LMFDB - Embedded newform 65.5.h.a.38.1

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			38.1
Character	$\chi$	$=$	65.38
Dual form			65.5.h.a.12.1

$q$-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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−5.46439	−	5.46439i	−1.36610	−	1.36610i	−0.865926	−	0.500172i	$-0.833270\pi$
$2$	−5.46439	−	5.46439i	−1.36610	−	1.36610i	−0.500172	−	0.865926i	$-0.666730\pi$
$3$	3.27217	+	3.27217i	0.363575	+	0.363575i	0.865127	−	0.501552i	$-0.167238\pi$
$3$	3.27217	+	3.27217i	0.363575	+	0.363575i	−0.501552	+	0.865127i	$0.667238\pi$
$4$			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	0.393330	−	0.919398i	$-0.371323\pi$
$7$	−25.7773	−	25.7773i	−0.526068	−	0.526068i	−0.919398	+	0.393330i	$0.871323\pi$
$8$	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	$0.0282528\pi$
$11$			21.4514i			0.177284i	−0.996064	+	0.0886422i	$0.971747\pi$
$12$	−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	0.212016	−	0.977266i	$-0.431997\pi$
$17$	343.703	−	343.703i	1.18928	−	1.18928i	0.977266	−	0.212016i	$-0.0680029\pi$
$18$	−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	0.904273	−	0.426955i	$-0.140414\pi$
$23$	252.501	+	252.501i	0.477317	+	0.477317i	−0.426955	+	0.904273i	$0.640414\pi$
$24$	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	$0.0656023\pi$
$29$			344.204i			0.409280i	−0.978837	+	0.204640i	$0.934398\pi$
$30$	839.753	+	306.743i	0.933058	+	0.340826i
$31$		−	1819.95i		−	1.89381i	−0.321518	−	0.946904i	$-0.604193\pi$
$31$		−	1819.95i		−	1.89381i	0.321518	−	0.946904i	$-0.395807\pi$
$32$	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	0.755132	−	0.655572i	$-0.227573\pi$
$37$	136.298	+	136.298i	0.0995602	+	0.0995602i	−0.655572	+	0.755132i	$0.727573\pi$
$38$	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	$0.113136\pi$
$41$			1169.94i			0.695981i	−0.937498	+	0.347990i	$0.886864\pi$
$42$	−921.820	+	921.820i	−0.522574	+	0.522574i
$43$	−1026.44	−	1026.44i	−0.555130	−	0.555130i	0.372787	−	0.927917i	$-0.378402\pi$
$43$	−1026.44	−	1026.44i	−0.555130	−	0.555130i	−0.927917	+	0.372787i	$0.878402\pi$
$44$	−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	0.416519	−	0.909127i	$-0.363250\pi$
$47$	−1088.17	−	1088.17i	−0.492608	−	0.492608i	−0.909127	+	0.416519i	$0.863250\pi$
$48$	−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	0.355657	−	0.934616i	$-0.384257\pi$
$53$	−1626.30	−	1626.30i	−0.578959	−	0.578959i	−0.934616	+	0.355657i	$0.884257\pi$
$54$	−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	0.998560	−	0.0536504i	$-0.0170856\pi$
$67$	4241.70	+	4241.70i	0.944909	+	0.944909i	−0.0536504	+	0.998560i	$0.517086\pi$
$68$	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	$0.0507189\pi$
$71$			1599.66i			0.317330i	−0.987332	+	0.158665i	$0.949281\pi$
$72$	−9025.36	−	9025.36i	−1.74100	−	1.74100i
$73$	880.019	−	880.019i	0.165138	−	0.165138i	−0.619701	−	0.784838i	$-0.712746\pi$
$73$	880.019	−	880.019i	0.165138	−	0.165138i	0.784838	+	0.619701i	$0.212746\pi$
$74$		−	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	$0.225376\pi$
$79$			8117.62i			1.30069i	−0.759638	+	0.650346i	$0.774624\pi$
$80$	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	−0.127591	−	0.991827i	$-0.540725\pi$
$83$	5953.72	−	5953.72i	0.864236	−	0.864236i	0.991827	+	0.127591i	$0.0407245\pi$
$84$	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	−0.991400	−	0.130869i	$-0.958223\pi$
$97$	−10559.4	−	10559.4i	−1.12227	−	1.12227i	−0.130869	−	0.991400i	$-0.541777\pi$
$98$	−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	0.287767	−	0.957701i	$-0.407087\pi$
$103$	−7107.33	−	7107.33i	−0.669934	−	0.669934i	−0.957701	+	0.287767i	$0.907087\pi$
$104$	−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	−0.985106	−	0.171951i	$-0.944993\pi$
$107$	−9309.81	+	9309.81i	−0.813155	+	0.813155i	0.171951	+	0.985106i	$0.444993\pi$
$108$	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	0.123952	−	0.992288i	$-0.460443\pi$
$113$	−11087.8	−	11087.8i	−0.868336	−	0.868336i	−0.992288	+	0.123952i	$0.960443\pi$
$114$			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	−0.130058	−	0.991506i	$-0.541516\pi$
$127$	13894.3	−	13894.3i	0.861448	−	0.861448i	0.991506	+	0.130058i	$0.0415165\pi$
$128$	−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	0.308174	−	0.951330i	$-0.400282\pi$
$137$	−12071.4	−	12071.4i	−0.643156	−	0.643156i	−0.951330	+	0.308174i	$0.900282\pi$
$138$	9029.65	−	9029.65i	0.474147	−	0.474147i
$139$			13504.0i			0.698927i	0.936950	+	0.349463i	$0.113636\pi$
$139$			13504.0i			0.698927i	−0.936950	+	0.349463i	$0.886364\pi$
$140$	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	$0.133124\pi$
$151$			18520.6i			0.812271i	−0.913813	+	0.406136i	$0.866876\pi$
$152$	−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	−0.0674084	+	0.997725i	$0.521473\pi$
$157$	−26254.5	+	26254.5i	−1.06513	+	1.06513i	−0.997725	+	0.0674084i	$0.978527\pi$
$158$	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	−0.733617	−	0.679564i	$-0.762169\pi$
$163$	−1436.13	+	1436.13i	−0.0540530	+	0.0540530i	0.679564	+	0.733617i	$0.262169\pi$
$164$	−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	0.464811	−	0.885410i	$-0.346122\pi$
$167$	−11730.1	−	11730.1i	−0.420599	−	0.420599i	−0.885410	+	0.464811i	$0.846122\pi$
$168$	−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	0.899661	−	0.436590i	$-0.143814\pi$
$173$	13859.2	+	13859.2i	0.463071	+	0.463071i	−0.436590	+	0.899661i	$0.643814\pi$
$174$	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	$0.119010\pi$
$179$			23404.8i			0.730464i	−0.930916	+	0.365232i	$0.880990\pi$
$180$	−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	−0.158614	−	0.987341i	$-0.550703\pi$
$193$	30869.2	−	30869.2i	0.828727	−	0.828727i	0.987341	+	0.158614i	$0.0507025\pi$
$194$			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	0.772234	−	0.635338i	$-0.219139\pi$
$197$	5312.79	+	5312.79i	0.136896	+	0.136896i	−0.635338	+	0.772234i	$0.719139\pi$
$198$	−6984.58	−	6984.58i	−0.178160	−	0.178160i
$199$		−	21849.2i		−	0.551735i	−0.961196	−	0.275867i	$-0.911035\pi$
$199$		−	21849.2i		−	0.551735i	0.961196	−	0.275867i	$-0.0889650\pi$
$200$	−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	−0.968506	−	0.248990i	$-0.919901\pi$
$223$	−35780.8	+	35780.8i	−0.719517	+	0.719517i	0.248990	+	0.968506i	$0.419901\pi$
$224$		−	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	0.998760	−	0.0497826i	$-0.0158528\pi$
$227$	48899.9	+	48899.9i	0.948978	+	0.948978i	−0.0497826	+	0.998760i	$0.515853\pi$
$228$	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	0.746015	−	0.665929i	$-0.231965\pi$
$233$	4347.81	+	4347.81i	0.0800864	+	0.0800864i	−0.665929	+	0.746015i	$0.731965\pi$
$234$	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	$-0.829472\pi$
$241$		−	59296.9i		−	1.02093i	0.859897	−	0.510467i	$-0.170528\pi$
$242$	−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	−0.984014	−	0.178088i	$-0.943009\pi$
$257$	−53230.6	+	53230.6i	−0.805926	+	0.805926i	0.178088	+	0.984014i	$0.443009\pi$
$258$	−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	0.877729	−	0.479157i	$-0.159058\pi$
$263$	27568.8	+	27568.8i	0.398572	+	0.398572i	−0.479157	+	0.877729i	$0.659058\pi$
$264$			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	$0.00907222\pi$
$269$			4124.20i			0.0569947i	−0.999594	+	0.0284974i	$0.990928\pi$
$270$	43123.7	−	118057.i	0.591546	−	1.61944i
$271$			70191.5i			0.955754i	0.878427	+	0.477877i	$0.158594\pi$
$271$			70191.5i			0.955754i	−0.878427	+	0.477877i	$0.841406\pi$
$272$	−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	−0.00109408	−	0.999999i	$-0.500348\pi$
$277$	76645.0	−	76645.0i	0.998905	−	0.998905i	0.999999	+	0.00109408i	$0.000348258\pi$
$278$	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	$-0.834915\pi$
$281$		−	78280.5i		−	0.991381i	0.868499	−	0.495691i	$-0.165085\pi$
$282$	−38914.0	+	38914.0i	−0.489336	+	0.489336i
$283$	−23247.4	−	23247.4i	−0.290269	−	0.290269i	0.546917	−	0.837187i	$-0.315801\pi$
$283$	−23247.4	−	23247.4i	−0.290269	−	0.290269i	−0.837187	+	0.546917i	$0.815801\pi$
$284$	−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	−0.606000	−	0.795465i	$-0.707227\pi$
$293$	16265.4	−	16265.4i	0.189465	−	0.189465i	0.795465	+	0.606000i	$0.207227\pi$
$294$	−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	0.984049	−	0.177900i	$-0.0569304\pi$
$307$	75978.7	+	75978.7i	0.806148	+	0.806148i	−0.177900	+	0.984049i	$0.556930\pi$
$308$	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	0.641706	−	0.766950i	$-0.278227\pi$
$313$	−12270.0	−	12270.0i	−0.125244	−	0.125244i	−0.766950	+	0.641706i	$0.778227\pi$
$314$	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	0.337721	−	0.941246i	$-0.390344\pi$
$317$	−60647.6	−	60647.6i	−0.603525	−	0.603525i	−0.941246	+	0.337721i	$0.890344\pi$
$318$	−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	$-0.801398\pi$
$331$		−	128017.i		−	1.16845i	0.811590	−	0.584227i	$-0.198602\pi$
$332$	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	0.397777	−	0.917482i	$-0.369782\pi$
$337$	149373.	−	149373.i	1.31526	−	1.31526i	0.917482	−	0.397777i	$-0.130218\pi$
$338$	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	−0.920716	−	0.390234i	$-0.872394\pi$
$347$	−63874.8	+	63874.8i	−0.530482	+	0.530482i	0.390234	+	0.920716i	$0.372394\pi$
$348$	−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	−0.779777	−	0.626057i	$-0.784668\pi$
$353$	−19154.9	+	19154.9i	−0.153720	+	0.153720i	0.626057	+	0.779777i	$0.284668\pi$
$354$		−	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	−0.747357	−	0.664423i	$-0.768677\pi$
$367$	−11170.3	+	11170.3i	−0.0829340	+	0.0829340i	0.664423	+	0.747357i	$0.268677\pi$
$368$	−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	0.367082	−	0.930189i	$-0.380357\pi$
$373$	−78344.5	−	78344.5i	−0.563107	−	0.563107i	−0.930189	+	0.367082i	$0.880357\pi$
$374$		−	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	−0.701381	−	0.712787i	$-0.747433\pi$
$383$	1673.15	−	1673.15i	0.0114061	−	0.0114061i	0.712787	+	0.701381i	$0.247433\pi$
$384$	−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	$0.0189551\pi$
$389$			18011.5i			0.119028i	−0.998227	+	0.0595141i	$0.981045\pi$
$390$	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	0.959622	−	0.281292i	$-0.0907628\pi$
$397$	106911.	+	106911.i	0.678331	+	0.678331i	−0.281292	+	0.959622i	$0.590763\pi$
$398$	−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	$-0.999788\pi$
$401$		−	213.754i		−	0.00132931i	1.00000		0.000664654i	$-0.000211566\pi$
$402$	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	$0.134484\pi$
$419$			143973.i			0.820074i	−0.912069	+	0.410037i	$0.865516\pi$
$420$	−63262.0	+	173189.i	−0.358628	+	0.981795i
$421$		−	12907.3i		−	0.0728235i	−0.999337	−	0.0364118i	$-0.988407\pi$
$421$		−	12907.3i		−	0.0728235i	0.999337	−	0.0364118i	$-0.0115928\pi$
$422$	−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	$-0.907988\pi$
$431$		−	105904.i		−	0.570110i	0.958511	−	0.285055i	$-0.0920119\pi$
$432$	−439715.	+	439715.i	−2.35616	+	2.35616i
$433$	221220.	+	221220.i	1.17991	+	1.17991i	0.979767	+	0.200143i	$0.0641407\pi$
$433$	221220.	+	221220.i	1.17991	+	1.17991i	0.200143	+	0.979767i	$0.435859\pi$
$434$	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	$0.233617\pi$
$439$			258166.i			1.33958i	−0.742548	+	0.669792i	$0.766383\pi$
$440$	−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	0.917393	−	0.397982i	$-0.130290\pi$
$443$	101934.	+	101934.i	0.519411	+	0.519411i	−0.397982	+	0.917393i	$0.630290\pi$
$444$	−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	0.974531	+	0.224251i	$0.0719934\pi$
$457$	250364.	+	250364.i	1.19878	+	1.19878i	0.224251	+	0.974531i	$0.428007\pi$
$458$	−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	$0.131500\pi$
$461$			170641.i			0.802936i	−0.915873	+	0.401468i	$0.868500\pi$
$462$	−19774.3	−	19774.3i	−0.0926442	−	0.0926442i
$463$	−163375.	+	163375.i	−0.762122	+	0.762122i	−0.976706	−	0.214584i	$-0.931161\pi$
$463$	−163375.	+	163375.i	−0.762122	+	0.762122i	0.214584	+	0.976706i	$0.431161\pi$
$464$		−	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	−0.558527	−	0.829486i	$-0.688633\pi$
$467$	59093.1	−	59093.1i	0.270959	−	0.270959i	0.829486	+	0.558527i	$0.188633\pi$
$468$	−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	0.914058	−	0.405584i	$-0.132932\pi$
$487$	120594.	+	120594.i	0.508473	+	0.508473i	−0.405584	+	0.914058i	$0.632932\pi$
$488$	−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	0.801984	−	0.597346i	$-0.203778\pi$
$503$	51775.2	+	51775.2i	0.204638	+	0.204638i	−0.597346	+	0.801984i	$0.703778\pi$
$504$			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	0.291172	−	0.956671i	$-0.405955\pi$
$523$	−182033.	−	182033.i	−0.665499	−	0.665499i	−0.956671	+	0.291172i	$0.905955\pi$
$524$			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	$0.108918\pi$
$541$			196412.i			0.671078i	−0.942026	+	0.335539i	$0.891082\pi$
$542$	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	0.244395	−	0.969676i	$-0.421411\pi$
$547$	363261.	−	363261.i	1.21407	−	1.21407i	0.969676	−	0.244395i	$-0.0785893\pi$
$548$	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	0.922866	−	0.385120i	$-0.125840\pi$
$557$	166835.	+	166835.i	0.537746	+	0.537746i	−0.385120	+	0.922866i	$0.625840\pi$
$558$	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	0.424280	−	0.905531i	$-0.360527\pi$
$563$	−152542.	−	152542.i	−0.481251	−	0.481251i	−0.905531	+	0.424280i	$0.860527\pi$
$564$	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	$-0.684954\pi$
$569$		−	541255.i		−	1.67177i	0.548903	−	0.835886i	$-0.315046\pi$
$570$	−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	0.296900	−	0.954908i	$-0.404047\pi$
$577$	−219070.	−	219070.i	−0.658008	−	0.658008i	−0.954908	+	0.296900i	$0.904047\pi$
$578$	−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	0.903761	−	0.428037i	$-0.140795\pi$
$587$	163920.	+	163920.i	0.475725	+	0.475725i	−0.428037	+	0.903761i	$0.640795\pi$
$588$	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	−0.0962586	+	0.995356i	$0.530688\pi$
$593$	−383865.	+	383865.i	−1.09161	+	1.09161i	−0.995356	+	0.0962586i	$0.969312\pi$
$594$		−	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	$0.201249\pi$
$599$			424071.i			1.18191i	−0.806704	+	0.590956i	$0.798751\pi$
$600$	−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	−0.890178	−	0.455613i	$-0.849420\pi$
$607$	−160115.	+	160115.i	−0.434565	+	0.434565i	0.455613	+	0.890178i	$0.349420\pi$
$608$	−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	−0.549955	−	0.835195i	$-0.685355\pi$
$613$	107184.	−	107184.i	0.285240	−	0.285240i	0.835195	+	0.549955i	$0.185355\pi$
$614$		−	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	0.808450	−	0.588566i	$-0.200307\pi$
$617$	83707.4	+	83707.4i	0.219884	+	0.219884i	−0.588566	+	0.808450i	$0.700307\pi$
$618$	−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	$-0.833588\pi$
$631$		−	397610.i		−	0.998616i	0.866425	−	0.499308i	$-0.166412\pi$
$632$	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	0.351212	−	0.936296i	$-0.385770\pi$
$643$	532319.	−	532319.i	1.28751	−	1.28751i	0.936296	−	0.351212i	$-0.114230\pi$
$644$	569118.			1.37224
$645$	157740.	+	57618.8i	0.379159	+	0.138499i
$646$	194512.			0.466102
$647$	−104638.	+	104638.i	−0.249967	+	0.249967i	−0.820957	−	0.570990i	$-0.806559\pi$
$647$	−104638.	+	104638.i	−0.249967	+	0.249967i	0.570990	+	0.820957i	$0.306559\pi$
$648$	−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	0.339442	−	0.940627i	$-0.389762\pi$
$653$	−256351.	−	256351.i	−0.601185	−	0.601185i	−0.940627	+	0.339442i	$0.889762\pi$
$654$			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	$-0.865247\pi$
$659$		−	356811.i		−	0.821613i	0.911723	−	0.410806i	$-0.134753\pi$
$660$	98384.9	−	45739.5i	0.225861	−	0.105003i
$661$			341864.i			0.782439i	0.920297	+	0.391219i	$0.127947\pi$
$661$			341864.i			0.782439i	−0.920297	+	0.391219i	$0.872053\pi$
$662$	−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	0.666272	−	0.745709i	$-0.267889\pi$
$673$	−35979.3	−	35979.3i	−0.0794370	−	0.0794370i	−0.745709	+	0.666272i	$0.767889\pi$
$674$	−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	−0.754228	−	0.656613i	$-0.771989\pi$
$677$	−44739.7	+	44739.7i	−0.0976148	+	0.0976148i	0.656613	+	0.754228i	$0.271989\pi$
$678$	−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	−0.409956	−	0.912105i	$-0.634456\pi$
$683$	234247.	−	234247.i	0.502150	−	0.502150i	0.912105	+	0.409956i	$0.134456\pi$
$684$	−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	$0.0775721\pi$
$691$			230428.i			0.482590i	−0.970452	+	0.241295i	$0.922428\pi$
$692$	−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	$0.161844\pi$
$719$			503336.i			0.973644i	−0.873501	+	0.486822i	$0.838156\pi$
$720$	−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	−0.923571	−	0.383428i	$-0.874743\pi$
$727$	−285481.	+	285481.i	−0.540142	+	0.540142i	0.383428	+	0.923571i	$0.374743\pi$
$728$	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	−0.685693	−	0.727891i	$-0.740501\pi$
$733$	22672.4	−	22672.4i	0.0421978	−	0.0421978i	0.727891	+	0.685693i	$0.240501\pi$
$734$	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	−0.697210	−	0.716867i	$-0.745575\pi$
$743$	10851.8	−	10851.8i	0.0196573	−	0.0196573i	0.716867	+	0.697210i	$0.245575\pi$
$744$		−	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	−0.194245	−	0.980953i	$-0.562226\pi$
$757$	450822.	−	450822.i	0.786708	−	0.786708i	0.980953	+	0.194245i	$0.0622257\pi$
$758$	−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	$0.189048\pi$
$761$			648161.i			1.11921i	−0.828758	+	0.559607i	$0.810952\pi$
$762$	−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	−0.627897	−	0.778297i	$-0.716084\pi$
$773$	89868.4	−	89868.4i	0.150400	−	0.150400i	0.778297	+	0.627897i	$0.216084\pi$
$774$	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	0.694247	−	0.719737i	$-0.255738\pi$
$787$	−15787.6	−	15787.6i	−0.0254898	−	0.0254898i	−0.719737	+	0.694247i	$0.755738\pi$
$788$	−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	−0.996712	−	0.0810247i	$-0.974181\pi$
$797$	−581653.	+	581653.i	−0.915687	+	0.915687i	0.0810247	+	0.996712i	$0.474181\pi$
$798$	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	$0.000618134\pi$
$809$			2541.90i			0.00388384i	−0.999998	+	0.00194192i	$0.999382\pi$
$810$	−318126.	+	147898.i	−0.484875	+	0.225420i
$811$		−	914702.i		−	1.39071i	−0.718665	−	0.695357i	$-0.755246\pi$
$811$		−	914702.i		−	1.39071i	0.718665	−	0.695357i	$-0.244754\pi$
$812$	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	$0.207585\pi$
$821$			818145.i			1.21379i	−0.794781	+	0.606896i	$0.792415\pi$
$822$	−431684.	+	431684.i	−0.638885	+	0.638885i
$823$	22874.7	+	22874.7i	0.0337719	+	0.0337719i	0.723791	−	0.690019i	$-0.242398\pi$
$823$	22874.7	+	22874.7i	0.0337719	+	0.0337719i	−0.690019	+	0.723791i	$0.742398\pi$
$824$	−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	0.257906	−	0.966170i	$-0.416967\pi$
$827$	−484402.	−	484402.i	−0.708263	−	0.708263i	−0.966170	+	0.257906i	$0.916967\pi$
$828$	657774.	+	657774.i	0.959437	+	0.959437i
$829$			168406.i			0.245046i	0.992466	+	0.122523i	$0.0390986\pi$
$829$			168406.i			0.245046i	−0.992466	+	0.122523i	$0.960901\pi$
$830$	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	−0.0497377	−	0.998762i	$-0.515839\pi$
$853$	690519.	−	690519.i	0.949025	−	0.949025i	0.998762	+	0.0497377i	$0.0158385\pi$
$854$		−	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	−0.898078	−	0.439837i	$-0.855036\pi$
$857$	−336555.	+	336555.i	−0.458241	+	0.458241i	0.439837	+	0.898078i	$0.355036\pi$
$858$	−12590.1	−	129031.i	−0.0171023	−	0.175275i
$859$			402315.i			0.545230i	0.962123	+	0.272615i	$0.0878884\pi$
$859$			402315.i			0.545230i	−0.962123	+	0.272615i	$0.912112\pi$
$860$	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	−0.215431	+	0.976519i	$0.569116\pi$
$863$	−887727.	+	887727.i	−1.19195	+	1.19195i	−0.976519	+	0.215431i	$0.930884\pi$
$864$	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	0.998406	+	0.0564405i	$0.0179751\pi$
$877$	811313.	+	811313.i	1.05485	+	1.05485i	0.0564405	+	0.998406i	$0.482025\pi$
$878$	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	−0.990779	−	0.135486i	$-0.956740\pi$
$883$	−878137.	−	878137.i	−1.12627	−	1.12627i	−0.135486	−	0.990779i	$-0.543260\pi$
$884$	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	0.297032	−	0.954867i	$-0.404003\pi$
$887$	984956.	−	984956.i	1.25190	−	1.25190i	0.954867	−	0.297032i	$-0.0959970\pi$
$888$	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	−0.0716988	−	0.997426i	$-0.522842\pi$
$907$	761549.	−	761549.i	0.925728	−	0.925728i	0.997426	+	0.0716988i	$0.0228420\pi$
$908$	−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	$0.128425\pi$
$919$			663151.i			0.785202i	−0.919709	+	0.392601i	$0.871575\pi$
$920$	−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	−0.982931	−	0.183973i	$-0.941104\pi$
$937$	−701460.	+	701460.i	−0.798958	+	0.798958i	0.183973	+	0.982931i	$0.441104\pi$
$938$	−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	$-0.791799\pi$
$941$		−	1.07751e6i		−	1.21686i	0.793607	−	0.608431i	$-0.208201\pi$
$942$	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	0.953714	−	0.300715i	$-0.0972252\pi$
$947$	585616.	+	585616.i	0.653000	+	0.653000i	−0.300715	+	0.953714i	$0.597225\pi$
$948$	−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	0.960505	−	0.278263i	$-0.0897587\pi$
$953$	619618.	+	619618.i	0.682242	+	0.682242i	−0.278263	+	0.960505i	$0.589759\pi$
$954$	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	0.728335	−	0.685221i	$-0.240294\pi$
$967$	40315.3	+	40315.3i	0.0431139	+	0.0431139i	−0.685221	+	0.728335i	$0.740294\pi$
$968$	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	0.778250	−	0.627955i	$-0.216108\pi$
$977$	143461.	+	143461.i	0.150295	+	0.150295i	−0.627955	+	0.778250i	$0.716108\pi$
$978$	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	−0.991140	−	0.132819i	$-0.957597\pi$
$983$	−829386.	+	829386.i	−0.858321	+	0.858321i	0.132819	+	0.991140i	$0.457597\pi$
$984$			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	−0.362001	−	0.932178i	$-0.617906\pi$
$997$	566761.	−	566761.i	0.570177	−	0.570177i	0.932178	+	0.362001i	$0.117906\pi$
$998$	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.38.1	yes	52
5.2	odd	4	inner	65.5.h.a.12.26	yes	52
13.12	even	2	inner	65.5.h.a.38.26	yes	52
65.12	odd	4	inner	65.5.h.a.12.1	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.h.a.12.1	✓	52	65.12	odd	4	inner
65.5.h.a.12.26	yes	52	5.2	odd	4	inner
65.5.h.a.38.1	yes	52	1.1	even	1	trivial
65.5.h.a.38.26	yes	52	13.12	even	2	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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