LMFDB - Embedded newform 51.5.f.a.38.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,5,Mod(38,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("51.38");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	51.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:	$5.27186811728$
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			38.20
Character	$\chi$	$=$	51.38
Dual form			51.5.f.a.47.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.32469 q^{2} +(8.98676 + 0.488073i) q^{3} +24.0018 q^{4} +(-17.5527 - 17.5527i) q^{5} +(56.8385 + 3.08692i) q^{6} +(2.97942 + 2.97942i) q^{7} +50.6087 q^{8} +(80.5236 + 8.77239i) q^{9} +O(q^{10})$	\(q+6.32469 q^{2} +(8.98676 + 0.488073i) q^{3} +24.0018 q^{4} +(-17.5527 - 17.5527i) q^{5} +(56.8385 + 3.08692i) q^{6} +(2.97942 + 2.97942i) q^{7} +50.6087 q^{8} +(80.5236 + 8.77239i) q^{9} +(-111.015 - 111.015i) q^{10} +(-162.427 + 162.427i) q^{11} +(215.698 + 11.7146i) q^{12} +3.77394 q^{13} +(18.8439 + 18.8439i) q^{14} +(-149.175 - 166.309i) q^{15} -63.9437 q^{16} +(217.840 + 189.912i) q^{17} +(509.287 + 55.4827i) q^{18} -434.838i q^{19} +(-421.295 - 421.295i) q^{20} +(25.3212 + 28.2295i) q^{21} +(-1027.30 + 1027.30i) q^{22} +(40.0377 - 40.0377i) q^{23} +(454.808 + 24.7008i) q^{24} -8.80729i q^{25} +23.8690 q^{26} +(719.364 + 118.137i) q^{27} +(71.5113 + 71.5113i) q^{28} +(-188.760 - 188.760i) q^{29} +(-943.484 - 1051.85i) q^{30} +(562.413 - 562.413i) q^{31} -1214.16 q^{32} +(-1538.96 + 1380.41i) q^{33} +(1377.77 + 1201.14i) q^{34} -104.594i q^{35} +(1932.71 + 210.553i) q^{36} +(243.262 - 243.262i) q^{37} -2750.22i q^{38} +(33.9155 + 1.84196i) q^{39} +(-888.318 - 888.318i) q^{40} +(-1779.90 + 1779.90i) q^{41} +(160.149 + 178.543i) q^{42} +316.313i q^{43} +(-3898.52 + 3898.52i) q^{44} +(-1259.42 - 1567.38i) q^{45} +(253.226 - 253.226i) q^{46} -318.493i q^{47} +(-574.646 - 31.2092i) q^{48} -2383.25i q^{49} -55.7034i q^{50} +(1864.99 + 1813.02i) q^{51} +90.5813 q^{52} +3970.87 q^{53} +(4549.76 + 747.179i) q^{54} +5702.04 q^{55} +(150.785 + 150.785i) q^{56} +(212.233 - 3907.78i) q^{57} +(-1193.85 - 1193.85i) q^{58} +3781.04 q^{59} +(-3580.45 - 3991.70i) q^{60} +(4985.82 + 4985.82i) q^{61} +(3557.09 - 3557.09i) q^{62} +(213.777 + 266.050i) q^{63} -6656.11 q^{64} +(-66.2428 - 66.2428i) q^{65} +(-9733.48 + 8730.68i) q^{66} +3570.56 q^{67} +(5228.55 + 4558.22i) q^{68} +(379.350 - 340.268i) q^{69} -661.523i q^{70} +(-5338.49 - 5338.49i) q^{71} +(4075.19 + 443.959i) q^{72} +(-3116.59 + 3116.59i) q^{73} +(1538.56 - 1538.56i) q^{74} +(4.29860 - 79.1490i) q^{75} -10436.9i q^{76} -967.874 q^{77} +(214.505 + 11.6498i) q^{78} +(-3478.45 - 3478.45i) q^{79} +(1122.38 + 1122.38i) q^{80} +(6407.09 + 1412.77i) q^{81} +(-11257.3 + 11257.3i) q^{82} -4527.74 q^{83} +(607.752 + 677.558i) q^{84} +(-490.217 - 7157.14i) q^{85} +2000.58i q^{86} +(-1604.21 - 1788.47i) q^{87} +(-8220.19 + 8220.19i) q^{88} +9568.91i q^{89} +(-7965.48 - 9913.22i) q^{90} +(11.2442 + 11.2442i) q^{91} +(960.975 - 960.975i) q^{92} +(5328.77 - 4779.77i) q^{93} -2014.37i q^{94} +(-7632.57 + 7632.57i) q^{95} +(-10911.4 - 592.601i) q^{96} +(-9237.30 + 9237.30i) q^{97} -15073.3i q^{98} +(-14504.0 + 11654.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7}+O(q^{10}) $ 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7	$ 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7} + 288 q^{10} - 234 q^{12} + 92 q^{13} + 960 q^{16} - 580 q^{18} - 1856 q^{21} + 120 q^{22} - 10 q^{24} + 378 q^{27} + 1648 q^{28} - 1248 q^{30} + 808 q^{31} + 2520 q^{33} - 5016 q^{34} - 5560 q^{37} + 152 q^{39} - 7020 q^{40} - 2696 q^{45} - 6620 q^{46} - 926 q^{48} + 11810 q^{51} + 5504 q^{52} + 6250 q^{54} + 9740 q^{55} + 16704 q^{57} + 4316 q^{58} + 9304 q^{61} + 27608 q^{63} - 6176 q^{64} + 23912 q^{67} - 3444 q^{69} - 54204 q^{72} + 14216 q^{73} - 5242 q^{75} - 25516 q^{78} + 4052 q^{79} + 6796 q^{81} + 14708 q^{82} - 59208 q^{84} - 32480 q^{85} - 28412 q^{88} - 21312 q^{90} - 38772 q^{91} - 56806 q^{96} - 92448 q^{97} - 18072 q^{99}+O(q^{100}) $ 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7 + 288 * q^10 - 234 * q^12 + 92 * q^13 + 960 * q^16 - 580 * q^18 - 1856 * q^21 + 120 * q^22 - 10 * q^24 + 378 * q^27 + 1648 * q^28 - 1248 * q^30 + 808 * q^31 + 2520 * q^33 - 5016 * q^34 - 5560 * q^37 + 152 * q^39 - 7020 * q^40 - 2696 * q^45 - 6620 * q^46 - 926 * q^48 + 11810 * q^51 + 5504 * q^52 + 6250 * q^54 + 9740 * q^55 + 16704 * q^57 + 4316 * q^58 + 9304 * q^61 + 27608 * q^63 - 6176 * q^64 + 23912 * q^67 - 3444 * q^69 - 54204 * q^72 + 14216 * q^73 - 5242 * q^75 - 25516 * q^78 + 4052 * q^79 + 6796 * q^81 + 14708 * q^82 - 59208 * q^84 - 32480 * q^85 - 28412 * q^88 - 21312 * q^90 - 38772 * q^91 - 56806 * q^96 - 92448 * q^97 - 18072 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	6.32469			1.58117			0.790587	−	0.612350i	$-0.209776\pi$
$2$	6.32469			1.58117			0.790587	+	0.612350i	$0.209776\pi$
$3$	8.98676	+	0.488073i	0.998528	+	0.0542304i
$3$	8.98676	+	0.488073i	0.998528	+	0.0542304i
$4$	24.0018			1.50011
$5$	−17.5527	−	17.5527i	−0.702107	−	0.702107i	0.262756	−	0.964862i	$-0.415369\pi$
$5$	−17.5527	−	17.5527i	−0.702107	−	0.702107i	−0.964862	+	0.262756i	$0.915369\pi$
$6$	56.8385	+	3.08692i	1.57885	+	0.0857477i
$7$	2.97942	+	2.97942i	0.0608045	+	0.0608045i	0.736855	−	0.676051i	$-0.236310\pi$
$7$	2.97942	+	2.97942i	0.0608045	+	0.0608045i	−0.676051	+	0.736855i	$0.736310\pi$
$8$	50.6087			0.790761
$9$	80.5236	+	8.77239i	0.994118	+	0.108301i
$10$	−111.015	−	111.015i	−1.11015	−	1.11015i
$11$	−162.427	+	162.427i	−1.34237	+	1.34237i	−0.448672	+	0.893697i	$0.648103\pi$
$11$	−162.427	+	162.427i	−1.34237	+	1.34237i	−0.893697	+	0.448672i	$0.851897\pi$
$12$	215.698	+	11.7146i	1.49790	+	0.0813515i
$13$	3.77394			0.0223310			0.0111655	−	0.999938i	$-0.496446\pi$
$13$	3.77394			0.0223310			0.0111655	+	0.999938i	$0.496446\pi$
$14$	18.8439	+	18.8439i	0.0961425	+	0.0961425i
$15$	−149.175	−	166.309i	−0.662998	−	0.739149i
$16$	−63.9437			−0.249780
$17$	217.840	+	189.912i	0.753773	+	0.657135i
$17$	217.840	+	189.912i	0.753773	+	0.657135i
$18$	509.287	+	55.4827i	1.57187	+	0.171243i
$19$		−	434.838i		−	1.20454i	−0.798293	−	0.602269i	$-0.794264\pi$
$19$		−	434.838i		−	1.20454i	0.798293	−	0.602269i	$-0.205736\pi$
$20$	−421.295	−	421.295i	−1.05324	−	1.05324i
$21$	25.3212	+	28.2295i	0.0574176	+	0.0640125i
$22$	−1027.30	+	1027.30i	−2.12252	+	2.12252i
$23$	40.0377	−	40.0377i	0.0756856	−	0.0756856i	−0.668251	−	0.743936i	$-0.732957\pi$
$23$	40.0377	−	40.0377i	0.0756856	−	0.0756856i	0.743936	+	0.668251i	$0.232957\pi$
$24$	454.808	+	24.7008i	0.789597	+	0.0428833i
$25$		−	8.80729i		−	0.0140917i
$26$	23.8690			0.0353092
$27$	719.364	+	118.137i	0.986782	+	0.162053i
$28$	71.5113	+	71.5113i	0.0912134	+	0.0912134i
$29$	−188.760	−	188.760i	−0.224447	−	0.224447i	0.585921	−	0.810368i	$-0.300733\pi$
$29$	−188.760	−	188.760i	−0.224447	−	0.224447i	−0.810368	+	0.585921i	$0.800733\pi$
$30$	−943.484	−	1051.85i	−1.04832	−	1.16872i
$31$	562.413	−	562.413i	0.585238	−	0.585238i	−0.351100	−	0.936338i	$-0.614192\pi$
$31$	562.413	−	562.413i	0.585238	−	0.585238i	0.936338	+	0.351100i	$0.114192\pi$
$32$	−1214.16			−1.18571
$33$	−1538.96	+	1380.41i	−1.41319	+	1.26760i
$34$	1377.77	+	1201.14i	1.19185	+	1.03904i
$35$		−	104.594i		−	0.0853825i
$36$	1932.71	+	210.553i	1.49129	+	0.162464i
$37$	243.262	−	243.262i	0.177693	−	0.177693i	−0.612656	−	0.790350i	$-0.709899\pi$
$37$	243.262	−	243.262i	0.177693	−	0.177693i	0.790350	+	0.612656i	$0.209899\pi$
$38$		−	2750.22i		−	1.90458i
$39$	33.9155	+	1.84196i	0.0222982	+	0.00121102i
$40$	−888.318	−	888.318i	−0.555199	−	0.555199i
$41$	−1779.90	+	1779.90i	−1.05884	+	1.05884i	−0.0606792	+	0.998157i	$0.519327\pi$
$41$	−1779.90	+	1779.90i	−1.05884	+	1.05884i	−0.998157	+	0.0606792i	$0.980673\pi$
$42$	160.149	+	178.543i	0.0907872	+	0.101215i
$43$			316.313i			0.171072i	0.996335	+	0.0855362i	$0.0272603\pi$
$43$			316.313i			0.171072i	−0.996335	+	0.0855362i	$0.972740\pi$
$44$	−3898.52	+	3898.52i	−2.01370	+	2.01370i
$45$	−1259.42	−	1567.38i	−0.621938	−	0.774016i
$46$	253.226	−	253.226i	0.119672	−	0.119672i
$47$		−	318.493i		−	0.144180i	−0.997398	−	0.0720898i	$-0.977033\pi$
$47$		−	318.493i		−	0.144180i	0.997398	−	0.0720898i	$-0.0229668\pi$
$48$	−574.646	−	31.2092i	−0.249413	−	0.0135457i
$49$		−	2383.25i		−	0.992606i
$50$		−	55.7034i		−	0.0222814i
$51$	1864.99	+	1813.02i	0.717027	+	0.697045i
$52$	90.5813			0.0334990
$53$	3970.87			1.41362			0.706812	−	0.707402i	$-0.250133\pi$
$53$	3970.87			1.41362			0.706812	+	0.707402i	$0.250133\pi$
$54$	4549.76	+	747.179i	1.56027	+	0.256234i
$55$	5702.04			1.88497
$56$	150.785	+	150.785i	0.0480818	+	0.0480818i
$57$	212.233	−	3907.78i	0.0653226	−	1.20277i
$58$	−1193.85	−	1193.85i	−0.354890	−	0.354890i
$59$	3781.04			1.08619			0.543097	−	0.839670i	$-0.317252\pi$
$59$	3781.04			1.08619			0.543097	+	0.839670i	$0.317252\pi$
$60$	−3580.45	−	3991.70i	−0.994570	−	1.10881i
$61$	4985.82	+	4985.82i	1.33992	+	1.33992i	0.896136	+	0.443779i	$0.146362\pi$
$61$	4985.82	+	4985.82i	1.33992	+	1.33992i	0.443779	+	0.896136i	$0.353638\pi$
$62$	3557.09	−	3557.09i	0.925362	−	0.925362i
$63$	213.777	+	266.050i	0.0538617	+	0.0670321i
$64$	−6656.11			−1.62503
$65$	−66.2428	−	66.2428i	−0.0156788	−	0.0156788i
$66$	−9733.48	+	8730.68i	−2.23450	+	2.00429i
$67$	3570.56			0.795402			0.397701	−	0.917515i	$-0.369808\pi$
$67$	3570.56			0.795402			0.397701	+	0.917515i	$0.369808\pi$
$68$	5228.55	+	4558.22i	1.13074	+	0.985775i
$69$	379.350	−	340.268i	0.0796787	−	0.0714698i
$70$		−	661.523i		−	0.135005i
$71$	−5338.49	−	5338.49i	−1.05901	−	1.05901i	−0.998146	−	0.0608690i	$-0.980613\pi$
$71$	−5338.49	−	5338.49i	−1.05901	−	1.05901i	−0.0608690	−	0.998146i	$-0.519387\pi$
$72$	4075.19	+	443.959i	0.786109	+	0.0856403i
$73$	−3116.59	+	3116.59i	−0.584836	+	0.584836i	−0.936228	−	0.351392i	$-0.885708\pi$
$73$	−3116.59	+	3116.59i	−0.584836	+	0.584836i	0.351392	+	0.936228i	$0.385708\pi$
$74$	1538.56	−	1538.56i	0.280964	−	0.280964i
$75$	4.29860	−	79.1490i	0.000764196	−	0.0140709i
$76$		−	10436.9i		−	1.80694i
$77$	−967.874			−0.163244
$78$	214.505	+	11.6498i	0.0352573	+	0.00191483i
$79$	−3478.45	−	3478.45i	−0.557354	−	0.557354i	0.371199	−	0.928553i	$-0.378947\pi$
$79$	−3478.45	−	3478.45i	−0.557354	−	0.557354i	−0.928553	+	0.371199i	$0.878947\pi$
$80$	1122.38	+	1122.38i	0.175372	+	0.175372i
$81$	6407.09	+	1412.77i	0.976542	+	0.215328i
$82$	−11257.3	+	11257.3i	−1.67420	+	1.67420i
$83$	−4527.74			−0.657242			−0.328621	−	0.944462i	$-0.606584\pi$
$83$	−4527.74			−0.657242			−0.328621	+	0.944462i	$0.606584\pi$
$84$	607.752	+	677.558i	0.0861327	+	0.0960258i
$85$	−490.217	−	7157.14i	−0.0678501	−	0.990608i
$86$			2000.58i			0.270495i
$87$	−1604.21	−	1788.47i	−0.211945	−	0.236289i
$88$	−8220.19	+	8220.19i	−1.06149	+	1.06149i
$89$			9568.91i			1.20804i	0.796968	+	0.604021i	$0.206436\pi$
$89$			9568.91i			1.20804i	−0.796968	+	0.604021i	$0.793564\pi$
$90$	−7965.48	−	9913.22i	−0.983392	−	1.22385i
$91$	11.2442	+	11.2442i	0.00135783	+	0.00135783i
$92$	960.975	−	960.975i	0.113537	−	0.113537i
$93$	5328.77	−	4779.77i	0.616114	−	0.552639i
$94$		−	2014.37i		−	0.227973i
$95$	−7632.57	+	7632.57i	−0.845714	+	0.845714i
$96$	−10911.4	−	592.601i	−1.18396	−	0.0643013i
$97$	−9237.30	+	9237.30i	−0.981752	+	0.981752i	−0.999836	−	0.0180849i	$-0.994243\pi$
$97$	−9237.30	+	9237.30i	−0.981752	+	0.981752i	0.0180849	+	0.999836i	$0.494243\pi$
$98$		−	15073.3i		−	1.56948i
$99$	−14504.0	+	11654.3i	−1.47985	+	1.18909i
$100$		−	211.390i		−	0.0211390i
$101$		−	17536.8i		−	1.71913i	−0.511028	−	0.859564i	$-0.670735\pi$
$101$		−	17536.8i		−	1.71913i	0.511028	−	0.859564i	$-0.329265\pi$
$102$	11795.5	+	11466.8i	1.13374	+	1.10215i
$103$	−7922.23			−0.746746			−0.373373	−	0.927681i	$-0.621799\pi$
$103$	−7922.23			−0.746746			−0.373373	+	0.927681i	$0.621799\pi$
$104$	190.994			0.0176585
$105$	51.0494	−	939.957i	0.00463033	−	0.0852569i
$106$	25114.5			2.23518
$107$	1947.90	+	1947.90i	0.170137	+	0.170137i	0.787040	−	0.616903i	$-0.211613\pi$
$107$	1947.90	+	1947.90i	0.170137	+	0.170137i	−0.616903	+	0.787040i	$0.711613\pi$
$108$	17266.0	+	2835.49i	1.48028	+	0.243098i
$109$	9239.87	+	9239.87i	0.777701	+	0.777701i	0.979439	−	0.201738i	$-0.0646591\pi$
$109$	9239.87	+	9239.87i	0.777701	+	0.777701i	−0.201738	+	0.979439i	$0.564659\pi$
$110$	36063.7			2.98047
$111$	2304.87	−	2067.41i	0.187068	−	0.167796i
$112$	−190.515	−	190.515i	−0.0151878	−	0.0151878i
$113$	99.7304	−	99.7304i	0.00781036	−	0.00781036i	−0.703191	−	0.711001i	$-0.748242\pi$
$113$	99.7304	−	99.7304i	0.00781036	−	0.00781036i	0.711001	+	0.703191i	$0.248242\pi$
$114$	1342.31	−	24715.5i	0.103286	−	1.90178i
$115$	−1405.54			−0.106279
$116$	−4530.57	−	4530.57i	−0.336695	−	0.336695i
$117$	303.891	+	33.1065i	0.0221997	+	0.00241848i
$118$	23913.9			1.71746
$119$	83.2102	+	1214.87i	0.00587601	+	0.0857896i
$120$	−7549.53	−	8416.66i	−0.524273	−	0.584490i
$121$		−	38123.8i		−	2.60391i
$122$	31533.8	+	31533.8i	2.11864	+	2.11864i
$123$	−16864.3	+	15126.8i	−1.11470	+	0.999857i
$124$	13498.9	−	13498.9i	0.877921	−	0.877921i
$125$	−11125.0	+	11125.0i	−0.712001	+	0.712001i
$126$	1352.07	+	1682.69i	0.0851646	+	0.105989i
$127$			17086.4i			1.05936i	0.848198	+	0.529680i	$0.177688\pi$
$127$			17086.4i			1.05936i	−0.848198	+	0.529680i	$0.822312\pi$
$128$	−22671.3			−1.38374
$129$	−154.384	+	2842.63i	−0.00927732	+	0.170821i
$130$	−418.966	−	418.966i	−0.0247909	−	0.0247909i
$131$	−18337.2	−	18337.2i	−1.06854	−	1.06854i	−0.997472	−	0.0710670i	$-0.977360\pi$
$131$	−18337.2	−	18337.2i	−1.06854	−	1.06854i	−0.0710670	−	0.997472i	$-0.522640\pi$
$132$	−36937.8	+	33132.3i	−2.11994	+	1.90153i
$133$	1295.57	−	1295.57i	0.0732413	−	0.0732413i
$134$	22582.7			1.25767
$135$	−10553.1	−	14700.4i	−0.579048	−	0.806605i
$136$	11024.6	+	9611.20i	0.596054	+	0.519637i
$137$			12756.7i			0.679667i	0.940486	+	0.339833i	$0.110371\pi$
$137$			12756.7i			0.679667i	−0.940486	+	0.339833i	$0.889629\pi$
$138$	2399.27	−	2152.09i	0.125986	−	0.113006i
$139$	−4373.36	+	4373.36i	−0.226353	+	0.226353i	−0.811167	−	0.584814i	$-0.801167\pi$
$139$	−4373.36	+	4373.36i	−0.226353	+	0.226353i	0.584814	+	0.811167i	$0.301167\pi$
$140$		−	2510.43i		−	0.128083i
$141$	155.448	−	2862.22i	0.00781892	−	0.143967i
$142$	−33764.3	−	33764.3i	−1.67449	−	1.67449i
$143$	−612.989	+	612.989i	−0.0299765	+	0.0299765i
$144$	−5148.98	−	560.939i	−0.248311	−	0.0270515i
$145$			6626.48i			0.315172i
$146$	−19711.5	+	19711.5i	−0.924727	+	0.924727i
$147$	1163.20	−	21417.7i	0.0538294	−	0.991145i
$148$	5838.72	−	5838.72i	0.266560	−	0.266560i
$149$		−	12690.3i		−	0.571610i	−0.958288	−	0.285805i	$-0.907739\pi$
$149$		−	12690.3i		−	0.571610i	0.958288	−	0.285805i	$-0.0922609\pi$
$150$	27.1874	−	500.593i	0.00120833	−	0.0222486i
$151$			21735.5i			0.953269i	0.879102	+	0.476635i	$0.158144\pi$
$151$			21735.5i			0.953269i	−0.879102	+	0.476635i	$0.841856\pi$
$152$		−	22006.6i		−	0.952501i
$153$	15875.3	+	17203.4i	0.678171	+	0.734904i
$154$	−6121.51			−0.258117
$155$	−19743.7			−0.821799
$156$	814.032	+	44.2103i	0.0334497	+	0.00181666i
$157$	27851.4			1.12992			0.564961	−	0.825118i	$-0.308891\pi$
$157$	27851.4			1.12992			0.564961	+	0.825118i	$0.308891\pi$
$158$	−22000.1	−	22000.1i	−0.881273	−	0.881273i
$159$	35685.2	+	1938.08i	1.41154	+	0.0766614i
$160$	21311.8	+	21311.8i	0.832493	+	0.832493i
$161$	238.578			0.00920405
$162$	40522.9	+	8935.33i	1.54408	+	0.340471i
$163$	1616.76	+	1616.76i	0.0608514	+	0.0608514i	0.736878	−	0.676026i	$-0.236299\pi$
$163$	1616.76	+	1616.76i	0.0608514	+	0.0608514i	−0.676026	+	0.736878i	$0.736299\pi$
$164$	−42720.8	+	42720.8i	−1.58837	+	1.58837i
$165$	51242.9	+	2783.02i	1.88220	+	0.102223i
$166$	−28636.6			−1.03921
$167$	−14998.8	−	14998.8i	−0.537804	−	0.537804i	0.385080	−	0.922883i	$-0.374174\pi$
$167$	−14998.8	−	14998.8i	−0.537804	−	0.537804i	−0.922883	+	0.385080i	$0.874174\pi$
$168$	1281.47	+	1428.66i	0.0454036	+	0.0506186i
$169$	−28546.8			−0.999501
$170$	−3100.47	−	45266.8i	−0.107283	−	1.56632i
$171$	3814.57	−	35014.7i	0.130453	−	1.19745i
$172$			7592.06i			0.256627i
$173$	24261.4	+	24261.4i	0.810632	+	0.810632i	0.984729	−	0.174097i	$-0.0557006\pi$
$173$	24261.4	+	24261.4i	0.810632	+	0.810632i	−0.174097	+	0.984729i	$0.555701\pi$
$174$	−10146.1	−	11311.5i	−0.335122	−	0.373613i
$175$	26.2406	−	26.2406i	0.000856837	−	0.000856837i
$176$	10386.2	−	10386.2i	0.335297	−	0.335297i
$177$	33979.3	+	1845.42i	1.08459	+	0.0589047i
$178$			60520.4i			1.91013i
$179$	−5992.98			−0.187041			−0.0935205	−	0.995617i	$-0.529812\pi$
$179$	−5992.98			−0.187041			−0.0935205	+	0.995617i	$0.529812\pi$
$180$	−30228.4	−	37619.9i	−0.932976	−	1.16111i
$181$	−14341.6	−	14341.6i	−0.437765	−	0.437765i	0.453494	−	0.891259i	$-0.350177\pi$
$181$	−14341.6	−	14341.6i	−0.437765	−	0.437765i	−0.891259	+	0.453494i	$0.850177\pi$
$182$	71.1159	+	71.1159i	0.00214696	+	0.00214696i
$183$	42372.9	+	47239.8i	1.26528	+	1.41061i
$184$	2026.25	−	2026.25i	0.0598492	−	0.0598492i
$185$	−8539.81			−0.249520
$186$	33702.8	−	30230.6i	0.974183	−	0.873818i
$187$	−66229.8	+	4536.30i	−1.89396	+	0.129724i
$188$		−	7644.39i		−	0.216285i
$189$	1791.31	+	2495.27i	0.0501472	+	0.0698544i
$190$	−48273.7	+	48273.7i	−1.33722	+	1.33722i
$191$		−	32031.6i		−	0.878036i	−0.898478	−	0.439018i	$-0.855326\pi$
$191$		−	32031.6i		−	0.878036i	0.898478	−	0.439018i	$-0.144674\pi$
$192$	−59816.9	−	3248.67i	−1.62264	−	0.0881259i
$193$	1422.30	+	1422.30i	0.0381836	+	0.0381836i	0.725941	−	0.687757i	$-0.241405\pi$
$193$	1422.30	+	1422.30i	0.0381836	+	0.0381836i	−0.687757	+	0.725941i	$0.741405\pi$
$194$	−58423.1	+	58423.1i	−1.55232	+	1.55232i
$195$	−562.977	−	627.639i	−0.0148054	−	0.0165060i
$196$		−	57202.1i		−	1.48902i
$197$	25724.4	−	25724.4i	0.662847	−	0.662847i	−0.293203	−	0.956050i	$-0.594721\pi$
$197$	25724.4	−	25724.4i	0.662847	−	0.662847i	0.956050	+	0.293203i	$0.0947213\pi$
$198$	−91733.6	+	73709.9i	−2.33990	+	1.88016i
$199$	5832.45	−	5832.45i	0.147280	−	0.147280i	−0.629622	−	0.776902i	$-0.716790\pi$
$199$	5832.45	−	5832.45i	0.147280	−	0.147280i	0.776902	+	0.629622i	$0.216790\pi$
$200$		−	445.725i		−	0.0111431i
$201$	32087.8	+	1742.70i	0.794232	+	0.0431350i
$202$		−	110915.i		−	2.71824i
$203$		−	1124.79i		−	0.0272948i
$204$	44763.0	+	43515.6i	1.07562	+	1.04564i
$205$	62484.2			1.48683
$206$	−50105.7			−1.18074
$207$	3575.20	−	2872.75i	0.0834373	−	0.0670436i
$208$	−241.320			−0.00557785
$209$	70629.3	+	70629.3i	1.61693	+	1.61693i
$210$	322.872	−	5944.94i	0.00732135	−	0.134806i
$211$	−50997.6	−	50997.6i	−1.14547	−	1.14547i	−0.987433	−	0.158040i	$-0.949482\pi$
$211$	−50997.6	−	50997.6i	−1.14547	−	1.14547i	−0.158040	−	0.987433i	$-0.550518\pi$
$212$	95307.9			2.12059
$213$	−45370.2	−	50581.3i	−1.00003	−	1.11489i
$214$	12319.9	+	12319.9i	0.269016	+	0.269016i
$215$	5552.13	−	5552.13i	0.120111	−	0.120111i
$216$	36406.1	+	5978.75i	0.780308	+	0.128145i
$217$	3351.33			0.0711702
$218$	58439.3	+	58439.3i	1.22968	+	1.22968i
$219$	−29529.2	+	26486.9i	−0.615691	+	0.552259i
$220$	136859.			2.82767
$221$	822.117	+	716.718i	0.0168325	+	0.0146745i
$222$	14577.6	−	13075.7i	0.295787	−	0.265314i
$223$			50397.0i			1.01343i	0.862113	+	0.506716i	$0.169141\pi$
$223$			50397.0i			1.01343i	−0.862113	+	0.506716i	$0.830859\pi$
$224$	−3617.50	−	3617.50i	−0.0720963	−	0.0720963i
$225$	77.2610	−	709.194i	0.00152614	−	0.0140088i
$226$	630.764	−	630.764i	0.0123495	−	0.0123495i
$227$	−42421.5	+	42421.5i	−0.823255	+	0.823255i	−0.986573	−	0.163319i	$-0.947780\pi$
$227$	−42421.5	+	42421.5i	−0.823255	+	0.823255i	0.163319	+	0.986573i	$0.447780\pi$
$228$	5093.96	−	93793.7i	0.0979910	−	1.80428i
$229$			2048.91i			0.0390708i	0.999809	+	0.0195354i	$0.00621870\pi$
$229$			2048.91i			0.0390708i	−0.999809	+	0.0195354i	$0.993781\pi$
$230$	−8889.59			−0.168045
$231$	−8698.05	−	472.394i	−0.163004	−	0.00885279i
$232$	−9552.89	−	9552.89i	−0.177484	−	0.177484i
$233$	−48218.0	−	48218.0i	−0.888172	−	0.888172i	0.106175	−	0.994347i	$-0.466139\pi$
$233$	−48218.0	−	48218.0i	−0.888172	−	0.888172i	−0.994347	+	0.106175i	$0.966139\pi$
$234$	1922.02	+	209.389i	0.0351016	+	0.00382403i
$235$	−5590.40	+	5590.40i	−0.101229	+	0.101229i
$236$	90751.6			1.62941
$237$	−29562.2	−	32957.7i	−0.526308	−	0.586759i
$238$	526.279	+	7683.66i	0.00929100	+	0.135648i
$239$			13742.8i			0.240591i	0.992738	+	0.120295i	$0.0383842\pi$
$239$			13742.8i			0.240591i	−0.992738	+	0.120295i	$0.961616\pi$
$240$	9538.78	+	10634.4i	0.165604	+	0.184625i
$241$	29410.5	−	29410.5i	0.506371	−	0.506371i	−0.407040	−	0.913410i	$-0.633439\pi$
$241$	29410.5	−	29410.5i	0.506371	−	0.506371i	0.913410	+	0.407040i	$0.133439\pi$
$242$		−	241121.i		−	4.11723i
$243$	56889.4	+	15823.3i	0.963427	+	0.267970i
$244$	119669.	+	119669.i	2.01002	+	2.01002i
$245$	−41832.3	+	41832.3i	−0.696915	+	0.696915i
$246$	−106661.	+	95672.6i	−1.76253	+	1.58095i
$247$		−	1641.06i		−	0.0268986i
$248$	28463.0	−	28463.0i	0.462783	−	0.462783i
$249$	−40689.7	−	2209.87i	−0.656275	−	0.0356425i
$250$	−70362.3	+	70362.3i	−1.12580	+	1.12580i
$251$		−	5886.02i		−	0.0934273i	−0.998908	−	0.0467137i	$-0.985125\pi$
$251$		−	5886.02i		−	0.0934273i	0.998908	−	0.0467137i	$-0.0148748\pi$
$252$	5131.02	+	6385.67i	0.0807984	+	0.100555i
$253$			13006.4i			0.203196i
$254$			108066.i			1.67503i
$255$	−912.246	−	64558.8i	−0.0140292	−	0.992830i
$256$	−36891.0			−0.562912
$257$	68531.9			1.03759			0.518796	−	0.854898i	$-0.326380\pi$
$257$	68531.9			1.03759			0.518796	+	0.854898i	$0.326380\pi$
$258$	−976.431	+	17978.7i	−0.0146690	+	0.270097i
$259$	1449.56			0.0216091
$260$	−1589.94	−	1589.94i	−0.0235199	−	0.0235199i
$261$	−13543.7	−	16855.5i	−0.198819	−	0.247435i
$262$	−115977.	−	115977.i	−1.68954	−	1.68954i
$263$	−45582.8			−0.659006			−0.329503	−	0.944154i	$-0.606881\pi$
$263$	−45582.8			−0.659006			−0.329503	+	0.944154i	$0.606881\pi$
$264$	−77884.9	+	69860.8i	−1.11750	+	1.00236i
$265$	−69699.4	−	69699.4i	−0.992515	−	0.992515i
$266$	8194.06	−	8194.06i	0.115807	−	0.115807i
$267$	−4670.33	+	85993.4i	−0.0655126	+	1.20627i
$268$	85699.7			1.19319
$269$	68791.7	+	68791.7i	0.950674	+	0.950674i	0.998839	−	0.0481655i	$-0.0153375\pi$
$269$	68791.7	+	68791.7i	0.950674	+	0.950674i	−0.0481655	+	0.998839i	$0.515338\pi$
$270$	−66745.4	−	92975.4i	−0.915575	−	1.27538i
$271$	76192.9			1.03747			0.518735	−	0.854935i	$-0.326403\pi$
$271$	76192.9			1.03747			0.518735	+	0.854935i	$0.326403\pi$
$272$	−13929.5	−	12143.7i	−0.188277	−	0.164139i
$273$	95.5606	+	106.537i	0.00128219	+	0.00142946i
$274$			80682.0i			1.07467i
$275$	1430.54	+	1430.54i	0.0189162	+	0.0189162i
$276$	9105.07	−	8167.02i	0.119527	−	0.107212i
$277$	81049.8	−	81049.8i	1.05631	−	1.05631i	0.0579954	−	0.998317i	$-0.481529\pi$
$277$	81049.8	−	81049.8i	1.05631	−	1.05631i	0.998317	−	0.0579954i	$-0.0184709\pi$
$278$	−27660.2	+	27660.2i	−0.357903	+	0.357903i
$279$	50221.2	−	40353.8i	0.645177	−	0.518413i
$280$		−	5293.34i		−	0.0675171i
$281$	−18775.4			−0.237781			−0.118890	−	0.992907i	$-0.537934\pi$
$281$	−18775.4			−0.237781			−0.118890	+	0.992907i	$0.537934\pi$
$282$	983.160	−	18102.6i	0.0123631	−	0.227637i
$283$	43416.8	+	43416.8i	0.542106	+	0.542106i	0.924146	−	0.382040i	$-0.124778\pi$
$283$	43416.8	+	43416.8i	0.542106	+	0.542106i	−0.382040	+	0.924146i	$0.624778\pi$
$284$	−128133.	−	128133.i	−1.58864	−	1.58864i
$285$	−72317.3	+	64866.8i	−0.890333	+	0.798606i
$286$	−3876.97	+	3876.97i	−0.0473980	+	0.0473980i
$287$	−10606.2			−0.128764
$288$	−97768.8	−	10651.1i	−1.17873	−	0.128413i
$289$	11387.8	+	82741.0i	0.136347	+	0.990661i
$290$			41910.5i			0.498341i
$291$	−87521.8	+	78504.9i	−1.03355	+	0.927066i
$292$	−74803.6	+	74803.6i	−0.877318	+	0.877318i
$293$			32671.6i			0.380571i	0.981729	+	0.190285i	$0.0609413\pi$
$293$			32671.6i			0.380571i	−0.981729	+	0.190285i	$0.939059\pi$
$294$	7356.88	−	135460.i	0.0851136	−	1.56717i
$295$	−66367.3	−	66367.3i	−0.762624	−	0.762624i
$296$	12311.2	−	12311.2i	0.140513	−	0.140513i
$297$	−136032.	+	97655.3i	−1.54216	+	1.10709i
$298$		−	80262.3i		−	0.903814i
$299$	151.100	−	151.100i	0.00169014	−	0.00169014i
$300$	103.174	−	1899.71i	0.00114638	−	0.0211079i
$301$	−942.429	+	942.429i	−0.0104020	+	0.0104020i
$302$			137470.i			1.50728i
$303$	8559.26	−	157599.i	0.0932290	−	1.71660i
$304$			27805.2i			0.300870i
$305$		−	175029.i		−	1.88153i
$306$	100406.	+	108806.i	1.07231	+	1.16201i
$307$	−25396.6			−0.269462			−0.134731	−	0.990882i	$-0.543017\pi$
$307$	−25396.6			−0.269462			−0.134731	+	0.990882i	$0.543017\pi$
$308$	−23230.7			−0.244884
$309$	−71195.1	−	3866.63i	−0.745647	−	0.0404963i
$310$	−124873.			−1.29941
$311$	60618.1	+	60618.1i	0.626732	+	0.626732i	0.947244	−	0.320512i	$-0.103855\pi$
$311$	60618.1	+	60618.1i	0.626732	+	0.626732i	−0.320512	+	0.947244i	$0.603855\pi$
$312$	1716.42	+	93.2193i	0.0176325	+	0.000957627i
$313$	42695.6	+	42695.6i	0.435808	+	0.435808i	0.890598	−	0.454791i	$-0.150286\pi$
$313$	42695.6	+	42695.6i	0.435808	+	0.435808i	−0.454791	+	0.890598i	$0.650286\pi$
$314$	176152.			1.78660
$315$	917.536	−	8422.25i	0.00924703	−	0.0848803i
$316$	−83488.8	−	83488.8i	−0.836092	−	0.836092i
$317$	109524.	−	109524.i	1.08991	−	1.08991i	0.0943713	−	0.995537i	$-0.469916\pi$
$317$	109524.	−	109524.i	1.08991	−	1.08991i	0.995537	−	0.0943713i	$-0.0300841\pi$
$318$	225698.	+	12257.7i	2.23190	+	0.121215i
$319$	61319.3			0.602581
$320$	116833.	+	116833.i	1.14094	+	1.14094i
$321$	16554.6	+	18456.0i	0.160660	+	0.179113i
$322$	1508.93			0.0145532
$323$	82581.0	−	94725.3i	0.791544	−	0.907948i
$324$	153781.	+	33908.9i	1.46492	+	0.323016i
$325$		−	33.2382i		−	0.000314681i
$326$	10225.5	+	10225.5i	0.0962167	+	0.0962167i
$327$	78526.7	+	87546.2i	0.734382	+	0.818732i
$328$	−90078.6	+	90078.6i	−0.837286	+	0.837286i
$329$	948.924	−	948.924i	0.00876677	−	0.00876677i
$330$	324095.	+	17601.7i	2.97608	+	0.161632i
$331$			57814.5i			0.527693i	0.964565	+	0.263846i	$0.0849912\pi$
$331$			57814.5i			0.527693i	−0.964565	+	0.263846i	$0.915009\pi$
$332$	−108674.			−0.985935
$333$	21722.3	−	17454.4i	0.195893	−	0.157404i
$334$	−94862.9	−	94862.9i	−0.850361	−	0.850361i
$335$	−62672.9	−	62672.9i	−0.558457	−	0.558457i
$336$	−1619.13	−	1805.10i	−0.0143418	−	0.0159890i
$337$	21125.3	−	21125.3i	0.186013	−	0.186013i	−0.607957	−	0.793970i	$-0.708011\pi$
$337$	21125.3	−	21125.3i	0.186013	−	0.186013i	0.793970	+	0.607957i	$0.208011\pi$
$338$	−180550.			−1.58039
$339$	944.929	−	847.577i	0.00822242	−	0.00737530i
$340$	−11766.1	−	171784.i	−0.101783	−	1.48602i
$341$			182702.i			1.57121i
$342$	24126.0	−	221457.i	0.206269	−	1.89338i
$343$	14254.3	−	14254.3i	0.121159	−	0.121159i
$344$			16008.2i			0.135277i
$345$	−12631.2	−	686.005i	−0.106122	−	0.00576354i
$346$	153446.	+	153446.i	1.28175	+	1.28175i
$347$	−1785.11	+	1785.11i	−0.0148254	+	0.0148254i	−0.714481	−	0.699655i	$-0.753337\pi$
$347$	−1785.11	+	1785.11i	−0.0148254	+	0.0148254i	0.699655	+	0.714481i	$0.253337\pi$
$348$	−38503.9	−	42926.4i	−0.317941	−	0.354459i
$349$			56038.4i			0.460081i	0.973181	+	0.230041i	$0.0738859\pi$
$349$			56038.4i			0.460081i	−0.973181	+	0.230041i	$0.926114\pi$
$350$	165.964	−	165.964i	0.00135481	−	0.00135481i
$351$	2714.84	+	445.842i	0.0220359	+	0.00361882i
$352$	197212.	−	197212.i	1.59165	−	1.59165i
$353$		−	161922.i		−	1.29944i	−0.760174	−	0.649719i	$-0.774886\pi$
$353$		−	161922.i		−	1.29944i	0.760174	−	0.649719i	$-0.225114\pi$
$354$	214908.	+	11671.7i	1.71493	+	0.0931385i
$355$			187410.i			1.48708i
$356$			229671.i			1.81220i
$357$	154.846	+	10958.3i	0.00121497	+	0.0859820i
$358$	−37903.8			−0.295744
$359$	−196594.			−1.52539			−0.762694	−	0.646759i	$-0.776124\pi$
$359$	−196594.			−1.52539			−0.762694	+	0.646759i	$0.776124\pi$
$360$	−63737.8	−	79323.2i	−0.491804	−	0.612062i
$361$	−58763.2			−0.450911
$362$	−90706.4	−	90706.4i	−0.692183	−	0.692183i
$363$	18607.2	−	342609.i	0.141211	−	2.60007i
$364$	269.880	+	269.880i	0.00203689	+	0.00203689i
$365$	109409.			0.821235
$366$	267996.	+	298777.i	2.00063	+	2.23042i
$367$	44146.9	+	44146.9i	0.327769	+	0.327769i	0.851738	−	0.523968i	$-0.175549\pi$
$367$	44146.9	+	44146.9i	0.327769	+	0.327769i	−0.523968	+	0.851738i	$0.675549\pi$
$368$	−2560.16	+	2560.16i	−0.0189048	+	0.0189048i
$369$	−158938.	+	127710.i	−1.16728	+	0.937935i
$370$	−54011.7			−0.394534
$371$	11830.9	+	11830.9i	0.0859547	+	0.0859547i
$372$	127900.	−	114723.i	0.924239	−	0.829019i
$373$	−176930.			−1.27170			−0.635848	−	0.771814i	$-0.719350\pi$
$373$	−176930.			−1.27170			−0.635848	+	0.771814i	$0.719350\pi$
$374$	−418883.	+	28690.7i	−2.99468	+	0.205115i
$375$	−105408.	+	94548.0i	−0.749565	+	0.672341i
$376$		−	16118.5i		−	0.114012i
$377$	−712.370	−	712.370i	−0.00501213	−	0.00501213i
$378$	11329.5	+	15781.8i	0.0792915	+	0.110452i
$379$	132908.	−	132908.i	0.925277	−	0.925277i	−0.0721190	−	0.997396i	$-0.522976\pi$
$379$	132908.	−	132908.i	0.925277	−	0.925277i	0.997396	+	0.0721190i	$0.0229761\pi$
$380$	−183195.	+	183195.i	−1.26866	+	1.26866i
$381$	−8339.42	+	153551.i	−0.0574495	+	1.05780i
$382$		−	202590.i		−	1.38833i
$383$	41992.7			0.286270			0.143135	−	0.989703i	$-0.454282\pi$
$383$	41992.7			0.286270			0.143135	+	0.989703i	$0.454282\pi$
$384$	−203741.	−	11065.2i	−1.38171	−	0.0750410i
$385$	16988.8	+	16988.8i	0.114615	+	0.114615i
$386$	8995.62	+	8995.62i	0.0603749	+	0.0603749i
$387$	−2774.82	+	25470.6i	−0.0185273	+	0.170066i
$388$	−221711.	+	221711.i	−1.47274	+	1.47274i
$389$	30713.9			0.202972			0.101486	−	0.994837i	$-0.467640\pi$
$389$	30713.9			0.202972			0.101486	+	0.994837i	$0.467640\pi$
$390$	−3560.66	−	3969.63i	−0.0234100	−	0.0260988i
$391$	16325.5	−	1118.19i	0.106785	−	0.00731409i
$392$		−	120613.i		−	0.784913i
$393$	−155842.	−	173742.i	−1.00902	−	1.12491i
$394$	162699.	−	162699.i	1.04808	−	1.04808i
$395$			122112.i			0.782644i
$396$	−348122.	+	279724.i	−2.21994	+	1.78377i
$397$	−49391.5	−	49391.5i	−0.313380	−	0.313380i	0.532837	−	0.846218i	$-0.321126\pi$
$397$	−49391.5	−	49391.5i	−0.313380	−	0.313380i	−0.846218	+	0.532837i	$0.821126\pi$
$398$	36888.5	−	36888.5i	0.232876	−	0.232876i
$399$	12275.3	−	11010.6i	0.0771055	−	0.0691616i
$400$			563.171i			0.00351982i
$401$	−77926.2	+	77926.2i	−0.484613	+	0.484613i	−0.906601	−	0.421989i	$-0.861332\pi$
$401$	−77926.2	+	77926.2i	−0.484613	+	0.484613i	0.421989	+	0.906601i	$0.361332\pi$
$402$	202945.	+	11022.0i	1.25582	+	0.0682039i
$403$	2122.52	−	2122.52i	0.0130690	−	0.0130690i
$404$		−	420915.i		−	2.57888i
$405$	−87663.7	−	137259.i	−0.534453	−	0.836820i
$406$		−	7113.96i		−	0.0431578i
$407$			79024.5i			0.477060i
$408$	94384.5	+	91754.3i	0.566997	+	0.551196i
$409$	−27872.1			−0.166619			−0.0833093	−	0.996524i	$-0.526549\pi$
$409$	−27872.1			−0.166619			−0.0833093	+	0.996524i	$0.526549\pi$
$410$	395193.			2.35094
$411$	−6226.19	+	114641.i	−0.0368586	+	0.678666i
$412$	−190147.			−1.12020
$413$	11265.3	+	11265.3i	0.0660454	+	0.0660454i
$414$	22612.1	−	18169.3i	0.131929	−	0.106008i
$415$	79473.9	+	79473.9i	0.461454	+	0.461454i
$416$	−4582.19			−0.0264780
$417$	−41436.9	+	37167.8i	−0.238295	+	0.213745i
$418$	446709.	+	446709.i	2.55665	+	2.55665i
$419$	89816.9	−	89816.9i	0.511600	−	0.511600i	−0.403417	−	0.915016i	$-0.632178\pi$
$419$	89816.9	−	89816.9i	0.511600	−	0.511600i	0.915016	+	0.403417i	$0.132178\pi$
$420$	1225.27	−	22560.6i	0.00694600	−	0.127895i
$421$	−56472.2			−0.318618			−0.159309	−	0.987229i	$-0.550927\pi$
$421$	−56472.2			−0.318618			−0.159309	+	0.987229i	$0.550927\pi$
$422$	−322544.	−	322544.i	−1.81119	−	1.81119i
$423$	2793.94	−	25646.2i	0.0156148	−	0.143332i
$424$	200960.			1.11784
$425$	1672.61	−	1918.58i	0.00926013	−	0.0106219i
$426$	−286952.	−	319911.i	−1.58121	−	1.76283i
$427$			29709.7i			0.162946i
$428$	46753.0	+	46753.0i	0.255224	+	0.255224i
$429$	−5807.97	+	5209.60i	−0.0315580	+	0.0283067i
$430$	35115.5	−	35115.5i	0.189916	−	0.189916i
$431$	53269.3	−	53269.3i	0.286763	−	0.286763i	−0.549036	−	0.835799i	$-0.685005\pi$
$431$	53269.3	−	53269.3i	0.286763	−	0.286763i	0.835799	+	0.549036i	$0.185005\pi$
$432$	−45998.8	−	7554.10i	−0.246479	−	0.0404777i
$433$		−	24641.5i		−	0.131429i	−0.997838	−	0.0657146i	$-0.979067\pi$
$433$		−	24641.5i		−	0.131429i	0.997838	−	0.0657146i	$-0.0209327\pi$
$434$	21196.2			0.112532
$435$	−3234.21	+	59550.6i	−0.0170919	+	0.314708i
$436$	221773.	+	221773.i	1.16664	+	1.16664i
$437$	−17409.9	−	17409.9i	−0.0911662	−	0.0911662i
$438$	−186763.	+	167522.i	−0.973514	+	0.873218i
$439$	−124319.	+	124319.i	−0.645073	+	0.645073i	−0.951798	−	0.306725i	$-0.900767\pi$
$439$	−124319.	+	124319.i	−0.645073	+	0.645073i	0.306725	+	0.951798i	$0.400767\pi$
$440$	288573.			1.49056
$441$	20906.8	−	191907.i	0.107500	−	0.986767i
$442$	5199.64	+	4533.02i	0.0266151	+	0.0232029i
$443$			17666.1i			0.0900190i	0.998987	+	0.0450095i	$0.0143318\pi$
$443$			17666.1i			0.0900190i	−0.998987	+	0.0450095i	$0.985668\pi$
$444$	55320.9	−	49621.4i	0.280623	−	0.251712i
$445$	167960.	−	167960.i	0.848175	−	0.848175i
$446$			318745.i			1.60241i
$447$	6193.80	−	114045.i	0.0309986	−	0.570769i
$448$	−19831.4	−	19831.4i	−0.0988090	−	0.0988090i
$449$	−118525.	+	118525.i	−0.587918	+	0.587918i	−0.937067	−	0.349149i	$-0.886471\pi$
$449$	−118525.	+	118525.i	−0.587918	+	0.587918i	0.349149	+	0.937067i	$0.386471\pi$
$450$	488.652	−	4485.44i	0.00241310	−	0.0221503i
$451$		−	578207.i		−	2.84270i
$452$	2393.71	−	2393.71i	0.0117164	−	0.0117164i
$453$	−10608.5	+	195332.i	−0.0516962	+	0.951866i
$454$	−268303.	+	268303.i	−1.30171	+	1.30171i
$455$		−	394.730i		−	0.00190668i
$456$	10740.8	−	197768.i	0.0516545	−	0.951099i
$457$			348562.i			1.66897i	0.551032	+	0.834484i	$0.314234\pi$
$457$			348562.i			1.66897i	−0.551032	+	0.834484i	$0.685766\pi$
$458$			12958.7i			0.0617777i
$459$	134271.	+	162351.i	0.637319	+	0.770600i
$460$	−33735.4			−0.159430
$461$	163942.			0.771414			0.385707	−	0.922621i	$-0.373958\pi$
$461$	163942.			0.771414			0.385707	+	0.922621i	$0.373958\pi$
$462$	−55012.5	−	2987.75i	−0.257737	−	0.0139978i
$463$	59684.5			0.278419			0.139210	−	0.990263i	$-0.455544\pi$
$463$	59684.5			0.278419			0.139210	+	0.990263i	$0.455544\pi$
$464$	12070.0	+	12070.0i	0.0560624	+	0.0560624i
$465$	−177432.	−	9636.38i	−0.820590	−	0.0445665i
$466$	−304964.	−	304964.i	−1.40435	−	1.40435i
$467$	−188838.			−0.865874			−0.432937	−	0.901424i	$-0.642523\pi$
$467$	−188838.			−0.865874			−0.432937	+	0.901424i	$0.642523\pi$
$468$	7293.93	+	794.615i	0.0333020	+	0.00362798i
$469$	10638.2	+	10638.2i	0.0483640	+	0.0483640i
$470$	−35357.6	+	35357.6i	−0.160061	+	0.160061i
$471$	250294.	+	13593.5i	1.12826	+	0.0612761i
$472$	191353.			0.858919
$473$	−51377.6	−	51377.6i	−0.229642	−	0.229642i
$474$	−186972.	−	208447.i	−0.832185	−	0.927768i
$475$	−3829.75			−0.0169739
$476$	1997.19	+	29158.9i	0.00881467	+	0.128694i
$477$	319749.	+	34834.0i	1.40531	+	0.153097i
$478$			86918.9i			0.380416i
$479$	110944.	+	110944.i	0.483539	+	0.483539i	0.906260	−	0.422721i	$-0.138925\pi$
$479$	110944.	+	110944.i	0.483539	+	0.483539i	−0.422721	+	0.906260i	$0.638925\pi$
$480$	181122.	+	201926.i	0.786121	+	0.876414i
$481$	918.058	−	918.058i	0.00396808	−	0.00396808i
$482$	186012.	−	186012.i	0.800660	−	0.800660i
$483$	2144.04	+	116.444i	0.00919051	+	0.000499139i
$484$		−	915038.i		−	3.90614i
$485$	324279.			1.37859
$486$	359808.	+	100078.i	1.52335	+	0.423707i
$487$	−291425.	−	291425.i	−1.22876	−	1.22876i	−0.964432	−	0.264332i	$-0.914848\pi$
$487$	−291425.	−	291425.i	−1.22876	−	1.22876i	−0.264332	−	0.964432i	$-0.585152\pi$
$488$	252326.	+	252326.i	1.05955	+	1.05955i
$489$	13740.3	+	15318.5i	0.0574619	+	0.0640619i
$490$	−264577.	+	264577.i	−1.10194	+	1.10194i
$491$	−220648.			−0.915243			−0.457621	−	0.889147i	$-0.651298\pi$
$491$	−220648.			−0.915243			−0.457621	+	0.889147i	$0.651298\pi$
$492$	−404773.	+	363071.i	−1.67217	+	1.49990i
$493$	−5271.75	−	76967.3i	−0.0216901	−	0.316674i
$494$		−	10379.2i		−	0.0425313i
$495$	459149.	+	50020.6i	1.87389	+	0.204145i
$496$	−35962.8	+	35962.8i	−0.146181	+	0.146181i
$497$		−	31811.2i		−	0.128786i
$498$	−257350.	−	13976.7i	−1.03768	−	0.0563569i
$499$	−114500.	−	114500.i	−0.459839	−	0.459839i	0.438763	−	0.898603i	$-0.355417\pi$
$499$	−114500.	−	114500.i	−0.459839	−	0.459839i	−0.898603	+	0.438763i	$0.855417\pi$
$500$	−267020.	+	267020.i	−1.06808	+	1.06808i
$501$	−127470.	−	142111.i	−0.507847	−	0.566178i
$502$		−	37227.2i		−	0.147725i
$503$	−86863.0	+	86863.0i	−0.343320	+	0.343320i	−0.857614	−	0.514294i	$-0.828054\pi$
$503$	−86863.0	+	86863.0i	−0.343320	+	0.343320i	0.514294	+	0.857614i	$0.328054\pi$
$504$	10819.0	+	13464.5i	0.0425917	+	0.0530063i
$505$	−307818.	+	307818.i	−1.20701	+	1.20701i
$506$			82261.3i			0.321288i
$507$	−256543.	−	13932.9i	−0.998031	−	0.0542033i
$508$			410104.i			1.58916i
$509$		−	16937.3i		−	0.0653744i	−0.999466	−	0.0326872i	$-0.989593\pi$
$509$		−	16937.3i		−	0.0653744i	0.999466	−	0.0326872i	$-0.0104065\pi$
$510$	−5769.68	−	408315.i	−0.0221825	−	1.56984i
$511$	−18571.3			−0.0711213
$512$	129416.			0.493682
$513$	51370.4	−	312807.i	0.195199	−	1.18862i
$514$	433443.			1.64061
$515$	139056.	+	139056.i	0.524296	+	0.524296i
$516$	−3705.48	+	68228.0i	−0.0139170	+	0.256250i
$517$	51731.7	+	51731.7i	0.193542	+	0.193542i
$518$	9168.03			0.0341678
$519$	206190.	+	229873.i	0.765478	+	0.853400i
$520$	−3352.46	−	3352.46i	−0.0123982	−	0.0123982i
$521$	200298.	−	200298.i	0.737907	−	0.737907i	−0.234265	−	0.972173i	$-0.575268\pi$
$521$	200298.	−	200298.i	0.737907	−	0.737907i	0.972173	+	0.234265i	$0.0752684\pi$
$522$	−85660.1	−	106606.i	−0.314367	−	0.391237i
$523$	304439.			1.11300			0.556502	−	0.830847i	$-0.312143\pi$
$523$	304439.			1.11300			0.556502	+	0.830847i	$0.312143\pi$
$524$	−440125.	−	440125.i	−1.60293	−	1.60293i
$525$	248.625	−	223.011i	0.000902042	−	0.000809109i
$526$	−288297.			−1.04200
$527$	229325.	−	15707.3i	0.825716	−	0.0565561i
$528$	98407.1	−	88268.6i	0.352987	−	0.316620i
$529$			276635.i			0.988543i
$530$	−440827.	−	440827.i	−1.56934	−	1.56934i
$531$	304463.	+	33168.8i	1.07980	+	0.117636i
$532$	31095.9	−	31095.9i	0.109870	−	0.109870i
$533$	−6717.26	+	6717.26i	−0.0236449	+	0.0236449i
$534$	−29538.4	+	543882.i	−0.103587	+	1.90731i
$535$		−	68381.7i		−	0.238909i
$536$	180701.			0.628973
$537$	−53857.4	−	2925.01i	−0.186766	−	0.0101433i
$538$	435087.	+	435087.i	1.50318	+	1.50318i
$539$	387102.	+	387102.i	1.33244	+	1.33244i
$540$	−253294.	−	352835.i	−0.868635	−	1.21000i
$541$	−7600.20	+	7600.20i	−0.0259675	+	0.0259675i	−0.719971	−	0.694004i	$-0.755845\pi$
$541$	−7600.20	+	7600.20i	−0.0259675	+	0.0259675i	0.694004	+	0.719971i	$0.255845\pi$
$542$	481897.			1.64042
$543$	−121885.	−	135885.i	−0.413381	−	0.460861i
$544$	−264494.	−	230584.i	−0.893753	−	0.779169i
$545$		−	324369.i		−	1.09206i
$546$	604.392	+	673.811i	0.00202737	+	0.00226023i
$547$	246447.	−	246447.i	0.823663	−	0.823663i	−0.162968	−	0.986631i	$-0.552107\pi$
$547$	246447.	−	246447.i	0.823663	−	0.823663i	0.986631	+	0.162968i	$0.0521069\pi$
$548$			306182.i			1.01957i
$549$	357739.	+	445214.i	1.18692	+	1.47715i
$550$	9047.71	+	9047.71i	0.0299098	+	0.0299098i
$551$	−82080.0	+	82080.0i	−0.270355	+	0.270355i
$552$	19198.4	−	17220.5i	0.0630068	−	0.0565155i
$553$		−	20727.5i		−	0.0677793i
$554$	512615.	−	512615.i	1.67021	−	1.67021i
$555$	−76745.1	−	4168.05i	−0.249152	−	0.0135315i
$556$	−104968.	+	104968.i	−0.339554	+	0.339554i
$557$		−	380833.i		−	1.22751i	−0.789498	−	0.613753i	$-0.789659\pi$
$557$		−	380833.i		−	1.22751i	0.789498	−	0.613753i	$-0.210341\pi$
$558$	317634.	−	255226.i	1.02014	−	0.819702i
$559$			1193.75i			0.00382022i
$560$			6688.10i			0.0213269i
$561$	−597405.	+	8441.62i	−1.89821	+	0.0268225i
$562$	−118749.			−0.375973
$563$	−474151.			−1.49589			−0.747945	−	0.663760i	$-0.768959\pi$
$563$	−474151.			−1.49589			−0.747945	+	0.663760i	$0.768959\pi$
$564$	3731.02	−	68698.2i	0.0117292	−	0.215967i
$565$	−3501.07			−0.0109674
$566$	274598.	+	274598.i	0.857164	+	0.857164i
$567$	14880.2	+	23298.7i	0.0462852	+	0.0724711i
$568$	−270174.	−	270174.i	−0.837427	−	0.837427i
$569$	147110.			0.454377			0.227188	−	0.973851i	$-0.427047\pi$
$569$	147110.			0.454377			0.227188	+	0.973851i	$0.427047\pi$
$570$	−457385.	+	410263.i	−1.40777	+	1.26274i
$571$	35106.0	+	35106.0i	0.107674	+	0.107674i	0.758891	−	0.651218i	$-0.225741\pi$
$571$	35106.0	+	35106.0i	0.107674	+	0.107674i	−0.651218	+	0.758891i	$0.725741\pi$
$572$	−14712.8	+	14712.8i	−0.0449680	+	0.0449680i
$573$	15633.8	−	287860.i	0.0476162	−	0.876744i
$574$	−67080.8			−0.203598
$575$	−352.623	−	352.623i	−0.00106654	−	0.00106654i
$576$	−535974.	−	58390.0i	−1.61547	−	0.175992i
$577$	64714.9			0.194381			0.0971903	−	0.995266i	$-0.469014\pi$
$577$	64714.9			0.194381			0.0971903	+	0.995266i	$0.469014\pi$
$578$	72024.6	+	523312.i	0.215588	+	1.56641i
$579$	12087.7	+	13476.1i	0.0360567	+	0.0401981i
$580$			159047.i			0.472792i
$581$	−13490.0	−	13490.0i	−0.0399633	−	0.0399633i
$582$	−553549.	+	496519.i	−1.63422	+	1.46585i
$583$	−644975.	+	644975.i	−1.89760	+	1.89760i
$584$	−157727.	+	157727.i	−0.462465	+	0.462465i
$585$	−4753.00	−	5915.22i	−0.0138885	−	0.0172846i
$586$			206638.i			0.601748i
$587$	−388137.			−1.12644			−0.563221	−	0.826306i	$-0.690438\pi$
$587$	−388137.			−1.12644			−0.563221	+	0.826306i	$0.690438\pi$
$588$	27918.8	−	514061.i	0.0807500	−	1.48683i
$589$	−244559.	−	244559.i	−0.704941	−	0.704941i
$590$	−419753.	−	419753.i	−1.20584	−	1.20584i
$591$	243735.	−	218624.i	0.697818	−	0.625925i
$592$	−15555.1	+	15555.1i	−0.0443843	+	0.0443843i
$593$	−208068.			−0.591693			−0.295846	−	0.955235i	$-0.595602\pi$
$593$	−208068.			−0.591693			−0.295846	+	0.955235i	$0.595602\pi$
$594$	−860363.	+	617640.i	−2.43842	+	1.75050i
$595$	19863.6	−	22784.7i	0.0561079	−	0.0643590i
$596$		−	304590.i		−	0.857478i
$597$	55261.5	−	49568.2i	0.155051	−	0.139077i
$598$	955.661	−	955.661i	0.00267240	−	0.00267240i
$599$		−	365100.i		−	1.01756i	−0.860898	−	0.508778i	$-0.830097\pi$
$599$		−	365100.i		−	1.01756i	0.860898	−	0.508778i	$-0.169903\pi$
$600$	217.547	−	4005.62i	0.000604296	−	0.0111267i
$601$	165308.	+	165308.i	0.457663	+	0.457663i	0.897888	−	0.440225i	$-0.145101\pi$
$601$	165308.	+	165308.i	0.457663	+	0.457663i	−0.440225	+	0.897888i	$0.645101\pi$
$602$	−5960.57	+	5960.57i	−0.0164473	+	0.0164473i
$603$	287514.	+	31322.4i	0.790724	+	0.0861430i
$604$			521690.i			1.43001i
$605$	−669174.	+	669174.i	−1.82822	+	1.82822i
$606$	54134.7	−	996767.i	0.147411	−	2.71424i
$607$	142750.	−	142750.i	0.387434	−	0.387434i	−0.486337	−	0.873771i	$-0.661667\pi$
$607$	142750.	−	142750.i	0.387434	−	0.387434i	0.873771	+	0.486337i	$0.161667\pi$
$608$			527965.i			1.42823i
$609$	548.981	−	10108.2i	0.00148021	−	0.0272546i
$610$		−	1.10701e6i		−	2.97502i
$611$		−	1201.97i		−	0.00321968i
$612$	381035.	+	412911.i	1.01733	+	1.10244i
$613$	23162.0			0.0616388			0.0308194	−	0.999525i	$-0.490188\pi$
$613$	23162.0			0.0616388			0.0308194	+	0.999525i	$0.490188\pi$
$614$	−160626.			−0.426067
$615$	561530.	+	30496.9i	1.48464	+	0.0806315i
$616$	−48982.8			−0.129087
$617$	−112072.	−	112072.i	−0.294393	−	0.294393i	0.544420	−	0.838813i	$-0.316750\pi$
$617$	−112072.	−	112072.i	−0.294393	−	0.294393i	−0.838813	+	0.544420i	$0.816750\pi$
$618$	−450287.	−	24455.3i	−1.17900	−	0.0640317i
$619$	98958.9	+	98958.9i	0.258270	+	0.258270i	0.824350	−	0.566080i	$-0.191541\pi$
$619$	98958.9	+	98958.9i	0.258270	+	0.258270i	−0.566080	+	0.824350i	$0.691541\pi$
$620$	−473884.			−1.23279
$621$	33531.6	−	24071.7i	0.0869503	−	0.0624201i
$622$	383391.	+	383391.i	0.990972	+	0.990972i
$623$	−28509.8	+	28509.8i	−0.0734545	+	0.0734545i
$624$	−2168.68	−	117.782i	−0.00556964	−	0.000302489i
$625$	385043.			0.985710
$626$	270037.	+	270037.i	0.689088	+	0.689088i
$627$	600256.	+	669200.i	1.52687	+	1.70224i
$628$	668483.			1.69501
$629$	99190.8	−	6793.91i	0.250709	−	0.0171719i
$630$	5803.14	−	53268.2i	0.0146212	−	0.134211i
$631$		−	638862.i		−	1.60453i	−0.596967	−	0.802266i	$-0.703628\pi$
$631$		−	638862.i		−	1.60453i	0.596967	−	0.802266i	$-0.296372\pi$
$632$	−176040.	−	176040.i	−0.440734	−	0.440734i
$633$	−433412.	−	483194.i	−1.08167	−	1.20591i
$634$	692705.	−	692705.i	1.72333	−	1.72333i
$635$	299912.	−	299912.i	0.743784	−	0.743784i
$636$	856508.	+	46517.2i	2.11747	+	0.115000i
$637$		−	8994.24i		−	0.0221659i
$638$	387826.			0.952786
$639$	−383043.	−	476706.i	−0.938093	−	1.16748i
$640$	397941.	+	397941.i	0.971536	+	0.971536i
$641$	182986.	+	182986.i	0.445351	+	0.445351i	0.893806	−	0.448454i	$-0.148025\pi$
$641$	182986.	+	182986.i	0.445351	+	0.445351i	−0.448454	+	0.893806i	$0.648025\pi$
$642$	104703.	+	116729.i	0.254031	+	0.283209i
$643$	440370.	−	440370.i	1.06511	−	1.06511i	0.0673858	−	0.997727i	$-0.478534\pi$
$643$	440370.	−	440370.i	1.06511	−	1.06511i	0.997727	−	0.0673858i	$-0.0214658\pi$
$644$	5726.30			0.0138071
$645$	52605.5	−	47185.8i	0.126448	−	0.113421i
$646$	522300.	−	599109.i	1.25157	−	1.43562i
$647$			663836.i			1.58581i	0.609343	+	0.792907i	$0.291433\pi$
$647$			663836.i			1.58581i	−0.609343	+	0.792907i	$0.708567\pi$
$648$	324254.	+	71498.4i	0.772211	+	0.170273i
$649$	−614141.	+	614141.i	−1.45807	+	1.45807i
$650$		−	210.222i		−	0.000497566i
$651$	30117.6	+	1635.70i	0.0710654	+	0.00385959i
$652$	38805.1	+	38805.1i	0.0912838	+	0.0912838i
$653$	500817.	−	500817.i	1.17450	−	1.17450i	0.193374	−	0.981125i	$-0.438057\pi$
$653$	500817.	−	500817.i	1.17450	−	1.17450i	0.981125	−	0.193374i	$-0.0619431\pi$
$654$	496657.	+	553703.i	1.16118	+	1.29456i
$655$			643733.i			1.50046i
$656$	113814.	−	113814.i	0.264476	−	0.264476i
$657$	−278299.	+	223619.i	−0.644734	+	0.518057i
$658$	6001.65	−	6001.65i	0.0138618	−	0.0138618i
$659$		−	208184.i		−	0.479377i	−0.970850	−	0.239689i	$-0.922955\pi$
$659$		−	208184.i		−	0.479377i	0.970850	−	0.239689i	$-0.0770453\pi$
$660$	1.22992e6	+	66797.3i	2.82350	+	0.153345i
$661$		−	356178.i		−	0.815200i	−0.913161	−	0.407600i	$-0.866366\pi$
$661$		−	356178.i		−	0.815200i	0.913161	−	0.407600i	$-0.133634\pi$
$662$			365659.i			0.834374i
$663$	7038.36	+	6842.22i	0.0160120	+	0.0155657i
$664$	−229143.			−0.519721
$665$	−45481.3			−0.102846
$666$	137387.	−	110393.i	0.309740	−	0.248883i
$667$	−15115.0			−0.0339748
$668$	−359998.	−	359998.i	−0.806765	−	0.806765i
$669$	−24597.4	+	452905.i	−0.0549588	+	1.01194i
$670$	−396387.	−	396387.i	−0.883018	−	0.883018i
$671$	−1.61966e6			−3.59732
$672$	−30744.0	−	34275.2i	−0.0680804	−	0.0759000i
$673$	−195092.	−	195092.i	−0.430734	−	0.430734i	0.458144	−	0.888878i	$-0.348514\pi$
$673$	−195092.	−	195092.i	−0.430734	−	0.430734i	−0.888878	+	0.458144i	$0.848514\pi$
$674$	133611.	−	133611.i	0.294119	−	0.294119i
$675$	1040.46	−	6335.65i	0.00228360	−	0.0139054i
$676$	−685172.			−1.49936
$677$	205841.	+	205841.i	0.449111	+	0.449111i	0.895059	−	0.445948i	$-0.147133\pi$
$677$	205841.	+	205841.i	0.449111	+	0.449111i	−0.445948	+	0.895059i	$0.647133\pi$
$678$	5976.39	−	5360.67i	0.0130011	−	0.0116616i
$679$	−55043.6			−0.119390
$680$	−24809.2	−	362214.i	−0.0536532	−	0.783334i
$681$	−401936.	+	360527.i	−0.866689	+	0.777398i
$682$			1.15553e6i			2.48435i
$683$	−331268.	−	331268.i	−0.710129	−	0.710129i	0.256433	−	0.966562i	$-0.417453\pi$
$683$	−331268.	−	331268.i	−0.710129	−	0.710129i	−0.966562	+	0.256433i	$0.917453\pi$
$684$	91556.4	−	840415.i	0.195694	−	1.79631i
$685$	223914.	−	223914.i	0.477199	−	0.477199i
$686$	90154.0	−	90154.0i	0.191574	−	0.191574i
$687$	−1000.02	+	18413.1i	−0.00211882	+	0.0390133i
$688$		−	20226.2i		−	0.0427305i
$689$	14985.8			0.0315677
$690$	−79888.6	−	4338.77i	−0.167798	−	0.00911315i
$691$	589286.	+	589286.i	1.23416	+	1.23416i	0.962353	+	0.271804i	$0.0876201\pi$
$691$	589286.	+	589286.i	1.23416	+	1.23416i	0.271804	+	0.962353i	$0.412380\pi$
$692$	582316.	+	582316.i	1.21604	+	1.21604i
$693$	−77936.7	−	8490.57i	−0.162284	−	0.0176795i
$694$	−11290.3	+	11290.3i	−0.0234415	+	0.0234415i
$695$	153528.			0.317848
$696$	−81187.0	−	90512.0i	−0.167598	−	0.186848i
$697$	−725760.	+	49709.7i	−1.49392	+	0.102324i
$698$			354425.i			0.727468i
$699$	−409789.	−	456857.i	−0.838699	−	0.935031i
$700$	629.821	−	629.821i	0.00128535	−	0.00128535i
$701$			517352.i			1.05281i	0.850234	+	0.526405i	$0.176461\pi$
$701$			517352.i			1.05281i	−0.850234	+	0.526405i	$0.823539\pi$
$702$	17170.5	+	2819.81i	0.0348425	+	0.00572198i
$703$	−105780.	−	105780.i	−0.214038	−	0.214038i
$704$	1.08113e6	−	1.08113e6i	2.18139	−	2.18139i
$705$	−52968.1	+	47511.0i	−0.106570	+	0.0955908i
$706$		−	1.02411e6i		−	2.05464i
$707$	52249.6	−	52249.6i	0.104531	−	0.104531i
$708$	815562.	+	44293.4i	1.62701	+	0.0883635i
$709$	−574326.	+	574326.i	−1.14253	+	1.14253i	−0.154539	+	0.987987i	$0.549389\pi$
$709$	−574326.	+	574326.i	−1.14253	+	1.14253i	−0.987987	+	0.154539i	$0.950611\pi$
$710$			1.18531e6i			2.35134i
$711$	−249583.	−	310611.i	−0.493714	−	0.614438i
$712$			484270.i			0.955273i
$713$		−	45035.5i		−	0.0885881i
$714$	979.355	+	69308.0i	0.00192107	+	0.135952i
$715$	21519.2			0.0420934
$716$	−143842.			−0.280582
$717$	−6707.49	+	123503.i	−0.0130473	+	0.240237i
$718$	−1.24339e6			−2.41190
$719$	−602309.	−	602309.i	−1.16510	−	1.16510i	−0.983345	−	0.181751i	$-0.941824\pi$
$719$	−602309.	−	602309.i	−1.16510	−	1.16510i	−0.181751	−	0.983345i	$-0.558176\pi$
$720$	80532.3	+	100224.i	0.155348	+	0.193334i
$721$	−23603.7	−	23603.7i	−0.0454055	−	0.0454055i
$722$	−371659.			−0.712969
$723$	278660.	−	249951.i	0.533086	−	0.478165i
$724$	−344224.	−	344224.i	−0.656696	−	0.656696i
$725$	−1662.46	+	1662.46i	−0.00316283	+	0.00316283i
$726$	117685.	−	2.16690e6i	0.223279	−	4.11117i
$727$	356405.			0.674333			0.337167	−	0.941445i	$-0.390531\pi$
$727$	356405.			0.674333			0.337167	+	0.941445i	$0.390531\pi$
$728$	569.053	+	569.053i	0.00107372	+	0.00107372i
$729$	503528.	+	169967.i	0.947478	+	0.319822i
$730$	691978.			1.29851
$731$	−60071.6	+	68905.7i	−0.112418	+	0.128950i
$732$	1.01702e6	+	1.13384e6i	1.89806	+	2.11607i
$733$		−	960075.i		−	1.78689i	−0.449176	−	0.893443i	$-0.648282\pi$
$733$		−	960075.i		−	1.78689i	0.449176	−	0.893443i	$-0.351718\pi$
$734$	279216.	+	279216.i	0.518260	+	0.518260i
$735$	−396354.	+	355520.i	−0.733684	+	0.658096i
$736$	−48612.3	+	48612.3i	−0.0897409	+	0.0897409i
$737$	−579954.	+	579954.i	−1.06772	+	1.06772i
$738$	−1.00524e6	+	807728.i	−1.84568	+	1.48304i
$739$			499843.i			0.915261i	0.889143	+	0.457630i	$0.151302\pi$
$739$			499843.i			0.915261i	−0.889143	+	0.457630i	$0.848698\pi$
$740$	−204970.			−0.374307
$741$	800.956	−	14747.8i	0.00145872	−	0.0268590i
$742$	74826.8	+	74826.8i	0.135909	+	0.135909i
$743$	32383.7	+	32383.7i	0.0586610	+	0.0586610i	0.735829	−	0.677168i	$-0.236793\pi$
$743$	32383.7	+	32383.7i	0.0586610	+	0.0586610i	−0.677168	+	0.735829i	$0.736793\pi$
$744$	269682.	−	241898.i	0.487199	−	0.437005i
$745$	−222749.	+	222749.i	−0.401331	+	0.401331i
$746$	−1.11903e6			−2.01077
$747$	−364590.	−	39719.1i	−0.653376	−	0.0711801i
$748$	−1.58963e6	+	108879.i	−2.84115	+	0.194600i
$749$			11607.2i			0.0206902i
$750$	−666671.	+	597987.i	−1.18519	+	1.06309i
$751$	−305516.	+	305516.i	−0.541694	+	0.541694i	−0.924025	−	0.382332i	$-0.875121\pi$
$751$	−305516.	+	305516.i	−0.541694	+	0.541694i	0.382332	+	0.924025i	$0.375121\pi$
$752$			20365.6i			0.0360132i
$753$	2872.81	−	52896.2i	0.00506660	−	0.0932898i
$754$	−4505.52	−	4505.52i	−0.00792506	−	0.00792506i
$755$	381516.	−	381516.i	0.669297	−	0.669297i
$756$	42994.6	+	59890.8i	0.0752264	+	0.104789i
$757$		−	435267.i		−	0.759563i	−0.925076	−	0.379782i	$-0.875999\pi$
$757$		−	435267.i		−	0.759563i	0.925076	−	0.379782i	$-0.124001\pi$
$758$	840601.	−	840601.i	1.46302	−	1.46302i
$759$	−6348.06	+	116885.i	−0.0110194	+	0.202897i
$760$	−386274.	+	386274.i	−0.668758	+	0.668758i
$761$		−	146824.i		−	0.253529i	−0.991933	−	0.126765i	$-0.959541\pi$
$761$		−	146824.i		−	0.253529i	0.991933	−	0.126765i	$-0.0404593\pi$
$762$	−52744.3	+	971166.i	−0.0908376	+	1.67257i
$763$			55058.9i			0.0945755i
$764$		−	768815.i		−	1.31715i
$765$	23311.3	−	580619.i	0.0398330	−	0.992130i
$766$	265591.			0.452643
$767$	14269.4			0.0242558
$768$	−331531.	−	18005.5i	−0.562084	−	0.0305270i
$769$	1858.29			0.00314240			0.00157120	−	0.999999i	$-0.499500\pi$
$769$	1858.29			0.00314240			0.00157120	+	0.999999i	$0.499500\pi$
$770$	107449.	+	107449.i	0.181226	+	0.181226i
$771$	615879.	+	33448.6i	1.03606	+	0.0562690i
$772$	34137.7	+	34137.7i	0.0572796	+	0.0572796i
$773$	1.00708e6			1.68540			0.842702	−	0.538381i	$-0.180964\pi$
$773$	1.00708e6			1.68540			0.842702	+	0.538381i	$0.180964\pi$
$774$	−17549.9	+	161094.i	−0.0292949	+	0.268904i
$775$	−4953.34	−	4953.34i	−0.00824697	−	0.00824697i
$776$	−467488.	+	467488.i	−0.776330	+	0.776330i
$777$	13026.9	+	707.492i	0.0215773	+	0.00117187i
$778$	194256.			0.320933
$779$	773970.	+	773970.i	1.27541	+	1.27541i
$780$	−13512.4	−	15064.5i	−0.0222098	−	0.0247608i
$781$	1.73423e6			2.84318
$782$	103254.	−	7072.18i	0.168846	−	0.0115648i
$783$	−113488.	−	158087.i	−0.185108	−	0.257853i
$784$			152394.i			0.247933i
$785$	−488867.	−	488867.i	−0.793326	−	0.793326i
$786$	−985653.	−	1.09886e6i	−1.59543	−	1.77868i
$787$	297485.	−	297485.i	0.480304	−	0.480304i	−0.424925	−	0.905229i	$-0.639699\pi$
$787$	297485.	−	297485.i	0.480304	−	0.480304i	0.905229	+	0.424925i	$0.139699\pi$
$788$	617431.	−	617431.i	0.994343	−	0.994343i
$789$	−409642.	−	22247.8i	−0.658037	−	0.0357382i
$790$			772322.i			1.23750i
$791$	594.278			0.000949810
$792$	−734030.	+	589809.i	−1.17021	+	0.940288i
$793$	18816.2	+	18816.2i	0.0299217	+	0.0299217i
$794$	−312386.	−	312386.i	−0.495508	−	0.495508i
$795$	−592353.	−	660390.i	−0.937230	−	1.04488i
$796$	139989.	−	139989.i	0.220937	−	0.220937i
$797$	88962.1			0.140052			0.0700258	−	0.997545i	$-0.477692\pi$
$797$	88962.1			0.140052			0.0700258	+	0.997545i	$0.477692\pi$
$798$	77637.3	−	69638.7i	0.121917	−	0.109357i
$799$	60485.6	−	69380.6i	0.0947455	−	0.108679i
$800$			10693.5i			0.0167086i
$801$	−83942.2	+	770523.i	−0.130832	+	1.20094i
$802$	−492859.	+	492859.i	−0.766257	+	0.766257i
$803$		−	1.01243e6i		−	1.57013i
$804$	770163.	+	41827.8i	1.19143	+	0.0647072i
$805$	−4187.69	−	4187.69i	−0.00646223	−	0.00646223i
$806$	13424.3	−	13424.3i	0.0206643	−	0.0206643i
$807$	584639.	+	651790.i	0.897719	+	1.00083i
$808$		−	887516.i		−	1.35942i
$809$	−431420.	+	431420.i	−0.659179	+	0.659179i	−0.955186	−	0.296007i	$-0.904345\pi$
$809$	−431420.	+	431420.i	−0.659179	+	0.659179i	0.296007	+	0.955186i	$0.404345\pi$
$810$	−554446.	−	868124.i	−0.845063	−	1.32316i
$811$	−411691.	+	411691.i	−0.625935	+	0.625935i	−0.947043	−	0.321107i	$-0.895945\pi$
$811$	−411691.	+	411691.i	−0.625935	+	0.625935i	0.321107	+	0.947043i	$0.395945\pi$
$812$		−	26997.0i		−	0.0409452i
$813$	684727.	+	37187.7i	1.03594	+	0.0562624i
$814$			499806.i			0.754315i
$815$		−	56757.0i		−	0.0854484i
$816$	−119254.	−	115931.i	−0.179099	−	0.174108i
$817$	137545.			0.206063
$818$	−176283.			−0.263453
$819$	806.782	+	1004.06i	0.00120279	+	0.00149690i
$820$	1.49973e6			2.23041
$821$	32937.5	+	32937.5i	0.0488657	+	0.0488657i	0.731117	−	0.682252i	$-0.238999\pi$
$821$	32937.5	+	32937.5i	0.0488657	+	0.0488657i	−0.682252	+	0.731117i	$0.738999\pi$
$822$	−39378.7	+	725069.i	−0.0582798	+	1.07309i
$823$	−316449.	−	316449.i	−0.467201	−	0.467201i	0.433805	−	0.901007i	$-0.357171\pi$
$823$	−316449.	−	316449.i	−0.467201	−	0.467201i	−0.901007	+	0.433805i	$0.857171\pi$
$824$	−400934.			−0.590497
$825$	12157.7	+	13554.1i	0.0178625	+	0.0199142i
$826$	71249.6	+	71249.6i	0.104429	+	0.104429i
$827$	−741524.	+	741524.i	−1.08421	+	1.08421i	−0.0881003	+	0.996112i	$0.528080\pi$
$827$	−741524.	+	741524.i	−1.08421	+	1.08421i	−0.996112	+	0.0881003i	$0.971920\pi$
$828$	85811.2	−	68951.1i	0.125165	−	0.100573i
$829$	1.29580e6			1.88550			0.942752	−	0.333495i	$-0.108228\pi$
$829$	1.29580e6			1.88550			0.942752	+	0.333495i	$0.108228\pi$
$830$	502648.	+	502648.i	0.729639	+	0.729639i
$831$	767933.	−	688816.i	1.11204	−	0.997474i
$832$	−25119.8			−0.0362885
$833$	452607.	−	519167.i	0.652276	−	0.748199i
$834$	−262076.	+	235075.i	−0.376786	+	0.337967i
$835$			526538.i			0.755191i
$836$	1.69523e6	+	1.69523e6i	2.42558	+	2.42558i
$837$	471022.	−	338138.i	0.672342	−	0.482662i
$838$	568065.	−	568065.i	0.808928	−	0.808928i
$839$	68939.3	−	68939.3i	0.0979362	−	0.0979362i	−0.656441	−	0.754377i	$-0.727939\pi$
$839$	68939.3	−	68939.3i	0.0979362	−	0.0979362i	0.754377	+	0.656441i	$0.227939\pi$
$840$	2583.54	−	47570.0i	0.00366148	−	0.0674178i
$841$		−	636020.i		−	0.899247i
$842$	−357169.			−0.503791
$843$	−168730.	−	9163.79i	−0.237431	−	0.0128950i
$844$	−1.22403e6	−	1.22403e6i	−1.71834	−	1.71834i
$845$	501072.	+	501072.i	0.701757	+	0.701757i
$846$	17670.8	−	162204.i	0.0246897	−	0.226632i
$847$	113587.	−	113587.i	0.158329	−	0.158329i
$848$	−253912.			−0.353095
$849$	368985.	+	411366.i	0.511910	+	0.570707i
$850$	10578.7	−	12134.5i	0.0146419	−	0.0167951i
$851$		−	19479.3i		−	0.0268977i
$852$	−1.08896e6	−	1.21404e6i	−1.50015	−	1.67245i
$853$	735044.	−	735044.i	1.01022	−	1.01022i	0.0102716	−	0.999947i	$-0.496730\pi$
$853$	735044.	−	735044.i	1.01022	−	1.01022i	0.999947	−	0.0102716i	$-0.00326959\pi$
$854$			187905.i			0.257646i
$855$	−681558.	+	547646.i	−0.932332	+	0.749148i
$856$	98580.6	+	98580.6i	0.134538	+	0.134538i
$857$	673627.	−	673627.i	0.917187	−	0.917187i	−0.0796371	−	0.996824i	$-0.525376\pi$
$857$	673627.	−	673627.i	0.917187	−	0.917187i	0.996824	+	0.0796371i	$0.0253762\pi$
$858$	−36733.6	+	32949.1i	−0.0498987	+	0.0447578i
$859$			367518.i			0.498073i	0.968494	+	0.249036i	$0.0801138\pi$
$859$			367518.i			0.498073i	−0.968494	+	0.249036i	$0.919886\pi$
$860$	133261.	−	133261.i	0.180180	−	0.180180i
$861$	−95315.0	−	5176.59i	−0.128575	−	0.00698293i
$862$	336912.	−	336912.i	0.453421	−	0.453421i
$863$			894596.i			1.20117i	0.799560	+	0.600586i	$0.205066\pi$
$863$			894596.i			1.20117i	−0.799560	+	0.600586i	$0.794934\pi$
$864$	−873425.	−	143437.i	−1.17003	−	0.192148i
$865$		−	851705.i		−	1.13830i
$866$		−	155850.i		−	0.207812i
$867$	61956.0	+	749131.i	0.0824225	+	0.996597i
$868$	80437.9			0.106763
$869$	1.12998e6			1.49635
$870$	−20455.4	+	376639.i	−0.0270252	+	0.497608i
$871$	13475.1			0.0177622
$872$	467617.	+	467617.i	0.614975	+	0.614975i
$873$	−824854.	+	662787.i	−1.08230	+	0.869652i
$874$	−110112.	−	110112.i	−0.144150	−	0.144150i
$875$	−66292.2			−0.0865857
$876$	−708752.	+	635732.i	−0.923604	+	0.828450i
$877$	423115.	+	423115.i	0.550122	+	0.550122i	0.926476	−	0.376354i	$-0.122822\pi$
$877$	423115.	+	423115.i	0.550122	+	0.550122i	−0.376354	+	0.926476i	$0.622822\pi$
$878$	−786281.	+	786281.i	−1.01997	+	1.01997i
$879$	−15946.1	+	293612.i	−0.0206385	+	0.380011i
$880$	−364610.			−0.470829
$881$	2070.44	+	2070.44i	0.00266754	+	0.00266754i	0.708439	−	0.705772i	$-0.249400\pi$
$881$	2070.44	+	2070.44i	0.00266754	+	0.00266754i	−0.705772	+	0.708439i	$0.749400\pi$
$882$	132229.	−	1.21376e6i	0.169977	−	1.56025i
$883$	−445078.			−0.570840			−0.285420	−	0.958403i	$-0.592133\pi$
$883$	−445078.			−0.570840			−0.285420	+	0.958403i	$0.592133\pi$
$884$	19732.3	+	17202.5i	0.0252506	+	0.0220134i
$885$	−564035.	−	628819.i	−0.720144	−	0.802859i
$886$			111733.i			0.142336i
$887$	−626923.	−	626923.i	−0.796832	−	0.796832i	0.185763	−	0.982595i	$-0.440524\pi$
$887$	−626923.	−	626923.i	−0.796832	−	0.796832i	−0.982595	+	0.185763i	$0.940524\pi$
$888$	116646.	−	104629.i	0.147926	−	0.132686i
$889$	−50907.6	+	50907.6i	−0.0644138	+	0.0644138i
$890$	1.06230e6	−	1.06230e6i	1.34111	−	1.34111i
$891$	−1.27015e6	+	811210.i	−1.59993	+	1.02183i
$892$			1.20962e6i			1.52026i
$893$	−138493.			−0.173670
$894$	39173.9	−	721298.i	0.0490142	−	0.902484i
$895$	105193.	+	105193.i	0.131323	+	0.131323i
$896$	−67547.2	−	67547.2i	−0.0841379	−	0.0841379i
$897$	1431.65	−	1284.15i	0.00177931	−	0.00159599i
$898$	−749634.	+	749634.i	−0.929601	+	0.929601i
$899$	−212322.			−0.262710
$900$	1854.40	−	17021.9i	0.00228938	−	0.0210147i
$901$	865016.	+	754116.i	1.06555	+	0.928942i
$902$		−	3.65699e6i		−	4.49480i
$903$	−8929.35	+	8009.40i	−0.0109508	+	0.00982256i
$904$	5047.23	−	5047.23i	0.00617612	−	0.00617612i
$905$			503468.i			0.614716i
$906$	−67095.6	+	1.23541e6i	−0.0817406	+	1.50507i
$907$	−572485.	−	572485.i	−0.695904	−	0.695904i	0.267620	−	0.963524i	$-0.413763\pi$
$907$	−572485.	−	572485.i	−0.695904	−	0.695904i	−0.963524	+	0.267620i	$0.913763\pi$
$908$	−1.01819e6	+	1.01819e6i	−1.23497	+	1.23497i
$909$	153840.	−	1.41213e6i	0.186184	−	1.70902i
$910$		−	2496.55i		−	0.00301479i
$911$	316154.	−	316154.i	0.380945	−	0.380945i	−0.490498	−	0.871442i	$-0.663185\pi$
$911$	316154.	−	316154.i	0.380945	−	0.380945i	0.871442	+	0.490498i	$0.163185\pi$
$912$	−13571.0	+	249878.i	−0.0163163	+	0.300427i
$913$	735425.	−	735425.i	0.882261	−	0.882261i
$914$			2.20455e6i			2.63893i
$915$	85427.1	−	1.57294e6i	0.102036	−	1.87876i
$916$			49177.5i			0.0586105i
$917$		−	109268.i		−	0.129944i
$918$	849223.	+	1.02682e6i	1.00771	+	1.21845i
$919$	−914882.			−1.08326			−0.541632	−	0.840616i	$-0.682193\pi$
$919$	−914882.			−1.08326			−0.541632	+	0.840616i	$0.682193\pi$
$920$	−71132.4			−0.0840411
$921$	−228233.	−	12395.4i	−0.269066	−	0.0146131i
$922$	1.03688e6			1.21974
$923$	−20147.2	−	20147.2i	−0.0236489	−	0.0236489i
$924$	−208768.	−	11338.3i	−0.244524	−	0.0132802i
$925$	−2142.48	−	2142.48i	−0.00250400	−	0.00250400i
$926$	377486.			0.440230
$927$	−637926.	−	69496.9i	−0.742354	−	0.0808735i
$928$	229185.	+	229185.i	0.266128	+	0.266128i
$929$	164673.	−	164673.i	0.190805	−	0.190805i	−0.605239	−	0.796044i	$-0.706922\pi$
$929$	164673.	−	164673.i	0.190805	−	0.190805i	0.796044	+	0.605239i	$0.206922\pi$
$930$	−1.12220e6	−	60947.2i	−1.29749	−	0.0704673i
$931$	−1.03633e6			−1.19563
$932$	−1.15732e6	−	1.15732e6i	−1.33236	−	1.33236i
$933$	515174.	+	574347.i	0.591822	+	0.659798i
$934$	−1.19434e6			−1.36910
$935$	1.24213e6	+	1.08289e6i	1.42084	+	1.23868i
$936$	15379.5	+	1675.48i	0.0175546	+	0.00191244i
$937$			489898.i			0.557991i	0.960292	+	0.278995i	$0.0900014\pi$
$937$			489898.i			0.557991i	−0.960292	+	0.278995i	$0.909999\pi$
$938$	67283.4	+	67283.4i	0.0764719	+	0.0764719i
$939$	362857.	+	404534.i	0.411532	+	0.458800i
$940$	−134179.	+	134179.i	−0.151855	+	0.151855i
$941$	−85300.4	+	85300.4i	−0.0963323	+	0.0963323i	−0.753631	−	0.657298i	$-0.771699\pi$
$941$	−85300.4	+	85300.4i	−0.0963323	+	0.0963323i	0.657298	+	0.753631i	$0.271699\pi$
$942$	1.58303e6	+	85975.0i	1.78397	+	0.0968881i
$943$			142526.i			0.160277i
$944$	−241774.			−0.271309
$945$	12356.4	−	75240.9i	0.0138365	−	0.0842540i
$946$	−324948.	−	324948.i	−0.363104	−	0.363104i
$947$	379994.	+	379994.i	0.423718	+	0.423718i	0.886482	−	0.462764i	$-0.153142\pi$
$947$	379994.	+	379994.i	0.423718	+	0.423718i	−0.462764	+	0.886482i	$0.653142\pi$
$948$	−709545.	−	791042.i	−0.789520	−	0.880204i
$949$	−11761.8	+	11761.8i	−0.0130600	+	0.0130600i
$950$	−24222.0			−0.0268387
$951$	1.03772e6	−	930808.i	1.14741	−	1.02920i
$952$	4211.16	+	61482.8i	0.00464652	+	0.0678390i
$953$			362391.i			0.399017i	0.979896	+	0.199508i	$0.0639345\pi$
$953$			362391.i			0.399017i	−0.979896	+	0.199508i	$0.936065\pi$
$954$	2.02231e6	+	220315.i	2.22204	+	0.242073i
$955$	−562241.	+	562241.i	−0.616475	+	0.616475i
$956$			329851.i			0.360913i
$957$	551061.	+	29928.3i	0.601695	+	0.0326782i
$958$	701685.	+	701685.i	0.764559	+	0.764559i
$959$	−38007.5	+	38007.5i	−0.0413268	+	0.0413268i
$960$	992923.	+	1.10697e6i	1.07739	+	1.20114i
$961$			290903.i			0.314994i
$962$	5806.44	−	5806.44i	0.00627422	−	0.00627422i
$963$	139764.	+	173940.i	0.150710	+	0.187562i
$964$	705904.	−	705904.i	0.759612	−	0.759612i
$965$		−	49930.4i		−	0.0536180i
$966$	13560.4	+	736.471i	0.0145318	+	0.000789226i
$967$		−	13396.7i		−	0.0143266i	−0.999974	−	0.00716332i	$-0.997720\pi$
$967$		−	13396.7i		−	0.0143266i	0.999974	−	0.00716332i	$-0.00228017\pi$
$968$		−	1.92939e6i		−	2.05907i
$969$	788368.	−	810968.i	0.839618	−	0.863686i
$970$	2.05096e6			2.17979
$971$	−486993.			−0.516517			−0.258258	−	0.966076i	$-0.583149\pi$
$971$	−486993.			−0.516517			−0.258258	+	0.966076i	$0.583149\pi$
$972$	1.36545e6	+	379788.i	1.44525	+	0.401984i
$973$	−26060.2			−0.0275265
$974$	−1.84317e6	−	1.84317e6i	−1.94289	−	1.94289i
$975$	16.2227	−	298.704i	1.70653e−5	−	0.000314218i
$976$	−318812.	−	318812.i	−0.334684	−	0.334684i
$977$	378654.			0.396692			0.198346	−	0.980132i	$-0.436443\pi$
$977$	378654.			0.396692			0.198346	+	0.980132i	$0.436443\pi$
$978$	86903.5	+	96885.1i	0.0908572	+	0.101293i
$979$	−1.55424e6	−	1.55424e6i	−1.62164	−	1.62164i
$980$	−1.00405e6	+	1.00405e6i	−1.04545	+	1.04545i
$981$	662971.	+	825083.i	0.688901	+	0.857353i
$982$	−1.39553e6			−1.44716
$983$	−1.27799e6	−	1.27799e6i	−1.32257	−	1.32257i	−0.911687	−	0.410886i	$-0.865219\pi$
$983$	−1.27799e6	−	1.27799e6i	−1.32257	−	1.32257i	−0.410886	−	0.911687i	$-0.634781\pi$
$984$	−853479.	+	765549.i	−0.881460	+	0.790648i
$985$	−903065.			−0.930779
$986$	−33342.2	−	486795.i	−0.0342958	−	0.500717i
$987$	8990.89	−	8064.60i	0.00922929	−	0.00827844i
$988$		−	39388.2i		−	0.0403508i
$989$	12664.4	+	12664.4i	0.0129477	+	0.0129477i
$990$	2.90398e6	+	316365.i	2.96294	+	0.322788i
$991$	−1.23159e6	+	1.23159e6i	−1.25406	+	1.25406i	−0.300180	+	0.953882i	$0.597047\pi$
$991$	−1.23159e6	+	1.23159e6i	−1.25406	+	1.25406i	−0.953882	+	0.300180i	$0.902953\pi$
$992$	−682862.	+	682862.i	−0.693920	+	0.693920i
$993$	−28217.7	+	519565.i	−0.0286170	+	0.526916i
$994$		−	201196.i		−	0.203633i
$995$	−204750.			−0.206813
$996$	−976624.	−	53040.7i	−0.984484	−	0.0534676i
$997$	−580051.	−	580051.i	−0.583547	−	0.583547i	0.352329	−	0.935876i	$-0.385390\pi$
$997$	−580051.	−	580051.i	−0.583547	−	0.583547i	−0.935876	+	0.352329i	$0.885390\pi$
$998$	−724180.	−	724180.i	−0.727086	−	0.727086i
$999$	203732.	−	146256.i	0.204140	−	0.146549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.5.f.a.38.20	yes	44
3.2	odd	2	inner	51.5.f.a.38.3	✓	44
17.13	even	4	inner	51.5.f.a.47.3	yes	44
51.47	odd	4	inner	51.5.f.a.47.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.5.f.a.38.3	✓	44	3.2	odd	2	inner
51.5.f.a.38.20	yes	44	1.1	even	1	trivial
51.5.f.a.47.3	yes	44	17.13	even	4	inner
51.5.f.a.47.20	yes	44	51.47	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+6.32469 q^{2} +(8.98676 + 0.488073i) q^{3} +24.0018 q^{4} +(-17.5527 - 17.5527i) q^{5} +(56.8385 + 3.08692i) q^{6} +(2.97942 + 2.97942i) q^{7} +50.6087 q^{8} +(80.5236 + 8.77239i) q^{9} +O(q^{10})\)	\(q+6.32469 q^{2} +(8.98676 + 0.488073i) q^{3} +24.0018 q^{4} +(-17.5527 - 17.5527i) q^{5} +(56.8385 + 3.08692i) q^{6} +(2.97942 + 2.97942i) q^{7} +50.6087 q^{8} +(80.5236 + 8.77239i) q^{9} +(-111.015 - 111.015i) q^{10} +(-162.427 + 162.427i) q^{11} +(215.698 + 11.7146i) q^{12} +3.77394 q^{13} +(18.8439 + 18.8439i) q^{14} +(-149.175 - 166.309i) q^{15} -63.9437 q^{16} +(217.840 + 189.912i) q^{17} +(509.287 + 55.4827i) q^{18} -434.838i q^{19} +(-421.295 - 421.295i) q^{20} +(25.3212 + 28.2295i) q^{21} +(-1027.30 + 1027.30i) q^{22} +(40.0377 - 40.0377i) q^{23} +(454.808 + 24.7008i) q^{24} -8.80729i q^{25} +23.8690 q^{26} +(719.364 + 118.137i) q^{27} +(71.5113 + 71.5113i) q^{28} +(-188.760 - 188.760i) q^{29} +(-943.484 - 1051.85i) q^{30} +(562.413 - 562.413i) q^{31} -1214.16 q^{32} +(-1538.96 + 1380.41i) q^{33} +(1377.77 + 1201.14i) q^{34} -104.594i q^{35} +(1932.71 + 210.553i) q^{36} +(243.262 - 243.262i) q^{37} -2750.22i q^{38} +(33.9155 + 1.84196i) q^{39} +(-888.318 - 888.318i) q^{40} +(-1779.90 + 1779.90i) q^{41} +(160.149 + 178.543i) q^{42} +316.313i q^{43} +(-3898.52 + 3898.52i) q^{44} +(-1259.42 - 1567.38i) q^{45} +(253.226 - 253.226i) q^{46} -318.493i q^{47} +(-574.646 - 31.2092i) q^{48} -2383.25i q^{49} -55.7034i q^{50} +(1864.99 + 1813.02i) q^{51} +90.5813 q^{52} +3970.87 q^{53} +(4549.76 + 747.179i) q^{54} +5702.04 q^{55} +(150.785 + 150.785i) q^{56} +(212.233 - 3907.78i) q^{57} +(-1193.85 - 1193.85i) q^{58} +3781.04 q^{59} +(-3580.45 - 3991.70i) q^{60} +(4985.82 + 4985.82i) q^{61} +(3557.09 - 3557.09i) q^{62} +(213.777 + 266.050i) q^{63} -6656.11 q^{64} +(-66.2428 - 66.2428i) q^{65} +(-9733.48 + 8730.68i) q^{66} +3570.56 q^{67} +(5228.55 + 4558.22i) q^{68} +(379.350 - 340.268i) q^{69} -661.523i q^{70} +(-5338.49 - 5338.49i) q^{71} +(4075.19 + 443.959i) q^{72} +(-3116.59 + 3116.59i) q^{73} +(1538.56 - 1538.56i) q^{74} +(4.29860 - 79.1490i) q^{75} -10436.9i q^{76} -967.874 q^{77} +(214.505 + 11.6498i) q^{78} +(-3478.45 - 3478.45i) q^{79} +(1122.38 + 1122.38i) q^{80} +(6407.09 + 1412.77i) q^{81} +(-11257.3 + 11257.3i) q^{82} -4527.74 q^{83} +(607.752 + 677.558i) q^{84} +(-490.217 - 7157.14i) q^{85} +2000.58i q^{86} +(-1604.21 - 1788.47i) q^{87} +(-8220.19 + 8220.19i) q^{88} +9568.91i q^{89} +(-7965.48 - 9913.22i) q^{90} +(11.2442 + 11.2442i) q^{91} +(960.975 - 960.975i) q^{92} +(5328.77 - 4779.77i) q^{93} -2014.37i q^{94} +(-7632.57 + 7632.57i) q^{95} +(-10911.4 - 592.601i) q^{96} +(-9237.30 + 9237.30i) q^{97} -15073.3i q^{98} +(-14504.0 + 11654.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7}+O(q^{10}) \) 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7	\( 44 q + 6 q^{3} + 312 q^{4} - 2 q^{6} - 4 q^{7} + 288 q^{10} - 234 q^{12} + 92 q^{13} + 960 q^{16} - 580 q^{18} - 1856 q^{21} + 120 q^{22} - 10 q^{24} + 378 q^{27} + 1648 q^{28} - 1248 q^{30} + 808 q^{31} + 2520 q^{33} - 5016 q^{34} - 5560 q^{37} + 152 q^{39} - 7020 q^{40} - 2696 q^{45} - 6620 q^{46} - 926 q^{48} + 11810 q^{51} + 5504 q^{52} + 6250 q^{54} + 9740 q^{55} + 16704 q^{57} + 4316 q^{58} + 9304 q^{61} + 27608 q^{63} - 6176 q^{64} + 23912 q^{67} - 3444 q^{69} - 54204 q^{72} + 14216 q^{73} - 5242 q^{75} - 25516 q^{78} + 4052 q^{79} + 6796 q^{81} + 14708 q^{82} - 59208 q^{84} - 32480 q^{85} - 28412 q^{88} - 21312 q^{90} - 38772 q^{91} - 56806 q^{96} - 92448 q^{97} - 18072 q^{99}+O(q^{100}) \) 44 * q + 6 * q^3 + 312 * q^4 - 2 * q^6 - 4 * q^7 + 288 * q^10 - 234 * q^12 + 92 * q^13 + 960 * q^16 - 580 * q^18 - 1856 * q^21 + 120 * q^22 - 10 * q^24 + 378 * q^27 + 1648 * q^28 - 1248 * q^30 + 808 * q^31 + 2520 * q^33 - 5016 * q^34 - 5560 * q^37 + 152 * q^39 - 7020 * q^40 - 2696 * q^45 - 6620 * q^46 - 926 * q^48 + 11810 * q^51 + 5504 * q^52 + 6250 * q^54 + 9740 * q^55 + 16704 * q^57 + 4316 * q^58 + 9304 * q^61 + 27608 * q^63 - 6176 * q^64 + 23912 * q^67 - 3444 * q^69 - 54204 * q^72 + 14216 * q^73 - 5242 * q^75 - 25516 * q^78 + 4052 * q^79 + 6796 * q^81 + 14708 * q^82 - 59208 * q^84 - 32480 * q^85 - 28412 * q^88 - 21312 * q^90 - 38772 * q^91 - 56806 * q^96 - 92448 * q^97 - 18072 * q^99

Introduction

L-functions

Modular forms

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Database

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