LMFDB - Embedded newform 147.6.c.d.146.16

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			146.16
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.52115i q^{2} +(-15.4465 + 2.09880i) q^{3} +29.6861 q^{4} -32.5134 q^{5} +(-3.19260 - 23.4966i) q^{6} +93.8341i q^{8} +(234.190 - 64.8384i) q^{9} +O(q^{10})$	\(q+1.52115i q^{2} +(-15.4465 + 2.09880i) q^{3} +29.6861 q^{4} -32.5134 q^{5} +(-3.19260 - 23.4966i) q^{6} +93.8341i q^{8} +(234.190 - 64.8384i) q^{9} -49.4578i q^{10} +321.521i q^{11} +(-458.547 + 62.3052i) q^{12} -609.147i q^{13} +(502.218 - 68.2391i) q^{15} +807.219 q^{16} -31.0202 q^{17} +(98.6292 + 356.239i) q^{18} +1316.86i q^{19} -965.194 q^{20} -489.084 q^{22} +3069.81i q^{23} +(-196.939 - 1449.41i) q^{24} -2067.88 q^{25} +926.607 q^{26} +(-3481.34 + 1493.05i) q^{27} -8104.22i q^{29} +(103.802 + 763.952i) q^{30} +5850.14i q^{31} +4230.60i q^{32} +(-674.809 - 4966.39i) q^{33} -47.1865i q^{34} +(6952.19 - 1924.80i) q^{36} -9764.56 q^{37} -2003.15 q^{38} +(1278.48 + 9409.20i) q^{39} -3050.86i q^{40} -19698.5 q^{41} -9705.30 q^{43} +9544.71i q^{44} +(-7614.30 + 2108.11i) q^{45} -4669.66 q^{46} -18224.2 q^{47} +(-12468.7 + 1694.19i) q^{48} -3145.57i q^{50} +(479.154 - 65.1052i) q^{51} -18083.2i q^{52} +33118.3i q^{53} +(-2271.15 - 5295.66i) q^{54} -10453.7i q^{55} +(-2763.83 - 20341.0i) q^{57} +12327.8 q^{58} +6677.29 q^{59} +(14908.9 - 2025.75i) q^{60} +35094.2i q^{61} -8898.97 q^{62} +19395.6 q^{64} +19805.4i q^{65} +(7554.64 - 1026.49i) q^{66} -19331.4 q^{67} -920.868 q^{68} +(-6442.93 - 47417.9i) q^{69} -21428.8i q^{71} +(6084.05 + 21975.0i) q^{72} -32945.3i q^{73} -14853.4i q^{74} +(31941.6 - 4340.07i) q^{75} +39092.5i q^{76} +(-14312.8 + 1944.76i) q^{78} +5143.35 q^{79} -26245.4 q^{80} +(50641.0 - 30369.0i) q^{81} -29964.4i q^{82} +65038.8 q^{83} +1008.57 q^{85} -14763.3i q^{86} +(17009.1 + 125182. i) q^{87} -30169.7 q^{88} +11478.5 q^{89} +(-3206.77 - 11582.5i) q^{90} +91130.7i q^{92} +(-12278.3 - 90364.3i) q^{93} -27721.8i q^{94} -42815.6i q^{95} +(-8879.18 - 65348.0i) q^{96} +132309. i q^{97} +(20846.9 + 75297.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.52115i			0.268905i	0.990920	+	0.134452i	$0.0429275\pi$
$2$			1.52115i			0.268905i	−0.990920	+	0.134452i	$0.957072\pi$
$3$	−15.4465	+	2.09880i	−0.990895	+	0.134638i
$3$	−15.4465	+	2.09880i	−0.990895	+	0.134638i
$4$	29.6861			0.927690
$5$	−32.5134			−0.581617			−0.290808	−	0.956781i	$-0.593924\pi$
$5$	−32.5134			−0.581617			−0.290808	+	0.956781i	$0.593924\pi$
$6$	−3.19260	−	23.4966i	−0.0362049	−	0.266456i
$7$		0			0
$7$		0			0
$8$			93.8341i			0.518365i
$9$	234.190	−	64.8384i	0.963745	−	0.266825i
$10$		−	49.4578i		−	0.156399i
$11$			321.521i			0.801176i	0.916258	+	0.400588i	$0.131194\pi$
$11$			321.521i			0.801176i	−0.916258	+	0.400588i	$0.868806\pi$
$12$	−458.547	+	62.3052i	−0.919243	+	0.124903i
$13$		−	609.147i		−	0.999686i	−0.866116	−	0.499843i	$-0.833391\pi$
$13$		−	609.147i		−	0.999686i	0.866116	−	0.499843i	$-0.166609\pi$
$14$		0			0
$15$	502.218	−	68.2391i	0.576321	−	0.0783078i
$16$	807.219			0.788299
$17$	−31.0202			−0.0260329			−0.0130164	−	0.999915i	$-0.504143\pi$
$17$	−31.0202			−0.0260329			−0.0130164	+	0.999915i	$0.504143\pi$
$18$	98.6292	+	356.239i	0.0717504	+	0.259156i
$19$			1316.86i			0.836867i	0.908247	+	0.418434i	$0.137421\pi$
$19$			1316.86i			0.836867i	−0.908247	+	0.418434i	$0.862579\pi$
$20$	−965.194			−0.539560
$21$		0			0
$22$	−489.084			−0.215440
$23$			3069.81i			1.21002i	0.796218	+	0.605010i	$0.206831\pi$
$23$			3069.81i			1.21002i	−0.796218	+	0.605010i	$0.793169\pi$
$24$	−196.939	−	1449.41i	−0.0697917	−	0.513645i
$25$	−2067.88			−0.661722
$26$	926.607			0.268820
$27$	−3481.34	+	1493.05i	−0.919045	+	0.394152i
$28$		0			0
$29$		−	8104.22i		−	1.78944i	−0.446632	−	0.894718i	$-0.647377\pi$
$29$		−	8104.22i		−	1.78944i	0.446632	−	0.894718i	$-0.352623\pi$
$30$	103.802	+	763.952i	0.0210573	+	0.154975i
$31$			5850.14i			1.09336i	0.837343	+	0.546678i	$0.184108\pi$
$31$			5850.14i			1.09336i	−0.837343	+	0.546678i	$0.815892\pi$
$32$			4230.60i			0.730342i
$33$	−674.809	−	4966.39i	−0.107869	−	0.793881i
$34$		−	47.1865i		−	0.00700036i
$35$		0			0
$36$	6952.19	−	1924.80i	0.894057	−	0.247531i
$37$	−9764.56			−1.17260			−0.586298	−	0.810095i	$-0.699415\pi$
$37$	−9764.56			−1.17260			−0.586298	+	0.810095i	$0.699415\pi$
$38$	−2003.15			−0.225038
$39$	1278.48	+	9409.20i	0.134596	+	0.990584i
$40$		−	3050.86i		−	0.301490i
$41$	−19698.5			−1.83009			−0.915046	−	0.403350i	$-0.867846\pi$
$41$	−19698.5			−1.83009			−0.915046	+	0.403350i	$0.867846\pi$
$42$		0			0
$43$	−9705.30			−0.800456			−0.400228	−	0.916416i	$-0.631069\pi$
$43$	−9705.30			−0.800456			−0.400228	+	0.916416i	$0.631069\pi$
$44$			9544.71i			0.743243i
$45$	−7614.30	+	2108.11i	−0.560530	+	0.155190i
$46$	−4669.66			−0.325380
$47$	−18224.2			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$47$	−18224.2			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$48$	−12468.7	+	1694.19i	−0.781122	+	0.106135i
$49$		0			0
$50$		−	3145.57i		−	0.177940i
$51$	479.154	−	65.1052i	0.0257958	−	0.00350502i
$52$		−	18083.2i		−	0.927399i
$53$			33118.3i			1.61949i	0.586782	+	0.809745i	$0.300395\pi$
$53$			33118.3i			1.61949i	−0.586782	+	0.809745i	$0.699605\pi$
$54$	−2271.15	−	5295.66i	−0.105989	−	0.247136i
$55$		−	10453.7i		−	0.465977i
$56$		0			0
$57$	−2763.83	−	20341.0i	−0.112674	−	0.829248i
$58$	12327.8			0.481188
$59$	6677.29			0.249730			0.124865	−	0.992174i	$-0.460150\pi$
$59$	6677.29			0.249730			0.124865	+	0.992174i	$0.460150\pi$
$60$	14908.9	−	2025.75i	0.534647	−	0.0726454i
$61$			35094.2i			1.20757i	0.797149	+	0.603783i	$0.206341\pi$
$61$			35094.2i			1.20757i	−0.797149	+	0.603783i	$0.793659\pi$
$62$	−8898.97			−0.294009
$63$		0			0
$64$	19395.6			0.591907
$65$			19805.4i			0.581434i
$66$	7554.64	−	1026.49i	0.213478	−	0.0290065i
$67$	−19331.4			−0.526110			−0.263055	−	0.964781i	$-0.584730\pi$
$67$	−19331.4			−0.526110			−0.263055	+	0.964781i	$0.584730\pi$
$68$	−920.868			−0.0241504
$69$	−6442.93	−	47417.9i	−0.162915	−	1.19900i
$70$		0			0
$71$		−	21428.8i		−	0.504489i	−0.967664	−	0.252245i	$-0.918831\pi$
$71$		−	21428.8i		−	0.504489i	0.967664	−	0.252245i	$-0.0811688\pi$
$72$	6084.05	+	21975.0i	0.138313	+	0.499572i
$73$		−	32945.3i		−	0.723581i	−0.932260	−	0.361790i	$-0.882166\pi$
$73$		−	32945.3i		−	0.723581i	0.932260	−	0.361790i	$-0.117834\pi$
$74$		−	14853.4i		−	0.315317i
$75$	31941.6	−	4340.07i	0.655697	−	0.0890931i
$76$			39092.5i			0.776354i
$77$		0			0
$78$	−14312.8	+	1944.76i	−0.266373	+	0.0361935i
$79$	5143.35			0.0927210			0.0463605	−	0.998925i	$-0.485238\pi$
$79$	5143.35			0.0927210			0.0463605	+	0.998925i	$0.485238\pi$
$80$	−26245.4			−0.458488
$81$	50641.0	−	30369.0i	0.857609	−	0.514302i
$82$		−	29964.4i		−	0.492120i
$83$	65038.8			1.03628			0.518140	−	0.855296i	$-0.326625\pi$
$83$	65038.8			1.03628			0.518140	+	0.855296i	$0.326625\pi$
$84$		0			0
$85$	1008.57			0.0151412
$86$		−	14763.3i		−	0.215246i
$87$	17009.1	+	125182.i	0.240926	+	1.77314i
$88$	−30169.7			−0.415302
$89$	11478.5			0.153607			0.0768034	−	0.997046i	$-0.475529\pi$
$89$	11478.5			0.153607			0.0768034	+	0.997046i	$0.475529\pi$
$90$	−3206.77	−	11582.5i	−0.0417312	−	0.150729i
$91$		0			0
$92$			91130.7i			1.12252i
$93$	−12278.3	−	90364.3i	−0.147208	−	1.08340i
$94$		−	27721.8i		−	0.323595i
$95$		−	42815.6i		−	0.486736i
$96$	−8879.18	−	65348.0i	−0.0983320	−	0.723693i
$97$			132309.i			1.42778i	0.700259	+	0.713889i	$0.253068\pi$
$97$			132309.i			1.42778i	−0.700259	+	0.713889i	$0.746932\pi$
$98$		0			0
$99$	20846.9	+	75297.1i	0.213774	+	0.772130i
$100$	−61387.3			−0.613873
$101$	86492.2			0.843671			0.421836	−	0.906672i	$-0.361386\pi$
$101$	86492.2			0.843671			0.421836	+	0.906672i	$0.361386\pi$
$102$	99.0351	+	728.868i	0.000942516	+	0.00693662i
$103$			93917.4i			0.872274i	0.899880	+	0.436137i	$0.143654\pi$
$103$			93917.4i			0.872274i	−0.899880	+	0.436137i	$0.856346\pi$
$104$	57158.7			0.518202
$105$		0			0
$106$	−50378.1			−0.435489
$107$		−	156675.i		−	1.32294i	−0.749970	−	0.661472i	$-0.769932\pi$
$107$		−	156675.i		−	1.32294i	0.749970	−	0.661472i	$-0.230068\pi$
$108$	−103347.	+	44322.7i	−0.852589	+	0.365651i
$109$	−181168.			−1.46054			−0.730272	−	0.683157i	$-0.760606\pi$
$109$	−181168.			−1.46054			−0.730272	+	0.683157i	$0.760606\pi$
$110$	15901.7			0.125303
$111$	150829.	−	20493.9i	1.16192	−	0.157876i
$112$		0			0
$113$			82928.7i			0.610955i	0.952199	+	0.305477i	$0.0988160\pi$
$113$			82928.7i			0.610955i	−0.952199	+	0.305477i	$0.901184\pi$
$114$	30941.7	−	4204.22i	0.222989	−	0.0302987i
$115$		−	99809.9i		−	0.703767i
$116$		−	240582.i		−	1.66004i
$117$	−39496.1	−	142656.i	−0.266741	−	0.963442i
$118$			10157.2i			0.0671535i
$119$		0			0
$120$	6403.15	+	47125.2i	0.0405920	+	0.298745i
$121$	57675.1			0.358117
$122$	−53383.7			−0.324720
$123$	304273.	−	41343.2i	1.81343	−	0.246400i
$124$			173668.i			1.01430i
$125$	168838.			0.966485
$126$		0			0
$127$	−52804.7			−0.290511			−0.145256	−	0.989394i	$-0.546400\pi$
$127$	−52804.7			−0.290511			−0.145256	+	0.989394i	$0.546400\pi$
$128$			164883.i			0.889509i
$129$	149913.	−	20369.5i	0.793168	−	0.107772i
$130$	−30127.1			−0.156350
$131$	205464.			1.04606			0.523030	−	0.852314i	$-0.324802\pi$
$131$	205464.			1.04606			0.523030	+	0.852314i	$0.324802\pi$
$132$	−20032.5	−	147433.i	−0.100069	−	0.736476i
$133$		0			0
$134$		−	29406.1i		−	0.141474i
$135$	113190.	−	48543.9i	0.534532	−	0.229245i
$136$		−	2910.75i		−	0.0134945i
$137$			93767.1i			0.426824i	0.976962	+	0.213412i	$0.0684577\pi$
$137$			93767.1i			0.426824i	−0.976962	+	0.213412i	$0.931542\pi$
$138$	72130.0	−	9800.69i	0.322417	−	0.0438086i
$139$		−	40339.4i		−	0.177089i	−0.996072	−	0.0885447i	$-0.971778\pi$
$139$		−	40339.4i		−	0.177089i	0.996072	−	0.0885447i	$-0.0282216\pi$
$140$		0			0
$141$	281500.	−	38248.9i	1.19242	−	0.162021i
$142$	32596.5			0.135660
$143$	195854.			0.800924
$144$	189043.	−	52338.7i	0.759720	−	0.210338i
$145$			263495.i			1.04077i
$146$	50115.0			0.194574
$147$		0			0
$148$	−289872.			−1.08781
$149$		−	158759.i		−	0.585832i	−0.956138	−	0.292916i	$-0.905374\pi$
$149$		−	158759.i		−	0.585832i	0.956138	−	0.292916i	$-0.0946256\pi$
$150$	6601.93	+	48588.1i	0.0239576	+	0.176320i
$151$	−161459.			−0.576260			−0.288130	−	0.957591i	$-0.593034\pi$
$151$	−161459.			−0.576260			−0.288130	+	0.957591i	$0.593034\pi$
$152$	−123567.			−0.433803
$153$	−7264.62	+	2011.30i	−0.0250891	+	0.00694621i
$154$		0			0
$155$		−	190208.i		−	0.635914i
$156$	37953.0	+	279322.i	0.124863	+	0.918955i
$157$		−	329790.i		−	1.06779i	−0.845549	−	0.533897i	$-0.820727\pi$
$157$		−	329790.i		−	1.06779i	0.845549	−	0.533897i	$-0.179273\pi$
$158$			7823.83i			0.0249331i
$159$	−69508.7	−	511562.i	−0.218045	−	1.60474i
$160$		−	137551.i		−	0.424779i
$161$		0			0
$162$	46196.0	+	77032.8i	0.138298	+	0.230615i
$163$	−295313.			−0.870589			−0.435295	−	0.900288i	$-0.643356\pi$
$163$	−295313.			−0.870589			−0.435295	+	0.900288i	$0.643356\pi$
$164$	−584771.			−1.69776
$165$	21940.3	+	161474.i	0.0627383	+	0.461734i
$166$			98934.1i			0.278661i
$167$	−539627.			−1.49728			−0.748640	−	0.662977i	$-0.769293\pi$
$167$	−539627.			−1.49728			−0.748640	+	0.662977i	$0.769293\pi$
$168$		0			0
$169$	233.200			0.000628075
$170$			1534.19i			0.00407153i
$171$	85383.3	+	308396.i	0.223297	+	0.806527i
$172$	−288112.			−0.742575
$173$	−245634.			−0.623984			−0.311992	−	0.950085i	$-0.600996\pi$
$173$	−245634.			−0.623984			−0.311992	+	0.950085i	$0.600996\pi$
$174$	−190421.	+	25873.5i	−0.476806	+	0.0647862i
$175$		0			0
$176$			259538.i			0.631567i
$177$	−103141.	+	14014.3i	−0.247456	+	0.0336232i
$178$			17460.6i			0.0413056i
$179$			795928.i			1.85670i	0.371709	+	0.928349i	$0.378772\pi$
$179$			795928.i			1.85670i	−0.371709	+	0.928349i	$0.621228\pi$
$180$	−226039.	+	62581.6i	−0.519998	+	0.143968i
$181$			717178.i			1.62716i	0.581452	+	0.813581i	$0.302485\pi$
$181$			717178.i			1.62716i	−0.581452	+	0.813581i	$0.697515\pi$
$182$		0			0
$183$	−73655.8	−	542083.i	−0.162585	−	1.19657i
$184$	−288053.			−0.627232
$185$	317479.			0.682001
$186$	137458.	−	18677.2i	0.291332	−	0.0395848i
$187$		−	9973.65i		−	0.0208569i
$188$	−541004.			−1.11636
$189$		0			0
$190$	65129.2			0.130886
$191$		−	53667.8i		−	0.106446i	−0.998583	−	0.0532231i	$-0.983051\pi$
$191$		−	53667.8i		−	0.106446i	0.998583	−	0.0532231i	$-0.0169495\pi$
$192$	−299595.	+	40707.5i	−0.586517	+	0.0796933i
$193$	−523027.			−1.01072			−0.505360	−	0.862909i	$-0.668640\pi$
$193$	−523027.			−1.01072			−0.505360	+	0.862909i	$0.668640\pi$
$194$	−201263.			−0.383936
$195$	−41567.6	−	305925.i	−0.0782832	−	0.576140i
$196$		0			0
$197$		−	682071.i		−	1.25217i	−0.779754	−	0.626086i	$-0.784656\pi$
$197$		−	682071.i		−	1.25217i	0.779754	−	0.626086i	$-0.215344\pi$
$198$	−114539.	+	31711.4i	−0.207629	+	0.0574847i
$199$			224421.i			0.401727i	0.979619	+	0.200863i	$0.0643747\pi$
$199$			224421.i			0.401727i	−0.979619	+	0.200863i	$0.935625\pi$
$200$		−	194038.i		−	0.343014i
$201$	298603.	−	40572.8i	0.521320	−	0.0708345i
$202$			131568.i			0.226867i
$203$		0			0
$204$	14224.2	−	1932.72i	0.0239306	−	0.00325157i
$205$	640463.			1.06441
$206$	−142863.			−0.234559
$207$	199042.	+	718920.i	0.322863	+	1.16615i
$208$		−	491715.i		−	0.788052i
$209$	−423399.			−0.670478
$210$		0			0
$211$	451968.			0.698878			0.349439	−	0.936959i	$-0.386372\pi$
$211$	451968.			0.698878			0.349439	+	0.936959i	$0.386372\pi$
$212$			983153.i			1.50239i
$213$	44974.8	+	331000.i	0.0679235	+	0.499896i
$214$	238328.			0.355746
$215$	315552.			0.465559
$216$	−140099.	−	326668.i	−0.204315	−	0.476401i
$217$		0			0
$218$		−	275584.i		−	0.392747i
$219$	69145.7	+	508891.i	0.0974216	+	0.716992i
$220$		−	310330.i		−	0.432283i
$221$			18895.8i			0.0260247i
$222$	31174.4	+	229434.i	0.0424537	+	0.312446i
$223$		−	1.07317e6i		−	1.44512i	−0.691306	−	0.722562i	$-0.742964\pi$
$223$		−	1.07317e6i		−	1.44512i	0.691306	−	0.722562i	$-0.257036\pi$
$224$		0			0
$225$	−484277.	+	134078.i	−0.637732	+	0.176564i
$226$	−126147.			−0.164289
$227$	276662.			0.356357			0.178178	−	0.983998i	$-0.442980\pi$
$227$	276662.			0.356357			0.178178	+	0.983998i	$0.442980\pi$
$228$	−82047.4	−	603843.i	−0.104527	−	0.769285i
$229$			615780.i			0.775955i	0.921669	+	0.387978i	$0.126826\pi$
$229$			615780.i			0.775955i	−0.921669	+	0.387978i	$0.873174\pi$
$230$	151826.			0.189246
$231$		0			0
$232$	760452.			0.927581
$233$		−	307953.i		−	0.371616i	−0.982586	−	0.185808i	$-0.940510\pi$
$233$		−	307953.i		−	0.371616i	0.982586	−	0.185808i	$-0.0594903\pi$
$234$	217002.	−	60079.7i	0.259074	−	0.0717279i
$235$	592529.			0.699906
$236$	198223.			0.231672
$237$	−79446.9	+	10794.9i	−0.0918768	+	0.0124838i
$238$		0			0
$239$		−	247221.i		−	0.279957i	−0.990155	−	0.139978i	$-0.955297\pi$
$239$		−	247221.i		−	0.279957i	0.990155	−	0.139978i	$-0.0447033\pi$
$240$	405400.	−	55083.9i	0.454313	−	0.0617300i
$241$		−	878437.i		−	0.974245i	−0.873334	−	0.487122i	$-0.838047\pi$
$241$		−	878437.i		−	0.974245i	0.873334	−	0.487122i	$-0.161953\pi$
$242$			87732.7i			0.0962993i
$243$	−718488.	+	575381.i	−0.780556	+	0.625086i
$244$			1.04181e6i			1.12025i
$245$		0			0
$246$	62889.4	+	462846.i	0.0662582	+	0.487640i
$247$	802163.			0.836605
$248$	−548943.			−0.566758
$249$	−1.00462e6	+	136504.i	−1.02684	+	0.139523i
$250$			256829.i			0.259892i
$251$	1.53832e6			1.54121			0.770607	−	0.637310i	$-0.219953\pi$
$251$	1.53832e6			1.54121			0.770607	+	0.637310i	$0.219953\pi$
$252$		0			0
$253$	−987010.			−0.969438
$254$		−	80324.1i		−	0.0781199i
$255$	−15578.9	+	2116.79i	−0.0150033	+	0.00203858i
$256$	369847.			0.352714
$257$	−441559.			−0.417019			−0.208510	−	0.978020i	$-0.566861\pi$
$257$	−441559.			−0.417019			−0.208510	+	0.978020i	$0.566861\pi$
$258$	30985.2	+	228041.i	0.0289804	+	0.213287i
$259$		0			0
$260$			587945.i			0.539390i
$261$	−525464.	−	1.89793e6i	−0.477465	−	1.72456i
$262$			312542.i			0.281290i
$263$		−	613396.i		−	0.546829i	−0.961896	−	0.273415i	$-0.911847\pi$
$263$		−	613396.i		−	0.546829i	0.961896	−	0.273415i	$-0.0881531\pi$
$264$	466016.	−	63320.1i	0.411520	−	0.0559155i
$265$		−	1.07679e6i		−	0.941922i
$266$		0			0
$267$	−177303.	+	24091.1i	−0.152208	+	0.0206813i
$268$	−573874.			−0.488067
$269$	976416.			0.822724			0.411362	−	0.911472i	$-0.365053\pi$
$269$	976416.			0.822724			0.411362	+	0.911472i	$0.365053\pi$
$270$	73842.8	+	172180.i	0.0616452	+	0.143738i
$271$		−	1.72538e6i		−	1.42712i	−0.700594	−	0.713560i	$-0.747082\pi$
$271$		−	1.72538e6i		−	1.42712i	0.700594	−	0.713560i	$-0.252918\pi$
$272$	−25040.1			−0.0205217
$273$		0			0
$274$	−142634.			−0.114775
$275$		−	664868.i		−	0.530156i
$276$	−191265.	−	1.40765e6i	−0.151134	−	1.11230i
$277$	549017.			0.429919			0.214959	−	0.976623i	$-0.431038\pi$
$277$	549017.			0.429919			0.214959	+	0.976623i	$0.431038\pi$
$278$	61362.5			0.0476202
$279$	379314.	+	1.37004e6i	0.291735	+	1.05372i
$280$		0			0
$281$			2.39784e6i			1.81156i	0.423743	+	0.905782i	$0.360716\pi$
$281$			2.39784e6i			1.81156i	−0.423743	+	0.905782i	$0.639284\pi$
$282$	58182.5	+	428205.i	0.0435682	+	0.320648i
$283$			2.32468e6i			1.72543i	0.505692	+	0.862714i	$0.331237\pi$
$283$			2.32468e6i			1.72543i	−0.505692	+	0.862714i	$0.668763\pi$
$284$		−	636137.i		−	0.468010i
$285$	89861.5	+	661353.i	0.0655332	+	0.482304i
$286$			297924.i			0.215372i
$287$		0			0
$288$	274305.	+	990763.i	0.194873	+	0.703864i
$289$	−1.41889e6			−0.999322
$290$	−400817.			−0.279867
$291$	−277691.	−	2.04372e6i	−0.192233	−	1.41478i
$292$		−	978018.i		−	0.671259i
$293$	1.52162e6			1.03547			0.517733	−	0.855542i	$-0.326776\pi$
$293$	1.52162e6			1.03547			0.517733	+	0.855542i	$0.326776\pi$
$294$		0			0
$295$	−217101.			−0.145247
$296$		−	916249.i		−	0.607833i
$297$	−480046.	−	1.11932e6i	−0.315785	−	0.736317i
$298$	241497.			0.157533
$299$	1.86997e6			1.20964
$300$	948221.	−	128840.i	0.608284	−	0.0826508i
$301$		0			0
$302$		−	245603.i		−	0.154959i
$303$	−1.33600e6	+	181530.i	−0.835990	+	0.113590i
$304$			1.06300e6i			0.659702i
$305$		−	1.14103e6i		−	0.702340i
$306$	−3059.50	−	11050.6i	−0.00186787	−	0.00674657i
$307$		−	93915.5i		−	0.0568711i	−0.999596	−	0.0284355i	$-0.990947\pi$
$307$		−	93915.5i		−	0.0568711i	0.999596	−	0.0284355i	$-0.00905253\pi$
$308$		0			0
$309$	−197114.	−	1.45070e6i	−0.117441	−	0.864332i
$310$	289335.			0.171000
$311$	421148.			0.246907			0.123453	−	0.992350i	$-0.460603\pi$
$311$	421148.			0.246907			0.123453	+	0.992350i	$0.460603\pi$
$312$	−882904.	+	119965.i	−0.513484	+	0.0697698i
$313$			598817.i			0.345488i	0.984967	+	0.172744i	$0.0552634\pi$
$313$			598817.i			0.345488i	−0.984967	+	0.172744i	$0.944737\pi$
$314$	501661.			0.287135
$315$		0			0
$316$	152686.			0.0860164
$317$			193835.i			0.108339i	0.998532	+	0.0541693i	$0.0172511\pi$
$317$			193835.i			0.108339i	−0.998532	+	0.0541693i	$0.982749\pi$
$318$	778166.	−	105734.i	0.431523	−	0.0586334i
$319$	2.60568e6			1.43365
$320$	−630616.			−0.344263
$321$	328831.	+	2.42009e6i	0.178119	+	1.31090i
$322$		0			0
$323$		−	40849.3i		−	0.0217861i
$324$	1.50333e6	−	901537.i	0.795596	−	0.477113i
$325$			1.25964e6i			0.661514i
$326$		−	449217.i		−	0.234106i
$327$	2.79841e6	−	380235.i	1.44724	−	0.196645i
$328$		−	1.84839e6i		−	0.948656i
$329$		0			0
$330$	−245627.	+	33374.6i	−0.124163	+	0.0168706i
$331$	2.67691e6			1.34296			0.671480	−	0.741022i	$-0.265659\pi$
$331$	2.67691e6			1.34296			0.671480	+	0.741022i	$0.265659\pi$
$332$	1.93075e6			0.961347
$333$	−2.28676e6	+	633118.i	−1.13008	+	0.312878i
$334$		−	820857.i		−	0.402625i
$335$	628529.			0.305994
$336$		0			0
$337$	610339.			0.292750			0.146375	−	0.989229i	$-0.453239\pi$
$337$	610339.			0.292750			0.146375	+	0.989229i	$0.453239\pi$
$338$			354.733i			0.000168892i
$339$	−174051.	−	1.28096e6i	−0.0822578	−	0.605392i
$340$	29940.5			0.0140463
$341$	−1.88094e6			−0.875971
$342$	−469118.	+	129881.i	−0.216879	+	0.0600456i
$343$		0			0
$344$		−	910688.i		−	0.414929i
$345$	209481.	+	1.54172e6i	0.0947539	+	0.697359i
$346$		−	373647.i		−	0.167792i
$347$		−	399806.i		−	0.178248i	−0.996021	−	0.0891241i	$-0.971593\pi$
$347$		−	399806.i		−	0.178248i	0.996021	−	0.0891241i	$-0.0284068\pi$
$348$	504935.	+	3.71616e6i	0.223505	+	1.64493i
$349$		−	2.11033e6i		−	0.927440i	−0.885982	−	0.463720i	$-0.846514\pi$
$349$		−	2.11033e6i		−	0.927440i	0.885982	−	0.463720i	$-0.153486\pi$
$350$		0			0
$351$	909484.	+	2.12065e6i	0.394028	+	0.918757i
$352$	−1.36023e6			−0.585133
$353$	−3.23135e6			−1.38021			−0.690107	−	0.723707i	$-0.742437\pi$
$353$	−3.23135e6			−1.38021			−0.690107	+	0.723707i	$0.742437\pi$
$354$	−21317.9	−	156893.i	−0.00904143	−	0.0665421i
$355$			696722.i			0.293419i
$356$	340752.			0.142500
$357$		0			0
$358$	−1.21073e6			−0.499275
$359$			1.26709e6i			0.518886i	0.965758	+	0.259443i	$0.0835389\pi$
$359$			1.26709e6i			0.518886i	−0.965758	+	0.259443i	$0.916461\pi$
$360$	−197813.	−	714481.i	−0.0804449	−	0.290559i
$361$	741971.			0.299653
$362$	−1.09094e6			−0.437552
$363$	−890879.	+	121049.i	−0.354856	+	0.0482162i
$364$		0			0
$365$			1.07116e6i			0.420846i
$366$	824593.	−	112042.i	0.321764	−	0.0437197i
$367$		−	1.90113e6i		−	0.736795i	−0.929668	−	0.368398i	$-0.879907\pi$
$367$		−	1.90113e6i		−	0.736795i	0.929668	−	0.368398i	$-0.120093\pi$
$368$			2.47801e6i			0.953857i
$369$	−4.61319e6	+	1.27722e6i	−1.76374	+	0.488314i
$370$			482934.i			0.183393i
$371$		0			0
$372$	−364494.	−	2.68256e6i	−0.136563	−	1.00506i
$373$	1.98473e6			0.738634			0.369317	−	0.929303i	$-0.379592\pi$
$373$	1.98473e6			0.738634			0.369317	+	0.929303i	$0.379592\pi$
$374$	15171.5			0.00560852
$375$	−2.60796e6	+	354358.i	−0.957685	+	0.130126i
$376$		−	1.71005e6i		−	0.623790i
$377$	−4.93666e6			−1.78887
$378$		0			0
$379$	4.48906e6			1.60531			0.802653	−	0.596446i	$-0.203421\pi$
$379$	4.48906e6			1.60531			0.802653	+	0.596446i	$0.203421\pi$
$380$		−	1.27103e6i		−	0.451540i
$381$	815649.	−	110827.i	0.287866	−	0.0391139i
$382$	81637.1			0.0286239
$383$	−78864.4			−0.0274716			−0.0137358	−	0.999906i	$-0.504372\pi$
$383$	−78864.4			−0.0274716			−0.0137358	+	0.999906i	$0.504372\pi$
$384$	−346056.	−	2.54687e6i	−0.119762	−	0.881410i
$385$		0			0
$386$		−	795605.i		−	0.271787i
$387$	−2.27288e6	+	629276.i	−0.771436	+	0.213581i
$388$			3.92774e6i			1.32454i
$389$			3.89610e6i			1.30544i	0.757600	+	0.652719i	$0.226372\pi$
$389$			3.89610e6i			1.30544i	−0.757600	+	0.652719i	$0.773628\pi$
$390$	465359.	−	63230.8i	0.154927	−	0.0210507i
$391$		−	95226.2i		−	0.0315003i
$392$		0			0
$393$	−3.17370e6	+	431227.i	−1.03654	+	0.140840i
$394$	1.03754e6			0.336715
$395$	−167228.			−0.0539281
$396$	618863.	+	2.23528e6i	0.198316	+	0.716297i
$397$		−	3.79135e6i		−	1.20731i	−0.797247	−	0.603654i	$-0.793711\pi$
$397$		−	3.79135e6i		−	1.20731i	0.797247	−	0.603654i	$-0.206289\pi$
$398$	−341379.			−0.108026
$399$		0			0
$400$	−1.66923e6			−0.521635
$401$			2.09311e6i			0.650026i	0.945710	+	0.325013i	$0.105369\pi$
$401$			2.09311e6i			0.650026i	−0.945710	+	0.325013i	$0.894631\pi$
$402$	61717.5	+	454222.i	0.0190477	+	0.140185i
$403$	3.56359e6			1.09301
$404$	2.56761e6			0.782666
$405$	−1.64651e6	+	987398.i	−0.498800	+	0.299126i
$406$		0			0
$407$		−	3.13951e6i		−	0.939456i
$408$	6109.09	+	44961.0i	0.00181688	+	0.0133717i
$409$		−	726821.i		−	0.214842i	−0.994214	−	0.107421i	$-0.965741\pi$
$409$		−	726821.i		−	0.214842i	0.994214	−	0.107421i	$-0.0342593\pi$
$410$			974244.i			0.286225i
$411$	−196799.	−	1.44838e6i	−0.0574669	−	0.422938i
$412$			2.78804e6i			0.809200i
$413$		0			0
$414$	−1.09359e6	+	302773.i	−0.313583	+	0.0868194i
$415$	−2.11463e6			−0.602718
$416$	2.57705e6			0.730113
$417$	84664.5	+	623104.i	0.0238430	+	0.175477i
$418$		−	644056.i		−	0.180295i
$419$	−5.13426e6			−1.42871			−0.714353	−	0.699786i	$-0.753279\pi$
$419$	−5.13426e6			−1.42871			−0.714353	+	0.699786i	$0.753279\pi$
$420$		0			0
$421$	3.76667e6			1.03574			0.517872	−	0.855458i	$-0.326724\pi$
$421$	3.76667e6			1.03574			0.517872	+	0.855458i	$0.326724\pi$
$422$			687513.i			0.187932i
$423$	−4.26792e6	+	1.18163e6i	−1.15975	+	0.321092i
$424$	−3.10763e6			−0.839487
$425$	64146.1			0.0172265
$426$	−503503.	+	68413.6i	−0.134424	+	0.0182650i
$427$		0			0
$428$		−	4.65108e6i		−	1.22728i
$429$	−3.02526e6	+	411058.i	−0.793632	+	0.107835i
$430$			480003.i			0.125191i
$431$		−	2.69991e6i		−	0.700094i	−0.936732	−	0.350047i	$-0.886166\pi$
$431$		−	2.69991e6i		−	0.700094i	0.936732	−	0.350047i	$-0.113834\pi$
$432$	−2.81020e6	+	1.20521e6i	−0.724483	+	0.310710i
$433$		−	513416.i		−	0.131598i	−0.997833	−	0.0657991i	$-0.979040\pi$
$433$		−	513416.i		−	0.131598i	0.997833	−	0.0657991i	$-0.0209596\pi$
$434$		0			0
$435$	−553024.	−	4.07008e6i	−0.140127	−	1.03129i
$436$	−5.37816e6			−1.35493
$437$	−4.04252e6			−1.01263
$438$	−774102.	+	105181.i	−0.192803	+	0.0261971i
$439$			1.98814e6i			0.492363i	0.969224	+	0.246181i	$0.0791759\pi$
$439$			1.98814e6i			0.492363i	−0.969224	+	0.246181i	$0.920824\pi$
$440$	980917.			0.241546
$441$		0			0
$442$	−28743.5			−0.00699816
$443$			6.80880e6i			1.64839i	0.566303	+	0.824197i	$0.308373\pi$
$443$			6.80880e6i			1.64839i	−0.566303	+	0.824197i	$0.691627\pi$
$444$	4.47751e6	−	608383.i	1.07790	−	0.146460i
$445$	−373205.			−0.0893403
$446$	1.63245e6			0.388601
$447$	333204.	+	2.45228e6i	0.0788754	+	0.580498i
$448$		0			0
$449$			217794.i			0.0509836i	0.999675	+	0.0254918i	$0.00811517\pi$
$449$			217794.i			0.0509836i	−0.999675	+	0.0254918i	$0.991885\pi$
$450$	−203954.	−	736661.i	−0.0474788	−	0.171489i
$451$		−	6.33348e6i		−	1.46623i
$452$			2.46183e6i			0.566777i
$453$	2.49397e6	−	338870.i	0.571013	−	0.0775867i
$454$			420846.i			0.0958261i
$455$		0			0
$456$	1.90868e6	−	259342.i	0.429853	−	0.0584064i
$457$	2.68841e6			0.602150			0.301075	−	0.953600i	$-0.402655\pi$
$457$	2.68841e6			0.602150			0.301075	+	0.953600i	$0.402655\pi$
$458$	−936697.			−0.208658
$459$	107992.	−	46314.6i	0.0239254	−	0.0102609i
$460$		−	2.96297e6i		−	0.652878i
$461$	−1.65552e6			−0.362813			−0.181406	−	0.983408i	$-0.558065\pi$
$461$	−1.65552e6			−0.362813			−0.181406	+	0.983408i	$0.558065\pi$
$462$		0			0
$463$	−5.86571e6			−1.27165			−0.635826	−	0.771832i	$-0.719340\pi$
$463$	−5.86571e6			−1.27165			−0.635826	+	0.771832i	$0.719340\pi$
$464$		−	6.54187e6i		−	1.41061i
$465$	399208.	+	2.93805e6i	0.0856184	+	0.630124i
$466$	468444.			0.0999293
$467$	447478.			0.0949466			0.0474733	−	0.998873i	$-0.484883\pi$
$467$	447478.			0.0949466			0.0474733	+	0.998873i	$0.484883\pi$
$468$	−1.17248e6	−	4.23490e6i	−0.247453	−	0.893776i
$469$		0			0
$470$			901328.i			0.188208i
$471$	692163.	+	5.09410e6i	0.143766	+	1.05807i
$472$			626558.i			0.129451i
$473$		−	3.12046e6i		−	0.641306i
$474$	−16420.7	−	120851.i	−0.00335695	−	0.0247061i
$475$		−	2.72312e6i		−	0.553774i
$476$		0			0
$477$	2.14734e6	+	7.75598e6i	0.432120	+	1.56078i
$478$	376062.			0.0752817
$479$	2.49211e6			0.496282			0.248141	−	0.968724i	$-0.420180\pi$
$479$	2.49211e6			0.496282			0.248141	+	0.968724i	$0.420180\pi$
$480$	288692.	+	2.12468e6i	0.0571915	+	0.420912i
$481$			5.94805e6i			1.17223i
$482$	1.33624e6			0.261979
$483$		0			0
$484$	1.71215e6			0.332221
$485$		−	4.30182e6i		−	0.830419i
$486$	−875243.	−	1.09293e6i	−0.168089	−	0.209895i
$487$	−3.02295e6			−0.577576			−0.288788	−	0.957393i	$-0.593252\pi$
$487$	−3.02295e6			−0.577576			−0.288788	+	0.957393i	$0.593252\pi$
$488$	−3.29303e6			−0.625960
$489$	4.56156e6	−	619803.i	0.862663	−	0.117215i
$490$		0			0
$491$			245385.i			0.0459351i	0.999736	+	0.0229676i	$0.00731145\pi$
$491$			245385.i			0.0459351i	−0.999736	+	0.0229676i	$0.992689\pi$
$492$	9.03267e6	−	1.22732e6i	1.68230	−	0.228583i
$493$			251394.i			0.0465841i
$494$			1.22021e6i			0.224967i
$495$	−677803.	−	2.44816e6i	−0.124334	−	0.449083i
$496$			4.72234e6i			0.861893i
$497$		0			0
$498$	−207643.	−	1.52819e6i	−0.0375184	−	0.276123i
$499$	3.65622e6			0.657326			0.328663	−	0.944447i	$-0.393402\pi$
$499$	3.65622e6			0.657326			0.328663	+	0.944447i	$0.393402\pi$
$500$	5.01214e6			0.896599
$501$	8.33537e6	−	1.13257e6i	1.48365	−	0.201591i
$502$			2.34003e6i			0.414440i
$503$	3.98843e6			0.702881			0.351440	−	0.936210i	$-0.385692\pi$
$503$	3.98843e6			0.702881			0.351440	+	0.936210i	$0.385692\pi$
$504$		0			0
$505$	−2.81215e6			−0.490693
$506$		−	1.50140e6i		−	0.260687i
$507$	−3602.13	+	489.441i	−0.000622357	+	8.45629e-5i
$508$	−1.56756e6			−0.269505
$509$	−6.53779e6			−1.11850			−0.559251	−	0.828999i	$-0.688911\pi$
$509$	−6.53779e6			−1.11850			−0.559251	+	0.828999i	$0.688911\pi$
$510$	−3219.96	−	23697.9i	−0.000548183	−	0.00403446i
$511$		0			0
$512$			5.83884e6i			0.984355i
$513$	−1.96614e6	−	4.58445e6i	−0.329853	−	0.769119i
$514$		−	671680.i		−	0.112138i
$515$		−	3.05357e6i		−	0.507329i
$516$	4.45033e6	−	604691.i	0.735814	−	0.0999790i
$517$		−	5.85946e6i		−	0.964120i
$518$		0			0
$519$	3.79419e6	−	515537.i	0.618302	−	0.0840121i
$520$	−1.85842e6			−0.301395
$521$	−8.72609e6			−1.40840			−0.704199	−	0.710003i	$-0.748694\pi$
$521$	−8.72609e6			−1.40840			−0.704199	+	0.710003i	$0.748694\pi$
$522$	2.88704e6	−	799312.i	0.463742	−	0.128393i
$523$			9.90012e6i			1.58265i	0.611393	+	0.791327i	$0.290610\pi$
$523$			9.90012e6i			1.58265i	−0.611393	+	0.791327i	$0.709390\pi$
$524$	6.09941e6			0.970420
$525$		0			0
$526$	933071.			0.147045
$527$		−	181472.i		−	0.0284632i
$528$	−544719.	−	4.00896e6i	−0.0850330	−	0.625816i
$529$	−2.98741e6			−0.464146
$530$	1.63796e6			0.253287
$531$	1.56376e6	−	432945.i	0.240676	−	0.0666341i
$532$		0			0
$533$			1.19993e7i			1.82952i
$534$	−36646.3	−	269705.i	−0.00556131	−	0.0409295i
$535$			5.09404e6i			0.769446i
$536$		−	1.81395e6i		−	0.272717i
$537$	−1.67050e6	−	1.22943e7i	−0.249983	−	1.83979i
$538$			1.48528e6i			0.221234i
$539$		0			0
$540$	3.36017e6	−	1.44108e6i	0.495880	−	0.212669i
$541$	6.07601e6			0.892535			0.446267	−	0.894900i	$-0.352753\pi$
$541$	6.07601e6			0.892535			0.446267	+	0.894900i	$0.352753\pi$
$542$	2.62456e6			0.383759
$543$	−1.50522e6	−	1.10779e7i	−0.219078	−	1.61235i
$544$		−	131234.i		−	0.0190129i
$545$	5.89037e6			0.849476
$546$		0			0
$547$	−6.64719e6			−0.949882			−0.474941	−	0.880018i	$-0.657531\pi$
$547$	−6.64719e6			−0.949882			−0.474941	+	0.880018i	$0.657531\pi$
$548$			2.78358e6i			0.395961i
$549$	2.27545e6	+	8.21871e6i	0.322208	+	1.16379i
$550$	1.01137e6			0.142561
$551$	1.06721e7			1.49752
$552$	4.44942e6	−	604566.i	0.621521	−	0.0844493i
$553$		0			0
$554$			835140.i			0.115607i
$555$	−4.90394e6	+	666325.i	−0.675792	+	0.0918234i
$556$		−	1.19752e6i		−	0.164284i
$557$		−	5.65506e6i		−	0.772323i	−0.922431	−	0.386162i	$-0.873801\pi$
$557$		−	5.65506e6i		−	0.772323i	0.922431	−	0.386162i	$-0.126199\pi$
$558$	−2.08405e6	+	576995.i	−0.283350	+	0.0784488i
$559$			5.91195e6i			0.800205i
$560$		0			0
$561$	20932.7	+	154058.i	0.00280814	+	0.0206670i
$562$	−3.64748e6			−0.487138
$563$	3.73556e6			0.496689			0.248345	−	0.968672i	$-0.420113\pi$
$563$	3.73556e6			0.496689			0.248345	+	0.968672i	$0.420113\pi$
$564$	8.35663e6	−	1.13546e6i	1.10620	−	0.150305i
$565$		−	2.69629e6i		−	0.355341i
$566$	−3.53620e6			−0.463976
$567$		0			0
$568$	2.01075e6			0.261510
$569$		−	9.77353e6i		−	1.26553i	−0.774346	−	0.632763i	$-0.781921\pi$
$569$		−	9.77353e6i		−	1.26553i	0.774346	−	0.632763i	$-0.218079\pi$
$570$	−1.00602e6	+	136693.i	−0.129694	+	0.0176222i
$571$	−1.41138e7			−1.81156			−0.905781	−	0.423745i	$-0.860715\pi$
$571$	−1.41138e7			−1.81156			−0.905781	+	0.423745i	$0.860715\pi$
$572$	5.81413e6			0.743010
$573$	112638.	+	828981.i	0.0143317	+	0.105477i
$574$		0			0
$575$		−	6.34801e6i		−	0.800697i
$576$	4.54226e6	−	1.25758e6i	0.570447	−	0.157935i
$577$		−	9.48980e6i		−	1.18664i	−0.804968	−	0.593318i	$-0.797818\pi$
$577$		−	9.48980e6i		−	1.18664i	0.804968	−	0.593318i	$-0.202182\pi$
$578$		−	2.15836e6i		−	0.268722i
$579$	8.07894e6	−	1.09773e6i	1.00152	−	0.136081i
$580$			7.82214e6i			0.965508i
$581$		0			0
$582$	3.10881e6	−	422411.i	0.380440	−	0.0516925i
$583$	−1.06482e7			−1.29750
$584$	3.09140e6			0.375079
$585$	1.28415e6	+	4.63823e6i	0.155141	+	0.560354i
$586$			2.31461e6i			0.278442i
$587$	1.15116e7			1.37893			0.689464	−	0.724320i	$-0.257846\pi$
$587$	1.15116e7			1.37893			0.689464	+	0.724320i	$0.257846\pi$
$588$		0			0
$589$	−7.70383e6			−0.914995
$590$		−	330244.i		−	0.0390576i
$591$	1.43153e6	+	1.05356e7i	0.168590	+	1.24077i
$592$	−7.88214e6			−0.924357
$593$	−6.09436e6			−0.711691			−0.355845	−	0.934545i	$-0.615807\pi$
$593$	−6.09436e6			−0.711691			−0.355845	+	0.934545i	$0.615807\pi$
$594$	1.70267e6	−	730224.i	0.197999	−	0.0849161i
$595$		0			0
$596$		−	4.71294e6i		−	0.543471i
$597$	−471015.	−	3.46652e6i	−0.0540877	−	0.398069i
$598$			2.84451e6i			0.325278i
$599$		−	508153.i		−	0.0578665i	−0.999581	−	0.0289333i	$-0.990789\pi$
$599$		−	508153.i		−	0.0578665i	0.999581	−	0.0289333i	$-0.00921103\pi$
$600$	407247.	+	2.99721e6i	0.0461827	+	0.339890i
$601$			7.48977e6i			0.845829i	0.906170	+	0.422914i	$0.138993\pi$
$601$			7.48977e6i			0.845829i	−0.906170	+	0.422914i	$0.861007\pi$
$602$		0			0
$603$	−4.52723e6	+	1.25342e6i	−0.507036	+	0.140379i
$604$	−4.79307e6			−0.534591
$605$	−1.87521e6			−0.208287
$606$	−276135.	−	2.03227e6i	−0.0305450	−	0.224802i
$607$			1.03012e7i			1.13479i	0.823446	+	0.567394i	$0.192048\pi$
$607$			1.03012e7i			1.13479i	−0.823446	+	0.567394i	$0.807952\pi$
$608$	−5.57112e6			−0.611200
$609$		0			0
$610$	1.73568e6			0.188863
$611$			1.11012e7i			1.20300i
$612$	−215658.	+	59707.6i	−0.0232749	+	0.00644393i
$613$	1.11662e7			1.20020			0.600098	−	0.799926i	$-0.295128\pi$
$613$	1.11662e7			1.20020			0.600098	+	0.799926i	$0.295128\pi$
$614$	142860.			0.0152929
$615$	−9.89293e6	+	1.34421e6i	−1.05472	+	0.143310i
$616$		0			0
$617$			6.80137e6i			0.719256i	0.933096	+	0.359628i	$0.117096\pi$
$617$			6.80137e6i			0.719256i	−0.933096	+	0.359628i	$0.882904\pi$
$618$	2.20673e6	−	299841.i	0.232423	−	0.0315805i
$619$		−	9.90152e6i		−	1.03866i	−0.854572	−	0.519332i	$-0.826181\pi$
$619$		−	9.90152e6i		−	1.03866i	0.854572	−	0.519332i	$-0.173819\pi$
$620$		−	5.64652e6i		−	0.589932i
$621$	−4.58337e6	−	1.06871e7i	−0.476932	−	1.11206i
$622$			640631.i			0.0663944i
$623$		0			0
$624$	1.03201e6	+	7.59528e6i	0.106102	+	0.780876i
$625$	972642.			0.0995985
$626$	−910893.			−0.0929034
$627$	6.54005e6	−	888632.i	0.664373	−	0.0902720i
$628$		−	9.79016e6i		−	0.990583i
$629$	302899.			0.0305261
$630$		0			0
$631$	7.75599e6			0.775468			0.387734	−	0.921771i	$-0.373258\pi$
$631$	7.75599e6			0.775468			0.387734	+	0.921771i	$0.373258\pi$
$632$			482622.i			0.0480633i
$633$	−6.98133e6	+	948591.i	−0.692515	+	0.0940957i
$634$	−294852.			−0.0291328
$635$	1.71686e6			0.168966
$636$	−2.06344e6	−	1.51863e7i	−0.202278	−	1.48871i
$637$		0			0
$638$			3.96364e6i			0.385516i
$639$	−1.38941e6	−	5.01841e6i	−0.134610	−	0.486199i
$640$		−	5.36089e6i		−	0.517353i
$641$			1.76528e7i			1.69695i	0.529235	+	0.848475i	$0.322479\pi$
$641$			1.76528e7i			1.69695i	−0.529235	+	0.848475i	$0.677521\pi$
$642$	−3.68133e6	+	500202.i	−0.352507	+	0.0478970i
$643$		−	1.18414e7i		−	1.12947i	−0.825273	−	0.564735i	$-0.808979\pi$
$643$		−	1.18414e7i		−	1.12947i	0.825273	−	0.564735i	$-0.191021\pi$
$644$		0			0
$645$	−4.87418e6	+	662281.i	−0.461320	+	0.0626820i
$646$	62138.2			0.00585838
$647$	2.83880e6			0.266609			0.133304	−	0.991075i	$-0.457441\pi$
$647$	2.83880e6			0.266609			0.133304	+	0.991075i	$0.457441\pi$
$648$	2.84965e6	+	4.75185e6i	0.266596	+	0.444555i
$649$			2.14689e6i			0.200078i
$650$	−1.91611e6			−0.177884
$651$		0			0
$652$	−8.76668e6			−0.807637
$653$			1.94768e6i			0.178745i	0.995998	+	0.0893724i	$0.0284861\pi$
$653$			1.94768e6i			0.178745i	−0.995998	+	0.0893724i	$0.971514\pi$
$654$	578396.	+	4.25682e6i	0.0528787	+	0.389171i
$655$	−6.68031e6			−0.608406
$656$	−1.59010e7			−1.44266
$657$	−2.13612e6	−	7.71547e6i	−0.193069	−	0.697347i
$658$		0			0
$659$		−	2.14961e7i		−	1.92818i	−0.265580	−	0.964089i	$-0.585563\pi$
$659$		−	2.14961e7i		−	1.92818i	0.265580	−	0.964089i	$-0.414437\pi$
$660$	651322.	+	4.79353e6i	0.0582017	+	0.428347i
$661$		−	2.58055e6i		−	0.229725i	−0.993381	−	0.114863i	$-0.963357\pi$
$661$		−	2.58055e6i		−	0.229725i	0.993381	−	0.114863i	$-0.0366428\pi$
$662$			4.07199e6i			0.361129i
$663$	−39658.6	−	291875.i	−0.00350392	−	0.0257877i
$664$			6.10286e6i			0.537172i
$665$		0			0
$666$	−963071.	−	3.47852e6i	−0.0841342	−	0.303885i
$667$	2.48784e7			2.16525
$668$	−1.60194e7			−1.38901
$669$	2.25236e6	+	1.65767e7i	0.194569	+	1.43197i
$670$			956090.i			0.0822833i
$671$	−1.12835e7			−0.967473
$672$		0			0
$673$	2.04614e7			1.74140			0.870698	−	0.491818i	$-0.163668\pi$
$673$	2.04614e7			1.74140			0.870698	+	0.491818i	$0.163668\pi$
$674$			928421.i			0.0787218i
$675$	7.19900e6	−	3.08744e6i	0.608153	−	0.260819i
$676$	6922.79			0.000582659
$677$	−5.99328e6			−0.502566			−0.251283	−	0.967914i	$-0.580852\pi$
$677$	−5.99328e6			−0.502566			−0.251283	+	0.967914i	$0.580852\pi$
$678$	1.94854e6	−	264759.i	0.162793	−	0.0221195i
$679$		0			0
$680$			94638.3i			0.00784864i
$681$	−4.27347e6	+	580659.i	−0.353112	+	0.0479793i
$682$		−	2.86121e6i		−	0.235553i
$683$		−	4.12451e6i		−	0.338315i	−0.985589	−	0.169157i	$-0.945895\pi$
$683$		−	4.12451e6i		−	0.338315i	0.985589	−	0.169157i	$-0.0541046\pi$
$684$	2.53470e6	+	9.15508e6i	0.207150	+	0.748207i
$685$		−	3.04868e6i		−	0.248248i
$686$		0			0
$687$	−1.29240e6	−	9.51166e6i	−0.104473	−	0.768890i
$688$	−7.83430e6			−0.630999
$689$	2.01739e7			1.61898
$690$	−2.34519e6	+	318653.i	−0.187523	+	0.0254798i
$691$			9.31269e6i			0.741959i	0.928641	+	0.370980i	$0.120978\pi$
$691$			9.31269e6i			0.741959i	−0.928641	+	0.370980i	$0.879022\pi$
$692$	−7.29191e6			−0.578864
$693$		0			0
$694$	608166.			0.0479318
$695$			1.31157e6i			0.102998i
$696$	−1.17463e7	+	1.59604e6i	−0.919135	+	0.124888i
$697$	611050.			0.0476426
$698$	3.21013e6			0.249393
$699$	646332.	+	4.75680e6i	0.0500337	+	0.368232i
$700$		0			0
$701$		−	3.77870e6i		−	0.290434i	−0.989400	−	0.145217i	$-0.953612\pi$
$701$		−	3.77870e6i		−	0.290434i	0.989400	−	0.145217i	$-0.0463880\pi$
$702$	−3.22583e6	+	1.38347e6i	−0.247058	+	0.105956i
$703$		−	1.28586e7i		−	0.981307i
$704$			6.23610e6i			0.474222i
$705$	−9.15251e6	+	1.24360e6i	−0.693533	+	0.0942341i
$706$		−	4.91538e6i		−	0.371146i
$707$		0			0
$708$	−3.06185e6	+	416030.i	−0.229562	+	0.0311919i
$709$	3.38082e6			0.252584			0.126292	−	0.991993i	$-0.459692\pi$
$709$	3.38082e6			0.252584			0.126292	+	0.991993i	$0.459692\pi$
$710$	−1.05982e6			−0.0789018
$711$	1.20452e6	−	333486.i	0.0893594	−	0.0247403i
$712$			1.07708e6i			0.0796244i
$713$	−1.79588e7			−1.32298
$714$		0			0
$715$	−6.36786e6			−0.465831
$716$			2.36280e7i			1.72244i
$717$	518868.	+	3.81871e6i	0.0376929	+	0.277408i
$718$	−1.92744e6			−0.139531
$719$	1.38747e7			1.00093			0.500463	−	0.865758i	$-0.333163\pi$
$719$	1.38747e7			1.00093			0.500463	+	0.865758i	$0.333163\pi$
$720$	−6.14641e6	+	1.70171e6i	−0.441866	+	0.122336i
$721$		0			0
$722$			1.12865e6i			0.0805781i
$723$	1.84367e6	+	1.35688e7i	0.131171	+	0.965374i
$724$			2.12902e7i			1.50950i
$725$			1.67586e7i			1.18411i
$726$	−184134.	−	1.35517e6i	−0.0129656	−	0.0954225i
$727$			1.00603e7i			0.705948i	0.935633	+	0.352974i	$0.114830\pi$
$727$			1.00603e7i			0.705948i	−0.935633	+	0.352974i	$0.885170\pi$
$728$		0			0
$729$	9.89053e6	−	1.03956e7i	0.689288	−	0.724487i
$730$	−1.62941e6			−0.113168
$731$	301060.			0.0208382
$732$	−2.18655e6	−	1.60923e7i	−0.150828	−	1.11005i
$733$		−	9.19873e6i		−	0.632365i	−0.948698	−	0.316182i	$-0.897599\pi$
$733$		−	9.19873e6i		−	0.632365i	0.948698	−	0.316182i	$-0.102401\pi$
$734$	2.89191e6			0.198128
$735$		0			0
$736$	−1.29871e7			−0.883728
$737$		−	6.21546e6i		−	0.421507i
$738$	−1.94284e6	−	7.01737e6i	−0.131310	−	0.474279i
$739$	−1.43134e6			−0.0964121			−0.0482061	−	0.998837i	$-0.515350\pi$
$739$	−1.43134e6			−0.0964121			−0.0482061	+	0.998837i	$0.515350\pi$
$740$	9.42470e6			0.632686
$741$	−1.23906e7	+	1.68358e6i	−0.828987	+	0.112639i
$742$		0			0
$743$		−	8.86521e6i		−	0.589138i	−0.955630	−	0.294569i	$-0.904824\pi$
$743$		−	8.86521e6i		−	0.589138i	0.955630	−	0.294569i	$-0.0951761\pi$
$744$	8.47925e6	−	1.15212e6i	0.561598	−	0.0763073i
$745$			5.16179e6i			0.340730i
$746$			3.01908e6i			0.198622i
$747$	1.52314e7	−	4.21701e6i	0.998710	−	0.276505i
$748$		−	296079.i		−	0.0193488i
$749$		0			0
$750$	−539033.	−	3.96711e6i	−0.0349914	−	0.257526i
$751$	−2.38638e7			−1.54397			−0.771987	−	0.635638i	$-0.780737\pi$
$751$	−2.38638e7			−1.54397			−0.771987	+	0.635638i	$0.780737\pi$
$752$	−1.47109e7			−0.948624
$753$	−2.37617e7	+	3.22863e6i	−1.52718	+	0.207506i
$754$		−	7.50942e6i		−	0.481036i
$755$	5.24956e6			0.335163
$756$		0			0
$757$	1.25214e7			0.794171			0.397086	−	0.917782i	$-0.370022\pi$
$757$	1.25214e7			0.794171			0.397086	+	0.917782i	$0.370022\pi$
$758$			6.82856e6i			0.431674i
$759$	1.52459e7	−	2.07154e6i	0.960612	−	0.130523i
$760$	4.01757e6			0.252307
$761$	−2.37933e7			−1.48934			−0.744668	−	0.667435i	$-0.767392\pi$
$761$	−2.37933e7			−1.48934			−0.744668	+	0.667435i	$0.767392\pi$
$762$	168584.	+	1.24073e6i	0.0105179	+	0.0774086i
$763$		0			0
$764$		−	1.59319e6i		−	0.0987492i
$765$	236197.	−	65394.1i	0.0145922	−	0.00404003i
$766$		−	119965.i		−	0.00738724i
$767$		−	4.06745e6i		−	0.249651i
$768$	−5.71285e6	+	776236.i	−0.349502	+	0.0474887i
$769$		−	6.93541e6i		−	0.422918i	−0.977387	−	0.211459i	$-0.932179\pi$
$769$		−	6.93541e6i		−	0.422918i	0.977387	−	0.211459i	$-0.0678215\pi$
$770$		0			0
$771$	6.82055e6	−	926745.i	0.413222	−	0.0561467i
$772$	−1.55266e7			−0.937634
$773$	−1.26437e7			−0.761074			−0.380537	−	0.924766i	$-0.624261\pi$
$773$	−1.26437e7			−0.761074			−0.380537	+	0.924766i	$0.624261\pi$
$774$	−957226.	−	3.45741e6i	−0.0574331	−	0.207443i
$775$		−	1.20974e7i		−	0.723499i
$776$	−1.24151e7			−0.740110
$777$		0			0
$778$	−5.92657e6			−0.351039
$779$		−	2.59402e7i		−	1.53154i
$780$	−1.23398e6	−	9.08170e6i	−0.0726226	−	0.534479i
$781$	6.88981e6			0.404185
$782$	144854.			0.00847057
$783$	1.21000e7	+	2.82135e7i	0.705310	+	1.64457i
$784$		0			0
$785$			1.07226e7i			0.621047i
$786$	−655964.	−	4.82769e6i	−0.0378724	−	0.278729i
$787$			3.06419e7i			1.76352i	0.471702	+	0.881758i	$0.343640\pi$
$787$			3.06419e7i			1.76352i	−0.471702	+	0.881758i	$0.656360\pi$
$788$		−	2.02480e7i		−	1.16163i
$789$	1.28740e6	+	9.47484e6i	0.0736241	+	0.541850i
$790$		−	254379.i		−	0.0145015i
$791$		0			0
$792$	−7.06543e6	+	1.95615e6i	−0.400245	+	0.110813i
$793$	2.13775e7			1.20719
$794$	5.76723e6			0.324651
$795$	2.25996e6	+	1.66326e7i	0.126819	+	0.933346i
$796$			6.66218e6i			0.372678i
$797$	1.19804e7			0.668073			0.334037	−	0.942560i	$-0.391589\pi$
$797$	1.19804e7			0.668073			0.334037	+	0.942560i	$0.391589\pi$
$798$		0			0
$799$	565317.			0.0313275
$800$		−	8.74837e6i		−	0.483284i
$801$	2.68815e6	−	744248.i	0.148038	−	0.0409861i
$802$	−3.18394e6			−0.174795
$803$	1.05926e7			0.579715
$804$	8.86436e6	−	1.20445e6i	0.483623	−	0.0657125i
$805$		0			0
$806$			5.42078e6i			0.293917i
$807$	−1.50822e7	+	2.04930e6i	−0.815233	+	0.110770i
$808$			8.11591e6i			0.437330i
$809$			1.88137e7i			1.01066i	0.862927	+	0.505328i	$0.168629\pi$
$809$			1.88137e7i			1.01066i	−0.862927	+	0.505328i	$0.831371\pi$
$810$	−1.50199e6	−	2.50459e6i	−0.0804365	−	0.134130i
$811$		−	1.91129e7i		−	1.02041i	−0.860053	−	0.510205i	$-0.829570\pi$
$811$		−	1.91129e7i		−	1.02041i	0.860053	−	0.510205i	$-0.170430\pi$
$812$		0			0
$813$	3.62122e6	+	2.66511e7i	0.192145	+	1.41413i
$814$	4.77569e6			0.252624
$815$	9.60161e6			0.506349
$816$	386782.	−	52554.2i	0.0203348	−	0.00276301i
$817$		−	1.27805e7i		−	0.669876i
$818$	1.10561e6			0.0577720
$819$		0			0
$820$	1.90129e7			0.987444
$821$		−	2.30126e7i		−	1.19154i	−0.803156	−	0.595768i	$-0.796848\pi$
$821$		−	2.30126e7i		−	1.19154i	0.803156	−	0.595768i	$-0.203152\pi$
$822$	2.20320e6	−	299361.i	0.113730	−	0.0154531i
$823$	2.63954e7			1.35840			0.679202	−	0.733951i	$-0.262326\pi$
$823$	2.63954e7			1.35840			0.679202	+	0.733951i	$0.262326\pi$
$824$	−8.81265e6			−0.452156
$825$	1.39543e6	+	1.02699e7i	0.0713793	+	0.525329i
$826$		0			0
$827$			1.88232e6i			0.0957039i	0.998854	+	0.0478520i	$0.0152376\pi$
$827$			1.88232e6i			0.0957039i	−0.998854	+	0.0478520i	$0.984762\pi$
$828$	5.90877e6	+	2.13419e7i	0.299517	+	1.08183i
$829$		−	4.83895e6i		−	0.244548i	−0.992496	−	0.122274i	$-0.960981\pi$
$829$		−	4.83895e6i		−	0.244548i	0.992496	−	0.122274i	$-0.0390187\pi$
$830$		−	3.21668e6i		−	0.162074i
$831$	−8.48041e6	+	1.15228e6i	−0.426004	+	0.0578835i
$832$		−	1.18148e7i		−	0.591721i
$833$		0			0
$834$	−947838.	+	128788.i	−0.0471866	+	0.00641150i
$835$	1.75451e7			0.870842
$836$	−1.25691e7			−0.621996
$837$	−8.73453e6	−	2.03663e7i	−0.430949	−	1.00484i
$838$		−	7.81001e6i		−	0.384186i
$839$	2.24112e7			1.09916			0.549579	−	0.835442i	$-0.314788\pi$
$839$	2.24112e7			1.09916			0.549579	+	0.835442i	$0.314788\pi$
$840$		0			0
$841$	−4.51672e7			−2.20208
$842$			5.72969e6i			0.278517i
$843$	−5.03259e6	−	3.70382e7i	−0.243906	−	1.79507i
$844$	1.34172e7			0.648342
$845$	−7582.11			−0.000365299
$846$	−1.79744e6	−	6.49216e6i	−0.0863430	−	0.311863i
$847$		0			0
$848$			2.67337e7i			1.27664i
$849$	−4.87904e6	−	3.59082e7i	−0.232309	−	1.70972i
$850$			97576.1i			0.00463230i
$851$		−	2.99754e7i		−	1.41886i
$852$	1.33513e6	+	9.82611e6i	0.0630120	+	0.463748i
$853$			5.61774e6i			0.264356i	0.991226	+	0.132178i	$0.0421970\pi$
$853$			5.61774e6i			0.264356i	−0.991226	+	0.132178i	$0.957803\pi$
$854$		0			0
$855$	−2.77610e6	−	1.00270e7i	−0.129873	−	0.469089i
$856$	1.47015e7			0.685768
$857$	1.15165e7			0.535636			0.267818	−	0.963470i	$-0.413697\pi$
$857$	1.15165e7			0.535636			0.267818	+	0.963470i	$0.413697\pi$
$858$	−625283.	−	4.60189e6i	−0.0289974	−	0.213411i
$859$			2.00096e7i			0.925240i	0.886557	+	0.462620i	$0.153091\pi$
$859$			2.00096e7i			0.925240i	−0.886557	+	0.462620i	$0.846909\pi$
$860$	9.36750e6			0.431894
$861$		0			0
$862$	4.10698e6			0.188259
$863$			1.81245e7i			0.828396i	0.910187	+	0.414198i	$0.135938\pi$
$863$			1.81245e7i			0.828396i	−0.910187	+	0.414198i	$0.864062\pi$
$864$	−6.31647e6	−	1.47281e7i	−0.287866	−	0.671218i
$865$	7.98639e6			0.362919
$866$	780986.			0.0353874
$867$	2.19170e7	−	2.97798e6i	0.990223	−	0.134547i
$868$		0			0
$869$			1.65370e6i			0.0742859i
$870$	6.19123e6	−	841236.i	0.277318	−	0.0376807i
$871$			1.17757e7i			0.525945i
$872$		−	1.69997e7i		−	0.757095i
$873$	8.57871e6	+	3.09855e7i	0.380966	+	1.37601i
$874$		−	6.14930e6i		−	0.272300i
$875$		0			0
$876$	2.05267e6	+	1.51070e7i	0.0903771	+	0.665147i
$877$	−1.55675e7			−0.683472			−0.341736	−	0.939796i	$-0.611015\pi$
$877$	−1.55675e7			−0.683472			−0.341736	+	0.939796i	$0.611015\pi$
$878$	−3.02427e6			−0.132399
$879$	−2.35037e7	+	3.19357e6i	−1.02604	+	0.139413i
$880$		−	8.43845e6i		−	0.367330i
$881$	1.64569e7			0.714343			0.357172	−	0.934039i	$-0.383741\pi$
$881$	1.64569e7			0.714343			0.357172	+	0.934039i	$0.383741\pi$
$882$		0			0
$883$	3.82610e7			1.65141			0.825705	−	0.564102i	$-0.190778\pi$
$883$	3.82610e7			1.65141			0.825705	+	0.564102i	$0.190778\pi$
$884$			560944.i			0.0241429i
$885$	3.35346e6	−	455652.i	0.143924	−	0.0195558i
$886$	−1.03572e7			−0.443261
$887$	3.82702e7			1.63325			0.816623	−	0.577172i	$-0.195844\pi$
$887$	3.82702e7			1.63325			0.816623	+	0.577172i	$0.195844\pi$
$888$	1.92302e6	+	1.41529e7i	0.0818375	+	0.602298i
$889$		0			0
$890$		−	567702.i		−	0.0240240i
$891$	9.76428e6	+	1.62821e7i	0.412046	+	0.687096i
$892$		−	3.18581e7i		−	1.34063i
$893$		−	2.39987e7i		−	1.00707i
$894$	−3.73029e6	+	506855.i	−0.156099	+	0.0212100i
$895$		−	2.58783e7i		−	1.07989i
$896$		0			0
$897$	−2.88845e7	+	3.92469e6i	−1.19863	+	0.162864i
$898$	−331299.			−0.0137097
$899$	4.74108e7			1.95649
$900$	−1.43763e7	+	3.98025e6i	−0.591617	+	0.163796i
$901$		−	1.02734e6i		−	0.0421600i
$902$	9.63420e6			0.394275
$903$		0			0
$904$	−7.78154e6			−0.316697
$905$		−	2.33179e7i		−	0.946384i
$906$	515473.	+	3.79372e6i	0.0208634	+	0.153548i
$907$	3.39948e7			1.37213			0.686064	−	0.727541i	$-0.259337\pi$
$907$	3.39948e7			1.37213			0.686064	+	0.727541i	$0.259337\pi$
$908$	8.21302e6			0.330589
$909$	2.02556e7	−	5.60801e6i	0.813084	−	0.225112i
$910$		0			0
$911$		−	8.36037e6i		−	0.333757i	−0.985978	−	0.166878i	$-0.946631\pi$
$911$		−	8.36037e6i		−	0.333757i	0.985978	−	0.166878i	$-0.0533687\pi$
$912$	−2.23102e6	−	1.64196e7i	−0.0888211	−	0.653695i
$913$			2.09114e7i			0.830243i
$914$			4.08949e6i			0.161921i
$915$	2.39480e6	+	1.76249e7i	0.0945618	+	0.695945i
$916$			1.82801e7i			0.719846i
$917$		0			0
$918$	70451.6	+	164272.i	0.00275921	+	0.00643365i
$919$	−1.41298e7			−0.551885			−0.275942	−	0.961174i	$-0.588990\pi$
$919$	−1.41298e7			−0.551885			−0.275942	+	0.961174i	$0.588990\pi$
$920$	9.36557e6			0.364808
$921$	197110.	+	1.45067e6i	0.00765702	+	0.0563532i
$922$		−	2.51830e6i		−	0.0975621i
$923$	−1.30533e7			−0.504331
$924$		0			0
$925$	2.01920e7			0.775933
$926$		−	8.92266e6i		−	0.341953i
$927$	6.08945e6	+	2.19945e7i	0.232744	+	0.840650i
$928$	3.42857e7			1.30690
$929$	623562.			0.0237050			0.0118525	−	0.999930i	$-0.496227\pi$
$929$	623562.			0.0237050			0.0118525	+	0.999930i	$0.496227\pi$
$930$	−4.46922e6	+	607257.i	−0.169443	+	0.0230232i
$931$		0			0
$932$		−	9.14192e6i		−	0.344745i
$933$	−6.50526e6	+	883905.i	−0.244659	+	0.0332431i
$934$			680683.i			0.0255316i
$935$			324277.i			0.0121307i
$936$	1.33860e7	−	3.70608e6i	0.499415	−	0.138269i
$937$			1.49765e7i			0.557264i	0.960398	+	0.278632i	$0.0898810\pi$
$937$			1.49765e7i			0.557264i	−0.960398	+	0.278632i	$0.910119\pi$
$938$		0			0
$939$	−1.25680e6	−	9.24964e6i	−0.0465159	−	0.342343i
$940$	1.75899e7			0.649296
$941$	−4.33219e7			−1.59490			−0.797451	−	0.603384i	$-0.793819\pi$
$941$	−4.33219e7			−1.59490			−0.797451	+	0.603384i	$0.793819\pi$
$942$	−7.74892e6	+	1.05289e6i	−0.284521	+	0.0386593i
$943$		−	6.04706e7i		−	2.21445i
$944$	5.39003e6			0.196862
$945$		0			0
$946$	4.74670e6			0.172450
$947$			3.10688e7i			1.12577i	0.826535	+	0.562886i	$0.190309\pi$
$947$			3.10688e7i			1.12577i	−0.826535	+	0.562886i	$0.809691\pi$
$948$	−2.35847e6	+	320458.i	−0.0852332	+	0.0115811i
$949$	−2.00685e7			−0.723353
$950$	4.14228e6			0.148912
$951$	−406820.	−	2.99407e6i	−0.0145865	−	0.107352i
$952$		0			0
$953$			1.75688e7i			0.626628i	0.949650	+	0.313314i	$0.101439\pi$
$953$			1.75688e7i			0.626628i	−0.949650	+	0.313314i	$0.898561\pi$
$954$	−1.17980e7	+	3.26643e6i	−0.419700	+	0.116199i
$955$			1.74492e6i			0.0619109i
$956$		−	7.33903e6i		−	0.259713i
$957$	−4.02487e7	+	5.46880e6i	−1.42060	+	0.193024i
$958$			3.79089e6i			0.133453i
$959$		0			0
$960$	9.74083e6	−	1.32354e6i	0.341128	−	0.0463509i
$961$	−5.59498e6			−0.195429
$962$	−9.04791e6			−0.315218
$963$	−1.01586e7	−	3.66918e7i	−0.352994	−	1.27498i
$964$		−	2.60774e7i		−	0.903797i
$965$	1.70053e7			0.587851
$966$		0			0
$967$	−3.21593e7			−1.10596			−0.552981	−	0.833194i	$-0.686510\pi$
$967$	−3.21593e7			−1.10596			−0.552981	+	0.833194i	$0.686510\pi$
$968$			5.41189e6i			0.185635i
$969$	85734.7	+	630980.i	0.00293324	+	0.0215877i
$970$	6.54373e6			0.223304
$971$	−2.10080e6			−0.0715050			−0.0357525	−	0.999361i	$-0.511383\pi$
$971$	−2.10080e6			−0.0715050			−0.0357525	+	0.999361i	$0.511383\pi$
$972$	−2.13291e7	+	1.70808e7i	−0.724114	+	0.579886i
$973$		0			0
$974$		−	4.59838e6i		−	0.155313i
$975$	−2.64374e6	−	1.94571e7i	−0.0890651	−	0.655491i
$976$			2.83287e7i			0.951924i
$977$			3.23677e7i			1.08486i	0.840100	+	0.542432i	$0.182496\pi$
$977$			3.23677e7i			1.08486i	−0.840100	+	0.542432i	$0.817504\pi$
$978$	942817.	+	6.93883e6i	0.0315196	+	0.231974i
$979$			3.69058e6i			0.123066i
$980$		0			0
$981$	−4.24277e7	+	1.17466e7i	−1.40759	+	0.389709i
$982$	−373269.			−0.0123522
$983$	−5.43338e7			−1.79344			−0.896718	−	0.442602i	$-0.854055\pi$
$983$	−5.43338e7			−1.79344			−0.896718	+	0.442602i	$0.854055\pi$
$984$	3.87940e6	+	2.85512e7i	0.127725	+	0.940018i
$985$			2.21764e7i			0.728284i
$986$	−382410.			−0.0125267
$987$		0			0
$988$	2.38131e7			0.776110
$989$		−	2.97934e7i		−	0.968567i
$990$	3.72403e6	−	1.03104e6i	0.120761	−	0.0334341i
$991$	−2.92192e6			−0.0945113			−0.0472556	−	0.998883i	$-0.515048\pi$
$991$	−2.92192e6			−0.0945113			−0.0472556	+	0.998883i	$0.515048\pi$
$992$	−2.47496e7			−0.798525
$993$	−4.13489e7	+	5.61830e6i	−1.33073	+	0.180814i
$994$		0			0
$995$		−	7.29668e6i		−	0.233651i
$996$	−2.98233e7	+	4.05226e6i	−0.952594	+	0.129434i
$997$		−	1.42613e7i		−	0.454383i	−0.973850	−	0.227192i	$-0.927046\pi$
$997$		−	1.42613e7i		−	0.454383i	0.973850	−	0.227192i	$-0.0729544\pi$
$998$			5.56168e6i			0.176758i
$999$	3.39938e7	−	1.45789e7i	1.07767	−	0.462181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.16	yes	40
3.2	odd	2	inner	147.6.c.d.146.25	yes	40
7.6	odd	2	inner	147.6.c.d.146.26	yes	40
21.20	even	2	inner	147.6.c.d.146.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.15	✓	40	21.20	even	2	inner
147.6.c.d.146.16	yes	40	1.1	even	1	trivial
147.6.c.d.146.25	yes	40	3.2	odd	2	inner
147.6.c.d.146.26	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)

\(f(q)\)	\(=\)	\(q+1.52115i q^{2} +(-15.4465 + 2.09880i) q^{3} +29.6861 q^{4} -32.5134 q^{5} +(-3.19260 - 23.4966i) q^{6} +93.8341i q^{8} +(234.190 - 64.8384i) q^{9} +O(q^{10})\)	\(q+1.52115i q^{2} +(-15.4465 + 2.09880i) q^{3} +29.6861 q^{4} -32.5134 q^{5} +(-3.19260 - 23.4966i) q^{6} +93.8341i q^{8} +(234.190 - 64.8384i) q^{9} -49.4578i q^{10} +321.521i q^{11} +(-458.547 + 62.3052i) q^{12} -609.147i q^{13} +(502.218 - 68.2391i) q^{15} +807.219 q^{16} -31.0202 q^{17} +(98.6292 + 356.239i) q^{18} +1316.86i q^{19} -965.194 q^{20} -489.084 q^{22} +3069.81i q^{23} +(-196.939 - 1449.41i) q^{24} -2067.88 q^{25} +926.607 q^{26} +(-3481.34 + 1493.05i) q^{27} -8104.22i q^{29} +(103.802 + 763.952i) q^{30} +5850.14i q^{31} +4230.60i q^{32} +(-674.809 - 4966.39i) q^{33} -47.1865i q^{34} +(6952.19 - 1924.80i) q^{36} -9764.56 q^{37} -2003.15 q^{38} +(1278.48 + 9409.20i) q^{39} -3050.86i q^{40} -19698.5 q^{41} -9705.30 q^{43} +9544.71i q^{44} +(-7614.30 + 2108.11i) q^{45} -4669.66 q^{46} -18224.2 q^{47} +(-12468.7 + 1694.19i) q^{48} -3145.57i q^{50} +(479.154 - 65.1052i) q^{51} -18083.2i q^{52} +33118.3i q^{53} +(-2271.15 - 5295.66i) q^{54} -10453.7i q^{55} +(-2763.83 - 20341.0i) q^{57} +12327.8 q^{58} +6677.29 q^{59} +(14908.9 - 2025.75i) q^{60} +35094.2i q^{61} -8898.97 q^{62} +19395.6 q^{64} +19805.4i q^{65} +(7554.64 - 1026.49i) q^{66} -19331.4 q^{67} -920.868 q^{68} +(-6442.93 - 47417.9i) q^{69} -21428.8i q^{71} +(6084.05 + 21975.0i) q^{72} -32945.3i q^{73} -14853.4i q^{74} +(31941.6 - 4340.07i) q^{75} +39092.5i q^{76} +(-14312.8 + 1944.76i) q^{78} +5143.35 q^{79} -26245.4 q^{80} +(50641.0 - 30369.0i) q^{81} -29964.4i q^{82} +65038.8 q^{83} +1008.57 q^{85} -14763.3i q^{86} +(17009.1 + 125182. i) q^{87} -30169.7 q^{88} +11478.5 q^{89} +(-3206.77 - 11582.5i) q^{90} +91130.7i q^{92} +(-12278.3 - 90364.3i) q^{93} -27721.8i q^{94} -42815.6i q^{95} +(-8879.18 - 65348.0i) q^{96} +132309. i q^{97} +(20846.9 + 75297.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 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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