LMFDB - Embedded newform 483.3.g.a.139.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(139,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("483.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.g (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.10
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.13389 q^{2} -1.73205i q^{3} +5.82124 q^{4} -7.50145i q^{5} +5.42805i q^{6} +(4.32864 + 5.50117i) q^{7} -5.70757 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.13389 q^{2} -1.73205i q^{3} +5.82124 q^{4} -7.50145i q^{5} +5.42805i q^{6} +(4.32864 + 5.50117i) q^{7} -5.70757 q^{8} -3.00000 q^{9} +23.5087i q^{10} +11.2741 q^{11} -10.0827i q^{12} +4.27394i q^{13} +(-13.5655 - 17.2400i) q^{14} -12.9929 q^{15} -5.39810 q^{16} +27.9296i q^{17} +9.40166 q^{18} +34.7317i q^{19} -43.6677i q^{20} +(9.52831 - 7.49742i) q^{21} -35.3317 q^{22} +4.79583 q^{23} +9.88580i q^{24} -31.2717 q^{25} -13.3940i q^{26} +5.19615i q^{27} +(25.1980 + 32.0237i) q^{28} -43.1450 q^{29} +40.7182 q^{30} +26.4407i q^{31} +39.7473 q^{32} -19.5273i q^{33} -87.5283i q^{34} +(41.2667 - 32.4710i) q^{35} -17.4637 q^{36} -10.1099 q^{37} -108.845i q^{38} +7.40268 q^{39} +42.8150i q^{40} +19.2526i q^{41} +(-29.8606 + 23.4961i) q^{42} -33.6446 q^{43} +65.6292 q^{44} +22.5043i q^{45} -15.0296 q^{46} +12.3743i q^{47} +9.34979i q^{48} +(-11.5258 + 47.6252i) q^{49} +98.0019 q^{50} +48.3755 q^{51} +24.8796i q^{52} -27.7362 q^{53} -16.2842i q^{54} -84.5720i q^{55} +(-24.7060 - 31.3983i) q^{56} +60.1571 q^{57} +135.212 q^{58} +73.4667i q^{59} -75.6347 q^{60} +65.6751i q^{61} -82.8621i q^{62} +(-12.9859 - 16.5035i) q^{63} -102.971 q^{64} +32.0607 q^{65} +61.1964i q^{66} +3.99282 q^{67} +162.585i q^{68} -8.30662i q^{69} +(-129.325 + 101.761i) q^{70} +104.091 q^{71} +17.1227 q^{72} +29.8094i q^{73} +31.6833 q^{74} +54.1642i q^{75} +202.182i q^{76} +(48.8015 + 62.0207i) q^{77} -23.1992 q^{78} +72.3676 q^{79} +40.4936i q^{80} +9.00000 q^{81} -60.3353i q^{82} -70.4907i q^{83} +(55.4666 - 43.6443i) q^{84} +209.513 q^{85} +105.438 q^{86} +74.7294i q^{87} -64.3477 q^{88} +35.0091i q^{89} -70.5260i q^{90} +(-23.5117 + 18.5003i) q^{91} +27.9177 q^{92} +45.7966 q^{93} -38.7796i q^{94} +260.538 q^{95} -68.8444i q^{96} +18.2434i q^{97} +(36.1205 - 149.252i) q^{98} -33.8223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.13389			−1.56694			−0.783472	−	0.621428i	$-0.786553\pi$
$2$	−3.13389			−1.56694			−0.783472	+	0.621428i	$0.786553\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	5.82124			1.45531
$5$		−	7.50145i		−	1.50029i	−0.661274	−	0.750145i	$-0.729984\pi$
$5$		−	7.50145i		−	1.50029i	0.661274	−	0.750145i	$-0.270016\pi$
$6$			5.42805i			0.904675i
$7$	4.32864	+	5.50117i	0.618377	+	0.785882i
$7$	4.32864	+	5.50117i	0.618377	+	0.785882i
$8$	−5.70757			−0.713446
$9$	−3.00000			−0.333333
$10$			23.5087i			2.35087i
$11$	11.2741			1.02492			0.512459	−	0.858712i	$-0.328735\pi$
$11$	11.2741			1.02492			0.512459	+	0.858712i	$0.328735\pi$
$12$		−	10.0827i		−	0.840224i
$13$			4.27394i			0.328765i	0.986397	+	0.164382i	$0.0525631\pi$
$13$			4.27394i			0.328765i	−0.986397	+	0.164382i	$0.947437\pi$
$14$	−13.5655	−	17.2400i	−0.968961	−	1.23143i
$15$	−12.9929			−0.866192
$16$	−5.39810			−0.337382
$17$			27.9296i			1.64292i	0.570267	+	0.821459i	$0.306840\pi$
$17$			27.9296i			1.64292i	−0.570267	+	0.821459i	$0.693160\pi$
$18$	9.40166			0.522314
$19$			34.7317i			1.82799i	0.405730	+	0.913993i	$0.367017\pi$
$19$			34.7317i			1.82799i	−0.405730	+	0.913993i	$0.632983\pi$
$20$		−	43.6677i		−	2.18339i
$21$	9.52831	−	7.49742i	0.453729	−	0.357020i
$22$	−35.3317			−1.60599
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$			9.88580i			0.411908i
$25$	−31.2717			−1.25087
$26$		−	13.3940i		−	0.515156i
$27$			5.19615i			0.192450i
$28$	25.1980	+	32.0237i	0.899930	+	1.14370i
$29$	−43.1450			−1.48776			−0.743880	−	0.668314i	$-0.767016\pi$
$29$	−43.1450			−1.48776			−0.743880	+	0.668314i	$0.767016\pi$
$30$	40.7182			1.35727
$31$			26.4407i			0.852926i	0.904505	+	0.426463i	$0.140241\pi$
$31$			26.4407i			0.852926i	−0.904505	+	0.426463i	$0.859759\pi$
$32$	39.7473			1.24210
$33$		−	19.5273i		−	0.591737i
$34$		−	87.5283i		−	2.57436i
$35$	41.2667	−	32.4710i	1.17905	−	0.927744i
$36$	−17.4637			−0.485104
$37$	−10.1099			−0.273240			−0.136620	−	0.990623i	$-0.543624\pi$
$37$	−10.1099			−0.273240			−0.136620	+	0.990623i	$0.543624\pi$
$38$		−	108.845i		−	2.86435i
$39$	7.40268			0.189812
$40$			42.8150i			1.07038i
$41$			19.2526i			0.469575i	0.972047	+	0.234787i	$0.0754394\pi$
$41$			19.2526i			0.469575i	−0.972047	+	0.234787i	$0.924561\pi$
$42$	−29.8606	+	23.4961i	−0.710968	+	0.559430i
$43$	−33.6446			−0.782432			−0.391216	−	0.920299i	$-0.627945\pi$
$43$	−33.6446			−0.782432			−0.391216	+	0.920299i	$0.627945\pi$
$44$	65.6292			1.49157
$45$			22.5043i			0.500096i
$46$	−15.0296			−0.326730
$47$			12.3743i			0.263283i	0.991297	+	0.131641i	$0.0420247\pi$
$47$			12.3743i			0.263283i	−0.991297	+	0.131641i	$0.957975\pi$
$48$			9.34979i			0.194787i
$49$	−11.5258	+	47.6252i	−0.235220	+	0.971942i
$50$	98.0019			1.96004
$51$	48.3755			0.948540
$52$			24.8796i			0.478455i
$53$	−27.7362			−0.523324			−0.261662	−	0.965160i	$-0.584271\pi$
$53$	−27.7362			−0.523324			−0.261662	+	0.965160i	$0.584271\pi$
$54$		−	16.2842i		−	0.301558i
$55$		−	84.5720i		−	1.53767i
$56$	−24.7060	−	31.3983i	−0.441178	−	0.560684i
$57$	60.1571			1.05539
$58$	135.212			2.33123
$59$			73.4667i			1.24520i	0.782541	+	0.622600i	$0.213923\pi$
$59$			73.4667i			1.24520i	−0.782541	+	0.622600i	$0.786077\pi$
$60$	−75.6347			−1.26058
$61$			65.6751i			1.07664i	0.842740	+	0.538321i	$0.180941\pi$
$61$			65.6751i			1.07664i	−0.842740	+	0.538321i	$0.819059\pi$
$62$		−	82.8621i		−	1.33649i
$63$	−12.9859	−	16.5035i	−0.206126	−	0.261961i
$64$	−102.971			−1.60892
$65$	32.0607			0.493242
$66$			61.1964i			0.927217i
$67$	3.99282			0.0595944			0.0297972	−	0.999556i	$-0.490514\pi$
$67$	3.99282			0.0595944			0.0297972	+	0.999556i	$0.490514\pi$
$68$			162.585i			2.39096i
$69$		−	8.30662i		−	0.120386i
$70$	−129.325	+	101.761i	−1.84750	+	1.45372i
$71$	104.091			1.46607			0.733035	−	0.680191i	$-0.238103\pi$
$71$	104.091			1.46607			0.733035	+	0.680191i	$0.238103\pi$
$72$	17.1227			0.237815
$73$			29.8094i			0.408347i	0.978935	+	0.204174i	$0.0654507\pi$
$73$			29.8094i			0.408347i	−0.978935	+	0.204174i	$0.934549\pi$
$74$	31.6833			0.428152
$75$			54.1642i			0.722189i
$76$			202.182i			2.66029i
$77$	48.8015	+	62.0207i	0.633785	+	0.805464i
$78$	−23.1992			−0.297425
$79$	72.3676			0.916046			0.458023	−	0.888940i	$-0.348558\pi$
$79$	72.3676			0.916046			0.458023	+	0.888940i	$0.348558\pi$
$80$			40.4936i			0.506170i
$81$	9.00000			0.111111
$82$		−	60.3353i		−	0.735797i
$83$		−	70.4907i		−	0.849285i	−0.905361	−	0.424642i	$-0.860400\pi$
$83$		−	70.4907i		−	0.849285i	0.905361	−	0.424642i	$-0.139600\pi$
$84$	55.4666	−	43.6443i	0.660317	−	0.519575i
$85$	209.513			2.46485
$86$	105.438			1.22603
$87$			74.7294i			0.858958i
$88$	−64.3477			−0.731223
$89$			35.0091i			0.393361i	0.980468	+	0.196680i	$0.0630161\pi$
$89$			35.0091i			0.393361i	−0.980468	+	0.196680i	$0.936984\pi$
$90$		−	70.5260i		−	0.783623i
$91$	−23.5117	+	18.5003i	−0.258370	+	0.203300i
$92$	27.9177			0.303453
$93$	45.7966			0.492437
$94$		−	38.7796i		−	0.412549i
$95$	260.538			2.74251
$96$		−	68.8444i		−	0.717129i
$97$			18.2434i			0.188076i	0.995569	+	0.0940380i	$0.0299775\pi$
$97$			18.2434i			0.188076i	−0.995569	+	0.0940380i	$0.970022\pi$
$98$	36.1205	−	149.252i	0.368577	−	1.52298i
$99$	−33.8223			−0.341639
$100$	−182.040			−1.82040
$101$		−	149.547i		−	1.48066i	−0.672244	−	0.740330i	$-0.734669\pi$
$101$		−	149.547i		−	1.48066i	0.672244	−	0.740330i	$-0.265331\pi$
$102$	−151.603			−1.48631
$103$			63.1457i			0.613065i	0.951860	+	0.306532i	$0.0991688\pi$
$103$			63.1457i			0.613065i	−0.951860	+	0.306532i	$0.900831\pi$
$104$		−	24.3938i		−	0.234556i
$105$	−56.2415	−	71.4761i	−0.535633	−	0.680725i
$106$	86.9220			0.820019
$107$	−165.331			−1.54515			−0.772573	−	0.634926i	$-0.781031\pi$
$107$	−165.331			−1.54515			−0.772573	+	0.634926i	$0.781031\pi$
$108$			30.2481i			0.280075i
$109$	148.829			1.36540			0.682702	−	0.730697i	$-0.260805\pi$
$109$	148.829			1.36540			0.682702	+	0.730697i	$0.260805\pi$
$110$			265.039i			2.40945i
$111$			17.5109i			0.157755i
$112$	−23.3664	−	29.6959i	−0.208629	−	0.265142i
$113$	−181.347			−1.60484			−0.802420	−	0.596760i	$-0.796455\pi$
$113$	−181.347			−1.60484			−0.802420	+	0.596760i	$0.796455\pi$
$114$	−188.526			−1.65373
$115$		−	35.9757i		−	0.312832i
$116$	−251.158			−2.16515
$117$		−	12.8218i		−	0.109588i
$118$		−	230.236i		−	1.95116i
$119$	−153.646	+	120.897i	−1.29114	+	1.01594i
$120$	74.1578			0.617981
$121$	6.10521			0.0504563
$122$		−	205.818i		−	1.68704i
$123$	33.3464			0.271109
$124$			153.918i			1.24127i
$125$			47.0467i			0.376374i
$126$	40.6964	+	51.7201i	0.322987	+	0.410477i
$127$	78.2741			0.616331			0.308166	−	0.951333i	$-0.400285\pi$
$127$	78.2741			0.616331			0.308166	+	0.951333i	$0.400285\pi$
$128$	163.711			1.27899
$129$			58.2741i			0.451737i
$130$	−100.475			−0.772882
$131$		−	187.084i		−	1.42812i	−0.700083	−	0.714062i	$-0.746854\pi$
$131$		−	187.084i		−	1.42812i	0.700083	−	0.714062i	$-0.253146\pi$
$132$		−	113.673i		−	0.861160i
$133$	−191.065	+	150.341i	−1.43658	+	1.13038i
$134$	−12.5131			−0.0933810
$135$	38.9787			0.288731
$136$		−	159.410i		−	1.17213i
$137$	−147.540			−1.07693			−0.538467	−	0.842647i	$-0.680996\pi$
$137$	−147.540			−1.07693			−0.538467	+	0.842647i	$0.680996\pi$
$138$			26.0320i			0.188638i
$139$		−	149.471i		−	1.07533i	−0.843157	−	0.537667i	$-0.819306\pi$
$139$		−	149.471i		−	1.07533i	0.843157	−	0.537667i	$-0.180694\pi$
$140$	240.224	−	189.022i	1.71588	−	1.35016i
$141$	21.4329			0.152006
$142$	−326.209			−2.29725
$143$			48.1848i			0.336957i
$144$	16.1943			0.112461
$145$			323.650i			2.23207i
$146$		−	93.4191i		−	0.639857i
$147$	82.4892	+	19.9633i	0.561151	+	0.135805i
$148$	−58.8522			−0.397650
$149$	79.9587			0.536635			0.268318	−	0.963330i	$-0.413532\pi$
$149$	79.9587			0.536635			0.268318	+	0.963330i	$0.413532\pi$
$150$		−	169.744i		−	1.13163i
$151$	130.801			0.866229			0.433114	−	0.901339i	$-0.357415\pi$
$151$	130.801			0.866229			0.433114	+	0.901339i	$0.357415\pi$
$152$		−	198.234i		−	1.30417i
$153$		−	83.7889i		−	0.547640i
$154$	−152.938	−	194.366i	−0.993105	−	1.26212i
$155$	198.343			1.27964
$156$	43.0928			0.276236
$157$		−	34.7618i		−	0.221413i	−0.993853	−	0.110706i	$-0.964689\pi$
$157$		−	34.7618i		−	0.221413i	0.993853	−	0.110706i	$-0.0353113\pi$
$158$	−226.792			−1.43539
$159$			48.0405i			0.302141i
$160$		−	298.162i		−	1.86351i
$161$	20.7594	+	26.3827i	0.128940	+	0.163868i
$162$	−28.2050			−0.174105
$163$	−70.5348			−0.432729			−0.216364	−	0.976313i	$-0.569420\pi$
$163$	−70.5348			−0.432729			−0.216364	+	0.976313i	$0.569420\pi$
$164$			112.074i			0.683377i
$165$	−146.483			−0.887776
$166$			220.910i			1.33078i
$167$		−	18.1771i		−	0.108845i	−0.998518	−	0.0544224i	$-0.982668\pi$
$167$		−	18.1771i		−	0.108845i	0.998518	−	0.0544224i	$-0.0173318\pi$
$168$	−54.3835	+	42.7920i	−0.323711	+	0.254714i
$169$	150.733			0.891914
$170$	−656.588			−3.86228
$171$		−	104.195i		−	0.609329i
$172$	−195.853			−1.13868
$173$		−	189.081i		−	1.09295i	−0.837475	−	0.546475i	$-0.815969\pi$
$173$		−	189.081i		−	1.09295i	0.837475	−	0.546475i	$-0.184031\pi$
$174$		−	234.193i		−	1.34594i
$175$	−135.364	−	172.031i	−0.773507	−	0.983034i
$176$	−60.8587			−0.345788
$177$	127.248			0.718916
$178$		−	109.715i		−	0.616374i
$179$	251.931			1.40743			0.703717	−	0.710480i	$-0.251522\pi$
$179$	251.931			1.40743			0.703717	+	0.710480i	$0.251522\pi$
$180$			131.003i			0.727796i
$181$		−	338.132i		−	1.86813i	−0.357097	−	0.934067i	$-0.616234\pi$
$181$		−	338.132i		−	1.86813i	0.357097	−	0.934067i	$-0.383766\pi$
$182$	73.6830	−	57.9780i	0.404851	−	0.318560i
$183$	113.753			0.621599
$184$	−27.3725			−0.148764
$185$			75.8388i			0.409940i
$186$	−143.521			−0.771621
$187$			314.881i			1.68386i
$188$			72.0337i			0.383158i
$189$	−28.5849	+	22.4923i	−0.151243	+	0.119007i
$190$	−816.497			−4.29735
$191$	−199.215			−1.04301			−0.521505	−	0.853248i	$-0.674629\pi$
$191$	−199.215			−1.04301			−0.521505	+	0.853248i	$0.674629\pi$
$192$			178.351i			0.928913i
$193$	25.3609			0.131403			0.0657017	−	0.997839i	$-0.479071\pi$
$193$	25.3609			0.131403			0.0657017	+	0.997839i	$0.479071\pi$
$194$		−	57.1726i		−	0.294704i
$195$		−	55.5308i		−	0.284773i
$196$	−67.0945	+	277.238i	−0.342319	+	1.41448i
$197$	−379.661			−1.92721			−0.963606	−	0.267326i	$-0.913860\pi$
$197$	−379.661			−1.92721			−0.963606	+	0.267326i	$0.913860\pi$
$198$	105.995			0.535329
$199$			33.7845i			0.169771i	0.996391	+	0.0848856i	$0.0270525\pi$
$199$			33.7845i			0.169771i	−0.996391	+	0.0848856i	$0.972948\pi$
$200$	178.485			0.892426
$201$		−	6.91577i		−	0.0344068i
$202$			468.662i			2.32011i
$203$	−186.759	−	237.348i	−0.919996	−	1.16920i
$204$	281.606			1.38042
$205$	144.422			0.704498
$206$		−	197.891i		−	0.960638i
$207$	−14.3875			−0.0695048
$208$		−	23.0712i		−	0.110919i
$209$			391.569i			1.87354i
$210$	176.254	+	223.998i	0.839307	+	1.06666i
$211$	116.720			0.553174			0.276587	−	0.960989i	$-0.410797\pi$
$211$	116.720			0.553174			0.276587	+	0.960989i	$0.410797\pi$
$212$	−161.459			−0.761599
$213$		−	180.291i		−	0.846436i
$214$	518.128			2.42116
$215$			252.383i			1.17387i
$216$		−	29.6574i		−	0.137303i
$217$	−145.455	+	114.452i	−0.670299	+	0.527429i
$218$	−466.413			−2.13951
$219$	51.6313			0.235759
$220$		−	492.314i		−	2.23779i
$221$	−119.370			−0.540134
$222$		−	54.8770i		−	0.247194i
$223$		−	318.913i		−	1.43010i	−0.699073	−	0.715051i	$-0.746404\pi$
$223$		−	318.913i		−	1.43010i	0.699073	−	0.715051i	$-0.253596\pi$
$224$	172.052	+	218.657i	0.768088	+	0.976147i
$225$	93.8151			0.416956
$226$	568.321			2.51469
$227$		−	222.231i		−	0.978990i	−0.872006	−	0.489495i	$-0.837181\pi$
$227$		−	222.231i		−	0.978990i	0.872006	−	0.489495i	$-0.162819\pi$
$228$	350.189			1.53592
$229$			151.091i			0.659784i	0.944019	+	0.329892i	$0.107012\pi$
$229$			151.091i			0.659784i	−0.944019	+	0.329892i	$0.892988\pi$
$230$			112.744i			0.490190i
$231$	107.423	−	84.5266i	0.465035	−	0.365916i
$232$	246.253			1.06144
$233$	386.475			1.65869			0.829347	−	0.558735i	$-0.188713\pi$
$233$	386.475			1.65869			0.829347	+	0.558735i	$0.188713\pi$
$234$			40.1821i			0.171719i
$235$	92.8250			0.395000
$236$			427.668i			1.81215i
$237$		−	125.344i		−	0.528879i
$238$	481.508	−	378.878i	2.02314	−	1.59192i
$239$	57.2687			0.239618			0.119809	−	0.992797i	$-0.461772\pi$
$239$	57.2687			0.239618			0.119809	+	0.992797i	$0.461772\pi$
$240$	70.1370			0.292237
$241$		−	38.4230i		−	0.159432i	−0.996818	−	0.0797158i	$-0.974599\pi$
$241$		−	38.4230i		−	0.159432i	0.996818	−	0.0797158i	$-0.0254013\pi$
$242$	−19.1330			−0.0790622
$243$		−	15.5885i		−	0.0641500i
$244$			382.311i			1.56685i
$245$	357.258	+	86.4601i	1.45819	+	0.352899i
$246$	−104.504			−0.424812
$247$	−148.441			−0.600977
$248$		−	150.912i		−	0.608516i
$249$	−122.093			−0.490335
$250$		−	147.439i		−	0.589756i
$251$			122.206i			0.486878i	0.969916	+	0.243439i	$0.0782756\pi$
$251$			122.206i			0.486878i	−0.969916	+	0.243439i	$0.921724\pi$
$252$	−75.5941	−	96.0710i	−0.299977	−	0.381234i
$253$	54.0687			0.213710
$254$	−245.302			−0.965756
$255$		−	362.886i		−	1.42308i
$256$	−101.166			−0.395179
$257$			202.717i			0.788781i	0.918943	+	0.394391i	$0.129044\pi$
$257$			202.717i			0.788781i	−0.918943	+	0.394391i	$0.870956\pi$
$258$		−	182.624i		−	0.707846i
$259$	−43.7621	−	55.6163i	−0.168966	−	0.214735i
$260$	186.633			0.717821
$261$	129.435			0.495920
$262$			586.300i			2.23779i
$263$	−494.192			−1.87906			−0.939528	−	0.342472i	$-0.888736\pi$
$263$	−494.192			−1.87906			−0.939528	+	0.342472i	$0.888736\pi$
$264$			111.453i			0.422172i
$265$			208.061i			0.785138i
$266$	598.777	−	471.152i	2.25104	−	1.77125i
$267$	60.6375			0.227107
$268$	23.2432			0.0867283
$269$			406.357i			1.51062i	0.655368	+	0.755310i	$0.272513\pi$
$269$			406.357i			1.51062i	−0.655368	+	0.755310i	$0.727487\pi$
$270$	−122.155			−0.452425
$271$			90.5084i			0.333979i	0.985959	+	0.166990i	$0.0534046\pi$
$271$			90.5084i			0.333979i	−0.985959	+	0.166990i	$0.946595\pi$
$272$		−	150.767i		−	0.554291i
$273$	32.0435	+	40.7234i	0.117376	+	0.149170i
$274$	462.373			1.68749
$275$	−352.560			−1.28204
$276$		−	48.3549i		−	0.175199i
$277$	355.574			1.28366			0.641830	−	0.766847i	$-0.278176\pi$
$277$	355.574			1.28366			0.641830	+	0.766847i	$0.278176\pi$
$278$			468.427i			1.68499i
$279$		−	79.3221i		−	0.284309i
$280$	−235.533	+	185.331i	−0.841188	+	0.661895i
$281$	278.099			0.989678			0.494839	−	0.868985i	$-0.335227\pi$
$281$	278.099			0.989678			0.494839	+	0.868985i	$0.335227\pi$
$282$	−67.1682			−0.238185
$283$			314.552i			1.11149i	0.831353	+	0.555745i	$0.187567\pi$
$283$			314.552i			1.11149i	−0.831353	+	0.555745i	$0.812433\pi$
$284$	605.939			2.13359
$285$		−	451.265i		−	1.58339i
$286$		−	151.006i		−	0.527992i
$287$	−105.912	+	83.3373i	−0.369030	+	0.290374i
$288$	−119.242			−0.414035
$289$	−491.064			−1.69918
$290$		−	1014.28i		−	3.49753i
$291$	31.5984			0.108586
$292$			173.527i			0.594272i
$293$			279.371i			0.953485i	0.879043	+	0.476742i	$0.158183\pi$
$293$			279.371i			0.953485i	−0.879043	+	0.476742i	$0.841817\pi$
$294$	−258.512	−	62.5626i	−0.879292	−	0.212798i
$295$	551.107			1.86816
$296$	57.7029			0.194942
$297$			58.5819i			0.197246i
$298$	−250.581			−0.840877
$299$			20.4971i			0.0685522i
$300$			315.303i			1.05101i
$301$	−145.635	−	185.085i	−0.483838	−	0.614899i
$302$	−409.914			−1.35733
$303$	−259.022			−0.854860
$304$		−	187.486i		−	0.616729i
$305$	492.658			1.61527
$306$			262.585i			0.858120i
$307$			351.377i			1.14455i	0.820062	+	0.572275i	$0.193939\pi$
$307$			351.377i			1.14455i	−0.820062	+	0.572275i	$0.806061\pi$
$308$	284.085	+	361.038i	0.922355	+	1.17220i
$309$	109.372			0.353953
$310$	−621.586			−2.00512
$311$			440.920i			1.41775i	0.705335	+	0.708874i	$0.250797\pi$
$311$			440.920i			1.41775i	−0.705335	+	0.708874i	$0.749203\pi$
$312$	−42.2513			−0.135421
$313$		−	356.503i		−	1.13899i	−0.821996	−	0.569493i	$-0.807139\pi$
$313$		−	356.503i		−	1.13899i	0.821996	−	0.569493i	$-0.192861\pi$
$314$			108.940i			0.346941i
$315$	−123.800	+	97.4131i	−0.393017	+	0.309248i
$316$	421.269			1.33313
$317$	568.098			1.79211			0.896053	−	0.443947i	$-0.146422\pi$
$317$	568.098			1.79211			0.896053	+	0.443947i	$0.146422\pi$
$318$		−	150.553i		−	0.473438i
$319$	−486.421			−1.52483
$320$			772.432i			2.41385i
$321$			286.361i			0.892091i
$322$	−65.0576	−	82.6804i	−0.202042	−	0.256771i
$323$	−970.044			−3.00323
$324$	52.3912			0.161701
$325$		−	133.653i		−	0.411241i
$326$	221.048			0.678061
$327$		−	257.779i		−	0.788316i
$328$		−	109.885i		−	0.335016i
$329$	−68.0731	+	53.5638i	−0.206909	+	0.162808i
$330$	459.061			1.39109
$331$	−463.183			−1.39934			−0.699672	−	0.714464i	$-0.746671\pi$
$331$	−463.183			−1.39934			−0.699672	+	0.714464i	$0.746671\pi$
$332$		−	410.343i		−	1.23597i
$333$	30.3297			0.0910802
$334$			56.9649i			0.170554i
$335$		−	29.9519i		−	0.0894088i
$336$	−51.4348	+	40.4719i	−0.153080	+	0.120452i
$337$	−31.8398			−0.0944802			−0.0472401	−	0.998884i	$-0.515043\pi$
$337$	−31.8398			−0.0944802			−0.0472401	+	0.998884i	$0.515043\pi$
$338$	−472.381			−1.39758
$339$			314.102i			0.926555i
$340$	1219.62			3.58713
$341$			298.095i			0.874179i
$342$			326.536i			0.954783i
$343$	−311.885	+	142.747i	−0.909286	+	0.416171i
$344$	192.029			0.558223
$345$	−62.3117			−0.180614
$346$			592.557i			1.71259i
$347$	−91.4067			−0.263420			−0.131710	−	0.991288i	$-0.542047\pi$
$347$	−91.4067			−0.263420			−0.131710	+	0.991288i	$0.542047\pi$
$348$			435.018i			1.25005i
$349$		−	108.310i		−	0.310344i	−0.987887	−	0.155172i	$-0.950407\pi$
$349$		−	108.310i		−	0.310344i	0.987887	−	0.155172i	$-0.0495931\pi$
$350$	424.215	+	539.125i	1.21204	+	1.54036i
$351$	−22.2080			−0.0632708
$352$	448.115			1.27305
$353$			29.3207i			0.0830616i	0.999137	+	0.0415308i	$0.0132235\pi$
$353$			29.3207i			0.0830616i	−0.999137	+	0.0415308i	$0.986777\pi$
$354$	−398.781			−1.12650
$355$		−	780.833i		−	2.19953i
$356$			203.796i			0.572462i
$357$	209.400	+	266.122i	0.586555	+	0.745440i
$358$	−789.522			−2.20537
$359$	−181.633			−0.505941			−0.252970	−	0.967474i	$-0.581407\pi$
$359$	−181.633			−0.505941			−0.252970	+	0.967474i	$0.581407\pi$
$360$		−	128.445i		−	0.356792i
$361$	−845.293			−2.34153
$362$			1059.67i			2.92726i
$363$		−	10.5745i		−	0.0291310i
$364$	−136.867	+	107.695i	−0.376009	+	0.295865i
$365$	223.613			0.612639
$366$	−356.488			−0.974011
$367$		−	144.912i		−	0.394856i	−0.980317	−	0.197428i	$-0.936741\pi$
$367$		−	144.912i		−	0.394856i	0.980317	−	0.197428i	$-0.0632588\pi$
$368$	−25.8884			−0.0703489
$369$		−	57.7577i		−	0.156525i
$370$		−	237.670i		−	0.642352i
$371$	−120.060	−	152.582i	−0.323611	−	0.411271i
$372$	266.593			0.716649
$373$	495.475			1.32835			0.664176	−	0.747576i	$-0.268783\pi$
$373$	495.475			1.32835			0.664176	+	0.747576i	$0.268783\pi$
$374$		−	986.802i		−	2.63851i
$375$	81.4873			0.217300
$376$		−	70.6271i		−	0.187838i
$377$		−	184.399i		−	0.489123i
$378$	89.5819	−	70.4882i	0.236989	−	0.186477i
$379$	1.78067			0.00469833			0.00234916	−	0.999997i	$-0.499252\pi$
$379$	1.78067			0.00469833			0.00234916	+	0.999997i	$0.499252\pi$
$380$	1516.66			3.99120
$381$		−	135.575i		−	0.355839i
$382$	624.317			1.63434
$383$		−	286.503i		−	0.748049i	−0.927419	−	0.374024i	$-0.877978\pi$
$383$		−	286.503i		−	0.748049i	0.927419	−	0.374024i	$-0.122022\pi$
$384$		−	283.555i		−	0.738425i
$385$	465.245	−	366.082i	1.20843	−	0.950861i
$386$	−79.4780			−0.205902
$387$	100.934			0.260811
$388$			106.199i			0.273709i
$389$	−155.753			−0.400394			−0.200197	−	0.979756i	$-0.564158\pi$
$389$	−155.753			−0.400394			−0.200197	+	0.979756i	$0.564158\pi$
$390$			174.027i			0.446224i
$391$			133.946i			0.342572i
$392$	65.7843	−	271.824i	0.167817	−	0.693428i
$393$	−324.039			−0.824527
$394$	1189.81			3.01983
$395$		−	542.862i		−	1.37433i
$396$	−196.888			−0.497191
$397$		−	424.990i		−	1.07050i	−0.844693	−	0.535252i	$-0.820217\pi$
$397$		−	424.990i		−	1.07050i	0.844693	−	0.535252i	$-0.179783\pi$
$398$		−	105.877i		−	0.266022i
$399$	260.398	+	330.935i	0.652627	+	0.829410i
$400$	168.808			0.422020
$401$	674.599			1.68229			0.841146	−	0.540808i	$-0.181881\pi$
$401$	674.599			1.68229			0.841146	+	0.540808i	$0.181881\pi$
$402$			21.6732i			0.0539135i
$403$	−113.006			−0.280412
$404$		−	870.547i		−	2.15482i
$405$		−	67.5130i		−	0.166699i
$406$	585.282	+	743.822i	1.44158	+	1.83207i
$407$	−113.980			−0.280049
$408$	−276.107			−0.676732
$409$		−	77.8563i		−	0.190358i	−0.995460	−	0.0951788i	$-0.969658\pi$
$409$		−	77.8563i		−	0.190358i	0.995460	−	0.0951788i	$-0.0303423\pi$
$410$	−452.602			−1.10391
$411$			255.547i			0.621768i
$412$			367.586i			0.892200i
$413$	−404.153	+	318.011i	−0.978579	+	0.770002i
$414$	45.0888			0.108910
$415$	−528.782			−1.27417
$416$			169.878i			0.408360i
$417$	−258.892			−0.620844
$418$		−	1227.13i		−	2.93572i
$419$		−	322.166i		−	0.768893i	−0.923147	−	0.384447i	$-0.874392\pi$
$419$		−	322.166i		−	0.768893i	0.923147	−	0.384447i	$-0.125608\pi$
$420$	−327.395	−	416.080i	−0.779513	−	0.990666i
$421$	185.709			0.441113			0.220557	−	0.975374i	$-0.429213\pi$
$421$	185.709			0.441113			0.220557	+	0.975374i	$0.429213\pi$
$422$	−365.786			−0.866792
$423$		−	37.1229i		−	0.0877609i
$424$	158.306			0.373363
$425$		−	873.406i		−	2.05507i
$426$			565.011i			1.32632i
$427$	−361.290	+	284.284i	−0.846113	+	0.665770i
$428$	−962.430			−2.24867
$429$	83.4586			0.194542
$430$		−	790.939i		−	1.83939i
$431$	521.194			1.20927			0.604633	−	0.796504i	$-0.293320\pi$
$431$	521.194			1.20927			0.604633	+	0.796504i	$0.293320\pi$
$432$		−	28.0494i		−	0.0649291i
$433$			43.3452i			0.100104i	0.998747	+	0.0500522i	$0.0159388\pi$
$433$			43.3452i			0.100104i	−0.998747	+	0.0500522i	$0.984061\pi$
$434$	455.839	−	358.680i	1.05032	−	0.826452i
$435$	560.578			1.28869
$436$	866.370			1.98709
$437$			166.568i			0.381161i
$438$	−161.807			−0.369422
$439$			310.098i			0.706372i	0.935553	+	0.353186i	$0.114902\pi$
$439$			310.098i			0.706372i	−0.935553	+	0.353186i	$0.885098\pi$
$440$			482.700i			1.09705i
$441$	34.5774	−	142.875i	0.0784068	−	0.323981i
$442$	374.091			0.846359
$443$	−5.19870			−0.0117352			−0.00586761	−	0.999983i	$-0.501868\pi$
$443$	−5.19870			−0.0117352			−0.00586761	+	0.999983i	$0.501868\pi$
$444$			101.935i			0.229583i
$445$	262.619			0.590155
$446$			999.436i			2.24089i
$447$		−	138.492i		−	0.309827i
$448$	−445.725	−	566.462i	−0.994921	−	1.26442i
$449$	−177.400			−0.395101			−0.197551	−	0.980293i	$-0.563299\pi$
$449$	−177.400			−0.395101			−0.197551	+	0.980293i	$0.563299\pi$
$450$	−294.006			−0.653346
$451$			217.055i			0.481275i
$452$	−1055.66			−2.33554
$453$		−	226.553i		−	0.500117i
$454$			696.446i			1.53402i
$455$	138.779	+	176.372i	0.305009	+	0.387630i
$456$	−343.351			−0.752962
$457$	766.797			1.67789			0.838946	−	0.544214i	$-0.183172\pi$
$457$	766.797			1.67789			0.838946	+	0.544214i	$0.183172\pi$
$458$		−	473.501i		−	1.03384i
$459$	−145.127			−0.316180
$460$		−	209.423i		−	0.455268i
$461$			13.7421i			0.0298094i	0.999889	+	0.0149047i	$0.00474448\pi$
$461$			13.7421i			0.0298094i	−0.999889	+	0.0149047i	$0.995256\pi$
$462$	−336.652	+	264.897i	−0.728683	+	0.573370i
$463$	−826.380			−1.78484			−0.892419	−	0.451208i	$-0.850993\pi$
$463$	−826.380			−1.78484			−0.892419	+	0.451208i	$0.850993\pi$
$464$	232.901			0.501943
$465$		−	343.541i		−	0.738798i
$466$	−1211.17			−2.59908
$467$		−	258.630i		−	0.553811i	−0.960897	−	0.276905i	$-0.910691\pi$
$467$		−	258.630i		−	0.553811i	0.960897	−	0.276905i	$-0.0893089\pi$
$468$		−	74.6389i		−	0.159485i
$469$	17.2835	+	21.9652i	0.0368518	+	0.0468341i
$470$	−290.903			−0.618943
$471$	−60.2093			−0.127833
$472$		−	419.316i		−	0.888382i
$473$	−379.312			−0.801928
$474$			392.815i			0.828724i
$475$		−	1086.12i		−	2.28657i
$476$	−894.409	+	703.772i	−1.87901	+	1.47851i
$477$	83.2085			0.174441
$478$	−179.473			−0.375468
$479$			789.164i			1.64752i	0.566936	+	0.823762i	$0.308129\pi$
$479$			789.164i			1.64752i	−0.566936	+	0.823762i	$0.691871\pi$
$480$	−516.432			−1.07590
$481$		−	43.2091i		−	0.0898318i
$482$			120.413i			0.249820i
$483$	45.6962	−	35.9564i	0.0946090	−	0.0744438i
$484$	35.5399			0.0734296
$485$	136.852			0.282168
$486$			48.8525i			0.100519i
$487$	−252.397			−0.518268			−0.259134	−	0.965841i	$-0.583437\pi$
$487$	−252.397			−0.518268			−0.259134	+	0.965841i	$0.583437\pi$
$488$		−	374.845i		−	0.768125i
$489$			122.170i			0.249836i
$490$	−1119.60	−	270.956i	−2.28491	−	0.552972i
$491$	−29.0870			−0.0592404			−0.0296202	−	0.999561i	$-0.509430\pi$
$491$	−29.0870			−0.0592404			−0.0296202	+	0.999561i	$0.509430\pi$
$492$	194.118			0.394548
$493$		−	1205.02i		−	2.44427i
$494$	465.198			0.941697
$495$			253.716i			0.512558i
$496$		−	142.730i		−	0.287761i
$497$	450.572	+	572.622i	0.906584	+	1.15216i
$498$	382.627			0.768327
$499$	942.450			1.88868			0.944338	−	0.328976i	$-0.106704\pi$
$499$	942.450			1.88868			0.944338	+	0.328976i	$0.106704\pi$
$500$			273.870i			0.547741i
$501$	−31.4836			−0.0628416
$502$		−	382.981i		−	0.762911i
$503$			15.1058i			0.0300314i	0.999887	+	0.0150157i	$0.00477982\pi$
$503$			15.1058i			0.0300314i	−0.999887	+	0.0150157i	$0.995220\pi$
$504$	74.1180	+	94.1949i	0.147059	+	0.186895i
$505$	−1121.82			−2.22142
$506$	−169.445			−0.334872
$507$		−	261.078i		−	0.514947i
$508$	455.653			0.896954
$509$		−	780.051i		−	1.53252i	−0.642533	−	0.766258i	$-0.722116\pi$
$509$		−	780.051i		−	1.53252i	0.642533	−	0.766258i	$-0.277884\pi$
$510$			1137.24i			2.22989i
$511$	−163.986	+	129.034i	−0.320913	+	0.252512i
$512$	−337.800			−0.659766
$513$	−180.471			−0.351796
$514$		−	635.291i		−	1.23598i
$515$	473.684			0.919775
$516$			339.228i			0.657418i
$517$			139.509i			0.269843i
$518$	137.145	+	174.295i	0.264759	+	0.336477i
$519$	−327.497			−0.631016
$520$	−182.989			−0.351902
$521$			831.656i			1.59627i	0.602480	+	0.798134i	$0.294179\pi$
$521$			831.656i			1.59627i	−0.602480	+	0.798134i	$0.705821\pi$
$522$	−405.635			−0.777078
$523$			292.428i			0.559135i	0.960126	+	0.279567i	$0.0901911\pi$
$523$			292.428i			0.559135i	−0.960126	+	0.279567i	$0.909809\pi$
$524$		−	1089.06i		−	2.07836i
$525$	−297.966	+	234.457i	−0.567555	+	0.446585i
$526$	1548.74			2.94437
$527$	−738.479			−1.40129
$528$			105.410i			0.199641i
$529$	23.0000			0.0434783
$530$		−	652.041i		−	1.23027i
$531$		−	220.400i		−	0.415066i
$532$	−1112.24	+	875.172i	−2.09067	+	1.64506i
$533$	−82.2843			−0.154380
$534$	−190.031			−0.355863
$535$			1240.22i			2.31817i
$536$	−22.7893			−0.0425174
$537$		−	436.357i		−	0.812583i
$538$		−	1273.48i		−	2.36705i
$539$	−129.943	+	536.931i	−0.241081	+	0.996161i
$540$	226.904			0.420193
$541$	526.964			0.974055			0.487027	−	0.873387i	$-0.338081\pi$
$541$	526.964			0.974055			0.487027	+	0.873387i	$0.338081\pi$
$542$		−	283.643i		−	0.523326i
$543$	−585.662			−1.07857
$544$			1110.13i			2.04068i
$545$		−	1116.43i		−	2.04850i
$546$	−100.421	−	127.623i	−0.183921	−	0.233741i
$547$	183.795			0.336005			0.168002	−	0.985787i	$-0.446268\pi$
$547$	183.795			0.336005			0.168002	+	0.985787i	$0.446268\pi$
$548$	−858.866			−1.56727
$549$		−	197.025i		−	0.358881i
$550$	1104.88			2.00888
$551$		−	1498.50i		−	2.71960i
$552$			47.4106i			0.0858888i
$553$	313.253	+	398.107i	0.566461	+	0.719904i
$554$	−1114.33			−2.01142
$555$	131.357			0.236679
$556$		−	870.110i		−	1.56495i
$557$	965.275			1.73299			0.866495	−	0.499186i	$-0.166368\pi$
$557$	965.275			1.73299			0.866495	+	0.499186i	$0.166368\pi$
$558$			248.586i			0.445495i
$559$		−	143.795i		−	0.257236i
$560$	−222.762	+	175.282i	−0.397790	+	0.313004i
$561$	545.390			0.972175
$562$	−871.532			−1.55077
$563$		−	978.039i		−	1.73719i	−0.495521	−	0.868596i	$-0.665023\pi$
$563$		−	978.039i		−	1.73719i	0.495521	−	0.868596i	$-0.334977\pi$
$564$	124.766			0.221216
$565$			1360.36i			2.40772i
$566$		−	985.769i		−	1.74164i
$567$	38.9577	+	49.5106i	0.0687085	+	0.0873202i
$568$	−594.106			−1.04596
$569$	−728.181			−1.27976			−0.639878	−	0.768476i	$-0.721015\pi$
$569$	−728.181			−1.27976			−0.639878	+	0.768476i	$0.721015\pi$
$570$			1414.21i			2.48108i
$571$	291.345			0.510236			0.255118	−	0.966910i	$-0.417886\pi$
$571$	291.345			0.510236			0.255118	+	0.966910i	$0.417886\pi$
$572$			280.496i			0.490377i
$573$			345.050i			0.602182i
$574$	331.915	−	261.170i	0.578249	−	0.455000i
$575$	−149.974			−0.260824
$576$	308.913			0.536308
$577$			861.204i			1.49255i	0.665635	+	0.746277i	$0.268161\pi$
$577$			861.204i			1.49255i	−0.665635	+	0.746277i	$0.731839\pi$
$578$	1538.94			2.66252
$579$		−	43.9263i		−	0.0758658i
$580$			1884.05i			3.24835i
$581$	387.781	−	305.128i	0.667438	−	0.525178i
$582$	−99.0259			−0.170148
$583$	−312.700			−0.536364
$584$		−	170.139i		−	0.291334i
$585$	−96.1822			−0.164414
$586$		−	875.517i		−	1.49406i
$587$		−	202.862i		−	0.345591i	−0.984958	−	0.172796i	$-0.944720\pi$
$587$		−	202.862i		−	0.345591i	0.984958	−	0.172796i	$-0.0552800\pi$
$588$	480.190	+	116.211i	0.816649	+	0.197638i
$589$	−918.331			−1.55914
$590$	−1727.11			−2.92730
$591$			657.592i			1.11268i
$592$	54.5743			0.0921863
$593$		−	733.958i		−	1.23770i	−0.785508	−	0.618852i	$-0.787598\pi$
$593$		−	733.958i		−	1.23770i	0.785508	−	0.618852i	$-0.212402\pi$
$594$		−	183.589i		−	0.309072i
$595$	906.904	+	1152.56i	1.52421	+	1.93708i
$596$	465.459			0.780971
$597$	58.5164			0.0980174
$598$		−	64.2356i		−	0.107417i
$599$	877.075			1.46423			0.732116	−	0.681180i	$-0.238533\pi$
$599$	877.075			1.46423			0.732116	+	0.681180i	$0.238533\pi$
$600$		−	309.146i		−	0.515243i
$601$			439.985i			0.732089i	0.930597	+	0.366044i	$0.119288\pi$
$601$			439.985i			0.732089i	−0.930597	+	0.366044i	$0.880712\pi$
$602$	456.404	+	580.034i	0.758146	+	0.963511i
$603$	−11.9785			−0.0198648
$604$	761.422			1.26063
$605$		−	45.7979i		−	0.0756990i
$606$	811.747			1.33952
$607$		−	506.073i		−	0.833729i	−0.908969	−	0.416864i	$-0.863129\pi$
$607$		−	506.073i		−	0.833729i	0.908969	−	0.416864i	$-0.136871\pi$
$608$			1380.49i			2.27055i
$609$	−411.099	+	323.476i	−0.675040	+	0.531160i
$610$	−1543.94			−2.53104
$611$	−52.8870			−0.0865580
$612$		−	487.755i		−	0.796986i
$613$	−260.150			−0.424389			−0.212194	−	0.977227i	$-0.568061\pi$
$613$	−260.150			−0.424389			−0.212194	+	0.977227i	$0.568061\pi$
$614$		−	1101.18i		−	1.79345i
$615$		−	250.146i		−	0.406742i
$616$	−278.538	−	353.988i	−0.452172	−	0.574655i
$617$	309.128			0.501018			0.250509	−	0.968114i	$-0.419402\pi$
$617$	309.128			0.501018			0.250509	+	0.968114i	$0.419402\pi$
$618$	−342.758			−0.554624
$619$			426.553i			0.689100i	0.938768	+	0.344550i	$0.111968\pi$
$619$			426.553i			0.689100i	−0.938768	+	0.344550i	$0.888032\pi$
$620$	1154.61			1.86227
$621$			24.9199i			0.0401286i
$622$		−	1381.79i		−	2.22153i
$623$	−192.591	+	151.542i	−0.309135	+	0.243245i
$624$	−39.9605			−0.0640392
$625$	−428.874			−0.686198
$626$			1117.24i			1.78473i
$627$	678.217			1.08169
$628$		−	202.357i		−	0.322225i
$629$		−	282.366i		−	0.448912i
$630$	387.976	−	305.282i	0.615835	−	0.484574i
$631$	172.410			0.273234			0.136617	−	0.990624i	$-0.456377\pi$
$631$	172.410			0.273234			0.136617	+	0.990624i	$0.456377\pi$
$632$	−413.043			−0.653549
$633$		−	202.164i		−	0.319375i
$634$	−1780.35			−2.80813
$635$		−	587.169i		−	0.924675i
$636$			279.655i			0.439710i
$637$	−203.547	−	49.2606i	−0.319540	−	0.0773321i
$638$	1524.39			2.38932
$639$	−312.273			−0.488690
$640$		−	1228.07i		−	1.91885i
$641$	−532.888			−0.831339			−0.415669	−	0.909516i	$-0.636453\pi$
$641$	−532.888			−0.831339			−0.415669	+	0.909516i	$0.636453\pi$
$642$		−	897.423i		−	1.39786i
$643$		−	351.230i		−	0.546236i	−0.961981	−	0.273118i	$-0.911945\pi$
$643$		−	351.230i		−	0.546236i	0.961981	−	0.273118i	$-0.0880549\pi$
$644$	120.846	+	153.580i	0.187648	+	0.238478i
$645$	437.140			0.677736
$646$	3040.01			4.70589
$647$			1040.71i			1.60851i	0.594282	+	0.804257i	$0.297436\pi$
$647$			1040.71i			1.60851i	−0.594282	+	0.804257i	$0.702564\pi$
$648$	−51.3681			−0.0792718
$649$			828.271i			1.27623i
$650$			418.854i			0.644391i
$651$	198.237	+	251.935i	0.304512	+	0.386997i
$652$	−410.600			−0.629755
$653$	−76.9921			−0.117905			−0.0589526	−	0.998261i	$-0.518776\pi$
$653$	−76.9921			−0.117905			−0.0589526	+	0.998261i	$0.518776\pi$
$654$			807.851i			1.23525i
$655$	−1403.40			−2.14260
$656$		−	103.927i		−	0.158426i
$657$		−	89.4281i		−	0.136116i
$658$	213.333	−	167.863i	0.324215	−	0.255111i
$659$	−303.868			−0.461105			−0.230553	−	0.973060i	$-0.574053\pi$
$659$	−303.868			−0.461105			−0.230553	+	0.973060i	$0.574053\pi$
$660$	−852.713			−1.29199
$661$			575.001i			0.869896i	0.900456	+	0.434948i	$0.143233\pi$
$661$			575.001i			0.869896i	−0.900456	+	0.434948i	$0.856767\pi$
$662$	1451.56			2.19269
$663$			206.754i			0.311846i
$664$			402.330i			0.605919i
$665$	1127.78	+	1433.27i	1.69590	+	2.15529i
$666$	−95.0498			−0.142717
$667$	−206.916			−0.310219
$668$		−	105.813i		−	0.158403i
$669$	−552.373			−0.825669
$670$			93.8660i			0.140098i
$671$			740.428i			1.10347i
$672$	378.725	−	298.002i	0.563578	−	0.443456i
$673$	1098.49			1.63222			0.816112	−	0.577894i	$-0.196125\pi$
$673$	1098.49			1.63222			0.816112	+	0.577894i	$0.196125\pi$
$674$	99.7824			0.148045
$675$		−	162.492i		−	0.240730i
$676$	877.456			1.29801
$677$			578.335i			0.854262i	0.904190	+	0.427131i	$0.140476\pi$
$677$			578.335i			0.854262i	−0.904190	+	0.427131i	$0.859524\pi$
$678$		−	984.360i		−	1.45186i
$679$	−100.360	+	78.9689i	−0.147805	+	0.116302i
$680$	−1195.81			−1.75854
$681$	−384.915			−0.565220
$682$		−	934.196i		−	1.36979i
$683$	−256.456			−0.375484			−0.187742	−	0.982218i	$-0.560117\pi$
$683$	−256.456			−0.375484			−0.187742	+	0.982218i	$0.560117\pi$
$684$		−	606.545i		−	0.886762i
$685$			1106.76i			1.61571i
$686$	977.413	−	447.352i	1.42480	−	0.652116i
$687$	261.697			0.380927
$688$	181.617			0.263978
$689$		−	118.543i		−	0.172051i
$690$	195.278			0.283011
$691$			37.0205i			0.0535753i	0.999641	+	0.0267876i	$0.00852779\pi$
$691$			37.0205i			0.0535753i	−0.999641	+	0.0267876i	$0.991472\pi$
$692$		−	1100.68i		−	1.59058i
$693$	−146.404	−	186.062i	−0.211262	−	0.268488i
$694$	286.458			0.412764
$695$	−1121.25			−1.61331
$696$		−	426.523i		−	0.612820i
$697$	−537.717			−0.771473
$698$			339.431i			0.486291i
$699$		−	669.395i		−	0.957647i
$700$	−787.986	−	1001.43i	−1.12569	−	1.43062i
$701$	302.539			0.431582			0.215791	−	0.976440i	$-0.430767\pi$
$701$	302.539			0.431582			0.215791	+	0.976440i	$0.430767\pi$
$702$	69.5975			0.0991417
$703$		−	351.134i		−	0.499480i
$704$	−1160.91			−1.64901
$705$		−	160.778i		−	0.228053i
$706$		−	91.8879i		−	0.130153i
$707$	822.682	−	647.333i	1.16362	−	0.915606i
$708$	740.742			1.04625
$709$	566.257			0.798670			0.399335	−	0.916805i	$-0.369241\pi$
$709$	566.257			0.798670			0.399335	+	0.916805i	$0.369241\pi$
$710$			2447.04i			3.44654i
$711$	−217.103			−0.305349
$712$		−	199.817i		−	0.280641i
$713$			126.805i			0.177847i
$714$	−656.236	−	833.996i	−0.919098	−	1.16806i
$715$	361.456			0.505533
$716$	1466.55			2.04825
$717$		−	99.1922i		−	0.138343i
$718$	569.216			0.792780
$719$		−	493.675i		−	0.686613i	−0.939223	−	0.343307i	$-0.888453\pi$
$719$		−	493.675i		−	0.686613i	0.939223	−	0.343307i	$-0.111547\pi$
$720$		−	121.481i		−	0.168723i
$721$	−347.375	+	273.335i	−0.481797	+	0.379105i
$722$	2649.05			3.66905
$723$	−66.5506			−0.0920478
$724$		−	1968.35i		−	2.71872i
$725$	1349.22			1.86099
$726$			33.1394i			0.0456466i
$727$			150.741i			0.207346i	0.994611	+	0.103673i	$0.0330595\pi$
$727$			150.741i			0.207346i	−0.994611	+	0.103673i	$0.966940\pi$
$728$	134.195	−	105.592i	0.184333	−	0.145044i
$729$	−27.0000			−0.0370370
$730$	−700.778			−0.959970
$731$		−	939.680i		−	1.28547i
$732$	662.182			0.904620
$733$		−	350.556i		−	0.478249i	−0.970989	−	0.239124i	$-0.923140\pi$
$733$		−	350.556i		−	0.478249i	0.970989	−	0.239124i	$-0.0768603\pi$
$734$			454.138i			0.618716i
$735$	149.753	−	618.788i	0.203746	−	0.841889i
$736$	190.621			0.258996
$737$	45.0155			0.0610793
$738$			181.006i			0.245266i
$739$	−387.696			−0.524623			−0.262311	−	0.964983i	$-0.584485\pi$
$739$	−387.696			−0.524623			−0.262311	+	0.964983i	$0.584485\pi$
$740$			441.476i			0.596590i
$741$			257.108i			0.346974i
$742$	376.254	+	478.173i	0.507081	+	0.644438i
$743$	8.60427			0.0115804			0.00579022	−	0.999983i	$-0.498157\pi$
$743$	8.60427			0.0115804			0.00579022	+	0.999983i	$0.498157\pi$
$744$	−261.387			−0.351327
$745$		−	599.806i		−	0.805108i
$746$	−1552.76			−2.08145
$747$			211.472i			0.283095i
$748$			1833.00i			2.45053i
$749$	−715.657	−	909.513i	−0.955483	−	1.21430i
$750$	−255.372			−0.340496
$751$	−661.282			−0.880536			−0.440268	−	0.897866i	$-0.645117\pi$
$751$	−661.282			−0.880536			−0.440268	+	0.897866i	$0.645117\pi$
$752$		−	66.7977i		−	0.0888267i
$753$	211.668			0.281099
$754$			577.886i			0.766428i
$755$		−	981.193i		−	1.29959i
$756$	−166.400	+	130.933i	−0.220106	+	0.173192i
$757$	−719.830			−0.950898			−0.475449	−	0.879743i	$-0.657714\pi$
$757$	−719.830			−0.950898			−0.475449	+	0.879743i	$0.657714\pi$
$758$	−5.58040			−0.00736201
$759$		−	93.6497i		−	0.123386i
$760$	−1487.04			−1.95663
$761$			1182.09i			1.55334i	0.629908	+	0.776670i	$0.283093\pi$
$761$			1182.09i			1.55334i	−0.629908	+	0.776670i	$0.716907\pi$
$762$			424.876i			0.557580i
$763$	644.227	+	818.734i	0.844334	+	1.07305i
$764$	−1159.68			−1.51790
$765$	−628.538			−0.821618
$766$			897.867i			1.17215i
$767$	−313.993			−0.409378
$768$			175.224i			0.228157i
$769$		−	934.836i		−	1.21565i	−0.794070	−	0.607826i	$-0.792042\pi$
$769$		−	934.836i		−	1.21565i	0.794070	−	0.607826i	$-0.207958\pi$
$770$	−1458.03	+	1147.26i	−1.89354	+	1.48995i
$771$	351.116			0.455403
$772$	147.632			0.191233
$773$			1265.08i			1.63658i	0.574804	+	0.818291i	$0.305078\pi$
$773$			1265.08i			1.63658i	−0.574804	+	0.818291i	$0.694922\pi$
$774$	−316.315			−0.408675
$775$		−	826.845i		−	1.06690i
$776$		−	104.125i		−	0.134182i
$777$	−96.3302	+	75.7981i	−0.123977	+	0.0975523i
$778$	488.113			0.627394
$779$	−668.675			−0.858376
$780$		−	323.258i		−	0.414434i
$781$	1173.53			1.50260
$782$		−	419.771i		−	0.536791i
$783$		−	224.188i		−	0.286319i
$784$	62.2175	−	257.086i	0.0793590	−	0.327915i
$785$	−260.764			−0.332183
$786$	1015.50			1.29199
$787$		−	915.629i		−	1.16344i	−0.813388	−	0.581721i	$-0.802380\pi$
$787$		−	915.629i		−	1.16344i	0.813388	−	0.581721i	$-0.197620\pi$
$788$	−2210.10			−2.80469
$789$			855.965i			1.08487i
$790$			1701.27i			2.15350i
$791$	−784.985	−	997.621i	−0.992396	−	1.26121i
$792$	193.043			0.243741
$793$	−280.692			−0.353962
$794$			1331.87i			1.67742i
$795$	360.373			0.453299
$796$			196.668i			0.247070i
$797$			836.329i			1.04935i	0.851304	+	0.524673i	$0.175812\pi$
$797$			836.329i			1.04935i	−0.851304	+	0.524673i	$0.824188\pi$
$798$	−816.059	−	1037.11i	−1.02263	−	1.29964i
$799$	−345.609			−0.432552
$800$	−1242.97			−1.55371
$801$		−	105.027i		−	0.131120i
$802$	−2114.12			−2.63606
$803$			336.073i			0.418522i
$804$		−	40.2584i		−	0.0500726i
$805$	197.908	−	155.726i	0.245849	−	0.193448i
$806$	354.148			0.439389
$807$	703.830			0.872156
$808$			853.548i			1.05637i
$809$	370.275			0.457695			0.228847	−	0.973462i	$-0.426504\pi$
$809$	370.275			0.457695			0.228847	+	0.973462i	$0.426504\pi$
$810$			211.578i			0.261208i
$811$			989.489i			1.22008i	0.792369	+	0.610042i	$0.208848\pi$
$811$			989.489i			1.22008i	−0.792369	+	0.610042i	$0.791152\pi$
$812$	−1087.17	−	1381.66i	−1.33888	−	1.70155i
$813$	156.765			0.192823
$814$	357.200			0.438821
$815$			529.113i			0.649218i
$816$	−261.136			−0.320020
$817$		−	1168.53i		−	1.43027i
$818$			243.993i			0.298280i
$819$	70.5351	−	55.5010i	0.0861234	−	0.0677668i
$820$	840.716			1.02526
$821$	−327.383			−0.398761			−0.199381	−	0.979922i	$-0.563893\pi$
$821$	−327.383			−0.398761			−0.199381	+	0.979922i	$0.563893\pi$
$822$		−	800.854i		−	0.974275i
$823$	457.253			0.555593			0.277797	−	0.960640i	$-0.410396\pi$
$823$	457.253			0.555593			0.277797	+	0.960640i	$0.410396\pi$
$824$		−	360.408i		−	0.437389i
$825$			610.652i			0.740184i
$826$	1266.57	−	996.610i	1.53338	−	1.20655i
$827$	−400.047			−0.483733			−0.241866	−	0.970310i	$-0.577760\pi$
$827$	−400.047			−0.483733			−0.241866	+	0.970310i	$0.577760\pi$
$828$	−83.7531			−0.101151
$829$			959.411i			1.15731i	0.815572	+	0.578656i	$0.196422\pi$
$829$			959.411i			1.15731i	−0.815572	+	0.578656i	$0.803578\pi$
$830$	1657.14			1.99656
$831$		−	615.871i		−	0.741121i
$832$		−	440.093i		−	0.528957i
$833$	−1330.15	−	321.911i	−1.59682	−	0.386448i
$834$	811.338			0.972828
$835$	−136.354			−0.163299
$836$			2279.42i			2.72658i
$837$	−137.390			−0.164146
$838$			1009.63i			1.20481i
$839$		−	152.541i		−	0.181813i	−0.995859	−	0.0909064i	$-0.971024\pi$
$839$		−	152.541i		−	0.181813i	0.995859	−	0.0909064i	$-0.0289764\pi$
$840$	321.002	+	407.955i	0.382145	+	0.485660i
$841$	1020.49			1.21343
$842$	−581.990			−0.691200
$843$		−	481.682i		−	0.571391i
$844$	679.453			0.805040
$845$		−	1130.72i		−	1.33813i
$846$			116.339i			0.137516i
$847$	26.4273	+	33.5858i	0.0312010	+	0.0396527i
$848$	149.723			0.176560
$849$	544.820			0.641719
$850$			2737.16i			3.22018i
$851$	−48.4854			−0.0569746
$852$		−	1049.52i		−	1.23183i
$853$		−	719.678i		−	0.843702i	−0.906665	−	0.421851i	$-0.861381\pi$
$853$		−	719.678i		−	0.843702i	0.906665	−	0.421851i	$-0.138619\pi$
$854$	1132.24	−	890.913i	1.32581	−	1.04322i
$855$	−781.615			−0.914169
$856$	943.636			1.10238
$857$		−	1184.28i		−	1.38190i	−0.722905	−	0.690948i	$-0.757193\pi$
$857$		−	1184.28i		−	1.38190i	0.722905	−	0.690948i	$-0.242807\pi$
$858$	−261.550			−0.304836
$859$		−	1592.26i		−	1.85362i	−0.375535	−	0.926808i	$-0.622541\pi$
$859$		−	1592.26i		−	1.85362i	0.375535	−	0.926808i	$-0.377459\pi$
$860$			1469.18i			1.70835i
$861$	144.345	+	183.444i	0.167648	+	0.213060i
$862$	−1633.36			−1.89485
$863$	768.365			0.890341			0.445171	−	0.895446i	$-0.353143\pi$
$863$	768.365			0.890341			0.445171	+	0.895446i	$0.353143\pi$
$864$			206.533i			0.239043i
$865$	−1418.38			−1.63974
$866$		−	135.839i		−	0.156858i
$867$			850.547i			0.981023i
$868$	−846.728	+	666.254i	−0.975493	+	0.767574i
$869$	815.879			0.938872
$870$	−1756.79			−2.01930
$871$			17.0651i			0.0195925i
$872$	−849.451			−0.974142
$873$		−	54.7301i		−	0.0626920i
$874$		−	522.004i		−	0.597258i
$875$	−258.812	+	203.648i	−0.295785	+	0.232741i
$876$	300.558			0.343103
$877$	597.791			0.681631			0.340816	−	0.940130i	$-0.389297\pi$
$877$	597.791			0.681631			0.340816	+	0.940130i	$0.389297\pi$
$878$		−	971.810i		−	1.10685i
$879$	483.885			0.550495
$880$			456.529i			0.518782i
$881$		−	221.241i		−	0.251125i	−0.992086	−	0.125562i	$-0.959926\pi$
$881$		−	221.241i		−	0.251125i	0.992086	−	0.125562i	$-0.0400735\pi$
$882$	−108.362	+	447.756i	−0.122859	+	0.507659i
$883$	481.374			0.545158			0.272579	−	0.962133i	$-0.412123\pi$
$883$	481.374			0.545158			0.272579	+	0.962133i	$0.412123\pi$
$884$	−694.879			−0.786062
$885$		−	954.545i		−	1.07858i
$886$	16.2921			0.0183884
$887$		−	26.9987i		−	0.0304383i	−0.999884	−	0.0152191i	$-0.995155\pi$
$887$		−	26.9987i		−	0.0304383i	0.999884	−	0.0152191i	$-0.00484459\pi$
$888$		−	99.9444i		−	0.112550i
$889$	338.820	+	430.599i	0.381125	+	0.484364i
$890$	−823.017			−0.924739
$891$	101.467			0.113880
$892$		−	1856.47i		−	2.08124i
$893$	−429.780			−0.481277
$894$			434.020i			0.485481i
$895$		−	1889.84i		−	2.11156i
$896$	708.644	+	900.600i	0.790897	+	1.00513i
$897$	35.5020			0.0395786
$898$	555.953			0.619101
$899$		−	1140.78i		−	1.26895i
$900$	546.120			0.606800
$901$		−	774.661i		−	0.859779i
$902$		−	680.226i		−	0.754131i
$903$	−320.576	+	252.247i	−0.355012	+	0.279344i
$904$	1035.05			1.14497
$905$	−2536.48			−2.80274
$906$			709.992i			0.783656i
$907$	1091.90			1.20386			0.601929	−	0.798549i	$-0.294399\pi$
$907$	1091.90			1.20386			0.601929	+	0.798549i	$0.294399\pi$
$908$		−	1293.66i		−	1.42473i
$909$			448.640i			0.493553i
$910$	−434.919	−	552.729i	−0.477932	−	0.607394i
$911$	1516.21			1.66433			0.832167	−	0.554526i	$-0.187100\pi$
$911$	1516.21			1.66433			0.832167	+	0.554526i	$0.187100\pi$
$912$	−324.734			−0.356068
$913$		−	794.718i		−	0.870447i
$914$	−2403.05			−2.62916
$915$		−	853.309i		−	0.932579i
$916$			879.535i			0.960191i
$917$	1029.18	−	809.819i	1.12234	−	0.883118i
$918$	454.810			0.495436
$919$	935.098			1.01752			0.508759	−	0.860909i	$-0.330105\pi$
$919$	935.098			1.01752			0.508759	+	0.860909i	$0.330105\pi$
$920$			205.334i			0.223189i
$921$	608.603			0.660807
$922$		−	43.0662i		−	0.0467096i
$923$			444.879i			0.481992i
$924$	625.336	−	492.050i	0.676770	−	0.532522i
$925$	316.154			0.341788
$926$	2589.78			2.79674
$927$		−	189.437i		−	0.204355i
$928$	−1714.90			−1.84795
$929$			1.92421i			0.00207127i	0.999999	+	0.00103563i	$0.000329653\pi$
$929$			1.92421i			0.00207127i	−0.999999	+	0.00103563i	$0.999670\pi$
$930$			1076.62i			1.15765i
$931$	−1654.10	−	400.311i	−1.77670	−	0.429979i
$932$	2249.77			2.41391
$933$	763.695			0.818537
$934$			810.516i			0.867790i
$935$	2362.06			2.52627
$936$			73.1814i			0.0781853i
$937$			625.905i			0.667989i	0.942575	+	0.333994i	$0.108397\pi$
$937$			625.905i			0.667989i	−0.942575	+	0.333994i	$0.891603\pi$
$938$	−54.1645	−	68.8365i	−0.0577446	−	0.0733864i
$939$	−617.481			−0.657594
$940$	540.357			0.574848
$941$			1573.60i			1.67227i	0.548525	+	0.836134i	$0.315189\pi$
$941$			1573.60i			1.67227i	−0.548525	+	0.836134i	$0.684811\pi$
$942$	188.689			0.200307
$943$			92.3320i			0.0979131i
$944$		−	396.581i		−	0.420107i
$945$	168.724	+	214.428i	0.178544	+	0.226908i
$946$	1188.72			1.25658
$947$	−853.456			−0.901220			−0.450610	−	0.892721i	$-0.648794\pi$
$947$	−853.456			−0.901220			−0.450610	+	0.892721i	$0.648794\pi$
$948$		−	729.660i		−	0.769684i
$949$	−127.403			−0.134250
$950$			3403.78i			3.58292i
$951$		−	983.974i		−	1.03467i
$952$	876.943	−	690.029i	0.921159	−	0.724820i
$953$	761.547			0.799105			0.399553	−	0.916710i	$-0.369166\pi$
$953$	761.547			0.799105			0.399553	+	0.916710i	$0.369166\pi$
$954$	−260.766			−0.273340
$955$			1494.40i			1.56482i
$956$	333.375			0.348718
$957$			842.506i			0.880362i
$958$		−	2473.15i		−	2.58158i
$959$	−638.647	−	811.643i	−0.665951	−	0.846343i
$960$	1337.89			1.39364
$961$	261.889			0.272518
$962$			135.412i			0.140761i
$963$	495.992			0.515049
$964$		−	223.670i		−	0.232022i
$965$		−	190.243i		−	0.197143i
$966$	−143.207	+	112.683i	−0.148247	+	0.116649i
$967$	−553.174			−0.572052			−0.286026	−	0.958222i	$-0.592334\pi$
$967$	−553.174			−0.572052			−0.286026	+	0.958222i	$0.592334\pi$
$968$	−34.8459			−0.0359978
$969$			1680.17i			1.73392i
$970$	−428.878			−0.442142
$971$			1633.85i			1.68265i	0.540532	+	0.841323i	$0.318223\pi$
$971$			1633.85i			1.68265i	−0.540532	+	0.841323i	$0.681777\pi$
$972$		−	90.7442i		−	0.0933582i
$973$	822.268	−	647.008i	0.845086	−	0.664962i
$974$	790.982			0.812097
$975$	−231.494			−0.237430
$976$		−	354.521i		−	0.363239i
$977$	407.640			0.417237			0.208618	−	0.977997i	$-0.433103\pi$
$977$	407.640			0.417237			0.208618	+	0.977997i	$0.433103\pi$
$978$		−	382.866i		−	0.391479i
$979$			394.696i			0.403162i
$980$	2079.68	+	503.305i	2.12213	+	0.513577i
$981$	−446.487			−0.455135
$982$	91.1554			0.0928263
$983$		−	202.707i		−	0.206213i	−0.994670	−	0.103106i	$-0.967122\pi$
$983$		−	202.707i		−	0.206213i	0.994670	−	0.103106i	$-0.0328782\pi$
$984$	−190.327			−0.193422
$985$			2848.01i			2.89138i
$986$			3776.41i			3.83003i
$987$	92.7752	+	117.906i	0.0939972	+	0.119459i
$988$	−864.113			−0.874609
$989$	−161.354			−0.163148
$990$		−	795.117i		−	0.803149i
$991$	−173.078			−0.174649			−0.0873247	−	0.996180i	$-0.527832\pi$
$991$	−173.078			−0.174649			−0.0873247	+	0.996180i	$0.527832\pi$
$992$			1050.95i			1.05942i
$993$			802.257i			0.807912i
$994$	−1412.04	−	1794.53i	−1.42057	−	1.80537i
$995$	253.432			0.254706
$996$	−710.735			−0.713590
$997$			548.574i			0.550224i	0.961412	+	0.275112i	$0.0887150\pi$
$997$			548.574i			0.550224i	−0.961412	+	0.275112i	$0.911285\pi$
$998$	−2953.53			−2.95945
$999$		−	52.5326i		−	0.0525852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.10	yes	60
7.6	odd	2	inner	483.3.g.a.139.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.9	✓	60	7.6	odd	2	inner
483.3.g.a.139.10	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.13389 q^{2} -1.73205i q^{3} +5.82124 q^{4} -7.50145i q^{5} +5.42805i q^{6} +(4.32864 + 5.50117i) q^{7} -5.70757 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.13389 q^{2} -1.73205i q^{3} +5.82124 q^{4} -7.50145i q^{5} +5.42805i q^{6} +(4.32864 + 5.50117i) q^{7} -5.70757 q^{8} -3.00000 q^{9} +23.5087i q^{10} +11.2741 q^{11} -10.0827i q^{12} +4.27394i q^{13} +(-13.5655 - 17.2400i) q^{14} -12.9929 q^{15} -5.39810 q^{16} +27.9296i q^{17} +9.40166 q^{18} +34.7317i q^{19} -43.6677i q^{20} +(9.52831 - 7.49742i) q^{21} -35.3317 q^{22} +4.79583 q^{23} +9.88580i q^{24} -31.2717 q^{25} -13.3940i q^{26} +5.19615i q^{27} +(25.1980 + 32.0237i) q^{28} -43.1450 q^{29} +40.7182 q^{30} +26.4407i q^{31} +39.7473 q^{32} -19.5273i q^{33} -87.5283i q^{34} +(41.2667 - 32.4710i) q^{35} -17.4637 q^{36} -10.1099 q^{37} -108.845i q^{38} +7.40268 q^{39} +42.8150i q^{40} +19.2526i q^{41} +(-29.8606 + 23.4961i) q^{42} -33.6446 q^{43} +65.6292 q^{44} +22.5043i q^{45} -15.0296 q^{46} +12.3743i q^{47} +9.34979i q^{48} +(-11.5258 + 47.6252i) q^{49} +98.0019 q^{50} +48.3755 q^{51} +24.8796i q^{52} -27.7362 q^{53} -16.2842i q^{54} -84.5720i q^{55} +(-24.7060 - 31.3983i) q^{56} +60.1571 q^{57} +135.212 q^{58} +73.4667i q^{59} -75.6347 q^{60} +65.6751i q^{61} -82.8621i q^{62} +(-12.9859 - 16.5035i) q^{63} -102.971 q^{64} +32.0607 q^{65} +61.1964i q^{66} +3.99282 q^{67} +162.585i q^{68} -8.30662i q^{69} +(-129.325 + 101.761i) q^{70} +104.091 q^{71} +17.1227 q^{72} +29.8094i q^{73} +31.6833 q^{74} +54.1642i q^{75} +202.182i q^{76} +(48.8015 + 62.0207i) q^{77} -23.1992 q^{78} +72.3676 q^{79} +40.4936i q^{80} +9.00000 q^{81} -60.3353i q^{82} -70.4907i q^{83} +(55.4666 - 43.6443i) q^{84} +209.513 q^{85} +105.438 q^{86} +74.7294i q^{87} -64.3477 q^{88} +35.0091i q^{89} -70.5260i q^{90} +(-23.5117 + 18.5003i) q^{91} +27.9177 q^{92} +45.7966 q^{93} -38.7796i q^{94} +260.538 q^{95} -68.8444i q^{96} +18.2434i q^{97} +(36.1205 - 149.252i) q^{98} -33.8223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Introduction

L-functions

Modular forms

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