LMFDB - Embedded newform 1805.2.b.l.1084.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.19
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61907i q^{2} -1.18857i q^{3} -0.621387 q^{4} +(0.326390 - 2.21212i) q^{5} +1.92438 q^{6} +2.23190i q^{7} +2.23207i q^{8} +1.58730 q^{9} +O(q^{10})$	\(q+1.61907i q^{2} -1.18857i q^{3} -0.621387 q^{4} +(0.326390 - 2.21212i) q^{5} +1.92438 q^{6} +2.23190i q^{7} +2.23207i q^{8} +1.58730 q^{9} +(3.58157 + 0.528448i) q^{10} +5.64478 q^{11} +0.738562i q^{12} +4.70049i q^{13} -3.61361 q^{14} +(-2.62926 - 0.387937i) q^{15} -4.85665 q^{16} -0.785842i q^{17} +2.56995i q^{18} +(-0.202814 + 1.37458i) q^{20} +2.65277 q^{21} +9.13929i q^{22} +5.13041i q^{23} +2.65297 q^{24} +(-4.78694 - 1.44403i) q^{25} -7.61043 q^{26} -5.45233i q^{27} -1.38688i q^{28} +3.03653 q^{29} +(0.628097 - 4.25695i) q^{30} -8.10416 q^{31} -3.39912i q^{32} -6.70922i q^{33} +1.27233 q^{34} +(4.93723 + 0.728470i) q^{35} -0.986329 q^{36} +0.985141i q^{37} +5.58687 q^{39} +(4.93761 + 0.728525i) q^{40} -1.41798 q^{41} +4.29502i q^{42} +1.52174i q^{43} -3.50759 q^{44} +(0.518079 - 3.51130i) q^{45} -8.30649 q^{46} +0.960695i q^{47} +5.77247i q^{48} +2.01861 q^{49} +(2.33798 - 7.75039i) q^{50} -0.934028 q^{51} -2.92083i q^{52} +4.41123i q^{53} +8.82770 q^{54} +(1.84240 - 12.4869i) q^{55} -4.98176 q^{56} +4.91635i q^{58} +9.87853 q^{59} +(1.63379 + 0.241059i) q^{60} +2.09604 q^{61} -13.1212i q^{62} +3.54270i q^{63} -4.20990 q^{64} +(10.3981 + 1.53419i) q^{65} +10.8627 q^{66} +3.24811i q^{67} +0.488312i q^{68} +6.09785 q^{69} +(-1.17944 + 7.99373i) q^{70} -7.17702 q^{71} +3.54297i q^{72} -15.1625i q^{73} -1.59501 q^{74} +(-1.71633 + 5.68961i) q^{75} +12.5986i q^{77} +9.04553i q^{78} +1.33973 q^{79} +(-1.58516 + 10.7435i) q^{80} -1.71857 q^{81} -2.29581i q^{82} +7.52545i q^{83} -1.64840 q^{84} +(-1.73838 - 0.256491i) q^{85} -2.46380 q^{86} -3.60912i q^{87} +12.5995i q^{88} +3.40299 q^{89} +(5.68504 + 0.838806i) q^{90} -10.4910 q^{91} -3.18797i q^{92} +9.63236i q^{93} -1.55543 q^{94} -4.04009 q^{96} +12.7601i q^{97} +3.26827i q^{98} +8.95997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} - 12 q^{40} - 60 q^{41} + 30 q^{44} + 9 q^{45} - 6 q^{46} - 12 q^{49} - 18 q^{50} - 30 q^{51} + 24 q^{54} + 33 q^{55} - 18 q^{56} + 60 q^{59} + 42 q^{60} + 30 q^{61} - 18 q^{65} + 36 q^{66} + 66 q^{69} - 9 q^{70} - 96 q^{71} - 24 q^{74} - 36 q^{75} + 72 q^{79} - 42 q^{80} - 96 q^{81} - 54 q^{84} - 27 q^{85} - 108 q^{86} + 84 q^{89} + 93 q^{90} - 96 q^{91} + 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.61907i			1.14486i	0.819955	+	0.572428i	$0.193998\pi$
$2$			1.61907i			1.14486i	−0.819955	+	0.572428i	$0.806002\pi$
$3$		−	1.18857i		−	0.686221i	−0.939295	−	0.343111i	$-0.888519\pi$
$3$		−	1.18857i		−	0.686221i	0.939295	−	0.343111i	$-0.111481\pi$
$4$	−0.621387			−0.310694
$5$	0.326390	−	2.21212i	0.145966	−	0.989290i
$5$	0.326390	−	2.21212i	0.145966	−	0.989290i
$6$	1.92438			0.785624
$7$			2.23190i			0.843580i	0.906694	+	0.421790i	$0.138598\pi$
$7$			2.23190i			0.843580i	−0.906694	+	0.421790i	$0.861402\pi$
$8$			2.23207i			0.789156i
$9$	1.58730			0.529100
$10$	3.58157	+	0.528448i	1.13259	+	0.167110i
$11$	5.64478			1.70197			0.850983	−	0.525194i	$-0.176007\pi$
$11$	5.64478			1.70197			0.850983	+	0.525194i	$0.176007\pi$
$12$			0.738562i			0.213204i
$13$			4.70049i			1.30368i	0.758355	+	0.651841i	$0.226003\pi$
$13$			4.70049i			1.30368i	−0.758355	+	0.651841i	$0.773997\pi$
$14$	−3.61361			−0.965777
$15$	−2.62926	−	0.387937i	−0.678872	−	0.100165i
$16$	−4.85665			−1.21416
$17$		−	0.785842i		−	0.190595i	−0.995449	−	0.0952973i	$-0.969620\pi$
$17$		−	0.785842i		−	0.190595i	0.995449	−	0.0952973i	$-0.0303802\pi$
$18$			2.56995i			0.605743i
$19$		0			0
$19$		0			0
$20$	−0.202814	+	1.37458i	−0.0453507	+	0.307366i
$21$	2.65277			0.578882
$22$			9.13929i			1.94850i
$23$			5.13041i			1.06976i	0.844927	+	0.534882i	$0.179644\pi$
$23$			5.13041i			1.06976i	−0.844927	+	0.534882i	$0.820356\pi$
$24$	2.65297			0.541536
$25$	−4.78694	−	1.44403i	−0.957388	−	0.288805i
$26$	−7.61043			−1.49253
$27$		−	5.45233i		−	1.04930i
$28$		−	1.38688i		−	0.262095i
$29$	3.03653			0.563869			0.281934	−	0.959434i	$-0.409024\pi$
$29$	3.03653			0.563869			0.281934	+	0.959434i	$0.409024\pi$
$30$	0.628097	−	4.25695i	0.114674	−	0.777210i
$31$	−8.10416			−1.45555			−0.727775	−	0.685816i	$-0.759445\pi$
$31$	−8.10416			−1.45555			−0.727775	+	0.685816i	$0.759445\pi$
$32$		−	3.39912i		−	0.600885i
$33$		−	6.70922i		−	1.16792i
$34$	1.27233			0.218203
$35$	4.93723	+	0.728470i	0.834545	+	0.123134i
$36$	−0.986329			−0.164388
$37$			0.985141i			0.161956i	0.996716	+	0.0809781i	$0.0258044\pi$
$37$			0.985141i			0.161956i	−0.996716	+	0.0809781i	$0.974196\pi$
$38$		0			0
$39$	5.58687			0.894615
$40$	4.93761	+	0.728525i	0.780704	+	0.115190i
$41$	−1.41798			−0.221451			−0.110726	−	0.993851i	$-0.535318\pi$
$41$	−1.41798			−0.221451			−0.110726	+	0.993851i	$0.535318\pi$
$42$			4.29502i			0.662737i
$43$			1.52174i			0.232063i	0.993246	+	0.116031i	$0.0370173\pi$
$43$			1.52174i			0.232063i	−0.993246	+	0.116031i	$0.962983\pi$
$44$	−3.50759			−0.528790
$45$	0.518079	−	3.51130i	0.0772306	−	0.523434i
$46$	−8.30649			−1.22473
$47$			0.960695i			0.140132i	0.997542	+	0.0700659i	$0.0223209\pi$
$47$			0.960695i			0.140132i	−0.997542	+	0.0700659i	$0.977679\pi$
$48$			5.77247i			0.833184i
$49$	2.01861			0.288373
$50$	2.33798	−	7.75039i	0.330640	−	1.09607i
$51$	−0.934028			−0.130790
$52$		−	2.92083i		−	0.405046i
$53$			4.41123i			0.605929i	0.953002	+	0.302964i	$0.0979763\pi$
$53$			4.41123i			0.605929i	−0.953002	+	0.302964i	$0.902024\pi$
$54$	8.82770			1.20130
$55$	1.84240	−	12.4869i	0.248429	−	1.68374i
$56$	−4.98176			−0.665716
$57$		0			0
$58$			4.91635i			0.645548i
$59$	9.87853			1.28608			0.643038	−	0.765835i	$-0.277674\pi$
$59$	9.87853			1.28608			0.643038	+	0.765835i	$0.277674\pi$
$60$	1.63379	+	0.241059i	0.210921	+	0.0311206i
$61$	2.09604			0.268370			0.134185	−	0.990956i	$-0.457158\pi$
$61$	2.09604			0.268370			0.134185	+	0.990956i	$0.457158\pi$
$62$		−	13.1212i		−	1.66639i
$63$			3.54270i			0.446339i
$64$	−4.20990			−0.526237
$65$	10.3981	+	1.53419i	1.28972	+	0.190293i
$66$	10.8627			1.33710
$67$			3.24811i			0.396820i	0.980119	+	0.198410i	$0.0635778\pi$
$67$			3.24811i			0.396820i	−0.980119	+	0.198410i	$0.936422\pi$
$68$			0.488312i			0.0592165i
$69$	6.09785			0.734095
$70$	−1.17944	+	7.99373i	−0.140971	+	0.955433i
$71$	−7.17702			−0.851755			−0.425878	−	0.904781i	$-0.640035\pi$
$71$	−7.17702			−0.851755			−0.425878	+	0.904781i	$0.640035\pi$
$72$			3.54297i			0.417543i
$73$		−	15.1625i		−	1.77463i	−0.461160	−	0.887317i	$-0.652567\pi$
$73$		−	15.1625i		−	1.77463i	0.461160	−	0.887317i	$-0.347433\pi$
$74$	−1.59501			−0.185416
$75$	−1.71633	+	5.68961i	−0.198184	+	0.656980i
$76$		0			0
$77$			12.5986i			1.43574i
$78$			9.04553i			1.02420i
$79$	1.33973			0.150731			0.0753655	−	0.997156i	$-0.475988\pi$
$79$	1.33973			0.150731			0.0753655	+	0.997156i	$0.475988\pi$
$80$	−1.58516	+	10.7435i	−0.177226	+	1.20116i
$81$	−1.71857			−0.190952
$82$		−	2.29581i		−	0.253530i
$83$			7.52545i			0.826026i	0.910725	+	0.413013i	$0.135524\pi$
$83$			7.52545i			0.826026i	−0.910725	+	0.413013i	$0.864476\pi$
$84$	−1.64840			−0.179855
$85$	−1.73838	−	0.256491i	−0.188553	−	0.0278203i
$86$	−2.46380			−0.265678
$87$		−	3.60912i		−	0.386939i
$88$			12.5995i			1.34312i
$89$	3.40299			0.360716			0.180358	−	0.983601i	$-0.442274\pi$
$89$	3.40299			0.360716			0.180358	+	0.983601i	$0.442274\pi$
$90$	5.68504	+	0.838806i	0.599256	+	0.0884179i
$91$	−10.4910			−1.09976
$92$		−	3.18797i		−	0.332369i
$93$			9.63236i			0.998829i
$94$	−1.55543			−0.160431
$95$		0			0
$96$	−4.04009			−0.412340
$97$			12.7601i			1.29559i	0.761816	+	0.647793i	$0.224308\pi$
$97$			12.7601i			1.29559i	−0.761816	+	0.647793i	$0.775692\pi$
$98$			3.26827i			0.330145i
$99$	8.95997			0.900511
$100$	2.97454	+	0.897299i	0.297454	+	0.0897299i
$101$	5.57300			0.554534			0.277267	−	0.960793i	$-0.410571\pi$
$101$	5.57300			0.554534			0.277267	+	0.960793i	$0.410571\pi$
$102$		−	1.51226i		−	0.149736i
$103$		−	3.30768i		−	0.325915i	−0.986633	−	0.162958i	$-0.947897\pi$
$103$		−	3.30768i		−	0.325915i	0.986633	−	0.162958i	$-0.0521034\pi$
$104$	−10.4918			−1.02881
$105$	0.865838	−	5.86825i	0.0844971	−	0.572682i
$106$	−7.14209			−0.693701
$107$		−	6.67267i		−	0.645071i	−0.946557	−	0.322536i	$-0.895465\pi$
$107$		−	6.67267i		−	0.645071i	0.946557	−	0.322536i	$-0.104535\pi$
$108$			3.38801i			0.326011i
$109$	15.6813			1.50199			0.750996	−	0.660307i	$-0.229574\pi$
$109$	15.6813			1.50199			0.750996	+	0.660307i	$0.229574\pi$
$110$	20.2172	+	2.98297i	1.92763	+	0.284415i
$111$	1.17091			0.111138
$112$		−	10.8396i		−	1.02424i
$113$			6.58139i			0.619125i	0.950879	+	0.309562i	$0.100183\pi$
$113$			6.58139i			0.619125i	−0.950879	+	0.309562i	$0.899817\pi$
$114$		0			0
$115$	11.3491	+	1.67451i	1.05831	+	0.156149i
$116$	−1.88686			−0.175190
$117$			7.46110i			0.689779i
$118$			15.9940i			1.47237i
$119$	1.75392			0.160782
$120$	0.865903	−	5.86869i	0.0790458	−	0.535736i
$121$	20.8636			1.89669
$122$			3.39363i			0.307245i
$123$			1.68537i			0.151965i
$124$	5.03582			0.452230
$125$	−4.75676	+	10.1180i	−0.425458	+	0.904978i
$126$	−5.73588			−0.510993
$127$		−	1.33460i		−	0.118427i	−0.998245	−	0.0592135i	$-0.981141\pi$
$127$		−	1.33460i		−	0.118427i	0.998245	−	0.0592135i	$-0.0188593\pi$
$128$		−	13.6144i		−	1.20335i
$129$	1.80869			0.159246
$130$	−2.48397	+	16.8352i	−0.217858	+	1.47654i
$131$	13.7788			1.20386			0.601930	−	0.798549i	$-0.294399\pi$
$131$	13.7788			1.20386			0.601930	+	0.798549i	$0.294399\pi$
$132$			4.16902i			0.362867i
$133$		0			0
$134$	−5.25892			−0.454302
$135$	−12.0612	−	1.77958i	−1.03806	−	0.153162i
$136$	1.75405			0.150409
$137$		−	11.7423i		−	1.00321i	−0.865097	−	0.501605i	$-0.832743\pi$
$137$		−	11.7423i		−	1.00321i	0.865097	−	0.501605i	$-0.167257\pi$
$138$			9.87284i			0.840432i
$139$	9.34145			0.792331			0.396166	−	0.918179i	$-0.370341\pi$
$139$	9.34145			0.792331			0.396166	+	0.918179i	$0.370341\pi$
$140$	−3.06793	−	0.452662i	−0.259288	−	0.0382569i
$141$	1.14185			0.0961614
$142$		−	11.6201i		−	0.975136i
$143$			26.5333i			2.21882i
$144$	−7.70897			−0.642414
$145$	0.991091	−	6.71716i	0.0823056	−	0.557830i
$146$	24.5491			2.03170
$147$		−	2.39926i		−	0.197887i
$148$		−	0.612154i		−	0.0503187i
$149$	−18.0234			−1.47653			−0.738265	−	0.674510i	$-0.764355\pi$
$149$	−18.0234			−1.47653			−0.738265	+	0.674510i	$0.764355\pi$
$150$	−9.21188	−	2.77885i	−0.752147	−	0.226892i
$151$	13.0159			1.05922			0.529611	−	0.848241i	$-0.322338\pi$
$151$	13.0159			1.05922			0.529611	+	0.848241i	$0.322338\pi$
$152$		0			0
$153$		−	1.24737i		−	0.100844i
$154$	−20.3980			−1.64372
$155$	−2.64511	+	17.9274i	−0.212461	+	1.43996i
$156$	−3.47161			−0.277951
$157$		−	10.5071i		−	0.838560i	−0.907857	−	0.419280i	$-0.862283\pi$
$157$		−	10.5071i		−	0.838560i	0.907857	−	0.419280i	$-0.137717\pi$
$158$			2.16911i			0.172565i
$159$	5.24305			0.415801
$160$	−7.51925	−	1.10944i	−0.594449	−	0.0877087i
$161$	−11.4506			−0.902432
$162$		−	2.78248i		−	0.218613i
$163$		−	3.62389i		−	0.283845i	−0.989878	−	0.141923i	$-0.954672\pi$
$163$		−	3.62389i		−	0.283845i	0.989878	−	0.141923i	$-0.0453284\pi$
$164$	0.881115			0.0688035
$165$	−14.8416	−	2.18982i	−1.15542	−	0.170477i
$166$	−12.1842			−0.945680
$167$		−	10.6399i		−	0.823344i	−0.911332	−	0.411672i	$-0.864945\pi$
$167$		−	10.6399i		−	0.823344i	0.911332	−	0.411672i	$-0.135055\pi$
$168$			5.92118i			0.456829i
$169$	−9.09465			−0.699588
$170$	0.415276	−	2.81455i	0.0318502	−	0.215866i
$171$		0			0
$172$		−	0.945588i		−	0.0721004i
$173$		−	19.4108i		−	1.47578i	−0.674923	−	0.737888i	$-0.735823\pi$
$173$		−	19.4108i		−	1.47578i	0.674923	−	0.737888i	$-0.264177\pi$
$174$	5.84342			0.442989
$175$	3.22293	−	10.6840i	0.243630	−	0.807633i
$176$	−27.4147			−2.06646
$177$		−	11.7413i		−	0.882532i
$178$			5.50967i			0.412967i
$179$	2.07052			0.154758			0.0773789	−	0.997002i	$-0.475345\pi$
$179$	2.07052			0.154758			0.0773789	+	0.997002i	$0.475345\pi$
$180$	−0.321927	+	2.18188i	−0.0239951	+	0.162627i
$181$	−21.6324			−1.60793			−0.803963	−	0.594679i	$-0.797279\pi$
$181$	−21.6324			−1.60793			−0.803963	+	0.594679i	$0.797279\pi$
$182$		−	16.9857i		−	1.25907i
$183$		−	2.49129i		−	0.184161i
$184$	−11.4514			−0.844211
$185$	2.17925	+	0.321540i	0.160222	+	0.0236401i
$186$	−15.5955			−1.14351
$187$		−	4.43590i		−	0.324385i
$188$		−	0.596963i		−	0.0435380i
$189$	12.1691			0.885169
$190$		0			0
$191$	−22.4061			−1.62125			−0.810626	−	0.585565i	$-0.800873\pi$
$191$	−22.4061			−1.62125			−0.810626	+	0.585565i	$0.800873\pi$
$192$			5.00376i			0.361115i
$193$		−	19.5987i		−	1.41075i	−0.708835	−	0.705374i	$-0.750779\pi$
$193$		−	19.5987i		−	1.41075i	0.708835	−	0.705374i	$-0.249221\pi$
$194$	−20.6594			−1.48326
$195$	1.82350	−	12.3588i	0.130583	−	0.885033i
$196$	−1.25434			−0.0895955
$197$		−	15.4597i		−	1.10146i	−0.834684	−	0.550729i	$-0.814350\pi$
$197$		−	15.4597i		−	1.10146i	0.834684	−	0.550729i	$-0.185650\pi$
$198$			14.5068i			1.03095i
$199$	1.37296			0.0973268			0.0486634	−	0.998815i	$-0.484504\pi$
$199$	1.37296			0.0973268			0.0486634	+	0.998815i	$0.484504\pi$
$200$	3.22317	−	10.6848i	0.227912	−	0.755529i
$201$	3.86061			0.272306
$202$			9.02307i			0.634861i
$203$			6.77723i			0.475668i
$204$	0.580393			0.0406356
$205$	−0.462815	+	3.13674i	−0.0323244	+	0.219080i
$206$	5.35536			0.373126
$207$			8.14350i			0.566013i
$208$		−	22.8287i		−	1.58288i
$209$		0			0
$210$	9.50110	+	1.40185i	0.655638	+	0.0967370i
$211$	−9.57190			−0.658957			−0.329478	−	0.944163i	$-0.606873\pi$
$211$	−9.57190			−0.658957			−0.329478	+	0.944163i	$0.606873\pi$
$212$		−	2.74108i		−	0.188258i
$213$			8.53039i			0.584492i
$214$	10.8035			0.738513
$215$	3.36627	+	0.496680i	0.229577	+	0.0338733i
$216$	12.1700			0.828062
$217$		−	18.0877i		−	1.22787i
$218$			25.3890i			1.71956i
$219$	−18.0217			−1.21779
$220$	−1.14484	+	7.75921i	−0.0771853	+	0.523126i
$221$	3.69385			0.248475
$222$			1.89578i			0.127237i
$223$		−	6.53750i		−	0.437783i	−0.975749	−	0.218892i	$-0.929756\pi$
$223$		−	6.53750i		−	0.437783i	0.975749	−	0.218892i	$-0.0702441\pi$
$224$	7.58650			0.506894
$225$	−7.59832	−	2.29210i	−0.506554	−	0.152807i
$226$	−10.6557			−0.708808
$227$			8.88867i			0.589962i	0.955503	+	0.294981i	$0.0953133\pi$
$227$			8.88867i			0.589962i	−0.955503	+	0.294981i	$0.904687\pi$
$228$		0			0
$229$	7.22494			0.477438			0.238719	−	0.971089i	$-0.423273\pi$
$229$	7.22494			0.477438			0.238719	+	0.971089i	$0.423273\pi$
$230$	−2.71115	+	18.3749i	−0.178768	+	1.21161i
$231$	14.9743			0.985238
$232$			6.77774i			0.444981i
$233$			24.9780i			1.63636i	0.574961	+	0.818181i	$0.305017\pi$
$233$			24.9780i			1.63636i	−0.574961	+	0.818181i	$0.694983\pi$
$234$	−12.0800			−0.789697
$235$	2.12517	+	0.313561i	0.138631	+	0.0204545i
$236$	−6.13839			−0.399575
$237$		−	1.59236i		−	0.103435i
$238$			2.83972i			0.184072i
$239$	−16.8187			−1.08791			−0.543956	−	0.839114i	$-0.683074\pi$
$239$	−16.8187			−1.08791			−0.543956	+	0.839114i	$0.683074\pi$
$240$	12.7694	+	1.88408i	0.824261	+	0.121617i
$241$	10.8463			0.698671			0.349335	−	0.936998i	$-0.386407\pi$
$241$	10.8463			0.698671			0.349335	+	0.936998i	$0.386407\pi$
$242$			33.7795i			2.17143i
$243$		−	14.3143i		−	0.918266i
$244$	−1.30245			−0.0833809
$245$	0.658853	−	4.46540i	0.0420926	−	0.285284i
$246$	−2.72873			−0.173978
$247$		0			0
$248$		−	18.0891i		−	1.14866i
$249$	8.94453			0.566837
$250$	−16.3817	−	7.70153i	−1.03607	−	0.487088i
$251$	6.37067			0.402113			0.201056	−	0.979580i	$-0.435563\pi$
$251$	6.37067			0.402113			0.201056	+	0.979580i	$0.435563\pi$
$252$		−	2.20139i		−	0.138675i
$253$			28.9600i			1.82070i
$254$	2.16082			0.135582
$255$	−0.304857	+	2.06618i	−0.0190909	+	0.129389i
$256$	13.6228			0.851425
$257$		−	13.6465i		−	0.851245i	−0.904901	−	0.425623i	$-0.860055\pi$
$257$		−	13.6465i		−	0.851245i	0.904901	−	0.425623i	$-0.139945\pi$
$258$			2.92840i			0.182314i
$259$	−2.19874			−0.136623
$260$	−6.46122	−	0.953328i	−0.400708	−	0.0591229i
$261$	4.81988			0.298343
$262$			22.3088i			1.37825i
$263$		−	10.2215i		−	0.630285i	−0.949044	−	0.315143i	$-0.897948\pi$
$263$		−	10.2215i		−	0.630285i	0.949044	−	0.315143i	$-0.102052\pi$
$264$	14.9754			0.921675
$265$	9.75816	+	1.43978i	0.599439	+	0.0884450i
$266$		0			0
$267$		−	4.04469i		−	0.247531i
$268$		−	2.01834i		−	0.123289i
$269$	−14.4499			−0.881028			−0.440514	−	0.897746i	$-0.645204\pi$
$269$	−14.4499			−0.881028			−0.440514	+	0.897746i	$0.645204\pi$
$270$	2.88127	−	19.5279i	0.175349	−	1.18843i
$271$	−16.2054			−0.984409			−0.492204	−	0.870480i	$-0.663809\pi$
$271$	−16.2054			−0.984409			−0.492204	+	0.870480i	$0.663809\pi$
$272$			3.81656i			0.231413i
$273$			12.4693i			0.754679i
$274$	19.0116			1.14853
$275$	−27.0212	−	8.15121i	−1.62944	−	0.491536i
$276$	−3.78912			−0.228079
$277$			28.5943i			1.71806i	0.511922	+	0.859032i	$0.328934\pi$
$277$			28.5943i			1.71806i	−0.511922	+	0.859032i	$0.671066\pi$
$278$			15.1245i			0.907105i
$279$	−12.8637			−0.770132
$280$	−1.62600	+	11.0203i	−0.0971719	+	0.658586i
$281$	−7.17770			−0.428186			−0.214093	−	0.976813i	$-0.568680\pi$
$281$	−7.17770			−0.428186			−0.214093	+	0.976813i	$0.568680\pi$
$282$			1.84874i			0.110091i
$283$			10.3656i			0.616173i	0.951358	+	0.308086i	$0.0996886\pi$
$283$			10.3656i			0.616173i	−0.951358	+	0.308086i	$0.900311\pi$
$284$	4.45970			0.264635
$285$		0			0
$286$	−42.9592			−2.54023
$287$		−	3.16480i		−	0.186812i
$288$		−	5.39542i		−	0.317928i
$289$	16.3825			0.963674
$290$	10.8755	+	1.60465i	0.638634	+	0.0942280i
$291$	15.1662			0.889059
$292$			9.42177i			0.551367i
$293$		−	9.09056i		−	0.531076i	−0.964100	−	0.265538i	$-0.914450\pi$
$293$		−	9.09056i		−	0.531076i	0.964100	−	0.265538i	$-0.0855496\pi$
$294$	3.88457			0.226553
$295$	3.22425	−	21.8525i	0.187723	−	1.27230i
$296$	−2.19890			−0.127809
$297$		−	30.7772i		−	1.78587i
$298$		−	29.1811i		−	1.69041i
$299$	−24.1155			−1.39463
$300$	1.06650	−	3.53545i	0.0615745	−	0.204119i
$301$	−3.39637			−0.195764
$302$			21.0737i			1.21266i
$303$		−	6.62390i		−	0.380533i
$304$		0			0
$305$	0.684125	−	4.63669i	0.0391729	−	0.265496i
$306$	2.01958			0.115451
$307$		−	14.6641i		−	0.836923i	−0.908235	−	0.418461i	$-0.862569\pi$
$307$		−	14.6641i		−	0.836923i	0.908235	−	0.418461i	$-0.137431\pi$
$308$		−	7.82861i		−	0.446076i
$309$	−3.93141			−0.223650
$310$	−29.0257	−	4.28262i	−1.64855	−	0.243237i
$311$	−31.5811			−1.79080			−0.895400	−	0.445263i	$-0.853110\pi$
$311$	−31.5811			−1.79080			−0.895400	+	0.445263i	$0.853110\pi$
$312$			12.4703i			0.705991i
$313$		−	8.99070i		−	0.508184i	−0.967180	−	0.254092i	$-0.918223\pi$
$313$		−	8.99070i		−	0.508184i	0.967180	−	0.254092i	$-0.0817766\pi$
$314$	17.0118			0.960030
$315$	7.83688	+	1.15630i	0.441558	+	0.0651502i
$316$	−0.832489			−0.0468312
$317$		−	10.4204i		−	0.585269i	−0.956224	−	0.292635i	$-0.905468\pi$
$317$		−	10.4204i		−	0.585269i	0.956224	−	0.292635i	$-0.0945320\pi$
$318$			8.48887i			0.476032i
$319$	17.1405			0.959685
$320$	−1.37407	+	9.31279i	−0.0768127	+	0.520601i
$321$	−7.93093			−0.442662
$322$		−	18.5393i		−	1.03315i
$323$		0			0
$324$	1.06790			0.0593276
$325$	6.78764	−	22.5010i	0.376510	−	1.24813i
$326$	5.86733			0.324962
$327$		−	18.6383i		−	1.03070i
$328$		−	3.16503i		−	0.174760i
$329$	−2.14418			−0.118212
$330$	3.54547	−	24.0296i	0.195172	−	1.32278i
$331$	4.03055			0.221539			0.110770	−	0.993846i	$-0.464668\pi$
$331$	4.03055			0.221539			0.110770	+	0.993846i	$0.464668\pi$
$332$		−	4.67622i		−	0.256641i
$333$			1.56372i			0.0856911i
$334$	17.2268			0.942609
$335$	7.18521	+	1.06015i	0.392570	+	0.0579222i
$336$	−12.8836			−0.702858
$337$		−	24.7816i		−	1.34994i	−0.737846	−	0.674969i	$-0.764157\pi$
$337$		−	24.7816i		−	1.34994i	0.737846	−	0.674969i	$-0.235843\pi$
$338$		−	14.7249i		−	0.800928i
$339$	7.82244			0.424857
$340$	1.08020	+	0.159380i	0.0585823	+	0.00864359i
$341$	−45.7462			−2.47730
$342$		0			0
$343$			20.1287i			1.08685i
$344$	−3.39663			−0.183134
$345$	1.99028	−	13.4892i	0.107153	−	0.726232i
$346$	31.4275			1.68955
$347$			28.6239i			1.53661i	0.640082	+	0.768306i	$0.278900\pi$
$347$			28.6239i			1.53661i	−0.640082	+	0.768306i	$0.721100\pi$
$348$			2.24266i			0.120219i
$349$	−10.2217			−0.547154			−0.273577	−	0.961850i	$-0.588207\pi$
$349$	−10.2217			−0.547154			−0.273577	+	0.961850i	$0.588207\pi$
$350$	17.2981	+	5.21814i	0.924623	+	0.278921i
$351$	25.6286			1.36796
$352$		−	19.1873i		−	1.02269i
$353$		−	17.7919i		−	0.946965i	−0.880803	−	0.473483i	$-0.842997\pi$
$353$		−	17.7919i		−	0.946965i	0.880803	−	0.473483i	$-0.157003\pi$
$354$	19.0100			1.01037
$355$	−2.34250	+	15.8764i	−0.124327	+	0.842632i
$356$	−2.11457			−0.112072
$357$		−	2.08466i		−	0.110332i
$358$			3.35231i			0.177175i
$359$	0.860591			0.0454202			0.0227101	−	0.999742i	$-0.492771\pi$
$359$	0.860591			0.0454202			0.0227101	+	0.999742i	$0.492771\pi$
$360$	7.83747	+	1.15639i	0.413071	+	0.0609470i
$361$		0			0
$362$		−	35.0244i		−	1.84084i
$363$		−	24.7978i		−	1.30155i
$364$	6.51900			0.341688
$365$	−33.5412	−	4.94888i	−1.75563	−	0.259036i
$366$	4.03357			0.210838
$367$		−	21.3109i		−	1.11242i	−0.831043	−	0.556209i	$-0.812256\pi$
$367$		−	21.3109i		−	1.11242i	0.831043	−	0.556209i	$-0.187744\pi$
$368$		−	24.9166i		−	1.29887i
$369$	−2.25076			−0.117170
$370$	−0.520596	+	3.52836i	−0.0270645	+	0.183430i
$371$	−9.84543			−0.511150
$372$		−	5.98542i		−	0.310330i
$373$			14.1725i			0.733822i	0.930256	+	0.366911i	$0.119585\pi$
$373$			14.1725i			0.733822i	−0.930256	+	0.366911i	$0.880415\pi$
$374$	7.18204			0.371374
$375$	12.0259	+	5.65375i	0.621015	+	0.291958i
$376$	−2.14434			−0.110586
$377$			14.2732i			0.735106i
$378$			19.7026i			1.01339i
$379$	−3.54496			−0.182092			−0.0910462	−	0.995847i	$-0.529021\pi$
$379$	−3.54496			−0.182092			−0.0910462	+	0.995847i	$0.529021\pi$
$380$		0			0
$381$	−1.58627			−0.0812671
$382$		−	36.2771i		−	1.85610i
$383$		−	7.70846i		−	0.393884i	−0.980415	−	0.196942i	$-0.936899\pi$
$383$		−	7.70846i		−	0.393884i	0.980415	−	0.196942i	$-0.0631011\pi$
$384$	−16.1816			−0.825764
$385$	27.8696	+	4.11205i	1.42037	+	0.209570i
$386$	31.7317			1.61510
$387$			2.41546i			0.122785i
$388$		−	7.92893i		−	0.402530i
$389$	−1.79987			−0.0912571			−0.0456285	−	0.998958i	$-0.514529\pi$
$389$	−1.79987			−0.0912571			−0.0456285	+	0.998958i	$0.514529\pi$
$390$	20.0098	+	2.95237i	1.01323	+	0.149499i
$391$	4.03169			0.203891
$392$			4.50568i			0.227571i
$393$		−	16.3771i		−	0.826114i
$394$	25.0303			1.26101
$395$	0.437273	−	2.96364i	0.0220016	−	0.149117i
$396$	−5.56761			−0.279783
$397$		−	17.6756i		−	0.887111i	−0.896247	−	0.443556i	$-0.853717\pi$
$397$		−	17.6756i		−	0.887111i	0.896247	−	0.443556i	$-0.146283\pi$
$398$			2.22292i			0.111425i
$399$		0			0
$400$	23.2485	+	7.01313i	1.16243	+	0.350657i
$401$	27.1151			1.35406			0.677032	−	0.735954i	$-0.263266\pi$
$401$	27.1151			1.35406			0.677032	+	0.735954i	$0.263266\pi$
$402$			6.25060i			0.311752i
$403$		−	38.0936i		−	1.89758i
$404$	−3.46299			−0.172290
$405$	−0.560924	+	3.80168i	−0.0278725	+	0.188907i
$406$	−10.9728			−0.544572
$407$			5.56090i			0.275644i
$408$		−	2.08482i		−	0.103214i
$409$	33.8712			1.67482			0.837411	−	0.546574i	$-0.184068\pi$
$409$	33.8712			1.67482			0.837411	+	0.546574i	$0.184068\pi$
$410$	−5.07861	−	0.749329i	−0.250815	−	0.0370067i
$411$	−13.9565			−0.688424
$412$			2.05535i			0.101260i
$413$			22.0479i			1.08491i
$414$	−13.1849			−0.648003
$415$	16.6472	+	2.45623i	0.817179	+	0.120572i
$416$	15.9775			0.783363
$417$		−	11.1030i		−	0.543714i
$418$		0			0
$419$	23.2338			1.13505			0.567524	−	0.823357i	$-0.307901\pi$
$419$	23.2338			1.13505			0.567524	+	0.823357i	$0.307901\pi$
$420$	−0.538020	+	3.64645i	−0.0262527	+	0.177929i
$421$	−19.3476			−0.942944			−0.471472	−	0.881881i	$-0.656277\pi$
$421$	−19.3476			−0.942944			−0.471472	+	0.881881i	$0.656277\pi$
$422$		−	15.4976i		−	0.754410i
$423$			1.52491i			0.0741438i
$424$	−9.84617			−0.478173
$425$	−1.13478	+	3.76178i	−0.0550447	+	0.182473i
$426$	−13.8113			−0.669159
$427$			4.67815i			0.226392i
$428$			4.14631i			0.200419i
$429$	31.5366			1.52260
$430$	−0.804159	+	5.45022i	−0.0387800	+	0.262833i
$431$	13.0559			0.628881			0.314440	−	0.949277i	$-0.398183\pi$
$431$	13.0559			0.628881			0.314440	+	0.949277i	$0.398183\pi$
$432$			26.4801i			1.27402i
$433$		−	5.82886i		−	0.280117i	−0.990143	−	0.140059i	$-0.955271\pi$
$433$		−	5.82886i		−	0.280117i	0.990143	−	0.140059i	$-0.0447291\pi$
$434$	29.2852			1.40574
$435$	−7.98381	−	1.17798i	−0.382794	−	0.0564799i
$436$	−9.74413			−0.466659
$437$		0			0
$438$		−	29.1783i		−	1.39419i
$439$	−6.49004			−0.309753			−0.154876	−	0.987934i	$-0.549498\pi$
$439$	−6.49004			−0.309753			−0.154876	+	0.987934i	$0.549498\pi$
$440$	27.8717	+	4.11236i	1.32873	+	0.196049i
$441$	3.20414			0.152578
$442$			5.98059i			0.284468i
$443$		−	9.20328i		−	0.437261i	−0.975808	−	0.218631i	$-0.929841\pi$
$443$		−	9.20328i		−	0.437261i	0.975808	−	0.218631i	$-0.0701589\pi$
$444$	−0.727588			−0.0345298
$445$	1.11070	−	7.52781i	0.0526522	−	0.356852i
$446$	10.5847			0.501198
$447$			21.4220i			1.01323i
$448$		−	9.39608i		−	0.443923i
$449$	−17.4646			−0.824206			−0.412103	−	0.911137i	$-0.635206\pi$
$449$	−17.4646			−0.824206			−0.412103	+	0.911137i	$0.635206\pi$
$450$	3.71108	−	12.3022i	0.174942	−	0.579931i
$451$	−8.00419			−0.376903
$452$		−	4.08959i		−	0.192358i
$453$		−	15.4703i		−	0.726860i
$454$	−14.3914			−0.675421
$455$	−3.42417	+	23.2074i	−0.160528	+	1.08798i
$456$		0			0
$457$			0.381827i			0.0178611i	0.999960	+	0.00893055i	$0.00284272\pi$
$457$			0.381827i			0.0178611i	−0.999960	+	0.00893055i	$0.997157\pi$
$458$			11.6977i			0.546597i
$459$	−4.28467			−0.199991
$460$	−7.05217	−	1.04052i	−0.328809	−	0.0485145i
$461$	8.51706			0.396679			0.198339	−	0.980133i	$-0.436445\pi$
$461$	8.51706			0.396679			0.198339	+	0.980133i	$0.436445\pi$
$462$			24.2445i			1.12795i
$463$			37.0178i			1.72036i	0.509988	+	0.860181i	$0.329650\pi$
$463$			37.0178i			1.72036i	−0.509988	+	0.860181i	$0.670350\pi$
$464$	−14.7474			−0.684629
$465$	21.3079	+	3.14390i	0.988131	+	0.145795i
$466$	−40.4411			−1.87340
$467$			25.9387i			1.20030i	0.799887	+	0.600151i	$0.204893\pi$
$467$			25.9387i			1.20030i	−0.799887	+	0.600151i	$0.795107\pi$
$468$		−	4.63623i		−	0.214310i
$469$	−7.24948			−0.334750
$470$	−0.507677	+	3.44080i	−0.0234174	+	0.158712i
$471$	−12.4885			−0.575438
$472$			22.0496i			1.01491i
$473$			8.58988i			0.394963i
$474$	2.57814			0.118418
$475$		0			0
$476$	−1.08986			−0.0499539
$477$			7.00195i			0.320597i
$478$		−	27.2307i		−	1.24550i
$479$	−11.8388			−0.540929			−0.270464	−	0.962730i	$-0.587177\pi$
$479$	−11.8388			−0.540929			−0.270464	+	0.962730i	$0.587177\pi$
$480$	−1.31864	+	8.93716i	−0.0601876	+	0.407924i
$481$	−4.63065			−0.211139
$482$			17.5609i			0.799877i
$483$			13.6098i			0.619268i
$484$	−12.9643			−0.589288
$485$	28.2267	+	4.16475i	1.28171	+	0.189112i
$486$	23.1759			1.05128
$487$			29.3813i			1.33139i	0.746223	+	0.665696i	$0.231865\pi$
$487$			29.3813i			1.33139i	−0.746223	+	0.665696i	$0.768135\pi$
$488$			4.67851i			0.211786i
$489$	−4.30725			−0.194781
$490$	7.22980	+	1.06673i	0.326609	+	0.0481899i
$491$	−4.81838			−0.217451			−0.108725	−	0.994072i	$-0.534677\pi$
$491$	−4.81838			−0.217451			−0.108725	+	0.994072i	$0.534677\pi$
$492$		−	1.04727i		−	0.0472145i
$493$		−	2.38623i		−	0.107470i
$494$		0			0
$495$	2.92444	−	19.8205i	0.131444	−	0.890866i
$496$	39.3591			1.76727
$497$		−	16.0184i		−	0.718524i
$498$			14.4818i			0.648946i
$499$	−0.188226			−0.00842614			−0.00421307	−	0.999991i	$-0.501341\pi$
$499$	−0.188226			−0.00842614			−0.00421307	+	0.999991i	$0.501341\pi$
$500$	2.95579	−	6.28717i	0.132187	−	0.281171i
$501$	−12.6463			−0.564996
$502$			10.3146i			0.460361i
$503$			2.27585i			0.101475i	0.998712	+	0.0507375i	$0.0161572\pi$
$503$			2.27585i			0.101475i	−0.998712	+	0.0507375i	$0.983843\pi$
$504$	−7.90756			−0.352231
$505$	1.81897	−	12.3281i	0.0809431	−	0.548595i
$506$	−46.8883			−2.08444
$507$			10.8096i			0.480072i
$508$			0.829306i			0.0367945i
$509$	−4.27456			−0.189467			−0.0947334	−	0.995503i	$-0.530200\pi$
$509$	−4.27456			−0.189467			−0.0947334	+	0.995503i	$0.530200\pi$
$510$	−3.34529	−	0.493585i	−0.148132	−	0.0218563i
$511$	33.8412			1.49705
$512$		−	5.17245i		−	0.228592i
$513$		0			0
$514$	22.0946			0.974552
$515$	−7.31698	−	1.07959i	−0.322425	−	0.0475725i
$516$	−1.12390			−0.0494769
$517$			5.42291i			0.238499i
$518$		−	3.55991i		−	0.156414i
$519$	−23.0711			−1.01271
$520$	−3.42443	+	23.2092i	−0.150171	+	1.01779i
$521$	−32.3273			−1.41629			−0.708143	−	0.706069i	$-0.750467\pi$
$521$	−32.3273			−1.41629			−0.708143	+	0.706069i	$0.750467\pi$
$522$			7.80373i			0.341560i
$523$		−	29.5161i		−	1.29065i	−0.763908	−	0.645325i	$-0.776722\pi$
$523$		−	29.5161i		−	1.29065i	0.763908	−	0.645325i	$-0.223278\pi$
$524$	−8.56197			−0.374031
$525$	−12.6987	−	3.83067i	−0.554215	−	0.167184i
$526$	16.5493			0.721585
$527$			6.36859i			0.277420i
$528$			32.5843i			1.41805i
$529$	−3.32109			−0.144395
$530$	−2.33110	+	15.7991i	−0.101257	+	0.686271i
$531$	15.6802			0.680463
$532$		0			0
$533$		−	6.66521i		−	0.288702i
$534$	6.54863			0.283387
$535$	−14.7607	−	2.17789i	−0.638162	−	0.0941584i
$536$	−7.25002			−0.313153
$537$		−	2.46096i		−	0.106198i
$538$		−	23.3954i		−	1.00865i
$539$	11.3946			0.490800
$540$	7.49467	+	1.10581i	0.322519	+	0.0475865i
$541$	18.8753			0.811515			0.405757	−	0.913981i	$-0.367008\pi$
$541$	18.8753			0.811515			0.405757	+	0.913981i	$0.367008\pi$
$542$		−	26.2377i		−	1.12701i
$543$			25.7117i			1.10339i
$544$	−2.67117			−0.114525
$545$	5.11820	−	34.6888i	0.219240	−	1.48590i
$546$	−20.1887			−0.863998
$547$		−	25.1190i		−	1.07401i	−0.843578	−	0.537006i	$-0.819555\pi$
$547$		−	25.1190i		−	1.07401i	0.843578	−	0.537006i	$-0.180445\pi$
$548$			7.29650i			0.311691i
$549$	3.32705			0.141995
$550$	13.1974	−	43.7492i	0.562738	−	1.86547i
$551$		0			0
$552$			13.6108i			0.579315i
$553$			2.99014i			0.127154i
$554$	−46.2961			−1.96693
$555$	0.382173	−	2.59019i	0.0162223	−	0.109947i
$556$	−5.80465			−0.246172
$557$			28.1731i			1.19373i	0.802340	+	0.596867i	$0.203588\pi$
$557$			28.1731i			1.19373i	−0.802340	+	0.596867i	$0.796412\pi$
$558$		−	20.8273i		−	0.881690i
$559$	−7.15292			−0.302536
$560$	−23.9784	−	3.53793i	−1.01327	−	0.149505i
$561$	−5.27238			−0.222600
$562$		−	11.6212i		−	0.490211i
$563$		−	20.4297i		−	0.861010i	−0.902588	−	0.430505i	$-0.858336\pi$
$563$		−	20.4297i		−	0.861010i	0.902588	−	0.430505i	$-0.141664\pi$
$564$	−0.709533			−0.0298767
$565$	14.5588	+	2.14810i	0.612494	+	0.0903711i
$566$	−16.7827			−0.705428
$567$		−	3.83568i		−	0.161083i
$568$		−	16.0196i		−	0.672168i
$569$	−35.8386			−1.50243			−0.751217	−	0.660056i	$-0.770533\pi$
$569$	−35.8386			−1.50243			−0.751217	+	0.660056i	$0.770533\pi$
$570$		0			0
$571$	−2.82827			−0.118359			−0.0591797	−	0.998247i	$-0.518848\pi$
$571$	−2.82827			−0.118359			−0.0591797	+	0.998247i	$0.518848\pi$
$572$		−	16.4874i		−	0.689374i
$573$			26.6313i			1.11254i
$574$	5.12403			0.213873
$575$	7.40844	−	24.5590i	0.308953	−	1.02418i
$576$	−6.68237			−0.278432
$577$		−	43.3132i		−	1.80315i	−0.432622	−	0.901575i	$-0.642411\pi$
$577$		−	43.3132i		−	1.80315i	0.432622	−	0.901575i	$-0.357589\pi$
$578$			26.5243i			1.10327i
$579$	−23.2945			−0.968085
$580$	−0.615851	+	4.17395i	−0.0255718	+	0.173314i
$581$	−16.7961			−0.696819
$582$			24.5552i			1.01784i
$583$			24.9004i			1.03127i
$584$	33.8437			1.40046
$585$	16.5048	+	2.43523i	0.682391	+	0.100684i
$586$	14.7183			0.608006
$587$			24.5741i			1.01428i	0.861863	+	0.507141i	$0.169298\pi$
$587$			24.5741i			1.01428i	−0.861863	+	0.507141i	$0.830702\pi$
$588$			1.49087i			0.0614824i
$589$		0			0
$590$	35.3807	+	5.22029i	1.45660	+	0.214916i
$591$	−18.3749			−0.755843
$592$		−	4.78449i		−	0.196641i
$593$		−	0.313720i		−	0.0128829i	−0.999979	−	0.00644147i	$-0.997950\pi$
$593$		−	0.313720i		−	0.0128829i	0.999979	−	0.00644147i	$-0.00205040\pi$
$594$	49.8304			2.04457
$595$	0.572462	−	3.87989i	0.0234687	−	0.159060i
$596$	11.1995			0.458748
$597$		−	1.63186i		−	0.0667877i
$598$		−	39.0446i		−	1.59665i
$599$	24.4964			1.00090			0.500448	−	0.865767i	$-0.333169\pi$
$599$	24.4964			1.00090			0.500448	+	0.865767i	$0.333169\pi$
$600$	−12.6996	−	3.83096i	−0.518460	−	0.156398i
$601$	7.83045			0.319411			0.159705	−	0.987165i	$-0.448946\pi$
$601$	7.83045			0.319411			0.159705	+	0.987165i	$0.448946\pi$
$602$		−	5.49896i		−	0.224121i
$603$			5.15574i			0.209958i
$604$	−8.08793			−0.329093
$605$	6.80965	−	46.1527i	0.276852	−	1.87637i
$606$	10.7246			0.435655
$607$			12.4142i			0.503876i	0.967743	+	0.251938i	$0.0810680\pi$
$607$			12.4142i			0.503876i	−0.967743	+	0.251938i	$0.918932\pi$
$608$		0			0
$609$	8.05522			0.326414
$610$	7.50712	+	1.10765i	0.303954	+	0.0448473i
$611$	−4.51574			−0.182687
$612$			0.775098i			0.0313315i
$613$		−	1.05853i		−	0.0427534i	−0.999771	−	0.0213767i	$-0.993195\pi$
$613$		−	1.05853i		−	0.0427534i	0.999771	−	0.0213767i	$-0.00680494\pi$
$614$	23.7422			0.958156
$615$	3.72824	+	0.550088i	0.150337	+	0.0221817i
$616$	−28.1210			−1.13303
$617$			28.5881i			1.15091i	0.817832	+	0.575457i	$0.195176\pi$
$617$			28.5881i			1.15091i	−0.817832	+	0.575457i	$0.804824\pi$
$618$		−	6.36522i		−	0.256047i
$619$	−9.41956			−0.378604			−0.189302	−	0.981919i	$-0.560623\pi$
$619$	−9.41956			−0.378604			−0.189302	+	0.981919i	$0.560623\pi$
$620$	1.64364	−	11.1398i	0.0660102	−	0.447386i
$621$	27.9727			1.12250
$622$		−	51.1320i		−	2.05021i
$623$			7.59514i			0.304293i
$624$	−27.1335			−1.08621
$625$	20.8296	+	13.8249i	0.833183	+	0.552997i
$626$	14.5566			0.581797
$627$		0			0
$628$			6.52899i			0.260535i
$629$	0.774165			0.0308680
$630$	−1.87213	+	12.6885i	−0.0745876	+	0.505520i
$631$	−39.6280			−1.57757			−0.788784	−	0.614671i	$-0.789289\pi$
$631$	−39.6280			−1.57757			−0.788784	+	0.614671i	$0.789289\pi$
$632$			2.99037i			0.118950i
$633$			11.3769i			0.452190i
$634$	16.8714			0.670049
$635$	−2.95230	−	0.435601i	−0.117159	−	0.0172863i
$636$	−3.25797			−0.129187
$637$			9.48846i			0.375947i
$638$			27.7517i			1.09870i
$639$	−11.3921			−0.450664
$640$	−30.1166	−	4.44358i	−1.19046	−	0.175648i
$641$	−19.6559			−0.776360			−0.388180	−	0.921584i	$-0.626896\pi$
$641$	−19.6559			−0.776360			−0.388180	+	0.921584i	$0.626896\pi$
$642$		−	12.8407i		−	0.506783i
$643$			28.7116i			1.13227i	0.824311	+	0.566137i	$0.191563\pi$
$643$			28.7116i			1.13227i	−0.824311	+	0.566137i	$0.808437\pi$
$644$	7.11524			0.280380
$645$	0.590339	−	4.00104i	0.0232446	−	0.157541i
$646$		0			0
$647$			17.4412i			0.685686i	0.939393	+	0.342843i	$0.111390\pi$
$647$			17.4412i			0.685686i	−0.939393	+	0.342843i	$0.888610\pi$
$648$		−	3.83597i		−	0.150691i
$649$	55.7622			2.18886
$650$	36.4307	+	10.9897i	1.42893	+	0.431050i
$651$	−21.4985			−0.842592
$652$			2.25184i			0.0881889i
$653$		−	30.3498i		−	1.18768i	−0.804584	−	0.593839i	$-0.797612\pi$
$653$		−	30.3498i		−	1.18768i	0.804584	−	0.593839i	$-0.202388\pi$
$654$	30.1767			1.18000
$655$	4.49726	−	30.4804i	0.175722	−	1.19097i
$656$	6.88664			0.268878
$657$		−	24.0674i		−	0.938959i
$658$		−	3.47157i		−	0.135336i
$659$	6.53865			0.254709			0.127355	−	0.991857i	$-0.459351\pi$
$659$	6.53865			0.254709			0.127355	+	0.991857i	$0.459351\pi$
$660$	9.22237	+	1.36073i	0.358980	+	0.0529662i
$661$	−23.7996			−0.925699			−0.462849	−	0.886437i	$-0.653173\pi$
$661$	−23.7996			−0.925699			−0.462849	+	0.886437i	$0.653173\pi$
$662$			6.52575i			0.253630i
$663$		−	4.39039i		−	0.170509i
$664$	−16.7973			−0.651863
$665$		0			0
$666$	−2.53176			−0.0981039
$667$			15.5786i			0.603207i
$668$			6.61152i			0.255808i
$669$	−7.77027			−0.300416
$670$	−1.71646	+	11.6334i	−0.0663126	+	0.449436i
$671$	11.8317			0.456757
$672$		−	9.01709i		−	0.347842i
$673$		−	49.9227i		−	1.92438i	−0.272381	−	0.962189i	$-0.587811\pi$
$673$		−	49.9227i		−	1.92438i	0.272381	−	0.962189i	$-0.412189\pi$
$674$	40.1231			1.54548
$675$	−7.87330	+	26.1000i	−0.303044	+	1.00459i
$676$	5.65130			0.217358
$677$		−	34.5826i		−	1.32912i	−0.747237	−	0.664558i	$-0.768620\pi$
$677$		−	34.5826i		−	1.32912i	0.747237	−	0.664558i	$-0.231380\pi$
$678$			12.6651i			0.486399i
$679$	−28.4792			−1.09293
$680$	0.572505	−	3.88018i	0.0219546	−	0.148798i
$681$	10.5648			0.404844
$682$		−	74.0663i		−	2.83614i
$683$			21.1277i			0.808429i	0.914664	+	0.404214i	$0.132455\pi$
$683$			21.1277i			0.808429i	−0.914664	+	0.404214i	$0.867545\pi$
$684$		0			0
$685$	−25.9753	−	3.83256i	−0.992466	−	0.146435i
$686$	−32.5897			−1.24428
$687$		−	8.58735i		−	0.327628i
$688$		−	7.39055i		−	0.281762i
$689$	−20.7350			−0.789939
$690$	21.8399	+	3.22239i	0.831431	+	0.122674i
$691$	27.8861			1.06084			0.530418	−	0.847736i	$-0.322035\pi$
$691$	27.8861			1.06084			0.530418	+	0.847736i	$0.322035\pi$
$692$			12.0616i			0.458514i
$693$			19.9978i			0.759653i
$694$	−46.3441			−1.75920
$695$	3.04895	−	20.6644i	0.115653	−	0.783845i
$696$	8.05582			0.305355
$697$			1.11431i			0.0422075i
$698$		−	16.5496i		−	0.626412i
$699$	29.6881			1.12291
$700$	−2.00268	+	6.63889i	−0.0756943	+	0.250926i
$701$	−39.3344			−1.48564			−0.742821	−	0.669490i	$-0.766513\pi$
$701$	−39.3344			−1.48564			−0.742821	+	0.669490i	$0.766513\pi$
$702$			41.4946i			1.56611i
$703$		0			0
$704$	−23.7639			−0.895637
$705$	0.372689	−	2.52591i	0.0140363	−	0.0951314i
$706$	28.8063			1.08414
$707$			12.4384i			0.467794i
$708$			7.29591i			0.274197i
$709$	−4.28832			−0.161051			−0.0805256	−	0.996753i	$-0.525660\pi$
$709$	−4.28832			−0.161051			−0.0805256	+	0.996753i	$0.525660\pi$
$710$	−25.7050	−	3.79268i	−0.964692	−	0.142337i
$711$	2.12655			0.0797519
$712$			7.59571i			0.284661i
$713$		−	41.5776i		−	1.55710i
$714$	3.37521			0.126314
$715$	58.6947	+	8.66018i	2.19506	+	0.323873i
$716$	−1.28659			−0.0480822
$717$			19.9902i			0.746549i
$718$			1.39336i			0.0519996i
$719$	3.93252			0.146658			0.0733291	−	0.997308i	$-0.476638\pi$
$719$	3.93252			0.146658			0.0733291	+	0.997308i	$0.476638\pi$
$720$	−2.51613	+	17.0532i	−0.0937706	+	0.635534i
$721$	7.38242			0.274936
$722$		0			0
$723$		−	12.8916i		−	0.479443i
$724$	13.4421			0.499572
$725$	−14.5357	−	4.38482i	−0.539841	−	0.162848i
$726$	40.1494			1.49008
$727$			20.0574i			0.743889i	0.928255	+	0.371944i	$0.121309\pi$
$727$			20.0574i			0.743889i	−0.928255	+	0.371944i	$0.878691\pi$
$728$		−	23.4168i		−	0.867883i
$729$	−22.1693			−0.821086
$730$	8.01258	−	54.3055i	0.296559	−	2.00994i
$731$	1.19585			0.0442300
$732$			1.54805i			0.0572177i
$733$		−	0.205782i		−	0.00760071i	−0.999993	−	0.00380036i	$-0.998790\pi$
$733$		−	0.205782i		−	0.00760071i	0.999993	−	0.00380036i	$-0.00120969\pi$
$734$	34.5038			1.27356
$735$	−5.30744	−	0.783093i	−0.195768	−	0.0288848i
$736$	17.4389			0.642805
$737$			18.3349i			0.675374i
$738$		−	3.64414i		−	0.134143i
$739$	−32.6116			−1.19964			−0.599819	−	0.800136i	$-0.704761\pi$
$739$	−32.6116			−1.19964			−0.599819	+	0.800136i	$0.704761\pi$
$740$	−1.35416	−	0.199801i	−0.0497798	−	0.00734482i
$741$		0			0
$742$		−	15.9404i		−	0.585192i
$743$			29.5603i			1.08446i	0.840230	+	0.542231i	$0.182420\pi$
$743$			29.5603i			1.08446i	−0.840230	+	0.542231i	$0.817580\pi$
$744$	−21.5001			−0.788232
$745$	−5.88264	+	39.8698i	−0.215523	+	1.46072i
$746$	−22.9462			−0.840120
$747$			11.9452i			0.437051i
$748$			2.75641i			0.100784i
$749$	14.8927			0.544169
$750$	−9.15381	+	19.4708i	−0.334250	+	0.710973i
$751$	37.0458			1.35182			0.675909	−	0.736985i	$-0.263751\pi$
$751$	37.0458			1.35182			0.675909	+	0.736985i	$0.263751\pi$
$752$		−	4.66576i		−	0.170143i
$753$		−	7.57198i		−	0.275938i
$754$	−23.1093			−0.841590
$755$	4.24827	−	28.7928i	0.154610	−	1.04788i
$756$	−7.56170			−0.275016
$757$		−	30.5480i		−	1.11029i	−0.831755	−	0.555143i	$-0.812664\pi$
$757$		−	30.5480i		−	1.11029i	0.831755	−	0.555143i	$-0.187336\pi$
$758$		−	5.73954i		−	0.208470i
$759$	34.4210			1.24940
$760$		0			0
$761$	−46.0692			−1.67001			−0.835004	−	0.550244i	$-0.814535\pi$
$761$	−46.0692			−1.67001			−0.835004	+	0.550244i	$0.814535\pi$
$762$		−	2.56828i		−	0.0930391i
$763$			34.9990i			1.26705i
$764$	13.9229			0.503712
$765$	−2.75933	−	0.407128i	−0.0997636	−	0.0147197i
$766$	12.4805			0.450940
$767$			46.4340i			1.67663i
$768$		−	16.1916i		−	0.584266i
$769$	−14.7199			−0.530814			−0.265407	−	0.964137i	$-0.585506\pi$
$769$	−14.7199			−0.530814			−0.265407	+	0.964137i	$0.585506\pi$
$770$	−6.65770	+	45.1228i	−0.239927	+	1.62611i
$771$	−16.2198			−0.584142
$772$			12.1784i			0.438310i
$773$		−	8.86483i		−	0.318846i	−0.987210	−	0.159423i	$-0.949037\pi$
$773$		−	8.86483i		−	0.318846i	0.987210	−	0.159423i	$-0.0509633\pi$
$774$	−3.91079			−0.140571
$775$	38.7941	+	11.7026i	1.39353	+	0.420370i
$776$	−28.4813			−1.02242
$777$			2.61336i			0.0937536i
$778$		−	2.91412i		−	0.104476i
$779$		0			0
$780$	−1.13310	+	7.67961i	−0.0405714	+	0.274974i
$781$	−40.5127			−1.44966
$782$			6.52759i			0.233426i
$783$		−	16.5561i		−	0.591668i
$784$	−9.80368			−0.350132
$785$	−23.2430	−	3.42942i	−0.829579	−	0.122401i
$786$	26.5156			0.945781
$787$			13.1846i			0.469979i	0.971998	+	0.234990i	$0.0755056\pi$
$787$			13.1846i			0.469979i	−0.971998	+	0.234990i	$0.924494\pi$
$788$			9.60645i			0.342216i
$789$	−12.1490			−0.432515
$790$	4.79833	+	0.707976i	0.170717	+	0.0251886i
$791$	−14.6890			−0.522281
$792$			19.9993i			0.710644i
$793$			9.85242i			0.349870i
$794$	28.6180			1.01561
$795$	1.71128	−	11.5983i	0.0606928	−	0.411348i
$796$	−0.853141			−0.0302388
$797$		−	38.1858i		−	1.35261i	−0.736621	−	0.676306i	$-0.763580\pi$
$797$		−	38.1858i		−	1.35261i	0.736621	−	0.676306i	$-0.236420\pi$
$798$		0			0
$799$	0.754954			0.0267084
$800$	−4.90841	+	16.2714i	−0.173539	+	0.575280i
$801$	5.40157			0.190855
$802$			43.9012i			1.55021i
$803$		−	85.5889i		−	3.02037i
$804$	−2.39893			−0.0846039
$805$	−3.73735	+	25.3300i	−0.131724	+	0.892766i
$806$	61.6761			2.17245
$807$			17.1747i			0.604580i
$808$			12.4393i			0.437614i
$809$	−43.7667			−1.53875			−0.769377	−	0.638795i	$-0.779433\pi$
$809$	−43.7667			−1.53875			−0.769377	+	0.638795i	$0.779433\pi$
$810$	−6.15519	−	0.908175i	−0.216271	−	0.0319100i
$811$	5.95225			0.209012			0.104506	−	0.994524i	$-0.466674\pi$
$811$	5.95225			0.209012			0.104506	+	0.994524i	$0.466674\pi$
$812$		−	4.21128i		−	0.147787i
$813$			19.2613i			0.675522i
$814$	−9.00349			−0.315572
$815$	−8.01648	−	1.18280i	−0.280805	−	0.0414317i
$816$	4.53625			0.158800
$817$		0			0
$818$			54.8398i			1.91743i
$819$	−16.6525			−0.581884
$820$	0.287587	−	1.94913i	0.0100430	−	0.0680666i
$821$	−7.97019			−0.278162			−0.139081	−	0.990281i	$-0.544415\pi$
$821$	−7.97019			−0.278162			−0.139081	+	0.990281i	$0.544415\pi$
$822$		−	22.5966i		−	0.788146i
$823$		−	28.1907i		−	0.982666i	−0.870972	−	0.491333i	$-0.836510\pi$
$823$		−	28.1907i		−	0.982666i	0.870972	−	0.491333i	$-0.163490\pi$
$824$	7.38297			0.257198
$825$	−9.68828	+	32.1166i	−0.337303	+	1.11816i
$826$	−35.6971			−1.24206
$827$			54.5094i			1.89548i	0.319048	+	0.947738i	$0.396637\pi$
$827$			54.5094i			1.89548i	−0.319048	+	0.947738i	$0.603363\pi$
$828$		−	5.06027i		−	0.175856i
$829$	8.40522			0.291925			0.145963	−	0.989290i	$-0.453372\pi$
$829$	8.40522			0.291925			0.145963	+	0.989290i	$0.453372\pi$
$830$	−3.97681	+	26.9530i	−0.138037	+	0.935552i
$831$	33.9863			1.17897
$832$		−	19.7886i		−	0.686046i
$833$		−	1.58631i		−	0.0549623i
$834$	17.9765			0.622474
$835$	−23.5368	−	3.47277i	−0.814525	−	0.120180i
$836$		0			0
$837$			44.1865i			1.52731i
$838$			37.6172i			1.29947i
$839$	37.7155			1.30208			0.651041	−	0.759042i	$-0.274333\pi$
$839$	37.7155			1.30208			0.651041	+	0.759042i	$0.274333\pi$
$840$	13.0983	+	1.93261i	0.451936	+	0.0666814i
$841$	−19.7795			−0.682052
$842$		−	31.3251i		−	1.07953i
$843$			8.53120i			0.293830i
$844$	5.94785			0.204734
$845$	−2.96840	+	20.1184i	−0.102116	+	0.692096i
$846$	−2.46894			−0.0848839
$847$			46.5654i			1.60001i
$848$		−	21.4238i		−	0.735696i
$849$	12.3203			0.422831
$850$	−6.09058	−	1.83728i	−0.208905	−	0.0630182i
$851$	−5.05418			−0.173255
$852$		−	5.30067i		−	0.181598i
$853$		−	41.2975i		−	1.41400i	−0.707214	−	0.707000i	$-0.750048\pi$
$853$		−	41.2975i		−	1.41400i	0.707214	−	0.707000i	$-0.249952\pi$
$854$	−7.57426			−0.259186
$855$		0			0
$856$	14.8939			0.509062
$857$			3.43473i			0.117328i	0.998278	+	0.0586640i	$0.0186841\pi$
$857$			3.43473i			0.117328i	−0.998278	+	0.0586640i	$0.981316\pi$
$858$			51.0600i			1.74316i
$859$	30.2921			1.03355			0.516777	−	0.856120i	$-0.327132\pi$
$859$	30.2921			1.03355			0.516777	+	0.856120i	$0.327132\pi$
$860$	−2.09175	−	0.308630i	−0.0713282	−	0.0105242i
$861$	−3.76158			−0.128194
$862$			21.1384i			0.719977i
$863$			23.8589i			0.812168i	0.913836	+	0.406084i	$0.133106\pi$
$863$			23.8589i			0.812168i	−0.913836	+	0.406084i	$0.866894\pi$
$864$	−18.5331			−0.630509
$865$	−42.9390	−	6.33549i	−1.45997	−	0.215413i
$866$	9.43733			0.320694
$867$		−	19.4717i		−	0.661293i
$868$			11.2395i			0.381492i
$869$	7.56246			0.256539
$870$	1.90723	−	12.9263i	0.0646613	−	0.438244i
$871$	−15.2677			−0.517328
$872$			35.0017i			1.18531i
$873$			20.2540i			0.685496i
$874$		0			0
$875$	−22.5823	−	10.6166i	−0.763422	−	0.358908i
$876$	11.1984			0.378360
$877$		−	13.2757i		−	0.448288i	−0.974556	−	0.224144i	$-0.928041\pi$
$877$		−	13.2757i		−	0.448288i	0.974556	−	0.224144i	$-0.0719586\pi$
$878$		−	10.5078i		−	0.354622i
$879$	−10.8048			−0.364436
$880$	−8.94789	+	60.6447i	−0.301633	+	2.04433i
$881$	20.1998			0.680547			0.340274	−	0.940326i	$-0.389480\pi$
$881$	20.1998			0.680547			0.340274	+	0.940326i	$0.389480\pi$
$882$			5.18773i			0.174680i
$883$		−	58.2506i		−	1.96029i	−0.198289	−	0.980144i	$-0.563538\pi$
$883$		−	58.2506i		−	1.96029i	0.198289	−	0.980144i	$-0.436462\pi$
$884$	−2.29531			−0.0771995
$885$	−25.9732	−	3.83225i	−0.873080	−	0.128820i
$886$	14.9008			0.500601
$887$			46.0826i			1.54730i	0.633612	+	0.773651i	$0.281571\pi$
$887$			46.0826i			1.54730i	−0.633612	+	0.773651i	$0.718429\pi$
$888$			2.61355i			0.0877050i
$889$	2.97871			0.0999026
$890$	12.1881	+	1.79830i	0.408544	+	0.0602792i
$891$	−9.70095			−0.324994
$892$			4.06232i			0.136016i
$893$		0			0
$894$	−34.6837			−1.16000
$895$	0.675796	−	4.58023i	0.0225894	−	0.153100i
$896$	30.3859			1.01512
$897$			28.6629i			0.957027i
$898$		−	28.2764i		−	0.943597i
$899$	−24.6085			−0.820739
$900$	4.72149	+	1.42428i	0.157383	+	0.0474761i
$901$	3.46653			0.115487
$902$		−	12.9593i		−	0.431499i
$903$			4.03683i			0.134337i
$904$	−14.6901			−0.488586
$905$	−7.06061	+	47.8535i	−0.234703	+	1.59071i
$906$	25.0476			0.832150
$907$		−	43.6873i		−	1.45061i	−0.688426	−	0.725306i	$-0.741698\pi$
$907$		−	43.6873i		−	1.45061i	0.688426	−	0.725306i	$-0.258302\pi$
$908$		−	5.52331i		−	0.183297i
$909$	8.84603			0.293404
$910$	−37.5745	−	5.54397i	−1.24558	−	0.183781i
$911$	30.7689			1.01942			0.509709	−	0.860347i	$-0.329753\pi$
$911$	30.7689			1.01942			0.509709	+	0.860347i	$0.329753\pi$
$912$		0			0
$913$			42.4795i			1.40587i
$914$	−0.618204			−0.0204484
$915$	−5.51103	−	0.813131i	−0.182189	−	0.0268813i
$916$	−4.48949			−0.148337
$917$			30.7530i			1.01555i
$918$		−	6.93718i		−	0.228961i
$919$	−12.0943			−0.398953			−0.199476	−	0.979903i	$-0.563924\pi$
$919$	−12.0943			−0.398953			−0.199476	+	0.979903i	$0.563924\pi$
$920$	−3.73763	+	25.3319i	−0.123226	+	0.835169i
$921$	−17.4293			−0.574314
$922$			13.7897i			0.454140i
$923$		−	33.7355i		−	1.11042i
$924$	−9.30485			−0.306107
$925$	1.42257	−	4.71581i	0.0467738	−	0.155055i
$926$	−59.9344			−1.96957
$927$		−	5.25028i		−	0.172442i
$928$		−	10.3215i		−	0.338820i
$929$	−15.9647			−0.523785			−0.261892	−	0.965097i	$-0.584347\pi$
$929$	−15.9647			−0.523785			−0.261892	+	0.965097i	$0.584347\pi$
$930$	−5.09020	+	34.4990i	−0.166914	+	1.13127i
$931$		0			0
$932$		−	15.5210i		−	0.508407i
$933$			37.5363i			1.22888i
$934$	−41.9966			−1.37417
$935$	−9.81275	−	1.44783i	−0.320911	−	0.0473492i
$936$	−16.6537			−0.544343
$937$		−	3.57961i		−	0.116941i	−0.998289	−	0.0584704i	$-0.981378\pi$
$937$		−	3.57961i		−	0.116941i	0.998289	−	0.0584704i	$-0.0186223\pi$
$938$		−	11.7374i		−	0.383240i
$939$	−10.6861			−0.348727
$940$	−1.32055	−	0.194843i	−0.0430717	−	0.00635507i
$941$	−34.7060			−1.13138			−0.565691	−	0.824617i	$-0.691391\pi$
$941$	−34.7060			−1.13138			−0.565691	+	0.824617i	$0.691391\pi$
$942$		−	20.2197i		−	0.658793i
$943$		−	7.27482i		−	0.236901i
$944$	−47.9766			−1.56151
$945$	3.97186	−	26.9194i	0.129205	−	0.875689i
$946$	−13.9076			−0.452176
$947$			44.9696i			1.46132i	0.682743	+	0.730658i	$0.260787\pi$
$947$			44.9696i			1.46132i	−0.682743	+	0.730658i	$0.739213\pi$
$948$			0.989471i			0.0321365i
$949$	71.2711			2.31356
$950$		0			0
$951$	−12.3854			−0.401624
$952$			3.91488i			0.126882i
$953$			1.67348i			0.0542095i	0.999633	+	0.0271047i	$0.00862876\pi$
$953$			1.67348i			0.0542095i	−0.999633	+	0.0271047i	$0.991371\pi$
$954$	−11.3366			−0.367037
$955$	−7.31313	+	49.5650i	−0.236647	+	1.60389i
$956$	10.4509			0.338007
$957$		−	20.3727i		−	0.658556i
$958$		−	19.1679i		−	0.619285i
$959$	26.2076			0.846288
$960$	11.0689	+	1.63317i	0.357247	+	0.0527105i
$961$	34.6774			1.11863
$962$		−	7.49735i		−	0.241724i
$963$		−	10.5915i		−	0.341307i
$964$	−6.73974			−0.217072
$965$	−43.3547	−	6.39683i	−1.39564	−	0.205921i
$966$	−22.0352			−0.708972
$967$		−	18.1691i		−	0.584279i	−0.956376	−	0.292140i	$-0.905633\pi$
$967$		−	18.1691i		−	0.584279i	0.956376	−	0.292140i	$-0.0943672\pi$
$968$			46.5689i			1.49678i
$969$		0			0
$970$	−6.74302	+	45.7011i	−0.216505	+	1.46737i
$971$	−4.64954			−0.149211			−0.0746054	−	0.997213i	$-0.523770\pi$
$971$	−4.64954			−0.149211			−0.0746054	+	0.997213i	$0.523770\pi$
$972$			8.89475i			0.285299i
$973$			20.8492i			0.668395i
$974$	−47.5703			−1.52425
$975$	−26.7440	−	8.06758i	−0.856493	−	0.258369i
$976$	−10.1797			−0.325845
$977$		−	13.7386i		−	0.439535i	−0.975552	−	0.219768i	$-0.929470\pi$
$977$		−	13.7386i		−	0.439535i	0.975552	−	0.219768i	$-0.0705299\pi$
$978$		−	6.97374i		−	0.222996i
$979$	19.2091			0.613926
$980$	−0.409403	+	2.77474i	−0.0130779	+	0.0886359i
$981$	24.8909			0.794704
$982$		−	7.80130i		−	0.248949i
$983$			8.41202i			0.268302i	0.990961	+	0.134151i	$0.0428307\pi$
$983$			8.41202i			0.268302i	−0.990961	+	0.134151i	$0.957169\pi$
$984$	−3.76187			−0.119924
$985$	−34.1987	−	5.04588i	−1.08966	−	0.160775i
$986$	3.86347			0.123038
$987$			2.54850i			0.0811198i
$988$		0			0
$989$	−7.80714			−0.248253
$990$	32.0908	+	4.73488i	1.01991	+	0.150484i
$991$	−18.5779			−0.590145			−0.295072	−	0.955475i	$-0.595344\pi$
$991$	−18.5779			−0.590145			−0.295072	+	0.955475i	$0.595344\pi$
$992$			27.5470i			0.874618i
$993$		−	4.79059i		−	0.152025i
$994$	25.9349			0.822605
$995$	0.448121	−	3.03716i	0.0142064	−	0.0962843i
$996$	−5.55801			−0.176112
$997$		−	38.4609i		−	1.21807i	−0.793143	−	0.609035i	$-0.791557\pi$
$997$		−	38.4609i		−	1.21807i	0.793143	−	0.609035i	$-0.208443\pi$
$998$		−	0.304751i		−	0.00964671i
$999$	5.37131			0.169941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.19		24
5.2	odd	4		9025.2.a.ct.1.6		24
5.3	odd	4		9025.2.a.ct.1.19		24
5.4	even	2	inner	1805.2.b.l.1084.6		24
19.14	odd	18		95.2.p.a.44.3	✓	48
19.15	odd	18		95.2.p.a.54.6	yes	48
19.18	odd	2		1805.2.b.k.1084.6		24
57.14	even	18		855.2.da.b.424.6		48
57.53	even	18		855.2.da.b.244.3		48
95.14	odd	18		95.2.p.a.44.6	yes	48
95.18	even	4		9025.2.a.cu.1.6		24
95.33	even	36		475.2.l.f.101.3		48
95.34	odd	18		95.2.p.a.54.3	yes	48
95.37	even	4		9025.2.a.cu.1.19		24
95.52	even	36		475.2.l.f.101.6		48
95.53	even	36		475.2.l.f.301.3		48
95.72	even	36		475.2.l.f.301.6		48
95.94	odd	2		1805.2.b.k.1084.19		24
285.14	even	18		855.2.da.b.424.3		48
285.224	even	18		855.2.da.b.244.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.3	✓	48	19.14	odd	18
95.2.p.a.44.6	yes	48	95.14	odd	18
95.2.p.a.54.3	yes	48	95.34	odd	18
95.2.p.a.54.6	yes	48	19.15	odd	18
475.2.l.f.101.3		48	95.33	even	36
475.2.l.f.101.6		48	95.52	even	36
475.2.l.f.301.3		48	95.53	even	36
475.2.l.f.301.6		48	95.72	even	36
855.2.da.b.244.3		48	57.53	even	18
855.2.da.b.244.6		48	285.224	even	18
855.2.da.b.424.3		48	285.14	even	18
855.2.da.b.424.6		48	57.14	even	18
1805.2.b.k.1084.6		24	19.18	odd	2
1805.2.b.k.1084.19		24	95.94	odd	2
1805.2.b.l.1084.6		24	5.4	even	2	inner
1805.2.b.l.1084.19		24	1.1	even	1	trivial
9025.2.a.ct.1.6		24	5.2	odd	4
9025.2.a.ct.1.19		24	5.3	odd	4
9025.2.a.cu.1.6		24	95.18	even	4
9025.2.a.cu.1.19		24	95.37	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61907i q^{2} -1.18857i q^{3} -0.621387 q^{4} +(0.326390 - 2.21212i) q^{5} +1.92438 q^{6} +2.23190i q^{7} +2.23207i q^{8} +1.58730 q^{9} +O(q^{10})\)	\(q+1.61907i q^{2} -1.18857i q^{3} -0.621387 q^{4} +(0.326390 - 2.21212i) q^{5} +1.92438 q^{6} +2.23190i q^{7} +2.23207i q^{8} +1.58730 q^{9} +(3.58157 + 0.528448i) q^{10} +5.64478 q^{11} +0.738562i q^{12} +4.70049i q^{13} -3.61361 q^{14} +(-2.62926 - 0.387937i) q^{15} -4.85665 q^{16} -0.785842i q^{17} +2.56995i q^{18} +(-0.202814 + 1.37458i) q^{20} +2.65277 q^{21} +9.13929i q^{22} +5.13041i q^{23} +2.65297 q^{24} +(-4.78694 - 1.44403i) q^{25} -7.61043 q^{26} -5.45233i q^{27} -1.38688i q^{28} +3.03653 q^{29} +(0.628097 - 4.25695i) q^{30} -8.10416 q^{31} -3.39912i q^{32} -6.70922i q^{33} +1.27233 q^{34} +(4.93723 + 0.728470i) q^{35} -0.986329 q^{36} +0.985141i q^{37} +5.58687 q^{39} +(4.93761 + 0.728525i) q^{40} -1.41798 q^{41} +4.29502i q^{42} +1.52174i q^{43} -3.50759 q^{44} +(0.518079 - 3.51130i) q^{45} -8.30649 q^{46} +0.960695i q^{47} +5.77247i q^{48} +2.01861 q^{49} +(2.33798 - 7.75039i) q^{50} -0.934028 q^{51} -2.92083i q^{52} +4.41123i q^{53} +8.82770 q^{54} +(1.84240 - 12.4869i) q^{55} -4.98176 q^{56} +4.91635i q^{58} +9.87853 q^{59} +(1.63379 + 0.241059i) q^{60} +2.09604 q^{61} -13.1212i q^{62} +3.54270i q^{63} -4.20990 q^{64} +(10.3981 + 1.53419i) q^{65} +10.8627 q^{66} +3.24811i q^{67} +0.488312i q^{68} +6.09785 q^{69} +(-1.17944 + 7.99373i) q^{70} -7.17702 q^{71} +3.54297i q^{72} -15.1625i q^{73} -1.59501 q^{74} +(-1.71633 + 5.68961i) q^{75} +12.5986i q^{77} +9.04553i q^{78} +1.33973 q^{79} +(-1.58516 + 10.7435i) q^{80} -1.71857 q^{81} -2.29581i q^{82} +7.52545i q^{83} -1.64840 q^{84} +(-1.73838 - 0.256491i) q^{85} -2.46380 q^{86} -3.60912i q^{87} +12.5995i q^{88} +3.40299 q^{89} +(5.68504 + 0.838806i) q^{90} -10.4910 q^{91} -3.18797i q^{92} +9.63236i q^{93} -1.55543 q^{94} -4.04009 q^{96} +12.7601i q^{97} +3.26827i q^{98} +8.95997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} - 12 q^{40} - 60 q^{41} + 30 q^{44} + 9 q^{45} - 6 q^{46} - 12 q^{49} - 18 q^{50} - 30 q^{51} + 24 q^{54} + 33 q^{55} - 18 q^{56} + 60 q^{59} + 42 q^{60} + 30 q^{61} - 18 q^{65} + 36 q^{66} + 66 q^{69} - 9 q^{70} - 96 q^{71} - 24 q^{74} - 36 q^{75} + 72 q^{79} - 42 q^{80} - 96 q^{81} - 54 q^{84} - 27 q^{85} - 108 q^{86} + 84 q^{89} + 93 q^{90} - 96 q^{91} + 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

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