LMFDB - Embedded newform 1690.2.c.g.1689.12

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			1689.12
Root			$2.20982i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.g.1689.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.666723i q^{3} +1.00000 q^{4} +(0.454429 - 2.18940i) q^{5} -0.666723i q^{6} +2.41461 q^{7} -1.00000 q^{8} +2.55548 q^{9} +(-0.454429 + 2.18940i) q^{10} -1.46118i q^{11} +0.666723i q^{12} -2.41461 q^{14} +(1.45973 + 0.302978i) q^{15} +1.00000 q^{16} +6.74749i q^{17} -2.55548 q^{18} +7.41659i q^{19} +(0.454429 - 2.18940i) q^{20} +1.60988i q^{21} +1.46118i q^{22} +7.48975i q^{23} -0.666723i q^{24} +(-4.58699 - 1.98986i) q^{25} +3.70397i q^{27} +2.41461 q^{28} +0.696556 q^{29} +(-1.45973 - 0.302978i) q^{30} -1.36837i q^{31} -1.00000 q^{32} +0.974200 q^{33} -6.74749i q^{34} +(1.09727 - 5.28656i) q^{35} +2.55548 q^{36} +9.25191 q^{37} -7.41659i q^{38} +(-0.454429 + 2.18940i) q^{40} -4.24884i q^{41} -1.60988i q^{42} -2.38573i q^{43} -1.46118i q^{44} +(1.16128 - 5.59498i) q^{45} -7.48975i q^{46} -2.77456 q^{47} +0.666723i q^{48} -1.16965 q^{49} +(4.58699 + 1.98986i) q^{50} -4.49870 q^{51} +7.04744i q^{53} -3.70397i q^{54} +(-3.19911 - 0.664001i) q^{55} -2.41461 q^{56} -4.94481 q^{57} -0.696556 q^{58} +0.0690364i q^{59} +(1.45973 + 0.302978i) q^{60} +5.91472 q^{61} +1.36837i q^{62} +6.17050 q^{63} +1.00000 q^{64} -0.974200 q^{66} +10.9958 q^{67} +6.74749i q^{68} -4.99359 q^{69} +(-1.09727 + 5.28656i) q^{70} +3.60919i q^{71} -2.55548 q^{72} +9.30157 q^{73} -9.25191 q^{74} +(1.32668 - 3.05825i) q^{75} +7.41659i q^{76} -3.52818i q^{77} +0.766732 q^{79} +(0.454429 - 2.18940i) q^{80} +5.19692 q^{81} +4.24884i q^{82} -16.5800 q^{83} +1.60988i q^{84} +(14.7730 + 3.06625i) q^{85} +2.38573i q^{86} +0.464410i q^{87} +1.46118i q^{88} -17.7481i q^{89} +(-1.16128 + 5.59498i) q^{90} +7.48975i q^{92} +0.912326 q^{93} +2.77456 q^{94} +(16.2379 + 3.37031i) q^{95} -0.666723i q^{96} -10.5209 q^{97} +1.16965 q^{98} -3.73401i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			0.666723i			0.384933i	0.981304	+	0.192466i	$0.0616486\pi$
$3$			0.666723i			0.384933i	−0.981304	+	0.192466i	$0.938351\pi$
$4$	1.00000			0.500000
$5$	0.454429	−	2.18940i	0.203227	−	0.979132i
$5$	0.454429	−	2.18940i	0.203227	−	0.979132i
$6$		−	0.666723i		−	0.272188i
$7$	2.41461			0.912638			0.456319	−	0.889816i	$-0.349168\pi$
$7$	2.41461			0.912638			0.456319	+	0.889816i	$0.349168\pi$
$8$	−1.00000			−0.353553
$9$	2.55548			0.851827
$10$	−0.454429	+	2.18940i	−0.143703	+	0.692351i
$11$		−	1.46118i		−	0.440561i	−0.975437	−	0.220281i	$-0.929303\pi$
$11$		−	1.46118i		−	0.440561i	0.975437	−	0.220281i	$-0.0706973\pi$
$12$			0.666723i			0.192466i
$13$		0			0
$13$		0			0
$14$	−2.41461			−0.645332
$15$	1.45973	+	0.302978i	0.376900	+	0.0782286i
$16$	1.00000			0.250000
$17$			6.74749i			1.63651i	0.574858	+	0.818253i	$0.305057\pi$
$17$			6.74749i			1.63651i	−0.574858	+	0.818253i	$0.694943\pi$
$18$	−2.55548			−0.602333
$19$			7.41659i			1.70148i	0.525585	+	0.850741i	$0.323846\pi$
$19$			7.41659i			1.70148i	−0.525585	+	0.850741i	$0.676154\pi$
$20$	0.454429	−	2.18940i	0.101613	−	0.489566i
$21$			1.60988i			0.351304i
$22$			1.46118i			0.311524i
$23$			7.48975i			1.56172i	0.624705	+	0.780861i	$0.285219\pi$
$23$			7.48975i			1.56172i	−0.624705	+	0.780861i	$0.714781\pi$
$24$		−	0.666723i		−	0.136094i
$25$	−4.58699	−	1.98986i	−0.917398	−	0.397972i
$26$		0			0
$27$			3.70397i			0.712829i
$28$	2.41461			0.456319
$29$	0.696556			0.129347			0.0646736	−	0.997906i	$-0.479399\pi$
$29$	0.696556			0.129347			0.0646736	+	0.997906i	$0.479399\pi$
$30$	−1.45973	−	0.302978i	−0.266508	−	0.0553160i
$31$		−	1.36837i		−	0.245767i	−0.992421	−	0.122884i	$-0.960786\pi$
$31$		−	1.36837i		−	0.245767i	0.992421	−	0.122884i	$-0.0392142\pi$
$32$	−1.00000			−0.176777
$33$	0.974200			0.169586
$34$		−	6.74749i		−	1.15718i
$35$	1.09727	−	5.28656i	0.185473	−	0.893593i
$36$	2.55548			0.425913
$37$	9.25191			1.52101			0.760503	−	0.649335i	$-0.224953\pi$
$37$	9.25191			1.52101			0.760503	+	0.649335i	$0.224953\pi$
$38$		−	7.41659i		−	1.20313i
$39$		0			0
$40$	−0.454429	+	2.18940i	−0.0718515	+	0.346175i
$41$		−	4.24884i		−	0.663558i	−0.943357	−	0.331779i	$-0.892351\pi$
$41$		−	4.24884i		−	0.663558i	0.943357	−	0.331779i	$-0.107649\pi$
$42$		−	1.60988i		−	0.248409i
$43$		−	2.38573i		−	0.363821i	−0.983315	−	0.181910i	$-0.941772\pi$
$43$		−	2.38573i		−	0.363821i	0.983315	−	0.181910i	$-0.0582281\pi$
$44$		−	1.46118i		−	0.220281i
$45$	1.16128	−	5.59498i	0.173114	−	0.834051i
$46$		−	7.48975i		−	1.10430i
$47$	−2.77456			−0.404711			−0.202356	−	0.979312i	$-0.564860\pi$
$47$	−2.77456			−0.404711			−0.202356	+	0.979312i	$0.564860\pi$
$48$			0.666723i			0.0962331i
$49$	−1.16965			−0.167092
$50$	4.58699	+	1.98986i	0.648698	+	0.281408i
$51$	−4.49870			−0.629944
$52$		0			0
$53$			7.04744i			0.968040i	0.875057	+	0.484020i	$0.160824\pi$
$53$			7.04744i			0.968040i	−0.875057	+	0.484020i	$0.839176\pi$
$54$		−	3.70397i		−	0.504046i
$55$	−3.19911	−	0.664001i	−0.431368	−	0.0895339i
$56$	−2.41461			−0.322666
$57$	−4.94481			−0.654956
$58$	−0.696556			−0.0914623
$59$			0.0690364i			0.00898777i	0.999990	+	0.00449389i	$0.00143045\pi$
$59$			0.0690364i			0.00898777i	−0.999990	+	0.00449389i	$0.998570\pi$
$60$	1.45973	+	0.302978i	0.188450	+	0.0391143i
$61$	5.91472			0.757302			0.378651	−	0.925539i	$-0.376388\pi$
$61$	5.91472			0.757302			0.378651	+	0.925539i	$0.376388\pi$
$62$			1.36837i			0.173784i
$63$	6.17050			0.777409
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.974200			−0.119916
$67$	10.9958			1.34335			0.671674	−	0.740847i	$-0.265576\pi$
$67$	10.9958			1.34335			0.671674	+	0.740847i	$0.265576\pi$
$68$			6.74749i			0.818253i
$69$	−4.99359			−0.601157
$70$	−1.09727	+	5.28656i	−0.131149	+	0.631865i
$71$			3.60919i			0.428332i	0.976797	+	0.214166i	$0.0687034\pi$
$71$			3.60919i			0.428332i	−0.976797	+	0.214166i	$0.931297\pi$
$72$	−2.55548			−0.301166
$73$	9.30157			1.08867			0.544333	−	0.838869i	$-0.316783\pi$
$73$	9.30157			1.08867			0.544333	+	0.838869i	$0.316783\pi$
$74$	−9.25191			−1.07551
$75$	1.32668	−	3.05825i	0.153192	−	0.353136i
$76$			7.41659i			0.850741i
$77$		−	3.52818i		−	0.402073i
$78$		0			0
$79$	0.766732			0.0862641			0.0431320	−	0.999069i	$-0.486266\pi$
$79$	0.766732			0.0862641			0.0431320	+	0.999069i	$0.486266\pi$
$80$	0.454429	−	2.18940i	0.0508067	−	0.244783i
$81$	5.19692			0.577436
$82$			4.24884i			0.469206i
$83$	−16.5800			−1.81989			−0.909947	−	0.414725i	$-0.863878\pi$
$83$	−16.5800			−1.81989			−0.909947	+	0.414725i	$0.863878\pi$
$84$			1.60988i			0.175652i
$85$	14.7730	+	3.06625i	1.60235	+	0.332582i
$86$			2.38573i			0.257260i
$87$			0.464410i			0.0497899i
$88$			1.46118i			0.155762i
$89$		−	17.7481i		−	1.88130i	−0.339384	−	0.940648i	$-0.610219\pi$
$89$		−	17.7481i		−	1.88130i	0.339384	−	0.940648i	$-0.389781\pi$
$90$	−1.16128	+	5.59498i	−0.122410	+	0.589763i
$91$		0			0
$92$			7.48975i			0.780861i
$93$	0.912326			0.0946038
$94$	2.77456			0.286174
$95$	16.2379	+	3.37031i	1.66597	+	0.345787i
$96$		−	0.666723i		−	0.0680471i
$97$	−10.5209			−1.06824			−0.534120	−	0.845409i	$-0.679357\pi$
$97$	−10.5209			−1.06824			−0.534120	+	0.845409i	$0.679357\pi$
$98$	1.16965			0.118152
$99$		−	3.73401i		−	0.375282i
$100$	−4.58699	−	1.98986i	−0.458699	−	0.198986i
$101$	−14.2473			−1.41765			−0.708827	−	0.705382i	$-0.750775\pi$
$101$	−14.2473			−1.41765			−0.708827	+	0.705382i	$0.750775\pi$
$102$	4.49870			0.445438
$103$		−	9.72411i		−	0.958145i	−0.877775	−	0.479072i	$-0.840973\pi$
$103$		−	9.72411i		−	0.958145i	0.877775	−	0.479072i	$-0.159027\pi$
$104$		0			0
$105$	3.52467	+	0.731575i	0.343973	+	0.0713944i
$106$		−	7.04744i		−	0.684508i
$107$		−	6.14900i		−	0.594446i	−0.954808	−	0.297223i	$-0.903939\pi$
$107$		−	6.14900i		−	0.594446i	0.954808	−	0.297223i	$-0.0960605\pi$
$108$			3.70397i			0.356414i
$109$		−	0.319202i		−	0.0305741i	−0.999883	−	0.0152870i	$-0.995134\pi$
$109$		−	0.319202i		−	0.0305741i	0.999883	−	0.0152870i	$-0.00486620\pi$
$110$	3.19911	+	0.664001i	0.305023	+	0.0633100i
$111$			6.16846i			0.585485i
$112$	2.41461			0.228159
$113$		−	1.95370i		−	0.183789i	−0.995769	−	0.0918945i	$-0.970708\pi$
$113$		−	1.95370i		−	0.183789i	0.995769	−	0.0918945i	$-0.0292923\pi$
$114$	4.94481			0.463124
$115$	16.3981	+	3.40356i	1.52913	+	0.317384i
$116$	0.696556			0.0646736
$117$		0			0
$118$		−	0.0690364i		−	0.00635531i
$119$			16.2926i			1.49354i
$120$	−1.45973	−	0.302978i	−0.133254	−	0.0276580i
$121$	8.86496			0.805906
$122$	−5.91472			−0.535494
$123$	2.83280			0.255425
$124$		−	1.36837i		−	0.122884i
$125$	−6.44107	+	9.13853i	−0.576107	+	0.817375i
$126$	−6.17050			−0.549711
$127$			9.73867i			0.864167i	0.901834	+	0.432084i	$0.142221\pi$
$127$			9.73867i			0.864167i	−0.901834	+	0.432084i	$0.857779\pi$
$128$	−1.00000			−0.0883883
$129$	1.59062			0.140046
$130$		0			0
$131$	10.6075			0.926778			0.463389	−	0.886155i	$-0.346633\pi$
$131$	10.6075			0.926778			0.463389	+	0.886155i	$0.346633\pi$
$132$	0.974200			0.0847932
$133$			17.9082i			1.55284i
$134$	−10.9958			−0.949890
$135$	8.10948	+	1.68319i	0.697953	+	0.144866i
$136$		−	6.74749i		−	0.578592i
$137$	6.40586			0.547289			0.273645	−	0.961831i	$-0.411771\pi$
$137$	6.40586			0.547289			0.273645	+	0.961831i	$0.411771\pi$
$138$	4.99359			0.425082
$139$	16.7981			1.42480			0.712398	−	0.701775i	$-0.247609\pi$
$139$	16.7981			1.42480			0.712398	+	0.701775i	$0.247609\pi$
$140$	1.09727	−	5.28656i	0.0927363	−	0.446796i
$141$		−	1.84986i		−	0.155786i
$142$		−	3.60919i		−	0.302877i
$143$		0			0
$144$	2.55548			0.212957
$145$	0.316535	−	1.52504i	0.0262868	−	0.126648i
$146$	−9.30157			−0.769804
$147$		−	0.779830i		−	0.0643193i
$148$	9.25191			0.760503
$149$		−	8.90415i		−	0.729456i	−0.931114	−	0.364728i	$-0.881162\pi$
$149$		−	8.90415i		−	0.729456i	0.931114	−	0.364728i	$-0.118838\pi$
$150$	−1.32668	+	3.05825i	−0.108323	+	0.249705i
$151$			17.1722i			1.39745i	0.715389	+	0.698726i	$0.246249\pi$
$151$			17.1722i			1.39745i	−0.715389	+	0.698726i	$0.753751\pi$
$152$		−	7.41659i		−	0.601565i
$153$			17.2431i			1.39402i
$154$			3.52818i			0.284308i
$155$	−2.99592	−	0.621829i	−0.240638	−	0.0499465i
$156$		0			0
$157$		−	11.0649i		−	0.883073i	−0.897243	−	0.441537i	$-0.854434\pi$
$157$		−	11.0649i		−	0.883073i	0.897243	−	0.441537i	$-0.145566\pi$
$158$	−0.766732			−0.0609979
$159$	−4.69869			−0.372630
$160$	−0.454429	+	2.18940i	−0.0359258	+	0.173088i
$161$			18.0848i			1.42529i
$162$	−5.19692			−0.408309
$163$	−15.2437			−1.19398			−0.596988	−	0.802250i	$-0.703636\pi$
$163$	−15.2437			−1.19398			−0.596988	+	0.802250i	$0.703636\pi$
$164$		−	4.24884i		−	0.331779i
$165$	0.442705	−	2.13292i	0.0344645	−	0.166047i
$166$	16.5800			1.28686
$167$	−8.69198			−0.672605			−0.336303	−	0.941754i	$-0.609177\pi$
$167$	−8.69198			−0.672605			−0.336303	+	0.941754i	$0.609177\pi$
$168$		−	1.60988i		−	0.124205i
$169$		0			0
$170$	−14.7730	−	3.06625i	−1.13304	−	0.235171i
$171$			18.9529i			1.44937i
$172$		−	2.38573i		−	0.181910i
$173$			3.39226i			0.257909i	0.991651	+	0.128954i	$0.0411621\pi$
$173$			3.39226i			0.257909i	−0.991651	+	0.128954i	$0.958838\pi$
$174$		−	0.464410i		−	0.0352068i
$175$	−11.0758	−	4.80474i	−0.837252	−	0.363204i
$176$		−	1.46118i		−	0.110140i
$177$	−0.0460281			−0.00345969
$178$			17.7481i			1.33028i
$179$	13.2996			0.994057			0.497029	−	0.867734i	$-0.334424\pi$
$179$	13.2996			0.994057			0.497029	+	0.867734i	$0.334424\pi$
$180$	1.16128	−	5.59498i	0.0865571	−	0.417025i
$181$	14.0010			1.04068			0.520341	−	0.853958i	$-0.325805\pi$
$181$	14.0010			1.04068			0.520341	+	0.853958i	$0.325805\pi$
$182$		0			0
$183$			3.94348i			0.291510i
$184$		−	7.48975i		−	0.552152i
$185$	4.20434	−	20.2562i	0.309109	−	1.48926i
$186$	−0.912326			−0.0668950
$187$	9.85927			0.720981
$188$	−2.77456			−0.202356
$189$			8.94364i			0.650554i
$190$	−16.2379	−	3.37031i	−1.17802	−	0.244508i
$191$	−18.7576			−1.35725			−0.678627	−	0.734483i	$-0.737425\pi$
$191$	−18.7576			−1.35725			−0.678627	+	0.734483i	$0.737425\pi$
$192$			0.666723i			0.0481166i
$193$	−24.3855			−1.75530			−0.877652	−	0.479299i	$-0.840891\pi$
$193$	−24.3855			−1.75530			−0.877652	+	0.479299i	$0.840891\pi$
$194$	10.5209			0.755360
$195$		0			0
$196$	−1.16965			−0.0835462
$197$	2.73133			0.194599			0.0972997	−	0.995255i	$-0.468979\pi$
$197$	2.73133			0.194599			0.0972997	+	0.995255i	$0.468979\pi$
$198$			3.73401i			0.265364i
$199$	11.2116			0.794771			0.397385	−	0.917652i	$-0.369918\pi$
$199$	11.2116			0.794771			0.397385	+	0.917652i	$0.369918\pi$
$200$	4.58699	+	1.98986i	0.324349	+	0.140704i
$201$			7.33113i			0.517098i
$202$	14.2473			1.00243
$203$	1.68191			0.118047
$204$	−4.49870			−0.314972
$205$	−9.30244	−	1.93080i	−0.649710	−	0.134853i
$206$			9.72411i			0.677511i
$207$			19.1399i			1.33032i
$208$		0			0
$209$	10.8369			0.749607
$210$	−3.52467	−	0.731575i	−0.243226	−	0.0504835i
$211$	13.7163			0.944266			0.472133	−	0.881527i	$-0.343484\pi$
$211$	13.7163			0.944266			0.472133	+	0.881527i	$0.343484\pi$
$212$			7.04744i			0.484020i
$213$	−2.40633			−0.164879
$214$			6.14900i			0.420337i
$215$	−5.22333	−	1.08415i	−0.356228	−	0.0739381i
$216$		−	3.70397i		−	0.252023i
$217$		−	3.30409i		−	0.224296i
$218$			0.319202i			0.0216191i
$219$			6.20157i			0.419063i
$220$	−3.19911	−	0.664001i	−0.215684	−	0.0447669i
$221$		0			0
$222$		−	6.16846i		−	0.414000i
$223$	−9.84353			−0.659172			−0.329586	−	0.944126i	$-0.606909\pi$
$223$	−9.84353			−0.659172			−0.329586	+	0.944126i	$0.606909\pi$
$224$	−2.41461			−0.161333
$225$	−11.7220	−	5.08505i	−0.781464	−	0.339003i
$226$			1.95370i			0.129959i
$227$	19.4038			1.28788			0.643939	−	0.765077i	$-0.277299\pi$
$227$	19.4038			1.28788			0.643939	+	0.765077i	$0.277299\pi$
$228$	−4.94481			−0.327478
$229$		−	16.7503i		−	1.10689i	−0.832885	−	0.553447i	$-0.813312\pi$
$229$		−	16.7503i		−	1.10689i	0.832885	−	0.553447i	$-0.186688\pi$
$230$	−16.3981	−	3.40356i	−1.08126	−	0.224424i
$231$	2.35231			0.154771
$232$	−0.696556			−0.0457311
$233$		−	16.7974i		−	1.10043i	−0.835022	−	0.550217i	$-0.814545\pi$
$233$		−	16.7974i		−	1.10043i	0.835022	−	0.550217i	$-0.185455\pi$
$234$		0			0
$235$	−1.26084	+	6.07463i	−0.0822482	+	0.396265i
$236$			0.0690364i			0.00449389i
$237$			0.511198i			0.0332059i
$238$		−	16.2926i		−	1.05609i
$239$		−	18.2819i		−	1.18256i	−0.806467	−	0.591278i	$-0.798623\pi$
$239$		−	18.2819i		−	1.18256i	0.806467	−	0.591278i	$-0.201377\pi$
$240$	1.45973	+	0.302978i	0.0942249	+	0.0195572i
$241$			7.86172i			0.506418i	0.967412	+	0.253209i	$0.0814860\pi$
$241$			7.86172i			0.506418i	−0.967412	+	0.253209i	$0.918514\pi$
$242$	−8.86496			−0.569861
$243$			14.5768i			0.935102i
$244$	5.91472			0.378651
$245$	−0.531521	+	2.56083i	−0.0339577	+	0.163605i
$246$	−2.83280			−0.180613
$247$		0			0
$248$			1.36837i			0.0868918i
$249$		−	11.0543i		−	0.700536i
$250$	6.44107	−	9.13853i	0.407369	−	0.577971i
$251$	−8.97087			−0.566236			−0.283118	−	0.959085i	$-0.591369\pi$
$251$	−8.97087			−0.566236			−0.283118	+	0.959085i	$0.591369\pi$
$252$	6.17050			0.388705
$253$	10.9439			0.688034
$254$		−	9.73867i		−	0.611059i
$255$	−2.04434	+	9.84948i	−0.128022	+	0.616799i
$256$	1.00000			0.0625000
$257$		−	24.2725i		−	1.51408i	−0.653369	−	0.757040i	$-0.726645\pi$
$257$		−	24.2725i		−	1.51408i	0.653369	−	0.757040i	$-0.273355\pi$
$258$	−1.59062			−0.0990278
$259$	22.3398			1.38813
$260$		0			0
$261$	1.78004			0.110181
$262$	−10.6075			−0.655331
$263$			28.7755i			1.77438i	0.461408	+	0.887188i	$0.347344\pi$
$263$			28.7755i			1.77438i	−0.461408	+	0.887188i	$0.652656\pi$
$264$	−0.974200			−0.0599578
$265$	15.4297	+	3.20256i	0.947839	+	0.196732i
$266$		−	17.9082i		−	1.09802i
$267$	11.8331			0.724172
$268$	10.9958			0.671674
$269$	26.2808			1.60237			0.801185	−	0.598417i	$-0.204203\pi$
$269$	26.2808			1.60237			0.801185	+	0.598417i	$0.204203\pi$
$270$	−8.10948	−	1.68319i	−0.493527	−	0.102436i
$271$		−	14.3647i		−	0.872594i	−0.899803	−	0.436297i	$-0.856290\pi$
$271$		−	14.3647i		−	0.872594i	0.899803	−	0.436297i	$-0.143710\pi$
$272$			6.74749i			0.409126i
$273$		0			0
$274$	−6.40586			−0.386992
$275$	−2.90753	+	6.70240i	−0.175331	+	0.404170i
$276$	−4.99359			−0.300579
$277$		−	9.92492i		−	0.596331i	−0.954514	−	0.298165i	$-0.903625\pi$
$277$		−	9.92492i		−	0.596331i	0.954514	−	0.298165i	$-0.0963747\pi$
$278$	−16.7981			−1.00748
$279$		−	3.49685i		−	0.209351i
$280$	−1.09727	+	5.28656i	−0.0655744	+	0.315933i
$281$		−	11.7992i		−	0.703880i	−0.936023	−	0.351940i	$-0.885522\pi$
$281$		−	11.7992i		−	0.703880i	0.936023	−	0.351940i	$-0.114478\pi$
$282$			1.84986i			0.110158i
$283$		−	13.0538i		−	0.775968i	−0.921666	−	0.387984i	$-0.873172\pi$
$283$		−	13.0538i		−	0.775968i	0.921666	−	0.387984i	$-0.126828\pi$
$284$			3.60919i			0.214166i
$285$	−2.24706	+	10.8262i	−0.133105	+	0.641288i
$286$		0			0
$287$		−	10.2593i		−	0.605588i
$288$	−2.55548			−0.150583
$289$	−28.5286			−1.67815
$290$	−0.316535	+	1.52504i	−0.0185876	+	0.0895536i
$291$		−	7.01455i		−	0.411200i
$292$	9.30157			0.544333
$293$	−16.2358			−0.948506			−0.474253	−	0.880389i	$-0.657282\pi$
$293$	−16.2358			−0.948506			−0.474253	+	0.880389i	$0.657282\pi$
$294$			0.779830i			0.0454806i
$295$	0.151149	+	0.0313721i	0.00880021	+	0.00182656i
$296$	−9.25191			−0.537757
$297$	5.41215			0.314045
$298$			8.90415i			0.515803i
$299$		0			0
$300$	1.32668	−	3.05825i	0.0765961	−	0.176568i
$301$		−	5.76062i		−	0.332036i
$302$		−	17.1722i		−	0.988148i
$303$		−	9.49897i		−	0.545701i
$304$			7.41659i			0.425370i
$305$	2.68782	−	12.9497i	0.153904	−	0.741499i
$306$		−	17.2431i		−	0.985721i
$307$	5.66589			0.323370			0.161685	−	0.986842i	$-0.448307\pi$
$307$	5.66589			0.323370			0.161685	+	0.986842i	$0.448307\pi$
$308$		−	3.52818i		−	0.201036i
$309$	6.48328			0.368821
$310$	2.99592	+	0.621829i	0.170157	+	0.0353175i
$311$	−20.5465			−1.16508			−0.582542	−	0.812801i	$-0.697942\pi$
$311$	−20.5465			−1.16508			−0.582542	+	0.812801i	$0.697942\pi$
$312$		0			0
$313$		−	11.0354i		−	0.623756i	−0.950122	−	0.311878i	$-0.899042\pi$
$313$		−	11.0354i		−	0.623756i	0.950122	−	0.311878i	$-0.100958\pi$
$314$			11.0649i			0.624427i
$315$	2.80405	−	13.5097i	0.157990	−	0.761186i
$316$	0.766732			0.0431320
$317$	17.0656			0.958501			0.479251	−	0.877678i	$-0.340909\pi$
$317$	17.0656			0.958501			0.479251	+	0.877678i	$0.340909\pi$
$318$	4.69869			0.263489
$319$		−	1.01779i		−	0.0569854i
$320$	0.454429	−	2.18940i	0.0254034	−	0.122391i
$321$	4.09968			0.228822
$322$		−	18.0848i		−	1.00783i
$323$	−50.0433			−2.78448
$324$	5.19692			0.288718
$325$		0			0
$326$	15.2437			0.844269
$327$	0.212820			0.0117689
$328$			4.24884i			0.234603i
$329$	−6.69949			−0.369355
$330$	−0.442705	+	2.13292i	−0.0243701	+	0.117413i
$331$			29.6977i			1.63233i	0.577817	+	0.816167i	$0.303905\pi$
$331$			29.6977i			1.63233i	−0.577817	+	0.816167i	$0.696095\pi$
$332$	−16.5800			−0.909947
$333$	23.6431			1.29563
$334$	8.69198			0.475604
$335$	4.99680	−	24.0742i	0.273004	−	1.31531i
$336$			1.60988i			0.0878260i
$337$			11.1216i			0.605833i	0.953017	+	0.302917i	$0.0979604\pi$
$337$			11.1216i			0.605833i	−0.953017	+	0.302917i	$0.902040\pi$
$338$		0			0
$339$	1.30258			0.0707464
$340$	14.7730	+	3.06625i	0.801177	+	0.166291i
$341$	−1.99944			−0.108275
$342$		−	18.9529i		−	1.02486i
$343$	−19.7265			−1.06513
$344$			2.38573i			0.128630i
$345$	−2.26923	+	10.9330i	−0.122171	+	0.588612i
$346$		−	3.39226i		−	0.182369i
$347$		−	19.1698i		−	1.02909i	−0.857463	−	0.514545i	$-0.827961\pi$
$347$		−	19.1698i		−	1.02909i	0.857463	−	0.514545i	$-0.172039\pi$
$348$			0.464410i			0.0248950i
$349$			2.07169i			0.110895i	0.998462	+	0.0554474i	$0.0176585\pi$
$349$			2.07169i			0.110895i	−0.998462	+	0.0554474i	$0.982341\pi$
$350$	11.0758	+	4.80474i	0.592026	+	0.256824i
$351$		0			0
$352$			1.46118i			0.0778810i
$353$	−14.2889			−0.760522			−0.380261	−	0.924879i	$-0.624166\pi$
$353$	−14.2889			−0.760522			−0.380261	+	0.924879i	$0.624166\pi$
$354$	0.0460281			0.00244637
$355$	7.90198	+	1.64012i	0.419394	+	0.0870486i
$356$		−	17.7481i		−	0.940648i
$357$	−10.8626			−0.574911
$358$	−13.2996			−0.702905
$359$			12.4966i			0.659543i	0.944061	+	0.329772i	$0.106972\pi$
$359$			12.4966i			0.659543i	−0.944061	+	0.329772i	$0.893028\pi$
$360$	−1.16128	+	5.59498i	−0.0612051	+	0.294881i
$361$	−36.0058			−1.89504
$362$	−14.0010			−0.735874
$363$			5.91047i			0.310219i
$364$		0			0
$365$	4.22690	−	20.3649i	0.221246	−	1.06595i
$366$		−	3.94348i		−	0.206129i
$367$		−	20.7194i		−	1.08154i	−0.841170	−	0.540772i	$-0.818132\pi$
$367$		−	20.7194i		−	1.08154i	0.841170	−	0.540772i	$-0.181868\pi$
$368$			7.48975i			0.390430i
$369$		−	10.8578i		−	0.565236i
$370$	−4.20434	+	20.2562i	−0.218573	+	1.05307i
$371$			17.0168i			0.883470i
$372$	0.912326			0.0473019
$373$			31.4926i			1.63063i	0.579020	+	0.815313i	$0.303435\pi$
$373$			31.4926i			1.63063i	−0.579020	+	0.815313i	$0.696565\pi$
$374$	−9.85927			−0.509811
$375$	−6.09286	−	4.29441i	−0.314634	−	0.221762i
$376$	2.77456			0.143087
$377$		0			0
$378$		−	8.94364i		−	0.460011i
$379$			7.87442i			0.404482i	0.979336	+	0.202241i	$0.0648224\pi$
$379$			7.87442i			0.404482i	−0.979336	+	0.202241i	$0.935178\pi$
$380$	16.2379	+	3.37031i	0.832987	+	0.172893i
$381$	−6.49299			−0.332646
$382$	18.7576			0.959723
$383$	8.03386			0.410511			0.205256	−	0.978708i	$-0.434197\pi$
$383$	8.03386			0.410511			0.205256	+	0.978708i	$0.434197\pi$
$384$		−	0.666723i		−	0.0340236i
$385$	−7.72460	−	1.60331i	−0.393682	−	0.0817120i
$386$	24.3855			1.24119
$387$		−	6.09669i		−	0.309912i
$388$	−10.5209			−0.534120
$389$	−21.5917			−1.09474			−0.547371	−	0.836890i	$-0.684371\pi$
$389$	−21.5917			−1.09474			−0.547371	+	0.836890i	$0.684371\pi$
$390$		0			0
$391$	−50.5370			−2.55577
$392$	1.16965			0.0590761
$393$			7.07224i			0.356747i
$394$	−2.73133			−0.137603
$395$	0.348425	−	1.67869i	0.0175312	−	0.0844639i
$396$		−	3.73401i		−	0.187641i
$397$	−36.8751			−1.85071			−0.925355	−	0.379102i	$-0.876233\pi$
$397$	−36.8751			−1.85071			−0.925355	+	0.379102i	$0.876233\pi$
$398$	−11.2116			−0.561988
$399$	−11.9398			−0.597737
$400$	−4.58699	−	1.98986i	−0.229349	−	0.0994929i
$401$			8.26837i			0.412902i	0.978457	+	0.206451i	$0.0661915\pi$
$401$			8.26837i			0.412902i	−0.978457	+	0.206451i	$0.933809\pi$
$402$		−	7.33113i		−	0.365644i
$403$		0			0
$404$	−14.2473			−0.708827
$405$	2.36163	−	11.3782i	0.117351	−	0.565386i
$406$	−1.68191			−0.0834719
$407$		−	13.5187i		−	0.670096i
$408$	4.49870			0.222719
$409$			3.02146i			0.149402i	0.997206	+	0.0747008i	$0.0238002\pi$
$409$			3.02146i			0.149402i	−0.997206	+	0.0747008i	$0.976200\pi$
$410$	9.30244	+	1.93080i	0.459415	+	0.0953553i
$411$			4.27093i			0.210669i
$412$		−	9.72411i		−	0.479072i
$413$			0.166696i			0.00820258i
$414$		−	19.1399i		−	0.940676i
$415$	−7.53444	+	36.3004i	−0.369851	+	1.78192i
$416$		0			0
$417$			11.1997i			0.548451i
$418$	−10.8369			−0.530052
$419$	35.0376			1.71170			0.855850	−	0.517223i	$-0.173034\pi$
$419$	35.0376			1.71170			0.855850	+	0.517223i	$0.173034\pi$
$420$	3.52467	+	0.731575i	0.171986	+	0.0356972i
$421$			9.81291i			0.478252i	0.970989	+	0.239126i	$0.0768609\pi$
$421$			9.81291i			0.478252i	−0.970989	+	0.239126i	$0.923139\pi$
$422$	−13.7163			−0.667697
$423$	−7.09033			−0.344744
$424$		−	7.04744i		−	0.342254i
$425$	13.4265	−	30.9506i	0.651283	−	1.50133i
$426$	2.40633			0.116587
$427$	14.2818			0.691143
$428$		−	6.14900i		−	0.297223i
$429$		0			0
$430$	5.22333	+	1.08415i	0.251891	+	0.0522821i
$431$		−	5.88552i		−	0.283495i	−0.989903	−	0.141748i	$-0.954728\pi$
$431$		−	5.88552i		−	0.283495i	0.989903	−	0.141748i	$-0.0452722\pi$
$432$			3.70397i			0.178207i
$433$		−	31.1096i		−	1.49503i	−0.664244	−	0.747516i	$-0.731246\pi$
$433$		−	31.1096i		−	1.49503i	0.664244	−	0.747516i	$-0.268754\pi$
$434$			3.30409i			0.158601i
$435$	1.01678	+	0.211041i	0.0487509	+	0.0101187i
$436$		−	0.319202i		−	0.0152870i
$437$	−55.5484			−2.65724
$438$		−	6.20157i		−	0.296322i
$439$	−2.69710			−0.128726			−0.0643629	−	0.997927i	$-0.520502\pi$
$439$	−2.69710			−0.128726			−0.0643629	+	0.997927i	$0.520502\pi$
$440$	3.19911	+	0.664001i	0.152511	+	0.0316550i
$441$	−2.98901			−0.142334
$442$		0			0
$443$		−	19.0859i		−	0.906799i	−0.891308	−	0.453399i	$-0.850211\pi$
$443$		−	19.0859i		−	0.906799i	0.891308	−	0.453399i	$-0.149789\pi$
$444$			6.16846i			0.292742i
$445$	−38.8578	−	8.06526i	−1.84204	−	0.382330i
$446$	9.84353			0.466105
$447$	5.93660			0.280791
$448$	2.41461			0.114080
$449$		−	18.3579i		−	0.866363i	−0.901307	−	0.433182i	$-0.857391\pi$
$449$		−	18.3579i		−	0.866363i	0.901307	−	0.433182i	$-0.142609\pi$
$450$	11.7220	+	5.08505i	0.552579	+	0.239711i
$451$	−6.20831			−0.292338
$452$		−	1.95370i		−	0.0918945i
$453$	−11.4491			−0.537925
$454$	−19.4038			−0.910668
$455$		0			0
$456$	4.94481			0.231562
$457$	−25.3873			−1.18757			−0.593785	−	0.804624i	$-0.702367\pi$
$457$	−25.3873			−1.18757			−0.593785	+	0.804624i	$0.702367\pi$
$458$			16.7503i			0.782692i
$459$	−24.9925			−1.16655
$460$	16.3981	+	3.40356i	0.764565	+	0.158692i
$461$		−	1.12031i		−	0.0521782i	−0.999660	−	0.0260891i	$-0.991695\pi$
$461$		−	1.12031i		−	0.0521782i	0.999660	−	0.0260891i	$-0.00830536\pi$
$462$	−2.35231			−0.109440
$463$	30.6952			1.42653			0.713264	−	0.700895i	$-0.247216\pi$
$463$	30.6952			1.42653			0.713264	+	0.700895i	$0.247216\pi$
$464$	0.696556			0.0323368
$465$	0.414587	−	1.99745i	0.0192260	−	0.0926296i
$466$			16.7974i			0.778124i
$467$		−	5.88670i		−	0.272404i	−0.990681	−	0.136202i	$-0.956510\pi$
$467$		−	5.88670i		−	0.272404i	0.990681	−	0.136202i	$-0.0434896\pi$
$468$		0			0
$469$	26.5505			1.22599
$470$	1.26084	−	6.07463i	0.0581582	−	0.280202i
$471$	7.37720			0.339924
$472$		−	0.0690364i		−	0.00317766i
$473$	−3.48597			−0.160285
$474$		−	0.511198i		−	0.0234801i
$475$	14.7580	−	34.0198i	0.677142	−	1.56094i
$476$			16.2926i			0.746768i
$477$			18.0096i			0.824602i
$478$			18.2819i			0.836194i
$479$			24.6962i			1.12840i	0.825638	+	0.564200i	$0.190815\pi$
$479$			24.6962i			1.12840i	−0.825638	+	0.564200i	$0.809185\pi$
$480$	−1.45973	−	0.302978i	−0.0666271	−	0.0138290i
$481$		0			0
$482$		−	7.86172i		−	0.358091i
$483$	−12.0576			−0.548639
$484$	8.86496			0.402953
$485$	−4.78102	+	23.0346i	−0.217095	+	1.04595i
$486$		−	14.5768i		−	0.661217i
$487$	6.85817			0.310774			0.155387	−	0.987854i	$-0.450338\pi$
$487$	6.85817			0.310774			0.155387	+	0.987854i	$0.450338\pi$
$488$	−5.91472			−0.267747
$489$		−	10.1633i		−	0.459600i
$490$	0.531521	−	2.56083i	0.0240117	−	0.115687i
$491$	32.0421			1.44604			0.723021	−	0.690826i	$-0.242753\pi$
$491$	32.0421			1.44604			0.723021	+	0.690826i	$0.242753\pi$
$492$	2.83280			0.127712
$493$			4.70000i			0.211677i
$494$		0			0
$495$	−8.17526	−	1.69684i	−0.367450	−	0.0762674i
$496$		−	1.36837i		−	0.0614418i
$497$			8.71480i			0.390912i
$498$			11.0543i			0.495354i
$499$		−	25.9861i		−	1.16330i	−0.813440	−	0.581648i	$-0.802408\pi$
$499$		−	25.9861i		−	1.16330i	0.813440	−	0.581648i	$-0.197592\pi$
$500$	−6.44107	+	9.13853i	−0.288053	+	0.408687i
$501$		−	5.79514i		−	0.258908i
$502$	8.97087			0.400389
$503$			7.96895i			0.355318i	0.984092	+	0.177659i	$0.0568524\pi$
$503$			7.96895i			0.355318i	−0.984092	+	0.177659i	$0.943148\pi$
$504$	−6.17050			−0.274856
$505$	−6.47437	+	31.1930i	−0.288105	+	1.38807i
$506$	−10.9439			−0.486513
$507$		0			0
$508$			9.73867i			0.432084i
$509$		−	26.5772i		−	1.17801i	−0.808128	−	0.589007i	$-0.799519\pi$
$509$		−	26.5772i		−	1.17801i	0.808128	−	0.589007i	$-0.200481\pi$
$510$	2.04434	−	9.84948i	0.0905250	−	0.436142i
$511$	22.4597			0.993558
$512$	−1.00000			−0.0441942
$513$	−27.4708			−1.21286
$514$			24.2725i			1.07062i
$515$	−21.2900	−	4.41892i	−0.938150	−	0.194721i
$516$	1.59062			0.0700232
$517$			4.05412i			0.178300i
$518$	−22.3398			−0.981554
$519$	−2.26170			−0.0992776
$520$		0			0
$521$	−16.3843			−0.717810			−0.358905	−	0.933374i	$-0.616850\pi$
$521$	−16.3843			−0.717810			−0.358905	+	0.933374i	$0.616850\pi$
$522$	−1.78004			−0.0779100
$523$			12.9757i			0.567390i	0.958915	+	0.283695i	$0.0915603\pi$
$523$			12.9757i			0.567390i	−0.958915	+	0.283695i	$0.908440\pi$
$524$	10.6075			0.463389
$525$	3.20343	−	7.38449i	0.139809	−	0.322285i
$526$		−	28.7755i		−	1.25467i
$527$	9.23308			0.402199
$528$	0.974200			0.0423966
$529$	−33.0964			−1.43897
$530$	−15.4297	−	3.20256i	−0.670223	−	0.139110i
$531$			0.176421i			0.00765602i
$532$			17.9082i			0.776418i
$533$		0			0
$534$	−11.8331			−0.512067
$535$	−13.4627	−	2.79428i	−0.582041	−	0.120807i
$536$	−10.9958			−0.474945
$537$			8.86713i			0.382645i
$538$	−26.2808			−1.13305
$539$			1.70906i			0.0736144i
$540$	8.10948	+	1.68319i	0.348976	+	0.0724329i
$541$		−	23.1606i		−	0.995753i	−0.867248	−	0.497877i	$-0.834113\pi$
$541$		−	23.1606i		−	0.995753i	0.867248	−	0.497877i	$-0.165887\pi$
$542$			14.3647i			0.617017i
$543$			9.33475i			0.400593i
$544$		−	6.74749i		−	0.289296i
$545$	−0.698864	−	0.145055i	−0.0299360	−	0.00621347i
$546$		0			0
$547$		−	13.3168i		−	0.569387i	−0.958619	−	0.284693i	$-0.908108\pi$
$547$		−	13.3168i		−	0.569387i	0.958619	−	0.284693i	$-0.0918917\pi$
$548$	6.40586			0.273645
$549$	15.1150			0.645091
$550$	2.90753	−	6.70240i	0.123978	−	0.285791i
$551$			5.16607i			0.220082i
$552$	4.99359			0.212541
$553$	1.85136			0.0787279
$554$			9.92492i			0.421669i
$555$	13.5053	+	2.80313i	0.573266	+	0.118986i
$556$	16.7981			0.712398
$557$	−3.02677			−0.128248			−0.0641242	−	0.997942i	$-0.520425\pi$
$557$	−3.02677			−0.128248			−0.0641242	+	0.997942i	$0.520425\pi$
$558$			3.49685i			0.148034i
$559$		0			0
$560$	1.09727	−	5.28656i	0.0463681	−	0.223398i
$561$			6.57340i			0.277529i
$562$			11.7992i			0.497718i
$563$			18.2744i			0.770175i	0.922880	+	0.385087i	$0.125829\pi$
$563$			18.2744i			0.770175i	−0.922880	+	0.385087i	$0.874171\pi$
$564$		−	1.84986i		−	0.0778932i
$565$	−4.27745	−	0.887820i	−0.179954	−	0.0373509i
$566$			13.0538i			0.548692i
$567$	12.5486			0.526990
$568$		−	3.60919i		−	0.151438i
$569$	−25.9020			−1.08587			−0.542933	−	0.839776i	$-0.682686\pi$
$569$	−25.9020			−1.08587			−0.542933	+	0.839776i	$0.682686\pi$
$570$	2.24706	−	10.8262i	0.0941192	−	0.453459i
$571$	37.9443			1.58792			0.793960	−	0.607970i	$-0.208016\pi$
$571$	37.9443			1.58792			0.793960	+	0.607970i	$0.208016\pi$
$572$		0			0
$573$		−	12.5061i		−	0.522451i
$574$			10.2593i			0.428215i
$575$	14.9035	−	34.3554i	0.621521	−	1.43272i
$576$	2.55548			0.106478
$577$	18.6481			0.776330			0.388165	−	0.921590i	$-0.373109\pi$
$577$	18.6481			0.776330			0.388165	+	0.921590i	$0.373109\pi$
$578$	28.5286			1.18663
$579$		−	16.2583i		−	0.675674i
$580$	0.316535	−	1.52504i	0.0131434	−	0.0633240i
$581$	−40.0343			−1.66090
$582$			7.01455i			0.290763i
$583$	10.2976			0.426481
$584$	−9.30157			−0.384902
$585$		0			0
$586$	16.2358			0.670695
$587$	−6.63680			−0.273930			−0.136965	−	0.990576i	$-0.543735\pi$
$587$	−6.63680			−0.273930			−0.136965	+	0.990576i	$0.543735\pi$
$588$		−	0.779830i		−	0.0321596i
$589$	10.1487			0.418168
$590$	−0.151149	−	0.0313721i	−0.00622269	−	0.00129157i
$591$			1.82104i			0.0749077i
$592$	9.25191			0.380251
$593$	−8.72953			−0.358479			−0.179239	−	0.983805i	$-0.557364\pi$
$593$	−8.72953			−0.358479			−0.179239	+	0.983805i	$0.557364\pi$
$594$	−5.41215			−0.222063
$595$	35.6710	+	7.40381i	1.46237	+	0.303527i
$596$		−	8.90415i		−	0.364728i
$597$			7.47504i			0.305933i
$598$		0			0
$599$	−38.0625			−1.55519			−0.777596	−	0.628765i	$-0.783561\pi$
$599$	−38.0625			−1.55519			−0.777596	+	0.628765i	$0.783561\pi$
$600$	−1.32668	+	3.05825i	−0.0541616	+	0.124853i
$601$	−2.03785			−0.0831256			−0.0415628	−	0.999136i	$-0.513234\pi$
$601$	−2.03785			−0.0831256			−0.0415628	+	0.999136i	$0.513234\pi$
$602$			5.76062i			0.234785i
$603$	28.0995			1.14430
$604$			17.1722i			0.698726i
$605$	4.02850	−	19.4090i	0.163782	−	0.789088i
$606$			9.49897i			0.385869i
$607$		−	1.61460i		−	0.0655347i	−0.999463	−	0.0327674i	$-0.989568\pi$
$607$		−	1.61460i		−	0.0655347i	0.999463	−	0.0327674i	$-0.0104320\pi$
$608$		−	7.41659i		−	0.300782i
$609$			1.12137i			0.0454402i
$610$	−2.68782	+	12.9497i	−0.108827	+	0.524319i
$611$		0			0
$612$			17.2431i			0.697010i
$613$	17.8032			0.719066			0.359533	−	0.933132i	$-0.382936\pi$
$613$	17.8032			0.719066			0.359533	+	0.933132i	$0.382936\pi$
$614$	−5.66589			−0.228657
$615$	1.28731	−	6.20215i	0.0519092	−	0.250095i
$616$			3.52818i			0.142154i
$617$	36.9565			1.48781			0.743906	−	0.668284i	$-0.232971\pi$
$617$	36.9565			1.48781			0.743906	+	0.668284i	$0.232971\pi$
$618$	−6.48328			−0.260796
$619$			31.6640i			1.27268i	0.771408	+	0.636341i	$0.219553\pi$
$619$			31.6640i			1.27268i	−0.771408	+	0.636341i	$0.780447\pi$
$620$	−2.99592	−	0.621829i	−0.120319	−	0.0249732i
$621$	−27.7418			−1.11324
$622$	20.5465			0.823839
$623$		−	42.8548i		−	1.71694i
$624$		0			0
$625$	17.0809	+	18.2549i	0.683237	+	0.730197i
$626$			11.0354i			0.441062i
$627$			7.22524i			0.288548i
$628$		−	11.0649i		−	0.441537i
$629$			62.4272i			2.48913i
$630$	−2.80405	+	13.5097i	−0.111716	+	0.538240i
$631$		−	7.35141i		−	0.292655i	−0.989236	−	0.146327i	$-0.953255\pi$
$631$		−	7.35141i		−	0.292655i	0.989236	−	0.146327i	$-0.0467453\pi$
$632$	−0.766732			−0.0304990
$633$			9.14494i			0.363479i
$634$	−17.0656			−0.677763
$635$	21.3219	+	4.42554i	0.846134	+	0.175622i
$636$	−4.69869			−0.186315
$637$		0			0
$638$			1.01779i			0.0402947i
$639$			9.22322i			0.364865i
$640$	−0.454429	+	2.18940i	−0.0179629	+	0.0865438i
$641$	−38.9606			−1.53885			−0.769425	−	0.638737i	$-0.779457\pi$
$641$	−38.9606			−1.53885			−0.769425	+	0.638737i	$0.779457\pi$
$642$	−4.09968			−0.161801
$643$	−0.528071			−0.0208251			−0.0104126	−	0.999946i	$-0.503314\pi$
$643$	−0.528071			−0.0208251			−0.0104126	+	0.999946i	$0.503314\pi$
$644$			18.0848i			0.712643i
$645$	0.722825	−	3.48251i	0.0284612	−	0.137124i
$646$	50.0433			1.96893
$647$		−	30.5439i		−	1.20081i	−0.799698	−	0.600403i	$-0.795007\pi$
$647$		−	30.5439i		−	1.20081i	0.799698	−	0.600403i	$-0.204993\pi$
$648$	−5.19692			−0.204154
$649$	0.100874			0.00395966
$650$		0			0
$651$	2.20291			0.0863390
$652$	−15.2437			−0.596988
$653$			11.9772i			0.468704i	0.972152	+	0.234352i	$0.0752968\pi$
$653$			11.9772i			0.468704i	−0.972152	+	0.234352i	$0.924703\pi$
$654$	−0.212820			−0.00832190
$655$	4.82034	−	23.2240i	0.188346	−	0.907438i
$656$		−	4.24884i		−	0.165889i
$657$	23.7700			0.927355
$658$	6.69949			0.261173
$659$	−4.01683			−0.156474			−0.0782368	−	0.996935i	$-0.524929\pi$
$659$	−4.01683			−0.156474			−0.0782368	+	0.996935i	$0.524929\pi$
$660$	0.442705	−	2.13292i	0.0172323	−	0.0830237i
$661$		−	40.3372i		−	1.56893i	−0.620170	−	0.784467i	$-0.712936\pi$
$661$		−	40.3372i		−	1.56893i	0.620170	−	0.784467i	$-0.287064\pi$
$662$		−	29.6977i		−	1.15423i
$663$		0			0
$664$	16.5800			0.643430
$665$	39.2083	+	8.13800i	1.52043	+	0.315578i
$666$	−23.6431			−0.916151
$667$			5.21703i			0.202004i
$668$	−8.69198			−0.336303
$669$		−	6.56291i		−	0.253737i
$670$	−4.99680	+	24.0742i	−0.193043	+	0.930067i
$671$		−	8.64245i		−	0.333638i
$672$		−	1.60988i		−	0.0621024i
$673$			41.3853i			1.59529i	0.603129	+	0.797644i	$0.293920\pi$
$673$			41.3853i			1.59529i	−0.603129	+	0.797644i	$0.706080\pi$
$674$		−	11.1216i		−	0.428389i
$675$	7.37037	−	16.9900i	0.283686	−	0.653947i
$676$		0			0
$677$			23.9115i			0.918995i	0.888179	+	0.459497i	$0.151970\pi$
$677$			23.9115i			0.918995i	−0.888179	+	0.459497i	$0.848030\pi$
$678$	−1.30258			−0.0500253
$679$	−25.4040			−0.974916
$680$	−14.7730	−	3.06625i	−0.566518	−	0.117585i
$681$			12.9370i			0.495746i
$682$	1.99944			0.0765623
$683$	−23.5399			−0.900729			−0.450364	−	0.892845i	$-0.648706\pi$
$683$	−23.5399			−0.900729			−0.450364	+	0.892845i	$0.648706\pi$
$684$			18.9529i			0.724684i
$685$	2.91101	−	14.0250i	0.111224	−	0.535868i
$686$	19.7265			0.753162
$687$	11.1678			0.426079
$688$		−	2.38573i		−	0.0909552i
$689$		0			0
$690$	2.26923	−	10.9330i	0.0863882	−	0.416212i
$691$		−	27.7945i		−	1.05735i	−0.848823	−	0.528677i	$-0.822688\pi$
$691$		−	27.7945i		−	1.05735i	0.848823	−	0.528677i	$-0.177312\pi$
$692$			3.39226i			0.128954i
$693$		−	9.01618i		−	0.342496i
$694$			19.1698i			0.727676i
$695$	7.63355	−	36.7779i	0.289557	−	1.39506i
$696$		−	0.464410i		−	0.0176034i
$697$	28.6690			1.08592
$698$		−	2.07169i		−	0.0784145i
$699$	11.1992			0.423593
$700$	−11.0758	−	4.80474i	−0.418626	−	0.181602i
$701$	−20.6527			−0.780042			−0.390021	−	0.920806i	$-0.627532\pi$
$701$	−20.6527			−0.780042			−0.390021	+	0.920806i	$0.627532\pi$
$702$		0			0
$703$			68.6176i			2.58796i
$704$		−	1.46118i		−	0.0550702i
$705$	−4.05010	−	0.840631i	−0.152535	−	0.0316600i
$706$	14.2889			0.537770
$707$	−34.4016			−1.29381
$708$	−0.0460281			−0.00172984
$709$			1.90959i			0.0717161i	0.999357	+	0.0358581i	$0.0114164\pi$
$709$			1.90959i			0.0717161i	−0.999357	+	0.0358581i	$0.988584\pi$
$710$	−7.90198	−	1.64012i	−0.296556	−	0.0615527i
$711$	1.95937			0.0734821
$712$			17.7481i			0.665138i
$713$	10.2488			0.383820
$714$	10.8626			0.406523
$715$		0			0
$716$	13.2996			0.497029
$717$	12.1889			0.455205
$718$		−	12.4966i		−	0.466367i
$719$	36.3672			1.35627			0.678135	−	0.734938i	$-0.262789\pi$
$719$	36.3672			1.35627			0.678135	+	0.734938i	$0.262789\pi$
$720$	1.16128	−	5.59498i	0.0432785	−	0.208513i
$721$		−	23.4799i		−	0.874439i
$722$	36.0058			1.34000
$723$	−5.24159			−0.194937
$724$	14.0010			0.520341
$725$	−3.19509	−	1.38605i	−0.118663	−	0.0514765i
$726$		−	5.91047i		−	0.219358i
$727$		−	2.25162i		−	0.0835080i	−0.999128	−	0.0417540i	$-0.986705\pi$
$727$		−	2.25162i		−	0.0835080i	0.999128	−	0.0417540i	$-0.0132946\pi$
$728$		0			0
$729$	5.87208			0.217485
$730$	−4.22690	+	20.3649i	−0.156445	+	0.753739i
$731$	16.0977			0.595395
$732$			3.94348i			0.145755i
$733$	−27.7157			−1.02370			−0.511851	−	0.859074i	$-0.671040\pi$
$733$	−27.7157			−1.02370			−0.511851	+	0.859074i	$0.671040\pi$
$734$			20.7194i			0.764766i
$735$	−1.70736	−	0.354377i	−0.0629771	−	0.0130714i
$736$		−	7.48975i		−	0.276076i
$737$		−	16.0668i		−	0.591827i
$738$			10.8578i			0.399682i
$739$			17.4826i			0.643108i	0.946891	+	0.321554i	$0.104205\pi$
$739$			17.4826i			0.643108i	−0.946891	+	0.321554i	$0.895795\pi$
$740$	4.20434	−	20.2562i	0.154555	−	0.744632i
$741$		0			0
$742$		−	17.0168i		−	0.624707i
$743$	45.4090			1.66589			0.832947	−	0.553353i	$-0.186652\pi$
$743$	45.4090			1.66589			0.832947	+	0.553353i	$0.186652\pi$
$744$	−0.912326			−0.0334475
$745$	−19.4948	−	4.04630i	−0.714234	−	0.148245i
$746$		−	31.4926i		−	1.15303i
$747$	−42.3699			−1.55023
$748$	9.85927			0.360491
$749$		−	14.8475i		−	0.542514i
$750$	6.09286	+	4.29441i	0.222480	+	0.156810i
$751$	23.3846			0.853315			0.426657	−	0.904413i	$-0.359691\pi$
$751$	23.3846			0.853315			0.426657	+	0.904413i	$0.359691\pi$
$752$	−2.77456			−0.101178
$753$		−	5.98108i		−	0.217963i
$754$		0			0
$755$	37.5969	+	7.80354i	1.36829	+	0.284000i
$756$			8.94364i			0.325277i
$757$		−	33.7347i		−	1.22611i	−0.790040	−	0.613055i	$-0.789941\pi$
$757$		−	33.7347i		−	1.22611i	0.790040	−	0.613055i	$-0.210059\pi$
$758$		−	7.87442i		−	0.286012i
$759$			7.29651i			0.264847i
$760$	−16.2379	−	3.37031i	−0.589011	−	0.122254i
$761$			13.4210i			0.486512i	0.969962	+	0.243256i	$0.0782155\pi$
$761$			13.4210i			0.486512i	−0.969962	+	0.243256i	$0.921785\pi$
$762$	6.49299			0.235216
$763$		−	0.770750i		−	0.0279030i
$764$	−18.7576			−0.678627
$765$	37.7521	+	7.83575i	1.36493	+	0.283302i
$766$	−8.03386			−0.290275
$767$		0			0
$768$			0.666723i			0.0240583i
$769$		−	18.6681i		−	0.673188i	−0.941650	−	0.336594i	$-0.890725\pi$
$769$		−	18.6681i		−	0.673188i	0.941650	−	0.336594i	$-0.109275\pi$
$770$	7.72460	+	1.60331i	0.278375	+	0.0577791i
$771$	16.1831			0.582818
$772$	−24.3855			−0.877652
$773$	−2.12110			−0.0762905			−0.0381453	−	0.999272i	$-0.512145\pi$
$773$	−2.12110			−0.0762905			−0.0381453	+	0.999272i	$0.512145\pi$
$774$			6.09669i			0.219141i
$775$	−2.72287	+	6.27671i	−0.0978084	+	0.225466i
$776$	10.5209			0.377680
$777$			14.8944i			0.534335i
$778$	21.5917			0.774099
$779$	31.5119			1.12903
$780$		0			0
$781$	5.27367			0.188707
$782$	50.5370			1.80720
$783$			2.58002i			0.0922024i
$784$	−1.16965			−0.0417731
$785$	−24.2255	−	5.02820i	−0.864645	−	0.179464i
$786$		−	7.07224i		−	0.252258i
$787$	1.88977			0.0673631			0.0336815	−	0.999433i	$-0.489277\pi$
$787$	1.88977			0.0673631			0.0336815	+	0.999433i	$0.489277\pi$
$788$	2.73133			0.0972997
$789$	−19.1853			−0.683015
$790$	−0.348425	+	1.67869i	−0.0123964	+	0.0597250i
$791$		−	4.71744i		−	0.167733i
$792$			3.73401i			0.132682i
$793$		0			0
$794$	36.8751			1.30865
$795$	−2.13522	+	10.2873i	−0.0757284	+	0.364854i
$796$	11.2116			0.397385
$797$			27.7575i			0.983222i	0.870815	+	0.491611i	$0.163592\pi$
$797$			27.7575i			0.983222i	−0.870815	+	0.491611i	$0.836408\pi$
$798$	11.9398			0.422664
$799$		−	18.7213i		−	0.662312i
$800$	4.58699	+	1.98986i	0.162175	+	0.0703521i
$801$		−	45.3549i		−	1.60254i
$802$		−	8.26837i		−	0.291966i
$803$		−	13.5912i		−	0.479624i
$804$			7.33113i			0.258549i
$805$	39.5951	+	8.21828i	1.39554	+	0.289656i
$806$		0			0
$807$			17.5220i			0.616804i
$808$	14.2473			0.501217
$809$	−22.3988			−0.787501			−0.393751	−	0.919217i	$-0.628823\pi$
$809$	−22.3988			−0.787501			−0.393751	+	0.919217i	$0.628823\pi$
$810$	−2.36163	+	11.3782i	−0.0829793	+	0.399788i
$811$			10.0371i			0.352450i	0.984350	+	0.176225i	$0.0563886\pi$
$811$			10.0371i			0.352450i	−0.984350	+	0.176225i	$0.943611\pi$
$812$	1.68191			0.0590236
$813$	9.57728			0.335890
$814$			13.5187i			0.473830i
$815$	−6.92717	+	33.3746i	−0.242648	+	1.16906i
$816$	−4.49870			−0.157486
$817$	17.6940			0.619034
$818$		−	3.02146i		−	0.105643i
$819$		0			0
$820$	−9.30244	−	1.93080i	−0.324855	−	0.0674264i
$821$			12.9086i			0.450513i	0.974299	+	0.225257i	$0.0723221\pi$
$821$			12.9086i			0.450513i	−0.974299	+	0.225257i	$0.927678\pi$
$822$		−	4.27093i		−	0.148966i
$823$			24.3811i			0.849870i	0.905224	+	0.424935i	$0.139703\pi$
$823$			24.3811i			0.849870i	−0.905224	+	0.424935i	$0.860297\pi$
$824$			9.72411i			0.338755i
$825$	−4.46864	−	1.93852i	−0.155578	−	0.0674906i
$826$		−	0.166696i		−	0.00580010i
$827$	−11.1712			−0.388461			−0.194230	−	0.980956i	$-0.562221\pi$
$827$	−11.1712			−0.388461			−0.194230	+	0.980956i	$0.562221\pi$
$828$			19.1399i			0.665158i
$829$	28.9931			1.00697			0.503487	−	0.864003i	$-0.332050\pi$
$829$	28.9931			1.00697			0.503487	+	0.864003i	$0.332050\pi$
$830$	7.53444	−	36.3004i	0.261524	−	1.26000i
$831$	6.61717			0.229547
$832$		0			0
$833$		−	7.89217i		−	0.273448i
$834$		−	11.1997i		−	0.387813i
$835$	−3.94989	+	19.0303i	−0.136691	+	0.658569i
$836$	10.8369			0.374804
$837$	5.06841			0.175190
$838$	−35.0376			−1.21036
$839$			24.0650i			0.830818i	0.909635	+	0.415409i	$0.136361\pi$
$839$			24.0650i			0.830818i	−0.909635	+	0.415409i	$0.863639\pi$
$840$	−3.52467	−	0.731575i	−0.121613	−	0.0252417i
$841$	−28.5148			−0.983269
$842$		−	9.81291i		−	0.338175i
$843$	7.86678			0.270946
$844$	13.7163			0.472133
$845$		0			0
$846$	7.09033			0.243771
$847$	21.4055			0.735500
$848$			7.04744i			0.242010i
$849$	8.70327			0.298695
$850$	−13.4265	+	30.9506i	−0.460527	+	1.06160i
$851$			69.2945i			2.37539i
$852$	−2.40633			−0.0824395
$853$	13.7936			0.472284			0.236142	−	0.971719i	$-0.424117\pi$
$853$	13.7936			0.472284			0.236142	+	0.971719i	$0.424117\pi$
$854$	−14.2818			−0.488712
$855$	41.4957	+	8.61277i	1.41912	+	0.294551i
$856$			6.14900i			0.210168i
$857$		−	14.1595i		−	0.483678i	−0.970316	−	0.241839i	$-0.922249\pi$
$857$		−	14.1595i		−	0.483678i	0.970316	−	0.241839i	$-0.0777506\pi$
$858$		0			0
$859$	−27.6665			−0.943968			−0.471984	−	0.881607i	$-0.656462\pi$
$859$	−27.6665			−0.943968			−0.471984	+	0.881607i	$0.656462\pi$
$860$	−5.22333	−	1.08415i	−0.178114	−	0.0369691i
$861$	6.84011			0.233110
$862$			5.88552i			0.200462i
$863$	−17.4318			−0.593386			−0.296693	−	0.954973i	$-0.595884\pi$
$863$	−17.4318			−0.593386			−0.296693	+	0.954973i	$0.595884\pi$
$864$		−	3.70397i		−	0.126011i
$865$	7.42704	+	1.54154i	0.252527	+	0.0524140i
$866$			31.1096i			1.05715i
$867$		−	19.0206i		−	0.645975i
$868$		−	3.30409i		−	0.112148i
$869$		−	1.12033i		−	0.0380046i
$870$	−1.01678	−	0.211041i	−0.0344721	−	0.00715497i
$871$		0			0
$872$			0.319202i			0.0108096i
$873$	−26.8861			−0.909956
$874$	55.5484			1.87895
$875$	−15.5527	+	22.0660i	−0.525777	+	0.745967i
$876$			6.20157i			0.209532i
$877$	2.17528			0.0734539			0.0367270	−	0.999325i	$-0.488307\pi$
$877$	2.17528			0.0734539			0.0367270	+	0.999325i	$0.488307\pi$
$878$	2.69710			0.0910229
$879$		−	10.8248i		−	0.365111i
$880$	−3.19911	−	0.664001i	−0.107842	−	0.0223835i
$881$	6.32823			0.213204			0.106602	−	0.994302i	$-0.466003\pi$
$881$	6.32823			0.213204			0.106602	+	0.994302i	$0.466003\pi$
$882$	2.98901			0.100645
$883$		−	28.5533i		−	0.960895i	−0.877024	−	0.480447i	$-0.840474\pi$
$883$		−	28.5533i		−	0.960895i	0.877024	−	0.480447i	$-0.159526\pi$
$884$		0			0
$885$	−0.0209165	+	0.100774i	−0.000703101	+	0.00338749i
$886$			19.0859i			0.641203i
$887$			21.3012i			0.715225i	0.933870	+	0.357613i	$0.116409\pi$
$887$			21.3012i			0.715225i	−0.933870	+	0.357613i	$0.883591\pi$
$888$		−	6.16846i		−	0.207000i
$889$			23.5151i			0.788672i
$890$	38.8578	+	8.06526i	1.30252	+	0.270348i
$891$		−	7.59362i		−	0.254396i
$892$	−9.84353			−0.329586
$893$		−	20.5778i		−	0.688609i
$894$	−5.93660			−0.198550
$895$	6.04372	−	29.1182i	0.202019	−	0.973313i
$896$	−2.41461			−0.0806665
$897$		0			0
$898$			18.3579i			0.612611i
$899$		−	0.953149i		−	0.0317893i
$900$	−11.7220	−	5.08505i	−0.390732	−	0.169502i
$901$	−47.5525			−1.58420
$902$	6.20831			0.206714
$903$	3.84073			0.127812
$904$			1.95370i			0.0649793i
$905$	6.36244	−	30.6538i	0.211495	−	1.01897i
$906$	11.4491			0.380370
$907$			46.5451i			1.54551i	0.634707	+	0.772753i	$0.281121\pi$
$907$			46.5451i			1.54551i	−0.634707	+	0.772753i	$0.718879\pi$
$908$	19.4038			0.643939
$909$	−36.4086			−1.20760
$910$		0			0
$911$	−29.3014			−0.970800			−0.485400	−	0.874292i	$-0.661326\pi$
$911$	−29.3014			−0.970800			−0.485400	+	0.874292i	$0.661326\pi$
$912$	−4.94481			−0.163739
$913$			24.2263i			0.801775i
$914$	25.3873			0.839739
$915$	8.63387	+	1.79203i	0.285427	+	0.0592427i
$916$		−	16.7503i		−	0.553447i
$917$	25.6129			0.845813
$918$	24.9925			0.824874
$919$	−29.4843			−0.972598			−0.486299	−	0.873792i	$-0.661654\pi$
$919$	−29.4843			−0.972598			−0.486299	+	0.873792i	$0.661654\pi$
$920$	−16.3981	−	3.40356i	−0.540629	−	0.112212i
$921$			3.77758i			0.124476i
$922$			1.12031i			0.0368956i
$923$		0			0
$924$	2.35231			0.0773855
$925$	−42.4384	−	18.4100i	−1.39537	−	0.605317i
$926$	−30.6952			−1.00871
$927$		−	24.8498i		−	0.816173i
$928$	−0.696556			−0.0228656
$929$		−	47.7459i		−	1.56649i	−0.621712	−	0.783246i	$-0.713562\pi$
$929$		−	47.7459i		−	1.56649i	0.621712	−	0.783246i	$-0.286438\pi$
$930$	−0.414587	+	1.99745i	−0.0135949	+	0.0654990i
$931$		−	8.67479i		−	0.284305i
$932$		−	16.7974i		−	0.550217i
$933$		−	13.6988i		−	0.448479i
$934$			5.88670i			0.192619i
$935$	4.48034	−	21.5859i	0.146523	−	0.705935i
$936$		0			0
$937$		−	29.2998i		−	0.957182i	−0.878038	−	0.478591i	$-0.841148\pi$
$937$		−	29.2998i		−	0.957182i	0.878038	−	0.478591i	$-0.158852\pi$
$938$	−26.5505			−0.866905
$939$	7.35753			0.240104
$940$	−1.26084	+	6.07463i	−0.0411241	+	0.198133i
$941$		−	7.48425i		−	0.243980i	−0.992531	−	0.121990i	$-0.961072\pi$
$941$		−	7.48425i		−	0.243980i	0.992531	−	0.121990i	$-0.0389275\pi$
$942$	−7.37720			−0.240362
$943$	31.8228			1.03629
$944$			0.0690364i			0.00224694i
$945$	19.5813	+	4.06425i	0.636978	+	0.132210i
$946$	3.48597			0.113339
$947$	15.9785			0.519230			0.259615	−	0.965712i	$-0.416404\pi$
$947$	15.9785			0.519230			0.259615	+	0.965712i	$0.416404\pi$
$948$			0.511198i			0.0166029i
$949$		0			0
$950$	−14.7580	+	34.0198i	−0.478811	+	1.10375i
$951$			11.3780i			0.368958i
$952$		−	16.2926i		−	0.528045i
$953$			44.7821i			1.45063i	0.688415	+	0.725317i	$0.258307\pi$
$953$			44.7821i			1.45063i	−0.688415	+	0.725317i	$0.741693\pi$
$954$		−	18.0096i		−	0.583082i
$955$	−8.52401	+	41.0680i	−0.275830	+	1.32893i
$956$		−	18.2819i		−	0.591278i
$957$	0.678585			0.0219355
$958$		−	24.6962i		−	0.797899i
$959$	15.4677			0.499477
$960$	1.45973	+	0.302978i	0.0471125	+	0.00977858i
$961$	29.1276			0.939599
$962$		0			0
$963$		−	15.7137i		−	0.506365i
$964$			7.86172i			0.253209i
$965$	−11.0815	+	53.3896i	−0.356725	+	1.71867i
$966$	12.0576			0.387946
$967$	−5.51993			−0.177509			−0.0887546	−	0.996054i	$-0.528289\pi$
$967$	−5.51993			−0.177509			−0.0887546	+	0.996054i	$0.528289\pi$
$968$	−8.86496			−0.284931
$969$		−	33.3650i		−	1.07184i
$970$	4.78102	−	23.0346i	0.153509	−	0.739597i
$971$	−38.6903			−1.24163			−0.620815	−	0.783957i	$-0.713198\pi$
$971$	−38.6903			−1.24163			−0.620815	+	0.783957i	$0.713198\pi$
$972$			14.5768i			0.467551i
$973$	40.5609			1.30032
$974$	−6.85817			−0.219750
$975$		0			0
$976$	5.91472			0.189326
$977$	22.0275			0.704722			0.352361	−	0.935864i	$-0.385379\pi$
$977$	22.0275			0.704722			0.352361	+	0.935864i	$0.385379\pi$
$978$			10.1633i			0.324987i
$979$	−25.9331			−0.828826
$980$	−0.531521	+	2.56083i	−0.0169788	+	0.0818027i
$981$		−	0.815716i		−	0.0260438i
$982$	−32.0421			−1.02251
$983$	−49.1575			−1.56788			−0.783941	−	0.620835i	$-0.786794\pi$
$983$	−49.1575			−1.56788			−0.783941	+	0.620835i	$0.786794\pi$
$984$	−2.83280			−0.0903064
$985$	1.24120	−	5.97999i	0.0395478	−	0.190538i
$986$		−	4.70000i		−	0.149679i
$987$		−	4.46670i		−	0.142177i
$988$		0			0
$989$	17.8685			0.568186
$990$	8.17526	+	1.69684i	0.259827	+	0.0539292i
$991$	−7.70733			−0.244831			−0.122416	−	0.992479i	$-0.539064\pi$
$991$	−7.70733			−0.244831			−0.122416	+	0.992479i	$0.539064\pi$
$992$			1.36837i			0.0434459i
$993$	−19.8001			−0.628338
$994$		−	8.71480i		−	0.276417i
$995$	5.09489	−	24.5468i	0.161519	−	0.778185i
$996$		−	11.0543i		−	0.350268i
$997$			23.9968i			0.759986i	0.924989	+	0.379993i	$0.124074\pi$
$997$			23.9968i			0.759986i	−0.924989	+	0.379993i	$0.875926\pi$
$998$			25.9861i			0.822575i
$999$			34.2688i			1.08422i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.5	✓	18	65.44	odd	4
1690.2.b.f.339.14	yes	18	13.5	odd	4
1690.2.b.g.339.5	yes	18	13.8	odd	4
1690.2.b.g.339.14	yes	18	65.34	odd	4
1690.2.c.g.1689.7		18	65.64	even	2	inner
1690.2.c.g.1689.12		18	1.1	even	1	trivial
1690.2.c.h.1689.7		18	5.4	even	2
1690.2.c.h.1689.12		18	13.12	even	2
8450.2.a.ct.1.5		9	65.8	even	4
8450.2.a.cw.1.5		9	65.57	even	4
8450.2.a.cx.1.5		9	65.18	even	4
8450.2.a.da.1.5		9	65.47	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)

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

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