LMFDB - Embedded newform 99.3.k.b.73.3

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			73.3
Root			$-1.32111 + 0.429256i$ of defining polynomial
Character	$\chi$	$=$	99.73
Dual form			99.3.k.b.19.3

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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	−0.554543	−	0.832155i	$-0.687107\pi$
$2$	0.816494	−	1.12381i	0.408247	−	0.561904i	0.962790	+	0.270252i	$0.0871069\pi$
$3$		0			0
$3$		0			0
$4$	0.639787	+	1.96906i	0.159947	+	0.492266i
$5$	3.53770	−	2.57029i	0.707540	−	0.514058i	−0.174839	−	0.984597i	$-0.555940\pi$
$5$	3.53770	−	2.57029i	0.707540	−	0.514058i	0.882379	+	0.470539i	$0.155940\pi$
$6$		0			0
$7$	0.582836	−	0.189375i	0.0832623	−	0.0270536i	−0.267090	−	0.963672i	$-0.586062\pi$
$7$	0.582836	−	0.189375i	0.0832623	−	0.0270536i	0.350352	+	0.936618i	$0.386062\pi$
$8$	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	−0.961895	−	0.273418i	$-0.911846\pi$
$13$	−5.26002	+	7.23980i	−0.404617	+	0.556907i	0.557278	+	0.830326i	$0.311846\pi$
$14$	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	0.754495	−	0.656306i	$-0.227882\pi$
$17$	−1.74830	−	2.40633i	−0.102841	−	0.141549i	−0.857336	+	0.514757i	$0.827882\pi$
$18$		0			0
$19$	−9.51507	−	3.09163i	−0.500793	−	0.162718i	0.0477179	−	0.998861i	$-0.484805\pi$
$19$	−9.51507	−	3.09163i	−0.500793	−	0.162718i	−0.548511	+	0.836143i	$0.684805\pi$
$20$	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	−0.825093	−	0.564996i	$-0.808878\pi$
$29$	−33.6548	+	10.9351i	−1.16051	+	0.377073i	−0.335418	+	0.942069i	$0.608878\pi$
$30$		0			0
$31$	40.7514	+	29.6076i	1.31456	+	0.955084i	0.999983	+	0.00585268i	$0.00186298\pi$
$31$	40.7514	+	29.6076i	1.31456	+	0.955084i	0.314578	+	0.949232i	$0.398137\pi$
$32$			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	0.958085	−	0.286483i	$-0.0924863\pi$
$37$	0.539730	+	1.66112i	0.0145873	+	0.0448951i	−0.943498	+	0.331378i	$0.892486\pi$
$38$	−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	−0.477104	−	0.878847i	$-0.658313\pi$
$41$	−56.5662	−	18.3795i	−1.37966	−	0.448279i	−0.902558	+	0.430567i	$0.858313\pi$
$42$		0			0
$43$		−	43.6490i		−	1.01509i	−0.861625	−	0.507546i	$-0.830553\pi$
$43$		−	43.6490i		−	1.01509i	0.861625	−	0.507546i	$-0.169447\pi$
$44$	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	−0.716366	−	0.697725i	$-0.754196\pi$
$47$	12.8450	−	39.5329i	0.273298	−	0.841126i	0.989665	−	0.143402i	$-0.0458040\pi$
$48$		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	0.962459	−	0.271427i	$-0.0874954\pi$
$53$	53.0919	+	38.5735i	1.00173	+	0.727802i	0.0392742	+	0.999228i	$0.487495\pi$
$54$		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	−0.983101	−	0.183066i	$-0.941398\pi$
$59$	−17.4262	−	53.6322i	−0.295359	−	0.909021i	0.687742	−	0.725955i	$-0.258602\pi$
$60$		0			0
$61$	−50.2917	−	69.2205i	−0.824454	−	1.13476i	−0.988930	−	0.148382i	$-0.952593\pi$
$61$	−50.2917	−	69.2205i	−0.824454	−	1.13476i	0.164477	−	0.986381i	$-0.447407\pi$
$62$	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	0.343834	−	0.939031i	$-0.388274\pi$
$71$	95.3640	−	69.2860i	1.34316	−	0.975859i	0.999322	−	0.0368288i	$-0.0117256\pi$
$72$		0			0
$73$	112.296	−	36.4872i	1.53830	−	0.499824i	0.587394	−	0.809301i	$-0.300154\pi$
$73$	112.296	−	36.4872i	1.53830	−	0.499824i	0.950907	+	0.309477i	$0.100154\pi$
$74$	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	0.0291902	+	0.999574i	$0.490707\pi$
$79$	−73.5080	+	101.175i	−0.930481	+	1.28070i	−0.959672	+	0.281124i	$0.909293\pi$
$80$	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	0.908887	−	0.417043i	$-0.136933\pi$
$83$	19.2057	+	26.4344i	0.231394	+	0.318487i	−0.677493	+	0.735530i	$0.736933\pi$
$84$		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	0.983320	+	0.181886i	$0.0582203\pi$
$97$	141.636	+	102.905i	1.46017	+	1.06087i	0.476847	+	0.878986i	$0.341780\pi$
$98$			67.5443i			0.689228i
$99$		0			0
$100$	−12.1704			−0.121704
$101$	−49.7038	+	68.4113i	−0.492116	+	0.677340i	−0.980777	−	0.195134i	$-0.937486\pi$
$101$	−49.7038	+	68.4113i	−0.492116	+	0.677340i	0.488660	+	0.872474i	$0.337486\pi$
$102$		0			0
$103$	−9.94484	−	30.6071i	−0.0965519	−	0.297156i	0.891103	−	0.453801i	$-0.149932\pi$
$103$	−9.94484	−	30.6071i	−0.0965519	−	0.297156i	−0.987655	+	0.156645i	$0.949932\pi$
$104$	−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	0.493591	−	0.869694i	$-0.335684\pi$
$107$	40.8441	+	13.2711i	0.381721	+	0.124029i	−0.111870	+	0.993723i	$0.535684\pi$
$108$		0			0
$109$		−	18.6259i		−	0.170879i	−0.996343	−	0.0854397i	$-0.972770\pi$
$109$		−	18.6259i		−	0.170879i	0.996343	−	0.0854397i	$-0.0272295\pi$
$110$	−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	0.404832	+	0.914391i	$0.367330\pi$
$113$	−51.9969	+	160.030i	−0.460149	+	1.41619i	−0.864982	+	0.501803i	$0.832670\pi$
$114$		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	0.528467	−	0.848954i	$-0.322767\pi$
$127$	−56.1647	−	77.3041i	−0.442242	−	0.608693i	−0.970708	+	0.240261i	$0.922767\pi$
$128$	−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	$-0.720582\pi$
$131$		−	201.569i		−	1.53869i	0.638833	−	0.769346i	$-0.279418\pi$
$132$		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	−0.904704	−	0.426040i	$-0.859908\pi$
$137$	−106.735	+	77.5473i	−0.779085	+	0.566039i	0.125619	+	0.992079i	$0.459908\pi$
$138$		0			0
$139$	53.2373	−	17.2978i	0.383002	−	0.124445i	−0.111187	−	0.993800i	$-0.535465\pi$
$139$	53.2373	−	17.2978i	0.383002	−	0.124445i	0.494189	+	0.869355i	$0.335465\pi$
$140$	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	0.864724	−	0.502247i	$-0.167493\pi$
$149$	17.8569	+	24.5779i	0.119845	+	0.164952i	−0.744879	+	0.667199i	$0.767493\pi$
$150$		0			0
$151$	107.960	+	35.0785i	0.714970	+	0.232308i	0.643841	−	0.765159i	$-0.277340\pi$
$151$	107.960	+	35.0785i	0.714970	+	0.232308i	0.0711288	+	0.997467i	$0.477340\pi$
$152$	−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	−0.926595	−	0.376061i	$-0.877278\pi$
$157$	6.92048	−	21.2991i	0.0440795	−	0.135663i	0.970674	+	0.240399i	$0.0772782\pi$
$158$	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	0.857092	−	0.515163i	$-0.172269\pi$
$163$	103.016	+	74.8454i	0.631999	+	0.459174i	−0.225093	+	0.974337i	$0.572269\pi$
$164$		−	123.141i		−	0.750862i
$165$		0			0
$166$	45.3886			0.273425
$167$	145.852	−	200.748i	0.873366	−	1.20208i	−0.104849	−	0.994488i	$-0.533436\pi$
$167$	145.852	−	200.748i	0.873366	−	1.20208i	0.978215	−	0.207597i	$-0.0665641\pi$
$168$		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	0.775038	−	0.631915i	$-0.217731\pi$
$173$	178.298	+	57.9327i	1.03063	+	0.334871i	0.255589	+	0.966786i	$0.417731\pi$
$174$		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	−0.968955	−	0.247238i	$-0.920477\pi$
$179$	−7.11182	+	21.8879i	−0.0397308	+	0.122279i	0.929224	+	0.369517i	$0.120477\pi$
$180$		0			0
$181$	112.686	−	81.8714i	0.622576	−	0.452328i	−0.231244	−	0.972896i	$-0.574280\pi$
$181$	112.686	−	81.8714i	0.622576	−	0.452328i	0.853820	+	0.520568i	$0.174280\pi$
$182$	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	0.854920	−	0.518760i	$-0.173606\pi$
$191$	−27.0541	−	83.2638i	−0.141644	−	0.435936i	−0.996564	+	0.0828237i	$0.973606\pi$
$192$		0			0
$193$	−82.9341	−	114.149i	−0.429710	−	0.591446i	0.538176	−	0.842832i	$-0.319113\pi$
$193$	−82.9341	−	114.149i	−0.429710	−	0.591446i	−0.967887	+	0.251387i	$0.919113\pi$
$194$	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	$-0.848292\pi$
$197$		−	180.754i		−	0.917532i	0.888557	−	0.458766i	$-0.151708\pi$
$198$		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	−0.878479	−	0.477781i	$-0.841441\pi$
$211$	−32.2024	+	44.3228i	−0.152618	+	0.210061i	0.725861	+	0.687841i	$0.241441\pi$
$212$	−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	−0.514292	−	0.857615i	$-0.671945\pi$
$223$	90.5096	−	278.560i	0.405873	−	1.24915i	0.920164	−	0.391532i	$-0.128055\pi$
$224$	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	−0.484023	−	0.875055i	$-0.660825\pi$
$227$	−82.0064	+	26.6455i	−0.361262	+	0.117381i	0.122762	+	0.992436i	$0.460825\pi$
$228$		0			0
$229$	−40.6339	−	29.5223i	−0.177441	−	0.128918i	0.495520	−	0.868597i	$-0.334978\pi$
$229$	−40.6339	−	29.5223i	−0.177441	−	0.128918i	−0.672961	+	0.739678i	$0.734978\pi$
$230$			174.009i			0.756563i
$231$		0			0
$232$	−298.396			−1.28619
$233$	−251.058	+	345.551i	−1.07750	+	1.48305i	−0.215257	+	0.976558i	$0.569059\pi$
$233$	−251.058	+	345.551i	−1.07750	+	1.48305i	−0.862243	+	0.506494i	$0.830941\pi$
$234$		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	0.270788	−	0.962639i	$-0.412716\pi$
$239$	−18.1556	−	5.89911i	−0.0759648	−	0.0246825i	−0.346753	+	0.937957i	$0.612716\pi$
$240$		0			0
$241$			53.8901i			0.223611i	0.993730	+	0.111805i	$0.0356633\pi$
$241$			53.8901i			0.223611i	−0.993730	+	0.111805i	$0.964337\pi$
$242$	−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	−0.288221	−	0.957564i	$-0.593064\pi$
$251$	−323.284	−	234.879i	−1.28798	−	0.935775i	−0.999763	+	0.0217890i	$0.993064\pi$
$252$		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	−0.705721	−	0.708490i	$-0.749377\pi$
$257$	−141.664	−	435.996i	−0.551221	−	1.69648i	0.154500	−	0.987993i	$-0.450623\pi$
$258$		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	$0.166163\pi$
$263$			262.279i			0.997259i	−0.866815	+	0.498630i	$0.833837\pi$
$264$		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	−0.691681	−	0.722203i	$-0.743130\pi$
$269$	−58.7944	+	42.7166i	−0.218566	+	0.158798i	0.473115	+	0.881001i	$0.343130\pi$
$270$		0			0
$271$	−191.391	+	62.1866i	−0.706238	+	0.229471i	−0.640047	−	0.768336i	$-0.721085\pi$
$271$	−191.391	+	62.1866i	−0.706238	+	0.229471i	−0.0661919	+	0.997807i	$0.521085\pi$
$272$	−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	−0.239751	−	0.970835i	$-0.577066\pi$
$277$	209.870	−	288.862i	0.757655	−	1.04282i	0.997405	−	0.0719881i	$-0.0229344\pi$
$278$	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	0.415207	−	0.909727i	$-0.363709\pi$
$281$	−162.502	−	223.665i	−0.578300	−	0.795962i	−0.993508	+	0.113765i	$0.963709\pi$
$282$		0			0
$283$	272.768	+	88.6277i	0.963844	+	0.313172i	0.748328	−	0.663328i	$-0.230857\pi$
$283$	272.768	+	88.6277i	0.963844	+	0.313172i	0.215516	+	0.976500i	$0.430857\pi$
$284$	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	−0.0570154	−	0.998373i	$-0.518158\pi$
$293$	141.720	−	46.0477i	0.483687	−	0.157160i	0.540703	+	0.841214i	$0.318158\pi$
$294$		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	$0.149143\pi$
$307$			277.276i			0.903179i	−0.892226	+	0.451590i	$0.850857\pi$
$308$	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	−0.791219	−	0.611533i	$-0.790553\pi$
$311$	64.7940	−	199.415i	0.208341	−	0.641207i	0.999560	−	0.0296738i	$-0.00944686\pi$
$312$		0			0
$313$	−86.4426	+	62.8042i	−0.276174	+	0.200652i	−0.717247	−	0.696819i	$-0.754598\pi$
$313$	−86.4426	+	62.8042i	−0.276174	+	0.200652i	0.441073	+	0.897471i	$0.354598\pi$
$314$	−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	0.998207	−	0.0598560i	$-0.0190641\pi$
$317$	396.169	+	287.833i	1.24974	+	0.907992i	0.251537	+	0.967848i	$0.419064\pi$
$318$		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	−0.914050	−	0.405601i	$-0.867062\pi$
$337$	−476.898	+	154.953i	−1.41513	+	0.459802i	−0.501076	+	0.865403i	$0.667062\pi$
$338$	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	0.945950	−	0.324313i	$-0.105133\pi$
$347$	119.783	+	164.867i	0.345195	+	0.475120i	−0.600755	+	0.799433i	$0.705133\pi$
$348$		0			0
$349$	401.860	+	130.572i	1.15146	+	0.374133i	0.821694	−	0.569929i	$-0.193029\pi$
$349$	401.860	+	130.572i	1.15146	+	0.374133i	0.329768	+	0.944062i	$0.393029\pi$
$350$	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	−0.801775	−	0.597625i	$-0.796111\pi$
$359$	−394.595	+	128.212i	−1.09915	+	0.357135i	−0.297375	+	0.954761i	$0.596111\pi$
$360$		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	0.932901	+	0.360133i	$0.117269\pi$
$367$	143.075	+	440.338i	0.389849	+	1.19983i	−0.543052	+	0.839699i	$0.682731\pi$
$368$	−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	$0.342233\pi$
$373$			656.230i			1.75933i	−0.475594	+	0.879665i	$0.657767\pi$
$374$	−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	0.00893516	−	0.999960i	$-0.497156\pi$
$379$	364.869	−	265.093i	0.962715	−	0.699453i	0.953780	+	0.300507i	$0.0971558\pi$
$380$	−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	0.869125	−	0.494592i	$-0.164682\pi$
$383$	255.582	+	185.691i	0.667315	+	0.484833i	−0.201810	+	0.979425i	$0.564682\pi$
$384$		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	0.999387	−	0.0349951i	$-0.0111416\pi$
$389$	66.2453	+	203.882i	0.170296	+	0.524119i	−0.829091	+	0.559114i	$0.811142\pi$
$390$		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	−0.694490	−	0.719502i	$-0.744370\pi$
$401$	−90.1495	+	65.4975i	−0.224812	+	0.163335i	0.469678	+	0.882838i	$0.344370\pi$
$402$		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	−0.637679	−	0.770302i	$-0.720105\pi$
$409$	119.418	−	164.365i	0.291976	−	0.401870i	0.929655	+	0.368432i	$0.120105\pi$
$410$	−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	−0.750907	−	0.660408i	$-0.770383\pi$
$421$	103.047	−	317.147i	0.244768	−	0.753317i	0.995675	−	0.0929092i	$-0.0296166\pi$
$422$	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	−0.0710952	+	0.997470i	$0.522649\pi$
$431$	−430.041	+	591.901i	−0.997775	+	1.37332i	−0.926680	+	0.375851i	$0.877351\pi$
$432$		0			0
$433$	−115.298	−	354.852i	−0.266278	−	0.819519i	−0.991396	−	0.130895i	$-0.958215\pi$
$433$	−115.298	−	354.852i	−0.266278	−	0.819519i	0.725119	−	0.688624i	$-0.241785\pi$
$434$	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	$-0.890946\pi$
$439$		−	294.954i		−	0.671878i	0.941884	−	0.335939i	$-0.109054\pi$
$440$	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	0.604696	+	0.796456i	$0.293295\pi$
$443$	−156.228	+	480.820i	−0.352659	+	1.08537i	−0.957355	+	0.288915i	$0.906705\pi$
$444$		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	0.563577	−	0.826064i	$-0.309425\pi$
$449$	−21.5081	−	15.6265i	−0.0479021	−	0.0348029i	−0.611479	+	0.791261i	$0.709425\pi$
$450$		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	0.680124	−	0.733097i	$-0.261926\pi$
$457$	−103.859	−	142.950i	−0.227262	−	0.312800i	−0.907387	+	0.420297i	$0.861926\pi$
$458$	−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	$0.0537781\pi$
$461$			155.031i			0.336292i	−0.985762	+	0.168146i	$0.946222\pi$
$462$		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	−0.271609	−	0.962408i	$-0.587556\pi$
$467$	261.410	−	189.925i	0.559764	−	0.406692i	0.831373	+	0.555715i	$0.187556\pi$
$468$		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	0.991651	−	0.128953i	$-0.0411615\pi$
$479$	269.472	+	370.897i	0.562572	+	0.774315i	−0.429078	+	0.903267i	$0.641162\pi$
$480$		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	−0.841650	−	0.540023i	$-0.818416\pi$
$487$	76.3014	−	234.832i	0.156676	−	0.482200i	0.998327	+	0.0578223i	$0.0184157\pi$
$488$	−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	−0.266771	−	0.963760i	$-0.585957\pi$
$491$	41.1903	−	13.3835i	0.0838906	−	0.0272577i	0.350662	+	0.936502i	$0.385957\pi$
$492$		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	−0.979518	−	0.201355i	$-0.935466\pi$
$499$	−152.407	−	469.060i	−0.305425	−	0.940000i	0.674094	−	0.738646i	$-0.264534\pi$
$500$	−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	0.577816	−	0.816167i	$-0.303905\pi$
$503$	284.470	+	92.4299i	0.565547	+	0.183757i	−0.0122686	+	0.999925i	$0.503905\pi$
$504$		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	−0.641274	−	0.767312i	$-0.721594\pi$
$509$	167.228	−	514.675i	0.328543	−	1.01115i	0.969816	−	0.243838i	$-0.0784064\pi$
$510$		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	0.993448	−	0.114281i	$-0.0364564\pi$
$521$	63.8533	+	196.520i	0.122559	+	0.377198i	−0.870889	+	0.491479i	$0.836456\pi$
$522$		0			0
$523$	−33.1163	−	45.5807i	−0.0633199	−	0.0871524i	0.776183	−	0.630508i	$-0.217153\pi$
$523$	−33.1163	−	45.5807i	−0.0633199	−	0.0871524i	−0.839503	+	0.543356i	$0.817153\pi$
$524$	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	−0.979916	−	0.199411i	$-0.936097\pi$
$541$	−263.713	+	362.970i	−0.487455	+	0.670924i	0.492461	+	0.870334i	$0.336097\pi$
$542$	−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	0.922758	−	0.385380i	$-0.125930\pi$
$547$	789.192	+	256.424i	1.44276	+	0.468782i	0.520006	+	0.854163i	$0.325930\pi$
$548$	−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	0.733076	−	0.680147i	$-0.238084\pi$
$557$	961.341	−	312.359i	1.72593	−	0.560788i	0.992851	+	0.119359i	$0.0380839\pi$
$558$		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	−0.804799	−	0.593548i	$-0.797727\pi$
$563$	4.72664	−	6.50566i	0.00839545	−	0.0115553i	0.813194	+	0.581993i	$0.197727\pi$
$564$		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	−0.300749	−	0.953703i	$-0.597237\pi$
$569$	−628.536	−	204.224i	−1.10463	−	0.358917i	−0.803884	+	0.594786i	$0.797237\pi$
$570$		0			0
$571$		−	472.496i		−	0.827489i	−0.910393	−	0.413745i	$-0.864221\pi$
$571$		−	472.496i		−	0.827489i	0.910393	−	0.413745i	$-0.135779\pi$
$572$	−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	−0.443785	−	0.896133i	$-0.646364\pi$
$577$	156.570	−	113.755i	0.271352	−	0.197149i	0.715137	+	0.698985i	$0.246364\pi$
$578$	−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	0.997794	+	0.0663796i	$0.0211448\pi$
$587$	134.763	+	414.757i	0.229579	+	0.706571i	−0.768216	+	0.640191i	$0.778855\pi$
$588$		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	$-0.746364\pi$
$593$		−	848.153i		−	1.43027i	0.698984	−	0.715137i	$-0.253636\pi$
$594$		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	−0.378416	+	0.925636i	$0.623531\pi$
$599$	−824.035	+	598.697i	−1.37569	+	0.999494i	−0.997269	+	0.0738582i	$0.976469\pi$
$600$		0			0
$601$	−556.691	+	180.880i	−0.926274	+	0.300965i	−0.733038	−	0.680188i	$-0.761898\pi$
$601$	−556.691	+	180.880i	−0.926274	+	0.300965i	−0.193236	+	0.981152i	$0.561898\pi$
$602$	−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	−0.0181180	+	0.999836i	$0.505767\pi$
$607$	−584.796	+	804.902i	−0.963420	+	1.32603i	−0.945302	+	0.326198i	$0.894233\pi$
$608$	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	−0.252614	−	0.967567i	$-0.581290\pi$
$613$	−628.757	−	204.295i	−1.02570	−	0.333272i	−0.773091	+	0.634296i	$0.781290\pi$
$614$	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	−0.974346	−	0.225055i	$-0.927744\pi$
$619$	−33.3019	+	102.493i	−0.0537995	+	0.165578i	0.920547	+	0.390633i	$0.127744\pi$
$620$	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	−0.997607	−	0.0691348i	$-0.977976\pi$
$631$	−145.864	−	448.922i	−0.231162	−	0.711445i	0.766445	−	0.642310i	$-0.222024\pi$
$632$	−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	0.702675	+	0.711511i	$0.251989\pi$
$641$	−182.054	+	560.306i	−0.284016	+	0.874112i	−0.986692	+	0.162602i	$0.948011\pi$
$642$		0			0
$643$	−798.095	+	579.850i	−1.24121	+	0.901788i	−0.997678	−	0.0681057i	$-0.978304\pi$
$643$	−798.095	+	579.850i	−1.24121	+	0.901788i	−0.243527	+	0.969894i	$0.578304\pi$
$644$	−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	0.0272850	−	0.999628i	$-0.491314\pi$
$647$	−591.996	−	430.110i	−0.914986	−	0.664776i	−0.942271	+	0.334852i	$0.891314\pi$
$648$		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	0.922976	−	0.384859i	$-0.125750\pi$
$653$	−32.6119	−	100.369i	−0.0499416	−	0.153705i	−0.972917	+	0.231154i	$0.925750\pi$
$654$		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	$-0.851505\pi$
$659$		−	592.799i		−	0.899543i	0.893144	−	0.449772i	$-0.148495\pi$
$660$		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	−0.549478	−	0.835508i	$-0.685173\pi$
$673$	279.252	−	384.357i	0.414936	−	0.571110i	0.964414	+	0.264398i	$0.0851733\pi$
$674$	−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	0.890314	−	0.455348i	$-0.150485\pi$
$677$	123.302	+	169.711i	0.182130	+	0.250681i	−0.708183	+	0.706029i	$0.750485\pi$
$678$		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	0.997086	−	0.0762896i	$-0.0243074\pi$
$691$	851.759	+	618.839i	1.23265	+	0.895570i	0.235561	+	0.971860i	$0.424307\pi$
$692$			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	0.837040	−	0.547142i	$-0.184284\pi$
$701$	836.024	+	271.641i	1.19262	+	0.387505i	0.355577	+	0.934647i	$0.384284\pi$
$702$		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	−0.918745	−	0.394851i	$-0.870796\pi$
$709$	−586.433	+	426.069i	−0.827127	+	0.600943i	0.0916181	+	0.995794i	$0.470796\pi$
$710$	−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	0.974917	+	0.222568i	$0.0714441\pi$
$719$	227.934	+	701.508i	0.317015	+	0.975672i	−0.657902	+	0.753103i	$0.728556\pi$
$720$		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	0.478324	−	0.878183i	$-0.341244\pi$
$733$	1012.62	−	329.022i	1.38148	−	0.448870i	0.903156	+	0.429314i	$0.141244\pi$
$734$	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	0.0282457	+	0.999601i	$0.491008\pi$
$739$	−688.127	+	947.126i	−0.931160	+	1.28163i	−0.959405	+	0.282030i	$0.908992\pi$
$740$	−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	0.439011	−	0.898482i	$-0.355329\pi$
$743$	−409.510	−	563.642i	−0.551158	−	0.758603i	−0.990169	+	0.139878i	$0.955329\pi$
$744$		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	−0.824062	−	0.566499i	$-0.808297\pi$
$751$	131.874	−	405.867i	0.175598	−	0.540435i	0.999660	+	0.0260640i	$0.00829738\pi$
$752$	−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	0.960357	−	0.278774i	$-0.0899280\pi$
$757$	750.939	+	545.589i	0.991993	+	0.720725i	0.0316368	+	0.999499i	$0.489928\pi$
$758$		−	626.489i		−	0.826502i
$759$		0			0
$760$	−368.910			−0.485408
$761$	28.3758	−	39.0559i	0.0372875	−	0.0513218i	−0.789966	−	0.613150i	$-0.789902\pi$
$761$	28.3758	−	39.0559i	0.0372875	−	0.0513218i	0.827254	+	0.561829i	$0.189902\pi$
$762$		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	$0.0914019\pi$
$769$			435.589i			0.566435i	−0.959056	+	0.283218i	$0.908598\pi$
$770$	−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	−0.855962	−	0.517039i	$-0.827034\pi$
$773$	108.555	−	334.098i	0.140434	−	0.432210i	0.996396	+	0.0848287i	$0.0270343\pi$
$774$		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	0.938986	−	0.343957i	$-0.111767\pi$
$787$	253.179	+	348.471i	0.321701	+	0.442783i	−0.617285	+	0.786740i	$0.711767\pi$
$788$	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	−0.371188	−	0.928558i	$-0.621050\pi$
$797$	316.584	−	230.011i	0.397219	−	0.288597i	0.768407	+	0.639961i	$0.221050\pi$
$798$		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	0.668439	−	0.743767i	$-0.266963\pi$
$809$	−198.597	−	273.345i	−0.245485	−	0.337881i	−0.913924	+	0.405886i	$0.866963\pi$
$810$		0			0
$811$	−1405.86	−	456.793i	−1.73349	−	0.563246i	−0.739546	−	0.673106i	$-0.764960\pi$
$811$	−1405.86	−	456.793i	−1.73349	−	0.563246i	−0.993947	+	0.109860i	$0.964960\pi$
$812$	−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	−0.316550	−	0.948576i	$-0.602525\pi$
$821$	−12.3858	+	4.02439i	−0.0150862	+	0.00490182i	0.301464	+	0.953478i	$0.402525\pi$
$822$		0			0
$823$	−8.15431	−	5.92445i	−0.00990803	−	0.00719860i	0.582820	−	0.812601i	$-0.301949\pi$
$823$	−8.15431	−	5.92445i	−0.00990803	−	0.00719860i	−0.592728	+	0.805403i	$0.701949\pi$
$824$		−	271.373i		−	0.329336i
$825$		0			0
$826$	−48.0058			−0.0581184
$827$	7.38327	−	10.1622i	0.00892778	−	0.0122880i	−0.804530	−	0.593912i	$-0.797583\pi$
$827$	7.38327	−	10.1622i	0.00892778	−	0.0122880i	0.813458	+	0.581624i	$0.197583\pi$
$828$		0			0
$829$	−63.4520	−	195.285i	−0.0765404	−	0.235567i	0.905465	−	0.424422i	$-0.139523\pi$
$829$	−63.4520	−	195.285i	−0.0765404	−	0.235567i	−0.982005	+	0.188854i	$0.939523\pi$
$830$	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	−0.509974	−	0.860190i	$-0.670345\pi$
$839$	342.489	−	1054.07i	0.408211	−	1.25634i	0.918184	−	0.396153i	$-0.129655\pi$
$840$		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	−0.947035	−	0.321129i	$-0.895938\pi$
$853$	−818.707	−	1126.85i	−0.959797	−	1.32105i	−0.0127620	−	0.999919i	$-0.504062\pi$
$854$	−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	$0.273323\pi$
$857$			1297.45i			1.51395i	−0.653444	+	0.756974i	$0.726677\pi$
$858$		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	−0.425652	−	0.904887i	$-0.639955\pi$
$863$	261.846	−	190.242i	0.303414	−	0.220443i	0.729065	+	0.684444i	$0.239955\pi$
$864$		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	−0.0480065	−	0.998847i	$-0.515287\pi$
$877$	−591.056	−	192.046i	−0.673952	−	0.218980i	−0.625946	+	0.779867i	$0.715287\pi$
$878$	−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	−0.811887	−	0.583815i	$-0.801559\pi$
$883$	166.093	−	511.183i	0.188101	−	0.578916i	0.999988	+	0.00489886i	$0.00155936\pi$
$884$	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	−0.0473806	−	0.998877i	$-0.515087\pi$
$887$	444.753	−	144.509i	0.501413	−	0.162919i	0.548793	+	0.835958i	$0.315087\pi$
$888$		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	−0.658454	−	0.752621i	$-0.728789\pi$
$907$	−132.551	+	96.3039i	−0.146142	+	0.106179i	0.512312	+	0.858800i	$0.328789\pi$
$908$	−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	0.926909	−	0.375287i	$-0.122456\pi$
$911$	780.199	+	566.848i	0.856420	+	0.622226i	−0.0704883	+	0.997513i	$0.522456\pi$
$912$		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	0.913437	+	0.406980i	$0.133418\pi$
$919$	935.754	+	1287.95i	1.01823	+	1.40147i	0.104794	+	0.994494i	$0.466582\pi$
$920$	−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	−0.946741	−	0.321996i	$-0.895646\pi$
$929$	−866.817	+	629.779i	−0.933064	+	0.677911i	0.0136770	+	0.999906i	$0.495646\pi$
$930$		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	−0.607477	−	0.794337i	$-0.707818\pi$
$937$	314.554	−	432.946i	0.335703	−	0.462056i	0.943180	+	0.332282i	$0.107818\pi$
$938$	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	0.962676	+	0.270657i	$0.0872409\pi$
$941$	868.169	+	1194.93i	0.922603	+	1.26985i	−0.0400733	+	0.999197i	$0.512759\pi$
$942$		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	−0.567987	−	0.823038i	$-0.692277\pi$
$953$	−518.173	+	168.365i	−0.543728	+	0.176668i	0.0242586	+	0.999706i	$0.492277\pi$
$954$		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	$-0.787609\pi$
$967$		−	1196.81i		−	1.23765i	0.785529	−	0.618824i	$-0.212391\pi$
$968$	−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	0.734213	+	0.678919i	$0.237551\pi$
$971$	−251.330	+	773.514i	−0.258836	+	0.796616i	−0.993050	+	0.117697i	$0.962449\pi$
$972$		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	0.833464	−	0.552574i	$-0.186354\pi$
$977$	552.483	+	401.403i	0.565490	+	0.410852i	−0.267974	+	0.963426i	$0.586354\pi$
$978$		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	−0.861935	−	0.507018i	$-0.830748\pi$
$983$	−454.768	−	1399.63i	−0.462633	−	1.42384i	0.399303	−	0.916819i	$-0.369252\pi$
$984$		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	−0.837119	−	0.547020i	$-0.815762\pi$
$997$	−1189.25	+	386.412i	−1.19283	+	0.387575i	−0.355713	+	0.934595i	$0.615762\pi$
$998$	−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.73.3	yes	16
3.2	odd	2	inner	99.3.k.b.73.2	yes	16
11.5	even	5		1089.3.c.l.604.11		16
11.6	odd	10		1089.3.c.l.604.5		16
11.8	odd	10	inner	99.3.k.b.19.3	yes	16
33.5	odd	10		1089.3.c.l.604.6		16
33.8	even	10	inner	99.3.k.b.19.2	✓	16
33.17	even	10		1089.3.c.l.604.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.k.b.19.2	✓	16	33.8	even	10	inner
99.3.k.b.19.3	yes	16	11.8	odd	10	inner
99.3.k.b.73.2	yes	16	3.2	odd	2	inner
99.3.k.b.73.3	yes	16	1.1	even	1	trivial
1089.3.c.l.604.5		16	11.6	odd	10
1089.3.c.l.604.6		16	33.5	odd	10
1089.3.c.l.604.11		16	11.5	even	5
1089.3.c.l.604.12		16	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.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

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