LMFDB - Embedded newform 147.6.c.d.146.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.7
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.29037i q^{2} +(-1.28755 - 15.5352i) q^{3} +13.5927 q^{4} -75.7260 q^{5} +(-66.6517 + 5.52407i) q^{6} -195.610i q^{8} +(-239.684 + 40.0047i) q^{9} +324.892i q^{10} -683.827i q^{11} +(-17.5013 - 211.166i) q^{12} +904.705i q^{13} +(97.5011 + 1176.42i) q^{15} -404.270 q^{16} -831.582 q^{17} +(171.635 + 1028.33i) q^{18} +46.6911i q^{19} -1029.32 q^{20} -2933.87 q^{22} +3225.98i q^{23} +(-3038.83 + 251.857i) q^{24} +2609.42 q^{25} +3881.52 q^{26} +(930.087 + 3672.04i) q^{27} -644.085i q^{29} +(5047.27 - 418.316i) q^{30} -818.506i q^{31} -4525.04i q^{32} +(-10623.4 + 880.462i) q^{33} +3567.79i q^{34} +(-3257.97 + 543.773i) q^{36} +12520.8 q^{37} +200.322 q^{38} +(14054.8 - 1164.85i) q^{39} +14812.7i q^{40} -3585.21 q^{41} -12749.4 q^{43} -9295.07i q^{44} +(18150.3 - 3029.40i) q^{45} +13840.7 q^{46} +5088.30 q^{47} +(520.519 + 6280.42i) q^{48} -11195.4i q^{50} +(1070.70 + 12918.8i) q^{51} +12297.4i q^{52} +29225.7i q^{53} +(15754.4 - 3990.42i) q^{54} +51783.4i q^{55} +(725.355 - 60.1172i) q^{57} -2763.36 q^{58} -14257.9 q^{59} +(1325.31 + 15990.7i) q^{60} -1026.97i q^{61} -3511.69 q^{62} -32350.7 q^{64} -68509.7i q^{65} +(3777.51 + 45578.2i) q^{66} -6569.50 q^{67} -11303.5 q^{68} +(50116.3 - 4153.62i) q^{69} +21670.0i q^{71} +(7825.31 + 46884.6i) q^{72} -56169.9i q^{73} -53719.0i q^{74} +(-3359.77 - 40537.9i) q^{75} +634.660i q^{76} +(-4997.66 - 60300.1i) q^{78} -24516.2 q^{79} +30613.8 q^{80} +(55848.2 - 19177.0i) q^{81} +15381.9i q^{82} -113500. q^{83} +62972.3 q^{85} +54699.8i q^{86} +(-10006.0 + 829.293i) q^{87} -133763. q^{88} -12023.0 q^{89} +(-12997.2 - 77871.7i) q^{90} +43849.9i q^{92} +(-12715.6 + 1053.87i) q^{93} -21830.7i q^{94} -3535.73i q^{95} +(-70297.4 + 5826.22i) q^{96} -131890. i q^{97} +(27356.3 + 163903. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51}+ \cdots - 258480 q^{99}+O(q^{100}) $ 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	4.29037i		−	0.758437i	−0.925307	−	0.379219i	$-0.876193\pi$
$2$		−	4.29037i		−	0.758437i	0.925307	−	0.379219i	$-0.123807\pi$
$3$	−1.28755	−	15.5352i	−0.0825965	−	0.996583i
$3$	−1.28755	−	15.5352i	−0.0825965	−	0.996583i
$4$	13.5927			0.424773
$5$	−75.7260			−1.35463			−0.677314	−	0.735694i	$-0.736856\pi$
$5$	−75.7260			−1.35463			−0.677314	+	0.735694i	$0.736856\pi$
$6$	−66.6517	+	5.52407i	−0.755846	+	0.0626442i
$7$		0			0
$7$		0			0
$8$		−	195.610i		−	1.08060i
$9$	−239.684	+	40.0047i	−0.986356	+	0.164628i
$10$			324.892i			1.02740i
$11$		−	683.827i		−	1.70398i	−0.523559	−	0.851989i	$-0.675396\pi$
$11$		−	683.827i		−	1.70398i	0.523559	−	0.851989i	$-0.324604\pi$
$12$	−17.5013	−	211.166i	−0.0350847	−	0.423321i
$13$			904.705i			1.48473i	0.669993	+	0.742367i	$0.266297\pi$
$13$			904.705i			1.48473i	−0.669993	+	0.742367i	$0.733703\pi$
$14$		0			0
$15$	97.5011	+	1176.42i	0.111887	+	1.35000i
$16$	−404.270			−0.394795
$17$	−831.582			−0.697883			−0.348941	−	0.937145i	$-0.613459\pi$
$17$	−831.582			−0.697883			−0.348941	+	0.937145i	$0.613459\pi$
$18$	171.635	+	1028.33i	0.124860	+	0.748089i
$19$			46.6911i			0.0296722i	0.999890	+	0.0148361i	$0.00472266\pi$
$19$			46.6911i			0.0296722i	−0.999890	+	0.0148361i	$0.995277\pi$
$20$	−1029.32			−0.575409
$21$		0			0
$22$	−2933.87			−1.29236
$23$			3225.98i			1.27158i	0.771863	+	0.635788i	$0.219325\pi$
$23$			3225.98i			1.27158i	−0.771863	+	0.635788i	$0.780675\pi$
$24$	−3038.83	+	251.857i	−1.07691	+	0.0892538i
$25$	2609.42			0.835016
$26$	3881.52			1.12608
$27$	930.087	+	3672.04i	0.245535	+	0.969388i
$28$		0			0
$29$		−	644.085i		−	0.142216i	−0.997469	−	0.0711080i	$-0.977347\pi$
$29$		−	644.085i		−	0.142216i	0.997469	−	0.0711080i	$-0.0226535\pi$
$30$	5047.27	−	418.316i	1.02389	−	0.0848596i
$31$		−	818.506i		−	0.152974i	−0.997071	−	0.0764870i	$-0.975630\pi$
$31$		−	818.506i		−	0.152974i	0.997071	−	0.0764870i	$-0.0243704\pi$
$32$		−	4525.04i		−	0.781173i
$33$	−10623.4	+	880.462i	−1.69816	+	0.140743i
$34$			3567.79i			0.529300i
$35$		0			0
$36$	−3257.97	+	543.773i	−0.418977	+	0.0699297i
$37$	12520.8			1.50359			0.751794	−	0.659398i	$-0.229189\pi$
$37$	12520.8			1.50359			0.751794	+	0.659398i	$0.229189\pi$
$38$	200.322			0.0225045
$39$	14054.8	−	1164.85i	1.47966	−	0.122634i
$40$			14812.7i			1.46381i
$41$	−3585.21			−0.333085			−0.166543	−	0.986034i	$-0.553260\pi$
$41$	−3585.21			−0.333085			−0.166543	+	0.986034i	$0.553260\pi$
$42$		0			0
$43$	−12749.4			−1.05153			−0.525763	−	0.850631i	$-0.676220\pi$
$43$	−12749.4			−1.05153			−0.525763	+	0.850631i	$0.676220\pi$
$44$		−	9295.07i		−	0.723804i
$45$	18150.3	−	3029.40i	1.33614	−	0.223010i
$46$	13840.7			0.964411
$47$	5088.30			0.335991			0.167996	−	0.985788i	$-0.446271\pi$
$47$	5088.30			0.335991			0.167996	+	0.985788i	$0.446271\pi$
$48$	520.519	+	6280.42i	0.0326087	+	0.393446i
$49$		0			0
$50$		−	11195.4i		−	0.633307i
$51$	1070.70	+	12918.8i	0.0576427	+	0.695498i
$52$			12297.4i			0.630675i
$53$			29225.7i			1.42914i	0.699562	+	0.714572i	$0.253378\pi$
$53$			29225.7i			1.42914i	−0.699562	+	0.714572i	$0.746622\pi$
$54$	15754.4	−	3990.42i	0.735220	−	0.186223i
$55$			51783.4i			2.30826i
$56$		0			0
$57$	725.355	−	60.1172i	0.0295708	−	0.00245082i
$58$	−2763.36			−0.107862
$59$	−14257.9			−0.533242			−0.266621	−	0.963801i	$-0.585907\pi$
$59$	−14257.9			−0.533242			−0.266621	+	0.963801i	$0.585907\pi$
$60$	1325.31	+	15990.7i	0.0475267	+	0.573443i
$61$		−	1026.97i		−	0.0353374i	−0.999844	−	0.0176687i	$-0.994376\pi$
$61$		−	1026.97i		−	0.0353374i	0.999844	−	0.0176687i	$-0.00562442\pi$
$62$	−3511.69			−0.116021
$63$		0			0
$64$	−32350.7			−0.987266
$65$		−	68509.7i		−	2.01126i
$66$	3777.51	+	45578.2i	0.106744	+	1.28795i
$67$	−6569.50			−0.178791			−0.0893954	−	0.995996i	$-0.528493\pi$
$67$	−6569.50			−0.178791			−0.0893954	+	0.995996i	$0.528493\pi$
$68$	−11303.5			−0.296442
$69$	50116.3	−	4153.62i	1.26723	−	0.105028i
$70$		0			0
$71$			21670.0i			0.510169i	0.966919	+	0.255084i	$0.0821032\pi$
$71$			21670.0i			0.510169i	−0.966919	+	0.255084i	$0.917897\pi$
$72$	7825.31	+	46884.6i	0.177898	+	1.06586i
$73$		−	56169.9i		−	1.23366i	−0.787096	−	0.616831i	$-0.788416\pi$
$73$		−	56169.9i		−	1.23366i	0.787096	−	0.616831i	$-0.211584\pi$
$74$		−	53719.0i		−	1.14038i
$75$	−3359.77	−	40537.9i	−0.0689693	−	0.832162i
$76$			634.660i			0.0126040i
$77$		0			0
$78$	−4997.66	−	60300.1i	−0.0930100	−	1.12223i
$79$	−24516.2			−0.441962			−0.220981	−	0.975278i	$-0.570926\pi$
$79$	−24516.2			−0.441962			−0.220981	+	0.975278i	$0.570926\pi$
$80$	30613.8			0.534801
$81$	55848.2	−	19177.0i	0.945795	−	0.324764i
$82$			15381.9i			0.252624i
$83$	−113500.			−1.80843			−0.904213	−	0.427083i	$-0.859541\pi$
$83$	−113500.			−1.80843			−0.904213	+	0.427083i	$0.859541\pi$
$84$		0			0
$85$	62972.3			0.945371
$86$			54699.8i			0.797517i
$87$	−10006.0	+	829.293i	−0.141730	+	0.0117465i
$88$	−133763.			−1.84132
$89$	−12023.0			−0.160893			−0.0804465	−	0.996759i	$-0.525635\pi$
$89$	−12023.0			−0.160893			−0.0804465	+	0.996759i	$0.525635\pi$
$90$	−12997.2	−	77871.7i	−0.169139	−	1.01338i
$91$		0			0
$92$			43849.9i			0.540131i
$93$	−12715.6	+	1053.87i	−0.152451	+	0.0126351i
$94$		−	21830.7i		−	0.254828i
$95$		−	3535.73i		−	0.0401948i
$96$	−70297.4	+	5826.22i	−0.778504	+	0.0645222i
$97$		−	131890.i		−	1.42326i	−0.702555	−	0.711630i	$-0.747957\pi$
$97$		−	131890.i		−	1.42326i	0.702555	−	0.711630i	$-0.252043\pi$
$98$		0			0
$99$	27356.3	+	163903.i	0.280523	+	1.68073i
$100$	35469.2			0.354692
$101$	−155285.			−1.51470			−0.757349	−	0.653010i	$-0.773506\pi$
$101$	−155285.			−1.51470			−0.757349	+	0.653010i	$0.773506\pi$
$102$	55426.3	−	4593.72i	0.527492	−	0.0437183i
$103$			117670.i			1.09288i	0.837497	+	0.546442i	$0.184018\pi$
$103$			117670.i			1.09288i	−0.837497	+	0.546442i	$0.815982\pi$
$104$	176969.			1.60440
$105$		0			0
$106$	125389.			1.08392
$107$			43888.8i			0.370591i	0.982683	+	0.185295i	$0.0593242\pi$
$107$			43888.8i			0.370591i	−0.982683	+	0.185295i	$0.940676\pi$
$108$	12642.4	+	49913.0i	0.104297	+	0.411769i
$109$	−141463.			−1.14045			−0.570223	−	0.821490i	$-0.693143\pi$
$109$	−141463.			−1.14045			−0.570223	+	0.821490i	$0.693143\pi$
$110$	222170.			1.75067
$111$	−16121.2	−	194514.i	−0.124191	−	1.49845i
$112$		0			0
$113$		−	150708.i		−	1.11030i	−0.831750	−	0.555151i	$-0.812661\pi$
$113$		−	150708.i		−	1.11030i	0.831750	−	0.555151i	$-0.187339\pi$
$114$	−257.925	−	3112.04i	−0.00185879	−	0.0224276i
$115$		−	244291.i		−	1.72251i
$116$		−	8754.87i		−	0.0604095i
$117$	−36192.5	−	216844.i	−0.244429	−	1.46448i
$118$			61171.5i			0.404431i
$119$		0			0
$120$	230119.	−	19072.2i	1.45881	−	0.120906i
$121$	−306568.			−1.90354
$122$	−4406.10			−0.0268012
$123$	4616.14	+	55697.0i	0.0275117	+	0.331947i
$124$		−	11125.7i		−	0.0649792i
$125$	39042.5			0.223492
$126$		0			0
$127$	−260441.			−1.43285			−0.716423	−	0.697667i	$-0.754222\pi$
$127$	−260441.			−1.43285			−0.716423	+	0.697667i	$0.754222\pi$
$128$		−	6004.61i		−	0.0323937i
$129$	16415.6	+	198065.i	0.0868523	+	1.04793i
$130$	−293932.			−1.52542
$131$	−214227.			−1.09067			−0.545337	−	0.838217i	$-0.683598\pi$
$131$	−214227.			−1.09067			−0.545337	+	0.838217i	$0.683598\pi$
$132$	−144401.	+	11967.9i	−0.721331	+	0.0597836i
$133$		0			0
$134$			28185.6i			0.135602i
$135$	−70431.7	−	278068.i	−0.332609	−	1.31316i
$136$			162665.i			0.754133i
$137$		−	28294.0i		−	0.128793i	−0.997924	−	0.0643966i	$-0.979488\pi$
$137$		−	28294.0i		−	0.128793i	0.997924	−	0.0643966i	$-0.0205123\pi$
$138$	−17820.6	−	215017.i	−0.0796570	−	0.961116i
$139$			10688.5i			0.0469223i	0.999725	+	0.0234612i	$0.00746861\pi$
$139$			10688.5i			0.0469223i	−0.999725	+	0.0234612i	$0.992531\pi$
$140$		0			0
$141$	−6551.44	−	79047.7i	−0.0277517	−	0.334843i
$142$	92972.5			0.386931
$143$	618661.			2.52996
$144$	96897.3	−	16172.7i	0.389409	−	0.0649946i
$145$			48774.0i			0.192650i
$146$	−240990.			−0.935656
$147$		0			0
$148$	170192.			0.638684
$149$			69026.4i			0.254712i	0.991857	+	0.127356i	$0.0406491\pi$
$149$			69026.4i			0.254712i	−0.991857	+	0.127356i	$0.959351\pi$
$150$	−173923.	+	14414.6i	−0.631143	+	0.0523089i
$151$	−124103.			−0.442933			−0.221467	−	0.975168i	$-0.571084\pi$
$151$	−124103.			−0.442933			−0.221467	+	0.975168i	$0.571084\pi$
$152$	9133.23			0.0320638
$153$	199317.	−	33267.2i	0.688361	−	0.114891i
$154$		0			0
$155$			61982.2i			0.207223i
$156$	191043.	−	15833.5i	0.628520	−	0.0520915i
$157$		−	231373.i		−	0.749142i	−0.927198	−	0.374571i	$-0.877790\pi$
$157$		−	231373.i		−	0.749142i	0.927198	−	0.374571i	$-0.122210\pi$
$158$			105183.i			0.335200i
$159$	454027.	−	37629.6i	1.42426	−	0.118042i
$160$			342663.i			1.05820i
$161$		0			0
$162$	−82276.5	−	239610.i	−0.246313	−	0.717326i
$163$	−65525.1			−0.193170			−0.0965848	−	0.995325i	$-0.530792\pi$
$163$	−65525.1			−0.193170			−0.0965848	+	0.995325i	$0.530792\pi$
$164$	−48732.8			−0.141485
$165$	804466.	−	66673.8i	2.30037	−	0.190654i
$166$			486957.i			1.37158i
$167$	454877.			1.26213			0.631063	−	0.775731i	$-0.282619\pi$
$167$	454877.			1.26213			0.631063	+	0.775731i	$0.282619\pi$
$168$		0			0
$169$	−447198.			−1.20443
$170$		−	270175.i		−	0.717005i
$171$	−1867.86	−	11191.1i	−0.00488489	−	0.0292674i
$172$	−173300.			−0.446660
$173$	−399209.			−1.01411			−0.507055	−	0.861914i	$-0.669266\pi$
$173$	−399209.			−1.01411			−0.507055	+	0.861914i	$0.669266\pi$
$174$	3557.97	+	42929.4i	0.00890901	+	0.107493i
$175$		0			0
$176$			276451.i			0.672723i
$177$	18357.7	+	221499.i	0.0440439	+	0.531420i
$178$			51583.0i			0.122027i
$179$			600133.i			1.39996i	0.714163	+	0.699979i	$0.246807\pi$
$179$			600133.i			1.39996i	−0.714163	+	0.699979i	$0.753193\pi$
$180$	246713.	−	41177.8i	0.567558	−	0.0947287i
$181$			167807.i			0.380726i	0.981714	+	0.190363i	$0.0609665\pi$
$181$			167807.i			0.380726i	−0.981714	+	0.190363i	$0.939034\pi$
$182$		0			0
$183$	−15954.3	+	1322.28i	−0.0352167	+	0.00291875i
$184$	631034.			1.37407
$185$	−948153.			−2.03680
$186$	4521.49	+	54554.8i	0.00958294	+	0.115625i
$187$			568658.i			1.18918i
$188$	69163.8			0.142720
$189$		0			0
$190$	−15169.6			−0.0304853
$191$			654116.i			1.29739i	0.761048	+	0.648696i	$0.224685\pi$
$191$			654116.i			1.29739i	−0.761048	+	0.648696i	$0.775315\pi$
$192$	41653.2	+	502575.i	0.0815447	+	0.983893i
$193$	929162.			1.79555			0.897776	−	0.440452i	$-0.145182\pi$
$193$	929162.			1.79555			0.897776	+	0.440452i	$0.145182\pi$
$194$	−565859.			−1.07945
$195$	−1.06431e6	+	88209.7i	−2.00439	+	0.166123i
$196$		0			0
$197$		−	265187.i		−	0.486840i	−0.969921	−	0.243420i	$-0.921731\pi$
$197$		−	265187.i		−	0.486840i	0.969921	−	0.243420i	$-0.0782693\pi$
$198$	703203.	−	117369.i	1.27473	−	0.212759i
$199$		−	739548.i		−	1.32383i	−0.749577	−	0.661917i	$-0.769743\pi$
$199$		−	739548.i		−	1.32383i	0.749577	−	0.661917i	$-0.230257\pi$
$200$		−	510429.i		−	0.902319i
$201$	8458.56	+	102058.i	0.0147675	+	0.178180i
$202$			666230.i			1.14880i
$203$		0			0
$204$	14553.8	+	175601.i	0.0244850	+	0.295429i
$205$	271494.			0.451206
$206$	504849.			0.828884
$207$	−129055.	−	773218.i	−0.209338	−	1.25423i
$208$		−	365745.i		−	0.586166i
$209$	31928.6			0.0505609
$210$		0			0
$211$	−782235.			−1.20957			−0.604785	−	0.796389i	$-0.706741\pi$
$211$	−782235.			−1.20957			−0.604785	+	0.796389i	$0.706741\pi$
$212$			397257.i			0.607061i
$213$	336648.	−	27901.3i	0.508426	−	0.0421381i
$214$	188299.			0.281070
$215$	965464.			1.42443
$216$	718286.	−	181934.i	1.04752	−	0.265326i
$217$		0			0
$218$			606926.i			0.864958i
$219$	−872610.	+	72321.6i	−1.22945	+	0.101896i
$220$			703878.i			0.980485i
$221$		−	752336.i		−	1.03617i
$222$	−834535.	+	69166.0i	−1.13648	+	0.0941912i
$223$			683761.i			0.920750i	0.887724	+	0.460375i	$0.152285\pi$
$223$			683761.i			0.920750i	−0.887724	+	0.460375i	$0.847715\pi$
$224$		0			0
$225$	−625438.	+	104389.i	−0.823622	+	0.137467i
$226$	−646594.			−0.842094
$227$	6601.90			0.00850363			0.00425182	−	0.999991i	$-0.498647\pi$
$227$	6601.90			0.00850363			0.00425182	+	0.999991i	$0.498647\pi$
$228$	9859.56	−	817.157i	0.0125609	−	0.00104104i
$229$		−	525219.i		−	0.661838i	−0.943659	−	0.330919i	$-0.892641\pi$
$229$		−	525219.i		−	0.661838i	0.943659	−	0.330919i	$-0.107359\pi$
$230$	−1.04810e6			−1.30642
$231$		0			0
$232$	−125989.			−0.153679
$233$		−	856277.i		−	1.03330i	−0.856198	−	0.516648i	$-0.827180\pi$
$233$		−	856277.i		−	1.03330i	0.856198	−	0.516648i	$-0.172820\pi$
$234$	−930340.	+	155279.i	−1.11071	+	0.185384i
$235$	−385316.			−0.455143
$236$	−193803.			−0.226507
$237$	31565.8	+	380863.i	0.0365045	+	0.440452i
$238$		0			0
$239$		−	601720.i		−	0.681396i	−0.940173	−	0.340698i	$-0.889337\pi$
$239$		−	601720.i		−	0.681396i	0.940173	−	0.340698i	$-0.110663\pi$
$240$	−39416.8	−	475591.i	−0.0441726	−	0.532973i
$241$			91693.7i			0.101694i	0.998706	+	0.0508472i	$0.0161921\pi$
$241$			91693.7i			0.101694i	−0.998706	+	0.0508472i	$0.983808\pi$
$242$			1.31529e6i			1.44372i
$243$	−369826.	−	842922.i	−0.401774	−	0.915739i
$244$		−	13959.4i		−	0.0150104i
$245$		0			0
$246$	238961.	−	19805.0i	0.251761	−	0.0208659i
$247$	−42241.7			−0.0440554
$248$	−160108.			−0.165304
$249$	146137.	+	1.76324e6i	0.149370	+	1.80225i
$250$		−	167507.i		−	0.169505i
$251$	673295.			0.674560			0.337280	−	0.941404i	$-0.390493\pi$
$251$	673295.			0.674560			0.337280	+	0.941404i	$0.390493\pi$
$252$		0			0
$253$	2.20601e6			2.16674
$254$			1.11739e6i			1.08672i
$255$	−81080.1	−	978287.i	−0.0780843	−	0.942141i
$256$	−1.06099e6			−1.01183
$257$	1.68970e6			1.59579			0.797895	−	0.602796i	$-0.205947\pi$
$257$	1.68970e6			1.59579			0.797895	+	0.602796i	$0.205947\pi$
$258$	849772.	−	70428.8i	0.794791	−	0.0658720i
$259$		0			0
$260$		−	931233.i		−	0.854329i
$261$	25766.4	+	154377.i	0.0234128	+	0.140275i
$262$			919111.i			0.827208i
$263$		−	1.46502e6i		−	1.30603i	−0.757345	−	0.653015i	$-0.773504\pi$
$263$		−	1.46502e6i		−	1.30603i	0.757345	−	0.653015i	$-0.226496\pi$
$264$	172227.	+	2.07804e6i	0.152087	+	1.83503i
$265$		−	2.21315e6i		−	1.93596i
$266$		0			0
$267$	15480.2	+	186779.i	0.0132892	+	0.160343i
$268$	−89297.4			−0.0759454
$269$	967037.			0.814821			0.407411	−	0.913245i	$-0.366432\pi$
$269$	967037.			0.814821			0.407411	+	0.913245i	$0.366432\pi$
$270$	−1.19302e6	+	302178.i	−0.995949	+	0.252263i
$271$		−	396860.i		−	0.328257i	−0.986439	−	0.164129i	$-0.947519\pi$
$271$		−	396860.i		−	0.328257i	0.986439	−	0.164129i	$-0.0524812\pi$
$272$	336184.			0.275521
$273$		0			0
$274$	−121392.			−0.0976816
$275$		−	1.78439e6i		−	1.42285i
$276$	681217.	−	56459.0i	0.538286	−	0.0446129i
$277$	1.27624e6			0.999385			0.499693	−	0.866203i	$-0.333446\pi$
$277$	1.27624e6			0.999385			0.499693	+	0.866203i	$0.333446\pi$
$278$	45857.6			0.0355876
$279$	32744.1	+	196183.i	0.0251839	+	0.150887i
$280$		0			0
$281$		−	223049.i		−	0.168514i	−0.996444	−	0.0842568i	$-0.973148\pi$
$281$		−	223049.i		−	0.168514i	0.996444	−	0.0842568i	$-0.0268516\pi$
$282$	−339144.	+	28108.1i	−0.253957	+	0.0210479i
$283$		−	1.02061e6i		−	0.757522i	−0.925494	−	0.378761i	$-0.876350\pi$
$283$		−	1.02061e6i		−	0.757522i	0.925494	−	0.378761i	$-0.123650\pi$
$284$			294555.i			0.216706i
$285$	−54928.2	+	4552.43i	−0.0400575	+	0.00331995i
$286$		−	2.65429e6i		−	1.91881i
$287$		0			0
$288$	181023.	+	1.08458e6i	0.128603	+	0.770515i
$289$	−728329.			−0.512959
$290$	209258.			0.146113
$291$	−2.04894e6	+	169816.i	−1.41840	+	0.117556i
$292$		−	763502.i		−	0.524026i
$293$	−749824.			−0.510259			−0.255129	−	0.966907i	$-0.582118\pi$
$293$	−749824.			−0.510259			−0.255129	+	0.966907i	$0.582118\pi$
$294$		0			0
$295$	1.07969e6			0.722345
$296$		−	2.44920e6i		−	1.62478i
$297$	2.51104e6	−	636018.i	1.65182	−	0.418387i
$298$	296149.			0.193183
$299$	−2.91856e6			−1.88795
$300$	−45668.4	−	551021.i	−0.0292963	−	0.353480i
$301$		0			0
$302$			532446.i			0.335937i
$303$	199937.	+	2.41238e6i	0.125109	+	1.50952i
$304$		−	18875.8i		−	0.0117145i
$305$			77768.7i			0.0478691i
$306$	−142729.	−	855144.i	−0.0871379	−	0.522078i
$307$		−	1.51886e6i		−	0.919757i	−0.887982	−	0.459879i	$-0.847893\pi$
$307$		−	1.51886e6i		−	0.919757i	0.887982	−	0.459879i	$-0.152107\pi$
$308$		0			0
$309$	1.82803e6	−	151507.i	1.08915	−	0.0902683i
$310$	265926.			0.157166
$311$	−1.30530e6			−0.765263			−0.382632	−	0.923901i	$-0.624982\pi$
$311$	−1.30530e6			−0.765263			−0.382632	+	0.923901i	$0.624982\pi$
$312$	−227857.	−	2.74925e6i	−0.132518	−	1.59892i
$313$		−	374621.i		−	0.216138i	−0.994143	−	0.108069i	$-0.965533\pi$
$313$		−	374621.i		−	0.216138i	0.994143	−	0.108069i	$-0.0344667\pi$
$314$	−992677.			−0.568177
$315$		0			0
$316$	−333242.			−0.187733
$317$			951664.i			0.531907i	0.963986	+	0.265953i	$0.0856867\pi$
$317$			951664.i			0.531907i	−0.963986	+	0.265953i	$0.914313\pi$
$318$	−161445.	−	1.94795e6i	−0.0895276	−	1.08021i
$319$	−440442.			−0.242333
$320$	2.44979e6			1.33738
$321$	681821.	−	56509.1i	0.369324	−	0.0306095i
$322$		0			0
$323$		−	38827.5i		−	0.0207077i
$324$	759130.	−	260668.i	0.401748	−	0.137951i
$325$			2.36076e6i			1.23978i
$326$			281127.i			0.146507i
$327$	182140.	+	2.19765e6i	0.0941969	+	1.13655i
$328$			701302.i			0.359932i
$329$		0			0
$330$	−286055.	−	3.45145e6i	−0.144599	−	1.74469i
$331$	1.38940e6			0.697037			0.348519	−	0.937302i	$-0.386685\pi$
$331$	1.38940e6			0.697037			0.348519	+	0.937302i	$0.386685\pi$
$332$	−1.54277e6			−0.768170
$333$	−3.00105e6	+	500893.i	−1.48307	+	0.247534i
$334$		−	1.95159e6i		−	0.957244i
$335$	497481.			0.242195
$336$		0			0
$337$	−354210.			−0.169897			−0.0849486	−	0.996385i	$-0.527073\pi$
$337$	−354210.			−0.169897			−0.0849486	+	0.996385i	$0.527073\pi$
$338$			1.91865e6i			0.913488i
$339$	−2.34128e6	+	194045.i	−1.10651	+	0.0917070i
$340$	855966.			0.401568
$341$	−559716.			−0.260664
$342$	−48014.1	+	8013.83i	−0.0221975	+	0.00370489i
$343$		0			0
$344$			2.49391e6i			1.13628i
$345$	−3.79510e6	+	314537.i	−1.71663	+	0.142273i
$346$			1.71275e6i			0.769138i
$347$			1.82666e6i			0.814391i	0.913341	+	0.407196i	$0.133493\pi$
$347$			1.82666e6i			0.814391i	−0.913341	+	0.407196i	$0.866507\pi$
$348$	−136009.	+	11272.4i	−0.0602030	+	0.00498961i
$349$		−	403109.i		−	0.177157i	−0.996069	−	0.0885786i	$-0.971768\pi$
$349$		−	403109.i		−	0.177157i	0.996069	−	0.0885786i	$-0.0282324\pi$
$350$		0			0
$351$	−3.32211e6	+	841454.i	−1.43928	+	0.364555i
$352$	−3.09434e6			−1.33110
$353$	−2.51507e6			−1.07427			−0.537135	−	0.843496i	$-0.680493\pi$
$353$	−2.51507e6			−1.07427			−0.537135	+	0.843496i	$0.680493\pi$
$354$	950311.	−	78761.5i	0.403049	−	0.0334046i
$355$		−	1.64099e6i		−	0.691089i
$356$	−163425.			−0.0683430
$357$		0			0
$358$	2.57479e6			1.06178
$359$		−	1.32306e6i		−	0.541805i	−0.962607	−	0.270903i	$-0.912678\pi$
$359$		−	1.32306e6i		−	0.541805i	0.962607	−	0.270903i	$-0.0873222\pi$
$360$	−592579.	−	3.55038e6i	−0.240985	−	1.44384i
$361$	2.47392e6			0.999120
$362$	719952.			0.288757
$363$	394722.	+	4.76259e6i	0.157226	+	1.89704i
$364$		0			0
$365$			4.25352e6i			1.67115i
$366$	5673.08	+	68449.6i	0.00221369	+	0.0267097i
$367$			1.51900e6i			0.588697i	0.955698	+	0.294348i	$0.0951026\pi$
$367$			1.51900e6i			0.588697i	−0.955698	+	0.294348i	$0.904897\pi$
$368$		−	1.30417e6i		−	0.502013i
$369$	859320.	−	143425.i	0.328540	−	0.0548353i
$370$			4.06793e6i			1.54479i
$371$		0			0
$372$	−172840.	+	14324.9i	−0.0647572	+	0.00536705i
$373$	1.94644e6			0.724385			0.362192	−	0.932103i	$-0.382028\pi$
$373$	1.94644e6			0.724385			0.362192	+	0.932103i	$0.382028\pi$
$374$	2.43975e6			0.901917
$375$	−50269.2	−	606533.i	−0.0184597	−	0.222729i
$376$		−	995320.i		−	0.363072i
$377$	582707.			0.211153
$378$		0			0
$379$	−2.70649e6			−0.967851			−0.483925	−	0.875109i	$-0.660789\pi$
$379$	−2.70649e6			−0.967851			−0.483925	+	0.875109i	$0.660789\pi$
$380$		−	48060.2i		−	0.0170737i
$381$	335331.	+	4.04599e6i	0.118348	+	1.42795i
$382$	2.80640e6			0.983990
$383$	−954838.			−0.332608			−0.166304	−	0.986075i	$-0.553183\pi$
$383$	−954838.			−0.332608			−0.166304	+	0.986075i	$0.553183\pi$
$384$	−93282.8	+	7731.24i	−0.0322830	+	0.00267560i
$385$		0			0
$386$		−	3.98645e6i		−	1.36181i
$387$	3.05584e6	−	510038.i	1.03718	−	0.173111i
$388$		−	1.79275e6i		−	0.604562i
$389$		−	2.90671e6i		−	0.973928i	−0.873422	−	0.486964i	$-0.838104\pi$
$389$		−	2.90671e6i		−	0.973928i	0.873422	−	0.486964i	$-0.161896\pi$
$390$	378452.	+	4.56629e6i	0.125994	+	1.52020i
$391$		−	2.68267e6i		−	0.887412i
$392$		0			0
$393$	275828.	+	3.32805e6i	0.0900859	+	1.08695i
$394$	−1.13775e6			−0.369237
$395$	1.85651e6			0.598694
$396$	371847.	+	2.22788e6i	0.119159	+	0.713928i
$397$			3.44376e6i			1.09662i	0.836275	+	0.548310i	$0.184729\pi$
$397$			3.44376e6i			1.09662i	−0.836275	+	0.548310i	$0.815271\pi$
$398$	−3.17294e6			−1.00405
$399$		0			0
$400$	−1.05491e6			−0.329660
$401$			3.46397e6i			1.07575i	0.843023	+	0.537877i	$0.180774\pi$
$401$			3.46397e6i			1.07575i	−0.843023	+	0.537877i	$0.819226\pi$
$402$	437868.	−	36290.4i	0.135138	−	0.0112002i
$403$	740507.			0.227126
$404$	−2.11075e6			−0.643403
$405$	−4.22916e6	+	1.45220e6i	−1.28120	+	0.439935i
$406$		0			0
$407$		−	8.56208e6i		−	2.56208i
$408$	2.52704e6	−	209440.i	0.751556	−	0.0622887i
$409$			1.17031e6i			0.345934i	0.984928	+	0.172967i	$0.0553354\pi$
$409$			1.17031e6i			0.345934i	−0.984928	+	0.172967i	$0.944665\pi$
$410$		−	1.16481e6i		−	0.342212i
$411$	−439553.	+	36430.0i	−0.128353	+	0.0106379i
$412$			1.59946e6i			0.464227i
$413$		0			0
$414$	−3.31739e6	+	553692.i	−0.951253	+	0.158770i
$415$	8.59490e6			2.44974
$416$	4.09383e6			1.15983
$417$	166048.	−	13762.0i	0.0467620	−	0.00387562i
$418$		−	136986.i		−	0.0383472i
$419$	2.44900e6			0.681481			0.340740	−	0.940157i	$-0.389322\pi$
$419$	2.44900e6			0.681481			0.340740	+	0.940157i	$0.389322\pi$
$420$		0			0
$421$	188332.			0.0517869			0.0258934	−	0.999665i	$-0.491757\pi$
$421$	188332.			0.0517869			0.0258934	+	0.999665i	$0.491757\pi$
$422$			3.35608e6i			0.917383i
$423$	−1.21959e6	+	203556.i	−0.331407	+	0.0553137i
$424$	5.71684e6			1.54433
$425$	−2.16995e6			−0.582743
$426$	−119707.	−	1.44435e6i	−0.0319591	−	0.385609i
$427$		0			0
$428$			596569.i			0.157417i
$429$	−796558.	−	9.61102e6i	−0.208965	−	2.52131i
$430$		−	4.14220e6i		−	1.08034i
$431$			4.99202e6i			1.29444i	0.762302	+	0.647221i	$0.224069\pi$
$431$			4.99202e6i			1.29444i	−0.762302	+	0.647221i	$0.775931\pi$
$432$	−376007.	−	1.48450e6i	−0.0969362	−	0.382710i
$433$			5.33397e6i			1.36720i	0.729859	+	0.683598i	$0.239586\pi$
$433$			5.33397e6i			1.36720i	−0.729859	+	0.683598i	$0.760414\pi$
$434$		0			0
$435$	757713.	−	62799.0i	0.191991	−	0.0159122i
$436$	−1.92286e6			−0.484431
$437$	−150625.			−0.0377305
$438$	310286.	+	3.74382e6i	0.0772818	+	0.932459i
$439$		−	92981.1i		−	0.0230268i	−0.999934	−	0.0115134i	$-0.996335\pi$
$439$		−	92981.1i		−	0.0230268i	0.999934	−	0.0115134i	$-0.00366491\pi$
$440$	1.01293e7			2.49430
$441$		0			0
$442$	−3.22780e6			−0.785870
$443$		−	4.76496e6i		−	1.15359i	−0.816890	−	0.576793i	$-0.804304\pi$
$443$		−	4.76496e6i		−	1.15359i	0.816890	−	0.576793i	$-0.195696\pi$
$444$	−219131.	−	2.64397e6i	−0.0527530	−	0.636501i
$445$	910452.			0.217950
$446$	2.93359e6			0.698331
$447$	1.07234e6	−	88875.0i	0.253842	−	0.0210383i
$448$		0			0
$449$			3.46959e6i			0.812200i	0.913829	+	0.406100i	$0.133112\pi$
$449$			3.46959e6i			0.812200i	−0.913829	+	0.406100i	$0.866888\pi$
$450$	447869.	+	2.68336e6i	0.104260	+	0.624666i
$451$			2.45166e6i			0.567570i
$452$		−	2.04854e6i		−	0.471626i
$453$	159788.	+	1.92796e6i	0.0365847	+	0.441420i
$454$		−	28324.6i		−	0.00644947i
$455$		0			0
$456$	−11759.5	−	141887.i	−0.00264836	−	0.0319543i
$457$	4.06259e6			0.909939			0.454969	−	0.890507i	$-0.349650\pi$
$457$	4.06259e6			0.909939			0.454969	+	0.890507i	$0.349650\pi$
$458$	−2.25338e6			−0.501963
$459$	−773443.	−	3.05360e6i	−0.171355	−	0.676519i
$460$		−	3.32058e6i		−	0.731677i
$461$	−4.24426e6			−0.930143			−0.465072	−	0.885273i	$-0.653971\pi$
$461$	−4.24426e6			−0.930143			−0.465072	+	0.885273i	$0.653971\pi$
$462$		0			0
$463$	1.11651e6			0.242053			0.121026	−	0.992649i	$-0.461381\pi$
$463$	1.11651e6			0.242053			0.121026	+	0.992649i	$0.461381\pi$
$464$			260385.i			0.0561462i
$465$	962905.	−	79805.2i	0.206515	−	0.0171159i
$466$	−3.67374e6			−0.783690
$467$	6.89759e6			1.46354			0.731771	−	0.681551i	$-0.238694\pi$
$467$	6.89759e6			1.46354			0.731771	+	0.681551i	$0.238694\pi$
$468$	−491954.	−	2.94750e6i	−0.103827	−	0.622069i
$469$		0			0
$470$			1.65315e6i			0.345197i
$471$	−3.59443e6	+	297905.i	−0.746582	+	0.0618765i
$472$			2.78898e6i			0.576222i
$473$			8.71841e6i			1.79178i
$474$	1.63404e6	−	135429.i	0.334055	−	0.0276864i
$475$			121837.i			0.0247768i
$476$		0			0
$477$	−1.16917e6	−	7.00495e6i	−0.235278	−	1.40964i
$478$	−2.58160e6			−0.516796
$479$	4.57012e6			0.910100			0.455050	−	0.890466i	$-0.349621\pi$
$479$	4.57012e6			0.910100			0.455050	+	0.890466i	$0.349621\pi$
$480$	5.32334e6	−	441196.i	1.05458	−	0.0874035i
$481$			1.13277e7i			2.23243i
$482$	393400.			0.0771288
$483$		0			0
$484$	−4.16709e6			−0.808574
$485$			9.98753e6i			1.92799i
$486$	−3.61645e6	+	1.58669e6i	−0.694531	+	0.304720i
$487$	−8.20765e6			−1.56818			−0.784091	−	0.620646i	$-0.786870\pi$
$487$	−8.20765e6			−1.56818			−0.784091	+	0.620646i	$0.786870\pi$
$488$	−200886.			−0.0381857
$489$	84366.9	+	1.01795e6i	0.0159551	+	0.192510i
$490$		0			0
$491$			3.42933e6i			0.641956i	0.947087	+	0.320978i	$0.104011\pi$
$491$			3.42933e6i			0.641956i	−0.947087	+	0.320978i	$0.895989\pi$
$492$	62746.0	+	757074.i	0.0116862	+	0.141002i
$493$			535609.i			0.0992501i
$494$			181232.i			0.0334132i
$495$	−2.07158e6	−	1.24117e7i	−0.380005	−	2.27676i
$496$			330898.i			0.0603934i
$497$		0			0
$498$	7.56497e6	−	626982.i	1.36689	−	0.113287i
$499$	−5.40504e6			−0.971734			−0.485867	−	0.874033i	$-0.661496\pi$
$499$	−5.40504e6			−0.971734			−0.485867	+	0.874033i	$0.661496\pi$
$500$	530694.			0.0949335
$501$	−585678.	−	7.06660e6i	−0.104247	−	1.25781i
$502$		−	2.88868e6i		−	0.511612i
$503$	−6.27690e6			−1.10618			−0.553090	−	0.833122i	$-0.686551\pi$
$503$	−6.27690e6			−1.10618			−0.553090	+	0.833122i	$0.686551\pi$
$504$		0			0
$505$	1.17591e7			2.05185
$506$		−	9.46461e6i		−	1.64334i
$507$	575791.	+	6.94731e6i	0.0994821	+	1.20032i
$508$	−3.54010e6			−0.608634
$509$	−9.68442e6			−1.65684			−0.828418	−	0.560111i	$-0.810759\pi$
$509$	−9.68442e6			−1.65684			−0.828418	+	0.560111i	$0.810759\pi$
$510$	−4.19721e6	+	347864.i	−0.714555	+	0.0592221i
$511$		0			0
$512$			4.35987e6i			0.735020i
$513$	−171451.	+	43426.8i	−0.0287639	+	0.00728558i
$514$		−	7.24942e6i		−	1.21031i
$515$		−	8.91070e6i		−	1.48045i
$516$	223132.	+	2.69224e6i	0.0368925	+	0.445133i
$517$		−	3.47951e6i		−	0.572522i
$518$		0			0
$519$	514002.	+	6.20178e6i	0.0837618	+	1.01064i
$520$	−1.34012e7			−2.17337
$521$	−9.71902e6			−1.56866			−0.784329	−	0.620346i	$-0.786992\pi$
$521$	−9.71902e6			−1.56866			−0.784329	+	0.620346i	$0.786992\pi$
$522$	662335.	−	110548.i	0.106390	−	0.0177571i
$523$		−	8.88406e6i		−	1.42022i	−0.704088	−	0.710112i	$-0.748644\pi$
$523$		−	8.88406e6i		−	1.42022i	0.704088	−	0.710112i	$-0.251356\pi$
$524$	−2.91192e6			−0.463289
$525$		0			0
$526$	−6.28546e6			−0.990542
$527$			680654.i			0.106758i
$528$	4.29472e6	−	355945.i	0.670424	−	0.0555645i
$529$	−3.97063e6			−0.616908
$530$	−9.49522e6			−1.46830
$531$	3.41739e6	−	570382.i	0.525966	−	0.0877868i
$532$		0			0
$533$		−	3.24356e6i		−	0.494543i
$534$	801353.	−	66415.8i	0.121610	−	0.0100790i
$535$		−	3.32352e6i		−	0.502012i
$536$			1.28506e6i			0.193201i
$537$	9.32318e6	−	772702.i	1.39517	−	0.115632i
$538$		−	4.14895e6i		−	0.617991i
$539$		0			0
$540$	−957360.	−	3.77971e6i	−0.141283	−	0.557794i
$541$	−1.68555e6			−0.247598			−0.123799	−	0.992307i	$-0.539508\pi$
$541$	−1.68555e6			−0.247598			−0.123799	+	0.992307i	$0.539508\pi$
$542$	−1.70268e6			−0.248963
$543$	2.60691e6	−	216060.i	0.379425	−	0.0314466i
$544$			3.76294e6i			0.545168i
$545$	1.07124e7			1.54488
$546$		0			0
$547$	787487.			0.112532			0.0562659	−	0.998416i	$-0.482081\pi$
$547$	787487.			0.112532			0.0562659	+	0.998416i	$0.482081\pi$
$548$		−	384593.i		−	0.0547079i
$549$	41083.8	+	246150.i	0.00581755	+	0.0348553i
$550$	−7.65571e6			−1.07914
$551$	30073.0			0.00421986
$552$	−812488.	−	9.80323e6i	−0.113493	−	1.36937i
$553$		0			0
$554$		−	5.47554e6i		−	0.757971i
$555$	1.22080e6	+	1.47297e7i	0.168233	+	2.02984i
$556$			145286.i			0.0199313i
$557$		−	1.09724e7i		−	1.49852i	−0.662274	−	0.749262i	$-0.730408\pi$
$557$		−	1.09724e7i		−	1.49852i	0.662274	−	0.749262i	$-0.269592\pi$
$558$	841698.	−	140484.i	0.114438	−	0.0191004i
$559$		−	1.15345e7i		−	1.56124i
$560$		0			0
$561$	8.83420e6	−	732176.i	1.18511	−	0.0982219i
$562$	−956964.			−0.127807
$563$	−1.48913e6			−0.197998			−0.0989991	−	0.995088i	$-0.531564\pi$
$563$	−1.48913e6			−0.197998			−0.0989991	+	0.995088i	$0.531564\pi$
$564$	−89052.0	−	1.07447e6i	−0.0117882	−	0.142232i
$565$			1.14125e7i			1.50405i
$566$	−4.37881e6			−0.574533
$567$		0			0
$568$	4.23887e6			0.551289
$569$		−	3.97438e6i		−	0.514623i	−0.966329	−	0.257311i	$-0.917163\pi$
$569$		−	3.97438e6i		−	0.514623i	0.966329	−	0.257311i	$-0.0828366\pi$
$570$	19531.6	+	235662.i	0.00251797	+	0.0303811i
$571$	−8.06090e6			−1.03465			−0.517325	−	0.855789i	$-0.673072\pi$
$571$	−8.06090e6			−1.03465			−0.517325	+	0.855789i	$0.673072\pi$
$572$	8.40930e6			1.07466
$573$	1.01618e7	−	842207.i	1.29296	−	0.107160i
$574$		0			0
$575$			8.41796e6i			1.06179i
$576$	7.75397e6	−	1.29418e6i	0.973796	−	0.162532i
$577$		−	1.43214e7i		−	1.79080i	−0.445264	−	0.895399i	$-0.646890\pi$
$577$		−	1.43214e7i		−	1.79080i	0.445264	−	0.895399i	$-0.353110\pi$
$578$			3.12480e6i			0.389048i
$579$	−1.19634e6	−	1.44347e7i	−0.148306	−	1.78942i
$580$			662971.i			0.0818323i
$581$		0			0
$582$	728572.	+	8.79072e6i	0.0891590	+	1.07576i
$583$	1.99853e7			2.43523
$584$	−1.09874e7			−1.33310
$585$	2.74071e6	+	1.64207e7i	0.331111	+	1.98382i
$586$			3.21702e6i			0.386999i
$587$	−4.72674e6			−0.566195			−0.283097	−	0.959091i	$-0.591362\pi$
$587$	−4.72674e6			−0.566195			−0.283097	+	0.959091i	$0.591362\pi$
$588$		0			0
$589$	38217.0			0.00453908
$590$		−	4.63227e6i		−	0.547853i
$591$	−4.11973e6	+	341441.i	−0.485176	+	0.0402112i
$592$	−5.06180e6			−0.593610
$593$	1.08122e7			1.26263			0.631317	−	0.775525i	$-0.282515\pi$
$593$	1.08122e7			1.26263			0.631317	+	0.775525i	$0.282515\pi$
$594$	−2.72875e6	−	1.07733e7i	−0.317320	−	1.25280i
$595$		0			0
$596$			938257.i			0.108195i
$597$	−1.14890e7	+	952206.i	−1.31931	+	0.109344i
$598$			1.25217e7i			1.43189i
$599$			1.19679e7i			1.36286i	0.731883	+	0.681430i	$0.238642\pi$
$599$			1.19679e7i			1.36286i	−0.731883	+	0.681430i	$0.761358\pi$
$600$	−7.92961e6	+	657203.i	−0.899235	+	0.0745283i
$601$			1.06577e7i			1.20359i	0.798651	+	0.601794i	$0.205547\pi$
$601$			1.06577e7i			1.20359i	−0.798651	+	0.601794i	$0.794453\pi$
$602$		0			0
$603$	1.57461e6	−	262811.i	0.176351	−	0.0294340i
$604$	−1.68689e6			−0.188146
$605$	2.32151e7			2.57859
$606$	1.03500e7	−	857805.i	1.14488	−	0.0948871i
$607$			3.11542e6i			0.343199i	0.985167	+	0.171599i	$0.0548934\pi$
$607$			3.11542e6i			0.343199i	−0.985167	+	0.171599i	$0.945107\pi$
$608$	211279.			0.0231792
$609$		0			0
$610$	333656.			0.0363057
$611$			4.60341e6i			0.498857i
$612$	2.70926e6	−	452192.i	0.292397	−	0.0488027i
$613$	−4.31540e6			−0.463842			−0.231921	−	0.972735i	$-0.574501\pi$
$613$	−4.31540e6			−0.463842			−0.231921	+	0.972735i	$0.574501\pi$
$614$	−6.51649e6			−0.697578
$615$	−349562.	−	4.21771e6i	−0.0372680	−	0.449665i
$616$		0			0
$617$		−	1.27346e7i		−	1.34671i	−0.739319	−	0.673355i	$-0.764853\pi$
$617$		−	1.27346e7i		−	1.34671i	0.739319	−	0.673355i	$-0.235147\pi$
$618$	−650019.	−	7.84293e6i	−0.0684629	−	0.826052i
$619$		−	1.19650e7i		−	1.25512i	−0.778569	−	0.627559i	$-0.784054\pi$
$619$		−	1.19650e7i		−	1.25512i	0.778569	−	0.627559i	$-0.215946\pi$
$620$			842507.i			0.0880226i
$621$	−1.18459e7	+	3.00045e6i	−1.23265	+	0.312217i
$622$			5.60024e6i			0.580404i
$623$		0			0
$624$	−5.68193e6	+	470916.i	−0.584163	+	0.0484152i
$625$	−1.11110e7			−1.13776
$626$	−1.60726e6			−0.163927
$627$	−41109.7	−	496017.i	−0.00417615	−	0.0503881i
$628$		−	3.14499e6i		−	0.318215i
$629$	−1.04121e7			−1.04933
$630$		0			0
$631$	−7.88130e6			−0.787996			−0.393998	−	0.919111i	$-0.628908\pi$
$631$	−7.88130e6			−0.787996			−0.393998	+	0.919111i	$0.628908\pi$
$632$			4.79560e6i			0.477585i
$633$	1.00717e6	+	1.21522e7i	0.0999062	+	1.20544i
$634$	4.08299e6			0.403418
$635$	1.97221e7			1.94097
$636$	6.17147e6	−	511489.i	0.604987	−	0.0501411i
$637$		0			0
$638$			1.88966e6i			0.183794i
$639$	−866904.	−	5.19397e6i	−0.0839883	−	0.503208i
$640$			454705.i			0.0438813i
$641$		−	8.37927e6i		−	0.805491i	−0.915312	−	0.402746i	$-0.868056\pi$
$641$		−	8.37927e6i		−	0.805491i	0.915312	−	0.402746i	$-0.131944\pi$
$642$	−242445.	−	2.92527e6i	−0.0232154	−	0.280109i
$643$		−	86587.1i		−	0.00825897i	−0.999991	−	0.00412949i	$-0.998686\pi$
$643$		−	86587.1i		−	0.00825897i	0.999991	−	0.00412949i	$-0.00131446\pi$
$644$		0			0
$645$	−1.24308e6	−	1.49987e7i	−0.117653	−	1.41956i
$646$	−166584.			−0.0157055
$647$	4.91422e6			0.461523			0.230762	−	0.973010i	$-0.425878\pi$
$647$	4.91422e6			0.461523			0.230762	+	0.973010i	$0.425878\pi$
$648$	−3.75121e6	−	1.09245e7i	−0.350941	−	1.02203i
$649$			9.74991e6i			0.908633i
$650$	1.01285e7			0.940292
$651$		0			0
$652$	−890665.			−0.0820532
$653$		−	1.74162e7i		−	1.59834i	−0.601103	−	0.799172i	$-0.705272\pi$
$653$		−	1.74162e7i		−	1.59834i	0.601103	−	0.799172i	$-0.294728\pi$
$654$	9.42872e6	−	781449.i	0.862002	−	0.0714424i
$655$	1.62225e7			1.47746
$656$	1.44940e6			0.131500
$657$	2.24706e6	+	1.34630e7i	0.203096	+	1.21683i
$658$		0			0
$659$		−	4.09851e6i		−	0.367631i	−0.982961	−	0.183816i	$-0.941155\pi$
$659$		−	4.09851e6i		−	0.367631i	0.982961	−	0.183816i	$-0.0588450\pi$
$660$	1.09349e7	−	906279.i	0.977134	−	0.0809846i
$661$			1.82046e6i			0.162061i	0.996712	+	0.0810304i	$0.0258211\pi$
$661$			1.82046e6i			0.162061i	−0.996712	+	0.0810304i	$0.974179\pi$
$662$		−	5.96102e6i		−	0.528659i
$663$	−1.16877e7	+	968671.i	−1.03263	+	0.0855840i
$664$			2.22017e7i			1.95419i
$665$		0			0
$666$	2.14901e6	+	1.28756e7i	0.187739	+	1.12482i
$667$	2.07781e6			0.180838
$668$	6.18302e6			0.536117
$669$	1.06224e7	−	880377.i	0.917604	−	0.0760507i
$670$		−	2.13438e6i		−	0.183690i
$671$	−702273.			−0.0602143
$672$		0			0
$673$	436008.			0.0371070			0.0185535	−	0.999828i	$-0.494094\pi$
$673$	436008.			0.0371070			0.0185535	+	0.999828i	$0.494094\pi$
$674$			1.51969e6i			0.128856i
$675$	2.42699e6	+	9.58190e6i	0.205026	+	0.809454i
$676$	−6.07864e6			−0.511611
$677$	−5.74216e6			−0.481508			−0.240754	−	0.970586i	$-0.577395\pi$
$677$	−5.74216e6			−0.481508			−0.240754	+	0.970586i	$0.577395\pi$
$678$	832523.	+	1.00450e7i	0.0695540	+	0.839217i
$679$		0			0
$680$		−	1.23180e7i		−	1.02157i
$681$	−8500.29	−	102562.i	−0.000702370	−	0.00847458i
$682$			2.40139e6i			0.197698i
$683$		−	2.30403e6i		−	0.188989i	−0.995525	−	0.0944943i	$-0.969877\pi$
$683$		−	2.30403e6i		−	0.188989i	0.995525	−	0.0944943i	$-0.0301234\pi$
$684$	−25389.4	−	152118.i	−0.00207497	−	0.0124320i
$685$			2.14259e6i			0.174467i
$686$		0			0
$687$	−8.15938e6	+	676247.i	−0.659577	+	0.0546655i
$688$	5.15422e6			0.415138
$689$	−2.64407e7			−2.12190
$690$	1.34948e6	+	1.62824e7i	0.107906	+	1.30195i
$691$		−	1.37249e7i		−	1.09349i	−0.837300	−	0.546744i	$-0.815867\pi$
$691$		−	1.37249e7i		−	1.09349i	0.837300	−	0.546744i	$-0.184133\pi$
$692$	−5.42634e6			−0.430766
$693$		0			0
$694$	7.83703e6			0.617665
$695$		−	809397.i		−	0.0635623i
$696$	162218.	+	1.95727e6i	0.0126933	+	0.153154i
$697$	2.98140e6			0.232454
$698$	−1.72949e6			−0.134363
$699$	−1.33024e7	+	1.10250e6i	−1.02976	+	0.0853465i
$700$		0			0
$701$			1.19545e7i			0.918836i	0.888220	+	0.459418i	$0.151942\pi$
$701$			1.19545e7i			0.918836i	−0.888220	+	0.459418i	$0.848058\pi$
$702$	3.61015e6	+	1.42531e7i	0.276492	+	1.09161i
$703$			584612.i			0.0446148i
$704$			2.21223e7i			1.68228i
$705$	496115.	+	5.98596e6i	0.0375932	+	0.453588i
$706$			1.07906e7i			0.814766i
$707$		0			0
$708$	249532.	+	3.01077e6i	0.0187087	+	0.225733i
$709$	−1.81040e7			−1.35257			−0.676283	−	0.736642i	$-0.736410\pi$
$709$	−1.81040e7			−1.35257			−0.676283	+	0.736642i	$0.736410\pi$
$710$	−7.04043e6			−0.524147
$711$	5.87614e6	−	980763.i	0.435932	−	0.0727595i
$712$			2.35181e6i			0.173861i
$713$	2.64049e6			0.194518
$714$		0			0
$715$	−4.68487e7			−3.42715
$716$			8.15745e6i			0.594664i
$717$	−9.34783e6	+	774745.i	−0.679068	+	0.0562809i
$718$	−5.67641e6			−0.410925
$719$	3.32191e6			0.239643			0.119822	−	0.992795i	$-0.461768\pi$
$719$	3.32191e6			0.239643			0.119822	+	0.992795i	$0.461768\pi$
$720$	−7.33764e6	+	1.22470e6i	−0.527504	+	0.0880434i
$721$		0			0
$722$		−	1.06140e7i		−	0.757770i
$723$	1.42448e6	−	118060.i	0.101347	−	0.00839960i
$724$			2.28095e6i			0.161722i
$725$		−	1.68069e6i		−	0.118753i
$726$	2.04333e7	−	1.69350e6i	1.43879	−	0.119246i
$727$		−	2.47810e6i		−	0.173893i	−0.996213	−	0.0869467i	$-0.972289\pi$
$727$		−	2.47810e6i		−	0.173893i	0.996213	−	0.0869467i	$-0.0277110\pi$
$728$		0			0
$729$	−1.26188e7	+	6.83063e6i	−0.879425	+	0.476038i
$730$	1.82492e7			1.26746
$731$	1.06022e7			0.733842
$732$	−216862.	+	17973.4i	−0.0149591	+	0.00123980i
$733$			1.81962e7i			1.25090i	0.780266	+	0.625448i	$0.215084\pi$
$733$			1.81962e7i			1.25090i	−0.780266	+	0.625448i	$0.784916\pi$
$734$	6.51706e6			0.446489
$735$		0			0
$736$	1.45977e7			0.993322
$737$			4.49240e6i			0.304656i
$738$	−615348.	−	3.68680e6i	−0.0415891	−	0.249177i
$739$	2.65912e7			1.79113			0.895564	−	0.444932i	$-0.146772\pi$
$739$	2.65912e7			1.79113			0.895564	+	0.444932i	$0.146772\pi$
$740$	−1.28880e7			−0.865178
$741$	54388.3	+	656233.i	0.00363882	+	0.0439048i
$742$		0			0
$743$			2.12846e7i			1.41447i	0.706980	+	0.707233i	$0.250057\pi$
$743$			2.12846e7i			1.41447i	−0.706980	+	0.707233i	$0.749943\pi$
$744$	206147.	+	2.48730e6i	0.0136535	+	0.164739i
$745$		−	5.22709e6i		−	0.345040i
$746$		−	8.35096e6i		−	0.549401i
$747$	2.72042e7	−	4.54053e6i	1.78375	−	0.297718i
$748$			7.72961e6i			0.505130i
$749$		0			0
$750$	−2.60225e6	+	215674.i	−0.168926	+	0.0140005i
$751$	2.87030e7			1.85707			0.928533	−	0.371251i	$-0.121071\pi$
$751$	2.87030e7			1.85707			0.928533	+	0.371251i	$0.121071\pi$
$752$	−2.05705e6			−0.132648
$753$	−866902.	−	1.04598e7i	−0.0557163	−	0.672256i
$754$		−	2.50003e6i		−	0.160146i
$755$	9.39779e6			0.600010
$756$		0			0
$757$	2.36595e7			1.50060			0.750302	−	0.661095i	$-0.229908\pi$
$757$	2.36595e7			1.50060			0.750302	+	0.661095i	$0.229908\pi$
$758$			1.16118e7i			0.734054i
$759$	−2.84036e6	−	3.42708e7i	−0.178965	−	2.15934i
$760$	−691623.			−0.0434346
$761$	−1.21252e7			−0.758973			−0.379487	−	0.925197i	$-0.623899\pi$
$761$	−1.21252e7			−0.758973			−0.379487	+	0.925197i	$0.623899\pi$
$762$	1.73588e7	−	1.43869e6i	1.08301	−	0.0897595i
$763$		0			0
$764$			8.89122e6i			0.551097i
$765$	−1.50935e7	+	2.51919e6i	−0.932472	+	0.155635i
$766$			4.09661e6i			0.252262i
$767$		−	1.28992e7i		−	0.791723i
$768$	1.36607e6	+	1.64826e7i	0.0835740	+	1.00838i
$769$		−	2.88689e7i		−	1.76041i	−0.474593	−	0.880206i	$-0.657405\pi$
$769$		−	2.88689e7i		−	1.76041i	0.474593	−	0.880206i	$-0.342595\pi$
$770$		0			0
$771$	−2.17557e6	−	2.62498e7i	−0.131807	−	1.59034i
$772$	1.26298e7			0.762702
$773$	−5.26593e6			−0.316976			−0.158488	−	0.987361i	$-0.550662\pi$
$773$	−5.26593e6			−0.316976			−0.158488	+	0.987361i	$0.550662\pi$
$774$	−2.18825e6	−	1.31107e7i	−0.131294	−	0.786635i
$775$		−	2.13583e6i		−	0.127736i
$776$	−2.57990e7			−1.53798
$777$		0			0
$778$	−1.24708e7			−0.738664
$779$		−	167398.i		−	0.00988338i
$780$	−1.44669e7	+	1.19901e6i	−0.851410	+	0.0705646i
$781$	1.48185e7			0.869317
$782$	−1.15096e7			−0.673046
$783$	2.36510e6	−	599055.i	0.137862	−	0.0349191i
$784$		0			0
$785$			1.75210e7i			1.01481i
$786$	1.42786e7	−	1.18340e6i	0.824382	−	0.0683245i
$787$			1.36972e7i			0.788306i	0.919045	+	0.394153i	$0.128962\pi$
$787$			1.36972e7i			0.788306i	−0.919045	+	0.394153i	$0.871038\pi$
$788$		−	3.60461e6i		−	0.206796i
$789$	−2.27593e7	+	1.88628e6i	−1.30157	+	0.107873i
$790$		−	7.96512e6i		−	0.454072i
$791$		0			0
$792$	3.20609e7	−	5.35115e6i	1.81620	−	0.303134i
$793$	929109.			0.0524667
$794$	1.47750e7			0.831718
$795$	−3.43817e7	+	2.84954e6i	−1.92934	+	0.159903i
$796$		−	1.00525e7i		−	0.562329i
$797$	−4.53096e6			−0.252665			−0.126332	−	0.991988i	$-0.540321\pi$
$797$	−4.53096e6			−0.252665			−0.126332	+	0.991988i	$0.540321\pi$
$798$		0			0
$799$	−4.23133e6			−0.234482
$800$		−	1.18077e7i		−	0.652292i
$801$	2.88172e6	−	480976.i	0.158698	−	0.0264876i
$802$	1.48617e7			0.815892
$803$	−3.84104e7			−2.10213
$804$	114975.	+	1.38725e6i	0.00627282	+	0.0756859i
$805$		0			0
$806$		−	3.17705e6i		−	0.172261i
$807$	−1.24511e6	−	1.50231e7i	−0.0673014	−	0.812037i
$808$			3.03752e7i			1.63678i
$809$			2.72004e7i			1.46118i	0.682815	+	0.730592i	$0.260756\pi$
$809$			2.72004e7i			1.46118i	−0.682815	+	0.730592i	$0.739244\pi$
$810$	6.23047e6	+	1.81447e7i	0.333663	+	0.971710i
$811$			1.05261e7i			0.561973i	0.959712	+	0.280987i	$0.0906616\pi$
$811$			1.05261e7i			0.561973i	−0.959712	+	0.280987i	$0.909338\pi$
$812$		0			0
$813$	−6.16530e6	+	510978.i	−0.327136	+	0.0271129i
$814$	−3.67345e7			−1.94318
$815$	4.96195e6			0.261673
$816$	−432854.	−	5.22268e6i	−0.0227571	−	0.274579i
$817$		−	595286.i		−	0.0312011i
$818$	5.02107e6			0.262369
$819$		0			0
$820$	3.69034e6			0.191660
$821$			1.28015e7i			0.662831i	0.943485	+	0.331415i	$0.107526\pi$
$821$			1.28015e7i			0.662831i	−0.943485	+	0.331415i	$0.892474\pi$
$822$	156298.	+	1.88584e6i	0.00806816	+	0.0973478i
$823$	−2.56260e7			−1.31881			−0.659404	−	0.751788i	$-0.729191\pi$
$823$	−2.56260e7			−1.31881			−0.659404	+	0.751788i	$0.729191\pi$
$824$	2.30175e7			1.18097
$825$	−2.77209e7	+	2.29750e6i	−1.41799	+	0.117522i
$826$		0			0
$827$		−	2.01621e7i		−	1.02511i	−0.858654	−	0.512556i	$-0.828699\pi$
$827$		−	2.01621e7i		−	1.02511i	0.858654	−	0.512556i	$-0.171301\pi$
$828$	−1.75420e6	−	1.05101e7i	−0.0889210	−	0.532761i
$829$		−	3.20634e7i		−	1.62040i	−0.586151	−	0.810202i	$-0.699358\pi$
$829$		−	3.20634e7i		−	1.62040i	0.586151	−	0.810202i	$-0.300642\pi$
$830$		−	3.68753e7i		−	1.85798i
$831$	−1.64322e6	−	1.98266e7i	−0.0825457	−	0.995970i
$832$		−	2.92679e7i		−	1.46583i
$833$		0			0
$834$	−59044.0	−	712407.i	−0.00293941	−	0.0354660i
$835$	−3.44460e7			−1.70971
$836$	433997.			0.0214769
$837$	3.00558e6	−	761282.i	0.148291	−	0.0375605i
$838$		−	1.05071e7i		−	0.516860i
$839$	2.55689e7			1.25403			0.627013	−	0.779009i	$-0.284277\pi$
$839$	2.55689e7			1.25403			0.627013	+	0.779009i	$0.284277\pi$
$840$		0			0
$841$	2.00963e7			0.979775
$842$		−	808015.i		−	0.0392771i
$843$	−3.46511e6	+	287187.i	−0.167938	+	0.0139186i
$844$	−1.06327e7			−0.513793
$845$	3.38645e7			1.63156
$846$	873330.	+	5.23247e6i	0.0419520	+	0.251351i
$847$		0			0
$848$		−	1.18151e7i		−	0.564219i
$849$	−1.58554e7	+	1.31409e6i	−0.754934	+	0.0625686i
$850$			9.30988e6i			0.441974i
$851$			4.03920e7i			1.91193i
$852$	4.57597e6	−	379255.i	0.215965	−	0.0178991i
$853$		−	1.91256e7i		−	0.900001i	−0.893028	−	0.450001i	$-0.851424\pi$
$853$		−	1.91256e7i		−	0.900001i	0.893028	−	0.450001i	$-0.148576\pi$
$854$		0			0
$855$	141446.	+	847459.i	0.00661721	+	0.0396464i
$856$	8.58508e6			0.400461
$857$	1.77319e7			0.824714			0.412357	−	0.911022i	$-0.364706\pi$
$857$	1.77319e7			0.824714			0.412357	+	0.911022i	$0.364706\pi$
$858$	−4.12348e7	+	3.41753e6i	−1.91226	+	0.158487i
$859$		−	3.21529e7i		−	1.48675i	−0.668875	−	0.743375i	$-0.733224\pi$
$859$		−	3.21529e7i		−	1.48675i	0.668875	−	0.743375i	$-0.266776\pi$
$860$	1.31233e7			0.605057
$861$		0			0
$862$	2.14176e7			0.981754
$863$			1.53188e7i			0.700161i	0.936720	+	0.350081i	$0.113846\pi$
$863$			1.53188e7i			0.700161i	−0.936720	+	0.350081i	$0.886154\pi$
$864$	1.66161e7	−	4.20868e6i	0.757260	−	0.191806i
$865$	3.02305e7			1.37374
$866$	2.28847e7			1.03693
$867$	937761.	+	1.13147e7i	0.0423686	+	0.511207i
$868$		0			0
$869$			1.67648e7i			0.753094i
$870$	−269431.	−	3.25087e6i	−0.0120684	−	0.145613i
$871$		−	5.94346e6i		−	0.265457i
$872$			2.76714e7i			1.23237i
$873$	5.27624e6	+	3.16121e7i	0.234309	+	1.40384i
$874$			646236.i			0.0286162i
$875$		0			0
$876$	−1.18611e7	+	983048.i	−0.522236	+	0.0432827i
$877$	−1.68420e7			−0.739425			−0.369713	−	0.929146i	$-0.620544\pi$
$877$	−1.68420e7			−0.739425			−0.369713	+	0.929146i	$0.620544\pi$
$878$	−398923.			−0.0174644
$879$	965437.	+	1.16487e7i	0.0421456	+	0.508515i
$880$		−	2.09345e7i		−	0.911289i
$881$	2.34232e7			1.01673			0.508367	−	0.861141i	$-0.330249\pi$
$881$	2.34232e7			1.01673			0.508367	+	0.861141i	$0.330249\pi$
$882$		0			0
$883$	2.30546e7			0.995077			0.497538	−	0.867442i	$-0.334237\pi$
$883$	2.30546e7			0.995077			0.497538	+	0.867442i	$0.334237\pi$
$884$		−	1.02263e7i		−	0.440137i
$885$	−1.39016e6	−	1.67732e7i	−0.0596631	−	0.719876i
$886$	−2.04434e7			−0.874923
$887$	−1.73521e7			−0.740531			−0.370265	−	0.928926i	$-0.620733\pi$
$887$	−1.73521e7			−0.740531			−0.370265	+	0.928926i	$0.620733\pi$
$888$	−3.80487e7	+	3.15347e6i	−1.61923	+	0.134201i
$889$		0			0
$890$		−	3.90618e6i		−	0.165302i
$891$	−1.31138e7	−	3.81905e7i	−0.553392	−	1.61161i
$892$			9.29417e6i			0.391110i
$893$			237578.i			0.00996961i
$894$	−381307.	−	4.60073e6i	−0.0159562	−	0.192523i
$895$		−	4.54457e7i		−	1.89642i
$896$		0			0
$897$	3.75780e6	+	4.53405e7i	0.155938	+	1.88150i
$898$	1.48858e7			0.616003
$899$	−527188.			−0.0217553
$900$	−8.50141e6	+	1.41893e6i	−0.349852	+	0.0583924i
$901$		−	2.43036e7i		−	0.997374i
$902$	1.05185e7			0.430466
$903$		0			0
$904$	−2.94800e7			−1.19979
$905$		−	1.27073e7i		−	0.515742i
$906$	8.27165e6	−	685551.i	0.334789	−	0.0277472i
$907$	−3.41252e7			−1.37739			−0.688696	−	0.725051i	$-0.741816\pi$
$907$	−3.41252e7			−1.37739			−0.688696	+	0.725051i	$0.741816\pi$
$908$	89737.9			0.00361211
$909$	3.72194e7	−	6.21213e6i	1.49403	−	0.249362i
$910$		0			0
$911$		−	1.86336e7i		−	0.743878i	−0.928257	−	0.371939i	$-0.878693\pi$
$911$		−	1.86336e7i		−	0.743878i	0.928257	−	0.371939i	$-0.121307\pi$
$912$	−293240.	+	24303.6i	−0.0116744	+	0.000967573i
$913$			7.76143e7i			3.08152i
$914$		−	1.74300e7i		−	0.690131i
$915$	1.20815e6	−	100131.i	0.0477055	−	0.00395382i
$916$		−	7.13916e6i		−	0.281131i
$917$		0			0
$918$	−1.31011e7	+	3.31836e6i	−0.513097	+	0.129962i
$919$	8.54259e6			0.333657			0.166829	−	0.985986i	$-0.446647\pi$
$919$	8.54259e6			0.333657			0.166829	+	0.985986i	$0.446647\pi$
$920$	−4.77856e7			−1.86135
$921$	−2.35959e7	+	1.95562e6i	−0.916614	+	0.0759687i
$922$			1.82094e7i			0.705455i
$923$	−1.96050e7			−0.757465
$924$		0			0
$925$	3.26722e7			1.25552
$926$		−	4.79024e6i		−	0.183582i
$927$	−4.70737e6	−	2.82037e7i	−0.179920	−	1.07797i
$928$	−2.91451e6			−0.111095
$929$	1.44120e7			0.547881			0.273940	−	0.961747i	$-0.411673\pi$
$929$	1.44120e7			0.547881			0.273940	+	0.961747i	$0.411673\pi$
$930$	−342394.	−	4.13122e6i	−0.0129813	−	0.156628i
$931$		0			0
$932$		−	1.16391e7i		−	0.438916i
$933$	1.68065e6	+	2.02782e7i	0.0632080	+	0.762648i
$934$		−	2.95932e7i		−	1.11000i
$935$		−	4.30621e7i		−	1.61089i
$936$	−4.24167e7	+	7.07960e6i	−1.58251	+	0.264131i
$937$			3.08762e7i			1.14888i	0.818547	+	0.574440i	$0.194780\pi$
$937$			3.08762e7i			1.14888i	−0.818547	+	0.574440i	$0.805220\pi$
$938$		0			0
$939$	−5.81981e6	+	482344.i	−0.215399	+	0.0178522i
$940$	−5.23750e6			−0.193332
$941$	4.32430e7			1.59199			0.795997	−	0.605301i	$-0.206947\pi$
$941$	4.32430e7			1.59199			0.795997	+	0.605301i	$0.206947\pi$
$942$	1.27812e6	+	1.54214e7i	0.0469294	+	0.566236i
$943$		−	1.15658e7i		−	0.423543i
$944$	5.76403e6			0.210522
$945$		0			0
$946$	3.74052e7			1.35895
$947$			9.47194e6i			0.343213i	0.985166	+	0.171607i	$0.0548958\pi$
$947$			9.47194e6i			0.343213i	−0.985166	+	0.171607i	$0.945104\pi$
$948$	429066.	+	5.17697e6i	0.0155061	+	0.187092i
$949$	5.08172e7			1.83166
$950$	522725.			0.0187916
$951$	1.47843e7	−	1.22532e6i	0.530089	−	0.0439336i
$952$		0			0
$953$		−	5.38831e7i		−	1.92185i	−0.276802	−	0.960927i	$-0.589275\pi$
$953$		−	5.38831e7i		−	1.92185i	0.276802	−	0.960927i	$-0.410725\pi$
$954$	−3.00538e7	+	5.01616e6i	−1.06913	+	0.178443i
$955$		−	4.95335e7i		−	1.75748i
$956$		−	8.17901e6i		−	0.289438i
$957$	567092.	+	6.84236e6i	0.0200158	+	0.241505i
$958$		−	1.96075e7i		−	0.690254i
$959$		0			0
$960$	−3.15423e6	−	3.80580e7i	−0.110463	−	1.33281i
$961$	2.79592e7			0.976599
$962$	4.85999e7			1.69316
$963$	−1.75576e6	−	1.05195e7i	−0.0610098	−	0.365534i
$964$			1.24637e6i			0.0431970i
$965$	−7.03617e7			−2.43230
$966$		0			0
$967$	−3.83707e7			−1.31957			−0.659787	−	0.751453i	$-0.729353\pi$
$967$	−3.83707e7			−1.31957			−0.659787	+	0.751453i	$0.729353\pi$
$968$			5.99676e7i			2.05697i
$969$	−603192.	+	49992.4i	−0.0206370	+	0.00171039i
$970$	4.28502e7			1.46226
$971$	−3.05234e7			−1.03893			−0.519463	−	0.854493i	$-0.673868\pi$
$971$	−3.05234e7			−1.03893			−0.519463	+	0.854493i	$0.673868\pi$
$972$	−5.02695e6	−	1.14576e7i	−0.170663	−	0.388981i
$973$		0			0
$974$			3.52138e7i			1.18937i
$975$	3.66748e7	−	3.03960e6i	1.23554	−	0.102401i
$976$			415176.i			0.0139511i
$977$		−	1.02939e7i		−	0.345018i	−0.985008	−	0.172509i	$-0.944813\pi$
$977$		−	1.02939e7i		−	0.345018i	0.985008	−	0.172509i	$-0.0551874\pi$
$978$	4.36736e6	−	361965.i	0.146006	−	0.0121010i
$979$			8.22164e6i			0.274158i
$980$		0			0
$981$	3.39064e7	−	5.65917e6i	1.12489	−	0.187750i
$982$	1.47131e7			0.486883
$983$	−5.35051e7			−1.76608			−0.883042	−	0.469294i	$-0.844508\pi$
$983$	−5.35051e7			−1.76608			−0.883042	+	0.469294i	$0.844508\pi$
$984$	1.08949e7	−	902963.i	0.358702	−	0.0297291i
$985$			2.00815e7i			0.659487i
$986$	2.29796e6			0.0752750
$987$		0			0
$988$	−574180.			−0.0187135
$989$		−	4.11295e7i		−	1.33710i
$990$	−5.32507e7	+	8.88785e6i	−1.72678	+	0.288210i
$991$	−1.40671e7			−0.455010			−0.227505	−	0.973777i	$-0.573057\pi$
$991$	−1.40671e7			−0.455010			−0.227505	+	0.973777i	$0.573057\pi$
$992$	−3.70377e6			−0.119499
$993$	−1.78892e6	−	2.15845e7i	−0.0575728	−	0.694656i
$994$		0			0
$995$			5.60030e7i			1.79330i
$996$	1.98640e6	+	2.39673e7i	0.0634481	+	0.765545i
$997$		−	1.77878e7i		−	0.566742i	−0.959010	−	0.283371i	$-0.908547\pi$
$997$		−	1.77878e7i		−	0.566742i	0.959010	−	0.283371i	$-0.0914528\pi$
$998$			2.31896e7i			0.737000i
$999$	1.16455e7	+	4.59770e7i	0.369184	+	1.45756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.7	✓	40
3.2	odd	2	inner	147.6.c.d.146.34	yes	40
7.6	odd	2	inner	147.6.c.d.146.33	yes	40
21.20	even	2	inner	147.6.c.d.146.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.7	✓	40	1.1	even	1	trivial
147.6.c.d.146.8	yes	40	21.20	even	2	inner
147.6.c.d.146.33	yes	40	7.6	odd	2	inner
147.6.c.d.146.34	yes	40	3.2	odd	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.29037i q^{2} +(-1.28755 - 15.5352i) q^{3} +13.5927 q^{4} -75.7260 q^{5} +(-66.6517 + 5.52407i) q^{6} -195.610i q^{8} +(-239.684 + 40.0047i) q^{9} +324.892i q^{10} -683.827i q^{11} +(-17.5013 - 211.166i) q^{12} +904.705i q^{13} +(97.5011 + 1176.42i) q^{15} -404.270 q^{16} -831.582 q^{17} +(171.635 + 1028.33i) q^{18} +46.6911i q^{19} -1029.32 q^{20} -2933.87 q^{22} +3225.98i q^{23} +(-3038.83 + 251.857i) q^{24} +2609.42 q^{25} +3881.52 q^{26} +(930.087 + 3672.04i) q^{27} -644.085i q^{29} +(5047.27 - 418.316i) q^{30} -818.506i q^{31} -4525.04i q^{32} +(-10623.4 + 880.462i) q^{33} +3567.79i q^{34} +(-3257.97 + 543.773i) q^{36} +12520.8 q^{37} +200.322 q^{38} +(14054.8 - 1164.85i) q^{39} +14812.7i q^{40} -3585.21 q^{41} -12749.4 q^{43} -9295.07i q^{44} +(18150.3 - 3029.40i) q^{45} +13840.7 q^{46} +5088.30 q^{47} +(520.519 + 6280.42i) q^{48} -11195.4i q^{50} +(1070.70 + 12918.8i) q^{51} +12297.4i q^{52} +29225.7i q^{53} +(15754.4 - 3990.42i) q^{54} +51783.4i q^{55} +(725.355 - 60.1172i) q^{57} -2763.36 q^{58} -14257.9 q^{59} +(1325.31 + 15990.7i) q^{60} -1026.97i q^{61} -3511.69 q^{62} -32350.7 q^{64} -68509.7i q^{65} +(3777.51 + 45578.2i) q^{66} -6569.50 q^{67} -11303.5 q^{68} +(50116.3 - 4153.62i) q^{69} +21670.0i q^{71} +(7825.31 + 46884.6i) q^{72} -56169.9i q^{73} -53719.0i q^{74} +(-3359.77 - 40537.9i) q^{75} +634.660i q^{76} +(-4997.66 - 60300.1i) q^{78} -24516.2 q^{79} +30613.8 q^{80} +(55848.2 - 19177.0i) q^{81} +15381.9i q^{82} -113500. q^{83} +62972.3 q^{85} +54699.8i q^{86} +(-10006.0 + 829.293i) q^{87} -133763. q^{88} -12023.0 q^{89} +(-12997.2 - 77871.7i) q^{90} +43849.9i q^{92} +(-12715.6 + 1053.87i) q^{93} -21830.7i q^{94} -3535.73i q^{95} +(-70297.4 + 5826.22i) q^{96} -131890. i q^{97} +(27356.3 + 163903. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9} - 3176 q^{15} + 3552 q^{16} - 4544 q^{18} + 21088 q^{22} + 30104 q^{25} + 44664 q^{30} - 59320 q^{36} - 26224 q^{37} - 16216 q^{39} + 21584 q^{43} - 27680 q^{46} + 95784 q^{51}+ \cdots - 258480 q^{99}+O(q^{100}) \) 40 * q - 640 * q^4 + 440 * q^9 - 3176 * q^15 + 3552 * q^16 - 4544 * q^18 + 21088 * q^22 + 30104 * q^25 + 44664 * q^30 - 59320 * q^36 - 26224 * q^37 - 16216 * q^39 + 21584 * q^43 - 27680 * q^46 + 95784 * q^51 - 130304 * q^57 - 131376 * q^58 + 329208 * q^60 + 53968 * q^64 - 187632 * q^67 + 606736 * q^72 + 70312 * q^78 - 597424 * q^79 + 755256 * q^81 + 108112 * q^85 - 1673072 * q^88 + 590480 * q^93 - 258480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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