LMFDB - Embedded newform 38.6.a.d.1.3

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:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 454x + 3760 $ x^3 - x^2 - 454*x + 3760
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$14.3926$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +18.3926 q^{3} +16.0000 q^{4} +42.3408 q^{5} +73.5705 q^{6} -127.237 q^{7} +64.0000 q^{8} +95.2889 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +18.3926 q^{3} +16.0000 q^{4} +42.3408 q^{5} +73.5705 q^{6} -127.237 q^{7} +64.0000 q^{8} +95.2889 q^{9} +169.363 q^{10} +381.793 q^{11} +294.282 q^{12} -726.498 q^{13} -508.950 q^{14} +778.758 q^{15} +256.000 q^{16} +1058.96 q^{17} +381.156 q^{18} -361.000 q^{19} +677.452 q^{20} -2340.23 q^{21} +1527.17 q^{22} -1566.71 q^{23} +1177.13 q^{24} -1332.26 q^{25} -2905.99 q^{26} -2716.80 q^{27} -2035.80 q^{28} +740.979 q^{29} +3115.03 q^{30} -7812.75 q^{31} +1024.00 q^{32} +7022.18 q^{33} +4235.84 q^{34} -5387.33 q^{35} +1524.62 q^{36} -457.587 q^{37} -1444.00 q^{38} -13362.2 q^{39} +2709.81 q^{40} -4251.13 q^{41} -9360.93 q^{42} +23354.2 q^{43} +6108.69 q^{44} +4034.60 q^{45} -6266.83 q^{46} +11928.2 q^{47} +4708.51 q^{48} -617.621 q^{49} -5329.04 q^{50} +19477.0 q^{51} -11624.0 q^{52} +17946.0 q^{53} -10867.2 q^{54} +16165.4 q^{55} -8143.20 q^{56} -6639.74 q^{57} +2963.92 q^{58} +47789.2 q^{59} +12460.1 q^{60} +8735.48 q^{61} -31251.0 q^{62} -12124.3 q^{63} +4096.00 q^{64} -30760.5 q^{65} +28088.7 q^{66} -1796.43 q^{67} +16943.3 q^{68} -28815.9 q^{69} -21549.3 q^{70} -45723.6 q^{71} +6098.49 q^{72} -73831.2 q^{73} -1830.35 q^{74} -24503.8 q^{75} -5776.00 q^{76} -48578.4 q^{77} -53448.9 q^{78} +61784.6 q^{79} +10839.2 q^{80} -73124.2 q^{81} -17004.5 q^{82} +82509.3 q^{83} -37443.7 q^{84} +44837.1 q^{85} +93416.7 q^{86} +13628.5 q^{87} +24434.7 q^{88} -6673.72 q^{89} +16138.4 q^{90} +92437.8 q^{91} -25067.3 q^{92} -143697. q^{93} +47712.8 q^{94} -15285.0 q^{95} +18834.1 q^{96} +163271. q^{97} -2470.48 q^{98} +36380.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9}+O(q^{10}) $ 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9} + 324 q^{10} + 363 q^{11} + 208 q^{12} + 501 q^{13} + 912 q^{14} - 670 q^{15} + 768 q^{16} - 1206 q^{17} + 944 q^{18} - 1083 q^{19} + 1296 q^{20} - 2085 q^{21} + 1452 q^{22} - 1077 q^{23} + 832 q^{24} - 3882 q^{25} + 2004 q^{26} - 5087 q^{27} + 3648 q^{28} - 8349 q^{29} - 2680 q^{30} - 7332 q^{31} + 3072 q^{32} - 15784 q^{33} - 4824 q^{34} - 1185 q^{35} + 3776 q^{36} - 1650 q^{37} - 4332 q^{38} + 773 q^{39} + 5184 q^{40} + 10140 q^{41} - 8340 q^{42} + 3777 q^{43} + 5808 q^{44} + 14005 q^{45} - 4308 q^{46} + 33231 q^{47} + 3328 q^{48} + 31269 q^{49} - 15528 q^{50} + 46935 q^{51} + 8016 q^{52} + 31029 q^{53} - 20348 q^{54} + 66003 q^{55} + 14592 q^{56} - 4693 q^{57} - 33396 q^{58} + 20409 q^{59} - 10720 q^{60} + 17115 q^{61} - 29328 q^{62} + 6327 q^{63} + 12288 q^{64} - 45348 q^{65} - 63136 q^{66} - 789 q^{67} - 19296 q^{68} - 151147 q^{69} - 4740 q^{70} + 19164 q^{71} + 15104 q^{72} - 76260 q^{73} - 6600 q^{74} - 69607 q^{75} - 17328 q^{76} - 97209 q^{77} + 3092 q^{78} + 68358 q^{79} + 20736 q^{80} - 197713 q^{81} + 40560 q^{82} + 6762 q^{83} - 33360 q^{84} - 45837 q^{85} + 15108 q^{86} + 66805 q^{87} + 23232 q^{88} - 85506 q^{89} + 56020 q^{90} + 345033 q^{91} - 17232 q^{92} + 15688 q^{93} + 132924 q^{94} - 29241 q^{95} + 13312 q^{96} + 105024 q^{97} + 125076 q^{98} + 158317 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9 + 324 * q^10 + 363 * q^11 + 208 * q^12 + 501 * q^13 + 912 * q^14 - 670 * q^15 + 768 * q^16 - 1206 * q^17 + 944 * q^18 - 1083 * q^19 + 1296 * q^20 - 2085 * q^21 + 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 - 5087 * q^27 + 3648 * q^28 - 8349 * q^29 - 2680 * q^30 - 7332 * q^31 + 3072 * q^32 - 15784 * q^33 - 4824 * q^34 - 1185 * q^35 + 3776 * q^36 - 1650 * q^37 - 4332 * q^38 + 773 * q^39 + 5184 * q^40 + 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 - 4308 * q^46 + 33231 * q^47 + 3328 * q^48 + 31269 * q^49 - 15528 * q^50 + 46935 * q^51 + 8016 * q^52 + 31029 * q^53 - 20348 * q^54 + 66003 * q^55 + 14592 * q^56 - 4693 * q^57 - 33396 * q^58 + 20409 * q^59 - 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 - 45348 * q^65 - 63136 * q^66 - 789 * q^67 - 19296 * q^68 - 151147 * q^69 - 4740 * q^70 + 19164 * q^71 + 15104 * q^72 - 76260 * q^73 - 6600 * q^74 - 69607 * q^75 - 17328 * q^76 - 97209 * q^77 + 3092 * q^78 + 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 - 33360 * q^84 - 45837 * q^85 + 15108 * q^86 + 66805 * q^87 + 23232 * q^88 - 85506 * q^89 + 56020 * q^90 + 345033 * q^91 - 17232 * q^92 + 15688 * q^93 + 132924 * q^94 - 29241 * q^95 + 13312 * q^96 + 105024 * q^97 + 125076 * q^98 + 158317 * 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
$3$	18.3926	1.17989	0.589944	−	0.807444i	$-0.299150\pi$
$3$	18.3926	1.17989	0.589944	+	0.807444i	$0.299150\pi$
$4$	16.0000	0.500000
$5$	42.3408	0.757415	0.378707	−	0.925517i	$-0.376369\pi$
$5$	42.3408	0.757415	0.378707	+	0.925517i	$0.376369\pi$
$6$	73.5705	0.834307
$7$	−127.237	−0.981454	−0.490727	−	0.871313i	$-0.663269\pi$
$7$	−127.237	−0.981454	−0.490727	+	0.871313i	$0.663269\pi$
$8$	64.0000	0.353553
$9$	95.2889	0.392135
$10$	169.363	0.535573
$11$	381.793	0.951363	0.475681	−	0.879618i	$-0.342202\pi$
$11$	381.793	0.951363	0.475681	+	0.879618i	$0.342202\pi$
$12$	294.282	0.589944
$13$	−726.498	−1.19227	−0.596137	−	0.802883i	$-0.703299\pi$
$13$	−726.498	−1.19227	−0.596137	+	0.802883i	$0.703299\pi$
$14$	−508.950	−0.693993
$15$	778.758	0.893664
$16$	256.000	0.250000
$17$	1058.96	0.888704	0.444352	−	0.895852i	$-0.353434\pi$
$17$	1058.96	0.888704	0.444352	+	0.895852i	$0.353434\pi$
$18$	381.156	0.277282
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	677.452	0.378707
$21$	−2340.23	−1.15801
$22$	1527.17	0.672715
$23$	−1566.71	−0.617545	−0.308772	−	0.951136i	$-0.599918\pi$
$23$	−1566.71	−0.617545	−0.308772	+	0.951136i	$0.599918\pi$
$24$	1177.13	0.417153
$25$	−1332.26	−0.426323
$26$	−2905.99	−0.843065
$27$	−2716.80	−0.717212
$28$	−2035.80	−0.490727
$29$	740.979	0.163610	0.0818052	−	0.996648i	$-0.473931\pi$
$29$	740.979	0.163610	0.0818052	+	0.996648i	$0.473931\pi$
$30$	3115.03	0.631916
$31$	−7812.75	−1.46016	−0.730079	−	0.683363i	$-0.760517\pi$
$31$	−7812.75	−1.46016	−0.730079	+	0.683363i	$0.760517\pi$
$32$	1024.00	0.176777
$33$	7022.18	1.12250
$34$	4235.84	0.628408
$35$	−5387.33	−0.743368
$36$	1524.62	0.196068
$37$	−457.587	−0.0549503	−0.0274751	−	0.999622i	$-0.508747\pi$
$37$	−457.587	−0.0549503	−0.0274751	+	0.999622i	$0.508747\pi$
$38$	−1444.00	−0.162221
$39$	−13362.2	−1.40675
$40$	2709.81	0.267786
$41$	−4251.13	−0.394952	−0.197476	−	0.980308i	$-0.563274\pi$
$41$	−4251.13	−0.394952	−0.197476	+	0.980308i	$0.563274\pi$
$42$	−9360.93	−0.818834
$43$	23354.2	1.92617	0.963083	−	0.269206i	$-0.0867612\pi$
$43$	23354.2	1.92617	0.963083	+	0.269206i	$0.0867612\pi$
$44$	6108.69	0.475681
$45$	4034.60	0.297009
$46$	−6266.83	−0.436670
$47$	11928.2	0.787645	0.393823	−	0.919186i	$-0.371152\pi$
$47$	11928.2	0.787645	0.393823	+	0.919186i	$0.371152\pi$
$48$	4708.51	0.294972
$49$	−617.621	−0.0367478
$50$	−5329.04	−0.301456
$51$	19477.0	1.04857
$52$	−11624.0	−0.596137
$53$	17946.0	0.877562	0.438781	−	0.898594i	$-0.355410\pi$
$53$	17946.0	0.877562	0.438781	+	0.898594i	$0.355410\pi$
$54$	−10867.2	−0.507146
$55$	16165.4	0.720576
$56$	−8143.20	−0.346996
$57$	−6639.74	−0.270685
$58$	2963.92	0.115690
$59$	47789.2	1.78731	0.893655	−	0.448754i	$-0.148132\pi$
$59$	47789.2	1.78731	0.893655	+	0.448754i	$0.148132\pi$
$60$	12460.1	0.446832
$61$	8735.48	0.300582	0.150291	−	0.988642i	$-0.451979\pi$
$61$	8735.48	0.300582	0.150291	+	0.988642i	$0.451979\pi$
$62$	−31251.0	−1.03249
$63$	−12124.3	−0.384863
$64$	4096.00	0.125000
$65$	−30760.5	−0.903046
$66$	28088.7	0.793728
$67$	−1796.43	−0.0488905	−0.0244452	−	0.999701i	$-0.507782\pi$
$67$	−1796.43	−0.0488905	−0.0244452	+	0.999701i	$0.507782\pi$
$68$	16943.3	0.444352
$69$	−28815.9	−0.728634
$70$	−21549.3	−0.525640
$71$	−45723.6	−1.07645	−0.538226	−	0.842801i	$-0.680905\pi$
$71$	−45723.6	−1.07645	−0.538226	+	0.842801i	$0.680905\pi$
$72$	6098.49	0.138641
$73$	−73831.2	−1.62156	−0.810779	−	0.585352i	$-0.800956\pi$
$73$	−73831.2	−1.62156	−0.810779	+	0.585352i	$0.800956\pi$
$74$	−1830.35	−0.0388557
$75$	−24503.8	−0.503014
$76$	−5776.00	−0.114708
$77$	−48578.4	−0.933719
$78$	−53448.9	−0.994722
$79$	61784.6	1.11381	0.556907	−	0.830575i	$-0.311988\pi$
$79$	61784.6	1.11381	0.556907	+	0.830575i	$0.311988\pi$
$80$	10839.2	0.189354
$81$	−73124.2	−1.23837
$82$	−17004.5	−0.279273
$83$	82509.3	1.31464	0.657321	−	0.753610i	$-0.271689\pi$
$83$	82509.3	1.31464	0.657321	+	0.753610i	$0.271689\pi$
$84$	−37443.7	−0.579003
$85$	44837.1	0.673117
$86$	93416.7	1.36200
$87$	13628.5	0.193042
$88$	24434.7	0.336358
$89$	−6673.72	−0.0893085	−0.0446543	−	0.999003i	$-0.514219\pi$
$89$	−6673.72	−0.0893085	−0.0446543	+	0.999003i	$0.514219\pi$
$90$	16138.4	0.210017
$91$	92437.8	1.17016
$92$	−25067.3	−0.308772
$93$	−143697.	−1.72282
$94$	47712.8	0.556949
$95$	−15285.0	−0.173763
$96$	18834.1	0.208577
$97$	163271.	1.76189	0.880944	−	0.473220i	$-0.156908\pi$
$97$	163271.	1.76189	0.880944	+	0.473220i	$0.156908\pi$
$98$	−2470.48	−0.0259846
$99$	36380.6	0.373063
$100$	−21316.2	−0.213162
$101$	−30090.6	−0.293513	−0.146757	−	0.989173i	$-0.546883\pi$
$101$	−30090.6	−0.293513	−0.146757	+	0.989173i	$0.546883\pi$
$102$	77908.2	0.741451
$103$	98753.1	0.917186	0.458593	−	0.888646i	$-0.348354\pi$
$103$	98753.1	0.917186	0.458593	+	0.888646i	$0.348354\pi$
$104$	−46495.9	−0.421533
$105$	−99087.2	−0.877090
$106$	71784.0	0.620530
$107$	−94862.2	−0.801002	−0.400501	−	0.916296i	$-0.631164\pi$
$107$	−94862.2	−0.801002	−0.400501	+	0.916296i	$0.631164\pi$
$108$	−43468.7	−0.358606
$109$	166646.	1.34347	0.671734	−	0.740792i	$-0.265550\pi$
$109$	166646.	1.34347	0.671734	+	0.740792i	$0.265550\pi$
$110$	64661.6	0.509524
$111$	−8416.24	−0.0648351
$112$	−32572.8	−0.245364
$113$	−167569.	−1.23451	−0.617257	−	0.786761i	$-0.711756\pi$
$113$	−167569.	−1.23451	−0.617257	+	0.786761i	$0.711756\pi$
$114$	−26559.0	−0.191403
$115$	−66335.6	−0.467737
$116$	11855.7	0.0818052
$117$	−69227.2	−0.467533
$118$	191157.	1.26382
$119$	−134739.	−0.872222
$120$	49840.5	0.315958
$121$	−15285.1	−0.0949087
$122$	34941.9	0.212543
$123$	−78189.4	−0.465999
$124$	−125004.	−0.730079
$125$	−188724.	−1.08032
$126$	−48497.3	−0.272139
$127$	88964.9	0.489451	0.244726	−	0.969592i	$-0.421302\pi$
$127$	88964.9	0.489451	0.244726	+	0.969592i	$0.421302\pi$
$128$	16384.0	0.0883883
$129$	429545.	2.27266
$130$	−123042.	−0.638550
$131$	375118.	1.90981	0.954904	−	0.296915i	$-0.0959577\pi$
$131$	375118.	1.90981	0.954904	+	0.296915i	$0.0959577\pi$
$132$	112355.	0.561251
$133$	45932.7	0.225161
$134$	−7185.73	−0.0345708
$135$	−115031.	−0.543227
$136$	67773.4	0.314204
$137$	−228683.	−1.04095	−0.520477	−	0.853875i	$-0.674246\pi$
$137$	−228683.	−1.04095	−0.520477	+	0.853875i	$0.674246\pi$
$138$	−115264.	−0.515222
$139$	135000.	0.592646	0.296323	−	0.955088i	$-0.404240\pi$
$139$	135000.	0.592646	0.296323	+	0.955088i	$0.404240\pi$
$140$	−86197.3	−0.371684
$141$	219391.	0.929333
$142$	−182894.	−0.761166
$143$	−277372.	−1.13429
$144$	24394.0	0.0980338
$145$	31373.6	0.123921
$146$	−295325.	−1.14662
$147$	−11359.7	−0.0433583
$148$	−7321.40	−0.0274751
$149$	−59731.8	−0.220414	−0.110207	−	0.993909i	$-0.535151\pi$
$149$	−59731.8	−0.220414	−0.110207	+	0.993909i	$0.535151\pi$
$150$	−98015.1	−0.355684
$151$	−431016.	−1.53834	−0.769168	−	0.639047i	$-0.779329\pi$
$151$	−431016.	−1.53834	−0.769168	+	0.639047i	$0.779329\pi$
$152$	−23104.0	−0.0811107
$153$	100907.	0.348492
$154$	−194314.	−0.660239
$155$	−330798.	−1.10594
$156$	−213795.	−0.703375
$157$	−230317.	−0.745722	−0.372861	−	0.927887i	$-0.621623\pi$
$157$	−230317.	−0.745722	−0.372861	+	0.927887i	$0.621623\pi$
$158$	247138.	0.787585
$159$	330074.	1.03543
$160$	43356.9	0.133893
$161$	199344.	0.606092
$162$	−292497.	−0.875656
$163$	573529.	1.69078	0.845388	−	0.534152i	$-0.179369\pi$
$163$	573529.	1.69078	0.845388	+	0.534152i	$0.179369\pi$
$164$	−68018.0	−0.197476
$165$	297324.	0.850199
$166$	330037.	0.929593
$167$	32331.8	0.0897095	0.0448548	−	0.998994i	$-0.485717\pi$
$167$	32331.8	0.0897095	0.0448548	+	0.998994i	$0.485717\pi$
$168$	−149775.	−0.409417
$169$	156507.	0.421518
$170$	179349.	0.475966
$171$	−34399.3	−0.0899620
$172$	373667.	0.963083
$173$	−640334.	−1.62664	−0.813319	−	0.581818i	$-0.802342\pi$
$173$	−640334.	−1.62664	−0.813319	+	0.581818i	$0.802342\pi$
$174$	54514.2	0.136501
$175$	169513.	0.418417
$176$	97739.0	0.237841
$177$	878970.	2.10883
$178$	−26694.9	−0.0631507
$179$	199033.	0.464292	0.232146	−	0.972681i	$-0.425425\pi$
$179$	199033.	0.464292	0.232146	+	0.972681i	$0.425425\pi$
$180$	64553.7	0.148505
$181$	−816331.	−1.85212	−0.926061	−	0.377374i	$-0.876827\pi$
$181$	−816331.	−1.85212	−0.926061	+	0.377374i	$0.876827\pi$
$182$	369751.	0.827430
$183$	160668.	0.354652
$184$	−100269.	−0.218335
$185$	−19374.6	−0.0416201
$186$	−574788.	−1.21822
$187$	404303.	0.845480
$188$	190851.	0.393823
$189$	345678.	0.703911
$190$	−61140.1	−0.122869
$191$	−263614.	−0.522859	−0.261430	−	0.965223i	$-0.584194\pi$
$191$	−263614.	−0.522859	−0.261430	+	0.965223i	$0.584194\pi$
$192$	75336.2	0.147486
$193$	−505817.	−0.977463	−0.488731	−	0.872434i	$-0.662540\pi$
$193$	−505817.	−0.977463	−0.488731	+	0.872434i	$0.662540\pi$
$194$	653082.	1.24584
$195$	−565766.	−1.06549
$196$	−9881.93	−0.0183739
$197$	864016.	1.58619	0.793097	−	0.609095i	$-0.208467\pi$
$197$	864016.	1.58619	0.793097	+	0.609095i	$0.208467\pi$
$198$	145523.	0.263795
$199$	−582580.	−1.04285	−0.521427	−	0.853296i	$-0.674600\pi$
$199$	−582580.	−1.04285	−0.521427	+	0.853296i	$0.674600\pi$
$200$	−85264.6	−0.150728
$201$	−33041.1	−0.0576853
$202$	−120363.	−0.207545
$203$	−94280.3	−0.160576
$204$	311633.	0.524285
$205$	−179996.	−0.299143
$206$	395012.	0.648549
$207$	−149290.	−0.242161
$208$	−185984.	−0.298069
$209$	−137827.	−0.218258
$210$	−396349.	−0.620197
$211$	374780.	0.579523	0.289761	−	0.957099i	$-0.406424\pi$
$211$	374780.	0.579523	0.289761	+	0.957099i	$0.406424\pi$
$212$	287136.	0.438781
$213$	−840977.	−1.27009
$214$	−379449.	−0.566394
$215$	988834.	1.45891
$216$	−173875.	−0.253573
$217$	994075.	1.43308
$218$	666582.	0.949976
$219$	−1.35795e6	−1.91326
$220$	258646.	0.360288
$221$	−769332.	−1.05958
$222$	−33664.9	−0.0458454
$223$	−773167.	−1.04114	−0.520572	−	0.853818i	$-0.674281\pi$
$223$	−773167.	−1.04114	−0.520572	+	0.853818i	$0.674281\pi$
$224$	−130291.	−0.173498
$225$	−126950.	−0.167176
$226$	−670274.	−0.872934
$227$	−490462.	−0.631743	−0.315871	−	0.948802i	$-0.602297\pi$
$227$	−490462.	−0.631743	−0.315871	+	0.948802i	$0.602297\pi$
$228$	−106236.	−0.135342
$229$	−57262.3	−0.0721573	−0.0360786	−	0.999349i	$-0.511487\pi$
$229$	−57262.3	−0.0721573	−0.0360786	+	0.999349i	$0.511487\pi$
$230$	−265342.	−0.330740
$231$	−893484.	−1.10168
$232$	47422.6	0.0578450
$233$	292508.	0.352979	0.176489	−	0.984303i	$-0.443526\pi$
$233$	292508.	0.352979	0.176489	+	0.984303i	$0.443526\pi$
$234$	−276909.	−0.330596
$235$	505049.	0.596574
$236$	764628.	0.893655
$237$	1.13638e6	1.31418
$238$	−538957.	−0.616754
$239$	445282.	0.504244	0.252122	−	0.967695i	$-0.418872\pi$
$239$	445282.	0.504244	0.252122	+	0.967695i	$0.418872\pi$
$240$	199362.	0.223416
$241$	−1.34568e6	−1.49244	−0.746222	−	0.665697i	$-0.768134\pi$
$241$	−1.34568e6	−1.49244	−0.746222	+	0.665697i	$0.768134\pi$
$242$	−61140.6	−0.0671106
$243$	−684766.	−0.743920
$244$	139768.	0.150291
$245$	−26150.5	−0.0278333
$246$	−312758.	−0.329511
$247$	262266.	0.273526
$248$	−500016.	−0.516244
$249$	1.51756e6	1.55113
$250$	−754895.	−0.763900
$251$	−1.09190e6	−1.09396	−0.546978	−	0.837147i	$-0.684222\pi$
$251$	−1.09190e6	−1.09396	−0.546978	+	0.837147i	$0.684222\pi$
$252$	−193989.	−0.192431
$253$	−598158.	−0.587509
$254$	355860.	0.346094
$255$	824673.	0.794203
$256$	65536.0	0.0625000
$257$	1.51625e6	1.43198	0.715992	−	0.698108i	$-0.245975\pi$
$257$	1.51625e6	1.43198	0.715992	+	0.698108i	$0.245975\pi$
$258$	1.71818e6	1.60701
$259$	58222.3	0.0539312
$260$	−492168.	−0.451523
$261$	70607.0	0.0641574
$262$	1.50047e6	1.35044
$263$	−183186.	−0.163306	−0.0816531	−	0.996661i	$-0.526020\pi$
$263$	−183186.	−0.163306	−0.0816531	+	0.996661i	$0.526020\pi$
$264$	449419.	0.396864
$265$	759847.	0.664679
$266$	183731.	0.159213
$267$	−122747.	−0.105374
$268$	−28742.9	−0.0244452
$269$	−1.10143e6	−0.928059	−0.464029	−	0.885820i	$-0.653597\pi$
$269$	−1.10143e6	−0.928059	−0.464029	+	0.885820i	$0.653597\pi$
$270$	−460125.	−0.384119
$271$	−1.02496e6	−0.847779	−0.423890	−	0.905714i	$-0.639336\pi$
$271$	−1.02496e6	−0.847779	−0.423890	+	0.905714i	$0.639336\pi$
$272$	271094.	0.222176
$273$	1.70017e6	1.38066
$274$	−914731.	−0.736066
$275$	−508647.	−0.405588
$276$	−461054.	−0.364317
$277$	2.38231e6	1.86551	0.932757	−	0.360505i	$-0.117396\pi$
$277$	2.38231e6	1.86551	0.932757	+	0.360505i	$0.117396\pi$
$278$	539998.	0.419064
$279$	−744468.	−0.572579
$280$	−344789.	−0.262820
$281$	1.97944e6	1.49547	0.747733	−	0.664000i	$-0.231143\pi$
$281$	1.97944e6	1.49547	0.747733	+	0.664000i	$0.231143\pi$
$282$	877565.	0.657138
$283$	70483.2	0.0523142	0.0261571	−	0.999658i	$-0.491673\pi$
$283$	70483.2	0.0523142	0.0261571	+	0.999658i	$0.491673\pi$
$284$	−731578.	−0.538226
$285$	−281132.	−0.205021
$286$	−1.10949e6	−0.802061
$287$	540903.	0.387627
$288$	97575.8	0.0693204
$289$	−298463.	−0.210206
$290$	125494.	0.0876253
$291$	3.00297e6	2.07883
$292$	−1.18130e6	−0.810779
$293$	842274.	0.573171	0.286586	−	0.958055i	$-0.407480\pi$
$293$	842274.	0.573171	0.286586	+	0.958055i	$0.407480\pi$
$294$	−45438.7	−0.0306590
$295$	2.02343e6	1.35373
$296$	−29285.6	−0.0194279
$297$	−1.03725e6	−0.682329
$298$	−238927.	−0.155857
$299$	1.13821e6	0.736283
$300$	−392060.	−0.251507
$301$	−2.97153e6	−1.89044
$302$	−1.72406e6	−1.08777
$303$	−553446.	−0.346313
$304$	−92416.0	−0.0573539
$305$	369867.	0.227665
$306$	403628.	0.246421
$307$	−2.79322e6	−1.69145	−0.845725	−	0.533619i	$-0.820832\pi$
$307$	−2.79322e6	−1.69145	−0.845725	+	0.533619i	$0.820832\pi$
$308$	−777254.	−0.466859
$309$	1.81633e6	1.08218
$310$	−1.32319e6	−0.782021
$311$	−1.49358e6	−0.875642	−0.437821	−	0.899062i	$-0.644250\pi$
$311$	−1.49358e6	−0.875642	−0.437821	+	0.899062i	$0.644250\pi$
$312$	−855182.	−0.497361
$313$	−395047.	−0.227923	−0.113961	−	0.993485i	$-0.536354\pi$
$313$	−395047.	−0.227923	−0.113961	+	0.993485i	$0.536354\pi$
$314$	−921268.	−0.527305
$315$	−513353.	−0.291501
$316$	988554.	0.556907
$317$	−2.17633e6	−1.21640	−0.608201	−	0.793783i	$-0.708108\pi$
$317$	−2.17633e6	−1.21640	−0.608201	+	0.793783i	$0.708108\pi$
$318$	1.32030e6	0.732156
$319$	282900.	0.155653
$320$	173428.	0.0946768
$321$	−1.74476e6	−0.945093
$322$	797376.	0.428572
$323$	−382284.	−0.203883
$324$	−1.16999e6	−0.619183
$325$	967884.	0.508294
$326$	2.29412e6	1.19556
$327$	3.06505e6	1.58514
$328$	−272072.	−0.139637
$329$	−1.51772e6	−0.773038
$330$	1.18930e6	0.601181
$331$	−2.05875e6	−1.03284	−0.516420	−	0.856335i	$-0.672736\pi$
$331$	−2.05875e6	−1.03284	−0.516420	+	0.856335i	$0.672736\pi$
$332$	1.32015e6	0.657321
$333$	−43603.0	−0.0215479
$334$	129327.	0.0634342
$335$	−76062.4	−0.0370303
$336$	−599099.	−0.289501
$337$	587423.	0.281758	0.140879	−	0.990027i	$-0.455007\pi$
$337$	587423.	0.281758	0.140879	+	0.990027i	$0.455007\pi$
$338$	626026.	0.298058
$339$	−3.08203e6	−1.45659
$340$	717394.	0.336558
$341$	−2.98285e6	−1.38914
$342$	−137597.	−0.0636128
$343$	2.21707e6	1.01752
$344$	1.49467e6	0.681002
$345$	−1.22009e6	−0.551878
$346$	−2.56133e6	−1.15021
$347$	3.01162e6	1.34269	0.671346	−	0.741144i	$-0.265716\pi$
$347$	3.01162e6	1.34269	0.671346	+	0.741144i	$0.265716\pi$
$348$	218057.	0.0965209
$349$	561200.	0.246635	0.123317	−	0.992367i	$-0.460647\pi$
$349$	561200.	0.246635	0.123317	+	0.992367i	$0.460647\pi$
$350$	678054.	0.295865
$351$	1.97375e6	0.855113
$352$	390956.	0.168179
$353$	1.93598e6	0.826922	0.413461	−	0.910522i	$-0.364320\pi$
$353$	1.93598e6	0.826922	0.413461	+	0.910522i	$0.364320\pi$
$354$	3.51588e6	1.49117
$355$	−1.93597e6	−0.815320
$356$	−106779.	−0.0446543
$357$	−2.47821e6	−1.02912
$358$	796130.	0.328304
$359$	−388348.	−0.159032	−0.0795161	−	0.996834i	$-0.525338\pi$
$359$	−388348.	−0.159032	−0.0795161	+	0.996834i	$0.525338\pi$
$360$	258215.	0.105009
$361$	130321.	0.0526316
$362$	−3.26532e6	−1.30965
$363$	−281134.	−0.111982
$364$	1.47900e6	0.585081
$365$	−3.12607e6	−1.22819
$366$	642674.	0.250777
$367$	3.42147e6	1.32601	0.663006	−	0.748614i	$-0.269280\pi$
$367$	3.42147e6	1.32601	0.663006	+	0.748614i	$0.269280\pi$
$368$	−401077.	−0.154386
$369$	−405085.	−0.154875
$370$	−77498.4	−0.0294299
$371$	−2.28340e6	−0.861287
$372$	−2.29915e6	−0.861411
$373$	−1.26109e6	−0.469325	−0.234663	−	0.972077i	$-0.575399\pi$
$373$	−1.26109e6	−0.469325	−0.234663	+	0.972077i	$0.575399\pi$
$374$	1.61721e6	0.597844
$375$	−3.47113e6	−1.27465
$376$	763405.	0.278475
$377$	−538320.	−0.195068
$378$	1.38271e6	0.497740
$379$	−3713.47	−0.00132795	−0.000663975	−	1.00000i	$-0.500211\pi$
$379$	−3713.47	−0.00132795	−0.000663975		1.00000i	$0.500211\pi$
$380$	−244560.	−0.0868814
$381$	1.63630e6	0.577498
$382$	−1.05446e6	−0.369717
$383$	3.31467e6	1.15463	0.577316	−	0.816521i	$-0.304100\pi$
$383$	3.31467e6	1.15463	0.577316	+	0.816521i	$0.304100\pi$
$384$	301345.	0.104288
$385$	−2.05685e6	−0.707212
$386$	−2.02327e6	−0.691171
$387$	2.22539e6	0.755318
$388$	2.61233e6	0.880944
$389$	722620.	0.242123	0.121061	−	0.992645i	$-0.461370\pi$
$389$	722620.	0.242123	0.121061	+	0.992645i	$0.461370\pi$
$390$	−2.26307e6	−0.753417
$391$	−1.65908e6	−0.548814
$392$	−39527.7	−0.0129923
$393$	6.89941e6	2.25336
$394$	3.45607e6	1.12161
$395$	2.61601e6	0.843619
$396$	582090.	0.186532
$397$	−15238.6	−0.00485253	−0.00242626	−	0.999997i	$-0.500772\pi$
$397$	−15238.6	−0.00485253	−0.00242626	+	0.999997i	$0.500772\pi$
$398$	−2.33032e6	−0.737408
$399$	844824.	0.265665
$400$	−341059.	−0.106581
$401$	−3.59956e6	−1.11786	−0.558932	−	0.829213i	$-0.688789\pi$
$401$	−3.59956e6	−1.11786	−0.558932	+	0.829213i	$0.688789\pi$
$402$	−132165.	−0.0407896
$403$	5.67595e6	1.74091
$404$	−481450.	−0.146757
$405$	−3.09614e6	−0.937956
$406$	−377121.	−0.113544
$407$	−174704.	−0.0522776
$408$	1.24653e6	0.370726
$409$	5.83495e6	1.72476	0.862381	−	0.506260i	$-0.168972\pi$
$409$	5.83495e6	1.72476	0.862381	+	0.506260i	$0.168972\pi$
$410$	−719984.	−0.211526
$411$	−4.20608e6	−1.22821
$412$	1.58005e6	0.458593
$413$	−6.08058e6	−1.75416
$414$	−597159.	−0.171234
$415$	3.49351e6	0.995730
$416$	−743934.	−0.210766
$417$	2.48300e6	0.699256
$418$	−551309.	−0.154331
$419$	5.97054e6	1.66142	0.830708	−	0.556708i	$-0.187936\pi$
$419$	5.97054e6	1.66142	0.830708	+	0.556708i	$0.187936\pi$
$420$	−1.58540e6	−0.438545
$421$	1.65047e6	0.453838	0.226919	−	0.973914i	$-0.427135\pi$
$421$	1.65047e6	0.453838	0.226919	+	0.973914i	$0.427135\pi$
$422$	1.49912e6	0.409784
$423$	1.13663e6	0.308864
$424$	1.14854e6	0.310265
$425$	−1.41081e6	−0.378875
$426$	−3.36391e6	−0.898091
$427$	−1.11148e6	−0.295007
$428$	−1.51779e6	−0.400501
$429$	−5.10160e6	−1.33833
$430$	3.95534e6	1.03160
$431$	2.35721e6	0.611231	0.305616	−	0.952155i	$-0.401138\pi$
$431$	2.35721e6	0.611231	0.305616	+	0.952155i	$0.401138\pi$
$432$	−695500.	−0.179303
$433$	−483266.	−0.123870	−0.0619351	−	0.998080i	$-0.519727\pi$
$433$	−483266.	−0.123870	−0.0619351	+	0.998080i	$0.519727\pi$
$434$	3.97630e6	1.01334
$435$	577043.	0.146213
$436$	2.66633e6	0.671734
$437$	565582.	0.141674
$438$	−5.43180e6	−1.35288
$439$	−3.28743e6	−0.814132	−0.407066	−	0.913399i	$-0.633448\pi$
$439$	−3.28743e6	−0.814132	−0.407066	+	0.913399i	$0.633448\pi$
$440$	1.03459e6	0.254762
$441$	−58852.4	−0.0144101
$442$	−3.07733e6	−0.749235
$443$	3.05552e6	0.739733	0.369867	−	0.929085i	$-0.379403\pi$
$443$	3.05552e6	0.739733	0.369867	+	0.929085i	$0.379403\pi$
$444$	−134660.	−0.0324176
$445$	−282570.	−0.0676436
$446$	−3.09267e6	−0.736201
$447$	−1.09863e6	−0.260064
$448$	−521165.	−0.122682
$449$	−3.85698e6	−0.902884	−0.451442	−	0.892300i	$-0.649090\pi$
$449$	−3.85698e6	−0.902884	−0.451442	+	0.892300i	$0.649090\pi$
$450$	−507798.	−0.118212
$451$	−1.62305e6	−0.375743
$452$	−2.68110e6	−0.617257
$453$	−7.92752e6	−1.81506
$454$	−1.96185e6	−0.446710
$455$	3.91389e6	0.886298
$456$	−424943.	−0.0957015
$457$	3.81819e6	0.855198	0.427599	−	0.903968i	$-0.359359\pi$
$457$	3.81819e6	0.855198	0.427599	+	0.903968i	$0.359359\pi$
$458$	−229049.	−0.0510229
$459$	−2.87698e6	−0.637389
$460$	−1.06137e6	−0.233869
$461$	−4.56025e6	−0.999392	−0.499696	−	0.866201i	$-0.666555\pi$
$461$	−4.56025e6	−0.999392	−0.499696	+	0.866201i	$0.666555\pi$
$462$	−3.57394e6	−0.779008
$463$	−5.10875e6	−1.10755	−0.553774	−	0.832667i	$-0.686813\pi$
$463$	−5.10875e6	−1.10755	−0.553774	+	0.832667i	$0.686813\pi$
$464$	189691.	0.0409026
$465$	−6.08424e6	−1.30489
$466$	1.17003e6	0.249594
$467$	−4.72680e6	−1.00294	−0.501470	−	0.865175i	$-0.667207\pi$
$467$	−4.72680e6	−1.00294	−0.501470	+	0.865175i	$0.667207\pi$
$468$	−1.10764e6	−0.233766
$469$	228574.	0.0479837
$470$	2.02020e6	0.421841
$471$	−4.23613e6	−0.879868
$472$	3.05851e6	0.631910
$473$	8.91646e6	1.83248
$474$	4.54553e6	0.929262
$475$	480946.	0.0978052
$476$	−2.15583e6	−0.436111
$477$	1.71005e6	0.344123
$478$	1.78113e6	0.356554
$479$	1.06702e6	0.212487	0.106243	−	0.994340i	$-0.466118\pi$
$479$	1.06702e6	0.212487	0.106243	+	0.994340i	$0.466118\pi$
$480$	797448.	0.157979
$481$	332436.	0.0655158
$482$	−5.38271e6	−1.05532
$483$	3.66646e6	0.715120
$484$	−244562.	−0.0474544
$485$	6.91300e6	1.33448
$486$	−2.73906e6	−0.526031
$487$	−2.94327e6	−0.562351	−0.281175	−	0.959656i	$-0.590724\pi$
$487$	−2.94327e6	−0.562351	−0.281175	+	0.959656i	$0.590724\pi$
$488$	559071.	0.106272
$489$	1.05487e7	1.99493
$490$	−104602.	−0.0196811
$491$	9.75253e6	1.82563	0.912817	−	0.408370i	$-0.133903\pi$
$491$	9.75253e6	1.82563	0.912817	+	0.408370i	$0.133903\pi$
$492$	−1.25103e6	−0.233000
$493$	784666.	0.145401
$494$	1.04906e6	0.193412
$495$	1.54038e6	0.282563
$496$	−2.00006e6	−0.365039
$497$	5.81776e6	1.05649
$498$	6.07025e6	1.09682
$499$	−1.58150e6	−0.284327	−0.142164	−	0.989843i	$-0.545406\pi$
$499$	−1.58150e6	−0.284327	−0.142164	+	0.989843i	$0.545406\pi$
$500$	−3.01958e6	−0.540159
$501$	594667.	0.105847
$502$	−4.36762e6	−0.773544
$503$	−1.02913e7	−1.81364	−0.906822	−	0.421514i	$-0.861499\pi$
$503$	−1.02913e7	−1.81364	−0.906822	+	0.421514i	$0.861499\pi$
$504$	−775956.	−0.136070
$505$	−1.27406e6	−0.222311
$506$	−2.39263e6	−0.415432
$507$	2.87857e6	0.497344
$508$	1.42344e6	0.244726
$509$	−5.02362e6	−0.859454	−0.429727	−	0.902959i	$-0.641390\pi$
$509$	−5.02362e6	−0.859454	−0.429727	+	0.902959i	$0.641390\pi$
$510$	3.29869e6	0.561586
$511$	9.39410e6	1.59149
$512$	262144.	0.0441942
$513$	980763.	0.164540
$514$	6.06501e6	1.01257
$515$	4.18128e6	0.694690
$516$	6.87272e6	1.13633
$517$	4.55411e6	0.749336
$518$	232889.	0.0381351
$519$	−1.17774e7	−1.91925
$520$	−1.96867e6	−0.319275
$521$	2.09428e6	0.338018	0.169009	−	0.985615i	$-0.445943\pi$
$521$	2.09428e6	0.338018	0.169009	+	0.985615i	$0.445943\pi$
$522$	282428.	0.0453661
$523$	−3.78110e6	−0.604454	−0.302227	−	0.953236i	$-0.597730\pi$
$523$	−3.78110e6	−0.604454	−0.302227	+	0.953236i	$0.597730\pi$
$524$	6.00189e6	0.954904
$525$	3.11780e6	0.493685
$526$	−732744.	−0.115475
$527$	−8.27338e6	−1.29765
$528$	1.79768e6	0.280625
$529$	−3.98177e6	−0.618639
$530$	3.03939e6	0.469999
$531$	4.55378e6	0.700868
$532$	734924.	0.112581
$533$	3.08844e6	0.470891
$534$	−490989.	−0.0745107
$535$	−4.01654e6	−0.606691
$536$	−114972.	−0.0172854
$537$	3.66073e6	0.547813
$538$	−4.40571e6	−0.656237
$539$	−235803.	−0.0349605
$540$	−1.84050e6	−0.271613
$541$	4.24352e6	0.623352	0.311676	−	0.950189i	$-0.399110\pi$
$541$	4.24352e6	0.623352	0.311676	+	0.950189i	$0.399110\pi$
$542$	−4.09983e6	−0.599470
$543$	−1.50145e7	−2.18530
$544$	1.08437e6	0.157102
$545$	7.05590e6	1.01756
$546$	6.80070e6	0.976274
$547$	6.71988e6	0.960270	0.480135	−	0.877195i	$-0.340588\pi$
$547$	6.71988e6	0.960270	0.480135	+	0.877195i	$0.340588\pi$
$548$	−3.65892e6	−0.520477
$549$	832394.	0.117869
$550$	−2.03459e6	−0.286794
$551$	−267493.	−0.0375348
$552$	−1.84422e6	−0.257611
$553$	−7.86132e6	−1.09316
$554$	9.52923e6	1.31912
$555$	−356350.	−0.0491071
$556$	2.15999e6	0.296323
$557$	−634310.	−0.0866290	−0.0433145	−	0.999061i	$-0.513792\pi$
$557$	−634310.	−0.0866290	−0.0433145	+	0.999061i	$0.513792\pi$
$558$	−2.97787e6	−0.404875
$559$	−1.69668e7	−2.29652
$560$	−1.37916e6	−0.185842
$561$	7.43620e6	0.997571
$562$	7.91776e6	1.05745
$563$	4.74103e6	0.630379	0.315190	−	0.949029i	$-0.397932\pi$
$563$	4.74103e6	0.630379	0.315190	+	0.949029i	$0.397932\pi$
$564$	3.51026e6	0.464666
$565$	−7.09498e6	−0.935040
$566$	281933.	0.0369917
$567$	9.30414e6	1.21540
$568$	−2.92631e6	−0.380583
$569$	−1.17115e7	−1.51647	−0.758234	−	0.651983i	$-0.773937\pi$
$569$	−1.17115e7	−1.51647	−0.758234	+	0.651983i	$0.773937\pi$
$570$	−1.12453e6	−0.144971
$571$	−64636.9	−0.00829642	−0.00414821	−	0.999991i	$-0.501320\pi$
$571$	−64636.9	−0.00829642	−0.00414821	+	0.999991i	$0.501320\pi$
$572$	−4.43795e6	−0.567143
$573$	−4.84855e6	−0.616916
$574$	2.16361e6	0.274094
$575$	2.08726e6	0.263274
$576$	390303.	0.0490169
$577$	2.26070e6	0.282685	0.141343	−	0.989961i	$-0.454858\pi$
$577$	2.26070e6	0.282685	0.141343	+	0.989961i	$0.454858\pi$
$578$	−1.19385e6	−0.148638
$579$	−9.30331e6	−1.15330
$580$	501978.	0.0619604
$581$	−1.04983e7	−1.29026
$582$	1.20119e7	1.46996
$583$	6.85166e6	0.834880
$584$	−4.72520e6	−0.573308
$585$	−2.93113e6	−0.354116
$586$	3.36910e6	0.405293
$587$	−6.43586e6	−0.770923	−0.385462	−	0.922724i	$-0.625958\pi$
$587$	−6.43586e6	−0.770923	−0.385462	+	0.922724i	$0.625958\pi$
$588$	−181755.	−0.0216792
$589$	2.82040e6	0.334983
$590$	8.09373e6	0.957235
$591$	1.58915e7	1.87153
$592$	−117142.	−0.0137376
$593$	−1.59757e7	−1.86562	−0.932808	−	0.360372i	$-0.882650\pi$
$593$	−1.59757e7	−1.86562	−0.932808	+	0.360372i	$0.882650\pi$
$594$	−4.14901e6	−0.482479
$595$	−5.70496e6	−0.660633
$596$	−955709.	−0.110207
$597$	−1.07152e7	−1.23045
$598$	4.55284e6	0.520630
$599$	1.57534e7	1.79393	0.896967	−	0.442097i	$-0.145765\pi$
$599$	1.57534e7	1.79393	0.896967	+	0.442097i	$0.145765\pi$
$600$	−1.56824e6	−0.177842
$601$	1.86110e6	0.210176	0.105088	−	0.994463i	$-0.466488\pi$
$601$	1.86110e6	0.210176	0.105088	+	0.994463i	$0.466488\pi$
$602$	−1.18861e7	−1.33674
$603$	−171180.	−0.0191717
$604$	−6.89625e6	−0.769168
$605$	−647185.	−0.0718852
$606$	−2.21378e6	−0.244880
$607$	−4.80555e6	−0.529385	−0.264693	−	0.964333i	$-0.585270\pi$
$607$	−4.80555e6	−0.529385	−0.264693	+	0.964333i	$0.585270\pi$
$608$	−369664.	−0.0405554
$609$	−1.73406e6	−0.189462
$610$	1.47947e6	0.160983
$611$	−8.66582e6	−0.939089
$612$	1.61451e6	0.174246
$613$	1.45069e7	1.55928	0.779641	−	0.626227i	$-0.215402\pi$
$613$	1.45069e7	1.55928	0.779641	+	0.626227i	$0.215402\pi$
$614$	−1.11729e7	−1.19604
$615$	−3.31060e6	−0.352955
$616$	−3.10902e6	−0.330120
$617$	5.83804e6	0.617382	0.308691	−	0.951162i	$-0.400109\pi$
$617$	5.83804e6	0.617382	0.308691	+	0.951162i	$0.400109\pi$
$618$	7.26532e6	0.765215
$619$	−3.44553e6	−0.361435	−0.180717	−	0.983535i	$-0.557842\pi$
$619$	−3.44553e6	−0.361435	−0.180717	+	0.983535i	$0.557842\pi$
$620$	−5.29277e6	−0.552972
$621$	4.25643e6	0.442911
$622$	−5.97430e6	−0.619172
$623$	849147.	0.0876522
$624$	−3.42073e6	−0.351687
$625$	−3.82740e6	−0.391925
$626$	−1.58019e6	−0.161166
$627$	−2.53501e6	−0.257520
$628$	−3.68507e6	−0.372861
$629$	−484566.	−0.0488345
$630$	−2.05341e6	−0.206122
$631$	5.33650e6	0.533560	0.266780	−	0.963757i	$-0.414040\pi$
$631$	5.33650e6	0.533560	0.266780	+	0.963757i	$0.414040\pi$
$632$	3.95421e6	0.393793
$633$	6.89319e6	0.683772
$634$	−8.70533e6	−0.860126
$635$	3.76684e6	0.370718
$636$	5.28119e6	0.517713
$637$	448700.	0.0438135
$638$	1.13160e6	0.110063
$639$	−4.35695e6	−0.422115
$640$	693711.	0.0669466
$641$	7.67654e6	0.737939	0.368970	−	0.929441i	$-0.379711\pi$
$641$	7.67654e6	0.737939	0.368970	+	0.929441i	$0.379711\pi$
$642$	−6.97906e6	−0.668281
$643$	−1.13614e7	−1.08369	−0.541844	−	0.840479i	$-0.682274\pi$
$643$	−1.13614e7	−1.08369	−0.541844	+	0.840479i	$0.682274\pi$
$644$	3.18950e6	0.303046
$645$	1.81873e7	1.72135
$646$	−1.52914e6	−0.144167
$647$	6.38485e6	0.599639	0.299819	−	0.953996i	$-0.403074\pi$
$647$	6.38485e6	0.599639	0.299819	+	0.953996i	$0.403074\pi$
$648$	−4.67995e6	−0.437828
$649$	1.82456e7	1.70038
$650$	3.87154e6	0.359418
$651$	1.82837e7	1.69087
$652$	9.17646e6	0.845388
$653$	1.71696e7	1.57572	0.787858	−	0.615857i	$-0.211190\pi$
$653$	1.71696e7	1.57572	0.787858	+	0.615857i	$0.211190\pi$
$654$	1.22602e7	1.12086
$655$	1.58828e7	1.44652
$656$	−1.08829e6	−0.0987380
$657$	−7.03529e6	−0.635871
$658$	−6.07086e6	−0.546620
$659$	2.50142e6	0.224375	0.112187	−	0.993687i	$-0.464214\pi$
$659$	2.50142e6	0.224375	0.112187	+	0.993687i	$0.464214\pi$
$660$	4.75719e6	0.425099
$661$	−2.60082e6	−0.231530	−0.115765	−	0.993277i	$-0.536932\pi$
$661$	−2.60082e6	−0.231530	−0.115765	+	0.993277i	$0.536932\pi$
$662$	−8.23500e6	−0.730329
$663$	−1.41500e7	−1.25018
$664$	5.28060e6	0.464796
$665$	1.94483e6	0.170540
$666$	−174412.	−0.0152367
$667$	−1.16090e6	−0.101037
$668$	517309.	0.0448548
$669$	−1.42206e7	−1.22843
$670$	−304249.	−0.0261844
$671$	3.33515e6	0.285962
$672$	−2.39640e6	−0.204708
$673$	5.73660e6	0.488222	0.244111	−	0.969747i	$-0.421504\pi$
$673$	5.73660e6	0.488222	0.244111	+	0.969747i	$0.421504\pi$
$674$	2.34969e6	0.199233
$675$	3.61948e6	0.305764
$676$	2.50411e6	0.210759
$677$	1.91455e7	1.60544	0.802721	−	0.596354i	$-0.203385\pi$
$677$	1.91455e7	1.60544	0.802721	+	0.596354i	$0.203385\pi$
$678$	−1.23281e7	−1.02996
$679$	−2.07741e7	−1.72921
$680$	2.86958e6	0.237983
$681$	−9.02088e6	−0.745386
$682$	−1.19314e7	−0.982270
$683$	−246438.	−0.0202142	−0.0101071	−	0.999949i	$-0.503217\pi$
$683$	−246438.	−0.0202142	−0.0101071	+	0.999949i	$0.503217\pi$
$684$	−550389.	−0.0449810
$685$	−9.68260e6	−0.788434
$686$	8.86826e6	0.719496
$687$	−1.05320e6	−0.0851375
$688$	5.97867e6	0.481541
$689$	−1.30377e7	−1.04630
$690$	−4.88035e6	−0.390236
$691$	−1.77933e7	−1.41763	−0.708813	−	0.705396i	$-0.750769\pi$
$691$	−1.77933e7	−1.41763	−0.708813	+	0.705396i	$0.750769\pi$
$692$	−1.02453e7	−0.813319
$693$	−4.62898e6	−0.366144
$694$	1.20465e7	0.949427
$695$	5.71598e6	0.448879
$696$	872227.	0.0682506
$697$	−4.50177e6	−0.350995
$698$	2.24480e6	0.174397
$699$	5.38000e6	0.416475
$700$	2.71221e6	0.209208
$701$	6.50720e6	0.500148	0.250074	−	0.968227i	$-0.419545\pi$
$701$	6.50720e6	0.500148	0.250074	+	0.968227i	$0.419545\pi$
$702$	7.89499e6	0.604657
$703$	165189.	0.0126065
$704$	1.56382e6	0.118920
$705$	9.28919e6	0.703890
$706$	7.74393e6	0.584722
$707$	3.82866e6	0.288070
$708$	1.40635e7	1.05441
$709$	−8.66886e6	−0.647659	−0.323829	−	0.946115i	$-0.604970\pi$
$709$	−8.66886e6	−0.647659	−0.323829	+	0.946115i	$0.604970\pi$
$710$	−7.74389e6	−0.576519
$711$	5.88739e6	0.436766
$712$	−427118.	−0.0315753
$713$	1.22403e7	0.901713
$714$	−9.91284e6	−0.727700
$715$	−1.17441e7	−0.859124
$716$	3.18452e6	0.232146
$717$	8.18991e6	0.594951
$718$	−1.55339e6	−0.112453
$719$	−5.47557e6	−0.395009	−0.197504	−	0.980302i	$-0.563284\pi$
$719$	−5.47557e6	−0.395009	−0.197504	+	0.980302i	$0.563284\pi$
$720$	1.03286e6	0.0742523
$721$	−1.25651e7	−0.900176
$722$	521284.	0.0372161
$723$	−2.47505e7	−1.76092
$724$	−1.30613e7	−0.926061
$725$	−987176.	−0.0697509
$726$	−1.12454e6	−0.0791830
$727$	1.67131e7	1.17279	0.586395	−	0.810025i	$-0.300547\pi$
$727$	1.67131e7	1.17279	0.586395	+	0.810025i	$0.300547\pi$
$728$	5.91602e6	0.413715
$729$	5.17455e6	0.360623
$730$	−1.25043e7	−0.868463
$731$	2.47311e7	1.71179
$732$	2.57070e6	0.177326
$733$	1.89538e7	1.30298	0.651489	−	0.758658i	$-0.274145\pi$
$733$	1.89538e7	1.30298	0.651489	+	0.758658i	$0.274145\pi$
$734$	1.36859e7	0.937632
$735$	−480977.	−0.0328402
$736$	−1.60431e6	−0.109168
$737$	−685866.	−0.0465126
$738$	−1.62034e6	−0.109513
$739$	−1.13520e7	−0.764646	−0.382323	−	0.924029i	$-0.624876\pi$
$739$	−1.13520e7	−0.764646	−0.382323	+	0.924029i	$0.624876\pi$
$740$	−309994.	−0.0208101
$741$	4.82376e6	0.322731
$742$	−9.13362e6	−0.609022
$743$	4.47868e6	0.297631	0.148815	−	0.988865i	$-0.452454\pi$
$743$	4.47868e6	0.297631	0.148815	+	0.988865i	$0.452454\pi$
$744$	−9.19661e6	−0.609110
$745$	−2.52909e6	−0.166945
$746$	−5.04436e6	−0.331863
$747$	7.86222e6	0.515518
$748$	6.46885e6	0.422740
$749$	1.20700e7	0.786147
$750$	−1.38845e7	−0.901317
$751$	−1.06842e7	−0.691260	−0.345630	−	0.938371i	$-0.612335\pi$
$751$	−1.06842e7	−0.691260	−0.345630	+	0.938371i	$0.612335\pi$
$752$	3.05362e6	0.196911
$753$	−2.00830e7	−1.29075
$754$	−2.15328e6	−0.137934
$755$	−1.82495e7	−1.16516
$756$	5.53085e6	0.351955
$757$	2.13637e7	1.35499	0.677496	−	0.735526i	$-0.263065\pi$
$757$	2.13637e7	1.35499	0.677496	+	0.735526i	$0.263065\pi$
$758$	−14853.9	−0.000939002 0
$759$	−1.10017e7	−0.693195
$760$	−978241.	−0.0614344
$761$	−1.30365e7	−0.816020	−0.408010	−	0.912977i	$-0.633777\pi$
$761$	−1.30365e7	−0.816020	−0.408010	+	0.912977i	$0.633777\pi$
$762$	6.54520e6	0.408353
$763$	−2.12036e7	−1.31855
$764$	−4.21782e6	−0.261430
$765$	4.27248e6	0.263953
$766$	1.32587e7	0.816448
$767$	−3.47188e7	−2.13096
$768$	1.20538e6	0.0737430
$769$	−2.54632e6	−0.155273	−0.0776366	−	0.996982i	$-0.524737\pi$
$769$	−2.54632e6	−0.155273	−0.0776366	+	0.996982i	$0.524737\pi$
$770$	−8.22738e6	−0.500075
$771$	2.78879e7	1.68958
$772$	−8.09307e6	−0.488731
$773$	−2.94957e7	−1.77546	−0.887729	−	0.460366i	$-0.847718\pi$
$773$	−2.94957e7	−1.77546	−0.887729	+	0.460366i	$0.847718\pi$
$774$	8.90158e6	0.534090
$775$	1.04086e7	0.622499
$776$	1.04493e7	0.622922
$777$	1.07086e6	0.0636327
$778$	2.89048e6	0.171207
$779$	1.53466e6	0.0906082
$780$	−9.05226e6	−0.532746
$781$	−1.74570e7	−1.02410
$782$	−6.63632e6	−0.388070
$783$	−2.01309e6	−0.117343
$784$	−158111.	−0.00918696
$785$	−9.75179e6	−0.564820
$786$	2.75976e7	1.59337
$787$	2.33229e6	0.134229	0.0671144	−	0.997745i	$-0.478621\pi$
$787$	2.33229e6	0.134229	0.0671144	+	0.997745i	$0.478621\pi$
$788$	1.38243e7	0.793097
$789$	−3.36927e6	−0.192683
$790$	1.04640e7	0.596529
$791$	2.13210e7	1.21162
$792$	2.32836e6	0.131898
$793$	−6.34631e6	−0.358376
$794$	−60954.3	−0.00343126
$795$	1.39756e7	0.784246
$796$	−9.32129e6	−0.521427
$797$	−1.36130e7	−0.759117	−0.379559	−	0.925168i	$-0.623924\pi$
$797$	−1.36130e7	−0.759117	−0.379559	+	0.925168i	$0.623924\pi$
$798$	3.37930e6	0.187853
$799$	1.26315e7	0.699983
$800$	−1.36423e6	−0.0753640
$801$	−635931.	−0.0350210
$802$	−1.43983e7	−0.790449
$803$	−2.81882e7	−1.54269
$804$	−528658.	−0.0288426
$805$	8.44038e6	0.459063
$806$	2.27038e7	1.23101
$807$	−2.02582e7	−1.09501
$808$	−1.92580e6	−0.103773
$809$	−1.98815e7	−1.06801	−0.534007	−	0.845480i	$-0.679314\pi$
$809$	−1.98815e7	−1.06801	−0.534007	+	0.845480i	$0.679314\pi$
$810$	−1.23845e7	−0.663235
$811$	3.08578e6	0.164745	0.0823725	−	0.996602i	$-0.473750\pi$
$811$	3.08578e6	0.164745	0.0823725	+	0.996602i	$0.473750\pi$
$812$	−1.50848e6	−0.0802880
$813$	−1.88517e7	−1.00028
$814$	−698815.	−0.0369659
$815$	2.42836e7	1.28062
$816$	4.98612e6	0.262143
$817$	−8.43086e6	−0.441893
$818$	2.33398e7	1.21959
$819$	8.80830e6	0.458862
$820$	−2.87994e6	−0.149571
$821$	−1.50937e7	−0.781515	−0.390757	−	0.920494i	$-0.627787\pi$
$821$	−1.50937e7	−0.781515	−0.390757	+	0.920494i	$0.627787\pi$
$822$	−1.68243e7	−0.868476
$823$	1.59595e7	0.821333	0.410667	−	0.911786i	$-0.365296\pi$
$823$	1.59595e7	0.821333	0.410667	+	0.911786i	$0.365296\pi$
$824$	6.32020e6	0.324274
$825$	−9.35536e6	−0.478548
$826$	−2.43223e7	−1.24038
$827$	−1.75451e7	−0.892058	−0.446029	−	0.895019i	$-0.647162\pi$
$827$	−1.75451e7	−0.892058	−0.446029	+	0.895019i	$0.647162\pi$
$828$	−2.38864e6	−0.121081
$829$	1.52529e7	0.770845	0.385422	−	0.922740i	$-0.374056\pi$
$829$	1.52529e7	0.770845	0.385422	+	0.922740i	$0.374056\pi$
$830$	1.39740e7	0.704087
$831$	4.38169e7	2.20110
$832$	−2.97574e6	−0.149034
$833$	−654035.	−0.0326579
$834$	9.93199e6	0.494449
$835$	1.36895e6	0.0679473
$836$	−2.20524e6	−0.109129
$837$	2.12257e7	1.04724
$838$	2.38822e7	1.17480
$839$	1.53885e7	0.754728	0.377364	−	0.926065i	$-0.376831\pi$
$839$	1.53885e7	0.754728	0.377364	+	0.926065i	$0.376831\pi$
$840$	−6.34158e6	−0.310098
$841$	−1.99621e7	−0.973232
$842$	6.60186e6	0.320912
$843$	3.64071e7	1.76448
$844$	5.99648e6	0.289761
$845$	6.62661e6	0.319264
$846$	4.54650e6	0.218399
$847$	1.94484e6	0.0931486
$848$	4.59418e6	0.219391
$849$	1.29637e6	0.0617249
$850$	−5.64324e6	−0.267905
$851$	716906.	0.0339342
$852$	−1.34556e7	−0.635046
$853$	1.91103e7	0.899278	0.449639	−	0.893210i	$-0.351553\pi$
$853$	1.91103e7	0.899278	0.449639	+	0.893210i	$0.351553\pi$
$854$	−4.44592e6	−0.208601
$855$	−1.45649e6	−0.0681385
$856$	−6.07118e6	−0.283197
$857$	−2.43080e6	−0.113057	−0.0565284	−	0.998401i	$-0.518003\pi$
$857$	−2.43080e6	−0.113057	−0.0565284	+	0.998401i	$0.518003\pi$
$858$	−2.04064e7	−0.946342
$859$	3.05663e7	1.41338	0.706692	−	0.707521i	$-0.250187\pi$
$859$	3.05663e7	1.41338	0.706692	+	0.707521i	$0.250187\pi$
$860$	1.58213e7	0.729453
$861$	9.94863e6	0.457357
$862$	9.42885e6	0.432206
$863$	9.33024e6	0.426448	0.213224	−	0.977003i	$-0.431604\pi$
$863$	9.33024e6	0.426448	0.213224	+	0.977003i	$0.431604\pi$
$864$	−2.78200e6	−0.126786
$865$	−2.71122e7	−1.23204
$866$	−1.93307e6	−0.0875895
$867$	−5.48951e6	−0.248020
$868$	1.59052e7	0.716539
$869$	2.35889e7	1.05964
$870$	2.30817e6	0.103388
$871$	1.30511e6	0.0582908
$872$	1.06653e7	0.474988
$873$	1.55579e7	0.690899
$874$	2.26233e6	0.100179
$875$	2.40127e7	1.06028
$876$	−2.17272e7	−0.956629
$877$	−2.97688e7	−1.30696	−0.653481	−	0.756943i	$-0.726692\pi$
$877$	−2.97688e7	−1.30696	−0.653481	+	0.756943i	$0.726692\pi$
$878$	−1.31497e7	−0.575678
$879$	1.54916e7	0.676278
$880$	4.13834e6	0.180144
$881$	−4.20040e6	−0.182327	−0.0911634	−	0.995836i	$-0.529059\pi$
$881$	−4.20040e6	−0.182327	−0.0911634	+	0.995836i	$0.529059\pi$
$882$	−235410.	−0.0101895
$883$	1.23924e7	0.534876	0.267438	−	0.963575i	$-0.413823\pi$
$883$	1.23924e7	0.534876	0.267438	+	0.963575i	$0.413823\pi$
$884$	−1.23093e7	−0.529789
$885$	3.72162e7	1.59726
$886$	1.22221e7	0.523070
$887$	−2.74194e7	−1.17017	−0.585084	−	0.810972i	$-0.698939\pi$
$887$	−2.74194e7	−1.17017	−0.585084	+	0.810972i	$0.698939\pi$
$888$	−538639.	−0.0229227
$889$	−1.13197e7	−0.480374
$890$	−1.13028e6	−0.0478312
$891$	−2.79183e7	−1.17813
$892$	−1.23707e7	−0.520572
$893$	−4.30608e6	−0.180698
$894$	−4.39450e6	−0.183893
$895$	8.42719e6	0.351662
$896$	−2.08466e6	−0.0867491
$897$	2.09347e7	0.868731
$898$	−1.54279e7	−0.638436
$899$	−5.78908e6	−0.238897
$900$	−2.03119e6	−0.0835882
$901$	1.90041e7	0.779893
$902$	−6.49220e6	−0.265690
$903$	−5.46542e7	−2.23051
$904$	−1.07244e7	−0.436467
$905$	−3.45641e7	−1.40282
$906$	−3.17101e7	−1.28344
$907$	−1.27225e7	−0.513516	−0.256758	−	0.966476i	$-0.582654\pi$
$907$	−1.27225e7	−0.513516	−0.256758	+	0.966476i	$0.582654\pi$
$908$	−7.84738e6	−0.315871
$909$	−2.86730e6	−0.115097
$910$	1.56555e7	0.626707
$911$	−276582.	−0.0110415	−0.00552076	−	0.999985i	$-0.501757\pi$
$911$	−276582.	−0.0110415	−0.00552076	+	0.999985i	$0.501757\pi$
$912$	−1.69977e6	−0.0676712
$913$	3.15015e7	1.25070
$914$	1.52728e7	0.604717
$915$	6.80283e6	0.268619
$916$	−916197.	−0.0360786
$917$	−4.77291e7	−1.87439
$918$	−1.15079e7	−0.450702
$919$	2.48623e7	0.971075	0.485538	−	0.874216i	$-0.338624\pi$
$919$	2.48623e7	0.971075	0.485538	+	0.874216i	$0.338624\pi$
$920$	−4.24548e6	−0.165370
$921$	−5.13747e7	−1.99572
$922$	−1.82410e7	−0.706677
$923$	3.32181e7	1.28343
$924$	−1.42957e7	−0.550842
$925$	609625.	0.0234266
$926$	−2.04350e7	−0.783155
$927$	9.41007e6	0.359661
$928$	758762.	0.0289225
$929$	−1.03940e7	−0.395133	−0.197566	−	0.980290i	$-0.563304\pi$
$929$	−1.03940e7	−0.395133	−0.197566	+	0.980290i	$0.563304\pi$
$930$	−2.43370e7	−0.922697
$931$	222961.	0.00843053
$932$	4.68014e6	0.176489
$933$	−2.74708e7	−1.03316
$934$	−1.89072e7	−0.709186
$935$	1.71185e7	0.640379
$936$	−4.43054e6	−0.165298
$937$	6.95767e6	0.258890	0.129445	−	0.991587i	$-0.458680\pi$
$937$	6.95767e6	0.258890	0.129445	+	0.991587i	$0.458680\pi$
$938$	914295.	0.0339296
$939$	−7.26595e6	−0.268923
$940$	8.08079e6	0.298287
$941$	−3.11961e7	−1.14849	−0.574243	−	0.818685i	$-0.694704\pi$
$941$	−3.11961e7	−1.14849	−0.574243	+	0.818685i	$0.694704\pi$
$942$	−1.69445e7	−0.622160
$943$	6.66027e6	0.243901
$944$	1.22340e7	0.446828
$945$	1.46363e7	0.533152
$946$	3.56659e7	1.29576
$947$	−6.85370e6	−0.248342	−0.124171	−	0.992261i	$-0.539627\pi$
$947$	−6.85370e6	−0.248342	−0.124171	+	0.992261i	$0.539627\pi$
$948$	1.81821e7	0.657088
$949$	5.36382e7	1.93334
$950$	1.92378e6	0.0691588
$951$	−4.00285e7	−1.43522
$952$	−8.62332e6	−0.308377
$953$	−6.47990e6	−0.231119	−0.115560	−	0.993301i	$-0.536866\pi$
$953$	−6.47990e6	−0.231119	−0.115560	+	0.993301i	$0.536866\pi$
$954$	6.84022e6	0.243332
$955$	−1.11616e7	−0.396021
$956$	7.12452e6	0.252122
$957$	5.20328e6	0.183653
$958$	4.26806e6	0.150251
$959$	2.90970e7	1.02165
$960$	3.18979e6	0.111708
$961$	3.24099e7	1.13206
$962$	1.32975e6	0.0463267
$963$	−9.03931e6	−0.314101
$964$	−2.15308e7	−0.746222
$965$	−2.14167e7	−0.740345
$966$	1.46658e7	0.505666
$967$	−1.13014e7	−0.388658	−0.194329	−	0.980936i	$-0.562253\pi$
$967$	−1.13014e7	−0.388658	−0.194329	+	0.980936i	$0.562253\pi$
$968$	−978249.	−0.0335553
$969$	−7.03121e6	−0.240559
$970$	2.76520e7	0.943620
$971$	−2.10630e7	−0.716923	−0.358461	−	0.933545i	$-0.616699\pi$
$971$	−2.10630e7	−0.716923	−0.358461	+	0.933545i	$0.616699\pi$
$972$	−1.09562e7	−0.371960
$973$	−1.71770e7	−0.581655
$974$	−1.17731e7	−0.397642
$975$	1.78019e7	0.599730
$976$	2.23628e6	0.0751454
$977$	1.26107e7	0.422670	0.211335	−	0.977414i	$-0.432219\pi$
$977$	1.26107e7	0.422670	0.211335	+	0.977414i	$0.432219\pi$
$978$	4.21948e7	1.41063
$979$	−2.54798e6	−0.0849648
$980$	−418409.	−0.0139167
$981$	1.58795e7	0.526821
$982$	3.90101e7	1.29092
$983$	3.62410e7	1.19623	0.598117	−	0.801409i	$-0.295916\pi$
$983$	3.62410e7	1.19623	0.598117	+	0.801409i	$0.295916\pi$
$984$	−5.00412e6	−0.164756
$985$	3.65831e7	1.20141
$986$	3.13867e6	0.102814
$987$	−2.79148e7	−0.912098
$988$	4.19625e6	0.136763
$989$	−3.65892e7	−1.18949
$990$	6.16153e6	0.199802
$991$	2.12245e7	0.686522	0.343261	−	0.939240i	$-0.388469\pi$
$991$	2.12245e7	0.686522	0.343261	+	0.939240i	$0.388469\pi$
$992$	−8.00026e6	−0.258122
$993$	−3.78658e7	−1.21864
$994$	2.32710e7	0.747050
$995$	−2.46669e7	−0.789872
$996$	2.42810e7	0.775566
$997$	536321.	0.0170878	0.00854392	−	0.999964i	$-0.497280\pi$
$997$	536321.	0.0170878	0.00854392	+	0.999964i	$0.497280\pi$
$998$	−6.32601e6	−0.201050
$999$	1.24317e6	0.0394110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.a.d.1.3	✓	3
3.2	odd	2		342.6.a.l.1.2		3
4.3	odd	2		304.6.a.h.1.1		3
5.4	even	2		950.6.a.f.1.1		3
19.18	odd	2		722.6.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.d.1.3	✓	3	1.1	even	1	trivial
304.6.a.h.1.1		3	4.3	odd	2
342.6.a.l.1.2		3	3.2	odd	2
722.6.a.d.1.1		3	19.18	odd	2
950.6.a.f.1.1		3	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +18.3926 q^{3} +16.0000 q^{4} +42.3408 q^{5} +73.5705 q^{6} -127.237 q^{7} +64.0000 q^{8} +95.2889 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +18.3926 q^{3} +16.0000 q^{4} +42.3408 q^{5} +73.5705 q^{6} -127.237 q^{7} +64.0000 q^{8} +95.2889 q^{9} +169.363 q^{10} +381.793 q^{11} +294.282 q^{12} -726.498 q^{13} -508.950 q^{14} +778.758 q^{15} +256.000 q^{16} +1058.96 q^{17} +381.156 q^{18} -361.000 q^{19} +677.452 q^{20} -2340.23 q^{21} +1527.17 q^{22} -1566.71 q^{23} +1177.13 q^{24} -1332.26 q^{25} -2905.99 q^{26} -2716.80 q^{27} -2035.80 q^{28} +740.979 q^{29} +3115.03 q^{30} -7812.75 q^{31} +1024.00 q^{32} +7022.18 q^{33} +4235.84 q^{34} -5387.33 q^{35} +1524.62 q^{36} -457.587 q^{37} -1444.00 q^{38} -13362.2 q^{39} +2709.81 q^{40} -4251.13 q^{41} -9360.93 q^{42} +23354.2 q^{43} +6108.69 q^{44} +4034.60 q^{45} -6266.83 q^{46} +11928.2 q^{47} +4708.51 q^{48} -617.621 q^{49} -5329.04 q^{50} +19477.0 q^{51} -11624.0 q^{52} +17946.0 q^{53} -10867.2 q^{54} +16165.4 q^{55} -8143.20 q^{56} -6639.74 q^{57} +2963.92 q^{58} +47789.2 q^{59} +12460.1 q^{60} +8735.48 q^{61} -31251.0 q^{62} -12124.3 q^{63} +4096.00 q^{64} -30760.5 q^{65} +28088.7 q^{66} -1796.43 q^{67} +16943.3 q^{68} -28815.9 q^{69} -21549.3 q^{70} -45723.6 q^{71} +6098.49 q^{72} -73831.2 q^{73} -1830.35 q^{74} -24503.8 q^{75} -5776.00 q^{76} -48578.4 q^{77} -53448.9 q^{78} +61784.6 q^{79} +10839.2 q^{80} -73124.2 q^{81} -17004.5 q^{82} +82509.3 q^{83} -37443.7 q^{84} +44837.1 q^{85} +93416.7 q^{86} +13628.5 q^{87} +24434.7 q^{88} -6673.72 q^{89} +16138.4 q^{90} +92437.8 q^{91} -25067.3 q^{92} -143697. q^{93} +47712.8 q^{94} -15285.0 q^{95} +18834.1 q^{96} +163271. q^{97} -2470.48 q^{98} +36380.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9}+O(q^{10}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9	\( 3 q + 12 q^{2} + 13 q^{3} + 48 q^{4} + 81 q^{5} + 52 q^{6} + 228 q^{7} + 192 q^{8} + 236 q^{9} + 324 q^{10} + 363 q^{11} + 208 q^{12} + 501 q^{13} + 912 q^{14} - 670 q^{15} + 768 q^{16} - 1206 q^{17} + 944 q^{18} - 1083 q^{19} + 1296 q^{20} - 2085 q^{21} + 1452 q^{22} - 1077 q^{23} + 832 q^{24} - 3882 q^{25} + 2004 q^{26} - 5087 q^{27} + 3648 q^{28} - 8349 q^{29} - 2680 q^{30} - 7332 q^{31} + 3072 q^{32} - 15784 q^{33} - 4824 q^{34} - 1185 q^{35} + 3776 q^{36} - 1650 q^{37} - 4332 q^{38} + 773 q^{39} + 5184 q^{40} + 10140 q^{41} - 8340 q^{42} + 3777 q^{43} + 5808 q^{44} + 14005 q^{45} - 4308 q^{46} + 33231 q^{47} + 3328 q^{48} + 31269 q^{49} - 15528 q^{50} + 46935 q^{51} + 8016 q^{52} + 31029 q^{53} - 20348 q^{54} + 66003 q^{55} + 14592 q^{56} - 4693 q^{57} - 33396 q^{58} + 20409 q^{59} - 10720 q^{60} + 17115 q^{61} - 29328 q^{62} + 6327 q^{63} + 12288 q^{64} - 45348 q^{65} - 63136 q^{66} - 789 q^{67} - 19296 q^{68} - 151147 q^{69} - 4740 q^{70} + 19164 q^{71} + 15104 q^{72} - 76260 q^{73} - 6600 q^{74} - 69607 q^{75} - 17328 q^{76} - 97209 q^{77} + 3092 q^{78} + 68358 q^{79} + 20736 q^{80} - 197713 q^{81} + 40560 q^{82} + 6762 q^{83} - 33360 q^{84} - 45837 q^{85} + 15108 q^{86} + 66805 q^{87} + 23232 q^{88} - 85506 q^{89} + 56020 q^{90} + 345033 q^{91} - 17232 q^{92} + 15688 q^{93} + 132924 q^{94} - 29241 q^{95} + 13312 q^{96} + 105024 q^{97} + 125076 q^{98} + 158317 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 + 13 * q^3 + 48 * q^4 + 81 * q^5 + 52 * q^6 + 228 * q^7 + 192 * q^8 + 236 * q^9 + 324 * q^10 + 363 * q^11 + 208 * q^12 + 501 * q^13 + 912 * q^14 - 670 * q^15 + 768 * q^16 - 1206 * q^17 + 944 * q^18 - 1083 * q^19 + 1296 * q^20 - 2085 * q^21 + 1452 * q^22 - 1077 * q^23 + 832 * q^24 - 3882 * q^25 + 2004 * q^26 - 5087 * q^27 + 3648 * q^28 - 8349 * q^29 - 2680 * q^30 - 7332 * q^31 + 3072 * q^32 - 15784 * q^33 - 4824 * q^34 - 1185 * q^35 + 3776 * q^36 - 1650 * q^37 - 4332 * q^38 + 773 * q^39 + 5184 * q^40 + 10140 * q^41 - 8340 * q^42 + 3777 * q^43 + 5808 * q^44 + 14005 * q^45 - 4308 * q^46 + 33231 * q^47 + 3328 * q^48 + 31269 * q^49 - 15528 * q^50 + 46935 * q^51 + 8016 * q^52 + 31029 * q^53 - 20348 * q^54 + 66003 * q^55 + 14592 * q^56 - 4693 * q^57 - 33396 * q^58 + 20409 * q^59 - 10720 * q^60 + 17115 * q^61 - 29328 * q^62 + 6327 * q^63 + 12288 * q^64 - 45348 * q^65 - 63136 * q^66 - 789 * q^67 - 19296 * q^68 - 151147 * q^69 - 4740 * q^70 + 19164 * q^71 + 15104 * q^72 - 76260 * q^73 - 6600 * q^74 - 69607 * q^75 - 17328 * q^76 - 97209 * q^77 + 3092 * q^78 + 68358 * q^79 + 20736 * q^80 - 197713 * q^81 + 40560 * q^82 + 6762 * q^83 - 33360 * q^84 - 45837 * q^85 + 15108 * q^86 + 66805 * q^87 + 23232 * q^88 - 85506 * q^89 + 56020 * q^90 + 345033 * q^91 - 17232 * q^92 + 15688 * q^93 + 132924 * q^94 - 29241 * q^95 + 13312 * q^96 + 105024 * q^97 + 125076 * q^98 + 158317 * q^99

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