LMFDB - Embedded newform 99.3.k.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 $ x^16 - 21x^14 + 227x^12 - 1488x^10 + 24225x^8 - 62832x^6 + 64372x^4 + 7986*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.3
Root			$-1.32111 - 0.429256i$ of defining polynomial
Character	$\chi$	$=$	99.19
Dual form			99.3.k.b.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.816494 + 1.12381i) q^{2} +(0.639787 - 1.96906i) q^{4} +(3.53770 + 2.57029i) q^{5} +(0.582836 + 0.189375i) q^{7} +(8.01969 - 2.60575i) q^{8} +O(q^{10})$	\(q+(0.816494 + 1.12381i) q^{2} +(0.639787 - 1.96906i) q^{4} +(3.53770 + 2.57029i) q^{5} +(0.582836 + 0.189375i) q^{7} +(8.01969 - 2.60575i) q^{8} +6.07432i q^{10} +(4.81000 + 9.89262i) q^{11} +(-5.26002 - 7.23980i) q^{13} +(0.263061 + 0.809619i) q^{14} +(2.77645 + 2.01721i) q^{16} +(-1.74830 + 2.40633i) q^{17} +(-9.51507 + 3.09163i) q^{19} +(7.32444 - 5.32152i) q^{20} +(-7.19005 + 13.4828i) q^{22} -28.6467 q^{23} +(-1.81649 - 5.59057i) q^{25} +(3.84136 - 11.8225i) q^{26} +(0.745782 - 1.02648i) q^{28} +(-33.6548 - 10.9351i) q^{29} +(40.7514 - 29.6076i) q^{31} -28.9624i q^{32} -4.13173 q^{34} +(1.57515 + 2.16801i) q^{35} +(0.539730 - 1.66112i) q^{37} +(-11.2434 - 8.16880i) q^{38} +(35.0688 + 11.3945i) q^{40} +(-56.5662 + 18.3795i) q^{41} +43.6490i q^{43} +(22.5566 - 3.14203i) q^{44} +(-23.3899 - 32.1934i) q^{46} +(12.8450 + 39.5329i) q^{47} +(-39.3380 - 28.5807i) q^{49} +(4.79957 - 6.60605i) q^{50} +(-17.6209 + 5.72538i) q^{52} +(53.0919 - 38.5735i) q^{53} +(-8.41054 + 47.3602i) q^{55} +5.16763 q^{56} +(-15.1900 - 46.7500i) q^{58} +(-17.4262 + 53.6322i) q^{59} +(-50.2917 + 69.2205i) q^{61} +(66.5465 + 21.6223i) q^{62} +(43.6539 - 31.7164i) q^{64} -39.1320i q^{65} +27.8960 q^{67} +(3.61967 + 4.98205i) q^{68} +(-1.15032 + 3.54033i) q^{70} +(95.3640 + 69.2860i) q^{71} +(112.296 + 36.4872i) q^{73} +(2.30746 - 0.749741i) q^{74} +20.7138i q^{76} +(0.930031 + 6.67667i) q^{77} +(-73.5080 - 101.175i) q^{79} +(4.63743 + 14.2726i) q^{80} +(-66.8409 - 48.5627i) q^{82} +(19.2057 - 26.4344i) q^{83} +(-12.3699 + 4.01923i) q^{85} +(-49.0530 + 35.6391i) q^{86} +(64.3525 + 66.8020i) q^{88} +19.9195 q^{89} +(-1.69469 - 5.21573i) q^{91} +(-18.3278 + 56.4072i) q^{92} +(-33.9395 + 46.7137i) q^{94} +(-41.6079 - 13.5192i) q^{95} +(141.636 - 102.905i) q^{97} -67.5443i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) $ 16 * q - 4 * q^4 + 30 * q^7	$ 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.816494	+	1.12381i	0.408247	+	0.561904i	0.962790	−	0.270252i	$-0.0871069\pi$
$2$	0.816494	+	1.12381i	0.408247	+	0.561904i	−0.554543	+	0.832155i	$0.687107\pi$
$3$		0			0
$3$		0			0
$4$	0.639787	−	1.96906i	0.159947	−	0.492266i
$5$	3.53770	+	2.57029i	0.707540	+	0.514058i	0.882379	−	0.470539i	$-0.155940\pi$
$5$	3.53770	+	2.57029i	0.707540	+	0.514058i	−0.174839	+	0.984597i	$0.555940\pi$
$6$		0			0
$7$	0.582836	+	0.189375i	0.0832623	+	0.0270536i	0.350352	−	0.936618i	$-0.386062\pi$
$7$	0.582836	+	0.189375i	0.0832623	+	0.0270536i	−0.267090	+	0.963672i	$0.586062\pi$
$8$	8.01969	−	2.60575i	1.00246	−	0.325719i
$9$		0			0
$10$			6.07432i			0.607432i
$11$	4.81000	+	9.89262i	0.437273	+	0.899329i
$11$	4.81000	+	9.89262i	0.437273	+	0.899329i
$12$		0			0
$13$	−5.26002	−	7.23980i	−0.404617	−	0.556907i	0.557278	−	0.830326i	$-0.311846\pi$
$13$	−5.26002	−	7.23980i	−0.404617	−	0.556907i	−0.961895	+	0.273418i	$0.911846\pi$
$14$	0.263061	+	0.809619i	0.0187901	+	0.0578299i
$15$		0			0
$16$	2.77645	+	2.01721i	0.173528	+	0.126075i
$17$	−1.74830	+	2.40633i	−0.102841	+	0.141549i	−0.857336	−	0.514757i	$-0.827882\pi$
$17$	−1.74830	+	2.40633i	−0.102841	+	0.141549i	0.754495	+	0.656306i	$0.227882\pi$
$18$		0			0
$19$	−9.51507	+	3.09163i	−0.500793	+	0.162718i	−0.548511	−	0.836143i	$-0.684805\pi$
$19$	−9.51507	+	3.09163i	−0.500793	+	0.162718i	0.0477179	+	0.998861i	$0.484805\pi$
$20$	7.32444	−	5.32152i	0.366222	−	0.266076i
$21$		0			0
$22$	−7.19005	+	13.4828i	−0.326821	+	0.612853i
$23$	−28.6467			−1.24551			−0.622755	−	0.782417i	$-0.713987\pi$
$23$	−28.6467			−1.24551			−0.622755	+	0.782417i	$0.713987\pi$
$24$		0			0
$25$	−1.81649	−	5.59057i	−0.0726595	−	0.223623i
$26$	3.84136	−	11.8225i	0.147745	−	0.454711i
$27$		0			0
$28$	0.745782	−	1.02648i	0.0266351	−	0.0366601i
$29$	−33.6548	−	10.9351i	−1.16051	−	0.377073i	−0.335418	−	0.942069i	$-0.608878\pi$
$29$	−33.6548	−	10.9351i	−1.16051	−	0.377073i	−0.825093	+	0.564996i	$0.808878\pi$
$30$		0			0
$31$	40.7514	−	29.6076i	1.31456	−	0.955084i	0.314578	−	0.949232i	$-0.398137\pi$
$31$	40.7514	−	29.6076i	1.31456	−	0.955084i	0.999983	−	0.00585268i	$-0.00186298\pi$
$32$		−	28.9624i		−	0.905074i
$33$		0			0
$34$	−4.13173			−0.121521
$35$	1.57515	+	2.16801i	0.0450043	+	0.0619431i
$36$		0			0
$37$	0.539730	−	1.66112i	0.0145873	−	0.0448951i	−0.943498	−	0.331378i	$-0.892486\pi$
$37$	0.539730	−	1.66112i	0.0145873	−	0.0448951i	0.958085	+	0.286483i	$0.0924863\pi$
$38$	−11.2434	−	8.16880i	−0.295879	−	0.214969i
$39$		0			0
$40$	35.0688	+	11.3945i	0.876720	+	0.284864i
$41$	−56.5662	+	18.3795i	−1.37966	+	0.448279i	−0.902558	−	0.430567i	$-0.858313\pi$
$41$	−56.5662	+	18.3795i	−1.37966	+	0.448279i	−0.477104	+	0.878847i	$0.658313\pi$
$42$		0			0
$43$			43.6490i			1.01509i	0.861625	+	0.507546i	$0.169447\pi$
$43$			43.6490i			1.01509i	−0.861625	+	0.507546i	$0.830553\pi$
$44$	22.5566	−	3.14203i	0.512649	−	0.0714098i
$45$		0			0
$46$	−23.3899	−	32.1934i	−0.508476	−	0.699857i
$47$	12.8450	+	39.5329i	0.273298	+	0.841126i	0.989665	+	0.143402i	$0.0458040\pi$
$47$	12.8450	+	39.5329i	0.273298	+	0.841126i	−0.716366	+	0.697725i	$0.754196\pi$
$48$		0			0
$49$	−39.3380	−	28.5807i	−0.802816	−	0.583280i
$50$	4.79957	−	6.60605i	0.0959915	−	0.132121i
$51$		0			0
$52$	−17.6209	+	5.72538i	−0.338864	+	0.110103i
$53$	53.0919	−	38.5735i	1.00173	−	0.727802i	0.0392742	−	0.999228i	$-0.487495\pi$
$53$	53.0919	−	38.5735i	1.00173	−	0.727802i	0.962459	+	0.271427i	$0.0874954\pi$
$54$		0			0
$55$	−8.41054	+	47.3602i	−0.152919	+	0.861095i
$56$	5.16763			0.0922791
$57$		0			0
$58$	−15.1900	−	46.7500i	−0.261896	−	0.806035i
$59$	−17.4262	+	53.6322i	−0.295359	+	0.909021i	0.687742	+	0.725955i	$0.258602\pi$
$59$	−17.4262	+	53.6322i	−0.295359	+	0.909021i	−0.983101	+	0.183066i	$0.941398\pi$
$60$		0			0
$61$	−50.2917	+	69.2205i	−0.824454	+	1.13476i	0.164477	+	0.986381i	$0.447407\pi$
$61$	−50.2917	+	69.2205i	−0.824454	+	1.13476i	−0.988930	+	0.148382i	$0.952593\pi$
$62$	66.5465	+	21.6223i	1.07333	+	0.348746i
$63$		0			0
$64$	43.6539	−	31.7164i	0.682092	−	0.495569i
$65$		−	39.1320i		−	0.602031i
$66$		0			0
$67$	27.8960			0.416359			0.208179	−	0.978091i	$-0.433246\pi$
$67$	27.8960			0.416359			0.208179	+	0.978091i	$0.433246\pi$
$68$	3.61967	+	4.98205i	0.0532305	+	0.0732655i
$69$		0			0
$70$	−1.15032	+	3.54033i	−0.0164332	+	0.0505762i
$71$	95.3640	+	69.2860i	1.34316	+	0.975859i	0.999322	+	0.0368288i	$0.0117256\pi$
$71$	95.3640	+	69.2860i	1.34316	+	0.975859i	0.343834	+	0.939031i	$0.388274\pi$
$72$		0			0
$73$	112.296	+	36.4872i	1.53830	+	0.499824i	0.950907	−	0.309477i	$-0.100154\pi$
$73$	112.296	+	36.4872i	1.53830	+	0.499824i	0.587394	+	0.809301i	$0.300154\pi$
$74$	2.30746	−	0.749741i	0.0311820	−	0.0101316i
$75$		0			0
$76$			20.7138i			0.272550i
$77$	0.930031	+	6.67667i	0.0120783	+	0.0867100i
$78$		0			0
$79$	−73.5080	−	101.175i	−0.930481	−	1.28070i	−0.959672	−	0.281124i	$-0.909293\pi$
$79$	−73.5080	−	101.175i	−0.930481	−	1.28070i	0.0291902	−	0.999574i	$-0.490707\pi$
$80$	4.63743	+	14.2726i	0.0579679	+	0.178407i
$81$		0			0
$82$	−66.8409	−	48.5627i	−0.815133	−	0.592229i
$83$	19.2057	−	26.4344i	0.231394	−	0.318487i	−0.677493	−	0.735530i	$-0.736933\pi$
$83$	19.2057	−	26.4344i	0.231394	−	0.318487i	0.908887	+	0.417043i	$0.136933\pi$
$84$		0			0
$85$	−12.3699	+	4.01923i	−0.145529	+	0.0472851i
$86$	−49.0530	+	35.6391i	−0.570384	+	0.414408i
$87$		0			0
$88$	64.3525	+	66.8020i	0.731278	+	0.759114i
$89$	19.9195			0.223815			0.111908	−	0.993719i	$-0.464304\pi$
$89$	19.9195			0.223815			0.111908	+	0.993719i	$0.464304\pi$
$90$		0			0
$91$	−1.69469	−	5.21573i	−0.0186230	−	0.0573157i
$92$	−18.3278	+	56.4072i	−0.199215	+	0.613122i
$93$		0			0
$94$	−33.9395	+	46.7137i	−0.361059	+	0.496954i
$95$	−41.6079	−	13.5192i	−0.437978	−	0.142308i
$96$		0			0
$97$	141.636	−	102.905i	1.46017	−	1.06087i	0.476847	−	0.878986i	$-0.341780\pi$
$97$	141.636	−	102.905i	1.46017	−	1.06087i	0.983320	−	0.181886i	$-0.0582203\pi$
$98$		−	67.5443i		−	0.689228i
$99$		0			0
$100$	−12.1704			−0.121704
$101$	−49.7038	−	68.4113i	−0.492116	−	0.677340i	0.488660	−	0.872474i	$-0.337486\pi$
$101$	−49.7038	−	68.4113i	−0.492116	−	0.677340i	−0.980777	+	0.195134i	$0.937486\pi$
$102$		0			0
$103$	−9.94484	+	30.6071i	−0.0965519	+	0.297156i	−0.987655	−	0.156645i	$-0.949932\pi$
$103$	−9.94484	+	30.6071i	−0.0965519	+	0.297156i	0.891103	+	0.453801i	$0.149932\pi$
$104$	−61.0488	−	44.3546i	−0.587008	−	0.426486i
$105$		0			0
$106$	86.6983	+	28.1700i	0.817909	+	0.265755i
$107$	40.8441	−	13.2711i	0.381721	−	0.124029i	−0.111870	−	0.993723i	$-0.535684\pi$
$107$	40.8441	−	13.2711i	0.381721	−	0.124029i	0.493591	+	0.869694i	$0.335684\pi$
$108$		0			0
$109$			18.6259i			0.170879i	0.996343	+	0.0854397i	$0.0272295\pi$
$109$			18.6259i			0.170879i	−0.996343	+	0.0854397i	$0.972770\pi$
$110$	−60.0909	+	29.2175i	−0.546281	+	0.265614i
$111$		0			0
$112$	1.23621	+	1.70149i	0.0110375	+	0.0151919i
$113$	−51.9969	−	160.030i	−0.460149	−	1.41619i	−0.864982	−	0.501803i	$-0.832670\pi$
$113$	−51.9969	−	160.030i	−0.460149	−	1.41619i	0.404832	−	0.914391i	$-0.367330\pi$
$114$		0			0
$115$	−101.344	−	73.6304i	−0.881249	−	0.640265i
$116$	−43.0639	+	59.2724i	−0.371240	+	0.510969i
$117$		0			0
$118$	−74.5006	+	24.2067i	−0.631361	+	0.205142i
$119$	−1.47467	+	1.07141i	−0.0123922	+	0.00900346i
$120$		0			0
$121$	−74.7277	+	95.1671i	−0.617584	+	0.786505i
$122$	−118.853			−0.974208
$123$		0			0
$124$	−32.2270	−	99.1846i	−0.259896	−	0.799876i
$125$	41.7252	−	128.417i	0.333802	−	1.02734i
$126$		0			0
$127$	−56.1647	+	77.3041i	−0.442242	+	0.608693i	−0.970708	−	0.240261i	$-0.922767\pi$
$127$	−56.1647	+	77.3041i	−0.442242	+	0.608693i	0.528467	+	0.848954i	$0.322767\pi$
$128$	−38.8931	−	12.6371i	−0.303852	−	0.0987277i
$129$		0			0
$130$	43.9768	−	31.9510i	0.338283	−	0.245777i
$131$			201.569i			1.53869i	0.638833	+	0.769346i	$0.279418\pi$
$131$			201.569i			1.53869i	−0.638833	+	0.769346i	$0.720582\pi$
$132$		0			0
$133$	−6.13120			−0.0460993
$134$	22.7769	+	31.3497i	0.169977	+	0.233953i
$135$		0			0
$136$	−7.75052	+	23.8537i	−0.0569891	+	0.175395i
$137$	−106.735	−	77.5473i	−0.779085	−	0.566039i	0.125619	−	0.992079i	$-0.459908\pi$
$137$	−106.735	−	77.5473i	−0.779085	−	0.566039i	−0.904704	+	0.426040i	$0.859908\pi$
$138$		0			0
$139$	53.2373	+	17.2978i	0.383002	+	0.124445i	0.494189	−	0.869355i	$-0.335465\pi$
$139$	53.2373	+	17.2978i	0.383002	+	0.124445i	−0.111187	+	0.993800i	$0.535465\pi$
$140$	5.27671	−	1.71451i	0.0376908	−	0.0122465i
$141$		0			0
$142$			163.742i			1.15312i
$143$	46.3198	−	86.8588i	0.323915	−	0.607404i
$144$		0			0
$145$	−90.9543	−	125.188i	−0.627271	−	0.863365i
$146$	50.6844	+	155.991i	0.347153	+	1.06843i
$147$		0			0
$148$	−2.92554	−	2.12553i	−0.0197671	−	0.0143617i
$149$	17.8569	−	24.5779i	0.119845	−	0.164952i	−0.744879	−	0.667199i	$-0.767493\pi$
$149$	17.8569	−	24.5779i	0.119845	−	0.164952i	0.864724	+	0.502247i	$0.167493\pi$
$150$		0			0
$151$	107.960	−	35.0785i	0.714970	−	0.232308i	0.0711288	−	0.997467i	$-0.477340\pi$
$151$	107.960	−	35.0785i	0.714970	−	0.232308i	0.643841	+	0.765159i	$0.277340\pi$
$152$	−68.2518	+	49.5879i	−0.449025	+	0.326236i
$153$		0			0
$154$	−6.74392	+	6.49663i	−0.0437917	+	0.0421859i
$155$	220.266			1.42107
$156$		0			0
$157$	6.92048	+	21.2991i	0.0440795	+	0.135663i	0.970674	−	0.240399i	$-0.0772782\pi$
$157$	6.92048	+	21.2991i	0.0440795	+	0.135663i	−0.926595	+	0.376061i	$0.877278\pi$
$158$	53.6825	−	165.218i	0.339763	−	1.04568i
$159$		0			0
$160$	74.4417	−	102.460i	0.465261	−	0.640376i
$161$	−16.6963	−	5.42497i	−0.103704	−	0.0336955i
$162$		0			0
$163$	103.016	−	74.8454i	0.631999	−	0.459174i	−0.225093	−	0.974337i	$-0.572269\pi$
$163$	103.016	−	74.8454i	0.631999	−	0.459174i	0.857092	+	0.515163i	$0.172269\pi$
$164$			123.141i			0.750862i
$165$		0			0
$166$	45.3886			0.273425
$167$	145.852	+	200.748i	0.873366	+	1.20208i	0.978215	+	0.207597i	$0.0665641\pi$
$167$	145.852	+	200.748i	0.873366	+	1.20208i	−0.104849	+	0.994488i	$0.533436\pi$
$168$		0			0
$169$	27.4770	−	84.5656i	0.162586	−	0.500388i
$170$	−14.6168	−	10.6197i	−0.0859813	−	0.0624690i
$171$		0			0
$172$	85.9476	+	27.9261i	0.499695	+	0.162361i
$173$	178.298	−	57.9327i	1.03063	−	0.334871i	0.255589	−	0.966786i	$-0.417731\pi$
$173$	178.298	−	57.9327i	1.03063	−	0.334871i	0.775038	+	0.631915i	$0.217731\pi$
$174$		0			0
$175$		−	3.60238i		−	0.0205850i
$176$	−6.60073	+	37.1691i	−0.0375042	+	0.211188i
$177$		0			0
$178$	16.2642	+	22.3857i	0.0913718	+	0.125762i
$179$	−7.11182	−	21.8879i	−0.0397308	−	0.122279i	0.929224	−	0.369517i	$-0.120477\pi$
$179$	−7.11182	−	21.8879i	−0.0397308	−	0.122279i	−0.968955	+	0.247238i	$0.920477\pi$
$180$		0			0
$181$	112.686	+	81.8714i	0.622576	+	0.452328i	0.853820	−	0.520568i	$-0.174280\pi$
$181$	112.686	+	81.8714i	0.622576	+	0.452328i	−0.231244	+	0.972896i	$0.574280\pi$
$182$	4.47777	−	6.16312i	0.0246031	−	0.0338633i
$183$		0			0
$184$	−229.738	+	74.6463i	−1.24858	+	0.405687i
$185$	6.17897	−	4.48928i	0.0333998	−	0.0242664i
$186$		0			0
$187$	−32.2142	−	5.72081i	−0.172269	−	0.0305926i
$188$	86.0609			0.457771
$189$		0			0
$190$	−18.7796	−	57.7976i	−0.0988398	−	0.304198i
$191$	−27.0541	+	83.2638i	−0.141644	+	0.435936i	−0.996564	−	0.0828237i	$-0.973606\pi$
$191$	−27.0541	+	83.2638i	−0.141644	+	0.435936i	0.854920	+	0.518760i	$0.173606\pi$
$192$		0			0
$193$	−82.9341	+	114.149i	−0.429710	+	0.591446i	−0.967887	−	0.251387i	$-0.919113\pi$
$193$	−82.9341	+	114.149i	−0.429710	+	0.591446i	0.538176	+	0.842832i	$0.319113\pi$
$194$	231.290	+	75.1507i	1.19222	+	0.387375i
$195$		0			0
$196$	−81.4452	+	59.1734i	−0.415537	+	0.301905i
$197$			180.754i			0.917532i	0.888557	+	0.458766i	$0.151708\pi$
$197$			180.754i			0.917532i	−0.888557	+	0.458766i	$0.848292\pi$
$198$		0			0
$199$	57.3438			0.288160			0.144080	−	0.989566i	$-0.453978\pi$
$199$	57.3438			0.288160			0.144080	+	0.989566i	$0.453978\pi$
$200$	−29.1353	−	40.1013i	−0.145677	−	0.200507i
$201$		0			0
$202$	36.2984	−	111.715i	0.179695	−	0.553044i
$203$	−17.5444	−	12.7468i	−0.0864257	−	0.0627919i
$204$		0			0
$205$	−247.355	−	80.3704i	−1.20661	−	0.392051i
$206$	−42.5163	+	13.8144i	−0.206390	+	0.0670602i
$207$		0			0
$208$		−	30.7115i		−	0.147651i
$209$	−76.3519	−	79.2582i	−0.365320	−	0.379226i
$210$		0			0
$211$	−32.2024	−	44.3228i	−0.152618	−	0.210061i	0.725861	−	0.687841i	$-0.241441\pi$
$211$	−32.2024	−	44.3228i	−0.152618	−	0.210061i	−0.878479	+	0.477781i	$0.841441\pi$
$212$	−41.9862	−	129.220i	−0.198048	−	0.609529i
$213$		0			0
$214$	48.2631	+	35.0652i	0.225528	+	0.163856i
$215$	−112.191	+	154.417i	−0.521816	+	0.718219i
$216$		0			0
$217$	29.3583	−	9.53910i	0.135292	−	0.0439590i
$218$	−20.9319	+	15.2079i	−0.0960178	+	0.0697610i
$219$		0			0
$220$	87.8743	+	46.8614i	0.399429	+	0.213006i
$221$	26.6174			0.120441
$222$		0			0
$223$	90.5096	+	278.560i	0.405873	+	1.24915i	0.920164	+	0.391532i	$0.128055\pi$
$223$	90.5096	+	278.560i	0.405873	+	1.24915i	−0.514292	+	0.857615i	$0.671945\pi$
$224$	5.48475	−	16.8803i	0.0244855	−	0.0753585i
$225$		0			0
$226$	137.388	−	189.098i	0.607910	−	0.836717i
$227$	−82.0064	−	26.6455i	−0.361262	−	0.117381i	0.122762	−	0.992436i	$-0.460825\pi$
$227$	−82.0064	−	26.6455i	−0.361262	−	0.117381i	−0.484023	+	0.875055i	$0.660825\pi$
$228$		0			0
$229$	−40.6339	+	29.5223i	−0.177441	+	0.128918i	−0.672961	−	0.739678i	$-0.734978\pi$
$229$	−40.6339	+	29.5223i	−0.177441	+	0.128918i	0.495520	+	0.868597i	$0.334978\pi$
$230$		−	174.009i		−	0.756563i
$231$		0			0
$232$	−298.396			−1.28619
$233$	−251.058	−	345.551i	−1.07750	−	1.48305i	−0.862243	−	0.506494i	$-0.830941\pi$
$233$	−251.058	−	345.551i	−1.07750	−	1.48305i	−0.215257	−	0.976558i	$-0.569059\pi$
$234$		0			0
$235$	−56.1692	+	172.871i	−0.239018	+	0.735622i
$236$	94.4562	+	68.6265i	0.400238	+	0.290790i
$237$		0			0
$238$	−2.40812	−	0.782445i	−0.0101181	−	0.00328759i
$239$	−18.1556	+	5.89911i	−0.0759648	+	0.0246825i	−0.346753	−	0.937957i	$-0.612716\pi$
$239$	−18.1556	+	5.89911i	−0.0759648	+	0.0246825i	0.270788	+	0.962639i	$0.412716\pi$
$240$		0			0
$241$		−	53.8901i		−	0.223611i	−0.993730	−	0.111805i	$-0.964337\pi$
$241$		−	53.8901i		−	0.223611i	0.993730	−	0.111805i	$-0.0356633\pi$
$242$	−167.964	−	6.27624i	−0.694067	−	0.0259349i
$243$		0			0
$244$	104.124	+	143.314i	0.426736	+	0.587352i
$245$	−65.7053	−	202.220i	−0.268185	−	0.825388i
$246$		0			0
$247$	72.4322	+	52.6251i	0.293248	+	0.213057i
$248$	249.663	−	343.632i	1.00671	−	1.38561i
$249$		0			0
$250$	178.384	−	57.9606i	0.713538	−	0.231842i
$251$	−323.284	+	234.879i	−1.28798	+	0.935775i	−0.999763	−	0.0217890i	$-0.993064\pi$
$251$	−323.284	+	234.879i	−1.28798	+	0.935775i	−0.288221	+	0.957564i	$0.593064\pi$
$252$		0			0
$253$	−137.791	−	283.391i	−0.544628	−	1.12012i
$254$	−132.733			−0.522571
$255$		0			0
$256$	−84.2515	−	259.299i	−0.329107	−	1.01289i
$257$	−141.664	+	435.996i	−0.551221	+	1.69648i	0.154500	+	0.987993i	$0.450623\pi$
$257$	−141.664	+	435.996i	−0.551221	+	1.69648i	−0.705721	+	0.708490i	$0.749377\pi$
$258$		0			0
$259$	0.629149	−	0.865949i	0.00242915	−	0.00334343i
$260$	−77.0534	−	25.0362i	−0.296359	−	0.0962930i
$261$		0			0
$262$	−226.524	+	164.579i	−0.864596	+	0.628166i
$263$		−	262.279i		−	0.997259i	−0.866815	−	0.498630i	$-0.833837\pi$
$263$		−	262.279i		−	0.997259i	0.866815	−	0.498630i	$-0.166163\pi$
$264$		0			0
$265$	286.968			1.08290
$266$	−5.00609	−	6.89029i	−0.0188199	−	0.0259033i
$267$		0			0
$268$	17.8475	−	54.9290i	0.0665952	−	0.204959i
$269$	−58.7944	−	42.7166i	−0.218566	−	0.158798i	0.473115	−	0.881001i	$-0.343130\pi$
$269$	−58.7944	−	42.7166i	−0.218566	−	0.158798i	−0.691681	+	0.722203i	$0.743130\pi$
$270$		0			0
$271$	−191.391	−	62.1866i	−0.706238	−	0.229471i	−0.0661919	−	0.997807i	$-0.521085\pi$
$271$	−191.391	−	62.1866i	−0.706238	−	0.229471i	−0.640047	+	0.768336i	$0.721085\pi$
$272$	−9.70813	+	3.15436i	−0.0356917	+	0.0115969i
$273$		0			0
$274$		−	183.266i		−	0.668854i
$275$	46.5681	−	44.8605i	0.169338	−	0.163129i
$276$		0			0
$277$	209.870	+	288.862i	0.757655	+	1.04282i	0.997405	+	0.0719881i	$0.0229344\pi$
$277$	209.870	+	288.862i	0.757655	+	1.04282i	−0.239751	+	0.970835i	$0.577066\pi$
$278$	24.0285	+	73.9520i	0.0864333	+	0.266014i
$279$		0			0
$280$	18.2815	+	13.2823i	0.0652912	+	0.0474368i
$281$	−162.502	+	223.665i	−0.578300	+	0.795962i	−0.993508	−	0.113765i	$-0.963709\pi$
$281$	−162.502	+	223.665i	−0.578300	+	0.795962i	0.415207	+	0.909727i	$0.363709\pi$
$282$		0			0
$283$	272.768	−	88.6277i	0.963844	−	0.313172i	0.215516	−	0.976500i	$-0.430857\pi$
$283$	272.768	−	88.6277i	0.963844	−	0.313172i	0.748328	+	0.663328i	$0.230857\pi$
$284$	197.441	−	143.449i	0.695216	−	0.505104i
$285$		0			0
$286$	135.432	−	18.8651i	0.473540	−	0.0659620i
$287$	−36.4494			−0.127001
$288$		0			0
$289$	86.5720	+	266.441i	0.299557	+	0.921942i
$290$	66.4234	−	204.430i	0.229046	−	0.704932i
$291$		0			0
$292$	143.691	−	197.774i	0.492093	−	0.677308i
$293$	141.720	+	46.0477i	0.483687	+	0.157160i	0.540703	−	0.841214i	$-0.318158\pi$
$293$	141.720	+	46.0477i	0.483687	+	0.157160i	−0.0570154	+	0.998373i	$0.518158\pi$
$294$		0			0
$295$	−199.499	+	144.945i	−0.676268	+	0.491337i
$296$		−	14.7281i		−	0.0497570i
$297$		0			0
$298$	42.2009			0.141614
$299$	150.682	+	207.397i	0.503954	+	0.693634i
$300$		0			0
$301$	−8.26602	+	25.4402i	−0.0274619	+	0.0845189i
$302$	127.570	+	92.6853i	0.422419	+	0.306905i
$303$		0			0
$304$	−32.6546	−	10.6101i	−0.107416	−	0.0349017i
$305$	−355.834	+	115.617i	−1.16667	+	0.379073i
$306$		0			0
$307$		−	277.276i		−	0.903179i	−0.892226	−	0.451590i	$-0.850857\pi$
$307$		−	277.276i		−	0.903179i	0.892226	−	0.451590i	$-0.149143\pi$
$308$	13.7418	+	2.44036i	0.0446162	+	0.00792324i
$309$		0			0
$310$	179.846	+	247.537i	0.580149	+	0.798506i
$311$	64.7940	+	199.415i	0.208341	+	0.641207i	0.999560	+	0.0296738i	$0.00944686\pi$
$311$	64.7940	+	199.415i	0.208341	+	0.641207i	−0.791219	+	0.611533i	$0.790553\pi$
$312$		0			0
$313$	−86.4426	−	62.8042i	−0.276174	−	0.200652i	0.441073	−	0.897471i	$-0.354598\pi$
$313$	−86.4426	−	62.8042i	−0.276174	−	0.200652i	−0.717247	+	0.696819i	$0.754598\pi$
$314$	−18.2855	+	25.1678i	−0.0582341	+	0.0801523i
$315$		0			0
$316$	−246.250	+	80.0114i	−0.779271	+	0.253201i
$317$	396.169	−	287.833i	1.24974	−	0.907992i	0.251537	−	0.967848i	$-0.419064\pi$
$317$	396.169	−	287.833i	1.24974	−	0.907992i	0.998207	+	0.0598560i	$0.0190641\pi$
$318$		0			0
$319$	−53.7030	−	385.532i	−0.168348	−	1.20857i
$320$	235.955			0.737359
$321$		0			0
$322$	−7.53584	−	23.1929i	−0.0234032	−	0.0720277i
$323$	9.19571	−	28.3015i	0.0284697	−	0.0876207i
$324$		0			0
$325$	−30.9198	+	42.5575i	−0.0951380	+	0.130946i
$326$	168.224	+	54.6592i	0.516023	+	0.167666i
$327$		0			0
$328$	−405.751	+	294.795i	−1.23704	+	0.898765i
$329$			25.4737i			0.0774278i
$330$		0			0
$331$	−333.988			−1.00903			−0.504514	−	0.863404i	$-0.668328\pi$
$331$	−333.988			−1.00903			−0.504514	+	0.863404i	$0.668328\pi$
$332$	−39.7635	−	54.7297i	−0.119770	−	0.164849i
$333$		0			0
$334$	−106.515	+	327.819i	−0.318907	+	0.981495i
$335$	98.6878	+	71.7009i	0.294590	+	0.214032i
$336$		0			0
$337$	−476.898	−	154.953i	−1.41513	−	0.459802i	−0.501076	−	0.865403i	$-0.667062\pi$
$337$	−476.898	−	154.953i	−1.41513	−	0.459802i	−0.914050	+	0.405601i	$0.867062\pi$
$338$	117.470	−	38.1684i	0.347545	−	0.112924i
$339$		0			0
$340$			26.9286i			0.0792019i
$341$	488.911	+	260.725i	1.43376	+	0.764590i
$342$		0			0
$343$	−35.1655	−	48.4012i	−0.102523	−	0.141111i
$344$	113.738	+	350.051i	0.330635	+	1.01759i
$345$		0			0
$346$	210.685	+	153.071i	0.608915	+	0.442403i
$347$	119.783	−	164.867i	0.345195	−	0.475120i	−0.600755	−	0.799433i	$-0.705133\pi$
$347$	119.783	−	164.867i	0.345195	−	0.475120i	0.945950	+	0.324313i	$0.105133\pi$
$348$		0			0
$349$	401.860	−	130.572i	1.15146	−	0.374133i	0.329768	−	0.944062i	$-0.393029\pi$
$349$	401.860	−	130.572i	1.15146	−	0.374133i	0.821694	+	0.569929i	$0.193029\pi$
$350$	4.04838	−	2.94132i	0.0115668	−	0.00840378i
$351$		0			0
$352$	286.514	−	139.309i	0.813959	−	0.395765i
$353$	−314.375			−0.890581			−0.445290	−	0.895386i	$-0.646900\pi$
$353$	−314.375			−0.890581			−0.445290	+	0.895386i	$0.646900\pi$
$354$		0			0
$355$	159.284	+	490.226i	0.448688	+	1.38092i
$356$	12.7443	−	39.2228i	0.0357985	−	0.110177i
$357$		0			0
$358$	18.7910	−	25.8637i	0.0524890	−	0.0722448i
$359$	−394.595	−	128.212i	−1.09915	−	0.357135i	−0.297375	−	0.954761i	$-0.596111\pi$
$359$	−394.595	−	128.212i	−1.09915	−	0.357135i	−0.801775	+	0.597625i	$0.796111\pi$
$360$		0			0
$361$	−211.077	+	153.356i	−0.584700	+	0.424810i
$362$			193.485i			0.534489i
$363$		0			0
$364$	−11.3543			−0.0311933
$365$	303.487	+	417.714i	0.831471	+	1.14442i
$366$		0			0
$367$	143.075	−	440.338i	0.389849	−	1.19983i	−0.543052	−	0.839699i	$-0.682731\pi$
$367$	143.075	−	440.338i	0.389849	−	1.19983i	0.932901	−	0.360133i	$-0.117269\pi$
$368$	−79.5362	−	57.7864i	−0.216131	−	0.157028i
$369$		0			0
$370$	10.0902	+	3.27850i	0.0272707	+	0.00886080i
$371$	38.2487	−	12.4278i	0.103096	−	0.0334980i
$372$		0			0
$373$		−	656.230i		−	1.75933i	−0.475594	−	0.879665i	$-0.657767\pi$
$373$		−	656.230i		−	1.75933i	0.475594	−	0.879665i	$-0.342233\pi$
$374$	−19.8736	−	40.8736i	−0.0531380	−	0.109288i
$375$		0			0
$376$	206.026	+	283.571i	0.547942	+	0.754177i
$377$	97.8571	+	301.173i	0.259568	+	0.798868i
$378$		0			0
$379$	364.869	+	265.093i	0.962715	+	0.699453i	0.953780	−	0.300507i	$-0.0971558\pi$
$379$	364.869	+	265.093i	0.962715	+	0.699453i	0.00893516	+	0.999960i	$0.497156\pi$
$380$	−53.2404	+	73.2791i	−0.140106	+	0.192840i
$381$		0			0
$382$	−115.662	+	37.5808i	−0.302780	+	0.0983792i
$383$	255.582	−	185.691i	0.667315	−	0.484833i	−0.201810	−	0.979425i	$-0.564682\pi$
$383$	255.582	−	185.691i	0.667315	−	0.484833i	0.869125	+	0.494592i	$0.164682\pi$
$384$		0			0
$385$	−13.8708	+	26.0105i	−0.0360281	+	0.0675598i
$386$	−195.997			−0.507763
$387$		0			0
$388$	−112.009	−	344.728i	−0.288682	−	0.888473i
$389$	66.2453	−	203.882i	0.170296	−	0.524119i	−0.829091	−	0.559114i	$-0.811142\pi$
$389$	66.2453	−	203.882i	0.170296	−	0.524119i	0.999387	+	0.0349951i	$0.0111416\pi$
$390$		0			0
$391$	50.0831	−	68.9335i	0.128090	−	0.176300i
$392$	−389.953	−	126.703i	−0.994778	−	0.323223i
$393$		0			0
$394$	−203.132	+	147.584i	−0.515564	+	0.374579i
$395$		−	546.864i		−	1.38447i
$396$		0			0
$397$	369.231			0.930052			0.465026	−	0.885297i	$-0.346045\pi$
$397$	369.231			0.930052			0.465026	+	0.885297i	$0.346045\pi$
$398$	46.8209	+	64.4434i	0.117640	+	0.161918i
$399$		0			0
$400$	6.23396	−	19.1862i	0.0155849	−	0.0479654i
$401$	−90.1495	−	65.4975i	−0.224812	−	0.163335i	0.469678	−	0.882838i	$-0.344370\pi$
$401$	−90.1495	−	65.4975i	−0.224812	−	0.163335i	−0.694490	+	0.719502i	$0.744370\pi$
$402$		0			0
$403$	−428.706	−	139.295i	−1.06379	−	0.345645i
$404$	−166.506	+	54.1011i	−0.412144	+	0.133914i
$405$		0			0
$406$		−	30.1242i		−	0.0741975i
$407$	19.0289	−	2.65065i	0.0467541	−	0.00651264i
$408$		0			0
$409$	119.418	+	164.365i	0.291976	+	0.401870i	0.929655	−	0.368432i	$-0.120105\pi$
$409$	119.418	+	164.365i	0.291976	+	0.401870i	−0.637679	+	0.770302i	$0.720105\pi$
$410$	−111.643	−	343.601i	−0.272299	−	0.838051i
$411$		0			0
$412$	53.9047	+	39.1640i	0.130837	+	0.0950584i
$413$	−20.3132	+	27.9587i	−0.0491845	+	0.0676967i
$414$		0			0
$415$	135.888	−	44.1528i	0.327442	−	0.106392i
$416$	−209.682	+	152.343i	−0.504042	+	0.366208i
$417$		0			0
$418$	26.7301	−	150.519i	0.0639475	−	0.360092i
$419$	−519.060			−1.23881			−0.619404	−	0.785073i	$-0.712626\pi$
$419$	−519.060			−1.23881			−0.619404	+	0.785073i	$0.712626\pi$
$420$		0			0
$421$	103.047	+	317.147i	0.244768	+	0.753317i	0.995675	+	0.0929092i	$0.0296166\pi$
$421$	103.047	+	317.147i	0.244768	+	0.753317i	−0.750907	+	0.660408i	$0.770383\pi$
$422$	23.5172	−	72.3785i	0.0557280	−	0.171513i
$423$		0			0
$424$	325.267	−	447.692i	0.767139	−	1.05588i
$425$	16.6285	+	5.40293i	0.0391259	+	0.0127128i
$426$		0			0
$427$	−42.4204	+	30.8202i	−0.0993453	+	0.0721786i
$428$		−	88.9153i		−	0.207746i
$429$		0			0
$430$	−265.138			−0.616599
$431$	−430.041	−	591.901i	−0.997775	−	1.37332i	−0.926680	−	0.375851i	$-0.877351\pi$
$431$	−430.041	−	591.901i	−0.997775	−	1.37332i	−0.0710952	−	0.997470i	$-0.522649\pi$
$432$		0			0
$433$	−115.298	+	354.852i	−0.266278	+	0.819519i	0.725119	+	0.688624i	$0.241785\pi$
$433$	−115.298	+	354.852i	−0.266278	+	0.819519i	−0.991396	+	0.130895i	$0.958215\pi$
$434$	34.6910	+	25.2045i	0.0799331	+	0.0580748i
$435$		0			0
$436$	36.6755	+	11.9166i	0.0841181	+	0.0273316i
$437$	272.576	−	88.5652i	0.623743	−	0.202666i
$438$		0			0
$439$			294.954i			0.671878i	0.941884	+	0.335939i	$0.109054\pi$
$439$			294.954i			0.671878i	−0.941884	+	0.335939i	$0.890946\pi$
$440$	55.9592	+	401.730i	0.127180	+	0.913023i
$441$		0			0
$442$	21.7330	+	29.9129i	0.0491696	+	0.0676761i
$443$	−156.228	−	480.820i	−0.352659	−	1.08537i	−0.957355	−	0.288915i	$-0.906705\pi$
$443$	−156.228	−	480.820i	−0.352659	−	1.08537i	0.604696	−	0.796456i	$-0.293295\pi$
$444$		0			0
$445$	70.4694	+	51.1990i	0.158358	+	0.115054i
$446$	−239.147	+	329.158i	−0.536204	+	0.738022i
$447$		0			0
$448$	31.4494	−	10.2185i	0.0701995	−	0.0228092i
$449$	−21.5081	+	15.6265i	−0.0479021	+	0.0348029i	−0.611479	−	0.791261i	$-0.709425\pi$
$449$	−21.5081	+	15.6265i	−0.0479021	+	0.0348029i	0.563577	+	0.826064i	$0.309425\pi$
$450$		0			0
$451$	−453.904	−	471.182i	−1.00644	−	1.04475i
$452$	−348.376			−0.770744
$453$		0			0
$454$	−37.0133	−	113.915i	−0.0815271	−	0.250915i
$455$	7.41062	−	22.8076i	0.0162871	−	0.0501265i
$456$		0			0
$457$	−103.859	+	142.950i	−0.227262	+	0.312800i	−0.907387	−	0.420297i	$-0.861926\pi$
$457$	−103.859	+	142.950i	−0.227262	+	0.312800i	0.680124	+	0.733097i	$0.261926\pi$
$458$	−66.3547	−	21.5600i	−0.144879	−	0.0470741i
$459$		0			0
$460$	−209.821	+	152.444i	−0.456133	+	0.331400i
$461$		−	155.031i		−	0.336292i	−0.985762	−	0.168146i	$-0.946222\pi$
$461$		−	155.031i		−	0.336292i	0.985762	−	0.168146i	$-0.0537781\pi$
$462$		0			0
$463$	−192.026			−0.414744			−0.207372	−	0.978262i	$-0.566491\pi$
$463$	−192.026			−0.414744			−0.207372	+	0.978262i	$0.566491\pi$
$464$	−71.3825	−	98.2496i	−0.153842	−	0.211745i
$465$		0			0
$466$	183.346	−	564.280i	0.393446	−	1.21090i
$467$	261.410	+	189.925i	0.559764	+	0.406692i	0.831373	−	0.555715i	$-0.187556\pi$
$467$	261.410	+	189.925i	0.559764	+	0.406692i	−0.271609	+	0.962408i	$0.587556\pi$
$468$		0			0
$469$	16.2588	+	5.28281i	0.0346670	+	0.0112640i
$470$	−240.136	+	78.0248i	−0.510927	+	0.166010i
$471$		0			0
$472$			475.522i			1.00746i
$473$	−431.802	+	209.952i	−0.912902	+	0.443872i
$474$		0			0
$475$	34.5680	+	47.5788i	0.0727747	+	0.100166i
$476$	1.16620	+	3.58920i	0.00245000	+	0.00754033i
$477$		0			0
$478$	−21.4534	−	15.5868i	−0.0448815	−	0.0326083i
$479$	269.472	−	370.897i	0.562572	−	0.774315i	−0.429078	−	0.903267i	$-0.641162\pi$
$479$	269.472	−	370.897i	0.562572	−	0.774315i	0.991651	+	0.128953i	$0.0411615\pi$
$480$		0			0
$481$	−14.8652	+	4.82998i	−0.0309047	+	0.0100415i
$482$	60.5621	−	44.0010i	0.125648	−	0.0912883i
$483$		0			0
$484$	139.580	+	208.030i	0.288389	+	0.429815i
$485$	765.561			1.57848
$486$		0			0
$487$	76.3014	+	234.832i	0.156676	+	0.482200i	0.998327	−	0.0578223i	$-0.0184157\pi$
$487$	76.3014	+	234.832i	0.156676	+	0.482200i	−0.841650	+	0.540023i	$0.818416\pi$
$488$	−222.952	+	686.175i	−0.456868	+	1.40610i
$489$		0			0
$490$	173.608	−	238.952i	0.354303	−	0.487656i
$491$	41.1903	+	13.3835i	0.0838906	+	0.0272577i	0.350662	−	0.936502i	$-0.385957\pi$
$491$	41.1903	+	13.3835i	0.0838906	+	0.0272577i	−0.266771	+	0.963760i	$0.585957\pi$
$492$		0			0
$493$	85.1523	−	61.8668i	0.172723	−	0.125490i
$494$			124.368i			0.251757i
$495$		0			0
$496$	172.869			0.348526
$497$	42.4606	+	58.4419i	0.0854337	+	0.117589i
$498$		0			0
$499$	−152.407	+	469.060i	−0.305425	+	0.940000i	0.674094	+	0.738646i	$0.264534\pi$
$499$	−152.407	+	469.060i	−0.305425	+	0.940000i	−0.979518	+	0.201355i	$0.935466\pi$
$500$	−226.166	−	164.319i	−0.452332	−	0.328639i
$501$		0			0
$502$	−527.918	−	171.531i	−1.05163	−	0.341695i
$503$	284.470	−	92.4299i	0.565547	−	0.183757i	−0.0122686	−	0.999925i	$-0.503905\pi$
$503$	284.470	−	92.4299i	0.565547	−	0.183757i	0.577816	+	0.816167i	$0.303905\pi$
$504$		0			0
$505$		−	369.772i		−	0.732222i
$506$	205.972	−	386.237i	0.407058	−	0.763315i
$507$		0			0
$508$	116.283	+	160.050i	0.228904	+	0.315059i
$509$	167.228	+	514.675i	0.328543	+	1.01115i	0.969816	+	0.243838i	$0.0784064\pi$
$509$	167.228	+	514.675i	0.328543	+	1.01115i	−0.641274	+	0.767312i	$0.721594\pi$
$510$		0			0
$511$	58.5404	+	42.5321i	0.114560	+	0.0832330i
$512$	126.463	−	174.061i	0.246997	−	0.339963i
$513$		0			0
$514$	−605.643	+	196.785i	−1.17829	+	0.382851i
$515$	−113.851	+	82.7176i	−0.221070	+	0.160617i
$516$		0			0
$517$	−329.299	+	317.224i	−0.636943	+	0.613587i
$518$	1.48686			0.00287038
$519$		0			0
$520$	−101.968	−	313.827i	−0.196093	−	0.603513i
$521$	63.8533	−	196.520i	0.122559	−	0.377198i	−0.870889	−	0.491479i	$-0.836456\pi$
$521$	63.8533	−	196.520i	0.122559	−	0.377198i	0.993448	+	0.114281i	$0.0364564\pi$
$522$		0			0
$523$	−33.1163	+	45.5807i	−0.0633199	+	0.0871524i	−0.839503	−	0.543356i	$-0.817153\pi$
$523$	−33.1163	+	45.5807i	−0.0633199	+	0.0871524i	0.776183	+	0.630508i	$0.217153\pi$
$524$	396.901	+	128.961i	0.757445	+	0.246109i
$525$		0			0
$526$	294.751	−	214.149i	0.560363	−	0.407128i
$527$			149.824i			0.284297i
$528$		0			0
$529$	291.635			0.551295
$530$	234.308	+	322.497i	0.442090	+	0.608485i
$531$		0			0
$532$	−3.92267	+	12.0727i	−0.00737343	+	0.0226931i
$533$	430.603	+	312.851i	0.807885	+	0.586963i
$534$		0			0
$535$	178.605	+	58.0322i	0.333841	+	0.108471i
$536$	223.717	−	72.6902i	0.417383	−	0.135616i
$537$		0			0
$538$		−	100.951i		−	0.187642i
$539$	93.5222	−	526.629i	0.173511	−	0.977049i
$540$		0			0
$541$	−263.713	−	362.970i	−0.487455	−	0.670924i	0.492461	−	0.870334i	$-0.336097\pi$
$541$	−263.713	−	362.970i	−0.487455	−	0.670924i	−0.979916	+	0.199411i	$0.936097\pi$
$542$	−86.3835	−	265.861i	−0.159379	−	0.490519i
$543$		0			0
$544$	69.6930	+	50.6349i	0.128112	+	0.0930789i
$545$	−47.8739	+	65.8927i	−0.0878420	+	0.120904i
$546$		0			0
$547$	789.192	−	256.424i	1.44276	−	0.468782i	0.520006	−	0.854163i	$-0.325930\pi$
$547$	789.192	−	256.424i	1.44276	−	0.468782i	0.922758	+	0.385380i	$0.125930\pi$
$548$	−220.983	+	160.554i	−0.403254	+	0.292981i
$549$		0			0
$550$	88.4370	+	15.7052i	0.160795	+	0.0285550i
$551$	354.036			0.642533
$552$		0			0
$553$	−23.6831	−	72.8891i	−0.0428266	−	0.131807i
$554$	−153.267	+	471.708i	−0.276655	+	0.851458i
$555$		0			0
$556$	68.1211	−	93.7606i	0.122520	−	0.168634i
$557$	961.341	+	312.359i	1.72593	+	0.560788i	0.992851	−	0.119359i	$-0.0380839\pi$
$557$	961.341	+	312.359i	1.72593	+	0.560788i	0.733076	+	0.680147i	$0.238084\pi$
$558$		0			0
$559$	316.010	−	229.594i	0.565312	−	0.410723i
$560$			9.19677i			0.0164228i
$561$		0			0
$562$	−384.039			−0.683343
$563$	4.72664	+	6.50566i	0.00839545	+	0.0115553i	0.813194	−	0.581993i	$-0.197727\pi$
$563$	4.72664	+	6.50566i	0.00839545	+	0.0115553i	−0.804799	+	0.593548i	$0.797727\pi$
$564$		0			0
$565$	227.374	−	699.785i	0.402432	−	1.23856i
$566$	322.314	+	234.175i	0.569459	+	0.413736i
$567$		0			0
$568$	945.332	+	307.157i	1.66432	+	0.540769i
$569$	−628.536	+	204.224i	−1.10463	+	0.358917i	−0.803884	−	0.594786i	$-0.797237\pi$
$569$	−628.536	+	204.224i	−1.10463	+	0.358917i	−0.300749	+	0.953703i	$0.597237\pi$
$570$		0			0
$571$			472.496i			0.827489i	0.910393	+	0.413745i	$0.135779\pi$
$571$			472.496i			0.827489i	−0.910393	+	0.413745i	$0.864221\pi$
$572$	−141.396	−	146.778i	−0.247195	−	0.256605i
$573$		0			0
$574$	−29.7607	−	40.9621i	−0.0518479	−	0.0713625i
$575$	52.0364	+	160.152i	0.0904981	+	0.278524i
$576$		0			0
$577$	156.570	+	113.755i	0.271352	+	0.197149i	0.715137	−	0.698985i	$-0.246364\pi$
$577$	156.570	+	113.755i	0.271352	+	0.197149i	−0.443785	+	0.896133i	$0.646364\pi$
$578$	−228.743	+	314.838i	−0.395749	+	0.544702i
$579$		0			0
$580$	−304.694	+	99.0012i	−0.525335	+	0.170692i
$581$	16.1998	−	11.7699i	0.0278826	−	0.0202579i
$582$		0			0
$583$	636.965	+	339.679i	1.09256	+	0.582639i
$584$	995.655			1.70489
$585$		0			0
$586$	63.9650	+	196.864i	0.109155	+	0.335946i
$587$	134.763	−	414.757i	0.229579	−	0.706571i	−0.768216	−	0.640191i	$-0.778855\pi$
$587$	134.763	−	414.757i	0.229579	−	0.706571i	0.997794	−	0.0663796i	$-0.0211448\pi$
$588$		0			0
$589$	−296.216	+	407.707i	−0.502914	+	0.692202i
$590$	−325.779	−	105.852i	−0.552168	−	0.179410i
$591$		0			0
$592$	4.84936	−	3.52326i	0.00819148	−	0.00595146i
$593$			848.153i			1.43027i	0.698984	+	0.715137i	$0.253636\pi$
$593$			848.153i			1.43027i	−0.698984	+	0.715137i	$0.746364\pi$
$594$		0			0
$595$	−7.97079			−0.0133963
$596$	−36.9708	−	50.8860i	−0.0620316	−	0.0853792i
$597$		0			0
$598$	−110.042	+	338.676i	−0.184017	+	0.566348i
$599$	−824.035	−	598.697i	−1.37569	−	0.999494i	−0.997269	−	0.0738582i	$-0.976469\pi$
$599$	−824.035	−	598.697i	−1.37569	−	0.999494i	−0.378416	−	0.925636i	$-0.623531\pi$
$600$		0			0
$601$	−556.691	−	180.880i	−0.926274	−	0.300965i	−0.193236	−	0.981152i	$-0.561898\pi$
$601$	−556.691	−	180.880i	−0.926274	−	0.300965i	−0.733038	+	0.680188i	$0.761898\pi$
$602$	−35.3390	+	11.4823i	−0.0587027	+	0.0190737i
$603$		0			0
$604$		−	235.024i		−	0.389112i
$605$	−508.971	+	144.601i	−0.841275	+	0.239009i
$606$		0			0
$607$	−584.796	−	804.902i	−0.963420	−	1.32603i	−0.945302	−	0.326198i	$-0.894233\pi$
$607$	−584.796	−	804.902i	−0.963420	−	1.32603i	−0.0181180	−	0.999836i	$-0.505767\pi$
$608$	89.5410	+	275.579i	0.147271	+	0.453255i
$609$		0			0
$610$	−420.468	−	305.488i	−0.689291	−	0.500799i
$611$	218.645	−	300.939i	0.357848	−	0.492536i
$612$		0			0
$613$	−628.757	+	204.295i	−1.02570	+	0.333272i	−0.773091	−	0.634296i	$-0.781290\pi$
$613$	−628.757	+	204.295i	−1.02570	+	0.333272i	−0.252614	+	0.967567i	$0.581290\pi$
$614$	311.605	−	226.394i	0.507500	−	0.368720i
$615$		0			0
$616$	24.8563	+	51.1214i	0.0403512	+	0.0829892i
$617$	−118.682			−0.192354			−0.0961770	−	0.995364i	$-0.530661\pi$
$617$	−118.682			−0.192354			−0.0961770	+	0.995364i	$0.530661\pi$
$618$		0			0
$619$	−33.3019	−	102.493i	−0.0537995	−	0.165578i	0.920547	−	0.390633i	$-0.127744\pi$
$619$	−33.3019	−	102.493i	−0.0537995	−	0.165578i	−0.974346	+	0.225055i	$0.927744\pi$
$620$	140.924	−	433.719i	0.227296	−	0.699546i
$621$		0			0
$622$	−171.201	+	235.637i	−0.275242	+	0.378838i
$623$	11.6098	+	3.77226i	0.0186354	+	0.00605499i
$624$		0			0
$625$	358.790	−	260.676i	0.574064	−	0.417082i
$626$		−	148.424i		−	0.237099i
$627$		0			0
$628$	46.3668			0.0738325
$629$	3.05359	+	4.20291i	0.00485467	+	0.00668188i
$630$		0			0
$631$	−145.864	+	448.922i	−0.231162	+	0.711445i	0.766445	+	0.642310i	$0.222024\pi$
$631$	−145.864	+	448.922i	−0.231162	+	0.711445i	−0.997607	+	0.0691348i	$0.977976\pi$
$632$	−853.149	−	619.849i	−1.34992	−	0.980774i
$633$		0			0
$634$	646.938	+	210.203i	1.02041	+	0.331551i
$635$	−397.388	+	129.119i	−0.625808	+	0.203337i
$636$		0			0
$637$			435.134i			0.683099i
$638$	389.416	−	375.137i	0.610370	−	0.587988i
$639$		0			0
$640$	−105.111	−	144.673i	−0.164236	−	0.226052i
$641$	−182.054	−	560.306i	−0.284016	−	0.874112i	−0.986692	−	0.162602i	$-0.948011\pi$
$641$	−182.054	−	560.306i	−0.284016	−	0.874112i	0.702675	−	0.711511i	$-0.251989\pi$
$642$		0			0
$643$	−798.095	−	579.850i	−1.24121	−	0.901788i	−0.243527	−	0.969894i	$-0.578304\pi$
$643$	−798.095	−	579.850i	−1.24121	−	0.901788i	−0.997678	+	0.0681057i	$0.978304\pi$
$644$	−21.3642	+	29.4053i	−0.0331743	+	0.0456605i
$645$		0			0
$646$	39.3137	−	12.7738i	0.0608571	−	0.0197737i
$647$	−591.996	+	430.110i	−0.914986	+	0.664776i	−0.942271	−	0.334852i	$-0.891314\pi$
$647$	−591.996	+	430.110i	−0.914986	+	0.664776i	0.0272850	+	0.999628i	$0.491314\pi$
$648$		0			0
$649$	−614.383	+	85.5809i	−0.946661	+	0.131866i
$650$	−73.0723			−0.112419
$651$		0			0
$652$	−81.4671	−	250.730i	−0.124950	−	0.384555i
$653$	−32.6119	+	100.369i	−0.0499416	+	0.153705i	−0.972917	−	0.231154i	$-0.925750\pi$
$653$	−32.6119	+	100.369i	−0.0499416	+	0.153705i	0.922976	+	0.384859i	$0.125750\pi$
$654$		0			0
$655$	−518.090	+	713.090i	−0.790977	+	1.08869i
$656$	−194.128	−	63.0761i	−0.295927	−	0.0961525i
$657$		0			0
$658$	−28.6276	+	20.7991i	−0.0435069	+	0.0316096i
$659$			592.799i			0.899543i	0.893144	+	0.449772i	$0.148495\pi$
$659$			592.799i			0.899543i	−0.893144	+	0.449772i	$0.851505\pi$
$660$		0			0
$661$	531.402			0.803936			0.401968	−	0.915654i	$-0.368326\pi$
$661$	531.402			0.803936			0.401968	+	0.915654i	$0.368326\pi$
$662$	−272.699	−	375.338i	−0.411932	−	0.566976i
$663$		0			0
$664$	85.1424	−	262.041i	0.128226	−	0.394641i
$665$	−21.6904	−	15.7590i	−0.0326171	−	0.0236977i
$666$		0			0
$667$	964.101	+	313.255i	1.44543	+	0.469648i
$668$	488.600	−	158.756i	0.731437	−	0.237658i
$669$		0			0
$670$			169.449i			0.252910i
$671$	−926.675	−	164.565i	−1.38104	−	0.245253i
$672$		0			0
$673$	279.252	+	384.357i	0.414936	+	0.571110i	0.964414	−	0.264398i	$-0.0851733\pi$
$673$	279.252	+	384.357i	0.414936	+	0.571110i	−0.549478	+	0.835508i	$0.685173\pi$
$674$	−215.246	−	662.459i	−0.319356	−	0.982877i
$675$		0			0
$676$	−148.936	−	108.208i	−0.220319	−	0.160071i
$677$	123.302	−	169.711i	0.182130	−	0.250681i	−0.708183	−	0.706029i	$-0.750485\pi$
$677$	123.302	−	169.711i	0.182130	−	0.250681i	0.890314	+	0.455348i	$0.150485\pi$
$678$		0			0
$679$	102.038	−	33.1542i	0.150277	−	0.0488280i
$680$	−88.7299	+	64.4660i	−0.130485	+	0.0948030i
$681$		0			0
$682$	106.188	+	762.322i	0.155701	+	1.11777i
$683$	−661.462			−0.968466			−0.484233	−	0.874939i	$-0.660901\pi$
$683$	−661.462			−0.968466			−0.484233	+	0.874939i	$0.660901\pi$
$684$		0			0
$685$	−178.276	−	548.678i	−0.260258	−	0.800990i
$686$	25.6812	−	79.0386i	0.0374361	−	0.115217i
$687$		0			0
$688$	−88.0490	+	121.189i	−0.127978	+	0.176147i
$689$	−558.529	−	181.477i	−0.810637	−	0.263392i
$690$		0			0
$691$	851.759	−	618.839i	1.23265	−	0.895570i	0.235561	−	0.971860i	$-0.424307\pi$
$691$	851.759	−	618.839i	1.23265	−	0.895570i	0.997086	+	0.0762896i	$0.0243074\pi$
$692$		−	388.145i		−	0.560904i
$693$		0			0
$694$	283.080			0.407896
$695$	143.877	+	198.030i	0.207017	+	0.284935i
$696$		0			0
$697$	54.6676	−	168.250i	0.0784327	−	0.241391i
$698$	474.854	+	345.002i	0.680307	+	0.494272i
$699$		0			0
$700$	−7.09332	−	2.30476i	−0.0101333	−	0.00329251i
$701$	836.024	−	271.641i	1.19262	−	0.387505i	0.355577	−	0.934647i	$-0.384284\pi$
$701$	836.024	−	271.641i	1.19262	−	0.387505i	0.837040	+	0.547142i	$0.184284\pi$
$702$		0			0
$703$			17.4743i			0.0248568i
$704$	523.734	+	279.295i	0.743940	+	0.396726i
$705$		0			0
$706$	−256.685	−	353.297i	−0.363577	−	0.500420i
$707$	−16.0137	−	49.2852i	−0.0226503	−	0.0697104i
$708$		0			0
$709$	−586.433	−	426.069i	−0.827127	−	0.600943i	0.0916181	−	0.995794i	$-0.470796\pi$
$709$	−586.433	−	426.069i	−0.827127	−	0.600943i	−0.918745	+	0.394851i	$0.870796\pi$
$710$	−420.865	+	579.272i	−0.592768	+	0.815875i
$711$		0			0
$712$	159.749	−	51.9054i	0.224366	−	0.0729009i
$713$	−1167.39	+	848.161i	−1.63730	+	1.18957i
$714$		0			0
$715$	387.118	−	188.225i	0.541424	−	0.263252i
$716$	−47.6487			−0.0665485
$717$		0			0
$718$	−178.099	−	548.132i	−0.248049	−	0.763416i
$719$	227.934	−	701.508i	0.317015	−	0.975672i	−0.657902	−	0.753103i	$-0.728556\pi$
$719$	227.934	−	701.508i	0.317015	−	0.975672i	0.974917	−	0.222568i	$-0.0714441\pi$
$720$		0			0
$721$	−11.5924	+	15.9556i	−0.0160783	+	0.0221298i
$722$	−344.686	−	111.995i	−0.477404	−	0.155118i
$723$		0			0
$724$	233.305	−	169.506i	0.322245	−	0.234125i
$725$			208.013i			0.286915i
$726$		0			0
$727$	−764.559			−1.05166			−0.525832	−	0.850589i	$-0.676246\pi$
$727$	−764.559			−1.05166			−0.525832	+	0.850589i	$0.676246\pi$
$728$	−27.1818	−	37.4126i	−0.0373377	−	0.0513909i
$729$		0			0
$730$	−221.635	+	682.122i	−0.303609	+	0.934413i
$731$	−105.034	−	76.3115i	−0.143685	−	0.104393i
$732$		0			0
$733$	1012.62	+	329.022i	1.38148	+	0.448870i	0.903156	−	0.429314i	$-0.141244\pi$
$733$	1012.62	+	329.022i	1.38148	+	0.448870i	0.478324	+	0.878183i	$0.341244\pi$
$734$	611.675	−	198.745i	0.833345	−	0.270770i
$735$		0			0
$736$			829.677i			1.12728i
$737$	134.180	+	275.965i	0.182062	+	0.374443i
$738$		0			0
$739$	−688.127	−	947.126i	−0.931160	−	1.28163i	−0.959405	−	0.282030i	$-0.908992\pi$
$739$	−688.127	−	947.126i	−0.931160	−	1.28163i	0.0282457	−	0.999601i	$-0.491008\pi$
$740$	−4.88645	−	15.0390i	−0.00660332	−	0.0203229i
$741$		0			0
$742$	45.1962	+	32.8370i	0.0609114	+	0.0442547i
$743$	−409.510	+	563.642i	−0.551158	+	0.758603i	−0.990169	−	0.139878i	$-0.955329\pi$
$743$	−409.510	+	563.642i	−0.551158	+	0.758603i	0.439011	+	0.898482i	$0.355329\pi$
$744$		0			0
$745$	126.345	−	41.0519i	0.169590	−	0.0551032i
$746$	737.476	−	535.808i	0.988574	−	0.718241i
$747$		0			0
$748$	−31.8749	+	59.7718i	−0.0426135	+	0.0799088i
$749$	26.3186			0.0351384
$750$		0			0
$751$	131.874	+	405.867i	0.175598	+	0.540435i	0.999660	−	0.0260640i	$-0.00829738\pi$
$751$	131.874	+	405.867i	0.175598	+	0.540435i	−0.824062	+	0.566499i	$0.808297\pi$
$752$	−44.0826	+	135.672i	−0.0586204	+	0.180415i
$753$		0			0
$754$	−258.561	+	355.878i	−0.342919	+	0.471987i
$755$	472.094	+	153.393i	0.625290	+	0.203169i
$756$		0			0
$757$	750.939	−	545.589i	0.991993	−	0.720725i	0.0316368	−	0.999499i	$-0.489928\pi$
$757$	750.939	−	545.589i	0.991993	−	0.720725i	0.960357	+	0.278774i	$0.0899280\pi$
$758$			626.489i			0.826502i
$759$		0			0
$760$	−368.910			−0.485408
$761$	28.3758	+	39.0559i	0.0372875	+	0.0513218i	0.827254	−	0.561829i	$-0.189902\pi$
$761$	28.3758	+	39.0559i	0.0372875	+	0.0513218i	−0.789966	+	0.613150i	$0.789902\pi$
$762$		0			0
$763$	−3.52727	+	10.8558i	−0.00462290	+	0.0142278i
$764$	146.643	+	106.542i	0.191941	+	0.139453i
$765$		0			0
$766$	417.362	+	135.609i	0.544859	+	0.177035i
$767$	479.948	−	155.945i	0.625748	−	0.203318i
$768$		0			0
$769$		−	435.589i		−	0.566435i	−0.959056	−	0.283218i	$-0.908598\pi$
$769$		−	435.589i		−	0.566435i	0.959056	−	0.283218i	$-0.0914019\pi$
$770$	−40.5562	+	5.64930i	−0.0526704	+	0.00733676i
$771$		0			0
$772$	171.706	+	236.334i	0.222418	+	0.306132i
$773$	108.555	+	334.098i	0.140434	+	0.432210i	0.996396	−	0.0848287i	$-0.0270343\pi$
$773$	108.555	+	334.098i	0.140434	+	0.432210i	−0.855962	+	0.517039i	$0.827034\pi$
$774$		0			0
$775$	−239.548	−	174.042i	−0.309094	−	0.224570i
$776$	867.733	−	1194.33i	1.11821	−	1.53909i
$777$		0			0
$778$	283.213	−	92.0215i	0.364027	−	0.118280i
$779$	481.408	−	349.764i	0.617982	−	0.448991i
$780$		0			0
$781$	−226.719	+	1276.67i	−0.290293	+	1.63466i
$782$	118.360			0.151356
$783$		0			0
$784$	−51.5666	−	158.706i	−0.0657738	−	0.202431i
$785$	−30.2622	+	93.1373i	−0.0385505	+	0.118646i
$786$		0			0
$787$	253.179	−	348.471i	0.321701	−	0.442783i	−0.617285	−	0.786740i	$-0.711767\pi$
$787$	253.179	−	348.471i	0.321701	−	0.442783i	0.938986	+	0.343957i	$0.111767\pi$
$788$	355.916	+	115.644i	0.451669	+	0.146756i
$789$		0			0
$790$	614.570	−	446.511i	0.777937	−	0.565204i
$791$		−	103.118i		−	0.130364i
$792$		0			0
$793$	765.678			0.965546
$794$	301.474	+	414.944i	0.379691	+	0.522599i
$795$		0			0
$796$	36.6879	−	112.914i	0.0460903	−	0.141851i
$797$	316.584	+	230.011i	0.397219	+	0.288597i	0.768407	−	0.639961i	$-0.221050\pi$
$797$	316.584	+	230.011i	0.397219	+	0.288597i	−0.371188	+	0.928558i	$0.621050\pi$
$798$		0			0
$799$	−117.586	−	38.2061i	−0.147167	−	0.0478174i
$800$	−161.916	+	52.6097i	−0.202395	+	0.0657622i
$801$		0			0
$802$		−	154.789i		−	0.193004i
$803$	179.191	+	1286.40i	0.223151	+	1.60200i
$804$		0			0
$805$	−45.1229	−	62.1064i	−0.0560533	−	0.0771508i
$806$	−193.495	−	595.517i	−0.240068	−	0.738854i
$807$		0			0
$808$	−576.872	−	419.122i	−0.713950	−	0.518715i
$809$	−198.597	+	273.345i	−0.245485	+	0.337881i	−0.913924	−	0.405886i	$-0.866963\pi$
$809$	−198.597	+	273.345i	−0.245485	+	0.337881i	0.668439	+	0.743767i	$0.266963\pi$
$810$		0			0
$811$	−1405.86	+	456.793i	−1.73349	+	0.563246i	−0.993947	−	0.109860i	$-0.964960\pi$
$811$	−1405.86	+	456.793i	−1.73349	+	0.563246i	−0.739546	+	0.673106i	$0.764960\pi$
$812$	−36.3239	+	26.3908i	−0.0447339	+	0.0325010i
$813$		0			0
$814$	18.5158	+	19.2206i	0.0227467	+	0.0236125i
$815$	556.814			0.683207
$816$		0			0
$817$	−134.947	−	415.323i	−0.165173	−	0.508351i
$818$	−87.2104	+	268.406i	−0.106614	+	0.328125i
$819$		0			0
$820$	−316.509	+	435.637i	−0.385987	+	0.531265i
$821$	−12.3858	−	4.02439i	−0.0150862	−	0.00490182i	0.301464	−	0.953478i	$-0.402525\pi$
$821$	−12.3858	−	4.02439i	−0.0150862	−	0.00490182i	−0.316550	+	0.948576i	$0.602525\pi$
$822$		0			0
$823$	−8.15431	+	5.92445i	−0.00990803	+	0.00719860i	−0.592728	−	0.805403i	$-0.701949\pi$
$823$	−8.15431	+	5.92445i	−0.00990803	+	0.00719860i	0.582820	+	0.812601i	$0.301949\pi$
$824$			271.373i			0.329336i
$825$		0			0
$826$	−48.0058			−0.0581184
$827$	7.38327	+	10.1622i	0.00892778	+	0.0122880i	0.813458	−	0.581624i	$-0.197583\pi$
$827$	7.38327	+	10.1622i	0.00892778	+	0.0122880i	−0.804530	+	0.593912i	$0.797583\pi$
$828$		0			0
$829$	−63.4520	+	195.285i	−0.0765404	+	0.235567i	−0.982005	−	0.188854i	$-0.939523\pi$
$829$	−63.4520	+	195.285i	−0.0765404	+	0.235567i	0.905465	+	0.424422i	$0.139523\pi$
$830$	160.571	+	116.662i	0.193459	+	0.140556i
$831$		0			0
$832$	−459.241	−	149.216i	−0.551972	−	0.179347i
$833$	137.549	−	44.6925i	0.165125	−	0.0536524i
$834$		0			0
$835$			1085.07i			1.29948i
$836$	−204.913	+	99.6333i	−0.245112	+	0.119179i
$837$		0			0
$838$	−423.809	−	583.324i	−0.505739	−	0.696090i
$839$	342.489	+	1054.07i	0.408211	+	1.25634i	0.918184	+	0.396153i	$0.129655\pi$
$839$	342.489	+	1054.07i	0.408211	+	1.25634i	−0.509974	+	0.860190i	$0.670345\pi$
$840$		0			0
$841$	332.688	+	241.712i	0.395586	+	0.287410i
$842$	−272.274	+	374.753i	−0.323366	+	0.445075i
$843$		0			0
$844$	−107.877	+	35.0514i	−0.127816	+	0.0415301i
$845$	314.564	−	228.544i	0.372265	−	0.270466i
$846$		0			0
$847$	−61.5763	+	41.3152i	−0.0726993	+	0.0487783i
$848$	225.218			0.265587
$849$		0			0
$850$	7.50522	+	23.0987i	0.00882968	+	0.0271749i
$851$	−15.4615	+	47.5856i	−0.0181686	+	0.0559173i
$852$		0			0
$853$	−818.707	+	1126.85i	−0.959797	+	1.32105i	−0.0127620	+	0.999919i	$0.504062\pi$
$853$	−818.707	+	1126.85i	−0.959797	+	1.32105i	−0.947035	+	0.321129i	$0.895938\pi$
$854$	−69.2720	−	22.5078i	−0.0811148	−	0.0263558i
$855$		0			0
$856$	292.976	−	212.859i	0.342262	−	0.248668i
$857$		−	1297.45i		−	1.51395i	−0.653444	−	0.756974i	$-0.726677\pi$
$857$		−	1297.45i		−	1.51395i	0.653444	−	0.756974i	$-0.273323\pi$
$858$		0			0
$859$	−406.557			−0.473290			−0.236645	−	0.971596i	$-0.576048\pi$
$859$	−406.557			−0.473290			−0.236645	+	0.971596i	$0.576048\pi$
$860$	232.279	+	319.704i	0.270092	+	0.371749i
$861$		0			0
$862$	314.057	−	966.567i	0.364335	−	1.12131i
$863$	261.846	+	190.242i	0.303414	+	0.220443i	0.729065	−	0.684444i	$-0.239955\pi$
$863$	261.846	+	190.242i	0.303414	+	0.220443i	−0.425652	+	0.904887i	$0.639955\pi$
$864$		0			0
$865$	779.670	+	253.330i	0.901353	+	0.292867i
$866$	−492.925	+	160.161i	−0.569198	+	0.184943i
$867$		0			0
$868$		−	63.9114i		−	0.0736306i
$869$	647.313	−	1213.84i	0.744894	−	1.39682i
$870$		0			0
$871$	−146.734	−	201.962i	−0.168466	−	0.231873i
$872$	48.5344	+	149.374i	0.0556587	+	0.171300i
$873$		0			0
$874$	322.086	+	234.010i	0.368520	+	0.267745i
$875$	48.6380	−	66.9444i	0.0555862	−	0.0765079i
$876$		0			0
$877$	−591.056	+	192.046i	−0.673952	+	0.218980i	−0.625946	−	0.779867i	$-0.715287\pi$
$877$	−591.056	+	192.046i	−0.673952	+	0.218980i	−0.0480065	+	0.998847i	$0.515287\pi$
$878$	−331.472	+	240.828i	−0.377531	+	0.274292i
$879$		0			0
$880$	−118.887	+	114.527i	−0.135099	+	0.130145i
$881$	−1346.48			−1.52835			−0.764176	−	0.645007i	$-0.776854\pi$
$881$	−1346.48			−1.52835			−0.764176	+	0.645007i	$0.776854\pi$
$882$		0			0
$883$	166.093	+	511.183i	0.188101	+	0.578916i	0.999988	−	0.00489886i	$-0.00155936\pi$
$883$	166.093	+	511.183i	0.188101	+	0.578916i	−0.811887	+	0.583815i	$0.801559\pi$
$884$	17.0295	−	52.4114i	0.0192641	−	0.0592889i
$885$		0			0
$886$	412.790	−	568.156i	0.465902	−	0.641260i
$887$	444.753	+	144.509i	0.501413	+	0.162919i	0.548793	−	0.835958i	$-0.315087\pi$
$887$	444.753	+	144.509i	0.501413	+	0.162919i	−0.0473806	+	0.998877i	$0.515087\pi$
$888$		0			0
$889$	−47.3743	+	34.4194i	−0.0532894	+	0.0387170i
$890$			120.998i			0.135952i
$891$		0			0
$892$	606.409			0.679831
$893$	−244.443	−	336.446i	−0.273732	−	0.376760i
$894$		0			0
$895$	31.0988	−	95.7124i	0.0347473	−	0.106941i
$896$	−20.2752	−	14.7308i	−0.0226285	−	0.0164406i
$897$		0			0
$898$	−35.1224	−	11.4120i	−0.0391118	−	0.0127082i
$899$	−1695.24	+	550.818i	−1.88570	+	0.612701i
$900$		0			0
$901$			195.195i			0.216642i
$902$	158.908	−	894.818i	0.176173	−	0.992038i
$903$		0			0
$904$	−833.998	−	1147.90i	−0.922564	−	1.26980i
$905$	188.217	+	579.273i	0.207975	+	0.640081i
$906$		0			0
$907$	−132.551	−	96.3039i	−0.146142	−	0.106179i	0.512312	−	0.858800i	$-0.328789\pi$
$907$	−132.551	−	96.3039i	−0.146142	−	0.106179i	−0.658454	+	0.752621i	$0.728789\pi$
$908$	−104.933	+	144.428i	−0.115565	+	0.159062i
$909$		0			0
$910$	31.6820	−	10.2941i	0.0348154	−	0.0113122i
$911$	780.199	−	566.848i	0.856420	−	0.622226i	−0.0704883	−	0.997513i	$-0.522456\pi$
$911$	780.199	−	566.848i	0.856420	−	0.622226i	0.926909	+	0.375287i	$0.122456\pi$
$912$		0			0
$913$	353.885	+	62.8453i	0.387607	+	0.0688338i
$914$	−245.448			−0.268542
$915$		0			0
$916$	32.1342	+	98.8988i	0.0350810	+	0.107968i
$917$	−38.1720	+	117.481i	−0.0416271	+	0.128115i
$918$		0			0
$919$	935.754	−	1287.95i	1.01823	−	1.40147i	0.104794	−	0.994494i	$-0.466582\pi$
$919$	935.754	−	1287.95i	1.01823	−	1.40147i	0.913437	−	0.406980i	$-0.133418\pi$
$920$	−1004.61	−	326.417i	−1.09196	−	0.354801i
$921$		0			0
$922$	174.225	−	126.582i	0.188964	−	0.137290i
$923$		−	1054.86i		−	1.14286i
$924$		0			0
$925$	−10.2670			−0.0110995
$926$	−156.788	−	215.801i	−0.169318	−	0.233046i
$927$		0			0
$928$	−316.707	+	974.724i	−0.341279	+	1.05035i
$929$	−866.817	−	629.779i	−0.933064	−	0.677911i	0.0136770	−	0.999906i	$-0.495646\pi$
$929$	−866.817	−	629.779i	−0.933064	−	0.677911i	−0.946741	+	0.321996i	$0.895646\pi$
$930$		0			0
$931$	462.665	+	150.329i	0.496955	+	0.161470i
$932$	−841.035	+	273.269i	−0.902398	+	0.293207i
$933$		0			0
$934$			448.847i			0.480564i
$935$	−99.2602	−	103.038i	−0.106161	−	0.110202i
$936$		0			0
$937$	314.554	+	432.946i	0.335703	+	0.462056i	0.943180	−	0.332282i	$-0.107818\pi$
$937$	314.554	+	432.946i	0.335703	+	0.462056i	−0.607477	+	0.794337i	$0.707818\pi$
$938$	7.33836	+	22.5851i	0.00782341	+	0.0240780i
$939$		0			0
$940$	304.458	+	221.202i	0.323891	+	0.235321i
$941$	868.169	−	1194.93i	0.922603	−	1.26985i	−0.0400733	−	0.999197i	$-0.512759\pi$
$941$	868.169	−	1194.93i	0.922603	−	1.26985i	0.962676	−	0.270657i	$-0.0872409\pi$
$942$		0			0
$943$	1620.44	−	526.511i	1.71838	−	0.558337i
$944$	−156.570	+	113.755i	−0.165858	+	0.120503i
$945$		0			0
$946$	−588.509	−	313.838i	−0.622103	−	0.331753i
$947$	425.172			0.448968			0.224484	−	0.974478i	$-0.427930\pi$
$947$	425.172			0.448968			0.224484	+	0.974478i	$0.427930\pi$
$948$		0			0
$949$	−326.519	−	1004.92i	−0.344067	−	1.05893i
$950$	−25.2448	+	77.6955i	−0.0265735	+	0.0817847i
$951$		0			0
$952$	−9.03457	+	12.4350i	−0.00949009	+	0.0130620i
$953$	−518.173	−	168.365i	−0.543728	−	0.176668i	0.0242586	−	0.999706i	$-0.492277\pi$
$953$	−518.173	−	168.365i	−0.543728	−	0.176668i	−0.567987	+	0.823038i	$0.692277\pi$
$954$		0			0
$955$	−309.721	+	225.026i	−0.324316	+	0.235629i
$956$			39.5237i			0.0413428i
$957$		0			0
$958$	636.839			0.664759
$959$	−47.5233	−	65.4102i	−0.0495551	−	0.0682067i
$960$		0			0
$961$	487.099	−	1499.14i	0.506867	−	1.55998i
$962$	−17.5653	−	12.7619i	−0.0182591	−	0.0132660i
$963$		0			0
$964$	−106.113	−	34.4782i	−0.110076	−	0.0357658i
$965$	−586.792	+	190.660i	−0.608075	+	0.197576i
$966$		0			0
$967$			1196.81i			1.23765i	0.785529	+	0.618824i	$0.212391\pi$
$967$			1196.81i			1.23765i	−0.785529	+	0.618824i	$0.787609\pi$
$968$	−351.311	+	957.932i	−0.362925	+	0.989599i
$969$		0			0
$970$	625.076	+	860.343i	0.644408	+	0.886952i
$971$	−251.330	−	773.514i	−0.258836	−	0.796616i	−0.993050	−	0.117697i	$-0.962449\pi$
$971$	−251.330	−	773.514i	−0.258836	−	0.796616i	0.734213	−	0.678919i	$-0.237551\pi$
$972$		0			0
$973$	27.7528	+	20.1636i	0.0285229	+	0.0207231i
$974$	−201.606	+	277.487i	−0.206987	+	0.284894i
$975$		0			0
$976$	−279.264	+	90.7385i	−0.286132	+	0.0929698i
$977$	552.483	−	401.403i	0.565490	−	0.410852i	−0.267974	−	0.963426i	$-0.586354\pi$
$977$	552.483	−	401.403i	0.565490	−	0.410852i	0.833464	+	0.552574i	$0.186354\pi$
$978$		0			0
$979$	95.8131	+	197.056i	0.0978683	+	0.201283i
$980$	−440.222			−0.449206
$981$		0			0
$982$	18.5911	+	57.2175i	0.0189319	+	0.0582663i
$983$	−454.768	+	1399.63i	−0.462633	+	1.42384i	0.399303	+	0.916819i	$0.369252\pi$
$983$	−454.768	+	1399.63i	−0.462633	+	1.42384i	−0.861935	+	0.507018i	$0.830748\pi$
$984$		0			0
$985$	−464.590	+	639.453i	−0.471665	+	0.649191i
$986$	139.053	+	45.1809i	0.141027	+	0.0458224i
$987$		0			0
$988$	149.963	−	108.955i	0.151785	−	0.110278i
$989$		−	1250.40i		−	1.26431i
$990$		0			0
$991$	−399.921			−0.403553			−0.201777	−	0.979432i	$-0.564671\pi$
$991$	−399.921			−0.403553			−0.201777	+	0.979432i	$0.564671\pi$
$992$	−857.507	−	1180.26i	−0.864422	−	1.18977i
$993$		0			0
$994$	−31.0087	+	95.4350i	−0.0311959	+	0.0960110i
$995$	202.865	+	147.390i	0.203885	+	0.148131i
$996$		0			0
$997$	−1189.25	−	386.412i	−1.19283	−	0.387575i	−0.355713	−	0.934595i	$-0.615762\pi$
$997$	−1189.25	−	386.412i	−1.19283	−	0.387575i	−0.837119	+	0.547020i	$0.815762\pi$
$998$	−651.572	+	211.709i	−0.652878	+	0.212133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.b.19.3	yes	16
3.2	odd	2	inner	99.3.k.b.19.2	✓	16
11.2	odd	10		1089.3.c.l.604.11		16
11.7	odd	10	inner	99.3.k.b.73.3	yes	16
11.9	even	5		1089.3.c.l.604.5		16
33.2	even	10		1089.3.c.l.604.6		16
33.20	odd	10		1089.3.c.l.604.12		16
33.29	even	10	inner	99.3.k.b.73.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.k.b.19.2	✓	16	3.2	odd	2	inner
99.3.k.b.19.3	yes	16	1.1	even	1	trivial
99.3.k.b.73.2	yes	16	33.29	even	10	inner
99.3.k.b.73.3	yes	16	11.7	odd	10	inner
1089.3.c.l.604.5		16	11.9	even	5
1089.3.c.l.604.6		16	33.2	even	10
1089.3.c.l.604.11		16	11.2	odd	10
1089.3.c.l.604.12		16	33.20	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.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.816494 + 1.12381i) q^{2} +(0.639787 - 1.96906i) q^{4} +(3.53770 + 2.57029i) q^{5} +(0.582836 + 0.189375i) q^{7} +(8.01969 - 2.60575i) q^{8} +O(q^{10})\)	\(q+(0.816494 + 1.12381i) q^{2} +(0.639787 - 1.96906i) q^{4} +(3.53770 + 2.57029i) q^{5} +(0.582836 + 0.189375i) q^{7} +(8.01969 - 2.60575i) q^{8} +6.07432i q^{10} +(4.81000 + 9.89262i) q^{11} +(-5.26002 - 7.23980i) q^{13} +(0.263061 + 0.809619i) q^{14} +(2.77645 + 2.01721i) q^{16} +(-1.74830 + 2.40633i) q^{17} +(-9.51507 + 3.09163i) q^{19} +(7.32444 - 5.32152i) q^{20} +(-7.19005 + 13.4828i) q^{22} -28.6467 q^{23} +(-1.81649 - 5.59057i) q^{25} +(3.84136 - 11.8225i) q^{26} +(0.745782 - 1.02648i) q^{28} +(-33.6548 - 10.9351i) q^{29} +(40.7514 - 29.6076i) q^{31} -28.9624i q^{32} -4.13173 q^{34} +(1.57515 + 2.16801i) q^{35} +(0.539730 - 1.66112i) q^{37} +(-11.2434 - 8.16880i) q^{38} +(35.0688 + 11.3945i) q^{40} +(-56.5662 + 18.3795i) q^{41} +43.6490i q^{43} +(22.5566 - 3.14203i) q^{44} +(-23.3899 - 32.1934i) q^{46} +(12.8450 + 39.5329i) q^{47} +(-39.3380 - 28.5807i) q^{49} +(4.79957 - 6.60605i) q^{50} +(-17.6209 + 5.72538i) q^{52} +(53.0919 - 38.5735i) q^{53} +(-8.41054 + 47.3602i) q^{55} +5.16763 q^{56} +(-15.1900 - 46.7500i) q^{58} +(-17.4262 + 53.6322i) q^{59} +(-50.2917 + 69.2205i) q^{61} +(66.5465 + 21.6223i) q^{62} +(43.6539 - 31.7164i) q^{64} -39.1320i q^{65} +27.8960 q^{67} +(3.61967 + 4.98205i) q^{68} +(-1.15032 + 3.54033i) q^{70} +(95.3640 + 69.2860i) q^{71} +(112.296 + 36.4872i) q^{73} +(2.30746 - 0.749741i) q^{74} +20.7138i q^{76} +(0.930031 + 6.67667i) q^{77} +(-73.5080 - 101.175i) q^{79} +(4.63743 + 14.2726i) q^{80} +(-66.8409 - 48.5627i) q^{82} +(19.2057 - 26.4344i) q^{83} +(-12.3699 + 4.01923i) q^{85} +(-49.0530 + 35.6391i) q^{86} +(64.3525 + 66.8020i) q^{88} +19.9195 q^{89} +(-1.69469 - 5.21573i) q^{91} +(-18.3278 + 56.4072i) q^{92} +(-33.9395 + 46.7137i) q^{94} +(-41.6079 - 13.5192i) q^{95} +(141.636 - 102.905i) q^{97} -67.5443i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) \) 16 * q - 4 * q^4 + 30 * q^7	\( 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more