LMFDB - Embedded newform 99.3.l.a.71.5

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			71.5
Character	$\chi$	$=$	99.71
Dual form			99.3.l.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.296118 - 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(-5.65537 - 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(-1.44634 + 1.99072i) q^{8} +O(q^{10})$	\(q+(0.296118 - 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(-5.65537 - 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(-1.44634 + 1.99072i) q^{8} -1.85145 q^{10} +(-0.122358 - 10.9993i) q^{11} +(5.77807 + 17.7831i) q^{13} +(-1.58689 + 2.18416i) q^{14} +(4.58769 - 14.1195i) q^{16} +(-9.12965 - 2.96640i) q^{17} +(-4.66262 - 3.38759i) q^{19} +(22.0732 - 7.17203i) q^{20} +(-1.09453 - 3.24532i) q^{22} +41.5830i q^{23} +(8.38122 + 6.08931i) q^{25} +(3.42197 + 4.70994i) q^{26} +(10.4582 - 32.1870i) q^{28} +(-10.2118 - 14.0553i) q^{29} +(-4.22647 - 13.0077i) q^{31} -14.4651i q^{32} -2.98886 q^{34} +(49.0378 - 15.9333i) q^{35} +(5.83617 - 4.24023i) q^{37} +(-1.70662 - 0.554514i) q^{38} +(11.8376 - 8.60055i) q^{40} +(-31.2326 + 42.9880i) q^{41} +43.3682 q^{43} +(25.6206 + 34.4512i) q^{44} +(4.00089 + 12.3135i) q^{46} +(11.0762 - 15.2451i) q^{47} +(8.09204 - 24.9047i) q^{49} +(3.06770 + 0.996758i) q^{50} +(-59.0422 - 42.8967i) q^{52} +(-51.8817 + 16.8574i) q^{53} +(-19.5197 + 62.4300i) q^{55} -21.3365i q^{56} +(-4.37620 - 3.17949i) q^{58} +(-20.7671 - 28.5835i) q^{59} +(-36.4184 + 112.084i) q^{61} +(-2.50306 - 3.44517i) q^{62} +(16.9590 + 52.1945i) q^{64} -111.187i q^{65} -91.5111 q^{67} +(35.6335 - 11.5780i) q^{68} +(12.9879 - 9.43628i) q^{70} +(-110.147 - 35.7890i) q^{71} +(42.8336 - 31.1204i) q^{73} +(1.32022 - 1.81713i) q^{74} +22.4946 q^{76} +(56.9185 + 76.5365i) q^{77} +(0.633214 + 1.94883i) q^{79} +(-51.8902 + 71.4207i) q^{80} +(-5.11246 + 15.7345i) q^{82} +(27.4089 + 8.90568i) q^{83} +(46.1806 + 33.5522i) q^{85} +(12.8421 - 4.17265i) q^{86} +(22.0736 + 15.6652i) q^{88} +134.980i q^{89} +(-131.168 - 95.2991i) q^{91} +(-95.3981 - 131.304i) q^{92} +(1.81306 - 5.58001i) q^{94} +(20.1440 + 27.7259i) q^{95} +(-3.08284 - 9.48799i) q^{97} -8.15330i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	0.296118	−	0.0962144i	0.148059	−	0.0481072i	−0.234050	−	0.972225i	$-0.575198\pi$
$2$	0.296118	−	0.0962144i	0.148059	−	0.0481072i	0.382109	+	0.924117i	$0.375198\pi$
$3$		0			0
$3$		0			0
$4$	−3.15764	+	2.29416i	−0.789410	+	0.573540i
$5$	−5.65537	−	1.83754i	−1.13107	−	0.367508i	−0.317090	−	0.948396i	$-0.602706\pi$
$5$	−5.65537	−	1.83754i	−1.13107	−	0.367508i	−0.813984	+	0.580887i	$0.802706\pi$
$6$		0			0
$7$	−7.01499	+	5.09669i	−1.00214	+	0.728099i	−0.962546	−	0.271117i	$-0.912607\pi$
$7$	−7.01499	+	5.09669i	−1.00214	+	0.728099i	−0.0395956	+	0.999216i	$0.512607\pi$
$8$	−1.44634	+	1.99072i	−0.180793	+	0.248840i
$9$		0			0
$10$	−1.85145			−0.185145
$11$	−0.122358	−	10.9993i	−0.0111235	−	0.999938i
$11$	−0.122358	−	10.9993i	−0.0111235	−	0.999938i
$12$		0			0
$13$	5.77807	+	17.7831i	0.444467	+	1.36793i	0.883067	+	0.469246i	$0.155474\pi$
$13$	5.77807	+	17.7831i	0.444467	+	1.36793i	−0.438601	+	0.898682i	$0.644526\pi$
$14$	−1.58689	+	2.18416i	−0.113349	+	0.156012i
$15$		0			0
$16$	4.58769	−	14.1195i	0.286731	−	0.882467i
$17$	−9.12965	−	2.96640i	−0.537038	−	0.174494i	0.0279257	−	0.999610i	$-0.491110\pi$
$17$	−9.12965	−	2.96640i	−0.537038	−	0.174494i	−0.564964	+	0.825116i	$0.691110\pi$
$18$		0			0
$19$	−4.66262	−	3.38759i	−0.245401	−	0.178294i	0.458285	−	0.888805i	$-0.348464\pi$
$19$	−4.66262	−	3.38759i	−0.245401	−	0.178294i	−0.703686	+	0.710511i	$0.748464\pi$
$20$	22.0732	−	7.17203i	1.10366	−	0.358601i
$21$		0			0
$22$	−1.09453	−	3.24532i	−0.0497512	−	0.147514i
$23$			41.5830i			1.80796i	0.427578	+	0.903979i	$0.359367\pi$
$23$			41.5830i			1.80796i	−0.427578	+	0.903979i	$0.640633\pi$
$24$		0			0
$25$	8.38122	+	6.08931i	0.335249	+	0.243572i
$26$	3.42197	+	4.70994i	0.131614	+	0.181152i
$27$		0			0
$28$	10.4582	−	32.1870i	0.373507	−	1.14954i
$29$	−10.2118	−	14.0553i	−0.352129	−	0.484665i	0.595805	−	0.803129i	$-0.296833\pi$
$29$	−10.2118	−	14.0553i	−0.352129	−	0.484665i	−0.947935	+	0.318464i	$0.896833\pi$
$30$		0			0
$31$	−4.22647	−	13.0077i	−0.136338	−	0.419604i	0.859458	−	0.511206i	$-0.170801\pi$
$31$	−4.22647	−	13.0077i	−0.136338	−	0.419604i	−0.995796	+	0.0916020i	$0.970801\pi$
$32$		−	14.4651i		−	0.452034i
$33$		0			0
$34$	−2.98886			−0.0879076
$35$	49.0378	−	15.9333i	1.40108	−	0.455238i
$36$		0			0
$37$	5.83617	−	4.24023i	0.157734	−	0.114601i	−0.506118	−	0.862464i	$-0.668920\pi$
$37$	5.83617	−	4.24023i	0.157734	−	0.114601i	0.663853	+	0.747863i	$0.268920\pi$
$38$	−1.70662	−	0.554514i	−0.0449110	−	0.0145925i
$39$		0			0
$40$	11.8376	−	8.60055i	0.295941	−	0.215014i
$41$	−31.2326	+	42.9880i	−0.761771	+	1.04849i	0.235294	+	0.971924i	$0.424395\pi$
$41$	−31.2326	+	42.9880i	−0.761771	+	1.04849i	−0.997065	+	0.0765632i	$0.975605\pi$
$42$		0			0
$43$	43.3682			1.00856			0.504282	−	0.863539i	$-0.331757\pi$
$43$	43.3682			1.00856			0.504282	+	0.863539i	$0.331757\pi$
$44$	25.6206	+	34.4512i	0.582285	+	0.782981i
$45$		0			0
$46$	4.00089	+	12.3135i	0.0869758	+	0.267684i
$47$	11.0762	−	15.2451i	0.235663	−	0.324363i	−0.674763	−	0.738035i	$-0.735754\pi$
$47$	11.0762	−	15.2451i	0.235663	−	0.324363i	0.910426	+	0.413672i	$0.135754\pi$
$48$		0			0
$49$	8.09204	−	24.9047i	0.165144	−	0.508260i
$50$	3.06770	+	0.996758i	0.0613541	+	0.0199352i
$51$		0			0
$52$	−59.0422	−	42.8967i	−1.13543	−	0.824937i
$53$	−51.8817	+	16.8574i	−0.978899	+	0.318064i	−0.754403	−	0.656411i	$-0.772074\pi$
$53$	−51.8817	+	16.8574i	−0.978899	+	0.318064i	−0.224496	+	0.974475i	$0.572074\pi$
$54$		0			0
$55$	−19.5197	+	62.4300i	−0.354904	+	1.13509i
$56$		−	21.3365i		−	0.381008i
$57$		0			0
$58$	−4.37620	−	3.17949i	−0.0754517	−	0.0548189i
$59$	−20.7671	−	28.5835i	−0.351985	−	0.484466i	0.595909	−	0.803052i	$-0.296792\pi$
$59$	−20.7671	−	28.5835i	−0.351985	−	0.484466i	−0.947894	+	0.318586i	$0.896792\pi$
$60$		0			0
$61$	−36.4184	+	112.084i	−0.597023	+	1.83745i	−0.0526365	+	0.998614i	$0.516762\pi$
$61$	−36.4184	+	112.084i	−0.597023	+	1.83745i	−0.544387	+	0.838834i	$0.683238\pi$
$62$	−2.50306	−	3.44517i	−0.0403720	−	0.0555673i
$63$		0			0
$64$	16.9590	+	52.1945i	0.264985	+	0.815539i
$65$		−	111.187i		−	1.71057i
$66$		0			0
$67$	−91.5111			−1.36584			−0.682919	−	0.730494i	$-0.739290\pi$
$67$	−91.5111			−1.36584			−0.682919	+	0.730494i	$0.739290\pi$
$68$	35.6335	−	11.5780i	0.524022	−	0.170265i
$69$		0			0
$70$	12.9879	−	9.43628i	0.185542	−	0.134804i
$71$	−110.147	−	35.7890i	−1.55137	−	0.504070i	−0.596883	−	0.802328i	$-0.703594\pi$
$71$	−110.147	−	35.7890i	−1.55137	−	0.504070i	−0.954485	+	0.298258i	$0.903594\pi$
$72$		0			0
$73$	42.8336	−	31.1204i	0.586762	−	0.426307i	−0.254394	−	0.967101i	$-0.581876\pi$
$73$	42.8336	−	31.1204i	0.586762	−	0.426307i	0.841156	+	0.540793i	$0.181876\pi$
$74$	1.32022	−	1.81713i	0.0178408	−	0.0245558i
$75$		0			0
$76$	22.4946			0.295981
$77$	56.9185	+	76.5365i	0.739201	+	0.993981i
$78$		0			0
$79$	0.633214	+	1.94883i	0.00801537	+	0.0246688i	0.954984	−	0.296657i	$-0.0958717\pi$
$79$	0.633214	+	1.94883i	0.00801537	+	0.0246688i	−0.946969	+	0.321325i	$0.895872\pi$
$80$	−51.8902	+	71.4207i	−0.648627	+	0.892759i
$81$		0			0
$82$	−5.11246	+	15.7345i	−0.0623470	+	0.191884i
$83$	27.4089	+	8.90568i	0.330227	+	0.107297i	0.469438	−	0.882965i	$-0.344457\pi$
$83$	27.4089	+	8.90568i	0.330227	+	0.107297i	−0.139211	+	0.990263i	$0.544457\pi$
$84$		0			0
$85$	46.1806	+	33.5522i	0.543302	+	0.394732i
$86$	12.8421	−	4.17265i	0.149327	−	0.0485192i
$87$		0			0
$88$	22.0736	+	15.6652i	0.250836	+	0.178014i
$89$			134.980i			1.51663i	0.651891	+	0.758313i	$0.273976\pi$
$89$			134.980i			1.51663i	−0.651891	+	0.758313i	$0.726024\pi$
$90$		0			0
$91$	−131.168	−	95.2991i	−1.44141	−	1.04724i
$92$	−95.3981	−	131.304i	−1.03694	−	1.42722i
$93$		0			0
$94$	1.81306	−	5.58001i	0.0192878	−	0.0593619i
$95$	20.1440	+	27.7259i	0.212042	+	0.291851i
$96$		0			0
$97$	−3.08284	−	9.48799i	−0.0317818	−	0.0978144i	0.933907	−	0.357515i	$-0.116376\pi$
$97$	−3.08284	−	9.48799i	−0.0317818	−	0.0978144i	−0.965689	+	0.259701i	$0.916376\pi$
$98$		−	8.15330i		−	0.0831970i
$99$		0			0
$100$	−40.4347			−0.404347
$101$	163.987	−	53.2825i	1.62363	−	0.527550i	0.650837	−	0.759218i	$-0.274418\pi$
$101$	163.987	−	53.2825i	1.62363	−	0.527550i	0.972795	+	0.231668i	$0.0744182\pi$
$102$		0			0
$103$	91.9355	−	66.7951i	0.892578	−	0.648496i	−0.0439711	−	0.999033i	$-0.514001\pi$
$103$	91.9355	−	66.7951i	0.892578	−	0.648496i	0.936549	+	0.350537i	$0.114001\pi$
$104$	−43.7582	−	14.2179i	−0.420752	−	0.136711i
$105$		0			0
$106$	−13.7411	+	9.98353i	−0.129633	+	0.0941842i
$107$	48.8875	−	67.2879i	0.456893	−	0.628859i	−0.516968	−	0.856005i	$-0.672939\pi$
$107$	48.8875	−	67.2879i	0.456893	−	0.628859i	0.973861	+	0.227146i	$0.0729395\pi$
$108$		0			0
$109$	125.432			1.15075			0.575377	−	0.817888i	$-0.304855\pi$
$109$	125.432			1.15075			0.575377	+	0.817888i	$0.304855\pi$
$110$	0.226540	+	20.3647i	0.00205945	+	0.185134i
$111$		0			0
$112$	39.7799	+	122.430i	0.355178	+	1.09313i
$113$	−59.4756	+	81.8612i	−0.526333	+	0.724435i	−0.986566	−	0.163363i	$-0.947766\pi$
$113$	−59.4756	+	81.8612i	−0.526333	+	0.724435i	0.460233	+	0.887798i	$0.347766\pi$
$114$		0			0
$115$	76.4105	−	235.167i	0.664439	−	2.04493i
$116$	64.4901	+	20.9541i	0.555949	+	0.180639i
$117$		0			0
$118$	−8.89966	−	6.46598i	−0.0754208	−	0.0547964i
$119$	79.1632	−	25.7217i	0.665237	−	0.216149i
$120$		0			0
$121$	−120.970	+	2.69171i	−0.999753	+	0.0222455i
$122$			36.6941i			0.300771i
$123$		0			0
$124$	43.1875	+	31.3775i	0.348286	+	0.253045i
$125$	51.1707	+	70.4305i	0.409366	+	0.563444i
$126$		0			0
$127$	38.3169	−	117.927i	0.301708	−	0.928561i	−0.679178	−	0.733974i	$-0.737663\pi$
$127$	38.3169	−	117.927i	0.301708	−	0.928561i	0.980885	−	0.194587i	$-0.0623366\pi$
$128$	44.0532	+	60.6340i	0.344166	+	0.473703i
$129$		0			0
$130$	−10.6978	−	32.9245i	−0.0822909	−	0.253265i
$131$		−	52.5607i		−	0.401227i	−0.979670	−	0.200614i	$-0.935706\pi$
$131$		−	52.5607i		−	0.401227i	0.979670	−	0.200614i	$-0.0642935\pi$
$132$		0			0
$133$	49.9738			0.375743
$134$	−27.0980	+	8.80469i	−0.202224	+	0.0657066i
$135$		0			0
$136$	19.1099	−	13.8841i	0.140514	−	0.102089i
$137$	−119.626	−	38.8689i	−0.873185	−	0.283715i	−0.162060	−	0.986781i	$-0.551814\pi$
$137$	−119.626	−	38.8689i	−0.873185	−	0.283715i	−0.711125	+	0.703066i	$0.751814\pi$
$138$		0			0
$139$	−43.4005	+	31.5323i	−0.312234	+	0.226851i	−0.732855	−	0.680385i	$-0.761812\pi$
$139$	−43.4005	+	31.5323i	−0.312234	+	0.226851i	0.420620	+	0.907237i	$0.361812\pi$
$140$	−118.290	+	162.812i	−0.844928	+	1.16294i
$141$		0			0
$142$	−36.0599			−0.253943
$143$	194.895	−	65.7307i	1.36290	−	0.459655i
$144$		0			0
$145$	31.9241	+	98.2523i	0.220166	+	0.677602i
$146$	9.68955	−	13.3365i	0.0663668	−	0.0913460i
$147$		0			0
$148$	−8.70077	+	26.7782i	−0.0587890	+	0.180934i
$149$	4.02993	+	1.30940i	0.0270465	+	0.00878795i	0.322509	−	0.946566i	$-0.395474\pi$
$149$	4.02993	+	1.30940i	0.0270465	+	0.00878795i	−0.295462	+	0.955354i	$0.595474\pi$
$150$		0			0
$151$	−76.3610	−	55.4795i	−0.505702	−	0.367414i	0.305489	−	0.952196i	$-0.401180\pi$
$151$	−76.3610	−	55.4795i	−0.505702	−	0.367414i	−0.811191	+	0.584782i	$0.801180\pi$
$152$	13.4875	−	4.38236i	0.0887336	−	0.0288313i
$153$		0			0
$154$	24.2185	+	17.1874i	0.157263	+	0.111607i
$155$			81.3299i			0.524709i
$156$		0			0
$157$	120.287	+	87.3939i	0.766162	+	0.556649i	0.900794	−	0.434247i	$-0.142985\pi$
$157$	120.287	+	87.3939i	0.766162	+	0.556649i	−0.134632	+	0.990896i	$0.542985\pi$
$158$	0.375011	+	0.516159i	0.00237349	+	0.00326683i
$159$		0			0
$160$	−26.5802	+	81.8054i	−0.166126	+	0.511284i
$161$	−211.936	−	291.705i	−1.31637	−	1.81183i
$162$		0			0
$163$	−28.3527	−	87.2606i	−0.173943	−	0.535341i	0.825641	−	0.564196i	$-0.190814\pi$
$163$	−28.3527	−	87.2606i	−0.173943	−	0.535341i	−0.999584	+	0.0288552i	$0.990814\pi$
$164$		−	207.393i		−	1.26459i
$165$		0			0
$166$	8.97310			0.0540548
$167$	13.5693	−	4.40895i	0.0812536	−	0.0264009i	−0.268108	−	0.963389i	$-0.586398\pi$
$167$	13.5693	−	4.40895i	0.0812536	−	0.0264009i	0.349362	+	0.936988i	$0.386398\pi$
$168$		0			0
$169$	−146.127	+	106.168i	−0.864660	+	0.628212i
$170$	16.9031	+	5.49215i	0.0994300	+	0.0323068i
$171$		0			0
$172$	−136.941	+	99.4936i	−0.796170	+	0.578451i
$173$	−136.531	+	187.919i	−0.789197	+	1.08624i	0.205011	+	0.978760i	$0.434277\pi$
$173$	−136.531	+	187.919i	−0.789197	+	1.08624i	−0.994208	+	0.107476i	$0.965723\pi$
$174$		0			0
$175$	−89.8295			−0.513312
$176$	−155.866	−	48.7339i	−0.885601	−	0.276897i
$177$		0			0
$178$	12.9870	+	39.9698i	0.0729606	+	0.224550i
$179$	84.4401	−	116.222i	0.471733	−	0.649284i	−0.505157	−	0.863027i	$-0.668566\pi$
$179$	84.4401	−	116.222i	0.471733	−	0.649284i	0.976890	+	0.213743i	$0.0685655\pi$
$180$		0			0
$181$	−74.0732	+	227.974i	−0.409244	+	1.25952i	0.508055	+	0.861324i	$0.330365\pi$
$181$	−74.0732	+	227.974i	−0.409244	+	1.25952i	−0.917299	+	0.398199i	$0.869635\pi$
$182$	−48.0103	−	15.5995i	−0.263793	−	0.0857114i
$183$		0			0
$184$	−82.7802	−	60.1433i	−0.449892	−	0.326866i
$185$	−40.7973	+	13.2558i	−0.220526	+	0.0716532i
$186$		0			0
$187$	−31.5113	+	100.783i	−0.168510	+	0.538946i
$188$			73.5489i			0.391218i
$189$		0			0
$190$	8.63262	+	6.27197i	0.0454349	+	0.0330104i
$191$	22.0606	+	30.3638i	0.115501	+	0.158973i	0.862853	−	0.505455i	$-0.168675\pi$
$191$	22.0606	+	30.3638i	0.115501	+	0.158973i	−0.747352	+	0.664428i	$0.768675\pi$
$192$		0			0
$193$	62.9072	−	193.608i	0.325944	−	1.00315i	−0.645069	−	0.764125i	$-0.723171\pi$
$193$	62.9072	−	193.608i	0.325944	−	1.00315i	0.971013	−	0.239028i	$-0.0768288\pi$
$194$	−1.82576	−	2.51295i	−0.00941115	−	0.0129533i
$195$		0			0
$196$	31.5837	+	97.2047i	0.161141	+	0.495942i
$197$			208.477i			1.05826i	0.848541	+	0.529129i	$0.177481\pi$
$197$			208.477i			1.05826i	−0.848541	+	0.529129i	$0.822519\pi$
$198$		0			0
$199$	−249.874			−1.25565			−0.627825	−	0.778355i	$-0.716055\pi$
$199$	−249.874			−1.25565			−0.627825	+	0.778355i	$0.716055\pi$
$200$	−24.2442	+	7.87743i	−0.121221	+	0.0393872i
$201$		0			0
$202$	43.4328	−	31.5558i	0.215014	−	0.156217i
$203$	143.271	+	46.5515i	0.705767	+	0.229318i
$204$		0			0
$205$	255.624	−	185.722i	1.24695	−	0.905960i
$206$	20.7971	−	28.6247i	0.100957	−	0.138955i
$207$		0			0
$208$	277.595			1.33459
$209$	−36.6907	+	51.7002i	−0.175554	+	0.247369i
$210$		0			0
$211$	37.5620	+	115.604i	0.178019	+	0.547885i	0.999758	−	0.0219776i	$-0.00699627\pi$
$211$	37.5620	+	115.604i	0.178019	+	0.547885i	−0.821740	+	0.569863i	$0.806996\pi$
$212$	125.150	−	172.254i	0.590331	−	0.812520i
$213$		0			0
$214$	8.00238	−	24.6288i	0.0373943	−	0.115088i
$215$	−245.263	−	79.6909i	−1.14076	−	0.370655i
$216$		0			0
$217$	95.9451	+	69.7082i	0.442143	+	0.321236i
$218$	37.1427	−	12.0684i	0.170379	−	0.0553595i
$219$		0			0
$220$	−81.5883	−	241.913i	−0.370856	−	1.09960i
$221$		−	179.493i		−	0.812186i
$222$		0			0
$223$	58.0972	+	42.2101i	0.260526	+	0.189283i	0.710379	−	0.703820i	$-0.248524\pi$
$223$	58.0972	+	42.2101i	0.260526	+	0.189283i	−0.449853	+	0.893103i	$0.648524\pi$
$224$	73.7241	+	101.473i	0.329125	+	0.453002i
$225$		0			0
$226$	−9.73555	+	29.9629i	−0.0430776	+	0.132579i
$227$	137.568	+	189.346i	0.606028	+	0.834125i	0.996243	−	0.0865981i	$-0.0275996\pi$
$227$	137.568	+	189.346i	0.606028	+	0.834125i	−0.390216	+	0.920723i	$0.627600\pi$
$228$		0			0
$229$	21.0536	+	64.7964i	0.0919372	+	0.282954i	0.986443	−	0.164102i	$-0.0524726\pi$
$229$	21.0536	+	64.7964i	0.0919372	+	0.282954i	−0.894506	+	0.447056i	$0.852473\pi$
$230$		−	76.9889i		−	0.334735i
$231$		0			0
$232$	42.7498			0.184267
$233$	101.511	−	32.9829i	0.435669	−	0.141558i	−0.0829673	−	0.996552i	$-0.526440\pi$
$233$	101.511	−	32.9829i	0.435669	−	0.141558i	0.518637	+	0.854995i	$0.326440\pi$
$234$		0			0
$235$	−90.6533	+	65.8635i	−0.385759	+	0.280270i
$236$	131.150	+	42.6133i	0.555721	+	0.180565i
$237$		0			0
$238$	20.9668	−	15.2333i	0.0880959	−	0.0640054i
$239$	204.895	−	282.014i	0.857302	−	1.17997i	−0.124904	−	0.992169i	$-0.539862\pi$
$239$	204.895	−	282.014i	0.857302	−	1.17997i	0.982206	−	0.187806i	$-0.0601377\pi$
$240$		0			0
$241$	−377.429			−1.56609			−0.783047	−	0.621962i	$-0.786336\pi$
$241$	−377.429			−1.56609			−0.783047	+	0.621962i	$0.786336\pi$
$242$	−35.5624	+	12.4361i	−0.146952	+	0.0513889i
$243$		0			0
$244$	−142.143	−	437.472i	−0.582554	−	1.79292i
$245$	−91.5270	+	125.976i	−0.373580	+	0.514188i
$246$		0			0
$247$	33.3009	−	102.489i	0.134821	−	0.414937i
$248$	32.0077	+	10.3999i	0.129063	+	0.0419352i
$249$		0			0
$250$	21.9290	+	15.9323i	0.0877159	+	0.0637293i
$251$	−286.896	+	93.2182i	−1.14301	+	0.371387i	−0.818507	−	0.574497i	$-0.805198\pi$
$251$	−286.896	+	93.2182i	−1.14301	+	0.371387i	−0.324506	+	0.945884i	$0.605198\pi$
$252$		0			0
$253$	457.385	−	5.08802i	1.80785	−	0.0201107i
$254$		−	38.6069i		−	0.151996i
$255$		0			0
$256$	−158.718	−	115.316i	−0.619994	−	0.450452i
$257$	8.80297	+	12.1162i	0.0342528	+	0.0471449i	0.825800	−	0.563963i	$-0.190724\pi$
$257$	8.80297	+	12.1162i	0.0342528	+	0.0471449i	−0.791547	+	0.611108i	$0.790724\pi$
$258$		0			0
$259$	−19.3296	+	59.4903i	−0.0746316	+	0.229692i
$260$	255.081	+	351.089i	0.981082	+	1.35034i
$261$		0			0
$262$	−5.05710	−	15.5642i	−0.0193019	−	0.0594052i
$263$			470.671i			1.78962i	0.446443	+	0.894812i	$0.352691\pi$
$263$			470.671i			1.78962i	−0.446443	+	0.894812i	$0.647309\pi$
$264$		0			0
$265$	324.386			1.22410
$266$	14.7981	−	4.80820i	0.0556320	−	0.0180759i
$267$		0			0
$268$	288.959	−	209.941i	1.07821	−	0.783362i
$269$	−190.046	−	61.7497i	−0.706491	−	0.229553i	−0.0663343	−	0.997797i	$-0.521130\pi$
$269$	−190.046	−	61.7497i	−0.706491	−	0.229553i	−0.640156	+	0.768245i	$0.721130\pi$
$270$		0			0
$271$	70.6026	−	51.2958i	0.260526	−	0.189283i	−0.449853	−	0.893103i	$-0.648524\pi$
$271$	70.6026	−	51.2958i	0.260526	−	0.189283i	0.710379	+	0.703819i	$0.248524\pi$
$272$	−83.7680	+	115.297i	−0.307971	+	0.423885i
$273$		0			0
$274$	−39.1632			−0.142931
$275$	65.9528	−	92.9328i	0.239828	−	0.337937i
$276$		0			0
$277$	−92.4637	−	284.574i	−0.333804	−	1.02734i	−0.967308	−	0.253604i	$-0.918384\pi$
$277$	−92.4637	−	284.574i	−0.333804	−	1.02734i	0.633504	−	0.773739i	$-0.281616\pi$
$278$	−9.81780	+	13.5130i	−0.0353158	+	0.0486080i
$279$		0			0
$280$	−39.2066	+	120.666i	−0.140024	+	0.430949i
$281$	284.085	+	92.3049i	1.01098	+	0.328487i	0.767245	−	0.641354i	$-0.221627\pi$
$281$	284.085	+	92.3049i	1.01098	+	0.328487i	0.243735	+	0.969842i	$0.421627\pi$
$282$		0			0
$283$	165.458	+	120.212i	0.584656	+	0.424777i	0.840400	−	0.541967i	$-0.182320\pi$
$283$	165.458	+	120.212i	0.584656	+	0.424777i	−0.255744	+	0.966745i	$0.582320\pi$
$284$	429.911	−	139.686i	1.51377	−	0.491854i
$285$		0			0
$286$	51.3875	−	38.2157i	0.179676	−	0.133621i
$287$		−	460.743i		−	1.60538i
$288$		0			0
$289$	−159.255	−	115.706i	−0.551055	−	0.400365i
$290$	18.9066	+	26.0227i	0.0651951	+	0.0897333i
$291$		0			0
$292$	−63.8579	+	196.534i	−0.218691	+	0.673063i
$293$	−60.4497	−	83.2019i	−0.206313	−	0.283965i	0.693304	−	0.720645i	$-0.256154\pi$
$293$	−60.4497	−	83.2019i	−0.206313	−	0.283965i	−0.899617	+	0.436680i	$0.856154\pi$
$294$		0			0
$295$	64.9224	+	199.811i	0.220076	+	0.677324i
$296$			17.7510i			0.0599697i
$297$		0			0
$298$	1.31932			0.00442724
$299$	−739.473	+	240.270i	−2.47316	+	0.803577i
$300$		0			0
$301$	−304.228	+	221.035i	−1.01072	+	0.734334i
$302$	−27.9497	−	9.08142i	−0.0925488	−	0.0300709i
$303$		0			0
$304$	−69.2217	+	50.2925i	−0.227703	+	0.165436i
$305$	411.919	−	566.958i	1.35055	−	1.85888i
$306$		0			0
$307$	39.5643			0.128874			0.0644369	−	0.997922i	$-0.479475\pi$
$307$	39.5643			0.128874			0.0644369	+	0.997922i	$0.479475\pi$
$308$	−355.315	−	111.095i	−1.15362	−	0.360697i
$309$		0			0
$310$	7.82510	+	24.0832i	0.0252423	+	0.0776877i
$311$	−81.9693	+	112.821i	−0.263567	+	0.362769i	−0.920205	−	0.391437i	$-0.871978\pi$
$311$	−81.9693	+	112.821i	−0.263567	+	0.362769i	0.656638	+	0.754206i	$0.271978\pi$
$312$		0			0
$313$	−69.8621	+	215.013i	−0.223201	+	0.686943i	0.775268	+	0.631633i	$0.217615\pi$
$313$	−69.8621	+	215.013i	−0.223201	+	0.686943i	−0.998469	+	0.0553107i	$0.982385\pi$
$314$	44.0278	+	14.3055i	0.140216	+	0.0455589i
$315$		0			0
$316$	−6.47039	−	4.70102i	−0.0204759	−	0.0148766i
$317$	−334.945	+	108.830i	−1.05661	+	0.343313i	−0.785259	−	0.619167i	$-0.787470\pi$
$317$	−334.945	+	108.830i	−1.05661	+	0.343313i	−0.271350	+	0.962481i	$0.587470\pi$
$318$		0			0
$319$	−153.349	+	114.042i	−0.480718	+	0.357499i
$320$		−	326.342i		−	1.01982i
$321$		0			0
$322$	−90.8241	−	65.9876i	−0.282062	−	0.204930i
$323$	32.5191	+	44.7587i	0.100678	+	0.138572i
$324$		0			0
$325$	−59.8594	+	184.228i	−0.184183	+	0.566856i
$326$	−16.7914	−	23.1114i	−0.0515075	−	0.0708940i
$327$		0			0
$328$	−40.4040	−	124.351i	−0.123183	−	0.379118i
$329$			163.396i			0.496644i
$330$		0			0
$331$	−84.8580			−0.256369			−0.128184	−	0.991750i	$-0.540915\pi$
$331$	−84.8580			−0.256369			−0.128184	+	0.991750i	$0.540915\pi$
$332$	−106.978	+	34.7594i	−0.322224	+	0.104697i
$333$		0			0
$334$	3.59392	−	2.61113i	0.0107602	−	0.00781776i
$335$	517.529	+	168.155i	1.54486	+	0.501956i
$336$		0			0
$337$	−426.493	+	309.865i	−1.26556	+	0.919482i	−0.999016	−	0.0443415i	$-0.985881\pi$
$337$	−426.493	+	309.865i	−1.26556	+	0.919482i	−0.266542	+	0.963823i	$0.585881\pi$
$338$	−33.0560	+	45.4977i	−0.0977989	+	0.134609i
$339$		0			0
$340$	−222.796			−0.655282
$341$	−142.559	+	48.0799i	−0.418062	+	0.140997i
$342$		0			0
$343$	−61.1288	−	188.135i	−0.178218	−	0.548499i
$344$	−62.7254	+	86.3341i	−0.182341	+	0.250971i
$345$		0			0
$346$	−22.3487	+	68.7823i	−0.0645917	+	0.198793i
$347$	−120.136	−	39.0345i	−0.346212	−	0.112491i	0.130749	−	0.991416i	$-0.458262\pi$
$347$	−120.136	−	39.0345i	−0.346212	−	0.112491i	−0.476961	+	0.878924i	$0.658262\pi$
$348$		0			0
$349$	365.235	+	265.359i	1.04652	+	0.760340i	0.971547	−	0.236845i	$-0.0761135\pi$
$349$	365.235	+	265.359i	1.04652	+	0.760340i	0.0749713	+	0.997186i	$0.476113\pi$
$350$	−26.6001	+	8.64290i	−0.0760003	+	0.0246940i
$351$		0			0
$352$	−159.106	+	1.76992i	−0.452006	+	0.00502818i
$353$			145.710i			0.412775i	0.978470	+	0.206388i	$0.0661708\pi$
$353$			145.710i			0.412775i	−0.978470	+	0.206388i	$0.933829\pi$
$354$		0			0
$355$	557.159	+	404.800i	1.56946	+	1.14028i
$356$	−309.665	−	426.217i	−0.869845	−	1.19724i
$357$		0			0
$358$	13.8220	−	42.5397i	0.0386089	−	0.118826i
$359$	−252.282	−	347.237i	−0.702736	−	0.967233i	−0.999923	−	0.0124137i	$-0.996048\pi$
$359$	−252.282	−	347.237i	−0.702736	−	0.967233i	0.297187	−	0.954819i	$-0.403952\pi$
$360$		0			0
$361$	−101.291	−	311.741i	−0.280584	−	0.863549i
$362$			74.6339i			0.206171i
$363$		0			0
$364$	632.812			1.73850
$365$	−299.425	+	97.2891i	−0.820342	+	0.266545i
$366$		0			0
$367$	−107.083	+	77.8000i	−0.291778	+	0.211989i	−0.724038	−	0.689760i	$-0.757716\pi$
$367$	−107.083	+	77.8000i	−0.291778	+	0.211989i	0.432260	+	0.901749i	$0.357716\pi$
$368$	587.130	+	190.770i	1.59546	+	0.518397i
$369$		0			0
$370$	−10.8054	+	7.85058i	−0.0292038	+	0.0212178i
$371$	278.033	−	382.679i	0.749414	−	1.03148i
$372$		0			0
$373$	−478.180			−1.28198			−0.640992	−	0.767547i	$-0.721477\pi$
$373$	−478.180			−1.28198			−0.640992	+	0.767547i	$0.721477\pi$
$374$	0.365711	+	32.8754i	0.000977837	+	0.0879022i
$375$		0			0
$376$	14.3287	+	44.0992i	0.0381082	+	0.117285i
$377$	190.942	−	262.809i	0.506476	−	0.697105i
$378$		0			0
$379$	−81.6441	+	251.275i	−0.215420	+	0.662994i	0.783704	+	0.621135i	$0.213328\pi$
$379$	−81.6441	+	251.275i	−0.215420	+	0.662994i	−0.999124	+	0.0418592i	$0.986672\pi$
$380$	−127.215	−	41.3347i	−0.334777	−	0.108775i
$381$		0			0
$382$	9.45396	+	6.86871i	0.0247486	+	0.0179809i
$383$	−224.859	+	73.0612i	−0.587100	+	0.190760i	−0.587479	−	0.809240i	$-0.699879\pi$
$383$	−224.859	+	73.0612i	−0.587100	+	0.190760i	0.000379005		1.00000i	$0.499879\pi$
$384$		0			0
$385$	−181.256	−	537.432i	−0.470795	−	1.39593i
$386$		−	63.3834i		−	0.164206i
$387$		0			0
$388$	31.5015	+	22.8871i	0.0811893	+	0.0589875i
$389$	300.486	+	413.583i	0.772457	+	1.06320i	0.996074	+	0.0885193i	$0.0282135\pi$
$389$	300.486	+	413.583i	0.772457	+	1.06320i	−0.223617	+	0.974677i	$0.571787\pi$
$390$		0			0
$391$	123.352	−	379.638i	0.315478	−	0.970942i
$392$	37.8745	+	52.1298i	0.0966187	+	0.132984i
$393$		0			0
$394$	20.0585	+	61.7336i	0.0509098	+	0.156684i
$395$		−	12.1849i		−	0.0308479i
$396$		0			0
$397$	389.224			0.980413			0.490207	−	0.871606i	$-0.336921\pi$
$397$	389.224			0.980413			0.490207	+	0.871606i	$0.336921\pi$
$398$	−73.9921	+	24.0415i	−0.185910	+	0.0604058i
$399$		0			0
$400$	124.428	−	90.4024i	0.311071	−	0.226006i
$401$	214.986	+	69.8532i	0.536125	+	0.174198i	0.564551	−	0.825398i	$-0.309049\pi$
$401$	214.986	+	69.8532i	0.536125	+	0.174198i	−0.0284257	+	0.999596i	$0.509049\pi$
$402$		0			0
$403$	206.897	−	150.319i	0.513391	−	0.373000i
$404$	−395.573	+	544.459i	−0.979140	+	1.34767i
$405$		0			0
$406$	46.9039			0.115527
$407$	−47.3537	−	63.6751i	−0.116348	−	0.156450i
$408$		0			0
$409$	−56.1688	−	172.870i	−0.137332	−	0.422664i	0.858614	−	0.512623i	$-0.171326\pi$
$409$	−56.1688	−	172.870i	−0.137332	−	0.422664i	−0.995945	+	0.0899593i	$0.971326\pi$
$410$	57.8256	−	79.5902i	0.141038	−	0.194122i
$411$		0			0
$412$	−137.061	+	421.829i	−0.332672	+	1.02386i
$413$	291.363	+	94.6694i	0.705478	+	0.229224i
$414$		0			0
$415$	−138.643	−	100.730i	−0.334079	−	0.242722i
$416$	257.234	−	83.5803i	0.618350	−	0.200914i
$417$		0			0
$418$	−5.89046	+	18.8395i	−0.0140920	+	0.0450706i
$419$			171.909i			0.410284i	0.978732	+	0.205142i	$0.0657656\pi$
$419$			171.909i			0.410284i	−0.978732	+	0.205142i	$0.934234\pi$
$420$		0			0
$421$	97.7668	+	71.0318i	0.232225	+	0.168722i	0.697813	−	0.716280i	$-0.254157\pi$
$421$	97.7668	+	71.0318i	0.232225	+	0.168722i	−0.465587	+	0.885002i	$0.654157\pi$
$422$	22.2455	+	30.6183i	0.0527145	+	0.0725552i
$423$		0			0
$424$	41.4804	−	127.663i	0.0978311	−	0.301093i
$425$	−58.4542	−	80.4553i	−0.137539	−	0.189307i
$426$		0			0
$427$	−315.784	−	971.884i	−0.739542	−	2.27608i
$428$			324.627i			0.758473i
$429$		0			0
$430$	−80.2942			−0.186731
$431$	−451.082	+	146.565i	−1.04659	+	0.340059i	−0.781331	−	0.624117i	$-0.785459\pi$
$431$	−451.082	+	146.565i	−1.04659	+	0.340059i	−0.265263	+	0.964176i	$0.585459\pi$
$432$		0			0
$433$	−205.673	+	149.430i	−0.474996	+	0.345105i	−0.799385	−	0.600819i	$-0.794841\pi$
$433$	−205.673	+	149.430i	−0.474996	+	0.345105i	0.324389	+	0.945924i	$0.394841\pi$
$434$	35.1179	+	11.4105i	0.0809169	+	0.0262915i
$435$		0			0
$436$	−396.070	+	287.761i	−0.908416	+	0.660003i
$437$	140.866	−	193.886i	0.322349	−	0.443675i
$438$		0			0
$439$	515.246			1.17368			0.586841	−	0.809703i	$-0.300372\pi$
$439$	515.246			1.17368			0.586841	+	0.809703i	$0.300372\pi$
$440$	−96.0486	−	129.154i	−0.218292	−	0.293531i
$441$		0			0
$442$	−17.2698	−	53.1511i	−0.0390720	−	0.120251i
$443$	309.199	−	425.576i	0.697966	−	0.960668i	−0.302007	−	0.953306i	$-0.597656\pi$
$443$	309.199	−	425.576i	0.697966	−	0.960668i	0.999973	−	0.00736244i	$-0.00234356\pi$
$444$		0			0
$445$	248.031	−	763.360i	0.557372	−	1.71542i
$446$	21.2648	+	6.90936i	0.0476790	+	0.0154918i
$447$		0			0
$448$	−384.987	−	279.709i	−0.859345	−	0.624351i
$449$	515.338	−	167.443i	1.14775	−	0.372925i	0.327452	−	0.944868i	$-0.393810\pi$
$449$	515.338	−	167.443i	1.14775	−	0.372925i	0.820293	+	0.571943i	$0.193810\pi$
$450$		0			0
$451$	476.660	+	338.277i	1.05690	+	0.750061i
$452$		−	394.935i		−	0.873749i
$453$		0			0
$454$	58.9542	+	42.8328i	0.129855	+	0.0943453i
$455$	566.687	+	779.978i	1.24547	+	1.71424i
$456$		0			0
$457$	37.8329	−	116.438i	0.0827854	−	0.254787i	−0.901093	−	0.433626i	$-0.857234\pi$
$457$	37.8329	−	116.438i	0.0827854	−	0.254787i	0.983878	+	0.178839i	$0.0572340\pi$
$458$	12.4687	+	17.1617i	0.0272242	+	0.0374709i
$459$		0			0
$460$	298.235	+	917.871i	0.648336	+	1.99537i
$461$			308.300i			0.668764i	0.942438	+	0.334382i	$0.108528\pi$
$461$			308.300i			0.668764i	−0.942438	+	0.334382i	$0.891472\pi$
$462$		0			0
$463$	369.654			0.798389			0.399195	−	0.916866i	$-0.369290\pi$
$463$	369.654			0.798389			0.399195	+	0.916866i	$0.369290\pi$
$464$	−245.301	+	79.7032i	−0.528667	+	0.171774i
$465$		0			0
$466$	26.8857	−	19.5336i	0.0576947	−	0.0419177i
$467$	103.523	+	33.6365i	0.221676	+	0.0720269i	0.417749	−	0.908562i	$-0.362819\pi$
$467$	103.523	+	33.6365i	0.221676	+	0.0720269i	−0.196073	+	0.980589i	$0.562819\pi$
$468$		0			0
$469$	641.950	−	466.404i	1.36876	−	0.994465i
$470$	−20.5070	+	28.2255i	−0.0436319	+	0.0600542i
$471$		0			0
$472$	86.9382			0.184191
$473$	−5.30645	−	477.021i	−0.0112187	−	1.00850i
$474$		0			0
$475$	−18.4503	−	56.7843i	−0.0388428	−	0.119546i
$476$	−190.959	+	262.833i	−0.401175	+	0.552170i
$477$		0			0
$478$	33.5392	−	103.223i	0.0701658	−	0.215948i
$479$	−287.864	−	93.5328i	−0.600969	−	0.195267i	−0.00729665	−	0.999973i	$-0.502323\pi$
$479$	−287.864	−	93.5328i	−0.600969	−	0.195267i	−0.593673	+	0.804707i	$0.702323\pi$
$480$		0			0
$481$	109.126	+	79.2847i	0.226873	+	0.164833i
$482$	−111.763	+	36.3141i	−0.231874	+	0.0753404i
$483$		0			0
$484$	375.805	−	286.024i	0.776456	−	0.590959i
$485$			59.3229i			0.122315i
$486$		0			0
$487$	−375.540	−	272.846i	−0.771130	−	0.560258i	0.131174	−	0.991359i	$-0.458125\pi$
$487$	−375.540	−	272.846i	−0.771130	−	0.560258i	−0.902304	+	0.431101i	$0.858125\pi$
$488$	−170.455	−	234.611i	−0.349293	−	0.480761i
$489$		0			0
$490$	−14.9820	+	46.1099i	−0.0305756	+	0.0941019i
$491$	204.017	+	280.805i	0.415513	+	0.571905i	0.964552	−	0.263892i	$-0.0850063\pi$
$491$	204.017	+	280.805i	0.415513	+	0.571905i	−0.549039	+	0.835797i	$0.685006\pi$
$492$		0			0
$493$	51.5361	+	158.612i	0.104536	+	0.321728i
$494$		−	33.5530i		−	0.0679210i
$495$		0			0
$496$	−203.052			−0.409379
$497$	955.087	−	310.326i	1.92170	−	0.624399i
$498$		0			0
$499$	−368.064	+	267.414i	−0.737603	+	0.535900i	−0.891960	−	0.452115i	$-0.850670\pi$
$499$	−368.064	+	267.414i	−0.737603	+	0.535900i	0.154356	+	0.988015i	$0.450670\pi$
$500$	−323.157	−	105.000i	−0.646315	−	0.210000i
$501$		0			0
$502$	−75.9860	+	55.2071i	−0.151367	+	0.109974i
$503$	−243.623	+	335.319i	−0.484341	+	0.666638i	−0.979332	−	0.202260i	$-0.935171\pi$
$503$	−243.623	+	335.319i	−0.484341	+	0.666638i	0.494991	+	0.868898i	$0.335171\pi$
$504$		0			0
$505$	−1025.31			−2.03033
$506$	134.950	−	45.5137i	0.266700	−	0.0899480i
$507$		0			0
$508$	149.553	+	460.277i	0.294396	+	0.906056i
$509$	88.1735	−	121.360i	0.173229	−	0.238429i	−0.713571	−	0.700583i	$-0.752923\pi$
$509$	88.1735	−	121.360i	0.173229	−	0.238429i	0.886800	+	0.462154i	$0.152923\pi$
$510$		0			0
$511$	−141.866	+	436.619i	−0.277625	+	0.854441i
$512$	−343.213	−	111.517i	−0.670337	−	0.217806i
$513$		0			0
$514$	3.77247	+	2.74086i	0.00733943	+	0.00533241i
$515$	−642.668	+	208.815i	−1.24790	+	0.405467i
$516$		0			0
$517$	−169.040	−	119.965i	−0.326964	−	0.232041i
$518$			19.4759i			0.0375983i
$519$		0			0
$520$	221.343	+	160.815i	0.425659	+	0.309260i
$521$	−256.909	−	353.605i	−0.493107	−	0.678704i	0.487850	−	0.872927i	$-0.337781\pi$
$521$	−256.909	−	353.605i	−0.493107	−	0.678704i	−0.980957	+	0.194224i	$0.937781\pi$
$522$		0			0
$523$	−126.781	+	390.193i	−0.242412	+	0.746067i	0.753639	+	0.657288i	$0.228297\pi$
$523$	−126.781	+	390.193i	−0.242412	+	0.746067i	−0.996051	+	0.0887790i	$0.971703\pi$
$524$	120.583	+	165.968i	0.230120	+	0.316733i
$525$		0			0
$526$	45.2854	+	139.374i	0.0860938	+	0.264970i
$527$			131.293i			0.249134i
$528$		0			0
$529$	−1200.15			−2.26871
$530$	96.0564	−	31.2106i	0.181238	−	0.0588879i
$531$		0			0
$532$	−157.799	+	114.648i	−0.296615	+	0.215504i
$533$	−944.922	−	307.024i	−1.77284	−	0.576030i
$534$		0			0
$535$	−400.121	+	290.705i	−0.747890	+	0.543374i
$536$	132.357	−	182.173i	0.246934	−	0.339875i
$537$		0			0
$538$	−62.2171			−0.115645
$539$	−274.925	−	85.9597i	−0.510066	−	0.159480i
$540$		0			0
$541$	−154.410	−	475.226i	−0.285416	−	0.878421i	−0.986274	−	0.165119i	$-0.947199\pi$
$541$	−154.410	−	475.226i	−0.285416	−	0.878421i	0.700857	−	0.713302i	$-0.252801\pi$
$542$	15.9713	−	21.9826i	0.0294673	−	0.0405583i
$543$		0			0
$544$	−42.9093	+	132.061i	−0.0788773	+	0.242759i
$545$	−709.365	−	230.487i	−1.30159	−	0.422911i
$546$		0			0
$547$	562.723	+	408.842i	1.02874	+	0.747426i	0.968057	−	0.250731i	$-0.0806709\pi$
$547$	562.723	+	408.842i	1.02874	+	0.747426i	0.0606867	+	0.998157i	$0.480671\pi$
$548$	466.908	−	151.708i	0.852022	−	0.276839i
$549$		0			0
$550$	10.5883	−	33.8646i	0.0192515	−	0.0615720i
$551$			100.128i			0.181720i
$552$		0			0
$553$	−14.3746	−	10.4437i	−0.0259938	−	0.0188856i
$554$	−54.7602	−	75.3710i	−0.0988452	−	0.136049i
$555$		0			0
$556$	64.7031	−	199.136i	0.116372	−	0.358157i
$557$	254.943	+	350.898i	0.457707	+	0.629979i	0.974031	−	0.226414i	$-0.0727002\pi$
$557$	254.943	+	350.898i	0.457707	+	0.629979i	−0.516325	+	0.856393i	$0.672700\pi$
$558$		0			0
$559$	250.585	+	771.220i	0.448273	+	1.37964i
$560$		−	765.484i		−	1.36694i
$561$		0			0
$562$	93.0037			0.165487
$563$	639.745	−	207.866i	1.13632	−	0.369211i	0.320343	−	0.947302i	$-0.396202\pi$
$563$	639.745	−	207.866i	1.13632	−	0.369211i	0.815973	+	0.578091i	$0.196202\pi$
$564$		0			0
$565$	486.780	−	353.666i	0.861557	−	0.625958i
$566$	60.5610	+	19.6775i	0.106998	+	0.0347658i
$567$		0			0
$568$	230.556	−	167.509i	0.405909	−	0.294910i
$569$	319.271	−	439.438i	0.561108	−	0.772299i	−0.430359	−	0.902658i	$-0.641613\pi$
$569$	319.271	−	439.438i	0.561108	−	0.772299i	0.991467	+	0.130359i	$0.0416129\pi$
$570$		0			0
$571$	607.861			1.06456			0.532278	−	0.846570i	$-0.321336\pi$
$571$	607.861			1.06456			0.532278	+	0.846570i	$0.321336\pi$
$572$	−464.610	+	654.673i	−0.812256	+	1.14453i
$573$		0			0
$574$	−44.3301	−	136.434i	−0.0772302	−	0.237690i
$575$	−253.212	+	348.516i	−0.440369	+	0.606115i
$576$		0			0
$577$	40.4970	−	124.637i	0.0701854	−	0.216009i	−0.909811	−	0.415022i	$-0.863774\pi$
$577$	40.4970	−	124.637i	0.0701854	−	0.216009i	0.979997	+	0.199014i	$0.0637738\pi$
$578$	−58.2907	−	18.9398i	−0.100849	−	0.0327678i
$579$		0			0
$580$	−326.211	−	237.006i	−0.562433	−	0.408632i
$581$	−237.663	+	77.2212i	−0.409058	+	0.132911i
$582$		0			0
$583$	191.768	+	568.600i	0.328933	+	0.975301i
$584$			130.281i			0.223083i
$585$		0			0
$586$	−25.9054	−	18.8214i	−0.0442072	−	0.0321184i
$587$	78.5679	+	108.139i	0.133846	+	0.184224i	0.870679	−	0.491851i	$-0.163680\pi$
$587$	78.5679	+	108.139i	0.133846	+	0.184224i	−0.736833	+	0.676075i	$0.763680\pi$
$588$		0			0
$589$	−24.3585	+	74.9677i	−0.0413557	+	0.127280i
$590$	38.4493	+	52.9210i	0.0651684	+	0.0896966i
$591$		0			0
$592$	−33.0952	−	101.857i	−0.0559040	−	0.172055i
$593$			164.004i			0.276567i	0.990393	+	0.138283i	$0.0441585\pi$
$593$			164.004i			0.276567i	−0.990393	+	0.138283i	$0.955841\pi$
$594$		0			0
$595$	−494.962			−0.831869
$596$	−15.7291	+	5.11068i	−0.0263910	+	0.00857497i
$597$		0			0
$598$	−195.854	+	142.296i	−0.327514	+	0.237953i
$599$	40.7149	+	13.2291i	0.0679714	+	0.0220852i	0.342805	−	0.939406i	$-0.388623\pi$
$599$	40.7149	+	13.2291i	0.0679714	+	0.0220852i	−0.274834	+	0.961492i	$0.588623\pi$
$600$		0			0
$601$	252.000	−	183.089i	0.419301	−	0.304640i	−0.358056	−	0.933700i	$-0.616560\pi$
$601$	252.000	−	183.089i	0.419301	−	0.304640i	0.777356	+	0.629060i	$0.216560\pi$
$602$	−68.8205	+	94.7233i	−0.114320	+	0.157348i
$603$		0			0
$604$	368.399			0.609933
$605$	689.076	+	207.065i	1.13897	+	0.342256i
$606$		0			0
$607$	347.998	+	1071.03i	0.573308	+	1.76446i	0.641871	+	0.766812i	$0.278158\pi$
$607$	347.998	+	1071.03i	0.573308	+	1.76446i	−0.0685637	+	0.997647i	$0.521842\pi$
$608$	−49.0019	+	67.4453i	−0.0805952	+	0.110930i
$609$		0			0
$610$	67.4269	−	207.519i	0.110536	−	0.340195i
$611$	335.103	+	108.881i	0.548450	+	0.178202i
$612$		0			0
$613$	−377.693	−	274.410i	−0.616139	−	0.447651i	0.235432	−	0.971891i	$-0.424350\pi$
$613$	−377.693	−	274.410i	−0.616139	−	0.447651i	−0.851571	+	0.524240i	$0.824350\pi$
$614$	11.7157	−	3.80665i	0.0190809	−	0.00619976i
$615$		0			0
$616$	−234.687	+	2.61069i	−0.380985	+	0.00423813i
$617$			130.650i			0.211750i	0.994379	+	0.105875i	$0.0337644\pi$
$617$			130.650i			0.211750i	−0.994379	+	0.105875i	$0.966236\pi$
$618$		0			0
$619$	−887.453	−	644.773i	−1.43369	−	1.04164i	−0.989315	−	0.145794i	$-0.953426\pi$
$619$	−887.453	−	644.773i	−1.43369	−	1.04164i	−0.444374	−	0.895841i	$-0.646574\pi$
$620$	−186.584	−	256.810i	−0.300941	−	0.414210i
$621$		0			0
$622$	−13.4175	+	41.2949i	−0.0215716	+	0.0663905i
$623$	−687.950	−	946.881i	−1.10425	−	1.51987i
$624$		0			0
$625$	−240.004	−	738.656i	−0.384006	−	1.18185i
$626$			70.3909i			0.112446i
$627$		0			0
$628$	−580.320			−0.924076
$629$	−65.8604	+	21.3993i	−0.104707	+	0.0340212i
$630$		0			0
$631$	939.823	−	682.821i	1.48942	−	1.08213i	0.515052	−	0.857159i	$-0.327773\pi$
$631$	939.823	−	682.821i	1.48942	−	1.08213i	0.974366	−	0.224967i	$-0.0722274\pi$
$632$	−4.79543	−	1.55813i	−0.00758770	−	0.00246539i
$633$		0			0
$634$	−88.7121	+	64.4531i	−0.139924	+	0.101661i
$635$	−433.392	+	596.513i	−0.682507	+	0.939391i
$636$		0			0
$637$	489.639			0.768664
$638$	−34.4368	+	48.5242i	−0.0539762	+	0.0760568i
$639$		0			0
$640$	−137.720	−	423.857i	−0.215187	−	0.662277i
$641$	228.036	−	313.864i	0.355750	−	0.489648i	−0.593208	−	0.805049i	$-0.702139\pi$
$641$	228.036	−	313.864i	0.355750	−	0.489648i	0.948958	+	0.315401i	$0.102139\pi$
$642$		0			0
$643$	−35.6219	+	109.633i	−0.0553995	+	0.170502i	−0.974928	−	0.222522i	$-0.928571\pi$
$643$	−35.6219	+	109.633i	−0.0553995	+	0.170502i	0.919528	+	0.393024i	$0.128571\pi$
$644$	1338.43	+	434.883i	2.07831	+	0.675285i
$645$		0			0
$646$	13.9359	+	10.1250i	0.0215726	+	0.0156734i
$647$	−173.649	+	56.4219i	−0.268391	+	0.0872054i	−0.440121	−	0.897939i	$-0.645064\pi$
$647$	−173.649	+	56.4219i	−0.268391	+	0.0872054i	0.171730	+	0.985144i	$0.445064\pi$
$648$		0			0
$649$	−311.858	+	231.922i	−0.480521	+	0.357352i
$650$			60.3125i			0.0927885i
$651$		0			0
$652$	289.717	+	210.492i	0.444352	+	0.322840i
$653$	6.35509	+	8.74703i	0.00973214	+	0.0133951i	0.813855	−	0.581068i	$-0.197365\pi$
$653$	6.35509	+	8.74703i	0.00973214	+	0.0133951i	−0.804123	+	0.594463i	$0.797365\pi$
$654$		0			0
$655$	−96.5825	+	297.250i	−0.147454	+	0.453817i
$656$	463.682	+	638.203i	0.706832	+	0.972871i
$657$		0			0
$658$	15.7210	+	48.3844i	0.0238921	+	0.0735325i
$659$		−	875.394i		−	1.32837i	−0.747569	−	0.664184i	$-0.768779\pi$
$659$		−	875.394i		−	1.32837i	0.747569	−	0.664184i	$-0.231221\pi$
$660$		0			0
$661$	1015.92			1.53695			0.768475	−	0.639880i	$-0.221016\pi$
$661$	1015.92			1.53695			0.768475	+	0.639880i	$0.221016\pi$
$662$	−25.1279	+	8.16456i	−0.0379576	+	0.0123332i
$663$		0			0
$664$	−57.3714	+	41.6827i	−0.0864027	+	0.0627752i
$665$	−282.620	−	91.8289i	−0.424993	−	0.138089i
$666$		0			0
$667$	584.461	−	424.636i	0.876253	−	0.636635i
$668$	−32.7323	+	45.0521i	−0.0490004	+	0.0674433i
$669$		0			0
$670$	169.428			0.252878
$671$	1237.31	+	386.863i	1.84398	+	0.576547i
$672$		0			0
$673$	−35.1655	−	108.228i	−0.0522519	−	0.160815i	0.921525	−	0.388318i	$-0.126944\pi$
$673$	−35.1655	−	108.228i	−0.0522519	−	0.160815i	−0.973777	+	0.227503i	$0.926944\pi$
$674$	−96.4786	+	132.791i	−0.143143	+	0.197020i
$675$		0			0
$676$	217.852	−	670.479i	0.322266	−	0.991834i
$677$	811.539	+	263.685i	1.19873	+	0.389490i	0.839293	−	0.543680i	$-0.182969\pi$
$677$	811.539	+	263.685i	1.19873	+	0.389490i	0.359435	+	0.933170i	$0.382969\pi$
$678$		0			0
$679$	69.9835	+	50.8460i	0.103068	+	0.0748836i
$680$	−133.586	+	43.4048i	−0.196450	+	0.0638305i
$681$		0			0
$682$	−37.5883	+	27.9535i	−0.0551148	+	0.0409876i
$683$			193.740i			0.283661i	0.989891	+	0.141830i	$0.0452987\pi$
$683$			193.740i			0.283661i	−0.989891	+	0.141830i	$0.954701\pi$
$684$		0			0
$685$	605.108	+	439.636i	0.883369	+	0.641805i
$686$	−36.2026	−	49.8286i	−0.0527735	−	0.0726365i
$687$		0			0
$688$	198.960	−	612.336i	0.289186	−	0.890024i
$689$	−599.551	−	825.212i	−0.870176	−	1.19769i
$690$		0			0
$691$	−78.3885	−	241.255i	−0.113442	−	0.349139i	0.878177	−	0.478336i	$-0.158760\pi$
$691$	−78.3885	−	241.255i	−0.113442	−	0.349139i	−0.991619	+	0.129197i	$0.958760\pi$
$692$		−	906.604i		−	1.31012i
$693$		0			0
$694$	−39.3300			−0.0566714
$695$	303.388	−	98.5768i	0.436530	−	0.141837i
$696$		0			0
$697$	412.662	−	299.817i	0.592055	−	0.430153i
$698$	133.684	+	43.4365i	0.191524	+	0.0622300i
$699$		0			0
$700$	283.649	−	206.083i	0.405213	−	0.294405i
$701$	−669.680	+	921.735i	−0.955321	+	1.31489i	−0.00619790	+	0.999981i	$0.501973\pi$
$701$	−669.680	+	921.735i	−0.955321	+	1.31489i	−0.949123	+	0.314906i	$0.898027\pi$
$702$		0			0
$703$	−41.5761			−0.0591409
$704$	572.029	−	192.924i	0.812541	−	0.274040i
$705$		0			0
$706$	14.0194	+	43.1472i	0.0198575	+	0.0611150i
$707$	−878.802	+	1209.57i	−1.24300	+	1.71084i
$708$		0			0
$709$	115.622	−	355.847i	0.163077	−	0.501899i	−0.835812	−	0.549015i	$-0.815003\pi$
$709$	115.622	−	355.847i	0.163077	−	0.501899i	0.998889	+	0.0471157i	$0.0150029\pi$
$710$	203.932	+	66.2615i	0.287228	+	0.0933261i
$711$		0			0
$712$	−268.707	−	195.227i	−0.377397	−	0.274195i
$713$	540.901	−	175.749i	0.758627	−	0.246493i
$714$		0			0
$715$	−1222.98	+	13.6047i	−1.71047	+	0.0190275i
$716$			560.706i			0.783109i
$717$		0			0
$718$	−108.114	−	78.5497i	−0.150577	−	0.109401i
$719$	−445.256	−	612.843i	−0.619272	−	0.852354i	0.378028	−	0.925794i	$-0.376602\pi$
$719$	−445.256	−	612.843i	−0.619272	−	0.852354i	−0.997300	+	0.0734400i	$0.976602\pi$
$720$		0			0
$721$	−304.493	+	937.134i	−0.422321	+	1.29977i
$722$	−59.9880	−	82.5664i	−0.0830859	−	0.114358i
$723$		0			0
$724$	−289.112	−	889.794i	−0.399326	−	1.22900i
$725$		−	179.983i		−	0.248252i
$726$		0			0
$727$	845.080			1.16242			0.581211	−	0.813753i	$-0.302579\pi$
$727$	845.080			1.16242			0.581211	+	0.813753i	$0.302579\pi$
$728$	379.428	−	123.284i	0.521192	−	0.169346i
$729$		0			0
$730$	−79.3044	+	57.6180i	−0.108636	+	0.0789288i
$731$	−395.937	−	128.648i	−0.541637	−	0.175989i
$732$		0			0
$733$	−1098.71	+	798.262i	−1.49893	+	1.08903i	−0.528121	+	0.849169i	$0.677103\pi$
$733$	−1098.71	+	798.262i	−1.49893	+	1.08903i	−0.970806	+	0.239865i	$0.922897\pi$
$734$	−24.2235	+	33.3408i	−0.0330021	+	0.0454235i
$735$		0			0
$736$	601.502			0.817258
$737$	11.1971	+	1006.56i	0.0151928	+	1.36575i
$738$		0			0
$739$	247.582	+	761.978i	0.335023	+	1.03109i	0.966711	+	0.255871i	$0.0823623\pi$
$739$	247.582	+	761.978i	0.335023	+	1.03109i	−0.631688	+	0.775223i	$0.717638\pi$
$740$	98.4122	−	135.453i	0.132989	−	0.183044i
$741$		0			0
$742$	45.5111	−	140.069i	0.0613357	−	0.188772i
$743$	−849.861	−	276.136i	−1.14382	−	0.371651i	−0.325010	−	0.945711i	$-0.605368\pi$
$743$	−849.861	−	276.136i	−1.14382	−	0.371651i	−0.818813	+	0.574060i	$0.805368\pi$
$744$		0			0
$745$	−20.3847	−	14.8103i	−0.0273620	−	0.0198796i
$746$	−141.598	+	46.0078i	−0.189809	+	0.0616727i
$747$		0			0
$748$	−131.711	−	390.528i	−0.176084	−	0.522096i
$749$			721.189i			0.962868i
$750$		0			0
$751$	−321.208	−	233.372i	−0.427708	−	0.310748i	0.353024	−	0.935614i	$-0.385153\pi$
$751$	−321.208	−	233.372i	−0.427708	−	0.310748i	−0.780732	+	0.624867i	$0.785153\pi$
$752$	−164.438	−	226.329i	−0.218667	−	0.300970i
$753$		0			0
$754$	31.2552	−	96.1936i	0.0414525	−	0.127578i
$755$	329.904	+	454.073i	0.436958	+	0.601422i
$756$		0			0
$757$	183.281	+	564.081i	0.242115	+	0.745153i	0.996098	+	0.0882586i	$0.0281302\pi$
$757$	183.281	+	564.081i	0.242115	+	0.745153i	−0.753983	+	0.656894i	$0.771870\pi$
$758$			82.2622i			0.108525i
$759$		0			0
$760$	−84.3296			−0.110960
$761$	−389.495	+	126.555i	−0.511820	+	0.166301i	−0.553530	−	0.832829i	$-0.686720\pi$
$761$	−389.495	+	126.555i	−0.511820	+	0.166301i	0.0417096	+	0.999130i	$0.486720\pi$
$762$		0			0
$763$	−879.906	+	639.289i	−1.15322	+	0.837862i
$764$	−139.319	−	45.2674i	−0.182354	−	0.0592506i
$765$		0			0
$766$	−59.5552	+	43.2694i	−0.0777483	+	0.0564874i
$767$	388.308	−	534.461i	0.506269	−	0.696820i
$768$		0			0
$769$	119.029			0.154784			0.0773921	−	0.997001i	$-0.475341\pi$
$769$	119.029			0.154784			0.0773921	+	0.997001i	$0.475341\pi$
$770$	−105.382	−	141.704i	−0.136859	−	0.184031i
$771$		0			0
$772$	245.530	+	755.665i	0.318045	+	0.978841i
$773$	412.352	−	567.554i	0.533444	−	0.734222i	−0.454207	−	0.890896i	$-0.650077\pi$
$773$	412.352	−	567.554i	0.533444	−	0.734222i	0.987650	+	0.156674i	$0.0500773\pi$
$774$		0			0
$775$	43.7852	−	134.757i	0.0564970	−	0.173880i
$776$	23.3468	+	7.58583i	0.0300861	+	0.00977556i
$777$		0			0
$778$	128.772	+	93.5582i	0.165516	+	0.120255i
$779$	291.252	−	94.6334i	0.373879	−	0.121481i
$780$		0			0
$781$	−380.177	+	1215.92i	−0.486782	+	1.55688i
$782$		−	124.286i		−	0.158933i
$783$		0			0
$784$	−314.518	−	228.511i	−0.401171	−	0.291468i
$785$	−519.680	−	715.278i	−0.662012	−	0.911182i
$786$		0			0
$787$	475.616	−	1463.80i	0.604341	−	1.85997i	0.103080	−	0.994673i	$-0.467130\pi$
$787$	475.616	−	1463.80i	0.604341	−	1.85997i	0.501261	−	0.865296i	$-0.332870\pi$
$788$	−478.279	−	658.295i	−0.606953	−	0.835400i
$789$		0			0
$790$	−1.17236	−	3.60817i	−0.00148401	−	0.00456730i
$791$		−	877.384i		−	1.10921i
$792$		0			0
$793$	−2203.63			−2.77885
$794$	115.256	−	37.4490i	0.145159	−	0.0471649i
$795$		0			0
$796$	789.013	−	573.251i	0.991222	−	0.720165i
$797$	−941.317	−	305.853i	−1.18108	−	0.383755i	−0.348310	−	0.937380i	$-0.613244\pi$
$797$	−941.317	−	305.853i	−1.18108	−	0.383755i	−0.832766	+	0.553625i	$0.813244\pi$
$798$		0			0
$799$	−146.345	+	106.326i	−0.183160	+	0.133073i
$800$	88.0824	−	121.235i	0.110103	−	0.151544i
$801$		0			0
$802$	70.3821			0.0877582
$803$	−347.545	−	467.333i	−0.432808	−	0.581984i
$804$		0			0
$805$	662.556	+	2039.14i	0.823051	+	2.53309i
$806$	46.8028	−	64.4186i	0.0580680	−	0.0799238i
$807$		0			0
$808$	−131.111	+	403.517i	−0.162266	+	0.499402i
$809$	−89.5017	−	29.0809i	−0.110632	−	0.0359467i	0.253178	−	0.967420i	$-0.418524\pi$
$809$	−89.5017	−	29.0809i	−0.110632	−	0.0359467i	−0.363810	+	0.931473i	$0.618524\pi$
$810$		0			0
$811$	299.589	+	217.664i	0.369407	+	0.268390i	0.756965	−	0.653455i	$-0.226681\pi$
$811$	299.589	+	217.664i	0.369407	+	0.268390i	−0.387558	+	0.921845i	$0.626681\pi$
$812$	−559.194	+	181.693i	−0.688663	+	0.223760i
$813$		0			0
$814$	−20.1487	−	14.2992i	−0.0247527	−	0.0175666i
$815$			545.590i			0.669436i
$816$		0			0
$817$	−202.210	−	146.914i	−0.247503	−	0.179821i
$818$	−33.2651	−	45.7855i	−0.0406664	−	0.0559725i
$819$		0			0
$820$	−381.093	+	1172.88i	−0.464748	+	1.43035i
$821$	−125.607	−	172.884i	−0.152993	−	0.210577i	0.725640	−	0.688075i	$-0.241544\pi$
$821$	−125.607	−	172.884i	−0.152993	−	0.210577i	−0.878633	+	0.477498i	$0.841544\pi$
$822$		0			0
$823$	32.2045	+	99.1154i	0.0391307	+	0.120432i	0.968714	−	0.248181i	$-0.0798328\pi$
$823$	32.2045	+	99.1154i	0.0391307	+	0.120432i	−0.929583	+	0.368613i	$0.879833\pi$
$824$			279.627i			0.339353i
$825$		0			0
$826$	95.3861			0.115480
$827$	1264.20	−	410.763i	1.52866	−	0.496690i	0.580436	−	0.814306i	$-0.302882\pi$
$827$	1264.20	−	410.763i	1.52866	−	0.496690i	0.948220	+	0.317615i	$0.102882\pi$
$828$		0			0
$829$	283.230	−	205.779i	0.341653	−	0.248225i	−0.403706	−	0.914889i	$-0.632278\pi$
$829$	283.230	−	205.779i	0.341653	−	0.248225i	0.745359	+	0.666663i	$0.232278\pi$
$830$	−50.7462	−	16.4884i	−0.0611400	−	0.0198656i
$831$		0			0
$832$	−830.188	+	603.167i	−0.997822	+	0.724960i
$833$	−147.755	+	203.367i	−0.177377	+	0.244138i
$834$		0			0
$835$	−84.8413			−0.101606
$836$	−2.75239	−	247.425i	−0.00329233	−	0.295963i
$837$		0			0
$838$	16.5401	+	50.9053i	0.0197376	+	0.0607461i
$839$	−906.466	+	1247.64i	−1.08041	+	1.48706i	−0.221347	+	0.975195i	$0.571045\pi$
$839$	−906.466	+	1247.64i	−1.08041	+	1.48706i	−0.859066	+	0.511865i	$0.828955\pi$
$840$		0			0
$841$	166.613	−	512.781i	0.198112	−	0.609727i
$842$	35.7847	+	11.6272i	0.0424997	+	0.0138090i
$843$		0			0
$844$	−383.821	−	278.862i	−0.454764	−	0.330405i
$845$	1021.49	−	331.903i	1.20887	−	0.392785i
$846$		0			0
$847$	834.885	−	635.429i	0.985697	−	0.750212i
$848$			809.878i			0.955044i
$849$		0			0
$850$	−25.0503	−	18.2001i	−0.0294709	−	0.0214119i
$851$	176.321	+	242.686i	0.207193	+	0.285177i
$852$		0			0
$853$	16.4190	−	50.5324i	0.0192485	−	0.0592408i	−0.940971	−	0.338488i	$-0.890085\pi$
$853$	16.4190	−	50.5324i	0.0192485	−	0.0592408i	0.960219	+	0.279247i	$0.0900847\pi$
$854$	−187.019	−	257.409i	−0.218991	−	0.301416i
$855$		0			0
$856$	63.2433	+	194.643i	0.0738823	+	0.227386i
$857$			668.807i			0.780405i	0.920729	+	0.390202i	$0.127595\pi$
$857$			668.807i			0.780405i	−0.920729	+	0.390202i	$0.872405\pi$
$858$		0			0
$859$	192.579			0.224189			0.112095	−	0.993698i	$-0.464244\pi$
$859$	192.579			0.224189			0.112095	+	0.993698i	$0.464244\pi$
$860$	957.277	−	311.038i	1.11311	−	0.361672i
$861$		0			0
$862$	−119.472	+	86.8012i	−0.138598	+	0.100697i
$863$	−809.418	−	262.996i	−0.937911	−	0.304746i	−0.200118	−	0.979772i	$-0.564132\pi$
$863$	−809.418	−	262.996i	−0.937911	−	0.304746i	−0.737794	+	0.675026i	$0.764132\pi$
$864$		0			0
$865$	1117.44	−	811.869i	1.29184	−	0.938577i
$866$	−46.5261	+	64.0377i	−0.0537253	+	0.0739465i
$867$		0			0
$868$	−462.882			−0.533274
$869$	21.3583	−	7.20338i	0.0245781	−	0.00828927i
$870$		0			0
$871$	−528.758	−	1627.35i	−0.607069	−	1.86837i
$872$	−181.418	+	249.700i	−0.208048	+	0.286354i
$873$		0			0
$874$	23.0584	−	70.9664i	0.0263826	−	0.0811973i
$875$	−717.925	−	233.268i	−0.820485	−	0.266592i
$876$		0			0
$877$	−356.476	−	258.995i	−0.406472	−	0.295319i	0.365700	−	0.930733i	$-0.380830\pi$
$877$	−356.476	−	258.995i	−0.406472	−	0.295319i	−0.772172	+	0.635414i	$0.780830\pi$
$878$	152.573	−	49.5741i	0.173774	−	0.0564625i
$879$		0			0
$880$	791.928	+	562.018i	0.899919	+	0.638657i
$881$			448.427i			0.508997i	0.967073	+	0.254499i	$0.0819104\pi$
$881$			448.427i			0.508997i	−0.967073	+	0.254499i	$0.918090\pi$
$882$		0			0
$883$	251.468	+	182.702i	0.284788	+	0.206911i	0.721003	−	0.692932i	$-0.243681\pi$
$883$	251.468	+	182.702i	0.284788	+	0.206911i	−0.436215	+	0.899842i	$0.643681\pi$
$884$	411.786	+	566.775i	0.465821	+	0.641148i
$885$		0			0
$886$	50.6127	−	155.770i	0.0571250	−	0.175813i
$887$	759.909	+	1045.92i	0.856718	+	1.17917i	0.982342	+	0.187093i	$0.0599066\pi$
$887$	759.909	+	1045.92i	0.856718	+	1.17917i	−0.125624	+	0.992078i	$0.540093\pi$
$888$		0			0
$889$	332.246	+	1022.55i	0.373730	+	1.15022i
$890$		−	249.908i		−	0.280796i
$891$		0			0
$892$	−280.287			−0.314223
$893$	−103.288	+	33.5603i	−0.115664	+	0.0375816i
$894$		0			0
$895$	−691.103	+	502.115i	−0.772182	+	0.561023i
$896$	−618.066	−	200.822i	−0.689806	−	0.224131i
$897$		0			0
$898$	136.490	−	99.1658i	0.151993	−	0.110430i
$899$	−139.668	+	192.236i	−0.155359	+	0.213833i
$900$		0			0
$901$	523.667			0.581206
$902$	173.695	+	54.3083i	0.192566	+	0.0602087i
$903$		0			0
$904$	−76.9406	−	236.799i	−0.0851113	−	0.261946i
$905$	837.822	−	1153.16i	0.925770	−	1.27421i
$906$		0			0
$907$	252.009	−	775.605i	0.277849	−	0.855132i	−0.710602	−	0.703594i	$-0.751577\pi$
$907$	252.009	−	775.605i	0.277849	−	0.855132i	0.988451	−	0.151538i	$-0.0484227\pi$
$908$	−868.782	−	282.284i	−0.956808	−	0.310886i
$909$		0			0
$910$	242.851	+	176.442i	0.266869	+	0.193892i
$911$	231.147	−	75.1044i	0.253729	−	0.0824417i	−0.179391	−	0.983778i	$-0.557413\pi$
$911$	231.147	−	75.1044i	0.253729	−	0.0824417i	0.433120	+	0.901336i	$0.357413\pi$
$912$		0			0
$913$	94.6027	−	302.569i	0.103617	−	0.331400i
$914$		−	38.1193i		−	0.0417061i
$915$		0			0
$916$	−215.133	−	156.303i	−0.234861	−	0.170637i
$917$	267.886	+	368.713i	0.292133	+	0.402086i
$918$		0			0
$919$	−89.7023	+	276.075i	−0.0976086	+	0.300408i	−0.987925	−	0.154935i	$-0.950483\pi$
$919$	−89.7023	+	276.075i	−0.0976086	+	0.300408i	0.890316	+	0.455343i	$0.150483\pi$
$920$	357.637	+	492.245i	0.388736	+	0.535049i
$921$		0			0
$922$	29.6629	+	91.2931i	0.0321724	+	0.0990164i
$923$		−	2165.54i		−	2.34620i
$924$		0			0
$925$	74.7343			0.0807938
$926$	109.461	−	35.5661i	0.118209	−	0.0384083i
$927$		0			0
$928$	−203.311	+	147.714i	−0.219085	+	0.159175i
$929$	280.633	+	91.1833i	0.302081	+	0.0981521i	0.456136	−	0.889910i	$-0.349233\pi$
$929$	280.633	+	91.1833i	0.302081	+	0.0981521i	−0.154055	+	0.988062i	$0.549233\pi$
$930$		0			0
$931$	−122.097	+	88.7089i	−0.131146	+	0.0952835i
$932$	−244.867	+	337.031i	−0.262733	+	0.361621i
$933$		0			0
$934$	33.8912			0.0362861
$935$	363.401	−	512.061i	0.388664	−	0.547659i
$936$		0			0
$937$	−283.722	−	873.206i	−0.302798	−	0.931917i	−0.980490	−	0.196570i	$-0.937020\pi$
$937$	−283.722	−	873.206i	−0.302798	−	0.931917i	0.677692	−	0.735346i	$-0.262980\pi$
$938$	145.218	−	199.875i	0.154816	−	0.213087i
$939$		0			0
$940$	135.149	−	415.946i	0.143776	−	0.442496i
$941$	949.293	+	308.444i	1.00881	+	0.327783i	0.766382	−	0.642385i	$-0.222055\pi$
$941$	949.293	+	308.444i	1.00881	+	0.327783i	0.242431	+	0.970169i	$0.422055\pi$
$942$		0			0
$943$	−1787.57	−	1298.75i	−1.89562	−	1.37725i
$944$	−498.857	+	162.088i	−0.528450	+	0.171704i
$945$		0			0
$946$	−47.4676	−	140.744i	−0.0501772	−	0.148778i
$947$		−	780.779i		−	0.824476i	−0.911076	−	0.412238i	$-0.864747\pi$
$947$		−	780.779i		−	0.824476i	0.911076	−	0.412238i	$-0.135253\pi$
$948$		0			0
$949$	800.912	+	581.897i	0.843954	+	0.613169i
$950$	−10.9269	−	15.0396i	−0.0115020	−	0.0158312i
$951$		0			0
$952$	−63.2925	+	194.794i	−0.0664838	+	0.204616i
$953$	54.7973	+	75.4220i	0.0574998	+	0.0791417i	0.836799	−	0.547511i	$-0.184425\pi$
$953$	54.7973	+	75.4220i	0.0574998	+	0.0791417i	−0.779299	+	0.626653i	$0.784425\pi$
$954$		0			0
$955$	−68.9661	−	212.256i	−0.0722158	−	0.222257i
$956$			1360.56i			1.42318i
$957$		0			0
$958$	−94.2409			−0.0983725
$959$	1037.28	−	337.033i	1.08163	−	0.351442i
$960$		0			0
$961$	626.127	−	454.908i	0.651537	−	0.473369i
$962$	39.9425	+	12.9781i	0.0415202	+	0.0134907i
$963$		0			0
$964$	1191.78	−	865.882i	1.23629	−	0.898217i
$965$	−711.527	+	979.333i	−0.737334	+	1.01485i
$966$		0			0
$967$	365.949			0.378437			0.189219	−	0.981935i	$-0.439405\pi$
$967$	365.949			0.378437			0.189219	+	0.981935i	$0.439405\pi$
$968$	169.606	−	244.711i	0.175213	−	0.252800i
$969$		0			0
$970$	5.70772	+	17.5666i	0.00588425	+	0.0181099i
$971$	−167.027	+	229.892i	−0.172015	+	0.236758i	−0.886317	−	0.463079i	$-0.846744\pi$
$971$	−167.027	+	229.892i	−0.172015	+	0.236758i	0.714302	+	0.699838i	$0.246744\pi$
$972$		0			0
$973$	143.744	−	442.398i	0.147733	−	0.454675i
$974$	−137.456	−	44.6621i	−0.141125	−	0.0458543i
$975$		0			0
$976$	1415.49	+	1028.42i	1.45030	+	1.05371i
$977$	−839.782	+	272.862i	−0.859552	+	0.279285i	−0.705441	−	0.708768i	$-0.749251\pi$
$977$	−839.782	+	272.862i	−0.859552	+	0.279285i	−0.154110	+	0.988054i	$0.549251\pi$
$978$		0			0
$979$	1484.68	−	16.5158i	1.51653	−	0.0168701i
$980$		−	607.765i		−	0.620168i
$981$		0			0
$982$	87.4305	+	63.5219i	0.0890331	+	0.0646863i
$983$	802.187	+	1104.12i	0.816060	+	1.12321i	0.990360	+	0.138518i	$0.0442338\pi$
$983$	802.187	+	1104.12i	0.816060	+	1.12321i	−0.174300	+	0.984693i	$0.555766\pi$
$984$		0			0
$985$	383.085	−	1179.01i	0.388919	−	1.19697i
$986$	30.5215	+	42.0092i	0.0309549	+	0.0426057i
$987$		0			0
$988$	129.975	+	400.022i	0.131554	+	0.404881i
$989$			1803.38i			1.82344i
$990$		0			0
$991$	−842.288			−0.849938			−0.424969	−	0.905208i	$-0.639715\pi$
$991$	−842.288			−0.849938			−0.424969	+	0.905208i	$0.639715\pi$
$992$	−188.158	+	61.1363i	−0.189675	+	0.0616293i
$993$		0			0
$994$	252.960	−	183.786i	0.254487	−	0.184896i
$995$	1413.13	+	459.154i	1.42023	+	0.461461i
$996$		0			0
$997$	296.438	−	215.375i	0.297330	−	0.216023i	−0.429111	−	0.903252i	$-0.641173\pi$
$997$	296.438	−	215.375i	0.297330	−	0.216023i	0.726441	+	0.687229i	$0.241173\pi$
$998$	−83.2611	+	114.599i	−0.0834280	+	0.114829i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.l.a.71.5	yes	32
3.2	odd	2	inner	99.3.l.a.71.4	yes	32
11.3	even	5		1089.3.b.i.485.8		16
11.8	odd	10		1089.3.b.j.485.9		16
11.9	even	5	inner	99.3.l.a.53.4	✓	32
33.8	even	10		1089.3.b.j.485.8		16
33.14	odd	10		1089.3.b.i.485.9		16
33.20	odd	10	inner	99.3.l.a.53.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.l.a.53.4	✓	32	11.9	even	5	inner
99.3.l.a.53.5	yes	32	33.20	odd	10	inner
99.3.l.a.71.4	yes	32	3.2	odd	2	inner
99.3.l.a.71.5	yes	32	1.1	even	1	trivial
1089.3.b.i.485.8		16	11.3	even	5
1089.3.b.i.485.9		16	33.14	odd	10
1089.3.b.j.485.8		16	33.8	even	10
1089.3.b.j.485.9		16	11.8	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)

\(f(q)\)	\(=\)	\(q+(0.296118 - 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(-5.65537 - 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(-1.44634 + 1.99072i) q^{8} +O(q^{10})\)	\(q+(0.296118 - 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(-5.65537 - 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(-1.44634 + 1.99072i) q^{8} -1.85145 q^{10} +(-0.122358 - 10.9993i) q^{11} +(5.77807 + 17.7831i) q^{13} +(-1.58689 + 2.18416i) q^{14} +(4.58769 - 14.1195i) q^{16} +(-9.12965 - 2.96640i) q^{17} +(-4.66262 - 3.38759i) q^{19} +(22.0732 - 7.17203i) q^{20} +(-1.09453 - 3.24532i) q^{22} +41.5830i q^{23} +(8.38122 + 6.08931i) q^{25} +(3.42197 + 4.70994i) q^{26} +(10.4582 - 32.1870i) q^{28} +(-10.2118 - 14.0553i) q^{29} +(-4.22647 - 13.0077i) q^{31} -14.4651i q^{32} -2.98886 q^{34} +(49.0378 - 15.9333i) q^{35} +(5.83617 - 4.24023i) q^{37} +(-1.70662 - 0.554514i) q^{38} +(11.8376 - 8.60055i) q^{40} +(-31.2326 + 42.9880i) q^{41} +43.3682 q^{43} +(25.6206 + 34.4512i) q^{44} +(4.00089 + 12.3135i) q^{46} +(11.0762 - 15.2451i) q^{47} +(8.09204 - 24.9047i) q^{49} +(3.06770 + 0.996758i) q^{50} +(-59.0422 - 42.8967i) q^{52} +(-51.8817 + 16.8574i) q^{53} +(-19.5197 + 62.4300i) q^{55} -21.3365i q^{56} +(-4.37620 - 3.17949i) q^{58} +(-20.7671 - 28.5835i) q^{59} +(-36.4184 + 112.084i) q^{61} +(-2.50306 - 3.44517i) q^{62} +(16.9590 + 52.1945i) q^{64} -111.187i q^{65} -91.5111 q^{67} +(35.6335 - 11.5780i) q^{68} +(12.9879 - 9.43628i) q^{70} +(-110.147 - 35.7890i) q^{71} +(42.8336 - 31.1204i) q^{73} +(1.32022 - 1.81713i) q^{74} +22.4946 q^{76} +(56.9185 + 76.5365i) q^{77} +(0.633214 + 1.94883i) q^{79} +(-51.8902 + 71.4207i) q^{80} +(-5.11246 + 15.7345i) q^{82} +(27.4089 + 8.90568i) q^{83} +(46.1806 + 33.5522i) q^{85} +(12.8421 - 4.17265i) q^{86} +(22.0736 + 15.6652i) q^{88} +134.980i q^{89} +(-131.168 - 95.2991i) q^{91} +(-95.3981 - 131.304i) q^{92} +(1.81306 - 5.58001i) q^{94} +(20.1440 + 27.7259i) q^{95} +(-3.08284 - 9.48799i) q^{97} -8.15330i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more