LMFDB - Embedded newform 561.2.g.b.67.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(67,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("561.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.g (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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 27x^{14} + 291x^{12} + 1585x^{10} + 4548x^{8} + 6536x^{6} + 4136x^{4} + 768x^{2} + 4 $ x^16 + 27x^14 + 291x^12 + 1585x^10 + 4548x^8 + 6536x^6 + 4136x^4 + 768*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.15
Root			$-2.43727i$ of defining polynomial
Character	$\chi$	$=$	561.67
Dual form			561.2.g.b.67.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43727 q^{2} -1.00000i q^{3} +3.94028 q^{4} -4.24270i q^{5} -2.43727i q^{6} +4.22123i q^{7} +4.72899 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.43727 q^{2} -1.00000i q^{3} +3.94028 q^{4} -4.24270i q^{5} -2.43727i q^{6} +4.22123i q^{7} +4.72899 q^{8} -1.00000 q^{9} -10.3406i q^{10} -1.00000i q^{11} -3.94028i q^{12} +0.715750 q^{13} +10.2883i q^{14} -4.24270 q^{15} +3.64526 q^{16} +(2.27710 + 3.43727i) q^{17} -2.43727 q^{18} -0.378933 q^{19} -16.7174i q^{20} +4.22123 q^{21} -2.43727i q^{22} -3.28094i q^{23} -4.72899i q^{24} -13.0005 q^{25} +1.74448 q^{26} +1.00000i q^{27} +16.6328i q^{28} -7.06349i q^{29} -10.3406 q^{30} +5.13399i q^{31} -0.573506 q^{32} -1.00000 q^{33} +(5.54990 + 8.37755i) q^{34} +17.9094 q^{35} -3.94028 q^{36} +7.87726i q^{37} -0.923562 q^{38} -0.715750i q^{39} -20.0637i q^{40} +10.4876i q^{41} +10.2883 q^{42} +2.47683 q^{43} -3.94028i q^{44} +4.24270i q^{45} -7.99654i q^{46} +7.10198 q^{47} -3.64526i q^{48} -10.8187 q^{49} -31.6856 q^{50} +(3.43727 - 2.27710i) q^{51} +2.82026 q^{52} -8.79599 q^{53} +2.43727i q^{54} -4.24270 q^{55} +19.9621i q^{56} +0.378933i q^{57} -17.2156i q^{58} +5.14417 q^{59} -16.7174 q^{60} +1.22451i q^{61} +12.5129i q^{62} -4.22123i q^{63} -8.68830 q^{64} -3.03671i q^{65} -2.43727 q^{66} +12.9368 q^{67} +(8.97241 + 13.5438i) q^{68} -3.28094 q^{69} +43.6500 q^{70} +3.30123i q^{71} -4.72899 q^{72} +2.16905i q^{73} +19.1990i q^{74} +13.0005i q^{75} -1.49310 q^{76} +4.22123 q^{77} -1.74448i q^{78} -6.60703i q^{79} -15.4657i q^{80} +1.00000 q^{81} +25.5612i q^{82} -5.19723 q^{83} +16.6328 q^{84} +(14.5833 - 9.66104i) q^{85} +6.03670 q^{86} -7.06349 q^{87} -4.72899i q^{88} -1.95847 q^{89} +10.3406i q^{90} +3.02134i q^{91} -12.9278i q^{92} +5.13399 q^{93} +17.3094 q^{94} +1.60770i q^{95} +0.573506i q^{96} +5.42839i q^{97} -26.3682 q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9	$ 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9} + 12 q^{13} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{21} - 56 q^{25} - 8 q^{26} - 36 q^{30} - 34 q^{32} - 16 q^{33} + 30 q^{34} + 8 q^{35} - 22 q^{36} + 44 q^{38} - 12 q^{42} - 24 q^{43} + 18 q^{47} - 34 q^{49} + 30 q^{50} + 14 q^{51} + 28 q^{52} - 26 q^{53} - 4 q^{55} - 2 q^{59} - 12 q^{60} - 38 q^{64} + 2 q^{66} + 30 q^{67} + 42 q^{68} - 28 q^{69} + 88 q^{70} + 6 q^{72} - 84 q^{76} + 2 q^{77} + 16 q^{81} - 52 q^{83} + 24 q^{84} + 40 q^{85} - 52 q^{86} - 26 q^{87} + 78 q^{89} + 20 q^{93} - 16 q^{94} - 70 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9 + 12 * q^13 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^21 - 56 * q^25 - 8 * q^26 - 36 * q^30 - 34 * q^32 - 16 * q^33 + 30 * q^34 + 8 * q^35 - 22 * q^36 + 44 * q^38 - 12 * q^42 - 24 * q^43 + 18 * q^47 - 34 * q^49 + 30 * q^50 + 14 * q^51 + 28 * q^52 - 26 * q^53 - 4 * q^55 - 2 * q^59 - 12 * q^60 - 38 * q^64 + 2 * q^66 + 30 * q^67 + 42 * q^68 - 28 * q^69 + 88 * q^70 + 6 * q^72 - 84 * q^76 + 2 * q^77 + 16 * q^81 - 52 * q^83 + 24 * q^84 + 40 * q^85 - 52 * q^86 - 26 * q^87 + 78 * q^89 + 20 * q^93 - 16 * q^94 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	2.43727			1.72341			0.861705	−	0.507410i	$-0.169397\pi$
$2$	2.43727			1.72341			0.861705	+	0.507410i	$0.169397\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	3.94028			1.97014
$5$		−	4.24270i		−	1.89739i	−0.316191	−	0.948696i	$-0.602404\pi$
$5$		−	4.24270i		−	1.89739i	0.316191	−	0.948696i	$-0.397596\pi$
$6$		−	2.43727i		−	0.995011i
$7$			4.22123i			1.59547i	0.603006	+	0.797737i	$0.293970\pi$
$7$			4.22123i			1.59547i	−0.603006	+	0.797737i	$0.706030\pi$
$8$	4.72899			1.67195
$9$	−1.00000			−0.333333
$10$		−	10.3406i		−	3.26998i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		−	3.94028i		−	1.13746i
$13$	0.715750			0.198513			0.0992567	−	0.995062i	$-0.468353\pi$
$13$	0.715750			0.198513			0.0992567	+	0.995062i	$0.468353\pi$
$14$			10.2883i			2.74965i
$15$	−4.24270			−1.09546
$16$	3.64526			0.911314
$17$	2.27710	+	3.43727i	0.552278	+	0.833660i
$17$	2.27710	+	3.43727i	0.552278	+	0.833660i
$18$	−2.43727			−0.574470
$19$	−0.378933			−0.0869332			−0.0434666	−	0.999055i	$-0.513840\pi$
$19$	−0.378933			−0.0869332			−0.0434666	+	0.999055i	$0.513840\pi$
$20$		−	16.7174i		−	3.73813i
$21$	4.22123			0.921147
$22$		−	2.43727i		−	0.519628i
$23$		−	3.28094i		−	0.684124i	−0.939677	−	0.342062i	$-0.888875\pi$
$23$		−	3.28094i		−	0.684124i	0.939677	−	0.342062i	$-0.111125\pi$
$24$		−	4.72899i		−	0.965301i
$25$	−13.0005			−2.60009
$26$	1.74448			0.342120
$27$			1.00000i			0.192450i
$28$			16.6328i			3.14331i
$29$		−	7.06349i		−	1.31166i	−0.754910	−	0.655829i	$-0.772319\pi$
$29$		−	7.06349i		−	1.31166i	0.754910	−	0.655829i	$-0.227681\pi$
$30$	−10.3406			−1.88793
$31$			5.13399i			0.922091i	0.887376	+	0.461046i	$0.152526\pi$
$31$			5.13399i			0.922091i	−0.887376	+	0.461046i	$0.847474\pi$
$32$	−0.573506			−0.101383
$33$	−1.00000			−0.174078
$34$	5.54990	+	8.37755i	0.951801	+	1.43674i
$35$	17.9094			3.02724
$36$	−3.94028			−0.656714
$37$			7.87726i			1.29501i	0.762060	+	0.647507i	$0.224188\pi$
$37$			7.87726i			1.29501i	−0.762060	+	0.647507i	$0.775812\pi$
$38$	−0.923562			−0.149822
$39$		−	0.715750i		−	0.114612i
$40$		−	20.0637i		−	3.17234i
$41$			10.4876i			1.63789i	0.573870	+	0.818946i	$0.305441\pi$
$41$			10.4876i			1.63789i	−0.573870	+	0.818946i	$0.694559\pi$
$42$	10.2883			1.58751
$43$	2.47683			0.377713			0.188857	−	0.982005i	$-0.439522\pi$
$43$	2.47683			0.377713			0.188857	+	0.982005i	$0.439522\pi$
$44$		−	3.94028i		−	0.594020i
$45$			4.24270i			0.632464i
$46$		−	7.99654i		−	1.17903i
$47$	7.10198			1.03593			0.517965	−	0.855402i	$-0.326690\pi$
$47$	7.10198			1.03593			0.517965	+	0.855402i	$0.326690\pi$
$48$		−	3.64526i		−	0.526147i
$49$	−10.8187			−1.54554
$50$	−31.6856			−4.48103
$51$	3.43727	−	2.27710i	0.481314	−	0.318858i
$52$	2.82026			0.391099
$53$	−8.79599			−1.20822			−0.604111	−	0.796900i	$-0.706472\pi$
$53$	−8.79599			−1.20822			−0.604111	+	0.796900i	$0.706472\pi$
$54$			2.43727i			0.331670i
$55$	−4.24270			−0.572085
$56$			19.9621i			2.66755i
$57$			0.378933i			0.0501909i
$58$		−	17.2156i		−	2.26052i
$59$	5.14417			0.669714			0.334857	−	0.942269i	$-0.391312\pi$
$59$	5.14417			0.669714			0.334857	+	0.942269i	$0.391312\pi$
$60$	−16.7174			−2.15821
$61$			1.22451i			0.156782i	0.996923	+	0.0783910i	$0.0249783\pi$
$61$			1.22451i			0.156782i	−0.996923	+	0.0783910i	$0.975022\pi$
$62$			12.5129i			1.58914i
$63$		−	4.22123i		−	0.531824i
$64$	−8.68830			−1.08604
$65$		−	3.03671i		−	0.376658i
$66$	−2.43727			−0.300007
$67$	12.9368			1.58048			0.790242	−	0.612794i	$-0.209955\pi$
$67$	12.9368			1.58048			0.790242	+	0.612794i	$0.209955\pi$
$68$	8.97241	+	13.5438i	1.08806	+	1.64243i
$69$	−3.28094			−0.394979
$70$	43.6500			5.21717
$71$			3.30123i			0.391784i	0.980625	+	0.195892i	$0.0627602\pi$
$71$			3.30123i			0.391784i	−0.980625	+	0.195892i	$0.937240\pi$
$72$	−4.72899			−0.557317
$73$			2.16905i			0.253868i	0.991911	+	0.126934i	$0.0405136\pi$
$73$			2.16905i			0.253868i	−0.991911	+	0.126934i	$0.959486\pi$
$74$			19.1990i			2.23184i
$75$			13.0005i			1.50116i
$76$	−1.49310			−0.171271
$77$	4.22123			0.481053
$78$		−	1.74448i		−	0.197523i
$79$		−	6.60703i		−	0.743349i	−0.928363	−	0.371675i	$-0.878784\pi$
$79$		−	6.60703i		−	0.743349i	0.928363	−	0.371675i	$-0.121216\pi$
$80$		−	15.4657i		−	1.72912i
$81$	1.00000			0.111111
$82$			25.5612i			2.82276i
$83$	−5.19723			−0.570470			−0.285235	−	0.958458i	$-0.592072\pi$
$83$	−5.19723			−0.570470			−0.285235	+	0.958458i	$0.592072\pi$
$84$	16.6328			1.81479
$85$	14.5833	−	9.66104i	1.58178	−	1.04789i
$86$	6.03670			0.650954
$87$	−7.06349			−0.757286
$88$		−	4.72899i		−	0.504112i
$89$	−1.95847			−0.207597			−0.103799	−	0.994598i	$-0.533100\pi$
$89$	−1.95847			−0.207597			−0.103799	+	0.994598i	$0.533100\pi$
$90$			10.3406i			1.08999i
$91$			3.02134i			0.316723i
$92$		−	12.9278i		−	1.34782i
$93$	5.13399			0.532370
$94$	17.3094			1.78533
$95$			1.60770i			0.164946i
$96$			0.573506i			0.0585333i
$97$			5.42839i			0.551170i	0.961277	+	0.275585i	$0.0888715\pi$
$97$			5.42839i			0.551170i	−0.961277	+	0.275585i	$0.911128\pi$
$98$	−26.3682			−2.66359
$99$			1.00000i			0.100504i
$100$	−51.2255			−5.12255
$101$	−6.27754			−0.624639			−0.312320	−	0.949977i	$-0.601106\pi$
$101$	−6.27754			−0.624639			−0.312320	+	0.949977i	$0.601106\pi$
$102$	8.37755	−	5.54990i	0.829501	−	0.549522i
$103$	−8.22864			−0.810792			−0.405396	−	0.914141i	$-0.632866\pi$
$103$	−8.22864			−0.810792			−0.405396	+	0.914141i	$0.632866\pi$
$104$	3.38478			0.331905
$105$		−	17.9094i		−	1.74778i
$106$	−21.4382			−2.08226
$107$		−	4.73702i		−	0.457945i	−0.973433	−	0.228973i	$-0.926463\pi$
$107$		−	4.73702i		−	0.457945i	0.973433	−	0.228973i	$-0.0735366\pi$
$108$			3.94028i			0.379154i
$109$		−	18.8516i		−	1.80565i	−0.430004	−	0.902827i	$-0.641488\pi$
$109$		−	18.8516i		−	1.80565i	0.430004	−	0.902827i	$-0.358512\pi$
$110$	−10.3406			−0.985937
$111$	7.87726			0.747676
$112$			15.3875i			1.45398i
$113$		−	19.7044i		−	1.85364i	−0.375507	−	0.926819i	$-0.622532\pi$
$113$		−	19.7044i		−	1.85364i	0.375507	−	0.926819i	$-0.377468\pi$
$114$			0.923562i			0.0864995i
$115$	−13.9200			−1.29805
$116$		−	27.8322i		−	2.58415i
$117$	−0.715750			−0.0661712
$118$	12.5377			1.15419
$119$	−14.5095	+	9.61215i	−1.33008	+	0.881144i
$120$	−20.0637			−1.83155
$121$	−1.00000			−0.0909091
$122$			2.98445i			0.270200i
$123$	10.4876			0.945638
$124$			20.2294i			1.81665i
$125$			33.9436i			3.03600i
$126$		−	10.2883i		−	0.916551i
$127$	1.97188			0.174976			0.0874882	−	0.996166i	$-0.472116\pi$
$127$	1.97188			0.174976			0.0874882	+	0.996166i	$0.472116\pi$
$128$	−20.0287			−1.77031
$129$		−	2.47683i		−	0.218073i
$130$		−	7.40128i		−	0.649136i
$131$		−	11.2485i		−	0.982785i	−0.870938	−	0.491393i	$-0.836488\pi$
$131$		−	11.2485i		−	0.982785i	0.870938	−	0.491393i	$-0.163512\pi$
$132$	−3.94028			−0.342958
$133$		−	1.59956i		−	0.138700i
$134$	31.5305			2.72382
$135$	4.24270			0.365153
$136$	10.7684	+	16.2548i	0.923381	+	1.39384i
$137$	−15.9194			−1.36009			−0.680045	−	0.733171i	$-0.738040\pi$
$137$	−15.9194			−1.36009			−0.680045	+	0.733171i	$0.738040\pi$
$138$	−7.99654			−0.680711
$139$		−	19.4962i		−	1.65365i	−0.562460	−	0.826824i	$-0.690145\pi$
$139$		−	19.4962i		−	1.65365i	0.562460	−	0.826824i	$-0.309855\pi$
$140$	70.5680			5.96408
$141$		−	7.10198i		−	0.598095i
$142$			8.04599i			0.675205i
$143$		−	0.715750i		−	0.0598541i
$144$	−3.64526			−0.303771
$145$	−29.9683			−2.48873
$146$			5.28655i			0.437518i
$147$			10.8187i			0.892315i
$148$			31.0386i			2.55136i
$149$	0.291720			0.0238986			0.0119493	−	0.999929i	$-0.496196\pi$
$149$	0.291720			0.0238986			0.0119493	+	0.999929i	$0.496196\pi$
$150$			31.6856i			2.58712i
$151$	−4.46189			−0.363103			−0.181552	−	0.983381i	$-0.558112\pi$
$151$	−4.46189			−0.363103			−0.181552	+	0.983381i	$0.558112\pi$
$152$	−1.79197			−0.145348
$153$	−2.27710	−	3.43727i	−0.184093	−	0.277887i
$154$	10.2883			0.829052
$155$	21.7820			1.74957
$156$		−	2.82026i		−	0.225801i
$157$	−1.76860			−0.141149			−0.0705747	−	0.997506i	$-0.522483\pi$
$157$	−1.76860			−0.141149			−0.0705747	+	0.997506i	$0.522483\pi$
$158$		−	16.1031i		−	1.28110i
$159$			8.79599i			0.697567i
$160$			2.43321i			0.192362i
$161$	13.8496			1.09150
$162$	2.43727			0.191490
$163$			14.2738i			1.11801i	0.829164	+	0.559005i	$0.188817\pi$
$163$			14.2738i			1.11801i	−0.829164	+	0.559005i	$0.811183\pi$
$164$			41.3242i			3.22688i
$165$			4.24270i			0.330293i
$166$	−12.6671			−0.983154
$167$		−	2.15961i		−	0.167116i	−0.996503	−	0.0835579i	$-0.973372\pi$
$167$		−	2.15961i		−	0.167116i	0.996503	−	0.0835579i	$-0.0266284\pi$
$168$	19.9621			1.54011
$169$	−12.4877			−0.960592
$170$	35.5434	−	23.5466i	2.72605	−	1.80594i
$171$	0.378933			0.0289777
$172$	9.75941			0.744148
$173$		−	13.2669i		−	1.00866i	−0.863510	−	0.504331i	$-0.831739\pi$
$173$		−	13.2669i		−	1.00866i	0.863510	−	0.504331i	$-0.168261\pi$
$174$	−17.2156			−1.30511
$175$		−	54.8779i		−	4.14838i
$176$		−	3.64526i		−	0.274772i
$177$		−	5.14417i		−	0.386659i
$178$	−4.77332			−0.357776
$179$	−15.6994			−1.17343			−0.586716	−	0.809793i	$-0.699579\pi$
$179$	−15.6994			−1.17343			−0.586716	+	0.809793i	$0.699579\pi$
$180$			16.7174i			1.24604i
$181$		−	5.02062i		−	0.373180i	−0.982438	−	0.186590i	$-0.940256\pi$
$181$		−	5.02062i		−	0.373180i	0.982438	−	0.186590i	$-0.0597436\pi$
$182$			7.36383i			0.545843i
$183$	1.22451			0.0905182
$184$		−	15.5155i		−	1.14382i
$185$	33.4208			2.45715
$186$	12.5129			0.917491
$187$	3.43727	−	2.27710i	0.251358	−	0.166518i
$188$	27.9838			2.04093
$189$	−4.22123			−0.307049
$190$			3.91839i			0.284270i
$191$	−9.34165			−0.675938			−0.337969	−	0.941157i	$-0.609740\pi$
$191$	−9.34165			−0.675938			−0.337969	+	0.941157i	$0.609740\pi$
$192$			8.68830i			0.627024i
$193$		−	18.6012i		−	1.33894i	−0.742839	−	0.669470i	$-0.766521\pi$
$193$		−	18.6012i		−	1.33894i	0.742839	−	0.669470i	$-0.233479\pi$
$194$			13.2305i			0.949891i
$195$	−3.03671			−0.217463
$196$	−42.6289			−3.04492
$197$			25.3351i			1.80505i	0.430637	+	0.902525i	$0.358289\pi$
$197$			25.3351i			1.80505i	−0.430637	+	0.902525i	$0.641711\pi$
$198$			2.43727i			0.173209i
$199$		−	13.2269i		−	0.937632i	−0.883296	−	0.468816i	$-0.844681\pi$
$199$		−	13.2269i		−	0.937632i	0.883296	−	0.468816i	$-0.155319\pi$
$200$	−61.4791			−4.34723
$201$		−	12.9368i		−	0.912493i
$202$	−15.3001			−1.07651
$203$	29.8166			2.09272
$204$	13.5438	−	8.97241i	0.948256	−	0.628194i
$205$	44.4958			3.10772
$206$	−20.0554			−1.39733
$207$			3.28094i			0.228041i
$208$	2.60909			0.180908
$209$			0.378933i			0.0262114i
$210$		−	43.6500i		−	3.01213i
$211$			8.65486i			0.595825i	0.954593	+	0.297913i	$0.0962904\pi$
$211$			8.65486i			0.595825i	−0.954593	+	0.297913i	$0.903710\pi$
$212$	−34.6587			−2.38037
$213$	3.30123			0.226197
$214$		−	11.5454i		−	0.789227i
$215$		−	10.5084i		−	0.716669i
$216$			4.72899i			0.321767i
$217$	−21.6717			−1.47117
$218$		−	45.9464i		−	3.11188i
$219$	2.16905			0.146571
$220$	−16.7174			−1.12709
$221$	1.62983	+	2.46023i	0.109635	+	0.165493i
$222$	19.1990			1.28855
$223$	25.7252			1.72269			0.861344	−	0.508021i	$-0.169623\pi$
$223$	25.7252			1.72269			0.861344	+	0.508021i	$0.169623\pi$
$224$		−	2.42090i		−	0.161753i
$225$	13.0005			0.866698
$226$		−	48.0251i		−	3.19458i
$227$			12.3676i			0.820869i	0.911890	+	0.410434i	$0.134623\pi$
$227$			12.3676i			0.820869i	−0.911890	+	0.410434i	$0.865377\pi$
$228$			1.49310i			0.0988832i
$229$	−9.39397			−0.620771			−0.310385	−	0.950611i	$-0.600458\pi$
$229$	−9.39397			−0.620771			−0.310385	+	0.950611i	$0.600458\pi$
$230$	−33.9269			−2.23707
$231$		−	4.22123i		−	0.277736i
$232$		−	33.4032i		−	2.19303i
$233$			9.48439i			0.621343i	0.950517	+	0.310672i	$0.100554\pi$
$233$			9.48439i			0.621343i	−0.950517	+	0.310672i	$0.899446\pi$
$234$	−1.74448			−0.114040
$235$		−	30.1315i		−	1.96557i
$236$	20.2695			1.31943
$237$	−6.60703			−0.429173
$238$	−35.3635	+	23.4274i	−2.29228	+	1.51857i
$239$	10.2531			0.663216			0.331608	−	0.943417i	$-0.392409\pi$
$239$	10.2531			0.663216			0.331608	+	0.943417i	$0.392409\pi$
$240$	−15.4657			−0.998308
$241$			15.3162i			0.986605i	0.869858	+	0.493303i	$0.164210\pi$
$241$			15.3162i			0.986605i	−0.869858	+	0.493303i	$0.835790\pi$
$242$	−2.43727			−0.156674
$243$		−	1.00000i		−	0.0641500i
$244$			4.82490i			0.308883i
$245$			45.9007i			2.93249i
$246$	25.5612			1.62972
$247$	−0.271222			−0.0172574
$248$			24.2786i			1.54169i
$249$			5.19723i			0.329361i
$250$			82.7296i			5.23228i
$251$	0.408562			0.0257882			0.0128941	−	0.999917i	$-0.495896\pi$
$251$	0.408562			0.0257882			0.0128941	+	0.999917i	$0.495896\pi$
$252$		−	16.6328i		−	1.04777i
$253$	−3.28094			−0.206271
$254$	4.80601			0.301556
$255$	−9.66104	−	14.5833i	−0.604998	−	0.913241i
$256$	−31.4388			−1.96492
$257$	30.5986			1.90869			0.954343	−	0.298712i	$-0.0965570\pi$
$257$	30.5986			1.90869			0.954343	+	0.298712i	$0.0965570\pi$
$258$		−	6.03670i		−	0.375829i
$259$	−33.2517			−2.06616
$260$		−	11.9655i		−	0.742069i
$261$			7.06349i			0.437219i
$262$		−	27.4156i		−	1.69374i
$263$	7.95428			0.490482			0.245241	−	0.969462i	$-0.421133\pi$
$263$	7.95428			0.490482			0.245241	+	0.969462i	$0.421133\pi$
$264$	−4.72899			−0.291049
$265$			37.3187i			2.29247i
$266$		−	3.89856i		−	0.239036i
$267$			1.95847i			0.119856i
$268$	50.9747			3.11378
$269$			7.48136i			0.456147i	0.973644	+	0.228073i	$0.0732426\pi$
$269$			7.48136i			0.456147i	−0.973644	+	0.228073i	$0.926757\pi$
$270$	10.3406			0.629308
$271$	19.3421			1.17495			0.587476	−	0.809242i	$-0.300122\pi$
$271$	19.3421			1.17495			0.587476	+	0.809242i	$0.300122\pi$
$272$	8.30061	+	12.5297i	0.503298	+	0.759726i
$273$	3.02134			0.182860
$274$	−38.8000			−2.34399
$275$			13.0005i			0.783958i
$276$	−12.9278			−0.778165
$277$			8.35713i			0.502131i	0.967970	+	0.251066i	$0.0807810\pi$
$277$			8.35713i			0.502131i	−0.967970	+	0.251066i	$0.919219\pi$
$278$		−	47.5176i		−	2.84991i
$279$		−	5.13399i		−	0.307364i
$280$	84.6933			5.06139
$281$	1.67139			0.0997068			0.0498534	−	0.998757i	$-0.484125\pi$
$281$	1.67139			0.0997068			0.0498534	+	0.998757i	$0.484125\pi$
$282$		−	17.3094i		−	1.03076i
$283$			11.8575i			0.704855i	0.935839	+	0.352427i	$0.114644\pi$
$283$			11.8575i			0.704855i	−0.935839	+	0.352427i	$0.885356\pi$
$284$			13.0078i			0.771870i
$285$	1.60770			0.0952318
$286$		−	1.74448i		−	0.103153i
$287$	−44.2707			−2.61321
$288$	0.573506			0.0337942
$289$	−6.62964	+	15.6540i	−0.389979	+	0.920824i
$290$	−73.0407			−4.28910
$291$	5.42839			0.318218
$292$			8.54666i			0.500155i
$293$	19.9672			1.16650			0.583249	−	0.812293i	$-0.301781\pi$
$293$	19.9672			1.16650			0.583249	+	0.812293i	$0.301781\pi$
$294$			26.3682i			1.53782i
$295$		−	21.8251i		−	1.27071i
$296$			37.2515i			2.16520i
$297$	1.00000			0.0580259
$298$	0.711000			0.0411871
$299$		−	2.34834i		−	0.135808i
$300$			51.2255i			2.95751i
$301$			10.4553i			0.602631i
$302$	−10.8748			−0.625776
$303$			6.27754i			0.360636i
$304$	−1.38131			−0.0792235
$305$	5.19521			0.297477
$306$	−5.54990	−	8.37755i	−0.317267	−	0.478913i
$307$	28.8522			1.64668			0.823341	−	0.567548i	$-0.192108\pi$
$307$	28.8522			1.64668			0.823341	+	0.567548i	$0.192108\pi$
$308$	16.6328			0.947743
$309$			8.22864i			0.468111i
$310$	53.0885			3.01522
$311$		−	26.5270i		−	1.50421i	−0.659044	−	0.752104i	$-0.729039\pi$
$311$		−	26.5270i		−	1.50421i	0.659044	−	0.752104i	$-0.270961\pi$
$312$		−	3.38478i		−	0.191625i
$313$		−	10.9351i		−	0.618086i	−0.951048	−	0.309043i	$-0.899991\pi$
$313$		−	10.9351i		−	0.618086i	0.951048	−	0.309043i	$-0.100009\pi$
$314$	−4.31055			−0.243258
$315$	−17.9094			−1.00908
$316$		−	26.0336i		−	1.46450i
$317$		−	9.61751i		−	0.540173i	−0.962836	−	0.270087i	$-0.912948\pi$
$317$		−	9.61751i		−	0.540173i	0.962836	−	0.270087i	$-0.0870523\pi$
$318$			21.4382i			1.20219i
$319$	−7.06349			−0.395480
$320$			36.8618i			2.06064i
$321$	−4.73702			−0.264395
$322$	33.7552			1.88110
$323$	−0.862868	−	1.30250i	−0.0480113	−	0.0724728i
$324$	3.94028			0.218905
$325$	−9.30509			−0.516154
$326$			34.7891i			1.92679i
$327$	−18.8516			−1.04249
$328$			49.5959i			2.73847i
$329$			29.9791i			1.65280i
$330$			10.3406i			0.569231i
$331$	−12.9335			−0.710891			−0.355446	−	0.934697i	$-0.615671\pi$
$331$	−12.9335			−0.710891			−0.355446	+	0.934697i	$0.615671\pi$
$332$	−20.4786			−1.12391
$333$		−	7.87726i		−	0.431671i
$334$		−	5.26356i		−	0.288009i
$335$		−	54.8870i		−	2.99880i
$336$	15.3875			0.839454
$337$			5.39290i			0.293770i	0.989154	+	0.146885i	$0.0469247\pi$
$337$			5.39290i			0.293770i	−0.989154	+	0.146885i	$0.953075\pi$
$338$	−30.4359			−1.65549
$339$	−19.7044			−1.07020
$340$	57.4623	−	38.0672i	3.11633	−	2.06448i
$341$	5.13399			0.278021
$342$	0.923562			0.0499405
$343$		−	16.1198i		−	0.870387i
$344$	11.7129			0.631517
$345$			13.9200i			0.749430i
$346$		−	32.3350i		−	1.73834i
$347$		−	23.1988i		−	1.24538i	−0.782469	−	0.622689i	$-0.786040\pi$
$347$		−	23.1988i		−	1.24538i	0.782469	−	0.622689i	$-0.213960\pi$
$348$	−27.8322			−1.49196
$349$	21.1320			1.13117			0.565584	−	0.824691i	$-0.308651\pi$
$349$	21.1320			1.13117			0.565584	+	0.824691i	$0.308651\pi$
$350$		−	133.752i		−	7.14936i
$351$			0.715750i			0.0382039i
$352$			0.573506i			0.0305680i
$353$	0.676527			0.0360079			0.0180040	−	0.999838i	$-0.494269\pi$
$353$	0.676527			0.0360079			0.0180040	+	0.999838i	$0.494269\pi$
$354$		−	12.5377i		−	0.666372i
$355$	14.0061			0.743368
$356$	−7.71693			−0.408996
$357$	9.61215	+	14.5095i	0.508729	+	0.767924i
$358$	−38.2638			−2.02230
$359$	11.0462			0.582996			0.291498	−	0.956571i	$-0.405846\pi$
$359$	11.0462			0.582996			0.291498	+	0.956571i	$0.405846\pi$
$360$			20.0637i			1.05745i
$361$	−18.8564			−0.992443
$362$		−	12.2366i		−	0.643142i
$363$			1.00000i			0.0524864i
$364$			11.9049i			0.623989i
$365$	9.20261			0.481686
$366$	2.98445			0.156000
$367$		−	10.6255i		−	0.554649i	−0.960776	−	0.277324i	$-0.910552\pi$
$367$		−	10.6255i		−	0.554649i	0.960776	−	0.277324i	$-0.0894476\pi$
$368$		−	11.9599i		−	0.623452i
$369$		−	10.4876i		−	0.545964i
$370$	81.4555			4.23467
$371$		−	37.1299i		−	1.92769i
$372$	20.2294			1.04884
$373$	−2.38485			−0.123483			−0.0617414	−	0.998092i	$-0.519665\pi$
$373$	−2.38485			−0.123483			−0.0617414	+	0.998092i	$0.519665\pi$
$374$	8.37755	−	5.54990i	0.433193	−	0.286979i
$375$	33.9436			1.75284
$376$	33.5852			1.73202
$377$		−	5.05570i		−	0.260382i
$378$	−10.2883			−0.529171
$379$			16.6509i			0.855297i	0.903945	+	0.427648i	$0.140658\pi$
$379$			16.6509i			0.855297i	−0.903945	+	0.427648i	$0.859342\pi$
$380$			6.33478i			0.324968i
$381$		−	1.97188i		−	0.101023i
$382$	−22.7681			−1.16492
$383$	−31.8733			−1.62865			−0.814324	−	0.580411i	$-0.802892\pi$
$383$	−31.8733			−1.62865			−0.814324	+	0.580411i	$0.802892\pi$
$384$			20.0287i			1.02209i
$385$		−	17.9094i		−	0.912746i
$386$		−	45.3360i		−	2.30754i
$387$	−2.47683			−0.125904
$388$			21.3894i			1.08588i
$389$	6.71638			0.340534			0.170267	−	0.985398i	$-0.445537\pi$
$389$	6.71638			0.340534			0.170267	+	0.985398i	$0.445537\pi$
$390$	−7.40128			−0.374779
$391$	11.2775	−	7.47103i	0.570327	−	0.377826i
$392$	−51.1617			−2.58406
$393$	−11.2485			−0.567411
$394$			61.7484i			3.11084i
$395$	−28.0316			−1.41042
$396$			3.94028i			0.198007i
$397$			7.22817i			0.362771i	0.983412	+	0.181386i	$0.0580582\pi$
$397$			7.22817i			0.362771i	−0.983412	+	0.181386i	$0.941942\pi$
$398$		−	32.2376i		−	1.61592i
$399$	−1.59956			−0.0800783
$400$	−47.3900			−2.36950
$401$			4.53406i			0.226420i	0.993571	+	0.113210i	$0.0361133\pi$
$401$			4.53406i			0.226420i	−0.993571	+	0.113210i	$0.963887\pi$
$402$		−	31.5305i		−	1.57260i
$403$			3.67465i			0.183048i
$404$	−24.7353			−1.23063
$405$		−	4.24270i		−	0.210821i
$406$	72.6711			3.60661
$407$	7.87726			0.390461
$408$	16.2548	−	10.7684i	0.804733	−	0.533114i
$409$	−15.6833			−0.775490			−0.387745	−	0.921767i	$-0.626746\pi$
$409$	−15.6833			−0.775490			−0.387745	+	0.921767i	$0.626746\pi$
$410$	108.448			5.35588
$411$			15.9194i			0.785248i
$412$	−32.4232			−1.59737
$413$			21.7147i			1.06851i
$414$			7.99654i			0.393009i
$415$			22.0503i			1.08241i
$416$	−0.410487			−0.0201258
$417$	−19.4962			−0.954735
$418$			0.923562i			0.0451729i
$419$			37.5264i			1.83329i	0.399707	+	0.916643i	$0.369112\pi$
$419$			37.5264i			1.83329i	−0.399707	+	0.916643i	$0.630888\pi$
$420$		−	70.5680i		−	3.44337i
$421$	−9.34096			−0.455251			−0.227625	−	0.973749i	$-0.573096\pi$
$421$	−9.34096			−0.455251			−0.227625	+	0.973749i	$0.573096\pi$
$422$			21.0942i			1.02685i
$423$	−7.10198			−0.345310
$424$	−41.5961			−2.02009
$425$	−29.6034	−	44.6861i	−1.43597	−	2.16760i
$426$	8.04599			0.389830
$427$	−5.16892			−0.250142
$428$		−	18.6652i		−	0.902217i
$429$	−0.715750			−0.0345568
$430$		−	25.6119i		−	1.23512i
$431$			18.7155i			0.901494i	0.892652	+	0.450747i	$0.148842\pi$
$431$			18.7155i			0.901494i	−0.892652	+	0.450747i	$0.851158\pi$
$432$			3.64526i			0.175382i
$433$	−21.5010			−1.03327			−0.516637	−	0.856204i	$-0.672816\pi$
$433$	−21.5010			−1.03327			−0.516637	+	0.856204i	$0.672816\pi$
$434$	−52.8198			−2.53543
$435$			29.9683i			1.43687i
$436$		−	74.2805i		−	3.55739i
$437$			1.24326i			0.0594731i
$438$	5.28655			0.252601
$439$			22.7852i			1.08748i	0.839255	+	0.543738i	$0.182991\pi$
$439$			22.7852i			1.08748i	−0.839255	+	0.543738i	$0.817009\pi$
$440$	−20.0637			−0.956498
$441$	10.8187			0.515178
$442$	3.97235	+	5.99624i	0.188945	+	0.285212i
$443$	−23.2543			−1.10485			−0.552423	−	0.833564i	$-0.686297\pi$
$443$	−23.2543			−1.10485			−0.552423	+	0.833564i	$0.686297\pi$
$444$	31.0386			1.47303
$445$			8.30920i			0.393894i
$446$	62.6993			2.96890
$447$		−	0.291720i		−	0.0137979i
$448$		−	36.6753i		−	1.73274i
$449$		−	21.7330i		−	1.02564i	−0.858495	−	0.512821i	$-0.828600\pi$
$449$		−	21.7330i		−	1.02564i	0.858495	−	0.512821i	$-0.171400\pi$
$450$	31.6856			1.49368
$451$	10.4876			0.493843
$452$		−	77.6411i		−	3.65193i
$453$			4.46189i			0.209638i
$454$			30.1433i			1.41469i
$455$	12.8186			0.600947
$456$			1.79197i			0.0839167i
$457$	8.88256			0.415508			0.207754	−	0.978181i	$-0.433385\pi$
$457$	8.88256			0.415508			0.207754	+	0.978181i	$0.433385\pi$
$458$	−22.8956			−1.06984
$459$	−3.43727	+	2.27710i	−0.160438	+	0.106286i
$460$	−54.8489			−2.55734
$461$	−2.00056			−0.0931754			−0.0465877	−	0.998914i	$-0.514835\pi$
$461$	−2.00056			−0.0931754			−0.0465877	+	0.998914i	$0.514835\pi$
$462$		−	10.2883i		−	0.478653i
$463$	29.0669			1.35085			0.675427	−	0.737427i	$-0.263959\pi$
$463$	29.0669			1.35085			0.675427	+	0.737427i	$0.263959\pi$
$464$		−	25.7482i		−	1.19533i
$465$		−	21.7820i		−	1.01011i
$466$			23.1160i			1.07083i
$467$	10.2830			0.475843			0.237921	−	0.971284i	$-0.423534\pi$
$467$	10.2830			0.475843			0.237921	+	0.971284i	$0.423534\pi$
$468$	−2.82026			−0.130366
$469$			54.6093i			2.52162i
$470$		−	73.4387i		−	3.38747i
$471$			1.76860i			0.0814926i
$472$	24.3267			1.11973
$473$		−	2.47683i		−	0.113885i
$474$	−16.1031			−0.739641
$475$	4.92631			0.226035
$476$	−57.1715	+	37.8746i	−2.62045	+	1.73598i
$477$	8.79599			0.402741
$478$	24.9895			1.14299
$479$			30.0311i			1.37216i	0.727528	+	0.686078i	$0.240669\pi$
$479$			30.0311i			1.37216i	−0.727528	+	0.686078i	$0.759331\pi$
$480$	2.43321			0.111060
$481$			5.63815i			0.257078i
$482$			37.3298i			1.70032i
$483$		−	13.8496i		−	0.630179i
$484$	−3.94028			−0.179104
$485$	23.0310			1.04578
$486$		−	2.43727i		−	0.110557i
$487$		−	35.1613i		−	1.59331i	−0.604433	−	0.796656i	$-0.706600\pi$
$487$		−	35.1613i		−	1.59331i	0.604433	−	0.796656i	$-0.293400\pi$
$488$			5.79068i			0.262132i
$489$	14.2738			0.645483
$490$			111.872i			5.05387i
$491$	15.4085			0.695374			0.347687	−	0.937611i	$-0.386967\pi$
$491$	15.4085			0.695374			0.347687	+	0.937611i	$0.386967\pi$
$492$	41.3242			1.86304
$493$	24.2791	−	16.0843i	1.09348	−	0.724399i
$494$	−0.661040			−0.0297416
$495$	4.24270			0.190695
$496$			18.7147i			0.840315i
$497$	−13.9352			−0.625081
$498$			12.6671i			0.567624i
$499$		−	16.0789i		−	0.719789i	−0.932993	−	0.359895i	$-0.882813\pi$
$499$		−	16.0789i		−	0.719789i	0.932993	−	0.359895i	$-0.117187\pi$
$500$			133.747i			5.98136i
$501$	−2.15961			−0.0964844
$502$	0.995776			0.0444437
$503$		−	17.1431i		−	0.764372i	−0.924085	−	0.382186i	$-0.875171\pi$
$503$		−	17.1431i		−	0.764372i	0.924085	−	0.382186i	$-0.124829\pi$
$504$		−	19.9621i		−	0.889184i
$505$			26.6337i			1.18518i
$506$	−7.99654			−0.355490
$507$			12.4877i			0.554598i
$508$	7.76978			0.344728
$509$	18.5177			0.820783			0.410391	−	0.911909i	$-0.365392\pi$
$509$	18.5177			0.820783			0.410391	+	0.911909i	$0.365392\pi$
$510$	−23.5466	−	35.5434i	−1.04266	−	1.57389i
$511$	−9.15604			−0.405039
$512$	−36.5673			−1.61606
$513$		−	0.378933i		−	0.0167303i
$514$	74.5770			3.28945
$515$			34.9116i			1.53839i
$516$		−	9.75941i		−	0.429634i
$517$		−	7.10198i		−	0.312345i
$518$	−81.0433			−3.56084
$519$	−13.2669			−0.582352
$520$		−	14.3606i		−	0.629753i
$521$			28.3472i			1.24191i	0.783845	+	0.620957i	$0.213256\pi$
$521$			28.3472i			1.24191i	−0.783845	+	0.620957i	$0.786744\pi$
$522$			17.2156i			0.753508i
$523$	−2.61455			−0.114326			−0.0571630	−	0.998365i	$-0.518205\pi$
$523$	−2.61455			−0.114326			−0.0571630	+	0.998365i	$0.518205\pi$
$524$		−	44.3222i		−	1.93623i
$525$	−54.8779			−2.39507
$526$	19.3867			0.845301
$527$	−17.6469	+	11.6906i	−0.768711	+	0.509250i
$528$	−3.64526			−0.158639
$529$	12.2354			0.531974
$530$			90.9557i			3.95086i
$531$	−5.14417			−0.223238
$532$		−	6.30273i		−	0.273258i
$533$			7.50653i			0.325144i
$534$			4.77332i			0.206562i
$535$	−20.0978			−0.868902
$536$	61.1781			2.64249
$537$			15.6994i			0.677481i
$538$			18.2341i			0.786128i
$539$			10.8187i			0.465996i
$540$	16.7174			0.719403
$541$		−	27.3439i		−	1.17561i	−0.809004	−	0.587803i	$-0.799993\pi$
$541$		−	27.3439i		−	1.17561i	0.809004	−	0.587803i	$-0.200007\pi$
$542$	47.1420			2.02492
$543$	−5.02062			−0.215455
$544$	−1.30593	−	1.97130i	−0.0559913	−	0.0845186i
$545$	−79.9815			−3.42603
$546$	7.36383			0.315143
$547$		−	6.97778i		−	0.298348i	−0.988811	−	0.149174i	$-0.952339\pi$
$547$		−	6.97778i		−	0.298348i	0.988811	−	0.149174i	$-0.0476615\pi$
$548$	−62.7271			−2.67957
$549$		−	1.22451i		−	0.0522607i
$550$			31.6856i			1.35108i
$551$			2.67659i			0.114027i
$552$	−15.5155			−0.660386
$553$	27.8898			1.18599
$554$			20.3686i			0.865378i
$555$		−	33.4208i		−	1.41863i
$556$		−	76.8207i		−	3.25792i
$557$	30.7672			1.30365			0.651825	−	0.758369i	$-0.274004\pi$
$557$	30.7672			1.30365			0.651825	+	0.758369i	$0.274004\pi$
$558$		−	12.5129i		−	0.529714i
$559$	1.77279			0.0749811
$560$	65.2843			2.75876
$561$	−2.27710	−	3.43727i	−0.0961392	−	0.145122i
$562$	4.07363			0.171836
$563$	3.07846			0.129742			0.0648708	−	0.997894i	$-0.479336\pi$
$563$	3.07846			0.129742			0.0648708	+	0.997894i	$0.479336\pi$
$564$		−	27.9838i		−	1.17833i
$565$	−83.6000			−3.51708
$566$			28.8999i			1.21475i
$567$			4.22123i			0.177275i
$568$			15.6115i			0.655044i
$569$	27.9064			1.16990			0.584949	−	0.811070i	$-0.301115\pi$
$569$	27.9064			1.16990			0.584949	+	0.811070i	$0.301115\pi$
$570$	3.91839			0.164123
$571$			20.1133i			0.841716i	0.907127	+	0.420858i	$0.138271\pi$
$571$			20.1133i			0.841716i	−0.907127	+	0.420858i	$0.861729\pi$
$572$		−	2.82026i		−	0.117921i
$573$			9.34165i			0.390253i
$574$	−107.900			−4.50364
$575$			42.6538i			1.77879i
$576$	8.68830			0.362013
$577$	−17.2602			−0.718553			−0.359276	−	0.933231i	$-0.616976\pi$
$577$	−17.2602			−0.718553			−0.359276	+	0.933231i	$0.616976\pi$
$578$	−16.1582	+	38.1530i	−0.672093	+	1.58696i
$579$	−18.6012			−0.773038
$580$	−118.083			−4.90315
$581$		−	21.9387i		−	0.910170i
$582$	13.2305			0.548420
$583$			8.79599i			0.364293i
$584$			10.2574i			0.424454i
$585$			3.03671i			0.125553i
$586$	48.6655			2.01036
$587$	7.25193			0.299319			0.149660	−	0.988738i	$-0.452182\pi$
$587$	7.25193			0.299319			0.149660	+	0.988738i	$0.452182\pi$
$588$			42.6289i			1.75799i
$589$		−	1.94544i		−	0.0801604i
$590$		−	53.1937i		−	2.18995i
$591$	25.3351			1.04215
$592$			28.7146i			1.18016i
$593$	−38.5847			−1.58449			−0.792243	−	0.610206i	$-0.791087\pi$
$593$	−38.5847			−1.58449			−0.792243	+	0.610206i	$0.791087\pi$
$594$	2.43727			0.100002
$595$	40.7814	+	61.5594i	1.67188	+	2.52369i
$596$	1.14946			0.0470836
$597$	−13.2269			−0.541342
$598$		−	5.72353i		−	0.234053i
$599$	−23.3445			−0.953829			−0.476915	−	0.878950i	$-0.658245\pi$
$599$	−23.3445			−0.953829			−0.476915	+	0.878950i	$0.658245\pi$
$600$			61.4791i			2.50987i
$601$			22.8079i			0.930355i	0.885217	+	0.465178i	$0.154010\pi$
$601$			22.8079i			0.930355i	−0.885217	+	0.465178i	$0.845990\pi$
$602$			25.4823i			1.03858i
$603$	−12.9368			−0.526828
$604$	−17.5811			−0.715365
$605$			4.24270i			0.172490i
$606$			15.3001i			0.621523i
$607$		−	4.14500i		−	0.168240i	−0.996456	−	0.0841201i	$-0.973192\pi$
$607$		−	4.14500i		−	0.168240i	0.996456	−	0.0841201i	$-0.0268080\pi$
$608$	0.217321			0.00881351
$609$		−	29.8166i		−	1.20823i
$610$	12.6621			0.512675
$611$	5.08325			0.205646
$612$	−8.97241	−	13.5438i	−0.362688	−	0.547476i
$613$	−28.0837			−1.13429			−0.567145	−	0.823618i	$-0.691952\pi$
$613$	−28.0837			−1.13429			−0.567145	+	0.823618i	$0.691952\pi$
$614$	70.3205			2.83791
$615$		−	44.4958i		−	1.79424i
$616$	19.9621			0.804297
$617$			28.2168i			1.13597i	0.823040	+	0.567983i	$0.192276\pi$
$617$			28.2168i			1.13597i	−0.823040	+	0.567983i	$0.807724\pi$
$618$			20.0554i			0.806747i
$619$			11.1752i			0.449168i	0.974455	+	0.224584i	$0.0721023\pi$
$619$			11.1752i			0.449168i	−0.974455	+	0.224584i	$0.927898\pi$
$620$	85.8270			3.44690
$621$	3.28094			0.131660
$622$		−	64.6534i		−	2.59237i
$623$		−	8.26715i		−	0.331216i
$624$		−	2.60909i		−	0.104447i
$625$	79.0099			3.16039
$626$		−	26.6517i		−	1.06522i
$627$	0.378933			0.0151331
$628$	−6.96877			−0.278084
$629$	−27.0763	+	17.9373i	−1.07960	+	0.715207i
$630$	−43.6500			−1.73906
$631$	14.0694			0.560094			0.280047	−	0.959986i	$-0.409650\pi$
$631$	14.0694			0.560094			0.280047	+	0.959986i	$0.409650\pi$
$632$		−	31.2446i		−	1.24284i
$633$	8.65486			0.344000
$634$		−	23.4405i		−	0.930940i
$635$		−	8.36611i		−	0.331999i
$636$			34.6587i			1.37431i
$637$	−7.74352			−0.306810
$638$	−17.2156			−0.681574
$639$		−	3.30123i		−	0.130595i
$640$			84.9758i			3.35896i
$641$			14.9672i			0.591168i	0.955317	+	0.295584i	$0.0955143\pi$
$641$			14.9672i			0.591168i	−0.955317	+	0.295584i	$0.904486\pi$
$642$	−11.5454			−0.455661
$643$			13.8960i			0.548003i	0.961729	+	0.274002i	$0.0883474\pi$
$643$			13.8960i			0.548003i	−0.961729	+	0.274002i	$0.911653\pi$
$644$	54.5713			2.15041
$645$	−10.5084			−0.413769
$646$	−2.10304	−	3.17453i	−0.0827431	−	0.124900i
$647$	32.8576			1.29176			0.645882	−	0.763437i	$-0.276490\pi$
$647$	32.8576			1.29176			0.645882	+	0.763437i	$0.276490\pi$
$648$	4.72899			0.185772
$649$		−	5.14417i		−	0.201926i
$650$	−22.6790			−0.889544
$651$			21.6717i			0.849382i
$652$			56.2428i			2.20264i
$653$		−	43.9818i		−	1.72114i	−0.509330	−	0.860571i	$-0.670107\pi$
$653$		−	43.9818i		−	1.72114i	0.509330	−	0.860571i	$-0.329893\pi$
$654$	−45.9464			−1.79665
$655$	−47.7239			−1.86473
$656$			38.2301i			1.49263i
$657$		−	2.16905i		−	0.0846226i
$658$			73.0670i			2.84845i
$659$	22.6350			0.881734			0.440867	−	0.897572i	$-0.354671\pi$
$659$	22.6350			0.881734			0.440867	+	0.897572i	$0.354671\pi$
$660$			16.7174i			0.650725i
$661$	15.7985			0.614490			0.307245	−	0.951630i	$-0.400593\pi$
$661$	15.7985			0.614490			0.307245	+	0.951630i	$0.400593\pi$
$662$	−31.5225			−1.22516
$663$	2.46023	−	1.62983i	0.0955473	−	0.0632975i
$664$	−24.5777			−0.953798
$665$	−6.78646			−0.263168
$666$		−	19.1990i		−	0.743946i
$667$	−23.1749			−0.897337
$668$		−	8.50948i		−	0.329242i
$669$		−	25.7252i		−	0.994595i
$670$		−	133.774i		−	5.16816i
$671$	1.22451			0.0472716
$672$	−2.42090			−0.0933882
$673$			23.1821i			0.893603i	0.894633	+	0.446802i	$0.147437\pi$
$673$			23.1821i			0.893603i	−0.894633	+	0.446802i	$0.852563\pi$
$674$			13.1439i			0.506286i
$675$		−	13.0005i		−	0.500388i
$676$	−49.2051			−1.89250
$677$		−	42.0292i		−	1.61531i	−0.589652	−	0.807657i	$-0.700735\pi$
$677$		−	42.0292i		−	1.61531i	0.589652	−	0.807657i	$-0.299265\pi$
$678$	−48.0251			−1.84439
$679$	−22.9145			−0.879377
$680$	68.9642	−	45.6869i	2.64466	−	1.75201i
$681$	12.3676			0.473929
$682$	12.5129			0.479144
$683$		−	9.28971i		−	0.355461i	−0.984079	−	0.177730i	$-0.943124\pi$
$683$		−	9.28971i		−	0.355461i	0.984079	−	0.177730i	$-0.0568755\pi$
$684$	1.49310			0.0570902
$685$			67.5413i			2.58062i
$686$		−	39.2883i		−	1.50003i
$687$			9.39397i			0.358402i
$688$	9.02868			0.344215
$689$	−6.29573			−0.239848
$690$			33.9269i			1.29158i
$691$		−	11.3748i		−	0.432717i	−0.976314	−	0.216358i	$-0.930582\pi$
$691$		−	11.3748i		−	0.432717i	0.976314	−	0.216358i	$-0.0694180\pi$
$692$		−	52.2753i		−	1.98721i
$693$	−4.22123			−0.160351
$694$		−	56.5418i		−	2.14630i
$695$	−82.7166			−3.13762
$696$	−33.4032			−1.26614
$697$	−36.0488	+	23.8814i	−1.36545	+	0.904571i
$698$	51.5043			1.94947
$699$	9.48439			0.358733
$700$		−	216.234i		−	8.17289i
$701$	−4.29848			−0.162351			−0.0811756	−	0.996700i	$-0.525867\pi$
$701$	−4.29848			−0.162351			−0.0811756	+	0.996700i	$0.525867\pi$
$702$			1.74448i			0.0658410i
$703$		−	2.98495i		−	0.112580i
$704$			8.68830i			0.327453i
$705$	−30.1315			−1.13482
$706$	1.64888			0.0620564
$707$		−	26.4989i		−	0.996595i
$708$		−	20.2695i		−	0.761773i
$709$			8.90982i			0.334615i	0.985905	+	0.167308i	$0.0535073\pi$
$709$			8.90982i			0.334615i	−0.985905	+	0.167308i	$0.946493\pi$
$710$	34.1367			1.28113
$711$			6.60703i			0.247783i
$712$	−9.26159			−0.347093
$713$	16.8443			0.630825
$714$	23.4274	+	35.3635i	0.876748	+	1.32345i
$715$	−3.03671			−0.113567
$716$	−61.8602			−2.31183
$717$		−	10.2531i		−	0.382908i
$718$	26.9226			1.00474
$719$		−	3.44675i		−	0.128542i	−0.997932	−	0.0642710i	$-0.979528\pi$
$719$		−	3.44675i		−	0.128542i	0.997932	−	0.0642710i	$-0.0204722\pi$
$720$			15.4657i			0.576373i
$721$		−	34.7349i		−	1.29360i
$722$	−45.9581			−1.71039
$723$	15.3162			0.569617
$724$		−	19.7827i		−	0.735217i
$725$			91.8287i			3.41043i
$726$			2.43727i			0.0904555i
$727$	0.127482			0.00472804			0.00236402	−	0.999997i	$-0.499248\pi$
$727$	0.127482			0.00472804			0.00236402	+	0.999997i	$0.499248\pi$
$728$			14.2879i			0.529545i
$729$	−1.00000			−0.0370370
$730$	22.4292			0.830143
$731$	5.63999	+	8.51353i	0.208602	+	0.314884i
$732$	4.82490			0.178334
$733$	26.9286			0.994630			0.497315	−	0.867570i	$-0.334319\pi$
$733$	26.9286			0.994630			0.497315	+	0.867570i	$0.334319\pi$
$734$		−	25.8973i		−	0.955887i
$735$	45.9007			1.69307
$736$			1.88164i			0.0693583i
$737$		−	12.9368i		−	0.476534i
$738$		−	25.5612i		−	0.940920i
$739$	12.7885			0.470434			0.235217	−	0.971943i	$-0.424420\pi$
$739$	12.7885			0.470434			0.235217	+	0.971943i	$0.424420\pi$
$740$	131.687			4.84093
$741$			0.271222i			0.00996357i
$742$		−	90.4954i		−	3.32219i
$743$		−	7.60880i		−	0.279140i	−0.990212	−	0.139570i	$-0.955428\pi$
$743$		−	7.60880i		−	0.279140i	0.990212	−	0.139570i	$-0.0445720\pi$
$744$	24.2786			0.890096
$745$		−	1.23768i		−	0.0453450i
$746$	−5.81252			−0.212811
$747$	5.19723			0.190157
$748$	13.5438	−	8.97241i	0.495211	−	0.328064i
$749$	19.9960			0.730640
$750$	82.7296			3.02086
$751$			17.3936i			0.634702i	0.948308	+	0.317351i	$0.102793\pi$
$751$			17.3936i			0.634702i	−0.948308	+	0.317351i	$0.897207\pi$
$752$	25.8885			0.944058
$753$		−	0.408562i		−	0.0148888i
$754$		−	12.3221i		−	0.448744i
$755$			18.9304i			0.688949i
$756$	−16.6328			−0.604930
$757$	−8.55925			−0.311091			−0.155546	−	0.987829i	$-0.549714\pi$
$757$	−8.55925			−0.311091			−0.155546	+	0.987829i	$0.549714\pi$
$758$			40.5826i			1.47403i
$759$			3.28094i			0.119091i
$760$			7.60279i			0.275782i
$761$	50.8614			1.84372			0.921862	−	0.387519i	$-0.126668\pi$
$761$	50.8614			1.84372			0.921862	+	0.387519i	$0.126668\pi$
$762$		−	4.80601i		−	0.174104i
$763$	79.5768			2.88087
$764$	−36.8087			−1.33169
$765$	−14.5833	+	9.66104i	−0.527260	+	0.349296i
$766$	−77.6837			−2.80683
$767$	3.68194			0.132947
$768$			31.4388i			1.13445i
$769$	−22.9559			−0.827812			−0.413906	−	0.910320i	$-0.635836\pi$
$769$	−22.9559			−0.827812			−0.413906	+	0.910320i	$0.635836\pi$
$770$		−	43.6500i		−	1.57304i
$771$		−	30.5986i		−	1.10198i
$772$		−	73.2938i		−	2.63790i
$773$	−14.7894			−0.531937			−0.265969	−	0.963982i	$-0.585692\pi$
$773$	−14.7894			−0.531937			−0.265969	+	0.963982i	$0.585692\pi$
$774$	−6.03670			−0.216985
$775$		−	66.7443i		−	2.39752i
$776$			25.6708i			0.921528i
$777$			33.2517i			1.19290i
$778$	16.3696			0.586880
$779$		−	3.97411i		−	0.142387i
$780$	−11.9655			−0.428434
$781$	3.30123			0.118127
$782$	27.4863	−	18.2089i	0.982907	−	0.651150i
$783$	7.06349			0.252429
$784$	−39.4371			−1.40847
$785$			7.50362i			0.267816i
$786$	−27.4156			−0.977882
$787$			6.18254i			0.220384i	0.993910	+	0.110192i	$0.0351465\pi$
$787$			6.18254i			0.220384i	−0.993910	+	0.110192i	$0.964853\pi$
$788$			99.8274i			3.55620i
$789$		−	7.95428i		−	0.283180i
$790$	−68.3206			−2.43074
$791$	83.1769			2.95743
$792$			4.72899i			0.168037i
$793$			0.876441i			0.0311234i
$794$			17.6170i			0.625204i
$795$	37.3187			1.32356
$796$		−	52.1178i		−	1.84727i
$797$	−31.8712			−1.12894			−0.564468	−	0.825455i	$-0.690919\pi$
$797$	−31.8712			−1.12894			−0.564468	+	0.825455i	$0.690919\pi$
$798$	−3.89856			−0.138008
$799$	16.1719	+	24.4114i	0.572121	+	0.863614i
$800$	7.45585			0.263604
$801$	1.95847			0.0691992
$802$			11.0507i			0.390214i
$803$	2.16905			0.0765440
$804$		−	50.9747i		−	1.79774i
$805$		−	58.7597i		−	2.07101i
$806$			8.95612i			0.315466i
$807$	7.48136			0.263356
$808$	−29.6864			−1.04437
$809$			7.45113i			0.261968i	0.991385	+	0.130984i	$0.0418136\pi$
$809$			7.45113i			0.261968i	−0.991385	+	0.130984i	$0.958186\pi$
$810$		−	10.3406i		−	0.363331i
$811$			24.9448i			0.875932i	0.898992	+	0.437966i	$0.144301\pi$
$811$			24.9448i			0.875932i	−0.898992	+	0.437966i	$0.855699\pi$
$812$	117.486			4.12294
$813$		−	19.3421i		−	0.678359i
$814$	19.1990			0.672925
$815$	60.5594			2.12130
$816$	12.5297	−	8.30061i	0.438628	−	0.290579i
$817$	−0.938553			−0.0328358
$818$	−38.2244			−1.33649
$819$		−	3.02134i		−	0.105574i
$820$	175.326			6.12265
$821$		−	41.8573i		−	1.46083i	−0.683004	−	0.730415i	$-0.739327\pi$
$821$		−	41.8573i		−	1.46083i	0.683004	−	0.730415i	$-0.260673\pi$
$822$			38.8000i			1.35330i
$823$			42.6238i			1.48577i	0.669417	+	0.742887i	$0.266544\pi$
$823$			42.6238i			1.48577i	−0.669417	+	0.742887i	$0.733456\pi$
$824$	−38.9131			−1.35560
$825$	13.0005			0.452618
$826$			52.9246i			1.84148i
$827$		−	25.4712i		−	0.885720i	−0.896591	−	0.442860i	$-0.853964\pi$
$827$		−	25.4712i		−	0.885720i	0.896591	−	0.442860i	$-0.146036\pi$
$828$			12.9278i			0.449274i
$829$	−28.6770			−0.995992			−0.497996	−	0.867179i	$-0.665931\pi$
$829$	−28.6770			−0.995992			−0.497996	+	0.867179i	$0.665931\pi$
$830$			53.7425i			1.86543i
$831$	8.35713			0.289906
$832$	−6.21866			−0.215593
$833$	−24.6354	−	37.1869i	−0.853565	−	1.28845i
$834$	−47.5176			−1.64540
$835$	−9.16258			−0.317084
$836$			1.49310i			0.0516401i
$837$	−5.13399			−0.177457
$838$			91.4620i			3.15950i
$839$			23.0068i			0.794283i	0.917757	+	0.397142i	$0.129998\pi$
$839$			23.0068i			0.794283i	−0.917757	+	0.397142i	$0.870002\pi$
$840$		−	84.6933i		−	2.92219i
$841$	−20.8929			−0.720446
$842$	−22.7664			−0.784583
$843$		−	1.67139i		−	0.0575657i
$844$			34.1026i			1.17386i
$845$			52.9815i			1.82262i
$846$	−17.3094			−0.595111
$847$		−	4.22123i		−	0.145043i
$848$	−32.0636			−1.10107
$849$	11.8575			0.406948
$850$	−72.1514	−	108.912i	−2.47477	−	3.73565i
$851$	25.8448			0.885950
$852$	13.0078			0.445639
$853$		−	5.54816i		−	0.189965i	−0.995479	−	0.0949826i	$-0.969720\pi$
$853$		−	5.54816i		−	0.189965i	0.995479	−	0.0949826i	$-0.0302796\pi$
$854$	−12.5981			−0.431096
$855$		−	1.60770i		−	0.0549821i
$856$		−	22.4013i		−	0.765662i
$857$		−	20.1175i		−	0.687202i	−0.939116	−	0.343601i	$-0.888353\pi$
$857$		−	20.1175i		−	0.687202i	0.939116	−	0.343601i	$-0.111647\pi$
$858$	−1.74448			−0.0595555
$859$	8.50097			0.290049			0.145025	−	0.989428i	$-0.453674\pi$
$859$	8.50097			0.290049			0.145025	+	0.989428i	$0.453674\pi$
$860$		−	41.4062i		−	1.41194i
$861$			44.2707i			1.50874i
$862$			45.6147i			1.55364i
$863$	14.9062			0.507413			0.253706	−	0.967281i	$-0.418350\pi$
$863$	14.9062			0.507413			0.253706	+	0.967281i	$0.418350\pi$
$864$		−	0.573506i		−	0.0195111i
$865$	−56.2874			−1.91383
$866$	−52.4038			−1.78075
$867$	15.6540	+	6.62964i	0.531638	+	0.225154i
$868$	−85.3927			−2.89842
$869$	−6.60703			−0.224128
$870$			73.0407i			2.47631i
$871$	9.25954			0.313748
$872$		−	89.1489i		−	3.01896i
$873$		−	5.42839i		−	0.183723i
$874$			3.03016i			0.102497i
$875$	−143.283			−4.84386
$876$	8.54666			0.288765
$877$		−	36.4674i		−	1.23142i	−0.787974	−	0.615709i	$-0.788870\pi$
$877$		−	36.4674i		−	1.23142i	0.787974	−	0.615709i	$-0.211130\pi$
$878$			55.5336i			1.87417i
$879$		−	19.9672i		−	0.673478i
$880$	−15.4657			−0.521349
$881$			10.2203i			0.344331i	0.985068	+	0.172165i	$0.0550763\pi$
$881$			10.2203i			0.344331i	−0.985068	+	0.172165i	$0.944924\pi$
$882$	26.3682			0.887863
$883$	−1.40940			−0.0474300			−0.0237150	−	0.999719i	$-0.507549\pi$
$883$	−1.40940			−0.0474300			−0.0237150	+	0.999719i	$0.507549\pi$
$884$	6.42201	+	9.69399i	0.215995	+	0.326044i
$885$	−21.8251			−0.733644
$886$	−56.6770			−1.90410
$887$			26.3409i			0.884439i	0.896907	+	0.442220i	$0.145809\pi$
$887$			26.3409i			0.884439i	−0.896907	+	0.442220i	$0.854191\pi$
$888$	37.2515			1.25008
$889$			8.32377i			0.279170i
$890$			20.2517i			0.678840i
$891$		−	1.00000i		−	0.0335013i
$892$	101.365			3.39394
$893$	−2.69118			−0.0900568
$894$		−	0.711000i		−	0.0237794i
$895$			66.6080i			2.22646i
$896$		−	84.5457i		−	2.82448i
$897$	−2.34834			−0.0784087
$898$		−	52.9691i		−	1.76760i
$899$	36.2639			1.20947
$900$	51.2255			1.70752
$901$	−20.0293	−	30.2342i	−0.667274	−	1.00725i
$902$	25.5612			0.851094
$903$	10.4553			0.347929
$904$		−	93.1821i		−	3.09919i
$905$	−21.3010			−0.708068
$906$			10.8748i			0.361292i
$907$			6.13163i			0.203598i	0.994805	+	0.101799i	$0.0324598\pi$
$907$			6.13163i			0.203598i	−0.994805	+	0.101799i	$0.967540\pi$
$908$			48.7320i			1.61723i
$909$	6.27754			0.208213
$910$	31.2425			1.03568
$911$		−	13.1370i		−	0.435247i	−0.976033	−	0.217624i	$-0.930169\pi$
$911$		−	13.1370i		−	0.435247i	0.976033	−	0.217624i	$-0.0698306\pi$
$912$			1.38131i			0.0457397i
$913$			5.19723i			0.172003i
$914$	21.6492			0.716091
$915$		−	5.19521i		−	0.171748i
$916$	−37.0149			−1.22301
$917$	47.4824			1.56801
$918$	−8.37755	+	5.54990i	−0.276500	+	0.183174i
$919$	54.4312			1.79552			0.897760	−	0.440484i	$-0.145193\pi$
$919$	54.4312			1.79552			0.897760	+	0.440484i	$0.145193\pi$
$920$	−65.8278			−2.17028
$921$		−	28.8522i		−	0.950712i
$922$	−4.87591			−0.160579
$923$			2.36286i			0.0777744i
$924$		−	16.6328i		−	0.547180i
$925$		−	102.408i		−	3.36716i
$926$	70.8439			2.32808
$927$	8.22864			0.270264
$928$			4.05096i			0.132979i
$929$		−	46.8992i		−	1.53871i	−0.638821	−	0.769356i	$-0.720577\pi$
$929$		−	46.8992i		−	1.53871i	0.638821	−	0.769356i	$-0.279423\pi$
$930$		−	53.0885i		−	1.74084i
$931$	4.09958			0.134358
$932$			37.3712i			1.22413i
$933$	−26.5270			−0.868455
$934$	25.0625			0.820072
$935$	−9.66104	−	14.5833i	−0.315950	−	0.476925i
$936$	−3.38478			−0.110635
$937$	22.6944			0.741395			0.370698	−	0.928754i	$-0.379119\pi$
$937$	22.6944			0.741395			0.370698	+	0.928754i	$0.379119\pi$
$938$			133.097i			4.34579i
$939$	−10.9351			−0.356852
$940$		−	118.727i		−	3.87244i
$941$		−	12.7975i		−	0.417187i	−0.978002	−	0.208593i	$-0.933111\pi$
$941$		−	12.7975i		−	0.417187i	0.978002	−	0.208593i	$-0.0668885\pi$
$942$			4.31055i			0.140445i
$943$	34.4093			1.12052
$944$	18.7518			0.610319
$945$			17.9094i			0.582592i
$946$		−	6.03670i		−	0.196270i
$947$		−	32.8509i		−	1.06751i	−0.845639	−	0.533755i	$-0.820780\pi$
$947$		−	32.8509i		−	1.06751i	0.845639	−	0.533755i	$-0.179220\pi$
$948$	−26.0336			−0.845531
$949$			1.55250i			0.0503962i
$950$	12.0067			0.389550
$951$	−9.61751			−0.311869
$952$	−68.6152	+	45.4557i	−2.22383	+	1.47323i
$953$	−6.22060			−0.201505			−0.100752	−	0.994912i	$-0.532125\pi$
$953$	−6.22060			−0.201505			−0.100752	+	0.994912i	$0.532125\pi$
$954$	21.4382			0.694087
$955$			39.6338i			1.28252i
$956$	40.4000			1.30663
$957$			7.06349i			0.228330i
$958$			73.1939i			2.36479i
$959$		−	67.1995i		−	2.16999i
$960$	36.8618			1.18971
$961$	4.64217			0.149747
$962$			13.7417i			0.443050i
$963$			4.73702i			0.152648i
$964$			60.3503i			1.94375i
$965$	−78.9191			−2.54049
$966$		−	33.7552i		−	1.08606i
$967$	−17.4446			−0.560980			−0.280490	−	0.959857i	$-0.590497\pi$
$967$	−17.4446			−0.560980			−0.280490	+	0.959857i	$0.590497\pi$
$968$	−4.72899			−0.151995
$969$	−1.30250	+	0.862868i	−0.0418422	+	0.0277193i
$970$	56.1328			1.80232
$971$	−52.1247			−1.67276			−0.836380	−	0.548150i	$-0.815332\pi$
$971$	−52.1247			−1.67276			−0.836380	+	0.548150i	$0.815332\pi$
$972$		−	3.94028i		−	0.126385i
$973$	82.2980			2.63835
$974$		−	85.6976i		−	2.74593i
$975$			9.30509i			0.298001i
$976$			4.46364i			0.142878i
$977$	29.0375			0.928993			0.464497	−	0.885575i	$-0.346235\pi$
$977$	29.0375			0.928993			0.464497	+	0.885575i	$0.346235\pi$
$978$	34.7891			1.11243
$979$			1.95847i			0.0625930i
$980$			180.862i			5.77741i
$981$			18.8516i			0.601885i
$982$	37.5546			1.19841
$983$		−	38.9960i		−	1.24378i	−0.783105	−	0.621889i	$-0.786365\pi$
$983$		−	38.9960i		−	1.24378i	0.783105	−	0.621889i	$-0.213635\pi$
$984$	49.5959			1.58106
$985$	107.489			3.42489
$986$	59.1748	−	39.2017i	1.88451	−	1.24844i
$987$	29.9791			0.954244
$988$	−1.06869			−0.0339995
$989$		−	8.12634i		−	0.258403i
$990$	10.3406			0.328646
$991$			35.9070i			1.14062i	0.821428	+	0.570312i	$0.193178\pi$
$991$			35.9070i			1.14062i	−0.821428	+	0.570312i	$0.806822\pi$
$992$		−	2.94438i		−	0.0934840i
$993$			12.9335i			0.410433i
$994$	−33.9639			−1.07727
$995$	−56.1178			−1.77906
$996$			20.4786i			0.648888i
$997$		−	10.8259i		−	0.342860i	−0.985196	−	0.171430i	$-0.945161\pi$
$997$		−	10.8259i		−	0.342860i	0.985196	−	0.171430i	$-0.0548388\pi$
$998$		−	39.1885i		−	1.24049i
$999$	−7.87726			−0.249225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.g.b.67.15	✓	16
3.2	odd	2		1683.2.g.c.1189.2		16
17.4	even	4		9537.2.a.bm.1.1		8
17.13	even	4		9537.2.a.bn.1.1		8
17.16	even	2	inner	561.2.g.b.67.16	yes	16
51.50	odd	2		1683.2.g.c.1189.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.g.b.67.15	✓	16	1.1	even	1	trivial
561.2.g.b.67.16	yes	16	17.16	even	2	inner
1683.2.g.c.1189.1		16	51.50	odd	2
1683.2.g.c.1189.2		16	3.2	odd	2
9537.2.a.bm.1.1		8	17.4	even	4
9537.2.a.bn.1.1		8	17.13	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.43727 q^{2} -1.00000i q^{3} +3.94028 q^{4} -4.24270i q^{5} -2.43727i q^{6} +4.22123i q^{7} +4.72899 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.43727 q^{2} -1.00000i q^{3} +3.94028 q^{4} -4.24270i q^{5} -2.43727i q^{6} +4.22123i q^{7} +4.72899 q^{8} -1.00000 q^{9} -10.3406i q^{10} -1.00000i q^{11} -3.94028i q^{12} +0.715750 q^{13} +10.2883i q^{14} -4.24270 q^{15} +3.64526 q^{16} +(2.27710 + 3.43727i) q^{17} -2.43727 q^{18} -0.378933 q^{19} -16.7174i q^{20} +4.22123 q^{21} -2.43727i q^{22} -3.28094i q^{23} -4.72899i q^{24} -13.0005 q^{25} +1.74448 q^{26} +1.00000i q^{27} +16.6328i q^{28} -7.06349i q^{29} -10.3406 q^{30} +5.13399i q^{31} -0.573506 q^{32} -1.00000 q^{33} +(5.54990 + 8.37755i) q^{34} +17.9094 q^{35} -3.94028 q^{36} +7.87726i q^{37} -0.923562 q^{38} -0.715750i q^{39} -20.0637i q^{40} +10.4876i q^{41} +10.2883 q^{42} +2.47683 q^{43} -3.94028i q^{44} +4.24270i q^{45} -7.99654i q^{46} +7.10198 q^{47} -3.64526i q^{48} -10.8187 q^{49} -31.6856 q^{50} +(3.43727 - 2.27710i) q^{51} +2.82026 q^{52} -8.79599 q^{53} +2.43727i q^{54} -4.24270 q^{55} +19.9621i q^{56} +0.378933i q^{57} -17.2156i q^{58} +5.14417 q^{59} -16.7174 q^{60} +1.22451i q^{61} +12.5129i q^{62} -4.22123i q^{63} -8.68830 q^{64} -3.03671i q^{65} -2.43727 q^{66} +12.9368 q^{67} +(8.97241 + 13.5438i) q^{68} -3.28094 q^{69} +43.6500 q^{70} +3.30123i q^{71} -4.72899 q^{72} +2.16905i q^{73} +19.1990i q^{74} +13.0005i q^{75} -1.49310 q^{76} +4.22123 q^{77} -1.74448i q^{78} -6.60703i q^{79} -15.4657i q^{80} +1.00000 q^{81} +25.5612i q^{82} -5.19723 q^{83} +16.6328 q^{84} +(14.5833 - 9.66104i) q^{85} +6.03670 q^{86} -7.06349 q^{87} -4.72899i q^{88} -1.95847 q^{89} +10.3406i q^{90} +3.02134i q^{91} -12.9278i q^{92} +5.13399 q^{93} +17.3094 q^{94} +1.60770i q^{95} +0.573506i q^{96} +5.42839i q^{97} -26.3682 q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9	\( 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9} + 12 q^{13} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{21} - 56 q^{25} - 8 q^{26} - 36 q^{30} - 34 q^{32} - 16 q^{33} + 30 q^{34} + 8 q^{35} - 22 q^{36} + 44 q^{38} - 12 q^{42} - 24 q^{43} + 18 q^{47} - 34 q^{49} + 30 q^{50} + 14 q^{51} + 28 q^{52} - 26 q^{53} - 4 q^{55} - 2 q^{59} - 12 q^{60} - 38 q^{64} + 2 q^{66} + 30 q^{67} + 42 q^{68} - 28 q^{69} + 88 q^{70} + 6 q^{72} - 84 q^{76} + 2 q^{77} + 16 q^{81} - 52 q^{83} + 24 q^{84} + 40 q^{85} - 52 q^{86} - 26 q^{87} + 78 q^{89} + 20 q^{93} - 16 q^{94} - 70 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9 + 12 * q^13 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^21 - 56 * q^25 - 8 * q^26 - 36 * q^30 - 34 * q^32 - 16 * q^33 + 30 * q^34 + 8 * q^35 - 22 * q^36 + 44 * q^38 - 12 * q^42 - 24 * q^43 + 18 * q^47 - 34 * q^49 + 30 * q^50 + 14 * q^51 + 28 * q^52 - 26 * q^53 - 4 * q^55 - 2 * q^59 - 12 * q^60 - 38 * q^64 + 2 * q^66 + 30 * q^67 + 42 * q^68 - 28 * q^69 + 88 * q^70 + 6 * q^72 - 84 * q^76 + 2 * q^77 + 16 * q^81 - 52 * q^83 + 24 * q^84 + 40 * q^85 - 52 * q^86 - 26 * q^87 + 78 * q^89 + 20 * q^93 - 16 * q^94 - 70 * q^98

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