LMFDB - Embedded newform 345.2.m.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	345.31
Dual form			345.2.m.a.256.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.139065 + 0.967216i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.00282 + 0.294454i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.937580 - 0.275298i) q^{6} +(1.72023 + 1.10553i) q^{7} +(-1.23611 + 2.70671i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.139065 + 0.967216i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.00282 + 0.294454i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.937580 - 0.275298i) q^{6} +(1.72023 + 1.10553i) q^{7} +(-1.23611 + 2.70671i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.822041 + 0.528294i) q^{10} +(-0.270777 - 1.88329i) q^{11} +(-0.148741 - 1.03452i) q^{12} +(0.240382 - 0.154484i) q^{13} +(-1.30851 + 1.51010i) q^{14} +(0.415415 - 0.909632i) q^{15} +(-0.687595 - 0.441890i) q^{16} +(-0.126693 + 0.0372005i) q^{17} +(-0.639905 - 0.738490i) q^{18} +(5.40582 + 1.58729i) q^{19} +(0.434173 + 0.950705i) q^{20} +(0.291012 - 2.02403i) q^{21} +1.85921 q^{22} +(-2.29407 + 4.21156i) q^{23} +2.97561 q^{24} +(-0.142315 + 0.989821i) q^{25} +(0.115991 + 0.253985i) q^{26} +(0.959493 + 0.281733i) q^{27} +(1.39955 + 1.61517i) q^{28} +(3.25088 - 0.954543i) q^{29} +(0.822041 + 0.528294i) q^{30} +(0.903693 - 1.97881i) q^{31} +(-3.37420 + 3.89403i) q^{32} +(-1.60062 + 1.02866i) q^{33} +(-0.0183624 - 0.127713i) q^{34} +(0.291012 + 2.02403i) q^{35} +(-0.879239 + 0.565053i) q^{36} +(-1.01567 + 1.17215i) q^{37} +(-2.28701 + 5.00786i) q^{38} +(-0.240382 - 0.154484i) q^{39} +(-2.85508 + 0.838326i) q^{40} +(-4.25082 - 4.90571i) q^{41} +(1.91721 + 0.562942i) q^{42} +(0.224358 + 0.491276i) q^{43} +(0.283003 - 1.96833i) q^{44} -1.00000 q^{45} +(-3.75447 - 2.80454i) q^{46} +1.57289 q^{47} +(-0.116320 + 0.809026i) q^{48} +(-1.17089 - 2.56390i) q^{49} +(-0.937580 - 0.275298i) q^{50} +(0.0864690 + 0.0997906i) q^{51} +(0.286548 - 0.0841381i) q^{52} +(-5.99659 - 3.85377i) q^{53} +(-0.405928 + 0.888858i) q^{54} +(1.24598 - 1.43793i) q^{55} +(-5.11874 + 3.28961i) q^{56} +(-0.801808 - 5.57670i) q^{57} +(0.471168 + 3.27704i) q^{58} +(1.49979 - 0.963859i) q^{59} +(0.684430 - 0.789875i) q^{60} +(2.99205 - 6.55168i) q^{61} +(1.78827 + 1.14925i) q^{62} +(-1.96201 + 0.576099i) q^{63} +(-4.36763 - 5.04052i) q^{64} +(0.274168 + 0.0805031i) q^{65} +(-0.772343 - 1.69119i) q^{66} +(1.59933 - 11.1236i) q^{67} -0.138004 q^{68} +(4.78396 + 0.337213i) q^{69} -1.99814 q^{70} +(0.764301 - 5.31583i) q^{71} +(-1.23611 - 2.70671i) q^{72} +(-2.58174 - 0.758068i) q^{73} +(-0.992475 - 1.14538i) q^{74} +(0.959493 - 0.281733i) q^{75} +(4.95367 + 3.18353i) q^{76} +(1.61623 - 3.53905i) q^{77} +(0.182848 - 0.211018i) q^{78} +(-3.30698 + 2.12527i) q^{79} +(-0.116320 - 0.809026i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(5.33602 - 3.42925i) q^{82} +(-10.0576 + 11.6071i) q^{83} +(0.887815 - 1.94404i) q^{84} +(-0.111081 - 0.0713872i) q^{85} +(-0.506370 + 0.148684i) q^{86} +(-2.21875 - 2.56057i) q^{87} +(5.43224 + 1.59505i) q^{88} +(-0.797756 - 1.74684i) q^{89} +(0.139065 - 0.967216i) q^{90} +0.584300 q^{91} +(-3.54064 + 3.54793i) q^{92} -2.17540 q^{93} +(-0.218734 + 1.52133i) q^{94} +(2.34047 + 5.12491i) q^{95} +(4.94383 + 1.45164i) q^{96} +(-9.45199 - 10.9082i) q^{97} +(2.64268 - 0.775960i) q^{98} +(1.60062 + 1.02866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	−0.139065	+	0.967216i	−0.0983336	+	0.683925i	0.879708	+	0.475515i	$0.157738\pi$
$2$	−0.139065	+	0.967216i	−0.0983336	+	0.683925i	−0.978041	+	0.208411i	$0.933171\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	1.00282	+	0.294454i	0.501409	+	0.147227i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.937580	−	0.275298i	0.382766	−	0.112390i
$7$	1.72023	+	1.10553i	0.650187	+	0.417850i	0.823734	−	0.566976i	$-0.191887\pi$
$7$	1.72023	+	1.10553i	0.650187	+	0.417850i	−0.173548	+	0.984825i	$0.555523\pi$
$8$	−1.23611	+	2.70671i	−0.437032	+	0.956966i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.822041	+	0.528294i	−0.259952	+	0.167061i
$11$	−0.270777	−	1.88329i	−0.0816423	−	0.567834i	−0.989050	−	0.147582i	$-0.952851\pi$
$11$	−0.270777	−	1.88329i	−0.0816423	−	0.567834i	0.907407	−	0.420252i	$-0.138058\pi$
$12$	−0.148741	−	1.03452i	−0.0429378	−	0.298639i
$13$	0.240382	−	0.154484i	0.0666700	−	0.0428462i	−0.506881	−	0.862016i	$-0.669202\pi$
$13$	0.240382	−	0.154484i	0.0666700	−	0.0428462i	0.573551	+	0.819170i	$0.305565\pi$
$14$	−1.30851	+	1.51010i	−0.349713	+	0.403590i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	−0.687595	−	0.441890i	−0.171899	−	0.110473i
$17$	−0.126693	+	0.0372005i	−0.0307276	+	0.00902244i	−0.297060	−	0.954859i	$-0.596006\pi$
$17$	−0.126693	+	0.0372005i	−0.0307276	+	0.00902244i	0.266333	+	0.963881i	$0.414188\pi$
$18$	−0.639905	−	0.738490i	−0.150827	−	0.174064i
$19$	5.40582	+	1.58729i	1.24018	+	0.364150i	0.835083	−	0.550123i	$-0.185419\pi$
$19$	5.40582	+	1.58729i	1.24018	+	0.364150i	0.405098	+	0.914273i	$0.367237\pi$
$20$	0.434173	+	0.950705i	0.0970840	+	0.212584i
$21$	0.291012	−	2.02403i	0.0635039	−	0.441680i
$22$	1.85921			0.396384
$23$	−2.29407	+	4.21156i	−0.478346	+	0.878171i
$23$	−2.29407	+	4.21156i	−0.478346	+	0.878171i
$24$	2.97561			0.607394
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	0.115991	+	0.253985i	0.0227477	+	0.0498105i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	1.39955	+	1.61517i	0.264491	+	0.305239i
$29$	3.25088	−	0.954543i	0.603673	−	0.177254i	0.0344069	−	0.999408i	$-0.489046\pi$
$29$	3.25088	−	0.954543i	0.603673	−	0.177254i	0.569266	+	0.822154i	$0.307228\pi$
$30$	0.822041	+	0.528294i	0.150084	+	0.0964528i
$31$	0.903693	−	1.97881i	0.162308	−	0.355405i	−0.810951	−	0.585113i	$-0.801050\pi$
$31$	0.903693	−	1.97881i	0.162308	−	0.355405i	0.973259	+	0.229708i	$0.0737773\pi$
$32$	−3.37420	+	3.89403i	−0.596479	+	0.688374i
$33$	−1.60062	+	1.02866i	−0.278632	+	0.179066i
$34$	−0.0183624	−	0.127713i	−0.00314912	−	0.0219026i
$35$	0.291012	+	2.02403i	0.0491899	+	0.342124i
$36$	−0.879239	+	0.565053i	−0.146540	+	0.0941755i
$37$	−1.01567	+	1.17215i	−0.166975	+	0.192700i	−0.833070	−	0.553167i	$-0.813419\pi$
$37$	−1.01567	+	1.17215i	−0.166975	+	0.192700i	0.666095	+	0.745867i	$0.267965\pi$
$38$	−2.28701	+	5.00786i	−0.371003	+	0.812383i
$39$	−0.240382	−	0.154484i	−0.0384920	−	0.0247373i
$40$	−2.85508	+	0.838326i	−0.451427	+	0.132551i
$41$	−4.25082	−	4.90571i	−0.663866	−	0.766143i	0.319537	−	0.947574i	$-0.396473\pi$
$41$	−4.25082	−	4.90571i	−0.663866	−	0.766143i	−0.983404	+	0.181431i	$0.941927\pi$
$42$	1.91721	+	0.562942i	0.295831	+	0.0868639i
$43$	0.224358	+	0.491276i	0.0342143	+	0.0749189i	0.925968	−	0.377603i	$-0.123252\pi$
$43$	0.224358	+	0.491276i	0.0342143	+	0.0749189i	−0.891753	+	0.452522i	$0.850524\pi$
$44$	0.283003	−	1.96833i	0.0426644	−	0.296737i
$45$	−1.00000			−0.149071
$46$	−3.75447	−	2.80454i	−0.553566	−	0.413507i
$47$	1.57289			0.229430			0.114715	−	0.993398i	$-0.463405\pi$
$47$	1.57289			0.229430			0.114715	+	0.993398i	$0.463405\pi$
$48$	−0.116320	+	0.809026i	−0.0167894	+	0.116773i
$49$	−1.17089	−	2.56390i	−0.167271	−	0.366272i
$50$	−0.937580	−	0.275298i	−0.132594	−	0.0389331i
$51$	0.0864690	+	0.0997906i	0.0121081	+	0.0139735i
$52$	0.286548	−	0.0841381i	0.0397371	−	0.0116679i
$53$	−5.99659	−	3.85377i	−0.823695	−	0.529357i	0.0595737	−	0.998224i	$-0.481026\pi$
$53$	−5.99659	−	3.85377i	−0.823695	−	0.529357i	−0.883269	+	0.468867i	$0.844662\pi$
$54$	−0.405928	+	0.888858i	−0.0552398	+	0.120958i
$55$	1.24598	−	1.43793i	0.168008	−	0.193891i
$56$	−5.11874	+	3.28961i	−0.684020	+	0.439593i
$57$	−0.801808	−	5.57670i	−0.106202	−	0.738651i
$58$	0.471168	+	3.27704i	0.0618673	+	0.430297i
$59$	1.49979	−	0.963859i	0.195256	−	0.125484i	−0.439360	−	0.898311i	$-0.644795\pi$
$59$	1.49979	−	0.963859i	0.195256	−	0.125484i	0.634616	+	0.772828i	$0.281158\pi$
$60$	0.684430	−	0.789875i	0.0883596	−	0.101972i
$61$	2.99205	−	6.55168i	0.383093	−	0.838856i	−0.615615	−	0.788047i	$-0.711093\pi$
$61$	2.99205	−	6.55168i	0.383093	−	0.838856i	0.998708	−	0.0508097i	$-0.0161802\pi$
$62$	1.78827	+	1.14925i	0.227110	+	0.145955i
$63$	−1.96201	+	0.576099i	−0.247190	+	0.0725817i
$64$	−4.36763	−	5.04052i	−0.545954	−	0.630064i
$65$	0.274168	+	0.0805031i	0.0340064	+	0.00998518i
$66$	−0.772343	−	1.69119i	−0.0950688	−	0.208172i
$67$	1.59933	−	11.1236i	0.195389	−	1.35896i	−0.622065	−	0.782966i	$-0.713706\pi$
$67$	1.59933	−	11.1236i	0.195389	−	1.35896i	0.817454	−	0.575994i	$-0.195385\pi$
$68$	−0.138004			−0.0167354
$69$	4.78396	+	0.337213i	0.575921	+	0.0405956i
$70$	−1.99814			−0.238824
$71$	0.764301	−	5.31583i	0.0907058	−	0.630873i	−0.892861	−	0.450331i	$-0.851306\pi$
$71$	0.764301	−	5.31583i	0.0907058	−	0.630873i	0.983567	−	0.180542i	$-0.0577851\pi$
$72$	−1.23611	−	2.70671i	−0.145677	−	0.318989i
$73$	−2.58174	−	0.758068i	−0.302170	−	0.0887252i	0.127133	−	0.991886i	$-0.459423\pi$
$73$	−2.58174	−	0.758068i	−0.302170	−	0.0887252i	−0.429303	+	0.903161i	$0.641241\pi$
$74$	−0.992475	−	1.14538i	−0.115373	−	0.133147i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	4.95367	+	3.18353i	0.568225	+	0.365176i
$77$	1.61623	−	3.53905i	0.184187	−	0.403312i
$78$	0.182848	−	0.211018i	0.0207035	−	0.0238931i
$79$	−3.30698	+	2.12527i	−0.372065	+	0.239112i	−0.713288	−	0.700871i	$-0.752795\pi$
$79$	−3.30698	+	2.12527i	−0.372065	+	0.239112i	0.341224	+	0.939982i	$0.389159\pi$
$80$	−0.116320	−	0.809026i	−0.0130050	−	0.0904519i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	5.33602	−	3.42925i	0.589265	−	0.378697i
$83$	−10.0576	+	11.6071i	−1.10397	+	1.27405i	−0.145340	+	0.989382i	$0.546428\pi$
$83$	−10.0576	+	11.6071i	−1.10397	+	1.27405i	−0.958627	+	0.284664i	$0.908118\pi$
$84$	0.887815	−	1.94404i	0.0968686	−	0.212113i
$85$	−0.111081	−	0.0713872i	−0.0120484	−	0.00774303i
$86$	−0.506370	+	0.148684i	−0.0546033	+	0.0160330i
$87$	−2.21875	−	2.56057i	−0.237875	−	0.274522i
$88$	5.43224	+	1.59505i	0.579079	+	0.170033i
$89$	−0.797756	−	1.74684i	−0.0845620	−	0.185165i	0.862627	−	0.505840i	$-0.168817\pi$
$89$	−0.797756	−	1.74684i	−0.0845620	−	0.185165i	−0.947189	+	0.320675i	$0.896090\pi$
$90$	0.139065	−	0.967216i	0.0146587	−	0.101954i
$91$	0.584300			0.0612512
$92$	−3.54064	+	3.54793i	−0.369138	+	0.369897i
$93$	−2.17540			−0.225578
$94$	−0.218734	+	1.52133i	−0.0225607	+	0.156913i
$95$	2.34047	+	5.12491i	0.240127	+	0.525804i
$96$	4.94383	+	1.45164i	0.504577	+	0.148157i
$97$	−9.45199	−	10.9082i	−0.959704	−	1.10756i	−0.994135	−	0.108150i	$-0.965507\pi$
$97$	−9.45199	−	10.9082i	−0.959704	−	1.10756i	0.0344304	−	0.999407i	$-0.489038\pi$
$98$	2.64268	−	0.775960i	0.266951	−	0.0783838i
$99$	1.60062	+	1.02866i	0.160868	+	0.103384i
$100$	−0.434173	+	0.950705i	−0.0434173	+	0.0950705i
$101$	7.82491	−	9.03043i	0.778607	−	0.898561i	−0.218401	−	0.975859i	$-0.570084\pi$
$101$	7.82491	−	9.03043i	0.778607	−	0.898561i	0.997008	+	0.0772983i	$0.0246294\pi$
$102$	−0.108544	+	0.0697569i	−0.0107474	+	0.00690696i
$103$	0.345207	+	2.40096i	0.0340142	+	0.236574i	0.999735	−	0.0230079i	$-0.00732430\pi$
$103$	0.345207	+	2.40096i	0.0340142	+	0.236574i	−0.965721	+	0.259582i	$0.916415\pi$
$104$	0.121005	+	0.841605i	0.0118655	+	0.0825262i
$105$	1.72023	−	1.10553i	0.167877	−	0.107888i
$106$	4.56135	−	5.26407i	0.443037	−	0.511292i
$107$	1.49252	−	3.26816i	0.144287	−	0.315945i	−0.823666	−	0.567075i	$-0.808075\pi$
$107$	1.49252	−	3.26816i	0.144287	−	0.315945i	0.967953	+	0.251130i	$0.0808022\pi$
$108$	0.879239	+	0.565053i	0.0846049	+	0.0543722i
$109$	−12.5280	+	3.67856i	−1.19997	+	0.352342i	−0.819840	−	0.572593i	$-0.805938\pi$
$109$	−12.5280	+	3.67856i	−1.19997	+	0.352342i	−0.380126	+	0.924935i	$0.624119\pi$
$110$	1.21752	+	1.40510i	0.116086	+	0.133971i
$111$	1.48815	+	0.436959i	0.141249	+	0.0414744i
$112$	−0.694301	−	1.52031i	−0.0656053	−	0.143656i
$113$	2.50387	−	17.4148i	0.235544	−	1.63824i	−0.437913	−	0.899017i	$-0.644282\pi$
$113$	2.50387	−	17.4148i	0.235544	−	1.63824i	0.673457	−	0.739226i	$-0.264809\pi$
$114$	5.50537			0.515625
$115$	−4.68518	+	1.02424i	−0.436895	+	0.0955113i
$116$	3.54111			0.328783
$117$	−0.0406655	+	0.282834i	−0.00375952	+	0.0261481i
$118$	0.723691	+	1.58466i	0.0666212	+	0.145880i
$119$	−0.259068	−	0.0760692i	−0.0237487	−	0.00697325i
$120$	1.94861	+	2.24882i	0.177883	+	0.205288i
$121$	7.08095	−	2.07915i	0.643723	−	0.189014i
$122$	5.92080	+	3.80507i	0.536044	+	0.344495i
$123$	−2.69653	+	5.90459i	−0.243138	+	0.532399i
$124$	1.48891	−	1.71829i	0.133708	−	0.154307i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	−0.284366	−	1.97781i	−0.0253333	−	0.176197i
$127$	−0.323209	−	2.24797i	−0.0286802	−	0.199475i	0.970444	−	0.241328i	$-0.0775829\pi$
$127$	−0.323209	−	2.24797i	−0.0286802	−	0.199475i	−0.999124	+	0.0418531i	$0.986674\pi$
$128$	−3.18653	+	2.04786i	−0.281652	+	0.181007i
$129$	0.353678	−	0.408167i	0.0311397	−	0.0359371i
$130$	−0.115991	+	0.253985i	−0.0101731	+	0.0222759i
$131$	14.1426	+	9.08888i	1.23564	+	0.794099i	0.984760	−	0.173919i	$-0.0556431\pi$
$131$	14.1426	+	9.08888i	1.23564	+	0.794099i	0.250882	+	0.968018i	$0.419279\pi$
$132$	−1.90802	+	0.560246i	−0.166072	+	0.0487631i
$133$	7.54448	+	8.70679i	0.654189	+	0.754975i
$134$	10.5365	+	3.09379i	0.910214	+	0.267263i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	0.0559162	−	0.388906i	0.00479477	−	0.0333484i
$137$	−8.19928			−0.700512			−0.350256	−	0.936654i	$-0.613905\pi$
$137$	−8.19928			−0.700512			−0.350256	+	0.936654i	$0.613905\pi$
$138$	−0.991438	+	4.58023i	−0.0843968	+	0.389895i
$139$	−18.8337			−1.59745			−0.798727	−	0.601693i	$-0.794493\pi$
$139$	−18.8337			−1.59745			−0.798727	+	0.601693i	$0.794493\pi$
$140$	−0.304152	+	2.11542i	−0.0257055	+	0.178786i
$141$	−0.653403	−	1.43075i	−0.0550265	−	0.120491i
$142$	5.03527	+	1.47849i	0.422550	+	0.124072i
$143$	−0.356029	−	0.410880i	−0.0297727	−	0.0343595i
$144$	0.784237	−	0.230273i	0.0653531	−	0.0191894i
$145$	2.85027	+	1.83176i	0.236702	+	0.152119i
$146$	1.09225	−	2.39168i	0.0903949	−	0.197937i
$147$	−1.84580	+	2.13017i	−0.152239	+	0.175693i
$148$	−1.36368	+	0.876381i	−0.112093	+	0.0720381i
$149$	0.194954	+	1.35594i	0.0159713	+	0.111083i	0.996248	−	0.0865492i	$-0.0275840\pi$
$149$	0.194954	+	1.35594i	0.0159713	+	0.111083i	−0.980276	+	0.197632i	$0.936675\pi$
$150$	0.139065	+	0.967216i	0.0113546	+	0.0789729i
$151$	−11.1370	+	7.15734i	−0.906320	+	0.582456i	−0.908658	−	0.417541i	$-0.862892\pi$
$151$	−11.1370	+	7.15734i	−0.906320	+	0.582456i	0.00233836	+	0.999997i	$0.499256\pi$
$152$	−10.9786	+	12.6699i	−0.890478	+	1.02767i
$153$	0.0548522	−	0.120109i	0.00443453	−	0.00971027i
$154$	3.19827	+	2.05540i	0.257724	+	0.165629i
$155$	2.08728	−	0.612880i	0.167654	−	0.0492277i
$156$	−0.195571	−	0.225701i	−0.0156582	−	0.0180705i
$157$	4.42626	+	1.29967i	0.353254	+	0.103725i	0.453545	−	0.891233i	$-0.350159\pi$
$157$	4.42626	+	1.29967i	0.353254	+	0.103725i	−0.100291	+	0.994958i	$0.531977\pi$
$158$	−1.59571	−	3.49412i	−0.126948	−	0.277977i
$159$	−1.01444	+	7.05561i	−0.0804506	+	0.559546i
$160$	−5.15254			−0.407344
$161$	−8.60232	+	4.70871i	−0.677958	+	0.371098i
$162$	0.977162			0.0767731
$163$	−2.34763	+	16.3281i	−0.183881	+	1.27892i	0.663598	+	0.748090i	$0.269029\pi$
$163$	−2.34763	+	16.3281i	−0.183881	+	1.27892i	−0.847479	+	0.530830i	$0.821880\pi$
$164$	−2.81829	−	6.17120i	−0.220072	−	0.481890i
$165$	−1.82559	−	0.536041i	−0.142122	−	0.0417308i
$166$	−9.82793	−	11.3420i	−0.762795	−	0.880312i
$167$	11.3855	−	3.34309i	0.881039	−	0.258696i	0.190235	−	0.981739i	$-0.439075\pi$
$167$	11.3855	−	3.34309i	0.881039	−	0.258696i	0.690804	+	0.723042i	$0.257257\pi$
$168$	5.11874	+	3.28961i	0.394919	+	0.253799i
$169$	−5.36648	+	11.7509i	−0.412806	+	0.903919i
$170$	0.0844942	−	0.0975116i	0.00648041	−	0.00747880i
$171$	−4.73966	+	3.04599i	−0.362451	+	0.232933i
$172$	0.0803323	+	0.558723i	0.00612528	+	0.0426023i
$173$	1.62913	+	11.3309i	0.123861	+	0.861470i	0.953117	+	0.302602i	$0.0978553\pi$
$173$	1.62913	+	11.3309i	0.123861	+	0.861470i	−0.829256	+	0.558868i	$0.811236\pi$
$174$	2.78517	−	1.78992i	0.211143	−	0.135694i
$175$	−1.33909	+	1.54539i	−0.101226	+	0.116820i
$176$	−0.646024	+	1.41460i	−0.0486959	+	0.106629i
$177$	−1.49979	−	0.963859i	−0.112731	−	0.0724480i
$178$	1.80051	−	0.528679i	0.134954	−	0.0396261i
$179$	−3.60191	−	4.15683i	−0.269220	−	0.310696i	0.605001	−	0.796225i	$-0.293173\pi$
$179$	−3.60191	−	4.15683i	−0.269220	−	0.310696i	−0.874221	+	0.485529i	$0.838627\pi$
$180$	−1.00282	−	0.294454i	−0.0747456	−	0.0219473i
$181$	8.88346	+	19.4521i	0.660302	+	1.44586i	0.882240	+	0.470800i	$0.156035\pi$
$181$	8.88346	+	19.4521i	0.660302	+	1.44586i	−0.221938	+	0.975061i	$0.571238\pi$
$182$	−0.0812555	+	0.565144i	−0.00602305	+	0.0418913i
$183$	−7.20256			−0.532428
$184$	−8.56375	−	11.4153i	−0.631328	−	0.841550i
$185$	−1.55097			−0.114030
$186$	0.302521	−	2.10408i	0.0221819	−	0.154279i
$187$	0.104365	+	0.228527i	0.00763192	+	0.0167116i
$188$	1.57732	+	0.463144i	0.115038	+	0.0337783i
$189$	1.33909	+	1.54539i	0.0974043	+	0.112411i
$190$	−5.28237	+	1.55104i	−0.383223	+	0.112524i
$191$	6.10051	+	3.92056i	0.441417	+	0.283682i	0.742411	−	0.669944i	$-0.233682\pi$
$191$	6.10051	+	3.92056i	0.441417	+	0.283682i	−0.300994	+	0.953626i	$0.597318\pi$
$192$	−2.77063	+	6.06684i	−0.199953	+	0.437837i
$193$	17.0555	−	19.6831i	1.22768	−	1.41682i	0.350568	−	0.936537i	$-0.385989\pi$
$193$	17.0555	−	19.6831i	1.22768	−	1.41682i	0.877114	−	0.480283i	$-0.159466\pi$
$194$	11.8650	−	7.62517i	0.851858	−	0.547456i
$195$	−0.0406655	−	0.282834i	−0.00291211	−	0.0202542i
$196$	−0.419243	−	2.91590i	−0.0299459	−	0.208279i
$197$	7.07214	−	4.54499i	0.503869	−	0.323817i	−0.263893	−	0.964552i	$-0.585007\pi$
$197$	7.07214	−	4.54499i	0.503869	−	0.323817i	0.767762	+	0.640735i	$0.221370\pi$
$198$	−1.21752	+	1.40510i	−0.0865255	+	0.0998558i
$199$	−6.50891	+	14.2525i	−0.461405	+	1.01034i	0.525761	+	0.850633i	$0.323781\pi$
$199$	−6.50891	+	14.2525i	−0.461405	+	1.01034i	−0.987165	+	0.159703i	$0.948946\pi$
$200$	−2.50324	−	1.60874i	−0.177006	−	0.113755i
$201$	−10.7827	+	3.16610i	−0.760556	+	0.223319i
$202$	7.64621	+	8.82419i	0.537985	+	0.620868i
$203$	6.64753	+	1.95189i	0.466565	+	0.136996i
$204$	0.0573289	+	0.125533i	0.00401383	+	0.00878906i
$205$	0.923791	−	6.42511i	0.0645204	−	0.448749i
$206$	−2.37026			−0.165144
$207$	−1.68059	−	4.49173i	−0.116809	−	0.312197i
$208$	−0.233551			−0.0161938
$209$	1.52557	−	10.6106i	0.105526	−	0.733947i
$210$	0.830059	+	1.81758i	0.0572795	+	0.125425i
$211$	11.8961	+	3.49302i	0.818963	+	0.240469i	0.664269	−	0.747493i	$-0.268743\pi$
$211$	11.8961	+	3.49302i	0.818963	+	0.240469i	0.154694	+	0.987962i	$0.450561\pi$
$212$	−4.87873	−	5.63035i	−0.335072	−	0.386694i
$213$	−5.15295	+	1.51304i	−0.353074	+	0.103672i
$214$	2.95346	+	1.89808i	0.201895	+	0.129750i
$215$	−0.224358	+	0.491276i	−0.0153011	+	0.0335047i
$216$	−1.94861	+	2.24882i	−0.132586	+	0.153013i
$217$	3.74219	−	2.40496i	0.254036	−	0.163259i
$218$	−1.81575	−	12.6288i	−0.122978	−	0.855334i
$219$	0.382932	+	2.66335i	0.0258761	+	0.179972i
$220$	1.67289	−	1.07510i	0.112786	−	0.0724835i
$221$	−0.0247079	+	0.0285144i	−0.00166203	+	0.00191809i
$222$	−0.629583	+	1.37859i	−0.0422548	+	0.0925252i
$223$	24.0814	+	15.4762i	1.61261	+	1.03636i	0.960517	+	0.278223i	$0.0897453\pi$
$223$	24.0814	+	15.4762i	1.61261	+	1.03636i	0.652093	+	0.758139i	$0.273891\pi$
$224$	−10.1094	+	2.96837i	−0.675460	+	0.198333i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	16.4956	+	4.84356i	1.09727	+	0.322189i
$227$	5.37555	+	11.7708i	0.356788	+	0.781256i	0.999880	+	0.0154676i	$0.00492369\pi$
$227$	5.37555	+	11.7708i	0.356788	+	0.781256i	−0.643093	+	0.765788i	$0.722349\pi$
$228$	0.838013	−	5.82851i	0.0554987	−	0.386002i
$229$	−25.2587			−1.66914			−0.834570	−	0.550902i	$-0.814284\pi$
$229$	−25.2587			−1.66914			−0.834570	+	0.550902i	$0.814284\pi$
$230$	−0.339123	−	4.67402i	−0.0223611	−	0.308196i
$231$	−3.89064			−0.255985
$232$	−1.43478	+	9.97910i	−0.0941978	+	0.655160i
$233$	−5.09222	−	11.1504i	−0.333602	−	0.730488i	0.666282	−	0.745700i	$-0.267885\pi$
$233$	−5.09222	−	11.1504i	−0.333602	−	0.730488i	−0.999884	+	0.0152125i	$0.995158\pi$
$234$	−0.267907	−	0.0786646i	−0.0175136	−	0.00514246i
$235$	1.03003	+	1.18871i	0.0671914	+	0.0775431i
$236$	1.78783	−	0.524955i	0.116378	−	0.0341716i
$237$	3.30698	+	2.12527i	0.214812	+	0.138051i
$238$	0.109603	−	0.239996i	0.00710448	−	0.0155566i
$239$	18.5251	−	21.3792i	1.19829	−	1.38290i	0.294102	−	0.955774i	$-0.404980\pi$
$239$	18.5251	−	21.3792i	1.19829	−	1.38290i	0.904191	−	0.427129i	$-0.140475\pi$
$240$	−0.687595	+	0.441890i	−0.0443840	+	0.0285239i
$241$	−0.483473	−	3.36263i	−0.0311432	−	0.216606i	0.968307	−	0.249763i	$-0.0803528\pi$
$241$	−0.483473	−	3.36263i	−0.0311432	−	0.216606i	−0.999450	+	0.0331575i	$0.989444\pi$
$242$	1.02628	+	7.13794i	0.0659719	+	0.458844i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	4.92965	−	5.68912i	0.315588	−	0.364208i
$245$	1.17089	−	2.56390i	0.0748057	−	0.163802i
$246$	−5.33602	−	3.42925i	−0.340212	−	0.218641i
$247$	1.54468	−	0.453558i	0.0982854	−	0.0288592i
$248$	4.23900	+	4.89207i	0.269177	+	0.310647i
$249$	14.7363	+	4.32696i	0.933874	+	0.274210i
$250$	−0.405928	−	0.888858i	−0.0256731	−	0.0562163i
$251$	−0.946306	+	6.58171i	−0.0597303	+	0.415434i	0.937916	+	0.346863i	$0.112753\pi$
$251$	−0.946306	+	6.58171i	−0.0597303	+	0.415434i	−0.997646	+	0.0685709i	$0.978156\pi$
$252$	−2.13718			−0.134629
$253$	8.55279	+	3.18001i	0.537709	+	0.199926i
$254$	2.21922			0.139246
$255$	−0.0187915	+	0.130698i	−0.00117677	+	0.00818462i
$256$	−7.07886	−	15.5005i	−0.442429	−	0.968784i
$257$	22.5727	+	6.62793i	1.40804	+	0.413439i	0.895439	−	0.445185i	$-0.146862\pi$
$257$	22.5727	+	6.62793i	1.40804	+	0.413439i	0.512606	+	0.858624i	$0.328680\pi$
$258$	0.345601	+	0.398845i	0.0215162	+	0.0248310i
$259$	−3.04303	+	0.893514i	−0.189085	+	0.0555202i
$260$	0.251236	+	0.161460i	0.0155810	+	0.0100133i
$261$	−1.40748	+	3.08194i	−0.0871205	+	0.190767i
$262$	−10.7576	+	12.4150i	−0.664609	+	0.767000i
$263$	3.73120	−	2.39789i	0.230075	−	0.147860i	−0.420524	−	0.907281i	$-0.638154\pi$
$263$	3.73120	−	2.39789i	0.230075	−	0.147860i	0.650600	+	0.759421i	$0.274518\pi$
$264$	−0.805726	−	5.60395i	−0.0495890	−	0.344899i
$265$	−1.01444	−	7.05561i	−0.0623167	−	0.433422i
$266$	−9.47052	+	6.08633i	−0.580675	+	0.373177i
$267$	−1.25758	+	1.45133i	−0.0769629	+	0.0888199i
$268$	4.87921	−	10.6840i	0.298045	−	0.652628i
$269$	7.05591	+	4.53456i	0.430206	+	0.276477i	0.737772	−	0.675050i	$-0.235878\pi$
$269$	7.05591	+	4.53456i	0.430206	+	0.276477i	−0.307566	+	0.951527i	$0.599514\pi$
$270$	−0.937580	+	0.275298i	−0.0570593	+	0.0167541i
$271$	16.6001	+	19.1575i	1.00838	+	1.16374i	0.986464	+	0.163978i	$0.0524326\pi$
$271$	16.6001	+	19.1575i	1.00838	+	1.16374i	0.0219206	+	0.999760i	$0.493022\pi$
$272$	0.103552	+	0.0304056i	0.00627877	+	0.00184361i
$273$	−0.242727	−	0.531498i	−0.0146905	−	0.0321677i
$274$	1.14023	−	7.93048i	0.0688839	−	0.479098i
$275$	1.90266			0.114735
$276$	4.69815	+	1.74682i	0.282795	+	0.105146i
$277$	−6.92351			−0.415994			−0.207997	−	0.978130i	$-0.566694\pi$
$277$	−6.92351			−0.415994			−0.207997	+	0.978130i	$0.566694\pi$
$278$	2.61910	−	18.2163i	0.157083	−	1.09254i
$279$	0.903693	+	1.97881i	0.0541027	+	0.118468i
$280$	−5.83819	−	1.71425i	−0.348898	−	0.102446i
$281$	−17.5918	−	20.3020i	−1.04944	−	1.21112i	−0.976888	−	0.213751i	$-0.931432\pi$
$281$	−17.5918	−	20.3020i	−1.04944	−	1.21112i	−0.0725500	−	0.997365i	$-0.523114\pi$
$282$	1.47471	−	0.433015i	0.0878179	−	0.0257857i
$283$	−22.9997	−	14.7810i	−1.36719	−	0.878641i	−0.368493	−	0.929630i	$-0.620126\pi$
$283$	−22.9997	−	14.7810i	−1.36719	−	0.878641i	−0.998699	+	0.0509893i	$0.983763\pi$
$284$	2.33172	−	5.10576i	0.138362	−	0.302971i
$285$	3.68951	−	4.25793i	0.218548	−	0.252218i
$286$	0.446920	−	0.287218i	0.0264270	−	0.0169836i
$287$	−1.88901	−	13.1383i	−0.111505	−	0.775532i
$288$	−0.733283	−	5.10009i	−0.0432091	−	0.300526i
$289$	−14.2866	+	9.18147i	−0.840391	+	0.540086i
$290$	−2.16807	+	2.50209i	−0.127314	+	0.146928i
$291$	−5.99593	+	13.1293i	−0.351488	+	0.769650i
$292$	−2.36580	−	1.52041i	−0.138448	−	0.0889752i
$293$	12.5964	−	3.69864i	0.735890	−	0.216077i	0.107751	−	0.994178i	$-0.465635\pi$
$293$	12.5964	−	3.69864i	0.735890	−	0.216077i	0.628139	+	0.778101i	$0.283817\pi$
$294$	−1.80365	−	2.08152i	−0.105191	−	0.121397i
$295$	1.71059	+	0.502275i	0.0995945	+	0.0292436i
$296$	−1.91718	−	4.19803i	−0.111434	−	0.244006i
$297$	0.270777	−	1.88329i	0.0157121	−	0.109280i
$298$	−1.33860			−0.0775428
$299$	0.0991666	+	1.36678i	0.00573495	+	0.0790431i
$300$	1.04515			0.0603420
$301$	−0.157170	+	1.09314i	−0.00905914	+	0.0630077i
$302$	−5.37393	−	11.7673i	−0.309235	−	0.677130i
$303$	−11.4649	−	3.36641i	−0.658644	−	0.193395i
$304$	−3.01561	−	3.48020i	−0.172957	−	0.199603i
$305$	6.91080	−	2.02920i	0.395712	−	0.116191i
$306$	0.108544	+	0.0697569i	0.00620504	+	0.00398774i
$307$	−12.1525	+	26.6103i	−0.693579	+	1.51873i	0.154007	+	0.988070i	$0.450782\pi$
$307$	−12.1525	+	26.6103i	−0.693579	+	1.51873i	−0.847586	+	0.530657i	$0.821945\pi$
$308$	2.66287	−	3.07312i	0.151731	−	0.175107i
$309$	2.04059	−	1.31141i	0.116085	−	0.0746034i
$310$	0.302521	+	2.10408i	0.0171820	+	0.119504i
$311$	−0.828542	−	5.76264i	−0.0469823	−	0.326769i	−0.999735	−	0.0230219i	$-0.992671\pi$
$311$	−0.828542	−	5.76264i	−0.0469823	−	0.326769i	0.952753	−	0.303747i	$-0.0982378\pi$
$312$	0.715284	−	0.459685i	0.0404950	−	0.0260245i
$313$	7.54691	−	8.70960i	0.426577	−	0.492296i	−0.501252	−	0.865301i	$-0.667127\pi$
$313$	7.54691	−	8.70960i	0.426577	−	0.492296i	0.927829	+	0.373005i	$0.121673\pi$
$314$	−1.87260	+	4.10041i	−0.105677	+	0.231400i
$315$	−1.72023	−	1.10553i	−0.0969241	−	0.0622893i
$316$	−3.94210	+	1.15750i	−0.221760	+	0.0651147i
$317$	−5.23538	−	6.04195i	−0.294048	−	0.339350i	0.589432	−	0.807818i	$-0.299352\pi$
$317$	−5.23538	−	6.04195i	−0.294048	−	0.339350i	−0.883480	+	0.468468i	$0.844806\pi$
$318$	−6.68322	−	1.96237i	−0.374777	−	0.110044i
$319$	−2.67795	−	5.86389i	−0.149936	−	0.328315i
$320$	0.949177	−	6.60167i	0.0530606	−	0.369045i
$321$	−3.59284			−0.200533
$322$	−3.35806	−	8.97512i	−0.187137	−	0.500164i
$323$	−0.743929			−0.0413933
$324$	0.148741	−	1.03452i	0.00826338	−	0.0574731i
$325$	0.118702	+	0.259921i	0.00658440	+	0.0144178i
$326$	−15.4664	−	4.54134i	−0.856603	−	0.251521i
$327$	8.55045	+	9.86775i	0.472841	+	0.545688i
$328$	18.5328	−	5.44173i	1.02330	−	0.300469i
$329$	2.70574	+	1.73887i	0.149172	+	0.0958672i
$330$	0.772343	−	1.69119i	0.0425161	−	0.0930972i
$331$	−1.26080	+	1.45504i	−0.0692998	+	0.0799762i	−0.789341	−	0.613955i	$-0.789578\pi$
$331$	−1.26080	+	1.45504i	−0.0692998	+	0.0799762i	0.720041	+	0.693932i	$0.244123\pi$
$332$	−13.5037	+	8.67831i	−0.741113	+	0.476284i
$333$	−0.220726	−	1.53519i	−0.0120957	−	0.0841277i
$334$	1.65017	+	11.4772i	0.0902932	+	0.628003i
$335$	9.45397	−	6.07570i	0.516525	−	0.331951i
$336$	−1.09450	+	1.26312i	−0.0597097	+	0.0689087i
$337$	4.45175	−	9.74798i	0.242502	−	0.531006i	−0.748771	−	0.662829i	$-0.769356\pi$
$337$	4.45175	−	9.74798i	0.242502	−	0.531006i	0.991273	+	0.131823i	$0.0420830\pi$
$338$	−10.6194	−	6.82468i	−0.577620	−	0.371214i
$339$	−16.8812	+	4.95676i	−0.916859	+	0.269214i
$340$	−0.0903734	−	0.104296i	−0.00490119	−	0.00565627i
$341$	−3.97138	−	1.16610i	−0.215062	−	0.0631480i
$342$	−2.28701	−	5.00786i	−0.123668	−	0.270794i
$343$	2.85733	−	19.8732i	0.154281	−	1.07305i
$344$	−1.60707			−0.0866476
$345$	2.87798	+	3.83630i	0.154945	+	0.206540i
$346$	−11.1860			−0.601361
$347$	4.42117	−	30.7499i	0.237341	−	1.65074i	−0.427690	−	0.903925i	$-0.640673\pi$
$347$	4.42117	−	30.7499i	0.237341	−	1.65074i	0.665031	−	0.746816i	$-0.268418\pi$
$348$	−1.47103	−	3.22110i	−0.0788554	−	0.172669i
$349$	3.84963	+	1.13035i	0.206066	+	0.0605065i	0.383137	−	0.923692i	$-0.374844\pi$
$349$	3.84963	+	1.13035i	0.206066	+	0.0605065i	−0.177070	+	0.984198i	$0.556662\pi$
$350$	−1.30851	−	1.51010i	−0.0699426	−	0.0807181i
$351$	0.274168	−	0.0805031i	0.0146340	−	0.00429694i
$352$	8.24725	+	5.30019i	0.439580	+	0.282501i
$353$	−5.22038	+	11.4310i	−0.277853	+	0.608413i	−0.996183	−	0.0872896i	$-0.972179\pi$
$353$	−5.22038	+	11.4310i	−0.277853	+	0.608413i	0.718330	+	0.695702i	$0.244907\pi$
$354$	1.14083	−	1.31659i	0.0606343	−	0.0699757i
$355$	4.51795	−	2.90351i	0.239788	−	0.154102i
$356$	−0.285640	−	1.98667i	−0.0151389	−	0.105293i
$357$	0.0384257	+	0.267257i	0.00203370	+	0.0141447i
$358$	4.52145	−	2.90576i	0.238966	−	0.153574i
$359$	−12.7378	+	14.7002i	−0.672274	+	0.775846i	−0.984730	−	0.174086i	$-0.944303\pi$
$359$	−12.7378	+	14.7002i	−0.672274	+	0.775846i	0.312456	+	0.949932i	$0.398848\pi$
$360$	1.23611	−	2.70671i	0.0651489	−	0.142656i
$361$	10.7196	+	6.88908i	0.564190	+	0.362583i
$362$	−20.0497	+	5.88713i	−1.05379	+	0.309421i
$363$	−4.83280	−	5.57735i	−0.253656	−	0.292735i
$364$	0.585946	+	0.172049i	0.0307119	+	0.00901783i
$365$	−1.11777	−	2.44758i	−0.0585069	−	0.128112i
$366$	1.00162	−	6.96643i	0.0523556	−	0.364141i
$367$	−25.3847			−1.32507			−0.662534	−	0.749032i	$-0.730519\pi$
$367$	−25.3847			−1.32507			−0.662534	+	0.749032i	$0.730519\pi$
$368$	3.43844	−	1.88212i	0.179241	−	0.0981123i
$369$	6.49118			0.337917
$370$	0.215685	−	1.50013i	0.0112130	−	0.0779878i
$371$	−6.05508	−	13.2588i	−0.314364	−	0.688361i
$372$	−2.18153	−	0.640554i	−0.113107	−	0.0332112i
$373$	−5.54711	−	6.40171i	−0.287219	−	0.331468i	0.593744	−	0.804654i	$-0.297649\pi$
$373$	−5.54711	−	6.40171i	−0.287219	−	0.331468i	−0.880962	+	0.473186i	$0.843104\pi$
$374$	−0.235549	+	0.0691634i	−0.0121799	+	0.00357635i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	−1.94427	+	4.25736i	−0.100268	+	0.219557i
$377$	0.633991	−	0.731665i	0.0326522	−	0.0376826i
$378$	−1.68095	+	1.08028i	−0.0864585	+	0.0555635i
$379$	2.61757	+	18.2056i	0.134456	+	0.935161i	0.939647	+	0.342145i	$0.111154\pi$
$379$	2.61757	+	18.2056i	0.134456	+	0.935161i	−0.805191	+	0.593015i	$0.797937\pi$
$380$	0.838013	+	5.82851i	0.0429891	+	0.298996i
$381$	−1.91056	+	1.22784i	−0.0978808	+	0.0629042i
$382$	−4.64039	+	5.35530i	−0.237423	+	0.274001i
$383$	−14.4382	+	31.6153i	−0.737760	+	1.61547i	0.0494448	+	0.998777i	$0.484255\pi$
$383$	−14.4382	+	31.6153i	−0.737760	+	1.61547i	−0.787205	+	0.616692i	$0.788472\pi$
$384$	3.18653	+	2.04786i	0.162612	+	0.104504i
$385$	3.73304	−	1.09612i	0.190254	−	0.0558635i
$386$	16.6660	+	19.2336i	0.848276	+	0.978963i
$387$	−0.518205	−	0.152159i	−0.0263418	−	0.00773466i
$388$	−6.26667	−	13.7221i	−0.318142	−	0.696634i
$389$	−4.09640	+	28.4911i	−0.207696	+	1.44455i	0.572955	+	0.819587i	$0.305797\pi$
$389$	−4.09640	+	28.4911i	−0.207696	+	1.44455i	−0.780651	+	0.624968i	$0.785112\pi$
$390$	0.279217			0.0141387
$391$	0.133971	−	0.618917i	0.00677520	−	0.0313000i
$392$	8.38709			0.423612
$393$	2.39250	−	16.6402i	0.120686	−	0.839386i
$394$	3.41250	+	7.47234i	0.171919	+	0.376451i
$395$	−3.77179	−	1.10750i	−0.189779	−	0.0557242i
$396$	1.30224	+	1.50286i	0.0654399	+	0.0755217i
$397$	20.6784	−	6.07172i	1.03782	−	0.304731i	0.281932	−	0.959434i	$-0.409025\pi$
$397$	20.6784	−	6.07172i	1.03782	−	0.304731i	0.755886	+	0.654704i	$0.227207\pi$
$398$	−12.8801	−	8.27755i	−0.645622	−	0.414916i
$399$	4.78589	−	10.4796i	0.239594	−	0.524638i
$400$	0.535247	−	0.617708i	0.0267624	−	0.0308854i
$401$	−21.8312	+	14.0301i	−1.09020	+	0.700628i	−0.956891	−	0.290447i	$-0.906196\pi$
$401$	−21.8312	+	14.0301i	−1.09020	+	0.700628i	−0.133307	+	0.991075i	$0.542560\pi$
$402$	−1.56280	−	10.8695i	−0.0779455	−	0.542123i
$403$	−0.0884635	−	0.615277i	−0.00440668	−	0.0306491i
$404$	10.5060	−	6.75180i	0.522693	−	0.335914i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	−2.81234	+	6.15816i	−0.139574	+	0.305625i
$407$	2.48252	+	1.59542i	0.123054	+	0.0790819i
$408$	−0.376989	+	0.110694i	−0.0186638	+	0.00548017i
$409$	−6.64533	−	7.66912i	−0.328590	−	0.379213i	0.567283	−	0.823523i	$-0.307995\pi$
$409$	−6.64533	−	7.66912i	−0.328590	−	0.379213i	−0.895873	+	0.444309i	$0.853449\pi$
$410$	6.08600	+	1.78701i	0.300566	+	0.0882542i
$411$	3.40611	+	7.45833i	0.168011	+	0.367892i
$412$	−0.360794	+	2.50938i	−0.0177750	+	0.123628i
$413$	3.64556			0.179386
$414$	4.57818	−	1.00085i	0.225005	−	0.0491892i
$415$	−15.3584			−0.753915
$416$	−0.209530	+	1.45732i	−0.0102731	+	0.0714508i
$417$	7.82381	+	17.1317i	0.383133	+	0.838945i
$418$	10.0505	+	2.95111i	0.491588	+	0.144343i
$419$	9.87640	+	11.3980i	0.482494	+	0.556827i	0.943844	−	0.330391i	$-0.107180\pi$
$419$	9.87640	+	11.3980i	0.482494	+	0.556827i	−0.461351	+	0.887218i	$0.652635\pi$
$420$	2.05061	−	0.602112i	0.100059	−	0.0293801i
$421$	−7.46530	−	4.79766i	−0.363836	−	0.233823i	0.345930	−	0.938260i	$-0.387563\pi$
$421$	−7.46530	−	4.79766i	−0.363836	−	0.233823i	−0.709767	+	0.704437i	$0.751200\pi$
$422$	−5.03283	+	11.0204i	−0.244995	+	0.536463i
$423$	−1.03003	+	1.18871i	−0.0500815	+	0.0577972i
$424$	17.8435	−	11.4673i	0.866557	−	0.556903i
$425$	−0.0187915	−	0.130698i	−0.000911522	−	0.00633978i
$426$	−0.746846	−	5.19443i	−0.0361848	−	0.251671i
$427$	12.3901	−	7.96262i	0.599598	−	0.385338i
$428$	2.45905	−	2.83789i	0.118863	−	0.137175i
$429$	−0.225849	+	0.494541i	−0.0109041	+	0.0238767i
$430$	−0.443970	−	0.285322i	−0.0214101	−	0.0137594i
$431$	0.195454	−	0.0573905i	0.00941469	−	0.00276440i	−0.277022	−	0.960864i	$-0.589347\pi$
$431$	0.195454	−	0.0573905i	0.00941469	−	0.00276440i	0.286437	+	0.958099i	$0.407529\pi$
$432$	−0.535247	−	0.617708i	−0.0257521	−	0.0297195i
$433$	−0.646443	−	0.189813i	−0.0310661	−	0.00912183i	0.266163	−	0.963928i	$-0.414244\pi$
$433$	−0.646443	−	0.189813i	−0.0310661	−	0.00912183i	−0.297229	+	0.954806i	$0.596062\pi$
$434$	1.80571	+	3.95395i	0.0866768	+	0.189796i
$435$	0.482180	−	3.35363i	0.0231187	−	0.160794i
$436$	−13.6465			−0.653548
$437$	−19.0863	+	19.1256i	−0.913022	+	0.914901i
$438$	−2.62929			−0.125632
$439$	5.00909	−	34.8390i	0.239071	−	1.66277i	−0.417627	−	0.908619i	$-0.637138\pi$
$439$	5.00909	−	34.8390i	0.239071	−	1.66277i	0.656697	−	0.754154i	$-0.271953\pi$
$440$	2.35190	+	5.14995i	0.112123	+	0.245514i
$441$	2.70444	+	0.794095i	0.128783	+	0.0378141i
$442$	−0.0241436	−	0.0278632i	−0.00114840	−	0.00132532i
$443$	−6.72423	+	1.97441i	−0.319478	+	0.0938072i	−0.437540	−	0.899199i	$-0.644150\pi$
$443$	−6.72423	+	1.97441i	−0.319478	+	0.0938072i	0.118062	+	0.993006i	$0.462332\pi$
$444$	1.36368	+	0.876381i	0.0647172	+	0.0415912i
$445$	0.797756	−	1.74684i	0.0378173	−	0.0828083i
$446$	−18.3177	+	21.1397i	−0.867367	+	1.00100i
$447$	1.15242	−	0.740614i	0.0545075	−	0.0350298i
$448$	−1.94092	−	13.4994i	−0.0916998	−	0.637786i
$449$	4.70364	+	32.7146i	0.221979	+	1.54390i	0.730540	+	0.682870i	$0.239268\pi$
$449$	4.70364	+	32.7146i	0.221979	+	1.54390i	−0.508561	+	0.861026i	$0.669823\pi$
$450$	0.822041	−	0.528294i	0.0387514	−	0.0249040i
$451$	−8.08786	+	9.33389i	−0.380843	+	0.439516i
$452$	7.63877	−	16.7266i	0.359297	−	0.786751i
$453$	11.1370	+	7.15734i	0.523264	+	0.336281i
$454$	−12.1325	+	3.56241i	−0.569405	+	0.167192i
$455$	0.382635	+	0.441584i	0.0179382	+	0.0207018i
$456$	16.0856	+	4.72316i	0.753278	+	0.221182i
$457$	4.78045	+	10.4677i	0.223620	+	0.489660i	0.987874	−	0.155255i	$-0.0496200\pi$
$457$	4.78045	+	10.4677i	0.223620	+	0.489660i	−0.764254	+	0.644915i	$0.776893\pi$
$458$	3.51259	−	24.4306i	0.164132	−	1.14157i
$459$	−0.132042			−0.00616318
$460$	−4.99998	−	0.352439i	−0.233125	−	0.0164326i
$461$	32.9862			1.53632			0.768161	−	0.640256i	$-0.221172\pi$
$461$	32.9862			1.53632			0.768161	+	0.640256i	$0.221172\pi$
$462$	0.541051	−	3.76309i	0.0251720	−	0.175075i
$463$	−6.61871	−	14.4930i	−0.307598	−	0.673545i	0.691195	−	0.722668i	$-0.257085\pi$
$463$	−6.61871	−	14.4930i	−0.307598	−	0.673545i	−0.998793	+	0.0491234i	$0.984357\pi$
$464$	−2.65709	−	0.780192i	−0.123352	−	0.0362195i
$465$	−1.42458	−	1.64406i	−0.0660634	−	0.0762413i
$466$	11.4930	−	3.37465i	0.532403	−	0.156328i
$467$	16.6582	+	10.7056i	0.770849	+	0.495394i	0.865985	−	0.500070i	$-0.166692\pi$
$467$	16.6582	+	10.7056i	0.770849	+	0.495394i	−0.0951363	+	0.995464i	$0.530329\pi$
$468$	−0.124062	+	0.271657i	−0.00573476	+	0.0125574i
$469$	15.0486	−	17.3670i	0.694880	−	0.801934i
$470$	−1.29298	+	0.830949i	−0.0596408	+	0.0383288i
$471$	−0.656516	−	4.56617i	−0.0302507	−	0.210398i
$472$	0.754972	+	5.25094i	0.0347504	+	0.241694i
$473$	0.864466	−	0.555558i	0.0397482	−	0.0255446i
$474$	−2.51548	+	2.90302i	−0.115540	+	0.133340i
$475$	−2.34047	+	5.12491i	−0.107388	+	0.235147i
$476$	−0.237399	−	0.152567i	−0.0108812	−	0.00699290i
$477$	6.83942	−	2.00823i	0.313156	−	0.0919508i
$478$	18.1021	+	20.8909i	0.827970	+	0.955528i
$479$	16.6164	+	4.87902i	0.759223	+	0.222928i	0.638357	−	0.769741i	$-0.279615\pi$
$479$	16.6164	+	4.87902i	0.759223	+	0.222928i	0.120867	+	0.992669i	$0.461433\pi$
$480$	2.14044	+	4.68692i	0.0976974	+	0.213927i
$481$	−0.0630710	+	0.438668i	−0.00287579	+	0.0200016i
$482$	3.31962			0.151205
$483$	7.85673	+	5.86888i	0.357493	+	0.267043i
$484$	7.71312			0.350596
$485$	2.05411	−	14.2867i	0.0932725	−	0.648724i
$486$	−0.405928	−	0.888858i	−0.0184133	−	0.0403194i
$487$	−13.8349	−	4.06230i	−0.626919	−	0.184080i	−0.0471857	−	0.998886i	$-0.515025\pi$
$487$	−13.8349	−	4.06230i	−0.626919	−	0.184080i	−0.579734	+	0.814806i	$0.696843\pi$
$488$	14.0350	+	16.1972i	0.635334	+	0.733214i
$489$	15.8278	−	4.64748i	0.715760	−	0.210166i
$490$	2.31702	+	1.48906i	0.104672	+	0.0672687i
$491$	−7.80386	+	17.0881i	−0.352183	+	0.771174i	0.647773	+	0.761833i	$0.275700\pi$
$491$	−7.80386	+	17.0881i	−0.352183	+	0.771174i	−0.999956	+	0.00934031i	$0.997027\pi$
$492$	−4.44276	+	5.12722i	−0.200295	+	0.231153i
$493$	−0.376354	+	0.241868i	−0.0169502	+	0.0108932i
$494$	0.223879	+	1.55711i	0.0100728	+	0.0700577i
$495$	0.270777	+	1.88329i	0.0121705	+	0.0846477i
$496$	−1.49579	+	0.961287i	−0.0671630	+	0.0431631i
$497$	7.19156	−	8.29951i	0.322586	−	0.372284i
$498$	−6.23441	+	13.6514i	−0.279370	+	0.611736i
$499$	7.26314	+	4.66774i	0.325143	+	0.208957i	0.693021	−	0.720917i	$-0.256279\pi$
$499$	7.26314	+	4.66774i	0.325143	+	0.208957i	−0.367878	+	0.929874i	$0.619916\pi$
$500$	−1.00282	+	0.294454i	−0.0448474	+	0.0131684i
$501$	−7.77070	−	8.96787i	−0.347169	−	0.400655i
$502$	−6.23433	−	1.83057i	−0.278252	−	0.0817021i
$503$	−3.33934	−	7.31213i	−0.148894	−	0.326032i	0.820459	−	0.571706i	$-0.193718\pi$
$503$	−3.33934	−	7.31213i	−0.148894	−	0.326032i	−0.969353	+	0.245674i	$0.920991\pi$
$504$	0.865937	−	6.02272i	0.0385719	−	0.268273i
$505$	11.9490			0.531722
$506$	−4.26515	+	7.83017i	−0.189609	+	0.348093i
$507$	12.9184			0.573724
$508$	0.337803	−	2.34947i	0.0149876	−	0.104241i
$509$	−3.65064	−	7.99378i	−0.161812	−	0.354318i	0.811308	−	0.584619i	$-0.198756\pi$
$509$	−3.65064	−	7.99378i	−0.161812	−	0.354318i	−0.973119	+	0.230301i	$0.926029\pi$
$510$	−0.123800	−	0.0363509i	−0.00548195	−	0.00160965i
$511$	−3.60313	−	4.15824i	−0.159393	−	0.183950i
$512$	8.70798	−	2.55689i	0.384842	−	0.113000i
$513$	4.73966	+	3.04599i	0.209261	+	0.134484i
$514$	−9.54971	+	20.9109i	−0.421219	+	0.922342i
$515$	−1.58847	+	1.83319i	−0.0699962	+	0.0807799i
$516$	0.474861	−	0.305175i	0.0209046	−	0.0134346i
$517$	−0.425903	−	2.96222i	−0.0187312	−	0.130278i
$518$	−0.441043	−	3.06752i	−0.0193783	−	0.134779i
$519$	9.63016	−	6.18893i	0.422717	−	0.271664i
$520$	−0.556801	+	0.642583i	−0.0244174	+	0.0281791i
$521$	−13.7958	+	30.2086i	−0.604406	+	1.32346i	0.321930	+	0.946764i	$0.395669\pi$
$521$	−13.7958	+	30.2086i	−0.604406	+	1.32346i	−0.926335	+	0.376700i	$0.877059\pi$
$522$	−2.78517	−	1.78992i	−0.121904	−	0.0783428i
$523$	−15.6321	+	4.58999i	−0.683543	+	0.200706i	−0.605025	−	0.796206i	$-0.706837\pi$
$523$	−15.6321	+	4.58999i	−0.683543	+	0.200706i	−0.0785179	+	0.996913i	$0.525019\pi$
$524$	11.5062	+	13.2788i	0.502649	+	0.580088i
$525$	1.96201	+	0.576099i	0.0856293	+	0.0251430i
$526$	1.80040	+	3.94234i	0.0785014	+	0.171894i
$527$	−0.0408790	+	0.284320i	−0.00178072	+	0.0123852i
$528$	1.55513			0.0676784
$529$	−12.4745	−	19.3232i	−0.542369	−	0.840140i
$530$	6.96537			0.302556
$531$	−0.253720	+	1.76466i	−0.0110105	+	0.0765798i
$532$	5.00199	+	10.9528i	0.216864	+	0.474865i
$533$	−1.77968	−	0.522560i	−0.0770863	−	0.0226346i
$534$	−1.22886	−	1.41818i	−0.0531781	−	0.0613708i
$535$	3.44730	−	1.01222i	0.149040	−	0.0437621i
$536$	28.1313	+	18.0789i	1.21509	+	0.780890i
$537$	−2.28490	+	5.00322i	−0.0986005	+	0.215905i
$538$	−5.36712	+	6.19399i	−0.231393	+	0.267042i
$539$	−4.51153	+	2.89938i	−0.194325	+	0.124885i
$540$	0.148741	+	1.03452i	0.00640079	+	0.0445185i
$541$	−0.389967	−	2.71228i	−0.0167660	−	0.116610i	0.979720	−	0.200373i	$-0.0642153\pi$
$541$	−0.389967	−	2.71228i	−0.0167660	−	0.116610i	−0.996486	+	0.0837628i	$0.973306\pi$
$542$	−20.8380	+	13.3918i	−0.895068	+	0.575225i
$543$	14.0039	−	16.1614i	0.600965	−	0.693550i
$544$	0.282628	−	0.618869i	0.0121176	−	0.0265338i
$545$	−10.9842	−	7.05910i	−0.470510	−	0.302378i
$546$	0.547828	−	0.160857i	0.0234449	−	0.00688403i
$547$	−11.4510	−	13.2152i	−0.489611	−	0.565041i	0.456151	−	0.889902i	$-0.349228\pi$
$547$	−11.4510	−	13.2152i	−0.489611	−	0.565041i	−0.945762	+	0.324862i	$0.894682\pi$
$548$	−8.22239	−	2.41431i	−0.351243	−	0.103134i
$549$	2.99205	+	6.55168i	0.127698	+	0.279619i
$550$	−0.264593	+	1.84028i	−0.0112823	+	0.0784699i
$551$	19.0888			0.813210
$552$	−6.82625	+	12.5320i	−0.290545	+	0.533396i
$553$	−8.03832			−0.341824
$554$	0.962816	−	6.69653i	0.0409061	−	0.284508i
$555$	0.644297	+	1.41081i	0.0273489	+	0.0598857i
$556$	−18.8868	−	5.54566i	−0.800978	−	0.235188i
$557$	−11.5062	−	13.2789i	−0.487534	−	0.562645i	0.457671	−	0.889122i	$-0.348684\pi$
$557$	−11.5062	−	13.2789i	−0.487534	−	0.562645i	−0.945205	+	0.326477i	$0.894138\pi$
$558$	−2.03961	+	0.598883i	−0.0863436	+	0.0253528i
$559$	0.129826	+	0.0834342i	0.00549106	+	0.00352889i
$560$	0.694301	−	1.52031i	0.0293396	−	0.0642447i
$561$	0.164521	−	0.189867i	0.00694609	−	0.00801621i
$562$	22.0828	−	14.1918i	0.931508	−	0.598644i
$563$	0.763399	+	5.30956i	0.0321734	+	0.223771i	0.999564	−	0.0295171i	$-0.00939696\pi$
$563$	0.763399	+	5.30956i	0.0321734	+	0.223771i	−0.967391	+	0.253288i	$0.918488\pi$
$564$	−0.233953	−	1.62718i	−0.00985122	−	0.0685167i
$565$	14.8009	−	9.51195i	0.622678	−	0.400171i
$566$	17.4949	−	20.1902i	0.735366	−	0.848657i
$567$	0.849459	−	1.86006i	0.0356739	−	0.0781150i
$568$	13.4436	+	8.63971i	0.564083	+	0.362514i
$569$	−38.7386	+	11.3747i	−1.62400	+	0.476851i	−0.962091	−	0.272729i	$-0.912074\pi$
$569$	−38.7386	+	11.3747i	−1.62400	+	0.476851i	−0.661914	+	0.749580i	$0.730256\pi$
$570$	3.60525	+	4.16068i	0.151007	+	0.174272i
$571$	20.5755	+	6.04150i	0.861056	+	0.252829i	0.682307	−	0.731066i	$-0.260977\pi$
$571$	20.5755	+	6.04150i	0.861056	+	0.252829i	0.178749	+	0.983895i	$0.442795\pi$
$572$	−0.236047	−	0.516872i	−0.00986963	−	0.0216115i
$573$	1.03202	−	7.17788i	0.0431134	−	0.299860i
$574$	12.9703			0.541371
$575$	−3.84221	−	2.87009i	−0.160231	−	0.119691i
$576$	6.66956			0.277898
$577$	−2.50336	+	17.4113i	−0.104216	+	0.724840i	0.868977	+	0.494852i	$0.164778\pi$
$577$	−2.50336	+	17.4113i	−0.104216	+	0.724840i	−0.973193	+	0.229988i	$0.926131\pi$
$578$	−6.89370	−	15.0951i	−0.286740	−	0.627873i
$579$	−24.9895	−	7.33757i	−1.03853	−	0.304939i
$580$	2.31893	+	2.67619i	0.0962884	+	0.111123i
$581$	−30.1334	+	8.84797i	−1.25014	+	0.367076i
$582$	−11.8650	−	7.62517i	−0.491820	−	0.316074i
$583$	−5.63405	+	12.3369i	−0.233339	+	0.510940i
$584$	5.24320	−	6.05097i	0.216965	−	0.250391i
$585$	−0.240382	+	0.154484i	−0.00993858	+	0.00638714i
$586$	1.82567	+	12.6978i	0.0754176	+	0.524541i
$587$	1.62210	+	11.2819i	0.0669512	+	0.465656i	0.995524	+	0.0945061i	$0.0301272\pi$
$587$	1.62210	+	11.2819i	0.0669512	+	0.465656i	−0.928573	+	0.371150i	$0.878964\pi$
$588$	−2.47824	+	1.59267i	−0.102201	+	0.0656804i
$589$	8.02616	−	9.26268i	0.330712	−	0.381662i
$590$	−0.723691	+	1.58466i	−0.0297939	+	0.0652395i
$591$	−7.07214	−	4.54499i	−0.290909	−	0.186956i
$592$	1.21633	−	0.357147i	0.0499909	−	0.0146786i
$593$	7.13570	+	8.23503i	0.293028	+	0.338172i	0.883106	−	0.469174i	$-0.155448\pi$
$593$	7.13570	+	8.23503i	0.293028	+	0.338172i	−0.590078	+	0.807346i	$0.700903\pi$
$594$	1.78390	+	0.523799i	0.0731942	+	0.0214917i
$595$	−0.112164	−	0.245605i	−0.00459828	−	0.0100688i
$596$	−0.203757	+	1.41716i	−0.00834623	+	0.0580493i
$597$	15.6685			0.641267
$598$	−1.33576	−	0.0941556i	−0.0546235	−	0.00385031i
$599$	24.7307			1.01047			0.505235	−	0.862982i	$-0.331406\pi$
$599$	24.7307			1.01047			0.505235	+	0.862982i	$0.331406\pi$
$600$	−0.423473	+	2.94532i	−0.0172882	+	0.120242i
$601$	−4.80779	−	10.5276i	−0.196114	−	0.429429i	0.785871	−	0.618391i	$-0.212215\pi$
$601$	−4.80779	−	10.5276i	−0.196114	−	0.429429i	−0.981984	+	0.188961i	$0.939488\pi$
$602$	−1.03545	−	0.304035i	−0.0422017	−	0.0123915i
$603$	7.35929	+	8.49308i	0.299694	+	0.345865i
$604$	−13.2759	+	3.89817i	−0.540190	+	0.158614i
$605$	6.20835	+	3.98987i	0.252406	+	0.162211i
$606$	4.85042	−	10.6209i	0.197035	−	0.431446i
$607$	2.61430	−	3.01706i	0.106111	−	0.122459i	−0.700210	−	0.713937i	$-0.746910\pi$
$607$	2.61430	−	3.01706i	0.106111	−	0.122459i	0.806321	+	0.591479i	$0.201456\pi$
$608$	−24.4213	+	15.6946i	−0.990414	+	0.636500i
$609$	−0.985982	−	6.85766i	−0.0399540	−	0.277886i
$610$	1.00162	+	6.96643i	0.0405545	+	0.282063i
$611$	0.378095	−	0.242987i	0.0152961	−	0.00983021i
$612$	0.0903734	−	0.104296i	0.00365313	−	0.00421594i
$613$	4.34059	−	9.50456i	0.175315	−	0.383886i	−0.801493	−	0.598004i	$-0.795961\pi$
$613$	4.34059	−	9.50456i	0.175315	−	0.383886i	0.976808	+	0.214118i	$0.0686879\pi$
$614$	−24.0479	−	15.4546i	−0.970494	−	0.623698i
$615$	−6.22824	+	1.82878i	−0.251147	+	0.0737434i
$616$	7.58134	+	8.74934i	0.305461	+	0.352521i
$617$	−25.4318	−	7.46746i	−1.02385	−	0.300628i	−0.273640	−	0.961832i	$-0.588228\pi$
$617$	−25.4318	−	7.46746i	−1.02385	−	0.300628i	−0.750206	+	0.661204i	$0.770046\pi$
$618$	0.984641	+	2.15606i	0.0396081	+	0.0867296i
$619$	−6.60123	+	45.9126i	−0.265326	+	1.84538i	0.225650	+	0.974208i	$0.427549\pi$
$619$	−6.60123	+	45.9126i	−0.265326	+	1.84538i	−0.490976	+	0.871173i	$0.663360\pi$
$620$	2.27363			0.0913110
$621$	−3.38768	+	3.39465i	−0.135943	+	0.136223i
$622$	5.68894			0.228106
$623$	0.558854	−	3.88692i	0.0223900	−	0.155726i
$624$	0.0970205	+	0.212445i	0.00388393	+	0.00850461i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	7.37456	+	8.51069i	0.294747	+	0.340156i
$627$	−10.2854	+	3.02008i	−0.410761	+	0.120610i
$628$	4.05604	+	2.60666i	0.161854	+	0.104017i
$629$	0.0850742	−	0.186286i	0.00339213	−	0.00742773i
$630$	1.30851	−	1.51010i	0.0521321	−	0.0601637i
$631$	24.9851	−	16.0570i	0.994642	−	0.639217i	0.0612672	−	0.998121i	$-0.480486\pi$
$631$	24.9851	−	16.0570i	0.994642	−	0.639217i	0.933374	+	0.358904i	$0.116849\pi$
$632$	−1.66468	−	11.5781i	−0.0662175	−	0.460553i
$633$	−1.76447	−	12.2721i	−0.0701313	−	0.487774i
$634$	6.57193	−	4.22352i	0.261005	−	0.167738i
$635$	1.48724	−	1.71637i	0.0590195	−	0.0681121i
$636$	−3.09485	+	6.77678i	−0.122719	+	0.268717i
$637$	−0.677545	−	0.435431i	−0.0268453	−	0.0172524i
$638$	6.04405	−	1.77469i	0.239286	−	0.0702608i
$639$	3.51693	+	4.05875i	0.139127	+	0.160562i
$640$	−3.63440	−	1.06716i	−0.143662	−	0.0421831i
$641$	−3.71294	−	8.13021i	−0.146652	−	0.321124i	0.822023	−	0.569454i	$-0.192845\pi$
$641$	−3.71294	−	8.13021i	−0.146652	−	0.321124i	−0.968675	+	0.248330i	$0.920118\pi$
$642$	0.499637	−	3.47505i	0.0197191	−	0.137149i
$643$	−28.8973			−1.13960			−0.569799	−	0.821784i	$-0.692979\pi$
$643$	−28.8973			−1.13960			−0.569799	+	0.821784i	$0.692979\pi$
$644$	−10.0131	+	2.18899i	−0.394570	+	0.0862583i
$645$	0.540082			0.0212657
$646$	0.103454	−	0.719540i	0.00407035	−	0.0283099i
$647$	−8.22108	−	18.0017i	−0.323204	−	0.707718i	0.676380	−	0.736553i	$-0.263548\pi$
$647$	−8.22108	−	18.0017i	−0.323204	−	0.707718i	−0.999584	+	0.0288347i	$0.990820\pi$
$648$	2.85508	+	0.838326i	0.112158	+	0.0329326i
$649$	−2.22134	−	2.56356i	−0.0871951	−	0.100629i
$650$	−0.267907	+	0.0786646i	−0.0105082	+	0.00308548i
$651$	−3.74219	−	2.40496i	−0.146668	−	0.0942578i
$652$	−7.16214	+	15.6829i	−0.280491	+	0.614189i
$653$	−12.1129	+	13.9790i	−0.474013	+	0.547041i	−0.941524	−	0.336947i	$-0.890606\pi$
$653$	−12.1129	+	13.9790i	−0.474013	+	0.547041i	0.467510	+	0.883988i	$0.345151\pi$
$654$	−10.7333	+	6.89788i	−0.419706	+	0.269729i
$655$	2.39250	+	16.6402i	0.0934826	+	0.650186i
$656$	0.755057	+	5.25153i	0.0294800	+	0.205038i
$657$	2.26359	−	1.45472i	0.0883111	−	0.0567541i
$658$	−2.05814	+	2.37522i	−0.0802346	+	0.0925957i
$659$	1.87947	−	4.11548i	0.0732139	−	0.160316i	−0.869486	−	0.493957i	$-0.835550\pi$
$659$	1.87947	−	4.11548i	0.0732139	−	0.160316i	0.942700	+	0.333641i	$0.108277\pi$
$660$	−1.67289	−	1.07510i	−0.0651173	−	0.0418483i
$661$	8.78008	−	2.57806i	0.341505	−	0.100275i	−0.106483	−	0.994315i	$-0.533959\pi$
$661$	8.78008	−	2.57806i	0.341505	−	0.100275i	0.447988	+	0.894040i	$0.352141\pi$
$662$	−1.23201	−	1.42181i	−0.0478832	−	0.0552602i
$663$	0.0362017	+	0.0106298i	0.00140596	+	0.000412826i
$664$	−18.9847	−	41.5708i	−0.736750	−	1.61326i
$665$	−1.63957	+	11.4035i	−0.0635799	+	0.442208i
$666$	1.51555			0.0587264
$667$	−3.43762	+	15.8811i	−0.133105	+	0.614917i
$668$	12.4020			0.479848
$669$	4.07385	−	28.3342i	0.157504	−	1.09547i
$670$	4.56180	+	9.98895i	0.176238	+	0.385907i
$671$	−13.1489	−	3.86087i	−0.507608	−	0.149047i
$672$	6.89970	+	7.96268i	0.266162	+	0.307167i
$673$	41.6402	−	12.2267i	1.60511	−	0.471304i	0.648150	−	0.761513i	$-0.275543\pi$
$673$	41.6402	−	12.2267i	1.60511	−	0.471304i	0.956963	+	0.290209i	$0.0937248\pi$
$674$	8.80932	+	5.66140i	0.339322	+	0.218069i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	−8.84171	+	10.2039i	−0.340066	+	0.392457i
$677$	−13.1485	+	8.45003i	−0.505338	+	0.324761i	−0.768348	−	0.640032i	$-0.778921\pi$
$677$	−13.1485	+	8.45003i	−0.505338	+	0.324761i	0.263010	+	0.964793i	$0.415285\pi$
$678$	−2.44668	−	17.0171i	−0.0939643	−	0.653536i
$679$	−4.20034	−	29.2140i	−0.161194	−	1.12113i
$680$	0.330533	−	0.212420i	0.0126753	−	0.00814595i
$681$	8.47402	−	9.77954i	0.324725	−	0.374753i
$682$	1.68015	−	3.67902i	0.0643363	−	0.140877i
$683$	29.4886	+	18.9512i	1.12835	+	0.725148i	0.965215	−	0.261456i	$-0.0842026\pi$
$683$	29.4886	+	18.9512i	1.12835	+	0.725148i	0.163136	+	0.986604i	$0.447839\pi$
$684$	−5.64992	+	1.65897i	−0.216030	+	0.0634321i
$685$	−5.36939	−	6.19661i	−0.205154	−	0.236760i
$686$	18.8243	+	5.52731i	0.718715	+	0.211034i
$687$	10.4928	+	22.9761i	0.400326	+	0.876592i
$688$	0.0628225	−	0.436940i	0.00239509	−	0.0166582i
$689$	−2.03682			−0.0775967
$690$	−4.11076	+	2.25013i	−0.156494	+	0.0856612i
$691$	−18.7462			−0.713138			−0.356569	−	0.934269i	$-0.616054\pi$
$691$	−18.7462			−0.713138			−0.356569	+	0.934269i	$0.616054\pi$
$692$	−1.70270	+	11.8425i	−0.0647268	+	0.450185i
$693$	1.61623	+	3.53905i	0.0613955	+	0.134437i
$694$	29.1270	+	8.55245i	1.10564	+	0.324647i
$695$	−12.3335	−	14.2336i	−0.467835	−	0.539910i
$696$	9.67334	−	2.84035i	0.366667	−	0.107663i
$697$	0.721045	+	0.463387i	0.0273115	+	0.0175520i
$698$	−1.62865	+	3.56624i	−0.0616451	+	0.134984i
$699$	−8.02738	+	9.26409i	−0.303624	+	0.350400i
$700$	−1.79791	+	1.15544i	−0.0679545	+	0.0436717i
$701$	−6.22365	−	43.2864i	−0.235064	−	1.63491i	−0.675669	−	0.737205i	$-0.736145\pi$
$701$	−6.22365	−	43.2864i	−0.235064	−	1.63491i	0.440605	−	0.897701i	$-0.354764\pi$
$702$	0.0397368	+	0.276375i	0.00149977	+	0.0104311i
$703$	−7.35108	+	4.72425i	−0.277251	+	0.178179i
$704$	−8.31012	+	9.59039i	−0.313199	+	0.361451i
$705$	0.653403	−	1.43075i	0.0246086	−	0.0538853i
$706$	−10.3303	−	6.63889i	−0.388786	−	0.249858i
$707$	23.4440	−	6.88379i	0.881704	−	0.258892i
$708$	−1.22021	−	1.40819i	−0.0458582	−	0.0529232i
$709$	−14.8321	−	4.35511i	−0.557032	−	0.163559i	−0.00891409	−	0.999960i	$-0.502837\pi$
$709$	−14.8321	−	4.35511i	−0.557032	−	0.163559i	−0.548118	+	0.836401i	$0.684656\pi$
$710$	2.18003	+	4.77361i	0.0818152	+	0.179150i
$711$	0.559442	−	3.89101i	0.0209807	−	0.145924i
$712$	5.71431			0.214153
$713$	6.26075	+	8.34549i	0.234467	+	0.312541i
$714$	−0.263839			−0.00987391
$715$	0.0773725	−	0.538138i	0.00289357	−	0.0201252i
$716$	−2.38807	−	5.22914i	−0.0892463	−	0.195422i
$717$	−27.1428	−	7.96984i	−1.01367	−	0.297639i
$718$	−12.4469	−	14.3645i	−0.464513	−	0.536077i
$719$	−23.8808	+	7.01205i	−0.890605	+	0.261505i	−0.694856	−	0.719149i	$-0.744532\pi$
$719$	−23.8808	+	7.01205i	−0.890605	+	0.261505i	−0.195749	+	0.980654i	$0.562714\pi$
$720$	0.687595	+	0.441890i	0.0256251	+	0.0164683i
$721$	−2.06049	+	4.51185i	−0.0767368	+	0.168030i
$722$	−8.15395	+	9.41016i	−0.303459	+	0.350210i
$723$	−2.85791	+	1.83667i	−0.106287	+	0.0683064i
$724$	3.18076	+	22.1226i	0.118212	+	0.822182i
$725$	0.482180	+	3.35363i	0.0179077	+	0.124551i
$726$	6.06657	−	3.89875i	0.225152	−	0.144696i
$727$	29.6396	−	34.2060i	1.09927	−	1.26863i	0.138780	−	0.990323i	$-0.455682\pi$
$727$	29.6396	−	34.2060i	1.09927	−	1.26863i	0.960493	−	0.278305i	$-0.0897727\pi$
$728$	−0.722260	+	1.58153i	−0.0267687	+	0.0586154i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	2.52278	−	0.740756i	0.0933724	−	0.0274166i
$731$	−0.0467004	−	0.0538951i	−0.00172727	−	0.00199338i
$732$	−7.22285	−	2.12082i	−0.266964	−	0.0783878i
$733$	3.53226	+	7.73457i	0.130467	+	0.285683i	0.963580	−	0.267420i	$-0.0861710\pi$
$733$	3.53226	+	7.73457i	0.130467	+	0.285683i	−0.833113	+	0.553103i	$0.813444\pi$
$734$	3.53011	−	24.5525i	0.130299	−	0.906248i
$735$	−2.81861			−0.103966
$736$	−8.65931	−	23.1438i	−0.319186	−	0.853092i
$737$	−21.3820			−0.787616
$738$	−0.902694	+	6.27838i	−0.0332286	+	0.231110i
$739$	11.6694	+	25.5523i	0.429264	+	0.939958i	0.993445	+	0.114307i	$0.0364647\pi$
$739$	11.6694	+	25.5523i	0.429264	+	0.939958i	−0.564181	+	0.825651i	$0.690808\pi$
$740$	−1.55534	−	0.456690i	−0.0571755	−	0.0167883i
$741$	−1.05425	−	1.21667i	−0.0387289	−	0.0446956i
$742$	13.6661	−	4.01274i	0.501700	−	0.147312i
$743$	−12.4045	−	7.97191i	−0.455078	−	0.292461i	0.292950	−	0.956128i	$-0.405363\pi$
$743$	−12.4045	−	7.97191i	−0.455078	−	0.292461i	−0.748028	+	0.663667i	$0.768999\pi$
$744$	2.68904	−	5.88817i	0.0985849	−	0.215871i
$745$	−0.897081	+	1.03529i	−0.0328665	+	0.0379300i
$746$	6.96324	−	4.47500i	0.254942	−	0.163842i
$747$	−2.18573	−	15.2021i	−0.0799717	−	0.556215i
$748$	0.0373683	+	0.259902i	0.00136632	+	0.00950296i
$749$	6.18052	−	3.97198i	0.225831	−	0.145133i
$750$	−0.639905	+	0.738490i	−0.0233660	+	0.0269658i
$751$	13.8357	−	30.2960i	0.504872	−	1.10552i	−0.469983	−	0.882676i	$-0.655740\pi$
$751$	13.8357	−	30.2960i	0.504872	−	1.10552i	0.974855	−	0.222840i	$-0.0715329\pi$
$752$	−1.08151	−	0.695046i	−0.0394387	−	0.0253457i
$753$	6.38004	−	1.87335i	0.232502	−	0.0682686i
$754$	0.619512	+	0.714955i	0.0225613	+	0.0260371i
$755$	−12.7024	−	3.72975i	−0.462287	−	0.135740i
$756$	0.887815	+	1.94404i	0.0322895	+	0.0707042i
$757$	−2.82364	+	19.6389i	−0.102627	+	0.713786i	0.871927	+	0.489635i	$0.162870\pi$
$757$	−2.82364	+	19.6389i	−0.102627	+	0.713786i	−0.974554	+	0.224151i	$0.928039\pi$
$758$	−17.9728			−0.652801
$759$	−0.660315	−	9.10091i	−0.0239679	−	0.330342i
$760$	−16.7647			−0.608120
$761$	−2.50041	+	17.3907i	−0.0906398	+	0.630414i	0.892972	+	0.450113i	$0.148616\pi$
$761$	−2.50041	+	17.3907i	−0.0906398	+	0.630414i	−0.983612	+	0.180301i	$0.942293\pi$
$762$	−0.921896	−	2.01867i	−0.0333968	−	0.0731287i
$763$	−25.6178	−	7.52207i	−0.927427	−	0.272317i
$764$	4.96328	+	5.72793i	0.179565	+	0.207229i
$765$	0.126693	−	0.0372005i	0.00458060	−	0.00134499i
$766$	−28.5710	−	18.3615i	−1.03231	−	0.663427i
$767$	0.211623	−	0.463389i	0.00764125	−	0.0167320i
$768$	−11.1591	+	12.8783i	−0.402670	+	0.464706i
$769$	36.5483	−	23.4882i	1.31797	−	0.847005i	0.322921	−	0.946426i	$-0.395335\pi$
$769$	36.5483	−	23.4882i	1.31797	−	0.847005i	0.995046	+	0.0994206i	$0.0316989\pi$
$770$	0.541051	+	3.76309i	0.0194981	+	0.135612i
$771$	−3.34805	−	23.2862i	−0.120577	−	0.838631i
$772$	22.8993	−	14.7165i	0.824165	−	0.529658i
$773$	−0.451113	+	0.520613i	−0.0162254	+	0.0187251i	−0.763804	−	0.645448i	$-0.776671\pi$
$773$	−0.451113	+	0.520613i	−0.0162254	+	0.0187251i	0.747579	+	0.664173i	$0.231216\pi$
$774$	0.219234	−	0.480056i	0.00788022	−	0.0172553i
$775$	1.83006	+	1.17611i	0.0657377	+	0.0422471i
$776$	41.2090	−	12.1001i	1.47932	−	0.434367i
$777$	2.07689	+	2.39686i	0.0745080	+	0.0859868i
$778$	−26.9874	−	7.92420i	−0.967544	−	0.284096i
$779$	−15.1924	−	33.2667i	−0.544324	−	1.19190i
$780$	0.0425017	−	0.295606i	0.00152180	−	0.0105844i
$781$	−10.2182			−0.365637
$782$	0.579996	+	0.215648i	0.0207406	+	0.00771156i
$783$	3.38812			0.121081
$784$	−0.327862	+	2.28033i	−0.0117094	+	0.0814404i
$785$	1.91636	+	4.19624i	0.0683979	+	0.149770i
$786$	15.7619	+	4.62812i	0.562210	+	0.165080i
$787$	−22.0928	−	25.4964i	−0.787523	−	0.908850i	0.210106	−	0.977679i	$-0.432619\pi$
$787$	−22.0928	−	25.4964i	−0.787523	−	0.908850i	−0.997628	+	0.0688289i	$0.978074\pi$
$788$	8.43036	−	2.47538i	0.300319	−	0.0881817i
$789$	−3.73120	−	2.39789i	−0.132834	−	0.0853673i
$790$	1.59571	−	3.49412i	0.0567728	−	0.124315i
$791$	23.5597	−	27.1894i	0.837687	−	0.966742i
$792$	−4.76282	+	3.06088i	−0.169239	+	0.108764i
$793$	−0.292895	−	2.03713i	−0.0104010	−	0.0723407i
$794$	2.99703	+	20.8448i	0.106361	+	0.739755i
$795$	−5.99659	+	3.85377i	−0.212677	+	0.136679i
$796$	−10.7240	+	12.3761i	−0.380101	+	0.438660i
$797$	3.87986	−	8.49570i	0.137432	−	0.300933i	−0.828385	−	0.560159i	$-0.810740\pi$
$797$	3.87986	−	8.49570i	0.137432	−	0.300933i	0.965817	+	0.259226i	$0.0834674\pi$
$798$	9.47052	+	6.08633i	0.335253	+	0.215454i
$799$	−0.199275	+	0.0585123i	−0.00704983	+	0.00207002i
$800$	−3.37420	−	3.89403i	−0.119296	−	0.137675i
$801$	1.84259	+	0.541035i	0.0651049	+	0.0191165i
$802$	−10.5342	−	23.0666i	−0.371974	−	0.814509i
$803$	−0.728589	+	5.06745i	−0.0257113	+	0.178826i
$804$	−11.7454			−0.414228
$805$	−9.19193	−	3.41765i	−0.323973	−	0.120456i
$806$	0.607408			0.0213950
$807$	1.19365	−	8.30200i	0.0420184	−	0.292244i
$808$	14.7703	+	32.3424i	0.519616	+	1.13780i
$809$	−31.8270	−	9.34525i	−1.11898	−	0.328562i	−0.330611	−	0.943767i	$-0.607255\pi$
$809$	−31.8270	−	9.34525i	−1.11898	−	0.328562i	−0.788367	+	0.615205i	$0.789073\pi$
$810$	0.639905	+	0.738490i	0.0224840	+	0.0259479i
$811$	24.0582	−	7.06412i	0.844797	−	0.248055i	0.169435	−	0.985541i	$-0.445806\pi$
$811$	24.0582	−	7.06412i	0.844797	−	0.248055i	0.675362	+	0.737486i	$0.263987\pi$
$812$	6.09152	+	3.91478i	0.213771	+	0.137382i
$813$	10.5304	−	23.0583i	0.369317	−	0.808691i
$814$	−1.88834	+	2.17926i	−0.0661864	+	0.0763832i
$815$	−13.8774	+	8.91844i	−0.486103	+	0.312399i
$816$	−0.0153592	−	0.106825i	−0.000537678	−	0.00373963i
$817$	0.433042	+	3.01187i	0.0151502	+	0.105372i
$818$	8.34182	−	5.36096i	0.291665	−	0.187442i
$819$	−0.382635	+	0.441584i	−0.0133703	+	0.0154302i
$820$	2.81829	−	6.17120i	0.0984191	−	0.215508i
$821$	−28.0758	−	18.0432i	−0.979852	−	0.629713i	−0.0504284	−	0.998728i	$-0.516059\pi$
$821$	−28.0758	−	18.0432i	−0.979852	−	0.629713i	−0.929423	+	0.369015i	$0.879695\pi$
$822$	−7.68749	+	2.25725i	−0.268132	+	0.0787306i
$823$	5.00115	+	5.77164i	0.174329	+	0.201187i	0.836190	−	0.548441i	$-0.184778\pi$
$823$	5.00115	+	5.77164i	0.174329	+	0.201187i	−0.661860	+	0.749627i	$0.730233\pi$
$824$	−6.92543	−	2.03349i	−0.241259	−	0.0708400i
$825$	−0.790393	−	1.73072i	−0.0275180	−	0.0602559i
$826$	−0.506969	+	3.52605i	−0.0176397	+	0.122687i
$827$	45.3203			1.57594			0.787970	−	0.615714i	$-0.211132\pi$
$827$	45.3203			1.57594			0.787970	+	0.615714i	$0.211132\pi$
$828$	−0.362719	−	4.99924i	−0.0126054	−	0.173736i
$829$	−4.75867			−0.165275			−0.0826377	−	0.996580i	$-0.526334\pi$
$829$	−4.75867			−0.165275			−0.0826377	+	0.996580i	$0.526334\pi$
$830$	2.13581	−	14.8549i	0.0741351	−	0.515621i
$831$	2.87613	+	6.29785i	0.0997719	+	0.218470i
$832$	−1.82858	−	0.536920i	−0.0633947	−	0.0186144i
$833$	0.243723	+	0.281271i	0.00844449	+	0.00974546i
$834$	−17.6581	+	5.18489i	−0.611451	+	0.179538i
$835$	9.98248	+	6.41535i	0.345458	+	0.222012i
$836$	4.65419	−	10.1912i	0.160968	−	0.352472i
$837$	1.42458	−	1.64406i	0.0492408	−	0.0568269i
$838$	−12.3978	+	7.96756i	−0.428273	+	0.275235i
$839$	1.13508	+	7.89463i	0.0391872	+	0.272553i	0.999989	−	0.00468310i	$-0.00149068\pi$
$839$	1.13508	+	7.89463i	0.0391872	+	0.272553i	−0.960802	+	0.277236i	$0.910582\pi$
$840$	0.865937	+	6.02272i	0.0298777	+	0.207804i
$841$	−14.7393	+	9.47238i	−0.508252	+	0.326634i
$842$	5.67853	−	6.55337i	0.195695	−	0.225844i
$843$	−11.1595	+	24.4358i	−0.384352	+	0.841614i
$844$	10.9011	+	7.00572i	0.375232	+	0.241147i
$845$	−12.3951	+	3.63952i	−0.426403	+	0.125203i
$846$	−1.00650	−	1.16157i	−0.0346042	−	0.0399354i
$847$	14.4794	+	4.25155i	0.497519	+	0.146085i
$848$	2.42028	+	5.29967i	0.0831127	+	0.181991i
$849$	−3.89086	+	27.0616i	−0.133534	+	0.928750i
$850$	0.129026			0.00442557
$851$	−2.60655	−	6.96655i	−0.0893513	−	0.238810i
$852$	−5.61299			−0.192298
$853$	−4.76777	+	33.1605i	−0.163245	+	1.13540i	0.729220	+	0.684279i	$0.239883\pi$
$853$	−4.76777	+	33.1605i	−0.163245	+	1.13540i	−0.892465	+	0.451116i	$0.851026\pi$
$854$	5.97855	+	13.0912i	0.204582	+	0.447972i
$855$	−5.40582	−	1.58729i	−0.184875	−	0.0542843i
$856$	7.00104	+	8.07963i	0.239291	+	0.276156i
$857$	−7.12428	+	2.09188i	−0.243361	+	0.0714572i	−0.401138	−	0.916017i	$-0.631385\pi$
$857$	−7.12428	+	2.09188i	−0.243361	+	0.0714572i	0.157777	+	0.987475i	$0.449567\pi$
$858$	−0.446920	−	0.287218i	−0.0152576	−	0.00980547i
$859$	4.96869	−	10.8799i	0.169530	−	0.371218i	−0.805729	−	0.592284i	$-0.798226\pi$
$859$	4.96869	−	10.8799i	0.169530	−	0.371218i	0.975259	+	0.221066i	$0.0709536\pi$
$860$	−0.369648	+	0.426597i	−0.0126049	+	0.0145468i
$861$	−11.1663	+	7.17617i	−0.380548	+	0.244563i
$862$	0.0283282	+	0.197027i	0.000964864	+	0.00671078i
$863$	−0.770397	−	5.35823i	−0.0262246	−	0.182396i	0.972499	−	0.232908i	$-0.0748240\pi$
$863$	−0.770397	−	5.35823i	−0.0262246	−	0.182396i	−0.998723	+	0.0505114i	$0.983915\pi$
$864$	−4.33459	+	2.78567i	−0.147466	+	0.0947705i
$865$	−7.49645	+	8.65136i	−0.254887	+	0.294155i
$866$	0.273488	−	0.598854i	0.00929349	−	0.0203499i
$867$	14.2866	+	9.18147i	0.485200	+	0.311819i
$868$	4.46088	−	1.30983i	0.151412	−	0.0444586i
$869$	4.89796	+	5.65255i	0.166152	+	0.191750i
$870$	3.17663	+	0.932744i	0.107698	+	0.0316230i
$871$	−1.33397	−	2.92098i	−0.0451997	−	0.0989736i
$872$	5.52925	−	38.4568i	0.187244	−	1.30231i
$873$	14.4336			0.488503
$874$	−15.8444	−	21.1203i	−0.535943	−	0.714404i
$875$	−2.04484			−0.0691283
$876$	−0.400223	+	2.78361i	−0.0135223	+	0.0940495i
$877$	−4.80966	−	10.5317i	−0.162411	−	0.355630i	0.810878	−	0.585216i	$-0.198990\pi$
$877$	−4.80966	−	10.5317i	−0.162411	−	0.355630i	−0.973288	+	0.229586i	$0.926263\pi$
$878$	33.0002	+	9.68974i	1.11370	+	0.327013i
$879$	−8.59713	−	9.92162i	−0.289974	−	0.334648i
$880$	−1.49214	+	0.438131i	−0.0502999	+	0.0147694i
$881$	−43.5397	−	27.9813i	−1.46689	−	0.942713i	−0.998238	−	0.0593300i	$-0.981104\pi$
$881$	−43.5397	−	27.9813i	−1.46689	−	0.942713i	−0.468652	−	0.883383i	$-0.655260\pi$
$882$	−1.14415	+	2.50535i	−0.0385257	+	0.0843594i
$883$	−33.3733	+	38.5148i	−1.12310	+	1.29613i	−0.172744	+	0.984967i	$0.555263\pi$
$883$	−33.3733	+	38.5148i	−1.12310	+	1.29613i	−0.950357	+	0.311161i	$0.899282\pi$
$884$	−0.0331737	+	0.0213195i	−0.00111575	+	0.000717051i
$885$	−0.253720	−	1.76466i	−0.00852870	−	0.0593184i
$886$	−0.974580	−	6.77835i	−0.0327417	−	0.227723i
$887$	36.3321	−	23.3492i	1.21991	−	0.783990i	0.237622	−	0.971358i	$-0.423632\pi$
$887$	36.3321	−	23.3492i	1.21991	−	0.783990i	0.982290	+	0.187368i	$0.0599955\pi$
$888$	−3.02224	+	3.48785i	−0.101420	+	0.117045i
$889$	1.92919	−	4.22434i	0.0647030	−	0.141680i
$890$	1.57863	+	1.01453i	0.0529160	+	0.0340070i
$891$	−1.82559	+	0.536041i	−0.0611595	+	0.0179581i
$892$	19.5922	+	22.6106i	0.655997	+	0.757060i
$893$	8.50278	+	2.49664i	0.284535	+	0.0835469i
$894$	0.556073	+	1.21763i	0.0185979	+	0.0407236i
$895$	0.782770	−	5.44429i	0.0261651	−	0.181982i
$896$	−7.74554			−0.258760
$897$	1.20207	−	0.657987i	0.0401361	−	0.0219695i
$898$	−32.2962			−1.07774
$899$	1.04893	−	7.29548i	0.0349838	−	0.243318i
$900$	−0.434173	−	0.950705i	−0.0144724	−	0.0316902i
$901$	0.903089	+	0.265171i	0.0300863	+	0.00883413i
$902$	−7.90316	−	9.12073i	−0.263146	−	0.303687i
$903$	1.05965	−	0.311141i	0.0352629	−	0.0103541i
$904$	44.0417	+	28.3039i	1.46480	+	0.941372i
$905$	−8.88346	+	19.4521i	−0.295296	+	0.646608i
$906$	−8.47147	+	9.77659i	−0.281446	+	0.324806i
$907$	15.9114	−	10.2256i	0.528330	−	0.339537i	−0.249130	−	0.968470i	$-0.580145\pi$
$907$	15.9114	−	10.2256i	0.528330	−	0.339537i	0.777459	+	0.628933i	$0.216508\pi$
$908$	1.92474	+	13.3868i	0.0638746	+	0.444257i
$909$	1.70052	+	11.8273i	0.0564025	+	0.392288i
$910$	−0.480318	+	0.308682i	−0.0159224	+	0.0102327i
$911$	36.4980	−	42.1209i	1.20923	−	1.39553i	0.314303	−	0.949323i	$-0.398229\pi$
$911$	36.4980	−	42.1209i	1.20923	−	1.39553i	0.894930	−	0.446206i	$-0.147225\pi$
$912$	−1.91297	+	4.18882i	−0.0633447	+	0.138706i
$913$	24.5830	+	15.7985i	0.813577	+	0.522854i
$914$	−10.7893	+	3.16804i	−0.356880	+	0.104789i
$915$	−4.71667	−	5.44333i	−0.155928	−	0.179951i
$916$	−25.3298	−	7.43751i	−0.836921	−	0.245742i
$917$	14.2805	+	31.2700i	0.471584	+	1.03262i
$918$	0.0183624	−	0.127713i	0.000606048	−	0.00421516i
$919$	12.2275			0.403347			0.201674	−	0.979453i	$-0.435362\pi$
$919$	12.2275			0.403347			0.201674	+	0.979453i	$0.435362\pi$
$920$	3.01908	−	13.9475i	0.0995361	−	0.459836i
$921$	29.2539			0.963948
$922$	−4.58722	+	31.9048i	−0.151072	+	1.05073i
$923$	−0.637488	−	1.39590i	−0.0209832	−	0.0459467i
$924$	−3.90161	−	1.14561i	−0.128353	−	0.0376880i
$925$	−1.01567	−	1.17215i	−0.0333951	−	0.0385399i
$926$	14.9383	−	4.38627i	0.490901	−	0.144142i
$927$	−2.04059	−	1.31141i	−0.0670218	−	0.0430723i
$928$	−7.25207	+	15.8798i	−0.238061	+	0.521281i
$929$	34.0715	−	39.3206i	1.11785	−	1.29007i	0.165111	−	0.986275i	$-0.447202\pi$
$929$	34.0715	−	39.3206i	1.11785	−	1.29007i	0.952739	−	0.303792i	$-0.0982527\pi$
$930$	1.78827	−	1.14925i	0.0586396	−	0.0376854i
$931$	−2.25999	−	15.7185i	−0.0740681	−	0.515155i
$932$	−1.82329	−	12.6813i	−0.0597238	−	0.415388i
$933$	−4.89769	+	3.14755i	−0.160343	+	0.103046i
$934$	−12.6712	+	14.6233i	−0.414613	+	0.478489i
$935$	−0.104365	+	0.228527i	−0.00341310	+	0.00747365i
$936$	−0.715284	−	0.459685i	−0.0233798	−	0.0150253i
$937$	58.4682	−	17.1678i	1.91007	−	0.560848i	0.927912	−	0.372798i	$-0.121602\pi$
$937$	58.4682	−	17.1678i	1.91007	−	0.560848i	0.982160	−	0.188049i	$-0.0602165\pi$
$938$	14.7049	+	16.9704i	0.480133	+	0.554103i
$939$	−11.0576	−	3.24681i	−0.360852	−	0.105956i
$940$	0.682907	+	1.49536i	0.0222740	+	0.0487732i
$941$	−2.01510	+	14.0153i	−0.0656903	+	0.456886i	0.930254	+	0.366916i	$0.119586\pi$
$941$	−2.01510	+	14.0153i	−0.0656903	+	0.456886i	−0.995944	+	0.0899704i	$0.971323\pi$
$942$	4.50777			0.146871
$943$	30.4124	−	6.64856i	0.990363	−	0.216507i
$944$	−1.45717			−0.0474268
$945$	−0.291012	+	2.02403i	−0.00946661	+	0.0658417i
$946$	0.417128	+	0.913384i	0.0135620	+	0.0296967i
$947$	18.9433	+	5.56226i	0.615575	+	0.180749i	0.574631	−	0.818412i	$-0.305145\pi$
$947$	18.9433	+	5.56226i	0.615575	+	0.180749i	0.0409436	+	0.999161i	$0.486964\pi$
$948$	2.69051	+	3.10501i	0.0873837	+	0.100846i
$949$	−0.737715	+	0.216613i	−0.0239472	+	0.00703154i
$950$	−4.63142	−	2.97643i	−0.150263	−	0.0965681i
$951$	−3.32110	+	7.27219i	−0.107694	+	0.235817i
$952$	0.526134	−	0.607191i	0.0170521	−	0.0196792i
$953$	−36.0467	+	23.1658i	−1.16767	+	0.750414i	−0.973079	−	0.230471i	$-0.925973\pi$
$953$	−36.0467	+	23.1658i	−1.16767	+	0.750414i	−0.194588	+	0.980885i	$0.562337\pi$
$954$	0.991275	+	6.89447i	0.0320937	+	0.223217i
$955$	1.03202	+	7.17788i	0.0333955	+	0.232271i
$956$	24.8725	−	15.9846i	0.804435	−	0.516979i
$957$	−4.22152	+	4.87189i	−0.136462	+	0.157486i
$958$	−7.02982	+	15.3932i	−0.227123	+	0.497330i
$959$	−14.1047	−	9.06452i	−0.455464	−	0.292709i
$960$	−6.39939	+	1.87903i	−0.206540	+	0.0606455i
$961$	17.2017	+	19.8518i	0.554892	+	0.640379i
$962$	−0.415516	−	0.122007i	−0.0133968	−	0.00393365i
$963$	1.49252	+	3.26816i	0.0480958	+	0.105315i
$964$	0.505303	−	3.51446i	0.0162747	−	0.113193i
$965$	26.0445			0.838401
$966$	−6.76907	+	6.78300i	−0.217791	+	0.218239i
$967$	−44.3215			−1.42528			−0.712642	−	0.701528i	$-0.752501\pi$
$967$	−44.3215			−1.42528			−0.712642	+	0.701528i	$0.752501\pi$
$968$	−3.12519	+	21.7361i	−0.100447	+	0.698626i
$969$	0.309039	+	0.676702i	0.00992777	+	0.0217388i
$970$	13.5326	+	3.97354i	0.434507	+	0.127583i
$971$	2.80191	+	3.23357i	0.0899175	+	0.103770i	0.798925	−	0.601430i	$-0.205402\pi$
$971$	2.80191	+	3.23357i	0.0899175	+	0.103770i	−0.709008	+	0.705201i	$0.750857\pi$
$972$	−1.00282	+	0.294454i	−0.0321654	+	0.00944461i
$973$	−32.3984	−	20.8212i	−1.03864	−	0.667496i
$974$	5.85306	−	12.8164i	0.187544	−	0.410665i
$975$	0.187122	−	0.215950i	0.00599269	−	0.00691594i
$976$	−4.95244	+	3.18274i	−0.158524	+	0.101877i
$977$	−0.827936	−	5.75842i	−0.0264880	−	0.184228i	0.972282	−	0.233811i	$-0.0751198\pi$
$977$	−0.827936	−	5.75842i	−0.0264880	−	0.184228i	−0.998770	+	0.0495831i	$0.984211\pi$
$978$	2.29402	+	15.9553i	0.0733546	+	0.510193i
$979$	−3.07380	+	1.97541i	−0.0982392	+	0.0631345i
$980$	1.92914	−	2.22635i	0.0616243	−	0.0711182i
$981$	5.42403	−	11.8770i	0.173176	−	0.379203i
$982$	−15.4426	−	9.92436i	−0.492794	−	0.316699i
$983$	32.5059	−	9.54460i	1.03678	−	0.304425i	0.281314	−	0.959616i	$-0.409230\pi$
$983$	32.5059	−	9.54460i	1.03678	−	0.304425i	0.755464	+	0.655190i	$0.227412\pi$
$984$	−12.6488	−	14.5975i	−0.403228	−	0.465350i
$985$	8.06614	+	2.36843i	0.257009	+	0.0754646i
$986$	−0.181601	−	0.397651i	−0.00578336	−	0.0126638i
$987$	0.457730	−	3.18358i	0.0145697	−	0.101335i
$988$	1.68258			0.0535300
$989$	−2.58373	−	0.182122i	−0.0821579	−	0.00579116i
$990$	−1.85921			−0.0590895
$991$	−1.71361	+	11.9184i	−0.0544345	+	0.378600i	0.944334	+	0.328988i	$0.106708\pi$
$991$	−1.71361	+	11.9184i	−0.0544345	+	0.378600i	−0.998769	+	0.0496121i	$0.984201\pi$
$992$	4.65631	+	10.1959i	0.147838	+	0.323720i
$993$	1.84731	+	0.542418i	0.0586225	+	0.0172131i
$994$	7.02733	+	8.10997i	0.222893	+	0.257232i
$995$	−15.0338	+	4.41432i	−0.476603	+	0.139943i
$996$	13.5037	+	8.67831i	0.427882	+	0.274983i
$997$	−24.8714	+	54.4607i	−0.787684	+	1.72479i	−0.104519	+	0.994523i	$0.533330\pi$
$997$	−24.8714	+	54.4607i	−0.787684	+	1.72479i	−0.683164	+	0.730265i	$0.739397\pi$
$998$	−5.52476	+	6.37591i	−0.174883	+	0.201826i
$999$	−1.30476	+	0.838519i	−0.0412808	+	0.0265296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.31.2	✓	30
23.3	even	11	inner	345.2.m.a.256.2	yes	30
23.7	odd	22		7935.2.a.bq.1.10		15
23.16	even	11		7935.2.a.bp.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.31.2	✓	30	1.1	even	1	trivial
345.2.m.a.256.2	yes	30	23.3	even	11	inner
7935.2.a.bp.1.10		15	23.16	even	11
7935.2.a.bq.1.10		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.139065 + 0.967216i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.00282 + 0.294454i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.937580 - 0.275298i) q^{6} +(1.72023 + 1.10553i) q^{7} +(-1.23611 + 2.70671i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.139065 + 0.967216i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.00282 + 0.294454i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.937580 - 0.275298i) q^{6} +(1.72023 + 1.10553i) q^{7} +(-1.23611 + 2.70671i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.822041 + 0.528294i) q^{10} +(-0.270777 - 1.88329i) q^{11} +(-0.148741 - 1.03452i) q^{12} +(0.240382 - 0.154484i) q^{13} +(-1.30851 + 1.51010i) q^{14} +(0.415415 - 0.909632i) q^{15} +(-0.687595 - 0.441890i) q^{16} +(-0.126693 + 0.0372005i) q^{17} +(-0.639905 - 0.738490i) q^{18} +(5.40582 + 1.58729i) q^{19} +(0.434173 + 0.950705i) q^{20} +(0.291012 - 2.02403i) q^{21} +1.85921 q^{22} +(-2.29407 + 4.21156i) q^{23} +2.97561 q^{24} +(-0.142315 + 0.989821i) q^{25} +(0.115991 + 0.253985i) q^{26} +(0.959493 + 0.281733i) q^{27} +(1.39955 + 1.61517i) q^{28} +(3.25088 - 0.954543i) q^{29} +(0.822041 + 0.528294i) q^{30} +(0.903693 - 1.97881i) q^{31} +(-3.37420 + 3.89403i) q^{32} +(-1.60062 + 1.02866i) q^{33} +(-0.0183624 - 0.127713i) q^{34} +(0.291012 + 2.02403i) q^{35} +(-0.879239 + 0.565053i) q^{36} +(-1.01567 + 1.17215i) q^{37} +(-2.28701 + 5.00786i) q^{38} +(-0.240382 - 0.154484i) q^{39} +(-2.85508 + 0.838326i) q^{40} +(-4.25082 - 4.90571i) q^{41} +(1.91721 + 0.562942i) q^{42} +(0.224358 + 0.491276i) q^{43} +(0.283003 - 1.96833i) q^{44} -1.00000 q^{45} +(-3.75447 - 2.80454i) q^{46} +1.57289 q^{47} +(-0.116320 + 0.809026i) q^{48} +(-1.17089 - 2.56390i) q^{49} +(-0.937580 - 0.275298i) q^{50} +(0.0864690 + 0.0997906i) q^{51} +(0.286548 - 0.0841381i) q^{52} +(-5.99659 - 3.85377i) q^{53} +(-0.405928 + 0.888858i) q^{54} +(1.24598 - 1.43793i) q^{55} +(-5.11874 + 3.28961i) q^{56} +(-0.801808 - 5.57670i) q^{57} +(0.471168 + 3.27704i) q^{58} +(1.49979 - 0.963859i) q^{59} +(0.684430 - 0.789875i) q^{60} +(2.99205 - 6.55168i) q^{61} +(1.78827 + 1.14925i) q^{62} +(-1.96201 + 0.576099i) q^{63} +(-4.36763 - 5.04052i) q^{64} +(0.274168 + 0.0805031i) q^{65} +(-0.772343 - 1.69119i) q^{66} +(1.59933 - 11.1236i) q^{67} -0.138004 q^{68} +(4.78396 + 0.337213i) q^{69} -1.99814 q^{70} +(0.764301 - 5.31583i) q^{71} +(-1.23611 - 2.70671i) q^{72} +(-2.58174 - 0.758068i) q^{73} +(-0.992475 - 1.14538i) q^{74} +(0.959493 - 0.281733i) q^{75} +(4.95367 + 3.18353i) q^{76} +(1.61623 - 3.53905i) q^{77} +(0.182848 - 0.211018i) q^{78} +(-3.30698 + 2.12527i) q^{79} +(-0.116320 - 0.809026i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(5.33602 - 3.42925i) q^{82} +(-10.0576 + 11.6071i) q^{83} +(0.887815 - 1.94404i) q^{84} +(-0.111081 - 0.0713872i) q^{85} +(-0.506370 + 0.148684i) q^{86} +(-2.21875 - 2.56057i) q^{87} +(5.43224 + 1.59505i) q^{88} +(-0.797756 - 1.74684i) q^{89} +(0.139065 - 0.967216i) q^{90} +0.584300 q^{91} +(-3.54064 + 3.54793i) q^{92} -2.17540 q^{93} +(-0.218734 + 1.52133i) q^{94} +(2.34047 + 5.12491i) q^{95} +(4.94383 + 1.45164i) q^{96} +(-9.45199 - 10.9082i) q^{97} +(2.64268 - 0.775960i) q^{98} +(1.60062 + 1.02866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more