LMFDB - Embedded newform 1690.2.c.e.1689.3

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 = [8,-8,0,8,-3] 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:	$8$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.3
Root			$-1.83766i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.e.1689.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.83766i q^{3} +1.00000 q^{4} +(2.21022 - 0.339024i) q^{5} +1.83766i q^{6} +4.79742 q^{7} -1.00000 q^{8} -0.376989 q^{9} +(-2.21022 + 0.339024i) q^{10} +1.65153i q^{11} -1.83766i q^{12} -4.79742 q^{14} +(-0.623011 - 4.06163i) q^{15} +1.00000 q^{16} -0.0805241i q^{17} +0.376989 q^{18} -4.24776i q^{19} +(2.21022 - 0.339024i) q^{20} -8.81603i q^{21} -1.65153i q^{22} +5.89928i q^{23} +1.83766i q^{24} +(4.77013 - 1.49863i) q^{25} -4.82020i q^{27} +4.79742 q^{28} -4.42044 q^{29} +(0.623011 + 4.06163i) q^{30} -4.06163i q^{31} -1.00000 q^{32} +3.03494 q^{33} +0.0805241i q^{34} +(10.6034 - 1.62644i) q^{35} -0.376989 q^{36} +1.81708 q^{37} +4.24776i q^{38} +(-2.21022 + 0.339024i) q^{40} -6.78855i q^{41} +8.81603i q^{42} +8.49552i q^{43} +1.65153i q^{44} +(-0.833228 + 0.127808i) q^{45} -5.89928i q^{46} -0.448597 q^{47} -1.83766i q^{48} +16.0153 q^{49} +(-4.77013 + 1.49863i) q^{50} -0.147976 q^{51} +11.5770i q^{53} +4.82020i q^{54} +(0.559907 + 3.65023i) q^{55} -4.79742 q^{56} -7.80593 q^{57} +4.42044 q^{58} -2.10800i q^{59} +(-0.623011 - 4.06163i) q^{60} -3.12832 q^{61} +4.06163i q^{62} -1.80858 q^{63} +1.00000 q^{64} -3.03494 q^{66} -4.00000 q^{67} -0.0805241i q^{68} +10.8409 q^{69} +(-10.6034 + 1.62644i) q^{70} +7.35063i q^{71} +0.376989 q^{72} +10.5752 q^{73} -1.81708 q^{74} +(-2.75398 - 8.76586i) q^{75} -4.24776i q^{76} +7.92308i q^{77} -14.6468 q^{79} +(2.21022 - 0.339024i) q^{80} -9.98885 q^{81} +6.78855i q^{82} +12.4289 q^{83} -8.81603i q^{84} +(-0.0272996 - 0.177976i) q^{85} -8.49552i q^{86} +8.12325i q^{87} -1.65153i q^{88} +8.35955i q^{89} +(0.833228 - 0.127808i) q^{90} +5.89928i q^{92} -7.46388 q^{93} +0.448597 q^{94} +(-1.44009 - 9.38847i) q^{95} +1.83766i q^{96} -5.80593 q^{97} -16.0153 q^{98} -0.622608i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 3 q^{5} + 10 q^{7} - 8 q^{8} - 16 q^{9} + 3 q^{10} - 10 q^{14} + 8 q^{15} + 8 q^{16} + 16 q^{18} - 3 q^{20} + 5 q^{25} + 10 q^{28} + 6 q^{29} - 8 q^{30} - 8 q^{32} - 20 q^{33}+ \cdots - 30 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 3 * q^5 + 10 * q^7 - 8 * q^8 - 16 * q^9 + 3 * q^10 - 10 * q^14 + 8 * q^15 + 8 * q^16 + 16 * q^18 - 3 * q^20 + 5 * q^25 + 10 * q^28 + 6 * q^29 - 8 * q^30 - 8 * q^32 - 20 * q^33 + 18 * q^35 - 16 * q^36 + 40 * q^37 + 3 * q^40 + 27 * q^45 - 6 * q^47 + 30 * q^49 - 5 * q^50 - 20 * q^51 - 8 * q^55 - 10 * q^56 - 24 * q^57 - 6 * q^58 + 8 * q^60 + 10 * q^61 - 50 * q^63 + 8 * q^64 + 20 * q^66 - 32 * q^67 + 4 * q^69 - 18 * q^70 + 16 * q^72 - 26 * q^73 - 40 * q^74 - 48 * q^75 + 4 * q^79 - 3 * q^80 - 16 * q^81 + 48 * q^83 - 5 * q^85 - 27 * q^90 + 36 * q^93 + 6 * q^94 - 24 * q^95 - 8 * q^97 - 30 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.83766i		−	1.06097i	−0.847693	−	0.530486i	$-0.822009\pi$
$3$		−	1.83766i		−	1.06097i	0.847693	−	0.530486i	$-0.177991\pi$
$4$	1.00000			0.500000
$5$	2.21022	−	0.339024i	0.988439	−	0.151616i
$5$	2.21022	−	0.339024i	0.988439	−	0.151616i
$6$			1.83766i			0.750221i
$7$	4.79742			1.81326			0.906628	−	0.421931i	$-0.138647\pi$
$7$	4.79742			1.81326			0.906628	+	0.421931i	$0.138647\pi$
$8$	−1.00000			−0.353553
$9$	−0.376989			−0.125663
$10$	−2.21022	+	0.339024i	−0.698932	+	0.107209i
$11$			1.65153i			0.497954i	0.968509	+	0.248977i	$0.0800944\pi$
$11$			1.65153i			0.497954i	−0.968509	+	0.248977i	$0.919906\pi$
$12$		−	1.83766i		−	0.530486i
$13$		0			0
$13$		0			0
$14$	−4.79742			−1.28217
$15$	−0.623011	−	4.06163i	−0.160861	−	1.04871i
$16$	1.00000			0.250000
$17$		−	0.0805241i		−	0.0195300i	−0.999952	−	0.00976499i	$-0.996892\pi$
$17$		−	0.0805241i		−	0.0195300i	0.999952	−	0.00976499i	$-0.00310834\pi$
$18$	0.376989			0.0888572
$19$		−	4.24776i		−	0.974502i	−0.873262	−	0.487251i	$-0.838000\pi$
$19$		−	4.24776i		−	0.974502i	0.873262	−	0.487251i	$-0.162000\pi$
$20$	2.21022	−	0.339024i	0.494220	−	0.0758081i
$21$		−	8.81603i		−	1.92382i
$22$		−	1.65153i		−	0.352107i
$23$			5.89928i			1.23009i	0.788494	+	0.615043i	$0.210861\pi$
$23$			5.89928i			1.23009i	−0.788494	+	0.615043i	$0.789139\pi$
$24$			1.83766i			0.375111i
$25$	4.77013	−	1.49863i	0.954025	−	0.299727i
$26$		0			0
$27$		−	4.82020i		−	0.927648i
$28$	4.79742			0.906628
$29$	−4.42044			−0.820854			−0.410427	−	0.911893i	$-0.634620\pi$
$29$	−4.42044			−0.820854			−0.410427	+	0.911893i	$0.634620\pi$
$30$	0.623011	+	4.06163i	0.113746	+	0.741548i
$31$		−	4.06163i		−	0.729490i	−0.931108	−	0.364745i	$-0.881156\pi$
$31$		−	4.06163i		−	0.729490i	0.931108	−	0.364745i	$-0.118844\pi$
$32$	−1.00000			−0.176777
$33$	3.03494			0.528316
$34$			0.0805241i			0.0138098i
$35$	10.6034	−	1.62644i	1.79229	−	0.274919i
$36$	−0.376989			−0.0628316
$37$	1.81708			0.298726			0.149363	−	0.988782i	$-0.452278\pi$
$37$	1.81708			0.298726			0.149363	+	0.988782i	$0.452278\pi$
$38$			4.24776i			0.689077i
$39$		0			0
$40$	−2.21022	+	0.339024i	−0.349466	+	0.0536044i
$41$		−	6.78855i		−	1.06019i	−0.847937	−	0.530097i	$-0.822156\pi$
$41$		−	6.78855i		−	1.06019i	0.847937	−	0.530097i	$-0.177844\pi$
$42$			8.81603i			1.36034i
$43$			8.49552i			1.29555i	0.761830	+	0.647777i	$0.224301\pi$
$43$			8.49552i			1.29555i	−0.761830	+	0.647777i	$0.775699\pi$
$44$			1.65153i			0.248977i
$45$	−0.833228	+	0.127808i	−0.124210	+	0.0190526i
$46$		−	5.89928i		−	0.869802i
$47$	−0.448597			−0.0654345			−0.0327173	−	0.999465i	$-0.510416\pi$
$47$	−0.448597			−0.0654345			−0.0327173	+	0.999465i	$0.510416\pi$
$48$		−	1.83766i		−	0.265243i
$49$	16.0153			2.28790
$50$	−4.77013	+	1.49863i	−0.674598	+	0.211939i
$51$	−0.147976			−0.0207208
$52$		0			0
$53$			11.5770i			1.59022i	0.606463	+	0.795112i	$0.292588\pi$
$53$			11.5770i			1.59022i	−0.606463	+	0.795112i	$0.707412\pi$
$54$			4.82020i			0.655946i
$55$	0.559907	+	3.65023i	0.0754979	+	0.492197i
$56$	−4.79742			−0.641083
$57$	−7.80593			−1.03392
$58$	4.42044			0.580432
$59$		−	2.10800i		−	0.274439i	−0.990541	−	0.137219i	$-0.956183\pi$
$59$		−	2.10800i		−	0.274439i	0.990541	−	0.137219i	$-0.0438165\pi$
$60$	−0.623011	−	4.06163i	−0.0804303	−	0.524354i
$61$	−3.12832			−0.400540			−0.200270	−	0.979741i	$-0.564182\pi$
$61$	−3.12832			−0.400540			−0.200270	+	0.979741i	$0.564182\pi$
$62$			4.06163i			0.515827i
$63$	−1.80858			−0.227859
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.03494			−0.373576
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		−	0.0805241i		−	0.00976499i
$69$	10.8409			1.30509
$70$	−10.6034	+	1.62644i	−1.26734	+	0.194397i
$71$			7.35063i			0.872360i	0.899859	+	0.436180i	$0.143669\pi$
$71$			7.35063i			0.872360i	−0.899859	+	0.436180i	$0.856331\pi$
$72$	0.376989			0.0444286
$73$	10.5752			1.23773			0.618866	−	0.785496i	$-0.287592\pi$
$73$	10.5752			1.23773			0.618866	+	0.785496i	$0.287592\pi$
$74$	−1.81708			−0.211231
$75$	−2.75398	−	8.76586i	−0.318002	−	1.01219i
$76$		−	4.24776i		−	0.487251i
$77$			7.92308i			0.902918i
$78$		0			0
$79$	−14.6468			−1.64789			−0.823947	−	0.566667i	$-0.808233\pi$
$79$	−14.6468			−1.64789			−0.823947	+	0.566667i	$0.808233\pi$
$80$	2.21022	−	0.339024i	0.247110	−	0.0379041i
$81$	−9.98885			−1.10987
$82$			6.78855i			0.749670i
$83$	12.4289			1.36425			0.682127	−	0.731234i	$-0.261055\pi$
$83$	12.4289			1.36425			0.682127	+	0.731234i	$0.261055\pi$
$84$		−	8.81603i		−	0.961908i
$85$	−0.0272996	−	0.177976i	−0.00296106	−	0.0193042i
$86$		−	8.49552i		−	0.916095i
$87$			8.12325i			0.870904i
$88$		−	1.65153i		−	0.176053i
$89$			8.35955i			0.886111i	0.896494	+	0.443055i	$0.146105\pi$
$89$			8.35955i			0.886111i	−0.896494	+	0.443055i	$0.853895\pi$
$90$	0.833228	−	0.127808i	0.0878300	−	0.0134722i
$91$		0			0
$92$			5.89928i			0.615043i
$93$	−7.46388			−0.773968
$94$	0.448597			0.0462692
$95$	−1.44009	−	9.38847i	−0.147750	−	0.963237i
$96$			1.83766i			0.187555i
$97$	−5.80593			−0.589503			−0.294751	−	0.955574i	$-0.595237\pi$
$97$	−5.80593			−0.589503			−0.294751	+	0.955574i	$0.595237\pi$
$98$	−16.0153			−1.61779
$99$		−	0.622608i		−	0.0625744i
$100$	4.77013	−	1.49863i	0.477013	−	0.149863i
$101$	1.23752			0.123138			0.0615688	−	0.998103i	$-0.480390\pi$
$101$	1.23752			0.123138			0.0615688	+	0.998103i	$0.480390\pi$
$102$	0.147976			0.0146518
$103$		−	9.38847i		−	0.925073i	−0.886600	−	0.462537i	$-0.846939\pi$
$103$		−	9.38847i		−	0.925073i	0.886600	−	0.462537i	$-0.153061\pi$
$104$		0			0
$105$	−2.98885	−	19.4853i	−0.291682	−	1.90157i
$106$		−	11.5770i		−	1.12446i
$107$		−	18.5066i		−	1.78910i	−0.446968	−	0.894550i	$-0.647496\pi$
$107$		−	18.5066i		−	1.78910i	0.446968	−	0.894550i	$-0.352504\pi$
$108$		−	4.82020i		−	0.463824i
$109$		−	9.08638i		−	0.870317i	−0.900354	−	0.435158i	$-0.856692\pi$
$109$		−	9.08638i		−	0.870317i	0.900354	−	0.435158i	$-0.143308\pi$
$110$	−0.559907	−	3.65023i	−0.0533851	−	0.348036i
$111$		−	3.33918i		−	0.316941i
$112$	4.79742			0.453314
$113$			15.9407i			1.49958i	0.661678	+	0.749788i	$0.269845\pi$
$113$			15.9407i			1.49958i	−0.661678	+	0.749788i	$0.730155\pi$
$114$	7.80593			0.731092
$115$	2.00000	+	13.0387i	0.186501	+	1.21587i
$116$	−4.42044			−0.410427
$117$		0			0
$118$			2.10800i			0.194058i
$119$		−	0.386309i		−	0.0354128i
$120$	0.623011	+	4.06163i	0.0568728	+	0.370774i
$121$	8.27246			0.752042
$122$	3.12832			0.283225
$123$	−12.4750			−1.12484
$124$		−	4.06163i		−	0.364745i
$125$	10.0349	−	4.92950i	0.897553	−	0.440908i
$126$	1.80858			0.161121
$127$		−	0.892954i		−	0.0792369i	−0.999215	−	0.0396184i	$-0.987386\pi$
$127$		−	0.892954i		−	0.0792369i	0.999215	−	0.0396184i	$-0.0126142\pi$
$128$	−1.00000			−0.0883883
$129$	15.6119			1.37455
$130$		0			0
$131$	−1.11770			−0.0976541			−0.0488271	−	0.998807i	$-0.515548\pi$
$131$	−1.11770			−0.0976541			−0.0488271	+	0.998807i	$0.515548\pi$
$132$	3.03494			0.264158
$133$		−	20.3783i		−	1.76702i
$134$	4.00000			0.345547
$135$	−1.63416	−	10.6537i	−0.140646	−	0.916923i
$136$			0.0805241i			0.00690489i
$137$	−8.20936			−0.701373			−0.350686	−	0.936493i	$-0.614052\pi$
$137$	−8.20936			−0.701373			−0.350686	+	0.936493i	$0.614052\pi$
$138$	−10.8409			−0.922836
$139$	−5.11770			−0.434078			−0.217039	−	0.976163i	$-0.569640\pi$
$139$	−5.11770			−0.434078			−0.217039	+	0.976163i	$0.569640\pi$
$140$	10.6034	−	1.62644i	0.896147	−	0.137460i
$141$			0.824367i			0.0694242i
$142$		−	7.35063i		−	0.616852i
$143$		0			0
$144$	−0.376989			−0.0314158
$145$	−9.77013	+	1.49863i	−0.811365	+	0.124455i
$146$	−10.5752			−0.875209
$147$		−	29.4306i		−	2.42740i
$148$	1.81708			0.149363
$149$		−	4.14215i		−	0.339338i	−0.985501	−	0.169669i	$-0.945730\pi$
$149$		−	4.14215i		−	0.339338i	0.985501	−	0.169669i	$-0.0542699\pi$
$150$	2.75398	+	8.76586i	0.224861	+	0.715730i
$151$		−	4.43389i		−	0.360825i	−0.983591	−	0.180412i	$-0.942257\pi$
$151$		−	4.43389i		−	0.360825i	0.983591	−	0.180412i	$-0.0577432\pi$
$152$			4.24776i			0.344539i
$153$			0.0303567i			0.00245420i
$154$		−	7.92308i		−	0.638460i
$155$	−1.37699	−	8.97708i	−0.110602	−	0.721056i
$156$		0			0
$157$		−	8.32411i		−	0.664337i	−0.943220	−	0.332168i	$-0.892220\pi$
$157$		−	8.32411i		−	0.664337i	0.943220	−	0.332168i	$-0.107780\pi$
$158$	14.6468			1.16524
$159$	21.2746			1.68718
$160$	−2.21022	+	0.339024i	−0.174733	+	0.0268022i
$161$			28.3014i			2.23046i
$162$	9.98885			0.784798
$163$	−0.943288			−0.0738840			−0.0369420	−	0.999317i	$-0.511762\pi$
$163$	−0.943288			−0.0738840			−0.0369420	+	0.999317i	$0.511762\pi$
$164$		−	6.78855i		−	0.530097i
$165$	6.70788	−	1.02892i	0.522208	−	0.0801012i
$166$	−12.4289			−0.964673
$167$	4.30062			0.332792			0.166396	−	0.986059i	$-0.446787\pi$
$167$	4.30062			0.332792			0.166396	+	0.986059i	$0.446787\pi$
$168$			8.81603i			0.680171i
$169$		0			0
$170$	0.0272996	+	0.177976i	0.00209379	+	0.0136501i
$171$			1.60136i			0.122459i
$172$			8.49552i			0.647777i
$173$		−	0.994872i		−	0.0756387i	−0.999285	−	0.0378194i	$-0.987959\pi$
$173$		−	0.994872i		−	0.0756387i	0.999285	−	0.0378194i	$-0.0120411\pi$
$174$		−	8.12325i		−	0.615822i
$175$	22.8843	−	7.18959i	1.72989	−	0.543482i
$176$			1.65153i			0.124489i
$177$	−3.87379			−0.291172
$178$		−	8.35955i		−	0.626575i
$179$	−20.4357			−1.52744			−0.763719	−	0.645549i	$-0.776629\pi$
$179$	−20.4357			−1.52744			−0.763719	+	0.645549i	$0.776629\pi$
$180$	−0.833228	+	0.127808i	−0.0621052	+	0.00952628i
$181$	−19.9522			−1.48303			−0.741517	−	0.670934i	$-0.765893\pi$
$181$	−19.9522			−1.48303			−0.741517	+	0.670934i	$0.765893\pi$
$182$		0			0
$183$			5.74878i			0.424962i
$184$		−	5.89928i		−	0.434901i
$185$	4.01615	−	0.616035i	0.295273	−	0.0452918i
$186$	7.46388			0.547278
$187$	0.132988			0.00972503
$188$	−0.448597			−0.0327173
$189$		−	23.1245i		−	1.68206i
$190$	1.44009	+	9.38847i	0.104475	+	0.681111i
$191$	−7.67972			−0.555685			−0.277843	−	0.960627i	$-0.589619\pi$
$191$	−7.67972			−0.555685			−0.277843	+	0.960627i	$0.589619\pi$
$192$		−	1.83766i		−	0.132622i
$193$	−15.1914			−1.09350			−0.546751	−	0.837295i	$-0.684136\pi$
$193$	−15.1914			−1.09350			−0.546751	+	0.837295i	$0.684136\pi$
$194$	5.80593			0.416841
$195$		0			0
$196$	16.0153			1.14395
$197$	3.01327			0.214686			0.107343	−	0.994222i	$-0.465766\pi$
$197$	3.01327			0.214686			0.107343	+	0.994222i	$0.465766\pi$
$198$			0.622608i			0.0442468i
$199$	−9.72106			−0.689107			−0.344554	−	0.938767i	$-0.611970\pi$
$199$	−9.72106			−0.689107			−0.344554	+	0.938767i	$0.611970\pi$
$200$	−4.77013	+	1.49863i	−0.337299	+	0.105969i
$201$			7.35063i			0.518474i
$202$	−1.23752			−0.0870714
$203$	−21.2067			−1.48842
$204$	−0.147976			−0.0103604
$205$	−2.30148	−	15.0042i	−0.160742	−	1.04794i
$206$			9.38847i			0.654126i
$207$		−	2.22397i		−	0.154576i
$208$		0			0
$209$	7.01529			0.485257
$210$	2.98885	+	19.4853i	0.206250	+	1.34462i
$211$	−4.79064			−0.329802			−0.164901	−	0.986310i	$-0.552730\pi$
$211$	−4.79064			−0.329802			−0.164901	+	0.986310i	$0.552730\pi$
$212$			11.5770i			0.795112i
$213$	13.5080			0.925550
$214$			18.5066i			1.26508i
$215$	2.88019	+	18.7769i	0.196427	+	1.28058i
$216$			4.82020i			0.327973i
$217$		−	19.4853i		−	1.32275i
$218$			9.08638i			0.615407i
$219$		−	19.4336i		−	1.31320i
$220$	0.559907	+	3.65023i	0.0377490	+	0.246099i
$221$		0			0
$222$			3.33918i			0.224111i
$223$	14.0434			0.940419			0.470209	−	0.882555i	$-0.344178\pi$
$223$	14.0434			0.940419			0.470209	+	0.882555i	$0.344178\pi$
$224$	−4.79742			−0.320541
$225$	−1.79829	+	0.564969i	−0.119886	+	0.0376646i
$226$		−	15.9407i		−	1.06036i
$227$	2.88019			0.191165			0.0955823	−	0.995422i	$-0.469529\pi$
$227$	2.88019			0.191165			0.0955823	+	0.995422i	$0.469529\pi$
$228$	−7.80593			−0.516960
$229$			6.70802i			0.443279i	0.975129	+	0.221639i	$0.0711408\pi$
$229$			6.70802i			0.443279i	−0.975129	+	0.221639i	$0.928859\pi$
$230$	−2.00000	−	13.0387i	−0.131876	−	0.859747i
$231$	14.5599			0.957972
$232$	4.42044			0.290216
$233$			17.5959i			1.15275i	0.817186	+	0.576374i	$0.195533\pi$
$233$			17.5959i			1.15275i	−0.817186	+	0.576374i	$0.804467\pi$
$234$		0			0
$235$	−0.991496	+	0.152085i	−0.0646781	+	0.00992094i
$236$		−	2.10800i		−	0.137219i
$237$			26.9158i			1.74837i
$238$			0.386309i			0.0250407i
$239$		−	11.3119i		−	0.731708i	−0.930672	−	0.365854i	$-0.880777\pi$
$239$		−	11.3119i		−	0.731708i	0.930672	−	0.365854i	$-0.119223\pi$
$240$	−0.623011	−	4.06163i	−0.0402152	−	0.262177i
$241$			5.08019i			0.327244i	0.986523	+	0.163622i	$0.0523177\pi$
$241$			5.08019i			0.327244i	−0.986523	+	0.163622i	$0.947682\pi$
$242$	−8.27246			−0.531774
$243$			3.89550i			0.249896i
$244$	−3.12832			−0.200270
$245$	35.3973	−	5.42957i	2.26145	−	0.346882i
$246$	12.4750			0.795379
$247$		0			0
$248$			4.06163i			0.257913i
$249$		−	22.8401i		−	1.44744i
$250$	−10.0349	+	4.92950i	−0.634665	+	0.311769i
$251$	−19.5704			−1.23527			−0.617637	−	0.786463i	$-0.711910\pi$
$251$	−19.5704			−1.23527			−0.617637	+	0.786463i	$0.711910\pi$
$252$	−1.80858			−0.113930
$253$	−9.74283			−0.612526
$254$			0.892954i			0.0560289i
$255$	−0.327059	+	0.0501674i	−0.0204812	+	0.00314160i
$256$	1.00000			0.0625000
$257$		−	1.98398i		−	0.123757i	−0.998084	−	0.0618786i	$-0.980291\pi$
$257$		−	1.98398i		−	0.123757i	0.998084	−	0.0618786i	$-0.0197091\pi$
$258$	−15.6119			−0.971952
$259$	8.71731			0.541668
$260$		0			0
$261$	1.66646			0.103151
$262$	1.11770			0.0690519
$263$			0.608563i			0.0375256i	0.999824	+	0.0187628i	$0.00597274\pi$
$263$			0.608563i			0.0375256i	−0.999824	+	0.0187628i	$0.994027\pi$
$264$	−3.03494			−0.186788
$265$	3.92488	+	25.5877i	0.241104	+	1.57184i
$266$			20.3783i			1.24947i
$267$	15.3620			0.940139
$268$	−4.00000			−0.244339
$269$	17.7448			1.08192			0.540961	−	0.841048i	$-0.318061\pi$
$269$	17.7448			1.08192			0.540961	+	0.841048i	$0.318061\pi$
$270$	1.63416	+	10.6537i	0.0994520	+	0.648363i
$271$		−	16.0279i		−	0.973626i	−0.873506	−	0.486813i	$-0.838159\pi$
$271$		−	16.0279i		−	0.973626i	0.873506	−	0.486813i	$-0.161841\pi$
$272$		−	0.0805241i		−	0.00488249i
$273$		0			0
$274$	8.20936			0.495945
$275$	2.47503	+	7.87799i	0.149250	+	0.475061i
$276$	10.8409			0.652544
$277$			11.9042i			0.715253i	0.933865	+	0.357626i	$0.116414\pi$
$277$			11.9042i			0.715253i	−0.933865	+	0.357626i	$0.883586\pi$
$278$	5.11770			0.306939
$279$			1.53119i			0.0916699i
$280$	−10.6034	+	1.62644i	−0.633672	+	0.0971986i
$281$			11.3975i			0.679920i	0.940440	+	0.339960i	$0.110413\pi$
$281$			11.3975i			0.679920i	−0.940440	+	0.339960i	$0.889587\pi$
$282$		−	0.824367i		−	0.0490904i
$283$			20.4123i			1.21339i	0.794935	+	0.606694i	$0.207505\pi$
$283$			20.4123i			1.21339i	−0.794935	+	0.606694i	$0.792495\pi$
$284$			7.35063i			0.436180i
$285$	−17.2528	+	2.64640i	−1.02197	+	0.156759i
$286$		0			0
$287$		−	32.5676i		−	1.92240i
$288$	0.376989			0.0222143
$289$	16.9935			0.999619
$290$	9.77013	−	1.49863i	0.573722	−	0.0880028i
$291$			10.6693i			0.625446i
$292$	10.5752			0.618866
$293$	−4.18768			−0.244647			−0.122323	−	0.992490i	$-0.539035\pi$
$293$	−4.18768			−0.244647			−0.122323	+	0.992490i	$0.539035\pi$
$294$			29.4306i			1.71643i
$295$	−0.714665	−	4.65915i	−0.0416094	−	0.271266i
$296$	−1.81708			−0.105616
$297$	7.96069			0.461926
$298$			4.14215i			0.239948i
$299$		0			0
$300$	−2.75398	−	8.76586i	−0.159001	−	0.506097i
$301$			40.7566i			2.34917i
$302$			4.43389i			0.255142i
$303$		−	2.27413i		−	0.130646i
$304$		−	4.24776i		−	0.243626i
$305$	−6.91427	+	1.06058i	−0.395910	+	0.0607284i
$306$		−	0.0303567i		−	0.00173538i
$307$	18.0170			1.02828			0.514142	−	0.857705i	$-0.328110\pi$
$307$	18.0170			1.02828			0.514142	+	0.857705i	$0.328110\pi$
$308$			7.92308i			0.451459i
$309$	−17.2528			−0.981478
$310$	1.37699	+	8.97708i	0.0782077	+	0.509864i
$311$	−5.17816			−0.293626			−0.146813	−	0.989164i	$-0.546902\pi$
$311$	−5.17816			−0.293626			−0.146813	+	0.989164i	$0.546902\pi$
$312$		0			0
$313$			32.6333i			1.84455i	0.386539	+	0.922273i	$0.373670\pi$
$313$			32.6333i			1.84455i	−0.386539	+	0.922273i	$0.626330\pi$
$314$			8.32411i			0.469757i
$315$	−3.99735	+	0.613152i	−0.225225	+	0.0345472i
$316$	−14.6468			−0.823947
$317$	−23.7385			−1.33328			−0.666642	−	0.745378i	$-0.732269\pi$
$317$	−23.7385			−1.33328			−0.666642	+	0.745378i	$0.732269\pi$
$318$	−21.2746			−1.19302
$319$		−	7.30047i		−	0.408748i
$320$	2.21022	−	0.339024i	0.123555	−	0.0189520i
$321$	−34.0088			−1.89819
$322$		−	28.3014i		−	1.57717i
$323$	−0.342047			−0.0190320
$324$	−9.98885			−0.554936
$325$		0			0
$326$	0.943288			0.0522439
$327$	−16.6977			−0.923383
$328$			6.78855i			0.374835i
$329$	−2.15211			−0.118650
$330$	−6.70788	+	1.02892i	−0.369257	+	0.0566401i
$331$		−	30.4752i		−	1.67507i	−0.546386	−	0.837534i	$-0.683997\pi$
$331$		−	30.4752i		−	1.67507i	0.546386	−	0.837534i	$-0.316003\pi$
$332$	12.4289			0.682127
$333$	−0.685020			−0.0375389
$334$	−4.30062			−0.235319
$335$	−8.84087	+	1.35610i	−0.483028	+	0.0740915i
$336$		−	8.81603i		−	0.480954i
$337$			19.2799i			1.05024i	0.851027	+	0.525121i	$0.175980\pi$
$337$			19.2799i			1.05024i	−0.851027	+	0.525121i	$0.824020\pi$
$338$		0			0
$339$	29.2936			1.59101
$340$	−0.0272996	−	0.177976i	−0.00148053	−	0.00965210i
$341$	6.70788			0.363252
$342$		−	1.60136i		−	0.0865916i
$343$	43.2502			2.33529
$344$		−	8.49552i		−	0.458048i
$345$	23.9607	−	3.67532i	1.29000	−	0.197872i
$346$			0.994872i			0.0534846i
$347$		−	15.3720i		−	0.825211i	−0.910910	−	0.412605i	$-0.864619\pi$
$347$		−	15.3720i		−	0.825211i	0.910910	−	0.412605i	$-0.135381\pi$
$348$			8.12325i			0.435452i
$349$		−	15.2035i		−	0.813827i	−0.913467	−	0.406913i	$-0.866605\pi$
$349$		−	15.2035i		−	0.813827i	0.913467	−	0.406913i	$-0.133395\pi$
$350$	−22.8843	+	7.18959i	−1.22322	+	0.384300i
$351$		0			0
$352$		−	1.65153i		−	0.0880267i
$353$	−26.9017			−1.43183			−0.715917	−	0.698185i	$-0.753991\pi$
$353$	−26.9017			−1.43183			−0.715917	+	0.698185i	$0.753991\pi$
$354$	3.87379			0.205890
$355$	2.49204	+	16.2465i	0.132264	+	0.862275i
$356$			8.35955i			0.443055i
$357$	−0.709903			−0.0375721
$358$	20.4357			1.08006
$359$			20.8348i			1.09962i	0.835291	+	0.549809i	$0.185299\pi$
$359$			20.8348i			1.09962i	−0.835291	+	0.549809i	$0.814701\pi$
$360$	0.833228	−	0.127808i	0.0439150	−	0.00673610i
$361$	0.956554			0.0503449
$362$	19.9522			1.04866
$363$		−	15.2020i		−	0.797896i
$364$		0			0
$365$	23.3735	−	3.58525i	1.22342	−	0.187660i
$366$		−	5.74878i		−	0.300494i
$367$		−	34.5729i		−	1.80469i	−0.431013	−	0.902346i	$-0.641844\pi$
$367$		−	34.5729i		−	1.80469i	0.431013	−	0.902346i	$-0.358156\pi$
$368$			5.89928i			0.307521i
$369$			2.55921i			0.133227i
$370$	−4.01615	+	0.616035i	−0.208790	+	0.0320261i
$371$			55.5398i			2.88348i
$372$	−7.46388			−0.386984
$373$			25.0064i			1.29478i	0.762158	+	0.647391i	$0.224140\pi$
$373$			25.0064i			1.29478i	−0.762158	+	0.647391i	$0.775860\pi$
$374$	−0.132988			−0.00687663
$375$	−9.05873	−	18.4408i	−0.467791	−	0.952279i
$376$	0.448597			0.0231346
$377$		0			0
$378$			23.1245i			1.18940i
$379$		−	3.75953i		−	0.193114i	−0.995327	−	0.0965571i	$-0.969217\pi$
$379$		−	3.75953i		−	0.193114i	0.995327	−	0.0965571i	$-0.0307830\pi$
$380$	−1.44009	−	9.38847i	−0.0738752	−	0.481618i
$381$	−1.64094			−0.0840682
$382$	7.67972			0.392929
$383$	3.93892			0.201269			0.100635	−	0.994923i	$-0.467913\pi$
$383$	3.93892			0.201269			0.100635	+	0.994923i	$0.467913\pi$
$384$			1.83766i			0.0937776i
$385$	2.68611	+	17.5117i	0.136897	+	0.892480i
$386$	15.1914			0.773223
$387$		−	3.20272i		−	0.162803i
$388$	−5.80593			−0.294751
$389$	−19.1589			−0.971394			−0.485697	−	0.874127i	$-0.661434\pi$
$389$	−19.1589			−0.971394			−0.485697	+	0.874127i	$0.661434\pi$
$390$		0			0
$391$	0.475035			0.0240235
$392$	−16.0153			−0.808894
$393$			2.05396i			0.103608i
$394$	−3.01327			−0.151806
$395$	−32.3726	+	4.96562i	−1.62884	+	0.249847i
$396$		−	0.622608i		−	0.0312872i
$397$	−6.45538			−0.323986			−0.161993	−	0.986792i	$-0.551792\pi$
$397$	−6.45538			−0.323986			−0.161993	+	0.986792i	$0.551792\pi$
$398$	9.72106			0.487273
$399$	−37.4484			−1.87476
$400$	4.77013	−	1.49863i	0.238506	−	0.0749317i
$401$			34.6424i			1.72996i	0.501807	+	0.864980i	$0.332669\pi$
$401$			34.6424i			1.72996i	−0.501807	+	0.864980i	$0.667331\pi$
$402$		−	7.35063i		−	0.366616i
$403$		0			0
$404$	1.23752			0.0615688
$405$	−22.0775	+	3.38646i	−1.09704	+	0.168275i
$406$	21.2067			1.05247
$407$			3.00096i			0.148752i
$408$	0.147976			0.00732590
$409$			18.6071i			0.920063i	0.887903	+	0.460031i	$0.152162\pi$
$409$			18.6071i			0.920063i	−0.887903	+	0.460031i	$0.847838\pi$
$410$	2.30148	+	15.0042i	0.113662	+	0.741003i
$411$			15.0860i			0.744137i
$412$		−	9.38847i		−	0.462537i
$413$		−	10.1130i		−	0.497628i
$414$			2.22397i			0.109302i
$415$	27.4707	−	4.21371i	1.34848	−	0.206843i
$416$		0			0
$417$			9.40459i			0.460545i
$418$	−7.01529			−0.343129
$419$	−22.9495			−1.12116			−0.560579	−	0.828101i	$-0.689421\pi$
$419$	−22.9495			−1.12116			−0.560579	+	0.828101i	$0.689421\pi$
$420$	−2.98885	−	19.4853i	−0.145841	−	0.950787i
$421$		−	34.8196i		−	1.69700i	−0.529194	−	0.848501i	$-0.677505\pi$
$421$		−	34.8196i		−	1.69700i	0.529194	−	0.848501i	$-0.322495\pi$
$422$	4.79064			0.233205
$423$	0.169116			0.00822271
$424$		−	11.5770i		−	0.562229i
$425$	−0.120676	−	0.384110i	−0.00585366	−	0.0186321i
$426$	−13.5080			−0.654463
$427$	−15.0079			−0.726282
$428$		−	18.5066i		−	0.894550i
$429$		0			0
$430$	−2.88019	−	18.7769i	−0.138895	−	0.905504i
$431$			20.4986i			0.987385i	0.869637	+	0.493692i	$0.164353\pi$
$431$			20.4986i			0.987385i	−0.869637	+	0.493692i	$0.835647\pi$
$432$		−	4.82020i		−	0.231912i
$433$		−	2.14503i		−	0.103083i	−0.998671	−	0.0515417i	$-0.983587\pi$
$433$		−	2.14503i		−	0.103083i	0.998671	−	0.0515417i	$-0.0164135\pi$
$434$			19.4853i			0.935326i
$435$	2.75398	+	17.9542i	0.132043	+	0.860836i
$436$		−	9.08638i		−	0.435158i
$437$	25.0587			1.19872
$438$			19.4336i			0.928573i
$439$	1.05195			0.0502068			0.0251034	−	0.999685i	$-0.492008\pi$
$439$	1.05195			0.0502068			0.0251034	+	0.999685i	$0.492008\pi$
$440$	−0.559907	−	3.65023i	−0.0266925	−	0.174018i
$441$	−6.03759			−0.287504
$442$		0			0
$443$			18.3043i			0.869665i	0.900511	+	0.434833i	$0.143193\pi$
$443$			18.3043i			0.869665i	−0.900511	+	0.434833i	$0.856807\pi$
$444$		−	3.33918i		−	0.158470i
$445$	2.83409	+	18.4764i	0.134349	+	0.875867i
$446$	−14.0434			−0.664976
$447$	−7.61186			−0.360029
$448$	4.79742			0.226657
$449$			13.9524i			0.658453i	0.944251	+	0.329226i	$0.106788\pi$
$449$			13.9524i			0.658453i	−0.944251	+	0.329226i	$0.893212\pi$
$450$	1.79829	−	0.564969i	0.0847720	−	0.0266329i
$451$	11.2115			0.527927
$452$			15.9407i			0.749788i
$453$	−8.14798			−0.382825
$454$	−2.88019			−0.135174
$455$		0			0
$456$	7.80593			0.365546
$457$	29.4331			1.37682			0.688411	−	0.725321i	$-0.258309\pi$
$457$	29.4331			1.37682			0.688411	+	0.725321i	$0.258309\pi$
$458$		−	6.70802i		−	0.313445i
$459$	−0.388142			−0.0181169
$460$	2.00000	+	13.0387i	0.0932505	+	0.607933i
$461$		−	9.09372i		−	0.423537i	−0.977320	−	0.211768i	$-0.932078\pi$
$461$		−	9.09372i		−	0.423537i	0.977320	−	0.211768i	$-0.0679223\pi$
$462$	−14.5599			−0.677388
$463$	−41.6642			−1.93630			−0.968150	−	0.250372i	$-0.919447\pi$
$463$	−41.6642			−1.93630			−0.968150	+	0.250372i	$0.919447\pi$
$464$	−4.42044			−0.205214
$465$	−16.4968	+	2.53044i	−0.765021	+	0.117346i
$466$		−	17.5959i		−	0.815116i
$467$		−	38.1079i		−	1.76342i	−0.471789	−	0.881712i	$-0.656391\pi$
$467$		−	38.1079i		−	1.76342i	0.471789	−	0.881712i	$-0.343609\pi$
$468$		0			0
$469$	−19.1897			−0.886098
$470$	0.991496	−	0.152085i	0.0457343	−	0.00701516i
$471$	−15.2969			−0.704843
$472$			2.10800i			0.0970288i
$473$	−14.0306			−0.645126
$474$		−	26.9158i		−	1.23628i
$475$	−6.36584	−	20.2623i	−0.292085	−	0.929700i
$476$		−	0.386309i		−	0.0177064i
$477$		−	4.36440i		−	0.199832i
$478$			11.3119i			0.517395i
$479$		−	15.0374i		−	0.687077i	−0.939139	−	0.343538i	$-0.888374\pi$
$479$		−	15.0374i		−	0.687077i	0.939139	−	0.343538i	$-0.111626\pi$
$480$	0.623011	+	4.06163i	0.0284364	+	0.185387i
$481$		0			0
$482$		−	5.08019i		−	0.231396i
$483$	52.0083			2.36646
$484$	8.27246			0.376021
$485$	−12.8324	+	1.96835i	−0.582688	+	0.0893782i
$486$		−	3.89550i		−	0.176703i
$487$	−4.56256			−0.206749			−0.103375	−	0.994642i	$-0.532964\pi$
$487$	−4.56256			−0.206749			−0.103375	+	0.994642i	$0.532964\pi$
$488$	3.12832			0.141612
$489$			1.73344i			0.0783890i
$490$	−35.3973	+	5.42957i	−1.59909	+	0.245283i
$491$	−8.41606			−0.379812			−0.189906	−	0.981802i	$-0.560818\pi$
$491$	−8.41606			−0.379812			−0.189906	+	0.981802i	$0.560818\pi$
$492$	−12.4750			−0.562418
$493$			0.355952i			0.0160313i
$494$		0			0
$495$	−0.211079	−	1.37610i	−0.00948730	−	0.0618511i
$496$		−	4.06163i		−	0.182372i
$497$			35.2641i			1.58181i
$498$			22.8401i			1.02349i
$499$			12.5587i			0.562206i	0.959678	+	0.281103i	$0.0907002\pi$
$499$			12.5587i			0.562206i	−0.959678	+	0.281103i	$0.909300\pi$
$500$	10.0349	−	4.92950i	0.448776	−	0.220454i
$501$		−	7.90307i		−	0.353083i
$502$	19.5704			0.873471
$503$		−	7.84324i		−	0.349713i	−0.984594	−	0.174856i	$-0.944054\pi$
$503$		−	7.84324i		−	0.349713i	0.984594	−	0.174856i	$-0.0559461\pi$
$504$	1.80858			0.0805605
$505$	2.73518	−	0.419548i	0.121714	−	0.0186697i
$506$	9.74283			0.433121
$507$		0			0
$508$		−	0.892954i		−	0.0396184i
$509$			36.2850i			1.60830i	0.594424	+	0.804152i	$0.297380\pi$
$509$			36.2850i			1.60830i	−0.594424	+	0.804152i	$0.702620\pi$
$510$	0.327059	−	0.0501674i	0.0144824	−	0.00222145i
$511$	50.7337			2.24433
$512$	−1.00000			−0.0441942
$513$	−20.4750			−0.903995
$514$			1.98398i			0.0875095i
$515$	−3.18292	−	20.7506i	−0.140256	−	0.914379i
$516$	15.6119			0.687274
$517$		−	0.740869i		−	0.0325834i
$518$	−8.71731			−0.383017
$519$	−1.82823			−0.0802506
$520$		0			0
$521$	1.95007			0.0854341			0.0427171	−	0.999087i	$-0.486399\pi$
$521$	1.95007			0.0854341			0.0427171	+	0.999087i	$0.486399\pi$
$522$	−1.66646			−0.0729388
$523$		−	9.08638i		−	0.397319i	−0.980069	−	0.198660i	$-0.936341\pi$
$523$		−	9.08638i		−	0.397319i	0.980069	−	0.198660i	$-0.0636589\pi$
$524$	−1.11770			−0.0488271
$525$	−13.2120	−	42.0536i	−0.576619	−	1.83537i
$526$		−	0.608563i		−	0.0265346i
$527$	−0.327059			−0.0142469
$528$	3.03494			0.132079
$529$	−11.8016			−0.513111
$530$	−3.92488	−	25.5877i	−0.170486	−	1.11146i
$531$			0.794695i			0.0344868i
$532$		−	20.3783i		−	0.883511i
$533$		0			0
$534$	−15.3620			−0.664779
$535$	−6.27418	−	40.9036i	−0.271257	−	1.76842i
$536$	4.00000			0.172774
$537$			37.5539i			1.62057i
$538$	−17.7448			−0.765035
$539$			26.4497i			1.13927i
$540$	−1.63416	−	10.6537i	−0.0703232	−	0.458462i
$541$			35.7827i			1.53842i	0.638997	+	0.769209i	$0.279350\pi$
$541$			35.7827i			1.53842i	−0.638997	+	0.769209i	$0.720650\pi$
$542$			16.0279i			0.688458i
$543$			36.6653i			1.57346i
$544$			0.0805241i			0.00345244i
$545$	−3.08050	−	20.0829i	−0.131954	−	0.860256i
$546$		0			0
$547$			29.0584i			1.24245i	0.783634	+	0.621223i	$0.213364\pi$
$547$			29.0584i			1.24245i	−0.783634	+	0.621223i	$0.786636\pi$
$548$	−8.20936			−0.350686
$549$	1.17934			0.0503331
$550$	−2.47503	−	7.87799i	−0.105536	−	0.335919i
$551$			18.7769i			0.799925i
$552$	−10.8409			−0.461418
$553$	−70.2669			−2.98805
$554$		−	11.9042i		−	0.505760i
$555$	−1.13206	−	7.38031i	−0.0480533	−	0.313277i
$556$	−5.11770			−0.217039
$557$	−33.0984			−1.40243			−0.701213	−	0.712952i	$-0.747358\pi$
$557$	−33.0984			−1.40243			−0.701213	+	0.712952i	$0.747358\pi$
$558$		−	1.53119i		−	0.0648204i
$559$		0			0
$560$	10.6034	−	1.62644i	0.448073	−	0.0687298i
$561$		−	0.244386i		−	0.0103180i
$562$		−	11.3975i		−	0.480776i
$563$		−	10.4632i		−	0.440971i	−0.975390	−	0.220485i	$-0.929236\pi$
$563$		−	10.4632i		−	0.440971i	0.975390	−	0.220485i	$-0.0707641\pi$
$564$			0.824367i			0.0347121i
$565$	5.40429	+	35.2325i	0.227360	+	1.48224i
$566$		−	20.4123i		−	0.857995i
$567$	−47.9207			−2.01248
$568$		−	7.35063i		−	0.308426i
$569$	8.63244			0.361891			0.180945	−	0.983493i	$-0.442084\pi$
$569$	8.63244			0.361891			0.180945	+	0.983493i	$0.442084\pi$
$570$	17.2528	−	2.64640i	0.722640	−	0.110845i
$571$	14.3069			0.598724			0.299362	−	0.954140i	$-0.403226\pi$
$571$	14.3069			0.598724			0.299362	+	0.954140i	$0.403226\pi$
$572$		0			0
$573$			14.1127i			0.589567i
$574$			32.5676i			1.35934i
$575$	8.84087	+	28.1403i	0.368690	+	1.17353i
$576$	−0.376989			−0.0157079
$577$	−11.9697			−0.498306			−0.249153	−	0.968464i	$-0.580152\pi$
$577$	−11.9697			−0.498306			−0.249153	+	0.968464i	$0.580152\pi$
$578$	−16.9935			−0.706837
$579$			27.9166i			1.16018i
$580$	−9.77013	+	1.49863i	−0.405682	+	0.0622274i
$581$	59.6269			2.47374
$582$		−	10.6693i		−	0.442257i
$583$	−19.1197			−0.791858
$584$	−10.5752			−0.437605
$585$		0			0
$586$	4.18768			0.172991
$587$	−5.50796			−0.227338			−0.113669	−	0.993519i	$-0.536260\pi$
$587$	−5.50796			−0.227338			−0.113669	+	0.993519i	$0.536260\pi$
$588$		−	29.4306i		−	1.21370i
$589$	−17.2528			−0.710889
$590$	0.714665	+	4.65915i	0.0294223	+	0.191814i
$591$		−	5.53735i		−	0.227776i
$592$	1.81708			0.0746816
$593$	24.6037			1.01035			0.505177	−	0.863016i	$-0.331427\pi$
$593$	24.6037			1.01035			0.505177	+	0.863016i	$0.331427\pi$
$594$	−7.96069			−0.326631
$595$	−0.130968	−	0.853826i	−0.00536916	−	0.0350035i
$596$		−	4.14215i		−	0.169669i
$597$			17.8640i			0.731124i
$598$		0			0
$599$	35.3159			1.44297			0.721484	−	0.692431i	$-0.243460\pi$
$599$	35.3159			1.44297			0.721484	+	0.692431i	$0.243460\pi$
$600$	2.75398	+	8.76586i	0.112431	+	0.357865i
$601$	34.9214			1.42447			0.712236	−	0.701940i	$-0.247682\pi$
$601$	34.9214			1.42447			0.712236	+	0.701940i	$0.247682\pi$
$602$		−	40.7566i		−	1.66111i
$603$	1.50796			0.0614088
$604$		−	4.43389i		−	0.180412i
$605$	18.2839	−	2.80456i	0.743348	−	0.114022i
$606$			2.27413i			0.0923804i
$607$			24.9627i			1.01320i	0.862180	+	0.506602i	$0.169099\pi$
$607$			24.9627i			1.01320i	−0.862180	+	0.506602i	$0.830901\pi$
$608$			4.24776i			0.172269i
$609$			38.9707i			1.57917i
$610$	6.91427	−	1.06058i	0.279950	−	0.0429415i
$611$		0			0
$612$			0.0303567i			0.00122710i
$613$	16.1266			0.651347			0.325674	−	0.945482i	$-0.394409\pi$
$613$	16.1266			0.651347			0.325674	+	0.945482i	$0.394409\pi$
$614$	−18.0170			−0.727107
$615$	−27.5725	+	4.22934i	−1.11183	+	0.170543i
$616$		−	7.92308i		−	0.319230i
$617$	28.5073			1.14766			0.573831	−	0.818974i	$-0.305457\pi$
$617$	28.5073			1.14766			0.573831	+	0.818974i	$0.305457\pi$
$618$	17.2528			0.694010
$619$		−	0.338217i		−	0.0135941i	−0.999977	−	0.00679705i	$-0.997836\pi$
$619$		−	0.338217i		−	0.0135941i	0.999977	−	0.00679705i	$-0.00216358\pi$
$620$	−1.37699	−	8.97708i	−0.0553012	−	0.360528i
$621$	28.4357			1.14109
$622$	5.17816			0.207625
$623$			40.1043i			1.60675i
$624$		0			0
$625$	20.5082	−	14.2973i	0.820328	−	0.571894i
$626$		−	32.6333i		−	1.30429i
$627$		−	12.8917i		−	0.514845i
$628$		−	8.32411i		−	0.332168i
$629$		−	0.146319i		−	0.00583412i
$630$	3.99735	−	0.613152i	0.159258	−	0.0244285i
$631$		−	32.1930i		−	1.28158i	−0.767715	−	0.640791i	$-0.778606\pi$
$631$		−	32.1930i		−	1.28158i	0.767715	−	0.640791i	$-0.221394\pi$
$632$	14.6468			0.582618
$633$			8.80357i			0.349910i
$634$	23.7385			0.942774
$635$	−0.302733	−	1.97362i	−0.0120136	−	0.0783208i
$636$	21.2746			0.843592
$637$		0			0
$638$			7.30047i			0.289028i
$639$		−	2.77111i		−	0.109623i
$640$	−2.21022	+	0.339024i	−0.0873665	+	0.0134011i
$641$	−12.5996			−0.497655			−0.248827	−	0.968548i	$-0.580045\pi$
$641$	−12.5996			−0.497655			−0.248827	+	0.968548i	$0.580045\pi$
$642$	34.0088			1.34222
$643$	19.4055			0.765280			0.382640	−	0.923898i	$-0.375015\pi$
$643$	19.4055			0.765280			0.382640	+	0.923898i	$0.375015\pi$
$644$			28.3014i			1.11523i
$645$	34.5056	−	5.29280i	1.35866	−	0.208404i
$646$	0.342047			0.0134577
$647$		−	18.6943i		−	0.734949i	−0.930034	−	0.367475i	$-0.880223\pi$
$647$		−	18.6943i		−	0.734949i	0.930034	−	0.367475i	$-0.119777\pi$
$648$	9.98885			0.392399
$649$	3.48143			0.136658
$650$		0			0
$651$	−35.8074			−1.40340
$652$	−0.943288			−0.0369420
$653$		−	17.8699i		−	0.699305i	−0.936879	−	0.349652i	$-0.886300\pi$
$653$		−	17.8699i		−	0.699305i	0.936879	−	0.349652i	$-0.113700\pi$
$654$	16.6977			0.652930
$655$	−2.47037	+	0.378928i	−0.0965252	+	0.0148059i
$656$		−	6.78855i		−	0.265048i
$657$	−3.98673			−0.155537
$658$	2.15211			0.0838979
$659$	39.0893			1.52270			0.761352	−	0.648339i	$-0.224536\pi$
$659$	39.0893			1.52270			0.761352	+	0.648339i	$0.224536\pi$
$660$	6.70788	−	1.02892i	0.261104	−	0.0400506i
$661$		−	40.3696i		−	1.57020i	−0.619372	−	0.785098i	$-0.712613\pi$
$661$		−	40.3696i		−	1.57020i	0.619372	−	0.785098i	$-0.287387\pi$
$662$			30.4752i			1.18445i
$663$		0			0
$664$	−12.4289			−0.482336
$665$	−6.90874	−	45.0405i	−0.267909	−	1.74659i
$666$	0.685020			0.0265440
$667$		−	26.0774i		−	1.00972i
$668$	4.30062			0.166396
$669$		−	25.8071i		−	0.997759i
$670$	8.84087	−	1.35610i	0.341553	−	0.0523906i
$671$		−	5.16650i		−	0.199451i
$672$			8.81603i			0.340086i
$673$		−	21.1833i		−	0.816558i	−0.912857	−	0.408279i	$-0.866129\pi$
$673$		−	21.1833i		−	0.816558i	0.912857	−	0.408279i	$-0.133871\pi$
$674$		−	19.2799i		−	0.742634i
$675$	−7.22372	−	22.9929i	−0.278041	−	0.884999i
$676$		0			0
$677$		−	2.48027i		−	0.0953245i	−0.998864	−	0.0476622i	$-0.984823\pi$
$677$		−	2.48027i		−	0.0953245i	0.998864	−	0.0476622i	$-0.0151771\pi$
$678$	−29.2936			−1.12501
$679$	−27.8535			−1.06892
$680$	0.0272996	+	0.177976i	0.00104689	+	0.00682506i
$681$		−	5.29280i		−	0.202820i
$682$	−6.70788			−0.256858
$683$	12.8579			0.491993			0.245997	−	0.969271i	$-0.420885\pi$
$683$	12.8579			0.491993			0.245997	+	0.969271i	$0.420885\pi$
$684$			1.60136i			0.0612295i
$685$	−18.1445	+	2.78317i	−0.693264	+	0.106339i
$686$	−43.2502			−1.65130
$687$	12.3271			0.470307
$688$			8.49552i			0.323888i
$689$		0			0
$690$	−23.9607	+	3.67532i	−0.912168	+	0.139917i
$691$			1.12646i			0.0428526i	0.999770	+	0.0214263i	$0.00682073\pi$
$691$			1.12646i			0.0428526i	−0.999770	+	0.0214263i	$0.993179\pi$
$692$		−	0.994872i		−	0.0378194i
$693$		−	2.98691i		−	0.113464i
$694$			15.3720i			0.583512i
$695$	−11.3112	+	1.73502i	−0.429060	+	0.0658132i
$696$		−	8.12325i		−	0.307911i
$697$	−0.546642			−0.0207055
$698$			15.2035i			0.575462i
$699$	32.3353			1.22303
$700$	22.8843	−	7.18959i	0.864946	−	0.271741i
$701$	9.39602			0.354883			0.177441	−	0.984131i	$-0.443218\pi$
$701$	9.39602			0.354883			0.177441	+	0.984131i	$0.443218\pi$
$702$		0			0
$703$		−	7.71852i		−	0.291110i
$704$			1.65153i			0.0622443i
$705$	0.279480	+	1.82203i	0.0105258	+	0.0686217i
$706$	26.9017			1.01246
$707$	5.93690			0.223280
$708$	−3.87379			−0.145586
$709$		−	17.8713i		−	0.671172i	−0.942010	−	0.335586i	$-0.891066\pi$
$709$		−	17.8713i		−	0.671172i	0.942010	−	0.335586i	$-0.108934\pi$
$710$	−2.49204	−	16.2465i	−0.0935247	−	0.609720i
$711$	5.52169			0.207079
$712$		−	8.35955i		−	0.313287i
$713$	23.9607			0.897335
$714$	0.709903			0.0265675
$715$		0			0
$716$	−20.4357			−0.763719
$717$	−20.7875			−0.776322
$718$		−	20.8348i		−	0.777547i
$719$	−2.31296			−0.0862588			−0.0431294	−	0.999069i	$-0.513733\pi$
$719$	−2.31296			−0.0862588			−0.0431294	+	0.999069i	$0.513733\pi$
$720$	−0.833228	+	0.127808i	−0.0310526	+	0.00476314i
$721$		−	45.0405i		−	1.67740i
$722$	−0.956554			−0.0355992
$723$	9.33566			0.347197
$724$	−19.9522			−0.741517
$725$	−21.0860	+	6.62462i	−0.783116	+	0.246032i
$726$			15.2020i			0.564198i
$727$		−	17.9866i		−	0.667087i	−0.942735	−	0.333543i	$-0.891756\pi$
$727$		−	17.9866i		−	0.667087i	0.942735	−	0.333543i	$-0.108244\pi$
$728$		0			0
$729$	−22.8079			−0.844739
$730$	−23.3735	+	3.58525i	−0.865091	+	0.132696i
$731$	0.684094			0.0253021
$732$			5.74878i			0.212481i
$733$	45.2898			1.67282			0.836408	−	0.548108i	$-0.184652\pi$
$733$	45.2898			1.67282			0.836408	+	0.548108i	$0.184652\pi$
$734$			34.5729i			1.27611i
$735$	−9.97769	−	65.0481i	−0.368033	−	2.39934i
$736$		−	5.89928i		−	0.217451i
$737$		−	6.60611i		−	0.243339i
$738$		−	2.55921i		−	0.0942058i
$739$			45.0044i			1.65551i	0.561088	+	0.827756i	$0.310383\pi$
$739$			45.0044i			1.65551i	−0.561088	+	0.827756i	$0.689617\pi$
$740$	4.01615	−	0.616035i	0.147636	−	0.0226459i
$741$		0			0
$742$		−	55.5398i		−	2.03893i
$743$	6.56669			0.240908			0.120454	−	0.992719i	$-0.461565\pi$
$743$	6.56669			0.240908			0.120454	+	0.992719i	$0.461565\pi$
$744$	7.46388			0.273639
$745$	−1.40429	−	9.15505i	−0.0514492	−	0.335415i
$746$		−	25.0064i		−	0.915549i
$747$	−4.68558			−0.171436
$748$	0.132988			0.00486251
$749$		−	88.7840i		−	3.24410i
$750$	9.05873	+	18.4408i	0.330778	+	0.673363i
$751$	27.3499			0.998013			0.499006	−	0.866598i	$-0.333698\pi$
$751$	27.3499			0.998013			0.499006	+	0.866598i	$0.333698\pi$
$752$	−0.448597			−0.0163586
$753$			35.9638i			1.31059i
$754$		0			0
$755$	−1.50320	−	9.79986i	−0.0547069	−	0.356653i
$756$		−	23.1245i		−	0.841031i
$757$			39.0526i			1.41939i	0.704509	+	0.709696i	$0.251167\pi$
$757$			39.0526i			1.41939i	−0.704509	+	0.709696i	$0.748833\pi$
$758$			3.75953i			0.136552i
$759$			17.9040i			0.649874i
$760$	1.44009	+	9.38847i	0.0522376	+	0.340556i
$761$			28.4342i			1.03074i	0.856968	+	0.515369i	$0.172345\pi$
$761$			28.4342i			1.03074i	−0.856968	+	0.515369i	$0.827655\pi$
$762$	1.64094			0.0594452
$763$		−	43.5912i		−	1.57811i
$764$	−7.67972			−0.277843
$765$	0.0102917	+	0.0670950i	0.000372096	+	0.00242583i
$766$	−3.93892			−0.142319
$767$		0			0
$768$		−	1.83766i		−	0.0663108i
$769$		−	29.2424i		−	1.05451i	−0.849708	−	0.527254i	$-0.823222\pi$
$769$		−	29.2424i		−	1.05451i	0.849708	−	0.527254i	$-0.176778\pi$
$770$	−2.68611	−	17.5117i	−0.0968008	−	0.631079i
$771$	−3.64587			−0.131303
$772$	−15.1914			−0.546751
$773$	−20.8212			−0.748887			−0.374444	−	0.927250i	$-0.622166\pi$
$773$	−20.8212			−0.748887			−0.374444	+	0.927250i	$0.622166\pi$
$774$			3.20272i			0.115119i
$775$	−6.08689	−	19.3745i	−0.218648	−	0.695951i
$776$	5.80593			0.208421
$777$		−	16.0194i		−	0.574694i
$778$	19.1589			0.686879
$779$	−28.8361			−1.03316
$780$		0			0
$781$	−12.1398			−0.434395
$782$	−0.475035			−0.0169872
$783$			21.3074i			0.761463i
$784$	16.0153			0.571974
$785$	−2.82208	−	18.3981i	−0.100724	−	0.656656i
$786$		−	2.05396i		−	0.0732622i
$787$	20.9569			0.747031			0.373516	−	0.927624i	$-0.378152\pi$
$787$	20.9569			0.747031			0.373516	+	0.927624i	$0.378152\pi$
$788$	3.01327			0.107343
$789$	1.11833			0.0398137
$790$	32.3726	−	4.96562i	1.15177	−	0.176669i
$791$			76.4744i			2.71912i
$792$			0.622608i			0.0221234i
$793$		0			0
$794$	6.45538			0.229093
$795$	47.0214	−	7.21259i	1.66768	−	0.255804i
$796$	−9.72106			−0.344554
$797$			18.5740i			0.657924i	0.944343	+	0.328962i	$0.106699\pi$
$797$			18.5740i			0.657924i	−0.944343	+	0.328962i	$0.893301\pi$
$798$	37.4484			1.32566
$799$			0.0361228i			0.00127793i
$800$	−4.77013	+	1.49863i	−0.168649	+	0.0529847i
$801$		−	3.15146i		−	0.111351i
$802$		−	34.6424i		−	1.22327i
$803$			17.4652i			0.616334i
$804$			7.35063i			0.259237i
$805$	9.59485	+	62.5522i	0.338174	+	2.20468i
$806$		0			0
$807$		−	32.6090i		−	1.14789i
$808$	−1.23752			−0.0435357
$809$	−28.1410			−0.989383			−0.494692	−	0.869069i	$-0.664719\pi$
$809$	−28.1410			−0.989383			−0.494692	+	0.869069i	$0.664719\pi$
$810$	22.0775	−	3.38646i	0.775725	−	0.118988i
$811$		−	17.1410i		−	0.601903i	−0.953639	−	0.300952i	$-0.902696\pi$
$811$		−	17.1410i		−	0.601903i	0.953639	−	0.300952i	$-0.0973043\pi$
$812$	−21.2067			−0.744210
$813$	−29.4538			−1.03299
$814$		−	3.00096i		−	0.105184i
$815$	−2.08487	+	0.319798i	−0.0730299	+	0.0112020i
$816$	−0.147976			−0.00518019
$817$	36.0869			1.26252
$818$		−	18.6071i		−	0.650583i
$819$		0			0
$820$	−2.30148	−	15.0042i	−0.0803712	−	0.523968i
$821$			13.3822i			0.467043i	0.972352	+	0.233521i	$0.0750249\pi$
$821$			13.3822i			0.467043i	−0.972352	+	0.233521i	$0.924975\pi$
$822$		−	15.0860i		−	0.526184i
$823$			21.6095i			0.753259i	0.926364	+	0.376629i	$0.122917\pi$
$823$			21.6095i			0.753259i	−0.926364	+	0.376629i	$0.877083\pi$
$824$			9.38847i			0.327063i
$825$	14.4771	−	4.54827i	0.504026	−	0.158350i
$826$			10.1130i			0.351876i
$827$	5.85827			0.203712			0.101856	−	0.994799i	$-0.467522\pi$
$827$	5.85827			0.203712			0.101856	+	0.994799i	$0.467522\pi$
$828$		−	2.22397i		−	0.0772882i
$829$	−21.2783			−0.739026			−0.369513	−	0.929225i	$-0.620476\pi$
$829$	−21.2783			−0.739026			−0.369513	+	0.929225i	$0.620476\pi$
$830$	−27.4707	+	4.21371i	−0.953521	+	0.146260i
$831$	21.8758			0.758864
$832$		0			0
$833$		−	1.28962i		−	0.0446826i
$834$		−	9.40459i		−	0.325654i
$835$	9.50531	−	1.45801i	0.328945	−	0.0504567i
$836$	7.01529			0.242629
$837$	−19.5778			−0.676709
$838$	22.9495			0.792778
$839$			19.5222i			0.673981i	0.941508	+	0.336990i	$0.109409\pi$
$839$			19.5222i			0.673981i	−0.941508	+	0.336990i	$0.890591\pi$
$840$	2.98885	+	19.4853i	0.103125	+	0.672308i
$841$	−9.45975			−0.326198
$842$			34.8196i			1.19996i
$843$	20.9448			0.721376
$844$	−4.79064			−0.164901
$845$		0			0
$846$	−0.169116			−0.00581433
$847$	39.6865			1.36364
$848$			11.5770i			0.397556i
$849$	37.5109			1.28737
$850$	0.120676	+	0.384110i	0.00413916	+	0.0131749i
$851$			10.7195i			0.367459i
$852$	13.5080			0.462775
$853$	−33.3923			−1.14333			−0.571665	−	0.820487i	$-0.693702\pi$
$853$	−33.3923			−1.14333			−0.571665	+	0.820487i	$0.693702\pi$
$854$	15.0079			0.513559
$855$	0.542899	+	3.53935i	0.0185668	+	0.121043i
$856$			18.5066i			0.632542i
$857$			22.7514i			0.777172i	0.921412	+	0.388586i	$0.127036\pi$
$857$			22.7514i			0.777172i	−0.921412	+	0.388586i	$0.872964\pi$
$858$		0			0
$859$	−7.99391			−0.272749			−0.136374	−	0.990657i	$-0.543545\pi$
$859$	−7.99391			−0.272749			−0.136374	+	0.990657i	$0.543545\pi$
$860$	2.88019	+	18.7769i	0.0982135	+	0.640288i
$861$	−59.8480			−2.03962
$862$		−	20.4986i		−	0.698186i
$863$	11.7205			0.398971			0.199486	−	0.979901i	$-0.436073\pi$
$863$	11.7205			0.398971			0.199486	+	0.979901i	$0.436073\pi$
$864$			4.82020i			0.163986i
$865$	−0.337286	−	2.19888i	−0.0114681	−	0.0747643i
$866$			2.14503i			0.0728909i
$867$		−	31.2283i		−	1.06057i
$868$		−	19.4853i		−	0.661376i
$869$		−	24.1896i		−	0.820575i
$870$	−2.75398	−	17.9542i	−0.0933686	−	0.608703i
$871$		0			0
$872$			9.08638i			0.307704i
$873$	2.18877			0.0740787
$874$	−25.0587			−0.847624
$875$	48.1419	−	23.6489i	1.62749	−	0.799478i
$876$		−	19.4336i		−	0.656600i
$877$	−1.72808			−0.0583530			−0.0291765	−	0.999574i	$-0.509288\pi$
$877$	−1.72808			−0.0583530			−0.0291765	+	0.999574i	$0.509288\pi$
$878$	−1.05195			−0.0355016
$879$			7.69553i			0.259564i
$880$	0.559907	+	3.65023i	0.0188745	+	0.123049i
$881$	33.5662			1.13087			0.565436	−	0.824792i	$-0.308708\pi$
$881$	33.5662			1.13087			0.565436	+	0.824792i	$0.308708\pi$
$882$	6.03759			0.203296
$883$		−	18.2526i		−	0.614249i	−0.951669	−	0.307124i	$-0.900633\pi$
$883$		−	18.2526i		−	0.614249i	0.951669	−	0.307124i	$-0.0993667\pi$
$884$		0			0
$885$	−8.56193	+	1.31331i	−0.287806	+	0.0441464i
$886$		−	18.3043i		−	0.614946i
$887$			23.4791i			0.788351i	0.919035	+	0.394176i	$0.128970\pi$
$887$			23.4791i			0.788351i	−0.919035	+	0.394176i	$0.871030\pi$
$888$			3.33918i			0.112055i
$889$		−	4.28388i		−	0.143677i
$890$	−2.83409	−	18.4764i	−0.0949989	−	0.619331i
$891$		−	16.4968i		−	0.552665i
$892$	14.0434			0.470209
$893$			1.90553i			0.0637661i
$894$	7.61186			0.254579
$895$	−45.1674	+	6.92820i	−1.50978	+	0.231584i
$896$	−4.79742			−0.160271
$897$		0			0
$898$		−	13.9524i		−	0.465596i
$899$			17.9542i			0.598805i
$900$	−1.79829	+	0.564969i	−0.0599429	+	0.0188323i
$901$	0.932228			0.0310570
$902$	−11.2115			−0.373301
$903$	74.8967			2.49241
$904$		−	15.9407i		−	0.530180i
$905$	−44.0987	+	6.76427i	−1.46589	+	0.224852i
$906$	8.14798			0.270698
$907$			26.6800i			0.885895i	0.896547	+	0.442948i	$0.146067\pi$
$907$			26.6800i			0.885895i	−0.896547	+	0.442948i	$0.853933\pi$
$908$	2.88019			0.0955823
$909$	−0.466531			−0.0154739
$910$		0			0
$911$	−33.1591			−1.09861			−0.549305	−	0.835622i	$-0.685108\pi$
$911$	−33.1591			−1.09861			−0.549305	+	0.835622i	$0.685108\pi$
$912$	−7.80593			−0.258480
$913$			20.5267i			0.679335i
$914$	−29.4331			−0.973559
$915$	1.94898	+	12.7061i	0.0644312	+	0.420049i
$916$			6.70802i			0.221639i
$917$	−5.36209			−0.177072
$918$	0.388142			0.0128106
$919$	38.5789			1.27260			0.636301	−	0.771441i	$-0.280464\pi$
$919$	38.5789			1.27260			0.636301	+	0.771441i	$0.280464\pi$
$920$	−2.00000	−	13.0387i	−0.0659380	−	0.429873i
$921$		−	33.1091i		−	1.09098i
$922$			9.09372i			0.299486i
$923$		0			0
$924$	14.5599			0.478986
$925$	8.66771	−	2.72314i	0.284992	−	0.0895363i
$926$	41.6642			1.36917
$927$			3.53935i			0.116248i
$928$	4.42044			0.145108
$929$		−	24.5973i		−	0.807011i	−0.914977	−	0.403505i	$-0.867792\pi$
$929$		−	24.5973i		−	0.807011i	0.914977	−	0.403505i	$-0.132208\pi$
$930$	16.4968	−	2.53044i	0.540952	−	0.0829763i
$931$		−	68.0291i		−	2.22956i
$932$			17.5959i			0.576374i
$933$			9.51568i			0.311530i
$934$			38.1079i			1.24693i
$935$	0.293932	−	0.0450861i	0.00961260	−	0.00147447i
$936$		0			0
$937$			25.6787i			0.838886i	0.907782	+	0.419443i	$0.137775\pi$
$937$			25.6787i			0.838886i	−0.907782	+	0.419443i	$0.862225\pi$
$938$	19.1897			0.626566
$939$	59.9690			1.95701
$940$	−0.991496	+	0.152085i	−0.0323390	+	0.00496047i
$941$			27.7630i			0.905047i	0.891752	+	0.452524i	$0.149476\pi$
$941$			27.7630i			0.905047i	−0.891752	+	0.452524i	$0.850524\pi$
$942$	15.2969			0.498399
$943$	40.0476			1.30413
$944$		−	2.10800i		−	0.0686097i
$945$	−7.83978	−	51.1103i	−0.255028	−	1.66262i
$946$	14.0306			0.456173
$947$	−10.0291			−0.325902			−0.162951	−	0.986634i	$-0.552101\pi$
$947$	−10.0291			−0.325902			−0.162951	+	0.986634i	$0.552101\pi$
$948$			26.9158i			0.874185i
$949$		0			0
$950$	6.36584	+	20.2623i	0.206535	+	0.657397i
$951$			43.6232i			1.41458i
$952$			0.386309i			0.0125203i
$953$			34.9592i			1.13244i	0.824254	+	0.566220i	$0.191595\pi$
$953$			34.9592i			1.13244i	−0.824254	+	0.566220i	$0.808405\pi$
$954$			4.36440i			0.141303i
$955$	−16.9739	+	2.60361i	−0.549261	+	0.0842509i
$956$		−	11.3119i		−	0.365854i
$957$	−13.4158			−0.433670
$958$			15.0374i			0.485837i
$959$	−39.3838			−1.27177
$960$	−0.623011	−	4.06163i	−0.0201076	−	0.131088i
$961$	14.5032			0.467845
$962$		0			0
$963$			6.97679i			0.224824i
$964$			5.08019i			0.163622i
$965$	−33.5764	+	5.15026i	−1.08086	+	0.165793i
$966$	−52.0083			−1.67334
$967$	8.61013			0.276883			0.138442	−	0.990371i	$-0.455791\pi$
$967$	8.61013			0.276883			0.138442	+	0.990371i	$0.455791\pi$
$968$	−8.27246			−0.265887
$969$			0.628566i			0.0201924i
$970$	12.8324	−	1.96835i	0.412022	−	0.0631999i
$971$	−28.4894			−0.914268			−0.457134	−	0.889398i	$-0.651124\pi$
$971$	−28.4894			−0.914268			−0.457134	+	0.889398i	$0.651124\pi$
$972$			3.89550i			0.124948i
$973$	−24.5518			−0.787094
$974$	4.56256			0.146194
$975$		0			0
$976$	−3.12832			−0.100135
$977$	23.1128			0.739444			0.369722	−	0.929142i	$-0.379453\pi$
$977$	23.1128			0.739444			0.369722	+	0.929142i	$0.379453\pi$
$978$		−	1.73344i		−	0.0554294i
$979$	−13.8060			−0.441242
$980$	35.3973	−	5.42957i	1.13072	−	0.173441i
$981$			3.42547i			0.109367i
$982$	8.41606			0.268567
$983$	−28.0211			−0.893736			−0.446868	−	0.894600i	$-0.647461\pi$
$983$	−28.0211			−0.893736			−0.446868	+	0.894600i	$0.647461\pi$
$984$	12.4750			0.397690
$985$	6.65997	−	1.02157i	0.212204	−	0.0325499i
$986$		−	0.355952i		−	0.0113358i
$987$			3.95484i			0.125884i
$988$		0			0
$989$	−50.1175			−1.59364
$990$	0.211079	+	1.37610i	0.00670853	+	0.0437353i
$991$	24.8714			0.790067			0.395034	−	0.918667i	$-0.370733\pi$
$991$	24.8714			0.790067			0.395034	+	0.918667i	$0.370733\pi$
$992$			4.06163i			0.128957i
$993$	−56.0030			−1.77720
$994$		−	35.2641i		−	1.11851i
$995$	−21.4857	+	3.29567i	−0.681141	+	0.104480i
$996$		−	22.8401i		−	0.723718i
$997$		−	26.6892i		−	0.845254i	−0.906304	−	0.422627i	$-0.861108\pi$
$997$		−	26.6892i		−	0.845254i	0.906304	−	0.422627i	$-0.138892\pi$
$998$		−	12.5587i		−	0.397539i
$999$		−	8.75869i		−	0.277113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.e.1689.3		8
5.4	even	2		1690.2.c.f.1689.6		8
13.5	odd	4		1690.2.b.e.339.11		16
13.8	odd	4		1690.2.b.e.339.3		16
13.9	even	3		130.2.m.b.49.2	yes	8
13.10	even	6		130.2.m.a.69.3	yes	8
13.12	even	2		1690.2.c.f.1689.3		8
39.23	odd	6		1170.2.bj.b.199.4		8
39.35	odd	6		1170.2.bj.a.829.1		8
52.23	odd	6		1040.2.df.c.849.2		8
52.35	odd	6		1040.2.df.a.49.3		8
65.8	even	4		8450.2.a.cr.1.6		8
65.9	even	6		130.2.m.a.49.3	✓	8
65.18	even	4		8450.2.a.cs.1.6		8
65.22	odd	12		650.2.m.e.101.3		16
65.23	odd	12		650.2.m.e.251.6		16
65.34	odd	4		1690.2.b.e.339.14		16
65.44	odd	4		1690.2.b.e.339.6		16
65.47	even	4		8450.2.a.cs.1.3		8
65.48	odd	12		650.2.m.e.101.6		16
65.49	even	6		130.2.m.b.69.2	yes	8
65.57	even	4		8450.2.a.cr.1.3		8
65.62	odd	12		650.2.m.e.251.3		16
65.64	even	2	inner	1690.2.c.e.1689.6		8
195.74	odd	6		1170.2.bj.b.829.4		8
195.179	odd	6		1170.2.bj.a.199.1		8
260.139	odd	6		1040.2.df.c.49.2		8
260.179	odd	6		1040.2.df.a.849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.3	✓	8	65.9	even	6
130.2.m.a.69.3	yes	8	13.10	even	6
130.2.m.b.49.2	yes	8	13.9	even	3
130.2.m.b.69.2	yes	8	65.49	even	6
650.2.m.e.101.3		16	65.22	odd	12
650.2.m.e.101.6		16	65.48	odd	12
650.2.m.e.251.3		16	65.62	odd	12
650.2.m.e.251.6		16	65.23	odd	12
1040.2.df.a.49.3		8	52.35	odd	6
1040.2.df.a.849.3		8	260.179	odd	6
1040.2.df.c.49.2		8	260.139	odd	6
1040.2.df.c.849.2		8	52.23	odd	6
1170.2.bj.a.199.1		8	195.179	odd	6
1170.2.bj.a.829.1		8	39.35	odd	6
1170.2.bj.b.199.4		8	39.23	odd	6
1170.2.bj.b.829.4		8	195.74	odd	6
1690.2.b.e.339.3		16	13.8	odd	4
1690.2.b.e.339.6		16	65.44	odd	4
1690.2.b.e.339.11		16	13.5	odd	4
1690.2.b.e.339.14		16	65.34	odd	4
1690.2.c.e.1689.3		8	1.1	even	1	trivial
1690.2.c.e.1689.6		8	65.64	even	2	inner
1690.2.c.f.1689.3		8	13.12	even	2
1690.2.c.f.1689.6		8	5.4	even	2
8450.2.a.cr.1.3		8	65.57	even	4
8450.2.a.cr.1.6		8	65.8	even	4
8450.2.a.cs.1.3		8	65.47	even	4
8450.2.a.cs.1.6		8	65.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.83766i q^{3} +1.00000 q^{4} +(2.21022 - 0.339024i) q^{5} +1.83766i q^{6} +4.79742 q^{7} -1.00000 q^{8} -0.376989 q^{9} +(-2.21022 + 0.339024i) q^{10} +1.65153i q^{11} -1.83766i q^{12} -4.79742 q^{14} +(-0.623011 - 4.06163i) q^{15} +1.00000 q^{16} -0.0805241i q^{17} +0.376989 q^{18} -4.24776i q^{19} +(2.21022 - 0.339024i) q^{20} -8.81603i q^{21} -1.65153i q^{22} +5.89928i q^{23} +1.83766i q^{24} +(4.77013 - 1.49863i) q^{25} -4.82020i q^{27} +4.79742 q^{28} -4.42044 q^{29} +(0.623011 + 4.06163i) q^{30} -4.06163i q^{31} -1.00000 q^{32} +3.03494 q^{33} +0.0805241i q^{34} +(10.6034 - 1.62644i) q^{35} -0.376989 q^{36} +1.81708 q^{37} +4.24776i q^{38} +(-2.21022 + 0.339024i) q^{40} -6.78855i q^{41} +8.81603i q^{42} +8.49552i q^{43} +1.65153i q^{44} +(-0.833228 + 0.127808i) q^{45} -5.89928i q^{46} -0.448597 q^{47} -1.83766i q^{48} +16.0153 q^{49} +(-4.77013 + 1.49863i) q^{50} -0.147976 q^{51} +11.5770i q^{53} +4.82020i q^{54} +(0.559907 + 3.65023i) q^{55} -4.79742 q^{56} -7.80593 q^{57} +4.42044 q^{58} -2.10800i q^{59} +(-0.623011 - 4.06163i) q^{60} -3.12832 q^{61} +4.06163i q^{62} -1.80858 q^{63} +1.00000 q^{64} -3.03494 q^{66} -4.00000 q^{67} -0.0805241i q^{68} +10.8409 q^{69} +(-10.6034 + 1.62644i) q^{70} +7.35063i q^{71} +0.376989 q^{72} +10.5752 q^{73} -1.81708 q^{74} +(-2.75398 - 8.76586i) q^{75} -4.24776i q^{76} +7.92308i q^{77} -14.6468 q^{79} +(2.21022 - 0.339024i) q^{80} -9.98885 q^{81} +6.78855i q^{82} +12.4289 q^{83} -8.81603i q^{84} +(-0.0272996 - 0.177976i) q^{85} -8.49552i q^{86} +8.12325i q^{87} -1.65153i q^{88} +8.35955i q^{89} +(0.833228 - 0.127808i) q^{90} +5.89928i q^{92} -7.46388 q^{93} +0.448597 q^{94} +(-1.44009 - 9.38847i) q^{95} +1.83766i q^{96} -5.80593 q^{97} -16.0153 q^{98} -0.622608i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 3 q^{5} + 10 q^{7} - 8 q^{8} - 16 q^{9} + 3 q^{10} - 10 q^{14} + 8 q^{15} + 8 q^{16} + 16 q^{18} - 3 q^{20} + 5 q^{25} + 10 q^{28} + 6 q^{29} - 8 q^{30} - 8 q^{32} - 20 q^{33}+ \cdots - 30 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 3 * q^5 + 10 * q^7 - 8 * q^8 - 16 * q^9 + 3 * q^10 - 10 * q^14 + 8 * q^15 + 8 * q^16 + 16 * q^18 - 3 * q^20 + 5 * q^25 + 10 * q^28 + 6 * q^29 - 8 * q^30 - 8 * q^32 - 20 * q^33 + 18 * q^35 - 16 * q^36 + 40 * q^37 + 3 * q^40 + 27 * q^45 - 6 * q^47 + 30 * q^49 - 5 * q^50 - 20 * q^51 - 8 * q^55 - 10 * q^56 - 24 * q^57 - 6 * q^58 + 8 * q^60 + 10 * q^61 - 50 * q^63 + 8 * q^64 + 20 * q^66 - 32 * q^67 + 4 * q^69 - 18 * q^70 + 16 * q^72 - 26 * q^73 - 40 * q^74 - 48 * q^75 + 4 * q^79 - 3 * q^80 - 16 * q^81 + 48 * q^83 - 5 * q^85 - 27 * q^90 + 36 * q^93 + 6 * q^94 - 24 * q^95 - 8 * q^97 - 30 * q^98

Introduction

L-functions

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