LMFDB - Embedded newform 99.3.l.a.80.3

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			80.3
Character	$\chi$	$=$	99.80
Dual form			99.3.l.a.26.3

$q$-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	0.416006	−	0.909362i	$-0.363429\pi$
$2$	−1.15480	−	1.58945i	−0.577401	−	0.794724i	−0.993407	+	0.114637i	$0.963429\pi$
$3$		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	$0.612273\pi$
$5$	−5.65603	+	7.78486i	−1.13121	+	1.55697i	−0.785758	+	0.618533i	$0.787727\pi$
$6$		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	−0.921328	−	0.388787i	$-0.872894\pi$
$17$	−4.53667	+	6.24419i	−0.266863	+	0.367306i	0.654464	+	0.756093i	$0.272894\pi$
$18$		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	$-0.960559\pi$
$23$		−	5.68512i		−	0.247179i	0.992333	−	0.123590i	$-0.0394407\pi$
$24$		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	−0.113812	−	0.993502i	$-0.536306\pi$
$29$	−22.9057	−	7.44253i	−0.789853	−	0.256639i	−0.676042	+	0.736863i	$0.736306\pi$
$30$		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	−0.0902795	−	0.995916i	$-0.528776\pi$
$41$	17.3048	−	5.62267i	0.422068	−	0.137138i	0.512347	+	0.858778i	$0.328776\pi$
$42$		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	0.111231	−	0.993795i	$-0.464521\pi$
$47$	36.9117	−	11.9934i	0.785356	−	0.255178i	0.674125	+	0.738617i	$0.264521\pi$
$48$		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	$0.0797158\pi$
$53$	47.9715	+	66.0271i	0.905123	+	1.24580i	−0.0636816	+	0.997970i	$0.520284\pi$
$54$		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	0.309013	−	0.951058i	$-0.400001\pi$
$59$	−0.000412921	0	0.000134166i	−6.99867e−6	0	2.27400e-6i	−0.309020	+	0.951055i	$0.600001\pi$
$60$		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	$0.447551\pi$
$71$	−58.5632	+	80.6053i	−0.824834	+	1.13529i	−0.988863	+	0.148831i	$0.952449\pi$
$72$		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	−0.974912	−	0.222589i	$-0.928549\pi$
$83$	−38.3421	+	52.7733i	−0.461953	+	0.635823i	0.512960	+	0.858413i	$0.328549\pi$
$84$		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	$-0.825853\pi$
$89$		−	92.5976i		−	1.04042i	0.854038	−	0.520211i	$-0.174147\pi$
$90$		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	0.945288	−	0.326238i	$-0.105781\pi$
$101$	34.6336	+	47.6691i	0.342907	+	0.471971i	−0.602381	+	0.798209i	$0.705781\pi$
$102$		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	−0.226138	−	0.974095i	$-0.572610\pi$
$107$	17.4915	−	5.68333i	0.163472	−	0.0531152i	0.389610	+	0.920980i	$0.372610\pi$
$108$		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	−0.267334	−	0.963604i	$-0.586143\pi$
$113$	9.35427	−	3.03939i	0.0827811	−	0.0268972i	0.350115	+	0.936707i	$0.386143\pi$
$114$		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	$0.219343\pi$
$131$			166.588i			1.27166i	−0.771827	+	0.635832i	$0.780657\pi$
$132$		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	−0.704790	−	0.709416i	$-0.748959\pi$
$137$	25.7144	−	35.3928i	0.187696	−	0.258342i	0.892487	+	0.451074i	$0.148959\pi$
$138$		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	−0.949309	−	0.314345i	$-0.898215\pi$
$149$	−53.1924	+	73.2130i	−0.356996	+	0.491363i	0.592313	+	0.805708i	$0.298215\pi$
$150$		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	0.835005	−	0.550243i	$-0.185465\pi$
$167$	8.96158	+	12.3346i	0.0536622	+	0.0738596i	−0.781343	+	0.624102i	$0.785465\pi$
$168$		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	−0.831857	−	0.554990i	$-0.812722\pi$
$173$	−203.903	+	66.2520i	−1.17863	+	0.382960i	−0.346772	+	0.937950i	$0.612722\pi$
$174$		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	−0.797105	−	0.603840i	$-0.793636\pi$
$179$	−194.582	+	63.2234i	−1.08705	+	0.353204i	−0.289943	+	0.957044i	$0.593636\pi$
$180$		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	−0.372030	−	0.928221i	$-0.621338\pi$
$191$	−232.753	−	75.6261i	−1.21860	−	0.395948i	−0.846573	+	0.532272i	$0.821338\pi$
$192$		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	$0.0778610\pi$
$197$			95.4172i			0.484351i	−0.970232	+	0.242176i	$0.922139\pi$
$198$		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	0.782331	−	0.622863i	$-0.214031\pi$
$227$	238.155	+	77.3812i	1.04914	+	0.340886i	0.266809	+	0.963749i	$0.414031\pi$
$228$		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	$-0.913871\pi$
$233$	−214.372	−	295.058i	−0.920052	−	1.26634i	0.0435636	−	0.999051i	$-0.486129\pi$
$234$		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	0.216943	−	0.976184i	$-0.430391\pi$
$239$	230.931	−	75.0342i	0.966240	−	0.313951i	0.749297	+	0.662234i	$0.230391\pi$
$240$		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	0.998954	−	0.0457326i	$-0.0145622\pi$
$251$	162.338	+	223.439i	0.646766	+	0.890197i	−0.352188	+	0.935929i	$0.614562\pi$
$252$		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	0.591693	−	0.806163i	$-0.298460\pi$
$257$	153.309	+	49.8130i	0.596532	+	0.193825i	0.00483877	+	0.999988i	$0.498460\pi$
$258$		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	$-0.966365\pi$
$263$		−	55.4784i		−	0.210944i	0.994422	−	0.105472i	$-0.0336354\pi$
$264$		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	−0.740682	−	0.671856i	$-0.765497\pi$
$269$	34.2101	−	47.0861i	0.127175	−	0.175041i	0.867856	+	0.496815i	$0.165497\pi$
$270$		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	−0.724085	−	0.689711i	$-0.757738\pi$
$281$	43.7302	−	60.1895i	0.155624	−	0.214198i	0.879709	+	0.475513i	$0.157738\pi$
$282$		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	0.331025	−	0.943622i	$-0.392606\pi$
$293$	12.9456	+	4.20629i	0.0441831	+	0.0143559i	−0.286842	+	0.957978i	$0.592606\pi$
$294$		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	−0.168077	−	0.985774i	$-0.553756\pi$
$311$	85.6398	−	27.8260i	0.275369	−	0.0894728i	0.443446	+	0.896301i	$0.353756\pi$
$312$		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	0.895221	−	0.445623i	$-0.147018\pi$
$317$	61.7422	+	84.9808i	0.194770	+	0.268078i	−0.700451	+	0.713701i	$0.747018\pi$
$318$		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	$-0.594781\pi$
$347$	245.149	−	337.419i	0.706482	−	0.972388i	0.999866	−	0.0163937i	$-0.00521852\pi$
$348$		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	$-0.843512\pi$
$353$		−	333.271i		−	0.944111i	0.881569	−	0.472056i	$-0.156488\pi$
$354$		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	0.881125	−	0.472883i	$-0.156787\pi$
$359$	472.450	+	153.508i	1.31602	+	0.427600i	0.434891	+	0.900483i	$0.356787\pi$
$360$		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	$-0.990296\pi$
$383$	−275.626	−	379.367i	−0.719651	−	0.990514i	0.279885	−	0.960034i	$-0.409704\pi$
$384$		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	−0.305518	−	0.952186i	$-0.598830\pi$
$389$	−432.711	−	140.596i	−1.11237	−	0.361430i	−0.806850	+	0.590756i	$0.798830\pi$
$390$		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	−0.857101	−	0.515148i	$-0.827737\pi$
$401$	−41.0252	+	56.4664i	−0.102307	+	0.140814i	0.754794	+	0.655962i	$0.227737\pi$
$402$		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	$0.119590\pi$
$419$			307.485i			0.733855i	−0.930250	+	0.366927i	$0.880410\pi$
$420$		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	0.720187	−	0.693781i	$-0.244056\pi$
$431$	−69.9030	−	96.2132i	−0.162188	−	0.223232i	−0.882374	+	0.470548i	$0.844056\pi$
$432$		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	0.241666	−	0.970359i	$-0.422306\pi$
$443$	446.341	−	145.025i	1.00754	−	0.327370i	0.765875	+	0.642989i	$0.222306\pi$
$444$		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	$0.107364\pi$
$449$	434.087	+	597.469i	0.966786	+	1.33067i	0.0231324	+	0.999732i	$0.492636\pi$
$450$		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	$-0.791610\pi$
$461$		−	561.409i		−	1.21781i	0.793244	−	0.608903i	$-0.208390\pi$
$462$		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	−0.418735	−	0.908109i	$-0.637526\pi$
$467$	268.209	−	369.158i	0.574324	−	0.790489i	0.993059	+	0.117619i	$0.0375263\pi$
$468$		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	−0.338927	−	0.940813i	$-0.610064\pi$
$479$	316.414	−	435.507i	0.660573	−	0.909201i	0.999500	+	0.0316118i	$0.0100640\pi$
$480$		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	0.499717	−	0.866188i	$-0.333437\pi$
$491$	193.879	+	62.9950i	0.394865	+	0.128299i	−0.104853	+	0.994488i	$0.533437\pi$
$492$		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	−0.0400708	−	0.999197i	$-0.512758\pi$
$503$	258.957	−	84.1401i	0.514824	−	0.167277i	0.554895	+	0.831920i	$0.312758\pi$
$504$		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	−0.997501	−	0.0706498i	$-0.977493\pi$
$509$	−897.352	+	291.567i	−1.76297	+	0.572824i	−0.765468	+	0.643473i	$0.777493\pi$
$510$		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	−0.00239665	−	0.999997i	$-0.500763\pi$
$521$	−308.494	−	100.236i	−0.592119	−	0.192391i	−0.589722	+	0.807606i	$0.700763\pi$
$522$		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	−0.128627	−	0.991693i	$-0.541057\pi$
$557$	−454.284	−	147.606i	−0.815590	−	0.265001i	−0.686964	+	0.726692i	$0.741057\pi$
$558$		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	0.980889	−	0.194567i	$-0.0623303\pi$
$563$	277.409	+	381.820i	0.492733	+	0.678189i	−0.488156	+	0.872756i	$0.662330\pi$
$564$		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	−0.414475	−	0.910061i	$-0.636035\pi$
$569$	−122.262	+	39.7253i	−0.214871	+	0.0698159i	0.199603	+	0.979877i	$0.436035\pi$
$570$		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	0.623030	−	0.782198i	$-0.285902\pi$
$587$	391.709	+	127.274i	0.667307	+	0.216821i	0.0442770	+	0.999019i	$0.485902\pi$
$588$		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	$-0.781963\pi$
$593$		−	750.336i		−	1.26532i	0.774429	−	0.632661i	$-0.218037\pi$
$594$		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	−0.987649	−	0.156682i	$-0.949920\pi$
$599$	−319.528	+	439.793i	−0.533436	+	0.734211i	0.454213	+	0.890893i	$0.349920\pi$
$600$		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	$-0.984217\pi$
$617$		−	61.1594i		−	0.0991238i	0.998771	−	0.0495619i	$-0.0157825\pi$
$618$		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	−0.556280	−	0.830995i	$-0.687772\pi$
$641$	−331.957	+	107.859i	−0.517874	+	0.168268i	0.0384062	+	0.999262i	$0.487772\pi$
$642$		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	0.782561	−	0.622574i	$-0.213913\pi$
$647$	−33.2345	−	45.7434i	−0.0513671	−	0.0707007i	−0.833928	+	0.551874i	$0.813913\pi$
$648$		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	0.692226	−	0.721681i	$-0.256630\pi$
$653$	540.720	+	175.691i	0.828055	+	0.269051i	0.135829	+	0.990732i	$0.456630\pi$
$654$		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	$-0.906703\pi$
$659$		−	380.801i		−	0.577847i	0.957352	−	0.288923i	$-0.0932973\pi$
$660$		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	$-0.584065\pi$
$677$	499.429	−	687.405i	0.737709	−	1.01537i	0.998747	−	0.0500409i	$-0.0159352\pi$
$678$		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	$0.208343\pi$
$683$			831.602i			1.21757i	−0.793334	+	0.608786i	$0.791657\pi$
$684$		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	−0.847665	−	0.530532i	$-0.821992\pi$
$701$	−856.342	+	278.242i	−1.22160	+	0.396922i	−0.373936	+	0.927454i	$0.621992\pi$
$702$		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	0.315845	−	0.948811i	$-0.397712\pi$
$719$	9.82994	+	3.19394i	0.0136717	+	0.00444220i	−0.302173	+	0.953253i	$0.597712\pi$
$720$		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	$0.424497\pi$
$743$	−566.208	+	779.319i	−0.762057	+	1.04888i	−0.997040	+	0.0768822i	$0.975503\pi$
$744$		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	$-0.979469\pi$
$761$	−571.395	−	786.458i	−0.750848	−	1.03345i	0.247073	−	0.968997i	$-0.420531\pi$
$762$		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	−0.217992	−	0.975951i	$-0.569951\pi$
$773$	138.598	−	45.0331i	0.179298	−	0.0582576i	0.397290	+	0.917693i	$0.369951\pi$
$774$		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	−0.924114	−	0.382117i	$-0.875195\pi$
$797$	−219.280	+	301.813i	−0.275132	+	0.378687i	0.648982	+	0.760804i	$0.275195\pi$
$798$		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	$-0.370692\pi$
$809$	927.680	−	1276.84i	1.14670	−	1.57830i	0.751546	−	0.659680i	$-0.229308\pi$
$810$		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	0.794542	−	0.607209i	$-0.207711\pi$
$821$	887.035	+	288.215i	1.08043	+	0.351054i	0.285890	+	0.958263i	$0.407711\pi$
$822$		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	0.985319	−	0.170726i	$-0.0546112\pi$
$827$	428.774	+	590.156i	0.518469	+	0.713611i	−0.466850	+	0.884337i	$0.654611\pi$
$828$		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	−0.806286	−	0.591525i	$-0.798526\pi$
$839$	−932.042	+	302.839i	−1.11090	+	0.360952i	−0.304609	+	0.952477i	$0.598526\pi$
$840$		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	$-0.791379\pi$
$857$		−	1044.64i		−	1.21895i	0.792804	−	0.609477i	$-0.208621\pi$
$858$		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	−0.971124	−	0.238575i	$-0.923320\pi$
$863$	−383.286	+	527.547i	−0.444132	+	0.611295i	0.526992	+	0.849870i	$0.323320\pi$
$864$		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	$0.0146417\pi$
$881$			81.0204i			0.0919641i	−0.998942	+	0.0459821i	$0.985358\pi$
$882$		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	0.977637	−	0.210299i	$-0.0674437\pi$
$887$	1459.07	+	474.081i	1.64495	+	0.534477i	0.667314	+	0.744776i	$0.267444\pi$
$888$		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	0.912362	−	0.409383i	$-0.134256\pi$
$911$	219.624	+	302.287i	0.241080	+	0.331819i	−0.671282	+	0.741202i	$0.734256\pi$
$912$		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	−0.623736	−	0.781635i	$-0.714386\pi$
$929$	290.209	−	399.438i	0.312388	−	0.429966i	0.936124	+	0.351670i	$0.114386\pi$
$930$		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	−0.999664	−	0.0259296i	$-0.991745\pi$
$941$	−626.791	+	862.704i	−0.666090	+	0.916794i	0.333574	+	0.942724i	$0.391745\pi$
$942$		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	$-0.966558\pi$
$947$		−	198.618i		−	0.209734i	0.994486	−	0.104867i	$-0.0334416\pi$
$948$		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	0.806700	−	0.590961i	$-0.201251\pi$
$953$	1059.71	+	344.322i	1.11198	+	0.361303i	0.305276	+	0.952264i	$0.401251\pi$
$954$		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	−0.365234	−	0.930916i	$-0.619011\pi$
$971$	−110.243	+	35.8200i	−0.113535	+	0.0368898i	0.251698	+	0.967806i	$0.419011\pi$
$972$		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	0.842009	−	0.539463i	$-0.181373\pi$
$977$	67.1734	+	92.4562i	0.0687547	+	0.0946328i	−0.773255	+	0.634095i	$0.781373\pi$
$978$		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	0.757861	−	0.652417i	$-0.226245\pi$
$983$	970.714	+	315.404i	0.987502	+	0.320859i	0.229641	+	0.973275i	$0.426245\pi$
$984$		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.80.3	yes	32
3.2	odd	2	inner	99.3.l.a.80.6	yes	32
11.2	odd	10		1089.3.b.j.485.5		16
11.4	even	5	inner	99.3.l.a.26.6	yes	32
11.9	even	5		1089.3.b.i.485.12		16
33.2	even	10		1089.3.b.j.485.12		16
33.20	odd	10		1089.3.b.i.485.5		16
33.26	odd	10	inner	99.3.l.a.26.3	✓	32

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