LMFDB - Embedded newform 1690.2.c.h.1689.5

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			1689.5
Root			$2.08395i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.h.1689.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.49535i q^{3} +1.00000 q^{4} +(-1.45979 - 1.69382i) q^{5} -1.49535i q^{6} -1.01867 q^{7} +1.00000 q^{8} +0.763924 q^{9} +(-1.45979 - 1.69382i) q^{10} -2.42025i q^{11} -1.49535i q^{12} -1.01867 q^{14} +(-2.53286 + 2.18289i) q^{15} +1.00000 q^{16} +5.04699i q^{17} +0.763924 q^{18} -7.36506i q^{19} +(-1.45979 - 1.69382i) q^{20} +1.52327i q^{21} -2.42025i q^{22} -4.52359i q^{23} -1.49535i q^{24} +(-0.738047 + 4.94523i) q^{25} -5.62839i q^{27} -1.01867 q^{28} -6.38898 q^{29} +(-2.53286 + 2.18289i) q^{30} -6.28274i q^{31} +1.00000 q^{32} -3.61912 q^{33} +5.04699i q^{34} +(1.48704 + 1.72544i) q^{35} +0.763924 q^{36} -1.80149 q^{37} -7.36506i q^{38} +(-1.45979 - 1.69382i) q^{40} -0.399553i q^{41} +1.52327i q^{42} +8.41814i q^{43} -2.42025i q^{44} +(-1.11517 - 1.29395i) q^{45} -4.52359i q^{46} +0.146040 q^{47} -1.49535i q^{48} -5.96231 q^{49} +(-0.738047 + 4.94523i) q^{50} +7.54702 q^{51} +1.52601i q^{53} -5.62839i q^{54} +(-4.09947 + 3.53305i) q^{55} -1.01867 q^{56} -11.0134 q^{57} -6.38898 q^{58} +3.23605i q^{59} +(-2.53286 + 2.18289i) q^{60} -14.1612 q^{61} -6.28274i q^{62} -0.778187 q^{63} +1.00000 q^{64} -3.61912 q^{66} -6.59001 q^{67} +5.04699i q^{68} -6.76435 q^{69} +(1.48704 + 1.72544i) q^{70} +1.36946i q^{71} +0.763924 q^{72} +15.9009 q^{73} -1.80149 q^{74} +(7.39485 + 1.10364i) q^{75} -7.36506i q^{76} +2.46544i q^{77} +3.53802 q^{79} +(-1.45979 - 1.69382i) q^{80} -6.12465 q^{81} -0.399553i q^{82} +4.64985 q^{83} +1.52327i q^{84} +(8.54869 - 7.36753i) q^{85} +8.41814i q^{86} +9.55376i q^{87} -2.42025i q^{88} +5.60882i q^{89} +(-1.11517 - 1.29395i) q^{90} -4.52359i q^{92} -9.39490 q^{93} +0.146040 q^{94} +(-12.4751 + 10.7514i) q^{95} -1.49535i q^{96} -8.27379 q^{97} -5.96231 q^{98} -1.84889i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	1.49535i		−	0.863342i	−0.902031	−	0.431671i	$-0.857924\pi$
$3$		−	1.49535i		−	0.863342i	0.902031	−	0.431671i	$-0.142076\pi$
$4$	1.00000			0.500000
$5$	−1.45979	−	1.69382i	−0.652836	−	0.757499i
$5$	−1.45979	−	1.69382i	−0.652836	−	0.757499i
$6$		−	1.49535i		−	0.610475i
$7$	−1.01867			−0.385021			−0.192511	−	0.981295i	$-0.561663\pi$
$7$	−1.01867			−0.385021			−0.192511	+	0.981295i	$0.561663\pi$
$8$	1.00000			0.353553
$9$	0.763924			0.254641
$10$	−1.45979	−	1.69382i	−0.461625	−	0.535633i
$11$		−	2.42025i		−	0.729733i	−0.931060	−	0.364866i	$-0.881115\pi$
$11$		−	2.42025i		−	0.729733i	0.931060	−	0.364866i	$-0.118885\pi$
$12$		−	1.49535i		−	0.431671i
$13$		0			0
$13$		0			0
$14$	−1.01867			−0.272251
$15$	−2.53286	+	2.18289i	−0.653980	+	0.563621i
$16$	1.00000			0.250000
$17$			5.04699i			1.22407i	0.790829	+	0.612037i	$0.209650\pi$
$17$			5.04699i			1.22407i	−0.790829	+	0.612037i	$0.790350\pi$
$18$	0.763924			0.180059
$19$		−	7.36506i		−	1.68966i	−0.535034	−	0.844830i	$-0.679701\pi$
$19$		−	7.36506i		−	1.68966i	0.535034	−	0.844830i	$-0.320299\pi$
$20$	−1.45979	−	1.69382i	−0.326418	−	0.378750i
$21$			1.52327i			0.332405i
$22$		−	2.42025i		−	0.515999i
$23$		−	4.52359i		−	0.943233i	−0.881804	−	0.471616i	$-0.843671\pi$
$23$		−	4.52359i		−	0.943233i	0.881804	−	0.471616i	$-0.156329\pi$
$24$		−	1.49535i		−	0.305237i
$25$	−0.738047	+	4.94523i	−0.147609	+	0.989046i
$26$		0			0
$27$		−	5.62839i		−	1.08318i
$28$	−1.01867			−0.192511
$29$	−6.38898			−1.18640			−0.593202	−	0.805054i	$-0.702136\pi$
$29$	−6.38898			−1.18640			−0.593202	+	0.805054i	$0.702136\pi$
$30$	−2.53286	+	2.18289i	−0.462434	+	0.398540i
$31$		−	6.28274i		−	1.12841i	−0.825634	−	0.564207i	$-0.809182\pi$
$31$		−	6.28274i		−	1.12841i	0.825634	−	0.564207i	$-0.190818\pi$
$32$	1.00000			0.176777
$33$	−3.61912			−0.630009
$34$			5.04699i			0.865551i
$35$	1.48704	+	1.72544i	0.251356	+	0.291653i
$36$	0.763924			0.127321
$37$	−1.80149			−0.296163			−0.148081	−	0.988975i	$-0.547310\pi$
$37$	−1.80149			−0.296163			−0.148081	+	0.988975i	$0.547310\pi$
$38$		−	7.36506i		−	1.19477i
$39$		0			0
$40$	−1.45979	−	1.69382i	−0.230812	−	0.267816i
$41$		−	0.399553i		−	0.0623997i	−0.999513	−	0.0311999i	$-0.990067\pi$
$41$		−	0.399553i		−	0.0623997i	0.999513	−	0.0311999i	$-0.00993284\pi$
$42$			1.52327i			0.235046i
$43$			8.41814i			1.28375i	0.766808	+	0.641877i	$0.221844\pi$
$43$			8.41814i			1.28375i	−0.766808	+	0.641877i	$0.778156\pi$
$44$		−	2.42025i		−	0.364866i
$45$	−1.11517	−	1.29395i	−0.166239	−	0.192891i
$46$		−	4.52359i		−	0.666966i
$47$	0.146040			0.0213021			0.0106511	−	0.999943i	$-0.496610\pi$
$47$	0.146040			0.0213021			0.0106511	+	0.999943i	$0.496610\pi$
$48$		−	1.49535i		−	0.215835i
$49$	−5.96231			−0.851758
$50$	−0.738047	+	4.94523i	−0.104376	+	0.699361i
$51$	7.54702			1.05679
$52$		0			0
$53$			1.52601i			0.209614i	0.994493	+	0.104807i	$0.0334225\pi$
$53$			1.52601i			0.209614i	−0.994493	+	0.104807i	$0.966578\pi$
$54$		−	5.62839i		−	0.765927i
$55$	−4.09947	+	3.53305i	−0.552772	+	0.476396i
$56$	−1.01867			−0.136126
$57$	−11.0134			−1.45875
$58$	−6.38898			−0.838914
$59$			3.23605i			0.421298i	0.977562	+	0.210649i	$0.0675578\pi$
$59$			3.23605i			0.421298i	−0.977562	+	0.210649i	$0.932442\pi$
$60$	−2.53286	+	2.18289i	−0.326990	+	0.281810i
$61$	−14.1612			−1.81316			−0.906580	−	0.422034i	$-0.861316\pi$
$61$	−14.1612			−1.81316			−0.906580	+	0.422034i	$0.861316\pi$
$62$		−	6.28274i		−	0.797909i
$63$	−0.778187			−0.0980424
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.61912			−0.445483
$67$	−6.59001			−0.805098			−0.402549	−	0.915398i	$-0.631876\pi$
$67$	−6.59001			−0.805098			−0.402549	+	0.915398i	$0.631876\pi$
$68$			5.04699i			0.612037i
$69$	−6.76435			−0.814332
$70$	1.48704	+	1.72544i	0.177736	+	0.206230i
$71$			1.36946i			0.162525i	0.996693	+	0.0812623i	$0.0258952\pi$
$71$			1.36946i			0.162525i	−0.996693	+	0.0812623i	$0.974105\pi$
$72$	0.763924			0.0900293
$73$	15.9009			1.86106			0.930531	−	0.366213i	$-0.119346\pi$
$73$	15.9009			1.86106			0.930531	+	0.366213i	$0.119346\pi$
$74$	−1.80149			−0.209419
$75$	7.39485	+	1.10364i	0.853884	+	0.127437i
$76$		−	7.36506i		−	0.844830i
$77$			2.46544i			0.280963i
$78$		0			0
$79$	3.53802			0.398059			0.199029	−	0.979994i	$-0.436221\pi$
$79$	3.53802			0.398059			0.199029	+	0.979994i	$0.436221\pi$
$80$	−1.45979	−	1.69382i	−0.163209	−	0.189375i
$81$	−6.12465			−0.680516
$82$		−	0.399553i		−	0.0441233i
$83$	4.64985			0.510387			0.255194	−	0.966890i	$-0.417861\pi$
$83$	4.64985			0.510387			0.255194	+	0.966890i	$0.417861\pi$
$84$			1.52327i			0.166203i
$85$	8.54869	−	7.36753i	0.927235	−	0.799120i
$86$			8.41814i			0.907751i
$87$			9.55376i			1.02427i
$88$		−	2.42025i		−	0.258000i
$89$			5.60882i			0.594533i	0.954794	+	0.297267i	$0.0960750\pi$
$89$			5.60882i			0.594533i	−0.954794	+	0.297267i	$0.903925\pi$
$90$	−1.11517	−	1.29395i	−0.117549	−	0.136394i
$91$		0			0
$92$		−	4.52359i		−	0.471616i
$93$	−9.39490			−0.974206
$94$	0.146040			0.0150629
$95$	−12.4751	+	10.7514i	−1.27992	+	1.10307i
$96$		−	1.49535i		−	0.152619i
$97$	−8.27379			−0.840076			−0.420038	−	0.907507i	$-0.637983\pi$
$97$	−8.27379			−0.840076			−0.420038	+	0.907507i	$0.637983\pi$
$98$	−5.96231			−0.602284
$99$		−	1.84889i		−	0.185820i
$100$	−0.738047	+	4.94523i	−0.0738047	+	0.494523i
$101$	19.9369			1.98379			0.991896	−	0.127053i	$-0.0405519\pi$
$101$	19.9369			1.98379			0.991896	+	0.127053i	$0.0405519\pi$
$102$	7.54702			0.747266
$103$		−	14.4702i		−	1.42579i	−0.701272	−	0.712893i	$-0.747384\pi$
$103$		−	14.4702i		−	1.42579i	0.701272	−	0.712893i	$-0.252616\pi$
$104$		0			0
$105$	2.58015	−	2.22365i	0.251796	−	0.217006i
$106$			1.52601i			0.148219i
$107$		−	6.49059i		−	0.627469i	−0.949511	−	0.313734i	$-0.898420\pi$
$107$		−	6.49059i		−	0.627469i	0.949511	−	0.313734i	$-0.101580\pi$
$108$		−	5.62839i		−	0.541592i
$109$		−	13.8750i		−	1.32899i	−0.747293	−	0.664494i	$-0.768647\pi$
$109$		−	13.8750i		−	1.32899i	0.747293	−	0.664494i	$-0.231353\pi$
$110$	−4.09947	+	3.53305i	−0.390869	+	0.336863i
$111$			2.69386i			0.255690i
$112$	−1.01867			−0.0962554
$113$		−	12.0565i		−	1.13418i	−0.823656	−	0.567089i	$-0.808069\pi$
$113$		−	12.0565i		−	1.13418i	0.823656	−	0.567089i	$-0.191931\pi$
$114$	−11.0134			−1.03149
$115$	−7.66214	+	6.60347i	−0.714498	+	0.615777i
$116$	−6.38898			−0.593202
$117$		0			0
$118$			3.23605i			0.297903i
$119$		−	5.14122i		−	0.471295i
$120$	−2.53286	+	2.18289i	−0.231217	+	0.199270i
$121$	5.14239			0.467490
$122$	−14.1612			−1.28210
$123$	−0.597472			−0.0538723
$124$		−	6.28274i		−	0.564207i
$125$	9.45372	−	5.96886i	0.845566	−	0.533871i
$126$	−0.778187			−0.0693264
$127$			18.2962i			1.62352i	0.583990	+	0.811761i	$0.301491\pi$
$127$			18.2962i			1.62352i	−0.583990	+	0.811761i	$0.698509\pi$
$128$	1.00000			0.0883883
$129$	12.5881			1.10832
$130$		0			0
$131$	21.8260			1.90694			0.953472	−	0.301481i	$-0.0974808\pi$
$131$	21.8260			1.90694			0.953472	+	0.301481i	$0.0974808\pi$
$132$	−3.61912			−0.315004
$133$			7.50257i			0.650556i
$134$	−6.59001			−0.569290
$135$	−9.53347	+	8.21625i	−0.820511	+	0.707142i
$136$			5.04699i			0.432776i
$137$	−8.05446			−0.688139			−0.344070	−	0.938944i	$-0.611806\pi$
$137$	−8.05446			−0.688139			−0.344070	+	0.938944i	$0.611806\pi$
$138$	−6.76435			−0.575820
$139$	12.8464			1.08962			0.544809	−	0.838560i	$-0.316602\pi$
$139$	12.8464			1.08962			0.544809	+	0.838560i	$0.316602\pi$
$140$	1.48704	+	1.72544i	0.125678	+	0.145827i
$141$		−	0.218381i		−	0.0183910i
$142$			1.36946i			0.114922i
$143$		0			0
$144$	0.763924			0.0636603
$145$	9.32654	+	10.8218i	0.774527	+	0.898699i
$146$	15.9009			1.31597
$147$			8.91575i			0.735358i
$148$	−1.80149			−0.148081
$149$		−	11.6532i		−	0.954669i	−0.878722	−	0.477335i	$-0.841603\pi$
$149$		−	11.6532i		−	0.954669i	0.878722	−	0.477335i	$-0.158397\pi$
$150$	7.39485	+	1.10364i	0.603787	+	0.0901118i
$151$			3.93672i			0.320365i	0.987087	+	0.160183i	$0.0512083\pi$
$151$			3.93672i			0.320365i	−0.987087	+	0.160183i	$0.948792\pi$
$152$		−	7.36506i		−	0.597385i
$153$			3.85552i			0.311700i
$154$			2.46544i			0.198671i
$155$	−10.6418	+	9.17146i	−0.854772	+	0.736669i
$156$		0			0
$157$		−	1.86131i		−	0.148548i	−0.997238	−	0.0742742i	$-0.976336\pi$
$157$		−	1.86131i		−	0.148548i	0.997238	−	0.0742742i	$-0.0236640\pi$
$158$	3.53802			0.281470
$159$	2.28193			0.180968
$160$	−1.45979	−	1.69382i	−0.115406	−	0.133908i
$161$			4.60805i			0.363165i
$162$	−6.12465			−0.481198
$163$	−23.0167			−1.80280			−0.901402	−	0.432984i	$-0.857461\pi$
$163$	−23.0167			−1.80280			−0.901402	+	0.432984i	$0.857461\pi$
$164$		−	0.399553i		−	0.0311999i
$165$	5.28315	+	6.13014i	0.411293	+	0.477231i
$166$	4.64985			0.360898
$167$	−6.11064			−0.472856			−0.236428	−	0.971649i	$-0.575977\pi$
$167$	−6.11064			−0.472856			−0.236428	+	0.971649i	$0.575977\pi$
$168$			1.52327i			0.117523i
$169$		0			0
$170$	8.54869	−	7.36753i	0.655654	−	0.565063i
$171$		−	5.62635i		−	0.430257i
$172$			8.41814i			0.641877i
$173$		−	23.0755i		−	1.75440i	−0.480125	−	0.877200i	$-0.659409\pi$
$173$		−	23.0755i		−	1.75440i	0.480125	−	0.877200i	$-0.340591\pi$
$174$			9.55376i			0.724269i
$175$	0.751828	−	5.03756i	0.0568328	−	0.380804i
$176$		−	2.42025i		−	0.182433i
$177$	4.83904			0.363724
$178$			5.60882i			0.420399i
$179$	7.81690			0.584263			0.292131	−	0.956378i	$-0.405636\pi$
$179$	7.81690			0.584263			0.292131	+	0.956378i	$0.405636\pi$
$180$	−1.11517	−	1.29395i	−0.0831196	−	0.0964453i
$181$	5.21467			0.387603			0.193802	−	0.981041i	$-0.437918\pi$
$181$	5.21467			0.387603			0.193802	+	0.981041i	$0.437918\pi$
$182$		0			0
$183$			21.1760i			1.56538i
$184$		−	4.52359i		−	0.333483i
$185$	2.62979	+	3.05139i	0.193346	+	0.224343i
$186$	−9.39490			−0.688868
$187$	12.2150			0.893248
$188$	0.146040			0.0106511
$189$			5.73348i			0.417049i
$190$	−12.4751	+	10.7514i	−0.905037	+	0.779990i
$191$	10.4143			0.753554			0.376777	−	0.926304i	$-0.377032\pi$
$191$	10.4143			0.753554			0.376777	+	0.926304i	$0.377032\pi$
$192$		−	1.49535i		−	0.107918i
$193$	1.40263			0.100964			0.0504819	−	0.998725i	$-0.483924\pi$
$193$	1.40263			0.100964			0.0504819	+	0.998725i	$0.483924\pi$
$194$	−8.27379			−0.594023
$195$		0			0
$196$	−5.96231			−0.425879
$197$	25.3455			1.80579			0.902897	−	0.429857i	$-0.141436\pi$
$197$	25.3455			1.80579			0.902897	+	0.429857i	$0.141436\pi$
$198$		−	1.84889i		−	0.131395i
$199$	13.7630			0.975636			0.487818	−	0.872945i	$-0.337793\pi$
$199$	13.7630			0.975636			0.487818	+	0.872945i	$0.337793\pi$
$200$	−0.738047	+	4.94523i	−0.0521878	+	0.349680i
$201$			9.85438i			0.695074i
$202$	19.9369			1.40275
$203$	6.50826			0.456791
$204$	7.54702			0.528397
$205$	−0.676771	+	0.583262i	−0.0472677	+	0.0407368i
$206$		−	14.4702i		−	1.00818i
$207$		−	3.45568i		−	0.240186i
$208$		0			0
$209$	−17.8253			−1.23300
$210$	2.58015	−	2.22365i	0.178047	−	0.153446i
$211$	9.82347			0.676275			0.338138	−	0.941097i	$-0.390203\pi$
$211$	9.82347			0.676275			0.338138	+	0.941097i	$0.390203\pi$
$212$			1.52601i			0.104807i
$213$	2.04782			0.140314
$214$		−	6.49059i		−	0.443688i
$215$	14.2588	−	12.2887i	0.972442	−	0.838081i
$216$		−	5.62839i		−	0.382963i
$217$			6.40004i			0.434463i
$218$		−	13.8750i		−	0.939737i
$219$		−	23.7775i		−	1.60673i
$220$	−4.09947	+	3.53305i	−0.276386	+	0.238198i
$221$		0			0
$222$			2.69386i			0.180800i
$223$	−19.3560			−1.29618			−0.648088	−	0.761565i	$-0.724431\pi$
$223$	−19.3560			−1.29618			−0.648088	+	0.761565i	$0.724431\pi$
$224$	−1.01867			−0.0680628
$225$	−0.563812	+	3.77778i	−0.0375875	+	0.251852i
$226$		−	12.0565i		−	0.801986i
$227$	20.7535			1.37746			0.688729	−	0.725019i	$-0.258169\pi$
$227$	20.7535			1.37746			0.688729	+	0.725019i	$0.258169\pi$
$228$	−11.0134			−0.729377
$229$		−	23.2933i		−	1.53927i	−0.638486	−	0.769634i	$-0.720439\pi$
$229$		−	23.2933i		−	1.53927i	0.638486	−	0.769634i	$-0.279561\pi$
$230$	−7.66214	+	6.60347i	−0.505226	+	0.435420i
$231$	3.68670			0.242567
$232$	−6.38898			−0.419457
$233$		−	0.585969i		−	0.0383881i	−0.999816	−	0.0191941i	$-0.993890\pi$
$233$		−	0.585969i		−	0.0383881i	0.999816	−	0.0191941i	$-0.00611003\pi$
$234$		0			0
$235$	−0.213187	−	0.247366i	−0.0139068	−	0.0161363i
$236$			3.23605i			0.210649i
$237$		−	5.29059i		−	0.343660i
$238$		−	5.14122i		−	0.333256i
$239$			9.56019i			0.618397i	0.950998	+	0.309199i	$0.100061\pi$
$239$			9.56019i			0.618397i	−0.950998	+	0.309199i	$0.899939\pi$
$240$	−2.53286	+	2.18289i	−0.163495	+	0.140905i
$241$			11.5135i			0.741650i	0.928703	+	0.370825i	$0.120925\pi$
$241$			11.5135i			0.741650i	−0.928703	+	0.370825i	$0.879075\pi$
$242$	5.14239			0.330565
$243$		−	7.72667i		−	0.495666i
$244$	−14.1612			−0.906580
$245$	8.70370	+	10.0991i	0.556059	+	0.645206i
$246$	−0.597472			−0.0380935
$247$		0			0
$248$		−	6.28274i		−	0.398954i
$249$		−	6.95316i		−	0.440639i
$250$	9.45372	−	5.96886i	0.597905	−	0.377504i
$251$	15.0024			0.946942			0.473471	−	0.880809i	$-0.343001\pi$
$251$	15.0024			0.946942			0.473471	+	0.880809i	$0.343001\pi$
$252$	−0.778187			−0.0490212
$253$	−10.9482			−0.688308
$254$			18.2962i			1.14800i
$255$	−11.0170	−	12.7833i	−0.689914	−	0.800521i
$256$	1.00000			0.0625000
$257$		−	0.902680i		−	0.0563077i	−0.999604	−	0.0281538i	$-0.991037\pi$
$257$		−	0.902680i		−	0.0563077i	0.999604	−	0.0281538i	$-0.00896283\pi$
$258$	12.5881			0.783699
$259$	1.83512			0.114029
$260$		0			0
$261$	−4.88069			−0.302107
$262$	21.8260			1.34841
$263$		−	17.5243i		−	1.08059i	−0.841475	−	0.540297i	$-0.818312\pi$
$263$		−	17.5243i		−	1.08059i	0.841475	−	0.540297i	$-0.181688\pi$
$264$	−3.61912			−0.222742
$265$	2.58479	−	2.22765i	0.158782	−	0.136844i
$266$			7.50257i			0.460012i
$267$	8.38715			0.513285
$268$	−6.59001			−0.402549
$269$	−3.17990			−0.193882			−0.0969410	−	0.995290i	$-0.530906\pi$
$269$	−3.17990			−0.193882			−0.0969410	+	0.995290i	$0.530906\pi$
$270$	−9.53347	+	8.21625i	−0.580189	+	0.500025i
$271$			13.8015i			0.838382i	0.907898	+	0.419191i	$0.137686\pi$
$271$			13.8015i			0.838382i	−0.907898	+	0.419191i	$0.862314\pi$
$272$			5.04699i			0.306019i
$273$		0			0
$274$	−8.05446			−0.486588
$275$	11.9687	+	1.78626i	0.721739	+	0.107716i
$276$	−6.76435			−0.407166
$277$		−	4.77040i		−	0.286626i	−0.989677	−	0.143313i	$-0.954225\pi$
$277$		−	4.77040i		−	0.286626i	0.989677	−	0.143313i	$-0.0457755\pi$
$278$	12.8464			0.770476
$279$		−	4.79954i		−	0.287341i
$280$	1.48704	+	1.72544i	0.0888678	+	0.103115i
$281$			5.70927i			0.340586i	0.985393	+	0.170293i	$0.0544715\pi$
$281$			5.70927i			0.340586i	−0.985393	+	0.170293i	$0.945529\pi$
$282$		−	0.218381i		−	0.0130044i
$283$		−	21.2228i		−	1.26157i	−0.775960	−	0.630783i	$-0.782734\pi$
$283$		−	21.2228i		−	1.26157i	0.775960	−	0.630783i	$-0.217266\pi$
$284$			1.36946i			0.0812623i
$285$	16.0771	+	18.6546i	0.952328	+	1.10500i
$286$		0			0
$287$			0.407013i			0.0240252i
$288$	0.763924			0.0450147
$289$	−8.47209			−0.498359
$290$	9.32654	+	10.8218i	0.547673	+	0.635476i
$291$			12.3722i			0.725272i
$292$	15.9009			0.930531
$293$	−23.9835			−1.40113			−0.700565	−	0.713588i	$-0.747069\pi$
$293$	−23.9835			−1.40113			−0.700565	+	0.713588i	$0.747069\pi$
$294$			8.91575i			0.519977i
$295$	5.48129	−	4.72395i	0.319133	−	0.275039i
$296$	−1.80149			−0.104709
$297$	−13.6221			−0.790435
$298$		−	11.6532i		−	0.675053i
$299$		0			0
$300$	7.39485	+	1.10364i	0.426942	+	0.0637187i
$301$		−	8.57531i		−	0.494273i
$302$			3.93672i			0.226533i
$303$		−	29.8126i		−	1.71269i
$304$		−	7.36506i		−	0.422415i
$305$	20.6724	+	23.9866i	1.18370	+	1.37347i
$306$			3.85552i			0.220405i
$307$	−17.0892			−0.975334			−0.487667	−	0.873030i	$-0.662152\pi$
$307$	−17.0892			−0.975334			−0.487667	+	0.873030i	$0.662152\pi$
$308$			2.46544i			0.140481i
$309$	−21.6380			−1.23094
$310$	−10.6418	+	9.17146i	−0.604415	+	0.520904i
$311$	−5.17968			−0.293713			−0.146856	−	0.989158i	$-0.546916\pi$
$311$	−5.17968			−0.293713			−0.146856	+	0.989158i	$0.546916\pi$
$312$		0			0
$313$			33.7809i			1.90941i	0.297556	+	0.954704i	$0.403828\pi$
$313$			33.7809i			1.90941i	−0.297556	+	0.954704i	$0.596172\pi$
$314$		−	1.86131i		−	0.105040i
$315$	1.13599	+	1.31811i	0.0640056	+	0.0742670i
$316$	3.53802			0.199029
$317$	23.3968			1.31409			0.657047	−	0.753850i	$-0.271805\pi$
$317$	23.3968			1.31409			0.657047	+	0.753850i	$0.271805\pi$
$318$	2.28193			0.127964
$319$			15.4629i			0.865757i
$320$	−1.45979	−	1.69382i	−0.0816045	−	0.0946874i
$321$	−9.70571			−0.541720
$322$			4.60805i			0.256796i
$323$	37.1714			2.06827
$324$	−6.12465			−0.340258
$325$		0			0
$326$	−23.0167			−1.27477
$327$	−20.7481			−1.14737
$328$		−	0.399553i		−	0.0220616i
$329$	−0.148767			−0.00820178
$330$	5.28315	+	6.13014i	0.290828	+	0.337453i
$331$		−	5.46645i		−	0.300463i	−0.988651	−	0.150232i	$-0.951998\pi$
$331$		−	5.46645i		−	0.300463i	0.988651	−	0.150232i	$-0.0480019\pi$
$332$	4.64985			0.255194
$333$	−1.37620			−0.0754153
$334$	−6.11064			−0.334359
$335$	9.62001	+	11.1623i	0.525597	+	0.609861i
$336$			1.52327i			0.0831013i
$337$			25.4138i			1.38438i	0.721717	+	0.692188i	$0.243353\pi$
$337$			25.4138i			1.38438i	−0.721717	+	0.692188i	$0.756647\pi$
$338$		0			0
$339$	−18.0287			−0.979184
$340$	8.54869	−	7.36753i	0.463618	−	0.399560i
$341$	−15.2058			−0.823440
$342$		−	5.62635i		−	0.304238i
$343$	13.2043			0.712967
$344$			8.41814i			0.453876i
$345$	9.87451	+	11.4576i	0.531626	+	0.616856i
$346$		−	23.0755i		−	1.24055i
$347$			17.1079i			0.918402i	0.888332	+	0.459201i	$0.151864\pi$
$347$			17.1079i			0.918402i	−0.888332	+	0.459201i	$0.848136\pi$
$348$			9.55376i			0.512136i
$349$			0.935233i			0.0500619i	0.999687	+	0.0250309i	$0.00796843\pi$
$349$			0.935233i			0.0500619i	−0.999687	+	0.0250309i	$0.992032\pi$
$350$	0.751828	−	5.03756i	0.0401869	−	0.269269i
$351$		0			0
$352$		−	2.42025i		−	0.129000i
$353$	0.243550			0.0129628			0.00648142	−	0.999979i	$-0.497937\pi$
$353$	0.243550			0.0129628			0.00648142	+	0.999979i	$0.497937\pi$
$354$	4.83904			0.257192
$355$	2.31961	−	1.99912i	0.123112	−	0.106102i
$356$			5.60882i			0.297267i
$357$	−7.68793			−0.406889
$358$	7.81690			0.413136
$359$		−	14.7698i		−	0.779520i	−0.920916	−	0.389760i	$-0.872558\pi$
$359$		−	14.7698i		−	0.779520i	0.920916	−	0.389760i	$-0.127442\pi$
$360$	−1.11517	−	1.29395i	−0.0587744	−	0.0681971i
$361$	−35.2441			−1.85495
$362$	5.21467			0.274077
$363$		−	7.68968i		−	0.403603i
$364$		0			0
$365$	−23.2120	−	26.9333i	−1.21497	−	1.40975i
$366$			21.1760i			1.10689i
$367$			3.29260i			0.171872i	0.996301	+	0.0859362i	$0.0273881\pi$
$367$			3.29260i			0.171872i	−0.996301	+	0.0859362i	$0.972612\pi$
$368$		−	4.52359i		−	0.235808i
$369$		−	0.305228i		−	0.0158896i
$370$	2.62979	+	3.05139i	0.136716	+	0.158634i
$371$		−	1.55450i		−	0.0807059i
$372$	−9.39490			−0.487103
$373$		−	18.9067i		−	0.978950i	−0.872017	−	0.489475i	$-0.837188\pi$
$373$		−	18.9067i		−	0.978950i	0.872017	−	0.489475i	$-0.162812\pi$
$374$	12.2150			0.631621
$375$	−8.92554	−	14.1366i	−0.460913	−	0.730012i
$376$	0.146040			0.00753144
$377$		0			0
$378$			5.73348i			0.294898i
$379$			13.7733i			0.707489i	0.935342	+	0.353744i	$0.115092\pi$
$379$			13.7733i			0.707489i	−0.935342	+	0.353744i	$0.884908\pi$
$380$	−12.4751	+	10.7514i	−0.639958	+	0.551536i
$381$	27.3592			1.40165
$382$	10.4143			0.532843
$383$	33.3243			1.70279			0.851395	−	0.524525i	$-0.175757\pi$
$383$	33.3243			1.70279			0.851395	+	0.524525i	$0.175757\pi$
$384$		−	1.49535i		−	0.0763093i
$385$	4.17601	−	3.59901i	0.212829	−	0.183423i
$386$	1.40263			0.0713922
$387$			6.43082i			0.326897i
$388$	−8.27379			−0.420038
$389$	−1.91117			−0.0969004			−0.0484502	−	0.998826i	$-0.515428\pi$
$389$	−1.91117			−0.0969004			−0.0484502	+	0.998826i	$0.515428\pi$
$390$		0			0
$391$	22.8305			1.15459
$392$	−5.96231			−0.301142
$393$		−	32.6375i		−	1.64634i
$394$	25.3455			1.27689
$395$	−5.16476	−	5.99277i	−0.259867	−	0.301529i
$396$		−	1.84889i		−	0.0929101i
$397$	13.5405			0.679579			0.339789	−	0.940502i	$-0.389644\pi$
$397$	13.5405			0.679579			0.339789	+	0.940502i	$0.389644\pi$
$398$	13.7630			0.689878
$399$	11.2190			0.561652
$400$	−0.738047	+	4.94523i	−0.0369024	+	0.247261i
$401$			28.9798i			1.44718i	0.690228	+	0.723592i	$0.257510\pi$
$401$			28.9798i			1.44718i	−0.690228	+	0.723592i	$0.742490\pi$
$402$			9.85438i			0.491492i
$403$		0			0
$404$	19.9369			0.991896
$405$	8.94068	+	10.3740i	0.444266	+	0.515490i
$406$	6.50826			0.323000
$407$			4.36005i			0.216120i
$408$	7.54702			0.373633
$409$			9.77252i			0.483220i	0.970373	+	0.241610i	$0.0776755\pi$
$409$			9.77252i			0.483220i	−0.970373	+	0.241610i	$0.922325\pi$
$410$	−0.676771	+	0.583262i	−0.0334233	+	0.0288053i
$411$			12.0442i			0.594099i
$412$		−	14.4702i		−	0.712893i
$413$		−	3.29647i		−	0.162209i
$414$		−	3.45568i		−	0.169837i
$415$	−6.78779	−	7.87601i	−0.333199	−	0.386618i
$416$		0			0
$417$		−	19.2099i		−	0.940712i
$418$	−17.8253			−0.871863
$419$	24.9288			1.21785			0.608926	−	0.793227i	$-0.291601\pi$
$419$	24.9288			1.21785			0.608926	+	0.793227i	$0.291601\pi$
$420$	2.58015	−	2.22365i	0.125898	−	0.108503i
$421$			12.7436i			0.621087i	0.950559	+	0.310544i	$0.100511\pi$
$421$			12.7436i			0.621087i	−0.950559	+	0.310544i	$0.899489\pi$
$422$	9.82347			0.478199
$423$	0.111564			0.00542441
$424$			1.52601i			0.0741097i
$425$	−24.9585	−	3.72492i	−1.21067	−	0.180685i
$426$	2.04782			0.0992172
$427$	14.4256			0.698105
$428$		−	6.49059i		−	0.313734i
$429$		0			0
$430$	14.2588	−	12.2887i	0.687621	−	0.592613i
$431$			22.2564i			1.07205i	0.844202	+	0.536026i	$0.180075\pi$
$431$			22.2564i			1.07205i	−0.844202	+	0.536026i	$0.819925\pi$
$432$		−	5.62839i		−	0.270796i
$433$		−	30.4130i		−	1.46156i	−0.682615	−	0.730778i	$-0.739157\pi$
$433$		−	30.4130i		−	1.46156i	0.682615	−	0.730778i	$-0.260843\pi$
$434$			6.40004i			0.307212i
$435$	16.1823	−	13.9465i	0.775884	−	0.668681i
$436$		−	13.8750i		−	0.664494i
$437$	−33.3165			−1.59374
$438$		−	23.7775i		−	1.13613i
$439$	−12.5984			−0.601287			−0.300644	−	0.953737i	$-0.597201\pi$
$439$	−12.5984			−0.601287			−0.300644	+	0.953737i	$0.597201\pi$
$440$	−4.09947	+	3.53305i	−0.195434	+	0.168431i
$441$	−4.55475			−0.216893
$442$		0			0
$443$			2.42243i			0.115093i	0.998343	+	0.0575467i	$0.0183278\pi$
$443$			2.42243i			0.115093i	−0.998343	+	0.0575467i	$0.981672\pi$
$444$			2.69386i			0.127845i
$445$	9.50032	−	8.18767i	0.450358	−	0.388133i
$446$	−19.3560			−0.916535
$447$	−17.4257			−0.824206
$448$	−1.01867			−0.0481277
$449$		−	29.0963i		−	1.37314i	−0.727065	−	0.686568i	$-0.759116\pi$
$449$		−	29.0963i		−	1.37314i	0.727065	−	0.686568i	$-0.240884\pi$
$450$	−0.563812	+	3.77778i	−0.0265784	+	0.178086i
$451$	−0.967019			−0.0455351
$452$		−	12.0565i		−	0.567089i
$453$	5.88677			0.276585
$454$	20.7535			0.974010
$455$		0			0
$456$	−11.0134			−0.515747
$457$	−5.25707			−0.245916			−0.122958	−	0.992412i	$-0.539238\pi$
$457$	−5.25707			−0.245916			−0.122958	+	0.992412i	$0.539238\pi$
$458$		−	23.2933i		−	1.08843i
$459$	28.4064			1.32590
$460$	−7.66214	+	6.60347i	−0.357249	+	0.307888i
$461$			21.6948i			1.01043i	0.862995	+	0.505213i	$0.168586\pi$
$461$			21.6948i			1.01043i	−0.862995	+	0.505213i	$0.831414\pi$
$462$	3.68670			0.171521
$463$	−6.17734			−0.287085			−0.143543	−	0.989644i	$-0.545849\pi$
$463$	−6.17734			−0.287085			−0.143543	+	0.989644i	$0.545849\pi$
$464$	−6.38898			−0.296601
$465$	13.7146	+	15.9133i	0.635997	+	0.737960i
$466$		−	0.585969i		−	0.0271445i
$467$			9.01521i			0.417174i	0.978004	+	0.208587i	$0.0668865\pi$
$467$			9.01521i			0.417174i	−0.978004	+	0.208587i	$0.933114\pi$
$468$		0			0
$469$	6.71305			0.309980
$470$	−0.213187	−	0.247366i	−0.00983360	−	0.0114101i
$471$	−2.78331			−0.128248
$472$			3.23605i			0.148951i
$473$	20.3740			0.936798
$474$		−	5.29059i		−	0.243005i
$475$	36.4219	+	5.43576i	1.67115	+	0.249410i
$476$		−	5.14122i		−	0.235647i
$477$			1.16576i			0.0533764i
$478$			9.56019i			0.437273i
$479$			14.3406i			0.655240i	0.944810	+	0.327620i	$0.106247\pi$
$479$			14.3406i			0.655240i	−0.944810	+	0.327620i	$0.893753\pi$
$480$	−2.53286	+	2.18289i	−0.115608	+	0.0996350i
$481$		0			0
$482$			11.5135i			0.524426i
$483$	6.89065			0.313535
$484$	5.14239			0.233745
$485$	12.0780	+	14.0143i	0.548432	+	0.636357i
$486$		−	7.72667i		−	0.350489i
$487$	−15.5121			−0.702921			−0.351460	−	0.936203i	$-0.614315\pi$
$487$	−15.5121			−0.702921			−0.351460	+	0.936203i	$0.614315\pi$
$488$	−14.1612			−0.641049
$489$			34.4180i			1.55644i
$490$	8.70370	+	10.0991i	0.393193	+	0.456230i
$491$	−2.60458			−0.117543			−0.0587715	−	0.998271i	$-0.518718\pi$
$491$	−2.60458			−0.117543			−0.0587715	+	0.998271i	$0.518718\pi$
$492$	−0.597472			−0.0269361
$493$		−	32.2451i		−	1.45225i
$494$		0			0
$495$	−3.13168	+	2.69898i	−0.140759	+	0.121310i
$496$		−	6.28274i		−	0.282103i
$497$		−	1.39503i		−	0.0625755i
$498$		−	6.95316i		−	0.311579i
$499$		−	4.88458i		−	0.218664i	−0.994005	−	0.109332i	$-0.965129\pi$
$499$		−	4.88458i		−	0.218664i	0.994005	−	0.109332i	$-0.0348712\pi$
$500$	9.45372	−	5.96886i	0.422783	−	0.266935i
$501$			9.13756i			0.408236i
$502$	15.0024			0.669589
$503$		−	1.67768i		−	0.0748041i	−0.999300	−	0.0374020i	$-0.988092\pi$
$503$		−	1.67768i		−	0.0748041i	0.999300	−	0.0374020i	$-0.0119082\pi$
$504$	−0.778187			−0.0346632
$505$	−29.1036	−	33.7694i	−1.29509	−	1.50272i
$506$	−10.9482			−0.486707
$507$		0			0
$508$			18.2962i			0.811761i
$509$			24.0762i			1.06716i	0.845750	+	0.533580i	$0.179154\pi$
$509$			24.0762i			1.06716i	−0.845750	+	0.533580i	$0.820846\pi$
$510$	−11.0170	−	12.7833i	−0.487843	−	0.566054i
$511$	−16.1978			−0.716549
$512$	1.00000			0.0441942
$513$	−41.4534			−1.83021
$514$		−	0.902680i		−	0.0398155i
$515$	−24.5098	+	21.1233i	−1.08003	+	0.930805i
$516$	12.5881			0.554159
$517$		−	0.353454i		−	0.0155449i
$518$	1.83512			0.0806307
$519$	−34.5060			−1.51465
$520$		0			0
$521$	4.74906			0.208060			0.104030	−	0.994574i	$-0.466826\pi$
$521$	4.74906			0.208060			0.104030	+	0.994574i	$0.466826\pi$
$522$	−4.88069			−0.213622
$523$			21.1351i			0.924174i	0.886835	+	0.462087i	$0.152899\pi$
$523$			21.1351i			0.924174i	−0.886835	+	0.462087i	$0.847101\pi$
$524$	21.8260			0.953472
$525$	−7.53292	−	1.12425i	−0.328764	−	0.0490661i
$526$		−	17.5243i		−	0.764095i
$527$	31.7089			1.38126
$528$	−3.61912			−0.157502
$529$	2.53718			0.110312
$530$	2.58479	−	2.22765i	0.112276	−	0.0967631i
$531$			2.47210i			0.107280i
$532$			7.50257i			0.325278i
$533$		0			0
$534$	8.38715			0.362948
$535$	−10.9939	+	9.47487i	−0.475307	+	0.409635i
$536$	−6.59001			−0.284645
$537$		−	11.6890i		−	0.504418i
$538$	−3.17990			−0.137095
$539$			14.4303i			0.621556i
$540$	−9.53347	+	8.21625i	−0.410255	+	0.353571i
$541$		−	16.3708i		−	0.703835i	−0.936031	−	0.351917i	$-0.885530\pi$
$541$		−	16.3708i		−	0.703835i	0.936031	−	0.351917i	$-0.114470\pi$
$542$			13.8015i			0.592825i
$543$		−	7.79776i		−	0.334634i
$544$			5.04699i			0.216388i
$545$	−23.5018	+	20.2546i	−1.00671	+	0.867612i
$546$		0			0
$547$			25.9050i			1.10762i	0.832643	+	0.553810i	$0.186827\pi$
$547$			25.9050i			1.10762i	−0.832643	+	0.553810i	$0.813173\pi$
$548$	−8.05446			−0.344070
$549$	−10.8181			−0.461706
$550$	11.9687	+	1.78626i	0.510347	+	0.0761664i
$551$			47.0552i			2.00462i
$552$	−6.76435			−0.287910
$553$	−3.60408			−0.153261
$554$		−	4.77040i		−	0.202675i
$555$	4.56291	−	3.93245i	0.193685	−	0.166923i
$556$	12.8464			0.544809
$557$	−18.3250			−0.776453			−0.388227	−	0.921564i	$-0.626912\pi$
$557$	−18.3250			−0.776453			−0.388227	+	0.921564i	$0.626912\pi$
$558$		−	4.79954i		−	0.203181i
$559$		0			0
$560$	1.48704	+	1.72544i	0.0628390	+	0.0729133i
$561$		−	18.2657i		−	0.771178i
$562$			5.70927i			0.240831i
$563$			17.3172i			0.729832i	0.931040	+	0.364916i	$0.118902\pi$
$563$			17.3172i			0.729832i	−0.931040	+	0.364916i	$0.881098\pi$
$564$		−	0.218381i		−	0.00919551i
$565$	−20.4215	+	17.5999i	−0.859139	+	0.740433i
$566$		−	21.2228i		−	0.892061i
$567$	6.23900			0.262013
$568$			1.36946i			0.0574612i
$569$	36.5689			1.53305			0.766524	−	0.642216i	$-0.221985\pi$
$569$	36.5689			1.53305			0.766524	+	0.642216i	$0.221985\pi$
$570$	16.0771	+	18.6546i	0.673397	+	0.781356i
$571$	−31.7878			−1.33028			−0.665139	−	0.746720i	$-0.731628\pi$
$571$	−31.7878			−1.33028			−0.665139	+	0.746720i	$0.731628\pi$
$572$		0			0
$573$		−	15.5731i		−	0.650575i
$574$			0.407013i			0.0169884i
$575$	22.3702	+	3.33862i	0.932900	+	0.139230i
$576$	0.763924			0.0318302
$577$	26.0002			1.08240			0.541202	−	0.840893i	$-0.317970\pi$
$577$	26.0002			1.08240			0.541202	+	0.840893i	$0.317970\pi$
$578$	−8.47209			−0.352393
$579$		−	2.09743i		−	0.0871663i
$580$	9.32654	+	10.8218i	0.387263	+	0.449350i
$581$	−4.73667			−0.196510
$582$			12.3722i			0.512845i
$583$	3.69333			0.152962
$584$	15.9009			0.657985
$585$		0			0
$586$	−23.9835			−0.990749
$587$	27.4016			1.13098			0.565492	−	0.824754i	$-0.308686\pi$
$587$	27.4016			1.13098			0.565492	+	0.824754i	$0.308686\pi$
$588$			8.91575i			0.367679i
$589$	−46.2728			−1.90664
$590$	5.48129	−	4.72395i	0.225661	−	0.194482i
$591$		−	37.9005i		−	1.55902i
$592$	−1.80149			−0.0740407
$593$	10.5439			0.432985			0.216492	−	0.976284i	$-0.430538\pi$
$593$	10.5439			0.432985			0.216492	+	0.976284i	$0.430538\pi$
$594$	−13.6221			−0.558922
$595$	−8.70830	+	7.50508i	−0.357005	+	0.307678i
$596$		−	11.6532i		−	0.477335i
$597$		−	20.5806i		−	0.842307i
$598$		0			0
$599$	15.3122			0.625640			0.312820	−	0.949812i	$-0.398726\pi$
$599$	15.3122			0.625640			0.312820	+	0.949812i	$0.398726\pi$
$600$	7.39485	+	1.10364i	0.301894	+	0.0450559i
$601$	12.1851			0.497041			0.248521	−	0.968627i	$-0.420056\pi$
$601$	12.1851			0.497041			0.248521	+	0.968627i	$0.420056\pi$
$602$		−	8.57531i		−	0.349504i
$603$	−5.03427			−0.205011
$604$			3.93672i			0.160183i
$605$	−7.50679	−	8.71028i	−0.305194	−	0.354123i
$606$		−	29.8126i		−	1.21105i
$607$		−	18.3971i		−	0.746716i	−0.927687	−	0.373358i	$-0.878206\pi$
$607$		−	18.3971i		−	0.746716i	0.927687	−	0.373358i	$-0.121794\pi$
$608$		−	7.36506i		−	0.298693i
$609$		−	9.73214i		−	0.394366i
$610$	20.6724	+	23.9866i	0.837000	+	0.971188i
$611$		0			0
$612$			3.85552i			0.155850i
$613$	−14.7497			−0.595734			−0.297867	−	0.954607i	$-0.596275\pi$
$613$	−14.7497			−0.595734			−0.297867	+	0.954607i	$0.596275\pi$
$614$	−17.0892			−0.689666
$615$	0.872182	+	1.01201i	0.0351698	+	0.0408082i
$616$			2.46544i			0.0993354i
$617$	12.2578			0.493482			0.246741	−	0.969081i	$-0.420640\pi$
$617$	12.2578			0.493482			0.246741	+	0.969081i	$0.420640\pi$
$618$	−21.6380			−0.870407
$619$		−	5.15917i		−	0.207365i	−0.994610	−	0.103682i	$-0.966937\pi$
$619$		−	5.15917i		−	0.207365i	0.994610	−	0.103682i	$-0.0330625\pi$
$620$	−10.6418	+	9.17146i	−0.427386	+	0.368335i
$621$	−25.4605			−1.02169
$622$	−5.17968			−0.207686
$623$		−	5.71354i		−	0.228908i
$624$		0			0
$625$	−23.9106	−	7.29963i	−0.956423	−	0.291985i
$626$			33.7809i			1.35016i
$627$			26.6551i			1.06450i
$628$		−	1.86131i		−	0.0742742i
$629$		−	9.09208i		−	0.362525i
$630$	1.13599	+	1.31811i	0.0452588	+	0.0525147i
$631$		−	11.4906i		−	0.457432i	−0.973493	−	0.228716i	$-0.926547\pi$
$631$		−	11.4906i		−	0.457432i	0.973493	−	0.228716i	$-0.0734527\pi$
$632$	3.53802			0.140735
$633$		−	14.6895i		−	0.583857i
$634$	23.3968			0.929205
$635$	30.9904	−	26.7085i	1.22982	−	1.05989i
$636$	2.28193			0.0904842
$637$		0			0
$638$			15.4629i			0.612183i
$639$			1.04616i			0.0413855i
$640$	−1.45979	−	1.69382i	−0.0577031	−	0.0669541i
$641$	−42.6494			−1.68455			−0.842275	−	0.539048i	$-0.818784\pi$
$641$	−42.6494			−1.68455			−0.842275	+	0.539048i	$0.818784\pi$
$642$	−9.70571			−0.383054
$643$	33.4244			1.31813			0.659064	−	0.752087i	$-0.270953\pi$
$643$	33.4244			1.31813			0.659064	+	0.752087i	$0.270953\pi$
$644$			4.60805i			0.181582i
$645$	−18.3759	−	21.3219i	−0.723550	−	0.839550i
$646$	37.1714			1.46249
$647$		−	21.1277i		−	0.830616i	−0.909681	−	0.415308i	$-0.863674\pi$
$647$		−	21.1277i		−	0.830616i	0.909681	−	0.415308i	$-0.136326\pi$
$648$	−6.12465			−0.240599
$649$	7.83206			0.307435
$650$		0			0
$651$	9.57032			0.375090
$652$	−23.0167			−0.901402
$653$			23.4000i			0.915711i	0.889027	+	0.457855i	$0.151382\pi$
$653$			23.4000i			0.915711i	−0.889027	+	0.457855i	$0.848618\pi$
$654$	−20.7481			−0.811314
$655$	−31.8613	−	36.9693i	−1.24492	−	1.44451i
$656$		−	0.399553i		−	0.0155999i
$657$	12.1471			0.473903
$658$	−0.148767			−0.00579953
$659$	−34.8524			−1.35766			−0.678829	−	0.734297i	$-0.737512\pi$
$659$	−34.8524			−1.35766			−0.678829	+	0.734297i	$0.737512\pi$
$660$	5.28315	+	6.13014i	0.205646	+	0.238616i
$661$			28.2985i			1.10068i	0.834939	+	0.550342i	$0.185503\pi$
$661$			28.2985i			1.10068i	−0.834939	+	0.550342i	$0.814497\pi$
$662$		−	5.46645i		−	0.212460i
$663$		0			0
$664$	4.64985			0.180449
$665$	12.7080	−	10.9522i	0.492795	−	0.424706i
$666$	−1.37620			−0.0533266
$667$			28.9011i			1.11905i
$668$	−6.11064			−0.236428
$669$			28.9441i			1.11904i
$670$	9.62001	+	11.1623i	0.371653	+	0.431237i
$671$			34.2737i			1.32312i
$672$			1.52327i			0.0587615i
$673$			12.7929i			0.493132i	0.969126	+	0.246566i	$0.0793022\pi$
$673$			12.7929i			0.493132i	−0.969126	+	0.246566i	$0.920698\pi$
$674$			25.4138i			0.978902i
$675$	27.8337	+	4.15402i	1.07132	+	0.159888i
$676$		0			0
$677$		−	31.8535i		−	1.22423i	−0.790769	−	0.612114i	$-0.790319\pi$
$677$		−	31.8535i		−	1.22423i	0.790769	−	0.612114i	$-0.209681\pi$
$678$	−18.0287			−0.692387
$679$	8.42827			0.323447
$680$	8.54869	−	7.36753i	0.327827	−	0.282532i
$681$		−	31.0338i		−	1.18922i
$682$	−15.2058			−0.582260
$683$	−51.5084			−1.97091			−0.985456	−	0.169928i	$-0.945646\pi$
$683$	−51.5084			−1.97091			−0.985456	+	0.169928i	$0.945646\pi$
$684$		−	5.62635i		−	0.215129i
$685$	11.7578	+	13.6428i	0.449242	+	0.521265i
$686$	13.2043			0.504144
$687$	−34.8317			−1.32891
$688$			8.41814i			0.320938i
$689$		0			0
$690$	9.87451	+	11.4576i	0.375916	+	0.436183i
$691$		−	42.1525i		−	1.60356i	−0.597622	−	0.801778i	$-0.703888\pi$
$691$		−	42.1525i		−	1.60356i	0.597622	−	0.801778i	$-0.296112\pi$
$692$		−	23.0755i		−	0.877200i
$693$			1.88341i			0.0715448i
$694$			17.1079i			0.649408i
$695$	−18.7530	−	21.7595i	−0.711342	−	0.825384i
$696$			9.55376i			0.362134i
$697$	2.01654			0.0763819
$698$			0.935233i			0.0353991i
$699$	−0.876230			−0.0331420
$700$	0.751828	−	5.03756i	0.0284164	−	0.190402i
$701$	31.6516			1.19546			0.597732	−	0.801696i	$-0.296069\pi$
$701$	31.6516			1.19546			0.597732	+	0.801696i	$0.296069\pi$
$702$		0			0
$703$			13.2681i			0.500414i
$704$		−	2.42025i		−	0.0912166i
$705$	−0.369898	+	0.318790i	−0.0139312	+	0.0120063i
$706$	0.243550			0.00916612
$707$	−20.3091			−0.763802
$708$	4.83904			0.181862
$709$			24.5801i			0.923126i	0.887108	+	0.461563i	$0.152711\pi$
$709$			24.5801i			0.923126i	−0.887108	+	0.461563i	$0.847289\pi$
$710$	2.31961	−	1.99912i	0.0870535	−	0.0750255i
$711$	2.70278			0.101362
$712$			5.60882i			0.210199i
$713$	−28.4205			−1.06436
$714$	−7.68793			−0.287714
$715$		0			0
$716$	7.81690			0.292131
$717$	14.2958			0.533888
$718$		−	14.7698i		−	0.551204i
$719$	−4.11098			−0.153314			−0.0766568	−	0.997058i	$-0.524425\pi$
$719$	−4.11098			−0.153314			−0.0766568	+	0.997058i	$0.524425\pi$
$720$	−1.11517	−	1.29395i	−0.0415598	−	0.0482226i
$721$			14.7403i			0.548959i
$722$	−35.2441			−1.31165
$723$	17.2167			0.640298
$724$	5.21467			0.193802
$725$	4.71537	−	31.5949i	0.175124	−	1.17341i
$726$		−	7.68968i		−	0.285391i
$727$		−	13.2521i		−	0.491492i	−0.969334	−	0.245746i	$-0.920967\pi$
$727$		−	13.2521i		−	0.491492i	0.969334	−	0.245746i	$-0.0790330\pi$
$728$		0			0
$729$	−29.9280			−1.10845
$730$	−23.2120	−	26.9333i	−0.859113	−	0.996846i
$731$	−42.4862			−1.57141
$732$			21.1760i			0.782688i
$733$	−11.6585			−0.430617			−0.215309	−	0.976546i	$-0.569076\pi$
$733$	−11.6585			−0.430617			−0.215309	+	0.976546i	$0.569076\pi$
$734$			3.29260i			0.121532i
$735$	15.1017	−	13.0151i	0.557033	−	0.480069i
$736$		−	4.52359i		−	0.166742i
$737$			15.9495i			0.587506i
$738$		−	0.305228i		−	0.0112356i
$739$		−	33.7614i		−	1.24193i	−0.783836	−	0.620967i	$-0.786740\pi$
$739$		−	33.7614i		−	1.24193i	0.783836	−	0.620967i	$-0.213260\pi$
$740$	2.62979	+	3.05139i	0.0966729	+	0.112171i
$741$		0			0
$742$		−	1.55450i		−	0.0570677i
$743$	32.1265			1.17861			0.589303	−	0.807912i	$-0.299402\pi$
$743$	32.1265			1.17861			0.589303	+	0.807912i	$0.299402\pi$
$744$	−9.39490			−0.344434
$745$	−19.7385	+	17.0112i	−0.723161	+	0.623243i
$746$		−	18.9067i		−	0.692222i
$747$	3.55213			0.129966
$748$	12.2150			0.446624
$749$			6.61178i			0.241589i
$750$	−8.92554	−	14.1366i	−0.325915	−	0.516197i
$751$	−40.3734			−1.47325			−0.736623	−	0.676304i	$-0.763581\pi$
$751$	−40.3734			−1.47325			−0.736623	+	0.676304i	$0.763581\pi$
$752$	0.146040			0.00532553
$753$		−	22.4338i		−	0.817534i
$754$		0			0
$755$	6.66809	−	5.74676i	0.242676	−	0.209146i
$756$			5.73348i			0.208525i
$757$			12.1790i			0.442652i	0.975200	+	0.221326i	$0.0710385\pi$
$757$			12.1790i			0.442652i	−0.975200	+	0.221326i	$0.928962\pi$
$758$			13.7733i			0.500270i
$759$			16.3714i			0.594245i
$760$	−12.4751	+	10.7514i	−0.452519	+	0.389995i
$761$		−	5.73188i		−	0.207781i	−0.994589	−	0.103890i	$-0.966871\pi$
$761$		−	5.73188i		−	0.207781i	0.994589	−	0.103890i	$-0.0331291\pi$
$762$	27.3592			0.991119
$763$			14.1341i			0.511689i
$764$	10.4143			0.376777
$765$	6.53055	−	5.62823i	0.236112	−	0.203489i
$766$	33.3243			1.20405
$767$		0			0
$768$		−	1.49535i		−	0.0539588i
$769$		−	50.3927i		−	1.81721i	−0.417661	−	0.908603i	$-0.637150\pi$
$769$		−	50.3927i		−	1.81721i	0.417661	−	0.908603i	$-0.362850\pi$
$770$	4.17601	−	3.59901i	0.150493	−	0.129699i
$771$	−1.34982			−0.0486127
$772$	1.40263			0.0504819
$773$	−31.9774			−1.15015			−0.575074	−	0.818102i	$-0.695027\pi$
$773$	−31.9774			−1.15015			−0.575074	+	0.818102i	$0.695027\pi$
$774$			6.43082i			0.231151i
$775$	31.0696	+	4.63696i	1.11605	+	0.166565i
$776$	−8.27379			−0.297012
$777$		−	2.74415i		−	0.0984459i
$778$	−1.91117			−0.0685189
$779$	−2.94273			−0.105434
$780$		0			0
$781$	3.31443			0.118600
$782$	22.8305			0.816416
$783$			35.9596i			1.28509i
$784$	−5.96231			−0.212940
$785$	−3.15272	+	2.71711i	−0.112525	+	0.0969778i
$786$		−	32.6375i		−	1.16414i
$787$	−23.1697			−0.825910			−0.412955	−	0.910751i	$-0.635503\pi$
$787$	−23.1697			−0.825910			−0.412955	+	0.910751i	$0.635503\pi$
$788$	25.3455			0.902897
$789$	−26.2050			−0.932921
$790$	−5.16476	−	5.99277i	−0.183754	−	0.213213i
$791$			12.2816i			0.436683i
$792$		−	1.84889i		−	0.0656974i
$793$		0			0
$794$	13.5405			0.480535
$795$	−3.33112	−	3.86517i	−0.118143	−	0.137083i
$796$	13.7630			0.487818
$797$			8.43667i			0.298842i	0.988774	+	0.149421i	$0.0477410\pi$
$797$			8.43667i			0.298842i	−0.988774	+	0.149421i	$0.952259\pi$
$798$	11.2190			0.397148
$799$			0.737063i			0.0260754i
$800$	−0.738047	+	4.94523i	−0.0260939	+	0.174840i
$801$			4.28471i			0.151393i
$802$			28.9798i			1.02331i
$803$		−	38.4842i		−	1.35808i
$804$			9.85438i			0.347537i
$805$	7.80520	−	6.72676i	0.275097	−	0.237087i
$806$		0			0
$807$			4.75507i			0.167386i
$808$	19.9369			0.701376
$809$	11.8560			0.416834			0.208417	−	0.978040i	$-0.433169\pi$
$809$	11.8560			0.416834			0.208417	+	0.978040i	$0.433169\pi$
$810$	8.94068	+	10.3740i	0.314143	+	0.364507i
$811$		−	16.6388i		−	0.584268i	−0.956377	−	0.292134i	$-0.905635\pi$
$811$		−	16.6388i		−	0.584268i	0.956377	−	0.292134i	$-0.0943653\pi$
$812$	6.50826			0.228395
$813$	20.6381			0.723810
$814$			4.36005i			0.152820i
$815$	33.5994	+	38.9861i	1.17694	+	1.36562i
$816$	7.54702			0.264199
$817$	62.0001			2.16911
$818$			9.77252i			0.341688i
$819$		0			0
$820$	−0.676771	+	0.583262i	−0.0236339	+	0.0203684i
$821$		−	25.6079i		−	0.893723i	−0.894603	−	0.446861i	$-0.852542\pi$
$821$		−	25.6079i		−	0.893723i	0.894603	−	0.446861i	$-0.147458\pi$
$822$			12.0442i			0.420091i
$823$		−	24.1832i		−	0.842974i	−0.906834	−	0.421487i	$-0.861508\pi$
$823$		−	24.1832i		−	0.842974i	0.906834	−	0.421487i	$-0.138492\pi$
$824$		−	14.4702i		−	0.504092i
$825$	2.67109	−	17.8974i	0.0929953	−	0.623107i
$826$		−	3.29647i		−	0.114699i
$827$	15.5125			0.539422			0.269711	−	0.962941i	$-0.413072\pi$
$827$	15.5125			0.539422			0.269711	+	0.962941i	$0.413072\pi$
$828$		−	3.45568i		−	0.120093i
$829$	47.4436			1.64779			0.823893	−	0.566746i	$-0.191798\pi$
$829$	47.4436			1.64779			0.823893	+	0.566746i	$0.191798\pi$
$830$	−6.78779	−	7.87601i	−0.235608	−	0.273380i
$831$	−7.13342			−0.247456
$832$		0			0
$833$		−	30.0917i		−	1.04262i
$834$		−	19.2099i		−	0.665184i
$835$	8.92023	+	10.3503i	0.308697	+	0.358188i
$836$	−17.8253			−0.616500
$837$	−35.3617			−1.22228
$838$	24.9288			0.861151
$839$		−	38.9320i		−	1.34408i	−0.740514	−	0.672040i	$-0.765418\pi$
$839$		−	38.9320i		−	1.34408i	0.740514	−	0.672040i	$-0.234582\pi$
$840$	2.58015	−	2.22365i	0.0890235	−	0.0767232i
$841$	11.8190			0.407552
$842$			12.7436i			0.439175i
$843$	8.53736			0.294042
$844$	9.82347			0.338138
$845$		0			0
$846$	0.111564			0.00383563
$847$	−5.23840			−0.179994
$848$			1.52601i			0.0524035i
$849$	−31.7356			−1.08916
$850$	−24.9585	−	3.72492i	−0.856070	−	0.127764i
$851$			8.14918i			0.279350i
$852$	2.04782			0.0701572
$853$	−11.8046			−0.404183			−0.202091	−	0.979367i	$-0.564774\pi$
$853$	−11.8046			−0.404183			−0.202091	+	0.979367i	$0.564774\pi$
$854$	14.4256			0.493635
$855$	−9.53001	+	8.21326i	−0.325920	+	0.280888i
$856$		−	6.49059i		−	0.221844i
$857$			26.7499i			0.913759i	0.889529	+	0.456880i	$0.151033\pi$
$857$			26.7499i			0.913759i	−0.889529	+	0.456880i	$0.848967\pi$
$858$		0			0
$859$	21.2441			0.724839			0.362420	−	0.932015i	$-0.381951\pi$
$859$	21.2441			0.724839			0.362420	+	0.932015i	$0.381951\pi$
$860$	14.2588	−	12.2887i	0.486221	−	0.419041i
$861$	0.608628			0.0207420
$862$			22.2564i			0.758055i
$863$	−9.36613			−0.318827			−0.159413	−	0.987212i	$-0.550960\pi$
$863$	−9.36613			−0.318827			−0.159413	+	0.987212i	$0.550960\pi$
$864$		−	5.62839i		−	0.191482i
$865$	−39.0858	+	33.6853i	−1.32896	+	1.14534i
$866$		−	30.4130i		−	1.03348i
$867$			12.6688i			0.430254i
$868$			6.40004i			0.217232i
$869$		−	8.56290i		−	0.290476i
$870$	16.1823	−	13.9465i	0.548633	−	0.472829i
$871$		0			0
$872$		−	13.8750i		−	0.469868i
$873$	−6.32055			−0.213918
$874$	−33.3165			−1.12695
$875$	−9.63023	+	6.08030i	−0.325561	+	0.205552i
$876$		−	23.7775i		−	0.803366i
$877$	−40.9589			−1.38308			−0.691542	−	0.722336i	$-0.743068\pi$
$877$	−40.9589			−1.38308			−0.691542	+	0.722336i	$0.743068\pi$
$878$	−12.5984			−0.425174
$879$			35.8637i			1.20965i
$880$	−4.09947	+	3.53305i	−0.138193	+	0.119099i
$881$	−32.8926			−1.10818			−0.554090	−	0.832457i	$-0.686934\pi$
$881$	−32.8926			−1.10818			−0.554090	+	0.832457i	$0.686934\pi$
$882$	−4.55475			−0.153366
$883$		−	28.2606i		−	0.951044i	−0.879704	−	0.475522i	$-0.842259\pi$
$883$		−	28.2606i		−	0.951044i	0.879704	−	0.475522i	$-0.157741\pi$
$884$		0			0
$885$	−7.06396	−	8.19646i	−0.237452	−	0.275521i
$886$			2.42243i			0.0813833i
$887$		−	6.76650i		−	0.227197i	−0.993527	−	0.113598i	$-0.963762\pi$
$887$		−	6.76650i		−	0.227197i	0.993527	−	0.113598i	$-0.0362377\pi$
$888$			2.69386i			0.0903999i
$889$		−	18.6378i		−	0.625091i
$890$	9.50032	−	8.18767i	0.318451	−	0.274451i
$891$			14.8232i			0.496595i
$892$	−19.3560			−0.648088
$893$		−	1.07559i		−	0.0359934i
$894$	−17.4257			−0.582802
$895$	−11.4110	−	13.2404i	−0.381428	−	0.442578i
$896$	−1.01867			−0.0340314
$897$		0			0
$898$		−	29.0963i		−	0.970954i
$899$			40.1403i			1.33875i
$900$	−0.563812	+	3.77778i	−0.0187937	+	0.125926i
$901$	−7.70177			−0.256583
$902$	−0.967019			−0.0321982
$903$	−12.8231			−0.426726
$904$		−	12.0565i		−	0.400993i
$905$	−7.61230	−	8.83271i	−0.253041	−	0.293609i
$906$	5.88677			0.195575
$907$			18.3605i			0.609649i	0.952409	+	0.304824i	$0.0985978\pi$
$907$			18.3605i			0.609649i	−0.952409	+	0.304824i	$0.901402\pi$
$908$	20.7535			0.688729
$909$	15.2302			0.505155
$910$		0			0
$911$	−4.36340			−0.144566			−0.0722830	−	0.997384i	$-0.523028\pi$
$911$	−4.36340			−0.144566			−0.0722830	+	0.997384i	$0.523028\pi$
$912$	−11.0134			−0.364689
$913$		−	11.2538i		−	0.372446i
$914$	−5.25707			−0.173889
$915$	35.8683	−	30.9125i	1.18577	−	1.02193i
$916$		−	23.2933i		−	0.769634i
$917$	−22.2335			−0.734215
$918$	28.4064			0.937551
$919$	42.7654			1.41070			0.705350	−	0.708859i	$-0.250790\pi$
$919$	42.7654			1.41070			0.705350	+	0.708859i	$0.250790\pi$
$920$	−7.66214	+	6.60347i	−0.252613	+	0.217710i
$921$			25.5544i			0.842047i
$922$			21.6948i			0.714479i
$923$		0			0
$924$	3.68670			0.121283
$925$	1.32958	−	8.90877i	0.0437164	−	0.292918i
$926$	−6.17734			−0.203000
$927$		−	11.0541i		−	0.363064i
$928$	−6.38898			−0.209728
$929$		−	22.2843i		−	0.731124i	−0.930787	−	0.365562i	$-0.880877\pi$
$929$		−	22.2843i		−	0.731124i	0.930787	−	0.365562i	$-0.119123\pi$
$930$	13.7146	+	15.9133i	0.449718	+	0.521817i
$931$			43.9128i			1.43918i
$932$		−	0.585969i		−	0.0191941i
$933$			7.74545i			0.253575i
$934$			9.01521i			0.294987i
$935$	−17.8313	−	20.6900i	−0.583144	−	0.676634i
$936$		0			0
$937$		−	28.0120i		−	0.915113i	−0.889180	−	0.457557i	$-0.848725\pi$
$937$		−	28.0120i		−	0.915113i	0.889180	−	0.457557i	$-0.151275\pi$
$938$	6.71305			0.219189
$939$	50.5143			1.64847
$940$	−0.213187	−	0.247366i	−0.00695340	−	0.00806817i
$941$			25.9180i			0.844904i	0.906385	+	0.422452i	$0.138831\pi$
$941$			25.9180i			0.844904i	−0.906385	+	0.422452i	$0.861169\pi$
$942$	−2.78331			−0.0906851
$943$	−1.80741			−0.0588575
$944$			3.23605i			0.105325i
$945$	9.71147	−	8.36965i	0.315914	−	0.272265i
$946$	20.3740			0.662416
$947$	39.2544			1.27560			0.637798	−	0.770204i	$-0.279846\pi$
$947$	39.2544			1.27560			0.637798	+	0.770204i	$0.279846\pi$
$948$		−	5.29059i		−	0.171830i
$949$		0			0
$950$	36.4219	+	5.43576i	1.18168	+	0.176359i
$951$		−	34.9864i		−	1.13451i
$952$		−	5.14122i		−	0.166628i
$953$			38.9069i			1.26032i	0.776466	+	0.630159i	$0.217010\pi$
$953$			38.9069i			1.26032i	−0.776466	+	0.630159i	$0.782990\pi$
$954$			1.16576i			0.0377428i
$955$	−15.2027	−	17.6400i	−0.491948	−	0.570817i
$956$			9.56019i			0.309199i
$957$	23.1225			0.747444
$958$			14.3406i			0.463325i
$959$	8.20485			0.264948
$960$	−2.53286	+	2.18289i	−0.0817475	+	0.0704526i
$961$	−8.47282			−0.273317
$962$		0			0
$963$		−	4.95832i		−	0.159780i
$964$			11.5135i			0.370825i
$965$	−2.04755	−	2.37581i	−0.0659128	−	0.0764800i
$966$	6.89065			0.221703
$967$	−49.1503			−1.58057			−0.790283	−	0.612742i	$-0.790066\pi$
$967$	−49.1503			−1.58057			−0.790283	+	0.612742i	$0.790066\pi$
$968$	5.14239			0.165283
$969$		−	55.5843i		−	1.78562i
$970$	12.0780	+	14.0143i	0.387800	+	0.449972i
$971$	2.29451			0.0736344			0.0368172	−	0.999322i	$-0.488278\pi$
$971$	2.29451			0.0736344			0.0368172	+	0.999322i	$0.488278\pi$
$972$		−	7.72667i		−	0.247833i
$973$	−13.0863			−0.419526
$974$	−15.5121			−0.497040
$975$		0			0
$976$	−14.1612			−0.453290
$977$	−40.4141			−1.29296			−0.646481	−	0.762930i	$-0.723760\pi$
$977$	−40.4141			−1.29296			−0.646481	+	0.762930i	$0.723760\pi$
$978$			34.4180i			1.10057i
$979$	13.5747			0.433851
$980$	8.70370	+	10.0991i	0.278029	+	0.322603i
$981$		−	10.5995i		−	0.338415i
$982$	−2.60458			−0.0831155
$983$	−5.97411			−0.190544			−0.0952722	−	0.995451i	$-0.530372\pi$
$983$	−5.97411			−0.190544			−0.0952722	+	0.995451i	$0.530372\pi$
$984$	−0.597472			−0.0190467
$985$	−36.9991	−	42.9307i	−1.17889	−	1.36789i
$986$		−	32.2451i		−	1.02689i
$987$			0.222459i			0.00708094i
$988$		0			0
$989$	38.0802			1.21088
$990$	−3.13168	+	2.69898i	−0.0995314	+	0.0857793i
$991$	−19.2849			−0.612604			−0.306302	−	0.951934i	$-0.599092\pi$
$991$	−19.2849			−0.612604			−0.306302	+	0.951934i	$0.599092\pi$
$992$		−	6.28274i		−	0.199477i
$993$	−8.17426			−0.259402
$994$		−	1.39503i		−	0.0442476i
$995$	−20.0911	−	23.3121i	−0.636930	−	0.739043i
$996$		−	6.95316i		−	0.220319i
$997$		−	52.5850i		−	1.66538i	−0.553736	−	0.832692i	$-0.686798\pi$
$997$		−	52.5850i		−	1.66538i	0.553736	−	0.832692i	$-0.313202\pi$
$998$		−	4.88458i		−	0.154619i
$999$			10.1395i			0.320799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.h.1689.5		18
5.4	even	2		1690.2.c.g.1689.14		18
13.5	odd	4		1690.2.b.g.339.2	yes	18
13.8	odd	4		1690.2.b.f.339.11	yes	18
13.12	even	2		1690.2.c.g.1689.5		18
65.8	even	4		8450.2.a.cx.1.8		9
65.18	even	4		8450.2.a.ct.1.8		9
65.34	odd	4		1690.2.b.f.339.8	✓	18
65.44	odd	4		1690.2.b.g.339.17	yes	18
65.47	even	4		8450.2.a.cw.1.2		9
65.57	even	4		8450.2.a.da.1.2		9
65.64	even	2	inner	1690.2.c.h.1689.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.8	✓	18	65.34	odd	4
1690.2.b.f.339.11	yes	18	13.8	odd	4
1690.2.b.g.339.2	yes	18	13.5	odd	4
1690.2.b.g.339.17	yes	18	65.44	odd	4
1690.2.c.g.1689.5		18	13.12	even	2
1690.2.c.g.1689.14		18	5.4	even	2
1690.2.c.h.1689.5		18	1.1	even	1	trivial
1690.2.c.h.1689.14		18	65.64	even	2	inner
8450.2.a.ct.1.8		9	65.18	even	4
8450.2.a.cw.1.2		9	65.47	even	4
8450.2.a.cx.1.8		9	65.8	even	4
8450.2.a.da.1.2		9	65.57	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.49535i q^{3} +1.00000 q^{4} +(-1.45979 - 1.69382i) q^{5} -1.49535i q^{6} -1.01867 q^{7} +1.00000 q^{8} +0.763924 q^{9} +(-1.45979 - 1.69382i) q^{10} -2.42025i q^{11} -1.49535i q^{12} -1.01867 q^{14} +(-2.53286 + 2.18289i) q^{15} +1.00000 q^{16} +5.04699i q^{17} +0.763924 q^{18} -7.36506i q^{19} +(-1.45979 - 1.69382i) q^{20} +1.52327i q^{21} -2.42025i q^{22} -4.52359i q^{23} -1.49535i q^{24} +(-0.738047 + 4.94523i) q^{25} -5.62839i q^{27} -1.01867 q^{28} -6.38898 q^{29} +(-2.53286 + 2.18289i) q^{30} -6.28274i q^{31} +1.00000 q^{32} -3.61912 q^{33} +5.04699i q^{34} +(1.48704 + 1.72544i) q^{35} +0.763924 q^{36} -1.80149 q^{37} -7.36506i q^{38} +(-1.45979 - 1.69382i) q^{40} -0.399553i q^{41} +1.52327i q^{42} +8.41814i q^{43} -2.42025i q^{44} +(-1.11517 - 1.29395i) q^{45} -4.52359i q^{46} +0.146040 q^{47} -1.49535i q^{48} -5.96231 q^{49} +(-0.738047 + 4.94523i) q^{50} +7.54702 q^{51} +1.52601i q^{53} -5.62839i q^{54} +(-4.09947 + 3.53305i) q^{55} -1.01867 q^{56} -11.0134 q^{57} -6.38898 q^{58} +3.23605i q^{59} +(-2.53286 + 2.18289i) q^{60} -14.1612 q^{61} -6.28274i q^{62} -0.778187 q^{63} +1.00000 q^{64} -3.61912 q^{66} -6.59001 q^{67} +5.04699i q^{68} -6.76435 q^{69} +(1.48704 + 1.72544i) q^{70} +1.36946i q^{71} +0.763924 q^{72} +15.9009 q^{73} -1.80149 q^{74} +(7.39485 + 1.10364i) q^{75} -7.36506i q^{76} +2.46544i q^{77} +3.53802 q^{79} +(-1.45979 - 1.69382i) q^{80} -6.12465 q^{81} -0.399553i q^{82} +4.64985 q^{83} +1.52327i q^{84} +(8.54869 - 7.36753i) q^{85} +8.41814i q^{86} +9.55376i q^{87} -2.42025i q^{88} +5.60882i q^{89} +(-1.11517 - 1.29395i) q^{90} -4.52359i q^{92} -9.39490 q^{93} +0.146040 q^{94} +(-12.4751 + 10.7514i) q^{95} -1.49535i q^{96} -8.27379 q^{97} -5.96231 q^{98} -1.84889i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) \) 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

Modular forms

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Representations

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Database

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