LMFDB - Embedded newform 1045.2.b.e.419.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.8
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66433i q^{2} -1.25863i q^{3} -0.769991 q^{4} +(-1.73458 + 1.41111i) q^{5} -2.09478 q^{6} +4.13429i q^{7} -2.04714i q^{8} +1.41584 q^{9} +O(q^{10})$	\(q-1.66433i q^{2} -1.25863i q^{3} -0.769991 q^{4} +(-1.73458 + 1.41111i) q^{5} -2.09478 q^{6} +4.13429i q^{7} -2.04714i q^{8} +1.41584 q^{9} +(2.34855 + 2.88691i) q^{10} +1.00000 q^{11} +0.969136i q^{12} -3.80507i q^{13} +6.88082 q^{14} +(1.77607 + 2.18320i) q^{15} -4.94710 q^{16} -2.64209i q^{17} -2.35643i q^{18} -1.00000 q^{19} +(1.33561 - 1.08654i) q^{20} +5.20355 q^{21} -1.66433i q^{22} -5.58456i q^{23} -2.57660 q^{24} +(1.01753 - 4.89537i) q^{25} -6.33289 q^{26} -5.55792i q^{27} -3.18337i q^{28} +6.34374 q^{29} +(3.63356 - 2.95596i) q^{30} +7.53516 q^{31} +4.13932i q^{32} -1.25863i q^{33} -4.39731 q^{34} +(-5.83394 - 7.17126i) q^{35} -1.09019 q^{36} +3.00157i q^{37} +1.66433i q^{38} -4.78918 q^{39} +(2.88874 + 3.55093i) q^{40} -4.89269 q^{41} -8.66042i q^{42} -10.6638i q^{43} -0.769991 q^{44} +(-2.45590 + 1.99791i) q^{45} -9.29455 q^{46} -6.54878i q^{47} +6.22657i q^{48} -10.0924 q^{49} +(-8.14750 - 1.69351i) q^{50} -3.32543 q^{51} +2.92987i q^{52} -7.14902i q^{53} -9.25022 q^{54} +(-1.73458 + 1.41111i) q^{55} +8.46347 q^{56} +1.25863i q^{57} -10.5581i q^{58} +7.34337 q^{59} +(-1.36756 - 1.68104i) q^{60} +4.72825 q^{61} -12.5410i q^{62} +5.85351i q^{63} -3.00501 q^{64} +(5.36937 + 6.60020i) q^{65} -2.09478 q^{66} +7.94790i q^{67} +2.03439i q^{68} -7.02891 q^{69} +(-11.9353 + 9.70960i) q^{70} +9.69764 q^{71} -2.89843i q^{72} +16.9975i q^{73} +4.99561 q^{74} +(-6.16147 - 1.28070i) q^{75} +0.769991 q^{76} +4.13429i q^{77} +7.97078i q^{78} -3.09141 q^{79} +(8.58113 - 6.98090i) q^{80} -2.74785 q^{81} +8.14304i q^{82} +1.51906i q^{83} -4.00669 q^{84} +(3.72829 + 4.58292i) q^{85} -17.7481 q^{86} -7.98443i q^{87} -2.04714i q^{88} -8.71704 q^{89} +(3.32519 + 4.08742i) q^{90} +15.7313 q^{91} +4.30007i q^{92} -9.48400i q^{93} -10.8993 q^{94} +(1.73458 - 1.41111i) q^{95} +5.20988 q^{96} +6.68784i q^{97} +16.7970i q^{98} +1.41584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.66433i		−	1.17686i	−0.808549	−	0.588429i	$-0.799747\pi$
$2$		−	1.66433i		−	1.17686i	0.808549	−	0.588429i	$-0.200253\pi$
$3$		−	1.25863i		−	0.726672i	−0.931658	−	0.363336i	$-0.881638\pi$
$3$		−	1.25863i		−	0.726672i	0.931658	−	0.363336i	$-0.118362\pi$
$4$	−0.769991			−0.384996
$5$	−1.73458	+	1.41111i	−0.775728	+	0.631068i
$5$	−1.73458	+	1.41111i	−0.775728	+	0.631068i
$6$	−2.09478			−0.855190
$7$			4.13429i			1.56261i	0.624146	+	0.781307i	$0.285447\pi$
$7$			4.13429i			1.56261i	−0.624146	+	0.781307i	$0.714553\pi$
$8$		−	2.04714i		−	0.723773i
$9$	1.41584			0.471948
$10$	2.34855	+	2.88691i	0.742677	+	0.912922i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			0.969136i			0.279765i
$13$		−	3.80507i		−	1.05534i	−0.849451	−	0.527668i	$-0.823066\pi$
$13$		−	3.80507i		−	1.05534i	0.849451	−	0.527668i	$-0.176934\pi$
$14$	6.88082			1.83898
$15$	1.77607	+	2.18320i	0.458579	+	0.563699i
$16$	−4.94710			−1.23677
$17$		−	2.64209i		−	0.640802i	−0.947282	−	0.320401i	$-0.896182\pi$
$17$		−	2.64209i		−	0.640802i	0.947282	−	0.320401i	$-0.103818\pi$
$18$		−	2.35643i		−	0.555416i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.33561	−	1.08654i	0.298652	−	0.242958i
$21$	5.20355			1.13551
$22$		−	1.66433i		−	0.354836i
$23$		−	5.58456i		−	1.16446i	−0.813023	−	0.582231i	$-0.802180\pi$
$23$		−	5.58456i		−	1.16446i	0.813023	−	0.582231i	$-0.197820\pi$
$24$	−2.57660			−0.525945
$25$	1.01753	−	4.89537i	0.203507	−	0.979074i
$26$	−6.33289			−1.24198
$27$		−	5.55792i		−	1.06962i
$28$		−	3.18337i		−	0.601600i
$29$	6.34374			1.17800			0.589001	−	0.808132i	$-0.299521\pi$
$29$	6.34374			1.17800			0.589001	+	0.808132i	$0.299521\pi$
$30$	3.63356	−	2.95596i	0.663394	−	0.539683i
$31$	7.53516			1.35336			0.676678	−	0.736279i	$-0.263419\pi$
$31$	7.53516			1.35336			0.676678	+	0.736279i	$0.263419\pi$
$32$			4.13932i			0.731735i
$33$		−	1.25863i		−	0.219100i
$34$	−4.39731			−0.754133
$35$	−5.83394	−	7.17126i	−0.986116	−	1.21216i
$36$	−1.09019			−0.181698
$37$			3.00157i			0.493456i	0.969085	+	0.246728i	$0.0793554\pi$
$37$			3.00157i			0.493456i	−0.969085	+	0.246728i	$0.920645\pi$
$38$			1.66433i			0.269990i
$39$	−4.78918			−0.766883
$40$	2.88874	+	3.55093i	0.456750	+	0.561451i
$41$	−4.89269			−0.764110			−0.382055	−	0.924140i	$-0.624783\pi$
$41$	−4.89269			−0.764110			−0.382055	+	0.924140i	$0.624783\pi$
$42$		−	8.66042i		−	1.33633i
$43$		−	10.6638i		−	1.62622i	−0.582110	−	0.813110i	$-0.697773\pi$
$43$		−	10.6638i		−	1.62622i	0.582110	−	0.813110i	$-0.302227\pi$
$44$	−0.769991			−0.116081
$45$	−2.45590	+	1.99791i	−0.366103	+	0.297831i
$46$	−9.29455			−1.37041
$47$		−	6.54878i		−	0.955238i	−0.878567	−	0.477619i	$-0.841500\pi$
$47$		−	6.54878i		−	0.955238i	0.878567	−	0.477619i	$-0.158500\pi$
$48$			6.22657i			0.898729i
$49$	−10.0924			−1.44177
$50$	−8.14750	−	1.69351i	−1.15223	−	0.239499i
$51$	−3.32543			−0.465653
$52$			2.92987i			0.406300i
$53$		−	7.14902i		−	0.981993i	−0.871161	−	0.490997i	$-0.836633\pi$
$53$		−	7.14902i		−	0.981993i	0.871161	−	0.490997i	$-0.163367\pi$
$54$	−9.25022			−1.25879
$55$	−1.73458	+	1.41111i	−0.233891	+	0.190274i
$56$	8.46347			1.13098
$57$			1.25863i			0.166710i
$58$		−	10.5581i		−	1.38634i
$59$	7.34337			0.956025			0.478012	−	0.878353i	$-0.341357\pi$
$59$	7.34337			0.956025			0.478012	+	0.878353i	$0.341357\pi$
$60$	−1.36756	−	1.68104i	−0.176551	−	0.217022i
$61$	4.72825			0.605391			0.302695	−	0.953087i	$-0.402114\pi$
$61$	4.72825			0.605391			0.302695	+	0.953087i	$0.402114\pi$
$62$		−	12.5410i		−	1.59271i
$63$			5.85351i			0.737473i
$64$	−3.00501			−0.375626
$65$	5.36937	+	6.60020i	0.665989	+	0.818654i
$66$	−2.09478			−0.257849
$67$			7.94790i			0.970990i	0.874239	+	0.485495i	$0.161361\pi$
$67$			7.94790i			0.970990i	−0.874239	+	0.485495i	$0.838639\pi$
$68$			2.03439i			0.246706i
$69$	−7.02891			−0.846182
$70$	−11.9353	+	9.70960i	−1.42654	+	1.16052i
$71$	9.69764			1.15090			0.575449	−	0.817838i	$-0.304827\pi$
$71$	9.69764			1.15090			0.575449	+	0.817838i	$0.304827\pi$
$72$		−	2.89843i		−	0.341583i
$73$			16.9975i			1.98940i	0.102798	+	0.994702i	$0.467221\pi$
$73$			16.9975i			1.98940i	−0.102798	+	0.994702i	$0.532779\pi$
$74$	4.99561			0.580727
$75$	−6.16147	−	1.28070i	−0.711465	−	0.147883i
$76$	0.769991			0.0883240
$77$			4.13429i			0.471146i
$78$			7.97078i			0.902513i
$79$	−3.09141			−0.347811			−0.173906	−	0.984762i	$-0.555639\pi$
$79$	−3.09141			−0.347811			−0.173906	+	0.984762i	$0.555639\pi$
$80$	8.58113	−	6.98090i	0.959400	−	0.780488i
$81$	−2.74785			−0.305317
$82$			8.14304i			0.899249i
$83$			1.51906i			0.166739i	0.996519	+	0.0833693i	$0.0265681\pi$
$83$			1.51906i			0.166739i	−0.996519	+	0.0833693i	$0.973432\pi$
$84$	−4.00669			−0.437166
$85$	3.72829	+	4.58292i	0.404390	+	0.497088i
$86$	−17.7481			−1.91383
$87$		−	7.98443i		−	0.856021i
$88$		−	2.04714i		−	0.218226i
$89$	−8.71704			−0.924005			−0.462002	−	0.886879i	$-0.652869\pi$
$89$	−8.71704			−0.924005			−0.462002	+	0.886879i	$0.652869\pi$
$90$	3.32519	+	4.08742i	0.350505	+	0.430852i
$91$	15.7313			1.64908
$92$			4.30007i			0.448313i
$93$		−	9.48400i		−	0.983445i
$94$	−10.8993			−1.12418
$95$	1.73458	−	1.41111i	0.177964	−	0.144777i
$96$	5.20988			0.531731
$97$			6.68784i			0.679048i	0.940597	+	0.339524i	$0.110266\pi$
$97$			6.68784i			0.679048i	−0.940597	+	0.339524i	$0.889734\pi$
$98$			16.7970i			1.69675i
$99$	1.41584			0.142298
$100$	−0.783493	+	3.76939i	−0.0783493	+	0.376939i
$101$	17.8311			1.77426			0.887128	−	0.461523i	$-0.152697\pi$
$101$	17.8311			1.77426			0.887128	+	0.461523i	$0.152697\pi$
$102$			5.53460i			0.548007i
$103$			11.5581i			1.13886i	0.822041	+	0.569429i	$0.192836\pi$
$103$			11.5581i			1.13886i	−0.822041	+	0.569429i	$0.807164\pi$
$104$	−7.78951			−0.763824
$105$	−9.02598	+	7.34279i	−0.880845	+	0.716583i
$106$	−11.8983			−1.15567
$107$			8.89809i			0.860210i	0.902779	+	0.430105i	$0.141524\pi$
$107$			8.89809i			0.860210i	−0.902779	+	0.430105i	$0.858476\pi$
$108$			4.27955i			0.411800i
$109$	−5.45885			−0.522863			−0.261432	−	0.965222i	$-0.584195\pi$
$109$	−5.45885			−0.522863			−0.261432	+	0.965222i	$0.584195\pi$
$110$	2.34855	+	2.88691i	0.223926	+	0.275256i
$111$	3.77788			0.358580
$112$		−	20.4527i		−	1.93260i
$113$			2.45792i			0.231221i	0.993295	+	0.115611i	$0.0368825\pi$
$113$			2.45792i			0.231221i	−0.993295	+	0.115611i	$0.963117\pi$
$114$	2.09478			0.196194
$115$	7.88044	+	9.68687i	0.734855	+	0.903306i
$116$	−4.88462			−0.453526
$117$		−	5.38739i		−	0.498064i
$118$		−	12.2218i		−	1.12511i
$119$	10.9232			1.00133
$120$	4.46931	−	3.63586i	0.407990	−	0.331907i
$121$	1.00000			0.0909091
$122$		−	7.86937i		−	0.712459i
$123$			6.15810i			0.555257i
$124$	−5.80201			−0.521036
$125$	5.14291	+	9.92726i	0.459996	+	0.887921i
$126$	9.74217			0.867902
$127$		−	19.9879i		−	1.77364i	−0.462116	−	0.886820i	$-0.652909\pi$
$127$		−	19.9879i		−	1.77364i	0.462116	−	0.886820i	$-0.347091\pi$
$128$			13.2800i			1.17379i
$129$	−13.4218			−1.18173
$130$	10.9849	−	8.93641i	0.963440	−	0.783775i
$131$	−6.36974			−0.556527			−0.278263	−	0.960505i	$-0.589759\pi$
$131$	−6.36974			−0.556527			−0.278263	+	0.960505i	$0.589759\pi$
$132$			0.969136i			0.0843524i
$133$		−	4.13429i		−	0.358488i
$134$	13.2279			1.14272
$135$	7.84285	+	9.64066i	0.675005	+	0.829736i
$136$	−5.40874			−0.463795
$137$		−	8.57793i		−	0.732862i	−0.930445	−	0.366431i	$-0.880580\pi$
$137$		−	8.57793i		−	0.732862i	0.930445	−	0.366431i	$-0.119420\pi$
$138$			11.6984i			0.995836i
$139$	−17.9590			−1.52326			−0.761629	−	0.648013i	$-0.775600\pi$
$139$	−17.9590			−1.52326			−0.761629	+	0.648013i	$0.775600\pi$
$140$	4.49208	+	5.52180i	0.379650	+	0.466678i
$141$	−8.24251			−0.694145
$142$		−	16.1401i		−	1.35444i
$143$		−	3.80507i		−	0.318196i
$144$	−7.00432			−0.583693
$145$	−11.0037	+	8.95171i	−0.913809	+	0.743399i
$146$	28.2894			2.34125
$147$			12.7026i			1.04769i
$148$		−	2.31118i		−	0.189978i
$149$	5.57782			0.456953			0.228477	−	0.973549i	$-0.426626\pi$
$149$	5.57782			0.456953			0.228477	+	0.973549i	$0.426626\pi$
$150$	−2.13151	+	10.2547i	−0.174037	+	0.837294i
$151$	−17.4741			−1.42202			−0.711011	−	0.703181i	$-0.751762\pi$
$151$	−17.4741			−1.42202			−0.711011	+	0.703181i	$0.751762\pi$
$152$			2.04714i			0.166045i
$153$		−	3.74080i		−	0.302425i
$154$	6.88082			0.554472
$155$	−13.0703	+	10.6329i	−1.04984	+	0.854059i
$156$	3.68763			0.295247
$157$		−	0.335336i		−	0.0267627i	−0.999910	−	0.0133814i	$-0.995740\pi$
$157$		−	0.335336i		−	0.0267627i	0.999910	−	0.0133814i	$-0.00425955\pi$
$158$			5.14513i			0.409324i
$159$	−8.99799			−0.713587
$160$	−5.84103	−	7.17997i	−0.461774	−	0.567627i
$161$	23.0882			1.81961
$162$			4.57332i			0.359314i
$163$		−	18.9776i		−	1.48644i	−0.669048	−	0.743219i	$-0.733298\pi$
$163$		−	18.9776i		−	1.48644i	0.669048	−	0.743219i	$-0.266702\pi$
$164$	3.76733			0.294179
$165$	1.77607	+	2.18320i	0.138267	+	0.169962i
$166$	2.52822			0.196228
$167$		−	2.50778i		−	0.194058i	−0.995282	−	0.0970289i	$-0.969066\pi$
$167$		−	2.50778i		−	0.194058i	0.995282	−	0.0970289i	$-0.0309339\pi$
$168$		−	10.6524i		−	0.821850i
$169$	−1.47856			−0.113735
$170$	7.62749	−	6.20510i	0.585002	−	0.475909i
$171$	−1.41584			−0.108272
$172$			8.21106i			0.626087i
$173$		−	8.73580i		−	0.664170i	−0.943249	−	0.332085i	$-0.892248\pi$
$173$		−	8.73580i		−	0.664170i	0.943249	−	0.332085i	$-0.107752\pi$
$174$	−13.2887			−1.00742
$175$	20.2389	+	4.20678i	1.52991	+	0.318003i
$176$	−4.94710			−0.372901
$177$		−	9.24260i		−	0.694716i
$178$			14.5080i			1.08742i
$179$	7.03056			0.525489			0.262744	−	0.964865i	$-0.415372\pi$
$179$	7.03056			0.525489			0.262744	+	0.964865i	$0.415372\pi$
$180$	1.89102	−	1.53838i	0.140948	−	0.114664i
$181$	4.57978			0.340412			0.170206	−	0.985408i	$-0.445557\pi$
$181$	4.57978			0.340412			0.170206	+	0.985408i	$0.445557\pi$
$182$		−	26.1820i		−	1.94074i
$183$		−	5.95113i		−	0.439920i
$184$	−11.4324			−0.842806
$185$	−4.23555	−	5.20647i	−0.311404	−	0.382787i
$186$	−15.7845			−1.15738
$187$		−	2.64209i		−	0.193209i
$188$			5.04251i			0.367763i
$189$	22.9781			1.67141
$190$	−2.34855	−	2.88691i	−0.170382	−	0.209439i
$191$	−15.1847			−1.09873			−0.549364	−	0.835583i	$-0.685130\pi$
$191$	−15.1847			−1.09873			−0.549364	+	0.835583i	$0.685130\pi$
$192$			3.78220i			0.272957i
$193$			10.0701i			0.724864i	0.932010	+	0.362432i	$0.118053\pi$
$193$			10.0701i			0.724864i	−0.932010	+	0.362432i	$0.881947\pi$
$194$	11.1308			0.799143
$195$	8.30722	−	6.75807i	0.594893	−	0.483955i
$196$	7.77103			0.555073
$197$		−	4.77076i		−	0.339902i	−0.985452	−	0.169951i	$-0.945639\pi$
$197$		−	4.77076i		−	0.339902i	0.985452	−	0.169951i	$-0.0543610\pi$
$198$		−	2.35643i		−	0.167464i
$199$	1.12545			0.0797808			0.0398904	−	0.999204i	$-0.487299\pi$
$199$	1.12545			0.0797808			0.0398904	+	0.999204i	$0.487299\pi$
$200$	−10.0215	−	2.08304i	−0.708627	−	0.147293i
$201$	10.0035			0.705591
$202$		−	29.6768i		−	2.08805i
$203$			26.2269i			1.84076i
$204$	2.56055			0.179274
$205$	8.48676	−	6.90412i	0.592741	−	0.482205i
$206$	19.2366			1.34027
$207$		−	7.90688i		−	0.549566i
$208$			18.8240i			1.30521i
$209$	−1.00000			−0.0691714
$210$	12.2208	+	15.0222i	0.843316	+	1.03663i
$211$	4.95441			0.341076			0.170538	−	0.985351i	$-0.445450\pi$
$211$	4.95441			0.341076			0.170538	+	0.985351i	$0.445450\pi$
$212$			5.50468i			0.378063i
$213$		−	12.2058i		−	0.836325i
$214$	14.8093			1.01235
$215$	15.0478	+	18.4973i	1.02625	+	1.26150i
$216$	−11.3778			−0.774164
$217$			31.1526i			2.11477i
$218$			9.08533i			0.615336i
$219$	21.3936			1.44564
$220$	1.33561	−	1.08654i	0.0900469	−	0.0732547i
$221$	−10.0534			−0.676262
$222$		−	6.28763i		−	0.421998i
$223$			3.36972i			0.225653i	0.993615	+	0.112826i	$0.0359904\pi$
$223$			3.36972i			0.225653i	−0.993615	+	0.112826i	$0.964010\pi$
$224$	−17.1131			−1.14342
$225$	1.44067	−	6.93108i	0.0960447	−	0.462072i
$226$	4.09078			0.272115
$227$			21.4571i			1.42416i	0.702101	+	0.712078i	$0.252246\pi$
$227$			21.4571i			1.42416i	−0.702101	+	0.712078i	$0.747754\pi$
$228$		−	0.969136i		−	0.0641826i
$229$	−4.58169			−0.302767			−0.151383	−	0.988475i	$-0.548373\pi$
$229$	−4.58169			−0.302767			−0.151383	+	0.988475i	$0.548373\pi$
$230$	16.1221	−	13.1156i	1.06306	−	0.864820i
$231$	5.20355			0.342369
$232$		−	12.9865i		−	0.852606i
$233$		−	12.2022i		−	0.799396i	−0.916647	−	0.399698i	$-0.869115\pi$
$233$		−	12.2022i		−	0.799396i	0.916647	−	0.399698i	$-0.130885\pi$
$234$	−8.96639			−0.586151
$235$	9.24106	+	11.3594i	0.602820	+	0.741005i
$236$	−5.65433			−0.368065
$237$			3.89095i			0.252745i
$238$		−	18.1798i		−	1.17842i
$239$	−27.5196			−1.78009			−0.890047	−	0.455869i	$-0.849329\pi$
$239$	−27.5196			−1.78009			−0.890047	+	0.455869i	$0.849329\pi$
$240$	−8.78638	−	10.8005i	−0.567159	−	0.697169i
$241$	−8.15118			−0.525064			−0.262532	−	0.964923i	$-0.584557\pi$
$241$	−8.15118			−0.525064			−0.262532	+	0.964923i	$0.584557\pi$
$242$		−	1.66433i		−	0.106987i
$243$		−	13.2152i		−	0.847758i
$244$	−3.64071			−0.233073
$245$	17.5060	−	14.2414i	1.11842	−	0.909852i
$246$	10.2491			0.653459
$247$			3.80507i			0.242111i
$248$		−	15.4255i		−	0.979522i
$249$	1.91194			0.121164
$250$	16.5222	−	8.55949i	1.04496	−	0.541350i
$251$	−15.0639			−0.950826			−0.475413	−	0.879763i	$-0.657701\pi$
$251$	−15.0639			−0.950826			−0.475413	+	0.879763i	$0.657701\pi$
$252$		−	4.50715i		−	0.283924i
$253$		−	5.58456i		−	0.351099i
$254$	−33.2664			−2.08732
$255$	5.76822	−	4.69254i	0.361220	−	0.293858i
$256$	16.0922			1.00576
$257$		−	10.7664i		−	0.671588i	−0.941935	−	0.335794i	$-0.890995\pi$
$257$		−	10.7664i		−	0.671588i	0.941935	−	0.335794i	$-0.109005\pi$
$258$			22.3384i			1.39073i
$259$	−12.4094			−0.771081
$260$	−4.13437	−	5.08209i	−0.256403	−	0.315178i
$261$	8.98175			0.555956
$262$			10.6013i			0.654953i
$263$			8.75501i			0.539857i	0.962880	+	0.269928i	$0.0870001\pi$
$263$			8.75501i			0.539857i	−0.962880	+	0.269928i	$0.913000\pi$
$264$	−2.57660			−0.158579
$265$	10.0881	+	12.4005i	0.619704	+	0.761760i
$266$	−6.88082			−0.421890
$267$			10.9716i			0.671448i
$268$		−	6.11981i		−	0.373827i
$269$	30.8940			1.88364			0.941822	−	0.336113i	$-0.109112\pi$
$269$	30.8940			1.88364			0.941822	+	0.336113i	$0.109112\pi$
$270$	16.0452	−	13.0531i	0.976482	−	0.794385i
$271$	−18.0422			−1.09598			−0.547991	−	0.836484i	$-0.684607\pi$
$271$	−18.0422			−1.09598			−0.547991	+	0.836484i	$0.684607\pi$
$272$			13.0707i			0.792527i
$273$		−	19.7999i		−	1.19834i
$274$	−14.2765			−0.862475
$275$	1.01753	−	4.89537i	0.0613596	−	0.295202i
$276$	5.41220			0.325776
$277$			22.7236i			1.36533i	0.730731	+	0.682666i	$0.239179\pi$
$277$			22.7236i			1.36533i	−0.730731	+	0.682666i	$0.760821\pi$
$278$			29.8896i			1.79266i
$279$	10.6686			0.638714
$280$	−14.6806	+	11.9429i	−0.877331	+	0.713724i
$281$	24.8693			1.48358			0.741790	−	0.670632i	$-0.233977\pi$
$281$	24.8693			1.48358			0.741790	+	0.670632i	$0.233977\pi$
$282$			13.7183i			0.816910i
$283$			30.6371i			1.82118i	0.413307	+	0.910592i	$0.364374\pi$
$283$			30.6371i			1.82118i	−0.413307	+	0.910592i	$0.635626\pi$
$284$	−7.46709			−0.443091
$285$	−1.77607	−	2.18320i	−0.105205	−	0.129321i
$286$	−6.33289			−0.374472
$287$		−	20.2278i		−	1.19401i
$288$			5.86063i			0.345341i
$289$	10.0193			0.589373
$290$	14.8986	+	18.3138i	0.874876	+	1.07542i
$291$	8.41754			0.493445
$292$		−	13.0879i		−	0.765912i
$293$		−	6.67638i		−	0.390038i	−0.980799	−	0.195019i	$-0.937523\pi$
$293$		−	6.67638i		−	0.390038i	0.980799	−	0.195019i	$-0.0624769\pi$
$294$	21.1413			1.23298
$295$	−12.7377	+	10.3623i	−0.741615	+	0.603316i
$296$	6.14464			0.357150
$297$		−	5.55792i		−	0.322504i
$298$		−	9.28333i		−	0.537769i
$299$	−21.2497			−1.22890
$300$	4.74428	+	0.986129i	0.273911	+	0.0569342i
$301$	44.0874			2.54115
$302$			29.0826i			1.67352i
$303$		−	22.4427i		−	1.28930i
$304$	4.94710			0.283735
$305$	−8.20153	+	6.67209i	−0.469618	+	0.382043i
$306$	−6.22592			−0.355912
$307$			6.23523i			0.355863i	0.984043	+	0.177932i	$0.0569406\pi$
$307$			6.23523i			0.355863i	−0.984043	+	0.177932i	$0.943059\pi$
$308$		−	3.18337i		−	0.181389i
$309$	14.5475			0.827576
$310$	17.6967	+	21.7533i	1.00511	+	1.23551i
$311$	10.7143			0.607550			0.303775	−	0.952744i	$-0.401753\pi$
$311$	10.7143			0.607550			0.303775	+	0.952744i	$0.401753\pi$
$312$			9.80413i			0.555049i
$313$		−	17.2646i		−	0.975855i	−0.872884	−	0.487928i	$-0.837753\pi$
$313$		−	17.2646i		−	0.975855i	0.872884	−	0.487928i	$-0.162247\pi$
$314$	−0.558109			−0.0314959
$315$	−8.25995	−	10.1534i	−0.465396	−	0.572079i
$316$	2.38036			0.133906
$317$			25.7380i			1.44559i	0.691064	+	0.722794i	$0.257142\pi$
$317$			25.7380i			1.44559i	−0.691064	+	0.722794i	$0.742858\pi$
$318$			14.9756i			0.839791i
$319$	6.34374			0.355181
$320$	5.21243	−	4.24040i	0.291383	−	0.237045i
$321$	11.1994			0.625091
$322$		−	38.4264i		−	2.14142i
$323$			2.64209i			0.147010i
$324$	2.11582			0.117546
$325$	−18.6272	−	3.87179i	−1.03325	−	0.214768i
$326$	−31.5849			−1.74933
$327$			6.87069i			0.379950i
$328$			10.0160i			0.553042i
$329$	27.0746			1.49267
$330$	3.63356	−	2.95596i	0.200021	−	0.162720i
$331$	19.3860			1.06555			0.532776	−	0.846256i	$-0.321149\pi$
$331$	19.3860			1.06555			0.532776	+	0.846256i	$0.321149\pi$
$332$		−	1.16966i		−	0.0641936i
$333$			4.24976i			0.232886i
$334$	−4.17377			−0.228379
$335$	−11.2154	−	13.7863i	−0.612761	−	0.753224i
$336$	−25.7425			−1.40437
$337$			23.5387i			1.28223i	0.767443	+	0.641117i	$0.221529\pi$
$337$			23.5387i			1.28223i	−0.767443	+	0.641117i	$0.778471\pi$
$338$			2.46081i			0.133850i
$339$	3.09361			0.168022
$340$	−2.87075	−	3.52881i	−0.155688	−	0.191377i
$341$	7.53516			0.408052
$342$			2.35643i			0.127421i
$343$		−	12.7847i		−	0.690309i
$344$	−21.8304			−1.17701
$345$	12.1922	−	9.91857i	0.656407	−	0.533998i
$346$	−14.5392			−0.781634
$347$		−	25.5573i		−	1.37199i	−0.727608	−	0.685993i	$-0.759368\pi$
$347$		−	25.5573i		−	1.37199i	0.727608	−	0.685993i	$-0.240632\pi$
$348$			6.14794i			0.329564i
$349$	−6.75120			−0.361383			−0.180692	−	0.983540i	$-0.557834\pi$
$349$	−6.75120			−0.361383			−0.180692	+	0.983540i	$0.557834\pi$
$350$	7.00147	−	33.6841i	0.374244	−	1.80049i
$351$	−21.1483			−1.12881
$352$			4.13932i			0.220626i
$353$			18.1264i			0.964771i	0.875959	+	0.482386i	$0.160230\pi$
$353$			18.1264i			0.964771i	−0.875959	+	0.482386i	$0.839770\pi$
$354$	−15.3827			−0.817582
$355$	−16.8213	+	13.6844i	−0.892783	+	0.726294i
$356$	6.71205			0.355738
$357$		−	13.7483i		−	0.727636i
$358$		−	11.7012i		−	0.618426i
$359$	−30.0381			−1.58535			−0.792675	−	0.609644i	$-0.791312\pi$
$359$	−30.0381			−1.58535			−0.792675	+	0.609644i	$0.791312\pi$
$360$	4.09001	+	5.02756i	0.215562	+	0.264976i
$361$	1.00000			0.0526316
$362$		−	7.62226i		−	0.400617i
$363$		−	1.25863i		−	0.0660611i
$364$	−12.1129			−0.634890
$365$	−23.9853	−	29.4835i	−1.25545	−	1.54324i
$366$	−9.90464			−0.517724
$367$			3.71003i			0.193662i	0.995301	+	0.0968309i	$0.0308706\pi$
$367$			3.71003i			0.193662i	−0.995301	+	0.0968309i	$0.969129\pi$
$368$			27.6274i			1.44018i
$369$	−6.92729			−0.360620
$370$	−8.66528	+	7.04935i	−0.450486	+	0.366478i
$371$	29.5561			1.53448
$372$			7.30259i			0.378622i
$373$		−	22.8775i		−	1.18455i	−0.805735	−	0.592277i	$-0.798229\pi$
$373$		−	22.8775i		−	1.18455i	0.805735	−	0.592277i	$-0.201771\pi$
$374$	−4.39731			−0.227380
$375$	12.4948	−	6.47303i	0.645227	−	0.334266i
$376$	−13.4063			−0.691376
$377$		−	24.1384i		−	1.24319i
$378$		−	38.2431i		−	1.96701i
$379$	−1.48762			−0.0764140			−0.0382070	−	0.999270i	$-0.512165\pi$
$379$	−1.48762			−0.0764140			−0.0382070	+	0.999270i	$0.512165\pi$
$380$	−1.33561	+	1.08654i	−0.0685154	+	0.0557385i
$381$	−25.1574			−1.28885
$382$			25.2724i			1.29305i
$383$			29.7901i			1.52220i	0.648634	+	0.761100i	$0.275341\pi$
$383$			29.7901i			1.52220i	−0.648634	+	0.761100i	$0.724659\pi$
$384$	16.7146			0.852962
$385$	−5.83394	−	7.17126i	−0.297325	−	0.365481i
$386$	16.7600			0.853062
$387$		−	15.0983i		−	0.767491i
$388$		−	5.14958i		−	0.261430i
$389$	10.6431			0.539628			0.269814	−	0.962913i	$-0.413038\pi$
$389$	10.6431			0.539628			0.269814	+	0.962913i	$0.413038\pi$
$390$	−11.2476	−	13.8260i	−0.569547	−	0.700104i
$391$	−14.7549			−0.746190
$392$			20.6605i			1.04351i
$393$			8.01716i			0.404412i
$394$	−7.94011			−0.400017
$395$	5.36230	−	4.36233i	0.269807	−	0.219492i
$396$	−1.09019			−0.0547840
$397$			10.1616i			0.509997i	0.966941	+	0.254999i	$0.0820750\pi$
$397$			10.1616i			0.509997i	−0.966941	+	0.254999i	$0.917925\pi$
$398$		−	1.87311i		−	0.0938907i
$399$	−5.20355			−0.260503
$400$	−5.03384	+	24.2179i	−0.251692	+	1.21089i
$401$	25.4722			1.27202			0.636011	−	0.771680i	$-0.280583\pi$
$401$	25.4722			1.27202			0.636011	+	0.771680i	$0.280583\pi$
$402$		−	16.6491i		−	0.830381i
$403$		−	28.6718i		−	1.42825i
$404$	−13.7298			−0.683081
$405$	4.76636	−	3.87752i	0.236842	−	0.192675i
$406$	43.6501			2.16632
$407$			3.00157i			0.148782i
$408$			6.80761i			0.337027i
$409$	−4.41274			−0.218196			−0.109098	−	0.994031i	$-0.534796\pi$
$409$	−4.41274			−0.218196			−0.109098	+	0.994031i	$0.534796\pi$
$410$	−11.4907	−	14.1248i	−0.567487	−	0.697572i
$411$	−10.7965			−0.532550
$412$		−	8.89967i		−	0.438455i
$413$			30.3596i			1.49390i
$414$	−13.1596			−0.646761
$415$	−2.14356	−	2.63493i	−0.105223	−	0.129344i
$416$	15.7504			0.772226
$417$			22.6037i			1.10691i
$418$			1.66433i			0.0814050i
$419$	12.1463			0.593384			0.296692	−	0.954973i	$-0.404117\pi$
$419$	12.1463			0.593384			0.296692	+	0.954973i	$0.404117\pi$
$420$	6.94992	−	5.65388i	0.339121	−	0.275881i
$421$	15.9860			0.779108			0.389554	−	0.921004i	$-0.372629\pi$
$421$	15.9860			0.779108			0.389554	+	0.921004i	$0.372629\pi$
$422$		−	8.24577i		−	0.401398i
$423$		−	9.27206i		−	0.450823i
$424$	−14.6350			−0.710740
$425$	−12.9340	−	2.68842i	−0.627392	−	0.130408i
$426$	−20.3144			−0.984236
$427$			19.5480i			0.945992i
$428$		−	6.85145i		−	0.331177i
$429$	−4.78918			−0.231224
$430$	30.7855	−	25.0446i	1.48461	−	1.20776i
$431$	2.80822			0.135267			0.0676336	−	0.997710i	$-0.478455\pi$
$431$	2.80822			0.135267			0.0676336	+	0.997710i	$0.478455\pi$
$432$			27.4956i			1.32288i
$433$			17.0633i			0.820011i	0.912083	+	0.410006i	$0.134473\pi$
$433$			17.0633i			0.820011i	−0.912083	+	0.410006i	$0.865527\pi$
$434$	51.8481			2.48879
$435$	11.2669	+	13.8496i	0.540207	+	0.664039i
$436$	4.20327			0.201300
$437$			5.58456i			0.267146i
$438$		−	35.6060i		−	1.70132i
$439$	−4.59307			−0.219215			−0.109608	−	0.993975i	$-0.534959\pi$
$439$	−4.59307			−0.219215			−0.109608	+	0.993975i	$0.534959\pi$
$440$	2.88874	+	3.55093i	0.137715	+	0.169284i
$441$	−14.2892			−0.680439
$442$			16.7321i			0.795864i
$443$		−	13.2967i		−	0.631747i	−0.948801	−	0.315873i	$-0.897703\pi$
$443$		−	13.2967i		−	0.631747i	0.948801	−	0.315873i	$-0.102297\pi$
$444$	−2.90893			−0.138052
$445$	15.1204	−	12.3007i	0.716776	−	0.583110i
$446$	5.60832			0.265561
$447$		−	7.02043i		−	0.332055i
$448$		−	12.4236i		−	0.586959i
$449$	4.22753			0.199510			0.0997548	−	0.995012i	$-0.468194\pi$
$449$	4.22753			0.199510			0.0997548	+	0.995012i	$0.468194\pi$
$450$	−11.5356	−	2.39775i	−0.543793	−	0.113031i
$451$	−4.89269			−0.230388
$452$		−	1.89257i		−	0.0890192i
$453$			21.9935i			1.03334i
$454$	35.7116			1.67603
$455$	−27.2871	+	22.1986i	−1.27924	+	1.04068i
$456$	2.57660			0.120660
$457$			39.3140i			1.83903i	0.393051	+	0.919517i	$0.371420\pi$
$457$			39.3140i			1.83903i	−0.393051	+	0.919517i	$0.628580\pi$
$458$			7.62545i			0.356314i
$459$	−14.6846			−0.685417
$460$	−6.06787	−	7.45881i	−0.282916	−	0.347769i
$461$	−32.6330			−1.51987			−0.759936	−	0.649998i	$-0.774770\pi$
$461$	−32.6330			−1.51987			−0.759936	+	0.649998i	$0.774770\pi$
$462$		−	8.66042i		−	0.402919i
$463$		−	9.25218i		−	0.429985i	−0.976616	−	0.214993i	$-0.931027\pi$
$463$		−	9.25218i		−	0.429985i	0.976616	−	0.214993i	$-0.0689728\pi$
$464$	−31.3831			−1.45692
$465$	13.3830	+	16.4508i	0.620620	+	0.762885i
$466$	−20.3085			−0.940775
$467$			30.3491i			1.40439i	0.711986	+	0.702194i	$0.247796\pi$
$467$			30.3491i			1.40439i	−0.711986	+	0.702194i	$0.752204\pi$
$468$			4.14824i			0.191753i
$469$	−32.8589			−1.51728
$470$	18.9058	−	15.3802i	0.872058	−	0.709434i
$471$	−0.422065			−0.0194477
$472$		−	15.0329i		−	0.691945i
$473$		−	10.6638i		−	0.490324i
$474$	6.47582			0.297444
$475$	−1.01753	+	4.89537i	−0.0466877	+	0.224615i
$476$	−8.41076			−0.385506
$477$		−	10.1219i		−	0.463450i
$478$			45.8016i			2.09492i
$479$	−22.0685			−1.00834			−0.504168	−	0.863606i	$-0.668201\pi$
$479$	−22.0685			−1.00834			−0.504168	+	0.863606i	$0.668201\pi$
$480$	−9.03695	+	7.35171i	−0.412478	+	0.335558i
$481$	11.4212			0.520762
$482$			13.5662i			0.617926i
$483$		−	29.0596i		−	1.32226i
$484$	−0.769991			−0.0349996
$485$	−9.43729	−	11.6006i	−0.428525	−	0.526756i
$486$	−21.9945			−0.997691
$487$		−	27.3741i		−	1.24044i	−0.784428	−	0.620220i	$-0.787043\pi$
$487$		−	27.3741i		−	1.24044i	0.784428	−	0.620220i	$-0.212957\pi$
$488$		−	9.67939i		−	0.438165i
$489$	−23.8858			−1.08015
$490$	−23.7024	−	29.1357i	−1.07077	−	1.31622i
$491$	24.6060			1.11045			0.555227	−	0.831699i	$-0.312631\pi$
$491$	24.6060			1.11045			0.555227	+	0.831699i	$0.312631\pi$
$492$		−	4.74168i		−	0.213771i
$493$		−	16.7608i		−	0.754866i
$494$	6.33289			0.284930
$495$	−2.45590	+	1.99791i	−0.110384	+	0.0897995i
$496$	−37.2772			−1.67379
$497$			40.0928i			1.79841i
$498$		−	3.18210i		−	0.142593i
$499$	22.4290			1.00406			0.502031	−	0.864850i	$-0.332586\pi$
$499$	22.4290			1.00406			0.502031	+	0.864850i	$0.332586\pi$
$500$	−3.95999	−	7.64390i	−0.177096	−	0.341846i
$501$	−3.15637			−0.141016
$502$			25.0713i			1.11899i
$503$			32.2644i			1.43860i	0.694701	+	0.719298i	$0.255537\pi$
$503$			32.2644i			1.43860i	−0.694701	+	0.719298i	$0.744463\pi$
$504$	11.9830			0.533763
$505$	−30.9294	+	25.1616i	−1.37634	+	1.11968i
$506$	−9.29455			−0.413193
$507$			1.86096i			0.0826482i
$508$			15.3905i			0.682843i
$509$	41.7294			1.84962			0.924811	−	0.380426i	$-0.124223\pi$
$509$	41.7294			1.84962			0.924811	+	0.380426i	$0.124223\pi$
$510$	−7.80994	−	9.60021i	−0.345830	−	0.425104i
$511$	−70.2725			−3.10867
$512$		−	0.222805i		−	0.00984669i
$513$			5.55792i			0.245388i
$514$	−17.9188			−0.790364
$515$	−16.3098	−	20.0485i	−0.718697	−	0.883444i
$516$	10.3347			0.454960
$517$		−	6.54878i		−	0.288015i
$518$			20.6533i			0.907453i
$519$	−10.9952			−0.482634
$520$	13.5115	−	10.9919i	0.592520	−	0.482025i
$521$	−24.2787			−1.06367			−0.531836	−	0.846848i	$-0.678498\pi$
$521$	−24.2787			−1.06367			−0.531836	+	0.846848i	$0.678498\pi$
$522$		−	14.9486i		−	0.654282i
$523$			3.57111i			0.156154i	0.996947	+	0.0780769i	$0.0248780\pi$
$523$			3.57111i			0.156154i	−0.996947	+	0.0780769i	$0.975122\pi$
$524$	4.90464			0.214260
$525$	5.29479	−	25.4733i	0.231084	−	1.11175i
$526$	14.5712			0.635335
$527$		−	19.9086i		−	0.867233i
$528$			6.22657i			0.270977i
$529$	−8.18736			−0.355972
$530$	20.6386	−	16.7898i	0.896483	−	0.729304i
$531$	10.3971			0.451194
$532$			3.18337i			0.138016i
$533$			18.6170i			0.806393i
$534$	18.2603			0.790199
$535$	−12.5562	−	15.4344i	−0.542851	−	0.667289i
$536$	16.2705			0.702777
$537$		−	8.84889i		−	0.381858i
$538$		−	51.4179i		−	2.21678i
$539$	−10.0924			−0.434709
$540$	−6.03892	−	7.42323i	−0.259874	−	0.319445i
$541$	−29.0917			−1.25075			−0.625376	−	0.780324i	$-0.715054\pi$
$541$	−29.0917			−1.25075			−0.625376	+	0.780324i	$0.715054\pi$
$542$			30.0281i			1.28982i
$543$		−	5.76426i		−	0.247368i
$544$	10.9365			0.468897
$545$	9.46882	−	7.70305i	0.405600	−	0.329962i
$546$	−32.9535			−1.41028
$547$			7.61063i			0.325407i	0.986675	+	0.162704i	$0.0520214\pi$
$547$			7.61063i			0.325407i	−0.986675	+	0.162704i	$0.947979\pi$
$548$			6.60493i			0.282149i
$549$	6.69447			0.285713
$550$	−8.14750	−	1.69351i	−0.347411	−	0.0722116i
$551$	−6.34374			−0.270252
$552$			14.3892i			0.612444i
$553$		−	12.7808i		−	0.543495i
$554$	37.8196			1.60680
$555$	−6.55303	+	5.33100i	−0.278161	+	0.226288i
$556$	13.8282			0.586448
$557$		−	34.8324i		−	1.47590i	−0.674858	−	0.737948i	$-0.735795\pi$
$557$		−	34.8324i		−	1.47590i	0.674858	−	0.737948i	$-0.264205\pi$
$558$		−	17.7561i		−	0.751675i
$559$	−40.5766			−1.71621
$560$	28.8611	+	35.4769i	1.21960	+	1.49917i
$561$	−3.32543			−0.140400
$562$		−	41.3908i		−	1.74596i
$563$			40.2832i			1.69773i	0.528607	+	0.848867i	$0.322715\pi$
$563$			40.2832i			1.69773i	−0.528607	+	0.848867i	$0.677285\pi$
$564$	6.34666			0.267243
$565$	−3.46839	−	4.26345i	−0.145916	−	0.179365i
$566$	50.9901			2.14328
$567$		−	11.3604i		−	0.477092i
$568$		−	19.8524i		−	0.832989i
$569$	−22.4278			−0.940221			−0.470111	−	0.882608i	$-0.655786\pi$
$569$	−22.4278			−0.940221			−0.470111	+	0.882608i	$0.655786\pi$
$570$	−3.63356	+	2.95596i	−0.152193	+	0.123812i
$571$	28.5385			1.19430			0.597149	−	0.802131i	$-0.296300\pi$
$571$	28.5385			1.19430			0.597149	+	0.802131i	$0.296300\pi$
$572$			2.92987i			0.122504i
$573$			19.1120i			0.798415i
$574$	−33.6657			−1.40518
$575$	−27.3385	−	5.68249i	−1.14009	−	0.236976i
$576$	−4.25462			−0.177276
$577$			35.9350i			1.49600i	0.663701	+	0.747998i	$0.268985\pi$
$577$			35.9350i			1.49600i	−0.663701	+	0.747998i	$0.731015\pi$
$578$		−	16.6755i		−	0.693608i
$579$	12.6746			0.526738
$580$	8.47277	−	6.89274i	0.351812	−	0.286205i
$581$	−6.28024			−0.260548
$582$		−	14.0096i		−	0.580715i
$583$		−	7.14902i		−	0.296082i
$584$	34.7962			1.43988
$585$	7.60220	+	9.34486i	0.314312	+	0.386362i
$586$	−11.1117			−0.459020
$587$		−	17.4907i		−	0.721920i	−0.932581	−	0.360960i	$-0.882449\pi$
$587$		−	17.4907i		−	0.721920i	0.932581	−	0.360960i	$-0.117551\pi$
$588$		−	9.78086i		−	0.403356i
$589$	−7.53516			−0.310481
$590$	17.2463	+	21.1996i	0.710018	+	0.872776i
$591$	−6.00463			−0.246997
$592$		−	14.8491i		−	0.610293i
$593$		−	32.0403i		−	1.31574i	−0.753132	−	0.657869i	$-0.771458\pi$
$593$		−	32.0403i		−	1.31574i	0.753132	−	0.657869i	$-0.228542\pi$
$594$	−9.25022			−0.379541
$595$	−18.9471	+	15.4138i	−0.776757	+	0.631905i
$596$	−4.29487			−0.175925
$597$		−	1.41652i		−	0.0579744i
$598$			35.3664i			1.44624i
$599$	2.86659			0.117126			0.0585629	−	0.998284i	$-0.481348\pi$
$599$	2.86659			0.117126			0.0585629	+	0.998284i	$0.481348\pi$
$600$	−2.62178	+	12.6134i	−0.107034	+	0.514939i
$601$	0.391875			0.0159849			0.00799245	−	0.999968i	$-0.497456\pi$
$601$	0.391875			0.0159849			0.00799245	+	0.999968i	$0.497456\pi$
$602$		−	73.3759i		−	2.99058i
$603$			11.2530i			0.458257i
$604$	13.4549			0.547472
$605$	−1.73458	+	1.41111i	−0.0705207	+	0.0573698i
$606$	−37.3521			−1.51733
$607$			23.3599i			0.948151i	0.880484	+	0.474075i	$0.157218\pi$
$607$			23.3599i			0.948151i	−0.880484	+	0.474075i	$0.842782\pi$
$608$		−	4.13932i		−	0.167871i
$609$	33.0100			1.33763
$610$	11.1045	+	13.6500i	0.449610	+	0.552674i
$611$	−24.9186			−1.00810
$612$			2.88038i			0.116432i
$613$		−	21.9771i		−	0.887648i	−0.896114	−	0.443824i	$-0.853621\pi$
$613$		−	21.9771i		−	0.887648i	0.896114	−	0.443824i	$-0.146379\pi$
$614$	10.3775			0.418800
$615$	−8.68975	−	10.6817i	−0.350405	−	0.430728i
$616$	8.46347			0.341003
$617$			20.9896i			0.845010i	0.906361	+	0.422505i	$0.138849\pi$
$617$			20.9896i			0.845010i	−0.906361	+	0.422505i	$0.861151\pi$
$618$		−	24.2118i		−	0.973940i
$619$	−4.96934			−0.199735			−0.0998673	−	0.995001i	$-0.531842\pi$
$619$	−4.96934			−0.199735			−0.0998673	+	0.995001i	$0.531842\pi$
$620$	10.0640	−	8.18727i	0.404182	−	0.328809i
$621$	−31.0386			−1.24554
$622$		−	17.8320i		−	0.715000i
$623$		−	36.0388i		−	1.44386i
$624$	23.6926			0.948461
$625$	−22.9292	−	9.96241i	−0.917170	−	0.398496i
$626$	−28.7340			−1.14844
$627$			1.25863i			0.0502649i
$628$			0.258206i			0.0103035i
$629$	7.93044			0.316207
$630$	−16.8986	+	13.7473i	−0.673255	+	0.547705i
$631$	12.8910			0.513181			0.256591	−	0.966520i	$-0.417401\pi$
$631$	12.8910			0.513181			0.256591	+	0.966520i	$0.417401\pi$
$632$			6.32855i			0.251736i
$633$		−	6.23578i		−	0.247850i
$634$	42.8364			1.70125
$635$	28.2051	+	34.6706i	1.11929	+	1.37586i
$636$	6.92837			0.274728
$637$			38.4021i			1.52155i
$638$		−	10.5581i		−	0.417998i
$639$	13.7303			0.543164
$640$	−18.7395	−	23.0351i	−0.740743	−	0.910544i
$641$	6.24599			0.246702			0.123351	−	0.992363i	$-0.460636\pi$
$641$	6.24599			0.246702			0.123351	+	0.992363i	$0.460636\pi$
$642$		−	18.6395i		−	0.735643i
$643$		−	4.14158i		−	0.163328i	−0.996660	−	0.0816640i	$-0.973977\pi$
$643$		−	4.14158i		−	0.163328i	0.996660	−	0.0816640i	$-0.0260234\pi$
$644$	−17.7777			−0.700540
$645$	23.2813	−	18.9397i	0.916699	−	0.745750i
$646$	4.39731			0.173010
$647$			0.463373i			0.0182171i	0.999959	+	0.00910853i	$0.00289938\pi$
$647$			0.463373i			0.0182171i	−0.999959	+	0.00910853i	$0.997101\pi$
$648$			5.62523i			0.220980i
$649$	7.34337			0.288252
$650$	−6.44393	+	31.0018i	−0.252752	+	1.21599i
$651$	39.2096			1.53675
$652$			14.6126i			0.572272i
$653$			5.98508i			0.234214i	0.993119	+	0.117107i	$0.0373621\pi$
$653$			5.98508i			0.234214i	−0.993119	+	0.117107i	$0.962638\pi$
$654$	11.4351			0.447147
$655$	11.0488	−	8.98841i	0.431713	−	0.351206i
$656$	24.2046			0.945031
$657$			24.0658i			0.938896i
$658$		−	45.0610i		−	1.75666i
$659$	−27.1167			−1.05632			−0.528158	−	0.849146i	$-0.677117\pi$
$659$	−27.1167			−1.05632			−0.528158	+	0.849146i	$0.677117\pi$
$660$	−1.36756	−	1.68104i	−0.0532321	−	0.0654345i
$661$	33.8878			1.31808			0.659041	−	0.752107i	$-0.270962\pi$
$661$	33.8878			1.31808			0.659041	+	0.752107i	$0.270962\pi$
$662$		−	32.2647i		−	1.25400i
$663$			12.6535i			0.491420i
$664$	3.10973			0.120681
$665$	5.83394	+	7.17126i	0.226231	+	0.278089i
$666$	7.07300			0.274073
$667$		−	35.4270i		−	1.37174i
$668$			1.93097i			0.0747114i
$669$	4.24123			0.163976
$670$	−22.9449	+	18.6660i	−0.886438	+	0.721132i
$671$	4.72825			0.182532
$672$			21.5391i			0.830891i
$673$			0.103566i			0.00399219i	0.999998	+	0.00199610i	$0.000635377\pi$
$673$			0.103566i			0.00399219i	−0.999998	+	0.00199610i	$0.999365\pi$
$674$	39.1761			1.50901
$675$	−27.2081	−	5.65538i	−1.04724	−	0.217676i
$676$	1.13848			0.0437876
$677$		−	36.4846i		−	1.40222i	−0.713054	−	0.701109i	$-0.752689\pi$
$677$		−	36.4846i		−	1.40222i	0.713054	−	0.701109i	$-0.247311\pi$
$678$		−	5.14879i		−	0.197738i
$679$	−27.6495			−1.06109
$680$	9.38188	−	7.63232i	0.359779	−	0.292686i
$681$	27.0066			1.03489
$682$		−	12.5410i		−	0.480219i
$683$		−	11.0961i		−	0.424579i	−0.977207	−	0.212290i	$-0.931908\pi$
$683$		−	11.0961i		−	0.424579i	0.977207	−	0.212290i	$-0.0680920\pi$
$684$	1.09019			0.0416844
$685$	12.1044	+	14.8791i	0.462486	+	0.568501i
$686$	−21.2780			−0.812396
$687$			5.76667i			0.220012i
$688$			52.7550i			2.01127i
$689$	−27.2025			−1.03633
$690$	−16.5078	−	20.2919i	−0.628440	−	0.772498i
$691$	11.8894			0.452293			0.226146	−	0.974093i	$-0.427387\pi$
$691$	11.8894			0.452293			0.226146	+	0.974093i	$0.427387\pi$
$692$			6.72649i			0.255703i
$693$			5.85351i			0.222357i
$694$	−42.5357			−1.61463
$695$	31.1512	−	25.3421i	1.18163	−	0.961279i
$696$	−16.3452			−0.619565
$697$			12.9269i			0.489643i
$698$			11.2362i			0.425297i
$699$	−15.3581			−0.580898
$700$	−15.5838	−	3.23919i	−0.589010	−	0.122430i
$701$	46.3021			1.74881			0.874403	−	0.485201i	$-0.161254\pi$
$701$	46.3021			1.74881			0.874403	+	0.485201i	$0.161254\pi$
$702$			35.1977i			1.32845i
$703$		−	3.00157i		−	0.113206i
$704$	−3.00501			−0.113255
$705$	14.2973	−	11.6311i	0.538467	−	0.438052i
$706$	30.1683			1.13540
$707$			73.7188i			2.77248i
$708$			7.11672i			0.267463i
$709$	−1.98659			−0.0746080			−0.0373040	−	0.999304i	$-0.511877\pi$
$709$	−1.98659			−0.0746080			−0.0373040	+	0.999304i	$0.511877\pi$
$710$	22.7754	+	27.9962i	0.854746	+	1.05068i
$711$	−4.37696			−0.164149
$712$			17.8450i			0.668770i
$713$		−	42.0806i		−	1.57593i
$714$	−22.8817			−0.856324
$715$	5.36937	+	6.60020i	0.200803	+	0.246833i
$716$	−5.41347			−0.202311
$717$			34.6370i			1.29354i
$718$			49.9933i			1.86573i
$719$	−25.3582			−0.945700			−0.472850	−	0.881143i	$-0.656775\pi$
$719$	−25.3582			−0.945700			−0.472850	+	0.881143i	$0.656775\pi$
$720$	12.1496	−	9.88387i	0.452787	−	0.368350i
$721$	−47.7847			−1.77960
$722$		−	1.66433i		−	0.0619399i
$723$			10.2593i			0.381549i
$724$	−3.52639			−0.131057
$725$	6.45497	−	31.0549i	0.239732	−	1.15335i
$726$	−2.09478			−0.0777445
$727$		−	30.4622i		−	1.12978i	−0.825166	−	0.564891i	$-0.808918\pi$
$727$		−	30.4622i		−	1.12978i	0.825166	−	0.564891i	$-0.191082\pi$
$728$		−	32.2041i		−	1.19356i
$729$	−24.8767			−0.921358
$730$	−49.0702	+	39.9195i	−1.81617	+	1.47749i
$731$	−28.1749			−1.04208
$732$			4.58232i			0.169367i
$733$			17.8574i			0.659577i	0.944055	+	0.329789i	$0.106977\pi$
$733$			17.8574i			0.659577i	−0.944055	+	0.329789i	$0.893023\pi$
$734$	6.17471			0.227913
$735$	−17.9247	−	22.0336i	−0.661163	−	0.812722i
$736$	23.1163			0.852077
$737$			7.94790i			0.292765i
$738$			11.5293i			0.424399i
$739$	−29.8916			−1.09958			−0.549789	−	0.835303i	$-0.685292\pi$
$739$	−29.8916			−1.09958			−0.549789	+	0.835303i	$0.685292\pi$
$740$	3.26134	+	4.00893i	0.119889	+	0.147371i
$741$	4.78918			0.175935
$742$		−	49.1911i		−	1.80586i
$743$			48.7230i			1.78747i	0.448591	+	0.893737i	$0.351926\pi$
$743$			48.7230i			1.78747i	−0.448591	+	0.893737i	$0.648074\pi$
$744$	−19.4151			−0.711791
$745$	−9.67518	+	7.87093i	−0.354471	+	0.288368i
$746$	−38.0757			−1.39405
$747$			2.15075i			0.0786920i
$748$			2.03439i			0.0743846i
$749$	−36.7873			−1.34418
$750$	−10.7733	−	20.7954i	−0.393384	−	0.759341i
$751$	49.7261			1.81453			0.907265	−	0.420559i	$-0.138166\pi$
$751$	49.7261			1.81453			0.907265	+	0.420559i	$0.138166\pi$
$752$			32.3975i			1.18141i
$753$			18.9599i			0.690939i
$754$	−40.1742			−1.46306
$755$	30.3102	−	24.6579i	1.10310	−	0.897392i
$756$	−17.6929			−0.643485
$757$			26.1383i			0.950014i	0.879982	+	0.475007i	$0.157555\pi$
$757$			26.1383i			0.950014i	−0.879982	+	0.475007i	$0.842445\pi$
$758$			2.47589i			0.0899284i
$759$	−7.02891			−0.255133
$760$	−2.88874	−	3.55093i	−0.104786	−	0.128806i
$761$	23.4157			0.848819			0.424410	−	0.905470i	$-0.360482\pi$
$761$	23.4157			0.848819			0.424410	+	0.905470i	$0.360482\pi$
$762$			41.8702i			1.51680i
$763$		−	22.5685i		−	0.817034i
$764$	11.6921			0.423005
$765$	5.27868	+	6.48871i	0.190851	+	0.234600i
$766$	49.5804			1.79141
$767$		−	27.9420i		−	1.00893i
$768$		−	20.2542i		−	0.730859i
$769$	−44.2884			−1.59708			−0.798541	−	0.601940i	$-0.794394\pi$
$769$	−44.2884			−1.59708			−0.798541	+	0.601940i	$0.794394\pi$
$770$	−11.9353	+	9.70960i	−0.430119	+	0.349910i
$771$	−13.5509			−0.488024
$772$		−	7.75391i		−	0.279069i
$773$		−	24.3892i		−	0.877220i	−0.898678	−	0.438610i	$-0.855471\pi$
$773$		−	24.3892i		−	0.877220i	0.898678	−	0.438610i	$-0.144529\pi$
$774$	−25.1286			−0.903229
$775$	7.66729	−	36.8874i	0.275417	−	1.32503i
$776$	13.6909			0.491476
$777$			15.6188i			0.560323i
$778$		−	17.7137i		−	0.635065i
$779$	4.89269			0.175299
$780$	−6.39649	+	5.20365i	−0.229031	+	0.186321i
$781$	9.69764			0.347009
$782$			24.5571i			0.878160i
$783$		−	35.2580i		−	1.26002i
$784$	49.9279			1.78314
$785$	0.473196	+	0.581667i	0.0168891	+	0.0207606i
$786$	13.3432			0.475936
$787$		−	52.1888i		−	1.86033i	−0.367141	−	0.930165i	$-0.619663\pi$
$787$		−	52.1888i		−	1.86033i	0.367141	−	0.930165i	$-0.380337\pi$
$788$			3.67344i			0.130861i
$789$	11.0193			0.392299
$790$	−7.26034	−	8.92464i	−0.258311	−	0.317524i
$791$	−10.1617			−0.361310
$792$		−	2.89843i		−	0.102991i
$793$		−	17.9913i		−	0.638891i
$794$	16.9123			0.600194
$795$	15.6077	−	12.6972i	0.553549	−	0.450322i
$796$	−0.866584			−0.0307152
$797$		−	7.66970i		−	0.271675i	−0.990731	−	0.135837i	$-0.956628\pi$
$797$		−	7.66970i		−	0.271675i	0.990731	−	0.135837i	$-0.0433724\pi$
$798$			8.66042i			0.306576i
$799$	−17.3025			−0.612119
$800$	20.2635	+	4.21190i	0.716422	+	0.148913i
$801$	−12.3420			−0.436083
$802$		−	42.3942i		−	1.49699i
$803$			16.9975i			0.599828i
$804$	−7.70259			−0.271649
$805$	−40.0484	+	32.5800i	−1.41152	+	1.14829i
$806$	−47.7193			−1.68084
$807$		−	38.8842i		−	1.36879i
$808$		−	36.5027i		−	1.28416i
$809$	1.23293			0.0433476			0.0216738	−	0.999765i	$-0.493100\pi$
$809$	1.23293			0.0433476			0.0216738	+	0.999765i	$0.493100\pi$
$810$	−6.45347	−	7.93280i	−0.226752	−	0.278730i
$811$	12.2439			0.429940			0.214970	−	0.976621i	$-0.431035\pi$
$811$	12.2439			0.429940			0.214970	+	0.976621i	$0.431035\pi$
$812$		−	20.1944i		−	0.708686i
$813$			22.7084i			0.796420i
$814$	4.99561			0.175096
$815$	26.7795	+	32.9181i	0.938043	+	1.15307i
$816$	16.4512			0.575907
$817$			10.6638i			0.373080i
$818$			7.34425i			0.256786i
$819$	22.2730			0.778283
$820$	−6.53473	+	5.31611i	−0.228203	+	0.185647i
$821$	21.2934			0.743145			0.371572	−	0.928404i	$-0.378819\pi$
$821$	21.2934			0.743145			0.371572	+	0.928404i	$0.378819\pi$
$822$			17.9689i			0.626736i
$823$		−	30.8939i		−	1.07690i	−0.842659	−	0.538448i	$-0.819011\pi$
$823$		−	30.8939i		−	1.07690i	0.842659	−	0.538448i	$-0.180989\pi$
$824$	23.6611			0.824275
$825$	−6.16147	−	1.28070i	−0.214515	−	0.0445883i
$826$	50.5284			1.75811
$827$		−	6.54249i		−	0.227505i	−0.993509	−	0.113752i	$-0.963713\pi$
$827$		−	6.54249i		−	0.227505i	0.993509	−	0.113752i	$-0.0362870\pi$
$828$			6.08823i			0.211580i
$829$	46.6368			1.61976			0.809881	−	0.586594i	$-0.199532\pi$
$829$	46.6368			1.61976			0.809881	+	0.586594i	$0.199532\pi$
$830$	−4.38539	+	3.56759i	−0.152219	+	0.123833i
$831$	28.6007			0.992148
$832$			11.4343i			0.396412i
$833$			26.6650i			0.923886i
$834$	37.6200			1.30267
$835$	3.53876	+	4.34995i	0.122464	+	0.150536i
$836$	0.769991			0.0266307
$837$		−	41.8799i		−	1.44758i
$838$		−	20.2154i		−	0.698329i
$839$	−20.6612			−0.713305			−0.356653	−	0.934237i	$-0.616082\pi$
$839$	−20.6612			−0.713305			−0.356653	+	0.934237i	$0.616082\pi$
$840$	15.0317	+	18.4774i	0.518643	+	0.637532i
$841$	11.2430			0.387690
$842$		−	26.6059i		−	0.916899i
$843$		−	31.3014i		−	1.07808i
$844$	−3.81485			−0.131313
$845$	2.56468	−	2.08641i	0.0882276	−	0.0717747i
$846$	−15.4318			−0.530555
$847$			4.13429i			0.142056i
$848$			35.3669i			1.21450i
$849$	38.5608			1.32340
$850$	−4.47442	+	21.5265i	−0.153471	+	0.738352i
$851$	16.7625			0.574610
$852$			9.39833i			0.321981i
$853$			21.9069i			0.750077i	0.927009	+	0.375038i	$0.122370\pi$
$853$			21.9069i			0.750077i	−0.927009	+	0.375038i	$0.877630\pi$
$854$	32.5343			1.11330
$855$	2.45590	−	1.99791i	0.0839899	−	0.0683272i
$856$	18.2156			0.622597
$857$			27.5927i			0.942547i	0.881987	+	0.471274i	$0.156206\pi$
$857$			27.5927i			0.942547i	−0.881987	+	0.471274i	$0.843794\pi$
$858$			7.97078i			0.272118i
$859$	−23.5111			−0.802187			−0.401094	−	0.916037i	$-0.631370\pi$
$859$	−23.5111			−0.802187			−0.401094	+	0.916037i	$0.631370\pi$
$860$	−11.5867	−	14.2427i	−0.395104	−	0.485673i
$861$	−25.4594			−0.867653
$862$		−	4.67381i		−	0.159190i
$863$		−	17.3336i		−	0.590042i	−0.955491	−	0.295021i	$-0.904673\pi$
$863$		−	17.3336i		−	0.590042i	0.955491	−	0.295021i	$-0.0953266\pi$
$864$	23.0060			0.782680
$865$	12.3272	+	15.1529i	0.419136	+	0.515215i
$866$	28.3990			0.965037
$867$		−	12.6107i		−	0.428280i
$868$		−	23.9872i		−	0.814178i
$869$	−3.09141			−0.104869
$870$	23.0503	−	18.7519i	0.781480	−	0.635747i
$871$	30.2423			1.02472
$872$			11.1750i			0.378435i
$873$			9.46895i			0.320475i
$874$	9.29455			0.314393
$875$	−41.0422	+	21.2623i	−1.38748	+	0.718796i
$876$	−16.4729			−0.556567
$877$		−	18.4351i		−	0.622509i	−0.950327	−	0.311254i	$-0.899251\pi$
$877$		−	18.4351i		−	0.622509i	0.950327	−	0.311254i	$-0.100749\pi$
$878$			7.64437i			0.257985i
$879$	−8.40310			−0.283430
$880$	8.58113	−	6.98090i	0.289270	−	0.235326i
$881$	−25.3130			−0.852818			−0.426409	−	0.904530i	$-0.640222\pi$
$881$	−25.3130			−0.852818			−0.426409	+	0.904530i	$0.640222\pi$
$882$			23.7820i			0.800780i
$883$			50.7804i			1.70890i	0.519535	+	0.854449i	$0.326105\pi$
$883$			50.7804i			1.70890i	−0.519535	+	0.854449i	$0.673895\pi$
$884$	7.74099			0.260358
$885$	13.0423	+	16.0320i	0.438413	+	0.538911i
$886$	−22.1301			−0.743477
$887$		−	27.0222i		−	0.907315i	−0.891176	−	0.453658i	$-0.850119\pi$
$887$		−	27.0222i		−	0.907315i	0.891176	−	0.453658i	$-0.149881\pi$
$888$		−	7.73384i		−	0.259531i
$889$	82.6358			2.77152
$890$	−20.4724	−	25.1653i	−0.686238	−	0.843544i
$891$	−2.74785			−0.0920564
$892$		−	2.59465i		−	0.0868753i
$893$			6.54878i			0.219147i
$894$	−11.6843			−0.390782
$895$	−12.1951	+	9.92090i	−0.407636	+	0.331619i
$896$	−54.9032			−1.83419
$897$			26.7455i			0.893007i
$898$		−	7.03600i		−	0.234794i
$899$	47.8011			1.59426
$900$	−1.10930	+	5.33687i	−0.0369768	+	0.177896i
$901$	−18.8884			−0.629263
$902$			8.14304i			0.271134i
$903$		−	55.4898i		−	1.84659i
$904$	5.03170			0.167352
$905$	−7.94399	+	6.46258i	−0.264067	+	0.214823i
$906$	36.6043			1.21610
$907$		−	12.2103i		−	0.405436i	−0.979237	−	0.202718i	$-0.935023\pi$
$907$		−	12.2103i		−	0.405436i	0.979237	−	0.202718i	$-0.0649775\pi$
$908$		−	16.5218i		−	0.548294i
$909$	25.2460			0.837357
$910$	36.9457	+	45.4148i	1.22474	+	1.50549i
$911$	−40.0238			−1.32605			−0.663024	−	0.748598i	$-0.730727\pi$
$911$	−40.0238			−1.32605			−0.663024	+	0.748598i	$0.730727\pi$
$912$		−	6.22657i		−	0.206182i
$913$			1.51906i			0.0502736i
$914$	65.4315			2.16428
$915$	8.39770	+	10.3227i	0.277619	+	0.341258i
$916$	3.52786			0.116564
$917$		−	26.3344i		−	0.869637i
$918$			24.4399i			0.806638i
$919$	12.6684			0.417891			0.208945	−	0.977927i	$-0.432997\pi$
$919$	12.6684			0.417891			0.208945	+	0.977927i	$0.432997\pi$
$920$	19.8304	−	16.1324i	0.653788	−	0.531868i
$921$	7.84786			0.258596
$922$			54.3121i			1.78867i
$923$		−	36.9002i		−	1.21458i
$924$	−4.00669			−0.131810
$925$	14.6938	+	3.05420i	0.483129	+	0.100422i
$926$	−15.3987			−0.506032
$927$			16.3645i			0.537482i
$928$			26.2587i			0.861985i
$929$	−26.1480			−0.857888			−0.428944	−	0.903331i	$-0.641114\pi$
$929$	−26.1480			−0.857888			−0.428944	+	0.903331i	$0.641114\pi$
$930$	27.3795	−	22.2737i	0.897808	−	0.730382i
$931$	10.0924			0.330764
$932$			9.39562i			0.307764i
$933$		−	13.4853i		−	0.441489i
$934$	50.5108			1.65277
$935$	3.72829	+	4.58292i	0.121928	+	0.149878i
$936$	−11.0287			−0.360486
$937$			7.59737i			0.248195i	0.992270	+	0.124098i	$0.0396036\pi$
$937$			7.59737i			0.248195i	−0.992270	+	0.124098i	$0.960396\pi$
$938$			54.6880i			1.78563i
$939$	−21.7298			−0.709126
$940$	−7.11553	−	8.74663i	−0.232083	−	0.285284i
$941$	11.6224			0.378880			0.189440	−	0.981892i	$-0.439333\pi$
$941$	11.6224			0.378880			0.189440	+	0.981892i	$0.439333\pi$
$942$			0.702454i			0.0228872i
$943$			27.3235i			0.889777i
$944$	−36.3283			−1.18239
$945$	−39.8573	+	32.4246i	−1.29656	+	1.05477i
$946$	−17.7481			−0.577041
$947$		−	30.7195i		−	0.998251i	−0.866530	−	0.499126i	$-0.833655\pi$
$947$		−	30.7195i		−	0.998251i	0.866530	−	0.499126i	$-0.166345\pi$
$948$		−	2.99600i		−	0.0973055i
$949$	64.6766			2.09949
$950$	8.14750	+	1.69351i	0.264340	+	0.0549448i
$951$	32.3946			1.05047
$952$		−	22.3613i		−	0.724733i
$953$		−	43.2509i		−	1.40103i	−0.713636	−	0.700516i	$-0.752953\pi$
$953$		−	43.2509i		−	1.40103i	0.713636	−	0.700516i	$-0.247047\pi$
$954$	−16.8462			−0.545415
$955$	26.3391	−	21.4273i	0.852314	−	0.693372i
$956$	21.1898			0.685328
$957$		−	7.98443i		−	0.258100i
$958$			36.7292i			1.18667i
$959$	35.4637			1.14518
$960$	−5.33710	−	6.56053i	−0.172254	−	0.211740i
$961$	25.7787			0.831570
$962$		−	19.0086i		−	0.612863i
$963$			12.5983i			0.405975i
$964$	6.27634			0.202147
$965$	−14.2101	−	17.4674i	−0.457438	−	0.562297i
$966$	−48.3647			−1.55611
$967$			9.17709i			0.295115i	0.989053	+	0.147558i	$0.0471412\pi$
$967$			9.17709i			0.295115i	−0.989053	+	0.147558i	$0.952859\pi$
$968$		−	2.04714i		−	0.0657976i
$969$	3.32543			0.106828
$970$	−19.3072	+	15.7068i	−0.619917	+	0.504313i
$971$	−45.3774			−1.45623			−0.728115	−	0.685455i	$-0.759603\pi$
$971$	−45.3774			−1.45623			−0.728115	+	0.685455i	$0.759603\pi$
$972$			10.1756i			0.326383i
$973$		−	74.2475i		−	2.38027i
$974$	−45.5595			−1.45982
$975$	−4.87316	+	23.4448i	−0.156066	+	0.750835i
$976$	−23.3911			−0.748731
$977$			13.2101i			0.422630i	0.977418	+	0.211315i	$0.0677745\pi$
$977$			13.2101i			0.422630i	−0.977418	+	0.211315i	$0.932225\pi$
$978$			39.7538i			1.27119i
$979$	−8.71704			−0.278598
$980$	−13.4795	+	10.9658i	−0.430586	+	0.350289i
$981$	−7.72889			−0.246765
$982$		−	40.9525i		−	1.30685i
$983$			21.0957i			0.672848i	0.941711	+	0.336424i	$0.109218\pi$
$983$			21.0957i			0.672848i	−0.941711	+	0.336424i	$0.890782\pi$
$984$	12.6065			0.401880
$985$	6.73207	+	8.27526i	0.214501	+	0.263672i
$986$	−27.8954			−0.888371
$987$		−	34.0769i		−	1.08468i
$988$		−	2.92987i		−	0.0932116i
$989$	−59.5529			−1.89367
$990$	3.32519	+	4.08742i	0.105681	+	0.129907i
$991$	1.29349			0.0410892			0.0205446	−	0.999789i	$-0.493460\pi$
$991$	1.29349			0.0410892			0.0205446	+	0.999789i	$0.493460\pi$
$992$			31.1904i			0.990297i
$993$		−	24.3999i		−	0.774307i
$994$	66.7277			2.11647
$995$	−1.95218	+	1.58813i	−0.0618882	+	0.0503471i
$996$	−1.47218			−0.0466477
$997$			0.429360i			0.0135980i	0.999977	+	0.00679898i	$0.00216420\pi$
$997$			0.429360i			0.0135980i	−0.999977	+	0.00679898i	$0.997836\pi$
$998$		−	37.3293i		−	1.18164i
$999$	16.6825			0.527812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.8	✓	30
5.2	odd	4		5225.2.a.bc.1.23		30
5.3	odd	4		5225.2.a.bc.1.8		30
5.4	even	2	inner	1045.2.b.e.419.23	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.8	✓	30	1.1	even	1	trivial
1045.2.b.e.419.23	yes	30	5.4	even	2	inner
5225.2.a.bc.1.8		30	5.3	odd	4
5225.2.a.bc.1.23		30	5.2	odd	4

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.66433i q^{2} -1.25863i q^{3} -0.769991 q^{4} +(-1.73458 + 1.41111i) q^{5} -2.09478 q^{6} +4.13429i q^{7} -2.04714i q^{8} +1.41584 q^{9} +O(q^{10})\)	\(q-1.66433i q^{2} -1.25863i q^{3} -0.769991 q^{4} +(-1.73458 + 1.41111i) q^{5} -2.09478 q^{6} +4.13429i q^{7} -2.04714i q^{8} +1.41584 q^{9} +(2.34855 + 2.88691i) q^{10} +1.00000 q^{11} +0.969136i q^{12} -3.80507i q^{13} +6.88082 q^{14} +(1.77607 + 2.18320i) q^{15} -4.94710 q^{16} -2.64209i q^{17} -2.35643i q^{18} -1.00000 q^{19} +(1.33561 - 1.08654i) q^{20} +5.20355 q^{21} -1.66433i q^{22} -5.58456i q^{23} -2.57660 q^{24} +(1.01753 - 4.89537i) q^{25} -6.33289 q^{26} -5.55792i q^{27} -3.18337i q^{28} +6.34374 q^{29} +(3.63356 - 2.95596i) q^{30} +7.53516 q^{31} +4.13932i q^{32} -1.25863i q^{33} -4.39731 q^{34} +(-5.83394 - 7.17126i) q^{35} -1.09019 q^{36} +3.00157i q^{37} +1.66433i q^{38} -4.78918 q^{39} +(2.88874 + 3.55093i) q^{40} -4.89269 q^{41} -8.66042i q^{42} -10.6638i q^{43} -0.769991 q^{44} +(-2.45590 + 1.99791i) q^{45} -9.29455 q^{46} -6.54878i q^{47} +6.22657i q^{48} -10.0924 q^{49} +(-8.14750 - 1.69351i) q^{50} -3.32543 q^{51} +2.92987i q^{52} -7.14902i q^{53} -9.25022 q^{54} +(-1.73458 + 1.41111i) q^{55} +8.46347 q^{56} +1.25863i q^{57} -10.5581i q^{58} +7.34337 q^{59} +(-1.36756 - 1.68104i) q^{60} +4.72825 q^{61} -12.5410i q^{62} +5.85351i q^{63} -3.00501 q^{64} +(5.36937 + 6.60020i) q^{65} -2.09478 q^{66} +7.94790i q^{67} +2.03439i q^{68} -7.02891 q^{69} +(-11.9353 + 9.70960i) q^{70} +9.69764 q^{71} -2.89843i q^{72} +16.9975i q^{73} +4.99561 q^{74} +(-6.16147 - 1.28070i) q^{75} +0.769991 q^{76} +4.13429i q^{77} +7.97078i q^{78} -3.09141 q^{79} +(8.58113 - 6.98090i) q^{80} -2.74785 q^{81} +8.14304i q^{82} +1.51906i q^{83} -4.00669 q^{84} +(3.72829 + 4.58292i) q^{85} -17.7481 q^{86} -7.98443i q^{87} -2.04714i q^{88} -8.71704 q^{89} +(3.32519 + 4.08742i) q^{90} +15.7313 q^{91} +4.30007i q^{92} -9.48400i q^{93} -10.8993 q^{94} +(1.73458 - 1.41111i) q^{95} +5.20988 q^{96} +6.68784i q^{97} +16.7970i q^{98} +1.41584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

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