LMFDB - Embedded newform 230.6.b.a.139.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.b (of order $2$, degree $1$, 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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.7
Character	$\chi$	$=$	230.139
Dual form			230.6.b.a.139.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} +1.04517i q^{3} -16.0000 q^{4} +(-54.3251 - 13.1829i) q^{5} +4.18067 q^{6} -135.681i q^{7} +64.0000i q^{8} +241.908 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} +1.04517i q^{3} -16.0000 q^{4} +(-54.3251 - 13.1829i) q^{5} +4.18067 q^{6} -135.681i q^{7} +64.0000i q^{8} +241.908 q^{9} +(-52.7315 + 217.300i) q^{10} +306.829 q^{11} -16.7227i q^{12} -653.597i q^{13} -542.725 q^{14} +(13.7783 - 56.7788i) q^{15} +256.000 q^{16} -535.653i q^{17} -967.631i q^{18} +1782.44 q^{19} +(869.201 + 210.926i) q^{20} +141.810 q^{21} -1227.31i q^{22} -529.000i q^{23} -66.8907 q^{24} +(2777.42 + 1432.32i) q^{25} -2614.39 q^{26} +506.809i q^{27} +2170.90i q^{28} -7755.06 q^{29} +(-227.115 - 55.1133i) q^{30} -6681.87 q^{31} -1024.00i q^{32} +320.687i q^{33} -2142.61 q^{34} +(-1788.67 + 7370.89i) q^{35} -3870.52 q^{36} -340.619i q^{37} -7129.78i q^{38} +683.118 q^{39} +(843.705 - 3476.80i) q^{40} -4453.12 q^{41} -567.238i q^{42} -10100.5i q^{43} -4909.26 q^{44} +(-13141.6 - 3189.04i) q^{45} -2116.00 q^{46} +3576.05i q^{47} +267.563i q^{48} -1602.41 q^{49} +(5729.29 - 11109.7i) q^{50} +559.847 q^{51} +10457.6i q^{52} -29257.9i q^{53} +2027.24 q^{54} +(-16668.5 - 4044.89i) q^{55} +8683.60 q^{56} +1862.95i q^{57} +31020.3i q^{58} -17852.6 q^{59} +(-220.453 + 908.460i) q^{60} -26240.0 q^{61} +26727.5i q^{62} -32822.3i q^{63} -4096.00 q^{64} +(-8616.30 + 35506.7i) q^{65} +1282.75 q^{66} +38922.3i q^{67} +8570.45i q^{68} +552.893 q^{69} +(29483.6 + 7154.68i) q^{70} -8169.37 q^{71} +15482.1i q^{72} +6736.85i q^{73} -1362.48 q^{74} +(-1497.02 + 2902.87i) q^{75} -28519.1 q^{76} -41630.9i q^{77} -2732.47i q^{78} -43302.1 q^{79} +(-13907.2 - 3374.82i) q^{80} +58253.9 q^{81} +17812.5i q^{82} -2541.36i q^{83} -2268.95 q^{84} +(-7061.45 + 29099.4i) q^{85} -40402.1 q^{86} -8105.34i q^{87} +19637.0i q^{88} -32376.1 q^{89} +(-12756.2 + 52566.6i) q^{90} -88680.9 q^{91} +8464.00i q^{92} -6983.67i q^{93} +14304.2 q^{94} +(-96831.4 - 23497.8i) q^{95} +1070.25 q^{96} -25477.7i q^{97} +6409.65i q^{98} +74224.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	$ 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) $ 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$			1.04517i			0.0670475i	0.999438	+	0.0335237i	$0.0106729\pi$
$3$			1.04517i			0.0670475i	−0.999438	+	0.0335237i	$0.989327\pi$
$4$	−16.0000			−0.500000
$5$	−54.3251	−	13.1829i	−0.971796	−	0.235823i
$5$	−54.3251	−	13.1829i	−0.971796	−	0.235823i
$6$	4.18067			0.0474097
$7$		−	135.681i		−	1.04659i	−0.852153	−	0.523293i	$-0.824703\pi$
$7$		−	135.681i		−	1.04659i	0.852153	−	0.523293i	$-0.175297\pi$
$8$			64.0000i			0.353553i
$9$	241.908			0.995505
$10$	−52.7315	+	217.300i	−0.166752	+	0.687164i
$11$	306.829			0.764565			0.382282	−	0.924046i	$-0.375138\pi$
$11$	306.829			0.764565			0.382282	+	0.924046i	$0.375138\pi$
$12$		−	16.7227i		−	0.0335237i
$13$		−	653.597i		−	1.07263i	−0.844016	−	0.536317i	$-0.819815\pi$
$13$		−	653.597i		−	1.07263i	0.844016	−	0.536317i	$-0.180185\pi$
$14$	−542.725			−0.740048
$15$	13.7783	−	56.7788i	0.0158113	−	0.0651565i
$16$	256.000			0.250000
$17$		−	535.653i		−	0.449533i	−0.974413	−	0.224766i	$-0.927838\pi$
$17$		−	535.653i		−	0.449533i	0.974413	−	0.224766i	$-0.0721619\pi$
$18$		−	967.631i		−	0.703928i
$19$	1782.44			1.13274			0.566372	−	0.824149i	$-0.308346\pi$
$19$	1782.44			1.13274			0.566372	+	0.824149i	$0.308346\pi$
$20$	869.201	+	210.926i	0.485898	+	0.117911i
$21$	141.810			0.0701710
$22$		−	1227.31i		−	0.540629i
$23$		−	529.000i		−	0.208514i
$23$		−	529.000i		−	0.208514i
$24$	−66.8907			−0.0237049
$25$	2777.42	+	1432.32i	0.888775	+	0.458343i
$26$	−2614.39			−0.758467
$27$			506.809i			0.133794i
$28$			2170.90i			0.523293i
$29$	−7755.06			−1.71234			−0.856171	−	0.516693i	$-0.827163\pi$
$29$	−7755.06			−1.71234			−0.856171	+	0.516693i	$0.827163\pi$
$30$	−227.115	−	55.1133i	−0.0460726	−	0.0111803i
$31$	−6681.87			−1.24880			−0.624401	−	0.781104i	$-0.714657\pi$
$31$	−6681.87			−1.24880			−0.624401	+	0.781104i	$0.714657\pi$
$32$		−	1024.00i		−	0.176777i
$33$			320.687i			0.0512622i
$34$	−2142.61			−0.317868
$35$	−1788.67	+	7370.89i	−0.246809	+	1.01707i
$36$	−3870.52			−0.497752
$37$		−	340.619i		−	0.0409039i	−0.999791	−	0.0204519i	$-0.993489\pi$
$37$		−	340.619i		−	0.0409039i	0.999791	−	0.0204519i	$-0.00651051\pi$
$38$		−	7129.78i		−	0.800972i
$39$	683.118			0.0719175
$40$	843.705	−	3476.80i	0.0833759	−	0.343582i
$41$	−4453.12			−0.413719			−0.206859	−	0.978371i	$-0.566324\pi$
$41$	−4453.12			−0.413719			−0.206859	+	0.978371i	$0.566324\pi$
$42$		−	567.238i		−	0.0496184i
$43$		−	10100.5i		−	0.833053i	−0.909124	−	0.416526i	$-0.863247\pi$
$43$		−	10100.5i		−	0.833053i	0.909124	−	0.416526i	$-0.136753\pi$
$44$	−4909.26			−0.382282
$45$	−13141.6	−	3189.04i	−0.967428	−	0.234763i
$46$	−2116.00			−0.147442
$47$			3576.05i			0.236134i	0.993006	+	0.118067i	$0.0376698\pi$
$47$			3576.05i			0.236134i	−0.993006	+	0.118067i	$0.962330\pi$
$48$			267.563i			0.0167619i
$49$	−1602.41			−0.0953420
$50$	5729.29	−	11109.7i	0.324097	−	0.628459i
$51$	559.847			0.0301400
$52$			10457.6i			0.536317i
$53$		−	29257.9i		−	1.43072i	−0.698757	−	0.715359i	$-0.746263\pi$
$53$		−	29257.9i		−	1.43072i	0.698757	−	0.715359i	$-0.253737\pi$
$54$	2027.24			0.0946063
$55$	−16668.5	−	4044.89i	−0.743001	−	0.180302i
$56$	8683.60			0.370024
$57$			1862.95i			0.0759477i
$58$			31020.3i			1.21081i
$59$	−17852.6			−0.667684			−0.333842	−	0.942629i	$-0.608345\pi$
$59$	−17852.6			−0.667684			−0.333842	+	0.942629i	$0.608345\pi$
$60$	−220.453	+	908.460i	−0.00790566	+	0.0325782i
$61$	−26240.0			−0.902899			−0.451450	−	0.892297i	$-0.649093\pi$
$61$	−26240.0			−0.902899			−0.451450	+	0.892297i	$0.649093\pi$
$62$			26727.5i			0.883037i
$63$		−	32822.3i		−	1.04188i
$64$	−4096.00			−0.125000
$65$	−8616.30	+	35506.7i	−0.252952	+	1.04238i
$66$	1282.75			0.0362478
$67$			38922.3i			1.05928i	0.848222	+	0.529641i	$0.177673\pi$
$67$			38922.3i			1.05928i	−0.848222	+	0.529641i	$0.822327\pi$
$68$			8570.45i			0.224766i
$69$	552.893			0.0139804
$70$	29483.6	+	7154.68i	0.719176	+	0.174520i
$71$	−8169.37			−0.192328			−0.0961641	−	0.995365i	$-0.530657\pi$
$71$	−8169.37			−0.192328			−0.0961641	+	0.995365i	$0.530657\pi$
$72$			15482.1i			0.351964i
$73$			6736.85i			0.147962i	0.997260	+	0.0739809i	$0.0235704\pi$
$73$			6736.85i			0.147962i	−0.997260	+	0.0739809i	$0.976430\pi$
$74$	−1362.48			−0.0289234
$75$	−1497.02	+	2902.87i	−0.0307308	+	0.0595902i
$76$	−28519.1			−0.566372
$77$		−	41630.9i		−	0.800183i
$78$		−	2732.47i		−	0.0508533i
$79$	−43302.1			−0.780623			−0.390311	−	0.920683i	$-0.627633\pi$
$79$	−43302.1			−0.780623			−0.390311	+	0.920683i	$0.627633\pi$
$80$	−13907.2	−	3374.82i	−0.242949	−	0.0589557i
$81$	58253.9			0.986534
$82$			17812.5i			0.292543i
$83$		−	2541.36i		−	0.0404922i	−0.999795	−	0.0202461i	$-0.993555\pi$
$83$		−	2541.36i		−	0.0404922i	0.999795	−	0.0202461i	$-0.00644497\pi$
$84$	−2268.95			−0.0350855
$85$	−7061.45	+	29099.4i	−0.106010	+	0.436854i
$86$	−40402.1			−0.589057
$87$		−	8105.34i		−	0.114808i
$88$			19637.0i			0.270314i
$89$	−32376.1			−0.433262			−0.216631	−	0.976254i	$-0.569507\pi$
$89$	−32376.1			−0.433262			−0.216631	+	0.976254i	$0.569507\pi$
$90$	−12756.2	+	52566.6i	−0.166002	+	0.684075i
$91$	−88680.9			−1.12260
$92$			8464.00i			0.104257i
$93$		−	6983.67i		−	0.0837291i
$94$	14304.2			0.166972
$95$	−96831.4	−	23497.8i	−1.10080	−	0.267127i
$96$	1070.25			0.0118524
$97$		−	25477.7i		−	0.274936i	−0.990506	−	0.137468i	$-0.956104\pi$
$97$		−	25477.7i		−	0.274936i	0.990506	−	0.137468i	$-0.0438964\pi$
$98$			6409.65i			0.0674170i
$99$	74224.2			0.761128
$100$	−44438.8	−	22917.2i	−0.444388	−	0.229172i
$101$	−61843.8			−0.603243			−0.301622	−	0.953428i	$-0.597528\pi$
$101$	−61843.8			−0.603243			−0.301622	+	0.953428i	$0.597528\pi$
$102$		−	2239.39i		−	0.0213122i
$103$			10670.5i			0.0991044i	0.998772	+	0.0495522i	$0.0157794\pi$
$103$			10670.5i			0.0991044i	−0.998772	+	0.0495522i	$0.984221\pi$
$104$	41830.2			0.379234
$105$	−7703.81	−	1869.46i	−0.0681919	−	0.0165479i
$106$	−117032.			−1.01167
$107$			155062.i			1.30932i	0.755922	+	0.654662i	$0.227189\pi$
$107$			155062.i			1.30932i	−0.755922	+	0.654662i	$0.772811\pi$
$108$		−	8108.95i		−	0.0668968i
$109$	190304.			1.53420			0.767101	−	0.641526i	$-0.221698\pi$
$109$	190304.			1.53420			0.767101	+	0.641526i	$0.221698\pi$
$110$	−16179.6	+	66673.9i	−0.127493	+	0.525381i
$111$	356.004			0.00274250
$112$		−	34734.4i		−	0.261646i
$113$			114452.i			0.843194i	0.906783	+	0.421597i	$0.138530\pi$
$113$			114452.i			0.843194i	−0.906783	+	0.421597i	$0.861470\pi$
$114$	7451.81			0.0537031
$115$	−6973.75	+	28738.0i	−0.0491724	+	0.202633i
$116$	124081.			0.856171
$117$		−	158110.i		−	1.06781i
$118$			71410.3i			0.472124i
$119$	−72678.1			−0.470474
$120$	3633.84	+	881.812i	0.0230363	+	0.00559014i
$121$	−66907.1			−0.415441
$122$			104960.i			0.638446i
$123$		−	4654.26i		−	0.0277388i
$124$	106910.			0.624401
$125$	−132002.	−	114425.i	−0.755621	−	0.655009i
$126$	−131289.			−0.736721
$127$		−	64538.9i		−	0.355068i	−0.984115	−	0.177534i	$-0.943188\pi$
$127$		−	64538.9i		−	0.355068i	0.984115	−	0.177534i	$-0.0568120\pi$
$128$			16384.0i			0.0883883i
$129$	10556.7			0.0558541
$130$	142027.	+	34465.2i	0.737075	+	0.178864i
$131$	48853.7			0.248725			0.124362	−	0.992237i	$-0.460311\pi$
$131$	48853.7			0.248725			0.124362	+	0.992237i	$0.460311\pi$
$132$		−	5131.00i		−	0.0256311i
$133$		−	241844.i		−	1.18551i
$134$	155689.			0.749026
$135$	6681.21	−	27532.4i	0.0315516	−	0.130020i
$136$	34281.8			0.158934
$137$		−	306438.i		−	1.39490i	−0.716636	−	0.697448i	$-0.754319\pi$
$137$		−	306438.i		−	1.39490i	0.716636	−	0.697448i	$-0.245681\pi$
$138$		−	2211.57i		−	0.00988561i
$139$	101761.			0.446731			0.223365	−	0.974735i	$-0.428296\pi$
$139$	101761.			0.446731			0.223365	+	0.974735i	$0.428296\pi$
$140$	28618.7	−	117934.i	0.123404	−	0.508534i
$141$	−3737.57			−0.0158322
$142$			32677.5i			0.135997i
$143$		−	200542.i		−	0.820099i
$144$	61928.4			0.248876
$145$	421294.	+	102234.i	1.66405	+	0.403809i
$146$	26947.4			0.104625
$147$		−	1674.79i		−	0.00639244i
$148$			5449.90i			0.0204519i
$149$	−388579.			−1.43388			−0.716941	−	0.697134i	$-0.754458\pi$
$149$	−388579.			−1.43388			−0.716941	+	0.697134i	$0.754458\pi$
$150$	11611.5	+	5988.06i	0.0421366	+	0.0217299i
$151$	119874.			0.427840			0.213920	−	0.976851i	$-0.431377\pi$
$151$	119874.			0.427840			0.213920	+	0.976851i	$0.431377\pi$
$152$			114076.i			0.400486i
$153$		−	129579.i		−	0.447512i
$154$	−166524.			−0.565815
$155$	362993.	+	88086.3i	1.21358	+	0.294496i
$156$	−10929.9			−0.0359587
$157$			103516.i			0.335165i	0.985858	+	0.167582i	$0.0535960\pi$
$157$			103516.i			0.335165i	−0.985858	+	0.167582i	$0.946404\pi$
$158$			173208.i			0.551984i
$159$	30579.4			0.0959261
$160$	−13499.3	+	55628.9i	−0.0416879	+	0.171791i
$161$	−71775.4			−0.218228
$162$		−	233015.i		−	0.697585i
$163$		−	576618.i		−	1.69988i	−0.526877	−	0.849942i	$-0.676637\pi$
$163$		−	576618.i		−	1.69988i	0.526877	−	0.849942i	$-0.323363\pi$
$164$	71250.0			0.206859
$165$	4227.58	−	17421.4i	0.0120888	−	0.0498164i
$166$	−10165.4			−0.0286323
$167$			75036.0i			0.208199i	0.994567	+	0.104100i	$0.0331960\pi$
$167$			75036.0i			0.208199i	−0.994567	+	0.104100i	$0.966804\pi$
$168$			9075.81i			0.0248092i
$169$	−55896.2			−0.150545
$170$	116398.	+	28245.8i	0.308902	+	0.0749604i
$171$	431187.			1.12765
$172$			161608.i			0.416526i
$173$		−	360825.i		−	0.916604i	−0.888796	−	0.458302i	$-0.848458\pi$
$173$		−	360825.i		−	0.916604i	0.888796	−	0.458302i	$-0.151542\pi$
$174$	−32421.3			−0.0811817
$175$	194339.	−	376844.i	0.479695	−	0.930180i
$176$	78548.2			0.191141
$177$		−	18658.9i		−	0.0447665i
$178$			129505.i			0.306362i
$179$	65448.4			0.152674			0.0763372	−	0.997082i	$-0.475677\pi$
$179$	65448.4			0.152674			0.0763372	+	0.997082i	$0.475677\pi$
$180$	210266.	+	51024.7i	0.483714	+	0.117381i
$181$	−273186.			−0.619815			−0.309907	−	0.950767i	$-0.600298\pi$
$181$	−273186.			−0.619815			−0.309907	+	0.950767i	$0.600298\pi$
$182$			354724.i			0.793801i
$183$		−	27425.2i		−	0.0605371i
$184$	33856.0			0.0737210
$185$	−4490.34	+	18504.1i	−0.00964606	+	0.0397502i
$186$	−27934.7			−0.0592054
$187$		−	164354.i		−	0.343697i
$188$		−	57216.8i		−	0.118067i
$189$	68764.6			0.140026
$190$	−93991.1	+	387326.i	−0.188887	+	0.778381i
$191$	147801.			0.293152			0.146576	−	0.989199i	$-0.453175\pi$
$191$	147801.			0.293152			0.146576	+	0.989199i	$0.453175\pi$
$192$		−	4281.00i		−	0.00838094i
$193$		−	764650.i		−	1.47764i	−0.673902	−	0.738821i	$-0.735383\pi$
$193$		−	764650.i		−	1.47764i	0.673902	−	0.738821i	$-0.264617\pi$
$194$	−101911.			−0.194409
$195$	−37110.4	−	9005.47i	−0.0698891	−	0.0169598i
$196$	25638.6			0.0476710
$197$			591367.i			1.08565i	0.839845	+	0.542827i	$0.182646\pi$
$197$			591367.i			1.08565i	−0.839845	+	0.542827i	$0.817354\pi$
$198$		−	296897.i		−	0.538199i
$199$	86059.6			0.154052			0.0770258	−	0.997029i	$-0.475458\pi$
$199$	86059.6			0.154052			0.0770258	+	0.997029i	$0.475458\pi$
$200$	−91668.6	+	177755.i	−0.162049	+	0.314230i
$201$	−40680.3			−0.0710222
$202$			247375.i			0.426558i
$203$			1.05222e6i			1.79211i
$204$	−8957.55			−0.0150700
$205$	241916.	+	58705.0i	0.402050	+	0.0975643i
$206$	42682.1			0.0700774
$207$		−	127969.i		−	0.207577i
$208$		−	167321.i		−	0.268159i
$209$	546905.			0.866057
$210$	−7477.84	+	30815.3i	−0.0117011	+	0.0482189i
$211$	−288580.			−0.446232			−0.223116	−	0.974792i	$-0.571623\pi$
$211$	−288580.			−0.446232			−0.223116	+	0.974792i	$0.571623\pi$
$212$			468127.i			0.715359i
$213$		−	8538.36i		−	0.0128951i
$214$	620250.			0.925832
$215$	−133154.	+	548711.i	−0.196453	+	0.809558i
$216$	−32435.8			−0.0473032
$217$			906605.i			1.30698i
$218$		−	761218.i		−	1.08484i
$219$	−7041.14			−0.00992047
$220$	266696.	+	64718.2i	0.371501	+	0.0901508i
$221$	−350101.			−0.482184
$222$		−	1424.01i		−	0.00193924i
$223$		−	605696.i		−	0.815628i	−0.913065	−	0.407814i	$-0.866291\pi$
$223$		−	605696.i		−	0.815628i	0.913065	−	0.407814i	$-0.133709\pi$
$224$	−138938.			−0.185012
$225$	671880.	+	346490.i	0.884780	+	0.456283i
$226$	457808.			0.596228
$227$		−	1.40723e6i		−	1.81260i	−0.422637	−	0.906299i	$-0.638895\pi$
$227$		−	1.40723e6i		−	1.81260i	0.422637	−	0.906299i	$-0.361105\pi$
$228$		−	29807.2i		−	0.0379739i
$229$	641101.			0.807863			0.403932	−	0.914789i	$-0.367643\pi$
$229$	641101.			0.807863			0.403932	+	0.914789i	$0.367643\pi$
$230$	114952.	+	27895.0i	0.143284	+	0.0347702i
$231$	43511.3			0.0536502
$232$		−	496324.i		−	0.605404i
$233$			287656.i			0.347123i	0.984823	+	0.173561i	$0.0555275\pi$
$233$			287656.i			0.347123i	−0.984823	+	0.173561i	$0.944472\pi$
$234$	−632441.			−0.755058
$235$	47142.7	−	194269.i	0.0556858	−	0.229474i
$236$	285641.			0.333842
$237$		−	45257.9i		−	0.0523388i
$238$			290712.i			0.332676i
$239$	392010.			0.443917			0.221959	−	0.975056i	$-0.428755\pi$
$239$	392010.			0.443917			0.221959	+	0.975056i	$0.428755\pi$
$240$	3527.25	−	14535.4i	0.00395283	−	0.0162891i
$241$	−1.43866e6			−1.59556			−0.797782	−	0.602946i	$-0.793993\pi$
$241$	−1.43866e6			−1.59556			−0.797782	+	0.602946i	$0.793993\pi$
$242$			267629.i			0.293761i
$243$			184040.i			0.199938i
$244$	419840.			0.451450
$245$	87051.2	+	21124.4i	0.0926530	+	0.0224838i
$246$	−18617.0			−0.0196143
$247$		−	1.16500e6i		−	1.21502i
$248$		−	427640.i		−	0.441518i
$249$	2656.15			0.00271490
$250$	−457702.	+	528006.i	−0.463162	+	0.534305i
$251$	−249195.			−0.249664			−0.124832	−	0.992178i	$-0.539839\pi$
$251$	−249195.			−0.249664			−0.124832	+	0.992178i	$0.539839\pi$
$252$			525157.i			0.520941i
$253$		−	162312.i		−	0.159423i
$254$	−258155.			−0.251071
$255$	−30413.7	−	7380.40i	−0.0292900	−	0.00710770i
$256$	65536.0			0.0625000
$257$			1.98012e6i			1.87007i	0.354553	+	0.935036i	$0.384633\pi$
$257$			1.98012e6i			1.87007i	−0.354553	+	0.935036i	$0.615367\pi$
$258$		−	42226.9i		−	0.0394948i
$259$	−46215.6			−0.0428094
$260$	137861.	−	568107.i	0.126476	−	0.521191i
$261$	−1.87601e6			−1.70464
$262$		−	195415.i		−	0.175875i
$263$			1.06254e6i			0.947232i	0.880731	+	0.473616i	$0.157052\pi$
$263$			1.06254e6i			0.947232i	−0.880731	+	0.473616i	$0.842948\pi$
$264$	−20524.0			−0.0181239
$265$	−385704.	+	1.58944e6i	−0.337396	+	1.39037i
$266$	−967378.			−0.838286
$267$		−	33838.5i		−	0.0290491i
$268$		−	622757.i		−	0.529641i
$269$	1.04680e6			0.882028			0.441014	−	0.897500i	$-0.354619\pi$
$269$	1.04680e6			0.882028			0.441014	+	0.897500i	$0.354619\pi$
$270$	−110130.	−	26724.8i	−0.0919381	−	0.0223103i
$271$	−2.08470e6			−1.72433			−0.862165	−	0.506627i	$-0.830892\pi$
$271$	−2.08470e6			−1.72433			−0.862165	+	0.506627i	$0.830892\pi$
$272$		−	137127.i		−	0.112383i
$273$		−	92686.4i		−	0.0752678i
$274$	−1.22575e6			−0.986340
$275$	852193.	+	439478.i	0.679526	+	0.350433i
$276$	−8846.29			−0.00699018
$277$		−	542605.i		−	0.424897i	−0.977172	−	0.212449i	$-0.931856\pi$
$277$		−	542605.i		−	0.424897i	0.977172	−	0.212449i	$-0.0681438\pi$
$278$		−	407046.i		−	0.315886i
$279$	−1.61640e6			−1.24319
$280$	−471737.	−	114475.i	−0.359588	−	0.0872600i
$281$	1.02759e6			0.776343			0.388171	−	0.921587i	$-0.373107\pi$
$281$	1.02759e6			0.776343			0.388171	+	0.921587i	$0.373107\pi$
$282$			14950.3i			0.0111951i
$283$		−	43529.6i		−	0.0323086i	−0.999870	−	0.0161543i	$-0.994858\pi$
$283$		−	43529.6i		−	0.0323086i	0.999870	−	0.0161543i	$-0.00514230\pi$
$284$	130710.			0.0961641
$285$	24559.1	−	101205.i	0.0179102	−	0.0738057i
$286$	−802169.			−0.579897
$287$			604206.i			0.432992i
$288$		−	247713.i		−	0.175982i
$289$	1.13293e6			0.797920
$290$	408936.	−	1.68518e6i	0.285536	−	1.17666i
$291$	26628.5			0.0184338
$292$		−	107790.i		−	0.0739809i
$293$			2.42131e6i			1.64771i	0.566800	+	0.823855i	$0.308181\pi$
$293$			2.42131e6i			1.64771i	−0.566800	+	0.823855i	$0.691819\pi$
$294$	−6699.15			−0.00452014
$295$	969843.	+	235349.i	0.648853	+	0.157455i
$296$	21799.6			0.0144617
$297$			155504.i			0.102294i
$298$			1.55432e6i			1.01391i
$299$	−345753.			−0.223660
$300$	23952.3	−	46445.9i	0.0153654	−	0.0297951i
$301$	−1.37045e6			−0.871861
$302$		−	479494.i		−	0.302528i
$303$		−	64637.1i		−	0.0404460i
$304$	456306.			0.283186
$305$	1.42549e6	+	345919.i	0.877434	+	0.212924i
$306$	−518314.			−0.316439
$307$		−	2.63008e6i		−	1.59266i	−0.604864	−	0.796329i	$-0.706773\pi$
$307$		−	2.63008e6i		−	1.59266i	0.604864	−	0.796329i	$-0.293227\pi$
$308$			666095.i			0.400091i
$309$	−11152.5			−0.00664470
$310$	352345.	−	1.45197e6i	0.208240	−	0.858132i
$311$	−3.01644e6			−1.76845			−0.884226	−	0.467060i	$-0.845313\pi$
$311$	−3.01644e6			−1.76845			−0.884226	+	0.467060i	$0.845313\pi$
$312$			43719.6i			0.0254267i
$313$		−	648480.i		−	0.374141i	−0.982346	−	0.187071i	$-0.940101\pi$
$313$		−	648480.i		−	0.374141i	0.982346	−	0.187071i	$-0.0598994\pi$
$314$	414064.			0.236997
$315$	−432693.	+	1.78308e6i	−0.245699	+	1.01250i
$316$	692834.			0.390311
$317$		−	1.16974e6i		−	0.653797i	−0.945059	−	0.326899i	$-0.893996\pi$
$317$		−	1.16974e6i		−	0.653797i	0.945059	−	0.326899i	$-0.106004\pi$
$318$		−	122318.i		−	0.0678300i
$319$	−2.37948e6			−1.30920
$320$	222515.	+	53997.1i	0.121475	+	0.0294778i
$321$	−162066.			−0.0877869
$322$			287102.i			0.154311i
$323$		−	954772.i		−	0.509206i
$324$	−932062.			−0.493267
$325$	936162.	−	1.81532e6i	0.491635	−	0.953331i
$326$	−2.30647e6			−1.20200
$327$			198900.i			0.102864i
$328$		−	285000.i		−	0.146272i
$329$	485203.			0.247135
$330$	−69685.4	−	16910.3i	−0.0352255	−	0.00854806i
$331$	1.04127e6			0.522387			0.261193	−	0.965287i	$-0.415884\pi$
$331$	1.04127e6			0.522387			0.261193	+	0.965287i	$0.415884\pi$
$332$			40661.8i			0.0202461i
$333$		−	82398.3i		−	0.0407200i
$334$	300144.			0.147219
$335$	513109.	−	2.11446e6i	0.249803	−	1.02941i
$336$	36303.3			0.0175427
$337$			4.10013e6i			1.96663i	0.181905	+	0.983316i	$0.441774\pi$
$337$			4.10013e6i			1.96663i	−0.181905	+	0.983316i	$0.558226\pi$
$338$			223585.i			0.106451i
$339$	−119621.			−0.0565340
$340$	112983.	−	465590.i	0.0530050	−	0.218427i
$341$	−2.05019e6			−0.954791
$342$		−	1.72475e6i		−	0.797371i
$343$		−	2.06298e6i		−	0.946802i
$344$	646433.			0.294529
$345$	−30036.0	−	7288.73i	−0.0135861	−	0.00329689i
$346$	−1.44330e6			−0.648137
$347$		−	2.67265e6i		−	1.19157i	−0.803145	−	0.595783i	$-0.796842\pi$
$347$		−	2.67265e6i		−	1.19157i	0.803145	−	0.595783i	$-0.203158\pi$
$348$			129685.i			0.0574041i
$349$	1.00646e6			0.442318			0.221159	−	0.975238i	$-0.429016\pi$
$349$	1.00646e6			0.442318			0.221159	+	0.975238i	$0.429016\pi$
$350$	−1.50738e6	−	777357.i	−0.657736	−	0.339196i
$351$	331249.			0.143512
$352$		−	314193.i		−	0.135157i
$353$			3.39241e6i			1.44901i	0.689270	+	0.724505i	$0.257932\pi$
$353$			3.39241e6i			1.44901i	−0.689270	+	0.724505i	$0.742068\pi$
$354$	−74635.7			−0.0316547
$355$	443802.	+	107696.i	0.186904	+	0.0453553i
$356$	518018.			0.216631
$357$		−	75960.7i		−	0.0315441i
$358$		−	261794.i		−	0.107957i
$359$	−2.58350e6			−1.05797			−0.528984	−	0.848632i	$-0.677427\pi$
$359$	−2.58350e6			−1.05797			−0.528984	+	0.848632i	$0.677427\pi$
$360$	204099.	−	841065.i	0.0830011	−	0.342037i
$361$	701011.			0.283111
$362$			1.09274e6i			0.438275i
$363$		−	69929.1i		−	0.0278543i
$364$	1.41889e6			0.561302
$365$	88811.2	−	365980.i	0.0348928	−	0.143789i
$366$	−109701.			−0.0428062
$367$			4066.82i			0.00157612i	1.00000		0.000788061i	$0.000250848\pi$
$367$			4066.82i			0.00157612i	−1.00000		0.000788061i	$0.999749\pi$
$368$		−	135424.i		−	0.0521286i
$369$	−1.07724e6			−0.411859
$370$	74016.6	+	17961.4i	0.0281077	+	0.00682080i
$371$	−3.96976e6			−1.49737
$372$			111739.i			0.0418645i
$373$		−	441354.i		−	0.164254i	−0.996622	−	0.0821269i	$-0.973829\pi$
$373$		−	441354.i		−	0.164254i	0.996622	−	0.0821269i	$-0.0261713\pi$
$374$	−657415.			−0.243030
$375$	119594.	−	137964.i	0.0439167	−	0.0506625i
$376$	−228867.			−0.0834861
$377$			5.06869e6i			1.83672i
$378$		−	275058.i		−	0.0990137i
$379$	4.59422e6			1.64291			0.821454	−	0.570275i	$-0.193163\pi$
$379$	4.59422e6			1.64291			0.821454	+	0.570275i	$0.193163\pi$
$380$	1.54930e6	+	375964.i	0.550399	+	0.133563i
$381$	67453.9			0.0238064
$382$		−	591202.i		−	0.207290i
$383$			4.04727e6i			1.40983i	0.709293	+	0.704913i	$0.249014\pi$
$383$			4.04727e6i			1.40983i	−0.709293	+	0.704913i	$0.750986\pi$
$384$	−17124.0			−0.00592622
$385$	−548816.	+	2.26160e6i	−0.188701	+	0.777614i
$386$	−3.05860e6			−1.04485
$387$		−	2.44339e6i		−	0.829308i
$388$			407644.i			0.137468i
$389$	1.84822e6			0.619270			0.309635	−	0.950855i	$-0.399793\pi$
$389$	1.84822e6			0.619270			0.309635	+	0.950855i	$0.399793\pi$
$390$	−36021.9	+	148442.i	−0.0119924	+	0.0494191i
$391$	−283360.			−0.0937340
$392$		−	102554.i		−	0.0337085i
$393$			51060.3i			0.0166764i
$394$	2.36547e6			0.767673
$395$	2.35239e6	+	570847.i	0.758606	+	0.184089i
$396$	−1.18759e6			−0.380564
$397$		−	2.19887e6i		−	0.700203i	−0.936712	−	0.350101i	$-0.886147\pi$
$397$		−	2.19887e6i		−	0.700203i	0.936712	−	0.350101i	$-0.113853\pi$
$398$		−	344238.i		−	0.108931i
$399$	252768.			0.0794858
$400$	711020.	+	366674.i	0.222194	+	0.114586i
$401$	431570.			0.134026			0.0670131	−	0.997752i	$-0.478653\pi$
$401$	431570.			0.134026			0.0670131	+	0.997752i	$0.478653\pi$
$402$			162721.i			0.0502203i
$403$			4.36725e6i			1.33951i
$404$	989501.			0.301622
$405$	−3.16464e6	−	767954.i	−0.958710	−	0.232647i
$406$	4.20887e6			1.26721
$407$		−	104512.i		−	0.0312737i
$408$			35830.2i			0.0106561i
$409$	3.34235e6			0.987969			0.493984	−	0.869471i	$-0.335540\pi$
$409$	3.34235e6			0.987969			0.493984	+	0.869471i	$0.335540\pi$
$410$	234820.	−	967665.i	0.0689883	−	0.284292i
$411$	320279.			0.0935242
$412$		−	170728.i		−	0.0495522i
$413$			2.42226e6i			0.698789i
$414$	−511877.			−0.146779
$415$	−33502.5	+	138060.i	−0.00954897	+	0.0393501i
$416$	−669283.			−0.189617
$417$			106358.i			0.0299522i
$418$		−	2.18762e6i		−	0.612395i
$419$	−3.04355e6			−0.846926			−0.423463	−	0.905914i	$-0.639186\pi$
$419$	−3.04355e6			−0.846926			−0.423463	+	0.905914i	$0.639186\pi$
$420$	123261.	+	29911.4i	0.0340959	+	0.00827395i
$421$	3.60005e6			0.989926			0.494963	−	0.868914i	$-0.335182\pi$
$421$	3.60005e6			0.989926			0.494963	+	0.868914i	$0.335182\pi$
$422$			1.15432e6i			0.315534i
$423$			865074.i			0.235073i
$424$	1.87251e6			0.505835
$425$	767228.	−	1.48773e6i	0.206040	−	0.399534i
$426$	−34153.4			−0.00911823
$427$			3.56028e6i			0.944962i
$428$		−	2.48100e6i		−	0.654662i
$429$	209600.			0.0549856
$430$	2.19485e6	+	532616.i	0.572444	+	0.138913i
$431$	3.69022e6			0.956885			0.478442	−	0.878119i	$-0.341202\pi$
$431$	3.69022e6			0.956885			0.478442	+	0.878119i	$0.341202\pi$
$432$			129743.i			0.0334484i
$433$			2.89868e6i			0.742985i	0.928436	+	0.371492i	$0.121154\pi$
$433$			2.89868e6i			0.742985i	−0.928436	+	0.371492i	$0.878846\pi$
$434$	3.62642e6			0.924174
$435$	−106852.	+	440323.i	−0.0270744	+	0.111570i
$436$	−3.04487e6			−0.767101
$437$		−	942913.i		−	0.236194i
$438$			28164.5i			0.00701483i
$439$	6.32986e6			1.56759			0.783795	−	0.621019i	$-0.213281\pi$
$439$	6.32986e6			1.56759			0.783795	+	0.621019i	$0.213281\pi$
$440$	258873.	−	1.06678e6i	0.0637463	−	0.262691i
$441$	−387636.			−0.0949134
$442$			1.40041e6i			0.340956i
$443$		−	5.30452e6i		−	1.28421i	−0.766616	−	0.642106i	$-0.778061\pi$
$443$		−	5.30452e6i		−	1.28421i	0.766616	−	0.642106i	$-0.221939\pi$
$444$	−5696.06			−0.00137125
$445$	1.75884e6	+	426811.i	0.421042	+	0.102173i
$446$	−2.42278e6			−0.576736
$447$		−	406130.i		−	0.0961382i
$448$			555751.i			0.130823i
$449$	1.85789e6			0.434916			0.217458	−	0.976070i	$-0.430224\pi$
$449$	1.85789e6			0.434916			0.217458	+	0.976070i	$0.430224\pi$
$450$	1.38596e6	−	2.68752e6i	0.322641	−	0.625634i
$451$	−1.36635e6			−0.316315
$452$		−	1.83123e6i		−	0.421597i
$453$			125288.i			0.0286856i
$454$	−5.62893e6			−1.28170
$455$	4.81759e6	+	1.16907e6i	1.09094	+	0.264735i
$456$	−119229.			−0.0268516
$457$		−	4.92996e6i		−	1.10421i	−0.833773	−	0.552107i	$-0.813824\pi$
$457$		−	4.92996e6i		−	1.10421i	0.833773	−	0.552107i	$-0.186176\pi$
$458$		−	2.56440e6i		−	0.571245i
$459$	271474.			0.0601446
$460$	111580.	−	459807.i	0.0245862	−	0.101317i
$461$	−6.84869e6			−1.50091			−0.750456	−	0.660920i	$-0.770166\pi$
$461$	−6.84869e6			−1.50091			−0.750456	+	0.660920i	$0.770166\pi$
$462$		−	174045.i		−	0.0379365i
$463$			2.39362e6i			0.518922i	0.965754	+	0.259461i	$0.0835450\pi$
$463$			2.39362e6i			0.518922i	−0.965754	+	0.259461i	$0.916455\pi$
$464$	−1.98530e6			−0.428085
$465$	−92064.9	+	379388.i	−0.0197452	+	0.0813676i
$466$	1.15062e6			0.245453
$467$			302196.i			0.0641205i	0.999486	+	0.0320602i	$0.0102068\pi$
$467$			302196.i			0.0641205i	−0.999486	+	0.0320602i	$0.989793\pi$
$468$			2.52976e6i			0.533906i
$469$	5.28103e6			1.10863
$470$	−777077.	−	188571.i	−0.162263	−	0.0393758i
$471$	−108192.			−0.0224720
$472$		−	1.14257e6i		−	0.236062i
$473$		−	3.09913e6i		−	0.636923i
$474$	−181032.			−0.0370091
$475$	4.95060e6	+	2.55304e6i	1.00676	+	0.519186i
$476$	1.16285e6			0.235237
$477$		−	7.07772e6i		−	1.42429i
$478$		−	1.56804e6i		−	0.313897i
$479$	−830579.			−0.165402			−0.0827012	−	0.996574i	$-0.526355\pi$
$479$	−830579.			−0.165402			−0.0827012	+	0.996574i	$0.526355\pi$
$480$	−58141.4	−	14109.0i	−0.0115181	−	0.00279507i
$481$	−222628.			−0.0438749
$482$			5.75462e6i			1.12823i
$483$		−	75017.3i		−	0.0146317i
$484$	1.07051e6			0.207720
$485$	−335870.	+	1.38408e6i	−0.0648361	+	0.267181i
$486$	736159.			0.141378
$487$		−	5.45624e6i		−	1.04249i	−0.853408	−	0.521244i	$-0.825468\pi$
$487$		−	5.45624e6i		−	1.04249i	0.853408	−	0.521244i	$-0.174532\pi$
$488$		−	1.67936e6i		−	0.319223i
$489$	602662.			0.113973
$490$	84497.7	−	348205.i	0.0158984	−	0.0655155i
$491$	9.06137e6			1.69625			0.848126	−	0.529795i	$-0.177731\pi$
$491$	9.06137e6			1.69625			0.848126	+	0.529795i	$0.177731\pi$
$492$			74468.1i			0.0138694i
$493$			4.15402e6i			0.769753i
$494$	−4.66000e6			−0.859150
$495$	−4.03223e6	−	978489.i	−0.739661	−	0.179491i
$496$	−1.71056e6			−0.312201
$497$			1.10843e6i			0.201288i
$498$		−	10624.6i		−	0.00191972i
$499$	5615.26			0.00100953			0.000504764	−	1.00000i	$-0.499839\pi$
$499$	5615.26			0.00100953			0.000504764		1.00000i	$0.499839\pi$
$500$	2.11202e6	+	1.83081e6i	0.377810	+	0.327505i
$501$	−78425.2			−0.0139592
$502$			996782.i			0.176539i
$503$			1.97299e6i			0.347700i	0.984772	+	0.173850i	$0.0556208\pi$
$503$			1.97299e6i			0.347700i	−0.984772	+	0.173850i	$0.944379\pi$
$504$	2.10063e6			0.368361
$505$	3.35967e6	+	815280.i	0.586230	+	0.142258i
$506$	−649250.			−0.112729
$507$		−	58420.9i		−	0.0100937i
$508$			1.03262e6i			0.177534i
$509$	7.64037e6			1.30713			0.653567	−	0.756869i	$-0.273272\pi$
$509$	7.64037e6			1.30713			0.653567	+	0.756869i	$0.273272\pi$
$510$	−29521.6	+	121655.i	−0.00502590	+	0.0207111i
$511$	914065.			0.154855
$512$		−	262144.i		−	0.0441942i
$513$			903360.i			0.151554i
$514$	7.92047e6			1.32234
$515$	140668.	−	579677.i	0.0233711	−	0.0963093i
$516$	−168908.			−0.0279271
$517$			1.09724e6i			0.180540i
$518$			184862.i			0.0302708i
$519$	377123.			0.0614560
$520$	−2.27243e6	−	551443.i	−0.368538	−	0.0894319i
$521$	−1.05953e7			−1.71008			−0.855041	−	0.518560i	$-0.826468\pi$
$521$	−1.05953e7			−1.71008			−0.855041	+	0.518560i	$0.826468\pi$
$522$			7.50404e6i			1.20537i
$523$		−	1.13458e7i		−	1.81376i	−0.421391	−	0.906879i	$-0.638458\pi$
$523$		−	1.13458e7i		−	1.81376i	0.421391	−	0.906879i	$-0.361542\pi$
$524$	−781660.			−0.124362
$525$	393865.	+	203117.i	0.0623662	+	0.0321624i
$526$	4.25016e6			0.669794
$527$			3.57916e6i			0.561378i
$528$			82095.9i			0.0128155i
$529$	−279841.			−0.0434783
$530$	6.35776e6	+	1.54282e6i	0.983138	+	0.238575i
$531$	−4.31868e6			−0.664683
$532$			3.86951e6i			0.592757i
$533$			2.91055e6i			0.443769i
$534$	−135354.			−0.0205408
$535$	2.04417e6	−	8.42377e6i	0.308768	−	1.27240i
$536$	−2.49103e6			−0.374513
$537$			68404.5i			0.0102364i
$538$		−	4.18720e6i		−	0.623688i
$539$	−491666.			−0.0728951
$540$	−106899.	+	440519.i	−0.0157758	+	0.0650100i
$541$	5.62252e6			0.825920			0.412960	−	0.910749i	$-0.364495\pi$
$541$	5.62252e6			0.825920			0.412960	+	0.910749i	$0.364495\pi$
$542$			8.33880e6i			1.21929i
$543$		−	285525.i		−	0.0415570i
$544$	−548509.			−0.0794669
$545$	−1.03383e7	−	2.50876e6i	−1.49093	−	0.361800i
$546$	−370745.			−0.0532224
$547$		−	1.29390e7i		−	1.84898i	−0.381205	−	0.924491i	$-0.624491\pi$
$547$		−	1.29390e7i		−	1.84898i	0.381205	−	0.924491i	$-0.375509\pi$
$548$			4.90301e6i			0.697448i
$549$	−6.34766e6			−0.898841
$550$	1.75791e6	−	3.40877e6i	0.247794	−	0.480498i
$551$	−1.38230e7			−1.93965
$552$			35385.2i			0.00494281i
$553$			5.87528e6i			0.816989i
$554$	−2.17042e6			−0.300448
$555$	−19339.9	−	4693.16i	−0.00266515	−	0.000646744i
$556$	−1.62818e6			−0.223365
$557$			8.69180e6i			1.18706i	0.804813	+	0.593529i	$0.202266\pi$
$557$			8.69180e6i			1.18706i	−0.804813	+	0.593529i	$0.797734\pi$
$558$			6.46558e6i			0.879067i
$559$	−6.60167e6			−0.893561
$560$	−457900.	+	1.88695e6i	−0.0617022	+	0.254267i
$561$	171777.			0.0230440
$562$		−	4.11035e6i		−	0.548957i
$563$		−	6.04038e6i		−	0.803143i	−0.915828	−	0.401572i	$-0.868464\pi$
$563$		−	6.04038e6i		−	0.803143i	0.915828	−	0.401572i	$-0.131536\pi$
$564$	59801.1			0.00791611
$565$	1.50881e6	−	6.21761e6i	0.198844	−	0.819412i
$566$	−174118.			−0.0228456
$567$		−	7.90396e6i		−	1.03249i
$568$		−	522840.i		−	0.0679983i
$569$	−1.93226e6			−0.250199			−0.125099	−	0.992144i	$-0.539925\pi$
$569$	−1.93226e6			−0.250199			−0.125099	+	0.992144i	$0.539925\pi$
$570$	−404820.	−	98236.4i	−0.0521885	−	0.0126644i
$571$	−1.36085e7			−1.74670			−0.873351	−	0.487091i	$-0.838058\pi$
$571$	−1.36085e7			−1.74670			−0.873351	+	0.487091i	$0.838058\pi$
$572$			3.20868e6i			0.410049i
$573$			154476.i			0.0196551i
$574$	2.41682e6			0.306172
$575$	757698.	−	1.46926e6i	0.0955711	−	0.185322i
$576$	−990854.			−0.124438
$577$		−	8.52471e6i		−	1.06596i	−0.846128	−	0.532979i	$-0.821072\pi$
$577$		−	8.52471e6i		−	1.06596i	0.846128	−	0.532979i	$-0.178928\pi$
$578$		−	4.53173e6i		−	0.564215i
$579$	799187.			0.0990722
$580$	−6.74071e6	−	1.63575e6i	−0.832023	−	0.201904i
$581$	−344815.			−0.0423785
$582$		−	106514.i		−	0.0130346i
$583$		−	8.97718e6i		−	1.09388i
$584$	−431159.			−0.0523124
$585$	−2.08435e6	+	8.58934e6i	−0.251814	+	1.03770i
$586$	9.68523e6			1.16511
$587$		−	1.19850e7i		−	1.43563i	−0.696235	−	0.717814i	$-0.745143\pi$
$587$		−	1.19850e7i		−	1.43563i	0.696235	−	0.717814i	$-0.254857\pi$
$588$			26796.6i			0.00319622i
$589$	−1.19101e7			−1.41457
$590$	941394.	−	3.87937e6i	0.111338	−	0.458808i
$591$	−618077.			−0.0727904
$592$		−	87198.5i		−	0.0102260i
$593$			543235.i			0.0634382i	0.999497	+	0.0317191i	$0.0100982\pi$
$593$			543235.i			0.0634382i	−0.999497	+	0.0317191i	$0.989902\pi$
$594$	622015.			0.0723327
$595$	3.94824e6	+	958107.i	0.457205	+	0.110949i
$596$	6.21726e6			0.716941
$597$			89946.6i			0.0103288i
$598$			1.38301e6i			0.158151i
$599$	−3.46311e6			−0.394366			−0.197183	−	0.980367i	$-0.563179\pi$
$599$	−3.46311e6			−0.394366			−0.197183	+	0.980367i	$0.563179\pi$
$600$	−185784.	−	95809.0i	−0.0210683	−	0.0108650i
$601$	1.59213e7			1.79801			0.899007	−	0.437933i	$-0.144289\pi$
$601$	1.59213e7			1.79801			0.899007	+	0.437933i	$0.144289\pi$
$602$			5.48181e6i			0.616499i
$603$			9.41561e6i			1.05452i
$604$	−1.91798e6			−0.213920
$605$	3.63473e6	+	882029.i	0.403724	+	0.0979703i
$606$	−258548.			−0.0285996
$607$		−	1.25730e7i		−	1.38505i	−0.721393	−	0.692526i	$-0.756498\pi$
$607$		−	1.25730e7i		−	1.38505i	0.721393	−	0.692526i	$-0.243502\pi$
$608$		−	1.82522e6i		−	0.200243i
$609$	−1.09974e6			−0.120157
$610$	1.38368e6	−	5.70196e6i	0.150560	−	0.620440i
$611$	2.33730e6			0.253286
$612$			2.07326e6i			0.223756i
$613$			1.71206e7i			1.84021i	0.391668	+	0.920107i	$0.371898\pi$
$613$			1.71206e7i			1.84021i	−0.391668	+	0.920107i	$0.628102\pi$
$614$	−1.05203e7			−1.12618
$615$	−61356.6	+	252843.i	−0.00654144	+	0.0269565i
$616$	2.66438e6			0.282907
$617$		−	483009.i		−	0.0510790i	−0.999674	−	0.0255395i	$-0.991870\pi$
$617$		−	483009.i		−	0.0510790i	0.999674	−	0.0255395i	$-0.00813036\pi$
$618$			44609.9i			0.00469851i
$619$	−3.91849e6			−0.411048			−0.205524	−	0.978652i	$-0.565890\pi$
$619$	−3.91849e6			−0.411048			−0.205524	+	0.978652i	$0.565890\pi$
$620$	−5.80789e6	−	1.40938e6i	−0.606791	−	0.147248i
$621$	268102.			0.0278979
$622$			1.20657e7i			1.25048i
$623$			4.39284e6i			0.453445i
$624$	174878.			0.0179794
$625$	5.66253e6	+	7.95633e6i	0.579843	+	0.814728i
$626$	−2.59392e6			−0.264558
$627$			571607.i			0.0580669i
$628$		−	1.65626e6i		−	0.167582i
$629$	−182454.			−0.0183876
$630$	7.13230e6	+	1.73077e6i	0.715943	+	0.173736i
$631$	1.65244e7			1.65216			0.826079	−	0.563554i	$-0.190566\pi$
$631$	1.65244e7			1.65216			0.826079	+	0.563554i	$0.190566\pi$
$632$		−	2.77133e6i		−	0.275992i
$633$		−	301615.i		−	0.0299187i
$634$	−4.67898e6			−0.462304
$635$	−850808.	+	3.50608e6i	−0.0837332	+	0.345054i
$636$	−489271.			−0.0479630
$637$			1.04733e6i			0.102267i
$638$			9.51790e6i			0.925741i
$639$	−1.97623e6			−0.191464
$640$	215988.	−	890062.i	0.0208440	−	0.0858955i
$641$	6.38520e6			0.613803			0.306902	−	0.951741i	$-0.400708\pi$
$641$	6.38520e6			0.613803			0.306902	+	0.951741i	$0.400708\pi$
$642$			648265.i			0.0620747i
$643$		−	9.78418e6i		−	0.933248i	−0.884456	−	0.466624i	$-0.845470\pi$
$643$		−	9.78418e6i		−	0.933248i	0.884456	−	0.466624i	$-0.154530\pi$
$644$	1.14841e6			0.109114
$645$	−573495.	−	139168.i	−0.0542788	−	0.0131717i
$646$	−3.81909e6			−0.360063
$647$			6.97062e6i			0.654652i	0.944911	+	0.327326i	$0.106148\pi$
$647$			6.97062e6i			0.654652i	−0.944911	+	0.327326i	$0.893852\pi$
$648$			3.72825e6i			0.348792i
$649$	−5.47769e6			−0.510488
$650$	−7.26126e6	−	3.74465e6i	−0.674107	−	0.347638i
$651$	−947553.			−0.0876297
$652$			9.22589e6i			0.849942i
$653$			5.21829e6i			0.478900i	0.970909	+	0.239450i	$0.0769671\pi$
$653$			5.21829e6i			0.478900i	−0.970909	+	0.239450i	$0.923033\pi$
$654$	795600.			0.0727361
$655$	−2.65398e6	−	644033.i	−0.241710	−	0.0586550i
$656$	−1.14000e6			−0.103430
$657$			1.62970e6i			0.147297i
$658$		−	1.94081e6i		−	0.174751i
$659$	−7.08617e6			−0.635621			−0.317810	−	0.948154i	$-0.602948\pi$
$659$	−7.08617e6			−0.635621			−0.317810	+	0.948154i	$0.602948\pi$
$660$	−67641.3	+	278742.i	−0.00604439	+	0.0249082i
$661$	2.35819e6			0.209930			0.104965	−	0.994476i	$-0.466527\pi$
$661$	2.35819e6			0.209930			0.104965	+	0.994476i	$0.466527\pi$
$662$		−	4.16507e6i		−	0.369383i
$663$		−	365914.i		−	0.0323292i
$664$	162647.			0.0143161
$665$	−3.18821e6	+	1.31382e7i	−0.279571	+	1.15208i
$666$	−329593.			−0.0287934
$667$			4.10243e6i			0.357048i
$668$		−	1.20058e6i		−	0.104100i
$669$	633053.			0.0546858
$670$	−8.45783e6	−	2.05243e6i	−0.727900	−	0.176637i
$671$	−8.05119e6			−0.690325
$672$		−	145213.i		−	0.0124046i
$673$		−	3.19055e6i		−	0.271536i	−0.990741	−	0.135768i	$-0.956650\pi$
$673$		−	3.19055e6i		−	0.271536i	0.990741	−	0.135768i	$-0.0433503\pi$
$674$	1.64005e7			1.39062
$675$	−725914.	+	1.40762e6i	−0.0613234	+	0.118912i
$676$	894340.			0.0752724
$677$		−	2.00247e7i		−	1.67917i	−0.543228	−	0.839585i	$-0.682798\pi$
$677$		−	2.00247e7i		−	1.67917i	0.543228	−	0.839585i	$-0.317202\pi$
$678$			478486.i			0.0399756i
$679$	−3.45685e6			−0.287744
$680$	−1.86236e6	−	451933.i	−0.154451	−	0.0374802i
$681$	1.47079e6			0.121530
$682$			8.20076e6i			0.675139i
$683$		−	4.07427e6i		−	0.334193i	−0.985941	−	0.167097i	$-0.946561\pi$
$683$		−	4.07427e6i		−	0.334193i	0.985941	−	0.167097i	$-0.0534392\pi$
$684$	−6.89899e6			−0.563826
$685$	−4.03974e6	+	1.66473e7i	−0.328948	+	1.35555i
$686$	−8.25191e6			−0.669490
$687$			670058.i			0.0541652i
$688$		−	2.58573e6i		−	0.208263i
$689$	−1.91229e7			−1.53464
$690$	−29154.9	+	120144.i	−0.00233125	+	0.00960680i
$691$	−9.95420e6			−0.793070			−0.396535	−	0.918020i	$-0.629787\pi$
$691$	−9.95420e6			−0.793070			−0.396535	+	0.918020i	$0.629787\pi$
$692$			5.77321e6i			0.458302i
$693$		−	1.00708e7i		−	0.796586i
$694$	−1.06906e7			−0.842565
$695$	−5.52819e6	−	1.34151e6i	−0.434131	−	0.105349i
$696$	518742.			0.0405908
$697$			2.38533e6i			0.185980i
$698$		−	4.02586e6i		−	0.312766i
$699$	−300648.			−0.0232737
$700$	−3.10943e6	+	6.02951e6i	−0.239848	+	0.465090i
$701$	−1.55324e7			−1.19383			−0.596916	−	0.802304i	$-0.703607\pi$
$701$	−1.55324e7			−1.19383			−0.596916	+	0.802304i	$0.703607\pi$
$702$		−	1.32500e6i		−	0.101478i
$703$		−	607135.i		−	0.0463337i
$704$	−1.25677e6			−0.0955706
$705$	203044.	+	49272.0i	0.0153857	+	0.00373360i
$706$	1.35696e7			1.02460
$707$			8.39104e6i			0.631346i
$708$			298543.i			0.0223833i
$709$	−1.85987e6			−0.138952			−0.0694762	−	0.997584i	$-0.522133\pi$
$709$	−1.85987e6			−0.138952			−0.0694762	+	0.997584i	$0.522133\pi$
$710$	430784.	−	1.77521e6i	0.0320711	−	0.132161i
$711$	−1.04751e7			−0.777114
$712$		−	2.07207e6i		−	0.153181i
$713$			3.53471e6i			0.260393i
$714$	−303843.			−0.0223051
$715$	−2.64373e6	+	1.08945e7i	−0.193398	+	0.796969i
$716$	−1.04717e6			−0.0763372
$717$			409716.i			0.0297636i
$718$			1.03340e7i			0.748097i
$719$	1.60336e7			1.15667			0.578333	−	0.815801i	$-0.303704\pi$
$719$	1.60336e7			1.15667			0.578333	+	0.815801i	$0.303704\pi$
$720$	−3.36426e6	−	816394.i	−0.241857	−	0.0586906i
$721$	1.44779e6			0.103721
$722$		−	2.80404e6i		−	0.200190i
$723$		−	1.50363e6i		−	0.106979i
$724$	4.37097e6			0.309907
$725$	−2.15391e7	−	1.11077e7i	−1.52189	−	0.784840i
$726$	−279717.			−0.0196959
$727$		−	9.42934e6i		−	0.661676i	−0.943688	−	0.330838i	$-0.892669\pi$
$727$		−	9.42934e6i		−	0.661676i	0.943688	−	0.330838i	$-0.107331\pi$
$728$		−	5.67558e6i		−	0.396900i
$729$	1.39633e7			0.973129
$730$	−1.46392e6	−	355245.i	−0.101674	−	0.0246729i
$731$	−5.41037e6			−0.374484
$732$			438803.i			0.0302686i
$733$			3.99434e6i			0.274590i	0.990530	+	0.137295i	$0.0438409\pi$
$733$			3.99434e6i			0.274590i	−0.990530	+	0.137295i	$0.956159\pi$
$734$	16267.3			0.00111449
$735$	−22078.5	+	90983.0i	−0.00150748	+	0.00621215i
$736$	−541696.			−0.0368605
$737$			1.19425e7i			0.809890i
$738$			4.30898e6i			0.291228i
$739$	−3.42020e6			−0.230378			−0.115189	−	0.993344i	$-0.536747\pi$
$739$	−3.42020e6			−0.230378			−0.115189	+	0.993344i	$0.536747\pi$
$740$	71845.5	−	296066.i	0.00482303	−	0.0198751i
$741$	1.21762e6			0.0814641
$742$			1.58790e7i			1.05880i
$743$		−	2.73023e7i		−	1.81437i	−0.420727	−	0.907187i	$-0.638225\pi$
$743$		−	2.73023e7i		−	1.81437i	0.420727	−	0.907187i	$-0.361775\pi$
$744$	446955.			0.0296027
$745$	2.11096e7	+	5.12259e6i	1.39344	+	0.338142i
$746$	−1.76542e6			−0.116145
$747$		−	614775.i		−	0.0403101i
$748$			2.62966e6i			0.171848i
$749$	2.10391e7			1.37032
$750$	−551854.	−	478375.i	−0.0358238	−	0.0310538i
$751$	2.36465e7			1.52991			0.764956	−	0.644082i	$-0.222761\pi$
$751$	2.36465e7			1.52991			0.764956	+	0.644082i	$0.222761\pi$
$752$			915469.i			0.0590336i
$753$		−	260451.i		−	0.0167393i
$754$	2.02747e7			1.29875
$755$	−6.51214e6	−	1.58028e6i	−0.415773	−	0.100894i
$756$	−1.10023e6			−0.0700132
$757$			2.48881e7i			1.57853i	0.614054	+	0.789264i	$0.289538\pi$
$757$			2.48881e7i			1.57853i	−0.614054	+	0.789264i	$0.710462\pi$
$758$		−	1.83769e7i		−	1.16171i
$759$	169644.			0.0106889
$760$	1.50386e6	−	6.19721e6i	0.0944436	−	0.389191i
$761$	1.44188e7			0.902544			0.451272	−	0.892386i	$-0.350970\pi$
$761$	1.44188e7			0.902544			0.451272	+	0.892386i	$0.350970\pi$
$762$		−	269816.i		−	0.0168337i
$763$		−	2.58207e7i		−	1.60567i
$764$	−2.36481e6			−0.146576
$765$	−1.70822e6	+	7.03936e6i	−0.105533	+	0.434890i
$766$	1.61891e7			0.996898
$767$			1.16684e7i			0.716181i
$768$			68496.1i			0.00419047i
$769$	2.31087e7			1.40916			0.704578	−	0.709626i	$-0.251136\pi$
$769$	2.31087e7			1.40916			0.704578	+	0.709626i	$0.251136\pi$
$770$	9.04641e6	+	2.19526e6i	0.549856	+	0.133432i
$771$	−2.06955e6			−0.125384
$772$			1.22344e7i			0.738821i
$773$		−	4.88438e6i		−	0.294009i	−0.989136	−	0.147005i	$-0.953037\pi$
$773$		−	4.88438e6i		−	0.294009i	0.989136	−	0.147005i	$-0.0469632\pi$
$774$	−9.77357e6			−0.586409
$775$	−1.85584e7	−	9.57059e6i	−1.10991	−	0.572380i
$776$	1.63057e6			0.0972045
$777$		−	48303.0i		−	0.00287026i
$778$		−	7.39289e6i		−	0.437890i
$779$	−7.93745e6			−0.468638
$780$	593767.	+	144088.i	0.0349446	+	0.00847988i
$781$	−2.50660e6			−0.147047
$782$			1.13344e6i			0.0662800i
$783$		−	3.93034e6i		−	0.229100i
$784$	−410218.			−0.0238355
$785$	1.36464e6	−	5.62351e6i	0.0790395	−	0.325712i
$786$	204241.			0.0117920
$787$			1.52231e7i			0.876123i	0.898945	+	0.438062i	$0.144335\pi$
$787$			1.52231e7i			0.876123i	−0.898945	+	0.438062i	$0.855665\pi$
$788$		−	9.46187e6i		−	0.542827i
$789$	−1.11053e6			−0.0635095
$790$	2.28339e6	−	9.40955e6i	0.130170	−	0.536416i
$791$	1.55290e7			0.882475
$792$			4.75035e6i			0.269099i
$793$			1.71504e7i			0.968481i
$794$	−8.79549e6			−0.495118
$795$	−1.66123e6	−	403125.i	−0.0932206	−	0.0226215i
$796$	−1.37695e6			−0.0770258
$797$		−	3.28940e7i		−	1.83430i	−0.398538	−	0.917152i	$-0.630482\pi$
$797$		−	3.28940e7i		−	1.83430i	0.398538	−	0.917152i	$-0.369518\pi$
$798$		−	1.01107e6i		−	0.0562049i
$799$	1.91552e6			0.106150
$800$	1.46670e6	−	2.84408e6i	0.0810244	−	0.157115i
$801$	−7.83204e6			−0.431314
$802$		−	1.72628e6i		−	0.0947709i
$803$			2.06706e6i			0.113126i
$804$	650885.			0.0355111
$805$	3.89920e6	+	946207.i	0.212073	+	0.0514632i
$806$	1.74690e7			0.947176
$807$			1.09408e6i			0.0591378i
$808$		−	3.95800e6i		−	0.213279i
$809$	−2.18817e7			−1.17547			−0.587733	−	0.809055i	$-0.699979\pi$
$809$	−2.18817e7			−1.17547			−0.587733	+	0.809055i	$0.699979\pi$
$810$	−3.07182e6	+	1.26586e7i	−0.164506	+	0.677910i
$811$	2.37397e7			1.26743			0.633713	−	0.773568i	$-0.281530\pi$
$811$	2.37397e7			1.26743			0.633713	+	0.773568i	$0.281530\pi$
$812$		−	1.68355e7i		−	0.896056i
$813$		−	2.17886e6i		−	0.115612i
$814$	−418047.			−0.0221138
$815$	−7.60149e6	+	3.13248e7i	−0.400871	+	1.65194i
$816$	143321.			0.00753501
$817$		−	1.80036e7i		−	0.943636i
$818$		−	1.33694e7i		−	0.698599i
$819$	−2.14526e7			−1.11756
$820$	−3.87066e6	−	939281.i	−0.201025	−	0.0487821i
$821$	1.15726e7			0.599201			0.299600	−	0.954065i	$-0.403147\pi$
$821$	1.15726e7			0.599201			0.299600	+	0.954065i	$0.403147\pi$
$822$		−	1.28112e6i		−	0.0661316i
$823$		−	5.24721e6i		−	0.270040i	−0.990843	−	0.135020i	$-0.956890\pi$
$823$		−	5.24721e6i		−	0.270040i	0.990843	−	0.135020i	$-0.0431099\pi$
$824$	−682914.			−0.0350387
$825$	−459327.	+	890684.i	−0.0234957	+	0.0455605i
$826$	9.68905e6			0.494118
$827$		−	2.92194e7i		−	1.48562i	−0.669504	−	0.742809i	$-0.733493\pi$
$827$		−	2.92194e7i		−	1.48562i	0.669504	−	0.742809i	$-0.266507\pi$
$828$			2.04751e6i			0.103789i
$829$	3.14372e7			1.58876			0.794379	−	0.607422i	$-0.207796\pi$
$829$	3.14372e7			1.58876			0.794379	+	0.607422i	$0.207796\pi$
$830$	552238.	+	134010.i	0.0278247	+	0.00675214i
$831$	567112.			0.0284883
$832$			2.67713e6i			0.134079i
$833$			858337.i			0.0428593i
$834$	425431.			0.0211794
$835$	989191.	−	4.07634e6i	0.0490980	−	0.202327i
$836$	−8.75048e6			−0.433028
$837$		−	3.38643e6i		−	0.167082i
$838$			1.21742e7i			0.598867i
$839$	3.78510e7			1.85640			0.928201	−	0.372079i	$-0.121355\pi$
$839$	3.78510e7			1.85640			0.928201	+	0.372079i	$0.121355\pi$
$840$	119645.	−	493044.i	0.00585057	−	0.0241095i
$841$	3.96299e7			1.93211
$842$		−	1.44002e7i		−	0.699983i
$843$			1.07400e6i			0.0520518i
$844$	4.61729e6			0.223116
$845$	3.03657e6	+	736874.i	0.146299	+	0.0355019i
$846$	3.46030e6			0.166222
$847$			9.07805e6i			0.434794i
$848$		−	7.49003e6i		−	0.357680i
$849$	45495.7			0.00216621
$850$	−5.95094e6	−	3.06891e6i	−0.282513	−	0.145692i
$851$	−180187.			−0.00852905
$852$			136614.i			0.00644756i
$853$			1.85096e7i			0.871015i	0.900185	+	0.435507i	$0.143431\pi$
$853$			1.85096e7i			0.871015i	−0.900185	+	0.435507i	$0.856569\pi$
$854$	1.42411e7			0.668189
$855$	−2.34243e7	−	5.68429e6i	−1.09585	−	0.265926i
$856$	−9.92400e6			−0.462916
$857$		−	5.18480e6i		−	0.241146i	−0.992704	−	0.120573i	$-0.961527\pi$
$857$		−	5.18480e6i		−	0.241146i	0.992704	−	0.120573i	$-0.0384732\pi$
$858$		−	838401.i		−	0.0388807i
$859$	−1.84018e7			−0.850896			−0.425448	−	0.904983i	$-0.639884\pi$
$859$	−1.84018e7			−0.850896			−0.425448	+	0.904983i	$0.639884\pi$
$860$	2.13046e6	−	8.77938e6i	0.0982264	−	0.404779i
$861$	−631496.			−0.0290310
$862$		−	1.47609e7i		−	0.676620i
$863$			5.74126e6i			0.262410i	0.991355	+	0.131205i	$0.0418846\pi$
$863$			5.74126e6i			0.262410i	−0.991355	+	0.131205i	$0.958115\pi$
$864$	518973.			0.0236516
$865$	−4.75672e6	+	1.96019e7i	−0.216156	+	0.890753i
$866$	1.15947e7			0.525369
$867$			1.18410e6i			0.0534986i
$868$		−	1.45057e7i		−	0.653490i
$869$	−1.32863e7			−0.596837
$870$	1.76129e6	+	427407.i	0.0788920	+	0.0191445i
$871$	2.54395e7			1.13622
$872$			1.21795e7i			0.542422i
$873$		−	6.16325e6i		−	0.273700i
$874$	−3.77165e6			−0.167014
$875$	−1.55254e7	+	1.79101e7i	−0.685524	+	0.790822i
$876$	112658.			0.00496024
$877$		−	6.60799e6i		−	0.290115i	−0.989423	−	0.145058i	$-0.953663\pi$
$877$		−	6.60799e6i		−	0.290115i	0.989423	−	0.145058i	$-0.0463367\pi$
$878$		−	2.53194e7i		−	1.10845i
$879$	−2.53067e6			−0.110475
$880$	−4.26713e6	−	1.03549e6i	−0.185750	−	0.0450754i
$881$	1.17611e7			0.510516			0.255258	−	0.966873i	$-0.417840\pi$
$881$	1.17611e7			0.510516			0.255258	+	0.966873i	$0.417840\pi$
$882$			1.55054e6i			0.0671139i
$883$		−	9.99352e6i		−	0.431337i	−0.976467	−	0.215668i	$-0.930807\pi$
$883$		−	9.99352e6i		−	0.431337i	0.976467	−	0.215668i	$-0.0691930\pi$
$884$	5.60162e6			0.241092
$885$	−245979.	+	1.01365e6i	−0.0105570	+	0.0435040i
$886$	−2.12181e7			−0.908075
$887$		−	1.59119e7i		−	0.679068i	−0.940594	−	0.339534i	$-0.889731\pi$
$887$		−	1.59119e7i		−	0.679068i	0.940594	−	0.339534i	$-0.110269\pi$
$888$			22784.2i			0.000969621i
$889$	−8.75672e6			−0.371610
$890$	1.70724e6	−	7.03534e6i	0.0722471	−	0.297722i
$891$	1.78740e7			0.754269
$892$			9.69113e6i			0.407814i
$893$			6.37412e6i			0.267480i
$894$	−1.62452e6			−0.0679800
$895$	−3.55549e6	−	862799.i	−0.148368	−	0.0360041i
$896$	2.22300e6			0.0925060
$897$		−	361369.i		−	0.0149958i
$898$		−	7.43158e6i		−	0.307532i
$899$	5.18183e7			2.13838
$900$	−1.07501e7	−	5.54383e6i	−0.442390	−	0.228141i
$901$	−1.56721e7			−0.643155
$902$			5.46539e6i			0.223668i
$903$		−	1.43235e6i		−	0.0584561i
$904$	−7.32493e6			−0.298114
$905$	1.48408e7	+	3.60138e6i	0.602333	+	0.146166i
$906$	501152.			0.0202838
$907$		−	9.67603e6i		−	0.390552i	−0.980748	−	0.195276i	$-0.937440\pi$
$907$		−	9.67603e6i		−	0.390552i	0.980748	−	0.195276i	$-0.0625603\pi$
$908$			2.25157e7i			0.906299i
$909$	−1.49605e7			−0.600532
$910$	4.67628e6	−	1.92704e7i	0.187196	−	0.771413i
$911$	3.08403e7			1.23118			0.615592	−	0.788065i	$-0.288917\pi$
$911$	3.08403e7			1.23118			0.615592	+	0.788065i	$0.288917\pi$
$912$			476916.i			0.0189869i
$913$		−	779762.i		−	0.0309589i
$914$	−1.97199e7			−0.780797
$915$	−361543.	+	1.48987e6i	−0.0142760	+	0.0588298i
$916$	−1.02576e7			−0.403932
$917$		−	6.62854e6i		−	0.260312i
$918$		−	1.08590e6i		−	0.0425286i
$919$	5.55331e6			0.216902			0.108451	−	0.994102i	$-0.465411\pi$
$919$	5.55331e6			0.216902			0.108451	+	0.994102i	$0.465411\pi$
$920$	−1.83923e6	−	446320.i	−0.0716418	−	0.0173851i
$921$	2.74887e6			0.106784
$922$			2.73948e7i			1.06131i
$923$			5.33948e6i			0.206298i
$924$	−696180.			−0.0268251
$925$	487876.	−	946043.i	0.0187480	−	0.0363544i
$926$	9.57447e6			0.366934
$927$			2.58128e6i			0.0986589i
$928$			7.94119e6i			0.302702i
$929$	−3.28078e7			−1.24720			−0.623602	−	0.781742i	$-0.714331\pi$
$929$	−3.28078e7			−1.24720			−0.623602	+	0.781742i	$0.714331\pi$
$930$	1.51755e6	+	368260.i	0.0575356	+	0.0139620i
$931$	−2.85621e6			−0.107998
$932$		−	4.60249e6i		−	0.173561i
$933$		−	3.15268e6i		−	0.118570i
$934$	1.20879e6			0.0453400
$935$	−2.16666e6	+	8.92852e6i	−0.0810515	+	0.334003i
$936$	1.01190e7			0.377529
$937$		−	2.75719e7i		−	1.02593i	−0.858410	−	0.512965i	$-0.828547\pi$
$937$		−	2.75719e7i		−	1.02593i	0.858410	−	0.512965i	$-0.171453\pi$
$938$		−	2.11241e7i		−	0.783920i
$939$	677770.			0.0250852
$940$	−754283.	+	3.10831e6i	−0.0278429	+	0.114737i
$941$	−3.67021e6			−0.135119			−0.0675595	−	0.997715i	$-0.521521\pi$
$941$	−3.67021e6			−0.135119			−0.0675595	+	0.997715i	$0.521521\pi$
$942$			432766.i			0.0158901i
$943$			2.35570e6i			0.0862663i
$944$	−4.57026e6			−0.166921
$945$	−3.73564e6	−	906515.i	−0.136077	−	0.0330214i
$946$	−1.23965e7			−0.450373
$947$			1.52856e7i			0.553871i	0.960888	+	0.276936i	$0.0893189\pi$
$947$			1.52856e7i			0.553871i	−0.960888	+	0.276936i	$0.910681\pi$
$948$			724127.i			0.0261694i
$949$	4.40319e6			0.158709
$950$	1.02121e7	−	1.98024e7i	0.367120	−	0.711884i
$951$	1.22258e6			0.0438355
$952$		−	4.65140e6i		−	0.166338i
$953$			5.42372e7i			1.93448i	0.253860	+	0.967241i	$0.418300\pi$
$953$			5.42372e7i			1.93448i	−0.253860	+	0.967241i	$0.581700\pi$
$954$	−2.83109e7			−1.00712
$955$	−8.02927e6	−	1.94844e6i	−0.284884	−	0.0691318i
$956$	−6.27216e6			−0.221959
$957$		−	2.48695e6i		−	0.0877783i
$958$			3.32231e6i			0.116957i
$959$	−4.15779e7			−1.45988
$960$	−56436.0	+	232566.i	−0.00197641	+	0.00814456i
$961$	1.60182e7			0.559508
$962$			890510.i			0.0310243i
$963$			3.75108e7i			1.30344i
$964$	2.30185e7			0.797782
$965$	−1.00803e7	+	4.15396e7i	−0.348462	+	1.43597i
$966$	−300069.			−0.0103461
$967$			3.94917e7i			1.35813i	0.734080	+	0.679063i	$0.237614\pi$
$967$			3.94917e7i			1.35813i	−0.734080	+	0.679063i	$0.762386\pi$
$968$		−	4.28206e6i		−	0.146880i
$969$	997896.			0.0341410
$970$	5.53631e6	+	1.34348e6i	0.188926	+	0.0458460i
$971$	2.88707e7			0.982672			0.491336	−	0.870970i	$-0.336509\pi$
$971$	2.88707e7			0.982672			0.491336	+	0.870970i	$0.336509\pi$
$972$		−	2.94464e6i		−	0.0999691i
$973$		−	1.38071e7i		−	0.467542i
$974$	−2.18250e7			−0.737150
$975$	1.89731e6	+	978445.i	0.0639185	+	0.0329629i
$976$	−6.71744e6			−0.225725
$977$			6.10164e6i			0.204508i	0.994758	+	0.102254i	$0.0326054\pi$
$977$			6.10164e6i			0.204508i	−0.994758	+	0.102254i	$0.967395\pi$
$978$		−	2.41065e6i		−	0.0805910i
$979$	−9.93393e6			−0.331257
$980$	−1.39282e6	−	337991.i	−0.0463265	−	0.0112419i
$981$	4.60361e7			1.52731
$982$		−	3.62455e7i		−	1.19943i
$983$			2.72036e7i			0.897930i	0.893549	+	0.448965i	$0.148207\pi$
$983$			2.72036e7i			0.897930i	−0.893549	+	0.448965i	$0.851793\pi$
$984$	297873.			0.00980715
$985$	7.79592e6	−	3.21260e7i	0.256022	−	1.05503i
$986$	1.66161e7			0.544298
$987$			507119.i			0.0165698i
$988$			1.86400e7i			0.607511i
$989$	−5.34317e6			−0.173704
$990$	−3.91396e6	+	1.61289e7i	−0.126919	+	0.523019i
$991$	2.79424e7			0.903815			0.451907	−	0.892065i	$-0.350744\pi$
$991$	2.79424e7			0.903815			0.451907	+	0.892065i	$0.350744\pi$
$992$			6.84224e6i			0.220759i
$993$			1.08830e6i			0.0350247i
$994$	4.43372e6			0.142332
$995$	−4.67519e6	−	1.13451e6i	−0.149707	−	0.0363289i
$996$	−42498.3			−0.00135745
$997$			4.11690e7i			1.31170i	0.754893	+	0.655848i	$0.227689\pi$
$997$			4.11690e7i			1.31170i	−0.754893	+	0.655848i	$0.772311\pi$
$998$		−	22461.0i		−	0.000713845i
$999$	172629.			0.00547268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.b.a.139.7	✓	26
5.4	even	2	inner	230.6.b.a.139.20	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.b.a.139.7	✓	26	1.1	even	1	trivial
230.6.b.a.139.20	yes	26	5.4	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} +1.04517i q^{3} -16.0000 q^{4} +(-54.3251 - 13.1829i) q^{5} +4.18067 q^{6} -135.681i q^{7} +64.0000i q^{8} +241.908 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} +1.04517i q^{3} -16.0000 q^{4} +(-54.3251 - 13.1829i) q^{5} +4.18067 q^{6} -135.681i q^{7} +64.0000i q^{8} +241.908 q^{9} +(-52.7315 + 217.300i) q^{10} +306.829 q^{11} -16.7227i q^{12} -653.597i q^{13} -542.725 q^{14} +(13.7783 - 56.7788i) q^{15} +256.000 q^{16} -535.653i q^{17} -967.631i q^{18} +1782.44 q^{19} +(869.201 + 210.926i) q^{20} +141.810 q^{21} -1227.31i q^{22} -529.000i q^{23} -66.8907 q^{24} +(2777.42 + 1432.32i) q^{25} -2614.39 q^{26} +506.809i q^{27} +2170.90i q^{28} -7755.06 q^{29} +(-227.115 - 55.1133i) q^{30} -6681.87 q^{31} -1024.00i q^{32} +320.687i q^{33} -2142.61 q^{34} +(-1788.67 + 7370.89i) q^{35} -3870.52 q^{36} -340.619i q^{37} -7129.78i q^{38} +683.118 q^{39} +(843.705 - 3476.80i) q^{40} -4453.12 q^{41} -567.238i q^{42} -10100.5i q^{43} -4909.26 q^{44} +(-13141.6 - 3189.04i) q^{45} -2116.00 q^{46} +3576.05i q^{47} +267.563i q^{48} -1602.41 q^{49} +(5729.29 - 11109.7i) q^{50} +559.847 q^{51} +10457.6i q^{52} -29257.9i q^{53} +2027.24 q^{54} +(-16668.5 - 4044.89i) q^{55} +8683.60 q^{56} +1862.95i q^{57} +31020.3i q^{58} -17852.6 q^{59} +(-220.453 + 908.460i) q^{60} -26240.0 q^{61} +26727.5i q^{62} -32822.3i q^{63} -4096.00 q^{64} +(-8616.30 + 35506.7i) q^{65} +1282.75 q^{66} +38922.3i q^{67} +8570.45i q^{68} +552.893 q^{69} +(29483.6 + 7154.68i) q^{70} -8169.37 q^{71} +15482.1i q^{72} +6736.85i q^{73} -1362.48 q^{74} +(-1497.02 + 2902.87i) q^{75} -28519.1 q^{76} -41630.9i q^{77} -2732.47i q^{78} -43302.1 q^{79} +(-13907.2 - 3374.82i) q^{80} +58253.9 q^{81} +17812.5i q^{82} -2541.36i q^{83} -2268.95 q^{84} +(-7061.45 + 29099.4i) q^{85} -40402.1 q^{86} -8105.34i q^{87} +19637.0i q^{88} -32376.1 q^{89} +(-12756.2 + 52566.6i) q^{90} -88680.9 q^{91} +8464.00i q^{92} -6983.67i q^{93} +14304.2 q^{94} +(-96831.4 - 23497.8i) q^{95} +1070.25 q^{96} -25477.7i q^{97} +6409.65i q^{98} +74224.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9}+O(q^{10}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9	\( 26 q - 416 q^{4} - 30 q^{5} - 72 q^{6} - 1400 q^{9} + 80 q^{10} - 1314 q^{11} + 808 q^{14} + 1280 q^{15} + 6656 q^{16} + 6630 q^{19} + 480 q^{20} - 10060 q^{21} + 1152 q^{24} - 10470 q^{25} - 376 q^{26} + 16084 q^{29} - 6200 q^{30} + 418 q^{31} + 3320 q^{34} - 3160 q^{35} + 22400 q^{36} + 71296 q^{39} - 1280 q^{40} - 35826 q^{41} + 21024 q^{44} - 83960 q^{45} - 55016 q^{46} + 53532 q^{49} - 20800 q^{50} - 25430 q^{51} + 98736 q^{54} - 110390 q^{55} - 12928 q^{56} + 126992 q^{59} - 20480 q^{60} - 63662 q^{61} - 106496 q^{64} - 88520 q^{65} - 18664 q^{66} - 9522 q^{69} - 116520 q^{70} - 106514 q^{71} + 183536 q^{74} - 44200 q^{75} - 106080 q^{76} + 324676 q^{79} - 7680 q^{80} - 170702 q^{81} + 160960 q^{84} + 120780 q^{85} - 42768 q^{86} + 465200 q^{89} + 61360 q^{90} - 468838 q^{91} + 107152 q^{94} + 309670 q^{95} - 18432 q^{96} + 523850 q^{99}+O(q^{100}) \) 26 * q - 416 * q^4 - 30 * q^5 - 72 * q^6 - 1400 * q^9 + 80 * q^10 - 1314 * q^11 + 808 * q^14 + 1280 * q^15 + 6656 * q^16 + 6630 * q^19 + 480 * q^20 - 10060 * q^21 + 1152 * q^24 - 10470 * q^25 - 376 * q^26 + 16084 * q^29 - 6200 * q^30 + 418 * q^31 + 3320 * q^34 - 3160 * q^35 + 22400 * q^36 + 71296 * q^39 - 1280 * q^40 - 35826 * q^41 + 21024 * q^44 - 83960 * q^45 - 55016 * q^46 + 53532 * q^49 - 20800 * q^50 - 25430 * q^51 + 98736 * q^54 - 110390 * q^55 - 12928 * q^56 + 126992 * q^59 - 20480 * q^60 - 63662 * q^61 - 106496 * q^64 - 88520 * q^65 - 18664 * q^66 - 9522 * q^69 - 116520 * q^70 - 106514 * q^71 + 183536 * q^74 - 44200 * q^75 - 106080 * q^76 + 324676 * q^79 - 7680 * q^80 - 170702 * q^81 + 160960 * q^84 + 120780 * q^85 - 42768 * q^86 + 465200 * q^89 + 61360 * q^90 - 468838 * q^91 + 107152 * q^94 + 309670 * q^95 - 18432 * q^96 + 523850 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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