LMFDB - Embedded newform 1805.2.b.g.1084.5

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:	$6$
Coefficient field:	6.0.4227136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 7x^{2} + 1 $ x^6 + 6x^4 + 7x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.5
Root			$1.15904i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.g.1084.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.862781i q^{2} -3.07914i q^{3} +1.25561 q^{4} +(-1.91223 - 1.15904i) q^{5} +2.65662 q^{6} -0.566520i q^{7} +2.80888i q^{8} -6.48108 q^{9} +O(q^{10})$	\(q+0.862781i q^{2} -3.07914i q^{3} +1.25561 q^{4} +(-1.91223 - 1.15904i) q^{5} +2.65662 q^{6} -0.566520i q^{7} +2.80888i q^{8} -6.48108 q^{9} +(1.00000 - 1.64984i) q^{10} -1.91223 q^{11} -3.86619i q^{12} -0.194531i q^{13} +0.488783 q^{14} +(-3.56885 + 5.88801i) q^{15} +0.0877708 q^{16} -5.29549i q^{17} -5.59175i q^{18} +(-2.40101 - 1.45530i) q^{20} -1.74439 q^{21} -1.64984i q^{22} +3.37540i q^{23} +8.64892 q^{24} +(2.31324 + 4.43271i) q^{25} +0.167838 q^{26} +10.7187i q^{27} -0.711327i q^{28} -8.73669 q^{29} +(-5.08007 - 3.07914i) q^{30} -5.65662 q^{31} +5.69348i q^{32} +5.88801i q^{33} +4.56885 q^{34} +(-0.656620 + 1.08332i) q^{35} -8.13770 q^{36} +0.955582i q^{37} -0.598988 q^{39} +(3.25561 - 5.37122i) q^{40} -10.0499 q^{41} -1.50503i q^{42} -4.93243i q^{43} -2.40101 q^{44} +(12.3933 + 7.51185i) q^{45} -2.91223 q^{46} -8.83942i q^{47} -0.270258i q^{48} +6.67906 q^{49} +(-3.82446 + 1.99582i) q^{50} -16.3055 q^{51} -0.244255i q^{52} +8.20610i q^{53} -9.24791 q^{54} +(3.65662 + 2.21635i) q^{55} +1.59128 q^{56} -7.53785i q^{58} +3.71425 q^{59} +(-4.48108 + 7.39304i) q^{60} -3.51122 q^{61} -4.88043i q^{62} +3.67166i q^{63} -4.73669 q^{64} +(-0.225470 + 0.371988i) q^{65} -5.08007 q^{66} +4.04365i q^{67} -6.64906i q^{68} +10.3933 q^{69} +(-0.934664 - 0.566520i) q^{70} -5.19533 q^{71} -18.2046i q^{72} +8.60409i q^{73} -0.824458 q^{74} +(13.6489 - 7.12278i) q^{75} +1.08332i q^{77} -0.516796i q^{78} +6.62648 q^{79} +(-0.167838 - 0.101730i) q^{80} +13.5611 q^{81} -8.67089i q^{82} -4.51737i q^{83} -2.19027 q^{84} +(-6.13770 + 10.1262i) q^{85} +4.25561 q^{86} +26.9014i q^{87} -5.37122i q^{88} +3.37352 q^{89} +(-6.48108 + 10.6927i) q^{90} -0.110206 q^{91} +4.23818i q^{92} +17.4175i q^{93} +7.62648 q^{94} +17.5310 q^{96} +15.1922i q^{97} +5.76256i q^{98} +12.3933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9}+O(q^{10}) $ 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9	$ 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} + 6 q^{10} + 2 q^{11} + 22 q^{14} - 4 q^{15} + 14 q^{16} - 20 q^{20} - 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} - 12 q^{29} + 6 q^{30} - 30 q^{31} + 10 q^{34} - 14 q^{36} + 2 q^{39} + 10 q^{40} - 12 q^{41} - 20 q^{44} + 30 q^{45} - 4 q^{46} - 2 q^{49} + 4 q^{50} - 40 q^{51} + 4 q^{54} + 18 q^{55} - 46 q^{56} + 20 q^{59} + 4 q^{60} - 2 q^{61} + 12 q^{64} + 20 q^{65} + 6 q^{66} + 18 q^{69} + 46 q^{70} + 2 q^{71} + 22 q^{74} + 28 q^{75} + 24 q^{79} + 22 q^{80} + 14 q^{81} + 48 q^{84} - 2 q^{85} + 16 q^{86} + 36 q^{89} - 8 q^{90} + 24 q^{91} + 30 q^{94} + 26 q^{96} + 30 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 + 6 * q^10 + 2 * q^11 + 22 * q^14 - 4 * q^15 + 14 * q^16 - 20 * q^20 - 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 - 12 * q^29 + 6 * q^30 - 30 * q^31 + 10 * q^34 - 14 * q^36 + 2 * q^39 + 10 * q^40 - 12 * q^41 - 20 * q^44 + 30 * q^45 - 4 * q^46 - 2 * q^49 + 4 * q^50 - 40 * q^51 + 4 * q^54 + 18 * q^55 - 46 * q^56 + 20 * q^59 + 4 * q^60 - 2 * q^61 + 12 * q^64 + 20 * q^65 + 6 * q^66 + 18 * q^69 + 46 * q^70 + 2 * q^71 + 22 * q^74 + 28 * q^75 + 24 * q^79 + 22 * q^80 + 14 * q^81 + 48 * q^84 - 2 * q^85 + 16 * q^86 + 36 * q^89 - 8 * q^90 + 24 * q^91 + 30 * q^94 + 26 * q^96 + 30 * q^99

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 $

$2$			0.862781i			0.610078i	0.952340	+	0.305039i	$0.0986696\pi$
$2$			0.862781i			0.610078i	−0.952340	+	0.305039i	$0.901330\pi$
$3$		−	3.07914i		−	1.77774i	−0.458159	−	0.888870i	$-0.651491\pi$
$3$		−	3.07914i		−	1.77774i	0.458159	−	0.888870i	$-0.348509\pi$
$4$	1.25561			0.627804
$5$	−1.91223	−	1.15904i	−0.855175	−	0.518340i
$5$	−1.91223	−	1.15904i	−0.855175	−	0.518340i
$6$	2.65662			1.08456
$7$		−	0.566520i		−	0.214124i	−0.994252	−	0.107062i	$-0.965856\pi$
$7$		−	0.566520i		−	0.214124i	0.994252	−	0.107062i	$-0.0341444\pi$
$8$			2.80888i			0.993088i
$9$	−6.48108			−2.16036
$10$	1.00000	−	1.64984i	0.316228	−	0.521724i
$11$	−1.91223			−0.576559			−0.288279	−	0.957546i	$-0.593083\pi$
$11$	−1.91223			−0.576559			−0.288279	+	0.957546i	$0.593083\pi$
$12$		−	3.86619i		−	1.11607i
$13$		−	0.194531i		−	0.0539533i	−0.999636	−	0.0269766i	$-0.991412\pi$
$13$		−	0.194531i		−	0.0539533i	0.999636	−	0.0269766i	$-0.00858797\pi$
$14$	0.488783			0.130633
$15$	−3.56885	+	5.88801i	−0.921473	+	1.52028i
$16$	0.0877708			0.0219427
$17$		−	5.29549i		−	1.28435i	−0.766560	−	0.642173i	$-0.778033\pi$
$17$		−	5.29549i		−	1.28435i	0.766560	−	0.642173i	$-0.221967\pi$
$18$		−	5.59175i		−	1.31799i
$19$		0			0
$19$		0			0
$20$	−2.40101	−	1.45530i	−0.536883	−	0.325416i
$21$	−1.74439			−0.380657
$22$		−	1.64984i		−	0.351746i
$23$			3.37540i			0.703819i	0.936034	+	0.351910i	$0.114468\pi$
$23$			3.37540i			0.703819i	−0.936034	+	0.351910i	$0.885532\pi$
$24$	8.64892			1.76545
$25$	2.31324	+	4.43271i	0.462648	+	0.886542i
$26$	0.167838			0.0329157
$27$			10.7187i			2.06282i
$28$		−	0.711327i		−	0.134428i
$29$	−8.73669			−1.62236			−0.811181	−	0.584795i	$-0.801175\pi$
$29$	−8.73669			−1.62236			−0.811181	+	0.584795i	$0.801175\pi$
$30$	−5.08007	−	3.07914i	−0.927489	−	0.562171i
$31$	−5.65662			−1.01596			−0.507980	−	0.861369i	$-0.669607\pi$
$31$	−5.65662			−1.01596			−0.507980	+	0.861369i	$0.669607\pi$
$32$			5.69348i			1.00648i
$33$			5.88801i			1.02497i
$34$	4.56885			0.783551
$35$	−0.656620	+	1.08332i	−0.110989	+	0.183114i
$36$	−8.13770			−1.35628
$37$			0.955582i			0.157097i	0.996910	+	0.0785484i	$0.0250285\pi$
$37$			0.955582i			0.157097i	−0.996910	+	0.0785484i	$0.974971\pi$
$38$		0			0
$39$	−0.598988			−0.0959149
$40$	3.25561	−	5.37122i	0.514757	−	0.849264i
$41$	−10.0499			−1.56954			−0.784768	−	0.619790i	$-0.787218\pi$
$41$	−10.0499			−1.56954			−0.784768	+	0.619790i	$0.787218\pi$
$42$		−	1.50503i		−	0.232231i
$43$		−	4.93243i		−	0.752189i	−0.926581	−	0.376094i	$-0.877267\pi$
$43$		−	4.93243i		−	0.752189i	0.926581	−	0.376094i	$-0.122733\pi$
$44$	−2.40101			−0.361966
$45$	12.3933	+	7.51185i	1.84749	+	1.11980i
$46$	−2.91223			−0.429385
$47$		−	8.83942i		−	1.28936i	−0.764452	−	0.644681i	$-0.776990\pi$
$47$		−	8.83942i		−	1.28936i	0.764452	−	0.644681i	$-0.223010\pi$
$48$		−	0.270258i		−	0.0390084i
$49$	6.67906			0.954151
$50$	−3.82446	+	1.99582i	−0.540860	+	0.282252i
$51$	−16.3055			−2.28323
$52$		−	0.244255i		−	0.0338721i
$53$			8.20610i			1.12719i	0.826050	+	0.563597i	$0.190583\pi$
$53$			8.20610i			1.12719i	−0.826050	+	0.563597i	$0.809417\pi$
$54$	−9.24791			−1.25848
$55$	3.65662	+	2.21635i	0.493059	+	0.298853i
$56$	1.59128			0.212644
$57$		0			0
$58$		−	7.53785i		−	0.989768i
$59$	3.71425			0.483554			0.241777	−	0.970332i	$-0.422270\pi$
$59$	3.71425			0.483554			0.241777	+	0.970332i	$0.422270\pi$
$60$	−4.48108	+	7.39304i	−0.578505	+	0.954438i
$61$	−3.51122			−0.449565			−0.224783	−	0.974409i	$-0.572167\pi$
$61$	−3.51122			−0.449565			−0.224783	+	0.974409i	$0.572167\pi$
$62$		−	4.88043i		−	0.619815i
$63$			3.67166i			0.462586i
$64$	−4.73669			−0.592086
$65$	−0.225470	+	0.371988i	−0.0279661	+	0.0461395i
$66$	−5.08007			−0.625313
$67$			4.04365i			0.494010i	0.969014	+	0.247005i	$0.0794464\pi$
$67$			4.04365i			0.494010i	−0.969014	+	0.247005i	$0.920554\pi$
$68$		−	6.64906i		−	0.806318i
$69$	10.3933			1.25121
$70$	−0.934664	−	0.566520i	−0.111714	−	0.0677121i
$71$	−5.19533			−0.616572			−0.308286	−	0.951294i	$-0.599755\pi$
$71$	−5.19533			−0.616572			−0.308286	+	0.951294i	$0.599755\pi$
$72$		−	18.2046i		−	2.14543i
$73$			8.60409i			1.00703i	0.863986	+	0.503516i	$0.167961\pi$
$73$			8.60409i			1.00703i	−0.863986	+	0.503516i	$0.832039\pi$
$74$	−0.824458			−0.0958413
$75$	13.6489	−	7.12278i	1.57604	−	0.822468i
$76$		0			0
$77$			1.08332i			0.123455i
$78$		−	0.516796i		−	0.0585156i
$79$	6.62648			0.745537			0.372769	−	0.927924i	$-0.378408\pi$
$79$	6.62648			0.745537			0.372769	+	0.927924i	$0.378408\pi$
$80$	−0.167838	−	0.101730i	−0.0187649	−	0.0113738i
$81$	13.5611			1.50679
$82$		−	8.67089i		−	0.957539i
$83$		−	4.51737i		−	0.495845i	−0.968780	−	0.247923i	$-0.920252\pi$
$83$		−	4.51737i		−	0.495845i	0.968780	−	0.247923i	$-0.0797479\pi$
$84$	−2.19027			−0.238978
$85$	−6.13770	+	10.1262i	−0.665727	+	1.09834i
$86$	4.25561			0.458894
$87$			26.9014i			2.88414i
$88$		−	5.37122i		−	0.572574i
$89$	3.37352			0.357592			0.178796	−	0.983886i	$-0.442780\pi$
$89$	3.37352			0.357592			0.178796	+	0.983886i	$0.442780\pi$
$90$	−6.48108	+	10.6927i	−0.683166	+	1.12711i
$91$	−0.110206			−0.0115527
$92$			4.23818i			0.441861i
$93$			17.4175i			1.80611i
$94$	7.62648			0.786612
$95$		0			0
$96$	17.5310			1.78925
$97$			15.1922i			1.54254i	0.636510	+	0.771268i	$0.280377\pi$
$97$			15.1922i			1.54254i	−0.636510	+	0.771268i	$0.719623\pi$
$98$			5.76256i			0.582107i
$99$	12.3933			1.24557
$100$	2.90453	+	5.56575i	0.290453	+	0.556575i
$101$	3.54136			0.352378			0.176189	−	0.984356i	$-0.443623\pi$
$101$	3.54136			0.352378			0.176189	+	0.984356i	$0.443623\pi$
$102$		−	14.0681i		−	1.39295i
$103$		−	15.6919i		−	1.54617i	−0.634301	−	0.773086i	$-0.718712\pi$
$103$		−	15.6919i		−	1.54617i	0.634301	−	0.773086i	$-0.281288\pi$
$104$	0.546415			0.0535804
$105$	3.33568	+	2.02182i	0.325529	+	0.197310i
$106$	−7.08007			−0.687677
$107$			1.05731i			0.102214i	0.998693	+	0.0511071i	$0.0162750\pi$
$107$			1.05731i			0.102214i	−0.998693	+	0.0511071i	$0.983725\pi$
$108$			13.4585i			1.29505i
$109$	−6.74439			−0.645996			−0.322998	−	0.946400i	$-0.604691\pi$
$109$	−6.74439			−0.645996			−0.322998	+	0.946400i	$0.604691\pi$
$110$	−1.91223	+	3.15486i	−0.182324	+	0.300804i
$111$	2.94237			0.279277
$112$		−	0.0497239i		−	0.00469847i
$113$			7.90091i			0.743255i	0.928382	+	0.371627i	$0.121200\pi$
$113$			7.90091i			0.743255i	−0.928382	+	0.371627i	$0.878800\pi$
$114$		0			0
$115$	3.91223	−	6.45453i	0.364817	−	0.601888i
$116$	−10.9699			−1.01853
$117$			1.26077i			0.116558i
$118$			3.20459i			0.295006i
$119$	−3.00000			−0.275010
$120$	−16.5387	−	10.0245i	−1.50977	−	0.915104i
$121$	−7.34338			−0.667580
$122$		−	3.02941i		−	0.274270i
$123$			30.9451i			2.79023i
$124$	−7.10250			−0.637824
$125$	0.714253	−	11.1575i	0.0638847	−	0.997957i
$126$	−3.16784			−0.282213
$127$		−	8.47636i		−	0.752155i	−0.926588	−	0.376078i	$-0.877273\pi$
$127$		−	8.47636i		−	0.752155i	0.926588	−	0.376078i	$-0.122727\pi$
$128$			7.30024i			0.645256i
$129$	−15.1876			−1.33720
$130$	−0.320945	−	0.194531i	−0.0281487	−	0.0170615i
$131$	1.87439			0.163766			0.0818830	−	0.996642i	$-0.473907\pi$
$131$	1.87439			0.163766			0.0818830	+	0.996642i	$0.473907\pi$
$132$			7.39304i			0.643482i
$133$		0			0
$134$	−3.48878			−0.301385
$135$	12.4234	−	20.4966i	1.06924	−	1.76407i
$136$	14.8744			1.27547
$137$		−	12.4614i		−	1.06465i	−0.846542	−	0.532323i	$-0.821319\pi$
$137$		−	12.4614i		−	1.06465i	0.846542	−	0.532323i	$-0.178681\pi$
$138$			8.96715i			0.763334i
$139$	0.313241			0.0265687			0.0132844	−	0.999912i	$-0.495771\pi$
$139$	0.313241			0.0265687			0.0132844	+	0.999912i	$0.495771\pi$
$140$	−0.824458	+	1.36022i	−0.0696794	+	0.114960i
$141$	−27.2178			−2.29215
$142$		−	4.48243i		−	0.376157i
$143$			0.371988i			0.0311072i
$144$	−0.568850			−0.0474041
$145$	16.7065	+	10.1262i	1.38740	+	0.840935i
$146$	−7.42345			−0.614369
$147$		−	20.5657i		−	1.69623i
$148$			1.19984i			0.0986260i
$149$	−4.36581			−0.357661			−0.178831	−	0.983880i	$-0.557231\pi$
$149$	−4.36581			−0.357661			−0.178831	+	0.983880i	$0.557231\pi$
$150$	6.14540	+	11.7760i	0.501770	+	0.961509i
$151$	−0.197977			−0.0161111			−0.00805555	−	0.999968i	$-0.502564\pi$
$151$	−0.197977			−0.0161111			−0.00805555	+	0.999968i	$0.502564\pi$
$152$		0			0
$153$			34.3205i			2.77465i
$154$	−0.934664			−0.0753174
$155$	10.8168	+	6.55626i	0.868823	+	0.526612i
$156$	−0.752095			−0.0602158
$157$		−	15.7700i		−	1.25858i	−0.777171	−	0.629290i	$-0.783346\pi$
$157$		−	15.7700i		−	1.25858i	0.777171	−	0.629290i	$-0.216654\pi$
$158$			5.71720i			0.454836i
$159$	25.2677			2.00386
$160$	6.59899	−	10.8872i	0.521696	−	0.860712i
$161$	1.91223			0.150705
$162$			11.7003i			0.919262i
$163$			9.18768i			0.719635i	0.933023	+	0.359817i	$0.117161\pi$
$163$			9.18768i			0.719635i	−0.933023	+	0.359817i	$0.882839\pi$
$164$	−12.6188			−0.985361
$165$	6.82446	−	11.2592i	0.531283	−	0.876530i
$166$	3.89750			0.302505
$167$		−	3.07021i		−	0.237580i	−0.992919	−	0.118790i	$-0.962099\pi$
$167$		−	3.07021i		−	0.237580i	0.992919	−	0.118790i	$-0.0379015\pi$
$168$		−	4.89978i		−	0.378026i
$169$	12.9622			0.997089
$170$	−8.73669	−	5.29549i	−0.670073	−	0.406146i
$171$		0			0
$172$		−	6.19320i		−	0.472227i
$173$		−	10.4135i		−	0.791726i	−0.918310	−	0.395863i	$-0.870446\pi$
$173$		−	10.4135i		−	0.791726i	0.918310	−	0.395863i	$-0.129554\pi$
$174$	−23.2101			−1.75955
$175$	2.51122	−	1.31050i	0.189830	−	0.0990642i
$176$	−0.167838			−0.0126513
$177$		−	11.4367i		−	0.859634i
$178$			2.91061i			0.218159i
$179$	−13.4432			−1.00479			−0.502397	−	0.864637i	$-0.667549\pi$
$179$	−13.4432			−1.00479			−0.502397	+	0.864637i	$0.667549\pi$
$180$	15.5611	+	9.43194i	1.15986	+	0.703015i
$181$	−7.96216			−0.591823			−0.295911	−	0.955215i	$-0.595623\pi$
$181$	−7.96216			−0.591823			−0.295911	+	0.955215i	$0.595623\pi$
$182$		−	0.0950835i		−	0.00704806i
$183$			10.8115i			0.799210i
$184$	−9.48108			−0.698954
$185$	1.10756	−	1.82729i	0.0814295	−	0.134345i
$186$	−15.0275			−1.10187
$187$			10.1262i			0.740501i
$188$		−	11.0988i		−	0.809467i
$189$	6.07236			0.441699
$190$		0			0
$191$	−14.0999			−1.02023			−0.510115	−	0.860106i	$-0.670397\pi$
$191$	−14.0999			−1.02023			−0.510115	+	0.860106i	$0.670397\pi$
$192$			14.5849i			1.05257i
$193$		−	3.97685i		−	0.286260i	−0.989704	−	0.143130i	$-0.954283\pi$
$193$		−	3.97685i		−	0.286260i	0.989704	−	0.143130i	$-0.0457167\pi$
$194$	−13.1076			−0.941068
$195$	1.14540	+	0.694253i	0.0820240	+	0.0497165i
$196$	8.38628			0.599020
$197$		−	18.3494i		−	1.30734i	−0.756781	−	0.653669i	$-0.773229\pi$
$197$		−	18.3494i		−	1.30734i	0.756781	−	0.653669i	$-0.226771\pi$
$198$			10.6927i			0.759898i
$199$	1.60669			0.113895			0.0569477	−	0.998377i	$-0.481863\pi$
$199$	1.60669			0.113895			0.0569477	+	0.998377i	$0.481863\pi$
$200$	−12.4509	+	6.49761i	−0.880414	+	0.459450i
$201$	12.4509			0.878222
$202$			3.05542i			0.214978i
$203$			4.94951i			0.347387i
$204$	−20.4734			−1.43342
$205$	19.2178	+	11.6483i	1.34223	+	0.813552i
$206$	13.5387			0.943287
$207$		−	21.8762i		−	1.52050i
$208$		−	0.0170742i		−	0.00118388i
$209$		0			0
$210$	−1.74439	+	2.87796i	−0.120374	+	0.198598i
$211$	6.09986			0.419931			0.209966	−	0.977709i	$-0.432665\pi$
$211$	6.09986			0.419931			0.209966	+	0.977709i	$0.432665\pi$
$212$			10.3036i			0.707658i
$213$			15.9971i			1.09611i
$214$	−0.912229			−0.0623587
$215$	−5.71690	+	9.43194i	−0.389889	+	0.643253i
$216$	−30.1076			−2.04856
$217$			3.20459i			0.217542i
$218$		−	5.81893i		−	0.394108i
$219$	26.4932			1.79024
$220$	4.59128	+	2.78287i	0.309544	+	0.187621i
$221$	−1.03014			−0.0692946
$222$			2.53862i			0.170381i
$223$		−	17.2253i		−	1.15349i	−0.816925	−	0.576744i	$-0.804323\pi$
$223$		−	17.2253i		−	1.15349i	0.816925	−	0.576744i	$-0.195677\pi$
$224$	3.22547			0.215511
$225$	−14.9923	−	28.7287i	−0.999486	−	1.91525i
$226$	−6.81675			−0.453444
$227$			1.18505i			0.0786542i	0.999226	+	0.0393271i	$0.0125214\pi$
$227$			1.18505i			0.0786542i	−0.999226	+	0.0393271i	$0.987479\pi$
$228$		0			0
$229$	−6.24791			−0.412873			−0.206437	−	0.978460i	$-0.566187\pi$
$229$	−6.24791			−0.412873			−0.206437	+	0.978460i	$0.566187\pi$
$230$	5.56885	+	3.37540i	0.367199	+	0.222567i
$231$	3.33568			0.219471
$232$		−	24.5403i		−	1.61115i
$233$		−	2.75687i		−	0.180609i	−0.995914	−	0.0903043i	$-0.971216\pi$
$233$		−	2.75687i		−	0.180609i	0.995914	−	0.0903043i	$-0.0287840\pi$
$234$	−1.08777			−0.0711098
$235$	−10.2453	+	16.9030i	−0.668327	+	1.10263i
$236$	4.66365			0.303578
$237$		−	20.4038i		−	1.32537i
$238$		−	2.58834i		−	0.167777i
$239$	−17.3055			−1.11940			−0.559701	−	0.828695i	$-0.689084\pi$
$239$	−17.3055			−1.11940			−0.559701	+	0.828695i	$0.689084\pi$
$240$	−0.313241	+	0.516796i	−0.0202196	+	0.0333590i
$241$	4.78662			0.308333			0.154167	−	0.988045i	$-0.450731\pi$
$241$	4.78662			0.308333			0.154167	+	0.988045i	$0.450731\pi$
$242$		−	6.33573i		−	0.407276i
$243$		−	9.60047i		−	0.615870i
$244$	−4.40872			−0.282239
$245$	−12.7719	−	7.74131i	−0.815966	−	0.494574i
$246$	−26.6988			−1.70226
$247$		0			0
$248$		−	15.8888i		−	1.00894i
$249$	−13.9096			−0.881484
$250$	9.62648	+	0.616244i	0.608832	+	0.0389747i
$251$	−26.2479			−1.65675			−0.828377	−	0.560172i	$-0.810735\pi$
$251$	−26.2479			−1.65675			−0.828377	+	0.560172i	$0.810735\pi$
$252$			4.61017i			0.290413i
$253$		−	6.45453i		−	0.405793i
$254$	7.31324			0.458874
$255$	31.1799	+	18.8988i	1.95256	+	1.18349i
$256$	−15.7719			−0.985743
$257$		−	22.2505i		−	1.38795i	−0.720000	−	0.693974i	$-0.755858\pi$
$257$		−	22.2505i		−	1.38795i	0.720000	−	0.693974i	$-0.244142\pi$
$258$		−	13.1036i		−	0.815794i
$259$	0.541356			0.0336382
$260$	−0.283102	+	0.467072i	−0.0175573	+	0.0289666i
$261$	56.6232			3.50489
$262$			1.61719i			0.0999101i
$263$			8.81341i			0.543458i	0.962374	+	0.271729i	$0.0875955\pi$
$263$			8.81341i			0.543458i	−0.962374	+	0.271729i	$0.912405\pi$
$264$	−16.5387			−1.01789
$265$	9.51122	−	15.6919i	0.584269	−	0.963948i
$266$		0			0
$267$		−	10.3875i		−	0.635706i
$268$			5.07724i			0.310142i
$269$	−4.76418			−0.290477			−0.145239	−	0.989397i	$-0.546395\pi$
$269$	−4.76418			−0.290477			−0.145239	+	0.989397i	$0.546395\pi$
$270$	17.6841	+	10.7187i	1.07622	+	0.652320i
$271$	3.51892			0.213759			0.106880	−	0.994272i	$-0.465914\pi$
$271$	3.51892			0.213759			0.106880	+	0.994272i	$0.465914\pi$
$272$		−	0.464790i		−	0.0281820i
$273$			0.339339i			0.0205377i
$274$	10.7514			0.649517
$275$	−4.42345	−	8.47636i	−0.266744	−	0.511144i
$276$	13.0499			0.785513
$277$		−	32.7724i		−	1.96910i	−0.175098	−	0.984551i	$-0.556024\pi$
$277$		−	32.7724i		−	1.96910i	0.175098	−	0.984551i	$-0.443976\pi$
$278$			0.270258i			0.0162090i
$279$	36.6610			2.19484
$280$	−3.04290	−	1.84437i	−0.181848	−	0.110222i
$281$	−9.91993			−0.591774			−0.295887	−	0.955223i	$-0.595615\pi$
$281$	−9.91993			−0.591774			−0.295887	+	0.955223i	$0.595615\pi$
$282$		−	23.4830i		−	1.39839i
$283$		−	2.47182i		−	0.146935i	−0.997298	−	0.0734673i	$-0.976594\pi$
$283$		−	2.47182i		−	0.146935i	0.997298	−	0.0734673i	$-0.0234064\pi$
$284$	−6.52330			−0.387087
$285$		0			0
$286$	−0.320945			−0.0189779
$287$			5.69348i			0.336076i
$288$		−	36.8999i		−	2.17435i
$289$	−11.0422			−0.649543
$290$	−8.73669	+	14.4141i	−0.513036	+	0.846425i
$291$	46.7789			2.74223
$292$			10.8034i			0.632219i
$293$		−	17.0284i		−	0.994812i	−0.867518	−	0.497406i	$-0.834286\pi$
$293$		−	17.0284i		−	0.994812i	0.867518	−	0.497406i	$-0.165714\pi$
$294$	17.7437			1.03483
$295$	−7.10250	−	4.30498i	−0.413524	−	0.250645i
$296$	−2.68411			−0.156011
$297$		−	20.4966i		−	1.18934i
$298$		−	3.76674i		−	0.218202i
$299$	0.656620			0.0379733
$300$	17.1377	−	8.94343i	0.989446	−	0.516349i
$301$	−2.79432			−0.161062
$302$		−	0.170810i		−	0.00982904i
$303$		−	10.9043i		−	0.626437i
$304$		0			0
$305$	6.71425	+	4.06965i	0.384457	+	0.233028i
$306$	−29.6111			−1.69275
$307$		−	20.9793i		−	1.19735i	−0.800992	−	0.598676i	$-0.795694\pi$
$307$		−	20.9793i		−	1.19735i	0.800992	−	0.598676i	$-0.204306\pi$
$308$			1.36022i			0.0775058i
$309$	−48.3176			−2.74869
$310$	−5.65662	+	9.33249i	−0.321274	+	0.530050i
$311$	−3.14805			−0.178509			−0.0892547	−	0.996009i	$-0.528449\pi$
$311$	−3.14805			−0.178509			−0.0892547	+	0.996009i	$0.528449\pi$
$312$		−	1.68248i		−	0.0952520i
$313$		−	12.2928i		−	0.694831i	−0.937711	−	0.347416i	$-0.887059\pi$
$313$		−	12.2928i		−	0.694831i	0.937711	−	0.347416i	$-0.112941\pi$
$314$	13.6060			0.767832
$315$	4.25561	−	7.02105i	0.239776	−	0.395592i
$316$	8.32027			0.468052
$317$			11.4619i			0.643765i	0.946780	+	0.321882i	$0.104316\pi$
$317$			11.4619i			0.643765i	−0.946780	+	0.321882i	$0.895684\pi$
$318$			21.8005i			1.22251i
$319$	16.7065			0.935387
$320$	9.05763	+	5.49002i	0.506337	+	0.306902i
$321$	3.25561			0.181710
$322$			1.64984i			0.0919417i
$323$		0			0
$324$	17.0275			0.945972
$325$	0.862301	−	0.449998i	0.0478318	−	0.0249614i
$326$	−7.92696			−0.439034
$327$			20.7669i			1.14841i
$328$		−	28.2290i		−	1.55869i
$329$	−5.00770			−0.276084
$330$	9.71425	+	5.88801i	0.534752	+	0.324124i
$331$	−5.85724			−0.321943			−0.160972	−	0.986959i	$-0.551463\pi$
$331$	−5.85724			−0.321943			−0.160972	+	0.986959i	$0.551463\pi$
$332$		−	5.67204i		−	0.311294i
$333$		−	6.19320i		−	0.339385i
$334$	2.64892			0.144942
$335$	4.68676	−	7.73238i	0.256065	−	0.422465i
$336$	−0.153107			−0.00835265
$337$			8.60995i			0.469014i	0.972114	+	0.234507i	$0.0753476\pi$
$337$			8.60995i			0.469014i	−0.972114	+	0.234507i	$0.924652\pi$
$338$			11.1835i			0.608302i
$339$	24.3280			1.32131
$340$	−7.70655	+	12.7145i	−0.417946	+	0.689543i
$341$	10.8168			0.585760
$342$		0			0
$343$		−	7.74945i		−	0.418431i
$344$	13.8546			0.746990
$345$	−19.8744	−	12.0463i	−1.07000	−	0.648550i
$346$	8.98459			0.483015
$347$			12.0901i			0.649033i	0.945880	+	0.324517i	$0.105202\pi$
$347$			12.0901i			0.649033i	−0.945880	+	0.324517i	$0.894798\pi$
$348$			33.7777i			1.81067i
$349$	−18.9819			−1.01608			−0.508040	−	0.861333i	$-0.669630\pi$
$349$	−18.9819			−1.01608			−0.508040	+	0.861333i	$0.669630\pi$
$350$	1.13067	+	2.16663i	0.0604369	+	0.115811i
$351$	2.08513			0.111296
$352$		−	10.8872i		−	0.580292i
$353$		−	7.71759i		−	0.410766i	−0.978682	−	0.205383i	$-0.934156\pi$
$353$		−	7.71759i		−	0.410766i	0.978682	−	0.205383i	$-0.0658440\pi$
$354$	9.86736			0.524444
$355$	9.93466	+	6.02161i	0.527277	+	0.319594i
$356$	4.23582			0.224498
$357$			9.23741i			0.488895i
$358$		−	11.5986i		−	0.613003i
$359$	7.03014			0.371037			0.185518	−	0.982641i	$-0.440604\pi$
$359$	7.03014			0.371037			0.185518	+	0.982641i	$0.440604\pi$
$360$	−21.0999	+	34.8113i	−1.11206	+	1.83472i
$361$		0			0
$362$		−	6.86960i		−	0.361058i
$363$			22.6113i			1.18678i
$364$	−0.138375			−0.00725284
$365$	9.97251	−	16.4530i	0.521985	−	0.861189i
$366$	−9.32797			−0.487581
$367$			33.7109i			1.75969i	0.475257	+	0.879847i	$0.342355\pi$
$367$			33.7109i			1.75969i	−0.475257	+	0.879847i	$0.657645\pi$
$368$			0.296261i			0.0154437i
$369$	65.1344			3.39076
$370$	1.57655	+	0.955582i	0.0819611	+	0.0496784i
$371$	4.64892			0.241360
$372$			21.8696i			1.13388i
$373$		−	10.0097i		−	0.518281i	−0.965840	−	0.259141i	$-0.916561\pi$
$373$		−	10.0097i		−	0.518281i	0.965840	−	0.259141i	$-0.0834393\pi$
$374$	−8.73669			−0.451763
$375$	−34.3555	−	2.19928i	−1.77411	−	0.113570i
$376$	24.8288			1.28045
$377$			1.69956i			0.0875317i
$378$			5.23912i			0.269471i
$379$	−35.8064			−1.83925			−0.919626	−	0.392796i	$-0.871508\pi$
$379$	−35.8064			−1.83925			−0.919626	+	0.392796i	$0.871508\pi$
$380$		0			0
$381$	−26.0999			−1.33714
$382$		−	12.1651i		−	0.622420i
$383$			16.2495i			0.830312i	0.909750	+	0.415156i	$0.136273\pi$
$383$			16.2495i			0.830312i	−0.909750	+	0.415156i	$0.863727\pi$
$384$	22.4784			1.14710
$385$	1.25561	−	2.07155i	0.0639917	−	0.105576i
$386$	3.43115			0.174641
$387$			31.9675i			1.62500i
$388$			19.0755i			0.968411i
$389$	19.3856			0.982889			0.491445	−	0.870909i	$-0.336469\pi$
$389$	19.3856			0.982889			0.491445	+	0.870909i	$0.336469\pi$
$390$	−0.598988	+	0.988232i	−0.0303310	+	0.0500411i
$391$	17.8744			0.903947
$392$			18.7607i			0.947556i
$393$		−	5.77149i		−	0.291133i
$394$	15.8315			0.797579
$395$	−12.6714	−	7.68037i	−0.637565	−	0.386442i
$396$	15.5611			0.781977
$397$		−	5.35414i		−	0.268717i	−0.990933	−	0.134358i	$-0.957103\pi$
$397$		−	5.35414i		−	0.268717i	0.990933	−	0.134358i	$-0.0428973\pi$
$398$			1.38622i			0.0694851i
$399$		0			0
$400$	0.203035	+	0.389063i	0.0101518	+	0.0194531i
$401$	−8.33832			−0.416396			−0.208198	−	0.978087i	$-0.566760\pi$
$401$	−8.33832			−0.416396			−0.208198	+	0.978087i	$0.566760\pi$
$402$			10.7424i			0.535784i
$403$			1.10039i			0.0548143i
$404$	4.44656			0.221225
$405$	−25.9320	−	15.7179i	−1.28857	−	0.781031i
$406$	−4.27034			−0.211933
$407$		−	1.82729i		−	0.0905755i
$408$		−	45.8003i		−	2.26745i
$409$	−35.3227			−1.74659			−0.873297	−	0.487188i	$-0.838023\pi$
$409$	−35.3227			−1.74659			−0.873297	+	0.487188i	$0.838023\pi$
$410$	−10.0499	+	16.5807i	−0.496331	+	0.818864i
$411$	−38.3702			−1.89266
$412$		−	19.7029i		−	0.970694i
$413$		−	2.10420i		−	0.103541i
$414$	18.8744			0.927626
$415$	−5.23582	+	8.63824i	−0.257016	+	0.424034i
$416$	1.10756			0.0543026
$417$		−	0.964511i		−	0.0472323i
$418$		0			0
$419$	−21.2453			−1.03790			−0.518949	−	0.854805i	$-0.673677\pi$
$419$	−21.2453			−1.03790			−0.518949	+	0.854805i	$0.673677\pi$
$420$	4.18830	+	2.53862i	0.204368	+	0.123872i
$421$	14.8744			0.724933			0.362467	−	0.931997i	$-0.381935\pi$
$421$	14.8744			0.724933			0.362467	+	0.931997i	$0.381935\pi$
$422$			5.26284i			0.256191i
$423$			57.2890i			2.78548i
$424$	−23.0499			−1.11940
$425$	23.4734	−	12.2497i	1.13863	−	0.594200i
$426$	−13.8020			−0.668710
$427$			1.98917i			0.0962629i
$428$			1.32757i			0.0641706i
$429$	1.14540			0.0553006
$430$	−8.13770	−	4.93243i	−0.392435	−	0.237863i
$431$	16.9518			0.816540			0.408270	−	0.912861i	$-0.366132\pi$
$431$	16.9518			0.816540			0.408270	+	0.912861i	$0.366132\pi$
$432$			0.940790i			0.0452638i
$433$		−	23.1459i		−	1.11232i	−0.831075	−	0.556161i	$-0.812274\pi$
$433$		−	23.1459i		−	1.11232i	0.831075	−	0.556161i	$-0.187726\pi$
$434$	−2.76486			−0.132717
$435$	31.1799	−	51.4417i	1.49496	−	2.46644i
$436$	−8.46832			−0.405559
$437$		0			0
$438$			22.8578i			1.09219i
$439$	33.5457			1.60105			0.800525	−	0.599299i	$-0.204554\pi$
$439$	33.5457			1.60105			0.800525	+	0.599299i	$0.204554\pi$
$440$	−6.22547	+	10.2710i	−0.296788	+	0.489651i
$441$	−43.2875			−2.06131
$442$		−	0.888784i		−	0.0422752i
$443$		−	31.3579i		−	1.48986i	−0.667144	−	0.744929i	$-0.732483\pi$
$443$		−	31.3579i		−	1.48986i	0.667144	−	0.744929i	$-0.267517\pi$
$444$	3.69446			0.175331
$445$	−6.45094	−	3.91005i	−0.305804	−	0.185354i
$446$	14.8616			0.703718
$447$			13.4429i			0.635829i
$448$			2.68343i			0.126780i
$449$	−16.0301			−0.756509			−0.378255	−	0.925702i	$-0.623476\pi$
$449$	−16.0301			−0.756509			−0.378255	+	0.925702i	$0.623476\pi$
$450$	24.7866	−	12.9351i	1.16845	−	0.609765i
$451$	19.2178			0.904929
$452$			9.92045i			0.466619i
$453$			0.609597i			0.0286414i
$454$	−1.02243			−0.0479853
$455$	0.210739	+	0.127733i	0.00987959	+	0.00598823i
$456$		0			0
$457$			15.3980i			0.720286i	0.932897	+	0.360143i	$0.117272\pi$
$457$			15.3980i			0.720286i	−0.932897	+	0.360143i	$0.882728\pi$
$458$		−	5.39057i		−	0.251885i
$459$	56.7609			2.64937
$460$	4.91223	−	8.10437i	0.229034	−	0.377868i
$461$	−5.81411			−0.270790			−0.135395	−	0.990792i	$-0.543230\pi$
$461$	−5.81411			−0.270790			−0.135395	+	0.990792i	$0.543230\pi$
$462$			2.87796i			0.133895i
$463$		−	32.6788i		−	1.51871i	−0.650675	−	0.759356i	$-0.725514\pi$
$463$		−	32.6788i		−	1.51871i	0.650675	−	0.759356i	$-0.274486\pi$
$464$	−0.766826			−0.0355990
$465$	20.1876	−	33.3063i	0.936179	−	1.54454i
$466$	2.37858			0.110185
$467$		−	6.59041i		−	0.304968i	−0.988306	−	0.152484i	$-0.951273\pi$
$467$		−	6.59041i		−	0.304968i	0.988306	−	0.152484i	$-0.0487272\pi$
$468$			1.58304i			0.0731759i
$469$	2.29081			0.105780
$470$	−14.5836	−	8.83942i	−0.672690	−	0.407732i
$471$	−48.5578			−2.23743
$472$			10.4329i			0.480212i
$473$			9.43194i			0.433681i
$474$	17.6040			0.808581
$475$		0			0
$476$	−3.76683			−0.172652
$477$		−	53.1844i		−	2.43515i
$478$		−	14.9309i		−	0.682923i
$479$	36.8064			1.68173			0.840864	−	0.541247i	$-0.182048\pi$
$479$	36.8064			1.68173			0.840864	+	0.541247i	$0.182048\pi$
$480$	−33.5233	−	20.3192i	−1.53012	−	0.927440i
$481$	0.185891			0.00847588
$482$			4.12980i			0.188107i
$483$		−	5.88801i		−	0.267914i
$484$	−9.22041			−0.419110
$485$	17.6084	−	29.0510i	0.799558	−	1.31914i
$486$	8.28310			0.375729
$487$		−	2.45475i		−	0.111235i	−0.998452	−	0.0556176i	$-0.982287\pi$
$487$		−	2.45475i		−	0.111235i	0.998452	−	0.0556176i	$-0.0177128\pi$
$488$		−	9.86258i		−	0.446458i
$489$	28.2901			1.27932
$490$	6.67906	−	11.0193i	0.301729	−	0.497803i
$491$	17.7943			0.803046			0.401523	−	0.915849i	$-0.368481\pi$
$491$	17.7943			0.803046			0.401523	+	0.915849i	$0.368481\pi$
$492$			38.8549i			1.75172i
$493$			46.2651i			2.08367i
$494$		0			0
$495$	−23.6988	−	14.3644i	−1.06518	−	0.645630i
$496$	−0.496486			−0.0222929
$497$			2.94326i			0.132023i
$498$		−	12.0009i		−	0.537774i
$499$	29.2798			1.31074			0.655371	−	0.755307i	$-0.272512\pi$
$499$	29.2798			1.31074			0.655371	+	0.755307i	$0.272512\pi$
$500$	0.896822	−	14.0095i	0.0401071	−	0.626522i
$501$	−9.45359			−0.422355
$502$		−	22.6462i		−	1.01075i
$503$			29.4378i			1.31257i	0.754515	+	0.656283i	$0.227872\pi$
$503$			29.4378i			1.31257i	−0.754515	+	0.656283i	$0.772128\pi$
$504$	−10.3132			−0.459388
$505$	−6.77188	−	4.10458i	−0.301345	−	0.182652i
$506$	5.56885			0.247566
$507$		−	39.9122i		−	1.77257i
$508$		−	10.6430i		−	0.472206i
$509$	6.69446			0.296727			0.148363	−	0.988933i	$-0.452599\pi$
$509$	6.69446			0.296727			0.148363	+	0.988933i	$0.452599\pi$
$510$	−16.3055	+	26.9014i	−0.722021	+	1.19122i
$511$	4.87439			0.215630
$512$			0.992797i			0.0438758i
$513$		0			0
$514$	19.1973			0.846757
$515$	−18.1876	+	30.0066i	−0.801443	+	1.32225i
$516$	−19.0697			−0.839498
$517$			16.9030i			0.743393i
$518$			0.467072i			0.0205220i
$519$	−32.0647			−1.40748
$520$	−1.04487	−	0.633318i	−0.0458206	−	0.0277728i
$521$	−20.0801			−0.879724			−0.439862	−	0.898065i	$-0.644973\pi$
$521$	−20.0801			−0.879724			−0.439862	+	0.898065i	$0.644973\pi$
$522$			48.8534i			2.13825i
$523$			36.4440i			1.59359i	0.604252	+	0.796793i	$0.293472\pi$
$523$			36.4440i			1.59359i	−0.604252	+	0.796793i	$0.706528\pi$
$524$	2.35350			0.102813
$525$	−4.03520	−	7.73238i	−0.176110	−	0.337469i
$526$	−7.60405			−0.331552
$527$			29.9546i			1.30484i
$528$			0.516796i			0.0224907i
$529$	11.6067			0.504639
$530$	13.5387	+	8.20610i	0.588084	+	0.356450i
$531$	−24.0724			−1.04465
$532$		0			0
$533$			1.95503i			0.0846816i
$534$	8.96216			0.387830
$535$	1.22547	−	2.02182i	0.0529817	−	0.0874111i
$536$	−11.3581			−0.490596
$537$			41.3936i			1.78626i
$538$		−	4.11045i		−	0.177214i
$539$	−12.7719			−0.550124
$540$	15.5990	−	25.7358i	0.671274	−	1.10749i
$541$	−14.6291			−0.628955			−0.314478	−	0.949265i	$-0.601829\pi$
$541$	−14.6291			−0.628955			−0.314478	+	0.949265i	$0.601829\pi$
$542$			3.03606i			0.130410i
$543$			24.5166i			1.05211i
$544$	30.1498			1.29266
$545$	12.8968	+	7.81704i	0.552439	+	0.334845i
$546$	−0.292775			−0.0125296
$547$			20.4186i			0.873038i	0.899695	+	0.436519i	$0.143789\pi$
$547$			20.4186i			0.873038i	−0.899695	+	0.436519i	$0.856211\pi$
$548$		−	15.6466i		−	0.668389i
$549$	22.7565			0.971223
$550$	7.31324	−	3.81647i	0.311838	−	0.162735i
$551$		0			0
$552$			29.1935i			1.24256i
$553$		−	3.75403i		−	0.159638i
$554$	28.2754			1.20131
$555$	−5.62648	−	3.41033i	−0.238831	−	0.144760i
$556$	0.393308			0.0166800
$557$		−	35.8798i		−	1.52028i	−0.649761	−	0.760138i	$-0.725131\pi$
$557$		−	35.8798i		−	1.52028i	0.649761	−	0.760138i	$-0.274869\pi$
$558$			31.6304i			1.33902i
$559$	−0.959512			−0.0405830
$560$	−0.0576321	+	0.0950835i	−0.00243540	+	0.00401801i
$561$	31.1799			1.31642
$562$		−	8.55873i		−	0.361028i
$563$		−	37.7708i		−	1.59185i	−0.605395	−	0.795925i	$-0.706985\pi$
$563$		−	37.7708i		−	1.59185i	0.605395	−	0.795925i	$-0.293015\pi$
$564$	−34.1749			−1.43902
$565$	9.15749	−	15.1083i	0.385258	−	0.635613i
$566$	2.13264			0.0896416
$567$		−	7.68266i		−	0.322641i
$568$		−	14.5931i		−	0.612311i
$569$	28.0844			1.17736			0.588681	−	0.808366i	$-0.299648\pi$
$569$	28.0844			1.17736			0.588681	+	0.808366i	$0.299648\pi$
$570$		0			0
$571$	20.6040			0.862253			0.431126	−	0.902292i	$-0.358116\pi$
$571$	20.6040			0.862253			0.431126	+	0.902292i	$0.358116\pi$
$572$			0.467072i			0.0195293i
$573$			43.4154i			1.81370i
$574$	−4.91223			−0.205032
$575$	−14.9622	+	7.80811i	−0.623965	+	0.325621i
$576$	30.6988			1.27912
$577$			43.8371i			1.82496i	0.409119	+	0.912481i	$0.365836\pi$
$577$			43.8371i			1.82496i	−0.409119	+	0.912481i	$0.634164\pi$
$578$		−	9.52702i		−	0.396272i
$579$	−12.2453			−0.508896
$580$	20.9769	+	12.7145i	0.871018	+	0.527942i
$581$	−2.55918			−0.106173
$582$			40.3600i			1.67297i
$583$		−	15.6919i		−	0.649894i
$584$	−24.1678			−1.00007
$585$	1.46129	−	2.41089i	0.0604169	−	0.0996779i
$586$	14.6918			0.606913
$587$			37.9809i			1.56764i	0.620987	+	0.783821i	$0.286732\pi$
$587$			37.9809i			1.56764i	−0.620987	+	0.783821i	$0.713268\pi$
$588$		−	25.8225i		−	1.06490i
$589$		0			0
$590$	3.71425	−	6.12790i	0.152913	−	0.252282i
$591$	−56.5002			−2.32411
$592$			0.0838722i			0.00344713i
$593$			5.38015i			0.220936i	0.993880	+	0.110468i	$0.0352350\pi$
$593$			5.38015i			0.220936i	−0.993880	+	0.110468i	$0.964765\pi$
$594$	17.6841			0.725588
$595$	5.73669	+	3.47713i	0.235181	+	0.142548i
$596$	−5.48175			−0.224541
$597$		−	4.94722i		−	0.202476i
$598$			0.566520i			0.0231667i
$599$	22.4285			0.916404			0.458202	−	0.888848i	$-0.348494\pi$
$599$	22.4285			0.916404			0.458202	+	0.888848i	$0.348494\pi$
$600$	20.0070	+	38.3381i	0.816783	+	1.56515i
$601$	29.5732			1.20632			0.603159	−	0.797621i	$-0.293909\pi$
$601$	29.5732			1.20632			0.603159	+	0.797621i	$0.293909\pi$
$602$		−	2.41089i		−	0.0982604i
$603$		−	26.2072i		−	1.06724i
$604$	−0.248581			−0.0101146
$605$	14.0422	+	8.51129i	0.570898	+	0.346033i
$606$	9.40804			0.382175
$607$		−	24.5915i		−	0.998139i	−0.866562	−	0.499069i	$-0.833675\pi$
$607$		−	24.5915i		−	0.998139i	0.866562	−	0.499069i	$-0.166325\pi$
$608$		0			0
$609$	15.2402			0.617564
$610$	−3.51122	+	5.79293i	−0.142165	+	0.234549i
$611$	−1.71954			−0.0695653
$612$			43.0931i			1.74194i
$613$		−	29.8901i		−	1.20725i	−0.797269	−	0.603624i	$-0.793723\pi$
$613$		−	29.8901i		−	1.20725i	0.797269	−	0.603624i	$-0.206277\pi$
$614$	18.1005			0.730478
$615$	35.8667	−	59.1741i	1.44628	−	2.38613i
$616$	−3.04290			−0.122602
$617$			40.7141i			1.63909i	0.573017	+	0.819544i	$0.305773\pi$
$617$			40.7141i			1.63909i	−0.573017	+	0.819544i	$0.694227\pi$
$618$		−	41.6875i		−	1.67692i
$619$	28.4784			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$619$	28.4784			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$620$	13.5816	+	8.23210i	0.545451	+	0.330609i
$621$	−36.1799			−1.45185
$622$		−	2.71608i		−	0.108905i
$623$		−	1.91116i		−	0.0765692i
$624$	−0.0525737			−0.00210463
$625$	−14.2978	+	20.5079i	−0.571913	+	0.820314i
$626$	10.6060			0.423902
$627$		0			0
$628$		−	19.8009i		−	0.790141i
$629$	5.06028			0.201766
$630$	6.05763	+	3.67166i	0.241342	+	0.146282i
$631$	42.4201			1.68872			0.844359	−	0.535777i	$-0.179981\pi$
$631$	42.4201			1.68872			0.844359	+	0.535777i	$0.179981\pi$
$632$			18.6130i			0.740384i
$633$		−	18.7823i		−	0.746529i
$634$	−9.88912			−0.392747
$635$	−9.82446	+	16.2087i	−0.389872	+	0.643224i
$636$	31.7263			1.25803
$637$		−	1.29929i		−	0.0514796i
$638$			14.4141i			0.570659i
$639$	33.6714			1.33202
$640$	8.46129	−	13.9597i	0.334462	−	0.551807i
$641$	29.5259			1.16620			0.583102	−	0.812399i	$-0.301839\pi$
$641$	29.5259			1.16620			0.583102	+	0.812399i	$0.301839\pi$
$642$			2.80888i			0.110858i
$643$			21.5970i			0.851704i	0.904793	+	0.425852i	$0.140026\pi$
$643$			21.5970i			0.851704i	−0.904793	+	0.425852i	$0.859974\pi$
$644$	2.40101			0.0946131
$645$	29.0422	+	17.6031i	1.14354	+	0.693122i
$646$		0			0
$647$			12.6128i			0.495861i	0.968778	+	0.247930i	$0.0797504\pi$
$647$			12.6128i			0.495861i	−0.968778	+	0.247930i	$0.920250\pi$
$648$			38.0916i			1.49638i
$649$	−7.10250			−0.278798
$650$	0.388250	+	0.743977i	0.0152284	+	0.0291812i
$651$	9.86736			0.386732
$652$			11.5361i			0.451790i
$653$		−	26.6312i		−	1.04216i	−0.853508	−	0.521080i	$-0.825529\pi$
$653$		−	26.6312i		−	1.04216i	0.853508	−	0.521080i	$-0.174471\pi$
$654$	−17.9173			−0.700621
$655$	−3.58426	−	2.17249i	−0.140049	−	0.0848864i
$656$	−0.882090			−0.0344398
$657$		−	55.7638i		−	2.17555i
$658$		−	4.32055i		−	0.168433i
$659$	39.9545			1.55640			0.778202	−	0.628014i	$-0.216132\pi$
$659$	39.9545			1.55640			0.778202	+	0.628014i	$0.216132\pi$
$660$	8.56885	−	14.1372i	0.333542	−	0.550289i
$661$	13.5233			0.525996			0.262998	−	0.964796i	$-0.415289\pi$
$661$	13.5233			0.525996			0.262998	+	0.964796i	$0.415289\pi$
$662$		−	5.05352i		−	0.196411i
$663$			3.17194i			0.123188i
$664$	12.6887			0.492418
$665$		0			0
$666$	5.34338			0.207052
$667$		−	29.4898i		−	1.14185i
$668$		−	3.85498i		−	0.149154i
$669$	−53.0389			−2.05060
$670$	6.67135	+	4.04365i	0.257737	+	0.156220i
$671$	6.71425			0.259201
$672$		−	9.93166i		−	0.383122i
$673$		−	34.4110i		−	1.32645i	−0.748421	−	0.663224i	$-0.769188\pi$
$673$		−	34.4110i		−	1.32645i	0.748421	−	0.663224i	$-0.230812\pi$
$674$	−7.42851			−0.286135
$675$	−47.5130	+	24.7950i	−1.82877	+	0.954359i
$676$	16.2754			0.625977
$677$		−	29.6650i		−	1.14012i	−0.821604	−	0.570059i	$-0.806920\pi$
$677$		−	29.6650i		−	1.14012i	0.821604	−	0.570059i	$-0.193080\pi$
$678$			20.9897i			0.806105i
$679$	8.60669			0.330295
$680$	−28.4432	−	17.2400i	−1.09075	−	0.661126i
$681$	3.64892			0.139827
$682$			9.33249i			0.357360i
$683$			27.8978i			1.06748i	0.845648	+	0.533740i	$0.179214\pi$
$683$			27.8978i			1.06748i	−0.845648	+	0.533740i	$0.820786\pi$
$684$		0			0
$685$	−14.4432	+	23.8290i	−0.551848	+	0.910458i
$686$	6.68608			0.255276
$687$			19.2381i			0.733981i
$688$		−	0.432924i		−	0.0165051i
$689$	1.59634			0.0608158
$690$	10.3933	−	17.1472i	0.395666	−	0.652784i
$691$	−49.6386			−1.88834			−0.944170	−	0.329459i	$-0.893134\pi$
$691$	−49.6386			−1.88834			−0.944170	+	0.329459i	$0.893134\pi$
$692$		−	13.0753i		−	0.497049i
$693$		−	7.02105i		−	0.266708i
$694$	−10.4312			−0.395961
$695$	−0.598988	−	0.363059i	−0.0227209	−	0.0137716i
$696$	−75.5629			−2.86420
$697$			53.2193i			2.01582i
$698$		−	16.3773i		−	0.619889i
$699$	−8.48878			−0.321075
$700$	3.15311	−	1.64547i	0.119176	−	0.0621930i
$701$	−49.9813			−1.88777			−0.943883	−	0.330279i	$-0.892857\pi$
$701$	−49.9813			−1.88777			−0.943883	+	0.330279i	$0.892857\pi$
$702$			1.79901i			0.0678991i
$703$		0			0
$704$	9.05763			0.341372
$705$	52.0466	+	31.5465i	1.96019	+	1.18811i
$706$	6.65859			0.250599
$707$		−	2.00625i		−	0.0754527i
$708$		−	14.3600i		−	0.539682i
$709$	−25.1876			−0.945941			−0.472971	−	0.881078i	$-0.656818\pi$
$709$	−25.1876			−0.945941			−0.472971	+	0.881078i	$0.656818\pi$
$710$	−5.19533	+	8.57144i	−0.194977	+	0.321680i
$711$	−42.9468			−1.61063
$712$			9.47580i			0.355121i
$713$		−	19.0933i		−	0.715051i
$714$	−7.96986			−0.298265
$715$	0.431150	−	0.711327i	0.0161241	−	0.0266021i
$716$	−16.8794			−0.630814
$717$			53.2861i			1.99001i
$718$			6.06547i			0.226361i
$719$	−17.1755			−0.640540			−0.320270	−	0.947326i	$-0.603774\pi$
$719$	−17.1755			−0.640540			−0.320270	+	0.947326i	$0.603774\pi$
$720$	1.08777	+	0.659321i	0.0405388	+	0.0245714i
$721$	−8.88979			−0.331073
$722$		0			0
$723$		−	14.7386i		−	0.548136i
$724$	−9.99735			−0.371549
$725$	−20.2101	−	38.7272i	−0.750583	−	1.43829i
$726$	−19.5086			−0.724031
$727$			1.05653i			0.0391845i	0.999808	+	0.0195922i	$0.00623680\pi$
$727$			1.05653i			0.0391845i	−0.999808	+	0.0195922i	$0.993763\pi$
$728$		−	0.309555i		−	0.0114729i
$729$	11.1223			0.411937
$730$	14.1953	+	8.60409i	0.525393	+	0.318452i
$731$	−26.1196			−0.966070
$732$			13.5750i			0.501748i
$733$			20.5025i			0.757277i	0.925545	+	0.378639i	$0.123608\pi$
$733$			20.5025i			0.757277i	−0.925545	+	0.378639i	$0.876392\pi$
$734$	−29.0851			−1.07355
$735$	−23.8365	+	39.3264i	−0.879224	+	1.45058i
$736$	−19.2178			−0.708376
$737$		−	7.73238i		−	0.284826i
$738$			56.1967i			2.06863i
$739$	−24.9096			−0.916314			−0.458157	−	0.888871i	$-0.651490\pi$
$739$	−24.9096			−0.916314			−0.458157	+	0.888871i	$0.651490\pi$
$740$	1.39066	−	2.29436i	0.0511218	−	0.0843425i
$741$		0			0
$742$			4.01100i			0.147248i
$743$		−	13.2573i		−	0.486364i	−0.969981	−	0.243182i	$-0.921809\pi$
$743$		−	13.2573i		−	0.486364i	0.969981	−	0.243182i	$-0.0781913\pi$
$744$	−48.9236			−1.79363
$745$	8.34844	+	5.06016i	0.305863	+	0.185390i
$746$	8.63615			0.316192
$747$			29.2774i			1.07120i
$748$			12.7145i			0.464889i
$749$	0.598988			0.0218866
$750$	1.89750	−	29.6412i	0.0692868	−	1.08235i
$751$	−24.8365			−0.906298			−0.453149	−	0.891435i	$-0.649700\pi$
$751$	−24.8365			−0.906298			−0.453149	+	0.891435i	$0.649700\pi$
$752$		−	0.775843i		−	0.0282921i
$753$			80.8209i			2.94528i
$754$	−1.46635			−0.0534012
$755$	0.378577	+	0.229463i	0.0137778	+	0.00835103i
$756$	7.62451			0.277301
$757$		−	48.4658i		−	1.76152i	−0.473562	−	0.880760i	$-0.657032\pi$
$757$		−	48.4658i		−	1.76152i	0.473562	−	0.880760i	$-0.342968\pi$
$758$		−	30.8931i		−	1.12209i
$759$	−19.8744			−0.721395
$760$		0			0
$761$	40.3726			1.46351			0.731753	−	0.681570i	$-0.238702\pi$
$761$	40.3726			1.46351			0.731753	+	0.681570i	$0.238702\pi$
$762$		−	22.5185i		−	0.815758i
$763$			3.82083i			0.138323i
$764$	−17.7039			−0.640505
$765$	39.7789	−	65.6287i	1.43821	−	2.37281i
$766$	−14.0198			−0.506556
$767$		−	0.722538i		−	0.0260893i
$768$			48.5638i			1.75239i
$769$	44.9545			1.62110			0.810550	−	0.585670i	$-0.199169\pi$
$769$	44.9545			1.62110			0.810550	+	0.585670i	$0.199169\pi$
$770$	1.78729	+	1.08332i	0.0644095	+	0.0390400i
$771$	−68.5123			−2.46741
$772$		−	4.99337i		−	0.179715i
$773$		−	3.68645i		−	0.132592i	−0.997800	−	0.0662962i	$-0.978882\pi$
$773$		−	3.68645i		−	0.132592i	0.997800	−	0.0662962i	$-0.0211182\pi$
$774$	−27.5809			−0.991376
$775$	−13.0851	−	25.0742i	−0.470032	−	0.900690i
$776$	−42.6731			−1.53187
$777$		−	1.66691i		−	0.0598000i
$778$			16.7255i			0.599639i
$779$		0			0
$780$	1.43818	+	0.871710i	0.0514950	+	0.0312122i
$781$	9.93466			0.355490
$782$			15.4217i			0.551478i
$783$		−	93.6461i		−	3.34664i
$784$	0.586226			0.0209366
$785$	−18.2780	+	30.1558i	−0.652371	+	1.07631i
$786$	4.97953			0.177614
$787$			45.7141i			1.62953i	0.579790	+	0.814766i	$0.303135\pi$
$787$			45.7141i			1.62953i	−0.579790	+	0.814766i	$0.696865\pi$
$788$		−	23.0396i		−	0.820753i
$789$	27.1377			0.966128
$790$	6.62648	−	10.9326i	0.235760	−	0.388965i
$791$	4.47602			0.159149
$792$			34.8113i			1.23697i
$793$			0.683042i			0.0242555i
$794$	4.61945			0.163938
$795$	−48.3176	−	29.2863i	−1.71365	−	1.03868i
$796$	2.01738			0.0715040
$797$		−	30.3378i		−	1.07462i	−0.843385	−	0.537310i	$-0.819441\pi$
$797$		−	30.3378i		−	1.07462i	0.843385	−	0.537310i	$-0.180559\pi$
$798$		0			0
$799$	−46.8091			−1.65599
$800$	−25.2376	+	13.1704i	−0.892282	+	0.465644i
$801$	−21.8640			−0.772528
$802$		−	7.19415i		−	0.254034i
$803$		−	16.4530i		−	0.580614i
$804$	15.6335			0.551351
$805$	−3.65662	−	2.21635i	−0.128879	−	0.0781162i
$806$	−0.949395			−0.0334410
$807$			14.6696i			0.516393i
$808$			9.94724i			0.349943i
$809$	−34.5585			−1.21501			−0.607506	−	0.794315i	$-0.707830\pi$
$809$	−34.5585			−1.21501			−0.607506	+	0.794315i	$0.707830\pi$
$810$	13.5611	−	22.3737i	0.476490	−	0.786130i
$811$	−33.2754			−1.16846			−0.584229	−	0.811589i	$-0.698603\pi$
$811$	−33.2754			−1.16846			−0.584229	+	0.811589i	$0.698603\pi$
$812$			6.21464i			0.218091i
$813$		−	10.8352i		−	0.380008i
$814$	1.57655			0.0552582
$815$	10.6489	−	17.5690i	0.373015	−	0.615414i
$816$	−1.43115			−0.0501003
$817$		0			0
$818$		−	30.4757i		−	1.06556i
$819$	0.714253			0.0249580
$820$	24.1300	+	14.6257i	0.842656	+	0.510752i
$821$	12.7013			0.443277			0.221638	−	0.975129i	$-0.428860\pi$
$821$	12.7013			0.443277			0.221638	+	0.975129i	$0.428860\pi$
$822$		−	33.1051i		−	1.15467i
$823$		−	12.0091i		−	0.418610i	−0.977850	−	0.209305i	$-0.932880\pi$
$823$		−	12.0091i		−	0.418610i	0.977850	−	0.209305i	$-0.0671201\pi$
$824$	44.0767			1.53549
$825$	−26.0999	+	13.6204i	−0.908680	+	0.474201i
$826$	1.81546			0.0631680
$827$			8.54544i			0.297154i	0.988901	+	0.148577i	$0.0474693\pi$
$827$			8.54544i			0.297154i	−0.988901	+	0.148577i	$0.952531\pi$
$828$		−	27.4680i		−	0.954578i
$829$	−27.1042			−0.941369			−0.470685	−	0.882302i	$-0.655993\pi$
$829$	−27.1042			−0.941369			−0.470685	+	0.882302i	$0.655993\pi$
$830$	−7.45291	−	4.51737i	−0.258694	−	0.156800i
$831$	−100.911			−3.50055
$832$			0.921434i			0.0319450i
$833$		−	35.3689i		−	1.22546i
$834$	0.832162			0.0288154
$835$	−3.55850	+	5.87094i	−0.123147	+	0.203172i
$836$		0			0
$837$		−	60.6317i		−	2.09574i
$838$		−	18.3300i		−	0.633200i
$839$	−36.4379			−1.25798			−0.628989	−	0.777414i	$-0.716531\pi$
$839$	−36.4379			−1.25798			−0.628989	+	0.777414i	$0.716531\pi$
$840$	−5.67906	+	9.36951i	−0.195946	+	0.323279i
$841$	47.3297			1.63206
$842$			12.8333i			0.442266i
$843$			30.5448i			1.05202i
$844$	7.65903			0.263635
$845$	−24.7866	−	15.0237i	−0.852686	−	0.516831i
$846$	−49.4278			−1.69936
$847$			4.16017i			0.142945i
$848$			0.720256i			0.0247337i
$849$	−7.61107			−0.261211
$850$	10.5688	+	20.2524i	0.362509	+	0.694651i
$851$	−3.22547			−0.110568
$852$			20.0861i			0.688140i
$853$		−	18.3471i		−	0.628192i	−0.949391	−	0.314096i	$-0.898299\pi$
$853$		−	18.3471i		−	0.628192i	0.949391	−	0.314096i	$-0.101701\pi$
$854$	−1.71622			−0.0587279
$855$		0			0
$856$	−2.96986			−0.101508
$857$		−	7.85783i		−	0.268418i	−0.990953	−	0.134209i	$-0.957151\pi$
$857$		−	7.85783i		−	0.268418i	0.990953	−	0.134209i	$-0.0428494\pi$
$858$			0.988232i			0.0337377i
$859$	34.3022			1.17038			0.585188	−	0.810897i	$-0.301021\pi$
$859$	34.3022			1.17038			0.585188	+	0.810897i	$0.301021\pi$
$860$	−7.17819	+	11.8428i	−0.244774	+	0.403837i
$861$	17.5310			0.597455
$862$			14.6257i			0.498153i
$863$			35.9451i			1.22359i	0.791018	+	0.611793i	$0.209551\pi$
$863$			35.9451i			1.22359i	−0.791018	+	0.611793i	$0.790449\pi$
$864$	−61.0268			−2.07617
$865$	−12.0697	+	19.9130i	−0.410383	+	0.677064i
$866$	19.9699			0.678604
$867$			34.0005i			1.15472i
$868$			4.02371i			0.136574i
$869$	−12.6714			−0.429846
$870$	44.3830	+	26.9014i	1.50472	+	0.912045i
$871$	0.786616			0.0266535
$872$		−	18.9442i		−	0.641531i
$873$		−	98.4620i		−	3.33243i
$874$		0			0
$875$	−6.32094	−	0.404638i	−0.213687	−	0.0136793i
$876$	33.2650			1.12392
$877$		−	25.2516i		−	0.852686i	−0.904561	−	0.426343i	$-0.859802\pi$
$877$		−	25.2516i		−	0.852686i	0.904561	−	0.426343i	$-0.140198\pi$
$878$			28.9426i			0.976766i
$879$	−52.4329			−1.76852
$880$	0.320945	+	0.194531i	0.0108190	+	0.00655765i
$881$	17.7796			0.599010			0.299505	−	0.954095i	$-0.403179\pi$
$881$	17.7796			0.599010			0.299505	+	0.954095i	$0.403179\pi$
$882$		−	37.3476i		−	1.25756i
$883$			7.55342i			0.254193i	0.991890	+	0.127096i	$0.0405658\pi$
$883$			7.55342i			0.254193i	−0.991890	+	0.127096i	$0.959434\pi$
$884$	−1.29345			−0.0435035
$885$	−13.2556	+	21.8696i	−0.445582	+	0.735138i
$886$	27.0550			0.908930
$887$		−	16.2406i		−	0.545306i	−0.962112	−	0.272653i	$-0.912099\pi$
$887$		−	16.2406i		−	0.545306i	0.962112	−	0.272653i	$-0.0879011\pi$
$888$			8.26475i			0.277347i
$889$	−4.80202			−0.161055
$890$	3.37352	−	5.56575i	0.113081	−	0.186564i
$891$	−25.9320			−0.868755
$892$		−	21.6282i		−	0.724165i
$893$		0			0
$894$	−11.5983			−0.387906
$895$	25.7065	+	15.5813i	0.859275	+	0.520825i
$896$	4.13573			0.138165
$897$		−	2.02182i		−	0.0675067i
$898$		−	13.8305i		−	0.461530i
$899$	49.4201			1.64825
$900$	−18.8245	−	36.0721i	−0.627482	−	1.20240i
$901$	43.4553			1.44771
$902$			16.5807i			0.552078i
$903$			8.60409i			0.286326i
$904$	−22.1927			−0.738118
$905$	15.2255	+	9.22848i	0.506112	+	0.306765i
$906$	−0.525949			−0.0174735
$907$		−	18.2535i		−	0.606097i	−0.952975	−	0.303049i	$-0.901996\pi$
$907$		−	18.2535i		−	0.606097i	0.952975	−	0.303049i	$-0.0980045\pi$
$908$			1.48795i			0.0493795i
$909$	−22.9518			−0.761263
$910$	−0.110206	+	0.181821i	−0.00365329	+	0.00602732i
$911$	−15.9019			−0.526853			−0.263426	−	0.964679i	$-0.584853\pi$
$911$	−15.9019			−0.526853			−0.263426	+	0.964679i	$0.584853\pi$
$912$		0			0
$913$			8.63824i			0.285884i
$914$	−13.2851			−0.439431
$915$	12.5310	−	20.6741i	0.414262	−	0.683465i
$916$	−7.84492			−0.259204
$917$		−	1.06188i		−	0.0350663i
$918$			48.9722i			1.61632i
$919$	30.0748			0.992075			0.496038	−	0.868301i	$-0.334788\pi$
$919$	30.0748			0.992075			0.496038	+	0.868301i	$0.334788\pi$
$920$	18.1300	+	10.9890i	0.597728	+	0.362296i
$921$	−64.5981			−2.12858
$922$		−	5.01630i		−	0.165203i
$923$			1.01065i			0.0332661i
$924$	4.18830			0.137785
$925$	−4.23582	+	2.21049i	−0.139273	+	0.0726805i
$926$	28.1947			0.926534
$927$			101.701i			3.34029i
$928$		−	49.7422i		−	1.63287i
$929$	36.8442			1.20882			0.604410	−	0.796673i	$-0.293409\pi$
$929$	36.8442			1.20882			0.604410	+	0.796673i	$0.293409\pi$
$930$	28.7360	+	17.4175i	0.942291	+	0.571142i
$931$		0			0
$932$		−	3.46155i		−	0.113387i
$933$			9.69327i			0.317343i
$934$	5.68608			0.186054
$935$	11.7367	−	19.3636i	0.383831	−	0.633257i
$936$	−3.54136			−0.115753
$937$			43.2321i			1.41233i	0.708047	+	0.706165i	$0.249576\pi$
$937$			43.2321i			1.41233i	−0.708047	+	0.706165i	$0.750424\pi$
$938$			1.97646i			0.0645338i
$939$	−37.8513			−1.23523
$940$	−12.8640	+	21.2235i	−0.419579	+	0.692236i
$941$	20.3203			0.662422			0.331211	−	0.943557i	$-0.392543\pi$
$941$	20.3203			0.662422			0.331211	+	0.943557i	$0.392543\pi$
$942$		−	41.8948i		−	1.36501i
$943$		−	33.9225i		−	1.10467i
$944$	0.326003			0.0106105
$945$	−11.6118	−	7.03813i	−0.377730	−	0.228950i
$946$	−8.13770			−0.264579
$947$			21.5050i			0.698819i	0.936970	+	0.349409i	$0.113618\pi$
$947$			21.5050i			0.698819i	−0.936970	+	0.349409i	$0.886382\pi$
$948$		−	25.6192i		−	0.832074i
$949$	1.67376			0.0543327
$950$		0			0
$951$	35.2928			1.14445
$952$		−	8.42663i		−	0.273109i
$953$		−	17.7301i		−	0.574333i	−0.957881	−	0.287166i	$-0.907287\pi$
$953$		−	17.7301i		−	0.574333i	0.957881	−	0.287166i	$-0.0927133\pi$
$954$	45.8865			1.48563
$955$	26.9622	+	16.3423i	0.872475	+	0.528825i
$956$	−21.7290			−0.702766
$957$		−	51.4417i		−	1.66288i
$958$			31.7559i			1.02599i
$959$	−7.05960			−0.227966
$960$	16.9045	−	27.8897i	0.545591	−	0.900136i
$961$	0.997355			0.0321727
$962$			0.160383i			0.00517095i
$963$		−	6.85253i		−	0.220820i
$964$	6.01012			0.193573
$965$	−4.60934	+	7.60465i	−0.148380	+	0.244802i
$966$	5.08007			0.163448
$967$			13.6530i			0.439052i	0.975607	+	0.219526i	$0.0704511\pi$
$967$			13.6530i			0.439052i	−0.975607	+	0.219526i	$0.929549\pi$
$968$		−	20.6267i		−	0.662966i
$969$		0			0
$970$	25.0647	+	15.1922i	0.804778	+	0.487793i
$971$	−27.9595			−0.897263			−0.448632	−	0.893717i	$-0.648089\pi$
$971$	−27.9595			−0.897263			−0.448632	+	0.893717i	$0.648089\pi$
$972$		−	12.0544i		−	0.386646i
$973$		−	0.177457i		−	0.00568901i
$974$	2.11791			0.0678622
$975$	−1.38560	−	2.65514i	−0.0443749	−	0.0850326i
$976$	−0.308182			−0.00986468
$977$			17.8540i			0.571200i	0.958349	+	0.285600i	$0.0921929\pi$
$977$			17.8540i			0.571200i	−0.958349	+	0.285600i	$0.907807\pi$
$978$			24.4082i			0.780488i
$979$	−6.45094			−0.206173
$980$	−16.0365	−	9.72006i	−0.512267	−	0.310496i
$981$	43.7109			1.39558
$982$			15.3526i			0.489921i
$983$			49.0443i			1.56427i	0.623108	+	0.782136i	$0.285870\pi$
$983$			49.0443i			1.56427i	−0.623108	+	0.782136i	$0.714130\pi$
$984$	−86.9210			−2.77094
$985$	−21.2677	+	35.0882i	−0.677645	+	1.11800i
$986$	−39.9166			−1.27120
$987$			15.4194i			0.490805i
$988$		0			0
$989$	16.6489			0.529405
$990$	12.3933	−	20.4469i	0.393885	−	0.649846i
$991$	25.0673			0.796289			0.398145	−	0.917323i	$-0.369654\pi$
$991$	25.0673			0.796289			0.398145	+	0.917323i	$0.369654\pi$
$992$		−	32.2059i		−	1.02254i
$993$			18.0352i			0.572331i
$994$	−2.53939			−0.0805445
$995$	−3.07236	−	1.86222i	−0.0974005	−	0.0590365i
$996$	−17.4650			−0.553400
$997$		−	30.0222i		−	0.950811i	−0.879767	−	0.475406i	$-0.842301\pi$
$997$		−	30.0222i		−	0.950811i	0.879767	−	0.475406i	$-0.157699\pi$
$998$			25.2620i			0.799656i
$999$	−10.2426			−0.324062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.g.1084.5		6
5.2	odd	4		9025.2.a.bt.1.2		6
5.3	odd	4		9025.2.a.bt.1.5		6
5.4	even	2	inner	1805.2.b.g.1084.2		6
19.8	odd	6		95.2.i.b.64.2	yes	12
19.12	odd	6		95.2.i.b.49.5	yes	12
19.18	odd	2		1805.2.b.f.1084.2		6
57.8	even	6		855.2.be.d.64.5		12
57.50	even	6		855.2.be.d.334.2		12
95.8	even	12		475.2.e.g.26.5		12
95.12	even	12		475.2.e.g.201.2		12
95.18	even	4		9025.2.a.bu.1.2		6
95.27	even	12		475.2.e.g.26.2		12
95.37	even	4		9025.2.a.bu.1.5		6
95.69	odd	6		95.2.i.b.49.2	✓	12
95.84	odd	6		95.2.i.b.64.5	yes	12
95.88	even	12		475.2.e.g.201.5		12
95.94	odd	2		1805.2.b.f.1084.5		6
285.164	even	6		855.2.be.d.334.5		12
285.179	even	6		855.2.be.d.64.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.2	✓	12	95.69	odd	6
95.2.i.b.49.5	yes	12	19.12	odd	6
95.2.i.b.64.2	yes	12	19.8	odd	6
95.2.i.b.64.5	yes	12	95.84	odd	6
475.2.e.g.26.2		12	95.27	even	12
475.2.e.g.26.5		12	95.8	even	12
475.2.e.g.201.2		12	95.12	even	12
475.2.e.g.201.5		12	95.88	even	12
855.2.be.d.64.2		12	285.179	even	6
855.2.be.d.64.5		12	57.8	even	6
855.2.be.d.334.2		12	57.50	even	6
855.2.be.d.334.5		12	285.164	even	6
1805.2.b.f.1084.2		6	19.18	odd	2
1805.2.b.f.1084.5		6	95.94	odd	2
1805.2.b.g.1084.2		6	5.4	even	2	inner
1805.2.b.g.1084.5		6	1.1	even	1	trivial
9025.2.a.bt.1.2		6	5.2	odd	4
9025.2.a.bt.1.5		6	5.3	odd	4
9025.2.a.bu.1.2		6	95.18	even	4
9025.2.a.bu.1.5		6	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)

\(f(q)\)	\(=\)	\(q+0.862781i q^{2} -3.07914i q^{3} +1.25561 q^{4} +(-1.91223 - 1.15904i) q^{5} +2.65662 q^{6} -0.566520i q^{7} +2.80888i q^{8} -6.48108 q^{9} +O(q^{10})\)	\(q+0.862781i q^{2} -3.07914i q^{3} +1.25561 q^{4} +(-1.91223 - 1.15904i) q^{5} +2.65662 q^{6} -0.566520i q^{7} +2.80888i q^{8} -6.48108 q^{9} +(1.00000 - 1.64984i) q^{10} -1.91223 q^{11} -3.86619i q^{12} -0.194531i q^{13} +0.488783 q^{14} +(-3.56885 + 5.88801i) q^{15} +0.0877708 q^{16} -5.29549i q^{17} -5.59175i q^{18} +(-2.40101 - 1.45530i) q^{20} -1.74439 q^{21} -1.64984i q^{22} +3.37540i q^{23} +8.64892 q^{24} +(2.31324 + 4.43271i) q^{25} +0.167838 q^{26} +10.7187i q^{27} -0.711327i q^{28} -8.73669 q^{29} +(-5.08007 - 3.07914i) q^{30} -5.65662 q^{31} +5.69348i q^{32} +5.88801i q^{33} +4.56885 q^{34} +(-0.656620 + 1.08332i) q^{35} -8.13770 q^{36} +0.955582i q^{37} -0.598988 q^{39} +(3.25561 - 5.37122i) q^{40} -10.0499 q^{41} -1.50503i q^{42} -4.93243i q^{43} -2.40101 q^{44} +(12.3933 + 7.51185i) q^{45} -2.91223 q^{46} -8.83942i q^{47} -0.270258i q^{48} +6.67906 q^{49} +(-3.82446 + 1.99582i) q^{50} -16.3055 q^{51} -0.244255i q^{52} +8.20610i q^{53} -9.24791 q^{54} +(3.65662 + 2.21635i) q^{55} +1.59128 q^{56} -7.53785i q^{58} +3.71425 q^{59} +(-4.48108 + 7.39304i) q^{60} -3.51122 q^{61} -4.88043i q^{62} +3.67166i q^{63} -4.73669 q^{64} +(-0.225470 + 0.371988i) q^{65} -5.08007 q^{66} +4.04365i q^{67} -6.64906i q^{68} +10.3933 q^{69} +(-0.934664 - 0.566520i) q^{70} -5.19533 q^{71} -18.2046i q^{72} +8.60409i q^{73} -0.824458 q^{74} +(13.6489 - 7.12278i) q^{75} +1.08332i q^{77} -0.516796i q^{78} +6.62648 q^{79} +(-0.167838 - 0.101730i) q^{80} +13.5611 q^{81} -8.67089i q^{82} -4.51737i q^{83} -2.19027 q^{84} +(-6.13770 + 10.1262i) q^{85} +4.25561 q^{86} +26.9014i q^{87} -5.37122i q^{88} +3.37352 q^{89} +(-6.48108 + 10.6927i) q^{90} -0.110206 q^{91} +4.23818i q^{92} +17.4175i q^{93} +7.62648 q^{94} +17.5310 q^{96} +15.1922i q^{97} +5.76256i q^{98} +12.3933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9}+O(q^{10}) \) 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9	\( 6 q - 2 q^{4} + 2 q^{5} + 12 q^{6} - 8 q^{9} + 6 q^{10} + 2 q^{11} + 22 q^{14} - 4 q^{15} + 14 q^{16} - 20 q^{20} - 20 q^{21} - 2 q^{24} + 6 q^{25} - 22 q^{26} - 12 q^{29} + 6 q^{30} - 30 q^{31} + 10 q^{34} - 14 q^{36} + 2 q^{39} + 10 q^{40} - 12 q^{41} - 20 q^{44} + 30 q^{45} - 4 q^{46} - 2 q^{49} + 4 q^{50} - 40 q^{51} + 4 q^{54} + 18 q^{55} - 46 q^{56} + 20 q^{59} + 4 q^{60} - 2 q^{61} + 12 q^{64} + 20 q^{65} + 6 q^{66} + 18 q^{69} + 46 q^{70} + 2 q^{71} + 22 q^{74} + 28 q^{75} + 24 q^{79} + 22 q^{80} + 14 q^{81} + 48 q^{84} - 2 q^{85} + 16 q^{86} + 36 q^{89} - 8 q^{90} + 24 q^{91} + 30 q^{94} + 26 q^{96} + 30 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 12 * q^6 - 8 * q^9 + 6 * q^10 + 2 * q^11 + 22 * q^14 - 4 * q^15 + 14 * q^16 - 20 * q^20 - 20 * q^21 - 2 * q^24 + 6 * q^25 - 22 * q^26 - 12 * q^29 + 6 * q^30 - 30 * q^31 + 10 * q^34 - 14 * q^36 + 2 * q^39 + 10 * q^40 - 12 * q^41 - 20 * q^44 + 30 * q^45 - 4 * q^46 - 2 * q^49 + 4 * q^50 - 40 * q^51 + 4 * q^54 + 18 * q^55 - 46 * q^56 + 20 * q^59 + 4 * q^60 - 2 * q^61 + 12 * q^64 + 20 * q^65 + 6 * q^66 + 18 * q^69 + 46 * q^70 + 2 * q^71 + 22 * q^74 + 28 * q^75 + 24 * q^79 + 22 * q^80 + 14 * q^81 + 48 * q^84 - 2 * q^85 + 16 * q^86 + 36 * q^89 - 8 * q^90 + 24 * q^91 + 30 * q^94 + 26 * q^96 + 30 * q^99

Introduction

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