LMFDB - Embedded newform 462.4.i.g.67.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,4,Mod(67,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("462.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	462.i (of order $3$, degree $2$, 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:	$27.2588824227$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 409 x^{10} - 1168 x^{9} + 132481 x^{8} - 260920 x^{7} + 13887112 x^{6} + 2274848 x^{5} + \cdots + 118041719184 $ x^12 + 409x^10 - 1168x^9 + 132481x^8 - 260920x^7 + 13887112x^6 + 2274848x^5 + 1083404428x^4 - 366535104x^3 + 12443125696x^2 + 7580572608x + 118041719184
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.6
Root			$-9.17891 - 15.8983i$ of defining polynomial
Character	$\chi$	$=$	462.67
Dual form			462.4.i.g.331.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.17891 + 15.8983i) q^{5} +6.00000 q^{6} +(-16.2056 - 8.96536i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.17891 + 15.8983i) q^{5} +6.00000 q^{6} +(-16.2056 - 8.96536i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(18.3578 - 31.7967i) q^{10} +(5.50000 - 9.52628i) q^{11} +(-6.00000 - 10.3923i) q^{12} -67.6178 q^{13} +(0.677163 + 37.0343i) q^{14} -55.0735 q^{15} +(-8.00000 - 13.8564i) q^{16} +(63.1695 - 109.413i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-48.2421 - 83.5578i) q^{19} -73.4313 q^{20} +(47.6011 - 28.6554i) q^{21} -22.0000 q^{22} +(22.4471 + 38.8796i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-106.005 + 183.606i) q^{25} +(67.6178 + 117.117i) q^{26} +27.0000 q^{27} +(63.4682 - 38.2072i) q^{28} +71.5903 q^{29} +(55.0735 + 95.3900i) q^{30} +(60.2676 - 104.387i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(16.5000 + 28.5788i) q^{33} -252.678 q^{34} +(-6.21562 - 339.935i) q^{35} +36.0000 q^{36} +(25.1768 + 43.6075i) q^{37} +(-96.4842 + 167.116i) q^{38} +(101.427 - 175.676i) q^{39} +(73.4313 + 127.187i) q^{40} +223.934 q^{41} +(-97.2338 - 53.7922i) q^{42} +309.673 q^{43} +(22.0000 + 38.1051i) q^{44} +(82.6102 - 143.085i) q^{45} +(44.8943 - 77.7592i) q^{46} +(208.750 + 361.565i) q^{47} +48.0000 q^{48} +(182.245 + 290.579i) q^{49} +424.019 q^{50} +(189.508 + 328.238i) q^{51} +(135.236 - 234.235i) q^{52} +(32.2650 - 55.8847i) q^{53} +(-27.0000 - 46.7654i) q^{54} +201.936 q^{55} +(-129.645 - 71.7229i) q^{56} +289.453 q^{57} +(-71.5903 - 123.998i) q^{58} +(149.664 - 259.226i) q^{59} +(110.147 - 190.780i) q^{60} +(-14.4886 - 25.0950i) q^{61} -241.070 q^{62} +(3.04723 + 166.654i) q^{63} +64.0000 q^{64} +(-620.658 - 1075.01i) q^{65} +(33.0000 - 57.1577i) q^{66} +(524.421 - 908.323i) q^{67} +(252.678 + 437.651i) q^{68} -134.683 q^{69} +(-582.569 + 350.701i) q^{70} -655.955 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-218.917 + 379.175i) q^{73} +(50.3536 - 87.2150i) q^{74} +(-318.014 - 550.817i) q^{75} +385.937 q^{76} +(-174.537 + 105.070i) q^{77} -405.707 q^{78} +(-683.459 - 1183.79i) q^{79} +(146.863 - 254.373i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-223.934 - 387.866i) q^{82} -481.837 q^{83} +(4.06298 + 222.206i) q^{84} +2319.31 q^{85} +(-309.673 - 536.369i) q^{86} +(-107.386 + 185.997i) q^{87} +(44.0000 - 76.2102i) q^{88} +(-169.305 - 293.244i) q^{89} -330.441 q^{90} +(1095.79 + 606.218i) q^{91} -179.577 q^{92} +(180.803 + 313.160i) q^{93} +(417.499 - 723.130i) q^{94} +(885.620 - 1533.94i) q^{95} +(-48.0000 - 83.1384i) q^{96} +396.192 q^{97} +(321.052 - 606.235i) q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 18 q^{3} - 24 q^{4} + 72 q^{6} - 8 q^{7} + 96 q^{8} - 54 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 18 * q^3 - 24 * q^4 + 72 * q^6 - 8 * q^7 + 96 * q^8 - 54 * q^9	\( 12 q - 12 q^{2} - 18 q^{3} - 24 q^{4} + 72 q^{6} - 8 q^{7} + 96 q^{8} - 54 q^{9} + 66 q^{11} - 72 q^{12} + 48 q^{13} - 16 q^{14} - 96 q^{16} + 2 q^{17} - 108 q^{18} - 120 q^{19} + 48 q^{21} - 264 q^{22} + 36 q^{23} - 144 q^{24} - 68 q^{25} - 48 q^{26} + 324 q^{27} + 64 q^{28} + 632 q^{29} - 392 q^{31} - 192 q^{32} + 198 q^{33} - 8 q^{34} - 318 q^{35} + 432 q^{36} - 348 q^{37} - 240 q^{38} - 72 q^{39} + 388 q^{41} - 48 q^{42} + 1360 q^{43} + 264 q^{44} + 72 q^{46} - 68 q^{47} + 576 q^{48} - 546 q^{49} + 272 q^{50} + 6 q^{51} - 96 q^{52} - 400 q^{53} - 324 q^{54} - 64 q^{56} + 720 q^{57} - 632 q^{58} - 340 q^{59} - 232 q^{61} + 1568 q^{62} - 72 q^{63} + 768 q^{64} - 1428 q^{65} + 396 q^{66} + 362 q^{67} + 8 q^{68} - 216 q^{69} - 1152 q^{70} - 40 q^{71} - 432 q^{72} - 1156 q^{73} - 696 q^{74} - 204 q^{75} + 960 q^{76} - 176 q^{77} + 288 q^{78} - 3336 q^{79} - 486 q^{81} - 388 q^{82} + 668 q^{83} - 96 q^{84} + 8000 q^{85} - 1360 q^{86} - 948 q^{87} + 528 q^{88} - 16 q^{89} + 1796 q^{91} - 288 q^{92} - 1176 q^{93} - 136 q^{94} - 404 q^{95} - 576 q^{96} - 1092 q^{97} + 768 q^{98} - 1188 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 18 * q^3 - 24 * q^4 + 72 * q^6 - 8 * q^7 + 96 * q^8 - 54 * q^9 + 66 * q^11 - 72 * q^12 + 48 * q^13 - 16 * q^14 - 96 * q^16 + 2 * q^17 - 108 * q^18 - 120 * q^19 + 48 * q^21 - 264 * q^22 + 36 * q^23 - 144 * q^24 - 68 * q^25 - 48 * q^26 + 324 * q^27 + 64 * q^28 + 632 * q^29 - 392 * q^31 - 192 * q^32 + 198 * q^33 - 8 * q^34 - 318 * q^35 + 432 * q^36 - 348 * q^37 - 240 * q^38 - 72 * q^39 + 388 * q^41 - 48 * q^42 + 1360 * q^43 + 264 * q^44 + 72 * q^46 - 68 * q^47 + 576 * q^48 - 546 * q^49 + 272 * q^50 + 6 * q^51 - 96 * q^52 - 400 * q^53 - 324 * q^54 - 64 * q^56 + 720 * q^57 - 632 * q^58 - 340 * q^59 - 232 * q^61 + 1568 * q^62 - 72 * q^63 + 768 * q^64 - 1428 * q^65 + 396 * q^66 + 362 * q^67 + 8 * q^68 - 216 * q^69 - 1152 * q^70 - 40 * q^71 - 432 * q^72 - 1156 * q^73 - 696 * q^74 - 204 * q^75 + 960 * q^76 - 176 * q^77 + 288 * q^78 - 3336 * q^79 - 486 * q^81 - 388 * q^82 + 668 * q^83 - 96 * q^84 + 8000 * q^85 - 1360 * q^86 - 948 * q^87 + 528 * q^88 - 16 * q^89 + 1796 * q^91 - 288 * q^92 - 1176 * q^93 - 136 * q^94 - 404 * q^95 - 576 * q^96 - 1092 * q^97 + 768 * q^98 - 1188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	9.17891	+	15.8983i	0.820987	+	1.42199i	0.904948	+	0.425522i	$0.139909\pi$
$5$	9.17891	+	15.8983i	0.820987	+	1.42199i	−0.0839614	+	0.996469i	$0.526757\pi$
$6$	6.00000			0.408248
$7$	−16.2056	−	8.96536i	−0.875022	−	0.484084i
$7$	−16.2056	−	8.96536i	−0.875022	−	0.484084i
$8$	8.00000			0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	18.3578	−	31.7967i	0.580525	−	1.00550i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	−67.6178			−1.44260			−0.721300	−	0.692622i	$-0.756455\pi$
$13$	−67.6178			−1.44260			−0.721300	+	0.692622i	$0.756455\pi$
$14$	0.677163	+	37.0343i	0.0129271	+	0.706989i
$15$	−55.0735			−0.947994
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	63.1695	−	109.413i	0.901226	−	1.56097i	0.0753216	−	0.997159i	$-0.476002\pi$
$17$	63.1695	−	109.413i	0.901226	−	1.56097i	0.825905	−	0.563810i	$-0.190665\pi$
$18$	−9.00000	+	15.5885i	−0.117851	+	0.204124i
$19$	−48.2421	−	83.5578i	−0.582500	−	1.00892i	−0.995182	−	0.0980443i	$-0.968741\pi$
$19$	−48.2421	−	83.5578i	−0.582500	−	1.00892i	0.412682	−	0.910875i	$-0.364592\pi$
$20$	−73.4313			−0.820987
$21$	47.6011	−	28.6554i	0.494639	−	0.297768i
$22$	−22.0000			−0.213201
$23$	22.4471	+	38.8796i	0.203502	+	0.352476i	0.949655	−	0.313299i	$-0.101434\pi$
$23$	22.4471	+	38.8796i	0.203502	+	0.352476i	−0.746152	+	0.665775i	$0.768101\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−106.005	+	183.606i	−0.848039	+	1.46885i
$26$	67.6178	+	117.117i	0.510036	+	0.883409i
$27$	27.0000			0.192450
$28$	63.4682	−	38.2072i	0.428370	−	0.257874i
$29$	71.5903			0.458414			0.229207	−	0.973378i	$-0.426387\pi$
$29$	71.5903			0.458414			0.229207	+	0.973378i	$0.426387\pi$
$30$	55.0735	+	95.3900i	0.335166	+	0.580525i
$31$	60.2676	−	104.387i	0.349174	−	0.604786i	−0.636929	−	0.770922i	$-0.719796\pi$
$31$	60.2676	−	104.387i	0.349174	−	0.604786i	0.986103	+	0.166136i	$0.0531290\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	16.5000	+	28.5788i	0.0870388	+	0.150756i
$34$	−252.678			−1.27453
$35$	−6.21562	−	339.935i	−0.0300180	−	1.64170i
$36$	36.0000			0.166667
$37$	25.1768	+	43.6075i	0.111866	+	0.193757i	0.916523	−	0.399983i	$-0.130984\pi$
$37$	25.1768	+	43.6075i	0.111866	+	0.193757i	−0.804657	+	0.593740i	$0.797651\pi$
$38$	−96.4842	+	167.116i	−0.411890	+	0.713414i
$39$	101.427	−	175.676i	0.416443	−	0.721300i
$40$	73.4313	+	127.187i	0.290263	+	0.502750i
$41$	223.934			0.852992			0.426496	−	0.904489i	$-0.359748\pi$
$41$	223.934			0.852992			0.426496	+	0.904489i	$0.359748\pi$
$42$	−97.2338	−	53.7922i	−0.357226	−	0.197626i
$43$	309.673			1.09825			0.549124	−	0.835741i	$-0.314961\pi$
$43$	309.673			1.09825			0.549124	+	0.835741i	$0.314961\pi$
$44$	22.0000	+	38.1051i	0.0753778	+	0.130558i
$45$	82.6102	−	143.085i	0.273662	−	0.473997i
$46$	44.8943	−	77.7592i	0.143898	−	0.249238i
$47$	208.750	+	361.565i	0.647857	+	1.12212i	0.983634	+	0.180179i	$0.0576679\pi$
$47$	208.750	+	361.565i	0.647857	+	1.12212i	−0.335777	+	0.941942i	$0.608999\pi$
$48$	48.0000			0.144338
$49$	182.245	+	290.579i	0.531325	+	0.847168i
$50$	424.019			1.19931
$51$	189.508	+	328.238i	0.520323	+	0.901226i
$52$	135.236	−	234.235i	0.360650	−	0.624664i
$53$	32.2650	−	55.8847i	0.0836216	−	0.144837i	−0.821181	−	0.570667i	$-0.806685\pi$
$53$	32.2650	−	55.8847i	0.0836216	−	0.144837i	0.904803	+	0.425830i	$0.140018\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	201.936			0.495074
$56$	−129.645	−	71.7229i	−0.309367	−	0.171150i
$57$	289.453			0.672613
$58$	−71.5903	−	123.998i	−0.162074	−	0.280720i
$59$	149.664	−	259.226i	0.330247	−	0.572005i	−0.652313	−	0.757950i	$-0.726201\pi$
$59$	149.664	−	259.226i	0.330247	−	0.572005i	0.982560	+	0.185945i	$0.0595345\pi$
$60$	110.147	−	190.780i	0.236998	−	0.410493i
$61$	−14.4886	−	25.0950i	−0.0304111	−	0.0526736i	0.850419	−	0.526106i	$-0.176348\pi$
$61$	−14.4886	−	25.0950i	−0.0304111	−	0.0526736i	−0.880830	+	0.473432i	$0.843015\pi$
$62$	−241.070			−0.493806
$63$	3.04723	+	166.654i	0.00609389	+	0.333278i
$64$	64.0000			0.125000
$65$	−620.658	−	1075.01i	−1.18436	−	2.05136i
$66$	33.0000	−	57.1577i	0.0615457	−	0.106600i
$67$	524.421	−	908.323i	0.956242	−	1.65626i	0.224740	−	0.974419i	$-0.427847\pi$
$67$	524.421	−	908.323i	0.956242	−	1.65626i	0.731501	−	0.681840i	$-0.238820\pi$
$68$	252.678	+	437.651i	0.450613	+	0.780485i
$69$	−134.683			−0.234984
$70$	−582.569	+	350.701i	−0.994718	+	0.598811i
$71$	−655.955			−1.09644			−0.548222	−	0.836333i	$-0.684695\pi$
$71$	−655.955			−1.09644			−0.548222	+	0.836333i	$0.684695\pi$
$72$	−36.0000	−	62.3538i	−0.0589256	−	0.102062i
$73$	−218.917	+	379.175i	−0.350990	+	0.607933i	−0.986423	−	0.164223i	$-0.947488\pi$
$73$	−218.917	+	379.175i	−0.350990	+	0.607933i	0.635433	+	0.772156i	$0.280822\pi$
$74$	50.3536	−	87.2150i	0.0791012	−	0.137007i
$75$	−318.014	−	550.817i	−0.489615	−	0.848039i
$76$	385.937			0.582500
$77$	−174.537	+	105.070i	−0.258317	+	0.155504i
$78$	−405.707			−0.588939
$79$	−683.459	−	1183.79i	−0.973357	−	1.68590i	−0.685254	−	0.728304i	$-0.740309\pi$
$79$	−683.459	−	1183.79i	−0.973357	−	1.68590i	−0.288103	−	0.957600i	$-0.593024\pi$
$80$	146.863	−	254.373i	0.205247	−	0.355498i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−223.934	−	387.866i	−0.301578	−	0.522349i
$83$	−481.837			−0.637210			−0.318605	−	0.947888i	$-0.603214\pi$
$83$	−481.837			−0.637210			−0.318605	+	0.947888i	$0.603214\pi$
$84$	4.06298	+	222.206i	0.00527747	+	0.288627i
$85$	2319.31			2.95958
$86$	−309.673	−	536.369i	−0.388289	−	0.672537i
$87$	−107.386	+	185.997i	−0.132333	+	0.229207i
$88$	44.0000	−	76.2102i	0.0533002	−	0.0923186i
$89$	−169.305	−	293.244i	−0.201643	−	0.349256i	0.747415	−	0.664358i	$-0.231295\pi$
$89$	−169.305	−	293.244i	−0.201643	−	0.349256i	−0.949058	+	0.315101i	$0.897961\pi$
$90$	−330.441			−0.387017
$91$	1095.79	+	606.218i	1.26231	+	0.698340i
$92$	−179.577			−0.203502
$93$	180.803	+	313.160i	0.201595	+	0.349174i
$94$	417.499	−	723.130i	0.458104	−	0.793459i
$95$	885.620	−	1533.94i	0.956449	−	1.65662i
$96$	−48.0000	−	83.1384i	−0.0510310	−	0.0883883i
$97$	396.192			0.414713			0.207357	−	0.978265i	$-0.433514\pi$
$97$	396.192			0.414713			0.207357	+	0.978265i	$0.433514\pi$
$98$	321.052	−	606.235i	0.330930	−	0.624888i
$99$	−99.0000			−0.100504
$100$	−424.019	−	734.423i	−0.424019	−	0.734423i
$101$	−320.687	+	555.447i	−0.315936	+	0.547218i	−0.979636	−	0.200781i	$-0.935652\pi$
$101$	−320.687	+	555.447i	−0.315936	+	0.547218i	0.663700	+	0.747999i	$0.268985\pi$
$102$	379.017	−	656.476i	0.367924	−	0.637263i
$103$	−243.590	−	421.911i	−0.233026	−	0.403613i	0.725671	−	0.688042i	$-0.241529\pi$
$103$	−243.590	−	421.911i	−0.233026	−	0.403613i	−0.958697	+	0.284429i	$0.908196\pi$
$104$	−540.943			−0.510036
$105$	892.500	+	493.754i	0.829515	+	0.458909i
$106$	−129.060			−0.118259
$107$	−893.340	−	1547.31i	−0.807125	−	1.39798i	−0.914847	−	0.403801i	$-0.867689\pi$
$107$	−893.340	−	1547.31i	−0.807125	−	1.39798i	0.107722	−	0.994181i	$-0.465644\pi$
$108$	−54.0000	+	93.5307i	−0.0481125	+	0.0833333i
$109$	−358.179	+	620.384i	−0.314746	+	0.545156i	−0.979383	−	0.202010i	$-0.935253\pi$
$109$	−358.179	+	620.384i	−0.314746	+	0.545156i	0.664638	+	0.747166i	$0.268586\pi$
$110$	−201.936	−	349.763i	−0.175035	−	0.303169i
$111$	−151.061			−0.129172
$112$	5.41730	+	296.275i	0.00457042	+	0.249958i
$113$	1340.44			1.11591			0.557955	−	0.829871i	$-0.311586\pi$
$113$	1340.44			1.11591			0.557955	+	0.829871i	$0.311586\pi$
$114$	−289.453	−	501.347i	−0.237805	−	0.411890i
$115$	−412.081	+	713.745i	−0.334145	+	0.578757i
$116$	−143.181	+	247.996i	−0.114603	+	0.198499i
$117$	304.280	+	527.029i	0.240433	+	0.416443i
$118$	−598.656			−0.467040
$119$	−2004.62	+	1206.76i	−1.54423	+	0.929613i
$120$	−440.588			−0.335166
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	−28.9773	+	50.1901i	−0.0215039	+	0.0372459i
$123$	−335.902	+	581.799i	−0.246238	+	0.426496i
$124$	241.070	+	417.546i	0.174587	+	0.302393i
$125$	−1597.31			−1.14294
$126$	285.607	−	171.932i	0.201936	−	0.121563i
$127$	2608.25			1.82240			0.911199	−	0.411967i	$-0.135158\pi$
$127$	2608.25			1.82240			0.911199	+	0.411967i	$0.135158\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−464.509	+	804.554i	−0.317037	+	0.549124i
$130$	−1241.32	+	2150.02i	−0.837466	+	1.45053i
$131$	−1099.18	−	1903.83i	−0.733095	−	1.26976i	−0.955554	−	0.294815i	$-0.904742\pi$
$131$	−1099.18	−	1903.83i	−0.733095	−	1.26976i	0.222459	−	0.974942i	$-0.428592\pi$
$132$	−132.000			−0.0870388
$133$	32.6678	+	1786.61i	0.0212982	+	1.16481i
$134$	−2097.68			−1.35233
$135$	247.831	+	429.255i	0.157999	+	0.273662i
$136$	505.356	−	875.302i	0.318632	−	0.551886i
$137$	415.419	−	719.526i	0.259063	−	0.448710i	−0.706928	−	0.707285i	$-0.749920\pi$
$137$	415.419	−	719.526i	0.259063	−	0.448710i	0.965991	+	0.258575i	$0.0832530\pi$
$138$	134.683	+	233.278i	0.0830795	+	0.143898i
$139$	2099.57			1.28117			0.640586	−	0.767886i	$-0.278691\pi$
$139$	2099.57			1.28117			0.640586	+	0.767886i	$0.278691\pi$
$140$	1190.00	+	658.338i	0.718381	+	0.397427i
$141$	−1252.50			−0.748081
$142$	655.955	+	1136.15i	0.387651	+	0.671432i
$143$	−371.898	+	644.146i	−0.217480	+	0.376687i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	657.121	+	1138.17i	0.376351	+	0.651860i
$146$	875.668			0.496375
$147$	−1028.31	+	37.6174i	−0.576964	+	0.0211063i
$148$	−201.414			−0.111866
$149$	−319.681	−	553.703i	−0.175767	−	0.304437i	0.764660	−	0.644434i	$-0.222907\pi$
$149$	−319.681	−	553.703i	−0.175767	−	0.304437i	−0.940426	+	0.339997i	$0.889574\pi$
$150$	−636.029	+	1101.63i	−0.346210	+	0.599654i
$151$	613.681	−	1062.93i	0.330733	−	0.572846i	−0.651923	−	0.758285i	$-0.726037\pi$
$151$	613.681	−	1062.93i	0.330733	−	0.572846i	0.982656	+	0.185439i	$0.0593708\pi$
$152$	−385.937	−	668.462i	−0.205945	−	0.356707i
$153$	−1137.05			−0.600817
$154$	356.524	+	197.238i	0.186555	+	0.103207i
$155$	2212.76			1.14667
$156$	405.707	+	702.705i	0.208221	+	0.360650i
$157$	47.0655	−	81.5198i	0.0239250	−	0.0414394i	−0.853815	−	0.520577i	$-0.825717\pi$
$157$	47.0655	−	81.5198i	0.0239250	−	0.0414394i	0.877740	+	0.479137i	$0.159050\pi$
$158$	−1366.92	+	2367.57i	−0.688267	+	1.19211i
$159$	96.7951	+	167.654i	0.0482789	+	0.0836216i
$160$	−587.450			−0.290263
$161$	−15.2004	−	831.315i	−0.00744073	−	0.406937i
$162$	162.000			0.0785674
$163$	−297.992	−	516.138i	−0.143194	−	0.248018i	0.785504	−	0.618857i	$-0.212404\pi$
$163$	−297.992	−	516.138i	−0.143194	−	0.248018i	−0.928698	+	0.370838i	$0.879070\pi$
$164$	−447.869	+	775.731i	−0.213248	+	0.369356i
$165$	−302.904	+	524.645i	−0.142915	+	0.247537i
$166$	481.837	+	834.565i	0.225288	+	0.390210i
$167$	3402.92			1.57680			0.788401	−	0.615162i	$-0.210909\pi$
$167$	3402.92			1.57680			0.788401	+	0.615162i	$0.210909\pi$
$168$	380.809	−	229.243i	0.174881	−	0.105277i
$169$	2375.17			1.08110
$170$	−2319.31	−	4017.16i	−1.04637	−	1.81236i
$171$	−434.179	+	752.020i	−0.194167	+	0.336306i
$172$	−619.346	+	1072.74i	−0.274562	+	0.475555i
$173$	1478.69	+	2561.17i	0.649844	+	1.12556i	0.983160	+	0.182747i	$0.0584990\pi$
$173$	1478.69	+	2561.17i	0.649844	+	1.12556i	−0.333316	+	0.942815i	$0.608168\pi$
$174$	429.542			0.187147
$175$	3363.97	−	2025.07i	1.45310	−	0.874750i
$176$	−176.000			−0.0753778
$177$	448.992	+	777.677i	0.190668	+	0.330247i
$178$	−338.609	+	586.488i	−0.142583	+	0.246962i
$179$	1507.88	−	2611.73i	0.629635	−	1.09056i	−0.357990	−	0.933725i	$-0.616538\pi$
$179$	1507.88	−	2611.73i	0.629635	−	1.09056i	0.987625	−	0.156834i	$-0.0501287\pi$
$180$	330.441	+	572.340i	0.136831	+	0.236998i
$181$	−4067.60			−1.67040			−0.835199	−	0.549947i	$-0.814648\pi$
$181$	−4067.60			−1.67040			−0.835199	+	0.549947i	$0.814648\pi$
$182$	−45.7883	−	2504.18i	−0.0186486	−	1.01990i
$183$	86.9318			0.0351157
$184$	179.577	+	311.037i	0.0719489	+	0.124619i
$185$	−462.191	+	800.539i	−0.183681	+	0.318145i
$186$	361.606	−	626.319i	0.142550	−	0.246903i
$187$	−694.864	−	1203.54i	−0.271730	−	0.470650i
$188$	−1670.00			−0.647857
$189$	−437.552	−	242.065i	−0.168398	−	0.0931620i
$190$	−3542.48			−1.35262
$191$	261.603	+	453.110i	0.0991044	+	0.171654i	0.911314	−	0.411712i	$-0.135069\pi$
$191$	261.603	+	453.110i	0.0991044	+	0.171654i	−0.812210	+	0.583365i	$0.801736\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	1349.78	−	2337.89i	0.503416	−	0.871942i	−0.496576	−	0.867993i	$-0.665410\pi$
$193$	1349.78	−	2337.89i	0.503416	−	0.871942i	0.999992	−	0.00394888i	$-0.00125697\pi$
$194$	−396.192	−	686.225i	−0.146623	−	0.253959i
$195$	3723.95			1.36758
$196$	−1371.08	+	50.1565i	−0.499666	+	0.0182786i
$197$	−2029.12			−0.733851			−0.366926	−	0.930250i	$-0.619590\pi$
$197$	−2029.12			−0.733851			−0.366926	+	0.930250i	$0.619590\pi$
$198$	99.0000	+	171.473i	0.0355335	+	0.0615457i
$199$	−1514.71	+	2623.56i	−0.539573	+	0.934568i	0.459354	+	0.888253i	$0.348081\pi$
$199$	−1514.71	+	2623.56i	−0.539573	+	0.934568i	−0.998927	+	0.0463145i	$0.985252\pi$
$200$	−848.039	+	1468.85i	−0.299827	+	0.519315i
$201$	1573.26	+	2724.97i	0.552086	+	0.956242i
$202$	1282.75			0.446801
$203$	−1160.17	−	641.833i	−0.401122	−	0.221911i
$204$	−1516.07			−0.520323
$205$	2055.47	+	3560.18i	0.700295	+	1.21295i
$206$	−487.180	+	843.821i	−0.164774	+	0.285397i
$207$	202.024	−	349.916i	0.0678341	−	0.117492i
$208$	540.943	+	936.940i	0.180325	+	0.312332i
$209$	−1061.33			−0.351261
$210$	−37.2937	−	2039.61i	−0.0122548	−	0.670221i
$211$	−2963.94			−0.967042			−0.483521	−	0.875333i	$-0.660642\pi$
$211$	−2963.94			−0.967042			−0.483521	+	0.875333i	$0.660642\pi$
$212$	129.060	+	223.539i	0.0418108	+	0.0724184i
$213$	983.932	−	1704.22i	0.316516	−	0.548222i
$214$	−1786.68	+	3094.62i	−0.570724	+	0.988523i
$215$	2842.46	+	4923.29i	0.901647	+	1.56170i
$216$	216.000			0.0680414
$217$	−1912.54	+	1151.33i	−0.598302	+	0.360172i
$218$	1432.71			0.445118
$219$	−656.751	−	1137.53i	−0.202644	−	0.350990i
$220$	−403.872	+	699.527i	−0.123768	+	0.214373i
$221$	−4271.38	+	7398.25i	−1.30011	+	2.25186i
$222$	151.061	+	261.645i	0.0456691	+	0.0791012i
$223$	−3784.44			−1.13643			−0.568217	−	0.822879i	$-0.692367\pi$
$223$	−3784.44			−1.13643			−0.568217	+	0.822879i	$0.692367\pi$
$224$	507.745	−	305.658i	0.151452	−	0.0911724i
$225$	1908.09			0.565359
$226$	−1340.44	−	2321.71i	−0.394534	−	0.683353i
$227$	956.961	−	1657.51i	0.279805	−	0.484637i	−0.691531	−	0.722347i	$-0.743063\pi$
$227$	956.961	−	1657.51i	0.279805	−	0.484637i	0.971336	+	0.237710i	$0.0763968\pi$
$228$	−578.905	+	1002.69i	−0.168153	+	0.291250i
$229$	−2321.88	−	4021.61i	−0.670018	−	1.16050i	−0.977899	−	0.209080i	$-0.932953\pi$
$229$	−2321.88	−	4021.61i	−0.670018	−	1.16050i	0.307881	−	0.951425i	$-0.400380\pi$
$230$	1648.32			0.472553
$231$	−11.1732	−	611.066i	−0.00318243	−	0.174049i
$232$	572.723			0.162074
$233$	−3450.52	−	5976.47i	−0.970176	−	1.68039i	−0.695015	−	0.718996i	$-0.744602\pi$
$233$	−3450.52	−	5976.47i	−0.970176	−	1.68039i	−0.275161	−	0.961398i	$-0.588731\pi$
$234$	608.560	−	1054.06i	0.170012	−	0.294470i
$235$	−3832.19	+	6637.55i	−1.06376	+	1.84249i
$236$	598.656	+	1036.90i	0.165124	+	0.286003i
$237$	4100.76			1.12394
$238$	4094.80	+	2265.35i	1.11524	+	0.616978i
$239$	955.361			0.258566			0.129283	−	0.991608i	$-0.458732\pi$
$239$	955.361			0.258566			0.129283	+	0.991608i	$0.458732\pi$
$240$	440.588	+	763.120i	0.118499	+	0.205247i
$241$	2324.19	−	4025.61i	0.621220	−	1.07598i	−0.368039	−	0.929810i	$-0.619971\pi$
$241$	2324.19	−	4025.61i	0.621220	−	1.07598i	0.989259	−	0.146174i	$-0.0466959\pi$
$242$	−121.000	+	209.578i	−0.0321412	+	0.0556702i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	115.909			0.0304111
$245$	−2946.91	+	5564.58i	−0.768454	+	1.45105i
$246$	1343.61			0.348233
$247$	3262.03	+	5649.99i	0.840315	+	1.45547i
$248$	482.141	−	835.092i	0.123452	−	0.213824i
$249$	722.755	−	1251.85i	0.183947	−	0.318605i
$250$	1597.31	+	2766.62i	0.404090	+	0.699905i
$251$	4375.91			1.10042			0.550209	−	0.835027i	$-0.314548\pi$
$251$	4375.91			1.10042			0.550209	+	0.835027i	$0.314548\pi$
$252$	−583.403	−	322.753i	−0.145837	−	0.0806807i
$253$	493.837			0.122717
$254$	−2608.25	−	4517.62i	−0.644315	−	1.11599i
$255$	−3478.96	+	6025.74i	−0.854357	+	1.47979i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1268.95	+	2197.89i	0.307997	+	0.533466i	0.977924	−	0.208961i	$-0.0670081\pi$
$257$	1268.95	+	2197.89i	0.307997	+	0.533466i	−0.669927	+	0.742427i	$0.733675\pi$
$258$	1858.04			0.448358
$259$	−17.0488	−	932.406i	−0.00409019	−	0.223694i
$260$	4965.26			1.18436
$261$	−322.157	−	557.992i	−0.0764023	−	0.132333i
$262$	−2198.35	+	3807.66i	−0.518376	+	0.897854i
$263$	2079.44	−	3601.69i	0.487542	−	0.844448i	−0.512355	−	0.858774i	$-0.671227\pi$
$263$	2079.44	−	3601.69i	0.487542	−	0.844448i	0.999897	+	0.0143255i	$0.00456011\pi$
$264$	132.000	+	228.631i	0.0307729	+	0.0533002i
$265$	1184.63			0.274609
$266$	3061.84	−	1843.20i	0.705764	−	0.424863i
$267$	1015.83			0.232838
$268$	2097.68	+	3633.29i	0.478121	+	0.828129i
$269$	16.7927	−	29.0859i	0.00380621	−	0.00659255i	−0.864116	−	0.503293i	$-0.832122\pi$
$269$	16.7927	−	29.0859i	0.00380621	−	0.00659255i	0.867922	+	0.496700i	$0.165455\pi$
$270$	495.661	−	858.510i	0.111722	−	0.193508i
$271$	−599.515	−	1038.39i	−0.134384	−	0.232759i	0.790978	−	0.611844i	$-0.209572\pi$
$271$	−599.515	−	1038.39i	−0.134384	−	0.232759i	−0.925362	+	0.379085i	$0.876239\pi$
$272$	−2021.42			−0.450613
$273$	−3218.68	+	1937.62i	−0.713566	+	0.429560i
$274$	−1661.67			−0.366370
$275$	1166.05	+	2019.66i	0.255693	+	0.442874i
$276$	269.366	−	466.555i	0.0587461	−	0.101751i
$277$	−3564.81	+	6174.44i	−0.773245	+	1.33930i	0.162531	+	0.986703i	$0.448034\pi$
$277$	−3564.81	+	6174.44i	−0.773245	+	1.33930i	−0.935776	+	0.352596i	$0.885299\pi$
$278$	−2099.57	−	3636.56i	−0.452963	−	0.784555i
$279$	−1084.82			−0.232782
$280$	−49.7249	−	2719.48i	−0.0106130	−	0.580428i
$281$	−6226.99			−1.32196			−0.660980	−	0.750403i	$-0.729859\pi$
$281$	−6226.99			−1.32196			−0.660980	+	0.750403i	$0.729859\pi$
$282$	1252.50	+	2169.39i	0.264486	+	0.458104i
$283$	−3842.56	+	6655.51i	−0.807126	+	1.39798i	0.107721	+	0.994181i	$0.465645\pi$
$283$	−3842.56	+	6655.51i	−0.807126	+	1.39798i	−0.914846	+	0.403802i	$0.867689\pi$
$284$	1311.91	−	2272.29i	0.274111	−	0.474774i
$285$	2656.86	+	4601.82i	0.552206	+	0.956449i
$286$	1487.59			0.307563
$287$	−3629.00	−	2007.65i	−0.746386	−	0.412920i
$288$	288.000			0.0589256
$289$	−5524.26	−	9568.30i	−1.12442	−	1.94755i
$290$	1314.24	−	2276.34i	0.266121	−	0.460935i
$291$	−594.288	+	1029.34i	−0.119717	+	0.207357i
$292$	−875.668	−	1516.70i	−0.175495	−	0.303966i
$293$	104.466			0.0208293			0.0104146	−	0.999946i	$-0.496685\pi$
$293$	104.466			0.0208293			0.0104146	+	0.999946i	$0.496685\pi$
$294$	1093.47	+	1743.47i	0.216913	+	0.345855i
$295$	5495.01			1.08451
$296$	201.414	+	348.860i	0.0395506	+	0.0685036i
$297$	148.500	−	257.210i	0.0290129	−	0.0502519i
$298$	−639.361	+	1107.41i	−0.124286	+	0.215269i
$299$	−1517.83	−	2628.95i	−0.293573	−	0.508483i
$300$	2544.12			0.489615
$301$	−5018.44	−	2776.33i	−0.960991	−	0.531644i
$302$	−2454.72			−0.467727
$303$	−962.062	−	1666.34i	−0.182406	−	0.315936i
$304$	−771.874	+	1336.92i	−0.145625	+	0.252230i
$305$	265.980	−	460.690i	0.0499343	−	0.0864887i
$306$	1137.05	+	1969.43i	0.212421	+	0.367924i
$307$	2238.32			0.416116			0.208058	−	0.978116i	$-0.433286\pi$
$307$	2238.32			0.416116			0.208058	+	0.978116i	$0.433286\pi$
$308$	−14.8976	−	814.755i	−0.00275607	−	0.150730i
$309$	1461.54			0.269075
$310$	−2212.76	−	3832.62i	−0.405408	−	0.702188i
$311$	−1063.23	+	1841.56i	−0.193859	+	0.335773i	−0.946526	−	0.322628i	$-0.895434\pi$
$311$	−1063.23	+	1841.56i	−0.193859	+	0.335773i	0.752667	+	0.658401i	$0.228767\pi$
$312$	811.414	−	1405.41i	0.147235	−	0.255018i
$313$	1825.47	+	3161.80i	0.329653	+	0.570976i	0.982443	−	0.186563i	$-0.0597348\pi$
$313$	1825.47	+	3161.80i	0.329653	+	0.570976i	−0.652790	+	0.757539i	$0.726401\pi$
$314$	−188.262			−0.0338351
$315$	−2621.56	+	1578.15i	−0.468915	+	0.282282i
$316$	5467.68			0.973357
$317$	−4075.96	−	7059.77i	−0.722173	−	1.25084i	−0.960127	−	0.279563i	$-0.909810\pi$
$317$	−4075.96	−	7059.77i	−0.722173	−	1.25084i	0.237955	−	0.971276i	$-0.423523\pi$
$318$	193.590	−	335.308i	0.0341384	−	0.0591294i
$319$	393.747	−	681.990i	0.0691084	−	0.119699i
$320$	587.450	+	1017.49i	0.102623	+	0.177749i
$321$	5360.04			0.931988
$322$	−1424.68	+	857.643i	−0.246566	+	0.148430i
$323$	−12189.7			−2.09986
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	7167.81	−	12415.0i	1.22338	−	2.11896i
$326$	−595.984	+	1032.28i	−0.101253	+	0.175376i
$327$	−1074.54	−	1861.15i	−0.181719	−	0.314746i
$328$	1791.47			0.301578
$329$	−141.358	−	7730.90i	−0.0236878	−	1.29550i
$330$	1211.62			0.202113
$331$	−984.754	−	1705.64i	−0.163526	−	0.283235i	0.772605	−	0.634887i	$-0.218953\pi$
$331$	−984.754	−	1705.64i	−0.163526	−	0.283235i	−0.936131	+	0.351652i	$0.885620\pi$
$332$	963.673	−	1669.13i	0.159302	−	0.275920i
$333$	226.591	−	392.467i	0.0372886	−	0.0645858i
$334$	−3402.92	−	5894.03i	−0.557483	−	0.965590i
$335$	19254.4			3.14025
$336$	−777.870	−	430.337i	−0.126298	−	0.0698715i
$337$	10182.0			1.64584			0.822920	−	0.568157i	$-0.192343\pi$
$337$	10182.0			1.64584			0.822920	+	0.568157i	$0.192343\pi$
$338$	−2375.17	−	4113.91i	−0.382225	−	0.662034i
$339$	−2010.66	+	3482.56i	−0.322136	+	0.557955i
$340$	−4638.61	+	8034.32i	−0.739895	+	1.28154i
$341$	−662.944	−	1148.25i	−0.105280	−	0.182350i
$342$	1736.72			0.274593
$343$	−348.245	−	6342.90i	−0.0548206	−	0.998496i
$344$	2477.38			0.388289
$345$	−1236.24	−	2141.23i	−0.192919	−	0.334145i
$346$	2957.39	−	5122.34i	0.459509	−	0.795893i
$347$	−3103.49	+	5375.40i	−0.480127	+	0.831605i	−0.999740	−	0.0227971i	$-0.992743\pi$
$347$	−3103.49	+	5375.40i	−0.480127	+	0.831605i	0.519613	+	0.854402i	$0.326076\pi$
$348$	−429.542	−	743.989i	−0.0661663	−	0.114603i
$349$	−10174.2			−1.56050			−0.780249	−	0.625470i	$-0.784907\pi$
$349$	−10174.2			−1.56050			−0.780249	+	0.625470i	$0.784907\pi$
$350$	−6871.50	−	3801.49i	−1.04942	−	0.580566i
$351$	−1825.68			−0.277629
$352$	176.000	+	304.841i	0.0266501	+	0.0461593i
$353$	−1078.13	+	1867.37i	−0.162558	+	0.281559i	−0.935785	−	0.352570i	$-0.885308\pi$
$353$	−1078.13	+	1867.37i	−0.162558	+	0.281559i	0.773227	+	0.634129i	$0.218641\pi$
$354$	897.984	−	1555.35i	0.134823	−	0.233520i
$355$	−6020.95	−	10428.6i	−0.900166	−	1.55913i
$356$	1354.44			0.201643
$357$	−128.328	−	7018.31i	−0.0190248	−	1.04047i
$358$	−6031.54			−0.890438
$359$	635.213	+	1100.22i	0.0933851	+	0.161748i	0.908933	−	0.416941i	$-0.136898\pi$
$359$	635.213	+	1100.22i	0.0933851	+	0.161748i	−0.815548	+	0.578689i	$0.803565\pi$
$360$	660.882	−	1144.68i	0.0967542	−	0.167583i
$361$	−1225.10	+	2121.94i	−0.178612	+	0.309365i
$362$	4067.60	+	7045.29i	0.590575	+	1.02291i
$363$	363.000			0.0524864
$364$	−4291.58	+	2583.49i	−0.617967	+	0.372010i
$365$	−8037.68			−1.15263
$366$	−86.9318	−	150.570i	−0.0124153	−	0.0215039i
$367$	3718.24	−	6440.19i	0.528857	−	0.916008i	−0.470576	−	0.882359i	$-0.655954\pi$
$367$	3718.24	−	6440.19i	0.528857	−	0.916008i	0.999434	−	0.0336487i	$-0.0107127\pi$
$368$	359.154	−	622.074i	0.0508756	−	0.0881191i
$369$	−1007.70	−	1745.40i	−0.142165	−	0.246238i
$370$	1848.76			0.259764
$371$	−1023.90	+	616.378i	−0.143284	+	0.0862555i
$372$	−1446.42			−0.201595
$373$	−3765.33	−	6521.75i	−0.522685	−	0.905317i	−0.999652	−	0.0263956i	$-0.991597\pi$
$373$	−3765.33	−	6521.75i	−0.522685	−	0.905317i	0.476966	−	0.878921i	$-0.341736\pi$
$374$	−1389.73	+	2407.08i	−0.192142	+	0.332800i
$375$	2395.96	−	4149.93i	0.329938	−	0.571470i
$376$	1670.00	+	2892.52i	0.229052	+	0.396730i
$377$	−4840.78			−0.661308
$378$	18.2834	+	999.927i	0.00248782	+	0.136060i
$379$	14616.7			1.98103			0.990514	−	0.137411i	$-0.0438781\pi$
$379$	14616.7			1.98103			0.990514	+	0.137411i	$0.0438781\pi$
$380$	3542.48	+	6135.76i	0.478225	+	0.828309i
$381$	−3912.37	+	6776.42i	−0.526081	+	0.911199i
$382$	523.206	−	906.220i	0.0700774	−	0.121378i
$383$	−3125.66	−	5413.80i	−0.417007	−	0.722278i	0.578630	−	0.815590i	$-0.303588\pi$
$383$	−3125.66	−	5413.80i	−0.417007	−	0.722278i	−0.995637	+	0.0933127i	$0.970254\pi$
$384$	384.000			0.0510310
$385$	−3272.50	−	1810.43i	−0.433200	−	0.239657i
$386$	−5399.12			−0.711938
$387$	−1393.53	−	2413.66i	−0.183041	−	0.317037i
$388$	−792.384	+	1372.45i	−0.103678	+	0.179576i
$389$	1431.86	−	2480.05i	0.186627	−	0.323248i	−0.757496	−	0.652839i	$-0.773578\pi$
$389$	1431.86	−	2480.05i	0.186627	−	0.323248i	0.944124	+	0.329592i	$0.106911\pi$
$390$	−3723.95	−	6450.07i	−0.483511	−	0.837466i
$391$	5671.90			0.733606
$392$	1457.96	+	2324.63i	0.187852	+	0.299519i
$393$	6595.05			0.846505
$394$	2029.12	+	3514.54i	0.259456	+	0.449390i
$395$	12546.8	−	21731.7i	1.59823	−	2.76821i
$396$	198.000	−	342.946i	0.0251259	−	0.0435194i
$397$	2465.81	+	4270.91i	0.311726	+	0.539926i	0.978736	−	0.205123i	$-0.0657594\pi$
$397$	2465.81	+	4270.91i	0.311726	+	0.539926i	−0.667010	+	0.745049i	$0.732426\pi$
$398$	6058.84			0.763071
$399$	−4690.76	−	2595.05i	−0.588551	−	0.325601i
$400$	3392.15			0.424019
$401$	6348.55	+	10996.0i	0.790602	+	1.36936i	0.925595	+	0.378516i	$0.123565\pi$
$401$	6348.55	+	10996.0i	0.790602	+	1.36936i	−0.134993	+	0.990847i	$0.543101\pi$
$402$	3146.52	−	5449.94i	0.390384	−	0.676165i
$403$	−4075.16	+	7058.39i	−0.503718	+	0.872465i
$404$	−1282.75	−	2221.79i	−0.157968	−	0.273609i
$405$	−1486.98			−0.182442
$406$	48.4783	+	2651.30i	0.00592596	+	0.324093i
$407$	553.890			0.0674577
$408$	1516.07	+	2625.90i	0.183962	+	0.318632i
$409$	−7671.47	+	13287.4i	−0.927457	+	1.60640i	−0.139896	+	0.990166i	$0.544677\pi$
$409$	−7671.47	+	13287.4i	−0.927457	+	1.60640i	−0.787561	+	0.616237i	$0.788656\pi$
$410$	4110.95	−	7120.37i	0.495183	−	0.857683i
$411$	1246.26	+	2158.58i	0.149570	+	0.259063i
$412$	1948.72			0.233026
$413$	−4749.45	+	2859.12i	−0.565872	+	0.340649i
$414$	−808.097			−0.0959319
$415$	−4422.73	−	7660.40i	−0.523141	−	0.906107i
$416$	1081.89	−	1873.88i	0.127509	−	0.220852i
$417$	−3149.35	+	5454.84i	−0.369843	+	0.640586i
$418$	1061.33	+	1838.27i	0.124189	+	0.215102i
$419$	−3302.54			−0.385058			−0.192529	−	0.981291i	$-0.561669\pi$
$419$	−3302.54			−0.385058			−0.192529	+	0.981291i	$0.561669\pi$
$420$	−3495.41	+	2104.20i	−0.406092	+	0.244463i
$421$	−644.096			−0.0745637			−0.0372818	−	0.999305i	$-0.511870\pi$
$421$	−644.096			−0.0745637			−0.0372818	+	0.999305i	$0.511870\pi$
$422$	2963.94	+	5133.69i	0.341901	+	0.592190i
$423$	1878.75	−	3254.09i	0.215952	−	0.374040i
$424$	258.120	−	447.077i	0.0295647	−	0.0512075i
$425$	13392.5	+	23196.5i	1.52855	+	2.64752i
$426$	−3935.73			−0.447621
$427$	9.81116	+	536.577i	0.00111193	+	0.0608121i
$428$	7146.72			0.807125
$429$	−1115.69	−	1932.44i	−0.125562	−	0.217480i
$430$	5684.92	−	9846.57i	0.637561	−	1.10429i
$431$	7305.38	−	12653.3i	0.816444	−	1.41412i	−0.0918415	−	0.995774i	$-0.529275\pi$
$431$	7305.38	−	12653.3i	0.816444	−	1.41412i	0.908286	−	0.418350i	$-0.137391\pi$
$432$	−216.000	−	374.123i	−0.0240563	−	0.0416667i
$433$	11015.1			1.22252			0.611259	−	0.791431i	$-0.290663\pi$
$433$	11015.1			1.22252			0.611259	+	0.791431i	$0.290663\pi$
$434$	3906.70	+	2161.28i	0.432091	+	0.239044i
$435$	−3942.73			−0.434573
$436$	−1432.71	−	2481.54i	−0.157373	−	0.272578i
$437$	2165.80	−	3751.27i	0.237080	−	0.410635i
$438$	−1313.50	+	2275.05i	−0.143291	+	0.248188i
$439$	167.391	+	289.930i	0.0181985	+	0.0315208i	0.874981	−	0.484157i	$-0.160874\pi$
$439$	167.391	+	289.930i	0.0181985	+	0.0315208i	−0.856783	+	0.515678i	$0.827540\pi$
$440$	1615.49			0.175035
$441$	1444.74	−	2728.06i	0.156002	−	0.294575i
$442$	17085.5			1.83863
$443$	−6117.85	−	10596.4i	−0.656135	−	1.13646i	−0.981608	−	0.190908i	$-0.938857\pi$
$443$	−6117.85	−	10596.4i	−0.656135	−	1.13646i	0.325473	−	0.945551i	$-0.394477\pi$
$444$	302.122	−	523.290i	0.0322929	−	0.0559330i
$445$	3108.06	−	5383.32i	0.331093	−	0.573470i
$446$	3784.44	+	6554.84i	0.401790	+	0.695921i
$447$	1918.08			0.202958
$448$	−1037.16	−	573.783i	−0.109378	−	0.0605105i
$449$	−2501.90			−0.262967			−0.131483	−	0.991318i	$-0.541974\pi$
$449$	−2501.90			−0.262967			−0.131483	+	0.991318i	$0.541974\pi$
$450$	−1908.09	−	3304.90i	−0.199885	−	0.346210i
$451$	1231.64	−	2133.26i	0.128593	−	0.222730i
$452$	−2680.88	+	4643.42i	−0.278978	+	0.483203i
$453$	1841.04	+	3188.78i	0.190949	+	0.330733i
$454$	−3827.84			−0.395704
$455$	420.287	+	22985.6i	0.0433040	+	2.36832i
$456$	2315.62			0.237805
$457$	−2874.50	−	4978.78i	−0.294231	−	0.509623i	0.680575	−	0.732678i	$-0.261730\pi$
$457$	−2874.50	−	4978.78i	−0.294231	−	0.509623i	−0.974806	+	0.223056i	$0.928397\pi$
$458$	−4643.76	+	8043.22i	−0.473774	+	0.820601i
$459$	1705.58	−	2954.14i	0.173441	−	0.300409i
$460$	−1648.32	−	2854.98i	−0.167073	−	0.289378i
$461$	−14131.8			−1.42773			−0.713867	−	0.700281i	$-0.753058\pi$
$461$	−14131.8			−1.42773			−0.713867	+	0.700281i	$0.753058\pi$
$462$	−1047.22	+	630.419i	−0.105457	+	0.0634843i
$463$	9861.71			0.989876			0.494938	−	0.868928i	$-0.335191\pi$
$463$	9861.71			0.989876			0.494938	+	0.868928i	$0.335191\pi$
$464$	−572.723	−	991.985i	−0.0573017	−	0.0992494i
$465$	−3319.15	+	5748.93i	−0.331014	+	0.573334i
$466$	−6901.04	+	11952.9i	−0.686018	+	1.18822i
$467$	1479.41	+	2562.42i	0.146593	+	0.253907i	0.929966	−	0.367645i	$-0.119836\pi$
$467$	1479.41	+	2562.42i	0.146593	+	0.253907i	−0.783373	+	0.621552i	$0.786502\pi$
$468$	−2434.24			−0.240433
$469$	−16642.0	+	10018.3i	−1.63850	+	0.986361i
$470$	15328.8			1.50439
$471$	141.196	+	244.559i	0.0138131	+	0.0239250i
$472$	1197.31	−	2073.81i	0.116760	−	0.202234i
$473$	1703.20	−	2950.03i	0.165567	−	0.286771i
$474$	−4100.76	−	7102.72i	−0.397371	−	0.688267i
$475$	20455.6			1.97593
$476$	−171.104	−	9357.75i	−0.0164759	−	0.901075i
$477$	−580.771			−0.0557477
$478$	−955.361	−	1654.73i	−0.0914168	−	0.158338i
$479$	−6545.24	+	11336.7i	−0.624342	+	1.08139i	0.364326	+	0.931272i	$0.381299\pi$
$479$	−6545.24	+	11336.7i	−0.624342	+	1.08139i	−0.988668	+	0.150120i	$0.952034\pi$
$480$	881.175	−	1526.24i	0.0837916	−	0.145131i
$481$	−1702.40	−	2948.64i	−0.161378	−	0.279515i
$482$	−9296.74			−0.878538
$483$	2182.62	+	1207.48i	0.205616	+	0.113752i
$484$	484.000			0.0454545
$485$	3636.61	+	6298.80i	0.340474	+	0.589719i
$486$	−243.000	+	420.888i	−0.0226805	+	0.0392837i
$487$	915.570	−	1585.81i	0.0851918	−	0.147557i	−0.820281	−	0.571961i	$-0.806183\pi$
$487$	915.570	−	1585.81i	0.0851918	−	0.147557i	0.905473	+	0.424404i	$0.139516\pi$
$488$	−115.909	−	200.760i	−0.0107520	−	0.0186229i
$489$	1787.95			0.165346
$490$	12585.0	−	460.383i	1.16027	−	0.0424448i
$491$	10387.8			0.954779			0.477390	−	0.878692i	$-0.341583\pi$
$491$	10387.8			0.954779			0.477390	+	0.878692i	$0.341583\pi$
$492$	−1343.61	−	2327.19i	−0.123119	−	0.213248i
$493$	4522.32	−	7832.89i	0.413134	−	0.715570i
$494$	6524.05	−	11300.0i	0.594192	−	1.02917i
$495$	−908.712	−	1573.94i	−0.0825123	−	0.142915i
$496$	−1928.56			−0.174587
$497$	10630.2	+	5880.87i	0.959412	+	0.530771i
$498$	−2891.02			−0.260140
$499$	−2912.19	−	5044.06i	−0.261258	−	0.452512i	0.705319	−	0.708890i	$-0.250804\pi$
$499$	−2912.19	−	5044.06i	−0.261258	−	0.452512i	−0.966576	+	0.256379i	$0.917471\pi$
$500$	3194.62	−	5533.24i	0.285735	−	0.494908i
$501$	−5104.38	+	8841.04i	−0.455183	+	0.788401i
$502$	−4375.91	−	7579.29i	−0.389056	−	0.673865i
$503$	−9157.00			−0.811711			−0.405855	−	0.913937i	$-0.633026\pi$
$503$	−9157.00			−0.811711			−0.405855	+	0.913937i	$0.633026\pi$
$504$	24.3779	+	1333.24i	0.00215452	+	0.117831i
$505$	−11774.2			−1.03752
$506$	−493.837	−	855.351i	−0.0433868	−	0.0751482i
$507$	−3562.75	+	6170.87i	−0.312086	+	0.540548i
$508$	−5216.49	+	9035.23i	−0.455599	+	0.789121i
$509$	−3455.75	−	5985.53i	−0.300930	−	0.521226i	0.675417	−	0.737436i	$-0.263964\pi$
$509$	−3455.75	−	5985.53i	−0.300930	−	0.521226i	−0.976347	+	0.216210i	$0.930630\pi$
$510$	13915.8			1.20824
$511$	6947.13	−	4182.10i	0.601415	−	0.362046i
$512$	512.000			0.0441942
$513$	−1302.54	−	2256.06i	−0.112102	−	0.194167i
$514$	2537.91	−	4395.78i	0.217786	−	0.377217i
$515$	4471.79	−	7745.36i	0.382622	−	0.662721i
$516$	−1858.04	−	3218.22i	−0.158518	−	0.274562i
$517$	4592.49			0.390672
$518$	−1597.93	+	961.935i	−0.135538	+	0.0815927i
$519$	−8872.16			−0.750375
$520$	−4965.26	−	8600.09i	−0.418733	−	0.725267i
$521$	−2704.76	+	4684.78i	−0.227443	+	0.393942i	−0.957049	−	0.289925i	$-0.906370\pi$
$521$	−2704.76	+	4684.78i	−0.227443	+	0.393942i	0.729607	+	0.683867i	$0.239703\pi$
$522$	−644.313	+	1115.98i	−0.0540246	+	0.0935733i
$523$	7901.91	+	13686.5i	0.660662	+	1.14430i	0.980442	+	0.196809i	$0.0630578\pi$
$523$	7901.91	+	13686.5i	0.660662	+	1.14430i	−0.319779	+	0.947492i	$0.603609\pi$
$524$	8793.40			0.733095
$525$	215.348	+	11777.5i	0.0179020	+	0.979067i
$526$	−8317.75			−0.689489
$527$	−7614.14	−	13188.1i	−0.629369	−	1.09010i
$528$	264.000	−	457.261i	0.0217597	−	0.0376889i
$529$	5075.75	−	8791.46i	0.417174	−	0.722566i
$530$	−1184.63	−	2051.84i	−0.0970889	−	0.168163i
$531$	−2693.95			−0.220165
$532$	−6254.35	−	3460.06i	−0.509700	−	0.281979i
$533$	−15142.0			−1.23053
$534$	−1015.83	−	1759.46i	−0.0823205	−	0.142583i
$535$	16399.8	−	28405.2i	1.32528	−	2.29545i
$536$	4195.37	−	7266.59i	0.338082	−	0.585576i
$537$	4523.65	+	7835.20i	0.363520	+	0.629635i
$538$	−67.1709			−0.00538280
$539$	3770.48	−	137.931i	0.301310	−	0.0110224i
$540$	−1982.64			−0.157999
$541$	3032.59	+	5252.61i	0.241001	+	0.417425i	0.961000	−	0.276550i	$-0.0891910\pi$
$541$	3032.59	+	5252.61i	0.241001	+	0.417425i	−0.719999	+	0.693975i	$0.755858\pi$
$542$	−1199.03	+	2076.78i	−0.0950235	+	0.164586i
$543$	6101.40	−	10567.9i	0.482203	−	0.835199i
$544$	2021.42	+	3501.21i	0.159316	+	0.275943i
$545$	−13150.8			−1.03361
$546$	6574.73	+	3637.31i	0.515334	+	0.285096i
$547$	−23098.9			−1.80555			−0.902775	−	0.430114i	$-0.858473\pi$
$547$	−23098.9			−1.80555			−0.902775	+	0.430114i	$0.858473\pi$
$548$	1661.67	+	2878.10i	0.129531	+	0.224355i
$549$	−130.398	+	225.855i	−0.0101370	+	0.0175579i
$550$	2332.11	−	4039.33i	0.180802	−	0.313159i
$551$	−3453.67	−	5981.93i	−0.267026	−	0.462502i
$552$	−1077.46			−0.0830795
$553$	462.813	+	25311.5i	0.0355892	+	1.94639i
$554$	14259.3			1.09353
$555$	−1386.57	−	2401.62i	−0.106048	−	0.183681i
$556$	−4199.13	+	7273.11i	−0.320293	+	0.554764i
$557$	10119.4	−	17527.2i	0.769786	−	1.33331i	−0.167892	−	0.985805i	$-0.553696\pi$
$557$	10119.4	−	17527.2i	0.769786	−	1.33331i	0.937679	−	0.347504i	$-0.112971\pi$
$558$	1084.82	+	1878.96i	0.0823010	+	0.142550i
$559$	−20939.4			−1.58433
$560$	−4660.55	+	2805.60i	−0.351686	+	0.211711i
$561$	4169.18			0.313767
$562$	6226.99	+	10785.5i	0.467384	+	0.809532i
$563$	−6726.07	+	11649.9i	−0.503499	+	0.872086i	0.496493	+	0.868041i	$0.334621\pi$
$563$	−6726.07	+	11649.9i	−0.503499	+	0.872086i	−0.999992	+	0.00404511i	$0.998712\pi$
$564$	2505.00	−	4338.78i	0.187020	−	0.323928i
$565$	12303.8	+	21310.7i	0.916147	+	1.58681i
$566$	15370.3			1.14145
$567$	1285.23	−	773.696i	0.0951933	−	0.0573054i
$568$	−5247.64			−0.387651
$569$	2314.11	+	4008.16i	0.170497	+	0.295309i	0.938594	−	0.345024i	$-0.112129\pi$
$569$	2314.11	+	4008.16i	0.170497	+	0.295309i	−0.768097	+	0.640334i	$0.778796\pi$
$570$	5313.72	−	9203.63i	0.390469	−	0.676312i
$571$	−11907.7	+	20624.8i	−0.872719	+	1.51159i	−0.0135454	+	0.999908i	$0.504312\pi$
$571$	−11907.7	+	20624.8i	−0.872719	+	1.51159i	−0.859173	+	0.511685i	$0.829022\pi$
$572$	−1487.59	−	2576.58i	−0.108740	−	0.188343i
$573$	−1569.62			−0.114436
$574$	151.640	+	8293.26i	0.0110267	+	0.603056i
$575$	−9518.02			−0.690311
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	2478.59	−	4293.05i	0.178831	−	0.309744i	−0.762650	−	0.646812i	$-0.776102\pi$
$577$	2478.59	−	4293.05i	0.178831	−	0.309744i	0.941480	+	0.337068i	$0.109435\pi$
$578$	−11048.5	+	19136.6i	−0.795083	+	1.37712i
$579$	4049.34	+	7013.66i	0.290647	+	0.503416i
$580$	−5256.97			−0.376351
$581$	7808.46	+	4319.84i	0.557572	+	0.308463i
$582$	2377.15			0.169306
$583$	−354.915	−	614.731i	−0.0252129	−	0.0436699i
$584$	−1751.34	+	3033.40i	−0.124094	+	0.214937i
$585$	−5585.92	+	9675.10i	−0.394785	+	0.683788i
$586$	−104.466	−	180.941i	−0.00736426	−	0.0127553i
$587$	1555.50			0.109374			0.0546868	−	0.998504i	$-0.482584\pi$
$587$	1555.50			0.109374			0.0546868	+	0.998504i	$0.482584\pi$
$588$	1926.31	−	3637.41i	0.135102	−	0.255109i
$589$	−11629.7			−0.813574
$590$	−5495.01	−	9517.64i	−0.383434	−	0.664127i
$591$	3043.68	−	5271.80i	0.211845	−	0.366926i
$592$	402.829	−	697.720i	0.0279665	−	0.0484394i
$593$	7149.55	+	12383.4i	0.495104	+	0.857546i	0.999984	−	0.00564372i	$-0.00179646\pi$
$593$	7149.55	+	12383.4i	0.495104	+	0.857546i	−0.504880	+	0.863190i	$0.668463\pi$
$594$	−594.000			−0.0410305
$595$	−37585.8	−	20793.4i	−2.58970	−	1.43268i
$596$	2557.44			0.175767
$597$	−4544.13	−	7870.67i	−0.311523	−	0.539573i
$598$	−3035.65	+	5257.91i	−0.207587	+	0.359552i
$599$	−14137.8	+	24487.4i	−0.964366	+	1.67033i	−0.253057	+	0.967451i	$0.581436\pi$
$599$	−14137.8	+	24487.4i	−0.964366	+	1.67033i	−0.711309	+	0.702879i	$0.751897\pi$
$600$	−2544.12	−	4406.54i	−0.173105	−	0.299827i
$601$	7291.40			0.494879			0.247440	−	0.968903i	$-0.420411\pi$
$601$	7291.40			0.494879			0.247440	+	0.968903i	$0.420411\pi$
$602$	209.699	+	11468.5i	0.0141972	+	0.776449i
$603$	−9439.57			−0.637494
$604$	2454.72	+	4251.70i	0.165366	+	0.286423i
$605$	1110.65	−	1923.70i	0.0746352	−	0.129272i
$606$	−1924.12	+	3332.68i	−0.128980	+	0.223401i
$607$	4518.58	+	7826.41i	0.302147	+	0.523335i	0.976622	−	0.214963i	$-0.0689632\pi$
$607$	4518.58	+	7826.41i	0.302147	+	0.523335i	−0.674475	+	0.738298i	$0.735630\pi$
$608$	3087.49			0.205945
$609$	3407.78	−	2051.45i	0.226749	−	0.136501i
$610$	−1063.92			−0.0706177
$611$	−14115.2	−	24448.2i	−0.934599	−	1.61877i
$612$	2274.10	−	3938.86i	0.150204	−	0.260162i
$613$	−5180.76	+	8973.33i	−0.341352	+	0.591239i	−0.984684	−	0.174348i	$-0.944218\pi$
$613$	−5180.76	+	8973.33i	−0.341352	+	0.591239i	0.643332	+	0.765587i	$0.277551\pi$
$614$	−2238.32	−	3876.88i	−0.147119	−	0.254818i
$615$	−12332.8			−0.808631
$616$	−1396.30	+	840.559i	−0.0913288	+	0.0549790i
$617$	23438.2			1.52932			0.764658	−	0.644436i	$-0.222908\pi$
$617$	23438.2			1.52932			0.764658	+	0.644436i	$0.222908\pi$
$618$	−1461.54	−	2531.46i	−0.0951324	−	0.164774i
$619$	3489.46	−	6043.92i	0.226580	−	0.392449i	−0.730212	−	0.683221i	$-0.760579\pi$
$619$	3489.46	−	6043.92i	0.226580	−	0.392449i	0.956792	+	0.290772i	$0.0939121\pi$
$620$	−4425.53	+	7665.24i	−0.286667	+	0.496522i
$621$	606.073	+	1049.75i	0.0391640	+	0.0678341i
$622$	4252.90			0.274157
$623$	114.647	+	6270.08i	0.00737276	+	0.403219i
$624$	−3245.66			−0.208221
$625$	−1410.94	−	2443.82i	−0.0903003	−	0.156405i
$626$	3650.93	−	6323.60i	0.233100	−	0.403741i
$627$	1591.99	−	2757.41i	0.101400	−	0.175630i
$628$	188.262	+	326.079i	0.0119625	+	0.0207197i
$629$	6361.62			0.403266
$630$	5355.00	+	2962.52i	0.338648	+	0.187349i
$631$	−9629.44			−0.607515			−0.303757	−	0.952749i	$-0.598241\pi$
$631$	−9629.44			−0.607515			−0.303757	+	0.952749i	$0.598241\pi$
$632$	−5467.68	−	9470.29i	−0.344134	−	0.596057i
$633$	4445.91	−	7700.54i	0.279161	−	0.483521i
$634$	−8151.92	+	14119.5i	−0.510653	+	0.884477i
$635$	23940.9	+	41466.8i	1.49616	+	2.59143i
$636$	−774.361			−0.0482789
$637$	−12323.0	−	19648.3i	−0.766490	−	1.22212i
$638$	−1574.99			−0.0977341
$639$	2951.80	+	5112.66i	0.182741	+	0.316516i
$640$	1174.90	−	2034.99i	0.0725657	−	0.125687i
$641$	−6677.97	+	11566.6i	−0.411488	+	0.712719i	−0.995053	−	0.0993483i	$-0.968324\pi$
$641$	−6677.97	+	11566.6i	−0.411488	+	0.712719i	0.583564	+	0.812067i	$0.301658\pi$
$642$	−5360.04	−	9283.86i	−0.329508	−	0.570724i
$643$	571.459			0.0350484			0.0175242	−	0.999846i	$-0.494422\pi$
$643$	571.459			0.0350484			0.0175242	+	0.999846i	$0.494422\pi$
$644$	2910.16	+	1609.97i	0.178069	+	0.0985122i
$645$	−17054.8			−1.04113
$646$	12189.7	+	21113.2i	0.742411	+	1.28589i
$647$	9946.35	−	17227.6i	0.604376	−	1.04681i	−0.387774	−	0.921755i	$-0.626756\pi$
$647$	9946.35	−	17227.6i	0.604376	−	1.04681i	0.992150	−	0.125055i	$-0.0399108\pi$
$648$	−324.000	+	561.184i	−0.0196419	+	0.0340207i
$649$	−1646.30	−	2851.48i	−0.0995733	−	0.172466i
$650$	−28671.3			−1.73012
$651$	−122.433	−	6695.91i	−0.00737101	−	0.403124i
$652$	2383.94			0.143194
$653$	12020.4	+	20820.0i	0.720361	+	1.24770i	0.960855	+	0.277051i	$0.0893570\pi$
$653$	12020.4	+	20820.0i	0.720361	+	1.24770i	−0.240495	+	0.970650i	$0.577310\pi$
$654$	−2149.07	+	3722.30i	−0.128494	+	0.222559i
$655$	20178.5	−	34950.1i	1.20372	−	2.08491i
$656$	−1791.47	−	3102.93i	−0.106624	−	0.184678i
$657$	3940.50			0.233993
$658$	−13249.0	+	7975.74i	−0.784952	+	0.472533i
$659$	−1521.61			−0.0899447			−0.0449724	−	0.998988i	$-0.514320\pi$
$659$	−1521.61			−0.0899447			−0.0449724	+	0.998988i	$0.514320\pi$
$660$	−1211.62	−	2098.58i	−0.0714577	−	0.123768i
$661$	9948.20	−	17230.8i	0.585386	−	1.01392i	−0.409441	−	0.912336i	$-0.634276\pi$
$661$	9948.20	−	17230.8i	0.585386	−	1.01392i	0.994827	−	0.101581i	$-0.0323902\pi$
$662$	−1969.51	+	3411.29i	−0.115630	+	0.200277i
$663$	−12814.1	−	22194.7i	−0.750618	−	1.30011i
$664$	−3854.69			−0.225288
$665$	−28104.3	+	16918.5i	−1.63886	+	0.986575i
$666$	−906.365			−0.0527341
$667$	1607.00	+	2783.40i	0.0932882	+	0.161580i
$668$	−6805.84	+	11788.1i	−0.394200	+	0.682775i
$669$	5676.66	−	9832.26i	0.328060	−	0.568217i
$670$	−19254.4	−	33349.7i	−1.11024	−	1.92300i
$671$	−318.750			−0.0183386
$672$	32.5038	+	1777.65i	0.00186587	+	0.102045i
$673$	6932.96			0.397097			0.198548	−	0.980091i	$-0.436377\pi$
$673$	6932.96			0.397097			0.198548	+	0.980091i	$0.436377\pi$
$674$	−10182.0	−	17635.7i	−0.581892	−	1.00787i
$675$	−2862.13	+	4957.35i	−0.163205	+	0.282680i
$676$	−4750.34	+	8227.83i	−0.270274	+	0.468128i
$677$	10447.2	+	18095.0i	0.593084	+	1.02725i	0.993814	+	0.111055i	$0.0354231\pi$
$677$	10447.2	+	18095.0i	0.593084	+	1.02725i	−0.400730	+	0.916196i	$0.631244\pi$
$678$	8042.63			0.455568
$679$	−6420.54	−	3552.01i	−0.362883	−	0.200756i
$680$	18554.5			1.04637
$681$	2870.88	+	4972.52i	0.161546	+	0.279805i
$682$	−1325.89	+	2296.50i	−0.0744441	+	0.128941i
$683$	−7000.76	+	12125.7i	−0.392206	+	0.679320i	−0.992740	−	0.120278i	$-0.961621\pi$
$683$	−7000.76	+	12125.7i	−0.392206	+	0.679320i	0.600534	+	0.799599i	$0.294955\pi$
$684$	−1736.72	−	3008.08i	−0.0970833	−	0.168153i
$685$	15252.4			0.850748
$686$	−10638.0	+	6946.07i	−0.592070	+	0.386592i
$687$	13931.3			0.773670
$688$	−2477.38	−	4290.95i	−0.137281	−	0.237778i
$689$	−2181.69	+	3778.80i	−0.120633	+	0.208942i
$690$	−2472.48	+	4282.47i	−0.136414	+	0.236277i
$691$	−9624.97	−	16670.9i	−0.529886	−	0.917789i	−0.999392	−	0.0348601i	$-0.988901\pi$
$691$	−9624.97	−	16670.9i	−0.529886	−	0.917789i	0.469506	−	0.882929i	$-0.344432\pi$
$692$	−11829.5			−0.649844
$693$	1604.36	+	887.571i	0.0879430	+	0.0486523i
$694$	12414.0			0.679002
$695$	19271.7	+	33379.6i	1.05183	+	1.82182i
$696$	−859.084	+	1487.98i	−0.0467866	+	0.0810368i
$697$	14145.8	−	24501.3i	0.768739	−	1.33149i
$698$	10174.2	+	17622.3i	0.551719	+	0.955605i
$699$	20703.1			1.12026
$700$	287.130	+	15703.3i	0.0155036	+	0.847897i
$701$	12292.2			0.662296			0.331148	−	0.943579i	$-0.392564\pi$
$701$	12292.2			0.662296			0.331148	+	0.943579i	$0.392564\pi$
$702$	1825.68	+	3162.17i	0.0981565	+	0.170012i
$703$	2429.16	−	4207.43i	0.130324	−	0.225727i
$704$	352.000	−	609.682i	0.0188445	−	0.0326396i
$705$	−11496.6	−	19912.6i	−0.614164	−	1.06376i
$706$	4312.51			0.229892
$707$	10176.7	−	6126.28i	0.541351	−	0.325888i
$708$	−3591.94			−0.190668
$709$	224.302	+	388.502i	0.0118813	+	0.0205790i	0.871905	−	0.489675i	$-0.162885\pi$
$709$	224.302	+	388.502i	0.0118813	+	0.0205790i	−0.860024	+	0.510254i	$0.829551\pi$
$710$	−12041.9	+	20857.2i	−0.636513	+	1.10247i
$711$	−6151.13	+	10654.1i	−0.324452	+	0.561968i
$712$	−1354.44	−	2345.95i	−0.0712917	−	0.123481i
$713$	5411.34			0.284231
$714$	−12027.7	+	7240.59i	−0.630430	+	0.379513i
$715$	−13654.5			−0.714194
$716$	6031.54	+	10446.9i	0.314817	+	0.545280i
$717$	−1433.04	+	2482.10i	−0.0746415	+	0.129283i
$718$	1270.43	−	2200.44i	0.0660332	−	0.114373i
$719$	−7742.27	−	13410.0i	−0.401583	−	0.695561i	0.592335	−	0.805692i	$-0.298206\pi$
$719$	−7742.27	−	13410.0i	−0.401583	−	0.695561i	−0.993917	+	0.110131i	$0.964873\pi$
$720$	−2643.53			−0.136831
$721$	164.950	+	9021.20i	0.00852021	+	0.465974i
$722$	4900.41			0.252596
$723$	6972.56	+	12076.8i	0.358661	+	0.621220i
$724$	8135.19	−	14090.6i	0.417600	−	0.723304i
$725$	−7588.92	+	13144.4i	−0.388752	+	0.673339i
$726$	−363.000	−	628.734i	−0.0185567	−	0.0321412i
$727$	−8496.38			−0.433443			−0.216722	−	0.976233i	$-0.569536\pi$
$727$	−8496.38			−0.433443			−0.216722	+	0.976233i	$0.569536\pi$
$728$	8766.31	+	4849.75i	0.446293	+	0.246900i
$729$	729.000			0.0370370
$730$	8037.68	+	13921.7i	0.407517	+	0.705841i
$731$	19561.9	−	33882.2i	0.989770	−	1.71433i
$732$	−173.864	+	301.140i	−0.00877894	+	0.0152056i
$733$	13041.0	+	22587.7i	0.657135	+	1.13819i	0.981354	+	0.192209i	$0.0615652\pi$
$733$	13041.0	+	22587.7i	0.657135	+	1.13819i	−0.324219	+	0.945982i	$0.605102\pi$
$734$	−14873.0			−0.747917
$735$	−10036.8	−	16003.2i	−0.503693	−	0.803110i
$736$	−1436.62			−0.0719489
$737$	−5768.63	−	9991.56i	−0.288318	−	0.499381i
$738$	−2015.41	+	3490.79i	−0.100526	+	0.174116i
$739$	−6375.90	+	11043.4i	−0.317376	+	0.549712i	−0.979940	−	0.199294i	$-0.936135\pi$
$739$	−6375.90	+	11043.4i	−0.317376	+	0.549712i	0.662563	+	0.749006i	$0.269469\pi$
$740$	−1848.76	−	3202.15i	−0.0918405	−	0.159072i
$741$	−19572.2			−0.970312
$742$	2091.50	+	1157.07i	0.103479	+	0.0572472i
$743$	−1188.60			−0.0586885			−0.0293442	−	0.999569i	$-0.509342\pi$
$743$	−1188.60			−0.0586885			−0.0293442	+	0.999569i	$0.509342\pi$
$744$	1446.42	+	2505.28i	0.0712748	+	0.123452i
$745$	5868.64	−	10164.8i	0.288604	−	0.499878i
$746$	−7530.67	+	13043.5i	−0.369594	+	0.640156i
$747$	2168.26	+	3755.54i	0.106202	+	0.183947i
$748$	5558.91			0.271730
$749$	604.937	+	33084.2i	0.0295112	+	1.61398i
$750$	−9583.85			−0.466603
$751$	−9066.02	−	15702.8i	−0.440511	−	0.762988i	0.557216	−	0.830367i	$-0.311869\pi$
$751$	−9066.02	−	15702.8i	−0.440511	−	0.762988i	−0.997727	+	0.0673796i	$0.978536\pi$
$752$	3340.00	−	5785.04i	0.161964	−	0.280530i
$753$	−6563.86	+	11368.9i	−0.317663	+	0.550209i
$754$	4840.78	+	8384.48i	0.233808	+	0.404967i
$755$	22531.7			1.08611
$756$	1713.64	−	1031.59i	0.0824398	−	0.0496280i
$757$	8989.79			0.431624			0.215812	−	0.976435i	$-0.430760\pi$
$757$	8989.79			0.431624			0.215812	+	0.976435i	$0.430760\pi$
$758$	−14616.7	−	25316.9i	−0.700399	−	1.21313i
$759$	−740.756	+	1283.03i	−0.0354252	+	0.0613583i
$760$	7084.96	−	12271.5i	0.338156	−	0.585703i
$761$	−9704.80	−	16809.2i	−0.462285	−	0.800701i	0.536790	−	0.843716i	$-0.319637\pi$
$761$	−9704.80	−	16809.2i	−0.462285	−	0.800701i	−0.999074	+	0.0430153i	$0.986304\pi$
$762$	15649.5			0.743991
$763$	11366.5	−	6842.50i	0.539311	−	0.324660i
$764$	−2092.83			−0.0991044
$765$	−10436.9	−	18077.2i	−0.493263	−	0.854357i
$766$	−6251.32	+	10827.6i	−0.294869	+	0.510728i
$767$	−10120.0	+	17528.3i	−0.476415	+	0.825175i
$768$	−384.000	−	665.108i	−0.0180422	−	0.0312500i
$769$	12916.7			0.605705			0.302852	−	0.953037i	$-0.402061\pi$
$769$	12916.7			0.605705			0.302852	+	0.953037i	$0.402061\pi$
$770$	136.744	+	7478.57i	0.00639987	+	0.350011i
$771$	−7613.72			−0.355644
$772$	5399.12	+	9351.55i	0.251708	+	0.435971i
$773$	−15331.0	+	26554.0i	−0.713346	+	1.23555i	0.250248	+	0.968182i	$0.419488\pi$
$773$	−15331.0	+	26554.0i	−0.713346	+	1.23555i	−0.963594	+	0.267370i	$0.913845\pi$
$774$	−2787.06	+	4827.32i	−0.129430	+	0.224179i
$775$	12777.3	+	22131.0i	0.592225	+	1.02576i
$776$	3169.54			0.146623
$777$	2448.03	+	1354.31i	0.113028	+	0.0625299i
$778$	−5727.42			−0.263931
$779$	−10803.1	−	18711.5i	−0.496868	−	0.860600i
$780$	−7447.89	+	12900.1i	−0.341894	+	0.592178i
$781$	−3607.75	+	6248.81i	−0.165295	+	0.286299i
$782$	−5671.90	−	9824.01i	−0.259369	−	0.449240i
$783$	1932.94			0.0882217
$784$	2568.42	−	4849.88i	0.117002	−	0.220931i
$785$	1728.04			0.0785686
$786$	−6595.05	−	11423.0i	−0.299285	−	0.518376i
$787$	2011.41	−	3483.86i	0.0911042	−	0.157797i	−0.816872	−	0.576819i	$-0.804294\pi$
$787$	2011.41	−	3483.86i	0.0911042	−	0.157797i	0.907976	+	0.419022i	$0.137627\pi$
$788$	4058.24	−	7029.07i	0.183463	−	0.317767i
$789$	6238.31	+	10805.1i	0.281483	+	0.487542i
$790$	−50187.3			−2.26023
$791$	−21722.6	−	12017.5i	−0.976445	−	0.540194i
$792$	−792.000			−0.0355335
$793$	979.689	+	1696.87i	0.0438711	+	0.0759870i
$794$	4931.62	−	8541.81i	0.220424	−	0.381785i
$795$	−1776.95	+	3077.76i	−0.0792727	+	0.137304i
$796$	−6058.84	−	10494.2i	−0.269787	−	0.467284i
$797$	−36952.9			−1.64233			−0.821167	−	0.570688i	$-0.806676\pi$
$797$	−36952.9			−1.64233			−0.821167	+	0.570688i	$0.806676\pi$
$798$	196.007	+	10719.7i	0.00869494	+	0.475530i
$799$	52746.4			2.33546
$800$	−3392.15	−	5875.38i	−0.149913	−	0.259658i
$801$	−1523.74	+	2639.20i	−0.0672144	+	0.116419i
$802$	12697.1	−	21992.0i	0.559040	−	0.968285i
$803$	2408.09	+	4170.93i	0.105828	+	0.183299i
$804$	−12586.1			−0.552086
$805$	13077.0	−	7872.23i	0.572551	−	0.344670i
$806$	16300.7			0.712365
$807$	50.3782	+	87.2576i	0.00219752	+	0.00380621i
$808$	−2565.50	+	4443.57i	−0.111700	+	0.193471i
$809$	13695.6	−	23721.5i	0.595195	−	1.03091i	−0.398325	−	0.917244i	$-0.630408\pi$
$809$	13695.6	−	23721.5i	0.595195	−	1.03091i	0.993519	−	0.113663i	$-0.0362583\pi$
$810$	1486.98	+	2575.53i	0.0645028	+	0.111722i
$811$	26312.6			1.13928			0.569642	−	0.821893i	$-0.307082\pi$
$811$	26312.6			1.13928			0.569642	+	0.821893i	$0.307082\pi$
$812$	4543.71	−	2735.27i	0.196371	−	0.118213i
$813$	3597.09			0.155173
$814$	−553.890	−	959.365i	−0.0238499	−	0.0413092i
$815$	5470.49	−	9475.16i	0.235120	−	0.407240i
$816$	3032.13	−	5251.81i	0.130081	−	0.225307i
$817$	−14939.3	−	25875.6i	−0.639730	−	1.10804i
$818$	30685.9			1.31162
$819$	−206.047	−	11268.8i	−0.00879105	−	0.480786i
$820$	−16443.8			−0.700295
$821$	6189.45	+	10720.4i	0.263110	+	0.455720i	0.967067	−	0.254523i	$-0.0819184\pi$
$821$	6189.45	+	10720.4i	0.263110	+	0.455720i	−0.703957	+	0.710243i	$0.748585\pi$
$822$	2492.51	−	4317.16i	0.105762	−	0.183185i
$823$	2993.43	−	5184.77i	0.126785	−	0.219599i	−0.795644	−	0.605764i	$-0.792867\pi$
$823$	2993.43	−	5184.77i	0.126785	−	0.219599i	0.922429	+	0.386166i	$0.126201\pi$
$824$	−1948.72	−	3375.29i	−0.0823871	−	0.142699i
$825$	−6996.32			−0.295249
$826$	9701.59	+	5367.17i	0.408670	+	0.226087i
$827$	−23312.8			−0.980250			−0.490125	−	0.871652i	$-0.663049\pi$
$827$	−23312.8			−0.980250			−0.490125	+	0.871652i	$0.663049\pi$
$828$	808.097	+	1399.67i	0.0339171	+	0.0587461i
$829$	−18536.6	+	32106.3i	−0.776600	+	1.34511i	0.157291	+	0.987552i	$0.449724\pi$
$829$	−18536.6	+	32106.3i	−0.776600	+	1.34511i	−0.933891	+	0.357558i	$0.883609\pi$
$830$	−8845.47	+	15320.8i	−0.369917	+	0.640714i
$831$	−10694.4	−	18523.3i	−0.446433	−	0.773245i
$832$	−4327.54			−0.180325
$833$	43305.3	−	1584.18i	1.80125	−	0.0658927i
$834$	12597.4			0.523036
$835$	31235.1	+	54100.8i	1.29453	+	2.24220i
$836$	2122.65	−	3676.54i	0.0878152	−	0.152100i
$837$	1627.23	−	2818.44i	0.0671985	−	0.116391i
$838$	3302.54	+	5720.16i	0.136139	+	0.235799i
$839$	21552.3			0.886852			0.443426	−	0.896311i	$-0.353763\pi$
$839$	21552.3			0.886852			0.443426	+	0.896311i	$0.353763\pi$
$840$	7140.00	+	3950.03i	0.293278	+	0.162249i
$841$	−19263.8			−0.789857
$842$	644.096	+	1115.61i	0.0263622	+	0.0456607i
$843$	9340.48	−	16178.2i	0.381617	−	0.660980i
$844$	5927.87	−	10267.4i	0.241760	−	0.418741i
$845$	21801.5	+	37761.2i	0.887566	+	1.53731i
$846$	−7514.99			−0.305403
$847$	40.9684	+	2240.58i	0.00166197	+	0.0908939i
$848$	−1032.48			−0.0418108
$849$	−11527.7	−	19966.5i	−0.465994	−	0.807126i
$850$	26785.1	−	46393.1i	1.08085	−	1.87208i
$851$	−1130.29	+	1957.73i	−0.0455300	+	0.0788602i
$852$	3935.73	+	6816.88i	0.158258	+	0.274111i
$853$	2118.11			0.0850207			0.0425104	−	0.999096i	$-0.486464\pi$
$853$	2118.11			0.0850207			0.0425104	+	0.999096i	$0.486464\pi$
$854$	919.567	−	553.570i	0.0368465	−	0.0221812i
$855$	−15941.2			−0.637633
$856$	−7146.72	−	12378.5i	−0.285362	−	0.494261i
$857$	15103.9	−	26160.7i	0.602030	−	1.04275i	−0.390483	−	0.920610i	$-0.627692\pi$
$857$	15103.9	−	26160.7i	0.602030	−	1.04275i	0.992513	−	0.122136i	$-0.0389745\pi$
$858$	−2231.39	+	3864.88i	−0.0887859	+	0.153782i
$859$	−19552.9	−	33866.7i	−0.776644	−	1.34519i	−0.933866	−	0.357624i	$-0.883587\pi$
$859$	−19552.9	−	33866.7i	−0.776644	−	1.34519i	0.157221	−	0.987563i	$-0.449746\pi$
$860$	−22739.7			−0.901647
$861$	10659.5	−	6416.93i	0.421923	−	0.253994i
$862$	−29221.5			−1.15463
$863$	4299.11	+	7446.27i	0.169575	+	0.293713i	0.938271	−	0.345902i	$-0.112427\pi$
$863$	4299.11	+	7446.27i	0.169575	+	0.293713i	−0.768695	+	0.639615i	$0.779094\pi$
$864$	−432.000	+	748.246i	−0.0170103	+	0.0294628i
$865$	−27145.6	+	47017.5i	−1.06703	+	1.84814i
$866$	−11015.1	−	19078.6i	−0.432225	−	0.748636i
$867$	33145.6			1.29836
$868$	−163.244	−	8927.88i	−0.00638348	−	0.349115i
$869$	−15036.1			−0.586956
$870$	3942.73	+	6829.01i	0.153645	+	0.266121i
$871$	−35460.2	+	61418.8i	−1.37947	+	2.38932i
$872$	−2865.43	+	4963.07i	−0.111279	+	0.192742i
$873$	−1782.86	−	3088.01i	−0.0691189	−	0.119717i
$874$	−8663.18			−0.335282
$875$	25885.4	+	14320.4i	1.00010	+	0.553279i
$876$	5254.01			0.202644
$877$	24543.8	+	42511.1i	0.945023	+	1.63683i	0.755706	+	0.654911i	$0.227294\pi$
$877$	24543.8	+	42511.1i	0.945023	+	1.63683i	0.189317	+	0.981916i	$0.439373\pi$
$878$	334.783	−	579.861i	0.0128683	−	0.0222885i
$879$	−156.699	+	271.411i	−0.00601289	+	0.0104146i
$880$	−1615.49	−	2798.11i	−0.0618842	−	0.107187i
$881$	23126.6			0.884397			0.442199	−	0.896917i	$-0.354199\pi$
$881$	23126.6			0.884397			0.442199	+	0.896917i	$0.354199\pi$
$882$	−6169.87	+	225.704i	−0.235545	+	0.00861663i
$883$	−32929.9			−1.25501			−0.627507	−	0.778611i	$-0.715925\pi$
$883$	−32929.9			−1.25501			−0.627507	+	0.778611i	$0.715925\pi$
$884$	−17085.5	−	29593.0i	−0.650055	−	1.12593i
$885$	−8242.51	+	14276.5i	−0.313072	+	0.542257i
$886$	−12235.7	+	21192.9i	−0.463958	+	0.803598i
$887$	−9092.62	−	15748.9i	−0.344194	−	0.596162i	0.641013	−	0.767530i	$-0.278515\pi$
$887$	−9092.62	−	15748.9i	−0.344194	−	0.596162i	−0.985207	+	0.171368i	$0.945181\pi$
$888$	−1208.49			−0.0456691
$889$	−42268.3	−	23383.9i	−1.59464	−	0.882193i
$890$	−12432.3			−0.468236
$891$	445.500	+	771.629i	0.0167506	+	0.0290129i
$892$	7568.88	−	13109.7i	0.284108	−	0.492090i
$893$	20141.1	−	34885.3i	0.754753	−	1.30727i
$894$	−1918.08	−	3322.22i	−0.0717565	−	0.124286i
$895$	55363.0			2.06769
$896$	43.3384	+	2370.20i	0.00161589	+	0.0883736i
$897$	9106.96			0.338988
$898$	2501.90	+	4333.42i	0.0929728	+	0.161034i
$899$	4314.58	−	7473.07i	0.160066	−	0.277242i
$900$	−3816.17	+	6609.81i	−0.141340	+	0.244808i
$901$	−4076.33	−	7060.41i	−0.150724	−	0.261061i
$902$	−4926.56			−0.181859
$903$	14740.8	−	8873.80i	0.543236	−	0.327023i
$904$	10723.5			0.394534
$905$	−37336.1	−	64668.0i	−1.37138	−	2.37529i
$906$	3682.08	−	6377.56i	0.135021	−	0.233863i
$907$	9721.35	−	16837.9i	0.355890	−	0.616419i	−0.631380	−	0.775474i	$-0.717511\pi$
$907$	9721.35	−	16837.9i	0.355890	−	0.616419i	0.987270	+	0.159054i	$0.0508445\pi$
$908$	3827.84	+	6630.02i	0.139903	+	0.242318i
$909$	5772.37			0.210624
$910$	39392.0	−	23713.6i	1.43498	−	0.863844i
$911$	−15347.9			−0.558175			−0.279088	−	0.960266i	$-0.590032\pi$
$911$	−15347.9			−0.558175			−0.279088	+	0.960266i	$0.590032\pi$
$912$	−2315.62	−	4010.77i	−0.0840766	−	0.145625i
$913$	−2650.10	+	4590.11i	−0.0960630	+	0.166386i
$914$	−5749.00	+	9957.56i	−0.208053	+	0.360358i
$915$	797.939	+	1382.07i	0.0288296	+	0.0499343i
$916$	18575.0			0.670018
$917$	744.321	+	40707.2i	0.0268044	+	1.46594i
$918$	−6822.30			−0.245283
$919$	8958.92	+	15517.3i	0.321575	+	0.556984i	0.980813	−	0.194950i	$-0.0624544\pi$
$919$	8958.92	+	15517.3i	0.321575	+	0.556984i	−0.659238	+	0.751934i	$0.729121\pi$
$920$	−3296.65	+	5709.96i	−0.118138	+	0.204621i
$921$	−3357.48	+	5815.33i	−0.120122	+	0.208058i
$922$	14131.8	+	24477.1i	0.504780	+	0.874305i
$923$	44354.2			1.58173
$924$	2139.14	+	1183.43i	0.0761608	+	0.0421341i
$925$	−10675.4			−0.379467
$926$	−9861.71	−	17081.0i	−0.349974	−	0.606173i
$927$	−2192.31	+	3797.20i	−0.0776753	+	0.134538i
$928$	−1145.45	+	1983.97i	−0.0405184	+	0.0701800i
$929$	3390.44	+	5872.42i	0.119738	+	0.207393i	0.919664	−	0.392706i	$-0.128461\pi$
$929$	3390.44	+	5872.42i	0.119738	+	0.207393i	−0.799926	+	0.600099i	$0.795128\pi$
$930$	13276.6			0.468125
$931$	15488.2	−	29246.1i	0.545227	−	1.02954i
$932$	27604.1			0.970176
$933$	−3189.68	−	5524.68i	−0.111924	−	0.193859i
$934$	2958.83	−	5124.84i	0.103657	−	0.179540i
$935$	12756.2	−	22094.4i	0.446173	−	0.772795i
$936$	2434.24	+	4216.23i	0.0850061	+	0.147235i
$937$	17559.0			0.612196			0.306098	−	0.952000i	$-0.400976\pi$
$937$	17559.0			0.612196			0.306098	+	0.952000i	$0.400976\pi$
$938$	33994.3	+	18806.5i	1.18332	+	0.654641i
$939$	−10952.8			−0.380651
$940$	−15328.8	−	26550.2i	−0.531882	−	0.921247i
$941$	−9543.48	+	16529.8i	−0.330615	+	0.572642i	−0.982633	−	0.185562i	$-0.940589\pi$
$941$	−9543.48	+	16529.8i	−0.330615	+	0.572642i	0.652018	+	0.758204i	$0.273923\pi$
$942$	282.393	−	489.119i	0.00976736	−	0.0169176i
$943$	5026.69	+	8706.48i	0.173586	+	0.300660i
$944$	−4789.25			−0.165124
$945$	−167.822	−	9178.24i	−0.00577697	−	0.315945i
$946$	−6812.80			−0.234147
$947$	18817.6	+	32593.1i	0.645713	+	1.11841i	0.984136	+	0.177414i	$0.0567731\pi$
$947$	18817.6	+	32593.1i	0.645713	+	1.11841i	−0.338423	+	0.940994i	$0.609894\pi$
$948$	−8201.51	+	14205.4i	−0.280984	+	0.486678i
$949$	14802.7	−	25639.0i	0.506339	−	0.877004i
$950$	−20455.6	−	35430.1i	−0.698597	−	1.21000i
$951$	24455.8			0.833893
$952$	−16037.0	+	9654.11i	−0.545969	+	0.328668i
$953$	4669.64			0.158725			0.0793623	−	0.996846i	$-0.474712\pi$
$953$	4669.64			0.158725			0.0793623	+	0.996846i	$0.474712\pi$
$954$	580.771	+	1005.92i	0.0197098	+	0.0341384i
$955$	−4802.46	+	8318.11i	−0.162727	+	0.281851i
$956$	−1910.72	+	3309.47i	−0.0646414	+	0.111962i
$957$	1181.24	+	2045.97i	0.0398998	+	0.0691084i
$958$	26181.0			0.882953
$959$	−13182.9	+	7935.99i	−0.443899	+	0.267223i
$960$	−3524.70			−0.118499
$961$	7631.13	+	13217.5i	0.256156	+	0.443675i
$962$	−3404.80	+	5897.29i	−0.114111	+	0.197647i
$963$	−8040.06	+	13925.8i	−0.269042	+	0.465994i
$964$	9296.74	+	16102.4i	0.310610	+	0.537992i
$965$	49558.0			1.65319
$966$	−91.2023	−	4987.89i	−0.00303767	−	0.166131i
$967$	−18584.4			−0.618028			−0.309014	−	0.951057i	$-0.599999\pi$
$967$	−18584.4			−0.618028			−0.309014	+	0.951057i	$0.599999\pi$
$968$	−484.000	−	838.313i	−0.0160706	−	0.0278351i
$969$	18284.6	−	31669.8i	0.606176	−	1.04993i
$970$	7273.22	−	12597.6i	0.240752	−	0.416994i
$971$	6388.17	+	11064.6i	0.211129	+	0.365686i	0.952068	−	0.305886i	$-0.0989527\pi$
$971$	6388.17	+	11064.6i	0.211129	+	0.365686i	−0.740939	+	0.671572i	$0.765619\pi$
$972$	972.000			0.0320750
$973$	−34024.8	−	18823.4i	−1.12105	−	0.620195i
$974$	−3662.28			−0.120479
$975$	21503.4	+	37245.1i	0.706319	+	1.22338i
$976$	−231.818	+	401.521i	−0.00760278	+	0.0131684i
$977$	20552.4	−	35597.8i	0.673009	−	1.16569i	−0.304038	−	0.952660i	$-0.598335\pi$
$977$	20552.4	−	35597.8i	0.673009	−	1.16569i	0.977047	−	0.213025i	$-0.0683317\pi$
$978$	−1787.95	−	3096.83i	−0.0584585	−	0.101253i
$979$	−3724.70			−0.121595
$980$	−13382.5	−	21337.6i	−0.436211	−	0.695514i
$981$	6447.22			0.209831
$982$	−10387.8	−	17992.3i	−0.337565	−	0.584681i
$983$	7399.43	−	12816.2i	0.240087	−	0.415842i	−0.720652	−	0.693297i	$-0.756158\pi$
$983$	7399.43	−	12816.2i	0.240087	−	0.415842i	0.960739	+	0.277455i	$0.0894908\pi$
$984$	−2687.21	+	4654.39i	−0.0870581	+	0.150789i
$985$	−18625.1	−	32259.6i	−0.602482	−	1.04353i
$986$	−18089.3			−0.584260
$987$	20297.5	+	11229.1i	0.654587	+	0.362134i
$988$	−26096.2			−0.840315
$989$	6951.27	+	12040.0i	0.223496	+	0.387107i
$990$	−1817.42	+	3147.87i	−0.0583450	+	0.101056i
$991$	24333.7	−	42147.2i	0.780005	−	1.35101i	−0.151933	−	0.988391i	$-0.548550\pi$
$991$	24333.7	−	42147.2i	0.780005	−	1.35101i	0.931938	−	0.362618i	$-0.118117\pi$
$992$	1928.56	+	3340.37i	0.0617258	+	0.106912i
$993$	5908.52			0.188823
$994$	−444.188	−	24292.8i	−0.0141738	−	0.775173i
$995$	−55613.6			−1.77193
$996$	2891.02	+	5007.39i	0.0919733	+	0.159302i
$997$	−1767.47	+	3061.34i	−0.0561447	+	0.0972455i	−0.892732	−	0.450589i	$-0.851214\pi$
$997$	−1767.47	+	3061.34i	−0.0561447	+	0.0972455i	0.836587	+	0.547834i	$0.184547\pi$
$998$	−5824.38	+	10088.1i	−0.184737	+	0.319974i
$999$	679.773	+	1177.40i	0.0215286	+	0.0372886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.4.i.g.67.6	✓	12
7.2	even	3	inner	462.4.i.g.331.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.i.g.67.6	✓	12	1.1	even	1	trivial
462.4.i.g.331.6	yes	12	7.2	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	462.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.17891 + 15.8983i) q^{5} +6.00000 q^{6} +(-16.2056 - 8.96536i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.17891 + 15.8983i) q^{5} +6.00000 q^{6} +(-16.2056 - 8.96536i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(18.3578 - 31.7967i) q^{10} +(5.50000 - 9.52628i) q^{11} +(-6.00000 - 10.3923i) q^{12} -67.6178 q^{13} +(0.677163 + 37.0343i) q^{14} -55.0735 q^{15} +(-8.00000 - 13.8564i) q^{16} +(63.1695 - 109.413i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-48.2421 - 83.5578i) q^{19} -73.4313 q^{20} +(47.6011 - 28.6554i) q^{21} -22.0000 q^{22} +(22.4471 + 38.8796i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-106.005 + 183.606i) q^{25} +(67.6178 + 117.117i) q^{26} +27.0000 q^{27} +(63.4682 - 38.2072i) q^{28} +71.5903 q^{29} +(55.0735 + 95.3900i) q^{30} +(60.2676 - 104.387i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(16.5000 + 28.5788i) q^{33} -252.678 q^{34} +(-6.21562 - 339.935i) q^{35} +36.0000 q^{36} +(25.1768 + 43.6075i) q^{37} +(-96.4842 + 167.116i) q^{38} +(101.427 - 175.676i) q^{39} +(73.4313 + 127.187i) q^{40} +223.934 q^{41} +(-97.2338 - 53.7922i) q^{42} +309.673 q^{43} +(22.0000 + 38.1051i) q^{44} +(82.6102 - 143.085i) q^{45} +(44.8943 - 77.7592i) q^{46} +(208.750 + 361.565i) q^{47} +48.0000 q^{48} +(182.245 + 290.579i) q^{49} +424.019 q^{50} +(189.508 + 328.238i) q^{51} +(135.236 - 234.235i) q^{52} +(32.2650 - 55.8847i) q^{53} +(-27.0000 - 46.7654i) q^{54} +201.936 q^{55} +(-129.645 - 71.7229i) q^{56} +289.453 q^{57} +(-71.5903 - 123.998i) q^{58} +(149.664 - 259.226i) q^{59} +(110.147 - 190.780i) q^{60} +(-14.4886 - 25.0950i) q^{61} -241.070 q^{62} +(3.04723 + 166.654i) q^{63} +64.0000 q^{64} +(-620.658 - 1075.01i) q^{65} +(33.0000 - 57.1577i) q^{66} +(524.421 - 908.323i) q^{67} +(252.678 + 437.651i) q^{68} -134.683 q^{69} +(-582.569 + 350.701i) q^{70} -655.955 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-218.917 + 379.175i) q^{73} +(50.3536 - 87.2150i) q^{74} +(-318.014 - 550.817i) q^{75} +385.937 q^{76} +(-174.537 + 105.070i) q^{77} -405.707 q^{78} +(-683.459 - 1183.79i) q^{79} +(146.863 - 254.373i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-223.934 - 387.866i) q^{82} -481.837 q^{83} +(4.06298 + 222.206i) q^{84} +2319.31 q^{85} +(-309.673 - 536.369i) q^{86} +(-107.386 + 185.997i) q^{87} +(44.0000 - 76.2102i) q^{88} +(-169.305 - 293.244i) q^{89} -330.441 q^{90} +(1095.79 + 606.218i) q^{91} -179.577 q^{92} +(180.803 + 313.160i) q^{93} +(417.499 - 723.130i) q^{94} +(885.620 - 1533.94i) q^{95} +(-48.0000 - 83.1384i) q^{96} +396.192 q^{97} +(321.052 - 606.235i) q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 18 q^{3} - 24 q^{4} + 72 q^{6} - 8 q^{7} + 96 q^{8} - 54 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 18 * q^3 - 24 * q^4 + 72 * q^6 - 8 * q^7 + 96 * q^8 - 54 * q^9	\( 12 q - 12 q^{2} - 18 q^{3} - 24 q^{4} + 72 q^{6} - 8 q^{7} + 96 q^{8} - 54 q^{9} + 66 q^{11} - 72 q^{12} + 48 q^{13} - 16 q^{14} - 96 q^{16} + 2 q^{17} - 108 q^{18} - 120 q^{19} + 48 q^{21} - 264 q^{22} + 36 q^{23} - 144 q^{24} - 68 q^{25} - 48 q^{26} + 324 q^{27} + 64 q^{28} + 632 q^{29} - 392 q^{31} - 192 q^{32} + 198 q^{33} - 8 q^{34} - 318 q^{35} + 432 q^{36} - 348 q^{37} - 240 q^{38} - 72 q^{39} + 388 q^{41} - 48 q^{42} + 1360 q^{43} + 264 q^{44} + 72 q^{46} - 68 q^{47} + 576 q^{48} - 546 q^{49} + 272 q^{50} + 6 q^{51} - 96 q^{52} - 400 q^{53} - 324 q^{54} - 64 q^{56} + 720 q^{57} - 632 q^{58} - 340 q^{59} - 232 q^{61} + 1568 q^{62} - 72 q^{63} + 768 q^{64} - 1428 q^{65} + 396 q^{66} + 362 q^{67} + 8 q^{68} - 216 q^{69} - 1152 q^{70} - 40 q^{71} - 432 q^{72} - 1156 q^{73} - 696 q^{74} - 204 q^{75} + 960 q^{76} - 176 q^{77} + 288 q^{78} - 3336 q^{79} - 486 q^{81} - 388 q^{82} + 668 q^{83} - 96 q^{84} + 8000 q^{85} - 1360 q^{86} - 948 q^{87} + 528 q^{88} - 16 q^{89} + 1796 q^{91} - 288 q^{92} - 1176 q^{93} - 136 q^{94} - 404 q^{95} - 576 q^{96} - 1092 q^{97} + 768 q^{98} - 1188 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 18 * q^3 - 24 * q^4 + 72 * q^6 - 8 * q^7 + 96 * q^8 - 54 * q^9 + 66 * q^11 - 72 * q^12 + 48 * q^13 - 16 * q^14 - 96 * q^16 + 2 * q^17 - 108 * q^18 - 120 * q^19 + 48 * q^21 - 264 * q^22 + 36 * q^23 - 144 * q^24 - 68 * q^25 - 48 * q^26 + 324 * q^27 + 64 * q^28 + 632 * q^29 - 392 * q^31 - 192 * q^32 + 198 * q^33 - 8 * q^34 - 318 * q^35 + 432 * q^36 - 348 * q^37 - 240 * q^38 - 72 * q^39 + 388 * q^41 - 48 * q^42 + 1360 * q^43 + 264 * q^44 + 72 * q^46 - 68 * q^47 + 576 * q^48 - 546 * q^49 + 272 * q^50 + 6 * q^51 - 96 * q^52 - 400 * q^53 - 324 * q^54 - 64 * q^56 + 720 * q^57 - 632 * q^58 - 340 * q^59 - 232 * q^61 + 1568 * q^62 - 72 * q^63 + 768 * q^64 - 1428 * q^65 + 396 * q^66 + 362 * q^67 + 8 * q^68 - 216 * q^69 - 1152 * q^70 - 40 * q^71 - 432 * q^72 - 1156 * q^73 - 696 * q^74 - 204 * q^75 + 960 * q^76 - 176 * q^77 + 288 * q^78 - 3336 * q^79 - 486 * q^81 - 388 * q^82 + 668 * q^83 - 96 * q^84 + 8000 * q^85 - 1360 * q^86 - 948 * q^87 + 528 * q^88 - 16 * q^89 + 1796 * q^91 - 288 * q^92 - 1176 * q^93 - 136 * q^94 - 404 * q^95 - 576 * q^96 - 1092 * q^97 + 768 * q^98 - 1188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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