LMFDB - Embedded newform 1805.2.b.l.1084.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.20
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.78468i q^{2} -2.38377i q^{3} -1.18508 q^{4} +(-1.16534 + 1.90840i) q^{5} +4.25426 q^{6} -4.23911i q^{7} +1.45438i q^{8} -2.68235 q^{9} +(-3.40588 - 2.07976i) q^{10} -0.490889 q^{11} +2.82495i q^{12} -4.16199i q^{13} +7.56544 q^{14} +(4.54918 + 2.77790i) q^{15} -4.96575 q^{16} +2.03619i q^{17} -4.78713i q^{18} +(1.38102 - 2.26160i) q^{20} -10.1050 q^{21} -0.876080i q^{22} +4.39525i q^{23} +3.46689 q^{24} +(-2.28396 - 4.44787i) q^{25} +7.42782 q^{26} -0.757211i q^{27} +5.02367i q^{28} -3.26270 q^{29} +(-4.95766 + 8.11882i) q^{30} -4.08833 q^{31} -5.95351i q^{32} +1.17017i q^{33} -3.63395 q^{34} +(8.08990 + 4.94000i) q^{35} +3.17879 q^{36} -2.14440i q^{37} -9.92123 q^{39} +(-2.77553 - 1.69484i) q^{40} -4.36602 q^{41} -18.0343i q^{42} +10.6241i q^{43} +0.581742 q^{44} +(3.12585 - 5.11898i) q^{45} -7.84410 q^{46} -2.62142i q^{47} +11.8372i q^{48} -10.9700 q^{49} +(7.93801 - 4.07614i) q^{50} +4.85381 q^{51} +4.93228i q^{52} -11.4341i q^{53} +1.35138 q^{54} +(0.572053 - 0.936812i) q^{55} +6.16526 q^{56} -5.82287i q^{58} -0.542306 q^{59} +(-5.39112 - 3.29203i) q^{60} -13.6423 q^{61} -7.29635i q^{62} +11.3708i q^{63} +0.693606 q^{64} +(7.94274 + 4.85014i) q^{65} -2.08837 q^{66} -7.15699i q^{67} -2.41305i q^{68} +10.4772 q^{69} +(-8.81632 + 14.4379i) q^{70} -6.03858 q^{71} -3.90114i q^{72} +2.05419i q^{73} +3.82707 q^{74} +(-10.6027 + 5.44444i) q^{75} +2.08093i q^{77} -17.7062i q^{78} +5.34029 q^{79} +(5.78678 - 9.47662i) q^{80} -9.85206 q^{81} -7.79193i q^{82} +8.11578i q^{83} +11.9753 q^{84} +(-3.88587 - 2.37286i) q^{85} -18.9605 q^{86} +7.77752i q^{87} -0.713937i q^{88} -4.34099 q^{89} +(9.13574 + 5.57863i) q^{90} -17.6431 q^{91} -5.20871i q^{92} +9.74562i q^{93} +4.67839 q^{94} -14.1918 q^{96} +5.64669i q^{97} -19.5780i q^{98} +1.31674 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 + 6 * q^10 + 12 * q^11 + 24 * q^14 + 9 * q^15 + 6 * q^16 + 21 * q^20 - 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 + 36 * q^29 - 18 * q^30 - 42 * q^31 + 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 - 12 * q^40 - 60 * q^41 + 30 * q^44 + 9 * q^45 - 6 * q^46 - 12 * q^49 - 18 * q^50 - 30 * q^51 + 24 * q^54 + 33 * q^55 - 18 * q^56 + 60 * q^59 + 42 * q^60 + 30 * q^61 - 18 * q^65 + 36 * q^66 + 66 * q^69 - 9 * q^70 - 96 * q^71 - 24 * q^74 - 36 * q^75 + 72 * q^79 - 42 * q^80 - 96 * q^81 - 54 * q^84 - 27 * q^85 - 108 * q^86 + 84 * q^89 + 93 * q^90 - 96 * q^91 + 36 * q^94 - 120 * q^96

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.78468i			1.26196i	0.775800	+	0.630979i	$0.217347\pi$
$2$			1.78468i			1.26196i	−0.775800	+	0.630979i	$0.782653\pi$
$3$		−	2.38377i		−	1.37627i	−0.725583	−	0.688134i	$-0.758430\pi$
$3$		−	2.38377i		−	1.37627i	0.725583	−	0.688134i	$-0.241570\pi$
$4$	−1.18508			−0.592538
$5$	−1.16534	+	1.90840i	−0.521156	+	0.853461i
$5$	−1.16534	+	1.90840i	−0.521156	+	0.853461i
$6$	4.25426			1.73679
$7$		−	4.23911i		−	1.60223i	−0.598509	−	0.801116i	$-0.704240\pi$
$7$		−	4.23911i		−	1.60223i	0.598509	−	0.801116i	$-0.295760\pi$
$8$			1.45438i			0.514199i
$9$	−2.68235			−0.894116
$10$	−3.40588	−	2.07976i	−1.07703	−	0.657677i
$11$	−0.490889			−0.148009			−0.0740043	−	0.997258i	$-0.523578\pi$
$11$	−0.490889			−0.148009			−0.0740043	+	0.997258i	$0.523578\pi$
$12$			2.82495i			0.815492i
$13$		−	4.16199i		−	1.15433i	−0.816628	−	0.577165i	$-0.804159\pi$
$13$		−	4.16199i		−	1.15433i	0.816628	−	0.577165i	$-0.195841\pi$
$14$	7.56544			2.02195
$15$	4.54918	+	2.77790i	1.17459	+	0.717251i
$16$	−4.96575			−1.24144
$17$			2.03619i			0.493850i	0.969035	+	0.246925i	$0.0794201\pi$
$17$			2.03619i			0.493850i	−0.969035	+	0.246925i	$0.920580\pi$
$18$		−	4.78713i		−	1.12834i
$19$		0			0
$19$		0			0
$20$	1.38102	−	2.26160i	0.308805	−	0.505709i
$21$	−10.1050			−2.20510
$22$		−	0.876080i		−	0.186781i
$23$			4.39525i			0.916472i	0.888830	+	0.458236i	$0.151519\pi$
$23$			4.39525i			0.916472i	−0.888830	+	0.458236i	$0.848481\pi$
$24$	3.46689			0.707677
$25$	−2.28396	−	4.44787i	−0.456793	−	0.889573i
$26$	7.42782			1.45672
$27$		−	0.757211i		−	0.145725i
$28$			5.02367i			0.949384i
$29$	−3.26270			−0.605869			−0.302934	−	0.953011i	$-0.597966\pi$
$29$	−3.26270			−0.605869			−0.302934	+	0.953011i	$0.597966\pi$
$30$	−4.95766	+	8.11882i	−0.905140	+	1.48229i
$31$	−4.08833			−0.734285			−0.367143	−	0.930165i	$-0.619664\pi$
$31$	−4.08833			−0.734285			−0.367143	+	0.930165i	$0.619664\pi$
$32$		−	5.95351i		−	1.05244i
$33$			1.17017i			0.203700i
$34$	−3.63395			−0.623218
$35$	8.08990	+	4.94000i	1.36744	+	0.835013i
$36$	3.17879			0.529798
$37$		−	2.14440i		−	0.352538i	−0.984342	−	0.176269i	$-0.943597\pi$
$37$		−	2.14440i		−	0.352538i	0.984342	−	0.176269i	$-0.0564028\pi$
$38$		0			0
$39$	−9.92123			−1.58867
$40$	−2.77553	−	1.69484i	−0.438849	−	0.267978i
$41$	−4.36602			−0.681857			−0.340929	−	0.940089i	$-0.610741\pi$
$41$	−4.36602			−0.681857			−0.340929	+	0.940089i	$0.610741\pi$
$42$		−	18.0343i		−	2.78275i
$43$			10.6241i			1.62015i	0.586324	+	0.810077i	$0.300575\pi$
$43$			10.6241i			1.62015i	−0.586324	+	0.810077i	$0.699425\pi$
$44$	0.581742			0.0877008
$45$	3.12585	−	5.11898i	0.465974	−	0.763093i
$46$	−7.84410			−1.15655
$47$		−	2.62142i		−	0.382373i	−0.981554	−	0.191187i	$-0.938766\pi$
$47$		−	2.62142i		−	0.382373i	0.981554	−	0.191187i	$-0.0612336\pi$
$48$			11.8372i			1.70855i
$49$	−10.9700			−1.56715
$50$	7.93801	−	4.07614i	1.12260	−	0.576453i
$51$	4.85381			0.679670
$52$			4.93228i			0.683985i
$53$		−	11.4341i		−	1.57059i	−0.619121	−	0.785296i	$-0.712511\pi$
$53$		−	11.4341i		−	1.57059i	0.619121	−	0.785296i	$-0.287489\pi$
$54$	1.35138			0.183899
$55$	0.572053	−	0.936812i	0.0771356	−	0.126320i
$56$	6.16526			0.823867
$57$		0			0
$58$		−	5.82287i		−	0.764581i
$59$	−0.542306			−0.0706022			−0.0353011	−	0.999377i	$-0.511239\pi$
$59$	−0.542306			−0.0706022			−0.0353011	+	0.999377i	$0.511239\pi$
$60$	−5.39112	−	3.29203i	−0.695991	−	0.424999i
$61$	−13.6423			−1.74671			−0.873356	−	0.487083i	$-0.838061\pi$
$61$	−13.6423			−1.74671			−0.873356	+	0.487083i	$0.838061\pi$
$62$		−	7.29635i		−	0.926637i
$63$			11.3708i			1.43258i
$64$	0.693606			0.0867007
$65$	7.94274	+	4.85014i	0.985176	+	0.601586i
$66$	−2.08837			−0.257061
$67$		−	7.15699i		−	0.874365i	−0.899373	−	0.437182i	$-0.855976\pi$
$67$		−	7.15699i		−	0.874365i	0.899373	−	0.437182i	$-0.144024\pi$
$68$		−	2.41305i		−	0.292625i
$69$	10.4772			1.26131
$70$	−8.81632	+	14.4379i	−1.05375	+	1.72566i
$71$	−6.03858			−0.716647			−0.358324	−	0.933597i	$-0.616652\pi$
$71$	−6.03858			−0.716647			−0.358324	+	0.933597i	$0.616652\pi$
$72$		−	3.90114i		−	0.459754i
$73$			2.05419i			0.240425i	0.992748	+	0.120212i	$0.0383576\pi$
$73$			2.05419i			0.240425i	−0.992748	+	0.120212i	$0.961642\pi$
$74$	3.82707			0.444888
$75$	−10.6027	+	5.44444i	−1.22429	+	0.628670i
$76$		0			0
$77$			2.08093i			0.237144i
$78$		−	17.7062i		−	2.00483i
$79$	5.34029			0.600830			0.300415	−	0.953809i	$-0.402875\pi$
$79$	5.34029			0.600830			0.300415	+	0.953809i	$0.402875\pi$
$80$	5.78678	−	9.47662i	0.646982	−	1.05952i
$81$	−9.85206			−1.09467
$82$		−	7.79193i		−	0.860475i
$83$			8.11578i			0.890823i	0.895326	+	0.445411i	$0.146943\pi$
$83$			8.11578i			0.890823i	−0.895326	+	0.445411i	$0.853057\pi$
$84$	11.9753			1.30661
$85$	−3.88587	−	2.37286i	−0.421482	−	0.257373i
$86$	−18.9605			−2.04457
$87$			7.77752i			0.833838i
$88$		−	0.713937i		−	0.0761060i
$89$	−4.34099			−0.460144			−0.230072	−	0.973174i	$-0.573896\pi$
$89$	−4.34099			−0.460144			−0.230072	+	0.973174i	$0.573896\pi$
$90$	9.13574	+	5.57863i	0.962992	+	0.588039i
$91$	−17.6431			−1.84950
$92$		−	5.20871i		−	0.543045i
$93$			9.74562i			1.01057i
$94$	4.67839			0.482539
$95$		0			0
$96$	−14.1918			−1.44844
$97$			5.64669i			0.573335i	0.958030	+	0.286667i	$0.0925475\pi$
$97$			5.64669i			0.573335i	−0.958030	+	0.286667i	$0.907453\pi$
$98$		−	19.5780i		−	1.97768i
$99$	1.31674			0.132337
$100$	2.70667	+	5.27106i	0.270667	+	0.527106i
$101$	−3.30082			−0.328444			−0.164222	−	0.986423i	$-0.552511\pi$
$101$	−3.30082			−0.328444			−0.164222	+	0.986423i	$0.552511\pi$
$102$			8.66250i			0.857715i
$103$			3.41567i			0.336556i	0.985740	+	0.168278i	$0.0538206\pi$
$103$			3.41567i			0.336556i	−0.985740	+	0.168278i	$0.946179\pi$
$104$	6.05310			0.593556
$105$	11.7758	−	19.2844i	1.14920	−	1.88197i
$106$	20.4062			1.98202
$107$		−	1.75252i		−	0.169422i	−0.996406	−	0.0847110i	$-0.973003\pi$
$107$		−	1.75252i		−	0.169422i	0.996406	−	0.0847110i	$-0.0269967\pi$
$108$			0.897354i			0.0863479i
$109$	−3.51923			−0.337081			−0.168541	−	0.985695i	$-0.553905\pi$
$109$	−3.51923			−0.337081			−0.168541	+	0.985695i	$0.553905\pi$
$110$	1.67191	+	1.02093i	0.159410	+	0.0973419i
$111$	−5.11176			−0.485186
$112$			21.0503i			1.98907i
$113$		−	13.2583i		−	1.24723i	−0.781731	−	0.623616i	$-0.785663\pi$
$113$		−	13.2583i		−	1.24723i	0.781731	−	0.623616i	$-0.214337\pi$
$114$		0			0
$115$	−8.38788	−	5.12196i	−0.782174	−	0.477625i
$116$	3.86655			0.359000
$117$			11.1639i			1.03210i
$118$		−	0.967842i		−	0.0890971i
$119$	8.63165			0.791262
$120$	−4.04011	+	6.61621i	−0.368810	+	0.603975i
$121$	−10.7590			−0.978093
$122$		−	24.3470i		−	2.20428i
$123$			10.4076i			0.938419i
$124$	4.84498			0.435092
$125$	11.1499	+	0.824566i	0.997277	+	0.0737514i
$126$	−20.2931			−1.80786
$127$		−	19.8082i		−	1.75769i	−0.477105	−	0.878846i	$-0.658314\pi$
$127$		−	19.8082i		−	1.75769i	0.477105	−	0.878846i	$-0.341686\pi$
$128$		−	10.6692i		−	0.943029i
$129$	25.3253			2.22977
$130$	−8.65594	+	14.1752i	−0.759176	+	1.24325i
$131$	−3.43004			−0.299684			−0.149842	−	0.988710i	$-0.547876\pi$
$131$	−3.43004			−0.299684			−0.149842	+	0.988710i	$0.547876\pi$
$132$		−	1.38674i		−	0.120700i
$133$		0			0
$134$	12.7729			1.10341
$135$	1.44506	+	0.882409i	0.124371	+	0.0759457i
$136$	−2.96139			−0.253937
$137$		−	0.608296i		−	0.0519702i	−0.999662	−	0.0259851i	$-0.991728\pi$
$137$		−	0.608296i		−	0.0519702i	0.999662	−	0.0259851i	$-0.00827225\pi$
$138$			18.6985i			1.59172i
$139$	8.45799			0.717397			0.358699	−	0.933453i	$-0.383221\pi$
$139$	8.45799			0.717397			0.358699	+	0.933453i	$0.383221\pi$
$140$	−9.58716	−	5.85428i	−0.810263	−	0.494777i
$141$	−6.24885			−0.526248
$142$		−	10.7769i		−	0.904379i
$143$			2.04308i			0.170851i
$144$	13.3199			1.10999
$145$	3.80216	−	6.22653i	0.315752	−	0.517085i
$146$	−3.66607			−0.303406
$147$			26.1500i			2.15682i
$148$			2.54128i			0.208892i
$149$	4.63735			0.379907			0.189953	−	0.981793i	$-0.439166\pi$
$149$	4.63735			0.379907			0.189953	+	0.981793i	$0.439166\pi$
$150$	−9.71657	−	18.9224i	−0.793355	−	1.54500i
$151$	−14.2109			−1.15646			−0.578232	−	0.815872i	$-0.696257\pi$
$151$	−14.2109			−1.15646			−0.578232	+	0.815872i	$0.696257\pi$
$152$		0			0
$153$		−	5.46178i		−	0.441559i
$154$	−3.71380			−0.299266
$155$	4.76429	−	7.80215i	0.382677	−	0.626684i
$156$	11.7574			0.941347
$157$		−	10.7281i		−	0.856194i	−0.903733	−	0.428097i	$-0.859184\pi$
$157$		−	10.7281i		−	0.856194i	0.903733	−	0.428097i	$-0.140816\pi$
$158$			9.53071i			0.758222i
$159$	−27.2562			−2.16156
$160$	11.3617	+	6.93786i	0.898218	+	0.548486i
$161$	18.6319			1.46840
$162$		−	17.5828i		−	1.38143i
$163$		−	16.9366i		−	1.32658i	−0.748363	−	0.663289i	$-0.769160\pi$
$163$		−	16.9366i		−	1.32658i	0.748363	−	0.663289i	$-0.230840\pi$
$164$	5.17406			0.404027
$165$	−2.23314	−	1.36364i	−0.173850	−	0.106159i
$166$	−14.4841			−1.12418
$167$			16.2567i			1.25798i	0.777412	+	0.628991i	$0.216532\pi$
$167$			16.2567i			1.25798i	−0.777412	+	0.628991i	$0.783468\pi$
$168$		−	14.6965i		−	1.13386i
$169$	−4.32219			−0.332476
$170$	4.23479	−	6.93503i	0.324794	−	0.531892i
$171$		0			0
$172$		−	12.5903i		−	0.960003i
$173$		−	8.59112i		−	0.653171i	−0.945168	−	0.326585i	$-0.894102\pi$
$173$		−	8.59112i		−	0.653171i	0.945168	−	0.326585i	$-0.105898\pi$
$174$	−13.8804			−1.05227
$175$	−18.8550	+	9.68197i	−1.42530	+	0.731888i
$176$	2.43763			0.183743
$177$			1.29273i			0.0971677i
$178$		−	7.74728i		−	0.580683i
$179$	−23.5276			−1.75853			−0.879267	−	0.476330i	$-0.841967\pi$
$179$	−23.5276			−1.75853			−0.879267	+	0.476330i	$0.841967\pi$
$180$	−3.70437	+	6.06639i	−0.276107	+	0.452162i
$181$	16.6135			1.23487			0.617434	−	0.786623i	$-0.288172\pi$
$181$	16.6135			1.23487			0.617434	+	0.786623i	$0.288172\pi$
$182$		−	31.4873i		−	2.33400i
$183$			32.5200i			2.40394i
$184$	−6.39234			−0.471250
$185$	4.09237	+	2.49896i	0.300877	+	0.183727i
$186$	−17.3928			−1.27530
$187$		−	0.999546i		−	0.0730941i
$188$			3.10658i			0.226571i
$189$	−3.20990			−0.233486
$190$		0			0
$191$	−12.8109			−0.926965			−0.463482	−	0.886106i	$-0.653400\pi$
$191$	−12.8109			−0.926965			−0.463482	+	0.886106i	$0.653400\pi$
$192$		−	1.65339i		−	0.119323i
$193$		−	9.63983i		−	0.693890i	−0.937885	−	0.346945i	$-0.887219\pi$
$193$		−	9.63983i		−	0.693890i	0.937885	−	0.346945i	$-0.112781\pi$
$194$	−10.0775			−0.723525
$195$	11.5616	−	18.9336i	0.827944	−	1.35587i
$196$	13.0003			0.928596
$197$		−	3.10241i		−	0.221038i	−0.993874	−	0.110519i	$-0.964749\pi$
$197$		−	3.10241i		−	0.221038i	0.993874	−	0.110519i	$-0.0352513\pi$
$198$			2.34995i			0.167004i
$199$	−0.524290			−0.0371659			−0.0185830	−	0.999827i	$-0.505915\pi$
$199$	−0.524290			−0.0371659			−0.0185830	+	0.999827i	$0.505915\pi$
$200$	6.46887	−	3.32174i	0.457418	−	0.234883i
$201$	−17.0606			−1.20336
$202$		−	5.89091i		−	0.414483i
$203$			13.8309i			0.970742i
$204$	−5.75214			−0.402731
$205$	5.08789	−	8.33209i	0.355354	−	0.581939i
$206$	−6.09586			−0.424719
$207$		−	11.7896i		−	0.819432i
$208$			20.6674i			1.43303i
$209$		0			0
$210$	34.4165	+	21.0160i	2.37497	+	1.45025i
$211$	19.0637			1.31240			0.656201	−	0.754586i	$-0.272162\pi$
$211$	19.0637			1.31240			0.656201	+	0.754586i	$0.272162\pi$
$212$			13.5503i			0.930636i
$213$			14.3946i			0.986299i
$214$	3.12768			0.213804
$215$	−20.2749	−	12.3806i	−1.38274	−	0.844353i
$216$	1.10127			0.0749319
$217$			17.3309i			1.17650i
$218$		−	6.28069i		−	0.425382i
$219$	4.89671			0.330889
$220$	−0.677927	+	1.11019i	−0.0457058	+	0.0748493i
$221$	8.47463			0.570065
$222$		−	9.12284i		−	0.612285i
$223$			3.16283i			0.211799i	0.994377	+	0.105899i	$0.0337721\pi$
$223$			3.16283i			0.211799i	−0.994377	+	0.105899i	$0.966228\pi$
$224$	−25.2376			−1.68626
$225$	6.12638	+	11.9307i	0.408426	+	0.795381i
$226$	23.6617			1.57395
$227$		−	9.04654i		−	0.600440i	−0.953870	−	0.300220i	$-0.902940\pi$
$227$		−	9.04654i		−	0.600440i	0.953870	−	0.300220i	$-0.0970600\pi$
$228$		0			0
$229$	17.8920			1.18234			0.591168	−	0.806549i	$-0.298667\pi$
$229$	17.8920			1.18234			0.591168	+	0.806549i	$0.298667\pi$
$230$	9.14105	−	14.9697i	0.602743	−	0.987071i
$231$	4.96046			0.326374
$232$		−	4.74519i		−	0.311537i
$233$			6.44330i			0.422114i	0.977474	+	0.211057i	$0.0676906\pi$
$233$			6.44330i			0.422114i	−0.977474	+	0.211057i	$0.932309\pi$
$234$	−19.9240			−1.30247
$235$	5.00271	+	3.05485i	0.326341	+	0.199276i
$236$	0.642674			0.0418345
$237$		−	12.7300i		−	0.826903i
$238$			15.4047i			0.998539i
$239$	13.4742			0.871571			0.435785	−	0.900051i	$-0.356471\pi$
$239$	13.4742			0.871571			0.435785	+	0.900051i	$0.356471\pi$
$240$	−22.5901	−	13.7943i	−1.45818	−	0.890421i
$241$	17.6351			1.13598			0.567990	−	0.823036i	$-0.307721\pi$
$241$	17.6351			1.13598			0.567990	+	0.823036i	$0.307721\pi$
$242$		−	19.2014i		−	1.23431i
$243$			21.2134i			1.36084i
$244$	16.1671			1.03499
$245$	12.7838	−	20.9352i	0.816729	−	1.33750i
$246$	−18.5742			−1.18424
$247$		0			0
$248$		−	5.94596i		−	0.377569i
$249$	19.3461			1.22601
$250$	−1.47158	+	19.8990i	−0.0930712	+	1.25852i
$251$	17.7326			1.11927			0.559636	−	0.828738i	$-0.310941\pi$
$251$	17.7326			1.11927			0.559636	+	0.828738i	$0.310941\pi$
$252$		−	13.4752i		−	0.848859i
$253$		−	2.15758i		−	0.135646i
$254$	35.3513			2.21813
$255$	−5.65635	+	9.26301i	−0.354214	+	0.580072i
$256$	20.4282			1.27676
$257$			27.7475i			1.73084i	0.501046	+	0.865421i	$0.332949\pi$
$257$			27.7475i			1.73084i	−0.501046	+	0.865421i	$0.667051\pi$
$258$			45.1975i			2.81387i
$259$	−9.09035			−0.564847
$260$	−9.41276	−	5.74779i	−0.583754	−	0.356463i
$261$	8.75170			0.541716
$262$		−	6.12152i		−	0.378189i
$263$		−	5.56032i		−	0.342864i	−0.985196	−	0.171432i	$-0.945161\pi$
$263$		−	5.56032i		−	0.342864i	0.985196	−	0.171432i	$-0.0548393\pi$
$264$	−1.70186			−0.104742
$265$	21.8208	+	13.3246i	1.34044	+	0.818523i
$266$		0			0
$267$			10.3479i			0.633282i
$268$			8.48158i			0.518095i
$269$	−4.62765			−0.282153			−0.141076	−	0.989999i	$-0.545056\pi$
$269$	−4.62765			−0.282153			−0.141076	+	0.989999i	$0.545056\pi$
$270$	−1.57482	+	2.57897i	−0.0958403	+	0.156951i
$271$	−7.60838			−0.462176			−0.231088	−	0.972933i	$-0.574229\pi$
$271$	−7.60838			−0.462176			−0.231088	+	0.972933i	$0.574229\pi$
$272$		−	10.1112i		−	0.613083i
$273$			42.0571i			2.54541i
$274$	1.08561			0.0655843
$275$	1.12117	+	2.18341i	0.0676093	+	0.131665i
$276$	−12.4163			−0.747376
$277$			7.53544i			0.452761i	0.974039	+	0.226380i	$0.0726892\pi$
$277$			7.53544i			0.452761i	−0.974039	+	0.226380i	$0.927311\pi$
$278$			15.0948i			0.905325i
$279$	10.9663			0.656536
$280$	−7.18462	+	11.7658i	−0.429363	+	0.703139i
$281$	18.2549			1.08900			0.544499	−	0.838762i	$-0.316720\pi$
$281$	18.2549			1.08900			0.544499	+	0.838762i	$0.316720\pi$
$282$		−	11.1522i		−	0.664103i
$283$			30.9333i			1.83880i	0.393328	+	0.919398i	$0.371324\pi$
$283$			30.9333i			1.83880i	−0.393328	+	0.919398i	$0.628676\pi$
$284$	7.15618			0.424641
$285$		0			0
$286$	−3.64624			−0.215607
$287$			18.5080i			1.09249i
$288$			15.9694i			0.941004i
$289$	12.8539			0.756112
$290$	11.1124	+	6.78563i	0.652540	+	0.398466i
$291$	13.4604			0.789063
$292$		−	2.43437i		−	0.142461i
$293$			21.8992i			1.27937i	0.768639	+	0.639683i	$0.220934\pi$
$293$			21.8992i			1.27937i	−0.768639	+	0.639683i	$0.779066\pi$
$294$	−46.6694			−2.72181
$295$	0.631971	−	1.03494i	0.0367948	−	0.0602563i
$296$	3.11877			0.181275
$297$			0.371707i			0.0215686i
$298$			8.27618i			0.479426i
$299$	18.2930			1.05791
$300$	12.5650	−	6.45208i	0.725440	−	0.372511i
$301$	45.0365			2.59586
$302$		−	25.3618i		−	1.45941i
$303$			7.86840i			0.452028i
$304$		0			0
$305$	15.8979	−	26.0349i	0.910309	−	1.49075i
$306$	9.74752			0.557229
$307$			5.45543i			0.311358i	0.987808	+	0.155679i	$0.0497565\pi$
$307$			5.45543i			0.311358i	−0.987808	+	0.155679i	$0.950243\pi$
$308$		−	2.46607i		−	0.140517i
$309$	8.14215			0.463191
$310$	13.9243	+	8.50273i	0.790849	+	0.482922i
$311$	6.69721			0.379764			0.189882	−	0.981807i	$-0.439189\pi$
$311$	6.69721			0.379764			0.189882	+	0.981807i	$0.439189\pi$
$312$		−	14.4292i		−	0.816892i
$313$		−	4.58279i		−	0.259035i	−0.991577	−	0.129517i	$-0.958657\pi$
$313$		−	4.58279i		−	0.259035i	0.991577	−	0.129517i	$-0.0413428\pi$
$314$	19.1462			1.08048
$315$	−21.6999	−	13.2508i	−1.22265	−	0.746598i
$316$	−6.32866			−0.356015
$317$			27.6794i			1.55463i	0.629113	+	0.777314i	$0.283418\pi$
$317$			27.6794i			1.55463i	−0.629113	+	0.777314i	$0.716582\pi$
$318$		−	48.6435i		−	2.72779i
$319$	1.60163			0.0896738
$320$	−0.808286	+	1.32368i	−0.0451846	+	0.0739957i
$321$	−4.17759			−0.233170
$322$			33.2520i			1.85306i
$323$		0			0
$324$	11.6754			0.648636
$325$	−18.5120	+	9.50584i	−1.02686	+	0.527289i
$326$	30.2264			1.67409
$327$			8.38903i			0.463914i
$328$		−	6.34983i		−	0.350611i
$329$	−11.1125			−0.612651
$330$	2.43366	−	3.98544i	0.133969	−	0.219391i
$331$	14.1302			0.776665			0.388332	−	0.921519i	$-0.373051\pi$
$331$	14.1302			0.776665			0.388332	+	0.921519i	$0.373051\pi$
$332$		−	9.61782i		−	0.527847i
$333$			5.75203i			0.315209i
$334$	−29.0130			−1.58752
$335$	13.6584	+	8.34032i	0.746237	+	0.455681i
$336$	50.1791			2.73749
$337$		−	14.9974i		−	0.816962i	−0.912767	−	0.408481i	$-0.866059\pi$
$337$		−	14.9974i		−	0.816962i	0.912767	−	0.408481i	$-0.133941\pi$
$338$		−	7.71372i		−	0.419571i
$339$	−31.6046			−1.71653
$340$	4.60505	+	2.81202i	0.249744	+	0.152503i
$341$	2.00692			0.108681
$342$		0			0
$343$			16.8294i			0.908703i
$344$	−15.4514			−0.833082
$345$	−12.2096	+	19.9948i	−0.657341	+	1.07648i
$346$	15.3324			0.824274
$347$		−	20.9133i		−	1.12268i	−0.827584	−	0.561342i	$-0.810285\pi$
$347$		−	20.9133i		−	1.12268i	0.827584	−	0.561342i	$-0.189715\pi$
$348$		−	9.21696i		−	0.494081i
$349$	3.13055			0.167574			0.0837872	−	0.996484i	$-0.473298\pi$
$349$	3.13055			0.167574			0.0837872	+	0.996484i	$0.473298\pi$
$350$	−17.2792	−	33.6501i	−0.923612	−	1.79867i
$351$	−3.15151			−0.168215
$352$			2.92251i			0.155771i
$353$		−	8.04538i		−	0.428212i	−0.976810	−	0.214106i	$-0.931316\pi$
$353$		−	8.04538i		−	0.428212i	0.976810	−	0.214106i	$-0.0686838\pi$
$354$	−2.30711			−0.122622
$355$	7.03700	−	11.5240i	0.373485	−	0.611631i
$356$	5.14441			0.272653
$357$		−	20.5758i		−	1.08899i
$358$		−	41.9891i		−	2.21920i
$359$	−30.5842			−1.61417			−0.807087	−	0.590432i	$-0.798957\pi$
$359$	−30.5842			−1.61417			−0.807087	+	0.590432i	$0.798957\pi$
$360$	7.44493	+	4.54616i	0.392382	+	0.239603i
$361$		0			0
$362$			29.6497i			1.55835i
$363$			25.6470i			1.34612i
$364$	20.9085			1.09590
$365$	−3.92021	−	2.39383i	−0.205193	−	0.125299i
$366$	−58.0377			−3.03368
$367$		−	9.95175i		−	0.519477i	−0.965679	−	0.259739i	$-0.916364\pi$
$367$		−	9.95175i		−	0.519477i	0.965679	−	0.259739i	$-0.0836364\pi$
$368$		−	21.8257i		−	1.13774i
$369$	11.7112			0.609659
$370$	−4.45984	+	7.30357i	−0.231856	+	0.379694i
$371$	−48.4703			−2.51645
$372$		−	11.5493i		−	0.598804i
$373$		−	9.27611i		−	0.480299i	−0.970736	−	0.240149i	$-0.922804\pi$
$373$		−	9.27611i		−	0.480299i	0.970736	−	0.240149i	$-0.0771964\pi$
$374$	1.78387			0.0922416
$375$	1.96557	−	26.5787i	0.101502	−	1.37252i
$376$	3.81253			0.196616
$377$			13.5793i			0.699372i
$378$		−	5.72864i		−	0.294649i
$379$	−21.1472			−1.08626			−0.543129	−	0.839649i	$-0.682761\pi$
$379$	−21.1472			−1.08626			−0.543129	+	0.839649i	$0.682761\pi$
$380$		0			0
$381$	−47.2181			−2.41906
$382$		−	22.8634i		−	1.16979i
$383$		−	15.1501i		−	0.774136i	−0.922051	−	0.387068i	$-0.873488\pi$
$383$		−	15.1501i		−	0.774136i	0.922051	−	0.387068i	$-0.126512\pi$
$384$	−25.4328			−1.29786
$385$	−3.97125	−	2.42499i	−0.202394	−	0.123589i
$386$	17.2040			0.875660
$387$		−	28.4974i		−	1.44860i
$388$		−	6.69177i		−	0.339723i
$389$	31.4483			1.59449			0.797247	−	0.603653i	$-0.206289\pi$
$389$	31.4483			1.59449			0.797247	+	0.603653i	$0.206289\pi$
$390$	33.7905	+	20.6337i	1.71105	+	1.04483i
$391$	−8.94958			−0.452600
$392$		−	15.9546i		−	0.805827i
$393$			8.17642i			0.412446i
$394$	5.53681			0.278940
$395$	−6.22326	+	10.1914i	−0.313126	+	0.512785i
$396$	−1.56043			−0.0784147
$397$		−	9.38559i		−	0.471049i	−0.971868	−	0.235525i	$-0.924319\pi$
$397$		−	9.38559i		−	0.471049i	0.971868	−	0.235525i	$-0.0756808\pi$
$398$		−	0.935689i		−	0.0469019i
$399$		0			0
$400$	11.3416	+	22.0870i	0.567079	+	1.10435i
$401$	−6.16049			−0.307640			−0.153820	−	0.988099i	$-0.549158\pi$
$401$	−6.16049			−0.307640			−0.153820	+	0.988099i	$0.549158\pi$
$402$		−	30.4477i		−	1.51859i
$403$			17.0156i			0.847607i
$404$	3.91173			0.194616
$405$	11.4810	−	18.8016i	0.570495	−	0.934261i
$406$	−24.6838			−1.22504
$407$			1.05266i			0.0521786i
$408$			7.05927i			0.349486i
$409$	2.28482			0.112977			0.0564885	−	0.998403i	$-0.482010\pi$
$409$	2.28482			0.112977			0.0564885	+	0.998403i	$0.482010\pi$
$410$	14.8701	+	9.08025i	0.734382	+	0.448442i
$411$	−1.45004			−0.0715250
$412$		−	4.04783i		−	0.199422i
$413$			2.29889i			0.113121i
$414$	21.0406			1.03409
$415$	−15.4881	−	9.45765i	−0.760283	−	0.464258i
$416$	−24.7785			−1.21486
$417$		−	20.1619i		−	0.987332i
$418$		0			0
$419$	22.6494			1.10649			0.553247	−	0.833017i	$-0.313389\pi$
$419$	22.6494			1.10649			0.553247	+	0.833017i	$0.313389\pi$
$420$	−13.9553	+	22.8536i	−0.680947	+	1.11514i
$421$	22.9969			1.12080			0.560400	−	0.828222i	$-0.310647\pi$
$421$	22.9969			1.12080			0.560400	+	0.828222i	$0.310647\pi$
$422$			34.0226i			1.65620i
$423$			7.03155i			0.341886i
$424$	16.6294			0.807597
$425$	9.05672	−	4.65059i	0.439315	−	0.225587i
$426$	−25.6897			−1.24467
$427$			57.8310i			2.79864i
$428$			2.07687i			0.100389i
$429$	4.87022			0.235137
$430$	22.0955	−	36.1842i	1.06554	−	1.74496i
$431$	−25.6319			−1.23465			−0.617323	−	0.786710i	$-0.711783\pi$
$431$	−25.6319			−1.23465			−0.617323	+	0.786710i	$0.711783\pi$
$432$			3.76012i			0.180909i
$433$		−	2.36330i		−	0.113573i	−0.998386	−	0.0567864i	$-0.981915\pi$
$433$		−	2.36330i		−	0.113573i	0.998386	−	0.0567864i	$-0.0180854\pi$
$434$	−30.9300			−1.48469
$435$	−14.8426	−	9.06346i	−0.711648	−	0.434560i
$436$	4.17056			0.199734
$437$		0			0
$438$			8.73906i			0.417568i
$439$	−6.31659			−0.301474			−0.150737	−	0.988574i	$-0.548165\pi$
$439$	−6.31659			−0.301474			−0.150737	+	0.988574i	$0.548165\pi$
$440$	1.36248	+	0.831980i	0.0649535	+	0.0396631i
$441$	29.4254			1.40121
$442$			15.1245i			0.719399i
$443$			31.5246i			1.49778i	0.662694	+	0.748890i	$0.269413\pi$
$443$			31.5246i			1.49778i	−0.662694	+	0.748890i	$0.730587\pi$
$444$	6.05782			0.287492
$445$	5.05874	−	8.28434i	0.239807	−	0.392716i
$446$	−5.64463			−0.267281
$447$		−	11.0544i		−	0.522854i
$448$		−	2.94027i		−	0.138915i
$449$	−15.0828			−0.711803			−0.355902	−	0.934523i	$-0.615826\pi$
$449$	−15.0828			−0.711803			−0.355902	+	0.934523i	$0.615826\pi$
$450$	−21.2925	+	10.9336i	−1.00374	+	0.515416i
$451$	2.14323			0.100921
$452$			15.7121i			0.739033i
$453$			33.8754i			1.59161i
$454$	16.1452			0.757730
$455$	20.5603	−	33.6701i	0.963880	−	1.57848i
$456$		0			0
$457$		−	20.1347i		−	0.941861i	−0.882170	−	0.470930i	$-0.843918\pi$
$457$		−	20.1347i		−	0.941861i	0.882170	−	0.470930i	$-0.156082\pi$
$458$			31.9314i			1.49206i
$459$	1.54183			0.0719664
$460$	9.94028	+	6.06992i	0.463468	+	0.283011i
$461$	−7.48489			−0.348606			−0.174303	−	0.984692i	$-0.555767\pi$
$461$	−7.48489			−0.348606			−0.174303	+	0.984692i	$0.555767\pi$
$462$			8.85283i			0.411871i
$463$		−	21.5973i		−	1.00371i	−0.864952	−	0.501855i	$-0.832651\pi$
$463$		−	21.5973i		−	1.00371i	0.864952	−	0.501855i	$-0.167349\pi$
$464$	16.2017			0.752147
$465$	−18.5985	−	11.3570i	−0.862486	−	0.526666i
$466$	−11.4992			−0.532691
$467$			27.0503i			1.25174i	0.779927	+	0.625870i	$0.215256\pi$
$467$			27.0503i			1.25174i	−0.779927	+	0.625870i	$0.784744\pi$
$468$		−	13.2301i		−	0.611561i
$469$	−30.3392			−1.40094
$470$	−5.45192	+	8.92823i	−0.251478	+	0.411828i
$471$	−25.5732			−1.17835
$472$		−	0.788717i		−	0.0363036i
$473$		−	5.21524i		−	0.239797i
$474$	22.7190			1.04352
$475$		0			0
$476$	−10.2292			−0.468853
$477$			30.6702i			1.40429i
$478$			24.0470i			1.09989i
$479$	38.0534			1.73870			0.869352	−	0.494193i	$-0.164536\pi$
$479$	38.0534			1.73870			0.869352	+	0.494193i	$0.164536\pi$
$480$	16.5383	−	27.0836i	0.754865	−	1.23619i
$481$	−8.92499			−0.406944
$482$			31.4731i			1.43356i
$483$		−	44.4142i		−	2.02092i
$484$	12.7503			0.579558
$485$	−10.7761	−	6.58032i	−0.489319	−	0.298797i
$486$	−37.8591			−1.71732
$487$		−	18.3353i		−	0.830851i	−0.909627	−	0.415426i	$-0.863633\pi$
$487$		−	18.3353i		−	0.830851i	0.909627	−	0.415426i	$-0.136367\pi$
$488$		−	19.8410i		−	0.898158i
$489$	−40.3730			−1.82573
$490$	37.3626	+	22.8150i	1.68787	+	1.03068i
$491$	−15.0675			−0.679986			−0.339993	−	0.940428i	$-0.610425\pi$
$491$	−15.0675			−0.679986			−0.339993	+	0.940428i	$0.610425\pi$
$492$		−	12.3338i		−	0.556049i
$493$		−	6.64350i		−	0.299208i
$494$		0			0
$495$	−1.53444	+	2.51285i	−0.0689682	+	0.112944i
$496$	20.3016			0.911568
$497$			25.5982i			1.14824i
$498$			34.5266i			1.54717i
$499$	−34.5299			−1.54577			−0.772886	−	0.634545i	$-0.781188\pi$
$499$	−34.5299			−1.54577			−0.772886	+	0.634545i	$0.781188\pi$
$500$	−13.2135	−	0.977174i	−0.590925	−	0.0437005i
$501$	38.7522			1.73132
$502$			31.6470i			1.41247i
$503$		−	30.8704i		−	1.37644i	−0.725501	−	0.688221i	$-0.758392\pi$
$503$		−	30.8704i		−	1.37644i	0.725501	−	0.688221i	$-0.241608\pi$
$504$	−16.5374			−0.736632
$505$	3.84658	−	6.29929i	0.171171	−	0.280315i
$506$	3.85059			0.171179
$507$			10.3031i			0.457577i
$508$			23.4742i			1.04150i
$509$	10.1777			0.451118			0.225559	−	0.974230i	$-0.427579\pi$
$509$	10.1777			0.451118			0.225559	+	0.974230i	$0.427579\pi$
$510$	−16.5315	−	10.0948i	−0.732027	−	0.447003i
$511$	8.70794			0.385217
$512$			15.1195i			0.668194i
$513$		0			0
$514$	−49.5204			−2.18425
$515$	−6.51845	−	3.98041i	−0.287237	−	0.175398i
$516$	−30.0124			−1.32122
$517$			1.28683i			0.0565946i
$518$		−	16.2234i		−	0.712813i
$519$	−20.4792			−0.898938
$520$	−7.05392	+	11.5517i	−0.309335	+	0.506577i
$521$	−16.5423			−0.724732			−0.362366	−	0.932036i	$-0.618031\pi$
$521$	−16.5423			−0.724732			−0.362366	+	0.932036i	$0.618031\pi$
$522$			15.6190i			0.683624i
$523$			7.99801i			0.349729i	0.984593	+	0.174864i	$0.0559487\pi$
$523$			7.99801i			0.349729i	−0.984593	+	0.174864i	$0.944051\pi$
$524$	4.06486			0.177574
$525$	23.0796	+	44.9459i	1.00727	+	1.96160i
$526$	9.92338			0.432680
$527$		−	8.32463i		−	0.362626i
$528$		−	5.81075i		−	0.252880i
$529$	3.68180			0.160078
$530$	−23.7801	+	38.9431i	−1.03294	+	1.69158i
$531$	1.45465			0.0631266
$532$		0			0
$533$			18.1713i			0.787088i
$534$	−18.4677			−0.799176
$535$	3.34450	+	2.04228i	0.144595	+	0.0882953i
$536$	10.4089			0.449598
$537$			56.0843i			2.42021i
$538$		−	8.25886i		−	0.356065i
$539$	5.38507			0.231952
$540$	−1.71251	−	1.04572i	−0.0736946	−	0.0450007i
$541$	5.20048			0.223586			0.111793	−	0.993732i	$-0.464341\pi$
$541$	5.20048			0.223586			0.111793	+	0.993732i	$0.464341\pi$
$542$		−	13.5785i		−	0.583247i
$543$		−	39.6026i		−	1.69951i
$544$	12.1225			0.519748
$545$	4.10110	−	6.71609i	0.175672	−	0.287686i
$546$	−75.0585			−3.21221
$547$			11.0339i			0.471777i	0.971780	+	0.235889i	$0.0758001\pi$
$547$			11.0339i			0.471777i	−0.971780	+	0.235889i	$0.924200\pi$
$548$			0.720878i			0.0307944i
$549$	36.5933			1.56176
$550$	−3.89668	+	2.00093i	−0.166155	+	0.0853201i
$551$		0			0
$552$			15.2379i			0.648566i
$553$		−	22.6381i		−	0.962669i
$554$	−13.4483			−0.571365
$555$	5.95694	−	9.75526i	0.252858	−	0.414088i
$556$	−10.0234			−0.425086
$557$			21.2817i			0.901735i	0.892591	+	0.450867i	$0.148885\pi$
$557$			21.2817i			0.901735i	−0.892591	+	0.450867i	$0.851115\pi$
$558$			19.5713i			0.828521i
$559$	44.2173			1.87019
$560$	−40.1724	−	24.5308i	−1.69759	−	1.03662i
$561$	−2.38269			−0.100597
$562$			32.5792i			1.37427i
$563$		−	14.7072i		−	0.619833i	−0.950764	−	0.309917i	$-0.899699\pi$
$563$		−	14.7072i		−	0.619833i	0.950764	−	0.309917i	$-0.100301\pi$
$564$	7.40537			0.311822
$565$	25.3020	+	15.4504i	1.06446	+	0.650003i
$566$	−55.2061			−2.32048
$567$			41.7639i			1.75392i
$568$		−	8.78236i		−	0.368500i
$569$	40.6551			1.70435			0.852174	−	0.523258i	$-0.175284\pi$
$569$	40.6551			1.70435			0.852174	+	0.523258i	$0.175284\pi$
$570$		0			0
$571$	−24.3240			−1.01793			−0.508964	−	0.860788i	$-0.669972\pi$
$571$	−24.3240			−1.01793			−0.508964	+	0.860788i	$0.669972\pi$
$572$		−	2.42120i		−	0.101236i
$573$			30.5382i			1.27575i
$574$	−33.0308			−1.37868
$575$	19.5495	−	10.0386i	0.815269	−	0.418638i
$576$	−1.86049			−0.0775204
$577$		−	33.6876i		−	1.40243i	−0.712949	−	0.701216i	$-0.752641\pi$
$577$		−	33.6876i		−	1.40243i	0.712949	−	0.701216i	$-0.247359\pi$
$578$			22.9401i			0.954182i
$579$	−22.9791			−0.954979
$580$	−4.50585	+	7.37892i	−0.187095	+	0.306393i
$581$	34.4037			1.42730
$582$			24.0225i			0.995764i
$583$			5.61287i			0.232461i
$584$	−2.98757			−0.123626
$585$	−21.3052	−	13.0098i	−0.880861	−	0.537887i
$586$	−39.0830			−1.61451
$587$			2.24977i			0.0928580i	0.998922	+	0.0464290i	$0.0147841\pi$
$587$			2.24977i			0.0928580i	−0.998922	+	0.0464290i	$0.985216\pi$
$588$		−	30.9898i		−	1.27800i
$589$		0			0
$590$	1.84703	+	1.12787i	0.0760409	+	0.0464335i
$591$	−7.39543			−0.304207
$592$			10.6486i			0.437653i
$593$		−	31.3871i		−	1.28891i	−0.764640	−	0.644457i	$-0.777083\pi$
$593$		−	31.3871i		−	1.28891i	0.764640	−	0.644457i	$-0.222917\pi$
$594$	−0.663377			−0.0272187
$595$	−10.0588	+	16.4726i	−0.412371	+	0.675312i
$596$	−5.49562			−0.225109
$597$			1.24979i			0.0511503i
$598$			32.6471i			1.33504i
$599$	10.4068			0.425212			0.212606	−	0.977138i	$-0.431805\pi$
$599$	10.4068			0.425212			0.212606	+	0.977138i	$0.431805\pi$
$600$	−7.91826	−	15.4203i	−0.323262	−	0.629530i
$601$	1.29592			0.0528616			0.0264308	−	0.999651i	$-0.491586\pi$
$601$	1.29592			0.0528616			0.0264308	+	0.999651i	$0.491586\pi$
$602$			80.3757i			3.27587i
$603$			19.1975i			0.781783i
$604$	16.8410			0.685249
$605$	12.5379	−	20.5325i	0.509739	−	0.834765i
$606$	−14.0426			−0.570440
$607$			5.50902i			0.223604i	0.993730	+	0.111802i	$0.0356623\pi$
$607$			5.50902i			0.223604i	−0.993730	+	0.111802i	$0.964338\pi$
$608$		0			0
$609$	32.9698			1.33600
$610$	46.4638	+	28.3726i	1.88127	+	1.14877i
$611$	−10.9103			−0.441385
$612$			6.47263i			0.261641i
$613$		−	40.6727i		−	1.64275i	−0.570386	−	0.821376i	$-0.693207\pi$
$613$		−	40.6727i		−	1.64275i	0.570386	−	0.821376i	$-0.306793\pi$
$614$	−9.73619			−0.392921
$615$	−19.8618	−	12.1284i	−0.800904	−	0.489062i
$616$	−3.02646			−0.121939
$617$		−	30.5053i		−	1.22810i	−0.789268	−	0.614049i	$-0.789540\pi$
$617$		−	30.5053i		−	1.22810i	0.789268	−	0.614049i	$-0.210460\pi$
$618$			14.5311i			0.584527i
$619$	−5.80411			−0.233287			−0.116643	−	0.993174i	$-0.537213\pi$
$619$	−5.80411			−0.233287			−0.116643	+	0.993174i	$0.537213\pi$
$620$	−5.64605	+	9.24615i	−0.226751	+	0.371334i
$621$	3.32813			0.133553
$622$			11.9524i			0.479246i
$623$			18.4019i			0.737258i
$624$	49.2663			1.97223
$625$	−14.5670	+	20.3175i	−0.582681	+	0.812701i
$626$	8.17881			0.326891
$627$		0			0
$628$			12.7136i			0.507328i
$629$	4.36642			0.174101
$630$	23.6484	−	38.7274i	0.942176	−	1.54294i
$631$	−23.3642			−0.930116			−0.465058	−	0.885280i	$-0.653967\pi$
$631$	−23.3642			−0.930116			−0.465058	+	0.885280i	$0.653967\pi$
$632$			7.76679i			0.308946i
$633$		−	45.4435i		−	1.80622i
$634$	−49.3987			−1.96187
$635$	37.8019	+	23.0833i	1.50012	+	0.916032i
$636$	32.3007			1.28080
$637$			45.6572i			1.80901i
$638$			2.85839i			0.113165i
$639$	16.1976			0.640766
$640$	20.3610	+	12.4332i	0.804839	+	0.491465i
$641$	−18.3459			−0.724621			−0.362311	−	0.932057i	$-0.618012\pi$
$641$	−18.3459			−0.724621			−0.362311	+	0.932057i	$0.618012\pi$
$642$		−	7.45565i		−	0.294251i
$643$			15.7630i			0.621633i	0.950470	+	0.310817i	$0.100603\pi$
$643$			15.7630i			0.621633i	−0.950470	+	0.310817i	$0.899397\pi$
$644$	−22.0803			−0.870084
$645$	−29.5126	+	48.3307i	−1.16206	+	1.90302i
$646$		0			0
$647$			25.0443i			0.984592i	0.870428	+	0.492296i	$0.163842\pi$
$647$			25.0443i			0.984592i	−0.870428	+	0.492296i	$0.836158\pi$
$648$		−	14.3286i		−	0.562880i
$649$	0.266212			0.0104497
$650$	−16.9649	−	33.0379i	−0.665417	−	1.29585i
$651$	41.3127			1.61917
$652$			20.0712i			0.786049i
$653$			2.98852i			0.116950i	0.998289	+	0.0584749i	$0.0186238\pi$
$653$			2.98852i			0.116950i	−0.998289	+	0.0584749i	$0.981376\pi$
$654$	−14.9717			−0.585440
$655$	3.99716	−	6.54588i	0.156182	−	0.255769i
$656$	21.6805			0.846482
$657$		−	5.51005i		−	0.214968i
$658$		−	19.8322i		−	0.773140i
$659$	−35.7695			−1.39338			−0.696691	−	0.717372i	$-0.745345\pi$
$659$	−35.7695			−1.39338			−0.696691	+	0.717372i	$0.745345\pi$
$660$	2.64644	+	1.61602i	0.103013	+	0.0629035i
$661$	−3.22147			−0.125301			−0.0626503	−	0.998036i	$-0.519955\pi$
$661$	−3.22147			−0.125301			−0.0626503	+	0.998036i	$0.519955\pi$
$662$			25.2178i			0.980118i
$663$		−	20.2015i		−	0.784563i
$664$	−11.8034			−0.458061
$665$		0			0
$666$	−10.2655			−0.397781
$667$		−	14.3404i		−	0.555262i
$668$		−	19.2655i		−	0.745403i
$669$	7.53945			0.291492
$670$	−14.8848	+	24.3758i	−0.575050	+	0.941720i
$671$	6.69684			0.258529
$672$			60.1605i			2.32074i
$673$			0.639706i			0.0246588i	0.999924	+	0.0123294i	$0.00392468\pi$
$673$			0.639706i			0.0246588i	−0.999924	+	0.0123294i	$0.996075\pi$
$674$	26.7656			1.03097
$675$	−3.36797	+	1.72944i	−0.129633	+	0.0665663i
$676$	5.12213			0.197005
$677$			25.8005i			0.991592i	0.868439	+	0.495796i	$0.165124\pi$
$677$			25.8005i			0.991592i	−0.868439	+	0.495796i	$0.834876\pi$
$678$		−	56.4041i		−	2.16618i
$679$	23.9369			0.918616
$680$	3.45103	−	5.65151i	0.132341	−	0.216726i
$681$	−21.5648			−0.826366
$682$			3.58170i			0.137150i
$683$		−	5.33696i		−	0.204213i	−0.994773	−	0.102107i	$-0.967442\pi$
$683$		−	5.33696i		−	0.204213i	0.994773	−	0.102107i	$-0.0325583\pi$
$684$		0			0
$685$	1.16087	+	0.708872i	0.0443546	+	0.0270846i
$686$	−30.0351			−1.14675
$687$		−	42.6503i		−	1.62721i
$688$		−	52.7564i		−	2.01132i
$689$	−47.5886			−1.81298
$690$	−35.6842	−	21.7901i	−1.35847	−	0.829536i
$691$	13.2507			0.504079			0.252040	−	0.967717i	$-0.418899\pi$
$691$	13.2507			0.504079			0.252040	+	0.967717i	$0.418899\pi$
$692$			10.1811i			0.387029i
$693$		−	5.58178i		−	0.212034i
$694$	37.3235			1.41678
$695$	−9.85644	+	16.1412i	−0.373876	+	0.612271i
$696$	−11.3114			−0.428759
$697$		−	8.89006i		−	0.336735i
$698$			5.58702i			0.211472i
$699$	15.3593			0.580943
$700$	22.3446	−	11.4739i	0.844547	−	0.433672i
$701$	40.8699			1.54363			0.771817	−	0.635845i	$-0.219348\pi$
$701$	40.8699			1.54363			0.771817	+	0.635845i	$0.219348\pi$
$702$		−	5.62443i		−	0.212280i
$703$		0			0
$704$	−0.340484			−0.0128325
$705$	7.28204	−	11.9253i	0.274257	−	0.449133i
$706$	14.3584			0.540386
$707$			13.9925i			0.526244i
$708$		−	1.53199i		−	0.0575756i
$709$	−7.35745			−0.276315			−0.138157	−	0.990410i	$-0.544118\pi$
$709$	−7.35745			−0.276315			−0.138157	+	0.990410i	$0.544118\pi$
$710$	20.5666	+	12.5588i	0.771853	+	0.471323i
$711$	−14.3245			−0.537211
$712$		−	6.31344i		−	0.236606i
$713$		−	17.9692i		−	0.672952i
$714$	36.7213			1.37426
$715$	−3.89901	−	2.38088i	−0.145815	−	0.0890399i
$716$	27.8820			1.04200
$717$		−	32.1193i		−	1.19952i
$718$		−	54.5830i		−	2.03702i
$719$	31.9597			1.19190			0.595948	−	0.803023i	$-0.296776\pi$
$719$	31.9597			1.19190			0.595948	+	0.803023i	$0.296776\pi$
$720$	−15.5222	+	25.4196i	−0.578477	+	0.947332i
$721$	14.4794			0.539240
$722$		0			0
$723$		−	42.0381i		−	1.56341i
$724$	−19.6882			−0.731707
$725$	7.45189	+	14.5121i	0.276756	+	0.538964i
$726$	−45.7717			−1.69875
$727$			29.3883i			1.08995i	0.838452	+	0.544976i	$0.183461\pi$
$727$			29.3883i			1.08995i	−0.838452	+	0.544976i	$0.816539\pi$
$728$		−	25.6598i		−	0.951014i
$729$	21.0116			0.778207
$730$	4.27222	−	6.99632i	0.158122	−	0.258945i
$731$	−21.6326			−0.800112
$732$		−	38.5387i		−	1.42443i
$733$		−	50.8285i		−	1.87739i	−0.344745	−	0.938696i	$-0.612035\pi$
$733$		−	50.8285i		−	1.87739i	0.344745	−	0.938696i	$-0.387965\pi$
$734$	17.7607			0.655559
$735$	−49.9046	−	30.4737i	−1.84076	−	1.12404i
$736$	26.1671			0.964534
$737$			3.51329i			0.129414i
$738$			20.9007i			0.769364i
$739$	−14.7245			−0.541650			−0.270825	−	0.962629i	$-0.587296\pi$
$739$	−14.7245			−0.541650			−0.270825	+	0.962629i	$0.587296\pi$
$740$	−4.84978	−	2.96146i	−0.178281	−	0.108865i
$741$		0			0
$742$		−	86.5039i		−	3.17566i
$743$		−	34.6568i		−	1.27144i	−0.771922	−	0.635718i	$-0.780704\pi$
$743$		−	34.6568i		−	1.27144i	0.771922	−	0.635718i	$-0.219296\pi$
$744$	−14.1738			−0.519636
$745$	−5.40409	+	8.84991i	−0.197991	+	0.324236i
$746$	16.5549			0.606117
$747$		−	21.7693i		−	0.796498i
$748$			1.18454i			0.0433110i
$749$	−7.42910			−0.271453
$750$	47.4345	+	3.50792i	1.73206	+	0.128091i
$751$	8.35539			0.304893			0.152446	−	0.988312i	$-0.451285\pi$
$751$	8.35539			0.304893			0.152446	+	0.988312i	$0.451285\pi$
$752$			13.0173i			0.474692i
$753$		−	42.2704i		−	1.54042i
$754$	−24.2348			−0.882578
$755$	16.5605	−	27.1200i	0.602698	−	0.986998i
$756$	3.80398			0.138349
$757$		−	13.8709i		−	0.504146i	−0.967708	−	0.252073i	$-0.918888\pi$
$757$		−	13.8709i		−	0.504146i	0.967708	−	0.252073i	$-0.0811123\pi$
$758$		−	37.7410i		−	1.37081i
$759$	−5.14317			−0.186685
$760$		0			0
$761$	44.3970			1.60939			0.804696	−	0.593687i	$-0.202328\pi$
$761$	44.3970			1.60939			0.804696	+	0.593687i	$0.202328\pi$
$762$		−	84.2692i		−	3.05275i
$763$			14.9184i			0.540082i
$764$	15.1819			0.549262
$765$	10.4232	+	6.36483i	0.376853	+	0.230121i
$766$	27.0381			0.976927
$767$			2.25707i			0.0814983i
$768$		−	48.6961i		−	1.75717i
$769$	−19.0001			−0.685160			−0.342580	−	0.939489i	$-0.611301\pi$
$769$	−19.0001			−0.685160			−0.342580	+	0.939489i	$0.611301\pi$
$770$	4.32784	−	7.08740i	0.155964	−	0.255412i
$771$	66.1436			2.38210
$772$			11.4239i			0.411157i
$773$			1.86738i			0.0671650i	0.999436	+	0.0335825i	$0.0106917\pi$
$773$			1.86738i			0.0671650i	−0.999436	+	0.0335825i	$0.989308\pi$
$774$	50.8587			1.82808
$775$	9.33759	+	18.1843i	0.335416	+	0.653200i
$776$	−8.21241			−0.294808
$777$			21.6693i			0.777381i
$778$			56.1252i			2.01218i
$779$		0			0
$780$	−13.7014	+	22.4378i	−0.490588	+	0.803403i
$781$	2.96427			0.106070
$782$		−	15.9721i		−	0.571162i
$783$			2.47055i			0.0882904i
$784$	54.4744			1.94552
$785$	20.4734	+	12.5019i	0.730728	+	0.446211i
$786$	−14.5923			−0.520489
$787$			12.9689i			0.462291i	0.972919	+	0.231146i	$0.0742474\pi$
$787$			12.9689i			0.462291i	−0.972919	+	0.231146i	$0.925753\pi$
$788$			3.67660i			0.130973i
$789$	−13.2545			−0.471873
$790$	−18.1884	−	11.1065i	−0.647113	−	0.395152i
$791$	−56.2032			−1.99836
$792$			1.91503i			0.0680476i
$793$			56.7790i			2.01628i
$794$	16.7503			0.594444
$795$	31.7627	−	52.0156i	1.12651	−	1.84480i
$796$	0.621324			0.0220222
$797$		−	29.9226i		−	1.05991i	−0.848025	−	0.529956i	$-0.822209\pi$
$797$		−	29.9226i		−	1.05991i	0.848025	−	0.529956i	$-0.177791\pi$
$798$		0			0
$799$	5.33772			0.188835
$800$	−26.4804	+	13.5976i	−0.936224	+	0.480748i
$801$	11.6441			0.411422
$802$		−	10.9945i		−	0.388229i
$803$		−	1.00838i		−	0.0355850i
$804$	20.2181			0.713038
$805$	−21.7125	+	35.5571i	−0.765266	+	1.25322i
$806$	−30.3674			−1.06964
$807$			11.0312i			0.388318i
$808$		−	4.80064i		−	0.168886i
$809$	−42.4578			−1.49274			−0.746369	−	0.665532i	$-0.768205\pi$
$809$	−42.4578			−1.49274			−0.746369	+	0.665532i	$0.768205\pi$
$810$	33.5549	+	20.4899i	1.17900	+	0.719941i
$811$	31.1514			1.09387			0.546936	−	0.837174i	$-0.315794\pi$
$811$	31.1514			1.09387			0.546936	+	0.837174i	$0.315794\pi$
$812$		−	16.3907i		−	0.575202i
$813$			18.1366i			0.636079i
$814$	−1.87867			−0.0658472
$815$	32.3218	+	19.7369i	1.13218	+	0.691354i
$816$	−24.1028			−0.843767
$817$		0			0
$818$			4.07767i			0.142572i
$819$	47.3250			1.65367
$820$	−6.02955	+	9.87417i	−0.210561	+	0.344821i
$821$	−6.20740			−0.216640			−0.108320	−	0.994116i	$-0.534547\pi$
$821$	−6.20740			−0.216640			−0.108320	+	0.994116i	$0.534547\pi$
$822$		−	2.58785i		−	0.0902616i
$823$			35.9702i			1.25384i	0.779083	+	0.626921i	$0.215685\pi$
$823$			35.9702i			1.25384i	−0.779083	+	0.626921i	$0.784315\pi$
$824$	−4.96766			−0.173057
$825$	5.20474	−	2.67262i	0.181206	−	0.0930486i
$826$	−4.10279			−0.142754
$827$		−	15.3837i		−	0.534945i	−0.963565	−	0.267473i	$-0.913811\pi$
$827$		−	15.3837i		−	0.534945i	0.963565	−	0.267473i	$-0.0861885\pi$
$828$			13.9716i			0.485545i
$829$	−24.1941			−0.840295			−0.420148	−	0.907456i	$-0.638022\pi$
$829$	−24.1941			−0.840295			−0.420148	+	0.907456i	$0.638022\pi$
$830$	16.8789	−	27.6413i	0.585874	−	0.959445i
$831$	17.9627			0.623120
$832$		−	2.88678i		−	0.100081i
$833$		−	22.3371i		−	0.773936i
$834$	35.9825			1.24597
$835$	−31.0243	−	18.9446i	−1.07364	−	0.655605i
$836$		0			0
$837$			3.09573i			0.107004i
$838$			40.4218i			1.39635i
$839$	12.4265			0.429012			0.214506	−	0.976723i	$-0.431186\pi$
$839$	12.4265			0.429012			0.214506	+	0.976723i	$0.431186\pi$
$840$	28.0468	+	17.1265i	0.967708	+	0.590919i
$841$	−18.3548			−0.632923
$842$			41.0420i			1.41440i
$843$		−	43.5155i		−	1.49875i
$844$	−22.5920			−0.777649
$845$	5.03683	−	8.24846i	0.173272	−	0.283756i
$846$	−12.5491			−0.431446
$847$			45.6087i			1.56713i
$848$			56.7787i			1.94979i
$849$	73.7379			2.53068
$850$	8.29982	+	16.1633i	0.284681	+	0.554398i
$851$	9.42518			0.323091
$852$		−	17.0587i		−	0.584420i
$853$		−	23.1527i		−	0.792734i	−0.918092	−	0.396367i	$-0.870271\pi$
$853$		−	23.1527i		−	0.792734i	0.918092	−	0.396367i	$-0.129729\pi$
$854$	−103.210			−3.53176
$855$		0			0
$856$	2.54882			0.0871167
$857$			2.84272i			0.0971054i	0.998821	+	0.0485527i	$0.0154609\pi$
$857$			2.84272i			0.0971054i	−0.998821	+	0.0485527i	$0.984539\pi$
$858$			8.69178i			0.296733i
$859$	25.8715			0.882725			0.441363	−	0.897329i	$-0.354495\pi$
$859$	25.8715			0.882725			0.441363	+	0.897329i	$0.354495\pi$
$860$	24.0273	+	14.6720i	0.819326	+	0.500311i
$861$	44.1188			1.50356
$862$		−	45.7447i		−	1.55807i
$863$		−	38.0032i		−	1.29365i	−0.762641	−	0.646823i	$-0.776097\pi$
$863$		−	38.0032i		−	1.29365i	0.762641	−	0.646823i	$-0.223903\pi$
$864$	−4.50806			−0.153367
$865$	16.3953	+	10.0116i	0.557456	+	0.340404i
$866$	4.21773			0.143324
$867$		−	30.6407i		−	1.04061i
$868$		−	20.5384i		−	0.697119i
$869$	−2.62149			−0.0889281
$870$	16.1754	−	26.4893i	0.548396	−	0.898071i
$871$	−29.7873			−1.00931
$872$		−	5.11828i		−	0.173327i
$873$		−	15.1464i		−	0.512628i
$874$		0			0
$875$	3.49542	−	47.2656i	0.118167	−	1.59787i
$876$	−5.80298			−0.196065
$877$		−	49.0943i		−	1.65780i	−0.559400	−	0.828898i	$-0.688968\pi$
$877$		−	49.0943i		−	1.65780i	0.559400	−	0.828898i	$-0.311032\pi$
$878$		−	11.2731i		−	0.380448i
$879$	52.2026			1.76075
$880$	−2.84067	+	4.65197i	−0.0957590	+	0.156818i
$881$	−55.7494			−1.87825			−0.939123	−	0.343581i	$-0.888360\pi$
$881$	−55.7494			−1.87825			−0.939123	+	0.343581i	$0.888360\pi$
$882$			52.5150i			1.76827i
$883$			16.6355i			0.559828i	0.960025	+	0.279914i	$0.0903060\pi$
$883$			16.6355i			0.559828i	−0.960025	+	0.279914i	$0.909694\pi$
$884$	−10.0431			−0.337786
$885$	−2.46705	−	1.50647i	−0.0829289	−	0.0506395i
$886$	−56.2613			−1.89014
$887$		−	43.3883i		−	1.45684i	−0.685133	−	0.728418i	$-0.740256\pi$
$887$		−	43.3883i		−	1.45684i	0.685133	−	0.728418i	$-0.259744\pi$
$888$		−	7.43441i		−	0.249483i
$889$	−83.9691			−2.81623
$890$	14.7849	+	9.02822i	0.495591	+	0.302626i
$891$	4.83627			0.162021
$892$		−	3.74820i		−	0.125499i
$893$		0			0
$894$	19.7285			0.659819
$895$	27.4176	−	44.9000i	0.916470	−	1.50084i
$896$	−45.2277			−1.51095
$897$		−	43.6062i		−	1.45597i
$898$		−	26.9180i		−	0.898266i
$899$	13.3390			0.444880
$900$	−7.26023	−	14.1388i	−0.242008	−	0.471294i
$901$	23.2820			0.775636
$902$			3.82498i			0.127358i
$903$		−	107.357i		−	3.57260i
$904$	19.2825			0.641326
$905$	−19.3603	+	31.7051i	−0.643559	+	1.05391i
$906$	−60.4567			−2.00854
$907$		−	19.8364i		−	0.658656i	−0.944216	−	0.329328i	$-0.893178\pi$
$907$		−	19.8364i		−	0.658656i	0.944216	−	0.329328i	$-0.106822\pi$
$908$			10.7208i			0.355784i
$909$	8.85395			0.293667
$910$	60.0904	+	36.6935i	1.99198	+	1.21638i
$911$	−15.4076			−0.510478			−0.255239	−	0.966878i	$-0.582154\pi$
$911$	−15.4076			−0.510478			−0.255239	+	0.966878i	$0.582154\pi$
$912$		0			0
$913$		−	3.98395i		−	0.131849i
$914$	35.9339			1.18859
$915$	−62.0610	−	37.8968i	−2.05167	−	1.25283i
$916$	−21.2034			−0.700579
$917$			14.5403i			0.480163i
$918$			2.75167i			0.0908186i
$919$	13.2561			0.437278			0.218639	−	0.975806i	$-0.429838\pi$
$919$	13.2561			0.437278			0.218639	+	0.975806i	$0.429838\pi$
$920$	7.44925	−	12.1991i	0.245595	−	0.402193i
$921$	13.0045			0.428512
$922$		−	13.3581i		−	0.439926i
$923$			25.1325i			0.827247i
$924$	−5.87853			−0.193389
$925$	−9.53801	+	4.89774i	−0.313608	+	0.161037i
$926$	38.5442			1.26664
$927$		−	9.16200i		−	0.300920i
$928$			19.4245i			0.637641i
$929$	−31.2016			−1.02369			−0.511846	−	0.859077i	$-0.671038\pi$
$929$	−31.2016			−1.02369			−0.511846	+	0.859077i	$0.671038\pi$
$930$	20.2685	−	33.1924i	0.664631	−	1.08842i
$931$		0			0
$932$		−	7.63580i		−	0.250119i
$933$		−	15.9646i		−	0.522658i
$934$	−48.2762			−1.57964
$935$	1.90753	+	1.16481i	0.0623830	+	0.0380934i
$936$	−16.2365			−0.530707
$937$		−	16.2187i		−	0.529840i	−0.964270	−	0.264920i	$-0.914654\pi$
$937$		−	16.2187i		−	0.529840i	0.964270	−	0.264920i	$-0.0853456\pi$
$938$		−	54.1458i		−	1.76792i
$939$	−10.9243			−0.356502
$940$	−5.92860	−	3.62023i	−0.193369	−	0.118079i
$941$	−35.1748			−1.14666			−0.573332	−	0.819323i	$-0.694350\pi$
$941$	−35.1748			−1.14666			−0.573332	+	0.819323i	$0.694350\pi$
$942$		−	45.6400i		−	1.48703i
$943$		−	19.1897i		−	0.624903i
$944$	2.69295			0.0876482
$945$	3.74063	−	6.12577i	0.121683	−	0.199271i
$946$	9.30752			0.302614
$947$		−	22.2784i		−	0.723950i	−0.932188	−	0.361975i	$-0.882103\pi$
$947$		−	22.2784i		−	0.723950i	0.932188	−	0.361975i	$-0.117897\pi$
$948$			15.0860i			0.489972i
$949$	8.54953			0.277530
$950$		0			0
$951$	65.9811			2.13958
$952$			12.5537i			0.406866i
$953$		−	4.25996i		−	0.137994i	−0.997617	−	0.0689968i	$-0.978020\pi$
$953$		−	4.25996i		−	0.137994i	0.997617	−	0.0689968i	$-0.0219798\pi$
$954$	−54.7364			−1.77216
$955$	14.9291	−	24.4483i	0.483093	−	0.791129i
$956$	−15.9679			−0.516439
$957$		−	3.81790i		−	0.123415i
$958$			67.9131i			2.19417i
$959$	−2.57863			−0.0832684
$960$	3.15533	+	1.92677i	0.101838	+	0.0621861i
$961$	−14.2856			−0.460825
$962$		−	15.9282i		−	0.513547i
$963$			4.70085i			0.151483i
$964$	−20.8990			−0.673111
$965$	18.3966	+	11.2337i	0.592208	+	0.361625i
$966$	79.2650			2.55031
$967$		−	1.21906i		−	0.0392023i	−0.999808	−	0.0196012i	$-0.993760\pi$
$967$		−	1.21906i		−	0.0392023i	0.999808	−	0.0196012i	$-0.00623964\pi$
$968$		−	15.6477i		−	0.502935i
$969$		0			0
$970$	11.7438	−	19.2319i	0.377069	−	0.617500i
$971$	4.34003			0.139278			0.0696391	−	0.997572i	$-0.477815\pi$
$971$	4.34003			0.139278			0.0696391	+	0.997572i	$0.477815\pi$
$972$		−	25.1395i		−	0.806349i
$973$		−	35.8543i		−	1.14944i
$974$	32.7226			1.04850
$975$	22.6597	+	44.1283i	0.725692	+	1.41324i
$976$	67.7440			2.16843
$977$		−	21.5270i		−	0.688710i	−0.938840	−	0.344355i	$-0.888098\pi$
$977$		−	21.5270i		−	0.688710i	0.938840	−	0.344355i	$-0.111902\pi$
$978$		−	72.0527i		−	2.30399i
$979$	2.13095			0.0681054
$980$	−15.1498	+	24.8098i	−0.483943	+	0.792520i
$981$	9.43980			0.301389
$982$		−	26.8906i		−	0.858114i
$983$			14.5998i			0.465661i	0.972517	+	0.232830i	$0.0747987\pi$
$983$			14.5998i			0.465661i	−0.972517	+	0.232830i	$0.925201\pi$
$984$	−15.1365			−0.482534
$985$	5.92064	+	3.61537i	0.188647	+	0.115195i
$986$	11.8565			0.377588
$987$			26.4896i			0.843172i
$988$		0			0
$989$	−46.6954			−1.48483
$990$	−4.48464	−	2.73849i	−0.142531	−	0.0870349i
$991$	−31.9286			−1.01425			−0.507123	−	0.861874i	$-0.669291\pi$
$991$	−31.9286			−1.01425			−0.507123	+	0.861874i	$0.669291\pi$
$992$			24.3399i			0.772792i
$993$		−	33.6831i		−	1.06890i
$994$	−45.6845			−1.44903
$995$	0.610976	−	1.00055i	0.0193692	−	0.0317197i
$996$	−22.9267			−0.726459
$997$			55.1812i			1.74761i	0.486280	+	0.873803i	$0.338353\pi$
$997$			55.1812i			1.74761i	−0.486280	+	0.873803i	$0.661647\pi$
$998$		−	61.6248i		−	1.95070i
$999$	−1.62377			−0.0513737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.20		24
5.2	odd	4		9025.2.a.ct.1.5		24
5.3	odd	4		9025.2.a.ct.1.20		24
5.4	even	2	inner	1805.2.b.l.1084.5		24
19.14	odd	18		95.2.p.a.44.2	✓	48
19.15	odd	18		95.2.p.a.54.7	yes	48
19.18	odd	2		1805.2.b.k.1084.5		24
57.14	even	18		855.2.da.b.424.7		48
57.53	even	18		855.2.da.b.244.2		48
95.14	odd	18		95.2.p.a.44.7	yes	48
95.18	even	4		9025.2.a.cu.1.5		24
95.33	even	36		475.2.l.f.101.2		48
95.34	odd	18		95.2.p.a.54.2	yes	48
95.37	even	4		9025.2.a.cu.1.20		24
95.52	even	36		475.2.l.f.101.7		48
95.53	even	36		475.2.l.f.301.2		48
95.72	even	36		475.2.l.f.301.7		48
95.94	odd	2		1805.2.b.k.1084.20		24
285.14	even	18		855.2.da.b.424.2		48
285.224	even	18		855.2.da.b.244.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.2	✓	48	19.14	odd	18
95.2.p.a.44.7	yes	48	95.14	odd	18
95.2.p.a.54.2	yes	48	95.34	odd	18
95.2.p.a.54.7	yes	48	19.15	odd	18
475.2.l.f.101.2		48	95.33	even	36
475.2.l.f.101.7		48	95.52	even	36
475.2.l.f.301.2		48	95.53	even	36
475.2.l.f.301.7		48	95.72	even	36
855.2.da.b.244.2		48	57.53	even	18
855.2.da.b.244.7		48	285.224	even	18
855.2.da.b.424.2		48	285.14	even	18
855.2.da.b.424.7		48	57.14	even	18
1805.2.b.k.1084.5		24	19.18	odd	2
1805.2.b.k.1084.20		24	95.94	odd	2
1805.2.b.l.1084.5		24	5.4	even	2	inner
1805.2.b.l.1084.20		24	1.1	even	1	trivial
9025.2.a.ct.1.5		24	5.2	odd	4
9025.2.a.ct.1.20		24	5.3	odd	4
9025.2.a.cu.1.5		24	95.18	even	4
9025.2.a.cu.1.20		24	95.37	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.78468i q^{2} -2.38377i q^{3} -1.18508 q^{4} +(-1.16534 + 1.90840i) q^{5} +4.25426 q^{6} -4.23911i q^{7} +1.45438i q^{8} -2.68235 q^{9} +(-3.40588 - 2.07976i) q^{10} -0.490889 q^{11} +2.82495i q^{12} -4.16199i q^{13} +7.56544 q^{14} +(4.54918 + 2.77790i) q^{15} -4.96575 q^{16} +2.03619i q^{17} -4.78713i q^{18} +(1.38102 - 2.26160i) q^{20} -10.1050 q^{21} -0.876080i q^{22} +4.39525i q^{23} +3.46689 q^{24} +(-2.28396 - 4.44787i) q^{25} +7.42782 q^{26} -0.757211i q^{27} +5.02367i q^{28} -3.26270 q^{29} +(-4.95766 + 8.11882i) q^{30} -4.08833 q^{31} -5.95351i q^{32} +1.17017i q^{33} -3.63395 q^{34} +(8.08990 + 4.94000i) q^{35} +3.17879 q^{36} -2.14440i q^{37} -9.92123 q^{39} +(-2.77553 - 1.69484i) q^{40} -4.36602 q^{41} -18.0343i q^{42} +10.6241i q^{43} +0.581742 q^{44} +(3.12585 - 5.11898i) q^{45} -7.84410 q^{46} -2.62142i q^{47} +11.8372i q^{48} -10.9700 q^{49} +(7.93801 - 4.07614i) q^{50} +4.85381 q^{51} +4.93228i q^{52} -11.4341i q^{53} +1.35138 q^{54} +(0.572053 - 0.936812i) q^{55} +6.16526 q^{56} -5.82287i q^{58} -0.542306 q^{59} +(-5.39112 - 3.29203i) q^{60} -13.6423 q^{61} -7.29635i q^{62} +11.3708i q^{63} +0.693606 q^{64} +(7.94274 + 4.85014i) q^{65} -2.08837 q^{66} -7.15699i q^{67} -2.41305i q^{68} +10.4772 q^{69} +(-8.81632 + 14.4379i) q^{70} -6.03858 q^{71} -3.90114i q^{72} +2.05419i q^{73} +3.82707 q^{74} +(-10.6027 + 5.44444i) q^{75} +2.08093i q^{77} -17.7062i q^{78} +5.34029 q^{79} +(5.78678 - 9.47662i) q^{80} -9.85206 q^{81} -7.79193i q^{82} +8.11578i q^{83} +11.9753 q^{84} +(-3.88587 - 2.37286i) q^{85} -18.9605 q^{86} +7.77752i q^{87} -0.713937i q^{88} -4.34099 q^{89} +(9.13574 + 5.57863i) q^{90} -17.6431 q^{91} -5.20871i q^{92} +9.74562i q^{93} +4.67839 q^{94} -14.1918 q^{96} +5.64669i q^{97} -19.5780i q^{98} +1.31674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 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

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