LMFDB - Embedded newform 147.6.c.d.146.8

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$0.123807\pi$
$2$			4.29037i			0.758437i	−0.925307	+	0.379219i	$0.876193\pi$
$3$	−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	$0.324604\pi$
$11$			683.827i			1.70398i	−0.523559	+	0.851989i	$0.675396\pi$
$12$	−17.5013	+	211.166i	−0.0350847	+	0.423321i
$13$		−	904.705i		−	1.48473i	−0.669993	−	0.742367i	$-0.733703\pi$
$13$		−	904.705i		−	1.48473i	0.669993	−	0.742367i	$-0.266297\pi$
$14$		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	$-0.995277\pi$
$19$		−	46.6911i		−	0.0296722i	0.999890	−	0.0148361i	$-0.00472266\pi$
$20$	−1029.32			−0.575409
$21$		0			0
$22$	−2933.87			−1.29236
$23$		−	3225.98i		−	1.27158i	−0.771863	−	0.635788i	$-0.780675\pi$
$23$		−	3225.98i		−	1.27158i	0.771863	−	0.635788i	$-0.219325\pi$
$24$	−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	$0.0226535\pi$
$29$			644.085i			0.142216i	−0.997469	+	0.0711080i	$0.977347\pi$
$30$	5047.27	+	418.316i	1.02389	+	0.0848596i
$31$			818.506i			0.152974i	0.997071	+	0.0764870i	$0.0243704\pi$
$31$			818.506i			0.152974i	−0.997071	+	0.0764870i	$0.975630\pi$
$32$			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	$-0.746622\pi$
$53$		−	29225.7i		−	1.42914i	0.699562	−	0.714572i	$-0.253378\pi$
$54$	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	$0.00562442\pi$
$61$			1026.97i			0.0353374i	−0.999844	+	0.0176687i	$0.994376\pi$
$62$	−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	$-0.917897\pi$
$71$		−	21670.0i		−	0.510169i	0.966919	−	0.255084i	$-0.0821032\pi$
$72$	7825.31	−	46884.6i	0.177898	−	1.06586i
$73$			56169.9i			1.23366i	0.787096	+	0.616831i	$0.211584\pi$
$73$			56169.9i			1.23366i	−0.787096	+	0.616831i	$0.788416\pi$
$74$			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	$0.252043\pi$
$97$			131890.i			1.42326i	−0.702555	+	0.711630i	$0.747957\pi$
$98$		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	$-0.815982\pi$
$103$		−	117670.i		−	1.09288i	0.837497	−	0.546442i	$-0.184018\pi$
$104$	176969.			1.60440
$105$		0			0
$106$	125389.			1.08392
$107$		−	43888.8i		−	0.370591i	−0.982683	−	0.185295i	$-0.940676\pi$
$107$		−	43888.8i		−	0.370591i	0.982683	−	0.185295i	$-0.0593242\pi$
$108$	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	$0.187339\pi$
$113$			150708.i			1.11030i	−0.831750	+	0.555151i	$0.812661\pi$
$114$	−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	$0.0205123\pi$
$137$			28294.0i			0.128793i	−0.997924	+	0.0643966i	$0.979488\pi$
$138$	−17820.6	+	215017.i	−0.0796570	+	0.961116i
$139$		−	10688.5i		−	0.0469223i	−0.999725	−	0.0234612i	$-0.992531\pi$
$139$		−	10688.5i		−	0.0469223i	0.999725	−	0.0234612i	$-0.00746861\pi$
$140$		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	$-0.959351\pi$
$149$		−	69026.4i		−	0.254712i	0.991857	−	0.127356i	$-0.0406491\pi$
$150$	−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	$0.122210\pi$
$157$			231373.i			0.749142i	−0.927198	+	0.374571i	$0.877790\pi$
$158$		−	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	$-0.753193\pi$
$179$		−	600133.i		−	1.39996i	0.714163	−	0.699979i	$-0.246807\pi$
$180$	246713.	+	41177.8i	0.567558	+	0.0947287i
$181$		−	167807.i		−	0.380726i	−0.981714	−	0.190363i	$-0.939034\pi$
$181$		−	167807.i		−	0.380726i	0.981714	−	0.190363i	$-0.0609665\pi$
$182$		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	$-0.775315\pi$
$191$		−	654116.i		−	1.29739i	0.761048	−	0.648696i	$-0.224685\pi$
$192$	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	$0.0782693\pi$
$197$			265187.i			0.486840i	−0.969921	+	0.243420i	$0.921731\pi$
$198$	703203.	+	117369.i	1.27473	+	0.212759i
$199$			739548.i			1.32383i	0.749577	+	0.661917i	$0.230257\pi$
$199$			739548.i			1.32383i	−0.749577	+	0.661917i	$0.769743\pi$
$200$			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	$-0.847715\pi$
$223$		−	683761.i		−	0.920750i	0.887724	−	0.460375i	$-0.152285\pi$
$224$		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	$0.107359\pi$
$229$			525219.i			0.661838i	−0.943659	+	0.330919i	$0.892641\pi$
$230$	−1.04810e6			−1.30642
$231$		0			0
$232$	−125989.			−0.153679
$233$			856277.i			1.03330i	0.856198	+	0.516648i	$0.172820\pi$
$233$			856277.i			1.03330i	−0.856198	+	0.516648i	$0.827180\pi$
$234$	−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	$0.110663\pi$
$239$			601720.i			0.681396i	−0.940173	+	0.340698i	$0.889337\pi$
$240$	−39416.8	+	475591.i	−0.0441726	+	0.532973i
$241$		−	91693.7i		−	0.101694i	−0.998706	−	0.0508472i	$-0.983808\pi$
$241$		−	91693.7i		−	0.101694i	0.998706	−	0.0508472i	$-0.0161921\pi$
$242$		−	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	$0.226496\pi$
$263$			1.46502e6i			1.30603i	−0.757345	+	0.653015i	$0.773504\pi$
$264$	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	$0.0524812\pi$
$271$			396860.i			0.328257i	−0.986439	+	0.164129i	$0.947519\pi$
$272$	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	$0.0268516\pi$
$281$			223049.i			0.168514i	−0.996444	+	0.0842568i	$0.973148\pi$
$282$	−339144.	−	28108.1i	−0.253957	−	0.0210479i
$283$			1.02061e6i			0.757522i	0.925494	+	0.378761i	$0.123650\pi$
$283$			1.02061e6i			0.757522i	−0.925494	+	0.378761i	$0.876350\pi$
$284$		−	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	$0.152107\pi$
$307$			1.51886e6i			0.919757i	−0.887982	+	0.459879i	$0.847893\pi$
$308$		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	$0.0344667\pi$
$313$			374621.i			0.216138i	−0.994143	+	0.108069i	$0.965533\pi$
$314$	−992677.			−0.568177
$315$		0			0
$316$	−333242.			−0.187733
$317$		−	951664.i		−	0.531907i	−0.963986	−	0.265953i	$-0.914313\pi$
$317$		−	951664.i		−	0.531907i	0.963986	−	0.265953i	$-0.0856867\pi$
$318$	−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	$-0.866507\pi$
$347$		−	1.82666e6i		−	0.814391i	0.913341	−	0.407196i	$-0.133493\pi$
$348$	−136009.	−	11272.4i	−0.0602030	−	0.00498961i
$349$			403109.i			0.177157i	0.996069	+	0.0885786i	$0.0282324\pi$
$349$			403109.i			0.177157i	−0.996069	+	0.0885786i	$0.971768\pi$
$350$		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	$0.0873222\pi$
$359$			1.32306e6i			0.541805i	−0.962607	+	0.270903i	$0.912678\pi$
$360$	−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	$-0.904897\pi$
$367$		−	1.51900e6i		−	0.588697i	0.955698	−	0.294348i	$-0.0951026\pi$
$368$			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	$0.161896\pi$
$389$			2.90671e6i			0.973928i	−0.873422	+	0.486964i	$0.838104\pi$
$390$	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	$-0.815271\pi$
$397$		−	3.44376e6i		−	1.09662i	0.836275	−	0.548310i	$-0.184729\pi$
$398$	−3.17294e6			−1.00405
$399$		0			0
$400$	−1.05491e6			−0.329660
$401$		−	3.46397e6i		−	1.07575i	−0.843023	−	0.537877i	$-0.819226\pi$
$401$		−	3.46397e6i		−	1.07575i	0.843023	−	0.537877i	$-0.180774\pi$
$402$	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	$-0.944665\pi$
$409$		−	1.17031e6i		−	0.345934i	0.984928	−	0.172967i	$-0.0553354\pi$
$410$			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	$-0.775931\pi$
$431$		−	4.99202e6i		−	1.29444i	0.762302	−	0.647221i	$-0.224069\pi$
$432$	−376007.	+	1.48450e6i	−0.0969362	+	0.382710i
$433$		−	5.33397e6i		−	1.36720i	−0.729859	−	0.683598i	$-0.760414\pi$
$433$		−	5.33397e6i		−	1.36720i	0.729859	−	0.683598i	$-0.239586\pi$
$434$		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	$0.00366491\pi$
$439$			92981.1i			0.0230268i	−0.999934	+	0.0115134i	$0.996335\pi$
$440$	1.01293e7			2.49430
$441$		0			0
$442$	−3.22780e6			−0.785870
$443$			4.76496e6i			1.15359i	0.816890	+	0.576793i	$0.195696\pi$
$443$			4.76496e6i			1.15359i	−0.816890	+	0.576793i	$0.804304\pi$
$444$	−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	$-0.866888\pi$
$449$		−	3.46959e6i		−	0.812200i	0.913829	−	0.406100i	$-0.133112\pi$
$450$	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	$-0.895989\pi$
$491$		−	3.42933e6i		−	0.641956i	0.947087	−	0.320978i	$-0.104011\pi$
$492$	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	$0.251356\pi$
$523$			8.88406e6i			1.42022i	−0.704088	+	0.710112i	$0.748644\pi$
$524$	−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	$0.269592\pi$
$557$			1.09724e7i			1.49852i	−0.662274	+	0.749262i	$0.730408\pi$
$558$	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	$0.0828366\pi$
$569$			3.97438e6i			0.514623i	−0.966329	+	0.257311i	$0.917163\pi$
$570$	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	$0.353110\pi$
$577$			1.43214e7i			1.79080i	−0.445264	+	0.895399i	$0.646890\pi$
$578$		−	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	$-0.761358\pi$
$599$		−	1.19679e7i		−	1.36286i	0.731883	−	0.681430i	$-0.238642\pi$
$600$	−7.92961e6	−	657203.i	−0.899235	−	0.0745283i
$601$		−	1.06577e7i		−	1.20359i	−0.798651	−	0.601794i	$-0.794453\pi$
$601$		−	1.06577e7i		−	1.20359i	0.798651	−	0.601794i	$-0.205547\pi$
$602$		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	$-0.945107\pi$
$607$		−	3.11542e6i		−	0.343199i	0.985167	−	0.171599i	$-0.0548934\pi$
$608$	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	$0.235147\pi$
$617$			1.27346e7i			1.34671i	−0.739319	+	0.673355i	$0.764853\pi$
$618$	−650019.	+	7.84293e6i	−0.0684629	+	0.826052i
$619$			1.19650e7i			1.25512i	0.778569	+	0.627559i	$0.215946\pi$
$619$			1.19650e7i			1.25512i	−0.778569	+	0.627559i	$0.784054\pi$
$620$		−	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	$0.131944\pi$
$641$			8.37927e6i			0.805491i	−0.915312	+	0.402746i	$0.868056\pi$
$642$	−242445.	+	2.92527e6i	−0.0232154	+	0.280109i
$643$			86587.1i			0.00825897i	0.999991	+	0.00412949i	$0.00131446\pi$
$643$			86587.1i			0.00825897i	−0.999991	+	0.00412949i	$0.998686\pi$
$644$		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	$0.294728\pi$
$653$			1.74162e7i			1.59834i	−0.601103	+	0.799172i	$0.705272\pi$
$654$	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	$0.0588450\pi$
$659$			4.09851e6i			0.367631i	−0.982961	+	0.183816i	$0.941155\pi$
$660$	1.09349e7	+	906279.i	0.977134	+	0.0809846i
$661$		−	1.82046e6i		−	0.162061i	−0.996712	−	0.0810304i	$-0.974179\pi$
$661$		−	1.82046e6i		−	0.162061i	0.996712	−	0.0810304i	$-0.0258211\pi$
$662$			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	$0.0301234\pi$
$683$			2.30403e6i			0.188989i	−0.995525	+	0.0944943i	$0.969877\pi$
$684$	−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	$0.184133\pi$
$691$			1.37249e7i			1.09349i	−0.837300	+	0.546744i	$0.815867\pi$
$692$	−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	$-0.848058\pi$
$701$		−	1.19545e7i		−	0.918836i	0.888220	−	0.459418i	$-0.151942\pi$
$702$	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	$0.0277110\pi$
$727$			2.47810e6i			0.173893i	−0.996213	+	0.0869467i	$0.972289\pi$
$728$		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	$-0.784916\pi$
$733$		−	1.81962e7i		−	1.25090i	0.780266	−	0.625448i	$-0.215084\pi$
$734$	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	$-0.749943\pi$
$743$		−	2.12846e7i		−	1.41447i	0.706980	−	0.707233i	$-0.250057\pi$
$744$	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	$0.342595\pi$
$769$			2.88689e7i			1.76041i	−0.474593	+	0.880206i	$0.657405\pi$
$770$		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	$-0.871038\pi$
$787$		−	1.36972e7i		−	0.788306i	0.919045	−	0.394153i	$-0.128962\pi$
$788$			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	$-0.739244\pi$
$809$		−	2.72004e7i		−	1.46118i	0.682815	−	0.730592i	$-0.260756\pi$
$810$	6.23047e6	−	1.81447e7i	0.333663	−	0.971710i
$811$		−	1.05261e7i		−	0.561973i	−0.959712	−	0.280987i	$-0.909338\pi$
$811$		−	1.05261e7i		−	0.561973i	0.959712	−	0.280987i	$-0.0906616\pi$
$812$		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	$-0.892474\pi$
$821$		−	1.28015e7i		−	0.662831i	0.943485	−	0.331415i	$-0.107526\pi$
$822$	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	$0.171301\pi$
$827$			2.01621e7i			1.02511i	−0.858654	+	0.512556i	$0.828699\pi$
$828$	−1.75420e6	+	1.05101e7i	−0.0889210	+	0.532761i
$829$			3.20634e7i			1.62040i	0.586151	+	0.810202i	$0.300642\pi$
$829$			3.20634e7i			1.62040i	−0.586151	+	0.810202i	$0.699358\pi$
$830$			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	$0.148576\pi$
$853$			1.91256e7i			0.900001i	−0.893028	+	0.450001i	$0.851424\pi$
$854$		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	$0.266776\pi$
$859$			3.21529e7i			1.48675i	−0.668875	+	0.743375i	$0.733224\pi$
$860$	1.31233e7			0.605057
$861$		0			0
$862$	2.14176e7			0.981754
$863$		−	1.53188e7i		−	0.700161i	−0.936720	−	0.350081i	$-0.886154\pi$
$863$		−	1.53188e7i		−	0.700161i	0.936720	−	0.350081i	$-0.113846\pi$
$864$	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	$0.121307\pi$
$911$			1.86336e7i			0.743878i	−0.928257	+	0.371939i	$0.878693\pi$
$912$	−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	$-0.805220\pi$
$937$		−	3.08762e7i		−	1.14888i	0.818547	−	0.574440i	$-0.194780\pi$
$938$		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	$-0.945104\pi$
$947$		−	9.47194e6i		−	0.343213i	0.985166	−	0.171607i	$-0.0548958\pi$
$948$	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	$0.410725\pi$
$953$			5.38831e7i			1.92185i	−0.276802	+	0.960927i	$0.589275\pi$
$954$	−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	$0.0551874\pi$
$977$			1.02939e7i			0.345018i	−0.985008	+	0.172509i	$0.944813\pi$
$978$	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	$0.0914528\pi$
$997$			1.77878e7i			0.566742i	−0.959010	+	0.283371i	$0.908547\pi$
$998$		−	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.146.8	yes	40
3.2	odd	2	inner	147.6.c.d.146.33	yes	40
7.6	odd	2	inner	147.6.c.d.146.34	yes	40
21.20	even	2	inner	147.6.c.d.146.7	✓	40

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

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