LMFDB - Embedded newform 165.3.e.a.56.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,3,Mod(56,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.56");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	165.e (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:	$4.49592436194$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			56.3
Character	$\chi$	$=$	165.56
Dual form			165.3.e.a.56.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.53441i q^{2} +(-0.569949 - 2.94536i) q^{3} -8.49206 q^{4} -2.23607i q^{5} +(-10.4101 + 2.01443i) q^{6} +0.0644394 q^{7} +15.8768i q^{8} +(-8.35032 + 3.35741i) q^{9} +O(q^{10})$	\(q-3.53441i q^{2} +(-0.569949 - 2.94536i) q^{3} -8.49206 q^{4} -2.23607i q^{5} +(-10.4101 + 2.01443i) q^{6} +0.0644394 q^{7} +15.8768i q^{8} +(-8.35032 + 3.35741i) q^{9} -7.90318 q^{10} -3.31662i q^{11} +(4.84004 + 25.0122i) q^{12} +15.8574 q^{13} -0.227755i q^{14} +(-6.58603 + 1.27444i) q^{15} +22.1468 q^{16} -16.7857i q^{17} +(11.8665 + 29.5134i) q^{18} -16.8487 q^{19} +18.9888i q^{20} +(-0.0367272 - 0.189797i) q^{21} -11.7223 q^{22} +11.3594i q^{23} +(46.7629 - 9.04895i) q^{24} -5.00000 q^{25} -56.0464i q^{26} +(14.6480 + 22.6812i) q^{27} -0.547223 q^{28} -37.8568i q^{29} +(4.50441 + 23.2777i) q^{30} +48.1838 q^{31} -14.7688i q^{32} +(-9.76866 + 1.89031i) q^{33} -59.3277 q^{34} -0.144091i q^{35} +(70.9114 - 28.5113i) q^{36} -68.4411 q^{37} +59.5502i q^{38} +(-9.03788 - 46.7057i) q^{39} +35.5015 q^{40} +17.2137i q^{41} +(-0.670822 + 0.129809i) q^{42} -12.6132 q^{43} +28.1650i q^{44} +(7.50740 + 18.6719i) q^{45} +40.1489 q^{46} -27.5079i q^{47} +(-12.6225 - 65.2304i) q^{48} -48.9958 q^{49} +17.6721i q^{50} +(-49.4401 + 9.56702i) q^{51} -134.662 q^{52} -47.7305i q^{53} +(80.1645 - 51.7722i) q^{54} -7.41620 q^{55} +1.02309i q^{56} +(9.60290 + 49.6255i) q^{57} -133.801 q^{58} +0.296634i q^{59} +(55.9289 - 10.8227i) q^{60} -45.3407 q^{61} -170.301i q^{62} +(-0.538089 + 0.216350i) q^{63} +36.3882 q^{64} -35.4581i q^{65} +(6.68112 + 34.5265i) q^{66} +96.1746 q^{67} +142.546i q^{68} +(33.4576 - 6.47429i) q^{69} -0.509276 q^{70} -108.324i q^{71} +(-53.3049 - 132.576i) q^{72} +102.908 q^{73} +241.899i q^{74} +(2.84974 + 14.7268i) q^{75} +143.080 q^{76} -0.213721i q^{77} +(-165.077 + 31.9436i) q^{78} -10.5452 q^{79} -49.5218i q^{80} +(58.4556 - 56.0709i) q^{81} +60.8403 q^{82} +30.7062i q^{83} +(0.311889 + 1.61177i) q^{84} -37.5341 q^{85} +44.5801i q^{86} +(-111.502 + 21.5764i) q^{87} +52.6573 q^{88} -133.145i q^{89} +(65.9941 - 26.5342i) q^{90} +1.02184 q^{91} -96.4649i q^{92} +(-27.4623 - 141.919i) q^{93} -97.2242 q^{94} +37.6748i q^{95} +(-43.4995 + 8.41747i) q^{96} +88.2514 q^{97} +173.171i q^{98} +(11.1353 + 27.6949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9}+O(q^{10}) $ 28 * q - 60 * q^4 - 4 * q^6 + 24 * q^7 - 16 * q^9	$ 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9} - 20 q^{10} + 40 q^{12} - 64 q^{13} + 172 q^{16} + 16 q^{18} + 56 q^{19} + 56 q^{21} - 140 q^{24} - 140 q^{25} - 96 q^{27} - 128 q^{28} - 40 q^{30} + 80 q^{31} - 32 q^{34} + 208 q^{36} + 72 q^{37} + 232 q^{39} - 60 q^{40} + 224 q^{42} - 360 q^{43} - 80 q^{45} + 264 q^{46} - 456 q^{48} + 332 q^{49} - 232 q^{51} + 488 q^{52} + 36 q^{54} - 16 q^{57} - 408 q^{58} - 360 q^{61} - 32 q^{63} - 300 q^{64} + 220 q^{66} - 16 q^{67} + 384 q^{69} + 240 q^{70} - 120 q^{72} + 464 q^{73} - 152 q^{76} + 16 q^{78} + 136 q^{79} + 48 q^{81} - 840 q^{82} - 392 q^{84} + 160 q^{85} + 32 q^{87} + 180 q^{90} - 32 q^{91} - 96 q^{93} + 520 q^{94} + 44 q^{96} - 136 q^{97}+O(q^{100}) $ 28 * q - 60 * q^4 - 4 * q^6 + 24 * q^7 - 16 * q^9 - 20 * q^10 + 40 * q^12 - 64 * q^13 + 172 * q^16 + 16 * q^18 + 56 * q^19 + 56 * q^21 - 140 * q^24 - 140 * q^25 - 96 * q^27 - 128 * q^28 - 40 * q^30 + 80 * q^31 - 32 * q^34 + 208 * q^36 + 72 * q^37 + 232 * q^39 - 60 * q^40 + 224 * q^42 - 360 * q^43 - 80 * q^45 + 264 * q^46 - 456 * q^48 + 332 * q^49 - 232 * q^51 + 488 * q^52 + 36 * q^54 - 16 * q^57 - 408 * q^58 - 360 * q^61 - 32 * q^63 - 300 * q^64 + 220 * q^66 - 16 * q^67 + 384 * q^69 + 240 * q^70 - 120 * q^72 + 464 * q^73 - 152 * q^76 + 16 * q^78 + 136 * q^79 + 48 * q^81 - 840 * q^82 - 392 * q^84 + 160 * q^85 + 32 * q^87 + 180 * q^90 - 32 * q^91 - 96 * q^93 + 520 * q^94 + 44 * q^96 - 136 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	3.53441i		−	1.76721i	−0.468238	−	0.883603i	$-0.655111\pi$
$2$		−	3.53441i		−	1.76721i	0.468238	−	0.883603i	$-0.344889\pi$
$3$	−0.569949	−	2.94536i	−0.189983	−	0.981787i
$3$	−0.569949	−	2.94536i	−0.189983	−	0.981787i
$4$	−8.49206			−2.12301
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−10.4101	+	2.01443i	−1.73502	+	0.335739i
$7$	0.0644394			0.00920563			0.00460281	−	0.999989i	$-0.498535\pi$
$7$	0.0644394			0.00920563			0.00460281	+	0.999989i	$0.498535\pi$
$8$			15.8768i			1.98460i
$9$	−8.35032	+	3.35741i	−0.927813	+	0.373046i
$10$	−7.90318			−0.790318
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	4.84004	+	25.0122i	0.403337	+	2.08435i
$13$	15.8574			1.21980			0.609898	−	0.792480i	$-0.291210\pi$
$13$	15.8574			1.21980			0.609898	+	0.792480i	$0.291210\pi$
$14$		−	0.227755i		−	0.0162682i
$15$	−6.58603	+	1.27444i	−0.439069	+	0.0849630i
$16$	22.1468			1.38418
$17$		−	16.7857i		−	0.987397i	−0.869633	−	0.493698i	$-0.835645\pi$
$17$		−	16.7857i		−	0.987397i	0.869633	−	0.493698i	$-0.164355\pi$
$18$	11.8665	+	29.5134i	0.659248	+	1.63964i
$19$	−16.8487			−0.886774			−0.443387	−	0.896330i	$-0.646223\pi$
$19$	−16.8487			−0.886774			−0.443387	+	0.896330i	$0.646223\pi$
$20$			18.9888i			0.949441i
$21$	−0.0367272	−	0.189797i	−0.00174891	−	0.00903797i
$22$	−11.7223			−0.532832
$23$			11.3594i			0.493888i	0.969030	+	0.246944i	$0.0794264\pi$
$23$			11.3594i			0.493888i	−0.969030	+	0.246944i	$0.920574\pi$
$24$	46.7629	−	9.04895i	1.94845	−	0.377040i
$25$	−5.00000			−0.200000
$26$		−	56.0464i		−	2.15563i
$27$	14.6480	+	22.6812i	0.542520	+	0.840043i
$28$	−0.547223			−0.0195437
$29$		−	37.8568i		−	1.30541i	−0.757614	−	0.652703i	$-0.773635\pi$
$29$		−	37.8568i		−	1.30541i	0.757614	−	0.652703i	$-0.226365\pi$
$30$	4.50441	+	23.2777i	0.150147	+	0.775924i
$31$	48.1838			1.55431			0.777157	−	0.629306i	$-0.216661\pi$
$31$	48.1838			1.55431			0.777157	+	0.629306i	$0.216661\pi$
$32$		−	14.7688i		−	0.461526i
$33$	−9.76866	+	1.89031i	−0.296020	+	0.0572820i
$34$	−59.3277			−1.74493
$35$		−	0.144091i		−	0.00411688i
$36$	70.9114	−	28.5113i	1.96976	−	0.791981i
$37$	−68.4411			−1.84976			−0.924879	−	0.380260i	$-0.875834\pi$
$37$	−68.4411			−1.84976			−0.924879	+	0.380260i	$0.875834\pi$
$38$			59.5502i			1.56711i
$39$	−9.03788	−	46.7057i	−0.231741	−	1.19758i
$40$	35.5015			0.887539
$41$			17.2137i			0.419847i	0.977718	+	0.209923i	$0.0673214\pi$
$41$			17.2137i			0.419847i	−0.977718	+	0.209923i	$0.932679\pi$
$42$	−0.670822	+	0.129809i	−0.0159719	+	0.00309069i
$43$	−12.6132			−0.293329			−0.146665	−	0.989186i	$-0.546854\pi$
$43$	−12.6132			−0.293329			−0.146665	+	0.989186i	$0.546854\pi$
$44$			28.1650i			0.640113i
$45$	7.50740	+	18.6719i	0.166831	+	0.414931i
$46$	40.1489			0.872802
$47$		−	27.5079i		−	0.585274i	−0.956224	−	0.292637i	$-0.905467\pi$
$47$		−	27.5079i		−	0.585274i	0.956224	−	0.292637i	$-0.0945328\pi$
$48$	−12.6225	−	65.2304i	−0.262970	−	1.35897i
$49$	−48.9958			−0.999915
$50$			17.6721i			0.353441i
$51$	−49.4401	+	9.56702i	−0.969414	+	0.187589i
$52$	−134.662			−2.58965
$53$		−	47.7305i		−	0.900576i	−0.892883	−	0.450288i	$-0.851321\pi$
$53$		−	47.7305i		−	0.900576i	0.892883	−	0.450288i	$-0.148679\pi$
$54$	80.1645	−	51.7722i	1.48453	−	0.958745i
$55$	−7.41620			−0.134840
$56$			1.02309i			0.0182695i
$57$	9.60290	+	49.6255i	0.168472	+	0.870623i
$58$	−133.801			−2.30692
$59$			0.296634i			0.00502770i	0.999997	+	0.00251385i	$0.000800184\pi$
$59$			0.296634i			0.00502770i	−0.999997	+	0.00251385i	$0.999200\pi$
$60$	55.9289	−	10.8227i	0.932149	−	0.180378i
$61$	−45.3407			−0.743290			−0.371645	−	0.928375i	$-0.621206\pi$
$61$	−45.3407			−0.743290			−0.371645	+	0.928375i	$0.621206\pi$
$62$		−	170.301i		−	2.74679i
$63$	−0.538089	+	0.216350i	−0.00854110	+	0.00343412i
$64$	36.3882			0.568565
$65$		−	35.4581i		−	0.545510i
$66$	6.68112	+	34.5265i	0.101229	+	0.523128i
$67$	96.1746			1.43544			0.717721	−	0.696331i	$-0.245185\pi$
$67$	96.1746			1.43544			0.717721	+	0.696331i	$0.245185\pi$
$68$			142.546i			2.09626i
$69$	33.4576	−	6.47429i	0.484893	−	0.0938303i
$70$	−0.509276			−0.00727538
$71$		−	108.324i		−	1.52569i	−0.646580	−	0.762846i	$-0.723801\pi$
$71$		−	108.324i		−	1.52569i	0.646580	−	0.762846i	$-0.276199\pi$
$72$	−53.3049	−	132.576i	−0.740345	−	1.84133i
$73$	102.908			1.40970			0.704848	−	0.709359i	$-0.251015\pi$
$73$	102.908			1.40970			0.704848	+	0.709359i	$0.251015\pi$
$74$			241.899i			3.26890i
$75$	2.84974	+	14.7268i	0.0379966	+	0.196357i
$76$	143.080			1.88263
$77$		−	0.213721i		−	0.00277560i
$78$	−165.077	+	31.9436i	−2.11637	+	0.409533i
$79$	−10.5452			−0.133483			−0.0667417	−	0.997770i	$-0.521260\pi$
$79$	−10.5452			−0.133483			−0.0667417	+	0.997770i	$0.521260\pi$
$80$		−	49.5218i		−	0.619022i
$81$	58.4556	−	56.0709i	0.721674	−	0.692233i
$82$	60.8403			0.741955
$83$			30.7062i			0.369954i	0.982743	+	0.184977i	$0.0592211\pi$
$83$			30.7062i			0.369954i	−0.982743	+	0.184977i	$0.940779\pi$
$84$	0.311889	+	1.61177i	0.00371297	+	0.0191877i
$85$	−37.5341			−0.441577
$86$			44.5801i			0.518373i
$87$	−111.502	+	21.5764i	−1.28163	+	0.248005i
$88$	52.6573			0.598378
$89$		−	133.145i		−	1.49601i	−0.663692	−	0.748006i	$-0.731011\pi$
$89$		−	133.145i		−	1.49601i	0.663692	−	0.748006i	$-0.268989\pi$
$90$	65.9941	−	26.5342i	0.733267	−	0.294825i
$91$	1.02184			0.0112290
$92$		−	96.4649i		−	1.04853i
$93$	−27.4623	−	141.919i	−0.295293	−	1.52601i
$94$	−97.2242			−1.03430
$95$			37.6748i			0.396577i
$96$	−43.4995	+	8.41747i	−0.453120	+	0.0876820i
$97$	88.2514			0.909808			0.454904	−	0.890541i	$-0.349674\pi$
$97$	88.2514			0.909808			0.454904	+	0.890541i	$0.349674\pi$
$98$			173.171i			1.76706i
$99$	11.1353	+	27.6949i	0.112478	+	0.279746i
$100$	42.4603			0.424603
$101$			39.2211i			0.388328i	0.980969	+	0.194164i	$0.0621993\pi$
$101$			39.2211i			0.388328i	−0.980969	+	0.194164i	$0.937801\pi$
$102$	33.8138	+	174.742i	0.331507	+	1.71315i
$103$	201.613			1.95741			0.978706	−	0.205267i	$-0.0658062\pi$
$103$	201.613			1.95741			0.978706	+	0.205267i	$0.0658062\pi$
$104$			251.764i			2.42080i
$105$	−0.424400	+	0.0821244i	−0.00404190	+	0.000782137i
$106$	−168.699			−1.59150
$107$			192.096i			1.79529i	0.440718	+	0.897646i	$0.354724\pi$
$107$			192.096i			1.79529i	−0.440718	+	0.897646i	$0.645276\pi$
$108$	−124.392	−	192.610i	−1.15178	−	1.78342i
$109$	137.434			1.26086			0.630431	−	0.776245i	$-0.282878\pi$
$109$	137.434			1.26086			0.630431	+	0.776245i	$0.282878\pi$
$110$			26.2119i			0.238290i
$111$	39.0079	+	201.584i	0.351423	+	1.81607i
$112$	1.42713			0.0127422
$113$		−	164.206i		−	1.45315i	−0.687087	−	0.726575i	$-0.741111\pi$
$113$		−	164.206i		−	1.45315i	0.687087	−	0.726575i	$-0.258889\pi$
$114$	175.397	−	33.9406i	1.53857	−	0.297724i
$115$	25.4004			0.220873
$116$			321.482i			2.77140i
$117$	−132.414	+	53.2397i	−1.13174	+	0.455040i
$118$	1.04843			0.00888497
$119$		−	1.08166i		−	0.00908961i
$120$	−20.2341	−	104.565i	−0.168617	−	0.871374i
$121$	−11.0000			−0.0909091
$122$			160.253i			1.31355i
$123$	50.7006	−	9.81093i	0.412200	−	0.0797637i
$124$	−409.179			−3.29983
$125$			11.1803i			0.0894427i
$126$	0.764668	+	1.90183i	0.00606879	+	0.0150939i
$127$	104.973			0.826558			0.413279	−	0.910605i	$-0.364383\pi$
$127$	104.973			0.826558			0.413279	+	0.910605i	$0.364383\pi$
$128$		−	187.686i		−	1.46630i
$129$	7.18886	+	37.1503i	0.0557276	+	0.287987i
$130$	−125.324			−0.964028
$131$			92.0290i			0.702512i	0.936279	+	0.351256i	$0.114245\pi$
$131$			92.0290i			0.702512i	−0.936279	+	0.351256i	$0.885755\pi$
$132$	82.9560	−	16.0526i	0.628455	−	0.121611i
$133$	−1.08572			−0.00816331
$134$		−	339.921i		−	2.53672i
$135$	50.7166	−	32.7540i	0.375679	−	0.242622i
$136$	266.503			1.95958
$137$			66.8499i			0.487956i	0.969781	+	0.243978i	$0.0784524\pi$
$137$			66.8499i			0.487956i	−0.969781	+	0.243978i	$0.921548\pi$
$138$	−22.8828	−	118.253i	−0.165817	−	0.856906i
$139$	−218.556			−1.57235			−0.786173	−	0.618007i	$-0.787940\pi$
$139$	−218.556			−1.57235			−0.786173	+	0.618007i	$0.787940\pi$
$140$			1.22363i			0.00874020i
$141$	−81.0207	+	15.6781i	−0.574615	+	0.111192i
$142$	−382.862			−2.69621
$143$		−	52.5929i		−	0.367783i
$144$	−184.933	+	74.3560i	−1.28426	+	0.516361i
$145$	−84.6503			−0.583795
$146$		−	363.718i		−	2.49122i
$147$	27.9251	+	144.311i	0.189967	+	0.981704i
$148$	581.206			3.92706
$149$		−	144.968i		−	0.972942i	−0.873697	−	0.486471i	$-0.838284\pi$
$149$		−	144.968i		−	0.972942i	0.873697	−	0.486471i	$-0.161716\pi$
$150$	52.0506	−	10.0722i	0.347004	−	0.0671478i
$151$	14.6810			0.0972252			0.0486126	−	0.998818i	$-0.484520\pi$
$151$	14.6810			0.0972252			0.0486126	+	0.998818i	$0.484520\pi$
$152$		−	267.503i		−	1.75989i
$153$	56.3567	+	140.166i	0.368344	+	0.916119i
$154$	−0.755379			−0.00490506
$155$		−	107.742i		−	0.695111i
$156$	76.7502	+	396.627i	0.491989	+	2.54248i
$157$	39.0660			0.248828			0.124414	−	0.992230i	$-0.460295\pi$
$157$	39.0660			0.248828			0.124414	+	0.992230i	$0.460295\pi$
$158$			37.2710i			0.235893i
$159$	−140.584	+	27.2040i	−0.884174	+	0.171094i
$160$	−33.0241			−0.206401
$161$			0.731994i			0.00454655i
$162$	−198.178	−	206.606i	−1.22332	−	1.27535i
$163$	−97.1186			−0.595820			−0.297910	−	0.954594i	$-0.596289\pi$
$163$	−97.1186			−0.595820			−0.297910	+	0.954594i	$0.596289\pi$
$164$		−	146.180i		−	0.891340i
$165$	4.22685	+	21.8434i	0.0256173	+	0.132384i
$166$	108.528			0.653785
$167$			11.1293i			0.0666423i	0.999445	+	0.0333211i	$0.0106084\pi$
$167$			11.1293i			0.0666423i	−0.999445	+	0.0333211i	$0.989392\pi$
$168$	3.01337	−	0.583109i	0.0179367	−	0.00347089i
$169$	82.4558			0.487904
$170$			132.661i			0.780358i
$171$	140.692	−	56.5680i	0.822760	−	0.330807i
$172$	107.112			0.622743
$173$		−	231.210i		−	1.33647i	−0.743949	−	0.668237i	$-0.767049\pi$
$173$		−	231.210i		−	1.33647i	0.743949	−	0.668237i	$-0.232951\pi$
$174$	76.2599	+	394.094i	0.438276	+	2.26491i
$175$	−0.322197			−0.00184113
$176$		−	73.4527i		−	0.417345i
$177$	0.873695	−	0.169066i	0.00493613	−	0.000955177i
$178$	−470.589			−2.64376
$179$		−	11.7705i		−	0.0657568i	−0.999459	−	0.0328784i	$-0.989533\pi$
$179$		−	11.7705i		−	0.0657568i	0.999459	−	0.0328784i	$-0.0104674\pi$
$180$	−63.7533	−	158.563i	−0.354185	−	0.880904i
$181$	−11.4370			−0.0631880			−0.0315940	−	0.999501i	$-0.510058\pi$
$181$	−11.4370			−0.0631880			−0.0315940	+	0.999501i	$0.510058\pi$
$182$		−	3.61160i		−	0.0198439i
$183$	25.8419	+	133.545i	0.141212	+	0.729753i
$184$	−180.351			−0.980169
$185$			153.039i			0.827237i
$186$	−501.599	+	97.0630i	−2.69677	+	0.521844i
$187$	−55.6720			−0.297711
$188$			233.599i			1.24255i
$189$	0.943911	+	1.46156i	0.00499424	+	0.00773312i
$190$	133.158			0.700833
$191$			340.558i			1.78303i	0.452995	+	0.891513i	$0.350356\pi$
$191$			340.558i			1.78303i	−0.452995	+	0.891513i	$0.649644\pi$
$192$	−20.7394	−	107.176i	−0.108018	−	0.558210i
$193$	0.482336			0.00249915			0.00124958	−	0.999999i	$-0.499602\pi$
$193$	0.482336			0.00249915			0.00124958	+	0.999999i	$0.499602\pi$
$194$		−	311.916i		−	1.60782i
$195$	−104.437	+	20.2093i	−0.535574	+	0.103638i
$196$	416.076			2.12283
$197$			172.800i			0.877155i	0.898693	+	0.438578i	$0.144518\pi$
$197$			172.800i			0.877155i	−0.898693	+	0.438578i	$0.855482\pi$
$198$	97.8850	−	39.3566i	0.494369	−	0.198771i
$199$	134.705			0.676912			0.338456	−	0.940982i	$-0.390095\pi$
$199$	134.705			0.676912			0.338456	+	0.940982i	$0.390095\pi$
$200$		−	79.3839i		−	0.396919i
$201$	−54.8146	−	283.269i	−0.272710	−	1.40930i
$202$	138.623			0.686255
$203$		−	2.43947i		−	0.0120171i
$204$	419.848	−	81.2436i	2.05808	−	0.398253i
$205$	38.4910			0.187761
$206$		−	712.585i		−	3.45915i
$207$	−38.1383	−	94.8548i	−0.184243	−	0.458236i
$208$	351.190			1.68841
$209$			55.8808i			0.267372i
$210$	0.290261	+	1.50000i	0.00138220	+	0.00714287i
$211$	82.9042			0.392911			0.196455	−	0.980513i	$-0.437057\pi$
$211$	82.9042			0.392911			0.196455	+	0.980513i	$0.437057\pi$
$212$			405.330i			1.91194i
$213$	−319.054	+	61.7392i	−1.49791	+	0.289856i
$214$	678.947			3.17265
$215$			28.2039i			0.131181i
$216$	−360.104	+	232.564i	−1.66715	+	1.07668i
$217$	3.10493			0.0143084
$218$		−	485.748i		−	2.22820i
$219$	−58.6522	−	303.101i	−0.267818	−	1.38402i
$220$	62.9788			0.286267
$221$		−	266.178i		−	1.20442i
$222$	712.480	−	137.870i	3.20937	−	0.621036i
$223$	152.628			0.684431			0.342215	−	0.939621i	$-0.388823\pi$
$223$	152.628			0.684431			0.342215	+	0.939621i	$0.388823\pi$
$224$		−	0.951694i		−	0.00424863i
$225$	41.7516	−	16.7871i	0.185563	−	0.0746091i
$226$	−580.372			−2.56802
$227$			15.0709i			0.0663915i	0.999449	+	0.0331957i	$0.0105685\pi$
$227$			15.0709i			0.0663915i	−0.999449	+	0.0331957i	$0.989432\pi$
$228$	−81.5483	−	421.423i	−0.357668	−	1.84835i
$229$	−74.5934			−0.325735			−0.162868	−	0.986648i	$-0.552074\pi$
$229$	−74.5934			−0.325735			−0.162868	+	0.986648i	$0.552074\pi$
$230$		−	89.7756i		−	0.390329i
$231$	−0.629487	+	0.121810i	−0.00272505	+	0.000527317i
$232$	601.044			2.59070
$233$			12.4686i			0.0535134i	0.999642	+	0.0267567i	$0.00851794\pi$
$233$			12.4686i			0.0535134i	−0.999642	+	0.0267567i	$0.991482\pi$
$234$	188.171	+	468.005i	0.804149	+	2.00002i
$235$	−61.5095			−0.261743
$236$		−	2.51903i		−	0.0106739i
$237$	6.01022	+	31.0594i	0.0253596	+	0.131052i
$238$	−3.82304			−0.0160632
$239$			298.857i			1.25045i	0.780445	+	0.625224i	$0.214992\pi$
$239$			298.857i			1.25045i	−0.780445	+	0.625224i	$0.785008\pi$
$240$	−145.860	+	28.2249i	−0.607748	+	0.117604i
$241$	−160.805			−0.667240			−0.333620	−	0.942708i	$-0.608270\pi$
$241$	−160.805			−0.667240			−0.333620	+	0.942708i	$0.608270\pi$
$242$			38.8785i			0.160655i
$243$	−198.466	−	140.215i	−0.816732	−	0.577018i
$244$	385.036			1.57802
$245$			109.558i			0.447176i
$246$	−34.6759	−	179.197i	−0.140959	−	0.728442i
$247$	−267.176			−1.08168
$248$			765.003i			3.08469i
$249$	90.4408	−	17.5010i	0.363216	−	0.0702850i
$250$	39.5159			0.158064
$251$		−	186.441i		−	0.742794i	−0.928474	−	0.371397i	$-0.878879\pi$
$251$		−	186.441i		−	0.742794i	0.928474	−	0.371397i	$-0.121121\pi$
$252$	4.56949	−	1.83725i	0.0181329	−	0.00729069i
$253$	37.6750			0.148913
$254$		−	371.017i		−	1.46070i
$255$	21.3925	+	110.551i	0.0838921	+	0.433535i
$256$	−517.807			−2.02268
$257$			138.232i			0.537868i	0.963159	+	0.268934i	$0.0866714\pi$
$257$			138.232i			0.537868i	−0.963159	+	0.268934i	$0.913329\pi$
$258$	131.305	−	25.4084i	0.508932	−	0.0984821i
$259$	−4.41030			−0.0170282
$260$			301.112i			1.15812i
$261$	127.101	+	316.116i	0.486976	+	1.21117i
$262$	325.268			1.24148
$263$			439.300i			1.67034i	0.549991	+	0.835171i	$0.314631\pi$
$263$			439.300i			1.67034i	−0.549991	+	0.835171i	$0.685369\pi$
$264$	−30.0120	−	155.095i	−0.113682	−	0.587480i
$265$	−106.729			−0.402750
$266$			3.83738i			0.0144262i
$267$	−392.160	+	75.8859i	−1.46877	+	0.284217i
$268$	−816.720			−3.04746
$269$		−	335.393i		−	1.24682i	−0.781897	−	0.623408i	$-0.785748\pi$
$269$		−	335.393i		−	1.24682i	0.781897	−	0.623408i	$-0.214252\pi$
$270$	−115.766	−	179.253i	−0.428764	−	0.663901i
$271$	−279.775			−1.03238			−0.516191	−	0.856474i	$-0.672650\pi$
$271$	−279.775			−1.03238			−0.516191	+	0.856474i	$0.672650\pi$
$272$		−	371.751i		−	1.36673i
$273$	−0.582396	−	3.00968i	−0.00213332	−	0.0110245i
$274$	236.275			0.862318
$275$			16.5831i			0.0603023i
$276$	−284.124	+	54.9801i	−1.02943	+	0.199203i
$277$	−124.104			−0.448027			−0.224014	−	0.974586i	$-0.571916\pi$
$277$	−124.104			−0.448027			−0.224014	+	0.974586i	$0.571916\pi$
$278$			772.467i			2.77866i
$279$	−402.350	+	161.773i	−1.44211	+	0.579831i
$280$	2.28770			0.00817035
$281$			0.751910i			0.00267584i	0.999999	+	0.00133792i	$0.000425873\pi$
$281$			0.751910i			0.00267584i	−0.999999	+	0.00133792i	$0.999574\pi$
$282$	55.4128	+	286.360i	0.196499	+	1.01546i
$283$	−257.050			−0.908304			−0.454152	−	0.890924i	$-0.650058\pi$
$283$	−257.050			−0.908304			−0.454152	+	0.890924i	$0.650058\pi$
$284$			919.895i			3.23907i
$285$	110.966	−	21.4727i	0.389355	−	0.0753429i
$286$	−185.885			−0.649947
$287$			1.10924i			0.00386495i
$288$	49.5850	+	123.324i	0.172170	+	0.428209i
$289$	7.23878			0.0250477
$290$			299.189i			1.03169i
$291$	−50.2988	−	259.932i	−0.172848	−	0.893238i
$292$	−873.899			−2.99280
$293$			276.104i			0.942336i	0.882044	+	0.471168i	$0.156167\pi$
$293$			276.104i			0.942336i	−0.882044	+	0.471168i	$0.843833\pi$
$294$	510.053	−	98.6989i	1.73487	−	0.335710i
$295$	0.663294			0.00224845
$296$		−	1086.62i		−	3.67103i
$297$	75.2249	−	48.5821i	0.253282	−	0.163576i
$298$	−512.378			−1.71939
$299$			180.130i			0.602443i
$300$	−24.2002	−	125.061i	−0.0806673	−	0.416870i
$301$	−0.812785			−0.00270028
$302$		−	51.8887i		−	0.171817i
$303$	115.520	−	22.3540i	0.381255	−	0.0737756i
$304$	−373.145			−1.22745
$305$			101.385i			0.332410i
$306$	495.405	−	199.188i	1.61897	−	0.650940i
$307$	464.370			1.51261			0.756303	−	0.654222i	$-0.227004\pi$
$307$	464.370			1.51261			0.756303	+	0.654222i	$0.227004\pi$
$308$			1.81493i			0.00589264i
$309$	−114.909	−	593.825i	−0.371875	−	1.92176i
$310$	−380.805			−1.22840
$311$			233.743i			0.751585i	0.926704	+	0.375793i	$0.122629\pi$
$311$			233.743i			0.751585i	−0.926704	+	0.375793i	$0.877371\pi$
$312$	741.535	−	143.492i	2.37672	−	0.459912i
$313$	508.543			1.62474			0.812368	−	0.583145i	$-0.198178\pi$
$313$	508.543			1.62474			0.812368	+	0.583145i	$0.198178\pi$
$314$		−	138.075i		−	0.439730i
$315$	0.483772	+	1.20320i	0.00153579	+	0.00381970i
$316$	89.5503			0.283387
$317$			29.7210i			0.0937572i	0.998901	+	0.0468786i	$0.0149274\pi$
$317$			29.7210i			0.0937572i	−0.998901	+	0.0468786i	$0.985073\pi$
$318$	96.1500	+	496.880i	0.302358	+	1.56252i
$319$	−125.557			−0.393595
$320$		−	81.3664i		−	0.254270i
$321$	565.793	−	109.485i	1.76259	−	0.341075i
$322$	2.58717			0.00803469
$323$			282.818i			0.875597i
$324$	−496.408	+	476.157i	−1.53212	+	1.46962i
$325$	−79.2868			−0.243959
$326$			343.257i			1.05294i
$327$	−78.3303	−	404.793i	−0.239542	−	1.23790i
$328$	−273.298			−0.833226
$329$		−	1.77259i		−	0.00538782i
$330$	77.2035	−	14.9394i	0.233950	−	0.0452710i
$331$	268.230			0.810364			0.405182	−	0.914236i	$-0.367208\pi$
$331$	268.230			0.810364			0.405182	+	0.914236i	$0.367208\pi$
$332$		−	260.759i		−	0.785418i
$333$	571.505	−	229.785i	1.71623	−	0.690045i
$334$	39.3354			0.117771
$335$		−	215.053i		−	0.641949i
$336$	−0.813389	−	4.20341i	−0.00242080	−	0.0125101i
$337$	456.085			1.35337			0.676685	−	0.736273i	$-0.263416\pi$
$337$	456.085			1.35337			0.676685	+	0.736273i	$0.263416\pi$
$338$		−	291.432i		−	0.862226i
$339$	−483.646	+	93.5890i	−1.42669	+	0.276074i
$340$	318.741			0.937475
$341$		−	159.807i		−	0.468644i
$342$	−199.935	−	497.263i	−0.584604	−	1.45399i
$343$	−6.31479			−0.0184105
$344$		−	200.256i		−	0.582141i
$345$	−14.4770	−	74.8135i	−0.0419622	−	0.216851i
$346$	−817.191			−2.36182
$347$		−	438.183i		−	1.26278i	−0.775467	−	0.631388i	$-0.782486\pi$
$347$		−	438.183i		−	1.26278i	0.775467	−	0.631388i	$-0.217514\pi$
$348$	946.881	−	183.228i	2.72092	−	0.526518i
$349$	−531.326			−1.52242			−0.761212	−	0.648503i	$-0.775395\pi$
$349$	−531.326			−1.52242			−0.761212	+	0.648503i	$0.775395\pi$
$350$			1.13878i			0.00325365i
$351$	232.279	+	359.663i	0.661764	+	1.02468i
$352$	−48.9826			−0.139155
$353$			305.442i			0.865276i	0.901568	+	0.432638i	$0.142417\pi$
$353$			305.442i			0.865276i	−0.901568	+	0.432638i	$0.857583\pi$
$354$	−0.597550	−	3.08800i	−0.00168799	−	0.00872316i
$355$	−242.220			−0.682310
$356$			1130.68i			3.17605i
$357$	−3.18589	+	0.616493i	−0.00892406	+	0.00172687i
$358$	−41.6017			−0.116206
$359$			401.993i			1.11976i	0.828574	+	0.559879i	$0.189153\pi$
$359$			401.993i			1.11976i	−0.828574	+	0.559879i	$0.810847\pi$
$360$	−296.449	+	119.193i	−0.823470	+	0.331093i
$361$	−77.1214			−0.213633
$362$			40.4232i			0.111666i
$363$	6.26944	+	32.3990i	0.0172712	+	0.0892534i
$364$	−8.67751			−0.0238393
$365$		−	230.109i		−	0.630435i
$366$	472.002	−	91.3358i	1.28962	−	0.249551i
$367$	2.75221			0.00749921			0.00374960	−	0.999993i	$-0.498806\pi$
$367$	2.75221			0.00749921			0.00374960	+	0.999993i	$0.498806\pi$
$368$			251.575i			0.683628i
$369$	−57.7935	−	143.740i	−0.156622	−	0.389539i
$370$	540.902			1.46190
$371$		−	3.07573i		−	0.00829037i
$372$	233.211	+	1205.18i	0.626912	+	3.23973i
$373$	377.063			1.01089			0.505446	−	0.862858i	$-0.331328\pi$
$373$	377.063			1.01089			0.505446	+	0.862858i	$0.331328\pi$
$374$			196.768i			0.526117i
$375$	32.9302	−	6.37222i	0.0878137	−	0.0169926i
$376$	436.737			1.16153
$377$		−	600.308i		−	1.59233i
$378$	5.16575	−	3.33617i	0.0136660	−	0.00882585i
$379$	530.824			1.40059			0.700295	−	0.713854i	$-0.253052\pi$
$379$	530.824			1.40059			0.700295	+	0.713854i	$0.253052\pi$
$380$		−	319.937i		−	0.841939i
$381$	−59.8291	−	309.183i	−0.157032	−	0.811504i
$382$	1203.67			3.15097
$383$			198.510i			0.518302i	0.965837	+	0.259151i	$0.0834427\pi$
$383$			198.510i			0.518302i	−0.965837	+	0.259151i	$0.916557\pi$
$384$	−552.803	+	106.971i	−1.43959	+	0.278571i
$385$	−0.477895			−0.00124129
$386$		−	1.70477i		−	0.00441651i
$387$	105.324	−	42.3476i	0.272155	−	0.109425i
$388$	−749.436			−1.93153
$389$			281.519i			0.723699i	0.932236	+	0.361850i	$0.117855\pi$
$389$			281.519i			0.723699i	−0.932236	+	0.361850i	$0.882145\pi$
$390$	71.4280	+	369.123i	0.183149	+	0.946470i
$391$	190.676			0.487663
$392$		−	777.896i		−	1.98443i
$393$	271.059	−	52.4518i	0.689717	−	0.133465i
$394$	610.745			1.55011
$395$			23.5798i			0.0596956i
$396$	−94.5614	−	235.186i	−0.238791	−	0.593905i
$397$	236.691			0.596198			0.298099	−	0.954535i	$-0.403647\pi$
$397$	236.691			0.596198			0.298099	+	0.954535i	$0.403647\pi$
$398$		−	476.105i		−	1.19624i
$399$	0.618805	+	3.19784i	0.00155089	+	0.00801463i
$400$	−110.734			−0.276835
$401$			112.420i			0.280349i	0.990127	+	0.140174i	$0.0447663\pi$
$401$			112.420i			0.280349i	−0.990127	+	0.140174i	$0.955234\pi$
$402$	−1001.19	+	193.737i	−2.49052	+	0.481934i
$403$	764.067			1.89595
$404$		−	333.068i		−	0.824425i
$405$	−125.378	−	130.711i	−0.309576	−	0.322742i
$406$	−8.62208			−0.0212367
$407$			226.993i			0.557723i
$408$	−151.893	−	784.949i	−0.372288	−	1.92390i
$409$	4.54083			0.0111023			0.00555114	−	0.999985i	$-0.498233\pi$
$409$	4.54083			0.0111023			0.00555114	+	0.999985i	$0.498233\pi$
$410$		−	136.043i		−	0.331812i
$411$	196.897	−	38.1010i	0.479069	−	0.0927033i
$412$	−1712.11			−4.15561
$413$			0.0191149i			4.62831e-5i
$414$	−335.256	+	134.796i	−0.809797	+	0.325595i
$415$	68.6611			0.165448
$416$		−	234.194i		−	0.562967i
$417$	124.566	+	643.727i	0.298719	+	1.54371i
$418$	197.506			0.472502
$419$			71.8408i			0.171458i	0.996318	+	0.0857289i	$0.0273219\pi$
$419$			71.8408i			0.171458i	−0.996318	+	0.0857289i	$0.972678\pi$
$420$	3.60403	−	0.697405i	0.00858102	−	0.00166049i
$421$	222.633			0.528819			0.264409	−	0.964411i	$-0.414823\pi$
$421$	222.633			0.528819			0.264409	+	0.964411i	$0.414823\pi$
$422$		−	293.018i		−	0.694354i
$423$	92.3553	+	229.700i	0.218334	+	0.543025i
$424$	757.807			1.78728
$425$			83.9287i			0.197479i
$426$	218.212	+	1127.67i	0.512234	+	2.64711i
$427$	−2.92173			−0.00684245
$428$		−	1631.29i		−	3.81143i
$429$	−154.905	+	29.9753i	−0.361084	+	0.0698724i
$430$	99.6842			0.231824
$431$		−	510.185i		−	1.18372i	−0.806039	−	0.591862i	$-0.798393\pi$
$431$		−	510.185i		−	1.18372i	0.806039	−	0.591862i	$-0.201607\pi$
$432$	324.407	+	502.315i	0.750943	+	1.16277i
$433$	−535.614			−1.23698			−0.618492	−	0.785791i	$-0.712256\pi$
$433$	−535.614			−1.23698			−0.618492	+	0.785791i	$0.712256\pi$
$434$		−	10.9741i		−	0.0252860i
$435$	48.2464	+	249.326i	0.110911	+	0.573163i
$436$	−1167.10			−2.67683
$437$		−	191.392i		−	0.437967i
$438$	−1071.28	+	207.301i	−2.44585	+	0.473290i
$439$	−522.019			−1.18911			−0.594555	−	0.804055i	$-0.702672\pi$
$439$	−522.019			−1.18911			−0.594555	+	0.804055i	$0.702672\pi$
$440$		−	117.745i		−	0.267603i
$441$	409.131	−	164.499i	0.927734	−	0.373014i
$442$	−940.781			−2.12846
$443$		−	575.259i		−	1.29855i	−0.760552	−	0.649277i	$-0.775072\pi$
$443$		−	575.259i		−	1.29855i	0.760552	−	0.649277i	$-0.224928\pi$
$444$	−331.257	−	1711.86i	−0.746075	−	3.85554i
$445$	−297.721			−0.669037
$446$		−	539.450i		−	1.20953i
$447$	−426.984	+	82.6246i	−0.955222	+	0.184842i
$448$	2.34483			0.00523400
$449$		−	529.067i		−	1.17832i	−0.808015	−	0.589161i	$-0.799458\pi$
$449$		−	529.067i		−	1.17832i	0.808015	−	0.589161i	$-0.200542\pi$
$450$	−59.3324	−	147.567i	−0.131850	−	0.327927i
$451$	57.0914			0.126589
$452$			1394.45i			3.08506i
$453$	−8.36742	−	43.2409i	−0.0184711	−	0.0954545i
$454$	53.2666			0.117327
$455$		−	2.28490i		−	0.00502176i
$456$	−787.893	+	152.463i	−1.72784	+	0.334349i
$457$	873.857			1.91216			0.956079	−	0.293108i	$-0.0946894\pi$
$457$	873.857			1.91216			0.956079	+	0.293108i	$0.0946894\pi$
$458$			263.644i			0.575641i
$459$	380.720	−	245.878i	0.829455	−	0.535683i
$460$	−215.702			−0.468918
$461$			172.562i			0.374321i	0.982329	+	0.187161i	$0.0599285\pi$
$461$			172.562i			0.374321i	−0.982329	+	0.187161i	$0.940071\pi$
$462$	0.430527	+	2.22486i	0.000931877	+	0.00481572i
$463$	−479.238			−1.03507			−0.517536	−	0.855661i	$-0.673151\pi$
$463$	−479.238			−1.03507			−0.517536	+	0.855661i	$0.673151\pi$
$464$		−	838.407i		−	1.80691i
$465$	−317.340	+	61.4075i	−0.682451	+	0.132059i
$466$	44.0692			0.0945692
$467$		−	699.697i		−	1.49828i	−0.662411	−	0.749140i	$-0.730467\pi$
$467$		−	699.697i		−	1.49828i	0.662411	−	0.749140i	$-0.269533\pi$
$468$	1124.47	−	452.114i	2.40271	−	0.966056i
$469$	6.19743			0.0132141
$470$			217.400i			0.462553i
$471$	−22.2656	−	115.064i	−0.0472731	−	0.244296i
$472$	−4.70959			−0.00997795
$473$			41.8331i			0.0884422i
$474$	109.777	−	21.2426i	0.231596	−	0.0448156i
$475$	84.2435			0.177355
$476$			9.18555i			0.0192974i
$477$	160.251	+	398.565i	0.335956	+	0.835566i
$478$	1056.28			2.20980
$479$			324.938i			0.678368i	0.940720	+	0.339184i	$0.110151\pi$
$479$			324.938i			0.678368i	−0.940720	+	0.339184i	$0.889849\pi$
$480$	18.8220	+	97.2679i	0.0392126	+	0.202641i
$481$	−1085.29			−2.25633
$482$			568.350i			1.17915i
$483$	2.15599	−	0.417199i	0.00446375	−	0.000863767i
$484$	93.4126			0.193001
$485$		−	197.336i		−	0.406878i
$486$	−495.578	+	701.460i	−1.01971	+	1.44333i
$487$	233.122			0.478690			0.239345	−	0.970935i	$-0.423067\pi$
$487$	233.122			0.478690			0.239345	+	0.970935i	$0.423067\pi$
$488$		−	719.864i		−	1.47513i
$489$	55.3526	+	286.049i	0.113196	+	0.584968i
$490$	387.223			0.790251
$491$			314.885i			0.641314i	0.947195	+	0.320657i	$0.103904\pi$
$491$			314.885i			0.641314i	−0.947195	+	0.320657i	$0.896096\pi$
$492$	−430.552	+	83.3150i	−0.875107	+	0.169339i
$493$	−635.454			−1.28895
$494$			944.309i			1.91156i
$495$	61.9276	−	24.8992i	0.125106	−	0.0503015i
$496$	1067.12			2.15144
$497$		−	6.98034i		−	0.0140450i
$498$	−61.8556	−	319.655i	−0.124208	−	0.641878i
$499$	673.348			1.34939			0.674697	−	0.738095i	$-0.264274\pi$
$499$	673.348			1.34939			0.674697	+	0.738095i	$0.264274\pi$
$500$		−	94.9441i		−	0.189888i
$501$	32.7797	−	6.34311i	0.0654286	−	0.0126609i
$502$	−658.960			−1.31267
$503$			452.712i			0.900025i	0.893022	+	0.450012i	$0.148580\pi$
$503$			452.712i			0.900025i	−0.893022	+	0.450012i	$0.851420\pi$
$504$	−3.43493	−	8.54312i	−0.00681534	−	0.0169506i
$505$	87.7010			0.173665
$506$		−	133.159i		−	0.263160i
$507$	−46.9956	−	242.862i	−0.0926934	−	0.479018i
$508$	−891.435			−1.75479
$509$			582.788i			1.14497i	0.819916	+	0.572484i	$0.194020\pi$
$509$			582.788i			1.14497i	−0.819916	+	0.572484i	$0.805980\pi$
$510$	390.734	−	75.6099i	0.766145	−	0.148255i
$511$	6.63131			0.0129771
$512$			1079.40i			2.10820i
$513$	−246.801	−	382.148i	−0.481093	−	0.744928i
$514$	488.569			0.950524
$515$		−	450.821i		−	0.875381i
$516$	−61.0482	−	315.483i	−0.118310	−	0.611401i
$517$	−91.2334			−0.176467
$518$			15.5878i			0.0300923i
$519$	−680.997	+	131.778i	−1.31213	+	0.253907i
$520$	562.961			1.08262
$521$		−	37.0696i		−	0.0711508i	−0.999367	−	0.0355754i	$-0.988674\pi$
$521$		−	37.0696i		−	0.0711508i	0.999367	−	0.0355754i	$-0.0113264\pi$
$522$	1117.28	−	449.226i	2.14039	−	0.860587i
$523$	−197.518			−0.377664			−0.188832	−	0.982009i	$-0.560470\pi$
$523$	−197.518			−0.377664			−0.188832	+	0.982009i	$0.560470\pi$
$524$		−	781.516i		−	1.49144i
$525$	0.183636	+	0.948987i	0.000349782	+	0.00180759i
$526$	1552.67			2.95184
$527$		−	808.800i		−	1.53473i
$528$	−216.345	+	41.8643i	−0.409744	+	0.0792884i
$529$	399.963			0.756075
$530$			377.223i			0.711742i
$531$	−0.995923	−	2.47699i	−0.00187556	−	0.00466476i
$532$	9.22000			0.0173308
$533$			272.964i			0.512127i
$534$	268.212	+	1386.06i	0.502269	+	2.59561i
$535$	429.540			0.802879
$536$			1526.94i			2.84877i
$537$	−34.6683	+	6.70857i	−0.0645592	+	0.0124927i
$538$	−1185.42			−2.20338
$539$			162.501i			0.301486i
$540$	−430.688	+	278.149i	−0.797571	+	0.515091i
$541$	−797.250			−1.47366			−0.736830	−	0.676078i	$-0.763678\pi$
$541$	−797.250			−1.47366			−0.736830	+	0.676078i	$0.763678\pi$
$542$			988.841i			1.82443i
$543$	6.51853	+	33.6862i	0.0120047	+	0.0620372i
$544$	−247.906			−0.455709
$545$		−	307.312i		−	0.563875i
$546$	−10.6375	+	2.05843i	−0.0194825	+	0.00377001i
$547$	−472.550			−0.863895			−0.431947	−	0.901899i	$-0.642173\pi$
$547$	−472.550			−0.863895			−0.431947	+	0.901899i	$0.642173\pi$
$548$		−	567.694i		−	1.03594i
$549$	378.609	−	152.227i	0.689634	−	0.277281i
$550$	58.6116			0.106566
$551$			637.837i			1.15760i
$552$	102.791	+	531.199i	0.186215	+	0.962317i
$553$	−0.679525			−0.00122880
$554$			438.633i			0.791756i
$555$	450.755	−	87.2243i	0.812171	−	0.157161i
$556$	1855.99			3.33811
$557$		−	528.445i		−	0.948734i	−0.880327	−	0.474367i	$-0.842677\pi$
$557$		−	528.445i		−	0.948734i	0.880327	−	0.474367i	$-0.157323\pi$
$558$	571.771	+	1422.07i	1.02468	+	2.54851i
$559$	−200.012			−0.357802
$560$		−	3.19115i		−	0.00569849i
$561$	31.7302	+	163.974i	0.0565601	+	0.292289i
$562$	2.65756			0.00472875
$563$		−	665.589i		−	1.18222i	−0.806592	−	0.591109i	$-0.798690\pi$
$563$		−	665.589i		−	1.18222i	0.806592	−	0.591109i	$-0.201310\pi$
$564$	688.033	−	133.139i	1.21992	−	0.236063i
$565$	−367.176			−0.649869
$566$			908.521i			1.60516i
$567$	3.76684	−	3.61317i	0.00664346	−	0.00637244i
$568$	1719.84			3.02788
$569$			108.689i			0.191018i	0.995429	+	0.0955088i	$0.0304478\pi$
$569$			108.689i			0.191018i	−0.995429	+	0.0955088i	$0.969552\pi$
$570$	−75.8934	−	392.200i	−0.133146	−	0.688069i
$571$	−106.808			−0.187054			−0.0935268	−	0.995617i	$-0.529814\pi$
$571$	−106.808			−0.187054			−0.0935268	+	0.995617i	$0.529814\pi$
$572$			446.622i			0.780808i
$573$	1003.07	−	194.101i	1.75055	−	0.338745i
$574$	3.92051			0.00683016
$575$		−	56.7971i		−	0.0987776i
$576$	−303.853	+	122.170i	−0.527522	+	0.212101i
$577$	−921.947			−1.59783			−0.798914	−	0.601445i	$-0.794592\pi$
$577$	−921.947			−1.59783			−0.798914	+	0.601445i	$0.794592\pi$
$578$		−	25.5848i		−	0.0442644i
$579$	−0.274907	−	1.42065i	−0.000474796	−	0.00245364i
$580$	718.855			1.23941
$581$			1.97869i			0.00340566i
$582$	−918.707	+	177.776i	−1.57853	+	0.305458i
$583$	−158.304			−0.271534
$584$			1633.84i			2.79768i
$585$	119.048	+	296.087i	0.203500	+	0.506131i
$586$	975.866			1.66530
$587$		−	648.849i		−	1.10536i	−0.833392	−	0.552682i	$-0.813604\pi$
$587$		−	648.849i		−	1.10536i	0.833392	−	0.552682i	$-0.186396\pi$
$588$	−237.142	−	1225.49i	−0.403302	−	2.08417i
$589$	−811.834			−1.37833
$590$		−	2.34435i		−	0.00397348i
$591$	508.957	−	98.4869i	0.861180	−	0.166645i
$592$	−1515.75			−2.56039
$593$			477.585i			0.805370i	0.915339	+	0.402685i	$0.131923\pi$
$593$			477.585i			0.805370i	−0.915339	+	0.402685i	$0.868077\pi$
$594$	−171.709	−	265.876i	−0.289072	−	0.447602i
$595$	−2.41867			−0.00406500
$596$			1231.08i			2.06557i
$597$	−76.7752	−	396.756i	−0.128602	−	0.664584i
$598$	636.655			1.06464
$599$		−	1174.94i		−	1.96150i	−0.195278	−	0.980748i	$-0.562561\pi$
$599$		−	1174.94i		−	1.96150i	0.195278	−	0.980748i	$-0.437439\pi$
$600$	−233.814	+	45.2447i	−0.389690	+	0.0754079i
$601$	−557.601			−0.927788			−0.463894	−	0.885891i	$-0.653548\pi$
$601$	−557.601			−0.927788			−0.463894	+	0.885891i	$0.653548\pi$
$602$			2.87272i			0.00477195i
$603$	−803.089	+	322.898i	−1.33182	+	0.535486i
$604$	−124.672			−0.206410
$605$			24.5967i			0.0406558i
$606$	−79.0083	−	408.296i	−0.130377	−	0.673756i
$607$	208.362			0.343265			0.171632	−	0.985161i	$-0.445096\pi$
$607$	208.362			0.343265			0.171632	+	0.985161i	$0.445096\pi$
$608$			248.835i			0.409269i
$609$	−7.18512	+	1.39037i	−0.0117982	+	0.00228304i
$610$	358.336			0.587436
$611$		−	436.203i		−	0.713916i
$612$	−478.584	−	1190.30i	−0.782000	−	1.94493i
$613$	−261.076			−0.425899			−0.212950	−	0.977063i	$-0.568307\pi$
$613$	−261.076			−0.425899			−0.212950	+	0.977063i	$0.568307\pi$
$614$		−	1641.27i		−	2.67308i
$615$	−21.9379	−	113.370i	−0.0356714	−	0.184341i
$616$	3.39320			0.00550845
$617$		−	198.406i		−	0.321566i	−0.986990	−	0.160783i	$-0.948598\pi$
$617$		−	198.406i		−	0.321566i	0.986990	−	0.160783i	$-0.0514020\pi$
$618$	−2098.82	+	406.137i	−3.39615	+	0.657179i
$619$	−177.495			−0.286745			−0.143373	−	0.989669i	$-0.545795\pi$
$619$	−177.495			−0.286745			−0.143373	+	0.989669i	$0.545795\pi$
$620$			914.953i			1.47573i
$621$	−257.645	+	166.393i	−0.414887	+	0.267944i
$622$	826.144			1.32821
$623$		−	8.57979i		−	0.0137717i
$624$	−200.160	−	1034.38i	−0.320770	−	1.65766i
$625$	25.0000			0.0400000
$626$		−	1797.40i		−	2.87124i
$627$	164.589	−	31.8492i	0.262503	−	0.0507962i
$628$	−331.751			−0.528266
$629$			1148.83i			1.82645i
$630$	4.25262	−	1.70985i	0.00675019	−	0.00271405i
$631$	860.308			1.36340			0.681702	−	0.731630i	$-0.261240\pi$
$631$	860.308			1.36340			0.681702	+	0.731630i	$0.261240\pi$
$632$		−	167.424i		−	0.264911i
$633$	−47.2512	−	244.183i	−0.0746464	−	0.385755i
$634$	105.046			0.165688
$635$		−	234.726i		−	0.369648i
$636$	1193.84	−	231.018i	1.87711	−	0.363235i
$637$	−776.945			−1.21969
$638$			443.769i			0.695563i
$639$	363.689	+	904.541i	0.569153	+	1.41556i
$640$	−419.679			−0.655748
$641$			63.1571i			0.0985291i	0.998786	+	0.0492645i	$0.0156877\pi$
$641$			63.1571i			0.0985291i	−0.998786	+	0.0492645i	$0.984312\pi$
$642$	−386.965	−	1999.74i	−0.602749	−	3.11487i
$643$	−340.765			−0.529960			−0.264980	−	0.964254i	$-0.585365\pi$
$643$	−340.765			−0.529960			−0.264980	+	0.964254i	$0.585365\pi$
$644$		−	6.21614i		−	0.00965239i
$645$	83.0707	−	16.0748i	0.128792	−	0.0249221i
$646$	999.595			1.54736
$647$			199.808i			0.308823i	0.988007	+	0.154411i	$0.0493481\pi$
$647$			199.808i			0.308823i	−0.988007	+	0.154411i	$0.950652\pi$
$648$	890.225	+	928.086i	1.37380	+	1.43223i
$649$	0.983824			0.00151591
$650$			280.232i			0.431126i
$651$	−1.76965	−	9.14515i	−0.00271836	−	0.0140479i
$652$	824.737			1.26493
$653$		−	1195.72i		−	1.83112i	−0.402178	−	0.915562i	$-0.631747\pi$
$653$		−	1195.72i		−	1.83112i	0.402178	−	0.915562i	$-0.368253\pi$
$654$	−1430.70	+	276.852i	−2.18762	+	0.423320i
$655$	205.783			0.314173
$656$			381.229i			0.581141i
$657$	−859.312	+	345.504i	−1.30793	+	0.525881i
$658$	−6.26507			−0.00952138
$659$			1050.34i			1.59383i	0.604089	+	0.796917i	$0.293537\pi$
$659$			1050.34i			1.59383i	−0.604089	+	0.796917i	$0.706463\pi$
$660$	−35.8947	−	185.495i	−0.0543859	−	0.281054i
$661$	−519.530			−0.785976			−0.392988	−	0.919544i	$-0.628559\pi$
$661$	−519.530			−0.785976			−0.392988	+	0.919544i	$0.628559\pi$
$662$		−	948.036i		−	1.43208i
$663$	−783.989	+	151.708i	−1.18249	+	0.228820i
$664$	−487.515			−0.734210
$665$			2.42774i			0.00365074i
$666$	−812.154	−	2019.93i	−1.21945	−	3.03293i
$667$	430.031			0.644725
$668$		−	94.5103i		−	0.141483i
$669$	−86.9902	−	449.545i	−0.130030	−	0.671966i
$670$	−760.086			−1.13446
$671$			150.378i			0.224110i
$672$	−2.80308	+	0.542417i	−0.00417125	+	0.000807168i
$673$	977.591			1.45259			0.726293	−	0.687385i	$-0.241241\pi$
$673$	977.591			1.45259			0.726293	+	0.687385i	$0.241241\pi$
$674$		−	1611.99i		−	2.39168i
$675$	−73.2402	−	113.406i	−0.108504	−	0.168009i
$676$	−700.219			−1.03583
$677$			998.266i			1.47454i	0.675596	+	0.737272i	$0.263886\pi$
$677$			998.266i			1.47454i	−0.675596	+	0.737272i	$0.736114\pi$
$678$	330.782	+	1709.40i	0.487879	+	2.52125i
$679$	5.68686			0.00837535
$680$		−	595.920i		−	0.876353i
$681$	44.3891	−	8.58962i	0.0651823	−	0.0126132i
$682$	−564.825			−0.828189
$683$			387.494i			0.567341i	0.958922	+	0.283671i	$0.0915522\pi$
$683$			387.494i			0.567341i	−0.958922	+	0.283671i	$0.908448\pi$
$684$	−1194.76	+	480.379i	−1.74673	+	0.702308i
$685$	149.481			0.218220
$686$			22.3191i			0.0325351i
$687$	42.5144	+	219.705i	0.0618842	+	0.319803i
$688$	−279.341			−0.406020
$689$		−	756.880i		−	1.09852i
$690$	−264.422	+	51.1675i	−0.383220	+	0.0741558i
$691$	−290.950			−0.421056			−0.210528	−	0.977588i	$-0.567518\pi$
$691$	−290.950			−0.421056			−0.210528	+	0.977588i	$0.567518\pi$
$692$			1963.45i			2.83735i
$693$	0.717550	+	1.78464i	0.00103543	+	0.00257524i
$694$	−1548.72			−2.23158
$695$			488.706i			0.703174i
$696$	−342.564	−	1770.29i	−0.492190	−	2.54352i
$697$	288.945			0.414555
$698$			1877.92i			2.69043i
$699$	36.7246	−	7.10648i	0.0525388	−	0.0101666i
$700$	2.73612			0.00390874
$701$			225.423i			0.321574i	0.986989	+	0.160787i	$0.0514032\pi$
$701$			225.423i			0.321574i	−0.986989	+	0.160787i	$0.948597\pi$
$702$	1271.20	−	820.970i	1.81082	−	1.16947i
$703$	1153.14			1.64032
$704$		−	120.686i		−	0.171429i
$705$	35.0573	+	181.168i	0.0497266	+	0.256976i
$706$	1079.56			1.52912
$707$			2.52738i			0.00357480i
$708$	−7.41947	+	1.43572i	−0.0104795	+	0.00202785i
$709$	−215.271			−0.303626			−0.151813	−	0.988409i	$-0.548511\pi$
$709$	−215.271			−0.303626			−0.151813	+	0.988409i	$0.548511\pi$
$710$			856.106i			1.20578i
$711$	88.0556	−	35.4045i	0.123848	−	0.0497954i
$712$	2113.91			2.96898
$713$			547.340i			0.767658i
$714$	2.17894	+	11.2602i	0.00305173	+	0.0157706i
$715$	−117.601			−0.164477
$716$			99.9555i			0.139603i
$717$	880.242	−	170.333i	1.22767	−	0.237564i
$718$	1420.81			1.97884
$719$			509.600i			0.708763i	0.935101	+	0.354381i	$0.115309\pi$
$719$			509.600i			0.708763i	−0.935101	+	0.354381i	$0.884691\pi$
$720$	166.265	+	413.522i	0.230924	+	0.574337i
$721$	12.9918			0.0180192
$722$			272.579i			0.377533i
$723$	91.6505	+	473.629i	0.126764	+	0.655088i
$724$	97.1240			0.134149
$725$			189.284i			0.261081i
$726$	114.511	−	22.1588i	0.157729	−	0.0305217i
$727$	−266.154			−0.366099			−0.183050	−	0.983104i	$-0.558597\pi$
$727$	−266.154			−0.366099			−0.183050	+	0.983104i	$0.558597\pi$
$728$			16.2235i			0.0222850i
$729$	−299.869	+	664.469i	−0.411344	+	0.911480i
$730$	−813.299			−1.11411
$731$			211.721i			0.289633i
$732$	−219.451	−	1134.07i	−0.299796	−	1.54928i
$733$	−327.146			−0.446311			−0.223156	−	0.974783i	$-0.571636\pi$
$733$	−327.146			−0.446311			−0.223156	+	0.974783i	$0.571636\pi$
$734$		−	9.72744i		−	0.0132526i
$735$	322.688	−	62.4425i	0.439031	−	0.0849558i
$736$	167.765			0.227942
$737$		−	318.975i		−	0.432802i
$738$	−508.036	+	204.266i	−0.688396	+	0.276783i
$739$	355.176			0.480617			0.240308	−	0.970697i	$-0.422751\pi$
$739$	355.176			0.480617			0.240308	+	0.970697i	$0.422751\pi$
$740$		−	1299.62i		−	1.75624i
$741$	152.277	+	786.930i	0.205501	+	1.06198i
$742$	−10.8709			−0.0146508
$743$		−	773.343i		−	1.04084i	−0.853911	−	0.520419i	$-0.825776\pi$
$743$		−	773.343i		−	1.04084i	0.853911	−	0.520419i	$-0.174224\pi$
$744$	2253.21	−	436.012i	3.02851	−	0.586038i
$745$	−324.159			−0.435113
$746$		−	1332.70i		−	1.78645i
$747$	−103.093	−	256.406i	−0.138010	−	0.343248i
$748$	472.770			0.632045
$749$			12.3786i			0.0165268i
$750$	−22.5220	−	116.389i	−0.0300294	−	0.155185i
$751$	−312.401			−0.415980			−0.207990	−	0.978131i	$-0.566692\pi$
$751$	−312.401			−0.415980			−0.207990	+	0.978131i	$0.566692\pi$
$752$		−	609.212i		−	0.810123i
$753$	−549.137	+	106.262i	−0.729266	+	0.141118i
$754$	−2121.74			−2.81397
$755$		−	32.8277i		−	0.0434804i
$756$	−8.01575	−	12.4116i	−0.0106028	−	0.0164175i
$757$	527.371			0.696659			0.348330	−	0.937372i	$-0.386749\pi$
$757$	527.371			0.696659			0.348330	+	0.937372i	$0.386749\pi$
$758$		−	1876.15i		−	2.47513i
$759$	−21.4728	−	110.966i	−0.0282909	−	0.146201i
$760$	−598.155			−0.787046
$761$		−	931.559i		−	1.22413i	−0.790809	−	0.612063i	$-0.790340\pi$
$761$		−	931.559i		−	1.22413i	0.790809	−	0.612063i	$-0.209660\pi$
$762$	−1092.78	+	211.461i	−1.43409	+	0.277508i
$763$	8.85616			0.0116070
$764$		−	2892.04i		−	3.78539i
$765$	313.421	−	126.017i	0.409701	−	0.164729i
$766$	701.614			0.915946
$767$			4.70383i			0.00613277i
$768$	295.123	+	1525.13i	0.384275	+	1.98584i
$769$	1360.03			1.76856			0.884282	−	0.466953i	$-0.154648\pi$
$769$	1360.03			1.76856			0.884282	+	0.466953i	$0.154648\pi$
$770$			1.68908i			0.00219361i
$771$	407.144	−	78.7852i	0.528072	−	0.102186i
$772$	−4.09603			−0.00530573
$773$			756.634i			0.978828i	0.872052	+	0.489414i	$0.162789\pi$
$773$			756.634i			0.978828i	−0.872052	+	0.489414i	$0.837211\pi$
$774$	−149.674	−	372.258i	−0.193377	−	0.480954i
$775$	−240.919			−0.310863
$776$			1401.15i			1.80560i
$777$	2.51365	+	12.9899i	0.00323507	+	0.0167181i
$778$	995.004			1.27893
$779$		−	290.029i		−	0.372309i
$780$	886.885	−	171.619i	1.13703	−	0.220024i
$781$	−359.271			−0.460014
$782$		−	673.929i		−	0.861801i
$783$	858.635	−	554.528i	1.09660	−	0.708209i
$784$	−1085.10			−1.38406
$785$		−	87.3543i		−	0.111279i
$786$	−185.386	−	958.033i	−0.235861	−	1.21887i
$787$	1235.86			1.57034			0.785172	−	0.619277i	$-0.212574\pi$
$787$	1235.86			1.57034			0.785172	+	0.619277i	$0.212574\pi$
$788$		−	1467.42i		−	1.86221i
$789$	1293.90	−	250.378i	1.63992	−	0.317336i
$790$	83.3405			0.105494
$791$		−	10.5813i		−	0.0133772i
$792$	−439.705	+	176.792i	−0.555183	+	0.223223i
$793$	−718.984			−0.906663
$794$		−	836.562i		−	1.05360i
$795$	60.8299	+	314.355i	0.0765156	+	0.395415i
$796$	−1143.93			−1.43709
$797$			89.5791i			0.112395i	0.998420	+	0.0561977i	$0.0178977\pi$
$797$			89.5791i			0.112395i	−0.998420	+	0.0561977i	$0.982102\pi$
$798$	11.3025	−	2.18711i	0.0141635	−	0.00274074i
$799$	−461.741			−0.577898
$800$			73.8441i			0.0923051i
$801$	447.023	+	1111.80i	0.558081	+	1.38802i
$802$	397.338			0.495434
$803$		−	341.306i		−	0.425039i
$804$	465.489	+	2405.54i	0.578966	+	2.99196i
$805$	1.63679			0.00203328
$806$		−	2700.53i		−	3.35053i
$807$	−987.855	+	191.157i	−1.22411	+	0.236874i
$808$	−622.704			−0.770674
$809$			567.123i			0.701018i	0.936559	+	0.350509i	$0.113991\pi$
$809$			567.123i			0.701018i	−0.936559	+	0.350509i	$0.886009\pi$
$810$	−461.985	+	443.139i	−0.570352	+	0.547085i
$811$	−226.203			−0.278918			−0.139459	−	0.990228i	$-0.544536\pi$
$811$	−226.203			−0.278918			−0.139459	+	0.990228i	$0.544536\pi$
$812$			20.7161i			0.0255124i
$813$	159.458	+	824.040i	0.196135	+	1.01358i
$814$	802.288			0.985612
$815$			217.164i			0.266459i
$816$	−1094.94	+	211.879i	−1.34184	+	0.259655i
$817$	212.515			0.260117
$818$		−	16.0492i		−	0.0196200i
$819$	−8.53267	+	3.43073i	−0.0104184	+	0.00418893i
$820$	−326.868			−0.398620
$821$		−	222.582i		−	0.271111i	−0.990770	−	0.135556i	$-0.956718\pi$
$821$		−	222.582i		−	0.271111i	0.990770	−	0.135556i	$-0.0432819\pi$
$822$	−134.665	−	695.916i	−0.163826	−	0.846613i
$823$	−259.507			−0.315319			−0.157659	−	0.987494i	$-0.550395\pi$
$823$	−259.507			−0.315319			−0.157659	+	0.987494i	$0.550395\pi$
$824$			3200.97i			3.88467i
$825$	48.8433	−	9.45153i	0.0592040	−	0.0114564i
$826$	0.0675600			8.17918e−5
$827$			18.2394i			0.0220549i	0.999939	+	0.0110275i	$0.00351022\pi$
$827$			18.2394i			0.0220549i	−0.999939	+	0.0110275i	$0.996490\pi$
$828$	323.872	+	805.512i	0.391150	+	0.972841i
$829$	1163.19			1.40313			0.701563	−	0.712607i	$-0.252486\pi$
$829$	1163.19			1.40313			0.701563	+	0.712607i	$0.252486\pi$
$830$		−	242.677i		−	0.292381i
$831$	70.7327	+	365.530i	0.0851176	+	0.439868i
$832$	577.020			0.693534
$833$			822.432i			0.987313i
$834$	2275.19	−	440.266i	2.72805	−	0.527897i
$835$	24.8858			0.0298033
$836$		−	474.543i		−	0.567635i
$837$	705.798	+	1092.86i	0.843247	+	1.30569i
$838$	253.915			0.303001
$839$			335.941i			0.400407i	0.979754	+	0.200203i	$0.0641603\pi$
$839$			335.941i			0.400407i	−0.979754	+	0.200203i	$0.935840\pi$
$840$	−1.30387	−	6.73810i	−0.00155223	−	0.00802155i
$841$	−592.136			−0.704085
$842$		−	786.875i		−	0.934531i
$843$	2.21465	−	0.428550i	0.00262710	−	0.000508363i
$844$	−704.027			−0.834156
$845$		−	184.377i		−	0.218197i
$846$	811.853	−	326.422i	0.959637	−	0.385841i
$847$	−0.708833			−0.000836875
$848$		−	1057.08i		−	1.24656i
$849$	146.505	+	757.106i	0.172562	+	0.891762i
$850$	296.639			0.348987
$851$		−	777.451i		−	0.913574i
$852$	2709.42	−	524.293i	3.18007	−	0.615367i
$853$	−1020.85			−1.19677			−0.598386	−	0.801208i	$-0.704191\pi$
$853$	−1020.85			−1.19677			−0.598386	+	0.801208i	$0.704191\pi$
$854$			10.3266i			0.0120920i
$855$	−126.490	−	314.597i	−0.147941	−	0.367949i
$856$	−3049.87			−3.56293
$857$		−	9.87597i		−	0.0115239i	−0.999983	−	0.00576194i	$-0.998166\pi$
$857$		−	9.87597i		−	0.0115239i	0.999983	−	0.00576194i	$-0.00183409\pi$
$858$	105.945	+	547.498i	0.123479	+	0.638110i
$859$	−867.169			−1.00951			−0.504755	−	0.863263i	$-0.668417\pi$
$859$	−867.169			−1.00951			−0.504755	+	0.863263i	$0.668417\pi$
$860$		−	239.509i		−	0.278499i
$861$	3.26712	−	0.632211i	0.00379456	−	0.000734275i
$862$	−1803.20			−2.09188
$863$			553.050i			0.640846i	0.947275	+	0.320423i	$0.103825\pi$
$863$			553.050i			0.640846i	−0.947275	+	0.320423i	$0.896175\pi$
$864$	334.974	−	216.334i	0.387701	−	0.250387i
$865$	−517.001			−0.597689
$866$			1893.08i			2.18600i
$867$	−4.12574	−	21.3208i	−0.00475863	−	0.0245915i
$868$	−26.3673			−0.0303770
$869$			34.9744i			0.0402467i
$870$	881.220	−	170.522i	1.01290	−	0.196003i
$871$	1525.08			1.75095
$872$			2182.01i			2.50230i
$873$	−736.927	+	296.296i	−0.844131	+	0.339400i
$874$	−676.456			−0.773977
$875$			0.720454i			0.000823376i
$876$	498.078	+	2573.95i	0.568582	+	2.93830i
$877$	210.788			0.240351			0.120175	−	0.992753i	$-0.461654\pi$
$877$	210.788			0.240351			0.120175	+	0.992753i	$0.461654\pi$
$878$			1845.03i			2.10140i
$879$	813.227	−	157.365i	0.925173	−	0.179028i
$880$	−164.245			−0.186642
$881$		−	228.326i		−	0.259166i	−0.991569	−	0.129583i	$-0.958636\pi$
$881$		−	228.326i		−	0.259166i	0.991569	−	0.129583i	$-0.0413639\pi$
$882$	−581.408	−	1446.04i	−0.659192	−	1.63950i
$883$	697.352			0.789753			0.394876	−	0.918734i	$-0.370787\pi$
$883$	697.352			0.789753			0.394876	+	0.918734i	$0.370787\pi$
$884$			2260.39i			2.55701i
$885$	−0.378044	−	1.95364i	−0.000427168	−	0.00220750i
$886$	−2033.20			−2.29481
$887$		−	110.277i		−	0.124326i	−0.998066	−	0.0621630i	$-0.980200\pi$
$887$		−	110.277i		−	0.124326i	0.998066	−	0.0621630i	$-0.0197998\pi$
$888$	−3200.50	+	619.320i	−3.60417	+	0.697432i
$889$	6.76439			0.00760898
$890$			1052.27i			1.18233i
$891$	−185.966	−	193.875i	−0.208716	−	0.217593i
$892$	−1296.13			−1.45306
$893$			463.472i			0.519006i
$894$	292.029	+	1509.14i	0.326655	+	1.68807i
$895$	−26.3196			−0.0294073
$896$		−	12.0944i		−	0.0134982i
$897$	530.549	−	102.665i	0.591471	−	0.114454i
$898$	−1869.94			−2.08234
$899$		−	1824.08i		−	2.02901i
$900$	−354.557	+	142.557i	−0.393952	+	0.158396i
$901$	−801.192			−0.889226
$902$		−	201.784i		−	0.223708i
$903$	0.463246	+	2.39395i	0.000513008	+	0.00265110i
$904$	2607.06			2.88392
$905$			25.5740i			0.0282586i
$906$	−152.831	+	29.5739i	−0.168688	+	0.0326423i
$907$	−224.008			−0.246977			−0.123488	−	0.992346i	$-0.539408\pi$
$907$	−224.008			−0.246977			−0.123488	+	0.992346i	$0.539408\pi$
$908$		−	127.983i		−	0.140950i
$909$	−131.681	−	327.509i	−0.144864	−	0.360295i
$910$	−8.07578			−0.00887448
$911$			522.340i			0.573370i	0.958025	+	0.286685i	$0.0925533\pi$
$911$			522.340i			0.573370i	−0.958025	+	0.286685i	$0.907447\pi$
$912$	212.674	+	1099.05i	0.233195	+	1.20510i
$913$	101.841			0.111545
$914$		−	3088.57i		−	3.37918i
$915$	298.615	−	57.7842i	0.326355	−	0.0631521i
$916$	633.452			0.691541
$917$			5.93030i			0.00646706i
$918$	−869.035	−	1345.62i	−0.946661	−	1.46582i
$919$	−840.034			−0.914074			−0.457037	−	0.889448i	$-0.651089\pi$
$919$	−840.034			−0.914074			−0.457037	+	0.889448i	$0.651089\pi$
$920$			403.277i			0.438345i
$921$	−264.667	−	1367.74i	−0.287369	−	1.48506i
$922$	609.905			0.661503
$923$		−	1717.73i		−	1.86103i
$924$	5.34564	−	1.03442i	0.00578532	−	0.00111950i
$925$	342.205			0.369952
$926$			1693.83i			1.82919i
$927$	−1683.54	+	676.899i	−1.81611	+	0.730204i
$928$	−559.100			−0.602478
$929$			673.974i			0.725483i	0.931890	+	0.362742i	$0.118159\pi$
$929$			673.974i			0.725483i	−0.931890	+	0.362742i	$0.881841\pi$
$930$	217.039	+	1121.61i	0.233376	+	1.20603i
$931$	825.516			0.886698
$932$		−	105.884i		−	0.113610i
$933$	688.458	−	133.222i	0.737897	−	0.142788i
$934$	−2473.02			−2.64777
$935$			124.486i			0.133141i
$936$	−845.274	−	2102.31i	−0.903071	−	2.24605i
$937$	−690.456			−0.736879			−0.368440	−	0.929652i	$-0.620108\pi$
$937$	−690.456			−0.736879			−0.368440	+	0.929652i	$0.620108\pi$
$938$		−	21.9043i		−	0.0233521i
$939$	−289.843	−	1497.84i	−0.308672	−	1.59515i
$940$	522.342			0.555683
$941$			1818.31i			1.93232i	0.257943	+	0.966160i	$0.416955\pi$
$941$			1818.31i			1.93232i	−0.257943	+	0.966160i	$0.583045\pi$
$942$	−406.682	+	78.6959i	−0.431722	+	0.0835413i
$943$	−195.538			−0.207357
$944$			6.56950i			0.00695922i
$945$	3.26815	−	2.11065i	0.00345836	−	0.00223349i
$946$	147.856			0.156295
$947$		−	530.793i		−	0.560499i	−0.959927	−	0.280250i	$-0.909583\pi$
$947$		−	530.793i		−	0.560499i	0.959927	−	0.280250i	$-0.0904173\pi$
$948$	−51.0391	−	263.758i	−0.0538387	−	0.278226i
$949$	1631.85			1.71954
$950$		−	297.751i		−	0.313422i
$951$	87.5392	−	16.9395i	0.0920496	−	0.0178123i
$952$	17.1733			0.0180392
$953$		−	1296.07i		−	1.35999i	−0.733216	−	0.679995i	$-0.761982\pi$
$953$		−	1296.07i		−	1.35999i	0.733216	−	0.679995i	$-0.238018\pi$
$954$	1408.69	−	566.393i	1.47662	−	0.593703i
$955$	761.511			0.797393
$956$		−	2537.91i		−	2.65472i
$957$	71.5609	+	369.810i	0.0747763	+	0.386426i
$958$	1148.46			1.19882
$959$			4.30777i			0.00449194i
$960$	−239.654	+	46.3747i	−0.249639	+	0.0483070i
$961$	1360.68			1.41590
$962$			3835.88i			3.98740i
$963$	−644.946	−	1604.06i	−0.669726	−	1.66569i
$964$	1365.56			1.41656
$965$		−	1.07854i		−	0.00111765i
$966$	−1.47455	−	7.62015i	−0.00152645	−	0.00788835i
$967$	−1511.16			−1.56273			−0.781367	−	0.624072i	$-0.785477\pi$
$967$	−1511.16			−1.56273			−0.781367	+	0.624072i	$0.785477\pi$
$968$		−	174.645i		−	0.180418i
$969$	833.001	−	161.192i	0.859650	−	0.166349i
$970$	−697.466			−0.719038
$971$			60.9018i			0.0627207i	0.999508	+	0.0313604i	$0.00998395\pi$
$971$			60.9018i			0.0627207i	−0.999508	+	0.0313604i	$0.990016\pi$
$972$	1685.38	+	1190.72i	1.73393	+	1.22502i
$973$	−14.0836			−0.0144744
$974$		−	823.949i		−	0.845943i
$975$	45.1894	+	233.528i	0.0463481	+	0.239516i
$976$	−1004.15			−1.02884
$977$			1075.50i			1.10081i	0.834896	+	0.550407i	$0.185528\pi$
$977$			1075.50i			1.10081i	−0.834896	+	0.550407i	$0.814472\pi$
$978$	1011.02	−	195.639i	1.03376	−	0.200040i
$979$	−441.592			−0.451064
$980$		−	930.373i		−	0.949360i
$981$	−1147.62	+	461.422i	−1.16984	+	0.470359i
$982$	1112.93			1.13333
$983$		−	601.095i		−	0.611490i	−0.952113	−	0.305745i	$-0.901095\pi$
$983$		−	601.095i		−	0.611490i	0.952113	−	0.305745i	$-0.0989055\pi$
$984$	155.766	+	804.962i	0.158299	+	0.818051i
$985$	386.392			0.392276
$986$			2245.96i			2.27785i
$987$	−5.22093	+	1.01029i	−0.00528969	+	0.00102359i
$988$	2268.87			2.29643
$989$		−	143.278i		−	0.144872i
$990$	−88.0041	−	218.878i	−0.0888930	−	0.221088i
$991$	−244.312			−0.246531			−0.123265	−	0.992374i	$-0.539337\pi$
$991$	−244.312			−0.246531			−0.123265	+	0.992374i	$0.539337\pi$
$992$		−	711.617i		−	0.717356i
$993$	−152.878	−	790.035i	−0.153955	−	0.795605i
$994$	−24.6714			−0.0248203
$995$		−	301.211i		−	0.302724i
$996$	−768.029	+	148.619i	−0.771113	+	0.149216i
$997$	19.1901			0.0192478			0.00962391	−	0.999954i	$-0.496937\pi$
$997$	19.1901			0.0192478			0.00962391	+	0.999954i	$0.496937\pi$
$998$		−	2379.89i		−	2.38466i
$999$	−1002.53	−	1552.32i	−1.00353	−	1.55388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.3.e.a.56.3	✓	28
3.2	odd	2	inner	165.3.e.a.56.26	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.3.e.a.56.3	✓	28	1.1	even	1	trivial
165.3.e.a.56.26	yes	28	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.53441i q^{2} +(-0.569949 - 2.94536i) q^{3} -8.49206 q^{4} -2.23607i q^{5} +(-10.4101 + 2.01443i) q^{6} +0.0644394 q^{7} +15.8768i q^{8} +(-8.35032 + 3.35741i) q^{9} +O(q^{10})\)	\(q-3.53441i q^{2} +(-0.569949 - 2.94536i) q^{3} -8.49206 q^{4} -2.23607i q^{5} +(-10.4101 + 2.01443i) q^{6} +0.0644394 q^{7} +15.8768i q^{8} +(-8.35032 + 3.35741i) q^{9} -7.90318 q^{10} -3.31662i q^{11} +(4.84004 + 25.0122i) q^{12} +15.8574 q^{13} -0.227755i q^{14} +(-6.58603 + 1.27444i) q^{15} +22.1468 q^{16} -16.7857i q^{17} +(11.8665 + 29.5134i) q^{18} -16.8487 q^{19} +18.9888i q^{20} +(-0.0367272 - 0.189797i) q^{21} -11.7223 q^{22} +11.3594i q^{23} +(46.7629 - 9.04895i) q^{24} -5.00000 q^{25} -56.0464i q^{26} +(14.6480 + 22.6812i) q^{27} -0.547223 q^{28} -37.8568i q^{29} +(4.50441 + 23.2777i) q^{30} +48.1838 q^{31} -14.7688i q^{32} +(-9.76866 + 1.89031i) q^{33} -59.3277 q^{34} -0.144091i q^{35} +(70.9114 - 28.5113i) q^{36} -68.4411 q^{37} +59.5502i q^{38} +(-9.03788 - 46.7057i) q^{39} +35.5015 q^{40} +17.2137i q^{41} +(-0.670822 + 0.129809i) q^{42} -12.6132 q^{43} +28.1650i q^{44} +(7.50740 + 18.6719i) q^{45} +40.1489 q^{46} -27.5079i q^{47} +(-12.6225 - 65.2304i) q^{48} -48.9958 q^{49} +17.6721i q^{50} +(-49.4401 + 9.56702i) q^{51} -134.662 q^{52} -47.7305i q^{53} +(80.1645 - 51.7722i) q^{54} -7.41620 q^{55} +1.02309i q^{56} +(9.60290 + 49.6255i) q^{57} -133.801 q^{58} +0.296634i q^{59} +(55.9289 - 10.8227i) q^{60} -45.3407 q^{61} -170.301i q^{62} +(-0.538089 + 0.216350i) q^{63} +36.3882 q^{64} -35.4581i q^{65} +(6.68112 + 34.5265i) q^{66} +96.1746 q^{67} +142.546i q^{68} +(33.4576 - 6.47429i) q^{69} -0.509276 q^{70} -108.324i q^{71} +(-53.3049 - 132.576i) q^{72} +102.908 q^{73} +241.899i q^{74} +(2.84974 + 14.7268i) q^{75} +143.080 q^{76} -0.213721i q^{77} +(-165.077 + 31.9436i) q^{78} -10.5452 q^{79} -49.5218i q^{80} +(58.4556 - 56.0709i) q^{81} +60.8403 q^{82} +30.7062i q^{83} +(0.311889 + 1.61177i) q^{84} -37.5341 q^{85} +44.5801i q^{86} +(-111.502 + 21.5764i) q^{87} +52.6573 q^{88} -133.145i q^{89} +(65.9941 - 26.5342i) q^{90} +1.02184 q^{91} -96.4649i q^{92} +(-27.4623 - 141.919i) q^{93} -97.2242 q^{94} +37.6748i q^{95} +(-43.4995 + 8.41747i) q^{96} +88.2514 q^{97} +173.171i q^{98} +(11.1353 + 27.6949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9}+O(q^{10}) \) 28 * q - 60 * q^4 - 4 * q^6 + 24 * q^7 - 16 * q^9	\( 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9} - 20 q^{10} + 40 q^{12} - 64 q^{13} + 172 q^{16} + 16 q^{18} + 56 q^{19} + 56 q^{21} - 140 q^{24} - 140 q^{25} - 96 q^{27} - 128 q^{28} - 40 q^{30} + 80 q^{31} - 32 q^{34} + 208 q^{36} + 72 q^{37} + 232 q^{39} - 60 q^{40} + 224 q^{42} - 360 q^{43} - 80 q^{45} + 264 q^{46} - 456 q^{48} + 332 q^{49} - 232 q^{51} + 488 q^{52} + 36 q^{54} - 16 q^{57} - 408 q^{58} - 360 q^{61} - 32 q^{63} - 300 q^{64} + 220 q^{66} - 16 q^{67} + 384 q^{69} + 240 q^{70} - 120 q^{72} + 464 q^{73} - 152 q^{76} + 16 q^{78} + 136 q^{79} + 48 q^{81} - 840 q^{82} - 392 q^{84} + 160 q^{85} + 32 q^{87} + 180 q^{90} - 32 q^{91} - 96 q^{93} + 520 q^{94} + 44 q^{96} - 136 q^{97}+O(q^{100}) \) 28 * q - 60 * q^4 - 4 * q^6 + 24 * q^7 - 16 * q^9 - 20 * q^10 + 40 * q^12 - 64 * q^13 + 172 * q^16 + 16 * q^18 + 56 * q^19 + 56 * q^21 - 140 * q^24 - 140 * q^25 - 96 * q^27 - 128 * q^28 - 40 * q^30 + 80 * q^31 - 32 * q^34 + 208 * q^36 + 72 * q^37 + 232 * q^39 - 60 * q^40 + 224 * q^42 - 360 * q^43 - 80 * q^45 + 264 * q^46 - 456 * q^48 + 332 * q^49 - 232 * q^51 + 488 * q^52 + 36 * q^54 - 16 * q^57 - 408 * q^58 - 360 * q^61 - 32 * q^63 - 300 * q^64 + 220 * q^66 - 16 * q^67 + 384 * q^69 + 240 * q^70 - 120 * q^72 + 464 * q^73 - 152 * q^76 + 16 * q^78 + 136 * q^79 + 48 * q^81 - 840 * q^82 - 392 * q^84 + 160 * q^85 + 32 * q^87 + 180 * q^90 - 32 * q^91 - 96 * q^93 + 520 * q^94 + 44 * q^96 - 136 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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