LMFDB - Embedded newform 250.4.d.c.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(51,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.d (of order $5$, degree $4$, not 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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.4
Character	$\chi$	$=$	250.201
Dual form			250.4.d.c.51.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(-0.0763140 - 0.234870i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.152628 + 0.469741i) q^{6} -19.9138 q^{7} +(2.47214 - 7.60845i) q^{8} +(21.7941 - 15.8344i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.0763140 - 0.234870i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.152628 + 0.469741i) q^{6} -19.9138 q^{7} +(2.47214 - 7.60845i) q^{8} +(21.7941 - 15.8344i) q^{9} +(1.78841 + 1.29936i) q^{11} +(0.799170 - 0.580631i) q^{12} +(9.95462 - 7.23245i) q^{13} +(32.2212 + 23.4101i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-23.0023 + 70.7939i) q^{17} -53.8780 q^{18} +(-15.5949 + 47.9960i) q^{19} +(1.51970 + 4.67716i) q^{21} +(-1.36622 - 4.20481i) q^{22} +(-161.248 - 117.154i) q^{23} -1.97566 q^{24} -24.6092 q^{26} +(-10.7766 - 7.82967i) q^{27} +(-24.6148 - 75.7565i) q^{28} +(74.5475 + 229.434i) q^{29} +(-15.8456 + 48.7679i) q^{31} +32.0000 q^{32} +(0.168700 - 0.519204i) q^{33} +(120.442 - 87.5061i) q^{34} +(87.1765 + 63.3374i) q^{36} +(-225.001 + 163.473i) q^{37} +(81.6557 - 59.3264i) q^{38} +(-2.45836 - 1.78611i) q^{39} +(-214.861 + 156.106i) q^{41} +(3.03940 - 9.35431i) q^{42} -103.714 q^{43} +(-2.73245 + 8.40961i) q^{44} +(123.183 + 379.117i) q^{46} +(127.174 + 391.402i) q^{47} +(3.19668 + 2.32252i) q^{48} +53.5589 q^{49} +18.3828 q^{51} +(39.8185 + 28.9298i) q^{52} +(132.965 + 409.226i) q^{53} +(8.23260 + 25.3373i) q^{54} +(-49.2296 + 151.513i) q^{56} +12.4629 q^{57} +(149.095 - 458.867i) q^{58} +(-445.750 + 323.856i) q^{59} +(413.338 + 300.308i) q^{61} +(82.9688 - 60.2804i) q^{62} +(-434.003 + 315.322i) q^{63} +(-51.7771 - 37.6183i) q^{64} +(-0.883322 + 0.641771i) q^{66} +(-23.5632 + 72.5200i) q^{67} -297.748 q^{68} +(-15.2104 + 46.8129i) q^{69} +(-264.409 - 813.766i) q^{71} +(-66.5969 - 204.964i) q^{72} +(417.952 + 303.660i) q^{73} +556.233 q^{74} -201.864 q^{76} +(-35.6140 - 25.8751i) q^{77} +(1.87802 + 5.77996i) q^{78} +(42.1044 + 129.584i) q^{79} +(223.748 - 688.626i) q^{81} +531.166 q^{82} +(283.533 - 872.626i) q^{83} +(-15.9145 + 11.5626i) q^{84} +(167.812 + 121.923i) q^{86} +(48.1981 - 35.0180i) q^{87} +(14.3073 - 10.3949i) q^{88} +(-1053.94 - 765.734i) q^{89} +(-198.234 + 144.026i) q^{91} +(246.365 - 758.234i) q^{92} +12.6634 q^{93} +(254.348 - 782.803i) q^{94} +(-2.44205 - 7.51585i) q^{96} +(-137.189 - 422.225i) q^{97} +(-86.6601 - 62.9623i) q^{98} +59.5513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9} - 106 q^{11} - 24 q^{12} + 14 q^{13} - 56 q^{14} - 128 q^{16} + 92 q^{17} + 848 q^{18} - 110 q^{19} - 36 q^{21} + 68 q^{22} + 124 q^{23} + 192 q^{24} + 808 q^{26} - 630 q^{27} - 112 q^{28} + 10 q^{29} - 486 q^{31} + 1024 q^{32} - 672 q^{33} - 616 q^{34} - 104 q^{36} - 88 q^{37} + 20 q^{38} - 1012 q^{39} - 96 q^{41} - 72 q^{42} + 1804 q^{43} + 136 q^{44} - 832 q^{46} - 328 q^{47} - 96 q^{48} + 2076 q^{49} + 884 q^{51} + 56 q^{52} + 1164 q^{53} + 120 q^{54} - 224 q^{56} + 2800 q^{57} + 20 q^{58} - 2250 q^{59} + 934 q^{61} + 768 q^{62} - 2976 q^{63} - 512 q^{64} + 16 q^{66} - 2248 q^{67} + 1728 q^{68} + 628 q^{69} - 2616 q^{71} - 1488 q^{72} - 3836 q^{73} + 2584 q^{74} + 800 q^{76} + 254 q^{77} + 1816 q^{78} + 2800 q^{79} - 5268 q^{81} + 2128 q^{82} + 304 q^{83} - 624 q^{84} - 692 q^{86} + 2660 q^{87} - 848 q^{88} - 4520 q^{89} + 3764 q^{91} - 1664 q^{92} + 5648 q^{93} - 656 q^{94} - 192 q^{96} - 6228 q^{97} - 2748 q^{98} + 2108 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9 - 106 * q^11 - 24 * q^12 + 14 * q^13 - 56 * q^14 - 128 * q^16 + 92 * q^17 + 848 * q^18 - 110 * q^19 - 36 * q^21 + 68 * q^22 + 124 * q^23 + 192 * q^24 + 808 * q^26 - 630 * q^27 - 112 * q^28 + 10 * q^29 - 486 * q^31 + 1024 * q^32 - 672 * q^33 - 616 * q^34 - 104 * q^36 - 88 * q^37 + 20 * q^38 - 1012 * q^39 - 96 * q^41 - 72 * q^42 + 1804 * q^43 + 136 * q^44 - 832 * q^46 - 328 * q^47 - 96 * q^48 + 2076 * q^49 + 884 * q^51 + 56 * q^52 + 1164 * q^53 + 120 * q^54 - 224 * q^56 + 2800 * q^57 + 20 * q^58 - 2250 * q^59 + 934 * q^61 + 768 * q^62 - 2976 * q^63 - 512 * q^64 + 16 * q^66 - 2248 * q^67 + 1728 * q^68 + 628 * q^69 - 2616 * q^71 - 1488 * q^72 - 3836 * q^73 + 2584 * q^74 + 800 * q^76 + 254 * q^77 + 1816 * q^78 + 2800 * q^79 - 5268 * q^81 + 2128 * q^82 + 304 * q^83 - 624 * q^84 - 692 * q^86 + 2660 * q^87 - 848 * q^88 - 4520 * q^89 + 3764 * q^91 - 1664 * q^92 + 5648 * q^93 - 656 * q^94 - 192 * q^96 - 6228 * q^97 - 2748 * q^98 + 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$3$	−0.0763140	−	0.234870i	−0.0146866	−	0.0452008i	0.943445	−	0.331530i	$-0.107565\pi$
$3$	−0.0763140	−	0.234870i	−0.0146866	−	0.0452008i	−0.958131	+	0.286329i	$0.907565\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.152628	+	0.469741i	−0.0103850	+	0.0319618i
$7$	−19.9138			−1.07524			−0.537622	−	0.843186i	$-0.680677\pi$
$7$	−19.9138			−1.07524			−0.537622	+	0.843186i	$0.680677\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	21.7941	−	15.8344i	0.807190	−	0.586458i
$10$		0			0
$11$	1.78841	+	1.29936i	0.0490206	+	0.0356155i	0.612026	−	0.790838i	$-0.290355\pi$
$11$	1.78841	+	1.29936i	0.0490206	+	0.0356155i	−0.563005	+	0.826453i	$0.690355\pi$
$12$	0.799170	−	0.580631i	0.0192250	−	0.0139678i
$13$	9.95462	−	7.23245i	0.212378	−	0.154302i	−0.476511	−	0.879169i	$-0.658099\pi$
$13$	9.95462	−	7.23245i	0.212378	−	0.154302i	0.688889	+	0.724867i	$0.258099\pi$
$14$	32.2212	+	23.4101i	0.615105	+	0.446900i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	−23.0023	+	70.7939i	−0.328170	+	1.01000i	0.641820	+	0.766856i	$0.278180\pi$
$17$	−23.0023	+	70.7939i	−0.328170	+	1.01000i	−0.969989	+	0.243147i	$0.921820\pi$
$18$	−53.8780			−0.705510
$19$	−15.5949	+	47.9960i	−0.188300	+	0.579529i	−0.999990	−	0.00456072i	$-0.998548\pi$
$19$	−15.5949	+	47.9960i	−0.188300	+	0.579529i	0.811689	+	0.584089i	$0.198548\pi$
$20$		0			0
$21$	1.51970	+	4.67716i	0.0157917	+	0.0486019i
$22$	−1.36622	−	4.20481i	−0.0132400	−	0.0407485i
$23$	−161.248	−	117.154i	−1.46185	−	1.06210i	−0.982876	−	0.184268i	$-0.941009\pi$
$23$	−161.248	−	117.154i	−1.46185	−	1.06210i	−0.478974	−	0.877829i	$-0.658991\pi$
$24$	−1.97566			−0.0168033
$25$		0			0
$26$	−24.6092			−0.185625
$27$	−10.7766	−	7.82967i	−0.0768133	−	0.0558082i
$28$	−24.6148	−	75.7565i	−0.166134	−	0.511309i
$29$	74.5475	+	229.434i	0.477349	+	1.46913i	0.842763	+	0.538285i	$0.180928\pi$
$29$	74.5475	+	229.434i	0.477349	+	1.46913i	−0.365414	+	0.930845i	$0.619072\pi$
$30$		0			0
$31$	−15.8456	+	48.7679i	−0.0918052	+	0.282547i	−0.986408	−	0.164315i	$-0.947459\pi$
$31$	−15.8456	+	48.7679i	−0.0918052	+	0.282547i	0.894603	+	0.446862i	$0.147459\pi$
$32$	32.0000			0.176777
$33$	0.168700	−	0.519204i	0.000889903	−	0.00273884i
$34$	120.442	−	87.5061i	0.607517	−	0.441387i
$35$		0			0
$36$	87.1765	+	63.3374i	0.403595	+	0.293229i
$37$	−225.001	+	163.473i	−0.999729	+	0.726345i	−0.962030	−	0.272944i	$-0.912003\pi$
$37$	−225.001	+	163.473i	−0.999729	+	0.726345i	−0.0376986	+	0.999289i	$0.512003\pi$
$38$	81.6557	−	59.3264i	0.348587	−	0.253263i
$39$	−2.45836	−	1.78611i	−0.0100937	−	0.00733348i
$40$		0			0
$41$	−214.861	+	156.106i	−0.818431	+	0.594625i	−0.916263	−	0.400578i	$-0.868809\pi$
$41$	−214.861	+	156.106i	−0.818431	+	0.594625i	0.0978313	+	0.995203i	$0.468809\pi$
$42$	3.03940	−	9.35431i	0.0111664	−	0.0343667i
$43$	−103.714			−0.367818			−0.183909	−	0.982943i	$-0.558875\pi$
$43$	−103.714			−0.367818			−0.183909	+	0.982943i	$0.558875\pi$
$44$	−2.73245	+	8.40961i	−0.00936210	+	0.0288136i
$45$		0			0
$46$	123.183	+	379.117i	0.394832	+	1.21517i
$47$	127.174	+	391.402i	0.394686	+	1.21472i	0.929206	+	0.369563i	$0.120493\pi$
$47$	127.174	+	391.402i	0.394686	+	1.21472i	−0.534520	+	0.845156i	$0.679507\pi$
$48$	3.19668	+	2.32252i	0.00961252	+	0.00698391i
$49$	53.5589			0.156148
$50$		0			0
$51$	18.3828			0.0504726
$52$	39.8185	+	28.9298i	0.106189	+	0.0771508i
$53$	132.965	+	409.226i	0.344608	+	1.06059i	0.961793	+	0.273776i	$0.0882728\pi$
$53$	132.965	+	409.226i	0.344608	+	1.06059i	−0.617186	+	0.786818i	$0.711727\pi$
$54$	8.23260	+	25.3373i	0.0207466	+	0.0638514i
$55$		0			0
$56$	−49.2296	+	151.513i	−0.117475	+	0.361550i
$57$	12.4629			0.0289607
$58$	149.095	−	458.867i	0.337537	−	1.03883i
$59$	−445.750	+	323.856i	−0.983589	+	0.714619i	−0.958508	−	0.285066i	$-0.907984\pi$
$59$	−445.750	+	323.856i	−0.983589	+	0.714619i	−0.0250809	+	0.999685i	$0.507984\pi$
$60$		0			0
$61$	413.338	+	300.308i	0.867583	+	0.630336i	0.929937	−	0.367718i	$-0.119861\pi$
$61$	413.338	+	300.308i	0.867583	+	0.630336i	−0.0623543	+	0.998054i	$0.519861\pi$
$62$	82.9688	−	60.2804i	0.169952	−	0.123478i
$63$	−434.003	+	315.322i	−0.867925	+	0.630585i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−0.883322	+	0.641771i	−0.00164742	+	0.00119692i
$67$	−23.5632	+	72.5200i	−0.0429657	+	0.132235i	−0.970238	−	0.242152i	$-0.922147\pi$
$67$	−23.5632	+	72.5200i	−0.0429657	+	0.132235i	0.927273	+	0.374387i	$0.122147\pi$
$68$	−297.748			−0.530990
$69$	−15.2104	+	46.8129i	−0.0265380	+	0.0816754i
$70$		0			0
$71$	−264.409	−	813.766i	−0.441965	−	1.36023i	−0.885778	−	0.464110i	$-0.846374\pi$
$71$	−264.409	−	813.766i	−0.441965	−	1.36023i	0.443812	−	0.896120i	$-0.353626\pi$
$72$	−66.5969	−	204.964i	−0.109007	−	0.335490i
$73$	417.952	+	303.660i	0.670104	+	0.486859i	0.870060	−	0.492946i	$-0.164080\pi$
$73$	417.952	+	303.660i	0.670104	+	0.486859i	−0.199956	+	0.979805i	$0.564080\pi$
$74$	556.233			0.873795
$75$		0			0
$76$	−201.864			−0.304676
$77$	−35.6140	−	25.8751i	−0.0527090	−	0.0382954i
$78$	1.87802	+	5.77996i	0.00272621	+	0.00839041i
$79$	42.1044	+	129.584i	0.0599634	+	0.184549i	0.976551	−	0.215285i	$-0.0690680\pi$
$79$	42.1044	+	129.584i	0.0599634	+	0.184549i	−0.916588	+	0.399833i	$0.869068\pi$
$80$		0			0
$81$	223.748	−	688.626i	0.306925	−	0.944617i
$82$	531.166			0.715335
$83$	283.533	−	872.626i	0.374962	−	1.15401i	−0.568543	−	0.822654i	$-0.692493\pi$
$83$	283.533	−	872.626i	0.374962	−	1.15401i	0.943504	−	0.331360i	$-0.107507\pi$
$84$	−15.9145	+	11.5626i	−0.0206716	+	0.0150188i
$85$		0			0
$86$	167.812	+	121.923i	0.210415	+	0.152875i
$87$	48.1981	−	35.0180i	0.0593952	−	0.0431531i
$88$	14.3073	−	10.3949i	0.0173314	−	0.0125920i
$89$	−1053.94	−	765.734i	−1.25526	−	0.911997i	−0.256741	−	0.966480i	$-0.582649\pi$
$89$	−1053.94	−	765.734i	−1.25526	−	0.911997i	−0.998515	+	0.0544837i	$0.982649\pi$
$90$		0			0
$91$	−198.234	+	144.026i	−0.228358	+	0.165912i
$92$	246.365	−	758.234i	0.279189	−	0.859254i
$93$	12.6634			0.0141197
$94$	254.348	−	782.803i	0.279085	−	0.858936i
$95$		0			0
$96$	−2.44205	−	7.51585i	−0.00259625	−	0.00799045i
$97$	−137.189	−	422.225i	−0.143603	−	0.441963i	0.853226	−	0.521541i	$-0.174643\pi$
$97$	−137.189	−	422.225i	−0.143603	−	0.441963i	−0.996829	+	0.0795779i	$0.974643\pi$
$98$	−86.6601	−	62.9623i	−0.0893265	−	0.0648995i
$99$	59.5513			0.0604559
$100$		0			0
$101$	−493.360			−0.486051			−0.243025	−	0.970020i	$-0.578140\pi$
$101$	−493.360			−0.486051			−0.243025	+	0.970020i	$0.578140\pi$
$102$	−29.7440	−	21.6103i	−0.0288734	−	0.0209778i
$103$	531.904	+	1637.03i	0.508835	+	1.56603i	0.794226	+	0.607623i	$0.207877\pi$
$103$	531.904	+	1637.03i	0.508835	+	1.56603i	−0.285391	+	0.958411i	$0.592123\pi$
$104$	−30.4186	−	93.6188i	−0.0286807	−	0.0882700i
$105$		0			0
$106$	265.931	−	818.451i	0.243675	−	0.749953i
$107$	−1241.00			−1.12124			−0.560618	−	0.828074i	$-0.689437\pi$
$107$	−1241.00			−1.12124			−0.560618	+	0.828074i	$0.689437\pi$
$108$	16.4652	−	50.6747i	0.0146700	−	0.0451498i
$109$	−142.969	+	103.873i	−0.125632	+	0.0912772i	−0.648827	−	0.760936i	$-0.724740\pi$
$109$	−142.969	+	103.873i	−0.125632	+	0.0912772i	0.523195	+	0.852213i	$0.324740\pi$
$110$		0			0
$111$	55.5657	+	40.3708i	0.0475140	+	0.0345210i
$112$	257.769	−	187.280i	0.217473	−	0.158003i
$113$	−155.126	+	112.705i	−0.129141	+	0.0938268i	−0.650481	−	0.759523i	$-0.725433\pi$
$113$	−155.126	+	112.705i	−0.129141	+	0.0938268i	0.521339	+	0.853349i	$0.325433\pi$
$114$	−20.1655	−	14.6511i	−0.0165673	−	0.0120368i
$115$		0			0
$116$	−780.672	+	567.191i	−0.624858	+	0.453986i
$117$	102.431	−	315.250i	0.0809379	−	0.249101i
$118$	1101.96			0.859688
$119$	458.064	−	1409.77i	0.352862	−	1.08600i
$120$		0			0
$121$	−409.792	−	1261.21i	−0.307882	−	0.947565i
$122$	−315.762	−	971.817i	−0.234326	−	0.721182i
$123$	53.0615	+	38.5515i	0.0388975	+	0.0282607i
$124$	−205.110			−0.148544
$125$		0			0
$126$	1072.92			0.758595
$127$	−248.648	−	180.653i	−0.173732	−	0.126224i	0.497521	−	0.867452i	$-0.334244\pi$
$127$	−248.648	−	180.653i	−0.173732	−	0.126224i	−0.671253	+	0.741228i	$0.734244\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	7.91481	+	24.3593i	0.00540201	+	0.0166257i
$130$		0			0
$131$	868.243	−	2672.18i	0.579074	−	1.78221i	−0.0427928	−	0.999084i	$-0.513626\pi$
$131$	868.243	−	2672.18i	0.579074	−	1.78221i	0.621867	−	0.783123i	$-0.286374\pi$
$132$	2.18369			0.00143989
$133$	310.553	−	955.783i	0.202469	−	0.623134i
$134$	123.378	−	89.6397i	0.0795394	−	0.0577887i
$135$		0			0
$136$	481.767	+	350.024i	0.303759	+	0.220694i
$137$	1586.38	−	1152.57i	0.989293	−	0.718764i	0.0295271	−	0.999564i	$-0.490600\pi$
$137$	1586.38	−	1152.57i	0.989293	−	0.718764i	0.959766	+	0.280800i	$0.0905999\pi$
$138$	79.6428	−	57.8639i	0.0491279	−	0.0356935i
$139$	1277.07	+	927.849i	0.779281	+	0.566181i	0.904763	−	0.425915i	$-0.140048\pi$
$139$	1277.07	+	927.849i	0.779281	+	0.566181i	−0.125482	+	0.992096i	$0.540048\pi$
$140$		0			0
$141$	82.2234	−	59.7388i	0.0491097	−	0.0356803i
$142$	−528.817	+	1627.53i	−0.312517	+	0.961828i
$143$	27.2005			0.0159064
$144$	−133.194	+	409.928i	−0.0770797	+	0.237227i
$145$		0			0
$146$	−319.287	−	982.665i	−0.180989	−	0.557027i
$147$	−4.08729	−	12.5794i	−0.00229329	−	0.00705803i
$148$	−900.005	−	653.892i	−0.499864	−	0.363173i
$149$	−1448.55			−0.796443			−0.398221	−	0.917289i	$-0.630372\pi$
$149$	−1448.55			−0.796443			−0.398221	+	0.917289i	$0.630372\pi$
$150$		0			0
$151$	−1804.96			−0.972754			−0.486377	−	0.873749i	$-0.661682\pi$
$151$	−1804.96			−0.972754			−0.486377	+	0.873749i	$0.661682\pi$
$152$	326.623	+	237.305i	0.174294	+	0.126632i
$153$	619.660	+	1907.12i	0.327428	+	1.00772i
$154$	27.2067	+	83.7336i	0.0142362	+	0.0438146i
$155$		0			0
$156$	3.75605	−	11.5599i	0.00192772	−	0.00593291i
$157$	1998.98			1.01615			0.508076	−	0.861312i	$-0.330357\pi$
$157$	1998.98			1.01615			0.508076	+	0.861312i	$0.330357\pi$
$158$	84.2087	−	259.168i	0.0424006	−	0.130495i
$159$	85.9678	−	62.4593i	0.0428786	−	0.0311531i
$160$		0			0
$161$	3211.06	+	2332.97i	1.57185	+	1.14201i
$162$	−1171.56	+	851.188i	−0.568188	+	0.412813i
$163$	−397.428	+	288.748i	−0.190975	+	0.138752i	−0.679164	−	0.733986i	$-0.737658\pi$
$163$	−397.428	+	288.748i	−0.190975	+	0.138752i	0.488189	+	0.872738i	$0.337658\pi$
$164$	−859.445	−	624.423i	−0.409216	−	0.297313i
$165$		0			0
$166$	−1484.60	+	1078.63i	−0.694140	+	0.504323i
$167$	105.206	−	323.790i	0.0487489	−	0.150034i	−0.923719	−	0.383071i	$-0.874866\pi$
$167$	105.206	−	323.790i	0.0487489	−	0.150034i	0.972468	+	0.233037i	$0.0748664\pi$
$168$	39.3428			0.0180676
$169$	−632.124	+	1945.48i	−0.287722	+	0.885516i
$170$		0			0
$171$	420.110	+	1292.97i	0.187875	+	0.578220i
$172$	−128.197	−	394.550i	−0.0568311	−	0.174908i
$173$	−1762.17	−	1280.29i	−0.774423	−	0.562651i	0.128877	−	0.991661i	$-0.458863\pi$
$173$	−1762.17	−	1280.29i	−0.774423	−	0.562651i	−0.903300	+	0.429009i	$0.858863\pi$
$174$	−119.152			−0.0519133
$175$		0			0
$176$	−35.3696			−0.0151482
$177$	110.081	+	79.9787i	0.0467470	+	0.0339637i
$178$	805.141	+	2477.97i	0.339033	+	1.04344i
$179$	−1063.04	−	3271.69i	−0.443884	−	1.36613i	−0.883703	−	0.468047i	$-0.844958\pi$
$179$	−1063.04	−	3271.69i	−0.443884	−	1.36613i	0.439820	−	0.898086i	$-0.355042\pi$
$180$		0			0
$181$	−624.898	+	1923.24i	−0.256621	+	0.789797i	0.736886	+	0.676018i	$0.236296\pi$
$181$	−624.898	+	1923.24i	−0.256621	+	0.789797i	−0.993506	+	0.113779i	$0.963704\pi$
$182$	490.062			0.199592
$183$	38.9899	−	119.999i	0.0157498	−	0.0484730i
$184$	−1289.99	+	937.229i	−0.516842	+	0.375508i
$185$		0			0
$186$	−20.4898	−	14.8867i	−0.00807732	−	0.00586852i
$187$	−133.124	+	96.7204i	−0.0520588	+	0.0378230i
$188$	−1331.78	+	967.598i	−0.516651	+	0.375369i
$189$	214.603	+	155.918i	0.0825930	+	0.0600074i
$190$		0			0
$191$	−3904.88	+	2837.06i	−1.47930	+	1.07478i	−0.501523	+	0.865144i	$0.667227\pi$
$191$	−3904.88	+	2837.06i	−1.47930	+	1.07478i	−0.977780	+	0.209633i	$0.932773\pi$
$192$	−4.88409	+	15.0317i	−0.00183583	+	0.00565010i
$193$	3075.17			1.14692			0.573460	−	0.819233i	$-0.305601\pi$
$193$	3075.17			1.14692			0.573460	+	0.819233i	$0.305601\pi$
$194$	−274.378	+	844.450i	−0.101542	+	0.312515i
$195$		0			0
$196$	66.2025	+	203.750i	0.0241263	+	0.0742530i
$197$	1308.56	+	4027.34i	0.473255	+	1.45653i	0.848297	+	0.529521i	$0.177628\pi$
$197$	1308.56	+	4027.34i	0.473255	+	1.45653i	−0.375042	+	0.927008i	$0.622372\pi$
$198$	−96.3561	−	70.0068i	−0.0345845	−	0.0251271i
$199$	4126.17			1.46983			0.734915	−	0.678159i	$-0.237222\pi$
$199$	4126.17			1.46983			0.734915	+	0.678159i	$0.237222\pi$
$200$		0			0
$201$	18.8310			0.00660814
$202$	798.273	+	579.979i	0.278051	+	0.202016i
$203$	−1484.52	−	4568.89i	−0.513267	−	1.57967i
$204$	22.7224	+	69.9322i	0.00779845	+	0.0240012i
$205$		0			0
$206$	1063.81	−	3274.06i	0.359801	−	1.10735i
$207$	−5369.31			−1.80287
$208$	−60.8372	+	187.238i	−0.0202803	+	0.0624163i
$209$	−90.2540	+	65.5734i	−0.0298708	+	0.0217024i
$210$		0			0
$211$	4109.67	+	2985.85i	1.34086	+	0.974192i	0.999412	+	0.0342918i	$0.0109176\pi$
$211$	4109.67	+	2985.85i	1.34086	+	0.974192i	0.341449	+	0.939900i	$0.389082\pi$
$212$	−1392.43	+	1011.66i	−0.451098	+	0.327742i
$213$	−170.951	+	124.203i	−0.0549925	+	0.0399544i
$214$	2007.99	+	1458.89i	0.641416	+	0.466016i
$215$		0			0
$216$	−86.2129	+	62.6373i	−0.0271576	+	0.0197312i
$217$	315.547	−	971.153i	0.0987129	−	0.303807i
$218$	353.438			0.109807
$219$	39.4251	−	121.338i	0.0121649	−	0.0374396i
$220$		0			0
$221$	283.034	+	871.089i	0.0861490	+	0.265139i
$222$	−42.4484	−	130.643i	−0.0128331	−	0.0394962i
$223$	−3992.51	−	2900.73i	−1.19892	−	0.871064i	−0.204740	−	0.978816i	$-0.565635\pi$
$223$	−3992.51	−	2900.73i	−1.19892	−	0.871064i	−0.994178	+	0.107752i	$0.965635\pi$
$224$	−637.241			−0.190078
$225$		0			0
$226$	383.492			0.112874
$227$	564.855	+	410.391i	0.165158	+	0.119994i	0.667294	−	0.744794i	$-0.267452\pi$
$227$	564.855	+	410.391i	0.165158	+	0.119994i	−0.502136	+	0.864788i	$0.667452\pi$
$228$	15.4050	+	47.4119i	0.00447467	+	0.0137716i
$229$	1916.69	+	5898.95i	0.553092	+	1.70224i	0.700929	+	0.713231i	$0.252769\pi$
$229$	1916.69	+	5898.95i	0.553092	+	1.70224i	−0.147836	+	0.989012i	$0.547231\pi$
$230$		0			0
$231$	−3.35945	+	10.3393i	−0.000956863	+	0.00294492i
$232$	1929.93			0.546146
$233$	844.535	−	2599.21i	0.237456	−	0.730815i	−0.759330	−	0.650706i	$-0.774473\pi$
$233$	844.535	−	2599.21i	0.237456	−	0.730815i	0.996786	−	0.0801094i	$-0.0255270\pi$
$234$	−536.335	+	389.670i	−0.149835	+	0.108861i
$235$		0			0
$236$	−1783.00	−	1295.43i	−0.491794	−	0.357310i
$237$	27.2223	−	19.7781i	0.00746108	−	0.00542079i
$238$	−2398.45	+	1742.58i	−0.653229	+	0.474599i
$239$	1197.49	+	870.027i	0.324097	+	0.235470i	0.737922	−	0.674886i	$-0.235807\pi$
$239$	1197.49	+	870.027i	0.324097	+	0.235470i	−0.413825	+	0.910357i	$0.635807\pi$
$240$		0			0
$241$	−209.377	+	152.121i	−0.0559633	+	0.0406597i	−0.615415	−	0.788203i	$-0.711012\pi$
$241$	−209.377	+	152.121i	−0.0559633	+	0.0406597i	0.559452	+	0.828863i	$0.311012\pi$
$242$	−819.583	+	2522.42i	−0.217706	+	0.670029i
$243$	−538.470			−0.142152
$244$	−631.525	+	1943.63i	−0.165694	+	0.509952i
$245$		0			0
$246$	−40.5354	−	124.755i	−0.0105059	−	0.0323337i
$247$	191.888	+	590.571i	0.0494314	+	0.152134i
$248$	331.875	+	241.122i	0.0849762	+	0.0617388i
$249$	−226.591			−0.0576693
$250$		0			0
$251$	−3432.35			−0.863139			−0.431570	−	0.902080i	$-0.642040\pi$
$251$	−3432.35			−0.863139			−0.431570	+	0.902080i	$0.642040\pi$
$252$	−1736.01	−	1261.29i	−0.433963	−	0.315292i
$253$	−136.154	−	419.038i	−0.0338336	−	0.104129i
$254$	189.950	+	584.607i	0.0469234	+	0.144415i
$255$		0			0
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	3106.91			0.754100			0.377050	−	0.926193i	$-0.376939\pi$
$257$	3106.91			0.754100			0.377050	+	0.926193i	$0.376939\pi$
$258$	15.8296	−	48.7185i	0.00381980	−	0.0117561i
$259$	4480.62	−	3255.36i	1.07495	−	0.780998i
$260$		0			0
$261$	5257.63	+	3819.89i	1.24689	+	0.905921i
$262$	−4546.18	+	3302.99i	−1.07200	+	0.778853i
$263$	−4010.07	+	2913.49i	−0.940195	+	0.683092i	−0.948468	−	0.316874i	$-0.897367\pi$
$263$	−4010.07	+	2913.49i	−0.940195	+	0.683092i	0.00827224	+	0.999966i	$0.497367\pi$
$264$	−3.53329	−	2.56708i	−0.000823708	−	0.000598459i
$265$		0			0
$266$	−1626.07	+	1181.41i	−0.374816	+	0.272320i
$267$	−99.4177	+	305.976i	−0.0227875	+	0.0701327i
$268$	−305.008			−0.0695200
$269$	740.660	−	2279.52i	0.167877	−	0.516671i	−0.831360	−	0.555734i	$-0.812437\pi$
$269$	740.660	−	2279.52i	0.167877	−	0.516671i	0.999237	+	0.0390628i	$0.0124373\pi$
$270$		0			0
$271$	−2005.70	−	6172.92i	−0.449586	−	1.38368i	−0.877375	−	0.479805i	$-0.840707\pi$
$271$	−2005.70	−	6172.92i	−0.449586	−	1.38368i	0.427789	−	0.903879i	$-0.359293\pi$
$272$	−368.037	−	1132.70i	−0.0820424	−	0.252501i
$273$	48.9553	+	35.5681i	0.0108532	+	0.00788528i
$274$	−3921.74			−0.864674
$275$		0			0
$276$	−196.888			−0.0429393
$277$	−3077.41	−	2235.87i	−0.667521	−	0.484983i	0.201673	−	0.979453i	$-0.435362\pi$
$277$	−3077.41	−	2235.87i	−0.667521	−	0.484983i	−0.869195	+	0.494470i	$0.835362\pi$
$278$	−975.598	−	3002.58i	−0.210477	−	0.647780i
$279$	426.866	+	1313.76i	0.0915978	+	0.281909i
$280$		0			0
$281$	78.9690	−	243.042i	0.0167647	−	0.0515966i	−0.942324	−	0.334702i	$-0.891364\pi$
$281$	78.9690	−	243.042i	0.0167647	−	0.0515966i	0.959089	+	0.283105i	$0.0913645\pi$
$282$	−203.268			−0.0429234
$283$	633.484	−	1949.66i	0.133063	−	0.409525i	−0.862221	−	0.506532i	$-0.830927\pi$
$283$	633.484	−	1949.66i	0.133063	−	0.409525i	0.995284	+	0.0970075i	$0.0309271\pi$
$284$	2768.92	−	2011.74i	0.578540	−	0.420334i
$285$		0			0
$286$	−44.0113	−	31.9761i	−0.00909945	−	0.00661114i
$287$	4278.70	−	3108.66i	0.880013	−	0.639367i
$288$	697.412	−	506.699i	0.142692	−	0.103672i
$289$	−507.968	−	369.060i	−0.103393	−	0.0751191i
$290$		0			0
$291$	−88.6986	+	64.4433i	−0.0178681	+	0.0129819i
$292$	−638.574	+	1965.33i	−0.127979	+	0.393878i
$293$	6743.02			1.34448			0.672238	−	0.740335i	$-0.265333\pi$
$293$	6743.02			1.34448			0.672238	+	0.740335i	$0.265333\pi$
$294$	−8.17459	+	25.1588i	−0.00162160	+	0.00499078i
$295$		0			0
$296$	687.542	+	2116.04i	0.135009	+	0.415514i
$297$	−9.09948	−	28.0053i	−0.00177780	−	0.00547150i
$298$	2343.81	+	1702.87i	0.455614	+	0.331023i
$299$	−2452.47			−0.474348
$300$		0			0
$301$	2065.33			0.395494
$302$	2920.49	+	2121.86i	0.556475	+	0.404303i
$303$	37.6503	+	115.876i	0.00713845	+	0.0219699i
$304$	−249.518	−	767.937i	−0.0470751	−	0.144882i
$305$		0			0
$306$	1239.32	−	3814.24i	0.231527	−	0.712566i
$307$	−4999.71			−0.929474			−0.464737	−	0.885449i	$-0.653851\pi$
$307$	−4999.71			−0.929474			−0.464737	+	0.885449i	$0.653851\pi$
$308$	54.4134	−	167.467i	0.0100665	−	0.0309816i
$309$	343.898	−	249.857i	0.0633129	−	0.0459995i
$310$		0			0
$311$	−5557.45	−	4037.73i	−1.01329	−	0.736201i	−0.0483961	−	0.998828i	$-0.515411\pi$
$311$	−5557.45	−	4037.73i	−1.01329	−	0.736201i	−0.964897	+	0.262627i	$0.915411\pi$
$312$	−19.6669	+	14.2889i	−0.00356865	+	0.00259278i
$313$	363.202	−	263.882i	0.0655892	−	0.0476533i	−0.554508	−	0.832179i	$-0.687093\pi$
$313$	363.202	−	263.882i	0.0655892	−	0.0476533i	0.620097	+	0.784525i	$0.287093\pi$
$314$	−3234.42	−	2349.94i	−0.581301	−	0.422340i
$315$		0			0
$316$	−440.923	+	320.349i	−0.0784932	+	0.0570286i
$317$	2069.60	−	6369.56i	0.366688	−	1.12855i	−0.582229	−	0.813025i	$-0.697819\pi$
$317$	2069.60	−	6369.56i	0.366688	−	1.12855i	0.948917	−	0.315525i	$-0.102181\pi$
$318$	−212.524			−0.0374772
$319$	−164.795	+	507.186i	−0.0289239	+	0.0890186i
$320$		0			0
$321$	94.7059	+	291.475i	0.0164672	+	0.0506808i
$322$	−2453.03	−	7549.66i	−0.424541	−	1.30660i
$323$	−3039.11	−	2208.04i	−0.523531	−	0.380368i
$324$	2896.25			0.496614
$325$		0			0
$326$	982.496			0.166918
$327$	35.3071	+	25.6521i	0.00597091	+	0.00433812i
$328$	656.558	+	2020.68i	0.110525	+	0.340162i
$329$	−2532.52	−	7794.29i	−0.424384	−	1.30612i
$330$		0			0
$331$	−130.339	+	401.141i	−0.0216437	+	0.0666125i	−0.961295	−	0.275521i	$-0.911150\pi$
$331$	−130.339	+	401.141i	−0.0216437	+	0.0666125i	0.939651	+	0.342134i	$0.111150\pi$
$332$	3670.13			0.606701
$333$	−2315.21	+	7125.50i	−0.381000	+	1.17260i
$334$	−550.865	+	400.227i	−0.0902454	+	0.0655672i
$335$		0			0
$336$	−63.6580	−	46.2503i	−0.0103358	−	0.00750940i
$337$	3694.07	−	2683.90i	0.597118	−	0.433832i	−0.247737	−	0.968827i	$-0.579687\pi$
$337$	3694.07	−	2683.90i	0.597118	−	0.433832i	0.844855	+	0.534996i	$0.179687\pi$
$338$	3309.85	−	2404.74i	0.532639	−	0.386985i
$339$	38.3094	+	27.8334i	0.00613770	+	0.00445930i
$340$		0			0
$341$	−91.7054	+	66.6279i	−0.0145634	+	0.0105809i
$342$	840.220	−	2585.93i	0.132848	−	0.408863i
$343$	5763.87			0.907346
$344$	−256.394	+	789.101i	−0.0401856	+	0.123679i
$345$		0			0
$346$	1346.18	+	4143.11i	0.209165	+	0.643742i
$347$	1897.93	+	5841.24i	0.293621	+	0.903672i	0.983681	+	0.179920i	$0.0575840\pi$
$347$	1897.93	+	5841.24i	0.293621	+	0.903672i	−0.690060	+	0.723752i	$0.742416\pi$
$348$	192.793	+	140.072i	0.0296976	+	0.0215766i
$349$	−7456.55			−1.14367			−0.571834	−	0.820369i	$-0.693768\pi$
$349$	−7456.55			−1.14367			−0.571834	+	0.820369i	$0.693768\pi$
$350$		0			0
$351$	−163.905			−0.0249248
$352$	57.2292	+	41.5794i	0.00866569	+	0.00629600i
$353$	2041.06	+	6281.74i	0.307747	+	0.947149i	0.978638	+	0.205592i	$0.0659121\pi$
$353$	2041.06	+	6281.74i	0.307747	+	0.947149i	−0.670890	+	0.741557i	$0.734088\pi$
$354$	−84.0946	−	258.816i	−0.0126259	−	0.0388586i
$355$		0			0
$356$	1610.28	−	4955.94i	0.239732	−	0.737821i
$357$	−366.071			−0.0542704
$358$	−2126.08	+	6543.39i	−0.313873	+	0.966002i
$359$	−861.031	+	625.575i	−0.126583	+	0.0919683i	−0.649275	−	0.760553i	$-0.724928\pi$
$359$	−861.031	+	625.575i	−0.126583	+	0.0919683i	0.522692	+	0.852522i	$0.324928\pi$
$360$		0			0
$361$	3488.63	+	2534.64i	0.508620	+	0.369534i
$362$	3272.01	−	2377.25i	0.475063	−	0.345154i
$363$	−264.948	+	192.496i	−0.0383089	+	0.0278331i
$364$	−792.937	−	576.102i	−0.114179	−	0.0829559i
$365$		0			0
$366$	−204.154	+	148.326i	−0.0291565	+	0.0211835i
$367$	−498.684	+	1534.79i	−0.0709295	+	0.218298i	−0.980237	−	0.197826i	$-0.936612\pi$
$367$	−498.684	+	1534.79i	−0.0709295	+	0.218298i	0.909308	+	0.416124i	$0.136612\pi$
$368$	3189.02			0.451737
$369$	−2210.88	+	6804.38i	−0.311907	+	0.959951i
$370$		0			0
$371$	−2647.85	−	8149.23i	−0.370537	−	1.14040i
$372$	15.6528	+	48.1743i	0.00218161	+	0.00671430i
$373$	6039.40	+	4387.88i	0.838360	+	0.609105i	0.921912	−	0.387399i	$-0.126626\pi$
$373$	6039.40	+	4387.88i	0.838360	+	0.609105i	−0.0835517	+	0.996503i	$0.526626\pi$
$374$	329.101			0.0455011
$375$		0			0
$376$	3292.35			0.451569
$377$	2401.46	+	1744.76i	0.328068	+	0.238355i
$378$	−163.942	−	504.562i	−0.0223076	−	0.0686558i
$379$	−2315.82	−	7127.35i	−0.313867	−	0.965982i	−0.976218	−	0.216789i	$-0.930442\pi$
$379$	−2315.82	−	7127.35i	−0.313867	−	0.965982i	0.662352	−	0.749193i	$-0.269558\pi$
$380$		0			0
$381$	−23.4548	+	72.1864i	−0.00315387	+	0.00970662i
$382$	9653.39			1.29296
$383$	−1357.19	+	4177.01i	−0.181069	+	0.557272i	−0.999859	−	0.0168213i	$-0.994645\pi$
$383$	−1357.19	+	4177.01i	−0.181069	+	0.557272i	0.818790	+	0.574093i	$0.194645\pi$
$384$	25.5734	−	18.5802i	0.00339854	−	0.00246918i
$385$		0			0
$386$	−4975.73	−	3615.08i	−0.656109	−	0.476691i
$387$	−2260.35	+	1642.24i	−0.296899	+	0.215710i
$388$	1436.66	−	1043.80i	0.187978	−	0.136574i
$389$	−4663.78	−	3388.43i	−0.607874	−	0.441646i	0.240791	−	0.970577i	$-0.422593\pi$
$389$	−4663.78	−	3388.43i	−0.607874	−	0.441646i	−0.848665	+	0.528931i	$0.822593\pi$
$390$		0			0
$391$	12002.8	−	8720.58i	1.55246	−	1.12792i
$392$	132.405	−	407.500i	0.0170598	−	0.0525048i
$393$	−693.874			−0.0890618
$394$	2617.13	−	8054.68i	0.334642	−	1.02992i
$395$		0			0
$396$	73.6095	+	226.547i	0.00934095	+	0.0287485i
$397$	493.669	+	1519.36i	0.0624094	+	0.192076i	0.977400	−	0.211399i	$-0.0678020\pi$
$397$	493.669	+	1519.36i	0.0624094	+	0.192076i	−0.914990	+	0.403476i	$0.867802\pi$
$398$	−6676.28	−	4850.60i	−0.840833	−	0.610901i
$399$	−248.184			−0.0311398
$400$		0			0
$401$	−4722.70			−0.588130			−0.294065	−	0.955785i	$-0.595008\pi$
$401$	−4722.70			−0.588130			−0.294065	+	0.955785i	$0.595008\pi$
$402$	−30.4692	−	22.1372i	−0.00378026	−	0.00274652i
$403$	194.974	+	600.068i	0.0241001	+	0.0741725i
$404$	−609.826	−	1876.85i	−0.0750990	−	0.231131i
$405$		0			0
$406$	−2969.05	+	9137.79i	−0.362934	+	1.11700i
$407$	−614.804			−0.0748764
$408$	45.4447	−	139.864i	0.00551434	−	0.0169714i
$409$	−4715.79	+	3426.22i	−0.570124	+	0.414219i	−0.835150	−	0.550022i	$-0.814619\pi$
$409$	−4715.79	+	3426.22i	−0.570124	+	0.414219i	0.265026	+	0.964241i	$0.414619\pi$
$410$		0			0
$411$	−391.767	−	284.635i	−0.0470181	−	0.0341606i
$412$	−5570.17	+	4046.96i	−0.666074	+	0.483931i
$413$	8876.57	−	6449.21i	1.05760	−	0.768389i
$414$	8687.73	+	6312.01i	1.03135	+	0.749319i
$415$		0			0
$416$	318.548	−	231.438i	0.0375435	−	0.0272769i
$417$	120.466	−	370.755i	0.0141468	−	0.0435394i
$418$	223.120			0.0261080
$419$	351.782	−	1082.68i	0.0410160	−	0.126234i	−0.928452	−	0.371453i	$-0.878860\pi$
$419$	351.782	−	1082.68i	0.0410160	−	0.126234i	0.969468	+	0.245219i	$0.0788597\pi$
$420$		0			0
$421$	−317.103	−	975.942i	−0.0367094	−	0.112980i	0.931023	−	0.364961i	$-0.118918\pi$
$421$	−317.103	−	975.942i	−0.0367094	−	0.112980i	−0.967732	+	0.251982i	$0.918918\pi$
$422$	−3139.51	−	9662.42i	−0.362154	−	1.11460i
$423$	8969.24	+	6516.53i	1.03097	+	0.749042i
$424$	3442.28			0.394274
$425$		0			0
$426$	422.615			0.0480652
$427$	−8231.13	−	5980.27i	−0.932863	−	0.677765i
$428$	−1533.96	−	4721.06i	−0.173241	−	0.533180i
$429$	−2.07578	−	6.38859i	−0.000233612	−	0.000718983i
$430$		0			0
$431$	−1729.47	+	5322.77i	−0.193285	+	0.594870i	0.806707	+	0.590951i	$0.201247\pi$
$431$	−1729.47	+	5322.77i	−0.193285	+	0.594870i	−0.999992	+	0.00391889i	$0.998753\pi$
$432$	213.130			0.0237366
$433$	271.516	−	835.639i	0.0301344	−	0.0927443i	−0.934858	−	0.355022i	$-0.884474\pi$
$433$	271.516	−	835.639i	0.0301344	−	0.0927443i	0.964993	+	0.262277i	$0.0844735\pi$
$434$	−1652.22	+	1200.41i	−0.182740	+	0.132769i
$435$		0			0
$436$	−571.875	−	415.491i	−0.0628161	−	0.0456386i
$437$	8137.55	−	5912.28i	0.890782	−	0.647191i
$438$	−206.433	+	149.982i	−0.0225199	+	0.0163617i
$439$	5667.04	+	4117.35i	0.616112	+	0.447632i	0.851561	−	0.524255i	$-0.175656\pi$
$439$	5667.04	+	4117.35i	0.616112	+	0.447632i	−0.235449	+	0.971887i	$0.575656\pi$
$440$		0			0
$441$	1167.27	−	848.071i	0.126041	−	0.0915744i
$442$	566.068	−	1742.18i	0.0609166	−	0.187482i
$443$	−17736.5			−1.90223			−0.951114	−	0.308839i	$-0.900060\pi$
$443$	−17736.5			−1.90223			−0.951114	+	0.308839i	$0.900060\pi$
$444$	−84.8968	+	261.285i	−0.00907437	+	0.0279281i
$445$		0			0
$446$	3050.01	+	9386.97i	0.323816	+	0.996605i
$447$	110.545	+	340.222i	0.0116971	+	0.0359999i
$448$	1031.08	+	749.122i	0.108736	+	0.0790015i
$449$	4292.26			0.451146			0.225573	−	0.974226i	$-0.427575\pi$
$449$	4292.26			0.451146			0.225573	+	0.974226i	$0.427575\pi$
$450$		0			0
$451$	−587.097			−0.0612979
$452$	−620.502	−	450.821i	−0.0645707	−	0.0469134i
$453$	137.744	+	423.932i	0.0142865	+	0.0439692i
$454$	−431.511	−	1328.05i	−0.0446075	−	0.137288i
$455$		0			0
$456$	30.8101	−	94.8237i	0.00316407	−	0.00973800i
$457$	−17409.6			−1.78203			−0.891015	−	0.453973i	$-0.850006\pi$
$457$	−17409.6			−1.78203			−0.891015	+	0.453973i	$0.850006\pi$
$458$	3833.37	−	11797.9i	0.391095	−	1.20367i
$459$	802.180	−	582.818i	0.0815742	−	0.0592671i
$460$		0			0
$461$	−11842.5	−	8604.09i	−1.19644	−	0.869267i	−0.202513	−	0.979279i	$-0.564911\pi$
$461$	−11842.5	−	8604.09i	−1.19644	−	0.869267i	−0.993930	+	0.110012i	$0.964911\pi$
$462$	17.5903	−	12.7801i	0.00177137	−	0.00128698i
$463$	−6102.97	+	4434.07i	−0.612590	+	0.445072i	−0.850325	−	0.526258i	$-0.823595\pi$
$463$	−6102.97	+	4434.07i	−0.612590	+	0.445072i	0.237736	+	0.971330i	$0.423595\pi$
$464$	−3122.69	−	2268.77i	−0.312429	−	0.226993i
$465$		0			0
$466$	−4422.04	+	3212.80i	−0.439586	+	0.319378i
$467$	−1090.40	+	3355.89i	−0.108046	+	0.332532i	−0.990433	−	0.137992i	$-0.955935\pi$
$467$	−1090.40	+	3355.89i	−0.108046	+	0.332532i	0.882387	+	0.470524i	$0.155935\pi$
$468$	1325.89			0.130960
$469$	469.232	−	1444.15i	0.0461986	−	0.142185i
$470$		0			0
$471$	−152.550	−	469.501i	−0.0149239	−	0.0459309i
$472$	1362.09	+	4192.09i	0.132829	+	0.408806i
$473$	−185.483	−	134.761i	−0.0180307	−	0.0131001i
$474$	−67.2971			−0.00652122
$475$		0			0
$476$	5929.30			0.570943
$477$	9377.69	+	6813.29i	0.900157	+	0.654002i
$478$	−914.801	−	2815.47i	−0.0875356	−	0.269407i
$479$	2295.73	+	7065.53i	0.218987	+	0.673971i	0.998847	+	0.0480172i	$0.0152902\pi$
$479$	2295.73	+	7065.53i	0.218987	+	0.673971i	−0.779860	+	0.625954i	$0.784710\pi$
$480$		0			0
$481$	−1057.49	+	3254.62i	−0.100244	+	0.308520i
$482$	517.608			0.0489137
$483$	302.897	−	932.221i	0.0285348	−	0.0878210i
$484$	4291.39	−	3117.88i	0.403023	−	0.292814i
$485$		0			0
$486$	871.262	+	633.009i	0.0813195	+	0.0590820i
$487$	−11340.5	+	8239.35i	−1.05521	+	0.766654i	−0.973196	−	0.229977i	$-0.926135\pi$
$487$	−11340.5	+	8239.35i	−1.05521	+	0.766654i	−0.0820130	+	0.996631i	$0.526135\pi$
$488$	3306.71	−	2402.46i	0.306737	−	0.222857i
$489$	98.1477	+	71.3085i	0.00907647	+	0.00659444i
$490$		0			0
$491$	2914.25	−	2117.33i	0.267858	−	0.194610i	−0.445746	−	0.895159i	$-0.647062\pi$
$491$	2914.25	−	2117.33i	0.267858	−	0.194610i	0.713604	+	0.700549i	$0.247062\pi$
$492$	−81.0708	+	249.510i	−0.00742877	+	0.0228634i
$493$	−17957.3			−1.64048
$494$	383.776	−	1181.14i	0.0349533	−	0.107575i
$495$		0			0
$496$	−253.530	−	780.286i	−0.0229513	−	0.0706368i
$497$	5265.38	+	16205.2i	0.475220	+	1.46258i
$498$	366.633	+	266.374i	0.0329904	+	0.0239689i
$499$	4905.02			0.440037			0.220019	−	0.975496i	$-0.429388\pi$
$499$	4905.02			0.440037			0.220019	+	0.975496i	$0.429388\pi$
$500$		0			0
$501$	−84.0774			−0.00749760
$502$	5553.66	+	4034.97i	0.493769	+	0.358744i
$503$	−5019.49	−	15448.4i	−0.444946	−	1.36940i	−0.882543	−	0.470232i	$-0.844170\pi$
$503$	−5019.49	−	15448.4i	−0.444946	−	1.36940i	0.437597	−	0.899171i	$-0.355830\pi$
$504$	1326.20	+	4081.61i	0.117209	+	0.360733i
$505$		0			0
$506$	−272.307	+	838.076i	−0.0239240	+	0.0736304i
$507$	505.175			0.0442517
$508$	379.901	−	1169.21i	0.0331798	−	0.102117i
$509$	−11603.2	+	8430.21i	−1.01042	+	0.734111i	−0.964297	−	0.264825i	$-0.914686\pi$
$509$	−11603.2	+	8430.21i	−1.01042	+	0.734111i	−0.0461207	+	0.998936i	$0.514686\pi$
$510$		0			0
$511$	−8323.01	−	6047.02i	−0.720525	−	0.523492i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	543.853	−	395.132i	0.0468064	−	0.0340068i
$514$	−5027.08	−	3652.39i	−0.431391	−	0.313424i
$515$		0			0
$516$	−82.8849	+	60.2194i	−0.00707133	+	0.00513762i
$517$	−281.131	+	865.232i	−0.0239151	+	0.0736032i
$518$	−11076.7			−0.939542
$519$	−166.224	+	511.585i	−0.0140586	+	0.0432680i
$520$		0			0
$521$	3425.75	+	10543.4i	0.288071	+	0.886591i	0.985461	+	0.169900i	$0.0543444\pi$
$521$	3425.75	+	10543.4i	0.288071	+	0.886591i	−0.697390	+	0.716692i	$0.745656\pi$
$522$	−4016.47	−	12361.4i	−0.336774	−	1.03649i
$523$	13.3330	+	9.68700i	0.00111475	+	0.000809910i	0.588342	−	0.808612i	$-0.299781\pi$
$523$	13.3330	+	9.68700i	0.00111475	+	0.000809910i	−0.587228	+	0.809422i	$0.699781\pi$
$524$	11238.8			0.936962
$525$		0			0
$526$	9913.43			0.821761
$527$	−3087.98	−	2243.55i	−0.255246	−	0.185447i
$528$	2.69919	+	8.30726i	0.000222476	+	0.000684710i
$529$	8516.18	+	26210.1i	0.699941	+	2.15420i
$530$		0			0
$531$	−4586.67	+	14116.3i	−0.374849	+	1.15367i
$532$	4019.88			0.327601
$533$	−1009.83	+	3107.95i	−0.0820652	+	0.252571i
$534$	520.558	−	378.207i	0.0421849	−	0.0306491i
$535$		0			0
$536$	493.514	+	358.559i	0.0397697	+	0.0288944i
$537$	−687.299	+	499.352i	−0.0552312	+	0.0401278i
$538$	−3878.15	+	2817.64i	−0.310778	+	0.225794i
$539$	95.7854	+	69.5921i	0.00765448	+	0.00556131i
$540$		0			0
$541$	19911.1	−	14466.2i	1.58233	−	1.14963i	0.668378	−	0.743822i	$-0.266989\pi$
$541$	19911.1	−	14466.2i	1.58233	−	1.14963i	0.913957	−	0.405811i	$-0.133011\pi$
$542$	−4011.41	+	12345.8i	−0.317905	+	0.978413i
$543$	499.400			0.0394683
$544$	−736.075	+	2265.40i	−0.0580128	+	0.178545i
$545$		0			0
$546$	−37.3986	−	115.101i	−0.00293134	−	0.00902173i
$547$	−1642.96	−	5056.52i	−0.128424	−	0.395249i	0.866085	−	0.499897i	$-0.166629\pi$
$547$	−1642.96	−	5056.52i	−0.128424	−	0.395249i	−0.994509	+	0.104647i	$0.966629\pi$
$548$	6345.50	+	4610.28i	0.494647	+	0.359382i
$549$	13763.5			1.06997
$550$		0			0
$551$	−12174.5			−0.941288
$552$	318.571	+	231.455i	0.0245639	+	0.0178467i
$553$	−838.458	−	2580.51i	−0.0644753	−	0.198435i
$554$	2350.93	+	7235.42i	0.180291	+	0.554880i
$555$		0			0
$556$	−1951.20	+	6005.17i	−0.148829	+	0.458050i
$557$	−9362.34			−0.712199			−0.356100	−	0.934448i	$-0.615894\pi$
$557$	−9362.34			−0.712199			−0.356100	+	0.934448i	$0.615894\pi$
$558$	853.732	−	2627.52i	0.0647694	−	0.199340i
$559$	−1032.43	+	750.105i	−0.0781166	+	0.0567550i
$560$		0			0
$561$	32.8760	+	23.8858i	0.00247420	+	0.00179761i
$562$	−413.487	+	300.416i	−0.0310354	+	0.0225485i
$563$	9823.74	−	7137.36i	0.735384	−	0.534288i	−0.155878	−	0.987776i	$-0.549821\pi$
$563$	9823.74	−	7137.36i	0.735384	−	0.534288i	0.891262	+	0.453488i	$0.149821\pi$
$564$	328.894	+	238.955i	0.0245548	+	0.0178401i
$565$		0			0
$566$	−3316.97	+	2409.92i	−0.246330	+	0.178969i
$567$	−4455.67	+	13713.1i	−0.330019	+	1.01569i
$568$	−6845.16			−0.505663
$569$	2883.62	−	8874.88i	0.212456	−	0.653874i	−0.786868	−	0.617121i	$-0.788299\pi$
$569$	2883.62	−	8874.88i	0.212456	−	0.653874i	0.999324	−	0.0367524i	$-0.0117013\pi$
$570$		0			0
$571$	5676.39	+	17470.1i	0.416024	+	1.28039i	0.911332	+	0.411672i	$0.135055\pi$
$571$	5676.39	+	17470.1i	0.416024	+	1.28039i	−0.495308	+	0.868717i	$0.664945\pi$
$572$	33.6217	+	103.477i	0.00245768	+	0.00756396i
$573$	964.337	+	700.632i	0.0703068	+	0.0510809i
$574$	−10577.5			−0.769160
$575$		0			0
$576$	−1724.10			−0.124718
$577$	−233.016	−	169.296i	−0.0168121	−	0.0122147i	0.579347	−	0.815081i	$-0.303307\pi$
$577$	−233.016	−	169.296i	−0.0168121	−	0.0122147i	−0.596160	+	0.802866i	$0.703307\pi$
$578$	388.053	+	1194.30i	0.0279254	+	0.0859455i
$579$	−234.678	−	722.266i	−0.0168444	−	0.0518417i
$580$		0			0
$581$	−5646.22	+	17377.3i	−0.403175	+	1.24085i
$582$	219.275			0.0156173
$583$	−293.933	+	904.633i	−0.0208807	+	0.0642643i
$584$	3343.62	−	2429.28i	0.236918	−	0.172131i
$585$		0			0
$586$	−10910.4	−	7926.90i	−0.769123	−	0.558801i
$587$	12259.0	−	8906.66i	0.861979	−	0.626264i	−0.0664436	−	0.997790i	$-0.521165\pi$
$587$	12259.0	−	8906.66i	0.861979	−	0.626264i	0.928423	+	0.371526i	$0.121165\pi$
$588$	42.8027	−	31.0980i	0.00300196	−	0.00218105i
$589$	−2093.55	−	1521.06i	−0.146457	−	0.106407i
$590$		0			0
$591$	846.041	−	614.685i	0.0588858	−	0.0427830i
$592$	1375.08	−	4232.08i	0.0954656	−	0.293813i
$593$	−8594.02			−0.595133			−0.297567	−	0.954701i	$-0.596175\pi$
$593$	−8594.02			−0.595133			−0.297567	+	0.954701i	$0.596175\pi$
$594$	−18.1990	+	56.0107i	−0.00125709	+	0.00386893i
$595$		0			0
$596$	−1790.51	−	5510.62i	−0.123057	−	0.378731i
$597$	−314.884	−	969.114i	−0.0215869	−	0.0664375i
$598$	3968.18	+	2883.05i	0.271356	+	0.197152i
$599$	−12431.0			−0.847942			−0.423971	−	0.905676i	$-0.639364\pi$
$599$	−12431.0			−0.847942			−0.423971	+	0.905676i	$0.639364\pi$
$600$		0			0
$601$	16440.3			1.11583			0.557913	−	0.829899i	$-0.311602\pi$
$601$	16440.3			1.11583			0.557913	+	0.829899i	$0.311602\pi$
$602$	−3341.78	−	2427.94i	−0.226247	−	0.164378i
$603$	634.769	+	1953.62i	0.0428686	+	0.131936i
$604$	−2231.06	−	6866.49i	−0.150299	−	0.462572i
$605$		0			0
$606$	75.3005	−	231.751i	0.00504765	−	0.0155351i
$607$	10367.1			0.693228			0.346614	−	0.938008i	$-0.387331\pi$
$607$	10367.1			0.693228			0.346614	+	0.938008i	$0.387331\pi$
$608$	−499.035	+	1535.87i	−0.0332871	+	0.102447i
$609$	−959.807	+	697.341i	−0.0638643	+	0.0464001i
$610$		0			0
$611$	4096.76	+	2976.47i	0.271256	+	0.197079i
$612$	−6489.16	+	4714.65i	−0.428609	+	0.311403i
$613$	11720.9	−	8515.76i	0.772274	−	0.561090i	−0.130376	−	0.991465i	$-0.541618\pi$
$613$	11720.9	−	8515.76i	0.772274	−	0.561090i	0.902650	+	0.430375i	$0.141618\pi$
$614$	8089.70	+	5877.51i	0.531716	+	0.386314i
$615$		0			0
$616$	−284.912	+	207.001i	−0.0186355	+	0.0135395i
$617$	−797.436	+	2454.25i	−0.0520317	+	0.160137i	−0.973696	−	0.227851i	$-0.926830\pi$
$617$	−797.436	+	2454.25i	−0.0520317	+	0.160137i	0.921664	+	0.387988i	$0.126830\pi$
$618$	−850.163			−0.0553375
$619$	1815.76	−	5588.34i	0.117903	−	0.362867i	−0.874639	−	0.484775i	$-0.838901\pi$
$619$	1815.76	−	5588.34i	0.117903	−	0.362867i	0.992541	+	0.121908i	$0.0389014\pi$
$620$		0			0
$621$	820.435	+	2525.04i	0.0530160	+	0.163166i
$622$	4245.52	+	13066.4i	0.273681	+	0.842304i
$623$	20988.0	+	15248.7i	1.34971	+	0.980618i
$624$	48.6193			0.00311912
$625$		0			0
$626$	−897.886			−0.0573270
$627$	22.2889	+	16.1938i	0.00141967	+	0.00103145i
$628$	2470.87	+	7604.57i	0.157004	+	0.483209i
$629$	−6397.33	−	19689.0i	−0.405530	−	1.24809i
$630$		0			0
$631$	−1241.27	+	3820.25i	−0.0783111	+	0.241017i	−0.982546	−	0.186018i	$-0.940442\pi$
$631$	−1241.27	+	3820.25i	−0.0783111	+	0.241017i	0.904235	+	0.427035i	$0.140442\pi$
$632$	1090.02			0.0686055
$633$	387.662	−	1193.10i	0.0243415	−	0.0749156i
$634$	−10836.5	+	7873.21i	−0.678824	+	0.493194i
$635$		0			0
$636$	343.871	+	249.837i	0.0214393	+	0.0155766i
$637$	533.158	−	387.362i	0.0331625	−	0.0240940i
$638$	862.876	−	626.916i	0.0535448	−	0.0389026i
$639$	−18648.0	−	13548.6i	−1.15447	−	0.838769i
$640$		0			0
$641$	−3281.65	+	2384.26i	−0.202211	+	0.146915i	−0.684283	−	0.729217i	$-0.739885\pi$
$641$	−3281.65	+	2384.26i	−0.202211	+	0.146915i	0.482071	+	0.876132i	$0.339885\pi$
$642$	189.412	−	582.950i	0.0116441	−	0.0358367i
$643$	−3520.39			−0.215911			−0.107955	−	0.994156i	$-0.534430\pi$
$643$	−3520.39			−0.215911			−0.107955	+	0.994156i	$0.534430\pi$
$644$	−4906.06	+	15099.3i	−0.300196	+	0.923907i
$645$		0			0
$646$	2321.67	+	7145.37i	0.141401	+	0.435187i
$647$	6582.66	+	20259.4i	0.399986	+	1.23103i	0.925010	+	0.379944i	$0.124057\pi$
$647$	6582.66	+	20259.4i	0.399986	+	1.23103i	−0.525023	+	0.851088i	$0.675943\pi$
$648$	−4686.24	−	3404.75i	−0.284094	−	0.206406i
$649$	−1217.99			−0.0736676
$650$		0			0
$651$	−252.176			−0.0151821
$652$	−1589.71	−	1154.99i	−0.0954876	−	0.0693758i
$653$	2749.81	+	8463.06i	0.164791	+	0.507175i	0.999021	−	0.0442423i	$-0.0140874\pi$
$653$	2749.81	+	8463.06i	0.164791	+	0.507175i	−0.834230	+	0.551417i	$0.814087\pi$
$654$	−26.9723	−	83.0121i	−0.00161269	−	0.00496335i
$655$		0			0
$656$	1313.12	−	4041.35i	0.0781533	−	0.240531i
$657$	13917.2			0.826424
$658$	−5065.04	+	15588.6i	−0.300085	+	0.923565i
$659$	17979.8	−	13063.1i	1.06281	−	0.772177i	0.0882040	−	0.996102i	$-0.471887\pi$
$659$	17979.8	−	13063.1i	1.06281	−	0.772177i	0.974606	+	0.223926i	$0.0718873\pi$
$660$		0			0
$661$	−22654.3	−	16459.3i	−1.33306	−	0.968522i	−0.999669	−	0.0257322i	$-0.991808\pi$
$661$	−22654.3	−	16459.3i	−1.33306	−	0.968522i	−0.333387	−	0.942790i	$-0.608192\pi$
$662$	682.463	−	495.838i	0.0400675	−	0.0291107i
$663$	182.994	−	132.953i	0.0107193	−	0.00778801i
$664$	−5938.40	−	4314.50i	−0.347070	−	0.252161i
$665$		0			0
$666$	12122.6	−	8807.60i	0.705318	−	0.512444i
$667$	14858.3	−	45729.3i	0.862545	−	2.65464i
$668$	1361.81			0.0788774
$669$	−376.611	+	1159.09i	−0.0217648	+	0.0669850i
$670$		0			0
$671$	349.012	+	1074.15i	0.0200797	+	0.0617989i
$672$	48.6304	+	149.669i	0.00279161	+	0.00859168i
$673$	−17047.7	−	12385.9i	−0.976436	−	0.709422i	−0.0195266	−	0.999809i	$-0.506216\pi$
$673$	−17047.7	−	12385.9i	−0.976436	−	0.709422i	−0.956909	+	0.290387i	$0.906216\pi$
$674$	−9132.24			−0.521900
$675$		0			0
$676$	−8182.39			−0.465543
$677$	−10063.0	−	7311.23i	−0.571277	−	0.415057i	0.264292	−	0.964443i	$-0.414862\pi$
$677$	−10063.0	−	7311.23i	−0.571277	−	0.415057i	−0.835569	+	0.549386i	$0.814862\pi$
$678$	−29.2658	−	90.0707i	−0.00165774	−	0.00510199i
$679$	2731.96	+	8408.10i	0.154408	+	0.475218i
$680$		0			0
$681$	53.2824	−	163.986i	0.00299822	−	0.00922756i
$682$	226.708			0.0127289
$683$	−1807.44	+	5562.74i	−0.101259	+	0.311643i	−0.988834	−	0.149020i	$-0.952388\pi$
$683$	−1807.44	+	5562.74i	−0.101259	+	0.311643i	0.887575	+	0.460663i	$0.152388\pi$
$684$	−4399.45	+	3196.39i	−0.245932	+	0.178680i
$685$		0			0
$686$	−9326.13	−	6775.83i	−0.519058	−	0.377117i
$687$	1239.22	−	900.345i	0.0688197	−	0.0500004i
$688$	1342.50	−	975.382i	0.0743929	−	0.0540496i
$689$	4283.33	+	3112.02i	0.236839	+	0.172073i
$690$		0			0
$691$	5923.87	−	4303.94i	0.326128	−	0.236946i	−0.412658	−	0.910886i	$-0.635399\pi$
$691$	5923.87	−	4303.94i	0.326128	−	0.236946i	0.738786	+	0.673940i	$0.235399\pi$
$692$	2692.35	−	8286.21i	0.147902	−	0.455194i
$693$	−1185.89			−0.0650048
$694$	3795.87	−	11682.5i	0.207621	−	0.638993i
$695$		0			0
$696$	−147.280	−	453.282i	−0.00802105	−	0.0246862i
$697$	−6109.03	−	18801.7i	−0.331989	−	1.02176i
$698$	12065.0	+	8765.70i	0.654248	+	0.475339i
$699$	−674.927			−0.0365209
$700$		0			0
$701$	15238.8			0.821060			0.410530	−	0.911847i	$-0.365344\pi$
$701$	15238.8			0.821060			0.410530	+	0.911847i	$0.365344\pi$
$702$	265.204	+	192.682i	0.0142585	+	0.0103594i
$703$	−4337.19	−	13348.5i	−0.232689	−	0.716143i
$704$	−43.7192	−	134.554i	−0.00234052	−	0.00720339i
$705$		0			0
$706$	4082.13	−	12563.5i	0.217610	−	0.669735i
$707$	9824.66			0.522623
$708$	−168.189	+	517.633i	−0.00892787	+	0.0274772i
$709$	9001.43	−	6539.92i	0.476807	−	0.346420i	−0.323281	−	0.946303i	$-0.604786\pi$
$709$	9001.43	−	6539.92i	0.476807	−	0.346420i	0.800088	+	0.599883i	$0.204786\pi$
$710$		0			0
$711$	2969.51	+	2157.47i	0.156632	+	0.113800i
$712$	−8431.54	+	6125.88i	−0.443800	+	0.322439i
$713$	8268.41	−	6007.35i	0.434298	−	0.315536i
$714$	592.315	+	430.342i	0.0310460	+	0.0225562i
$715$		0			0
$716$	11132.3	−	8088.07i	0.581051	−	0.422158i
$717$	112.958	−	347.650i	0.00588355	−	0.0181077i
$718$	2128.59			0.110638
$719$	−8073.67	+	24848.2i	−0.418772	+	1.28885i	0.490061	+	0.871688i	$0.336974\pi$
$719$	−8073.67	+	24848.2i	−0.418772	+	1.28885i	−0.908833	+	0.417160i	$0.863026\pi$
$720$		0			0
$721$	−10592.2	−	32599.5i	−0.547122	−	1.68387i
$722$	−2665.07	−	8202.26i	−0.137374	−	0.422793i
$723$	51.7071	+	37.5674i	0.00265976	+	0.00193243i
$724$	−8088.85			−0.415221
$725$		0			0
$726$	654.986			0.0334832
$727$	3162.84	+	2297.94i	0.161352	+	0.117229i	0.665532	−	0.746370i	$-0.268205\pi$
$727$	3162.84	+	2297.94i	0.161352	+	0.117229i	−0.504179	+	0.863599i	$0.668205\pi$
$728$	605.750	+	1864.31i	0.0308387	+	0.0949118i
$729$	−6000.10	−	18466.4i	−0.304837	−	0.938191i
$730$		0			0
$731$	2385.66	−	7342.30i	0.120707	−	0.371498i
$732$	504.696			0.0254837
$733$	−1440.84	+	4434.46i	−0.0726040	+	0.223452i	−0.980773	−	0.195151i	$-0.937480\pi$
$733$	−1440.84	+	4434.46i	−0.0726040	+	0.223452i	0.908169	+	0.418603i	$0.137480\pi$
$734$	2611.15	−	1897.11i	0.131307	−	0.0953999i
$735$		0			0
$736$	−5159.94	−	3748.92i	−0.258421	−	0.187754i
$737$	−136.370	+	99.0787i	−0.00681582	+	0.00495198i
$738$	11576.3	−	8410.67i	0.577411	−	0.419514i
$739$	14248.6	+	10352.2i	0.709261	+	0.515308i	0.882935	−	0.469495i	$-0.155564\pi$
$739$	14248.6	+	10352.2i	0.709261	+	0.515308i	−0.173674	+	0.984803i	$0.555564\pi$
$740$		0			0
$741$	124.064	−	90.1377i	0.00615061	−	0.00446868i
$742$	−5295.69	+	16298.5i	−0.262009	+	0.806382i
$743$	26680.2			1.31737			0.658683	−	0.752421i	$-0.271114\pi$
$743$	26680.2			1.31737			0.658683	+	0.752421i	$0.271114\pi$
$744$	31.3056	−	96.3486i	0.00154263	−	0.00474773i
$745$		0			0
$746$	−4613.69	−	14199.5i	−0.226433	−	0.696890i
$747$	−7638.11	−	23507.7i	−0.374115	−	1.15141i
$748$	−532.497	−	386.881i	−0.0260294	−	0.0189115i
$749$	24713.1			1.20560
$750$		0			0
$751$	8017.53			0.389566			0.194783	−	0.980846i	$-0.437600\pi$
$751$	8017.53			0.389566			0.194783	+	0.980846i	$0.437600\pi$
$752$	−5327.14	−	3870.39i	−0.258325	−	0.187684i
$753$	261.936	+	806.157i	0.0126766	+	0.0390146i
$754$	−1834.55	−	5646.17i	−0.0886081	−	0.272708i
$755$		0			0
$756$	−327.885	+	1009.12i	−0.0157739	+	0.0485470i
$757$	−4716.28			−0.226441			−0.113221	−	0.993570i	$-0.536117\pi$
$757$	−4716.28			−0.226441			−0.113221	+	0.993570i	$0.536117\pi$
$758$	−4631.63	+	14254.7i	−0.221937	+	0.683052i
$759$	−88.0291	+	63.9569i	−0.00420982	+	0.00305861i
$760$		0			0
$761$	4294.37	+	3120.04i	0.204561	+	0.148622i	0.685349	−	0.728214i	$-0.259650\pi$
$761$	4294.37	+	3120.04i	0.204561	+	0.148622i	−0.480789	+	0.876837i	$0.659650\pi$
$762$	122.811	−	89.2273i	0.00583854	−	0.00424195i
$763$	2847.05	−	2068.50i	0.135085	−	0.0981452i
$764$	−15619.5	−	11348.2i	−0.739652	−	0.537388i
$765$		0			0
$766$	7106.35	−	5163.07i	0.335200	−	0.243537i
$767$	−2095.00	+	6447.73i	−0.0986257	+	0.303539i
$768$	−63.2210			−0.00297043
$769$	12806.7	−	39415.0i	0.600548	−	1.84830i	0.0756466	−	0.997135i	$-0.475898\pi$
$769$	12806.7	−	39415.0i	0.600548	−	1.84830i	0.524902	−	0.851163i	$-0.324102\pi$
$770$		0			0
$771$	−237.100	−	729.720i	−0.0110752	−	0.0340859i
$772$	3801.12	+	11698.6i	0.177209	+	0.545393i
$773$	−6750.04	−	4904.19i	−0.314078	−	0.228191i	0.419566	−	0.907725i	$-0.362182\pi$
$773$	−6750.04	−	4904.19i	−0.314078	−	0.228191i	−0.733644	+	0.679534i	$0.762182\pi$
$774$	5587.89			0.259499
$775$		0			0
$776$	−3551.63			−0.164299
$777$	−1106.52	−	803.936i	−0.0510892	−	0.0371184i
$778$	3562.81	+	10965.2i	0.164181	+	0.505297i
$779$	−4141.73	−	12746.9i	−0.190492	−	0.586273i
$780$		0			0
$781$	584.501	−	1798.91i	0.0267799	−	0.0824201i
$782$	−29672.7			−1.35690
$783$	993.020	−	3056.20i	0.0453227	−	0.139489i
$784$	−693.281	+	503.698i	−0.0315817	+	0.0229454i
$785$		0			0
$786$	1122.71	+	815.697i	0.0509488	+	0.0370165i
$787$	6549.52	−	4758.50i	0.296652	−	0.215530i	−0.429496	−	0.903069i	$-0.641309\pi$
$787$	6549.52	−	4758.50i	0.296652	−	0.215530i	0.726148	+	0.687539i	$0.241309\pi$
$788$	−13703.4	+	9956.14i	−0.619499	+	0.450092i
$789$	990.315	+	719.506i	0.0446846	+	0.0324653i
$790$		0			0
$791$	3089.14	−	2244.39i	0.138859	−	0.100887i
$792$	147.219	−	453.093i	0.00660505	−	0.0203282i
$793$	6286.59			0.281517
$794$	987.338	−	3038.71i	0.0441301	−	0.135819i
$795$		0			0
$796$	5100.22	+	15696.9i	0.227101	+	0.698946i
$797$	−6192.35	−	19058.1i	−0.275212	−	0.847016i	−0.989163	−	0.146821i	$-0.953096\pi$
$797$	−6192.35	−	19058.1i	−0.275212	−	0.847016i	0.713951	−	0.700196i	$-0.246904\pi$
$798$	401.571	+	291.758i	0.0178139	+	0.0129425i
$799$	−30634.1			−1.35639
$800$		0			0
$801$	−35094.7			−1.54808
$802$	7641.48	+	5551.86i	0.336447	+	0.244443i
$803$	352.908	+	1086.14i	0.0155091	+	0.0477322i
$804$	23.2764	+	71.6374i	0.00102101	+	0.00314236i
$805$		0			0
$806$	389.948	−	1200.14i	0.0170414	−	0.0524479i
$807$	−591.913			−0.0258195
$808$	−1219.65	+	3753.71i	−0.0531030	+	0.163434i
$809$	−3586.40	+	2605.67i	−0.155860	+	0.113239i	−0.662982	−	0.748635i	$-0.730709\pi$
$809$	−3586.40	+	2605.67i	−0.155860	+	0.113239i	0.507122	+	0.861874i	$0.330709\pi$
$810$		0			0
$811$	4379.53	+	3181.92i	0.189625	+	0.137771i	0.678548	−	0.734557i	$-0.262610\pi$
$811$	4379.53	+	3181.92i	0.189625	+	0.137771i	−0.488922	+	0.872327i	$0.662610\pi$
$812$	15546.1	−	11294.9i	0.671875	−	0.488146i
$813$	−1296.77	+	942.161i	−0.0559407	+	0.0406433i
$814$	994.774	+	722.746i	0.0428339	+	0.0311207i
$815$		0			0
$816$	−237.952	+	172.882i	−0.0102083	+	0.00741677i
$817$	1617.40	−	4977.85i	0.0692603	−	0.213161i
$818$	11658.1			0.498307
$819$	−2039.79	+	6277.82i	−0.0870280	+	0.267845i
$820$		0			0
$821$	6717.03	+	20672.9i	0.285537	+	0.878793i	0.986237	+	0.165337i	$0.0528711\pi$
$821$	6717.03	+	20672.9i	0.285537	+	0.878793i	−0.700700	+	0.713456i	$0.747129\pi$
$822$	299.283	+	921.099i	0.0126991	+	0.0390840i
$823$	20823.2	+	15129.0i	0.881959	+	0.640780i	0.933769	−	0.357877i	$-0.116499\pi$
$823$	20823.2	+	15129.0i	0.881959	+	0.640780i	−0.0518104	+	0.998657i	$0.516499\pi$
$824$	13770.2			0.582170
$825$		0			0
$826$	−21944.1			−0.924374
$827$	2545.13	+	1849.15i	0.107017	+	0.0777523i	0.640007	−	0.768369i	$-0.278932\pi$
$827$	2545.13	+	1849.15i	0.107017	+	0.0777523i	−0.532990	+	0.846122i	$0.678932\pi$
$828$	−6636.84	−	20426.1i	−0.278558	−	0.857313i
$829$	3738.37	+	11505.5i	0.156621	+	0.482031i	0.998322	−	0.0579142i	$-0.0184450\pi$
$829$	3738.37	+	11505.5i	0.156621	+	0.482031i	−0.841700	+	0.539945i	$0.818445\pi$
$830$		0			0
$831$	−290.289	+	893.419i	−0.0121180	+	0.0372953i
$832$	−787.493			−0.0328142
$833$	−1231.98	+	3791.64i	−0.0512432	+	0.157710i
$834$	−630.766	+	458.278i	−0.0261890	+	0.0190274i
$835$		0			0
$836$	−361.016	−	262.293i	−0.0149354	−	0.0108512i
$837$	552.599	−	401.486i	0.0228203	−	0.0165799i
$838$	−1841.96	+	1338.26i	−0.0759300	+	0.0551664i
$839$	1198.70	+	870.909i	0.0493252	+	0.0358369i	0.612175	−	0.790723i	$-0.290295\pi$
$839$	1198.70	+	870.909i	0.0493252	+	0.0358369i	−0.562849	+	0.826559i	$0.690295\pi$
$840$		0			0
$841$	−27351.4	+	19871.9i	−1.12146	+	0.814791i
$842$	−634.205	+	1951.88i	−0.0259574	+	0.0798888i
$843$	−63.1097			−0.00257842
$844$	−6279.02	+	19324.8i	−0.256082	+	0.788138i
$845$		0			0
$846$	−6851.89	−	21087.9i	−0.278455	−	0.856996i
$847$	8160.50	+	25115.4i	0.331049	+	1.01886i
$848$	−5569.73	−	4046.65i	−0.225549	−	0.163871i
$849$	−506.262			−0.0204651
$850$		0			0
$851$	55432.5			2.23290
$852$	−683.806	−	496.814i	−0.0274962	−	0.0199772i
$853$	−5268.61	−	16215.1i	−0.211481	−	0.650873i	−0.999385	−	0.0350740i	$-0.988833\pi$
$853$	−5268.61	−	16215.1i	−0.211481	−	0.650873i	0.787903	−	0.615799i	$-0.211167\pi$
$854$	6288.03	+	19352.6i	0.251958	+	0.775446i
$855$		0			0
$856$	−3067.93	+	9442.12i	−0.122500	+	0.377015i
$857$	−5794.04			−0.230946			−0.115473	−	0.993311i	$-0.536838\pi$
$857$	−5794.04			−0.230946			−0.115473	+	0.993311i	$0.536838\pi$
$858$	−4.15155	+	12.7772i	−0.000165188	+	0.000508398i
$859$	16171.8	−	11749.5i	0.642346	−	0.466692i	−0.218310	−	0.975880i	$-0.570054\pi$
$859$	16171.8	−	11749.5i	0.642346	−	0.466692i	0.860655	+	0.509188i	$0.170054\pi$
$860$		0			0
$861$	−1056.66	−	767.706i	−0.0418243	−	0.0303872i
$862$	9055.64	−	6579.31i	0.357815	−	0.259968i
$863$	−39553.6	+	28737.4i	−1.56016	+	1.13353i	−0.624288	+	0.781194i	$0.714611\pi$
$863$	−39553.6	+	28737.4i	−1.56016	+	1.13353i	−0.935875	+	0.352331i	$0.885389\pi$
$864$	−344.852	−	250.549i	−0.0135788	−	0.00986558i
$865$		0			0
$866$	−1421.67	+	1032.91i	−0.0557858	+	0.0405307i
$867$	−47.9162	+	147.471i	−0.00187696	+	0.00577667i
$868$	4084.52			0.159721
$869$	−93.0758	+	286.458i	−0.00363335	+	0.0111823i
$870$		0			0
$871$	289.935	+	892.329i	0.0112791	+	0.0347134i
$872$	436.873	+	1344.56i	0.0169661	+	0.0522161i
$873$	−9675.58	−	7029.72i	−0.375107	−	0.272531i
$874$	−20117.1			−0.778572
$875$		0			0
$876$	510.330			0.0196832
$877$	5126.68	+	3724.75i	0.197395	+	0.143416i	0.682092	−	0.731266i	$-0.261070\pi$
$877$	5126.68	+	3724.75i	0.197395	+	0.143416i	−0.484697	+	0.874682i	$0.661070\pi$
$878$	−4329.24	−	13324.0i	−0.166406	−	0.512146i
$879$	−514.587	−	1583.74i	−0.0197458	−	0.0607714i
$880$		0			0
$881$	6049.04	−	18617.0i	0.231325	−	0.711945i	−0.766263	−	0.642527i	$-0.777886\pi$
$881$	6049.04	−	18617.0i	0.231325	−	0.711945i	0.997588	−	0.0694177i	$-0.0221141\pi$
$882$	−2885.65			−0.110164
$883$	14467.5	−	44526.5i	0.551384	−	1.69698i	−0.153924	−	0.988083i	$-0.549191\pi$
$883$	14467.5	−	44526.5i	0.551384	−	1.69698i	0.705307	−	0.708902i	$-0.250809\pi$
$884$	−2963.97	+	2153.45i	−0.112771	+	0.0819326i
$885$		0			0
$886$	28698.3	+	20850.5i	1.08819	+	0.790617i
$887$	−2613.54	+	1898.84i	−0.0989334	+	0.0718793i	−0.636152	−	0.771564i	$-0.719475\pi$
$887$	−2613.54	+	1898.84i	−0.0989334	+	0.0718793i	0.537219	+	0.843443i	$0.319475\pi$
$888$	444.525	−	322.966i	0.0167987	−	0.0122050i
$889$	4951.53	+	3597.49i	0.186804	+	0.135721i
$890$		0			0
$891$	1294.92	−	940.817i	0.0486886	−	0.0353744i
$892$	6100.02	−	18773.9i	0.228973	−	0.704706i
$893$	−20769.0			−0.778284
$894$	221.089	−	680.443i	0.00827107	−	0.0254557i
$895$		0			0
$896$	−787.673	−	2424.21i	−0.0293687	−	0.0903875i
$897$	187.158	+	576.013i	0.00696658	+	0.0214409i
$898$	−6945.03	−	5045.86i	−0.258083	−	0.187508i
$899$	−12370.2			−0.458922
$900$		0			0
$901$	−32029.2			−1.18429
$902$	949.944	+	690.174i	0.0350661	+	0.0254770i
$903$	−157.614	−	485.085i	−0.00580848	−	0.0178767i
$904$	474.022	+	1458.89i	0.0174400	+	0.0536747i
$905$		0			0
$906$	275.488	−	847.864i	0.0101021	−	0.0310909i
$907$	24727.7			0.905258			0.452629	−	0.891699i	$-0.350486\pi$
$907$	24727.7			0.905258			0.452629	+	0.891699i	$0.350486\pi$
$908$	−863.022	+	2656.11i	−0.0315423	+	0.0970772i
$909$	−10752.3	+	7812.04i	−0.392335	+	0.285048i
$910$		0			0
$911$	10203.7	+	7413.45i	0.371092	+	0.269614i	0.757664	−	0.652645i	$-0.226341\pi$
$911$	10203.7	+	7413.45i	0.371092	+	0.269614i	−0.386572	+	0.922259i	$0.626341\pi$
$912$	−161.324	+	117.209i	−0.00585742	+	0.00425566i
$913$	1640.93	−	1192.20i	0.0594817	−	0.0432160i
$914$	28169.4	+	20466.2i	1.01943	+	0.740660i
$915$		0			0
$916$	−20071.8	+	14583.0i	−0.724007	+	0.526022i
$917$	−17290.0	+	53213.1i	−0.622646	+	1.91631i
$918$	−1983.10			−0.0712985
$919$	−9253.51	+	28479.4i	−0.332149	+	1.02225i	0.635960	+	0.771722i	$0.280604\pi$
$919$	−9253.51	+	28479.4i	−0.332149	+	1.02225i	−0.968109	+	0.250528i	$0.919396\pi$
$920$		0			0
$921$	381.548	+	1174.28i	0.0136508	+	0.0420130i
$922$	9046.87	+	27843.4i	0.323148	+	0.994548i
$923$	−8517.61	−	6188.41i	−0.303749	−	0.220687i
$924$	−43.4856			−0.00154824
$925$		0			0
$926$	15087.4			0.535423
$927$	37513.7	+	27255.3i	1.32914	+	0.965676i
$928$	2385.52	+	7341.88i	0.0843842	+	0.259708i
$929$	3387.87	+	10426.8i	0.119647	+	0.368237i	0.992888	−	0.119052i	$-0.0379856\pi$
$929$	3387.87	+	10426.8i	0.119647	+	0.368237i	−0.873240	+	0.487290i	$0.837986\pi$
$930$		0			0
$931$	−835.244	+	2570.62i	−0.0294028	+	0.0904925i
$932$	10931.9			0.384212
$933$	−524.230	+	1613.42i	−0.0183950	+	0.0566140i
$934$	5709.39	−	4148.11i	0.200018	−	0.145322i
$935$		0			0
$936$	−2145.34	−	1558.68i	−0.0749174	−	0.0544306i
$937$	−39386.2	+	28615.8i	−1.37320	+	0.997691i	−0.375725	+	0.926731i	$0.622606\pi$
$937$	−39386.2	+	28615.8i	−1.37320	+	0.997691i	−0.997479	+	0.0709603i	$0.977394\pi$
$938$	−2456.93	+	1785.07i	−0.0855242	+	0.0621370i
$939$	−89.6954	−	65.1675i	−0.00311725	−	0.00226482i
$940$		0			0
$941$	−10133.1	+	7362.13i	−0.351041	+	0.255046i	−0.749306	−	0.662224i	$-0.769613\pi$
$941$	−10133.1	+	7362.13i	−0.351041	+	0.255046i	0.398265	+	0.917271i	$0.369613\pi$
$942$	−305.100	+	939.001i	−0.0105528	+	0.0324780i
$943$	52934.3			1.82797
$944$	2724.18	−	8384.17i	0.0939244	−	0.289069i
$945$		0			0
$946$	141.696	+	436.096i	0.00486992	+	0.0149881i
$947$	−10330.1	−	31792.8i	−0.354470	−	1.09095i	−0.956316	−	0.292335i	$-0.905568\pi$
$947$	−10330.1	−	31792.8i	−0.354470	−	1.09095i	0.601846	−	0.798612i	$-0.294432\pi$
$948$	108.889	+	79.1125i	0.00373054	+	0.00271040i
$949$	6356.76			0.217439
$950$		0			0
$951$	−1653.96			−0.0563968
$952$	−9593.81	−	6970.31i	−0.326615	−	0.237299i
$953$	10938.2	+	33664.4i	0.371799	+	1.14428i	0.945613	+	0.325293i	$0.105463\pi$
$953$	10938.2	+	33664.4i	0.371799	+	1.14428i	−0.573815	+	0.818985i	$0.694537\pi$
$954$	−7163.92	−	22048.3i	−0.243124	−	0.748259i
$955$		0			0
$956$	−1829.60	+	5630.94i	−0.0618970	+	0.190499i
$957$	131.699			0.00444851
$958$	4591.46	−	14131.1i	0.154847	−	0.476570i
$959$	−31590.7	+	22952.0i	−1.06373	+	0.772846i
$960$		0			0
$961$	21974.2	+	15965.2i	0.737612	+	0.535907i
$962$	5537.09	−	4022.93i	0.185575	−	0.134828i
$963$	−27046.6	+	19650.5i	−0.905051	+	0.657558i
$964$	−837.507	−	608.485i	−0.0279816	−	0.0203298i
$965$		0			0
$966$	−1585.99	+	1152.29i	−0.0528244	+	0.0383792i
$967$	−6943.26	+	21369.2i	−0.230900	+	0.710637i	0.766739	+	0.641959i	$0.221878\pi$
$967$	−6943.26	+	21369.2i	−0.230900	+	0.710637i	−0.997639	+	0.0686780i	$0.978122\pi$
$968$	−10608.9			−0.352255
$969$	−286.677	+	882.301i	−0.00950401	+	0.0292503i
$970$		0			0
$971$	17654.3	+	54334.4i	0.583475	+	1.79575i	0.605309	+	0.795990i	$0.293049\pi$
$971$	17654.3	+	54334.4i	0.583475	+	1.79575i	−0.0218342	+	0.999762i	$0.506951\pi$
$972$	−665.585	−	2048.46i	−0.0219636	−	0.0675971i
$973$	−25431.4	−	18477.0i	−0.837917	−	0.608782i
$974$	28035.2			0.922287
$975$		0			0
$976$	−8174.63			−0.268098
$977$	−26432.7	−	19204.5i	−0.865566	−	0.628870i	0.0638277	−	0.997961i	$-0.479669\pi$
$977$	−26432.7	−	19204.5i	−0.865566	−	0.628870i	−0.929393	+	0.369091i	$0.879669\pi$
$978$	−74.9782	−	230.759i	−0.00245147	−	0.00754485i
$979$	−889.921	−	2738.90i	−0.0290521	−	0.0894132i
$980$		0			0
$981$	−1471.12	+	4527.63i	−0.0478788	+	0.147356i
$982$	−7204.42			−0.234116
$983$	−15775.3	+	48551.3i	−0.511854	+	1.57533i	0.277079	+	0.960847i	$0.410634\pi$
$983$	−15775.3	+	48551.3i	−0.511854	+	1.57533i	−0.788933	+	0.614479i	$0.789366\pi$
$984$	424.492	−	308.412i	0.0137524	−	0.00999167i
$985$		0			0
$986$	29055.5	+	21110.0i	0.938453	+	0.681826i
$987$	−1637.38	+	1189.63i	−0.0528048	+	0.0383650i
$988$	−2009.48	+	1459.97i	−0.0647065	+	0.0470121i
$989$	16723.6	+	12150.4i	0.537696	+	0.390659i
$990$		0			0
$991$	−44985.3	+	32683.7i	−1.44198	+	1.04766i	−0.454359	+	0.890819i	$0.650132\pi$
$991$	−44985.3	+	32683.7i	−1.44198	+	1.04766i	−0.987624	+	0.156843i	$0.949868\pi$
$992$	−507.060	+	1560.57i	−0.0162290	+	0.0499478i
$993$	104.163			0.00332881
$994$	10530.8	−	32410.3i	0.336032	−	1.03420i
$995$		0			0
$996$	−280.082	−	862.005i	−0.00891039	−	0.0274234i
$997$	3094.69	+	9524.47i	0.0983047	+	0.302551i	0.988101	−	0.153808i	$-0.0491536\pi$
$997$	3094.69	+	9524.47i	0.0983047	+	0.302551i	−0.889796	+	0.456358i	$0.849154\pi$
$998$	−7936.48	−	5766.19i	−0.251728	−	0.182891i
$999$	3704.69			0.117329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.d.c.201.4		32
5.2	odd	4		250.4.e.b.49.6		32
5.3	odd	4		50.4.e.a.9.3	✓	32
5.4	even	2		250.4.d.d.201.5		32
25.2	odd	20		50.4.e.a.39.3	yes	32
25.6	even	5		1250.4.a.n.1.8		16
25.11	even	5	inner	250.4.d.c.51.4		32
25.14	even	10		250.4.d.d.51.5		32
25.19	even	10		1250.4.a.m.1.9		16
25.23	odd	20		250.4.e.b.199.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.3	✓	32	5.3	odd	4
50.4.e.a.39.3	yes	32	25.2	odd	20
250.4.d.c.51.4		32	25.11	even	5	inner
250.4.d.c.201.4		32	1.1	even	1	trivial
250.4.d.d.51.5		32	25.14	even	10
250.4.d.d.201.5		32	5.4	even	2
250.4.e.b.49.6		32	5.2	odd	4
250.4.e.b.199.6		32	25.23	odd	20
1250.4.a.m.1.9		16	25.19	even	10
1250.4.a.n.1.8		16	25.6	even	5

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.0763140 - 0.234870i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.152628 + 0.469741i) q^{6} -19.9138 q^{7} +(2.47214 - 7.60845i) q^{8} +(21.7941 - 15.8344i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(-0.0763140 - 0.234870i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-0.152628 + 0.469741i) q^{6} -19.9138 q^{7} +(2.47214 - 7.60845i) q^{8} +(21.7941 - 15.8344i) q^{9} +(1.78841 + 1.29936i) q^{11} +(0.799170 - 0.580631i) q^{12} +(9.95462 - 7.23245i) q^{13} +(32.2212 + 23.4101i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(-23.0023 + 70.7939i) q^{17} -53.8780 q^{18} +(-15.5949 + 47.9960i) q^{19} +(1.51970 + 4.67716i) q^{21} +(-1.36622 - 4.20481i) q^{22} +(-161.248 - 117.154i) q^{23} -1.97566 q^{24} -24.6092 q^{26} +(-10.7766 - 7.82967i) q^{27} +(-24.6148 - 75.7565i) q^{28} +(74.5475 + 229.434i) q^{29} +(-15.8456 + 48.7679i) q^{31} +32.0000 q^{32} +(0.168700 - 0.519204i) q^{33} +(120.442 - 87.5061i) q^{34} +(87.1765 + 63.3374i) q^{36} +(-225.001 + 163.473i) q^{37} +(81.6557 - 59.3264i) q^{38} +(-2.45836 - 1.78611i) q^{39} +(-214.861 + 156.106i) q^{41} +(3.03940 - 9.35431i) q^{42} -103.714 q^{43} +(-2.73245 + 8.40961i) q^{44} +(123.183 + 379.117i) q^{46} +(127.174 + 391.402i) q^{47} +(3.19668 + 2.32252i) q^{48} +53.5589 q^{49} +18.3828 q^{51} +(39.8185 + 28.9298i) q^{52} +(132.965 + 409.226i) q^{53} +(8.23260 + 25.3373i) q^{54} +(-49.2296 + 151.513i) q^{56} +12.4629 q^{57} +(149.095 - 458.867i) q^{58} +(-445.750 + 323.856i) q^{59} +(413.338 + 300.308i) q^{61} +(82.9688 - 60.2804i) q^{62} +(-434.003 + 315.322i) q^{63} +(-51.7771 - 37.6183i) q^{64} +(-0.883322 + 0.641771i) q^{66} +(-23.5632 + 72.5200i) q^{67} -297.748 q^{68} +(-15.2104 + 46.8129i) q^{69} +(-264.409 - 813.766i) q^{71} +(-66.5969 - 204.964i) q^{72} +(417.952 + 303.660i) q^{73} +556.233 q^{74} -201.864 q^{76} +(-35.6140 - 25.8751i) q^{77} +(1.87802 + 5.77996i) q^{78} +(42.1044 + 129.584i) q^{79} +(223.748 - 688.626i) q^{81} +531.166 q^{82} +(283.533 - 872.626i) q^{83} +(-15.9145 + 11.5626i) q^{84} +(167.812 + 121.923i) q^{86} +(48.1981 - 35.0180i) q^{87} +(14.3073 - 10.3949i) q^{88} +(-1053.94 - 765.734i) q^{89} +(-198.234 + 144.026i) q^{91} +(246.365 - 758.234i) q^{92} +12.6634 q^{93} +(254.348 - 782.803i) q^{94} +(-2.44205 - 7.51585i) q^{96} +(-137.189 - 422.225i) q^{97} +(-86.6601 - 62.9623i) q^{98} +59.5513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9	\( 32 q - 16 q^{2} - 6 q^{3} - 32 q^{4} - 12 q^{6} + 112 q^{7} - 64 q^{8} - 26 q^{9} - 106 q^{11} - 24 q^{12} + 14 q^{13} - 56 q^{14} - 128 q^{16} + 92 q^{17} + 848 q^{18} - 110 q^{19} - 36 q^{21} + 68 q^{22} + 124 q^{23} + 192 q^{24} + 808 q^{26} - 630 q^{27} - 112 q^{28} + 10 q^{29} - 486 q^{31} + 1024 q^{32} - 672 q^{33} - 616 q^{34} - 104 q^{36} - 88 q^{37} + 20 q^{38} - 1012 q^{39} - 96 q^{41} - 72 q^{42} + 1804 q^{43} + 136 q^{44} - 832 q^{46} - 328 q^{47} - 96 q^{48} + 2076 q^{49} + 884 q^{51} + 56 q^{52} + 1164 q^{53} + 120 q^{54} - 224 q^{56} + 2800 q^{57} + 20 q^{58} - 2250 q^{59} + 934 q^{61} + 768 q^{62} - 2976 q^{63} - 512 q^{64} + 16 q^{66} - 2248 q^{67} + 1728 q^{68} + 628 q^{69} - 2616 q^{71} - 1488 q^{72} - 3836 q^{73} + 2584 q^{74} + 800 q^{76} + 254 q^{77} + 1816 q^{78} + 2800 q^{79} - 5268 q^{81} + 2128 q^{82} + 304 q^{83} - 624 q^{84} - 692 q^{86} + 2660 q^{87} - 848 q^{88} - 4520 q^{89} + 3764 q^{91} - 1664 q^{92} + 5648 q^{93} - 656 q^{94} - 192 q^{96} - 6228 q^{97} - 2748 q^{98} + 2108 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 6 * q^3 - 32 * q^4 - 12 * q^6 + 112 * q^7 - 64 * q^8 - 26 * q^9 - 106 * q^11 - 24 * q^12 + 14 * q^13 - 56 * q^14 - 128 * q^16 + 92 * q^17 + 848 * q^18 - 110 * q^19 - 36 * q^21 + 68 * q^22 + 124 * q^23 + 192 * q^24 + 808 * q^26 - 630 * q^27 - 112 * q^28 + 10 * q^29 - 486 * q^31 + 1024 * q^32 - 672 * q^33 - 616 * q^34 - 104 * q^36 - 88 * q^37 + 20 * q^38 - 1012 * q^39 - 96 * q^41 - 72 * q^42 + 1804 * q^43 + 136 * q^44 - 832 * q^46 - 328 * q^47 - 96 * q^48 + 2076 * q^49 + 884 * q^51 + 56 * q^52 + 1164 * q^53 + 120 * q^54 - 224 * q^56 + 2800 * q^57 + 20 * q^58 - 2250 * q^59 + 934 * q^61 + 768 * q^62 - 2976 * q^63 - 512 * q^64 + 16 * q^66 - 2248 * q^67 + 1728 * q^68 + 628 * q^69 - 2616 * q^71 - 1488 * q^72 - 3836 * q^73 + 2584 * q^74 + 800 * q^76 + 254 * q^77 + 1816 * q^78 + 2800 * q^79 - 5268 * q^81 + 2128 * q^82 + 304 * q^83 - 624 * q^84 - 692 * q^86 + 2660 * q^87 - 848 * q^88 - 4520 * q^89 + 3764 * q^91 - 1664 * q^92 + 5648 * q^93 - 656 * q^94 - 192 * q^96 - 6228 * q^97 - 2748 * q^98 + 2108 * q^99

Introduction

L-functions

Modular forms

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