LMFDB - Embedded newform 21.8.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,8,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.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:	$6.56008553517$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1065}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 266 $ x^2 - x - 266
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-15.8172$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.8172 q^{2} -27.0000 q^{3} +11.6455 q^{4} -506.343 q^{5} -319.064 q^{6} +343.000 q^{7} -1374.98 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+11.8172 q^{2} -27.0000 q^{3} +11.6455 q^{4} -506.343 q^{5} -319.064 q^{6} +343.000 q^{7} -1374.98 q^{8} +729.000 q^{9} -5983.55 q^{10} +2559.69 q^{11} -314.428 q^{12} -845.345 q^{13} +4053.29 q^{14} +13671.3 q^{15} -17739.0 q^{16} -23364.3 q^{17} +8614.72 q^{18} -16591.1 q^{19} -5896.61 q^{20} -9261.00 q^{21} +30248.3 q^{22} +58426.2 q^{23} +37124.5 q^{24} +178259. q^{25} -9989.58 q^{26} -19683.0 q^{27} +3994.40 q^{28} -252068. q^{29} +161556. q^{30} +151032. q^{31} -33627.2 q^{32} -69111.6 q^{33} -276100. q^{34} -173676. q^{35} +8489.56 q^{36} -305435. q^{37} -196060. q^{38} +22824.3 q^{39} +696213. q^{40} -657709. q^{41} -109439. q^{42} +53085.2 q^{43} +29808.8 q^{44} -369124. q^{45} +690432. q^{46} -1.05001e6 q^{47} +478953. q^{48} +117649. q^{49} +2.10651e6 q^{50} +630837. q^{51} -9844.44 q^{52} +1.53677e6 q^{53} -232597. q^{54} -1.29608e6 q^{55} -471618. q^{56} +447961. q^{57} -2.97873e6 q^{58} +320564. q^{59} +159209. q^{60} +645385. q^{61} +1.78477e6 q^{62} +250047. q^{63} +1.87321e6 q^{64} +428035. q^{65} -816703. q^{66} -2.84308e6 q^{67} -272089. q^{68} -1.57751e6 q^{69} -2.05236e6 q^{70} +650129. q^{71} -1.00236e6 q^{72} +5.07847e6 q^{73} -3.60938e6 q^{74} -4.81298e6 q^{75} -193212. q^{76} +877973. q^{77} +269719. q^{78} +283873. q^{79} +8.98203e6 q^{80} +531441. q^{81} -7.77226e6 q^{82} -6.30268e6 q^{83} -107849. q^{84} +1.18304e7 q^{85} +627317. q^{86} +6.80584e6 q^{87} -3.51952e6 q^{88} -7.02180e6 q^{89} -4.36200e6 q^{90} -289953. q^{91} +680401. q^{92} -4.07786e6 q^{93} -1.24082e7 q^{94} +8.40081e6 q^{95} +907935. q^{96} +1.01269e7 q^{97} +1.39028e6 q^{98} +1.86601e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 9 q^{2} - 54 q^{3} + 317 q^{4} - 360 q^{5} + 243 q^{6} + 686 q^{7} - 5067 q^{8} + 1458 q^{9}+O(q^{10}) $ 2 * q - 9 * q^2 - 54 * q^3 + 317 * q^4 - 360 * q^5 + 243 * q^6 + 686 * q^7 - 5067 * q^8 + 1458 * q^9	\( 2 q - 9 q^{2} - 54 q^{3} + 317 q^{4} - 360 q^{5} + 243 q^{6} + 686 q^{7} - 5067 q^{8} + 1458 q^{9} - 9030 q^{10} - 4932 q^{11} - 8559 q^{12} + 7708 q^{13} - 3087 q^{14} + 9720 q^{15} + 20033 q^{16} - 28584 q^{17} - 6561 q^{18} - 63728 q^{19} + 38790 q^{20} - 18522 q^{21} + 186204 q^{22} + 82260 q^{23} + 136809 q^{24} + 121550 q^{25} - 188046 q^{26} - 39366 q^{27} + 108731 q^{28} - 435996 q^{29} + 243810 q^{30} - 29240 q^{31} - 347355 q^{32} + 133164 q^{33} - 167442 q^{34} - 123480 q^{35} + 231093 q^{36} - 709556 q^{37} + 785196 q^{38} - 208116 q^{39} + 155910 q^{40} - 25056 q^{41} + 83349 q^{42} + 496216 q^{43} - 2257812 q^{44} - 262440 q^{45} + 194280 q^{46} - 1575000 q^{47} - 540891 q^{48} + 235298 q^{49} + 3287025 q^{50} + 771768 q^{51} + 2601958 q^{52} + 2057436 q^{53} + 177147 q^{54} - 2392440 q^{55} - 1737981 q^{56} + 1720656 q^{57} + 850122 q^{58} - 1101024 q^{59} - 1047330 q^{60} + 28996 q^{61} + 5537520 q^{62} + 500094 q^{63} + 3569321 q^{64} + 1679760 q^{65} - 5027508 q^{66} - 4480784 q^{67} - 1865934 q^{68} - 2221020 q^{69} - 3097290 q^{70} + 54540 q^{71} - 3693843 q^{72} + 666604 q^{73} + 4803282 q^{74} - 3281850 q^{75} - 14586668 q^{76} - 1691676 q^{77} + 5077242 q^{78} + 2322952 q^{79} + 14509710 q^{80} + 1062882 q^{81} - 20942298 q^{82} - 7384392 q^{83} - 2935737 q^{84} + 11066520 q^{85} - 8597412 q^{86} + 11771892 q^{87} + 24139932 q^{88} + 1784448 q^{89} - 6582870 q^{90} + 2643844 q^{91} + 7958160 q^{92} + 789480 q^{93} - 1479360 q^{94} + 1502640 q^{95} + 9378585 q^{96} + 16266412 q^{97} - 1058841 q^{98} - 3595428 q^{99}+O(q^{100}) \) 2 * q - 9 * q^2 - 54 * q^3 + 317 * q^4 - 360 * q^5 + 243 * q^6 + 686 * q^7 - 5067 * q^8 + 1458 * q^9 - 9030 * q^10 - 4932 * q^11 - 8559 * q^12 + 7708 * q^13 - 3087 * q^14 + 9720 * q^15 + 20033 * q^16 - 28584 * q^17 - 6561 * q^18 - 63728 * q^19 + 38790 * q^20 - 18522 * q^21 + 186204 * q^22 + 82260 * q^23 + 136809 * q^24 + 121550 * q^25 - 188046 * q^26 - 39366 * q^27 + 108731 * q^28 - 435996 * q^29 + 243810 * q^30 - 29240 * q^31 - 347355 * q^32 + 133164 * q^33 - 167442 * q^34 - 123480 * q^35 + 231093 * q^36 - 709556 * q^37 + 785196 * q^38 - 208116 * q^39 + 155910 * q^40 - 25056 * q^41 + 83349 * q^42 + 496216 * q^43 - 2257812 * q^44 - 262440 * q^45 + 194280 * q^46 - 1575000 * q^47 - 540891 * q^48 + 235298 * q^49 + 3287025 * q^50 + 771768 * q^51 + 2601958 * q^52 + 2057436 * q^53 + 177147 * q^54 - 2392440 * q^55 - 1737981 * q^56 + 1720656 * q^57 + 850122 * q^58 - 1101024 * q^59 - 1047330 * q^60 + 28996 * q^61 + 5537520 * q^62 + 500094 * q^63 + 3569321 * q^64 + 1679760 * q^65 - 5027508 * q^66 - 4480784 * q^67 - 1865934 * q^68 - 2221020 * q^69 - 3097290 * q^70 + 54540 * q^71 - 3693843 * q^72 + 666604 * q^73 + 4803282 * q^74 - 3281850 * q^75 - 14586668 * q^76 - 1691676 * q^77 + 5077242 * q^78 + 2322952 * q^79 + 14509710 * q^80 + 1062882 * q^81 - 20942298 * q^82 - 7384392 * q^83 - 2935737 * q^84 + 11066520 * q^85 - 8597412 * q^86 + 11771892 * q^87 + 24139932 * q^88 + 1784448 * q^89 - 6582870 * q^90 + 2643844 * q^91 + 7958160 * q^92 + 789480 * q^93 - 1479360 * q^94 + 1502640 * q^95 + 9378585 * q^96 + 16266412 * q^97 - 1058841 * q^98 - 3595428 * 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 $

$2$	11.8172	1.04450	0.522250	−	0.852792i	$-0.325093\pi$
$2$	11.8172	1.04450	0.522250	+	0.852792i	$0.325093\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	11.6455	0.0909803
$5$	−506.343	−1.81155	−0.905775	−	0.423760i	$-0.860710\pi$
$5$	−506.343	−1.81155	−0.905775	+	0.423760i	$0.860710\pi$
$6$	−319.064	−0.603042
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1374.98	−0.949471
$9$	729.000	0.333333
$10$	−5983.55	−1.89216
$11$	2559.69	0.579846	0.289923	−	0.957050i	$-0.406370\pi$
$11$	2559.69	0.579846	0.289923	+	0.957050i	$0.406370\pi$
$12$	−314.428	−0.0525275
$13$	−845.345	−0.106717	−0.0533583	−	0.998575i	$-0.516993\pi$
$13$	−845.345	−0.106717	−0.0533583	+	0.998575i	$0.516993\pi$
$14$	4053.29	0.394784
$15$	13671.3	1.04590
$16$	−17739.0	−1.08270
$17$	−23364.3	−1.15341	−0.576703	−	0.816954i	$-0.695661\pi$
$17$	−23364.3	−1.15341	−0.576703	+	0.816954i	$0.695661\pi$
$18$	8614.72	0.348167
$19$	−16591.1	−0.554930	−0.277465	−	0.960736i	$-0.589494\pi$
$19$	−16591.1	−0.554930	−0.277465	+	0.960736i	$0.589494\pi$
$20$	−5896.61	−0.164815
$21$	−9261.00	−0.218218
$22$	30248.3	0.605649
$23$	58426.2	1.00129	0.500645	−	0.865652i	$-0.333096\pi$
$23$	58426.2	1.00129	0.500645	+	0.865652i	$0.333096\pi$
$24$	37124.5	0.548177
$25$	178259.	2.28171
$26$	−9989.58	−0.111466
$27$	−19683.0	−0.192450
$28$	3994.40	0.0343873
$29$	−252068.	−1.91922	−0.959611	−	0.281331i	$-0.909224\pi$
$29$	−252068.	−1.91922	−0.959611	+	0.281331i	$0.909224\pi$
$30$	161556.	1.09244
$31$	151032.	0.910548	0.455274	−	0.890351i	$-0.349541\pi$
$31$	151032.	0.910548	0.455274	+	0.890351i	$0.349541\pi$
$32$	−33627.2	−0.181412
$33$	−69111.6	−0.334774
$34$	−276100.	−1.20473
$35$	−173676.	−0.684701
$36$	8489.56	0.0303268
$37$	−305435.	−0.991317	−0.495659	−	0.868517i	$-0.665073\pi$
$37$	−305435.	−0.991317	−0.495659	+	0.868517i	$0.665073\pi$
$38$	−196060.	−0.579625
$39$	22824.3	0.0616129
$40$	696213.	1.72001
$41$	−657709.	−1.49036	−0.745178	−	0.666865i	$-0.767636\pi$
$41$	−657709.	−1.49036	−0.745178	+	0.666865i	$0.767636\pi$
$42$	−109439.	−0.227929
$43$	53085.2	0.101820	0.0509101	−	0.998703i	$-0.483788\pi$
$43$	53085.2	0.101820	0.0509101	+	0.998703i	$0.483788\pi$
$44$	29808.8	0.0527546
$45$	−369124.	−0.603850
$46$	690432.	1.04585
$47$	−1.05001e6	−1.47520	−0.737600	−	0.675237i	$-0.764041\pi$
$47$	−1.05001e6	−1.47520	−0.737600	+	0.675237i	$0.764041\pi$
$48$	478953.	0.625099
$49$	117649.	0.142857
$50$	2.10651e6	2.38325
$51$	630837.	0.665920
$52$	−9844.44	−0.00970911
$53$	1.53677e6	1.41789	0.708946	−	0.705263i	$-0.249171\pi$
$53$	1.53677e6	1.41789	0.708946	+	0.705263i	$0.249171\pi$
$54$	−232597.	−0.201014
$55$	−1.29608e6	−1.05042
$56$	−471618.	−0.358866
$57$	447961.	0.320389
$58$	−2.97873e6	−2.00463
$59$	320564.	0.203204	0.101602	−	0.994825i	$-0.467603\pi$
$59$	320564.	0.203204	0.101602	+	0.994825i	$0.467603\pi$
$60$	159209.	0.0951562
$61$	645385.	0.364053	0.182026	−	0.983294i	$-0.441734\pi$
$61$	645385.	0.364053	0.182026	+	0.983294i	$0.441734\pi$
$62$	1.78477e6	0.951067
$63$	250047.	0.125988
$64$	1.87321e6	0.893218
$65$	428035.	0.193322
$66$	−816703.	−0.349672
$67$	−2.84308e6	−1.15486	−0.577428	−	0.816442i	$-0.695944\pi$
$67$	−2.84308e6	−1.15486	−0.577428	+	0.816442i	$0.695944\pi$
$68$	−272089.	−0.104937
$69$	−1.57751e6	−0.578095
$70$	−2.05236e6	−0.715170
$71$	650129.	0.215573	0.107787	−	0.994174i	$-0.465624\pi$
$71$	650129.	0.215573	0.107787	+	0.994174i	$0.465624\pi$
$72$	−1.00236e6	−0.316490
$73$	5.07847e6	1.52793	0.763963	−	0.645260i	$-0.223251\pi$
$73$	5.07847e6	1.52793	0.763963	+	0.645260i	$0.223251\pi$
$74$	−3.60938e6	−1.03543
$75$	−4.81298e6	−1.31735
$76$	−193212.	−0.0504877
$77$	877973.	0.219161
$78$	269719.	0.0643546
$79$	283873.	0.0647783	0.0323892	−	0.999475i	$-0.489688\pi$
$79$	283873.	0.0647783	0.0323892	+	0.999475i	$0.489688\pi$
$80$	8.98203e6	1.96137
$81$	531441.	0.111111
$82$	−7.77226e6	−1.55668
$83$	−6.30268e6	−1.20991	−0.604954	−	0.796261i	$-0.706808\pi$
$83$	−6.30268e6	−1.20991	−0.604954	+	0.796261i	$0.706808\pi$
$84$	−107849.	−0.0198535
$85$	1.18304e7	2.08945
$86$	627317.	0.106351
$87$	6.80584e6	1.10806
$88$	−3.51952e6	−0.550547
$89$	−7.02180e6	−1.05580	−0.527902	−	0.849305i	$-0.677021\pi$
$89$	−7.02180e6	−1.05580	−0.527902	+	0.849305i	$0.677021\pi$
$90$	−4.36200e6	−0.630721
$91$	−289953.	−0.0403351
$92$	680401.	0.0910977
$93$	−4.07786e6	−0.525705
$94$	−1.24082e7	−1.54085
$95$	8.40081e6	1.00528
$96$	907935.	0.104738
$97$	1.01269e7	1.12662	0.563308	−	0.826247i	$-0.309529\pi$
$97$	1.01269e7	1.12662	0.563308	+	0.826247i	$0.309529\pi$
$98$	1.39028e6	0.149214
$99$	1.86601e6	0.193282
$100$	2.07591e6	0.207591
$101$	6.62293e6	0.639625	0.319813	−	0.947481i	$-0.396380\pi$
$101$	6.62293e6	0.639625	0.319813	+	0.947481i	$0.396380\pi$
$102$	7.45471e6	0.695553
$103$	1.46463e7	1.32068	0.660339	−	0.750968i	$-0.270413\pi$
$103$	1.46463e7	1.32068	0.660339	+	0.750968i	$0.270413\pi$
$104$	1.16233e6	0.101324
$105$	4.68925e6	0.395312
$106$	1.81603e7	1.48099
$107$	−1.40846e7	−1.11148	−0.555739	−	0.831357i	$-0.687564\pi$
$107$	−1.40846e7	−1.11148	−0.555739	+	0.831357i	$0.687564\pi$
$108$	−229218.	−0.0175092
$109$	−6.60705e6	−0.488669	−0.244335	−	0.969691i	$-0.578569\pi$
$109$	−6.60705e6	−0.488669	−0.244335	+	0.969691i	$0.578569\pi$
$110$	−1.53160e7	−1.09716
$111$	8.24674e6	0.572337
$112$	−6.08448e6	−0.409223
$113$	−1.43861e6	−0.0937926	−0.0468963	−	0.998900i	$-0.514933\pi$
$113$	−1.43861e6	−0.0937926	−0.0468963	+	0.998900i	$0.514933\pi$
$114$	5.29362e6	0.334646
$115$	−2.95837e7	−1.81389
$116$	−2.93546e6	−0.174611
$117$	−616256.	−0.0355722
$118$	3.78816e6	0.212247
$119$	−8.01397e6	−0.435947
$120$	−1.87977e7	−0.993050
$121$	−1.29352e7	−0.663779
$122$	7.62662e6	0.380253
$123$	1.77581e7	0.860458
$124$	1.75884e6	0.0828419
$125$	−5.07020e7	−2.32188
$126$	2.95485e6	0.131595
$127$	−2.19250e7	−0.949789	−0.474894	−	0.880043i	$-0.657514\pi$
$127$	−2.19250e7	−0.949789	−0.474894	+	0.880043i	$0.657514\pi$
$128$	2.64404e7	1.11438
$129$	−1.43330e6	−0.0587859
$130$	5.05816e6	0.201925
$131$	2.73673e7	1.06361	0.531805	−	0.846867i	$-0.321514\pi$
$131$	2.73673e7	1.06361	0.531805	+	0.846867i	$0.321514\pi$
$132$	−804837.	−0.0304579
$133$	−5.69076e6	−0.209744
$134$	−3.35972e7	−1.20625
$135$	9.96636e6	0.348633
$136$	3.21255e7	1.09513
$137$	−6.59982e6	−0.219286	−0.109643	−	0.993971i	$-0.534971\pi$
$137$	−6.59982e6	−0.219286	−0.109643	+	0.993971i	$0.534971\pi$
$138$	−1.86417e7	−0.603821
$139$	−5.73763e6	−0.181209	−0.0906047	−	0.995887i	$-0.528880\pi$
$139$	−5.73763e6	−0.181209	−0.0906047	+	0.995887i	$0.528880\pi$
$140$	−2.02254e6	−0.0622943
$141$	2.83503e7	0.851708
$142$	7.68268e6	0.225166
$143$	−2.16382e6	−0.0618792
$144$	−1.29317e7	−0.360901
$145$	1.27633e8	3.47676
$146$	6.00131e7	1.59592
$147$	−3.17652e6	−0.0824786
$148$	−3.55694e6	−0.0901903
$149$	4.77602e7	1.18281	0.591404	−	0.806375i	$-0.298574\pi$
$149$	4.77602e7	1.18281	0.591404	+	0.806375i	$0.298574\pi$
$150$	−5.68758e7	−1.37597
$151$	4.28872e6	0.101370	0.0506849	−	0.998715i	$-0.483860\pi$
$151$	4.28872e6	0.101370	0.0506849	+	0.998715i	$0.483860\pi$
$152$	2.28125e7	0.526890
$153$	−1.70326e7	−0.384469
$154$	1.03752e7	0.228914
$155$	−7.64740e7	−1.64950
$156$	265800.	0.00560556
$157$	−3.79498e7	−0.782637	−0.391319	−	0.920255i	$-0.627981\pi$
$157$	−3.79498e7	−0.782637	−0.391319	+	0.920255i	$0.627981\pi$
$158$	3.35458e6	0.0676610
$159$	−4.14928e7	−0.818620
$160$	1.70269e7	0.328637
$161$	2.00402e7	0.378452
$162$	6.28013e6	0.116056
$163$	−1.08347e8	−1.95956	−0.979782	−	0.200069i	$-0.935883\pi$
$163$	−1.08347e8	−1.95956	−0.979782	+	0.200069i	$0.935883\pi$
$164$	−7.65934e6	−0.135593
$165$	3.49942e7	0.606460
$166$	−7.44799e7	−1.26375
$167$	3.73178e7	0.620024	0.310012	−	0.950733i	$-0.399667\pi$
$167$	3.73178e7	0.620024	0.310012	+	0.950733i	$0.399667\pi$
$168$	1.27337e7	0.207192
$169$	−6.20339e7	−0.988612
$170$	1.39802e8	2.18243
$171$	−1.20949e7	−0.184977
$172$	618203.	0.00926363
$173$	−3.17763e7	−0.466598	−0.233299	−	0.972405i	$-0.574952\pi$
$173$	−3.17763e7	−0.466598	−0.233299	+	0.972405i	$0.574952\pi$
$174$	8.04258e7	1.15737
$175$	6.11427e7	0.862405
$176$	−4.54063e7	−0.627801
$177$	−8.65522e6	−0.117320
$178$	−8.29778e7	−1.10279
$179$	−5.17703e7	−0.674676	−0.337338	−	0.941384i	$-0.609526\pi$
$179$	−5.17703e7	−0.674676	−0.337338	+	0.941384i	$0.609526\pi$
$180$	−4.29863e6	−0.0549384
$181$	2.17212e6	0.0272276	0.0136138	−	0.999907i	$-0.495666\pi$
$181$	2.17212e6	0.0272276	0.0136138	+	0.999907i	$0.495666\pi$
$182$	−3.42643e6	−0.0421300
$183$	−1.74254e7	−0.210186
$184$	−8.03349e7	−0.950697
$185$	1.54655e8	1.79582
$186$	−4.81888e7	−0.549099
$187$	−5.98054e7	−0.668798
$188$	−1.22279e7	−0.134214
$189$	−6.75127e6	−0.0727393
$190$	9.92738e7	1.05002
$191$	−1.21738e8	−1.26419	−0.632093	−	0.774892i	$-0.717804\pi$
$191$	−1.21738e8	−1.26419	−0.632093	+	0.774892i	$0.717804\pi$
$192$	−5.05768e7	−0.515700
$193$	2.69330e7	0.269671	0.134835	−	0.990868i	$-0.456949\pi$
$193$	2.69330e7	0.269671	0.134835	+	0.990868i	$0.456949\pi$
$194$	1.19671e8	1.17675
$195$	−1.15569e7	−0.111615
$196$	1.37008e6	0.0129972
$197$	4.90383e6	0.0456987	0.0228493	−	0.999739i	$-0.492726\pi$
$197$	4.90383e6	0.0456987	0.0228493	+	0.999739i	$0.492726\pi$
$198$	2.20510e7	0.201883
$199$	4.85555e6	0.0436770	0.0218385	−	0.999762i	$-0.493048\pi$
$199$	4.85555e6	0.0436770	0.0218385	+	0.999762i	$0.493048\pi$
$200$	−2.45102e8	−2.16642
$201$	7.67632e7	0.666756
$202$	7.82643e7	0.668089
$203$	−8.64594e7	−0.725398
$204$	7.34640e6	0.0605856
$205$	3.33027e8	2.69985
$206$	1.73077e8	1.37945
$207$	4.25927e7	0.333764
$208$	1.49956e7	0.115542
$209$	−4.24681e7	−0.321774
$210$	5.54136e7	0.412904
$211$	−1.49124e8	−1.09285	−0.546424	−	0.837509i	$-0.684011\pi$
$211$	−1.49124e8	−1.09285	−0.546424	+	0.837509i	$0.684011\pi$
$212$	1.78964e7	0.129000
$213$	−1.75535e7	−0.124461
$214$	−1.66440e8	−1.16094
$215$	−2.68793e7	−0.184452
$216$	2.70638e7	0.182726
$217$	5.18039e7	0.344155
$218$	−7.80766e7	−0.510415
$219$	−1.37119e8	−0.882149
$220$	−1.50935e7	−0.0955675
$221$	1.97509e7	0.123088
$222$	9.74531e7	0.597806
$223$	1.68773e8	1.01915	0.509574	−	0.860427i	$-0.329803\pi$
$223$	1.68773e8	1.01915	0.509574	+	0.860427i	$0.329803\pi$
$224$	−1.15341e7	−0.0685673
$225$	1.29951e8	0.760570
$226$	−1.70003e7	−0.0979664
$227$	2.07785e8	1.17903	0.589513	−	0.807759i	$-0.299320\pi$
$227$	2.07785e8	1.17903	0.589513	+	0.807759i	$0.299320\pi$
$228$	5.21672e6	0.0291491
$229$	−1.43204e8	−0.788008	−0.394004	−	0.919109i	$-0.628910\pi$
$229$	−1.43204e8	−0.788008	−0.394004	+	0.919109i	$0.628910\pi$
$230$	−3.49596e8	−1.89461
$231$	−2.37053e7	−0.126533
$232$	3.46589e8	1.82225
$233$	−3.12790e7	−0.161997	−0.0809985	−	0.996714i	$-0.525811\pi$
$233$	−3.12790e7	−0.161997	−0.0809985	+	0.996714i	$0.525811\pi$
$234$	−7.28240e6	−0.0371552
$235$	5.31666e8	2.67240
$236$	3.73312e6	0.0184876
$237$	−7.66458e6	−0.0373998
$238$	−9.47024e7	−0.455346
$239$	−1.03833e8	−0.491973	−0.245986	−	0.969273i	$-0.579112\pi$
$239$	−1.03833e8	−0.491973	−0.245986	+	0.969273i	$0.579112\pi$
$240$	−2.42515e8	−1.13240
$241$	−3.08497e8	−1.41968	−0.709841	−	0.704362i	$-0.751233\pi$
$241$	−3.08497e8	−1.41968	−0.709841	+	0.704362i	$0.751233\pi$
$242$	−1.52857e8	−0.693317
$243$	−1.43489e7	−0.0641500
$244$	7.51582e6	0.0331216
$245$	−5.95708e7	−0.258793
$246$	2.09851e8	0.898748
$247$	1.40252e7	0.0592203
$248$	−2.07666e8	−0.864539
$249$	1.70172e8	0.698540
$250$	−5.99154e8	−2.42520
$251$	−7.36890e7	−0.294133	−0.147067	−	0.989127i	$-0.546983\pi$
$251$	−7.36890e7	−0.294133	−0.147067	+	0.989127i	$0.546983\pi$
$252$	2.91192e6	0.0114624
$253$	1.49553e8	0.580594
$254$	−2.59092e8	−0.992054
$255$	−3.19420e8	−1.20635
$256$	7.26790e7	0.270750
$257$	4.70274e8	1.72816	0.864082	−	0.503352i	$-0.167900\pi$
$257$	4.70274e8	1.72816	0.864082	+	0.503352i	$0.167900\pi$
$258$	−1.69376e7	−0.0614019
$259$	−1.04764e8	−0.374683
$260$	4.98467e6	0.0175885
$261$	−1.83758e8	−0.639741
$262$	3.23404e8	1.11094
$263$	2.92938e8	0.992957	0.496479	−	0.868049i	$-0.334626\pi$
$263$	2.92938e8	0.992957	0.496479	+	0.868049i	$0.334626\pi$
$264$	9.50271e7	0.317858
$265$	−7.78133e8	−2.56858
$266$	−6.72486e7	−0.219078
$267$	1.89589e8	0.609569
$268$	−3.31091e7	−0.105069
$269$	2.78907e7	0.0873627	0.0436813	−	0.999046i	$-0.486091\pi$
$269$	2.78907e7	0.0873627	0.0436813	+	0.999046i	$0.486091\pi$
$270$	1.17774e8	0.364147
$271$	−2.04533e8	−0.624266	−0.312133	−	0.950038i	$-0.601044\pi$
$271$	−2.04533e8	−0.624266	−0.312133	+	0.950038i	$0.601044\pi$
$272$	4.14460e8	1.24880
$273$	7.82874e6	0.0232875
$274$	−7.79912e7	−0.229044
$275$	4.56286e8	1.32304
$276$	−1.83708e7	−0.0525953
$277$	1.39644e8	0.394769	0.197385	−	0.980326i	$-0.436755\pi$
$277$	1.39644e8	0.394769	0.197385	+	0.980326i	$0.436755\pi$
$278$	−6.78025e7	−0.189273
$279$	1.10102e8	0.303516
$280$	2.38801e8	0.650104
$281$	2.41823e8	0.650167	0.325083	−	0.945685i	$-0.394608\pi$
$281$	2.41823e8	0.650167	0.325083	+	0.945685i	$0.394608\pi$
$282$	3.35020e8	0.889609
$283$	−1.02768e8	−0.269528	−0.134764	−	0.990878i	$-0.543028\pi$
$283$	−1.02768e8	−0.269528	−0.134764	+	0.990878i	$0.543028\pi$
$284$	7.57106e6	0.0196129
$285$	−2.26822e8	−0.580401
$286$	−2.55702e7	−0.0646328
$287$	−2.25594e8	−0.563302
$288$	−2.45143e7	−0.0604707
$289$	1.35554e8	0.330347
$290$	1.50826e9	3.63148
$291$	−2.73426e8	−0.650452
$292$	5.91412e7	0.139011
$293$	−7.21625e8	−1.67600	−0.838002	−	0.545667i	$-0.816276\pi$
$293$	−7.21625e8	−1.67600	−0.838002	+	0.545667i	$0.816276\pi$
$294$	−3.75375e7	−0.0861489
$295$	−1.62315e8	−0.368114
$296$	4.19967e8	0.941227
$297$	−5.03823e7	−0.111591
$298$	5.64390e8	1.23544
$299$	−4.93903e7	−0.106854
$300$	−5.60495e7	−0.119853
$301$	1.82082e7	0.0384844
$302$	5.06805e7	0.105881
$303$	−1.78819e8	−0.369288
$304$	2.94310e8	0.600825
$305$	−3.26786e8	−0.659500
$306$	−2.01277e8	−0.401578
$307$	8.06683e7	0.159118	0.0795588	−	0.996830i	$-0.474649\pi$
$307$	8.06683e7	0.159118	0.0795588	+	0.996830i	$0.474649\pi$
$308$	1.02244e7	0.0199394
$309$	−3.95449e8	−0.762493
$310$	−9.03706e8	−1.72290
$311$	−4.34178e8	−0.818477	−0.409239	−	0.912427i	$-0.634206\pi$
$311$	−4.34178e8	−0.818477	−0.409239	+	0.912427i	$0.634206\pi$
$312$	−3.13830e7	−0.0584996
$313$	3.75382e8	0.691940	0.345970	−	0.938246i	$-0.387550\pi$
$313$	3.75382e8	0.691940	0.345970	+	0.938246i	$0.387550\pi$
$314$	−4.48459e8	−0.817464
$315$	−1.26610e8	−0.228234
$316$	3.30584e6	0.00589355
$317$	2.42984e8	0.428421	0.214210	−	0.976788i	$-0.431282\pi$
$317$	2.42984e8	0.428421	0.214210	+	0.976788i	$0.431282\pi$
$318$	−4.90327e8	−0.855049
$319$	−6.45216e8	−1.11285
$320$	−9.48489e8	−1.61811
$321$	3.80284e8	0.641712
$322$	2.36818e8	0.395293
$323$	3.87641e8	0.640060
$324$	6.18889e6	0.0101089
$325$	−1.50690e8	−0.243496
$326$	−1.28035e9	−2.04676
$327$	1.78390e8	0.282133
$328$	9.04337e8	1.41505
$329$	−3.60154e8	−0.557574
$330$	4.13532e8	0.633447
$331$	−7.70250e8	−1.16744	−0.583719	−	0.811956i	$-0.698403\pi$
$331$	−7.70250e8	−1.16744	−0.583719	+	0.811956i	$0.698403\pi$
$332$	−7.33978e7	−0.110078
$333$	−2.22662e8	−0.330439
$334$	4.40991e8	0.647615
$335$	1.43958e9	2.09208
$336$	1.64281e8	0.236265
$337$	6.61836e8	0.941989	0.470994	−	0.882136i	$-0.343895\pi$
$337$	6.61836e8	0.941989	0.470994	+	0.882136i	$0.343895\pi$
$338$	−7.33065e8	−1.03260
$339$	3.88425e7	0.0541512
$340$	1.37770e8	0.190099
$341$	3.86595e8	0.527977
$342$	−1.42928e8	−0.193208
$343$	4.03536e7	0.0539949
$344$	−7.29911e7	−0.0966753
$345$	7.98760e8	1.04725
$346$	−3.75506e8	−0.487361
$347$	1.43073e9	1.83825	0.919125	−	0.393967i	$-0.128897\pi$
$347$	1.43073e9	1.83825	0.919125	+	0.393967i	$0.128897\pi$
$348$	7.92573e7	0.100812
$349$	−4.71857e8	−0.594184	−0.297092	−	0.954849i	$-0.596017\pi$
$349$	−4.71857e8	−0.594184	−0.297092	+	0.954849i	$0.596017\pi$
$350$	7.22534e8	0.900782
$351$	1.66389e7	0.0205376
$352$	−8.60752e7	−0.105191
$353$	−5.95148e8	−0.720135	−0.360067	−	0.932926i	$-0.617246\pi$
$353$	−5.95148e8	−0.720135	−0.360067	+	0.932926i	$0.617246\pi$
$354$	−1.02280e8	−0.122541
$355$	−3.29188e8	−0.390522
$356$	−8.17722e7	−0.0960574
$357$	2.16377e8	0.251694
$358$	−6.11778e8	−0.704699
$359$	2.42278e8	0.276365	0.138183	−	0.990407i	$-0.455874\pi$
$359$	2.42278e8	0.276365	0.138183	+	0.990407i	$0.455874\pi$
$360$	5.07539e8	0.573338
$361$	−6.18606e8	−0.692052
$362$	2.56684e7	0.0284392
$363$	3.49250e8	0.383233
$364$	−3.37664e6	−0.00366970
$365$	−2.57145e9	−2.76791
$366$	−2.05919e8	−0.219539
$367$	−1.32152e8	−0.139554	−0.0697769	−	0.997563i	$-0.522229\pi$
$367$	−1.32152e8	−0.139554	−0.0697769	+	0.997563i	$0.522229\pi$
$368$	−1.03642e9	−1.08410
$369$	−4.79470e8	−0.496786
$370$	1.82758e9	1.87573
$371$	5.27112e8	0.535913
$372$	−4.74887e7	−0.0478288
$373$	1.42291e9	1.41970	0.709850	−	0.704353i	$-0.248763\pi$
$373$	1.42291e9	1.41970	0.709850	+	0.704353i	$0.248763\pi$
$374$	−7.06731e8	−0.698560
$375$	1.36895e9	1.34054
$376$	1.44374e9	1.40066
$377$	2.13085e8	0.204813
$378$	−7.97809e7	−0.0759762
$379$	1.27451e9	1.20256	0.601280	−	0.799038i	$-0.294657\pi$
$379$	1.27451e9	1.20256	0.601280	+	0.799038i	$0.294657\pi$
$380$	9.78315e7	0.0914610
$381$	5.91976e8	0.548361
$382$	−1.43860e9	−1.32044
$383$	1.46548e9	1.33286	0.666429	−	0.745569i	$-0.267822\pi$
$383$	1.46548e9	1.33286	0.666429	+	0.745569i	$0.267822\pi$
$384$	−7.13890e8	−0.643387
$385$	−4.44556e8	−0.397021
$386$	3.18271e8	0.281671
$387$	3.86991e7	0.0339401
$388$	1.17933e8	0.102500
$389$	−1.26046e9	−1.08568	−0.542842	−	0.839835i	$-0.682652\pi$
$389$	−1.26046e9	−1.08568	−0.542842	+	0.839835i	$0.682652\pi$
$390$	−1.36570e8	−0.116582
$391$	−1.36509e9	−1.15490
$392$	−1.61765e8	−0.135639
$393$	−7.38918e8	−0.614076
$394$	5.79494e7	0.0477323
$395$	−1.43737e8	−0.117349
$396$	2.17306e7	0.0175849
$397$	1.50525e9	1.20737	0.603687	−	0.797221i	$-0.293698\pi$
$397$	1.50525e9	1.20737	0.603687	+	0.797221i	$0.293698\pi$
$398$	5.73789e7	0.0456206
$399$	1.53650e8	0.121096
$400$	−3.16213e9	−2.47041
$401$	8.79522e8	0.681148	0.340574	−	0.940218i	$-0.389379\pi$
$401$	8.79522e8	0.681148	0.340574	+	0.940218i	$0.389379\pi$
$402$	9.07124e8	0.696427
$403$	−1.27674e8	−0.0971706
$404$	7.71272e7	0.0581933
$405$	−2.69092e8	−0.201283
$406$	−1.02171e9	−0.757678
$407$	−7.81818e8	−0.574811
$408$	−8.67389e8	−0.632271
$409$	−8.87855e8	−0.641668	−0.320834	−	0.947135i	$-0.603963\pi$
$409$	−8.87855e8	−0.641668	−0.320834	+	0.947135i	$0.603963\pi$
$410$	3.93543e9	2.82000
$411$	1.78195e8	0.126605
$412$	1.70563e8	0.120156
$413$	1.09953e8	0.0768039
$414$	5.03325e8	0.348616
$415$	3.19132e9	2.19181
$416$	2.84266e7	0.0193597
$417$	1.54916e8	0.104621
$418$	−5.01853e8	−0.336093
$419$	−1.54425e9	−1.02558	−0.512788	−	0.858515i	$-0.671387\pi$
$419$	−1.54425e9	−1.02558	−0.512788	+	0.858515i	$0.671387\pi$
$420$	5.46085e7	0.0359656
$421$	−4.18620e7	−0.0273422	−0.0136711	−	0.999907i	$-0.504352\pi$
$421$	−4.18620e7	−0.0273422	−0.0136711	+	0.999907i	$0.504352\pi$
$422$	−1.76223e9	−1.14148
$423$	−7.65458e8	−0.491734
$424$	−2.11303e9	−1.34625
$425$	−4.16490e9	−2.63174
$426$	−2.07432e8	−0.130000
$427$	2.21367e8	0.137599
$428$	−1.64022e8	−0.101123
$429$	5.84231e7	0.0357260
$430$	−3.17638e8	−0.192660
$431$	2.88819e9	1.73762	0.868810	−	0.495146i	$-0.164885\pi$
$431$	2.88819e9	1.73762	0.868810	+	0.495146i	$0.164885\pi$
$432$	3.49157e8	0.208366
$433$	2.10632e8	0.124686	0.0623428	−	0.998055i	$-0.480143\pi$
$433$	2.10632e8	0.124686	0.0623428	+	0.998055i	$0.480143\pi$
$434$	6.12176e8	0.359470
$435$	−3.44609e9	−2.00731
$436$	−7.69423e7	−0.0444593
$437$	−9.69357e8	−0.555646
$438$	−1.62035e9	−0.921404
$439$	1.20723e9	0.681025	0.340513	−	0.940240i	$-0.389399\pi$
$439$	1.20723e9	0.681025	0.340513	+	0.940240i	$0.389399\pi$
$440$	1.78209e9	0.997343
$441$	8.57661e7	0.0476190
$442$	2.33400e8	0.128565
$443$	−1.54375e9	−0.843652	−0.421826	−	0.906677i	$-0.638611\pi$
$443$	−1.54375e9	−0.843652	−0.421826	+	0.906677i	$0.638611\pi$
$444$	9.60373e7	0.0520714
$445$	3.55544e9	1.91264
$446$	1.99442e9	1.06450
$447$	−1.28953e9	−0.682894
$448$	6.42512e8	0.337605
$449$	1.46438e9	0.763467	0.381734	−	0.924272i	$-0.375327\pi$
$449$	1.46438e9	0.763467	0.381734	+	0.924272i	$0.375327\pi$
$450$	1.53565e9	0.794415
$451$	−1.68353e9	−0.864177
$452$	−1.67533e7	−0.00853328
$453$	−1.15795e8	−0.0585259
$454$	2.45543e9	1.23149
$455$	1.46816e8	0.0730690
$456$	−6.15937e8	−0.304200
$457$	−3.26783e9	−1.60159	−0.800797	−	0.598936i	$-0.795590\pi$
$457$	−3.26783e9	−1.60159	−0.800797	+	0.598936i	$0.795590\pi$
$458$	−1.69226e9	−0.823074
$459$	4.59880e8	0.221973
$460$	−3.44517e8	−0.165028
$461$	1.54907e9	0.736405	0.368203	−	0.929746i	$-0.379973\pi$
$461$	1.54907e9	0.736405	0.368203	+	0.929746i	$0.379973\pi$
$462$	−2.80129e8	−0.132163
$463$	2.32804e9	1.09008	0.545038	−	0.838411i	$-0.316515\pi$
$463$	2.32804e9	1.09008	0.545038	+	0.838411i	$0.316515\pi$
$464$	4.47144e9	2.07795
$465$	2.06480e9	0.952340
$466$	−3.69629e8	−0.169206
$467$	1.02555e9	0.465961	0.232981	−	0.972481i	$-0.425152\pi$
$467$	1.02555e9	0.465961	0.232981	+	0.972481i	$0.425152\pi$
$468$	−7.17660e6	−0.00323637
$469$	−9.75177e8	−0.436494
$470$	6.28279e9	2.79132
$471$	1.02464e9	0.451856
$472$	−4.40769e8	−0.192936
$473$	1.35882e8	0.0590400
$474$	−9.05737e7	−0.0390641
$475$	−2.95751e9	−1.26619
$476$	−9.33265e7	−0.0396626
$477$	1.12030e9	0.472631
$478$	−1.22701e9	−0.513866
$479$	−9.84494e8	−0.409297	−0.204649	−	0.978836i	$-0.565605\pi$
$479$	−9.84494e8	−0.409297	−0.204649	+	0.978836i	$0.565605\pi$
$480$	−4.59727e8	−0.189739
$481$	2.58198e8	0.105790
$482$	−3.64556e9	−1.48286
$483$	−5.41085e8	−0.218500
$484$	−1.50636e8	−0.0603908
$485$	−5.12769e9	−2.04092
$486$	−1.69563e8	−0.0670047
$487$	−2.48196e9	−0.973742	−0.486871	−	0.873474i	$-0.661862\pi$
$487$	−2.48196e9	−0.973742	−0.486871	+	0.873474i	$0.661862\pi$
$488$	−8.87392e8	−0.345658
$489$	2.92536e9	1.13135
$490$	−7.03958e8	−0.270309
$491$	2.05647e9	0.784036	0.392018	−	0.919957i	$-0.371777\pi$
$491$	2.05647e9	0.784036	0.392018	+	0.919957i	$0.371777\pi$
$492$	2.06802e8	0.0782847
$493$	5.88941e9	2.21364
$494$	1.65738e8	0.0618556
$495$	−9.44843e8	−0.350140
$496$	−2.67916e9	−0.985853
$497$	2.22994e8	0.0814791
$498$	2.01096e9	0.729625
$499$	−2.48409e9	−0.894984	−0.447492	−	0.894288i	$-0.647683\pi$
$499$	−2.48409e9	−0.894984	−0.447492	+	0.894288i	$0.647683\pi$
$500$	−5.90449e8	−0.211245
$501$	−1.00758e9	−0.357971
$502$	−8.70795e8	−0.307222
$503$	3.98238e9	1.39526	0.697630	−	0.716458i	$-0.254238\pi$
$503$	3.98238e9	1.39526	0.697630	+	0.716458i	$0.254238\pi$
$504$	−3.43810e8	−0.119622
$505$	−3.35348e9	−1.15871
$506$	1.76729e9	0.606431
$507$	1.67492e9	0.570775
$508$	−2.55327e8	−0.0864121
$509$	−3.08817e8	−0.103798	−0.0518990	−	0.998652i	$-0.516527\pi$
$509$	−3.08817e8	−0.103798	−0.0518990	+	0.998652i	$0.516527\pi$
$510$	−3.77464e9	−1.26003
$511$	1.74191e9	0.577502
$512$	−2.52551e9	−0.831580
$513$	3.26563e8	0.106796
$514$	5.55730e9	1.80507
$515$	−7.41604e9	−2.39247
$516$	−1.66915e7	−0.00534836
$517$	−2.68770e9	−0.855389
$518$	−1.23802e9	−0.391356
$519$	8.57961e8	0.269390
$520$	−5.88540e8	−0.183554
$521$	−2.20724e9	−0.683783	−0.341891	−	0.939739i	$-0.611068\pi$
$521$	−2.20724e9	−0.683783	−0.341891	+	0.939739i	$0.611068\pi$
$522$	−2.17150e9	−0.668209
$523$	−3.71386e9	−1.13519	−0.567596	−	0.823307i	$-0.692127\pi$
$523$	−3.71386e9	−1.13519	−0.567596	+	0.823307i	$0.692127\pi$
$524$	3.18706e8	0.0967676
$525$	−1.65085e9	−0.497910
$526$	3.46170e9	1.03714
$527$	−3.52876e9	−1.05023
$528$	1.22597e9	0.362461
$529$	8.79528e6	0.00258318
$530$	−9.19533e9	−2.68288
$531$	2.33691e8	0.0677347
$532$	−6.62716e7	−0.0190826
$533$	5.55991e8	0.159046
$534$	2.24040e9	0.636695
$535$	7.13163e9	2.01350
$536$	3.90919e9	1.09650
$537$	1.39780e9	0.389524
$538$	3.29589e8	0.0912503
$539$	3.01145e8	0.0828351
$540$	1.16063e8	0.0317187
$541$	2.70994e9	0.735815	0.367907	−	0.929862i	$-0.380074\pi$
$541$	2.70994e9	0.735815	0.367907	+	0.929862i	$0.380074\pi$
$542$	−2.41700e9	−0.652046
$543$	−5.86473e7	−0.0157199
$544$	7.85678e8	0.209242
$545$	3.34544e9	0.885248
$546$	9.25135e7	0.0243238
$547$	1.96269e9	0.512739	0.256370	−	0.966579i	$-0.417474\pi$
$547$	1.96269e9	0.512739	0.256370	+	0.966579i	$0.417474\pi$
$548$	−7.68581e7	−0.0199507
$549$	4.70486e8	0.121351
$550$	5.39201e9	1.38192
$551$	4.18210e9	1.06503
$552$	2.16904e9	0.548885
$553$	9.73686e7	0.0244839
$554$	1.65020e9	0.412337
$555$	−4.17568e9	−1.03682
$556$	−6.68174e7	−0.0164865
$557$	6.90420e8	0.169286	0.0846429	−	0.996411i	$-0.473025\pi$
$557$	6.90420e8	0.169286	0.0846429	+	0.996411i	$0.473025\pi$
$558$	1.30110e9	0.317022
$559$	−4.48753e7	−0.0108659
$560$	3.08084e9	0.741328
$561$	1.61475e9	0.386131
$562$	2.85766e9	0.679099
$563$	−1.69677e9	−0.400723	−0.200362	−	0.979722i	$-0.564212\pi$
$563$	−1.69677e9	−0.400723	−0.200362	+	0.979722i	$0.564212\pi$
$564$	3.30153e8	0.0774886
$565$	7.28431e8	0.169910
$566$	−1.21442e9	−0.281522
$567$	1.82284e8	0.0419961
$568$	−8.93915e8	−0.204681
$569$	−4.75305e9	−1.08163	−0.540816	−	0.841141i	$-0.681885\pi$
$569$	−4.75305e9	−1.08163	−0.540816	+	0.841141i	$0.681885\pi$
$570$	−2.68039e9	−0.606228
$571$	−4.11471e9	−0.924939	−0.462470	−	0.886635i	$-0.653037\pi$
$571$	−4.11471e9	−0.924939	−0.462470	+	0.886635i	$0.653037\pi$
$572$	−2.51987e7	−0.00562979
$573$	3.28694e9	0.729878
$574$	−2.66588e9	−0.588369
$575$	1.04150e10	2.28466
$576$	1.36557e9	0.297739
$577$	−2.88913e9	−0.626112	−0.313056	−	0.949735i	$-0.601353\pi$
$577$	−2.88913e9	−0.626112	−0.313056	+	0.949735i	$0.601353\pi$
$578$	1.60186e9	0.345047
$579$	−7.27190e8	−0.155694
$580$	1.48635e9	0.316317
$581$	−2.16182e9	−0.457302
$582$	−3.23113e9	−0.679397
$583$	3.93365e9	0.822159
$584$	−6.98279e9	−1.45072
$585$	3.12037e8	0.0644408
$586$	−8.52757e9	−1.75059
$587$	−7.67395e9	−1.56598	−0.782989	−	0.622035i	$-0.786306\pi$
$587$	−7.67395e9	−1.56598	−0.782989	+	0.622035i	$0.786306\pi$
$588$	−3.69921e7	−0.00750393
$589$	−2.50579e9	−0.505290
$590$	−1.91811e9	−0.384495
$591$	−1.32403e8	−0.0263842
$592$	5.41811e9	1.07330
$593$	7.22960e8	0.142371	0.0711857	−	0.997463i	$-0.477322\pi$
$593$	7.22960e8	0.142371	0.0711857	+	0.997463i	$0.477322\pi$
$594$	−5.95377e8	−0.116557
$595$	4.05782e9	0.789739
$596$	5.56190e8	0.107612
$597$	−1.31100e8	−0.0252169
$598$	−5.83653e8	−0.111609
$599$	7.88643e9	1.49929	0.749647	−	0.661838i	$-0.230223\pi$
$599$	7.88643e9	1.49929	0.749647	+	0.661838i	$0.230223\pi$
$600$	6.61776e9	1.25078
$601$	−1.37657e9	−0.258664	−0.129332	−	0.991601i	$-0.541283\pi$
$601$	−1.37657e9	−0.258664	−0.129332	+	0.991601i	$0.541283\pi$
$602$	2.15170e8	0.0401970
$603$	−2.07261e9	−0.384952
$604$	4.99442e7	0.00922265
$605$	6.54964e9	1.20247
$606$	−2.11314e9	−0.385721
$607$	−4.96380e9	−0.900853	−0.450427	−	0.892813i	$-0.648728\pi$
$607$	−4.96380e9	−0.900853	−0.450427	+	0.892813i	$0.648728\pi$
$608$	5.57914e8	0.100671
$609$	2.33440e9	0.418809
$610$	−3.86169e9	−0.688847
$611$	8.87621e8	0.157428
$612$	−1.98353e8	−0.0349791
$613$	1.64394e9	0.288254	0.144127	−	0.989559i	$-0.453963\pi$
$613$	1.64394e9	0.288254	0.144127	+	0.989559i	$0.453963\pi$
$614$	9.53271e8	0.166198
$615$	−8.99172e9	−1.55876
$616$	−1.20720e9	−0.208087
$617$	−1.46189e9	−0.250563	−0.125281	−	0.992121i	$-0.539983\pi$
$617$	−1.46189e9	−0.250563	−0.125281	+	0.992121i	$0.539983\pi$
$618$	−4.67309e9	−0.796424
$619$	−5.81126e9	−0.984812	−0.492406	−	0.870366i	$-0.663882\pi$
$619$	−5.81126e9	−0.984812	−0.492406	+	0.870366i	$0.663882\pi$
$620$	−8.90576e8	−0.150072
$621$	−1.15000e9	−0.192698
$622$	−5.13076e9	−0.854899
$623$	−2.40848e9	−0.399056
$624$	−4.04880e8	−0.0667084
$625$	1.17462e10	1.92449
$626$	4.43596e9	0.722732
$627$	1.14664e9	0.185776
$628$	−4.41943e8	−0.0712046
$629$	7.13629e9	1.14339
$630$	−1.49617e9	−0.238390
$631$	−1.17184e10	−1.85681	−0.928403	−	0.371575i	$-0.878818\pi$
$631$	−1.17184e10	−1.85681	−0.928403	+	0.371575i	$0.878818\pi$
$632$	−3.90321e8	−0.0615052
$633$	4.02635e9	0.630956
$634$	2.87138e9	0.447485
$635$	1.11016e10	1.72059
$636$	−4.83203e8	−0.0744783
$637$	−9.94540e7	−0.0152452
$638$	−7.62463e9	−1.16237
$639$	4.73944e8	0.0718578
$640$	−1.33879e10	−2.01875
$641$	−1.81574e9	−0.272302	−0.136151	−	0.990688i	$-0.543473\pi$
$641$	−1.81574e9	−0.272302	−0.136151	+	0.990688i	$0.543473\pi$
$642$	4.49387e9	0.670268
$643$	5.81427e9	0.862496	0.431248	−	0.902233i	$-0.358073\pi$
$643$	5.81427e9	0.862496	0.431248	+	0.902233i	$0.358073\pi$
$644$	2.33378e8	0.0344317
$645$	7.25742e8	0.106494
$646$	4.58082e9	0.668543
$647$	7.06120e8	0.102497	0.0512487	−	0.998686i	$-0.483680\pi$
$647$	7.06120e8	0.102497	0.0512487	+	0.998686i	$0.483680\pi$
$648$	−7.30721e8	−0.105497
$649$	8.20543e8	0.117827
$650$	−1.78073e9	−0.254332
$651$	−1.39871e9	−0.198698
$652$	−1.26175e9	−0.178282
$653$	4.13387e9	0.580980	0.290490	−	0.956878i	$-0.406182\pi$
$653$	4.13387e9	0.580980	0.290490	+	0.956878i	$0.406182\pi$
$654$	2.10807e9	0.294688
$655$	−1.38573e10	−1.92678
$656$	1.16671e10	1.61361
$657$	3.70220e9	0.509309
$658$	−4.25600e9	−0.582386
$659$	−8.52636e9	−1.16055	−0.580276	−	0.814420i	$-0.697055\pi$
$659$	−8.52636e9	−1.16055	−0.580276	+	0.814420i	$0.697055\pi$
$660$	4.07524e8	0.0551759
$661$	−9.50126e7	−0.0127961	−0.00639803	−	0.999980i	$-0.502037\pi$
$661$	−9.50126e7	−0.0127961	−0.00639803	+	0.999980i	$0.502037\pi$
$662$	−9.10217e9	−1.21939
$663$	−5.33275e8	−0.0710647
$664$	8.66607e9	1.14877
$665$	2.88148e9	0.379961
$666$	−2.63123e9	−0.345144
$667$	−1.47274e10	−1.92170
$668$	4.34584e8	0.0564100
$669$	−4.55688e9	−0.588405
$670$	1.70117e10	2.18518
$671$	1.65198e9	0.211095
$672$	3.11422e8	0.0395874
$673$	3.00696e9	0.380255	0.190127	−	0.981759i	$-0.439110\pi$
$673$	3.00696e9	0.380255	0.190127	+	0.981759i	$0.439110\pi$
$674$	7.82103e9	0.983907
$675$	−3.50866e9	−0.439115
$676$	−7.22415e8	−0.0899442
$677$	2.63630e9	0.326538	0.163269	−	0.986582i	$-0.447796\pi$
$677$	2.63630e9	0.326538	0.163269	+	0.986582i	$0.447796\pi$
$678$	4.59008e8	0.0565609
$679$	3.47353e9	0.425820
$680$	−1.62666e10	−1.98387
$681$	−5.61019e9	−0.680711
$682$	4.56845e9	0.551472
$683$	8.25370e9	0.991234	0.495617	−	0.868541i	$-0.334942\pi$
$683$	8.25370e9	0.991234	0.495617	+	0.868541i	$0.334942\pi$
$684$	−1.40851e8	−0.0168292
$685$	3.34178e9	0.397247
$686$	4.76865e8	0.0563977
$687$	3.86650e9	0.454957
$688$	−9.41679e8	−0.110241
$689$	−1.29910e9	−0.151313
$690$	9.43909e9	1.09385
$691$	−6.56349e9	−0.756767	−0.378383	−	0.925649i	$-0.623520\pi$
$691$	−6.56349e9	−0.756767	−0.378383	+	0.925649i	$0.623520\pi$
$692$	−3.70051e8	−0.0424512
$693$	6.40042e8	0.0730537
$694$	1.69072e10	1.92005
$695$	2.90521e9	0.328270
$696$	−9.35790e9	−1.05207
$697$	1.53669e10	1.71899
$698$	−5.57601e9	−0.620625
$699$	8.44533e8	0.0935290
$700$	7.12036e8	0.0784619
$701$	5.91004e9	0.648003	0.324002	−	0.946057i	$-0.394972\pi$
$701$	5.91004e9	0.648003	0.324002	+	0.946057i	$0.394972\pi$
$702$	1.96625e8	0.0214515
$703$	5.06751e9	0.550112
$704$	4.79484e9	0.517929
$705$	−1.43550e10	−1.54291
$706$	−7.03297e9	−0.752181
$707$	2.27167e9	0.241756
$708$	−1.00794e8	−0.0106738
$709$	1.85087e10	1.95035	0.975177	−	0.221428i	$-0.0710717\pi$
$709$	1.85087e10	1.95035	0.975177	+	0.221428i	$0.0710717\pi$
$710$	−3.89008e9	−0.407900
$711$	2.06944e8	0.0215928
$712$	9.65484e9	1.00246
$713$	8.82422e9	0.911723
$714$	2.55697e9	0.262894
$715$	1.09564e9	0.112097
$716$	−6.02890e8	−0.0613822
$717$	2.80348e9	0.284041
$718$	2.86304e9	0.288663
$719$	−1.54172e10	−1.54687	−0.773436	−	0.633874i	$-0.781464\pi$
$719$	−1.54172e10	−1.54687	−0.773436	+	0.633874i	$0.781464\pi$
$720$	6.54790e9	0.653790
$721$	5.02367e9	0.499169
$722$	−7.31017e9	−0.722849
$723$	8.32941e9	0.819654
$724$	2.52954e7	0.00247718
$725$	−4.49333e10	−4.37911
$726$	4.12714e9	0.400287
$727$	4.10902e9	0.396614	0.198307	−	0.980140i	$-0.436456\pi$
$727$	4.10902e9	0.396614	0.198307	+	0.980140i	$0.436456\pi$
$728$	3.98680e8	0.0382970
$729$	3.87420e8	0.0370370
$730$	−3.03872e10	−2.89109
$731$	−1.24030e9	−0.117440
$732$	−2.02927e8	−0.0191228
$733$	−5.22793e9	−0.490305	−0.245152	−	0.969485i	$-0.578838\pi$
$733$	−5.22793e9	−0.490305	−0.245152	+	0.969485i	$0.578838\pi$
$734$	−1.56166e9	−0.145764
$735$	1.60841e9	0.149414
$736$	−1.96471e9	−0.181646
$737$	−7.27741e9	−0.669638
$738$	−5.66598e9	−0.518893
$739$	−1.81752e10	−1.65662	−0.828310	−	0.560269i	$-0.810698\pi$
$739$	−1.81752e10	−1.65662	−0.828310	+	0.560269i	$0.810698\pi$
$740$	1.80103e9	0.163384
$741$	−3.78681e8	−0.0341908
$742$	6.22897e9	0.559761
$743$	−1.66110e9	−0.148571	−0.0742855	−	0.997237i	$-0.523668\pi$
$743$	−1.66110e9	−0.148571	−0.0742855	+	0.997237i	$0.523668\pi$
$744$	5.60698e9	0.499142
$745$	−2.41831e10	−2.14271
$746$	1.68148e10	1.48288
$747$	−4.59466e9	−0.403302
$748$	−6.96463e8	−0.0608475
$749$	−4.83101e9	−0.420099
$750$	1.61772e10	1.40019
$751$	−1.44056e10	−1.24106	−0.620530	−	0.784183i	$-0.713083\pi$
$751$	−1.44056e10	−1.24106	−0.620530	+	0.784183i	$0.713083\pi$
$752$	1.86261e10	1.59720
$753$	1.98960e9	0.169818
$754$	2.51806e9	0.213927
$755$	−2.17157e9	−0.183636
$756$	−7.86218e7	−0.00661784
$757$	−1.07107e10	−0.897395	−0.448698	−	0.893684i	$-0.648112\pi$
$757$	−1.07107e10	−0.897395	−0.448698	+	0.893684i	$0.648112\pi$
$758$	1.50611e10	1.25607
$759$	−4.03793e9	−0.335206
$760$	−1.15510e10	−0.954487
$761$	−9.76867e9	−0.803506	−0.401753	−	0.915748i	$-0.631599\pi$
$761$	−9.76867e9	−0.803506	−0.401753	+	0.915748i	$0.631599\pi$
$762$	6.99548e9	0.572763
$763$	−2.26622e9	−0.184700
$764$	−1.41770e9	−0.115016
$765$	8.62435e9	0.696484
$766$	1.73178e10	1.39217
$767$	−2.70987e8	−0.0216852
$768$	−1.96233e9	−0.156318
$769$	6.79202e9	0.538588	0.269294	−	0.963058i	$-0.413210\pi$
$769$	6.79202e9	0.538588	0.269294	+	0.963058i	$0.413210\pi$
$770$	−5.25339e9	−0.414689
$771$	−1.26974e10	−0.997756
$772$	3.13647e8	0.0245347
$773$	−3.67331e9	−0.286042	−0.143021	−	0.989720i	$-0.545682\pi$
$773$	−3.67331e9	−0.286042	−0.143021	+	0.989720i	$0.545682\pi$
$774$	4.57314e8	0.0354504
$775$	2.69227e10	2.07761
$776$	−1.39243e10	−1.06969
$777$	2.82863e9	0.216323
$778$	−1.48950e10	−1.13400
$779$	1.09121e10	0.827044
$780$	−1.34586e8	−0.0101547
$781$	1.66413e9	0.124999
$782$	−1.61315e10	−1.20629
$783$	4.96146e9	0.369354
$784$	−2.08698e9	−0.154672
$785$	1.92156e10	1.41779
$786$	−8.73191e9	−0.641402
$787$	2.64976e10	1.93774	0.968868	−	0.247579i	$-0.0796348\pi$
$787$	2.64976e10	1.93774	0.968868	+	0.247579i	$0.0796348\pi$
$788$	5.71075e7	0.00415768
$789$	−7.90933e9	−0.573284
$790$	−1.69857e9	−0.122571
$791$	−4.93444e8	−0.0354503
$792$	−2.56573e9	−0.183516
$793$	−5.45573e8	−0.0388505
$794$	1.77878e10	1.26110
$795$	2.10096e10	1.48297
$796$	5.65452e7	0.00397375
$797$	−1.78272e10	−1.24732	−0.623662	−	0.781694i	$-0.714356\pi$
$797$	−1.78272e10	−1.24732	−0.623662	+	0.781694i	$0.714356\pi$
$798$	1.81571e9	0.126484
$799$	2.45328e10	1.70151
$800$	−5.99435e9	−0.413930
$801$	−5.11889e9	−0.351935
$802$	1.03935e10	0.711459
$803$	1.29993e10	0.885962
$804$	8.93945e8	0.0606617
$805$	−1.01472e10	−0.685585
$806$	−1.50875e9	−0.101495
$807$	−7.53048e8	−0.0504389
$808$	−9.10641e9	−0.607306
$809$	−1.50221e10	−0.997498	−0.498749	−	0.866746i	$-0.666207\pi$
$809$	−1.50221e10	−0.997498	−0.498749	+	0.866746i	$0.666207\pi$
$810$	−3.17990e9	−0.210240
$811$	8.10208e9	0.533363	0.266682	−	0.963785i	$-0.414073\pi$
$811$	8.10208e9	0.533363	0.266682	+	0.963785i	$0.414073\pi$
$812$	−1.00686e9	−0.0659969
$813$	5.52238e9	0.360420
$814$	−9.23888e9	−0.600390
$815$	5.48607e10	3.54985
$816$	−1.11904e10	−0.720993
$817$	−8.80743e8	−0.0565031
$818$	−1.04919e10	−0.670223
$819$	−2.11376e8	−0.0134450
$820$	3.87825e9	0.245634
$821$	2.59355e10	1.63566	0.817832	−	0.575457i	$-0.195176\pi$
$821$	2.59355e10	1.63566	0.817832	+	0.575457i	$0.195176\pi$
$822$	2.10576e9	0.132239
$823$	1.32431e10	0.828116	0.414058	−	0.910250i	$-0.364111\pi$
$823$	1.32431e10	0.828116	0.414058	+	0.910250i	$0.364111\pi$
$824$	−2.01383e10	−1.25395
$825$	−1.23197e10	−0.763858
$826$	1.29934e9	0.0802217
$827$	−1.01074e10	−0.621401	−0.310701	−	0.950508i	$-0.600564\pi$
$827$	−1.01074e10	−0.621401	−0.310701	+	0.950508i	$0.600564\pi$
$828$	4.96012e8	0.0303659
$829$	−2.30939e10	−1.40785	−0.703924	−	0.710275i	$-0.748571\pi$
$829$	−2.30939e10	−1.40785	−0.703924	+	0.710275i	$0.748571\pi$
$830$	3.77124e10	2.28934
$831$	−3.77039e9	−0.227920
$832$	−1.58351e9	−0.0953212
$833$	−2.74879e9	−0.164772
$834$	1.83067e9	0.109277
$835$	−1.88956e10	−1.12320
$836$	−4.94562e8	−0.0292751
$837$	−2.97276e9	−0.175235
$838$	−1.82486e10	−1.07121
$839$	1.02801e10	0.600939	0.300469	−	0.953791i	$-0.402857\pi$
$839$	1.02801e10	0.600939	0.300469	+	0.953791i	$0.402857\pi$
$840$	−6.44762e9	−0.375338
$841$	4.62885e10	2.68341
$842$	−4.94691e8	−0.0285589
$843$	−6.52921e9	−0.375374
$844$	−1.73662e9	−0.0994276
$845$	3.14105e10	1.79092
$846$	−9.04554e9	−0.513616
$847$	−4.43676e9	−0.250885
$848$	−2.72608e10	−1.53516
$849$	2.77473e9	0.155612
$850$	−4.92173e10	−2.74885
$851$	−1.78454e10	−0.992597
$852$	−2.04419e8	−0.0113235
$853$	−2.37327e10	−1.30926	−0.654628	−	0.755951i	$-0.727175\pi$
$853$	−2.37327e10	−1.30926	−0.654628	+	0.755951i	$0.727175\pi$
$854$	2.61593e9	0.143722
$855$	6.12419e9	0.335094
$856$	1.93660e10	1.05532
$857$	−2.81461e10	−1.52751	−0.763757	−	0.645504i	$-0.776647\pi$
$857$	−2.81461e10	−1.52751	−0.763757	+	0.645504i	$0.776647\pi$
$858$	6.90396e8	0.0373158
$859$	−2.04412e10	−1.10035	−0.550174	−	0.835050i	$-0.685439\pi$
$859$	−2.04412e10	−1.10035	−0.550174	+	0.835050i	$0.685439\pi$
$860$	−3.13023e8	−0.0167815
$861$	6.09104e9	0.325222
$862$	3.41302e10	1.81494
$863$	−2.98198e10	−1.57931	−0.789655	−	0.613552i	$-0.789740\pi$
$863$	−2.98198e10	−1.57931	−0.789655	+	0.613552i	$0.789740\pi$
$864$	6.61885e8	0.0349128
$865$	1.60897e10	0.845265
$866$	2.48907e9	0.130234
$867$	−3.65996e9	−0.190726
$868$	6.03282e8	0.0313113
$869$	7.26627e8	0.0375615
$870$	−4.07231e10	−2.09664
$871$	2.40338e9	0.123242
$872$	9.08457e9	0.463977
$873$	7.38251e9	0.375538
$874$	−1.14551e10	−0.580373
$875$	−1.73908e10	−0.877589
$876$	−1.59681e9	−0.0802582
$877$	−5.96932e9	−0.298831	−0.149416	−	0.988774i	$-0.547739\pi$
$877$	−5.96932e9	−0.298831	−0.149416	+	0.988774i	$0.547739\pi$
$878$	1.42660e10	0.711331
$879$	1.94839e10	0.967642
$880$	2.29912e10	1.13729
$881$	7.92595e8	0.0390513	0.0195257	−	0.999809i	$-0.493784\pi$
$881$	7.92595e8	0.0390513	0.0195257	+	0.999809i	$0.493784\pi$
$882$	1.01351e9	0.0497381
$883$	−7.96340e9	−0.389257	−0.194628	−	0.980877i	$-0.562350\pi$
$883$	−7.96340e9	−0.389257	−0.194628	+	0.980877i	$0.562350\pi$
$884$	2.30009e8	0.0111986
$885$	4.38251e9	0.212531
$886$	−1.82427e10	−0.881195
$887$	3.15162e10	1.51635	0.758177	−	0.652049i	$-0.226090\pi$
$887$	3.15162e10	1.51635	0.758177	+	0.652049i	$0.226090\pi$
$888$	−1.13391e10	−0.543418
$889$	−7.52028e9	−0.358986
$890$	4.20152e10	1.99775
$891$	1.36032e9	0.0644273
$892$	1.96545e9	0.0927224
$893$	1.74209e10	0.818634
$894$	−1.52385e10	−0.713283
$895$	2.62135e10	1.22221
$896$	9.06905e9	0.421195
$897$	1.33354e9	0.0616924
$898$	1.73048e10	0.797442
$899$	−3.80703e10	−1.74754
$900$	1.51334e9	0.0691969
$901$	−3.59056e10	−1.63541
$902$	−1.98946e10	−0.902633
$903$	−4.91622e8	−0.0222190
$904$	1.97806e9	0.0890534
$905$	−1.09984e9	−0.0493242
$906$	−1.36837e9	−0.0611303
$907$	1.36004e10	0.605238	0.302619	−	0.953112i	$-0.402139\pi$
$907$	1.36004e10	0.605238	0.302619	+	0.953112i	$0.402139\pi$
$908$	2.41976e9	0.107268
$909$	4.82812e9	0.213208
$910$	1.73495e9	0.0763206
$911$	−2.57065e10	−1.12650	−0.563248	−	0.826288i	$-0.690448\pi$
$911$	−2.57065e10	−1.12650	−0.563248	+	0.826288i	$0.690448\pi$
$912$	−7.94637e9	−0.346886
$913$	−1.61329e10	−0.701560
$914$	−3.86165e10	−1.67286
$915$	8.82323e9	0.380762
$916$	−1.66768e9	−0.0716932
$917$	9.38699e9	0.402007
$918$	5.43448e9	0.231851
$919$	2.55630e10	1.08644	0.543222	−	0.839589i	$-0.317204\pi$
$919$	2.55630e10	1.08644	0.543222	+	0.839589i	$0.317204\pi$
$920$	4.06771e10	1.72223
$921$	−2.17804e9	−0.0918666
$922$	1.83056e10	0.769175
$923$	−5.49583e8	−0.0230053
$924$	−2.76059e8	−0.0115120
$925$	−5.44464e10	−2.26190
$926$	2.75109e10	1.13859
$927$	1.06771e10	0.440226
$928$	8.47636e9	0.348170
$929$	−2.35583e10	−0.964027	−0.482014	−	0.876164i	$-0.660094\pi$
$929$	−2.35583e10	−0.964027	−0.482014	+	0.876164i	$0.660094\pi$
$930$	2.44001e10	0.994720
$931$	−1.95193e9	−0.0792757
$932$	−3.64259e8	−0.0147385
$933$	1.17228e10	0.472548
$934$	1.21192e10	0.486696
$935$	3.02821e10	1.21156
$936$	8.47341e8	0.0337748
$937$	1.01871e10	0.404542	0.202271	−	0.979330i	$-0.435168\pi$
$937$	1.01871e10	0.404542	0.202271	+	0.979330i	$0.435168\pi$
$938$	−1.15238e10	−0.455918
$939$	−1.01353e10	−0.399492
$940$	6.19150e9	0.243136
$941$	4.37637e10	1.71218	0.856092	−	0.516823i	$-0.172886\pi$
$941$	4.37637e10	1.71218	0.856092	+	0.516823i	$0.172886\pi$
$942$	1.21084e10	0.471963
$943$	−3.84274e10	−1.49228
$944$	−5.68648e9	−0.220010
$945$	3.41846e9	0.131771
$946$	1.60574e9	0.0616673
$947$	−4.71763e10	−1.80509	−0.902545	−	0.430596i	$-0.858303\pi$
$947$	−4.71763e10	−1.80509	−0.902545	+	0.430596i	$0.858303\pi$
$948$	−8.92577e7	−0.00340265
$949$	−4.29305e9	−0.163055
$950$	−3.49494e10	−1.32254
$951$	−6.56057e9	−0.247349
$952$	1.10191e10	0.413919
$953$	2.44973e10	0.916840	0.458420	−	0.888736i	$-0.348416\pi$
$953$	2.44973e10	0.916840	0.458420	+	0.888736i	$0.348416\pi$
$954$	1.32388e10	0.493663
$955$	6.16415e10	2.29014
$956$	−1.20918e9	−0.0447598
$957$	1.74208e10	0.642506
$958$	−1.16339e10	−0.427511
$959$	−2.26374e9	−0.0828822
$960$	2.56092e10	0.934215
$961$	−4.70198e9	−0.170903
$962$	3.05117e9	0.110498
$963$	−1.02677e10	−0.370492
$964$	−3.59259e9	−0.129163
$965$	−1.36373e10	−0.488522
$966$	−6.39409e9	−0.228223
$967$	−1.72004e10	−0.611712	−0.305856	−	0.952078i	$-0.598943\pi$
$967$	−1.72004e10	−0.611712	−0.305856	+	0.952078i	$0.598943\pi$
$968$	1.77856e10	0.630239
$969$	−1.04663e10	−0.369539
$970$	−6.05948e10	−2.13174
$971$	1.52302e10	0.533874	0.266937	−	0.963714i	$-0.413988\pi$
$971$	1.52302e10	0.533874	0.266937	+	0.963714i	$0.413988\pi$
$972$	−1.67100e8	−0.00583639
$973$	−1.96801e9	−0.0684907
$974$	−2.93298e10	−1.01707
$975$	4.06863e9	0.140583
$976$	−1.14485e10	−0.394161
$977$	−2.92918e10	−1.00488	−0.502441	−	0.864612i	$-0.667564\pi$
$977$	−2.92918e10	−1.00488	−0.502441	+	0.864612i	$0.667564\pi$
$978$	3.45695e10	1.18170
$979$	−1.79736e10	−0.612204
$980$	−6.93730e8	−0.0235450
$981$	−4.81654e9	−0.162890
$982$	2.43016e10	0.818926
$983$	−4.01674e10	−1.34877	−0.674383	−	0.738382i	$-0.735590\pi$
$983$	−4.01674e10	−1.34877	−0.674383	+	0.738382i	$0.735590\pi$
$984$	−2.44171e10	−0.816980
$985$	−2.48302e9	−0.0827854
$986$	6.95961e10	2.31215
$987$	9.72415e9	0.321915
$988$	1.63330e8	0.00538788
$989$	3.10157e9	0.101952
$990$	−1.11654e10	−0.365721
$991$	4.55984e10	1.48831	0.744153	−	0.668010i	$-0.232854\pi$
$991$	4.55984e10	1.48831	0.744153	+	0.668010i	$0.232854\pi$
$992$	−5.07879e9	−0.165184
$993$	2.07967e10	0.674020
$994$	2.63516e9	0.0851049
$995$	−2.45858e9	−0.0791230
$996$	1.98174e9	0.0635534
$997$	4.73495e10	1.51315	0.756576	−	0.653906i	$-0.226871\pi$
$997$	4.73495e10	1.51315	0.756576	+	0.653906i	$0.226871\pi$
$998$	−2.93549e10	−0.934811
$999$	6.01187e9	0.190779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.a.b.1.2	✓	2
3.2	odd	2		63.8.a.f.1.1		2
4.3	odd	2		336.8.a.n.1.1		2
5.4	even	2		525.8.a.e.1.1		2
7.2	even	3		147.8.e.h.67.1		4
7.3	odd	6		147.8.e.g.79.1		4
7.4	even	3		147.8.e.h.79.1		4
7.5	odd	6		147.8.e.g.67.1		4
7.6	odd	2		147.8.a.c.1.2		2
21.20	even	2		441.8.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.a.b.1.2	✓	2	1.1	even	1	trivial
63.8.a.f.1.1		2	3.2	odd	2
147.8.a.c.1.2		2	7.6	odd	2
147.8.e.g.67.1		4	7.5	odd	6
147.8.e.g.79.1		4	7.3	odd	6
147.8.e.h.67.1		4	7.2	even	3
147.8.e.h.79.1		4	7.4	even	3
336.8.a.n.1.1		2	4.3	odd	2
441.8.a.m.1.1		2	21.20	even	2
525.8.a.e.1.1		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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+11.8172 q^{2} -27.0000 q^{3} +11.6455 q^{4} -506.343 q^{5} -319.064 q^{6} +343.000 q^{7} -1374.98 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+11.8172 q^{2} -27.0000 q^{3} +11.6455 q^{4} -506.343 q^{5} -319.064 q^{6} +343.000 q^{7} -1374.98 q^{8} +729.000 q^{9} -5983.55 q^{10} +2559.69 q^{11} -314.428 q^{12} -845.345 q^{13} +4053.29 q^{14} +13671.3 q^{15} -17739.0 q^{16} -23364.3 q^{17} +8614.72 q^{18} -16591.1 q^{19} -5896.61 q^{20} -9261.00 q^{21} +30248.3 q^{22} +58426.2 q^{23} +37124.5 q^{24} +178259. q^{25} -9989.58 q^{26} -19683.0 q^{27} +3994.40 q^{28} -252068. q^{29} +161556. q^{30} +151032. q^{31} -33627.2 q^{32} -69111.6 q^{33} -276100. q^{34} -173676. q^{35} +8489.56 q^{36} -305435. q^{37} -196060. q^{38} +22824.3 q^{39} +696213. q^{40} -657709. q^{41} -109439. q^{42} +53085.2 q^{43} +29808.8 q^{44} -369124. q^{45} +690432. q^{46} -1.05001e6 q^{47} +478953. q^{48} +117649. q^{49} +2.10651e6 q^{50} +630837. q^{51} -9844.44 q^{52} +1.53677e6 q^{53} -232597. q^{54} -1.29608e6 q^{55} -471618. q^{56} +447961. q^{57} -2.97873e6 q^{58} +320564. q^{59} +159209. q^{60} +645385. q^{61} +1.78477e6 q^{62} +250047. q^{63} +1.87321e6 q^{64} +428035. q^{65} -816703. q^{66} -2.84308e6 q^{67} -272089. q^{68} -1.57751e6 q^{69} -2.05236e6 q^{70} +650129. q^{71} -1.00236e6 q^{72} +5.07847e6 q^{73} -3.60938e6 q^{74} -4.81298e6 q^{75} -193212. q^{76} +877973. q^{77} +269719. q^{78} +283873. q^{79} +8.98203e6 q^{80} +531441. q^{81} -7.77226e6 q^{82} -6.30268e6 q^{83} -107849. q^{84} +1.18304e7 q^{85} +627317. q^{86} +6.80584e6 q^{87} -3.51952e6 q^{88} -7.02180e6 q^{89} -4.36200e6 q^{90} -289953. q^{91} +680401. q^{92} -4.07786e6 q^{93} -1.24082e7 q^{94} +8.40081e6 q^{95} +907935. q^{96} +1.01269e7 q^{97} +1.39028e6 q^{98} +1.86601e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 9 q^{2} - 54 q^{3} + 317 q^{4} - 360 q^{5} + 243 q^{6} + 686 q^{7} - 5067 q^{8} + 1458 q^{9}+O(q^{10}) \) 2 * q - 9 * q^2 - 54 * q^3 + 317 * q^4 - 360 * q^5 + 243 * q^6 + 686 * q^7 - 5067 * q^8 + 1458 * q^9	\( 2 q - 9 q^{2} - 54 q^{3} + 317 q^{4} - 360 q^{5} + 243 q^{6} + 686 q^{7} - 5067 q^{8} + 1458 q^{9} - 9030 q^{10} - 4932 q^{11} - 8559 q^{12} + 7708 q^{13} - 3087 q^{14} + 9720 q^{15} + 20033 q^{16} - 28584 q^{17} - 6561 q^{18} - 63728 q^{19} + 38790 q^{20} - 18522 q^{21} + 186204 q^{22} + 82260 q^{23} + 136809 q^{24} + 121550 q^{25} - 188046 q^{26} - 39366 q^{27} + 108731 q^{28} - 435996 q^{29} + 243810 q^{30} - 29240 q^{31} - 347355 q^{32} + 133164 q^{33} - 167442 q^{34} - 123480 q^{35} + 231093 q^{36} - 709556 q^{37} + 785196 q^{38} - 208116 q^{39} + 155910 q^{40} - 25056 q^{41} + 83349 q^{42} + 496216 q^{43} - 2257812 q^{44} - 262440 q^{45} + 194280 q^{46} - 1575000 q^{47} - 540891 q^{48} + 235298 q^{49} + 3287025 q^{50} + 771768 q^{51} + 2601958 q^{52} + 2057436 q^{53} + 177147 q^{54} - 2392440 q^{55} - 1737981 q^{56} + 1720656 q^{57} + 850122 q^{58} - 1101024 q^{59} - 1047330 q^{60} + 28996 q^{61} + 5537520 q^{62} + 500094 q^{63} + 3569321 q^{64} + 1679760 q^{65} - 5027508 q^{66} - 4480784 q^{67} - 1865934 q^{68} - 2221020 q^{69} - 3097290 q^{70} + 54540 q^{71} - 3693843 q^{72} + 666604 q^{73} + 4803282 q^{74} - 3281850 q^{75} - 14586668 q^{76} - 1691676 q^{77} + 5077242 q^{78} + 2322952 q^{79} + 14509710 q^{80} + 1062882 q^{81} - 20942298 q^{82} - 7384392 q^{83} - 2935737 q^{84} + 11066520 q^{85} - 8597412 q^{86} + 11771892 q^{87} + 24139932 q^{88} + 1784448 q^{89} - 6582870 q^{90} + 2643844 q^{91} + 7958160 q^{92} + 789480 q^{93} - 1479360 q^{94} + 1502640 q^{95} + 9378585 q^{96} + 16266412 q^{97} - 1058841 q^{98} - 3595428 q^{99}+O(q^{100}) \) 2 * q - 9 * q^2 - 54 * q^3 + 317 * q^4 - 360 * q^5 + 243 * q^6 + 686 * q^7 - 5067 * q^8 + 1458 * q^9 - 9030 * q^10 - 4932 * q^11 - 8559 * q^12 + 7708 * q^13 - 3087 * q^14 + 9720 * q^15 + 20033 * q^16 - 28584 * q^17 - 6561 * q^18 - 63728 * q^19 + 38790 * q^20 - 18522 * q^21 + 186204 * q^22 + 82260 * q^23 + 136809 * q^24 + 121550 * q^25 - 188046 * q^26 - 39366 * q^27 + 108731 * q^28 - 435996 * q^29 + 243810 * q^30 - 29240 * q^31 - 347355 * q^32 + 133164 * q^33 - 167442 * q^34 - 123480 * q^35 + 231093 * q^36 - 709556 * q^37 + 785196 * q^38 - 208116 * q^39 + 155910 * q^40 - 25056 * q^41 + 83349 * q^42 + 496216 * q^43 - 2257812 * q^44 - 262440 * q^45 + 194280 * q^46 - 1575000 * q^47 - 540891 * q^48 + 235298 * q^49 + 3287025 * q^50 + 771768 * q^51 + 2601958 * q^52 + 2057436 * q^53 + 177147 * q^54 - 2392440 * q^55 - 1737981 * q^56 + 1720656 * q^57 + 850122 * q^58 - 1101024 * q^59 - 1047330 * q^60 + 28996 * q^61 + 5537520 * q^62 + 500094 * q^63 + 3569321 * q^64 + 1679760 * q^65 - 5027508 * q^66 - 4480784 * q^67 - 1865934 * q^68 - 2221020 * q^69 - 3097290 * q^70 + 54540 * q^71 - 3693843 * q^72 + 666604 * q^73 + 4803282 * q^74 - 3281850 * q^75 - 14586668 * q^76 - 1691676 * q^77 + 5077242 * q^78 + 2322952 * q^79 + 14509710 * q^80 + 1062882 * q^81 - 20942298 * q^82 - 7384392 * q^83 - 2935737 * q^84 + 11066520 * q^85 - 8597412 * q^86 + 11771892 * q^87 + 24139932 * q^88 + 1784448 * q^89 - 6582870 * q^90 + 2643844 * q^91 + 7958160 * q^92 + 789480 * q^93 - 1479360 * q^94 + 1502640 * q^95 + 9378585 * q^96 + 16266412 * q^97 - 1058841 * q^98 - 3595428 * q^99

Introduction

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