LMFDB - Embedded newform 1690.2.c.g.1689.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,-18,0,18,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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			1689.9
Root			$0.506152i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.g.1689.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -0.0670024i q^{3} +1.00000 q^{4} +(1.50791 - 1.65112i) q^{5} +0.0670024i q^{6} -5.03568 q^{7} -1.00000 q^{8} +2.99551 q^{9} +(-1.50791 + 1.65112i) q^{10} +3.28967i q^{11} -0.0670024i q^{12} +5.03568 q^{14} +(-0.110629 - 0.101034i) q^{15} +1.00000 q^{16} -0.516695i q^{17} -2.99551 q^{18} +5.26981i q^{19} +(1.50791 - 1.65112i) q^{20} +0.337403i q^{21} -3.28967i q^{22} +0.524116i q^{23} +0.0670024i q^{24} +(-0.452390 - 4.97949i) q^{25} -0.401714i q^{27} -5.03568 q^{28} -6.36392 q^{29} +(0.110629 + 0.101034i) q^{30} -6.84648i q^{31} -1.00000 q^{32} +0.220416 q^{33} +0.516695i q^{34} +(-7.59337 + 8.31450i) q^{35} +2.99551 q^{36} -5.49639 q^{37} -5.26981i q^{38} +(-1.50791 + 1.65112i) q^{40} +5.54869i q^{41} -0.337403i q^{42} +9.35921i q^{43} +3.28967i q^{44} +(4.51697 - 4.94595i) q^{45} -0.524116i q^{46} -1.65182 q^{47} -0.0670024i q^{48} +18.3580 q^{49} +(0.452390 + 4.97949i) q^{50} -0.0346198 q^{51} +9.30982i q^{53} +0.401714i q^{54} +(5.43164 + 4.96055i) q^{55} +5.03568 q^{56} +0.353090 q^{57} +6.36392 q^{58} +12.8188i q^{59} +(-0.110629 - 0.101034i) q^{60} -11.5310 q^{61} +6.84648i q^{62} -15.0844 q^{63} +1.00000 q^{64} -0.220416 q^{66} -3.38856 q^{67} -0.516695i q^{68} +0.0351171 q^{69} +(7.59337 - 8.31450i) q^{70} -3.86643i q^{71} -2.99551 q^{72} +6.43004 q^{73} +5.49639 q^{74} +(-0.333638 + 0.0303112i) q^{75} +5.26981i q^{76} -16.5657i q^{77} +7.28413 q^{79} +(1.50791 - 1.65112i) q^{80} +8.95962 q^{81} -5.54869i q^{82} +2.57870 q^{83} +0.337403i q^{84} +(-0.853124 - 0.779131i) q^{85} -9.35921i q^{86} +0.426398i q^{87} -3.28967i q^{88} +4.82497i q^{89} +(-4.51697 + 4.94595i) q^{90} +0.524116i q^{92} -0.458731 q^{93} +1.65182 q^{94} +(8.70109 + 7.94642i) q^{95} +0.0670024i q^{96} +1.88098 q^{97} -18.3580 q^{98} +9.85425i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 2 q^{5} + 2 q^{7} - 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} - 14 q^{15} + 18 q^{16} + 16 q^{18} + 2 q^{20} - 22 q^{25} + 2 q^{28} - 30 q^{29} + 14 q^{30} - 18 q^{32} + 28 q^{33}+ \cdots + 20 q^{98}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 2 * q^5 + 2 * q^7 - 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 - 14 * q^15 + 18 * q^16 + 16 * q^18 + 2 * q^20 - 22 * q^25 + 2 * q^28 - 30 * q^29 + 14 * q^30 - 18 * q^32 + 28 * q^33 - 4 * q^35 - 16 * q^36 - 20 * q^37 - 2 * q^40 - 20 * q^45 + 10 * q^47 - 20 * q^49 + 22 * q^50 - 24 * q^51 - 2 * q^56 + 24 * q^57 + 30 * q^58 - 14 * q^60 - 38 * q^61 - 78 * q^63 + 18 * q^64 - 28 * q^66 + 2 * q^67 - 28 * q^69 + 4 * q^70 + 16 * q^72 + 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 + 2 * q^80 + 106 * q^81 + 2 * q^83 + 16 * q^85 + 20 * q^90 - 56 * q^93 - 10 * q^94 + 54 * q^95 - 12 * q^97 + 20 * q^98

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	0.0670024i		−	0.0386839i	−0.999813	−	0.0193419i	$-0.993843\pi$
$3$		−	0.0670024i		−	0.0386839i	0.999813	−	0.0193419i	$-0.00615711\pi$
$4$	1.00000			0.500000
$5$	1.50791	−	1.65112i	0.674360	−	0.738403i
$5$	1.50791	−	1.65112i	0.674360	−	0.738403i
$6$			0.0670024i			0.0273536i
$7$	−5.03568			−1.90331			−0.951653	−	0.307174i	$-0.900617\pi$
$7$	−5.03568			−1.90331			−0.951653	+	0.307174i	$0.900617\pi$
$8$	−1.00000			−0.353553
$9$	2.99551			0.998504
$10$	−1.50791	+	1.65112i	−0.476844	+	0.522130i
$11$			3.28967i			0.991874i	0.868358	+	0.495937i	$0.165175\pi$
$11$			3.28967i			0.991874i	−0.868358	+	0.495937i	$0.834825\pi$
$12$		−	0.0670024i		−	0.0193419i
$13$		0			0
$13$		0			0
$14$	5.03568			1.34584
$15$	−0.110629	−	0.101034i	−0.0285643	−	0.0260868i
$16$	1.00000			0.250000
$17$		−	0.516695i		−	0.125317i	−0.998035	−	0.0626584i	$-0.980042\pi$
$17$		−	0.516695i		−	0.125317i	0.998035	−	0.0626584i	$-0.0199579\pi$
$18$	−2.99551			−0.706049
$19$			5.26981i			1.20898i	0.796614	+	0.604489i	$0.206623\pi$
$19$			5.26981i			1.20898i	−0.796614	+	0.604489i	$0.793377\pi$
$20$	1.50791	−	1.65112i	0.337180	−	0.369201i
$21$			0.337403i			0.0736273i
$22$		−	3.28967i		−	0.701361i
$23$			0.524116i			0.109286i	0.998506	+	0.0546429i	$0.0174020\pi$
$23$			0.524116i			0.109286i	−0.998506	+	0.0546429i	$0.982598\pi$
$24$			0.0670024i			0.0136768i
$25$	−0.452390	−	4.97949i	−0.0904780	−	0.995898i
$26$		0			0
$27$		−	0.401714i		−	0.0773099i
$28$	−5.03568			−0.951653
$29$	−6.36392			−1.18175			−0.590875	−	0.806763i	$-0.701217\pi$
$29$	−6.36392			−1.18175			−0.590875	+	0.806763i	$0.701217\pi$
$30$	0.110629	+	0.101034i	0.0201980	+	0.0184462i
$31$		−	6.84648i		−	1.22966i	−0.788658	−	0.614832i	$-0.789224\pi$
$31$		−	6.84648i		−	1.22966i	0.788658	−	0.614832i	$-0.210776\pi$
$32$	−1.00000			−0.176777
$33$	0.220416			0.0383695
$34$			0.516695i			0.0886124i
$35$	−7.59337	+	8.31450i	−1.28351	+	1.40541i
$36$	2.99551			0.499252
$37$	−5.49639			−0.903600			−0.451800	−	0.892119i	$-0.649218\pi$
$37$	−5.49639			−0.903600			−0.451800	+	0.892119i	$0.649218\pi$
$38$		−	5.26981i		−	0.854876i
$39$		0			0
$40$	−1.50791	+	1.65112i	−0.238422	+	0.261065i
$41$			5.54869i			0.866560i	0.901259	+	0.433280i	$0.142644\pi$
$41$			5.54869i			0.866560i	−0.901259	+	0.433280i	$0.857356\pi$
$42$		−	0.337403i		−	0.0520624i
$43$			9.35921i			1.42727i	0.700520	+	0.713633i	$0.252952\pi$
$43$			9.35921i			1.42727i	−0.700520	+	0.713633i	$0.747048\pi$
$44$			3.28967i			0.495937i
$45$	4.51697	−	4.94595i	0.673351	−	0.737298i
$46$		−	0.524116i		−	0.0772767i
$47$	−1.65182			−0.240942			−0.120471	−	0.992717i	$-0.538440\pi$
$47$	−1.65182			−0.240942			−0.120471	+	0.992717i	$0.538440\pi$
$48$		−	0.0670024i		−	0.00967097i
$49$	18.3580			2.62258
$50$	0.452390	+	4.97949i	0.0639776	+	0.704207i
$51$	−0.0346198			−0.00484774
$52$		0			0
$53$			9.30982i			1.27880i	0.768873	+	0.639401i	$0.220818\pi$
$53$			9.30982i			1.27880i	−0.768873	+	0.639401i	$0.779182\pi$
$54$			0.401714i			0.0546663i
$55$	5.43164	+	4.96055i	0.732403	+	0.668880i
$56$	5.03568			0.672921
$57$	0.353090			0.0467679
$58$	6.36392			0.835624
$59$			12.8188i			1.66887i	0.551108	+	0.834434i	$0.314205\pi$
$59$			12.8188i			1.66887i	−0.551108	+	0.834434i	$0.685795\pi$
$60$	−0.110629	−	0.101034i	−0.0142821	−	0.0130434i
$61$	−11.5310			−1.47639			−0.738196	−	0.674586i	$-0.764322\pi$
$61$	−11.5310			−1.47639			−0.738196	+	0.674586i	$0.764322\pi$
$62$			6.84648i			0.869503i
$63$	−15.0844			−1.90046
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.220416			−0.0271314
$67$	−3.38856			−0.413978			−0.206989	−	0.978343i	$-0.566366\pi$
$67$	−3.38856			−0.413978			−0.206989	+	0.978343i	$0.566366\pi$
$68$		−	0.516695i		−	0.0626584i
$69$	0.0351171			0.00422760
$70$	7.59337	−	8.31450i	0.907581	−	0.993773i
$71$		−	3.86643i		−	0.458861i	−0.973325	−	0.229430i	$-0.926314\pi$
$71$		−	3.86643i		−	0.458861i	0.973325	−	0.229430i	$-0.0736863\pi$
$72$	−2.99551			−0.353024
$73$	6.43004			0.752579			0.376290	−	0.926502i	$-0.377200\pi$
$73$	6.43004			0.752579			0.376290	+	0.926502i	$0.377200\pi$
$74$	5.49639			0.638942
$75$	−0.333638	+	0.0303112i	−0.0385252	+	0.00350004i
$76$			5.26981i			0.604489i
$77$		−	16.5657i		−	1.88784i
$78$		0			0
$79$	7.28413			0.819528			0.409764	−	0.912191i	$-0.365611\pi$
$79$	7.28413			0.819528			0.409764	+	0.912191i	$0.365611\pi$
$80$	1.50791	−	1.65112i	0.168590	−	0.184601i
$81$	8.95962			0.995513
$82$		−	5.54869i		−	0.612750i
$83$	2.57870			0.283050			0.141525	−	0.989935i	$-0.454800\pi$
$83$	2.57870			0.283050			0.141525	+	0.989935i	$0.454800\pi$
$84$			0.337403i			0.0368136i
$85$	−0.853124	−	0.779131i	−0.0925343	−	0.0845086i
$86$		−	9.35921i		−	1.00923i
$87$			0.426398i			0.0457147i
$88$		−	3.28967i		−	0.350680i
$89$			4.82497i			0.511446i	0.966750	+	0.255723i	$0.0823135\pi$
$89$			4.82497i			0.511446i	−0.966750	+	0.255723i	$0.917687\pi$
$90$	−4.51697	+	4.94595i	−0.476131	+	0.521348i
$91$		0			0
$92$			0.524116i			0.0546429i
$93$	−0.458731			−0.0475681
$94$	1.65182			0.170372
$95$	8.70109	+	7.94642i	0.892713	+	0.815286i
$96$			0.0670024i			0.00683841i
$97$	1.88098			0.190985			0.0954925	−	0.995430i	$-0.469557\pi$
$97$	1.88098			0.190985			0.0954925	+	0.995430i	$0.469557\pi$
$98$	−18.3580			−1.85444
$99$			9.85425i			0.990390i
$100$	−0.452390	−	4.97949i	−0.0452390	−	0.497949i
$101$	−3.10344			−0.308804			−0.154402	−	0.988008i	$-0.549345\pi$
$101$	−3.10344			−0.308804			−0.154402	+	0.988008i	$0.549345\pi$
$102$	0.0346198			0.00342787
$103$			14.9509i			1.47316i	0.676351	+	0.736580i	$0.263560\pi$
$103$			14.9509i			1.47316i	−0.676351	+	0.736580i	$0.736440\pi$
$104$		0			0
$105$	0.557092	+	0.508774i	0.0543666	+	0.0496513i
$106$		−	9.30982i		−	0.904250i
$107$			15.3210i			1.48113i	0.671983	+	0.740567i	$0.265443\pi$
$107$			15.3210i			1.48113i	−0.671983	+	0.740567i	$0.734557\pi$
$108$		−	0.401714i		−	0.0386549i
$109$			4.19883i			0.402175i	0.979573	+	0.201087i	$0.0644475\pi$
$109$			4.19883i			0.402175i	−0.979573	+	0.201087i	$0.935553\pi$
$110$	−5.43164	−	4.96055i	−0.517887	−	0.472970i
$111$			0.368271i			0.0349548i
$112$	−5.03568			−0.475827
$113$		−	11.7363i		−	1.10406i	−0.833825	−	0.552029i	$-0.813854\pi$
$113$		−	11.7363i		−	1.10406i	0.833825	−	0.552029i	$-0.186146\pi$
$114$	−0.353090			−0.0330699
$115$	0.865378	+	0.790322i	0.0806970	+	0.0736979i
$116$	−6.36392			−0.590875
$117$		0			0
$118$		−	12.8188i		−	1.18007i
$119$			2.60191i			0.238516i
$120$	0.110629	+	0.101034i	0.0100990	+	0.00922309i
$121$	0.178043			0.0161857
$122$	11.5310			1.04397
$123$	0.371776			0.0335219
$124$		−	6.84648i		−	0.614832i
$125$	−8.90390	−	6.76170i	−0.796389	−	0.604785i
$126$	15.0844			1.34383
$127$			9.96441i			0.884198i	0.896966	+	0.442099i	$0.145766\pi$
$127$			9.96441i			0.884198i	−0.896966	+	0.442099i	$0.854234\pi$
$128$	−1.00000			−0.0883883
$129$	0.627090			0.0552122
$130$		0			0
$131$	−3.43248			−0.299897			−0.149948	−	0.988694i	$-0.547911\pi$
$131$	−3.43248			−0.299897			−0.149948	+	0.988694i	$0.547911\pi$
$132$	0.220416			0.0191848
$133$		−	26.5371i		−	2.30106i
$134$	3.38856			0.292727
$135$	−0.663277	−	0.605750i	−0.0570858	−	0.0521347i
$136$			0.516695i			0.0443062i
$137$	17.1983			1.46935			0.734677	−	0.678417i	$-0.237334\pi$
$137$	17.1983			1.46935			0.734677	+	0.678417i	$0.237334\pi$
$138$	−0.0351171			−0.00298936
$139$	6.56328			0.556690			0.278345	−	0.960481i	$-0.410214\pi$
$139$	6.56328			0.556690			0.278345	+	0.960481i	$0.410214\pi$
$140$	−7.59337	+	8.31450i	−0.641757	+	0.702704i
$141$			0.110676i			0.00932057i
$142$			3.86643i			0.324464i
$143$		0			0
$144$	2.99551			0.249626
$145$	−9.59625	+	10.5076i	−0.796925	+	0.872608i
$146$	−6.43004			−0.532154
$147$		−	1.23003i		−	0.101451i
$148$	−5.49639			−0.451800
$149$		−	12.7625i		−	1.04554i	−0.852473	−	0.522772i	$-0.824898\pi$
$149$		−	12.7625i		−	1.04554i	0.852473	−	0.522772i	$-0.175102\pi$
$150$	0.333638	−	0.0303112i	0.0272414	−	0.00247490i
$151$			9.73737i			0.792416i	0.918161	+	0.396208i	$0.129674\pi$
$151$			9.73737i			0.792416i	−0.918161	+	0.396208i	$0.870326\pi$
$152$		−	5.26981i		−	0.427438i
$153$		−	1.54776i		−	0.125129i
$154$			16.5657i			1.33491i
$155$	−11.3043	−	10.3239i	−0.907987	−	0.829235i
$156$		0			0
$157$			21.3156i			1.70117i	0.525835	+	0.850587i	$0.323753\pi$
$157$			21.3156i			1.70117i	−0.525835	+	0.850587i	$0.676247\pi$
$158$	−7.28413			−0.579494
$159$	0.623781			0.0494690
$160$	−1.50791	+	1.65112i	−0.119211	+	0.130532i
$161$		−	2.63928i		−	0.208004i
$162$	−8.95962			−0.703934
$163$	−1.27897			−0.100177			−0.0500883	−	0.998745i	$-0.515950\pi$
$163$	−1.27897			−0.100177			−0.0500883	+	0.998745i	$0.515950\pi$
$164$			5.54869i			0.433280i
$165$	0.332369	−	0.363933i	0.0258749	−	0.0283322i
$166$	−2.57870			−0.200146
$167$	1.90682			0.147554			0.0737770	−	0.997275i	$-0.476495\pi$
$167$	1.90682			0.147554			0.0737770	+	0.997275i	$0.476495\pi$
$168$		−	0.337403i		−	0.0260312i
$169$		0			0
$170$	0.853124	+	0.779131i	0.0654317	+	0.0597566i
$171$			15.7858i			1.20717i
$172$			9.35921i			0.713633i
$173$			0.112802i			0.00857615i	0.999991	+	0.00428807i	$0.00136494\pi$
$173$			0.112802i			0.00857615i	−0.999991	+	0.00428807i	$0.998635\pi$
$174$		−	0.426398i		−	0.0323252i
$175$	2.27809	+	25.0751i	0.172207	+	1.89550i
$176$			3.28967i			0.247969i
$177$	0.858892			0.0645583
$178$		−	4.82497i		−	0.361647i
$179$	−9.78320			−0.731231			−0.365615	−	0.930766i	$-0.619141\pi$
$179$	−9.78320			−0.731231			−0.365615	+	0.930766i	$0.619141\pi$
$180$	4.51697	−	4.94595i	0.336675	−	0.368649i
$181$	−8.36184			−0.621531			−0.310765	−	0.950487i	$-0.600585\pi$
$181$	−8.36184			−0.621531			−0.310765	+	0.950487i	$0.600585\pi$
$182$		0			0
$183$			0.772604i			0.0571126i
$184$		−	0.524116i		−	0.0386384i
$185$	−8.28808	+	9.07519i	−0.609352	+	0.667221i
$186$	0.458731			0.0336358
$187$	1.69976			0.124299
$188$	−1.65182			−0.120471
$189$			2.02290i			0.147144i
$190$	−8.70109	−	7.94642i	−0.631243	−	0.576494i
$191$	−9.25588			−0.669732			−0.334866	−	0.942266i	$-0.608691\pi$
$191$	−9.25588			−0.669732			−0.334866	+	0.942266i	$0.608691\pi$
$192$		−	0.0670024i		−	0.00483548i
$193$	−17.5149			−1.26075			−0.630374	−	0.776292i	$-0.717098\pi$
$193$	−17.5149			−1.26075			−0.630374	+	0.776292i	$0.717098\pi$
$194$	−1.88098			−0.135047
$195$		0			0
$196$	18.3580			1.31129
$197$	20.2809			1.44496			0.722479	−	0.691393i	$-0.243003\pi$
$197$	20.2809			1.44496			0.722479	+	0.691393i	$0.243003\pi$
$198$		−	9.85425i		−	0.700311i
$199$	−27.0802			−1.91966			−0.959832	−	0.280577i	$-0.909474\pi$
$199$	−27.0802			−1.91966			−0.959832	+	0.280577i	$0.909474\pi$
$200$	0.452390	+	4.97949i	0.0319888	+	0.352103i
$201$			0.227042i			0.0160143i
$202$	3.10344			0.218357
$203$	32.0466			2.24923
$204$	−0.0346198			−0.00242387
$205$	9.16155	+	8.36695i	0.639870	+	0.584373i
$206$		−	14.9509i		−	1.04168i
$207$			1.57000i			0.109122i
$208$		0			0
$209$	−17.3360			−1.19915
$210$	−0.557092	−	0.508774i	−0.0384430	−	0.0351088i
$211$	−11.9828			−0.824928			−0.412464	−	0.910974i	$-0.635332\pi$
$211$	−11.9828			−0.824928			−0.412464	+	0.910974i	$0.635332\pi$
$212$			9.30982i			0.639401i
$213$	−0.259060			−0.0177505
$214$		−	15.3210i		−	1.04732i
$215$	15.4532	+	14.1129i	1.05390	+	0.962491i
$216$			0.401714i			0.0273332i
$217$			34.4766i			2.34043i
$218$		−	4.19883i		−	0.284380i
$219$		−	0.430828i		−	0.0291127i
$220$	5.43164	+	4.96055i	0.366201	+	0.334440i
$221$		0			0
$222$		−	0.368271i		−	0.0247167i
$223$	12.7910			0.856546			0.428273	−	0.903649i	$-0.359122\pi$
$223$	12.7910			0.856546			0.428273	+	0.903649i	$0.359122\pi$
$224$	5.03568			0.336460
$225$	−1.35514	−	14.9161i	−0.0903426	−	0.994408i
$226$			11.7363i			0.780687i
$227$	−5.83533			−0.387305			−0.193652	−	0.981070i	$-0.562033\pi$
$227$	−5.83533			−0.387305			−0.193652	+	0.981070i	$0.562033\pi$
$228$	0.353090			0.0233840
$229$			15.2208i			1.00582i	0.864340	+	0.502909i	$0.167737\pi$
$229$			15.2208i			1.00582i	−0.864340	+	0.502909i	$0.832263\pi$
$230$	−0.865378	−	0.790322i	−0.0570614	−	0.0521123i
$231$	−1.10994			−0.0730290
$232$	6.36392			0.417812
$233$			18.4629i			1.20955i	0.796398	+	0.604773i	$0.206736\pi$
$233$			18.4629i			1.20955i	−0.796398	+	0.604773i	$0.793264\pi$
$234$		0			0
$235$	−2.49080	+	2.72734i	−0.162482	+	0.177912i
$236$			12.8188i			0.834434i
$237$		−	0.488054i		−	0.0317025i
$238$		−	2.60191i		−	0.168657i
$239$		−	3.76483i		−	0.243526i	−0.992559	−	0.121763i	$-0.961145\pi$
$239$		−	3.76483i		−	0.243526i	0.992559	−	0.121763i	$-0.0388548\pi$
$240$	−0.110629	−	0.101034i	−0.00714107	−	0.00652171i
$241$			15.4771i			0.996965i	0.866900	+	0.498482i	$0.166109\pi$
$241$			15.4771i			0.996965i	−0.866900	+	0.498482i	$0.833891\pi$
$242$	−0.178043			−0.0114450
$243$		−	1.80546i		−	0.115820i
$244$	−11.5310			−0.738196
$245$	27.6823	−	30.3113i	1.76856	−	1.93652i
$246$	−0.371776			−0.0237035
$247$		0			0
$248$			6.84648i			0.434752i
$249$		−	0.172779i		−	0.0109495i
$250$	8.90390	+	6.76170i	0.563132	+	0.427647i
$251$	−1.26747			−0.0800019			−0.0400010	−	0.999200i	$-0.512736\pi$
$251$	−1.26747			−0.0800019			−0.0400010	+	0.999200i	$0.512736\pi$
$252$	−15.0844			−0.950229
$253$	−1.72417			−0.108398
$254$		−	9.96441i		−	0.625223i
$255$	−0.0522037	+	0.0571614i	−0.00326912	+	0.00357959i
$256$	1.00000			0.0625000
$257$		−	29.7338i		−	1.85474i	−0.374143	−	0.927371i	$-0.622063\pi$
$257$		−	29.7338i		−	1.85474i	0.374143	−	0.927371i	$-0.377937\pi$
$258$	−0.627090			−0.0390409
$259$	27.6780			1.71983
$260$		0			0
$261$	−19.0632			−1.17998
$262$	3.43248			0.212059
$263$		−	20.2454i		−	1.24839i	−0.781270	−	0.624193i	$-0.785428\pi$
$263$		−	20.2454i		−	1.24839i	0.781270	−	0.624193i	$-0.214572\pi$
$264$	−0.220416			−0.0135657
$265$	15.3716	+	14.0384i	0.944271	+	0.862373i
$266$			26.5371i			1.62709i
$267$	0.323285			0.0197847
$268$	−3.38856			−0.206989
$269$	−12.2284			−0.745576			−0.372788	−	0.927917i	$-0.621598\pi$
$269$	−12.2284			−0.745576			−0.372788	+	0.927917i	$0.621598\pi$
$270$	0.663277	+	0.605750i	0.0403658	+	0.0368648i
$271$		−	13.3526i		−	0.811114i	−0.914070	−	0.405557i	$-0.867078\pi$
$271$		−	13.3526i		−	0.811114i	0.914070	−	0.405557i	$-0.132922\pi$
$272$		−	0.516695i		−	0.0313292i
$273$		0			0
$274$	−17.1983			−1.03899
$275$	16.3809	−	1.48822i	0.987806	−	0.0897428i
$276$	0.0351171			0.00211380
$277$			9.36534i			0.562709i	0.959604	+	0.281354i	$0.0907837\pi$
$277$			9.36534i			0.562709i	−0.959604	+	0.281354i	$0.909216\pi$
$278$	−6.56328			−0.393640
$279$		−	20.5087i		−	1.22782i
$280$	7.59337	−	8.31450i	0.453791	−	0.496887i
$281$		−	20.5996i		−	1.22887i	−0.788968	−	0.614434i	$-0.789384\pi$
$281$		−	20.5996i		−	1.22887i	0.788968	−	0.614434i	$-0.210616\pi$
$282$		−	0.110676i		−	0.00659064i
$283$		−	14.4039i		−	0.856225i	−0.903726	−	0.428112i	$-0.859179\pi$
$283$		−	14.4039i		−	0.856225i	0.903726	−	0.428112i	$-0.140821\pi$
$284$		−	3.86643i		−	0.229430i
$285$	0.532430	−	0.582994i	0.0315384	−	0.0345336i
$286$		0			0
$287$		−	27.9414i		−	1.64933i
$288$	−2.99551			−0.176512
$289$	16.7330			0.984296
$290$	9.59625	−	10.5076i	0.563511	−	0.617027i
$291$		−	0.126031i		−	0.00738804i
$292$	6.43004			0.376290
$293$	−15.0823			−0.881117			−0.440559	−	0.897724i	$-0.645220\pi$
$293$	−15.0823			−0.881117			−0.440559	+	0.897724i	$0.645220\pi$
$294$			1.23003i			0.0717370i
$295$	21.1654	+	19.3297i	1.23230	+	1.12542i
$296$	5.49639			0.319471
$297$	1.32151			0.0766816
$298$			12.7625i			0.739311i
$299$		0			0
$300$	−0.333638	+	0.0303112i	−0.0192626	+	0.00175002i
$301$		−	47.1300i		−	2.71653i
$302$		−	9.73737i		−	0.560323i
$303$			0.207938i			0.0119457i
$304$			5.26981i			0.302244i
$305$	−17.3877	+	19.0390i	−0.995619	+	1.09017i
$306$			1.54776i			0.0884798i
$307$	−1.59681			−0.0911346			−0.0455673	−	0.998961i	$-0.514510\pi$
$307$	−1.59681			−0.0911346			−0.0455673	+	0.998961i	$0.514510\pi$
$308$		−	16.5657i		−	0.943920i
$309$	1.00175			0.0569875
$310$	11.3043	+	10.3239i	0.642044	+	0.586358i
$311$	−3.52287			−0.199764			−0.0998819	−	0.994999i	$-0.531846\pi$
$311$	−3.52287			−0.199764			−0.0998819	+	0.994999i	$0.531846\pi$
$312$		0			0
$313$		−	20.7603i		−	1.17344i	−0.809788	−	0.586722i	$-0.800418\pi$
$313$		−	20.7603i		−	1.17344i	0.809788	−	0.586722i	$-0.199582\pi$
$314$		−	21.3156i		−	1.20291i
$315$	−22.7460	+	24.9062i	−1.28159	+	1.40330i
$316$	7.28413			0.409764
$317$	4.92085			0.276382			0.138191	−	0.990406i	$-0.455871\pi$
$317$	4.92085			0.276382			0.138191	+	0.990406i	$0.455871\pi$
$318$	−0.623781			−0.0349799
$319$		−	20.9352i		−	1.17215i
$320$	1.50791	−	1.65112i	0.0842950	−	0.0923004i
$321$	1.02654			0.0572960
$322$			2.63928i			0.147081i
$323$	2.72288			0.151505
$324$	8.95962			0.497756
$325$		0			0
$326$	1.27897			0.0708355
$327$	0.281332			0.0155577
$328$		−	5.54869i		−	0.306375i
$329$	8.31801			0.458587
$330$	−0.332369	+	0.363933i	−0.0182963	+	0.0200339i
$331$		−	14.1568i		−	0.778126i	−0.921211	−	0.389063i	$-0.872799\pi$
$331$		−	14.1568i		−	0.778126i	0.921211	−	0.389063i	$-0.127201\pi$
$332$	2.57870			0.141525
$333$	−16.4645			−0.902248
$334$	−1.90682			−0.104336
$335$	−5.10965	+	5.59491i	−0.279170	+	0.305683i
$336$			0.337403i			0.0184068i
$337$			18.7663i			1.02227i	0.859502	+	0.511133i	$0.170774\pi$
$337$			18.7663i			1.02227i	−0.859502	+	0.511133i	$0.829226\pi$
$338$		0			0
$339$	−0.786361			−0.0427093
$340$	−0.853124	−	0.779131i	−0.0462672	−	0.0422543i
$341$	22.5227			1.21967
$342$		−	15.7858i		−	0.853597i
$343$	−57.1954			−3.08826
$344$		−	9.35921i		−	0.504615i
$345$	0.0529535	−	0.0579825i	0.00285092	−	0.00312167i
$346$		−	0.112802i		−	0.00606425i
$347$		−	32.2646i		−	1.73205i	−0.499997	−	0.866027i	$-0.666665\pi$
$347$		−	32.2646i		−	1.73205i	0.499997	−	0.866027i	$-0.333335\pi$
$348$			0.426398i			0.0228573i
$349$			8.62949i			0.461926i	0.972963	+	0.230963i	$0.0741876\pi$
$349$			8.62949i			0.461926i	−0.972963	+	0.230963i	$0.925812\pi$
$350$	−2.27809	−	25.0751i	−0.121769	−	1.34032i
$351$		0			0
$352$		−	3.28967i		−	0.175340i
$353$	−19.0692			−1.01495			−0.507474	−	0.861667i	$-0.669421\pi$
$353$	−19.0692			−1.01495			−0.507474	+	0.861667i	$0.669421\pi$
$354$	−0.858892			−0.0456496
$355$	−6.38394	−	5.83025i	−0.338824	−	0.309437i
$356$			4.82497i			0.255723i
$357$	0.174334			0.00922674
$358$	9.78320			0.517058
$359$			2.70589i			0.142811i	0.997447	+	0.0714056i	$0.0227485\pi$
$359$			2.70589i			0.142811i	−0.997447	+	0.0714056i	$0.977252\pi$
$360$	−4.51697	+	4.94595i	−0.238065	+	0.260674i
$361$	−8.77090			−0.461627
$362$	8.36184			0.439489
$363$		−	0.0119293i		−	0.000626126i
$364$		0			0
$365$	9.69595	−	10.6168i	0.507509	−	0.555707i
$366$		−	0.772604i		−	0.0403847i
$367$		−	7.80278i		−	0.407302i	−0.979044	−	0.203651i	$-0.934719\pi$
$367$		−	7.80278i		−	0.407302i	0.979044	−	0.203651i	$-0.0652807\pi$
$368$			0.524116i			0.0273214i
$369$			16.6212i			0.865263i
$370$	8.28808	−	9.07519i	0.430877	−	0.471797i
$371$		−	46.8812i		−	2.43395i
$372$	−0.458731			−0.0237841
$373$		−	14.0835i		−	0.729218i	−0.931161	−	0.364609i	$-0.881203\pi$
$373$		−	14.0835i		−	0.729218i	0.931161	−	0.364609i	$-0.118797\pi$
$374$	−1.69976			−0.0878923
$375$	−0.453050	+	0.596583i	−0.0233954	+	0.0308074i
$376$	1.65182			0.0851859
$377$		0			0
$378$		−	2.02290i		−	0.104047i
$379$		−	0.236252i		−	0.0121354i	−0.999982	−	0.00606772i	$-0.998069\pi$
$379$		−	0.236252i		−	0.0121354i	0.999982	−	0.00606772i	$-0.00193143\pi$
$380$	8.70109	+	7.94642i	0.446356	+	0.407643i
$381$	0.667640			0.0342042
$382$	9.25588			0.473572
$383$	11.7086			0.598281			0.299140	−	0.954209i	$-0.403300\pi$
$383$	11.7086			0.598281			0.299140	+	0.954209i	$0.403300\pi$
$384$			0.0670024i			0.00341920i
$385$	−27.3520	−	24.9797i	−1.39399	−	1.27308i
$386$	17.5149			0.891483
$387$			28.0356i			1.42513i
$388$	1.88098			0.0954925
$389$	−2.05842			−0.104366			−0.0521830	−	0.998638i	$-0.516618\pi$
$389$	−2.05842			−0.104366			−0.0521830	+	0.998638i	$0.516618\pi$
$390$		0			0
$391$	0.270808			0.0136953
$392$	−18.3580			−0.927221
$393$			0.229984i			0.0116012i
$394$	−20.2809			−1.02174
$395$	10.9838	−	12.0270i	0.552657	−	0.605142i
$396$			9.85425i			0.495195i
$397$	10.6417			0.534091			0.267046	−	0.963684i	$-0.413953\pi$
$397$	10.6417			0.534091			0.267046	+	0.963684i	$0.413953\pi$
$398$	27.0802			1.35741
$399$	−1.77805			−0.0890137
$400$	−0.452390	−	4.97949i	−0.0226195	−	0.248975i
$401$		−	7.49704i		−	0.374384i	−0.982323	−	0.187192i	$-0.940061\pi$
$401$		−	7.49704i		−	0.374384i	0.982323	−	0.187192i	$-0.0599387\pi$
$402$		−	0.227042i		−	0.0113238i
$403$		0			0
$404$	−3.10344			−0.154402
$405$	13.5103	−	14.7934i	0.671334	−	0.735090i
$406$	−32.0466			−1.59045
$407$		−	18.0813i		−	0.896258i
$408$	0.0346198			0.00171394
$409$			21.5011i			1.06316i	0.847007	+	0.531582i	$0.178402\pi$
$409$			21.5011i			1.06316i	−0.847007	+	0.531582i	$0.821598\pi$
$410$	−9.16155	−	8.36695i	−0.452457	−	0.413214i
$411$		−	1.15233i		−	0.0568403i
$412$			14.9509i			0.736580i
$413$		−	64.5514i		−	3.17637i
$414$		−	1.57000i		−	0.0771611i
$415$	3.88847	−	4.25775i	0.190877	−	0.209005i
$416$		0			0
$417$		−	0.439756i		−	0.0215349i
$418$	17.3360			0.847930
$419$	−12.8640			−0.628449			−0.314224	−	0.949349i	$-0.601744\pi$
$419$	−12.8640			−0.628449			−0.314224	+	0.949349i	$0.601744\pi$
$420$	0.557092	+	0.508774i	0.0271833	+	0.0248256i
$421$			4.00323i			0.195105i	0.995230	+	0.0975527i	$0.0311015\pi$
$421$			4.00323i			0.195105i	−0.995230	+	0.0975527i	$0.968899\pi$
$422$	11.9828			0.583312
$423$	−4.94803			−0.240581
$424$		−	9.30982i		−	0.452125i
$425$	−2.57288	+	0.233747i	−0.124803	+	0.0113384i
$426$	0.259060			0.0125515
$427$	58.0663			2.81003
$428$			15.3210i			0.740567i
$429$		0			0
$430$	−15.4532	−	14.1129i	−0.745218	−	0.680584i
$431$			21.6439i			1.04255i	0.853389	+	0.521274i	$0.174543\pi$
$431$			21.6439i			1.04255i	−0.853389	+	0.521274i	$0.825457\pi$
$432$		−	0.401714i		−	0.0193275i
$433$			1.51015i			0.0725733i	0.999341	+	0.0362866i	$0.0115529\pi$
$433$			1.51015i			0.0725733i	−0.999341	+	0.0362866i	$0.988447\pi$
$434$		−	34.4766i		−	1.65493i
$435$	0.704034	+	0.642972i	0.0337559	+	0.0308281i
$436$			4.19883i			0.201087i
$437$	−2.76199			−0.132124
$438$			0.430828i			0.0205858i
$439$	−16.1800			−0.772229			−0.386114	−	0.922451i	$-0.626183\pi$
$439$	−16.1800			−0.772229			−0.386114	+	0.922451i	$0.626183\pi$
$440$	−5.43164	−	4.96055i	−0.258944	−	0.236485i
$441$	54.9917			2.61865
$442$		0			0
$443$		−	3.49878i		−	0.166232i	−0.996540	−	0.0831161i	$-0.973513\pi$
$443$		−	3.49878i		−	0.166232i	0.996540	−	0.0831161i	$-0.0264872\pi$
$444$			0.368271i			0.0174774i
$445$	7.96660	+	7.27564i	0.377653	+	0.344898i
$446$	−12.7910			−0.605669
$447$	−0.855118			−0.0404457
$448$	−5.03568			−0.237913
$449$		−	7.98505i		−	0.376838i	−0.982089	−	0.188419i	$-0.939664\pi$
$449$		−	7.98505i		−	0.376838i	0.982089	−	0.188419i	$-0.0603363\pi$
$450$	1.35514	+	14.9161i	0.0638818	+	0.703153i
$451$	−18.2534			−0.859518
$452$		−	11.7363i		−	0.552029i
$453$	0.652428			0.0306537
$454$	5.83533			0.273866
$455$		0			0
$456$	−0.353090			−0.0165350
$457$	−17.4867			−0.817992			−0.408996	−	0.912536i	$-0.634121\pi$
$457$	−17.4867			−0.817992			−0.408996	+	0.912536i	$0.634121\pi$
$458$		−	15.2208i		−	0.711220i
$459$	−0.207563			−0.00968823
$460$	0.865378	+	0.790322i	0.0403485	+	0.0368490i
$461$		−	15.0988i		−	0.703222i	−0.936146	−	0.351611i	$-0.885634\pi$
$461$		−	15.0988i		−	0.703222i	0.936146	−	0.351611i	$-0.114366\pi$
$462$	1.10994			0.0516393
$463$	12.3107			0.572127			0.286064	−	0.958211i	$-0.407653\pi$
$463$	12.3107			0.572127			0.286064	+	0.958211i	$0.407653\pi$
$464$	−6.36392			−0.295438
$465$	−0.691726	+	0.757419i	−0.0320780	+	0.0351245i
$466$		−	18.4629i		−	0.855278i
$467$		−	9.27853i		−	0.429359i	−0.976685	−	0.214680i	$-0.931129\pi$
$467$		−	9.27853i		−	0.429359i	0.976685	−	0.214680i	$-0.0688707\pi$
$468$		0			0
$469$	17.0637			0.787928
$470$	2.49080	−	2.72734i	0.114892	−	0.125803i
$471$	1.42820			0.0658080
$472$		−	12.8188i		−	0.590034i
$473$	−30.7888			−1.41567
$474$			0.488054i			0.0224171i
$475$	26.2410	−	2.38401i	1.20402	−	0.109386i
$476$			2.60191i			0.119258i
$477$			27.8877i			1.27689i
$478$			3.76483i			0.172199i
$479$		−	38.6780i		−	1.76724i	−0.468201	−	0.883622i	$-0.655098\pi$
$479$		−	38.6780i		−	1.76724i	0.468201	−	0.883622i	$-0.344902\pi$
$480$	0.110629	+	0.101034i	0.00504950	+	0.00461155i
$481$		0			0
$482$		−	15.4771i		−	0.704961i
$483$	−0.176838			−0.00804642
$484$	0.178043			0.00809286
$485$	2.83636	−	3.10573i	0.128793	−	0.141024i
$486$			1.80546i			0.0818972i
$487$	19.3496			0.876812			0.438406	−	0.898777i	$-0.355543\pi$
$487$	19.3496			0.876812			0.438406	+	0.898777i	$0.355543\pi$
$488$	11.5310			0.521983
$489$			0.0856940i			0.00387522i
$490$	−27.6823	+	30.3113i	−1.25056	+	1.36933i
$491$	−27.7335			−1.25160			−0.625798	−	0.779986i	$-0.715226\pi$
$491$	−27.7335			−1.25160			−0.625798	+	0.779986i	$0.715226\pi$
$492$	0.371776			0.0167609
$493$			3.28820i			0.148093i
$494$		0			0
$495$	16.2705	+	14.8594i	0.731307	+	0.667879i
$496$		−	6.84648i		−	0.307416i
$497$			19.4701i			0.873353i
$498$			0.172779i			0.00774243i
$499$			22.2962i			0.998116i	0.866569	+	0.499058i	$0.166321\pi$
$499$			22.2962i			0.998116i	−0.866569	+	0.499058i	$0.833679\pi$
$500$	−8.90390	−	6.76170i	−0.398195	−	0.302392i
$501$		−	0.127761i		−	0.00570796i
$502$	1.26747			0.0565699
$503$		−	5.15651i		−	0.229918i	−0.993370	−	0.114959i	$-0.963326\pi$
$503$		−	5.15651i		−	0.229918i	0.993370	−	0.114959i	$-0.0366736\pi$
$504$	15.0844			0.671914
$505$	−4.67972	+	5.12415i	−0.208245	+	0.228021i
$506$	1.72417			0.0766488
$507$		0			0
$508$			9.96441i			0.442099i
$509$		−	9.11596i		−	0.404058i	−0.979380	−	0.202029i	$-0.935246\pi$
$509$		−	9.11596i		−	0.404058i	0.979380	−	0.202029i	$-0.0647535\pi$
$510$	0.0522037	−	0.0571614i	0.00231162	−	0.00253115i
$511$	−32.3796			−1.43239
$512$	−1.00000			−0.0441942
$513$	2.11696			0.0934659
$514$			29.7338i			1.31150i
$515$	24.6858	+	22.5447i	1.08779	+	0.993439i
$516$	0.627090			0.0276061
$517$		−	5.43393i		−	0.238984i
$518$	−27.6780			−1.21610
$519$	0.00755798			0.000331759
$520$		0			0
$521$	−28.0573			−1.22921			−0.614606	−	0.788834i	$-0.710685\pi$
$521$	−28.0573			−1.22921			−0.614606	+	0.788834i	$0.710685\pi$
$522$	19.0632			0.834373
$523$		−	20.2889i		−	0.887170i	−0.896232	−	0.443585i	$-0.853706\pi$
$523$		−	20.2889i		−	0.887170i	0.896232	−	0.443585i	$-0.146294\pi$
$524$	−3.43248			−0.149948
$525$	1.68009	−	0.152638i	0.0733253	−	0.00666165i
$526$			20.2454i			0.882743i
$527$	−3.53754			−0.154098
$528$	0.220416			0.00959238
$529$	22.7253			0.988057
$530$	−15.3716	−	14.0384i	−0.667701	−	0.609790i
$531$			38.3989i			1.66637i
$532$		−	26.5371i		−	1.15053i
$533$		0			0
$534$	−0.323285			−0.0139899
$535$	25.2967	+	23.1027i	1.09367	+	0.998816i
$536$	3.38856			0.146363
$537$			0.655498i			0.0282868i
$538$	12.2284			0.527202
$539$			60.3920i			2.60127i
$540$	−0.663277	−	0.605750i	−0.0285429	−	0.0260673i
$541$			34.8443i			1.49807i	0.662529	+	0.749036i	$0.269483\pi$
$541$			34.8443i			1.49807i	−0.662529	+	0.749036i	$0.730517\pi$
$542$			13.3526i			0.573544i
$543$			0.560264i			0.0240432i
$544$			0.516695i			0.0221531i
$545$	6.93276	+	6.33147i	0.296967	+	0.271210i
$546$		0			0
$547$		−	6.66151i		−	0.284825i	−0.989807	−	0.142413i	$-0.954514\pi$
$547$		−	6.66151i		−	0.284825i	0.989807	−	0.142413i	$-0.0454860\pi$
$548$	17.1983			0.734677
$549$	−34.5412			−1.47418
$550$	−16.3809	+	1.48822i	−0.698484	+	0.0634577i
$551$		−	33.5367i		−	1.42871i
$552$	−0.0351171			−0.00149468
$553$	−36.6805			−1.55981
$554$		−	9.36534i		−	0.397895i
$555$	0.608060	+	0.555321i	0.0258107	+	0.0235721i
$556$	6.56328			0.278345
$557$	1.12641			0.0477277			0.0238638	−	0.999715i	$-0.492403\pi$
$557$	1.12641			0.0477277			0.0238638	+	0.999715i	$0.492403\pi$
$558$			20.5087i			0.868202i
$559$		0			0
$560$	−7.59337	+	8.31450i	−0.320878	+	0.351352i
$561$		−	0.113888i		−	0.00480835i
$562$			20.5996i			0.868941i
$563$			12.0651i			0.508484i	0.967141	+	0.254242i	$0.0818260\pi$
$563$			12.0651i			0.508484i	−0.967141	+	0.254242i	$0.918174\pi$
$564$			0.110676i			0.00466028i
$565$	−19.3780	−	17.6973i	−0.815240	−	0.744533i
$566$			14.4039i			0.605442i
$567$	−45.1177			−1.89477
$568$			3.86643i			0.162232i
$569$	26.4132			1.10730			0.553650	−	0.832750i	$-0.313235\pi$
$569$	26.4132			1.10730			0.553650	+	0.832750i	$0.313235\pi$
$570$	−0.532430	+	0.582994i	−0.0223010	+	0.0244189i
$571$	−29.7751			−1.24605			−0.623025	−	0.782202i	$-0.714096\pi$
$571$	−29.7751			−1.24605			−0.623025	+	0.782202i	$0.714096\pi$
$572$		0			0
$573$			0.620167i			0.0259078i
$574$			27.9414i			1.16625i
$575$	2.60983	−	0.237105i	0.108838	−	0.00988796i
$576$	2.99551			0.124813
$577$	28.5908			1.19025			0.595126	−	0.803633i	$-0.297102\pi$
$577$	28.5908			1.19025			0.595126	+	0.803633i	$0.297102\pi$
$578$	−16.7330			−0.696002
$579$			1.17354i			0.0487706i
$580$	−9.59625	+	10.5076i	−0.398462	+	0.436304i
$581$	−12.9855			−0.538730
$582$			0.126031i			0.00522413i
$583$	−30.6263			−1.26841
$584$	−6.43004			−0.266077
$585$		0			0
$586$	15.0823			0.623044
$587$	−1.57376			−0.0649562			−0.0324781	−	0.999472i	$-0.510340\pi$
$587$	−1.57376			−0.0649562			−0.0324781	+	0.999472i	$0.510340\pi$
$588$		−	1.23003i		−	0.0507257i
$589$	36.0796			1.48664
$590$	−21.1654	−	19.3297i	−0.871366	−	0.795790i
$591$		−	1.35887i		−	0.0558965i
$592$	−5.49639			−0.225900
$593$	31.9506			1.31205			0.656027	−	0.754737i	$-0.272236\pi$
$593$	31.9506			1.31205			0.656027	+	0.754737i	$0.272236\pi$
$594$	−1.32151			−0.0542221
$595$	4.29606	+	3.92345i	0.176121	+	0.160846i
$596$		−	12.7625i		−	0.522772i
$597$			1.81444i			0.0742600i
$598$		0			0
$599$	29.2165			1.19375			0.596877	−	0.802332i	$-0.296408\pi$
$599$	29.2165			1.19375			0.596877	+	0.802332i	$0.296408\pi$
$600$	0.333638	−	0.0303112i	0.0136207	−	0.00123745i
$601$	24.1056			0.983287			0.491643	−	0.870797i	$-0.336396\pi$
$601$	24.1056			0.983287			0.491643	+	0.870797i	$0.336396\pi$
$602$			47.1300i			1.92087i
$603$	−10.1505			−0.413359
$604$			9.73737i			0.396208i
$605$	0.268473	−	0.293970i	0.0109150	−	0.0119516i
$606$		−	0.207938i		−	0.00844690i
$607$		−	22.1386i		−	0.898579i	−0.893386	−	0.449290i	$-0.851677\pi$
$607$		−	22.1386i		−	0.898579i	0.893386	−	0.449290i	$-0.148323\pi$
$608$		−	5.26981i		−	0.213719i
$609$		−	2.14720i		−	0.0870091i
$610$	17.3877	−	19.0390i	0.704009	−	0.770868i
$611$		0			0
$612$		−	1.54776i		−	0.0625647i
$613$	−37.1880			−1.50201			−0.751004	−	0.660297i	$-0.770430\pi$
$613$	−37.1880			−1.50201			−0.751004	+	0.660297i	$0.770430\pi$
$614$	1.59681			0.0644419
$615$	0.560606	−	0.613846i	0.0226058	−	0.0247527i
$616$			16.5657i			0.667453i
$617$	−40.8840			−1.64593			−0.822963	−	0.568094i	$-0.807681\pi$
$617$	−40.8840			−1.64593			−0.822963	+	0.568094i	$0.807681\pi$
$618$	−1.00175			−0.0402963
$619$		−	17.3785i		−	0.698501i	−0.937029	−	0.349250i	$-0.886436\pi$
$619$		−	17.3785i		−	0.698501i	0.937029	−	0.349250i	$-0.113564\pi$
$620$	−11.3043	−	10.3239i	−0.453994	−	0.414618i
$621$	0.210545			0.00844887
$622$	3.52287			0.141254
$623$		−	24.2970i		−	0.973438i
$624$		0			0
$625$	−24.5907	+	4.50534i	−0.983627	+	0.180214i
$626$			20.7603i			0.829750i
$627$			1.16155i			0.0463879i
$628$			21.3156i			0.850587i
$629$			2.83995i			0.113236i
$630$	22.7460	−	24.9062i	0.906223	−	0.992286i
$631$		−	1.17310i		−	0.0467005i	−0.999727	−	0.0233503i	$-0.992567\pi$
$631$		−	1.17310i		−	0.0467005i	0.999727	−	0.0233503i	$-0.00743330\pi$
$632$	−7.28413			−0.289747
$633$			0.802875i			0.0319114i
$634$	−4.92085			−0.195432
$635$	16.4524	+	15.0255i	0.652895	+	0.596268i
$636$	0.623781			0.0247345
$637$		0			0
$638$			20.9352i			0.828834i
$639$		−	11.5819i		−	0.458174i
$640$	−1.50791	+	1.65112i	−0.0596055	+	0.0652662i
$641$	30.0814			1.18815			0.594073	−	0.804411i	$-0.297519\pi$
$641$	30.0814			1.18815			0.594073	+	0.804411i	$0.297519\pi$
$642$	−1.02654			−0.0405144
$643$	39.2988			1.54979			0.774896	−	0.632089i	$-0.217802\pi$
$643$	39.2988			1.54979			0.774896	+	0.632089i	$0.217802\pi$
$644$		−	2.63928i		−	0.104002i
$645$	0.945598	−	1.03540i	0.0372329	−	0.0407689i
$646$	−2.72288			−0.107130
$647$			47.8194i			1.87997i	0.341211	+	0.939987i	$0.389163\pi$
$647$			47.8194i			1.87997i	−0.341211	+	0.939987i	$0.610837\pi$
$648$	−8.95962			−0.351967
$649$	−42.1697			−1.65531
$650$		0			0
$651$	2.31002			0.0905368
$652$	−1.27897			−0.0500883
$653$		−	32.7143i		−	1.28021i	−0.768288	−	0.640104i	$-0.778891\pi$
$653$		−	32.7143i		−	1.28021i	0.768288	−	0.640104i	$-0.221109\pi$
$654$	−0.281332			−0.0110009
$655$	−5.17588	+	5.66743i	−0.202238	+	0.221445i
$656$			5.54869i			0.216640i
$657$	19.2613			0.751453
$658$	−8.31801			−0.324270
$659$	41.9069			1.63246			0.816231	−	0.577725i	$-0.196060\pi$
$659$	41.9069			1.63246			0.816231	+	0.577725i	$0.196060\pi$
$660$	0.332369	−	0.363933i	0.0129374	−	0.0141661i
$661$			21.6745i			0.843039i	0.906819	+	0.421520i	$0.138503\pi$
$661$			21.6745i			0.843039i	−0.906819	+	0.421520i	$0.861497\pi$
$662$			14.1568i			0.550218i
$663$		0			0
$664$	−2.57870			−0.100073
$665$	−43.8159	−	40.0156i	−1.69911	−	1.55174i
$666$	16.4645			0.637986
$667$		−	3.33543i		−	0.129149i
$668$	1.90682			0.0737770
$669$		−	0.857025i		−	0.0331345i
$670$	5.10965	−	5.59491i	0.197403	−	0.216150i
$671$		−	37.9332i		−	1.46440i
$672$		−	0.337403i		−	0.0130156i
$673$			37.9352i			1.46230i	0.682219	+	0.731148i	$0.261015\pi$
$673$			37.9352i			1.46230i	−0.682219	+	0.731148i	$0.738985\pi$
$674$		−	18.7663i		−	0.722851i
$675$	−2.00033	+	0.181731i	−0.0769928	+	0.00699484i
$676$		0			0
$677$			10.4768i			0.402654i	0.979524	+	0.201327i	$0.0645254\pi$
$677$			10.4768i			0.402654i	−0.979524	+	0.201327i	$0.935475\pi$
$678$	0.786361			0.0302000
$679$	−9.47203			−0.363503
$680$	0.853124	+	0.779131i	0.0327158	+	0.0298783i
$681$			0.390981i			0.0149824i
$682$	−22.5227			−0.862438
$683$	−24.4591			−0.935903			−0.467952	−	0.883754i	$-0.655008\pi$
$683$	−24.4591			−0.935903			−0.467952	+	0.883754i	$0.655008\pi$
$684$			15.7858i			0.603584i
$685$	25.9336	−	28.3965i	0.990873	−	1.08498i
$686$	57.1954			2.18373
$687$	1.01983			0.0389089
$688$			9.35921i			0.356817i
$689$		0			0
$690$	−0.0529535	+	0.0579825i	−0.00201591	+	0.00220735i
$691$		−	20.4414i		−	0.777626i	−0.921317	−	0.388813i	$-0.872885\pi$
$691$		−	20.4414i		−	0.777626i	0.921317	−	0.388813i	$-0.127115\pi$
$692$			0.112802i			0.00428807i
$693$		−	49.6228i		−	1.88502i
$694$			32.2646i			1.22475i
$695$	9.89687	−	10.8368i	0.375410	−	0.411062i
$696$		−	0.426398i		−	0.0161626i
$697$	2.86698			0.108594
$698$		−	8.62949i		−	0.326631i
$699$	1.23706			0.0467899
$700$	2.27809	+	25.0751i	0.0861037	+	0.947750i
$701$	−11.4168			−0.431208			−0.215604	−	0.976481i	$-0.569172\pi$
$701$	−11.4168			−0.431208			−0.215604	+	0.976481i	$0.569172\pi$
$702$		0			0
$703$		−	28.9649i		−	1.09243i
$704$			3.28967i			0.123984i
$705$	0.182739	+	0.166889i	0.00688234	+	0.00628542i
$706$	19.0692			0.717677
$707$	15.6279			0.587748
$708$	0.858892			0.0322791
$709$			39.7802i			1.49398i	0.664836	+	0.746989i	$0.268501\pi$
$709$			39.7802i			1.49398i	−0.664836	+	0.746989i	$0.731499\pi$
$710$	6.38394	+	5.83025i	0.239585	+	0.218805i
$711$	21.8197			0.818302
$712$		−	4.82497i		−	0.180823i
$713$	3.58835			0.134385
$714$	−0.174334			−0.00652429
$715$		0			0
$716$	−9.78320			−0.365615
$717$	−0.252253			−0.00942054
$718$		−	2.70589i		−	0.100983i
$719$	21.4776			0.800980			0.400490	−	0.916301i	$-0.368840\pi$
$719$	21.4776			0.800980			0.400490	+	0.916301i	$0.368840\pi$
$720$	4.51697	−	4.94595i	0.168338	−	0.184325i
$721$		−	75.2881i		−	2.80387i
$722$	8.77090			0.326419
$723$	1.03700			0.0385665
$724$	−8.36184			−0.310765
$725$	2.87897	+	31.6891i	0.106922	+	1.17690i
$726$			0.0119293i			0.000442738i
$727$			26.5625i			0.985148i	0.870271	+	0.492574i	$0.163944\pi$
$727$			26.5625i			0.985148i	−0.870271	+	0.492574i	$0.836056\pi$
$728$		0			0
$729$	26.7579			0.991033
$730$	−9.69595	+	10.6168i	−0.358863	+	0.392944i
$731$	4.83585			0.178861
$732$			0.772604i			0.0285563i
$733$	28.8341			1.06501			0.532505	−	0.846427i	$-0.321251\pi$
$733$	28.8341			1.06501			0.532505	+	0.846427i	$0.321251\pi$
$734$			7.80278i			0.288006i
$735$	−2.03093	−	1.85478i	−0.0749121	−	0.0684148i
$736$		−	0.524116i		−	0.0193192i
$737$		−	11.1473i		−	0.410614i
$738$		−	16.6212i		−	0.611833i
$739$		−	9.48392i		−	0.348872i	−0.984669	−	0.174436i	$-0.944190\pi$
$739$		−	9.48392i		−	0.348872i	0.984669	−	0.174436i	$-0.0558102\pi$
$740$	−8.28808	+	9.07519i	−0.304676	+	0.333611i
$741$		0			0
$742$			46.8812i			1.72106i
$743$	10.2767			0.377017			0.188508	−	0.982072i	$-0.439635\pi$
$743$	10.2767			0.377017			0.188508	+	0.982072i	$0.439635\pi$
$744$	0.458731			0.0168179
$745$	−21.0724	−	19.2447i	−0.772033	−	0.705073i
$746$			14.0835i			0.515635i
$747$	7.72454			0.282626
$748$	1.69976			0.0621493
$749$		−	77.1514i		−	2.81905i
$750$	0.453050	−	0.596583i	0.0165431	−	0.0217841i
$751$	−29.7407			−1.08525			−0.542627	−	0.839974i	$-0.682570\pi$
$751$	−29.7407			−1.08525			−0.542627	+	0.839974i	$0.682570\pi$
$752$	−1.65182			−0.0602355
$753$			0.0849235i			0.00309478i
$754$		0			0
$755$	16.0776	+	14.6831i	0.585123	+	0.534374i
$756$			2.02290i			0.0735722i
$757$		−	2.50703i		−	0.0911197i	−0.998962	−	0.0455599i	$-0.985493\pi$
$757$		−	2.50703i		−	0.0911197i	0.998962	−	0.0455599i	$-0.0145072\pi$
$758$			0.236252i			0.00858106i
$759$			0.115524i			0.00419324i
$760$	−8.70109	−	7.94642i	−0.315622	−	0.288247i
$761$		−	36.3569i		−	1.31794i	−0.752170	−	0.658969i	$-0.770993\pi$
$761$		−	36.3569i		−	1.31794i	0.752170	−	0.658969i	$-0.229007\pi$
$762$	−0.667640			−0.0241860
$763$		−	21.1439i		−	0.765462i
$764$	−9.25588			−0.334866
$765$	−2.55554	−	2.33390i	−0.0923959	−	0.0843822i
$766$	−11.7086			−0.423048
$767$		0			0
$768$		−	0.0670024i		−	0.00241774i
$769$			9.73400i			0.351017i	0.984478	+	0.175509i	$0.0561570\pi$
$769$			9.73400i			0.351017i	−0.984478	+	0.175509i	$0.943843\pi$
$770$	27.3520	+	24.9797i	0.985698	+	0.900206i
$771$	−1.99224			−0.0717486
$772$	−17.5149			−0.630374
$773$	−40.0014			−1.43875			−0.719375	−	0.694621i	$-0.755572\pi$
$773$	−40.0014			−1.43875			−0.719375	+	0.694621i	$0.755572\pi$
$774$		−	28.0356i		−	1.00772i
$775$	−34.0920	+	3.09728i	−1.22462	+	0.111257i
$776$	−1.88098			−0.0675234
$777$		−	1.85449i		−	0.0665296i
$778$	2.05842			0.0737979
$779$	−29.2405			−1.04765
$780$		0			0
$781$	12.7193			0.455132
$782$	−0.270808			−0.00968407
$783$			2.55647i			0.0913610i
$784$	18.3580			0.655644
$785$	35.1947	+	32.1422i	1.25615	+	1.14720i
$786$		−	0.229984i		−	0.00820327i
$787$	−46.0334			−1.64091			−0.820456	−	0.571710i	$-0.806280\pi$
$787$	−46.0334			−1.64091			−0.820456	+	0.571710i	$0.806280\pi$
$788$	20.2809			0.722479
$789$	−1.35649			−0.0482924
$790$	−10.9838	+	12.0270i	−0.390787	+	0.427900i
$791$			59.1002i			2.10136i
$792$		−	9.85425i		−	0.350156i
$793$		0			0
$794$	−10.6417			−0.377660
$795$	0.940608	−	1.02994i	0.0333599	−	0.0365281i
$796$	−27.0802			−0.959832
$797$			5.63521i			0.199610i	0.995007	+	0.0998048i	$0.0318218\pi$
$797$			5.63521i			0.199610i	−0.995007	+	0.0998048i	$0.968178\pi$
$798$	1.77805			0.0629422
$799$			0.853484i			0.0301941i
$800$	0.452390	+	4.97949i	0.0159944	+	0.176052i
$801$			14.4533i			0.510680i
$802$			7.49704i			0.264730i
$803$			21.1527i			0.746464i
$804$			0.227042i			0.00800714i
$805$	−4.35777	−	3.97981i	−0.153591	−	0.140270i
$806$		0			0
$807$			0.819330i			0.0288418i
$808$	3.10344			0.109179
$809$	35.5797			1.25092			0.625459	−	0.780257i	$-0.284912\pi$
$809$	35.5797			1.25092			0.625459	+	0.780257i	$0.284912\pi$
$810$	−13.5103	+	14.7934i	−0.474705	+	0.519787i
$811$		−	23.1724i		−	0.813694i	−0.913496	−	0.406847i	$-0.866628\pi$
$811$		−	23.1724i		−	0.813694i	0.913496	−	0.406847i	$-0.133372\pi$
$812$	32.0466			1.12462
$813$	−0.894658			−0.0313770
$814$			18.0813i			0.633750i
$815$	−1.92857	+	2.11173i	−0.0675550	+	0.0739706i
$816$	−0.0346198			−0.00121194
$817$	−49.3213			−1.72553
$818$		−	21.5011i		−	0.751770i
$819$		0			0
$820$	9.16155	+	8.36695i	0.319935	+	0.292186i
$821$			22.8480i			0.797401i	0.917081	+	0.398701i	$0.130539\pi$
$821$			22.8480i			0.797401i	−0.917081	+	0.398701i	$0.869461\pi$
$822$			1.15233i			0.0401922i
$823$			23.7086i			0.826431i	0.910633	+	0.413216i	$0.135594\pi$
$823$			23.7086i			0.826431i	−0.910633	+	0.413216i	$0.864406\pi$
$824$		−	14.9509i		−	0.520840i
$825$	−0.0997140	−	1.09756i	−0.00347160	−	0.0382122i
$826$			64.5514i			2.24603i
$827$	47.3108			1.64516			0.822579	−	0.568650i	$-0.192534\pi$
$827$	47.3108			1.64516			0.822579	+	0.568650i	$0.192534\pi$
$828$			1.57000i			0.0545611i
$829$	43.6231			1.51509			0.757547	−	0.652781i	$-0.226398\pi$
$829$	43.6231			1.51509			0.757547	+	0.652781i	$0.226398\pi$
$830$	−3.88847	+	4.25775i	−0.134971	+	0.147789i
$831$	0.627501			0.0217678
$832$		0			0
$833$		−	9.48550i		−	0.328653i
$834$			0.439756i			0.0152275i
$835$	2.87532	−	3.14838i	0.0995045	−	0.108954i
$836$	−17.3360			−0.599577
$837$	−2.75032			−0.0950651
$838$	12.8640			0.444380
$839$			33.9488i			1.17204i	0.810296	+	0.586021i	$0.199306\pi$
$839$			33.9488i			1.17204i	−0.810296	+	0.586021i	$0.800694\pi$
$840$	−0.557092	−	0.508774i	−0.0192215	−	0.0175544i
$841$	11.4995			0.396534
$842$		−	4.00323i		−	0.137960i
$843$	−1.38022			−0.0475374
$844$	−11.9828			−0.412464
$845$		0			0
$846$	4.94803			0.170117
$847$	−0.896566			−0.0308064
$848$			9.30982i			0.319701i
$849$	−0.965098			−0.0331221
$850$	2.57288	−	0.233747i	0.0882489	−	0.00801747i
$851$		−	2.88075i		−	0.0987507i
$852$	−0.259060			−0.00887526
$853$	−30.4292			−1.04187			−0.520937	−	0.853595i	$-0.674417\pi$
$853$	−30.4292			−1.04187			−0.520937	+	0.853595i	$0.674417\pi$
$854$	−58.0663			−1.98699
$855$	26.0642	+	23.8036i	0.891377	+	0.814066i
$856$		−	15.3210i		−	0.523660i
$857$		−	50.9646i		−	1.74092i	−0.492240	−	0.870459i	$-0.663822\pi$
$857$		−	50.9646i		−	1.74092i	0.492240	−	0.870459i	$-0.336178\pi$
$858$		0			0
$859$	−38.5183			−1.31423			−0.657114	−	0.753791i	$-0.728223\pi$
$859$	−38.5183			−1.31423			−0.657114	+	0.753791i	$0.728223\pi$
$860$	15.4532	+	14.1129i	0.526949	+	0.481246i
$861$	−1.87214			−0.0638024
$862$		−	21.6439i		−	0.737193i
$863$	56.6567			1.92862			0.964308	−	0.264784i	$-0.0853008\pi$
$863$	56.6567			1.92862			0.964308	+	0.264784i	$0.0853008\pi$
$864$			0.401714i			0.0136666i
$865$	0.186249	+	0.170095i	0.00633265	+	0.00578341i
$866$		−	1.51015i		−	0.0513170i
$867$		−	1.12115i		−	0.0380764i
$868$			34.4766i			1.17021i
$869$			23.9624i			0.812869i
$870$	−0.704034	−	0.642972i	−0.0238690	−	0.0217988i
$871$		0			0
$872$		−	4.19883i		−	0.142190i
$873$	5.63451			0.190699
$874$	2.76199			0.0934258
$875$	44.8372	+	34.0497i	1.51577	+	1.15109i
$876$		−	0.430828i		−	0.0145563i
$877$	41.9193			1.41551			0.707757	−	0.706456i	$-0.249707\pi$
$877$	41.9193			1.41551			0.707757	+	0.706456i	$0.249707\pi$
$878$	16.1800			0.546048
$879$			1.01055i			0.0340850i
$880$	5.43164	+	4.96055i	0.183101	+	0.167220i
$881$	−1.17194			−0.0394836			−0.0197418	−	0.999805i	$-0.506284\pi$
$881$	−1.17194			−0.0394836			−0.0197418	+	0.999805i	$0.506284\pi$
$882$	−54.9917			−1.85167
$883$			24.3462i			0.819314i	0.912240	+	0.409657i	$0.134352\pi$
$883$			24.3462i			0.819314i	−0.912240	+	0.409657i	$0.865648\pi$
$884$		0			0
$885$	1.29514	−	1.41813i	0.0435355	−	0.0476700i
$886$			3.49878i			0.117544i
$887$			8.57827i			0.288030i	0.989575	+	0.144015i	$0.0460014\pi$
$887$			8.57827i			0.288030i	−0.989575	+	0.144015i	$0.953999\pi$
$888$		−	0.368271i		−	0.0123584i
$889$		−	50.1775i		−	1.68290i
$890$	−7.96660	−	7.27564i	−0.267041	−	0.243880i
$891$			29.4742i			0.987424i
$892$	12.7910			0.428273
$893$		−	8.70475i		−	0.291293i
$894$	0.855118			0.0285994
$895$	−14.7522	+	16.1532i	−0.493112	+	0.539943i
$896$	5.03568			0.168230
$897$		0			0
$898$			7.98505i			0.266465i
$899$			43.5704i			1.45316i
$900$	−1.35514	−	14.9161i	−0.0451713	−	0.497204i
$901$	4.81033			0.160255
$902$	18.2534			0.607771
$903$	−3.15782			−0.105086
$904$			11.7363i			0.390344i
$905$	−12.6089	+	13.8064i	−0.419135	+	0.458940i
$906$	−0.652428			−0.0216755
$907$		−	25.2134i		−	0.837197i	−0.908172	−	0.418598i	$-0.862522\pi$
$907$		−	25.2134i		−	0.837197i	0.908172	−	0.418598i	$-0.137478\pi$
$908$	−5.83533			−0.193652
$909$	−9.29638			−0.308341
$910$		0			0
$911$	27.1861			0.900715			0.450358	−	0.892848i	$-0.351296\pi$
$911$	27.1861			0.900715			0.450358	+	0.892848i	$0.351296\pi$
$912$	0.353090			0.0116920
$913$			8.48310i			0.280750i
$914$	17.4867			0.578408
$915$	1.27566	+	1.16502i	0.0421721	+	0.0385144i
$916$			15.2208i			0.502909i
$917$	17.2848			0.570796
$918$	0.207563			0.00685061
$919$	−13.6082			−0.448893			−0.224446	−	0.974486i	$-0.572057\pi$
$919$	−13.6082			−0.448893			−0.224446	+	0.974486i	$0.572057\pi$
$920$	−0.865378	−	0.790322i	−0.0285307	−	0.0260562i
$921$			0.106990i			0.00352544i
$922$			15.0988i			0.497253i
$923$		0			0
$924$	−1.10994			−0.0365145
$925$	2.48651	+	27.3692i	0.0817559	+	0.899894i
$926$	−12.3107			−0.404555
$927$			44.7857i			1.47095i
$928$	6.36392			0.208906
$929$		−	14.8556i		−	0.487396i	−0.969851	−	0.243698i	$-0.921639\pi$
$929$		−	14.8556i		−	0.487396i	0.969851	−	0.243698i	$-0.0783606\pi$
$930$	0.691726	−	0.757419i	0.0226826	−	0.0248367i
$931$			96.7434i			3.17064i
$932$			18.4629i			0.604773i
$933$			0.236041i			0.00772764i
$934$			9.27853i			0.303603i
$935$	2.56309	−	2.80650i	0.0838219	−	0.0917824i
$936$		0			0
$937$			47.7682i			1.56052i	0.625457	+	0.780259i	$0.284913\pi$
$937$			47.7682i			1.56052i	−0.625457	+	0.780259i	$0.715087\pi$
$938$	−17.0637			−0.557149
$939$	−1.39099			−0.0453934
$940$	−2.49080	+	2.72734i	−0.0812408	+	0.0889561i
$941$			11.2464i			0.366623i	0.983055	+	0.183311i	$0.0586816\pi$
$941$			11.2464i			0.366623i	−0.983055	+	0.183311i	$0.941318\pi$
$942$	−1.42820			−0.0465333
$943$	−2.90816			−0.0947026
$944$			12.8188i			0.417217i
$945$	3.34005	+	3.05036i	0.108652	+	0.0992282i
$946$	30.7888			1.00103
$947$	−35.7394			−1.16137			−0.580687	−	0.814127i	$-0.697216\pi$
$947$	−35.7394			−1.16137			−0.580687	+	0.814127i	$0.697216\pi$
$948$		−	0.488054i		−	0.0158513i
$949$		0			0
$950$	−26.2410	+	2.38401i	−0.851370	+	0.0773475i
$951$		−	0.329709i		−	0.0106915i
$952$		−	2.60191i		−	0.0843283i
$953$			40.0847i			1.29847i	0.760587	+	0.649236i	$0.224911\pi$
$953$			40.0847i			1.29847i	−0.760587	+	0.649236i	$0.775089\pi$
$954$		−	27.8877i		−	0.902896i
$955$	−13.9571	+	15.2826i	−0.451640	+	0.494532i
$956$		−	3.76483i		−	0.121763i
$957$	−1.40271			−0.0453432
$958$			38.6780i			1.24963i
$959$	−86.6053			−2.79663
$960$	−0.110629	−	0.101034i	−0.00357054	−	0.00326086i
$961$	−15.8742			−0.512072
$962$		0			0
$963$			45.8941i			1.47892i
$964$			15.4771i			0.498482i
$965$	−26.4109	+	28.9191i	−0.850198	+	0.930940i
$966$	0.176838			0.00568968
$967$	−24.2441			−0.779639			−0.389820	−	0.920891i	$-0.627463\pi$
$967$	−24.2441			−0.779639			−0.389820	+	0.920891i	$0.627463\pi$
$968$	−0.178043			−0.00572251
$969$		−	0.182440i		−	0.00586081i
$970$	−2.83636	+	3.10573i	−0.0910701	+	0.0997190i
$971$	−33.3744			−1.07104			−0.535519	−	0.844523i	$-0.679884\pi$
$971$	−33.3744			−1.07104			−0.535519	+	0.844523i	$0.679884\pi$
$972$		−	1.80546i		−	0.0579101i
$973$	−33.0506			−1.05955
$974$	−19.3496			−0.620000
$975$		0			0
$976$	−11.5310			−0.369098
$977$	−6.21560			−0.198855			−0.0994273	−	0.995045i	$-0.531701\pi$
$977$	−6.21560			−0.198855			−0.0994273	+	0.995045i	$0.531701\pi$
$978$		−	0.0856940i		−	0.00274019i
$979$	−15.8726			−0.507290
$980$	27.6823	−	30.3113i	0.884280	−	0.968259i
$981$			12.5776i			0.401573i
$982$	27.7335			0.885011
$983$	−42.7293			−1.36285			−0.681427	−	0.731886i	$-0.738640\pi$
$983$	−42.7293			−1.36285			−0.681427	+	0.731886i	$0.738640\pi$
$984$	−0.371776			−0.0118518
$985$	30.5819	−	33.4863i	0.974421	−	1.06696i
$986$		−	3.28820i		−	0.104718i
$987$		−	0.557327i		−	0.0177399i
$988$		0			0
$989$	−4.90531			−0.155980
$990$	−16.2705	−	14.8594i	−0.517112	−	0.472262i
$991$	40.0026			1.27072			0.635362	−	0.772214i	$-0.280851\pi$
$991$	40.0026			1.27072			0.635362	+	0.772214i	$0.280851\pi$
$992$			6.84648i			0.217376i
$993$	−0.948538			−0.0301009
$994$		−	19.4701i		−	0.617554i
$995$	−40.8346	+	44.7126i	−1.29454	+	1.41749i
$996$		−	0.172779i		−	0.00547473i
$997$		−	15.9741i		−	0.505904i	−0.967479	−	0.252952i	$-0.918599\pi$
$997$		−	15.9741i		−	0.505904i	0.967479	−	0.252952i	$-0.0814014\pi$
$998$		−	22.2962i		−	0.705775i
$999$			2.20797i			0.0698572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.g.1689.9		18
5.4	even	2		1690.2.c.h.1689.10		18
13.5	odd	4		1690.2.b.g.339.15	yes	18
13.8	odd	4		1690.2.b.f.339.6	✓	18
13.12	even	2		1690.2.c.h.1689.9		18
65.8	even	4		8450.2.a.cw.1.4		9
65.18	even	4		8450.2.a.da.1.4		9
65.34	odd	4		1690.2.b.f.339.13	yes	18
65.44	odd	4		1690.2.b.g.339.4	yes	18
65.47	even	4		8450.2.a.cx.1.6		9
65.57	even	4		8450.2.a.ct.1.6		9
65.64	even	2	inner	1690.2.c.g.1689.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.6	✓	18	13.8	odd	4
1690.2.b.f.339.13	yes	18	65.34	odd	4
1690.2.b.g.339.4	yes	18	65.44	odd	4
1690.2.b.g.339.15	yes	18	13.5	odd	4
1690.2.c.g.1689.9		18	1.1	even	1	trivial
1690.2.c.g.1689.10		18	65.64	even	2	inner
1690.2.c.h.1689.9		18	13.12	even	2
1690.2.c.h.1689.10		18	5.4	even	2
8450.2.a.ct.1.6		9	65.57	even	4
8450.2.a.cw.1.4		9	65.8	even	4
8450.2.a.cx.1.6		9	65.47	even	4
8450.2.a.da.1.4		9	65.18	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0670024i q^{3} +1.00000 q^{4} +(1.50791 - 1.65112i) q^{5} +0.0670024i q^{6} -5.03568 q^{7} -1.00000 q^{8} +2.99551 q^{9} +(-1.50791 + 1.65112i) q^{10} +3.28967i q^{11} -0.0670024i q^{12} +5.03568 q^{14} +(-0.110629 - 0.101034i) q^{15} +1.00000 q^{16} -0.516695i q^{17} -2.99551 q^{18} +5.26981i q^{19} +(1.50791 - 1.65112i) q^{20} +0.337403i q^{21} -3.28967i q^{22} +0.524116i q^{23} +0.0670024i q^{24} +(-0.452390 - 4.97949i) q^{25} -0.401714i q^{27} -5.03568 q^{28} -6.36392 q^{29} +(0.110629 + 0.101034i) q^{30} -6.84648i q^{31} -1.00000 q^{32} +0.220416 q^{33} +0.516695i q^{34} +(-7.59337 + 8.31450i) q^{35} +2.99551 q^{36} -5.49639 q^{37} -5.26981i q^{38} +(-1.50791 + 1.65112i) q^{40} +5.54869i q^{41} -0.337403i q^{42} +9.35921i q^{43} +3.28967i q^{44} +(4.51697 - 4.94595i) q^{45} -0.524116i q^{46} -1.65182 q^{47} -0.0670024i q^{48} +18.3580 q^{49} +(0.452390 + 4.97949i) q^{50} -0.0346198 q^{51} +9.30982i q^{53} +0.401714i q^{54} +(5.43164 + 4.96055i) q^{55} +5.03568 q^{56} +0.353090 q^{57} +6.36392 q^{58} +12.8188i q^{59} +(-0.110629 - 0.101034i) q^{60} -11.5310 q^{61} +6.84648i q^{62} -15.0844 q^{63} +1.00000 q^{64} -0.220416 q^{66} -3.38856 q^{67} -0.516695i q^{68} +0.0351171 q^{69} +(7.59337 - 8.31450i) q^{70} -3.86643i q^{71} -2.99551 q^{72} +6.43004 q^{73} +5.49639 q^{74} +(-0.333638 + 0.0303112i) q^{75} +5.26981i q^{76} -16.5657i q^{77} +7.28413 q^{79} +(1.50791 - 1.65112i) q^{80} +8.95962 q^{81} -5.54869i q^{82} +2.57870 q^{83} +0.337403i q^{84} +(-0.853124 - 0.779131i) q^{85} -9.35921i q^{86} +0.426398i q^{87} -3.28967i q^{88} +4.82497i q^{89} +(-4.51697 + 4.94595i) q^{90} +0.524116i q^{92} -0.458731 q^{93} +1.65182 q^{94} +(8.70109 + 7.94642i) q^{95} +0.0670024i q^{96} +1.88098 q^{97} -18.3580 q^{98} +9.85425i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 2 q^{5} + 2 q^{7} - 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} - 14 q^{15} + 18 q^{16} + 16 q^{18} + 2 q^{20} - 22 q^{25} + 2 q^{28} - 30 q^{29} + 14 q^{30} - 18 q^{32} + 28 q^{33}+ \cdots + 20 q^{98}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 2 * q^5 + 2 * q^7 - 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 - 14 * q^15 + 18 * q^16 + 16 * q^18 + 2 * q^20 - 22 * q^25 + 2 * q^28 - 30 * q^29 + 14 * q^30 - 18 * q^32 + 28 * q^33 - 4 * q^35 - 16 * q^36 - 20 * q^37 - 2 * q^40 - 20 * q^45 + 10 * q^47 - 20 * q^49 + 22 * q^50 - 24 * q^51 - 2 * q^56 + 24 * q^57 + 30 * q^58 - 14 * q^60 - 38 * q^61 - 78 * q^63 + 18 * q^64 - 28 * q^66 + 2 * q^67 - 28 * q^69 + 4 * q^70 + 16 * q^72 + 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 + 2 * q^80 + 106 * q^81 + 2 * q^83 + 16 * q^85 + 20 * q^90 - 56 * q^93 - 10 * q^94 + 54 * q^95 - 12 * q^97 + 20 * q^98

Introduction

L-functions

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