LMFDB - Embedded newform 1690.2.b.g.339.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.339"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			339.3
Root			$-2.90009i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.g.339.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -0.303663i q^{3} -1.00000 q^{4} +(1.92689 - 1.13450i) q^{5} -0.303663 q^{6} +1.08593i q^{7} +1.00000i q^{8} +2.90779 q^{9} +(-1.13450 - 1.92689i) q^{10} +0.403887 q^{11} +0.303663i q^{12} +1.08593 q^{14} +(-0.344506 - 0.585124i) q^{15} +1.00000 q^{16} +5.21387i q^{17} -2.90779i q^{18} +0.844510 q^{19} +(-1.92689 + 1.13450i) q^{20} +0.329755 q^{21} -0.403887i q^{22} -1.76217i q^{23} +0.303663 q^{24} +(2.42580 - 4.37213i) q^{25} -1.79397i q^{27} -1.08593i q^{28} +5.96747 q^{29} +(-0.585124 + 0.344506i) q^{30} +5.25338 q^{31} -1.00000i q^{32} -0.122645i q^{33} +5.21387 q^{34} +(1.23199 + 2.09246i) q^{35} -2.90779 q^{36} +4.42321i q^{37} -0.844510i q^{38} +(1.13450 + 1.92689i) q^{40} -3.20196 q^{41} -0.329755i q^{42} +11.4865i q^{43} -0.403887 q^{44} +(5.60299 - 3.29890i) q^{45} -1.76217 q^{46} -11.5048i q^{47} -0.303663i q^{48} +5.82076 q^{49} +(-4.37213 - 2.42580i) q^{50} +1.58326 q^{51} +10.7632i q^{53} -1.79397 q^{54} +(0.778246 - 0.458212i) q^{55} -1.08593 q^{56} -0.256446i q^{57} -5.96747i q^{58} -7.28501 q^{59} +(0.344506 + 0.585124i) q^{60} -2.64135 q^{61} -5.25338i q^{62} +3.15764i q^{63} -1.00000 q^{64} -0.122645 q^{66} -10.5992i q^{67} -5.21387i q^{68} -0.535105 q^{69} +(2.09246 - 1.23199i) q^{70} +12.4325 q^{71} +2.90779i q^{72} -2.92837i q^{73} +4.42321 q^{74} +(-1.32765 - 0.736626i) q^{75} -0.844510 q^{76} +0.438592i q^{77} -15.8880 q^{79} +(1.92689 - 1.13450i) q^{80} +8.17860 q^{81} +3.20196i q^{82} -12.6626i q^{83} -0.329755 q^{84} +(5.91515 + 10.0465i) q^{85} +11.4865 q^{86} -1.81210i q^{87} +0.403887i q^{88} +6.99770 q^{89} +(-3.29890 - 5.60299i) q^{90} +1.76217i q^{92} -1.59525i q^{93} -11.5048 q^{94} +(1.62728 - 0.958100i) q^{95} -0.303663 q^{96} -9.47384i q^{97} -5.82076i q^{98} +1.17442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{4} + 14 q^{6} - 16 q^{9} + 2 q^{10} + 8 q^{11} - 2 q^{14} + 8 q^{15} + 18 q^{16} - 12 q^{19} + 16 q^{21} - 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} - 12 q^{31} - 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) $ 18 * q - 18 * q^4 + 14 * q^6 - 16 * q^9 + 2 * q^10 + 8 * q^11 - 2 * q^14 + 8 * q^15 + 18 * q^16 - 12 * q^19 + 16 * q^21 - 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 - 12 * q^31 - 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 + 54 * q^41 - 8 * q^44 + 20 * q^45 + 22 * q^46 + 20 * q^49 + 8 * q^50 + 24 * q^51 - 68 * q^54 + 2 * q^56 - 40 * q^59 - 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 - 6 * q^70 - 20 * q^71 + 20 * q^74 - 72 * q^75 + 12 * q^76 + 28 * q^79 + 106 * q^81 - 16 * q^84 + 56 * q^85 + 82 * q^86 - 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 + 14 * q^96 - 32 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.303663i		−	0.175320i	−0.996150	−	0.0876598i	$-0.972061\pi$
$3$		−	0.303663i		−	0.175320i	0.996150	−	0.0876598i	$-0.0279389\pi$
$4$	−1.00000			−0.500000
$5$	1.92689	−	1.13450i	0.861731	−	0.507365i
$5$	1.92689	−	1.13450i	0.861731	−	0.507365i
$6$	−0.303663			−0.123970
$7$			1.08593i			0.410441i	0.978716	+	0.205221i	$0.0657912\pi$
$7$			1.08593i			0.410441i	−0.978716	+	0.205221i	$0.934209\pi$
$8$			1.00000i			0.353553i
$9$	2.90779			0.969263
$10$	−1.13450	−	1.92689i	−0.358762	−	0.609336i
$11$	0.403887			0.121777			0.0608883	−	0.998145i	$-0.480607\pi$
$11$	0.403887			0.121777			0.0608883	+	0.998145i	$0.480607\pi$
$12$			0.303663i			0.0876598i
$13$		0			0
$13$		0			0
$14$	1.08593			0.290226
$15$	−0.344506	−	0.585124i	−0.0889511	−	0.151078i
$16$	1.00000			0.250000
$17$			5.21387i			1.26455i	0.774745	+	0.632274i	$0.217878\pi$
$17$			5.21387i			1.26455i	−0.774745	+	0.632274i	$0.782122\pi$
$18$		−	2.90779i		−	0.685372i
$19$	0.844510			0.193744			0.0968719	−	0.995297i	$-0.469116\pi$
$19$	0.844510			0.193744			0.0968719	+	0.995297i	$0.469116\pi$
$20$	−1.92689	+	1.13450i	−0.430866	+	0.253683i
$21$	0.329755			0.0719585
$22$		−	0.403887i		−	0.0861091i
$23$		−	1.76217i		−	0.367438i	−0.982979	−	0.183719i	$-0.941186\pi$
$23$		−	1.76217i		−	0.367438i	0.982979	−	0.183719i	$-0.0588137\pi$
$24$	0.303663			0.0619849
$25$	2.42580	−	4.37213i	0.485161	−	0.874425i
$26$		0			0
$27$		−	1.79397i		−	0.345251i
$28$		−	1.08593i		−	0.205221i
$29$	5.96747			1.10813			0.554066	−	0.832473i	$-0.313076\pi$
$29$	5.96747			1.10813			0.554066	+	0.832473i	$0.313076\pi$
$30$	−0.585124	+	0.344506i	−0.106829	+	0.0628980i
$31$	5.25338			0.943534			0.471767	−	0.881723i	$-0.343616\pi$
$31$	5.25338			0.943534			0.471767	+	0.881723i	$0.343616\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	0.122645i		−	0.0213498i
$34$	5.21387			0.894171
$35$	1.23199	+	2.09246i	0.208244	+	0.353690i
$36$	−2.90779			−0.484632
$37$			4.42321i			0.727171i	0.931561	+	0.363586i	$0.118448\pi$
$37$			4.42321i			0.727171i	−0.931561	+	0.363586i	$0.881552\pi$
$38$		−	0.844510i		−	0.136998i
$39$		0			0
$40$	1.13450	+	1.92689i	0.179381	+	0.304668i
$41$	−3.20196			−0.500062			−0.250031	−	0.968238i	$-0.580441\pi$
$41$	−3.20196			−0.500062			−0.250031	+	0.968238i	$0.580441\pi$
$42$		−	0.329755i		−	0.0508823i
$43$			11.4865i			1.75168i	0.482601	+	0.875840i	$0.339692\pi$
$43$			11.4865i			1.75168i	−0.482601	+	0.875840i	$0.660308\pi$
$44$	−0.403887			−0.0608883
$45$	5.60299	−	3.29890i	0.835244	−	0.491771i
$46$	−1.76217			−0.259818
$47$		−	11.5048i		−	1.67814i	−0.544022	−	0.839071i	$-0.683099\pi$
$47$		−	11.5048i		−	1.67814i	0.544022	−	0.839071i	$-0.316901\pi$
$48$		−	0.303663i		−	0.0438299i
$49$	5.82076			0.831538
$50$	−4.37213	−	2.42580i	−0.618312	−	0.343060i
$51$	1.58326			0.221700
$52$		0			0
$53$			10.7632i			1.47844i	0.673463	+	0.739221i	$0.264806\pi$
$53$			10.7632i			1.47844i	−0.673463	+	0.739221i	$0.735194\pi$
$54$	−1.79397			−0.244129
$55$	0.778246	−	0.458212i	0.104939	−	0.0617852i
$56$	−1.08593			−0.145113
$57$		−	0.256446i		−	0.0339671i
$58$		−	5.96747i		−	0.783567i
$59$	−7.28501			−0.948428			−0.474214	−	0.880410i	$-0.657268\pi$
$59$	−7.28501			−0.948428			−0.474214	+	0.880410i	$0.657268\pi$
$60$	0.344506	+	0.585124i	0.0444756	+	0.0755392i
$61$	−2.64135			−0.338190			−0.169095	−	0.985600i	$-0.554084\pi$
$61$	−2.64135			−0.338190			−0.169095	+	0.985600i	$0.554084\pi$
$62$		−	5.25338i		−	0.667179i
$63$			3.15764i			0.397826i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−0.122645			−0.0150966
$67$		−	10.5992i		−	1.29490i	−0.762106	−	0.647452i	$-0.775835\pi$
$67$		−	10.5992i		−	1.29490i	0.762106	−	0.647452i	$-0.224165\pi$
$68$		−	5.21387i		−	0.632274i
$69$	−0.535105			−0.0644191
$70$	2.09246	−	1.23199i	0.250097	−	0.147251i
$71$	12.4325			1.47546			0.737732	−	0.675094i	$-0.235897\pi$
$71$	12.4325			1.47546			0.737732	+	0.675094i	$0.235897\pi$
$72$			2.90779i			0.342686i
$73$		−	2.92837i		−	0.342740i	−0.985207	−	0.171370i	$-0.945181\pi$
$73$		−	2.92837i		−	0.342740i	0.985207	−	0.171370i	$-0.0548193\pi$
$74$	4.42321			0.514188
$75$	−1.32765	−	0.736626i	−0.153304	−	0.0850582i
$76$	−0.844510			−0.0968719
$77$			0.438592i			0.0499822i
$78$		0			0
$79$	−15.8880			−1.78754			−0.893772	−	0.448522i	$-0.851951\pi$
$79$	−15.8880			−1.78754			−0.893772	+	0.448522i	$0.851951\pi$
$80$	1.92689	−	1.13450i	0.215433	−	0.126841i
$81$	8.17860			0.908734
$82$			3.20196i			0.353597i
$83$		−	12.6626i		−	1.38990i	−0.719056	−	0.694952i	$-0.755426\pi$
$83$		−	12.6626i		−	1.38990i	0.719056	−	0.694952i	$-0.244574\pi$
$84$	−0.329755			−0.0359792
$85$	5.91515	+	10.0465i	0.641588	+	1.08970i
$86$	11.4865			1.23863
$87$		−	1.81210i		−	0.194277i
$88$			0.403887i			0.0430545i
$89$	6.99770			0.741755			0.370877	−	0.928682i	$-0.379057\pi$
$89$	6.99770			0.741755			0.370877	+	0.928682i	$0.379057\pi$
$90$	−3.29890	−	5.60299i	−0.347734	−	0.590607i
$91$		0			0
$92$			1.76217i			0.183719i
$93$		−	1.59525i		−	0.165420i
$94$	−11.5048			−1.18663
$95$	1.62728	−	0.958100i	0.166955	−	0.0982989i
$96$	−0.303663			−0.0309924
$97$		−	9.47384i		−	0.961923i	−0.876742	−	0.480961i	$-0.840288\pi$
$97$		−	9.47384i		−	0.961923i	0.876742	−	0.480961i	$-0.159712\pi$
$98$		−	5.82076i		−	0.587986i
$99$	1.17442			0.118034
$100$	−2.42580	+	4.37213i	−0.242580	+	0.437213i
$101$	6.61025			0.657744			0.328872	−	0.944374i	$-0.393331\pi$
$101$	6.61025			0.657744			0.328872	+	0.944374i	$0.393331\pi$
$102$		−	1.58326i		−	0.156766i
$103$			9.21082i			0.907569i	0.891111	+	0.453784i	$0.149926\pi$
$103$			9.21082i			0.907569i	−0.891111	+	0.453784i	$0.850074\pi$
$104$		0			0
$105$	0.635402	−	0.374108i	0.0620088	−	0.0365092i
$106$	10.7632			1.04542
$107$		−	6.97470i		−	0.674270i	−0.941456	−	0.337135i	$-0.890542\pi$
$107$		−	6.97470i		−	0.674270i	0.941456	−	0.337135i	$-0.109458\pi$
$108$			1.79397i			0.172625i
$109$	3.29363			0.315473			0.157736	−	0.987481i	$-0.449580\pi$
$109$	3.29363			0.315473			0.157736	+	0.987481i	$0.449580\pi$
$110$	−0.458212	−	0.778246i	−0.0436888	−	0.0742029i
$111$	1.34316			0.127487
$112$			1.08593i			0.102610i
$113$		−	10.0934i		−	0.949508i	−0.880119	−	0.474754i	$-0.842537\pi$
$113$		−	10.0934i		−	0.949508i	0.880119	−	0.474754i	$-0.157463\pi$
$114$	−0.256446			−0.0240184
$115$	−1.99919	−	3.39551i	−0.186425	−	0.316633i
$116$	−5.96747			−0.554066
$117$		0			0
$118$			7.28501i			0.670640i
$119$	−5.66187			−0.519023
$120$	0.585124	−	0.344506i	0.0534143	−	0.0314490i
$121$	−10.8369			−0.985170
$122$			2.64135i			0.239137i
$123$			0.972316i			0.0876708i
$124$	−5.25338			−0.471767
$125$	−0.285938	−	11.1767i	−0.0255751	−	0.999673i
$126$	3.15764			0.281305
$127$		−	6.06998i		−	0.538624i	−0.963053	−	0.269312i	$-0.913204\pi$
$127$		−	6.06998i		−	0.538624i	0.963053	−	0.269312i	$-0.0867963\pi$
$128$			1.00000i			0.0883883i
$129$	3.48803			0.307104
$130$		0			0
$131$	0.534787			0.0467246			0.0233623	−	0.999727i	$-0.492563\pi$
$131$	0.534787			0.0467246			0.0233623	+	0.999727i	$0.492563\pi$
$132$			0.122645i			0.0106749i
$133$			0.917075i			0.0795205i
$134$	−10.5992			−0.915636
$135$	−2.03527	−	3.45679i	−0.175168	−	0.297513i
$136$	−5.21387			−0.447085
$137$			11.9809i			1.02360i	0.859105	+	0.511799i	$0.171021\pi$
$137$			11.9809i			1.02360i	−0.859105	+	0.511799i	$0.828979\pi$
$138$			0.535105i			0.0455512i
$139$	−2.69002			−0.228165			−0.114082	−	0.993471i	$-0.536393\pi$
$139$	−2.69002			−0.228165			−0.114082	+	0.993471i	$0.536393\pi$
$140$	−1.23199	−	2.09246i	−0.104122	−	0.176845i
$141$	−3.49357			−0.294211
$142$		−	12.4325i		−	1.04331i
$143$		0			0
$144$	2.90779			0.242316
$145$	11.4987	−	6.77011i	0.954911	−	0.562227i
$146$	−2.92837			−0.242354
$147$		−	1.76755i		−	0.145785i
$148$		−	4.42321i		−	0.363586i
$149$	−17.5424			−1.43713			−0.718565	−	0.695460i	$-0.755201\pi$
$149$	−17.5424			−1.43713			−0.718565	+	0.695460i	$0.755201\pi$
$150$	−0.736626	+	1.32765i	−0.0601452	+	0.108402i
$151$	−17.5381			−1.42723			−0.713615	−	0.700538i	$-0.752943\pi$
$151$	−17.5381			−1.42723			−0.713615	+	0.700538i	$0.752943\pi$
$152$			0.844510i			0.0684988i
$153$			15.1608i			1.22568i
$154$	0.438592			0.0353427
$155$	10.1227	−	5.95997i	0.813073	−	0.478717i
$156$		0			0
$157$		−	10.5663i		−	0.843279i	−0.906764	−	0.421639i	$-0.861455\pi$
$157$		−	10.5663i		−	0.843279i	0.906764	−	0.421639i	$-0.138545\pi$
$158$			15.8880i			1.26398i
$159$	3.26839			0.259200
$160$	−1.13450	−	1.92689i	−0.0896904	−	0.152334i
$161$	1.91359			0.150812
$162$		−	8.17860i		−	0.642572i
$163$		−	19.0637i		−	1.49318i	−0.665282	−	0.746592i	$-0.731689\pi$
$163$		−	19.0637i		−	1.49318i	0.665282	−	0.746592i	$-0.268311\pi$
$164$	3.20196			0.250031
$165$	−0.139142	−	0.236324i	−0.0108322	−	0.0183978i
$166$	−12.6626			−0.982811
$167$		−	10.6825i		−	0.826637i	−0.910587	−	0.413319i	$-0.864370\pi$
$167$		−	10.6825i		−	0.826637i	0.910587	−	0.413319i	$-0.135630\pi$
$168$			0.329755i			0.0254412i
$169$		0			0
$170$	10.0465	−	5.91515i	0.770535	−	0.453671i
$171$	2.45566			0.187789
$172$		−	11.4865i		−	0.875840i
$173$			15.8983i			1.20872i	0.796710	+	0.604362i	$0.206572\pi$
$173$			15.8983i			1.20872i	−0.796710	+	0.604362i	$0.793428\pi$
$174$	−1.81210			−0.137375
$175$	4.74780	+	2.63424i	0.358900	+	0.199130i
$176$	0.403887			0.0304442
$177$			2.21219i			0.166278i
$178$		−	6.99770i		−	0.524500i
$179$	25.2779			1.88936			0.944680	−	0.327995i	$-0.106373\pi$
$179$	25.2779			1.88936			0.944680	+	0.327995i	$0.106373\pi$
$180$	−5.60299	+	3.29890i	−0.417622	+	0.245885i
$181$	17.8082			1.32367			0.661837	−	0.749648i	$-0.269777\pi$
$181$	17.8082			1.32367			0.661837	+	0.749648i	$0.269777\pi$
$182$		0			0
$183$			0.802079i			0.0592914i
$184$	1.76217			0.129909
$185$	5.01815	+	8.52303i	0.368942	+	0.626626i
$186$	−1.59525			−0.116970
$187$			2.10581i			0.153992i
$188$			11.5048i			0.839071i
$189$	1.94812			0.141705
$190$	−0.958100	−	1.62728i	−0.0695078	−	0.118055i
$191$	−10.4612			−0.756947			−0.378474	−	0.925612i	$-0.623551\pi$
$191$	−10.4612			−0.756947			−0.378474	+	0.925612i	$0.623551\pi$
$192$			0.303663i			0.0219150i
$193$			14.6561i			1.05497i	0.849565	+	0.527483i	$0.176864\pi$
$193$			14.6561i			1.05497i	−0.849565	+	0.527483i	$0.823136\pi$
$194$	−9.47384			−0.680182
$195$		0			0
$196$	−5.82076			−0.415769
$197$			10.3360i			0.736406i	0.929745	+	0.368203i	$0.120027\pi$
$197$			10.3360i			0.736406i	−0.929745	+	0.368203i	$0.879973\pi$
$198$		−	1.17442i		−	0.0834623i
$199$	−5.21516			−0.369693			−0.184846	−	0.982767i	$-0.559179\pi$
$199$	−5.21516			−0.369693			−0.184846	+	0.982767i	$0.559179\pi$
$200$	4.37213	+	2.42580i	0.309156	+	0.171530i
$201$	−3.21860			−0.227022
$202$		−	6.61025i		−	0.465096i
$203$			6.48023i			0.454823i
$204$	−1.58326			−0.110850
$205$	−6.16982	+	3.63264i	−0.430919	+	0.253714i
$206$	9.21082			0.641748
$207$		−	5.12402i		−	0.356144i
$208$		0			0
$209$	0.341087			0.0235935
$210$	−0.374108	−	0.635402i	−0.0258159	−	0.0438469i
$211$	−12.3086			−0.847361			−0.423681	−	0.905812i	$-0.639262\pi$
$211$	−12.3086			−0.847361			−0.423681	+	0.905812i	$0.639262\pi$
$212$		−	10.7632i		−	0.739221i
$213$		−	3.77528i		−	0.258678i
$214$	−6.97470			−0.476781
$215$	13.0315	+	22.1333i	0.888742	+	1.50948i
$216$	1.79397			0.122065
$217$			5.70478i			0.387266i
$218$		−	3.29363i		−	0.223073i
$219$	−0.889236			−0.0600890
$220$	−0.778246	+	0.458212i	−0.0524693	+	0.0308926i
$221$		0			0
$222$		−	1.34316i		−	0.0901472i
$223$			9.35143i			0.626218i	0.949717	+	0.313109i	$0.101371\pi$
$223$			9.35143i			0.626218i	−0.949717	+	0.313109i	$0.898629\pi$
$224$	1.08593			0.0725565
$225$	7.05372	−	12.7132i	0.470248	−	0.847548i
$226$	−10.0934			−0.671403
$227$			13.1715i			0.874224i	0.899407	+	0.437112i	$0.143999\pi$
$227$			13.1715i			0.874224i	−0.899407	+	0.437112i	$0.856001\pi$
$228$			0.256446i			0.0169836i
$229$	−13.6752			−0.903680			−0.451840	−	0.892099i	$-0.649232\pi$
$229$	−13.6752			−0.903680			−0.451840	+	0.892099i	$0.649232\pi$
$230$	−3.39551	+	1.99919i	−0.223893	+	0.131823i
$231$	0.133184			0.00876286
$232$			5.96747i			0.391784i
$233$			27.7357i			1.81703i	0.417855	+	0.908514i	$0.362782\pi$
$233$			27.7357i			1.81703i	−0.417855	+	0.908514i	$0.637218\pi$
$234$		0			0
$235$	−13.0522	−	22.1684i	−0.851431	−	1.44611i
$236$	7.28501			0.474214
$237$			4.82460i			0.313392i
$238$			5.66187i			0.367005i
$239$	−17.7552			−1.14849			−0.574243	−	0.818685i	$-0.694703\pi$
$239$	−17.7552			−1.14849			−0.574243	+	0.818685i	$0.694703\pi$
$240$	−0.344506	−	0.585124i	−0.0222378	−	0.0377696i
$241$	3.83937			0.247316			0.123658	−	0.992325i	$-0.460537\pi$
$241$	3.83937			0.247316			0.123658	+	0.992325i	$0.460537\pi$
$242$			10.8369i			0.696621i
$243$		−	7.86546i		−	0.504569i
$244$	2.64135			0.169095
$245$	11.2160	−	6.60368i	0.716562	−	0.421894i
$246$	0.972316			0.0619926
$247$		0			0
$248$			5.25338i			0.333590i
$249$	−3.84517			−0.243678
$250$	−11.1767	+	0.285938i	−0.706875	+	0.0180843i
$251$	14.4338			0.911054			0.455527	−	0.890222i	$-0.349451\pi$
$251$	14.4338			0.911054			0.455527	+	0.890222i	$0.349451\pi$
$252$		−	3.15764i		−	0.198913i
$253$		−	0.711719i		−	0.0447454i
$254$	−6.06998			−0.380865
$255$	3.05076	−	1.79621i	0.191046	−	0.112483i
$256$	1.00000			0.0625000
$257$		−	11.0755i		−	0.690868i	−0.938443	−	0.345434i	$-0.887732\pi$
$257$		−	11.0755i		−	0.690868i	0.938443	−	0.345434i	$-0.112268\pi$
$258$		−	3.48803i		−	0.217155i
$259$	−4.80328			−0.298461
$260$		0			0
$261$	17.3521			1.07407
$262$		−	0.534787i		−	0.0330393i
$263$			1.74154i			0.107388i	0.998557	+	0.0536941i	$0.0170996\pi$
$263$			1.74154i			0.107388i	−0.998557	+	0.0536941i	$0.982900\pi$
$264$	0.122645			0.00754831
$265$	12.2109	+	20.7395i	0.750110	+	1.27402i
$266$	0.917075			0.0562295
$267$		−	2.12494i		−	0.130044i
$268$			10.5992i			0.647452i
$269$	10.0411			0.612220			0.306110	−	0.951996i	$-0.400973\pi$
$269$	10.0411			0.612220			0.306110	+	0.951996i	$0.400973\pi$
$270$	−3.45679	+	2.03527i	−0.210374	+	0.123863i
$271$	−10.3097			−0.626271			−0.313136	−	0.949708i	$-0.601379\pi$
$271$	−10.3097			−0.626271			−0.313136	+	0.949708i	$0.601379\pi$
$272$			5.21387i			0.316137i
$273$		0			0
$274$	11.9809			0.723794
$275$	0.979751	−	1.76585i	0.0590812	−	0.106485i
$276$	0.535105			0.0322096
$277$		−	29.7990i		−	1.79045i	−0.445616	−	0.895224i	$-0.647015\pi$
$277$		−	29.7990i		−	1.79045i	0.445616	−	0.895224i	$-0.352985\pi$
$278$			2.69002i			0.161337i
$279$	15.2757			0.914533
$280$	−2.09246	+	1.23199i	−0.125048	+	0.0736253i
$281$	−17.5437			−1.04657			−0.523285	−	0.852158i	$-0.675294\pi$
$281$	−17.5437			−1.04657			−0.523285	+	0.852158i	$0.675294\pi$
$282$			3.49357i			0.208039i
$283$			25.9299i			1.54137i	0.637214	+	0.770687i	$0.280087\pi$
$283$			25.9299i			1.54137i	−0.637214	+	0.770687i	$0.719913\pi$
$284$	−12.4325			−0.737732
$285$	−0.290939	−	0.494143i	−0.0172337	−	0.0292705i
$286$		0			0
$287$		−	3.47709i		−	0.205246i
$288$		−	2.90779i		−	0.171343i
$289$	−10.1844			−0.599083
$290$	−6.77011	−	11.4987i	−0.397555	−	0.675224i
$291$	−2.87685			−0.168644
$292$			2.92837i			0.171370i
$293$		−	26.1627i		−	1.52844i	−0.644954	−	0.764221i	$-0.723124\pi$
$293$		−	26.1627i		−	1.52844i	0.644954	−	0.764221i	$-0.276876\pi$
$294$	−1.76755			−0.103086
$295$	−14.0374	+	8.26487i	−0.817290	+	0.481199i
$296$	−4.42321			−0.257094
$297$		−	0.724564i		−	0.0420434i
$298$			17.5424i			1.01620i
$299$		0			0
$300$	1.32765	+	0.736626i	0.0766520	+	0.0425291i
$301$	−12.4735			−0.718962
$302$			17.5381i			1.00920i
$303$		−	2.00729i		−	0.115316i
$304$	0.844510			0.0484360
$305$	−5.08959	+	2.99662i	−0.291429	+	0.171586i
$306$	15.1608			0.866687
$307$			2.68863i			0.153448i	0.997052	+	0.0767240i	$0.0244460\pi$
$307$			2.68863i			0.153448i	−0.997052	+	0.0767240i	$0.975554\pi$
$308$		−	0.438592i		−	0.0249911i
$309$	2.79698			0.159115
$310$	−5.95997	−	10.1227i	−0.338504	−	0.574929i
$311$	−31.0278			−1.75943			−0.879713	−	0.475506i	$-0.842265\pi$
$311$	−31.0278			−1.75943			−0.879713	+	0.475506i	$0.842265\pi$
$312$		0			0
$313$			14.7399i			0.833151i	0.909101	+	0.416575i	$0.136770\pi$
$313$			14.7399i			0.833151i	−0.909101	+	0.416575i	$0.863230\pi$
$314$	−10.5663			−0.596288
$315$	3.58236	+	6.08443i	0.201843	+	0.342819i
$316$	15.8880			0.893772
$317$			14.7416i			0.827971i	0.910284	+	0.413985i	$0.135864\pi$
$317$			14.7416i			0.827971i	−0.910284	+	0.413985i	$0.864136\pi$
$318$		−	3.26839i		−	0.183282i
$319$	2.41019			0.134944
$320$	−1.92689	+	1.13450i	−0.107716	+	0.0634207i
$321$	−2.11796			−0.118213
$322$		−	1.91359i		−	0.106640i
$323$			4.40316i			0.244999i
$324$	−8.17860			−0.454367
$325$		0			0
$326$	−19.0637			−1.05584
$327$		−	1.00015i		−	0.0553086i
$328$		−	3.20196i		−	0.176799i
$329$	12.4933			0.688779
$330$	−0.236324	+	0.139142i	−0.0130092	+	0.00765950i
$331$	9.55973			0.525450			0.262725	−	0.964871i	$-0.415379\pi$
$331$	9.55973			0.525450			0.262725	+	0.964871i	$0.415379\pi$
$332$			12.6626i			0.694952i
$333$			12.8618i			0.704820i
$334$	−10.6825			−0.584521
$335$	−12.0249	−	20.4236i	−0.656990	−	1.11586i
$336$	0.329755			0.0179896
$337$		−	7.58566i		−	0.413217i	−0.978424	−	0.206609i	$-0.933757\pi$
$337$		−	7.58566i		−	0.413217i	0.978424	−	0.206609i	$-0.0662427\pi$
$338$		0			0
$339$	−3.06499			−0.166467
$340$	−5.91515	−	10.0465i	−0.320794	−	0.544850i
$341$	2.12177			0.114900
$342$		−	2.45566i		−	0.132787i
$343$			13.9224i			0.751739i
$344$	−11.4865			−0.619313
$345$	−1.03109	+	0.607079i	−0.0555120	+	0.0326840i
$346$	15.8983			0.854697
$347$			8.88467i			0.476954i	0.971148	+	0.238477i	$0.0766482\pi$
$347$			8.88467i			0.476954i	−0.971148	+	0.238477i	$0.923352\pi$
$348$			1.81210i			0.0971386i
$349$	22.3237			1.19496			0.597480	−	0.801884i	$-0.296169\pi$
$349$	22.3237			1.19496			0.597480	+	0.801884i	$0.296169\pi$
$350$	2.63424	−	4.74780i	0.140806	−	0.253781i
$351$		0			0
$352$		−	0.403887i		−	0.0215273i
$353$			31.0186i			1.65095i	0.564438	+	0.825476i	$0.309093\pi$
$353$			31.0186i			1.65095i	−0.564438	+	0.825476i	$0.690907\pi$
$354$	2.21219			0.117576
$355$	23.9560	−	14.1047i	1.27145	−	0.748599i
$356$	−6.99770			−0.370877
$357$			1.71930i			0.0909950i
$358$		−	25.2779i		−	1.33598i
$359$	15.1402			0.799072			0.399536	−	0.916718i	$-0.369171\pi$
$359$	15.1402			0.799072			0.399536	+	0.916718i	$0.369171\pi$
$360$	3.29890	+	5.60299i	0.173867	+	0.295303i
$361$	−18.2868			−0.962463
$362$		−	17.8082i		−	0.935979i
$363$			3.29075i			0.172720i
$364$		0			0
$365$	−3.32224	−	5.64264i	−0.173894	−	0.295349i
$366$	0.802079			0.0419253
$367$			20.8201i			1.08680i	0.839474	+	0.543401i	$0.182863\pi$
$367$			20.8201i			1.08680i	−0.839474	+	0.543401i	$0.817137\pi$
$368$		−	1.76217i		−	0.0918595i
$369$	−9.31063			−0.484692
$370$	8.52303	−	5.01815i	0.443091	−	0.260881i
$371$	−11.6881			−0.606814
$372$			1.59525i			0.0827100i
$373$			0.901633i			0.0466848i	0.999728	+	0.0233424i	$0.00743079\pi$
$373$			0.901633i			0.0466848i	−0.999728	+	0.0233424i	$0.992569\pi$
$374$	2.10581			0.108889
$375$	−3.39394	+	0.0868286i	−0.175262	+	0.00448381i
$376$	11.5048			0.593313
$377$		0			0
$378$		−	1.94812i		−	0.100201i
$379$	−15.7125			−0.807096			−0.403548	−	0.914959i	$-0.632223\pi$
$379$	−15.7125			−0.807096			−0.403548	+	0.914959i	$0.632223\pi$
$380$	−1.62728	+	0.958100i	−0.0834775	+	0.0491495i
$381$	−1.84323			−0.0944314
$382$			10.4612i			0.535242i
$383$			38.0352i			1.94351i	0.235993	+	0.971755i	$0.424166\pi$
$383$			38.0352i			1.94351i	−0.235993	+	0.971755i	$0.575834\pi$
$384$	0.303663			0.0154962
$385$	0.497584	+	0.845118i	0.0253592	+	0.0430712i
$386$	14.6561			0.745974
$387$			33.4004i			1.69784i
$388$			9.47384i			0.480961i
$389$	−3.64514			−0.184816			−0.0924079	−	0.995721i	$-0.529456\pi$
$389$	−3.64514			−0.184816			−0.0924079	+	0.995721i	$0.529456\pi$
$390$		0			0
$391$	9.18773			0.464643
$392$			5.82076i			0.293993i
$393$		−	0.162395i		−	0.00819173i
$394$	10.3360			0.520718
$395$	−30.6145	+	18.0250i	−1.54038	+	0.906938i
$396$	−1.17442			−0.0590168
$397$		−	1.08366i		−	0.0543872i	−0.999630	−	0.0271936i	$-0.991343\pi$
$397$		−	1.08366i		−	0.0543872i	0.999630	−	0.0271936i	$-0.00865706\pi$
$398$			5.21516i			0.261412i
$399$	0.278481			0.0139415
$400$	2.42580	−	4.37213i	0.121290	−	0.218606i
$401$	−6.16953			−0.308091			−0.154046	−	0.988064i	$-0.549230\pi$
$401$	−6.16953			−0.308091			−0.154046	+	0.988064i	$0.549230\pi$
$402$			3.21860i			0.160529i
$403$		0			0
$404$	−6.61025			−0.328872
$405$	15.7593	−	9.27866i	0.783084	−	0.461060i
$406$	6.48023			0.321608
$407$			1.78648i			0.0885524i
$408$			1.58326i			0.0783829i
$409$	−19.8455			−0.981299			−0.490649	−	0.871357i	$-0.663240\pi$
$409$	−19.8455			−0.981299			−0.490649	+	0.871357i	$0.663240\pi$
$410$	3.63264	+	6.16982i	0.179403	+	0.304706i
$411$	3.63816			0.179457
$412$		−	9.21082i		−	0.453784i
$413$		−	7.91099i		−	0.389274i
$414$	−5.12402			−0.251832
$415$	−14.3658	−	24.3995i	−0.705189	−	1.19772i
$416$		0			0
$417$			0.816859i			0.0400018i
$418$		−	0.341087i		−	0.0166831i
$419$	−4.45670			−0.217724			−0.108862	−	0.994057i	$-0.534721\pi$
$419$	−4.45670			−0.217724			−0.108862	+	0.994057i	$0.534721\pi$
$420$	−0.635402	+	0.374108i	−0.0310044	+	0.0182546i
$421$	16.7557			0.816624			0.408312	−	0.912842i	$-0.366118\pi$
$421$	16.7557			0.816624			0.408312	+	0.912842i	$0.366118\pi$
$422$			12.3086i			0.599175i
$423$		−	33.4534i		−	1.62656i
$424$	−10.7632			−0.522708
$425$	22.7957	+	12.6478i	1.10575	+	0.613509i
$426$	−3.77528			−0.182913
$427$		−	2.86831i		−	0.138807i
$428$			6.97470i			0.337135i
$429$		0			0
$430$	22.1333	−	13.0315i	1.06736	−	0.628436i
$431$	−17.3440			−0.835433			−0.417717	−	0.908577i	$-0.637170\pi$
$431$	−17.3440			−0.835433			−0.417717	+	0.908577i	$0.637170\pi$
$432$		−	1.79397i		−	0.0863126i
$433$		−	4.41765i		−	0.212299i	−0.994350	−	0.106149i	$-0.966148\pi$
$433$		−	4.41765i		−	0.212299i	0.994350	−	0.106149i	$-0.0338521\pi$
$434$	5.70478			0.273838
$435$	−2.05583	−	3.49171i	−0.0985695	−	0.167415i
$436$	−3.29363			−0.157736
$437$		−	1.48817i		−	0.0711889i
$438$			0.889236i			0.0424893i
$439$	−33.1534			−1.58232			−0.791162	−	0.611607i	$-0.790523\pi$
$439$	−33.1534			−1.58232			−0.791162	+	0.611607i	$0.790523\pi$
$440$	0.458212	+	0.778246i	0.0218444	+	0.0371014i
$441$	16.9256			0.805979
$442$		0			0
$443$			19.2632i			0.915224i	0.889152	+	0.457612i	$0.151295\pi$
$443$			19.2632i			0.915224i	−0.889152	+	0.457612i	$0.848705\pi$
$444$	−1.34316			−0.0637437
$445$	13.4838	−	7.93892i	0.639193	−	0.376341i
$446$	9.35143			0.442803
$447$			5.32697i			0.251957i
$448$		−	1.08593i		−	0.0513052i
$449$	4.55734			0.215074			0.107537	−	0.994201i	$-0.465704\pi$
$449$	4.55734			0.215074			0.107537	+	0.994201i	$0.465704\pi$
$450$	−12.7132	−	7.05372i	−0.599307	−	0.332516i
$451$	−1.29323			−0.0608959
$452$			10.0934i			0.474754i
$453$			5.32566i			0.250222i
$454$	13.1715			0.618170
$455$		0			0
$456$	0.256446			0.0120092
$457$		−	15.9598i		−	0.746570i	−0.927717	−	0.373285i	$-0.878231\pi$
$457$		−	15.9598i		−	0.746570i	0.927717	−	0.373285i	$-0.121769\pi$
$458$			13.6752i			0.638998i
$459$	9.35354			0.436586
$460$	1.99919	+	3.39551i	0.0932127	+	0.158316i
$461$	−22.2437			−1.03599			−0.517996	−	0.855383i	$-0.673322\pi$
$461$	−22.2437			−1.03599			−0.517996	+	0.855383i	$0.673322\pi$
$462$		−	0.133184i		−	0.00619628i
$463$			31.0149i			1.44138i	0.693256	+	0.720692i	$0.256176\pi$
$463$			31.0149i			1.44138i	−0.693256	+	0.720692i	$0.743824\pi$
$464$	5.96747			0.277033
$465$	−1.80982	−	3.07388i	−0.0839284	−	0.142548i
$466$	27.7357			1.28483
$467$		−	0.841337i		−	0.0389324i	−0.999811	−	0.0194662i	$-0.993803\pi$
$467$		−	0.841337i		−	0.0389324i	0.999811	−	0.0194662i	$-0.00619668\pi$
$468$		0			0
$469$	11.5100			0.531482
$470$	−22.1684	+	13.0522i	−1.02255	+	0.602053i
$471$	−3.20858			−0.147843
$472$		−	7.28501i		−	0.335320i
$473$			4.63927i			0.213314i
$474$	4.82460			0.221601
$475$	2.04861	−	3.69230i	0.0939969	−	0.169414i
$476$	5.66187			0.259512
$477$			31.2972i			1.43300i
$478$			17.7552i			0.812102i
$479$	7.63429			0.348819			0.174410	−	0.984673i	$-0.444198\pi$
$479$	7.63429			0.348819			0.174410	+	0.984673i	$0.444198\pi$
$480$	−0.585124	+	0.344506i	−0.0267071	+	0.0157245i
$481$		0			0
$482$		−	3.83937i		−	0.174879i
$483$		−	0.581085i		−	0.0264403i
$484$	10.8369			0.492585
$485$	−10.7481	−	18.2550i	−0.488046	−	0.828919i
$486$	−7.86546			−0.356784
$487$			23.2958i			1.05563i	0.849358	+	0.527817i	$0.176989\pi$
$487$			23.2958i			1.05563i	−0.849358	+	0.527817i	$0.823011\pi$
$488$		−	2.64135i		−	0.119568i
$489$	−5.78893			−0.261784
$490$	−6.60368	−	11.2160i	−0.298324	−	0.506686i
$491$	36.2972			1.63807			0.819034	−	0.573745i	$-0.194510\pi$
$491$	36.2972			1.63807			0.819034	+	0.573745i	$0.194510\pi$
$492$		−	0.972316i		−	0.0438354i
$493$			31.1136i			1.40129i
$494$		0			0
$495$	2.26298	−	1.33238i	0.101713	−	0.0598862i
$496$	5.25338			0.235884
$497$			13.5008i			0.605591i
$498$			3.84517i			0.172306i
$499$	18.9398			0.847863			0.423932	−	0.905694i	$-0.360650\pi$
$499$	18.9398			0.847863			0.423932	+	0.905694i	$0.360650\pi$
$500$	0.285938	+	11.1767i	0.0127875	+	0.499836i
$501$	−3.24388			−0.144926
$502$		−	14.4338i		−	0.644213i
$503$		−	35.7640i		−	1.59464i	−0.603560	−	0.797318i	$-0.706251\pi$
$503$		−	35.7640i		−	1.59464i	0.603560	−	0.797318i	$-0.293749\pi$
$504$	−3.15764			−0.140653
$505$	12.7372	−	7.49935i	0.566799	−	0.333717i
$506$	−0.711719			−0.0316398
$507$		0			0
$508$			6.06998i			0.269312i
$509$	3.11873			0.138235			0.0691176	−	0.997609i	$-0.477982\pi$
$509$	3.11873			0.138235			0.0691176	+	0.997609i	$0.477982\pi$
$510$	−1.79621	−	3.05076i	−0.0795375	−	0.135090i
$511$	3.17999			0.140675
$512$		−	1.00000i		−	0.0441942i
$513$		−	1.51503i		−	0.0668902i
$514$	−11.0755			−0.488517
$515$	10.4497	+	17.7482i	0.460469	+	0.782080i
$516$	−3.48803			−0.153552
$517$		−	4.64663i		−	0.204359i
$518$			4.80328i			0.211044i
$519$	4.82772			0.211913
$520$		0			0
$521$	38.4309			1.68369			0.841844	−	0.539721i	$-0.181470\pi$
$521$	38.4309			1.68369			0.841844	+	0.539721i	$0.181470\pi$
$522$		−	17.3521i		−	0.759483i
$523$		−	23.8519i		−	1.04297i	−0.853260	−	0.521485i	$-0.825378\pi$
$523$		−	23.8519i		−	1.04297i	0.853260	−	0.521485i	$-0.174622\pi$
$524$	−0.534787			−0.0233623
$525$	0.799921	−	1.44173i	0.0349114	−	0.0629223i
$526$	1.74154			0.0759349
$527$			27.3904i			1.19314i
$528$		−	0.122645i		−	0.00533746i
$529$	19.8948			0.864989
$530$	20.7395	−	12.2109i	0.900867	−	0.530408i
$531$	−21.1833			−0.919276
$532$		−	0.917075i		−	0.0397603i
$533$		0			0
$534$	−2.12494			−0.0919551
$535$	−7.91283	−	13.4395i	−0.342101	−	0.581040i
$536$	10.5992			0.457818
$537$		−	7.67595i		−	0.331242i
$538$		−	10.0411i		−	0.432905i
$539$	2.35093			0.101262
$540$	2.03527	+	3.45679i	0.0875841	+	0.148757i
$541$	−5.36874			−0.230820			−0.115410	−	0.993318i	$-0.536818\pi$
$541$	−5.36874			−0.230820			−0.115410	+	0.993318i	$0.536818\pi$
$542$			10.3097i			0.442841i
$543$		−	5.40769i		−	0.232066i
$544$	5.21387			0.223543
$545$	6.34647	−	3.73664i	0.271853	−	0.160060i
$546$		0			0
$547$		−	28.1689i		−	1.20442i	−0.798339	−	0.602208i	$-0.794288\pi$
$547$		−	28.1689i		−	1.20442i	0.798339	−	0.602208i	$-0.205712\pi$
$548$		−	11.9809i		−	0.511799i
$549$	−7.68049			−0.327795
$550$	−1.76585	−	0.979751i	−0.0752959	−	0.0417767i
$551$	5.03959			0.214694
$552$		−	0.535105i		−	0.0227756i
$553$		−	17.2532i		−	0.733682i
$554$	−29.7990			−1.26604
$555$	2.58813	−	1.52382i	0.109860	−	0.0646827i
$556$	2.69002			0.114082
$557$		−	15.1505i		−	0.641947i	−0.947088	−	0.320974i	$-0.895990\pi$
$557$		−	15.1505i		−	0.641947i	0.947088	−	0.320974i	$-0.104010\pi$
$558$		−	15.2757i		−	0.646672i
$559$		0			0
$560$	1.23199	+	2.09246i	0.0520610	+	0.0884225i
$561$	0.639457			0.0269979
$562$			17.5437i			0.740037i
$563$			32.5894i			1.37348i	0.726904	+	0.686739i	$0.240958\pi$
$563$			32.5894i			1.37348i	−0.726904	+	0.686739i	$0.759042\pi$
$564$	3.49357			0.147106
$565$	−11.4510	−	19.4489i	−0.481747	−	0.818220i
$566$	25.9299			1.08992
$567$			8.88136i			0.372982i
$568$			12.4325i			0.521655i
$569$	−21.7554			−0.912033			−0.456016	−	0.889971i	$-0.650724\pi$
$569$	−21.7554			−0.912033			−0.456016	+	0.889971i	$0.650724\pi$
$570$	−0.494143	+	0.290939i	−0.0206974	+	0.0121861i
$571$	−24.2853			−1.01631			−0.508155	−	0.861266i	$-0.669672\pi$
$571$	−24.2853			−1.01631			−0.508155	+	0.861266i	$0.669672\pi$
$572$		0			0
$573$			3.17668i			0.132708i
$574$	−3.47709			−0.145131
$575$	−7.70443	−	4.27468i	−0.321297	−	0.178266i
$576$	−2.90779			−0.121158
$577$		−	23.1332i		−	0.963048i	−0.876433	−	0.481524i	$-0.840083\pi$
$577$		−	23.1332i		−	0.963048i	0.876433	−	0.481524i	$-0.159917\pi$
$578$			10.1844i			0.423616i
$579$	4.45050			0.184956
$580$	−11.4987	+	6.77011i	−0.477455	+	0.281114i
$581$	13.7507			0.570474
$582$			2.87685i			0.119249i
$583$			4.34713i			0.180040i
$584$	2.92837			0.121177
$585$		0			0
$586$	−26.1627			−1.08077
$587$			4.60818i			0.190200i	0.995468	+	0.0950999i	$0.0303171\pi$
$587$			4.60818i			0.190200i	−0.995468	+	0.0950999i	$0.969683\pi$
$588$			1.76755i			0.0728925i
$589$	4.43653			0.182804
$590$	8.26487	+	14.0374i	0.340259	+	0.577911i
$591$	3.13864			0.129106
$592$			4.42321i			0.181793i
$593$			1.27629i			0.0524111i	0.999657	+	0.0262056i	$0.00834244\pi$
$593$			1.27629i			0.0524111i	−0.999657	+	0.0262056i	$0.991658\pi$
$594$	−0.724564			−0.0297292
$595$	−10.9098	+	6.42342i	−0.447258	+	0.263334i
$596$	17.5424			0.718565
$597$			1.58365i			0.0648144i
$598$		0			0
$599$	−21.3539			−0.872497			−0.436249	−	0.899826i	$-0.643693\pi$
$599$	−21.3539			−0.872497			−0.436249	+	0.899826i	$0.643693\pi$
$600$	0.736626	−	1.32765i	0.0300726	−	0.0542011i
$601$	−2.74727			−0.112063			−0.0560317	−	0.998429i	$-0.517845\pi$
$601$	−2.74727			−0.112063			−0.0560317	+	0.998429i	$0.517845\pi$
$602$			12.4735i			0.508383i
$603$		−	30.8204i		−	1.25510i
$604$	17.5381			0.713615
$605$	−20.8815	+	12.2945i	−0.848952	+	0.499841i
$606$	−2.00729			−0.0815404
$607$		−	22.9135i		−	0.930030i	−0.885303	−	0.465015i	$-0.846049\pi$
$607$		−	22.9135i		−	0.930030i	0.885303	−	0.465015i	$-0.153951\pi$
$608$		−	0.844510i		−	0.0342494i
$609$	1.96780			0.0797394
$610$	2.99662	+	5.08959i	0.121330	+	0.206071i
$611$		0			0
$612$		−	15.1608i		−	0.612840i
$613$			16.5575i			0.668752i	0.942440	+	0.334376i	$0.108526\pi$
$613$			16.5575i			0.668752i	−0.942440	+	0.334376i	$0.891474\pi$
$614$	2.68863			0.108504
$615$	1.10310	+	1.87354i	0.0444811	+	0.0755486i
$616$	−0.438592			−0.0176714
$617$		−	11.3693i		−	0.457712i	−0.973460	−	0.228856i	$-0.926502\pi$
$617$		−	11.3693i		−	0.457712i	0.973460	−	0.228856i	$-0.0734985\pi$
$618$		−	2.79698i		−	0.112511i
$619$	47.1109			1.89355			0.946773	−	0.321901i	$-0.104322\pi$
$619$	47.1109			1.89355			0.946773	+	0.321901i	$0.104322\pi$
$620$	−10.1227	+	5.95997i	−0.406536	+	0.239358i
$621$	−3.16129			−0.126858
$622$			31.0278i			1.24410i
$623$			7.59898i			0.304447i
$624$		0			0
$625$	−13.2310	−	21.2118i	−0.529238	−	0.848473i
$626$	14.7399			0.589127
$627$		−	0.103575i		−	0.00413640i
$628$			10.5663i			0.421639i
$629$	−23.0620			−0.919543
$630$	6.08443	−	3.58236i	0.242409	−	0.142725i
$631$	−8.39389			−0.334156			−0.167078	−	0.985944i	$-0.553433\pi$
$631$	−8.39389			−0.334156			−0.167078	+	0.985944i	$0.553433\pi$
$632$		−	15.8880i		−	0.631992i
$633$			3.73767i			0.148559i
$634$	14.7416			0.585464
$635$	−6.88642	−	11.6962i	−0.273279	−	0.464149i
$636$	−3.26839			−0.129600
$637$		0			0
$638$		−	2.41019i		−	0.0954201i
$639$	36.1510			1.43011
$640$	1.13450	+	1.92689i	0.0448452	+	0.0761670i
$641$	−36.5728			−1.44454			−0.722268	−	0.691613i	$-0.756901\pi$
$641$	−36.5728			−1.44454			−0.722268	+	0.691613i	$0.756901\pi$
$642$			2.11796i			0.0835891i
$643$		−	46.0372i		−	1.81553i	−0.419478	−	0.907766i	$-0.637787\pi$
$643$		−	46.0372i		−	1.81553i	0.419478	−	0.907766i	$-0.362213\pi$
$644$	−1.91359			−0.0754059
$645$	6.72105	−	3.95719i	0.264641	−	0.155814i
$646$	4.40316			0.173240
$647$		−	27.8549i		−	1.09509i	−0.836776	−	0.547545i	$-0.815563\pi$
$647$		−	27.8549i		−	1.09509i	0.836776	−	0.547545i	$-0.184437\pi$
$648$			8.17860i			0.321286i
$649$	−2.94232			−0.115496
$650$		0			0
$651$	1.73233			0.0678953
$652$			19.0637i			0.746592i
$653$			4.98456i			0.195061i	0.995233	+	0.0975304i	$0.0310943\pi$
$653$			4.98456i			0.195061i	−0.995233	+	0.0975304i	$0.968906\pi$
$654$	−1.00015			−0.0391091
$655$	1.03048	−	0.606718i	0.0402640	−	0.0237064i
$656$	−3.20196			−0.125016
$657$		−	8.51508i		−	0.332205i
$658$		−	12.4933i		−	0.487040i
$659$	−27.8625			−1.08537			−0.542684	−	0.839937i	$-0.682592\pi$
$659$	−27.8625			−1.08537			−0.542684	+	0.839937i	$0.682592\pi$
$660$	0.139142	+	0.236324i	0.00541608	+	0.00919891i
$661$	−37.9173			−1.47481			−0.737406	−	0.675450i	$-0.763949\pi$
$661$	−37.9173			−1.47481			−0.737406	+	0.675450i	$0.763949\pi$
$662$		−	9.55973i		−	0.371549i
$663$		0			0
$664$	12.6626			0.491405
$665$	1.04043	+	1.76710i	0.0403460	+	0.0685253i
$666$	12.8618			0.498383
$667$		−	10.5157i		−	0.407170i
$668$			10.6825i			0.413319i
$669$	2.83968			0.109788
$670$	−20.4236	+	12.0249i	−0.789032	+	0.464562i
$671$	−1.06681			−0.0411837
$672$		−	0.329755i		−	0.0127206i
$673$		−	5.08337i		−	0.195949i	−0.995189	−	0.0979747i	$-0.968764\pi$
$673$		−	5.08337i		−	0.195949i	0.995189	−	0.0979747i	$-0.0312364\pi$
$674$	−7.58566			−0.292189
$675$	−7.84348	−	4.35183i	−0.301896	−	0.167502i
$676$		0			0
$677$			40.3815i			1.55199i	0.630740	+	0.775994i	$0.282751\pi$
$677$			40.3815i			1.55199i	−0.630740	+	0.775994i	$0.717249\pi$
$678$			3.06499i			0.117710i
$679$	10.2879			0.394813
$680$	−10.0465	+	5.91515i	−0.385267	+	0.226836i
$681$	3.99970			0.153269
$682$		−	2.12177i		−	0.0812468i
$683$			14.8432i			0.567959i	0.958830	+	0.283980i	$0.0916548\pi$
$683$			14.8432i			0.567959i	−0.958830	+	0.283980i	$0.908345\pi$
$684$	−2.45566			−0.0938944
$685$	13.5924	+	23.0859i	0.519339	+	0.882067i
$686$	13.9224			0.531560
$687$			4.15264i			0.158433i
$688$			11.4865i			0.437920i
$689$		0			0
$690$	0.607079	+	1.03109i	0.0231111	+	0.0392529i
$691$	−31.8114			−1.21016			−0.605081	−	0.796164i	$-0.706859\pi$
$691$	−31.8114			−1.21016			−0.605081	+	0.796164i	$0.706859\pi$
$692$		−	15.8983i		−	0.604362i
$693$			1.27533i			0.0484459i
$694$	8.88467			0.337257
$695$	−5.18338	+	3.05184i	−0.196617	+	0.115763i
$696$	1.81210			0.0686874
$697$		−	16.6946i		−	0.632353i
$698$		−	22.3237i		−	0.844964i
$699$	8.42230			0.318561
$700$	−4.74780	−	2.63424i	−0.179450	−	0.0995650i
$701$	−2.75131			−0.103915			−0.0519577	−	0.998649i	$-0.516546\pi$
$701$	−2.75131			−0.103915			−0.0519577	+	0.998649i	$0.516546\pi$
$702$		0			0
$703$			3.73544i			0.140885i
$704$	−0.403887			−0.0152221
$705$	−6.73172	+	3.96346i	−0.253531	+	0.149273i
$706$	31.0186			1.16740
$707$			7.17824i			0.269966i
$708$		−	2.21219i		−	0.0831390i
$709$	28.7721			1.08056			0.540279	−	0.841486i	$-0.318319\pi$
$709$	28.7721			1.08056			0.540279	+	0.841486i	$0.318319\pi$
$710$	−14.1047	−	23.9560i	−0.529340	−	0.899053i
$711$	−46.1991			−1.73260
$712$			6.99770i			0.262250i
$713$		−	9.25735i		−	0.346690i
$714$	1.71930			0.0643432
$715$		0			0
$716$	−25.2779			−0.944680
$717$			5.39158i			0.201352i
$718$		−	15.1402i		−	0.565029i
$719$	−33.1840			−1.23756			−0.618778	−	0.785566i	$-0.712372\pi$
$719$	−33.1840			−1.23756			−0.618778	+	0.785566i	$0.712372\pi$
$720$	5.60299	−	3.29890i	0.208811	−	0.122943i
$721$	−10.0023			−0.372504
$722$			18.2868i			0.680564i
$723$		−	1.16587i		−	0.0433593i
$724$	−17.8082			−0.661837
$725$	14.4759	−	26.0905i	0.537622	−	0.968978i
$726$	3.29075			0.122131
$727$		−	37.6129i		−	1.39499i	−0.716591	−	0.697493i	$-0.754299\pi$
$727$		−	37.6129i		−	1.39499i	0.716591	−	0.697493i	$-0.245701\pi$
$728$		0			0
$729$	22.1474			0.820273
$730$	−5.64264	+	3.32224i	−0.208844	+	0.122962i
$731$	−59.8893			−2.21509
$732$		−	0.802079i		−	0.0296457i
$733$		−	19.0778i		−	0.704654i	−0.935877	−	0.352327i	$-0.885391\pi$
$733$		−	19.0778i		−	0.704654i	0.935877	−	0.352327i	$-0.114609\pi$
$734$	20.8201			0.768484
$735$	−2.00529	−	3.40587i	−0.0739662	−	0.125627i
$736$	−1.76217			−0.0649545
$737$		−	4.28090i		−	0.157689i
$738$			9.31063i			0.342729i
$739$	−40.5137			−1.49032			−0.745160	−	0.666886i	$-0.767627\pi$
$739$	−40.5137			−1.49032			−0.745160	+	0.666886i	$0.767627\pi$
$740$	−5.01815	−	8.52303i	−0.184471	−	0.313313i
$741$		0			0
$742$			11.6881i			0.429082i
$743$			11.8075i			0.433176i	0.976263	+	0.216588i	$0.0694929\pi$
$743$			11.8075i			0.433176i	−0.976263	+	0.216588i	$0.930507\pi$
$744$	1.59525			0.0584848
$745$	−33.8023	+	19.9019i	−1.23842	+	0.729150i
$746$	0.901633			0.0330111
$747$		−	36.8203i		−	1.34718i
$748$		−	2.10581i		−	0.0769962i
$749$	7.57401			0.276748
$750$	0.0868286	+	3.39394i	0.00317053	+	0.123929i
$751$	−14.0149			−0.511409			−0.255705	−	0.966755i	$-0.582307\pi$
$751$	−14.0149			−0.511409			−0.255705	+	0.966755i	$0.582307\pi$
$752$		−	11.5048i		−	0.419536i
$753$		−	4.38301i		−	0.159726i
$754$		0			0
$755$	−33.7940	+	19.8970i	−1.22989	+	0.724127i
$756$	−1.94812			−0.0708526
$757$		−	31.2552i		−	1.13599i	−0.823032	−	0.567994i	$-0.807720\pi$
$757$		−	31.2552i		−	1.13599i	0.823032	−	0.567994i	$-0.192280\pi$
$758$			15.7125i			0.570703i
$759$	−0.216122			−0.00784474
$760$	0.958100	+	1.62728i	0.0347539	+	0.0590275i
$761$	−34.1575			−1.23821			−0.619103	−	0.785310i	$-0.712504\pi$
$761$	−34.1575			−1.23821			−0.619103	+	0.785310i	$0.712504\pi$
$762$			1.84323i			0.0667731i
$763$			3.57664i			0.129483i
$764$	10.4612			0.378474
$765$	17.2000	+	29.2132i	0.621868	+	1.05621i
$766$	38.0352			1.37427
$767$		0			0
$768$		−	0.303663i		−	0.0109575i
$769$	44.2201			1.59462			0.797308	−	0.603572i	$-0.206256\pi$
$769$	44.2201			1.59462			0.797308	+	0.603572i	$0.206256\pi$
$770$	0.845118	−	0.497584i	0.0304559	−	0.0179317i
$771$	−3.36320			−0.121123
$772$		−	14.6561i		−	0.527483i
$773$			2.04145i			0.0734259i	0.999326	+	0.0367129i	$0.0116887\pi$
$773$			2.04145i			0.0734259i	−0.999326	+	0.0367129i	$0.988311\pi$
$774$	33.4004			1.20055
$775$	12.7437	−	22.9684i	0.457766	−	0.825050i
$776$	9.47384			0.340091
$777$			1.45858i			0.0523261i
$778$			3.64514i			0.130685i
$779$	−2.70409			−0.0968840
$780$		0			0
$781$	5.02132			0.179677
$782$		−	9.18773i		−	0.328552i
$783$		−	10.7055i		−	0.382583i
$784$	5.82076			0.207884
$785$	−11.9875	−	20.3600i	−0.427851	−	0.726680i
$786$	−0.162395			−0.00579243
$787$			3.39520i			0.121026i	0.998167	+	0.0605130i	$0.0192737\pi$
$787$			3.39520i			0.121026i	−0.998167	+	0.0605130i	$0.980726\pi$
$788$		−	10.3360i		−	0.368203i
$789$	0.528841			0.0188273
$790$	18.0250	+	30.6145i	0.641302	+	1.08921i
$791$	10.9607			0.389717
$792$			1.17442i			0.0417312i
$793$		0			0
$794$	−1.08366			−0.0384576
$795$	6.29782	−	3.70800i	0.223361	−	0.131509i
$796$	5.21516			0.184846
$797$			24.4659i			0.866626i	0.901244	+	0.433313i	$0.142655\pi$
$797$			24.4659i			0.866626i	−0.901244	+	0.433313i	$0.857345\pi$
$798$		−	0.278481i		−	0.00985814i
$799$	59.9843			2.12209
$800$	−4.37213	−	2.42580i	−0.154578	−	0.0857651i
$801$	20.3478			0.718955
$802$			6.16953i			0.217854i
$803$		−	1.18273i		−	0.0417377i
$804$	3.21860			0.113511
$805$	3.68727	−	2.17097i	0.129959	−	0.0765167i
$806$		0			0
$807$		−	3.04912i		−	0.107334i
$808$			6.61025i			0.232548i
$809$	17.6948			0.622117			0.311058	−	0.950391i	$-0.399317\pi$
$809$	17.6948			0.622117			0.311058	+	0.950391i	$0.399317\pi$
$810$	−9.27866	−	15.7593i	−0.326019	−	0.553724i
$811$	2.82931			0.0993505			0.0496753	−	0.998765i	$-0.484181\pi$
$811$	2.82931			0.0993505			0.0496753	+	0.998765i	$0.484181\pi$
$812$		−	6.48023i		−	0.227411i
$813$			3.13068i			0.109798i
$814$	1.78648			0.0626160
$815$	−21.6278	−	36.7336i	−0.757590	−	1.28672i
$816$	1.58326			0.0554251
$817$			9.70050i			0.339377i
$818$			19.8455i			0.693883i
$819$		0			0
$820$	6.16982	−	3.63264i	0.215460	−	0.126857i
$821$	26.1300			0.911942			0.455971	−	0.889995i	$-0.349292\pi$
$821$	26.1300			0.911942			0.455971	+	0.889995i	$0.349292\pi$
$822$		−	3.63816i		−	0.126895i
$823$		−	1.85316i		−	0.0645970i	−0.999478	−	0.0322985i	$-0.989717\pi$
$823$		−	1.85316i		−	0.0645970i	0.999478	−	0.0322985i	$-0.0102827\pi$
$824$	−9.21082			−0.320874
$825$	−0.536221	−	0.297514i	−0.0186688	−	0.0103581i
$826$	−7.91099			−0.275258
$827$			19.9886i			0.695072i	0.937667	+	0.347536i	$0.112982\pi$
$827$			19.9886i			0.695072i	−0.937667	+	0.347536i	$0.887018\pi$
$828$			5.12402i			0.178072i
$829$	−41.6506			−1.44658			−0.723292	−	0.690542i	$-0.757372\pi$
$829$	−41.6506			−1.44658			−0.723292	+	0.690542i	$0.757372\pi$
$830$	−24.3995	+	14.3658i	−0.846918	+	0.498644i
$831$	−9.04884			−0.313901
$832$		0			0
$833$			30.3487i			1.05152i
$834$	0.816859			0.0282855
$835$	−12.1193	−	20.5840i	−0.419407	−	0.712339i
$836$	−0.341087			−0.0117967
$837$		−	9.42442i		−	0.325756i
$838$			4.45670i			0.153954i
$839$	−25.9421			−0.895622			−0.447811	−	0.894128i	$-0.647796\pi$
$839$	−25.9421			−0.895622			−0.447811	+	0.894128i	$0.647796\pi$
$840$	0.374108	+	0.635402i	0.0129080	+	0.0219234i
$841$	6.61068			0.227955
$842$		−	16.7557i		−	0.577441i
$843$			5.32737i			0.183484i
$844$	12.3086			0.423681
$845$		0			0
$846$	−33.4534			−1.15015
$847$		−	11.7680i		−	0.404355i
$848$			10.7632i			0.369610i
$849$	7.87395			0.270233
$850$	12.6478	−	22.7957i	0.433816	−	0.781885i
$851$	7.79445			0.267190
$852$			3.77528i			0.129339i
$853$		−	33.6674i		−	1.15275i	−0.817186	−	0.576374i	$-0.804467\pi$
$853$		−	33.6674i		−	1.15275i	0.817186	−	0.576374i	$-0.195533\pi$
$854$	−2.86831			−0.0981516
$855$	4.73178	−	2.78595i	0.161823	−	0.0952775i
$856$	6.97470			0.238391
$857$			6.39008i			0.218281i	0.994026	+	0.109140i	$0.0348098\pi$
$857$			6.39008i			0.218281i	−0.994026	+	0.109140i	$0.965190\pi$
$858$		0			0
$859$	−29.6345			−1.01112			−0.505558	−	0.862792i	$-0.668713\pi$
$859$	−29.6345			−1.01112			−0.505558	+	0.862792i	$0.668713\pi$
$860$	−13.0315	−	22.1333i	−0.444371	−	0.754739i
$861$	−1.05586			−0.0359837
$862$			17.3440i			0.590741i
$863$		−	15.7244i		−	0.535264i	−0.963521	−	0.267632i	$-0.913759\pi$
$863$		−	15.7244i		−	0.535264i	0.963521	−	0.267632i	$-0.0862412\pi$
$864$	−1.79397			−0.0610323
$865$	18.0367	+	30.6342i	0.613265	+	1.04160i
$866$	−4.41765			−0.150118
$867$			3.09262i			0.105031i
$868$		−	5.70478i		−	0.193633i
$869$	−6.41698			−0.217681
$870$	−3.49171	+	2.05583i	−0.118380	+	0.0696992i
$871$		0			0
$872$			3.29363i			0.111537i
$873$		−	27.5479i		−	0.932356i
$874$	−1.48817			−0.0503381
$875$	12.1371	−	0.310507i	0.410307	−	0.0104971i
$876$	0.889236			0.0300445
$877$		−	30.3994i		−	1.02651i	−0.858235	−	0.513257i	$-0.828439\pi$
$877$		−	30.3994i		−	1.02651i	0.858235	−	0.513257i	$-0.171561\pi$
$878$			33.1534i			1.11887i
$879$	−7.94464			−0.267966
$880$	0.778246	−	0.458212i	0.0262347	−	0.0154463i
$881$	41.3933			1.39458			0.697288	−	0.716791i	$-0.254390\pi$
$881$	41.3933			1.39458			0.697288	+	0.716791i	$0.254390\pi$
$882$		−	16.9256i		−	0.569913i
$883$		−	24.4503i		−	0.822819i	−0.911451	−	0.411410i	$-0.865037\pi$
$883$		−	24.4503i		−	0.822819i	0.911451	−	0.411410i	$-0.134963\pi$
$884$		0			0
$885$	2.50973	+	4.26264i	0.0843637	+	0.143287i
$886$	19.2632			0.647161
$887$		−	37.1737i		−	1.24817i	−0.781357	−	0.624085i	$-0.785472\pi$
$887$		−	37.1737i		−	1.24817i	0.781357	−	0.624085i	$-0.214528\pi$
$888$			1.34316i			0.0450736i
$889$	6.59155			0.221074
$890$	−7.93892	−	13.4838i	−0.266113	−	0.451978i
$891$	3.30323			0.110663
$892$		−	9.35143i		−	0.313109i
$893$		−	9.71589i		−	0.325130i
$894$	5.32697			0.178161
$895$	48.7077	−	28.6779i	1.62812	−	0.958595i
$896$	−1.08593			−0.0362782
$897$		0			0
$898$		−	4.55734i		−	0.152081i
$899$	31.3494			1.04556
$900$	−7.05372	+	12.7132i	−0.235124	+	0.423774i
$901$	−56.1180			−1.86956
$902$			1.29323i			0.0430599i
$903$			3.78775i			0.126048i
$904$	10.0934			0.335702
$905$	34.3144	−	20.2035i	1.14065	−	0.671586i
$906$	5.32566			0.176933
$907$		−	32.4758i		−	1.07834i	−0.842196	−	0.539171i	$-0.818738\pi$
$907$		−	32.4758i		−	1.07834i	0.842196	−	0.539171i	$-0.181262\pi$
$908$		−	13.1715i		−	0.437112i
$909$	19.2212			0.637527
$910$		0			0
$911$	16.8692			0.558900			0.279450	−	0.960160i	$-0.409848\pi$
$911$	16.8692			0.558900			0.279450	+	0.960160i	$0.409848\pi$
$912$		−	0.256446i		−	0.00849178i
$913$		−	5.11428i		−	0.169258i
$914$	−15.9598			−0.527905
$915$	0.909962	+	1.54552i	0.0300824	+	0.0510932i
$916$	13.6752			0.451840
$917$			0.580739i			0.0191777i
$918$		−	9.35354i		−	0.308713i
$919$	5.75843			0.189953			0.0949765	−	0.995480i	$-0.469722\pi$
$919$	5.75843			0.189953			0.0949765	+	0.995480i	$0.469722\pi$
$920$	3.39551	−	1.99919i	0.111947	−	0.0659113i
$921$	0.816435			0.0269025
$922$			22.2437i			0.732556i
$923$		0			0
$924$	−0.133184			−0.00438143
$925$	19.3388	+	10.7298i	0.635857	+	0.352795i
$926$	31.0149			1.01921
$927$			26.7831i			0.879673i
$928$		−	5.96747i		−	0.195892i
$929$	−43.2786			−1.41992			−0.709962	−	0.704240i	$-0.751288\pi$
$929$	−43.2786			−1.41992			−0.709962	+	0.704240i	$0.751288\pi$
$930$	−3.07388	+	1.80982i	−0.100796	+	0.0593464i
$931$	4.91569			0.161105
$932$		−	27.7357i		−	0.908514i
$933$			9.42198i			0.308462i
$934$	−0.841337			−0.0275294
$935$	2.38905	+	4.05767i	0.0781304	+	0.132700i
$936$		0			0
$937$			13.9713i			0.456424i	0.973611	+	0.228212i	$0.0732879\pi$
$937$			13.9713i			0.456424i	−0.973611	+	0.228212i	$0.926712\pi$
$938$		−	11.5100i		−	0.375815i
$939$	4.47597			0.146068
$940$	13.0522	+	22.1684i	0.425716	+	0.723054i
$941$	27.2678			0.888905			0.444452	−	0.895803i	$-0.353398\pi$
$941$	27.2678			0.888905			0.444452	+	0.895803i	$0.353398\pi$
$942$			3.20858i			0.104541i
$943$			5.64240i			0.183742i
$944$	−7.28501			−0.237107
$945$	3.75382	−	2.21015i	0.122112	−	0.0718963i
$946$	4.63927			0.150836
$947$		−	11.4663i		−	0.372605i	−0.982492	−	0.186302i	$-0.940350\pi$
$947$		−	11.4663i		−	0.372605i	0.982492	−	0.186302i	$-0.0596504\pi$
$948$		−	4.82460i		−	0.156696i
$949$		0			0
$950$	−3.69230	−	2.04861i	−0.119794	−	0.0664658i
$951$	4.47647			0.145160
$952$		−	5.66187i		−	0.183502i
$953$			19.2137i			0.622392i	0.950346	+	0.311196i	$0.100730\pi$
$953$			19.2137i			0.622392i	−0.950346	+	0.311196i	$0.899270\pi$
$954$	31.2972			1.01328
$955$	−20.1576	+	11.8683i	−0.652285	+	0.384049i
$956$	17.7552			0.574243
$957$		−	0.731883i		−	0.0236584i
$958$		−	7.63429i		−	0.246653i
$959$	−13.0104			−0.420127
$960$	0.344506	+	0.585124i	0.0111189	+	0.0188848i
$961$	−3.40205			−0.109743
$962$		0			0
$963$		−	20.2810i		−	0.653545i
$964$	−3.83937			−0.123658
$965$	16.6274	+	28.2406i	0.535253	+	0.909097i
$966$	−0.581085			−0.0186961
$967$		−	40.2200i		−	1.29339i	−0.762749	−	0.646695i	$-0.776151\pi$
$967$		−	40.2200i		−	1.29339i	0.762749	−	0.646695i	$-0.223849\pi$
$968$		−	10.8369i		−	0.348310i
$969$	1.33708			0.0429531
$970$	−18.2550	+	10.7481i	−0.586134	+	0.345101i
$971$	40.8959			1.31241			0.656207	−	0.754581i	$-0.272160\pi$
$971$	40.8959			1.31241			0.656207	+	0.754581i	$0.272160\pi$
$972$			7.86546i			0.252285i
$973$		−	2.92117i		−	0.0936483i
$974$	23.2958			0.746446
$975$		0			0
$976$	−2.64135			−0.0845475
$977$			19.5975i			0.626981i	0.949591	+	0.313490i	$0.101498\pi$
$977$			19.5975i			0.626981i	−0.949591	+	0.313490i	$0.898502\pi$
$978$			5.78893i			0.185110i
$979$	2.82628			0.0903284
$980$	−11.2160	+	6.60368i	−0.358281	+	0.210947i
$981$	9.57719			0.305776
$982$		−	36.2972i		−	1.15829i
$983$		−	11.7949i		−	0.376198i	−0.982150	−	0.188099i	$-0.939767\pi$
$983$		−	11.7949i		−	0.376198i	0.982150	−	0.188099i	$-0.0602325\pi$
$984$	−0.972316			−0.0309963
$985$	11.7262	+	19.9162i	0.373627	+	0.634584i
$986$	31.1136			0.990858
$987$		−	3.79375i		−	0.120757i
$988$		0			0
$989$	20.2412			0.643634
$990$	−1.33238	−	2.26298i	−0.0423459	−	0.0719221i
$991$	25.3114			0.804043			0.402022	−	0.915630i	$-0.368308\pi$
$991$	25.3114			0.804043			0.402022	+	0.915630i	$0.368308\pi$
$992$		−	5.25338i		−	0.166795i
$993$		−	2.90293i		−	0.0921217i
$994$	13.5008			0.428218
$995$	−10.0490	+	5.91661i	−0.318576	+	0.187569i
$996$	3.84517			0.121839
$997$		−	18.7441i		−	0.593632i	−0.954935	−	0.296816i	$-0.904075\pi$
$997$		−	18.7441i		−	0.593632i	0.954935	−	0.296816i	$-0.0959248\pi$
$998$		−	18.9398i		−	0.599530i
$999$	7.93513			0.251056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.g.339.3	yes	18
5.2	odd	4		8450.2.a.da.1.3		9
5.3	odd	4		8450.2.a.ct.1.7		9
5.4	even	2	inner	1690.2.b.g.339.16	yes	18
13.5	odd	4		1690.2.c.g.1689.8		18
13.8	odd	4		1690.2.c.h.1689.8		18
13.12	even	2		1690.2.b.f.339.12	yes	18
65.12	odd	4		8450.2.a.cw.1.3		9
65.34	odd	4		1690.2.c.g.1689.11		18
65.38	odd	4		8450.2.a.cx.1.7		9
65.44	odd	4		1690.2.c.h.1689.11		18
65.64	even	2		1690.2.b.f.339.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.7	✓	18	65.64	even	2
1690.2.b.f.339.12	yes	18	13.12	even	2
1690.2.b.g.339.3	yes	18	1.1	even	1	trivial
1690.2.b.g.339.16	yes	18	5.4	even	2	inner
1690.2.c.g.1689.8		18	13.5	odd	4
1690.2.c.g.1689.11		18	65.34	odd	4
1690.2.c.h.1689.8		18	13.8	odd	4
1690.2.c.h.1689.11		18	65.44	odd	4
8450.2.a.ct.1.7		9	5.3	odd	4
8450.2.a.cw.1.3		9	65.12	odd	4
8450.2.a.cx.1.7		9	65.38	odd	4
8450.2.a.da.1.3		9	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.303663i q^{3} -1.00000 q^{4} +(1.92689 - 1.13450i) q^{5} -0.303663 q^{6} +1.08593i q^{7} +1.00000i q^{8} +2.90779 q^{9} +(-1.13450 - 1.92689i) q^{10} +0.403887 q^{11} +0.303663i q^{12} +1.08593 q^{14} +(-0.344506 - 0.585124i) q^{15} +1.00000 q^{16} +5.21387i q^{17} -2.90779i q^{18} +0.844510 q^{19} +(-1.92689 + 1.13450i) q^{20} +0.329755 q^{21} -0.403887i q^{22} -1.76217i q^{23} +0.303663 q^{24} +(2.42580 - 4.37213i) q^{25} -1.79397i q^{27} -1.08593i q^{28} +5.96747 q^{29} +(-0.585124 + 0.344506i) q^{30} +5.25338 q^{31} -1.00000i q^{32} -0.122645i q^{33} +5.21387 q^{34} +(1.23199 + 2.09246i) q^{35} -2.90779 q^{36} +4.42321i q^{37} -0.844510i q^{38} +(1.13450 + 1.92689i) q^{40} -3.20196 q^{41} -0.329755i q^{42} +11.4865i q^{43} -0.403887 q^{44} +(5.60299 - 3.29890i) q^{45} -1.76217 q^{46} -11.5048i q^{47} -0.303663i q^{48} +5.82076 q^{49} +(-4.37213 - 2.42580i) q^{50} +1.58326 q^{51} +10.7632i q^{53} -1.79397 q^{54} +(0.778246 - 0.458212i) q^{55} -1.08593 q^{56} -0.256446i q^{57} -5.96747i q^{58} -7.28501 q^{59} +(0.344506 + 0.585124i) q^{60} -2.64135 q^{61} -5.25338i q^{62} +3.15764i q^{63} -1.00000 q^{64} -0.122645 q^{66} -10.5992i q^{67} -5.21387i q^{68} -0.535105 q^{69} +(2.09246 - 1.23199i) q^{70} +12.4325 q^{71} +2.90779i q^{72} -2.92837i q^{73} +4.42321 q^{74} +(-1.32765 - 0.736626i) q^{75} -0.844510 q^{76} +0.438592i q^{77} -15.8880 q^{79} +(1.92689 - 1.13450i) q^{80} +8.17860 q^{81} +3.20196i q^{82} -12.6626i q^{83} -0.329755 q^{84} +(5.91515 + 10.0465i) q^{85} +11.4865 q^{86} -1.81210i q^{87} +0.403887i q^{88} +6.99770 q^{89} +(-3.29890 - 5.60299i) q^{90} +1.76217i q^{92} -1.59525i q^{93} -11.5048 q^{94} +(1.62728 - 0.958100i) q^{95} -0.303663 q^{96} -9.47384i q^{97} -5.82076i q^{98} +1.17442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{4} + 14 q^{6} - 16 q^{9} + 2 q^{10} + 8 q^{11} - 2 q^{14} + 8 q^{15} + 18 q^{16} - 12 q^{19} + 16 q^{21} - 14 q^{24} + 22 q^{25} - 30 q^{29} - 14 q^{30} - 12 q^{31} - 24 q^{34} - 4 q^{35} + 16 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) \) 18 * q - 18 * q^4 + 14 * q^6 - 16 * q^9 + 2 * q^10 + 8 * q^11 - 2 * q^14 + 8 * q^15 + 18 * q^16 - 12 * q^19 + 16 * q^21 - 14 * q^24 + 22 * q^25 - 30 * q^29 - 14 * q^30 - 12 * q^31 - 24 * q^34 - 4 * q^35 + 16 * q^36 - 2 * q^40 + 54 * q^41 - 8 * q^44 + 20 * q^45 + 22 * q^46 + 20 * q^49 + 8 * q^50 + 24 * q^51 - 68 * q^54 + 2 * q^56 - 40 * q^59 - 8 * q^60 - 38 * q^61 - 18 * q^64 - 28 * q^66 + 28 * q^69 - 6 * q^70 - 20 * q^71 + 20 * q^74 - 72 * q^75 + 12 * q^76 + 28 * q^79 + 106 * q^81 - 16 * q^84 + 56 * q^85 + 82 * q^86 - 86 * q^89 - 20 * q^90 - 10 * q^94 - 54 * q^95 + 14 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

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Database

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