LMFDB - Embedded newform 230.5.f.a.93.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, 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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.15
Character	$\chi$	$=$	230.93
Dual form			230.5.f.a.47.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} +(4.47696 + 4.47696i) q^{3} -8.00000i q^{4} +(-20.9409 - 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 + 15.4160i) q^{7} +(16.0000 + 16.0000i) q^{8} -40.9136i q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} +(4.47696 + 4.47696i) q^{3} -8.00000i q^{4} +(-20.9409 - 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 + 15.4160i) q^{7} +(16.0000 + 16.0000i) q^{8} -40.9136i q^{9} +(69.1933 - 14.5701i) q^{10} +133.641 q^{11} +(35.8157 - 35.8157i) q^{12} +(-27.8077 - 27.8077i) q^{13} -61.6638i q^{14} +(-32.6150 - 154.888i) q^{15} -64.0000 q^{16} +(-6.97609 + 6.97609i) q^{17} +(81.8272 + 81.8272i) q^{18} +581.940i q^{19} +(-109.246 + 167.527i) q^{20} -138.033 q^{21} +(-267.283 + 267.283i) q^{22} +(-77.9968 - 77.9968i) q^{23} +143.263i q^{24} +(252.039 + 571.928i) q^{25} +111.231 q^{26} +(545.803 - 545.803i) q^{27} +(123.328 + 123.328i) q^{28} +1422.24i q^{29} +(375.006 + 244.546i) q^{30} -109.874 q^{31} +(128.000 - 128.000i) q^{32} +(598.307 + 598.307i) q^{33} -27.9044i q^{34} +(533.340 - 112.306i) q^{35} -327.309 q^{36} +(347.767 - 347.767i) q^{37} +(-1163.88 - 1163.88i) q^{38} -248.988i q^{39} +(-116.561 - 553.546i) q^{40} -1500.74 q^{41} +(276.067 - 276.067i) q^{42} +(687.304 + 687.304i) q^{43} -1069.13i q^{44} +(-558.708 + 856.766i) q^{45} +311.987 q^{46} +(-97.5012 + 97.5012i) q^{47} +(-286.526 - 286.526i) q^{48} +1925.70i q^{49} +(-1647.93 - 639.777i) q^{50} -62.4634 q^{51} +(-222.461 + 222.461i) q^{52} +(2457.09 + 2457.09i) q^{53} +2183.21i q^{54} +(-2798.56 - 1824.98i) q^{55} -493.310 q^{56} +(-2605.32 + 2605.32i) q^{57} +(-2844.48 - 2844.48i) q^{58} +3828.70i q^{59} +(-1239.10 + 260.920i) q^{60} -5066.25 q^{61} +(219.748 - 219.748i) q^{62} +(630.722 + 630.722i) q^{63} +512.000i q^{64} +(202.581 + 962.051i) q^{65} -2393.23 q^{66} +(1522.51 - 1522.51i) q^{67} +(55.8087 + 55.8087i) q^{68} -698.377i q^{69} +(-842.068 + 1291.29i) q^{70} -1397.47 q^{71} +(654.618 - 654.618i) q^{72} +(1262.48 + 1262.48i) q^{73} +1391.07i q^{74} +(-1432.13 + 3688.87i) q^{75} +4655.52 q^{76} +(-2060.21 + 2060.21i) q^{77} +(497.975 + 497.975i) q^{78} +5010.15i q^{79} +(1340.21 + 873.970i) q^{80} +1573.07 q^{81} +(3001.47 - 3001.47i) q^{82} +(3638.73 + 3638.73i) q^{83} +1104.27i q^{84} +(241.349 - 50.8213i) q^{85} -2749.21 q^{86} +(-6367.32 + 6367.32i) q^{87} +(2138.26 + 2138.26i) q^{88} +12022.9i q^{89} +(-596.117 - 2830.95i) q^{90} +857.363 q^{91} +(-623.974 + 623.974i) q^{92} +(-491.903 - 491.903i) q^{93} -390.005i q^{94} +(7946.84 - 12186.3i) q^{95} +1146.10 q^{96} +(897.842 - 897.842i) q^{97} +(-3851.39 - 3851.39i) q^{98} -5467.75i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$	4.47696	+	4.47696i	0.497440	+	0.497440i	0.910640	−	0.413200i	$-0.135589\pi$
$3$	4.47696	+	4.47696i	0.497440	+	0.497440i	−0.413200	+	0.910640i	$0.635589\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−20.9409	−	13.6558i	−0.837634	−	0.546231i
$5$	−20.9409	−	13.6558i	−0.837634	−	0.546231i
$6$	−17.9078			−0.497440
$7$	−15.4160	+	15.4160i	−0.314611	+	0.314611i	−0.846693	−	0.532082i	$-0.821410\pi$
$7$	−15.4160	+	15.4160i	−0.314611	+	0.314611i	0.532082	+	0.846693i	$0.321410\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$		−	40.9136i		−	0.505106i
$10$	69.1933	−	14.5701i	0.691933	−	0.145701i
$11$	133.641			1.10447			0.552237	−	0.833687i	$-0.313774\pi$
$11$	133.641			1.10447			0.552237	+	0.833687i	$0.313774\pi$
$12$	35.8157	−	35.8157i	0.248720	−	0.248720i
$13$	−27.8077	−	27.8077i	−0.164542	−	0.164542i	0.620033	−	0.784576i	$-0.287119\pi$
$13$	−27.8077	−	27.8077i	−0.164542	−	0.164542i	−0.784576	+	0.620033i	$0.787119\pi$
$14$		−	61.6638i		−	0.314611i
$15$	−32.6150	−	154.888i	−0.144956	−	0.688391i
$16$	−64.0000			−0.250000
$17$	−6.97609	+	6.97609i	−0.0241387	+	0.0241387i	−0.719073	−	0.694934i	$-0.755433\pi$
$17$	−6.97609	+	6.97609i	−0.0241387	+	0.0241387i	0.694934	+	0.719073i	$0.255433\pi$
$18$	81.8272	+	81.8272i	0.252553	+	0.252553i
$19$			581.940i			1.61202i	0.591901	+	0.806011i	$0.298378\pi$
$19$			581.940i			1.61202i	−0.591901	+	0.806011i	$0.701622\pi$
$20$	−109.246	+	167.527i	−0.273116	+	0.418817i
$21$	−138.033			−0.313001
$22$	−267.283	+	267.283i	−0.552237	+	0.552237i
$23$	−77.9968	−	77.9968i	−0.147442	−	0.147442i
$23$	−77.9968	−	77.9968i	−0.147442	−	0.147442i
$24$			143.263i			0.248720i
$25$	252.039	+	571.928i	0.403262	+	0.915084i
$26$	111.231			0.164542
$27$	545.803	−	545.803i	0.748700	−	0.748700i
$28$	123.328	+	123.328i	0.157306	+	0.157306i
$29$			1422.24i			1.69113i	0.533871	+	0.845566i	$0.320737\pi$
$29$			1422.24i			1.69113i	−0.533871	+	0.845566i	$0.679263\pi$
$30$	375.006	+	244.546i	0.416673	+	0.271717i
$31$	−109.874			−0.114333			−0.0571666	−	0.998365i	$-0.518207\pi$
$31$	−109.874			−0.114333			−0.0571666	+	0.998365i	$0.518207\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	598.307	+	598.307i	0.549409	+	0.549409i
$34$		−	27.9044i		−	0.0241387i
$35$	533.340	−	112.306i	0.435380	−	0.0916786i
$36$	−327.309			−0.252553
$37$	347.767	−	347.767i	0.254030	−	0.254030i	−0.568591	−	0.822621i	$-0.692511\pi$
$37$	347.767	−	347.767i	0.254030	−	0.254030i	0.822621	+	0.568591i	$0.192511\pi$
$38$	−1163.88	−	1163.88i	−0.806011	−	0.806011i
$39$		−	248.988i		−	0.163700i
$40$	−116.561	−	553.546i	−0.0728507	−	0.345966i
$41$	−1500.74			−0.892764			−0.446382	−	0.894842i	$-0.647288\pi$
$41$	−1500.74			−0.892764			−0.446382	+	0.894842i	$0.647288\pi$
$42$	276.067	−	276.067i	0.156500	−	0.156500i
$43$	687.304	+	687.304i	0.371716	+	0.371716i	0.868102	−	0.496386i	$-0.165340\pi$
$43$	687.304	+	687.304i	0.371716	+	0.371716i	−0.496386	+	0.868102i	$0.665340\pi$
$44$		−	1069.13i		−	0.552237i
$45$	−558.708	+	856.766i	−0.275905	+	0.423094i
$46$	311.987			0.147442
$47$	−97.5012	+	97.5012i	−0.0441382	+	0.0441382i	−0.728831	−	0.684693i	$-0.759936\pi$
$47$	−97.5012	+	97.5012i	−0.0441382	+	0.0441382i	0.684693	+	0.728831i	$0.259936\pi$
$48$	−286.526	−	286.526i	−0.124360	−	0.124360i
$49$			1925.70i			0.802040i
$50$	−1647.93	−	639.777i	−0.659173	−	0.255911i
$51$	−62.4634			−0.0240151
$52$	−222.461	+	222.461i	−0.0822712	+	0.0822712i
$53$	2457.09	+	2457.09i	0.874722	+	0.874722i	0.992983	−	0.118261i	$-0.0377319\pi$
$53$	2457.09	+	2457.09i	0.874722	+	0.874722i	−0.118261	+	0.992983i	$0.537732\pi$
$54$			2183.21i			0.748700i
$55$	−2798.56	−	1824.98i	−0.925145	−	0.603298i
$56$	−493.310			−0.157306
$57$	−2605.32	+	2605.32i	−0.801884	+	0.801884i
$58$	−2844.48	−	2844.48i	−0.845566	−	0.845566i
$59$			3828.70i			1.09989i	0.835202	+	0.549943i	$0.185351\pi$
$59$			3828.70i			1.09989i	−0.835202	+	0.549943i	$0.814649\pi$
$60$	−1239.10	+	260.920i	−0.344195	+	0.0724778i
$61$	−5066.25			−1.36153			−0.680765	−	0.732502i	$-0.738352\pi$
$61$	−5066.25			−1.36153			−0.680765	+	0.732502i	$0.738352\pi$
$62$	219.748	−	219.748i	0.0571666	−	0.0571666i
$63$	630.722	+	630.722i	0.158912	+	0.158912i
$64$			512.000i			0.125000i
$65$	202.581	+	962.051i	0.0479481	+	0.227704i
$66$	−2393.23			−0.549409
$67$	1522.51	−	1522.51i	0.339164	−	0.339164i	−0.516889	−	0.856052i	$-0.672910\pi$
$67$	1522.51	−	1522.51i	0.339164	−	0.339164i	0.856052	+	0.516889i	$0.172910\pi$
$68$	55.8087	+	55.8087i	0.0120694	+	0.0120694i
$69$		−	698.377i		−	0.146687i
$70$	−842.068	+	1291.29i	−0.171851	+	0.263529i
$71$	−1397.47			−0.277221			−0.138611	−	0.990347i	$-0.544264\pi$
$71$	−1397.47			−0.277221			−0.138611	+	0.990347i	$0.544264\pi$
$72$	654.618	−	654.618i	0.126277	−	0.126277i
$73$	1262.48	+	1262.48i	0.236907	+	0.236907i	0.815568	−	0.578661i	$-0.196425\pi$
$73$	1262.48	+	1262.48i	0.236907	+	0.236907i	−0.578661	+	0.815568i	$0.696425\pi$
$74$			1391.07i			0.254030i
$75$	−1432.13	+	3688.87i	−0.254601	+	0.655799i
$76$	4655.52			0.806011
$77$	−2060.21	+	2060.21i	−0.347480	+	0.347480i
$78$	497.975	+	497.975i	0.0818500	+	0.0818500i
$79$			5010.15i			0.802780i	0.915907	+	0.401390i	$0.131473\pi$
$79$			5010.15i			0.802780i	−0.915907	+	0.401390i	$0.868527\pi$
$80$	1340.21	+	873.970i	0.209409	+	0.136558i
$81$	1573.07			0.239761
$82$	3001.47	−	3001.47i	0.446382	−	0.446382i
$83$	3638.73	+	3638.73i	0.528194	+	0.528194i	0.920034	−	0.391839i	$-0.128161\pi$
$83$	3638.73	+	3638.73i	0.528194	+	0.528194i	−0.391839	+	0.920034i	$0.628161\pi$
$84$			1104.27i			0.156500i
$85$	241.349	−	50.8213i	0.0334047	−	0.00703409i
$86$	−2749.21			−0.371716
$87$	−6367.32	+	6367.32i	−0.841237	+	0.841237i
$88$	2138.26	+	2138.26i	0.276118	+	0.276118i
$89$			12022.9i			1.51786i	0.651175	+	0.758928i	$0.274276\pi$
$89$			12022.9i			1.51786i	−0.651175	+	0.758928i	$0.725724\pi$
$90$	−596.117	−	2830.95i	−0.0735947	−	0.349500i
$91$	857.363			0.103534
$92$	−623.974	+	623.974i	−0.0737210	+	0.0737210i
$93$	−491.903	−	491.903i	−0.0568740	−	0.0568740i
$94$		−	390.005i		−	0.0441382i
$95$	7946.84	−	12186.3i	0.880537	−	1.35028i
$96$	1146.10			0.124360
$97$	897.842	−	897.842i	0.0954238	−	0.0954238i	−0.657783	−	0.753207i	$-0.728506\pi$
$97$	897.842	−	897.842i	0.0954238	−	0.0954238i	0.753207	+	0.657783i	$0.228506\pi$
$98$	−3851.39	−	3851.39i	−0.401020	−	0.401020i
$99$		−	5467.75i		−	0.557877i
$100$	4575.42	−	2016.31i	0.457542	−	0.201631i
$101$	6434.40			0.630762			0.315381	−	0.948965i	$-0.397868\pi$
$101$	6434.40			0.630762			0.315381	+	0.948965i	$0.397868\pi$
$102$	124.927	−	124.927i	0.0120076	−	0.0120076i
$103$	−13926.1	−	13926.1i	−1.31267	−	1.31267i	−0.919444	−	0.393221i	$-0.871361\pi$
$103$	−13926.1	−	13926.1i	−1.31267	−	1.31267i	−0.393221	−	0.919444i	$-0.628639\pi$
$104$		−	889.845i		−	0.0822712i
$105$	2890.53	+	1884.95i	0.262180	+	0.170971i
$106$	−9828.37			−0.874722
$107$	8513.25	−	8513.25i	0.743581	−	0.743581i	−0.229684	−	0.973265i	$-0.573769\pi$
$107$	8513.25	−	8513.25i	0.743581	−	0.743581i	0.973265	+	0.229684i	$0.0737694\pi$
$108$	−4366.42	−	4366.42i	−0.374350	−	0.374350i
$109$			6247.33i			0.525826i	0.964820	+	0.262913i	$0.0846832\pi$
$109$			6247.33i			0.525826i	−0.964820	+	0.262913i	$0.915317\pi$
$110$	9247.08	−	1947.17i	0.764221	−	0.160923i
$111$	3113.88			0.252730
$112$	986.621	−	986.621i	0.0786528	−	0.0786528i
$113$	2797.66	+	2797.66i	0.219098	+	0.219098i	0.808118	−	0.589020i	$-0.200486\pi$
$113$	2797.66	+	2797.66i	0.219098	+	0.219098i	−0.589020	+	0.808118i	$0.700486\pi$
$114$		−	10421.3i		−	0.801884i
$115$	568.212	+	2698.43i	0.0429650	+	0.204040i
$116$	11377.9			0.845566
$117$	−1137.71	+	1137.71i	−0.0831114	+	0.0831114i
$118$	−7657.41	−	7657.41i	−0.549943	−	0.549943i
$119$		−	215.086i		−	0.0151886i
$120$	1956.37	−	3000.05i	0.135859	−	0.208337i
$121$	3218.99			0.219861
$122$	10132.5	−	10132.5i	0.680765	−	0.680765i
$123$	−6718.74	−	6718.74i	−0.444097	−	0.444097i
$124$			878.994i			0.0571666i
$125$	2532.21	−	15418.4i	0.162061	−	0.986781i
$126$	−2522.89			−0.158912
$127$	8109.16	−	8109.16i	0.502769	−	0.502769i	−0.409529	−	0.912297i	$-0.634307\pi$
$127$	8109.16	−	8109.16i	0.502769	−	0.502769i	0.912297	+	0.409529i	$0.134307\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$			6154.06i			0.369813i
$130$	−2329.26	−	1518.94i	−0.137826	−	0.0898782i
$131$	30412.4			1.77218			0.886090	−	0.463514i	$-0.153412\pi$
$131$	30412.4			1.77218			0.886090	+	0.463514i	$0.153412\pi$
$132$	4786.46	−	4786.46i	0.274705	−	0.274705i
$133$	−8971.15	−	8971.15i	−0.507160	−	0.507160i
$134$			6090.02i			0.339164i
$135$	−18882.9	+	3976.21i	−1.03610	+	0.218173i
$136$	−223.235			−0.0120694
$137$	−2657.43	+	2657.43i	−0.141586	+	0.141586i	−0.774347	−	0.632761i	$-0.781922\pi$
$137$	−2657.43	+	2657.43i	−0.141586	+	0.141586i	0.632761	+	0.774347i	$0.281922\pi$
$138$	1396.75	+	1396.75i	0.0733436	+	0.0733436i
$139$		−	1120.78i		−	0.0580085i	−0.999579	−	0.0290043i	$-0.990766\pi$
$139$		−	1120.78i		−	0.0580085i	0.999579	−	0.0290043i	$-0.00923364\pi$
$140$	−898.451	−	4266.72i	−0.0458393	−	0.217690i
$141$	−873.019			−0.0439122
$142$	2794.94	−	2794.94i	0.138611	−	0.138611i
$143$	−3716.25	−	3716.25i	−0.181733	−	0.181733i
$144$			2618.47i			0.126277i
$145$	19421.8	−	29783.0i	0.923750	−	1.41655i
$146$	−5049.91			−0.236907
$147$	−8621.27	+	8621.27i	−0.398967	+	0.398967i
$148$	−2782.14	−	2782.14i	−0.127015	−	0.127015i
$149$			16434.1i			0.740243i	0.928983	+	0.370122i	$0.120684\pi$
$149$			16434.1i			0.740243i	−0.928983	+	0.370122i	$0.879316\pi$
$150$	−4513.48	−	10242.0i	−0.200599	−	0.455200i
$151$	25320.6			1.11051			0.555253	−	0.831682i	$-0.312621\pi$
$151$	25320.6			1.11051			0.555253	+	0.831682i	$0.312621\pi$
$152$	−9311.04	+	9311.04i	−0.403005	+	0.403005i
$153$	285.417	+	285.417i	0.0121926	+	0.0121926i
$154$		−	8240.83i		−	0.347480i
$155$	2300.86	+	1500.42i	0.0957694	+	0.0624524i
$156$	−1991.90			−0.0818500
$157$	19257.5	−	19257.5i	0.781271	−	0.781271i	−0.198774	−	0.980045i	$-0.563696\pi$
$157$	19257.5	−	19257.5i	0.781271	−	0.781271i	0.980045	+	0.198774i	$0.0636961\pi$
$158$	−10020.3	−	10020.3i	−0.401390	−	0.401390i
$159$			22000.6i			0.870244i
$160$	−4428.37	+	932.489i	−0.172983	+	0.0364254i
$161$	2404.79			0.0927738
$162$	−3146.15	+	3146.15i	−0.119881	+	0.119881i
$163$	23703.8	+	23703.8i	0.892162	+	0.892162i	0.994726	−	0.102564i	$-0.0327048\pi$
$163$	23703.8	+	23703.8i	0.892162	+	0.892162i	−0.102564	+	0.994726i	$0.532705\pi$
$164$			12005.9i			0.446382i
$165$	−4358.71	−	20699.4i	−0.160099	−	0.760309i
$166$	−14554.9			−0.528194
$167$	907.579	−	907.579i	0.0325425	−	0.0325425i	−0.690648	−	0.723191i	$-0.742675\pi$
$167$	907.579	−	907.579i	0.0325425	−	0.0325425i	0.723191	+	0.690648i	$0.242675\pi$
$168$	−2208.53	−	2208.53i	−0.0782501	−	0.0782501i
$169$		−	27014.5i		−	0.945852i
$170$	−381.056	+	584.341i	−0.0131853	+	0.0202194i
$171$	23809.3			0.814242
$172$	5498.43	−	5498.43i	0.185858	−	0.185858i
$173$	21438.6	+	21438.6i	0.716314	+	0.716314i	0.967848	−	0.251534i	$-0.0809351\pi$
$173$	21438.6	+	21438.6i	0.716314	+	0.716314i	−0.251534	+	0.967848i	$0.580935\pi$
$174$		−	25469.3i		−	0.841237i
$175$	−12702.2	−	4931.39i	−0.414767	−	0.161025i
$176$	−8553.04			−0.276118
$177$	−17141.0	+	17141.0i	−0.547128	+	0.547128i
$178$	−24045.9	−	24045.9i	−0.758928	−	0.758928i
$179$			20851.2i			0.650767i	0.945582	+	0.325384i	$0.105493\pi$
$179$			20851.2i			0.650767i	−0.945582	+	0.325384i	$0.894507\pi$
$180$	6854.13	+	4469.66i	0.211547	+	0.137952i
$181$	−17991.9			−0.549185			−0.274593	−	0.961561i	$-0.588543\pi$
$181$	−17991.9			−0.549185			−0.274593	+	0.961561i	$0.588543\pi$
$182$	−1714.73	+	1714.73i	−0.0517669	+	0.0517669i
$183$	−22681.4	−	22681.4i	−0.677279	−	0.677279i
$184$		−	2495.90i		−	0.0737210i
$185$	−12031.6	+	2533.51i	−0.351544	+	0.0740251i
$186$	1967.61			0.0568740
$187$	−932.294	+	932.294i	−0.0266606	+	0.0266606i
$188$	780.010	+	780.010i	0.0220691	+	0.0220691i
$189$			16828.1i			0.471099i
$190$	8478.95	+	40266.3i	0.234874	+	1.11541i
$191$	35596.9			0.975764			0.487882	−	0.872910i	$-0.337770\pi$
$191$	35596.9			0.975764			0.487882	+	0.872910i	$0.337770\pi$
$192$	−2292.20	+	2292.20i	−0.0621800	+	0.0621800i
$193$	−9427.48	−	9427.48i	−0.253094	−	0.253094i	0.569144	−	0.822238i	$-0.307275\pi$
$193$	−9427.48	−	9427.48i	−0.253094	−	0.253094i	−0.822238	+	0.569144i	$0.807275\pi$
$194$			3591.37i			0.0954238i
$195$	−3400.12	+	5214.01i	−0.0894181	+	0.137121i
$196$	15405.6			0.401020
$197$	−28233.3	+	28233.3i	−0.727492	+	0.727492i	−0.970120	−	0.242627i	$-0.921991\pi$
$197$	−28233.3	+	28233.3i	−0.727492	+	0.727492i	0.242627	+	0.970120i	$0.421991\pi$
$198$	10935.5	+	10935.5i	0.278938	+	0.278938i
$199$		−	2118.93i		−	0.0535069i	−0.999642	−	0.0267534i	$-0.991483\pi$
$199$		−	2118.93i		−	0.0535069i	0.999642	−	0.0267534i	$-0.00851690\pi$
$200$	−5118.22	+	13183.5i	−0.127955	+	0.329587i
$201$	13632.4			0.337427
$202$	−12868.8	+	12868.8i	−0.315381	+	0.315381i
$203$	−21925.2	−	21925.2i	−0.532049	−	0.532049i
$204$			499.707i			0.0120076i
$205$	31426.7	+	20493.7i	0.747810	+	0.487656i
$206$	55704.3			1.31267
$207$	−3191.13	+	3191.13i	−0.0744739	+	0.0744739i
$208$	1779.69	+	1779.69i	0.0411356	+	0.0411356i
$209$			77771.2i			1.78043i
$210$	−9550.98	+	2011.16i	−0.216575	+	0.0456046i
$211$	−86409.8			−1.94088			−0.970439	−	0.241348i	$-0.922410\pi$
$211$	−86409.8			−1.94088			−0.970439	+	0.241348i	$0.922410\pi$
$212$	19656.7	−	19656.7i	0.437361	−	0.437361i
$213$	−6256.43	−	6256.43i	−0.137901	−	0.137901i
$214$			34053.0i			0.743581i
$215$	−5007.06	−	23778.4i	−0.108319	−	0.514406i
$216$	17465.7			0.374350
$217$	1693.82	−	1693.82i	0.0359705	−	0.0359705i
$218$	−12494.7	−	12494.7i	−0.262913	−	0.262913i
$219$			11304.1i			0.235694i
$220$	−14599.8	+	22388.5i	−0.301649	+	0.462572i
$221$	387.977			0.00794368
$222$	−6227.76	+	6227.76i	−0.126365	+	0.126365i
$223$	−53920.4	−	53920.4i	−1.08428	−	1.08428i	−0.996105	−	0.0881796i	$-0.971895\pi$
$223$	−53920.4	−	53920.4i	−1.08428	−	1.08428i	−0.0881796	−	0.996105i	$-0.528105\pi$
$224$			3946.48i			0.0786528i
$225$	23399.6	−	10311.8i	0.462215	−	0.203690i
$226$	−11190.7			−0.219098
$227$	−58185.9	+	58185.9i	−1.12919	+	1.12919i	−0.138879	+	0.990309i	$0.544350\pi$
$227$	−58185.9	+	58185.9i	−1.12919	+	1.12919i	−0.990309	+	0.138879i	$0.955650\pi$
$228$	20842.6	+	20842.6i	0.400942	+	0.400942i
$229$		−	102779.i		−	1.95989i	−0.199260	−	0.979947i	$-0.563854\pi$
$229$		−	102779.i		−	1.95989i	0.199260	−	0.979947i	$-0.436146\pi$
$230$	−6533.28	−	4260.43i	−0.123502	−	0.0805374i
$231$	−18446.9			−0.345701
$232$	−22755.9	+	22755.9i	−0.422783	+	0.422783i
$233$	−7978.96	−	7978.96i	−0.146972	−	0.146972i	0.629792	−	0.776764i	$-0.283140\pi$
$233$	−7978.96	−	7978.96i	−0.146972	−	0.146972i	−0.776764	+	0.629792i	$0.783140\pi$
$234$		−	4550.85i		−	0.0831114i
$235$	3373.22	−	710.304i	0.0610813	−	0.0128620i
$236$	30629.6			0.549943
$237$	−22430.2	+	22430.2i	−0.399335	+	0.399335i
$238$	430.172	+	430.172i	0.00759431	+	0.00759431i
$239$			27188.7i			0.475985i	0.971267	+	0.237992i	$0.0764894\pi$
$239$			27188.7i			0.475985i	−0.971267	+	0.237992i	$0.923511\pi$
$240$	2087.36	+	9912.82i	0.0362389	+	0.172098i
$241$	93444.7			1.60887			0.804434	−	0.594041i	$-0.202468\pi$
$241$	93444.7			1.60887			0.804434	+	0.594041i	$0.202468\pi$
$242$	−6437.98	+	6437.98i	−0.109931	+	0.109931i
$243$	−37167.4	−	37167.4i	−0.629434	−	0.629434i
$244$			40530.0i			0.680765i
$245$	26296.9	−	40325.7i	0.438099	−	0.671816i
$246$	26875.0			0.444097
$247$	16182.4	−	16182.4i	0.265246	−	0.265246i
$248$	−1757.99	−	1757.99i	−0.0285833	−	0.0285833i
$249$			32580.9i			0.525490i
$250$	25772.5	+	35901.3i	0.412360	+	0.574421i
$251$	−86697.4			−1.37613			−0.688064	−	0.725650i	$-0.741539\pi$
$251$	−86697.4			−1.37613			−0.688064	+	0.725650i	$0.741539\pi$
$252$	5045.78	−	5045.78i	0.0794561	−	0.0794561i
$253$	−10423.6	−	10423.6i	−0.162846	−	0.162846i
$254$			32436.6i			0.502769i
$255$	1308.04	+	852.987i	0.0201159	+	0.0131178i
$256$	4096.00			0.0625000
$257$	−43371.9	+	43371.9i	−0.656663	+	0.656663i	−0.954589	−	0.297926i	$-0.903705\pi$
$257$	−43371.9	+	43371.9i	−0.656663	+	0.656663i	0.297926	+	0.954589i	$0.403705\pi$
$258$	−12308.1	−	12308.1i	−0.184907	−	0.184907i
$259$			10722.3i			0.159841i
$260$	7696.41	−	1620.65i	0.113852	−	0.0239741i
$261$	58189.1			0.854202
$262$	−60824.7	+	60824.7i	−0.886090	+	0.886090i
$263$	19131.9	+	19131.9i	0.276597	+	0.276597i	0.831749	−	0.555152i	$-0.187340\pi$
$263$	19131.9	+	19131.9i	0.276597	+	0.276597i	−0.555152	+	0.831749i	$0.687340\pi$
$264$			19145.8i			0.274705i
$265$	−17900.1	−	85007.2i	−0.254896	−	1.21050i
$266$	35884.6			0.507160
$267$	−53826.2	+	53826.2i	−0.755042	+	0.755042i
$268$	−12180.0	−	12180.0i	−0.169582	−	0.169582i
$269$		−	93021.2i		−	1.28552i	−0.766070	−	0.642758i	$-0.777790\pi$
$269$		−	93021.2i		−	1.28552i	0.766070	−	0.642758i	$-0.222210\pi$
$270$	29813.5	−	45718.3i	0.408964	−	0.627137i
$271$	−83220.8			−1.13316			−0.566582	−	0.824005i	$-0.691735\pi$
$271$	−83220.8			−1.13316			−0.566582	+	0.824005i	$0.691735\pi$
$272$	446.470	−	446.470i	0.00603468	−	0.00603468i
$273$	3838.38	+	3838.38i	0.0515018	+	0.0515018i
$274$		−	10629.7i		−	0.141586i
$275$	33682.8	+	76433.1i	0.445393	+	1.01069i
$276$	−5587.02			−0.0733436
$277$	−67889.2	+	67889.2i	−0.884792	+	0.884792i	−0.994017	−	0.109225i	$-0.965163\pi$
$277$	−67889.2	+	67889.2i	−0.884792	+	0.884792i	0.109225	+	0.994017i	$0.465163\pi$
$278$	2241.57	+	2241.57i	0.0290043	+	0.0290043i
$279$			4495.35i			0.0577505i
$280$	10330.3	+	6736.54i	0.131765	+	0.0859253i
$281$	37774.9			0.478400			0.239200	−	0.970970i	$-0.423115\pi$
$281$	37774.9			0.478400			0.239200	+	0.970970i	$0.423115\pi$
$282$	1746.04	−	1746.04i	0.0219561	−	0.0219561i
$283$	19303.8	+	19303.8i	0.241030	+	0.241030i	0.817276	−	0.576246i	$-0.195483\pi$
$283$	19303.8	+	19303.8i	0.241030	+	0.241030i	−0.576246	+	0.817276i	$0.695483\pi$
$284$			11179.8i			0.138611i
$285$	90135.4	−	18980.0i	1.10970	−	0.233671i
$286$	14865.0			0.181733
$287$	23135.3	−	23135.3i	0.280874	−	0.280874i
$288$	−5236.94	−	5236.94i	−0.0631383	−	0.0631383i
$289$			83423.7i			0.998835i
$290$	20722.3	+	98409.6i	0.246400	+	1.17015i
$291$	8039.21			0.0949353
$292$	10099.8	−	10099.8i	0.118453	−	0.118453i
$293$	−28464.3	−	28464.3i	−0.331562	−	0.331562i	0.521617	−	0.853180i	$-0.325329\pi$
$293$	−28464.3	−	28464.3i	−0.331562	−	0.331562i	−0.853180	+	0.521617i	$0.825329\pi$
$294$		−	34485.1i		−	0.398967i
$295$	52283.9	−	80176.3i	0.600792	−	0.921302i
$296$	11128.5			0.127015
$297$	72941.8	−	72941.8i	0.826920	−	0.826920i
$298$	−32868.3	−	32868.3i	−0.370122	−	0.370122i
$299$			4337.82i			0.0485209i
$300$	29510.9	+	11457.0i	0.327899	+	0.127300i
$301$	−21190.9			−0.233892
$302$	−50641.3	+	50641.3i	−0.555253	+	0.555253i
$303$	28806.6	+	28806.6i	0.313766	+	0.313766i
$304$		−	37244.1i		−	0.403005i
$305$	106092.	+	69183.6i	1.14046	+	0.743710i
$306$	−1141.67			−0.0121926
$307$	−10051.9	+	10051.9i	−0.106652	+	0.106652i	−0.758419	−	0.651767i	$-0.774028\pi$
$307$	−10051.9	+	10051.9i	−0.106652	+	0.106652i	0.651767	+	0.758419i	$0.274028\pi$
$308$	16481.7	+	16481.7i	0.173740	+	0.173740i
$309$		−	124693.i		−	1.30594i
$310$	−7602.56	+	1600.88i	−0.0791109	+	0.0166585i
$311$	−85798.1			−0.887068			−0.443534	−	0.896258i	$-0.646275\pi$
$311$	−85798.1			−0.887068			−0.443534	+	0.896258i	$0.646275\pi$
$312$	3983.80	−	3983.80i	0.0409250	−	0.0409250i
$313$	−98508.8	−	98508.8i	−1.00551	−	1.00551i	−0.999985	−	0.00552498i	$-0.998241\pi$
$313$	−98508.8	−	98508.8i	−1.00551	−	1.00551i	−0.00552498	−	0.999985i	$-0.501759\pi$
$314$			77030.2i			0.781271i
$315$	−4594.86	−	21820.9i	−0.0463075	−	0.219913i
$316$	40081.2			0.401390
$317$	96104.3	−	96104.3i	0.956366	−	0.956366i	−0.0427210	−	0.999087i	$-0.513603\pi$
$317$	96104.3	−	96104.3i	0.956366	−	0.956366i	0.999087	+	0.0427210i	$0.0136027\pi$
$318$	−44001.3	−	44001.3i	−0.435122	−	0.435122i
$319$			190070.i			1.86781i
$320$	6991.76	−	10721.7i	0.0682789	−	0.104704i
$321$	76227.0			0.739774
$322$	−4809.58	+	4809.58i	−0.0463869	+	0.0463869i
$323$	−4059.66	−	4059.66i	−0.0389121	−	0.0389121i
$324$		−	12584.6i		−	0.119881i
$325$	8895.35	−	22912.6i	0.0842164	−	0.216924i
$326$	−94815.4			−0.892162
$327$	−27969.1	+	27969.1i	−0.261567	+	0.261567i
$328$	−24011.8	−	24011.8i	−0.223191	−	0.223191i
$329$		−	3006.15i		−	0.0277727i
$330$	50116.2	+	32681.4i	0.460204	+	0.300105i
$331$	−11449.0			−0.104499			−0.0522494	−	0.998634i	$-0.516639\pi$
$331$	−11449.0			−0.104499			−0.0522494	+	0.998634i	$0.516639\pi$
$332$	29109.8	−	29109.8i	0.264097	−	0.264097i
$333$	−14228.4	−	14228.4i	−0.128312	−	0.128312i
$334$			3630.32i			0.0325425i
$335$	−52673.6	+	11091.6i	−0.469357	+	0.0988332i
$336$	8834.13			0.0782501
$337$	142320.	−	142320.i	1.25316	−	1.25316i	0.298865	−	0.954295i	$-0.403392\pi$
$337$	142320.	−	142320.i	1.25316	−	1.25316i	0.954295	−	0.298865i	$-0.0966082\pi$
$338$	54028.9	+	54028.9i	0.472926	+	0.472926i
$339$			25050.1i			0.217976i
$340$	−406.571	−	1930.79i	−0.00351705	−	0.0167024i
$341$	−14683.7			−0.126278
$342$	−47618.5	+	47618.5i	−0.407121	+	0.407121i
$343$	−66700.1	−	66700.1i	−0.566942	−	0.566942i
$344$			21993.7i			0.185858i
$345$	−9536.89	+	14624.6i	−0.0801251	+	0.122870i
$346$	−85754.3			−0.716314
$347$	−6898.82	+	6898.82i	−0.0572949	+	0.0572949i	−0.735174	−	0.677879i	$-0.762899\pi$
$347$	−6898.82	+	6898.82i	−0.0572949	+	0.0572949i	0.677879	+	0.735174i	$0.262899\pi$
$348$	50938.6	+	50938.6i	0.420619	+	0.420619i
$349$			120582.i			0.989989i	0.868896	+	0.494994i	$0.164830\pi$
$349$			120582.i			0.989989i	−0.868896	+	0.494994i	$0.835170\pi$
$350$	35267.2	−	15541.7i	0.287896	−	0.126871i
$351$	−30355.0			−0.246386
$352$	17106.1	−	17106.1i	0.138059	−	0.138059i
$353$	99139.7	+	99139.7i	0.795606	+	0.795606i	0.982399	−	0.186793i	$-0.0598095\pi$
$353$	99139.7	+	99139.7i	0.795606	+	0.795606i	−0.186793	+	0.982399i	$0.559809\pi$
$354$		−	68563.8i		−	0.547128i
$355$	29264.3	+	19083.6i	0.232210	+	0.151427i
$356$	96183.5			0.758928
$357$	962.932	−	962.932i	0.00755543	−	0.00755543i
$358$	−41702.5	−	41702.5i	−0.325384	−	0.325384i
$359$		−	66147.1i		−	0.513242i	−0.966512	−	0.256621i	$-0.917391\pi$
$359$		−	66147.1i		−	0.513242i	0.966512	−	0.256621i	$-0.0826092\pi$
$360$	−22647.6	+	4768.94i	−0.174750	+	0.0367974i
$361$	−208333.			−1.59861
$362$	35983.7	−	35983.7i	0.274593	−	0.274593i
$363$	14411.3	+	14411.3i	0.109368	+	0.109368i
$364$		−	6858.90i		−	0.0517669i
$365$	−9197.24	−	43677.5i	−0.0690354	−	0.327847i
$366$	90725.6			0.677279
$367$	−109978.	+	109978.i	−0.816531	+	0.816531i	−0.985604	−	0.169073i	$-0.945923\pi$
$367$	−109978.	+	109978.i	−0.816531	+	0.816531i	0.169073	+	0.985604i	$0.445923\pi$
$368$	4991.79	+	4991.79i	0.0368605	+	0.0368605i
$369$			61400.6i			0.450941i
$370$	18996.1	−	29130.2i	0.138759	−	0.212784i
$371$	−75756.9			−0.550395
$372$	−3935.22	+	3935.22i	−0.0284370	+	0.0284370i
$373$	−62523.6	−	62523.6i	−0.449393	−	0.449393i	0.445760	−	0.895153i	$-0.352934\pi$
$373$	−62523.6	−	62523.6i	−0.449393	−	0.449393i	−0.895153	+	0.445760i	$0.852934\pi$
$374$		−	3729.17i		−	0.0266606i
$375$	80364.4	−	57691.2i	0.571480	−	0.410249i
$376$	−3120.04			−0.0220691
$377$	39549.2	−	39549.2i	0.278263	−	0.278263i
$378$	−33656.3	−	33656.3i	−0.235550	−	0.235550i
$379$		−	110606.i		−	0.770014i	−0.922914	−	0.385007i	$-0.874199\pi$
$379$		−	110606.i		−	0.770014i	0.922914	−	0.385007i	$-0.125801\pi$
$380$	−97490.5	−	63574.8i	−0.675142	−	0.440268i
$381$	72608.8			0.500195
$382$	−71193.7	+	71193.7i	−0.487882	+	0.487882i
$383$	−1184.54	−	1184.54i	−0.00807515	−	0.00807515i	0.703058	−	0.711133i	$-0.251818\pi$
$383$	−1184.54	−	1184.54i	−0.00807515	−	0.00807515i	−0.711133	+	0.703058i	$0.751818\pi$
$384$		−	9168.82i		−	0.0621800i
$385$	71276.3	−	15008.8i	0.480865	−	0.101257i
$386$	37709.9			0.253094
$387$	28120.1	−	28120.1i	0.187756	−	0.187756i
$388$	−7182.74	−	7182.74i	−0.0477119	−	0.0477119i
$389$		−	45967.0i		−	0.303771i	−0.988398	−	0.151886i	$-0.951465\pi$
$389$		−	45967.0i		−	0.303771i	0.988398	−	0.151886i	$-0.0485345\pi$
$390$	−3627.79	−	17228.3i	−0.0238513	−	0.113269i
$391$	1088.23			0.00711812
$392$	−30811.2	+	30811.2i	−0.200510	+	0.200510i
$393$	136155.	+	136155.i	0.881553	+	0.881553i
$394$		−	112933.i		−	0.727492i
$395$	68417.5	−	104917.i	0.438504	−	0.672436i
$396$	−43742.0			−0.278938
$397$	−159089.	+	159089.i	−1.00939	+	1.00939i	−0.00943206	+	0.999956i	$0.503002\pi$
$397$	−159089.	+	159089.i	−1.00939	+	1.00939i	−0.999956	+	0.00943206i	$0.996998\pi$
$398$	4237.85	+	4237.85i	0.0267534	+	0.0267534i
$399$		−	80327.0i		−	0.504564i
$400$	−16130.5	−	36603.4i	−0.100816	−	0.228771i
$401$	126144.			0.784475			0.392238	−	0.919864i	$-0.371701\pi$
$401$	126144.			0.784475			0.392238	+	0.919864i	$0.371701\pi$
$402$	−27264.8	+	27264.8i	−0.168714	+	0.168714i
$403$	3055.34	+	3055.34i	0.0188127	+	0.0188127i
$404$		−	51475.2i		−	0.315381i
$405$	−32941.5	−	21481.5i	−0.200832	−	0.130965i
$406$	87700.9			0.532049
$407$	46476.0	−	46476.0i	0.280569	−	0.280569i
$408$	−999.414	−	999.414i	−0.00600379	−	0.00600379i
$409$		−	147744.i		−	0.883208i	−0.897210	−	0.441604i	$-0.854410\pi$
$409$		−	147744.i		−	0.883208i	0.897210	−	0.441604i	$-0.145590\pi$
$410$	−103841.	+	21866.0i	−0.617733	+	0.130077i
$411$	−23794.4			−0.140861
$412$	−111409.	+	111409.i	−0.656333	+	0.656333i
$413$	−59023.1	−	59023.1i	−0.346036	−	0.346036i
$414$		−	12764.5i		−	0.0744739i
$415$	−26508.4	−	125888.i	−0.153917	−	0.730950i
$416$	−7118.76			−0.0411356
$417$	5017.70	−	5017.70i	0.0288558	−	0.0288558i
$418$	−155542.	−	155542.i	−0.890217	−	0.890217i
$419$		−	203624.i		−	1.15985i	−0.814672	−	0.579923i	$-0.803083\pi$
$419$		−	203624.i		−	1.15985i	0.814672	−	0.579923i	$-0.196917\pi$
$420$	15079.6	−	23124.3i	0.0854854	−	0.131090i
$421$	−113865.			−0.642431			−0.321215	−	0.947006i	$-0.604091\pi$
$421$	−113865.			−0.642431			−0.321215	+	0.947006i	$0.604091\pi$
$422$	172820.	−	172820.i	0.970439	−	0.970439i
$423$	3989.13	+	3989.13i	0.0222945	+	0.0222945i
$424$			78627.0i			0.437361i
$425$	−5748.07	−	2231.57i	−0.0318232	−	0.0123547i
$426$	25025.7			0.137901
$427$	78101.1	−	78101.1i	0.428352	−	0.428352i
$428$	−68106.0	−	68106.0i	−0.371790	−	0.371790i
$429$		−	33275.0i		−	0.180802i
$430$	57570.9	+	37542.7i	0.311362	+	0.203043i
$431$	−310369.			−1.67080			−0.835400	−	0.549643i	$-0.814764\pi$
$431$	−310369.			−1.67080			−0.835400	+	0.549643i	$0.814764\pi$
$432$	−34931.4	+	34931.4i	−0.187175	+	0.187175i
$433$	−136164.	−	136164.i	−0.726248	−	0.726248i	0.243622	−	0.969870i	$-0.421664\pi$
$433$	−136164.	−	136164.i	−0.726248	−	0.726248i	−0.969870	+	0.243622i	$0.921664\pi$
$434$			6775.26i			0.0359705i
$435$	220288.	−	46386.4i	1.16416	−	0.245139i
$436$	49978.7			0.262913
$437$	45389.4	−	45389.4i	0.237680	−	0.237680i
$438$	−22608.2	−	22608.2i	−0.117847	−	0.117847i
$439$			297445.i			1.54339i	0.635990	+	0.771697i	$0.280592\pi$
$439$			297445.i			1.54339i	−0.635990	+	0.771697i	$0.719408\pi$
$440$	−15577.4	−	73976.6i	−0.0804617	−	0.382111i
$441$	78787.2			0.405115
$442$	−775.955	+	775.955i	−0.00397184	+	0.00397184i
$443$	196943.	+	196943.i	1.00354	+	1.00354i	0.999994	+	0.00354489i	$0.00112838\pi$
$443$	196943.	+	196943.i	1.00354	+	1.00354i	0.00354489	+	0.999994i	$0.498872\pi$
$444$		−	24911.0i		−	0.126365i
$445$	164183.	−	251771.i	0.829100	−	1.27141i
$446$	215681.			1.08428
$447$	−73575.0	+	73575.0i	−0.368227	+	0.368227i
$448$	−7892.97	−	7892.97i	−0.0393264	−	0.0393264i
$449$			277579.i			1.37687i	0.725298	+	0.688435i	$0.241702\pi$
$449$			277579.i			1.37687i	−0.725298	+	0.688435i	$0.758298\pi$
$450$	−26175.6	+	67422.9i	−0.129262	+	0.332953i
$451$	−200560.			−0.986034
$452$	22381.3	−	22381.3i	0.109549	−	0.109549i
$453$	113360.	+	113360.i	0.552410	+	0.552410i
$454$		−	232744.i		−	1.12919i
$455$	−17953.9	−	11708.0i	−0.0867234	−	0.0565534i
$456$	−83370.3			−0.400942
$457$	204991.	−	204991.i	0.981527	−	0.981527i	−0.0183054	−	0.999832i	$-0.505827\pi$
$457$	204991.	−	204991.i	0.981527	−	0.981527i	0.999832	+	0.0183054i	$0.00582713\pi$
$458$	205558.	+	205558.i	0.979947	+	0.979947i
$459$			7615.14i			0.0361453i
$460$	21587.4	−	4545.70i	0.102020	−	0.0214825i
$461$	−3099.86			−0.0145861			−0.00729306	−	0.999973i	$-0.502321\pi$
$461$	−3099.86			−0.0145861			−0.00729306	+	0.999973i	$0.502321\pi$
$462$	36893.9	−	36893.9i	0.172850	−	0.172850i
$463$	62253.8	+	62253.8i	0.290405	+	0.290405i	0.837240	−	0.546835i	$-0.184168\pi$
$463$	62253.8	+	62253.8i	0.290405	+	0.290405i	−0.546835	+	0.837240i	$0.684168\pi$
$464$		−	91023.5i		−	0.422783i
$465$	3583.55	+	17018.2i	0.0165732	+	0.0787059i
$466$	31915.8			0.146972
$467$	186901.	−	186901.i	0.856993	−	0.856993i	−0.133990	−	0.990983i	$-0.542779\pi$
$467$	186901.	−	186901.i	0.856993	−	0.856993i	0.990983	+	0.133990i	$0.0427789\pi$
$468$	9101.69	+	9101.69i	0.0415557	+	0.0415557i
$469$			46941.7i			0.213409i
$470$	−5325.82	+	8167.04i	−0.0241097	+	0.0369717i
$471$	172431.			0.777271
$472$	−61259.2	+	61259.2i	−0.274971	+	0.274971i
$473$	91852.1	+	91852.1i	0.410551	+	0.410551i
$474$		−	89721.0i		−	0.399335i
$475$	−332827.	+	146672.i	−1.47514	+	0.650068i
$476$	−1720.69			−0.00759431
$477$	100529.	−	100529.i	0.441828	−	0.441828i
$478$	−54377.5	−	54377.5i	−0.237992	−	0.237992i
$479$			83978.2i			0.366012i	0.983112	+	0.183006i	$0.0585828\pi$
$479$			83978.2i			0.366012i	−0.983112	+	0.183006i	$0.941417\pi$
$480$	−24000.4	−	15650.9i	−0.104168	−	0.0679294i
$481$	−19341.2			−0.0835974
$482$	−186889.	+	186889.i	−0.804434	+	0.804434i
$483$	10766.2	+	10766.2i	0.0461494	+	0.0461494i
$484$		−	25751.9i		−	0.109931i
$485$	−31062.3	+	6540.85i	−0.132054	+	0.0278068i
$486$	148670.			0.629434
$487$	−239611.	+	239611.i	−1.01030	+	1.01030i	−0.0103487	+	0.999946i	$0.503294\pi$
$487$	−239611.	+	239611.i	−1.01030	+	1.01030i	−0.999946	+	0.0103487i	$0.996706\pi$
$488$	−81060.0	−	81060.0i	−0.340382	−	0.340382i
$489$			212242.i			0.887594i
$490$	28057.7	+	133245.i	0.116858	+	0.554958i
$491$	58812.0			0.243951			0.121976	−	0.992533i	$-0.461077\pi$
$491$	58812.0			0.243951			0.121976	+	0.992533i	$0.461077\pi$
$492$	−53749.9	+	53749.9i	−0.222048	+	0.222048i
$493$	−9921.69	−	9921.69i	−0.0408218	−	0.0408218i
$494$			64729.5i			0.265246i
$495$	−74666.4	+	114499.i	−0.304730	+	0.467297i
$496$	7031.95			0.0285833
$497$	21543.4	−	21543.4i	0.0872169	−	0.0872169i
$498$	−65161.8	−	65161.8i	−0.262745	−	0.262745i
$499$		−	173676.i		−	0.697489i	−0.937218	−	0.348745i	$-0.886608\pi$
$499$		−	173676.i		−	0.697489i	0.937218	−	0.348745i	$-0.113392\pi$
$500$	−123348.	−	20257.7i	−0.493390	−	0.0810307i
$501$	8126.39			0.0323759
$502$	173395.	−	173395.i	0.688064	−	0.688064i
$503$	−11620.5	−	11620.5i	−0.0459291	−	0.0459291i	0.683769	−	0.729698i	$-0.260339\pi$
$503$	−11620.5	−	11620.5i	−0.0459291	−	0.0459291i	−0.729698	+	0.683769i	$0.760339\pi$
$504$			20183.1i			0.0794561i
$505$	−134742.	−	87866.8i	−0.528348	−	0.344542i
$506$	41694.4			0.162846
$507$	120943.	−	120943.i	0.470505	−	0.470505i
$508$	−64873.3	−	64873.3i	−0.251384	−	0.251384i
$509$			326727.i			1.26110i	0.776149	+	0.630550i	$0.217171\pi$
$509$			326727.i			1.26110i	−0.776149	+	0.630550i	$0.782829\pi$
$510$	−4322.05	+	910.100i	−0.0166169	+	0.00349904i
$511$	−38924.6			−0.149067
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	317624.	+	317624.i	1.20692	+	1.20692i
$514$		−	173488.i		−	0.656663i
$515$	101452.	+	481795.i	0.382514	+	1.81655i
$516$	49232.5			0.184907
$517$	−13030.2	+	13030.2i	−0.0487494	+	0.0487494i
$518$	−21444.6	−	21444.6i	−0.0799207	−	0.0799207i
$519$			191959.i			0.712647i
$520$	−12151.5	+	18634.1i	−0.0449391	+	0.0689131i
$521$	397121.			1.46301			0.731505	−	0.681836i	$-0.238818\pi$
$521$	397121.			1.46301			0.731505	+	0.681836i	$0.238818\pi$
$522$	−116378.	+	116378.i	−0.427101	+	0.427101i
$523$	299724.	+	299724.i	1.09577	+	1.09577i	0.994900	+	0.100866i	$0.0321613\pi$
$523$	299724.	+	299724.i	1.09577	+	1.09577i	0.100866	+	0.994900i	$0.467839\pi$
$524$		−	243299.i		−	0.886090i
$525$	−34789.8	−	78945.0i	−0.126221	−	0.286422i
$526$	−76527.7			−0.276597
$527$	766.493	−	766.493i	0.00275986	−	0.00275986i
$528$	−38291.6	−	38291.6i	−0.137352	−	0.137352i
$529$			12167.0i			0.0434783i
$530$	205815.	+	134214.i	0.732697	+	0.477800i
$531$	156646.			0.555559
$532$	−71769.2	+	71769.2i	−0.253580	+	0.253580i
$533$	41732.0	+	41732.0i	0.146898	+	0.146898i
$534$		−	215305.i		−	0.755042i
$535$	−294530.	+	62019.7i	−1.02902	+	0.216682i
$536$	48720.2			0.169582
$537$	−93350.2	+	93350.2i	−0.323718	+	0.323718i
$538$	186042.	+	186042.i	0.642758	+	0.642758i
$539$			257353.i			0.885831i
$540$	31809.7	+	151064.i	0.109087	+	0.518050i
$541$	−329750.			−1.12665			−0.563326	−	0.826235i	$-0.690478\pi$
$541$	−329750.			−1.12665			−0.563326	+	0.826235i	$0.690478\pi$
$542$	166442.	−	166442.i	0.566582	−	0.566582i
$543$	−80548.9	−	80548.9i	−0.273187	−	0.273187i
$544$			1785.88i			0.00603468i
$545$	85312.3	−	130825.i	0.287222	−	0.440450i
$546$	−15353.5			−0.0515018
$547$	−306007.	+	306007.i	−1.02272	+	1.02272i	−0.0229849	+	0.999736i	$0.507317\pi$
$547$	−306007.	+	306007.i	−1.02272	+	1.02272i	−0.999736	+	0.0229849i	$0.992683\pi$
$548$	21259.4	+	21259.4i	0.0707931	+	0.0707931i
$549$			207279.i			0.687717i
$550$	−220232.	−	85500.7i	−0.728039	−	0.282647i
$551$	−827659.			−2.72614
$552$	11174.0	−	11174.0i	0.0366718	−	0.0366718i
$553$	−77236.2	−	77236.2i	−0.252564	−	0.252564i
$554$		−	271557.i		−	0.884792i
$555$	−65207.3	−	42522.5i	−0.211695	−	0.138049i
$556$	−8966.26			−0.0290043
$557$	272348.	−	272348.i	0.877837	−	0.877837i	−0.115474	−	0.993311i	$-0.536839\pi$
$557$	272348.	−	272348.i	0.877837	−	0.877837i	0.993311	+	0.115474i	$0.0368387\pi$
$558$	−8990.71	−	8990.71i	−0.0288752	−	0.0288752i
$559$		−	38224.6i		−	0.122326i
$560$	−34133.8	+	7187.60i	−0.108845	+	0.0229197i
$561$	−8347.69			−0.0265241
$562$	−75549.8	+	75549.8i	−0.239200	+	0.239200i
$563$	−122342.	−	122342.i	−0.385974	−	0.385974i	0.487275	−	0.873249i	$-0.337991\pi$
$563$	−122342.	−	122342.i	−0.385974	−	0.385974i	−0.873249	+	0.487275i	$0.837991\pi$
$564$			6984.15i			0.0219561i
$565$	−20381.2	−	96789.8i	−0.0638458	−	0.303202i
$566$	−77215.4			−0.241030
$567$	−24250.4	+	24250.4i	−0.0754315	+	0.0754315i
$568$	−22359.6	−	22359.6i	−0.0693053	−	0.0693053i
$569$			190163.i			0.587355i	0.955905	+	0.293678i	$0.0948792\pi$
$569$			190163.i			0.587355i	−0.955905	+	0.293678i	$0.905121\pi$
$570$	−142311.	+	218231.i	−0.438014	+	0.671686i
$571$	−167852.			−0.514818			−0.257409	−	0.966303i	$-0.582869\pi$
$571$	−167852.			−0.514818			−0.257409	+	0.966303i	$0.582869\pi$
$572$	−29730.0	+	29730.0i	−0.0908663	+	0.0908663i
$573$	159366.	+	159366.i	0.485384	+	0.485384i
$574$			92541.1i			0.280874i
$575$	24950.3	−	64266.8i	0.0754640	−	0.194380i
$576$	20947.8			0.0631383
$577$	170670.	−	170670.i	0.512633	−	0.512633i	−0.402700	−	0.915332i	$-0.631928\pi$
$577$	170670.	−	170670.i	0.512633	−	0.512633i	0.915332	+	0.402700i	$0.131928\pi$
$578$	−166847.	−	166847.i	−0.499417	−	0.499417i
$579$		−	84413.0i		−	0.251798i
$580$	−238264.	−	155375.i	−0.708275	−	0.461875i
$581$	−112189.			−0.332352
$582$	−16078.4	+	16078.4i	−0.0474676	+	0.0474676i
$583$	328369.	+	328369.i	0.966107	+	0.966107i
$584$			40399.3i			0.118453i
$585$	39361.0	−	8288.31i	0.115015	−	0.0242189i
$586$	113857.			0.331562
$587$	−125647.	+	125647.i	−0.364651	+	0.364651i	−0.865522	−	0.500871i	$-0.833013\pi$
$587$	−125647.	+	125647.i	−0.364651	+	0.364651i	0.500871	+	0.865522i	$0.333013\pi$
$588$	68970.2	+	68970.2i	0.199483	+	0.199483i
$589$		−	63940.2i		−	0.184308i
$590$	55784.8	+	264921.i	0.160255	+	0.761047i
$591$	−252798.			−0.723768
$592$	−22257.1	+	22257.1i	−0.0635075	+	0.0635075i
$593$	−8108.29	−	8108.29i	−0.0230579	−	0.0230579i	0.695484	−	0.718542i	$-0.255190\pi$
$593$	−8108.29	−	8108.29i	−0.0230579	−	0.0230579i	−0.718542	+	0.695484i	$0.755190\pi$
$594$			291767.i			0.826920i
$595$	−2937.17	+	4504.09i	−0.00829650	+	0.0127225i
$596$	131473.			0.370122
$597$	9486.35	−	9486.35i	0.0266165	−	0.0266165i
$598$	−8675.63	−	8675.63i	−0.0242604	−	0.0242604i
$599$		−	193242.i		−	0.538578i	−0.963059	−	0.269289i	$-0.913211\pi$
$599$		−	193242.i		−	0.538578i	0.963059	−	0.269289i	$-0.0867887\pi$
$600$	−81936.0	+	36107.8i	−0.227600	+	0.100299i
$601$	6464.17			0.0178963			0.00894816	−	0.999960i	$-0.497152\pi$
$601$	6464.17			0.0178963			0.00894816	+	0.999960i	$0.497152\pi$
$602$	42381.8	−	42381.8i	0.116946	−	0.116946i
$603$	−62291.2	−	62291.2i	−0.171314	−	0.171314i
$604$		−	202565.i		−	0.555253i
$605$	−67408.4	−	43957.8i	−0.184163	−	0.120095i
$606$	−115226.			−0.313766
$607$	417558.	−	417558.i	1.13329	−	1.13329i	0.143658	−	0.989627i	$-0.454113\pi$
$607$	417558.	−	417558.i	1.13329	−	1.13329i	0.989627	−	0.143658i	$-0.0458866\pi$
$608$	74488.3	+	74488.3i	0.201503	+	0.201503i
$609$		−	196317.i		−	0.529325i
$610$	−350550.	+	73816.0i	−0.942087	+	0.198377i
$611$	5422.56			0.0145252
$612$	2283.34	−	2283.34i	0.00609631	−	0.00609631i
$613$	94239.1	+	94239.1i	0.250790	+	0.250790i	0.821294	−	0.570505i	$-0.193252\pi$
$613$	94239.1	+	94239.1i	0.250790	+	0.250790i	−0.570505	+	0.821294i	$0.693252\pi$
$614$		−	40207.5i		−	0.106652i
$615$	48946.5	+	232446.i	0.129411	+	0.614570i
$616$	−65926.6			−0.173740
$617$	−408173.	+	408173.i	−1.07220	+	1.07220i	−0.0750142	+	0.997182i	$0.523900\pi$
$617$	−408173.	+	408173.i	−1.07220	+	1.07220i	−0.997182	+	0.0750142i	$0.976100\pi$
$618$	249386.	+	249386.i	0.652972	+	0.652972i
$619$		−	402928.i		−	1.05159i	−0.850611	−	0.525795i	$-0.823768\pi$
$619$		−	402928.i		−	1.05159i	0.850611	−	0.525795i	$-0.176232\pi$
$620$	12003.4	−	18406.9i	0.0312262	−	0.0478847i
$621$	−85141.7			−0.220780
$622$	171596.	−	171596.i	0.443534	−	0.443534i
$623$	−185345.	−	185345.i	−0.477534	−	0.477534i
$624$			15935.2i			0.0409250i
$625$	−263578.	+	288296.i	−0.674759	+	0.738038i
$626$	394035.			1.00551
$627$	−348179.	+	348179.i	−0.885660	+	0.885660i
$628$	−154060.	−	154060.i	−0.390635	−	0.390635i
$629$			4852.11i			0.0122639i
$630$	52831.5	+	34452.0i	0.133110	+	0.0868028i
$631$	495085.			1.24343			0.621714	−	0.783244i	$-0.286436\pi$
$631$	495085.			1.24343			0.621714	+	0.783244i	$0.286436\pi$
$632$	−80162.4	+	80162.4i	−0.200695	+	0.200695i
$633$	−386853.	−	386853.i	−0.965470	−	0.965470i
$634$			384417.i			0.956366i
$635$	−280550.	+	59075.8i	−0.695765	+	0.146508i
$636$	176005.			0.435122
$637$	53549.1	−	53549.1i	0.131969	−	0.131969i
$638$	−380141.	−	380141.i	−0.933905	−	0.933905i
$639$			57175.6i			0.140026i
$640$	7459.91	+	35427.0i	0.0182127	+	0.0864916i
$641$	130080.			0.316588			0.158294	−	0.987392i	$-0.449401\pi$
$641$	130080.			0.316588			0.158294	+	0.987392i	$0.449401\pi$
$642$	−152454.	+	152454.i	−0.369887	+	0.369887i
$643$	−83774.8	−	83774.8i	−0.202624	−	0.202624i	0.598499	−	0.801123i	$-0.295764\pi$
$643$	−83774.8	−	83774.8i	−0.202624	−	0.202624i	−0.801123	+	0.598499i	$0.795764\pi$
$644$		−	19238.3i		−	0.0463869i
$645$	84038.6	−	128871.i	0.202004	−	0.309768i
$646$	16238.7			0.0389121
$647$	159581.	−	159581.i	0.381217	−	0.381217i	−0.490323	−	0.871541i	$-0.663121\pi$
$647$	159581.	−	159581.i	0.381217	−	0.381217i	0.871541	+	0.490323i	$0.163121\pi$
$648$	25169.2	+	25169.2i	0.0599403	+	0.0599403i
$649$			511673.i			1.21479i
$650$	28034.5	+	63615.9i	0.0663537	+	0.150570i
$651$	15166.3			0.0357864
$652$	189631.	−	189631.i	0.446081	−	0.446081i
$653$	63954.6	+	63954.6i	0.149984	+	0.149984i	0.778111	−	0.628127i	$-0.216178\pi$
$653$	63954.6	+	63954.6i	0.149984	+	0.149984i	−0.628127	+	0.778111i	$0.716178\pi$
$654$		−	111876.i		−	0.261567i
$655$	−636861.	−	415305.i	−1.48444	−	0.968020i
$656$	96047.2			0.223191
$657$	51652.5	−	51652.5i	0.119663	−	0.119663i
$658$	6012.30	+	6012.30i	0.0138864	+	0.0138864i
$659$			52015.9i			0.119775i	0.998205	+	0.0598873i	$0.0190741\pi$
$659$			52015.9i			0.119775i	−0.998205	+	0.0598873i	$0.980926\pi$
$660$	−165595.	+	34869.7i	−0.380154	+	0.0800497i
$661$	386314.			0.884173			0.442086	−	0.896972i	$-0.354238\pi$
$661$	386314.			0.884173			0.442086	+	0.896972i	$0.354238\pi$
$662$	22898.0	−	22898.0i	0.0522494	−	0.0522494i
$663$	1736.96	+	1736.96i	0.00395151	+	0.00395151i
$664$			116439.i			0.264097i
$665$	65355.5	+	310372.i	0.147788	+	0.701841i
$666$	56913.7			0.128312
$667$	110930.	−	110930.i	0.249344	−	0.249344i
$668$	−7260.63	−	7260.63i	−0.0162713	−	0.0162713i
$669$		−	482799.i		−	1.07873i
$670$	83164.0	−	127530.i	0.185262	−	0.284095i
$671$	−677060.			−1.50377
$672$	−17668.3	+	17668.3i	−0.0391251	+	0.0391251i
$673$	344390.	+	344390.i	0.760362	+	0.760362i	0.976388	−	0.216026i	$-0.0693095\pi$
$673$	344390.	+	344390.i	0.760362	+	0.760362i	−0.216026	+	0.976388i	$0.569310\pi$
$674$			569281.i			1.25316i
$675$	449723.	+	174596.i	0.987047	+	0.383201i
$676$	−216116.			−0.472926
$677$	265651.	−	265651.i	0.579608	−	0.579608i	−0.355187	−	0.934795i	$-0.615583\pi$
$677$	265651.	−	265651.i	0.579608	−	0.579608i	0.934795	+	0.355187i	$0.115583\pi$
$678$	−50100.1	−	50100.1i	−0.108988	−	0.108988i
$679$			27682.2i			0.0600428i
$680$	4674.73	+	3048.45i	0.0101097	+	0.00659266i
$681$	−520992.			−1.12341
$682$	29367.5	−	29367.5i	0.0631390	−	0.0631390i
$683$	292240.	+	292240.i	0.626467	+	0.626467i	0.947177	−	0.320710i	$-0.103922\pi$
$683$	292240.	+	292240.i	0.626467	+	0.626467i	−0.320710	+	0.947177i	$0.603922\pi$
$684$		−	190474.i		−	0.407121i
$685$	91938.2	−	19359.6i	0.195936	−	0.0412586i
$686$	266801.			0.566942
$687$	460137.	−	460137.i	0.974930	−	0.974930i
$688$	−43987.4	−	43987.4i	−0.0929291	−	0.0929291i
$689$		−	136652.i		−	0.287857i
$690$	−10175.5	−	48323.0i	−0.0213725	−	0.101498i
$691$	231240.			0.484292			0.242146	−	0.970240i	$-0.422149\pi$
$691$	231240.			0.484292			0.242146	+	0.970240i	$0.422149\pi$
$692$	171509.	−	171509.i	0.358157	−	0.358157i
$693$	84290.5	+	84290.5i	0.175514	+	0.175514i
$694$		−	27595.3i		−	0.0572949i
$695$	−15305.2	+	23470.2i	−0.0316861	+	0.0485899i
$696$	−203754.			−0.420619
$697$	10469.3	−	10469.3i	0.0215502	−	0.0215502i
$698$	−241163.	−	241163.i	−0.494994	−	0.494994i
$699$		−	71443.0i		−	0.146219i
$700$	−39451.1	+	101618.i	−0.0805125	+	0.207383i
$701$	238530.			0.485407			0.242704	−	0.970101i	$-0.421966\pi$
$701$	238530.			0.485407			0.242704	+	0.970101i	$0.421966\pi$
$702$	60710.0	−	60710.0i	0.123193	−	0.123193i
$703$	202380.	+	202380.i	0.409502	+	0.409502i
$704$			68424.3i			0.138059i
$705$	18281.8	+	11921.8i	0.0367824	+	0.0239862i
$706$	−396559.			−0.795606
$707$	−99192.4	+	99192.4i	−0.198445	+	0.198445i
$708$	137128.	+	137128.i	0.273564	+	0.273564i
$709$			360860.i			0.717872i	0.933362	+	0.358936i	$0.116860\pi$
$709$			360860.i			0.717872i	−0.933362	+	0.358936i	$0.883140\pi$
$710$	−96695.7	+	20361.4i	−0.191818	+	0.0403915i
$711$	204983.			0.405489
$712$	−192367.	+	192367.i	−0.379464	+	0.379464i
$713$	8569.84	+	8569.84i	0.0168575	+	0.0168575i
$714$			3851.73i			0.00755543i
$715$	27073.1	+	128570.i	0.0529574	+	0.251494i
$716$	166810.			0.325384
$717$	−121723.	+	121723.i	−0.236774	+	0.236774i
$718$	132294.	+	132294.i	0.256621	+	0.256621i
$719$		−	687332.i		−	1.32956i	−0.747038	−	0.664781i	$-0.768525\pi$
$719$		−	687332.i		−	1.32956i	0.747038	−	0.664781i	$-0.231475\pi$
$720$	35757.3	−	54833.0i	0.0689762	−	0.105774i
$721$	429367.			0.825958
$722$	416666.	−	416666.i	0.799307	−	0.799307i
$723$	418348.	+	418348.i	0.800316	+	0.800316i
$724$			143935.i			0.274593i
$725$	−813420.	+	358461.i	−1.54753	+	0.681970i
$726$	−57645.2			−0.109368
$727$	77256.9	−	77256.9i	0.146173	−	0.146173i	−0.630233	−	0.776406i	$-0.717041\pi$
$727$	77256.9	−	77256.9i	0.146173	−	0.146173i	0.776406	+	0.630233i	$0.217041\pi$
$728$	13717.8	+	13717.8i	0.0258834	+	0.0258834i
$729$		−	460213.i		−	0.865972i
$730$	105749.	+	68960.5i	0.198441	+	0.129406i
$731$	−9589.38			−0.0179455
$732$	−181451.	+	181451.i	−0.338640	+	0.338640i
$733$	−377934.	−	377934.i	−0.703409	−	0.703409i	0.261731	−	0.965141i	$-0.415707\pi$
$733$	−377934.	−	377934.i	−0.703409	−	0.703409i	−0.965141	+	0.261731i	$0.915707\pi$
$734$		−	439911.i		−	0.816531i
$735$	298267.	−	62806.6i	0.552116	−	0.116260i
$736$	−19967.2			−0.0368605
$737$	203470.	−	203470.i	0.374597	−	0.374597i
$738$	−122801.	−	122801.i	−0.225470	−	0.225470i
$739$			65835.1i			0.120550i	0.998182	+	0.0602752i	$0.0191978\pi$
$739$			65835.1i			0.120550i	−0.998182	+	0.0602752i	$0.980802\pi$
$740$	20268.1	+	96252.6i	0.0370125	+	0.175772i
$741$	144896.			0.263888
$742$	151514.	−	151514.i	0.275197	−	0.275197i
$743$	−121704.	−	121704.i	−0.220459	−	0.220459i	0.588233	−	0.808692i	$-0.299824\pi$
$743$	−121704.	−	121704.i	−0.220459	−	0.220459i	−0.808692	+	0.588233i	$0.799824\pi$
$744$		−	15740.9i		−	0.0284370i
$745$	224421.	−	344145.i	0.404344	−	0.620053i
$746$	250094.			0.449393
$747$	148874.	−	148874.i	0.266794	−	0.266794i
$748$	7458.35	+	7458.35i	0.0133303	+	0.0133303i
$749$			262480.i			0.467878i
$750$	−45346.4	+	276111.i	−0.0806158	+	0.490864i
$751$	121197.			0.214888			0.107444	−	0.994211i	$-0.465733\pi$
$751$	121197.			0.214888			0.107444	+	0.994211i	$0.465733\pi$
$752$	6240.08	−	6240.08i	0.0110345	−	0.0110345i
$753$	−388141.	−	388141.i	−0.684541	−	0.684541i
$754$			158197.i			0.278263i
$755$	−530236.	−	345773.i	−0.930198	−	0.606593i
$756$	134625.			0.235550
$757$	547316.	−	547316.i	0.955095	−	0.955095i	−0.0439395	−	0.999034i	$-0.513991\pi$
$757$	547316.	−	547316.i	0.955095	−	0.955095i	0.999034	+	0.0439395i	$0.0139909\pi$
$758$	221211.	+	221211.i	0.385007	+	0.385007i
$759$		−	93332.0i		−	0.162012i
$760$	322131.	−	67831.6i	0.557705	−	0.117437i
$761$	652879.			1.12736			0.563681	−	0.825992i	$-0.309385\pi$
$761$	652879.			1.12736			0.563681	+	0.825992i	$0.309385\pi$
$762$	−145218.	+	145218.i	−0.250097	+	0.250097i
$763$	−96308.6	−	96308.6i	−0.165431	−	0.165431i
$764$		−	284775.i		−	0.487882i
$765$	−2079.28	−	9874.47i	−0.00355297	−	0.0168730i
$766$	4738.14			0.00807515
$767$	106467.	−	106467.i	0.180978	−	0.180978i
$768$	18337.6	+	18337.6i	0.0310900	+	0.0310900i
$769$		−	322701.i		−	0.545692i	−0.962058	−	0.272846i	$-0.912035\pi$
$769$		−	322701.i		−	0.545692i	0.962058	−	0.272846i	$-0.0879649\pi$
$770$	−112535.	+	172570.i	−0.189804	+	0.291061i
$771$	−388349.			−0.653301
$772$	−75419.8	+	75419.8i	−0.126547	+	0.126547i
$773$	−684980.	−	684980.i	−1.14636	−	1.14636i	−0.987264	−	0.159091i	$-0.949144\pi$
$773$	−684980.	−	684980.i	−1.14636	−	1.14636i	−0.159091	−	0.987264i	$-0.550856\pi$
$774$			112480.i			0.187756i
$775$	−27692.6	−	62840.1i	−0.0461063	−	0.104625i
$776$	28731.0			0.0477119
$777$	−48003.4	+	48003.4i	−0.0795116	+	0.0795116i
$778$	91933.9	+	91933.9i	0.151886	+	0.151886i
$779$		−	873338.i		−	1.43916i
$780$	41712.1	+	27201.0i	0.0685603	+	0.0447090i
$781$	−186760.			−0.306183
$782$	−2176.45	+	2176.45i	−0.00355906	+	0.00355906i
$783$	776264.	+	776264.i	1.26615	+	1.26615i
$784$		−	123245.i		−	0.200510i
$785$	−666247.	+	140293.i	−1.08117	+	0.227665i
$786$	−544620.			−0.881553
$787$	455092.	−	455092.i	0.734768	−	0.734768i	−0.236792	−	0.971560i	$-0.576096\pi$
$787$	455092.	−	455092.i	0.734768	−	0.734768i	0.971560	+	0.236792i	$0.0760961\pi$
$788$	225866.	+	225866.i	0.363746	+	0.363746i
$789$			171306.i			0.275181i
$790$	72998.6	+	346669.i	0.116966	+	0.555470i
$791$	−86257.3			−0.137861
$792$	87484.0	−	87484.0i	0.139469	−	0.139469i
$793$	140881.	+	140881.i	0.224029	+	0.224029i
$794$		−	636354.i		−	1.00939i
$795$	300436.	−	460712.i	0.475354	−	0.728946i
$796$	−16951.4			−0.0267534
$797$	641033.	−	641033.i	1.00917	−	1.00917i	0.00921058	−	0.999958i	$-0.497068\pi$
$797$	641033.	−	641033.i	1.00917	−	1.00917i	0.999958	−	0.00921058i	$-0.00293186\pi$
$798$	160654.	+	160654.i	0.252282	+	0.252282i
$799$		−	1360.35i		−	0.00213088i
$800$	105468.	+	40945.8i	0.164793	+	0.0639777i
$801$	491902.			0.766679
$802$	−252289.	+	252289.i	−0.392238	+	0.392238i
$803$	168719.	+	168719.i	0.261657	+	0.261657i
$804$		−	109059.i		−	0.168714i
$805$	−50358.4	−	32839.3i	−0.0777105	−	0.0506760i
$806$	−12221.4			−0.0188127
$807$	416452.	−	416452.i	0.639467	−	0.639467i
$808$	102950.	+	102950.i	0.157690	+	0.157690i
$809$		−	475560.i		−	0.726621i	−0.931668	−	0.363311i	$-0.881646\pi$
$809$		−	475560.i		−	0.726621i	0.931668	−	0.363311i	$-0.118354\pi$
$810$	108846.	−	22919.9i	0.165899	−	0.0349335i
$811$	555596.			0.844729			0.422364	−	0.906426i	$-0.361200\pi$
$811$	555596.			0.844729			0.422364	+	0.906426i	$0.361200\pi$
$812$	−175402.	+	175402.i	−0.266025	+	0.266025i
$813$	−372576.	−	372576.i	−0.563682	−	0.563682i
$814$			185904.i			0.280569i
$815$	−172684.	−	820074.i	−0.259979	−	1.23463i
$816$	3997.66			0.00600379
$817$	−399969.	+	399969.i	−0.599215	+	0.599215i
$818$	295488.	+	295488.i	0.441604	+	0.441604i
$819$		−	35077.8i		−	0.0522956i
$820$	163950.	−	251414.i	0.243828	−	0.373905i
$821$	−648338.			−0.961867			−0.480934	−	0.876757i	$-0.659702\pi$
$821$	−648338.			−0.961867			−0.480934	+	0.876757i	$0.659702\pi$
$822$	47588.9	−	47588.9i	0.0704306	−	0.0704306i
$823$	−421156.	−	421156.i	−0.621790	−	0.621790i	0.324199	−	0.945989i	$-0.394905\pi$
$823$	−421156.	−	421156.i	−0.621790	−	0.621790i	−0.945989	+	0.324199i	$0.894905\pi$
$824$		−	445634.i		−	0.656333i
$825$	−191392.	+	492985.i	−0.281200	+	0.724312i
$826$	236092.			0.346036
$827$	231159.	−	231159.i	0.337986	−	0.337986i	−0.517623	−	0.855609i	$-0.673183\pi$
$827$	231159.	−	231159.i	0.337986	−	0.337986i	0.855609	+	0.517623i	$0.173183\pi$
$828$	25529.0	+	25529.0i	0.0372369	+	0.0372369i
$829$		−	1.21019e6i		−	1.76095i	−0.474096	−	0.880473i	$-0.657225\pi$
$829$		−	1.21019e6i		−	1.76095i	0.474096	−	0.880473i	$-0.342775\pi$
$830$	304793.	+	198759.i	0.442434	+	0.288516i
$831$	−607875.			−0.880262
$832$	14237.5	−	14237.5i	0.0205678	−	0.0205678i
$833$	−13433.8	−	13433.8i	−0.0193602	−	0.0193602i
$834$			20070.8i			0.0288558i
$835$	−31399.2	+	6611.78i	−0.0450345	+	0.00948299i
$836$	622169.			0.890217
$837$	−59969.7	+	59969.7i	−0.0856014	+	0.0856014i
$838$	407247.	+	407247.i	0.579923	+	0.579923i
$839$		−	286832.i		−	0.407477i	−0.979025	−	0.203739i	$-0.934691\pi$
$839$		−	286832.i		−	0.407477i	0.979025	−	0.203739i	$-0.0653093\pi$
$840$	16089.3	+	76407.8i	0.0228023	+	0.108288i
$841$	−1.31549e6			−1.85993
$842$	227730.	−	227730.i	0.321215	−	0.321215i
$843$	169117.	+	169117.i	0.237975	+	0.237975i
$844$			691278.i			0.970439i
$845$	−368904.	+	565706.i	−0.516654	+	0.792278i
$846$	−15956.5			−0.0222945
$847$	−49623.8	+	49623.8i	−0.0691708	+	0.0691708i
$848$	−157254.	−	157254.i	−0.218680	−	0.218680i
$849$			172845.i			0.239796i
$850$	15959.3	−	7032.99i	0.0220890	−	0.00973424i
$851$	−54249.4			−0.0749094
$852$	−50051.4	+	50051.4i	−0.0689505	+	0.0689505i
$853$	648590.	+	648590.i	0.891399	+	0.891399i	0.994655	−	0.103256i	$-0.0329261\pi$
$853$	648590.	+	648590.i	0.891399	+	0.891399i	−0.103256	+	0.994655i	$0.532926\pi$
$854$			312404.i			0.428352i
$855$	−498586.	−	325134.i	−0.682037	−	0.444765i
$856$	272424.			0.371790
$857$	220314.	−	220314.i	0.299972	−	0.299972i	−0.541031	−	0.841003i	$-0.681966\pi$
$857$	220314.	−	220314.i	0.299972	−	0.299972i	0.841003	+	0.541031i	$0.181966\pi$
$858$	66550.0	+	66550.0i	0.0904011	+	0.0904011i
$859$		−	52637.7i		−	0.0713363i	−0.999364	−	0.0356682i	$-0.988644\pi$
$859$		−	52637.7i		−	0.0713363i	0.999364	−	0.0356682i	$-0.0113559\pi$
$860$	−190227.	+	40056.4i	−0.257203	+	0.0541596i
$861$	207152.			0.279436
$862$	620739.	−	620739.i	0.835400	−	0.835400i
$863$	949999.	+	949999.i	1.27556	+	1.27556i	0.943126	+	0.332435i	$0.107870\pi$
$863$	949999.	+	949999.i	1.27556	+	1.27556i	0.332435	+	0.943126i	$0.392130\pi$
$864$		−	139725.i		−	0.187175i
$865$	−156182.	−	741703.i	−0.208736	−	0.991283i
$866$	544654.			0.726248
$867$	−373485.	+	373485.i	−0.496861	+	0.496861i
$868$	−13550.5	−	13550.5i	−0.0179853	−	0.0179853i
$869$			669563.i			0.886649i
$870$	−347803.	+	533349.i	−0.459510	+	0.704649i
$871$	−84674.6			−0.111614
$872$	−99957.4	+	99957.4i	−0.131456	+	0.131456i
$873$	−36734.0	−	36734.0i	−0.0481992	−	0.0481992i
$874$			181558.i			0.237680i
$875$	198654.	+	276726.i	0.259466	+	0.361439i
$876$	90433.0			0.117847
$877$	−534065.	+	534065.i	−0.694376	+	0.694376i	−0.963192	−	0.268816i	$-0.913368\pi$
$877$	−534065.	+	534065.i	−0.694376	+	0.694376i	0.268816	+	0.963192i	$0.413368\pi$
$878$	−594889.	−	594889.i	−0.771697	−	0.771697i
$879$		−	254867.i		−	0.329865i
$880$	179108.	+	116798.i	0.231286	+	0.150825i
$881$	−1.00777e6			−1.29841			−0.649204	−	0.760614i	$-0.724898\pi$
$881$	−1.00777e6			−1.29841			−0.649204	+	0.760614i	$0.724898\pi$
$882$	−157574.	+	157574.i	−0.202558	+	0.202558i
$883$	522706.	+	522706.i	0.670403	+	0.670403i	0.957809	−	0.287406i	$-0.0927929\pi$
$883$	522706.	+	522706.i	0.670403	+	0.670403i	−0.287406	+	0.957809i	$0.592793\pi$
$884$		−	3103.82i		−	0.00397184i
$885$	593020.	−	124873.i	0.757151	−	0.159435i
$886$	−787774.			−1.00354
$887$	−511630.	+	511630.i	−0.650292	+	0.650292i	−0.953063	−	0.302771i	$-0.902088\pi$
$887$	−511630.	+	511630.i	−0.650292	+	0.650292i	0.302771	+	0.953063i	$0.402088\pi$
$888$	49822.1	+	49822.1i	0.0631824	+	0.0631824i
$889$			250021.i			0.316353i
$890$	175176.	+	831906.i	0.221154	+	1.05025i
$891$	210227.			0.264810
$892$	−431363.	+	431363.i	−0.542142	+	0.542142i
$893$	−56739.8	−	56739.8i	−0.0711517	−	0.0711517i
$894$		−	294300.i		−	0.368227i
$895$	284740.	−	436643.i	0.355470	−	0.545105i
$896$	31571.9			0.0393264
$897$	−19420.2	+	19420.2i	−0.0241362	+	0.0241362i
$898$	−555157.	−	555157.i	−0.688435	−	0.688435i
$899$		−	156268.i		−	0.193353i
$900$	−82494.6	−	187197.i	−0.101845	−	0.231107i
$901$	−34281.8			−0.0422293
$902$	401121.	−	401121.i	0.493017	−	0.493017i
$903$	−94870.8	−	94870.8i	−0.116347	−	0.116347i
$904$			89525.3i			0.109549i
$905$	376765.	+	245693.i	0.460016	+	0.299982i
$906$	−453438.			−0.552410
$907$	784298.	−	784298.i	0.953382	−	0.953382i	−0.0455791	−	0.998961i	$-0.514513\pi$
$907$	784298.	−	784298.i	0.953382	−	0.953382i	0.998961	+	0.0455791i	$0.0145133\pi$
$908$	465487.	+	465487.i	0.564594	+	0.564594i
$909$		−	263255.i		−	0.318602i
$910$	59323.8	−	12491.9i	0.0716384	−	0.0150850i
$911$	−1.57547e6			−1.89834			−0.949171	−	0.314762i	$-0.898075\pi$
$911$	−1.57547e6			−1.89834			−0.949171	+	0.314762i	$0.898075\pi$
$912$	166741.	−	166741.i	0.200471	−	0.200471i
$913$	486285.	+	486285.i	0.583377	+	0.583377i
$914$			819964.i			0.981527i
$915$	165236.	+	784701.i	0.197361	+	0.937264i
$916$	−822230.			−0.979947
$917$	−468836.	+	468836.i	−0.557548	+	0.557548i
$918$	−15230.3	−	15230.3i	−0.0180727	−	0.0180727i
$919$		−	575240.i		−	0.681111i	−0.940224	−	0.340556i	$-0.889385\pi$
$919$		−	575240.i		−	0.681111i	0.940224	−	0.340556i	$-0.110615\pi$
$920$	−34083.4	+	52266.2i	−0.0402687	+	0.0617512i
$921$	−90003.6			−0.106106
$922$	6199.71	−	6199.71i	0.00729306	−	0.00729306i
$923$	38860.4	+	38860.4i	0.0456146	+	0.0456146i
$924$			147576.i			0.172850i
$925$	286549.	+	111247.i	0.334900	+	0.130018i
$926$	−249015.			−0.290405
$927$	−569766.	+	569766.i	−0.663036	+	0.663036i
$928$	182047.	+	182047.i	0.211392	+	0.211392i
$929$			1.41732e6i			1.64225i	0.570752	+	0.821123i	$0.306652\pi$
$929$			1.41732e6i			1.64225i	−0.570752	+	0.821123i	$0.693348\pi$
$930$	−41203.5	−	26869.3i	−0.0476396	−	0.0310663i
$931$	−1.12064e6			−1.29290
$932$	−63831.7	+	63831.7i	−0.0734859	+	0.0734859i
$933$	−384115.	−	384115.i	−0.441263	−	0.441263i
$934$			747603.i			0.856993i
$935$	32254.2	−	6791.83i	0.0368947	−	0.00776897i
$936$	−36406.8			−0.0415557
$937$	−1.10376e6	+	1.10376e6i	−1.25717	+	1.25717i	−0.304735	+	0.952437i	$0.598568\pi$
$937$	−1.10376e6	+	1.10376e6i	−1.25717	+	1.25717i	−0.952437	+	0.304735i	$0.901432\pi$
$938$	−93883.5	−	93883.5i	−0.106705	−	0.106705i
$939$		−	882040.i		−	1.00036i
$940$	−5682.43	−	26985.7i	−0.00643100	−	0.0305407i
$941$	305672.			0.345205			0.172602	−	0.984992i	$-0.444782\pi$
$941$	305672.			0.345205			0.172602	+	0.984992i	$0.444782\pi$
$942$	−344861.	+	344861.i	−0.388636	+	0.388636i
$943$	117053.	+	117053.i	0.131631	+	0.131631i
$944$		−	245037.i		−	0.274971i
$945$	229801.	−	352396.i	0.257329	−	0.394609i
$946$	−367408.			−0.410551
$947$	377220.	−	377220.i	0.420624	−	0.420624i	−0.464794	−	0.885419i	$-0.653872\pi$
$947$	377220.	−	377220.i	0.420624	−	0.420624i	0.885419	+	0.464794i	$0.153872\pi$
$948$	179442.	+	179442.i	0.199667	+	0.199667i
$949$		−	70213.0i		−	0.0779624i
$950$	372312.	−	958998.i	0.412534	−	1.06260i
$951$	860510.			0.951470
$952$	3441.38	−	3441.38i	0.00379716	−	0.00379716i
$953$	−349391.	−	349391.i	−0.384703	−	0.384703i	0.488090	−	0.872793i	$-0.337694\pi$
$953$	−349391.	−	349391.i	−0.384703	−	0.384703i	−0.872793	+	0.488090i	$0.837694\pi$
$954$			402114.i			0.441828i
$955$	−745429.	−	486103.i	−0.817334	−	0.532993i
$956$	217510.			0.237992
$957$	−850937.	+	850937.i	−0.929124	+	0.929124i
$958$	−167956.	−	167956.i	−0.183006	−	0.183006i
$959$		−	81933.6i		−	0.0890892i
$960$	79302.6	−	16698.9i	0.0860488	−	0.0181194i
$961$	−911449.			−0.986928
$962$	38682.4	−	38682.4i	0.0417987	−	0.0417987i
$963$	−348308.	−	348308.i	−0.375587	−	0.375587i
$964$		−	747558.i		−	0.804434i
$965$	68679.9	+	326159.i	0.0737522	+	0.350247i
$966$	−43064.6			−0.0461494
$967$	103657.	−	103657.i	0.110853	−	0.110853i	−0.649505	−	0.760358i	$-0.725024\pi$
$967$	103657.	−	103657.i	0.110853	−	0.110853i	0.760358	+	0.649505i	$0.225024\pi$
$968$	51503.8	+	51503.8i	0.0549653	+	0.0549653i
$969$		−	36349.9i		−	0.0387129i
$970$	49043.0	−	75206.4i	0.0521235	−	0.0799302i
$971$	−119158.			−0.126381			−0.0631907	−	0.998001i	$-0.520128\pi$
$971$	−119158.			−0.126381			−0.0631907	+	0.998001i	$0.520128\pi$
$972$	−297339.	+	297339.i	−0.314717	+	0.314717i
$973$	17277.9	+	17277.9i	0.0182501	+	0.0182501i
$974$		−	958443.i		−	1.01030i
$975$	142403.	−	62754.6i	0.149799	−	0.0660140i
$976$	324240.			0.340382
$977$	−747694.	+	747694.i	−0.783312	+	0.783312i	−0.980388	−	0.197076i	$-0.936855\pi$
$977$	−747694.	+	747694.i	−0.783312	+	0.783312i	0.197076	+	0.980388i	$0.436855\pi$
$978$	−424485.	−	424485.i	−0.443797	−	0.443797i
$979$			1.60676e6i			1.67643i
$980$	−322606.	−	210375.i	−0.335908	−	0.219050i
$981$	255601.			0.265598
$982$	−117624.	+	117624.i	−0.121976	+	0.121976i
$983$	477597.	+	477597.i	0.494259	+	0.494259i	0.909645	−	0.415386i	$-0.136353\pi$
$983$	477597.	+	477597.i	0.494259	+	0.494259i	−0.415386	+	0.909645i	$0.636353\pi$
$984$		−	215000.i		−	0.222048i
$985$	976776.	−	205681.i	1.00675	−	0.211993i
$986$	39686.8			0.0408218
$987$	13458.4	−	13458.4i	0.0138153	−	0.0138153i
$988$	−129459.	−	129459.i	−0.132623	−	0.132623i
$989$		−	107215.i		−	0.109613i
$990$	−79665.9	−	378331.i	−0.0812834	−	0.386013i
$991$	552759.			0.562844			0.281422	−	0.959584i	$-0.409194\pi$
$991$	552759.			0.562844			0.281422	+	0.959584i	$0.409194\pi$
$992$	−14063.9	+	14063.9i	−0.0142917	+	0.0142917i
$993$	−51256.7	−	51256.7i	−0.0519819	−	0.0519819i
$994$			86173.5i			0.0872169i
$995$	−28935.6	+	44372.1i	−0.0292271	+	0.0448192i
$996$	260647.			0.262745
$997$	−187575.	+	187575.i	−0.188705	+	0.188705i	−0.795136	−	0.606431i	$-0.792601\pi$
$997$	−187575.	+	187575.i	−0.188705	+	0.188705i	0.606431	+	0.795136i	$0.292601\pi$
$998$	347351.	+	347351.i	0.348745	+	0.348745i
$999$		−	379624.i		−	0.380385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.a.93.15	yes	44
5.2	odd	4	inner	230.5.f.a.47.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.a.47.15	✓	44	5.2	odd	4	inner
230.5.f.a.93.15	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +(4.47696 + 4.47696i) q^{3} -8.00000i q^{4} +(-20.9409 - 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 + 15.4160i) q^{7} +(16.0000 + 16.0000i) q^{8} -40.9136i q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} +(4.47696 + 4.47696i) q^{3} -8.00000i q^{4} +(-20.9409 - 13.6558i) q^{5} -17.9078 q^{6} +(-15.4160 + 15.4160i) q^{7} +(16.0000 + 16.0000i) q^{8} -40.9136i q^{9} +(69.1933 - 14.5701i) q^{10} +133.641 q^{11} +(35.8157 - 35.8157i) q^{12} +(-27.8077 - 27.8077i) q^{13} -61.6638i q^{14} +(-32.6150 - 154.888i) q^{15} -64.0000 q^{16} +(-6.97609 + 6.97609i) q^{17} +(81.8272 + 81.8272i) q^{18} +581.940i q^{19} +(-109.246 + 167.527i) q^{20} -138.033 q^{21} +(-267.283 + 267.283i) q^{22} +(-77.9968 - 77.9968i) q^{23} +143.263i q^{24} +(252.039 + 571.928i) q^{25} +111.231 q^{26} +(545.803 - 545.803i) q^{27} +(123.328 + 123.328i) q^{28} +1422.24i q^{29} +(375.006 + 244.546i) q^{30} -109.874 q^{31} +(128.000 - 128.000i) q^{32} +(598.307 + 598.307i) q^{33} -27.9044i q^{34} +(533.340 - 112.306i) q^{35} -327.309 q^{36} +(347.767 - 347.767i) q^{37} +(-1163.88 - 1163.88i) q^{38} -248.988i q^{39} +(-116.561 - 553.546i) q^{40} -1500.74 q^{41} +(276.067 - 276.067i) q^{42} +(687.304 + 687.304i) q^{43} -1069.13i q^{44} +(-558.708 + 856.766i) q^{45} +311.987 q^{46} +(-97.5012 + 97.5012i) q^{47} +(-286.526 - 286.526i) q^{48} +1925.70i q^{49} +(-1647.93 - 639.777i) q^{50} -62.4634 q^{51} +(-222.461 + 222.461i) q^{52} +(2457.09 + 2457.09i) q^{53} +2183.21i q^{54} +(-2798.56 - 1824.98i) q^{55} -493.310 q^{56} +(-2605.32 + 2605.32i) q^{57} +(-2844.48 - 2844.48i) q^{58} +3828.70i q^{59} +(-1239.10 + 260.920i) q^{60} -5066.25 q^{61} +(219.748 - 219.748i) q^{62} +(630.722 + 630.722i) q^{63} +512.000i q^{64} +(202.581 + 962.051i) q^{65} -2393.23 q^{66} +(1522.51 - 1522.51i) q^{67} +(55.8087 + 55.8087i) q^{68} -698.377i q^{69} +(-842.068 + 1291.29i) q^{70} -1397.47 q^{71} +(654.618 - 654.618i) q^{72} +(1262.48 + 1262.48i) q^{73} +1391.07i q^{74} +(-1432.13 + 3688.87i) q^{75} +4655.52 q^{76} +(-2060.21 + 2060.21i) q^{77} +(497.975 + 497.975i) q^{78} +5010.15i q^{79} +(1340.21 + 873.970i) q^{80} +1573.07 q^{81} +(3001.47 - 3001.47i) q^{82} +(3638.73 + 3638.73i) q^{83} +1104.27i q^{84} +(241.349 - 50.8213i) q^{85} -2749.21 q^{86} +(-6367.32 + 6367.32i) q^{87} +(2138.26 + 2138.26i) q^{88} +12022.9i q^{89} +(-596.117 - 2830.95i) q^{90} +857.363 q^{91} +(-623.974 + 623.974i) q^{92} +(-491.903 - 491.903i) q^{93} -390.005i q^{94} +(7946.84 - 12186.3i) q^{95} +1146.10 q^{96} +(897.842 - 897.842i) q^{97} +(-3851.39 - 3851.39i) q^{98} -5467.75i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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