LMFDB - Embedded newform 65.5.h.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(12,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("65.12");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.h (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:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.1
Character	$\chi$	$=$	65.12
Dual form			65.5.h.a.38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.46439 + 5.46439i) q^{2} +(3.27217 - 3.27217i) q^{3} -43.7192i q^{4} +(-8.57761 - 23.4824i) q^{5} +35.7609i q^{6} +(-25.7773 + 25.7773i) q^{7} +(151.468 + 151.468i) q^{8} +59.5857i q^{9} +O(q^{10})$	\(q+(-5.46439 + 5.46439i) q^{2} +(3.27217 - 3.27217i) q^{3} -43.7192i q^{4} +(-8.57761 - 23.4824i) q^{5} +35.7609i q^{6} +(-25.7773 + 25.7773i) q^{7} +(151.468 + 151.468i) q^{8} +59.5857i q^{9} +(175.189 + 81.4458i) q^{10} -21.4514i q^{11} +(-143.057 - 143.057i) q^{12} +(-16.4121 + 168.201i) q^{13} -281.715i q^{14} +(-104.906 - 48.7712i) q^{15} -955.859 q^{16} +(343.703 + 343.703i) q^{17} +(-325.600 - 325.600i) q^{18} -51.7835 q^{19} +(-1026.63 + 375.006i) q^{20} +168.696i q^{21} +(117.219 + 117.219i) q^{22} +(252.501 - 252.501i) q^{23} +991.262 q^{24} +(-477.849 + 402.846i) q^{25} +(-829.435 - 1008.80i) q^{26} +(460.021 + 460.021i) q^{27} +(1126.96 + 1126.96i) q^{28} -344.204i q^{29} +(839.753 - 306.743i) q^{30} +1819.95i q^{31} +(2799.69 - 2799.69i) q^{32} +(-70.1928 - 70.1928i) q^{33} -3756.25 q^{34} +(826.422 + 384.206i) q^{35} +2605.04 q^{36} +(136.298 - 136.298i) q^{37} +(282.966 - 282.966i) q^{38} +(496.680 + 604.087i) q^{39} +(2257.61 - 4856.08i) q^{40} -1169.94i q^{41} +(-921.820 - 921.820i) q^{42} +(-1026.44 + 1026.44i) q^{43} -937.838 q^{44} +(1399.22 - 511.103i) q^{45} +2759.53i q^{46} +(-1088.17 + 1088.17i) q^{47} +(-3127.74 + 3127.74i) q^{48} +1072.06i q^{49} +(409.845 - 4812.47i) q^{50} +2249.31 q^{51} +(7353.62 + 717.524i) q^{52} +(-1626.30 + 1626.30i) q^{53} -5027.47 q^{54} +(-503.731 + 184.002i) q^{55} -7808.90 q^{56} +(-169.445 + 169.445i) q^{57} +(1880.87 + 1880.87i) q^{58} +665.197 q^{59} +(-2132.23 + 4586.41i) q^{60} -2881.26 q^{61} +(-9944.91 - 9944.91i) q^{62} +(-1535.96 - 1535.96i) q^{63} +15303.5i q^{64} +(4090.55 - 1057.37i) q^{65} +767.122 q^{66} +(4241.70 - 4241.70i) q^{67} +(15026.4 - 15026.4i) q^{68} -1652.45i q^{69} +(-6615.35 + 2416.44i) q^{70} -1599.66i q^{71} +(-9025.36 + 9025.36i) q^{72} +(880.019 + 880.019i) q^{73} +1489.57i q^{74} +(-245.422 + 2881.79i) q^{75} +2263.93i q^{76} +(552.960 + 552.960i) q^{77} +(-6015.02 - 586.912i) q^{78} -8117.62i q^{79} +(8198.99 + 22445.9i) q^{80} -1815.91 q^{81} +(6393.03 + 6393.03i) q^{82} +(5953.72 + 5953.72i) q^{83} +7375.24 q^{84} +(5122.82 - 11019.1i) q^{85} -11217.7i q^{86} +(-1126.30 - 1126.30i) q^{87} +(3249.21 - 3249.21i) q^{88} +7869.21 q^{89} +(-4853.01 + 10438.7i) q^{90} +(-3912.72 - 4758.84i) q^{91} +(-11039.1 - 11039.1i) q^{92} +(5955.19 + 5955.19i) q^{93} -11892.4i q^{94} +(444.179 + 1216.00i) q^{95} -18322.2i q^{96} +(-10559.4 + 10559.4i) q^{97} +(-5858.15 - 5858.15i) q^{98} +1278.20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3}+O(q^{10}) $ 52 * q - 4 * q^3	$ 52 q - 4 q^{3} + 36 q^{10} + 24 q^{12} - 82 q^{13} - 1464 q^{16} + 356 q^{17} + 2440 q^{22} + 1136 q^{23} + 1172 q^{25} - 3580 q^{26} - 880 q^{27} + 3096 q^{30} + 1616 q^{35} - 5672 q^{36} - 5828 q^{38} + 8072 q^{40} - 1512 q^{42} - 7744 q^{43} + 4996 q^{48} + 24856 q^{51} + 15132 q^{52} - 19144 q^{53} - 12668 q^{55} - 2232 q^{56} - 3128 q^{61} - 1380 q^{62} - 18530 q^{65} - 3240 q^{66} + 29576 q^{68} - 25624 q^{75} - 28740 q^{77} + 51516 q^{78} - 34844 q^{81} + 11180 q^{82} + 8420 q^{87} + 31980 q^{88} + 75392 q^{90} - 9720 q^{91} - 70436 q^{92} + 12184 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 + 36 * q^10 + 24 * q^12 - 82 * q^13 - 1464 * q^16 + 356 * q^17 + 2440 * q^22 + 1136 * q^23 + 1172 * q^25 - 3580 * q^26 - 880 * q^27 + 3096 * q^30 + 1616 * q^35 - 5672 * q^36 - 5828 * q^38 + 8072 * q^40 - 1512 * q^42 - 7744 * q^43 + 4996 * q^48 + 24856 * q^51 + 15132 * q^52 - 19144 * q^53 - 12668 * q^55 - 2232 * q^56 - 3128 * q^61 - 1380 * q^62 - 18530 * q^65 - 3240 * q^66 + 29576 * q^68 - 25624 * q^75 - 28740 * q^77 + 51516 * q^78 - 34844 * q^81 + 11180 * q^82 + 8420 * q^87 + 31980 * q^88 + 75392 * q^90 - 9720 * q^91 - 70436 * q^92 + 12184 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−5.46439	+	5.46439i	−1.36610	+	1.36610i	−0.500172	+	0.865926i	$0.666730\pi$
$2$	−5.46439	+	5.46439i	−1.36610	+	1.36610i	−0.865926	+	0.500172i	$0.833270\pi$
$3$	3.27217	−	3.27217i	0.363575	−	0.363575i	−0.501552	−	0.865127i	$-0.667238\pi$
$3$	3.27217	−	3.27217i	0.363575	−	0.363575i	0.865127	+	0.501552i	$0.167238\pi$
$4$		−	43.7192i		−	2.73245i
$5$	−8.57761	−	23.4824i	−0.343104	−	0.939297i
$5$	−8.57761	−	23.4824i	−0.343104	−	0.939297i
$6$			35.7609i			0.993358i
$7$	−25.7773	+	25.7773i	−0.526068	+	0.526068i	−0.919398	−	0.393330i	$-0.871323\pi$
$7$	−25.7773	+	25.7773i	−0.526068	+	0.526068i	0.393330	+	0.919398i	$0.371323\pi$
$8$	151.468	+	151.468i	2.36669	+	2.36669i
$9$			59.5857i			0.735627i
$10$	175.189	+	81.4458i	1.75189	+	0.814458i
$11$		−	21.4514i		−	0.177284i	−0.996064	−	0.0886422i	$-0.971747\pi$
$11$		−	21.4514i		−	0.177284i	0.996064	−	0.0886422i	$-0.0282528\pi$
$12$	−143.057	−	143.057i	−0.993450	−	0.993450i
$13$	−16.4121	+	168.201i	−0.0971131	+	0.995273i
$13$	−16.4121	+	168.201i	−0.0971131	+	0.995273i
$14$		−	281.715i		−	1.43732i
$15$	−104.906	−	48.7712i	−0.466249	−	0.216761i
$16$	−955.859			−3.73382
$17$	343.703	+	343.703i	1.18928	+	1.18928i	0.977266	+	0.212016i	$0.0680029\pi$
$17$	343.703	+	343.703i	1.18928	+	1.18928i	0.212016	+	0.977266i	$0.431997\pi$
$18$	−325.600	−	325.600i	−1.00494	−	1.00494i
$19$	−51.7835			−0.143445			−0.0717223	−	0.997425i	$-0.522850\pi$
$19$	−51.7835			−0.143445			−0.0717223	+	0.997425i	$0.522850\pi$
$20$	−1026.63	+	375.006i	−2.56658	+	0.937515i
$21$			168.696i			0.382530i
$22$	117.219	+	117.219i	0.242188	+	0.242188i
$23$	252.501	−	252.501i	0.477317	−	0.477317i	−0.426955	−	0.904273i	$-0.640414\pi$
$23$	252.501	−	252.501i	0.477317	−	0.477317i	0.904273	+	0.426955i	$0.140414\pi$
$24$	991.262			1.72094
$25$	−477.849	+	402.846i	−0.764559	+	0.644554i
$26$	−829.435	−	1008.80i	−1.22697	−	1.49231i
$27$	460.021	+	460.021i	0.631030	+	0.631030i
$28$	1126.96	+	1126.96i	1.43745	+	1.43745i
$29$		−	344.204i		−	0.409280i	−0.978837	−	0.204640i	$-0.934398\pi$
$29$		−	344.204i		−	0.409280i	0.978837	−	0.204640i	$-0.0656023\pi$
$30$	839.753	−	306.743i	0.933058	−	0.340826i
$31$			1819.95i			1.89381i	0.321518	+	0.946904i	$0.395807\pi$
$31$			1819.95i			1.89381i	−0.321518	+	0.946904i	$0.604193\pi$
$32$	2799.69	−	2799.69i	2.73407	−	2.73407i
$33$	−70.1928	−	70.1928i	−0.0644562	−	0.0644562i
$34$	−3756.25			−3.24935
$35$	826.422	+	384.206i	0.674630	+	0.313638i
$36$	2605.04			2.01006
$37$	136.298	−	136.298i	0.0995602	−	0.0995602i	−0.655572	−	0.755132i	$-0.727573\pi$
$37$	136.298	−	136.298i	0.0995602	−	0.0995602i	0.755132	+	0.655572i	$0.227573\pi$
$38$	282.966	−	282.966i	0.195960	−	0.195960i
$39$	496.680	+	604.087i	0.326549	+	0.397164i
$40$	2257.61	−	4856.08i	1.41101	−	3.03505i
$41$		−	1169.94i		−	0.695981i	−0.937498	−	0.347990i	$-0.886864\pi$
$41$		−	1169.94i		−	0.695981i	0.937498	−	0.347990i	$-0.113136\pi$
$42$	−921.820	−	921.820i	−0.522574	−	0.522574i
$43$	−1026.44	+	1026.44i	−0.555130	+	0.555130i	−0.927917	−	0.372787i	$-0.878402\pi$
$43$	−1026.44	+	1026.44i	−0.555130	+	0.555130i	0.372787	+	0.927917i	$0.378402\pi$
$44$	−937.838			−0.484420
$45$	1399.22	−	511.103i	0.690972	−	0.252397i
$46$			2759.53i			1.30412i
$47$	−1088.17	+	1088.17i	−0.492608	+	0.492608i	−0.909127	−	0.416519i	$-0.863250\pi$
$47$	−1088.17	+	1088.17i	−0.492608	+	0.492608i	0.416519	+	0.909127i	$0.363250\pi$
$48$	−3127.74	+	3127.74i	−1.35752	+	1.35752i
$49$			1072.06i			0.446505i
$50$	409.845	−	4812.47i	0.163938	−	1.92499i
$51$	2249.31			0.864786
$52$	7353.62	+	717.524i	2.71953	+	0.265357i
$53$	−1626.30	+	1626.30i	−0.578959	+	0.578959i	−0.934616	−	0.355657i	$-0.884257\pi$
$53$	−1626.30	+	1626.30i	−0.578959	+	0.578959i	0.355657	+	0.934616i	$0.384257\pi$
$54$	−5027.47			−1.72410
$55$	−503.731	+	184.002i	−0.166523	+	0.0608271i
$56$	−7808.90			−2.49008
$57$	−169.445	+	169.445i	−0.0521529	+	0.0521529i
$58$	1880.87	+	1880.87i	0.559116	+	0.559116i
$59$	665.197			0.191094			0.0955468	−	0.995425i	$-0.469540\pi$
$59$	665.197			0.191094			0.0955468	+	0.995425i	$0.469540\pi$
$60$	−2132.23	+	4586.41i	−0.592287	+	1.27400i
$61$	−2881.26			−0.774324			−0.387162	−	0.922012i	$-0.626545\pi$
$61$	−2881.26			−0.774324			−0.387162	+	0.922012i	$0.626545\pi$
$62$	−9944.91	−	9944.91i	−2.58713	−	2.58713i
$63$	−1535.96	−	1535.96i	−0.386990	−	0.386990i
$64$			15303.5i			3.73621i
$65$	4090.55	−	1057.37i	0.968177	−	0.250265i
$66$	767.122			0.176107
$67$	4241.70	−	4241.70i	0.944909	−	0.944909i	−0.0536504	−	0.998560i	$-0.517086\pi$
$67$	4241.70	−	4241.70i	0.944909	−	0.944909i	0.998560	+	0.0536504i	$0.0170856\pi$
$68$	15026.4	−	15026.4i	3.24965	−	3.24965i
$69$		−	1652.45i		−	0.347081i
$70$	−6615.35	+	2416.44i	−1.35007	+	0.493151i
$71$		−	1599.66i		−	0.317330i	−0.987332	−	0.158665i	$-0.949281\pi$
$71$		−	1599.66i		−	0.317330i	0.987332	−	0.158665i	$-0.0507189\pi$
$72$	−9025.36	+	9025.36i	−1.74100	+	1.74100i
$73$	880.019	+	880.019i	0.165138	+	0.165138i	0.784838	−	0.619701i	$-0.212746\pi$
$73$	880.019	+	880.019i	0.165138	+	0.165138i	−0.619701	+	0.784838i	$0.712746\pi$
$74$			1489.57i			0.272018i
$75$	−245.422	+	2881.79i	−0.0436306	+	0.512318i
$76$			2263.93i			0.391955i
$77$	552.960	+	552.960i	0.0932637	+	0.0932637i
$78$	−6015.02	−	586.912i	−0.988663	−	0.0964681i
$79$		−	8117.62i		−	1.30069i	−0.759638	−	0.650346i	$-0.774624\pi$
$79$		−	8117.62i		−	1.30069i	0.759638	−	0.650346i	$-0.225376\pi$
$80$	8198.99	+	22445.9i	1.28109	+	3.50717i
$81$	−1815.91			−0.276773
$82$	6393.03	+	6393.03i	0.950778	+	0.950778i
$83$	5953.72	+	5953.72i	0.864236	+	0.864236i	0.991827	−	0.127591i	$-0.0407245\pi$
$83$	5953.72	+	5953.72i	0.864236	+	0.864236i	−0.127591	+	0.991827i	$0.540725\pi$
$84$	7375.24			1.04524
$85$	5122.82	−	11019.1i	0.709041	−	1.52514i
$86$		−	11217.7i		−	1.51672i
$87$	−1126.30	−	1126.30i	−0.148804	−	0.148804i
$88$	3249.21	−	3249.21i	0.419578	−	0.419578i
$89$	7869.21			0.993462			0.496731	−	0.867905i	$-0.334534\pi$
$89$	7869.21			0.993462			0.496731	+	0.867905i	$0.334534\pi$
$90$	−4853.01	+	10438.7i	−0.599137	+	1.28873i
$91$	−3912.72	−	4758.84i	−0.472493	−	0.574670i
$92$	−11039.1	−	11039.1i	−1.30424	−	1.30424i
$93$	5955.19	+	5955.19i	0.688541	+	0.688541i
$94$		−	11892.4i		−	1.34590i
$95$	444.179	+	1216.00i	0.0492165	+	0.134737i
$96$		−	18322.2i		−	1.98808i
$97$	−10559.4	+	10559.4i	−1.12227	+	1.12227i	−0.130869	+	0.991400i	$0.541777\pi$
$97$	−10559.4	+	10559.4i	−1.12227	+	1.12227i	−0.991400	+	0.130869i	$0.958223\pi$
$98$	−5858.15	−	5858.15i	−0.609970	−	0.609970i
$99$	1278.20			0.130415
$100$	17612.1	+	20891.2i	1.76121	+	2.08912i
$101$	7415.57			0.726946			0.363473	−	0.931605i	$-0.381591\pi$
$101$	7415.57			0.726946			0.363473	+	0.931605i	$0.381591\pi$
$102$	−12291.1	+	12291.1i	−1.18138	+	1.18138i
$103$	−7107.33	+	7107.33i	−0.669934	+	0.669934i	−0.957701	−	0.287767i	$-0.907087\pi$
$103$	−7107.33	+	7107.33i	−0.669934	+	0.669934i	0.287767	+	0.957701i	$0.407087\pi$
$104$	−27963.1	+	22991.2i	−2.58534	+	2.12567i
$105$	3961.39	−	1447.01i	0.359310	−	0.131248i
$106$		−	17773.4i		−	1.58183i
$107$	−9309.81	−	9309.81i	−0.813155	−	0.813155i	0.171951	−	0.985106i	$-0.444993\pi$
$107$	−9309.81	−	9309.81i	−0.813155	−	0.813155i	−0.985106	+	0.171951i	$0.944993\pi$
$108$	20111.7	−	20111.7i	1.72426	−	1.72426i
$109$	−13781.1			−1.15993			−0.579965	−	0.814641i	$-0.696934\pi$
$109$	−13781.1			−1.15993			−0.579965	+	0.814641i	$0.696934\pi$
$110$	1747.13	−	3758.04i	0.144391	−	0.310582i
$111$		−	891.981i		−	0.0723952i
$112$	24639.5	−	24639.5i	1.96424	−	1.96424i
$113$	−11087.8	+	11087.8i	−0.868336	+	0.868336i	−0.992288	−	0.123952i	$-0.960443\pi$
$113$	−11087.8	+	11087.8i	−0.868336	+	0.868336i	0.123952	+	0.992288i	$0.460443\pi$
$114$		−	1851.83i		−	0.142492i
$115$	−8095.19	−	3763.48i	−0.612112	−	0.284573i
$116$	−15048.3			−1.11834
$117$	−10022.4	−	977.928i	−0.732149	−	0.0714390i
$118$	−3634.90	+	3634.90i	−0.261053	+	0.261053i
$119$	−17719.5			−1.25129
$120$	−8502.66	−	23277.2i	−0.590463	−	1.61648i
$121$	14180.8			0.968570
$122$	15744.3	−	15744.3i	1.05780	−	1.05780i
$123$	−3828.26	−	3828.26i	−0.253041	−	0.253041i
$124$	79566.6			5.17473
$125$	13558.6	+	7765.60i	0.867751	+	0.496998i
$126$	16786.2			1.05733
$127$	13894.3	+	13894.3i	0.861448	+	0.861448i	0.991506	−	0.130058i	$-0.0415165\pi$
$127$	13894.3	+	13894.3i	0.861448	+	0.861448i	−0.130058	+	0.991506i	$0.541516\pi$
$128$	−38829.2	−	38829.2i	−2.36995	−	2.36995i
$129$			6717.35i			0.403663i
$130$	−16574.5	+	28130.2i	−0.980739	+	1.66451i
$131$	21883.2			1.27517			0.637584	−	0.770381i	$-0.279934\pi$
$131$	21883.2			1.27517			0.637584	+	0.770381i	$0.279934\pi$
$132$	−3068.77	+	3068.77i	−0.176123	+	0.176123i
$133$	1334.84	−	1334.84i	0.0754617	−	0.0754617i
$134$			46356.6i			2.58168i
$135$	6856.53	−	14748.3i	0.376216	−	0.809234i
$136$			104120.i			5.62933i
$137$	−12071.4	+	12071.4i	−0.643156	+	0.643156i	−0.951330	−	0.308174i	$-0.900282\pi$
$137$	−12071.4	+	12071.4i	−0.643156	+	0.643156i	0.308174	+	0.951330i	$0.400282\pi$
$138$	9029.65	+	9029.65i	0.474147	+	0.474147i
$139$		−	13504.0i		−	0.698927i	−0.936950	−	0.349463i	$-0.886364\pi$
$139$		−	13504.0i		−	0.698927i	0.936950	−	0.349463i	$-0.113636\pi$
$140$	16797.2	−	36130.5i	0.856999	−	1.84339i
$141$			7121.37i			0.358200i
$142$	8741.17	+	8741.17i	0.433504	+	0.433504i
$143$	3608.15	+	352.063i	0.176446	+	0.0172166i
$144$		−	56955.6i		−	2.74670i
$145$	−8082.75	+	2952.45i	−0.384435	+	0.140426i
$146$	−9617.54			−0.451189
$147$	3507.96	+	3507.96i	0.162338	+	0.162338i
$148$	−5958.83	−	5958.83i	−0.272043	−	0.272043i
$149$	−17291.8			−0.778875			−0.389437	−	0.921053i	$-0.627331\pi$
$149$	−17291.8			−0.778875			−0.389437	+	0.921053i	$0.627331\pi$
$150$	−14406.1	−	17088.3i	−0.640273	−	0.759480i
$151$		−	18520.6i		−	0.812271i	−0.913813	−	0.406136i	$-0.866876\pi$
$151$		−	18520.6i		−	0.812271i	0.913813	−	0.406136i	$-0.133124\pi$
$152$	−7843.57	−	7843.57i	−0.339490	−	0.339490i
$153$	−20479.8	+	20479.8i	−0.874867	+	0.874867i
$154$	−6043.18			−0.254815
$155$	42736.8	−	15610.8i	1.77885	−	0.649774i
$156$	26410.2	−	21714.4i	1.08523	−	0.892277i
$157$	−26254.5	−	26254.5i	−1.06513	−	1.06513i	−0.997725	−	0.0674084i	$-0.978527\pi$
$157$	−26254.5	−	26254.5i	−1.06513	−	1.06513i	−0.0674084	−	0.997725i	$-0.521473\pi$
$158$	44357.9	+	44357.9i	1.77687	+	1.77687i
$159$			10643.1i			0.420990i
$160$	−89758.3	−	41728.9i	−3.50618	−	1.63004i
$161$			13017.6i			0.502203i
$162$	9922.83	−	9922.83i	0.378099	−	0.378099i
$163$	−1436.13	−	1436.13i	−0.0540530	−	0.0540530i	0.679564	−	0.733617i	$-0.262169\pi$
$163$	−1436.13	−	1436.13i	−0.0540530	−	0.0540530i	−0.733617	+	0.679564i	$0.762169\pi$
$164$	−51149.0			−1.90173
$165$	−1046.21	+	2250.38i	−0.0384283	+	0.0826587i
$166$	−65066.9			−2.36126
$167$	−11730.1	+	11730.1i	−0.420599	+	0.420599i	−0.885410	−	0.464811i	$-0.846122\pi$
$167$	−11730.1	+	11730.1i	−0.420599	+	0.420599i	0.464811	+	0.885410i	$0.346122\pi$
$168$	−25552.1	+	25552.1i	−0.905332	+	0.905332i
$169$	−28022.3	−	5521.08i	−0.981138	−	0.193308i
$170$	32219.7	+	88205.9i	1.11487	+	3.05211i
$171$		−	3085.56i		−	0.105522i
$172$	44874.9	+	44874.9i	1.51686	+	1.51686i
$173$	13859.2	−	13859.2i	0.463071	−	0.463071i	−0.436590	−	0.899661i	$-0.643814\pi$
$173$	13859.2	−	13859.2i	0.463071	−	0.463071i	0.899661	+	0.436590i	$0.143814\pi$
$174$	12309.1			0.406561
$175$	1933.37	−	22702.0i	0.0631305	−	0.741289i
$176$			20504.5i			0.661949i
$177$	2176.64	−	2176.64i	0.0694768	−	0.0694768i
$178$	−43000.5	+	43000.5i	−1.35717	+	1.35717i
$179$		−	23404.8i		−	0.730464i	−0.930916	−	0.365232i	$-0.880990\pi$
$179$		−	23404.8i		−	0.730464i	0.930916	−	0.365232i	$-0.119010\pi$
$180$	−22345.0	−	61172.7i	−0.689661	−	1.88804i
$181$	13154.0			0.401514			0.200757	−	0.979641i	$-0.435660\pi$
$181$	13154.0			0.401514			0.200757	+	0.979641i	$0.435660\pi$
$182$	47384.8	+	4623.54i	1.43053	+	0.139583i
$183$	−9427.99	+	9427.99i	−0.281525	+	0.281525i
$184$	76491.8			2.25933
$185$	−4369.72	−	2031.50i	−0.127676	−	0.0593571i
$186$	−65083.0			−1.88123
$187$	7372.91	−	7372.91i	0.210841	−	0.210841i
$188$	47573.9	+	47573.9i	1.34603	+	1.34603i
$189$	−23716.2			−0.663930
$190$	−9071.89	−	4217.55i	−0.251299	−	0.116830i
$191$	−6587.32			−0.180569			−0.0902843	−	0.995916i	$-0.528778\pi$
$191$	−6587.32			−0.180569			−0.0902843	+	0.995916i	$0.528778\pi$
$192$	50075.7	+	50075.7i	1.35839	+	1.35839i
$193$	30869.2	+	30869.2i	0.828727	+	0.828727i	0.987341	−	0.158614i	$-0.0507025\pi$
$193$	30869.2	+	30869.2i	0.828727	+	0.828727i	−0.158614	+	0.987341i	$0.550703\pi$
$194$		−	115402.i		−	3.06626i
$195$	9925.10	−	16844.9i	0.261015	−	0.442995i
$196$	46869.5			1.22005
$197$	5312.79	−	5312.79i	0.136896	−	0.136896i	−0.635338	−	0.772234i	$-0.719139\pi$
$197$	5312.79	−	5312.79i	0.136896	−	0.136896i	0.772234	+	0.635338i	$0.219139\pi$
$198$	−6984.58	+	6984.58i	−0.178160	+	0.178160i
$199$			21849.2i			0.551735i	0.961196	+	0.275867i	$0.0889650\pi$
$199$			21849.2i			0.551735i	−0.961196	+	0.275867i	$0.911035\pi$
$200$	−133398.	−	11360.6i	−3.33494	−	0.284014i
$201$		−	27759.2i		−	0.687091i
$202$	−40521.6	+	40521.6i	−0.993079	+	0.993079i
$203$	8872.67	+	8872.67i	0.215309	+	0.215309i
$204$		−	98337.9i		−	2.36298i
$205$	−27473.1	+	10035.3i	−0.653733	+	0.238794i
$206$		−	77674.5i		−	1.83039i
$207$	15045.4	+	15045.4i	0.351127	+	0.351127i
$208$	15687.7	−	160777.i	0.362603	−	3.71617i
$209$			1110.83i			0.0254305i
$210$	−13739.6	+	29553.6i	−0.311555	+	0.670150i
$211$	16504.0			0.370701			0.185351	−	0.982672i	$-0.440658\pi$
$211$	16504.0			0.370701			0.185351	+	0.982672i	$0.440658\pi$
$212$	71100.3	+	71100.3i	1.58198	+	1.58198i
$213$	−5234.36	−	5234.36i	−0.115373	−	0.115373i
$214$	101745.			2.22170
$215$	32907.6	+	15298.8i	0.711900	+	0.330965i
$216$			139357.i			2.98691i
$217$	−46913.4	−	46913.4i	−0.996271	−	0.996271i
$218$	75305.5	−	75305.5i	1.58458	−	1.58458i
$219$	5759.15			0.120080
$220$	8044.41	+	22022.7i	0.166207	+	0.455015i
$221$	−63452.1	+	52170.3i	−1.29916	+	1.06817i
$222$	4874.14	+	4874.14i	0.0988989	+	0.0988989i
$223$	−35780.8	−	35780.8i	−0.719517	−	0.719517i	0.248990	−	0.968506i	$-0.419901\pi$
$223$	−35780.8	−	35780.8i	−0.719517	−	0.719517i	−0.968506	+	0.248990i	$0.919901\pi$
$224$			144337.i			2.87662i
$225$	−24003.9	−	28473.0i	−0.474151	−	0.562430i
$226$		−	121176.i		−	2.37247i
$227$	48899.9	−	48899.9i	0.948978	−	0.948978i	−0.0497826	−	0.998760i	$-0.515853\pi$
$227$	48899.9	−	48899.9i	0.948978	−	0.948978i	0.998760	+	0.0497826i	$0.0158528\pi$
$228$	7407.98	+	7407.98i	0.142505	+	0.142505i
$229$	7286.01			0.138937			0.0694686	−	0.997584i	$-0.477870\pi$
$229$	7286.01			0.138937			0.0694686	+	0.997584i	$0.477870\pi$
$230$	64800.4	−	23670.1i	1.22496	−	0.447451i
$231$	3618.76			0.0678167
$232$	52136.1	−	52136.1i	0.968640	−	0.968640i
$233$	4347.81	−	4347.81i	0.0800864	−	0.0800864i	−0.665929	−	0.746015i	$-0.731965\pi$
$233$	4347.81	−	4347.81i	0.0800864	−	0.0800864i	0.746015	+	0.665929i	$0.231965\pi$
$234$	60110.1	−	49422.5i	1.09778	−	0.902595i
$235$	34886.8	+	16219.0i	0.631722	+	0.293689i
$236$		−	29081.8i		−	0.522153i
$237$	−26562.3	−	26562.3i	−0.472899	−	0.472899i
$238$	96826.1	−	96826.1i	1.70938	−	1.70938i
$239$	15560.7			0.272416			0.136208	−	0.990680i	$-0.456508\pi$
$239$	15560.7			0.272416			0.136208	+	0.990680i	$0.456508\pi$
$240$	100275.	+	46618.3i	1.74089	+	0.809346i
$241$			59296.9i			1.02093i	0.859897	+	0.510467i	$0.170528\pi$
$241$			59296.9i			1.02093i	−0.859897	+	0.510467i	$0.829472\pi$
$242$	−77489.7	+	77489.7i	−1.32316	+	1.32316i
$243$	−43203.7	+	43203.7i	−0.731658	+	0.731658i
$244$			125966.i			2.11580i
$245$	25174.5	−	9195.70i	0.419401	−	0.153198i
$246$	41838.2			0.691358
$247$	849.877	−	8710.05i	0.0139304	−	0.142767i
$248$	−275665.	+	275665.i	−4.48206	+	4.48206i
$249$	38963.2			0.628429
$250$	−116524.	+	31655.3i	−1.86438	+	0.506485i
$251$	85507.8			1.35725			0.678623	−	0.734487i	$-0.262577\pi$
$251$	85507.8			1.35725			0.678623	+	0.734487i	$0.262577\pi$
$252$	−67151.0	+	67151.0i	−1.05743	+	1.05743i
$253$	−5416.50	−	5416.50i	−0.0846209	−	0.0846209i
$254$	−151848.			−2.35364
$255$	−19293.7	−	52819.3i	−0.296712	−	0.812291i
$256$	179500.			2.73896
$257$	−53230.6	−	53230.6i	−0.805926	−	0.805926i	0.178088	−	0.984014i	$-0.443009\pi$
$257$	−53230.6	−	53230.6i	−0.805926	−	0.805926i	−0.984014	+	0.178088i	$0.943009\pi$
$258$	−36706.3	−	36706.3i	−0.551443	−	0.551443i
$259$			7026.79i			0.104751i
$260$	−46227.3	−	178835.i	−0.683835	−	2.64549i
$261$	20509.7			0.301077
$262$	−119578.	+	119578.i	−1.74201	+	1.74201i
$263$	27568.8	−	27568.8i	0.398572	−	0.398572i	−0.479157	−	0.877729i	$-0.659058\pi$
$263$	27568.8	−	27568.8i	0.398572	−	0.398572i	0.877729	+	0.479157i	$0.159058\pi$
$264$		−	21264.0i		−	0.305096i
$265$	52139.1	+	24239.7i	0.742458	+	0.345171i
$266$			14588.2i			0.206176i
$267$	25749.4	−	25749.4i	0.361198	−	0.361198i
$268$	−185444.	−	185444.i	−2.58192	−	2.58192i
$269$		−	4124.20i		−	0.0569947i	−0.999594	−	0.0284974i	$-0.990928\pi$
$269$		−	4124.20i		−	0.0569947i	0.999594	−	0.0284974i	$-0.00907222\pi$
$270$	43123.7	+	118057.i	0.591546	+	1.61944i
$271$		−	70191.5i		−	0.955754i	−0.878427	−	0.477877i	$-0.841406\pi$
$271$		−	70191.5i		−	0.955754i	0.878427	−	0.477877i	$-0.158594\pi$
$272$	−328531.	−	328531.i	−4.44057	−	4.44057i
$273$	−28374.8	−	2768.66i	−0.380722	−	0.0371487i
$274$		−	131926.i		−	1.75723i
$275$	8641.62	+	10250.5i	0.114269	+	0.135544i
$276$	−72243.9			−0.948381
$277$	76645.0	+	76645.0i	0.998905	+	0.998905i	0.999999	−	0.00109408i	$-0.000348258\pi$
$277$	76645.0	+	76645.0i	0.998905	+	0.998905i	−0.00109408	+	0.999999i	$0.500348\pi$
$278$	73791.0	+	73791.0i	0.954803	+	0.954803i
$279$	−108443.			−1.39313
$280$	66981.7	+	183372.i	0.854359	+	2.33893i
$281$			78280.5i			0.991381i	0.868499	+	0.495691i	$0.165085\pi$
$281$			78280.5i			0.991381i	−0.868499	+	0.495691i	$0.834915\pi$
$282$	−38914.0	−	38914.0i	−0.489336	−	0.489336i
$283$	−23247.4	+	23247.4i	−0.290269	+	0.290269i	−0.837187	−	0.546917i	$-0.815801\pi$
$283$	−23247.4	+	23247.4i	−0.290269	+	0.290269i	0.546917	+	0.837187i	$0.315801\pi$
$284$	−69935.8			−0.867087
$285$	5432.41	+	2525.54i	0.0668810	+	0.0310932i
$286$	−21640.2	+	17792.6i	−0.264563	+	0.217524i
$287$	30158.0	+	30158.0i	0.366133	+	0.366133i
$288$	166822.	+	166822.i	2.01126	+	2.01126i
$289$			152742.i			1.82878i
$290$	28034.0	−	60300.7i	0.333341	−	0.717012i
$291$			69104.6i			0.816057i
$292$	38473.7	−	38473.7i	0.451230	−	0.451230i
$293$	16265.4	+	16265.4i	0.189465	+	0.189465i	0.795465	−	0.606000i	$-0.207227\pi$
$293$	16265.4	+	16265.4i	0.189465	+	0.189465i	−0.606000	+	0.795465i	$0.707227\pi$
$294$	−38337.8			−0.443539
$295$	−5705.80	−	15620.4i	−0.0655651	−	0.179494i
$296$	41289.7			0.471257
$297$	9868.10	−	9868.10i	0.111872	−	0.111872i
$298$	94489.2	−	94489.2i	1.06402	−	1.06402i
$299$	38326.9	+	46615.0i	0.428707	+	0.521415i
$300$	125989.	+	10729.7i	1.39988	+	0.119218i
$301$		−	52917.5i		−	0.584072i
$302$	101204.	+	101204.i	1.10964	+	1.10964i
$303$	24265.0	−	24265.0i	0.264299	−	0.264299i
$304$	49497.7			0.535597
$305$	24714.3	+	67659.0i	0.265674	+	0.727321i
$306$		−	223819.i		−	2.39031i
$307$	75978.7	−	75978.7i	0.806148	−	0.806148i	−0.177900	−	0.984049i	$-0.556930\pi$
$307$	75978.7	−	75978.7i	0.806148	−	0.806148i	0.984049	+	0.177900i	$0.0569304\pi$
$308$	24175.0	−	24175.0i	0.254838	−	0.254838i
$309$			46512.8i			0.487142i
$310$	−148227.	+	318834.i	−1.54243	+	3.31774i
$311$	189518.			1.95943			0.979714	−	0.200399i	$-0.0642240\pi$
$311$	189518.			1.95943			0.979714	+	0.200399i	$0.0642240\pi$
$312$	−16268.7	+	166731.i	−0.167126	+	1.71281i
$313$	−12270.0	+	12270.0i	−0.125244	+	0.125244i	−0.766950	−	0.641706i	$-0.778227\pi$
$313$	−12270.0	+	12270.0i	−0.125244	+	0.125244i	0.641706	+	0.766950i	$0.278227\pi$
$314$	286930.			2.91015
$315$	−22893.2	+	49243.0i	−0.230720	+	0.496276i
$316$	−354896.			−3.55407
$317$	−60647.6	+	60647.6i	−0.603525	+	0.603525i	−0.941246	−	0.337721i	$-0.890344\pi$
$317$	−60647.6	+	60647.6i	−0.603525	+	0.603525i	0.337721	+	0.941246i	$0.390344\pi$
$318$	−58157.8	−	58157.8i	−0.575114	−	0.575114i
$319$	−7383.67			−0.0725589
$320$	359363.	−	131267.i	3.50941	−	1.28191i
$321$	−60926.6			−0.591285
$322$	−71133.2	−	71133.2i	−0.686058	−	0.686058i
$323$	−17798.1	−	17798.1i	−0.170596	−	0.170596i
$324$			79389.9i			0.756268i
$325$	−59916.7	−	86986.4i	−0.567259	−	0.823540i
$326$	15695.2			0.147683
$327$	−45094.3	+	45094.3i	−0.421722	+	0.421722i
$328$	177210.	−	177210.i	1.64717	−	1.64717i
$329$		−	56100.3i		−	0.518291i
$330$	−6580.07	−	18013.9i	−0.0604231	−	0.165417i
$331$			128017.i			1.16845i	0.811590	+	0.584227i	$0.198602\pi$
$331$			128017.i			1.16845i	−0.811590	+	0.584227i	$0.801398\pi$
$332$	260292.	−	260292.i	2.36148	−	2.36148i
$333$	8121.41	+	8121.41i	0.0732391	+	0.0732391i
$334$		−	128195.i		−	1.14916i
$335$	−135989.	−	63221.7i	−1.21175	−	0.563348i
$336$		−	161249.i		−	1.42830i
$337$	149373.	+	149373.i	1.31526	+	1.31526i	0.917482	+	0.397777i	$0.130218\pi$
$337$	149373.	+	149373.i	1.31526	+	1.31526i	0.397777	+	0.917482i	$0.369782\pi$
$338$	183294.	−	122955.i	1.60441	−	1.07625i
$339$			72562.4i			0.631411i
$340$	−481747.	−	223966.i	−4.16736	−	1.93742i
$341$	39040.5			0.335743
$342$	16860.7	+	16860.7i	0.144153	+	0.144153i
$343$	−89526.2	−	89526.2i	−0.760960	−	0.760960i
$344$	−310945.			−2.62765
$345$	−38803.6	+	14174.1i	−0.326012	+	0.119085i
$346$			151465.i			1.26520i
$347$	−63874.8	−	63874.8i	−0.530482	−	0.530482i	0.390234	−	0.920716i	$-0.372394\pi$
$347$	−63874.8	−	63874.8i	−0.530482	−	0.530482i	−0.920716	+	0.390234i	$0.872394\pi$
$348$	−49240.7	+	49240.7i	−0.406599	+	0.406599i
$349$	−44220.0			−0.363051			−0.181526	−	0.983386i	$-0.558104\pi$
$349$	−44220.0			−0.363051			−0.181526	+	0.983386i	$0.558104\pi$
$350$	113488.	+	134617.i	0.926431	+	1.09892i
$351$	−84926.0	+	69826.2i	−0.689329	+	0.566766i
$352$	−60057.4	−	60057.4i	−0.484709	−	0.484709i
$353$	−19154.9	−	19154.9i	−0.153720	−	0.153720i	0.626057	−	0.779777i	$-0.284668\pi$
$353$	−19154.9	−	19154.9i	−0.153720	−	0.153720i	−0.779777	+	0.626057i	$0.784668\pi$
$354$			23788.0i			0.189824i
$355$	−37563.9	+	13721.3i	−0.298067	+	0.108877i
$356$		−	344035.i		−	2.71458i
$357$	−57981.2	+	57981.2i	−0.454936	+	0.454936i
$358$	127893.	+	127893.i	0.997886	+	0.997886i
$359$	162120.			1.25791			0.628953	−	0.777443i	$-0.283484\pi$
$359$	162120.			1.25791			0.628953	+	0.777443i	$0.283484\pi$
$360$	289353.	+	134521.i	2.23266	+	1.03797i
$361$	−127639.			−0.979424
$362$	−71878.6	+	71878.6i	−0.548507	+	0.548507i
$363$	46402.2	−	46402.2i	0.352148	−	0.352148i
$364$	−208052.	+	171061.i	−1.57025	+	1.29106i
$365$	13116.5	−	28213.4i	0.0984539	−	0.211773i
$366$		−	103036.i		−	0.769181i
$367$	−11170.3	−	11170.3i	−0.0829340	−	0.0829340i	0.664423	−	0.747357i	$-0.268677\pi$
$367$	−11170.3	−	11170.3i	−0.0829340	−	0.0829340i	−0.747357	+	0.664423i	$0.768677\pi$
$368$	−241355.	+	241355.i	−1.78222	+	1.78222i
$369$	69712.0			0.511982
$370$	34978.7	−	12777.0i	0.255506	−	0.0933306i
$371$		−	83843.2i		−	0.609144i
$372$	260356.	−	260356.i	1.88140	−	1.88140i
$373$	−78344.5	+	78344.5i	−0.563107	+	0.563107i	−0.930189	−	0.367082i	$-0.880357\pi$
$373$	−78344.5	+	78344.5i	−0.563107	+	0.563107i	0.367082	+	0.930189i	$0.380357\pi$
$374$			80576.9i			0.576059i
$375$	69776.6	−	18955.8i	0.496189	−	0.134797i
$376$	−329647.			−2.33171
$377$	57895.6	+	5649.12i	0.407345	+	0.0397464i
$378$	129595.	−	129595.i	0.906993	−	0.906993i
$379$	138532.			0.964431			0.482215	−	0.876053i	$-0.339832\pi$
$379$	138532.			0.964431			0.482215	+	0.876053i	$0.339832\pi$
$380$	53162.6	−	19419.1i	0.368162	−	0.134482i
$381$	90929.1			0.626402
$382$	35995.7	−	35995.7i	0.246674	−	0.246674i
$383$	1673.15	+	1673.15i	0.0114061	+	0.0114061i	0.712787	−	0.701381i	$-0.247433\pi$
$383$	1673.15	+	1673.15i	0.0114061	+	0.0114061i	−0.701381	+	0.712787i	$0.747433\pi$
$384$	−254112.			−1.72331
$385$	8241.77	−	17727.9i	0.0556031	−	0.119601i
$386$	−337363.			−2.26424
$387$	−61160.9	−	61160.9i	−0.408368	−	0.408368i
$388$	461649.	+	461649.i	3.06654	+	3.06654i
$389$		−	18011.5i		−	0.119028i	−0.998227	−	0.0595141i	$-0.981045\pi$
$389$		−	18011.5i		−	0.119028i	0.998227	−	0.0595141i	$-0.0189551\pi$
$390$	37812.4	+	146282.i	0.248602	+	0.961747i
$391$	173570.			1.13533
$392$	−162383.	+	162383.i	−1.05674	+	1.05674i
$393$	71605.5	−	71605.5i	0.463619	−	0.463619i
$394$			58062.3i			0.374026i
$395$	−190621.	+	69629.8i	−1.22174	+	0.446273i
$396$		−	55881.8i		−	0.356353i
$397$	106911.	−	106911.i	0.678331	−	0.678331i	−0.281292	−	0.959622i	$-0.590763\pi$
$397$	106911.	−	106911.i	0.678331	−	0.678331i	0.959622	+	0.281292i	$0.0907628\pi$
$398$	−119393.	−	119393.i	−0.753723	−	0.753723i
$399$		−	8735.67i		−	0.0548719i
$400$	456756.	−	385064.i	2.85473	−	2.40665i
$401$			213.754i			0.00132931i	1.00000		0.000664654i	$0.000211566\pi$
$401$			213.754i			0.00132931i	−1.00000		0.000664654i	$0.999788\pi$
$402$	151687.	+	151687.i	0.938633	+	0.938633i
$403$	−306118.	−	29869.2i	−1.88486	−	0.183914i
$404$		−	324203.i		−	1.98634i
$405$	15576.1	+	42641.9i	0.0949620	+	0.259972i
$406$	−96967.5			−0.588266
$407$	−2923.78	−	2923.78i	−0.0176505	−	0.0176505i
$408$	340699.	+	340699.i	2.04668	+	2.04668i
$409$	−38574.0			−0.230594			−0.115297	−	0.993331i	$-0.536782\pi$
$409$	−38574.0			−0.230594			−0.115297	+	0.993331i	$0.536782\pi$
$410$	95287.0	−	204961.i	0.566847	−	1.21928i
$411$			78999.5i			0.467671i
$412$	310726.	+	310726.i	1.83056	+	1.83056i
$413$	−17147.0	+	17147.0i	−0.100528	+	0.100528i
$414$	−164428.			−0.959348
$415$	88739.1	−	190877.i	0.515251	−	1.10830i
$416$	424963.	+	516861.i	2.45564	+	2.98667i
$417$	−44187.3	−	44187.3i	−0.254112	−	0.254112i
$418$	−6070.01	−	6070.01i	−0.0347406	−	0.0347406i
$419$		−	143973.i		−	0.820074i	−0.912069	−	0.410037i	$-0.865516\pi$
$419$		−	143973.i		−	0.820074i	0.912069	−	0.410037i	$-0.134484\pi$
$420$	−63262.0	−	173189.i	−0.358628	−	0.981795i
$421$			12907.3i			0.0728235i	0.999337	+	0.0364118i	$0.0115928\pi$
$421$			12907.3i			0.0728235i	−0.999337	+	0.0364118i	$0.988407\pi$
$422$	−90184.3	+	90184.3i	−0.506414	+	0.506414i
$423$	−64839.5	−	64839.5i	−0.362376	−	0.362376i
$424$	−492665.			−2.74044
$425$	−302697.	−	25778.6i	−1.67583	−	0.142719i
$426$	57205.2			0.315222
$427$	74271.2	−	74271.2i	0.407347	−	0.407347i
$428$	−407017.	+	407017.i	−2.22190	+	2.22190i
$429$	12958.5	−	10654.5i	0.0704110	−	0.0578920i
$430$	−263419.	+	96221.0i	−1.42466	+	0.520395i
$431$			105904.i			0.570110i	0.958511	+	0.285055i	$0.0920119\pi$
$431$			105904.i			0.570110i	−0.958511	+	0.285055i	$0.907988\pi$
$432$	−439715.	−	439715.i	−2.35616	−	2.35616i
$433$	221220.	−	221220.i	1.17991	−	1.17991i	0.200143	−	0.979767i	$-0.435859\pi$
$433$	221220.	−	221220.i	1.17991	−	1.17991i	0.979767	−	0.200143i	$-0.0641407\pi$
$434$	512707.			2.72201
$435$	−16787.2	+	36109.1i	−0.0887158	+	0.190826i
$436$			602500.i			3.16945i
$437$	−13075.4	+	13075.4i	−0.0684686	+	0.0684686i
$438$	−31470.3	+	31470.3i	−0.164041	+	0.164041i
$439$		−	258166.i		−	1.33958i	−0.742548	−	0.669792i	$-0.766383\pi$
$439$		−	258166.i		−	1.33958i	0.742548	−	0.669792i	$-0.233617\pi$
$440$	−104170.	−	48428.9i	−0.538067	−	0.250149i
$441$	−63879.4			−0.328461
$442$	61648.0	−	631806.i	0.315555	−	3.23399i
$443$	101934.	−	101934.i	0.519411	−	0.519411i	−0.397982	−	0.917393i	$-0.630290\pi$
$443$	101934.	−	101934.i	0.519411	−	0.519411i	0.917393	+	0.397982i	$0.130290\pi$
$444$	−38996.7			−0.197816
$445$	−67499.0	−	184788.i	−0.340861	−	0.933156i
$446$	391041.			1.96586
$447$	−56581.8	+	56581.8i	−0.283179	+	0.283179i
$448$	−394483.	−	394483.i	−1.96550	−	1.96550i
$449$	−157201.			−0.779761			−0.389880	−	0.920865i	$-0.627484\pi$
$449$	−157201.			−0.779761			−0.389880	+	0.920865i	$0.627484\pi$
$450$	286754.	+	24420.9i	1.41607	+	0.120597i
$451$	−25097.0			−0.123387
$452$	484749.	+	484749.i	2.37268	+	2.37268i
$453$	−60602.6	−	60602.6i	−0.295322	−	0.295322i
$454$			534416.i			2.59279i
$455$	−78187.3	+	132700.i	−0.377671	+	0.640983i
$456$	−51331.0			−0.246860
$457$	250364.	−	250364.i	1.19878	−	1.19878i	0.224251	−	0.974531i	$-0.428007\pi$
$457$	250364.	−	250364.i	1.19878	−	1.19878i	0.974531	−	0.224251i	$-0.0719934\pi$
$458$	−39813.6	+	39813.6i	−0.189802	+	0.189802i
$459$			316221.i			1.50095i
$460$	−164536.	+	353915.i	−0.777581	+	1.67257i
$461$		−	170641.i		−	0.802936i	−0.915873	−	0.401468i	$-0.868500\pi$
$461$		−	170641.i		−	0.802936i	0.915873	−	0.401468i	$-0.131500\pi$
$462$	−19774.3	+	19774.3i	−0.0926442	+	0.0926442i
$463$	−163375.	−	163375.i	−0.762122	−	0.762122i	0.214584	−	0.976706i	$-0.431161\pi$
$463$	−163375.	−	163375.i	−0.762122	−	0.762122i	−0.976706	+	0.214584i	$0.931161\pi$
$464$			329011.i			1.52818i
$465$	88761.0	−	190924.i	0.410503	−	0.882986i
$466$			47516.3i			0.218812i
$467$	59093.1	+	59093.1i	0.270959	+	0.270959i	0.829486	−	0.558527i	$-0.188633\pi$
$467$	59093.1	+	59093.1i	0.270959	+	0.270959i	−0.558527	+	0.829486i	$0.688633\pi$
$468$	−42754.2	+	438171.i	−0.195203	+	2.00056i
$469$			218679.i			0.994173i
$470$	−279262.	+	102008.i	−1.26420	+	0.461785i
$471$	−171819.			−0.774512
$472$	100756.	+	100756.i	0.452260	+	0.452260i
$473$	22018.5	+	22018.5i	0.0984159	+	0.0984159i
$474$	290293.			1.29205
$475$	24744.7	−	20860.8i	0.109672	−	0.0924579i
$476$			774680.i			3.41908i
$477$	−96904.1	−	96904.1i	−0.425898	−	0.425898i
$478$	−85029.7	+	85029.7i	−0.372147	+	0.372147i
$479$	199800.			0.870813			0.435406	−	0.900234i	$-0.356605\pi$
$479$	199800.			0.870813			0.435406	+	0.900234i	$0.356605\pi$
$480$	−430249.	+	157160.i	−1.86740	+	0.682120i
$481$	20688.5	+	25162.4i	0.0894210	+	0.108758i
$482$	−324022.	−	324022.i	−1.39470	−	1.39470i
$483$	42595.8	+	42595.8i	0.182588	+	0.182588i
$484$		−	619974.i		−	2.64657i
$485$	338536.	+	157386.i	1.43920	+	0.669088i
$486$		−	472164.i		−	1.99903i
$487$	120594.	−	120594.i	0.508473	−	0.508473i	−0.405584	−	0.914058i	$-0.632932\pi$
$487$	120594.	−	120594.i	0.508473	−	0.508473i	0.914058	+	0.405584i	$0.132932\pi$
$488$	−436420.	−	436420.i	−1.83259	−	1.83259i
$489$	−9398.56			−0.0393046
$490$	−87314.6	+	187812.i	−0.363659	+	0.782226i
$491$	−170182.			−0.705910			−0.352955	−	0.935640i	$-0.614823\pi$
$491$	−170182.			−0.705910			−0.352955	+	0.935640i	$0.614823\pi$
$492$	−167368.	+	167368.i	−0.691422	+	0.691422i
$493$	118304.	−	118304.i	0.486749	−	0.486749i
$494$	42951.1	+	52239.2i	0.176003	+	0.214064i
$495$	−10963.9	−	30015.2i	−0.0447460	−	0.122499i
$496$		−	1.73961e6i		−	7.07114i
$497$	41234.9	+	41234.9i	0.166937	+	0.166937i
$498$	−212910.	+	212910.i	−0.858495	+	0.858495i
$499$	−227089.			−0.912002			−0.456001	−	0.889979i	$-0.650719\pi$
$499$	−227089.			−0.912002			−0.456001	+	0.889979i	$0.650719\pi$
$500$	339506.	−	592771.i	1.35802	−	2.37109i
$501$			76765.7i			0.305838i
$502$	−467248.	+	467248.i	−1.85413	+	1.85413i
$503$	51775.2	−	51775.2i	0.204638	−	0.204638i	−0.597346	−	0.801984i	$-0.703778\pi$
$503$	51775.2	−	51775.2i	0.204638	−	0.204638i	0.801984	+	0.597346i	$0.203778\pi$
$504$		−	465299.i		−	1.83177i
$505$	−63607.9	−	174136.i	−0.249418	−	0.682818i
$506$	59195.8			0.231201
$507$	−109760.	+	73627.9i	−0.426999	+	0.286435i
$508$	607447.	−	607447.i	2.35386	−	2.35386i
$509$	−226873.			−0.875682			−0.437841	−	0.899052i	$-0.644257\pi$
$509$	−226873.			−0.875682			−0.437841	+	0.899052i	$0.644257\pi$
$510$	394053.	+	183197.i	1.51501	+	0.704332i
$511$	−45369.1			−0.173747
$512$	−359593.	+	359593.i	−1.37174	+	1.37174i
$513$	−23821.5	−	23821.5i	−0.0905179	−	0.0905179i
$514$	581746.			2.20195
$515$	227861.	+	105933.i	0.859124	+	0.399410i
$516$	293677.			1.10299
$517$	23342.8	+	23342.8i	0.0873318	+	0.0873318i
$518$	−38397.2	−	38397.2i	−0.143100	−	0.143100i
$519$		−	90699.7i		−	0.336722i
$520$	779747.	+	459431.i	2.88368	+	1.69908i
$521$	−112555.			−0.414656			−0.207328	−	0.978272i	$-0.566477\pi$
$521$	−112555.			−0.414656			−0.207328	+	0.978272i	$0.566477\pi$
$522$	−112073.	+	112073.i	−0.411301	+	0.411301i
$523$	−182033.	+	182033.i	−0.665499	+	0.665499i	−0.956671	−	0.291172i	$-0.905955\pi$
$523$	−182033.	+	182033.i	−0.665499	+	0.665499i	0.291172	+	0.956671i	$0.405955\pi$
$524$		−	956714.i		−	3.48433i
$525$	−67958.5	−	80611.2i	−0.246561	−	0.292467i
$526$			301294.i			1.08898i
$527$	−625521.	+	625521.i	−2.25227	+	2.25227i
$528$	67094.4	+	67094.4i	0.240668	+	0.240668i
$529$			152328.i			0.544337i
$530$	−417364.	+	152454.i	−1.48581	+	0.542733i
$531$			39636.2i			0.140573i
$532$	−58358.1	−	58358.1i	−0.206195	−	0.206195i
$533$	196786.	+	19201.3i	0.692691	+	0.0675889i
$534$			281410.i			0.986863i
$535$	−138761.	+	298473.i	−0.484797	+	1.04279i
$536$	1.28497e6			4.47262
$537$	−76584.6	−	76584.6i	−0.265578	−	0.265578i
$538$	22536.2	+	22536.2i	0.0778604	+	0.0778604i
$539$	22997.2			0.0791584
$540$	−644783.	−	299762.i	−2.21119	−	1.02799i
$541$		−	196412.i		−	0.671078i	−0.942026	−	0.335539i	$-0.891082\pi$
$541$		−	196412.i		−	0.671078i	0.942026	−	0.335539i	$-0.108918\pi$
$542$	383554.	+	383554.i	1.30565	+	1.30565i
$543$	43042.2	−	43042.2i	0.145980	−	0.145980i
$544$	1.92452e6			6.50317
$545$	118209.	+	323615.i	0.397977	+	1.08952i
$546$	170180.	−	139922.i	0.570853	−	0.469355i
$547$	363261.	+	363261.i	1.21407	+	1.21407i	0.969676	+	0.244395i	$0.0785893\pi$
$547$	363261.	+	363261.i	1.21407	+	1.21407i	0.244395	+	0.969676i	$0.421411\pi$
$548$	527752.	+	527752.i	1.75739	+	1.75739i
$549$		−	171682.i		−	0.569613i
$550$	−103234.	−	8791.75i	−0.341270	−	0.0290636i
$551$			17824.1i			0.0587090i
$552$	250294.	−	250294.i	0.821435	−	0.821435i
$553$	209251.	+	209251.i	0.684253	+	0.684253i
$554$	−837637.			−2.72921
$555$	−20945.9	+	7651.07i	−0.0680006	+	0.0248391i
$556$	−590382.			−1.90978
$557$	166835.	−	166835.i	0.537746	−	0.537746i	−0.385120	−	0.922866i	$-0.625840\pi$
$557$	166835.	−	166835.i	0.537746	−	0.537746i	0.922866	+	0.385120i	$0.125840\pi$
$558$	592575.	−	592575.i	1.90316	−	1.90316i
$559$	−155802.	−	189494.i	−0.498596	−	0.606417i
$560$	−789943.	−	367247.i	−2.51895	−	1.17107i
$561$		−	48250.9i		−	0.153313i
$562$	−427755.	−	427755.i	−1.35432	−	1.35432i
$563$	−152542.	+	152542.i	−0.481251	+	0.481251i	−0.905531	−	0.424280i	$-0.860527\pi$
$563$	−152542.	+	152542.i	−0.481251	+	0.481251i	0.424280	+	0.905531i	$0.360527\pi$
$564$	311341.			0.978763
$565$	355475.	+	165261.i	1.11356	+	0.517696i
$566$		−	254066.i		−	0.793073i
$567$	46809.2	−	46809.2i	0.145601	−	0.145601i
$568$	242298.	−	242298.i	0.751022	−	0.751022i
$569$			541255.i			1.67177i	0.548903	+	0.835886i	$0.315046\pi$
$569$			541255.i			1.67177i	−0.548903	+	0.835886i	$0.684954\pi$
$570$	−43485.4	+	15884.2i	−0.133842	+	0.0488896i
$571$	364649.			1.11842			0.559208	−	0.829028i	$-0.311105\pi$
$571$	364649.			1.11842			0.559208	+	0.829028i	$0.311105\pi$
$572$	15391.9	−	157745.i	0.0470436	−	0.482131i
$573$	−21554.9	+	21554.9i	−0.0656502	+	0.0656502i
$574$	−329591.			−1.00035
$575$	−18938.3	+	222376.i	−0.0572802	+	0.672594i
$576$	−911870.			−2.74845
$577$	−219070.	+	219070.i	−0.658008	+	0.658008i	−0.954908	−	0.296900i	$-0.904047\pi$
$577$	−219070.	+	219070.i	−0.658008	+	0.658008i	0.296900	+	0.954908i	$0.404047\pi$
$578$	−834641.	−	834641.i	−2.49830	−	2.49830i
$579$	202019.			0.602608
$580$	129079.	+	353371.i	0.383706	+	1.05045i
$581$	−306942.			−0.909293
$582$	−377614.	−	377614.i	−1.11481	−	1.11481i
$583$	34886.4	+	34886.4i	0.102640	+	0.102640i
$584$			266590.i			0.781661i
$585$	63004.1	+	243738.i	0.184101	+	0.712217i
$586$	−177761.			−0.517655
$587$	163920.	−	163920.i	0.475725	−	0.475725i	−0.428037	−	0.903761i	$-0.640795\pi$
$587$	163920.	−	163920.i	0.475725	−	0.475725i	0.903761	+	0.428037i	$0.140795\pi$
$588$	153365.	−	153365.i	0.443580	−	0.443580i
$589$		−	94243.4i		−	0.271657i
$590$	116535.	+	54177.5i	0.334774	+	0.155638i
$591$		−	34768.7i		−	0.0995438i
$592$	−130282.	+	130282.i	−0.371740	+	0.371740i
$593$	−383865.	−	383865.i	−1.09161	−	1.09161i	−0.995356	−	0.0962586i	$-0.969312\pi$
$593$	−383865.	−	383865.i	−1.09161	−	1.09161i	−0.0962586	−	0.995356i	$-0.530688\pi$
$594$			107846.i			0.305656i
$595$	151991.	+	416096.i	0.429322	+	1.17533i
$596$			755983.i			2.12823i
$597$	71494.5	+	71494.5i	0.200597	+	0.200597i
$598$	−464156.	−	45289.7i	−1.29796	−	0.126648i
$599$		−	424071.i		−	1.18191i	−0.806704	−	0.590956i	$-0.798751\pi$
$599$		−	424071.i		−	1.18191i	0.806704	−	0.590956i	$-0.201249\pi$
$600$	−473674.	+	399326.i	−1.31576	+	1.10924i
$601$	240497.			0.665826			0.332913	−	0.942958i	$-0.391968\pi$
$601$	240497.			0.665826			0.332913	+	0.942958i	$0.391968\pi$
$602$	289162.	+	289162.i	0.797900	+	0.797900i
$603$	252745.	+	252745.i	0.695100	+	0.695100i
$604$	−809705.			−2.21949
$605$	−121638.	−	333001.i	−0.332321	−	0.909775i
$606$			265187.i			0.722117i
$607$	−160115.	−	160115.i	−0.434565	−	0.434565i	0.455613	−	0.890178i	$-0.349420\pi$
$607$	−160115.	−	160115.i	−0.434565	−	0.434565i	−0.890178	+	0.455613i	$0.849420\pi$
$608$	−144978.	+	144978.i	−0.392189	+	0.392189i
$609$	58065.8			0.156562
$610$	−504764.	−	234666.i	−1.35653	−	0.630654i
$611$	−165173.	−	200891.i	−0.442441	−	0.538119i
$612$	895359.	+	895359.i	2.39053	+	2.39053i
$613$	107184.	+	107184.i	0.285240	+	0.285240i	0.835195	−	0.549955i	$-0.185355\pi$
$613$	107184.	+	107184.i	0.285240	+	0.285240i	−0.549955	+	0.835195i	$0.685355\pi$
$614$			830355.i			2.20256i
$615$	−57059.5	+	122734.i	−0.150861	+	0.324501i
$616$			167512.i			0.441453i
$617$	83707.4	−	83707.4i	0.219884	−	0.219884i	−0.588566	−	0.808450i	$-0.700307\pi$
$617$	83707.4	−	83707.4i	0.219884	−	0.219884i	0.808450	+	0.588566i	$0.200307\pi$
$618$	−254164.	−	254164.i	−0.665484	−	0.665484i
$619$	270731.			0.706572			0.353286	−	0.935515i	$-0.385064\pi$
$619$	270731.			0.706572			0.353286	+	0.935515i	$0.385064\pi$
$620$	−682492.	−	1.86842e6i	−1.77547	−	4.86061i
$621$	232311.			0.602403
$622$	−1.03560e6	+	1.03560e6i	−2.67677	+	2.67677i
$623$	−202847.	+	202847.i	−0.522628	+	0.522628i
$624$	−474756.	−	577422.i	−1.21927	−	1.48294i
$625$	66054.6	−	385000.i	0.169100	−	0.985599i
$626$		−	134096.i		−	0.342191i
$627$	3634.83	+	3634.83i	0.00924590	+	0.00924590i
$628$	−1.14782e6	+	1.14782e6i	−2.91042	+	2.91042i
$629$	93691.9			0.236810
$630$	−143985.	−	394181.i	−0.362775	−	0.993148i
$631$			397610.i			0.998616i	0.866425	+	0.499308i	$0.166412\pi$
$631$			397610.i			0.998616i	−0.866425	+	0.499308i	$0.833588\pi$
$632$	1.22956e6	−	1.22956e6i	3.07834	−	3.07834i
$633$	54003.9	−	54003.9i	0.134778	−	0.134778i
$634$		−	662805.i		−	1.64895i
$635$	207092.	−	445452.i	0.513589	−	1.10472i
$636$	465305.			1.15033
$637$	−180321.	−	17594.7i	−0.444394	−	0.0433615i
$638$	40347.3	−	40347.3i	0.0991226	−	0.0991226i
$639$	95316.9			0.233436
$640$	−578743.	+	1.24487e6i	−1.41295	+	3.03923i
$641$	418012.			1.01736			0.508678	−	0.860957i	$-0.330134\pi$
$641$	418012.			1.01736			0.508678	+	0.860957i	$0.330134\pi$
$642$	332927.	−	332927.i	0.807754	−	0.807754i
$643$	532319.	+	532319.i	1.28751	+	1.28751i	0.936296	+	0.351212i	$0.114230\pi$
$643$	532319.	+	532319.i	1.28751	+	1.28751i	0.351212	+	0.936296i	$0.385770\pi$
$644$	569118.			1.37224
$645$	157740.	−	57618.8i	0.379159	−	0.138499i
$646$	194512.			0.466102
$647$	−104638.	−	104638.i	−0.249967	−	0.249967i	0.570990	−	0.820957i	$-0.306559\pi$
$647$	−104638.	−	104638.i	−0.249967	−	0.249967i	−0.820957	+	0.570990i	$0.806559\pi$
$648$	−275053.	−	275053.i	−0.655037	−	0.655037i
$649$		−	14269.4i		−	0.0338779i
$650$	802736.	+	147919.i	1.89997	+	0.350104i
$651$	−307018.			−0.724439
$652$	−62786.6	+	62786.6i	−0.147697	+	0.147697i
$653$	−256351.	+	256351.i	−0.601185	+	0.601185i	−0.940627	−	0.339442i	$-0.889762\pi$
$653$	−256351.	+	256351.i	−0.601185	+	0.601185i	0.339442	+	0.940627i	$0.389762\pi$
$654$		−	492826.i		−	1.15223i
$655$	−187705.	−	513870.i	−0.437516	−	1.19776i
$656$			1.11830e6i			2.59867i
$657$	−52436.6	+	52436.6i	−0.121480	+	0.121480i
$658$	306554.	+	306554.i	0.708036	+	0.708036i
$659$			356811.i			0.821613i	0.911723	+	0.410806i	$0.134753\pi$
$659$			356811.i			0.821613i	−0.911723	+	0.410806i	$0.865247\pi$
$660$	98384.9	+	45739.5i	0.225861	+	0.105003i
$661$		−	341864.i		−	0.782439i	−0.920297	−	0.391219i	$-0.872053\pi$
$661$		−	341864.i		−	0.782439i	0.920297	−	0.391219i	$-0.127947\pi$
$662$	−699535.	−	699535.i	−1.59622	−	1.59622i
$663$	−36915.9	+	378337.i	−0.0839821	+	0.860699i
$664$			1.80360e6i			4.09076i
$665$	−42795.1	−	19895.6i	−0.0967722	−	0.0449897i
$666$	−88757.2			−0.200104
$667$	−86911.9	−	86911.9i	−0.195356	−	0.195356i
$668$	512829.	+	512829.i	1.14926	+	1.14926i
$669$	−234162.			−0.523196
$670$	1.08857e6	−	397629.i	2.42496	−	0.885785i
$671$			61807.1i			0.137276i
$672$	472297.	+	472297.i	1.04587	+	1.04587i
$673$	−35979.3	+	35979.3i	−0.0794370	+	0.0794370i	−0.745709	−	0.666272i	$-0.767889\pi$
$673$	−35979.3	+	35979.3i	−0.0794370	+	0.0794370i	0.666272	+	0.745709i	$0.267889\pi$
$674$	−1.63246e6			−3.59355
$675$	−405139.	−	34502.9i	−0.889193	−	0.0757265i
$676$	−241377.	+	1.22511e6i	−0.528205	+	2.68091i
$677$	−44739.7	−	44739.7i	−0.0976148	−	0.0976148i	0.656613	−	0.754228i	$-0.271989\pi$
$677$	−44739.7	−	44739.7i	−0.0976148	−	0.0976148i	−0.754228	+	0.656613i	$0.771989\pi$
$678$	−396509.	−	396509.i	−0.862569	−	0.862569i
$679$		−	544388.i		−	1.18078i
$680$	2.44499e6	−	893102.i	5.28762	−	1.93145i
$681$		−	320018.i		−	0.690049i
$682$	−213332.	+	213332.i	−0.458657	+	0.458657i
$683$	234247.	+	234247.i	0.502150	+	0.502150i	0.912105	−	0.409956i	$-0.134456\pi$
$683$	234247.	+	234247.i	0.502150	+	0.502150i	−0.409956	+	0.912105i	$0.634456\pi$
$684$	−134898.			−0.288333
$685$	387010.	+	179922.i	0.824785	+	0.383445i
$686$	978412.			2.07909
$687$	23841.1	−	23841.1i	0.0505141	−	0.0505141i
$688$	981127.	−	981127.i	2.07276	−	2.07276i
$689$	−246854.	−	300236.i	−0.519998	−	0.632447i
$690$	134585.	−	289491.i	0.282683	−	0.608047i
$691$		−	230428.i		−	0.482590i	−0.970452	−	0.241295i	$-0.922428\pi$
$691$		−	230428.i		−	0.482590i	0.970452	−	0.241295i	$-0.0775721\pi$
$692$	−605915.	−	605915.i	−1.26532	−	1.26532i
$693$	−32948.5	+	32948.5i	−0.0686072	+	0.0686072i
$694$	698074.			1.44938
$695$	−317106.	+	115832.i	−0.656500	+	0.239805i
$696$		−	341197.i		−	0.704346i
$697$	402113.	−	402113.i	0.827718	−	0.827718i
$698$	241636.	−	241636.i	0.495964	−	0.495964i
$699$		−	28453.6i		−	0.0582348i
$700$	−992512.	−	84525.4i	−2.02553	−	0.172501i
$701$	−520603.			−1.05943			−0.529713	−	0.848177i	$-0.677701\pi$
$701$	−520603.			−1.05943			−0.529713	+	0.848177i	$0.677701\pi$
$702$	82511.5	−	845627.i	0.167433	−	1.71595i
$703$	−7057.99	+	7057.99i	−0.0142814	+	0.0142814i
$704$	328282.			0.662371
$705$	167227.	−	61084.4i	0.336456	−	0.122900i
$706$	209340.			0.419994
$707$	−191154.	+	191154.i	−0.382423	+	0.382423i
$708$	−95160.9	−	95160.9i	−0.189842	−	0.189842i
$709$	−420877.			−0.837265			−0.418633	−	0.908156i	$-0.637490\pi$
$709$	−420877.			−0.837265			−0.418633	+	0.908156i	$0.637490\pi$
$710$	130285.	−	280242.i	0.258452	−	0.555926i
$711$	483695.			0.956824
$712$	1.19194e6	+	1.19194e6i	2.35122	+	2.35122i
$713$	459538.	+	459538.i	0.903947	+	0.903947i
$714$		−	633664.i		−	1.24298i
$715$	−22682.0	−	87748.1i	−0.0443680	−	0.171643i
$716$	−1.02324e6			−1.99596
$717$	50917.3	−	50917.3i	0.0990437	−	0.0990437i
$718$	−885888.	+	885888.i	−1.71842	+	1.71842i
$719$		−	503336.i		−	0.973644i	−0.873501	−	0.486822i	$-0.838156\pi$
$719$		−	503336.i		−	0.973644i	0.873501	−	0.486822i	$-0.161844\pi$
$720$	−1.33745e6	+	488543.i	−2.57997	+	0.942405i
$721$		−	366416.i		−	0.704862i
$722$	697472.	−	697472.i	1.33799	−	1.33799i
$723$	194030.	+	194030.i	0.371186	+	0.371186i
$724$		−	575082.i		−	1.09712i
$725$	138661.	+	164478.i	0.263803	+	0.312918i
$726$			507119.i			0.962137i
$727$	−285481.	−	285481.i	−0.540142	−	0.540142i	0.383428	−	0.923571i	$-0.374743\pi$
$727$	−285481.	−	285481.i	−0.540142	−	0.540142i	−0.923571	+	0.383428i	$0.874743\pi$
$728$	128161.	−	1.31347e6i	0.241820	−	2.47831i
$729$			135651.i			0.255252i
$730$	82495.5	+	225843.i	0.154805	+	0.423800i
$731$	−705577.			−1.32041
$732$	412184.	+	412184.i	0.769252	+	0.769252i
$733$	22672.4	+	22672.4i	0.0421978	+	0.0421978i	0.727891	−	0.685693i	$-0.240501\pi$
$733$	22672.4	+	22672.4i	0.0421978	+	0.0421978i	−0.685693	+	0.727891i	$0.740501\pi$
$734$	122078.			0.226592
$735$	52285.5	−	112465.i	0.0967847	−	0.208183i
$736$		−	1.41385e6i		−	2.61004i
$737$	−90990.4	−	90990.4i	−0.167518	−	0.167518i
$738$	−380934.	+	380934.i	−0.699418	+	0.699418i
$739$	259786.			0.475693			0.237847	−	0.971303i	$-0.423558\pi$
$739$	259786.			0.475693			0.237847	+	0.971303i	$0.423558\pi$
$740$	−88815.3	+	191040.i	−0.162190	+	0.348869i
$741$	−25719.9	−	31281.8i	−0.0468417	−	0.0569711i
$742$	458152.	+	458152.i	0.832150	+	0.832150i
$743$	10851.8	+	10851.8i	0.0196573	+	0.0196573i	0.716867	−	0.697210i	$-0.245575\pi$
$743$	10851.8	+	10851.8i	0.0196573	+	0.0196573i	−0.697210	+	0.716867i	$0.745575\pi$
$744$			1.80405e6i			3.25913i
$745$	148322.	+	406053.i	0.267235	+	0.731595i
$746$		−	856211.i		−	1.53852i
$747$	−354757.	+	354757.i	−0.635755	+	0.635755i
$748$	−322337.	−	322337.i	−0.576113	−	0.576113i
$749$	479964.			0.855549
$750$	−277705.	+	484868.i	−0.493697	+	0.861988i
$751$	−105745.			−0.187491			−0.0937455	−	0.995596i	$-0.529884\pi$
$751$	−105745.			−0.187491			−0.0937455	+	0.995596i	$0.529884\pi$
$752$	1.04014e6	−	1.04014e6i	1.83931	−	1.83931i
$753$	279796.	−	279796.i	0.493460	−	0.493460i
$754$	−347233.	+	285495.i	−0.610771	+	0.502176i
$755$	−434909.	+	158863.i	−0.762964	+	0.278694i
$756$			1.03685e6i			1.81415i
$757$	450822.	+	450822.i	0.786708	+	0.786708i	0.980953	−	0.194245i	$-0.0622257\pi$
$757$	450822.	+	450822.i	0.786708	+	0.786708i	−0.194245	+	0.980953i	$0.562226\pi$
$758$	−756992.	+	756992.i	−1.31751	+	1.31751i
$759$	−35447.5			−0.0615321
$760$	−116907.	+	251465.i	−0.202401	+	0.435362i
$761$		−	648161.i		−	1.11921i	−0.828758	−	0.559607i	$-0.810952\pi$
$761$		−	648161.i		−	1.11921i	0.828758	−	0.559607i	$-0.189048\pi$
$762$	−496872.	+	496872.i	−0.855726	+	0.855726i
$763$	355241.	−	355241.i	0.610202	−	0.610202i
$764$			287992.i			0.493394i
$765$	656582.	+	305247.i	1.12193	+	0.521590i
$766$	−18285.5			−0.0311637
$767$	−10917.3	+	111887.i	−0.0185577	+	0.190190i
$768$	587357.	−	587357.i	0.995817	−	0.995817i
$769$	396429.			0.670367			0.335183	−	0.942153i	$-0.391202\pi$
$769$	396429.			0.670367			0.335183	+	0.942153i	$0.391202\pi$
$770$	51836.1	+	141909.i	0.0874280	+	0.239347i
$771$	−348360.			−0.586029
$772$	1.34958e6	−	1.34958e6i	2.26445	−	2.26445i
$773$	89868.4	+	89868.4i	0.150400	+	0.150400i	0.778297	−	0.627897i	$-0.216084\pi$
$773$	89868.4	+	89868.4i	0.150400	+	0.150400i	−0.627897	+	0.778297i	$0.716084\pi$
$774$	668415.			1.11574
$775$	−733160.	−	869661.i	−1.22066	−	1.44793i
$776$	−3.19884e6			−5.31213
$777$	22992.9	+	22992.9i	0.0380848	+	0.0380848i
$778$	98421.7	+	98421.7i	0.162604	+	0.162604i
$779$			60583.8i			0.0998348i
$780$	−736444.	−	433917.i	−1.21046	−	0.713210i
$781$	−34315.0			−0.0562576
$782$	−948456.	+	948456.i	−1.55097	+	1.55097i
$783$	158341.	−	158341.i	0.258268	−	0.258268i
$784$		−	1.02474e6i		−	1.66717i
$785$	−391318.	+	841720.i	−0.635025	+	1.36593i
$786$			782562.i			1.26670i
$787$	−15787.6	+	15787.6i	−0.0254898	+	0.0254898i	−0.719737	−	0.694247i	$-0.755738\pi$
$787$	−15787.6	+	15787.6i	−0.0254898	+	0.0254898i	0.694247	+	0.719737i	$0.255738\pi$
$788$	−232271.	−	232271.i	−0.374061	−	0.374061i
$789$		−	180420.i		−	0.289822i
$790$	661146.	−	1.42212e6i	1.05936	−	2.27867i
$791$		−	571627.i		−	0.913608i
$792$	193607.	+	193607.i	0.308653	+	0.308653i
$793$	47287.6	−	484631.i	0.0751970	−	0.770664i
$794$			1.16841e6i			1.85333i
$795$	249925.	−	91292.0i	0.395435	−	0.144444i
$796$	955230.			1.50759
$797$	−581653.	−	581653.i	−0.915687	−	0.915687i	0.0810247	−	0.996712i	$-0.474181\pi$
$797$	−581653.	−	581653.i	−0.915687	−	0.915687i	−0.996712	+	0.0810247i	$0.974181\pi$
$798$	47735.1	+	47735.1i	0.0749604	+	0.0749604i
$799$	−748015.			−1.17170
$800$	−209985.	+	2.46568e6i	−0.328101	+	3.85262i
$801$			468893.i			0.730817i
$802$	−1168.04	−	1168.04i	−0.00181596	−	0.00181596i
$803$	18877.6	−	18877.6i	0.0292763	−	0.0292763i
$804$	−1.21361e6			−1.87744
$805$	305685.	−	111660.i	0.471718	−	0.172308i
$806$	1.83596e6	−	1.50953e6i	2.82614	−	2.32365i
$807$	−13495.1	−	13495.1i	−0.0207219	−	0.0207219i
$808$	1.12322e6	+	1.12322e6i	1.72046	+	1.72046i
$809$		−	2541.90i		−	0.00388384i	−0.999998	−	0.00194192i	$-0.999382\pi$
$809$		−	2541.90i		−	0.00388384i	0.999998	−	0.00194192i	$-0.000618134\pi$
$810$	−318126.	−	147898.i	−0.484875	−	0.225420i
$811$			914702.i			1.39071i	0.718665	+	0.695357i	$0.244754\pi$
$811$			914702.i			1.39071i	−0.718665	+	0.695357i	$0.755246\pi$
$812$	387906.	−	387906.i	0.588321	−	0.588321i
$813$	−229679.	−	229679.i	−0.347488	−	0.347488i
$814$	31953.4			0.0482246
$815$	−21405.3	+	46042.5i	−0.0322260	+	0.0693177i
$816$	−2.15002e6			−3.22896
$817$	53152.5	−	53152.5i	0.0796305	−	0.0796305i
$818$	210784.	−	210784.i	0.315014	−	0.315014i
$819$	283559.	−	233142.i	0.422742	−	0.347579i
$820$	438736.	+	1.20110e6i	0.652493	+	1.78629i
$821$		−	818145.i		−	1.21379i	−0.794781	−	0.606896i	$-0.792415\pi$
$821$		−	818145.i		−	1.21379i	0.794781	−	0.606896i	$-0.207585\pi$
$822$	−431684.	−	431684.i	−0.638885	−	0.638885i
$823$	22874.7	−	22874.7i	0.0337719	−	0.0337719i	−0.690019	−	0.723791i	$-0.742398\pi$
$823$	22874.7	−	22874.7i	0.0337719	−	0.0337719i	0.723791	+	0.690019i	$0.242398\pi$
$824$	−2.15307e6			−3.17106
$825$	61818.5	+	5264.65i	0.0908260	+	0.00773503i
$826$		−	187396.i		−	0.274663i
$827$	−484402.	+	484402.i	−0.708263	+	0.708263i	−0.966170	−	0.257906i	$-0.916967\pi$
$827$	−484402.	+	484402.i	−0.708263	+	0.708263i	0.257906	+	0.966170i	$0.416967\pi$
$828$	657774.	−	657774.i	0.959437	−	0.959437i
$829$		−	168406.i		−	0.245046i	−0.992466	−	0.122523i	$-0.960901\pi$
$829$		−	168406.i		−	0.245046i	0.992466	−	0.122523i	$-0.0390986\pi$
$830$	558119.	+	1.52793e6i	0.810159	+	2.21793i
$831$	501592.			0.726354
$832$	−2.57407e6	−	251163.i	−3.71855	−	0.362835i
$833$	−368469.	+	368469.i	−0.531020	+	0.531020i
$834$	482914.			0.694285
$835$	376067.	+	174835.i	0.539377	+	0.250758i
$836$	48564.6			0.0694875
$837$	−837215.	+	837215.i	−1.19505	+	1.19505i
$838$	786725.	+	786725.i	1.12030	+	1.12030i
$839$	−316440.			−0.449539			−0.224770	−	0.974412i	$-0.572163\pi$
$839$	−316440.			−0.449539			−0.224770	+	0.974412i	$0.572163\pi$
$840$	819201.	+	380849.i	1.16100	+	0.539752i
$841$	588804.			0.832490
$842$	−70530.6	−	70530.6i	−0.0994841	−	0.0994841i
$843$	256147.	+	256147.i	0.360441	+	0.360441i
$844$		−	721541.i		−	1.01292i
$845$	110716.	+	705389.i	0.155059	+	0.987905i
$846$	708617.			0.990081
$847$	−365544.	+	365544.i	−0.509534	+	0.509534i
$848$	1.55451e6	−	1.55451e6i	2.16173	−	2.16173i
$849$			152139.i			0.211069i
$850$	1.79492e6	−	1.51319e6i	2.48432	−	2.09438i
$851$		−	68830.7i		−	0.0950436i
$852$	−228842.	+	228842.i	−0.315251	+	0.315251i
$853$	690519.	+	690519.i	0.949025	+	0.949025i	0.998762	−	0.0497377i	$-0.0158385\pi$
$853$	690519.	+	690519.i	0.949025	+	0.949025i	−0.0497377	+	0.998762i	$0.515839\pi$
$854$			811694.i			1.11295i
$855$	−72456.5	+	26466.7i	−0.0991163	+	0.0362050i
$856$		−	2.82028e6i		−	3.84898i
$857$	−336555.	−	336555.i	−0.458241	−	0.458241i	0.439837	−	0.898078i	$-0.355036\pi$
$857$	−336555.	−	336555.i	−0.458241	−	0.458241i	−0.898078	+	0.439837i	$0.855036\pi$
$858$	−12590.1	+	129031.i	−0.0171023	+	0.175275i
$859$		−	402315.i		−	0.545230i	−0.962123	−	0.272615i	$-0.912112\pi$
$859$		−	402315.i		−	0.545230i	0.962123	−	0.272615i	$-0.0878884\pi$
$860$	668852.	−	1.43869e6i	0.904343	−	1.94523i
$861$	197365.			0.266234
$862$	−578702.	−	578702.i	−0.778827	−	0.778827i
$863$	−887727.	−	887727.i	−1.19195	−	1.19195i	−0.976519	−	0.215431i	$-0.930884\pi$
$863$	−887727.	−	887727.i	−1.19195	−	1.19195i	−0.215431	−	0.976519i	$-0.569116\pi$
$864$	2.57584e6			3.45057
$865$	−444328.	−	206570.i	−0.593843	−	0.276079i
$866$			2.41767e6i			3.22374i
$867$	499798.	+	499798.i	0.664900	+	0.664900i
$868$	−2.05102e6	+	2.05102e6i	−2.72226	+	2.72226i
$869$	−174134.			−0.230592
$870$	−105582.	−	289046.i	−0.139493	−	0.381882i
$871$	643843.	+	783074.i	0.848680	+	1.03221i
$872$	−2.08741e6	−	2.08741e6i	−2.74520	−	2.74520i
$873$	−629191.	−	629191.i	−0.825570	−	0.825570i
$874$		−	142898.i		−	0.187070i
$875$	−549681.	+	149329.i	−0.717951	+	0.195041i
$876$		−	251785.i		−	0.328112i
$877$	811313.	−	811313.i	1.05485	−	1.05485i	0.0564405	−	0.998406i	$-0.482025\pi$
$877$	811313.	−	811313.i	1.05485	−	1.05485i	0.998406	−	0.0564405i	$-0.0179751\pi$
$878$	1.41072e6	+	1.41072e6i	1.83000	+	1.83000i
$879$	106446.			0.137769
$880$	481496.	−	175880.i	0.621767	−	0.227118i
$881$	124925.			0.160952			0.0804760	−	0.996757i	$-0.474356\pi$
$881$	124925.			0.160952			0.0804760	+	0.996757i	$0.474356\pi$
$882$	349062.	−	349062.i	0.448710	−	0.448710i
$883$	−878137.	+	878137.i	−1.12627	+	1.12627i	−0.135486	+	0.990779i	$0.543260\pi$
$883$	−878137.	+	878137.i	−1.12627	+	1.12627i	−0.990779	+	0.135486i	$0.956740\pi$
$884$	2.28084e6	+	2.77407e6i	2.91871	+	3.54988i
$885$	−69783.2	−	32442.4i	−0.0890972	−	0.0414216i
$886$			1.11401e6i			1.41913i
$887$	984956.	+	984956.i	1.25190	+	1.25190i	0.954867	+	0.297032i	$0.0959970\pi$
$887$	984956.	+	984956.i	1.25190	+	1.25190i	0.297032	+	0.954867i	$0.404003\pi$
$888$	135107.	−	135107.i	0.171337	−	0.171337i
$889$	−716316.			−0.906360
$890$	1.37860e6	+	640914.i	1.74043	+	0.809133i
$891$			38953.8i			0.0490675i
$892$	−1.56431e6	+	1.56431e6i	−1.96604	+	1.96604i
$893$	56349.4	−	56349.4i	0.0706620	−	0.0706620i
$894$		−	618370.i		−	0.773701i
$895$	−549602.	+	200757.i	−0.686123	+	0.250626i
$896$	2.00183e6			2.49351
$897$	277945.	+	27120.3i	0.345441	+	0.0337061i
$898$	859006.	−	859006.i	1.06523	−	1.06523i
$899$	626434.			0.775097
$900$	−1.24482e6	+	1.04943e6i	−1.53681	+	1.29559i
$901$	−1.11792e6			−1.37709
$902$	137140.	−	137140.i	0.168558	−	0.168558i
$903$	−173155.	−	173155.i	−0.212354	−	0.212354i
$904$	−3.35890e6			−4.11017
$905$	−112830.	−	308888.i	−0.137761	−	0.377141i
$906$	662313.			0.806876
$907$	761549.	+	761549.i	0.925728	+	0.925728i	0.997426	−	0.0716988i	$-0.0228420\pi$
$907$	761549.	+	761549.i	0.925728	+	0.925728i	−0.0716988	+	0.997426i	$0.522842\pi$
$908$	−2.13786e6	−	2.13786e6i	−2.59303	−	2.59303i
$909$			441862.i			0.534760i
$910$	−297876.	−	1.15237e6i	−0.359711	−	1.39158i
$911$	263398.			0.317377			0.158688	−	0.987329i	$-0.449273\pi$
$911$	263398.			0.317377			0.158688	+	0.987329i	$0.449273\pi$
$912$	161965.	−	161965.i	0.194730	−	0.194730i
$913$	127716.	−	127716.i	0.153216	−	0.153216i
$914$			2.73618e6i			3.27531i
$915$	302262.	+	140522.i	0.361028	+	0.167843i
$916$		−	318538.i		−	0.379639i
$917$	−564090.	+	564090.i	−0.670825	+	0.670825i
$918$	−1.72795e6	−	1.72795e6i	−2.05044	−	2.05044i
$919$		−	663151.i		−	0.785202i	−0.919709	−	0.392601i	$-0.871575\pi$
$919$		−	663151.i		−	0.785202i	0.919709	−	0.392601i	$-0.128425\pi$
$920$	−656117.	−	1.79621e6i	−0.775185	−	2.12218i
$921$		−	497231.i		−	0.586191i
$922$	932449.	+	932449.i	1.09689	+	1.09689i
$923$	269065.	+	26253.8i	0.315830	+	0.0308169i
$924$		−	158209.i		−	0.185305i
$925$	−10222.7	+	120037.i	−0.0119477	+	0.140292i
$926$	1.78549e6			2.08227
$927$	−423495.	−	423495.i	−0.492821	−	0.492821i
$928$	−963666.	−	963666.i	−1.11900	−	1.11900i
$929$	−678632.			−0.786327			−0.393163	−	0.919469i	$-0.628619\pi$
$929$	−678632.			−0.786327			−0.393163	+	0.919469i	$0.628619\pi$
$930$	558257.	+	1.52831e6i	0.645458	+	1.76703i
$931$		−	55515.0i		−	0.0640488i
$932$	−190083.	−	190083.i	−0.218832	−	0.218832i
$933$	620136.	−	620136.i	0.712399	−	0.712399i
$934$	−645816.			−0.740312
$935$	−236376.	−	109892.i	−0.270383	−	0.125702i
$936$	−1.36995e6	−	1.66620e6i	−1.56370	−	1.90185i
$937$	−701460.	−	701460.i	−0.798958	−	0.798958i	0.183973	−	0.982931i	$-0.441104\pi$
$937$	−701460.	−	701460.i	−0.798958	−	0.798958i	−0.982931	+	0.183973i	$0.941104\pi$
$938$	−1.19495e6	−	1.19495e6i	−1.35814	−	1.35814i
$939$			80299.3i			0.0910711i
$940$	709081.	−	1.52522e6i	0.802491	−	1.72615i
$941$			1.07751e6i			1.21686i	0.793607	+	0.608431i	$0.208201\pi$
$941$			1.07751e6i			1.21686i	−0.793607	+	0.608431i	$0.791799\pi$
$942$	938884.	−	938884.i	1.05806	−	1.05806i
$943$	−295412.	−	295412.i	−0.332204	−	0.332204i
$944$	−635834.			−0.713510
$945$	203429.	+	556915.i	0.227797	+	0.623627i
$946$	−240635.			−0.268892
$947$	585616.	−	585616.i	0.653000	−	0.653000i	−0.300715	−	0.953714i	$-0.597225\pi$
$947$	585616.	−	585616.i	0.653000	−	0.653000i	0.953714	+	0.300715i	$0.0972252\pi$
$948$	−1.16128e6	+	1.16128e6i	−1.29217	+	1.29217i
$949$	−162463.	+	133577.i	−0.180394	+	0.148320i
$950$	−21223.2	+	249206.i	−0.0235160	+	0.276129i
$951$			396899.i			0.438853i
$952$	−2.68394e6	−	2.68394e6i	−2.96141	−	2.96141i
$953$	619618.	−	619618.i	0.682242	−	0.682242i	−0.278263	−	0.960505i	$-0.589759\pi$
$953$	619618.	−	619618.i	0.682242	−	0.682242i	0.960505	+	0.278263i	$0.0897587\pi$
$954$	1.05904e6			1.16364
$955$	56503.5	+	154686.i	0.0619539	+	0.169608i
$956$		−	680300.i		−	0.744363i
$957$	−24160.7	+	24160.7i	−0.0263806	+	0.0263806i
$958$	−1.09179e6	+	1.09179e6i	−1.18962	+	1.18962i
$959$		−	622337.i		−	0.676688i
$960$	746370.	−	1.60543e6i	0.809863	−	1.74200i
$961$	−2.38869e6			−2.58651
$962$	−250548.	−	24447.0i	−0.270732	−	0.0264165i
$963$	554732.	−	554732.i	0.598178	−	0.598178i
$964$	2.59241e6			2.78965
$965$	460100.	−	989669.i	0.494081	−	1.06276i
$966$	−465521.			−0.498867
$967$	40315.3	−	40315.3i	0.0431139	−	0.0431139i	−0.685221	−	0.728335i	$-0.740294\pi$
$967$	40315.3	−	40315.3i	0.0431139	−	0.0431139i	0.728335	+	0.685221i	$0.240294\pi$
$968$	2.14795e6	+	2.14795e6i	2.29231	+	2.29231i
$969$	−116477.			−0.124049
$970$	−2.70991e6	+	989871.i	−2.88013	+	1.05205i
$971$	829357.			0.879636			0.439818	−	0.898087i	$-0.355043\pi$
$971$	829357.			0.879636			0.439818	+	0.898087i	$0.355043\pi$
$972$	1.88883e6	+	1.88883e6i	1.99922	+	1.99922i
$973$	348096.	+	348096.i	0.367683	+	0.367683i
$974$			1.31795e6i			1.38925i
$975$	−480693.	−	88576.6i	−0.505659	−	0.0931772i
$976$	2.75408e6			2.89119
$977$	143461.	−	143461.i	0.150295	−	0.150295i	−0.627955	−	0.778250i	$-0.716108\pi$
$977$	143461.	−	143461.i	0.150295	−	0.150295i	0.778250	+	0.627955i	$0.216108\pi$
$978$	51357.4	−	51357.4i	0.0536940	−	0.0536940i
$979$		−	168806.i		−	0.176125i
$980$	−402028.	−	1.10061e6i	−0.418605	−	1.14599i
$981$		−	821159.i		−	0.853276i
$982$	929939.	−	929939.i	0.964343	−	0.964343i
$983$	−829386.	−	829386.i	−0.858321	−	0.858321i	0.132819	−	0.991140i	$-0.457597\pi$
$983$	−829386.	−	829386.i	−0.858321	−	0.858321i	−0.991140	+	0.132819i	$0.957597\pi$
$984$		−	1.15972e6i		−	1.19774i
$985$	−170328.	−	79186.2i	−0.175555	−	0.0816163i
$986$			1.29292e6i			1.32989i
$987$	−183570.	−	183570.i	−0.188438	−	0.188438i
$988$	−380796.	−	37155.9i	−0.390102	−	0.0380640i
$989$			518352.i			0.529946i
$990$	223926.	+	104104.i	0.228472	+	0.106218i
$991$	−1.45085e6			−1.47733			−0.738663	−	0.674075i	$-0.764542\pi$
$991$	−1.45085e6			−1.47733			−0.738663	+	0.674075i	$0.764542\pi$
$992$	5.09530e6	+	5.09530e6i	5.17781	+	5.17781i
$993$	418894.	+	418894.i	0.424821	+	0.424821i
$994$	−450648.			−0.456105
$995$	513073.	−	187414.i	0.518243	−	0.189303i
$996$		−	1.70344e6i		−	1.71715i
$997$	566761.	+	566761.i	0.570177	+	0.570177i	0.932178	−	0.362001i	$-0.117906\pi$
$997$	566761.	+	566761.i	0.570177	+	0.570177i	−0.362001	+	0.932178i	$0.617906\pi$
$998$	1.24090e6	−	1.24090e6i	1.24588	−	1.24588i
$999$	125400.			0.125651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.h.a.12.1	✓	52
5.3	odd	4	inner	65.5.h.a.38.26	yes	52
13.12	even	2	inner	65.5.h.a.12.26	yes	52
65.38	odd	4	inner	65.5.h.a.38.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.h.a.12.1	✓	52	1.1	even	1	trivial
65.5.h.a.12.26	yes	52	13.12	even	2	inner
65.5.h.a.38.1	yes	52	65.38	odd	4	inner
65.5.h.a.38.26	yes	52	5.3	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.46439 + 5.46439i) q^{2} +(3.27217 - 3.27217i) q^{3} -43.7192i q^{4} +(-8.57761 - 23.4824i) q^{5} +35.7609i q^{6} +(-25.7773 + 25.7773i) q^{7} +(151.468 + 151.468i) q^{8} +59.5857i q^{9} +O(q^{10})\)	\(q+(-5.46439 + 5.46439i) q^{2} +(3.27217 - 3.27217i) q^{3} -43.7192i q^{4} +(-8.57761 - 23.4824i) q^{5} +35.7609i q^{6} +(-25.7773 + 25.7773i) q^{7} +(151.468 + 151.468i) q^{8} +59.5857i q^{9} +(175.189 + 81.4458i) q^{10} -21.4514i q^{11} +(-143.057 - 143.057i) q^{12} +(-16.4121 + 168.201i) q^{13} -281.715i q^{14} +(-104.906 - 48.7712i) q^{15} -955.859 q^{16} +(343.703 + 343.703i) q^{17} +(-325.600 - 325.600i) q^{18} -51.7835 q^{19} +(-1026.63 + 375.006i) q^{20} +168.696i q^{21} +(117.219 + 117.219i) q^{22} +(252.501 - 252.501i) q^{23} +991.262 q^{24} +(-477.849 + 402.846i) q^{25} +(-829.435 - 1008.80i) q^{26} +(460.021 + 460.021i) q^{27} +(1126.96 + 1126.96i) q^{28} -344.204i q^{29} +(839.753 - 306.743i) q^{30} +1819.95i q^{31} +(2799.69 - 2799.69i) q^{32} +(-70.1928 - 70.1928i) q^{33} -3756.25 q^{34} +(826.422 + 384.206i) q^{35} +2605.04 q^{36} +(136.298 - 136.298i) q^{37} +(282.966 - 282.966i) q^{38} +(496.680 + 604.087i) q^{39} +(2257.61 - 4856.08i) q^{40} -1169.94i q^{41} +(-921.820 - 921.820i) q^{42} +(-1026.44 + 1026.44i) q^{43} -937.838 q^{44} +(1399.22 - 511.103i) q^{45} +2759.53i q^{46} +(-1088.17 + 1088.17i) q^{47} +(-3127.74 + 3127.74i) q^{48} +1072.06i q^{49} +(409.845 - 4812.47i) q^{50} +2249.31 q^{51} +(7353.62 + 717.524i) q^{52} +(-1626.30 + 1626.30i) q^{53} -5027.47 q^{54} +(-503.731 + 184.002i) q^{55} -7808.90 q^{56} +(-169.445 + 169.445i) q^{57} +(1880.87 + 1880.87i) q^{58} +665.197 q^{59} +(-2132.23 + 4586.41i) q^{60} -2881.26 q^{61} +(-9944.91 - 9944.91i) q^{62} +(-1535.96 - 1535.96i) q^{63} +15303.5i q^{64} +(4090.55 - 1057.37i) q^{65} +767.122 q^{66} +(4241.70 - 4241.70i) q^{67} +(15026.4 - 15026.4i) q^{68} -1652.45i q^{69} +(-6615.35 + 2416.44i) q^{70} -1599.66i q^{71} +(-9025.36 + 9025.36i) q^{72} +(880.019 + 880.019i) q^{73} +1489.57i q^{74} +(-245.422 + 2881.79i) q^{75} +2263.93i q^{76} +(552.960 + 552.960i) q^{77} +(-6015.02 - 586.912i) q^{78} -8117.62i q^{79} +(8198.99 + 22445.9i) q^{80} -1815.91 q^{81} +(6393.03 + 6393.03i) q^{82} +(5953.72 + 5953.72i) q^{83} +7375.24 q^{84} +(5122.82 - 11019.1i) q^{85} -11217.7i q^{86} +(-1126.30 - 1126.30i) q^{87} +(3249.21 - 3249.21i) q^{88} +7869.21 q^{89} +(-4853.01 + 10438.7i) q^{90} +(-3912.72 - 4758.84i) q^{91} +(-11039.1 - 11039.1i) q^{92} +(5955.19 + 5955.19i) q^{93} -11892.4i q^{94} +(444.179 + 1216.00i) q^{95} -18322.2i q^{96} +(-10559.4 + 10559.4i) q^{97} +(-5858.15 - 5858.15i) q^{98} +1278.20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3}+O(q^{10}) \) 52 * q - 4 * q^3	\( 52 q - 4 q^{3} + 36 q^{10} + 24 q^{12} - 82 q^{13} - 1464 q^{16} + 356 q^{17} + 2440 q^{22} + 1136 q^{23} + 1172 q^{25} - 3580 q^{26} - 880 q^{27} + 3096 q^{30} + 1616 q^{35} - 5672 q^{36} - 5828 q^{38} + 8072 q^{40} - 1512 q^{42} - 7744 q^{43} + 4996 q^{48} + 24856 q^{51} + 15132 q^{52} - 19144 q^{53} - 12668 q^{55} - 2232 q^{56} - 3128 q^{61} - 1380 q^{62} - 18530 q^{65} - 3240 q^{66} + 29576 q^{68} - 25624 q^{75} - 28740 q^{77} + 51516 q^{78} - 34844 q^{81} + 11180 q^{82} + 8420 q^{87} + 31980 q^{88} + 75392 q^{90} - 9720 q^{91} - 70436 q^{92} + 12184 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 + 36 * q^10 + 24 * q^12 - 82 * q^13 - 1464 * q^16 + 356 * q^17 + 2440 * q^22 + 1136 * q^23 + 1172 * q^25 - 3580 * q^26 - 880 * q^27 + 3096 * q^30 + 1616 * q^35 - 5672 * q^36 - 5828 * q^38 + 8072 * q^40 - 1512 * q^42 - 7744 * q^43 + 4996 * q^48 + 24856 * q^51 + 15132 * q^52 - 19144 * q^53 - 12668 * q^55 - 2232 * q^56 - 3128 * q^61 - 1380 * q^62 - 18530 * q^65 - 3240 * q^66 + 29576 * q^68 - 25624 * q^75 - 28740 * q^77 + 51516 * q^78 - 34844 * q^81 + 11180 * q^82 + 8420 * q^87 + 31980 * q^88 + 75392 * q^90 - 9720 * q^91 - 70436 * q^92 + 12184 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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