LMFDB - Embedded newform 41.2.g.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, 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:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	41.8
Dual form			41.2.g.a.36.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.746800 - 1.02788i) q^{2} +(-0.604406 - 0.604406i) q^{3} +(0.119203 + 0.366868i) q^{4} +(-3.27974 + 1.06565i) q^{5} +(-1.07263 + 0.169888i) q^{6} +(1.70635 + 0.270260i) q^{7} +(2.88281 + 0.936683i) q^{8} -2.26939i q^{9} +O(q^{10})$	\(q+(0.746800 - 1.02788i) q^{2} +(-0.604406 - 0.604406i) q^{3} +(0.119203 + 0.366868i) q^{4} +(-3.27974 + 1.06565i) q^{5} +(-1.07263 + 0.169888i) q^{6} +(1.70635 + 0.270260i) q^{7} +(2.88281 + 0.936683i) q^{8} -2.26939i q^{9} +(-1.35394 + 4.16701i) q^{10} +(-3.99164 + 2.03384i) q^{11} +(0.149691 - 0.293784i) q^{12} +(-0.380129 - 2.40004i) q^{13} +(1.55210 - 1.55210i) q^{14} +(2.62638 + 1.33821i) q^{15} +(2.49153 - 1.81020i) q^{16} +(-0.138725 - 0.272263i) q^{17} +(-2.33266 - 1.69478i) q^{18} +(0.274489 - 1.73306i) q^{19} +(-0.781908 - 1.07620i) q^{20} +(-0.867983 - 1.19468i) q^{21} +(-0.890407 + 5.62181i) q^{22} +(3.75048 + 2.72488i) q^{23} +(-1.17625 - 2.30853i) q^{24} +(5.57599 - 4.05119i) q^{25} +(-2.75084 - 1.40162i) q^{26} +(-3.18485 + 3.18485i) q^{27} +(0.104252 + 0.658222i) q^{28} +(4.39273 - 8.62121i) q^{29} +(3.33690 - 1.70024i) q^{30} +(-2.28469 + 7.03157i) q^{31} +2.14948i q^{32} +(3.64184 + 1.18331i) q^{33} +(-0.383454 - 0.0607331i) q^{34} +(-5.88439 + 0.931996i) q^{35} +(0.832566 - 0.270517i) q^{36} +(2.28152 + 7.02179i) q^{37} +(-1.57639 - 1.57639i) q^{38} +(-1.22085 + 1.68035i) q^{39} -10.4531 q^{40} +(-5.99000 - 2.26271i) q^{41} -1.87620 q^{42} +(-1.53275 + 2.10964i) q^{43} +(-1.22197 - 1.22197i) q^{44} +(2.41838 + 7.44299i) q^{45} +(5.60172 - 1.82011i) q^{46} +(6.25754 - 0.991097i) q^{47} +(-2.60000 - 0.411799i) q^{48} +(-3.81880 - 1.24080i) q^{49} -8.75689i q^{50} +(-0.0807112 + 0.248404i) q^{51} +(0.835185 - 0.425548i) q^{52} +(-0.556161 + 1.09153i) q^{53} +(0.895204 + 5.65210i) q^{54} +(10.9242 - 10.9242i) q^{55} +(4.66595 + 2.37742i) q^{56} +(-1.21337 + 0.881567i) q^{57} +(-5.58110 - 10.9535i) q^{58} +(2.66945 + 1.93947i) q^{59} +(-0.177874 + 1.12305i) q^{60} +(-0.655043 - 0.901590i) q^{61} +(5.52141 + 7.59957i) q^{62} +(0.613323 - 3.87237i) q^{63} +(7.19247 + 5.22564i) q^{64} +(3.80433 + 7.46641i) q^{65} +(3.93602 - 2.85969i) q^{66} +(-9.09493 - 4.63410i) q^{67} +(0.0833482 - 0.0833482i) q^{68} +(-0.619877 - 3.91375i) q^{69} +(-3.43648 + 6.74448i) q^{70} +(0.475905 - 0.242486i) q^{71} +(2.12570 - 6.54222i) q^{72} -8.56300i q^{73} +(8.92141 + 2.89874i) q^{74} +(-5.81873 - 0.921596i) q^{75} +(0.668523 - 0.105884i) q^{76} +(-7.36081 + 2.39167i) q^{77} +(0.815474 + 2.50977i) q^{78} +(-6.09837 - 6.09837i) q^{79} +(-6.24253 + 8.59210i) q^{80} -2.95827 q^{81} +(-6.79914 + 4.46722i) q^{82} +9.88122 q^{83} +(0.334823 - 0.460844i) q^{84} +(0.745119 + 0.745119i) q^{85} +(1.02381 + 3.15096i) q^{86} +(-7.86570 + 2.55572i) q^{87} +(-13.4122 + 2.12429i) q^{88} +(-14.4489 - 2.28848i) q^{89} +(9.45656 + 3.07262i) q^{90} -4.19804i q^{91} +(-0.552606 + 1.70075i) q^{92} +(5.63081 - 2.86904i) q^{93} +(3.65440 - 7.17217i) q^{94} +(0.946582 + 5.97648i) q^{95} +(1.29916 - 1.29916i) q^{96} +(8.80540 + 4.48657i) q^{97} +(-4.12728 + 2.99864i) q^{98} +(4.61557 + 9.05857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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 $

$2$	0.746800	−	1.02788i	0.528067	−	0.726822i	−0.458767	−	0.888557i	$-0.651709\pi$
$2$	0.746800	−	1.02788i	0.528067	−	0.726822i	0.986834	+	0.161734i	$0.0517087\pi$
$3$	−0.604406	−	0.604406i	−0.348954	−	0.348954i	0.510766	−	0.859720i	$-0.329362\pi$
$3$	−0.604406	−	0.604406i	−0.348954	−	0.348954i	−0.859720	+	0.510766i	$0.829362\pi$
$4$	0.119203	+	0.366868i	0.0596014	+	0.183434i
$5$	−3.27974	+	1.06565i	−1.46674	+	0.476574i	−0.930123	−	0.367249i	$-0.880300\pi$
$5$	−3.27974	+	1.06565i	−1.46674	+	0.476574i	−0.536621	+	0.843823i	$0.680300\pi$
$6$	−1.07263	+	0.169888i	−0.437899	+	0.0693564i
$7$	1.70635	+	0.270260i	0.644940	+	0.102149i	0.470332	−	0.882489i	$-0.344134\pi$
$7$	1.70635	+	0.270260i	0.644940	+	0.102149i	0.174608	+	0.984638i	$0.444134\pi$
$8$	2.88281	+	0.936683i	1.01923	+	0.331167i
$9$		−	2.26939i		−	0.756462i
$10$	−1.35394	+	4.16701i	−0.428155	+	1.31773i
$11$	−3.99164	+	2.03384i	−1.20352	+	0.613226i	−0.936569	−	0.350483i	$-0.886018\pi$
$11$	−3.99164	+	2.03384i	−1.20352	+	0.613226i	−0.266955	+	0.963709i	$0.586018\pi$
$12$	0.149691	−	0.293784i	0.0432120	−	0.0848082i
$13$	−0.380129	−	2.40004i	−0.105429	−	0.665651i	−0.982637	−	0.185540i	$-0.940597\pi$
$13$	−0.380129	−	2.40004i	−0.105429	−	0.665651i	0.877208	−	0.480111i	$-0.159403\pi$
$14$	1.55210	−	1.55210i	0.414816	−	0.414816i
$15$	2.62638	+	1.33821i	0.678129	+	0.345524i
$16$	2.49153	−	1.81020i	0.622883	−	0.452551i
$17$	−0.138725	−	0.272263i	−0.0336457	−	0.0660334i	0.873572	−	0.486695i	$-0.161798\pi$
$17$	−0.138725	−	0.272263i	−0.0336457	−	0.0660334i	−0.907217	+	0.420662i	$0.861798\pi$
$18$	−2.33266	−	1.69478i	−0.549814	−	0.399463i
$19$	0.274489	−	1.73306i	0.0629721	−	0.397590i	−0.935989	−	0.352028i	$-0.885492\pi$
$19$	0.274489	−	1.73306i	0.0629721	−	0.397590i	0.998962	−	0.0455621i	$-0.0145079\pi$
$20$	−0.781908	−	1.07620i	−0.174840	−	0.240646i
$21$	−0.867983	−	1.19468i	−0.189409	−	0.260700i
$22$	−0.890407	+	5.62181i	−0.189835	+	1.19857i
$23$	3.75048	+	2.72488i	0.782029	+	0.568178i	0.905587	−	0.424160i	$-0.139431\pi$
$23$	3.75048	+	2.72488i	0.782029	+	0.568178i	−0.123558	+	0.992337i	$0.539431\pi$
$24$	−1.17625	−	2.30853i	−0.240102	−	0.471226i
$25$	5.57599	−	4.05119i	1.11520	−	0.810239i
$26$	−2.75084	−	1.40162i	−0.539483	−	0.274880i
$27$	−3.18485	+	3.18485i	−0.612925	+	0.612925i
$28$	0.104252	+	0.658222i	0.0197018	+	0.124392i
$29$	4.39273	−	8.62121i	0.815709	−	1.60092i	0.0165007	−	0.999864i	$-0.494747\pi$
$29$	4.39273	−	8.62121i	0.815709	−	1.60092i	0.799208	−	0.601055i	$-0.205253\pi$
$30$	3.33690	−	1.70024i	0.609232	−	0.310419i
$31$	−2.28469	+	7.03157i	−0.410343	+	1.26291i	0.506007	+	0.862529i	$0.331121\pi$
$31$	−2.28469	+	7.03157i	−0.410343	+	1.26291i	−0.916350	+	0.400378i	$0.868879\pi$
$32$			2.14948i			0.379978i
$33$	3.64184	+	1.18331i	0.633963	+	0.205987i
$34$	−0.383454	−	0.0607331i	−0.0657618	−	0.0104156i
$35$	−5.88439	+	0.931996i	−0.994644	+	0.157536i
$36$	0.832566	−	0.270517i	0.138761	−	0.0450862i
$37$	2.28152	+	7.02179i	0.375079	+	1.15438i	0.943425	+	0.331585i	$0.107583\pi$
$37$	2.28152	+	7.02179i	0.375079	+	1.15438i	−0.568346	+	0.822790i	$0.692417\pi$
$38$	−1.57639	−	1.57639i	−0.255724	−	0.255724i
$39$	−1.22085	+	1.68035i	−0.195492	+	0.269071i
$40$	−10.4531			−1.65277
$41$	−5.99000	−	2.26271i	−0.935481	−	0.353376i
$41$	−5.99000	−	2.26271i	−0.935481	−	0.353376i
$42$	−1.87620			−0.289503
$43$	−1.53275	+	2.10964i	−0.233742	+	0.321718i	−0.909735	−	0.415190i	$-0.863715\pi$
$43$	−1.53275	+	2.10964i	−0.233742	+	0.321718i	0.675993	+	0.736908i	$0.263715\pi$
$44$	−1.22197	−	1.22197i	−0.184218	−	0.184218i
$45$	2.41838	+	7.44299i	0.360510	+	1.10954i
$46$	5.60172	−	1.82011i	0.825928	−	0.268360i
$47$	6.25754	−	0.991097i	0.912756	−	0.144566i	0.317645	−	0.948210i	$-0.397108\pi$
$47$	6.25754	−	0.991097i	0.912756	−	0.144566i	0.595111	+	0.803643i	$0.297108\pi$
$48$	−2.60000	−	0.411799i	−0.375277	−	0.0594381i
$49$	−3.81880	−	1.24080i	−0.545543	−	0.177258i
$50$		−	8.75689i		−	1.23841i
$51$	−0.0807112	+	0.248404i	−0.0113018	+	0.0347835i
$52$	0.835185	−	0.425548i	0.115819	−	0.0590129i
$53$	−0.556161	+	1.09153i	−0.0763946	+	0.149933i	−0.926045	−	0.377414i	$-0.876813\pi$
$53$	−0.556161	+	1.09153i	−0.0763946	+	0.149933i	0.849650	+	0.527347i	$0.176813\pi$
$54$	0.895204	+	5.65210i	0.121822	+	0.769153i
$55$	10.9242	−	10.9242i	1.47301	−	1.47301i
$56$	4.66595	+	2.37742i	0.623513	+	0.317696i
$57$	−1.21337	+	0.881567i	−0.160715	+	0.116766i
$58$	−5.58110	−	10.9535i	−0.732834	−	1.43827i
$59$	2.66945	+	1.93947i	0.347533	+	0.252497i	0.747833	−	0.663887i	$-0.231094\pi$
$59$	2.66945	+	1.93947i	0.347533	+	0.252497i	−0.400300	+	0.916384i	$0.631094\pi$
$60$	−0.177874	+	1.12305i	−0.0229635	+	0.144986i
$61$	−0.655043	−	0.901590i	−0.0838697	−	0.115437i	0.765021	−	0.644006i	$-0.222729\pi$
$61$	−0.655043	−	0.901590i	−0.0838697	−	0.115437i	−0.848890	+	0.528569i	$0.822729\pi$
$62$	5.52141	+	7.59957i	0.701220	+	0.965147i
$63$	0.613323	−	3.87237i	0.0772715	−	0.487873i
$64$	7.19247	+	5.22564i	0.899059	+	0.653205i
$65$	3.80433	+	7.46641i	0.471869	+	0.926095i
$66$	3.93602	−	2.85969i	0.484491	−	0.352003i
$67$	−9.09493	−	4.63410i	−1.11112	−	0.566145i	−0.200628	−	0.979667i	$-0.564298\pi$
$67$	−9.09493	−	4.63410i	−1.11112	−	0.566145i	−0.910494	+	0.413522i	$0.864298\pi$
$68$	0.0833482	−	0.0833482i	0.0101075	−	0.0101075i
$69$	−0.619877	−	3.91375i	−0.0746245	−	0.471160i
$70$	−3.43648	+	6.74448i	−0.410738	+	0.806119i
$71$	0.475905	−	0.242486i	0.0564795	−	0.0287777i	−0.425523	−	0.904948i	$-0.639910\pi$
$71$	0.475905	−	0.242486i	0.0564795	−	0.0287777i	0.482002	+	0.876170i	$0.339910\pi$
$72$	2.12570	−	6.54222i	0.250516	−	0.771008i
$73$		−	8.56300i		−	1.00222i	−0.865383	−	0.501112i	$-0.832925\pi$
$73$		−	8.56300i		−	1.00222i	0.865383	−	0.501112i	$-0.167075\pi$
$74$	8.92141	+	2.89874i	1.03709	+	0.336972i
$75$	−5.81873	−	0.921596i	−0.671889	−	0.106417i
$76$	0.668523	−	0.105884i	0.0766848	−	0.0121457i
$77$	−7.36081	+	2.39167i	−0.838842	+	0.272556i
$78$	0.815474	+	2.50977i	0.0923343	+	0.284176i
$79$	−6.09837	−	6.09837i	−0.686120	−	0.686120i	0.275252	−	0.961372i	$-0.411239\pi$
$79$	−6.09837	−	6.09837i	−0.686120	−	0.686120i	−0.961372	+	0.275252i	$0.911239\pi$
$80$	−6.24253	+	8.59210i	−0.697936	+	0.960626i
$81$	−2.95827			−0.328697
$82$	−6.79914	+	4.46722i	−0.750839	+	0.493322i
$83$	9.88122			1.08460			0.542302	−	0.840183i	$-0.317553\pi$
$83$	9.88122			1.08460			0.542302	+	0.840183i	$0.317553\pi$
$84$	0.334823	−	0.460844i	0.0365322	−	0.0502822i
$85$	0.745119	+	0.745119i	0.0808195	+	0.0808195i
$86$	1.02381	+	3.15096i	0.110400	+	0.339777i
$87$	−7.86570	+	2.55572i	−0.843292	+	0.274002i
$88$	−13.4122	+	2.12429i	−1.42975	+	0.226450i
$89$	−14.4489	−	2.28848i	−1.53158	−	0.242579i	−0.666996	−	0.745062i	$-0.732420\pi$
$89$	−14.4489	−	2.28848i	−1.53158	−	0.242579i	−0.864587	+	0.502483i	$0.832420\pi$
$90$	9.45656	+	3.07262i	0.996809	+	0.323883i
$91$		−	4.19804i		−	0.440074i
$92$	−0.552606	+	1.70075i	−0.0576131	+	0.177315i
$93$	5.63081	−	2.86904i	0.583888	−	0.297506i
$94$	3.65440	−	7.17217i	0.376923	−	0.739753i
$95$	0.946582	+	5.97648i	0.0971172	+	0.613174i
$96$	1.29916	−	1.29916i	0.132595	−	0.132595i
$97$	8.80540	+	4.48657i	0.894053	+	0.455543i	0.839745	−	0.542982i	$-0.182705\pi$
$97$	8.80540	+	4.48657i	0.894053	+	0.455543i	0.0543082	+	0.998524i	$0.482705\pi$
$98$	−4.12728	+	2.99864i	−0.416918	+	0.302909i
$99$	4.61557	+	9.05857i	0.463882	+	0.910420i
$100$	2.15093	+	1.56274i	0.215093	+	0.156274i
$101$	0.271981	−	1.71722i	0.0270631	−	0.170870i	−0.970455	−	0.241283i	$-0.922432\pi$
$101$	0.271981	−	1.71722i	0.0270631	−	0.170870i	0.997518	+	0.0704133i	$0.0224318\pi$
$102$	0.195054	+	0.268469i	0.0193133	+	0.0265824i
$103$	4.97027	+	6.84100i	0.489736	+	0.674063i	0.980339	−	0.197320i	$-0.0632236\pi$
$103$	4.97027	+	6.84100i	0.489736	+	0.674063i	−0.490603	+	0.871383i	$0.663224\pi$
$104$	1.15223	−	7.27492i	0.112986	−	0.713365i
$105$	4.11987	+	2.99326i	0.402058	+	0.292112i
$106$	0.706621	+	1.38682i	0.0686331	+	0.134700i
$107$	−0.277133	+	0.201349i	−0.0267915	+	0.0194651i	−0.601100	−	0.799174i	$-0.705271\pi$
$107$	−0.277133	+	0.201349i	−0.0267915	+	0.0194651i	0.574309	+	0.818639i	$0.305271\pi$
$108$	−1.54806	−	0.788778i	−0.148962	−	0.0759002i
$109$	0.0194034	−	0.0194034i	0.00185851	−	0.00185851i	−0.706177	−	0.708035i	$-0.749582\pi$
$109$	0.0194034	−	0.0194034i	0.00185851	−	0.00185851i	0.708035	+	0.706177i	$0.249582\pi$
$110$	−3.07059	−	19.3869i	−0.292769	−	1.84847i
$111$	2.86505	−	5.62298i	0.271939	−	0.533709i
$112$	4.74065	−	2.41548i	0.447950	−	0.228242i
$113$	−1.43672	+	4.42177i	−0.135155	+	0.415965i	−0.995614	−	0.0935546i	$-0.970177\pi$
$113$	−1.43672	+	4.42177i	−0.135155	+	0.415965i	0.860459	+	0.509520i	$0.170177\pi$
$114$			1.90556i			0.178472i
$115$	−15.2044	−	4.94020i	−1.41782	−	0.460676i
$116$	3.68647	+	0.583880i	0.342280	+	0.0542119i
$117$	−5.44661	+	0.862659i	−0.503539	+	0.0797528i
$118$	3.98709	−	1.29548i	0.367041	−	0.119259i
$119$	−0.163132	−	0.502068i	−0.0149543	−	0.0460245i
$120$	6.31789	+	6.31789i	0.576742	+	0.576742i
$121$	5.33103	−	7.33753i	0.484639	−	0.667049i
$122$	−1.41591			−0.128191
$123$	2.25280	+	4.98799i	0.203128	+	0.449752i
$124$	−2.85200			−0.256117
$125$	−3.83568	+	5.27936i	−0.343074	+	0.472200i
$126$	−3.52231	−	3.52231i	−0.313792	−	0.313792i
$127$	−6.46903	−	19.9096i	−0.574034	−	1.76669i	−0.639446	−	0.768836i	$-0.720836\pi$
$127$	−6.46903	−	19.9096i	−0.574034	−	1.76669i	0.0654117	−	0.997858i	$-0.479164\pi$
$128$	6.65413	−	2.16206i	0.588147	−	0.191101i
$129$	2.20148	−	0.348681i	0.193830	−	0.0306996i
$130$	10.5157	+	1.66552i	0.922285	+	0.146076i
$131$	13.7334	+	4.46226i	1.19989	+	0.389869i	0.839722	−	0.543016i	$-0.182718\pi$
$131$	13.7334	+	4.46226i	1.19989	+	0.389869i	0.360172	+	0.932886i	$0.382718\pi$
$132$			1.47713i			0.128567i
$133$	0.936750	−	2.88302i	0.0812265	−	0.249990i
$134$	−11.5554	+	5.88777i	−0.998235	+	0.508626i
$135$	7.05154	−	13.8394i	0.606900	−	1.19111i
$136$	−0.144894	−	0.914824i	−0.0124245	−	0.0784455i
$137$	0.668766	−	0.668766i	0.0571365	−	0.0571365i	−0.677961	−	0.735098i	$-0.737136\pi$
$137$	0.668766	−	0.668766i	0.0571365	−	0.0571365i	0.735098	+	0.677961i	$0.237136\pi$
$138$	−4.48580	−	2.28563i	−0.381857	−	0.194566i
$139$	−6.13162	+	4.45488i	−0.520077	+	0.377858i	−0.816633	−	0.577157i	$-0.804162\pi$
$139$	−6.13162	+	4.45488i	−0.520077	+	0.377858i	0.296556	+	0.955016i	$0.404162\pi$
$140$	−1.04336	−	2.04770i	−0.0881796	−	0.173062i
$141$	−4.38112	−	3.18307i	−0.368957	−	0.268063i
$142$	0.106159	−	0.670262i	0.00890868	−	0.0562472i
$143$	6.39863	+	8.80696i	0.535081	+	0.736475i
$144$	−4.10805	−	5.65425i	−0.342338	−	0.471187i
$145$	−5.21979	+	32.9564i	−0.433480	+	2.73688i
$146$	−8.80175	−	6.39485i	−0.728438	−	0.529241i
$147$	1.55816	+	3.05806i	0.128515	+	0.252224i
$148$	−2.30411	+	1.67403i	−0.189397	+	0.137605i
$149$	8.57816	+	4.37079i	0.702750	+	0.358069i	0.768573	−	0.639762i	$-0.220967\pi$
$149$	8.57816	+	4.37079i	0.702750	+	0.358069i	−0.0658226	+	0.997831i	$0.520967\pi$
$150$	−5.29272	+	5.29272i	−0.432149	+	0.432149i
$151$	2.81584	+	17.7785i	0.229150	+	1.44679i	0.787051	+	0.616887i	$0.211607\pi$
$151$	2.81584	+	17.7785i	0.229150	+	1.44679i	−0.557902	+	0.829907i	$0.688393\pi$
$152$	2.41463	−	4.73897i	0.195852	−	0.384381i
$153$	−0.617869	+	0.314820i	−0.0499518	+	0.0254517i
$154$	−3.03869	+	9.35214i	−0.244865	+	0.753617i
$155$		−	25.4964i		−	2.04792i
$156$	−0.761995	−	0.247587i	−0.0610084	−	0.0198228i
$157$	10.9681	+	1.73718i	0.875350	+	0.138642i	0.577912	−	0.816099i	$-0.303868\pi$
$157$	10.9681	+	1.73718i	0.875350	+	0.138642i	0.297438	+	0.954741i	$0.403868\pi$
$158$	−10.8227	+	1.71414i	−0.861005	+	0.136370i
$159$	0.995874	−	0.323579i	0.0789779	−	0.0256615i
$160$	−2.29060	−	7.04973i	−0.181087	−	0.557330i
$161$	5.66321	+	5.66321i	0.446324	+	0.446324i
$162$	−2.20924	+	3.04075i	−0.173574	+	0.238904i
$163$	1.98697			0.155631			0.0778156	−	0.996968i	$-0.475205\pi$
$163$	1.98697			0.155631			0.0778156	+	0.996968i	$0.475205\pi$
$164$	0.116093	−	2.46726i	0.00906536	−	0.192661i
$165$	−13.2053			−1.02803
$166$	7.37930	−	10.1567i	0.572744	−	0.788315i
$167$	3.26398	+	3.26398i	0.252574	+	0.252574i	0.822025	−	0.569451i	$-0.192844\pi$
$167$	3.26398	+	3.26398i	0.252574	+	0.252574i	−0.569451	+	0.822025i	$0.692844\pi$
$168$	−1.38320	−	4.25706i	−0.106716	−	0.328439i
$169$	6.74805	−	2.19257i	0.519081	−	0.168660i
$170$	1.32235	−	0.209439i	0.101420	−	0.0160633i
$171$	−3.93297	−	0.622922i	−0.300762	−	0.0476360i
$172$	−0.956669	−	0.310841i	−0.0729453	−	0.0237014i
$173$			3.45816i			0.262919i	0.991322	+	0.131460i	$0.0419663\pi$
$173$			3.45816i			0.262919i	−0.991322	+	0.131460i	$0.958034\pi$
$174$	−3.24713	+	9.99363i	−0.246164	+	0.757615i
$175$	10.6095	−	5.40580i	0.802001	−	0.408640i
$176$	−6.26363	+	12.2931i	−0.472139	+	0.926624i
$177$	−0.441205	−	2.78566i	−0.0331630	−	0.209383i
$178$	−13.1427	+	13.1427i	−0.985091	+	0.985091i
$179$	−14.1878	−	7.22903i	−1.06044	−	0.540323i	−0.165366	−	0.986232i	$-0.552881\pi$
$179$	−14.1878	−	7.22903i	−1.06044	−	0.540323i	−0.895078	+	0.445909i	$0.852881\pi$
$180$	−2.44232	+	1.77445i	−0.182040	+	0.132260i
$181$	−1.10429	−	2.16728i	−0.0820810	−	0.161093i	0.846318	−	0.532678i	$-0.178814\pi$
$181$	−1.10429	−	2.16728i	−0.0820810	−	0.161093i	−0.928399	+	0.371585i	$0.878814\pi$
$182$	−4.31509	−	3.13510i	−0.319856	−	0.232389i
$183$	−0.149014	+	0.940839i	−0.0110154	+	0.0695488i
$184$	8.25959	+	11.3683i	0.608905	+	0.838085i
$185$	−14.9656	−	20.5983i	−1.10029	−	1.51442i
$186$	1.25605	−	7.93041i	0.0920983	−	0.581486i
$187$	1.10748	+	0.804630i	0.0809869	+	0.0588404i
$188$	1.10952	+	2.17755i	0.0809199	+	0.158814i
$189$	−6.29521	+	4.57374i	−0.457909	+	0.332691i
$190$	6.85003	+	3.49026i	0.496953	+	0.253210i
$191$	−4.58243	+	4.58243i	−0.331573	+	0.331573i	−0.853184	−	0.521610i	$-0.825331\pi$
$191$	−4.58243	+	4.58243i	−0.331573	+	0.331573i	0.521610	+	0.853184i	$0.325331\pi$
$192$	−1.18877	−	7.50559i	−0.0857919	−	0.541669i
$193$	−0.572698	+	1.12398i	−0.0412237	+	0.0809060i	−0.910700	−	0.413069i	$-0.864457\pi$
$193$	−0.572698	+	1.12398i	−0.0412237	+	0.0809060i	0.869476	+	0.493975i	$0.164457\pi$
$194$	11.1875	−	5.70034i	0.803219	−	0.409260i
$195$	2.21339	−	6.81211i	0.158504	−	0.487825i
$196$		−	1.54890i		−	0.110636i
$197$	−3.22508	−	1.04789i	−0.229777	−	0.0746592i	0.191865	−	0.981421i	$-0.438546\pi$
$197$	−3.22508	−	1.04789i	−0.229777	−	0.0746592i	−0.421643	+	0.906762i	$0.638546\pi$
$198$	12.7580	+	2.02068i	0.906675	+	0.143603i
$199$	7.65101	−	1.21180i	0.542365	−	0.0859023i	0.120760	−	0.992682i	$-0.461467\pi$
$199$	7.65101	−	1.21180i	0.542365	−	0.0859023i	0.421605	+	0.906779i	$0.361467\pi$
$200$	19.8692	−	6.45590i	1.40497	−	0.456501i
$201$	2.69615	+	8.29791i	0.190172	+	0.585290i
$202$	−1.56198	−	1.56198i	−0.109901	−	0.109901i
$203$	9.82550	−	13.5236i	0.689615	−	0.949174i
$204$	−0.100752			−0.00705408
$205$	22.0569	+	1.03785i	1.54052	+	0.0724868i
$206$	10.7435			0.748538
$207$	6.18381	−	8.51129i	0.429805	−	0.591575i
$208$	−5.29166	−	5.29166i	−0.366911	−	0.366911i
$209$	2.42910	+	7.47600i	0.168024	+	0.517126i
$210$	6.15344	−	1.99937i	0.424627	−	0.137970i
$211$	−15.0249	+	2.37972i	−1.03436	+	0.163826i	−0.650453	−	0.759546i	$-0.725421\pi$
$211$	−15.0249	+	2.37972i	−1.03436	+	0.163826i	−0.383905	+	0.923372i	$0.625421\pi$
$212$	−0.466743	−	0.0739248i	−0.0320560	−	0.00507717i
$213$	−0.434200	−	0.141080i	−0.0297509	−	0.00966664i
$214$			0.435228i			0.0297515i
$215$	2.77886	−	8.55246i	0.189517	−	0.583273i
$216$	−12.1645	+	6.19813i	−0.827691	+	0.421730i
$217$	−5.79884	+	11.3809i	−0.393651	+	0.772584i
$218$	−0.00545394	−	0.0344348i	−0.000369387	−	0.00233222i
$219$	−5.17553	+	5.17553i	−0.349730	+	0.349730i
$220$	5.30992	+	2.70554i	0.357995	+	0.182407i
$221$	−0.600708	+	0.436440i	−0.0404080	+	0.0293581i
$222$	−3.64014	−	7.14417i	−0.244310	−	0.479486i
$223$	−2.35953	−	1.71430i	−0.158006	−	0.114798i	0.505973	−	0.862549i	$-0.331134\pi$
$223$	−2.35953	−	1.71430i	−0.158006	−	0.114798i	−0.663979	+	0.747751i	$0.731134\pi$
$224$	−0.580917	+	3.66777i	−0.0388142	+	0.245063i
$225$	−9.19372	−	12.6541i	−0.612915	−	0.843605i
$226$	3.47212	+	4.77896i	0.230962	+	0.317892i
$227$	2.59992	−	16.4153i	0.172563	−	1.08952i	−0.737591	−	0.675248i	$-0.764037\pi$
$227$	2.59992	−	16.4153i	0.172563	−	1.08952i	0.910154	−	0.414271i	$-0.135963\pi$
$228$	−0.468056	−	0.340063i	−0.0309978	−	0.0225212i
$229$	5.63479	+	11.0589i	0.372358	+	0.730793i	0.998815	−	0.0486625i	$-0.0154959\pi$
$229$	5.63479	+	11.0589i	0.372358	+	0.730793i	−0.626458	+	0.779455i	$0.715496\pi$
$230$	−16.4326	+	11.9390i	−1.08353	+	0.787232i
$231$	5.89446	+	3.00338i	0.387827	+	0.197608i
$232$	20.7387	−	20.7387i	1.36157	−	1.36157i
$233$	0.476691	+	3.00971i	0.0312291	+	0.197173i	0.998370	−	0.0570669i	$-0.0181748\pi$
$233$	0.476691	+	3.00971i	0.0312291	+	0.197173i	−0.967141	+	0.254240i	$0.918175\pi$
$234$	−3.18082	+	6.24271i	−0.207937	+	0.408099i
$235$	−19.4669	+	9.91890i	−1.26988	+	0.647038i
$236$	−0.393324	+	1.21053i	−0.0256032	+	0.0787985i
$237$			7.37179i			0.478849i
$238$	−0.637893	−	0.207264i	−0.0413485	−	0.0134349i
$239$	−13.5302	−	2.14297i	−0.875193	−	0.138617i	−0.297354	−	0.954767i	$-0.596104\pi$
$239$	−13.5302	−	2.14297i	−0.875193	−	0.138617i	−0.577840	+	0.816150i	$0.696104\pi$
$240$	8.96614	−	1.42010i	0.578762	−	0.0916669i
$241$	−12.5581	+	4.08039i	−0.808941	+	0.262841i	−0.684149	−	0.729342i	$-0.739826\pi$
$241$	−12.5581	+	4.08039i	−0.808941	+	0.262841i	−0.124792	+	0.992183i	$0.539826\pi$
$242$	−3.56091	−	10.9593i	−0.228904	−	0.704493i
$243$	11.3425	+	11.3425i	0.727625	+	0.727625i
$244$	0.252682	−	0.347786i	0.0161763	−	0.0222647i
$245$	13.8469			0.884648
$246$	6.80946	+	1.40942i	0.434155	+	0.0898616i
$247$	−4.26374			−0.271295
$248$	−13.1727	+	18.1307i	−0.836467	+	1.15130i
$249$	−5.97227	−	5.97227i	−0.378477	−	0.378477i
$250$	2.56207	+	7.88525i	0.162040	+	0.498707i
$251$	−19.8271	+	6.44222i	−1.25148	+	0.406630i	−0.858450	−	0.512897i	$-0.828572\pi$
$251$	−19.8271	+	6.44222i	−1.25148	+	0.406630i	−0.393027	+	0.919527i	$0.628572\pi$
$252$	1.49376	−	0.236588i	0.0940980	−	0.0149037i
$253$	−20.5125	−	3.24887i	−1.28961	−	0.204255i
$254$	−25.2958	−	8.21912i	−1.58720	−	0.515713i
$255$		−	0.900709i		−	0.0564046i
$256$	−2.74760	+	8.45624i	−0.171725	+	0.528515i
$257$	16.3088	−	8.30974i	1.01731	−	0.518348i	0.135916	−	0.990720i	$-0.456602\pi$
$257$	16.3088	−	8.30974i	1.01731	−	0.518348i	0.881399	+	0.472373i	$0.156602\pi$
$258$	1.28567	−	2.52326i	0.0800420	−	0.157091i
$259$	1.99537	+	12.5982i	0.123986	+	0.782817i
$260$	−2.28570	+	2.28570i	−0.141753	+	0.141753i
$261$	−19.5649	−	9.96879i	−1.21103	−	0.617053i
$262$	14.8428	−	10.7839i	0.916991	−	0.666233i
$263$	9.77669	+	19.1878i	0.602857	+	1.18317i	0.967700	+	0.252104i	$0.0811225\pi$
$263$	9.77669	+	19.1878i	0.602857	+	1.18317i	−0.364844	+	0.931069i	$0.618878\pi$
$264$	9.39036	+	6.82250i	0.577937	+	0.419896i
$265$	0.660875	−	4.17260i	0.0405972	−	0.256321i
$266$	−2.26384	−	3.11591i	−0.138805	−	0.191049i
$267$	7.34985	+	10.1162i	0.449803	+	0.619101i
$268$	0.615963	−	3.88904i	0.0376259	−	0.237561i
$269$	2.38656	+	1.73394i	0.145511	+	0.105720i	0.658159	−	0.752879i	$-0.271335\pi$
$269$	2.38656	+	1.73394i	0.145511	+	0.105720i	−0.512648	+	0.858599i	$0.671335\pi$
$270$	−8.95920	−	17.5834i	−0.545240	−	1.07009i
$271$	9.08621	−	6.60152i	0.551948	−	0.401014i	−0.276555	−	0.960998i	$-0.589193\pi$
$271$	9.08621	−	6.60152i	0.551948	−	0.401014i	0.828503	+	0.559984i	$0.189193\pi$
$272$	−0.838488	−	0.427231i	−0.0508408	−	0.0259047i
$273$	−2.53732	+	2.53732i	−0.153566	+	0.153566i
$274$	−0.187978	−	1.18685i	−0.0113562	−	0.0717000i
$275$	−14.0179	+	27.5116i	−0.845308	+	1.65901i
$276$	1.36194	−	0.693943i	0.0819792	−	0.0417705i
$277$	9.15694	−	28.1822i	0.550187	−	1.69330i	−0.158138	−	0.987417i	$-0.550549\pi$
$277$	9.15694	−	28.1822i	0.550187	−	1.69330i	0.708326	−	0.705886i	$-0.249451\pi$
$278$			9.62949i			0.577538i
$279$	15.9573	+	5.18485i	0.955341	+	0.310409i
$280$	−17.8366	−	2.82504i	−1.06594	−	0.168828i
$281$	2.43464	−	0.385610i	0.145239	−	0.0230036i	−0.0833917	−	0.996517i	$-0.526575\pi$
$281$	2.43464	−	0.385610i	0.145239	−	0.0230036i	0.228630	+	0.973513i	$0.426575\pi$
$282$	−6.54365	+	2.12616i	−0.389669	+	0.126611i
$283$	−4.97243	−	15.3036i	−0.295580	−	0.909703i	−0.983026	−	0.183467i	$-0.941268\pi$
$283$	−4.97243	−	15.3036i	−0.295580	−	0.909703i	0.687446	−	0.726236i	$-0.258732\pi$
$284$	0.145689	+	0.145689i	0.00864507	+	0.00864507i
$285$	3.04010	−	4.18434i	0.180080	−	0.247859i
$286$	13.8310			0.817845
$287$	−9.60953	−	5.47984i	−0.567233	−	0.323465i
$288$	4.87800			0.287439
$289$	9.93747	−	13.6777i	0.584557	−	0.804574i
$290$	29.9772	+	29.9772i	1.76032	+	1.76032i
$291$	−2.61032	−	8.03375i	−0.153020	−	0.470947i
$292$	3.14149	−	1.02073i	0.183842	−	0.0597339i
$293$	26.1450	−	4.14096i	1.52741	−	0.241917i	0.664502	−	0.747286i	$-0.268644\pi$
$293$	26.1450	−	4.14096i	1.52741	−	0.241917i	0.862904	+	0.505369i	$0.168644\pi$
$294$	4.30695	+	0.682154i	0.251187	+	0.0397840i
$295$	−10.8219	−	3.51625i	−0.630075	−	0.204724i
$296$			22.3796i			1.30079i
$297$	6.23529	−	19.1903i	0.361808	−	1.11353i
$298$	10.8988	−	5.55323i	0.631352	−	0.321690i
$299$	5.11416	−	10.0371i	0.295759	−	0.580461i
$300$	−0.355504	−	2.24456i	−0.0205250	−	0.129590i
$301$	−3.18556	+	3.18556i	−0.183612	+	0.183612i
$302$	20.3771	+	10.3826i	1.17257	+	0.597454i
$303$	−1.20228	+	0.873511i	−0.0690695	+	0.0501819i
$304$	−2.45329	−	4.81485i	−0.140706	−	0.276150i
$305$	3.10915	+	2.25893i	0.178030	+	0.129346i
$306$	−0.137827	+	0.870205i	−0.00787904	+	0.0497463i
$307$	6.74688	+	9.28628i	0.385065	+	0.529996i	0.956917	−	0.290360i	$-0.0937751\pi$
$307$	6.74688	+	9.28628i	0.385065	+	0.529996i	−0.571853	+	0.820356i	$0.693775\pi$
$308$	−1.75486	−	2.41535i	−0.0999922	−	0.137627i
$309$	1.13068	−	7.13881i	0.0643219	−	0.406113i
$310$	−26.2073	−	19.0407i	−1.48847	−	1.08144i
$311$	−8.36318	−	16.4137i	−0.474232	−	0.930733i	−0.996936	−	0.0782190i	$-0.975077\pi$
$311$	−8.36318	−	16.4137i	−0.474232	−	0.930733i	0.522704	−	0.852514i	$-0.324923\pi$
$312$	−5.09343	+	3.70059i	−0.288358	+	0.209505i
$313$	−12.8108	−	6.52744i	−0.724110	−	0.368953i	0.0527652	−	0.998607i	$-0.483197\pi$
$313$	−12.8108	−	6.52744i	−0.724110	−	0.368953i	−0.776875	+	0.629654i	$0.783197\pi$
$314$	9.97659	−	9.97659i	0.563012	−	0.563012i
$315$	2.11506	+	13.3540i	0.119170	+	0.752410i
$316$	1.51036	−	2.96424i	0.0849642	−	0.166752i
$317$	−21.3431	+	10.8749i	−1.19875	+	0.610794i	−0.935292	−	0.353877i	$-0.884863\pi$
$317$	−21.3431	+	10.8749i	−1.19875	+	0.610794i	−0.263459	+	0.964671i	$0.584863\pi$
$318$	0.411117	−	1.26529i	0.0230543	−	0.0709539i
$319$			43.3469i			2.42696i
$320$	−29.1581	−	9.47406i	−1.62999	−	0.529616i
$321$	0.289198	+	0.0458044i	0.0161414	+	0.00255655i
$322$	10.0504	−	1.59183i	0.560087	−	0.0887091i
$323$	−0.509925	+	0.165685i	−0.0283730	+	0.00921894i
$324$	−0.352634	−	1.08530i	−0.0195908	−	0.0602942i
$325$	−11.8426	−	11.8426i	−0.656910	−	0.656910i
$326$	1.48387	−	2.04237i	0.0821838	−	0.113116i
$327$	−0.0234550			−0.00129707
$328$	−15.1486	−	12.1337i	−0.836442	−	0.669972i
$329$	10.9454			0.603441
$330$	−9.86170	+	13.5735i	−0.542869	+	0.747195i
$331$	−0.797529	−	0.797529i	−0.0438362	−	0.0438362i	0.684849	−	0.728685i	$-0.259868\pi$
$331$	−0.797529	−	0.797529i	−0.0438362	−	0.0438362i	−0.728685	+	0.684849i	$0.759868\pi$
$332$	1.17787	+	3.62511i	0.0646439	+	0.198954i
$333$	15.9351	−	5.17764i	0.873241	−	0.283733i
$334$	5.79252	−	0.917445i	0.316953	−	0.0502004i
$335$	34.7673	+	5.50660i	1.89954	+	0.300858i
$336$	−4.32522	−	1.40535i	−0.235960	−	0.0766680i
$337$			9.36237i			0.510001i	0.966941	+	0.255000i	$0.0820756\pi$
$337$			9.36237i			0.510001i	−0.966941	+	0.255000i	$0.917924\pi$
$338$	2.78574	−	8.57362i	0.151524	−	0.466343i
$339$	3.54091	−	1.80418i	0.192316	−	0.0979898i
$340$	−0.184540	+	0.362180i	−0.0100081	+	0.0196420i
$341$	−5.18142	−	32.7142i	−0.280590	−	1.77157i
$342$	−3.57743	+	3.57743i	−0.193446	+	0.193446i
$343$	−16.9561	−	8.63958i	−0.915545	−	0.466494i
$344$	−6.39469	+	4.64601i	−0.344779	+	0.250496i
$345$	6.20373	+	12.1755i	0.333998	+	0.655507i
$346$	3.55458	+	2.58255i	0.191095	+	0.138839i
$347$	−1.06889	+	6.74870i	−0.0573810	+	0.362289i	0.942245	+	0.334926i	$0.108711\pi$
$347$	−1.06889	+	6.74870i	−0.0573810	+	0.362289i	−0.999626	+	0.0273636i	$0.991289\pi$
$348$	−1.87523	−	2.58103i	−0.100523	−	0.138358i
$349$	2.17419	+	2.99251i	0.116382	+	0.160185i	0.863233	−	0.504805i	$-0.168436\pi$
$349$	2.17419	+	2.99251i	0.116382	+	0.160185i	−0.746852	+	0.664990i	$0.768436\pi$
$350$	2.36663	−	14.9423i	0.126502	−	0.798702i
$351$	8.85441	+	6.43311i	0.472614	+	0.343374i
$352$	−4.37170	−	8.57994i	−0.233012	−	0.457312i
$353$	−2.84588	+	2.06765i	−0.151471	+	0.110050i	−0.660939	−	0.750439i	$-0.729842\pi$
$353$	−2.84588	+	2.06765i	−0.151471	+	0.110050i	0.509469	+	0.860489i	$0.329842\pi$
$354$	−3.19282	−	1.62682i	−0.169697	−	0.0864647i
$355$	−1.30244	+	1.30244i	−0.0691263	+	0.0691263i
$356$	−0.882778	−	5.57364i	−0.0467872	−	0.295403i
$357$	−0.204855	+	0.402051i	−0.0108421	+	0.0212788i
$358$	−18.0260	+	9.18472i	−0.952705	+	0.485428i
$359$	−4.61076	+	14.1905i	−0.243347	+	0.748944i	0.752557	+	0.658527i	$0.228820\pi$
$359$	−4.61076	+	14.1905i	−0.243347	+	0.748944i	−0.995904	+	0.0904171i	$0.971180\pi$
$360$			23.7220i			1.25026i
$361$	15.1419	+	4.91991i	0.796944	+	0.258943i
$362$	−3.05239	−	0.483452i	−0.160430	−	0.0254097i
$363$	−7.65696	+	1.21274i	−0.401886	+	0.0636525i
$364$	1.54013	−	0.500418i	0.0807247	−	0.0262290i
$365$	9.12518	+	28.0844i	0.477634	+	1.47001i
$366$	0.855788	+	0.855788i	0.0447327	+	0.0447327i
$367$	−10.3592	+	14.2583i	−0.540748	+	0.744276i	−0.988721	−	0.149771i	$-0.952146\pi$
$367$	−10.3592	+	14.2583i	−0.540748	+	0.744276i	0.447972	+	0.894047i	$0.352146\pi$
$368$	14.2770			0.744242
$369$	−5.13497	+	13.5936i	−0.267316	+	0.707656i
$370$	−32.3489			−1.68174
$371$	−1.24400	+	1.71222i	−0.0645854	+	0.0888942i
$372$	1.72377	+	1.72377i	0.0893732	+	0.0893732i
$373$	0.925209	+	2.84750i	0.0479055	+	0.147438i	0.972148	−	0.234368i	$-0.0753022\pi$
$373$	0.925209	+	2.84750i	0.0479055	+	0.147438i	−0.924242	+	0.381806i	$0.875302\pi$
$374$	1.65413	−	0.537460i	0.0855330	−	0.0277914i
$375$	5.50919	−	0.872570i	0.284493	−	0.0450593i
$376$	18.9677	+	3.00418i	0.978183	+	0.154929i
$377$	−22.3610	−	7.26554i	−1.15165	−	0.374194i
$378$			9.88640i			0.508502i
$379$	9.87141	−	30.3811i	0.507060	−	1.56057i	−0.290220	−	0.956960i	$-0.593728\pi$
$379$	9.87141	−	30.3811i	0.507060	−	1.56057i	0.797280	−	0.603610i	$-0.206272\pi$
$380$	−2.07975	+	1.05968i	−0.106689	+	0.0543606i
$381$	−8.12359	+	15.9434i	−0.416184	+	0.816807i
$382$	1.28804	+	8.13236i	0.0659018	+	0.416088i
$383$	1.77733	−	1.77733i	0.0908173	−	0.0908173i	−0.660239	−	0.751056i	$-0.729545\pi$
$383$	1.77733	−	1.77733i	0.0908173	−	0.0908173i	0.751056	+	0.660239i	$0.229545\pi$
$384$	−5.32856	−	2.71504i	−0.271922	−	0.138551i
$385$	21.5928	−	15.6881i	1.10047	−	0.799540i
$386$	0.727631	+	1.42806i	0.0370354	+	0.0726861i
$387$	4.78760	+	3.47839i	0.243367	+	0.176817i
$388$	−0.596354	+	3.76523i	−0.0302753	+	0.191151i
$389$	−20.3807	−	28.0517i	−1.03334	−	1.42228i	−0.902406	−	0.430886i	$-0.858201\pi$
$389$	−20.3807	−	28.0517i	−1.03334	−	1.42228i	−0.130938	−	0.991391i	$-0.541799\pi$
$390$	−5.34908	−	7.36238i	−0.270861	−	0.372809i
$391$	0.221600	−	1.39913i	0.0112068	−	0.0707568i
$392$	−9.84665	−	7.15401i	−0.497331	−	0.361332i
$393$	−5.60355	−	10.9976i	−0.282662	−	0.554755i
$394$	−3.48560	+	2.53244i	−0.175602	+	0.127582i
$395$	26.4998	+	13.5023i	1.33335	+	0.679376i
$396$	−2.77311	+	2.77311i	−0.139354	+	0.139354i
$397$	5.37624	+	33.9443i	0.269826	+	1.70361i	0.634867	+	0.772622i	$0.281055\pi$
$397$	5.37624	+	33.9443i	0.269826	+	1.70361i	−0.365041	+	0.930992i	$0.618945\pi$
$398$	4.46818	−	8.76931i	0.223970	−	0.439566i
$399$	−2.30869	+	1.17634i	−0.115579	+	0.0588906i
$400$	6.55927	−	20.1874i	0.327963	−	1.00937i
$401$		−	8.02435i		−	0.400717i	−0.979723	−	0.200359i	$-0.935789\pi$
$401$		−	8.02435i		−	0.400717i	0.979723	−	0.200359i	$-0.0642107\pi$
$402$	10.5428	+	3.42555i	0.525825	+	0.170851i
$403$	17.7445	+	2.81045i	0.883917	+	0.139999i
$404$	0.662414	−	0.104916i	0.0329563	−	0.00521977i
$405$	9.70236	−	3.15249i	0.482114	−	0.156648i
$406$	−6.56302	−	20.1989i	−0.325717	−	1.00246i
$407$	−23.3882	−	23.3882i	−1.15931	−	1.15931i
$408$	−0.465351	+	0.640500i	−0.0230383	+	0.0317095i
$409$	6.97227			0.344757			0.172378	−	0.985031i	$-0.444855\pi$
$409$	6.97227			0.344757			0.172378	+	0.985031i	$0.444855\pi$
$410$	17.5389	−	21.8968i	0.866184	−	1.08141i
$411$	−0.808413			−0.0398760
$412$	−1.91727	+	2.63890i	−0.0944573	+	0.130009i
$413$	4.03086	+	4.03086i	0.198346	+	0.198346i
$414$	−4.13053	−	12.7125i	−0.203004	−	0.624783i
$415$	−32.4078	+	10.5299i	−1.59084	+	0.516894i
$416$	5.15883	−	0.817078i	0.252932	−	0.0400606i
$417$	6.39855	+	1.01343i	0.313338	+	0.0496279i
$418$	9.49850	+	3.08625i	0.464587	+	0.150953i
$419$			15.4578i			0.755163i	0.925976	+	0.377581i	$0.123244\pi$
$419$			15.4578i			0.755163i	−0.925976	+	0.377581i	$0.876756\pi$
$420$	−0.607032	+	1.86825i	−0.0296201	+	0.0911614i
$421$	−19.0239	+	9.69316i	−0.927168	+	0.472416i	−0.851286	−	0.524701i	$-0.824177\pi$
$421$	−19.0239	+	9.69316i	−0.927168	+	0.472416i	−0.0758813	+	0.997117i	$0.524177\pi$
$422$	−8.77455	+	17.2210i	−0.427139	+	0.838307i
$423$	−2.24918	−	14.2008i	−0.109359	−	0.690466i
$424$	−2.62572	+	2.62572i	−0.127516	+	0.127516i
$425$	−1.87652	−	0.956133i	−0.0910245	−	0.0463793i
$426$	−0.469274	+	0.340948i	−0.0227364	+	0.0165190i
$427$	−0.874071	−	1.71546i	−0.0422993	−	0.0830170i
$428$	−0.106904	−	0.0776700i	−0.00516738	−	0.00375432i
$429$	1.45561	−	9.19036i	0.0702775	−	0.443715i
$430$	−6.71566	−	9.24332i	−0.323858	−	0.445752i
$431$	−5.97602	−	8.22528i	−0.287855	−	0.396198i	0.640461	−	0.767991i	$-0.278743\pi$
$431$	−5.97602	−	8.22528i	−0.287855	−	0.396198i	−0.928316	+	0.371793i	$0.878743\pi$
$432$	−2.16993	+	13.7004i	−0.104401	+	0.659160i
$433$	−16.6045	−	12.0639i	−0.797962	−	0.579754i	0.112353	−	0.993668i	$-0.464161\pi$
$433$	−16.6045	−	12.0639i	−0.797962	−	0.579754i	−0.910316	+	0.413915i	$0.864161\pi$
$434$	7.36762	+	14.4598i	0.353657	+	0.694091i
$435$	23.0740	−	16.7642i	1.10631	−	0.803782i
$436$	0.00943141	+	0.00480554i	0.000451683	+	0.000230144i
$437$	5.75184	−	5.75184i	0.275148	−	0.275148i
$438$	1.45475	+	9.18492i	0.0695106	+	0.438873i
$439$	−1.86410	+	3.65850i	−0.0889687	+	0.174611i	−0.931203	−	0.364500i	$-0.881240\pi$
$439$	−1.86410	+	3.65850i	−0.0889687	+	0.174611i	0.842235	+	0.539111i	$0.181240\pi$
$440$	41.7248	−	21.2599i	1.98915	−	1.01352i
$441$	−2.81586	+	8.66633i	−0.134089	+	0.412682i
$442$			0.943390i			0.0448725i
$443$	6.70132	+	2.17739i	0.318389	+	0.103451i	0.463852	−	0.885913i	$-0.346467\pi$
$443$	6.70132	+	2.17739i	0.318389	+	0.103451i	−0.145463	+	0.989364i	$0.546467\pi$
$444$	2.40441	+	0.380822i	0.114108	+	0.0180730i
$445$	49.8274	−	7.89189i	2.36205	−	0.374111i
$446$	−3.52420	+	1.14508i	−0.166875	+	0.0542211i
$447$	−2.54296	−	7.82643i	−0.120278	−	0.370177i
$448$	10.8606	+	10.8606i	0.513116	+	0.513116i
$449$	−8.08754	+	11.1316i	−0.381675	+	0.525330i	−0.956027	−	0.293278i	$-0.905254\pi$
$449$	−8.08754	+	11.1316i	−0.381675	+	0.525330i	0.574352	+	0.818608i	$0.305254\pi$
$450$	−19.8728			−0.936811
$451$	28.5119	−	3.15078i	1.34257	−	0.148364i
$452$	−1.79347			−0.0843577
$453$	9.04353	−	12.4474i	0.424902	−	0.584828i
$454$	−14.9313	−	14.9313i	−0.700762	−	0.700762i
$455$	4.47365	+	13.7685i	0.209728	+	0.645477i
$456$	−4.32368	+	1.40485i	−0.202475	+	0.0657880i
$457$	−1.52547	+	0.241611i	−0.0713587	+	0.0113021i	−0.192012	−	0.981393i	$-0.561501\pi$
$457$	−1.52547	+	0.241611i	−0.0713587	+	0.0113021i	0.120653	+	0.992695i	$0.461501\pi$
$458$	15.5753	+	2.46689i	0.727787	+	0.115270i
$459$	1.30893	+	0.425298i	0.0610958	+	0.0198512i
$460$		−	6.16689i		−	0.287533i
$461$	−9.62660	+	29.6276i	−0.448355	+	1.37990i	0.430407	+	0.902635i	$0.358370\pi$
$461$	−9.62660	+	29.6276i	−0.448355	+	1.37990i	−0.878762	+	0.477261i	$0.841630\pi$
$462$	7.48910	−	3.81589i	0.348424	−	0.177531i
$463$	−13.9772	+	27.4318i	−0.649577	+	1.27487i	0.297764	+	0.954639i	$0.403759\pi$
$463$	−13.9772	+	27.4318i	−0.649577	+	1.27487i	−0.947341	+	0.320227i	$0.896241\pi$
$464$	−4.66153	−	29.4317i	−0.216406	−	1.36633i
$465$	−15.4102	+	15.4102i	−0.714630	+	0.714630i
$466$	3.44962	+	1.75767i	0.159801	+	0.0814224i
$467$	−0.689868	+	0.501219i	−0.0319233	+	0.0231936i	−0.603632	−	0.797263i	$-0.706281\pi$
$467$	−0.689868	+	0.501219i	−0.0319233	+	0.0231936i	0.571709	+	0.820456i	$0.306281\pi$
$468$	−0.965733	−	1.89536i	−0.0446410	−	0.0876129i
$469$	−14.2667	−	10.3654i	−0.658777	−	0.478629i
$470$	−4.34245	+	27.4172i	−0.200302	+	1.26466i
$471$	−5.57923	−	7.67915i	−0.257077	−	0.353837i
$472$	5.87886	+	8.09156i	0.270596	+	0.372444i
$473$	1.82749	−	11.5383i	0.0840280	−	0.530532i
$474$	7.57733	+	5.50525i	0.348038	+	0.252865i
$475$	−5.49040	−	10.7755i	−0.251917	−	0.494414i
$476$	0.164747	−	0.119696i	0.00755117	−	0.00548624i
$477$	2.47710	+	1.26214i	0.113419	+	0.0577896i
$478$	−12.3070	+	12.3070i	−0.562911	+	0.562911i
$479$	−0.752997	−	4.75424i	−0.0344053	−	0.217227i	0.964496	−	0.264099i	$-0.0850746\pi$
$479$	−0.752997	−	4.75424i	−0.0344053	−	0.217227i	−0.998901	+	0.0468724i	$0.985075\pi$
$480$	−2.87645	+	5.64535i	−0.131291	+	0.257674i
$481$	15.9853	−	8.14491i	0.728866	−	0.371376i
$482$	−5.18426	+	15.9555i	−0.236137	+	0.726754i
$483$		−	6.84577i		−	0.311493i
$484$	3.32738	+	1.08113i	0.151245	+	0.0491423i
$485$	−33.6605	−	5.33131i	−1.52845	−	0.242082i
$486$	20.1294	−	3.18819i	0.913089	−	0.144619i
$487$	−35.1859	+	11.4326i	−1.59442	+	0.518060i	−0.965720	−	0.259585i	$-0.916414\pi$
$487$	−35.1859	+	11.4326i	−1.59442	+	0.518060i	−0.628704	+	0.777645i	$0.716414\pi$
$488$	−1.04386	−	3.21268i	−0.0472535	−	0.145431i
$489$	−1.20094	−	1.20094i	−0.0543082	−	0.0543082i
$490$	10.3409	−	14.2330i	0.467154	−	0.642982i
$491$	16.4508			0.742413			0.371206	−	0.928550i	$-0.378944\pi$
$491$	16.4508			0.742413			0.371206	+	0.928550i	$0.378944\pi$
$492$	−1.56140	+	1.42106i	−0.0703932	+	0.0640664i
$493$	−2.95661			−0.133159
$494$	−3.18416	+	4.38262i	−0.143262	+	0.197184i
$495$	−24.7912	−	24.7912i	−1.11428	−	1.11428i
$496$	7.03618	+	21.6551i	0.315934	+	0.972344i
$497$	0.877595	−	0.285148i	0.0393655	−	0.0127906i
$498$	−10.5989	+	1.67870i	−0.474947	+	0.0752243i
$499$	−2.45675	−	0.389111i	−0.109979	−	0.0174190i	0.101202	−	0.994866i	$-0.467731\pi$
$499$	−2.45675	−	0.389111i	−0.109979	−	0.0174190i	−0.211181	+	0.977447i	$0.567731\pi$
$500$	−2.39405	−	0.777875i	−0.107065	−	0.0347876i
$501$		−	3.94554i		−	0.176274i
$502$	−8.18505	+	25.1910i	−0.365317	+	1.12433i
$503$	−31.9595	+	16.2842i	−1.42501	+	0.726076i	−0.985102	−	0.171969i	$-0.944987\pi$
$503$	−31.9595	+	16.2842i	−1.42501	+	0.726076i	−0.439903	+	0.898045i	$0.644987\pi$
$504$	5.39528	−	10.5888i	0.240325	−	0.471664i
$505$	0.937931	+	5.92187i	0.0417374	+	0.263520i
$506$	−18.6582	+	18.6582i	−0.829459	+	0.829459i
$507$	−5.40377	−	2.75336i	−0.239990	−	0.122281i
$508$	6.53309	−	4.74657i	0.289859	−	0.210595i
$509$	−2.56872	−	5.04140i	−0.113857	−	0.223456i	0.827045	−	0.562135i	$-0.190020\pi$
$509$	−2.56872	−	5.04140i	−0.113857	−	0.223456i	−0.940902	+	0.338679i	$0.890020\pi$
$510$	−0.925822	−	0.672649i	−0.0409961	−	0.0297854i
$511$	2.31423	−	14.6115i	0.102376	−	0.646374i
$512$	14.8651	+	20.4600i	0.656949	+	0.904213i
$513$	4.64532	+	6.39373i	0.205096	+	0.282290i
$514$	3.63797	−	22.9692i	0.160464	−	1.01313i
$515$	−23.5913	−	17.1401i	−1.03956	−	0.755283i
$516$	0.390343	+	0.766091i	0.0171839	+	0.0337253i
$517$	−22.9621	+	16.6830i	−1.00987	+	0.733715i
$518$	14.4397	+	7.35737i	0.634442	+	0.323264i
$519$	2.09013	−	2.09013i	0.0917467	−	0.0917467i
$520$	3.97351	+	25.0877i	0.174250	+	1.10017i
$521$	15.5944	−	30.6057i	0.683203	−	1.34086i	−0.245268	−	0.969455i	$-0.578876\pi$
$521$	15.5944	−	30.6057i	0.683203	−	1.34086i	0.928471	−	0.371405i	$-0.121124\pi$
$522$	−24.8578	+	12.6657i	−1.08800	+	0.554361i
$523$	1.50152	−	4.62119i	0.0656567	−	0.202070i	−0.912846	−	0.408304i	$-0.866120\pi$
$523$	1.50152	−	4.62119i	0.0656567	−	0.202070i	0.978503	+	0.206233i	$0.0661205\pi$
$524$			5.57027i			0.243338i
$525$	−9.67973	−	3.14514i	−0.422458	−	0.137265i
$526$	27.0241	+	4.28019i	1.17831	+	0.186625i
$527$	2.23138	−	0.353416i	0.0972004	−	0.0153950i
$528$	11.2158	−	3.64423i	0.488104	−	0.158595i
$529$	−0.466276	−	1.43505i	−0.0202729	−	0.0623934i
$530$	−3.79540	−	3.79540i	−0.164862	−	0.164862i
$531$	4.40140	−	6.05801i	0.191005	−	0.262895i
$532$	1.16935			0.0506978
$533$	−3.15363	+	15.2364i	−0.136599	+	0.659960i
$534$	15.8871			0.687503
$535$	0.694356	−	0.955700i	0.0300196	−	0.0413185i
$536$	−21.8783	−	21.8783i	−0.944999	−	0.944999i
$537$	4.20591	+	12.9445i	0.181498	+	0.558595i
$538$	3.56457	−	1.15820i	0.153679	−	0.0499335i
$539$	17.7669	−	2.81399i	0.765273	−	0.121207i
$540$	5.91781	+	0.937288i	0.254662	+	0.0403345i
$541$	26.4078	+	8.58041i	1.13536	+	0.368901i	0.815610	−	0.578601i	$-0.196401\pi$
$541$	26.4078	+	8.58041i	1.13536	+	0.368901i	0.319749	+	0.947502i	$0.396401\pi$
$542$		−	14.2696i		−	0.612931i
$543$	−0.642482	+	1.97736i	−0.0275716	+	0.0848565i
$544$	0.585223	−	0.298186i	0.0250912	−	0.0127846i
$545$	−0.0429608	+	0.0843152i	−0.00184024	+	0.00361167i
$546$	0.713196	+	4.50294i	0.0305220	+	0.192708i
$547$	28.2679	−	28.2679i	1.20865	−	1.20865i	0.237183	−	0.971465i	$-0.423776\pi$
$547$	28.2679	−	28.2679i	1.20865	−	1.20865i	0.971465	−	0.237183i	$-0.0762240\pi$
$548$	0.325068	+	0.165630i	0.0138862	+	0.00707537i
$549$	−2.04605	+	1.48655i	−0.0873235	+	0.0634442i
$550$	17.8101	+	34.9544i	0.759427	+	1.49046i
$551$	−13.7353	−	9.97927i	−0.585143	−	0.425131i
$552$	1.87895	−	11.8632i	0.0799736	−	0.504933i
$553$	−8.75782	−	12.0541i	−0.372420	−	0.512593i
$554$	−22.1295	−	30.4587i	−0.940194	−	1.29407i
$555$	−3.40448	+	21.4950i	−0.144512	+	0.912414i
$556$	−2.36526	−	1.71846i	−0.100309	−	0.0728790i
$557$	5.77051	+	11.3253i	0.244504	+	0.479867i	0.980346	−	0.197287i	$-0.0632131\pi$
$557$	5.77051	+	11.3253i	0.244504	+	0.479867i	−0.735841	+	0.677154i	$0.763213\pi$
$558$	17.2464	−	12.5302i	0.730097	−	0.530446i
$559$	5.64587	+	2.87671i	0.238795	+	0.121672i
$560$	−12.9740	+	12.9740i	−0.548253	+	0.548253i
$561$	−0.183043	−	1.15569i	−0.00772810	−	0.0487933i
$562$	1.42183	−	2.79050i	0.0599763	−	0.117710i
$563$	7.15381	−	3.64505i	0.301497	−	0.153621i	−0.296697	−	0.954972i	$-0.595885\pi$
$563$	7.15381	−	3.64505i	0.301497	−	0.153621i	0.598194	+	0.801351i	$0.295885\pi$
$564$	0.645526	−	1.98673i	0.0271816	−	0.0836563i
$565$		−	16.0333i		−	0.674526i
$566$	−19.4437	−	6.31763i	−0.817278	−	0.265550i
$567$	−5.04785	−	0.799501i	−0.211990	−	0.0335759i
$568$	1.59908	−	0.253269i	0.0670958	−	0.0106269i
$569$	0.559666	−	0.181847i	0.0234624	−	0.00762341i	−0.297262	−	0.954796i	$-0.596074\pi$
$569$	0.559666	−	0.181847i	0.0234624	−	0.00762341i	0.320725	+	0.947172i	$0.396074\pi$
$570$	−2.03066	−	6.24974i	−0.0850551	−	0.261773i
$571$	23.7361	+	23.7361i	0.993324	+	0.993324i	0.999978	−	0.00665379i	$-0.00211798\pi$
$571$	23.7361	+	23.7361i	0.993324	+	0.993324i	−0.00665379	+	0.999978i	$0.502118\pi$
$572$	−2.46826	+	3.39727i	−0.103203	+	0.142047i
$573$	5.53930			0.231408
$574$	−12.8090	+	5.78512i	−0.534639	+	0.241466i
$575$	31.9517			1.33248
$576$	11.8590	−	16.3225i	0.494125	−	0.680104i
$577$	29.1837	+	29.1837i	1.21493	+	1.21493i	0.969385	+	0.245547i	$0.0789675\pi$
$577$	29.1837	+	29.1837i	1.21493	+	1.21493i	0.245547	+	0.969385i	$0.421033\pi$
$578$	−6.63781	−	20.4291i	−0.276097	−	0.849738i
$579$	1.02548	−	0.333200i	0.0426177	−	0.0138473i
$580$	−12.7129	+	2.01352i	−0.527874	+	0.0836070i
$581$	16.8608	+	2.67049i	0.699506	+	0.110791i
$582$	−10.2071	−	3.31650i	−0.423100	−	0.137473i
$583$		−	5.48813i		−	0.227295i
$584$	8.02082	−	24.6855i	0.331904	−	1.02149i
$585$	16.9442	−	8.63349i	0.700555	−	0.356951i
$586$	15.2687	−	29.9664i	0.630742	−	1.23790i
$587$	3.80777	+	24.0413i	0.157164	+	0.992292i	0.932612	+	0.360881i	$0.117524\pi$
$587$	3.80777	+	24.0413i	0.157164	+	0.992292i	−0.775448	+	0.631411i	$0.782476\pi$
$588$	−0.936167	+	0.936167i	−0.0386069	+	0.0386069i
$589$	11.5590	+	5.88959i	0.476279	+	0.242676i
$590$	−11.6961	+	8.49770i	−0.481520	+	0.349845i
$591$	1.31591	+	2.58261i	0.0541292	+	0.106234i
$592$	18.3953	+	13.3650i	0.756044	+	0.549298i
$593$	6.57408	−	41.5071i	0.269965	−	1.70449i	−0.364220	−	0.931313i	$-0.618664\pi$
$593$	6.57408	−	41.5071i	0.269965	−	1.70449i	0.634185	−	0.773181i	$-0.281336\pi$
$594$	−15.0688	−	20.7404i	−0.618280	−	0.850990i
$595$	1.07006	+	1.47281i	0.0438681	+	0.0603793i
$596$	−0.580964	+	3.66806i	−0.0237972	+	0.150250i
$597$	−5.35674	−	3.89190i	−0.219237	−	0.159285i
$598$	−6.49770	−	12.7525i	−0.265711	−	0.521487i
$599$	13.7976	−	10.0245i	0.563755	−	0.409592i	−0.269076	−	0.963119i	$-0.586718\pi$
$599$	13.7976	−	10.0245i	0.563755	−	0.409592i	0.832831	+	0.553527i	$0.186718\pi$
$600$	−15.9111	−	8.10710i	−0.649567	−	0.330971i
$601$	−17.8450	+	17.8450i	−0.727912	+	0.727912i	−0.970203	−	0.242292i	$-0.922101\pi$
$601$	−17.8450	+	17.8450i	−0.727912	+	0.727912i	0.242292	+	0.970203i	$0.422101\pi$
$602$	0.895403	+	5.65335i	0.0364939	+	0.230413i
$603$	−10.5166	+	20.6399i	−0.428267	+	0.840522i
$604$	−6.18671	+	3.15229i	−0.251734	+	0.128265i
$605$	−9.66513	+	29.7462i	−0.392944	+	1.20936i
$606$			1.88815i			0.0767006i
$607$	−0.0810629	−	0.0263389i	−0.00329024	−	0.00106906i	0.307371	−	0.951590i	$-0.400551\pi$
$607$	−0.0810629	−	0.0263389i	−0.00329024	−	0.00106906i	−0.310662	+	0.950521i	$0.600551\pi$
$608$	3.72517	+	0.590008i	0.151075	+	0.0239280i
$609$	−14.1124	+	2.23518i	−0.571862	+	0.0905741i
$610$	4.64383	−	1.50887i	0.188023	−	0.0610924i
$611$	−4.75734	−	14.6416i	−0.192461	−	0.592336i
$612$	−0.189149	−	0.189149i	−0.00764590	−	0.00764590i
$613$	−13.7750	+	18.9597i	−0.556369	+	0.765776i	−0.990859	−	0.134900i	$-0.956929\pi$
$613$	−13.7750	+	18.9597i	−0.556369	+	0.765776i	0.434490	+	0.900677i	$0.356929\pi$
$614$	14.5838			0.588553
$615$	−12.7041	−	13.9586i	−0.512277	−	0.562866i
$616$	−23.4601			−0.945233
$617$	−24.1173	+	33.1947i	−0.970927	+	1.33637i	−0.0293501	+	0.999569i	$0.509344\pi$
$617$	−24.1173	+	33.1947i	−0.970927	+	1.33637i	−0.941577	+	0.336797i	$0.890656\pi$
$618$	−6.49346	−	6.49346i	−0.261205	−	0.261205i
$619$	−8.20387	−	25.2489i	−0.329741	−	1.01484i	−0.969255	−	0.246059i	$-0.920864\pi$
$619$	−8.20387	−	25.2489i	−0.329741	−	1.01484i	0.639513	−	0.768780i	$-0.279136\pi$
$620$	9.35382	−	3.03924i	0.375658	−	0.122059i
$621$	−20.6231	+	3.26637i	−0.827575	+	0.131075i
$622$	−23.1169	−	3.66136i	−0.926904	−	0.146807i
$623$	−24.0365	−	7.80992i	−0.963001	−	0.312898i
$624$			6.39663i			0.256070i
$625$	−3.69513	+	11.3724i	−0.147805	+	0.454897i
$626$	−16.2766	+	8.29332i	−0.650542	+	0.331468i
$627$	3.05038	−	5.98671i	0.121820	−	0.239086i
$628$	0.670113	+	4.23092i	0.0267404	+	0.168832i
$629$	1.59527	−	1.59527i	0.0636075	−	0.0636075i
$630$	15.3058	+	7.79870i	0.609798	+	0.310708i
$631$	16.7720	−	12.1856i	0.667683	−	0.485100i	−0.201566	−	0.979475i	$-0.564603\pi$
$631$	16.7720	−	12.1856i	0.667683	−	0.485100i	0.869249	+	0.494375i	$0.164603\pi$
$632$	−11.8682	−	23.2927i	−0.472093	−	0.926534i
$633$	10.5195	+	7.64285i	0.418112	+	0.303776i
$634$	−4.76097	+	30.0596i	−0.189082	+	1.19382i
$635$	42.4335	+	58.4047i	1.68392	+	2.31772i
$636$	0.237422	+	0.326783i	0.00941438	+	0.0129578i
$637$	−1.52634	+	9.63693i	−0.0604758	+	0.381829i
$638$	44.5555	+	32.3714i	1.76397	+	1.28160i
$639$	−0.550293	−	1.08001i	−0.0217693	−	0.0427246i
$640$	−19.5198	+	14.1820i	−0.771588	+	0.560592i
$641$	9.14683	+	4.66054i	0.361278	+	0.184080i	0.625202	−	0.780463i	$-0.285017\pi$
$641$	9.14683	+	4.66054i	0.361278	+	0.184080i	−0.263924	+	0.964544i	$0.585017\pi$
$642$	0.263054	−	0.263054i	0.0103819	−	0.0103819i
$643$	−6.58374	−	41.5681i	−0.259637	−	1.63929i	−0.680921	−	0.732357i	$-0.738420\pi$
$643$	−6.58374	−	41.5681i	−0.259637	−	1.63929i	0.421284	−	0.906929i	$-0.361580\pi$
$644$	−1.40258	+	2.75272i	−0.0552695	+	0.108473i
$645$	−6.84872	+	3.48960i	−0.269668	+	0.137403i
$646$	−0.210508	+	0.647876i	−0.00828232	+	0.0254904i
$647$		−	15.8237i		−	0.622093i	−0.950395	−	0.311046i	$-0.899321\pi$
$647$		−	15.8237i		−	0.622093i	0.950395	−	0.311046i	$-0.100679\pi$
$648$	−8.52814	−	2.77096i	−0.335017	−	0.108854i
$649$	−14.6001	−	2.31242i	−0.573102	−	0.0907705i
$650$	−21.0169	+	3.32875i	−0.824350	+	0.130564i
$651$	10.3835	−	3.37381i	0.406963	−	0.132230i
$652$	0.236852	+	0.728955i	0.00927583	+	0.0285481i
$653$	−27.7138	−	27.7138i	−1.08452	−	1.08452i	−0.996081	−	0.0884422i	$-0.971811\pi$
$653$	−27.7138	−	27.7138i	−1.08452	−	1.08452i	−0.0884422	−	0.996081i	$-0.528189\pi$
$654$	−0.0175162	+	0.0241090i	−0.000684939	+	0.000942737i
$655$	−49.7972			−1.94574
$656$	−19.0203	+	5.20550i	−0.742616	+	0.203241i
$657$	−19.4328			−0.758144
$658$	8.17404	−	11.2506i	0.318657	−	0.438594i
$659$	25.4024	+	25.4024i	0.989538	+	0.989538i	0.999946	−	0.0104074i	$-0.00331284\pi$
$659$	25.4024	+	25.4024i	0.989538	+	0.989538i	−0.0104074	+	0.999946i	$0.503313\pi$
$660$	−1.57410	−	4.84459i	−0.0612719	−	0.188576i
$661$	23.3250	−	7.57876i	0.907238	−	0.294779i	0.182017	−	0.983295i	$-0.441738\pi$
$661$	23.3250	−	7.57876i	0.907238	−	0.294779i	0.725221	+	0.688516i	$0.241738\pi$
$662$	−1.41536	+	0.224171i	−0.0550096	+	0.00871266i
$663$	0.626858	+	0.0992846i	0.0243452	+	0.00385590i
$664$	28.4857	+	9.25557i	1.10546	+	0.359186i
$665$			10.4538i			0.405381i
$666$	6.57836	−	20.2461i	0.254906	−	0.784521i
$667$	39.9666	−	20.3640i	1.54751	−	0.788498i
$668$	−0.808375	+	1.58652i	−0.0312770	+	0.0613845i
$669$	0.389982	+	2.46225i	0.0150776	+	0.0951960i
$670$	31.6244	−	31.6244i	1.22176	−	1.22176i
$671$	4.44839	+	2.26657i	0.171728	+	0.0874998i
$672$	2.56793	−	1.86571i	0.0990601	−	0.0719714i
$673$	3.77384	+	7.40657i	0.145471	+	0.285502i	0.952232	−	0.305375i	$-0.0987818\pi$
$673$	3.77384	+	7.40657i	0.145471	+	0.285502i	−0.806762	+	0.590877i	$0.798782\pi$
$674$	9.62341	+	6.99182i	0.370680	+	0.269315i
$675$	−4.85625	+	30.6611i	−0.186917	+	1.18015i
$676$	1.60877	+	2.21428i	0.0618758	+	0.0851648i
$677$	23.9553	+	32.9717i	0.920678	+	1.26720i	0.963386	+	0.268117i	$0.0864015\pi$
$677$	23.9553	+	32.9717i	0.920678	+	1.26720i	−0.0427079	+	0.999088i	$0.513598\pi$
$678$	0.789864	−	4.98700i	0.0303345	−	0.191525i
$679$	13.8126	+	10.0354i	0.530078	+	0.385124i
$680$	1.45010	+	2.84598i	0.0556087	+	0.109138i
$681$	−11.4929	+	8.35008i	−0.440409	+	0.319976i
$682$	−37.4958	−	19.1051i	−1.43579	−	0.731571i
$683$	26.6543	−	26.6543i	1.01990	−	1.01990i	0.0201019	−	0.999798i	$-0.493601\pi$
$683$	26.6543	−	26.6543i	1.01990	−	1.01990i	0.999798	−	0.0201019i	$-0.00639908\pi$
$684$	−0.240291	−	1.51714i	−0.00918775	−	0.0580092i
$685$	−1.48071	+	2.90605i	−0.0565749	+	0.111034i
$686$	−21.5433	+	10.9769i	−0.822527	+	0.419099i
$687$	3.27837	−	10.0898i	0.125077	−	0.384949i
$688$			8.03083i			0.306172i
$689$	2.83112	+	0.919887i	0.107857	+	0.0350449i
$690$	17.1479	+	2.71597i	0.652811	+	0.103395i
$691$	−46.6639	+	7.39084i	−1.77518	+	0.281161i	−0.956211	−	0.292678i	$-0.905454\pi$
$691$	−46.6639	+	7.39084i	−1.77518	+	0.281161i	−0.818968	+	0.573839i	$0.805454\pi$
$692$	−1.26869	+	0.412222i	−0.0482283	+	0.0156703i
$693$	5.42762	+	16.7045i	0.206178	+	0.634552i
$694$	6.13862	+	6.13862i	0.233019	+	0.233019i
$695$	15.3628	−	21.1450i	0.582743	−	0.802077i
$696$	−25.0693			−0.950248
$697$	0.214909	+	1.94475i	0.00814027	+	0.0736626i
$698$	4.69963			0.177884
$699$	1.53097	−	2.10720i	0.0579067	−	0.0797017i
$700$	3.24789	+	3.24789i	0.122759	+	0.122759i
$701$	−7.16445	−	22.0499i	−0.270597	−	0.832813i	−0.990351	−	0.138583i	$-0.955745\pi$
$701$	−7.16445	−	22.0499i	−0.270597	−	0.832813i	0.719753	−	0.694230i	$-0.244255\pi$
$702$	13.2250	−	4.29705i	0.499144	−	0.162182i
$703$	12.7954	−	2.02659i	0.482588	−	0.0764344i
$704$	−39.3379	−	6.23051i	−1.48260	−	0.234821i
$705$	17.7610	+	5.77090i	0.668918	+	0.217345i
$706$			4.46935i			0.168206i
$707$	0.928190	−	2.85667i	0.0349082	−	0.107436i
$708$	0.969377	−	0.493922i	0.0364314	−	0.0185627i
$709$	3.28431	−	6.44583i	0.123345	−	0.242078i	−0.821074	−	0.570821i	$-0.806625\pi$
$709$	3.28431	−	6.44583i	0.123345	−	0.242078i	0.944419	+	0.328743i	$0.106625\pi$
$710$	0.366092	+	2.31141i	0.0137392	+	0.0867458i
$711$	−13.8396	+	13.8396i	−0.519024	+	0.519024i
$712$	−39.5100	−	20.1313i	−1.48070	−	0.754454i
$713$	−27.7289	+	20.1462i	−1.03846	+	0.754482i
$714$	0.260275	+	0.510819i	0.00974055	+	0.0191169i
$715$	−30.3710	−	22.0658i	−1.13581	−	0.825215i
$716$	0.960881	−	6.06677i	0.0359098	−	0.226726i
$717$	6.88249	+	9.47294i	0.257031	+	0.353773i
$718$	11.1428	+	15.3368i	0.415846	+	0.572363i
$719$	3.36289	−	21.2325i	0.125415	−	0.791837i	−0.842156	−	0.539235i	$-0.818714\pi$
$719$	3.36289	−	21.2325i	0.125415	−	0.791837i	0.967570	−	0.252602i	$-0.0812864\pi$
$720$	19.4988	+	14.1667i	0.726677	+	0.527962i
$721$	6.63219	+	13.0164i	0.246996	+	0.484757i
$722$	16.3651	−	11.8899i	0.609046	−	0.442497i
$723$	10.0564	+	5.12401i	0.374003	+	0.190564i
$724$	0.663474	−	0.663474i	0.0246578	−	0.0246578i
$725$	−10.4324	−	65.8676i	−0.387450	−	2.44626i
$726$	−4.47166	+	8.77613i	−0.165959	+	0.325713i
$727$	33.2699	−	16.9518i	1.23391	−	0.628709i	0.289406	−	0.957206i	$-0.406542\pi$
$727$	33.2699	−	16.9518i	1.23391	−	0.628709i	0.944505	+	0.328498i	$0.106542\pi$
$728$	3.93223	−	12.1022i	0.145738	−	0.448536i
$729$		−	4.83620i		−	0.179119i
$730$	35.6821	+	11.5938i	1.32066	+	0.429107i
$731$	0.787008	+	0.124650i	0.0291085	+	0.00461034i
$732$	−0.362927	+	0.0574819i	−0.0134142	+	0.00212459i
$733$	12.3995	−	4.02883i	0.457984	−	0.148808i	−0.0709338	−	0.997481i	$-0.522598\pi$
$733$	12.3995	−	4.02883i	0.457984	−	0.148808i	0.528918	+	0.848673i	$0.322598\pi$
$734$	6.91954	+	21.2962i	0.255405	+	0.786056i
$735$	−8.36917	−	8.36917i	−0.308702	−	0.308702i
$736$	−5.85708	+	8.06158i	−0.215895	+	0.297154i
$737$	45.7287			1.68444
$738$	10.1378	+	15.4299i	0.373179	+	0.567981i
$739$	−7.51921			−0.276599			−0.138299	−	0.990390i	$-0.544164\pi$
$739$	−7.51921			−0.276599			−0.138299	+	0.990390i	$0.544164\pi$
$740$	5.77294	−	7.94577i	0.212217	−	0.292092i
$741$	2.57703	+	2.57703i	0.0946696	+	0.0946696i
$742$	0.830942	+	2.55738i	0.0305048	+	0.0938842i
$743$	−24.0292	+	7.80755i	−0.881545	+	0.286431i	−0.714599	−	0.699535i	$-0.753391\pi$
$743$	−24.0292	+	7.80755i	−0.881545	+	0.286431i	−0.166946	+	0.985966i	$0.553391\pi$
$744$	18.9200	−	2.99663i	0.693639	−	0.109862i
$745$	−32.7919	−	5.19372i	−1.20140	−	0.190283i
$746$	3.61784	+	1.17551i	0.132459	+	0.0430384i
$747$		−	22.4243i		−	0.820462i
$748$	−0.163179	+	0.502213i	−0.00596641	+	0.0183627i
$749$	−0.527303	+	0.268674i	−0.0192672	+	0.00981715i
$750$	3.21736	−	6.31443i	0.117481	−	0.230570i
$751$	3.97360	+	25.0883i	0.144999	+	0.915486i	0.947713	+	0.319123i	$0.103388\pi$
$751$	3.97360	+	25.0883i	0.144999	+	0.915486i	−0.802715	+	0.596363i	$0.796612\pi$
$752$	13.7968	−	13.7968i	0.503117	−	0.503117i
$753$	15.8774	+	8.08992i	0.578603	+	0.294813i
$754$	−24.1673	+	17.5586i	−0.880122	+	0.639446i
$755$	−28.1809	−	55.3082i	−1.02561	−	2.01287i
$756$	−2.42837	−	1.76431i	−0.0883188	−	0.0641674i
$757$	2.10412	−	13.2849i	0.0764754	−	0.482847i	−0.919490	−	0.393113i	$-0.871398\pi$
$757$	2.10412	−	13.2849i	0.0764754	−	0.482847i	0.995966	−	0.0897341i	$-0.0286017\pi$
$758$	−23.8562	−	32.8352i	−0.866496	−	1.19263i
$759$	10.4343	+	14.3616i	0.378740	+	0.521291i
$760$	−2.86925	+	18.1157i	−0.104079	+	0.657127i
$761$	6.67949	+	4.85293i	0.242131	+	0.175919i	0.702232	−	0.711948i	$-0.252187\pi$
$761$	6.67949	+	4.85293i	0.242131	+	0.175919i	−0.460101	+	0.887867i	$0.652187\pi$
$762$	10.3213	+	20.2566i	0.373900	+	0.733821i
$763$	0.0383529	−	0.0278650i	0.00138847	−	0.00100878i
$764$	−2.22739	−	1.13491i	−0.0805841	−	0.0410596i
$765$	1.69096	−	1.69096i	0.0611368	−	0.0611368i
$766$	−0.499575	−	3.15419i	−0.0180504	−	0.113966i
$767$	3.64006	−	7.14403i	0.131435	−	0.257956i
$768$	6.77167	−	3.45034i	0.244352	−	0.124503i
$769$	13.5745	−	41.7779i	0.489508	−	1.50655i	−0.335837	−	0.941920i	$-0.609019\pi$
$769$	13.5745	−	41.7779i	0.489508	−	1.50655i	0.825344	−	0.564630i	$-0.190981\pi$
$770$		−	33.9108i		−	1.22206i
$771$	−14.8796	−	4.83467i	−0.535876	−	0.174117i
$772$	−0.480621	−	0.0761228i	−0.0172979	−	0.00273972i
$773$	−34.7813	+	5.50882i	−1.25100	+	0.198139i	−0.746565	−	0.665312i	$-0.768298\pi$
$773$	−34.7813	+	5.50882i	−1.25100	+	0.198139i	−0.504433	+	0.863451i	$0.668298\pi$
$774$	7.15076	−	2.32342i	0.257029	−	0.0835137i
$775$	15.7468	+	48.4637i	0.565642	+	1.74087i
$776$	21.1818	+	21.1818i	0.760383	+	0.760383i
$777$	6.40845	−	8.82047i	0.229902	−	0.316433i
$778$	−44.0542			−1.57942
$779$	−5.56560	+	9.75992i	−0.199408	+	0.349685i
$780$	2.76299			0.0989308
$781$	−1.40646	+	1.93583i	−0.0503272	+	0.0692694i
$782$	−1.27265	−	1.27265i	−0.0455097	−	0.0455097i
$783$	13.4671	+	41.4474i	0.481274	+	1.48121i
$784$	−11.7608	+	3.82130i	−0.420027	+	0.136475i
$785$	−37.8237	+	5.99069i	−1.34999	+	0.213817i
$786$	−15.4889	−	2.45321i	−0.552472	−	0.0875030i
$787$	−23.1388	−	7.51826i	−0.824810	−	0.267997i	−0.133952	−	0.990988i	$-0.542767\pi$
$787$	−23.1388	−	7.51826i	−0.824810	−	0.267997i	−0.690858	+	0.722991i	$0.742767\pi$
$788$		−	1.30809i		−	0.0465988i
$789$	5.68816	−	17.5063i	0.202504	−	0.623242i
$790$	33.6689	−	17.1551i	1.19788	−	0.610352i
$791$	−3.64658	+	7.15681i	−0.129657	+	0.254467i
$792$	4.82083	+	30.4375i	0.171301	+	1.08155i
$793$	−1.91485	+	1.91485i	−0.0679983	+	0.0679983i
$794$	38.9057	+	19.8234i	1.38071	+	0.703507i
$795$	−2.92138	+	2.12251i	−0.103611	+	0.0752776i
$796$	1.35659	+	2.66246i	0.0480831	+	0.0943684i
$797$	31.9272	+	23.1965i	1.13092	+	0.821661i	0.985828	−	0.167758i	$-0.0536527\pi$
$797$	31.9272	+	23.1965i	1.13092	+	0.821661i	0.145090	+	0.989418i	$0.453653\pi$
$798$	−0.514996	+	3.25155i	−0.0182306	+	0.115104i
$799$	−1.13792	−	1.56621i	−0.0402566	−	0.0554084i
$800$	8.70795	+	11.9855i	0.307873	+	0.423750i
$801$	−5.19345	+	32.7902i	−0.183502	+	1.15858i
$802$	−8.24809	−	5.99259i	−0.291250	−	0.211606i
$803$	17.4158	+	34.1804i	0.614590	+	1.20620i
$804$	−2.72285	+	1.97827i	−0.0960275	+	0.0697681i
$805$	−24.6089	−	12.5389i	−0.867349	−	0.441936i
$806$	16.1404	−	16.1404i	0.568522	−	0.568522i
$807$	−0.394449	−	2.49046i	−0.0138853	−	0.0876682i
$808$	2.39256	−	4.69566i	0.0841699	−	0.165193i
$809$	5.75888	−	2.93430i	0.202472	−	0.103164i	−0.349815	−	0.936819i	$-0.613755\pi$
$809$	5.75888	−	2.93430i	0.202472	−	0.103164i	0.552286	+	0.833654i	$0.313755\pi$
$810$	4.00534	−	12.3272i	0.140733	−	0.433132i
$811$		−	32.7119i		−	1.14867i	−0.818620	−	0.574336i	$-0.805260\pi$
$811$		−	32.7119i		−	1.14867i	0.818620	−	0.574336i	$-0.194740\pi$
$812$	6.13262	+	1.99261i	0.215213	+	0.0699269i
$813$	−9.48177	−	1.50176i	−0.332540	−	0.0526692i
$814$	−41.5066	+	6.57400i	−1.45481	+	0.230419i
$815$	−6.51673	+	2.11742i	−0.228271	+	0.0741698i
$816$	0.248566	+	0.765009i	0.00870157	+	0.0267807i
$817$	3.23541	+	3.23541i	0.113193	+	0.113193i
$818$	5.20689	−	7.16667i	0.182055	−	0.250577i
$819$	−9.52698			−0.332900
$820$	2.24849	+	8.21569i	0.0785206	+	0.286904i
$821$	42.4481			1.48145			0.740725	−	0.671808i	$-0.234482\pi$
$821$	42.4481			1.48145			0.740725	+	0.671808i	$0.234482\pi$
$822$	−0.603723	+	0.830953i	−0.0210572	+	0.0289828i
$823$	1.50529	+	1.50529i	0.0524710	+	0.0524710i	0.732855	−	0.680384i	$-0.238187\pi$
$823$	1.50529	+	1.50529i	0.0524710	+	0.0524710i	−0.680384	+	0.732855i	$0.738187\pi$
$824$	7.92053	+	24.3769i	0.275925	+	0.849209i
$825$	25.1007	−	8.15570i	0.873893	−	0.283945i
$826$	7.15350	−	1.13300i	0.248902	−	0.0394222i
$827$	−51.3821	−	8.13812i	−1.78673	−	0.282990i	−0.826650	−	0.562716i	$-0.809757\pi$
$827$	−51.3821	−	8.13812i	−1.78673	−	0.282990i	−0.960080	+	0.279726i	$0.909757\pi$
$828$	3.85965	+	1.25408i	0.134132	+	0.0435821i
$829$		−	25.8047i		−	0.896234i	−0.893975	−	0.448117i	$-0.852095\pi$
$829$		−	25.8047i		−	0.896234i	0.893975	−	0.448117i	$-0.147905\pi$
$830$	−13.3786	+	41.1752i	−0.464379	+	1.42921i
$831$	−22.5680	+	11.4990i	−0.782875	+	0.398895i
$832$	9.80766	−	19.2486i	0.340020	−	0.667326i
$833$	0.191938	+	1.21185i	0.00665025	+	0.0419880i
$834$	5.82013	−	5.82013i	0.201534	−	0.201534i
$835$	−14.1833	−	7.22673i	−0.490832	−	0.250091i
$836$	−2.45315	+	1.78232i	−0.0848440	+	0.0616428i
$837$	−15.1181	−	29.6709i	−0.522557	−	1.02558i
$838$	15.8888	+	11.5439i	0.548869	+	0.398777i
$839$	−8.15795	+	51.5073i	−0.281644	+	1.77823i	0.289299	+	0.957239i	$0.406578\pi$
$839$	−8.15795	+	51.5073i	−0.281644	+	1.77823i	−0.570943	+	0.820990i	$0.693422\pi$
$840$	9.07308	+	12.4880i	0.313051	+	0.430878i
$841$	−37.9834	−	52.2797i	−1.30977	−	1.80275i
$842$	−4.24362	+	26.7932i	−0.146245	+	0.923353i
$843$	−1.70458	−	1.23845i	−0.0587088	−	0.0426545i
$844$	−2.66405	−	5.22850i	−0.0917005	−	0.179972i
$845$	−19.7953	+	14.3821i	−0.680980	+	0.494761i
$846$	−16.2764	−	8.29325i	−0.559595	−	0.285128i
$847$	11.0797	−	11.0797i	0.380701	−	0.380701i
$848$	0.590194	+	3.72634i	0.0202674	+	0.127963i
$849$	−6.24420	+	12.2549i	−0.214301	+	0.420588i
$850$	−2.38418	+	1.21480i	−0.0817766	+	0.0416672i
$851$	−10.5768	+	32.5520i	−0.362567	+	1.11587i
$852$		−	0.176111i		−	0.00603347i
$853$	1.08259	+	0.351756i	0.0370673	+	0.0120439i	0.327492	−	0.944854i	$-0.393797\pi$
$853$	1.08259	+	0.351756i	0.0370673	+	0.0120439i	−0.290425	+	0.956898i	$0.593797\pi$
$854$	−2.41605	−	0.382664i	−0.0826755	−	0.0130945i
$855$	13.5629	−	2.14816i	0.463843	−	0.0734655i
$856$	−0.987523	+	0.320866i	−0.0337529	+	0.0109670i
$857$	−7.83870	−	24.1250i	−0.267765	−	0.824095i	−0.991044	−	0.133539i	$-0.957366\pi$
$857$	−7.83870	−	24.1250i	−0.267765	−	0.824095i	0.723279	−	0.690556i	$-0.242634\pi$
$858$	−8.35956	−	8.35956i	−0.285391	−	0.285391i
$859$	−19.3856	+	26.6820i	−0.661428	+	0.910378i	−0.999528	−	0.0307324i	$-0.990216\pi$
$859$	−19.3856	+	26.6820i	−0.661428	+	0.910378i	0.338099	+	0.941110i	$0.390216\pi$
$860$	3.46887			0.118288
$861$	2.49601	+	9.12011i	0.0850638	+	0.310813i
$862$	−12.9175			−0.439972
$863$	2.84191	−	3.91155i	0.0967396	−	0.133151i	−0.757903	−	0.652367i	$-0.773776\pi$
$863$	2.84191	−	3.91155i	0.0967396	−	0.133151i	0.854643	+	0.519216i	$0.173776\pi$
$864$	−6.84577	−	6.84577i	−0.232898	−	0.232898i
$865$	−3.68520	−	11.3419i	−0.125300	−	0.385635i
$866$	−24.8005	+	8.05818i	−0.842756	+	0.273828i
$867$	−14.2732	+	2.26065i	−0.484743	+	0.0767757i
$868$	−4.86652	−	0.770781i	−0.165180	−	0.0261620i
$869$	36.7456	+	11.9394i	1.24651	+	0.405015i
$870$		−	36.2368i		−	1.22854i
$871$	−7.66477	+	23.5897i	−0.259711	+	0.799307i
$872$	0.0741111	−	0.0377615i	0.00250972	−	0.00127877i
$873$	10.1818	−	19.9828i	0.344601	−	0.676317i
$874$	−1.61674	−	10.2077i	−0.0546870	−	0.345280i
$875$	−7.97182	+	7.97182i	−0.269497	+	0.269497i
$876$	−2.51568	−	1.28180i	−0.0849968	−	0.0433080i
$877$	0.997552	−	0.724764i	0.0336850	−	0.0244736i	−0.570815	−	0.821078i	$-0.693373\pi$
$877$	0.997552	−	0.724764i	0.0336850	−	0.0244736i	0.604500	+	0.796605i	$0.293373\pi$
$878$	2.36840	+	4.64825i	0.0799296	+	0.156871i
$879$	−18.3050	−	13.2994i	−0.617413	−	0.448577i
$880$	7.44294	−	46.9929i	0.250901	−	1.58413i
$881$	23.2592	+	32.0135i	0.783622	+	1.07856i	0.994873	+	0.101131i	$0.0322463\pi$
$881$	23.2592	+	32.0135i	0.783622	+	1.07856i	−0.211251	+	0.977432i	$0.567754\pi$
$882$	6.80508	+	9.36639i	0.229139	+	0.315383i
$883$	−0.703339	+	4.44071i	−0.0236692	+	0.149442i	−0.996693	−	0.0812653i	$-0.974104\pi$
$883$	−0.703339	+	4.44071i	−0.0236692	+	0.149442i	0.973023	+	0.230707i	$0.0741039\pi$
$884$	−0.231722	−	0.168356i	−0.00779365	−	0.00566242i
$885$	4.41558	+	8.66607i	0.148428	+	0.291307i
$886$	7.24265	−	5.26209i	0.243321	−	0.176783i
$887$	−26.7808	−	13.6455i	−0.899212	−	0.458171i	−0.0576530	−	0.998337i	$-0.518362\pi$
$887$	−26.7808	−	13.6455i	−0.899212	−	0.458171i	−0.841559	+	0.540165i	$0.818362\pi$
$888$	13.5264	−	13.5264i	0.453915	−	0.453915i
$889$	−5.65768	−	35.7212i	−0.189752	−	1.19805i
$890$	29.0992	−	57.1104i	0.975407	−	1.91434i
$891$	11.8083	−	6.01665i	0.395594	−	0.201565i
$892$	0.347659	−	1.06999i	0.0116405	−	0.0358258i
$893$		−	11.1167i		−	0.372007i
$894$	−9.94373	−	3.23091i	−0.332568	−	0.108058i
$895$	54.2359	+	8.59011i	1.81290	+	0.287136i
$896$	11.9386	−	1.89089i	0.398841	−	0.0631702i
$897$	−9.15752	+	2.97546i	−0.305761	+	0.0993477i
$898$	5.40214	+	16.6261i	0.180272	+	0.554820i
$899$	50.5846	+	50.5846i	1.68709	+	1.68709i
$900$	3.54646	−	4.88128i	0.118215	−	0.162709i
$901$	0.374336			0.0124709
$902$	18.0541	−	31.6599i	0.601135	−	1.05416i
$903$	3.85074			0.128145
$904$	−8.28360	+	11.4014i	−0.275508	+	0.379205i
$905$	5.93134	+	5.93134i	0.197164	+	0.197164i
$906$	−6.04070	−	18.5914i	−0.200689	−	0.617657i
$907$	44.9026	−	14.5898i	1.49097	−	0.484445i	0.553599	−	0.832783i	$-0.313254\pi$
$907$	44.9026	−	14.5898i	1.49097	−	0.484445i	0.937369	+	0.348339i	$0.113254\pi$
$908$	6.33216	−	1.00291i	0.210140	−	0.0332829i
$909$	−3.89703	−	0.617229i	−0.129256	−	0.0204722i
$910$	17.4933	+	5.68392i	0.579897	+	0.188420i
$911$		−	58.9483i		−	1.95305i	−0.215414	−	0.976523i	$-0.569110\pi$
$911$		−	58.9483i		−	1.95305i	0.215414	−	0.976523i	$-0.430890\pi$
$912$	−1.42734	+	4.39290i	−0.0472640	+	0.145464i
$913$	−39.4423	+	20.0968i	−1.30535	+	0.665108i
$914$	−0.890876	+	1.74844i	−0.0294676	+	0.0578334i
$915$	−0.513879	−	3.24450i	−0.0169883	−	0.107260i
$916$	−3.38548	+	3.38548i	−0.111859	+	0.111859i
$917$	22.2281	+	11.3258i	0.734036	+	0.374010i
$918$	1.41467	−	1.02782i	0.0466910	−	0.0339230i
$919$	5.62090	+	11.0316i	0.185416	+	0.363900i	0.964939	−	0.262474i	$-0.0845383\pi$
$919$	5.62090	+	11.0316i	0.185416	+	0.363900i	−0.779523	+	0.626374i	$0.784538\pi$
$920$	−39.2040	−	28.4834i	−1.29252	−	0.939069i
$921$	1.53483	−	9.69055i	0.0505744	−	0.319314i
$922$	23.2646	+	32.0209i	0.766177	+	1.05455i
$923$	−0.762880	−	1.05001i	−0.0251105	−	0.0345616i
$924$	−0.399208	+	2.52050i	−0.0131330	+	0.0829184i
$925$	41.1683	+	29.9106i	1.35361	+	0.983453i
$926$	17.7585	+	34.8530i	0.583581	+	1.14534i
$927$	15.5249	−	11.2795i	0.509903	−	0.370466i
$928$	18.5311	+	9.44207i	0.608313	+	0.309951i
$929$	−41.7616	+	41.7616i	−1.37015	+	1.37015i	−0.509945	+	0.860207i	$0.670334\pi$
$929$	−41.7616	+	41.7616i	−1.37015	+	1.37015i	−0.860207	+	0.509945i	$0.829666\pi$
$930$	4.33153	+	27.3482i	0.142036	+	0.896782i
$931$	−3.19860	+	6.27761i	−0.104830	+	0.205740i
$932$	−1.04734	+	0.533648i	−0.0343069	+	0.0174802i
$933$	−4.86576	+	14.9753i	−0.159298	+	0.490269i
$934$			1.08341i			0.0354504i
$935$	−4.48970	−	1.45879i	−0.146829	−	0.0477076i
$936$	−16.5096	−	2.61486i	−0.539633	−	0.0854695i
$937$	14.8935	−	2.35889i	0.486549	−	0.0770617i	0.0916592	−	0.995790i	$-0.470783\pi$
$937$	14.8935	−	2.35889i	0.486549	−	0.0770617i	0.394889	+	0.918729i	$0.370783\pi$
$938$	−21.3088	+	6.92365i	−0.695757	+	0.226065i
$939$	3.79771	+	11.6882i	0.123934	+	0.381429i
$940$	−5.95944	−	5.95944i	−0.194376	−	0.194376i
$941$	11.2887	−	15.5376i	0.368002	−	0.506511i	−0.584354	−	0.811499i	$-0.698652\pi$
$941$	11.2887	−	15.5376i	0.368002	−	0.506511i	0.952356	+	0.304987i	$0.0986522\pi$
$942$	−12.0598			−0.392931
$943$	−16.2998	−	24.8083i	−0.530793	−	0.807870i
$944$	10.1619			0.330740
$945$	15.7726	−	21.7092i	0.513084	−	0.706200i
$946$	−10.4952	−	10.4952i	−0.341230	−	0.341230i
$947$	−10.9296	−	33.6378i	−0.355164	−	1.09308i	−0.955914	−	0.293646i	$-0.905131\pi$
$947$	−10.9296	−	33.6378i	−0.355164	−	1.09308i	0.600750	−	0.799437i	$-0.294869\pi$
$948$	−2.70447	+	0.878737i	−0.0878372	+	0.0285400i
$949$	−20.5515	+	3.25504i	−0.667131	+	0.105663i
$950$	−15.1762	−	2.40367i	−0.492380	−	0.0779854i
$951$	19.4728	+	6.32709i	0.631448	+	0.205170i
$952$		−	1.60017i		−	0.0518618i
$953$	−1.20952	+	3.72252i	−0.0391802	+	0.120584i	−0.968734	−	0.248103i	$-0.920193\pi$
$953$	−1.20952	+	3.72252i	−0.0391802	+	0.120584i	0.929553	+	0.368688i	$0.120193\pi$
$954$	3.14723	−	1.60359i	0.101895	−	0.0519183i
$955$	10.1459	−	19.9125i	0.328314	−	0.644352i
$956$	−0.826645	−	5.21923i	−0.0267356	−	0.168802i
$957$	26.1991	−	26.1991i	0.846897	−	0.846897i
$958$	−5.44913	−	2.77647i	−0.176053	−	0.0897037i
$959$	1.32189	−	0.960409i	0.0426861	−	0.0310132i
$960$	11.8972	+	23.3495i	0.383980	+	0.753603i
$961$	−19.1436	−	13.9086i	−0.617535	−	0.448666i
$962$	3.56581	−	22.5136i	0.114966	−	0.725868i
$963$	0.456939	+	0.628922i	0.0147246	+	0.0202667i
$964$	−2.99393	−	4.12079i	−0.0964279	−	0.132722i
$965$	0.680525	−	4.29667i	0.0219069	−	0.138315i
$966$	−7.03664	−	5.11242i	−0.226400	−	0.164489i
$967$	−15.2042	−	29.8398i	−0.488933	−	0.959584i	−0.995261	−	0.0972434i	$-0.968997\pi$
$967$	−15.2042	−	29.8398i	−0.488933	−	0.959584i	0.506328	−	0.862341i	$-0.331003\pi$
$968$	22.2413	−	16.1593i	0.714863	−	0.519378i
$969$	0.408343	+	0.208061i	0.0131179	+	0.00668389i
$970$	−30.6176	+	30.6176i	−0.983073	+	0.983073i
$971$	3.19917	+	20.1988i	0.102666	+	0.648209i	0.984331	+	0.176332i	$0.0564233\pi$
$971$	3.19917	+	20.1988i	0.102666	+	0.648209i	−0.881665	+	0.471877i	$0.843577\pi$
$972$	−2.80916	+	5.51328i	−0.0901038	+	0.176839i
$973$	−11.6667	+	5.94447i	−0.374017	+	0.190571i
$974$	−14.5255	+	44.7048i	−0.465426	+	1.43243i
$975$			14.3155i			0.458463i
$976$	−3.26412	−	1.06058i	−0.104482	−	0.0339483i
$977$	−6.07624	−	0.962381i	−0.194396	−	0.0307893i	0.0584771	−	0.998289i	$-0.481376\pi$
$977$	−6.07624	−	0.962381i	−0.194396	−	0.0307893i	−0.252873	+	0.967499i	$0.581376\pi$
$978$	−2.13128	+	0.337561i	−0.0681508	+	0.0107940i
$979$	62.3293	−	20.2520i	1.99205	−	0.647257i
$980$	1.65059	+	5.08000i	0.0527262	+	0.162275i
$981$	−0.0440337	−	0.0440337i	−0.00140589	−	0.00140589i
$982$	12.2854	−	16.9094i	0.392044	−	0.539602i
$983$	−21.3411			−0.680674			−0.340337	−	0.940304i	$-0.610541\pi$
$983$	−21.3411			−0.680674			−0.340337	+	0.940304i	$0.610541\pi$
$984$	1.82222	+	16.4896i	0.0580904	+	0.525670i
$985$	11.6941			0.372605
$986$	−2.20800	+	3.03905i	−0.0703170	+	0.0967831i
$987$	−6.61548	−	6.61548i	−0.210573	−	0.210573i
$988$	−0.508249	−	1.56423i	−0.0161696	−	0.0497648i
$989$	−11.4971	+	3.73563i	−0.365586	+	0.118786i
$990$	−43.9964	+	6.96835i	−1.39830	+	0.221469i
$991$	39.8821	+	6.31670i	1.26690	+	0.200657i	0.753473	−	0.657479i	$-0.228377\pi$
$991$	39.8821	+	6.31670i	1.26690	+	0.200657i	0.513423	+	0.858136i	$0.328377\pi$
$992$	−15.1142	−	4.91090i	−0.479876	−	0.155921i
$993$			0.964063i			0.0305936i
$994$	0.362290	−	1.11501i	0.0114911	−	0.0353661i
$995$	−23.8019	+	12.1277i	−0.754572	+	0.384474i
$996$	1.47913	−	2.90295i	0.0468679	−	0.0919834i
$997$	4.43858	+	28.0241i	0.140571	+	0.887531i	0.952669	+	0.304010i	$0.0983255\pi$
$997$	4.43858	+	28.0241i	0.140571	+	0.887531i	−0.812098	+	0.583521i	$0.801674\pi$
$998$	−2.23466	+	2.23466i	−0.0707370	+	0.0707370i
$999$	−29.6296	−	15.0971i	−0.937440	−	0.477650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.8.3	✓	24
3.2	odd	2		369.2.u.a.172.1		24
4.3	odd	2		656.2.bs.d.49.3		24
41.6	odd	40		1681.2.a.m.1.6		24
41.35	odd	40		1681.2.a.m.1.5		24
41.36	even	20	inner	41.2.g.a.36.3	yes	24
123.77	odd	20		369.2.u.a.118.1		24
164.159	odd	20		656.2.bs.d.241.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.3	✓	24	1.1	even	1	trivial
41.2.g.a.36.3	yes	24	41.36	even	20	inner
369.2.u.a.118.1		24	123.77	odd	20
369.2.u.a.172.1		24	3.2	odd	2
656.2.bs.d.49.3		24	4.3	odd	2
656.2.bs.d.241.3		24	164.159	odd	20
1681.2.a.m.1.5		24	41.35	odd	40
1681.2.a.m.1.6		24	41.6	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.746800 - 1.02788i) q^{2} +(-0.604406 - 0.604406i) q^{3} +(0.119203 + 0.366868i) q^{4} +(-3.27974 + 1.06565i) q^{5} +(-1.07263 + 0.169888i) q^{6} +(1.70635 + 0.270260i) q^{7} +(2.88281 + 0.936683i) q^{8} -2.26939i q^{9} +O(q^{10})\)	\(q+(0.746800 - 1.02788i) q^{2} +(-0.604406 - 0.604406i) q^{3} +(0.119203 + 0.366868i) q^{4} +(-3.27974 + 1.06565i) q^{5} +(-1.07263 + 0.169888i) q^{6} +(1.70635 + 0.270260i) q^{7} +(2.88281 + 0.936683i) q^{8} -2.26939i q^{9} +(-1.35394 + 4.16701i) q^{10} +(-3.99164 + 2.03384i) q^{11} +(0.149691 - 0.293784i) q^{12} +(-0.380129 - 2.40004i) q^{13} +(1.55210 - 1.55210i) q^{14} +(2.62638 + 1.33821i) q^{15} +(2.49153 - 1.81020i) q^{16} +(-0.138725 - 0.272263i) q^{17} +(-2.33266 - 1.69478i) q^{18} +(0.274489 - 1.73306i) q^{19} +(-0.781908 - 1.07620i) q^{20} +(-0.867983 - 1.19468i) q^{21} +(-0.890407 + 5.62181i) q^{22} +(3.75048 + 2.72488i) q^{23} +(-1.17625 - 2.30853i) q^{24} +(5.57599 - 4.05119i) q^{25} +(-2.75084 - 1.40162i) q^{26} +(-3.18485 + 3.18485i) q^{27} +(0.104252 + 0.658222i) q^{28} +(4.39273 - 8.62121i) q^{29} +(3.33690 - 1.70024i) q^{30} +(-2.28469 + 7.03157i) q^{31} +2.14948i q^{32} +(3.64184 + 1.18331i) q^{33} +(-0.383454 - 0.0607331i) q^{34} +(-5.88439 + 0.931996i) q^{35} +(0.832566 - 0.270517i) q^{36} +(2.28152 + 7.02179i) q^{37} +(-1.57639 - 1.57639i) q^{38} +(-1.22085 + 1.68035i) q^{39} -10.4531 q^{40} +(-5.99000 - 2.26271i) q^{41} -1.87620 q^{42} +(-1.53275 + 2.10964i) q^{43} +(-1.22197 - 1.22197i) q^{44} +(2.41838 + 7.44299i) q^{45} +(5.60172 - 1.82011i) q^{46} +(6.25754 - 0.991097i) q^{47} +(-2.60000 - 0.411799i) q^{48} +(-3.81880 - 1.24080i) q^{49} -8.75689i q^{50} +(-0.0807112 + 0.248404i) q^{51} +(0.835185 - 0.425548i) q^{52} +(-0.556161 + 1.09153i) q^{53} +(0.895204 + 5.65210i) q^{54} +(10.9242 - 10.9242i) q^{55} +(4.66595 + 2.37742i) q^{56} +(-1.21337 + 0.881567i) q^{57} +(-5.58110 - 10.9535i) q^{58} +(2.66945 + 1.93947i) q^{59} +(-0.177874 + 1.12305i) q^{60} +(-0.655043 - 0.901590i) q^{61} +(5.52141 + 7.59957i) q^{62} +(0.613323 - 3.87237i) q^{63} +(7.19247 + 5.22564i) q^{64} +(3.80433 + 7.46641i) q^{65} +(3.93602 - 2.85969i) q^{66} +(-9.09493 - 4.63410i) q^{67} +(0.0833482 - 0.0833482i) q^{68} +(-0.619877 - 3.91375i) q^{69} +(-3.43648 + 6.74448i) q^{70} +(0.475905 - 0.242486i) q^{71} +(2.12570 - 6.54222i) q^{72} -8.56300i q^{73} +(8.92141 + 2.89874i) q^{74} +(-5.81873 - 0.921596i) q^{75} +(0.668523 - 0.105884i) q^{76} +(-7.36081 + 2.39167i) q^{77} +(0.815474 + 2.50977i) q^{78} +(-6.09837 - 6.09837i) q^{79} +(-6.24253 + 8.59210i) q^{80} -2.95827 q^{81} +(-6.79914 + 4.46722i) q^{82} +9.88122 q^{83} +(0.334823 - 0.460844i) q^{84} +(0.745119 + 0.745119i) q^{85} +(1.02381 + 3.15096i) q^{86} +(-7.86570 + 2.55572i) q^{87} +(-13.4122 + 2.12429i) q^{88} +(-14.4489 - 2.28848i) q^{89} +(9.45656 + 3.07262i) q^{90} -4.19804i q^{91} +(-0.552606 + 1.70075i) q^{92} +(5.63081 - 2.86904i) q^{93} +(3.65440 - 7.17217i) q^{94} +(0.946582 + 5.97648i) q^{95} +(1.29916 - 1.29916i) q^{96} +(8.80540 + 4.48657i) q^{97} +(-4.12728 + 2.99864i) q^{98} +(4.61557 + 9.05857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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