LMFDB - Embedded newform 1690.2.b.d.339.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(339,1690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1690.339");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.5
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.d.339.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.52434i q^{3} -1.00000 q^{4} +(-0.469882 - 2.18614i) q^{5} +2.52434 q^{6} -2.37228i q^{7} -1.00000i q^{8} -3.37228 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.52434i q^{3} -1.00000 q^{4} +(-0.469882 - 2.18614i) q^{5} +2.52434 q^{6} -2.37228i q^{7} -1.00000i q^{8} -3.37228 q^{9} +(2.18614 - 0.469882i) q^{10} +1.58457 q^{11} +2.52434i q^{12} +2.37228 q^{14} +(-5.51856 + 1.18614i) q^{15} +1.00000 q^{16} -5.98844i q^{17} -3.37228i q^{18} -3.46410 q^{19} +(0.469882 + 2.18614i) q^{20} -5.98844 q^{21} +1.58457i q^{22} -6.63325i q^{23} -2.52434 q^{24} +(-4.55842 + 2.05446i) q^{25} +0.939764i q^{27} +2.37228i q^{28} +2.74456 q^{29} +(-1.18614 - 5.51856i) q^{30} +3.46410 q^{31} +1.00000i q^{32} -4.00000i q^{33} +5.98844 q^{34} +(-5.18614 + 1.11469i) q^{35} +3.37228 q^{36} +9.11684i q^{37} -3.46410i q^{38} +(-2.18614 + 0.469882i) q^{40} +10.0974 q^{41} -5.98844i q^{42} +0.644810i q^{43} -1.58457 q^{44} +(1.58457 + 7.37228i) q^{45} +6.63325 q^{46} +10.3723i q^{47} -2.52434i q^{48} +1.37228 q^{49} +(-2.05446 - 4.55842i) q^{50} -15.1168 q^{51} -5.04868i q^{53} -0.939764 q^{54} +(-0.744563 - 3.46410i) q^{55} -2.37228 q^{56} +8.74456i q^{57} +2.74456i q^{58} -6.63325 q^{59} +(5.51856 - 1.18614i) q^{60} -6.74456 q^{61} +3.46410i q^{62} +8.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +4.00000i q^{67} +5.98844i q^{68} -16.7446 q^{69} +(-1.11469 - 5.18614i) q^{70} -12.6217 q^{71} +3.37228i q^{72} -10.0000i q^{73} -9.11684 q^{74} +(5.18614 + 11.5070i) q^{75} +3.46410 q^{76} -3.75906i q^{77} +4.74456 q^{79} +(-0.469882 - 2.18614i) q^{80} -7.74456 q^{81} +10.0974i q^{82} +8.74456i q^{83} +5.98844 q^{84} +(-13.0916 + 2.81386i) q^{85} -0.644810 q^{86} -6.92820i q^{87} -1.58457i q^{88} -1.87953 q^{89} +(-7.37228 + 1.58457i) q^{90} +6.63325i q^{92} -8.74456i q^{93} -10.3723 q^{94} +(1.62772 + 7.57301i) q^{95} +2.52434 q^{96} +6.74456i q^{97} +1.37228i q^{98} -5.34363 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^9	$ 8 q - 8 q^{4} - 4 q^{9} + 6 q^{10} - 4 q^{14} + 8 q^{16} - 2 q^{25} - 24 q^{29} + 2 q^{30} - 30 q^{35} + 4 q^{36} - 6 q^{40} - 12 q^{49} - 52 q^{51} + 40 q^{55} + 4 q^{56} - 8 q^{61} - 8 q^{64} + 32 q^{66} - 88 q^{69} - 4 q^{74} + 30 q^{75} - 8 q^{79} - 16 q^{81} - 36 q^{90} - 60 q^{94} + 36 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^9 + 6 * q^10 - 4 * q^14 + 8 * q^16 - 2 * q^25 - 24 * q^29 + 2 * q^30 - 30 * q^35 + 4 * q^36 - 6 * q^40 - 12 * q^49 - 52 * q^51 + 40 * q^55 + 4 * q^56 - 8 * q^61 - 8 * q^64 + 32 * q^66 - 88 * q^69 - 4 * q^74 + 30 * q^75 - 8 * q^79 - 16 * q^81 - 36 * q^90 - 60 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	2.52434i		−	1.45743i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$		−	2.52434i		−	1.45743i	0.684819	−	0.728714i	$-0.259881\pi$
$4$	−1.00000			−0.500000
$5$	−0.469882	−	2.18614i	−0.210138	−	0.977672i
$5$	−0.469882	−	2.18614i	−0.210138	−	0.977672i
$6$	2.52434			1.03056
$7$		−	2.37228i		−	0.896638i	−0.893874	−	0.448319i	$-0.852023\pi$
$7$		−	2.37228i		−	0.896638i	0.893874	−	0.448319i	$-0.147977\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−3.37228			−1.12409
$10$	2.18614	−	0.469882i	0.691318	−	0.148590i
$11$	1.58457			0.477767			0.238884	−	0.971048i	$-0.423219\pi$
$11$	1.58457			0.477767			0.238884	+	0.971048i	$0.423219\pi$
$12$			2.52434i			0.728714i
$13$		0			0
$13$		0			0
$14$	2.37228			0.634019
$15$	−5.51856	+	1.18614i	−1.42489	+	0.306260i
$16$	1.00000			0.250000
$17$		−	5.98844i		−	1.45241i	−0.687478	−	0.726205i	$-0.741282\pi$
$17$		−	5.98844i		−	1.45241i	0.687478	−	0.726205i	$-0.258718\pi$
$18$		−	3.37228i		−	0.794854i
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$	0.469882	+	2.18614i	0.105069	+	0.488836i
$21$	−5.98844			−1.30678
$22$			1.58457i			0.337832i
$23$		−	6.63325i		−	1.38313i	−0.722315	−	0.691564i	$-0.756922\pi$
$23$		−	6.63325i		−	1.38313i	0.722315	−	0.691564i	$-0.243078\pi$
$24$	−2.52434			−0.515278
$25$	−4.55842	+	2.05446i	−0.911684	+	0.410891i
$26$		0			0
$27$			0.939764i			0.180858i
$28$			2.37228i			0.448319i
$29$	2.74456			0.509652			0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456			0.509652			0.254826	+	0.966987i	$0.417982\pi$
$30$	−1.18614	−	5.51856i	−0.216559	−	1.00755i
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$			1.00000i			0.176777i
$33$		−	4.00000i		−	0.696311i
$34$	5.98844			1.02701
$35$	−5.18614	+	1.11469i	−0.876618	+	0.188417i
$36$	3.37228			0.562047
$37$			9.11684i			1.49880i	0.662118	+	0.749400i	$0.269658\pi$
$37$			9.11684i			1.49880i	−0.662118	+	0.749400i	$0.730342\pi$
$38$		−	3.46410i		−	0.561951i
$39$		0			0
$40$	−2.18614	+	0.469882i	−0.345659	+	0.0742949i
$41$	10.0974			1.57694			0.788471	−	0.615072i	$-0.210873\pi$
$41$	10.0974			1.57694			0.788471	+	0.615072i	$0.210873\pi$
$42$		−	5.98844i		−	0.924036i
$43$			0.644810i			0.0983326i	0.998791	+	0.0491663i	$0.0156564\pi$
$43$			0.644810i			0.0983326i	−0.998791	+	0.0491663i	$0.984344\pi$
$44$	−1.58457			−0.238884
$45$	1.58457	+	7.37228i	0.236214	+	1.09899i
$46$	6.63325			0.978019
$47$			10.3723i			1.51295i	0.654021	+	0.756476i	$0.273081\pi$
$47$			10.3723i			1.51295i	−0.654021	+	0.756476i	$0.726919\pi$
$48$		−	2.52434i		−	0.364357i
$49$	1.37228			0.196040
$50$	−2.05446	−	4.55842i	−0.290544	−	0.644658i
$51$	−15.1168			−2.11678
$52$		0			0
$53$		−	5.04868i		−	0.693489i	−0.937960	−	0.346744i	$-0.887287\pi$
$53$		−	5.04868i		−	0.693489i	0.937960	−	0.346744i	$-0.112713\pi$
$54$	−0.939764			−0.127886
$55$	−0.744563	−	3.46410i	−0.100397	−	0.467099i
$56$	−2.37228			−0.317009
$57$			8.74456i			1.15825i
$58$			2.74456i			0.360379i
$59$	−6.63325			−0.863576			−0.431788	−	0.901975i	$-0.642117\pi$
$59$	−6.63325			−0.863576			−0.431788	+	0.901975i	$0.642117\pi$
$60$	5.51856	−	1.18614i	0.712443	−	0.153130i
$61$	−6.74456			−0.863553			−0.431776	−	0.901981i	$-0.642113\pi$
$61$	−6.74456			−0.863553			−0.431776	+	0.901981i	$0.642113\pi$
$62$			3.46410i			0.439941i
$63$			8.00000i			1.00791i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.00000			0.492366
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			5.98844i			0.726205i
$69$	−16.7446			−2.01581
$70$	−1.11469	−	5.18614i	−0.133231	−	0.619862i
$71$	−12.6217			−1.49792			−0.748959	−	0.662616i	$-0.769446\pi$
$71$	−12.6217			−1.49792			−0.748959	+	0.662616i	$0.769446\pi$
$72$			3.37228i			0.397427i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	−9.11684			−1.05981
$75$	5.18614	+	11.5070i	0.598844	+	1.32871i
$76$	3.46410			0.397360
$77$		−	3.75906i		−	0.428384i
$78$		0			0
$79$	4.74456			0.533805			0.266903	−	0.963724i	$-0.414000\pi$
$79$	4.74456			0.533805			0.266903	+	0.963724i	$0.414000\pi$
$80$	−0.469882	−	2.18614i	−0.0525344	−	0.244418i
$81$	−7.74456			−0.860507
$82$			10.0974i			1.11507i
$83$			8.74456i			0.959840i	0.877312	+	0.479920i	$0.159334\pi$
$83$			8.74456i			0.959840i	−0.877312	+	0.479920i	$0.840666\pi$
$84$	5.98844			0.653392
$85$	−13.0916	+	2.81386i	−1.41998	+	0.305206i
$86$	−0.644810			−0.0695317
$87$		−	6.92820i		−	0.742781i
$88$		−	1.58457i		−	0.168916i
$89$	−1.87953			−0.199230			−0.0996148	−	0.995026i	$-0.531761\pi$
$89$	−1.87953			−0.199230			−0.0996148	+	0.995026i	$0.531761\pi$
$90$	−7.37228	+	1.58457i	−0.777107	+	0.167029i
$91$		0			0
$92$			6.63325i			0.691564i
$93$		−	8.74456i		−	0.906769i
$94$	−10.3723			−1.06982
$95$	1.62772	+	7.57301i	0.167000	+	0.776975i
$96$	2.52434			0.257639
$97$			6.74456i			0.684807i	0.939553	+	0.342403i	$0.111241\pi$
$97$			6.74456i			0.684807i	−0.939553	+	0.342403i	$0.888759\pi$
$98$			1.37228i			0.138621i
$99$	−5.34363			−0.537055
$100$	4.55842	−	2.05446i	0.455842	−	0.205446i
$101$	14.7446			1.46714			0.733569	−	0.679615i	$-0.237853\pi$
$101$	14.7446			1.46714			0.733569	+	0.679615i	$0.237853\pi$
$102$		−	15.1168i		−	1.49679i
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$		0			0
$105$	2.81386	+	13.0916i	0.274605	+	1.27761i
$106$	5.04868			0.490371
$107$			13.5615i			1.31104i	0.755180	+	0.655518i	$0.227549\pi$
$107$			13.5615i			1.31104i	−0.755180	+	0.655518i	$0.772451\pi$
$108$		−	0.939764i		−	0.0904288i
$109$	−2.81929			−0.270039			−0.135020	−	0.990843i	$-0.543110\pi$
$109$	−2.81929			−0.270039			−0.135020	+	0.990843i	$0.543110\pi$
$110$	3.46410	−	0.744563i	0.330289	−	0.0709913i
$111$	23.0140			2.18439
$112$		−	2.37228i		−	0.224160i
$113$		−	3.75906i		−	0.353622i	−0.984245	−	0.176811i	$-0.943422\pi$
$113$		−	3.75906i		−	0.353622i	0.984245	−	0.176811i	$-0.0565782\pi$
$114$	−8.74456			−0.819003
$115$	−14.5012	+	3.11684i	−1.35225	+	0.290647i
$116$	−2.74456			−0.254826
$117$		0			0
$118$		−	6.63325i		−	0.610640i
$119$	−14.2063			−1.30229
$120$	1.18614	+	5.51856i	0.108279	+	0.503773i
$121$	−8.48913			−0.771739
$122$		−	6.74456i		−	0.610624i
$123$		−	25.4891i		−	2.29828i
$124$	−3.46410			−0.311086
$125$	6.63325	+	9.00000i	0.593296	+	0.804984i
$126$	−8.00000			−0.712697
$127$			3.46410i			0.307389i	0.988118	+	0.153695i	$0.0491172\pi$
$127$			3.46410i			0.307389i	−0.988118	+	0.153695i	$0.950883\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.62772			0.143313
$130$		0			0
$131$	−1.62772			−0.142214			−0.0711072	−	0.997469i	$-0.522653\pi$
$131$	−1.62772			−0.142214			−0.0711072	+	0.997469i	$0.522653\pi$
$132$			4.00000i			0.348155i
$133$			8.21782i			0.712576i
$134$	−4.00000			−0.345547
$135$	2.05446	−	0.441578i	0.176819	−	0.0380050i
$136$	−5.98844			−0.513504
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		−	16.7446i		−	1.42539i
$139$	6.37228			0.540490			0.270245	−	0.962792i	$-0.412895\pi$
$139$	6.37228			0.540490			0.270245	+	0.962792i	$0.412895\pi$
$140$	5.18614	−	1.11469i	0.438309	−	0.0942087i
$141$	26.1831			2.20502
$142$		−	12.6217i		−	1.05919i
$143$		0			0
$144$	−3.37228			−0.281023
$145$	−1.28962	−	6.00000i	−0.107097	−	0.498273i
$146$	10.0000			0.827606
$147$		−	3.46410i		−	0.285714i
$148$		−	9.11684i		−	0.749400i
$149$	17.0256			1.39479			0.697394	−	0.716688i	$-0.254343\pi$
$149$	17.0256			1.39479			0.697394	+	0.716688i	$0.254343\pi$
$150$	−11.5070	+	5.18614i	−0.939542	+	0.423447i
$151$	−7.57301			−0.616283			−0.308142	−	0.951341i	$-0.599707\pi$
$151$	−7.57301			−0.616283			−0.308142	+	0.951341i	$0.599707\pi$
$152$			3.46410i			0.280976i
$153$			20.1947i			1.63264i
$154$	3.75906			0.302913
$155$	−1.62772	−	7.57301i	−0.130742	−	0.608279i
$156$		0			0
$157$		−	15.1460i		−	1.20878i	−0.796687	−	0.604392i	$-0.793416\pi$
$157$		−	15.1460i		−	1.20878i	0.796687	−	0.604392i	$-0.206584\pi$
$158$			4.74456i			0.377457i
$159$	−12.7446			−1.01071
$160$	2.18614	−	0.469882i	0.172830	−	0.0371474i
$161$	−15.7359			−1.24017
$162$		−	7.74456i		−	0.608470i
$163$		−	24.7446i		−	1.93814i	−0.246779	−	0.969072i	$-0.579372\pi$
$163$		−	24.7446i		−	1.93814i	0.246779	−	0.969072i	$-0.420628\pi$
$164$	−10.0974			−0.788471
$165$	−8.74456	+	1.87953i	−0.680763	+	0.146321i
$166$	−8.74456			−0.678710
$167$		−	17.4891i		−	1.35335i	−0.736282	−	0.676675i	$-0.763420\pi$
$167$		−	17.4891i		−	1.35335i	0.736282	−	0.676675i	$-0.236580\pi$
$168$			5.98844i			0.462018i
$169$		0			0
$170$	−2.81386	−	13.0916i	−0.215813	−	1.00408i
$171$	11.6819			0.893339
$172$		−	0.644810i		−	0.0491663i
$173$			18.9051i			1.43733i	0.695358	+	0.718663i	$0.255246\pi$
$173$			18.9051i			1.43733i	−0.695358	+	0.718663i	$0.744754\pi$
$174$	6.92820			0.525226
$175$	4.87375	+	10.8139i	0.368421	+	0.817451i
$176$	1.58457			0.119442
$177$			16.7446i			1.25860i
$178$		−	1.87953i		−	0.140877i
$179$	−4.88316			−0.364984			−0.182492	−	0.983207i	$-0.558416\pi$
$179$	−4.88316			−0.364984			−0.182492	+	0.983207i	$0.558416\pi$
$180$	−1.58457	−	7.37228i	−0.118107	−	0.549497i
$181$	3.48913			0.259345			0.129672	−	0.991557i	$-0.458607\pi$
$181$	3.48913			0.259345			0.129672	+	0.991557i	$0.458607\pi$
$182$		0			0
$183$			17.0256i			1.25857i
$184$	−6.63325			−0.489010
$185$	19.9307	−	4.28384i	1.46533	−	0.314954i
$186$	8.74456			0.641182
$187$		−	9.48913i		−	0.693914i
$188$		−	10.3723i		−	0.756476i
$189$	2.22938			0.162164
$190$	−7.57301	+	1.62772i	−0.549404	+	0.118087i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$			2.52434i			0.182178i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−6.74456			−0.484231
$195$		0			0
$196$	−1.37228			−0.0980201
$197$		−	4.37228i		−	0.311512i	−0.987796	−	0.155756i	$-0.950219\pi$
$197$		−	4.37228i		−	0.311512i	0.987796	−	0.155756i	$-0.0497814\pi$
$198$		−	5.34363i		−	0.379755i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	2.05446	+	4.55842i	0.145272	+	0.322329i
$201$	10.0974			0.712212
$202$			14.7446i			1.03742i
$203$		−	6.51087i		−	0.456974i
$204$	15.1168			1.05839
$205$	−4.74456	−	22.0742i	−0.331375	−	1.54173i
$206$	10.3923			0.724066
$207$			22.3692i			1.55477i
$208$		0			0
$209$	−5.48913			−0.379691
$210$	−13.0916	+	2.81386i	−0.903404	+	0.194175i
$211$	3.11684			0.214572			0.107286	−	0.994228i	$-0.465784\pi$
$211$	3.11684			0.214572			0.107286	+	0.994228i	$0.465784\pi$
$212$			5.04868i			0.346744i
$213$			31.8614i			2.18311i
$214$	−13.5615			−0.927042
$215$	1.40965	−	0.302985i	0.0961370	−	0.0206634i
$216$	0.939764			0.0639428
$217$		−	8.21782i		−	0.557862i
$218$		−	2.81929i		−	0.190947i
$219$	−25.2434			−1.70579
$220$	0.744563	+	3.46410i	0.0501984	+	0.233550i
$221$		0			0
$222$			23.0140i			1.54460i
$223$		−	15.1168i		−	1.01230i	−0.862446	−	0.506149i	$-0.831068\pi$
$223$		−	15.1168i		−	1.01230i	0.862446	−	0.506149i	$-0.168932\pi$
$224$	2.37228			0.158505
$225$	15.3723	−	6.92820i	1.02482	−	0.461880i
$226$	3.75906			0.250049
$227$		−	5.48913i		−	0.364326i	−0.983268	−	0.182163i	$-0.941690\pi$
$227$		−	5.48913i		−	0.364326i	0.983268	−	0.182163i	$-0.0583099\pi$
$228$		−	8.74456i		−	0.579123i
$229$	24.8935			1.64501			0.822505	−	0.568758i	$-0.192576\pi$
$229$	24.8935			1.64501			0.822505	+	0.568758i	$0.192576\pi$
$230$	−3.11684	−	14.5012i	−0.205519	−	0.956182i
$231$	−9.48913			−0.624339
$232$		−	2.74456i		−	0.180189i
$233$			7.86797i			0.515448i	0.966219	+	0.257724i	$0.0829725\pi$
$233$			7.86797i			0.515448i	−0.966219	+	0.257724i	$0.917028\pi$
$234$		0			0
$235$	22.6753	−	4.87375i	1.47917	−	0.317928i
$236$	6.63325			0.431788
$237$		−	11.9769i		−	0.777982i
$238$		−	14.2063i		−	0.920855i
$239$	9.45254			0.611434			0.305717	−	0.952122i	$-0.401104\pi$
$239$	9.45254			0.611434			0.305717	+	0.952122i	$0.401104\pi$
$240$	−5.51856	+	1.18614i	−0.356221	+	0.0765651i
$241$	8.21782			0.529357			0.264678	−	0.964337i	$-0.414734\pi$
$241$	8.21782			0.529357			0.264678	+	0.964337i	$0.414734\pi$
$242$		−	8.48913i		−	0.545702i
$243$			22.3692i			1.43498i
$244$	6.74456			0.431776
$245$	−0.644810	−	3.00000i	−0.0411954	−	0.191663i
$246$	25.4891			1.62513
$247$		0			0
$248$		−	3.46410i		−	0.219971i
$249$	22.0742			1.39890
$250$	−9.00000	+	6.63325i	−0.569210	+	0.419524i
$251$	22.9783			1.45037			0.725187	−	0.688552i	$-0.241753\pi$
$251$	22.9783			1.45037			0.725187	+	0.688552i	$0.241753\pi$
$252$		−	8.00000i		−	0.503953i
$253$		−	10.5109i		−	0.660813i
$254$	−3.46410			−0.217357
$255$	7.10313	+	33.0475i	0.444815	+	2.06952i
$256$	1.00000			0.0625000
$257$		−	14.2063i		−	0.886162i	−0.896481	−	0.443081i	$-0.853885\pi$
$257$		−	14.2063i		−	0.886162i	0.896481	−	0.443081i	$-0.146115\pi$
$258$			1.62772i			0.101337i
$259$	21.6277			1.34388
$260$		0			0
$261$	−9.25544			−0.572897
$262$		−	1.62772i		−	0.100561i
$263$		−	18.0202i		−	1.11117i	−0.831458	−	0.555587i	$-0.812493\pi$
$263$		−	18.0202i		−	1.11117i	0.831458	−	0.555587i	$-0.187507\pi$
$264$	−4.00000			−0.246183
$265$	−11.0371	+	2.37228i	−0.678005	+	0.145728i
$266$	−8.21782			−0.503867
$267$			4.74456i			0.290363i
$268$		−	4.00000i		−	0.244339i
$269$	2.74456			0.167339			0.0836695	−	0.996494i	$-0.473336\pi$
$269$	2.74456			0.167339			0.0836695	+	0.996494i	$0.473336\pi$
$270$	0.441578	+	2.05446i	0.0268736	+	0.125030i
$271$	−21.4294			−1.30174			−0.650872	−	0.759187i	$-0.725597\pi$
$271$	−21.4294			−1.30174			−0.650872	+	0.759187i	$0.725597\pi$
$272$		−	5.98844i		−	0.363102i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−7.22316	+	3.25544i	−0.435573	+	0.196310i
$276$	16.7446			1.00790
$277$		−	23.3639i		−	1.40380i	−0.712277	−	0.701899i	$-0.752336\pi$
$277$		−	23.3639i		−	1.40380i	0.712277	−	0.701899i	$-0.247664\pi$
$278$			6.37228i			0.382184i
$279$	−11.6819			−0.699379
$280$	1.11469	+	5.18614i	0.0666156	+	0.309931i
$281$	−1.87953			−0.112123			−0.0560616	−	0.998427i	$-0.517854\pi$
$281$	−1.87953			−0.112123			−0.0560616	+	0.998427i	$0.517854\pi$
$282$			26.1831i			1.55918i
$283$		−	17.3205i		−	1.02960i	−0.857311	−	0.514799i	$-0.827867\pi$
$283$		−	17.3205i		−	1.02960i	0.857311	−	0.514799i	$-0.172133\pi$
$284$	12.6217			0.748959
$285$	19.1168	−	4.10891i	1.13238	−	0.243391i
$286$		0			0
$287$		−	23.9538i		−	1.41395i
$288$		−	3.37228i		−	0.198714i
$289$	−18.8614			−1.10949
$290$	6.00000	−	1.28962i	0.352332	−	0.0757291i
$291$	17.0256			0.998056
$292$			10.0000i			0.585206i
$293$		−	2.13859i		−	0.124938i	−0.998047	−	0.0624690i	$-0.980103\pi$
$293$		−	2.13859i		−	0.124938i	0.998047	−	0.0624690i	$-0.0198974\pi$
$294$	3.46410			0.202031
$295$	3.11684	+	14.5012i	0.181470	+	0.844293i
$296$	9.11684			0.529906
$297$			1.48913i			0.0864078i
$298$			17.0256i			0.986264i
$299$		0			0
$300$	−5.18614	−	11.5070i	−0.299422	−	0.664357i
$301$	1.52967			0.0881688
$302$		−	7.57301i		−	0.435778i
$303$		−	37.2203i		−	2.13825i
$304$	−3.46410			−0.198680
$305$	3.16915	+	14.7446i	0.181465	+	0.844271i
$306$	−20.1947			−1.15445
$307$		−	18.2337i		−	1.04065i	−0.853968	−	0.520326i	$-0.825811\pi$
$307$		−	18.2337i		−	1.04065i	0.853968	−	0.520326i	$-0.174189\pi$
$308$			3.75906i			0.214192i
$309$	−26.2337			−1.49238
$310$	7.57301	−	1.62772i	0.430118	−	0.0924482i
$311$	−3.25544			−0.184599			−0.0922995	−	0.995731i	$-0.529422\pi$
$311$	−3.25544			−0.184599			−0.0922995	+	0.995731i	$0.529422\pi$
$312$		0			0
$313$			12.3267i			0.696748i	0.937356	+	0.348374i	$0.113266\pi$
$313$			12.3267i			0.696748i	−0.937356	+	0.348374i	$0.886734\pi$
$314$	15.1460			0.854740
$315$	17.4891	−	3.75906i	0.985401	−	0.211799i
$316$	−4.74456			−0.266903
$317$			16.9783i			0.953594i	0.879014	+	0.476797i	$0.158202\pi$
$317$			16.9783i			0.953594i	−0.879014	+	0.476797i	$0.841798\pi$
$318$		−	12.7446i		−	0.714680i
$319$	4.34896			0.243495
$320$	0.469882	+	2.18614i	0.0262672	+	0.122209i
$321$	34.2337			1.91074
$322$		−	15.7359i		−	0.876929i
$323$			20.7446i			1.15426i
$324$	7.74456			0.430253
$325$		0			0
$326$	24.7446			1.37047
$327$			7.11684i			0.393562i
$328$		−	10.0974i		−	0.557533i
$329$	24.6060			1.35657
$330$	−1.87953	−	8.74456i	−0.103465	−	0.481372i
$331$	10.3923			0.571213			0.285606	−	0.958347i	$-0.407805\pi$
$331$	10.3923			0.571213			0.285606	+	0.958347i	$0.407805\pi$
$332$		−	8.74456i		−	0.479920i
$333$		−	30.7446i		−	1.68479i
$334$	17.4891			0.956962
$335$	8.74456	−	1.87953i	0.477766	−	0.102690i
$336$	−5.98844			−0.326696
$337$			1.52967i			0.0833265i	0.999132	+	0.0416632i	$0.0132657\pi$
$337$			1.52967i			0.0833265i	−0.999132	+	0.0416632i	$0.986734\pi$
$338$		0			0
$339$	−9.48913			−0.515379
$340$	13.0916	−	2.81386i	0.709990	−	0.152603i
$341$	5.48913			0.297253
$342$			11.6819i			0.631686i
$343$		−	19.8614i		−	1.07242i
$344$	0.644810			0.0347658
$345$	7.86797	+	36.6060i	0.423597	+	1.97080i
$346$	−18.9051			−1.01634
$347$		−	20.8395i		−	1.11872i	−0.828924	−	0.559362i	$-0.811046\pi$
$347$		−	20.8395i		−	1.11872i	0.828924	−	0.559362i	$-0.188954\pi$
$348$			6.92820i			0.371391i
$349$	27.4728			1.47058			0.735292	−	0.677751i	$-0.237045\pi$
$349$	27.4728			1.47058			0.735292	+	0.677751i	$0.237045\pi$
$350$	−10.8139	+	4.87375i	−0.578025	+	0.260513i
$351$		0			0
$352$			1.58457i			0.0844581i
$353$			11.4891i			0.611504i	0.952111	+	0.305752i	$0.0989079\pi$
$353$			11.4891i			0.611504i	−0.952111	+	0.305752i	$0.901092\pi$
$354$	−16.7446			−0.889963
$355$	5.93070	+	27.5928i	0.314769	+	1.46447i
$356$	1.87953			0.0996148
$357$			35.8614i			1.89799i
$358$		−	4.88316i		−	0.258083i
$359$	2.87419			0.151694			0.0758471	−	0.997119i	$-0.475834\pi$
$359$	2.87419			0.151694			0.0758471	+	0.997119i	$0.475834\pi$
$360$	7.37228	−	1.58457i	0.388553	−	0.0835144i
$361$	−7.00000			−0.368421
$362$			3.48913i			0.183384i
$363$			21.4294i			1.12475i
$364$		0			0
$365$	−21.8614	+	4.69882i	−1.14428	+	0.245947i
$366$	−17.0256			−0.889940
$367$			4.75372i			0.248142i	0.992273	+	0.124071i	$0.0395951\pi$
$367$			4.75372i			0.248142i	−0.992273	+	0.124071i	$0.960405\pi$
$368$		−	6.63325i		−	0.345782i
$369$	−34.0511			−1.77263
$370$	4.28384	+	19.9307i	0.222706	+	1.03615i
$371$	−11.9769			−0.621809
$372$			8.74456i			0.453384i
$373$		−	9.50744i		−	0.492277i	−0.969235	−	0.246138i	$-0.920838\pi$
$373$		−	9.50744i		−	0.492277i	0.969235	−	0.246138i	$-0.0791618\pi$
$374$	9.48913			0.490671
$375$	22.7190	−	16.7446i	1.17321	−	0.864685i
$376$	10.3723			0.534910
$377$		0			0
$378$			2.22938i			0.114667i
$379$	−17.3205			−0.889695			−0.444847	−	0.895606i	$-0.646742\pi$
$379$	−17.3205			−0.889695			−0.444847	+	0.895606i	$0.646742\pi$
$380$	−1.62772	−	7.57301i	−0.0835002	−	0.388487i
$381$	8.74456			0.447998
$382$		0			0
$383$		−	16.8832i		−	0.862689i	−0.902187	−	0.431344i	$-0.858039\pi$
$383$		−	16.8832i		−	0.862689i	0.902187	−	0.431344i	$-0.141961\pi$
$384$	−2.52434			−0.128820
$385$	−8.21782	+	1.76631i	−0.418819	+	0.0900196i
$386$	−14.0000			−0.712581
$387$		−	2.17448i		−	0.110535i
$388$		−	6.74456i		−	0.342403i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−39.7228			−2.00887
$392$		−	1.37228i		−	0.0693107i
$393$			4.10891i			0.207267i
$394$	4.37228			0.220272
$395$	−2.22938	−	10.3723i	−0.112172	−	0.521886i
$396$	5.34363			0.268527
$397$			8.51087i			0.427149i	0.976927	+	0.213574i	$0.0685105\pi$
$397$			8.51087i			0.427149i	−0.976927	+	0.213574i	$0.931489\pi$
$398$		−	8.00000i		−	0.401004i
$399$	20.7446			1.03853
$400$	−4.55842	+	2.05446i	−0.227921	+	0.102723i
$401$	−32.1716			−1.60657			−0.803286	−	0.595593i	$-0.796917\pi$
$401$	−32.1716			−1.60657			−0.803286	+	0.595593i	$0.796917\pi$
$402$			10.0974i			0.503610i
$403$		0			0
$404$	−14.7446			−0.733569
$405$	3.63903	+	16.9307i	0.180825	+	0.841293i
$406$	6.51087			0.323129
$407$			14.4463i			0.716077i
$408$			15.1168i			0.748395i
$409$	−5.63858			−0.278810			−0.139405	−	0.990235i	$-0.544519\pi$
$409$	−5.63858			−0.278810			−0.139405	+	0.990235i	$0.544519\pi$
$410$	22.0742	−	4.74456i	1.09017	−	0.234317i
$411$	15.1460			0.747098
$412$			10.3923i			0.511992i
$413$			15.7359i			0.774315i
$414$	−22.3692			−1.09939
$415$	19.1168	−	4.10891i	0.938409	−	0.201699i
$416$		0			0
$417$		−	16.0858i		−	0.787725i
$418$		−	5.48913i		−	0.268482i
$419$	19.1168			0.933919			0.466959	−	0.884279i	$-0.345349\pi$
$419$	19.1168			0.933919			0.466959	+	0.884279i	$0.345349\pi$
$420$	−2.81386	−	13.0916i	−0.137302	−	0.638803i
$421$	11.0371			0.537916			0.268958	−	0.963152i	$-0.413321\pi$
$421$	11.0371			0.537916			0.268958	+	0.963152i	$0.413321\pi$
$422$			3.11684i			0.151726i
$423$		−	34.9783i		−	1.70070i
$424$	−5.04868			−0.245185
$425$	12.3030	+	27.2978i	0.596782	+	1.32414i
$426$	−31.8614			−1.54369
$427$			16.0000i			0.774294i
$428$		−	13.5615i		−	0.655518i
$429$		0			0
$430$	0.302985	+	1.40965i	0.0146112	+	0.0679792i
$431$	−26.4781			−1.27540			−0.637702	−	0.770283i	$-0.720115\pi$
$431$	−26.4781			−1.27540			−0.637702	+	0.770283i	$0.720115\pi$
$432$			0.939764i			0.0452144i
$433$			34.4010i			1.65320i	0.562786	+	0.826602i	$0.309729\pi$
$433$			34.4010i			1.65320i	−0.562786	+	0.826602i	$0.690271\pi$
$434$	8.21782			0.394468
$435$	−15.1460	+	3.25544i	−0.726196	+	0.156086i
$436$	2.81929			0.135020
$437$			22.9783i			1.09920i
$438$		−	25.2434i		−	1.20618i
$439$	−22.2337			−1.06116			−0.530578	−	0.847636i	$-0.678025\pi$
$439$	−22.2337			−1.06116			−0.530578	+	0.847636i	$0.678025\pi$
$440$	−3.46410	+	0.744563i	−0.165145	+	0.0354956i
$441$	−4.62772			−0.220368
$442$		0			0
$443$		−	4.40387i		−	0.209234i	−0.994513	−	0.104617i	$-0.966638\pi$
$443$		−	4.40387i		−	0.209234i	0.994513	−	0.104617i	$-0.0333617\pi$
$444$	−23.0140			−1.09220
$445$	0.883156	+	4.10891i	0.0418656	+	0.194781i
$446$	15.1168			0.715803
$447$		−	42.9783i		−	2.03280i
$448$			2.37228i			0.112080i
$449$	−7.51811			−0.354802			−0.177401	−	0.984139i	$-0.556769\pi$
$449$	−7.51811			−0.354802			−0.177401	+	0.984139i	$0.556769\pi$
$450$	6.92820	+	15.3723i	0.326599	+	0.724656i
$451$	16.0000			0.753411
$452$			3.75906i			0.176811i
$453$			19.1168i			0.898188i
$454$	5.48913			0.257617
$455$		0			0
$456$	8.74456			0.409502
$457$		−	24.9783i		−	1.16843i	−0.811598	−	0.584217i	$-0.801402\pi$
$457$		−	24.9783i		−	1.16843i	0.811598	−	0.584217i	$-0.198598\pi$
$458$			24.8935i			1.16320i
$459$	5.62772			0.262679
$460$	14.5012	−	3.11684i	0.676123	−	0.145324i
$461$	1.63948			0.0763580			0.0381790	−	0.999271i	$-0.487844\pi$
$461$	1.63948			0.0763580			0.0381790	+	0.999271i	$0.487844\pi$
$462$		−	9.48913i		−	0.441474i
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$	2.74456			0.127413
$465$	−19.1168	+	4.10891i	−0.886522	+	0.190546i
$466$	−7.86797			−0.364477
$467$		−	27.4179i		−	1.26875i	−0.773027	−	0.634374i	$-0.781258\pi$
$467$		−	27.4179i		−	1.26875i	0.773027	−	0.634374i	$-0.218742\pi$
$468$		0			0
$469$	9.48913			0.438167
$470$	4.87375	+	22.6753i	0.224809	+	1.04593i
$471$	−38.2337			−1.76172
$472$			6.63325i			0.305320i
$473$			1.02175i			0.0469801i
$474$	11.9769			0.550116
$475$	15.7908	−	7.11684i	0.724533	−	0.326543i
$476$	14.2063			0.651143
$477$			17.0256i			0.779547i
$478$			9.45254i			0.432349i
$479$	18.2603			0.834333			0.417167	−	0.908830i	$-0.363023\pi$
$479$	18.2603			0.834333			0.417167	+	0.908830i	$0.363023\pi$
$480$	−1.18614	−	5.51856i	−0.0541397	−	0.251887i
$481$		0			0
$482$			8.21782i			0.374312i
$483$			39.7228i			1.80745i
$484$	8.48913			0.385869
$485$	14.7446	−	3.16915i	0.669516	−	0.143904i
$486$	−22.3692			−1.01469
$487$		−	1.48913i		−	0.0674787i	−0.999431	−	0.0337394i	$-0.989258\pi$
$487$		−	1.48913i		−	0.0674787i	0.999431	−	0.0337394i	$-0.0107416\pi$
$488$			6.74456i			0.305312i
$489$	−62.4636			−2.82470
$490$	3.00000	−	0.644810i	0.135526	−	0.0291296i
$491$	25.6277			1.15656			0.578281	−	0.815837i	$-0.303724\pi$
$491$	25.6277			1.15656			0.578281	+	0.815837i	$0.303724\pi$
$492$			25.4891i			1.14914i
$493$		−	16.4356i		−	0.740224i
$494$		0			0
$495$	2.51087	+	11.6819i	0.112855	+	0.525063i
$496$	3.46410			0.155543
$497$			29.9422i			1.34309i
$498$			22.0742i			0.989170i
$499$	16.0309			0.717641			0.358821	−	0.933407i	$-0.383179\pi$
$499$	16.0309			0.717641			0.358821	+	0.933407i	$0.383179\pi$
$500$	−6.63325	−	9.00000i	−0.296648	−	0.402492i
$501$	−44.1485			−1.97241
$502$			22.9783i			1.02557i
$503$			6.63325i			0.295762i	0.989005	+	0.147881i	$0.0472453\pi$
$503$			6.63325i			0.295762i	−0.989005	+	0.147881i	$0.952755\pi$
$504$	8.00000			0.356348
$505$	−6.92820	−	32.2337i	−0.308301	−	1.43438i
$506$	10.5109			0.467265
$507$		0			0
$508$		−	3.46410i		−	0.153695i
$509$	3.16915			0.140470			0.0702350	−	0.997530i	$-0.477625\pi$
$509$	3.16915			0.140470			0.0702350	+	0.997530i	$0.477625\pi$
$510$	−33.0475	+	7.10313i	−1.46337	+	0.314532i
$511$	−23.7228			−1.04944
$512$			1.00000i			0.0441942i
$513$		−	3.25544i		−	0.143731i
$514$	14.2063			0.626611
$515$	−22.7190	+	4.88316i	−1.00112	+	0.215178i
$516$	−1.62772			−0.0716563
$517$			16.4356i			0.722839i
$518$			21.6277i			0.950267i
$519$	47.7228			2.09480
$520$		0			0
$521$	18.6060			0.815142			0.407571	−	0.913173i	$-0.366376\pi$
$521$	18.6060			0.815142			0.407571	+	0.913173i	$0.366376\pi$
$522$		−	9.25544i		−	0.405099i
$523$		−	10.3923i		−	0.454424i	−0.973845	−	0.227212i	$-0.927039\pi$
$523$		−	10.3923i		−	0.454424i	0.973845	−	0.227212i	$-0.0729610\pi$
$524$	1.62772			0.0711072
$525$	27.2978	−	12.3030i	1.19138	−	0.536946i
$526$	18.0202			0.785719
$527$		−	20.7446i		−	0.903647i
$528$		−	4.00000i		−	0.174078i
$529$	−21.0000			−0.913043
$530$	−2.37228	−	11.0371i	−0.103045	−	0.479422i
$531$	22.3692			0.970740
$532$		−	8.21782i		−	0.356288i
$533$		0			0
$534$	−4.74456			−0.205317
$535$	29.6472	−	6.37228i	1.28176	−	0.275498i
$536$	4.00000			0.172774
$537$			12.3267i			0.531938i
$538$			2.74456i			0.118326i
$539$	2.17448			0.0936615
$540$	−2.05446	+	0.441578i	−0.0884097	+	0.0190025i
$541$	30.5321			1.31268			0.656339	−	0.754466i	$-0.272104\pi$
$541$	30.5321			1.31268			0.656339	+	0.754466i	$0.272104\pi$
$542$		−	21.4294i		−	0.920472i
$543$		−	8.80773i		−	0.377976i
$544$	5.98844			0.256752
$545$	1.32473	+	6.16337i	0.0567454	+	0.264010i
$546$		0			0
$547$			21.4294i			0.916256i	0.888886	+	0.458128i	$0.151480\pi$
$547$			21.4294i			0.916256i	−0.888886	+	0.458128i	$0.848520\pi$
$548$		−	6.00000i		−	0.256307i
$549$	22.7446			0.970714
$550$	−3.25544	−	7.22316i	−0.138812	−	0.307996i
$551$	−9.50744			−0.405031
$552$			16.7446i			0.712696i
$553$		−	11.2554i		−	0.478630i
$554$	23.3639			0.992635
$555$	−10.8139	−	50.3118i	−0.459023	−	2.13562i
$556$	−6.37228			−0.270245
$557$			1.11684i			0.0473222i	0.999720	+	0.0236611i	$0.00753226\pi$
$557$			1.11684i			0.0473222i	−0.999720	+	0.0236611i	$0.992468\pi$
$558$		−	11.6819i		−	0.494535i
$559$		0			0
$560$	−5.18614	+	1.11469i	−0.219154	+	0.0471043i
$561$	−23.9538			−1.01133
$562$		−	1.87953i		−	0.0792831i
$563$			1.82462i			0.0768988i	0.999261	+	0.0384494i	$0.0122418\pi$
$563$			1.82462i			0.0768988i	−0.999261	+	0.0384494i	$0.987758\pi$
$564$	−26.1831			−1.10251
$565$	−8.21782	+	1.76631i	−0.345726	+	0.0743093i
$566$	17.3205			0.728035
$567$			18.3723i			0.771563i
$568$			12.6217i			0.529594i
$569$	16.3723			0.686362			0.343181	−	0.939269i	$-0.388496\pi$
$569$	16.3723			0.686362			0.343181	+	0.939269i	$0.388496\pi$
$570$	4.10891	+	19.1168i	0.172103	+	0.800716i
$571$	−12.8832			−0.539143			−0.269572	−	0.962980i	$-0.586882\pi$
$571$	−12.8832			−0.539143			−0.269572	+	0.962980i	$0.586882\pi$
$572$		0			0
$573$		0			0
$574$	23.9538			0.999811
$575$	13.6277	+	30.2372i	0.568315	+	1.26098i
$576$	3.37228			0.140512
$577$			20.9783i			0.873336i	0.899623	+	0.436668i	$0.143842\pi$
$577$			20.9783i			0.873336i	−0.899623	+	0.436668i	$0.856158\pi$
$578$		−	18.8614i		−	0.784531i
$579$	35.3407			1.46871
$580$	1.28962	+	6.00000i	0.0535486	+	0.249136i
$581$	20.7446			0.860629
$582$			17.0256i			0.705732i
$583$		−	8.00000i		−	0.331326i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	2.13859			0.0883445
$587$			19.7228i			0.814048i	0.913418	+	0.407024i	$0.133433\pi$
$587$			19.7228i			0.814048i	−0.913418	+	0.407024i	$0.866567\pi$
$588$			3.46410i			0.142857i
$589$	−12.0000			−0.494451
$590$	−14.5012	+	3.11684i	−0.597006	+	0.128318i
$591$	−11.0371			−0.454006
$592$			9.11684i			0.374700i
$593$		−	32.2337i		−	1.32368i	−0.749646	−	0.661839i	$-0.769776\pi$
$593$		−	32.2337i		−	1.32368i	0.749646	−	0.661839i	$-0.230224\pi$
$594$	−1.48913			−0.0610996
$595$	6.67527	+	31.0569i	0.273659	+	1.27321i
$596$	−17.0256			−0.697394
$597$			20.1947i			0.826514i
$598$		0			0
$599$	31.7228			1.29616			0.648080	−	0.761573i	$-0.275572\pi$
$599$	31.7228			1.29616			0.648080	+	0.761573i	$0.275572\pi$
$600$	11.5070	−	5.18614i	0.469771	−	0.211723i
$601$	−32.3723			−1.32049			−0.660246	−	0.751049i	$-0.729548\pi$
$601$	−32.3723			−1.32049			−0.660246	+	0.751049i	$0.729548\pi$
$602$			1.52967i			0.0623447i
$603$		−	13.4891i		−	0.549320i
$604$	7.57301			0.308142
$605$	3.98889	+	18.5584i	0.162171	+	0.754507i
$606$	37.2203			1.51197
$607$		−	3.46410i		−	0.140604i	−0.997526	−	0.0703018i	$-0.977604\pi$
$607$		−	3.46410i		−	0.140604i	0.997526	−	0.0703018i	$-0.0223962\pi$
$608$		−	3.46410i		−	0.140488i
$609$	−16.4356			−0.666006
$610$	−14.7446	+	3.16915i	−0.596990	+	0.128315i
$611$		0			0
$612$		−	20.1947i		−	0.816322i
$613$		−	19.4891i		−	0.787158i	−0.919291	−	0.393579i	$-0.871237\pi$
$613$		−	19.4891i		−	0.787158i	0.919291	−	0.393579i	$-0.128763\pi$
$614$	18.2337			0.735852
$615$	−55.7228	+	11.9769i	−2.24696	+	0.482954i
$616$	−3.75906			−0.151457
$617$			14.7446i			0.593594i	0.954941	+	0.296797i	$0.0959184\pi$
$617$			14.7446i			0.593594i	−0.954941	+	0.296797i	$0.904082\pi$
$618$		−	26.2337i		−	1.05527i
$619$	9.10268			0.365868			0.182934	−	0.983125i	$-0.441441\pi$
$619$	9.10268			0.365868			0.182934	+	0.983125i	$0.441441\pi$
$620$	1.62772	+	7.57301i	0.0653708	+	0.304140i
$621$	6.23369			0.250149
$622$		−	3.25544i		−	0.130531i
$623$			4.45877i			0.178637i
$624$		0			0
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$	−12.3267			−0.492675
$627$			13.8564i			0.553372i
$628$			15.1460i			0.604392i
$629$	54.5957			2.17687
$630$	3.75906	+	17.4891i	0.149764	+	0.696783i
$631$	−40.4443			−1.61006			−0.805031	−	0.593232i	$-0.797852\pi$
$631$	−40.4443			−1.61006			−0.805031	+	0.593232i	$0.797852\pi$
$632$		−	4.74456i		−	0.188729i
$633$		−	7.86797i		−	0.312724i
$634$	−16.9783			−0.674292
$635$	7.57301	−	1.62772i	0.300526	−	0.0645940i
$636$	12.7446			0.505355
$637$		0			0
$638$			4.34896i			0.172177i
$639$	42.5639			1.68380
$640$	−2.18614	+	0.469882i	−0.0864148	+	0.0185737i
$641$	16.9783			0.670601			0.335300	−	0.942111i	$-0.391162\pi$
$641$	16.9783			0.670601			0.335300	+	0.942111i	$0.391162\pi$
$642$			34.2337i			1.35110i
$643$		−	37.4891i		−	1.47843i	−0.673471	−	0.739213i	$-0.735197\pi$
$643$		−	37.4891i		−	1.47843i	0.673471	−	0.739213i	$-0.264803\pi$
$644$	15.7359			0.620083
$645$	−0.764836	−	3.55842i	−0.0301154	−	0.140113i
$646$	−20.7446			−0.816184
$647$			21.0796i			0.828723i	0.910112	+	0.414362i	$0.135995\pi$
$647$			21.0796i			0.828723i	−0.910112	+	0.414362i	$0.864005\pi$
$648$			7.74456i			0.304235i
$649$	−10.5109			−0.412588
$650$		0			0
$651$	−20.7446			−0.813044
$652$			24.7446i			0.969072i
$653$			17.0256i			0.666261i	0.942881	+	0.333131i	$0.108105\pi$
$653$			17.0256i			0.666261i	−0.942881	+	0.333131i	$0.891895\pi$
$654$	−7.11684			−0.278291
$655$	0.764836	+	3.55842i	0.0298846	+	0.139039i
$656$	10.0974			0.394235
$657$			33.7228i			1.31565i
$658$			24.6060i			0.959241i
$659$	−40.4674			−1.57639			−0.788193	−	0.615429i	$-0.788983\pi$
$659$	−40.4674			−1.57639			−0.788193	+	0.615429i	$0.788983\pi$
$660$	8.74456	−	1.87953i	0.340382	−	0.0731605i
$661$	−9.50744			−0.369797			−0.184898	−	0.982758i	$-0.559196\pi$
$661$	−9.50744			−0.369797			−0.184898	+	0.982758i	$0.559196\pi$
$662$			10.3923i			0.403908i
$663$		0			0
$664$	8.74456			0.339355
$665$	17.9653	−	3.86141i	0.696665	−	0.149739i
$666$	30.7446			1.19133
$667$		−	18.2054i		−	0.704915i
$668$			17.4891i			0.676675i
$669$	−38.1600			−1.47535
$670$	1.87953	+	8.74456i	0.0726125	+	0.337832i
$671$	−10.6873			−0.412577
$672$		−	5.98844i		−	0.231009i
$673$		−	9.74749i		−	0.375738i	−0.982194	−	0.187869i	$-0.939842\pi$
$673$		−	9.74749i		−	0.375738i	0.982194	−	0.187869i	$-0.0601581\pi$
$674$	−1.52967			−0.0589207
$675$	−1.93070	−	4.28384i	−0.0743128	−	0.164885i
$676$		0			0
$677$			39.0998i			1.50273i	0.659889	+	0.751363i	$0.270603\pi$
$677$			39.0998i			1.50273i	−0.659889	+	0.751363i	$0.729397\pi$
$678$		−	9.48913i		−	0.364428i
$679$	16.0000			0.614024
$680$	2.81386	+	13.0916i	0.107907	+	0.502039i
$681$	−13.8564			−0.530979
$682$			5.48913i			0.210189i
$683$			8.74456i			0.334601i	0.985906	+	0.167301i	$0.0535051\pi$
$683$			8.74456i			0.334601i	−0.985906	+	0.167301i	$0.946495\pi$
$684$	−11.6819			−0.446670
$685$	13.1168	−	2.81929i	0.501169	−	0.107720i
$686$	19.8614			0.758312
$687$		−	62.8397i		−	2.39748i
$688$			0.644810i			0.0245832i
$689$		0			0
$690$	−36.6060	+	7.86797i	−1.39357	+	0.299528i
$691$	−39.3947			−1.49865			−0.749323	−	0.662204i	$-0.769621\pi$
$691$	−39.3947			−1.49865			−0.749323	+	0.662204i	$0.769621\pi$
$692$		−	18.9051i		−	0.718663i
$693$			12.6766i			0.481544i
$694$	20.8395			0.791057
$695$	−2.99422	−	13.9307i	−0.113577	−	0.528422i
$696$	−6.92820			−0.262613
$697$		−	60.4674i		−	2.29037i
$698$			27.4728i			1.03986i
$699$	19.8614			0.751227
$700$	−4.87375	−	10.8139i	−0.184210	−	0.408725i
$701$	−16.9783			−0.641260			−0.320630	−	0.947205i	$-0.603895\pi$
$701$	−16.9783			−0.641260			−0.320630	+	0.947205i	$0.603895\pi$
$702$		0			0
$703$		−	31.5817i		−	1.19113i
$704$	−1.58457			−0.0597209
$705$	−12.3030	−	57.2400i	−0.463357	−	2.15578i
$706$	−11.4891			−0.432399
$707$		−	34.9783i		−	1.31549i
$708$		−	16.7446i		−	0.629299i
$709$	−20.7846			−0.780582			−0.390291	−	0.920691i	$-0.627626\pi$
$709$	−20.7846			−0.780582			−0.390291	+	0.920691i	$0.627626\pi$
$710$	−27.5928	+	5.93070i	−1.03554	+	0.222575i
$711$	−16.0000			−0.600047
$712$			1.87953i			0.0704383i
$713$		−	22.9783i		−	0.860542i
$714$	−35.8614			−1.34208
$715$		0			0
$716$	4.88316			0.182492
$717$		−	23.8614i		−	0.891121i
$718$			2.87419i			0.107264i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$	1.58457	+	7.37228i	0.0590536	+	0.274749i
$721$	−24.6535			−0.918143
$722$		−	7.00000i		−	0.260513i
$723$		−	20.7446i		−	0.771499i
$724$	−3.48913			−0.129672
$725$	−12.5109	+	5.63858i	−0.464642	+	0.209412i
$726$	−21.4294			−0.795320
$727$		−	2.17448i		−	0.0806470i	−0.999187	−	0.0403235i	$-0.987161\pi$
$727$		−	2.17448i		−	0.0806470i	0.999187	−	0.0403235i	$-0.0128389\pi$
$728$		0			0
$729$	33.2337			1.23088
$730$	−4.69882	−	21.8614i	−0.173911	−	0.809127i
$731$	3.86141			0.142819
$732$		−	17.0256i		−	0.629283i
$733$			16.0951i			0.594486i	0.954802	+	0.297243i	$0.0960671\pi$
$733$			16.0951i			0.594486i	−0.954802	+	0.297243i	$0.903933\pi$
$734$	−4.75372			−0.175463
$735$	−7.57301	+	1.62772i	−0.279335	+	0.0600393i
$736$	6.63325			0.244505
$737$			6.33830i			0.233474i
$738$		−	34.0511i		−	1.25344i
$739$	28.1176			1.03432			0.517161	−	0.855888i	$-0.326989\pi$
$739$	28.1176			1.03432			0.517161	+	0.855888i	$0.326989\pi$
$740$	−19.9307	+	4.28384i	−0.732667	+	0.157477i
$741$		0			0
$742$		−	11.9769i		−	0.439685i
$743$		−	7.11684i		−	0.261092i	−0.991442	−	0.130546i	$-0.958327\pi$
$743$		−	7.11684i		−	0.261092i	0.991442	−	0.130546i	$-0.0416730\pi$
$744$	−8.74456			−0.320591
$745$	−8.00000	−	37.2203i	−0.293097	−	1.36364i
$746$	9.50744			0.348092
$747$		−	29.4891i		−	1.07895i
$748$			9.48913i			0.346957i
$749$	32.1716			1.17552
$750$	16.7446	+	22.7190i	0.611425	+	0.829582i
$751$	−25.4891			−0.930111			−0.465056	−	0.885281i	$-0.653966\pi$
$751$	−25.4891			−0.930111			−0.465056	+	0.885281i	$0.653966\pi$
$752$			10.3723i			0.378238i
$753$		−	58.0049i		−	2.11381i
$754$		0			0
$755$	3.55842	+	16.5557i	0.129504	+	0.602523i
$756$	−2.22938			−0.0810819
$757$		−	45.4381i		−	1.65148i	−0.564055	−	0.825738i	$-0.690759\pi$
$757$		−	45.4381i		−	1.65148i	0.564055	−	0.825738i	$-0.309241\pi$
$758$		−	17.3205i		−	0.629109i
$759$	−26.5330			−0.963087
$760$	7.57301	−	1.62772i	0.274702	−	0.0590436i
$761$	−1.87953			−0.0681328			−0.0340664	−	0.999420i	$-0.510846\pi$
$761$	−1.87953			−0.0681328			−0.0340664	+	0.999420i	$0.510846\pi$
$762$			8.74456i			0.316782i
$763$			6.68815i			0.242127i
$764$		0			0
$765$	44.1485	−	9.48913i	1.59619	−	0.343080i
$766$	16.8832			0.610013
$767$		0			0
$768$		−	2.52434i		−	0.0910892i
$769$	−16.4356			−0.592685			−0.296342	−	0.955082i	$-0.595767\pi$
$769$	−16.4356			−0.592685			−0.296342	+	0.955082i	$0.595767\pi$
$770$	−1.76631	−	8.21782i	−0.0636535	−	0.296150i
$771$	−35.8614			−1.29152
$772$		−	14.0000i		−	0.503871i
$773$			30.6060i			1.10082i	0.834894	+	0.550410i	$0.185529\pi$
$773$			30.6060i			1.10082i	−0.834894	+	0.550410i	$0.814471\pi$
$774$	2.17448			0.0781601
$775$	−15.7908	+	7.11684i	−0.567224	+	0.255645i
$776$	6.74456			0.242116
$777$		−	54.5957i		−	1.95861i
$778$		−	6.00000i		−	0.215110i
$779$	−34.9783			−1.25323
$780$		0			0
$781$	−20.0000			−0.715656
$782$		−	39.7228i		−	1.42048i
$783$			2.57924i			0.0921745i
$784$	1.37228			0.0490100
$785$	−33.1113	+	7.11684i	−1.18179	+	0.254011i
$786$	−4.10891			−0.146560
$787$			44.0000i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$787$			44.0000i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$788$			4.37228i			0.155756i
$789$	−45.4891			−1.61946
$790$	10.3723	−	2.22938i	0.369029	−	0.0793179i
$791$	−8.91754			−0.317071
$792$			5.34363i			0.189878i
$793$		0			0
$794$	−8.51087			−0.302040
$795$	5.98844	+	27.8614i	0.212388	+	0.988142i
$796$	8.00000			0.283552
$797$		−	25.2434i		−	0.894166i	−0.894492	−	0.447083i	$-0.852463\pi$
$797$		−	25.2434i		−	0.894166i	0.894492	−	0.447083i	$-0.147537\pi$
$798$			20.7446i			0.734350i
$799$	62.1138			2.19743
$800$	−2.05446	−	4.55842i	−0.0726360	−	0.161165i
$801$	6.33830			0.223953
$802$		−	32.1716i		−	1.13602i
$803$		−	15.8457i		−	0.559184i
$804$	−10.0974			−0.356106
$805$	7.39403	+	34.4010i	0.260605	+	1.21247i
$806$		0			0
$807$		−	6.92820i		−	0.243884i
$808$		−	14.7446i		−	0.518712i
$809$	39.3505			1.38349			0.691746	−	0.722141i	$-0.256842\pi$
$809$	39.3505			1.38349			0.691746	+	0.722141i	$0.256842\pi$
$810$	−16.9307	+	3.63903i	−0.594884	+	0.127862i
$811$	−41.9740			−1.47391			−0.736953	−	0.675944i	$-0.763736\pi$
$811$	−41.9740			−1.47391			−0.736953	+	0.675944i	$0.763736\pi$
$812$			6.51087i			0.228487i
$813$			54.0951i			1.89720i
$814$	−14.4463			−0.506343
$815$	−54.0951	+	11.6270i	−1.89487	+	0.407277i
$816$	−15.1168			−0.529195
$817$		−	2.23369i		−	0.0781468i
$818$		−	5.63858i		−	0.197148i
$819$		0			0
$820$	4.74456	+	22.0742i	0.165687	+	0.770866i
$821$	−25.5932			−0.893210			−0.446605	−	0.894731i	$-0.647367\pi$
$821$	−25.5932			−0.893210			−0.446605	+	0.894731i	$0.647367\pi$
$822$			15.1460i			0.528278i
$823$		−	54.5408i		−	1.90117i	−0.310462	−	0.950586i	$-0.600484\pi$
$823$		−	54.5408i		−	1.90117i	0.310462	−	0.950586i	$-0.399516\pi$
$824$	−10.3923			−0.362033
$825$	8.21782	+	18.2337i	0.286108	+	0.634816i
$826$	−15.7359			−0.547523
$827$			15.2554i			0.530484i	0.964182	+	0.265242i	$0.0854518\pi$
$827$			15.2554i			0.530484i	−0.964182	+	0.265242i	$0.914548\pi$
$828$		−	22.3692i		−	0.777383i
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$	4.10891	+	19.1168i	0.142622	+	0.663555i
$831$	−58.9783			−2.04593
$832$		0			0
$833$		−	8.21782i		−	0.284731i
$834$	16.0858			0.557005
$835$	−38.2337	+	8.21782i	−1.32313	+	0.284390i
$836$	5.48913			0.189845
$837$			3.25544i			0.112524i
$838$			19.1168i			0.660380i
$839$	−13.5615			−0.468193			−0.234097	−	0.972213i	$-0.575213\pi$
$839$	−13.5615			−0.468193			−0.234097	+	0.972213i	$0.575213\pi$
$840$	13.0916	−	2.81386i	0.451702	−	0.0970874i
$841$	−21.4674			−0.740254
$842$			11.0371i			0.380364i
$843$			4.74456i			0.163411i
$844$	−3.11684			−0.107286
$845$		0			0
$846$	34.9783			1.20258
$847$			20.1386i			0.691970i
$848$		−	5.04868i		−	0.173372i
$849$	−43.7228			−1.50056
$850$	−27.2978	+	12.3030i	−0.936308	+	0.421989i
$851$	60.4743			2.07303
$852$		−	31.8614i		−	1.09155i
$853$		−	5.11684i		−	0.175197i	−0.996156	−	0.0875987i	$-0.972081\pi$
$853$		−	5.11684i		−	0.175197i	0.996156	−	0.0875987i	$-0.0279193\pi$
$854$	−16.0000			−0.547509
$855$	−5.48913	−	25.5383i	−0.187724	−	0.873393i
$856$	13.5615			0.463521
$857$			22.7739i			0.777943i	0.921250	+	0.388972i	$0.127170\pi$
$857$			22.7739i			0.777943i	−0.921250	+	0.388972i	$0.872830\pi$
$858$		0			0
$859$	−32.4674			−1.10777			−0.553886	−	0.832592i	$-0.686856\pi$
$859$	−32.4674			−1.10777			−0.553886	+	0.832592i	$0.686856\pi$
$860$	−1.40965	+	0.302985i	−0.0480685	+	0.0103317i
$861$	−60.4674			−2.06072
$862$		−	26.4781i		−	0.901848i
$863$		−	3.86141i		−	0.131444i	−0.997838	−	0.0657219i	$-0.979065\pi$
$863$		−	3.86141i		−	0.131444i	0.997838	−	0.0657219i	$-0.0209350\pi$
$864$	−0.939764			−0.0319714
$865$	41.3292	−	8.88316i	1.40523	−	0.302036i
$866$	−34.4010			−1.16899
$867$			47.6126i			1.61701i
$868$			8.21782i			0.278931i
$869$	7.51811			0.255034
$870$	−3.25544	−	15.1460i	−0.110370	−	0.513498i
$871$		0			0
$872$			2.81929i			0.0954733i
$873$		−	22.7446i		−	0.769787i
$874$	−22.9783			−0.777251
$875$	21.3505	−	15.7359i	0.721780	−	0.531972i
$876$	25.2434			0.852895
$877$		−	47.3505i		−	1.59891i	−0.600723	−	0.799457i	$-0.705121\pi$
$877$		−	47.3505i		−	1.59891i	0.600723	−	0.799457i	$-0.294879\pi$
$878$		−	22.2337i		−	0.750351i
$879$	−5.39853			−0.182088
$880$	−0.744563	−	3.46410i	−0.0250992	−	0.116775i
$881$	54.6060			1.83972			0.919861	−	0.392245i	$-0.128301\pi$
$881$	54.6060			1.83972			0.919861	+	0.392245i	$0.128301\pi$
$882$		−	4.62772i		−	0.155823i
$883$			58.6497i			1.97372i	0.161581	+	0.986859i	$0.448341\pi$
$883$			58.6497i			1.97372i	−0.161581	+	0.986859i	$0.551659\pi$
$884$		0			0
$885$	36.6060	−	7.86797i	1.23050	−	0.264479i
$886$	4.40387			0.147951
$887$		−	45.7330i		−	1.53556i	−0.640711	−	0.767782i	$-0.721360\pi$
$887$		−	45.7330i		−	1.53556i	0.640711	−	0.767782i	$-0.278640\pi$
$888$		−	23.0140i		−	0.772299i
$889$	8.21782			0.275617
$890$	−4.10891	+	0.883156i	−0.137731	+	0.0296035i
$891$	−12.2718			−0.411122
$892$			15.1168i			0.506149i
$893$		−	35.9306i		−	1.20237i
$894$	42.9783			1.43741
$895$	2.29451	+	10.6753i	0.0766969	+	0.356835i
$896$	−2.37228			−0.0792524
$897$		0			0
$898$		−	7.51811i		−	0.250883i
$899$	9.50744			0.317091
$900$	−15.3723	+	6.92820i	−0.512409	+	0.230940i
$901$	−30.2337			−1.00723
$902$			16.0000i			0.532742i
$903$		−	3.86141i		−	0.128500i
$904$	−3.75906			−0.125024
$905$	−1.63948	−	7.62772i	−0.0544981	−	0.253554i
$906$	−19.1168			−0.635115
$907$			0.644810i			0.0214106i	0.999943	+	0.0107053i	$0.00340766\pi$
$907$			0.644810i			0.0214106i	−0.999943	+	0.0107053i	$0.996592\pi$
$908$			5.48913i			0.182163i
$909$	−49.7228			−1.64920
$910$		0			0
$911$	34.9783			1.15888			0.579441	−	0.815014i	$-0.303271\pi$
$911$	34.9783			1.15888			0.579441	+	0.815014i	$0.303271\pi$
$912$			8.74456i			0.289561i
$913$			13.8564i			0.458580i
$914$	24.9783			0.826207
$915$	37.2203	−	8.00000i	1.23046	−	0.264472i
$916$	−24.8935			−0.822505
$917$			3.86141i			0.127515i
$918$			5.62772i			0.185742i
$919$	42.9783			1.41772			0.708861	−	0.705348i	$-0.249209\pi$
$919$	42.9783			1.41772			0.708861	+	0.705348i	$0.249209\pi$
$920$	3.11684	+	14.5012i	0.102759	+	0.478091i
$921$	−46.0280			−1.51667
$922$			1.63948i			0.0539933i
$923$		0			0
$924$	9.48913			0.312169
$925$	−18.7302	−	41.5584i	−0.615844	−	1.36643i
$926$	16.0000			0.525793
$927$			35.0458i			1.15105i
$928$			2.74456i			0.0900947i
$929$	−47.9075			−1.57179			−0.785897	−	0.618357i	$-0.787799\pi$
$929$	−47.9075			−1.57179			−0.785897	+	0.618357i	$0.787799\pi$
$930$	−4.10891	−	19.1168i	−0.134737	−	0.626866i
$931$	−4.75372			−0.155797
$932$		−	7.86797i		−	0.257724i
$933$			8.21782i			0.269039i
$934$	27.4179			0.897140
$935$	−20.7446	+	4.45877i	−0.678420	+	0.145817i
$936$		0			0
$937$			30.2921i			0.989598i	0.869007	+	0.494799i	$0.164758\pi$
$937$			30.2921i			0.989598i	−0.869007	+	0.494799i	$0.835242\pi$
$938$			9.48913i			0.309831i
$939$	31.1168			1.01546
$940$	−22.6753	+	4.87375i	−0.739586	+	0.158964i
$941$	40.6295			1.32448			0.662241	−	0.749291i	$-0.269605\pi$
$941$	40.6295			1.32448			0.662241	+	0.749291i	$0.269605\pi$
$942$		−	38.2337i		−	1.24572i
$943$		−	66.9783i		−	2.18111i
$944$	−6.63325			−0.215894
$945$	−1.04755	−	4.87375i	−0.0340767	−	0.158543i
$946$	−1.02175			−0.0332199
$947$		−	29.4891i		−	0.958268i	−0.877742	−	0.479134i	$-0.840951\pi$
$947$		−	29.4891i		−	0.958268i	0.877742	−	0.479134i	$-0.159049\pi$
$948$			11.9769i			0.388991i
$949$		0			0
$950$	7.11684	+	15.7908i	0.230901	+	0.512322i
$951$	42.8588			1.38979
$952$			14.2063i			0.460428i
$953$			16.0858i			0.521070i	0.965464	+	0.260535i	$0.0838989\pi$
$953$			16.0858i			0.521070i	−0.965464	+	0.260535i	$0.916101\pi$
$954$	−17.0256			−0.551223
$955$		0			0
$956$	−9.45254			−0.305717
$957$		−	10.9783i		−	0.354876i
$958$			18.2603i			0.589963i
$959$	14.2337			0.459630
$960$	5.51856	−	1.18614i	0.178111	−	0.0382825i
$961$	−19.0000			−0.612903
$962$		0			0
$963$		−	45.7330i		−	1.47373i
$964$	−8.21782			−0.264678
$965$	30.6060	−	6.57835i	0.985241	−	0.211764i
$966$	−39.7228			−1.27806
$967$		−	5.35053i		−	0.172062i	−0.996292	−	0.0860308i	$-0.972582\pi$
$967$		−	5.35053i		−	0.172062i	0.996292	−	0.0860308i	$-0.0274183\pi$
$968$			8.48913i			0.272851i
$969$	52.3663			1.68225
$970$	3.16915	+	14.7446i	0.101755	+	0.473419i
$971$	−12.6060			−0.404545			−0.202272	−	0.979329i	$-0.564833\pi$
$971$	−12.6060			−0.404545			−0.202272	+	0.979329i	$0.564833\pi$
$972$		−	22.3692i		−	0.717492i
$973$		−	15.1168i		−	0.484624i
$974$	1.48913			0.0477147
$975$		0			0
$976$	−6.74456			−0.215888
$977$			25.7228i			0.822946i	0.911422	+	0.411473i	$0.134986\pi$
$977$			25.7228i			0.822946i	−0.911422	+	0.411473i	$0.865014\pi$
$978$		−	62.4636i		−	1.99737i
$979$	−2.97825			−0.0951853
$980$	0.644810	+	3.00000i	0.0205977	+	0.0958315i
$981$	9.50744			0.303549
$982$			25.6277i			0.817813i
$983$			42.0951i			1.34263i	0.741174	+	0.671313i	$0.234269\pi$
$983$			42.0951i			1.34263i	−0.741174	+	0.671313i	$0.765731\pi$
$984$	−25.4891			−0.812564
$985$	−9.55842	+	2.05446i	−0.304557	+	0.0654604i
$986$	16.4356			0.523418
$987$		−	62.1138i		−	1.97710i
$988$		0			0
$989$	4.27719			0.136007
$990$	−11.6819	+	2.51087i	−0.371276	+	0.0798008i
$991$	−1.76631			−0.0561088			−0.0280544	−	0.999606i	$-0.508931\pi$
$991$	−1.76631			−0.0561088			−0.0280544	+	0.999606i	$0.508931\pi$
$992$			3.46410i			0.109985i
$993$		−	26.2337i		−	0.832501i
$994$	−29.9422			−0.949709
$995$	3.75906	+	17.4891i	0.119170	+	0.554443i
$996$	−22.0742			−0.699449
$997$		−	4.34896i		−	0.137733i	−0.997626	−	0.0688665i	$-0.978062\pi$
$997$		−	4.34896i		−	0.137733i	0.997626	−	0.0688665i	$-0.0219383\pi$
$998$			16.0309i			0.507449i
$999$	−8.56768			−0.271069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.d.339.5		8
5.2	odd	4		8450.2.a.cj.1.1		4
5.3	odd	4		8450.2.a.cn.1.4		4
5.4	even	2	inner	1690.2.b.d.339.4		8
13.5	odd	4		130.2.c.b.129.1	yes	4
13.8	odd	4		130.2.c.a.129.1	✓	4
13.12	even	2	inner	1690.2.b.d.339.1		8
39.5	even	4		1170.2.f.a.649.3		4
39.8	even	4		1170.2.f.b.649.2		4
52.31	even	4		1040.2.f.c.129.4		4
52.47	even	4		1040.2.f.d.129.4		4
65.8	even	4		650.2.d.e.51.8		8
65.12	odd	4		8450.2.a.cn.1.1		4
65.18	even	4		650.2.d.e.51.4		8
65.34	odd	4		130.2.c.b.129.4	yes	4
65.38	odd	4		8450.2.a.cj.1.4		4
65.44	odd	4		130.2.c.a.129.4	yes	4
65.47	even	4		650.2.d.e.51.1		8
65.57	even	4		650.2.d.e.51.5		8
65.64	even	2	inner	1690.2.b.d.339.8		8
195.44	even	4		1170.2.f.b.649.1		4
195.164	even	4		1170.2.f.a.649.4		4
260.99	even	4		1040.2.f.c.129.1		4
260.239	even	4		1040.2.f.d.129.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.c.a.129.1	✓	4	13.8	odd	4
130.2.c.a.129.4	yes	4	65.44	odd	4
130.2.c.b.129.1	yes	4	13.5	odd	4
130.2.c.b.129.4	yes	4	65.34	odd	4
650.2.d.e.51.1		8	65.47	even	4
650.2.d.e.51.4		8	65.18	even	4
650.2.d.e.51.5		8	65.57	even	4
650.2.d.e.51.8		8	65.8	even	4
1040.2.f.c.129.1		4	260.99	even	4
1040.2.f.c.129.4		4	52.31	even	4
1040.2.f.d.129.1		4	260.239	even	4
1040.2.f.d.129.4		4	52.47	even	4
1170.2.f.a.649.3		4	39.5	even	4
1170.2.f.a.649.4		4	195.164	even	4
1170.2.f.b.649.1		4	195.44	even	4
1170.2.f.b.649.2		4	39.8	even	4
1690.2.b.d.339.1		8	13.12	even	2	inner
1690.2.b.d.339.4		8	5.4	even	2	inner
1690.2.b.d.339.5		8	1.1	even	1	trivial
1690.2.b.d.339.8		8	65.64	even	2	inner
8450.2.a.cj.1.1		4	5.2	odd	4
8450.2.a.cj.1.4		4	65.38	odd	4
8450.2.a.cn.1.1		4	65.12	odd	4
8450.2.a.cn.1.4		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.52434i q^{3} -1.00000 q^{4} +(-0.469882 - 2.18614i) q^{5} +2.52434 q^{6} -2.37228i q^{7} -1.00000i q^{8} -3.37228 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.52434i q^{3} -1.00000 q^{4} +(-0.469882 - 2.18614i) q^{5} +2.52434 q^{6} -2.37228i q^{7} -1.00000i q^{8} -3.37228 q^{9} +(2.18614 - 0.469882i) q^{10} +1.58457 q^{11} +2.52434i q^{12} +2.37228 q^{14} +(-5.51856 + 1.18614i) q^{15} +1.00000 q^{16} -5.98844i q^{17} -3.37228i q^{18} -3.46410 q^{19} +(0.469882 + 2.18614i) q^{20} -5.98844 q^{21} +1.58457i q^{22} -6.63325i q^{23} -2.52434 q^{24} +(-4.55842 + 2.05446i) q^{25} +0.939764i q^{27} +2.37228i q^{28} +2.74456 q^{29} +(-1.18614 - 5.51856i) q^{30} +3.46410 q^{31} +1.00000i q^{32} -4.00000i q^{33} +5.98844 q^{34} +(-5.18614 + 1.11469i) q^{35} +3.37228 q^{36} +9.11684i q^{37} -3.46410i q^{38} +(-2.18614 + 0.469882i) q^{40} +10.0974 q^{41} -5.98844i q^{42} +0.644810i q^{43} -1.58457 q^{44} +(1.58457 + 7.37228i) q^{45} +6.63325 q^{46} +10.3723i q^{47} -2.52434i q^{48} +1.37228 q^{49} +(-2.05446 - 4.55842i) q^{50} -15.1168 q^{51} -5.04868i q^{53} -0.939764 q^{54} +(-0.744563 - 3.46410i) q^{55} -2.37228 q^{56} +8.74456i q^{57} +2.74456i q^{58} -6.63325 q^{59} +(5.51856 - 1.18614i) q^{60} -6.74456 q^{61} +3.46410i q^{62} +8.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +4.00000i q^{67} +5.98844i q^{68} -16.7446 q^{69} +(-1.11469 - 5.18614i) q^{70} -12.6217 q^{71} +3.37228i q^{72} -10.0000i q^{73} -9.11684 q^{74} +(5.18614 + 11.5070i) q^{75} +3.46410 q^{76} -3.75906i q^{77} +4.74456 q^{79} +(-0.469882 - 2.18614i) q^{80} -7.74456 q^{81} +10.0974i q^{82} +8.74456i q^{83} +5.98844 q^{84} +(-13.0916 + 2.81386i) q^{85} -0.644810 q^{86} -6.92820i q^{87} -1.58457i q^{88} -1.87953 q^{89} +(-7.37228 + 1.58457i) q^{90} +6.63325i q^{92} -8.74456i q^{93} -10.3723 q^{94} +(1.62772 + 7.57301i) q^{95} +2.52434 q^{96} +6.74456i q^{97} +1.37228i q^{98} -5.34363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^9	\( 8 q - 8 q^{4} - 4 q^{9} + 6 q^{10} - 4 q^{14} + 8 q^{16} - 2 q^{25} - 24 q^{29} + 2 q^{30} - 30 q^{35} + 4 q^{36} - 6 q^{40} - 12 q^{49} - 52 q^{51} + 40 q^{55} + 4 q^{56} - 8 q^{61} - 8 q^{64} + 32 q^{66} - 88 q^{69} - 4 q^{74} + 30 q^{75} - 8 q^{79} - 16 q^{81} - 36 q^{90} - 60 q^{94} + 36 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^9 + 6 * q^10 - 4 * q^14 + 8 * q^16 - 2 * q^25 - 24 * q^29 + 2 * q^30 - 30 * q^35 + 4 * q^36 - 6 * q^40 - 12 * q^49 - 52 * q^51 + 40 * q^55 + 4 * q^56 - 8 * q^61 - 8 * q^64 + 32 * q^66 - 88 * q^69 - 4 * q^74 + 30 * q^75 - 8 * q^79 - 16 * q^81 - 36 * q^90 - 60 * q^94 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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