LMFDB - Embedded newform 418.2.s.a.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(107,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.s (of order $30$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			145.4
Character	$\chi$	$=$	418.145
Dual form			418.2.s.a.369.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 - 0.207912i) q^{2} +(-0.222075 + 0.498789i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.572934 + 0.636307i) q^{5} +(-0.113518 + 0.534061i) q^{6} +(-2.17900 + 2.99913i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.80792 + 2.00790i) q^{9} +O(q^{10})$	\(q+(0.978148 - 0.207912i) q^{2} +(-0.222075 + 0.498789i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.572934 + 0.636307i) q^{5} +(-0.113518 + 0.534061i) q^{6} +(-2.17900 + 2.99913i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.80792 + 2.00790i) q^{9} +(-0.428118 + 0.741522i) q^{10} +(-3.17725 + 0.951342i) q^{11} +0.545993i q^{12} +(3.46427 + 3.84746i) q^{13} +(-1.50783 + 3.38663i) q^{14} +(-0.190149 - 0.427081i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.554807 - 0.499551i) q^{17} +(2.18588 + 1.58813i) q^{18} +(3.57524 - 2.49352i) q^{19} +(-0.264591 + 0.814329i) q^{20} +(-1.01203 - 1.75289i) q^{21} +(-2.91003 + 1.59114i) q^{22} +(3.96120 - 6.86100i) q^{23} +(0.113518 + 0.534061i) q^{24} +(0.446008 + 4.24349i) q^{25} +(4.18849 + 3.04312i) q^{26} +(-2.96082 + 0.962029i) q^{27} +(-0.770756 + 3.62612i) q^{28} +(1.10809 - 0.493356i) q^{29} +(-0.274789 - 0.378214i) q^{30} +(-6.32104 - 2.05383i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.231070 - 1.79605i) q^{33} +(-0.646546 - 0.373283i) q^{34} +(-0.659949 - 3.10481i) q^{35} +(2.46830 + 1.09896i) q^{36} +(-2.29228 + 3.15505i) q^{37} +(2.97868 - 3.18236i) q^{38} +(-2.68840 + 0.873513i) q^{39} +(-0.0895010 + 0.851545i) q^{40} +(3.07895 + 1.37084i) q^{41} +(-1.35436 - 1.50417i) q^{42} +(5.26978 - 3.04251i) q^{43} +(-2.51562 + 2.16140i) q^{44} -2.31346 q^{45} +(2.44816 - 7.53465i) q^{46} +(-0.348275 - 3.31362i) q^{47} +(0.222075 + 0.498789i) q^{48} +(-2.08365 - 6.41280i) q^{49} +(1.31853 + 4.05803i) q^{50} +(0.372379 - 0.165794i) q^{51} +(4.72967 + 2.10578i) q^{52} +(-0.688966 + 0.620348i) q^{53} +(-2.69610 + 1.55660i) q^{54} +(1.21501 - 2.56677i) q^{55} +3.70713i q^{56} +(0.449767 + 2.33704i) q^{57} +(0.981306 - 0.712960i) q^{58} +(-7.04299 - 0.740248i) q^{59} +(-0.347419 - 0.312818i) q^{60} +(1.56819 - 7.37774i) q^{61} +(-6.60993 - 0.694731i) q^{62} +(-9.96140 + 1.04698i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.43296 q^{65} +(-0.147399 - 1.80484i) q^{66} +(7.95547 + 4.59309i) q^{67} +(-0.710027 - 0.230702i) q^{68} +(2.54251 + 3.49946i) q^{69} +(-1.29105 - 2.89976i) q^{70} +(-0.313847 - 0.282589i) q^{71} +(2.64285 + 0.561755i) q^{72} +(-7.11796 - 0.748127i) q^{73} +(-1.58622 + 3.56270i) q^{74} +(-2.21565 - 0.719909i) q^{75} +(2.25194 - 3.73212i) q^{76} +(4.07003 - 11.6020i) q^{77} +(-2.44804 + 1.41337i) q^{78} +(11.2711 - 2.39574i) q^{79} +(0.0895010 + 0.851545i) q^{80} +(-0.669598 + 6.37080i) q^{81} +(3.29668 + 0.700730i) q^{82} +(11.9260 - 3.87498i) q^{83} +(-1.63750 - 1.18972i) q^{84} +(0.635735 - 0.0668185i) q^{85} +(4.52205 - 4.07167i) q^{86} +0.662268i q^{87} +(-2.01127 + 2.63720i) q^{88} +(-1.64726 - 0.951047i) q^{89} +(-2.26290 + 0.480995i) q^{90} +(-19.0877 + 2.00619i) q^{91} +(0.828117 - 7.87900i) q^{92} +(2.42817 - 2.69676i) q^{93} +(-1.02960 - 3.16880i) q^{94} +(-0.461734 + 3.70357i) q^{95} +(0.320926 + 0.441717i) q^{96} +(-1.38694 - 6.52504i) q^{97} +(-3.37141 - 5.83945i) q^{98} +(-7.65442 - 4.65965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) $ 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$3$	−0.222075	+	0.498789i	−0.128215	+	0.287976i	−0.966234	−	0.257665i	$-0.917047\pi$
$3$	−0.222075	+	0.498789i	−0.128215	+	0.287976i	0.838019	+	0.545641i	$0.183714\pi$
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	−0.572934	+	0.636307i	−0.256224	+	0.284565i	−0.857509	−	0.514469i	$-0.827989\pi$
$5$	−0.572934	+	0.636307i	−0.256224	+	0.284565i	0.601285	+	0.799035i	$0.294656\pi$
$6$	−0.113518	+	0.534061i	−0.0463436	+	0.218030i
$7$	−2.17900	+	2.99913i	−0.823583	+	1.13357i	0.165500	+	0.986210i	$0.447076\pi$
$7$	−2.17900	+	2.99913i	−0.823583	+	1.13357i	−0.989084	+	0.147356i	$0.952924\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.80792	+	2.00790i	0.602640	+	0.669299i
$10$	−0.428118	+	0.741522i	−0.135383	+	0.234490i
$11$	−3.17725	+	0.951342i	−0.957978	+	0.286841i
$11$	−3.17725	+	0.951342i	−0.957978	+	0.286841i
$12$			0.545993i			0.157615i
$13$	3.46427	+	3.84746i	0.960814	+	1.06709i	0.997701	+	0.0677731i	$0.0215894\pi$
$13$	3.46427	+	3.84746i	0.960814	+	1.06709i	−0.0368863	+	0.999319i	$0.511744\pi$
$14$	−1.50783	+	3.38663i	−0.402983	+	0.905116i
$15$	−0.190149	−	0.427081i	−0.0490962	−	0.110272i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	−0.554807	−	0.499551i	−0.134561	−	0.121159i	0.599102	−	0.800672i	$-0.295524\pi$
$17$	−0.554807	−	0.499551i	−0.134561	−	0.121159i	−0.733663	+	0.679514i	$0.762191\pi$
$18$	2.18588	+	1.58813i	0.515216	+	0.374326i
$19$	3.57524	−	2.49352i	0.820217	−	0.572052i
$19$	3.57524	−	2.49352i	0.820217	−	0.572052i
$20$	−0.264591	+	0.814329i	−0.0591644	+	0.182089i
$21$	−1.01203	−	1.75289i	−0.220844	−	0.382513i
$22$	−2.91003	+	1.59114i	−0.620420	+	0.339233i
$23$	3.96120	−	6.86100i	0.825968	−	1.43062i	−0.0752100	−	0.997168i	$-0.523963\pi$
$23$	3.96120	−	6.86100i	0.825968	−	1.43062i	0.901178	−	0.433450i	$-0.142704\pi$
$24$	0.113518	+	0.534061i	0.0231718	+	0.109015i
$25$	0.446008	+	4.24349i	0.0892017	+	0.848697i
$26$	4.18849	+	3.04312i	0.821431	+	0.596805i
$27$	−2.96082	+	0.962029i	−0.569810	+	0.185143i
$28$	−0.770756	+	3.62612i	−0.145659	+	0.685272i
$29$	1.10809	−	0.493356i	0.205768	−	0.0916138i	−0.301265	−	0.953540i	$-0.597409\pi$
$29$	1.10809	−	0.493356i	0.205768	−	0.0916138i	0.507033	+	0.861927i	$0.330742\pi$
$30$	−0.274789	−	0.378214i	−0.0501693	−	0.0690522i
$31$	−6.32104	−	2.05383i	−1.13529	−	0.368879i	−0.319707	−	0.947516i	$-0.603585\pi$
$31$	−6.32104	−	2.05383i	−1.13529	−	0.368879i	−0.815585	+	0.578637i	$0.803585\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.231070	−	1.79605i	0.0402242	−	0.312652i
$34$	−0.646546	−	0.373283i	−0.110882	−	0.0640176i
$35$	−0.659949	−	3.10481i	−0.111552	−	0.524809i
$36$	2.46830	+	1.09896i	0.411384	+	0.183160i
$37$	−2.29228	+	3.15505i	−0.376849	+	0.518688i	−0.954746	−	0.297422i	$-0.903873\pi$
$37$	−2.29228	+	3.15505i	−0.376849	+	0.518688i	0.577898	+	0.816109i	$0.303873\pi$
$38$	2.97868	−	3.18236i	0.483206	−	0.516248i
$39$	−2.68840	+	0.873513i	−0.430488	+	0.139874i
$40$	−0.0895010	+	0.851545i	−0.0141514	+	0.134641i
$41$	3.07895	+	1.37084i	0.480851	+	0.214089i	0.632823	−	0.774296i	$-0.281896\pi$
$41$	3.07895	+	1.37084i	0.480851	+	0.214089i	−0.151973	+	0.988385i	$0.548563\pi$
$42$	−1.35436	−	1.50417i	−0.208983	−	0.232099i
$43$	5.26978	−	3.04251i	0.803634	−	0.463978i	−0.0411062	−	0.999155i	$-0.513088\pi$
$43$	5.26978	−	3.04251i	0.803634	−	0.463978i	0.844740	+	0.535176i	$0.179755\pi$
$44$	−2.51562	+	2.16140i	−0.379244	+	0.325843i
$45$	−2.31346			−0.344870
$46$	2.44816	−	7.53465i	0.360961	−	1.11092i
$47$	−0.348275	−	3.31362i	−0.0508011	−	0.483341i	−0.990113	−	0.140275i	$-0.955201\pi$
$47$	−0.348275	−	3.31362i	−0.0508011	−	0.483341i	0.939311	−	0.343066i	$-0.111465\pi$
$48$	0.222075	+	0.498789i	0.0320538	+	0.0719940i
$49$	−2.08365	−	6.41280i	−0.297664	−	0.916115i
$50$	1.31853	+	4.05803i	0.186469	+	0.573891i
$51$	0.372379	−	0.165794i	0.0521435	−	0.0232158i
$52$	4.72967	+	2.10578i	0.655887	+	0.292020i
$53$	−0.688966	+	0.620348i	−0.0946368	+	0.0852113i	−0.715091	−	0.699031i	$-0.753615\pi$
$53$	−0.688966	+	0.620348i	−0.0946368	+	0.0852113i	0.620454	+	0.784242i	$0.286948\pi$
$54$	−2.69610	+	1.55660i	−0.366893	+	0.211826i
$55$	1.21501	−	2.56677i	0.163832	−	0.346103i
$56$			3.70713i			0.495386i
$57$	0.449767	+	2.33704i	0.0595730	+	0.309549i
$58$	0.981306	−	0.712960i	0.128852	−	0.0936163i
$59$	−7.04299	−	0.740248i	−0.916919	−	0.0963721i	−0.365700	−	0.930733i	$-0.619170\pi$
$59$	−7.04299	−	0.740248i	−0.916919	−	0.0963721i	−0.551219	+	0.834361i	$0.685837\pi$
$60$	−0.347419	−	0.312818i	−0.0448516	−	0.0403846i
$61$	1.56819	−	7.37774i	0.200786	−	0.944623i	−0.756167	−	0.654379i	$-0.772930\pi$
$61$	1.56819	−	7.37774i	0.200786	−	0.944623i	0.956953	−	0.290244i	$-0.0937365\pi$
$62$	−6.60993	−	0.694731i	−0.839461	−	0.0882309i
$63$	−9.96140	+	1.04698i	−1.25502	+	0.131908i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−4.43296			−0.549841
$66$	−0.147399	−	1.80484i	−0.0181435	−	0.222161i
$67$	7.95547	+	4.59309i	0.971915	+	0.561135i	0.899819	−	0.436262i	$-0.143698\pi$
$67$	7.95547	+	4.59309i	0.971915	+	0.561135i	0.0720954	+	0.997398i	$0.477031\pi$
$68$	−0.710027	−	0.230702i	−0.0861034	−	0.0279767i
$69$	2.54251	+	3.49946i	0.306082	+	0.421286i
$70$	−1.29105	−	2.89976i	−0.154311	−	0.346587i
$71$	−0.313847	−	0.282589i	−0.0372468	−	0.0335371i	0.650297	−	0.759680i	$-0.274644\pi$
$71$	−0.313847	−	0.282589i	−0.0372468	−	0.0335371i	−0.687544	+	0.726143i	$0.741311\pi$
$72$	2.64285	+	0.561755i	0.311463	+	0.0662035i
$73$	−7.11796	−	0.748127i	−0.833094	−	0.0875617i	−0.321629	−	0.946866i	$-0.604230\pi$
$73$	−7.11796	−	0.748127i	−0.833094	−	0.0875617i	−0.511465	+	0.859304i	$0.670897\pi$
$74$	−1.58622	+	3.56270i	−0.184394	+	0.414155i
$75$	−2.21565	−	0.719909i	−0.255841	−	0.0831279i
$76$	2.25194	−	3.73212i	0.258316	−	0.428104i
$77$	4.07003	−	11.6020i	0.463823	−	1.32217i
$78$	−2.44804	+	1.41337i	−0.277185	+	0.160033i
$79$	11.2711	−	2.39574i	1.26809	−	0.269541i	0.475730	−	0.879592i	$-0.342184\pi$
$79$	11.2711	−	2.39574i	1.26809	−	0.269541i	0.792363	+	0.610050i	$0.208851\pi$
$80$	0.0895010	+	0.851545i	0.0100065	+	0.0952056i
$81$	−0.669598	+	6.37080i	−0.0743998	+	0.707867i
$82$	3.29668	+	0.700730i	0.364057	+	0.0773827i
$83$	11.9260	−	3.87498i	1.30905	−	0.425335i	0.430327	−	0.902673i	$-0.358398\pi$
$83$	11.9260	−	3.87498i	1.30905	−	0.425335i	0.878720	+	0.477338i	$0.158398\pi$
$84$	−1.63750	−	1.18972i	−0.178666	−	0.129809i
$85$	0.635735	−	0.0668185i	0.0689552	−	0.00724748i
$86$	4.52205	−	4.07167i	0.487625	−	0.439060i
$87$			0.662268i			0.0710026i
$88$	−2.01127	+	2.63720i	−0.214402	+	0.281126i
$89$	−1.64726	−	0.951047i	−0.174609	−	0.100811i	0.410148	−	0.912019i	$-0.365477\pi$
$89$	−1.64726	−	0.951047i	−0.174609	−	0.100811i	−0.584757	+	0.811208i	$0.698810\pi$
$90$	−2.26290	+	0.480995i	−0.238531	+	0.0507013i
$91$	−19.0877	+	2.00619i	−2.00093	+	0.210306i
$92$	0.828117	−	7.87900i	0.0863371	−	0.821443i
$93$	2.42817	−	2.69676i	0.251790	−	0.279641i
$94$	−1.02960	−	3.16880i	−0.106196	−	0.326836i
$95$	−0.461734	+	3.70357i	−0.0473729	+	0.379979i
$96$	0.320926	+	0.441717i	0.0327544	+	0.0450826i
$97$	−1.38694	−	6.52504i	−0.140822	−	0.662517i	−0.990759	−	0.135632i	$-0.956693\pi$
$97$	−1.38694	−	6.52504i	−0.140822	−	0.662517i	0.849937	−	0.526885i	$-0.176640\pi$
$98$	−3.37141	−	5.83945i	−0.340564	−	0.589874i
$99$	−7.65442	−	4.65965i	−0.769298	−	0.468313i
$100$	2.13343	+	3.69521i	0.213343	+	0.369521i
$101$	3.71140	−	3.34176i	0.369298	−	0.332518i	−0.463497	−	0.886098i	$-0.653406\pi$
$101$	3.71140	−	3.34176i	0.369298	−	0.332518i	0.832796	+	0.553581i	$0.186739\pi$
$102$	0.329772	−	0.239593i	0.0326522	−	0.0237232i
$103$	−2.58905	+	3.56352i	−0.255107	+	0.351125i	−0.917292	−	0.398216i	$-0.869629\pi$
$103$	−2.58905	+	3.56352i	−0.255107	+	0.351125i	0.662185	+	0.749341i	$0.269629\pi$
$104$	5.06413	+	1.07641i	0.496579	+	0.105551i
$105$	1.69521	+	0.360327i	0.165435	+	0.0351643i
$106$	−0.544933	+	0.750036i	−0.0529286	+	0.0728499i
$107$	13.5513	−	9.84562i	1.31006	−	0.951812i	0.310058	−	0.950718i	$-0.399652\pi$
$107$	13.5513	−	9.84562i	1.31006	−	0.951812i	0.999999	−	0.00109471i	$-0.000348457\pi$
$108$	−2.31355	+	2.08313i	−0.222622	+	0.200449i
$109$	−6.41414	−	11.1096i	−0.614363	−	1.06411i	−0.990496	−	0.137543i	$-0.956080\pi$
$109$	−6.41414	−	11.1096i	−0.614363	−	1.06411i	0.376133	−	0.926566i	$-0.377254\pi$
$110$	0.654798	−	2.76329i	0.0624326	−	0.263469i
$111$	−1.06465	−	1.84402i	−0.101052	−	0.175027i
$112$	0.770756	+	3.62612i	0.0728296	+	0.342636i
$113$	4.99544	+	6.87563i	0.469931	+	0.646805i	0.976531	−	0.215376i	$-0.0690979\pi$
$113$	4.99544	+	6.87563i	0.469931	+	0.646805i	−0.506600	+	0.862181i	$0.669098\pi$
$114$	0.925836	+	2.19246i	0.0867125	+	0.205343i
$115$	2.09620	+	6.45144i	0.195472	+	0.601600i
$116$	0.811629	−	0.901406i	0.0753579	−	0.0836934i
$117$	−1.46219	+	13.9118i	−0.135179	+	1.28614i
$118$	−7.04299	+	0.740248i	−0.648360	+	0.0681454i
$119$	2.70714	−	0.575421i	0.248163	−	0.0527487i
$120$	−0.404866	−	0.233749i	−0.0369590	−	0.0213383i
$121$	9.18990	−	6.04531i	0.835445	−	0.549574i
$122$		−	7.54257i		−	0.682872i
$123$	−1.36752	+	1.23132i	−0.123305	+	0.111024i
$124$	−6.60993	+	0.694731i	−0.593589	+	0.0623887i
$125$	−6.41924	−	4.66385i	−0.574154	−	0.417148i
$126$	−9.52604	+	3.09520i	−0.848647	+	0.275742i
$127$	−13.5611	−	2.88250i	−1.20335	−	0.255781i	−0.437752	−	0.899096i	$-0.644225\pi$
$127$	−13.5611	−	2.88250i	−1.20335	−	0.255781i	−0.765601	+	0.643315i	$0.777558\pi$
$128$	0.104528	−	0.994522i	0.00923910	−	0.0879041i
$129$	0.347283	+	3.30418i	0.0305766	+	0.290916i
$130$	−4.33609	+	0.921664i	−0.380300	+	0.0808353i
$131$	−8.77836	+	5.06819i	−0.766969	+	0.442810i	−0.831792	−	0.555087i	$-0.812685\pi$
$131$	−8.77836	+	5.06819i	−0.766969	+	0.442810i	0.0648232	+	0.997897i	$0.479352\pi$
$132$	−0.519426	−	1.73476i	−0.0452102	−	0.150991i
$133$	−0.312056	+	16.1560i	−0.0270587	+	1.40090i
$134$	8.73658	+	2.83869i	0.754725	+	0.245225i
$135$	1.08421	−	2.43517i	0.0933137	−	0.209586i
$136$	−0.742477	−	0.0780375i	−0.0636669	−	0.00669166i
$137$	20.1076	+	4.27400i	1.71791	+	0.365152i	0.958418	−	0.285369i	$-0.0921161\pi$
$137$	20.1076	+	4.27400i	1.71791	+	0.365152i	0.759488	+	0.650521i	$0.225449\pi$
$138$	3.21453	+	2.89437i	0.273639	+	0.246385i
$139$	5.34198	+	11.9983i	0.453101	+	1.01768i	0.985264	+	0.171039i	$0.0547124\pi$
$139$	5.34198	+	11.9983i	0.453101	+	1.01768i	−0.532164	+	0.846641i	$0.678621\pi$
$140$	−1.86573	−	2.56796i	−0.157683	−	0.217033i
$141$	1.73014	+	0.562156i	0.145704	+	0.0473421i
$142$	−0.365742	−	0.211161i	−0.0306924	−	0.0177203i
$143$	−14.6671	−	8.92865i	−1.22652	−	0.746651i
$144$	2.70189			0.225158
$145$	−0.320939	+	0.987749i	−0.0266525	+	0.0820281i
$146$	−7.11796	+	0.748127i	−0.589086	+	0.0619155i
$147$	3.66136	+	0.384825i	0.301984	+	0.0317398i
$148$	−0.810826	+	3.81464i	−0.0666495	+	0.313561i
$149$	−3.23630	−	2.91398i	−0.265128	−	0.238723i	0.525834	−	0.850587i	$-0.323753\pi$
$149$	−3.23630	−	2.91398i	−0.265128	−	0.238723i	−0.790963	+	0.611864i	$0.790420\pi$
$150$	−2.31691	−	0.243517i	−0.189175	−	0.0198831i
$151$	−10.9573	+	7.96095i	−0.891693	+	0.647853i	−0.936319	−	0.351151i	$-0.885791\pi$
$151$	−10.9573	+	7.96095i	−0.891693	+	0.647853i	0.0446256	+	0.999004i	$0.485791\pi$
$152$	1.42678	−	4.11877i	0.115727	−	0.334077i
$153$		−	2.01714i		−	0.163076i
$154$	1.56890	−	12.1947i	0.126426	−	0.982673i
$155$	4.92840	−	2.84541i	0.395859	−	0.228549i
$156$	−2.10068	+	1.89146i	−0.168189	+	0.151438i
$157$	17.8804	+	7.96087i	1.42701	+	0.635347i	0.967511	−	0.252830i	$-0.0813613\pi$
$157$	17.8804	+	7.96087i	1.42701	+	0.635347i	0.459502	+	0.888177i	$0.348028\pi$
$158$	10.5267	−	4.68677i	0.837455	−	0.372859i
$159$	−0.156420	−	0.481413i	−0.0124049	−	0.0381785i
$160$	0.264591	+	0.814329i	0.0209178	+	0.0643783i
$161$	11.9456	+	26.8303i	0.941446	+	2.11452i
$162$	0.669598	+	6.37080i	0.0526086	+	0.500538i
$163$	−2.05671	+	6.32991i	−0.161094	+	0.495797i	−0.998727	−	0.0504365i	$-0.983939\pi$
$163$	−2.05671	+	6.32991i	−0.161094	+	0.495797i	0.837633	+	0.546233i	$0.183939\pi$
$164$	3.37033			0.263178
$165$	1.01045	+	1.17605i	0.0786635	+	0.0915553i
$166$	10.8597	−	6.26986i	0.842877	−	0.486635i
$167$	−16.0284	−	17.8013i	−1.24031	−	1.37751i	−0.899232	−	0.437471i	$-0.855874\pi$
$167$	−16.0284	−	17.8013i	−1.24031	−	1.37751i	−0.341080	−	0.940034i	$-0.610793\pi$
$168$	−1.84908	−	0.823262i	−0.142659	−	0.0635160i
$169$	−1.44292	+	13.7284i	−0.110994	+	1.05603i
$170$	0.607951	−	0.197535i	0.0466277	−	0.0151503i
$171$	11.4705	+	2.67064i	0.877169	+	0.204229i
$172$	3.57668	−	4.92288i	0.272720	−	0.375366i
$173$	15.9855	+	7.11720i	1.21535	+	0.541110i	0.911378	−	0.411569i	$-0.135019\pi$
$173$	15.9855	+	7.11720i	1.21535	+	0.541110i	0.303975	+	0.952680i	$0.401686\pi$
$174$	0.137693	+	0.647796i	0.0104385	+	0.0491093i
$175$	−13.6986	−	7.90890i	−1.03552	−	0.597857i
$176$	−1.41901	+	2.99773i	−0.106962	+	0.225963i
$177$	1.93330	−	3.34858i	0.145316	−	0.251694i
$178$	−1.80900	−	0.587779i	−0.135590	−	0.0440559i
$179$	−6.85131	−	9.43002i	−0.512091	−	0.704833i	0.472179	−	0.881503i	$-0.343468\pi$
$179$	−6.85131	−	9.43002i	−0.512091	−	0.704833i	−0.984270	+	0.176670i	$0.943468\pi$
$180$	−2.11345	+	0.940968i	−0.157527	+	0.0701356i
$181$	−2.06365	+	9.70870i	−0.153390	+	0.721642i	0.832470	+	0.554070i	$0.186926\pi$
$181$	−2.06365	+	9.70870i	−0.153390	+	0.721642i	−0.985860	+	0.167572i	$0.946407\pi$
$182$	−18.2534	+	5.93090i	−1.35303	+	0.439628i
$183$	3.33168	+	2.42061i	0.246285	+	0.178937i
$184$	−0.828117	−	7.87900i	−0.0610496	−	0.580848i
$185$	−0.694259	−	3.26623i	−0.0510429	−	0.240138i
$186$	1.81443	−	3.14268i	0.133040	−	0.230432i
$187$	2.23801	+	1.05939i	0.163659	+	0.0774701i
$188$	−1.66593	−	2.88548i	−0.121501	−	0.210445i
$189$	3.56637	−	10.9762i	0.259415	−	0.798398i
$190$	0.318372	+	3.71864i	0.0230972	+	0.269779i
$191$	−9.69630	−	7.04477i	−0.701599	−	0.509742i	0.178853	−	0.983876i	$-0.442761\pi$
$191$	−9.69630	−	7.04477i	−0.701599	−	0.509742i	−0.880453	+	0.474134i	$0.842761\pi$
$192$	0.405752	+	0.365340i	0.0292826	+	0.0263662i
$193$	5.65863	−	6.28454i	0.407317	−	0.452371i	−0.504229	−	0.863570i	$-0.668223\pi$
$193$	5.65863	−	6.28454i	0.407317	−	0.452371i	0.911546	+	0.411199i	$0.134890\pi$
$194$	−2.71326	−	6.09409i	−0.194801	−	0.437530i
$195$	0.984450	−	2.21111i	0.0704980	−	0.158341i
$196$	−4.51183	−	5.01089i	−0.322273	−	0.357921i
$197$		−	12.8338i		−	0.914372i	−0.889371	−	0.457186i	$-0.848857\pi$
$197$		−	12.8338i		−	0.914372i	0.889371	−	0.457186i	$-0.151143\pi$
$198$	−8.45594	−	2.96638i	−0.600938	−	0.210812i
$199$	−10.8328	+	18.7630i	−0.767919	+	1.33007i	0.170771	+	0.985311i	$0.445374\pi$
$199$	−10.8328	+	18.7630i	−0.767919	+	1.33007i	−0.938689	+	0.344764i	$0.887959\pi$
$200$	2.85509	+	3.17090i	0.201885	+	0.224216i
$201$	−4.05770	+	2.94809i	−0.286208	+	0.207942i
$202$	2.93551	−	4.04038i	0.206542	−	0.284280i
$203$	−0.934897	+	4.39834i	−0.0656169	+	0.308703i
$204$	0.272751	−	0.302921i	0.0190964	−	0.0212087i
$205$	−2.63630	+	1.17376i	−0.184127	+	0.0819788i
$206$	−1.79158	+	4.02395i	−0.124825	+	0.280362i
$207$	20.9377	−	4.45045i	1.45527	−	0.309328i
$208$	5.17726			0.358979
$209$	−8.98727	+	11.3238i	−0.621663	+	0.783285i
$210$	1.73308			0.119594
$211$	13.6592	−	2.90335i	0.940337	−	0.199875i	0.287850	−	0.957675i	$-0.407059\pi$
$211$	13.6592	−	2.90335i	0.940337	−	0.199875i	0.652486	+	0.757801i	$0.273726\pi$
$212$	−0.377084	+	0.846944i	−0.0258982	+	0.0581683i
$213$	0.210650	−	0.0937874i	0.0144335	−	0.00642620i
$214$	11.2082	−	12.4480i	0.766176	−	0.850925i
$215$	−1.08326	+	5.09636i	−0.0738780	+	0.347569i
$216$	−1.82989	+	2.51862i	−0.124508	+	0.171371i
$217$	19.9332	−	14.4823i	1.35316	−	0.983125i
$218$	−8.58380	−	9.53327i	−0.581368	−	0.645675i
$219$	1.95388	−	3.38422i	0.132031	−	0.228684i
$220$	0.0659690	−	2.83905i	0.00444763	−	0.191408i
$221$		−	3.86517i		−	0.260000i
$222$	−1.42478	−	1.58237i	−0.0956247	−	0.106202i
$223$	−4.90879	+	11.0253i	−0.328717	+	0.738311i	−0.999996	−	0.00289442i	$-0.999079\pi$
$223$	−4.90879	+	11.0253i	−0.328717	+	0.738311i	0.671279	+	0.741205i	$0.265745\pi$
$224$	1.50783	+	3.38663i	0.100746	+	0.226279i
$225$	−7.71414	+	8.56742i	−0.514276	+	0.571161i
$226$	6.31580	+	5.68677i	0.420121	+	0.378278i
$227$	24.1886	+	17.5740i	1.60545	+	1.16643i	0.875886	+	0.482518i	$0.160278\pi$
$227$	24.1886	+	17.5740i	1.60545	+	1.16643i	0.729566	+	0.683910i	$0.239722\pi$
$228$	1.36144	+	1.95206i	0.0901637	+	0.129278i
$229$	−4.08424	+	12.5700i	−0.269894	+	0.830649i	0.720631	+	0.693319i	$0.243852\pi$
$229$	−4.08424	+	12.5700i	−0.269894	+	0.830649i	−0.990525	+	0.137330i	$0.956148\pi$
$230$	3.39172	+	5.87464i	0.223644	+	0.387362i
$231$	4.88309	+	4.60660i	0.321284	+	0.303092i
$232$	0.606480	−	1.05045i	0.0398174	−	0.0689657i
$233$	−0.112467	−	0.529113i	−0.00736793	−	0.0346634i	0.974310	−	0.225211i	$-0.0723071\pi$
$233$	−0.112467	−	0.529113i	−0.00736793	−	0.0346634i	−0.981678	+	0.190547i	$0.938974\pi$
$234$	1.46219	+	13.9118i	0.0955861	+	0.909441i
$235$	2.30802	+	1.67687i	0.150558	+	0.109387i
$236$	−6.73518	+	2.18839i	−0.438423	+	0.142452i
$237$	−1.30805	+	6.15391i	−0.0849673	+	0.399740i
$238$	2.52835	−	1.12569i	0.163888	−	0.0729678i
$239$	9.90308	+	13.6304i	0.640577	+	0.881679i	0.998646	−	0.0520165i	$-0.0165648\pi$
$239$	9.90308	+	13.6304i	0.640577	+	0.881679i	−0.358069	+	0.933695i	$0.616565\pi$
$240$	−0.444617	−	0.144465i	−0.0286999	−	0.00932517i
$241$	1.80820	−	3.13190i	0.116477	−	0.201744i	−0.801892	−	0.597468i	$-0.796173\pi$
$241$	1.80820	−	3.13190i	0.116477	−	0.201744i	0.918369	+	0.395725i	$0.129507\pi$
$242$	7.73218	−	7.82390i	0.497044	−	0.502939i
$243$	−11.1173	−	6.41857i	−0.713175	−	0.411752i
$244$	−1.56819	−	7.37774i	−0.100393	−	0.472312i
$245$	5.27430	+	2.34827i	0.336963	+	0.150026i
$246$	−1.08163	+	1.48873i	−0.0689620	+	0.0949181i
$247$	21.9793	+	5.11739i	1.39851	+	0.325612i
$248$	−6.32104	+	2.05383i	−0.401386	+	0.130418i
$249$	−0.715664	+	6.80909i	−0.0453534	+	0.431508i
$250$	−7.24863	−	3.22730i	−0.458444	−	0.204112i
$251$	−6.11794	−	6.79466i	−0.386161	−	0.428875i	0.518454	−	0.855106i	$-0.326508\pi$
$251$	−6.11794	−	6.79466i	−0.386161	−	0.428875i	−0.904615	+	0.426231i	$0.859841\pi$
$252$	−8.67434	+	5.00813i	−0.546432	+	0.315483i
$253$	−6.05858	+	25.5676i	−0.380900	+	1.60742i
$254$	−13.8641			−0.869909
$255$	−0.107853	+	0.331937i	−0.00675400	+	0.0207867i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	−3.09962	−	6.96187i	−0.193349	−	0.434269i	0.790691	−	0.612215i	$-0.209721\pi$
$257$	−3.09962	−	6.96187i	−0.193349	−	0.434269i	−0.984040	+	0.177946i	$0.943055\pi$
$258$	1.02667	+	3.15977i	0.0639177	+	0.196719i
$259$	−4.46755	−	13.7497i	−0.277600	−	0.854365i
$260$	−4.04971	+	1.80305i	−0.251152	+	0.111820i
$261$	2.99395	+	1.33299i	0.185321	+	0.0825102i
$262$	−7.53280	+	6.78256i	−0.465378	+	0.419028i
$263$	5.09555	−	2.94192i	0.314205	−	0.181407i	−0.334601	−	0.942360i	$-0.608602\pi$
$263$	5.09555	−	2.94192i	0.314205	−	0.181407i	0.648807	+	0.760953i	$0.275268\pi$
$264$	−0.868752	−	1.58885i	−0.0534680	−	0.0977872i
$265$		−	0.793812i		−	0.0487635i
$266$	3.05378	+	15.8678i	0.187239	+	0.972919i
$267$	0.840188	−	0.610432i	0.0514187	−	0.0373578i
$268$	9.13586	+	0.960217i	0.558061	+	0.0586546i
$269$	−9.62339	−	8.66494i	−0.586748	−	0.528310i	0.321409	−	0.946941i	$-0.395844\pi$
$269$	−9.62339	−	8.66494i	−0.586748	−	0.528310i	−0.908157	+	0.418630i	$0.862510\pi$
$270$	0.554215	−	2.60738i	0.0337284	−	0.158680i
$271$	−25.5610	−	2.68656i	−1.55272	−	0.163197i	−0.711030	−	0.703162i	$-0.751771\pi$
$271$	−25.5610	−	2.68656i	−1.55272	−	0.163197i	−0.841688	+	0.539965i	$0.818438\pi$
$272$	−0.742477	+	0.0780375i	−0.0450193	+	0.00473172i
$273$	3.23823	−	9.96624i	0.195986	−	0.603184i
$274$	20.5568			1.24188
$275$	−5.45409	−	13.0583i	−0.328894	−	0.787447i
$276$	3.74606	+	2.16279i	0.225486	+	0.130184i
$277$	26.3055	+	8.54717i	1.58054	+	0.513550i	0.962197	−	0.272356i	$-0.0878028\pi$
$277$	26.3055	+	8.54717i	1.58054	+	0.513550i	0.618347	+	0.785905i	$0.287803\pi$
$278$	7.71982	+	10.6254i	0.463004	+	0.637271i
$279$	−7.30405	−	16.4052i	−0.437282	−	0.982151i
$280$	−2.35887	−	2.12394i	−0.140970	−	0.126930i
$281$	−14.7355	−	3.13213i	−0.879046	−	0.186847i	−0.253783	−	0.967261i	$-0.581675\pi$
$281$	−14.7355	−	3.13213i	−0.879046	−	0.186847i	−0.625263	+	0.780414i	$0.715008\pi$
$282$	1.80921	+	0.190156i	0.107737	+	0.0113236i
$283$	−7.33683	+	16.4788i	−0.436129	+	0.979563i	0.553090	+	0.833122i	$0.313449\pi$
$283$	−7.33683	+	16.4788i	−0.436129	+	0.979563i	−0.989219	+	0.146441i	$0.953218\pi$
$284$	−0.401652	−	0.130505i	−0.0238337	−	0.00774404i
$285$	−1.74476	−	1.05278i	−0.103351	−	0.0623613i
$286$	−16.2030	−	5.68407i	−0.958101	−	0.336106i
$287$	−10.8203	+	6.24712i	−0.638704	+	0.368756i
$288$	2.64285	−	0.561755i	0.155731	−	0.0331017i
$289$	−1.71872	−	16.3526i	−0.101101	−	0.961916i
$290$	−0.108561	+	1.03289i	−0.00637493	+	0.0606534i
$291$	3.56262	+	0.757259i	0.208845	+	0.0443913i
$292$	−6.80687	+	2.21169i	−0.398342	+	0.129429i
$293$	−19.3596	−	14.0656i	−1.13100	−	0.821720i	−0.145160	−	0.989408i	$-0.546370\pi$
$293$	−19.3596	−	14.0656i	−1.13100	−	0.821720i	−0.985840	+	0.167688i	$0.946370\pi$
$294$	3.66136	−	0.384825i	0.213535	−	0.0224434i
$295$	4.50619	−	4.05739i	0.262361	−	0.236231i
$296$			3.89986i			0.226675i
$297$	8.49206	−	5.87337i	0.492760	−	0.340807i
$298$	−3.77143	−	2.17744i	−0.218473	−	0.126136i
$299$	40.1201	−	8.52778i	2.32020	−	0.493174i
$300$	−2.31691	+	0.243517i	−0.133767	+	0.0140595i
$301$	−2.35795	+	22.4344i	−0.135910	+	1.29310i
$302$	−9.06269	+	10.0651i	−0.521499	+	0.579184i
$303$	0.842624	+	2.59333i	0.0484075	+	0.148983i
$304$	0.539260	−	4.32541i	0.0309287	−	0.248079i
$305$	3.79604	+	5.22481i	0.217361	+	0.299171i
$306$	−0.419388	−	1.97306i	−0.0239748	−	0.112793i
$307$	2.45449	+	4.25129i	0.140085	+	0.242634i	0.927528	−	0.373753i	$-0.121929\pi$
$307$	2.45449	+	4.25129i	0.140085	+	0.242634i	−0.787444	+	0.616387i	$0.788596\pi$
$308$	−1.00079	−	12.2544i	−0.0570256	−	0.698257i
$309$	−1.20248	−	2.08276i	−0.0684069	−	0.118484i
$310$	4.22911	−	3.80791i	0.240197	−	0.216275i
$311$	−6.01255	+	4.36837i	−0.340940	+	0.247708i	−0.745058	−	0.666999i	$-0.767578\pi$
$311$	−6.01255	+	4.36837i	−0.340940	+	0.247708i	0.404118	+	0.914707i	$0.367578\pi$
$312$	−1.66152	+	2.28689i	−0.0940651	+	0.129470i
$313$	−17.3833	−	3.69493i	−0.982561	−	0.208850i	−0.311495	−	0.950248i	$-0.600830\pi$
$313$	−17.3833	−	3.69493i	−0.982561	−	0.208850i	−0.671066	+	0.741398i	$0.734163\pi$
$314$	19.1448	+	4.06936i	1.08041	+	0.229647i
$315$	5.04101	−	6.93836i	0.284029	−	0.390932i
$316$	9.32219	−	6.77296i	0.524414	−	0.381009i
$317$	−2.94173	+	2.64875i	−0.165224	+	0.148769i	−0.747595	−	0.664154i	$-0.768792\pi$
$317$	−2.94173	+	2.64875i	−0.165224	+	0.148769i	0.582371	+	0.812923i	$0.302125\pi$
$318$	−0.253094	−	0.438371i	−0.0141928	−	0.0245826i
$319$	−3.05135	+	2.62169i	−0.170843	+	0.146787i
$320$	0.428118	+	0.741522i	0.0239325	+	0.0414523i
$321$	1.90147	+	8.94573i	0.106130	+	0.499302i
$322$	17.2629	+	23.7603i	0.962023	+	1.32411i
$323$	−3.22921	−	0.402594i	−0.179678	−	0.0224009i
$324$	1.97953	+	6.09237i	0.109974	+	0.338465i
$325$	−14.7815	+	16.4166i	−0.819932	+	0.910627i
$326$	−0.695706	+	6.61920i	−0.0385316	+	0.366604i
$327$	6.96578	−	0.732133i	0.385208	−	0.0404870i
$328$	3.29668	−	0.700730i	0.182029	−	0.0386914i
$329$	10.6969	+	6.17584i	0.589737	+	0.340485i
$330$	1.23288	+	0.940265i	0.0678681	+	0.0517599i
$331$			18.3449i			1.00833i	0.863608	+	0.504163i	$0.168199\pi$
$331$			18.3449i			1.00833i	−0.863608	+	0.504163i	$0.831801\pi$
$332$	9.31882	−	8.39071i	0.511437	−	0.460500i
$333$	−10.4793	+	1.10142i	−0.574261	+	0.0603573i
$334$	−19.3792	−	14.0798i	−1.06038	−	0.770413i
$335$	−7.48057	+	2.43058i	−0.408707	+	0.132797i
$336$	−1.97984	−	0.420827i	−0.108009	−	0.0229580i
$337$	2.36153	−	22.4685i	0.128641	−	1.22394i	−0.719624	−	0.694364i	$-0.755686\pi$
$337$	2.36153	−	22.4685i	0.128641	−	1.22394i	0.848265	−	0.529572i	$-0.177648\pi$
$338$	1.44292	+	13.7284i	0.0784844	+	0.746729i
$339$	−4.53885	+	0.964763i	−0.246517	+	0.0523987i
$340$	0.553596	−	0.319619i	0.0300229	−	0.0173338i
$341$	22.0375	+	0.512069i	1.19339	+	0.0277301i
$342$	11.7751	+	0.227438i	0.636723	+	0.0122984i
$343$	−0.906740	−	0.294618i	−0.0489594	−	0.0159079i
$344$	2.47500	−	5.55894i	0.133443	−	0.299718i
$345$	−3.68342	−	0.387143i	−0.198309	−	0.0208431i
$346$	17.1159	+	3.63810i	0.920157	+	0.195585i
$347$	−17.1639	−	15.4545i	−0.921409	−	0.829640i	0.0643289	−	0.997929i	$-0.479509\pi$
$347$	−17.1639	−	15.4545i	−0.921409	−	0.829640i	−0.985738	+	0.168288i	$0.946176\pi$
$348$	0.269369	+	0.605012i	0.0144397	+	0.0324320i
$349$	1.73019	+	2.38140i	0.0926149	+	0.127473i	0.852810	−	0.522222i	$-0.174897\pi$
$349$	1.73019	+	2.38140i	0.0926149	+	0.127473i	−0.760195	+	0.649695i	$0.774897\pi$
$350$	−15.0436	−	4.88797i	−0.804116	−	0.261273i
$351$	−13.9584	−	8.05891i	−0.745046	−	0.430153i
$352$	−0.764741	+	3.22725i	−0.0407608	+	0.172013i
$353$	−14.3065			−0.761456			−0.380728	−	0.924687i	$-0.624326\pi$
$353$	−14.3065			−0.761456			−0.380728	+	0.924687i	$0.624326\pi$
$354$	1.19485	−	3.67736i	0.0635054	−	0.195449i
$355$	0.359627	−	0.0377983i	0.0190870	−	0.00200612i
$356$	−1.89167	−	0.198823i	−0.100258	−	0.0105376i
$357$	−0.314176	+	1.47808i	−0.0166279	+	0.0782283i
$358$	−8.66221	−	7.79949i	−0.457812	−	0.412216i
$359$	31.4749	+	3.30815i	1.66118	+	0.174597i	0.888082	−	0.459685i	$-0.152038\pi$
$359$	31.4749	+	3.30815i	1.66118	+	0.174597i	0.773101	+	0.634283i	$0.218704\pi$
$360$	−1.87163	+	1.35982i	−0.0986433	+	0.0716686i
$361$	6.56474	−	17.8299i	0.345513	−	0.938414i
$362$			9.92560i			0.521678i
$363$	0.974489	+	5.92634i	0.0511474	+	0.311052i
$364$	−16.6214	+	9.59640i	−0.871201	+	0.502988i
$365$	4.55416	−	4.10058i	0.238375	−	0.214634i
$366$	3.76215	+	1.67502i	0.196651	+	0.0875545i
$367$	−29.1575	+	12.9818i	−1.52201	+	0.677642i	−0.986027	−	0.166588i	$-0.946725\pi$
$367$	−29.1575	+	12.9818i	−1.52201	+	0.677642i	−0.535982	+	0.844229i	$0.680059\pi$
$368$	−2.44816	−	7.53465i	−0.127619	−	0.392771i
$369$	2.81399	+	8.66057i	0.146490	+	0.450851i
$370$	−1.35817	−	3.05051i	−0.0706081	−	0.158588i
$371$	−0.359250	−	3.41804i	−0.0186513	−	0.177456i
$372$	1.12138	−	3.45124i	0.0581407	−	0.178939i
$373$	−11.7402			−0.607886			−0.303943	−	0.952690i	$-0.598303\pi$
$373$	−11.7402			−0.607886			−0.303943	+	0.952690i	$0.598303\pi$
$374$	2.40936	+	0.570930i	0.124585	+	0.0295221i
$375$	3.75183	−	2.16612i	0.193744	−	0.111858i
$376$	−2.22946	−	2.47606i	−0.114975	−	0.127693i
$377$	5.73690	+	2.55423i	0.295465	+	0.131550i
$378$	1.20636	−	11.4778i	0.0620487	−	0.590354i
$379$	−7.40075	+	2.40465i	−0.380151	+	0.123519i	−0.492858	−	0.870110i	$-0.664048\pi$
$379$	−7.40075	+	2.40465i	−0.380151	+	0.123519i	0.112707	+	0.993628i	$0.464048\pi$
$380$	1.08456	+	3.57119i	0.0556370	+	0.183198i
$381$	4.44935	−	6.12400i	0.227947	−	0.313742i
$382$	−10.9491	−	4.87485i	−0.560205	−	0.249419i
$383$	−7.03448	−	33.0946i	−0.359445	−	1.69106i	−0.671510	−	0.740995i	$-0.734354\pi$
$383$	−7.03448	−	33.0946i	−0.359445	−	1.69106i	0.312065	−	0.950061i	$-0.398979\pi$
$384$	0.472844	+	0.272996i	0.0241297	+	0.0139313i
$385$	5.05057	+	9.23695i	0.257401	+	0.470759i
$386$	4.22834	−	7.32370i	0.215217	−	0.372767i
$387$	15.6364	+	5.08057i	0.794842	+	0.258260i
$388$	−3.92100	−	5.39680i	−0.199059	−	0.273981i
$389$	6.84128	−	3.04593i	0.346867	−	0.154435i	−0.225906	−	0.974149i	$-0.572534\pi$
$389$	6.84128	−	3.04593i	0.346867	−	0.154435i	0.572773	+	0.819714i	$0.305868\pi$
$390$	0.503222	−	2.36747i	0.0254816	−	0.119882i
$391$	−5.62512	+	1.82771i	−0.284475	+	0.0924314i
$392$	−5.45506	−	3.96333i	−0.275522	−	0.200178i
$393$	−0.578501	−	5.50407i	−0.0291815	−	0.277644i
$394$	−2.66830	−	12.5534i	−0.134427	−	0.632430i
$395$	−4.93314	+	8.54445i	−0.248213	+	0.429918i
$396$	−8.88791	−	1.14347i	−0.446634	−	0.0574616i
$397$	−1.43530	−	2.48601i	−0.0720356	−	0.124769i	0.827758	−	0.561086i	$-0.189616\pi$
$397$	−1.43530	−	2.48601i	−0.0720356	−	0.124769i	−0.899793	+	0.436316i	$0.856283\pi$
$398$	−6.69506	+	20.6053i	−0.335593	+	1.03285i
$399$	−7.98914	−	3.74350i	−0.399957	−	0.187409i
$400$	3.45196	+	2.50800i	0.172598	+	0.125400i
$401$	−20.5792	−	18.5296i	−1.02767	−	0.925322i	−0.0304321	−	0.999537i	$-0.509688\pi$
$401$	−20.5792	−	18.5296i	−1.02767	−	0.925322i	−0.997242	+	0.0742146i	$0.976355\pi$
$402$	−3.35608	+	3.72731i	−0.167386	+	0.185901i
$403$	−13.9957	−	31.4349i	−0.697177	−	1.56589i
$404$	2.03132	−	4.56242i	0.101062	−	0.226989i
$405$	−3.67015	−	4.07612i	−0.182371	−	0.202544i
$406$			4.49660i			0.223163i
$407$	4.28162	−	12.2052i	0.212232	−	0.604987i
$408$	0.203810	−	0.353009i	0.0100901	−	0.0174766i
$409$	−19.7499	−	21.9345i	−0.976569	−	1.08459i	−0.996399	−	0.0847865i	$-0.972979\pi$
$409$	−19.7499	−	21.9345i	−0.976569	−	1.08459i	0.0198301	−	0.999803i	$-0.493687\pi$
$410$	−2.33466	+	1.69623i	−0.115300	+	0.0837707i
$411$	−6.59722	+	9.08029i	−0.325417	+	0.447898i
$412$	−0.915801	+	4.30850i	−0.0451183	+	0.212265i
$413$	17.5668	−	19.5099i	0.864404	−	0.960017i
$414$	19.5549	−	8.70639i	0.961070	−	0.427896i
$415$	−4.36711	+	9.80869i	−0.214373	+	0.481490i
$416$	5.06413	−	1.07641i	0.248289	−	0.0527755i
$417$	−7.17093			−0.351162
$418$	−6.43652	+	12.9449i	−0.314821	+	0.633157i
$419$	6.40785			0.313044			0.156522	−	0.987674i	$-0.449972\pi$
$419$	6.40785			0.313044			0.156522	+	0.987674i	$0.449972\pi$
$420$	1.69521	−	0.360327i	0.0827176	−	0.0175822i
$421$	11.6993	−	26.2770i	0.570187	−	1.28066i	−0.366475	−	0.930428i	$-0.619436\pi$
$421$	11.6993	−	26.2770i	0.570187	−	1.28066i	0.936662	−	0.350234i	$-0.113898\pi$
$422$	12.7571	−	5.67981i	0.621004	−	0.276489i
$423$	6.02375	−	6.69005i	0.292885	−	0.325281i
$424$	−0.192754	+	0.906836i	−0.00936096	+	0.0440398i
$425$	1.87239	−	2.57712i	0.0908241	−	0.125009i
$426$	0.186547	−	0.135534i	0.00903824	−	0.00656667i
$427$	18.7097	+	20.7793i	0.905428	+	1.00558i
$428$	8.37519	−	14.5063i	0.404830	−	0.701186i
$429$	7.71071	−	5.33296i	0.372277	−	0.257478i
$430$			5.21021i			0.251259i
$431$	−6.43568	−	7.14754i	−0.309996	−	0.344285i	0.567935	−	0.823074i	$-0.307743\pi$
$431$	−6.43568	−	7.14754i	−0.309996	−	0.344285i	−0.877930	+	0.478789i	$0.841076\pi$
$432$	−1.26625	+	2.84404i	−0.0609224	+	0.136834i
$433$	−11.3572	−	25.5088i	−0.545794	−	1.22587i	−0.950299	−	0.311338i	$-0.899223\pi$
$433$	−11.3572	−	25.5088i	−0.545794	−	1.22587i	0.404506	−	0.914536i	$-0.367444\pi$
$434$	16.4866	−	18.3102i	0.791382	−	0.878919i
$435$	−0.421406	−	0.379435i	−0.0202049	−	0.0181925i
$436$	−10.3783	−	7.54027i	−0.497030	−	0.361114i
$437$	−2.94577	−	34.4071i	−0.140915	−	1.64591i
$438$	1.20756	−	3.71650i	0.0576997	−	0.177581i
$439$	0.122980	+	0.213008i	0.00586954	+	0.0101663i	0.868945	−	0.494908i	$-0.164798\pi$
$439$	0.122980	+	0.213008i	0.00586954	+	0.0101663i	−0.863076	+	0.505075i	$0.831465\pi$
$440$	−0.525744	−	2.79072i	−0.0250638	−	0.133042i
$441$	9.10918	−	15.7776i	0.433771	−	0.751313i
$442$	−0.803615	−	3.78071i	−0.0382241	−	0.179830i
$443$	−0.907163	−	8.63108i	−0.0431006	−	0.410075i	−0.994707	−	0.102755i	$-0.967234\pi$
$443$	−0.907163	−	8.63108i	−0.0431006	−	0.410075i	0.951606	−	0.307320i	$-0.0994323\pi$
$444$	−1.72264	−	1.25157i	−0.0817527	−	0.0593968i
$445$	1.54893	−	0.503278i	0.0734263	−	0.0238576i
$446$	−2.50923	+	11.8050i	−0.118815	+	0.558983i
$447$	2.17216	−	0.967110i	0.102740	−	0.0457427i
$448$	2.17900	+	2.99913i	0.102948	+	0.141696i
$449$	−6.48143	−	2.10595i	−0.305878	−	0.0993857i	0.152056	−	0.988372i	$-0.451410\pi$
$449$	−6.48143	−	2.10595i	−0.305878	−	0.0993857i	−0.457934	+	0.888986i	$0.651410\pi$
$450$	−5.76430	+	9.98406i	−0.271732	+	0.470653i
$451$	−11.0867	−	1.42636i	−0.522054	−	0.0671647i
$452$	7.36013	+	4.24937i	0.346191	+	0.199874i
$453$	−1.53749	−	7.23332i	−0.0722376	−	0.339851i
$454$	27.3138	+	12.1609i	1.28190	+	0.570739i
$455$	9.65940	−	13.2950i	0.452840	−	0.623280i
$456$	1.73755	+	1.62634i	0.0813681	+	0.0761604i
$457$	38.8314	−	12.6171i	1.81645	−	0.590202i	0.816538	−	0.577292i	$-0.195891\pi$
$457$	38.8314	−	12.6171i	1.81645	−	0.590202i	0.999917	−	0.0129096i	$-0.00410938\pi$
$458$	−1.38154	+	13.1445i	−0.0645551	+	0.614201i
$459$	2.12327	+	0.945339i	0.0991056	+	0.0441247i
$460$	4.53901	+	5.04108i	0.211632	+	0.235042i
$461$	−18.3837	+	10.6138i	−0.856214	+	0.494335i	−0.862743	−	0.505643i	$-0.831255\pi$
$461$	−18.3837	+	10.6138i	−0.856214	+	0.494335i	0.00652854	+	0.999979i	$0.497922\pi$
$462$	5.73415	+	3.49068i	0.266777	+	0.162401i
$463$	−8.63302			−0.401211			−0.200605	−	0.979672i	$-0.564291\pi$
$463$	−8.63302			−0.401211			−0.200605	+	0.979672i	$0.564291\pi$
$464$	0.374825	−	1.15359i	0.0174008	−	0.0535543i
$465$	0.324786	+	3.09013i	0.0150616	+	0.143301i
$466$	−0.220018	−	0.494168i	−0.0101921	−	0.0228919i
$467$	−5.53623	−	17.0388i	−0.256186	−	0.788460i	−0.993594	−	0.113012i	$-0.963950\pi$
$467$	−5.53623	−	17.0388i	−0.256186	−	0.788460i	0.737407	−	0.675448i	$-0.236050\pi$
$468$	4.32266	+	13.3038i	0.199815	+	0.614967i
$469$	−31.1102	+	13.8512i	−1.43654	+	0.639587i
$470$	2.60622	+	1.16036i	0.120216	+	0.0535236i
$471$	−7.94160	+	7.15064i	−0.365929	+	0.329484i
$472$	−6.13301	+	3.54089i	−0.282294	+	0.162983i
$473$	−13.8490	+	14.6802i	−0.636776	+	0.674996i
$474$			6.29139i			0.288973i
$475$	12.1758	+	14.0594i	0.558664	+	0.645088i
$476$	2.23905	−	1.62677i	0.102627	−	0.0745627i
$477$	−2.49119	−	0.261834i	−0.114064	−	0.0119886i
$478$	12.5206	+	11.2736i	0.572679	+	0.515642i
$479$	2.11487	−	9.94969i	0.0966310	−	0.454613i	−0.903054	−	0.429526i	$-0.858681\pi$
$479$	2.11487	−	9.94969i	0.0966310	−	0.454613i	0.999685	−	0.0250866i	$-0.00798614\pi$
$480$	−0.464937	−	0.0488669i	−0.0212214	−	0.00223046i
$481$	−20.0800	+	2.11049i	−0.915569	+	0.0962302i
$482$	1.11753	−	3.43941i	0.0509022	−	0.156661i
$483$	−16.0355			−0.729639
$484$	5.93654	−	9.26054i	0.269843	−	0.420933i
$485$	4.94655	+	2.85589i	0.224611	+	0.129679i
$486$	−12.2089	−	3.96690i	−0.553805	−	0.179942i
$487$	−4.59576	−	6.32552i	−0.208254	−	0.286637i	0.692094	−	0.721807i	$-0.256688\pi$
$487$	−4.59576	−	6.32552i	−0.208254	−	0.286637i	−0.900348	+	0.435170i	$0.856688\pi$
$488$	−3.06784	−	6.89048i	−0.138874	−	0.311917i
$489$	−2.70054	−	2.43158i	−0.122123	−	0.109960i
$490$	5.64728	+	1.20037i	0.255118	+	0.0542270i
$491$	31.9676	+	3.35993i	1.44268	+	0.151632i	0.793299	−	0.608833i	$-0.208362\pi$
$491$	31.9676	+	3.35993i	1.44268	+	0.151632i	0.649380	+	0.760464i	$0.275029\pi$
$492$	−0.748466	+	1.68108i	−0.0337435	+	0.0757891i
$493$	−0.861235	−	0.279832i	−0.0387881	−	0.0126030i
$494$	22.5630	+	0.435808i	1.01516	+	0.0196079i
$495$	7.35044	−	2.20089i	0.330378	−	0.0989226i
$496$	−5.75589	+	3.32317i	−0.258447	+	0.149215i
$497$	1.53139	−	0.325507i	0.0686923	−	0.0146010i
$498$	0.715664	+	6.80909i	0.0320697	+	0.305122i
$499$	−3.79830	+	36.1384i	−0.170035	+	1.61778i	0.493577	+	0.869702i	$0.335689\pi$
$499$	−3.79830	+	36.1384i	−0.170035	+	1.61778i	−0.663613	+	0.748076i	$0.730978\pi$
$500$	−7.76123	−	1.64970i	−0.347093	−	0.0737768i
$501$	12.4386	−	4.04155i	0.555716	−	0.180563i
$502$	−7.39694	−	5.37419i	−0.330141	−	0.239862i
$503$	−22.2945	+	2.34324i	−0.994062	+	0.104480i	−0.587569	−	0.809174i	$-0.699915\pi$
$503$	−22.2945	+	2.34324i	−0.994062	+	0.104480i	−0.406493	+	0.913654i	$0.633248\pi$
$504$	−7.44354	+	6.70219i	−0.331561	+	0.298539i
$505$			4.27620i			0.190288i
$506$	−0.610384	+	26.2685i	−0.0271349	+	1.16778i
$507$	−6.52716	−	3.76846i	−0.289881	−	0.167363i
$508$	−13.5611	+	2.88250i	−0.601677	+	0.127890i
$509$	−30.4158	+	3.19683i	−1.34816	+	0.141697i	−0.750933	−	0.660378i	$-0.770396\pi$
$509$	−30.4158	+	3.19683i	−1.34816	+	0.141697i	−0.597223	+	0.802075i	$0.703729\pi$
$510$	−0.0364824	+	0.347107i	−0.00161547	+	0.0153702i
$511$	17.7537	−	19.7175i	0.785379	−	0.872252i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−8.18682	+	10.8223i	−0.361457	+	0.477818i
$514$	−4.47934	−	6.16529i	−0.197575	−	0.271939i
$515$	−0.784141	−	3.68910i	−0.0345534	−	0.162561i
$516$	1.66119	+	2.87726i	0.0731297	+	0.126664i
$517$	4.25894	+	10.1969i	0.187308	+	0.448458i
$518$	−7.22865	−	12.5204i	−0.317608	−	0.550114i
$519$	−7.09996	+	6.39283i	−0.311654	+	0.280614i
$520$	−3.58634	+	2.60563i	−0.157271	+	0.114264i
$521$	−12.2658	+	16.8824i	−0.537375	+	0.739634i	−0.988232	−	0.152963i	$-0.951119\pi$
$521$	−12.2658	+	16.8824i	−0.537375	+	0.739634i	0.450857	+	0.892596i	$0.351119\pi$
$522$	3.20567	+	0.681387i	0.140308	+	0.0298235i
$523$	36.6988	+	7.80056i	1.60473	+	0.341095i	0.921278	−	0.388905i	$-0.127147\pi$
$523$	36.6988	+	7.80056i	1.60473	+	0.341095i	0.683447	+	0.730000i	$0.260480\pi$
$524$	−5.95802	+	8.20051i	−0.260277	+	0.358241i
$525$	6.98700	−	5.07635i	0.304938	−	0.221550i
$526$	4.37255	−	3.93706i	0.190652	−	0.171664i
$527$	2.48097	+	4.29716i	0.108073	+	0.187187i
$528$	−1.18011	−	1.37351i	−0.0513576	−	0.0597744i
$529$	−19.8822	−	34.4370i	−0.864445	−	1.49726i
$530$	−0.165043	−	0.776465i	−0.00716900	−	0.0337275i
$531$	−11.2468	−	15.4799i	−0.488070	−	0.671771i
$532$	6.28616	+	14.8862i	0.272539	+	0.645397i
$533$	5.39206	+	16.5951i	0.233556	+	0.718812i
$534$	0.694912	−	0.771778i	0.0300718	−	0.0333981i
$535$	−1.49918	+	14.2637i	−0.0648150	+	0.616674i
$536$	9.13586	−	0.960217i	0.394609	−	0.0414751i
$537$	6.22510	−	1.32319i	0.268633	−	0.0570997i
$538$	−11.2146	−	6.47477i	−0.483497	−	0.279147i
$539$	12.7210	+	18.3928i	0.547934	+	0.792236i
$540$		−	2.66563i		−	0.114710i
$541$	−1.17387	+	1.05696i	−0.0504687	+	0.0454422i	−0.693979	−	0.719995i	$-0.744144\pi$
$541$	−1.17387	+	1.05696i	−0.0504687	+	0.0454422i	0.643510	+	0.765437i	$0.277477\pi$
$542$	−25.5610	+	2.68656i	−1.09794	+	0.115398i
$543$	−4.38431	−	3.18539i	−0.188149	−	0.136698i
$544$	−0.710027	+	0.230702i	−0.0304422	+	0.00989126i
$545$	10.7440	+	2.28371i	0.460223	+	0.0978233i
$546$	1.09537	−	10.4217i	0.0468774	−	0.446008i
$547$	0.434026	+	4.12948i	0.0185576	+	0.176564i	0.999875	−	0.0158339i	$-0.00504029\pi$
$547$	0.434026	+	4.12948i	0.0185576	+	0.176564i	−0.981317	+	0.192398i	$0.938374\pi$
$548$	20.1076	−	4.27400i	0.858953	−	0.182576i
$549$	17.6489	−	10.1896i	0.753237	−	0.434881i
$550$	−8.04988	−	11.6390i	−0.343248	−	0.496289i
$551$	2.73152	−	4.52692i	0.116367	−	0.192853i
$552$	4.11387	+	1.33668i	0.175098	+	0.0568927i
$553$	−17.3745	+	39.0237i	−0.738837	+	1.65946i
$554$	27.5077	+	2.89118i	1.16869	+	0.122834i
$555$	1.78334	+	0.379060i	0.0756985	+	0.0160902i
$556$	9.76028	+	8.78819i	0.413928	+	0.372702i
$557$	4.72348	+	10.6091i	0.200140	+	0.449523i	0.985535	−	0.169473i	$-0.0542066\pi$
$557$	4.72348	+	10.6091i	0.200140	+	0.449523i	−0.785395	+	0.618996i	$0.787540\pi$
$558$	−10.5553	−	14.5281i	−0.446840	−	0.615022i
$559$	29.9618	+	9.73519i	1.26725	+	0.411755i
$560$	−2.74892	−	1.58709i	−0.116163	−	0.0670667i
$561$	−1.02542	+	0.881030i	−0.0432932	+	0.0371971i
$562$	−15.0647			−0.635466
$563$	−9.18952	+	28.2824i	−0.387292	+	1.19196i	0.547511	+	0.836798i	$0.315575\pi$
$563$	−9.18952	+	28.2824i	−0.387292	+	1.19196i	−0.934804	+	0.355165i	$0.884425\pi$
$564$	1.80921	−	0.190156i	0.0761815	−	0.00800700i
$565$	−7.23707	−	0.760646i	−0.304466	−	0.0320006i
$566$	−3.75037	+	17.6441i	−0.157640	+	0.741637i
$567$	−17.6478	−	15.8902i	−0.741139	−	0.667325i
$568$	−0.420009	−	0.0441447i	−0.0176232	−	0.00185227i
$569$	8.36826	−	6.07990i	0.350816	−	0.254883i	−0.398395	−	0.917214i	$-0.630433\pi$
$569$	8.36826	−	6.07990i	0.350816	−	0.254883i	0.749211	+	0.662331i	$0.230433\pi$
$570$	−1.92552	−	0.667018i	−0.0806512	−	0.0279383i
$571$			11.9399i			0.499670i	0.968288	+	0.249835i	$0.0803764\pi$
$571$			11.9399i			0.499670i	−0.968288	+	0.249835i	$0.919624\pi$
$572$	−17.0307	−	2.19108i	−0.712088	−	0.0916135i
$573$	5.66716	−	3.27194i	0.236749	−	0.136687i
$574$	−9.28503	+	8.36028i	−0.387550	+	0.348951i
$575$	30.8813	+	13.7492i	1.28784	+	0.573383i
$576$	2.46830	−	1.09896i	0.102846	−	0.0457899i
$577$	9.76753	+	30.0614i	0.406628	+	1.25147i	0.919529	+	0.393023i	$0.128571\pi$
$577$	9.76753	+	30.0614i	0.406628	+	1.25147i	−0.512901	+	0.858448i	$0.671429\pi$
$578$	−5.08105	−	15.6379i	−0.211344	−	0.650450i
$579$	1.87802	+	4.21810i	0.0780479	+	0.175298i
$580$	0.108561	+	1.03289i	0.00450776	+	0.0428885i
$581$	−14.3651	+	44.2112i	−0.595964	+	1.83419i
$582$	3.64221			0.150975
$583$	1.59886	−	2.62645i	0.0662179	−	0.108776i
$584$	−6.19829	+	3.57858i	−0.256487	+	0.148083i
$585$	−8.01443	−	8.90092i	−0.331356	−	0.368008i
$586$	−21.8610	−	9.73312i	−0.903068	−	0.402072i
$587$	2.43663	−	23.1830i	0.100570	−	0.956864i	−0.821596	−	0.570070i	$-0.806916\pi$
$587$	2.43663	−	23.1830i	0.100570	−	0.956864i	0.922166	−	0.386794i	$-0.126417\pi$
$588$	3.50134	−	1.13766i	0.144393	−	0.0469161i
$589$	−27.7205	+	8.41868i	−1.14220	+	0.346886i
$590$	3.56414	−	4.90562i	0.146733	−	0.201961i
$591$	6.40138	+	2.85008i	0.263317	+	0.117236i
$592$	0.810826	+	3.81464i	0.0333248	+	0.156781i
$593$	38.1110	+	22.0034i	1.56503	+	0.903572i	0.996735	+	0.0807484i	$0.0257310\pi$
$593$	38.1110	+	22.0034i	1.56503	+	0.903572i	0.568297	+	0.822823i	$0.307602\pi$
$594$	7.08535	−	7.51062i	0.290715	−	0.308164i
$595$	−1.18487	+	2.05225i	−0.0485748	+	0.0841341i
$596$	−4.14173	−	1.34573i	−0.169652	−	0.0551233i
$597$	−6.95308	−	9.57010i	−0.284571	−	0.391678i
$598$	37.4703	−	16.6829i	1.53228	−	0.682213i
$599$	−8.62485	+	40.5767i	−0.352402	+	1.65792i	0.343027	+	0.939326i	$0.388548\pi$
$599$	−8.62485	+	40.5767i	−0.352402	+	1.65792i	−0.695429	+	0.718595i	$0.744786\pi$
$600$	−2.21565	+	0.719909i	−0.0904536	+	0.0293902i
$601$	11.5611	+	8.39962i	0.471587	+	0.342628i	0.798059	−	0.602579i	$-0.205860\pi$
$601$	11.5611	+	8.39962i	0.471587	+	0.342628i	−0.326473	+	0.945207i	$0.605860\pi$
$602$	2.35795	+	22.4344i	0.0961028	+	0.914357i
$603$	5.16038	+	24.2777i	0.210147	+	0.988664i
$604$	−6.77199	+	11.7294i	−0.275548	+	0.477264i
$605$	−1.41852	+	9.31116i	−0.0576712	+	0.378552i
$606$	1.36339	+	2.36147i	0.0553841	+	0.0959281i
$607$	2.90206	−	8.93161i	0.117791	−	0.362523i	−0.874728	−	0.484614i	$-0.838960\pi$
$607$	2.90206	−	8.93161i	0.117791	−	0.362523i	0.992519	+	0.122091i	$0.0389601\pi$
$608$	−0.371828	−	4.34301i	−0.0150796	−	0.176132i
$609$	−1.98623	−	1.44308i	−0.0804860	−	0.0584765i
$610$	4.79939	+	4.32139i	0.194322	+	0.174968i
$611$	11.5425	−	12.8192i	0.466959	−	0.518610i
$612$	−0.820446	−	1.84275i	−0.0331646	−	0.0744888i
$613$	10.2469	−	23.0148i	0.413867	−	0.929560i	−0.579543	−	0.814942i	$-0.696769\pi$
$613$	10.2469	−	23.0148i	0.413867	−	0.929560i	0.993410	−	0.114619i	$-0.0365646\pi$
$614$	3.28474	+	3.64808i	0.132561	+	0.147224i
$615$		−	1.57562i		−	0.0635352i
$616$	−3.52675	−	11.7785i	−0.142097	−	0.474569i
$617$	−8.60701	+	14.9078i	−0.346505	+	0.600164i	−0.985626	−	0.168942i	$-0.945965\pi$
$617$	−8.60701	+	14.9078i	−0.346505	+	0.600164i	0.639121	+	0.769106i	$0.279298\pi$
$618$	−1.60924	−	1.78724i	−0.0647330	−	0.0718933i
$619$	14.7571	−	10.7217i	0.593139	−	0.430941i	−0.250298	−	0.968169i	$-0.580529\pi$
$619$	14.7571	−	10.7217i	0.593139	−	0.430941i	0.843437	+	0.537228i	$0.180529\pi$
$620$	3.34499	−	4.60398i	0.134338	−	0.184900i
$621$	−5.12793	+	24.1250i	−0.205777	+	0.968103i
$622$	−4.97292	+	5.52299i	−0.199396	+	0.221452i
$623$	6.44169	−	2.86803i	0.258081	−	0.114905i
$624$	−1.14974	+	2.58236i	−0.0460265	+	0.103377i
$625$	−14.2227	+	3.02312i	−0.568906	+	0.120925i
$626$	−17.7716			−0.710297
$627$	−3.65235	−	6.99749i	−0.145861	−	0.279453i
$628$	19.5726			0.781030
$629$	2.84788	−	0.605336i	0.113553	−	0.0241363i
$630$	3.48829	−	7.83483i	0.138977	−	0.312147i
$631$	−36.2892	+	16.1570i	−1.44465	+	0.643200i	−0.971340	−	0.237695i	$-0.923608\pi$
$631$	−36.2892	+	16.1570i	−1.44465	+	0.643200i	−0.473311	+	0.880895i	$0.656941\pi$
$632$	7.71029	−	8.56315i	0.306699	−	0.340624i
$633$	−1.58521	+	7.45781i	−0.0630063	+	0.296421i
$634$	−2.32674	+	3.20249i	−0.0924068	+	0.127187i
$635$	9.60377	−	6.97754i	0.381114	−	0.276895i
$636$	−0.338705	−	0.376170i	−0.0134305	−	0.0149161i
$637$	17.4547	−	30.2324i	0.691579	−	1.19785i
$638$	−2.43959	+	3.19881i	−0.0965843	+	0.126642i
$639$		−	1.14107i		−	0.0451400i
$640$	0.572934	+	0.636307i	0.0226472	+	0.0251522i
$641$	16.6318	−	37.3556i	0.656916	−	1.47546i	−0.210357	−	0.977625i	$-0.567463\pi$
$641$	16.6318	−	37.3556i	0.656916	−	1.47546i	0.867273	−	0.497833i	$-0.165871\pi$
$642$	3.71984	+	8.35491i	0.146811	+	0.329742i
$643$	31.1679	−	34.6154i	1.22914	−	1.36510i	0.320648	−	0.947199i	$-0.396099\pi$
$643$	31.1679	−	34.6154i	1.22914	−	1.36510i	0.908493	−	0.417900i	$-0.137234\pi$
$644$	21.8257	+	19.6520i	0.860053	+	0.774395i
$645$	−2.30144	−	1.67209i	−0.0906191	−	0.0658387i
$646$	−3.24235	+	0.277594i	−0.127568	+	0.0109218i
$647$	6.69480	−	20.6045i	0.263200	−	0.810046i	−0.728903	−	0.684617i	$-0.759969\pi$
$647$	6.69480	−	20.6045i	0.263200	−	0.810046i	0.992103	−	0.125429i	$-0.0400306\pi$
$648$	3.20295	+	5.54767i	0.125824	+	0.217933i
$649$	23.0816	−	4.34834i	0.906032	−	0.170687i
$650$	−11.0453	+	19.1311i	−0.433234	+	0.750382i
$651$	2.79696	+	13.1587i	0.109621	+	0.515728i
$652$	0.695706	+	6.61920i	0.0272459	+	0.259228i
$653$	26.6243	+	19.3437i	1.04189	+	0.756977i	0.970653	−	0.240482i	$-0.0773056\pi$
$653$	26.6243	+	19.3437i	1.04189	+	0.756977i	0.0712360	+	0.997459i	$0.477306\pi$
$654$	6.66134	−	2.16440i	0.260479	−	0.0846348i
$655$	1.80449	−	8.48947i	0.0705074	−	0.331711i
$656$	3.07895	−	1.37084i	0.120213	−	0.0535221i
$657$	−11.3665	−	15.6447i	−0.443450	−	0.610357i
$658$	11.7471	+	3.81688i	0.457951	+	0.148797i
$659$	−6.64208	+	11.5044i	−0.258739	+	0.448149i	−0.965904	−	0.258899i	$-0.916640\pi$
$659$	−6.64208	+	11.5044i	−0.258739	+	0.448149i	0.707165	+	0.707048i	$0.249974\pi$
$660$	1.40144	+	0.663387i	0.0545508	+	0.0258223i
$661$	−18.6797	−	10.7847i	−0.726555	−	0.419477i	0.0906055	−	0.995887i	$-0.471120\pi$
$661$	−18.6797	−	10.7847i	−0.726555	−	0.419477i	−0.817161	+	0.576410i	$0.804453\pi$
$662$	3.81412	+	17.9440i	0.148240	+	0.697414i
$663$	1.92791	+	0.858359i	0.0748737	+	0.0333359i
$664$	7.37066	−	10.1448i	0.286037	−	0.393696i
$665$	−10.1014	−	9.45488i	−0.391715	−	0.366644i
$666$	−10.0213	+	3.25611i	−0.388317	+	0.126172i
$667$	1.00447	−	9.55692i	0.0388933	−	0.370045i
$668$	−21.8831	−	9.74297i	−0.846682	−	0.376967i
$669$	−4.40919	−	4.89690i	−0.170469	−	0.189325i
$670$	−6.81175	+	3.93277i	−0.263161	+	0.151936i
$671$	2.03623	+	24.9329i	0.0786077	+	0.962522i
$672$	−2.02407			−0.0780801
$673$	−3.82134	+	11.7609i	−0.147302	+	0.453349i	−0.997300	−	0.0734373i	$-0.976603\pi$
$673$	−3.82134	+	11.7609i	−0.147302	+	0.453349i	0.849998	+	0.526786i	$0.176603\pi$
$674$	−2.36153	−	22.4685i	−0.0909629	−	0.865454i
$675$	−5.40291	−	12.1351i	−0.207958	−	0.467081i
$676$	4.26569	+	13.1284i	0.164065	+	0.504940i
$677$	−4.82451	−	14.8483i	−0.185421	−	0.570667i	0.814534	−	0.580115i	$-0.196992\pi$
$677$	−4.82451	−	14.8483i	−0.185421	−	0.570667i	−0.999955	+	0.00944833i	$0.996992\pi$
$678$	−4.23908	+	1.88736i	−0.162801	+	0.0724837i
$679$	22.5916	+	10.0584i	0.866985	+	0.386007i
$680$	0.475046	−	0.427733i	0.0182172	−	0.0164028i
$681$	−14.1374	+	8.16224i	−0.541747	+	0.312778i
$682$	21.6623	−	4.08096i	0.829494	−	0.156268i
$683$			25.0801i			0.959662i	0.877361	+	0.479831i	$0.159302\pi$
$683$			25.0801i			0.959662i	−0.877361	+	0.479831i	$0.840698\pi$
$684$	11.5651	−	2.22571i	0.442201	−	0.0851021i
$685$	−14.2399	+	10.3459i	−0.544078	+	0.395296i
$686$	−0.948180	−	0.0996578i	−0.0362017	−	0.00380495i
$687$	−5.36277	−	4.82866i	−0.204602	−	0.184225i
$688$	1.26515	−	5.95205i	0.0482333	−	0.226920i
$689$	−4.77352	−	0.501717i	−0.181857	−	0.0191139i
$690$	−3.68342	+	0.387143i	−0.140225	+	0.0147383i
$691$	−2.54109	+	7.82068i	−0.0966678	+	0.297513i	−0.987685	−	0.156457i	$-0.949993\pi$
$691$	−2.54109	+	7.82068i	−0.0966678	+	0.297513i	0.891017	+	0.453970i	$0.149993\pi$
$692$	17.4983			0.665185
$693$	30.6539	−	12.8032i	1.16444	−	0.486355i
$694$	−20.0020	−	11.5482i	−0.759267	−	0.438363i
$695$	−10.6952	−	3.47508i	−0.405692	−	0.131817i
$696$	0.389271	+	0.535786i	0.0147553	+	0.0203089i
$697$	−1.02342	−	2.29864i	−0.0387648	−	0.0870672i
$698$	2.18750	+	1.96963i	0.0827981	+	0.0745518i
$699$	0.288892	+	0.0614059i	0.0109269	+	0.00232258i
$700$	−15.7312	−	1.65341i	−0.594582	−	0.0624931i
$701$	−9.14681	+	20.5441i	−0.345470	+	0.775939i	0.654335	+	0.756205i	$0.272949\pi$
$701$	−9.14681	+	20.5441i	−0.345470	+	0.775939i	−0.999805	+	0.0197343i	$0.993718\pi$
$702$	−15.3290	−	4.98068i	−0.578554	−	0.187984i
$703$	−0.328280	+	16.9959i	−0.0123813	+	0.641013i
$704$	−0.0770454	+	3.31573i	−0.00290376	+	0.124966i
$705$	−1.34896	+	0.778822i	−0.0508047	+	0.0293321i
$706$	−13.9938	+	2.97448i	−0.526664	+	0.111946i
$707$	1.93525	+	18.4127i	0.0727826	+	0.692480i
$708$	0.404170	−	3.84542i	0.0151896	−	0.144520i
$709$	22.8448	+	4.85582i	0.857956	+	0.182364i	0.615828	−	0.787880i	$-0.288821\pi$
$709$	22.8448	+	4.85582i	0.857956	+	0.182364i	0.242128	+	0.970244i	$0.422155\pi$
$710$	0.343909	−	0.111743i	0.0129067	−	0.00419364i
$711$	25.1875	+	18.2998i	0.944606	+	0.686297i
$712$	−1.89167	+	0.198823i	−0.0708935	+	0.00745120i
$713$	−39.1302	+	35.2330i	−1.46544	+	1.31949i
$714$			1.51110i			0.0565515i
$715$	14.0846	−	4.21726i	0.526736	−	0.157717i
$716$	−10.0945	−	5.82807i	−0.377250	−	0.217805i
$717$	−8.99793	+	1.91257i	−0.336034	+	0.0714262i
$718$	31.4749	−	3.30815i	1.17463	−	0.123459i
$719$	−0.832056	+	7.91649i	−0.0310305	+	0.295235i	0.967990	+	0.250988i	$0.0807555\pi$
$719$	−0.832056	+	7.91649i	−0.0310305	+	0.295235i	−0.999021	+	0.0442470i	$0.985911\pi$
$720$	−1.54800	+	1.71923i	−0.0576907	+	0.0640720i
$721$	−5.04594	−	15.5298i	−0.187921	−	0.578361i
$722$	2.71424	−	18.8051i	0.101014	−	0.699854i
$723$	1.16060	+	1.59743i	0.0431632	+	0.0594091i
$724$	2.06365	+	9.70870i	0.0766949	+	0.360821i
$725$	2.58777	+	4.48214i	0.0961073	+	0.166463i
$726$	2.18535	+	5.59422i	0.0811059	+	0.207621i
$727$	−2.93168	−	5.07782i	−0.108730	−	0.188326i	0.806526	−	0.591199i	$-0.201345\pi$
$727$	−2.93168	−	5.07782i	−0.108730	−	0.188326i	−0.915256	+	0.402873i	$0.868012\pi$
$728$	−14.2630	+	12.8425i	−0.528623	+	0.475974i
$729$	−9.87704	+	7.17609i	−0.365816	+	0.265781i
$730$	3.60208	−	4.95783i	0.133319	−	0.183498i
$731$	−4.44360	−	0.944516i	−0.164353	−	0.0349342i
$732$	4.02819	+	0.856219i	0.148886	+	0.0316468i
$733$	16.5520	−	22.7818i	0.611360	−	0.841465i	−0.385328	−	0.922780i	$-0.625912\pi$
$733$	16.5520	−	22.7818i	0.611360	−	0.841465i	0.996689	+	0.0813143i	$0.0259118\pi$
$734$	−25.8213	+	18.7603i	−0.953081	+	0.692454i
$735$	−2.34258	+	2.10927i	−0.0864075	+	0.0778017i
$736$	−3.96120	−	6.86100i	−0.146012	−	0.252900i
$737$	−29.6461	−	7.02505i	−1.09203	−	0.258771i
$738$	4.55313	+	7.88625i	0.167603	+	0.290297i
$739$	0.702423	+	3.30464i	0.0258391	+	0.121563i	0.989177	−	0.146728i	$-0.0468743\pi$
$739$	0.702423	+	3.30464i	0.0258391	+	0.121563i	−0.963338	+	0.268291i	$0.913541\pi$
$740$	−1.96273	−	2.70147i	−0.0721515	−	0.0993080i
$741$	−7.43356	+	9.82659i	−0.273079	+	0.360989i
$742$	−1.06205	−	3.26865i	−0.0389890	−	0.119996i
$743$	−36.1179	+	40.1129i	−1.32504	+	1.47160i	−0.558298	+	0.829640i	$0.688546\pi$
$743$	−36.1179	+	40.1129i	−1.32504	+	1.47160i	−0.766737	+	0.641961i	$0.778121\pi$
$744$	0.379318	−	3.60897i	0.0139065	−	0.132311i
$745$	3.70837	−	0.389766i	0.135864	−	0.0142799i
$746$	−11.4837	+	2.44093i	−0.420447	+	0.0893688i
$747$	29.3418	+	16.9405i	1.07356	+	0.619820i
$748$	2.47541	+	0.0575195i	0.0905101	+	0.00210312i
$749$			62.0958i			2.26893i
$750$	3.21948	−	2.89884i	0.117559	−	0.105851i
$751$	21.8152	−	2.29287i	0.796048	−	0.0836680i	0.302232	−	0.953234i	$-0.402268\pi$
$751$	21.8152	−	2.29287i	0.796048	−	0.0836680i	0.493816	+	0.869566i	$0.335602\pi$
$752$	−2.69554	−	1.95842i	−0.0982962	−	0.0714163i
$753$	4.74774	−	1.54264i	0.173017	−	0.0562168i
$754$	6.14259	+	1.30565i	0.223700	+	0.0475489i
$755$	1.21220	−	11.5333i	0.0441165	−	0.419740i
$756$	−1.20636	−	11.4778i	−0.0438750	−	0.417443i
$757$	28.6725	−	6.09454i	1.04212	−	0.221510i	0.345104	−	0.938564i	$-0.387844\pi$
$757$	28.6725	−	6.09454i	1.04212	−	0.221510i	0.697017	+	0.717055i	$0.254510\pi$
$758$	−6.73908	+	3.89081i	−0.244774	+	0.141320i
$759$	−11.4074	−	8.69989i	−0.414062	−	0.315786i
$760$	1.80336	+	3.26765i	0.0654146	+	0.118530i
$761$	−36.6652	−	11.9132i	−1.32911	−	0.431855i	−0.443497	−	0.896276i	$-0.646262\pi$
$761$	−36.6652	−	11.9132i	−1.32911	−	0.431855i	−0.885614	+	0.464421i	$0.846262\pi$
$762$	3.07887	−	6.91525i	0.111536	−	0.250513i
$763$	47.2956	+	4.97097i	1.71222	+	0.179961i
$764$	−11.7234	−	2.49188i	−0.424137	−	0.0901531i
$765$	1.28352	+	1.15569i	0.0464058	+	0.0417840i
$766$	−13.7615	−	30.9089i	−0.497224	−	1.11678i
$767$	−21.5507	−	29.6620i	−0.778151	−	1.07103i
$768$	0.519270	+	0.168721i	0.0187375	+	0.00608820i
$769$	2.67214	+	1.54276i	0.0963600	+	0.0556335i	0.547406	−	0.836867i	$-0.315616\pi$
$769$	2.67214	+	1.54276i	0.0963600	+	0.0556335i	−0.451046	+	0.892501i	$0.648949\pi$
$770$	6.86067	+	7.98503i	0.247241	+	0.287760i
$771$	4.16085			0.149849
$772$	2.61326	−	8.04278i	0.0940533	−	0.289466i
$773$	31.7305	−	3.33501i	1.14127	−	0.119952i	0.485024	−	0.874501i	$-0.338811\pi$
$773$	31.7305	−	3.33501i	1.14127	−	0.119952i	0.656244	+	0.754549i	$0.272144\pi$
$774$	16.3510	+	1.71856i	0.587725	+	0.0617723i
$775$	5.89616	−	27.7393i	0.211796	−	0.996424i
$776$	−4.95738	−	4.46364i	−0.177959	−	0.160235i
$777$	7.85033	+	0.825103i	0.281629	+	0.0296004i
$778$	6.05849	−	4.40175i	0.217208	−	0.157811i
$779$	14.4262	−	2.77634i	0.516872	−	0.0994726i
$780$		−	2.42036i		−	0.0866629i
$781$	1.26601	+	0.599281i	0.0453014	+	0.0214440i
$782$	−5.12220	+	2.95730i	−0.183169	+	0.105753i
$783$	−2.80625	+	2.52676i	−0.100287	+	0.0902989i
$784$	−6.15987	−	2.74255i	−0.219995	−	0.0979483i
$785$	−15.3099	+	6.81639i	−0.546432	+	0.243287i
$786$	−1.71022	−	5.26352i	−0.0610016	−	0.187743i
$787$	−11.8599	−	36.5011i	−0.422760	−	1.30112i	−0.905123	−	0.425151i	$-0.860221\pi$
$787$	−11.8599	−	36.5011i	−0.422760	−	1.30112i	0.482362	−	0.875972i	$-0.339779\pi$
$788$	−5.21999	−	11.7243i	−0.185954	−	0.417660i
$789$	0.335801	+	3.19494i	0.0119548	+	0.113743i
$790$	−3.04885	+	9.38339i	−0.108473	+	0.333846i
$791$	−31.5060			−1.12022
$792$	−8.93143	+	0.729416i	−0.317364	+	0.0259187i
$793$	33.8182	−	19.5249i	1.20092	−	0.693350i
$794$	−1.92081	−	2.13327i	−0.0681669	−	0.0757070i
$795$	0.395945	+	0.176286i	0.0140427	+	0.00625222i
$796$	−2.26468	+	21.5470i	−0.0802694	+	0.763712i
$797$	−20.6503	+	6.70970i	−0.731473	+	0.237670i	−0.650990	−	0.759086i	$-0.725646\pi$
$797$	−20.6503	+	6.70970i	−0.731473	+	0.237670i	−0.0804824	+	0.996756i	$0.525646\pi$
$798$	−8.59287	−	2.00066i	−0.304184	−	0.0708225i
$799$	−1.46209	+	2.01240i	−0.0517252	+	0.0711936i
$800$	3.89797	+	1.73549i	0.137814	+	0.0613588i
$801$	−1.06851	−	5.02695i	−0.0377540	−	0.177618i
$802$	−23.9820	−	13.8460i	−0.846833	−	0.488919i
$803$	23.3273	−	4.39462i	0.823202	−	0.155083i
$804$	−2.50779	+	4.34363i	−0.0884431	+	0.153188i
$805$	−23.9163	−	7.77089i	−0.842940	−	0.273888i
$806$	−20.2256	−	27.8381i	−0.712416	−	0.980557i
$807$	6.45909	−	2.87577i	0.227371	−	0.101232i
$808$	1.03835	−	4.88505i	0.0365290	−	0.171855i
$809$	26.7559	−	8.69353i	0.940688	−	0.305648i	0.201762	−	0.979435i	$-0.435333\pi$
$809$	26.7559	−	8.69353i	0.940688	−	0.305648i	0.738926	+	0.673786i	$0.235333\pi$
$810$	−4.43742	−	3.22398i	−0.155915	−	0.113279i
$811$	1.19121	+	11.3336i	0.0418291	+	0.397977i	0.995326	+	0.0965737i	$0.0307883\pi$
$811$	1.19121	+	11.3336i	0.0418291	+	0.397977i	−0.953497	+	0.301403i	$0.902545\pi$
$812$	0.934897	+	4.39834i	0.0328084	+	0.154352i
$813$	7.01648	−	12.1529i	0.246079	−	0.426221i
$814$	1.65047	−	12.8286i	0.0578488	−	0.449644i
$815$	−2.84941	−	4.93532i	−0.0998104	−	0.172877i
$816$	0.125962	−	0.387670i	0.00440954	−	0.0135712i
$817$	11.2542	−	24.0180i	0.393735	−	0.840284i
$818$	−23.8787	−	17.3489i	−0.834901	−	0.606591i
$819$	−38.5372	−	34.6990i	−1.34660	−	1.21248i
$820$	−1.93097	+	2.14456i	−0.0674325	+	0.0748914i
$821$	−12.1278	−	27.2395i	−0.423264	−	0.950665i	−0.991775	−	0.127990i	$-0.959147\pi$
$821$	−12.1278	−	27.2395i	−0.423264	−	0.950665i	0.568512	−	0.822675i	$-0.307519\pi$
$822$	−4.56515	+	10.2535i	−0.159228	+	0.357632i
$823$	0.358487	+	0.398140i	0.0124961	+	0.0138783i	0.749360	−	0.662162i	$-0.230361\pi$
$823$	0.358487	+	0.398140i	0.0124961	+	0.0138783i	−0.736864	+	0.676041i	$0.763694\pi$
$824$			4.40476i			0.153447i
$825$	7.72457	+	0.179491i	0.268935	+	0.00624906i
$826$	13.1266	−	22.7359i	0.456731	−	0.791082i
$827$	−4.68211	−	5.20002i	−0.162813	−	0.180822i	0.656218	−	0.754571i	$-0.272155\pi$
$827$	−4.68211	−	5.20002i	−0.162813	−	0.180822i	−0.819031	+	0.573749i	$0.805488\pi$
$828$	17.3174	−	12.5818i	0.601821	−	0.437249i
$829$	−6.81051	+	9.37387i	−0.236539	+	0.325568i	−0.910740	−	0.412980i	$-0.864488\pi$
$829$	−6.81051	+	9.37387i	−0.236539	+	0.325568i	0.674201	+	0.738548i	$0.264488\pi$
$830$	−2.23234	+	10.5023i	−0.0774856	+	0.364541i
$831$	−10.1050	+	11.2228i	−0.350540	+	0.389314i
$832$	4.72967	−	2.10578i	0.163972	−	0.0730049i
$833$	−2.04750	+	4.59876i	−0.0709416	+	0.159337i
$834$	−7.01423	+	1.49092i	−0.242883	+	0.0516264i
$835$	20.5103			0.709788
$836$	−3.60447	+	14.0003i	−0.124663	+	0.484210i
$837$	20.6913			0.715196
$838$	6.26782	−	1.33227i	0.216518	−	0.0460224i
$839$	5.94426	−	13.3510i	0.205219	−	0.460929i	−0.781388	−	0.624045i	$-0.785488\pi$
$839$	5.94426	−	13.3510i	0.205219	−	0.460929i	0.986607	+	0.163117i	$0.0521547\pi$
$840$	1.58325	−	0.704906i	0.0546272	−	0.0243216i
$841$	−18.4203	+	20.4578i	−0.635183	+	0.705442i
$842$	5.98032	−	28.1352i	0.206095	−	0.969602i
$843$	4.83466	−	6.65434i	0.166515	−	0.229188i
$844$	11.2974	−	8.20803i	0.388872	−	0.282532i
$845$	−7.90881	−	8.78362i	−0.272071	−	0.302166i
$846$	4.50117	−	7.79626i	0.154754	−	0.268041i
$847$	−1.89406	+	40.7344i	−0.0650807	+	1.39965i
$848$			0.927095i			0.0318366i
$849$	−6.59012	−	7.31906i	−0.226172	−	0.251190i
$850$	1.29566	−	2.91010i	0.0444407	−	0.0998155i
$851$	12.5666	+	28.2251i	0.430779	+	0.967545i
$852$	0.154291	−	0.171358i	0.00528594	−	0.00587063i
$853$	12.9674	+	11.6759i	0.443995	+	0.399775i	0.860575	−	0.509324i	$-0.170105\pi$
$853$	12.9674	+	11.6759i	0.443995	+	0.399775i	−0.416580	+	0.909099i	$0.636771\pi$
$854$	22.6211	+	16.4352i	0.774080	+	0.562402i
$855$	−8.27117	+	5.76864i	−0.282868	+	0.197283i
$856$	5.17615	−	15.9306i	0.176917	−	0.544495i
$857$	9.80662	+	16.9856i	0.334988	+	0.580216i	0.983482	−	0.181003i	$-0.0579345\pi$
$857$	9.80662	+	16.9856i	0.334988	+	0.580216i	−0.648495	+	0.761219i	$0.724601\pi$
$858$	6.43343	−	6.81957i	0.219634	−	0.232816i
$859$	25.5619	−	44.2746i	0.872162	−	1.51063i	0.0124060	−	0.999923i	$-0.496051\pi$
$859$	25.5619	−	44.2746i	0.872162	−	1.51063i	0.859756	−	0.510705i	$-0.170616\pi$
$860$	1.08326	+	5.09636i	0.0369390	+	0.173784i
$861$	−0.713069	−	6.78439i	−0.0243013	−	0.231212i
$862$	−7.78110	−	5.65330i	−0.265025	−	0.192552i
$863$	−3.62828	+	1.17890i	−0.123508	+	0.0401302i	−0.370119	−	0.928984i	$-0.620683\pi$
$863$	−3.62828	+	1.17890i	−0.123508	+	0.0401302i	0.246611	+	0.969115i	$0.420683\pi$
$864$	−0.647269	+	3.04516i	−0.0220205	+	0.103598i
$865$	−13.6873	+	6.09400i	−0.465384	+	0.207202i
$866$	−16.4126	−	22.5900i	−0.557724	−	0.767641i
$867$	8.53817	+	2.77422i	0.289971	+	0.0942174i
$868$	12.3194	−	21.3379i	0.418148	−	0.724254i
$869$	−33.5318	+	18.3345i	−1.13749	+	0.621955i
$870$	−0.491086	−	0.283529i	−0.0166494	−	0.00961252i
$871$	9.88813	+	46.5200i	0.335047	+	1.57627i
$872$	−11.7192	−	5.21773i	−0.396863	−	0.176695i
$873$	10.5941	−	14.5816i	0.358557	−	0.493511i
$874$	−10.0350	−	33.0427i	−0.339440	−	1.11769i
$875$	27.9750	−	9.08963i	0.945728	−	0.307286i
$876$	0.408472	−	3.88635i	0.0138010	−	0.131308i
$877$	−51.9943	−	23.1494i	−1.75572	−	0.781699i	−0.990430	−	0.138019i	$-0.955927\pi$
$877$	−51.9943	−	23.1494i	−1.75572	−	0.781699i	−0.765295	−	0.643680i	$-0.777407\pi$
$878$	0.164580	+	0.182785i	0.00555431	+	0.00616868i
$879$	11.3150	−	6.53275i	0.381647	−	0.220344i
$880$	−1.09448	−	2.62043i	−0.0368949	−	0.0883347i
$881$	−13.0197			−0.438644			−0.219322	−	0.975653i	$-0.570385\pi$
$881$	−13.0197			−0.438644			−0.219322	+	0.975653i	$0.570385\pi$
$882$	5.62979	−	17.3267i	0.189565	−	0.583420i
$883$	2.35549	+	22.4110i	0.0792686	+	0.754191i	0.959891	+	0.280372i	$0.0904579\pi$
$883$	2.35549	+	22.4110i	0.0792686	+	0.754191i	−0.880623	+	0.473818i	$0.842875\pi$
$884$	−1.57211	−	3.53101i	−0.0528757	−	0.118761i
$885$	1.02307	+	3.14869i	0.0343901	+	0.105842i
$886$	−2.68184	−	8.25386i	−0.0900983	−	0.277294i
$887$	16.0646	−	7.15240i	0.539395	−	0.240154i	−0.118911	−	0.992905i	$-0.537940\pi$
$887$	16.0646	−	7.15240i	0.539395	−	0.240154i	0.658306	+	0.752751i	$0.271273\pi$
$888$	−1.94521	−	0.866062i	−0.0652769	−	0.0290632i
$889$	38.1946	−	34.3906i	1.28101	−	1.15342i
$890$	1.41044	−	0.814320i	0.0472782	−	0.0272961i
$891$	−3.93333	−	20.8787i	−0.131772	−	0.699462i
$892$			12.0687i			0.404091i
$893$	−9.50773	−	10.9786i	−0.318164	−	0.367383i
$894$	1.92362	−	1.39759i	0.0643356	−	0.0467426i
$895$	9.92574	+	1.04324i	0.331781	+	0.0348716i
$896$	2.75494	+	2.48055i	0.0920359	+	0.0828695i
$897$	−4.65611	+	21.9053i	−0.155463	+	0.731395i
$898$	−6.77765	−	0.712360i	−0.226173	−	0.0237717i
$899$	−8.01758	+	0.842682i	−0.267401	+	0.0281050i
$900$	−3.56253	+	10.9643i	−0.118751	+	0.365478i
$901$	0.692138			0.0230585
$902$	−11.1410	+	0.909870i	−0.370955	+	0.0302953i
$903$	−10.6664	−	6.15824i	−0.354955	−	0.204933i
$904$	8.08279	+	2.62626i	0.268830	+	0.0873480i
$905$	−4.99538	−	6.87555i	−0.166052	−	0.228551i
$906$	−3.00778	−	6.75559i	−0.0999269	−	0.224439i
$907$	−23.5423	−	21.1976i	−0.781710	−	0.703855i	0.178252	−	0.983985i	$-0.442956\pi$
$907$	−23.5423	−	21.1976i	−0.781710	−	0.703855i	−0.959962	+	0.280130i	$0.909622\pi$
$908$	29.2454	+	6.21629i	0.970541	+	0.206295i
$909$	13.4198	+	1.41048i	0.445108	+	0.0467827i
$910$	6.68413	−	15.0128i	0.221577	−	0.497670i
$911$	−25.0485	−	8.13874i	−0.829893	−	0.269648i	−0.136893	−	0.990586i	$-0.543711\pi$
$911$	−25.0485	−	8.13874i	−0.829893	−	0.269648i	−0.693000	+	0.720937i	$0.743711\pi$
$912$	2.03771	+	1.22954i	0.0674754	+	0.0407143i
$913$	−34.2054	+	23.6575i	−1.13203	+	0.782949i
$914$	35.3596	−	20.4149i	1.16959	−	0.675263i
$915$	−3.44908	+	0.733125i	−0.114023	+	0.0242364i
$916$	1.38154	+	13.1445i	0.0456474	+	0.434306i
$917$	3.92785	−	37.3710i	0.129709	−	1.23410i
$918$	2.27342	+	0.483229i	0.0750339	+	0.0159489i
$919$	−54.5728	+	17.7318i	−1.80019	+	0.584918i	−0.999892	−	0.0146823i	$-0.995326\pi$
$919$	−54.5728	+	17.7318i	−1.80019	+	0.584918i	−0.800300	+	0.599600i	$0.795326\pi$
$920$	5.48792	+	3.98721i	0.180931	+	0.131454i
$921$	−2.66558	+	0.280164i	−0.0878338	+	0.00923171i
$922$	−15.7752	+	14.2041i	−0.519530	+	0.467786i
$923$		−	2.18647i		−	0.0719687i
$924$	6.33460	+	2.22221i	0.208393	+	0.0731052i
$925$	−14.4108	−	8.32008i	−0.473824	−	0.273563i
$926$	−8.44437	+	1.79491i	−0.277499	+	0.0589843i
$927$	−11.8360	+	1.24401i	−0.388745	+	0.0408587i
$928$	0.126789	−	1.20632i	0.00416205	−	0.0395993i
$929$	−26.2384	+	29.1407i	−0.860856	+	0.956077i	−0.999412	−	0.0342775i	$-0.989087\pi$
$929$	−26.2384	+	29.1407i	−0.860856	+	0.956077i	0.138557	+	0.990354i	$0.455754\pi$
$930$	0.960163	+	2.95508i	0.0314850	+	0.0969008i
$931$	−23.4400	−	17.7317i	−0.768214	−	0.581134i
$932$	−0.317953	−	0.437625i	−0.0104149	−	0.0143349i
$933$	−0.843658	−	3.96910i	−0.0276201	−	0.129942i
$934$	−8.95781	−	15.5154i	−0.293109	−	0.507679i
$935$	−1.95633	+	0.817101i	−0.0639787	+	0.0267221i
$936$	6.99420	+	12.1143i	0.228613	+	0.395969i
$937$	21.7462	−	19.5804i	0.710417	−	0.639662i	−0.232536	−	0.972588i	$-0.574702\pi$
$937$	21.7462	−	19.5804i	0.710417	−	0.639662i	0.942953	+	0.332925i	$0.108036\pi$
$938$	−27.5506	+	20.0167i	−0.899558	+	0.653567i
$939$	5.70339	−	7.85004i	0.186123	−	0.256176i
$940$	2.79052	+	0.593144i	0.0910168	+	0.0193462i
$941$	−28.1748	−	5.98873i	−0.918472	−	0.195227i	−0.275663	−	0.961254i	$-0.588897\pi$
$941$	−28.1748	−	5.98873i	−0.918472	−	0.195227i	−0.642808	+	0.766027i	$0.722231\pi$
$942$	−6.28135	+	8.64554i	−0.204657	+	0.281687i
$943$	21.6016	−	15.6945i	0.703446	−	0.511083i
$944$	−5.26279	+	4.73864i	−0.171289	+	0.154230i
$945$	4.94091	+	8.55791i	0.160728	+	0.278389i
$946$	−10.4942	+	17.2388i	−0.341194	+	0.560480i
$947$	26.2020	+	45.3833i	0.851452	+	1.47476i	0.879898	+	0.475163i	$0.157611\pi$
$947$	26.2020	+	45.3833i	0.851452	+	1.47476i	−0.0284455	+	0.999595i	$0.509056\pi$
$948$	1.30805	+	6.15391i	0.0424836	+	0.199870i
$949$	−21.7801	−	29.9777i	−0.707012	−	0.973119i
$950$	14.8328	+	11.2206i	0.481241	+	0.364046i
$951$	−0.667881	−	2.05553i	−0.0216575	−	0.0666550i
$952$	1.85190	−	2.05674i	0.0600204	−	0.0666594i
$953$	−3.43231	+	32.6562i	−0.111183	+	1.05784i	0.786618	+	0.617440i	$0.211830\pi$
$953$	−3.43231	+	32.6562i	−0.111183	+	1.05784i	−0.897802	+	0.440400i	$0.854837\pi$
$954$	−2.49119	+	0.261834i	−0.0806552	+	0.00847720i
$955$	10.0380	−	2.13364i	0.324821	−	0.0690429i
$956$	14.5909	+	8.42406i	0.471904	+	0.272454i
$957$	−0.630043	−	2.10419i	−0.0203664	−	0.0680189i
$958$		−	10.1720i		−	0.328641i
$959$	−56.6326	+	50.9922i	−1.82876	+	1.64663i
$960$	−0.464937	+	0.0488669i	−0.0150058	+	0.00157717i
$961$	10.6578	+	7.74335i	0.343800	+	0.249785i
$962$	−19.2024	+	6.23924i	−0.619110	+	0.201161i
$963$	44.2687	+	9.40961i	1.42654	+	0.303220i
$964$	0.378018	−	3.59660i	0.0121751	−	0.115839i
$965$	0.756882	+	7.20125i	0.0243649	+	0.231816i
$966$	−15.6851	+	3.33396i	−0.504658	+	0.107268i
$967$	12.7002	−	7.33245i	0.408410	−	0.235796i	−0.281696	−	0.959504i	$-0.590897\pi$
$967$	12.7002	−	7.33245i	0.408410	−	0.235796i	0.690106	+	0.723708i	$0.257564\pi$
$968$	3.88144	−	10.2924i	0.124754	−	0.330812i
$969$	0.917937	−	1.52129i	0.0294884	−	0.0488708i
$970$	5.43223	+	1.76504i	0.174418	+	0.0566720i
$971$	2.56130	−	5.75278i	0.0821961	−	0.184615i	−0.867772	−	0.496963i	$-0.834449\pi$
$971$	2.56130	−	5.75278i	0.0821961	−	0.184615i	0.949968	+	0.312347i	$0.101115\pi$
$972$	−12.7668	−	1.34185i	−0.409496	−	0.0430398i
$973$	−47.6246	−	10.1229i	−1.52677	−	0.324526i
$974$	−5.81048	−	5.23178i	−0.186180	−	0.167637i
$975$	−4.90579	−	11.0186i	−0.157111	−	0.352877i
$976$	−4.43341	−	6.10206i	−0.141910	−	0.195322i
$977$	3.66312	+	1.19022i	0.117194	+	0.0380785i	0.367027	−	0.930210i	$-0.380376\pi$
$977$	3.66312	+	1.19022i	0.117194	+	0.0380785i	−0.249833	+	0.968289i	$0.580376\pi$
$978$	−3.14709	−	1.81697i	−0.100633	−	0.0581003i
$979$	6.13854	+	1.45461i	0.196189	+	0.0464895i
$980$	5.77344			0.184426
$981$	10.7107	−	32.9642i	0.341967	−	1.05247i
$982$	31.9676	−	3.35993i	1.02013	−	0.107220i
$983$	−5.56216	−	0.584607i	−0.177405	−	0.0186461i	0.0154091	−	0.999881i	$-0.495095\pi$
$983$	−5.56216	−	0.584607i	−0.177405	−	0.0186461i	−0.192815	+	0.981235i	$0.561762\pi$
$984$	−0.382594	+	1.79996i	−0.0121966	+	0.0573807i
$985$	8.16626	+	7.35293i	0.260199	+	0.234284i
$986$	−0.900595	−	0.0946564i	−0.0286808	−	0.00301447i
$987$	−5.45595	+	3.96398i	−0.173665	+	0.126175i
$988$	22.1605	−	4.26482i	0.705020	−	0.135682i
$989$		−	48.2080i		−	1.53292i
$990$	6.73223	−	3.68104i	0.213964	−	0.116991i
$991$	35.5619	−	20.5317i	1.12966	−	0.652211i	0.185812	−	0.982585i	$-0.440508\pi$
$991$	35.5619	−	20.5317i	1.12966	−	0.652211i	0.943850	+	0.330375i	$0.107175\pi$
$992$	−4.93919	+	4.44727i	−0.156819	+	0.141201i
$993$	−9.15023	−	4.07395i	−0.290374	−	0.129283i
$994$	1.43025	−	0.636789i	0.0453648	−	0.0201977i
$995$	−5.73255	−	17.6430i	−0.181734	−	0.559320i
$996$	2.11571	+	6.51150i	0.0670389	+	0.206325i
$997$	7.33239	+	16.4688i	0.232219	+	0.521573i	0.991641	−	0.129025i	$-0.0411849\pi$
$997$	7.33239	+	16.4688i	0.232219	+	0.521573i	−0.759422	+	0.650598i	$0.774518\pi$
$998$	3.79830	+	36.1384i	0.120233	+	1.14394i
$999$	3.75178	−	11.5468i	0.118701	−	0.365324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.145.4	✓	80
11.6	odd	10		418.2.s.b.259.4	yes	80
19.8	odd	6		418.2.s.b.255.4	yes	80
209.160	even	30	inner	418.2.s.a.369.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.145.4	✓	80	1.1	even	1	trivial
418.2.s.a.369.4	yes	80	209.160	even	30	inner
418.2.s.b.255.4	yes	80	19.8	odd	6
418.2.s.b.259.4	yes	80	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.s (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 - 0.207912i) q^{2} +(-0.222075 + 0.498789i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.572934 + 0.636307i) q^{5} +(-0.113518 + 0.534061i) q^{6} +(-2.17900 + 2.99913i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.80792 + 2.00790i) q^{9} +O(q^{10})\)	\(q+(0.978148 - 0.207912i) q^{2} +(-0.222075 + 0.498789i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.572934 + 0.636307i) q^{5} +(-0.113518 + 0.534061i) q^{6} +(-2.17900 + 2.99913i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.80792 + 2.00790i) q^{9} +(-0.428118 + 0.741522i) q^{10} +(-3.17725 + 0.951342i) q^{11} +0.545993i q^{12} +(3.46427 + 3.84746i) q^{13} +(-1.50783 + 3.38663i) q^{14} +(-0.190149 - 0.427081i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.554807 - 0.499551i) q^{17} +(2.18588 + 1.58813i) q^{18} +(3.57524 - 2.49352i) q^{19} +(-0.264591 + 0.814329i) q^{20} +(-1.01203 - 1.75289i) q^{21} +(-2.91003 + 1.59114i) q^{22} +(3.96120 - 6.86100i) q^{23} +(0.113518 + 0.534061i) q^{24} +(0.446008 + 4.24349i) q^{25} +(4.18849 + 3.04312i) q^{26} +(-2.96082 + 0.962029i) q^{27} +(-0.770756 + 3.62612i) q^{28} +(1.10809 - 0.493356i) q^{29} +(-0.274789 - 0.378214i) q^{30} +(-6.32104 - 2.05383i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.231070 - 1.79605i) q^{33} +(-0.646546 - 0.373283i) q^{34} +(-0.659949 - 3.10481i) q^{35} +(2.46830 + 1.09896i) q^{36} +(-2.29228 + 3.15505i) q^{37} +(2.97868 - 3.18236i) q^{38} +(-2.68840 + 0.873513i) q^{39} +(-0.0895010 + 0.851545i) q^{40} +(3.07895 + 1.37084i) q^{41} +(-1.35436 - 1.50417i) q^{42} +(5.26978 - 3.04251i) q^{43} +(-2.51562 + 2.16140i) q^{44} -2.31346 q^{45} +(2.44816 - 7.53465i) q^{46} +(-0.348275 - 3.31362i) q^{47} +(0.222075 + 0.498789i) q^{48} +(-2.08365 - 6.41280i) q^{49} +(1.31853 + 4.05803i) q^{50} +(0.372379 - 0.165794i) q^{51} +(4.72967 + 2.10578i) q^{52} +(-0.688966 + 0.620348i) q^{53} +(-2.69610 + 1.55660i) q^{54} +(1.21501 - 2.56677i) q^{55} +3.70713i q^{56} +(0.449767 + 2.33704i) q^{57} +(0.981306 - 0.712960i) q^{58} +(-7.04299 - 0.740248i) q^{59} +(-0.347419 - 0.312818i) q^{60} +(1.56819 - 7.37774i) q^{61} +(-6.60993 - 0.694731i) q^{62} +(-9.96140 + 1.04698i) q^{63} +(0.309017 - 0.951057i) q^{64} -4.43296 q^{65} +(-0.147399 - 1.80484i) q^{66} +(7.95547 + 4.59309i) q^{67} +(-0.710027 - 0.230702i) q^{68} +(2.54251 + 3.49946i) q^{69} +(-1.29105 - 2.89976i) q^{70} +(-0.313847 - 0.282589i) q^{71} +(2.64285 + 0.561755i) q^{72} +(-7.11796 - 0.748127i) q^{73} +(-1.58622 + 3.56270i) q^{74} +(-2.21565 - 0.719909i) q^{75} +(2.25194 - 3.73212i) q^{76} +(4.07003 - 11.6020i) q^{77} +(-2.44804 + 1.41337i) q^{78} +(11.2711 - 2.39574i) q^{79} +(0.0895010 + 0.851545i) q^{80} +(-0.669598 + 6.37080i) q^{81} +(3.29668 + 0.700730i) q^{82} +(11.9260 - 3.87498i) q^{83} +(-1.63750 - 1.18972i) q^{84} +(0.635735 - 0.0668185i) q^{85} +(4.52205 - 4.07167i) q^{86} +0.662268i q^{87} +(-2.01127 + 2.63720i) q^{88} +(-1.64726 - 0.951047i) q^{89} +(-2.26290 + 0.480995i) q^{90} +(-19.0877 + 2.00619i) q^{91} +(0.828117 - 7.87900i) q^{92} +(2.42817 - 2.69676i) q^{93} +(-1.02960 - 3.16880i) q^{94} +(-0.461734 + 3.70357i) q^{95} +(0.320926 + 0.441717i) q^{96} +(-1.38694 - 6.52504i) q^{97} +(-3.37141 - 5.83945i) q^{98} +(-7.65442 - 4.65965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Introduction

L-functions

Modular forms

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