LMFDB - Embedded newform 99.3.l.a.80.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(26,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("99.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.l (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			80.6
Character	$\chi$	$=$	99.80
Dual form			99.3.l.a.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15480 + 1.58945i) q^{2} +(0.0432885 - 0.133228i) q^{4} +(5.65603 - 7.78486i) q^{5} +(-1.61633 + 4.97456i) q^{7} +(7.73579 - 2.51351i) q^{8} +O(q^{10})$	\(q+(1.15480 + 1.58945i) q^{2} +(0.0432885 - 0.133228i) q^{4} +(5.65603 - 7.78486i) q^{5} +(-1.61633 + 4.97456i) q^{7} +(7.73579 - 2.51351i) q^{8} +18.9052 q^{10} +(-9.06319 + 6.23366i) q^{11} +(-13.9350 + 10.1244i) q^{13} +(-9.77335 + 3.17555i) q^{14} +(12.4751 + 9.06367i) q^{16} +(4.53667 - 6.24419i) q^{17} +(4.33521 + 13.3424i) q^{19} +(-0.792322 - 1.09054i) q^{20} +(-20.3743 - 7.20684i) q^{22} +5.68512i q^{23} +(-20.8879 - 64.2864i) q^{25} +(-32.1844 - 10.4574i) q^{26} +(0.592783 + 0.430682i) q^{28} +(22.9057 + 7.44253i) q^{29} +(-12.1481 + 8.82612i) q^{31} -2.24031i q^{32} +15.1638 q^{34} +(29.5842 + 40.7192i) q^{35} +(-2.36563 + 7.28065i) q^{37} +(-16.2007 + 22.2984i) q^{38} +(24.1865 - 74.4385i) q^{40} +(-17.3048 + 5.62267i) q^{41} -53.6955 q^{43} +(0.438168 + 1.47732i) q^{44} +(-9.03621 + 6.56519i) q^{46} +(-36.9117 + 11.9934i) q^{47} +(17.5081 + 12.7204i) q^{49} +(78.0585 - 107.438i) q^{50} +(0.745630 + 2.29481i) q^{52} +(-47.9715 - 66.0271i) q^{53} +(-2.73355 + 105.813i) q^{55} +42.5448i q^{56} +(14.6221 + 45.0022i) q^{58} +(0.000412921 + 0.000134166i) q^{59} +(-3.86696 - 2.80951i) q^{61} +(-28.0573 - 9.11638i) q^{62} +(53.4611 - 38.8418i) q^{64} +165.746i q^{65} +111.796 q^{67} +(-0.635517 - 0.874715i) q^{68} +(-30.5571 + 94.0452i) q^{70} +(58.5632 - 80.6053i) q^{71} +(-10.5980 + 32.6171i) q^{73} +(-14.3041 + 4.64767i) q^{74} +1.96525 q^{76} +(-16.3606 - 55.1611i) q^{77} +(49.9398 - 36.2834i) q^{79} +(141.119 - 45.8523i) q^{80} +(-28.9205 - 21.0120i) q^{82} +(38.3421 - 52.7733i) q^{83} +(-22.9506 - 70.6347i) q^{85} +(-62.0076 - 85.3462i) q^{86} +(-54.4426 + 71.0027i) q^{88} +92.5976i q^{89} +(-27.8408 - 85.6851i) q^{91} +(0.757419 + 0.246100i) q^{92} +(-61.6886 - 44.8194i) q^{94} +(128.389 + 41.7160i) q^{95} +(42.4116 - 30.8138i) q^{97} +42.5178i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^7	$ 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	1.15480	+	1.58945i	0.577401	+	0.794724i	0.993407	−	0.114637i	$-0.0365706\pi$
$2$	1.15480	+	1.58945i	0.577401	+	0.794724i	−0.416006	+	0.909362i	$0.636571\pi$
$3$		0			0
$3$		0			0
$4$	0.0432885	−	0.133228i	0.0108221	−	0.0333071i
$5$	5.65603	−	7.78486i	1.13121	−	1.55697i	0.345448	−	0.938438i	$-0.387727\pi$
$5$	5.65603	−	7.78486i	1.13121	−	1.55697i	0.785758	−	0.618533i	$-0.212273\pi$
$6$		0			0
$7$	−1.61633	+	4.97456i	−0.230905	+	0.710651i	0.766734	+	0.641965i	$0.221881\pi$
$7$	−1.61633	+	4.97456i	−0.230905	+	0.710651i	−0.997638	+	0.0686861i	$0.978119\pi$
$8$	7.73579	−	2.51351i	0.966973	−	0.314189i
$9$		0			0
$10$	18.9052			1.89052
$11$	−9.06319	+	6.23366i	−0.823927	+	0.566696i
$11$	−9.06319	+	6.23366i	−0.823927	+	0.566696i
$12$		0			0
$13$	−13.9350	+	10.1244i	−1.07193	+	0.778800i	−0.976258	−	0.216613i	$-0.930499\pi$
$13$	−13.9350	+	10.1244i	−1.07193	+	0.778800i	−0.0956692	+	0.995413i	$0.530499\pi$
$14$	−9.77335	+	3.17555i	−0.698097	+	0.226825i
$15$		0			0
$16$	12.4751	+	9.06367i	0.779692	+	0.566479i
$17$	4.53667	−	6.24419i	0.266863	−	0.367306i	−0.654464	−	0.756093i	$-0.727106\pi$
$17$	4.53667	−	6.24419i	0.266863	−	0.367306i	0.921328	+	0.388787i	$0.127106\pi$
$18$		0			0
$19$	4.33521	+	13.3424i	0.228169	+	0.702231i	0.997954	+	0.0639288i	$0.0203630\pi$
$19$	4.33521	+	13.3424i	0.228169	+	0.702231i	−0.769786	+	0.638302i	$0.779637\pi$
$20$	−0.792322	−	1.09054i	−0.0396161	−	0.0545269i
$21$		0			0
$22$	−20.3743	−	7.20684i	−0.926104	−	0.327584i
$23$			5.68512i			0.247179i	0.992333	+	0.123590i	$0.0394407\pi$
$23$			5.68512i			0.247179i	−0.992333	+	0.123590i	$0.960559\pi$
$24$		0			0
$25$	−20.8879	−	64.2864i	−0.835516	−	2.57145i
$26$	−32.1844	−	10.4574i	−1.23786	−	0.402206i
$27$		0			0
$28$	0.592783	+	0.430682i	0.0211708	+	0.0153815i
$29$	22.9057	+	7.44253i	0.789853	+	0.256639i	0.676042	−	0.736863i	$-0.263694\pi$
$29$	22.9057	+	7.44253i	0.789853	+	0.256639i	0.113812	+	0.993502i	$0.463694\pi$
$30$		0			0
$31$	−12.1481	+	8.82612i	−0.391874	+	0.284713i	−0.766223	−	0.642575i	$-0.777866\pi$
$31$	−12.1481	+	8.82612i	−0.391874	+	0.284713i	0.374349	+	0.927288i	$0.377866\pi$
$32$		−	2.24031i		−	0.0700097i
$33$		0			0
$34$	15.1638			0.445994
$35$	29.5842	+	40.7192i	0.845263	+	1.16340i
$36$		0			0
$37$	−2.36563	+	7.28065i	−0.0639359	+	0.196774i	−0.977922	−	0.208972i	$-0.932988\pi$
$37$	−2.36563	+	7.28065i	−0.0639359	+	0.196774i	0.913986	+	0.405746i	$0.132988\pi$
$38$	−16.2007	+	22.2984i	−0.426335	+	0.586800i
$39$		0			0
$40$	24.1865	−	74.4385i	0.604663	−	1.86096i
$41$	−17.3048	+	5.62267i	−0.422068	+	0.137138i	−0.512347	−	0.858778i	$-0.671224\pi$
$41$	−17.3048	+	5.62267i	−0.422068	+	0.137138i	0.0902795	+	0.995916i	$0.471224\pi$
$42$		0			0
$43$	−53.6955			−1.24873			−0.624366	−	0.781132i	$-0.714642\pi$
$43$	−53.6955			−1.24873			−0.624366	+	0.781132i	$0.714642\pi$
$44$	0.438168	+	1.47732i	0.00995836	+	0.0335754i
$45$		0			0
$46$	−9.03621	+	6.56519i	−0.196439	+	0.142722i
$47$	−36.9117	+	11.9934i	−0.785356	+	0.255178i	−0.674125	−	0.738617i	$-0.735479\pi$
$47$	−36.9117	+	11.9934i	−0.785356	+	0.255178i	−0.111231	+	0.993795i	$0.535479\pi$
$48$		0			0
$49$	17.5081	+	12.7204i	0.357309	+	0.259600i
$50$	78.0585	−	107.438i	1.56117	−	2.14877i
$51$		0			0
$52$	0.745630	+	2.29481i	0.0143390	+	0.0441310i
$53$	−47.9715	−	66.0271i	−0.905123	−	1.24580i	−0.968805	−	0.247825i	$-0.920284\pi$
$53$	−47.9715	−	66.0271i	−0.905123	−	1.24580i	0.0636816	−	0.997970i	$-0.479716\pi$
$54$		0			0
$55$	−2.73355	+	105.813i	−0.0497010	+	1.92388i
$56$			42.5448i			0.759728i
$57$		0			0
$58$	14.6221	+	45.0022i	0.252105	+	0.775899i
$59$	0.000412921	0	0.000134166i	6.99867e−6	0	2.27400e-6i	0.309020	−	0.951055i	$-0.399999\pi$
$59$	0.000412921	0	0.000134166i	6.99867e−6	0	2.27400e-6i	−0.309013	+	0.951058i	$0.599999\pi$
$60$		0			0
$61$	−3.86696	−	2.80951i	−0.0633928	−	0.0460576i	0.555638	−	0.831425i	$-0.312474\pi$
$61$	−3.86696	−	2.80951i	−0.0633928	−	0.0460576i	−0.619030	+	0.785367i	$0.712474\pi$
$62$	−28.0573	−	9.11638i	−0.452537	−	0.147038i
$63$		0			0
$64$	53.4611	−	38.8418i	0.835330	−	0.606903i
$65$			165.746i			2.54994i
$66$		0			0
$67$	111.796			1.66860			0.834298	−	0.551313i	$-0.185873\pi$
$67$	111.796			1.66860			0.834298	+	0.551313i	$0.185873\pi$
$68$	−0.635517	−	0.874715i	−0.00934585	−	0.0128635i
$69$		0			0
$70$	−30.5571	+	94.0452i	−0.436530	+	1.34350i
$71$	58.5632	−	80.6053i	0.824834	−	1.13529i	−0.164029	−	0.986456i	$-0.552449\pi$
$71$	58.5632	−	80.6053i	0.824834	−	1.13529i	0.988863	−	0.148831i	$-0.0475509\pi$
$72$		0			0
$73$	−10.5980	+	32.6171i	−0.145177	+	0.446810i	−0.997034	−	0.0769653i	$-0.975477\pi$
$73$	−10.5980	+	32.6171i	−0.145177	+	0.446810i	0.851856	+	0.523775i	$0.175477\pi$
$74$	−14.3041	+	4.64767i	−0.193298	+	0.0628063i
$75$		0			0
$76$	1.96525			0.0258585
$77$	−16.3606	−	55.1611i	−0.212475	−	0.716377i
$78$		0			0
$79$	49.9398	−	36.2834i	0.632150	−	0.459284i	−0.224995	−	0.974360i	$-0.572236\pi$
$79$	49.9398	−	36.2834i	0.632150	−	0.459284i	0.857144	+	0.515076i	$0.172236\pi$
$80$	141.119	−	45.8523i	1.76398	−	0.573153i
$81$		0			0
$82$	−28.9205	−	21.0120i	−0.352690	−	0.256244i
$83$	38.3421	−	52.7733i	0.461953	−	0.635823i	−0.512960	−	0.858413i	$-0.671451\pi$
$83$	38.3421	−	52.7733i	0.461953	−	0.635823i	0.974912	+	0.222589i	$0.0714509\pi$
$84$		0			0
$85$	−22.9506	−	70.6347i	−0.270007	−	0.830996i
$86$	−62.0076	−	85.3462i	−0.721019	−	0.992397i
$87$		0			0
$88$	−54.4426	+	71.0027i	−0.618666	+	0.806849i
$89$			92.5976i			1.04042i	0.854038	+	0.520211i	$0.174147\pi$
$89$			92.5976i			1.04042i	−0.854038	+	0.520211i	$0.825853\pi$
$90$		0			0
$91$	−27.8408	−	85.6851i	−0.305943	−	0.941595i
$92$	0.757419	+	0.246100i	0.00823282	+	0.00267500i
$93$		0			0
$94$	−61.6886	−	44.8194i	−0.656261	−	0.476802i
$95$	128.389	+	41.7160i	1.35146	+	0.439116i
$96$		0			0
$97$	42.4116	−	30.8138i	0.437233	−	0.317668i	−0.347302	−	0.937753i	$-0.612902\pi$
$97$	42.4116	−	30.8138i	0.437233	−	0.317668i	0.784534	+	0.620085i	$0.212902\pi$
$98$			42.5178i			0.433855i
$99$		0			0
$100$	−9.46897			−0.0946897
$101$	−34.6336	−	47.6691i	−0.342907	−	0.471971i	0.602381	−	0.798209i	$-0.294219\pi$
$101$	−34.6336	−	47.6691i	−0.342907	−	0.471971i	−0.945288	+	0.326238i	$0.894219\pi$
$102$		0			0
$103$	−29.8866	+	91.9816i	−0.290161	+	0.893025i	0.694642	+	0.719355i	$0.255563\pi$
$103$	−29.8866	+	91.9816i	−0.290161	+	0.893025i	−0.984804	+	0.173670i	$0.944437\pi$
$104$	−82.3508	+	113.346i	−0.791834	+	1.08987i
$105$		0			0
$106$	49.5491	−	152.497i	0.467445	−	1.43865i
$107$	−17.4915	+	5.68333i	−0.163472	+	0.0531152i	−0.389610	−	0.920980i	$-0.627390\pi$
$107$	−17.4915	+	5.68333i	−0.163472	+	0.0531152i	0.226138	+	0.974095i	$0.427390\pi$
$108$		0			0
$109$	50.6495			0.464674			0.232337	−	0.972635i	$-0.425363\pi$
$109$	50.6495			0.464674			0.232337	+	0.972635i	$0.425363\pi$
$110$	−171.342	+	117.849i	−1.55765	+	1.07135i
$111$		0			0
$112$	−65.2516	+	47.4081i	−0.582604	+	0.423286i
$113$	−9.35427	+	3.03939i	−0.0827811	+	0.0268972i	−0.350115	−	0.936707i	$-0.613857\pi$
$113$	−9.35427	+	3.03939i	−0.0827811	+	0.0268972i	0.267334	+	0.963604i	$0.413857\pi$
$114$		0			0
$115$	44.2579	+	32.1552i	0.384851	+	0.279611i
$116$	1.98311	−	2.72952i	0.0170958	−	0.0235303i
$117$		0			0
$118$	0.000263592	0	0.000811253i	2.23383e−6	0	6.87502e-6i
$119$	23.7293	+	32.6606i	0.199406	+	0.274459i
$120$		0			0
$121$	43.2830	−	112.994i	0.357711	−	0.933832i
$122$		−	9.39077i		−	0.0769736i
$123$		0			0
$124$	0.650015	+	2.00054i	0.00524206	+	0.0161334i
$125$	−389.812	−	126.657i	−3.11849	−	1.01326i
$126$		0			0
$127$	−174.328	−	126.656i	−1.37266	−	0.997294i	−0.997524	−	0.0703233i	$-0.977597\pi$
$127$	−174.328	−	126.656i	−1.37266	−	0.997294i	−0.375133	−	0.926971i	$-0.622403\pi$
$128$	114.951	+	37.3500i	0.898058	+	0.291797i
$129$		0			0
$130$	−263.445	+	191.404i	−2.02650	+	1.47234i
$131$		−	166.588i		−	1.27166i	−0.771827	−	0.635832i	$-0.780657\pi$
$131$		−	166.588i		−	1.27166i	0.771827	−	0.635832i	$-0.219343\pi$
$132$		0			0
$133$	−73.3797			−0.551727
$134$	129.102	+	177.694i	0.963450	+	1.32607i
$135$		0			0
$136$	19.3999	−	59.7067i	0.142646	−	0.439020i
$137$	−25.7144	+	35.3928i	−0.187696	+	0.258342i	−0.892487	−	0.451074i	$-0.851041\pi$
$137$	−25.7144	+	35.3928i	−0.187696	+	0.258342i	0.704790	+	0.709416i	$0.251041\pi$
$138$		0			0
$139$	−31.8516	+	98.0291i	−0.229148	+	0.705245i	0.768696	+	0.639614i	$0.220906\pi$
$139$	−31.8516	+	98.0291i	−0.229148	+	0.705245i	−0.997844	+	0.0656308i	$0.979094\pi$
$140$	6.70560	−	2.17878i	0.0478972	−	0.0155627i
$141$		0			0
$142$	195.747			1.37850
$143$	63.1840	−	178.626i	0.441846	−	1.24913i
$144$		0			0
$145$	187.495	−	136.223i	1.29307	−	0.939468i
$146$	−64.0818	+	20.8214i	−0.438917	+	0.142613i
$147$		0			0
$148$	0.867584	+	0.630337i	0.00586205	+	0.00425903i
$149$	53.1924	−	73.2130i	0.356996	−	0.491363i	−0.592313	−	0.805708i	$-0.701785\pi$
$149$	53.1924	−	73.2130i	0.356996	−	0.491363i	0.949309	+	0.314345i	$0.101785\pi$
$150$		0			0
$151$	74.2733	+	228.590i	0.491876	+	1.51384i	0.821769	+	0.569821i	$0.192988\pi$
$151$	74.2733	+	228.590i	0.491876	+	1.51384i	−0.329892	+	0.944019i	$0.607012\pi$
$152$	67.0724	+	92.3173i	0.441266	+	0.607351i
$153$		0			0
$154$	68.7825	−	89.7044i	0.446639	−	0.582496i
$155$			144.492i			0.932207i
$156$		0			0
$157$	−9.14801	−	28.1547i	−0.0582676	−	0.179329i	0.917687	−	0.397305i	$-0.130055\pi$
$157$	−9.14801	−	28.1547i	−0.0582676	−	0.179329i	−0.975954	+	0.217976i	$0.930055\pi$
$158$	115.341	+	37.4766i	0.730008	+	0.237194i
$159$		0			0
$160$	−17.4405	−	12.6713i	−0.109003	−	0.0791953i
$161$	−28.2810	−	9.18905i	−0.175658	−	0.0570748i
$162$		0			0
$163$	−169.962	+	123.484i	−1.04271	+	0.757573i	−0.970813	−	0.239839i	$-0.922905\pi$
$163$	−169.962	+	123.484i	−1.04271	+	0.757573i	−0.0718974	+	0.997412i	$0.522905\pi$
$164$			2.54888i			0.0155420i
$165$		0			0
$166$	128.158			0.772036
$167$	−8.96158	−	12.3346i	−0.0536622	−	0.0738596i	0.781343	−	0.624102i	$-0.214535\pi$
$167$	−8.96158	−	12.3346i	−0.0536622	−	0.0738596i	−0.835005	+	0.550243i	$0.814535\pi$
$168$		0			0
$169$	39.4581	−	121.440i	0.233480	−	0.718578i
$170$	85.7668	−	118.048i	0.504511	−	0.694399i
$171$		0			0
$172$	−2.32440	+	7.15375i	−0.0135139	+	0.0415916i
$173$	203.903	−	66.2520i	1.17863	−	0.382960i	0.346772	−	0.937950i	$-0.387278\pi$
$173$	203.903	−	66.2520i	1.17863	−	0.382960i	0.831857	+	0.554990i	$0.187278\pi$
$174$		0			0
$175$	353.558			2.02033
$176$	−169.564	−	4.38046i	−0.963431	−	0.0248890i
$177$		0			0
$178$	−147.179	+	106.932i	−0.826849	+	0.600741i
$179$	194.582	−	63.2234i	1.08705	−	0.353204i	0.289943	−	0.957044i	$-0.406364\pi$
$179$	194.582	−	63.2234i	1.08705	−	0.353204i	0.797105	+	0.603840i	$0.206364\pi$
$180$		0			0
$181$	−110.640	−	80.3847i	−0.611271	−	0.444114i	0.238591	−	0.971120i	$-0.423315\pi$
$181$	−110.640	−	80.3847i	−0.611271	−	0.444114i	−0.849862	+	0.527006i	$0.823315\pi$
$182$	104.042	−	143.201i	0.571657	−	0.786818i
$183$		0			0
$184$	14.2896	+	43.9789i	0.0776609	+	0.239016i
$185$	43.2988	+	59.5956i	0.234047	+	0.322139i
$186$		0			0
$187$	−2.19257	+	84.8724i	−0.0117250	+	0.453863i
$188$			5.43686i			0.0289195i
$189$		0			0
$190$	81.9581	+	252.241i	0.431358	+	1.32758i
$191$	232.753	+	75.6261i	1.21860	+	0.395948i	0.846573	−	0.532272i	$-0.178662\pi$
$191$	232.753	+	75.6261i	1.21860	+	0.395948i	0.372030	+	0.928221i	$0.378662\pi$
$192$		0			0
$193$	12.7310	+	9.24963i	0.0659639	+	0.0479256i	0.620279	−	0.784382i	$-0.287020\pi$
$193$	12.7310	+	9.24963i	0.0659639	+	0.0479256i	−0.554315	+	0.832307i	$0.687020\pi$
$194$	97.9540	+	31.8272i	0.504918	+	0.164058i
$195$		0			0
$196$	2.45262	−	1.78193i	0.0125133	−	0.00909148i
$197$		−	95.4172i		−	0.484351i	−0.970232	−	0.242176i	$-0.922139\pi$
$197$		−	95.4172i		−	0.484351i	0.970232	−	0.242176i	$-0.0778610\pi$
$198$		0			0
$199$	−65.2214			−0.327746			−0.163873	−	0.986481i	$-0.552399\pi$
$199$	−65.2214			−0.327746			−0.163873	+	0.986481i	$0.552399\pi$
$200$	−323.169	−	444.804i	−1.61584	−	2.22402i
$201$		0			0
$202$	35.7726	−	110.097i	0.177092	−	0.545033i
$203$	−74.0466	+	101.916i	−0.364762	+	0.502051i
$204$		0			0
$205$	−54.1047	+	166.517i	−0.263926	+	0.812279i
$206$	−180.713	+	58.7173i	−0.877248	+	0.285035i
$207$		0			0
$208$	−265.605			−1.27695
$209$	−122.463	−	93.9005i	−0.585946	−	0.449285i
$210$		0			0
$211$	222.580	−	161.714i	1.05488	−	0.766415i	0.0817453	−	0.996653i	$-0.473951\pi$
$211$	222.580	−	161.714i	1.05488	−	0.766415i	0.973134	+	0.230238i	$0.0739506\pi$
$212$	−10.8733	+	3.53295i	−0.0512891	+	0.0166649i
$213$		0			0
$214$	−29.2326	−	21.2387i	−0.136601	−	0.0992462i
$215$	−303.703	+	418.011i	−1.41257	+	1.94424i
$216$		0			0
$217$	−24.2707	−	74.6974i	−0.111846	−	0.344228i
$218$	58.4902	+	80.5048i	0.268304	+	0.369288i
$219$		0			0
$220$	13.9790	+	4.94469i	0.0635410	+	0.0224759i
$221$			132.944i			0.601558i
$222$		0			0
$223$	56.5219	+	173.956i	0.253461	+	0.780074i	0.994129	+	0.108202i	$0.0345094\pi$
$223$	56.5219	+	173.956i	0.253461	+	0.780074i	−0.740668	+	0.671872i	$0.765491\pi$
$224$	11.1445	+	3.62108i	0.0497525	+	0.0161656i
$225$		0			0
$226$	−15.6333	−	11.3582i	−0.0691738	−	0.0502577i
$227$	−238.155	−	77.3812i	−1.04914	−	0.340886i	−0.266809	−	0.963749i	$-0.585969\pi$
$227$	−238.155	−	77.3812i	−1.04914	−	0.340886i	−0.782331	+	0.622863i	$0.785969\pi$
$228$		0			0
$229$	283.549	−	206.010i	1.23820	−	0.899608i	0.240726	−	0.970593i	$-0.422614\pi$
$229$	283.549	−	206.010i	1.23820	−	0.899608i	0.997477	+	0.0709854i	$0.0226144\pi$
$230$			107.479i			0.467298i
$231$		0			0
$232$	195.901			0.844400
$233$	214.372	+	295.058i	0.920052	+	1.26634i	0.963616	+	0.267292i	$0.0861289\pi$
$233$	214.372	+	295.058i	0.920052	+	1.26634i	−0.0435636	+	0.999051i	$0.513871\pi$
$234$		0			0
$235$	−115.407	+	355.187i	−0.491095	+	1.51144i
$236$	3.57495e−5	0	4.92049e-5i	1.51481e−7	0	2.08495e-7i
$237$		0			0
$238$	−24.5097	+	75.4331i	−0.102982	+	0.316946i
$239$	−230.931	+	75.0342i	−0.966240	+	0.313951i	−0.749297	−	0.662234i	$-0.769609\pi$
$239$	−230.931	+	75.0342i	−0.966240	+	0.313951i	−0.216943	+	0.976184i	$0.569609\pi$
$240$		0			0
$241$	−418.345			−1.73587			−0.867935	−	0.496677i	$-0.834553\pi$
$241$	−418.345			−1.73587			−0.867935	+	0.496677i	$0.834553\pi$
$242$	229.581	−	61.6893i	0.948682	−	0.254914i
$243$		0			0
$244$	−0.541702	+	0.393569i	−0.00222009	+	0.00161299i
$245$	198.053	−	64.3513i	0.808379	−	0.262658i
$246$		0			0
$247$	−195.495	−	142.036i	−0.791478	−	0.575043i
$248$	−71.7906	+	98.8113i	−0.289478	+	0.398433i
$249$		0			0
$250$	−248.840	−	765.850i	−0.995359	−	3.06340i
$251$	−162.338	−	223.439i	−0.646766	−	0.890197i	0.352188	−	0.935929i	$-0.385438\pi$
$251$	−162.338	−	223.439i	−0.646766	−	0.890197i	−0.998954	+	0.0457326i	$0.985438\pi$
$252$		0			0
$253$	−35.4391	−	51.5254i	−0.140076	−	0.203658i
$254$		−	423.348i		−	1.66672i
$255$		0			0
$256$	−8.30108	−	25.5481i	−0.0324261	−	0.0997972i
$257$	−153.309	−	49.8130i	−0.596532	−	0.193825i	−0.00483877	−	0.999988i	$-0.501540\pi$
$257$	−153.309	−	49.8130i	−0.596532	−	0.193825i	−0.591693	+	0.806163i	$0.701540\pi$
$258$		0			0
$259$	−32.3944	−	23.5359i	−0.125075	−	0.0908722i
$260$	22.0821	+	7.17491i	0.0849311	+	0.0275958i
$261$		0			0
$262$	264.783	−	192.376i	1.01062	−	0.734260i
$263$			55.4784i			0.210944i	0.994422	+	0.105472i	$0.0336354\pi$
$263$			55.4784i			0.210944i	−0.994422	+	0.105472i	$0.966365\pi$
$264$		0			0
$265$	−785.340			−2.96355
$266$	−84.7390	−	116.633i	−0.318568	−	0.438471i
$267$		0			0
$268$	4.83948	−	14.8944i	0.0180578	−	0.0555761i
$269$	−34.2101	+	47.0861i	−0.127175	+	0.175041i	−0.867856	−	0.496815i	$-0.834503\pi$
$269$	−34.2101	+	47.0861i	−0.127175	+	0.175041i	0.740682	+	0.671856i	$0.234503\pi$
$270$		0			0
$271$	131.612	−	405.060i	0.485653	−	1.49469i	−0.345380	−	0.938463i	$-0.612250\pi$
$271$	131.612	−	405.060i	0.485653	−	1.49469i	0.831033	−	0.556223i	$-0.187750\pi$
$272$	113.191	−	36.7779i	0.416142	−	0.135213i
$273$		0			0
$274$	−85.9501			−0.313686
$275$	590.050	+	452.432i	2.14564	+	1.64521i
$276$		0			0
$277$	103.461	−	75.1686i	0.373504	−	0.271367i	−0.385158	−	0.922851i	$-0.625853\pi$
$277$	103.461	−	75.1686i	0.373504	−	0.271367i	0.758663	+	0.651484i	$0.225853\pi$
$278$	−192.594	+	62.5777i	−0.692786	+	0.225100i
$279$		0			0
$280$	331.205	+	240.635i	1.18288	+	0.859409i
$281$	−43.7302	+	60.1895i	−0.155624	+	0.214198i	−0.879709	−	0.475513i	$-0.842262\pi$
$281$	−43.7302	+	60.1895i	−0.155624	+	0.214198i	0.724085	+	0.689711i	$0.242262\pi$
$282$		0			0
$283$	152.758	+	470.142i	0.539782	+	1.66128i	0.733083	+	0.680139i	$0.238081\pi$
$283$	152.758	+	470.142i	0.539782	+	1.66128i	−0.193301	+	0.981139i	$0.561919\pi$
$284$	−8.20379	−	11.2916i	−0.0288866	−	0.0397590i
$285$		0			0
$286$	356.882	−	105.850i	1.24784	−	0.370104i
$287$		−	95.1718i		−	0.331609i
$288$		0			0
$289$	70.8974	+	218.200i	0.245320	+	0.755016i
$290$	433.038	+	140.703i	1.49324	+	0.485182i
$291$		0			0
$292$	3.88676	+	2.82389i	0.0133108	+	0.00967087i
$293$	−12.9456	−	4.20629i	−0.0441831	−	0.0143559i	0.286842	−	0.957978i	$-0.407394\pi$
$293$	−12.9456	−	4.20629i	−0.0441831	−	0.0143559i	−0.331025	+	0.943622i	$0.607394\pi$
$294$		0			0
$295$	0.00337996	−	0.00245568i	1.14575e−5	−	8.32436e-6i
$296$			62.2676i			0.210363i
$297$		0			0
$298$	177.795			0.596628
$299$	−57.5585	−	79.2225i	−0.192503	−	0.264958i
$300$		0			0
$301$	86.7897	−	267.111i	0.288338	−	0.887413i
$302$	−277.561	+	382.030i	−0.919075	+	1.26500i
$303$		0			0
$304$	−66.8490	+	205.740i	−0.219898	+	0.676777i
$305$	−43.7433	+	14.2131i	−0.143421	+	0.0466002i
$306$		0			0
$307$	−215.268			−0.701198			−0.350599	−	0.936526i	$-0.614022\pi$
$307$	−215.268			−0.701198			−0.350599	+	0.936526i	$0.614022\pi$
$308$	−8.05724	−	0.208148i	−0.0261599	−	0.000675806i
$309$		0			0
$310$	−229.663	+	166.860i	−0.740847	+	0.538257i
$311$	−85.6398	+	27.8260i	−0.275369	+	0.0894728i	−0.443446	−	0.896301i	$-0.646244\pi$
$311$	−85.6398	+	27.8260i	−0.275369	+	0.0894728i	0.168077	+	0.985774i	$0.446244\pi$
$312$		0			0
$313$	−208.941	−	151.805i	−0.667544	−	0.484999i	0.201658	−	0.979456i	$-0.435367\pi$
$313$	−208.941	−	151.805i	−0.667544	−	0.484999i	−0.869202	+	0.494457i	$0.835367\pi$
$314$	34.1863	−	47.0534i	0.108873	−	0.149851i
$315$		0			0
$316$	−2.67216	−	8.22405i	−0.00845619	−	0.0260255i
$317$	−61.7422	−	84.9808i	−0.194770	−	0.268078i	0.700451	−	0.713701i	$-0.252982\pi$
$317$	−61.7422	−	84.9808i	−0.194770	−	0.268078i	−0.895221	+	0.445623i	$0.852982\pi$
$318$		0			0
$319$	−253.993	+	75.3335i	−0.796218	+	0.236155i
$320$		−	635.878i		−	1.98712i
$321$		0			0
$322$	−18.0534	−	55.5627i	−0.0560665	−	0.172555i
$323$	102.980	+	33.4602i	0.318823	+	0.103592i
$324$		0			0
$325$	941.935	+	684.356i	2.89826	+	2.10571i
$326$	−392.544	−	127.545i	−1.20412	−	0.391244i
$327$		0			0
$328$	−119.733	+	86.9915i	−0.365041	+	0.265218i
$329$		−	203.005i		−	0.617036i
$330$		0			0
$331$	258.731			0.781664			0.390832	−	0.920462i	$-0.372187\pi$
$331$	258.731			0.781664			0.390832	+	0.920462i	$0.372187\pi$
$332$	−5.37113	−	7.39273i	−0.0161781	−	0.0222673i
$333$		0			0
$334$	9.25629	−	28.4879i	0.0277135	−	0.0852933i
$335$	632.321	−	870.316i	1.88753	−	2.59796i
$336$		0			0
$337$	−113.715	+	349.979i	−0.337433	+	1.03851i	0.628078	+	0.778150i	$0.283842\pi$
$337$	−113.715	+	349.979i	−0.337433	+	1.03851i	−0.965511	+	0.260362i	$0.916158\pi$
$338$	238.588	−	77.5221i	0.705883	−	0.229355i
$339$		0			0
$340$	−10.4040			−0.0306001
$341$	55.0817	−	155.720i	0.161530	−	0.456657i
$342$		0			0
$343$	−298.926	+	217.183i	−0.871505	+	0.633186i
$344$	−415.377	+	134.964i	−1.20749	+	0.392337i
$345$		0			0
$346$	340.772	+	247.585i	0.984889	+	0.715564i
$347$	−245.149	+	337.419i	−0.706482	+	0.972388i	0.293384	+	0.955995i	$0.405219\pi$
$347$	−245.149	+	337.419i	−0.706482	+	0.972388i	−0.999866	+	0.0163937i	$0.994781\pi$
$348$		0			0
$349$	86.4724	+	266.135i	0.247772	+	0.762564i	0.995168	+	0.0981851i	$0.0313037\pi$
$349$	86.4724	+	266.135i	0.247772	+	0.762564i	−0.747396	+	0.664379i	$0.768696\pi$
$350$	408.290	+	561.963i	1.16654	+	1.60561i
$351$		0			0
$352$	13.9653	+	20.3044i	0.0396742	+	0.0576828i
$353$			333.271i			0.944111i	0.881569	+	0.472056i	$0.156488\pi$
$353$			333.271i			0.944111i	−0.881569	+	0.472056i	$0.843512\pi$
$354$		0			0
$355$	−296.266	−	911.812i	−0.834551	−	2.56848i
$356$	12.3366	+	4.00841i	0.0346534	+	0.0112596i
$357$		0			0
$358$	325.194	+	236.267i	0.908363	+	0.659964i
$359$	−472.450	−	153.508i	−1.31602	−	0.427600i	−0.434891	−	0.900483i	$-0.643213\pi$
$359$	−472.450	−	153.508i	−1.31602	−	0.427600i	−0.881125	+	0.472883i	$0.843213\pi$
$360$		0			0
$361$	132.830	−	96.5064i	0.367949	−	0.267331i
$362$		−	268.685i		−	0.742224i
$363$		0			0
$364$	−12.6209			−0.0346727
$365$	193.977	+	266.987i	0.531445	+	0.731471i
$366$		0			0
$367$	51.0462	−	157.104i	0.139090	−	0.428076i	−0.857113	−	0.515128i	$-0.827744\pi$
$367$	51.0462	−	157.104i	0.139090	−	0.428076i	0.996204	+	0.0870514i	$0.0277444\pi$
$368$	−51.5281	+	70.9223i	−0.140022	+	0.192724i
$369$		0			0
$370$	−44.7227	+	137.642i	−0.120872	+	0.372006i
$371$	405.994	−	131.915i	1.09432	−	0.355567i
$372$		0			0
$373$	393.501			1.05496			0.527481	−	0.849567i	$-0.323136\pi$
$373$	393.501			1.05496			0.527481	+	0.849567i	$0.323136\pi$
$374$	−137.432	+	94.5259i	−0.367466	+	0.252743i
$375$		0			0
$376$	−255.396	+	185.556i	−0.679245	+	0.493500i
$377$	−394.544	+	128.195i	−1.04654	+	0.340040i
$378$		0			0
$379$	−153.017	−	111.173i	−0.403739	−	0.293334i	0.367323	−	0.930093i	$-0.380274\pi$
$379$	−153.017	−	111.173i	−0.403739	−	0.293334i	−0.771062	+	0.636760i	$0.780274\pi$
$380$	11.1155	−	15.2992i	0.0292513	−	0.0402610i
$381$		0			0
$382$	148.580	+	457.282i	0.388953	+	1.19707i
$383$	275.626	+	379.367i	0.719651	+	0.990514i	0.999535	+	0.0304804i	$0.00970371\pi$
$383$	275.626	+	379.367i	0.719651	+	0.990514i	−0.279885	+	0.960034i	$0.590296\pi$
$384$		0			0
$385$	−521.957	−	184.628i	−1.35573	−	0.479553i
$386$			30.9168i			0.0800954i
$387$		0			0
$388$	−2.26934	−	6.98431i	−0.00584881	−	0.0180008i
$389$	432.711	+	140.596i	1.11237	+	0.361430i	0.806850	−	0.590756i	$-0.201170\pi$
$389$	432.711	+	140.596i	1.11237	+	0.361430i	0.305518	+	0.952186i	$0.401170\pi$
$390$		0			0
$391$	35.4990	+	25.7915i	0.0907903	+	0.0659630i
$392$	167.412	+	54.3954i	0.427071	+	0.138764i
$393$		0			0
$394$	151.661	−	110.188i	0.384926	−	0.279665i
$395$		−	593.994i		−	1.50378i
$396$		0			0
$397$	168.638			0.424782			0.212391	−	0.977185i	$-0.431875\pi$
$397$	168.638			0.424782			0.212391	+	0.977185i	$0.431875\pi$
$398$	−75.3178	−	103.666i	−0.189241	−	0.260468i
$399$		0			0
$400$	322.092	−	991.298i	0.805231	−	2.47825i
$401$	41.0252	−	56.4664i	0.102307	−	0.140814i	−0.754794	−	0.655962i	$-0.772263\pi$
$401$	41.0252	−	56.4664i	0.102307	−	0.140814i	0.857101	+	0.515148i	$0.172263\pi$
$402$		0			0
$403$	79.9253	−	245.985i	0.198326	−	0.610384i
$404$	−7.85011	+	2.55066i	−0.0194310	+	0.00631350i
$405$		0			0
$406$	−247.500			−0.609606
$407$	−23.9450	−	80.7325i	−0.0588328	−	0.198360i
$408$		0			0
$409$	−448.126	+	325.583i	−1.09566	+	0.796046i	−0.980347	−	0.197283i	$-0.936788\pi$
$409$	−448.126	+	325.583i	−1.09566	+	0.796046i	−0.115317	+	0.993329i	$0.536788\pi$
$410$	−327.151	+	106.298i	−0.797929	+	0.259263i
$411$		0			0
$412$	10.9608	+	7.96349i	0.0266039	+	0.0193289i
$413$	−0.00133484	+	0.00183724i	−3.23205e−6	+	4.44853e-6i
$414$		0			0
$415$	−193.969	−	596.975i	−0.467395	−	1.43849i
$416$	22.6818	+	31.2188i	0.0545235	+	0.0750452i
$417$		0			0
$418$	7.82980	−	303.085i	0.0187316	−	0.725083i
$419$		−	307.485i		−	0.733855i	−0.930250	−	0.366927i	$-0.880410\pi$
$419$		−	307.485i		−	0.733855i	0.930250	−	0.366927i	$-0.119590\pi$
$420$		0			0
$421$	−1.09596	−	3.37301i	−0.00260322	−	0.00801189i	0.949746	−	0.313020i	$-0.101341\pi$
$421$	−1.09596	−	3.37301i	−0.00260322	−	0.00801189i	−0.952350	+	0.305008i	$0.901341\pi$
$422$	514.071	+	167.032i	1.21818	+	0.395810i
$423$		0			0
$424$	−537.057	−	390.195i	−1.26664	−	0.920271i
$425$	−496.178	−	161.218i	−1.16748	−	0.379337i
$426$		0			0
$427$	20.2264	−	14.6953i	0.0473686	−	0.0344153i
$428$			2.57638i			0.00601959i
$429$		0			0
$430$	−1015.12			−2.36076
$431$	69.9030	+	96.2132i	0.162188	+	0.223232i	0.882374	−	0.470548i	$-0.155944\pi$
$431$	69.9030	+	96.2132i	0.162188	+	0.223232i	−0.720187	+	0.693781i	$0.755944\pi$
$432$		0			0
$433$	61.6340	−	189.690i	0.142342	−	0.438083i	−0.854318	−	0.519751i	$-0.826025\pi$
$433$	61.6340	−	189.690i	0.142342	−	0.438083i	0.996660	+	0.0816680i	$0.0260247\pi$
$434$	90.6999	−	124.838i	0.208986	−	0.287644i
$435$		0			0
$436$	2.19254	−	6.74795i	0.00502876	−	0.0154769i
$437$	−75.8532	+	24.6462i	−0.173577	+	0.0563986i
$438$		0			0
$439$	−7.94474			−0.0180973			−0.00904867	−	0.999959i	$-0.502880\pi$
$439$	−7.94474			−0.0180973			−0.00904867	+	0.999959i	$0.502880\pi$
$440$	244.817	+	825.421i	0.556402	+	1.87596i
$441$		0			0
$442$	−211.308	+	153.524i	−0.478073	+	0.347340i
$443$	−446.341	+	145.025i	−1.00754	+	0.327370i	−0.765875	−	0.642989i	$-0.777694\pi$
$443$	−446.341	+	145.025i	−1.00754	+	0.327370i	−0.241666	+	0.970359i	$0.577694\pi$
$444$		0			0
$445$	720.859	+	523.735i	1.61991	+	1.17693i
$446$	−211.223	+	290.724i	−0.473595	+	0.651847i
$447$		0			0
$448$	106.810	+	328.727i	0.238415	+	0.733765i
$449$	−434.087	−	597.469i	−0.966786	−	1.33067i	−0.943654	−	0.330935i	$-0.892636\pi$
$449$	−434.087	−	597.469i	−0.966786	−	1.33067i	−0.0231324	−	0.999732i	$-0.507364\pi$
$450$		0			0
$451$	121.787	−	158.831i	0.270037	−	0.352176i
$452$			1.37782i			0.00304828i
$453$		0			0
$454$	−152.028	−	467.895i	−0.334864	−	1.03060i
$455$	−824.515	−	267.901i	−1.81212	−	0.588794i
$456$		0			0
$457$	146.584	+	106.500i	0.320753	+	0.233041i	0.736497	−	0.676441i	$-0.236479\pi$
$457$	146.584	+	106.500i	0.320753	+	0.233041i	−0.415744	+	0.909482i	$0.636479\pi$
$458$	654.885	+	212.785i	1.42988	+	0.464596i
$459$		0			0
$460$	6.19984	−	4.50445i	0.0134779	−	0.00979228i
$461$			561.409i			1.21781i	0.793244	+	0.608903i	$0.208390\pi$
$461$			561.409i			1.21781i	−0.793244	+	0.608903i	$0.791610\pi$
$462$		0			0
$463$	379.155			0.818909			0.409454	−	0.912331i	$-0.365719\pi$
$463$	379.155			0.818909			0.409454	+	0.912331i	$0.365719\pi$
$464$	218.294	+	300.456i	0.470462	+	0.647535i
$465$		0			0
$466$	−221.422	+	681.467i	−0.475155	+	1.46238i
$467$	−268.209	+	369.158i	−0.574324	+	0.790489i	−0.993059	−	0.117619i	$-0.962474\pi$
$467$	−268.209	+	369.158i	−0.574324	+	0.790489i	0.418735	+	0.908109i	$0.362474\pi$
$468$		0			0
$469$	−180.699	+	556.136i	−0.385287	+	1.18579i
$470$	−697.825	+	226.737i	−1.48473	+	0.482419i
$471$		0			0
$472$	0.00353150			7.48199e−6
$473$	486.652	−	334.719i	1.02886	−	0.707651i
$474$		0			0
$475$	767.181	−	557.389i	1.61512	−	1.17345i
$476$	5.37853	−	1.74759i	0.0112994	−	0.00367141i
$477$		0			0
$478$	−385.943	−	280.404i	−0.807412	−	0.586619i
$479$	−316.414	+	435.507i	−0.660573	+	0.909201i	−0.999500	−	0.0316118i	$-0.989936\pi$
$479$	−316.414	+	435.507i	−0.660573	+	0.909201i	0.338927	+	0.940813i	$0.389936\pi$
$480$		0			0
$481$	−40.7471	−	125.407i	−0.0847134	−	0.260721i
$482$	−483.106	−	664.938i	−1.00229	−	1.37954i
$483$		0			0
$484$	−13.1803	−	10.6578i	−0.0272320	−	0.0220203i
$485$		−	504.452i		−	1.04011i
$486$		0			0
$487$	60.1626	+	185.162i	0.123537	+	0.380208i	0.993632	−	0.112676i	$-0.0359424\pi$
$487$	60.1626	+	185.162i	0.123537	+	0.380208i	−0.870095	+	0.492885i	$0.835942\pi$
$488$	−36.9757	−	12.0141i	−0.0757700	−	0.0246192i
$489$		0			0
$490$	330.995	+	240.482i	0.675500	+	0.490780i
$491$	−193.879	−	62.9950i	−0.394865	−	0.128299i	0.104853	−	0.994488i	$-0.466563\pi$
$491$	−193.879	−	62.9950i	−0.394865	−	0.128299i	−0.499717	+	0.866188i	$0.666563\pi$
$492$		0			0
$493$	150.388	−	109.264i	0.305048	−	0.221630i
$494$		−	474.752i		−	0.961037i
$495$		0			0
$496$	−231.546			−0.466826
$497$	306.318	+	421.611i	0.616335	+	0.848312i
$498$		0			0
$499$	−264.246	+	813.267i	−0.529552	+	1.62979i	0.225584	+	0.974224i	$0.427571\pi$
$499$	−264.246	+	813.267i	−0.529552	+	1.62979i	−0.755135	+	0.655569i	$0.772429\pi$
$500$	−33.7487	+	46.4511i	−0.0674974	+	0.0929022i
$501$		0			0
$502$	167.677	−	516.057i	0.334018	−	1.02800i
$503$	−258.957	+	84.1401i	−0.514824	+	0.167277i	−0.554895	−	0.831920i	$-0.687242\pi$
$503$	−258.957	+	84.1401i	−0.514824	+	0.167277i	0.0400708	+	0.999197i	$0.487242\pi$
$504$		0			0
$505$	−566.986			−1.12274
$506$	40.9718	−	115.830i	0.0809719	−	0.228914i
$507$		0			0
$508$	−24.4206	+	17.7426i	−0.0480720	+	0.0349264i
$509$	897.352	−	291.567i	1.76297	−	0.572824i	0.765468	−	0.643473i	$-0.222507\pi$
$509$	897.352	−	291.567i	1.76297	−	0.572824i	0.997501	+	0.0706498i	$0.0225073\pi$
$510$		0			0
$511$	−145.126	−	105.440i	−0.284004	−	0.206341i
$512$	315.197	−	433.831i	0.615619	−	0.847327i
$513$		0			0
$514$	−97.8660	−	301.200i	−0.190401	−	0.585993i
$515$	547.024	+	752.914i	1.06218	+	1.46197i
$516$		0			0
$517$	259.776	−	338.793i	0.502468	−	0.655306i
$518$		−	78.6685i		−	0.151870i
$519$		0			0
$520$	416.605	+	1282.18i	0.801163	+	2.46573i
$521$	308.494	+	100.236i	0.592119	+	0.192391i	0.589722	−	0.807606i	$-0.299237\pi$
$521$	308.494	+	100.236i	0.592119	+	0.192391i	0.00239665	+	0.999997i	$0.499237\pi$
$522$		0			0
$523$	−98.0023	−	71.2028i	−0.187385	−	0.136143i	0.490138	−	0.871645i	$-0.336946\pi$
$523$	−98.0023	−	71.2028i	−0.187385	−	0.136143i	−0.677523	+	0.735502i	$0.736946\pi$
$524$	−22.1942	−	7.21135i	−0.0423554	−	0.0137621i
$525$		0			0
$526$	−88.1801	+	64.0666i	−0.167643	+	0.121800i
$527$			115.896i			0.219917i
$528$		0			0
$529$	496.679			0.938902
$530$	−906.913	−	1248.26i	−1.71116	−	2.35520i
$531$		0			0
$532$	−3.17649	+	9.77624i	−0.00597085	+	0.0183764i
$533$	184.217	−	253.553i	0.345623	−	0.475709i
$534$		0			0
$535$	−54.6885	+	168.314i	−0.102221	+	0.314605i
$536$	864.830	−	281.000i	1.61349	−	0.524254i
$537$		0			0
$538$	−114.347			−0.212540
$539$	−237.974	−	6.14776i	−0.441510	−	0.0114059i
$540$		0			0
$541$	482.965	−	350.895i	0.892727	−	0.648604i	−0.0438604	−	0.999038i	$-0.513966\pi$
$541$	482.965	−	350.895i	0.892727	−	0.648604i	0.936588	+	0.350433i	$0.113966\pi$
$542$	795.808	−	258.574i	1.46828	−	0.477073i
$543$		0			0
$544$	−13.9889	−	10.1635i	−0.0257149	−	0.0186830i
$545$	286.475	−	394.299i	0.525643	−	0.723485i
$546$		0			0
$547$	−104.567	−	321.823i	−0.191164	−	0.588343i	−1.00000		0.000308188i	$-0.999902\pi$
$547$	−104.567	−	321.823i	−0.191164	−	0.588343i	0.808836	−	0.588035i	$-0.200098\pi$
$548$	3.60219	+	4.95798i	0.00657333	+	0.00904742i
$549$		0			0
$550$	−37.7256	+	1460.32i	−0.0685920	+	2.65513i
$551$			337.882i			0.613217i
$552$		0			0
$553$	99.7746	+	307.075i	0.180424	+	0.555289i
$554$	238.953	+	77.6406i	0.431324	+	0.140146i
$555$		0			0
$556$	11.6814	+	8.48706i	0.0210098	+	0.0152645i
$557$	454.284	+	147.606i	0.815590	+	0.265001i	0.686964	−	0.726692i	$-0.258943\pi$
$557$	454.284	+	147.606i	0.815590	+	0.265001i	0.128627	+	0.991693i	$0.458943\pi$
$558$		0			0
$559$	748.249	−	543.635i	1.33855	−	0.972513i
$560$			776.116i			1.38592i
$561$		0			0
$562$	−146.168			−0.260085
$563$	−277.409	−	381.820i	−0.492733	−	0.678189i	0.488156	−	0.872756i	$-0.337670\pi$
$563$	−277.409	−	381.820i	−0.492733	−	0.678189i	−0.980889	+	0.194567i	$0.937670\pi$
$564$		0			0
$565$	−29.2468	+	90.0125i	−0.0517643	+	0.159314i
$566$	−570.861	+	785.722i	−1.00859	+	1.38820i
$567$		0			0
$568$	250.430	−	770.745i	0.440898	−	1.35694i
$569$	122.262	−	39.7253i	0.214871	−	0.0698159i	−0.199603	−	0.979877i	$-0.563965\pi$
$569$	122.262	−	39.7253i	0.214871	−	0.0698159i	0.414475	+	0.910061i	$0.363965\pi$
$570$		0			0
$571$	266.234			0.466259			0.233130	−	0.972446i	$-0.425103\pi$
$571$	266.234			0.466259			0.233130	+	0.972446i	$0.425103\pi$
$572$	−21.0629	−	16.1503i	−0.0368232	−	0.0282348i
$573$		0			0
$574$	151.271	−	109.905i	0.263538	−	0.191471i
$575$	365.476	−	118.750i	0.635610	−	0.206522i
$576$		0			0
$577$	−583.296	−	423.789i	−1.01091	−	0.734470i	−0.0465112	−	0.998918i	$-0.514810\pi$
$577$	−583.296	−	423.789i	−1.01091	−	0.734470i	−0.964400	+	0.264448i	$0.914810\pi$
$578$	−264.945	+	364.665i	−0.458382	+	0.630908i
$579$		0			0
$580$	−10.0324	−	30.8765i	−0.0172972	−	0.0532353i
$581$	200.551	+	276.034i	0.345182	+	0.475102i
$582$		0			0
$583$	846.366	+	299.379i	1.45174	+	0.513514i
$584$			278.957i			0.477667i
$585$		0			0
$586$	−8.26396	−	25.4339i	−0.0141023	−	0.0434025i
$587$	−391.709	−	127.274i	−0.667307	−	0.216821i	−0.0442770	−	0.999019i	$-0.514098\pi$
$587$	−391.709	−	127.274i	−0.667307	−	0.216821i	−0.623030	+	0.782198i	$0.714098\pi$
$588$		0			0
$589$	−170.426	−	123.822i	−0.289348	−	0.210224i
$590$	0.00780637	+	0.00253644i	1.32311e−5	+	4.29906e-6i
$591$		0			0
$592$	−95.5008	+	69.3854i	−0.161319	+	0.117205i
$593$			750.336i			1.26532i	0.774429	+	0.632661i	$0.218037\pi$
$593$			750.336i			1.26532i	−0.774429	+	0.632661i	$0.781963\pi$
$594$		0			0
$595$	388.472			0.652895
$596$	−7.45143	−	10.2560i	−0.0125024	−	0.0172081i
$597$		0			0
$598$	59.4514	−	182.973i	0.0994171	−	0.305974i
$599$	319.528	−	439.793i	0.533436	−	0.734211i	−0.454213	−	0.890893i	$-0.650080\pi$
$599$	319.528	−	439.793i	0.533436	−	0.734211i	0.987649	+	0.156682i	$0.0500796\pi$
$600$		0			0
$601$	−227.497	+	700.163i	−0.378530	+	1.16500i	0.562535	+	0.826773i	$0.309826\pi$
$601$	−227.497	+	700.163i	−0.378530	+	1.16500i	−0.941066	+	0.338224i	$0.890174\pi$
$602$	524.785	−	170.513i	0.871735	−	0.283244i
$603$		0			0
$604$	33.6698			0.0557447
$605$	−634.830	−	976.048i	−1.04931	−	1.61330i
$606$		0			0
$607$	−452.759	+	328.949i	−0.745896	+	0.541925i	−0.894552	−	0.446964i	$-0.852505\pi$
$607$	−452.759	+	328.949i	−0.745896	+	0.541925i	0.148656	+	0.988889i	$0.452505\pi$
$608$	29.8911	−	9.71220i	0.0491630	−	0.0159740i
$609$		0			0
$610$	−73.1058	−	53.1145i	−0.119846	−	0.0870729i
$611$	392.941	−	540.837i	0.643112	−	0.885168i
$612$		0			0
$613$	−33.9655	−	104.535i	−0.0554086	−	0.170530i	0.919522	−	0.393038i	$-0.128576\pi$
$613$	−33.9655	−	104.535i	−0.0554086	−	0.170530i	−0.974931	+	0.222508i	$0.928576\pi$
$614$	−248.592	−	342.157i	−0.404872	−	0.557259i
$615$		0			0
$616$	−265.210	−	385.592i	−0.430535	−	0.625961i
$617$			61.1594i			0.0991238i	0.998771	+	0.0495619i	$0.0157825\pi$
$617$			61.1594i			0.0991238i	−0.998771	+	0.0495619i	$0.984217\pi$
$618$		0			0
$619$	25.2833	+	77.8139i	0.0408454	+	0.125709i	0.969400	−	0.245487i	$-0.0789478\pi$
$619$	25.2833	+	77.8139i	0.0408454	+	0.125709i	−0.928555	+	0.371196i	$0.878948\pi$
$620$	19.2504	+	6.25484i	0.0310491	+	0.0100885i
$621$		0			0
$622$	−143.125	−	103.986i	−0.230105	−	0.167181i
$623$	−460.632	−	149.668i	−0.739377	−	0.240238i
$624$		0			0
$625$	−1823.67	+	1324.97i	−2.91786	+	2.11995i
$626$		−	507.406i		−	0.810553i
$627$		0			0
$628$	−4.14700			−0.00660351
$629$	34.7297	+	47.8014i	0.0552142	+	0.0759958i
$630$		0			0
$631$	2.87142	−	8.83732i	0.00455058	−	0.0140053i	−0.948755	−	0.316011i	$-0.897656\pi$
$631$	2.87142	−	8.83732i	0.00455058	−	0.0140053i	0.953306	+	0.302006i	$0.0976563\pi$
$632$	295.125	−	406.205i	0.466970	−	0.642729i
$633$		0			0
$634$	63.7726	−	196.272i	0.100588	−	0.309577i
$635$	−1972.00	+	640.743i	−3.10552	+	1.00904i
$636$		0			0
$637$	−372.763			−0.585185
$638$	−413.051	−	316.714i	−0.647415	−	0.496417i
$639$		0			0
$640$	940.933	−	683.628i	1.47021	−	1.06817i
$641$	331.957	−	107.859i	0.517874	−	0.168268i	−0.0384062	−	0.999262i	$-0.512228\pi$
$641$	331.957	−	107.859i	0.517874	−	0.168268i	0.556280	+	0.830995i	$0.312228\pi$
$642$		0			0
$643$	−733.104	−	532.631i	−1.14013	−	0.828353i	−0.152993	−	0.988227i	$-0.548891\pi$
$643$	−733.104	−	532.631i	−1.14013	−	0.828353i	−0.987137	+	0.159874i	$0.948891\pi$
$644$	−2.44848	+	3.37005i	−0.00380199	+	0.00523299i
$645$		0			0
$646$	65.7381	+	202.321i	0.101762	+	0.313191i
$647$	33.2345	+	45.7434i	0.0513671	+	0.0707007i	0.833928	−	0.551874i	$-0.186087\pi$
$647$	33.2345	+	45.7434i	0.0513671	+	0.0707007i	−0.782561	+	0.622574i	$0.786087\pi$
$648$		0			0
$649$	−0.00457873	+	0.00135804i	−7.05506e−6	+	2.09250e-6i
$650$			2287.45i			3.51916i
$651$		0			0
$652$	9.09423	+	27.9892i	0.0139482	+	0.0429282i
$653$	−540.720	−	175.691i	−0.828055	−	0.269051i	−0.135829	−	0.990732i	$-0.543370\pi$
$653$	−540.720	−	175.691i	−0.828055	−	0.269051i	−0.692226	+	0.721681i	$0.743370\pi$
$654$		0			0
$655$	−1296.86	−	942.227i	−1.97995	−	1.43851i
$656$	−266.840	−	86.7017i	−0.406769	−	0.132167i
$657$		0			0
$658$	322.666	−	234.430i	0.490374	−	0.356277i
$659$			380.801i			0.577847i	0.957352	+	0.288923i	$0.0932973\pi$
$659$			380.801i			0.577847i	−0.957352	+	0.288923i	$0.906703\pi$
$660$		0			0
$661$	350.773			0.530671			0.265335	−	0.964156i	$-0.414517\pi$
$661$	350.773			0.530671			0.265335	+	0.964156i	$0.414517\pi$
$662$	298.783	+	411.239i	0.451333	+	0.621207i
$663$		0			0
$664$	163.960	−	504.616i	0.246927	−	0.759965i
$665$	−415.038	+	571.250i	−0.624117	+	0.859023i
$666$		0			0
$667$	−42.3117	+	130.222i	−0.0634358	+	0.195235i
$668$	−2.03125	+	0.659992i	−0.00304079	+	0.000988011i
$669$		0			0
$670$	2113.53			3.15452
$671$	52.5606	+	1.35784i	0.0783317	+	0.00202360i
$672$		0			0
$673$	390.671	−	283.839i	0.580491	−	0.421752i	−0.258410	−	0.966035i	$-0.583198\pi$
$673$	390.671	−	283.839i	0.580491	−	0.421752i	0.838901	+	0.544284i	$0.183198\pi$
$674$	−687.591	+	223.412i	−1.02017	+	0.331472i
$675$		0			0
$676$	−14.4711	−	10.5139i	−0.0214070	−	0.0155531i
$677$	−499.429	+	687.405i	−0.737709	+	1.01537i	0.261038	+	0.965328i	$0.415935\pi$
$677$	−499.429	+	687.405i	−0.737709	+	1.01537i	−0.998747	+	0.0500409i	$0.984065\pi$
$678$		0			0
$679$	84.7340	+	260.784i	0.124792	+	0.384071i
$680$	−355.082	−	488.728i	−0.522179	−	0.718718i
$681$		0			0
$682$	311.117	−	92.2763i	0.456184	−	0.135302i
$683$		−	831.602i		−	1.21757i	−0.793334	−	0.608786i	$-0.791657\pi$
$683$		−	831.602i		−	1.21757i	0.793334	−	0.608786i	$-0.208343\pi$
$684$		0			0
$685$	130.087	+	400.366i	0.189908	+	0.584475i
$686$	−690.402	−	224.325i	−1.00642	−	0.327004i
$687$		0			0
$688$	−669.855	−	486.678i	−0.973626	−	0.707381i
$689$	1336.97	+	434.408i	1.94045	+	0.630491i
$690$		0			0
$691$	−736.820	+	535.331i	−1.06631	+	0.774719i	−0.975245	−	0.221126i	$-0.929027\pi$
$691$	−736.820	+	535.331i	−1.06631	+	0.774719i	−0.0910643	+	0.995845i	$0.529027\pi$
$692$		−	30.0336i		−	0.0434011i
$693$		0			0
$694$	−819.409			−1.18070
$695$	582.989	+	802.415i	0.838833	+	1.15455i
$696$		0			0
$697$	−43.3971	+	133.563i	−0.0622627	+	0.191625i
$698$	−323.149	+	444.776i	−0.462964	+	0.637216i
$699$		0			0
$700$	15.3050	−	47.1039i	0.0218643	−	0.0672913i
$701$	856.342	−	278.242i	1.22160	−	0.396922i	0.373936	−	0.927454i	$-0.378008\pi$
$701$	856.342	−	278.242i	1.22160	−	0.396922i	0.847665	+	0.530532i	$0.178008\pi$
$702$		0			0
$703$	−107.397			−0.152769
$704$	−242.402	+	685.289i	−0.344321	+	0.973422i
$705$		0			0
$706$	−529.718	+	384.862i	−0.750308	+	0.545131i
$707$	293.112	−	95.2379i	0.414586	−	0.134707i
$708$		0			0
$709$	746.154	+	542.113i	1.05240	+	0.764616i	0.972668	−	0.232200i	$-0.0745924\pi$
$709$	746.154	+	542.113i	1.05240	+	0.764616i	0.0797356	+	0.996816i	$0.474592\pi$
$710$	1107.15	−	1523.86i	1.55937	−	2.14628i
$711$		0			0
$712$	232.745	+	716.315i	0.326889	+	1.00606i
$713$	−50.1776	−	69.0635i	−0.0703753	−	0.0968632i
$714$		0			0
$715$	−1033.21	−	1502.19i	−1.44504	−	2.10097i
$716$		−	28.6606i		−	0.0400288i
$717$		0			0
$718$	−301.593	−	928.206i	−0.420045	−	1.29277i
$719$	−9.82994	−	3.19394i	−0.0136717	−	0.00444220i	0.302173	−	0.953253i	$-0.402288\pi$
$719$	−9.82994	−	3.19394i	−0.0136717	−	0.00444220i	−0.315845	+	0.948811i	$0.602288\pi$
$720$		0			0
$721$	−409.261	−	297.346i	−0.567630	−	0.412407i
$722$	306.784	+	99.6802i	0.424909	+	0.138061i
$723$		0			0
$724$	−15.4989	+	11.2606i	−0.0214074	+	0.0155534i
$725$		−	1627.99i		−	2.24550i
$726$		0			0
$727$	119.809			0.164799			0.0823995	−	0.996599i	$-0.473742\pi$
$727$	119.809			0.164799			0.0823995	+	0.996599i	$0.473742\pi$
$728$	−430.741	−	592.864i	−0.591677	−	0.814373i
$729$		0			0
$730$	−200.357	+	616.635i	−0.274461	+	0.844705i
$731$	−243.599	+	335.285i	−0.333240	+	0.458666i
$732$		0			0
$733$	393.151	−	1210.00i	0.536359	−	1.65074i	−0.204334	−	0.978901i	$-0.565503\pi$
$733$	393.151	−	1210.00i	0.536359	−	1.65074i	0.740693	−	0.671843i	$-0.234497\pi$
$734$	308.657	−	100.289i	0.420514	−	0.136633i
$735$		0			0
$736$	12.7364			0.0173049
$737$	−1013.23	+	696.898i	−1.37480	+	0.945588i
$738$		0			0
$739$	136.706	−	99.3227i	0.184988	−	0.134402i	−0.491437	−	0.870913i	$-0.663528\pi$
$739$	136.706	−	99.3227i	0.184988	−	0.134402i	0.676425	+	0.736511i	$0.263528\pi$
$740$	9.81416	−	3.18882i	0.0132624	−	0.00430921i
$741$		0			0
$742$	678.515	+	492.970i	0.914441	+	0.664380i
$743$	566.208	−	779.319i	0.762057	−	1.04888i	−0.234983	−	0.971999i	$-0.575503\pi$
$743$	566.208	−	779.319i	0.762057	−	1.04888i	0.997040	−	0.0768822i	$-0.0244965\pi$
$744$		0			0
$745$	−269.095	−	828.190i	−0.361202	−	1.11167i
$746$	454.416	+	625.450i	0.609137	+	0.838405i
$747$		0			0
$748$	11.2125	+	3.96611i	0.0149900	+	0.00530229i
$749$		−	96.1986i		−	0.128436i
$750$		0			0
$751$	−127.573	−	392.629i	−0.169871	−	0.522808i	0.829491	−	0.558519i	$-0.188630\pi$
$751$	−127.573	−	392.629i	−0.169871	−	0.522808i	−0.999362	+	0.0357111i	$0.988630\pi$
$752$	−569.180	−	184.938i	−0.756889	−	0.245928i
$753$		0			0
$754$	−659.380	−	479.067i	−0.874509	−	0.635368i
$755$	2199.63	+	714.704i	2.91342	+	0.946627i
$756$		0			0
$757$	−729.792	+	530.225i	−0.964058	+	0.700429i	−0.954090	−	0.299521i	$-0.903173\pi$
$757$	−729.792	+	530.225i	−0.964058	+	0.700429i	−0.00996868	+	0.999950i	$0.503173\pi$
$758$		−	371.596i		−	0.490233i
$759$		0			0
$760$	1098.04			1.44479
$761$	571.395	+	786.458i	0.750848	+	1.03345i	0.997921	+	0.0644566i	$0.0205314\pi$
$761$	571.395	+	786.458i	0.750848	+	1.03345i	−0.247073	+	0.968997i	$0.579469\pi$
$762$		0			0
$763$	−81.8665	+	251.959i	−0.107295	+	0.330222i
$764$	20.1511	−	27.7356i	0.0263757	−	0.0363031i
$765$		0			0
$766$	−284.691	+	876.187i	−0.371659	+	1.14385i
$767$	−0.00711243	+	0.00231097i	−9.27305e−6	+	3.01300e-6i
$768$		0			0
$769$	1404.29			1.82613			0.913064	−	0.407817i	$-0.133710\pi$
$769$	1404.29			1.82613			0.913064	+	0.407817i	$0.133710\pi$
$770$	−309.300	−	1042.83i	−0.401689	−	1.35433i
$771$		0			0
$772$	1.78342	−	1.29573i	0.00231013	−	0.00167841i
$773$	−138.598	+	45.0331i	−0.179298	+	0.0582576i	−0.397290	−	0.917693i	$-0.630049\pi$
$773$	−138.598	+	45.0331i	−0.179298	+	0.0582576i	0.217992	+	0.975951i	$0.430049\pi$
$774$		0			0
$775$	821.147	+	596.599i	1.05955	+	0.769805i
$776$	250.636	−	344.971i	0.322985	−	0.444550i
$777$		0			0
$778$	276.225	+	850.133i	0.355045	+	1.09272i
$779$	−150.040	−	206.512i	−0.192605	−	0.265099i
$780$		0			0
$781$	−28.3035	+	1095.60i	−0.0362401	+	1.40282i
$782$			86.2080i			0.110240i
$783$		0			0
$784$	103.122	+	317.376i	0.131533	+	0.404816i
$785$	−270.921	−	88.0277i	−0.345123	−	0.112137i
$786$		0			0
$787$	740.082	+	537.701i	0.940383	+	0.683228i	0.948513	−	0.316739i	$-0.102588\pi$
$787$	740.082	+	537.701i	0.940383	+	0.683228i	−0.00812966	+	0.999967i	$0.502588\pi$
$788$	−12.7123	−	4.13047i	−0.0161323	−	0.00524171i
$789$		0			0
$790$	944.124	−	685.946i	1.19509	−	0.868286i
$791$		−	51.4460i		−	0.0650392i
$792$		0			0
$793$	82.3310			0.103822
$794$	194.744	+	268.042i	0.245269	+	0.337584i
$795$		0			0
$796$	−2.82334	+	8.68934i	−0.00354691	+	0.0109163i
$797$	219.280	−	301.813i	0.275132	−	0.378687i	−0.648982	−	0.760804i	$-0.724805\pi$
$797$	219.280	−	301.813i	0.275132	−	0.378687i	0.924114	+	0.382117i	$0.124805\pi$
$798$		0			0
$799$	−92.5677	+	284.894i	−0.115854	+	0.356563i
$800$	−144.021	+	46.7954i	−0.180027	+	0.0584942i
$801$		0			0
$802$	137.126			0.170981
$803$	−107.273	−	361.680i	−0.133590	−	0.450410i
$804$		0			0
$805$	−231.494	+	168.190i	−0.287570	+	0.208932i
$806$	483.278	−	157.027i	0.599600	−	0.194822i
$807$		0			0
$808$	−387.735	−	281.706i	−0.479870	−	0.348646i
$809$	−927.680	+	1276.84i	−1.14670	+	1.57830i	−0.395153	+	0.918615i	$0.629308\pi$
$809$	−927.680	+	1276.84i	−1.14670	+	1.57830i	−0.751546	+	0.659680i	$0.770692\pi$
$810$		0			0
$811$	222.549	+	684.936i	0.274413	+	0.844558i	0.989374	+	0.145393i	$0.0464447\pi$
$811$	222.549	+	684.936i	0.274413	+	0.844558i	−0.714960	+	0.699165i	$0.753555\pi$
$812$	10.3728	+	14.2769i	0.0127744	+	0.0175824i
$813$		0			0
$814$	100.668	−	131.289i	0.123671	−	0.161289i
$815$			2021.56i			2.48044i
$816$		0			0
$817$	−232.781	−	716.426i	−0.284921	−	0.876898i
$818$	−1034.99	−	336.290i	−1.26527	−	0.411113i
$819$		0			0
$820$	19.8427	+	14.4166i	0.0241984	+	0.0175812i
$821$	−887.035	−	288.215i	−1.08043	−	0.351054i	−0.285890	−	0.958263i	$-0.592289\pi$
$821$	−887.035	−	288.215i	−1.08043	−	0.351054i	−0.794542	+	0.607209i	$0.792289\pi$
$822$		0			0
$823$	−403.890	+	293.443i	−0.490753	+	0.356553i	−0.805474	−	0.592631i	$-0.798089\pi$
$823$	−403.890	+	293.443i	−0.490753	+	0.356553i	0.314721	+	0.949184i	$0.398089\pi$
$824$			786.670i			0.954697i
$825$		0			0
$826$	−0.00446168			−5.40155e−6
$827$	−428.774	−	590.156i	−0.518469	−	0.713611i	0.466850	−	0.884337i	$-0.345389\pi$
$827$	−428.774	−	590.156i	−0.518469	−	0.713611i	−0.985319	+	0.170726i	$0.945389\pi$
$828$		0			0
$829$	−457.435	+	1407.84i	−0.551792	+	1.69824i	0.152477	+	0.988307i	$0.451275\pi$
$829$	−457.435	+	1407.84i	−0.551792	+	1.69824i	−0.704269	+	0.709934i	$0.748725\pi$
$830$	724.866	−	997.692i	0.873332	−	1.20204i
$831$		0			0
$832$	−351.734	+	1082.52i	−0.422757	+	1.30111i
$833$	158.857	−	51.6158i	0.190705	−	0.0619638i
$834$		0			0
$835$	−146.710			−0.175700
$836$	−17.8114	+	12.2507i	−0.0213055	+	0.0146539i
$837$		0			0
$838$	488.732	−	355.085i	0.583212	−	0.423729i
$839$	932.042	−	302.839i	1.11090	−	0.360952i	0.304609	−	0.952477i	$-0.401474\pi$
$839$	932.042	−	302.839i	1.11090	−	0.360952i	0.806286	+	0.591525i	$0.201474\pi$
$840$		0			0
$841$	−211.101	−	153.374i	−0.251012	−	0.182371i
$842$	4.09561	−	5.63712i	0.00486414	−	0.00669492i
$843$		0			0
$844$	−11.9097	−	36.6542i	−0.0141110	−	0.0434292i
$845$	−722.214	−	994.042i	−0.854691	−	1.17638i
$846$		0			0
$847$	492.134	+	397.949i	0.581032	+	0.469834i
$848$		−	1258.49i		−	1.48407i
$849$		0			0
$850$	−316.740	−	974.825i	−0.372635	−	1.14685i
$851$	−41.3914	−	13.4489i	−0.0486385	−	0.0158036i
$852$		0			0
$853$	1124.90	+	817.288i	1.31876	+	0.958134i	0.999947	+	0.0103159i	$0.00328372\pi$
$853$	1124.90	+	817.288i	1.31876	+	0.958134i	0.318812	+	0.947818i	$0.396716\pi$
$854$	46.7150	+	15.1786i	0.0547014	+	0.0177735i
$855$		0			0
$856$	−121.025	+	87.9300i	−0.141385	+	0.102722i
$857$			1044.64i			1.21895i	0.792804	+	0.609477i	$0.208621\pi$
$857$			1044.64i			1.21895i	−0.792804	+	0.609477i	$0.791379\pi$
$858$		0			0
$859$	480.571			0.559454			0.279727	−	0.960080i	$-0.409756\pi$
$859$	480.571			0.559454			0.279727	+	0.960080i	$0.409756\pi$
$860$	42.5441	+	58.5569i	0.0494699	+	0.0680894i
$861$		0			0
$862$	−72.2018	+	222.214i	−0.0837608	+	0.257789i
$863$	383.286	−	527.547i	0.444132	−	0.611295i	−0.526992	−	0.849870i	$-0.676680\pi$
$863$	383.286	−	527.547i	0.444132	−	0.611295i	0.971124	+	0.238575i	$0.0766804\pi$
$864$		0			0
$865$	637.518	−	1962.08i	0.737014	−	2.26830i
$866$	372.678	−	121.090i	0.430344	−	0.139827i
$867$		0			0
$868$	−11.0024			−0.0126756
$869$	−226.436	+	640.151i	−0.260571	+	0.736653i
$870$		0			0
$871$	−1557.88	+	1131.87i	−1.78861	+	1.29950i
$872$	391.814	−	127.308i	0.449328	−	0.145995i
$873$		0			0
$874$	−126.769	−	92.1032i	−0.145045	−	0.105381i
$875$	1260.13	−	1734.42i	1.44015	−	1.98219i
$876$		0			0
$877$	−107.579	−	331.093i	−0.122667	−	0.377530i	0.870802	−	0.491634i	$-0.163600\pi$
$877$	−107.579	−	331.093i	−0.122667	−	0.377530i	−0.993469	+	0.114104i	$0.963600\pi$
$878$	−9.17460	−	12.6278i	−0.0104494	−	0.0143824i
$879$		0			0
$880$	−993.160	+	1295.25i	−1.12859	+	1.47188i
$881$		−	81.0204i		−	0.0919641i	−0.998942	−	0.0459821i	$-0.985358\pi$
$881$		−	81.0204i		−	0.0919641i	0.998942	−	0.0459821i	$-0.0146417\pi$
$882$		0			0
$883$	301.483	+	927.871i	0.341431	+	1.05082i	0.963467	+	0.267827i	$0.0863057\pi$
$883$	301.483	+	927.871i	0.341431	+	1.05082i	−0.622036	+	0.782989i	$0.713694\pi$
$884$	17.7119	+	5.75496i	0.0200361	+	0.00651013i
$885$		0			0
$886$	−745.945	−	541.961i	−0.841924	−	0.611694i
$887$	−1459.07	−	474.081i	−1.64495	−	0.534477i	−0.667314	−	0.744776i	$-0.732556\pi$
$887$	−1459.07	−	474.081i	−1.64495	−	0.534477i	−0.977637	+	0.210299i	$0.932556\pi$
$888$		0			0
$889$	911.831	−	662.484i	1.02568	−	0.745201i
$890$			1750.58i			1.96694i
$891$		0			0
$892$	25.6227			0.0287250
$893$	−320.040	−	440.497i	−0.358387	−	0.493278i
$894$		0			0
$895$	608.375	−	1872.38i	0.679748	−	2.09205i
$896$	−371.600	+	511.463i	−0.414732	+	0.570829i
$897$		0			0
$898$	448.363	−	1379.92i	0.499290	−	1.53666i
$899$	−343.950	+	111.756i	−0.382592	+	0.124312i
$900$		0			0
$901$	−629.917			−0.699131
$902$	393.094	+	10.1551i	0.435803	+	0.0112584i
$903$		0			0
$904$	−64.7231	+	47.0241i	−0.0715963	+	0.0520178i
$905$	−1251.57	+	406.659i	−1.38295	+	0.449346i
$906$		0			0
$907$	−841.629	−	611.479i	−0.927926	−	0.674178i	0.0175578	−	0.999846i	$-0.494411\pi$
$907$	−841.629	−	611.479i	−0.927926	−	0.674178i	−0.945484	+	0.325668i	$0.894411\pi$
$908$	−20.6187	+	28.3792i	−0.0227078	+	0.0312547i
$909$		0			0
$910$	−526.336	−	1619.90i	−0.578392	−	1.78011i
$911$	−219.624	−	302.287i	−0.241080	−	0.331819i	0.671282	−	0.741202i	$-0.265744\pi$
$911$	−219.624	−	302.287i	−0.241080	−	0.331819i	−0.912362	+	0.409383i	$0.865744\pi$
$912$		0			0
$913$	−18.5307	+	717.307i	−0.0202965	+	0.785659i
$914$			355.974i			0.389468i
$915$		0			0
$916$	−15.1720	−	46.6946i	−0.0165633	−	0.0509766i
$917$	828.702	+	269.262i	0.903710	+	0.293633i
$918$		0			0
$919$	−3.84227	−	2.79157i	−0.00418092	−	0.00303762i	0.585693	−	0.810533i	$-0.300822\pi$
$919$	−3.84227	−	2.79157i	−0.00418092	−	0.00303762i	−0.589874	+	0.807495i	$0.700822\pi$
$920$	423.192	+	137.503i	0.459991	+	0.149460i
$921$		0			0
$922$	−892.331	+	648.316i	−0.967821	+	0.703163i
$923$			1716.16i			1.85932i
$924$		0			0
$925$	517.460			0.559416
$926$	437.849	+	602.647i	0.472839	+	0.650807i
$927$		0			0
$928$	16.6736	−	51.3159i	0.0179672	−	0.0552974i
$929$	−290.209	+	399.438i	−0.312388	+	0.429966i	−0.936124	−	0.351670i	$-0.885614\pi$
$929$	−290.209	+	399.438i	−0.312388	+	0.429966i	0.623736	+	0.781635i	$0.285614\pi$
$930$		0			0
$931$	−93.8192	+	288.746i	−0.100772	+	0.310146i
$932$	48.5899	−	15.7878i	0.0521351	−	0.0169397i
$933$		0			0
$934$	−896.487			−0.959836
$935$	648.318	+	497.110i	0.693389	+	0.531668i
$936$		0			0
$937$	475.006	−	345.112i	0.506944	−	0.368316i	−0.304719	−	0.952442i	$-0.598563\pi$
$937$	475.006	−	345.112i	0.506944	−	0.368316i	0.811663	+	0.584126i	$0.198563\pi$
$938$	−1092.62	+	355.014i	−1.16484	+	0.378480i
$939$		0			0
$940$	42.3252	+	30.7511i	0.0450268	+	0.0327139i
$941$	626.791	−	862.704i	0.666090	−	0.916794i	−0.333574	−	0.942724i	$-0.608255\pi$
$941$	626.791	−	862.704i	0.666090	−	0.916794i	0.999664	+	0.0259296i	$0.00825458\pi$
$942$		0			0
$943$	−31.9656	−	98.3799i	−0.0338977	−	0.104326i
$944$	0.00393518	+	0.00541632i	4.16863e−6	+	5.73762e-6i
$945$		0			0
$946$	1094.01	+	386.975i	1.15645	+	0.409064i
$947$			198.618i			0.209734i	0.994486	+	0.104867i	$0.0334416\pi$
$947$			198.618i			0.209734i	−0.994486	+	0.104867i	$0.966558\pi$
$948$		0			0
$949$	−182.546	−	561.819i	−0.192356	−	0.592012i
$950$	1771.88	+	575.720i	1.86514	+	0.606021i
$951$		0			0
$952$	265.658	+	193.012i	0.279052	+	0.202743i
$953$	−1059.71	−	344.322i	−1.11198	−	0.361303i	−0.305276	−	0.952264i	$-0.598749\pi$
$953$	−1059.71	−	344.322i	−1.11198	−	0.361303i	−0.806700	+	0.590961i	$0.798749\pi$
$954$		0			0
$955$	1905.20	−	1384.21i	1.99497	−	1.44943i
$956$			34.0147i			0.0355802i
$957$		0			0
$958$	−1057.61			−1.10398
$959$	−134.501	−	185.124i	−0.140251	−	0.193039i
$960$		0			0
$961$	−227.289	+	699.524i	−0.236513	+	0.727913i
$962$	152.273	−	209.586i	0.158288	−	0.217864i
$963$		0			0
$964$	−18.1095	+	55.7354i	−0.0187858	+	0.0578168i
$965$	144.014	−	46.7930i	0.149237	−	0.0484902i
$966$		0			0
$967$	−983.820			−1.01739			−0.508697	−	0.860945i	$-0.669873\pi$
$967$	−983.820			−1.01739			−0.508697	+	0.860945i	$0.669873\pi$
$968$	50.8172	−	982.887i	0.0524971	−	1.01538i
$969$		0			0
$970$	801.801	−	582.542i	0.826599	−	0.600559i
$971$	110.243	−	35.8200i	0.113535	−	0.0368898i	−0.251698	−	0.967806i	$-0.580989\pi$
$971$	110.243	−	35.8200i	0.113535	−	0.0368898i	0.365234	+	0.930916i	$0.380989\pi$
$972$		0			0
$973$	−436.169	−	316.895i	−0.448272	−	0.325689i
$974$	−224.829	+	309.450i	−0.230830	+	0.317711i
$975$		0			0
$976$	−22.7761	−	70.0978i	−0.0233362	−	0.0718215i
$977$	−67.1734	−	92.4562i	−0.0687547	−	0.0946328i	0.773255	−	0.634095i	$-0.218627\pi$
$977$	−67.1734	−	92.4562i	−0.0687547	−	0.0946328i	−0.842009	+	0.539463i	$0.818627\pi$
$978$		0			0
$979$	−577.222	−	839.230i	−0.589603	−	0.857232i
$980$		−	29.1719i		−	0.0297673i
$981$		0			0
$982$	−123.764	−	380.907i	−0.126033	−	0.387889i
$983$	−970.714	−	315.404i	−0.987502	−	0.320859i	−0.229641	−	0.973275i	$-0.573755\pi$
$983$	−970.714	−	315.404i	−0.987502	−	0.320859i	−0.757861	+	0.652417i	$0.773755\pi$
$984$		0			0
$985$	−742.809	−	539.682i	−0.754121	−	0.547901i
$986$	347.338	+	112.857i	0.352270	+	0.114459i
$987$		0			0
$988$	−27.3858	+	19.8970i	−0.0277185	+	0.0201386i
$989$		−	305.265i		−	0.308661i
$990$		0			0
$991$	544.638			0.549584			0.274792	−	0.961504i	$-0.411391\pi$
$991$	544.638			0.549584			0.274792	+	0.961504i	$0.411391\pi$
$992$	19.7732	+	27.2155i	0.0199327	+	0.0274350i
$993$		0			0
$994$	−316.392	+	973.755i	−0.318302	+	0.979632i
$995$	−368.894	+	507.739i	−0.370748	+	0.510291i
$996$		0			0
$997$	386.146	−	1188.43i	0.387308	−	1.19201i	−0.547485	−	0.836816i	$-0.684415\pi$
$997$	386.146	−	1188.43i	0.387308	−	1.19201i	0.934792	−	0.355195i	$-0.115585\pi$
$998$	−1597.80	+	519.156i	−1.60100	+	0.520196i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.80.6	yes	32
3.2	odd	2	inner	99.3.l.a.80.3	yes	32
11.2	odd	10		1089.3.b.j.485.12		16
11.4	even	5	inner	99.3.l.a.26.3	✓	32
11.9	even	5		1089.3.b.i.485.5		16
33.2	even	10		1089.3.b.j.485.5		16
33.20	odd	10		1089.3.b.i.485.12		16
33.26	odd	10	inner	99.3.l.a.26.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.26.3	✓	32	11.4	even	5	inner
99.3.l.a.26.6	yes	32	33.26	odd	10	inner
99.3.l.a.80.3	yes	32	3.2	odd	2	inner
99.3.l.a.80.6	yes	32	1.1	even	1	trivial
1089.3.b.i.485.5		16	11.9	even	5
1089.3.b.i.485.12		16	33.20	odd	10
1089.3.b.j.485.5		16	33.2	even	10
1089.3.b.j.485.12		16	11.2	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15480 + 1.58945i) q^{2} +(0.0432885 - 0.133228i) q^{4} +(5.65603 - 7.78486i) q^{5} +(-1.61633 + 4.97456i) q^{7} +(7.73579 - 2.51351i) q^{8} +O(q^{10})\)	\(q+(1.15480 + 1.58945i) q^{2} +(0.0432885 - 0.133228i) q^{4} +(5.65603 - 7.78486i) q^{5} +(-1.61633 + 4.97456i) q^{7} +(7.73579 - 2.51351i) q^{8} +18.9052 q^{10} +(-9.06319 + 6.23366i) q^{11} +(-13.9350 + 10.1244i) q^{13} +(-9.77335 + 3.17555i) q^{14} +(12.4751 + 9.06367i) q^{16} +(4.53667 - 6.24419i) q^{17} +(4.33521 + 13.3424i) q^{19} +(-0.792322 - 1.09054i) q^{20} +(-20.3743 - 7.20684i) q^{22} +5.68512i q^{23} +(-20.8879 - 64.2864i) q^{25} +(-32.1844 - 10.4574i) q^{26} +(0.592783 + 0.430682i) q^{28} +(22.9057 + 7.44253i) q^{29} +(-12.1481 + 8.82612i) q^{31} -2.24031i q^{32} +15.1638 q^{34} +(29.5842 + 40.7192i) q^{35} +(-2.36563 + 7.28065i) q^{37} +(-16.2007 + 22.2984i) q^{38} +(24.1865 - 74.4385i) q^{40} +(-17.3048 + 5.62267i) q^{41} -53.6955 q^{43} +(0.438168 + 1.47732i) q^{44} +(-9.03621 + 6.56519i) q^{46} +(-36.9117 + 11.9934i) q^{47} +(17.5081 + 12.7204i) q^{49} +(78.0585 - 107.438i) q^{50} +(0.745630 + 2.29481i) q^{52} +(-47.9715 - 66.0271i) q^{53} +(-2.73355 + 105.813i) q^{55} +42.5448i q^{56} +(14.6221 + 45.0022i) q^{58} +(0.000412921 + 0.000134166i) q^{59} +(-3.86696 - 2.80951i) q^{61} +(-28.0573 - 9.11638i) q^{62} +(53.4611 - 38.8418i) q^{64} +165.746i q^{65} +111.796 q^{67} +(-0.635517 - 0.874715i) q^{68} +(-30.5571 + 94.0452i) q^{70} +(58.5632 - 80.6053i) q^{71} +(-10.5980 + 32.6171i) q^{73} +(-14.3041 + 4.64767i) q^{74} +1.96525 q^{76} +(-16.3606 - 55.1611i) q^{77} +(49.9398 - 36.2834i) q^{79} +(141.119 - 45.8523i) q^{80} +(-28.9205 - 21.0120i) q^{82} +(38.3421 - 52.7733i) q^{83} +(-22.9506 - 70.6347i) q^{85} +(-62.0076 - 85.3462i) q^{86} +(-54.4426 + 71.0027i) q^{88} +92.5976i q^{89} +(-27.8408 - 85.6851i) q^{91} +(0.757419 + 0.246100i) q^{92} +(-61.6886 - 44.8194i) q^{94} +(128.389 + 41.7160i) q^{95} +(42.4116 - 30.8138i) q^{97} +42.5178i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^7	\( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

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