465422i
$254$		0			0
$255$	−10.6978	−	6.17638i	−0.669922	−	0.386780i
$256$		0			0
$257$	4.53161	−	7.84898i	0.282674	−	0.489606i	−0.689368	−	0.724411i	$-0.742112\pi$
$257$	4.53161	−	7.84898i	0.282674	−	0.489606i	0.972042	+	0.234805i	$0.0754452\pi$
$258$		0			0
$259$	−2.73715	−	4.66007i	−0.170078	−	0.289563i
$260$		0			0
$261$	3.44881	+	5.97351i	0.213476	+	0.369751i
$262$		0			0
$263$	−14.7945			−0.912269			−0.456134	−	0.889911i	$-0.650766\pi$
$263$	−14.7945			−0.912269			−0.456134	+	0.889911i	$0.650766\pi$
$264$		0			0
$265$			14.0455i			0.862811i
$266$		0			0
$267$	0.309964	+	0.178958i	0.0189695	+	0.0109520i
$268$		0			0
$269$	−14.6738	−	25.4158i	−0.894678	−	1.54963i	−0.834203	−	0.551457i	$-0.814072\pi$
$269$	−14.6738	−	25.4158i	−0.894678	−	1.54963i	−0.0604745	−	0.998170i	$-0.519261\pi$
$270$		0			0
$271$	9.80478	+	5.66079i	0.595598	+	0.343869i	0.767308	−	0.641279i	$-0.221596\pi$
$271$	9.80478	+	5.66079i	0.595598	+	0.343869i	−0.171710	+	0.985148i	$0.554929\pi$
$272$		0			0
$273$	−4.17022	+	4.00173i	−0.252393	+	0.242196i
$274$		0			0
$275$	−29.2906	−	16.9109i	−1.76629	−	1.01977i
$276$		0			0
$277$	−9.30823	−	16.1223i	−0.559277	−	0.968697i	−0.997557	−	0.0698581i	$-0.977745\pi$
$277$	−9.30823	−	16.1223i	−0.559277	−	0.968697i	0.438280	−	0.898839i	$-0.355588\pi$
$278$		0			0
$279$	−23.3401	−	13.4754i	−1.39734	−	0.806753i
$280$		0			0
$281$			9.63428i			0.574733i	0.957821	+	0.287366i	$0.0927797\pi$
$281$			9.63428i			0.574733i	−0.957821	+	0.287366i	$0.907220\pi$
$282$		0			0
$283$	−17.7476			−1.05498			−0.527492	−	0.849560i	$-0.676867\pi$
$283$	−17.7476			−1.05498			−0.527492	+	0.849560i	$0.676867\pi$
$284$		0			0
$285$	4.04873	+	7.01260i	0.239826	+	0.415391i
$286$		0			0
$287$	0.770934	−	0.00576334i	0.0455068	−	0.000340199i
$288$		0			0
$289$	−4.31844	+	7.47976i	−0.254026	+	0.439986i
$290$		0			0
$291$	−2.99676	−	1.73018i	−0.175673	−	0.101425i
$292$		0			0
$293$	−21.2670	−	12.2785i	−1.24243	−	0.717320i	−0.272845	−	0.962058i	$-0.587965\pi$
$293$	−21.2670	−	12.2785i	−1.24243	−	0.717320i	−0.969589	+	0.244738i	$0.921298\pi$
$294$		0			0
$295$	−13.5859	+	23.5316i	−0.791005	+	1.37006i
$296$		0			0
$297$			10.2930i			0.597259i
$298$		0			0
$299$	−12.1596	−	12.8627i	−0.703208	−	0.743869i
$300$		0			0
$301$	−2.65170	+	1.55751i	−0.152841	+	0.0897731i
$302$		0			0
$303$	0.981632			0.0563933
$304$		0			0
$305$	−46.3523	+	26.7615i	−2.65413	+	1.53236i
$306$		0			0
$307$		−	3.59068i		−	0.204931i	−0.994737	−	0.102466i	$-0.967327\pi$
$307$		−	3.59068i		−	0.204931i	0.994737	−	0.102466i	$-0.0326731\pi$
$308$		0			0
$309$	2.23040	+	3.86317i	0.126883	+	0.219768i
$310$		0			0
$311$	4.31915	−	7.48098i	0.244916	−	0.424208i	−0.717192	−	0.696876i	$-0.754573\pi$
$311$	4.31915	−	7.48098i	0.244916	−	0.424208i	0.962108	+	0.272668i	$0.0879062\pi$
$312$		0			0
$313$	9.01786	+	15.6194i	0.509720	+	0.882861i	0.999937	+	0.0112601i	$0.00358428\pi$
$313$	9.01786	+	15.6194i	0.509720	+	0.882861i	−0.490217	+	0.871601i	$0.663082\pi$
$314$		0			0
$315$	−28.0494	+	0.209691i	−1.58040	+	0.0118148i
$316$		0			0
$317$	12.6003	−	7.27477i	0.707702	−	0.408592i	−0.102508	−	0.994732i	$-0.532687\pi$
$317$	12.6003	−	7.27477i	0.707702	−	0.408592i	0.810210	+	0.586140i	$0.199353\pi$
$318$		0			0
$319$	−6.84254	+	3.95055i	−0.383109	+	0.221188i
$320$		0			0
$321$	−2.80423	+	4.85707i	−0.156517	+	0.271095i
$322$		0			0
$323$	14.5539	−	8.40272i	0.809803	−	0.467540i
$324$		0			0
$325$	27.7766	+	29.3827i	1.54077	+	1.62986i
$326$		0			0
$327$	5.97549	+	3.44995i	0.330445	+	0.190783i
$328$		0			0
$329$	11.1213	−	0.0831403i	0.613135	−	0.00458367i
$330$		0			0
$331$		−	28.5151i		−	1.56733i	−0.621182	−	0.783666i	$-0.713347\pi$
$331$		−	28.5151i		−	1.56733i	0.621182	−	0.783666i	$-0.286653\pi$
$332$		0			0
$333$	4.65770	+	2.68912i	0.255240	+	0.147363i
$334$		0			0
$335$	8.32856	+	14.4255i	0.455038	+	0.788149i
$336$		0			0
$337$	6.02834			0.328385			0.164192	−	0.986428i	$-0.447498\pi$
$337$	6.02834			0.328385			0.164192	+	0.986428i	$0.447498\pi$
$338$		0			0
$339$	−4.28183	+	7.41634i	−0.232557	+	0.402801i
$340$		0			0
$341$	15.4359	−	26.7357i	0.835899	−	1.44782i
$342$		0			0
$343$	0.415318	+	18.5156i	0.0224251	+	0.999749i
$344$		0			0
$345$			11.9769i			0.644813i
$346$		0			0
$347$	2.16529	+	3.75039i	0.116239	+	0.201331i	0.918274	−	0.395945i	$-0.129583\pi$
$347$	2.16529	+	3.75039i	0.116239	+	0.201331i	−0.802036	+	0.597276i	$0.796250\pi$
$348$		0			0
$349$	−2.85466	+	1.64814i	−0.152806	+	0.0882228i	−0.574454	−	0.818537i	$-0.694785\pi$
$349$	−2.85466	+	1.64814i	−0.152806	+	0.0882228i	0.421647	+	0.906760i	$0.361452\pi$
$350$		0			0
$351$	3.51739	−	11.7917i	0.187745	−	0.629396i
$352$		0			0
$353$			20.5841i			1.09558i	0.836616	+	0.547790i	$0.184531\pi$
$353$			20.5841i			1.09558i	−0.836616	+	0.547790i	$0.815469\pi$
$354$		0			0
$355$	−5.14752			−0.273202
$356$		0			0
$357$	−0.0606749	−	8.11618i	−0.00321125	−	0.429554i
$358$		0			0
$359$	12.9348	−	7.46793i	0.682674	−	0.394142i	−0.118188	−	0.992991i	$-0.537708\pi$
$359$	12.9348	−	7.46793i	0.682674	−	0.394142i	0.800862	+	0.598849i	$0.204375\pi$
$360$		0			0
$361$	7.98372			0.420196
$362$		0			0
$363$	1.15358			0.0605471
$364$		0			0
$365$	−60.0482			−3.14307
$366$		0			0
$367$	−5.01214			−0.261631			−0.130816	−	0.991407i	$-0.541760\pi$
$367$	−5.01214			−0.261631			−0.130816	+	0.991407i	$0.541760\pi$
$368$		0			0
$369$	−0.664429	+	0.383608i	−0.0345888	+	0.0199698i
$370$		0			0
$371$	−7.95753	+	4.67395i	−0.413135	+	0.242659i
$372$		0			0
$373$	17.0022			0.880338			0.440169	−	0.897915i	$-0.354918\pi$
$373$	17.0022			0.880338			0.440169	+	0.897915i	$0.354918\pi$
$374$		0			0
$375$		−	15.1608i		−	0.782902i
$376$		0			0
$377$	9.18889	−	2.18750i	0.473252	−	0.112662i
$378$		0			0
$379$	24.9003	−	14.3762i	1.27904	−	0.738454i	0.302369	−	0.953191i	$-0.402223\pi$
$379$	24.9003	−	14.3762i	1.27904	−	0.738454i	0.976672	+	0.214737i	$0.0688894\pi$
$380$		0			0
$381$	−1.01494	−	1.75793i	−0.0519972	−	0.0900617i
$382$		0			0
$383$			29.8622i			1.52589i	0.646465	+	0.762944i	$0.276247\pi$
$383$			29.8622i			1.52589i	−0.646465	+	0.762944i	$0.723753\pi$
$384$		0			0
$385$	−0.240198	−	32.1301i	−0.0122416	−	1.63750i
$386$		0			0
$387$	1.53018	−	2.65035i	0.0777834	−	0.134725i
$388$		0			0
$389$	−4.17584	+	7.23276i	−0.211723	+	0.366715i	−0.952254	−	0.305307i	$-0.901241\pi$
$389$	−4.17584	+	7.23276i	−0.211723	+	0.366715i	0.740531	+	0.672023i	$0.234574\pi$
$390$		0			0
$391$	24.8568			1.25706
$392$		0			0
$393$	−3.68693	−	6.38595i	−0.185981	−	0.322129i
$394$		0			0
$395$	24.1310	+	13.9320i	1.21416	+	0.700996i
$396$		0			0
$397$			2.86213i			0.143646i	0.997417	+	0.0718232i	$0.0228817\pi$
$397$			2.86213i			0.143646i	−0.997417	+	0.0718232i	$0.977118\pi$
$398$		0			0
$399$	−2.62571	+	4.62741i	−0.131450	+	0.231660i
$400$		0			0
$401$	−14.6879	−	8.48009i	−0.733481	−	0.423476i	0.0862132	−	0.996277i	$-0.472523\pi$
$401$	−14.6879	−	8.48009i	−0.733481	−	0.423476i	−0.819694	+	0.572801i	$0.805857\pi$
$402$		0			0
$403$	−26.8198	+	25.3538i	−1.33599	+	1.26296i
$404$		0			0
$405$	20.3340	−	11.7398i	1.01040	−	0.583357i
$406$		0			0
$407$	−3.08034	+	5.33531i	−0.152687	+	0.264462i
$408$		0			0
$409$	8.05450	−	4.65027i	0.398269	−	0.229941i	−0.287468	−	0.957790i	$-0.592813\pi$
$409$	8.05450	−	4.65027i	0.398269	−	0.229941i	0.685737	+	0.727849i	$0.259480\pi$
$410$		0			0
$411$	1.81702	−	1.04906i	0.0896270	−	0.0517462i
$412$		0			0
$413$	−17.8529	+	0.133464i	−0.878482	+	0.00656735i
$414$		0			0
$415$	−21.1387	−	36.6134i	−1.03766	−	1.79728i
$416$		0			0
$417$	2.78081	−	4.81650i	0.136177	−	0.235865i
$418$		0			0
$419$	10.1471	+	17.5753i	0.495718	+	0.858608i	0.999988	−	0.00493765i	$-0.00157171\pi$
$419$	10.1471	+	17.5753i	0.495718	+	0.858608i	−0.504270	+	0.863546i	$0.668238\pi$
$420$		0			0
$421$			6.82905i			0.332827i	0.986056	+	0.166414i	$0.0532187\pi$
$421$			6.82905i			0.332827i	−0.986056	+	0.166414i	$0.946781\pi$
$422$		0			0
$423$	−9.58485	+	5.53381i	−0.466031	+	0.269063i
$424$		0			0
$425$	−56.7812			−2.75429
$426$		0			0
$427$	−30.5865	−	17.3556i	−1.48018	−	0.839894i
$428$		0			0
$429$	6.31349	+	1.88327i	0.304818	+	0.0909252i
$430$		0			0
$431$			9.67781i			0.466164i	0.972457	+	0.233082i	$0.0748810\pi$
$431$			9.67781i			0.466164i	−0.972457	+	0.233082i	$0.925119\pi$
$432$		0			0
$433$	9.67518	−	16.7579i	0.464960	−	0.805334i	−0.534240	−	0.845333i	$-0.679402\pi$
$433$	9.67518	−	16.7579i	0.464960	−	0.805334i	0.999200	+	0.0399991i	$0.0127355\pi$
$434$		0			0
$435$	−5.53507	−	3.19568i	−0.265386	−	0.153221i
$436$		0			0
$437$	−14.1111	−	8.14703i	−0.675024	−	0.389725i
$438$		0			0
$439$	−8.69109	+	15.0534i	−0.414803	+	0.718460i	−0.995408	−	0.0957255i	$-0.969483\pi$
$439$	−8.69109	+	15.0534i	−0.414803	+	0.718460i	0.580605	+	0.814186i	$0.302816\pi$
$440$		0			0
$441$	−9.45281	−	15.8217i	−0.450134	−	0.753412i
$442$		0			0
$443$	6.61637	+	11.4599i	0.314353	+	0.544476i	0.979300	−	0.202415i	$-0.0648790\pi$
$443$	6.61637	+	11.4599i	0.314353	+	0.544476i	−0.664946	+	0.746891i	$0.731546\pi$
$444$		0			0
$445$	2.37874			0.112763
$446$		0			0
$447$		−	3.74844i		−	0.177295i
$448$		0			0
$449$	6.12896	+	3.53855i	0.289243	+	0.166995i	0.637601	−	0.770367i	$-0.279927\pi$
$449$	6.12896	+	3.53855i	0.289243	+	0.166995i	−0.348357	+	0.937362i	$0.613260\pi$
$450$		0			0
$451$	−0.439416	−	0.761091i	−0.0206913	−	0.0358384i
$452$		0			0
$453$	−10.3393	−	5.96941i	−0.485784	−	0.280467i
$454$		0			0
$455$	−10.7045	+	36.8906i	−0.501837	+	1.72946i
$456$		0			0
$457$	28.9889	+	16.7367i	1.35604	+	0.782911i	0.989088	−	0.147328i	$-0.0470672\pi$
$457$	28.9889	+	16.7367i	1.35604	+	0.782911i	0.366954	+	0.930239i	$0.380401\pi$
$458$		0			0
$459$	8.64009	+	14.9651i	0.403285	+	0.698510i
$460$		0			0
$461$	7.21129	+	4.16344i	0.335863	+	0.193911i	0.658441	−	0.752632i	$-0.271216\pi$
$461$	7.21129	+	4.16344i	0.335863	+	0.193911i	−0.322578	+	0.946543i	$0.604549\pi$
$462$		0			0
$463$			4.45810i			0.207186i	0.994620	+	0.103593i	$0.0330339\pi$
$463$			4.45810i			0.207186i	−0.994620	+	0.103593i	$0.966966\pi$
$464$		0			0
$465$	24.9728			1.15808
$466$		0			0
$467$	−16.0477	−	27.7954i	−0.742599	−	1.28622i	−0.951308	−	0.308241i	$-0.900260\pi$
$467$	−16.0477	−	27.7954i	−0.742599	−	1.28622i	0.208710	−	0.977978i	$-0.433074\pi$
$468$		0			0
$469$	−5.40129	+	9.51894i	−0.249408	+	0.439544i
$470$		0			0
$471$	5.65551	−	9.79564i	0.260592	−	0.451359i
$472$		0			0
$473$	3.03593	+	1.75279i	0.139592	+	0.0805936i
$474$		0			0
$475$	32.2344	+	18.6106i	1.47902	+	0.853911i
$476$		0			0
$477$	4.59195	−	7.95348i	0.210251	−	0.364165i
$478$		0			0
$479$		−	19.3554i		−	0.884371i	−0.896924	−	0.442185i	$-0.854203\pi$
$479$		−	19.3554i		−	0.884371i	0.896924	−	0.442185i	$-0.145797\pi$
$480$		0			0
$481$	5.35209	−	5.05955i	0.244034	−	0.230695i
$482$		0			0
$483$	−6.78552	+	3.98555i	−0.308752	+	0.181349i
$484$		0			0
$485$	−22.9979			−1.04428
$486$		0			0
$487$	5.07742	−	2.93145i	0.230080	−	0.132837i	−0.380529	−	0.924769i	$-0.624258\pi$
$487$	5.07742	−	2.93145i	0.230080	−	0.132837i	0.610609	+	0.791932i	$0.290925\pi$
$488$		0			0
$489$			11.4415i			0.517403i
$490$		0			0
$491$	5.13898	+	8.90098i	0.231919	+	0.401696i	0.958373	−	0.285520i	$-0.0921662\pi$
$491$	5.13898	+	8.90098i	0.231919	+	0.401696i	−0.726454	+	0.687215i	$0.758833\pi$
$492$		0			0
$493$	−6.63230	+	11.4875i	−0.298704	+	0.517370i
$494$		0			0
$495$	15.9875	+	27.6912i	0.718587	+	1.24463i
$496$		0			0
$497$	−1.71295	−	2.91634i	−0.0768361	−	0.130816i
$498$		0			0
$499$	26.5363	−	15.3208i	1.18793	−	0.685851i	0.230094	−	0.973168i	$-0.426097\pi$
$499$	26.5363	−	15.3208i	1.18793	−	0.685851i	0.957835	+	0.287317i	$0.0927634\pi$
$500$		0			0
$501$	−7.47438	+	4.31534i	−0.333931	+	0.192795i
$502$		0			0
$503$	1.91528	−	3.31736i	0.0853981	−	0.147914i	−0.820163	−	0.572130i	$-0.806117\pi$
$503$	1.91528	−	3.31736i	0.0853981	−	0.147914i	0.905561	+	0.424216i	$0.139450\pi$
$504$		0			0
$505$	5.64997	−	3.26201i	0.251420	−	0.145158i
$506$		0			0
$507$	−6.58923	−	4.31499i	−0.292638	−	0.191635i
$508$		0			0
$509$	−16.3952	−	9.46577i	−0.726704	−	0.419563i	0.0905109	−	0.995895i	$-0.471150\pi$
$509$	−16.3952	−	9.46577i	−0.726704	−	0.419563i	−0.817215	+	0.576333i	$0.804483\pi$
$510$		0			0
$511$	−19.9823	−	34.0205i	−0.883965	−	1.50498i
$512$		0			0
$513$		−	11.3275i		−	0.500120i
$514$		0			0
$515$	25.6750	+	14.8235i	1.13138	+	0.653201i
$516$		0			0
$517$	−6.33888	−	10.9793i	−0.278784	−	0.482868i
$518$		0			0
$519$	12.1173			0.531888
$520$		0			0
$521$	22.1534	−	38.3709i	0.970559	−	1.68106i	0.276686	−	0.960960i	$-0.410764\pi$
$521$	22.1534	−	38.3709i	0.970559	−	1.68106i	0.693873	−	0.720097i	$-0.255903\pi$
$522$		0			0
$523$	11.4413	−	19.8169i	0.500293	−	0.866532i	−0.499707	−	0.866194i	$-0.666559\pi$
$523$	11.4413	−	19.8169i	0.500293	−	0.866532i	1.00000		0.000337913i	$-0.000107561\pi$
$524$		0			0
$525$	15.5004	−	9.10434i	0.676493	−	0.397346i
$526$		0			0
$527$		−	51.8284i		−	2.25768i
$528$		0			0
$529$	−0.550191	−	0.952958i	−0.0239213	−	0.0414330i
$530$		0			0
$531$	15.3865	−	8.88338i	0.667716	−	0.385506i
$532$		0			0
$533$	0.243313	+	1.02207i	0.0105391	+	0.0442709i
$534$		0			0
$535$			37.2744i			1.61151i
$536$		0			0
$537$	14.1788			0.611859
$538$		0			0
$539$	18.1234	−	10.8280i	0.780631	−	0.466396i
$540$		0			0
$541$	1.49131	−	0.861006i	0.0641163	−	0.0370175i	−0.467599	−	0.883941i	$-0.654881\pi$
$541$	1.49131	−	0.861006i	0.0641163	−	0.0370175i	0.531715	+	0.846923i	$0.321548\pi$
$542$		0			0
$543$	−3.12206			−0.133981
$544$		0			0
$545$	45.8574			1.96432
$546$		0			0
$547$	21.7554			0.930195			0.465098	−	0.885259i	$-0.346019\pi$
$547$	21.7554			0.930195			0.465098	+	0.885259i	$0.346019\pi$
$548$		0			0
$549$	34.9968			1.49363
$550$		0			0
$551$	7.53025	−	4.34759i	0.320800	−	0.185214i
$552$		0			0
$553$	0.136864	+	18.3076i	0.00582005	+	0.778519i
$554$		0			0
$555$	−4.98351			−0.211538
$556$		0			0
$557$			20.2913i			0.859768i	0.902884	+	0.429884i	$0.141446\pi$
$557$			20.2913i			0.859768i	−0.902884	+	0.429884i	$0.858554\pi$
$558$		0			0
$559$	−2.87901	−	3.04548i	−0.121769	−	0.128810i
$560$		0			0
$561$	−8.01255	+	4.62605i	−0.338290	+	0.195312i
$562$		0			0
$563$	−6.08156	−	10.5336i	−0.256307	−	0.443937i	0.708943	−	0.705266i	$-0.249172\pi$
$563$	−6.08156	−	10.5336i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$564$		0			0
$565$			56.9149i			2.39443i
$566$		0			0
$567$	13.4178	+	7.61360i	0.563494	+	0.319741i
$568$		0			0
$569$	−2.60362	+	4.50961i	−0.109150	+	0.189052i	−0.915426	−	0.402486i	$-0.868146\pi$
$569$	−2.60362	+	4.50961i	−0.109150	+	0.189052i	0.806276	+	0.591539i	$0.201479\pi$
$570$		0			0
$571$	7.11158	−	12.3176i	0.297611	−	0.515477i	−0.677978	−	0.735082i	$-0.737144\pi$
$571$	7.11158	−	12.3176i	0.297611	−	0.515477i	0.975589	+	0.219605i	$0.0704770\pi$
$572$		0			0
$573$	13.5344			0.565406
$574$		0			0
$575$	27.5267	+	47.6776i	1.14794	+	1.98829i
$576$		0			0
$577$	8.49045	+	4.90196i	0.353462	+	0.204071i	0.666209	−	0.745765i	$-0.267916\pi$
$577$	8.49045	+	4.90196i	0.353462	+	0.204071i	−0.312747	+	0.949836i	$0.601249\pi$
$578$		0			0
$579$			6.25032i			0.259754i
$580$		0			0
$581$	13.7090	−	24.1601i	0.568747	−	1.00233i
$582$		0			0
$583$	9.11057	+	5.25999i	0.377321	+	0.217847i
$584$		0			0
$585$	−8.85262	−	37.1867i	−0.366011	−	1.53748i
$586$		0			0
$587$	−14.4001	+	8.31388i	−0.594354	+	0.343151i	−0.766817	−	0.641865i	$-0.778161\pi$
$587$	−14.4001	+	8.31388i	−0.594354	+	0.343151i	0.172463	+	0.985016i	$0.444827\pi$
$588$		0			0
$589$	−16.9872	+	29.4228i	−0.699947	+	1.21234i
$590$		0			0
$591$	14.0248	−	8.09724i	0.576904	−	0.333076i
$592$		0			0
$593$	−27.2185	+	15.7146i	−1.11773	+	0.645322i	−0.940821	−	0.338905i	$-0.889944\pi$
$593$	−27.2185	+	15.7146i	−1.11773	+	0.645322i	−0.176910	+	0.984227i	$0.556610\pi$
$594$		0			0
$595$	−27.3197	−	46.5126i	−1.12000	−	1.90683i
$596$		0			0
$597$	0.0266291	+	0.0461230i	0.00108986	+	0.00188769i
$598$		0			0
$599$	−19.9208	+	34.5039i	−0.813943	+	1.40979i	0.0961406	+	0.995368i	$0.469350\pi$
$599$	−19.9208	+	34.5039i	−0.813943	+	1.40979i	−0.910084	+	0.414424i	$0.863983\pi$
$600$		0			0
$601$	−4.75064	−	8.22836i	−0.193783	−	0.335642i	0.752718	−	0.658343i	$-0.228742\pi$
$601$	−4.75064	−	8.22836i	−0.193783	−	0.335642i	−0.946501	+	0.322701i	$0.895409\pi$
$602$		0			0
$603$		−	10.8915i		−	0.443536i
$604$		0			0
$605$	6.63964	−	3.83340i	0.269940	−	0.155850i
$606$		0			0
$607$	3.68363			0.149514			0.0747569	−	0.997202i	$-0.476182\pi$
$607$	3.68363			0.149514			0.0747569	+	0.997202i	$0.476182\pi$
$608$		0			0
$609$	−0.0313934	−	4.19934i	−0.00127212	−	0.170166i
$610$		0			0
$611$	3.50997	+	14.7441i	0.141998	+	0.596483i
$612$		0			0
$613$		−	28.1993i		−	1.13896i	−0.822006	−	0.569479i	$-0.807145\pi$
$613$		−	28.1993i		−	1.13896i	0.822006	−	0.569479i	$-0.192855\pi$
$614$		0			0
$615$	0.355453	−	0.615662i	0.0143332	−	0.0248259i
$616$		0			0
$617$	−4.12127	−	2.37942i	−0.165916	−	0.0957917i	0.414743	−	0.909939i	$-0.363872\pi$
$617$	−4.12127	−	2.37942i	−0.165916	−	0.0957917i	−0.580659	+	0.814147i	$0.697205\pi$
$618$		0			0
$619$	−18.7796	−	10.8424i	−0.754815	−	0.435793i	0.0726159	−	0.997360i	$-0.476865\pi$
$619$	−18.7796	−	10.8424i	−0.754815	−	0.435793i	−0.827431	+	0.561567i	$0.810199\pi$
$620$		0			0
$621$	8.37717	−	14.5097i	0.336164	−	0.582254i
$622$		0			0
$623$	0.791576	+	1.34768i	0.0317138	+	0.0539938i
$624$		0			0
$625$	−22.3445	−	38.7018i	−0.893779	−	1.54807i
$626$		0			0
$627$	6.06492			0.242210
$628$		0			0
$629$			10.3428i			0.412393i
$630$		0			0
$631$	−32.0785	−	18.5205i	−1.27702	−	0.737290i	−0.300724	−	0.953711i	$-0.597228\pi$
$631$	−32.0785	−	18.5205i	−1.27702	−	0.737290i	−0.976300	+	0.216421i	$0.930562\pi$
$632$		0			0
$633$	−7.39079	−	12.8012i	−0.293757	−	0.508803i
$634$		0			0
$635$	−11.6834	−	6.74542i	−0.463642	−	0.267684i
$636$		0			0
$637$	−24.4626	+	6.21142i	−0.969243	+	0.246105i
$638$		0			0
$639$	2.91486	+	1.68289i	0.115310	+	0.0665742i
$640$		0			0
$641$	−0.310057	−	0.537034i	−0.0122465	−	0.0212116i	0.859837	−	0.510568i	$-0.170565\pi$
$641$	−0.310057	−	0.537034i	−0.0122465	−	0.0212116i	−0.872084	+	0.489357i	$0.837232\pi$
$642$		0			0
$643$	11.5598	+	6.67403i	0.455872	+	0.263198i	0.710307	−	0.703892i	$-0.248556\pi$
$643$	11.5598	+	6.67403i	0.455872	+	0.263198i	−0.254435	+	0.967090i	$0.581889\pi$
$644$		0			0
$645$			2.83574i			0.111657i
$646$		0			0
$647$	6.52504			0.256526			0.128263	−	0.991740i	$-0.459060\pi$
$647$	6.52504			0.256526			0.128263	+	0.991740i	$0.459060\pi$
$648$		0			0
$649$	10.1757	+	17.6249i	0.399433	+	0.691838i
$650$		0			0
$651$	8.31021	+	14.1484i	0.325703	+	0.554519i
$652$		0			0
$653$	4.15183	−	7.19118i	0.162474	−	0.281413i	−0.773282	−	0.634063i	$-0.781386\pi$
$653$	4.15183	−	7.19118i	0.162474	−	0.281413i	0.935755	+	0.352650i	$0.114719\pi$
$654$		0			0
$655$	−42.4417	−	24.5037i	−1.65833	−	0.957439i
$656$		0			0
$657$	34.0031	+	19.6317i	1.32659	+	0.765906i
$658$		0			0
$659$	5.41342	−	9.37632i	0.210877	−	0.365250i	−0.741112	−	0.671381i	$-0.765701\pi$
$659$	5.41342	−	9.37632i	0.210877	−	0.365250i	0.951989	+	0.306131i	$0.0990347\pi$
$660$		0			0
$661$		−	16.0233i		−	0.623236i	−0.950207	−	0.311618i	$-0.899129\pi$
$661$		−	16.0233i		−	0.623236i	0.950207	−	0.311618i	$-0.100871\pi$
$662$		0			0
$663$	10.7601	−	2.56154i	0.417888	−	0.0994818i
$664$		0			0
$665$	0.264339	+	35.3593i	0.0102506	+	1.37117i
$666$		0			0
$667$	12.8610			0.497978
$668$		0			0
$669$	−1.36526	+	0.788235i	−0.0527841	+	0.0304749i
$670$		0			0
$671$			40.0883i			1.54759i
$672$		0			0
$673$	7.99990	+	13.8562i	0.308373	+	0.534119i	0.978007	−	0.208573i	$-0.0668820\pi$
$673$	7.99990	+	13.8562i	0.308373	+	0.534119i	−0.669633	+	0.742692i	$0.733549\pi$
$674$		0			0
$675$	−19.1363	+	33.1450i	−0.736556	+	1.27575i
$676$		0			0
$677$	−4.80538	−	8.32316i	−0.184686	−	0.319885i	0.758785	−	0.651341i	$-0.225793\pi$
$677$	−4.80538	−	8.32316i	−0.184686	−	0.319885i	−0.943471	+	0.331456i	$0.892460\pi$
$678$		0			0
$679$	−7.65302	−	13.0295i	−0.293696	−	0.500026i
$680$		0			0
$681$	−7.76514	+	4.48321i	−0.297561	+	0.171797i
$682$		0			0
$683$	−15.8268	+	9.13760i	−0.605595	+	0.349641i	−0.771240	−	0.636545i	$-0.780363\pi$
$683$	−15.8268	+	9.13760i	−0.605595	+	0.349641i	0.165644	+	0.986186i	$0.447030\pi$
$684$		0			0
$685$	6.97214	−	12.0761i	0.266392	−	0.461404i
$686$		0			0
$687$	−1.69535	+	0.978812i	−0.0646817	+	0.0373440i
$688$		0			0
$689$	−8.63967	−	9.13923i	−0.329145	−	0.348177i
$690$		0			0
$691$	−19.3973	−	11.1990i	−0.737908	−	0.426031i	0.0834002	−	0.996516i	$-0.473422\pi$
$691$	−19.3973	−	11.1990i	−0.737908	−	0.426031i	−0.821308	+	0.570485i	$0.806755\pi$
$692$		0			0
$693$	−10.3683	+	18.2726i	−0.393861	+	0.694119i
$694$		0			0
$695$		−	36.9631i		−	1.40209i
$696$		0			0
$697$	−1.27774	−	0.737706i	−0.0483980	−	0.0279426i
$698$		0			0
$699$	3.29688	+	5.71036i	0.124699	+	0.215985i
$700$		0			0
$701$	−25.9923			−0.981715			−0.490858	−	0.871240i	$-0.663317\pi$
$701$	−25.9923			−0.981715			−0.490858	+	0.871240i	$0.663317\pi$
$702$		0			0
$703$	3.38993	−	5.87154i	0.127854	−	0.221449i
$704$		0			0
$705$	5.12765	−	8.88136i	0.193119	−	0.334491i
$706$		0			0
$707$	3.72824	+	2.11550i	0.140215	+	0.0795616i
$708$		0			0
$709$		−	1.43956i		−	0.0540640i	−0.999635	−	0.0270320i	$-0.991394\pi$
$709$		−	1.43956i		−	0.0540640i	0.999635	−	0.0270320i	$-0.00860560\pi$
$710$		0			0
$711$	−9.10966	−	15.7784i	−0.341639	−	0.591736i
$712$		0			0
$713$	−43.5189	+	25.1257i	−1.62980	+	0.940964i
$714$		0			0
$715$	42.5967	−	10.1405i	1.59303	−	0.379234i
$716$		0			0
$717$		−	8.65134i		−	0.323090i
$718$		0			0
$719$	40.8771			1.52446			0.762228	−	0.647308i	$-0.224105\pi$
$719$	40.8771			1.52446			0.762228	+	0.647308i	$0.224105\pi$
$720$		0			0
$721$	0.145621	+	19.4791i	0.00542322	+	0.725438i
$722$		0			0
$723$	13.3013	−	7.67949i	0.494680	−	0.285603i
$724$		0			0
$725$	−29.3788			−1.09110
$726$		0			0
$727$	−22.0673			−0.818432			−0.409216	−	0.912438i	$-0.634198\pi$
$727$	−22.0673			−0.818432			−0.409216	+	0.912438i	$0.634198\pi$
$728$		0			0
$729$	−9.14930			−0.338863
$730$		0			0
$731$	5.88529			0.217675
$732$		0			0
$733$	−10.1099	+	5.83696i	−0.373418	+	0.215593i	−0.674951	−	0.737863i	$-0.735835\pi$
$733$	−10.1099	+	5.83696i	−0.373418	+	0.215593i	0.301533	+	0.953456i	$0.402502\pi$
$734$		0			0
$735$	14.9157	+	8.31678i	0.550175	+	0.306769i
$736$		0			0
$737$	12.4760			0.459560
$738$		0			0
$739$			29.1737i			1.07317i	0.843846	+	0.536585i	$0.180286\pi$
$739$			29.1737i			1.07317i	−0.843846	+	0.536585i	$0.819714\pi$
$740$		0			0
$741$	−6.94803	−	2.07255i	−0.255242	−	0.0761370i
$742$		0			0
$743$	20.1398	−	11.6277i	0.738858	−	0.426580i	−0.0827959	−	0.996567i	$-0.526385\pi$
$743$	20.1398	−	11.6277i	0.738858	−	0.426580i	0.821654	+	0.569987i	$0.193052\pi$
$744$		0			0
$745$	−12.4562	−	21.5749i	−0.456362	−	0.790441i
$746$		0			0
$747$			27.6438i			1.01143i
$748$		0			0
$749$	−21.1179	+	12.4038i	−0.771632	+	0.453226i
$750$		0			0
$751$	−16.8130	+	29.1210i	−0.613517	+	1.06264i	0.377126	+	0.926162i	$0.376912\pi$
$751$	−16.8130	+	29.1210i	−0.613517	+	1.06264i	−0.990643	+	0.136480i	$0.956421\pi$
$752$		0			0
$753$	−6.47052	+	11.2073i	−0.235799	+	0.408416i
$754$		0			0
$755$	−79.3466			−2.88772
$756$		0			0
$757$	10.7585	+	18.6343i	0.391025	+	0.677275i	0.992585	−	0.121552i	$-0.0387872\pi$
$757$	10.7585	+	18.6343i	0.391025	+	0.677275i	−0.601560	+	0.798828i	$0.705454\pi$
$758$		0			0
$759$	7.76873	+	4.48528i	0.281987	+	0.162805i
$760$		0			0
$761$		−	1.30767i		−	0.0474029i	−0.999719	−	0.0237014i	$-0.992455\pi$
$761$		−	1.30767i		−	0.0474029i	0.999719	−	0.0237014i	$-0.00754511\pi$
$762$		0			0
$763$	15.2600	+	25.9806i	0.552449	+	0.940561i
$764$		0			0
$765$	46.4889	+	26.8404i	1.68081	+	0.970416i
$766$		0			0
$767$	−5.63451	−	23.6686i	−0.203451	−	0.854624i
$768$		0			0
$769$	−31.1392	+	17.9782i	−1.12291	+	0.648312i	−0.942142	−	0.335214i	$-0.891191\pi$
$769$	−31.1392	+	17.9782i	−1.12291	+	0.648312i	−0.180767	+	0.983526i	$0.557858\pi$
$770$		0			0
$771$	2.74558	−	4.75549i	0.0988798	−	0.171265i
$772$		0			0
$773$	37.8302	−	21.8413i	1.36066	−	0.785576i	0.370947	−	0.928654i	$-0.379033\pi$
$773$	37.8302	−	21.8413i	1.36066	−	0.785576i	0.989711	+	0.143078i	$0.0456998\pi$
$774$		0			0
$775$	99.4119	−	57.3955i	3.57098	−	2.06171i
$776$		0			0
$777$	−1.65837	−	2.82342i	−0.0594935	−	0.101290i
$778$		0			0
$779$	0.483580	+	0.837584i	0.0173260	+	0.0300096i
$780$		0			0
$781$	−1.92772	+	3.33892i	−0.0689794	+	0.119476i
$782$		0			0
$783$	4.47041	+	7.74297i	0.159759	+	0.276711i
$784$		0			0
$785$		−	75.1742i		−	2.68308i
$786$		0			0
$787$	−16.8292	+	9.71634i	−0.599896	+	0.346350i	−0.769001	−	0.639248i	$-0.779246\pi$
$787$	−16.8292	+	9.71634i	−0.599896	+	0.346350i	0.169105	+	0.985598i	$0.445912\pi$
$788$		0			0
$789$	−8.96361			−0.319113
$790$		0			0
$791$	−32.2453	+	18.9396i	−1.14651	+	0.673415i
$792$		0			0
$793$	13.6993	−	45.9255i	0.486475	−	1.63086i
$794$		0			0
$795$			8.50983i			0.301813i
$796$		0			0
$797$	8.40446	−	14.5570i	0.297701	−	0.515634i	−0.677908	−	0.735146i	$-0.737113\pi$
$797$	8.40446	−	14.5570i	0.297701	−	0.515634i	0.975610	+	0.219513i	$0.0704467\pi$
$798$		0			0
$799$	−18.4323	−	10.6419i	−0.652090	−	0.376484i
$800$		0			0
$801$	−1.34700	−	0.777689i	−0.0475938	−	0.0274783i
$802$		0			0
$803$	−22.4878	+	38.9500i	−0.793577	+	1.37452i
$804$		0			0
$805$	−25.8112	+	45.4882i	−0.909724	+	1.60325i
$806$		0			0
$807$	−8.89047	−	15.3988i	−0.312960	−	0.542062i
$808$		0			0
$809$	−19.3130			−0.679008			−0.339504	−	0.940605i	$-0.610259\pi$
$809$	−19.3130			−0.679008			−0.339504	+	0.940605i	$0.610259\pi$
$810$		0			0
$811$			21.4951i			0.754795i	0.926051	+	0.377397i	$0.123181\pi$
$811$			21.4951i			0.754795i	−0.926051	+	0.377397i	$0.876819\pi$
$812$		0			0
$813$	5.94046	+	3.42973i	0.208341	+	0.120286i
$814$		0			0
$815$	38.0207	+	65.8538i	1.33181	+	2.30676i
$816$		0			0
$817$	−3.34105	−	1.92896i	−0.116889	−	0.0674857i
$818$		0			0
$819$	18.1223	−	17.3901i	0.633245	−	0.607660i
$820$		0			0
$821$	−42.1884	−	24.3575i	−1.47239	−	0.850082i	−0.472868	−	0.881134i	$-0.656781\pi$
$821$	−42.1884	−	24.3575i	−1.47239	−	0.850082i	−0.999518	+	0.0310515i	$0.990114\pi$
$822$		0			0
$823$	9.05247	+	15.6793i	0.315549	+	0.546547i	0.979554	−	0.201181i	$-0.0644780\pi$
$823$	9.05247	+	15.6793i	0.315549	+	0.546547i	−0.664005	+	0.747728i	$0.731145\pi$
$824$		0			0
$825$	−17.7464	−	10.2459i	−0.617850	−	0.356716i
$826$		0			0
$827$			43.6958i			1.51945i	0.650244	+	0.759726i	$0.274667\pi$
$827$			43.6958i			1.51945i	−0.650244	+	0.759726i	$0.725333\pi$
$828$		0			0
$829$	−30.4929			−1.05906			−0.529530	−	0.848291i	$-0.677632\pi$
$829$	−30.4929			−1.05906			−0.529530	+	0.848291i	$0.677632\pi$
$830$		0			0
$831$	−5.63961	−	9.76810i	−0.195636	−	0.338852i
$832$		0			0
$833$	17.2606	−	30.9561i	0.598045	−	1.07256i
$834$		0			0
$835$	−28.6802	+	49.6755i	−0.992518	+	1.71909i
$836$		0			0
$837$	−30.2539	−	17.4671i	−1.04573	−	0.603752i
$838$		0			0
$839$	−27.3088	−	15.7668i	−0.942806	−	0.544329i	−0.0519670	−	0.998649i	$-0.516549\pi$
$839$	−27.3088	−	15.7668i	−0.942806	−	0.544329i	−0.890839	+	0.454320i	$0.849882\pi$
$840$		0			0
$841$	11.0684	−	19.1711i	0.381670	−	0.661072i
$842$		0			0
$843$			5.83716i			0.201042i
$844$		0			0
$845$	−52.2645	−	2.93940i	−1.79795	−	0.101118i
$846$		0			0
$847$	4.38130	+	2.48606i	0.150543	+	0.0854220i
$848$		0			0
$849$	−10.7528			−0.369035
$850$		0			0
$851$	8.68453	−	5.01402i	0.297702	−	0.171878i
$852$		0			0
$853$			49.9618i			1.71066i	0.518085	+	0.855329i	$0.326645\pi$
$853$			49.9618i			1.71066i	−0.518085	+	0.855329i	$0.673355\pi$
$854$		0			0
$855$	−17.5944	−	30.4743i	−0.601715	−	1.04220i
$856$		0			0
$857$	−20.4955	+	35.4993i	−0.700113	+	1.21263i	0.268313	+	0.963332i	$0.413534\pi$
$857$	−20.4955	+	35.4993i	−0.700113	+	1.21263i	−0.968426	+	0.249300i	$0.919799\pi$
$858$		0			0
$859$	22.7071	+	39.3298i	0.774756	+	1.34192i	0.934931	+	0.354829i	$0.115461\pi$
$859$	22.7071	+	39.3298i	0.774756	+	1.34192i	−0.160175	+	0.987089i	$0.551206\pi$
$860$		0			0
$861$	0.467089	−	0.00349186i	0.0159183	−	0.000119002i
$862$		0			0
$863$	−45.5827	+	26.3172i	−1.55165	+	0.895848i	−0.553647	+	0.832751i	$0.686764\pi$
$863$	−45.5827	+	26.3172i	−1.55165	+	0.895848i	−0.998007	+	0.0630969i	$0.979902\pi$
$864$		0			0
$865$	69.7432	−	40.2662i	2.37134	−	1.36909i
$866$		0			0
$867$	−2.61643	+	4.53179i	−0.0888587	+	0.153908i
$868$		0			0
$869$	18.0739	−	10.4350i	0.613114	−	0.353982i
$870$		0			0
$871$	−14.2926	−	4.26340i	−0.484288	−	0.144460i
$872$		0			0
$873$	13.0229	+	7.51876i	0.440757	+	0.254471i
$874$		0			0
$875$	32.6729	−	57.5810i	1.10455	−	1.94659i
$876$		0			0
$877$			11.7224i			0.395838i	0.980218	+	0.197919i	$0.0634183\pi$
$877$			11.7224i			0.395838i	−0.980218	+	0.197919i	$0.936582\pi$
$878$		0			0
$879$	−12.8851	−	7.43924i	−0.434605	−	0.250919i
$880$		0			0
$881$	−14.5273	−	25.1619i	−0.489435	−	0.847727i	0.510491	−	0.859883i	$-0.329464\pi$
$881$	−14.5273	−	25.1619i	−0.489435	−	0.847727i	−0.999926	+	0.0121562i	$0.996130\pi$
$882$		0			0
$883$	−41.9709			−1.41243			−0.706216	−	0.707996i	$-0.749599\pi$
$883$	−41.9709			−1.41243			−0.706216	+	0.707996i	$0.749599\pi$
$884$		0			0
$885$	−8.23137	+	14.2572i	−0.276695	+	0.479249i
$886$		0			0
$887$	−18.4327	+	31.9265i	−0.618911	+	1.07199i	0.370774	+	0.928723i	$0.379093\pi$
$887$	−18.4327	+	31.9265i	−0.618911	+	1.07199i	−0.989685	+	0.143262i	$0.954241\pi$
$888$		0			0
$889$	−0.0662649	−	8.86394i	−0.00222245	−	0.297287i
$890$		0			0
$891$		−	17.5861i		−	0.589155i
$892$		0			0
$893$	6.97597	+	12.0827i	0.233442	+	0.404333i
$894$		0			0
$895$	81.6086	−	47.1167i	2.72787	−	1.57494i
$896$		0			0
$897$	−7.36719	−	7.79317i	−0.245983	−	0.260206i
$898$		0			0
$899$		−	26.8162i		−	0.894370i
$900$		0			0
$901$	17.6613			0.588383
$902$		0			0
$903$	−1.60660	+	0.943652i	−0.0534642	+	0.0314028i
$904$		0			0
$905$	−17.9696	+	10.3748i	−0.597331	+	0.344869i
$906$		0			0
$907$	31.0746			1.03181			0.515907	−	0.856645i	$-0.327455\pi$
$907$	31.0746			1.03181			0.515907	+	0.856645i	$0.327455\pi$
$908$		0			0
$909$	−4.26583			−0.141489
$910$		0			0
$911$	12.7180			0.421365			0.210682	−	0.977555i	$-0.432431\pi$
$911$	12.7180			0.421365			0.210682	+	0.977555i	$0.432431\pi$
$912$		0			0
$913$	−31.6654			−1.04797
$914$		0			0
$915$	−28.0837	+	16.2141i	−0.928417	+	0.536022i
$916$		0			0
$917$	−0.240717	−	32.1995i	−0.00794918	−	1.06332i
$918$		0			0
$919$	−10.5876			−0.349253			−0.174627	−	0.984635i	$-0.555872\pi$
$919$	−10.5876			−0.349253			−0.174627	+	0.984635i	$0.555872\pi$
$920$		0			0
$921$		−	2.17550i		−	0.0716852i
$922$		0			0
$923$	3.34942	−	3.16634i	0.110247	−	0.104221i
$924$		0			0
$925$	−19.8384	+	11.4537i	−0.652282	+	0.376595i
$926$		0			0
$927$	−9.69255	−	16.7880i	−0.318345	−	0.551390i
$928$		0			0
$929$		−	15.4183i		−	0.505857i	−0.967485	−	0.252928i	$-0.918606\pi$
$929$		−	15.4183i		−	0.505857i	0.967485	−	0.252928i	$-0.0813937\pi$
$930$		0			0
$931$	−19.9449	+	11.9163i	−0.653668	+	0.390541i
$932$		0			0
$933$	2.61686	−	4.53253i	0.0856721	−	0.148388i
$934$		0			0
$935$	−30.7452	+	53.2522i	−1.00548	+	1.74153i
$936$		0			0
$937$	−1.66353			−0.0543452			−0.0271726	−	0.999631i	$-0.508650\pi$
$937$	−1.66353			−0.0543452			−0.0271726	+	0.999631i	$0.508650\pi$
$938$		0			0
$939$	5.46369	+	9.46339i	0.178301	+	0.308826i
$940$		0			0
$941$	−25.8392	−	14.9183i	−0.842335	−	0.486322i	0.0157224	−	0.999876i	$-0.494995\pi$
$941$	−25.8392	−	14.9183i	−0.842335	−	0.486322i	−0.858057	+	0.513554i	$0.828329\pi$
$942$		0			0
$943$			1.43052i			0.0465840i
$944$		0			0
$945$	−36.3581	+	0.271806i	−1.18273	+	0.00884184i
$946$		0			0
$947$	5.43043	+	3.13526i	0.176465	+	0.101882i	0.585631	−	0.810578i	$-0.300847\pi$
$947$	5.43043	+	3.13526i	0.176465	+	0.101882i	−0.409166	+	0.912460i	$0.634180\pi$
$948$		0			0
$949$	39.0725	−	36.9368i	1.26835	−	1.19902i
$950$		0			0
$951$	7.63418	−	4.40759i	0.247555	−	0.142926i
$952$		0			0
$953$	10.6219	−	18.3977i	0.344078	−	0.595960i	−0.641108	−	0.767451i	$-0.721525\pi$
$953$	10.6219	−	18.3977i	0.344078	−	0.595960i	0.985186	+	0.171491i	$0.0548583\pi$
$954$		0			0
$955$	77.8996	−	44.9754i	2.52077	−	1.45537i
$956$		0			0
$957$	−4.14572	+	2.39353i	−0.134012	+	0.0773719i
$958$		0			0
$959$	9.16187	−	0.0684922i	0.295852	−	0.00221173i
$960$		0			0
$961$	36.8891	+	63.8938i	1.18997	+	2.06109i
$962$		0			0
$963$	12.1862	−	21.1072i	0.392696	−	0.680169i
$964$		0			0
$965$	20.7701	+	35.9749i	0.668614	+	1.15807i
$966$		0			0
$967$			28.1083i			0.903902i	0.892043	+	0.451951i	$0.149272\pi$
$967$			28.1083i			0.903902i	−0.892043	+	0.451951i	$0.850728\pi$
$968$		0			0
$969$	8.81785	−	5.09099i	0.283270	−	0.163546i
$970$		0			0
$971$	19.0275			0.610621			0.305310	−	0.952253i	$-0.401240\pi$
$971$	19.0275			0.610621			0.305310	+	0.952253i	$0.401240\pi$
$972$		0			0
$973$	20.9415	−	12.3002i	0.671354	−	0.394327i
$974$		0			0
$975$	16.8291	+	17.8022i	0.538964	+	0.570127i
$976$		0			0
$977$			60.5225i			1.93629i	0.250400	+	0.968143i	$0.419438\pi$
$977$			60.5225i			1.93629i	−0.250400	+	0.968143i	$0.580562\pi$
$978$		0			0
$979$	0.890828	−	1.54296i	0.0284710	−	0.0493132i
$980$		0			0
$981$	−25.9674	−	14.9923i	−0.829075	−	0.478666i
$982$		0			0
$983$	38.4381	+	22.1922i	1.22598	+	0.707823i	0.966188	−	0.257840i	$-0.0830109\pi$
$983$	38.4381	+	22.1922i	1.22598	+	0.707823i	0.259797	+	0.965663i	$0.416344\pi$
$984$		0			0
$985$	53.8151	−	93.2104i	1.71469	−	2.96993i
$986$		0			0
$987$	6.73808	−	0.0503725i	0.214476	−	0.00160337i
$988$		0			0
$989$	−2.85310	−	4.94172i	−0.0907234	−	0.157138i
$990$		0			0
$991$	45.4599			1.44408			0.722040	−	0.691851i	$-0.243205\pi$
$991$	45.4599			1.44408			0.722040	+	0.691851i	$0.243205\pi$
$992$		0			0
$993$		−	17.2766i		−	0.548255i
$994$		0			0
$995$	0.306538	+	0.176980i	0.00971791	+	0.00561064i
$996$		0			0
$997$	−16.3250	−	28.2758i	−0.517018	−	0.895502i	−0.999805	−	0.0197639i	$-0.993709\pi$
$997$	−16.3250	−	28.2758i	−0.517018	−	0.895502i	0.482786	−	0.875738i	$-0.339625\pi$
$998$		0			0
$999$	6.03740	+	3.48569i	0.191015	+	0.110283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	364.2.bq.a.361.6	yes	18
3.2	odd	2		3276.2.fe.i.361.1		18
7.2	even	3		364.2.bb.a.205.4	✓	18
7.3	odd	6		2548.2.u.d.1765.6		18
7.4	even	3		2548.2.u.e.1765.4		18
7.5	odd	6		2548.2.bb.f.569.6		18
7.6	odd	2		2548.2.bq.f.361.4		18
13.4	even	6		364.2.bb.a.277.4	yes	18
21.2	odd	6		3276.2.hi.i.1297.9		18
39.17	odd	6		3276.2.hi.i.1369.9		18
91.4	even	6		2548.2.u.e.589.4		18
91.17	odd	6		2548.2.u.d.589.6		18
91.30	even	6	inner	364.2.bq.a.121.6	yes	18
91.69	odd	6		2548.2.bb.f.1733.6		18
91.82	odd	6		2548.2.bq.f.1941.4		18
273.212	odd	6		3276.2.fe.i.2305.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.4	✓	18	7.2	even	3
364.2.bb.a.277.4	yes	18	13.4	even	6
364.2.bq.a.121.6	yes	18	91.30	even	6	inner
364.2.bq.a.361.6	yes	18	1.1	even	1	trivial
2548.2.u.d.589.6		18	91.17	odd	6
2548.2.u.d.1765.6		18	7.3	odd	6
2548.2.u.e.589.4		18	91.4	even	6
2548.2.u.e.1765.4		18	7.4	even	3
2548.2.bb.f.569.6		18	7.5	odd	6
2548.2.bb.f.1733.6		18	91.69	odd	6
2548.2.bq.f.361.4		18	7.6	odd	2
2548.2.bq.f.1941.4		18	91.82	odd	6
3276.2.fe.i.361.1		18	3.2	odd	2
3276.2.fe.i.2305.1		18	273.212	odd	6
3276.2.hi.i.1297.9		18	21.2	odd	6
3276.2.hi.i.1369.9		18	39.17	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:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.605874 q^{3} +(3.48722 - 2.01335i) q^{5} +(2.30111 + 1.30571i) q^{7} -2.63292 q^{9} -3.01596i q^{11} +(-1.03064 + 3.45511i) q^{13} +(2.11282 - 1.21984i) q^{15} +(-2.53164 - 4.38494i) q^{17} +3.31908i q^{19} +(1.39418 + 0.791096i) q^{21} +(-2.45461 + 4.25150i) q^{23} +(5.60715 - 9.71187i) q^{25} -3.41284 q^{27} +(-1.30988 - 2.26878i) q^{29} +(8.86474 + 5.11806i) q^{31} -1.82729i q^{33} +(10.6533 - 0.0796422i) q^{35} +(-1.76903 - 1.02135i) q^{37} +(-0.624435 + 2.09336i) q^{39} +(0.252355 - 0.145697i) q^{41} +(-0.581173 + 1.00662i) q^{43} +(-9.18157 + 5.30098i) q^{45} +(3.64039 - 2.10178i) q^{47} +(3.59024 + 6.00917i) q^{49} +(-1.53386 - 2.65672i) q^{51} +(-1.74405 + 3.02079i) q^{53} +(-6.07218 - 10.5173i) q^{55} +2.01094i q^{57} +(-5.84388 + 3.37397i) q^{59} -13.2920 q^{61} +(-6.05864 - 3.43783i) q^{63} +(3.36229 + 14.1238i) q^{65} +4.13667i q^{67} +(-1.48718 + 2.57588i) q^{69} +(-1.10708 - 0.639174i) q^{71} +(-12.9146 - 7.45626i) q^{73} +(3.39722 - 5.88417i) q^{75} +(3.93797 - 6.94006i) q^{77} +(3.45991 + 5.99274i) q^{79} +5.83100 q^{81} -10.4993i q^{83} +(-17.6568 - 10.1942i) q^{85} +(-0.793622 - 1.37459i) q^{87} +(0.511598 + 0.295371i) q^{89} +(-6.88298 + 6.60489i) q^{91} +(5.37092 + 3.10090i) q^{93} +(6.68246 + 11.5744i) q^{95} +(-4.94617 - 2.85568i) q^{97} +7.94077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} + q^{7} + 12 q^{9} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 7 q^{21} - 6 q^{23} + 5 q^{25} - 20 q^{27} + 2 q^{29} + 9 q^{31} + 3 q^{35} + 18 q^{37} + 11 q^{39} - 9 q^{41} - 14 q^{43} + 30 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) \) 18 * q - 2 * q^3 + q^7 + 12 * q^9 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 7 * q^21 - 6 * q^23 + 5 * q^25 - 20 * q^27 + 2 * q^29 + 9 * q^31 + 3 * q^35 + 18 * q^37 + 11 * q^39 - 9 * q^41 - 14 * q^43 + 30 * q^45 + 36 * q^47 - 11 * q^49 + 2 * q^51 - 13 * q^53 - q^55 - 42 * q^61 - 32 * q^63 + 30 * q^65 - q^69 - 45 * q^71 - 33 * q^73 + 25 * q^75 - 9 * q^77 - 14 * q^79 + 2 * q^81 - 30 * q^85 + 2 * q^87 - 9 * q^89 + 21 * q^93 + 30 * q^95 - 18 * q^97

Introduction

L-functions

Modular forms

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