LMFDB - Embedded newform 1690.2.c.h.1689.11

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			1689.11
Root			$2.90009i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.h.1689.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +0.303663i q^{3} +1.00000 q^{4} +(1.13450 - 1.92689i) q^{5} +0.303663i q^{6} +1.08593 q^{7} +1.00000 q^{8} +2.90779 q^{9} +(1.13450 - 1.92689i) q^{10} +0.403887i q^{11} +0.303663i q^{12} +1.08593 q^{14} +(0.585124 + 0.344506i) q^{15} +1.00000 q^{16} +5.21387i q^{17} +2.90779 q^{18} -0.844510i q^{19} +(1.13450 - 1.92689i) q^{20} +0.329755i q^{21} +0.403887i q^{22} -1.76217i q^{23} +0.303663i q^{24} +(-2.42580 - 4.37213i) q^{25} +1.79397i q^{27} +1.08593 q^{28} +5.96747 q^{29} +(0.585124 + 0.344506i) q^{30} -5.25338i q^{31} +1.00000 q^{32} -0.122645 q^{33} +5.21387i q^{34} +(1.23199 - 2.09246i) q^{35} +2.90779 q^{36} +4.42321 q^{37} -0.844510i q^{38} +(1.13450 - 1.92689i) q^{40} +3.20196i q^{41} +0.329755i q^{42} +11.4865i q^{43} +0.403887i q^{44} +(3.29890 - 5.60299i) q^{45} -1.76217i q^{46} -11.5048 q^{47} +0.303663i q^{48} -5.82076 q^{49} +(-2.42580 - 4.37213i) q^{50} -1.58326 q^{51} -10.7632i q^{53} +1.79397i q^{54} +(0.778246 + 0.458212i) q^{55} +1.08593 q^{56} +0.256446 q^{57} +5.96747 q^{58} -7.28501i q^{59} +(0.585124 + 0.344506i) q^{60} -2.64135 q^{61} -5.25338i q^{62} +3.15764 q^{63} +1.00000 q^{64} -0.122645 q^{66} +10.5992 q^{67} +5.21387i q^{68} +0.535105 q^{69} +(1.23199 - 2.09246i) q^{70} -12.4325i q^{71} +2.90779 q^{72} -2.92837 q^{73} +4.42321 q^{74} +(1.32765 - 0.736626i) q^{75} -0.844510i q^{76} +0.438592i q^{77} -15.8880 q^{79} +(1.13450 - 1.92689i) q^{80} +8.17860 q^{81} +3.20196i q^{82} +12.6626 q^{83} +0.329755i q^{84} +(10.0465 + 5.91515i) q^{85} +11.4865i q^{86} +1.81210i q^{87} +0.403887i q^{88} +6.99770i q^{89} +(3.29890 - 5.60299i) q^{90} -1.76217i q^{92} +1.59525 q^{93} -11.5048 q^{94} +(-1.62728 - 0.958100i) q^{95} +0.303663i q^{96} +9.47384 q^{97} -5.82076 q^{98} +1.17442i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) $ 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			0.303663i			0.175320i	0.996150	+	0.0876598i	$0.0279389\pi$
$3$			0.303663i			0.175320i	−0.996150	+	0.0876598i	$0.972061\pi$
$4$	1.00000			0.500000
$5$	1.13450	−	1.92689i	0.507365	−	0.861731i
$5$	1.13450	−	1.92689i	0.507365	−	0.861731i
$6$			0.303663i			0.123970i
$7$	1.08593			0.410441			0.205221	−	0.978716i	$-0.434209\pi$
$7$	1.08593			0.410441			0.205221	+	0.978716i	$0.434209\pi$
$8$	1.00000			0.353553
$9$	2.90779			0.969263
$10$	1.13450	−	1.92689i	0.358762	−	0.609336i
$11$			0.403887i			0.121777i	0.998145	+	0.0608883i	$0.0193933\pi$
$11$			0.403887i			0.121777i	−0.998145	+	0.0608883i	$0.980607\pi$
$12$			0.303663i			0.0876598i
$13$		0			0
$13$		0			0
$14$	1.08593			0.290226
$15$	0.585124	+	0.344506i	0.151078	+	0.0889511i
$16$	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	$0.782122\pi$
$18$	2.90779			0.685372
$19$		−	0.844510i		−	0.193744i	−0.995297	−	0.0968719i	$-0.969116\pi$
$19$		−	0.844510i		−	0.193744i	0.995297	−	0.0968719i	$-0.0308837\pi$
$20$	1.13450	−	1.92689i	0.253683	−	0.430866i
$21$			0.329755i			0.0719585i
$22$			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	$-0.0588137\pi$
$24$			0.303663i			0.0619849i
$25$	−2.42580	−	4.37213i	−0.485161	−	0.874425i
$26$		0			0
$27$			1.79397i			0.345251i
$28$	1.08593			0.205221
$29$	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
$31$		−	5.25338i		−	0.943534i	−0.881723	−	0.471767i	$-0.843616\pi$
$31$		−	5.25338i		−	0.943534i	0.881723	−	0.471767i	$-0.156384\pi$
$32$	1.00000			0.176777
$33$	−0.122645			−0.0213498
$34$			5.21387i			0.894171i
$35$	1.23199	−	2.09246i	0.208244	−	0.353690i
$36$	2.90779			0.484632
$37$	4.42321			0.727171			0.363586	−	0.931561i	$-0.381552\pi$
$37$	4.42321			0.727171			0.363586	+	0.931561i	$0.381552\pi$
$38$		−	0.844510i		−	0.136998i
$39$		0			0
$40$	1.13450	−	1.92689i	0.179381	−	0.304668i
$41$			3.20196i			0.500062i	0.968238	+	0.250031i	$0.0804409\pi$
$41$			3.20196i			0.500062i	−0.968238	+	0.250031i	$0.919559\pi$
$42$			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	$0.660308\pi$
$44$			0.403887i			0.0608883i
$45$	3.29890	−	5.60299i	0.491771	−	0.835244i
$46$		−	1.76217i		−	0.259818i
$47$	−11.5048			−1.67814			−0.839071	−	0.544022i	$-0.816901\pi$
$47$	−11.5048			−1.67814			−0.839071	+	0.544022i	$0.816901\pi$
$48$			0.303663i			0.0438299i
$49$	−5.82076			−0.831538
$50$	−2.42580	−	4.37213i	−0.343060	−	0.618312i
$51$	−1.58326			−0.221700
$52$		0			0
$53$		−	10.7632i		−	1.47844i	−0.673463	−	0.739221i	$-0.735194\pi$
$53$		−	10.7632i		−	1.47844i	0.673463	−	0.739221i	$-0.264806\pi$
$54$			1.79397i			0.244129i
$55$	0.778246	+	0.458212i	0.104939	+	0.0617852i
$56$	1.08593			0.145113
$57$	0.256446			0.0339671
$58$	5.96747			0.783567
$59$		−	7.28501i		−	0.948428i	−0.880410	−	0.474214i	$-0.842732\pi$
$59$		−	7.28501i		−	0.948428i	0.880410	−	0.474214i	$-0.157268\pi$
$60$	0.585124	+	0.344506i	0.0755392	+	0.0444756i
$61$	−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
$63$	3.15764			0.397826
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.122645			−0.0150966
$67$	10.5992			1.29490			0.647452	−	0.762106i	$-0.275835\pi$
$67$	10.5992			1.29490			0.647452	+	0.762106i	$0.275835\pi$
$68$			5.21387i			0.632274i
$69$	0.535105			0.0644191
$70$	1.23199	−	2.09246i	0.147251	−	0.250097i
$71$		−	12.4325i		−	1.47546i	−0.675094	−	0.737732i	$-0.735897\pi$
$71$		−	12.4325i		−	1.47546i	0.675094	−	0.737732i	$-0.264103\pi$
$72$	2.90779			0.342686
$73$	−2.92837			−0.342740			−0.171370	−	0.985207i	$-0.554819\pi$
$73$	−2.92837			−0.342740			−0.171370	+	0.985207i	$0.554819\pi$
$74$	4.42321			0.514188
$75$	1.32765	−	0.736626i	0.153304	−	0.0850582i
$76$		−	0.844510i		−	0.0968719i
$77$			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	$0.851951\pi$
$80$	1.13450	−	1.92689i	0.126841	−	0.215433i
$81$	8.17860			0.908734
$82$			3.20196i			0.353597i
$83$	12.6626			1.38990			0.694952	−	0.719056i	$-0.255426\pi$
$83$	12.6626			1.38990			0.694952	+	0.719056i	$0.255426\pi$
$84$			0.329755i			0.0359792i
$85$	10.0465	+	5.91515i	1.08970	+	0.641588i
$86$			11.4865i			1.23863i
$87$			1.81210i			0.194277i
$88$			0.403887i			0.0430545i
$89$			6.99770i			0.741755i	0.928682	+	0.370877i	$0.120943\pi$
$89$			6.99770i			0.741755i	−0.928682	+	0.370877i	$0.879057\pi$
$90$	3.29890	−	5.60299i	0.347734	−	0.590607i
$91$		0			0
$92$		−	1.76217i		−	0.183719i
$93$	1.59525			0.165420
$94$	−11.5048			−1.18663
$95$	−1.62728	−	0.958100i	−0.166955	−	0.0982989i
$96$			0.303663i			0.0309924i
$97$	9.47384			0.961923			0.480961	−	0.876742i	$-0.340288\pi$
$97$	9.47384			0.961923			0.480961	+	0.876742i	$0.340288\pi$
$98$	−5.82076			−0.587986
$99$			1.17442i			0.118034i
$100$	−2.42580	−	4.37213i	−0.242580	−	0.437213i
$101$	−6.61025			−0.657744			−0.328872	−	0.944374i	$-0.606669\pi$
$101$	−6.61025			−0.657744			−0.328872	+	0.944374i	$0.606669\pi$
$102$	−1.58326			−0.156766
$103$			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
$106$		−	10.7632i		−	1.04542i
$107$			6.97470i			0.674270i	0.941456	+	0.337135i	$0.109458\pi$
$107$			6.97470i			0.674270i	−0.941456	+	0.337135i	$0.890542\pi$
$108$			1.79397i			0.172625i
$109$		−	3.29363i		−	0.315473i	−0.987481	−	0.157736i	$-0.949580\pi$
$109$		−	3.29363i		−	0.315473i	0.987481	−	0.157736i	$-0.0504196\pi$
$110$	0.778246	+	0.458212i	0.0742029	+	0.0436888i
$111$			1.34316i			0.127487i
$112$	1.08593			0.102610
$113$			10.0934i			0.949508i	0.880119	+	0.474754i	$0.157463\pi$
$113$			10.0934i			0.949508i	−0.880119	+	0.474754i	$0.842537\pi$
$114$	0.256446			0.0240184
$115$	−3.39551	−	1.99919i	−0.316633	−	0.186425i
$116$	5.96747			0.554066
$117$		0			0
$118$		−	7.28501i		−	0.670640i
$119$			5.66187i			0.519023i
$120$	0.585124	+	0.344506i	0.0534143	+	0.0314490i
$121$	10.8369			0.985170
$122$	−2.64135			−0.239137
$123$	−0.972316			−0.0876708
$124$		−	5.25338i		−	0.471767i
$125$	−11.1767	−	0.285938i	−0.999673	−	0.0255751i
$126$	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	$-0.0867963\pi$
$128$	1.00000			0.0883883
$129$	−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	$0.492563\pi$
$132$	−0.122645			−0.0106749
$133$		−	0.917075i		−	0.0795205i
$134$	10.5992			0.915636
$135$	3.45679	+	2.03527i	0.297513	+	0.175168i
$136$			5.21387i			0.447085i
$137$	11.9809			1.02360			0.511799	−	0.859105i	$-0.328979\pi$
$137$	11.9809			1.02360			0.511799	+	0.859105i	$0.328979\pi$
$138$	0.535105			0.0455512
$139$	−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
$141$		−	3.49357i		−	0.294211i
$142$		−	12.4325i		−	1.04331i
$143$		0			0
$144$	2.90779			0.242316
$145$	6.77011	−	11.4987i	0.562227	−	0.954911i
$146$	−2.92837			−0.242354
$147$		−	1.76755i		−	0.145785i
$148$	4.42321			0.363586
$149$			17.5424i			1.43713i	0.695460	+	0.718565i	$0.255201\pi$
$149$			17.5424i			1.43713i	−0.695460	+	0.718565i	$0.744799\pi$
$150$	1.32765	−	0.736626i	0.108402	−	0.0601452i
$151$		−	17.5381i		−	1.42723i	−0.700538	−	0.713615i	$-0.747057\pi$
$151$		−	17.5381i		−	1.42723i	0.700538	−	0.713615i	$-0.252943\pi$
$152$		−	0.844510i		−	0.0684988i
$153$			15.1608i			1.22568i
$154$			0.438592i			0.0353427i
$155$	−10.1227	−	5.95997i	−0.813073	−	0.478717i
$156$		0			0
$157$			10.5663i			0.843279i	0.906764	+	0.421639i	$0.138545\pi$
$157$			10.5663i			0.843279i	−0.906764	+	0.421639i	$0.861455\pi$
$158$	−15.8880			−1.26398
$159$	3.26839			0.259200
$160$	1.13450	−	1.92689i	0.0896904	−	0.152334i
$161$		−	1.91359i		−	0.150812i
$162$	8.17860			0.642572
$163$	−19.0637			−1.49318			−0.746592	−	0.665282i	$-0.768311\pi$
$163$	−19.0637			−1.49318			−0.746592	+	0.665282i	$0.768311\pi$
$164$			3.20196i			0.250031i
$165$	−0.139142	+	0.236324i	−0.0108322	+	0.0183978i
$166$	12.6626			0.982811
$167$	−10.6825			−0.826637			−0.413319	−	0.910587i	$-0.635630\pi$
$167$	−10.6825			−0.826637			−0.413319	+	0.910587i	$0.635630\pi$
$168$			0.329755i			0.0254412i
$169$		0			0
$170$	10.0465	+	5.91515i	0.770535	+	0.453671i
$171$		−	2.45566i		−	0.187789i
$172$			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	$0.793428\pi$
$174$			1.81210i			0.137375i
$175$	−2.63424	−	4.74780i	−0.199130	−	0.358900i
$176$			0.403887i			0.0304442i
$177$	2.21219			0.166278
$178$			6.99770i			0.524500i
$179$	−25.2779			−1.88936			−0.944680	−	0.327995i	$-0.893627\pi$
$179$	−25.2779			−1.88936			−0.944680	+	0.327995i	$0.893627\pi$
$180$	3.29890	−	5.60299i	0.245885	−	0.417622i
$181$	−17.8082			−1.32367			−0.661837	−	0.749648i	$-0.730223\pi$
$181$	−17.8082			−1.32367			−0.661837	+	0.749648i	$0.730223\pi$
$182$		0			0
$183$		−	0.802079i		−	0.0592914i
$184$		−	1.76217i		−	0.129909i
$185$	5.01815	−	8.52303i	0.368942	−	0.626626i
$186$	1.59525			0.116970
$187$	−2.10581			−0.153992
$188$	−11.5048			−0.839071
$189$			1.94812i			0.141705i
$190$	−1.62728	−	0.958100i	−0.118055	−	0.0695078i
$191$	−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
$193$	14.6561			1.05497			0.527483	−	0.849565i	$-0.323136\pi$
$193$	14.6561			1.05497			0.527483	+	0.849565i	$0.323136\pi$
$194$	9.47384			0.680182
$195$		0			0
$196$	−5.82076			−0.415769
$197$	−10.3360			−0.736406			−0.368203	−	0.929745i	$-0.620027\pi$
$197$	−10.3360			−0.736406			−0.368203	+	0.929745i	$0.620027\pi$
$198$			1.17442i			0.0834623i
$199$	5.21516			0.369693			0.184846	−	0.982767i	$-0.440821\pi$
$199$	5.21516			0.369693			0.184846	+	0.982767i	$0.440821\pi$
$200$	−2.42580	−	4.37213i	−0.171530	−	0.309156i
$201$			3.21860i			0.227022i
$202$	−6.61025			−0.465096
$203$	6.48023			0.454823
$204$	−1.58326			−0.110850
$205$	6.16982	+	3.63264i	0.430919	+	0.253714i
$206$			9.21082i			0.641748i
$207$		−	5.12402i		−	0.356144i
$208$		0			0
$209$	0.341087			0.0235935
$210$	0.635402	+	0.374108i	0.0438469	+	0.0258159i
$211$	−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
$213$	3.77528			0.258678
$214$			6.97470i			0.476781i
$215$	22.1333	+	13.0315i	1.50948	+	0.888742i
$216$			1.79397i			0.122065i
$217$		−	5.70478i		−	0.387266i
$218$		−	3.29363i		−	0.223073i
$219$		−	0.889236i		−	0.0600890i
$220$	0.778246	+	0.458212i	0.0524693	+	0.0308926i
$221$		0			0
$222$			1.34316i			0.0901472i
$223$	−9.35143			−0.626218			−0.313109	−	0.949717i	$-0.601371\pi$
$223$	−9.35143			−0.626218			−0.313109	+	0.949717i	$0.601371\pi$
$224$	1.08593			0.0725565
$225$	−7.05372	−	12.7132i	−0.470248	−	0.847548i
$226$			10.0934i			0.671403i
$227$	−13.1715			−0.874224			−0.437112	−	0.899407i	$-0.643999\pi$
$227$	−13.1715			−0.874224			−0.437112	+	0.899407i	$0.643999\pi$
$228$	0.256446			0.0169836
$229$		−	13.6752i		−	0.903680i	−0.892099	−	0.451840i	$-0.850768\pi$
$229$		−	13.6752i		−	0.903680i	0.892099	−	0.451840i	$-0.149232\pi$
$230$	−3.39551	−	1.99919i	−0.223893	−	0.131823i
$231$	−0.133184			−0.00876286
$232$	5.96747			0.391784
$233$			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
$236$		−	7.28501i		−	0.474214i
$237$		−	4.82460i		−	0.313392i
$238$			5.66187i			0.367005i
$239$			17.7552i			1.14849i	0.818685	+	0.574243i	$0.194703\pi$
$239$			17.7552i			1.14849i	−0.818685	+	0.574243i	$0.805297\pi$
$240$	0.585124	+	0.344506i	0.0377696	+	0.0222378i
$241$			3.83937i			0.247316i	0.992325	+	0.123658i	$0.0394625\pi$
$241$			3.83937i			0.247316i	−0.992325	+	0.123658i	$0.960537\pi$
$242$	10.8369			0.696621
$243$			7.86546i			0.504569i
$244$	−2.64135			−0.169095
$245$	−6.60368	+	11.2160i	−0.421894	+	0.716562i
$246$	−0.972316			−0.0619926
$247$		0			0
$248$		−	5.25338i		−	0.333590i
$249$			3.84517i			0.243678i
$250$	−11.1767	−	0.285938i	−0.706875	−	0.0180843i
$251$	−14.4338			−0.911054			−0.455527	−	0.890222i	$-0.650549\pi$
$251$	−14.4338			−0.911054			−0.455527	+	0.890222i	$0.650549\pi$
$252$	3.15764			0.198913
$253$	0.711719			0.0447454
$254$		−	6.06998i		−	0.380865i
$255$	−1.79621	+	3.05076i	−0.112483	+	0.191046i
$256$	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	$-0.112268\pi$
$258$	−3.48803			−0.217155
$259$	4.80328			0.298461
$260$		0			0
$261$	17.3521			1.07407
$262$	0.534787			0.0330393
$263$		−	1.74154i		−	0.107388i	−0.998557	−	0.0536941i	$-0.982900\pi$
$263$		−	1.74154i		−	0.107388i	0.998557	−	0.0536941i	$-0.0170996\pi$
$264$	−0.122645			−0.00754831
$265$	−20.7395	−	12.2109i	−1.27402	−	0.750110i
$266$		−	0.917075i		−	0.0562295i
$267$	−2.12494			−0.130044
$268$	10.5992			0.647452
$269$	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
$271$		−	10.3097i		−	0.626271i	−0.949708	−	0.313136i	$-0.898621\pi$
$271$		−	10.3097i		−	0.626271i	0.949708	−	0.313136i	$-0.101379\pi$
$272$			5.21387i			0.316137i
$273$		0			0
$274$	11.9809			0.723794
$275$	1.76585	−	0.979751i	0.106485	−	0.0590812i
$276$	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	$-0.352985\pi$
$278$	−2.69002			−0.161337
$279$		−	15.2757i		−	0.914533i
$280$	1.23199	−	2.09246i	0.0736253	−	0.125048i
$281$		−	17.5437i		−	1.04657i	−0.852158	−	0.523285i	$-0.824706\pi$
$281$		−	17.5437i		−	1.04657i	0.852158	−	0.523285i	$-0.175294\pi$
$282$		−	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	$0.719913\pi$
$284$		−	12.4325i		−	0.737732i
$285$	0.290939	−	0.494143i	0.0172337	−	0.0292705i
$286$		0			0
$287$			3.47709i			0.205246i
$288$	2.90779			0.171343
$289$	−10.1844			−0.599083
$290$	6.77011	−	11.4987i	0.397555	−	0.675224i
$291$			2.87685i			0.168644i
$292$	−2.92837			−0.171370
$293$	−26.1627			−1.52844			−0.764221	−	0.644954i	$-0.776876\pi$
$293$	−26.1627			−1.52844			−0.764221	+	0.644954i	$0.776876\pi$
$294$		−	1.76755i		−	0.103086i
$295$	−14.0374	−	8.26487i	−0.817290	−	0.481199i
$296$	4.42321			0.257094
$297$	−0.724564			−0.0420434
$298$			17.5424i			1.01620i
$299$		0			0
$300$	1.32765	−	0.736626i	0.0766520	−	0.0425291i
$301$			12.4735i			0.718962i
$302$		−	17.5381i		−	1.00920i
$303$		−	2.00729i		−	0.115316i
$304$		−	0.844510i		−	0.0484360i
$305$	−2.99662	+	5.08959i	−0.171586	+	0.291429i
$306$			15.1608i			0.866687i
$307$	2.68863			0.153448			0.0767240	−	0.997052i	$-0.475554\pi$
$307$	2.68863			0.153448			0.0767240	+	0.997052i	$0.475554\pi$
$308$			0.438592i			0.0249911i
$309$	−2.79698			−0.159115
$310$	−10.1227	−	5.95997i	−0.574929	−	0.338504i
$311$	31.0278			1.75943			0.879713	−	0.475506i	$-0.157735\pi$
$311$	31.0278			1.75943			0.879713	+	0.475506i	$0.157735\pi$
$312$		0			0
$313$		−	14.7399i		−	0.833151i	−0.909101	−	0.416575i	$-0.863230\pi$
$313$		−	14.7399i		−	0.833151i	0.909101	−	0.416575i	$-0.136770\pi$
$314$			10.5663i			0.596288i
$315$	3.58236	−	6.08443i	0.201843	−	0.342819i
$316$	−15.8880			−0.893772
$317$	−14.7416			−0.827971			−0.413985	−	0.910284i	$-0.635864\pi$
$317$	−14.7416			−0.827971			−0.413985	+	0.910284i	$0.635864\pi$
$318$	3.26839			0.183282
$319$			2.41019i			0.134944i
$320$	1.13450	−	1.92689i	0.0634207	−	0.107716i
$321$	−2.11796			−0.118213
$322$		−	1.91359i		−	0.106640i
$323$	4.40316			0.244999
$324$	8.17860			0.454367
$325$		0			0
$326$	−19.0637			−1.05584
$327$	1.00015			0.0553086
$328$			3.20196i			0.176799i
$329$	−12.4933			−0.688779
$330$	−0.139142	+	0.236324i	−0.00765950	+	0.0130092i
$331$		−	9.55973i		−	0.525450i	−0.964871	−	0.262725i	$-0.915379\pi$
$331$		−	9.55973i		−	0.525450i	0.964871	−	0.262725i	$-0.0846212\pi$
$332$	12.6626			0.694952
$333$	12.8618			0.704820
$334$	−10.6825			−0.584521
$335$	12.0249	−	20.4236i	0.656990	−	1.11586i
$336$			0.329755i			0.0179896i
$337$		−	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
$340$	10.0465	+	5.91515i	0.544850	+	0.320794i
$341$	2.12177			0.114900
$342$		−	2.45566i		−	0.132787i
$343$	−13.9224			−0.751739
$344$			11.4865i			0.619313i
$345$	0.607079	−	1.03109i	0.0326840	−	0.0555120i
$346$			15.8983i			0.854697i
$347$		−	8.88467i		−	0.476954i	−0.971148	−	0.238477i	$-0.923352\pi$
$347$		−	8.88467i		−	0.476954i	0.971148	−	0.238477i	$-0.0766482\pi$
$348$			1.81210i			0.0971386i
$349$			22.3237i			1.19496i	0.801884	+	0.597480i	$0.203831\pi$
$349$			22.3237i			1.19496i	−0.801884	+	0.597480i	$0.796169\pi$
$350$	−2.63424	−	4.74780i	−0.140806	−	0.253781i
$351$		0			0
$352$			0.403887i			0.0215273i
$353$	−31.0186			−1.65095			−0.825476	−	0.564438i	$-0.809093\pi$
$353$	−31.0186			−1.65095			−0.825476	+	0.564438i	$0.809093\pi$
$354$	2.21219			0.117576
$355$	−23.9560	−	14.1047i	−1.27145	−	0.748599i
$356$			6.99770i			0.370877i
$357$	−1.71930			−0.0909950
$358$	−25.2779			−1.33598
$359$			15.1402i			0.799072i	0.916718	+	0.399536i	$0.130829\pi$
$359$			15.1402i			0.799072i	−0.916718	+	0.399536i	$0.869171\pi$
$360$	3.29890	−	5.60299i	0.173867	−	0.295303i
$361$	18.2868			0.962463
$362$	−17.8082			−0.935979
$363$			3.29075i			0.172720i
$364$		0			0
$365$	−3.32224	+	5.64264i	−0.173894	+	0.295349i
$366$		−	0.802079i		−	0.0419253i
$367$		−	20.8201i		−	1.08680i	−0.839474	−	0.543401i	$-0.817137\pi$
$367$		−	20.8201i		−	1.08680i	0.839474	−	0.543401i	$-0.182863\pi$
$368$		−	1.76217i		−	0.0918595i
$369$			9.31063i			0.484692i
$370$	5.01815	−	8.52303i	0.260881	−	0.443091i
$371$		−	11.6881i		−	0.606814i
$372$	1.59525			0.0827100
$373$		−	0.901633i		−	0.0466848i	−0.999728	−	0.0233424i	$-0.992569\pi$
$373$		−	0.901633i		−	0.0466848i	0.999728	−	0.0233424i	$-0.00743079\pi$
$374$	−2.10581			−0.108889
$375$	0.0868286	−	3.39394i	0.00448381	−	0.175262i
$376$	−11.5048			−0.593313
$377$		0			0
$378$			1.94812i			0.100201i
$379$			15.7125i			0.807096i	0.914959	+	0.403548i	$0.132223\pi$
$379$			15.7125i			0.807096i	−0.914959	+	0.403548i	$0.867777\pi$
$380$	−1.62728	−	0.958100i	−0.0834775	−	0.0491495i
$381$	1.84323			0.0944314
$382$	−10.4612			−0.535242
$383$	−38.0352			−1.94351			−0.971755	−	0.235993i	$-0.924166\pi$
$383$	−38.0352			−1.94351			−0.971755	+	0.235993i	$0.924166\pi$
$384$			0.303663i			0.0154962i
$385$	0.845118	+	0.497584i	0.0430712	+	0.0253592i
$386$	14.6561			0.745974
$387$			33.4004i			1.69784i
$388$	9.47384			0.480961
$389$	3.64514			0.184816			0.0924079	−	0.995721i	$-0.470544\pi$
$389$	3.64514			0.184816			0.0924079	+	0.995721i	$0.470544\pi$
$390$		0			0
$391$	9.18773			0.464643
$392$	−5.82076			−0.293993
$393$			0.162395i			0.00819173i
$394$	−10.3360			−0.520718
$395$	−18.0250	+	30.6145i	−0.906938	+	1.54038i
$396$			1.17442i			0.0590168i
$397$	−1.08366			−0.0543872			−0.0271936	−	0.999630i	$-0.508657\pi$
$397$	−1.08366			−0.0543872			−0.0271936	+	0.999630i	$0.508657\pi$
$398$	5.21516			0.261412
$399$	0.278481			0.0139415
$400$	−2.42580	−	4.37213i	−0.121290	−	0.218606i
$401$		−	6.16953i		−	0.308091i	−0.988064	−	0.154046i	$-0.950770\pi$
$401$		−	6.16953i		−	0.308091i	0.988064	−	0.154046i	$-0.0492303\pi$
$402$			3.21860i			0.160529i
$403$		0			0
$404$	−6.61025			−0.328872
$405$	9.27866	−	15.7593i	0.461060	−	0.783084i
$406$	6.48023			0.321608
$407$			1.78648i			0.0885524i
$408$	−1.58326			−0.0783829
$409$			19.8455i			0.981299i	0.871357	+	0.490649i	$0.163240\pi$
$409$			19.8455i			0.981299i	−0.871357	+	0.490649i	$0.836760\pi$
$410$	6.16982	+	3.63264i	0.304706	+	0.179403i
$411$			3.63816i			0.179457i
$412$			9.21082i			0.453784i
$413$		−	7.91099i		−	0.389274i
$414$		−	5.12402i		−	0.251832i
$415$	14.3658	−	24.3995i	0.705189	−	1.19772i
$416$		0			0
$417$		−	0.816859i		−	0.0400018i
$418$	0.341087			0.0166831
$419$	−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
$421$		−	16.7557i		−	0.816624i	−0.912842	−	0.408312i	$-0.866118\pi$
$421$		−	16.7557i		−	0.816624i	0.912842	−	0.408312i	$-0.133882\pi$
$422$	−12.3086			−0.599175
$423$	−33.4534			−1.62656
$424$		−	10.7632i		−	0.522708i
$425$	22.7957	−	12.6478i	1.10575	−	0.613509i
$426$	3.77528			0.182913
$427$	−2.86831			−0.138807
$428$			6.97470i			0.337135i
$429$		0			0
$430$	22.1333	+	13.0315i	1.06736	+	0.628436i
$431$			17.3440i			0.835433i	0.908577	+	0.417717i	$0.137170\pi$
$431$			17.3440i			0.835433i	−0.908577	+	0.417717i	$0.862830\pi$
$432$			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	$-0.0338521\pi$
$434$		−	5.70478i		−	0.273838i
$435$	3.49171	+	2.05583i	0.167415	+	0.0985695i
$436$		−	3.29363i		−	0.157736i
$437$	−1.48817			−0.0711889
$438$		−	0.889236i		−	0.0424893i
$439$	33.1534			1.58232			0.791162	−	0.611607i	$-0.209477\pi$
$439$	33.1534			1.58232			0.791162	+	0.611607i	$0.209477\pi$
$440$	0.778246	+	0.458212i	0.0371014	+	0.0218444i
$441$	−16.9256			−0.805979
$442$		0			0
$443$		−	19.2632i		−	0.915224i	−0.889152	−	0.457612i	$-0.848705\pi$
$443$		−	19.2632i		−	0.915224i	0.889152	−	0.457612i	$-0.151295\pi$
$444$			1.34316i			0.0637437i
$445$	13.4838	+	7.93892i	0.639193	+	0.376341i
$446$	−9.35143			−0.442803
$447$	−5.32697			−0.251957
$448$	1.08593			0.0513052
$449$			4.55734i			0.215074i	0.994201	+	0.107537i	$0.0342965\pi$
$449$			4.55734i			0.215074i	−0.994201	+	0.107537i	$0.965704\pi$
$450$	−7.05372	−	12.7132i	−0.332516	−	0.599307i
$451$	−1.29323			−0.0608959
$452$			10.0934i			0.474754i
$453$	5.32566			0.250222
$454$	−13.1715			−0.618170
$455$		0			0
$456$	0.256446			0.0120092
$457$	15.9598			0.746570			0.373285	−	0.927717i	$-0.378231\pi$
$457$	15.9598			0.746570			0.373285	+	0.927717i	$0.378231\pi$
$458$		−	13.6752i		−	0.638998i
$459$	−9.35354			−0.436586
$460$	−3.39551	−	1.99919i	−0.158316	−	0.0932127i
$461$			22.2437i			1.03599i	0.855383	+	0.517996i	$0.173322\pi$
$461$			22.2437i			1.03599i	−0.855383	+	0.517996i	$0.826678\pi$
$462$	−0.133184			−0.00619628
$463$	31.0149			1.44138			0.720692	−	0.693256i	$-0.243824\pi$
$463$	31.0149			1.44138			0.720692	+	0.693256i	$0.243824\pi$
$464$	5.96747			0.277033
$465$	1.80982	−	3.07388i	0.0839284	−	0.142548i
$466$			27.7357i			1.28483i
$467$		−	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
$470$	−13.0522	+	22.1684i	−0.602053	+	1.02255i
$471$	−3.20858			−0.147843
$472$		−	7.28501i		−	0.335320i
$473$	−4.63927			−0.213314
$474$		−	4.82460i		−	0.221601i
$475$	−3.69230	+	2.04861i	−0.169414	+	0.0939969i
$476$			5.66187i			0.259512i
$477$		−	31.2972i		−	1.43300i
$478$			17.7552i			0.812102i
$479$			7.63429i			0.348819i	0.984673	+	0.174410i	$0.0558017\pi$
$479$			7.63429i			0.348819i	−0.984673	+	0.174410i	$0.944198\pi$
$480$	0.585124	+	0.344506i	0.0267071	+	0.0157245i
$481$		0			0
$482$			3.83937i			0.174879i
$483$	0.581085			0.0264403
$484$	10.8369			0.492585
$485$	10.7481	−	18.2550i	0.488046	−	0.828919i
$486$			7.86546i			0.356784i
$487$	−23.2958			−1.05563			−0.527817	−	0.849358i	$-0.676989\pi$
$487$	−23.2958			−1.05563			−0.527817	+	0.849358i	$0.676989\pi$
$488$	−2.64135			−0.119568
$489$		−	5.78893i		−	0.261784i
$490$	−6.60368	+	11.2160i	−0.298324	+	0.506686i
$491$	−36.2972			−1.63807			−0.819034	−	0.573745i	$-0.805490\pi$
$491$	−36.2972			−1.63807			−0.819034	+	0.573745i	$0.805490\pi$
$492$	−0.972316			−0.0438354
$493$			31.1136i			1.40129i
$494$		0			0
$495$	2.26298	+	1.33238i	0.101713	+	0.0598862i
$496$		−	5.25338i		−	0.235884i
$497$		−	13.5008i		−	0.605591i
$498$			3.84517i			0.172306i
$499$		−	18.9398i		−	0.847863i	−0.905694	−	0.423932i	$-0.860650\pi$
$499$		−	18.9398i		−	0.847863i	0.905694	−	0.423932i	$-0.139350\pi$
$500$	−11.1767	−	0.285938i	−0.499836	−	0.0127875i
$501$		−	3.24388i		−	0.144926i
$502$	−14.4338			−0.644213
$503$			35.7640i			1.59464i	0.603560	+	0.797318i	$0.293749\pi$
$503$			35.7640i			1.59464i	−0.603560	+	0.797318i	$0.706251\pi$
$504$	3.15764			0.140653
$505$	−7.49935	+	12.7372i	−0.333717	+	0.566799i
$506$	0.711719			0.0316398
$507$		0			0
$508$		−	6.06998i		−	0.269312i
$509$		−	3.11873i		−	0.138235i	−0.997609	−	0.0691176i	$-0.977982\pi$
$509$		−	3.11873i		−	0.138235i	0.997609	−	0.0691176i	$-0.0220184\pi$
$510$	−1.79621	+	3.05076i	−0.0795375	+	0.135090i
$511$	−3.17999			−0.140675
$512$	1.00000			0.0441942
$513$	1.51503			0.0668902
$514$		−	11.0755i		−	0.488517i
$515$	17.7482	+	10.4497i	0.782080	+	0.460469i
$516$	−3.48803			−0.153552
$517$		−	4.64663i		−	0.204359i
$518$	4.80328			0.211044
$519$	−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	$0.181470\pi$
$522$	17.3521			0.759483
$523$			23.8519i			1.04297i	0.853260	+	0.521485i	$0.174622\pi$
$523$			23.8519i			1.04297i	−0.853260	+	0.521485i	$0.825378\pi$
$524$	0.534787			0.0233623
$525$	1.44173	−	0.799921i	0.0629223	−	0.0349114i
$526$		−	1.74154i		−	0.0759349i
$527$	27.3904			1.19314
$528$	−0.122645			−0.00533746
$529$	19.8948			0.864989
$530$	−20.7395	−	12.2109i	−0.900867	−	0.530408i
$531$		−	21.1833i		−	0.919276i
$532$		−	0.917075i		−	0.0397603i
$533$		0			0
$534$	−2.12494			−0.0919551
$535$	13.4395	+	7.91283i	0.581040	+	0.342101i
$536$	10.5992			0.457818
$537$		−	7.67595i		−	0.331242i
$538$	10.0411			0.432905
$539$		−	2.35093i		−	0.101262i
$540$	3.45679	+	2.03527i	0.148757	+	0.0875841i
$541$		−	5.36874i		−	0.230820i	−0.993318	−	0.115410i	$-0.963182\pi$
$541$		−	5.36874i		−	0.230820i	0.993318	−	0.115410i	$-0.0368182\pi$
$542$		−	10.3097i		−	0.442841i
$543$		−	5.40769i		−	0.232066i
$544$			5.21387i			0.223543i
$545$	−6.34647	−	3.73664i	−0.271853	−	0.160060i
$546$		0			0
$547$			28.1689i			1.20442i	0.798339	+	0.602208i	$0.205712\pi$
$547$			28.1689i			1.20442i	−0.798339	+	0.602208i	$0.794288\pi$
$548$	11.9809			0.511799
$549$	−7.68049			−0.327795
$550$	1.76585	−	0.979751i	0.0752959	−	0.0417767i
$551$		−	5.03959i		−	0.214694i
$552$	0.535105			0.0227756
$553$	−17.2532			−0.733682
$554$		−	29.7990i		−	1.26604i
$555$	2.58813	+	1.52382i	0.109860	+	0.0646827i
$556$	−2.69002			−0.114082
$557$	−15.1505			−0.641947			−0.320974	−	0.947088i	$-0.604010\pi$
$557$	−15.1505			−0.641947			−0.320974	+	0.947088i	$0.604010\pi$
$558$		−	15.2757i		−	0.646672i
$559$		0			0
$560$	1.23199	−	2.09246i	0.0520610	−	0.0884225i
$561$		−	0.639457i		−	0.0269979i
$562$		−	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	$0.759042\pi$
$564$		−	3.49357i		−	0.147106i
$565$	19.4489	+	11.4510i	0.818220	+	0.481747i
$566$			25.9299i			1.08992i
$567$	8.88136			0.372982
$568$		−	12.4325i		−	0.521655i
$569$	21.7554			0.912033			0.456016	−	0.889971i	$-0.349276\pi$
$569$	21.7554			0.912033			0.456016	+	0.889971i	$0.349276\pi$
$570$	0.290939	−	0.494143i	0.0121861	−	0.0206974i
$571$	24.2853			1.01631			0.508155	−	0.861266i	$-0.330328\pi$
$571$	24.2853			1.01631			0.508155	+	0.861266i	$0.330328\pi$
$572$		0			0
$573$		−	3.17668i		−	0.132708i
$574$			3.47709i			0.145131i
$575$	−7.70443	+	4.27468i	−0.321297	+	0.178266i
$576$	2.90779			0.121158
$577$	23.1332			0.963048			0.481524	−	0.876433i	$-0.340083\pi$
$577$	23.1332			0.963048			0.481524	+	0.876433i	$0.340083\pi$
$578$	−10.1844			−0.423616
$579$			4.45050i			0.184956i
$580$	6.77011	−	11.4987i	0.281114	−	0.477455i
$581$	13.7507			0.570474
$582$			2.87685i			0.119249i
$583$	4.34713			0.180040
$584$	−2.92837			−0.121177
$585$		0			0
$586$	−26.1627			−1.08077
$587$	−4.60818			−0.190200			−0.0950999	−	0.995468i	$-0.530317\pi$
$587$	−4.60818			−0.190200			−0.0950999	+	0.995468i	$0.530317\pi$
$588$		−	1.76755i		−	0.0728925i
$589$	−4.43653			−0.182804
$590$	−14.0374	−	8.26487i	−0.577911	−	0.340259i
$591$		−	3.13864i		−	0.129106i
$592$	4.42321			0.181793
$593$	1.27629			0.0524111			0.0262056	−	0.999657i	$-0.491658\pi$
$593$	1.27629			0.0524111			0.0262056	+	0.999657i	$0.491658\pi$
$594$	−0.724564			−0.0297292
$595$	10.9098	+	6.42342i	0.447258	+	0.263334i
$596$			17.5424i			0.718565i
$597$			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	$0.643693\pi$
$600$	1.32765	−	0.736626i	0.0542011	−	0.0300726i
$601$	−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
$603$	30.8204			1.25510
$604$		−	17.5381i		−	0.713615i
$605$	12.2945	−	20.8815i	0.499841	−	0.848952i
$606$		−	2.00729i		−	0.0815404i
$607$			22.9135i			0.930030i	0.885303	+	0.465015i	$0.153951\pi$
$607$			22.9135i			0.930030i	−0.885303	+	0.465015i	$0.846049\pi$
$608$		−	0.844510i		−	0.0342494i
$609$			1.96780i			0.0797394i
$610$	−2.99662	+	5.08959i	−0.121330	+	0.206071i
$611$		0			0
$612$			15.1608i			0.612840i
$613$	−16.5575			−0.668752			−0.334376	−	0.942440i	$-0.608526\pi$
$613$	−16.5575			−0.668752			−0.334376	+	0.942440i	$0.608526\pi$
$614$	2.68863			0.108504
$615$	−1.10310	+	1.87354i	−0.0444811	+	0.0755486i
$616$			0.438592i			0.0176714i
$617$	11.3693			0.457712			0.228856	−	0.973460i	$-0.426502\pi$
$617$	11.3693			0.457712			0.228856	+	0.973460i	$0.426502\pi$
$618$	−2.79698			−0.112511
$619$			47.1109i			1.89355i	0.321901	+	0.946773i	$0.395678\pi$
$619$			47.1109i			1.89355i	−0.321901	+	0.946773i	$0.604322\pi$
$620$	−10.1227	−	5.95997i	−0.406536	−	0.239358i
$621$	3.16129			0.126858
$622$	31.0278			1.24410
$623$			7.59898i			0.304447i
$624$		0			0
$625$	−13.2310	+	21.2118i	−0.529238	+	0.848473i
$626$		−	14.7399i		−	0.589127i
$627$			0.103575i			0.00413640i
$628$			10.5663i			0.421639i
$629$			23.0620i			0.919543i
$630$	3.58236	−	6.08443i	0.142725	−	0.242409i
$631$		−	8.39389i		−	0.334156i	−0.985944	−	0.167078i	$-0.946567\pi$
$631$		−	8.39389i		−	0.334156i	0.985944	−	0.167078i	$-0.0534331\pi$
$632$	−15.8880			−0.631992
$633$		−	3.73767i		−	0.148559i
$634$	−14.7416			−0.585464
$635$	−11.6962	−	6.88642i	−0.464149	−	0.273279i
$636$	3.26839			0.129600
$637$		0			0
$638$			2.41019i			0.0954201i
$639$		−	36.1510i		−	1.43011i
$640$	1.13450	−	1.92689i	0.0448452	−	0.0761670i
$641$	36.5728			1.44454			0.722268	−	0.691613i	$-0.243099\pi$
$641$	36.5728			1.44454			0.722268	+	0.691613i	$0.243099\pi$
$642$	−2.11796			−0.0835891
$643$	46.0372			1.81553			0.907766	−	0.419478i	$-0.137787\pi$
$643$	46.0372			1.81553			0.907766	+	0.419478i	$0.137787\pi$
$644$		−	1.91359i		−	0.0754059i
$645$	−3.95719	+	6.72105i	−0.155814	+	0.264641i
$646$	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	$-0.184437\pi$
$648$	8.17860			0.321286
$649$	2.94232			0.115496
$650$		0			0
$651$	1.73233			0.0678953
$652$	−19.0637			−0.746592
$653$		−	4.98456i		−	0.195061i	−0.995233	−	0.0975304i	$-0.968906\pi$
$653$		−	4.98456i		−	0.195061i	0.995233	−	0.0975304i	$-0.0310943\pi$
$654$	1.00015			0.0391091
$655$	0.606718	−	1.03048i	0.0237064	−	0.0402640i
$656$			3.20196i			0.125016i
$657$	−8.51508			−0.332205
$658$	−12.4933			−0.487040
$659$	−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
$661$		−	37.9173i		−	1.47481i	−0.675450	−	0.737406i	$-0.736051\pi$
$661$		−	37.9173i		−	1.47481i	0.675450	−	0.737406i	$-0.263949\pi$
$662$		−	9.55973i		−	0.371549i
$663$		0			0
$664$	12.6626			0.491405
$665$	−1.76710	−	1.04043i	−0.0685253	−	0.0403460i
$666$	12.8618			0.498383
$667$		−	10.5157i		−	0.407170i
$668$	−10.6825			−0.413319
$669$		−	2.83968i		−	0.109788i
$670$	12.0249	−	20.4236i	0.464562	−	0.789032i
$671$		−	1.06681i		−	0.0411837i
$672$			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	$-0.0312364\pi$
$674$		−	7.58566i		−	0.292189i
$675$	7.84348	−	4.35183i	0.301896	−	0.167502i
$676$		0			0
$677$		−	40.3815i		−	1.55199i	−0.630740	−	0.775994i	$-0.717249\pi$
$677$		−	40.3815i		−	1.55199i	0.630740	−	0.775994i	$-0.282751\pi$
$678$	−3.06499			−0.117710
$679$	10.2879			0.394813
$680$	10.0465	+	5.91515i	0.385267	+	0.226836i
$681$		−	3.99970i		−	0.153269i
$682$	2.12177			0.0812468
$683$	14.8432			0.567959			0.283980	−	0.958830i	$-0.408345\pi$
$683$	14.8432			0.567959			0.283980	+	0.958830i	$0.408345\pi$
$684$		−	2.45566i		−	0.0938944i
$685$	13.5924	−	23.0859i	0.519339	−	0.882067i
$686$	−13.9224			−0.531560
$687$	4.15264			0.158433
$688$			11.4865i			0.437920i
$689$		0			0
$690$	0.607079	−	1.03109i	0.0231111	−	0.0392529i
$691$			31.8114i			1.21016i	0.796164	+	0.605081i	$0.206859\pi$
$691$			31.8114i			1.21016i	−0.796164	+	0.605081i	$0.793141\pi$
$692$			15.8983i			0.604362i
$693$			1.27533i			0.0484459i
$694$		−	8.88467i		−	0.337257i
$695$	−3.05184	+	5.18338i	−0.115763	+	0.196617i
$696$			1.81210i			0.0686874i
$697$	−16.6946			−0.632353
$698$			22.3237i			0.844964i
$699$	−8.42230			−0.318561
$700$	−2.63424	−	4.74780i	−0.0995650	−	0.179450i
$701$	2.75131			0.103915			0.0519577	−	0.998649i	$-0.483454\pi$
$701$	2.75131			0.103915			0.0519577	+	0.998649i	$0.483454\pi$
$702$		0			0
$703$		−	3.73544i		−	0.140885i
$704$			0.403887i			0.0152221i
$705$	−6.73172	−	3.96346i	−0.253531	−	0.149273i
$706$	−31.0186			−1.16740
$707$	−7.17824			−0.269966
$708$	2.21219			0.0831390
$709$			28.7721i			1.08056i	0.841486	+	0.540279i	$0.181681\pi$
$709$			28.7721i			1.08056i	−0.841486	+	0.540279i	$0.818319\pi$
$710$	−23.9560	−	14.1047i	−0.899053	−	0.529340i
$711$	−46.1991			−1.73260
$712$			6.99770i			0.262250i
$713$	−9.25735			−0.346690
$714$	−1.71930			−0.0643432
$715$		0			0
$716$	−25.2779			−0.944680
$717$	−5.39158			−0.201352
$718$			15.1402i			0.565029i
$719$	33.1840			1.23756			0.618778	−	0.785566i	$-0.287628\pi$
$719$	33.1840			1.23756			0.618778	+	0.785566i	$0.287628\pi$
$720$	3.29890	−	5.60299i	0.122943	−	0.208811i
$721$			10.0023i			0.372504i
$722$	18.2868			0.680564
$723$	−1.16587			−0.0433593
$724$	−17.8082			−0.661837
$725$	−14.4759	−	26.0905i	−0.537622	−	0.968978i
$726$			3.29075i			0.122131i
$727$		−	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
$730$	−3.32224	+	5.64264i	−0.122962	+	0.208844i
$731$	−59.8893			−2.21509
$732$		−	0.802079i		−	0.0296457i
$733$	19.0778			0.704654			0.352327	−	0.935877i	$-0.385391\pi$
$733$	19.0778			0.704654			0.352327	+	0.935877i	$0.385391\pi$
$734$		−	20.8201i		−	0.768484i
$735$	−3.40587	−	2.00529i	−0.125627	−	0.0739662i
$736$		−	1.76217i		−	0.0649545i
$737$			4.28090i			0.157689i
$738$			9.31063i			0.342729i
$739$		−	40.5137i		−	1.49032i	−0.666886	−	0.745160i	$-0.732373\pi$
$739$		−	40.5137i		−	1.49032i	0.666886	−	0.745160i	$-0.267627\pi$
$740$	5.01815	−	8.52303i	0.184471	−	0.313313i
$741$		0			0
$742$		−	11.6881i		−	0.429082i
$743$	−11.8075			−0.433176			−0.216588	−	0.976263i	$-0.569493\pi$
$743$	−11.8075			−0.433176			−0.216588	+	0.976263i	$0.569493\pi$
$744$	1.59525			0.0584848
$745$	33.8023	+	19.9019i	1.23842	+	0.729150i
$746$		−	0.901633i		−	0.0330111i
$747$	36.8203			1.34718
$748$	−2.10581			−0.0769962
$749$			7.57401i			0.276748i
$750$	0.0868286	−	3.39394i	0.00317053	−	0.123929i
$751$	14.0149			0.511409			0.255705	−	0.966755i	$-0.417693\pi$
$751$	14.0149			0.511409			0.255705	+	0.966755i	$0.417693\pi$
$752$	−11.5048			−0.419536
$753$		−	4.38301i		−	0.159726i
$754$		0			0
$755$	−33.7940	−	19.8970i	−1.22989	−	0.724127i
$756$			1.94812i			0.0708526i
$757$			31.2552i			1.13599i	0.823032	+	0.567994i	$0.192280\pi$
$757$			31.2552i			1.13599i	−0.823032	+	0.567994i	$0.807720\pi$
$758$			15.7125i			0.570703i
$759$			0.216122i			0.00784474i
$760$	−1.62728	−	0.958100i	−0.0590275	−	0.0347539i
$761$		−	34.1575i		−	1.23821i	−0.785310	−	0.619103i	$-0.787496\pi$
$761$		−	34.1575i		−	1.23821i	0.785310	−	0.619103i	$-0.212504\pi$
$762$	1.84323			0.0667731
$763$		−	3.57664i		−	0.129483i
$764$	−10.4612			−0.378474
$765$	29.2132	+	17.2000i	1.05621	+	0.621868i
$766$	−38.0352			−1.37427
$767$		0			0
$768$			0.303663i			0.0109575i
$769$		−	44.2201i		−	1.59462i	−0.603572	−	0.797308i	$-0.706256\pi$
$769$		−	44.2201i		−	1.59462i	0.603572	−	0.797308i	$-0.293744\pi$
$770$	0.845118	+	0.497584i	0.0304559	+	0.0179317i
$771$	3.36320			0.121123
$772$	14.6561			0.527483
$773$	−2.04145			−0.0734259			−0.0367129	−	0.999326i	$-0.511689\pi$
$773$	−2.04145			−0.0734259			−0.0367129	+	0.999326i	$0.511689\pi$
$774$			33.4004i			1.20055i
$775$	−22.9684	+	12.7437i	−0.825050	+	0.457766i
$776$	9.47384			0.340091
$777$			1.45858i			0.0523261i
$778$	3.64514			0.130685
$779$	2.70409			0.0968840
$780$		0			0
$781$	5.02132			0.179677
$782$	9.18773			0.328552
$783$			10.7055i			0.382583i
$784$	−5.82076			−0.207884
$785$	20.3600	+	11.9875i	0.726680	+	0.427851i
$786$			0.162395i			0.00579243i
$787$	3.39520			0.121026			0.0605130	−	0.998167i	$-0.480726\pi$
$787$	3.39520			0.121026			0.0605130	+	0.998167i	$0.480726\pi$
$788$	−10.3360			−0.368203
$789$	0.528841			0.0188273
$790$	−18.0250	+	30.6145i	−0.641302	+	1.08921i
$791$			10.9607i			0.389717i
$792$			1.17442i			0.0417312i
$793$		0			0
$794$	−1.08366			−0.0384576
$795$	3.70800	−	6.29782i	0.131509	−	0.223361i
$796$	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	$0.857345\pi$
$798$	0.278481			0.00985814
$799$		−	59.9843i		−	2.12209i
$800$	−2.42580	−	4.37213i	−0.0857651	−	0.154578i
$801$			20.3478i			0.718955i
$802$		−	6.16953i		−	0.217854i
$803$		−	1.18273i		−	0.0417377i
$804$			3.21860i			0.113511i
$805$	−3.68727	−	2.17097i	−0.129959	−	0.0765167i
$806$		0			0
$807$			3.04912i			0.107334i
$808$	−6.61025			−0.232548
$809$	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
$811$		−	2.82931i		−	0.0993505i	−0.998765	−	0.0496753i	$-0.984181\pi$
$811$		−	2.82931i		−	0.0993505i	0.998765	−	0.0496753i	$-0.0158186\pi$
$812$	6.48023			0.227411
$813$	3.13068			0.109798
$814$			1.78648i			0.0626160i
$815$	−21.6278	+	36.7336i	−0.757590	+	1.28672i
$816$	−1.58326			−0.0554251
$817$	9.70050			0.339377
$818$			19.8455i			0.693883i
$819$		0			0
$820$	6.16982	+	3.63264i	0.215460	+	0.126857i
$821$		−	26.1300i		−	0.911942i	−0.889995	−	0.455971i	$-0.849292\pi$
$821$		−	26.1300i		−	0.911942i	0.889995	−	0.455971i	$-0.150708\pi$
$822$			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	$-0.0102827\pi$
$824$			9.21082i			0.320874i
$825$	0.297514	+	0.536221i	0.0103581	+	0.0186688i
$826$		−	7.91099i		−	0.275258i
$827$	19.9886			0.695072			0.347536	−	0.937667i	$-0.387018\pi$
$827$	19.9886			0.695072			0.347536	+	0.937667i	$0.387018\pi$
$828$		−	5.12402i		−	0.178072i
$829$	41.6506			1.44658			0.723292	−	0.690542i	$-0.242628\pi$
$829$	41.6506			1.44658			0.723292	+	0.690542i	$0.242628\pi$
$830$	14.3658	−	24.3995i	0.498644	−	0.846918i
$831$	9.04884			0.313901
$832$		0			0
$833$		−	30.3487i		−	1.05152i
$834$		−	0.816859i		−	0.0282855i
$835$	−12.1193	+	20.5840i	−0.419407	+	0.712339i
$836$	0.341087			0.0117967
$837$	9.42442			0.325756
$838$	−4.45670			−0.153954
$839$		−	25.9421i		−	0.895622i	−0.894128	−	0.447811i	$-0.852204\pi$
$839$		−	25.9421i		−	0.895622i	0.894128	−	0.447811i	$-0.147796\pi$
$840$	0.635402	+	0.374108i	0.0219234	+	0.0129080i
$841$	6.61068			0.227955
$842$		−	16.7557i		−	0.577441i
$843$	5.32737			0.183484
$844$	−12.3086			−0.423681
$845$		0			0
$846$	−33.4534			−1.15015
$847$	11.7680			0.404355
$848$		−	10.7632i		−	0.369610i
$849$	−7.87395			−0.270233
$850$	22.7957	−	12.6478i	0.781885	−	0.433816i
$851$		−	7.79445i		−	0.267190i
$852$	3.77528			0.129339
$853$	−33.6674			−1.15275			−0.576374	−	0.817186i	$-0.695533\pi$
$853$	−33.6674			−1.15275			−0.576374	+	0.817186i	$0.695533\pi$
$854$	−2.86831			−0.0981516
$855$	−4.73178	−	2.78595i	−0.161823	−	0.0952775i
$856$			6.97470i			0.238391i
$857$			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	$0.668713\pi$
$860$	22.1333	+	13.0315i	0.754739	+	0.444371i
$861$	−1.05586			−0.0359837
$862$			17.3440i			0.590741i
$863$	15.7244			0.535264			0.267632	−	0.963521i	$-0.413759\pi$
$863$	15.7244			0.535264			0.267632	+	0.963521i	$0.413759\pi$
$864$			1.79397i			0.0610323i
$865$	30.6342	+	18.0367i	1.04160	+	0.613265i
$866$		−	4.41765i		−	0.150118i
$867$		−	3.09262i		−	0.105031i
$868$		−	5.70478i		−	0.193633i
$869$		−	6.41698i		−	0.217681i
$870$	3.49171	+	2.05583i	0.118380	+	0.0696992i
$871$		0			0
$872$		−	3.29363i		−	0.111537i
$873$	27.5479			0.932356
$874$	−1.48817			−0.0503381
$875$	−12.1371	−	0.310507i	−0.410307	−	0.0104971i
$876$		−	0.889236i		−	0.0300445i
$877$	30.3994			1.02651			0.513257	−	0.858235i	$-0.328439\pi$
$877$	30.3994			1.02651			0.513257	+	0.858235i	$0.328439\pi$
$878$	33.1534			1.11887
$879$		−	7.94464i		−	0.267966i
$880$	0.778246	+	0.458212i	0.0262347	+	0.0154463i
$881$	−41.3933			−1.39458			−0.697288	−	0.716791i	$-0.745610\pi$
$881$	−41.3933			−1.39458			−0.697288	+	0.716791i	$0.745610\pi$
$882$	−16.9256			−0.569913
$883$		−	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
$886$		−	19.2632i		−	0.647161i
$887$			37.1737i			1.24817i	0.781357	+	0.624085i	$0.214528\pi$
$887$			37.1737i			1.24817i	−0.781357	+	0.624085i	$0.785472\pi$
$888$			1.34316i			0.0450736i
$889$		−	6.59155i		−	0.221074i
$890$	13.4838	+	7.93892i	0.451978	+	0.266113i
$891$			3.30323i			0.110663i
$892$	−9.35143			−0.313109
$893$			9.71589i			0.325130i
$894$	−5.32697			−0.178161
$895$	−28.6779	+	48.7077i	−0.958595	+	1.62812i
$896$	1.08593			0.0362782
$897$		0			0
$898$			4.55734i			0.152081i
$899$		−	31.3494i		−	1.04556i
$900$	−7.05372	−	12.7132i	−0.235124	−	0.423774i
$901$	56.1180			1.86956
$902$	−1.29323			−0.0430599
$903$	−3.78775			−0.126048
$904$			10.0934i			0.335702i
$905$	−20.2035	+	34.3144i	−0.671586	+	1.14065i
$906$	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	$-0.181262\pi$
$908$	−13.1715			−0.437112
$909$	−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	$0.409848\pi$
$912$	0.256446			0.00849178
$913$			5.11428i			0.169258i
$914$	15.9598			0.527905
$915$	−1.54552	−	0.909962i	−0.0510932	−	0.0300824i
$916$		−	13.6752i		−	0.451840i
$917$	0.580739			0.0191777
$918$	−9.35354			−0.308713
$919$	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
$921$			0.816435i			0.0269025i
$922$			22.2437i			0.732556i
$923$		0			0
$924$	−0.133184			−0.00438143
$925$	−10.7298	−	19.3388i	−0.352795	−	0.635857i
$926$	31.0149			1.01921
$927$			26.7831i			0.879673i
$928$	5.96747			0.195892
$929$			43.2786i			1.41992i	0.704240	+	0.709962i	$0.251288\pi$
$929$			43.2786i			1.41992i	−0.704240	+	0.709962i	$0.748712\pi$
$930$	1.80982	−	3.07388i	0.0593464	−	0.100796i
$931$			4.91569i			0.161105i
$932$			27.7357i			0.908514i
$933$			9.42198i			0.308462i
$934$		−	0.841337i		−	0.0275294i
$935$	−2.38905	+	4.05767i	−0.0781304	+	0.132700i
$936$		0			0
$937$		−	13.9713i		−	0.456424i	−0.973611	−	0.228212i	$-0.926712\pi$
$937$		−	13.9713i		−	0.456424i	0.973611	−	0.228212i	$-0.0732879\pi$
$938$	11.5100			0.375815
$939$	4.47597			0.146068
$940$	−13.0522	+	22.1684i	−0.425716	+	0.723054i
$941$		−	27.2678i		−	0.888905i	−0.895803	−	0.444452i	$-0.853398\pi$
$941$		−	27.2678i		−	0.888905i	0.895803	−	0.444452i	$-0.146602\pi$
$942$	−3.20858			−0.104541
$943$	5.64240			0.183742
$944$		−	7.28501i		−	0.237107i
$945$	3.75382	+	2.21015i	0.122112	+	0.0718963i
$946$	−4.63927			−0.150836
$947$	−11.4663			−0.372605			−0.186302	−	0.982492i	$-0.559650\pi$
$947$	−11.4663			−0.372605			−0.186302	+	0.982492i	$0.559650\pi$
$948$		−	4.82460i		−	0.156696i
$949$		0			0
$950$	−3.69230	+	2.04861i	−0.119794	+	0.0664658i
$951$		−	4.47647i		−	0.145160i
$952$			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	$0.899270\pi$
$954$		−	31.2972i		−	1.01328i
$955$	−11.8683	+	20.1576i	−0.384049	+	0.652285i
$956$			17.7552i			0.574243i
$957$	−0.731883			−0.0236584
$958$			7.63429i			0.246653i
$959$	13.0104			0.420127
$960$	0.585124	+	0.344506i	0.0188848	+	0.0111189i
$961$	3.40205			0.109743
$962$		0			0
$963$			20.2810i			0.653545i
$964$			3.83937i			0.123658i
$965$	16.6274	−	28.2406i	0.535253	−	0.909097i
$966$	0.581085			0.0186961
$967$	40.2200			1.29339			0.646695	−	0.762749i	$-0.276151\pi$
$967$	40.2200			1.29339			0.646695	+	0.762749i	$0.276151\pi$
$968$	10.8369			0.348310
$969$			1.33708i			0.0429531i
$970$	10.7481	−	18.2550i	0.345101	−	0.586134i
$971$	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
$973$	−2.92117			−0.0936483
$974$	−23.2958			−0.746446
$975$		0			0
$976$	−2.64135			−0.0845475
$977$	−19.5975			−0.626981			−0.313490	−	0.949591i	$-0.601498\pi$
$977$	−19.5975			−0.626981			−0.313490	+	0.949591i	$0.601498\pi$
$978$		−	5.78893i		−	0.185110i
$979$	−2.82628			−0.0903284
$980$	−6.60368	+	11.2160i	−0.210947	+	0.358281i
$981$		−	9.57719i		−	0.305776i
$982$	−36.2972			−1.15829
$983$	−11.7949			−0.376198			−0.188099	−	0.982150i	$-0.560233\pi$
$983$	−11.7949			−0.376198			−0.188099	+	0.982150i	$0.560233\pi$
$984$	−0.972316			−0.0309963
$985$	−11.7262	+	19.9162i	−0.373627	+	0.634584i
$986$			31.1136i			0.990858i
$987$		−	3.79375i		−	0.120757i
$988$		0			0
$989$	20.2412			0.643634
$990$	2.26298	+	1.33238i	0.0719221	+	0.0423459i
$991$	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
$993$	2.90293			0.0921217
$994$		−	13.5008i		−	0.428218i
$995$	5.91661	−	10.0490i	0.187569	−	0.318576i
$996$			3.84517i			0.121839i
$997$			18.7441i			0.593632i	0.954935	+	0.296816i	$0.0959248\pi$
$997$			18.7441i			0.593632i	−0.954935	+	0.296816i	$0.904075\pi$
$998$		−	18.9398i		−	0.599530i
$999$			7.93513i			0.251056i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.7	✓	18	13.5	odd	4
1690.2.b.f.339.12	yes	18	65.44	odd	4
1690.2.b.g.339.3	yes	18	65.34	odd	4
1690.2.b.g.339.16	yes	18	13.8	odd	4
1690.2.c.g.1689.8		18	5.4	even	2
1690.2.c.g.1689.11		18	13.12	even	2
1690.2.c.h.1689.8		18	65.64	even	2	inner
1690.2.c.h.1689.11		18	1.1	even	1	trivial
8450.2.a.ct.1.7		9	65.47	even	4
8450.2.a.cw.1.3		9	65.18	even	4
8450.2.a.cx.1.7		9	65.57	even	4
8450.2.a.da.1.3		9	65.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.303663i q^{3} +1.00000 q^{4} +(1.13450 - 1.92689i) q^{5} +0.303663i q^{6} +1.08593 q^{7} +1.00000 q^{8} +2.90779 q^{9} +(1.13450 - 1.92689i) q^{10} +0.403887i q^{11} +0.303663i q^{12} +1.08593 q^{14} +(0.585124 + 0.344506i) q^{15} +1.00000 q^{16} +5.21387i q^{17} +2.90779 q^{18} -0.844510i q^{19} +(1.13450 - 1.92689i) q^{20} +0.329755i q^{21} +0.403887i q^{22} -1.76217i q^{23} +0.303663i q^{24} +(-2.42580 - 4.37213i) q^{25} +1.79397i q^{27} +1.08593 q^{28} +5.96747 q^{29} +(0.585124 + 0.344506i) q^{30} -5.25338i q^{31} +1.00000 q^{32} -0.122645 q^{33} +5.21387i q^{34} +(1.23199 - 2.09246i) q^{35} +2.90779 q^{36} +4.42321 q^{37} -0.844510i q^{38} +(1.13450 - 1.92689i) q^{40} +3.20196i q^{41} +0.329755i q^{42} +11.4865i q^{43} +0.403887i q^{44} +(3.29890 - 5.60299i) q^{45} -1.76217i q^{46} -11.5048 q^{47} +0.303663i q^{48} -5.82076 q^{49} +(-2.42580 - 4.37213i) q^{50} -1.58326 q^{51} -10.7632i q^{53} +1.79397i q^{54} +(0.778246 + 0.458212i) q^{55} +1.08593 q^{56} +0.256446 q^{57} +5.96747 q^{58} -7.28501i q^{59} +(0.585124 + 0.344506i) q^{60} -2.64135 q^{61} -5.25338i q^{62} +3.15764 q^{63} +1.00000 q^{64} -0.122645 q^{66} +10.5992 q^{67} +5.21387i q^{68} +0.535105 q^{69} +(1.23199 - 2.09246i) q^{70} -12.4325i q^{71} +2.90779 q^{72} -2.92837 q^{73} +4.42321 q^{74} +(1.32765 - 0.736626i) q^{75} -0.844510i q^{76} +0.438592i q^{77} -15.8880 q^{79} +(1.13450 - 1.92689i) q^{80} +8.17860 q^{81} +3.20196i q^{82} +12.6626 q^{83} +0.329755i q^{84} +(10.0465 + 5.91515i) q^{85} +11.4865i q^{86} +1.81210i q^{87} +0.403887i q^{88} +6.99770i q^{89} +(3.29890 - 5.60299i) q^{90} -1.76217i q^{92} +1.59525 q^{93} -11.5048 q^{94} +(-1.62728 - 0.958100i) q^{95} +0.303663i q^{96} +9.47384 q^{97} -5.82076 q^{98} +1.17442i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) \) 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Introduction

L-functions

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