LMFDB - Embedded newform 1690.2.b.f.339.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(339,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, 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("1690.339"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-18,0,-14,0,0,-16,2,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 29x^{16} + 336x^{14} + 1977x^{12} + 6147x^{10} + 9369x^{8} + 5559x^{6} + 1342x^{4} + 116x^{2} + 1 $ x^18 + 29x^16 + 336x^14 + 1977x^12 + 6147x^10 + 9369x^8 + 5559x^6 + 1342x^4 + 116x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.5
Root			$-2.20982i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.f.339.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -0.666723i q^{3} -1.00000 q^{4} +(-2.18940 + 0.454429i) q^{5} -0.666723 q^{6} -2.41461i q^{7} +1.00000i q^{8} +2.55548 q^{9} +(0.454429 + 2.18940i) q^{10} +1.46118 q^{11} +0.666723i q^{12} -2.41461 q^{14} +(0.302978 + 1.45973i) q^{15} +1.00000 q^{16} +6.74749i q^{17} -2.55548i q^{18} +7.41659 q^{19} +(2.18940 - 0.454429i) q^{20} -1.60988 q^{21} -1.46118i q^{22} +7.48975i q^{23} +0.666723 q^{24} +(4.58699 - 1.98986i) q^{25} -3.70397i q^{27} +2.41461i q^{28} +0.696556 q^{29} +(1.45973 - 0.302978i) q^{30} -1.36837 q^{31} -1.00000i q^{32} -0.974200i q^{33} +6.74749 q^{34} +(1.09727 + 5.28656i) q^{35} -2.55548 q^{36} -9.25191i q^{37} -7.41659i q^{38} +(-0.454429 - 2.18940i) q^{40} -4.24884 q^{41} +1.60988i q^{42} -2.38573i q^{43} -1.46118 q^{44} +(-5.59498 + 1.16128i) q^{45} +7.48975 q^{46} +2.77456i q^{47} -0.666723i q^{48} +1.16965 q^{49} +(-1.98986 - 4.58699i) q^{50} +4.49870 q^{51} -7.04744i q^{53} -3.70397 q^{54} +(-3.19911 + 0.664001i) q^{55} +2.41461 q^{56} -4.94481i q^{57} -0.696556i q^{58} -0.0690364 q^{59} +(-0.302978 - 1.45973i) q^{60} +5.91472 q^{61} +1.36837i q^{62} -6.17050i q^{63} -1.00000 q^{64} -0.974200 q^{66} +10.9958i q^{67} -6.74749i q^{68} +4.99359 q^{69} +(5.28656 - 1.09727i) q^{70} +3.60919 q^{71} +2.55548i q^{72} -9.30157i q^{73} -9.25191 q^{74} +(-1.32668 - 3.05825i) q^{75} -7.41659 q^{76} -3.52818i q^{77} +0.766732 q^{79} +(-2.18940 + 0.454429i) q^{80} +5.19692 q^{81} +4.24884i q^{82} -16.5800i q^{83} +1.60988 q^{84} +(-3.06625 - 14.7730i) q^{85} -2.38573 q^{86} -0.464410i q^{87} +1.46118i q^{88} +17.7481 q^{89} +(1.16128 + 5.59498i) q^{90} -7.48975i q^{92} +0.912326i q^{93} +2.77456 q^{94} +(-16.2379 + 3.37031i) q^{95} -0.666723 q^{96} -10.5209i q^{97} -1.16965i q^{98} +3.73401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{4} - 14 q^{6} - 16 q^{9} + 2 q^{10} - 8 q^{11} - 2 q^{14} - 8 q^{15} + 18 q^{16} + 12 q^{19} - 16 q^{21} + 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} + 12 q^{31} + 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots + 32 q^{99}+O(q^{100}) $ 18 * q - 18 * q^4 - 14 * q^6 - 16 * q^9 + 2 * q^10 - 8 * q^11 - 2 * q^14 - 8 * q^15 + 18 * q^16 + 12 * q^19 - 16 * q^21 + 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 + 12 * q^31 + 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 - 54 * q^41 + 8 * q^44 - 20 * q^45 - 22 * q^46 + 20 * q^49 - 8 * q^50 + 24 * q^51 + 68 * q^54 + 2 * q^56 + 40 * q^59 + 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 + 6 * q^70 + 20 * q^71 + 20 * q^74 - 72 * q^75 - 12 * q^76 + 28 * q^79 + 106 * q^81 + 16 * q^84 - 56 * q^85 - 82 * q^86 + 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 - 14 * q^96 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.666723i		−	0.384933i	−0.981304	−	0.192466i	$-0.938351\pi$
$3$		−	0.666723i		−	0.384933i	0.981304	−	0.192466i	$-0.0616486\pi$
$4$	−1.00000			−0.500000
$5$	−2.18940	+	0.454429i	−0.979132	+	0.203227i
$5$	−2.18940	+	0.454429i	−0.979132	+	0.203227i
$6$	−0.666723			−0.272188
$7$		−	2.41461i		−	0.912638i	−0.889816	−	0.456319i	$-0.849168\pi$
$7$		−	2.41461i		−	0.912638i	0.889816	−	0.456319i	$-0.150832\pi$
$8$			1.00000i			0.353553i
$9$	2.55548			0.851827
$10$	0.454429	+	2.18940i	0.143703	+	0.692351i
$11$	1.46118			0.440561			0.220281	−	0.975437i	$-0.429303\pi$
$11$	1.46118			0.440561			0.220281	+	0.975437i	$0.429303\pi$
$12$			0.666723i			0.192466i
$13$		0			0
$13$		0			0
$14$	−2.41461			−0.645332
$15$	0.302978	+	1.45973i	0.0782286	+	0.376900i
$16$	1.00000			0.250000
$17$			6.74749i			1.63651i	0.574858	+	0.818253i	$0.305057\pi$
$17$			6.74749i			1.63651i	−0.574858	+	0.818253i	$0.694943\pi$
$18$		−	2.55548i		−	0.602333i
$19$	7.41659			1.70148			0.850741	−	0.525585i	$-0.176154\pi$
$19$	7.41659			1.70148			0.850741	+	0.525585i	$0.176154\pi$
$20$	2.18940	−	0.454429i	0.489566	−	0.101613i
$21$	−1.60988			−0.351304
$22$		−	1.46118i		−	0.311524i
$23$			7.48975i			1.56172i	0.624705	+	0.780861i	$0.285219\pi$
$23$			7.48975i			1.56172i	−0.624705	+	0.780861i	$0.714781\pi$
$24$	0.666723			0.136094
$25$	4.58699	−	1.98986i	0.917398	−	0.397972i
$26$		0			0
$27$		−	3.70397i		−	0.712829i
$28$			2.41461i			0.456319i
$29$	0.696556			0.129347			0.0646736	−	0.997906i	$-0.479399\pi$
$29$	0.696556			0.129347			0.0646736	+	0.997906i	$0.479399\pi$
$30$	1.45973	−	0.302978i	0.266508	−	0.0553160i
$31$	−1.36837			−0.245767			−0.122884	−	0.992421i	$-0.539214\pi$
$31$	−1.36837			−0.245767			−0.122884	+	0.992421i	$0.539214\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	0.974200i		−	0.169586i
$34$	6.74749			1.15718
$35$	1.09727	+	5.28656i	0.185473	+	0.893593i
$36$	−2.55548			−0.425913
$37$		−	9.25191i		−	1.52101i	−0.649335	−	0.760503i	$-0.724953\pi$
$37$		−	9.25191i		−	1.52101i	0.649335	−	0.760503i	$-0.275047\pi$
$38$		−	7.41659i		−	1.20313i
$39$		0			0
$40$	−0.454429	−	2.18940i	−0.0718515	−	0.346175i
$41$	−4.24884			−0.663558			−0.331779	−	0.943357i	$-0.607649\pi$
$41$	−4.24884			−0.663558			−0.331779	+	0.943357i	$0.607649\pi$
$42$			1.60988i			0.248409i
$43$		−	2.38573i		−	0.363821i	−0.983315	−	0.181910i	$-0.941772\pi$
$43$		−	2.38573i		−	0.363821i	0.983315	−	0.181910i	$-0.0582281\pi$
$44$	−1.46118			−0.220281
$45$	−5.59498	+	1.16128i	−0.834051	+	0.173114i
$46$	7.48975			1.10430
$47$			2.77456i			0.404711i	0.979312	+	0.202356i	$0.0648597\pi$
$47$			2.77456i			0.404711i	−0.979312	+	0.202356i	$0.935140\pi$
$48$		−	0.666723i		−	0.0962331i
$49$	1.16965			0.167092
$50$	−1.98986	−	4.58699i	−0.281408	−	0.648698i
$51$	4.49870			0.629944
$52$		0			0
$53$		−	7.04744i		−	0.968040i	−0.875057	−	0.484020i	$-0.839176\pi$
$53$		−	7.04744i		−	0.968040i	0.875057	−	0.484020i	$-0.160824\pi$
$54$	−3.70397			−0.504046
$55$	−3.19911	+	0.664001i	−0.431368	+	0.0895339i
$56$	2.41461			0.322666
$57$		−	4.94481i		−	0.654956i
$58$		−	0.696556i		−	0.0914623i
$59$	−0.0690364			−0.00898777			−0.00449389	−	0.999990i	$-0.501430\pi$
$59$	−0.0690364			−0.00898777			−0.00449389	+	0.999990i	$0.501430\pi$
$60$	−0.302978	−	1.45973i	−0.0391143	−	0.188450i
$61$	5.91472			0.757302			0.378651	−	0.925539i	$-0.376388\pi$
$61$	5.91472			0.757302			0.378651	+	0.925539i	$0.376388\pi$
$62$			1.36837i			0.173784i
$63$		−	6.17050i		−	0.777409i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.974200			−0.119916
$67$			10.9958i			1.34335i	0.740847	+	0.671674i	$0.234424\pi$
$67$			10.9958i			1.34335i	−0.740847	+	0.671674i	$0.765576\pi$
$68$		−	6.74749i		−	0.818253i
$69$	4.99359			0.601157
$70$	5.28656	−	1.09727i	0.631865	−	0.131149i
$71$	3.60919			0.428332			0.214166	−	0.976797i	$-0.431297\pi$
$71$	3.60919			0.428332			0.214166	+	0.976797i	$0.431297\pi$
$72$			2.55548i			0.301166i
$73$		−	9.30157i		−	1.08867i	−0.838869	−	0.544333i	$-0.816783\pi$
$73$		−	9.30157i		−	1.08867i	0.838869	−	0.544333i	$-0.183217\pi$
$74$	−9.25191			−1.07551
$75$	−1.32668	−	3.05825i	−0.153192	−	0.353136i
$76$	−7.41659			−0.850741
$77$		−	3.52818i		−	0.402073i
$78$		0			0
$79$	0.766732			0.0862641			0.0431320	−	0.999069i	$-0.486266\pi$
$79$	0.766732			0.0862641			0.0431320	+	0.999069i	$0.486266\pi$
$80$	−2.18940	+	0.454429i	−0.244783	+	0.0508067i
$81$	5.19692			0.577436
$82$			4.24884i			0.469206i
$83$		−	16.5800i		−	1.81989i	−0.414725	−	0.909947i	$-0.636122\pi$
$83$		−	16.5800i		−	1.81989i	0.414725	−	0.909947i	$-0.363878\pi$
$84$	1.60988			0.175652
$85$	−3.06625	−	14.7730i	−0.332582	−	1.60235i
$86$	−2.38573			−0.257260
$87$		−	0.464410i		−	0.0497899i
$88$			1.46118i			0.155762i
$89$	17.7481			1.88130			0.940648	−	0.339384i	$-0.110219\pi$
$89$	17.7481			1.88130			0.940648	+	0.339384i	$0.110219\pi$
$90$	1.16128	+	5.59498i	0.122410	+	0.589763i
$91$		0			0
$92$		−	7.48975i		−	0.780861i
$93$			0.912326i			0.0946038i
$94$	2.77456			0.286174
$95$	−16.2379	+	3.37031i	−1.66597	+	0.345787i
$96$	−0.666723			−0.0680471
$97$		−	10.5209i		−	1.06824i	−0.845409	−	0.534120i	$-0.820643\pi$
$97$		−	10.5209i		−	1.06824i	0.845409	−	0.534120i	$-0.179357\pi$
$98$		−	1.16965i		−	0.118152i
$99$	3.73401			0.375282
$100$	−4.58699	+	1.98986i	−0.458699	+	0.198986i
$101$	14.2473			1.41765			0.708827	−	0.705382i	$-0.249225\pi$
$101$	14.2473			1.41765			0.708827	+	0.705382i	$0.249225\pi$
$102$		−	4.49870i		−	0.445438i
$103$		−	9.72411i		−	0.958145i	−0.877775	−	0.479072i	$-0.840973\pi$
$103$		−	9.72411i		−	0.958145i	0.877775	−	0.479072i	$-0.159027\pi$
$104$		0			0
$105$	3.52467	−	0.731575i	0.343973	−	0.0713944i
$106$	−7.04744			−0.684508
$107$			6.14900i			0.594446i	0.954808	+	0.297223i	$0.0960605\pi$
$107$			6.14900i			0.594446i	−0.954808	+	0.297223i	$0.903939\pi$
$108$			3.70397i			0.356414i
$109$	−0.319202			−0.0305741			−0.0152870	−	0.999883i	$-0.504866\pi$
$109$	−0.319202			−0.0305741			−0.0152870	+	0.999883i	$0.504866\pi$
$110$	0.664001	+	3.19911i	0.0633100	+	0.305023i
$111$	−6.16846			−0.585485
$112$		−	2.41461i		−	0.228159i
$113$			1.95370i			0.183789i	0.995769	+	0.0918945i	$0.0292923\pi$
$113$			1.95370i			0.183789i	−0.995769	+	0.0918945i	$0.970708\pi$
$114$	−4.94481			−0.463124
$115$	−3.40356	−	16.3981i	−0.317384	−	1.52913i
$116$	−0.696556			−0.0646736
$117$		0			0
$118$			0.0690364i			0.00635531i
$119$	16.2926			1.49354
$120$	−1.45973	+	0.302978i	−0.133254	+	0.0276580i
$121$	−8.86496			−0.805906
$122$		−	5.91472i		−	0.535494i
$123$			2.83280i			0.255425i
$124$	1.36837			0.122884
$125$	−9.13853	+	6.44107i	−0.817375	+	0.576107i
$126$	−6.17050			−0.549711
$127$			9.73867i			0.864167i	0.901834	+	0.432084i	$0.142221\pi$
$127$			9.73867i			0.864167i	−0.901834	+	0.432084i	$0.857779\pi$
$128$			1.00000i			0.0883883i
$129$	−1.59062			−0.140046
$130$		0			0
$131$	10.6075			0.926778			0.463389	−	0.886155i	$-0.346633\pi$
$131$	10.6075			0.926778			0.463389	+	0.886155i	$0.346633\pi$
$132$			0.974200i			0.0847932i
$133$		−	17.9082i		−	1.55284i
$134$	10.9958			0.949890
$135$	1.68319	+	8.10948i	0.144866	+	0.697953i
$136$	−6.74749			−0.578592
$137$		−	6.40586i		−	0.547289i	−0.961831	−	0.273645i	$-0.911771\pi$
$137$		−	6.40586i		−	0.547289i	0.961831	−	0.273645i	$-0.0882292\pi$
$138$		−	4.99359i		−	0.425082i
$139$	16.7981			1.42480			0.712398	−	0.701775i	$-0.247609\pi$
$139$	16.7981			1.42480			0.712398	+	0.701775i	$0.247609\pi$
$140$	−1.09727	−	5.28656i	−0.0927363	−	0.446796i
$141$	1.84986			0.155786
$142$		−	3.60919i		−	0.302877i
$143$		0			0
$144$	2.55548			0.212957
$145$	−1.52504	+	0.316535i	−0.126648	+	0.0262868i
$146$	−9.30157			−0.769804
$147$		−	0.779830i		−	0.0643193i
$148$			9.25191i			0.760503i
$149$	−8.90415			−0.729456			−0.364728	−	0.931114i	$-0.618838\pi$
$149$	−8.90415			−0.729456			−0.364728	+	0.931114i	$0.618838\pi$
$150$	−3.05825	+	1.32668i	−0.249705	+	0.108323i
$151$	−17.1722			−1.39745			−0.698726	−	0.715389i	$-0.746249\pi$
$151$	−17.1722			−1.39745			−0.698726	+	0.715389i	$0.746249\pi$
$152$			7.41659i			0.601565i
$153$			17.2431i			1.39402i
$154$	−3.52818			−0.284308
$155$	2.99592	−	0.621829i	0.240638	−	0.0499465i
$156$		0			0
$157$			11.0649i			0.883073i	0.897243	+	0.441537i	$0.145566\pi$
$157$			11.0649i			0.883073i	−0.897243	+	0.441537i	$0.854434\pi$
$158$		−	0.766732i		−	0.0609979i
$159$	−4.69869			−0.372630
$160$	0.454429	+	2.18940i	0.0359258	+	0.173088i
$161$	18.0848			1.42529
$162$		−	5.19692i		−	0.408309i
$163$			15.2437i			1.19398i	0.802250	+	0.596988i	$0.203636\pi$
$163$			15.2437i			1.19398i	−0.802250	+	0.596988i	$0.796364\pi$
$164$	4.24884			0.331779
$165$	0.442705	+	2.13292i	0.0344645	+	0.166047i
$166$	−16.5800			−1.28686
$167$			8.69198i			0.672605i	0.941754	+	0.336303i	$0.109177\pi$
$167$			8.69198i			0.672605i	−0.941754	+	0.336303i	$0.890823\pi$
$168$		−	1.60988i		−	0.124205i
$169$		0			0
$170$	−14.7730	+	3.06625i	−1.13304	+	0.235171i
$171$	18.9529			1.44937
$172$			2.38573i			0.181910i
$173$			3.39226i			0.257909i	0.991651	+	0.128954i	$0.0411621\pi$
$173$			3.39226i			0.257909i	−0.991651	+	0.128954i	$0.958838\pi$
$174$	−0.464410			−0.0352068
$175$	−4.80474	−	11.0758i	−0.363204	−	0.837252i
$176$	1.46118			0.110140
$177$			0.0460281i			0.00345969i
$178$		−	17.7481i		−	1.33028i
$179$	−13.2996			−0.994057			−0.497029	−	0.867734i	$-0.665576\pi$
$179$	−13.2996			−0.994057			−0.497029	+	0.867734i	$0.665576\pi$
$180$	5.59498	−	1.16128i	0.417025	−	0.0865571i
$181$	−14.0010			−1.04068			−0.520341	−	0.853958i	$-0.674195\pi$
$181$	−14.0010			−1.04068			−0.520341	+	0.853958i	$0.674195\pi$
$182$		0			0
$183$		−	3.94348i		−	0.291510i
$184$	−7.48975			−0.552152
$185$	4.20434	+	20.2562i	0.309109	+	1.48926i
$186$	0.912326			0.0668950
$187$			9.85927i			0.720981i
$188$		−	2.77456i		−	0.202356i
$189$	−8.94364			−0.650554
$190$	3.37031	+	16.2379i	0.244508	+	1.17802i
$191$	−18.7576			−1.35725			−0.678627	−	0.734483i	$-0.737425\pi$
$191$	−18.7576			−1.35725			−0.678627	+	0.734483i	$0.737425\pi$
$192$			0.666723i			0.0481166i
$193$			24.3855i			1.75530i	0.479299	+	0.877652i	$0.340891\pi$
$193$			24.3855i			1.75530i	−0.479299	+	0.877652i	$0.659109\pi$
$194$	−10.5209			−0.755360
$195$		0			0
$196$	−1.16965			−0.0835462
$197$			2.73133i			0.194599i	0.995255	+	0.0972997i	$0.0310205\pi$
$197$			2.73133i			0.194599i	−0.995255	+	0.0972997i	$0.968979\pi$
$198$		−	3.73401i		−	0.265364i
$199$	−11.2116			−0.794771			−0.397385	−	0.917652i	$-0.630082\pi$
$199$	−11.2116			−0.794771			−0.397385	+	0.917652i	$0.630082\pi$
$200$	1.98986	+	4.58699i	0.140704	+	0.324349i
$201$	7.33113			0.517098
$202$		−	14.2473i		−	1.00243i
$203$		−	1.68191i		−	0.118047i
$204$	−4.49870			−0.314972
$205$	9.30244	−	1.93080i	0.649710	−	0.134853i
$206$	−9.72411			−0.677511
$207$			19.1399i			1.33032i
$208$		0			0
$209$	10.8369			0.749607
$210$	−0.731575	−	3.52467i	−0.0504835	−	0.243226i
$211$	13.7163			0.944266			0.472133	−	0.881527i	$-0.343484\pi$
$211$	13.7163			0.944266			0.472133	+	0.881527i	$0.343484\pi$
$212$			7.04744i			0.484020i
$213$		−	2.40633i		−	0.164879i
$214$	6.14900			0.420337
$215$	1.08415	+	5.22333i	0.0739381	+	0.356228i
$216$	3.70397			0.252023
$217$			3.30409i			0.224296i
$218$			0.319202i			0.0216191i
$219$	−6.20157			−0.419063
$220$	3.19911	−	0.664001i	0.215684	−	0.0447669i
$221$		0			0
$222$			6.16846i			0.414000i
$223$		−	9.84353i		−	0.659172i	−0.944126	−	0.329586i	$-0.893091\pi$
$223$		−	9.84353i		−	0.659172i	0.944126	−	0.329586i	$-0.106909\pi$
$224$	−2.41461			−0.161333
$225$	11.7220	−	5.08505i	0.781464	−	0.339003i
$226$	1.95370			0.129959
$227$			19.4038i			1.28788i	0.765077	+	0.643939i	$0.222701\pi$
$227$			19.4038i			1.28788i	−0.765077	+	0.643939i	$0.777299\pi$
$228$			4.94481i			0.327478i
$229$	16.7503			1.10689			0.553447	−	0.832885i	$-0.313312\pi$
$229$	16.7503			1.10689			0.553447	+	0.832885i	$0.313312\pi$
$230$	−16.3981	+	3.40356i	−1.08126	+	0.224424i
$231$	−2.35231			−0.154771
$232$			0.696556i			0.0457311i
$233$		−	16.7974i		−	1.10043i	−0.835022	−	0.550217i	$-0.814545\pi$
$233$		−	16.7974i		−	1.10043i	0.835022	−	0.550217i	$-0.185455\pi$
$234$		0			0
$235$	−1.26084	−	6.07463i	−0.0822482	−	0.396265i
$236$	0.0690364			0.00449389
$237$		−	0.511198i		−	0.0332059i
$238$		−	16.2926i		−	1.05609i
$239$	−18.2819			−1.18256			−0.591278	−	0.806467i	$-0.701377\pi$
$239$	−18.2819			−1.18256			−0.591278	+	0.806467i	$0.701377\pi$
$240$	0.302978	+	1.45973i	0.0195572	+	0.0942249i
$241$	−7.86172			−0.506418			−0.253209	−	0.967412i	$-0.581486\pi$
$241$	−7.86172			−0.506418			−0.253209	+	0.967412i	$0.581486\pi$
$242$			8.86496i			0.569861i
$243$		−	14.5768i		−	0.935102i
$244$	−5.91472			−0.378651
$245$	−2.56083	+	0.531521i	−0.163605	+	0.0339577i
$246$	2.83280			0.180613
$247$		0			0
$248$		−	1.36837i		−	0.0868918i
$249$	−11.0543			−0.700536
$250$	6.44107	+	9.13853i	0.407369	+	0.577971i
$251$	8.97087			0.566236			0.283118	−	0.959085i	$-0.408631\pi$
$251$	8.97087			0.566236			0.283118	+	0.959085i	$0.408631\pi$
$252$			6.17050i			0.388705i
$253$			10.9439i			0.688034i
$254$	9.73867			0.611059
$255$	−9.84948	+	2.04434i	−0.616799	+	0.128022i
$256$	1.00000			0.0625000
$257$		−	24.2725i		−	1.51408i	−0.653369	−	0.757040i	$-0.726645\pi$
$257$		−	24.2725i		−	1.51408i	0.653369	−	0.757040i	$-0.273355\pi$
$258$			1.59062i			0.0990278i
$259$	−22.3398			−1.38813
$260$		0			0
$261$	1.78004			0.110181
$262$		−	10.6075i		−	0.655331i
$263$		−	28.7755i		−	1.77438i	−0.461408	−	0.887188i	$-0.652656\pi$
$263$		−	28.7755i		−	1.77438i	0.461408	−	0.887188i	$-0.347344\pi$
$264$	0.974200			0.0599578
$265$	3.20256	+	15.4297i	0.196732	+	0.947839i
$266$	−17.9082			−1.09802
$267$		−	11.8331i		−	0.724172i
$268$		−	10.9958i		−	0.671674i
$269$	26.2808			1.60237			0.801185	−	0.598417i	$-0.204203\pi$
$269$	26.2808			1.60237			0.801185	+	0.598417i	$0.204203\pi$
$270$	8.10948	−	1.68319i	0.493527	−	0.102436i
$271$	14.3647			0.872594			0.436297	−	0.899803i	$-0.356290\pi$
$271$	14.3647			0.872594			0.436297	+	0.899803i	$0.356290\pi$
$272$			6.74749i			0.409126i
$273$		0			0
$274$	−6.40586			−0.386992
$275$	6.70240	−	2.90753i	0.404170	−	0.175331i
$276$	−4.99359			−0.300579
$277$		−	9.92492i		−	0.596331i	−0.954514	−	0.298165i	$-0.903625\pi$
$277$		−	9.92492i		−	0.596331i	0.954514	−	0.298165i	$-0.0963747\pi$
$278$		−	16.7981i		−	1.00748i
$279$	−3.49685			−0.209351
$280$	−5.28656	+	1.09727i	−0.315933	+	0.0655744i
$281$	11.7992			0.703880			0.351940	−	0.936023i	$-0.385522\pi$
$281$	11.7992			0.703880			0.351940	+	0.936023i	$0.385522\pi$
$282$		−	1.84986i		−	0.110158i
$283$		−	13.0538i		−	0.775968i	−0.921666	−	0.387984i	$-0.873172\pi$
$283$		−	13.0538i		−	0.775968i	0.921666	−	0.387984i	$-0.126828\pi$
$284$	−3.60919			−0.214166
$285$	2.24706	+	10.8262i	0.133105	+	0.641288i
$286$		0			0
$287$			10.2593i			0.605588i
$288$		−	2.55548i		−	0.150583i
$289$	−28.5286			−1.67815
$290$	0.316535	+	1.52504i	0.0185876	+	0.0895536i
$291$	−7.01455			−0.411200
$292$			9.30157i			0.544333i
$293$			16.2358i			0.948506i	0.880389	+	0.474253i	$0.157282\pi$
$293$			16.2358i			0.948506i	−0.880389	+	0.474253i	$0.842718\pi$
$294$	−0.779830			−0.0454806
$295$	0.151149	−	0.0313721i	0.00880021	−	0.00182656i
$296$	9.25191			0.537757
$297$		−	5.41215i		−	0.314045i
$298$			8.90415i			0.515803i
$299$		0			0
$300$	1.32668	+	3.05825i	0.0765961	+	0.176568i
$301$	−5.76062			−0.332036
$302$			17.1722i			0.988148i
$303$		−	9.49897i		−	0.545701i
$304$	7.41659			0.425370
$305$	−12.9497	+	2.68782i	−0.741499	+	0.153904i
$306$	17.2431			0.985721
$307$		−	5.66589i		−	0.323370i	−0.986842	−	0.161685i	$-0.948307\pi$
$307$		−	5.66589i		−	0.323370i	0.986842	−	0.161685i	$-0.0516928\pi$
$308$			3.52818i			0.201036i
$309$	−6.48328			−0.368821
$310$	−0.621829	−	2.99592i	−0.0353175	−	0.170157i
$311$	20.5465			1.16508			0.582542	−	0.812801i	$-0.302058\pi$
$311$	20.5465			1.16508			0.582542	+	0.812801i	$0.302058\pi$
$312$		0			0
$313$			11.0354i			0.623756i	0.950122	+	0.311878i	$0.100958\pi$
$313$			11.0354i			0.623756i	−0.950122	+	0.311878i	$0.899042\pi$
$314$	11.0649			0.624427
$315$	2.80405	+	13.5097i	0.157990	+	0.761186i
$316$	−0.766732			−0.0431320
$317$			17.0656i			0.958501i	0.877678	+	0.479251i	$0.159091\pi$
$317$			17.0656i			0.958501i	−0.877678	+	0.479251i	$0.840909\pi$
$318$			4.69869i			0.263489i
$319$	1.01779			0.0569854
$320$	2.18940	−	0.454429i	0.122391	−	0.0254034i
$321$	4.09968			0.228822
$322$		−	18.0848i		−	1.00783i
$323$			50.0433i			2.78448i
$324$	−5.19692			−0.288718
$325$		0			0
$326$	15.2437			0.844269
$327$			0.212820i			0.0117689i
$328$		−	4.24884i		−	0.234603i
$329$	6.69949			0.369355
$330$	2.13292	−	0.442705i	0.117413	−	0.0243701i
$331$	29.6977			1.63233			0.816167	−	0.577817i	$-0.196095\pi$
$331$	29.6977			1.63233			0.816167	+	0.577817i	$0.196095\pi$
$332$			16.5800i			0.909947i
$333$		−	23.6431i		−	1.29563i
$334$	8.69198			0.475604
$335$	−4.99680	−	24.0742i	−0.273004	−	1.31531i
$336$	−1.60988			−0.0878260
$337$			11.1216i			0.605833i	0.953017	+	0.302917i	$0.0979604\pi$
$337$			11.1216i			0.605833i	−0.953017	+	0.302917i	$0.902040\pi$
$338$		0			0
$339$	1.30258			0.0707464
$340$	3.06625	+	14.7730i	0.166291	+	0.801177i
$341$	−1.99944			−0.108275
$342$		−	18.9529i		−	1.02486i
$343$		−	19.7265i		−	1.06513i
$344$	2.38573			0.128630
$345$	−10.9330	+	2.26923i	−0.588612	+	0.122171i
$346$	3.39226			0.182369
$347$			19.1698i			1.02909i	0.857463	+	0.514545i	$0.172039\pi$
$347$			19.1698i			1.02909i	−0.857463	+	0.514545i	$0.827961\pi$
$348$			0.464410i			0.0248950i
$349$	−2.07169			−0.110895			−0.0554474	−	0.998462i	$-0.517659\pi$
$349$	−2.07169			−0.110895			−0.0554474	+	0.998462i	$0.517659\pi$
$350$	−11.0758	+	4.80474i	−0.592026	+	0.256824i
$351$		0			0
$352$		−	1.46118i		−	0.0778810i
$353$		−	14.2889i		−	0.760522i	−0.924879	−	0.380261i	$-0.875834\pi$
$353$		−	14.2889i		−	0.760522i	0.924879	−	0.380261i	$-0.124166\pi$
$354$	0.0460281			0.00244637
$355$	−7.90198	+	1.64012i	−0.419394	+	0.0870486i
$356$	−17.7481			−0.940648
$357$		−	10.8626i		−	0.574911i
$358$			13.2996i			0.702905i
$359$	−12.4966			−0.659543			−0.329772	−	0.944061i	$-0.606972\pi$
$359$	−12.4966			−0.659543			−0.329772	+	0.944061i	$0.606972\pi$
$360$	−1.16128	−	5.59498i	−0.0612051	−	0.294881i
$361$	36.0058			1.89504
$362$			14.0010i			0.735874i
$363$			5.91047i			0.310219i
$364$		0			0
$365$	4.22690	+	20.3649i	0.221246	+	1.06595i
$366$	−3.94348			−0.206129
$367$			20.7194i			1.08154i	0.841170	+	0.540772i	$0.181868\pi$
$367$			20.7194i			1.08154i	−0.841170	+	0.540772i	$0.818132\pi$
$368$			7.48975i			0.390430i
$369$	−10.8578			−0.565236
$370$	20.2562	−	4.20434i	1.05307	−	0.218573i
$371$	−17.0168			−0.883470
$372$		−	0.912326i		−	0.0473019i
$373$		−	31.4926i		−	1.63063i	−0.579020	−	0.815313i	$-0.696565\pi$
$373$		−	31.4926i		−	1.63063i	0.579020	−	0.815313i	$-0.303435\pi$
$374$	9.85927			0.509811
$375$	4.29441	+	6.09286i	0.221762	+	0.314634i
$376$	−2.77456			−0.143087
$377$		0			0
$378$			8.94364i			0.460011i
$379$	7.87442			0.404482			0.202241	−	0.979336i	$-0.435178\pi$
$379$	7.87442			0.404482			0.202241	+	0.979336i	$0.435178\pi$
$380$	16.2379	−	3.37031i	0.832987	−	0.172893i
$381$	6.49299			0.332646
$382$			18.7576i			0.959723i
$383$			8.03386i			0.410511i	0.978708	+	0.205256i	$0.0658025\pi$
$383$			8.03386i			0.410511i	−0.978708	+	0.205256i	$0.934197\pi$
$384$	0.666723			0.0340236
$385$	1.60331	+	7.72460i	0.0817120	+	0.393682i
$386$	24.3855			1.24119
$387$		−	6.09669i		−	0.309912i
$388$			10.5209i			0.534120i
$389$	21.5917			1.09474			0.547371	−	0.836890i	$-0.315629\pi$
$389$	21.5917			1.09474			0.547371	+	0.836890i	$0.315629\pi$
$390$		0			0
$391$	−50.5370			−2.55577
$392$			1.16965i			0.0590761i
$393$		−	7.07224i		−	0.356747i
$394$	2.73133			0.137603
$395$	−1.67869	+	0.348425i	−0.0844639	+	0.0175312i
$396$	−3.73401			−0.187641
$397$			36.8751i			1.85071i	0.379102	+	0.925355i	$0.376233\pi$
$397$			36.8751i			1.85071i	−0.379102	+	0.925355i	$0.623767\pi$
$398$			11.2116i			0.561988i
$399$	−11.9398			−0.597737
$400$	4.58699	−	1.98986i	0.229349	−	0.0994929i
$401$	−8.26837			−0.412902			−0.206451	−	0.978457i	$-0.566191\pi$
$401$	−8.26837			−0.412902			−0.206451	+	0.978457i	$0.566191\pi$
$402$		−	7.33113i		−	0.365644i
$403$		0			0
$404$	−14.2473			−0.708827
$405$	−11.3782	+	2.36163i	−0.565386	+	0.117351i
$406$	−1.68191			−0.0834719
$407$		−	13.5187i		−	0.670096i
$408$			4.49870i			0.222719i
$409$	3.02146			0.149402			0.0747008	−	0.997206i	$-0.476200\pi$
$409$	3.02146			0.149402			0.0747008	+	0.997206i	$0.476200\pi$
$410$	−1.93080	−	9.30244i	−0.0953553	−	0.459415i
$411$	−4.27093			−0.210669
$412$			9.72411i			0.479072i
$413$			0.166696i			0.00820258i
$414$	19.1399			0.940676
$415$	7.53444	+	36.3004i	0.369851	+	1.78192i
$416$		0			0
$417$		−	11.1997i		−	0.548451i
$418$		−	10.8369i		−	0.530052i
$419$	35.0376			1.71170			0.855850	−	0.517223i	$-0.173034\pi$
$419$	35.0376			1.71170			0.855850	+	0.517223i	$0.173034\pi$
$420$	−3.52467	+	0.731575i	−0.171986	+	0.0356972i
$421$	9.81291			0.478252			0.239126	−	0.970989i	$-0.423139\pi$
$421$	9.81291			0.478252			0.239126	+	0.970989i	$0.423139\pi$
$422$		−	13.7163i		−	0.667697i
$423$			7.09033i			0.344744i
$424$	7.04744			0.342254
$425$	13.4265	+	30.9506i	0.651283	+	1.50133i
$426$	−2.40633			−0.116587
$427$		−	14.2818i		−	0.691143i
$428$		−	6.14900i		−	0.297223i
$429$		0			0
$430$	5.22333	−	1.08415i	0.251891	−	0.0522821i
$431$	−5.88552			−0.283495			−0.141748	−	0.989903i	$-0.545272\pi$
$431$	−5.88552			−0.283495			−0.141748	+	0.989903i	$0.545272\pi$
$432$		−	3.70397i		−	0.178207i
$433$		−	31.1096i		−	1.49503i	−0.664244	−	0.747516i	$-0.731246\pi$
$433$		−	31.1096i		−	1.49503i	0.664244	−	0.747516i	$-0.268754\pi$
$434$	3.30409			0.158601
$435$	0.211041	+	1.01678i	0.0101187	+	0.0487509i
$436$	0.319202			0.0152870
$437$			55.5484i			2.65724i
$438$			6.20157i			0.296322i
$439$	2.69710			0.128726			0.0643629	−	0.997927i	$-0.479498\pi$
$439$	2.69710			0.128726			0.0643629	+	0.997927i	$0.479498\pi$
$440$	−0.664001	−	3.19911i	−0.0316550	−	0.152511i
$441$	2.98901			0.142334
$442$		0			0
$443$			19.0859i			0.906799i	0.891308	+	0.453399i	$0.149789\pi$
$443$			19.0859i			0.906799i	−0.891308	+	0.453399i	$0.850211\pi$
$444$	6.16846			0.292742
$445$	−38.8578	+	8.06526i	−1.84204	+	0.382330i
$446$	−9.84353			−0.466105
$447$			5.93660i			0.280791i
$448$			2.41461i			0.114080i
$449$	18.3579			0.866363			0.433182	−	0.901307i	$-0.357391\pi$
$449$	18.3579			0.866363			0.433182	+	0.901307i	$0.357391\pi$
$450$	−5.08505	−	11.7220i	−0.239711	−	0.552579i
$451$	−6.20831			−0.292338
$452$		−	1.95370i		−	0.0918945i
$453$			11.4491i			0.537925i
$454$	19.4038			0.910668
$455$		0			0
$456$	4.94481			0.231562
$457$		−	25.3873i		−	1.18757i	−0.804624	−	0.593785i	$-0.797633\pi$
$457$		−	25.3873i		−	1.18757i	0.804624	−	0.593785i	$-0.202367\pi$
$458$		−	16.7503i		−	0.782692i
$459$	24.9925			1.16655
$460$	3.40356	+	16.3981i	0.158692	+	0.764565i
$461$	−1.12031			−0.0521782			−0.0260891	−	0.999660i	$-0.508305\pi$
$461$	−1.12031			−0.0521782			−0.0260891	+	0.999660i	$0.508305\pi$
$462$			2.35231i			0.109440i
$463$		−	30.6952i		−	1.42653i	−0.700895	−	0.713264i	$-0.747216\pi$
$463$		−	30.6952i		−	1.42653i	0.700895	−	0.713264i	$-0.252784\pi$
$464$	0.696556			0.0323368
$465$	−0.414587	−	1.99745i	−0.0192260	−	0.0926296i
$466$	−16.7974			−0.778124
$467$		−	5.88670i		−	0.272404i	−0.990681	−	0.136202i	$-0.956510\pi$
$467$		−	5.88670i		−	0.272404i	0.990681	−	0.136202i	$-0.0434896\pi$
$468$		0			0
$469$	26.5505			1.22599
$470$	−6.07463	+	1.26084i	−0.280202	+	0.0581582i
$471$	7.37720			0.339924
$472$		−	0.0690364i		−	0.00317766i
$473$		−	3.48597i		−	0.160285i
$474$	−0.511198			−0.0234801
$475$	34.0198	−	14.7580i	1.56094	−	0.677142i
$476$	−16.2926			−0.746768
$477$		−	18.0096i		−	0.824602i
$478$			18.2819i			0.836194i
$479$	−24.6962			−1.12840			−0.564200	−	0.825638i	$-0.690815\pi$
$479$	−24.6962			−1.12840			−0.564200	+	0.825638i	$0.690815\pi$
$480$	1.45973	−	0.302978i	0.0666271	−	0.0138290i
$481$		0			0
$482$			7.86172i			0.358091i
$483$		−	12.0576i		−	0.548639i
$484$	8.86496			0.402953
$485$	4.78102	+	23.0346i	0.217095	+	1.04595i
$486$	−14.5768			−0.661217
$487$			6.85817i			0.310774i	0.987854	+	0.155387i	$0.0496624\pi$
$487$			6.85817i			0.310774i	−0.987854	+	0.155387i	$0.950338\pi$
$488$			5.91472i			0.267747i
$489$	10.1633			0.459600
$490$	0.531521	+	2.56083i	0.0240117	+	0.115687i
$491$	−32.0421			−1.44604			−0.723021	−	0.690826i	$-0.757247\pi$
$491$	−32.0421			−1.44604			−0.723021	+	0.690826i	$0.757247\pi$
$492$		−	2.83280i		−	0.127712i
$493$			4.70000i			0.211677i
$494$		0			0
$495$	−8.17526	+	1.69684i	−0.367450	+	0.0762674i
$496$	−1.36837			−0.0614418
$497$		−	8.71480i		−	0.390912i
$498$			11.0543i			0.495354i
$499$	−25.9861			−1.16330			−0.581648	−	0.813440i	$-0.697592\pi$
$499$	−25.9861			−1.16330			−0.581648	+	0.813440i	$0.697592\pi$
$500$	9.13853	−	6.44107i	0.408687	−	0.288053i
$501$	5.79514			0.258908
$502$		−	8.97087i		−	0.400389i
$503$		−	7.96895i		−	0.355318i	−0.984092	−	0.177659i	$-0.943148\pi$
$503$		−	7.96895i		−	0.355318i	0.984092	−	0.177659i	$-0.0568524\pi$
$504$	6.17050			0.274856
$505$	−31.1930	+	6.47437i	−1.38807	+	0.288105i
$506$	10.9439			0.486513
$507$		0			0
$508$		−	9.73867i		−	0.432084i
$509$	−26.5772			−1.17801			−0.589007	−	0.808128i	$-0.700481\pi$
$509$	−26.5772			−1.17801			−0.589007	+	0.808128i	$0.700481\pi$
$510$	2.04434	+	9.84948i	0.0905250	+	0.436142i
$511$	−22.4597			−0.993558
$512$		−	1.00000i		−	0.0441942i
$513$		−	27.4708i		−	1.21286i
$514$	−24.2725			−1.07062
$515$	4.41892	+	21.2900i	0.194721	+	0.938150i
$516$	1.59062			0.0700232
$517$			4.05412i			0.178300i
$518$			22.3398i			0.981554i
$519$	2.26170			0.0992776
$520$		0			0
$521$	−16.3843			−0.717810			−0.358905	−	0.933374i	$-0.616850\pi$
$521$	−16.3843			−0.717810			−0.358905	+	0.933374i	$0.616850\pi$
$522$		−	1.78004i		−	0.0779100i
$523$		−	12.9757i		−	0.567390i	−0.958915	−	0.283695i	$-0.908440\pi$
$523$		−	12.9757i		−	0.567390i	0.958915	−	0.283695i	$-0.0915603\pi$
$524$	−10.6075			−0.463389
$525$	−7.38449	+	3.20343i	−0.322285	+	0.139809i
$526$	−28.7755			−1.25467
$527$		−	9.23308i		−	0.402199i
$528$		−	0.974200i		−	0.0423966i
$529$	−33.0964			−1.43897
$530$	15.4297	−	3.20256i	0.670223	−	0.139110i
$531$	−0.176421			−0.00765602
$532$			17.9082i			0.776418i
$533$		0			0
$534$	−11.8331			−0.512067
$535$	−2.79428	−	13.4627i	−0.120807	−	0.582041i
$536$	−10.9958			−0.474945
$537$			8.86713i			0.382645i
$538$		−	26.2808i		−	1.13305i
$539$	1.70906			0.0736144
$540$	−1.68319	−	8.10948i	−0.0724329	−	0.348976i
$541$	23.1606			0.995753			0.497877	−	0.867248i	$-0.334113\pi$
$541$	23.1606			0.995753			0.497877	+	0.867248i	$0.334113\pi$
$542$		−	14.3647i		−	0.617017i
$543$			9.33475i			0.400593i
$544$	6.74749			0.289296
$545$	0.698864	−	0.145055i	0.0299360	−	0.00621347i
$546$		0			0
$547$			13.3168i			0.569387i	0.958619	+	0.284693i	$0.0918917\pi$
$547$			13.3168i			0.569387i	−0.958619	+	0.284693i	$0.908108\pi$
$548$			6.40586i			0.273645i
$549$	15.1150			0.645091
$550$	−2.90753	−	6.70240i	−0.123978	−	0.285791i
$551$	5.16607			0.220082
$552$			4.99359i			0.212541i
$553$		−	1.85136i		−	0.0787279i
$554$	−9.92492			−0.421669
$555$	13.5053	−	2.80313i	0.573266	−	0.118986i
$556$	−16.7981			−0.712398
$557$			3.02677i			0.128248i	0.997942	+	0.0641242i	$0.0204254\pi$
$557$			3.02677i			0.128248i	−0.997942	+	0.0641242i	$0.979575\pi$
$558$			3.49685i			0.148034i
$559$		0			0
$560$	1.09727	+	5.28656i	0.0463681	+	0.223398i
$561$	6.57340			0.277529
$562$		−	11.7992i		−	0.497718i
$563$			18.2744i			0.770175i	0.922880	+	0.385087i	$0.125829\pi$
$563$			18.2744i			0.770175i	−0.922880	+	0.385087i	$0.874171\pi$
$564$	−1.84986			−0.0778932
$565$	−0.887820	−	4.27745i	−0.0373509	−	0.179954i
$566$	−13.0538			−0.548692
$567$		−	12.5486i		−	0.526990i
$568$			3.60919i			0.151438i
$569$	25.9020			1.08587			0.542933	−	0.839776i	$-0.317314\pi$
$569$	25.9020			1.08587			0.542933	+	0.839776i	$0.317314\pi$
$570$	10.8262	−	2.24706i	0.453459	−	0.0941192i
$571$	−37.9443			−1.58792			−0.793960	−	0.607970i	$-0.791984\pi$
$571$	−37.9443			−1.58792			−0.793960	+	0.607970i	$0.791984\pi$
$572$		0			0
$573$			12.5061i			0.522451i
$574$	10.2593			0.428215
$575$	14.9035	+	34.3554i	0.621521	+	1.43272i
$576$	−2.55548			−0.106478
$577$			18.6481i			0.776330i	0.921590	+	0.388165i	$0.126891\pi$
$577$			18.6481i			0.776330i	−0.921590	+	0.388165i	$0.873109\pi$
$578$			28.5286i			1.18663i
$579$	16.2583			0.675674
$580$	1.52504	−	0.316535i	0.0633240	−	0.0131434i
$581$	−40.0343			−1.66090
$582$			7.01455i			0.290763i
$583$		−	10.2976i		−	0.426481i
$584$	9.30157			0.384902
$585$		0			0
$586$	16.2358			0.670695
$587$		−	6.63680i		−	0.273930i	−0.990576	−	0.136965i	$-0.956265\pi$
$587$		−	6.63680i		−	0.273930i	0.990576	−	0.136965i	$-0.0437348\pi$
$588$			0.779830i			0.0321596i
$589$	−10.1487			−0.418168
$590$	−0.0313721	−	0.151149i	−0.00129157	−	0.00622269i
$591$	1.82104			0.0749077
$592$		−	9.25191i		−	0.380251i
$593$			8.72953i			0.358479i	0.983805	+	0.179239i	$0.0573636\pi$
$593$			8.72953i			0.358479i	−0.983805	+	0.179239i	$0.942636\pi$
$594$	−5.41215			−0.222063
$595$	−35.6710	+	7.40381i	−1.46237	+	0.303527i
$596$	8.90415			0.364728
$597$			7.47504i			0.305933i
$598$		0			0
$599$	−38.0625			−1.55519			−0.777596	−	0.628765i	$-0.783561\pi$
$599$	−38.0625			−1.55519			−0.777596	+	0.628765i	$0.783561\pi$
$600$	3.05825	−	1.32668i	0.124853	−	0.0541616i
$601$	−2.03785			−0.0831256			−0.0415628	−	0.999136i	$-0.513234\pi$
$601$	−2.03785			−0.0831256			−0.0415628	+	0.999136i	$0.513234\pi$
$602$			5.76062i			0.234785i
$603$			28.0995i			1.14430i
$604$	17.1722			0.698726
$605$	19.4090	−	4.02850i	0.789088	−	0.163782i
$606$	−9.49897			−0.385869
$607$			1.61460i			0.0655347i	0.999463	+	0.0327674i	$0.0104320\pi$
$607$			1.61460i			0.0655347i	−0.999463	+	0.0327674i	$0.989568\pi$
$608$		−	7.41659i		−	0.300782i
$609$	−1.12137			−0.0454402
$610$	2.68782	+	12.9497i	0.108827	+	0.524319i
$611$		0			0
$612$		−	17.2431i		−	0.697010i
$613$			17.8032i			0.719066i	0.933132	+	0.359533i	$0.117064\pi$
$613$			17.8032i			0.719066i	−0.933132	+	0.359533i	$0.882936\pi$
$614$	−5.66589			−0.228657
$615$	−1.28731	−	6.20215i	−0.0519092	−	0.250095i
$616$	3.52818			0.142154
$617$			36.9565i			1.48781i	0.668284	+	0.743906i	$0.267029\pi$
$617$			36.9565i			1.48781i	−0.668284	+	0.743906i	$0.732971\pi$
$618$			6.48328i			0.260796i
$619$	−31.6640			−1.27268			−0.636341	−	0.771408i	$-0.719553\pi$
$619$	−31.6640			−1.27268			−0.636341	+	0.771408i	$0.719553\pi$
$620$	−2.99592	+	0.621829i	−0.120319	+	0.0249732i
$621$	27.7418			1.11324
$622$		−	20.5465i		−	0.823839i
$623$		−	42.8548i		−	1.71694i
$624$		0			0
$625$	17.0809	−	18.2549i	0.683237	−	0.730197i
$626$	11.0354			0.441062
$627$		−	7.22524i		−	0.288548i
$628$		−	11.0649i		−	0.441537i
$629$	62.4272			2.48913
$630$	13.5097	−	2.80405i	0.538240	−	0.111716i
$631$	7.35141			0.292655			0.146327	−	0.989236i	$-0.453255\pi$
$631$	7.35141			0.292655			0.146327	+	0.989236i	$0.453255\pi$
$632$			0.766732i			0.0304990i
$633$		−	9.14494i		−	0.363479i
$634$	17.0656			0.677763
$635$	−4.42554	−	21.3219i	−0.175622	−	0.846134i
$636$	4.69869			0.186315
$637$		0			0
$638$		−	1.01779i		−	0.0402947i
$639$	9.22322			0.364865
$640$	−0.454429	−	2.18940i	−0.0179629	−	0.0865438i
$641$	38.9606			1.53885			0.769425	−	0.638737i	$-0.220543\pi$
$641$	38.9606			1.53885			0.769425	+	0.638737i	$0.220543\pi$
$642$		−	4.09968i		−	0.161801i
$643$		−	0.528071i		−	0.0208251i	−0.999946	−	0.0104126i	$-0.996686\pi$
$643$		−	0.528071i		−	0.0208251i	0.999946	−	0.0104126i	$-0.00331448\pi$
$644$	−18.0848			−0.712643
$645$	3.48251	−	0.722825i	0.137124	−	0.0284612i
$646$	50.0433			1.96893
$647$		−	30.5439i		−	1.20081i	−0.799698	−	0.600403i	$-0.795007\pi$
$647$		−	30.5439i		−	1.20081i	0.799698	−	0.600403i	$-0.204993\pi$
$648$			5.19692i			0.204154i
$649$	−0.100874			−0.00395966
$650$		0			0
$651$	2.20291			0.0863390
$652$		−	15.2437i		−	0.596988i
$653$		−	11.9772i		−	0.468704i	−0.972152	−	0.234352i	$-0.924703\pi$
$653$		−	11.9772i		−	0.468704i	0.972152	−	0.234352i	$-0.0752968\pi$
$654$	0.212820			0.00832190
$655$	−23.2240	+	4.82034i	−0.907438	+	0.188346i
$656$	−4.24884			−0.165889
$657$		−	23.7700i		−	0.927355i
$658$		−	6.69949i		−	0.261173i
$659$	−4.01683			−0.156474			−0.0782368	−	0.996935i	$-0.524929\pi$
$659$	−4.01683			−0.156474			−0.0782368	+	0.996935i	$0.524929\pi$
$660$	−0.442705	−	2.13292i	−0.0172323	−	0.0830237i
$661$	40.3372			1.56893			0.784467	−	0.620170i	$-0.212936\pi$
$661$	40.3372			1.56893			0.784467	+	0.620170i	$0.212936\pi$
$662$		−	29.6977i		−	1.15423i
$663$		0			0
$664$	16.5800			0.643430
$665$	8.13800	+	39.2083i	0.315578	+	1.52043i
$666$	−23.6431			−0.916151
$667$			5.21703i			0.202004i
$668$		−	8.69198i		−	0.336303i
$669$	−6.56291			−0.253737
$670$	−24.0742	+	4.99680i	−0.930067	+	0.193043i
$671$	8.64245			0.333638
$672$			1.60988i			0.0621024i
$673$			41.3853i			1.59529i	0.603129	+	0.797644i	$0.293920\pi$
$673$			41.3853i			1.59529i	−0.603129	+	0.797644i	$0.706080\pi$
$674$	11.1216			0.428389
$675$	−7.37037	−	16.9900i	−0.283686	−	0.653947i
$676$		0			0
$677$		−	23.9115i		−	0.918995i	−0.888179	−	0.459497i	$-0.848030\pi$
$677$		−	23.9115i		−	0.918995i	0.888179	−	0.459497i	$-0.151970\pi$
$678$		−	1.30258i		−	0.0500253i
$679$	−25.4040			−0.974916
$680$	14.7730	−	3.06625i	0.566518	−	0.117585i
$681$	12.9370			0.495746
$682$			1.99944i			0.0765623i
$683$			23.5399i			0.900729i	0.892845	+	0.450364i	$0.148706\pi$
$683$			23.5399i			0.900729i	−0.892845	+	0.450364i	$0.851294\pi$
$684$	−18.9529			−0.724684
$685$	2.91101	+	14.0250i	0.111224	+	0.535868i
$686$	−19.7265			−0.753162
$687$		−	11.1678i		−	0.426079i
$688$		−	2.38573i		−	0.0909552i
$689$		0			0
$690$	2.26923	+	10.9330i	0.0863882	+	0.416212i
$691$	−27.7945			−1.05735			−0.528677	−	0.848823i	$-0.677312\pi$
$691$	−27.7945			−1.05735			−0.528677	+	0.848823i	$0.677312\pi$
$692$		−	3.39226i		−	0.128954i
$693$		−	9.01618i		−	0.342496i
$694$	19.1698			0.727676
$695$	−36.7779	+	7.63355i	−1.39506	+	0.289557i
$696$	0.464410			0.0176034
$697$		−	28.6690i		−	1.08592i
$698$			2.07169i			0.0784145i
$699$	−11.1992			−0.423593
$700$	4.80474	+	11.0758i	0.181602	+	0.418626i
$701$	20.6527			0.780042			0.390021	−	0.920806i	$-0.372468\pi$
$701$	20.6527			0.780042			0.390021	+	0.920806i	$0.372468\pi$
$702$		0			0
$703$		−	68.6176i		−	2.58796i
$704$	−1.46118			−0.0550702
$705$	−4.05010	+	0.840631i	−0.152535	+	0.0316600i
$706$	−14.2889			−0.537770
$707$		−	34.4016i		−	1.29381i
$708$		−	0.0460281i		−	0.00172984i
$709$	−1.90959			−0.0717161			−0.0358581	−	0.999357i	$-0.511416\pi$
$709$	−1.90959			−0.0717161			−0.0358581	+	0.999357i	$0.511416\pi$
$710$	1.64012	+	7.90198i	0.0615527	+	0.296556i
$711$	1.95937			0.0734821
$712$			17.7481i			0.665138i
$713$		−	10.2488i		−	0.383820i
$714$	−10.8626			−0.406523
$715$		0			0
$716$	13.2996			0.497029
$717$			12.1889i			0.455205i
$718$			12.4966i			0.466367i
$719$	−36.3672			−1.35627			−0.678135	−	0.734938i	$-0.737211\pi$
$719$	−36.3672			−1.35627			−0.678135	+	0.734938i	$0.737211\pi$
$720$	−5.59498	+	1.16128i	−0.208513	+	0.0432785i
$721$	−23.4799			−0.874439
$722$		−	36.0058i		−	1.34000i
$723$			5.24159i			0.194937i
$724$	14.0010			0.520341
$725$	3.19509	−	1.38605i	0.118663	−	0.0514765i
$726$	5.91047			0.219358
$727$		−	2.25162i		−	0.0835080i	−0.999128	−	0.0417540i	$-0.986705\pi$
$727$		−	2.25162i		−	0.0835080i	0.999128	−	0.0417540i	$-0.0132946\pi$
$728$		0			0
$729$	5.87208			0.217485
$730$	20.3649	−	4.22690i	0.753739	−	0.156445i
$731$	16.0977			0.595395
$732$			3.94348i			0.145755i
$733$		−	27.7157i		−	1.02370i	−0.859074	−	0.511851i	$-0.828960\pi$
$733$		−	27.7157i		−	1.02370i	0.859074	−	0.511851i	$-0.171040\pi$
$734$	20.7194			0.764766
$735$	0.354377	+	1.70736i	0.0130714	+	0.0629771i
$736$	7.48975			0.276076
$737$			16.0668i			0.591827i
$738$			10.8578i			0.399682i
$739$	−17.4826			−0.643108			−0.321554	−	0.946891i	$-0.604205\pi$
$739$	−17.4826			−0.643108			−0.321554	+	0.946891i	$0.604205\pi$
$740$	−4.20434	−	20.2562i	−0.154555	−	0.744632i
$741$		0			0
$742$			17.0168i			0.624707i
$743$			45.4090i			1.66589i	0.553353	+	0.832947i	$0.313348\pi$
$743$			45.4090i			1.66589i	−0.553353	+	0.832947i	$0.686652\pi$
$744$	−0.912326			−0.0334475
$745$	19.4948	−	4.04630i	0.714234	−	0.148245i
$746$	−31.4926			−1.15303
$747$		−	42.3699i		−	1.55023i
$748$		−	9.85927i		−	0.360491i
$749$	14.8475			0.542514
$750$	6.09286	−	4.29441i	0.222480	−	0.156810i
$751$	−23.3846			−0.853315			−0.426657	−	0.904413i	$-0.640309\pi$
$751$	−23.3846			−0.853315			−0.426657	+	0.904413i	$0.640309\pi$
$752$			2.77456i			0.101178i
$753$		−	5.98108i		−	0.217963i
$754$		0			0
$755$	37.5969	−	7.80354i	1.36829	−	0.284000i
$756$	8.94364			0.325277
$757$			33.7347i			1.22611i	0.790040	+	0.613055i	$0.210059\pi$
$757$			33.7347i			1.22611i	−0.790040	+	0.613055i	$0.789941\pi$
$758$		−	7.87442i		−	0.286012i
$759$	7.29651			0.264847
$760$	−3.37031	−	16.2379i	−0.122254	−	0.589011i
$761$	−13.4210			−0.486512			−0.243256	−	0.969962i	$-0.578215\pi$
$761$	−13.4210			−0.486512			−0.243256	+	0.969962i	$0.578215\pi$
$762$		−	6.49299i		−	0.235216i
$763$			0.770750i			0.0279030i
$764$	18.7576			0.678627
$765$	−7.83575	−	37.7521i	−0.283302	−	1.36493i
$766$	8.03386			0.290275
$767$		0			0
$768$		−	0.666723i		−	0.0240583i
$769$	−18.6681			−0.673188			−0.336594	−	0.941650i	$-0.609275\pi$
$769$	−18.6681			−0.673188			−0.336594	+	0.941650i	$0.609275\pi$
$770$	7.72460	−	1.60331i	0.278375	−	0.0577791i
$771$	−16.1831			−0.582818
$772$		−	24.3855i		−	0.877652i
$773$		−	2.12110i		−	0.0762905i	−0.999272	−	0.0381453i	$-0.987855\pi$
$773$		−	2.12110i		−	0.0762905i	0.999272	−	0.0381453i	$-0.0121450\pi$
$774$	−6.09669			−0.219141
$775$	−6.27671	+	2.72287i	−0.225466	+	0.0978084i
$776$	10.5209			0.377680
$777$			14.8944i			0.534335i
$778$		−	21.5917i		−	0.774099i
$779$	−31.5119			−1.12903
$780$		0			0
$781$	5.27367			0.188707
$782$			50.5370i			1.80720i
$783$		−	2.58002i		−	0.0922024i
$784$	1.16965			0.0417731
$785$	−5.02820	−	24.2255i	−0.179464	−	0.864645i
$786$	−7.07224			−0.252258
$787$		−	1.88977i		−	0.0673631i	−0.999433	−	0.0336815i	$-0.989277\pi$
$787$		−	1.88977i		−	0.0673631i	0.999433	−	0.0336815i	$-0.0107232\pi$
$788$		−	2.73133i		−	0.0972997i
$789$	−19.1853			−0.683015
$790$	0.348425	+	1.67869i	0.0123964	+	0.0597250i
$791$	4.71744			0.167733
$792$			3.73401i			0.132682i
$793$		0			0
$794$	36.8751			1.30865
$795$	10.2873	−	2.13522i	0.364854	−	0.0757284i
$796$	11.2116			0.397385
$797$			27.7575i			0.983222i	0.870815	+	0.491611i	$0.163592\pi$
$797$			27.7575i			0.983222i	−0.870815	+	0.491611i	$0.836408\pi$
$798$			11.9398i			0.422664i
$799$	−18.7213			−0.662312
$800$	−1.98986	−	4.58699i	−0.0703521	−	0.162175i
$801$	45.3549			1.60254
$802$			8.26837i			0.291966i
$803$		−	13.5912i		−	0.479624i
$804$	−7.33113			−0.258549
$805$	−39.5951	+	8.21828i	−1.39554	+	0.289656i
$806$		0			0
$807$		−	17.5220i		−	0.616804i
$808$			14.2473i			0.501217i
$809$	−22.3988			−0.787501			−0.393751	−	0.919217i	$-0.628823\pi$
$809$	−22.3988			−0.787501			−0.393751	+	0.919217i	$0.628823\pi$
$810$	2.36163	+	11.3782i	0.0829793	+	0.399788i
$811$	10.0371			0.352450			0.176225	−	0.984350i	$-0.443611\pi$
$811$	10.0371			0.352450			0.176225	+	0.984350i	$0.443611\pi$
$812$			1.68191i			0.0590236i
$813$		−	9.57728i		−	0.335890i
$814$	−13.5187			−0.473830
$815$	−6.92717	−	33.3746i	−0.242648	−	1.16906i
$816$	4.49870			0.157486
$817$		−	17.6940i		−	0.619034i
$818$		−	3.02146i		−	0.105643i
$819$		0			0
$820$	−9.30244	+	1.93080i	−0.324855	+	0.0674264i
$821$	12.9086			0.450513			0.225257	−	0.974299i	$-0.427678\pi$
$821$	12.9086			0.450513			0.225257	+	0.974299i	$0.427678\pi$
$822$			4.27093i			0.148966i
$823$			24.3811i			0.849870i	0.905224	+	0.424935i	$0.139703\pi$
$823$			24.3811i			0.849870i	−0.905224	+	0.424935i	$0.860297\pi$
$824$	9.72411			0.338755
$825$	−1.93852	−	4.46864i	−0.0674906	−	0.155578i
$826$	0.166696			0.00580010
$827$			11.1712i			0.388461i	0.980956	+	0.194230i	$0.0622209\pi$
$827$			11.1712i			0.388461i	−0.980956	+	0.194230i	$0.937779\pi$
$828$		−	19.1399i		−	0.665158i
$829$	−28.9931			−1.00697			−0.503487	−	0.864003i	$-0.667950\pi$
$829$	−28.9931			−1.00697			−0.503487	+	0.864003i	$0.667950\pi$
$830$	36.3004	−	7.53444i	1.26000	−	0.261524i
$831$	−6.61717			−0.229547
$832$		0			0
$833$			7.89217i			0.273448i
$834$	−11.1997			−0.387813
$835$	−3.94989	−	19.0303i	−0.136691	−	0.658569i
$836$	−10.8369			−0.374804
$837$			5.06841i			0.175190i
$838$		−	35.0376i		−	1.21036i
$839$	−24.0650			−0.830818			−0.415409	−	0.909635i	$-0.636361\pi$
$839$	−24.0650			−0.830818			−0.415409	+	0.909635i	$0.636361\pi$
$840$	0.731575	+	3.52467i	0.0252417	+	0.121613i
$841$	−28.5148			−0.983269
$842$		−	9.81291i		−	0.338175i
$843$		−	7.86678i		−	0.270946i
$844$	−13.7163			−0.472133
$845$		0			0
$846$	7.09033			0.243771
$847$			21.4055i			0.735500i
$848$		−	7.04744i		−	0.242010i
$849$	−8.70327			−0.298695
$850$	30.9506	−	13.4265i	1.06160	−	0.460527i
$851$	69.2945			2.37539
$852$			2.40633i			0.0824395i
$853$		−	13.7936i		−	0.472284i	−0.971719	−	0.236142i	$-0.924117\pi$
$853$		−	13.7936i		−	0.472284i	0.971719	−	0.236142i	$-0.0758831\pi$
$854$	−14.2818			−0.488712
$855$	−41.4957	+	8.61277i	−1.41912	+	0.294551i
$856$	−6.14900			−0.210168
$857$		−	14.1595i		−	0.483678i	−0.970316	−	0.241839i	$-0.922249\pi$
$857$		−	14.1595i		−	0.483678i	0.970316	−	0.241839i	$-0.0777506\pi$
$858$		0			0
$859$	−27.6665			−0.943968			−0.471984	−	0.881607i	$-0.656462\pi$
$859$	−27.6665			−0.943968			−0.471984	+	0.881607i	$0.656462\pi$
$860$	−1.08415	−	5.22333i	−0.0369691	−	0.178114i
$861$	6.84011			0.233110
$862$			5.88552i			0.200462i
$863$		−	17.4318i		−	0.593386i	−0.954973	−	0.296693i	$-0.904116\pi$
$863$		−	17.4318i		−	0.593386i	0.954973	−	0.296693i	$-0.0958839\pi$
$864$	−3.70397			−0.126011
$865$	−1.54154	−	7.42704i	−0.0524140	−	0.252527i
$866$	−31.1096			−1.05715
$867$			19.0206i			0.645975i
$868$		−	3.30409i		−	0.112148i
$869$	1.12033			0.0380046
$870$	1.01678	−	0.211041i	0.0344721	−	0.00715497i
$871$		0			0
$872$		−	0.319202i		−	0.0108096i
$873$		−	26.8861i		−	0.909956i
$874$	55.5484			1.87895
$875$	15.5527	+	22.0660i	0.525777	+	0.745967i
$876$	6.20157			0.209532
$877$			2.17528i			0.0734539i	0.999325	+	0.0367270i	$0.0116932\pi$
$877$			2.17528i			0.0734539i	−0.999325	+	0.0367270i	$0.988307\pi$
$878$		−	2.69710i		−	0.0910229i
$879$	10.8248			0.365111
$880$	−3.19911	+	0.664001i	−0.107842	+	0.0223835i
$881$	−6.32823			−0.213204			−0.106602	−	0.994302i	$-0.533997\pi$
$881$	−6.32823			−0.213204			−0.106602	+	0.994302i	$0.533997\pi$
$882$		−	2.98901i		−	0.100645i
$883$		−	28.5533i		−	0.960895i	−0.877024	−	0.480447i	$-0.840474\pi$
$883$		−	28.5533i		−	0.960895i	0.877024	−	0.480447i	$-0.159526\pi$
$884$		0			0
$885$	−0.0209165	−	0.100774i	−0.000703101	−	0.00338749i
$886$	19.0859			0.641203
$887$		−	21.3012i		−	0.715225i	−0.933870	−	0.357613i	$-0.883591\pi$
$887$		−	21.3012i		−	0.715225i	0.933870	−	0.357613i	$-0.116409\pi$
$888$		−	6.16846i		−	0.207000i
$889$	23.5151			0.788672
$890$	8.06526	+	38.8578i	0.270348	+	1.30252i
$891$	7.59362			0.254396
$892$			9.84353i			0.329586i
$893$			20.5778i			0.688609i
$894$	5.93660			0.198550
$895$	29.1182	−	6.04372i	0.973313	−	0.202019i
$896$	2.41461			0.0806665
$897$		0			0
$898$		−	18.3579i		−	0.612611i
$899$	−0.953149			−0.0317893
$900$	−11.7220	+	5.08505i	−0.390732	+	0.169502i
$901$	47.5525			1.58420
$902$			6.20831i			0.206714i
$903$			3.84073i			0.127812i
$904$	−1.95370			−0.0649793
$905$	30.6538	−	6.36244i	1.01897	−	0.211495i
$906$	11.4491			0.380370
$907$			46.5451i			1.54551i	0.634707	+	0.772753i	$0.281121\pi$
$907$			46.5451i			1.54551i	−0.634707	+	0.772753i	$0.718879\pi$
$908$		−	19.4038i		−	0.643939i
$909$	36.4086			1.20760
$910$		0			0
$911$	−29.3014			−0.970800			−0.485400	−	0.874292i	$-0.661326\pi$
$911$	−29.3014			−0.970800			−0.485400	+	0.874292i	$0.661326\pi$
$912$		−	4.94481i		−	0.163739i
$913$		−	24.2263i		−	0.801775i
$914$	−25.3873			−0.839739
$915$	1.79203	+	8.63387i	0.0592427	+	0.285427i
$916$	−16.7503			−0.553447
$917$		−	25.6129i		−	0.845813i
$918$		−	24.9925i		−	0.824874i
$919$	−29.4843			−0.972598			−0.486299	−	0.873792i	$-0.661654\pi$
$919$	−29.4843			−0.972598			−0.486299	+	0.873792i	$0.661654\pi$
$920$	16.3981	−	3.40356i	0.540629	−	0.112212i
$921$	−3.77758			−0.124476
$922$			1.12031i			0.0368956i
$923$		0			0
$924$	2.35231			0.0773855
$925$	−18.4100	−	42.4384i	−0.605317	−	1.39537i
$926$	−30.6952			−1.00871
$927$		−	24.8498i		−	0.816173i
$928$		−	0.696556i		−	0.0228656i
$929$	−47.7459			−1.56649			−0.783246	−	0.621712i	$-0.786438\pi$
$929$	−47.7459			−1.56649			−0.783246	+	0.621712i	$0.786438\pi$
$930$	−1.99745	+	0.414587i	−0.0654990	+	0.0135949i
$931$	8.67479			0.284305
$932$			16.7974i			0.550217i
$933$		−	13.6988i		−	0.448479i
$934$	−5.88670			−0.192619
$935$	−4.48034	−	21.5859i	−0.146523	−	0.705935i
$936$		0			0
$937$			29.2998i			0.957182i	0.878038	+	0.478591i	$0.158852\pi$
$937$			29.2998i			0.957182i	−0.878038	+	0.478591i	$0.841148\pi$
$938$		−	26.5505i		−	0.866905i
$939$	7.35753			0.240104
$940$	1.26084	+	6.07463i	0.0411241	+	0.198133i
$941$	−7.48425			−0.243980			−0.121990	−	0.992531i	$-0.538928\pi$
$941$	−7.48425			−0.243980			−0.121990	+	0.992531i	$0.538928\pi$
$942$		−	7.37720i		−	0.240362i
$943$		−	31.8228i		−	1.03629i
$944$	−0.0690364			−0.00224694
$945$	19.5813	−	4.06425i	0.636978	−	0.132210i
$946$	−3.48597			−0.113339
$947$		−	15.9785i		−	0.519230i	−0.965712	−	0.259615i	$-0.916404\pi$
$947$		−	15.9785i		−	0.519230i	0.965712	−	0.259615i	$-0.0835957\pi$
$948$			0.511198i			0.0166029i
$949$		0			0
$950$	−14.7580	−	34.0198i	−0.478811	−	1.10375i
$951$	11.3780			0.368958
$952$			16.2926i			0.528045i
$953$			44.7821i			1.45063i	0.688415	+	0.725317i	$0.258307\pi$
$953$			44.7821i			1.45063i	−0.688415	+	0.725317i	$0.741693\pi$
$954$	−18.0096			−0.583082
$955$	41.0680	−	8.52401i	1.32893	−	0.275830i
$956$	18.2819			0.591278
$957$		−	0.678585i		−	0.0219355i
$958$			24.6962i			0.797899i
$959$	−15.4677			−0.499477
$960$	−0.302978	−	1.45973i	−0.00977858	−	0.0471125i
$961$	−29.1276			−0.939599
$962$		0			0
$963$			15.7137i			0.506365i
$964$	7.86172			0.253209
$965$	−11.0815	−	53.3896i	−0.356725	−	1.71867i
$966$	−12.0576			−0.387946
$967$		−	5.51993i		−	0.177509i	−0.996054	−	0.0887546i	$-0.971711\pi$
$967$		−	5.51993i		−	0.177509i	0.996054	−	0.0887546i	$-0.0282887\pi$
$968$		−	8.86496i		−	0.284931i
$969$	33.3650			1.07184
$970$	23.0346	−	4.78102i	0.739597	−	0.153509i
$971$	−38.6903			−1.24163			−0.620815	−	0.783957i	$-0.713198\pi$
$971$	−38.6903			−1.24163			−0.620815	+	0.783957i	$0.713198\pi$
$972$			14.5768i			0.467551i
$973$		−	40.5609i		−	1.30032i
$974$	6.85817			0.219750
$975$		0			0
$976$	5.91472			0.189326
$977$			22.0275i			0.704722i	0.935864	+	0.352361i	$0.114621\pi$
$977$			22.0275i			0.704722i	−0.935864	+	0.352361i	$0.885379\pi$
$978$		−	10.1633i		−	0.324987i
$979$	25.9331			0.828826
$980$	2.56083	−	0.531521i	0.0818027	−	0.0169788i
$981$	−0.815716			−0.0260438
$982$			32.0421i			1.02251i
$983$			49.1575i			1.56788i	0.620835	+	0.783941i	$0.286794\pi$
$983$			49.1575i			1.56788i	−0.620835	+	0.783941i	$0.713206\pi$
$984$	−2.83280			−0.0903064
$985$	−1.24120	−	5.97999i	−0.0395478	−	0.190538i
$986$	4.70000			0.149679
$987$		−	4.46670i		−	0.142177i
$988$		0			0
$989$	17.8685			0.568186
$990$	1.69684	+	8.17526i	0.0539292	+	0.259827i
$991$	−7.70733			−0.244831			−0.122416	−	0.992479i	$-0.539064\pi$
$991$	−7.70733			−0.244831			−0.122416	+	0.992479i	$0.539064\pi$
$992$			1.36837i			0.0434459i
$993$		−	19.8001i		−	0.628338i
$994$	−8.71480			−0.276417
$995$	24.5468	−	5.09489i	0.778185	−	0.161519i
$996$	11.0543			0.350268
$997$		−	23.9968i		−	0.759986i	−0.924989	−	0.379993i	$-0.875926\pi$
$997$		−	23.9968i		−	0.759986i	0.924989	−	0.379993i	$-0.124074\pi$
$998$			25.9861i			0.822575i
$999$	−34.2688			−1.08422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.f.339.5	✓	18
5.2	odd	4		8450.2.a.cx.1.5		9
5.3	odd	4		8450.2.a.cw.1.5		9
5.4	even	2	inner	1690.2.b.f.339.14	yes	18
13.5	odd	4		1690.2.c.g.1689.7		18
13.8	odd	4		1690.2.c.h.1689.7		18
13.12	even	2		1690.2.b.g.339.14	yes	18
65.12	odd	4		8450.2.a.ct.1.5		9
65.34	odd	4		1690.2.c.g.1689.12		18
65.38	odd	4		8450.2.a.da.1.5		9
65.44	odd	4		1690.2.c.h.1689.12		18
65.64	even	2		1690.2.b.g.339.5	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.5	✓	18	1.1	even	1	trivial
1690.2.b.f.339.14	yes	18	5.4	even	2	inner
1690.2.b.g.339.5	yes	18	65.64	even	2
1690.2.b.g.339.14	yes	18	13.12	even	2
1690.2.c.g.1689.7		18	13.5	odd	4
1690.2.c.g.1689.12		18	65.34	odd	4
1690.2.c.h.1689.7		18	13.8	odd	4
1690.2.c.h.1689.12		18	65.44	odd	4
8450.2.a.ct.1.5		9	65.12	odd	4
8450.2.a.cw.1.5		9	5.3	odd	4
8450.2.a.cx.1.5		9	5.2	odd	4
8450.2.a.da.1.5		9	65.38	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.666723i q^{3} -1.00000 q^{4} +(-2.18940 + 0.454429i) q^{5} -0.666723 q^{6} -2.41461i q^{7} +1.00000i q^{8} +2.55548 q^{9} +(0.454429 + 2.18940i) q^{10} +1.46118 q^{11} +0.666723i q^{12} -2.41461 q^{14} +(0.302978 + 1.45973i) q^{15} +1.00000 q^{16} +6.74749i q^{17} -2.55548i q^{18} +7.41659 q^{19} +(2.18940 - 0.454429i) q^{20} -1.60988 q^{21} -1.46118i q^{22} +7.48975i q^{23} +0.666723 q^{24} +(4.58699 - 1.98986i) q^{25} -3.70397i q^{27} +2.41461i q^{28} +0.696556 q^{29} +(1.45973 - 0.302978i) q^{30} -1.36837 q^{31} -1.00000i q^{32} -0.974200i q^{33} +6.74749 q^{34} +(1.09727 + 5.28656i) q^{35} -2.55548 q^{36} -9.25191i q^{37} -7.41659i q^{38} +(-0.454429 - 2.18940i) q^{40} -4.24884 q^{41} +1.60988i q^{42} -2.38573i q^{43} -1.46118 q^{44} +(-5.59498 + 1.16128i) q^{45} +7.48975 q^{46} +2.77456i q^{47} -0.666723i q^{48} +1.16965 q^{49} +(-1.98986 - 4.58699i) q^{50} +4.49870 q^{51} -7.04744i q^{53} -3.70397 q^{54} +(-3.19911 + 0.664001i) q^{55} +2.41461 q^{56} -4.94481i q^{57} -0.696556i q^{58} -0.0690364 q^{59} +(-0.302978 - 1.45973i) q^{60} +5.91472 q^{61} +1.36837i q^{62} -6.17050i q^{63} -1.00000 q^{64} -0.974200 q^{66} +10.9958i q^{67} -6.74749i q^{68} +4.99359 q^{69} +(5.28656 - 1.09727i) q^{70} +3.60919 q^{71} +2.55548i q^{72} -9.30157i q^{73} -9.25191 q^{74} +(-1.32668 - 3.05825i) q^{75} -7.41659 q^{76} -3.52818i q^{77} +0.766732 q^{79} +(-2.18940 + 0.454429i) q^{80} +5.19692 q^{81} +4.24884i q^{82} -16.5800i q^{83} +1.60988 q^{84} +(-3.06625 - 14.7730i) q^{85} -2.38573 q^{86} -0.464410i q^{87} +1.46118i q^{88} +17.7481 q^{89} +(1.16128 + 5.59498i) q^{90} -7.48975i q^{92} +0.912326i q^{93} +2.77456 q^{94} +(-16.2379 + 3.37031i) q^{95} -0.666723 q^{96} -10.5209i q^{97} -1.16965i q^{98} +3.73401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{4} - 14 q^{6} - 16 q^{9} + 2 q^{10} - 8 q^{11} - 2 q^{14} - 8 q^{15} + 18 q^{16} + 12 q^{19} - 16 q^{21} + 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} + 12 q^{31} + 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots + 32 q^{99}+O(q^{100}) \) 18 * q - 18 * q^4 - 14 * q^6 - 16 * q^9 + 2 * q^10 - 8 * q^11 - 2 * q^14 - 8 * q^15 + 18 * q^16 + 12 * q^19 - 16 * q^21 + 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 + 12 * q^31 + 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 - 54 * q^41 + 8 * q^44 - 20 * q^45 - 22 * q^46 + 20 * q^49 - 8 * q^50 + 24 * q^51 + 68 * q^54 + 2 * q^56 + 40 * q^59 + 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 + 6 * q^70 + 20 * q^71 + 20 * q^74 - 72 * q^75 - 12 * q^76 + 28 * q^79 + 106 * q^81 + 16 * q^84 - 56 * q^85 - 82 * q^86 + 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 - 14 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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