LMFDB - Embedded newform 1805.2.b.k.1084.24

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			1084.24
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.68669i q^{2} +2.14658i q^{3} -5.21828 q^{4} +(-1.71227 + 1.43810i) q^{5} -5.76720 q^{6} +2.78303i q^{7} -8.64651i q^{8} -1.60782 q^{9} +(-3.86371 - 4.60034i) q^{10} -2.37999 q^{11} -11.2015i q^{12} -0.0404924i q^{13} -7.47713 q^{14} +(-3.08699 - 3.67554i) q^{15} +12.7939 q^{16} -1.81575i q^{17} -4.31971i q^{18} +(8.93512 - 7.50439i) q^{20} -5.97401 q^{21} -6.39429i q^{22} +2.54434i q^{23} +18.5605 q^{24} +(0.863754 - 4.92483i) q^{25} +0.108790 q^{26} +2.98843i q^{27} -14.5226i q^{28} -2.94820 q^{29} +(9.87501 - 8.29379i) q^{30} -2.88614 q^{31} +17.0802i q^{32} -5.10885i q^{33} +4.87834 q^{34} +(-4.00227 - 4.76531i) q^{35} +8.39006 q^{36} -0.227089i q^{37} +0.0869204 q^{39} +(12.4345 + 14.8052i) q^{40} +8.03741 q^{41} -16.0503i q^{42} -5.13269i q^{43} +12.4195 q^{44} +(2.75303 - 2.31220i) q^{45} -6.83583 q^{46} +11.0764i q^{47} +27.4632i q^{48} -0.745270 q^{49} +(13.2315 + 2.32064i) q^{50} +3.89765 q^{51} +0.211301i q^{52} -5.71448i q^{53} -8.02897 q^{54} +(4.07519 - 3.42266i) q^{55} +24.0635 q^{56} -7.92088i q^{58} -11.6165 q^{59} +(16.1088 + 19.1800i) q^{60} +4.58383 q^{61} -7.75415i q^{62} -4.47462i q^{63} -20.3012 q^{64} +(0.0582320 + 0.0693341i) q^{65} +13.7259 q^{66} +4.85278i q^{67} +9.47508i q^{68} -5.46163 q^{69} +(12.8029 - 10.7528i) q^{70} -7.76927 q^{71} +13.9020i q^{72} +4.24767i q^{73} +0.610118 q^{74} +(10.5716 + 1.85412i) q^{75} -6.62359i q^{77} +0.233528i q^{78} -11.6104 q^{79} +(-21.9066 + 18.3989i) q^{80} -11.2384 q^{81} +21.5940i q^{82} -4.47055i q^{83} +31.1741 q^{84} +(2.61122 + 3.10906i) q^{85} +13.7899 q^{86} -6.32855i q^{87} +20.5786i q^{88} -15.3931 q^{89} +(6.21216 + 7.39652i) q^{90} +0.112692 q^{91} -13.2771i q^{92} -6.19534i q^{93} -29.7588 q^{94} -36.6640 q^{96} +5.59540i q^{97} -2.00231i q^{98} +3.82660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.68669i			1.89977i	0.312594	+	0.949887i	$0.398802\pi$
$2$			2.68669i			1.89977i	−0.312594	+	0.949887i	$0.601198\pi$
$3$			2.14658i			1.23933i	0.784866	+	0.619665i	$0.212732\pi$
$3$			2.14658i			1.23933i	−0.784866	+	0.619665i	$0.787268\pi$
$4$	−5.21828			−2.60914
$5$	−1.71227	+	1.43810i	−0.765752	+	0.643137i
$5$	−1.71227	+	1.43810i	−0.765752	+	0.643137i
$6$	−5.76720			−2.35445
$7$			2.78303i			1.05189i	0.850519	+	0.525944i	$0.176288\pi$
$7$			2.78303i			1.05189i	−0.850519	+	0.525944i	$0.823712\pi$
$8$		−	8.64651i		−	3.05700i
$9$	−1.60782			−0.535940
$10$	−3.86371	−	4.60034i	−1.22181	−	1.45475i
$11$	−2.37999			−0.717594			−0.358797	−	0.933416i	$-0.616813\pi$
$11$	−2.37999			−0.717594			−0.358797	+	0.933416i	$0.616813\pi$
$12$		−	11.2015i		−	3.23359i
$13$		−	0.0404924i		−	0.0112306i	−0.999984	−	0.00561529i	$-0.998213\pi$
$13$		−	0.0404924i		−	0.0112306i	0.999984	−	0.00561529i	$-0.00178741\pi$
$14$	−7.47713			−1.99835
$15$	−3.08699	−	3.67554i	−0.797059	−	0.949019i
$16$	12.7939			3.19847
$17$		−	1.81575i		−	0.440384i	−0.975457	−	0.220192i	$-0.929332\pi$
$17$		−	1.81575i		−	0.440384i	0.975457	−	0.220192i	$-0.0706683\pi$
$18$		−	4.31971i		−	1.01816i
$19$		0			0
$19$		0			0
$20$	8.93512	−	7.50439i	1.99795	−	1.67803i
$21$	−5.97401			−1.30364
$22$		−	6.39429i		−	1.36327i
$23$			2.54434i			0.530531i	0.964175	+	0.265265i	$0.0854595\pi$
$23$			2.54434i			0.530531i	−0.964175	+	0.265265i	$0.914540\pi$
$24$	18.5605			3.78864
$25$	0.863754	−	4.92483i	0.172751	−	0.984966i
$26$	0.108790			0.0213356
$27$			2.98843i			0.575124i
$28$		−	14.5226i		−	2.74452i
$29$	−2.94820			−0.547467			−0.273733	−	0.961806i	$-0.588259\pi$
$29$	−2.94820			−0.547467			−0.273733	+	0.961806i	$0.588259\pi$
$30$	9.87501	−	8.29379i	1.80292	−	1.51423i
$31$	−2.88614			−0.518366			−0.259183	−	0.965828i	$-0.583453\pi$
$31$	−2.88614			−0.518366			−0.259183	+	0.965828i	$0.583453\pi$
$32$			17.0802i			3.01937i
$33$		−	5.10885i		−	0.889337i
$34$	4.87834			0.836629
$35$	−4.00227	−	4.76531i	−0.676507	−	0.805484i
$36$	8.39006			1.39834
$37$		−	0.227089i		−	0.0373333i	−0.999826	−	0.0186666i	$-0.994058\pi$
$37$		−	0.227089i		−	0.0373333i	0.999826	−	0.0186666i	$-0.00594212\pi$
$38$		0			0
$39$	0.0869204			0.0139184
$40$	12.4345	+	14.8052i	1.96607	+	2.34091i
$41$	8.03741			1.25523			0.627616	−	0.778523i	$-0.284031\pi$
$41$	8.03741			1.25523			0.627616	+	0.778523i	$0.284031\pi$
$42$		−	16.0503i		−	2.47661i
$43$		−	5.13269i		−	0.782727i	−0.920236	−	0.391364i	$-0.872003\pi$
$43$		−	5.13269i		−	0.782727i	0.920236	−	0.391364i	$-0.127997\pi$
$44$	12.4195			1.87230
$45$	2.75303	−	2.31220i	0.410397	−	0.344683i
$46$	−6.83583			−1.00789
$47$			11.0764i			1.61566i	0.589417	+	0.807829i	$0.299358\pi$
$47$			11.0764i			1.61566i	−0.589417	+	0.807829i	$0.700642\pi$
$48$			27.4632i			3.96397i
$49$	−0.745270			−0.106467
$50$	13.2315	+	2.32064i	1.87121	+	0.328188i
$51$	3.89765			0.545781
$52$			0.211301i			0.0293022i
$53$		−	5.71448i		−	0.784945i	−0.919764	−	0.392472i	$-0.871620\pi$
$53$		−	5.71448i		−	0.784945i	0.919764	−	0.392472i	$-0.128380\pi$
$54$	−8.02897			−1.09260
$55$	4.07519	−	3.42266i	0.549499	−	0.461511i
$56$	24.0635			3.21562
$57$		0			0
$58$		−	7.92088i		−	1.04006i
$59$	−11.6165			−1.51234			−0.756172	−	0.654373i	$-0.772933\pi$
$59$	−11.6165			−1.51234			−0.756172	+	0.654373i	$0.772933\pi$
$60$	16.1088	+	19.1800i	2.07964	+	2.47612i
$61$	4.58383			0.586899			0.293450	−	0.955975i	$-0.405197\pi$
$61$	4.58383			0.586899			0.293450	+	0.955975i	$0.405197\pi$
$62$		−	7.75415i		−	0.984778i
$63$		−	4.47462i		−	0.563749i
$64$	−20.3012			−2.53765
$65$	0.0582320	+	0.0693341i	0.00722280	+	0.00859983i
$66$	13.7259			1.68954
$67$			4.85278i			0.592862i	0.955054	+	0.296431i	$0.0957965\pi$
$67$			4.85278i			0.592862i	−0.955054	+	0.296431i	$0.904204\pi$
$68$			9.47508i			1.14902i
$69$	−5.46163			−0.657503
$70$	12.8029	−	10.7528i	1.53024	−	1.28521i
$71$	−7.76927			−0.922043			−0.461022	−	0.887389i	$-0.652517\pi$
$71$	−7.76927			−0.922043			−0.461022	+	0.887389i	$0.652517\pi$
$72$			13.9020i			1.63837i
$73$			4.24767i			0.497152i	0.968612	+	0.248576i	$0.0799627\pi$
$73$			4.24767i			0.497152i	−0.968612	+	0.248576i	$0.920037\pi$
$74$	0.610118			0.0709248
$75$	10.5716	+	1.85412i	1.22070	+	0.214095i
$76$		0			0
$77$		−	6.62359i		−	0.754828i
$78$			0.233528i			0.0264418i
$79$	−11.6104			−1.30628			−0.653138	−	0.757239i	$-0.726548\pi$
$79$	−11.6104			−1.30628			−0.653138	+	0.757239i	$0.726548\pi$
$80$	−21.9066	+	18.3989i	−2.44924	+	2.05706i
$81$	−11.2384			−1.24871
$82$			21.5940i			2.38466i
$83$		−	4.47055i		−	0.490707i	−0.969434	−	0.245354i	$-0.921096\pi$
$83$		−	4.47055i		−	0.490707i	0.969434	−	0.245354i	$-0.0789040\pi$
$84$	31.1741			3.40137
$85$	2.61122	+	3.10906i	0.283227	+	0.337224i
$86$	13.7899			1.48700
$87$		−	6.32855i		−	0.678492i
$88$			20.5786i			2.19369i
$89$	−15.3931			−1.63167			−0.815835	−	0.578285i	$-0.803722\pi$
$89$	−15.3931			−1.63167			−0.815835	+	0.578285i	$0.803722\pi$
$90$	6.21216	+	7.39652i	0.654819	+	0.779661i
$91$	0.112692			0.0118133
$92$		−	13.2771i		−	1.38423i
$93$		−	6.19534i		−	0.642427i
$94$	−29.7588			−3.06939
$95$		0			0
$96$	−36.6640			−3.74200
$97$			5.59540i			0.568127i	0.958805	+	0.284064i	$0.0916827\pi$
$97$			5.59540i			0.568127i	−0.958805	+	0.284064i	$0.908317\pi$
$98$		−	2.00231i		−	0.202263i
$99$	3.82660			0.384588
$100$	−4.50731	+	25.6991i	−0.450731	+	2.56991i
$101$	11.9572			1.18979			0.594894	−	0.803804i	$-0.297194\pi$
$101$	11.9572			1.18979			0.594894	+	0.803804i	$0.297194\pi$
$102$			10.4718i			1.03686i
$103$			14.0940i			1.38873i	0.719624	+	0.694363i	$0.244314\pi$
$103$			14.0940i			1.38873i	−0.719624	+	0.694363i	$0.755686\pi$
$104$	−0.350118			−0.0343319
$105$	10.2291	−	8.59121i	0.998261	−	0.838416i
$106$	15.3530			1.49122
$107$		−	11.7250i		−	1.13350i	−0.823891	−	0.566748i	$-0.808201\pi$
$107$		−	11.7250i		−	1.13350i	0.823891	−	0.566748i	$-0.191799\pi$
$108$		−	15.5945i		−	1.50058i
$109$	6.71229			0.642921			0.321461	−	0.946923i	$-0.395826\pi$
$109$	6.71229			0.642921			0.321461	+	0.946923i	$0.395826\pi$
$110$	9.19561	+	10.9488i	0.876767	+	1.04392i
$111$	0.487466			0.0462683
$112$			35.6058i			3.36444i
$113$		−	2.46603i		−	0.231985i	−0.993250	−	0.115992i	$-0.962995\pi$
$113$		−	2.46603i		−	0.231985i	0.993250	−	0.115992i	$-0.0370048\pi$
$114$		0			0
$115$	−3.65900	−	4.35660i	−0.341204	−	0.406255i
$116$	15.3845			1.42842
$117$			0.0651045i			0.00601892i
$118$		−	31.2100i		−	2.87311i
$119$	5.05329			0.463234
$120$	−31.7806	+	26.6917i	−2.90115	+	2.43661i
$121$	−5.33564			−0.485058
$122$			12.3153i			1.11498i
$123$			17.2530i			1.55565i
$124$	15.0607			1.35249
$125$	5.60340	+	9.67481i	0.501183	+	0.865341i
$126$	12.0219			1.07099
$127$			0.739025i			0.0655778i	0.999462	+	0.0327889i	$0.0104389\pi$
$127$			0.739025i			0.0655778i	−0.999462	+	0.0327889i	$0.989561\pi$
$128$		−	20.3827i		−	1.80160i
$129$	11.0177			0.970058
$130$	−0.186279	+	0.156451i	−0.0163377	+	0.0137217i
$131$	−10.9122			−0.953406			−0.476703	−	0.879064i	$-0.658168\pi$
$131$	−10.9122			−0.953406			−0.476703	+	0.879064i	$0.658168\pi$
$132$			26.6594i			2.32040i
$133$		0			0
$134$	−13.0379			−1.12630
$135$	−4.29765	−	5.11701i	−0.369883	−	0.440402i
$136$	−15.6999			−1.34625
$137$			4.59040i			0.392184i	0.980585	+	0.196092i	$0.0628251\pi$
$137$			4.59040i			0.392184i	−0.980585	+	0.196092i	$0.937175\pi$
$138$		−	14.6737i		−	1.24911i
$139$	7.84530			0.665429			0.332715	−	0.943028i	$-0.392035\pi$
$139$	7.84530			0.665429			0.332715	+	0.943028i	$0.392035\pi$
$140$	20.8850	+	24.8667i	1.76510	+	2.10162i
$141$	−23.7764			−2.00233
$142$		−	20.8736i		−	1.75167i
$143$			0.0963716i			0.00805900i
$144$	−20.5703			−1.71419
$145$	5.04812	−	4.23980i	0.419224	−	0.352096i
$146$	−11.4122			−0.944477
$147$		−	1.59978i		−	0.131948i
$148$			1.18502i			0.0974077i
$149$	21.7400			1.78101			0.890503	−	0.454977i	$-0.150352\pi$
$149$	21.7400			1.78101			0.890503	+	0.454977i	$0.150352\pi$
$150$	−4.98144	+	28.4024i	−0.406733	+	2.31905i
$151$	9.68916			0.788493			0.394247	−	0.919005i	$-0.371006\pi$
$151$	9.68916			0.788493			0.394247	+	0.919005i	$0.371006\pi$
$152$		0			0
$153$			2.91940i			0.236019i
$154$	17.7955			1.43400
$155$	4.94186	−	4.15055i	0.396940	−	0.333380i
$156$	−0.453575			−0.0363151
$157$			7.37956i			0.588953i	0.955659	+	0.294476i	$0.0951452\pi$
$157$			7.37956i			0.588953i	−0.955659	+	0.294476i	$0.904855\pi$
$158$		−	31.1936i		−	2.48163i
$159$	12.2666			0.972806
$160$	−24.5629	−	29.2459i	−1.94187	−	2.31209i
$161$	−7.08097			−0.558058
$162$		−	30.1940i		−	2.37226i
$163$		−	4.90311i		−	0.384041i	−0.981391	−	0.192021i	$-0.938496\pi$
$163$		−	4.90311i		−	0.384041i	0.981391	−	0.192021i	$-0.0615040\pi$
$164$	−41.9415			−3.27508
$165$	7.34702	+	8.74774i	0.571965	+	0.681011i
$166$	12.0110			0.932232
$167$		−	10.0918i		−	0.780923i	−0.920619	−	0.390462i	$-0.872315\pi$
$167$		−	10.0918i		−	0.780923i	0.920619	−	0.390462i	$-0.127685\pi$
$168$			51.6544i			3.98522i
$169$	12.9984			0.999874
$170$	−8.35305	+	7.01553i	−0.640650	+	0.538067i
$171$		0			0
$172$			26.7838i			2.04225i
$173$			4.87931i			0.370967i	0.982647	+	0.185484i	$0.0593852\pi$
$173$			4.87931i			0.370967i	−0.982647	+	0.185484i	$0.940615\pi$
$174$	17.0028			1.28898
$175$	13.7060	+	2.40386i	1.03607	+	0.181714i
$176$	−30.4494			−2.29521
$177$		−	24.9359i		−	1.87429i
$178$		−	41.3565i		−	3.09980i
$179$	−23.8844			−1.78521			−0.892604	−	0.450842i	$-0.851124\pi$
$179$	−23.8844			−1.78521			−0.892604	+	0.450842i	$0.851124\pi$
$180$	−14.3661	+	12.0657i	−1.07078	+	0.899325i
$181$	2.56750			0.190841			0.0954204	−	0.995437i	$-0.469580\pi$
$181$	2.56750			0.190841			0.0954204	+	0.995437i	$0.469580\pi$
$182$			0.302767i			0.0224426i
$183$			9.83957i			0.727362i
$184$	21.9996			1.62183
$185$	0.326577	+	0.388839i	0.0240104	+	0.0285880i
$186$	16.6449			1.22047
$187$			4.32146i			0.316017i
$188$		−	57.7998i		−	4.21548i
$189$	−8.31690			−0.604965
$190$		0			0
$191$	9.28746			0.672017			0.336008	−	0.941859i	$-0.390923\pi$
$191$	9.28746			0.672017			0.336008	+	0.941859i	$0.390923\pi$
$192$		−	43.5783i		−	3.14499i
$193$		−	24.8317i		−	1.78742i	−0.448643	−	0.893711i	$-0.648093\pi$
$193$		−	24.8317i		−	1.78742i	0.448643	−	0.893711i	$-0.351907\pi$
$194$	−15.0331			−1.07931
$195$	−0.148831	+	0.125000i	−0.0106580	+	0.00895143i
$196$	3.88903			0.277788
$197$		−	4.17316i		−	0.297325i	−0.988888	−	0.148663i	$-0.952503\pi$
$197$		−	4.17316i		−	0.297325i	0.988888	−	0.148663i	$-0.0474969\pi$
$198$			10.2809i			0.730629i
$199$	−22.3867			−1.58695			−0.793475	−	0.608603i	$-0.791730\pi$
$199$	−22.3867			−1.58695			−0.793475	+	0.608603i	$0.791730\pi$
$200$	−42.5826	−	7.46846i	−3.01104	−	0.528100i
$201$	−10.4169			−0.734752
$202$			32.1253i			2.26033i
$203$		−	8.20493i		−	0.575873i
$204$	−20.3391			−1.42402
$205$	−13.7622	+	11.5586i	−0.961196	+	0.807286i
$206$	−37.8663			−2.63827
$207$		−	4.09083i		−	0.284333i
$208$		−	0.518056i		−	0.0359207i
$209$		0			0
$210$	23.0819	+	27.4825i	1.59280	+	1.89647i
$211$	1.68159			0.115765			0.0578827	−	0.998323i	$-0.481565\pi$
$211$	1.68159			0.115765			0.0578827	+	0.998323i	$0.481565\pi$
$212$			29.8198i			2.04803i
$213$		−	16.6774i		−	1.14272i
$214$	31.5013			2.15339
$215$	7.38130	+	8.78856i	0.503400	+	0.599375i
$216$	25.8395			1.75816
$217$		−	8.03222i		−	0.545263i
$218$			18.0338i			1.22140i
$219$	−9.11798			−0.616136
$220$	−21.2655	+	17.8604i	−1.43372	+	1.20415i
$221$	−0.0735240			−0.00494576
$222$			1.30967i			0.0878992i
$223$		−	9.61157i		−	0.643638i	−0.946801	−	0.321819i	$-0.895706\pi$
$223$		−	9.61157i		−	0.643638i	0.946801	−	0.321819i	$-0.104294\pi$
$224$	−47.5346			−3.17604
$225$	−1.38876	+	7.91824i	−0.0925841	+	0.527882i
$226$	6.62545			0.440719
$227$		−	23.4650i		−	1.55743i	−0.627379	−	0.778714i	$-0.715872\pi$
$227$		−	23.4650i		−	1.55743i	0.627379	−	0.778714i	$-0.284128\pi$
$228$		0			0
$229$	1.19088			0.0786952			0.0393476	−	0.999226i	$-0.487472\pi$
$229$	1.19088			0.0786952			0.0393476	+	0.999226i	$0.487472\pi$
$230$	11.7048	−	9.83059i	0.771792	−	0.648210i
$231$	14.2181			0.935482
$232$			25.4916i			1.67361i
$233$			23.1405i			1.51598i	0.652263	+	0.757992i	$0.273820\pi$
$233$			23.1405i			1.51598i	−0.652263	+	0.757992i	$0.726180\pi$
$234$	−0.174915			−0.0114346
$235$	−15.9289	−	18.9658i	−1.03909	−	1.23719i
$236$	60.6183			3.94592
$237$		−	24.9228i		−	1.61891i
$238$			13.5766i			0.880040i
$239$	−9.68715			−0.626610			−0.313305	−	0.949653i	$-0.601436\pi$
$239$	−9.68715			−0.626610			−0.313305	+	0.949653i	$0.601436\pi$
$240$	−39.4947	−	47.0244i	−2.54937	−	3.03541i
$241$	15.7854			1.01682			0.508412	−	0.861114i	$-0.330233\pi$
$241$	15.7854			1.01682			0.508412	+	0.861114i	$0.330233\pi$
$242$		−	14.3352i		−	0.921501i
$243$		−	15.1588i		−	0.972439i
$244$	−23.9197			−1.53130
$245$	1.27611	−	1.07177i	0.0815274	−	0.0684729i
$246$	−46.3533			−2.95538
$247$		0			0
$248$			24.9550i			1.58465i
$249$	9.59642			0.608148
$250$	−25.9932	+	15.0546i	−1.64395	+	0.952135i
$251$	5.47929			0.345850			0.172925	−	0.984935i	$-0.444678\pi$
$251$	5.47929			0.345850			0.172925	+	0.984935i	$0.444678\pi$
$252$			23.3498i			1.47090i
$253$		−	6.05550i		−	0.380706i
$254$	−1.98553			−0.124583
$255$	−6.67385	+	5.60520i	−0.417932	+	0.351012i
$256$	14.1595			0.884969
$257$		−	3.54799i		−	0.221318i	−0.993858	−	0.110659i	$-0.964704\pi$
$257$		−	3.54799i		−	0.221318i	0.993858	−	0.110659i	$-0.0352961\pi$
$258$			29.6012i			1.84289i
$259$	0.631997			0.0392704
$260$	−0.303871	−	0.361805i	−0.0188453	−	0.0224382i
$261$	4.74017			0.293409
$262$		−	29.3177i		−	1.81126i
$263$			26.3476i			1.62466i	0.583196	+	0.812332i	$0.301802\pi$
$263$			26.3476i			1.62466i	−0.583196	+	0.812332i	$0.698198\pi$
$264$	−44.1737			−2.71870
$265$	8.21798	+	9.78475i	0.504827	+	0.601073i
$266$		0			0
$267$		−	33.0427i		−	2.02218i
$268$		−	25.3232i		−	1.54686i
$269$	−23.1165			−1.40943			−0.704717	−	0.709488i	$-0.748926\pi$
$269$	−23.1165			−1.40943			−0.704717	+	0.709488i	$0.748926\pi$
$270$	13.7478	−	11.5464i	0.836664	−	0.702694i
$271$	18.4658			1.12172			0.560860	−	0.827911i	$-0.310471\pi$
$271$	18.4658			1.12172			0.560860	+	0.827911i	$0.310471\pi$
$272$		−	23.2305i		−	1.40856i
$273$			0.241902i			0.0146406i
$274$	−12.3330			−0.745061
$275$	−2.05573	+	11.7210i	−0.123965	+	0.706806i
$276$	28.5003			1.71552
$277$		−	29.9708i		−	1.80077i	−0.435095	−	0.900384i	$-0.643285\pi$
$277$		−	29.9708i		−	1.80077i	0.435095	−	0.900384i	$-0.356715\pi$
$278$			21.0778i			1.26417i
$279$	4.64039			0.277813
$280$	−41.2033	+	34.6057i	−2.46237	+	2.06808i
$281$	−3.97918			−0.237378			−0.118689	−	0.992931i	$-0.537869\pi$
$281$	−3.97918			−0.237378			−0.118689	+	0.992931i	$0.537869\pi$
$282$		−	63.8797i		−	3.80398i
$283$			9.04931i			0.537925i	0.963151	+	0.268963i	$0.0866808\pi$
$283$			9.04931i			0.537925i	−0.963151	+	0.268963i	$0.913319\pi$
$284$	40.5423			2.40574
$285$		0			0
$286$	−0.258920			−0.0153103
$287$			22.3684i			1.32036i
$288$		−	27.4618i		−	1.61820i
$289$	13.7031			0.806062
$290$	11.3910	+	13.5627i	0.668903	+	0.796430i
$291$	−12.0110			−0.704097
$292$		−	22.1656i		−	1.29714i
$293$		−	2.33643i		−	0.136496i	−0.997668	−	0.0682479i	$-0.978259\pi$
$293$		−	2.33643i		−	0.136496i	0.997668	−	0.0682479i	$-0.0217409\pi$
$294$	4.29812			0.250671
$295$	19.8907	−	16.7057i	1.15808	−	0.972644i
$296$	−1.96353			−0.114128
$297$		−	7.11244i		−	0.412706i
$298$			58.4084i			3.38351i
$299$	0.103026			0.00595817
$300$	−55.1653	−	9.67532i	−3.18497	−	0.558605i
$301$	14.2844			0.823341
$302$			26.0317i			1.49796i
$303$			25.6672i			1.47454i
$304$		0			0
$305$	−7.84876	+	6.59199i	−0.449419	+	0.377456i
$306$	−7.84350			−0.448383
$307$			7.60114i			0.433820i	0.976192	+	0.216910i	$0.0695978\pi$
$307$			7.60114i			0.433820i	−0.976192	+	0.216910i	$0.930402\pi$
$308$			34.5638i			1.96945i
$309$	−30.2540			−1.72109
$310$	11.1512	+	13.2772i	0.633347	+	0.754095i
$311$	−18.8241			−1.06742			−0.533709	−	0.845668i	$-0.679202\pi$
$311$	−18.8241			−1.06742			−0.533709	+	0.845668i	$0.679202\pi$
$312$		−	0.751558i		−	0.0425486i
$313$		−	22.2112i		−	1.25545i	−0.778436	−	0.627724i	$-0.783987\pi$
$313$		−	22.2112i		−	1.25545i	0.778436	−	0.627724i	$-0.216013\pi$
$314$	−19.8265			−1.11888
$315$	6.43493	+	7.66176i	0.362567	+	0.431691i
$316$	60.5865			3.40826
$317$			4.07272i			0.228747i	0.993438	+	0.114373i	$0.0364860\pi$
$317$			4.07272i			0.228747i	−0.993438	+	0.114373i	$0.963514\pi$
$318$			32.9565i			1.84811i
$319$	7.01669			0.392859
$320$	34.7613	−	29.1951i	1.94321	−	1.63206i
$321$	25.1686			1.40478
$322$		−	19.0243i		−	1.06018i
$323$		0			0
$324$	58.6450			3.25806
$325$	−0.199418	−	0.0349755i	−0.0110617	−	0.00194009i
$326$	13.1731			0.729591
$327$			14.4085i			0.796792i
$328$		−	69.4955i		−	3.83725i
$329$	−30.8260			−1.69949
$330$	−23.5024	+	19.7391i	−1.29377	+	1.08660i
$331$	20.7878			1.14260			0.571301	−	0.820741i	$-0.306439\pi$
$331$	20.7878			1.14260			0.571301	+	0.820741i	$0.306439\pi$
$332$			23.3286i			1.28032i
$333$			0.365119i			0.0200084i
$334$	27.1134			1.48358
$335$	−6.97878	−	8.30929i	−0.381291	−	0.453985i
$336$	−76.4309			−4.16965
$337$			26.1722i			1.42569i	0.701320	+	0.712846i	$0.252594\pi$
$337$			26.1722i			1.42569i	−0.701320	+	0.712846i	$0.747406\pi$
$338$			34.9225i			1.89953i
$339$	5.29354			0.287506
$340$	−13.6261	−	16.2239i	−0.738978	−	0.879866i
$341$	6.86899			0.371976
$342$		0			0
$343$			17.4071i			0.939896i
$344$	−44.3798			−2.39280
$345$	9.35179	−	7.85435i	0.503484	−	0.422864i
$346$	−13.1092			−0.704754
$347$		−	20.5989i		−	1.10580i	−0.833246	−	0.552902i	$-0.813520\pi$
$347$		−	20.5989i		−	1.10580i	0.833246	−	0.552902i	$-0.186480\pi$
$348$			33.0242i			1.77028i
$349$	25.0306			1.33986			0.669929	−	0.742425i	$-0.266324\pi$
$349$	25.0306			1.33986			0.669929	+	0.742425i	$0.266324\pi$
$350$	−6.45841	+	36.8236i	−0.345216	+	1.96830i
$351$	0.121009			0.00645897
$352$		−	40.6506i		−	2.16669i
$353$		−	7.21257i		−	0.383886i	−0.981406	−	0.191943i	$-0.938521\pi$
$353$		−	7.21257i		−	0.383886i	0.981406	−	0.191943i	$-0.0614789\pi$
$354$	66.9948			3.56073
$355$	13.3031	−	11.1730i	0.706056	−	0.593000i
$356$	80.3257			4.25726
$357$			10.8473i			0.574100i
$358$		−	64.1700i		−	3.39149i
$359$	−15.8081			−0.834322			−0.417161	−	0.908833i	$-0.636975\pi$
$359$	−15.8081			−0.834322			−0.417161	+	0.908833i	$0.636975\pi$
$360$	−19.9925	−	23.8041i	−1.05370	−	1.25458i
$361$		0			0
$362$			6.89807i			0.362554i
$363$		−	11.4534i		−	0.601148i
$364$	−0.588057			−0.0308226
$365$	−6.10857	−	7.27317i	−0.319737	−	0.380695i
$366$	−26.4358			−1.38182
$367$			2.64262i			0.137944i	0.997619	+	0.0689719i	$0.0219719\pi$
$367$			2.64262i			0.137944i	−0.997619	+	0.0689719i	$0.978028\pi$
$368$			32.5520i			1.69689i
$369$	−12.9227			−0.672729
$370$	−1.04469	+	0.877409i	−0.0543107	+	0.0456143i
$371$	15.9036			0.825673
$372$			32.3290i			1.67618i
$373$		−	6.16440i		−	0.319181i	−0.987183	−	0.159590i	$-0.948983\pi$
$373$		−	6.16440i		−	0.319181i	0.987183	−	0.159590i	$-0.0510173\pi$
$374$	−11.6104			−0.600360
$375$	−20.7678	+	12.0282i	−1.07244	+	0.621131i
$376$	95.7722			4.93907
$377$			0.119380i			0.00614837i
$378$		−	22.3449i		−	1.14930i
$379$	−0.156142			−0.00802047			−0.00401024	−	0.999992i	$-0.501277\pi$
$379$	−0.156142			−0.00802047			−0.00401024	+	0.999992i	$0.501277\pi$
$380$		0			0
$381$	−1.58638			−0.0812726
$382$			24.9525i			1.27668i
$383$			16.1220i			0.823796i	0.911230	+	0.411898i	$0.135134\pi$
$383$			16.1220i			0.823796i	−0.911230	+	0.411898i	$0.864866\pi$
$384$	43.7532			2.23277
$385$	9.52537	+	11.3414i	0.485458	+	0.578011i
$386$	66.7149			3.39570
$387$			8.25243i			0.419495i
$388$		−	29.1984i		−	1.48232i
$389$	−2.71507			−0.137660			−0.0688298	−	0.997628i	$-0.521927\pi$
$389$	−2.71507			−0.137660			−0.0688298	+	0.997628i	$0.521927\pi$
$390$	−0.335836	−	0.399863i	−0.0170057	−	0.0202479i
$391$	4.61987			0.233637
$392$			6.44399i			0.325470i
$393$		−	23.4240i		−	1.18158i
$394$	11.2120			0.564851
$395$	19.8802	−	16.6969i	1.00028	−	0.840114i
$396$	−19.9683			−1.00344
$397$		−	15.8528i		−	0.795631i	−0.917465	−	0.397815i	$-0.869768\pi$
$397$		−	15.8528i		−	0.795631i	0.917465	−	0.397815i	$-0.130232\pi$
$398$		−	60.1460i		−	3.01485i
$399$		0			0
$400$	11.0508	−	63.0077i	0.552539	−	3.15039i
$401$	−3.32547			−0.166066			−0.0830331	−	0.996547i	$-0.526461\pi$
$401$	−3.32547			−0.166066			−0.0830331	+	0.996547i	$0.526461\pi$
$402$		−	27.9870i		−	1.39586i
$403$			0.116867i			0.00582155i
$404$	−62.3962			−3.10433
$405$	19.2432	−	16.1619i	0.956200	−	0.803090i
$406$	22.0441			1.09403
$407$			0.540471i			0.0267901i
$408$		−	33.7011i		−	1.66845i
$409$	−7.49029			−0.370371			−0.185185	−	0.982704i	$-0.559289\pi$
$409$	−7.49029			−0.370371			−0.185185	+	0.982704i	$0.559289\pi$
$410$	−31.0543	−	36.9748i	−1.53366	−	1.82606i
$411$	−9.85367			−0.486046
$412$		−	73.5467i		−	3.62338i
$413$		−	32.3292i		−	1.59082i
$414$	10.9908			0.540168
$415$	6.42909	+	7.65481i	0.315592	+	0.375760i
$416$	0.691617			0.0339093
$417$			16.8406i			0.824687i
$418$		0			0
$419$	−14.4108			−0.704012			−0.352006	−	0.935998i	$-0.614500\pi$
$419$	−14.4108			−0.704012			−0.352006	+	0.935998i	$0.614500\pi$
$420$	−53.3785	+	44.8313i	−2.60460	+	2.18755i
$421$	−35.7661			−1.74314			−0.871568	−	0.490275i	$-0.836896\pi$
$421$	−35.7661			−1.74314			−0.871568	+	0.490275i	$0.836896\pi$
$422$			4.51790i			0.219928i
$423$		−	17.8089i		−	0.865896i
$424$	−49.4103			−2.39958
$425$	−8.94225	−	1.56836i	−0.433763	−	0.0760766i
$426$	44.8069			2.17090
$427$			12.7569i			0.617352i
$428$			61.1842i			2.95745i
$429$	−0.206870			−0.00998777
$430$	−23.6121	+	19.8312i	−1.13868	+	0.956347i
$431$	10.3894			0.500440			0.250220	−	0.968189i	$-0.419497\pi$
$431$	10.3894			0.500440			0.250220	+	0.968189i	$0.419497\pi$
$432$			38.2337i			1.83952i
$433$			35.0812i			1.68589i	0.537997	+	0.842947i	$0.319181\pi$
$433$			35.0812i			1.68589i	−0.537997	+	0.842947i	$0.680819\pi$
$434$	21.5801			1.03588
$435$	9.10107	+	10.8362i	0.436363	+	0.519556i
$436$	−35.0266			−1.67747
$437$		0			0
$438$		−	24.4972i		−	1.17052i
$439$	−19.1269			−0.912876			−0.456438	−	0.889755i	$-0.650875\pi$
$439$	−19.1269			−0.912876			−0.456438	+	0.889755i	$0.650875\pi$
$440$	−29.5941	−	35.2362i	−1.41084	−	1.67982i
$441$	1.19826			0.0570600
$442$		−	0.197536i		−	0.00939583i
$443$			22.9916i			1.09236i	0.837667	+	0.546181i	$0.183919\pi$
$443$			22.9916i			1.09236i	−0.837667	+	0.546181i	$0.816081\pi$
$444$	−2.54374			−0.120720
$445$	26.3572	−	22.1368i	1.24945	−	1.04939i
$446$	25.8233			1.22277
$447$			46.6666i			2.20726i
$448$		−	56.4990i		−	2.66933i
$449$	−15.7738			−0.744414			−0.372207	−	0.928150i	$-0.621399\pi$
$449$	−15.7738			−0.744414			−0.372207	+	0.928150i	$0.621399\pi$
$450$	−21.2738	−	3.73117i	−1.00286	−	0.175889i
$451$	−19.1290			−0.900748
$452$			12.8684i			0.605281i
$453$			20.7986i			0.977203i
$454$	63.0431			2.95876
$455$	−0.192959	+	0.162062i	−0.00904606	+	0.00759757i
$456$		0			0
$457$		−	34.6414i		−	1.62046i	−0.586114	−	0.810229i	$-0.699343\pi$
$457$		−	34.6414i		−	1.62046i	0.586114	−	0.810229i	$-0.300657\pi$
$458$			3.19951i			0.149503i
$459$	5.42624			0.253275
$460$	19.0937	+	22.7339i	0.890248	+	1.05998i
$461$	24.5628			1.14400			0.572001	−	0.820253i	$-0.306167\pi$
$461$	24.5628			1.14400			0.572001	+	0.820253i	$0.306167\pi$
$462$			38.1996i			1.77720i
$463$			7.70610i			0.358133i	0.983837	+	0.179067i	$0.0573077\pi$
$463$			7.70610i			0.358133i	−0.983837	+	0.179067i	$0.942692\pi$
$464$	−37.7190			−1.75106
$465$	8.90950	+	10.6081i	0.413168	+	0.491939i
$466$	−62.1713			−2.88003
$467$		−	6.51888i		−	0.301658i	−0.988560	−	0.150829i	$-0.951806\pi$
$467$		−	6.51888i		−	0.301658i	0.988560	−	0.150829i	$-0.0481942\pi$
$468$		−	0.339734i		−	0.0157042i
$469$	−13.5055			−0.623624
$470$	50.9552	−	42.7960i	2.35039	−	1.97403i
$471$	−15.8408			−0.729907
$472$			100.442i			4.62324i
$473$			12.2157i			0.561681i
$474$	66.9597			3.07556
$475$		0			0
$476$	−26.3695			−1.20864
$477$			9.18786i			0.420683i
$478$		−	26.0263i		−	1.19042i
$479$	−12.3748			−0.565420			−0.282710	−	0.959205i	$-0.591233\pi$
$479$	−12.3748			−0.565420			−0.282710	+	0.959205i	$0.591233\pi$
$480$	62.7787	−	52.7264i	2.86544	−	2.40662i
$481$	−0.00919540			−0.000419274
$482$			42.4103i			1.93174i
$483$		−	15.1999i		−	0.691619i
$484$	27.8429			1.26559
$485$	−8.04673	−	9.58086i	−0.365383	−	0.435044i
$486$	40.7270			1.84741
$487$		−	38.7209i		−	1.75461i	−0.479931	−	0.877306i	$-0.659338\pi$
$487$		−	38.7209i		−	1.75461i	0.479931	−	0.877306i	$-0.340662\pi$
$488$		−	39.6341i		−	1.79415i
$489$	10.5249			0.475954
$490$	2.87951	+	3.42849i	0.130083	+	0.154884i
$491$	−31.4089			−1.41747			−0.708733	−	0.705477i	$-0.750733\pi$
$491$	−31.4089			−1.41747			−0.708733	+	0.705477i	$0.750733\pi$
$492$		−	90.0308i		−	4.05890i
$493$			5.35319i			0.241095i
$494$		0			0
$495$	−6.55218	+	5.50302i	−0.294498	+	0.247342i
$496$	−36.9250			−1.65798
$497$		−	21.6221i		−	0.969886i
$498$			25.7826i			1.15534i
$499$	−19.4261			−0.869633			−0.434817	−	0.900519i	$-0.643187\pi$
$499$	−19.4261			−0.869633			−0.434817	+	0.900519i	$0.643187\pi$
$500$	−29.2401	−	50.4859i	−1.30766	−	2.25780i
$501$	21.6628			0.967822
$502$			14.7211i			0.657036i
$503$		−	4.25810i		−	0.189859i	−0.995484	−	0.0949297i	$-0.969737\pi$
$503$		−	4.25810i		−	0.189859i	0.995484	−	0.0949297i	$-0.0302626\pi$
$504$	−38.6898			−1.72338
$505$	−20.4740	+	17.1957i	−0.911083	+	0.765197i
$506$	16.2692			0.723255
$507$			27.9021i			1.23917i
$508$		−	3.85644i		−	0.171102i
$509$	7.33745			0.325227			0.162613	−	0.986690i	$-0.448008\pi$
$509$	7.33745			0.325227			0.162613	+	0.986690i	$0.448008\pi$
$510$	−15.0594	−	17.9305i	−0.666842	−	0.793977i
$511$	−11.8214			−0.522948
$512$		−	2.72331i		−	0.120354i
$513$		0			0
$514$	9.53234			0.420453
$515$	−20.2686	−	24.1328i	−0.893141	−	1.06342i
$516$	−57.4937			−2.53102
$517$		−	26.3617i		−	1.15939i
$518$			1.69798i			0.0746049i
$519$	−10.4739			−0.459751
$520$	0.599498	−	0.503504i	0.0262897	−	0.0220801i
$521$	−7.96809			−0.349088			−0.174544	−	0.984649i	$-0.555845\pi$
$521$	−7.96809			−0.349088			−0.174544	+	0.984649i	$0.555845\pi$
$522$			12.7354i			0.557411i
$523$		−	15.6754i		−	0.685436i	−0.939438	−	0.342718i	$-0.888652\pi$
$523$		−	15.6754i		−	0.685436i	0.939438	−	0.342718i	$-0.111348\pi$
$524$	56.9431			2.48757
$525$	−5.16008	+	29.4210i	−0.225204	+	1.28404i
$526$	−70.7878			−3.08649
$527$			5.24050i			0.228280i
$528$		−	65.3621i		−	2.84452i
$529$	16.5264			0.718537
$530$	−26.2886	+	22.0791i	−1.14190	+	0.959056i
$531$	18.6773			0.810526
$532$		0			0
$533$		−	0.325454i		−	0.0140970i
$534$	88.7752			3.84168
$535$	16.8617	+	20.0764i	0.728993	+	0.867977i
$536$	41.9597			1.81238
$537$		−	51.2700i		−	2.21246i
$538$		−	62.1066i		−	2.67761i
$539$	1.77374			0.0764002
$540$	22.4264	+	26.7020i	0.965077	+	1.14907i
$541$	29.1267			1.25225			0.626127	−	0.779721i	$-0.284639\pi$
$541$	29.1267			1.25225			0.626127	+	0.779721i	$0.284639\pi$
$542$			49.6119i			2.13101i
$543$			5.51135i			0.236515i
$544$	31.0133			1.32968
$545$	−11.4933	+	9.65293i	−0.492318	+	0.413486i
$546$	−0.649915			−0.0278138
$547$		−	14.4668i		−	0.618557i	−0.950972	−	0.309279i	$-0.899912\pi$
$547$		−	14.4668i		−	0.618557i	0.950972	−	0.309279i	$-0.100088\pi$
$548$		−	23.9540i		−	1.02326i
$549$	−7.36997			−0.314543
$550$	−31.4908	−	5.52309i	−1.34277	−	0.235506i
$551$		0			0
$552$			47.2240i			2.00999i
$553$		−	32.3122i		−	1.37406i
$554$	80.5220			3.42105
$555$	−0.834675	+	0.701024i	−0.0354300	+	0.0297568i
$556$	−40.9390			−1.73620
$557$			33.6775i			1.42696i	0.700675	+	0.713480i	$0.252882\pi$
$557$			33.6775i			1.42696i	−0.700675	+	0.713480i	$0.747118\pi$
$558$			12.4673i			0.527782i
$559$	−0.207835			−0.00879048
$560$	−51.2046	−	60.9669i	−2.16379	−	2.57632i
$561$	−9.27638			−0.391649
$562$		−	10.6908i		−	0.450964i
$563$			24.9154i			1.05006i	0.851084	+	0.525030i	$0.175946\pi$
$563$			24.9154i			1.05006i	−0.851084	+	0.525030i	$0.824054\pi$
$564$	124.072			5.22437
$565$	3.54639	+	4.22252i	0.149198	+	0.177643i
$566$	−24.3126			−1.02194
$567$		−	31.2768i		−	1.31350i
$568$			67.1771i			2.81869i
$569$	−19.7304			−0.827141			−0.413571	−	0.910472i	$-0.635719\pi$
$569$	−19.7304			−0.827141			−0.413571	+	0.910472i	$0.635719\pi$
$570$		0			0
$571$	−13.8463			−0.579452			−0.289726	−	0.957110i	$-0.593564\pi$
$571$	−13.8463			−0.579452			−0.289726	+	0.957110i	$0.593564\pi$
$572$		−	0.502894i		−	0.0210271i
$573$			19.9363i			0.832851i
$574$	−60.0968			−2.50839
$575$	12.5304	+	2.19768i	0.522554	+	0.0916496i
$576$	32.6407			1.36003
$577$			41.6653i			1.73455i	0.497830	+	0.867275i	$0.334130\pi$
$577$			41.6653i			1.73455i	−0.497830	+	0.867275i	$0.665870\pi$
$578$			36.8158i			1.53134i
$579$	53.3032			2.21521
$580$	−26.3425	+	22.1244i	−1.09381	+	0.918668i
$581$	12.4417			0.516169
$582$		−	32.2698i		−	1.33763i
$583$			13.6004i			0.563272i
$584$	36.7275			1.51980
$585$	−0.0936266	−	0.111477i	−0.00387099	−	0.00460899i
$586$	6.27726			0.259311
$587$			16.1707i			0.667436i	0.942673	+	0.333718i	$0.108303\pi$
$587$			16.1707i			0.667436i	−0.942673	+	0.333718i	$0.891697\pi$
$588$			8.34812i			0.344271i
$589$		0			0
$590$	44.8830	+	53.4400i	1.84780	+	2.20009i
$591$	8.95804			0.368485
$592$		−	2.90536i		−	0.119409i
$593$			22.4662i			0.922578i	0.887250	+	0.461289i	$0.152613\pi$
$593$			22.4662i			0.922578i	−0.887250	+	0.461289i	$0.847387\pi$
$594$	19.1089			0.784047
$595$	−8.65260	+	7.26711i	−0.354722	+	0.297923i
$596$	−113.445			−4.64690
$597$		−	48.0549i		−	1.96676i
$598$			0.276799i			0.0113192i
$599$	−2.16008			−0.0882584			−0.0441292	−	0.999026i	$-0.514051\pi$
$599$	−2.16008			−0.0882584			−0.0441292	+	0.999026i	$0.514051\pi$
$600$	16.0317	−	91.4071i	0.654490	−	3.73168i
$601$	−17.0595			−0.695870			−0.347935	−	0.937519i	$-0.613117\pi$
$601$	−17.0595			−0.695870			−0.347935	+	0.937519i	$0.613117\pi$
$602$			38.3778i			1.56416i
$603$		−	7.80240i		−	0.317738i
$604$	−50.5608			−2.05729
$605$	9.13607	−	7.67317i	0.371434	−	0.311959i
$606$	−68.9597			−2.80130
$607$		−	3.47625i		−	0.141097i	−0.997508	−	0.0705483i	$-0.977525\pi$
$607$		−	3.47625i		−	0.141097i	0.997508	−	0.0705483i	$-0.0224749\pi$
$608$		0			0
$609$	17.6126			0.713697
$610$	−17.7106	−	21.0872i	−0.717082	−	0.853794i
$611$	0.448510			0.0181448
$612$		−	15.2342i		−	0.615807i
$613$			18.5830i			0.750561i	0.926911	+	0.375281i	$0.122454\pi$
$613$			18.5830i			0.750561i	−0.926911	+	0.375281i	$0.877546\pi$
$614$	−20.4219			−0.824160
$615$	−24.8114	−	29.5418i	−1.00049	−	1.19124i
$616$	−57.2710			−2.30751
$617$		−	19.8681i		−	0.799861i	−0.916545	−	0.399931i	$-0.869034\pi$
$617$		−	19.8681i		−	0.799861i	0.916545	−	0.399931i	$-0.130966\pi$
$618$		−	81.2831i		−	3.26968i
$619$	8.42415			0.338595			0.169298	−	0.985565i	$-0.445850\pi$
$619$	8.42415			0.338595			0.169298	+	0.985565i	$0.445850\pi$
$620$	−25.7880	+	21.6587i	−1.03567	+	0.869835i
$621$	−7.60357			−0.305121
$622$		−	50.5745i		−	2.02785i
$623$		−	42.8396i		−	1.71633i
$624$	1.11205			0.0445176
$625$	−23.5079	−	8.50768i	−0.940314	−	0.340307i
$626$	59.6744			2.38507
$627$		0			0
$628$		−	38.5086i		−	1.53666i
$629$	−0.412337			−0.0164410
$630$	−20.5847	+	17.2886i	−0.820116	+	0.688796i
$631$	1.60577			0.0639245			0.0319623	−	0.999489i	$-0.489824\pi$
$631$	1.60577			0.0639245			0.0319623	+	0.999489i	$0.489824\pi$
$632$			100.390i			3.99329i
$633$			3.60967i			0.143472i
$634$	−10.9421			−0.434567
$635$	−1.06279	−	1.26541i	−0.0421755	−	0.0502163i
$636$	−64.0106			−2.53819
$637$			0.0301778i			0.00119569i
$638$			18.8516i			0.746343i
$639$	12.4916			0.494160
$640$	29.3123	+	34.9008i	1.15867	+	1.37957i
$641$	−45.8457			−1.81080			−0.905398	−	0.424563i	$-0.860428\pi$
$641$	−45.8457			−1.81080			−0.905398	+	0.424563i	$0.860428\pi$
$642$			67.6202i			2.66876i
$643$		−	18.3274i		−	0.722763i	−0.932418	−	0.361381i	$-0.882305\pi$
$643$		−	18.3274i		−	0.722763i	0.932418	−	0.361381i	$-0.117695\pi$
$644$	36.9505			1.45605
$645$	−18.8654	+	15.8446i	−0.742823	+	0.623880i
$646$		0			0
$647$			25.1770i			0.989808i	0.868948	+	0.494904i	$0.164797\pi$
$647$			25.1770i			0.989808i	−0.868948	+	0.494904i	$0.835203\pi$
$648$			97.1727i			3.81731i
$649$	27.6472			1.08525
$650$	0.0939682	−	0.535774i	0.00368574	−	0.0210148i
$651$	17.2418			0.675761
$652$			25.5858i			1.00202i
$653$		−	0.698581i		−	0.0273376i	−0.999907	−	0.0136688i	$-0.995649\pi$
$653$		−	0.698581i		−	0.0273376i	0.999907	−	0.0136688i	$-0.00435105\pi$
$654$	−38.7111			−1.51372
$655$	18.6847	−	15.6928i	0.730072	−	0.613170i
$656$	102.830			4.01483
$657$		−	6.82949i		−	0.266444i
$658$		−	82.8197i		−	3.22865i
$659$	−20.3631			−0.793232			−0.396616	−	0.917985i	$-0.629816\pi$
$659$	−20.3631			−0.793232			−0.396616	+	0.917985i	$0.629816\pi$
$660$	−38.3388	−	45.6482i	−1.49234	−	1.77685i
$661$	−34.7369			−1.35111			−0.675554	−	0.737311i	$-0.736095\pi$
$661$	−34.7369			−1.35111			−0.675554	+	0.737311i	$0.736095\pi$
$662$			55.8504i			2.17069i
$663$		−	0.157825i		−	0.00612943i
$664$	−38.6547			−1.50009
$665$		0			0
$666$	−0.980960			−0.0380114
$667$		−	7.50121i		−	0.290448i
$668$			52.6616i			2.03754i
$669$	20.6320			0.797681
$670$	22.3245	−	18.7498i	0.862469	−	0.724367i
$671$	−10.9095			−0.421155
$672$		−	102.037i		−	3.93617i
$673$			25.5533i			0.985009i	0.870310	+	0.492505i	$0.163919\pi$
$673$			25.5533i			0.985009i	−0.870310	+	0.492505i	$0.836081\pi$
$674$	−70.3166			−2.70849
$675$	14.7175	+	2.58127i	0.566477	+	0.0993531i
$676$	−67.8291			−2.60881
$677$		−	38.0431i		−	1.46212i	−0.682315	−	0.731058i	$-0.739027\pi$
$677$		−	38.0431i		−	1.46212i	0.682315	−	0.731058i	$-0.260973\pi$
$678$			14.2221i			0.546196i
$679$	−15.5722			−0.597606
$680$	26.8825	−	22.5780i	1.03090	−	0.865825i
$681$	50.3696			1.93017
$682$			18.4548i			0.706671i
$683$			31.7070i			1.21324i	0.794994	+	0.606618i	$0.207474\pi$
$683$			31.7070i			1.21324i	−0.794994	+	0.606618i	$0.792526\pi$
$684$		0			0
$685$	−6.60144	−	7.86001i	−0.252228	−	0.300316i
$686$	−46.7675			−1.78559
$687$			2.55631i			0.0975294i
$688$		−	65.6671i		−	2.50353i
$689$	−0.231393			−0.00881538
$690$	21.1022	+	25.1253i	0.803346	+	0.956505i
$691$	4.11055			0.156373			0.0781864	−	0.996939i	$-0.475087\pi$
$691$	4.11055			0.156373			0.0781864	+	0.996939i	$0.475087\pi$
$692$		−	25.4616i		−	0.967906i
$693$			10.6495i			0.404543i
$694$	55.3427			2.10078
$695$	−13.4333	+	11.2823i	−0.509554	+	0.427962i
$696$	−54.7199			−2.07415
$697$		−	14.5939i		−	0.552784i
$698$			67.2494i			2.54543i
$699$	−49.6730			−1.87881
$700$	−71.5215	−	12.5440i	−2.70326	−	0.474119i
$701$	−4.44612			−0.167928			−0.0839638	−	0.996469i	$-0.526758\pi$
$701$	−4.44612			−0.167928			−0.0839638	+	0.996469i	$0.526758\pi$
$702$			0.325113i			0.0122706i
$703$		0			0
$704$	48.3168			1.82101
$705$	40.7117	−	34.1928i	1.53329	−	1.28777i
$706$	19.3779			0.729297
$707$			33.2774i			1.25152i
$708$			130.122i			4.89030i
$709$	−3.35571			−0.126027			−0.0630133	−	0.998013i	$-0.520071\pi$
$709$	−3.35571			−0.126027			−0.0630133	+	0.998013i	$0.520071\pi$
$710$	30.0183	+	35.7413i	1.12657	+	1.34135i
$711$	18.6675			0.700086
$712$			133.097i			4.98802i
$713$		−	7.34331i		−	0.275009i
$714$	−29.1433			−1.09066
$715$	−0.138592	−	0.165014i	−0.00518304	−	0.00617119i
$716$	124.636			4.65786
$717$		−	20.7943i		−	0.776577i
$718$		−	42.4715i		−	1.58502i
$719$	−41.0927			−1.53250			−0.766249	−	0.642544i	$-0.777879\pi$
$719$	−41.0927			−1.53250			−0.766249	+	0.642544i	$0.777879\pi$
$720$	35.2219	−	29.5821i	1.31264	−	1.10246i
$721$	−39.2242			−1.46078
$722$		0			0
$723$			33.8846i			1.26018i
$724$	−13.3979			−0.497931
$725$	−2.54652	+	14.5194i	−0.0945753	+	0.539236i
$726$	30.7717			1.14204
$727$			12.0665i			0.447522i	0.974644	+	0.223761i	$0.0718335\pi$
$727$			12.0665i			0.447522i	−0.974644	+	0.223761i	$0.928166\pi$
$728$		−	0.974391i		−	0.0361133i
$729$	−1.17546			−0.0435356
$730$	19.5407	−	16.4118i	0.723235	−	0.607428i
$731$	−9.31966			−0.344700
$732$		−	51.3456i		−	1.89779i
$733$		−	13.6350i		−	0.503619i	−0.967777	−	0.251809i	$-0.918974\pi$
$733$		−	13.6350i		−	0.503619i	0.967777	−	0.251809i	$-0.0810256\pi$
$734$	−7.09990			−0.262062
$735$	2.30064	+	2.73927i	0.0848606	+	0.101039i
$736$	−43.4577			−1.60187
$737$		−	11.5496i		−	0.425434i
$738$		−	34.7193i		−	1.27803i
$739$	−38.2167			−1.40582			−0.702911	−	0.711278i	$-0.748117\pi$
$739$	−38.2167			−1.40582			−0.702911	+	0.711278i	$0.748117\pi$
$740$	−1.70417	−	2.02907i	−0.0626465	−	0.0745901i
$741$		0			0
$742$			42.7280i			1.56859i
$743$			6.07323i			0.222805i	0.993775	+	0.111403i	$0.0355343\pi$
$743$			6.07323i			0.222805i	−0.993775	+	0.111403i	$0.964466\pi$
$744$	−53.5681			−1.96390
$745$	−37.2247	+	31.2642i	−1.36381	+	1.14543i
$746$	16.5618			0.606371
$747$			7.18785i			0.262990i
$748$		−	22.5506i		−	0.824532i
$749$	32.6310			1.19231
$750$	−32.3159	−	55.7965i	−1.18001	−	2.03740i
$751$	0.204498			0.00746224			0.00373112	−	0.999993i	$-0.498812\pi$
$751$	0.204498			0.00746224			0.00373112	+	0.999993i	$0.498812\pi$
$752$			141.710i			5.16764i
$753$			11.7618i			0.428622i
$754$	−0.320736			−0.0116805
$755$	−16.5905	+	13.9340i	−0.603790	+	0.507109i
$756$	43.3999			1.57844
$757$		−	18.3853i		−	0.668225i	−0.942533	−	0.334112i	$-0.891563\pi$
$757$		−	18.3853i		−	0.668225i	0.942533	−	0.334112i	$-0.108437\pi$
$758$		−	0.419504i		−	0.0152371i
$759$	12.9986			0.471820
$760$		0			0
$761$	−31.4304			−1.13935			−0.569675	−	0.821870i	$-0.692931\pi$
$761$	−31.4304			−1.13935			−0.569675	+	0.821870i	$0.692931\pi$
$762$		−	4.26210i		−	0.154400i
$763$			18.6805i			0.676281i
$764$	−48.4646			−1.75339
$765$	−4.19837	−	4.99880i	−0.151793	−	0.180732i
$766$	−43.3147			−1.56503
$767$			0.470382i			0.0169845i
$768$			30.3946i			1.09677i
$769$	21.5939			0.778697			0.389348	−	0.921091i	$-0.372700\pi$
$769$	21.5939			0.778697			0.389348	+	0.921091i	$0.372700\pi$
$770$	−30.4708	+	25.5917i	−1.09809	+	0.922260i
$771$	7.61606			0.274286
$772$			129.579i			4.66363i
$773$		−	37.0897i		−	1.33402i	−0.745047	−	0.667012i	$-0.767573\pi$
$773$		−	37.0897i		−	1.33402i	0.745047	−	0.667012i	$-0.232427\pi$
$774$	−22.1717			−0.796945
$775$	−2.49292	+	14.2137i	−0.0895482	+	0.510573i
$776$	48.3807			1.73677
$777$			1.35663i			0.0486690i
$778$		−	7.29454i		−	0.261522i
$779$		0			0
$780$	0.776644	−	0.652285i	0.0278083	−	0.0233555i
$781$	18.4908			0.661653
$782$			12.4121i			0.443857i
$783$		−	8.81049i		−	0.314861i
$784$	−9.53491			−0.340532
$785$	−10.6125	−	12.6358i	−0.378777	−	0.450991i
$786$	62.9329			2.24474
$787$		−	2.00316i		−	0.0714049i	−0.999362	−	0.0357025i	$-0.988633\pi$
$787$		−	2.00316i		−	0.0714049i	0.999362	−	0.0357025i	$-0.0113669\pi$
$788$			21.7767i			0.775764i
$789$	−56.5573			−2.01349
$790$	44.8594	+	53.4119i	1.59603	+	1.90031i
$791$	6.86305			0.244022
$792$		−	33.0867i		−	1.17569i
$793$		−	0.185610i		−	0.00659122i
$794$	42.5916			1.51152
$795$	−21.0038	+	17.6406i	−0.744927	+	0.625647i
$796$	116.820			4.14058
$797$		−	12.8587i		−	0.455480i	−0.973722	−	0.227740i	$-0.926866\pi$
$797$		−	12.8587i		−	0.455480i	0.973722	−	0.227740i	$-0.0731336\pi$
$798$		0			0
$799$	20.1119			0.711509
$800$	84.1169	+	14.7531i	2.97398	+	0.521600i
$801$	24.7494			0.874477
$802$		−	8.93451i		−	0.315488i
$803$		−	10.1094i		−	0.356754i
$804$	54.3584			1.91707
$805$	12.1245	−	10.1831i	0.427334	−	0.358908i
$806$	−0.313984			−0.0110596
$807$		−	49.6214i		−	1.74676i
$808$		−	103.388i		−	3.63719i
$809$	−21.1972			−0.745255			−0.372627	−	0.927981i	$-0.621543\pi$
$809$	−21.1972			−0.745255			−0.372627	+	0.927981i	$0.621543\pi$
$810$	43.4219	+	51.7003i	1.52569	+	1.81656i
$811$	−8.94877			−0.314234			−0.157117	−	0.987580i	$-0.550220\pi$
$811$	−8.94877			−0.314234			−0.157117	+	0.987580i	$0.550220\pi$
$812$			42.8157i			1.50253i
$813$			39.6384i			1.39018i
$814$	−1.45208			−0.0508952
$815$	7.05114	+	8.39546i	0.246991	+	0.294080i
$816$	49.8662			1.74567
$817$		0			0
$818$		−	20.1240i		−	0.703621i
$819$	−0.181188			−0.00633122
$820$	71.8152	−	60.3159i	2.50790	−	2.10632i
$821$	−3.45820			−0.120692			−0.0603459	−	0.998178i	$-0.519220\pi$
$821$	−3.45820			−0.120692			−0.0603459	+	0.998178i	$0.519220\pi$
$822$		−	26.4737i		−	0.923377i
$823$			18.1282i			0.631910i	0.948774	+	0.315955i	$0.102325\pi$
$823$			18.1282i			0.631910i	−0.948774	+	0.315955i	$0.897675\pi$
$824$	121.864			4.24534
$825$	−25.1602	−	4.41279i	−0.875966	−	0.153634i
$826$	86.8584			3.02219
$827$			29.3890i			1.02195i	0.859594	+	0.510977i	$0.170716\pi$
$827$			29.3890i			1.02195i	−0.859594	+	0.510977i	$0.829284\pi$
$828$			21.3471i			0.741864i
$829$	3.46778			0.120441			0.0602204	−	0.998185i	$-0.480820\pi$
$829$	3.46778			0.120441			0.0602204	+	0.998185i	$0.480820\pi$
$830$	−20.5661	+	17.2729i	−0.713858	+	0.599553i
$831$	64.3347			2.23175
$832$			0.822047i			0.0284993i
$833$			1.35322i			0.0468864i
$834$	−45.2454			−1.56672
$835$	14.5129	+	17.2798i	0.502240	+	0.597993i
$836$		0			0
$837$		−	8.62503i		−	0.298125i
$838$		−	38.7172i		−	1.33746i
$839$	−39.8304			−1.37510			−0.687548	−	0.726139i	$-0.741313\pi$
$839$	−39.8304			−1.37510			−0.687548	+	0.726139i	$0.741313\pi$
$840$	−74.2840	−	88.4463i	−2.56304	−	3.05169i
$841$	−20.3081			−0.700280
$842$		−	96.0924i		−	3.31156i
$843$		−	8.54163i		−	0.294189i
$844$	−8.77500			−0.302048
$845$	−22.2567	+	18.6929i	−0.765655	+	0.643055i
$846$	47.8468			1.64501
$847$		−	14.8493i		−	0.510227i
$848$		−	73.1105i		−	2.51063i
$849$	−19.4251			−0.666667
$850$	4.21369	−	24.0250i	0.144528	−	0.824051i
$851$	0.577792			0.0198064
$852$			87.0273i			2.98151i
$853$			16.0111i			0.548210i	0.961700	+	0.274105i	$0.0883816\pi$
$853$			16.0111i			0.548210i	−0.961700	+	0.274105i	$0.911618\pi$
$854$	−34.2739			−1.17283
$855$		0			0
$856$	−101.380			−3.46510
$857$			16.2443i			0.554896i	0.960741	+	0.277448i	$0.0894886\pi$
$857$			16.2443i			0.554896i	−0.960741	+	0.277448i	$0.910511\pi$
$858$		−	0.555794i		−	0.0189745i
$859$	56.2376			1.91880			0.959401	−	0.282046i	$-0.0910132\pi$
$859$	56.2376			1.91880			0.959401	+	0.282046i	$0.0910132\pi$
$860$	−38.5177	−	45.8612i	−1.31344	−	1.56385i
$861$	−48.0156			−1.63637
$862$			27.9131i			0.950724i
$863$		−	14.1589i		−	0.481974i	−0.970528	−	0.240987i	$-0.922529\pi$
$863$		−	14.1589i		−	0.481974i	0.970528	−	0.240987i	$-0.0774711\pi$
$864$	−51.0429			−1.73651
$865$	−7.01693	−	8.35472i	−0.238583	−	0.284069i
$866$	−94.2521			−3.20282
$867$			29.4148i			0.998978i
$868$			41.9144i			1.42267i
$869$	27.6327			0.937377
$870$	−29.1135	+	24.4517i	−0.987040	+	0.828991i
$871$	0.196501			0.00665818
$872$		−	58.0379i		−	1.96541i
$873$		−	8.99640i		−	0.304482i
$874$		0			0
$875$	−26.9253	+	15.5944i	−0.910242	+	0.527188i
$876$	47.5802			1.60759
$877$			6.40787i			0.216379i	0.994130	+	0.108189i	$0.0345052\pi$
$877$			6.40787i			0.216379i	−0.994130	+	0.108189i	$0.965495\pi$
$878$		−	51.3879i		−	1.73426i
$879$	5.01534			0.169163
$880$	52.1376	−	43.7891i	1.75756	−	1.47613i
$881$	−11.6117			−0.391208			−0.195604	−	0.980683i	$-0.562667\pi$
$881$	−11.6117			−0.391208			−0.195604	+	0.980683i	$0.562667\pi$
$882$			3.21935i			0.108401i
$883$			26.4253i			0.889283i	0.895709	+	0.444642i	$0.146669\pi$
$883$			26.4253i			0.889283i	−0.895709	+	0.444642i	$0.853331\pi$
$884$	0.383669			0.0129042
$885$	35.8602	+	42.6970i	1.20543	+	1.43524i
$886$	−61.7712			−2.07524
$887$			39.0608i			1.31153i	0.754964	+	0.655766i	$0.227654\pi$
$887$			39.0608i			1.31153i	−0.754964	+	0.655766i	$0.772346\pi$
$888$		−	4.21488i		−	0.141442i
$889$	−2.05673			−0.0689805
$890$	59.4747	+	70.8136i	1.99360	+	2.37368i
$891$	26.7472			0.896066
$892$			50.1559i			1.67934i
$893$		0			0
$894$	−125.379			−4.19329
$895$	40.8967	−	34.3482i	1.36703	−	1.14813i
$896$	56.7258			1.89508
$897$			0.221155i			0.00738414i
$898$		−	42.3794i		−	1.41422i
$899$	8.50891			0.283788
$900$	7.24695	−	41.3196i	0.241565	−	1.37732i
$901$	−10.3761			−0.345677
$902$		−	51.3935i		−	1.71122i
$903$			30.6627i			1.02039i
$904$	−21.3226			−0.709178
$905$	−4.39626	+	3.69232i	−0.146137	+	0.122737i
$906$	−55.8793			−1.85647
$907$		−	57.3392i		−	1.90392i	−0.306228	−	0.951958i	$-0.599067\pi$
$907$		−	57.3392i		−	1.90392i	0.306228	−	0.951958i	$-0.400933\pi$
$908$			122.447i			4.06355i
$909$	−19.2251			−0.637655
$910$	−0.435409	−	0.518420i	−0.0144337	−	0.0171855i
$911$	22.2118			0.735909			0.367954	−	0.929844i	$-0.380058\pi$
$911$	22.2118			0.735909			0.367954	+	0.929844i	$0.380058\pi$
$912$		0			0
$913$			10.6399i			0.352129i
$914$	93.0706			3.07850
$915$	−14.1503	−	16.8480i	−0.467793	−	0.556979i
$916$	−6.21432			−0.205327
$917$		−	30.3691i		−	1.00288i
$918$			14.5786i			0.481165i
$919$	−48.0529			−1.58512			−0.792560	−	0.609794i	$-0.791252\pi$
$919$	−48.0529			−1.58512			−0.792560	+	0.609794i	$0.791252\pi$
$920$	−37.6694	+	31.6376i	−1.24192	+	1.04306i
$921$	−16.3165			−0.537647
$922$			65.9924i			2.17334i
$923$			0.314597i			0.0103551i
$924$	−74.1940			−2.44080
$925$	−1.11838	−	0.196149i	−0.0367720	−	0.00644935i
$926$	−20.7039			−0.680372
$927$		−	22.6607i		−	0.744274i
$928$		−	50.3557i		−	1.65301i
$929$	−8.15190			−0.267455			−0.133728	−	0.991018i	$-0.542695\pi$
$929$	−8.15190			−0.267455			−0.133728	+	0.991018i	$0.542695\pi$
$930$	−28.5007	+	23.9370i	−0.934573	+	0.784926i
$931$		0			0
$932$		−	120.754i		−	3.95542i
$933$		−	40.4076i		−	1.32288i
$934$	17.5142			0.573082
$935$	−6.21468	−	7.39952i	−0.203242	−	0.241990i
$936$	0.562927			0.0183998
$937$			35.1525i			1.14838i	0.818721	+	0.574191i	$0.194683\pi$
$937$			35.1525i			1.14838i	−0.818721	+	0.574191i	$0.805317\pi$
$938$		−	36.2849i		−	1.18474i
$939$	47.6781			1.55592
$940$	83.1217	+	98.9689i	2.71113	+	3.22801i
$941$	−14.9909			−0.488690			−0.244345	−	0.969688i	$-0.578573\pi$
$941$	−14.9909			−0.488690			−0.244345	+	0.969688i	$0.578573\pi$
$942$		−	42.5593i		−	1.38666i
$943$			20.4499i			0.665939i
$944$	−148.621			−4.83719
$945$	14.2408	−	11.9605i	0.463253	−	0.389075i
$946$	−32.8199			−1.06707
$947$		−	32.9872i		−	1.07194i	−0.844237	−	0.535970i	$-0.819946\pi$
$947$		−	32.9872i		−	1.07194i	0.844237	−	0.535970i	$-0.180054\pi$
$948$			130.054i			4.22396i
$949$	0.171999			0.00558331
$950$		0			0
$951$	−8.74244			−0.283493
$952$		−	43.6933i		−	1.41611i
$953$		−	28.9498i		−	0.937777i	−0.883257	−	0.468888i	$-0.844655\pi$
$953$		−	28.9498i		−	0.937777i	0.883257	−	0.468888i	$-0.155345\pi$
$954$	−24.6849			−0.799203
$955$	−15.9027	+	13.3563i	−0.514598	+	0.432198i
$956$	50.5503			1.63491
$957$			15.0619i			0.486882i
$958$		−	33.2473i		−	1.07417i
$959$	−12.7752			−0.412534
$960$	62.6698	+	74.6179i	2.02266	+	2.40828i
$961$	−22.6702			−0.731297
$962$		−	0.0247052i		−	0.000796526i
$963$			18.8517i			0.607486i
$964$	−82.3725			−2.65304
$965$	35.7103	+	42.5186i	1.14956	+	1.36872i
$966$	40.8373			1.31392
$967$		−	33.3659i		−	1.07297i	−0.843909	−	0.536487i	$-0.819751\pi$
$967$		−	33.3659i		−	1.07297i	0.843909	−	0.536487i	$-0.180249\pi$
$968$			46.1347i			1.48283i
$969$		0			0
$970$	25.7408	−	21.6190i	0.826486	−	0.694146i
$971$	−6.80851			−0.218495			−0.109248	−	0.994015i	$-0.534844\pi$
$971$	−6.80851			−0.218495			−0.109248	+	0.994015i	$0.534844\pi$
$972$			79.1030i			2.53723i
$973$			21.8337i			0.699957i
$974$	104.031			3.33337
$975$	0.0750778	−	0.428068i	0.00240442	−	0.0137091i
$976$	58.6450			1.87718
$977$			0.0669330i			0.00214138i	0.999999	+	0.00107069i	$0.000340811\pi$
$977$			0.0669330i			0.00214138i	−0.999999	+	0.00107069i	$0.999659\pi$
$978$			28.2772i			0.904205i
$979$	36.6355			1.17088
$980$	−6.65908	+	5.59280i	−0.212716	+	0.178655i
$981$	−10.7922			−0.344567
$982$		−	84.3859i		−	2.69286i
$983$			50.3061i			1.60451i	0.596979	+	0.802257i	$0.296368\pi$
$983$			50.3061i			1.60451i	−0.596979	+	0.802257i	$0.703632\pi$
$984$	149.178			4.75562
$985$	6.00141	+	7.14559i	0.191221	+	0.227677i
$986$	−14.3823			−0.458027
$987$		−	66.1705i		−	2.10623i
$988$		0			0
$989$	13.0593			0.415261
$990$	−14.7849	−	17.6036i	−0.469894	−	0.559480i
$991$	4.24805			0.134944			0.0674718	−	0.997721i	$-0.478507\pi$
$991$	4.24805			0.134944			0.0674718	+	0.997721i	$0.478507\pi$
$992$		−	49.2957i		−	1.56514i
$993$			44.6228i			1.41606i
$994$	58.0919			1.84256
$995$	38.3321	−	32.1942i	1.21521	−	1.02063i
$996$	−50.0768			−1.58674
$997$		−	46.0208i		−	1.45749i	−0.684784	−	0.728746i	$-0.740103\pi$
$997$		−	46.0208i		−	1.45749i	0.684784	−	0.728746i	$-0.259897\pi$
$998$		−	52.1919i		−	1.65211i
$999$	0.678641			0.0214712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.24		24
5.2	odd	4		9025.2.a.cu.1.1		24
5.3	odd	4		9025.2.a.cu.1.24		24
5.4	even	2	inner	1805.2.b.k.1084.1		24
19.4	even	9		95.2.p.a.54.1	yes	48
19.5	even	9		95.2.p.a.44.8	yes	48
19.18	odd	2		1805.2.b.l.1084.1		24
57.5	odd	18		855.2.da.b.424.1		48
57.23	odd	18		855.2.da.b.244.8		48
95.4	even	18		95.2.p.a.54.8	yes	48
95.18	even	4		9025.2.a.ct.1.1		24
95.23	odd	36		475.2.l.f.301.8		48
95.24	even	18		95.2.p.a.44.1	✓	48
95.37	even	4		9025.2.a.ct.1.24		24
95.42	odd	36		475.2.l.f.301.1		48
95.43	odd	36		475.2.l.f.101.8		48
95.62	odd	36		475.2.l.f.101.1		48
95.94	odd	2		1805.2.b.l.1084.24		24
285.119	odd	18		855.2.da.b.424.8		48
285.194	odd	18		855.2.da.b.244.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.1	✓	48	95.24	even	18
95.2.p.a.44.8	yes	48	19.5	even	9
95.2.p.a.54.1	yes	48	19.4	even	9
95.2.p.a.54.8	yes	48	95.4	even	18
475.2.l.f.101.1		48	95.62	odd	36
475.2.l.f.101.8		48	95.43	odd	36
475.2.l.f.301.1		48	95.42	odd	36
475.2.l.f.301.8		48	95.23	odd	36
855.2.da.b.244.1		48	285.194	odd	18
855.2.da.b.244.8		48	57.23	odd	18
855.2.da.b.424.1		48	57.5	odd	18
855.2.da.b.424.8		48	285.119	odd	18
1805.2.b.k.1084.1		24	5.4	even	2	inner
1805.2.b.k.1084.24		24	1.1	even	1	trivial
1805.2.b.l.1084.1		24	19.18	odd	2
1805.2.b.l.1084.24		24	95.94	odd	2
9025.2.a.ct.1.1		24	95.18	even	4
9025.2.a.ct.1.24		24	95.37	even	4
9025.2.a.cu.1.1		24	5.2	odd	4
9025.2.a.cu.1.24		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.68669i q^{2} +2.14658i q^{3} -5.21828 q^{4} +(-1.71227 + 1.43810i) q^{5} -5.76720 q^{6} +2.78303i q^{7} -8.64651i q^{8} -1.60782 q^{9} +(-3.86371 - 4.60034i) q^{10} -2.37999 q^{11} -11.2015i q^{12} -0.0404924i q^{13} -7.47713 q^{14} +(-3.08699 - 3.67554i) q^{15} +12.7939 q^{16} -1.81575i q^{17} -4.31971i q^{18} +(8.93512 - 7.50439i) q^{20} -5.97401 q^{21} -6.39429i q^{22} +2.54434i q^{23} +18.5605 q^{24} +(0.863754 - 4.92483i) q^{25} +0.108790 q^{26} +2.98843i q^{27} -14.5226i q^{28} -2.94820 q^{29} +(9.87501 - 8.29379i) q^{30} -2.88614 q^{31} +17.0802i q^{32} -5.10885i q^{33} +4.87834 q^{34} +(-4.00227 - 4.76531i) q^{35} +8.39006 q^{36} -0.227089i q^{37} +0.0869204 q^{39} +(12.4345 + 14.8052i) q^{40} +8.03741 q^{41} -16.0503i q^{42} -5.13269i q^{43} +12.4195 q^{44} +(2.75303 - 2.31220i) q^{45} -6.83583 q^{46} +11.0764i q^{47} +27.4632i q^{48} -0.745270 q^{49} +(13.2315 + 2.32064i) q^{50} +3.89765 q^{51} +0.211301i q^{52} -5.71448i q^{53} -8.02897 q^{54} +(4.07519 - 3.42266i) q^{55} +24.0635 q^{56} -7.92088i q^{58} -11.6165 q^{59} +(16.1088 + 19.1800i) q^{60} +4.58383 q^{61} -7.75415i q^{62} -4.47462i q^{63} -20.3012 q^{64} +(0.0582320 + 0.0693341i) q^{65} +13.7259 q^{66} +4.85278i q^{67} +9.47508i q^{68} -5.46163 q^{69} +(12.8029 - 10.7528i) q^{70} -7.76927 q^{71} +13.9020i q^{72} +4.24767i q^{73} +0.610118 q^{74} +(10.5716 + 1.85412i) q^{75} -6.62359i q^{77} +0.233528i q^{78} -11.6104 q^{79} +(-21.9066 + 18.3989i) q^{80} -11.2384 q^{81} +21.5940i q^{82} -4.47055i q^{83} +31.1741 q^{84} +(2.61122 + 3.10906i) q^{85} +13.7899 q^{86} -6.32855i q^{87} +20.5786i q^{88} -15.3931 q^{89} +(6.21216 + 7.39652i) q^{90} +0.112692 q^{91} -13.2771i q^{92} -6.19534i q^{93} -29.7588 q^{94} -36.6640 q^{96} +5.59540i q^{97} -2.00231i q^{98} +3.82660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 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

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Representations

Groups

Database

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