LMFDB - Embedded newform 147.6.c.d.146.24

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			146.24
Character	$\chi$	$=$	147.146
Dual form			147.6.c.d.146.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.54010i q^{2} +(-2.32648 - 15.4139i) q^{3} -10.7729 q^{4} -13.6838 q^{5} +(100.808 - 15.2154i) q^{6} +138.827i q^{8} +(-232.175 + 71.7202i) q^{9} +O(q^{10})$	\(q+6.54010i q^{2} +(-2.32648 - 15.4139i) q^{3} -10.7729 q^{4} -13.6838 q^{5} +(100.808 - 15.2154i) q^{6} +138.827i q^{8} +(-232.175 + 71.7202i) q^{9} -89.4937i q^{10} -214.762i q^{11} +(25.0631 + 166.053i) q^{12} -219.576i q^{13} +(31.8352 + 210.921i) q^{15} -1252.68 q^{16} +2125.60 q^{17} +(-469.058 - 1518.45i) q^{18} +1220.59i q^{19} +147.415 q^{20} +1404.57 q^{22} +3302.00i q^{23} +(2139.86 - 322.979i) q^{24} -2937.75 q^{25} +1436.05 q^{26} +(1645.64 + 3411.86i) q^{27} +5636.75i q^{29} +(-1379.45 + 208.206i) q^{30} +5580.55i q^{31} -3750.17i q^{32} +(-3310.32 + 499.640i) q^{33} +13901.6i q^{34} +(2501.21 - 772.638i) q^{36} -373.824 q^{37} -7982.80 q^{38} +(-3384.51 + 510.839i) q^{39} -1899.69i q^{40} -10975.4 q^{41} +20780.3 q^{43} +2313.62i q^{44} +(3177.05 - 981.408i) q^{45} -21595.4 q^{46} +15115.7 q^{47} +(2914.33 + 19308.6i) q^{48} -19213.2i q^{50} +(-4945.17 - 32763.7i) q^{51} +2365.48i q^{52} +24313.5i q^{53} +(-22313.9 + 10762.6i) q^{54} +2938.77i q^{55} +(18814.1 - 2839.69i) q^{57} -36864.9 q^{58} -39091.9 q^{59} +(-342.959 - 2272.24i) q^{60} +14042.1i q^{61} -36497.4 q^{62} -15559.2 q^{64} +3004.64i q^{65} +(-3267.70 - 21649.8i) q^{66} -44537.1 q^{67} -22899.0 q^{68} +(50896.6 - 7682.05i) q^{69} +41525.1i q^{71} +(-9956.71 - 32232.2i) q^{72} +2864.09i q^{73} -2444.84i q^{74} +(6834.63 + 45282.1i) q^{75} -13149.4i q^{76} +(-3340.94 - 22135.0i) q^{78} +33937.5 q^{79} +17141.4 q^{80} +(48761.4 - 33303.3i) q^{81} -71780.2i q^{82} -9963.09 q^{83} -29086.4 q^{85} +135905. i q^{86} +(86884.1 - 13113.8i) q^{87} +29814.8 q^{88} +115771. q^{89} +(6418.51 + 20778.2i) q^{90} -35572.3i q^{92} +(86017.9 - 12983.1i) q^{93} +98858.4i q^{94} -16702.4i q^{95} +(-57804.7 + 8724.71i) q^{96} -98824.0i q^{97} +(15402.8 + 49862.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			6.54010i			1.15614i	0.815988	+	0.578069i	$0.196194\pi$
$2$			6.54010i			1.15614i	−0.815988	+	0.578069i	$0.803806\pi$
$3$	−2.32648	−	15.4139i	−0.149244	−	0.988800i
$3$	−2.32648	−	15.4139i	−0.149244	−	0.988800i
$4$	−10.7729			−0.336655
$5$	−13.6838			−0.244784			−0.122392	−	0.992482i	$-0.539057\pi$
$5$	−13.6838			−0.244784			−0.122392	+	0.992482i	$0.539057\pi$
$6$	100.808	−	15.2154i	1.14319	−	0.172547i
$7$		0			0
$7$		0			0
$8$			138.827i			0.766919i
$9$	−232.175	+	71.7202i	−0.955453	+	0.295145i
$10$		−	89.4937i		−	0.283004i
$11$		−	214.762i		−	0.535151i	−0.963537	−	0.267575i	$-0.913778\pi$
$11$		−	214.762i		−	0.535151i	0.963537	−	0.267575i	$-0.0862224\pi$
$12$	25.0631	+	166.053i	0.0502436	+	0.332884i
$13$		−	219.576i		−	0.360351i	−0.983634	−	0.180175i	$-0.942333\pi$
$13$		−	219.576i		−	0.360351i	0.983634	−	0.180175i	$-0.0576666\pi$
$14$		0			0
$15$	31.8352	+	210.921i	0.0365325	+	0.242043i
$16$	−1252.68			−1.22332
$17$	2125.60			1.78385			0.891926	−	0.452181i	$-0.149354\pi$
$17$	2125.60			1.78385			0.891926	+	0.452181i	$0.149354\pi$
$18$	−469.058	−	1518.45i	−0.341228	−	1.10463i
$19$			1220.59i			0.775687i	0.921725	+	0.387844i	$0.126780\pi$
$19$			1220.59i			0.775687i	−0.921725	+	0.387844i	$0.873220\pi$
$20$	147.415			0.0824077
$21$		0			0
$22$	1404.57			0.618708
$23$			3302.00i			1.30154i	0.759275	+	0.650770i	$0.225554\pi$
$23$			3302.00i			1.30154i	−0.759275	+	0.650770i	$0.774446\pi$
$24$	2139.86	−	322.979i	0.758330	−	0.114458i
$25$	−2937.75			−0.940081
$26$	1436.05			0.416615
$27$	1645.64	+	3411.86i	0.434435	+	0.900703i
$28$		0			0
$29$			5636.75i			1.24461i	0.782774	+	0.622306i	$0.213804\pi$
$29$			5636.75i			1.24461i	−0.782774	+	0.622306i	$0.786196\pi$
$30$	−1379.45	+	208.206i	−0.279835	+	0.0422366i
$31$			5580.55i			1.04297i	0.853260	+	0.521486i	$0.174622\pi$
$31$			5580.55i			1.04297i	−0.853260	+	0.521486i	$0.825378\pi$
$32$		−	3750.17i		−	0.647406i
$33$	−3310.32	+	499.640i	−0.529157	+	0.0798680i
$34$			13901.6i			2.06238i
$35$		0			0
$36$	2501.21	−	772.638i	0.321657	−	0.0993619i
$37$	−373.824			−0.0448913			−0.0224457	−	0.999748i	$-0.507145\pi$
$37$	−373.824			−0.0448913			−0.0224457	+	0.999748i	$0.507145\pi$
$38$	−7982.80			−0.896802
$39$	−3384.51	+	510.839i	−0.356315	+	0.0537802i
$40$		−	1899.69i		−	0.187729i
$41$	−10975.4			−1.01967			−0.509836	−	0.860272i	$-0.670294\pi$
$41$	−10975.4			−1.01967			−0.509836	+	0.860272i	$0.670294\pi$
$42$		0			0
$43$	20780.3			1.71388			0.856940	−	0.515417i	$-0.172363\pi$
$43$	20780.3			1.71388			0.856940	+	0.515417i	$0.172363\pi$
$44$			2313.62i			0.180161i
$45$	3177.05	−	981.408i	0.233880	−	0.0722468i
$46$	−21595.4			−1.50476
$47$	15115.7			0.998124			0.499062	−	0.866566i	$-0.333678\pi$
$47$	15115.7			0.998124			0.499062	+	0.866566i	$0.333678\pi$
$48$	2914.33	+	19308.6i	0.182573	+	1.20962i
$49$		0			0
$50$		−	19213.2i		−	1.08686i
$51$	−4945.17	−	32763.7i	−0.266229	−	1.76387i
$52$			2365.48i			0.121314i
$53$			24313.5i			1.18894i	0.804119	+	0.594468i	$0.202637\pi$
$53$			24313.5i			1.18894i	−0.804119	+	0.594468i	$0.797363\pi$
$54$	−22313.9	+	10762.6i	−1.04134	+	0.502267i
$55$			2938.77i			0.130996i
$56$		0			0
$57$	18814.1	−	2839.69i	0.767000	−	0.115767i
$58$	−36864.9			−1.43894
$59$	−39091.9			−1.46203			−0.731016	−	0.682361i	$-0.760953\pi$
$59$	−39091.9			−1.46203			−0.731016	+	0.682361i	$0.760953\pi$
$60$	−342.959	−	2272.24i	−0.0122988	−	0.0814847i
$61$			14042.1i			0.483180i	0.970378	+	0.241590i	$0.0776688\pi$
$61$			14042.1i			0.483180i	−0.970378	+	0.241590i	$0.922331\pi$
$62$	−36497.4			−1.20582
$63$		0			0
$64$	−15559.2			−0.474828
$65$			3004.64i			0.0882082i
$66$	−3267.70	−	21649.8i	−0.0923384	−	0.611779i
$67$	−44537.1			−1.21209			−0.606045	−	0.795430i	$-0.707245\pi$
$67$	−44537.1			−1.21209			−0.606045	+	0.795430i	$0.707245\pi$
$68$	−22899.0			−0.600542
$69$	50896.6	−	7682.05i	1.28696	−	0.194247i
$70$		0			0
$71$			41525.1i			0.977607i	0.872394	+	0.488804i	$0.162566\pi$
$71$			41525.1i			0.977607i	−0.872394	+	0.488804i	$0.837434\pi$
$72$	−9956.71	−	32232.2i	−0.226352	−	0.732754i
$73$			2864.09i			0.0629042i	0.999505	+	0.0314521i	$0.0100132\pi$
$73$			2864.09i			0.0629042i	−0.999505	+	0.0314521i	$0.989987\pi$
$74$		−	2444.84i		−	0.0519006i
$75$	6834.63	+	45282.1i	0.140301	+	0.929552i
$76$		−	13149.4i		−	0.261139i
$77$		0			0
$78$	−3340.94	−	22135.0i	−0.0621773	−	0.411949i
$79$	33937.5			0.611804			0.305902	−	0.952063i	$-0.401042\pi$
$79$	33937.5			0.611804			0.305902	+	0.952063i	$0.401042\pi$
$80$	17141.4			0.299449
$81$	48761.4	−	33303.3i	0.825779	−	0.563994i
$82$		−	71780.2i		−	1.17888i
$83$	−9963.09			−0.158745			−0.0793723	−	0.996845i	$-0.525292\pi$
$83$	−9963.09			−0.158745			−0.0793723	+	0.996845i	$0.525292\pi$
$84$		0			0
$85$	−29086.4			−0.436659
$86$			135905.i			1.98148i
$87$	86884.1	−	13113.8i	1.23067	−	0.185751i
$88$	29814.8			0.410417
$89$	115771.			1.54926			0.774632	−	0.632413i	$-0.217935\pi$
$89$	115771.			1.54926			0.774632	+	0.632413i	$0.217935\pi$
$90$	6418.51	+	20778.2i	0.0835272	+	0.270397i
$91$		0			0
$92$		−	35572.3i		−	0.438169i
$93$	86017.9	−	12983.1i	1.03129	−	0.155657i
$94$			98858.4i			1.15397i
$95$		−	16702.4i		−	0.189876i
$96$	−57804.7	+	8724.71i	−0.640155	+	0.0966214i
$97$		−	98824.0i		−	1.06643i	−0.845979	−	0.533216i	$-0.820983\pi$
$97$		−	98824.0i		−	1.06643i	0.845979	−	0.533216i	$-0.179017\pi$
$98$		0			0
$99$	15402.8	+	49862.4i	0.157947	+	0.511311i
$100$	31648.2			0.316482
$101$	87992.6			0.858307			0.429153	−	0.903232i	$-0.358812\pi$
$101$	87992.6			0.858307			0.429153	+	0.903232i	$0.358812\pi$
$102$	214278.	−	32341.9i	2.03928	−	0.307798i
$103$		−	157176.i		−	1.45980i	−0.683554	−	0.729900i	$-0.739567\pi$
$103$		−	157176.i		−	1.45980i	0.683554	−	0.729900i	$-0.260433\pi$
$104$	30483.0			0.276360
$105$		0			0
$106$	−159013.			−1.37457
$107$			28166.9i			0.237837i	0.992904	+	0.118918i	$0.0379427\pi$
$107$			28166.9i			0.237837i	−0.992904	+	0.118918i	$0.962057\pi$
$108$	−17728.4	−	36755.8i	−0.146254	−	0.303226i
$109$	−10890.3			−0.0877954			−0.0438977	−	0.999036i	$-0.513978\pi$
$109$	−10890.3			−0.0877954			−0.0438977	+	0.999036i	$0.513978\pi$
$110$	−19219.9			−0.151450
$111$	869.694	+	5762.07i	0.00669976	+	0.0443886i
$112$		0			0
$113$			139346.i			1.02659i	0.858212	+	0.513295i	$0.171575\pi$
$113$			139346.i			1.02659i	−0.858212	+	0.513295i	$0.828425\pi$
$114$	18571.8	+	123046.i	0.133842	+	0.886758i
$115$		−	45184.1i		−	0.318596i
$116$		−	60724.4i		−	0.419004i
$117$	15748.0	+	50980.0i	0.106356	+	0.344298i
$118$		−	255665.i		−	1.69031i
$119$		0			0
$120$	−29281.6	+	4419.59i	−0.185627	+	0.0280175i
$121$	114928.			0.713614
$122$	−91837.0			−0.558622
$123$	25534.1	+	169173.i	0.152180	+	1.00825i
$124$		−	60119.0i		−	0.351121i
$125$	82961.8			0.474901
$126$		0			0
$127$	−94742.0			−0.521235			−0.260617	−	0.965442i	$-0.583926\pi$
$127$	−94742.0			−0.521235			−0.260617	+	0.965442i	$0.583926\pi$
$128$		−	221764.i		−	1.19637i
$129$	−48344.9	−	320305.i	−0.255786	−	1.69468i
$130$	−19650.6			−0.101981
$131$	−87332.2			−0.444628			−0.222314	−	0.974975i	$-0.571361\pi$
$131$	−87332.2			−0.444628			−0.222314	+	0.974975i	$0.571361\pi$
$132$	35661.9	−	5382.60i	0.178143	−	0.0268879i
$133$		0			0
$134$		−	291277.i		−	1.40134i
$135$	−22518.6	−	46687.4i	−0.106343	−	0.220478i
$136$			295091.i			1.36807i
$137$			152664.i			0.694921i	0.937695	+	0.347461i	$0.112956\pi$
$137$			152664.i			0.694921i	−0.937695	+	0.347461i	$0.887044\pi$
$138$	50241.4	+	332869.i	0.224576	+	1.48791i
$139$		−	240237.i		−	1.05464i	−0.849667	−	0.527319i	$-0.823197\pi$
$139$		−	240237.i		−	1.05464i	0.849667	−	0.527319i	$-0.176803\pi$
$140$		0			0
$141$	−35166.5	−	232992.i	−0.148964	−	0.986945i
$142$	−271578.			−1.13025
$143$	−47156.5			−0.192842
$144$	290840.	−	89842.3i	1.16882	−	0.361056i
$145$		−	77132.4i		−	0.304661i
$146$	−18731.4			−0.0727259
$147$		0			0
$148$	4027.18			0.0151129
$149$		−	342046.i		−	1.26217i	−0.775712	−	0.631087i	$-0.782609\pi$
$149$		−	342046.i		−	1.26217i	0.775712	−	0.631087i	$-0.217391\pi$
$150$	−296150.	+	44699.2i	−1.07469	+	0.162208i
$151$	−510494.			−1.82200			−0.911001	−	0.412405i	$-0.864689\pi$
$151$	−510494.			−1.82200			−0.911001	+	0.412405i	$0.864689\pi$
$152$	−169451.			−0.594889
$153$	−493511.	+	152448.i	−1.70439	+	0.526495i
$154$		0			0
$155$		−	76363.4i		−	0.255303i
$156$	36461.1	−	5503.24i	0.119955	−	0.0181053i
$157$		−	228128.i		−	0.738635i	−0.929303	−	0.369318i	$-0.879591\pi$
$157$		−	228128.i		−	0.738635i	0.929303	−	0.369318i	$-0.120409\pi$
$158$			221955.i			0.707330i
$159$	374766.	−	56565.0i	1.17562	−	0.177442i
$160$			51316.8i			0.158475i
$161$		0			0
$162$	217807.	+	318905.i	0.652055	+	0.954714i
$163$	193098.			0.569258			0.284629	−	0.958638i	$-0.408130\pi$
$163$	193098.			0.569258			0.284629	+	0.958638i	$0.408130\pi$
$164$	118237.			0.343277
$165$	45297.8	−	6837.00i	0.129529	−	0.0195504i
$166$		−	65159.7i		−	0.183531i
$167$	304213.			0.844085			0.422043	−	0.906576i	$-0.361313\pi$
$167$	304213.			0.844085			0.422043	+	0.906576i	$0.361313\pi$
$168$		0			0
$169$	323080.			0.870147
$170$		−	190228.i		−	0.504838i
$171$	−87541.2	−	283391.i	−0.228940	−	0.741133i
$172$	−223865.			−0.576985
$173$	−531106.			−1.34917			−0.674583	−	0.738199i	$-0.735677\pi$
$173$	−531106.			−1.34917			−0.674583	+	0.738199i	$0.735677\pi$
$174$	85765.6	+	568231.i	0.214753	+	1.42283i
$175$		0			0
$176$			269028.i			0.654659i
$177$	90946.6	+	602558.i	0.218199	+	1.44566i
$178$			757155.i			1.79116i
$179$		−	552319.i		−	1.28842i	−0.764849	−	0.644209i	$-0.777187\pi$
$179$		−	552319.i		−	1.28842i	0.764849	−	0.644209i	$-0.222813\pi$
$180$	−34226.1	+	10572.7i	−0.0787366	+	0.0243222i
$181$			713046.i			1.61779i	0.587955	+	0.808893i	$0.299933\pi$
$181$			713046.i			1.61779i	−0.587955	+	0.808893i	$0.700067\pi$
$182$		0			0
$183$	216444.	−	32668.8i	0.477768	−	0.0721116i
$184$	−458407.			−0.998176
$185$	5115.34			0.0109887
$186$	84910.5	+	562566.i	0.179961	+	1.19231i
$187$		−	456498.i		−	0.954630i
$188$	−162841.			−0.336023
$189$		0			0
$190$	109235.			0.219523
$191$			378348.i			0.750427i	0.926938	+	0.375213i	$0.122431\pi$
$191$			378348.i			0.750427i	−0.926938	+	0.375213i	$0.877569\pi$
$192$	36198.1	+	239827.i	0.0708652	+	0.469510i
$193$	−471993.			−0.912100			−0.456050	−	0.889954i	$-0.650736\pi$
$193$	−471993.			−0.912100			−0.456050	+	0.889954i	$0.650736\pi$
$194$	646319.			1.23294
$195$	46313.1	−	6990.24i	0.0872203	−	0.0131645i
$196$		0			0
$197$			58245.7i			0.106930i	0.998570	+	0.0534648i	$0.0170265\pi$
$197$			58245.7i			0.106930i	−0.998570	+	0.0534648i	$0.982974\pi$
$198$	−326105.	+	100736.i	−0.591146	+	0.182608i
$199$		−	4649.32i		−	0.00832255i	−0.999991	−	0.00416128i	$-0.998675\pi$
$199$		−	4649.32i		−	0.00832255i	0.999991	−	0.00416128i	$-0.00132458\pi$
$200$		−	407840.i		−	0.720966i
$201$	103615.	+	686489.i	0.180897	+	1.19852i
$202$			575480.i			0.992321i
$203$		0			0
$204$	53274.0	+	352962.i	0.0896273	+	0.593816i
$205$	150186.			0.249599
$206$	1.02795e6			1.68773
$207$	−236820.	−	766642.i	−0.384143	−	1.24356i
$208$			275057.i			0.440824i
$209$	262137.			0.415110
$210$		0			0
$211$	262985.			0.406653			0.203327	−	0.979111i	$-0.434825\pi$
$211$	262985.			0.406653			0.203327	+	0.979111i	$0.434825\pi$
$212$		−	261929.i		−	0.400261i
$213$	640062.	−	96607.3i	0.966658	−	0.145902i
$214$	−184214.			−0.274972
$215$	−284354.			−0.419530
$216$	−473659.	+	228459.i	−0.690766	+	0.333176i
$217$		0			0
$218$		−	71223.4i		−	0.101504i
$219$	44146.7	−	6663.26i	0.0621997	−	0.00938807i
$220$		−	31659.2i		−	0.0441005i
$221$		−	466730.i		−	0.642813i
$222$	−37684.5	+	5687.89i	−0.0513193	+	0.00774584i
$223$		−	578908.i		−	0.779557i	−0.920909	−	0.389778i	$-0.872552\pi$
$223$		−	578908.i		−	0.779557i	0.920909	−	0.389778i	$-0.127448\pi$
$224$		0			0
$225$	682073.	−	210696.i	0.898203	−	0.277460i
$226$	−911335.			−1.18688
$227$	−268266.			−0.345542			−0.172771	−	0.984962i	$-0.555272\pi$
$227$	−268266.			−0.345542			−0.172771	+	0.984962i	$0.555272\pi$
$228$	−202683.	+	30591.8i	−0.258214	+	0.0389734i
$229$			626856.i			0.789912i	0.918700	+	0.394956i	$0.129240\pi$
$229$			626856.i			0.789912i	−0.918700	+	0.394956i	$0.870760\pi$
$230$	295508.			0.368341
$231$		0			0
$232$	−782534.			−0.954516
$233$			698449.i			0.842839i	0.906866	+	0.421420i	$0.138468\pi$
$233$			698449.i			0.842839i	−0.906866	+	0.421420i	$0.861532\pi$
$234$	−333414.	+	102994.i	−0.398056	+	0.122962i
$235$	−206841.			−0.244325
$236$	421135.			0.492200
$237$	−78955.0	−	523108.i	−0.0913080	−	0.604952i
$238$		0			0
$239$			332169.i			0.376153i	0.982154	+	0.188076i	$0.0602252\pi$
$239$			332169.i			0.376153i	−0.982154	+	0.188076i	$0.939775\pi$
$240$	−39879.3	−	264216.i	−0.0446909	−	0.296095i
$241$		−	913349.i		−	1.01296i	−0.862250	−	0.506482i	$-0.830946\pi$
$241$		−	913349.i		−	1.01296i	0.862250	−	0.506482i	$-0.169054\pi$
$242$			751642.i			0.825036i
$243$	−626775.	−	674123.i	−0.680920	−	0.732358i
$244$		−	151275.i		−	0.162665i
$245$		0			0
$246$	−1.10641e6	+	166995.i	−1.16568	+	0.175941i
$247$	268012.			0.279520
$248$	−774732.			−0.799875
$249$	23179.0	+	153570.i	0.0236917	+	0.156967i
$250$			542578.i			0.549051i
$251$	−110541.			−0.110748			−0.0553742	−	0.998466i	$-0.517635\pi$
$251$	−110541.			−0.110748			−0.0553742	+	0.998466i	$0.517635\pi$
$252$		0			0
$253$	709145.			0.696520
$254$		−	619622.i		−	0.602619i
$255$	67668.9	+	448333.i	0.0651686	+	0.431768i
$256$	952467.			0.908343
$257$	−791581.			−0.747588			−0.373794	−	0.927512i	$-0.621943\pi$
$257$	−791581.			−0.747588			−0.373794	+	0.927512i	$0.621943\pi$
$258$	2.09482e6	−	316181.i	1.95929	−	0.295724i
$259$		0			0
$260$		−	32368.8i		−	0.0296957i
$261$	−404269.	−	1.30871e6i	−0.367341	−	1.18917i
$262$		−	571162.i		−	0.514051i
$263$			2.03678e6i			1.81575i	0.419243	+	0.907874i	$0.362296\pi$
$263$			2.03678e6i			1.81575i	−0.419243	+	0.907874i	$0.637704\pi$
$264$	−69363.6	−	459562.i	−0.0612522	−	0.405821i
$265$		−	332703.i		−	0.291033i
$266$		0			0
$267$	−269339.	−	1.78448e6i	−0.231218	−	1.53191i
$268$	479796.			0.408056
$269$	−1.61111e6			−1.35751			−0.678755	−	0.734365i	$-0.737480\pi$
$269$	−1.61111e6			−1.35751			−0.678755	+	0.734365i	$0.737480\pi$
$270$	305340.	−	147274.i	0.254903	−	0.122947i
$271$		−	1.44324e6i		−	1.19376i	−0.802332	−	0.596878i	$-0.796408\pi$
$271$		−	1.44324e6i		−	1.19376i	0.802332	−	0.596878i	$-0.203592\pi$
$272$	−2.66269e6			−2.18222
$273$		0			0
$274$	−998439.			−0.803425
$275$			630918.i			0.503085i
$276$	−548307.	+	82758.3i	−0.433262	+	0.0653941i
$277$	1.98019e6			1.55062			0.775312	−	0.631579i	$-0.217593\pi$
$277$	1.98019e6			1.55062			0.775312	+	0.631579i	$0.217593\pi$
$278$	1.57118e6			1.21931
$279$	−400238.	−	1.29566e6i	−0.307828	−	0.996510i
$280$		0			0
$281$			116002.i			0.0876392i	0.999039	+	0.0438196i	$0.0139527\pi$
$281$			116002.i			0.0876392i	−0.999039	+	0.0438196i	$0.986047\pi$
$282$	1.52379e6	−	229992.i	1.14104	−	0.172223i
$283$			742994.i			0.551466i	0.961234	+	0.275733i	$0.0889206\pi$
$283$			742994.i			0.551466i	−0.961234	+	0.275733i	$0.911079\pi$
$284$		−	447347.i		−	0.329116i
$285$	−257449.	+	38857.8i	−0.187749	+	0.0283378i
$286$		−	308409.i		−	0.222952i
$287$		0			0
$288$	268963.	+	870697.i	0.191078	+	0.618565i
$289$	3.09831e6			2.18213
$290$	504454.			0.352230
$291$	−1.52326e6	+	229912.i	−1.05449	+	0.159158i
$292$		−	30854.7i		−	0.0211770i
$293$	−197531.			−0.134421			−0.0672104	−	0.997739i	$-0.521410\pi$
$293$	−197531.			−0.134421			−0.0672104	+	0.997739i	$0.521410\pi$
$294$		0			0
$295$	534927.			0.357882
$296$		−	51896.9i		−	0.0344280i
$297$	732738.	−	353421.i	0.482012	−	0.232488i
$298$	2.23702e6			1.45925
$299$	725039.			0.469011
$300$	−73629.1	−	487822.i	−0.0472331	−	0.312938i
$301$		0			0
$302$		−	3.33869e6i		−	2.10648i
$303$	−204713.	−	1.35631e6i	−0.128097	−	0.848694i
$304$		−	1.52901e6i		−	0.948913i
$305$		−	192150.i		−	0.118275i
$306$	−997028.	−	3.22761e6i	−0.608701	−	1.97051i
$307$			37022.2i			0.0224190i	0.999937	+	0.0112095i	$0.00356817\pi$
$307$			37022.2i			0.0224190i	−0.999937	+	0.0112095i	$0.996432\pi$
$308$		0			0
$309$	−2.42269e6	+	365667.i	−1.44345	+	0.217866i
$310$	499424.			0.295165
$311$	−992927.			−0.582125			−0.291063	−	0.956704i	$-0.594009\pi$
$311$	−992927.			−0.582125			−0.291063	+	0.956704i	$0.594009\pi$
$312$	−70918.3	−	469862.i	−0.0412450	−	0.273265i
$313$			2.17965e6i			1.25755i	0.777587	+	0.628776i	$0.216444\pi$
$313$			2.17965e6i			1.25755i	−0.777587	+	0.628776i	$0.783556\pi$
$314$	1.49198e6			0.853964
$315$		0			0
$316$	−365607.			−0.205967
$317$			2.29088e6i			1.28043i	0.768198	+	0.640213i	$0.221154\pi$
$317$			2.29088e6i			1.28043i	−0.768198	+	0.640213i	$0.778846\pi$
$318$	369941.	+	2.45101e6i	0.205147	+	1.35918i
$319$	1.21056e6			0.666054
$320$	212909.			0.116230
$321$	434161.	−	65529.7i	0.235173	−	0.0354957i
$322$		0			0
$323$			2.59449e6i			1.38371i
$324$	−525304.	+	358774.i	−0.278002	+	0.189871i
$325$			645059.i			0.338759i
$326$			1.26288e6i			0.658140i
$327$	25336.0	+	167861.i	0.0131029	+	0.0868121i
$328$		−	1.52368e6i		−	0.782005i
$329$		0			0
$330$	44714.7	+	296253.i	0.0226030	+	0.149754i
$331$	−1.71782e6			−0.861802			−0.430901	−	0.902399i	$-0.641804\pi$
$331$	−1.71782e6			−0.861802			−0.430901	+	0.902399i	$0.641804\pi$
$332$	107332.			0.0534421
$333$	86792.5	−	26810.7i	0.0428915	−	0.0132494i
$334$			1.98958e6i			0.975879i
$335$	609439.			0.296700
$336$		0			0
$337$	−2.13570e6			−1.02439			−0.512196	−	0.858868i	$-0.671168\pi$
$337$	−2.13570e6			−1.02439			−0.512196	+	0.858868i	$0.671168\pi$
$338$			2.11297e6i			1.00601i
$339$	2.14786e6	−	324185.i	1.01509	−	0.153212i
$340$	313346.			0.147003
$341$	1.19849e6			0.558147
$342$	1.85341e6	−	572528.i	0.856851	−	0.264686i
$343$		0			0
$344$			2.88487e6i			1.31441i
$345$	−696461.	+	105120.i	−0.315028	+	0.0475486i
$346$		−	3.47349e6i		−	1.55982i
$347$		−	3.13549e6i		−	1.39792i	−0.715162	−	0.698958i	$-0.753647\pi$
$347$		−	3.13549e6i		−	1.39792i	0.715162	−	0.698958i	$-0.246353\pi$
$348$	−935998.	+	141274.i	−0.414311	+	0.0625338i
$349$			1.73339e6i			0.761785i	0.924619	+	0.380893i	$0.124383\pi$
$349$			1.73339e6i			0.761785i	−0.924619	+	0.380893i	$0.875617\pi$
$350$		0			0
$351$	749161.	−	361342.i	0.324569	−	0.156549i
$352$	−805395.			−0.346460
$353$	2.04453e6			0.873288			0.436644	−	0.899634i	$-0.356167\pi$
$353$	2.04453e6			0.873288			0.436644	+	0.899634i	$0.356167\pi$
$354$	−3.94079e6	+	594800.i	−1.67138	+	0.252268i
$355$		−	568222.i		−	0.239303i
$356$	−1.24720e6			−0.521567
$357$		0			0
$358$	3.61222e6			1.48959
$359$		−	1.71555e6i		−	0.702535i	−0.936275	−	0.351267i	$-0.885751\pi$
$359$		−	1.71555e6i		−	0.702535i	0.936275	−	0.351267i	$-0.114249\pi$
$360$	136246.	+	441060.i	0.0554074	+	0.179367i
$361$	986252.			0.398309
$362$	−4.66340e6			−1.87038
$363$	−267378.	−	1.77149e6i	−0.106503	−	0.705622i
$364$		0			0
$365$		−	39191.8i		−	0.0153979i
$366$	213657.	+	1.41556e6i	0.0833710	+	0.552366i
$367$		−	58977.6i		−	0.0228571i	−0.999935	−	0.0114286i	$-0.996362\pi$
$367$		−	58977.6i		−	0.0228571i	0.999935	−	0.0114286i	$-0.00363791\pi$
$368$		−	4.13634e6i		−	1.59220i
$369$	2.54821e6	−	787157.i	0.974248	−	0.300951i
$370$			33454.9i			0.0127044i
$371$		0			0
$372$	−926666.	+	139866.i	−0.347189	+	0.0524027i
$373$	−1.46594e6			−0.545563			−0.272782	−	0.962076i	$-0.587944\pi$
$373$	−1.46594e6			−0.545563			−0.272782	+	0.962076i	$0.587944\pi$
$374$	2.98554e6			1.10368
$375$	−193009.	−	1.27876e6i	−0.0708761	−	0.469582i
$376$			2.09847e6i			0.765480i
$377$	1.23769e6			0.448497
$378$		0			0
$379$	1.23905e6			0.443089			0.221544	−	0.975150i	$-0.428890\pi$
$379$	1.23905e6			0.443089			0.221544	+	0.975150i	$0.428890\pi$
$380$			179934.i			0.0639226i
$381$	220416.	+	1.46034e6i	0.0777911	+	0.515397i
$382$	−2.47444e6			−0.867597
$383$	3.75246e6			1.30713			0.653566	−	0.756869i	$-0.273272\pi$
$383$	3.75246e6			1.30713			0.653566	+	0.756869i	$0.273272\pi$
$384$	−3.41824e6	+	515930.i	−1.18297	+	0.178551i
$385$		0			0
$386$		−	3.08688e6i		−	1.05451i
$387$	−4.82466e6	+	1.49037e6i	−1.63753	+	0.505843i
$388$			1.06463e6i			0.359019i
$389$			5.20547e6i			1.74416i	0.489365	+	0.872079i	$0.337229\pi$
$389$			5.20547e6i			1.74416i	−0.489365	+	0.872079i	$0.662771\pi$
$390$	45716.9	+	302892.i	0.0152200	+	0.100839i
$391$			7.01873e6i			2.32176i
$392$		0			0
$393$	203177.	+	1.34613e6i	0.0663579	+	0.439648i
$394$	−380933.			−0.123625
$395$	−464396.			−0.149760
$396$	−165933.	−	537165.i	−0.0531736	−	0.172135i
$397$			693163.i			0.220729i	0.993891	+	0.110364i	$0.0352018\pi$
$397$			693163.i			0.220729i	−0.993891	+	0.110364i	$0.964798\pi$
$398$	30407.0			0.00962201
$399$		0			0
$400$	3.68006e6			1.15002
$401$		−	5.51502e6i		−	1.71272i	−0.516379	−	0.856360i	$-0.672721\pi$
$401$		−	5.51502e6i		−	1.71272i	0.516379	−	0.856360i	$-0.327279\pi$
$402$	−4.48971e6	+	677651.i	−1.38565	+	0.209142i
$403$	1.22535e6			0.375836
$404$	−947939.			−0.288953
$405$	−667244.	+	455717.i	−0.202138	+	0.138057i
$406$		0			0
$407$			80283.2i			0.0240236i
$408$	4.54849e6	−	686523.i	1.35275	−	0.204176i
$409$			846702.i			0.250278i	0.992139	+	0.125139i	$0.0399376\pi$
$409$			846702.i			0.250278i	−0.992139	+	0.125139i	$0.960062\pi$
$410$			982229.i			0.288571i
$411$	2.35315e6	−	355171.i	0.687139	−	0.103713i
$412$			1.69325e6i			0.491448i
$413$		0			0
$414$	5.01392e6	−	1.54883e6i	1.43773	−	0.444122i
$415$	136333.			0.0388581
$416$	−823447.			−0.233293
$417$	−3.70299e6	+	558908.i	−1.04283	+	0.157398i
$418$			1.71440e6i			0.479924i
$419$	1.55316e6			0.432196			0.216098	−	0.976372i	$-0.430667\pi$
$419$	1.55316e6			0.432196			0.216098	+	0.976372i	$0.430667\pi$
$420$		0			0
$421$	−3.72316e6			−1.02378			−0.511889	−	0.859052i	$-0.671054\pi$
$421$	−3.72316e6			−1.02378			−0.511889	+	0.859052i	$0.671054\pi$
$422$			1.71995e6i			0.470147i
$423$	−3.50949e6	+	1.08410e6i	−0.953660	+	0.294591i
$424$	−3.37538e6			−0.911818
$425$	−6.24448e6			−1.67697
$426$	631822.	+	4.18607e6i	0.168683	+	1.11759i
$427$		0			0
$428$		−	303440.i		−	0.0800689i
$429$	109709.	+	726865.i	0.0287805	+	0.190682i
$430$		−	1.85970e6i		−	0.485035i
$431$			1.13242e6i			0.293640i	0.989163	+	0.146820i	$0.0469039\pi$
$431$			1.13242e6i			0.293640i	−0.989163	+	0.146820i	$0.953096\pi$
$432$	−2.06145e6	−	4.27396e6i	−0.531452	−	1.10185i
$433$			3.94540e6i			1.01128i	0.862745	+	0.505639i	$0.168743\pi$
$433$			3.94540e6i			1.01128i	−0.862745	+	0.505639i	$0.831257\pi$
$434$		0			0
$435$	−1.18891e6	+	179447.i	−0.301249	+	0.0454688i
$436$	117320.			0.0295567
$437$	−4.03040e6			−1.00959
$438$	43578.4	+	288724.i	0.0108539	+	0.0719114i
$439$		−	3.95535e6i		−	0.979543i	−0.871851	−	0.489771i	$-0.837080\pi$
$439$		−	3.95535e6i		−	0.979543i	0.871851	−	0.489771i	$-0.162920\pi$
$440$	−407981.			−0.100464
$441$		0			0
$442$	3.05246e6			0.743180
$443$		−	5.57901e6i		−	1.35067i	−0.737513	−	0.675333i	$-0.764000\pi$
$443$		−	5.57901e6i		−	1.35067i	0.737513	−	0.675333i	$-0.236000\pi$
$444$	−9369.17	−	62074.5i	−0.00225550	−	0.0149436i
$445$	−1.58419e6			−0.379235
$446$	3.78612e6			0.901275
$447$	−5.27226e6	+	795765.i	−1.24804	+	0.188372i
$448$		0			0
$449$			1.07609e6i			0.251902i	0.992036	+	0.125951i	$0.0401982\pi$
$449$			1.07609e6i			0.251902i	−0.992036	+	0.125951i	$0.959802\pi$
$450$	1.37797e6	+	4.46082e6i	0.320782	+	1.03845i
$451$			2.35710e6i			0.545678i
$452$		−	1.50116e6i		−	0.345606i
$453$	1.18766e6	+	7.86870e6i	0.271923	+	1.80160i
$454$		−	1.75449e6i		−	0.399495i
$455$		0			0
$456$	394226.	+	2.61190e6i	0.0887836	+	0.588227i
$457$	2.12525e6			0.476013			0.238007	−	0.971264i	$-0.423506\pi$
$457$	2.12525e6			0.476013			0.238007	+	0.971264i	$0.423506\pi$
$458$	−4.09970e6			−0.913248
$459$	3.49796e6	+	7.25224e6i	0.774968	+	1.60672i
$460$			486765.i			0.107257i
$461$	−2.43758e6			−0.534202			−0.267101	−	0.963669i	$-0.586066\pi$
$461$	−2.43758e6			−0.534202			−0.267101	+	0.963669i	$0.586066\pi$
$462$		0			0
$463$	860872.			0.186632			0.0933160	−	0.995637i	$-0.470253\pi$
$463$	860872.			0.186632			0.0933160	+	0.995637i	$0.470253\pi$
$464$		−	7.06103e6i		−	1.52256i
$465$	−1.17706e6	+	177658.i	−0.252444	+	0.0381024i
$466$	−4.56793e6			−0.974438
$467$	−4.54709e6			−0.964808			−0.482404	−	0.875949i	$-0.660236\pi$
$467$	−4.54709e6			−0.964808			−0.482404	+	0.875949i	$0.660236\pi$
$468$	−169652.	−	549204.i	−0.0358051	−	0.115910i
$469$		0			0
$470$		−	1.35276e6i		−	0.282473i
$471$	−3.51634e6	+	530736.i	−0.730363	+	0.110237i
$472$		−	5.42702e6i		−	1.12126i
$473$		−	4.46282e6i		−	0.917183i
$474$	3.42118e6	−	516374.i	0.699408	−	0.105565i
$475$		−	3.58580e6i		−	0.729209i
$476$		0			0
$477$	−1.74377e6	−	5.64500e6i	−0.350909	−	1.13597i
$478$	−2.17242e6			−0.434884
$479$	9.92765e6			1.97700			0.988502	−	0.151205i	$-0.0483155\pi$
$479$	9.92765e6			1.97700			0.988502	+	0.151205i	$0.0483155\pi$
$480$	790991.	−	119388.i	0.156700	−	0.0236514i
$481$			82082.5i			0.0161766i
$482$	5.97340e6			1.17113
$483$		0			0
$484$	−1.23812e6			−0.240241
$485$			1.35229e6i			0.261045i
$486$	4.40883e6	−	4.09917e6i	0.846707	−	0.787237i
$487$	6.45121e6			1.23259			0.616295	−	0.787515i	$-0.288633\pi$
$487$	6.45121e6			1.23259			0.616295	+	0.787515i	$0.288633\pi$
$488$	−1.94943e6			−0.370559
$489$	−449239.	−	2.97639e6i	−0.0849582	−	0.562882i
$490$		0			0
$491$		−	2.49579e6i		−	0.467202i	−0.972333	−	0.233601i	$-0.924949\pi$
$491$		−	2.49579e6i		−	0.467202i	0.972333	−	0.233601i	$-0.0750509\pi$
$492$	−275077.	−	1.82249e6i	−0.0512320	−	0.339433i
$493$			1.19815e7i			2.22020i
$494$			1.75283e6i			0.323163i
$495$	−210769.	−	682309.i	−0.0386629	−	0.125161i
$496$		−	6.99063e6i		−	1.27589i
$497$		0			0
$498$	−1.00436e6	+	151593.i	−0.181475	+	0.0273908i
$499$	−2.95128e6			−0.530590			−0.265295	−	0.964167i	$-0.585469\pi$
$499$	−2.95128e6			−0.530590			−0.265295	+	0.964167i	$0.585469\pi$
$500$	−893742.			−0.159878
$501$	−707746.	−	4.68910e6i	−0.125975	−	0.834632i
$502$		−	722947.i		−	0.128040i
$503$	3.38420e6			0.596398			0.298199	−	0.954504i	$-0.403614\pi$
$503$	3.38420e6			0.596398			0.298199	+	0.954504i	$0.403614\pi$
$504$		0			0
$505$	−1.20408e6			−0.210100
$506$			4.63788e6i			0.805273i
$507$	−751639.	−	4.97991e6i	−0.129864	−	0.860402i
$508$	1.02065e6			0.175476
$509$	7.01495e6			1.20014			0.600068	−	0.799949i	$-0.295140\pi$
$509$	7.01495e6			1.20014			0.600068	+	0.799949i	$0.295140\pi$
$510$	−2.93215e6	+	442562.i	−0.499184	+	0.0753439i
$511$		0			0
$512$		−	867221.i		−	0.146202i
$513$	−4.16449e6	+	2.00865e6i	−0.698664	+	0.336986i
$514$		−	5.17702e6i		−	0.864315i
$515$			2.15077e6i			0.357336i
$516$	520817.	+	3.45062e6i	0.0861115	+	0.570523i
$517$		−	3.24629e6i		−	0.534146i
$518$		0			0
$519$	1.23561e6	+	8.18639e6i	0.201355	+	1.33406i
$520$	−417125.			−0.0676485
$521$	523192.			0.0844436			0.0422218	−	0.999108i	$-0.486556\pi$
$521$	523192.			0.0844436			0.0422218	+	0.999108i	$0.486556\pi$
$522$	8.55911e6	−	2.64396e6i	1.37484	−	0.424696i
$523$		−	2.67455e6i		−	0.427559i	−0.976882	−	0.213779i	$-0.931423\pi$
$523$		−	2.67455e6i		−	0.427559i	0.976882	−	0.213779i	$-0.0685774\pi$
$524$	940825.			0.149686
$525$		0			0
$526$	−1.33208e7			−2.09926
$527$			1.18620e7i			1.86051i
$528$	4.14676e6	−	625888.i	0.647328	−	0.0977039i
$529$	−4.46687e6			−0.694007
$530$	2.17591e6			0.336474
$531$	9.07616e6	−	2.80368e6i	1.39690	−	0.431511i
$532$		0			0
$533$			2.40993e6i			0.367440i
$534$	1.16707e7	−	1.76151e6i	1.77110	−	0.267320i
$535$		−	385431.i		−	0.0582187i
$536$		−	6.18296e6i		−	0.929575i
$537$	−8.51337e6	+	1.28496e6i	−1.27399	+	0.192289i
$538$		−	1.05368e7i		−	1.56947i
$539$		0			0
$540$	242592.	+	502960.i	0.0358008	+	0.0742248i
$541$	6.47264e6			0.950798			0.475399	−	0.879770i	$-0.342304\pi$
$541$	6.47264e6			0.950798			0.475399	+	0.879770i	$0.342304\pi$
$542$	9.43894e6			1.38015
$543$	1.09908e7	−	1.65889e6i	1.59967	−	0.241445i
$544$		−	7.97137e6i		−	1.15488i
$545$	149021.			0.0214909
$546$		0			0
$547$	5.63101e6			0.804671			0.402335	−	0.915492i	$-0.368199\pi$
$547$	5.63101e6			0.804671			0.402335	+	0.915492i	$0.368199\pi$
$548$		−	1.64464e6i		−	0.233948i
$549$	−1.00710e6	−	3.26023e6i	−0.142608	−	0.461655i
$550$	−4.12627e6			−0.581635
$551$	−6.88018e6			−0.965429
$552$	1.06648e6	+	7.06583e6i	0.148972	+	0.986996i
$553$		0			0
$554$			1.29506e7i			1.79273i
$555$	−11900.8	−	78847.3i	−0.00163999	−	0.0108656i
$556$			2.58806e6i			0.355049i
$557$		−	8.24134e6i		−	1.12554i	−0.826614	−	0.562769i	$-0.809736\pi$
$557$		−	8.24134e6i		−	1.12554i	0.826614	−	0.562769i	$-0.190264\pi$
$558$	8.47378e6	−	2.61760e6i	1.15210	−	0.355891i
$559$		−	4.56284e6i		−	0.617598i
$560$		0			0
$561$	−7.03640e6	+	1.06203e6i	−0.943938	+	0.142473i
$562$	−758662.			−0.101323
$563$	−6.84376e6			−0.909964			−0.454982	−	0.890501i	$-0.650354\pi$
$563$	−6.84376e6			−0.909964			−0.454982	+	0.890501i	$0.650354\pi$
$564$	378846.	+	2.51001e6i	0.0501494	+	0.332260i
$565$		−	1.90678e6i		−	0.251293i
$566$	−4.85925e6			−0.637571
$567$		0			0
$568$	−5.76480e6			−0.749745
$569$			4.31871e6i			0.559208i	0.960115	+	0.279604i	$0.0902032\pi$
$569$			4.31871e6i			0.559208i	−0.960115	+	0.279604i	$0.909797\pi$
$570$	−254134.	−	1.68374e6i	−0.0327624	−	0.217064i
$571$	1.07499e7			1.37979			0.689894	−	0.723910i	$-0.257657\pi$
$571$	1.07499e7			1.37979			0.689894	+	0.723910i	$0.257657\pi$
$572$	508015.			0.0649211
$573$	5.83181e6	−	880221.i	0.742023	−	0.111997i
$574$		0			0
$575$		−	9.70046e6i		−	1.22355i
$576$	3.61245e6	−	1.11591e6i	0.453676	−	0.140143i
$577$			1.33918e7i			1.67455i	0.546780	+	0.837276i	$0.315853\pi$
$577$			1.33918e7i			1.67455i	−0.546780	+	0.837276i	$0.684147\pi$
$578$			2.02633e7i			2.52284i
$579$	1.09808e6	+	7.27524e6i	0.136125	+	0.901885i
$580$			830943.i			0.102566i
$581$		0			0
$582$	−1.50365e6	−	9.96228e6i	−0.184009	−	1.21913i
$583$	5.22163e6			0.636260
$584$	−397614.			−0.0482424
$585$	−215493.	−	697602.i	−0.0260342	−	0.0842787i
$586$		−	1.29187e6i		−	0.155409i
$587$	−1.59393e7			−1.90930			−0.954652	−	0.297723i	$-0.903773\pi$
$587$	−1.59393e7			−1.90930			−0.954652	+	0.297723i	$0.903773\pi$
$588$		0			0
$589$	−6.81158e6			−0.809020
$590$			3.49848e6i			0.413761i
$591$	897791.	−	135508.i	0.105732	−	0.0159586i
$592$	468281.			0.0549164
$593$	1.24008e7			1.44815			0.724076	−	0.689720i	$-0.242266\pi$
$593$	1.24008e7			1.44815			0.724076	+	0.689720i	$0.242266\pi$
$594$	2.31141e6	+	4.79218e6i	0.268788	+	0.557272i
$595$		0			0
$596$			3.68485e6i			0.424917i
$597$	−71664.0	+	10816.6i	−0.00822934	+	0.00124209i
$598$			4.74183e6i			0.542242i
$599$		−	1.42156e6i		−	0.161882i	−0.996719	−	0.0809412i	$-0.974207\pi$
$599$		−	1.42156e6i		−	0.161882i	0.996719	−	0.0809412i	$-0.0257926\pi$
$600$	−6.28639e6	+	948832.i	−0.712891	+	0.107600i
$601$			1.85823e6i			0.209852i	0.994480	+	0.104926i	$0.0334606\pi$
$601$			1.85823e6i			0.209852i	−0.994480	+	0.104926i	$0.966539\pi$
$602$		0			0
$603$	1.03404e7	−	3.19421e6i	1.15809	−	0.357742i
$604$	5.49953e6			0.613385
$605$	−1.57266e6			−0.174681
$606$	8.87038e6	−	1.33885e6i	0.981207	−	0.148098i
$607$		−	1.70561e7i		−	1.87892i	−0.342664	−	0.939458i	$-0.611329\pi$
$607$		−	1.70561e7i		−	1.87892i	0.342664	−	0.939458i	$-0.388671\pi$
$608$	4.57744e6			0.502184
$609$		0			0
$610$	1.25668e6			0.136742
$611$		−	3.31904e6i		−	0.359675i
$612$	5.31656e6	−	1.64232e6i	0.573789	−	0.177247i
$613$	−1.17965e7			−1.26795			−0.633977	−	0.773352i	$-0.718579\pi$
$613$	−1.17965e7			−1.26795			−0.633977	+	0.773352i	$0.718579\pi$
$614$	−242129.			−0.0259194
$615$	−349404.	−	2.31494e6i	−0.0372512	−	0.246804i
$616$		0			0
$617$		−	1.66971e7i		−	1.76575i	−0.469610	−	0.882874i	$-0.655606\pi$
$617$		−	1.66971e7i		−	1.76575i	0.469610	−	0.882874i	$-0.344394\pi$
$618$	−2.39150e6	−	1.58447e7i	−0.251883	−	1.66883i
$619$		−	1.19716e7i		−	1.25582i	−0.778287	−	0.627908i	$-0.783911\pi$
$619$		−	1.19716e7i		−	1.25582i	0.778287	−	0.627908i	$-0.216089\pi$
$620$			822658.i			0.0859489i
$621$	−1.12660e7	+	5.43390e6i	−1.17230	+	0.565434i
$622$		−	6.49385e6i		−	0.673017i
$623$		0			0
$624$	4.23970e6	−	639916.i	0.435887	−	0.0657903i
$625$	8.04524e6			0.823833
$626$	−1.42551e7			−1.45390
$627$	−609857.	−	4.04055e6i	−0.0619526	−	0.410461i
$628$			2.45761e6i			0.248665i
$629$	−794599.			−0.0800795
$630$		0			0
$631$	1.00990e7			1.00973			0.504864	−	0.863199i	$-0.331543\pi$
$631$	1.00990e7			1.00973			0.504864	+	0.863199i	$0.331543\pi$
$632$			4.71145e6i			0.469204i
$633$	−611829.	−	4.05361e6i	−0.0606905	−	0.402099i
$634$	−1.49826e7			−1.48035
$635$	1.29643e6			0.127590
$636$	−4.03733e6	+	609372.i	−0.395778	+	0.0597365i
$637$		0			0
$638$			7.91719e6i			0.770051i
$639$	−2.97819e6	−	9.64108e6i	−0.288536	−	0.934057i
$640$			3.03459e6i			0.292853i
$641$			1.32054e7i			1.26942i	0.772750	+	0.634711i	$0.218881\pi$
$641$			1.32054e7i			1.26942i	−0.772750	+	0.634711i	$0.781119\pi$
$642$	428571.	+	2.83945e6i	0.0410379	+	0.271893i
$643$			1.08135e7i			1.03143i	0.856760	+	0.515715i	$0.172474\pi$
$643$			1.08135e7i			1.03143i	−0.856760	+	0.515715i	$0.827526\pi$
$644$		0			0
$645$	661545.	+	4.38300e6i	0.0626123	+	0.414832i
$646$	−1.69682e7			−1.59976
$647$	−1.43826e7			−1.35075			−0.675376	−	0.737474i	$-0.736018\pi$
$647$	−1.43826e7			−1.35075			−0.675376	+	0.737474i	$0.736018\pi$
$648$	4.62340e6	+	6.76941e6i	0.432537	+	0.633305i
$649$			8.39546e6i			0.782407i
$650$	−4.21875e6			−0.391652
$651$		0			0
$652$	−2.08023e6			−0.191643
$653$		−	2.61347e6i		−	0.239848i	−0.992783	−	0.119924i	$-0.961735\pi$
$653$		−	2.61347e6i		−	0.239848i	0.992783	−	0.119924i	$-0.0382650\pi$
$654$	−1.09783e6	+	165700.i	−0.100367	+	0.0151488i
$655$	1.19504e6			0.108838
$656$	1.37486e7			1.24738
$657$	−205413.	−	664970.i	−0.0185659	−	0.0601020i
$658$		0			0
$659$			9.51511e6i			0.853494i	0.904371	+	0.426747i	$0.140340\pi$
$659$			9.51511e6i			0.853494i	−0.904371	+	0.426747i	$0.859660\pi$
$660$	−487991.	+	73654.6i	−0.0436066	+	0.00658173i
$661$		−	4.18215e6i		−	0.372302i	−0.982521	−	0.186151i	$-0.940399\pi$
$661$		−	4.18215e6i		−	0.372302i	0.982521	−	0.186151i	$-0.0596014\pi$
$662$		−	1.12347e7i		−	0.996362i
$663$	−7.19411e6	+	1.08584e6i	−0.635614	+	0.0959359i
$664$		−	1.38315e6i		−	0.121744i
$665$		0			0
$666$	175345.	+	567632.i	0.0153182	+	0.0495885i
$667$	−1.86126e7			−1.61991
$668$	−3.27727e6			−0.284165
$669$	−8.92322e6	+	1.34682e6i	−0.770826	+	0.116344i
$670$			3.98579e6i			0.343027i
$671$	3.01572e6			0.258574
$672$		0			0
$673$	−9.30210e6			−0.791669			−0.395834	−	0.918322i	$-0.629545\pi$
$673$	−9.30210e6			−0.791669			−0.395834	+	0.918322i	$0.629545\pi$
$674$		−	1.39677e7i		−	1.18434i
$675$	−4.83447e6	−	1.00232e7i	−0.408404	−	0.846734i
$676$	−3.48052e6			−0.292939
$677$	−1.55632e7			−1.30505			−0.652527	−	0.757765i	$-0.726291\pi$
$677$	−1.55632e7			−1.30505			−0.652527	+	0.757765i	$0.726291\pi$
$678$	2.12020e6	+	1.40472e7i	0.177135	+	1.17359i
$679$		0			0
$680$		−	4.03798e6i		−	0.334882i
$681$	624117.	+	4.13502e6i	0.0515701	+	0.341673i
$682$			7.83825e6i			0.645295i
$683$		−	453291.i		−	0.0371813i	−0.999827	−	0.0185907i	$-0.994082\pi$
$683$		−	453291.i		−	0.0371813i	0.999827	−	0.0185907i	$-0.00591794\pi$
$684$	943076.	+	3.05296e6i	0.0770738	+	0.249506i
$685$		−	2.08903e6i		−	0.170106i
$686$		0			0
$687$	9.66227e6	−	1.45837e6i	0.781066	−	0.117890i
$688$	−2.60310e7			−2.09662
$689$	5.33866e6			0.428434
$690$	−687495.	−	4.55493e6i	−0.0549727	−	0.364216i
$691$		−	5.01610e6i		−	0.399642i	−0.979832	−	0.199821i	$-0.935964\pi$
$691$		−	5.01610e6i		−	0.399642i	0.979832	−	0.199821i	$-0.0640361\pi$
$692$	5.72157e6			0.454203
$693$		0			0
$694$	2.05064e7			1.61618
$695$			3.28737e6i			0.258159i
$696$	1.82055e6	+	1.20619e7i	0.142456	+	0.943826i
$697$	−2.33293e7			−1.81894
$698$	−1.13365e7			−0.880729
$699$	1.07658e7	−	1.62493e6i	0.833400	−	0.125789i
$700$		0			0
$701$		−	6.60749e6i		−	0.507857i	−0.967223	−	0.253929i	$-0.918277\pi$
$701$		−	6.60749e6i		−	0.507857i	0.967223	−	0.253929i	$-0.0817228\pi$
$702$	2.36321e6	+	4.89959e6i	0.180992	+	0.375247i
$703$		−	456286.i		−	0.0348216i
$704$			3.34152e6i			0.254105i
$705$	481212.	+	3.18822e6i	0.0364640	+	0.241588i
$706$			1.33715e7i			1.00964i
$707$		0			0
$708$	−979763.	−	6.49132e6i	−0.0734578	−	0.486687i
$709$	2.58924e7			1.93444			0.967222	−	0.253932i	$-0.0817239\pi$
$709$	2.58924e7			1.93444			0.967222	+	0.253932i	$0.0817239\pi$
$710$	3.71623e6			0.276667
$711$	−7.87944e6	+	2.43401e6i	−0.584550	+	0.180571i
$712$			1.60722e7i			1.18816i
$713$	−1.84270e7			−1.35747
$714$		0			0
$715$	645282.			0.0472046
$716$			5.95010e6i			0.433752i
$717$	5.12001e6	−	772785.i	0.371940	−	0.0561385i
$718$	1.12199e7			0.812227
$719$	1.80330e7			1.30091			0.650455	−	0.759545i	$-0.274578\pi$
$719$	1.80330e7			1.30091			0.650455	+	0.759545i	$0.274578\pi$
$720$	−3.97982e6	+	1.22939e6i	−0.286109	+	0.0883808i
$721$		0			0
$722$			6.45019e6i			0.460500i
$723$	−1.40782e7	+	2.12489e6i	−1.00162	+	0.151179i
$724$		−	7.68161e6i		−	0.544635i
$725$		−	1.65594e7i		−	1.17004i
$726$	1.15857e7	−	1.74868e6i	0.815796	−	0.123132i
$727$			2.03511e7i			1.42808i	0.700107	+	0.714038i	$0.253136\pi$
$727$			2.03511e7i			1.42808i	−0.700107	+	0.714038i	$0.746864\pi$
$728$		0			0
$729$	−8.93266e6	+	1.12294e7i	−0.622533	+	0.782594i
$730$	256318.			0.0178021
$731$	4.41705e7			3.05731
$732$	−2.33174e6	+	351939.i	−0.160843	+	0.0242767i
$733$		−	3.00997e6i		−	0.206920i	−0.994634	−	0.103460i	$-0.967009\pi$
$733$		−	3.00997e6i		−	0.206920i	0.994634	−	0.103460i	$-0.0329913\pi$
$734$	385720.			0.0264260
$735$		0			0
$736$	1.23831e7			0.842625
$737$			9.56488e6i			0.648651i
$738$	5.14809e6	+	1.66656e7i	0.347941	+	1.12636i
$739$	−2.82754e6			−0.190457			−0.0952287	−	0.995455i	$-0.530358\pi$
$739$	−2.82754e6			−0.190457			−0.0952287	+	0.995455i	$0.530358\pi$
$740$	−55107.3			−0.00369939
$741$	−623526.	−	4.13111e6i	−0.0417166	−	0.276389i
$742$		0			0
$743$			8.50642e6i			0.565295i	0.959224	+	0.282647i	$0.0912126\pi$
$743$			8.50642e6i			0.565295i	−0.959224	+	0.282647i	$0.908787\pi$
$744$	1.80240e6	+	1.19416e7i	0.119376	+	0.790917i
$745$			4.68051e6i			0.308960i
$746$		−	9.58742e6i		−	0.630746i
$747$	2.31318e6	−	714555.i	0.151673	−	0.0468527i
$748$			4.91783e6i			0.321380i
$749$		0			0
$750$	8.36323e6	−	1.26230e6i	0.542902	−	0.0819425i
$751$	8.89808e6			0.575701			0.287850	−	0.957675i	$-0.407059\pi$
$751$	8.89808e6			0.575701			0.287850	+	0.957675i	$0.407059\pi$
$752$	−1.89351e7			−1.22102
$753$	257171.	+	1.70386e6i	0.0165285	+	0.109508i
$754$			8.09464e6i			0.518524i
$755$	6.98553e6			0.445997
$756$		0			0
$757$	6.17988e6			0.391959			0.195979	−	0.980608i	$-0.437211\pi$
$757$	6.17988e6			0.391959			0.195979	+	0.980608i	$0.437211\pi$
$758$			8.10351e6i			0.512272i
$759$	−1.64981e6	−	1.09307e7i	−0.103951	−	0.688719i
$760$	2.31875e6			0.145619
$761$	5.57067e6			0.348695			0.174347	−	0.984684i	$-0.444218\pi$
$761$	5.57067e6			0.348695			0.174347	+	0.984684i	$0.444218\pi$
$762$	−9.55078e6	+	1.44154e6i	−0.595870	+	0.0899372i
$763$		0			0
$764$		−	4.07593e6i		−	0.252635i
$765$	6.75312e6	−	2.08608e6i	0.417207	−	0.128878i
$766$			2.45415e7i			1.51123i
$767$			8.58363e6i			0.526844i
$768$	−2.21590e6	−	1.46812e7i	−0.135565	−	0.898170i
$769$			9.05216e6i			0.551996i	0.961158	+	0.275998i	$0.0890084\pi$
$769$			9.05216e6i			0.551996i	−0.961158	+	0.275998i	$0.910992\pi$
$770$		0			0
$771$	1.84160e6	+	1.22013e7i	0.111573	+	0.739215i
$772$	5.08476e6			0.307063
$773$	1.74174e7			1.04842			0.524208	−	0.851590i	$-0.324361\pi$
$773$	1.74174e7			1.04842			0.524208	+	0.851590i	$0.324361\pi$
$774$	−9.74715e6	−	3.15538e7i	−0.584824	−	1.89321i
$775$		−	1.63943e7i		−	0.980478i
$776$	1.37195e7			0.817867
$777$		0			0
$778$	−3.40443e7			−2.01649
$779$		−	1.33965e7i		−	0.790946i
$780$	−498929.	+	75305.4i	−0.0293631	+	0.00443190i
$781$	8.91801e6			0.523167
$782$	−4.59032e7			−2.68427
$783$	−1.92318e7	+	9.27604e6i	−1.12103	+	0.540703i
$784$		0			0
$785$			3.12167e6i			0.180806i
$786$	−8.80382e6	+	1.32880e6i	−0.508293	+	0.0767189i
$787$		−	2.46984e7i		−	1.42145i	−0.703470	−	0.710725i	$-0.748367\pi$
$787$		−	2.46984e7i		−	1.42145i	0.703470	−	0.710725i	$-0.251633\pi$
$788$		−	627477.i		−	0.0359984i
$789$	3.13947e7	−	4.73854e6i	1.79541	−	0.270989i
$790$		−	3.03719e6i		−	0.173143i
$791$		0			0
$792$	−6.92225e6	+	2.13832e6i	−0.392134	+	0.121132i
$793$	3.08331e6			0.174114
$794$	−4.53335e6			−0.255193
$795$	−5.12824e6	+	774027.i	−0.287773	+	0.0434349i
$796$			50086.8i			0.00280182i
$797$	3.00275e7			1.67445			0.837226	−	0.546857i	$-0.184176\pi$
$797$	3.00275e7			1.67445			0.837226	+	0.546857i	$0.184176\pi$
$798$		0			0
$799$	3.21300e7			1.78051
$800$			1.10171e7i			0.608614i
$801$	−2.68792e7	+	8.30313e6i	−1.48025	+	0.457257i
$802$	3.60688e7			1.98014
$803$	615098.			0.0336632
$804$	−1.11624e6	−	7.39551e6i	−0.0608998	−	0.403486i
$805$		0			0
$806$			8.01393e6i			0.434518i
$807$	3.74821e6	+	2.48334e7i	0.202600	+	1.34231i
$808$			1.22158e7i			0.658252i
$809$		−	4.00234e6i		−	0.215002i	−0.994205	−	0.107501i	$-0.965715\pi$
$809$		−	4.00234e6i		−	0.215002i	0.994205	−	0.107501i	$-0.0342849\pi$
$810$	−2.98043e6	−	4.36384e6i	−0.159613	−	0.233699i
$811$		−	2.52234e7i		−	1.34664i	−0.739352	−	0.673319i	$-0.764868\pi$
$811$		−	2.52234e7i		−	1.34664i	0.739352	−	0.673319i	$-0.235132\pi$
$812$		0			0
$813$	−2.22459e7	+	3.35767e6i	−1.18039	+	0.178161i
$814$	−525060.			−0.0277746
$815$	−2.64232e6			−0.139345
$816$	6.19470e6	+	4.10424e7i	0.325683	+	2.15778i
$817$			2.53643e7i			1.32943i
$818$	−5.53752e6			−0.289355
$819$		0			0
$820$	−1.61794e6			−0.0840287
$821$		−	2.33112e7i		−	1.20700i	−0.797363	−	0.603500i	$-0.793772\pi$
$821$		−	2.33112e7i		−	1.20700i	0.797363	−	0.603500i	$-0.206228\pi$
$822$	2.32285e6	+	1.53898e7i	0.119906	+	0.794427i
$823$	1.66216e7			0.855409			0.427705	−	0.903919i	$-0.359322\pi$
$823$	1.66216e7			0.855409			0.427705	+	0.903919i	$0.359322\pi$
$824$	2.18203e7			1.11955
$825$	9.72489e6	−	1.46782e6i	0.497450	−	0.0750823i
$826$		0			0
$827$		−	314522.i		−	0.0159915i	−0.999968	−	0.00799573i	$-0.997455\pi$
$827$		−	314522.i		−	0.0159915i	0.999968	−	0.00799573i	$-0.00254515\pi$
$828$	2.55125e6	+	8.25899e6i	0.129323	+	0.418650i
$829$		−	2.81284e7i		−	1.42154i	−0.703426	−	0.710769i	$-0.748347\pi$
$829$		−	2.81284e7i		−	1.42154i	0.703426	−	0.710769i	$-0.251653\pi$
$830$			891635.i			0.0449254i
$831$	−4.60687e6	−	3.05223e7i	−0.231421	−	1.53326i
$832$			3.41641e6i			0.171105i
$833$		0			0
$834$	−3.65532e6	−	2.42179e7i	−0.181974	−	1.20565i
$835$	−4.16280e6			−0.206619
$836$	−2.82399e6			−0.139749
$837$	−1.90401e7	+	9.18356e6i	−0.939408	+	0.453103i
$838$			1.01578e7i			0.499678i
$839$	−673488.			−0.0330313			−0.0165156	−	0.999864i	$-0.505257\pi$
$839$	−673488.			−0.0330313			−0.0165156	+	0.999864i	$0.505257\pi$
$840$		0			0
$841$	−1.12618e7			−0.549057
$842$		−	2.43498e7i		−	1.18363i
$843$	1.78803e6	−	269876.i	0.0866576	−	0.0130796i
$844$	−2.83312e6			−0.136902
$845$	−4.42097e6			−0.212998
$846$	−7.09015e6	−	2.29524e7i	−0.340588	−	1.10256i
$847$		0			0
$848$		−	3.04570e7i		−	1.45445i
$849$	1.14524e7	−	1.72856e6i	0.545290	−	0.0823030i
$850$		−	4.08396e7i		−	1.93880i
$851$		−	1.23437e6i		−	0.0584279i
$852$	−6.89535e6	+	1.04075e6i	−0.325430	+	0.0491185i
$853$		−	1.51428e7i		−	0.712579i	−0.934376	−	0.356289i	$-0.884042\pi$
$853$		−	1.51428e7i		−	0.712579i	0.934376	−	0.356289i	$-0.115958\pi$
$854$		0			0
$855$	1.19790e6	+	3.87788e6i	0.0560409	+	0.181417i
$856$	−3.91033e6			−0.182402
$857$	−2.02980e7			−0.944062			−0.472031	−	0.881582i	$-0.656479\pi$
$857$	−2.02980e7			−0.944062			−0.472031	+	0.881582i	$0.656479\pi$
$858$	−4.75377e6	+	717507.i	−0.220455	+	0.0332742i
$859$		−	5.92069e6i		−	0.273772i	−0.990587	−	0.136886i	$-0.956291\pi$
$859$		−	5.92069e6i		−	0.273772i	0.990587	−	0.136886i	$-0.0437094\pi$
$860$	3.06333e6			0.141237
$861$		0			0
$862$	−7.40617e6			−0.339489
$863$		−	3.06323e7i		−	1.40008i	−0.714103	−	0.700041i	$-0.753165\pi$
$863$		−	3.06323e7i		−	1.40008i	0.714103	−	0.700041i	$-0.246835\pi$
$864$	1.27951e7	−	6.17143e6i	0.583120	−	0.281256i
$865$	7.26757e6			0.330254
$866$	−2.58033e7			−1.16918
$867$	−7.20817e6	−	4.77570e7i	−0.325670	−	2.15769i
$868$		0			0
$869$		−	7.28849e6i		−	0.327407i
$870$	−1.17360e6	−	7.77559e6i	−0.0525682	−	0.348285i
$871$			9.77926e6i			0.436778i
$872$		−	1.51186e6i		−	0.0673319i
$873$	7.08768e6	+	2.29445e7i	0.314752	+	1.01892i
$874$		−	2.63592e7i		−	1.16722i
$875$		0			0
$876$	−475590.	+	71782.9i	−0.0209398	+	0.00316054i
$877$	2.62128e7			1.15084			0.575419	−	0.817859i	$-0.304839\pi$
$877$	2.62128e7			1.15084			0.575419	+	0.817859i	$0.304839\pi$
$878$	2.58684e7			1.13249
$879$	459553.	+	3.04472e6i	0.0200615	+	0.132915i
$880$		−	3.68133e6i		−	0.160250i
$881$	−6.70446e6			−0.291021			−0.145510	−	0.989357i	$-0.546482\pi$
$881$	−6.70446e6			−0.291021			−0.145510	+	0.989357i	$0.546482\pi$
$882$		0			0
$883$	−9.02754e6			−0.389644			−0.194822	−	0.980839i	$-0.562413\pi$
$883$	−9.02754e6			−0.389644			−0.194822	+	0.980839i	$0.562413\pi$
$884$			5.02805e6i			0.216406i
$885$	−1.24450e6	−	8.24530e6i	−0.0534117	−	0.353874i
$886$	3.64873e7			1.56156
$887$	2.22675e7			0.950306			0.475153	−	0.879903i	$-0.342393\pi$
$887$	2.22675e7			0.950306			0.475153	+	0.879903i	$0.342393\pi$
$888$	−799932.	+	120737.i	−0.0340424	+	0.00513817i
$889$		0			0
$890$		−	1.03608e7i		−	0.438448i
$891$	−7.15228e6	−	1.04721e7i	−0.301822	−	0.441916i
$892$			6.23655e6i			0.262441i
$893$			1.84501e7i			0.774232i
$894$	−5.20438e6	−	3.44811e7i	−0.217784	−	1.44290i
$895$			7.55784e6i			0.315384i
$896$		0			0
$897$	−1.68679e6	−	1.11757e7i	−0.0699971	−	0.463759i
$898$	−7.03772e6			−0.291233
$899$	−3.14562e7			−1.29810
$900$	−7.34793e6	+	2.26982e6i	−0.302384	+	0.0934082i
$901$			5.16808e7i			2.12089i
$902$	−1.54157e7			−0.630879
$903$		0			0
$904$	−1.93450e7			−0.787312
$905$		−	9.75721e6i		−	0.396008i
$906$	−5.14621e7	+	7.76739e6i	−2.08289	+	0.314380i
$907$	3.88768e6			0.156918			0.0784590	−	0.996917i	$-0.475000\pi$
$907$	3.88768e6			0.156918			0.0784590	+	0.996917i	$0.475000\pi$
$908$	2.89002e6			0.116328
$909$	−2.04297e7	+	6.31085e6i	−0.820071	+	0.253325i
$910$		0			0
$911$		−	4.73756e6i		−	0.189129i	−0.995519	−	0.0945646i	$-0.969854\pi$
$911$		−	4.73756e6i		−	0.189129i	0.995519	−	0.0945646i	$-0.0301459\pi$
$912$	−2.35680e7	+	3.55721e6i	−0.938285	+	0.141619i
$913$			2.13970e6i			0.0849523i
$914$			1.38993e7i			0.550337i
$915$	−2.96178e6	+	447034.i	−0.116950	+	0.0176518i
$916$		−	6.75308e6i		−	0.265928i
$917$		0			0
$918$	−4.74304e7	+	2.28770e7i	−1.85759	+	0.895970i
$919$	3.21381e7			1.25525			0.627626	−	0.778515i	$-0.284027\pi$
$919$	3.21381e7			1.25525			0.627626	+	0.778515i	$0.284027\pi$
$920$	6.27277e6			0.244337
$921$	570655.	−	86131.5i	0.0221679	−	0.00334590i
$922$		−	1.59420e7i		−	0.617611i
$923$	9.11789e6			0.352282
$924$		0			0
$925$	1.09820e6			0.0422015
$926$			5.63019e6i			0.215772i
$927$	1.12727e7	+	3.64923e7i	0.430852	+	1.39477i
$928$	2.11388e7			0.805768
$929$	−2.91091e7			−1.10660			−0.553298	−	0.832984i	$-0.686631\pi$
$929$	−2.91091e7			−1.10660			−0.553298	+	0.832984i	$0.686631\pi$
$930$	−1.16190e6	−	7.69806e6i	−0.0440516	−	0.291860i
$931$		0			0
$932$		−	7.52435e6i		−	0.283746i
$933$	2.31003e6	+	1.53049e7i	0.0868787	+	0.575606i
$934$		−	2.97384e7i		−	1.11545i
$935$			6.24665e6i			0.233678i
$936$	−7.07740e6	+	2.18625e6i	−0.264049	+	0.0815662i
$937$			4.78152e6i			0.177917i	0.996035	+	0.0889583i	$0.0283538\pi$
$937$			4.78152e6i			0.177917i	−0.996035	+	0.0889583i	$0.971646\pi$
$938$		0			0
$939$	3.35968e7	−	5.07092e6i	1.24347	−	0.187682i
$940$	2.22829e6			0.0822530
$941$	4.59812e6			0.169280			0.0846401	−	0.996412i	$-0.473026\pi$
$941$	4.59812e6			0.169280			0.0846401	+	0.996412i	$0.473026\pi$
$942$	−3.47107e6	−	2.29972e7i	−0.127449	−	0.844400i
$943$		−	3.62407e7i		−	1.32714i
$944$	4.89696e7			1.78853
$945$		0			0
$946$	2.91873e7			1.06039
$947$			2.07134e7i			0.750543i	0.926915	+	0.375271i	$0.122450\pi$
$947$			2.07134e7i			0.750543i	−0.926915	+	0.375271i	$0.877550\pi$
$948$	850578.	+	5.63542e6i	0.0307393	+	0.203660i
$949$	628884.			0.0226676
$950$	2.34515e7			0.843066
$951$	3.53113e7	−	5.32969e6i	1.26608	−	0.191096i
$952$		0			0
$953$			3.05528e7i			1.08973i	0.838524	+	0.544865i	$0.183419\pi$
$953$			3.05528e7i			1.08973i	−0.838524	+	0.544865i	$0.816581\pi$
$954$	3.69189e7	−	1.14045e7i	1.31334	−	0.405699i
$955$		−	5.17726e6i		−	0.183693i
$956$		−	3.57844e6i		−	0.126634i
$957$	−2.81635e6	−	1.86594e7i	−0.0994046	−	0.658595i
$958$			6.49279e7i			2.28569i
$959$		0			0
$960$	−495329.	−	3.28176e6i	−0.0173467	−	0.114929i
$961$	−2.51338e6			−0.0877911
$962$	−536828.			−0.0187024
$963$	−2.02013e6	−	6.53964e6i	−0.0701963	−	0.227242i
$964$			9.83946e6i			0.341019i
$965$	6.45868e6			0.223268
$966$		0			0
$967$	−2.08371e7			−0.716590			−0.358295	−	0.933608i	$-0.616642\pi$
$967$	−2.08371e7			−0.716590			−0.358295	+	0.933608i	$0.616642\pi$
$968$			1.59552e7i			0.547284i
$969$	3.99911e7	−	6.03604e6i	1.36822	−	0.206511i
$970$	−8.84413e6			−0.301805
$971$	1.45477e7			0.495162			0.247581	−	0.968867i	$-0.420364\pi$
$971$	1.45477e7			0.495162			0.247581	+	0.968867i	$0.420364\pi$
$972$	6.75221e6	+	7.26229e6i	0.229235	+	0.246552i
$973$		0			0
$974$			4.21916e7i			1.42504i
$975$	9.94285e6	−	1.50072e6i	0.334965	−	0.0505577i
$976$		−	1.75903e7i		−	0.591082i
$977$		−	7.99910e6i		−	0.268105i	−0.990974	−	0.134052i	$-0.957201\pi$
$977$		−	7.99910e6i		−	0.268105i	0.990974	−	0.134052i	$-0.0427990\pi$
$978$	1.94659e7	−	2.93807e6i	0.650769	−	0.0982234i
$979$		−	2.48633e7i		−	0.829089i
$980$		0			0
$981$	2.52844e6	−	781051.i	0.0838843	−	0.0259124i
$982$	1.63227e7			0.540149
$983$	4.53255e6			0.149609			0.0748047	−	0.997198i	$-0.476167\pi$
$983$	4.53255e6			0.149609			0.0748047	+	0.997198i	$0.476167\pi$
$984$	−2.34858e7	+	3.54482e6i	−0.773247	+	0.116710i
$985$		−	797025.i		−	0.0261747i
$986$	−7.83600e7			−2.56686
$987$		0			0
$988$	−2.88728e6			−0.0941016
$989$			6.86165e7i			2.23068i
$990$	4.46237e6	−	1.37845e6i	0.144703	−	0.0446996i
$991$	9.67681e6			0.313003			0.156501	−	0.987678i	$-0.449978\pi$
$991$	9.67681e6			0.313003			0.156501	+	0.987678i	$0.449978\pi$
$992$	2.09280e7			0.675226
$993$	3.99648e6	+	2.64783e7i	0.128619	+	0.852150i
$994$		0			0
$995$			63620.5i			0.00203723i
$996$	−249706.	−	1.65440e6i	−0.00797591	−	0.0528436i
$997$			2.97775e7i			0.948748i	0.880323	+	0.474374i	$0.157326\pi$
$997$			2.97775e7i			0.948748i	−0.880323	+	0.474374i	$0.842674\pi$
$998$		−	1.93017e7i		−	0.613435i
$999$	−615178.	−	1.27543e6i	−0.0195024	−	0.0404338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.d.146.24	yes	40
3.2	odd	2	inner	147.6.c.d.146.17	✓	40
7.6	odd	2	inner	147.6.c.d.146.18	yes	40
21.20	even	2	inner	147.6.c.d.146.23	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.c.d.146.17	✓	40	3.2	odd	2	inner
147.6.c.d.146.18	yes	40	7.6	odd	2	inner
147.6.c.d.146.23	yes	40	21.20	even	2	inner
147.6.c.d.146.24	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+6.54010i q^{2} +(-2.32648 - 15.4139i) q^{3} -10.7729 q^{4} -13.6838 q^{5} +(100.808 - 15.2154i) q^{6} +138.827i q^{8} +(-232.175 + 71.7202i) q^{9} +O(q^{10})\)	\(q+6.54010i q^{2} +(-2.32648 - 15.4139i) q^{3} -10.7729 q^{4} -13.6838 q^{5} +(100.808 - 15.2154i) q^{6} +138.827i q^{8} +(-232.175 + 71.7202i) q^{9} -89.4937i q^{10} -214.762i q^{11} +(25.0631 + 166.053i) q^{12} -219.576i q^{13} +(31.8352 + 210.921i) q^{15} -1252.68 q^{16} +2125.60 q^{17} +(-469.058 - 1518.45i) q^{18} +1220.59i q^{19} +147.415 q^{20} +1404.57 q^{22} +3302.00i q^{23} +(2139.86 - 322.979i) q^{24} -2937.75 q^{25} +1436.05 q^{26} +(1645.64 + 3411.86i) q^{27} +5636.75i q^{29} +(-1379.45 + 208.206i) q^{30} +5580.55i q^{31} -3750.17i q^{32} +(-3310.32 + 499.640i) q^{33} +13901.6i q^{34} +(2501.21 - 772.638i) q^{36} -373.824 q^{37} -7982.80 q^{38} +(-3384.51 + 510.839i) q^{39} -1899.69i q^{40} -10975.4 q^{41} +20780.3 q^{43} +2313.62i q^{44} +(3177.05 - 981.408i) q^{45} -21595.4 q^{46} +15115.7 q^{47} +(2914.33 + 19308.6i) q^{48} -19213.2i q^{50} +(-4945.17 - 32763.7i) q^{51} +2365.48i q^{52} +24313.5i q^{53} +(-22313.9 + 10762.6i) q^{54} +2938.77i q^{55} +(18814.1 - 2839.69i) q^{57} -36864.9 q^{58} -39091.9 q^{59} +(-342.959 - 2272.24i) q^{60} +14042.1i q^{61} -36497.4 q^{62} -15559.2 q^{64} +3004.64i q^{65} +(-3267.70 - 21649.8i) q^{66} -44537.1 q^{67} -22899.0 q^{68} +(50896.6 - 7682.05i) q^{69} +41525.1i q^{71} +(-9956.71 - 32232.2i) q^{72} +2864.09i q^{73} -2444.84i q^{74} +(6834.63 + 45282.1i) q^{75} -13149.4i q^{76} +(-3340.94 - 22135.0i) q^{78} +33937.5 q^{79} +17141.4 q^{80} +(48761.4 - 33303.3i) q^{81} -71780.2i q^{82} -9963.09 q^{83} -29086.4 q^{85} +135905. i q^{86} +(86884.1 - 13113.8i) q^{87} +29814.8 q^{88} +115771. q^{89} +(6418.51 + 20778.2i) q^{90} -35572.3i q^{92} +(86017.9 - 12983.1i) q^{93} +98858.4i q^{94} -16702.4i q^{95} +(-57804.7 + 8724.71i) q^{96} -98824.0i q^{97} +(15402.8 + 49862.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 640 q^{4} + 440 q^{9}+O(q^{10}) \) 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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