LMFDB - Embedded newform 1805.2.b.l.1084.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,2,Mod(1084,1805)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [24,0,0,-18,-3,-12,0,0,-12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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			1084.21
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.96177i q^{2} -0.187708i q^{3} -1.84854 q^{4} +(1.81111 - 1.31144i) q^{5} +0.368240 q^{6} -0.677067i q^{7} +0.297123i q^{8} +2.96477 q^{9} +(2.57274 + 3.55299i) q^{10} +2.84069 q^{11} +0.346987i q^{12} -4.76663i q^{13} +1.32825 q^{14} +(-0.246168 - 0.339961i) q^{15} -4.27997 q^{16} -5.18394i q^{17} +5.81619i q^{18} +(-3.34792 + 2.42425i) q^{20} -0.127091 q^{21} +5.57278i q^{22} +1.05091i q^{23} +0.0557724 q^{24} +(1.56026 - 4.75032i) q^{25} +9.35103 q^{26} -1.11964i q^{27} +1.25159i q^{28} -1.42605 q^{29} +(0.666925 - 0.482924i) q^{30} -0.271064 q^{31} -7.80208i q^{32} -0.533221i q^{33} +10.1697 q^{34} +(-0.887932 - 1.22625i) q^{35} -5.48050 q^{36} +0.603754i q^{37} -0.894735 q^{39} +(0.389658 + 0.538123i) q^{40} -6.73563 q^{41} -0.249324i q^{42} -5.62944i q^{43} -5.25114 q^{44} +(5.36953 - 3.88810i) q^{45} -2.06165 q^{46} -7.89538i q^{47} +0.803386i q^{48} +6.54158 q^{49} +(9.31905 + 3.06088i) q^{50} -0.973067 q^{51} +8.81132i q^{52} -6.88829i q^{53} +2.19647 q^{54} +(5.14481 - 3.72539i) q^{55} +0.201172 q^{56} -2.79757i q^{58} -10.1227 q^{59} +(0.455051 + 0.628432i) q^{60} -7.47195 q^{61} -0.531765i q^{62} -2.00735i q^{63} +6.74594 q^{64} +(-6.25114 - 8.63291i) q^{65} +1.04606 q^{66} +4.11733i q^{67} +9.58273i q^{68} +0.197265 q^{69} +(2.40561 - 1.74192i) q^{70} +7.60546 q^{71} +0.880900i q^{72} +16.1274i q^{73} -1.18443 q^{74} +(-0.891675 - 0.292874i) q^{75} -1.92334i q^{77} -1.75527i q^{78} +14.8468 q^{79} +(-7.75152 + 5.61292i) q^{80} +8.68413 q^{81} -13.2138i q^{82} +14.1815i q^{83} +0.234933 q^{84} +(-6.79841 - 9.38870i) q^{85} +11.0437 q^{86} +0.267680i q^{87} +0.844034i q^{88} +8.23788 q^{89} +(7.62757 + 10.5338i) q^{90} -3.22733 q^{91} -1.94266i q^{92} +0.0508809i q^{93} +15.4889 q^{94} -1.46451 q^{96} -5.72847i q^{97} +12.8331i q^{98} +8.42198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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 $

$2$			1.96177i			1.38718i	0.720369	+	0.693591i	$0.243972\pi$
$2$			1.96177i			1.38718i	−0.720369	+	0.693591i	$0.756028\pi$
$3$		−	0.187708i		−	0.108373i	−0.998531	−	0.0541867i	$-0.982743\pi$
$3$		−	0.187708i		−	0.108373i	0.998531	−	0.0541867i	$-0.0172566\pi$
$4$	−1.84854			−0.924272
$5$	1.81111	−	1.31144i	0.809955	−	0.586493i
$5$	1.81111	−	1.31144i	0.809955	−	0.586493i
$6$	0.368240			0.150333
$7$		−	0.677067i		−	0.255907i	−0.991780	−	0.127954i	$-0.959159\pi$
$7$		−	0.677067i		−	0.255907i	0.991780	−	0.127954i	$-0.0408409\pi$
$8$			0.297123i			0.105049i
$9$	2.96477			0.988255
$10$	2.57274	+	3.55299i	0.813572	+	1.12355i
$11$	2.84069			0.856500			0.428250	−	0.903660i	$-0.359130\pi$
$11$	2.84069			0.856500			0.428250	+	0.903660i	$0.359130\pi$
$12$			0.346987i			0.100166i
$13$		−	4.76663i		−	1.32203i	−0.750375	−	0.661013i	$-0.770127\pi$
$13$		−	4.76663i		−	1.32203i	0.750375	−	0.661013i	$-0.229873\pi$
$14$	1.32825			0.354990
$15$	−0.246168	−	0.339961i	−0.0635602	−	0.0877775i
$16$	−4.27997			−1.06999
$17$		−	5.18394i		−	1.25729i	−0.777693	−	0.628645i	$-0.783610\pi$
$17$		−	5.18394i		−	1.25729i	0.777693	−	0.628645i	$-0.216390\pi$
$18$			5.81619i			1.37089i
$19$		0			0
$19$		0			0
$20$	−3.34792	+	2.42425i	−0.748618	+	0.542079i
$21$	−0.127091			−0.0277336
$22$			5.57278i			1.18812i
$23$			1.05091i			0.219131i	0.993980	+	0.109565i	$0.0349459\pi$
$23$			1.05091i			0.219131i	−0.993980	+	0.109565i	$0.965054\pi$
$24$	0.0557724			0.0113845
$25$	1.56026	−	4.75032i	0.312053	−	0.950065i
$26$	9.35103			1.83389
$27$		−	1.11964i		−	0.215474i
$28$			1.25159i			0.236528i
$29$	−1.42605			−0.264810			−0.132405	−	0.991196i	$-0.542270\pi$
$29$	−1.42605			−0.264810			−0.132405	+	0.991196i	$0.542270\pi$
$30$	0.666925	−	0.482924i	0.121763	−	0.0881695i
$31$	−0.271064			−0.0486845			−0.0243422	−	0.999704i	$-0.507749\pi$
$31$	−0.271064			−0.0486845			−0.0243422	+	0.999704i	$0.507749\pi$
$32$		−	7.80208i		−	1.37923i
$33$		−	0.533221i		−	0.0928218i
$34$	10.1697			1.74409
$35$	−0.887932	−	1.22625i	−0.150088	−	0.207273i
$36$	−5.48050			−0.913416
$37$			0.603754i			0.0992566i	0.998768	+	0.0496283i	$0.0158037\pi$
$37$			0.603754i			0.0992566i	−0.998768	+	0.0496283i	$0.984196\pi$
$38$		0			0
$39$	−0.894735			−0.143272
$40$	0.389658	+	0.538123i	0.0616104	+	0.0850848i
$41$	−6.73563			−1.05193			−0.525965	−	0.850506i	$-0.676296\pi$
$41$	−6.73563			−1.05193			−0.525965	+	0.850506i	$0.676296\pi$
$42$		−	0.249324i		−	0.0384715i
$43$		−	5.62944i		−	0.858482i	−0.903190	−	0.429241i	$-0.858781\pi$
$43$		−	5.62944i		−	0.858482i	0.903190	−	0.429241i	$-0.141219\pi$
$44$	−5.25114			−0.791639
$45$	5.36953	−	3.88810i	0.800442	−	0.579604i
$46$	−2.06165			−0.303974
$47$		−	7.89538i		−	1.15166i	−0.817570	−	0.575829i	$-0.804679\pi$
$47$		−	7.89538i		−	1.15166i	0.817570	−	0.575829i	$-0.195321\pi$
$48$			0.803386i			0.115959i
$49$	6.54158			0.934511
$50$	9.31905	+	3.06088i	1.31791	+	0.432874i
$51$	−0.973067			−0.136257
$52$			8.81132i			1.22191i
$53$		−	6.88829i		−	0.946180i	−0.881014	−	0.473090i	$-0.843139\pi$
$53$		−	6.88829i		−	0.946180i	0.881014	−	0.473090i	$-0.156861\pi$
$54$	2.19647			0.298901
$55$	5.14481	−	3.72539i	0.693726	−	0.502331i
$56$	0.201172			0.0268828
$57$		0			0
$58$		−	2.79757i		−	0.367339i
$59$	−10.1227			−1.31786			−0.658930	−	0.752204i	$-0.728991\pi$
$59$	−10.1227			−1.31786			−0.658930	+	0.752204i	$0.728991\pi$
$60$	0.455051	+	0.628432i	0.0587469	+	0.0811303i
$61$	−7.47195			−0.956686			−0.478343	−	0.878173i	$-0.658762\pi$
$61$	−7.47195			−0.956686			−0.478343	+	0.878173i	$0.658762\pi$
$62$		−	0.531765i		−	0.0675342i
$63$		−	2.00735i		−	0.252902i
$64$	6.74594			0.843243
$65$	−6.25114	−	8.63291i	−0.775358	−	1.07078i
$66$	1.04606			0.128761
$67$			4.11733i			0.503012i	0.967856	+	0.251506i	$0.0809259\pi$
$67$			4.11733i			0.503012i	−0.967856	+	0.251506i	$0.919074\pi$
$68$			9.58273i			1.16208i
$69$	0.197265			0.0237480
$70$	2.40561	−	1.74192i	0.287526	−	0.208199i
$71$	7.60546			0.902603			0.451301	−	0.892372i	$-0.350960\pi$
$71$	7.60546			0.902603			0.451301	+	0.892372i	$0.350960\pi$
$72$			0.880900i			0.103815i
$73$			16.1274i			1.88757i	0.330565	+	0.943783i	$0.392761\pi$
$73$			16.1274i			1.88757i	−0.330565	+	0.943783i	$0.607239\pi$
$74$	−1.18443			−0.137687
$75$	−0.891675	−	0.292874i	−0.102962	−	0.0338182i
$76$		0			0
$77$		−	1.92334i		−	0.219185i
$78$		−	1.75527i		−	0.198745i
$79$	14.8468			1.67039			0.835196	−	0.549953i	$-0.185354\pi$
$79$	14.8468			1.67039			0.835196	+	0.549953i	$0.185354\pi$
$80$	−7.75152	+	5.61292i	−0.866646	+	0.627543i
$81$	8.68413			0.964904
$82$		−	13.2138i		−	1.45922i
$83$			14.1815i			1.55662i	0.627878	+	0.778312i	$0.283924\pi$
$83$			14.1815i			1.55662i	−0.627878	+	0.778312i	$0.716076\pi$
$84$	0.234933			0.0256333
$85$	−6.79841	−	9.38870i	−0.737391	−	1.01835i
$86$	11.0437			1.19087
$87$			0.267680i			0.0286983i
$88$			0.844034i			0.0899743i
$89$	8.23788			0.873214			0.436607	−	0.899652i	$-0.356180\pi$
$89$	8.23788			0.873214			0.436607	+	0.899652i	$0.356180\pi$
$90$	7.62757	+	10.5338i	0.804016	+	1.11036i
$91$	−3.22733			−0.338316
$92$		−	1.94266i		−	0.202536i
$93$			0.0508809i			0.00527610i
$94$	15.4889			1.59756
$95$		0			0
$96$	−1.46451			−0.149471
$97$		−	5.72847i		−	0.581638i	−0.956778	−	0.290819i	$-0.906072\pi$
$97$		−	5.72847i		−	0.581638i	0.956778	−	0.290819i	$-0.0939277\pi$
$98$			12.8331i			1.29634i
$99$	8.42198			0.846441
$100$	−2.88422	+	8.78118i	−0.288422	+	0.878118i
$101$	−2.02231			−0.201228			−0.100614	−	0.994926i	$-0.532081\pi$
$101$	−2.02231			−0.201228			−0.100614	+	0.994926i	$0.532081\pi$
$102$		−	1.90893i		−	0.189013i
$103$			18.2358i			1.79683i	0.439147	+	0.898415i	$0.355281\pi$
$103$			18.2358i			1.79683i	−0.439147	+	0.898415i	$0.644719\pi$
$104$	1.41627			0.138877
$105$	−0.230176	+	0.166672i	−0.0224629	+	0.0162655i
$106$	13.5133			1.31252
$107$			6.21341i			0.600673i	0.953833	+	0.300337i	$0.0970990\pi$
$107$			6.21341i			0.600673i	−0.953833	+	0.300337i	$0.902901\pi$
$108$			2.06969i			0.199156i
$109$	15.9885			1.53142			0.765711	−	0.643185i	$-0.222387\pi$
$109$	15.9885			1.53142			0.765711	+	0.643185i	$0.222387\pi$
$110$	7.30836	+	10.0929i	0.696824	+	0.962324i
$111$	0.113330			0.0107568
$112$			2.89783i			0.273819i
$113$			7.88392i			0.741657i	0.928701	+	0.370828i	$0.120926\pi$
$113$			7.88392i			0.741657i	−0.928701	+	0.370828i	$0.879074\pi$
$114$		0			0
$115$	1.37821	+	1.90333i	0.128519	+	0.177486i
$116$	2.63611			0.244756
$117$		−	14.1319i		−	1.30650i
$118$		−	19.8584i		−	1.82811i
$119$	−3.50988			−0.321750
$120$	0.101010	−	0.0731420i	0.00922092	−	0.00667692i
$121$	−2.93048			−0.266407
$122$		−	14.6583i		−	1.32710i
$123$			1.26433i			0.114001i
$124$	0.501073			0.0449977
$125$	−3.40394	−	10.6496i	−0.304457	−	0.952526i
$126$	3.93795			0.350821
$127$			15.7743i			1.39974i	0.714270	+	0.699871i	$0.246759\pi$
$127$			15.7743i			1.39974i	−0.714270	+	0.699871i	$0.753241\pi$
$128$		−	2.37017i		−	0.209495i
$129$	−1.05669			−0.0930366
$130$	16.9358	−	12.2633i	1.48537	−	1.07556i
$131$	−4.06624			−0.355269			−0.177634	−	0.984097i	$-0.556844\pi$
$131$	−4.06624			−0.355269			−0.177634	+	0.984097i	$0.556844\pi$
$132$			0.985682i			0.0857926i
$133$		0			0
$134$	−8.07726			−0.697769
$135$	−1.46833	−	2.02779i	−0.126374	−	0.174524i
$136$	1.54027			0.132077
$137$			2.61201i			0.223159i	0.993756	+	0.111580i	$0.0355910\pi$
$137$			2.61201i			0.223159i	−0.993756	+	0.111580i	$0.964409\pi$
$138$			0.386989i			0.0329427i
$139$	−8.97126			−0.760932			−0.380466	−	0.924795i	$-0.624236\pi$
$139$	−8.97126			−0.760932			−0.380466	+	0.924795i	$0.624236\pi$
$140$	1.64138	+	2.26677i	0.138722	+	0.191577i
$141$	−1.48203			−0.124809
$142$			14.9202i			1.25207i
$143$		−	13.5405i		−	1.13232i
$144$	−12.6891			−1.05743
$145$	−2.58273	+	1.87017i	−0.214484	+	0.155309i
$146$	−31.6382			−2.61840
$147$		−	1.22791i		−	0.101276i
$148$		−	1.11607i		−	0.0917401i
$149$	1.72807			0.141569			0.0707846	−	0.997492i	$-0.477450\pi$
$149$	1.72807			0.141569			0.0707846	+	0.997492i	$0.477450\pi$
$150$	0.574552	−	1.74926i	0.0469120	−	0.142827i
$151$	−11.0738			−0.901177			−0.450589	−	0.892732i	$-0.648786\pi$
$151$	−11.0738			−0.901177			−0.450589	+	0.892732i	$0.648786\pi$
$152$		0			0
$153$		−	15.3692i		−	1.24252i
$154$	3.77315			0.304049
$155$	−0.490927	+	0.355483i	−0.0394322	+	0.0285531i
$156$	1.65396			0.132423
$157$			1.96462i			0.156794i	0.996922	+	0.0783970i	$0.0249802\pi$
$157$			1.96462i			0.156794i	−0.996922	+	0.0783970i	$0.975020\pi$
$158$			29.1259i			2.31714i
$159$	−1.29299			−0.102541
$160$	−10.2319	−	14.1305i	−0.808906	−	1.11711i
$161$	0.711540			0.0560772
$162$			17.0363i			1.33850i
$163$			20.1311i			1.57679i	0.615169	+	0.788395i	$0.289088\pi$
$163$			20.1311i			1.57679i	−0.615169	+	0.788395i	$0.710912\pi$
$164$	12.4511			0.972269
$165$	−0.699286	−	0.965723i	−0.0544393	−	0.0751815i
$166$	−27.8209			−2.15932
$167$			17.8567i			1.38179i	0.722956	+	0.690895i	$0.242783\pi$
$167$			17.8567i			1.38179i	−0.722956	+	0.690895i	$0.757217\pi$
$168$		−	0.0377617i		−	0.00291338i
$169$	−9.72076			−0.747751
$170$	18.4185	−	13.3369i	1.41263	−	1.02289i
$171$		0			0
$172$			10.4063i			0.793470i
$173$			2.72218i			0.206963i	0.994631	+	0.103482i	$0.0329983\pi$
$173$			2.72218i			0.206963i	−0.994631	+	0.103482i	$0.967002\pi$
$174$	−0.525127			−0.0398098
$175$	−3.21629	−	1.05640i	−0.243129	−	0.0798566i
$176$	−12.1581			−0.916450
$177$			1.90011i			0.142821i
$178$			16.1608i			1.21131i
$179$	7.71634			0.576746			0.288373	−	0.957518i	$-0.406886\pi$
$179$	7.71634			0.576746			0.288373	+	0.957518i	$0.406886\pi$
$180$	−9.92580	+	7.18733i	−0.739826	+	0.535712i
$181$	1.07040			0.0795625			0.0397812	−	0.999208i	$-0.487334\pi$
$181$	1.07040			0.0795625			0.0397812	+	0.999208i	$0.487334\pi$
$182$		−	6.33128i		−	0.469306i
$183$			1.40255i			0.103679i
$184$	−0.312251			−0.0230194
$185$	0.791786	+	1.09347i	0.0582133	+	0.0803933i
$186$	−0.0998166			−0.00731891
$187$		−	14.7260i		−	1.07687i
$188$			14.5949i			1.06445i
$189$	−0.758069			−0.0551414
$190$		0			0
$191$	5.38296			0.389497			0.194749	−	0.980853i	$-0.437611\pi$
$191$	5.38296			0.389497			0.194749	+	0.980853i	$0.437611\pi$
$192$		−	1.26627i		−	0.0913851i
$193$		−	15.4699i		−	1.11355i	−0.830664	−	0.556774i	$-0.812039\pi$
$193$		−	15.4699i		−	1.11355i	0.830664	−	0.556774i	$-0.187961\pi$
$194$	11.2379			0.806837
$195$	−1.62047	+	1.17339i	−0.116044	+	0.0840282i
$196$	−12.0924			−0.863742
$197$			21.2328i			1.51278i	0.654124	+	0.756388i	$0.273038\pi$
$197$			21.2328i			1.51278i	−0.654124	+	0.756388i	$0.726962\pi$
$198$			16.5220i			1.17417i
$199$	−7.58119			−0.537416			−0.268708	−	0.963222i	$-0.586597\pi$
$199$	−7.58119			−0.537416			−0.268708	+	0.963222i	$0.586597\pi$
$200$	1.41143	+	0.463590i	0.0998032	+	0.0327808i
$201$	0.772857			0.0545131
$202$		−	3.96732i		−	0.279139i
$203$			0.965529i			0.0677668i
$204$	1.79876			0.125938
$205$	−12.1990	+	8.83336i	−0.852015	+	0.616949i
$206$	−35.7745			−2.49253
$207$			3.11572i			0.216557i
$208$			20.4011i			1.41456i
$209$		0			0
$210$	−0.326972	−	0.451553i	−0.0225632	−	0.0311601i
$211$	13.2991			0.915548			0.457774	−	0.889069i	$-0.348647\pi$
$211$	13.2991			0.915548			0.457774	+	0.889069i	$0.348647\pi$
$212$			12.7333i			0.874527i
$213$		−	1.42761i		−	0.0978181i
$214$	−12.1893			−0.833243
$215$	−7.38266	−	10.1956i	−0.503493	−	0.695331i
$216$	0.332669			0.0226353
$217$			0.183528i			0.0124587i
$218$			31.3658i			2.12436i
$219$	3.02724			0.204562
$220$	−9.51041	+	6.88654i	−0.641192	+	0.464290i
$221$	−24.7099			−1.66217
$222$			0.222327i			0.0149216i
$223$		−	19.8794i		−	1.33122i	−0.746299	−	0.665611i	$-0.768171\pi$
$223$		−	19.8794i		−	1.33122i	0.746299	−	0.665611i	$-0.231829\pi$
$224$	−5.28253			−0.352954
$225$	4.62582	−	14.0836i	0.308388	−	0.938906i
$226$	−15.4664			−1.02881
$227$		−	27.3022i		−	1.81211i	−0.423163	−	0.906054i	$-0.639080\pi$
$227$		−	27.3022i		−	1.81211i	0.423163	−	0.906054i	$-0.360920\pi$
$228$		0			0
$229$	14.6429			0.967633			0.483816	−	0.875170i	$-0.339250\pi$
$229$	14.6429			0.967633			0.483816	+	0.875170i	$0.339250\pi$
$230$	−3.73389	+	2.70373i	−0.246205	+	0.178279i
$231$	−0.361026			−0.0237538
$232$		−	0.423711i		−	0.0278180i
$233$			6.62933i			0.434302i	0.976138	+	0.217151i	$0.0696764\pi$
$233$			6.62933i			0.434302i	−0.976138	+	0.217151i	$0.930324\pi$
$234$	27.7236			1.81235
$235$	−10.3543	−	14.2994i	−0.675439	−	0.932791i
$236$	18.7122			1.21806
$237$		−	2.78686i		−	0.181026i
$238$		−	6.88557i		−	0.446325i
$239$	12.6792			0.820148			0.410074	−	0.912052i	$-0.365503\pi$
$239$	12.6792			0.820148			0.410074	+	0.912052i	$0.365503\pi$
$240$	1.05359	+	1.45502i	0.0680090	+	0.0939214i
$241$	−14.1138			−0.909151			−0.454575	−	0.890708i	$-0.650209\pi$
$241$	−14.1138			−0.909151			−0.454575	+	0.890708i	$0.650209\pi$
$242$		−	5.74893i		−	0.369555i
$243$		−	4.98899i		−	0.320044i
$244$	13.8122			0.884237
$245$	11.8475	−	8.57887i	0.756912	−	0.548084i
$246$	−2.48033			−0.158140
$247$		0			0
$248$		−	0.0805392i		−	0.00511425i
$249$	2.66199			0.168696
$250$	20.8920	−	6.67774i	1.32133	−	0.422338i
$251$	6.97395			0.440192			0.220096	−	0.975478i	$-0.429363\pi$
$251$	6.97395			0.440192			0.220096	+	0.975478i	$0.429363\pi$
$252$			3.71067i			0.233750i
$253$			2.98532i			0.187686i
$254$	−30.9455			−1.94169
$255$	−1.76234	+	1.27612i	−0.110362	+	0.0799135i
$256$	18.1416			1.13385
$257$		−	15.7808i		−	0.984379i	−0.870488	−	0.492189i	$-0.836197\pi$
$257$		−	15.7808i		−	0.984379i	0.870488	−	0.492189i	$-0.163803\pi$
$258$		−	2.07299i		−	0.129059i
$259$	0.408782			0.0254005
$260$	11.5555	+	15.9583i	0.716642	+	0.989692i
$261$	−4.22789			−0.261700
$262$		−	7.97703i		−	0.492822i
$263$			19.8933i			1.22667i	0.789822	+	0.613336i	$0.210173\pi$
$263$			19.8933i			1.22667i	−0.789822	+	0.613336i	$0.789827\pi$
$264$	0.158432			0.00975082
$265$	−9.03357	−	12.4755i	−0.554928	−	0.766363i
$266$		0			0
$267$		−	1.54632i		−	0.0946331i
$268$		−	7.61107i		−	0.464920i
$269$	−11.3590			−0.692568			−0.346284	−	0.938130i	$-0.612557\pi$
$269$	−11.3590			−0.692568			−0.346284	+	0.938130i	$0.612557\pi$
$270$	3.97805	−	2.88053i	0.242097	−	0.175303i
$271$	23.8877			1.45107			0.725536	−	0.688184i	$-0.241592\pi$
$271$	23.8877			1.45107			0.725536	+	0.688184i	$0.241592\pi$
$272$			22.1871i			1.34529i
$273$			0.605796i			0.0366645i
$274$	−5.12416			−0.309562
$275$	4.43223	−	13.4942i	0.267273	−	0.813731i
$276$	−0.364653			−0.0219496
$277$		−	4.69303i		−	0.281977i	−0.990011	−	0.140988i	$-0.954972\pi$
$277$		−	4.69303i		−	0.281977i	0.990011	−	0.140988i	$-0.0450280\pi$
$278$		−	17.5996i		−	1.05555i
$279$	−0.803640			−0.0481127
$280$	0.364346	−	0.263825i	0.0217738	−	0.0157665i
$281$	−22.4556			−1.33959			−0.669795	−	0.742546i	$-0.733618\pi$
$281$	−22.4556			−1.33959			−0.669795	+	0.742546i	$0.733618\pi$
$282$		−	2.90740i		−	0.173133i
$283$			10.8830i			0.646926i	0.946241	+	0.323463i	$0.104847\pi$
$283$			10.8830i			0.646926i	−0.946241	+	0.323463i	$0.895153\pi$
$284$	−14.0590			−0.834250
$285$		0			0
$286$	26.5634			1.57073
$287$			4.56048i			0.269197i
$288$		−	23.1313i		−	1.36303i
$289$	−9.87320			−0.580777
$290$	−3.66884	−	5.06672i	−0.215442	−	0.297528i
$291$	−1.07528			−0.0630340
$292$		−	29.8122i		−	1.74462i
$293$			12.4712i			0.728576i	0.931286	+	0.364288i	$0.118688\pi$
$293$			12.4712i			0.728576i	−0.931286	+	0.364288i	$0.881312\pi$
$294$	2.40887			0.140488
$295$	−18.3333	+	13.2753i	−1.06741	+	0.772916i
$296$	−0.179389			−0.0104268
$297$		−	3.18054i		−	0.184553i
$298$			3.39008i			0.196382i
$299$	5.00932			0.289697
$300$	1.64830	+	0.541391i	0.0951646	+	0.0312572i
$301$	−3.81151			−0.219692
$302$		−	21.7244i		−	1.25010i
$303$			0.379605i			0.0218077i
$304$		0			0
$305$	−13.5326	+	9.79900i	−0.774872	+	0.561089i
$306$	30.1508			1.72360
$307$		−	4.17858i		−	0.238484i	−0.992865	−	0.119242i	$-0.961954\pi$
$307$		−	4.17858i		−	0.238484i	0.992865	−	0.119242i	$-0.0380465\pi$
$308$			3.55538i			0.202586i
$309$	3.42302			0.194729
$310$	−0.697376	−	0.963086i	−0.0396083	−	0.0546996i
$311$	−12.0909			−0.685611			−0.342806	−	0.939406i	$-0.611377\pi$
$311$	−12.0909			−0.685611			−0.342806	+	0.939406i	$0.611377\pi$
$312$		−	0.265846i		−	0.0150506i
$313$		−	9.57859i		−	0.541414i	−0.962662	−	0.270707i	$-0.912743\pi$
$313$		−	9.57859i		−	0.541414i	0.962662	−	0.270707i	$-0.0872574\pi$
$314$	−3.85414			−0.217502
$315$	−2.63251	−	3.63553i	−0.148325	−	0.204839i
$316$	−27.4449			−1.54390
$317$			11.1692i			0.627324i	0.949535	+	0.313662i	$0.101556\pi$
$317$			11.1692i			0.627324i	−0.949535	+	0.313662i	$0.898444\pi$
$318$		−	2.53655i		−	0.142243i
$319$	−4.05095			−0.226810
$320$	12.2177	−	8.84688i	0.682989	−	0.494556i
$321$	1.16631			0.0650970
$322$			1.39588i			0.0777893i
$323$		0			0
$324$	−16.0530			−0.891833
$325$	−22.6430	−	7.43720i	−1.25601	−	0.412542i
$326$	−39.4926			−2.18729
$327$		−	3.00118i		−	0.165965i
$328$		−	2.00131i		−	0.110504i
$329$	−5.34570			−0.294718
$330$	1.89453	−	1.37184i	0.104290	−	0.0755172i
$331$	21.6878			1.19207			0.596034	−	0.802959i	$-0.296742\pi$
$331$	21.6878			1.19207			0.596034	+	0.802959i	$0.296742\pi$
$332$		−	26.2151i		−	1.43874i
$333$			1.78999i			0.0980909i
$334$	−35.0307			−1.91679
$335$	5.39962	+	7.45696i	0.295013	+	0.407417i
$336$	0.543947			0.0296747
$337$		−	0.0528499i		−	0.00287892i	−0.999999	−	0.00143946i	$-0.999542\pi$
$337$		−	0.0528499i		−	0.00287892i	0.999999	−	0.00143946i	$-0.000458194\pi$
$338$		−	19.0699i		−	1.03727i
$339$	1.47988			0.0803758
$340$	12.5672	+	17.3554i	0.681550	+	0.941230i
$341$	−0.770008			−0.0416983
$342$		0			0
$343$		−	9.16856i		−	0.495056i
$344$	1.67264			0.0901825
$345$	0.357270	−	0.258701i	0.0192348	−	0.0139280i
$346$	−5.34029			−0.287096
$347$			25.3863i			1.36281i	0.731908	+	0.681403i	$0.238630\pi$
$347$			25.3863i			1.36281i	−0.731908	+	0.681403i	$0.761370\pi$
$348$		−	0.494819i		−	0.0265251i
$349$	15.6199			0.836114			0.418057	−	0.908421i	$-0.362711\pi$
$349$	15.6199			0.836114			0.418057	+	0.908421i	$0.362711\pi$
$350$	2.07242	−	6.30962i	0.110776	−	0.337263i
$351$	−5.33689			−0.284862
$352$		−	22.1633i		−	1.18131i
$353$		−	12.4713i		−	0.663779i	−0.943318	−	0.331890i	$-0.892314\pi$
$353$		−	12.4713i		−	0.663779i	0.943318	−	0.331890i	$-0.107686\pi$
$354$	−3.72758			−0.198119
$355$	13.7744	−	9.97409i	0.731067	−	0.529370i
$356$	−15.2281			−0.807087
$357$			0.658832i			0.0348691i
$358$			15.1377i			0.800051i
$359$	33.6430			1.77561			0.887804	−	0.460223i	$-0.152230\pi$
$359$	33.6430			1.77561			0.887804	+	0.460223i	$0.152230\pi$
$360$	1.15524	+	1.59541i	0.0608868	+	0.0840855i
$361$		0			0
$362$			2.09989i			0.110368i
$363$			0.550075i			0.0288714i
$364$	5.96586			0.312696
$365$	21.1500	+	29.2085i	1.10704	+	1.52884i
$366$	−2.75147			−0.143822
$367$		−	25.6100i		−	1.33683i	−0.743787	−	0.668416i	$-0.766973\pi$
$367$		−	25.6100i		−	1.33683i	0.743787	−	0.668416i	$-0.233027\pi$
$368$		−	4.49789i		−	0.234469i
$369$	−19.9696			−1.03957
$370$	−2.14513	+	1.55330i	−0.111520	+	0.0807524i
$371$	−4.66384			−0.242134
$372$		−	0.0940555i		−	0.00487655i
$373$		−	21.7610i		−	1.12674i	−0.826204	−	0.563372i	$-0.809504\pi$
$373$		−	21.7610i		−	1.12674i	0.826204	−	0.563372i	$-0.190496\pi$
$374$	28.8890			1.49381
$375$	−1.99901	+	0.638947i	−0.103228	+	0.0329951i
$376$	2.34590			0.120980
$377$			6.79743i			0.350085i
$378$		−	1.48716i		−	0.0764911i
$379$	−6.63029			−0.340575			−0.170288	−	0.985394i	$-0.554470\pi$
$379$	−6.63029			−0.340575			−0.170288	+	0.985394i	$0.554470\pi$
$380$		0			0
$381$	2.96096			0.151695
$382$			10.5601i			0.540303i
$383$			27.0219i			1.38075i	0.723450	+	0.690377i	$0.242555\pi$
$383$			27.0219i			1.38075i	−0.723450	+	0.690377i	$0.757445\pi$
$384$	−0.444900			−0.0227037
$385$	−2.52234	−	3.48338i	−0.128550	−	0.177530i
$386$	30.3484			1.54469
$387$		−	16.6900i		−	0.848399i
$388$			10.5893i			0.537591i
$389$	−25.9896			−1.31773			−0.658863	−	0.752263i	$-0.728962\pi$
$389$	−25.9896			−1.31773			−0.658863	+	0.752263i	$0.728962\pi$
$390$	−2.30192	−	3.17898i	−0.116562	−	0.160974i
$391$	5.44788			0.275511
$392$			1.94365i			0.0981693i
$393$			0.763266i			0.0385017i
$394$	−41.6539			−2.09849
$395$	26.8892	−	19.4706i	1.35294	−	0.979672i
$396$	−15.5684			−0.782341
$397$			21.3475i			1.07140i	0.844409	+	0.535699i	$0.179952\pi$
$397$			21.3475i			1.07140i	−0.844409	+	0.535699i	$0.820048\pi$
$398$		−	14.8726i		−	0.745494i
$399$		0			0
$400$	−6.67789	+	20.3313i	−0.333894	+	1.01656i
$401$	−26.0611			−1.30143			−0.650716	−	0.759321i	$-0.725531\pi$
$401$	−26.0611			−1.30143			−0.650716	+	0.759321i	$0.725531\pi$
$402$			1.51617i			0.0756196i
$403$			1.29206i			0.0643621i
$404$	3.73834			0.185989
$405$	15.7279	−	11.3887i	0.781528	−	0.565909i
$406$	−1.89415			−0.0940049
$407$			1.71508i			0.0850133i
$408$		−	0.289121i		−	0.0143136i
$409$	−23.3472			−1.15444			−0.577222	−	0.816587i	$-0.695863\pi$
$409$	−23.3472			−1.15444			−0.577222	+	0.816587i	$0.695863\pi$
$410$	−17.3290	−	23.9316i	−0.855820	−	1.18190i
$411$	0.490296			0.0241845
$412$		−	33.7097i		−	1.66076i
$413$			6.85374i			0.337250i
$414$	−6.11232			−0.300404
$415$	18.5982	+	25.6843i	0.912948	+	1.26079i
$416$	−37.1896			−1.82337
$417$			1.68398i			0.0824648i
$418$		0			0
$419$	−21.9951			−1.07453			−0.537265	−	0.843413i	$-0.680543\pi$
$419$	−21.9951			−1.07453			−0.537265	+	0.843413i	$0.680543\pi$
$420$	0.425491	−	0.308100i	0.0207618	−	0.0150338i
$421$	−3.73114			−0.181845			−0.0909223	−	0.995858i	$-0.528982\pi$
$421$	−3.73114			−0.181845			−0.0909223	+	0.995858i	$0.528982\pi$
$422$			26.0898i			1.27003i
$423$		−	23.4079i		−	1.13813i
$424$	2.04667			0.0993951
$425$	−24.6254	−	8.08831i	−1.19451	−	0.392341i
$426$	2.80064			0.135691
$427$			5.05902i			0.244823i
$428$		−	11.4858i		−	0.555185i
$429$	−2.54167			−0.122713
$430$	20.0013	−	14.4831i	0.964550	−	0.698436i
$431$	24.9141			1.20007			0.600035	−	0.799974i	$-0.295153\pi$
$431$	24.9141			1.20007			0.600035	+	0.799974i	$0.295153\pi$
$432$			4.79201i			0.230556i
$433$		−	10.9722i		−	0.527292i	−0.964619	−	0.263646i	$-0.915075\pi$
$433$		−	10.9722i		−	0.527292i	0.964619	−	0.263646i	$-0.0849251\pi$
$434$	−0.360041			−0.0172825
$435$	0.351046	+	0.484799i	0.0168314	+	0.0232444i
$436$	−29.5555			−1.41545
$437$		0			0
$438$			5.93875i			0.283765i
$439$	−8.51973			−0.406624			−0.203312	−	0.979114i	$-0.565171\pi$
$439$	−8.51973			−0.406624			−0.203312	+	0.979114i	$0.565171\pi$
$440$	1.10690	+	1.52864i	0.0527693	+	0.0728751i
$441$	19.3943			0.923536
$442$		−	48.4752i		−	2.30573i
$443$			9.41714i			0.447422i	0.974656	+	0.223711i	$0.0718171\pi$
$443$			9.41714i			0.447422i	−0.974656	+	0.223711i	$0.928183\pi$
$444$	−0.209495			−0.00994218
$445$	14.9197	−	10.8035i	0.707264	−	0.512134i
$446$	38.9988			1.84665
$447$		−	0.324373i		−	0.0153423i
$448$		−	4.56746i		−	0.215792i
$449$	9.72743			0.459066			0.229533	−	0.973301i	$-0.426280\pi$
$449$	9.72743			0.459066			0.229533	+	0.973301i	$0.426280\pi$
$450$	27.6288	+	9.07479i	1.30243	+	0.427790i
$451$	−19.1339			−0.900978
$452$		−	14.5738i		−	0.685492i
$453$			2.07865i			0.0976636i
$454$	53.5606			2.51372
$455$	−5.84506	+	4.23244i	−0.274021	+	0.198420i
$456$		0			0
$457$		−	10.4686i		−	0.489700i	−0.969561	−	0.244850i	$-0.921261\pi$
$457$		−	10.4686i		−	0.489700i	0.969561	−	0.244850i	$-0.0787387\pi$
$458$			28.7261i			1.34228i
$459$	−5.80412			−0.270913
$460$	−2.54768	−	3.51838i	−0.118786	−	0.164045i
$461$	−22.6739			−1.05603			−0.528014	−	0.849236i	$-0.677063\pi$
$461$	−22.6739			−1.05603			−0.528014	+	0.849236i	$0.677063\pi$
$462$		−	0.708251i		−	0.0329508i
$463$		−	35.6376i		−	1.65622i	−0.560566	−	0.828110i	$-0.689416\pi$
$463$		−	35.6376i		−	1.65622i	0.560566	−	0.828110i	$-0.310584\pi$
$464$	6.10344			0.283345
$465$	0.0667271	+	0.0921510i	0.00309439	+	0.00427340i
$466$	−13.0052			−0.602456
$467$		−	2.90160i		−	0.134270i	−0.997744	−	0.0671350i	$-0.978614\pi$
$467$		−	2.90160i		−	0.134270i	0.997744	−	0.0671350i	$-0.0213858\pi$
$468$			26.1235i			1.20756i
$469$	2.78771			0.128725
$470$	28.0522	−	20.3127i	1.29395	−	0.936957i
$471$	0.368776			0.0169923
$472$		−	3.00768i		−	0.138440i
$473$		−	15.9915i		−	0.735290i
$474$	5.46718			0.251116
$475$		0			0
$476$	6.48816			0.297384
$477$		−	20.4222i		−	0.935067i
$478$			24.8736i			1.13769i
$479$	−29.3510			−1.34108			−0.670540	−	0.741874i	$-0.733937\pi$
$479$	−29.3510			−1.34108			−0.670540	+	0.741874i	$0.733937\pi$
$480$	−2.65240	+	1.92062i	−0.121065	+	0.0876639i
$481$	2.87787			0.131220
$482$		−	27.6881i		−	1.26116i
$483$		−	0.133562i		−	0.00607728i
$484$	5.41712			0.246233
$485$	−7.51253	−	10.3749i	−0.341126	−	0.471100i
$486$	9.78725			0.443959
$487$		−	3.41683i		−	0.154831i	−0.996999	−	0.0774157i	$-0.975333\pi$
$487$		−	3.41683i		−	0.154831i	0.996999	−	0.0774157i	$-0.0246669\pi$
$488$		−	2.22009i		−	0.100499i
$489$	3.77877			0.170882
$490$	16.8298	+	23.2422i	0.760292	+	1.04997i
$491$	−25.1863			−1.13664			−0.568320	−	0.822808i	$-0.692406\pi$
$491$	−25.1863			−1.13664			−0.568320	+	0.822808i	$0.692406\pi$
$492$		−	2.33718i		−	0.105368i
$493$			7.39253i			0.332943i
$494$		0			0
$495$	15.2532	−	11.0449i	0.685579	−	0.496431i
$496$	1.16015			0.0520921
$497$		−	5.14941i		−	0.230983i
$498$			5.22220i			0.234013i
$499$	34.7335			1.55488			0.777442	−	0.628955i	$-0.216517\pi$
$499$	34.7335			1.55488			0.777442	+	0.628955i	$0.216517\pi$
$500$	6.29233	+	19.6862i	0.281401	+	0.880393i
$501$	3.35184			0.149749
$502$			13.6813i			0.610626i
$503$		−	22.4582i		−	1.00136i	−0.865631	−	0.500682i	$-0.833083\pi$
$503$		−	22.4582i		−	1.00136i	0.865631	−	0.500682i	$-0.166917\pi$
$504$	0.596429			0.0265670
$505$	−3.66264	+	2.65214i	−0.162985	+	0.118019i
$506$	−5.85652			−0.260354
$507$			1.82467i			0.0810363i
$508$		−	29.1594i		−	1.29374i
$509$	2.34801			0.104074			0.0520369	−	0.998645i	$-0.483429\pi$
$509$	2.34801			0.104074			0.0520369	+	0.998645i	$0.483429\pi$
$510$	−2.50345	−	3.45730i	−0.110855	−	0.153092i
$511$	10.9193			0.483042
$512$			30.8493i			1.36336i
$513$		0			0
$514$	30.9583			1.36551
$515$	23.9152	+	33.0272i	1.05383	+	1.45535i
$516$	1.95334			0.0859911
$517$		−	22.4283i		−	0.986396i
$518$			0.801937i			0.0352351i
$519$	0.510975			0.0224293
$520$	2.56503	−	1.85736i	0.112484	−	0.0814504i
$521$	−1.52393			−0.0667645			−0.0333822	−	0.999443i	$-0.510628\pi$
$521$	−1.52393			−0.0667645			−0.0333822	+	0.999443i	$0.510628\pi$
$522$		−	8.29415i		−	0.363025i
$523$			13.4269i			0.587117i	0.955941	+	0.293559i	$0.0948396\pi$
$523$			13.4269i			0.587117i	−0.955941	+	0.293559i	$0.905160\pi$
$524$	7.51662			0.328365
$525$	−0.198296	+	0.603724i	−0.00865433	+	0.0263487i
$526$	−39.0261			−1.70162
$527$			1.40518i			0.0612105i
$528$			2.28217i			0.0993187i
$529$	21.8956			0.951982
$530$	24.4740	−	17.7218i	1.06308	−	0.769785i
$531$	−30.0114			−1.30238
$532$		0			0
$533$			32.1063i			1.39068i
$534$	3.03352			0.131273
$535$	8.14850	+	11.2532i	0.352290	+	0.486518i
$536$	−1.22335			−0.0528408
$537$		−	1.44842i		−	0.0625039i
$538$		−	22.2837i		−	0.960718i
$539$	18.5826			0.800409
$540$	2.71427	+	3.74845i	0.116804	+	0.161308i
$541$	16.2283			0.697709			0.348854	−	0.937177i	$-0.386571\pi$
$541$	16.2283			0.697709			0.348854	+	0.937177i	$0.386571\pi$
$542$			46.8621i			2.01290i
$543$		−	0.200924i		−	0.00862245i
$544$	−40.4455			−1.73409
$545$	28.9570	−	20.9679i	1.24038	−	0.898168i
$546$	−1.18843			−0.0508602
$547$		−	9.91482i		−	0.423927i	−0.977278	−	0.211964i	$-0.932014\pi$
$547$		−	9.91482i		−	0.423927i	0.977278	−	0.211964i	$-0.0679858\pi$
$548$		−	4.82841i		−	0.206260i
$549$	−22.1526			−0.945449
$550$	26.4725	+	8.69501i	1.12879	+	0.370757i
$551$		0			0
$552$			0.0586120i			0.00249469i
$553$		−	10.0523i		−	0.427466i
$554$	9.20665			0.391153
$555$	0.205253	−	0.148625i	0.00871250	−	0.00630877i
$556$	16.5838			0.703308
$557$			22.8831i			0.969589i	0.874628	+	0.484795i	$0.161106\pi$
$557$			22.8831i			0.969589i	−0.874628	+	0.484795i	$0.838894\pi$
$558$		−	1.57656i		−	0.0667410i
$559$	−26.8335			−1.13493
$560$	3.80032	+	5.24830i	0.160593	+	0.221781i
$561$	−2.76418			−0.116704
$562$		−	44.0528i		−	1.85826i
$563$			12.4801i			0.525972i	0.964800	+	0.262986i	$0.0847074\pi$
$563$			12.4801i			0.525972i	−0.964800	+	0.262986i	$0.915293\pi$
$564$	2.73959			0.115358
$565$	10.3393	+	14.2787i	0.434976	+	0.600708i
$566$	−21.3499			−0.897403
$567$		−	5.87974i		−	0.246926i
$568$			2.25976i			0.0948173i
$569$	1.90233			0.0797500			0.0398750	−	0.999205i	$-0.487304\pi$
$569$	1.90233			0.0797500			0.0398750	+	0.999205i	$0.487304\pi$
$570$		0			0
$571$	−12.2153			−0.511193			−0.255596	−	0.966784i	$-0.582272\pi$
$571$	−12.2153			−0.511193			−0.255596	+	0.966784i	$0.582272\pi$
$572$			25.0302i			1.04657i
$573$		−	1.01042i		−	0.0422111i
$574$	−8.94661			−0.373424
$575$	4.99219	+	1.63970i	0.208189	+	0.0683804i
$576$	20.0001			0.833339
$577$			25.2903i			1.05285i	0.850221	+	0.526425i	$0.176468\pi$
$577$			25.2903i			1.05285i	−0.850221	+	0.526425i	$0.823532\pi$
$578$		−	19.3690i		−	0.805643i
$579$	−2.90383			−0.120679
$580$	4.77429	−	3.45709i	0.198242	−	0.143548i
$581$	9.60184			0.398351
$582$		−	2.10945i		−	0.0874396i
$583$		−	19.5675i		−	0.810403i
$584$	−4.79181			−0.198287
$585$	−18.5332	−	25.5945i	−0.766252	−	1.05820i
$586$	−24.4657			−1.01067
$587$			6.32179i			0.260928i	0.991453	+	0.130464i	$0.0416467\pi$
$587$			6.32179i			0.260928i	−0.991453	+	0.130464i	$0.958353\pi$
$588$			2.26984i			0.0936067i
$589$		0			0
$590$	−26.0430	−	35.9658i	−1.07217	−	1.48069i
$591$	3.98557			0.163945
$592$		−	2.58405i		−	0.106204i
$593$			0.583715i			0.0239703i	0.999928	+	0.0119851i	$0.00381508\pi$
$593$			0.583715i			0.0239703i	−0.999928	+	0.0119851i	$0.996185\pi$
$594$	6.23948			0.256009
$595$	−6.35678	+	4.60298i	−0.260603	+	0.188704i
$596$	−3.19442			−0.130848
$597$			1.42305i			0.0582416i
$598$			9.82714i			0.401862i
$599$	42.5221			1.73740			0.868702	−	0.495335i	$-0.164955\pi$
$599$	42.5221			1.73740			0.868702	+	0.495335i	$0.164955\pi$
$600$	0.0870197	−	0.264937i	0.00355256	−	0.0108160i
$601$	−16.2762			−0.663920			−0.331960	−	0.943294i	$-0.607710\pi$
$601$	−16.2762			−0.663920			−0.331960	+	0.943294i	$0.607710\pi$
$602$		−	7.47731i		−	0.304752i
$603$			12.2069i			0.497105i
$604$	20.4705			0.832932
$605$	−5.30743	+	3.84314i	−0.215778	+	0.156246i
$606$	−0.744698			−0.0302513
$607$		−	6.86749i		−	0.278743i	−0.990240	−	0.139371i	$-0.955492\pi$
$607$		−	6.86749i		−	0.278743i	0.990240	−	0.139371i	$-0.0445082\pi$
$608$		0			0
$609$	0.181238			0.00734412
$610$	−19.2234	−	26.5478i	−0.778332	−	1.07489i
$611$	−37.6343			−1.52252
$612$			28.4106i			1.14843i
$613$			5.84296i			0.235995i	0.993014	+	0.117997i	$0.0376475\pi$
$613$			5.84296i			0.235995i	−0.993014	+	0.117997i	$0.962353\pi$
$614$	8.19741			0.330821
$615$	1.65809	+	2.28985i	0.0668608	+	0.0923357i
$616$	0.571468			0.0230251
$617$			38.5625i			1.55247i	0.630444	+	0.776234i	$0.282873\pi$
$617$			38.5625i			1.55247i	−0.630444	+	0.776234i	$0.717127\pi$
$618$			6.71517i			0.270124i
$619$	−10.9201			−0.438917			−0.219459	−	0.975622i	$-0.570429\pi$
$619$	−10.9201			−0.438917			−0.219459	+	0.975622i	$0.570429\pi$
$620$	0.907500	−	0.657126i	0.0364461	−	0.0263908i
$621$	1.17664			0.0472170
$622$		−	23.7195i		−	0.951067i
$623$		−	5.57760i		−	0.223462i
$624$	3.82944			0.153300
$625$	−20.1312	−	14.8235i	−0.805246	−	0.592941i
$626$	18.7910			0.751039
$627$		0			0
$628$		−	3.63169i		−	0.144920i
$629$	3.12982			0.124794
$630$	7.13208	−	5.16438i	0.284149	−	0.205754i
$631$	8.11401			0.323014			0.161507	−	0.986872i	$-0.448365\pi$
$631$	8.11401			0.323014			0.161507	+	0.986872i	$0.448365\pi$
$632$			4.41131i			0.175473i
$633$		−	2.49635i		−	0.0992210i
$634$	−21.9114			−0.870212
$635$	20.6870	+	28.5690i	0.820938	+	1.13373i
$636$	2.39015			0.0947755
$637$		−	31.1813i		−	1.23545i
$638$		−	7.94704i		−	0.314626i
$639$	22.5484			0.892002
$640$	−3.10833	−	4.29264i	−0.122867	−	0.169682i
$641$	−13.9078			−0.549323			−0.274662	−	0.961541i	$-0.588566\pi$
$641$	−13.9078			−0.549323			−0.274662	+	0.961541i	$0.588566\pi$
$642$			2.28803i			0.0903013i
$643$		−	38.1086i		−	1.50286i	−0.659815	−	0.751428i	$-0.729365\pi$
$643$		−	38.1086i		−	1.50286i	0.659815	−	0.751428i	$-0.270635\pi$
$644$	−1.31531			−0.0518306
$645$	−1.91379	+	1.38579i	−0.0753554	+	0.0545653i
$646$		0			0
$647$			28.6072i			1.12466i	0.826912	+	0.562332i	$0.190096\pi$
$647$			28.6072i			1.12466i	−0.826912	+	0.562332i	$0.809904\pi$
$648$			2.58025i			0.101362i
$649$	−28.7554			−1.12875
$650$	14.5901	−	44.4204i	0.572270	−	1.74231i
$651$	0.0344498			0.00135019
$652$		−	37.2132i		−	1.45738i
$653$		−	11.8861i		−	0.465139i	−0.972580	−	0.232569i	$-0.925287\pi$
$653$		−	11.8861i		−	0.465139i	0.972580	−	0.232569i	$-0.0747132\pi$
$654$	5.88762			0.230224
$655$	−7.36442	+	5.33262i	−0.287752	+	0.208363i
$656$	28.8283			1.12556
$657$			47.8139i			1.86540i
$658$		−	10.4870i		−	0.408827i
$659$	−36.9129			−1.43792			−0.718961	−	0.695051i	$-0.755382\pi$
$659$	−36.9129			−1.43792			−0.718961	+	0.695051i	$0.755382\pi$
$660$	1.29266	+	1.78518i	0.0503167	+	0.0694881i
$661$	9.04095			0.351652			0.175826	−	0.984421i	$-0.443740\pi$
$661$	9.04095			0.351652			0.175826	+	0.984421i	$0.443740\pi$
$662$			42.5465i			1.65361i
$663$			4.63825i			0.180135i
$664$	−4.21365			−0.163521
$665$		0			0
$666$	−3.51155			−0.136070
$667$		−	1.49865i		−	0.0580280i
$668$		−	33.0088i		−	1.27715i
$669$	−3.73152			−0.144269
$670$	−14.6288	+	10.5928i	−0.565161	+	0.409236i
$671$	−21.2255			−0.819401
$672$			0.991575i			0.0382508i
$673$		−	39.8365i		−	1.53558i	−0.640700	−	0.767791i	$-0.721356\pi$
$673$		−	39.8365i		−	1.53558i	0.640700	−	0.767791i	$-0.278644\pi$
$674$	0.103679			0.00399358
$675$	−5.31863	−	1.74693i	−0.204714	−	0.0672392i
$676$	17.9692			0.691125
$677$		−	18.0388i		−	0.693288i	−0.937997	−	0.346644i	$-0.887321\pi$
$677$		−	18.0388i		−	0.693288i	0.937997	−	0.346644i	$-0.112679\pi$
$678$			2.90318i			0.111496i
$679$	−3.87856			−0.148845
$680$	2.78960	−	2.01996i	0.106976	−	0.0774620i
$681$	−5.12484			−0.196384
$682$		−	1.51058i		−	0.0578430i
$683$		−	15.4271i		−	0.590301i	−0.955451	−	0.295151i	$-0.904630\pi$
$683$		−	15.4271i		−	0.590301i	0.955451	−	0.295151i	$-0.0953698\pi$
$684$		0			0
$685$	3.42549	+	4.73065i	0.130881	+	0.180749i
$686$	17.9866			0.686732
$687$		−	2.74860i		−	0.104866i
$688$			24.0939i			0.918570i
$689$	−32.8339			−1.25087
$690$	0.507512	+	0.700881i	0.0193207	+	0.0266821i
$691$	3.03824			0.115580			0.0577901	−	0.998329i	$-0.481595\pi$
$691$	3.03824			0.115580			0.0577901	+	0.998329i	$0.481595\pi$
$692$		−	5.03206i		−	0.191290i
$693$		−	5.70225i		−	0.216611i
$694$	−49.8020			−1.89046
$695$	−16.2480	+	11.7652i	−0.616321	+	0.446281i
$696$	−0.0795340			−0.00301473
$697$			34.9171i			1.32258i
$698$			30.6427i			1.15984i
$699$	1.24438			0.0470668
$700$	5.94545	+	1.95281i	0.224717	+	0.0738092i
$701$	−45.7925			−1.72956			−0.864780	−	0.502151i	$-0.832542\pi$
$701$	−45.7925			−1.72956			−0.864780	+	0.502151i	$0.832542\pi$
$702$		−	10.4697i		−	0.395155i
$703$		0			0
$704$	19.1631			0.722238
$705$	−2.68412	+	1.94359i	−0.101090	+	0.0731996i
$706$	24.4658			0.920782
$707$			1.36924i			0.0514957i
$708$		−	3.51244i		−	0.132005i
$709$	−22.0549			−0.828289			−0.414144	−	0.910211i	$-0.635919\pi$
$709$	−22.0549			−0.828289			−0.414144	+	0.910211i	$0.635919\pi$
$710$	19.5669	+	27.0221i	0.734332	+	1.01412i
$711$	44.0172			1.65077
$712$			2.44766i			0.0917301i
$713$		−	0.284865i		−	0.0106683i
$714$	−1.29248			−0.0483698
$715$	−17.7575	−	24.5234i	−0.664094	−	0.917124i
$716$	−14.2640			−0.533070
$717$		−	2.37999i		−	0.0888822i
$718$			65.9998i			2.46309i
$719$	7.09458			0.264583			0.132292	−	0.991211i	$-0.457766\pi$
$719$	7.09458			0.264583			0.132292	+	0.991211i	$0.457766\pi$
$720$	−22.9814	+	16.6410i	−0.856468	+	0.620173i
$721$	12.3469			0.459822
$722$		0			0
$723$			2.64928i			0.0985277i
$724$	−1.97869			−0.0735374
$725$	−2.22501	+	6.77418i	−0.0826347	+	0.251587i
$726$	−1.07912			−0.0400499
$727$			28.2127i			1.04635i	0.852225	+	0.523176i	$0.175253\pi$
$727$			28.2127i			1.04635i	−0.852225	+	0.523176i	$0.824747\pi$
$728$		−	0.958914i		−	0.0355397i
$729$	25.1159			0.930219
$730$	−57.3004	+	41.4915i	−2.12078	+	1.53567i
$731$	−29.1827			−1.07936
$732$		−	2.59267i		−	0.0958278i
$733$		−	1.03586i		−	0.0382604i	−0.999817	−	0.0191302i	$-0.993910\pi$
$733$		−	1.03586i		−	0.0382604i	0.999817	−	0.0191302i	$-0.00608970\pi$
$734$	50.2410			1.85443
$735$	−1.61032	−	2.22388i	−0.0593977	−	0.0820291i
$736$	8.19932			0.302231
$737$			11.6961i			0.430830i
$738$		−	39.1757i		−	1.44208i
$739$	−19.4150			−0.714191			−0.357095	−	0.934068i	$-0.616233\pi$
$739$	−19.4150			−0.714191			−0.357095	+	0.934068i	$0.616233\pi$
$740$	−1.46365	−	2.02132i	−0.0538049	−	0.0743053i
$741$		0			0
$742$		−	9.14938i		−	0.335884i
$743$		−	12.7028i		−	0.466021i	−0.972474	−	0.233011i	$-0.925142\pi$
$743$		−	12.7028i		−	0.466021i	0.972474	−	0.233011i	$-0.0748577\pi$
$744$	−0.0151179			−0.000554248
$745$	3.12973	−	2.26626i	0.114665	−	0.0830293i
$746$	42.6901			1.56300
$747$			42.0449i			1.53834i
$748$			27.2216i			0.995319i
$749$	4.20690			0.153717
$750$	−1.25347	−	3.92160i	−0.0457702	−	0.143197i
$751$	4.61794			0.168511			0.0842555	−	0.996444i	$-0.473149\pi$
$751$	4.61794			0.168511			0.0842555	+	0.996444i	$0.473149\pi$
$752$			33.7920i			1.23227i
$753$		−	1.30907i		−	0.0477051i
$754$	−13.3350			−0.485632
$755$	−20.0560	+	14.5227i	−0.729912	+	0.528534i
$756$	1.40132			0.0509656
$757$		−	6.81005i		−	0.247515i	−0.992312	−	0.123758i	$-0.960505\pi$
$757$		−	6.81005i		−	0.247515i	0.992312	−	0.123758i	$-0.0394946\pi$
$758$		−	13.0071i		−	0.472439i
$759$	0.560370			0.0203401
$760$		0			0
$761$	24.4864			0.887632			0.443816	−	0.896118i	$-0.353624\pi$
$761$	24.4864			0.887632			0.443816	+	0.896118i	$0.353624\pi$
$762$			5.80873i			0.210428i
$763$		−	10.8253i		−	0.391902i
$764$	−9.95063			−0.360001
$765$	−20.1557	−	27.8353i	−0.728730	−	1.00639i
$766$	−53.0107			−1.91536
$767$			48.2511i			1.74225i
$768$		−	3.40533i		−	0.122879i
$769$	−2.99156			−0.107878			−0.0539391	−	0.998544i	$-0.517178\pi$
$769$	−2.99156			−0.107878			−0.0539391	+	0.998544i	$0.517178\pi$
$770$	6.83360	−	4.94825i	0.246266	−	0.178323i
$771$	−2.96218			−0.106680
$772$			28.5968i			1.02922i
$773$			19.7642i			0.710869i	0.934701	+	0.355434i	$0.115667\pi$
$773$			19.7642i			0.710869i	−0.934701	+	0.355434i	$0.884333\pi$
$774$	32.7419			1.17688
$775$	−0.422931	+	1.28764i	−0.0151921	+	0.0462534i
$776$	1.70206			0.0611003
$777$		−	0.0767318i		−	0.00275274i
$778$		−	50.9857i		−	1.82792i
$779$		0			0
$780$	2.99550	−	2.16906i	0.107256	−	0.0776649i
$781$	21.6048			0.773079
$782$			10.6875i			0.382184i
$783$			1.59665i			0.0570596i
$784$	−27.9978			−0.999921
$785$	2.57648	+	3.55815i	0.0919585	+	0.126996i
$786$	−1.49735			−0.0534088
$787$		−	23.5466i		−	0.839346i	−0.907675	−	0.419673i	$-0.862145\pi$
$787$		−	23.5466i		−	0.839346i	0.907675	−	0.419673i	$-0.137855\pi$
$788$		−	39.2498i		−	1.39822i
$789$	3.73413			0.132939
$790$	38.1968	+	52.7504i	1.35898	+	1.87677i
$791$	5.33795			0.189795
$792$			2.50236i			0.0889176i
$793$			35.6160i			1.26476i
$794$	−41.8788			−1.48622
$795$	−2.34175	+	1.69567i	−0.0830533	+	0.0601394i
$796$	14.0142			0.496719
$797$		−	5.96976i		−	0.211460i	−0.994395	−	0.105730i	$-0.966282\pi$
$797$		−	5.96976i		−	0.211460i	0.994395	−	0.105730i	$-0.0337179\pi$
$798$		0			0
$799$	−40.9291			−1.44797
$800$	−37.0624	−	12.1733i	−1.31035	−	0.430391i
$801$	24.4234			0.862958
$802$		−	51.1260i		−	1.80532i
$803$			45.8129i			1.61670i
$804$	−1.42866			−0.0503849
$805$	1.28868	−	0.933140i	0.0454200	−	0.0328889i
$806$	−2.53473			−0.0892819
$807$			2.13217i			0.0750559i
$808$		−	0.600876i		−	0.0211387i
$809$	25.9066			0.910829			0.455414	−	0.890280i	$-0.349491\pi$
$809$	25.9066			0.910829			0.455414	+	0.890280i	$0.349491\pi$
$810$	22.3420	+	30.8546i	0.785018	+	1.08412i
$811$	−27.6473			−0.970828			−0.485414	−	0.874284i	$-0.661331\pi$
$811$	−27.6473			−0.970828			−0.485414	+	0.874284i	$0.661331\pi$
$812$		−	1.78482i		−	0.0626350i
$813$		−	4.48391i		−	0.157258i
$814$	−3.36459			−0.117929
$815$	26.4007	+	36.4597i	0.924776	+	1.27713i
$816$	4.16470			0.145794
$817$		0			0
$818$		−	45.8018i		−	1.60142i
$819$	−9.56828			−0.334343
$820$	22.5504	−	16.3289i	0.787493	−	0.570228i
$821$	−10.3541			−0.361362			−0.180681	−	0.983542i	$-0.557830\pi$
$821$	−10.3541			−0.361362			−0.180681	+	0.983542i	$0.557830\pi$
$822$			0.961847i			0.0335483i
$823$		−	42.3497i		−	1.47622i	−0.674683	−	0.738108i	$-0.735719\pi$
$823$		−	42.3497i		−	1.47622i	0.674683	−	0.738108i	$-0.264281\pi$
$824$	−5.41829			−0.188755
$825$	−2.53297	−	0.831965i	−0.0881867	−	0.0289653i
$826$	−13.4455			−0.467827
$827$			22.5822i			0.785260i	0.919696	+	0.392630i	$0.128435\pi$
$827$			22.5822i			0.785260i	−0.919696	+	0.392630i	$0.871565\pi$
$828$		−	5.75954i		−	0.200158i
$829$	−12.6489			−0.439315			−0.219657	−	0.975577i	$-0.570494\pi$
$829$	−12.6489			−0.439315			−0.219657	+	0.975577i	$0.570494\pi$
$830$	−50.3868	+	36.4853i	−1.74895	+	1.26642i
$831$	−0.880920			−0.0305588
$832$		−	32.1554i		−	1.11479i
$833$		−	33.9111i		−	1.17495i
$834$	−3.30358			−0.114394
$835$	23.4179	+	32.3404i	0.810409	+	1.11919i
$836$		0			0
$837$			0.303492i			0.0104902i
$838$		−	43.1493i		−	1.49057i
$839$	46.1433			1.59304			0.796522	−	0.604610i	$-0.206671\pi$
$839$	46.1433			1.59304			0.796522	+	0.604610i	$0.206671\pi$
$840$	−0.0495221	−	0.0683907i	−0.00170867	−	0.00235970i
$841$	−26.9664			−0.929876
$842$		−	7.31964i		−	0.252252i
$843$			4.21511i			0.145176i
$844$	−24.5840			−0.846215
$845$	−17.6054	+	12.7482i	−0.605644	+	0.438550i
$846$	45.9210			1.57880
$847$			1.98413i			0.0681756i
$848$			29.4817i			1.01241i
$849$	2.04282			0.0701095
$850$	15.8674	−	48.3093i	0.544248	−	1.65700i
$851$	−0.634494			−0.0217502
$852$			2.63900i			0.0904105i
$853$		−	37.4633i		−	1.28272i	−0.767241	−	0.641359i	$-0.778371\pi$
$853$		−	37.4633i		−	1.28272i	0.767241	−	0.641359i	$-0.221629\pi$
$854$	−9.92463			−0.339614
$855$		0			0
$856$	−1.84615			−0.0631000
$857$		−	33.8342i		−	1.15575i	−0.816124	−	0.577876i	$-0.803882\pi$
$857$		−	33.8342i		−	1.15575i	0.816124	−	0.577876i	$-0.196118\pi$
$858$		−	4.98617i		−	0.170225i
$859$	21.2143			0.723822			0.361911	−	0.932213i	$-0.382124\pi$
$859$	21.2143			0.723822			0.361911	+	0.932213i	$0.382124\pi$
$860$	13.6472	+	18.8469i	0.465365	+	0.642675i
$861$	0.856039			0.0291737
$862$			48.8758i			1.66472i
$863$		−	29.1392i		−	0.991909i	−0.868348	−	0.495955i	$-0.834818\pi$
$863$		−	29.1392i		−	0.991909i	0.868348	−	0.495955i	$-0.165182\pi$
$864$	−8.73548			−0.297187
$865$	3.56997	+	4.93017i	0.121382	+	0.167631i
$866$	21.5250			0.731450
$867$			1.85328i			0.0629407i
$868$		−	0.339260i		−	0.0115152i
$869$	42.1751			1.43069
$870$	−0.951065	+	0.688672i	−0.0322441	+	0.0233482i
$871$	19.6258			0.664995
$872$			4.75055i			0.160874i
$873$		−	16.9836i		−	0.574806i
$874$		0			0
$875$	−7.21047	+	2.30470i	−0.243758	+	0.0779129i
$876$	−5.59599			−0.189071
$877$		−	6.43824i		−	0.217404i	−0.994074	−	0.108702i	$-0.965331\pi$
$877$		−	6.43824i		−	0.217404i	0.994074	−	0.108702i	$-0.0346694\pi$
$878$		−	16.7137i		−	0.564062i
$879$	2.34095			0.0789582
$880$	−22.0197	+	15.9446i	−0.742283	+	0.537491i
$881$	14.3999			0.485145			0.242573	−	0.970133i	$-0.422009\pi$
$881$	14.3999			0.485145			0.242573	+	0.970133i	$0.422009\pi$
$882$			38.0471i			1.28111i
$883$			25.8016i			0.868292i	0.900843	+	0.434146i	$0.142950\pi$
$883$			25.8016i			0.868292i	−0.900843	+	0.434146i	$0.857050\pi$
$884$	45.6773			1.53630
$885$	2.49188	+	3.44131i	0.0837635	+	0.115679i
$886$	−18.4743			−0.620655
$887$			25.9435i			0.871099i	0.900165	+	0.435549i	$0.143446\pi$
$887$			25.9435i			0.871099i	−0.900165	+	0.435549i	$0.856554\pi$
$888$			0.0336728i			0.00112999i
$889$	10.6803			0.358204
$890$	21.1939	+	29.2691i	0.710422	+	0.981103i
$891$	24.6689			0.826440
$892$			36.7479i			1.23041i
$893$		0			0
$894$	0.636346			0.0212826
$895$	13.9752	−	10.1195i	0.467138	−	0.338257i
$896$	−1.60476			−0.0536114
$897$		−	0.940291i		−	0.0313954i
$898$			19.0830i			0.636808i
$899$	0.386549			0.0128921
$900$	−8.55102	+	26.0341i	−0.285034	+	0.867805i
$901$	−35.7085			−1.18962
$902$		−	37.5362i		−	1.24982i
$903$			0.715452i			0.0238087i
$904$	−2.34249			−0.0779102
$905$	1.93862	−	1.40377i	0.0644420	−	0.0466628i
$906$	−4.07784			−0.135477
$907$			29.9257i			0.993665i	0.867846	+	0.496832i	$0.165504\pi$
$907$			29.9257i			0.993665i	−0.867846	+	0.496832i	$0.834496\pi$
$908$			50.4692i			1.67488i
$909$	−5.99569			−0.198864
$910$	−8.30308	−	11.4667i	−0.275244	−	0.380116i
$911$	−3.36120			−0.111362			−0.0556808	−	0.998449i	$-0.517733\pi$
$911$	−3.36120			−0.111362			−0.0556808	+	0.998449i	$0.517733\pi$
$912$		0			0
$913$			40.2853i			1.33325i
$914$	20.5370			0.679302
$915$	1.83935	+	2.54017i	0.0608071	+	0.0839755i
$916$	−27.0681			−0.894355
$917$			2.75312i			0.0909160i
$918$		−	11.3863i		−	0.375806i
$919$	−6.92467			−0.228424			−0.114212	−	0.993456i	$-0.536434\pi$
$919$	−6.92467			−0.228424			−0.114212	+	0.993456i	$0.536434\pi$
$920$	−0.565522	+	0.409497i	−0.0186447	+	0.0135007i
$921$	−0.784353			−0.0258453
$922$		−	44.4809i		−	1.46490i
$923$		−	36.2524i		−	1.19326i
$924$	0.667373			0.0219550
$925$	2.86803	+	0.942016i	0.0943002	+	0.0309733i
$926$	69.9128			2.29748
$927$			54.0650i			1.77573i
$928$			11.1261i			0.365233i
$929$	−27.3408			−0.897024			−0.448512	−	0.893777i	$-0.648046\pi$
$929$	−27.3408			−0.897024			−0.448512	+	0.893777i	$0.648046\pi$
$930$	−0.180779	+	0.130903i	−0.00592798	+	0.00429248i
$931$		0			0
$932$		−	12.2546i		−	0.401413i
$933$			2.26956i			0.0743020i
$934$	5.69227			0.186257
$935$	−19.3122	−	26.6704i	−0.631576	−	0.872215i
$936$	4.19892			0.137246
$937$			37.1376i			1.21323i	0.794995	+	0.606617i	$0.207474\pi$
$937$			37.1376i			1.21323i	−0.794995	+	0.606617i	$0.792526\pi$
$938$			5.46885i			0.178564i
$939$	−1.79798			−0.0586748
$940$	19.1404	+	26.4331i	0.624290	+	0.862153i
$941$	−50.6874			−1.65236			−0.826180	−	0.563406i	$-0.809491\pi$
$941$	−50.6874			−1.65236			−0.826180	+	0.563406i	$0.809491\pi$
$942$			0.723453i			0.0235714i
$943$		−	7.07858i		−	0.230510i
$944$	43.3248			1.41010
$945$	−1.37295	+	0.994160i	−0.0446620	+	0.0323400i
$946$	31.3717			1.01998
$947$		−	4.06669i		−	0.132150i	−0.997815	−	0.0660749i	$-0.978952\pi$
$947$		−	4.06669i		−	0.132150i	0.997815	−	0.0660749i	$-0.0210476\pi$
$948$			5.15163i			0.167317i
$949$	76.8732			2.49541
$950$		0			0
$951$	2.09655			0.0679852
$952$		−	1.04286i		−	0.0337994i
$953$			14.8332i			0.480495i	0.970712	+	0.240247i	$0.0772286\pi$
$953$			14.8332i			0.480495i	−0.970712	+	0.240247i	$0.922771\pi$
$954$	40.0636			1.29711
$955$	9.74914	−	7.05941i	0.315475	−	0.228437i
$956$	−23.4380			−0.758040
$957$			0.760397i			0.0245801i
$958$		−	57.5798i		−	1.86032i
$959$	1.76851			0.0571081
$960$	−1.66063	−	2.29336i	−0.0535967	−	0.0740178i
$961$	−30.9265			−0.997630
$962$			5.64573i			0.182026i
$963$			18.4213i			0.593619i
$964$	26.0900			0.840302
$965$	−20.2878	−	28.0178i	−0.653088	−	0.901924i
$966$	0.262018			0.00843028
$967$			56.7201i			1.82400i	0.410194	+	0.911998i	$0.365461\pi$
$967$			56.7201i			1.82400i	−0.410194	+	0.911998i	$0.634539\pi$
$968$		−	0.870712i		−	0.0279858i
$969$		0			0
$970$	20.3532	−	14.7379i	0.653501	−	0.473204i
$971$	12.5938			0.404154			0.202077	−	0.979370i	$-0.435231\pi$
$971$	12.5938			0.404154			0.202077	+	0.979370i	$0.435231\pi$
$972$			9.22236i			0.295807i
$973$			6.07415i			0.194728i
$974$	6.70304			0.214779
$975$	−1.39602	+	4.25028i	−0.0447085	+	0.136118i
$976$	31.9798			1.02365
$977$			36.8973i			1.18045i	0.807239	+	0.590224i	$0.200961\pi$
$977$			36.8973i			1.18045i	−0.807239	+	0.590224i	$0.799039\pi$
$978$			7.41309i			0.237044i
$979$	23.4013			0.747908
$980$	−21.9007	+	15.8584i	−0.699592	+	0.506579i
$981$	47.4022			1.51344
$982$		−	49.4097i		−	1.57673i
$983$			9.56063i			0.304937i	0.988308	+	0.152468i	$0.0487222\pi$
$983$			9.56063i			0.304937i	−0.988308	+	0.152468i	$0.951278\pi$
$984$	−0.375662			−0.0119757
$985$	27.8455	+	38.4550i	0.887231	+	1.22528i
$986$	−14.5024			−0.461852
$987$			1.00343i			0.0319396i
$988$		0			0
$989$	5.91606			0.188120
$990$	21.6676	+	29.9232i	0.688640	+	0.951022i
$991$	16.2633			0.516621			0.258310	−	0.966062i	$-0.416834\pi$
$991$	16.2633			0.516621			0.258310	+	0.966062i	$0.416834\pi$
$992$			2.11486i			0.0671469i
$993$		−	4.07097i		−	0.129188i
$994$	10.1020			0.320415
$995$	−13.7304	+	9.94226i	−0.435283	+	0.315191i
$996$	−4.92080			−0.155921
$997$			36.6404i			1.16041i	0.814469	+	0.580207i	$0.197028\pi$
$997$			36.6404i			1.16041i	−0.814469	+	0.580207i	$0.802972\pi$
$998$			68.1391i			2.15690i
$999$	0.675985			0.0213872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.21		24
5.2	odd	4		9025.2.a.ct.1.4		24
5.3	odd	4		9025.2.a.ct.1.21		24
5.4	even	2	inner	1805.2.b.l.1084.4		24
19.3	odd	18		95.2.p.a.9.8	yes	48
19.13	odd	18		95.2.p.a.74.1	yes	48
19.18	odd	2		1805.2.b.k.1084.4		24
57.32	even	18		855.2.da.b.739.8		48
57.41	even	18		855.2.da.b.199.1		48
95.3	even	36		475.2.l.f.351.1		48
95.13	even	36		475.2.l.f.226.1		48
95.18	even	4		9025.2.a.cu.1.4		24
95.22	even	36		475.2.l.f.351.8		48
95.32	even	36		475.2.l.f.226.8		48
95.37	even	4		9025.2.a.cu.1.21		24
95.79	odd	18		95.2.p.a.9.1	✓	48
95.89	odd	18		95.2.p.a.74.8	yes	48
95.94	odd	2		1805.2.b.k.1084.21		24
285.89	even	18		855.2.da.b.739.1		48
285.269	even	18		855.2.da.b.199.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.1	✓	48	95.79	odd	18
95.2.p.a.9.8	yes	48	19.3	odd	18
95.2.p.a.74.1	yes	48	19.13	odd	18
95.2.p.a.74.8	yes	48	95.89	odd	18
475.2.l.f.226.1		48	95.13	even	36
475.2.l.f.226.8		48	95.32	even	36
475.2.l.f.351.1		48	95.3	even	36
475.2.l.f.351.8		48	95.22	even	36
855.2.da.b.199.1		48	57.41	even	18
855.2.da.b.199.8		48	285.269	even	18
855.2.da.b.739.1		48	285.89	even	18
855.2.da.b.739.8		48	57.32	even	18
1805.2.b.k.1084.4		24	19.18	odd	2
1805.2.b.k.1084.21		24	95.94	odd	2
1805.2.b.l.1084.4		24	5.4	even	2	inner
1805.2.b.l.1084.21		24	1.1	even	1	trivial
9025.2.a.ct.1.4		24	5.2	odd	4
9025.2.a.ct.1.21		24	5.3	odd	4
9025.2.a.cu.1.4		24	95.18	even	4
9025.2.a.cu.1.21		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.96177i q^{2} -0.187708i q^{3} -1.84854 q^{4} +(1.81111 - 1.31144i) q^{5} +0.368240 q^{6} -0.677067i q^{7} +0.297123i q^{8} +2.96477 q^{9} +(2.57274 + 3.55299i) q^{10} +2.84069 q^{11} +0.346987i q^{12} -4.76663i q^{13} +1.32825 q^{14} +(-0.246168 - 0.339961i) q^{15} -4.27997 q^{16} -5.18394i q^{17} +5.81619i q^{18} +(-3.34792 + 2.42425i) q^{20} -0.127091 q^{21} +5.57278i q^{22} +1.05091i q^{23} +0.0557724 q^{24} +(1.56026 - 4.75032i) q^{25} +9.35103 q^{26} -1.11964i q^{27} +1.25159i q^{28} -1.42605 q^{29} +(0.666925 - 0.482924i) q^{30} -0.271064 q^{31} -7.80208i q^{32} -0.533221i q^{33} +10.1697 q^{34} +(-0.887932 - 1.22625i) q^{35} -5.48050 q^{36} +0.603754i q^{37} -0.894735 q^{39} +(0.389658 + 0.538123i) q^{40} -6.73563 q^{41} -0.249324i q^{42} -5.62944i q^{43} -5.25114 q^{44} +(5.36953 - 3.88810i) q^{45} -2.06165 q^{46} -7.89538i q^{47} +0.803386i q^{48} +6.54158 q^{49} +(9.31905 + 3.06088i) q^{50} -0.973067 q^{51} +8.81132i q^{52} -6.88829i q^{53} +2.19647 q^{54} +(5.14481 - 3.72539i) q^{55} +0.201172 q^{56} -2.79757i q^{58} -10.1227 q^{59} +(0.455051 + 0.628432i) q^{60} -7.47195 q^{61} -0.531765i q^{62} -2.00735i q^{63} +6.74594 q^{64} +(-6.25114 - 8.63291i) q^{65} +1.04606 q^{66} +4.11733i q^{67} +9.58273i q^{68} +0.197265 q^{69} +(2.40561 - 1.74192i) q^{70} +7.60546 q^{71} +0.880900i q^{72} +16.1274i q^{73} -1.18443 q^{74} +(-0.891675 - 0.292874i) q^{75} -1.92334i q^{77} -1.75527i q^{78} +14.8468 q^{79} +(-7.75152 + 5.61292i) q^{80} +8.68413 q^{81} -13.2138i q^{82} +14.1815i q^{83} +0.234933 q^{84} +(-6.79841 - 9.38870i) q^{85} +11.0437 q^{86} +0.267680i q^{87} +0.844034i q^{88} +8.23788 q^{89} +(7.62757 + 10.5338i) q^{90} -3.22733 q^{91} -1.94266i q^{92} +0.0508809i q^{93} +15.4889 q^{94} -1.46451 q^{96} -5.72847i q^{97} +12.8331i q^{98} +8.42198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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