LMFDB - Embedded newform 414.2.m.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(1.23371 + 1.21571i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.213728 - 0.300139i) q^{5} +(1.55235 - 0.768242i) q^{6} +(1.08956 + 4.49122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.0441053 + 2.99968i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(1.23371 + 1.21571i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.213728 - 0.300139i) q^{5} +(1.55235 - 0.768242i) q^{6} +(1.08956 + 4.49122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.0441053 + 2.99968i) q^{9} +(-0.353536 + 0.103807i) q^{10} +(-0.0153105 - 0.00295086i) q^{11} +(-0.218264 - 1.71824i) q^{12} +(-0.919036 + 3.78832i) q^{13} +(4.60056 + 0.439300i) q^{14} +(0.101202 - 0.630118i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.199869 - 1.39012i) q^{17} +(2.84912 + 0.939418i) q^{18} +(0.504497 - 3.50885i) q^{19} +(-0.0175321 + 0.368044i) q^{20} +(-4.11581 + 6.86546i) q^{21} +(-0.00779613 + 0.0135033i) q^{22} +(3.19748 - 3.57437i) q^{23} +(-1.69513 - 0.355722i) q^{24} +(1.59094 - 4.59671i) q^{25} +(3.27938 + 2.10753i) q^{26} +(-3.59232 + 3.75436i) q^{27} +(1.91984 - 4.20385i) q^{28} +(2.25220 - 1.77115i) q^{29} +(-0.562362 - 0.301728i) q^{30} +(-0.204088 - 4.28433i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(-0.0153014 - 0.0222536i) q^{33} +(-1.37903 - 0.265787i) q^{34} +(1.11512 - 1.28692i) q^{35} +(1.81961 - 2.38517i) q^{36} +(4.05410 + 8.87723i) q^{37} +(-3.15086 - 1.62438i) q^{38} +(-5.73932 + 3.55642i) q^{39} +(0.342067 + 0.136943i) q^{40} +(1.30720 + 1.83570i) q^{41} +(5.14172 + 6.13491i) q^{42} +(0.0435160 - 0.913513i) q^{43} +(0.0102108 + 0.0117839i) q^{44} +(0.890894 - 0.654353i) q^{45} +(-2.33199 - 4.19068i) q^{46} +(-3.49454 - 6.05272i) q^{47} +(-0.890580 + 1.48555i) q^{48} +(-12.7620 + 6.57929i) q^{49} +(-3.82355 - 3.00687i) q^{50} +(1.44340 - 1.95799i) q^{51} +(3.06419 - 2.40971i) q^{52} +(6.69941 + 1.96712i) q^{53} +(2.37294 + 4.62268i) q^{54} +(0.00238662 + 0.00522596i) q^{55} +(-3.34473 - 3.18919i) q^{56} +(4.88815 - 3.71560i) q^{57} +(-0.937114 - 2.70761i) q^{58} +(0.751327 - 3.09701i) q^{59} +(-0.469063 + 0.432747i) q^{60} +(-8.63524 - 4.45178i) q^{61} +(-4.11544 - 1.20840i) q^{62} +(-13.4241 + 3.46640i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.33345 - 0.533832i) q^{65} +(-0.0260343 + 0.00718140i) q^{66} +(-2.67489 + 0.515544i) q^{67} +(-0.702207 + 1.21626i) q^{68} +(8.29017 - 0.522554i) q^{69} +(-0.851419 - 1.47470i) q^{70} +(-2.15137 - 2.48281i) q^{71} +(-1.65885 - 2.49964i) q^{72} +(0.697486 - 4.85112i) q^{73} +(9.71496 - 0.927666i) q^{74} +(7.55102 - 3.73691i) q^{75} +(-2.56559 + 2.44629i) q^{76} +(-0.00342873 - 0.0719779i) q^{77} +(1.48368 + 6.58685i) q^{78} +(1.47134 + 1.40292i) q^{79} +(0.241291 - 0.278464i) q^{80} +(-8.99611 + 0.264603i) q^{81} +(2.16229 - 0.634904i) q^{82} +(9.91802 - 13.9279i) q^{83} +(7.47919 - 2.85240i) q^{84} +(-0.374512 + 0.357096i) q^{85} +(-0.849038 - 0.339904i) q^{86} +(4.93177 + 0.552924i) q^{87} +(0.0144754 - 0.00579506i) q^{88} +(1.05571 + 0.678467i) q^{89} +(-0.326981 - 1.05591i) q^{90} -18.0155 q^{91} +(-4.72292 + 0.833096i) q^{92} +(4.95671 - 5.53375i) q^{93} +(-6.86278 + 1.32269i) q^{94} +(-1.16097 + 0.598522i) q^{95} +(1.11257 + 1.32748i) q^{96} +(-2.34105 + 0.223543i) q^{97} +(2.04338 + 14.2120i) q^{98} +(0.00817634 - 0.0460567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	1.23371	+	1.21571i	0.712286	+	0.701890i
$3$	1.23371	+	1.21571i	0.712286	+	0.701890i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.213728	−	0.300139i	−0.0955822	−	0.134226i	0.764015	−	0.645198i	$-0.223225\pi$
$5$	−0.213728	−	0.300139i	−0.0955822	−	0.134226i	−0.859598	+	0.510972i	$0.829286\pi$
$6$	1.55235	−	0.768242i	0.633746	−	0.313634i
$7$	1.08956	+	4.49122i	0.411814	+	1.69752i	0.679219	+	0.733936i	$0.262319\pi$
$7$	1.08956	+	4.49122i	0.411814	+	1.69752i	−0.267405	+	0.963584i	$0.586166\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.0441053	+	2.99968i	0.0147018	+	0.999892i
$10$	−0.353536	+	0.103807i	−0.111798	+	0.0328268i
$11$	−0.0153105	−	0.00295086i	−0.00461629	−	0.000889717i	0.186943	−	0.982371i	$-0.440142\pi$
$11$	−0.0153105	−	0.00295086i	−0.00461629	−	0.000889717i	−0.191559	+	0.981481i	$0.561354\pi$
$12$	−0.218264	−	1.71824i	−0.0630075	−	0.496014i
$13$	−0.919036	+	3.78832i	−0.254895	+	1.05069i	0.690129	+	0.723687i	$0.257554\pi$
$13$	−0.919036	+	3.78832i	−0.254895	+	1.05069i	−0.945023	+	0.327003i	$0.893961\pi$
$14$	4.60056	+	0.439300i	1.22955	+	0.117408i
$15$	0.101202	−	0.630118i	0.0261303	−	0.162696i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−0.199869	−	1.39012i	−0.0484753	−	0.337153i	−0.999598	−	0.0283410i	$-0.990978\pi$
$17$	−0.199869	−	1.39012i	−0.0484753	−	0.337153i	0.951123	−	0.308812i	$-0.0999315\pi$
$18$	2.84912	+	0.939418i	0.671544	+	0.221423i
$19$	0.504497	−	3.50885i	0.115740	−	0.804986i	−0.846423	−	0.532511i	$-0.821249\pi$
$19$	0.504497	−	3.50885i	0.115740	−	0.804986i	0.962163	−	0.272475i	$-0.0878423\pi$
$20$	−0.0175321	+	0.368044i	−0.00392029	+	0.0822970i
$21$	−4.11581	+	6.86546i	−0.898143	+	1.49817i
$22$	−0.00779613	+	0.0135033i	−0.00166214	+	0.00287891i
$23$	3.19748	−	3.57437i	0.666720	−	0.745308i
$23$	3.19748	−	3.57437i	0.666720	−	0.745308i
$24$	−1.69513	−	0.355722i	−0.346017	−	0.0726115i
$25$	1.59094	−	4.59671i	0.318187	−	0.919342i
$26$	3.27938	+	2.10753i	0.643138	+	0.413320i
$27$	−3.59232	+	3.75436i	−0.691342	+	0.722528i
$28$	1.91984	−	4.20385i	0.362815	−	0.794454i
$29$	2.25220	−	1.77115i	0.418222	−	0.328894i	−0.386773	−	0.922175i	$-0.626410\pi$
$29$	2.25220	−	1.77115i	0.418222	−	0.328894i	0.804995	+	0.593281i	$0.202168\pi$
$30$	−0.562362	−	0.301728i	−0.102673	−	0.0550877i
$31$	−0.204088	−	4.28433i	−0.0366552	−	0.769488i	−0.940124	−	0.340833i	$-0.889291\pi$
$31$	−0.204088	−	4.28433i	−0.0366552	−	0.769488i	0.903468	−	0.428655i	$-0.141012\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	−0.0153014	−	0.0222536i	−0.00266363	−	0.00387386i
$34$	−1.37903	−	0.265787i	−0.236502	−	0.0455821i
$35$	1.11512	−	1.28692i	0.188490	−	0.217529i
$36$	1.81961	−	2.38517i	0.303268	−	0.397528i
$37$	4.05410	+	8.87723i	0.666489	+	1.45941i	0.876349	+	0.481677i	$0.159972\pi$
$37$	4.05410	+	8.87723i	0.666489	+	1.45941i	−0.209860	+	0.977732i	$0.567301\pi$
$38$	−3.15086	−	1.62438i	−0.511138	−	0.263510i
$39$	−5.73932	+	3.55642i	−0.919026	+	0.569484i
$40$	0.342067	+	0.136943i	0.0540856	+	0.0216526i
$41$	1.30720	+	1.83570i	0.204150	+	0.286689i	0.903939	−	0.427661i	$-0.140662\pi$
$41$	1.30720	+	1.83570i	0.204150	+	0.286689i	−0.699789	+	0.714349i	$0.746723\pi$
$42$	5.14172	+	6.13491i	0.793385	+	0.946638i
$43$	0.0435160	−	0.913513i	0.00663613	−	0.139310i	−0.993118	−	0.117121i	$-0.962634\pi$
$43$	0.0435160	−	0.913513i	0.00663613	−	0.139310i	0.999754	−	0.0221887i	$-0.00706345\pi$
$44$	0.0102108	+	0.0117839i	0.00153933	+	0.00177648i
$45$	0.890894	−	0.654353i	0.132807	−	0.0975452i
$46$	−2.33199	−	4.19068i	−0.343833	−	0.617882i
$47$	−3.49454	−	6.05272i	−0.509731	−	0.882880i	−0.999936	−	0.0112732i	$-0.996412\pi$
$47$	−3.49454	−	6.05272i	−0.509731	−	0.882880i	0.490205	−	0.871607i	$-0.336922\pi$
$48$	−0.890580	+	1.48555i	−0.128544	+	0.214421i
$49$	−12.7620	+	6.57929i	−1.82315	+	0.939898i
$50$	−3.82355	−	3.00687i	−0.540731	−	0.425236i
$51$	1.44340	−	1.95799i	0.202116	−	0.274174i
$52$	3.06419	−	2.40971i	0.424927	−	0.334166i
$53$	6.69941	+	1.96712i	0.920235	+	0.270205i	0.707343	−	0.706870i	$-0.249894\pi$
$53$	6.69941	+	1.96712i	0.920235	+	0.270205i	0.212892	+	0.977076i	$0.431712\pi$
$54$	2.37294	+	4.62268i	0.322917	+	0.629067i
$55$	0.00238662	+	0.00522596i	0.000321811	+	0.000704669i
$56$	−3.34473	−	3.18919i	−0.446958	−	0.426174i
$57$	4.88815	−	3.71560i	0.647451	−	0.492144i
$58$	−0.937114	−	2.70761i	−0.123049	−	0.355527i
$59$	0.751327	−	3.09701i	0.0978145	−	0.403197i	−0.901764	−	0.432229i	$-0.857727\pi$
$59$	0.751327	−	3.09701i	0.0978145	−	0.403197i	0.999578	+	0.0290320i	$0.00924246\pi$
$60$	−0.469063	+	0.432747i	−0.0605558	+	0.0558674i
$61$	−8.63524	−	4.45178i	−1.10563	−	0.569992i	−0.193999	−	0.981002i	$-0.562146\pi$
$61$	−8.63524	−	4.45178i	−1.10563	−	0.569992i	−0.911631	+	0.411010i	$0.865176\pi$
$62$	−4.11544	−	1.20840i	−0.522662	−	0.153467i
$63$	−13.4241	+	3.46640i	−1.69128	+	0.436726i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	1.33345	−	0.533832i	0.165394	−	0.0662137i
$66$	−0.0260343	+	0.00718140i	−0.00320460	+	0.000883969i
$67$	−2.67489	+	0.515544i	−0.326790	+	0.0629837i	−0.350008	−	0.936747i	$-0.613821\pi$
$67$	−2.67489	+	0.515544i	−0.326790	+	0.0629837i	0.0232175	+	0.999730i	$0.492609\pi$
$68$	−0.702207	+	1.21626i	−0.0851551	+	0.147493i
$69$	8.29017	−	0.522554i	0.998019	−	0.0629081i
$70$	−0.851419	−	1.47470i	−0.101764	−	0.176260i
$71$	−2.15137	−	2.48281i	−0.255321	−	0.294656i	0.613590	−	0.789625i	$-0.289725\pi$
$71$	−2.15137	−	2.48281i	−0.255321	−	0.294656i	−0.868911	+	0.494969i	$0.835179\pi$
$72$	−1.65885	−	2.49964i	−0.195497	−	0.294586i
$73$	0.697486	−	4.85112i	0.0816345	−	0.567781i	−0.907419	−	0.420226i	$-0.861951\pi$
$73$	0.697486	−	4.85112i	0.0816345	−	0.567781i	0.989054	−	0.147554i	$-0.0471402\pi$
$74$	9.71496	−	0.927666i	1.12934	−	0.107839i
$75$	7.55102	−	3.73691i	0.871916	−	0.431501i
$76$	−2.56559	+	2.44629i	−0.294293	+	0.280608i
$77$	−0.00342873	−	0.0719779i	−0.000390740	−	0.00820264i
$78$	1.48368	+	6.58685i	0.167993	+	0.745814i
$79$	1.47134	+	1.40292i	0.165539	+	0.157841i	0.768321	−	0.640065i	$-0.221093\pi$
$79$	1.47134	+	1.40292i	0.165539	+	0.157841i	−0.602782	+	0.797906i	$0.705941\pi$
$80$	0.241291	−	0.278464i	0.0269771	−	0.0311332i
$81$	−8.99611	+	0.264603i	−0.999568	+	0.0294004i
$82$	2.16229	−	0.634904i	0.238784	−	0.0701134i
$83$	9.91802	−	13.9279i	1.08864	−	1.52879i	0.262832	−	0.964842i	$-0.415344\pi$
$83$	9.91802	−	13.9279i	1.08864	−	1.52879i	0.825812	−	0.563945i	$-0.190717\pi$
$84$	7.47919	−	2.85240i	0.816047	−	0.311222i
$85$	−0.374512	+	0.357096i	−0.0406215	+	0.0387325i
$86$	−0.849038	−	0.339904i	−0.0915542	−	0.0366528i
$87$	4.93177	+	0.552924i	0.528741	+	0.0592797i
$88$	0.0144754	−	0.00579506i	0.00154308	−	0.000617756i
$89$	1.05571	+	0.678467i	0.111906	+	0.0719173i	0.595396	−	0.803432i	$-0.296995\pi$
$89$	1.05571	+	0.678467i	0.111906	+	0.0719173i	−0.483491	+	0.875349i	$0.660631\pi$
$90$	−0.326981	−	1.05591i	−0.0344669	−	0.111303i
$91$	−18.0155			−1.88854
$92$	−4.72292	+	0.833096i	−0.492398	+	0.0868563i
$93$	4.95671	−	5.53375i	0.513987	−	0.573823i
$94$	−6.86278	+	1.32269i	−0.707842	+	0.136425i
$95$	−1.16097	+	0.598522i	−0.119113	+	0.0614070i
$96$	1.11257	+	1.32748i	0.113551	+	0.135485i
$97$	−2.34105	+	0.223543i	−0.237697	+	0.0226973i	−0.213225	−	0.977003i	$-0.568397\pi$
$97$	−2.34105	+	0.223543i	−0.237697	+	0.0226973i	−0.0244725	+	0.999701i	$0.507791\pi$
$98$	2.04338	+	14.2120i	0.206412	+	1.43563i
$99$	0.00817634	−	0.0460567i	0.000821753	−	0.00462887i
$100$	−4.09206	+	2.62980i	−0.409206	+	0.262980i
$101$	9.36047	−	13.1449i	0.931402	−	1.30797i	−0.0199294	−	0.999801i	$-0.506344\pi$
$101$	9.36047	−	13.1449i	0.931402	−	1.30797i	0.951331	−	0.308170i	$-0.0997165\pi$
$102$	−1.37822	−	2.00441i	−0.136464	−	0.198466i
$103$	5.18251	+	14.9739i	0.510647	+	1.47542i	0.845926	+	0.533300i	$0.179048\pi$
$103$	5.18251	+	14.9739i	0.510647	+	1.47542i	−0.335279	+	0.942119i	$0.608830\pi$
$104$	−1.27498	−	3.68380i	−0.125022	−	0.361227i
$105$	2.94026	−	0.232028i	0.286940	−	0.0226436i
$106$	4.05010	−	5.68756i	0.393380	−	0.552425i
$107$	−12.7459	+	8.19129i	−1.23219	+	0.791882i	−0.984231	−	0.176888i	$-0.943397\pi$
$107$	−12.7459	+	8.19129i	−1.23219	+	0.791882i	−0.247962	+	0.968770i	$0.579761\pi$
$108$	5.14455	−	0.730506i	0.495034	−	0.0702930i
$109$	0.160886	+	1.11899i	0.0154101	+	0.107179i	0.996075	−	0.0885164i	$-0.0282126\pi$
$109$	0.160886	+	1.11899i	0.0154101	+	0.107179i	−0.980665	+	0.195696i	$0.937303\pi$
$110$	0.00571913		0.000546110i	0.000545297		5.20696e-5i
$111$	−5.79053	+	15.8806i	−0.549613	+	1.50732i
$112$	−4.10774	+	2.11769i	−0.388145	+	0.200103i
$113$	−5.11691	+	0.986204i	−0.481359	+	0.0927743i	−0.424158	−	0.905588i	$-0.639430\pi$
$113$	−5.11691	+	0.986204i	−0.481359	+	0.0927743i	−0.0572011	+	0.998363i	$0.518218\pi$
$114$	−1.91249	−	5.83456i	−0.179121	−	0.546456i
$115$	−1.75620	−	0.195745i	−0.163767	−	0.0182533i
$116$	−2.86520			−0.266027
$117$	−11.4043	−	2.58972i	−1.05432	−	0.239420i
$118$	−2.68094	−	1.72294i	−0.246801	−	0.158609i
$119$	6.02556	−	2.41227i	0.552362	−	0.221132i
$120$	0.255531	+	0.584803i	0.0233266	+	0.0533849i
$121$	−10.2118	−	4.08820i	−0.928347	−	0.371654i
$122$	−7.03124	+	6.70428i	−0.636579	+	0.606977i
$123$	−0.618970	+	3.85391i	−0.0558107	+	0.347495i
$124$	−2.48797	+	3.49387i	−0.223426	+	0.313759i
$125$	−3.48736	+	1.02398i	−0.311919	+	0.0915876i
$126$	−1.11485	+	13.8196i	−0.0993187	+	1.23115i
$127$	−5.10810	+	5.89506i	−0.453270	+	0.523102i	−0.935683	−	0.352842i	$-0.885215\pi$
$127$	−5.10810	+	5.89506i	−0.453270	+	0.523102i	0.482412	+	0.875944i	$0.339761\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	1.16425	−	1.07411i	0.102507	−	0.0945703i
$130$	−0.0683436	−	1.43471i	−0.00599413	−	0.125832i
$131$	−14.2752	+	13.6114i	−1.24723	+	1.18923i	−0.273411	+	0.961897i	$0.588152\pi$
$131$	−14.2752	+	13.6114i	−1.24723	+	1.18923i	−0.973817	+	0.227333i	$0.927000\pi$
$132$	−0.00172855	+	0.0269512i	−0.000150451	+	0.00234580i
$133$	16.3087	−	1.55729i	1.41414	−	0.135034i
$134$	−0.387683	+	2.69640i	−0.0334907	+	0.232933i
$135$	1.89461	+	0.275782i	0.163062	+	0.0237356i
$136$	0.919696	+	1.06139i	0.0788632	+	0.0910130i
$137$	6.62205	+	11.4697i	0.565760	+	0.979925i	0.996979	+	0.0776773i	$0.0247504\pi$
$137$	6.62205	+	11.4697i	0.565760	+	0.979925i	−0.431219	+	0.902247i	$0.641916\pi$
$138$	2.21764	−	8.00513i	0.188778	−	0.681442i
$139$	9.58720	−	16.6055i	0.813176	−	1.40846i	−0.0974547	−	0.995240i	$-0.531070\pi$
$139$	9.58720	−	16.6055i	0.813176	−	1.40846i	0.910630	−	0.413222i	$-0.135597\pi$
$140$	−1.67207	+	0.322264i	−0.141315	+	0.0272363i
$141$	3.04708	−	11.7157i	0.256610	−	0.986638i
$142$	−3.04991	+	1.22100i	−0.255942	+	0.102464i
$143$	0.0252497	−	0.0552891i	0.00211148	−	0.00462350i
$144$	−2.90472	+	0.750062i	−0.242060	+	0.0625052i
$145$	−1.01295	−	0.297429i	−0.0841208	−	0.0247001i
$146$	−4.35619	−	2.24577i	−0.360521	−	0.185861i
$147$	−23.7432	−	7.39795i	−1.95831	−	0.610173i
$148$	2.30081	−	9.48405i	0.189125	−	0.779584i
$149$	−5.01179	−	14.4806i	−0.410582	−	1.18630i	−0.940954	−	0.338534i	$-0.890069\pi$
$149$	−5.01179	−	14.4806i	−0.410582	−	1.18630i	0.530373	−	0.847765i	$-0.322052\pi$
$150$	−1.06169	−	8.35794i	−0.0866866	−	0.682423i
$151$	−11.8174	−	11.2678i	−0.961683	−	0.916962i	0.0349145	−	0.999390i	$-0.488884\pi$
$151$	−11.8174	−	11.2678i	−0.961683	−	0.916962i	−0.996597	+	0.0824278i	$0.973733\pi$
$152$	1.47262	+	3.22459i	0.119445	+	0.261548i
$153$	4.16109	−	0.660854i	0.336404	−	0.0534269i
$154$	−0.0691406	−	0.0203015i	−0.00557151	−	0.00163594i
$155$	−1.24228	+	0.976937i	−0.0997820	+	0.0784694i
$156$	6.70984	+	0.752273i	0.537217	+	0.0602300i
$157$	18.4262	+	14.4905i	1.47057	+	1.15647i	0.953839	+	0.300319i	$0.0970930\pi$
$157$	18.4262	+	14.4905i	1.47057	+	1.15647i	0.516729	+	0.856149i	$0.327149\pi$
$158$	1.80699	−	0.931568i	0.143756	−	0.0741116i
$159$	5.87371	+	10.5714i	0.465816	+	0.838367i
$160$	−0.184230	−	0.319096i	−0.0145647	−	0.0252268i
$161$	19.5371	+	10.4661i	1.53974	+	0.824843i
$162$	−2.69229	+	8.58787i	−0.211526	+	0.674727i
$163$	1.54630	+	1.78452i	0.121115	+	0.139775i	0.813069	−	0.582167i	$-0.197795\pi$
$163$	1.54630	+	1.78452i	0.121115	+	0.139775i	−0.691953	+	0.721942i	$0.743250\pi$
$164$	0.107229	−	2.25102i	0.00837319	−	0.175775i
$165$	−0.00340884	+	0.00934878i	−0.000265378	+	0.000727802i
$166$	−9.91802	−	13.9279i	−0.769788	−	1.08102i
$167$	−15.5357	−	6.21957i	−1.20219	−	0.481284i	−0.317856	−	0.948139i	$-0.602963\pi$
$167$	−15.5357	−	6.21957i	−1.20219	−	0.481284i	−0.884334	+	0.466854i	$0.845387\pi$
$168$	−0.249313	−	8.00077i	−0.0192349	−	0.617273i
$169$	−1.95186	−	1.00625i	−0.150143	−	0.0774041i
$170$	0.214965	+	0.470709i	0.0164871	+	0.0361017i
$171$	10.5477	+	1.35857i	0.806601	+	0.103892i
$172$	−0.598902	+	0.691170i	−0.0456659	+	0.0527012i
$173$	18.6698	+	3.59830i	1.41944	+	0.273574i	0.840506	−	0.541803i	$-0.182258\pi$
$173$	18.6698	+	3.59830i	1.41944	+	0.273574i	0.578931	+	0.815377i	$0.303470\pi$
$174$	2.13554	−	4.47968i	0.161895	−	0.339604i
$175$	22.3782	+	2.13686i	1.69163	+	0.161532i
$176$	−0.000741910	−	0.0155746i	−5.59236e−5	−	0.00117398i
$177$	4.69199	−	2.90744i	0.352671	−	0.218536i
$178$	0.986442	−	0.775746i	0.0739369	−	0.0581447i
$179$	−3.78534	+	8.28875i	−0.282930	+	0.619530i	−0.996729	−	0.0808208i	$-0.974246\pi$
$179$	−3.78534	+	8.28875i	−0.282930	+	0.619530i	0.713799	+	0.700351i	$0.246973\pi$
$180$	−1.10478	−	0.0363579i	−0.0823458	−	0.00270996i
$181$	14.4973	+	9.31682i	1.07757	+	0.692514i	0.953995	−	0.299821i	$-0.0969270\pi$
$181$	14.4973	+	9.31682i	1.07757	+	0.692514i	0.123577	+	0.992335i	$0.460563\pi$
$182$	−5.89229	+	17.0247i	−0.436766	+	1.26195i
$183$	−5.24137	−	15.9902i	−0.387453	−	1.18203i
$184$	−0.757439	+	4.73564i	−0.0558391	+	0.349116i
$185$	1.79793	−	3.11411i	0.132187	−	0.228954i
$186$	−3.60822	−	6.49401i	−0.264567	−	0.476164i
$187$	−0.00104195	+	0.0218732i	−7.61948e−5	+	0.00159953i
$188$	−0.994650	+	6.91794i	−0.0725423	+	0.504543i
$189$	−20.7757	−	12.0433i	−1.51121	−	0.876020i
$190$	0.185887	+	1.29287i	0.0134857	+	0.0937950i
$191$	2.93715	+	12.1071i	0.212525	+	0.876039i	0.973763	+	0.227566i	$0.0730768\pi$
$191$	2.93715	+	12.1071i	0.212525	+	0.876039i	−0.761238	+	0.648473i	$0.775408\pi$
$192$	1.61835	−	0.617203i	0.116794	−	0.0445428i
$193$	−5.82226	−	0.555959i	−0.419096	−	0.0400188i	−0.116622	−	0.993176i	$-0.537206\pi$
$193$	−5.82226	−	0.555959i	−0.419096	−	0.0400188i	−0.302474	+	0.953158i	$0.597813\pi$
$194$	−0.554433	+	2.28541i	−0.0398060	+	0.164083i
$195$	2.29408	+	0.962487i	0.164282	+	0.0689251i
$196$	14.0987	+	2.71730i	1.00705	+	0.194093i
$197$	21.3449	−	6.26742i	1.52076	−	0.446535i	0.588552	−	0.808459i	$-0.299698\pi$
$197$	21.3449	−	6.26742i	1.52076	−	0.446535i	0.932208	+	0.361924i	$0.117880\pi$
$198$	−0.0408494	−	0.0227903i	−0.00290304	−	0.00161964i
$199$	20.8529	−	13.4013i	1.47822	−	0.949995i	0.480906	−	0.876772i	$-0.340308\pi$
$199$	20.8529	−	13.4013i	1.47822	−	0.949995i	0.997316	−	0.0732231i	$-0.0233285\pi$
$200$	1.14679	+	4.72712i	0.0810901	+	0.334258i
$201$	−3.92681	−	2.61586i	−0.276976	−	0.184508i
$202$	−9.36047	−	13.1449i	−0.658601	−	0.924875i
$203$	10.4085	+	8.18533i	0.730533	+	0.574498i
$204$	−2.34494	+	0.646837i	−0.164179	+	0.0452876i
$205$	0.271582	−	0.784684i	0.0189681	−	0.0548047i
$206$	15.8453			1.10400
$207$	10.8630	+	9.43375i	0.755029	+	0.655691i
$208$	−3.89820			−0.270292
$209$	−0.0180782	+	0.0522336i	−0.00125050	+	0.00361307i
$210$	0.742398	−	2.85444i	0.0512303	−	0.196975i
$211$	9.15653	+	7.20078i	0.630362	+	0.495722i	0.881472	−	0.472237i	$-0.156553\pi$
$211$	9.15653	+	7.20078i	0.630362	+	0.495722i	−0.251110	+	0.967959i	$0.580796\pi$
$212$	−4.05010	−	5.68756i	−0.278162	−	0.390624i
$213$	0.364200	−	5.67853i	0.0249546	−	0.389086i
$214$	3.57200	+	14.7240i	0.244177	+	1.00651i
$215$	−0.283482	+	0.182183i	−0.0193333	+	0.0124248i
$216$	0.992288	−	5.10053i	0.0675166	−	0.347047i
$217$	19.0195	−	5.58462i	1.29113	−	0.379109i
$218$	1.11006	+	0.213947i	0.0751829	+	0.0144903i
$219$	6.75805	−	5.13696i	0.456666	−	0.347124i
$220$	0.00135447	−	0.00558319i	9.13182e−5	−	0.000376419i
$221$	5.44990	+	0.520402i	0.366600	+	0.0350060i
$222$	13.1133	+	10.6661i	0.880104	+	0.715861i
$223$	−4.86777	−	20.0652i	−0.325970	−	1.34367i	−0.865165	−	0.501487i	$-0.832787\pi$
$223$	−4.86777	−	20.0652i	−0.325970	−	1.34367i	0.539195	−	0.842181i	$-0.318729\pi$
$224$	0.657706	+	4.57445i	0.0439449	+	0.305643i
$225$	13.8588	+	4.56955i	0.923920	+	0.304637i
$226$	−0.741615	+	5.15804i	−0.0493315	+	0.343108i
$227$	0.0484890	−	1.01791i	0.00321833	−	0.0675610i	−0.996687	−	0.0813352i	$-0.974082\pi$
$227$	0.0484890	−	1.01791i	0.00321833	−	0.0675610i	0.999905	+	0.0137742i	$0.00438461\pi$
$228$	−6.13918	−	0.100991i	−0.406577	−	0.00668830i
$229$	−7.87686	+	13.6431i	−0.520518	+	0.901563i	0.479198	+	0.877707i	$0.340928\pi$
$229$	−7.87686	+	13.6431i	−0.520518	+	0.901563i	−0.999715	+	0.0238562i	$0.992406\pi$
$230$	−0.759376	+	1.59559i	−0.0500718	+	0.105210i
$231$	0.0832740	−	0.0929685i	0.00547903	−	0.00611688i
$232$	−0.937114	+	2.70761i	−0.0615245	+	0.177763i
$233$	−13.7137	−	8.81328i	−0.898416	−	0.577377i	0.00790376	−	0.999969i	$-0.497484\pi$
$233$	−13.7137	−	8.81328i	−0.898416	−	0.577377i	−0.906320	+	0.422592i	$0.861120\pi$
$234$	−6.17726	+	9.93002i	−0.403820	+	0.649145i
$235$	−1.06978	+	2.34249i	−0.0697846	+	0.152807i
$236$	−2.50503	+	1.96998i	−0.163064	+	0.128235i
$237$	0.109673	+	3.51953i	0.00712400	+	0.228618i
$238$	−0.308830	−	6.48313i	−0.0200184	−	0.420239i
$239$	−13.1140	−	1.25223i	−0.848273	−	0.0810002i	−0.338140	−	0.941096i	$-0.609798\pi$
$239$	−13.1140	−	1.25223i	−0.848273	−	0.0810002i	−0.510133	+	0.860096i	$0.670404\pi$
$240$	0.636215	−	0.0502064i	0.0410675	−	0.00324081i
$241$	6.01141	+	1.15860i	0.387229	+	0.0746322i	0.379150	−	0.925335i	$-0.376216\pi$
$241$	6.01141	+	1.15860i	0.387229	+	0.0746322i	0.00807854	+	0.999967i	$0.497428\pi$
$242$	−7.20331	+	8.31306i	−0.463046	+	0.534384i
$243$	−11.4203	−	10.6102i	−0.732614	−	0.680645i
$244$	4.03585	+	8.83729i	0.258369	+	0.565749i
$245$	4.70231	+	2.42421i	0.300420	+	0.154877i
$246$	3.43950	+	1.84542i	0.219295	+	0.117660i
$247$	12.8290	+	5.13596i	0.816290	+	0.326793i
$248$	2.48797	+	3.49387i	0.157986	+	0.221861i
$249$	29.1683	−	5.12565i	1.84847	−	0.324825i
$250$	−0.172941	+	3.63047i	−0.0109377	+	0.229611i
$251$	−10.8473	−	12.5184i	−0.684673	−	0.790155i	0.301924	−	0.953332i	$-0.402371\pi$
$251$	−10.8473	−	12.5184i	−0.684673	−	0.790155i	−0.986597	+	0.163177i	$0.947826\pi$
$252$	12.6949	+	5.57347i	0.799702	+	0.351096i
$253$	−0.0595024	+	0.0452901i	−0.00374089	+	0.00284736i
$254$	3.90014	+	6.75524i	0.244717	+	0.423861i
$255$	−0.896166	−	0.0147422i	−0.0561201	−	0.000923191i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−18.8736	−	14.8424i	−1.17730	−	0.925841i	−0.178986	−	0.983852i	$-0.557282\pi$
$257$	−18.8736	−	14.8424i	−1.17730	−	0.925841i	−0.998316	+	0.0580107i	$0.981524\pi$
$258$	−0.634247	−	1.45153i	−0.0394865	−	0.0903681i
$259$	−35.4524	+	27.8801i	−2.20290	+	1.73238i
$260$	−1.37815	−	0.404662i	−0.0854694	−	0.0250961i
$261$	5.41220	+	6.67774i	0.335007	+	0.413342i
$262$	8.19379	+	17.9419i	0.506214	+	1.10845i
$263$	−17.3251	−	16.5195i	−1.06831	−	1.01863i	−0.999780	−	0.0209853i	$-0.993320\pi$
$263$	−17.3251	−	16.5195i	−1.06831	−	1.01863i	−0.0685329	−	0.997649i	$-0.521832\pi$
$264$	0.0249036	+	0.0104484i	0.00153271	+	0.000643053i
$265$	−0.841442	−	2.43119i	−0.0516894	−	0.149347i
$266$	3.86241	−	15.9211i	0.236820	−	0.976183i
$267$	0.477633	+	2.12048i	0.0292307	+	0.129771i
$268$	2.42130	+	1.24827i	0.147904	+	0.0762499i
$269$	−1.52727	−	0.448446i	−0.0931190	−	0.0273422i	0.234841	−	0.972034i	$-0.424543\pi$
$269$	−1.52727	−	0.448446i	−0.0931190	−	0.0273422i	−0.327960	+	0.944692i	$0.606361\pi$
$270$	0.880282	−	1.70021i	0.0535722	−	0.103472i
$271$	3.98489	−	8.72570i	0.242065	−	0.530049i	−0.749136	−	0.662417i	$-0.769531\pi$
$271$	3.98489	−	8.72570i	0.242065	−	0.530049i	0.991201	+	0.132368i	$0.0422581\pi$
$272$	1.30381	−	0.521968i	0.0790553	−	0.0316490i
$273$	−22.2260	−	21.9016i	−1.34518	−	1.32554i
$274$	13.0048	−	2.50646i	0.785646	−	0.151421i
$275$	−0.0379222	+	0.0656833i	−0.00228680	+	0.00396085i
$276$	−6.83954	−	4.71389i	−0.411692	−	0.283743i
$277$	10.6666	+	18.4751i	0.640893	+	1.11006i	0.985234	+	0.171214i	$0.0547689\pi$
$277$	10.6666	+	18.4751i	0.640893	+	1.11006i	−0.344341	+	0.938845i	$0.611898\pi$
$278$	−12.5566	−	14.4910i	−0.753093	−	0.869115i
$279$	12.8426	−	0.801159i	0.768866	−	0.0479641i
$280$	−0.242339	+	1.68551i	−0.0144825	+	0.100728i
$281$	−32.6030	+	3.11321i	−1.94493	+	0.185718i	−0.992783	−	0.119923i	$-0.961735\pi$
$281$	−32.6030	+	3.11321i	−1.94493	+	0.185718i	−0.952147	+	0.305641i	$0.901129\pi$
$282$	−10.0747	−	6.71131i	−0.599941	−	0.399653i
$283$	10.9620	−	10.4522i	0.651621	−	0.621319i	−0.290387	−	0.956909i	$-0.593784\pi$
$283$	10.9620	−	10.4522i	0.651621	−	0.621319i	0.942008	+	0.335590i	$0.108936\pi$
$284$	0.156318	+	3.28151i	0.00927575	+	0.194722i
$285$	−2.15993	−	0.672996i	−0.127943	−	0.0398649i
$286$	−0.0439899	−	0.0419442i	−0.00260117	−	0.00248022i
$287$	−6.82028	+	7.87102i	−0.402588	+	0.464612i
$288$	−0.241232	+	2.99029i	−0.0142147	+	0.176204i
$289$	14.4189	−	4.23377i	0.848170	−	0.249045i
$290$	−0.612373	+	0.859958i	−0.0359598	+	0.0504985i
$291$	−3.15995	−	2.57024i	−0.185239	−	0.150670i
$292$	−3.54702	+	3.38208i	−0.207574	+	0.197921i
$293$	19.7581	+	7.90997i	1.15428	+	0.462105i	0.868256	−	0.496117i	$-0.165241\pi$
$293$	19.7581	+	7.90997i	1.15428	+	0.462105i	0.286027	+	0.958222i	$0.407665\pi$
$294$	−14.7567	+	20.0177i	−0.860629	+	1.16746i
$295$	−1.09012	+	0.436416i	−0.0634690	+	0.0254091i
$296$	−8.20992	−	5.27619i	−0.477192	−	0.306673i
$297$	0.0660788	−	0.0468808i	0.00383428	−	0.00272030i
$298$	−15.3234			−0.887660
$299$	10.6023	+	15.3980i	0.613144	+	0.890491i
$300$	−8.24551	−	1.73032i	−0.476055	−	0.0999000i
$301$	4.15020	−	0.799885i	0.239214	−	0.0461046i
$302$	−14.5132	+	7.48206i	−0.835140	+	0.430544i
$303$	27.5286	−	4.83751i	1.58148	−	0.277908i
$304$	3.52888	−	0.336968i	0.202395	−	0.0193264i
$305$	0.509442	+	3.54325i	0.0291706	+	0.202886i
$306$	0.736452	−	4.14838i	0.0421002	−	0.237147i
$307$	−19.9348	+	12.8113i	−1.13774	+	0.731180i	−0.967161	−	0.254165i	$-0.918200\pi$
$307$	−19.9348	+	12.8113i	−1.13774	+	0.731180i	−0.170577	+	0.985344i	$0.554563\pi$
$308$	−0.0417986	+	0.0586979i	−0.00238170	+	0.00334462i
$309$	−11.8101	+	24.7739i	−0.671854	+	1.40934i
$310$	0.516897	+	1.49348i	0.0293578	+	0.0848238i
$311$	4.66161	+	13.4688i	0.264336	+	0.763747i	0.996575	+	0.0826996i	$0.0263542\pi$
$311$	4.66161	+	13.4688i	0.264336	+	0.763747i	−0.732239	+	0.681048i	$0.761525\pi$
$312$	2.90547	−	6.09476i	0.164490	−	0.345048i
$313$	−5.01016	+	7.03579i	−0.283191	+	0.397686i	−0.931529	−	0.363666i	$-0.881525\pi$
$313$	−5.01016	+	7.03579i	−0.283191	+	0.397686i	0.648338	+	0.761352i	$0.275464\pi$
$314$	19.7201	−	12.6734i	1.11287	−	0.715199i
$315$	3.90952	+	3.28824i	0.220277	+	0.185271i
$316$	−0.289324	−	2.01229i	−0.0162758	−	0.113200i
$317$	−4.91698	+	0.469514i	−0.276165	+	0.0263705i	−0.232220	−	0.972663i	$-0.574599\pi$
$317$	−4.91698	+	0.469514i	−0.276165	+	0.0263705i	−0.0439453	+	0.999034i	$0.513993\pi$
$318$	11.9111	−	2.09310i	0.667941	−	0.117375i
$319$	−0.0397086	+	0.0204712i	−0.00222326	+	0.00114617i
$320$	−0.361802	+	0.0697317i	−0.0202254	+	0.00389812i
$321$	−25.6830	−	5.38958i	−1.43349	−	0.300817i
$322$	16.2804	−	15.0395i	0.907272	−	0.838117i
$323$	−4.97856			−0.277014
$324$	7.23499	+	5.35303i	0.401944	+	0.297391i
$325$	15.9517	+	10.2515i	0.884839	+	0.568651i
$326$	2.19212	−	0.877593i	0.121410	−	0.0486054i
$327$	−1.16187	+	1.57610i	−0.0642517	+	0.0871585i
$328$	−2.09214	−	0.837568i	−0.115519	−	0.0462469i
$329$	23.3766	−	22.2895i	1.28879	−	1.22886i
$330$	0.00771968	+	0.00627905i	0.000424955	+	0.000345650i
$331$	4.49061	−	6.30618i	0.246826	−	0.346619i	−0.672513	−	0.740086i	$-0.734785\pi$
$331$	4.49061	−	6.30618i	0.246826	−	0.346619i	0.919339	+	0.393467i	$0.128724\pi$
$332$	−16.4058	+	4.81716i	−0.900383	+	0.264376i
$333$	−26.4500	+	12.5525i	−1.44945	+	0.687873i
$334$	−10.9587	+	12.6471i	−0.599635	+	0.692016i
$335$	0.726435	+	0.692655i	0.0396894	+	0.0378438i
$336$	−7.64228	−	2.38119i	−0.416920	−	0.129905i
$337$	0.589038	+	12.3654i	0.0320869	+	0.673588i	0.956419	+	0.291998i	$0.0943202\pi$
$337$	0.589038	+	12.3654i	0.0320869	+	0.673588i	−0.924332	+	0.381589i	$0.875377\pi$
$338$	−1.58930	+	1.51540i	−0.0864466	+	0.0824266i
$339$	−7.51175	−	5.00398i	−0.407982	−	0.271779i
$340$	0.515128	−	0.0491888i	0.0279368	−	0.00266764i
$341$	−0.00951775	+	0.0661974i	−0.000515415	+	0.00358479i
$342$	4.73365	−	9.52321i	0.255967	−	0.514956i
$343$	−22.2689	−	25.6997i	−1.20241	−	1.38766i
$344$	0.457275	+	0.792023i	0.0246546	+	0.0427030i
$345$	−1.92868	−	2.37652i	−0.103837	−	0.127948i
$346$	9.50668	−	16.4661i	0.511083	−	0.885221i
$347$	−35.0377	+	6.75296i	−1.88092	+	0.362518i	−0.994878	−	0.101084i	$-0.967769\pi$
$347$	−35.0377	+	6.75296i	−1.88092	+	0.362518i	−0.886044	+	0.463602i	$0.846557\pi$
$348$	−3.53483	−	3.48324i	−0.189487	−	0.186721i
$349$	−11.0490	+	4.42337i	−0.591441	+	0.236777i	−0.648023	−	0.761621i	$-0.724404\pi$
$349$	−11.0490	+	4.42337i	−0.591441	+	0.236777i	0.0565820	+	0.998398i	$0.481980\pi$
$350$	9.33853	−	20.4485i	0.499166	−	1.09302i
$351$	−10.9213	−	17.0592i	−0.582933	−	0.910555i
$352$	−0.0149607	−	0.00439285i	−0.000797407	−	0.000234140i
$353$	−5.16798	−	2.66428i	−0.275064	−	0.141805i	0.315176	−	0.949033i	$-0.397936\pi$
$353$	−5.16798	−	2.66428i	−0.275064	−	0.141805i	−0.590240	+	0.807228i	$0.700967\pi$
$354$	−1.21293	−	5.38486i	−0.0644665	−	0.286202i
$355$	−0.285382	+	1.17636i	−0.0151465	+	0.0624346i
$356$	−0.410448	−	1.18591i	−0.0217537	−	0.0628531i
$357$	10.3664	+	4.34927i	0.548650	+	0.230188i
$358$	6.59481	+	6.28814i	0.348546	+	0.332338i
$359$	7.37368	+	16.1461i	0.389168	+	0.852159i	0.998255	+	0.0590551i	$0.0188088\pi$
$359$	7.37368	+	16.1461i	0.389168	+	0.852159i	−0.609087	+	0.793103i	$0.708464\pi$
$360$	−0.395698	+	1.03213i	−0.0208551	+	0.0543981i
$361$	6.17284	+	1.81251i	0.324886	+	0.0953952i
$362$	13.5460	−	10.6527i	0.711962	−	0.559893i
$363$	−7.62842	−	17.4583i	−0.400388	−	0.916321i
$364$	14.1611	+	11.1364i	0.742245	+	0.583708i
$365$	−1.60508	+	0.827479i	−0.0840140	+	0.0433122i
$366$	−16.8250	−	0.276776i	−0.879457	−	0.0144673i
$367$	−10.1169	−	17.5229i	−0.528096	−	0.914688i	−0.999464	−	0.0327517i	$-0.989573\pi$
$367$	−10.1169	−	17.5229i	−0.528096	−	0.914688i	0.471368	−	0.881937i	$-0.343760\pi$
$368$	4.22745	+	2.26466i	0.220371	+	0.118053i
$369$	−5.44886	+	4.00214i	−0.283657	+	0.208343i
$370$	−2.35479	−	2.71757i	−0.122420	−	0.141280i
$371$	−1.53539	+	32.2318i	−0.0797134	+	1.67339i
$372$	−7.31697	+	1.28579i	−0.379367	+	0.0666650i
$373$	6.67242	+	9.37010i	0.345485	+	0.485166i	0.950359	−	0.311155i	$-0.100716\pi$
$373$	6.67242	+	9.37010i	0.345485	+	0.485166i	−0.604874	+	0.796321i	$0.706777\pi$
$374$	0.0203294	+	0.00813866i	0.00105121	+	0.000420840i
$375$	−5.54727	−	2.97631i	−0.286460	−	0.153696i
$376$	6.21214	+	3.20258i	0.320367	+	0.165161i
$377$	4.63982	+	10.1598i	0.238963	+	0.523255i
$378$	−18.1760	+	15.6941i	−0.934871	+	0.807216i
$379$	−3.49782	+	4.03670i	−0.179671	+	0.207351i	−0.838440	−	0.544994i	$-0.816532\pi$
$379$	−3.49782	+	4.03670i	−0.179671	+	0.207351i	0.658769	+	0.752345i	$0.271077\pi$
$380$	1.28257	+	0.247194i	0.0657942	+	0.0126808i
$381$	−13.4686	+	1.06286i	−0.690018	+	0.0544522i
$382$	12.4019	+	1.18423i	0.634535	+	0.0605907i
$383$	0.458989	+	9.63537i	0.0234532	+	0.492344i	0.979784	+	0.200058i	$0.0641130\pi$
$383$	0.458989	+	9.63537i	0.0234532	+	0.492344i	−0.956331	+	0.292286i	$0.905584\pi$
$384$	−0.0539465	−	1.73121i	−0.00275295	−	0.0883455i
$385$	−0.0208706	+	0.0164128i	−0.00106366	+	0.000836474i
$386$	−2.42966	+	5.32021i	−0.123666	+	0.270791i
$387$	2.74216	+	0.0902431i	0.139392	+	0.00458732i
$388$	1.97837	+	1.27142i	0.100437	+	0.0645467i
$389$	0.350045	−	1.01139i	0.0177480	−	0.0512794i	−0.935779	−	0.352587i	$-0.885302\pi$
$389$	0.350045	−	1.01139i	0.0177480	−	0.0512794i	0.953527	+	0.301308i	$0.0974232\pi$
$390$	1.65987	−	1.85311i	0.0840508	−	0.0938357i
$391$	−5.60788	−	3.73047i	−0.283603	−	0.188658i
$392$	7.17908	−	12.4345i	0.362598	−	0.628038i
$393$	−34.1590	−	0.561924i	−1.72309	−	0.0283453i
$394$	1.05851	−	22.2208i	0.0533268	−	1.11947i
$395$	0.106605	−	0.741451i	0.00536386	−	0.0373065i
$396$	−0.0348974	+	0.0311487i	−0.00175366	+	0.00156528i
$397$	−0.0610836	−	0.424846i	−0.00306570	−	0.0213224i	0.988231	−	0.152968i	$-0.0488831\pi$
$397$	−0.0610836	−	0.424846i	−0.00306570	−	0.0213224i	−0.991297	+	0.131645i	$0.957974\pi$
$398$	−5.84396	−	24.0891i	−0.292931	−	1.20748i
$399$	22.0135	+	17.9054i	1.10205	+	0.896389i
$400$	4.84221	+	0.462375i	0.242111	+	0.0231188i
$401$	−0.303094	+	1.24937i	−0.0151358	+	0.0623906i	−0.978879	−	0.204442i	$-0.934462\pi$
$401$	−0.303094	+	1.24937i	−0.0151358	+	0.0623906i	0.963743	+	0.266833i	$0.0859771\pi$
$402$	−3.75632	+	2.85527i	−0.187348	+	0.142408i
$403$	16.4180	+	3.16430i	0.817837	+	0.157625i
$404$	−15.4835	+	4.54636i	−0.770333	+	0.226190i
$405$	2.00214	+	2.64353i	0.0994872	+	0.131358i
$406$	11.1394	−	7.15888i	0.552841	−	0.355289i
$407$	−0.0358748	−	0.147878i	−0.00177825	−	0.00733004i
$408$	−0.155693	+	2.42753i	−0.00770795	+	0.120181i
$409$	−11.8667	−	16.6645i	−0.586771	−	0.824004i	0.409315	−	0.912393i	$-0.365768\pi$
$409$	−11.8667	−	16.6645i	−0.586771	−	0.824004i	−0.996086	+	0.0883888i	$0.971828\pi$
$410$	−0.652701	−	0.513290i	−0.0322346	−	0.0253496i
$411$	−5.77412	+	22.2009i	−0.284816	+	1.09509i
$412$	5.18251	−	14.9739i	0.255324	−	0.737710i
$413$	14.7280			0.724716
$414$	12.4678	−	7.18005i	0.612761	−	0.352880i
$415$	−6.30007			−0.309259
$416$	−1.27498	+	3.68380i	−0.0625109	+	0.180613i
$417$	32.0153	−	8.83124i	1.56780	−	0.432467i
$418$	0.0434480	+	0.0341679i	0.00212511	+	0.00167120i
$419$	−2.65352	−	3.72634i	−0.129633	−	0.182044i	0.744658	−	0.667446i	$-0.232613\pi$
$419$	−2.65352	−	3.72634i	−0.129633	−	0.182044i	−0.874291	+	0.485402i	$0.838673\pi$
$420$	−2.45463	−	1.63516i	−0.119774	−	0.0797877i
$421$	1.64130	+	6.76553i	0.0799921	+	0.329732i	0.997721	−	0.0674756i	$-0.0214945\pi$
$421$	1.64130	+	6.76553i	0.0799921	+	0.329732i	−0.917729	+	0.397208i	$0.869979\pi$
$422$	9.79955	−	6.29779i	0.477034	−	0.306571i
$423$	18.0021	−	10.7494i	0.875291	−	0.522656i
$424$	−6.69941	+	1.96712i	−0.325352	+	0.0955320i
$425$	−6.70795	−	1.29285i	−0.325383	−	0.0627125i
$426$	−5.24709	−	2.20143i	−0.254222	−	0.106660i
$427$	10.5853	−	43.6332i	0.512259	−	2.11156i
$428$	15.0825	+	1.44020i	0.729039	+	0.0696148i
$429$	0.0983663	−	0.0375147i	0.00474917	−	0.00181123i
$430$	0.0794450	+	0.327477i	0.00383118	+	0.0157923i
$431$	0.391107	+	2.72021i	0.0188390	+	0.131028i	0.997070	−	0.0764889i	$-0.0243710\pi$
$431$	0.391107	+	2.72021i	0.0188390	+	0.131028i	−0.978231	+	0.207517i	$0.933462\pi$
$432$	−4.49546	−	2.60593i	−0.216288	−	0.125378i
$433$	3.57601	−	24.8717i	0.171852	−	1.19526i	−0.703115	−	0.711076i	$-0.748208\pi$
$433$	3.57601	−	24.8717i	0.171852	−	1.19526i	0.874968	−	0.484182i	$-0.160883\pi$
$434$	0.943189	−	19.8000i	0.0452745	−	0.950429i
$435$	−0.888104	−	1.59839i	−0.0425813	−	0.0766371i
$436$	0.565246	−	0.979035i	0.0270704	−	0.0468873i
$437$	−10.9288	−	13.0227i	−0.522797	−	0.622962i
$438$	−2.64409	−	8.06650i	−0.126340	−	0.385432i
$439$	−8.87830	+	25.6522i	−0.423738	+	1.22431i	0.508056	+	0.861324i	$0.330364\pi$
$439$	−8.87830	+	25.6522i	−0.423738	+	1.22431i	−0.931794	+	0.362987i	$0.881757\pi$
$440$	−0.00483312	−	0.00310606i	−0.000230410	−	0.000148075i
$441$	−20.2986	−	37.9918i	−0.966600	−	1.80913i
$442$	2.27427	−	4.97995i	0.108176	−	0.236872i
$443$	16.0415	−	12.6152i	0.762154	−	0.599364i	−0.159581	−	0.987185i	$-0.551014\pi$
$443$	16.0415	−	12.6152i	0.762154	−	0.599364i	0.921735	+	0.387820i	$0.126772\pi$
$444$	14.3684	−	8.90351i	0.681893	−	0.422542i
$445$	−0.0220015	−	0.461869i	−0.00104297	−	0.0218947i
$446$	−20.5538	−	1.96265i	−0.973249	−	0.0929340i
$447$	11.4211	−	23.9578i	0.540199	−	1.13317i
$448$	4.53797	+	0.874622i	0.214399	+	0.0413220i
$449$	−6.76189	+	7.80364i	−0.319113	+	0.368276i	−0.892530	−	0.450987i	$-0.851072\pi$
$449$	−6.76189	+	7.80364i	−0.319113	+	0.368276i	0.573417	+	0.819264i	$0.305617\pi$
$450$	8.85100	−	11.6020i	0.417240	−	0.546925i
$451$	−0.0145970	−	0.0319629i	−0.000687344	−	0.00150507i
$452$	4.63180	+	2.38786i	0.217861	+	0.112315i
$453$	−0.880856	−	28.2677i	−0.0413862	−	1.32813i
$454$	−0.946065	−	0.378747i	−0.0444010	−	0.0177755i
$455$	3.85042	+	5.40716i	0.180510	+	0.253491i
$456$	−2.10336	+	5.76850i	−0.0984991	+	0.270135i
$457$	−0.749944	+	15.7433i	−0.0350809	+	0.736439i	0.910980	+	0.412450i	$0.135327\pi$
$457$	−0.749944	+	15.7433i	−0.0350809	+	0.736439i	−0.946061	+	0.323989i	$0.894976\pi$
$458$	10.3165	+	11.9059i	0.482058	+	0.556325i
$459$	5.93701	+	4.24337i	0.277116	+	0.198064i
$460$	1.25947	+	1.23948i	0.0587229	+	0.0577909i
$461$	−14.2166	−	24.6239i	−0.662133	−	1.14685i	−0.980054	−	0.198731i	$-0.936318\pi$
$461$	−14.2166	−	24.6239i	−0.662133	−	1.14685i	0.317921	−	0.948117i	$-0.397015\pi$
$462$	−0.0606190	−	0.109101i	−0.00282025	−	0.00507584i
$463$	9.98681	−	5.14856i	0.464126	−	0.239274i	−0.210270	−	0.977643i	$-0.567434\pi$
$463$	9.98681	−	5.14856i	0.464126	−	0.239274i	0.674396	+	0.738370i	$0.264404\pi$
$464$	2.25220	+	1.77115i	0.104556	+	0.0822234i
$465$	−2.72029	−	0.304984i	−0.126150	−	0.0141433i
$466$	−12.8139	+	10.0769i	−0.593592	+	0.466806i
$467$	−7.95549	−	2.33594i	−0.368136	−	0.108095i	0.0924317	−	0.995719i	$-0.470536\pi$
$467$	−7.95549	−	2.33594i	−0.368136	−	0.108095i	−0.460568	+	0.887625i	$0.652354\pi$
$468$	7.36349	+	9.08531i	0.340377	+	0.419968i
$469$	−5.22987	−	11.4518i	−0.241493	−	0.528796i
$470$	1.86376	+	1.77709i	0.0859689	+	0.0819712i
$471$	5.11642	+	40.2780i	0.235752	+	1.85591i
$472$	1.04232	+	3.01157i	0.0479764	+	0.138619i
$473$	−0.00336190	+	0.0138579i	−0.000154580	+	0.000637189i
$474$	3.36183	+	1.04748i	0.154414	+	0.0481125i
$475$	−15.3265	−	7.90138i	−0.703230	−	0.362540i
$476$	−6.22757	−	1.82858i	−0.285440	−	0.0838128i
$477$	−5.60526	+	20.1828i	−0.256647	+	0.924108i
$478$	−5.47252	+	11.9832i	−0.250307	+	0.548097i
$479$	−13.9227	+	5.57381i	−0.636145	+	0.254674i	−0.667240	−	0.744842i	$-0.732525\pi$
$479$	−13.9227	+	5.57381i	−0.636145	+	0.254674i	0.0310956	+	0.999516i	$0.490100\pi$
$480$	0.160640	−	0.617645i	0.00733220	−	0.0281915i
$481$	−37.3556	+	7.19971i	−1.70327	+	0.328278i
$482$	3.06102	−	5.30184i	0.139426	−	0.241492i
$483$	11.3795	+	36.6636i	0.517786	+	1.66825i
$484$	5.49988	+	9.52607i	0.249994	+	0.433003i
$485$	0.567442	+	0.654863i	0.0257662	+	0.0297358i
$486$	−13.7619	+	7.32195i	−0.624251	+	0.332130i
$487$	2.34655	−	16.3206i	0.106332	−	0.739559i	−0.864989	−	0.501790i	$-0.832675\pi$
$487$	2.34655	−	16.3206i	0.106332	−	0.739559i	0.971322	−	0.237769i	$-0.0764160\pi$
$488$	9.67124	−	0.923492i	0.437797	−	0.0418045i
$489$	−0.261769	+	4.08144i	−0.0118376	+	0.184569i
$490$	3.82886	−	3.65081i	0.172970	−	0.164927i
$491$	0.986014	+	20.6990i	0.0444982	+	0.934132i	0.905190	+	0.425006i	$0.139728\pi$
$491$	0.986014	+	20.6990i	0.0444982	+	0.934132i	−0.860692	+	0.509126i	$0.829969\pi$
$492$	2.86887	−	2.64676i	0.129339	−	0.119325i
$493$	−2.91225	−	2.77682i	−0.131161	−	0.125062i
$494$	9.04944	−	10.4436i	0.407153	−	0.469880i
$495$	−0.0155709	+	0.00738957i	−0.000699861	+	0.000332137i
$496$	4.11544	−	1.20840i	0.184789	−	0.0542589i
$497$	8.80681	−	12.3674i	0.395040	−	0.554755i
$498$	4.69627	−	29.2405i	0.210445	−	1.31030i
$499$	−25.8668	+	24.6639i	−1.15796	+	1.10411i	−0.164920	+	0.986307i	$0.552737\pi$
$499$	−25.8668	+	24.6639i	−1.15796	+	1.10411i	−0.993037	+	0.117803i	$0.962415\pi$
$500$	3.37423	+	1.35084i	0.150900	+	0.0604113i
$501$	−11.6055	−	26.5601i	−0.518494	−	1.18662i
$502$	−15.3777	+	6.15630i	−0.686340	+	0.274769i
$503$	4.36209	+	2.80335i	0.194496	+	0.124995i	0.634264	−	0.773116i	$-0.281303\pi$
$503$	4.36209	+	2.80335i	0.194496	+	0.124995i	−0.439768	+	0.898111i	$0.644939\pi$
$504$	9.41902	−	10.1738i	0.419557	−	0.453175i
$505$	−5.94591			−0.264590
$506$	0.0233378	+	0.0710428i	0.00103749	+	0.00315824i
$507$	−1.18473	−	3.61432i	−0.0526156	−	0.160518i
$508$	7.65932	−	1.47621i	0.339827	−	0.0654963i
$509$	−31.5556	+	16.2681i	−1.39868	+	0.721069i	−0.982158	−	0.188057i	$-0.939781\pi$
$509$	−31.5556	+	16.2681i	−1.39868	+	0.721069i	−0.416521	+	0.909126i	$0.636751\pi$
$510$	−0.307038	+	0.842056i	−0.0135959	+	0.0372869i
$511$	22.5474	−	2.15301i	0.997437	−	0.0952437i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	11.3612	+	14.4990i	0.501609	+	0.640146i
$514$	−20.1990	+	12.9811i	−0.890939	+	0.572572i
$515$	3.38660	−	4.75581i	0.149231	−	0.209566i
$516$	−1.57914	+	0.124616i	−0.0695176	+	0.00548593i
$517$	0.0356424	+	0.102982i	0.00156755	+	0.00452915i
$518$	14.7514	+	42.6212i	0.648137	+	1.87267i
$519$	18.6587	+	27.1363i	0.819026	+	1.19115i
$520$	−0.833156	+	1.17000i	−0.0365363	+	0.0513081i
$521$	5.36723	−	3.44931i	0.235142	−	0.151117i	−0.417764	−	0.908556i	$-0.637186\pi$
$521$	5.36723	−	3.44931i	0.235142	−	0.151117i	0.652906	+	0.757439i	$0.273550\pi$
$522$	8.08063	−	2.93046i	0.353679	−	0.128263i
$523$	−1.66735	−	11.5967i	−0.0729082	−	0.507088i	−0.993252	−	0.115977i	$-0.963000\pi$
$523$	−1.66735	−	11.5967i	−0.0729082	−	0.507088i	0.920344	−	0.391111i	$-0.127909\pi$
$524$	19.6350	−	1.87492i	0.857760	−	0.0819062i
$525$	25.0105	+	29.8417i	1.09155	+	1.30240i
$526$	−21.2774	+	10.9693i	−0.927739	+	0.478283i
$527$	−5.91494	+	1.14001i	−0.257659	+	0.0496596i
$528$	0.0180189	−	0.0201166i	0.000784171	−	0.000875461i
$529$	−2.55227	−	22.8580i	−0.110968	−	0.993824i
$530$	−2.57268			−0.111750
$531$	9.32317	+	2.11714i	0.404591	+	0.0918762i
$532$	−13.7822	−	8.85725i	−0.597532	−	0.384011i
$533$	−8.15559	+	3.26501i	−0.353258	+	0.141423i
$534$	2.16007	+	0.242176i	0.0934754	+	0.0104800i
$535$	5.18269	+	2.07484i	0.224067	+	0.0897030i
$536$	1.97154	−	1.87986i	0.0851576	−	0.0811976i
$537$	−14.7467	+	5.62408i	−0.636369	+	0.242697i
$538$	−0.923301	+	1.29660i	−0.0398063	+	0.0559002i
$539$	0.214808	−	0.0630732i	0.00925242	−	0.00271676i
$540$	−1.31879	−	1.38795i	−0.0567516	−	0.0597279i
$541$	−21.9393	+	25.3193i	−0.943244	+	1.08856i	0.0527025	+	0.998610i	$0.483216\pi$
$541$	−21.9393	+	25.3193i	−0.943244	+	1.08856i	−0.995946	+	0.0899510i	$0.971329\pi$
$542$	−6.94246	−	6.61963i	−0.298204	−	0.284337i
$543$	6.55894	+	29.1187i	0.281471	+	1.24960i
$544$	−0.0668247	−	1.40282i	−0.00286509	−	0.0601455i
$545$	0.301466	−	0.287447i	0.0129134	−	0.0123129i
$546$	−27.9664	+	13.8403i	−1.19685	+	0.592309i
$547$	16.2145	−	1.54830i	0.693283	−	0.0662005i	0.257535	−	0.966269i	$-0.417090\pi$
$547$	16.2145	−	1.54830i	0.693283	−	0.0662005i	0.435748	+	0.900069i	$0.356484\pi$
$548$	1.88483	−	13.1093i	0.0805160	−	0.560001i
$549$	12.9730	−	26.0993i	0.553675	−	1.11389i
$550$	0.0496676	+	0.0573194i	0.00211783	+	0.00244411i
$551$	−5.07847	−	8.79616i	−0.216350	−	0.374729i
$552$	−6.69162	+	4.92161i	−0.284814	+	0.209477i
$553$	−4.69771	+	8.13668i	−0.199767	+	0.346007i
$554$	20.9476	−	4.03733i	0.889980	−	0.171530i
$555$	6.00399	−	1.65616i	0.254855	−	0.0703002i
$556$	−17.8009	+	7.12641i	−0.754926	+	0.302227i
$557$	−16.2904	+	35.6710i	−0.690246	+	1.51143i	0.161165	+	0.986927i	$0.448475\pi$
$557$	−16.2904	+	35.6710i	−0.690246	+	1.51143i	−0.851411	+	0.524500i	$0.824252\pi$
$558$	3.44331	−	12.3983i	0.145767	−	0.524862i
$559$	3.42069	+	1.00440i	0.144680	+	0.0424818i
$560$	1.51354	+	0.780285i	0.0639588	+	0.0329731i
$561$	−0.0278769	+	0.0257186i	−0.00117696	+	0.00108584i
$562$	−7.72140	+	31.8281i	−0.325708	+	1.34259i
$563$	−11.0871	−	32.0342i	−0.467267	−	1.35008i	−0.894956	−	0.446154i	$-0.852793\pi$
$563$	−11.0871	−	32.0342i	−0.467267	−	1.35008i	0.427689	−	0.903926i	$-0.359328\pi$
$564$	−9.63732	+	7.32556i	−0.405804	+	0.308462i
$565$	1.38963	+	1.32501i	0.0584621	+	0.0557435i
$566$	−6.29204	−	13.7776i	−0.264474	−	0.579118i
$567$	−10.9902	−	40.1152i	−0.461544	−	1.68468i
$568$	3.15216	+	0.925557i	0.132262	+	0.0388355i
$569$	−4.91437	+	3.86470i	−0.206021	+	0.162017i	−0.715839	−	0.698266i	$-0.753955\pi$
$569$	−4.91437	+	3.86470i	−0.206021	+	0.162017i	0.509817	+	0.860283i	$0.329713\pi$
$570$	−1.34243	+	1.82102i	−0.0562281	+	0.0762743i
$571$	6.50642	+	5.11670i	0.272285	+	0.214127i	0.744959	−	0.667110i	$-0.232469\pi$
$571$	6.50642	+	5.11670i	0.272285	+	0.214127i	−0.472674	+	0.881237i	$0.656711\pi$
$572$	−0.0540250	+	0.0278518i	−0.00225890	+	0.00116454i
$573$	−11.0951	+	18.5074i	−0.463504	+	0.773159i
$574$	5.20743	+	9.01953i	0.217354	+	0.376468i
$575$	−11.3434	−	20.3845i	−0.473051	−	0.850091i
$576$	2.74692	+	1.20599i	0.114455	+	0.0502496i
$577$	−18.3319	−	21.1561i	−0.763165	−	0.880739i	0.232610	−	0.972570i	$-0.425274\pi$
$577$	−18.3319	−	21.1561i	−0.763165	−	0.880739i	−0.995775	+	0.0918308i	$0.970728\pi$
$578$	0.715043	−	15.0106i	0.0297419	−	0.624359i
$579$	−6.50713	−	7.76407i	−0.270427	−	0.322664i
$580$	0.612373	+	0.859958i	0.0254274	+	0.0357078i
$581$	73.3595	+	29.3687i	3.04346	+	1.21842i
$582$	−3.46240	+	2.14551i	−0.143521	+	0.0889342i
$583$	−0.0967666	−	0.0498866i	−0.00400766	−	0.00206609i
$584$	2.03595	+	4.45811i	0.0842483	+	0.184478i
$585$	1.66013	+	3.97636i	0.0686381	+	0.164402i
$586$	13.9372	−	16.0844i	0.575739	−	0.664439i
$587$	−8.90059	−	1.71545i	−0.367367	−	0.0708041i	0.00222717	−	0.999998i	$-0.499291\pi$
$587$	−8.90059	−	1.71545i	−0.367367	−	0.0708041i	−0.369594	+	0.929193i	$0.620503\pi$
$588$	14.0903	+	20.4923i	0.581075	+	0.845087i
$589$	−15.1360	−	1.44532i	−0.623670	−	0.0595532i
$590$	0.0558720	+	1.17290i	0.00230021	+	0.0482874i
$591$	33.9529	+	18.2169i	1.39663	+	0.749345i
$592$	−7.67121	+	6.03271i	−0.315285	+	0.247943i
$593$	5.61000	−	12.2842i	0.230375	−	0.504451i	−0.758776	−	0.651351i	$-0.774202\pi$
$593$	5.61000	−	12.2842i	0.230375	−	0.504451i	0.989151	+	0.146901i	$0.0469297\pi$
$594$	−0.0226901	−	0.0777777i	−0.000930987	−	0.00319126i
$595$	−2.01185	−	1.29294i	−0.0824777	−	0.0530052i
$596$	−5.01179	+	14.4806i	−0.205291	+	0.593149i
$597$	42.0186	+	8.81760i	1.71971	+	0.360880i
$598$	18.0188	−	4.98294i	0.736844	−	0.203767i
$599$	13.1255	−	22.7341i	0.536295	−	0.928890i	−0.462805	−	0.886460i	$-0.653157\pi$
$599$	13.1255	−	22.7341i	0.536295	−	0.928890i	0.999099	−	0.0424294i	$-0.0135098\pi$
$600$	−4.33199	+	7.22608i	−0.176853	+	0.295003i
$601$	−1.43990	+	30.2272i	−0.0587347	+	1.23299i	0.756551	+	0.653934i	$0.226883\pi$
$601$	−1.43990	+	30.2272i	−0.0587347	+	1.23299i	−0.815286	+	0.579058i	$0.803420\pi$
$602$	0.601505	−	4.18356i	0.0245155	−	0.170509i
$603$	−1.66444	−	8.00108i	−0.0677813	−	0.325829i
$604$	2.32376	+	16.1621i	0.0945525	+	0.657627i
$605$	0.955526	+	3.93873i	0.0388477	+	0.160132i
$606$	4.43227	−	27.5967i	0.180049	−	1.12104i
$607$	−22.3930	−	2.13827i	−0.908903	−	0.0867897i	−0.369879	−	0.929080i	$-0.620601\pi$
$607$	−22.3930	−	2.13827i	−0.908903	−	0.0867897i	−0.539024	+	0.842290i	$0.681207\pi$
$608$	0.835750	−	3.44501i	0.0338941	−	0.139714i
$609$	2.89014	+	22.7521i	0.117114	+	0.921960i
$610$	3.51499	+	0.677459i	0.142318	+	0.0274295i
$611$	26.1412	−	7.67576i	1.05756	−	0.310528i
$612$	−3.67935	−	2.05275i	−0.148729	−	0.0829775i
$613$	−24.8902	+	15.9960i	−1.00531	+	0.646071i	−0.936174	−	0.351536i	$-0.885659\pi$
$613$	−24.8902	+	15.9960i	−1.00531	+	0.646071i	−0.0691324	+	0.997607i	$0.522023\pi$
$614$	5.58667	+	23.0286i	0.225459	+	0.929357i
$615$	1.28900	−	0.637912i	0.0519776	−	0.0257231i
$616$	0.0417986	+	0.0586979i	0.00168411	+	0.00236501i
$617$	−5.88554	−	4.62844i	−0.236943	−	0.186334i	0.492626	−	0.870241i	$-0.336037\pi$
$617$	−5.88554	−	4.62844i	−0.236943	−	0.186334i	−0.729569	+	0.683907i	$0.760279\pi$
$618$	19.5486	+	19.2633i	0.786362	+	0.774885i
$619$	5.55330	−	16.0452i	0.223206	−	0.644912i	−0.776681	−	0.629894i	$-0.783098\pi$
$619$	5.55330	−	16.0452i	0.223206	−	0.644912i	0.999887	−	0.0150177i	$-0.00478045\pi$
$620$	1.58040			0.0634703
$621$	1.93313	+	24.8448i	0.0775740	+	0.996987i
$622$	14.2527			0.571482
$623$	−1.89688	+	5.48067i	−0.0759968	+	0.219578i
$624$	−4.80927	−	4.73908i	−0.192525	−	0.189715i
$625$	−18.0651	−	14.2065i	−0.722602	−	0.568261i
$626$	5.01016	+	7.03579i	0.200246	+	0.281207i
$627$	−0.0858042	+	0.0424635i	−0.00342669	+	0.00169583i
$628$	−5.52651	−	22.7806i	−0.220532	−	0.909045i
$629$	11.5301	−	7.40996i	0.459736	−	0.295454i
$630$	4.38607	−	2.61902i	0.174745	−	0.104344i
$631$	41.6902	−	12.2414i	1.65966	−	0.487321i	0.688399	−	0.725332i	$-0.258314\pi$
$631$	41.6902	−	12.2414i	1.65966	−	0.487321i	0.971262	+	0.238012i	$0.0764956\pi$
$632$	−1.99625	−	0.384745i	−0.0794065	−	0.0153043i
$633$	2.54250	+	20.0154i	0.101055	+	0.795540i
$634$	−1.16449	+	4.80011i	−0.0462480	+	0.190637i
$635$	2.86108	+	0.273200i	0.113539	+	0.0108416i
$636$	1.91776	−	11.9406i	0.0760440	−	0.473474i
$637$	−13.1957	−	54.3932i	−0.522831	−	2.15514i
$638$	0.00635790	+	0.0442202i	0.000251712	+	0.00175069i
$639$	7.35275	−	6.56292i	0.290870	−	0.259625i
$640$	−0.0524374	+	0.364710i	−0.00207277	+	0.0144164i
$641$	−1.99066	+	41.7891i	−0.0786263	+	1.65057i	0.523395	+	0.852090i	$0.324665\pi$
$641$	−1.99066	+	41.7891i	−0.0786263	+	1.65057i	−0.602022	+	0.798480i	$0.705638\pi$
$642$	−13.4933	+	22.5077i	−0.532536	+	0.888309i
$643$	9.02299	−	15.6283i	0.355832	−	0.616319i	−0.631428	−	0.775435i	$-0.717531\pi$
$643$	9.02299	−	15.6283i	0.355832	−	0.616319i	0.987260	+	0.159115i	$0.0508642\pi$
$644$	−8.88750	−	20.3039i	−0.350217	−	0.800087i
$645$	−0.571217	−	0.119870i	−0.0224917	−	0.00471987i
$646$	−1.62833	+	4.70474i	−0.0640656	+	0.185106i
$647$	−13.2116	−	8.49056i	−0.519400	−	0.333798i	0.254535	−	0.967064i	$-0.418078\pi$
$647$	−13.2116	−	8.49056i	−0.519400	−	0.333798i	−0.773935	+	0.633266i	$0.781714\pi$
$648$	7.42495	−	5.08626i	0.291680	−	0.199807i
$649$	−0.0206420	+	0.0451997i	−0.000810271	+	0.00177425i
$650$	14.9050	−	11.7214i	0.584621	−	0.459751i
$651$	30.2539	+	16.2323i	1.18574	+	0.636194i
$652$	−0.112353	−	2.35859i	−0.00440010	−	0.0923695i
$653$	42.1312	+	4.02304i	1.64872	+	0.157434i	0.877646	−	0.479310i	$-0.159113\pi$
$653$	42.1312	+	4.02304i	1.64872	+	0.157434i	0.771075	+	0.636744i	$0.219719\pi$
$654$	1.10940	+	1.61346i	0.0433811	+	0.0630914i
$655$	7.13631	+	1.37541i	0.278839	+	0.0537418i
$656$	−1.47578	+	1.70314i	−0.0576193	+	0.0664963i
$657$	14.5826	+	1.87827i	0.568919	+	0.0732783i
$658$	−13.4179	−	29.3811i	−0.523084	−	1.14539i
$659$	4.23431	+	2.18294i	0.164945	+	0.0850352i	0.538722	−	0.842483i	$-0.318907\pi$
$659$	4.23431	+	2.18294i	0.164945	+	0.0850352i	−0.373777	+	0.927519i	$0.621938\pi$
$660$	0.00845857	−	0.00524143i	0.000329249	−	0.000204022i
$661$	17.5728	+	7.03508i	0.683502	+	0.273633i	0.687315	−	0.726360i	$-0.258789\pi$
$661$	17.5728	+	7.03508i	0.683502	+	0.273633i	−0.00381264	+	0.999993i	$0.501214\pi$
$662$	−4.49061	−	6.30618i	−0.174532	−	0.245097i
$663$	6.09096	+	7.26752i	0.236553	+	0.282247i
$664$	−0.813573	+	17.0790i	−0.0315727	+	0.662793i
$665$	−3.95303	−	4.56204i	−0.153292	−	0.176908i
$666$	3.21118	+	29.1008i	0.124431	+	1.12763i
$667$	0.870612	−	13.7134i	0.0337102	−	0.530985i
$668$	8.36722	+	14.4925i	0.323738	+	0.560730i
$669$	18.3880	−	30.6726i	0.710922	−	1.18587i
$670$	0.892153	−	0.459937i	0.0344669	−	0.0177689i
$671$	0.119073	+	0.0936403i	0.00459677	+	0.00361494i
$672$	−4.74977	+	6.44314i	−0.183226	+	0.248550i
$673$	13.0951	−	10.2981i	0.504780	−	0.396964i	−0.333037	−	0.942914i	$-0.608074\pi$
$673$	13.0951	−	10.2981i	0.504780	−	0.396964i	0.837818	+	0.545950i	$0.183831\pi$
$674$	11.8780	+	3.48769i	0.457523	+	0.134341i
$675$	11.5426	+	22.4858i	0.444274	+	0.865478i
$676$	0.912240	+	1.99753i	0.0350862	+	0.0768280i
$677$	33.0815	+	31.5432i	1.27143	+	1.21230i	0.965546	+	0.260233i	$0.0837995\pi$
$677$	33.0815	+	31.5432i	1.27143	+	1.21230i	0.305881	+	0.952070i	$0.401049\pi$
$678$	−7.18562	+	5.46197i	−0.275962	+	0.209766i
$679$	−3.55468	−	10.2706i	−0.136416	−	0.394149i
$680$	0.121999	−	0.502885i	0.00467843	−	0.0192848i
$681$	1.29730	−	1.19686i	0.0497127	−	0.0458638i
$682$	0.0594437	+	0.0306453i	0.00227622	+	0.00117347i
$683$	18.0005	+	5.28541i	0.688768	+	0.202241i	0.607344	−	0.794439i	$-0.292235\pi$
$683$	18.0005	+	5.28541i	0.688768	+	0.202241i	0.0814242	+	0.996680i	$0.474053\pi$
$684$	−7.45122	−	7.58804i	−0.284904	−	0.290136i
$685$	2.02720	−	4.43894i	0.0774552	−	0.169603i
$686$	−31.5697	+	12.6386i	−1.20534	+	0.482544i
$687$	−26.3039	+	7.25576i	−1.00356	+	0.276825i
$688$	0.898022	−	0.173080i	0.0342368	−	0.00659860i
$689$	−13.6091	+	23.5716i	−0.518465	+	0.898008i
$690$	−2.87663	+	1.04532i	−0.109511	+	0.0397948i
$691$	5.79797	+	10.0424i	0.220565	+	0.382030i	0.954980	−	0.296671i	$-0.0958766\pi$
$691$	5.79797	+	10.0424i	0.220565	+	0.382030i	−0.734415	+	0.678701i	$0.762543\pi$
$692$	−12.4511	−	14.3693i	−0.473320	−	0.546241i
$693$	0.215759	−	0.0134597i	0.00819601	−	0.000511291i
$694$	−5.07815	+	35.3193i	−0.192764	+	1.34070i
$695$	−7.03303	+	0.671573i	−0.266778	+	0.0254742i
$696$	−4.44780	+	2.20116i	−0.168593	+	0.0834349i
$697$	2.29058	−	2.18406i	0.0867619	−	0.0827273i
$698$	0.566299	+	11.8881i	0.0214347	+	0.449971i
$699$	−6.20446	−	27.5450i	−0.234674	−	1.04185i
$700$	−16.2695	−	15.5130i	−0.614931	−	0.586336i
$701$	−1.33915	+	1.54546i	−0.0505789	+	0.0583712i	−0.780475	−	0.625187i	$-0.785023\pi$
$701$	−1.33915	+	1.54546i	−0.0505789	+	0.0583712i	0.729896	+	0.683558i	$0.239568\pi$
$702$	−19.6930	+	4.74106i	−0.743264	+	0.178940i
$703$	33.1942	−	9.74669i	1.25194	−	0.367603i
$704$	−0.00904440	+	0.0127011i	−0.000340874	+	0.000478690i
$705$	−4.16758	+	1.58942i	−0.156960	+	0.0598611i
$706$	−4.20802	+	4.01234i	−0.158371	+	0.151007i
$707$	69.2356	+	27.7177i	2.60387	+	1.04243i
$708$	−5.48541	−	0.614996i	−0.206154	−	0.0231130i
$709$	−16.4522	+	6.58647i	−0.617875	+	0.247360i	−0.659418	−	0.751777i	$-0.729197\pi$
$709$	−16.4522	+	6.58647i	−0.617875	+	0.247360i	0.0415424	+	0.999137i	$0.486773\pi$
$710$	1.01832	+	0.654435i	0.0382169	+	0.0245605i
$711$	−4.14342	+	4.47542i	−0.155390	+	0.167842i
$712$	−1.25493			−0.0470305
$713$	−15.9663	−	12.9696i	−0.597944	−	0.485714i
$714$	7.50059	−	8.37378i	0.280703	−	0.313381i
$715$	−0.0219910	+	0.00423842i	−0.000822417	+	0.000158508i
$716$	8.09924	−	4.17545i	0.302683	−	0.156044i
$717$	−14.6566	−	17.4877i	−0.547359	−	0.653089i
$718$	17.6698	−	1.68726i	0.659430	−	0.0629679i
$719$	−6.80772	−	47.3487i	−0.253885	−	1.76581i	−0.574409	−	0.818568i	$-0.694768\pi$
$719$	−6.80772	−	47.3487i	−0.253885	−	1.76581i	0.320524	−	0.947240i	$-0.396141\pi$
$720$	0.845944	+	0.711512i	0.0315265	+	0.0265165i
$721$	−61.6042	+	39.5906i	−2.29426	+	1.47443i
$722$	3.73176	−	5.24052i	0.138882	−	0.195032i
$723$	6.00784	+	8.73750i	0.223434	+	0.324951i
$724$	−5.63634	−	16.2851i	−0.209473	−	0.605232i
$725$	−4.55834	−	13.1705i	−0.169293	−	0.489139i
$726$	−18.9931	+	1.49882i	−0.704900	+	0.0556266i
$727$	−7.53612	+	10.5830i	−0.279499	+	0.392502i	−0.930331	−	0.366720i	$-0.880481\pi$
$727$	−7.53612	+	10.5830i	−0.279499	+	0.392502i	0.650832	+	0.759222i	$0.274420\pi$
$728$	15.1556	−	9.73991i	0.561704	−	0.360985i
$729$	−1.19050	−	26.9737i	−0.0440926	−	0.999027i
$730$	0.256996	+	1.78745i	0.00951186	+	0.0661564i
$731$	−1.27859	+	0.122091i	−0.0472904	+	0.00451568i
$732$	−5.76447	+	15.8091i	−0.213061	+	0.584322i
$733$	−26.1118	+	13.4616i	−0.964461	+	0.497214i	−0.867154	−	0.498040i	$-0.834053\pi$
$733$	−26.1118	+	13.4616i	−0.964461	+	0.497214i	−0.0973071	+	0.995254i	$0.531023\pi$
$734$	−19.8681	+	3.82925i	−0.733344	+	0.141340i
$735$	2.85418	+	8.70742i	0.105278	+	0.321178i
$736$	3.52277	−	3.25425i	0.129851	−	0.119953i
$737$	0.0424753			0.00156460
$738$	1.99988	+	6.45815i	0.0736164	+	0.237728i
$739$	18.6588	+	11.9913i	0.686376	+	0.441107i	0.836796	−	0.547515i	$-0.184426\pi$
$739$	18.6588	+	11.9913i	0.686376	+	0.441107i	−0.150419	+	0.988622i	$0.548062\pi$
$740$	−3.33828	+	1.33645i	−0.122718	+	0.0491288i
$741$	9.58350	+	21.9326i	0.352059	+	0.805715i
$742$	29.9569	+	11.9929i	1.09975	+	0.440274i
$743$	9.85614	−	9.39781i	0.361587	−	0.344772i	−0.487407	−	0.873175i	$-0.662057\pi$
$743$	9.85614	−	9.39781i	0.361587	−	0.344772i	0.848994	+	0.528402i	$0.177209\pi$
$744$	−1.17808	+	7.33509i	−0.0431904	+	0.268917i
$745$	−3.27504	+	4.59915i	−0.119988	+	0.168500i
$746$	11.0371	−	3.24078i	0.404097	−	0.118653i
$747$	42.2166	+	29.1365i	1.54463	+	1.06605i
$748$	0.0143401	−	0.0165494i	0.000524327	−	0.000605106i
$749$	−50.6763	−	48.3197i	−1.85167	−	1.76556i
$750$	−4.62695	+	4.26872i	−0.168952	+	0.155872i
$751$	−1.12679	−	23.6542i	−0.0411170	−	0.863153i	−0.921379	−	0.388665i	$-0.872936\pi$
$751$	−1.12679	−	23.6542i	−0.0411170	−	0.863153i	0.880262	−	0.474488i	$-0.157367\pi$
$752$	5.05824	−	4.82302i	0.184455	−	0.175877i
$753$	1.83631	−	28.6312i	0.0669187	−	1.04338i
$754$	11.1185	−	1.06169i	0.404913	−	0.0386645i
$755$	−0.856215	+	5.95511i	−0.0311608	+	0.216728i
$756$	8.88614	+	22.3093i	0.323186	+	0.811383i
$757$	−27.7523	−	32.0279i	−1.00867	−	1.16407i	−0.986407	−	0.164321i	$-0.947457\pi$
$757$	−27.7523	−	32.0279i	−1.00867	−	1.16407i	−0.0222679	−	0.999752i	$-0.507089\pi$
$758$	2.67066	+	4.62572i	0.0970028	+	0.168014i
$759$	−0.128469	−	0.0164625i	−0.00466312	−	0.000597552i
$760$	0.653085	−	1.13118i	0.0236899	−	0.0410321i
$761$	10.8088	−	2.08322i	0.391818	−	0.0755166i	0.0104624	−	0.999945i	$-0.496670\pi$
$761$	10.8088	−	2.08322i	0.391818	−	0.0755166i	0.381355	+	0.924429i	$0.375458\pi$
$762$	−3.40074	+	13.0755i	−0.123196	+	0.473674i
$763$	−4.85031	+	1.94177i	−0.175593	+	0.0702968i
$764$	5.17536	−	11.3324i	0.187238	−	0.409994i
$765$	−1.08769	−	1.10766i	−0.0393256	−	0.0400477i
$766$	9.25555	+	2.71767i	0.334417	+	0.0981936i
$767$	11.0420	+	5.69253i	0.398702	+	0.205545i
$768$	−1.65364	−	0.515244i	−0.0596706	−	0.0185923i
$769$	−11.3046	+	46.5983i	−0.407655	+	1.68038i	0.284537	+	0.958665i	$0.408160\pi$
$769$	−11.3046	+	46.5983i	−0.407655	+	1.68038i	−0.692192	+	0.721713i	$0.743355\pi$
$770$	0.00868401	+	0.0250908i	0.000312950	+	0.000904210i
$771$	−5.24065	−	41.2560i	−0.188738	−	1.48580i
$772$	4.23294	+	4.03610i	0.152347	+	0.145262i
$773$	19.1582	+	41.9505i	0.689071	+	1.50886i	0.852737	+	0.522340i	$0.174941\pi$
$773$	19.1582	+	41.9505i	0.689071	+	1.50886i	−0.163666	+	0.986516i	$0.552332\pi$
$774$	0.982154	−	2.56183i	0.0353028	−	0.0920831i
$775$	−20.0185	−	5.87796i	−0.719086	−	0.211143i
$776$	1.84856	−	1.45372i	0.0663594	−	0.0521856i
$777$	−77.6322	−	8.70372i	−2.78504	−	0.312244i
$778$	−0.841274	−	0.661585i	−0.0301611	−	0.0237190i
$779$	7.10070	−	3.66066i	0.254409	−	0.131157i
$780$	−1.20830	−	2.17467i	−0.0432640	−	0.0778657i
$781$	0.0256121	+	0.0443615i	0.000916474	+	0.00158738i
$782$	−5.35945	+	4.07933i	−0.191654	+	0.145877i
$783$	−1.44108	+	14.8181i	−0.0514998	+	0.529555i
$784$	−9.40259	−	10.8512i	−0.335807	−	0.387542i
$785$	0.410976	−	8.62745i	0.0146684	−	0.307927i
$786$	−11.7033	+	32.0964i	−0.417444	+	1.14484i
$787$	−12.0180	−	16.8769i	−0.428396	−	0.601598i	0.542805	−	0.839859i	$-0.317362\pi$
$787$	−12.0180	−	16.8769i	−0.428396	−	0.601598i	−0.971201	+	0.238261i	$0.923423\pi$
$788$	−20.6525	−	8.26800i	−0.735714	−	0.294535i
$789$	−1.29140	−	41.4426i	−0.0459751	−	1.47540i
$790$	−0.665805	−	0.343246i	−0.0236883	−	0.0122122i
$791$	−10.0044	−	21.9066i	−0.355716	−	0.778910i
$792$	0.0180217	+	0.0431658i	0.000640375	+	0.00153383i
$793$	24.8008	−	28.6217i	0.880704	−	1.01639i
$794$	−0.421458	−	0.0812294i	−0.0149570	−	0.00288272i
$795$	1.91752	−	4.02234i	0.0680073	−	0.142658i
$796$	−24.6756	−	2.35624i	−0.874604	−	0.0835146i
$797$	−0.975879	−	20.4862i	−0.0345674	−	0.725660i	−0.947924	−	0.318498i	$-0.896822\pi$
$797$	−0.975879	−	20.4862i	−0.0345674	−	0.725660i	0.913356	−	0.407162i	$-0.133481\pi$
$798$	24.1205	−	14.9465i	0.853856	−	0.529100i
$799$	−7.71555	+	6.06758i	−0.272957	+	0.214655i
$800$	2.02068	−	4.42467i	0.0714417	−	0.156436i
$801$	−1.98862	+	3.19673i	−0.0702643	+	0.112951i
$802$	1.08152	+	0.695054i	0.0381900	+	0.0245432i
$803$	−0.0249938	+	0.0722149i	−0.000882012	+	0.00254841i
$804$	1.46966	+	4.48360i	0.0518310	+	0.158124i
$805$	−1.03435	−	8.10075i	−0.0364560	−	0.285514i
$806$	8.36006	−	14.4800i	0.294470	−	0.510038i
$807$	−1.33903	−	2.40996i	−0.0471361	−	0.0848348i
$808$	−0.767837	+	16.1189i	−0.0270124	+	0.567060i
$809$	6.15973	−	42.8418i	0.216564	−	1.50624i	−0.534024	−	0.845469i	$-0.679321\pi$
$809$	6.15973	−	42.8418i	0.216564	−	1.50624i	0.750589	−	0.660770i	$-0.229770\pi$
$810$	3.15298	−	1.02741i	0.110784	−	0.0360995i
$811$	5.21106	+	36.2437i	0.182985	+	1.27269i	0.849657	+	0.527336i	$0.176809\pi$
$811$	5.21106	+	36.2437i	0.182985	+	1.27269i	−0.666672	+	0.745352i	$0.732282\pi$
$812$	−3.12179	−	12.8682i	−0.109554	−	0.451586i
$813$	15.5241	−	5.92056i	0.544455	−	0.207643i
$814$	−0.151478	−	0.0144644i	−0.00530931	−	0.000506978i
$815$	0.205118	−	0.845509i	0.00718498	−	0.0296169i
$816$	2.24309	+	0.941097i	0.0785240	+	0.0329450i
$817$	−3.18343	−	0.613556i	−0.111374	−	0.0214656i
$818$	−19.6291	+	5.76364i	−0.686317	+	0.201521i
$819$	−0.794579	−	54.0406i	−0.0277648	−	1.88833i
$820$	−0.698537	+	0.448923i	−0.0243940	+	0.0156771i
$821$	8.05828	+	33.2167i	0.281236	+	1.15927i	0.920644	+	0.390403i	$0.127664\pi$
$821$	8.05828	+	33.2167i	0.281236	+	1.15927i	−0.639408	+	0.768868i	$0.720820\pi$
$822$	19.0913	+	12.7177i	0.665885	+	0.443582i
$823$	8.58901	+	12.0616i	0.299394	+	0.420440i	0.936680	−	0.350188i	$-0.113882\pi$
$823$	8.58901	+	12.0616i	0.299394	+	0.420440i	−0.637286	+	0.770628i	$0.719943\pi$
$824$	−12.4553	−	9.79494i	−0.433900	−	0.341223i
$825$	−0.126637	+	0.0349320i	−0.00440893	+	0.00121618i
$826$	4.81705	−	13.9179i	0.167606	−	0.484267i
$827$	−29.2989			−1.01882			−0.509412	−	0.860523i	$-0.670137\pi$
$827$	−29.2989			−1.01882			−0.509412	+	0.860523i	$0.670137\pi$
$828$	−2.70732	−	14.1305i	−0.0940860	−	0.491068i
$829$	11.5797			0.402181			0.201091	−	0.979573i	$-0.435551\pi$
$829$	11.5797			0.402181			0.201091	+	0.979573i	$0.435551\pi$
$830$	−2.06055	+	5.95358i	−0.0715228	+	0.206652i
$831$	−9.30077	+	35.7604i	−0.322640	+	1.24051i
$832$	3.06419	+	2.40971i	0.106232	+	0.0835416i
$833$	11.6967	+	16.4258i	0.405268	+	0.569119i
$834$	2.12567	−	33.1429i	0.0736059	−	1.14765i
$835$	1.45369	+	5.99218i	0.0503069	+	0.207368i
$836$	0.0464991	−	0.0298832i	0.00160820	−	0.00103353i
$837$	16.8181	+	14.6244i	0.581318	+	0.505495i
$838$	−4.38928	+	1.28881i	−0.151625	+	0.0445211i
$839$	−31.9441	−	6.15672i	−1.10283	−	0.212553i	−0.394823	−	0.918757i	$-0.629194\pi$
$839$	−31.9441	−	6.15672i	−1.10283	−	0.212553i	−0.708009	+	0.706204i	$0.750406\pi$
$840$	−2.34806	+	1.78482i	−0.0810158	+	0.0615821i
$841$	−4.90158	+	20.2046i	−0.169020	+	0.696710i
$842$	6.93025	+	0.661759i	0.238832	+	0.0228057i
$843$	−44.0075	−	35.7949i	−1.51570	−	1.23284i
$844$	−2.74630	−	11.3204i	−0.0945314	−	0.389664i
$845$	0.115151	+	0.800894i	0.00396132	+	0.0275516i
$846$	−4.27033	−	20.5278i	−0.146817	−	0.705759i
$847$	7.23461	−	50.3178i	0.248584	−	1.72894i
$848$	−0.332228	+	6.97433i	−0.0114088	+	0.239500i
$849$	26.2308	+	0.431504i	0.900238	+	0.0148092i
$850$	−3.41570	+	5.91617i	−0.117158	+	0.202923i
$851$	44.6934	+	13.8939i	1.53207	+	0.476277i
$852$	−3.79651	+	4.23849i	−0.130066	+	0.145208i
$853$	−5.78158	+	16.7048i	−0.197957	+	0.571960i	−0.999668	−	0.0257516i	$-0.991802\pi$
$853$	−5.78158	+	16.7048i	−0.197957	+	0.571960i	0.801711	+	0.597712i	$0.203923\pi$
$854$	−37.7713	−	24.2741i	−1.29251	−	0.830644i
$855$	−1.84658	−	3.45614i	−0.0631516	−	0.118197i
$856$	6.29399	−	13.7819i	0.215124	−	0.471056i
$857$	42.6662	−	33.5530i	1.45745	−	1.14615i	0.496980	−	0.867762i	$-0.334442\pi$
$857$	42.6662	−	33.5530i	1.45745	−	1.14615i	0.960469	−	0.278388i	$-0.0898002\pi$
$858$	−0.00327897	−	0.105226i	−0.000111942	−	0.00359236i
$859$	−0.981833	−	20.6112i	−0.0334997	−	0.703246i	−0.951682	−	0.307087i	$-0.900646\pi$
$859$	−0.981833	−	20.6112i	−0.0334997	−	0.703246i	0.918182	−	0.396159i	$-0.129657\pi$
$860$	0.335450	+	0.0320316i	0.0114387	+	0.00109227i
$861$	−17.9831	+	1.41913i	−0.612864	+	0.0483637i
$862$	2.69852	+	0.520097i	0.0919119	+	0.0177146i
$863$	−33.5518	+	38.7208i	−1.14212	+	1.31807i	−0.201153	+	0.979560i	$0.564469\pi$
$863$	−33.5518	+	38.7208i	−1.14212	+	1.31807i	−0.940962	+	0.338511i	$0.890077\pi$
$864$	−3.93293	+	3.39589i	−0.133801	+	0.115531i
$865$	−2.91027	−	6.37259i	−0.0989520	−	0.216675i
$866$	−22.3342	−	11.5141i	−0.758946	−	0.391264i
$867$	22.9358	+	12.3059i	0.778942	+	0.417931i
$868$	−18.4025	−	7.36725i	−0.624622	−	0.250061i
$869$	−0.0183872	−	0.0258211i	−0.000623741	−	0.000875922i
$870$	−1.80095	+	0.316476i	−0.0610580	+	0.0107295i
$871$	0.505281	−	10.6072i	0.0171208	−	0.359410i
$872$	−0.740315	−	0.854369i	−0.0250702	−	0.0289326i
$873$	−0.773809	−	7.01252i	−0.0261895	−	0.237338i
$874$	−15.8810	+	6.06843i	−0.537182	+	0.205268i
$875$	−8.39860	−	14.5468i	−0.283924	−	0.491771i
$876$	−8.48764	−	0.139624i	−0.286771	−	0.00471746i
$877$	20.8748	−	10.7617i	0.704891	−	0.363396i	−0.0682177	−	0.997670i	$-0.521731\pi$
$877$	20.8748	−	10.7617i	0.704891	−	0.363396i	0.773108	+	0.634274i	$0.218701\pi$
$878$	21.3375	+	16.7800i	0.720106	+	0.566298i
$879$	14.7597	+	33.7788i	0.497832	+	1.13933i
$880$	−0.00451599	+	0.00355141i	−0.000152234	+	0.000119718i
$881$	−10.3373	−	3.03530i	−0.348272	−	0.102262i	0.102918	−	0.994690i	$-0.467182\pi$
$881$	−10.3373	−	3.03530i	−0.348272	−	0.102262i	−0.451190	+	0.892428i	$0.649000\pi$
$882$	−42.5413	+	6.75630i	−1.43244	+	0.227496i
$883$	2.61609	+	5.72844i	0.0880384	+	0.192777i	0.948530	−	0.316688i	$-0.102571\pi$
$883$	2.61609	+	5.72844i	0.0880384	+	0.192777i	−0.860491	+	0.509465i	$0.829843\pi$
$884$	−3.96222	−	3.77797i	−0.133264	−	0.127067i
$885$	−1.87545	−	0.786849i	−0.0630425	−	0.0264496i
$886$	−6.67468	−	19.2852i	−0.224240	−	0.647900i
$887$	10.3557	−	42.6866i	0.347709	−	1.43328i	−0.482536	−	0.875876i	$-0.660284\pi$
$887$	10.3557	−	42.6866i	0.347709	−	1.43328i	0.830245	−	0.557399i	$-0.188201\pi$
$888$	−3.71438	−	16.4902i	−0.124647	−	0.553374i
$889$	−32.0415	−	16.5186i	−1.07464	−	0.554015i
$890$	−0.443663	−	0.130271i	−0.0148716	−	0.00436670i
$891$	0.138516	+	0.0224950i	0.00464045	+	0.000753612i
$892$	−8.57718	+	18.7814i	−0.287185	+	0.628848i
$893$	−23.0011	+	9.20825i	−0.769702	+	0.308142i
$894$	−18.9047	−	18.6288i	−0.632268	−	0.623039i
$895$	3.29681	−	0.635409i	0.110200	−	0.0212394i
$896$	2.31074	−	4.00233i	0.0771965	−	0.133708i
$897$	−5.63936	+	31.8860i	−0.188293	+	1.06464i
$898$	5.16285	+	8.94231i	0.172286	+	0.298409i
$899$	−8.04782	−	9.28768i	−0.268410	−	0.309761i
$900$	−8.06904	−	12.1589i	−0.268968	−	0.405295i
$901$	1.39553	−	9.70614i	0.0464919	−	0.323359i
$902$	−0.0349792	+	0.00334011i	−0.00116468	+	0.000111213i
$903$	6.09259	+	4.05860i	0.202749	+	0.135062i
$904$	3.77144	−	3.59606i	0.125436	−	0.119603i
$905$	−0.302129	−	6.34247i	−0.0100431	−	0.210831i
$906$	−27.0011	−	8.41306i	−0.897053	−	0.279505i
$907$	1.96022	+	1.86907i	0.0650882	+	0.0620614i	0.721925	−	0.691971i	$-0.243258\pi$
$907$	1.96022	+	1.86907i	0.0650882	+	0.0620614i	−0.656837	+	0.754033i	$0.728106\pi$
$908$	−0.667344	+	0.770156i	−0.0221466	+	0.0255585i
$909$	39.8434	+	27.4986i	1.32152	+	0.912072i
$910$	6.36912	−	1.87014i	0.211134	−	0.0619946i
$911$	−29.5782	+	41.5368i	−0.979969	+	1.37617i	−0.0540146	+	0.998540i	$0.517202\pi$
$911$	−29.5782	+	41.5368i	−0.979969	+	1.37617i	−0.925955	+	0.377634i	$0.876738\pi$
$912$	4.76329	+	3.87437i	0.157728	+	0.128293i
$913$	−0.192949	+	0.183977i	−0.00638568	+	0.00608874i
$914$	14.6321	+	5.85781i	0.483987	+	0.193759i
$915$	−3.67905	+	4.99069i	−0.121626	+	0.164987i
$916$	14.6253	−	5.85507i	0.483232	−	0.193457i
$917$	−76.6852	−	49.2826i	−2.53237	−	1.62745i
$918$	5.95179	−	4.22261i	0.196438	−	0.139367i
$919$	−19.1725			−0.632444			−0.316222	−	0.948685i	$-0.602414\pi$
$919$	−19.1725			−0.632444			−0.316222	+	0.948685i	$0.602414\pi$
$920$	1.58324	−	0.784803i	0.0521978	−	0.0258742i
$921$	−40.1687	−	8.42938i	−1.32360	−	0.277758i
$922$	−27.9194	+	5.38102i	−0.919476	+	0.177214i
$923$	11.3829	−	5.86828i	0.374672	−	0.193157i
$924$	−0.122927	+	0.0216016i	−0.00404401	+	0.000710640i
$925$	47.2559	−	4.51239i	1.55376	−	0.148366i
$926$	−1.59903	−	11.1215i	−0.0525473	−	0.365474i
$927$	−44.6882	+	16.2063i	−1.46775	+	0.532284i
$928$	2.41036	−	1.54904i	0.0791238	−	0.0508498i
$929$	−11.4876	+	16.1320i	−0.376895	+	0.529275i	−0.958838	−	0.283955i	$-0.908353\pi$
$929$	−11.4876	+	16.1320i	−0.376895	+	0.529275i	0.581942	+	0.813230i	$0.302293\pi$
$930$	−1.17793	+	2.47092i	−0.0386258	+	0.0810247i
$931$	16.6473	+	48.0993i	0.545595	+	1.57639i
$932$	5.33171	+	15.4050i	0.174646	+	0.504607i
$933$	−10.6231	+	22.2839i	−0.347784	+	0.729541i
$934$	−4.80945	+	6.75393i	−0.157370	+	0.220995i
$935$	0.00678770	−	0.00436219i	0.000221982	−	0.000142659i
$936$	10.9940	−	3.98699i	0.359350	−	0.130319i
$937$	3.97051	+	27.6155i	0.129711	+	0.902159i	0.945919	+	0.324402i	$0.105163\pi$
$937$	3.97051	+	27.6155i	0.129711	+	0.902159i	−0.816208	+	0.577757i	$0.803928\pi$
$938$	−12.5325	+	1.19671i	−0.409200	+	0.0390739i
$939$	−14.7346	+	2.58926i	−0.480845	+	0.0844973i
$940$	2.28893	−	1.18003i	0.0746567	−	0.0384882i
$941$	−9.53340	+	1.83741i	−0.310780	+	0.0598979i	−0.342256	−	0.939607i	$-0.611191\pi$
$941$	−9.53340	+	1.83741i	−0.310780	+	0.0598979i	0.0314765	+	0.999504i	$0.489979\pi$
$942$	39.7361	+	8.33862i	1.29467	+	0.271687i
$943$	10.7412	+	1.19721i	0.349783	+	0.0389865i
$944$	3.18685			0.103723
$945$	0.825691	+	8.80959i	0.0268597	+	0.286576i
$946$	0.0119962	+	0.00770948i	0.000390030	+	0.000250657i
$947$	53.2924	−	21.3351i	1.73177	−	0.693297i	0.731841	−	0.681475i	$-0.238661\pi$
$947$	53.2924	−	21.3351i	1.73177	−	0.693297i	0.999930	−	0.0118213i	$-0.00376293\pi$
$948$	2.08942	−	2.83433i	0.0678612	−	0.0920548i
$949$	17.7366	+	7.10065i	0.575753	+	0.230497i
$950$	−12.4796	+	11.8993i	−0.404893	+	0.386065i
$951$	−6.63694	−	5.39836i	−0.215218	−	0.175054i
$952$	−3.76485	+	5.28699i	−0.122019	+	0.171352i
$953$	−25.9455	+	7.61828i	−0.840457	+	0.246780i	−0.673503	−	0.739184i	$-0.735211\pi$
$953$	−25.9455	+	7.61828i	−0.840457	+	0.246780i	−0.166954	+	0.985965i	$0.553393\pi$
$954$	17.2395	+	11.8981i	0.558149	+	0.385216i
$955$	3.00606	−	3.46918i	0.0972740	−	0.112260i
$956$	9.53420	+	9.09084i	0.308358	+	0.294019i
$957$	−0.0738762	−	0.0230185i	−0.00238808	−	0.000744082i
$958$	0.713585	+	14.9800i	0.0230549	+	0.483981i
$959$	−44.2979	+	42.2380i	−1.43045	+	1.36394i
$960$	−0.531134	−	0.353817i	−0.0171423	−	0.0114194i
$961$	12.5458	−	1.19798i	0.404704	−	0.0386445i
$962$	−5.41410	+	37.6559i	−0.174558	+	1.21407i
$963$	−25.1334	−	37.8723i	−0.809912	−	1.22042i
$964$	−4.00908	−	4.62673i	−0.129124	−	0.149017i
$965$	1.07752	+	1.86631i	0.0346865	+	0.0600788i
$966$	38.3690	+	1.23783i	1.23450	+	0.0398266i
$967$	−15.7984	+	27.3636i	−0.508041	+	0.879954i	0.491915	+	0.870643i	$0.336297\pi$
$967$	−15.7984	+	27.3636i	−0.508041	+	0.879954i	−0.999957	+	0.00931044i	$0.997036\pi$
$968$	10.8010	−	2.08172i	0.347157	−	0.0669089i
$969$	−6.14212	−	6.05247i	−0.197313	−	0.194433i
$970$	0.804438	−	0.322049i	0.0258290	−	0.0103404i
$971$	4.01131	−	8.78354i	0.128729	−	0.281877i	−0.834283	−	0.551337i	$-0.814118\pi$
$971$	4.01131	−	8.78354i	0.128729	−	0.281877i	0.963012	+	0.269460i	$0.0868451\pi$
$972$	2.41818	+	15.3998i	0.0775632	+	0.493947i
$973$	85.0248	+	24.9655i	2.72577	+	0.800358i
$974$	−14.6555	−	7.55545i	−0.469594	−	0.242092i
$975$	7.21695	+	32.0400i	0.231127	+	1.02610i
$976$	2.29045	−	9.44138i	0.0733156	−	0.302211i
$977$	−8.07637	−	23.3351i	−0.258386	−	0.746557i	−0.997346	−	0.0728079i	$-0.976804\pi$
$977$	−8.07637	−	23.3351i	−0.258386	−	0.746557i	0.738960	−	0.673749i	$-0.235317\pi$
$978$	3.77135	+	1.58228i	0.120595	+	0.0505958i
$979$	−0.0141615	−	0.0135029i	−0.000452602	−	0.000431555i
$980$	−2.19772	−	4.81233i	−0.0702036	−	0.153724i
$981$	−3.34950	+	0.531958i	−0.106941	+	0.0169841i
$982$	19.8831	+	5.83819i	0.634494	+	0.186304i
$983$	−2.40354	+	1.89016i	−0.0766609	+	0.0602868i	−0.655754	−	0.754975i	$-0.727649\pi$
$983$	−2.40354	+	1.89016i	−0.0766609	+	0.0602868i	0.579093	+	0.815261i	$0.303407\pi$
$984$	−1.56287	−	3.57676i	−0.0498225	−	0.114023i
$985$	−6.44311	−	5.06691i	−0.205294	−	0.161445i
$986$	−3.57660	+	1.84387i	−0.113902	+	0.0587207i
$987$	55.9376	+	0.920189i	1.78051	+	0.0292899i
$988$	−6.90944	−	11.9675i	−0.219818	−	0.380737i
$989$	−3.12610	−	3.07648i	−0.0994040	−	0.0978264i
$990$	0.00189040	+	0.0171314i	6.00808e−5	+	0.000544473i
$991$	7.08221	+	8.17331i	0.224974	+	0.259634i	0.857004	−	0.515310i	$-0.172323\pi$
$991$	7.08221	+	8.17331i	0.224974	+	0.259634i	−0.632030	+	0.774944i	$0.717778\pi$
$992$	0.204088	−	4.28433i	0.00647979	−	0.136028i
$993$	13.2066	−	2.32075i	0.419099	−	0.0736469i
$994$	−8.80681	−	12.3674i	−0.279335	−	0.392271i
$995$	−8.47912	−	3.39453i	−0.268806	−	0.107614i
$996$	−26.0963	−	14.0016i	−0.826893	−	0.443658i
$997$	16.6256	+	8.57107i	0.526537	+	0.271449i	0.700933	−	0.713227i	$-0.252767\pi$
$997$	16.6256	+	8.57107i	0.526537	+	0.271449i	−0.174396	+	0.984676i	$0.555797\pi$
$998$	14.8472	+	32.5109i	0.469981	+	1.02912i
$999$	−47.8920	−	16.6693i	−1.51523	−	0.527393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.9	✓	240
9.7	even	3	inner	414.2.m.a.151.11	yes	240
23.16	even	11	inner	414.2.m.a.85.11	yes	240
207.16	even	33	inner	414.2.m.a.223.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.9	✓	240	1.1	even	1	trivial
414.2.m.a.85.11	yes	240	23.16	even	11	inner
414.2.m.a.151.11	yes	240	9.7	even	3	inner
414.2.m.a.223.9	yes	240	207.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.23371 + 1.21571i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.213728 - 0.300139i) q^{5} +(1.55235 - 0.768242i) q^{6} +(1.08956 + 4.49122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.0441053 + 2.99968i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.23371 + 1.21571i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.213728 - 0.300139i) q^{5} +(1.55235 - 0.768242i) q^{6} +(1.08956 + 4.49122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.0441053 + 2.99968i) q^{9} +(-0.353536 + 0.103807i) q^{10} +(-0.0153105 - 0.00295086i) q^{11} +(-0.218264 - 1.71824i) q^{12} +(-0.919036 + 3.78832i) q^{13} +(4.60056 + 0.439300i) q^{14} +(0.101202 - 0.630118i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-0.199869 - 1.39012i) q^{17} +(2.84912 + 0.939418i) q^{18} +(0.504497 - 3.50885i) q^{19} +(-0.0175321 + 0.368044i) q^{20} +(-4.11581 + 6.86546i) q^{21} +(-0.00779613 + 0.0135033i) q^{22} +(3.19748 - 3.57437i) q^{23} +(-1.69513 - 0.355722i) q^{24} +(1.59094 - 4.59671i) q^{25} +(3.27938 + 2.10753i) q^{26} +(-3.59232 + 3.75436i) q^{27} +(1.91984 - 4.20385i) q^{28} +(2.25220 - 1.77115i) q^{29} +(-0.562362 - 0.301728i) q^{30} +(-0.204088 - 4.28433i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(-0.0153014 - 0.0222536i) q^{33} +(-1.37903 - 0.265787i) q^{34} +(1.11512 - 1.28692i) q^{35} +(1.81961 - 2.38517i) q^{36} +(4.05410 + 8.87723i) q^{37} +(-3.15086 - 1.62438i) q^{38} +(-5.73932 + 3.55642i) q^{39} +(0.342067 + 0.136943i) q^{40} +(1.30720 + 1.83570i) q^{41} +(5.14172 + 6.13491i) q^{42} +(0.0435160 - 0.913513i) q^{43} +(0.0102108 + 0.0117839i) q^{44} +(0.890894 - 0.654353i) q^{45} +(-2.33199 - 4.19068i) q^{46} +(-3.49454 - 6.05272i) q^{47} +(-0.890580 + 1.48555i) q^{48} +(-12.7620 + 6.57929i) q^{49} +(-3.82355 - 3.00687i) q^{50} +(1.44340 - 1.95799i) q^{51} +(3.06419 - 2.40971i) q^{52} +(6.69941 + 1.96712i) q^{53} +(2.37294 + 4.62268i) q^{54} +(0.00238662 + 0.00522596i) q^{55} +(-3.34473 - 3.18919i) q^{56} +(4.88815 - 3.71560i) q^{57} +(-0.937114 - 2.70761i) q^{58} +(0.751327 - 3.09701i) q^{59} +(-0.469063 + 0.432747i) q^{60} +(-8.63524 - 4.45178i) q^{61} +(-4.11544 - 1.20840i) q^{62} +(-13.4241 + 3.46640i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.33345 - 0.533832i) q^{65} +(-0.0260343 + 0.00718140i) q^{66} +(-2.67489 + 0.515544i) q^{67} +(-0.702207 + 1.21626i) q^{68} +(8.29017 - 0.522554i) q^{69} +(-0.851419 - 1.47470i) q^{70} +(-2.15137 - 2.48281i) q^{71} +(-1.65885 - 2.49964i) q^{72} +(0.697486 - 4.85112i) q^{73} +(9.71496 - 0.927666i) q^{74} +(7.55102 - 3.73691i) q^{75} +(-2.56559 + 2.44629i) q^{76} +(-0.00342873 - 0.0719779i) q^{77} +(1.48368 + 6.58685i) q^{78} +(1.47134 + 1.40292i) q^{79} +(0.241291 - 0.278464i) q^{80} +(-8.99611 + 0.264603i) q^{81} +(2.16229 - 0.634904i) q^{82} +(9.91802 - 13.9279i) q^{83} +(7.47919 - 2.85240i) q^{84} +(-0.374512 + 0.357096i) q^{85} +(-0.849038 - 0.339904i) q^{86} +(4.93177 + 0.552924i) q^{87} +(0.0144754 - 0.00579506i) q^{88} +(1.05571 + 0.678467i) q^{89} +(-0.326981 - 1.05591i) q^{90} -18.0155 q^{91} +(-4.72292 + 0.833096i) q^{92} +(4.95671 - 5.53375i) q^{93} +(-6.86278 + 1.32269i) q^{94} +(-1.16097 + 0.598522i) q^{95} +(1.11257 + 1.32748i) q^{96} +(-2.34105 + 0.223543i) q^{97} +(2.04338 + 14.2120i) q^{98} +(0.00817634 - 0.0460567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

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Database

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