LMFDB - Embedded newform 38.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.a (trivial)

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:	yes
Analytic conductor:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1441}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 360 $ x^2 - x - 360
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$19.4803$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} -64.0000 q^{8} +62.5592 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} -64.0000 q^{8} +62.5592 q^{9} +317.763 q^{10} +311.520 q^{11} -279.684 q^{12} +901.401 q^{13} -531.684 q^{14} +1388.64 q^{15} +256.000 q^{16} -157.803 q^{17} -250.237 q^{18} +361.000 q^{19} -1271.05 q^{20} -2323.49 q^{21} -1246.08 q^{22} -2522.53 q^{23} +1118.74 q^{24} +3185.83 q^{25} -3605.61 q^{26} +3154.15 q^{27} +2126.74 q^{28} +4738.28 q^{29} -5554.58 q^{30} -6587.76 q^{31} -1024.00 q^{32} -5445.44 q^{33} +631.210 q^{34} -10559.3 q^{35} +1000.95 q^{36} +8508.60 q^{37} -1444.00 q^{38} -15756.7 q^{39} +5084.21 q^{40} +19741.1 q^{41} +9293.97 q^{42} +10985.0 q^{43} +4984.32 q^{44} -4969.75 q^{45} +10090.1 q^{46} +15085.5 q^{47} -4474.94 q^{48} +860.995 q^{49} -12743.3 q^{50} +2758.43 q^{51} +14422.4 q^{52} +21699.6 q^{53} -12616.6 q^{54} -24747.4 q^{55} -8506.94 q^{56} -6310.37 q^{57} -18953.1 q^{58} -40676.1 q^{59} +22218.3 q^{60} +6151.79 q^{61} +26351.0 q^{62} +8315.44 q^{63} +4096.00 q^{64} -71608.0 q^{65} +21781.8 q^{66} +62760.3 q^{67} -2524.84 q^{68} +44094.5 q^{69} +42237.4 q^{70} -55311.0 q^{71} -4003.79 q^{72} -48528.1 q^{73} -34034.4 q^{74} -55689.2 q^{75} +5776.00 q^{76} +41407.5 q^{77} +63026.9 q^{78} +31017.6 q^{79} -20336.8 q^{80} -70337.2 q^{81} -78964.4 q^{82} +41068.7 q^{83} -37175.9 q^{84} +12536.0 q^{85} -43939.8 q^{86} -82826.3 q^{87} -19937.3 q^{88} -17065.6 q^{89} +19879.0 q^{90} +119815. q^{91} -40360.5 q^{92} +115156. q^{93} -60341.9 q^{94} -28678.1 q^{95} +17899.8 q^{96} +139045. q^{97} -3443.98 q^{98} +19488.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9} + 180 q^{10} + 661 q^{11} + 48 q^{12} + 1613 q^{13} - 456 q^{14} + 2094 q^{15} + 512 q^{16} + 64 q^{17} - 956 q^{18} + 722 q^{19} - 720 q^{20} - 2711 q^{21} - 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} + 1791 q^{27} + 1824 q^{28} - 2481 q^{29} - 8376 q^{30} - 1180 q^{31} - 2048 q^{32} + 1712 q^{33} - 256 q^{34} - 11211 q^{35} + 3824 q^{36} + 10488 q^{37} - 2888 q^{38} - 1183 q^{39} + 2880 q^{40} + 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} + 12740 q^{46} - 12155 q^{47} + 768 q^{48} - 15588 q^{49} - 4988 q^{50} + 7301 q^{51} + 25808 q^{52} + 20585 q^{53} - 7164 q^{54} - 12711 q^{55} - 7296 q^{56} + 1083 q^{57} + 9924 q^{58} - 78581 q^{59} + 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} - 47100 q^{65} - 6848 q^{66} + 7805 q^{67} + 1024 q^{68} + 30527 q^{69} + 44844 q^{70} - 62488 q^{71} - 15296 q^{72} + 16218 q^{73} - 41952 q^{74} - 95397 q^{75} + 11552 q^{76} + 34795 q^{77} + 4732 q^{78} + 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} - 43376 q^{84} + 20175 q^{85} - 45212 q^{86} - 230679 q^{87} - 42304 q^{88} + 128188 q^{89} - 4428 q^{90} + 106351 q^{91} - 50960 q^{92} + 225908 q^{93} + 48620 q^{94} - 16245 q^{95} - 3072 q^{96} + 178558 q^{97} + 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9 + 180 * q^10 + 661 * q^11 + 48 * q^12 + 1613 * q^13 - 456 * q^14 + 2094 * q^15 + 512 * q^16 + 64 * q^17 - 956 * q^18 + 722 * q^19 - 720 * q^20 - 2711 * q^21 - 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 + 1791 * q^27 + 1824 * q^28 - 2481 * q^29 - 8376 * q^30 - 1180 * q^31 - 2048 * q^32 + 1712 * q^33 - 256 * q^34 - 11211 * q^35 + 3824 * q^36 + 10488 * q^37 - 2888 * q^38 - 1183 * q^39 + 2880 * q^40 + 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 + 12740 * q^46 - 12155 * q^47 + 768 * q^48 - 15588 * q^49 - 4988 * q^50 + 7301 * q^51 + 25808 * q^52 + 20585 * q^53 - 7164 * q^54 - 12711 * q^55 - 7296 * q^56 + 1083 * q^57 + 9924 * q^58 - 78581 * q^59 + 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 - 47100 * q^65 - 6848 * q^66 + 7805 * q^67 + 1024 * q^68 + 30527 * q^69 + 44844 * q^70 - 62488 * q^71 - 15296 * q^72 + 16218 * q^73 - 41952 * q^74 - 95397 * q^75 + 11552 * q^76 + 34795 * q^77 + 4732 * q^78 + 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 - 43376 * q^84 + 20175 * q^85 - 45212 * q^86 - 230679 * q^87 - 42304 * q^88 + 128188 * q^89 - 4428 * q^90 + 106351 * q^91 - 50960 * q^92 + 225908 * q^93 + 48620 * q^94 - 16245 * q^95 - 3072 * q^96 + 178558 * q^97 + 62352 * q^98 + 81151 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−17.4803	−1.12136	−0.560679	−	0.828033i	$-0.689460\pi$
$3$	−17.4803	−1.12136	−0.560679	+	0.828033i	$0.689460\pi$
$4$	16.0000	0.500000
$5$	−79.4408	−1.42108	−0.710540	−	0.703657i	$-0.751549\pi$
$5$	−79.4408	−1.42108	−0.710540	+	0.703657i	$0.751549\pi$
$6$	69.9210	0.792920
$7$	132.921	1.02529	0.512647	−	0.858599i	$-0.328665\pi$
$7$	132.921	1.02529	0.512647	+	0.858599i	$0.328665\pi$
$8$	−64.0000	−0.353553
$9$	62.5592	0.257445
$10$	317.763	1.00485
$11$	311.520	0.776254	0.388127	−	0.921606i	$-0.373122\pi$
$11$	311.520	0.776254	0.388127	+	0.921606i	$0.373122\pi$
$12$	−279.684	−0.560679
$13$	901.401	1.47931	0.739656	−	0.672985i	$-0.234988\pi$
$13$	901.401	1.47931	0.739656	+	0.672985i	$0.234988\pi$
$14$	−531.684	−0.724993
$15$	1388.64	1.59354
$16$	256.000	0.250000
$17$	−157.803	−0.132432	−0.0662158	−	0.997805i	$-0.521093\pi$
$17$	−157.803	−0.132432	−0.0662158	+	0.997805i	$0.521093\pi$
$18$	−250.237	−0.182041
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−1271.05	−0.710540
$21$	−2323.49	−1.14972
$22$	−1246.08	−0.548894
$23$	−2522.53	−0.994299	−0.497150	−	0.867665i	$-0.665620\pi$
$23$	−2522.53	−0.994299	−0.497150	+	0.867665i	$0.665620\pi$
$24$	1118.74	0.396460
$25$	3185.83	1.01947
$26$	−3605.61	−1.04603
$27$	3154.15	0.832670
$28$	2126.74	0.512647
$29$	4738.28	1.04623	0.523113	−	0.852263i	$-0.324770\pi$
$29$	4738.28	1.04623	0.523113	+	0.852263i	$0.324770\pi$
$30$	−5554.58	−1.12680
$31$	−6587.76	−1.23121	−0.615607	−	0.788053i	$-0.711089\pi$
$31$	−6587.76	−1.23121	−0.615607	+	0.788053i	$0.711089\pi$
$32$	−1024.00	−0.176777
$33$	−5445.44	−0.870459
$34$	631.210	0.0936433
$35$	−10559.3	−1.45702
$36$	1000.95	0.128723
$37$	8508.60	1.02177	0.510886	−	0.859648i	$-0.329317\pi$
$37$	8508.60	1.02177	0.510886	+	0.859648i	$0.329317\pi$
$38$	−1444.00	−0.162221
$39$	−15756.7	−1.65884
$40$	5084.21	0.502427
$41$	19741.1	1.83405	0.917027	−	0.398826i	$-0.130582\pi$
$41$	19741.1	1.83405	0.917027	+	0.398826i	$0.130582\pi$
$42$	9293.97	0.812977
$43$	10985.0	0.905997	0.452999	−	0.891511i	$-0.350354\pi$
$43$	10985.0	0.905997	0.452999	+	0.891511i	$0.350354\pi$
$44$	4984.32	0.388127
$45$	−4969.75	−0.365850
$46$	10090.1	0.703076
$47$	15085.5	0.996127	0.498063	−	0.867141i	$-0.334045\pi$
$47$	15085.5	0.996127	0.498063	+	0.867141i	$0.334045\pi$
$48$	−4474.94	−0.280340
$49$	860.995	0.0512284
$50$	−12743.3	−0.720872
$51$	2758.43	0.148503
$52$	14422.4	0.739656
$53$	21699.6	1.06112	0.530558	−	0.847649i	$-0.321982\pi$
$53$	21699.6	1.06112	0.530558	+	0.847649i	$0.321982\pi$
$54$	−12616.6	−0.588787
$55$	−24747.4	−1.10312
$56$	−8506.94	−0.362496
$57$	−6310.37	−0.257257
$58$	−18953.1	−0.739794
$59$	−40676.1	−1.52128	−0.760639	−	0.649175i	$-0.775114\pi$
$59$	−40676.1	−1.52128	−0.760639	+	0.649175i	$0.775114\pi$
$60$	22218.3	0.796770
$61$	6151.79	0.211679	0.105839	−	0.994383i	$-0.466247\pi$
$61$	6151.79	0.211679	0.105839	+	0.994383i	$0.466247\pi$
$62$	26351.0	0.870600
$63$	8315.44	0.263957
$64$	4096.00	0.125000
$65$	−71608.0	−2.10222
$66$	21781.8	0.615508
$67$	62760.3	1.70804	0.854019	−	0.520241i	$-0.174158\pi$
$67$	62760.3	1.70804	0.854019	+	0.520241i	$0.174158\pi$
$68$	−2524.84	−0.0662158
$69$	44094.5	1.11497
$70$	42237.4	1.03027
$71$	−55311.0	−1.30216	−0.651081	−	0.759008i	$-0.725684\pi$
$71$	−55311.0	−1.30216	−0.651081	+	0.759008i	$0.725684\pi$
$72$	−4003.79	−0.0910207
$73$	−48528.1	−1.06583	−0.532913	−	0.846170i	$-0.678903\pi$
$73$	−48528.1	−1.06583	−0.532913	+	0.846170i	$0.678903\pi$
$74$	−34034.4	−0.722502
$75$	−55689.2	−1.14319
$76$	5776.00	0.114708
$77$	41407.5	0.795889
$78$	63026.9	1.17298
$79$	31017.6	0.559166	0.279583	−	0.960121i	$-0.409804\pi$
$79$	31017.6	0.559166	0.279583	+	0.960121i	$0.409804\pi$
$80$	−20336.8	−0.355270
$81$	−70337.2	−1.19117
$82$	−78964.4	−1.29687
$83$	41068.7	0.654358	0.327179	−	0.944962i	$-0.393902\pi$
$83$	41068.7	0.654358	0.327179	+	0.944962i	$0.393902\pi$
$84$	−37175.9	−0.574861
$85$	12536.0	0.188196
$86$	−43939.8	−0.640637
$87$	−82826.3	−1.17320
$88$	−19937.3	−0.274447
$89$	−17065.6	−0.228373	−0.114187	−	0.993459i	$-0.536426\pi$
$89$	−17065.6	−0.228373	−0.114187	+	0.993459i	$0.536426\pi$
$90$	19879.0	0.258695
$91$	119815.	1.51673
$92$	−40360.5	−0.497150
$93$	115156.	1.38063
$94$	−60341.9	−0.704368
$95$	−28678.1	−0.326018
$96$	17899.8	0.198230
$97$	139045.	1.50047	0.750234	−	0.661172i	$-0.229941\pi$
$97$	139045.	1.50047	0.750234	+	0.661172i	$0.229941\pi$
$98$	−3443.98	−0.0362239
$99$	19488.4	0.199843
$100$	50973.3	0.509733
$101$	−122253.	−1.19249	−0.596247	−	0.802801i	$-0.703342\pi$
$101$	−122253.	−1.19249	−0.596247	+	0.802801i	$0.703342\pi$
$102$	−11033.7	−0.105008
$103$	−71932.4	−0.668084	−0.334042	−	0.942558i	$-0.608413\pi$
$103$	−71932.4	−0.668084	−0.334042	+	0.942558i	$0.608413\pi$
$104$	−57689.7	−0.523016
$105$	184580.	1.63385
$106$	−86798.5	−0.750322
$107$	14833.3	0.125250	0.0626249	−	0.998037i	$-0.480053\pi$
$107$	14833.3	0.125250	0.0626249	+	0.998037i	$0.480053\pi$
$108$	50466.4	0.416335
$109$	140025.	1.12886	0.564429	−	0.825482i	$-0.309096\pi$
$109$	140025.	1.12886	0.564429	+	0.825482i	$0.309096\pi$
$110$	98989.5	0.780023
$111$	−148733.	−1.14577
$112$	34027.8	0.256324
$113$	235172.	1.73256	0.866282	−	0.499555i	$-0.166503\pi$
$113$	235172.	1.73256	0.866282	+	0.499555i	$0.166503\pi$
$114$	25241.5	0.181908
$115$	200392.	1.41298
$116$	75812.5	0.523113
$117$	56391.0	0.380842
$118$	162704.	1.07571
$119$	−20975.3	−0.135781
$120$	−88873.3	−0.563401
$121$	−64006.4	−0.397430
$122$	−24607.2	−0.149679
$123$	−345080.	−2.05663
$124$	−105404.	−0.615607
$125$	−4832.71	−0.0276640
$126$	−33261.8	−0.186646
$127$	−24783.9	−0.136351	−0.0681757	−	0.997673i	$-0.521718\pi$
$127$	−24783.9	−0.136351	−0.0681757	+	0.997673i	$0.521718\pi$
$128$	−16384.0	−0.0883883
$129$	−192020.	−1.01595
$130$	286432.	1.48649
$131$	−152549.	−0.776661	−0.388331	−	0.921520i	$-0.626948\pi$
$131$	−152549.	−0.776661	−0.388331	+	0.921520i	$0.626948\pi$
$132$	−87127.1	−0.435230
$133$	47984.5	0.235219
$134$	−251041.	−1.20777
$135$	−250568.	−1.18329
$136$	10099.4	0.0468216
$137$	192265.	0.875184	0.437592	−	0.899174i	$-0.355831\pi$
$137$	192265.	0.875184	0.437592	+	0.899174i	$0.355831\pi$
$138$	−176378.	−0.788400
$139$	−342833.	−1.50503	−0.752515	−	0.658575i	$-0.771159\pi$
$139$	−342833.	−1.50503	−0.752515	+	0.658575i	$0.771159\pi$
$140$	−168950.	−0.728512
$141$	−263698.	−1.11702
$142$	221244.	0.920768
$143$	280804.	1.14832
$144$	16015.2	0.0643614
$145$	−376413.	−1.48677
$146$	194112.	0.753652
$147$	−15050.4	−0.0574454
$148$	136138.	0.510886
$149$	335859.	1.23934	0.619671	−	0.784862i	$-0.287266\pi$
$149$	335859.	1.23934	0.619671	+	0.784862i	$0.287266\pi$
$150$	222757.	0.808356
$151$	266683.	0.951816	0.475908	−	0.879495i	$-0.342120\pi$
$151$	266683.	0.951816	0.475908	+	0.879495i	$0.342120\pi$
$152$	−23104.0	−0.0811107
$153$	−9872.01	−0.0340939
$154$	−165630.	−0.562778
$155$	523337.	1.74965
$156$	−252108.	−0.829420
$157$	−173779.	−0.562664	−0.281332	−	0.959611i	$-0.590776\pi$
$157$	−173779.	−0.562664	−0.281332	+	0.959611i	$0.590776\pi$
$158$	−124071.	−0.395390
$159$	−379315.	−1.18989
$160$	81347.3	0.251214
$161$	−335298.	−1.01945
$162$	281349.	0.842282
$163$	−406317.	−1.19783	−0.598917	−	0.800811i	$-0.704402\pi$
$163$	−406317.	−1.19783	−0.598917	+	0.800811i	$0.704402\pi$
$164$	315858.	0.917027
$165$	432590.	1.23699
$166$	−164275.	−0.462701
$167$	−319695.	−0.887043	−0.443522	−	0.896264i	$-0.646271\pi$
$167$	−319695.	−0.887043	−0.443522	+	0.896264i	$0.646271\pi$
$168$	148704.	0.406488
$169$	441231.	1.18836
$170$	−50143.8	−0.133075
$171$	22583.9	0.0590620
$172$	175759.	0.452999
$173$	−427313.	−1.08550	−0.542752	−	0.839893i	$-0.682618\pi$
$173$	−427313.	−1.08550	−0.542752	+	0.839893i	$0.682618\pi$
$174$	331305.	0.829574
$175$	423464.	1.04525
$176$	79749.1	0.194064
$177$	711028.	1.70590
$178$	68262.2	0.161484
$179$	361946.	0.844329	0.422164	−	0.906519i	$-0.361271\pi$
$179$	361946.	0.844329	0.422164	+	0.906519i	$0.361271\pi$
$180$	−79516.1	−0.182925
$181$	−416686.	−0.945393	−0.472697	−	0.881225i	$-0.656719\pi$
$181$	−416686.	−0.945393	−0.472697	+	0.881225i	$0.656719\pi$
$182$	−479261.	−1.07249
$183$	−107535.	−0.237368
$184$	161442.	0.351538
$185$	−675930.	−1.45202
$186$	−460623.	−0.976255
$187$	−49158.6	−0.102801
$188$	241368.	0.498063
$189$	419253.	0.853732
$190$	114712.	0.230530
$191$	581586.	1.15353	0.576767	−	0.816909i	$-0.304314\pi$
$191$	581586.	1.15353	0.576767	+	0.816909i	$0.304314\pi$
$192$	−71599.1	−0.140170
$193$	−182832.	−0.353312	−0.176656	−	0.984273i	$-0.556528\pi$
$193$	−182832.	−0.353312	−0.176656	+	0.984273i	$0.556528\pi$
$194$	−556181.	−1.06099
$195$	1.25173e6	2.35734
$196$	13775.9	0.0256142
$197$	−93344.9	−0.171366	−0.0856831	−	0.996322i	$-0.527307\pi$
$197$	−93344.9	−0.171366	−0.0856831	+	0.996322i	$0.527307\pi$
$198$	−77953.8	−0.141310
$199$	723166.	1.29451	0.647255	−	0.762274i	$-0.275917\pi$
$199$	723166.	1.29451	0.647255	+	0.762274i	$0.275917\pi$
$200$	−203893.	−0.360436
$201$	−1.09707e6	−1.91532
$202$	489012.	0.843221
$203$	629817.	1.07269
$204$	44134.8	0.0742517
$205$	−1.56825e6	−2.60634
$206$	287730.	0.472407
$207$	−157808.	−0.255978
$208$	230759.	0.369828
$209$	112459.	0.178085
$210$	−738320.	−1.15530
$211$	85741.4	0.132582	0.0662910	−	0.997800i	$-0.478883\pi$
$211$	85741.4	0.132582	0.0662910	+	0.997800i	$0.478883\pi$
$212$	347194.	0.530558
$213$	966850.	1.46019
$214$	−59333.0	−0.0885650
$215$	−872653.	−1.28749
$216$	−201866.	−0.294393
$217$	−875652.	−1.26236
$218$	−560100.	−0.798223
$219$	848283.	1.19517
$220$	−395958.	−0.551559
$221$	−142243.	−0.195908
$222$	594930.	0.810184
$223$	111106.	0.149615	0.0748076	−	0.997198i	$-0.476166\pi$
$223$	111106.	0.149615	0.0748076	+	0.997198i	$0.476166\pi$
$224$	−136111.	−0.181248
$225$	199303.	0.262457
$226$	−940688.	−1.22511
$227$	−314299.	−0.404835	−0.202418	−	0.979299i	$-0.564880\pi$
$227$	−314299.	−0.404835	−0.202418	+	0.979299i	$0.564880\pi$
$228$	−100966.	−0.128629
$229$	1.45815e6	1.83744	0.918718	−	0.394913i	$-0.129225\pi$
$229$	1.45815e6	1.83744	0.918718	+	0.394913i	$0.129225\pi$
$230$	−801568.	−0.999127
$231$	−723814.	−0.892477
$232$	−303250.	−0.369897
$233$	1.38626e6	1.67284	0.836418	−	0.548091i	$-0.184645\pi$
$233$	1.38626e6	1.67284	0.836418	+	0.548091i	$0.184645\pi$
$234$	−225564.	−0.269296
$235$	−1.19840e6	−1.41558
$236$	−650817.	−0.760639
$237$	−542196.	−0.627026
$238$	83901.1	0.0960119
$239$	365117.	0.413464	0.206732	−	0.978398i	$-0.433717\pi$
$239$	365117.	0.413464	0.206732	+	0.978398i	$0.433717\pi$
$240$	355493.	0.398385
$241$	−312312.	−0.346374	−0.173187	−	0.984889i	$-0.555407\pi$
$241$	−312312.	−0.346374	−0.173187	+	0.984889i	$0.555407\pi$
$242$	256026.	0.281025
$243$	463054.	0.503056
$244$	98428.7	0.105839
$245$	−68398.1	−0.0727996
$246$	1.38032e6	1.45426
$247$	325406.	0.339377
$248$	421617.	0.435300
$249$	−717891.	−0.733771
$250$	19330.8	0.0195614
$251$	−970095.	−0.971919	−0.485959	−	0.873981i	$-0.661530\pi$
$251$	−970095.	−0.971919	−0.485959	+	0.873981i	$0.661530\pi$
$252$	133047.	0.131979
$253$	−785819.	−0.771829
$254$	99135.5	0.0964151
$255$	−219132.	−0.211035
$256$	65536.0	0.0625000
$257$	1.28988e6	1.21819	0.609096	−	0.793096i	$-0.291532\pi$
$257$	1.28988e6	1.21819	0.609096	+	0.793096i	$0.291532\pi$
$258$	768079.	0.718384
$259$	1.13097e6	1.04762
$260$	−1.14573e6	−1.05111
$261$	296423.	0.269346
$262$	610197.	0.549183
$263$	−501426.	−0.447011	−0.223505	−	0.974703i	$-0.571750\pi$
$263$	−501426.	−0.447011	−0.223505	+	0.974703i	$0.571750\pi$
$264$	348508.	0.307754
$265$	−1.72384e6	−1.50793
$266$	−191938.	−0.166325
$267$	298310.	0.256089
$268$	1.00416e6	0.854019
$269$	1.42986e6	1.20479	0.602397	−	0.798197i	$-0.294213\pi$
$269$	1.42986e6	1.20479	0.602397	+	0.798197i	$0.294213\pi$
$270$	1.00227e6	0.836713
$271$	−709506.	−0.586857	−0.293429	−	0.955981i	$-0.594796\pi$
$271$	−709506.	−0.586857	−0.293429	+	0.955981i	$0.594796\pi$
$272$	−40397.4	−0.0331079
$273$	−2.09440e6	−1.70080
$274$	−769061.	−0.618849
$275$	992450.	0.791365
$276$	705512.	0.557483
$277$	−766740.	−0.600411	−0.300205	−	0.953875i	$-0.597055\pi$
$277$	−766740.	−0.600411	−0.300205	+	0.953875i	$0.597055\pi$
$278$	1.37133e6	1.06422
$279$	−412125.	−0.316970
$280$	675798.	0.515136
$281$	5975.32	0.00451435	0.00225718	−	0.999997i	$-0.499282\pi$
$281$	5975.32	0.00451435	0.00225718	+	0.999997i	$0.499282\pi$
$282$	1.05479e6	0.789849
$283$	−189246.	−0.140463	−0.0702314	−	0.997531i	$-0.522374\pi$
$283$	−189246.	−0.140463	−0.0702314	+	0.997531i	$0.522374\pi$
$284$	−884975.	−0.651081
$285$	501301.	0.365583
$286$	−1.12322e6	−0.811986
$287$	2.62401e6	1.88044
$288$	−64060.7	−0.0455104
$289$	−1.39496e6	−0.982462
$290$	1.50565e6	1.05131
$291$	−2.43055e6	−1.68256
$292$	−776449.	−0.532913
$293$	986180.	0.671100	0.335550	−	0.942022i	$-0.391078\pi$
$293$	986180.	0.671100	0.335550	+	0.942022i	$0.391078\pi$
$294$	60201.7	0.0406200
$295$	3.23134e6	2.16186
$296$	−544551.	−0.361251
$297$	982580.	0.646363
$298$	−1.34343e6	−0.876347
$299$	−2.27381e6	−1.47088
$300$	−891027.	−0.571594
$301$	1.46013e6	0.928914
$302$	−1.06673e6	−0.673035
$303$	2.13702e6	1.33721
$304$	92416.0	0.0573539
$305$	−488703.	−0.300812
$306$	39488.0	0.0241080
$307$	−1.45722e6	−0.882428	−0.441214	−	0.897402i	$-0.645452\pi$
$307$	−1.45722e6	−0.882428	−0.441214	+	0.897402i	$0.645452\pi$
$308$	662520.	0.397944
$309$	1.25740e6	0.749162
$310$	−2.09335e6	−1.23719
$311$	2.40526e6	1.41014	0.705069	−	0.709138i	$-0.250916\pi$
$311$	2.40526e6	1.41014	0.705069	+	0.709138i	$0.250916\pi$
$312$	1.00843e6	0.586488
$313$	−3.20380e6	−1.84843	−0.924217	−	0.381867i	$-0.875281\pi$
$313$	−3.20380e6	−1.84843	−0.924217	+	0.381867i	$0.875281\pi$
$314$	695117.	0.397863
$315$	−660585.	−0.375104
$316$	496282.	0.279583
$317$	−603046.	−0.337056	−0.168528	−	0.985697i	$-0.553901\pi$
$317$	−603046.	−0.337056	−0.168528	+	0.985697i	$0.553901\pi$
$318$	1.51726e6	0.841380
$319$	1.47607e6	0.812137
$320$	−325389.	−0.177635
$321$	−259289.	−0.140450
$322$	1.34119e6	0.720860
$323$	−56966.7	−0.0303819
$324$	−1.12540e6	−0.595584
$325$	2.87171e6	1.50811
$326$	1.62527e6	0.846996
$327$	−2.44767e6	−1.26585
$328$	−1.26343e6	−0.648436
$329$	2.00518e6	1.02132
$330$	−1.73036e6	−0.874685
$331$	−3.77416e6	−1.89344	−0.946719	−	0.322062i	$-0.895624\pi$
$331$	−3.77416e6	−1.89344	−0.946719	+	0.322062i	$0.895624\pi$
$332$	657099.	0.327179
$333$	532292.	0.263051
$334$	1.27878e6	0.627234
$335$	−4.98572e6	−2.42726
$336$	−594814.	−0.287431
$337$	−2.12850e6	−1.02094	−0.510470	−	0.859896i	$-0.670528\pi$
$337$	−2.12850e6	−1.02094	−0.510470	+	0.859896i	$0.670528\pi$
$338$	−1.76492e6	−0.840300
$339$	−4.11087e6	−1.94283
$340$	200575.	0.0940979
$341$	−2.05222e6	−0.955735
$342$	−90335.5	−0.0417632
$343$	−2.11956e6	−0.972770
$344$	−703037.	−0.320318
$345$	−3.50290e6	−1.58446
$346$	1.70925e6	0.767567
$347$	2.40305e6	1.07137	0.535685	−	0.844418i	$-0.320053\pi$
$347$	2.40305e6	1.07137	0.535685	+	0.844418i	$0.320053\pi$
$348$	−1.32522e6	−0.586598
$349$	3.71870e6	1.63428	0.817141	−	0.576438i	$-0.195558\pi$
$349$	3.71870e6	1.63428	0.817141	+	0.576438i	$0.195558\pi$
$350$	−1.69386e6	−0.739106
$351$	2.84315e6	1.23178
$352$	−318996.	−0.137224
$353$	−2.04192e6	−0.872174	−0.436087	−	0.899905i	$-0.643636\pi$
$353$	−2.04192e6	−0.872174	−0.436087	+	0.899905i	$0.643636\pi$
$354$	−2.84411e6	−1.20625
$355$	4.39394e6	1.85048
$356$	−273049.	−0.114187
$357$	366653.	0.152260
$358$	−1.44778e6	−0.597030
$359$	−949493.	−0.388826	−0.194413	−	0.980920i	$-0.562280\pi$
$359$	−949493.	−0.388826	−0.194413	+	0.980920i	$0.562280\pi$
$360$	318064.	0.129348
$361$	130321.	0.0526316
$362$	1.66674e6	0.668494
$363$	1.11885e6	0.445661
$364$	1.91704e6	0.758365
$365$	3.85511e6	1.51462
$366$	430139.	0.167844
$367$	1.74418e6	0.675967	0.337984	−	0.941152i	$-0.390255\pi$
$367$	1.74418e6	0.675967	0.337984	+	0.941152i	$0.390255\pi$
$368$	−645768.	−0.248575
$369$	1.23499e6	0.472169
$370$	2.70372e6	1.02673
$371$	2.88434e6	1.08796
$372$	1.84249e6	0.690316
$373$	4.59987e6	1.71188	0.855940	−	0.517076i	$-0.172980\pi$
$373$	4.59987e6	1.71188	0.855940	+	0.517076i	$0.172980\pi$
$374$	196634.	0.0726910
$375$	84477.0	0.0310213
$376$	−965471.	−0.352184
$377$	4.27109e6	1.54770
$378$	−1.67701e6	−0.603680
$379$	−6993.69	−0.00250097	−0.00125048	−	0.999999i	$-0.500398\pi$
$379$	−6993.69	−0.00250097	−0.00125048	+	0.999999i	$0.500398\pi$
$380$	−458850.	−0.163009
$381$	433228.	0.152899
$382$	−2.32634e6	−0.815672
$383$	1.37680e6	0.479594	0.239797	−	0.970823i	$-0.422919\pi$
$383$	1.37680e6	0.479594	0.239797	+	0.970823i	$0.422919\pi$
$384$	286396.	0.0991150
$385$	−3.28944e6	−1.13102
$386$	731327.	0.249829
$387$	687210.	0.233245
$388$	2.22472e6	0.750234
$389$	1.40115e6	0.469473	0.234736	−	0.972059i	$-0.424577\pi$
$389$	1.40115e6	0.469473	0.234736	+	0.972059i	$0.424577\pi$
$390$	−5.00690e6	−1.66689
$391$	398062.	0.131677
$392$	−55103.7	−0.0181120
$393$	2.66660e6	0.870916
$394$	373380.	0.121174
$395$	−2.46407e6	−0.794620
$396$	311815.	0.0999215
$397$	3.33402e6	1.06168	0.530839	−	0.847473i	$-0.321877\pi$
$397$	3.33402e6	1.06168	0.530839	+	0.847473i	$0.321877\pi$
$398$	−2.89266e6	−0.915357
$399$	−838781.	−0.263764
$400$	815574.	0.254867
$401$	−5.32612e6	−1.65406	−0.827028	−	0.562161i	$-0.809970\pi$
$401$	−5.32612e6	−1.65406	−0.827028	+	0.562161i	$0.809970\pi$
$402$	4.38826e6	1.35434
$403$	−5.93822e6	−1.82135
$404$	−1.95605e6	−0.596247
$405$	5.58764e6	1.69274
$406$	−2.51927e6	−0.758506
$407$	2.65060e6	0.793155
$408$	−176539.	−0.0525039
$409$	−3.00861e6	−0.889319	−0.444659	−	0.895700i	$-0.646675\pi$
$409$	−3.00861e6	−0.889319	−0.444659	+	0.895700i	$0.646675\pi$
$410$	6.27300e6	1.84296
$411$	−3.36085e6	−0.981395
$412$	−1.15092e6	−0.334042
$413$	−5.40670e6	−1.55976
$414$	631231.	0.181004
$415$	−3.26253e6	−0.929895
$416$	−923035.	−0.261508
$417$	5.99280e6	1.68768
$418$	−449835.	−0.125925
$419$	2.47470e6	0.688633	0.344317	−	0.938854i	$-0.388111\pi$
$419$	2.47470e6	0.688633	0.344317	+	0.938854i	$0.388111\pi$
$420$	2.95328e6	0.816924
$421$	−3.25587e6	−0.895286	−0.447643	−	0.894212i	$-0.647737\pi$
$421$	−3.25587e6	−0.895286	−0.447643	+	0.894212i	$0.647737\pi$
$422$	−342966.	−0.0937496
$423$	943736.	0.256448
$424$	−1.38878e6	−0.375161
$425$	−502733.	−0.135010
$426$	−3.86740e6	−1.03251
$427$	817702.	0.217033
$428$	237332.	0.0626249
$429$	−4.90853e6	−1.28768
$430$	3.49061e6	0.910396
$431$	−3.54756e6	−0.919891	−0.459945	−	0.887947i	$-0.652131\pi$
$431$	−3.54756e6	−0.919891	−0.459945	+	0.887947i	$0.652131\pi$
$432$	807462.	0.208168
$433$	2.58960e6	0.663763	0.331881	−	0.943321i	$-0.392317\pi$
$433$	2.58960e6	0.663763	0.331881	+	0.943321i	$0.392317\pi$
$434$	3.50261e6	0.892621
$435$	6.57979e6	1.66720
$436$	2.24040e6	0.564429
$437$	−910634.	−0.228108
$438$	−3.39313e6	−0.845114
$439$	−3.47682e6	−0.861036	−0.430518	−	0.902582i	$-0.641669\pi$
$439$	−3.47682e6	−0.861036	−0.430518	+	0.902582i	$0.641669\pi$
$440$	1.58383e6	0.390011
$441$	53863.2	0.0131885
$442$	568974.	0.138528
$443$	−3.22496e6	−0.780756	−0.390378	−	0.920655i	$-0.627656\pi$
$443$	−3.22496e6	−0.780756	−0.390378	+	0.920655i	$0.627656\pi$
$444$	−2.37972e6	−0.572886
$445$	1.35570e6	0.324537
$446$	−444424.	−0.105794
$447$	−5.87089e6	−1.38975
$448$	544444.	0.128162
$449$	−4.47721e6	−1.04807	−0.524036	−	0.851696i	$-0.675574\pi$
$449$	−4.47721e6	−1.04807	−0.524036	+	0.851696i	$0.675574\pi$
$450$	−797213.	−0.185585
$451$	6.14975e6	1.42369
$452$	3.76275e6	0.866282
$453$	−4.66169e6	−1.06733
$454$	1.25720e6	0.286262
$455$	−9.51821e6	−2.15539
$456$	403864.	0.0909542
$457$	563938.	0.126311	0.0631555	−	0.998004i	$-0.479884\pi$
$457$	563938.	0.126311	0.0631555	+	0.998004i	$0.479884\pi$
$458$	−5.83259e6	−1.29926
$459$	−497733.	−0.110272
$460$	3.20627e6	0.706489
$461$	−3.05325e6	−0.669130	−0.334565	−	0.942373i	$-0.608589\pi$
$461$	−3.05325e6	−0.669130	−0.334565	+	0.942373i	$0.608589\pi$
$462$	2.89526e6	0.631076
$463$	7.31911e6	1.58674	0.793370	−	0.608740i	$-0.208325\pi$
$463$	7.31911e6	1.58674	0.793370	+	0.608740i	$0.208325\pi$
$464$	1.21300e6	0.261557
$465$	−9.14806e6	−1.96199
$466$	−5.54502e6	−1.18287
$467$	−3.83007e6	−0.812671	−0.406336	−	0.913724i	$-0.633194\pi$
$467$	−3.83007e6	−0.812671	−0.406336	+	0.913724i	$0.633194\pi$
$468$	902256.	0.190421
$469$	8.34216e6	1.75124
$470$	4.79361e6	1.00096
$471$	3.03771e6	0.630948
$472$	2.60327e6	0.537853
$473$	3.42203e6	0.703284
$474$	2.16879e6	0.443374
$475$	1.15009e6	0.233882
$476$	−335604.	−0.0678907
$477$	1.35751e6	0.273179
$478$	−1.46047e6	−0.292363
$479$	−852140.	−0.169696	−0.0848481	−	0.996394i	$-0.527040\pi$
$479$	−852140.	−0.169696	−0.0848481	+	0.996394i	$0.527040\pi$
$480$	−1.42197e6	−0.281701
$481$	7.66967e6	1.51152
$482$	1.24925e6	0.244924
$483$	5.86109e6	1.14317
$484$	−1.02410e6	−0.198715
$485$	−1.10459e7	−2.13228
$486$	−1.85222e6	−0.355714
$487$	−1.76953e6	−0.338093	−0.169046	−	0.985608i	$-0.554069\pi$
$487$	−1.76953e6	−0.338093	−0.169046	+	0.985608i	$0.554069\pi$
$488$	−393715.	−0.0748397
$489$	7.10253e6	1.34320
$490$	273592.	0.0514771
$491$	−1.12702e6	−0.210973	−0.105487	−	0.994421i	$-0.533640\pi$
$491$	−1.12702e6	−0.210973	−0.105487	+	0.994421i	$0.533640\pi$
$492$	−5.52127e6	−1.02832
$493$	−747713.	−0.138553
$494$	−1.30162e6	−0.239976
$495$	−1.54818e6	−0.283993
$496$	−1.68647e6	−0.307803
$497$	−7.35199e6	−1.33510
$498$	2.87156e6	0.518854
$499$	−5.96123e6	−1.07173	−0.535864	−	0.844304i	$-0.680014\pi$
$499$	−5.96123e6	−1.07173	−0.535864	+	0.844304i	$0.680014\pi$
$500$	−77323.4	−0.0138320
$501$	5.58835e6	0.994694
$502$	3.88038e6	0.687250
$503$	−5.66845e6	−0.998951	−0.499476	−	0.866328i	$-0.666474\pi$
$503$	−5.66845e6	−0.998951	−0.499476	+	0.866328i	$0.666474\pi$
$504$	−532188.	−0.0933230
$505$	9.71188e6	1.69463
$506$	3.14327e6	0.545765
$507$	−7.71283e6	−1.33258
$508$	−396542.	−0.0681757
$509$	8.42220e6	1.44089	0.720446	−	0.693512i	$-0.243937\pi$
$509$	8.42220e6	1.44089	0.720446	+	0.693512i	$0.243937\pi$
$510$	876526.	0.149224
$511$	−6.45040e6	−1.09278
$512$	−262144.	−0.0441942
$513$	1.13865e6	0.191028
$514$	−5.15951e6	−0.861392
$515$	5.71436e6	0.949401
$516$	−3.07232e6	−0.507974
$517$	4.69943e6	0.773247
$518$	−4.52389e6	−0.740777
$519$	7.46955e6	1.21724
$520$	4.58291e6	0.743247
$521$	5.81861e6	0.939128	0.469564	−	0.882899i	$-0.344411\pi$
$521$	5.81861e6	0.939128	0.469564	+	0.882899i	$0.344411\pi$
$522$	−1.18569e6	−0.190457
$523$	4.81037e6	0.768996	0.384498	−	0.923126i	$-0.374375\pi$
$523$	4.81037e6	0.768996	0.384498	+	0.923126i	$0.374375\pi$
$524$	−2.44079e6	−0.388331
$525$	−7.40226e6	−1.17210
$526$	2.00571e6	0.316084
$527$	1.03957e6	0.163052
$528$	−1.39403e6	−0.217615
$529$	−73173.3	−0.0113688
$530$	6.89534e6	1.06627
$531$	−2.54466e6	−0.391646
$532$	767752.	0.117609
$533$	1.77947e7	2.71314
$534$	−1.19324e6	−0.181082
$535$	−1.17836e6	−0.177990
$536$	−4.01666e6	−0.603883
$537$	−6.32691e6	−0.946795
$538$	−5.71944e6	−0.851918
$539$	268217.	0.0397662
$540$	−4.00909e6	−0.591645
$541$	3.11994e6	0.458304	0.229152	−	0.973391i	$-0.426405\pi$
$541$	3.11994e6	0.458304	0.229152	+	0.973391i	$0.426405\pi$
$542$	2.83802e6	0.414971
$543$	7.28378e6	1.06012
$544$	161590.	0.0234108
$545$	−1.11237e7	−1.60420
$546$	8.37760e6	1.20265
$547$	2.61616e6	0.373848	0.186924	−	0.982374i	$-0.440148\pi$
$547$	2.61616e6	0.373848	0.186924	+	0.982374i	$0.440148\pi$
$548$	3.07624e6	0.437592
$549$	384851.	0.0544957
$550$	−3.96980e6	−0.559580
$551$	1.71052e6	0.240021
$552$	−2.82205e6	−0.394200
$553$	4.12290e6	0.573310
$554$	3.06696e6	0.424555
$555$	1.18154e7	1.62823
$556$	−5.48532e6	−0.752515
$557$	1.91062e6	0.260937	0.130469	−	0.991452i	$-0.458352\pi$
$557$	1.91062e6	0.260937	0.130469	+	0.991452i	$0.458352\pi$
$558$	1.64850e6	0.224132
$559$	9.90185e6	1.34025
$560$	−2.70319e6	−0.364256
$561$	859305.	0.115276
$562$	−23901.3	−0.00319213
$563$	84059.8	0.0111768	0.00558840	−	0.999984i	$-0.498221\pi$
$563$	84059.8	0.0111768	0.00558840	+	0.999984i	$0.498221\pi$
$564$	−4.21917e6	−0.558508
$565$	−1.86822e7	−2.46211
$566$	756986.	0.0993222
$567$	−9.34930e6	−1.22130
$568$	3.53990e6	0.460384
$569$	−2.22862e6	−0.288572	−0.144286	−	0.989536i	$-0.546089\pi$
$569$	−2.22862e6	−0.288572	−0.144286	+	0.989536i	$0.546089\pi$
$570$	−2.00520e6	−0.258506
$571$	8.28284e6	1.06314	0.531568	−	0.847015i	$-0.321603\pi$
$571$	8.28284e6	1.06314	0.531568	+	0.847015i	$0.321603\pi$
$572$	4.49287e6	0.574161
$573$	−1.01663e7	−1.29353
$574$	−1.04960e7	−1.32968
$575$	−8.03637e6	−1.01366
$576$	256243.	0.0321807
$577$	−1.50122e7	−1.87717	−0.938585	−	0.345047i	$-0.887863\pi$
$577$	−1.50122e7	−1.87717	−0.938585	+	0.345047i	$0.887863\pi$
$578$	5.57982e6	0.694705
$579$	3.19595e6	0.396190
$580$	−6.02260e6	−0.743385
$581$	5.45889e6	0.670910
$582$	9.72218e6	1.18975
$583$	6.75986e6	0.823695
$584$	3.10580e6	0.376826
$585$	−4.47974e6	−0.541207
$586$	−3.94472e6	−0.474539
$587$	−4.07944e6	−0.488658	−0.244329	−	0.969692i	$-0.578568\pi$
$587$	−4.07944e6	−0.488658	−0.244329	+	0.969692i	$0.578568\pi$
$588$	−240807.	−0.0287227
$589$	−2.37818e6	−0.282460
$590$	−1.29253e7	−1.52866
$591$	1.63169e6	0.192163
$592$	2.17820e6	0.255443
$593$	−545602.	−0.0637147	−0.0318573	−	0.999492i	$-0.510142\pi$
$593$	−545602.	−0.0637147	−0.0318573	+	0.999492i	$0.510142\pi$
$594$	−3.93032e6	−0.457048
$595$	1.66629e6	0.192956
$596$	5.37374e6	0.619671
$597$	−1.26411e7	−1.45161
$598$	9.09526e6	1.04007
$599$	−8.45396e6	−0.962704	−0.481352	−	0.876527i	$-0.659854\pi$
$599$	−8.45396e6	−0.962704	−0.481352	+	0.876527i	$0.659854\pi$
$600$	3.56411e6	0.404178
$601$	−5.39862e6	−0.609673	−0.304836	−	0.952405i	$-0.598602\pi$
$601$	−5.39862e6	−0.609673	−0.304836	+	0.952405i	$0.598602\pi$
$602$	−5.84052e6	−0.656841
$603$	3.92623e6	0.439727
$604$	4.26693e6	0.475908
$605$	5.08472e6	0.564779
$606$	−8.54806e6	−0.945553
$607$	−1.14275e7	−1.25886	−0.629432	−	0.777055i	$-0.716712\pi$
$607$	−1.14275e7	−1.25886	−0.629432	+	0.777055i	$0.716712\pi$
$608$	−369664.	−0.0405554
$609$	−1.10094e7	−1.20287
$610$	1.95481e6	0.212706
$611$	1.35981e7	1.47358
$612$	−157952.	−0.0170470
$613$	−894639.	−0.0961605	−0.0480802	−	0.998843i	$-0.515310\pi$
$613$	−894639.	−0.0961605	−0.0480802	+	0.998843i	$0.515310\pi$
$614$	5.82888e6	0.623971
$615$	2.74134e7	2.92264
$616$	−2.65008e6	−0.281389
$617$	1.18925e7	1.25765	0.628826	−	0.777546i	$-0.283536\pi$
$617$	1.18925e7	1.25765	0.628826	+	0.777546i	$0.283536\pi$
$618$	−5.02958e6	−0.529738
$619$	1.03513e7	1.08585	0.542924	−	0.839782i	$-0.317317\pi$
$619$	1.03513e7	1.08585	0.542924	+	0.839782i	$0.317317\pi$
$620$	8.37339e6	0.874826
$621$	−7.95645e6	−0.827923
$622$	−9.62106e6	−0.997118
$623$	−2.26837e6	−0.234150
$624$	−4.03372e6	−0.414710
$625$	−9.57182e6	−0.980154
$626$	1.28152e7	1.30704
$627$	−1.96581e6	−0.199697
$628$	−2.78047e6	−0.281332
$629$	−1.34268e6	−0.135315
$630$	2.64234e6	0.265239
$631$	−1.17088e6	−0.117068	−0.0585342	−	0.998285i	$-0.518643\pi$
$631$	−1.17088e6	−0.117068	−0.0585342	+	0.998285i	$0.518643\pi$
$632$	−1.98513e6	−0.197695
$633$	−1.49878e6	−0.148672
$634$	2.41219e6	0.238335
$635$	1.96885e6	0.193766
$636$	−6.06904e6	−0.594946
$637$	776102.	0.0757828
$638$	−5.90427e6	−0.574268
$639$	−3.46021e6	−0.335236
$640$	1.30156e6	0.125607
$641$	−4.72990e6	−0.454681	−0.227341	−	0.973815i	$-0.573003\pi$
$641$	−4.72990e6	−0.454681	−0.227341	+	0.973815i	$0.573003\pi$
$642$	1.03716e6	0.0993131
$643$	−1.49075e7	−1.42193	−0.710963	−	0.703229i	$-0.751741\pi$
$643$	−1.49075e7	−1.42193	−0.710963	+	0.703229i	$0.751741\pi$
$644$	−5.36476e6	−0.509725
$645$	1.52542e7	1.44374
$646$	227867.	0.0214832
$647$	−4.27732e6	−0.401708	−0.200854	−	0.979621i	$-0.564372\pi$
$647$	−4.27732e6	−0.401708	−0.200854	+	0.979621i	$0.564372\pi$
$648$	4.50158e6	0.421141
$649$	−1.26714e7	−1.18090
$650$	−1.14869e7	−1.06639
$651$	1.53066e7	1.41555
$652$	−6.50108e6	−0.598917
$653$	2.25370e6	0.206829	0.103415	−	0.994638i	$-0.467023\pi$
$653$	2.25370e6	0.206829	0.103415	+	0.994638i	$0.467023\pi$
$654$	9.79069e6	0.895094
$655$	1.21186e7	1.10370
$656$	5.05372e6	0.458513
$657$	−3.03588e6	−0.274392
$658$	−8.02071e6	−0.722184
$659$	−2.93133e6	−0.262937	−0.131468	−	0.991320i	$-0.541969\pi$
$659$	−2.93133e6	−0.262937	−0.131468	+	0.991320i	$0.541969\pi$
$660$	6.92144e6	0.618496
$661$	6.56037e6	0.584016	0.292008	−	0.956416i	$-0.405677\pi$
$661$	6.56037e6	0.584016	0.292008	+	0.956416i	$0.405677\pi$
$662$	1.50967e7	1.33886
$663$	2.48645e6	0.219683
$664$	−2.62840e6	−0.231351
$665$	−3.81192e6	−0.334264
$666$	−2.12917e6	−0.186005
$667$	−1.19525e7	−1.04026
$668$	−5.11512e6	−0.443522
$669$	−1.94216e6	−0.167772
$670$	1.99429e7	1.71633
$671$	1.91640e6	0.164316
$672$	2.37926e6	0.203244
$673$	−3.19596e6	−0.271996	−0.135998	−	0.990709i	$-0.543424\pi$
$673$	−3.19596e6	−0.271996	−0.135998	+	0.990709i	$0.543424\pi$
$674$	8.51402e6	0.721913
$675$	1.00486e7	0.848880
$676$	7.05970e6	0.594182
$677$	−2.06961e6	−0.173547	−0.0867734	−	0.996228i	$-0.527656\pi$
$677$	−2.06961e6	−0.173547	−0.0867734	+	0.996228i	$0.527656\pi$
$678$	1.64435e7	1.37379
$679$	1.84820e7	1.53842
$680$	−802301.	−0.0665373
$681$	5.49402e6	0.453965
$682$	8.20887e6	0.675807
$683$	−2.61594e6	−0.214574	−0.107287	−	0.994228i	$-0.534216\pi$
$683$	−2.61594e6	−0.214574	−0.107287	+	0.994228i	$0.534216\pi$
$684$	361342.	0.0295310
$685$	−1.52737e7	−1.24371
$686$	8.47824e6	0.687852
$687$	−2.54888e7	−2.06043
$688$	2.81215e6	0.226499
$689$	1.95601e7	1.56972
$690$	1.40116e7	1.12038
$691$	−1.40203e7	−1.11703	−0.558513	−	0.829496i	$-0.688628\pi$
$691$	−1.40203e7	−1.11703	−0.558513	+	0.829496i	$0.688628\pi$
$692$	−6.83701e6	−0.542752
$693$	2.59042e6	0.204898
$694$	−9.61221e6	−0.757573
$695$	2.72349e7	2.13877
$696$	5.30088e6	0.414787
$697$	−3.11520e6	−0.242887
$698$	−1.48748e7	−1.15561
$699$	−2.42321e7	−1.87585
$700$	6.77543e6	0.522627
$701$	3.42664e6	0.263375	0.131687	−	0.991291i	$-0.457961\pi$
$701$	3.42664e6	0.263375	0.131687	+	0.991291i	$0.457961\pi$
$702$	−1.13726e7	−0.870999
$703$	3.07161e6	0.234411
$704$	1.27598e6	0.0970318
$705$	2.09484e7	1.58737
$706$	8.16770e6	0.616720
$707$	−1.62500e7	−1.22266
$708$	1.13764e7	0.852950
$709$	8.04969e6	0.601400	0.300700	−	0.953719i	$-0.402780\pi$
$709$	8.04969e6	0.601400	0.300700	+	0.953719i	$0.402780\pi$
$710$	−1.75758e7	−1.30848
$711$	1.94044e6	0.143955
$712$	1.09220e6	0.0807422
$713$	1.66178e7	1.22420
$714$	−1.46661e6	−0.107664
$715$	−2.23073e7	−1.63186
$716$	5.79114e6	0.422164
$717$	−6.38234e6	−0.463641
$718$	3.79797e6	0.274942
$719$	−2.66646e7	−1.92359	−0.961795	−	0.273771i	$-0.911729\pi$
$719$	−2.66646e7	−1.92359	−0.961795	+	0.273771i	$0.911729\pi$
$720$	−1.27226e6	−0.0914626
$721$	−9.56132e6	−0.684983
$722$	−521284.	−0.0372161
$723$	5.45929e6	0.388410
$724$	−6.66698e6	−0.472697
$725$	1.50954e7	1.06659
$726$	−4.47540e6	−0.315130
$727$	1.25706e7	0.882102	0.441051	−	0.897482i	$-0.354606\pi$
$727$	1.25706e7	0.882102	0.441051	+	0.897482i	$0.354606\pi$
$728$	−7.66817e6	−0.536245
$729$	8.99764e6	0.627061
$730$	−1.54204e7	−1.07100
$731$	−1.73345e6	−0.119983
$732$	−1.72056e6	−0.118684
$733$	−1.12272e7	−0.771814	−0.385907	−	0.922538i	$-0.626111\pi$
$733$	−1.12272e7	−0.771814	−0.385907	+	0.922538i	$0.626111\pi$
$734$	−6.97671e6	−0.477981
$735$	1.19562e6	0.0816345
$736$	2.58307e6	0.175769
$737$	1.95511e7	1.32587
$738$	−4.93996e6	−0.333874
$739$	1.05677e7	0.711820	0.355910	−	0.934520i	$-0.384171\pi$
$739$	1.05677e7	0.711820	0.355910	+	0.934520i	$0.384171\pi$
$740$	−1.08149e7	−0.726010
$741$	−5.68818e6	−0.380564
$742$	−1.15373e7	−0.769301
$743$	−5.83579e6	−0.387817	−0.193909	−	0.981020i	$-0.562117\pi$
$743$	−5.83579e6	−0.387817	−0.193909	+	0.981020i	$0.562117\pi$
$744$	−7.36997e6	−0.488127
$745$	−2.66809e7	−1.76120
$746$	−1.83995e7	−1.21048
$747$	2.56923e6	0.168462
$748$	−786538.	−0.0514003
$749$	1.97165e6	0.128418
$750$	−337908.	−0.0219354
$751$	4.48767e6	0.290349	0.145175	−	0.989406i	$-0.453626\pi$
$751$	4.48767e6	0.290349	0.145175	+	0.989406i	$0.453626\pi$
$752$	3.86188e6	0.249032
$753$	1.69575e7	1.08987
$754$	−1.70844e7	−1.09439
$755$	−2.11855e7	−1.35261
$756$	6.70805e6	0.426866
$757$	7.81327e6	0.495557	0.247778	−	0.968817i	$-0.420300\pi$
$757$	7.81327e6	0.495557	0.247778	+	0.968817i	$0.420300\pi$
$758$	27974.8	0.00176845
$759$	1.37363e7	0.865497
$760$	1.83540e6	0.115265
$761$	1.81639e7	1.13697	0.568483	−	0.822695i	$-0.307531\pi$
$761$	1.81639e7	1.13697	0.568483	+	0.822695i	$0.307531\pi$
$762$	−1.73291e6	−0.108116
$763$	1.86123e7	1.15741
$764$	9.30537e6	0.576767
$765$	784240.	0.0484502
$766$	−5.50720e6	−0.339124
$767$	−3.66655e7	−2.25045
$768$	−1.14559e6	−0.0700849
$769$	−4.47189e6	−0.272694	−0.136347	−	0.990661i	$-0.543536\pi$
$769$	−4.47189e6	−0.272694	−0.136347	+	0.990661i	$0.543536\pi$
$770$	1.31578e7	0.799753
$771$	−2.25474e7	−1.36603
$772$	−2.92531e6	−0.176656
$773$	−2.53207e7	−1.52415	−0.762075	−	0.647489i	$-0.775819\pi$
$773$	−2.53207e7	−1.52415	−0.762075	+	0.647489i	$0.775819\pi$
$774$	−2.74884e6	−0.164929
$775$	−2.09875e7	−1.25518
$776$	−8.89889e6	−0.530496
$777$	−1.97697e7	−1.17475
$778$	−5.60460e6	−0.331967
$779$	7.12654e6	0.420761
$780$	2.00276e7	1.17867
$781$	−1.72305e7	−1.01081
$782$	−1.59225e6	−0.0931095
$783$	1.49452e7	0.871161
$784$	220415.	0.0128071
$785$	1.38052e7	0.799590
$786$	−1.06664e7	−0.615831
$787$	4.73524e6	0.272524	0.136262	−	0.990673i	$-0.456491\pi$
$787$	4.73524e6	0.272524	0.136262	+	0.990673i	$0.456491\pi$
$788$	−1.49352e6	−0.0856831
$789$	8.76506e6	0.501259
$790$	9.85626e6	0.561881
$791$	3.12593e7	1.77639
$792$	−1.24726e6	−0.0706552
$793$	5.54523e6	0.313139
$794$	−1.33361e7	−0.750719
$795$	3.01331e7	1.69093
$796$	1.15707e7	0.647255
$797$	1.54780e7	0.863116	0.431558	−	0.902085i	$-0.357964\pi$
$797$	1.54780e7	0.863116	0.431558	+	0.902085i	$0.357964\pi$
$798$	3.35512e6	0.186510
$799$	−2.38053e6	−0.131919
$800$	−3.26229e6	−0.180218
$801$	−1.06761e6	−0.0587937
$802$	2.13045e7	1.16959
$803$	−1.51175e7	−0.827351
$804$	−1.75530e7	−0.957662
$805$	2.66363e7	1.44872
$806$	2.37529e7	1.28789
$807$	−2.49943e7	−1.35101
$808$	7.82420e6	0.421611
$809$	5.54794e6	0.298031	0.149015	−	0.988835i	$-0.452390\pi$
$809$	5.54794e6	0.298031	0.149015	+	0.988835i	$0.452390\pi$
$810$	−2.23506e7	−1.19695
$811$	9.82955e6	0.524785	0.262392	−	0.964961i	$-0.415489\pi$
$811$	9.82955e6	0.524785	0.262392	+	0.964961i	$0.415489\pi$
$812$	1.00771e7	0.536345
$813$	1.24023e7	0.658078
$814$	−1.06024e7	−0.560845
$815$	3.22782e7	1.70222
$816$	706158.	0.0371258
$817$	3.96557e6	0.207850
$818$	1.20344e7	0.628843
$819$	7.49555e6	0.390475
$820$	−2.50920e7	−1.30317
$821$	1.78229e7	0.922830	0.461415	−	0.887185i	$-0.347342\pi$
$821$	1.78229e7	0.922830	0.461415	+	0.887185i	$0.347342\pi$
$822$	1.34434e7	0.693951
$823$	−1.29509e7	−0.666502	−0.333251	−	0.942838i	$-0.608146\pi$
$823$	−1.29509e7	−0.666502	−0.333251	+	0.942838i	$0.608146\pi$
$824$	4.60367e6	0.236204
$825$	−1.73483e7	−0.887404
$826$	2.16268e7	1.10292
$827$	−2.57276e7	−1.30808	−0.654042	−	0.756458i	$-0.726928\pi$
$827$	−2.57276e7	−1.30808	−0.654042	+	0.756458i	$0.726928\pi$
$828$	−2.52492e6	−0.127989
$829$	2.26984e7	1.14712	0.573559	−	0.819164i	$-0.305562\pi$
$829$	2.26984e7	1.14712	0.573559	+	0.819164i	$0.305562\pi$
$830$	1.30501e7	0.657535
$831$	1.34028e7	0.673276
$832$	3.69214e6	0.184914
$833$	−135867.	−0.00678426
$834$	−2.39712e7	−1.19337
$835$	2.53968e7	1.26056
$836$	1.79934e6	0.0890424
$837$	−2.07788e7	−1.02519
$838$	−9.89881e6	−0.486937
$839$	−9.22885e6	−0.452629	−0.226315	−	0.974054i	$-0.572668\pi$
$839$	−9.22885e6	−0.452629	−0.226315	+	0.974054i	$0.572668\pi$
$840$	−1.18131e7	−0.577652
$841$	1.94015e6	0.0945898
$842$	1.30235e7	0.633063
$843$	−104450.	−0.00506221
$844$	1.37186e6	0.0662910
$845$	−3.50517e7	−1.68876
$846$	−3.77495e6	−0.181336
$847$	−8.50780e6	−0.407482
$848$	5.55511e6	0.265279
$849$	3.30807e6	0.157509
$850$	2.01093e6	0.0954662
$851$	−2.14632e7	−1.01595
$852$	1.54696e7	0.730096
$853$	−3.17055e7	−1.49198	−0.745989	−	0.665959i	$-0.768023\pi$
$853$	−3.17055e7	−1.49198	−0.745989	+	0.665959i	$0.768023\pi$
$854$	−3.27081e6	−0.153465
$855$	−1.79408e6	−0.0839318
$856$	−949328.	−0.0442825
$857$	3.01353e7	1.40160	0.700799	−	0.713359i	$-0.252827\pi$
$857$	3.01353e7	1.40160	0.700799	+	0.713359i	$0.252827\pi$
$858$	1.96341e7	0.910528
$859$	−1.58417e7	−0.732520	−0.366260	−	0.930513i	$-0.619362\pi$
$859$	−1.58417e7	−0.732520	−0.366260	+	0.930513i	$0.619362\pi$
$860$	−1.39624e7	−0.643747
$861$	−4.58683e7	−2.10865
$862$	1.41902e7	0.650461
$863$	−2.32831e7	−1.06418	−0.532089	−	0.846689i	$-0.678593\pi$
$863$	−2.32831e7	−1.06418	−0.532089	+	0.846689i	$0.678593\pi$
$864$	−3.22985e6	−0.147197
$865$	3.39461e7	1.54259
$866$	−1.03584e7	−0.469351
$867$	2.43842e7	1.10169
$868$	−1.40104e7	−0.631178
$869$	9.66261e6	0.434055
$870$	−2.63191e7	−1.17889
$871$	5.65722e7	2.52672
$872$	−8.96160e6	−0.399111
$873$	8.69856e6	0.386289
$874$	3.64254e6	0.161297
$875$	−642369.	−0.0283638
$876$	1.35725e7	0.597586
$877$	2.89258e7	1.26995	0.634975	−	0.772532i	$-0.281010\pi$
$877$	2.89258e7	1.26995	0.634975	+	0.772532i	$0.281010\pi$
$878$	1.39073e7	0.608844
$879$	−1.72387e7	−0.752544
$880$	−6.33533e6	−0.275780
$881$	−2.35636e7	−1.02283	−0.511413	−	0.859335i	$-0.670878\pi$
$881$	−2.35636e7	−1.02283	−0.511413	+	0.859335i	$0.670878\pi$
$882$	−215453.	−0.00932569
$883$	−1.91319e6	−0.0825764	−0.0412882	−	0.999147i	$-0.513146\pi$
$883$	−1.91319e6	−0.0825764	−0.0412882	+	0.999147i	$0.513146\pi$
$884$	−2.27589e6	−0.0979538
$885$	−5.64846e7	−2.42422
$886$	1.28998e7	0.552078
$887$	3.48791e7	1.48852	0.744262	−	0.667888i	$-0.232801\pi$
$887$	3.48791e7	1.48852	0.744262	+	0.667888i	$0.232801\pi$
$888$	9.51888e6	0.405092
$889$	−3.29430e6	−0.139800
$890$	−5.42280e6	−0.229482
$891$	−2.19114e7	−0.924648
$892$	1.77770e6	0.0748076
$893$	5.44586e6	0.228527
$894$	2.34836e7	0.982699
$895$	−2.87533e7	−1.19986
$896$	−2.17778e6	−0.0906241
$897$	3.97468e7	1.64938
$898$	1.79088e7	0.741099
$899$	−3.12146e7	−1.28813
$900$	3.18885e6	0.131229
$901$	−3.42426e6	−0.140525
$902$	−2.45990e7	−1.00670
$903$	−2.55235e7	−1.04165
$904$	−1.50510e7	−0.612554
$905$	3.31018e7	1.34348
$906$	1.86467e7	0.754714
$907$	1.34601e7	0.543287	0.271644	−	0.962398i	$-0.412433\pi$
$907$	1.34601e7	0.543287	0.271644	+	0.962398i	$0.412433\pi$
$908$	−5.02878e6	−0.202418
$909$	−7.64806e6	−0.307002
$910$	3.80728e7	1.52409
$911$	−1.42316e7	−0.568144	−0.284072	−	0.958803i	$-0.591685\pi$
$911$	−1.42316e7	−0.568144	−0.284072	+	0.958803i	$0.591685\pi$
$912$	−1.61546e6	−0.0643143
$913$	1.27937e7	0.507948
$914$	−2.25575e6	−0.0893154
$915$	8.54265e6	0.337318
$916$	2.33303e7	0.918718
$917$	−2.02770e7	−0.796307
$918$	1.99093e6	0.0779740
$919$	1.48289e7	0.579188	0.289594	−	0.957150i	$-0.406480\pi$
$919$	1.48289e7	0.579188	0.289594	+	0.957150i	$0.406480\pi$
$920$	−1.28251e7	−0.499563
$921$	2.54726e7	0.989518
$922$	1.22130e7	0.473146
$923$	−4.98574e7	−1.92631
$924$	−1.15810e7	−0.446238
$925$	2.71070e7	1.04166
$926$	−2.92764e7	−1.12199
$927$	−4.50003e6	−0.171995
$928$	−4.85200e6	−0.184948
$929$	1.48557e7	0.564748	0.282374	−	0.959304i	$-0.408878\pi$
$929$	1.48557e7	0.564748	0.282374	+	0.959304i	$0.408878\pi$
$930$	3.65922e7	1.38734
$931$	310819.	0.0117526
$932$	2.21801e7	0.836418
$933$	−4.20446e7	−1.58127
$934$	1.53203e7	0.574645
$935$	3.90520e6	0.146088
$936$	−3.60902e6	−0.134648
$937$	9.74272e6	0.362519	0.181260	−	0.983435i	$-0.441983\pi$
$937$	9.74272e6	0.362519	0.181260	+	0.983435i	$0.441983\pi$
$938$	−3.33686e7	−1.23832
$939$	5.60032e7	2.07276
$940$	−1.91744e7	−0.707788
$941$	−2.16418e6	−0.0796745	−0.0398373	−	0.999206i	$-0.512684\pi$
$941$	−2.16418e6	−0.0796745	−0.0398373	+	0.999206i	$0.512684\pi$
$942$	−1.21508e7	−0.446148
$943$	−4.97976e7	−1.82360
$944$	−1.04131e7	−0.380320
$945$	−3.33058e7	−1.21322
$946$	−1.36881e7	−0.497297
$947$	1.60138e7	0.580254	0.290127	−	0.956988i	$-0.406302\pi$
$947$	1.60138e7	0.580254	0.290127	+	0.956988i	$0.406302\pi$
$948$	−8.67514e6	−0.313513
$949$	−4.37433e7	−1.57669
$950$	−4.60034e6	−0.165379
$951$	1.05414e7	0.377961
$952$	1.34242e6	0.0480060
$953$	−2.67154e6	−0.0952860	−0.0476430	−	0.998864i	$-0.515171\pi$
$953$	−2.67154e6	−0.0952860	−0.0476430	+	0.998864i	$0.515171\pi$
$954$	−5.43005e6	−0.193167
$955$	−4.62016e7	−1.63926
$956$	5.84188e6	0.206732
$957$	−2.58020e7	−0.910697
$958$	3.40856e6	0.119993
$959$	2.55561e7	0.897321
$960$	5.68789e6	0.199192
$961$	1.47694e7	0.515888
$962$	−3.06787e7	−1.06881
$963$	927957.	0.0322450
$964$	−4.99699e6	−0.173187
$965$	1.45243e7	0.502085
$966$	−2.34443e7	−0.808342
$967$	−7.08291e6	−0.243582	−0.121791	−	0.992556i	$-0.538864\pi$
$967$	−7.08291e6	−0.243582	−0.121791	+	0.992556i	$0.538864\pi$
$968$	4.09641e6	0.140513
$969$	995793.	0.0340690
$970$	4.41834e7	1.50775
$971$	2.85104e7	0.970411	0.485205	−	0.874400i	$-0.338745\pi$
$971$	2.85104e7	0.970411	0.485205	+	0.874400i	$0.338745\pi$
$972$	7.40887e6	0.251528
$973$	−4.55697e7	−1.54310
$974$	7.07813e6	0.239068
$975$	−5.01983e7	−1.69113
$976$	1.57486e6	0.0529197
$977$	−2.48752e7	−0.833739	−0.416869	−	0.908966i	$-0.636873\pi$
$977$	−2.48752e7	−0.833739	−0.416869	+	0.908966i	$0.636873\pi$
$978$	−2.84101e7	−0.949786
$979$	−5.31626e6	−0.177276
$980$	−1.09437e6	−0.0363998
$981$	8.75985e6	0.290619
$982$	4.50808e6	0.149181
$983$	−2.66082e6	−0.0878277	−0.0439138	−	0.999035i	$-0.513983\pi$
$983$	−2.66082e6	−0.0878277	−0.0439138	+	0.999035i	$0.513983\pi$
$984$	2.20851e7	0.727129
$985$	7.41539e6	0.243525
$986$	2.99085e6	0.0979721
$987$	−3.50510e7	−1.14527
$988$	5.20649e6	0.169689
$989$	−2.77099e7	−0.900833
$990$	6.19271e6	0.200813
$991$	5.19709e7	1.68103	0.840516	−	0.541786i	$-0.182252\pi$
$991$	5.19709e7	1.68103	0.840516	+	0.541786i	$0.182252\pi$
$992$	6.74587e6	0.217650
$993$	6.59734e7	2.12322
$994$	2.94080e7	0.944058
$995$	−5.74489e7	−1.83960
$996$	−1.14863e7	−0.366885
$997$	−1.86644e7	−0.594672	−0.297336	−	0.954773i	$-0.596098\pi$
$997$	−1.86644e7	−0.594672	−0.297336	+	0.954773i	$0.596098\pi$
$998$	2.38449e7	0.757826
$999$	2.68374e7	0.850799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.a.c.1.1	✓	2
3.2	odd	2		342.6.a.i.1.2		2
4.3	odd	2		304.6.a.f.1.2		2
5.4	even	2		950.6.a.d.1.2		2
19.18	odd	2		722.6.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.c.1.1	✓	2	1.1	even	1	trivial
304.6.a.f.1.2		2	4.3	odd	2
342.6.a.i.1.2		2	3.2	odd	2
722.6.a.c.1.2		2	19.18	odd	2
950.6.a.d.1.2		2	5.4	even	2

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} -64.0000 q^{8} +62.5592 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} -64.0000 q^{8} +62.5592 q^{9} +317.763 q^{10} +311.520 q^{11} -279.684 q^{12} +901.401 q^{13} -531.684 q^{14} +1388.64 q^{15} +256.000 q^{16} -157.803 q^{17} -250.237 q^{18} +361.000 q^{19} -1271.05 q^{20} -2323.49 q^{21} -1246.08 q^{22} -2522.53 q^{23} +1118.74 q^{24} +3185.83 q^{25} -3605.61 q^{26} +3154.15 q^{27} +2126.74 q^{28} +4738.28 q^{29} -5554.58 q^{30} -6587.76 q^{31} -1024.00 q^{32} -5445.44 q^{33} +631.210 q^{34} -10559.3 q^{35} +1000.95 q^{36} +8508.60 q^{37} -1444.00 q^{38} -15756.7 q^{39} +5084.21 q^{40} +19741.1 q^{41} +9293.97 q^{42} +10985.0 q^{43} +4984.32 q^{44} -4969.75 q^{45} +10090.1 q^{46} +15085.5 q^{47} -4474.94 q^{48} +860.995 q^{49} -12743.3 q^{50} +2758.43 q^{51} +14422.4 q^{52} +21699.6 q^{53} -12616.6 q^{54} -24747.4 q^{55} -8506.94 q^{56} -6310.37 q^{57} -18953.1 q^{58} -40676.1 q^{59} +22218.3 q^{60} +6151.79 q^{61} +26351.0 q^{62} +8315.44 q^{63} +4096.00 q^{64} -71608.0 q^{65} +21781.8 q^{66} +62760.3 q^{67} -2524.84 q^{68} +44094.5 q^{69} +42237.4 q^{70} -55311.0 q^{71} -4003.79 q^{72} -48528.1 q^{73} -34034.4 q^{74} -55689.2 q^{75} +5776.00 q^{76} +41407.5 q^{77} +63026.9 q^{78} +31017.6 q^{79} -20336.8 q^{80} -70337.2 q^{81} -78964.4 q^{82} +41068.7 q^{83} -37175.9 q^{84} +12536.0 q^{85} -43939.8 q^{86} -82826.3 q^{87} -19937.3 q^{88} -17065.6 q^{89} +19879.0 q^{90} +119815. q^{91} -40360.5 q^{92} +115156. q^{93} -60341.9 q^{94} -28678.1 q^{95} +17899.8 q^{96} +139045. q^{97} -3443.98 q^{98} +19488.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9	\( 2 q - 8 q^{2} + 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} - 128 q^{8} + 239 q^{9} + 180 q^{10} + 661 q^{11} + 48 q^{12} + 1613 q^{13} - 456 q^{14} + 2094 q^{15} + 512 q^{16} + 64 q^{17} - 956 q^{18} + 722 q^{19} - 720 q^{20} - 2711 q^{21} - 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} + 1791 q^{27} + 1824 q^{28} - 2481 q^{29} - 8376 q^{30} - 1180 q^{31} - 2048 q^{32} + 1712 q^{33} - 256 q^{34} - 11211 q^{35} + 3824 q^{36} + 10488 q^{37} - 2888 q^{38} - 1183 q^{39} + 2880 q^{40} + 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} + 12740 q^{46} - 12155 q^{47} + 768 q^{48} - 15588 q^{49} - 4988 q^{50} + 7301 q^{51} + 25808 q^{52} + 20585 q^{53} - 7164 q^{54} - 12711 q^{55} - 7296 q^{56} + 1083 q^{57} + 9924 q^{58} - 78581 q^{59} + 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} - 47100 q^{65} - 6848 q^{66} + 7805 q^{67} + 1024 q^{68} + 30527 q^{69} + 44844 q^{70} - 62488 q^{71} - 15296 q^{72} + 16218 q^{73} - 41952 q^{74} - 95397 q^{75} + 11552 q^{76} + 34795 q^{77} + 4732 q^{78} + 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} - 43376 q^{84} + 20175 q^{85} - 45212 q^{86} - 230679 q^{87} - 42304 q^{88} + 128188 q^{89} - 4428 q^{90} + 106351 q^{91} - 50960 q^{92} + 225908 q^{93} + 48620 q^{94} - 16245 q^{95} - 3072 q^{96} + 178558 q^{97} + 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 - 128 * q^8 + 239 * q^9 + 180 * q^10 + 661 * q^11 + 48 * q^12 + 1613 * q^13 - 456 * q^14 + 2094 * q^15 + 512 * q^16 + 64 * q^17 - 956 * q^18 + 722 * q^19 - 720 * q^20 - 2711 * q^21 - 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 + 1791 * q^27 + 1824 * q^28 - 2481 * q^29 - 8376 * q^30 - 1180 * q^31 - 2048 * q^32 + 1712 * q^33 - 256 * q^34 - 11211 * q^35 + 3824 * q^36 + 10488 * q^37 - 2888 * q^38 - 1183 * q^39 + 2880 * q^40 + 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 + 12740 * q^46 - 12155 * q^47 + 768 * q^48 - 15588 * q^49 - 4988 * q^50 + 7301 * q^51 + 25808 * q^52 + 20585 * q^53 - 7164 * q^54 - 12711 * q^55 - 7296 * q^56 + 1083 * q^57 + 9924 * q^58 - 78581 * q^59 + 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 - 47100 * q^65 - 6848 * q^66 + 7805 * q^67 + 1024 * q^68 + 30527 * q^69 + 44844 * q^70 - 62488 * q^71 - 15296 * q^72 + 16218 * q^73 - 41952 * q^74 - 95397 * q^75 + 11552 * q^76 + 34795 * q^77 + 4732 * q^78 + 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 - 43376 * q^84 + 20175 * q^85 - 45212 * q^86 - 230679 * q^87 - 42304 * q^88 + 128188 * q^89 - 4428 * q^90 + 106351 * q^91 - 50960 * q^92 + 225908 * q^93 + 48620 * q^94 - 16245 * q^95 - 3072 * q^96 + 178558 * q^97 + 62352 * q^98 + 81151 * q^99

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