LMFDB - Embedded newform 1805.2.b.l.1084.18

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			1084.18
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.l.1084.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.47917i q^{2} +2.48321i q^{3} -0.187941 q^{4} +(0.111989 + 2.23326i) q^{5} -3.67308 q^{6} -3.24988i q^{7} +2.68034i q^{8} -3.16631 q^{9} +(-3.30337 + 0.165651i) q^{10} -4.18399 q^{11} -0.466696i q^{12} +1.78413i q^{13} +4.80712 q^{14} +(-5.54565 + 0.278093i) q^{15} -4.34056 q^{16} +6.33226i q^{17} -4.68351i q^{18} +(-0.0210474 - 0.419722i) q^{20} +8.07011 q^{21} -6.18883i q^{22} -1.43368i q^{23} -6.65584 q^{24} +(-4.97492 + 0.500204i) q^{25} -2.63904 q^{26} -0.412988i q^{27} +0.610785i q^{28} -0.339390 q^{29} +(-0.411347 - 8.20295i) q^{30} +2.77865 q^{31} -1.05974i q^{32} -10.3897i q^{33} -9.36648 q^{34} +(7.25782 - 0.363952i) q^{35} +0.595080 q^{36} +2.70482i q^{37} -4.43037 q^{39} +(-5.98590 + 0.300170i) q^{40} +7.13821 q^{41} +11.9371i q^{42} -9.89425i q^{43} +0.786344 q^{44} +(-0.354594 - 7.07120i) q^{45} +2.12065 q^{46} -0.445441i q^{47} -10.7785i q^{48} -3.56169 q^{49} +(-0.739886 - 7.35874i) q^{50} -15.7243 q^{51} -0.335312i q^{52} -7.23734i q^{53} +0.610879 q^{54} +(-0.468563 - 9.34395i) q^{55} +8.71078 q^{56} -0.502015i q^{58} +3.14263 q^{59} +(1.04226 - 0.0522651i) q^{60} -3.06562 q^{61} +4.11009i q^{62} +10.2901i q^{63} -7.11359 q^{64} +(-3.98444 + 0.199804i) q^{65} +15.3681 q^{66} -8.55254i q^{67} -1.19009i q^{68} +3.56011 q^{69} +(0.538346 + 10.7355i) q^{70} -12.8928 q^{71} -8.48680i q^{72} +1.82227i q^{73} -4.00089 q^{74} +(-1.24211 - 12.3537i) q^{75} +13.5974i q^{77} -6.55327i q^{78} +0.698700 q^{79} +(-0.486097 - 9.69361i) q^{80} -8.47340 q^{81} +10.5586i q^{82} +0.552985i q^{83} -1.51671 q^{84} +(-14.1416 + 0.709146i) q^{85} +14.6353 q^{86} -0.842775i q^{87} -11.2145i q^{88} +6.82870 q^{89} +(10.4595 - 0.524504i) q^{90} +5.79822 q^{91} +0.269446i q^{92} +6.89995i q^{93} +0.658883 q^{94} +2.63155 q^{96} +13.2006i q^{97} -5.26835i q^{98} +13.2478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.47917i			1.04593i	0.852354	+	0.522965i	$0.175174\pi$
$2$			1.47917i			1.04593i	−0.852354	+	0.522965i	$0.824826\pi$
$3$			2.48321i			1.43368i	0.697238	+	0.716840i	$0.254412\pi$
$3$			2.48321i			1.43368i	−0.697238	+	0.716840i	$0.745588\pi$
$4$	−0.187941			−0.0939705
$5$	0.111989	+	2.23326i	0.0500832	+	0.998745i
$5$	0.111989	+	2.23326i	0.0500832	+	0.998745i
$6$	−3.67308			−1.49953
$7$		−	3.24988i		−	1.22834i	−0.789175	−	0.614169i	$-0.789491\pi$
$7$		−	3.24988i		−	1.22834i	0.789175	−	0.614169i	$-0.210509\pi$
$8$			2.68034i			0.947644i
$9$	−3.16631			−1.05544
$10$	−3.30337	+	0.165651i	−1.04462	+	0.0523836i
$11$	−4.18399			−1.26152			−0.630760	−	0.775978i	$-0.717257\pi$
$11$	−4.18399			−1.26152			−0.630760	+	0.775978i	$0.717257\pi$
$12$		−	0.466696i		−	0.134724i
$13$			1.78413i			0.494830i	0.968910	+	0.247415i	$0.0795811\pi$
$13$			1.78413i			0.494830i	−0.968910	+	0.247415i	$0.920419\pi$
$14$	4.80712			1.28476
$15$	−5.54565	+	0.278093i	−1.43188	+	0.0718033i
$16$	−4.34056			−1.08514
$17$			6.33226i			1.53580i	0.640571	+	0.767899i	$0.278698\pi$
$17$			6.33226i			1.53580i	−0.640571	+	0.767899i	$0.721302\pi$
$18$		−	4.68351i		−	1.10391i
$19$		0			0
$19$		0			0
$20$	−0.0210474	−	0.419722i	−0.00470635	−	0.0938526i
$21$	8.07011			1.76104
$22$		−	6.18883i		−	1.31946i
$23$		−	1.43368i		−	0.298942i	−0.988766	−	0.149471i	$-0.952243\pi$
$23$		−	1.43368i		−	0.298942i	0.988766	−	0.149471i	$-0.0477571\pi$
$24$	−6.65584			−1.35862
$25$	−4.97492	+	0.500204i	−0.994983	+	0.100041i
$26$	−2.63904			−0.517558
$27$		−	0.412988i		−	0.0794796i
$28$			0.610785i			0.115428i
$29$	−0.339390			−0.0630231			−0.0315116	−	0.999503i	$-0.510032\pi$
$29$	−0.339390			−0.0630231			−0.0315116	+	0.999503i	$0.510032\pi$
$30$	−0.411347	−	8.20295i	−0.0751013	−	1.49765i
$31$	2.77865			0.499060			0.249530	−	0.968367i	$-0.419724\pi$
$31$	2.77865			0.499060			0.249530	+	0.968367i	$0.419724\pi$
$32$		−	1.05974i		−	0.187337i
$33$		−	10.3897i		−	1.80862i
$34$	−9.36648			−1.60634
$35$	7.25782	−	0.363952i	1.22680	−	0.0615191i
$36$	0.595080			0.0991800
$37$			2.70482i			0.444670i	0.974970	+	0.222335i	$0.0713679\pi$
$37$			2.70482i			0.444670i	−0.974970	+	0.222335i	$0.928632\pi$
$38$		0			0
$39$	−4.43037			−0.709427
$40$	−5.98590	+	0.300170i	−0.946455	+	0.0474611i
$41$	7.13821			1.11480			0.557401	−	0.830244i	$-0.311799\pi$
$41$	7.13821			1.11480			0.557401	+	0.830244i	$0.311799\pi$
$42$			11.9371i			1.84193i
$43$		−	9.89425i		−	1.50886i	−0.656381	−	0.754429i	$-0.727914\pi$
$43$		−	9.89425i		−	1.50886i	0.656381	−	0.754429i	$-0.272086\pi$
$44$	0.786344			0.118546
$45$	−0.354594	−	7.07120i	−0.0528597	−	1.05411i
$46$	2.12065			0.312673
$47$		−	0.445441i		−	0.0649743i	−0.999472	−	0.0324871i	$-0.989657\pi$
$47$		−	0.445441i		−	0.0649743i	0.999472	−	0.0324871i	$-0.0103428\pi$
$48$		−	10.7785i		−	1.55574i
$49$	−3.56169			−0.508813
$50$	−0.739886	−	7.35874i	−0.104636	−	1.04068i
$51$	−15.7243			−2.20184
$52$		−	0.335312i		−	0.0464994i
$53$		−	7.23734i		−	0.994125i	−0.867715	−	0.497062i	$-0.834412\pi$
$53$		−	7.23734i		−	0.994125i	0.867715	−	0.497062i	$-0.165588\pi$
$54$	0.610879			0.0831301
$55$	−0.468563	−	9.34395i	−0.0631810	−	1.25994i
$56$	8.71078			1.16403
$57$		0			0
$58$		−	0.502015i		−	0.0659178i
$59$	3.14263			0.409136			0.204568	−	0.978852i	$-0.434421\pi$
$59$	3.14263			0.409136			0.204568	+	0.978852i	$0.434421\pi$
$60$	1.04226	−	0.0522651i	0.134555	−	0.00674739i
$61$	−3.06562			−0.392512			−0.196256	−	0.980553i	$-0.562878\pi$
$61$	−3.06562			−0.392512			−0.196256	+	0.980553i	$0.562878\pi$
$62$			4.11009i			0.521982i
$63$			10.2901i			1.29643i
$64$	−7.11359			−0.889198
$65$	−3.98444	+	0.199804i	−0.494209	+	0.0247827i
$66$	15.3681			1.89169
$67$		−	8.55254i		−	1.04486i	−0.852682	−	0.522430i	$-0.825026\pi$
$67$		−	8.55254i		−	1.04486i	0.852682	−	0.522430i	$-0.174974\pi$
$68$		−	1.19009i		−	0.144320i
$69$	3.56011			0.428587
$70$	0.538346	+	10.7355i	0.0643447	+	1.28314i
$71$	−12.8928			−1.53009			−0.765046	−	0.643975i	$-0.777284\pi$
$71$	−12.8928			−1.53009			−0.765046	+	0.643975i	$0.777284\pi$
$72$		−	8.48680i		−	1.00018i
$73$			1.82227i			0.213281i	0.994298	+	0.106640i	$0.0340093\pi$
$73$			1.82227i			0.213281i	−0.994298	+	0.106640i	$0.965991\pi$
$74$	−4.00089			−0.465094
$75$	−1.24211	−	12.3537i	−0.143426	−	1.42649i
$76$		0			0
$77$			13.5974i			1.54957i
$78$		−	6.55327i		−	0.742012i
$79$	0.698700			0.0786099			0.0393050	−	0.999227i	$-0.487486\pi$
$79$	0.698700			0.0786099			0.0393050	+	0.999227i	$0.487486\pi$
$80$	−0.486097	−	9.69361i	−0.0543473	−	1.08378i
$81$	−8.47340			−0.941489
$82$			10.5586i			1.16600i
$83$			0.552985i			0.0606980i	0.999539	+	0.0303490i	$0.00966188\pi$
$83$			0.552985i			0.0606980i	−0.999539	+	0.0303490i	$0.990338\pi$
$84$	−1.51671			−0.165486
$85$	−14.1416	+	0.709146i	−1.53387	+	0.0769177i
$86$	14.6353			1.57816
$87$		−	0.842775i		−	0.0903550i
$88$		−	11.2145i		−	1.19547i
$89$	6.82870			0.723841			0.361920	−	0.932209i	$-0.382121\pi$
$89$	6.82870			0.723841			0.361920	+	0.932209i	$0.382121\pi$
$90$	10.4595	−	0.524504i	1.10253	−	0.0552876i
$91$	5.79822			0.607818
$92$			0.269446i			0.0280917i
$93$			6.89995i			0.715492i
$94$	0.658883			0.0679586
$95$		0			0
$96$	2.63155			0.268582
$97$			13.2006i			1.34032i	0.742217	+	0.670160i	$0.233774\pi$
$97$			13.2006i			1.34032i	−0.742217	+	0.670160i	$0.766226\pi$
$98$		−	5.26835i		−	0.532183i
$99$	13.2478			1.33146
$100$	0.934991	−	0.0940088i	0.0934991	−	0.00940088i
$101$	17.2757			1.71899			0.859496	−	0.511142i	$-0.170777\pi$
$101$	17.2757			1.71899			0.859496	+	0.511142i	$0.170777\pi$
$102$		−	23.2589i		−	2.30297i
$103$			13.8286i			1.36257i	0.732017	+	0.681286i	$0.238579\pi$
$103$			13.8286i			1.36257i	−0.732017	+	0.681286i	$0.761421\pi$
$104$	−4.78209			−0.468922
$105$	0.903768	+	18.0227i	0.0881987	+	1.75883i
$106$	10.7052			1.03979
$107$			3.26460i			0.315600i	0.987471	+	0.157800i	$0.0504402\pi$
$107$			3.26460i			0.315600i	−0.987471	+	0.157800i	$0.949560\pi$
$108$			0.0776174i			0.00746874i
$109$	−3.22094			−0.308510			−0.154255	−	0.988031i	$-0.549298\pi$
$109$	−3.22094			−0.308510			−0.154255	+	0.988031i	$0.549298\pi$
$110$	13.8213	−	0.693084i	1.31781	−	0.0660829i
$111$	−6.71663			−0.637514
$112$			14.1063i			1.33292i
$113$			4.71007i			0.443086i	0.975151	+	0.221543i	$0.0711093\pi$
$113$			4.71007i			0.443086i	−0.975151	+	0.221543i	$0.928891\pi$
$114$		0			0
$115$	3.20177	−	0.160557i	0.298567	−	0.0149720i
$116$	0.0637853			0.00592232
$117$		−	5.64913i		−	0.522262i
$118$			4.64849i			0.427928i
$119$	20.5791			1.88648
$120$	−0.745384	−	14.8642i	−0.0680440	−	1.35691i
$121$	6.50577			0.591434
$122$		−	4.53457i		−	0.410541i
$123$			17.7257i			1.59827i
$124$	−0.522222			−0.0468969
$125$	−1.67422	−	11.0543i	−0.149747	−	0.988724i
$126$	−15.2208			−1.35598
$127$		−	0.592012i		−	0.0525325i	−0.999655	−	0.0262663i	$-0.991638\pi$
$127$		−	0.592012i		−	0.0525325i	0.999655	−	0.0262663i	$-0.00836177\pi$
$128$		−	12.6417i		−	1.11738i
$129$	24.5695			2.16322
$130$	−0.295544	−	5.89366i	−0.0259210	−	0.516908i
$131$	−20.5490			−1.79538			−0.897689	−	0.440629i	$-0.854755\pi$
$131$	−20.5490			−1.79538			−0.897689	+	0.440629i	$0.854755\pi$
$132$			1.95265i			0.169957i
$133$		0			0
$134$	12.6507			1.09285
$135$	0.922310	−	0.0462503i	0.0793798	−	0.00398059i
$136$	−16.9726			−1.45539
$137$			8.75406i			0.747910i	0.927447	+	0.373955i	$0.121999\pi$
$137$			8.75406i			0.747910i	−0.927447	+	0.373955i	$0.878001\pi$
$138$			5.26601i			0.448272i
$139$	−7.68939			−0.652205			−0.326103	−	0.945334i	$-0.605736\pi$
$139$	−7.68939			−0.652205			−0.326103	+	0.945334i	$0.605736\pi$
$140$	−1.36404	+	0.0684015i	−0.115283	+	0.00578098i
$141$	1.10612			0.0931523
$142$		−	19.0706i		−	1.60037i
$143$		−	7.46480i		−	0.624238i
$144$	13.7436			1.14530
$145$	−0.0380081	−	0.757947i	−0.00315640	−	0.0629440i
$146$	−2.69545			−0.223077
$147$		−	8.84442i		−	0.729475i
$148$		−	0.508347i		−	0.0417859i
$149$	14.9414			1.22404			0.612022	−	0.790841i	$-0.290356\pi$
$149$	14.9414			1.22404			0.612022	+	0.790841i	$0.290356\pi$
$150$	18.2733	−	1.83729i	1.49201	−	0.150014i
$151$	−13.1424			−1.06951			−0.534757	−	0.845006i	$-0.679597\pi$
$151$	−13.1424			−1.06951			−0.534757	+	0.845006i	$0.679597\pi$
$152$		0			0
$153$		−	20.0499i		−	1.62094i
$154$	−20.1129			−1.62075
$155$	0.311179	+	6.20545i	0.0249945	+	0.498434i
$156$	0.832649			0.0666653
$157$			10.8372i			0.864902i	0.901657	+	0.432451i	$0.142351\pi$
$157$			10.8372i			0.864902i	−0.901657	+	0.432451i	$0.857649\pi$
$158$			1.03350i			0.0822205i
$159$	17.9718			1.42526
$160$	2.36668	−	0.118680i	0.187102	−	0.00938245i
$161$	−4.65927			−0.367202
$162$		−	12.5336i		−	0.984732i
$163$		−	8.44554i		−	0.661506i	−0.943717	−	0.330753i	$-0.892697\pi$
$163$		−	8.44554i		−	0.661506i	0.943717	−	0.330753i	$-0.107303\pi$
$164$	−1.34156			−0.104758
$165$	23.2029	−	1.16354i	1.80635	−	0.0905813i
$166$	−0.817959			−0.0634859
$167$			19.9012i			1.54000i	0.638041	+	0.770002i	$0.279745\pi$
$167$			19.9012i			1.54000i	−0.638041	+	0.770002i	$0.720255\pi$
$168$			21.6307i			1.66884i
$169$	9.81686			0.755143
$170$	−1.04895	−	20.9178i	−0.0804506	−	1.60432i
$171$		0			0
$172$			1.85954i			0.141788i
$173$			11.7211i			0.891135i	0.895248	+	0.445568i	$0.146998\pi$
$173$			11.7211i			0.891135i	−0.895248	+	0.445568i	$0.853002\pi$
$174$	1.24661			0.0945050
$175$	1.62560	+	16.1679i	0.122884	+	1.22218i
$176$	18.1609			1.36893
$177$			7.80380i			0.586570i
$178$			10.1008i			0.757087i
$179$	7.08378			0.529467			0.264733	−	0.964322i	$-0.414716\pi$
$179$	7.08378			0.529467			0.264733	+	0.964322i	$0.414716\pi$
$180$	0.0666427	+	1.32897i	0.00496726	+	0.0990556i
$181$	−9.28177			−0.689908			−0.344954	−	0.938620i	$-0.612106\pi$
$181$	−9.28177			−0.689908			−0.344954	+	0.938620i	$0.612106\pi$
$182$			8.57654i			0.635735i
$183$		−	7.61257i		−	0.562737i
$184$	3.84274			0.283291
$185$	−6.04057	+	0.302912i	−0.444112	+	0.0222705i
$186$	−10.2062			−0.748355
$187$		−	26.4941i		−	1.93744i
$188$			0.0837167i			0.00610567i
$189$	−1.34216			−0.0976277
$190$		0			0
$191$	8.12426			0.587850			0.293925	−	0.955828i	$-0.405038\pi$
$191$	8.12426			0.587850			0.293925	+	0.955828i	$0.405038\pi$
$192$		−	17.6645i		−	1.27483i
$193$			7.72342i			0.555944i	0.960589	+	0.277972i	$0.0896623\pi$
$193$			7.72342i			0.555944i	−0.960589	+	0.277972i	$0.910338\pi$
$194$	−19.5259			−1.40188
$195$	−0.496155	−	9.89418i	−0.0355304	−	0.708537i
$196$	0.669388			0.0478135
$197$			3.56762i			0.254183i	0.991891	+	0.127091i	$0.0405641\pi$
$197$			3.56762i			0.254183i	−0.991891	+	0.127091i	$0.959436\pi$
$198$			19.5958i			1.39261i
$199$	8.76938			0.621645			0.310822	−	0.950468i	$-0.399396\pi$
$199$	8.76938			0.621645			0.310822	+	0.950468i	$0.399396\pi$
$200$	−1.34072	−	13.3345i	−0.0948030	−	0.942890i
$201$	21.2377			1.49799
$202$			25.5536i			1.79795i
$203$			1.10298i			0.0774137i
$204$	2.95524			0.206908
$205$	0.799405	+	15.9415i	0.0558328	+	1.11340i
$206$	−20.4548			−1.42516
$207$			4.53946i			0.315515i
$208$		−	7.74414i		−	0.536960i
$209$		0			0
$210$	−26.6586	+	1.33683i	−1.83962	+	0.0922497i
$211$	−11.8171			−0.813526			−0.406763	−	0.913534i	$-0.633343\pi$
$211$	−11.8171			−0.813526			−0.406763	+	0.913534i	$0.633343\pi$
$212$			1.36019i			0.0934184i
$213$		−	32.0155i		−	2.19366i
$214$	−4.82889			−0.330096
$215$	22.0964	−	1.10805i	1.50696	−	0.0755685i
$216$	1.10695			0.0753183
$217$		−	9.03026i		−	0.613014i
$218$		−	4.76431i		−	0.322680i
$219$	−4.52507			−0.305776
$220$	0.0880622	+	1.75611i	0.00593715	+	0.118397i
$221$	−11.2976			−0.759959
$222$		−	9.93503i		−	0.666796i
$223$			8.89760i			0.595827i	0.954593	+	0.297914i	$0.0962908\pi$
$223$			8.89760i			0.595827i	−0.954593	+	0.297914i	$0.903709\pi$
$224$	−3.44402			−0.230113
$225$	15.7521	−	1.58380i	1.05014	−	0.105587i
$226$	−6.96698			−0.463437
$227$			26.4080i			1.75276i	0.481620	+	0.876380i	$0.340049\pi$
$227$			26.4080i			1.75276i	−0.481620	+	0.876380i	$0.659951\pi$
$228$		0			0
$229$	−21.7852			−1.43961			−0.719804	−	0.694177i	$-0.755768\pi$
$229$	−21.7852			−1.43961			−0.719804	+	0.694177i	$0.755768\pi$
$230$	0.237490	+	4.73596i	0.0156596	+	0.312280i
$231$	−33.7653			−2.22159
$232$		−	0.909681i		−	0.0597235i
$233$		−	10.0009i		−	0.655183i	−0.944820	−	0.327591i	$-0.893763\pi$
$233$		−	10.0009i		−	0.655183i	0.944820	−	0.327591i	$-0.106237\pi$
$234$	8.35601			0.546250
$235$	0.994787	−	0.0498847i	0.0648927	−	0.00325412i
$236$	−0.590630			−0.0384467
$237$			1.73502i			0.112701i
$238$			30.4399i			1.97313i
$239$	−17.8365			−1.15374			−0.576872	−	0.816834i	$-0.695727\pi$
$239$	−17.8365			−1.15374			−0.576872	+	0.816834i	$0.695727\pi$
$240$	24.0712	−	1.20708i	1.55379	−	0.0779166i
$241$	17.1442			1.10435			0.552177	−	0.833727i	$-0.313797\pi$
$241$	17.1442			1.10435			0.552177	+	0.833727i	$0.313797\pi$
$242$			9.62314i			0.618599i
$243$		−	22.2802i		−	1.42927i
$244$	0.576156			0.0368846
$245$	−0.398872	−	7.95419i	−0.0254830	−	0.508175i
$246$	−26.2192			−1.67168
$247$		0			0
$248$			7.44772i			0.472931i
$249$	−1.37318			−0.0870215
$250$	16.3511	−	2.47646i	1.03414	−	0.156625i
$251$	9.69585			0.611997			0.305998	−	0.952032i	$-0.401010\pi$
$251$	9.69585			0.611997			0.305998	+	0.952032i	$0.401010\pi$
$252$		−	1.93394i		−	0.121827i
$253$			5.99848i			0.377121i
$254$	0.875685			0.0549454
$255$	−1.76096	−	35.1165i	−0.110275	−	2.19908i
$256$	4.47200			0.279500
$257$			10.0506i			0.626942i	0.949598	+	0.313471i	$0.101492\pi$
$257$			10.0506i			0.626942i	−0.949598	+	0.313471i	$0.898508\pi$
$258$			36.3424i			2.26258i
$259$	8.79033			0.546205
$260$	0.748840	−	0.0375514i	0.0464411	−	0.00232884i
$261$	1.07461			0.0665170
$262$		−	30.3955i		−	1.87784i
$263$			21.8306i			1.34613i	0.739583	+	0.673065i	$0.235023\pi$
$263$			21.8306i			1.34613i	−0.739583	+	0.673065i	$0.764977\pi$
$264$	27.8480			1.71392
$265$	16.1629	−	0.810506i	0.992877	−	0.0497890i
$266$		0			0
$267$			16.9571i			1.03776i
$268$			1.60737i			0.0981860i
$269$	15.4551			0.942312			0.471156	−	0.882050i	$-0.343837\pi$
$269$	15.4551			0.942312			0.471156	+	0.882050i	$0.343837\pi$
$270$	0.0684120	+	1.36425i	0.00416342	+	0.0830258i
$271$	5.16319			0.313642			0.156821	−	0.987627i	$-0.449875\pi$
$271$	5.16319			0.313642			0.156821	+	0.987627i	$0.449875\pi$
$272$		−	27.4855i		−	1.66656i
$273$			14.3982i			0.871416i
$274$	−12.9487			−0.782262
$275$	20.8150	−	2.09285i	1.25519	−	0.126203i
$276$	−0.669091			−0.0402746
$277$		−	5.57030i		−	0.334687i	−0.985899	−	0.167343i	$-0.946481\pi$
$277$		−	5.57030i		−	0.334687i	0.985899	−	0.167343i	$-0.0535189\pi$
$278$		−	11.3739i		−	0.682161i
$279$	−8.79807			−0.526726
$280$	0.975516	+	19.4534i	0.0582982	+	1.16257i
$281$	−27.2729			−1.62697			−0.813483	−	0.581589i	$-0.802431\pi$
$281$	−27.2729			−1.62697			−0.813483	+	0.581589i	$0.802431\pi$
$282$			1.63614i			0.0974308i
$283$		−	15.0458i		−	0.894379i	−0.894439	−	0.447190i	$-0.852425\pi$
$283$		−	15.0458i		−	0.894379i	0.894439	−	0.447190i	$-0.147575\pi$
$284$	2.42308			0.143784
$285$		0			0
$286$	11.0417			0.652910
$287$		−	23.1983i		−	1.36935i
$288$			3.35547i			0.197723i
$289$	−23.0975			−1.35868
$290$	1.12113	−	0.0562204i	0.0658351	−	0.00330138i
$291$	−32.7799			−1.92159
$292$		−	0.342479i		−	0.0200421i
$293$			7.82882i			0.457364i	0.973501	+	0.228682i	$0.0734416\pi$
$293$			7.82882i			0.457364i	−0.973501	+	0.228682i	$0.926558\pi$
$294$	13.0824			0.762981
$295$	0.351942	+	7.01832i	0.0204908	+	0.408622i
$296$	−7.24985			−0.421389
$297$			1.72794i			0.100265i
$298$			22.1008i			1.28026i
$299$	2.55787			0.147925
$300$	0.233443	+	2.32178i	0.0134779	+	0.134048i
$301$	−32.1551			−1.85339
$302$		−	19.4398i		−	1.11864i
$303$			42.8990i			2.46449i
$304$		0			0
$305$	−0.343317	−	6.84633i	−0.0196583	−	0.392020i
$306$	29.6572			1.69539
$307$		−	15.7146i		−	0.896879i	−0.893813	−	0.448439i	$-0.851980\pi$
$307$		−	15.7146i		−	0.896879i	0.893813	−	0.448439i	$-0.148020\pi$
$308$		−	2.55552i		−	0.145614i
$309$	−34.3393			−1.95349
$310$	−9.17891	+	0.460287i	−0.521327	+	0.0261425i
$311$	17.9812			1.01962			0.509810	−	0.860287i	$-0.329716\pi$
$311$	17.9812			1.01962			0.509810	+	0.860287i	$0.329716\pi$
$312$		−	11.8749i		−	0.672285i
$313$			21.2005i			1.19832i	0.800628	+	0.599161i	$0.204499\pi$
$313$			21.2005i			1.19832i	−0.800628	+	0.599161i	$0.795501\pi$
$314$	−16.0300			−0.904627
$315$	−22.9805	+	1.15239i	−1.29481	+	0.0649296i
$316$	−0.131314			−0.00738702
$317$			3.06442i			0.172115i	0.996290	+	0.0860575i	$0.0274269\pi$
$317$			3.06442i			0.172115i	−0.996290	+	0.0860575i	$0.972573\pi$
$318$			26.5833i			1.49072i
$319$	1.42000			0.0795050
$320$	−0.796647	−	15.8865i	−0.0445339	−	0.888082i
$321$	−8.10666			−0.452470
$322$		−	6.89184i		−	0.384067i
$323$		0			0
$324$	1.59250			0.0884722
$325$	−0.892431	−	8.87592i	−0.0495031	−	0.492347i
$326$	12.4924			0.691889
$327$		−	7.99825i		−	0.442304i
$328$			19.1328i			1.05643i
$329$	−1.44763			−0.0798103
$330$	1.72107	+	34.3211i	0.0947418	+	1.88931i
$331$	25.9509			1.42639			0.713195	−	0.700966i	$-0.247247\pi$
$331$	25.9509			1.42639			0.713195	+	0.700966i	$0.247247\pi$
$332$		−	0.103929i		−	0.00570383i
$333$		−	8.56431i		−	0.469321i
$334$	−29.4373			−1.61074
$335$	19.1001	−	0.957795i	1.04355	−	0.0523299i
$336$	−35.0288			−1.91098
$337$			10.0575i			0.547865i	0.961749	+	0.273933i	$0.0883245\pi$
$337$			10.0575i			0.547865i	−0.961749	+	0.273933i	$0.911676\pi$
$338$			14.5208i			0.789828i
$339$	−11.6961			−0.635243
$340$	2.65779	−	0.133278i	0.144139	−	0.00722800i
$341$	−11.6258			−0.629574
$342$		0			0
$343$		−	11.1741i		−	0.603343i
$344$	26.5200			1.42986
$345$	0.398695	+	7.95066i	0.0214650	+	0.428049i
$346$	−17.3374			−0.932065
$347$		−	6.81801i		−	0.366010i	−0.983112	−	0.183005i	$-0.941418\pi$
$347$		−	6.81801i		−	0.366010i	0.983112	−	0.183005i	$-0.0585824\pi$
$348$			0.158392i			0.00849071i
$349$	−31.5966			−1.69133			−0.845663	−	0.533718i	$-0.820795\pi$
$349$	−31.5966			−1.69133			−0.845663	+	0.533718i	$0.820795\pi$
$350$	−23.9150	+	2.40454i	−1.27831	+	0.128528i
$351$	0.736826			0.0393289
$352$			4.43394i			0.236330i
$353$		−	6.30657i		−	0.335665i	−0.985816	−	0.167832i	$-0.946323\pi$
$353$		−	6.30657i		−	0.335665i	0.985816	−	0.167832i	$-0.0536767\pi$
$354$	−11.5431			−0.613511
$355$	−1.44386	−	28.7930i	−0.0766320	−	1.52817i
$356$	−1.28339			−0.0680197
$357$			51.1020i			2.70461i
$358$			10.4781i			0.553785i
$359$	−4.17666			−0.220436			−0.110218	−	0.993907i	$-0.535155\pi$
$359$	−4.17666			−0.220436			−0.110218	+	0.993907i	$0.535155\pi$
$360$	18.9532	−	0.950432i	0.998924	−	0.0500922i
$361$		0			0
$362$		−	13.7293i		−	0.721596i
$363$			16.1552i			0.847927i
$364$	−1.08972			−0.0571170
$365$	−4.06961	+	0.204075i	−0.213013	+	0.0106818i
$366$	11.2603			0.588584
$367$			16.5710i			0.864998i	0.901634	+	0.432499i	$0.142368\pi$
$367$			16.5710i			0.864998i	−0.901634	+	0.432499i	$0.857632\pi$
$368$			6.22295i			0.324394i
$369$	−22.6018			−1.17660
$370$	−0.448057	−	8.93503i	−0.0232934	−	0.464510i
$371$	−23.5204			−1.22112
$372$		−	1.29678i		−	0.0672352i
$373$			37.0004i			1.91581i	0.287085	+	0.957905i	$0.407314\pi$
$373$			37.0004i			1.91581i	−0.287085	+	0.957905i	$0.592686\pi$
$374$	39.1893			2.02643
$375$	27.4500	−	4.15744i	1.41751	−	0.214689i
$376$	1.19393			0.0615725
$377$		−	0.605517i		−	0.0311857i
$378$		−	1.98528i		−	0.102112i
$379$	31.5147			1.61880			0.809400	−	0.587257i	$-0.199792\pi$
$379$	31.5147			1.61880			0.809400	+	0.587257i	$0.199792\pi$
$380$		0			0
$381$	1.47009			0.0753148
$382$			12.0171i			0.614851i
$383$			3.09813i			0.158307i	0.996862	+	0.0791536i	$0.0252218\pi$
$383$			3.09813i			0.158307i	−0.996862	+	0.0791536i	$0.974778\pi$
$384$	31.3919			1.60196
$385$	−30.3667	+	1.52277i	−1.54763	+	0.0776076i
$386$	−11.4243			−0.581479
$387$			31.3283i			1.59251i
$388$		−	2.48094i		−	0.125951i
$389$	−26.0318			−1.31986			−0.659931	−	0.751326i	$-0.729415\pi$
$389$	−26.0318			−1.31986			−0.659931	+	0.751326i	$0.729415\pi$
$390$	14.6352	−	0.733897i	0.741081	−	0.0371623i
$391$	9.07840			0.459115
$392$		−	9.54655i		−	0.482174i
$393$		−	51.0275i		−	2.57400i
$394$	−5.27712			−0.265857
$395$	0.0782471	+	1.56038i	0.00393704	+	0.0785113i
$396$	−2.48981			−0.125118
$397$		−	12.6607i		−	0.635423i	−0.948187	−	0.317712i	$-0.897086\pi$
$397$		−	12.6607i		−	0.635423i	0.948187	−	0.317712i	$-0.102914\pi$
$398$			12.9714i			0.650197i
$399$		0			0
$400$	21.5939	−	2.17116i	1.07970	−	0.108558i
$401$	9.22180			0.460515			0.230257	−	0.973130i	$-0.426043\pi$
$401$	9.22180			0.460515			0.230257	+	0.973130i	$0.426043\pi$
$402$			31.4142i			1.56680i
$403$			4.95748i			0.246950i
$404$	−3.24681			−0.161535
$405$	−0.948932	−	18.9233i	−0.0471528	−	0.940308i
$406$	−1.63149			−0.0809693
$407$		−	11.3169i		−	0.560960i
$408$		−	42.1465i		−	2.08656i
$409$	34.4572			1.70380			0.851899	−	0.523706i	$-0.175451\pi$
$409$	34.4572			1.70380			0.851899	+	0.523706i	$0.175451\pi$
$410$	−23.5802	+	1.18245i	−1.16454	+	0.0583973i
$411$	−21.7381			−1.07226
$412$		−	2.59896i		−	0.128042i
$413$		−	10.2132i		−	0.502557i
$414$	−6.71464			−0.330006
$415$	−1.23496	+	0.0619286i	−0.0606219	+	0.00303995i
$416$	1.89072			0.0927001
$417$		−	19.0943i		−	0.935053i
$418$		0			0
$419$	7.86047			0.384009			0.192005	−	0.981394i	$-0.438501\pi$
$419$	7.86047			0.384009			0.192005	+	0.981394i	$0.438501\pi$
$420$	−0.169855	−	3.38720i	−0.00828808	−	0.165278i
$421$	−10.4922			−0.511360			−0.255680	−	0.966761i	$-0.582299\pi$
$421$	−10.4922			−0.511360			−0.255680	+	0.966761i	$0.582299\pi$
$422$		−	17.4796i		−	0.850892i
$423$			1.41041i			0.0685763i
$424$	19.3985			0.942076
$425$	−3.16742	−	31.5025i	−0.153642	−	1.52809i
$426$	47.3563			2.29442
$427$			9.96288i			0.482138i
$428$		−	0.613552i		−	0.0296571i
$429$	18.5366			0.894957
$430$	1.63900	+	32.6844i	0.0790394	+	1.57618i
$431$	−29.8923			−1.43986			−0.719931	−	0.694046i	$-0.755827\pi$
$431$	−29.8923			−1.43986			−0.719931	+	0.694046i	$0.755827\pi$
$432$			1.79260i			0.0862465i
$433$		−	6.79977i		−	0.326776i	−0.986562	−	0.163388i	$-0.947758\pi$
$433$		−	6.79977i		−	0.326776i	0.986562	−	0.163388i	$-0.0522422\pi$
$434$	13.3573			0.641170
$435$	1.88214	−	0.0943820i	0.0902416	−	0.00452527i
$436$	0.605347			0.0289908
$437$		0			0
$438$		−	6.69335i		−	0.319820i
$439$	7.96606			0.380199			0.190100	−	0.981765i	$-0.439119\pi$
$439$	7.96606			0.380199			0.190100	+	0.981765i	$0.439119\pi$
$440$	25.0450	−	1.25591i	1.19397	−	0.0598731i
$441$	11.2774			0.537021
$442$		−	16.7111i		−	0.794864i
$443$		−	21.7893i		−	1.03524i	−0.855610	−	0.517621i	$-0.826818\pi$
$443$		−	21.7893i		−	1.03524i	0.855610	−	0.517621i	$-0.173182\pi$
$444$	1.26233			0.0599076
$445$	0.764743	+	15.2503i	0.0362523	+	0.722932i
$446$	−13.1611			−0.623194
$447$			37.1025i			1.75489i
$448$			23.1183i			1.09224i
$449$	18.7837			0.886458			0.443229	−	0.896409i	$-0.353833\pi$
$449$	18.7837			0.886458			0.443229	+	0.896409i	$0.353833\pi$
$450$	2.34271	+	23.3001i	0.110436	+	1.09838i
$451$	−29.8662			−1.40634
$452$		−	0.885215i		−	0.0416370i
$453$		−	32.6353i		−	1.53334i
$454$	−39.0619			−1.83327
$455$	0.649339	+	12.9489i	0.0304415	+	0.607055i
$456$		0			0
$457$		−	28.2368i		−	1.32086i	−0.750887	−	0.660431i	$-0.770373\pi$
$457$		−	28.2368i		−	1.32086i	0.750887	−	0.660431i	$-0.229627\pi$
$458$		−	32.2240i		−	1.50573i
$459$	2.61515			0.122065
$460$	−0.601745	+	0.0301752i	−0.0280565	+	0.00140692i
$461$	−0.196008			−0.00912900			−0.00456450	−	0.999990i	$-0.501453\pi$
$461$	−0.196008			−0.00912900			−0.00456450	+	0.999990i	$0.501453\pi$
$462$		−	49.9445i		−	2.32363i
$463$			13.9641i			0.648967i	0.945891	+	0.324484i	$0.105191\pi$
$463$			13.9641i			0.648967i	−0.945891	+	0.324484i	$0.894809\pi$
$464$	1.47314			0.0683889
$465$	−15.4094	+	0.772722i	−0.714594	+	0.0358341i
$466$	14.7931			0.685275
$467$			32.1025i			1.48553i	0.669555	+	0.742763i	$0.266485\pi$
$467$			32.1025i			1.48553i	−0.669555	+	0.742763i	$0.733515\pi$
$468$			1.06170i			0.0490772i
$469$	−27.7947			−1.28344
$470$	0.0737880	+	1.47146i	0.00340358	+	0.0678733i
$471$	−26.9110			−1.23999
$472$			8.42333i			0.387715i
$473$			41.3974i			1.90346i
$474$	−2.56638			−0.117878
$475$		0			0
$476$	−3.86765			−0.177273
$477$			22.9157i			1.04924i
$478$		−	26.3831i		−	1.20674i
$479$	1.98226			0.0905717			0.0452858	−	0.998974i	$-0.485580\pi$
$479$	1.98226			0.0905717			0.0452858	+	0.998974i	$0.485580\pi$
$480$	0.294706	+	5.87694i	0.0134514	+	0.268245i
$481$	−4.82576			−0.220036
$482$			25.3591i			1.15508i
$483$		−	11.5699i		−	0.526450i
$484$	−1.22270			−0.0555774
$485$	−29.4804	+	1.47833i	−1.33864	+	0.0671275i
$486$	32.9561			1.49492
$487$			8.58916i			0.389212i	0.980881	+	0.194606i	$0.0623428\pi$
$487$			8.58916i			0.389212i	−0.980881	+	0.194606i	$0.937657\pi$
$488$		−	8.21691i		−	0.371962i
$489$	20.9720			0.948387
$490$	11.7656	−	0.589999i	0.531516	−	0.0266535i
$491$	25.9002			1.16886			0.584430	−	0.811444i	$-0.301318\pi$
$491$	25.9002			1.16886			0.584430	+	0.811444i	$0.301318\pi$
$492$		−	3.33138i		−	0.150190i
$493$		−	2.14910i		−	0.0967908i
$494$		0			0
$495$	1.48362	+	29.5858i	0.0666836	+	1.32979i
$496$	−12.0609			−0.541550
$497$			41.9000i			1.87947i
$498$		−	2.03116i		−	0.0910185i
$499$	21.2038			0.949214			0.474607	−	0.880198i	$-0.342590\pi$
$499$	21.2038			0.949214			0.474607	+	0.880198i	$0.342590\pi$
$500$	0.314655	+	2.07755i	0.0140718	+	0.0929109i
$501$	−49.4189			−2.20787
$502$			14.3418i			0.640106i
$503$			25.5162i			1.13771i	0.822438	+	0.568855i	$0.192614\pi$
$503$			25.5162i			1.13771i	−0.822438	+	0.568855i	$0.807386\pi$
$504$	−27.5810			−1.22856
$505$	1.93469	+	38.5811i	0.0860927	+	1.71684i
$506$	−8.87277			−0.394443
$507$			24.3773i			1.08263i
$508$			0.111263i			0.00493651i
$509$	−17.0407			−0.755314			−0.377657	−	0.925946i	$-0.623270\pi$
$509$	−17.0407			−0.755314			−0.377657	+	0.925946i	$0.623270\pi$
$510$	51.9432	−	2.60475i	2.30008	−	0.115340i
$511$	5.92215			0.261981
$512$		−	18.6685i		−	0.825039i
$513$		0			0
$514$	−14.8666			−0.655738
$515$	−30.8829	+	1.54866i	−1.36086	+	0.0682420i
$516$	−4.61761			−0.203279
$517$			1.86372i			0.0819664i
$518$			13.0024i			0.571292i
$519$	−29.1058			−1.27760
$520$	−0.535544	−	10.6797i	−0.0234851	−	0.468334i
$521$	−21.7817			−0.954274			−0.477137	−	0.878829i	$-0.658325\pi$
$521$	−21.7817			−0.954274			−0.477137	+	0.878829i	$0.658325\pi$
$522$			1.58954i			0.0695721i
$523$			17.4855i			0.764589i	0.924041	+	0.382294i	$0.124866\pi$
$523$			17.4855i			0.764589i	−0.924041	+	0.382294i	$0.875134\pi$
$524$	3.86201			0.168713
$525$	−40.1481	+	4.03670i	−1.75221	+	0.176176i
$526$	−32.2911			−1.40796
$527$			17.5951i			0.766455i
$528$			45.0972i			1.96260i
$529$	20.9446			0.910634
$530$	1.19887	+	23.9076i	0.0520758	+	1.03848i
$531$	−9.95056			−0.431817
$532$		0			0
$533$			12.7355i			0.551637i
$534$	−25.0824			−1.08542
$535$	−7.29070	+	0.365600i	−0.315204	+	0.0158063i
$536$	22.9237			0.990154
$537$			17.5905i			0.759086i
$538$			22.8607i			0.985593i
$539$	14.9021			0.641878
$540$	−0.173340	+	0.00869233i	−0.00745936	+	0.000374058i
$541$	14.8091			0.636691			0.318346	−	0.947975i	$-0.396873\pi$
$541$	14.8091			0.636691			0.318346	+	0.947975i	$0.396873\pi$
$542$			7.63724i			0.328047i
$543$		−	23.0485i		−	0.989108i
$544$	6.71054			0.287712
$545$	−0.360711	−	7.19320i	−0.0154512	−	0.308123i
$546$	−21.2973			−0.911441
$547$		−	26.5735i		−	1.13620i	−0.822959	−	0.568100i	$-0.807679\pi$
$547$		−	26.5735i		−	1.13620i	0.822959	−	0.568100i	$-0.192321\pi$
$548$		−	1.64525i		−	0.0702815i
$549$	9.70671			0.414272
$550$	3.09568	+	30.7889i	0.132000	+	1.31284i
$551$		0			0
$552$			9.54231i			0.406148i
$553$		−	2.27069i		−	0.0965595i
$554$	8.23942			0.350059
$555$	−0.752192	−	15.0000i	−0.0319288	−	0.636714i
$556$	1.44515			0.0612881
$557$			16.0752i			0.681129i	0.940221	+	0.340565i	$0.110618\pi$
$557$			16.0752i			0.681129i	−0.940221	+	0.340565i	$0.889382\pi$
$558$		−	13.0138i		−	0.550919i
$559$	17.6527			0.746628
$560$	−31.5030	+	1.57976i	−1.33125	+	0.0667569i
$561$	65.7903			2.77767
$562$		−	40.3413i		−	1.70169i
$563$			2.03145i			0.0856155i	0.999083	+	0.0428078i	$0.0136303\pi$
$563$			2.03145i			0.0856155i	−0.999083	+	0.0428078i	$0.986370\pi$
$564$	−0.207886			−0.00875357
$565$	−10.5188	+	0.527478i	−0.442530	+	0.0221912i
$566$	22.2553			0.935459
$567$			27.5375i			1.15647i
$568$		−	34.5571i		−	1.44998i
$569$	−12.8224			−0.537543			−0.268772	−	0.963204i	$-0.586618\pi$
$569$	−12.8224			−0.537543			−0.268772	+	0.963204i	$0.586618\pi$
$570$		0			0
$571$	12.9168			0.540551			0.270276	−	0.962783i	$-0.412885\pi$
$571$	12.9168			0.540551			0.270276	+	0.962783i	$0.412885\pi$
$572$			1.40294i			0.0586600i
$573$			20.1742i			0.842789i
$574$	34.3142			1.43225
$575$	0.717130	+	7.13242i	0.0299064	+	0.297442i
$576$	22.5238			0.938493
$577$			8.11359i			0.337773i	0.985635	+	0.168887i	$0.0540172\pi$
$577$			8.11359i			0.337773i	−0.985635	+	0.168887i	$0.945983\pi$
$578$		−	34.1651i		−	1.42108i
$579$	−19.1789			−0.797046
$580$	0.00714329	+	0.142449i	0.000296609	+	0.00591489i
$581$	1.79713			0.0745577
$582$		−	48.4869i		−	2.00985i
$583$			30.2809i			1.25411i
$584$	−4.88431			−0.202114
$585$	12.6160	−	0.632643i	0.521607	−	0.0261566i
$586$	−11.5801			−0.478371
$587$		−	32.5617i		−	1.34396i	−0.740568	−	0.671982i	$-0.765443\pi$
$587$		−	32.5617i		−	1.34396i	0.740568	−	0.671982i	$-0.234557\pi$
$588$			1.66223i			0.0685492i
$589$		0			0
$590$	−10.3813	+	0.520581i	−0.427391	+	0.0214320i
$591$	−8.85914			−0.364416
$592$		−	11.7404i		−	0.482529i
$593$			11.4752i			0.471231i	0.971846	+	0.235616i	$0.0757106\pi$
$593$			11.4752i			0.471231i	−0.971846	+	0.235616i	$0.924289\pi$
$594$	−2.55591			−0.104870
$595$	2.30464	+	45.9584i	0.0944809	+	1.88411i
$596$	−2.80809			−0.115024
$597$			21.7762i			0.891239i
$598$			3.78352i			0.154720i
$599$	33.2099			1.35692			0.678460	−	0.734637i	$-0.262648\pi$
$599$	33.2099			1.35692			0.678460	+	0.734637i	$0.262648\pi$
$600$	33.1123	−	3.32928i	1.35180	−	0.135917i
$601$	−27.3180			−1.11433			−0.557163	−	0.830403i	$-0.688110\pi$
$601$	−27.3180			−1.11433			−0.557163	+	0.830403i	$0.688110\pi$
$602$		−	47.5628i		−	1.93851i
$603$			27.0800i			1.10278i
$604$	2.47000			0.100503
$605$	0.728578	+	14.5291i	0.0296209	+	0.590692i
$606$	−63.4549			−2.57768
$607$		−	25.7405i		−	1.04478i	−0.852708	−	0.522388i	$-0.825041\pi$
$607$		−	25.7405i		−	1.04478i	0.852708	−	0.522388i	$-0.174959\pi$
$608$		0			0
$609$	−2.73892			−0.110986
$610$	10.1269	−	0.507824i	0.410025	−	0.0205612i
$611$	0.794727			0.0321512
$612$			3.76820i			0.152320i
$613$		−	40.6039i		−	1.63997i	−0.572382	−	0.819987i	$-0.693980\pi$
$613$		−	40.6039i		−	1.63997i	0.572382	−	0.819987i	$-0.306020\pi$
$614$	23.2445			0.938073
$615$	−39.5860	+	1.98509i	−1.59626	+	0.0800464i
$616$	−36.4458			−1.46844
$617$			14.2113i			0.572125i	0.958211	+	0.286063i	$0.0923465\pi$
$617$			14.2113i			0.572125i	−0.958211	+	0.286063i	$0.907653\pi$
$618$		−	50.7936i		−	2.04322i
$619$	29.5635			1.18826			0.594129	−	0.804370i	$-0.297497\pi$
$619$	29.5635			1.18826			0.594129	+	0.804370i	$0.297497\pi$
$620$	−0.0584834	−	1.16626i	−0.00234875	−	0.0468381i
$621$	−0.592091			−0.0237598
$622$			26.5973i			1.06645i
$623$		−	22.1924i		−	0.889121i
$624$	19.2303			0.769828
$625$	24.4996	−	4.97694i	0.979984	−	0.199078i
$626$	−31.3591			−1.25336
$627$		0			0
$628$		−	2.03675i		−	0.0812753i
$629$	−17.1276			−0.682923
$630$	−1.70457	−	33.9921i	−0.0679118	−	1.35428i
$631$	−1.70763			−0.0679798			−0.0339899	−	0.999422i	$-0.510821\pi$
$631$	−1.70763			−0.0679798			−0.0339899	+	0.999422i	$0.510821\pi$
$632$			1.87276i			0.0744942i
$633$		−	29.3444i		−	1.16634i
$634$	−4.53280			−0.180020
$635$	1.32212	−	0.0662991i	0.0524666	−	0.00263100i
$636$	−3.37764			−0.133932
$637$		−	6.35454i		−	0.251776i
$638$			2.10043i			0.0831567i
$639$	40.8226			1.61492
$640$	28.2322	−	1.41573i	1.11597	−	0.0559618i
$641$	−2.76200			−0.109092			−0.0545462	−	0.998511i	$-0.517371\pi$
$641$	−2.76200			−0.109092			−0.0545462	+	0.998511i	$0.517371\pi$
$642$		−	11.9911i		−	0.473252i
$643$		−	21.6971i		−	0.855648i	−0.903862	−	0.427824i	$-0.859280\pi$
$643$		−	21.6971i		−	0.855648i	0.903862	−	0.427824i	$-0.140720\pi$
$644$	0.875668			0.0345061
$645$	2.75152	+	54.8700i	0.108341	+	2.16050i
$646$		0			0
$647$		−	28.0268i		−	1.10185i	−0.834556	−	0.550923i	$-0.814276\pi$
$647$		−	28.0268i		−	1.10185i	0.834556	−	0.550923i	$-0.185724\pi$
$648$		−	22.7116i		−	0.892196i
$649$	−13.1487			−0.516133
$650$	13.1290	−	1.32006i	0.514961	−	0.0517768i
$651$	22.4240			0.878866
$652$			1.58726i			0.0621620i
$653$		−	7.59308i		−	0.297140i	−0.988902	−	0.148570i	$-0.952533\pi$
$653$		−	7.59308i		−	0.297140i	0.988902	−	0.148570i	$-0.0474671\pi$
$654$	11.8308			0.462620
$655$	−2.30128	−	45.8914i	−0.0899183	−	1.79313i
$656$	−30.9838			−1.20972
$657$		−	5.76988i		−	0.225104i
$658$		−	2.14129i		−	0.0834761i
$659$	7.18394			0.279847			0.139923	−	0.990162i	$-0.455314\pi$
$659$	7.18394			0.279847			0.139923	+	0.990162i	$0.455314\pi$
$660$	−4.36079	+	0.218677i	−0.169743	+	0.00851198i
$661$	28.8678			1.12283			0.561413	−	0.827536i	$-0.310258\pi$
$661$	28.8678			1.12283			0.561413	+	0.827536i	$0.310258\pi$
$662$			38.3857i			1.49190i
$663$		−	28.0543i		−	1.08954i
$664$	−1.48219			−0.0575201
$665$		0			0
$666$	12.6681			0.490877
$667$			0.486575i			0.0188403i
$668$		−	3.74026i		−	0.144715i
$669$	−22.0946			−0.854226
$670$	1.41674	+	28.2522i	0.0547334	+	1.09148i
$671$	12.8265			0.495162
$672$		−	8.55222i		−	0.329909i
$673$		−	23.3191i		−	0.898885i	−0.893309	−	0.449442i	$-0.851623\pi$
$673$		−	23.3191i		−	0.898885i	0.893309	−	0.449442i	$-0.148377\pi$
$674$	−14.8767			−0.573029
$675$	0.206578	+	2.05458i	0.00795119	+	0.0790808i
$676$	−1.84499			−0.0709612
$677$		−	17.5099i		−	0.672958i	−0.941691	−	0.336479i	$-0.890764\pi$
$677$		−	17.5099i		−	0.672958i	0.941691	−	0.336479i	$-0.109236\pi$
$678$		−	17.3005i		−	0.664420i
$679$	42.9004			1.64636
$680$	−1.90075	−	37.9043i	−0.0728906	−	1.45356i
$681$	−65.5765			−2.51290
$682$		−	17.1966i		−	0.658491i
$683$		−	22.0114i		−	0.842243i	−0.907004	−	0.421122i	$-0.861637\pi$
$683$		−	22.0114i		−	0.842243i	0.907004	−	0.421122i	$-0.138363\pi$
$684$		0			0
$685$	−19.5501	+	0.980363i	−0.746971	+	0.0374577i
$686$	16.5283			0.631055
$687$		−	54.0972i		−	2.06394i
$688$			42.9466i			1.63732i
$689$	12.9124			0.491923
$690$	−11.7604	+	0.589737i	−0.447710	+	0.0224509i
$691$	−2.65623			−0.101048			−0.0505238	−	0.998723i	$-0.516089\pi$
$691$	−2.65623			−0.101048			−0.0505238	+	0.998723i	$0.516089\pi$
$692$		−	2.20287i		−	0.0837404i
$693$		−	43.0538i		−	1.63548i
$694$	10.0850			0.382821
$695$	−0.861130	−	17.1724i	−0.0326645	−	0.651387i
$696$	2.25893			0.0856244
$697$			45.2010i			1.71211i
$698$		−	46.7367i		−	1.76901i
$699$	24.8344			0.939322
$700$	−0.305517	−	3.03861i	−0.0115475	−	0.114848i
$701$	−7.36728			−0.278258			−0.139129	−	0.990274i	$-0.544430\pi$
$701$	−7.36728			−0.278258			−0.139129	+	0.990274i	$0.544430\pi$
$702$			1.08989i			0.0411352i
$703$		0			0
$704$	29.7632			1.12174
$705$	0.123874	+	2.47026i	0.00466537	+	0.0930354i
$706$	9.32848			0.351082
$707$		−	56.1438i		−	2.11150i
$708$		−	1.46666i		−	0.0551203i
$709$	5.99178			0.225026			0.112513	−	0.993650i	$-0.464110\pi$
$709$	5.99178			0.225026			0.112513	+	0.993650i	$0.464110\pi$
$710$	42.5897	−	2.13571i	1.59836	−	0.0801517i
$711$	−2.21230			−0.0829679
$712$			18.3032i			0.685943i
$713$		−	3.98368i		−	0.149190i
$714$	−75.5885			−2.82883
$715$	16.6709	−	0.835979i	0.623455	−	0.0312639i
$716$	−1.33133			−0.0497543
$717$		−	44.2916i		−	1.65410i
$718$		−	6.17798i		−	0.230560i
$719$	−13.5815			−0.506504			−0.253252	−	0.967400i	$-0.581500\pi$
$719$	−13.5815			−0.506504			−0.253252	+	0.967400i	$0.581500\pi$
$720$	1.53914	+	30.6930i	0.0573602	+	1.14386i
$721$	44.9412			1.67370
$722$		0			0
$723$			42.5725i			1.58329i
$724$	1.74443			0.0648311
$725$	1.68844	−	0.169764i	0.0627070	−	0.00630488i
$726$	−23.8962			−0.886872
$727$		−	41.2448i		−	1.52968i	−0.644218	−	0.764842i	$-0.722817\pi$
$727$		−	41.2448i		−	1.52968i	0.644218	−	0.764842i	$-0.277183\pi$
$728$			15.5412i			0.575995i
$729$	29.9060			1.10763
$730$	−0.301862	−	6.01963i	−0.0111724	−	0.222797i
$731$	62.6529			2.31730
$732$			1.43071i			0.0528807i
$733$			0.123848i			0.00457443i	0.999997	+	0.00228722i	$0.000728044\pi$
$733$			0.123848i			0.00457443i	−0.999997	+	0.00228722i	$0.999272\pi$
$734$	−24.5113			−0.904728
$735$	19.7519	−	0.990482i	0.728560	−	0.0365345i
$736$	−1.51932			−0.0560030
$737$			35.7837i			1.31811i
$738$		−	33.4319i		−	1.23065i
$739$	36.5134			1.34317			0.671584	−	0.740928i	$-0.265614\pi$
$739$	36.5134			1.34317			0.671584	+	0.740928i	$0.265614\pi$
$740$	1.13527	−	0.0569295i	0.0417334	−	0.00209277i
$741$		0			0
$742$		−	34.7907i		−	1.27721i
$743$			9.06197i			0.332451i	0.986088	+	0.166226i	$0.0531580\pi$
$743$			9.06197i			0.332451i	−0.986088	+	0.166226i	$0.946842\pi$
$744$	−18.4942			−0.678032
$745$	1.67328	+	33.3680i	0.0613041	+	1.22251i
$746$	−54.7299			−2.00380
$747$		−	1.75092i		−	0.0640630i
$748$			4.97933i			0.182062i
$749$	10.6095			0.387664
$750$	6.14956	+	40.6032i	0.224550	+	1.48262i
$751$	4.08610			0.149104			0.0745519	−	0.997217i	$-0.476247\pi$
$751$	4.08610			0.149104			0.0745519	+	0.997217i	$0.476247\pi$
$752$			1.93346i			0.0705062i
$753$			24.0768i			0.877407i
$754$	0.895663			0.0326181
$755$	−1.47181	−	29.3504i	−0.0535647	−	1.06817i
$756$	0.252247			0.00917413
$757$		−	34.4597i		−	1.25246i	−0.779638	−	0.626230i	$-0.784597\pi$
$757$		−	34.4597i		−	1.25246i	0.779638	−	0.626230i	$-0.215403\pi$
$758$			46.6155i			1.69315i
$759$	−14.8955			−0.540671
$760$		0			0
$761$	20.5813			0.746072			0.373036	−	0.927817i	$-0.378317\pi$
$761$	20.5813			0.746072			0.373036	+	0.927817i	$0.378317\pi$
$762$			2.17451i			0.0787741i
$763$			10.4676i			0.378954i
$764$	−1.52688			−0.0552406
$765$	44.7767	−	2.24538i	1.61890	−	0.0811818i
$766$	−4.58266			−0.165578
$767$			5.60688i			0.202453i
$768$			11.1049i			0.400714i
$769$	30.3550			1.09463			0.547315	−	0.836927i	$-0.315650\pi$
$769$	30.3550			1.09463			0.547315	+	0.836927i	$0.315650\pi$
$770$	−2.25244	−	44.9174i	−0.0811722	−	1.61871i
$771$	−24.9578			−0.898834
$772$		−	1.45155i		−	0.0522424i
$773$			19.5225i			0.702176i	0.936343	+	0.351088i	$0.114188\pi$
$773$			19.5225i			0.702176i	−0.936343	+	0.351088i	$0.885812\pi$
$774$	−46.3398			−1.66565
$775$	−13.8235	+	1.38989i	−0.496556	+	0.0499263i
$776$	−35.3822			−1.27015
$777$			21.8282i			0.783083i
$778$		−	38.5054i		−	1.38048i
$779$		0			0
$780$	0.0932479	+	1.85952i	0.00333881	+	0.0665816i
$781$	53.9433			1.93024
$782$			13.4285i			0.480202i
$783$			0.140164i			0.00500905i
$784$	15.4597			0.552134
$785$	−24.2023	+	1.21365i	−0.863817	+	0.0433171i
$786$	75.4783			2.69222
$787$			35.2236i			1.25559i	0.778380	+	0.627793i	$0.216042\pi$
$787$			35.2236i			1.25559i	−0.778380	+	0.627793i	$0.783958\pi$
$788$		−	0.670503i		−	0.0238857i
$789$	−54.2098			−1.92992
$790$	−2.30807	+	0.115741i	−0.0821173	+	0.00411787i
$791$	15.3071			0.544259
$792$			35.5087i			1.26175i
$793$		−	5.46948i		−	0.194227i
$794$	18.7273			0.664608
$795$	2.01265	+	40.1357i	0.0713814	+	1.42347i
$796$	−1.64813			−0.0584163
$797$		−	28.7940i		−	1.01994i	−0.860193	−	0.509969i	$-0.829657\pi$
$797$		−	28.7940i		−	1.01994i	0.860193	−	0.509969i	$-0.170343\pi$
$798$		0			0
$799$	2.82065			0.0997874
$800$	0.530086	+	5.27212i	0.0187414	+	0.186397i
$801$	−21.6218			−0.763969
$802$			13.6406i			0.481666i
$803$		−	7.62436i		−	0.269058i
$804$	−3.99144			−0.140767
$805$	−0.521789	−	10.4054i	−0.0183906	−	0.366741i
$806$	−7.33295			−0.258292
$807$			38.3781i			1.35097i
$808$			46.3047i			1.62899i
$809$	48.0068			1.68783			0.843915	−	0.536478i	$-0.180245\pi$
$809$	48.0068			1.68783			0.843915	+	0.536478i	$0.180245\pi$
$810$	27.9908	−	1.40363i	0.983496	−	0.0493186i
$811$	9.62886			0.338115			0.169057	−	0.985606i	$-0.445928\pi$
$811$	9.62886			0.338115			0.169057	+	0.985606i	$0.445928\pi$
$812$		−	0.207294i		−	0.00727461i
$813$			12.8213i			0.449662i
$814$	16.7397			0.586725
$815$	18.8611	−	0.945812i	0.660675	−	0.0331303i
$816$	68.2523			2.38931
$817$		0			0
$818$			50.9680i			1.78205i
$819$	−18.3590			−0.641514
$820$	−0.150241	−	2.99606i	−0.00524664	−	0.104627i
$821$	−25.7257			−0.897834			−0.448917	−	0.893573i	$-0.648190\pi$
$821$	−25.7257			−0.897834			−0.448917	+	0.893573i	$0.648190\pi$
$822$		−	32.1544i		−	1.12151i
$823$			13.4584i			0.469132i	0.972100	+	0.234566i	$0.0753668\pi$
$823$			13.4584i			0.469132i	−0.972100	+	0.234566i	$0.924633\pi$
$824$	−37.0654			−1.29123
$825$	5.19697	+	51.6879i	0.180935	+	1.79954i
$826$	15.1070			0.525640
$827$		−	0.172408i		−	0.00599520i	−0.999996	−	0.00299760i	$-0.999046\pi$
$827$		−	0.172408i		−	0.00599520i	0.999996	−	0.00299760i	$-0.000954168\pi$
$828$		−	0.853152i		−	0.0296491i
$829$	−42.3791			−1.47189			−0.735943	−	0.677044i	$-0.763261\pi$
$829$	−42.3791			−1.47189			−0.735943	+	0.677044i	$0.763261\pi$
$830$	−0.0916028	−	1.82672i	−0.00317958	−	0.0634063i
$831$	13.8322			0.479834
$832$		−	12.6916i		−	0.440002i
$833$		−	22.5536i		−	0.781435i
$834$	28.2437			0.978001
$835$	−44.4447	+	2.22873i	−1.53807	+	0.0771284i
$836$		0			0
$837$		−	1.14755i		−	0.0396651i
$838$			11.6270i			0.401647i
$839$	45.1399			1.55840			0.779200	−	0.626775i	$-0.215625\pi$
$839$	45.1399			1.55840			0.779200	+	0.626775i	$0.215625\pi$
$840$	−48.3069	+	2.42241i	−1.66675	+	0.0835810i
$841$	−28.8848			−0.996028
$842$		−	15.5198i		−	0.534847i
$843$		−	67.7243i		−	2.33255i
$844$	2.22093			0.0764475
$845$	1.09939	+	21.9236i	0.0378200	+	0.754196i
$846$	−2.08623			−0.0717260
$847$		−	21.1430i		−	0.726481i
$848$			31.4141i			1.07876i
$849$	37.3618			1.28225
$850$	46.5975	−	4.68515i	1.59828	−	0.160699i
$851$	3.87784			0.132931
$852$			6.01702i			0.206140i
$853$			46.3405i			1.58667i	0.608787	+	0.793333i	$0.291656\pi$
$853$			46.3405i			1.58667i	−0.608787	+	0.793333i	$0.708344\pi$
$854$	−14.7368			−0.504283
$855$		0			0
$856$	−8.75023			−0.299077
$857$		−	21.8934i		−	0.747863i	−0.927456	−	0.373931i	$-0.878010\pi$
$857$		−	21.8934i		−	0.747863i	0.927456	−	0.373931i	$-0.121990\pi$
$858$			27.4188i			0.936063i
$859$	−33.4020			−1.13966			−0.569830	−	0.821762i	$-0.692991\pi$
$859$	−33.4020			−1.13966			−0.569830	+	0.821762i	$0.692991\pi$
$860$	−4.15283	+	0.208248i	−0.141610	+	0.00710121i
$861$	57.6062			1.96321
$862$		−	44.2158i		−	1.50600i
$863$		−	27.1254i		−	0.923359i	−0.887047	−	0.461680i	$-0.847247\pi$
$863$		−	27.1254i		−	0.923359i	0.887047	−	0.461680i	$-0.152753\pi$
$864$	−0.437660			−0.0148895
$865$	−26.1762	+	1.31263i	−0.890017	+	0.0446309i
$866$	10.0580			0.341785
$867$		−	57.3558i		−	1.94791i
$868$			1.69716i			0.0576052i
$869$	−2.92335			−0.0991680
$870$	0.139607	+	2.78400i	0.00473312	+	0.0943864i
$871$	15.2589			0.517027
$872$		−	8.63321i		−	0.292358i
$873$		−	41.7973i		−	1.41462i
$874$		0			0
$875$	−35.9250	+	5.44102i	−1.21449	+	0.183940i
$876$	0.850447			0.0287339
$877$			49.0823i			1.65739i	0.559700	+	0.828695i	$0.310916\pi$
$877$			49.0823i			1.65739i	−0.559700	+	0.828695i	$0.689084\pi$
$878$			11.7832i			0.397662i
$879$	−19.4406			−0.655714
$880$	2.03383	+	40.5580i	0.0685602	+	1.36721i
$881$	37.9778			1.27951			0.639753	−	0.768581i	$-0.279037\pi$
$881$	37.9778			1.27951			0.639753	+	0.768581i	$0.279037\pi$
$882$			16.6812i			0.561686i
$883$		−	33.2100i		−	1.11761i	−0.829300	−	0.558803i	$-0.811261\pi$
$883$		−	33.2100i		−	1.11761i	0.829300	−	0.558803i	$-0.188739\pi$
$884$	2.12328			0.0714137
$885$	−17.4279	+	0.873944i	−0.585834	+	0.0293773i
$886$	32.2301			1.08279
$887$		−	26.2525i		−	0.881474i	−0.897636	−	0.440737i	$-0.854717\pi$
$887$		−	26.2525i		−	0.881474i	0.897636	−	0.440737i	$-0.145283\pi$
$888$		−	18.0029i		−	0.604136i
$889$	−1.92396			−0.0645277
$890$	−22.5577	+	1.13118i	−0.756137	+	0.0379174i
$891$	35.4526			1.18771
$892$		−	1.67222i		−	0.0559902i
$893$		0			0
$894$	−54.8808			−1.83549
$895$	0.793309	+	15.8199i	0.0265174	+	0.528802i
$896$	−41.0839			−1.37252
$897$			6.35172i			0.212078i
$898$			27.7843i			0.927173i
$899$	−0.943045			−0.0314523
$900$	−2.96047	+	0.297661i	−0.0986825	+	0.00992204i
$901$	45.8287			1.52677
$902$		−	44.1772i		−	1.47094i
$903$		−	79.8477i		−	2.65716i
$904$	−12.6246			−0.419888
$905$	−1.03946	−	20.7286i	−0.0345528	−	0.689043i
$906$	48.2731			1.60377
$907$		−	7.92760i		−	0.263231i	−0.991301	−	0.131616i	$-0.957983\pi$
$907$		−	7.92760i		−	0.263231i	0.991301	−	0.131616i	$-0.0420165\pi$
$908$		−	4.96315i		−	0.164708i
$909$	−54.7002			−1.81429
$910$	−19.1537	+	0.960482i	−0.634938	+	0.0318397i
$911$	0.619746			0.0205331			0.0102665	−	0.999947i	$-0.496732\pi$
$911$	0.619746			0.0205331			0.0102665	+	0.999947i	$0.496732\pi$
$912$		0			0
$913$		−	2.31369i		−	0.0765718i
$914$	41.7670			1.38153
$915$	17.0009	−	0.852527i	0.562031	−	0.0281837i
$916$	4.09434			0.135281
$917$			66.7818i			2.20533i
$918$			3.86824i			0.127671i
$919$	35.0574			1.15644			0.578219	−	0.815882i	$-0.303748\pi$
$919$	35.0574			1.15644			0.578219	+	0.815882i	$0.303748\pi$
$920$	0.430346	+	8.58184i	0.0141881	+	0.282935i
$921$	39.0226			1.28584
$922$		−	0.289929i		−	0.00954830i
$923$		−	23.0025i		−	0.757135i
$924$	6.34588			0.208764
$925$	−1.35296	−	13.4563i	−0.0444851	−	0.442439i
$926$	−20.6553			−0.678775
$927$		−	43.7857i		−	1.43811i
$928$			0.359665i			0.0118066i
$929$	−12.0434			−0.395132			−0.197566	−	0.980290i	$-0.563304\pi$
$929$	−12.0434			−0.395132			−0.197566	+	0.980290i	$0.563304\pi$
$930$	−1.14299	−	22.7931i	−0.0374800	−	0.747416i
$931$		0			0
$932$			1.87959i			0.0615679i
$933$			44.6511i			1.46181i
$934$	−47.4850			−1.55376
$935$	59.1683	−	2.96706i	1.93501	−	0.0970333i
$936$	15.1416			0.494918
$937$			14.9304i			0.487757i	0.969806	+	0.243878i	$0.0784197\pi$
$937$			14.9304i			0.487757i	−0.969806	+	0.243878i	$0.921580\pi$
$938$		−	41.1131i		−	1.34239i
$939$	−52.6452			−1.71801
$940$	−0.186961	+	0.00937539i	−0.00609800	+	0.000305792i
$941$	−19.4198			−0.633068			−0.316534	−	0.948581i	$-0.602519\pi$
$941$	−19.4198			−0.633068			−0.316534	+	0.948581i	$0.602519\pi$
$942$		−	39.8059i		−	1.29695i
$943$		−	10.2339i		−	0.333261i
$944$	−13.6408			−0.443970
$945$	−0.150308	−	2.99739i	−0.00488951	−	0.0975052i
$946$	−61.2338			−1.99088
$947$			16.7369i			0.543878i	0.962315	+	0.271939i	$0.0876648\pi$
$947$			16.7369i			0.543878i	−0.962315	+	0.271939i	$0.912335\pi$
$948$		−	0.326081i		−	0.0105906i
$949$	−3.25117			−0.105538
$950$		0			0
$951$	−7.60959			−0.246758
$952$			55.1589i			1.78771i
$953$		−	53.1772i		−	1.72258i	−0.508114	−	0.861290i	$-0.669657\pi$
$953$		−	53.1772i		−	1.72258i	0.508114	−	0.861290i	$-0.330343\pi$
$954$	−33.8962			−1.09743
$955$	0.909831	+	18.1436i	0.0294414	+	0.587113i
$956$	3.35220			0.108418
$957$			3.52616i			0.113985i
$958$			2.93209i			0.0947317i
$959$	28.4496			0.918686
$960$	39.4495	−	1.97824i	1.27323	−	0.0638474i
$961$	−23.2791			−0.750939
$962$		−	7.13812i		−	0.230142i
$963$		−	10.3367i		−	0.333096i
$964$	−3.22209			−0.103777
$965$	−17.2484	+	0.864942i	−0.555247	+	0.0278435i
$966$	17.1139			0.550630
$967$			30.0281i			0.965637i	0.875720	+	0.482819i	$0.160387\pi$
$967$			30.0281i			0.965637i	−0.875720	+	0.482819i	$0.839613\pi$
$968$			17.4377i			0.560469i
$969$		0			0
$970$	−2.18670	−	43.6065i	−0.0702107	−	1.40012i
$971$	−24.1413			−0.774732			−0.387366	−	0.921926i	$-0.626615\pi$
$971$	−24.1413			−0.774732			−0.387366	+	0.921926i	$0.626615\pi$
$972$			4.18736i			0.134310i
$973$			24.9896i			0.801128i
$974$	−12.7048			−0.407089
$975$	22.0407	−	2.21609i	0.705869	−	0.0709717i
$976$	13.3065			0.425931
$977$			9.57680i			0.306389i	0.988196	+	0.153195i	$0.0489561\pi$
$977$			9.57680i			0.306389i	−0.988196	+	0.153195i	$0.951044\pi$
$978$			31.0211i			0.991947i
$979$	−28.5712			−0.913140
$980$	0.0749645	+	1.49492i	0.00239465	+	0.0477535i
$981$	10.1985			0.325613
$982$			38.3108i			1.22255i
$983$			31.1715i			0.994216i	0.867689	+	0.497108i	$0.165605\pi$
$983$			31.1715i			0.994216i	−0.867689	+	0.497108i	$0.834395\pi$
$984$	−47.5108			−1.51459
$985$	−7.96743	+	0.399536i	−0.253864	+	0.0127303i
$986$	3.17889			0.101236
$987$		−	3.59476i		−	0.114422i
$988$		0			0
$989$	−14.1851			−0.451061
$990$	−43.7625	+	2.19452i	−1.39086	+	0.0697464i
$991$	48.6643			1.54587			0.772937	−	0.634483i	$-0.218787\pi$
$991$	48.6643			1.54587			0.772937	+	0.634483i	$0.218787\pi$
$992$		−	2.94464i		−	0.0934925i
$993$			64.4414i			2.04499i
$994$	−61.9771			−1.96580
$995$	0.982078	+	19.5843i	0.0311340	+	0.620865i
$996$	0.258076			0.00817746
$997$			31.8954i			1.01014i	0.863080	+	0.505068i	$0.168533\pi$
$997$			31.8954i			1.01014i	−0.863080	+	0.505068i	$0.831467\pi$
$998$			31.3641i			0.992812i
$999$	1.11706			0.0353422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.l.1084.18		24
5.2	odd	4		9025.2.a.ct.1.7		24
5.3	odd	4		9025.2.a.ct.1.18		24
5.4	even	2	inner	1805.2.b.l.1084.7		24
19.3	odd	18		95.2.p.a.9.7	yes	48
19.13	odd	18		95.2.p.a.74.2	yes	48
19.18	odd	2		1805.2.b.k.1084.7		24
57.32	even	18		855.2.da.b.739.7		48
57.41	even	18		855.2.da.b.199.2		48
95.3	even	36		475.2.l.f.351.2		48
95.13	even	36		475.2.l.f.226.2		48
95.18	even	4		9025.2.a.cu.1.7		24
95.22	even	36		475.2.l.f.351.7		48
95.32	even	36		475.2.l.f.226.7		48
95.37	even	4		9025.2.a.cu.1.18		24
95.79	odd	18		95.2.p.a.9.2	✓	48
95.89	odd	18		95.2.p.a.74.7	yes	48
95.94	odd	2		1805.2.b.k.1084.18		24
285.89	even	18		855.2.da.b.739.2		48
285.269	even	18		855.2.da.b.199.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.2	✓	48	95.79	odd	18
95.2.p.a.9.7	yes	48	19.3	odd	18
95.2.p.a.74.2	yes	48	19.13	odd	18
95.2.p.a.74.7	yes	48	95.89	odd	18
475.2.l.f.226.2		48	95.13	even	36
475.2.l.f.226.7		48	95.32	even	36
475.2.l.f.351.2		48	95.3	even	36
475.2.l.f.351.7		48	95.22	even	36
855.2.da.b.199.2		48	57.41	even	18
855.2.da.b.199.7		48	285.269	even	18
855.2.da.b.739.2		48	285.89	even	18
855.2.da.b.739.7		48	57.32	even	18
1805.2.b.k.1084.7		24	19.18	odd	2
1805.2.b.k.1084.18		24	95.94	odd	2
1805.2.b.l.1084.7		24	5.4	even	2	inner
1805.2.b.l.1084.18		24	1.1	even	1	trivial
9025.2.a.ct.1.7		24	5.2	odd	4
9025.2.a.ct.1.18		24	5.3	odd	4
9025.2.a.cu.1.7		24	95.18	even	4
9025.2.a.cu.1.18		24	95.37	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.47917i q^{2} +2.48321i q^{3} -0.187941 q^{4} +(0.111989 + 2.23326i) q^{5} -3.67308 q^{6} -3.24988i q^{7} +2.68034i q^{8} -3.16631 q^{9} +(-3.30337 + 0.165651i) q^{10} -4.18399 q^{11} -0.466696i q^{12} +1.78413i q^{13} +4.80712 q^{14} +(-5.54565 + 0.278093i) q^{15} -4.34056 q^{16} +6.33226i q^{17} -4.68351i q^{18} +(-0.0210474 - 0.419722i) q^{20} +8.07011 q^{21} -6.18883i q^{22} -1.43368i q^{23} -6.65584 q^{24} +(-4.97492 + 0.500204i) q^{25} -2.63904 q^{26} -0.412988i q^{27} +0.610785i q^{28} -0.339390 q^{29} +(-0.411347 - 8.20295i) q^{30} +2.77865 q^{31} -1.05974i q^{32} -10.3897i q^{33} -9.36648 q^{34} +(7.25782 - 0.363952i) q^{35} +0.595080 q^{36} +2.70482i q^{37} -4.43037 q^{39} +(-5.98590 + 0.300170i) q^{40} +7.13821 q^{41} +11.9371i q^{42} -9.89425i q^{43} +0.786344 q^{44} +(-0.354594 - 7.07120i) q^{45} +2.12065 q^{46} -0.445441i q^{47} -10.7785i q^{48} -3.56169 q^{49} +(-0.739886 - 7.35874i) q^{50} -15.7243 q^{51} -0.335312i q^{52} -7.23734i q^{53} +0.610879 q^{54} +(-0.468563 - 9.34395i) q^{55} +8.71078 q^{56} -0.502015i q^{58} +3.14263 q^{59} +(1.04226 - 0.0522651i) q^{60} -3.06562 q^{61} +4.11009i q^{62} +10.2901i q^{63} -7.11359 q^{64} +(-3.98444 + 0.199804i) q^{65} +15.3681 q^{66} -8.55254i q^{67} -1.19009i q^{68} +3.56011 q^{69} +(0.538346 + 10.7355i) q^{70} -12.8928 q^{71} -8.48680i q^{72} +1.82227i q^{73} -4.00089 q^{74} +(-1.24211 - 12.3537i) q^{75} +13.5974i q^{77} -6.55327i q^{78} +0.698700 q^{79} +(-0.486097 - 9.69361i) q^{80} -8.47340 q^{81} +10.5586i q^{82} +0.552985i q^{83} -1.51671 q^{84} +(-14.1416 + 0.709146i) q^{85} +14.6353 q^{86} -0.842775i q^{87} -11.2145i q^{88} +6.82870 q^{89} +(10.4595 - 0.524504i) q^{90} +5.79822 q^{91} +0.269446i q^{92} +6.89995i q^{93} +0.658883 q^{94} +2.63155 q^{96} +13.2006i q^{97} -5.26835i q^{98} +13.2478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} + 6 q^{10} + 12 q^{11} + 24 q^{14} + 9 q^{15} + 6 q^{16} + 21 q^{20} - 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} + 36 q^{29} - 18 q^{30} - 42 q^{31} + 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 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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