LMFDB - Embedded newform 37.6.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.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:	$5.93420133308$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 160x^{5} + 156x^{4} + 6495x^{3} - 2943x^{2} - 64880x + 53844 $ x^7 - x^6 - 160x^5 + 156x^4 + 6495x^3 - 2943x^2 - 64880*x + 53844
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.30071$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.30071 q^{2} -0.151013 q^{3} -13.5039 q^{4} +95.6487 q^{5} +0.649463 q^{6} -203.420 q^{7} +195.699 q^{8} -242.977 q^{9} +O(q^{10})$	\(q-4.30071 q^{2} -0.151013 q^{3} -13.5039 q^{4} +95.6487 q^{5} +0.649463 q^{6} -203.420 q^{7} +195.699 q^{8} -242.977 q^{9} -411.358 q^{10} -149.306 q^{11} +2.03926 q^{12} -996.592 q^{13} +874.851 q^{14} -14.4442 q^{15} -409.522 q^{16} -214.370 q^{17} +1044.98 q^{18} -1427.12 q^{19} -1291.63 q^{20} +30.7190 q^{21} +642.123 q^{22} +588.114 q^{23} -29.5531 q^{24} +6023.68 q^{25} +4286.06 q^{26} +73.3888 q^{27} +2746.95 q^{28} +7014.56 q^{29} +62.1203 q^{30} -6451.60 q^{31} -4501.13 q^{32} +22.5472 q^{33} +921.943 q^{34} -19456.9 q^{35} +3281.13 q^{36} -1369.00 q^{37} +6137.63 q^{38} +150.498 q^{39} +18718.4 q^{40} -8739.29 q^{41} -132.114 q^{42} +3772.67 q^{43} +2016.21 q^{44} -23240.5 q^{45} -2529.31 q^{46} -19586.5 q^{47} +61.8431 q^{48} +24572.7 q^{49} -25906.1 q^{50} +32.3726 q^{51} +13457.8 q^{52} +34141.8 q^{53} -315.624 q^{54} -14280.9 q^{55} -39809.1 q^{56} +215.513 q^{57} -30167.6 q^{58} +20577.0 q^{59} +195.052 q^{60} +2078.42 q^{61} +27746.5 q^{62} +49426.4 q^{63} +32462.8 q^{64} -95322.7 q^{65} -96.9689 q^{66} +1381.93 q^{67} +2894.82 q^{68} -88.8128 q^{69} +83678.4 q^{70} +42350.5 q^{71} -47550.4 q^{72} -18761.5 q^{73} +5887.68 q^{74} -909.653 q^{75} +19271.6 q^{76} +30371.9 q^{77} -647.250 q^{78} -71044.9 q^{79} -39170.3 q^{80} +59032.4 q^{81} +37585.2 q^{82} -23099.0 q^{83} -414.826 q^{84} -20504.2 q^{85} -16225.2 q^{86} -1059.29 q^{87} -29219.1 q^{88} +42552.8 q^{89} +99950.5 q^{90} +202727. q^{91} -7941.81 q^{92} +974.274 q^{93} +84235.7 q^{94} -136502. q^{95} +679.729 q^{96} -114226. q^{97} -105680. q^{98} +36278.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * 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 $

$2$	−4.30071	−0.760266	−0.380133	−	0.924932i	$-0.624122\pi$
$2$	−4.30071	−0.760266	−0.380133	+	0.924932i	$0.624122\pi$
$3$	−0.151013	−0.00968748	−0.00484374	−	0.999988i	$-0.501542\pi$
$3$	−0.151013	−0.00968748	−0.00484374	+	0.999988i	$0.501542\pi$
$4$	−13.5039	−0.421996
$5$	95.6487	1.71102	0.855508	−	0.517789i	$-0.173245\pi$
$5$	95.6487	1.71102	0.855508	+	0.517789i	$0.173245\pi$
$6$	0.649463	0.00736506
$7$	−203.420	−1.56909	−0.784546	−	0.620071i	$-0.787104\pi$
$7$	−203.420	−1.56909	−0.784546	+	0.620071i	$0.787104\pi$
$8$	195.699	1.08109
$9$	−242.977	−0.999906
$10$	−411.358	−1.30083
$11$	−149.306	−0.372046	−0.186023	−	0.982545i	$-0.559560\pi$
$11$	−149.306	−0.372046	−0.186023	+	0.982545i	$0.559560\pi$
$12$	2.03926	0.00408808
$13$	−996.592	−1.63553	−0.817766	−	0.575551i	$-0.804787\pi$
$13$	−996.592	−1.63553	−0.817766	+	0.575551i	$0.804787\pi$
$14$	874.851	1.19293
$15$	−14.4442	−0.0165754
$16$	−409.522	−0.399924
$17$	−214.370	−0.179904	−0.0899521	−	0.995946i	$-0.528671\pi$
$17$	−214.370	−0.179904	−0.0899521	+	0.995946i	$0.528671\pi$
$18$	1044.98	0.760195
$19$	−1427.12	−0.906935	−0.453467	−	0.891273i	$-0.649813\pi$
$19$	−1427.12	−0.906935	−0.453467	+	0.891273i	$0.649813\pi$
$20$	−1291.63	−0.722042
$21$	30.7190	0.0152006
$22$	642.123	0.282854
$23$	588.114	0.231815	0.115908	−	0.993260i	$-0.463022\pi$
$23$	588.114	0.231815	0.115908	+	0.993260i	$0.463022\pi$
$24$	−29.5531	−0.0104731
$25$	6023.68	1.92758
$26$	4286.06	1.24344
$27$	73.3888	0.0193741
$28$	2746.95	0.662150
$29$	7014.56	1.54884	0.774418	−	0.632675i	$-0.218043\pi$
$29$	7014.56	1.54884	0.774418	+	0.632675i	$0.218043\pi$
$30$	62.1203	0.0126017
$31$	−6451.60	−1.20577	−0.602883	−	0.797830i	$-0.705981\pi$
$31$	−6451.60	−1.20577	−0.602883	+	0.797830i	$0.705981\pi$
$32$	−4501.13	−0.777046
$33$	22.5472	0.00360419
$34$	921.943	0.136775
$35$	−19456.9	−2.68474
$36$	3281.13	0.421956
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	6137.63	0.689512
$39$	150.498	0.0158442
$40$	18718.4	1.84977
$41$	−8739.29	−0.811926	−0.405963	−	0.913890i	$-0.633064\pi$
$41$	−8739.29	−0.811926	−0.405963	+	0.913890i	$0.633064\pi$
$42$	−132.114	−0.0115565
$43$	3772.67	0.311155	0.155578	−	0.987824i	$-0.450276\pi$
$43$	3772.67	0.311155	0.155578	+	0.987824i	$0.450276\pi$
$44$	2016.21	0.157002
$45$	−23240.5	−1.71086
$46$	−2529.31	−0.176241
$47$	−19586.5	−1.29334	−0.646668	−	0.762772i	$-0.723838\pi$
$47$	−19586.5	−1.29334	−0.646668	+	0.762772i	$0.723838\pi$
$48$	61.8431	0.00387426
$49$	24572.7	1.46205
$50$	−25906.1	−1.46547
$51$	32.3726	0.00174282
$52$	13457.8	0.690187
$53$	34141.8	1.66954	0.834769	−	0.550601i	$-0.185601\pi$
$53$	34141.8	1.66954	0.834769	+	0.550601i	$0.185601\pi$
$54$	−315.624	−0.0147294
$55$	−14280.9	−0.636576
$56$	−39809.1	−1.69634
$57$	215.513	0.00878592
$58$	−30167.6	−1.17753
$59$	20577.0	0.769579	0.384789	−	0.923004i	$-0.374274\pi$
$59$	20577.0	0.769579	0.384789	+	0.923004i	$0.374274\pi$
$60$	195.052	0.00699476
$61$	2078.42	0.0715168	0.0357584	−	0.999360i	$-0.488615\pi$
$61$	2078.42	0.0715168	0.0357584	+	0.999360i	$0.488615\pi$
$62$	27746.5	0.916703
$63$	49426.4	1.56894
$64$	32462.8	0.990686
$65$	−95322.7	−2.79842
$66$	−96.9689	−0.00274014
$67$	1381.93	0.0376097	0.0188049	−	0.999823i	$-0.494014\pi$
$67$	1381.93	0.0376097	0.0188049	+	0.999823i	$0.494014\pi$
$68$	2894.82	0.0759188
$69$	−88.8128	−0.00224571
$70$	83678.4	2.04112
$71$	42350.5	0.997039	0.498520	−	0.866878i	$-0.333877\pi$
$71$	42350.5	0.997039	0.498520	+	0.866878i	$0.333877\pi$
$72$	−47550.4	−1.08099
$73$	−18761.5	−0.412060	−0.206030	−	0.978546i	$-0.566054\pi$
$73$	−18761.5	−0.412060	−0.206030	+	0.978546i	$0.566054\pi$
$74$	5887.68	0.124987
$75$	−909.653	−0.0186734
$76$	19271.6	0.382723
$77$	30371.9	0.583774
$78$	−647.250	−0.0120458
$79$	−71044.9	−1.28075	−0.640376	−	0.768061i	$-0.721222\pi$
$79$	−71044.9	−1.28075	−0.640376	+	0.768061i	$0.721222\pi$
$80$	−39170.3	−0.684276
$81$	59032.4	0.999718
$82$	37585.2	0.617280
$83$	−23099.0	−0.368043	−0.184021	−	0.982922i	$-0.558912\pi$
$83$	−23099.0	−0.368043	−0.184021	+	0.982922i	$0.558912\pi$
$84$	−414.826	−0.00641457
$85$	−20504.2	−0.307819
$86$	−16225.2	−0.236561
$87$	−1059.29	−0.0150043
$88$	−29219.1	−0.402217
$89$	42552.8	0.569447	0.284724	−	0.958610i	$-0.408098\pi$
$89$	42552.8	0.569447	0.284724	+	0.958610i	$0.408098\pi$
$90$	99950.5	1.30071
$91$	202727.	2.56630
$92$	−7941.81	−0.0978250
$93$	974.274	0.0116808
$94$	84235.7	0.983279
$95$	−136502.	−1.55178
$96$	679.729	0.00752762
$97$	−114226.	−1.23264	−0.616320	−	0.787496i	$-0.711377\pi$
$97$	−114226.	−1.23264	−0.616320	+	0.787496i	$0.711377\pi$
$98$	−105680.	−1.11155
$99$	36278.0	0.372011
$100$	−81342.9	−0.813429
$101$	−1611.28	−0.0157169	−0.00785846	−	0.999969i	$-0.502501\pi$
$101$	−1611.28	−0.0157169	−0.00785846	+	0.999969i	$0.502501\pi$
$102$	−139.225	−0.00132501
$103$	−203406.	−1.88917	−0.944583	−	0.328272i	$-0.893534\pi$
$103$	−203406.	−1.88917	−0.944583	+	0.328272i	$0.893534\pi$
$104$	−195032.	−1.76816
$105$	2938.24	0.0260084
$106$	−146834.	−1.26929
$107$	20036.2	0.169183	0.0845915	−	0.996416i	$-0.473041\pi$
$107$	20036.2	0.169183	0.0845915	+	0.996416i	$0.473041\pi$
$108$	−991.033	−0.00817577
$109$	41553.6	0.334999	0.167499	−	0.985872i	$-0.446431\pi$
$109$	41553.6	0.334999	0.167499	+	0.985872i	$0.446431\pi$
$110$	61418.3	0.483967
$111$	206.737	0.00159261
$112$	83304.9	0.627517
$113$	92507.7	0.681525	0.340763	−	0.940149i	$-0.389315\pi$
$113$	92507.7	0.681525	0.340763	+	0.940149i	$0.389315\pi$
$114$	−926.861	−0.00667963
$115$	56252.3	0.396639
$116$	−94723.6	−0.653602
$117$	242149.	1.63538
$118$	−88496.0	−0.585084
$119$	43607.1	0.282286
$120$	−2826.71	−0.0179196
$121$	−138759.	−0.861582
$122$	−8938.68	−0.0543718
$123$	1319.75	0.00786552
$124$	87121.5	0.508828
$125$	277255.	1.58710
$126$	−212569.	−1.19282
$127$	−233143.	−1.28267	−0.641333	−	0.767262i	$-0.721618\pi$
$127$	−233143.	−1.28267	−0.641333	+	0.767262i	$0.721618\pi$
$128$	4423.11	0.0238618
$129$	−569.721	−0.00301431
$130$	409956.	2.12754
$131$	−156326.	−0.795892	−0.397946	−	0.917409i	$-0.630277\pi$
$131$	−156326.	−0.795892	−0.397946	+	0.917409i	$0.630277\pi$
$132$	−304.474	−0.00152095
$133$	290304.	1.42306
$134$	−5943.30	−0.0285934
$135$	7019.55	0.0331493
$136$	−41952.0	−0.194494
$137$	−290776.	−1.32360	−0.661801	−	0.749680i	$-0.730208\pi$
$137$	−290776.	−1.32360	−0.661801	+	0.749680i	$0.730208\pi$
$138$	381.958	0.00170733
$139$	315964.	1.38708	0.693538	−	0.720420i	$-0.256051\pi$
$139$	315964.	1.38708	0.693538	+	0.720420i	$0.256051\pi$
$140$	262743.	1.13295
$141$	2957.81	0.0125292
$142$	−182137.	−0.758015
$143$	148797.	0.608492
$144$	99504.5	0.399886
$145$	670933.	2.65008
$146$	80687.8	0.313275
$147$	−3710.79	−0.0141636
$148$	18486.8	0.0693757
$149$	48499.9	0.178968	0.0894840	−	0.995988i	$-0.471478\pi$
$149$	48499.9	0.178968	0.0894840	+	0.995988i	$0.471478\pi$
$150$	3912.16	0.0141967
$151$	−343529.	−1.22609	−0.613043	−	0.790050i	$-0.710055\pi$
$151$	−343529.	−1.22609	−0.613043	+	0.790050i	$0.710055\pi$
$152$	−279286.	−0.980483
$153$	52087.0	0.179887
$154$	−130621.	−0.443823
$155$	−617087.	−2.06308
$156$	−2032.31	−0.00668618
$157$	−25494.2	−0.0825454	−0.0412727	−	0.999148i	$-0.513141\pi$
$157$	−25494.2	−0.0825454	−0.0412727	+	0.999148i	$0.513141\pi$
$158$	305544.	0.973713
$159$	−5155.85	−0.0161736
$160$	−430528.	−1.32954
$161$	−119634.	−0.363739
$162$	−253881.	−0.760052
$163$	−139754.	−0.411997	−0.205999	−	0.978552i	$-0.566044\pi$
$163$	−139754.	−0.411997	−0.205999	+	0.978552i	$0.566044\pi$
$164$	118014.	0.342629
$165$	2156.61	0.00616682
$166$	99342.2	0.279810
$167$	−198243.	−0.550055	−0.275027	−	0.961436i	$-0.588687\pi$
$167$	−198243.	−0.550055	−0.275027	+	0.961436i	$0.588687\pi$
$168$	6011.69	0.0164332
$169$	621902.	1.67496
$170$	88182.7	0.234024
$171$	346757.	0.906850
$172$	−50945.6	−0.131306
$173$	−472977.	−1.20150	−0.600752	−	0.799436i	$-0.705132\pi$
$173$	−472977.	−1.20150	−0.600752	+	0.799436i	$0.705132\pi$
$174$	4555.70	0.0114073
$175$	−1.22534e6	−3.02454
$176$	61144.2	0.148790
$177$	−3107.40	−0.00745528
$178$	−183008.	−0.432931
$179$	636182.	1.48405	0.742026	−	0.670371i	$-0.233865\pi$
$179$	636182.	1.48405	0.742026	+	0.670371i	$0.233865\pi$
$180$	313836.	0.721974
$181$	177290.	0.402243	0.201121	−	0.979566i	$-0.435541\pi$
$181$	177290.	0.402243	0.201121	+	0.979566i	$0.435541\pi$
$182$	−871869.	−1.95107
$183$	−313.868	−0.000692818 0
$184$	115093.	0.250614
$185$	−130943.	−0.281289
$186$	−4190.07	−0.00888054
$187$	32006.7	0.0669326
$188$	264493.	0.545782
$189$	−14928.8	−0.0303997
$190$	587056.	1.17977
$191$	462159.	0.916660	0.458330	−	0.888782i	$-0.348448\pi$
$191$	462159.	0.916660	0.458330	+	0.888782i	$0.348448\pi$
$192$	−4902.30	−0.00959725
$193$	−554416.	−1.07138	−0.535689	−	0.844415i	$-0.679948\pi$
$193$	−554416.	−1.07138	−0.535689	+	0.844415i	$0.679948\pi$
$194$	491254.	0.937134
$195$	14395.0	0.0271096
$196$	−331826.	−0.616979
$197$	−190797.	−0.350273	−0.175136	−	0.984544i	$-0.556037\pi$
$197$	−190797.	−0.350273	−0.175136	+	0.984544i	$0.556037\pi$
$198$	−156021.	−0.282827
$199$	−235339.	−0.421271	−0.210636	−	0.977565i	$-0.567553\pi$
$199$	−235339.	−0.421271	−0.210636	+	0.977565i	$0.567553\pi$
$200$	1.17883e6	2.08389
$201$	−208.690	−0.000364343 0
$202$	6929.65	0.0119490
$203$	−1.42690e6	−2.43027
$204$	−437.155	−0.000735462 0
$205$	−835902.	−1.38922
$206$	874790.	1.43627
$207$	−142898.	−0.231793
$208$	408126.	0.654088
$209$	213078.	0.337421
$210$	−12636.5	−0.0197733
$211$	937821.	1.45015	0.725077	−	0.688668i	$-0.241804\pi$
$211$	937821.	1.45015	0.725077	+	0.688668i	$0.241804\pi$
$212$	−461046.	−0.704538
$213$	−6395.46	−0.00965880
$214$	−86170.1	−0.128624
$215$	360851.	0.532392
$216$	14362.1	0.0209452
$217$	1.31238e6	1.89196
$218$	−178710.	−0.254688
$219$	2833.23	0.00399182
$220$	192848.	0.268632
$221$	213639.	0.294239
$222$	−889.115	−0.00121081
$223$	63085.9	0.0849514	0.0424757	−	0.999098i	$-0.486476\pi$
$223$	63085.9	0.0849514	0.0424757	+	0.999098i	$0.486476\pi$
$224$	915620.	1.21926
$225$	−1.46362e6	−1.92740
$226$	−397849.	−0.518140
$227$	−674787.	−0.869165	−0.434583	−	0.900632i	$-0.643104\pi$
$227$	−674787.	−0.869165	−0.434583	+	0.900632i	$0.643104\pi$
$228$	−2910.26	−0.00370762
$229$	683420.	0.861191	0.430595	−	0.902545i	$-0.358304\pi$
$229$	683420.	0.861191	0.430595	+	0.902545i	$0.358304\pi$
$230$	−241925.	−0.301551
$231$	−4586.54	−0.00565530
$232$	1.37274e6	1.67444
$233$	1.14697e6	1.38408	0.692042	−	0.721857i	$-0.256711\pi$
$233$	1.14697e6	1.38408	0.692042	+	0.721857i	$0.256711\pi$
$234$	−1.04141e6	−1.24332
$235$	−1.87342e6	−2.21292
$236$	−277870.	−0.324759
$237$	10728.7	0.0124073
$238$	−187542.	−0.214613
$239$	485107.	0.549342	0.274671	−	0.961538i	$-0.411431\pi$
$239$	485107.	0.549342	0.274671	+	0.961538i	$0.411431\pi$
$240$	5915.21	0.00662891
$241$	−866321.	−0.960808	−0.480404	−	0.877047i	$-0.659510\pi$
$241$	−866321.	−0.960808	−0.480404	+	0.877047i	$0.659510\pi$
$242$	596761.	0.655031
$243$	−26748.1	−0.0290588
$244$	−28066.7	−0.0301798
$245$	2.35034e6	2.50159
$246$	−5675.85	−0.00597988
$247$	1.42225e6	1.48332
$248$	−1.26257e6	−1.30355
$249$	3488.25	0.00356541
$250$	−1.19239e6	−1.20662
$251$	−105910.	−0.106109	−0.0530547	−	0.998592i	$-0.516896\pi$
$251$	−105910.	−0.106109	−0.0530547	+	0.998592i	$0.516896\pi$
$252$	−667447.	−0.662088
$253$	−87809.1	−0.0862458
$254$	1.00268e6	0.975168
$255$	3096.40	0.00298199
$256$	−1.05783e6	−1.00883
$257$	−611794.	−0.577793	−0.288896	−	0.957360i	$-0.593288\pi$
$257$	−611794.	−0.577793	−0.288896	+	0.957360i	$0.593288\pi$
$258$	2450.21	0.00229168
$259$	278482.	0.257957
$260$	1.28722e6	1.18092
$261$	−1.70438e6	−1.54869
$262$	672315.	0.605090
$263$	−970861.	−0.865501	−0.432751	−	0.901514i	$-0.642457\pi$
$263$	−970861.	−0.865501	−0.432751	+	0.901514i	$0.642457\pi$
$264$	4412.46	0.00389647
$265$	3.26562e6	2.85661
$266$	−1.24852e6	−1.08191
$267$	−6426.03	−0.00551651
$268$	−18661.4	−0.0158711
$269$	−1.02444e6	−0.863185	−0.431593	−	0.902069i	$-0.642048\pi$
$269$	−1.02444e6	−0.863185	−0.431593	+	0.902069i	$0.642048\pi$
$270$	−30189.1	−0.0252023
$271$	−647490.	−0.535562	−0.267781	−	0.963480i	$-0.586290\pi$
$271$	−647490.	−0.535562	−0.267781	+	0.963480i	$0.586290\pi$
$272$	87789.2	0.0719480
$273$	−30614.3	−0.0248610
$274$	1.25054e6	1.00629
$275$	−899372.	−0.717146
$276$	1199.32	0.000947678 0
$277$	−494374.	−0.387130	−0.193565	−	0.981087i	$-0.562005\pi$
$277$	−494374.	−0.387130	−0.193565	+	0.981087i	$0.562005\pi$
$278$	−1.35887e6	−1.05455
$279$	1.56759e6	1.20565
$280$	−3.80769e6	−2.90246
$281$	1.52161e6	1.14958	0.574789	−	0.818301i	$-0.305084\pi$
$281$	1.52161e6	1.14958	0.574789	+	0.818301i	$0.305084\pi$
$282$	−12720.7	−0.00952550
$283$	−1.85659e6	−1.37800	−0.689002	−	0.724760i	$-0.741951\pi$
$283$	−1.85659e6	−1.37800	−0.689002	+	0.724760i	$0.741951\pi$
$284$	−571895.	−0.420746
$285$	20613.6	0.0150328
$286$	−639935.	−0.462616
$287$	1.77775e6	1.27399
$288$	1.09367e6	0.776973
$289$	−1.37390e6	−0.967634
$290$	−2.88549e6	−2.01477
$291$	17249.6	0.0119412
$292$	253353.	0.173887
$293$	770421.	0.524275	0.262137	−	0.965031i	$-0.415573\pi$
$293$	770421.	0.524275	0.262137	+	0.965031i	$0.415573\pi$
$294$	15959.0	0.0107681
$295$	1.96817e6	1.31676
$296$	−267912.	−0.177731
$297$	−10957.4	−0.00720803
$298$	−208584.	−0.136063
$299$	−586109.	−0.379141
$300$	12283.8	0.00788008
$301$	−767436.	−0.488231
$302$	1.47742e6	0.932151
$303$	243.324	0.000152257 0
$304$	584437.	0.362705
$305$	198798.	0.122366
$306$	−224011.	−0.136762
$307$	−488953.	−0.296088	−0.148044	−	0.988981i	$-0.547298\pi$
$307$	−488953.	−0.296088	−0.148044	+	0.988981i	$0.547298\pi$
$308$	−410137.	−0.246350
$309$	30716.9	0.0183013
$310$	2.65391e6	1.56849
$311$	752508.	0.441174	0.220587	−	0.975367i	$-0.429203\pi$
$311$	752508.	0.441174	0.220587	+	0.975367i	$0.429203\pi$
$312$	29452.4	0.0171291
$313$	1.91026e6	1.10213	0.551063	−	0.834463i	$-0.314222\pi$
$313$	1.91026e6	1.10213	0.551063	+	0.834463i	$0.314222\pi$
$314$	109643.	0.0627564
$315$	4.72757e6	2.68449
$316$	959381.	0.540472
$317$	1.15176e6	0.643746	0.321873	−	0.946783i	$-0.395688\pi$
$317$	1.15176e6	0.643746	0.321873	+	0.946783i	$0.395688\pi$
$318$	22173.8	0.0122962
$319$	−1.04732e6	−0.576237
$320$	3.10502e6	1.69508
$321$	−3025.73	−0.00163896
$322$	514512.	0.276539
$323$	305931.	0.163161
$324$	−797165.	−0.421877
$325$	−6.00315e6	−3.15261
$326$	601041.	0.313228
$327$	−6275.14	−0.00324529
$328$	−1.71027e6	−0.877769
$329$	3.98428e6	2.02936
$330$	−9274.95	−0.00468842
$331$	−2.47258e6	−1.24045	−0.620226	−	0.784423i	$-0.712959\pi$
$331$	−2.47258e6	−1.24045	−0.620226	+	0.784423i	$0.712959\pi$
$332$	311926.	0.155312
$333$	332636.	0.164384
$334$	852585.	0.418188
$335$	132180.	0.0643508
$336$	−12580.1	−0.00607906
$337$	−3.47861e6	−1.66852	−0.834259	−	0.551373i	$-0.814104\pi$
$337$	−3.47861e6	−1.66852	−0.834259	+	0.551373i	$0.814104\pi$
$338$	−2.67462e6	−1.27342
$339$	−13969.9	−0.00660226
$340$	276886.	0.129898
$341$	963263.	0.448600
$342$	−1.49130e6	−0.689447
$343$	−1.57969e6	−0.724998
$344$	738308.	0.336389
$345$	−8494.83	−0.00384244
$346$	2.03414e6	0.913462
$347$	665279.	0.296606	0.148303	−	0.988942i	$-0.452619\pi$
$347$	665279.	0.296606	0.148303	+	0.988942i	$0.452619\pi$
$348$	14304.5	0.00633176
$349$	3.16244e6	1.38982	0.694910	−	0.719096i	$-0.255444\pi$
$349$	3.16244e6	1.38982	0.694910	+	0.719096i	$0.255444\pi$
$350$	5.26982e6	2.29946
$351$	−73138.7	−0.0316869
$352$	672047.	0.289097
$353$	−2.29723e6	−0.981222	−0.490611	−	0.871379i	$-0.663226\pi$
$353$	−2.29723e6	−0.981222	−0.490611	+	0.871379i	$0.663226\pi$
$354$	13364.0	0.00566799
$355$	4.05077e6	1.70595
$356$	−574628.	−0.240304
$357$	−6585.23	−0.00273464
$358$	−2.73604e6	−1.12827
$359$	1.25901e6	0.515576	0.257788	−	0.966201i	$-0.417006\pi$
$359$	1.25901e6	0.515576	0.257788	+	0.966201i	$0.417006\pi$
$360$	−4.54814e6	−1.84960
$361$	−439431.	−0.177469
$362$	−762474.	−0.305812
$363$	20954.3	0.00834656
$364$	−2.73759e6	−1.08297
$365$	−1.79451e6	−0.705041
$366$	1349.86	0.000526726 0
$367$	2.73649e6	1.06055	0.530273	−	0.847827i	$-0.322090\pi$
$367$	2.73649e6	1.06055	0.530273	+	0.847827i	$0.322090\pi$
$368$	−240846.	−0.0927084
$369$	2.12345e6	0.811850
$370$	563149.	0.213855
$371$	−6.94511e6	−2.61966
$372$	−13156.5	−0.00492926
$373$	2.13544e6	0.794722	0.397361	−	0.917662i	$-0.369926\pi$
$373$	2.13544e6	0.794722	0.397361	+	0.917662i	$0.369926\pi$
$374$	−137652.	−0.0508866
$375$	−41869.0	−0.0153750
$376$	−3.83305e6	−1.39822
$377$	−6.99065e6	−2.53317
$378$	64204.3	0.0231118
$379$	−562437.	−0.201129	−0.100565	−	0.994931i	$-0.532065\pi$
$379$	−562437.	−0.201129	−0.100565	+	0.994931i	$0.532065\pi$
$380$	1.84331e6	0.654845
$381$	35207.7	0.0124258
$382$	−1.98761e6	−0.696905
$383$	−4.67625e6	−1.62892	−0.814462	−	0.580216i	$-0.802968\pi$
$383$	−4.67625e6	−1.62892	−0.814462	+	0.580216i	$0.802968\pi$
$384$	−667.947	−0.000231161 0
$385$	2.90503e6	0.998846
$386$	2.38439e6	0.814532
$387$	−916672.	−0.311126
$388$	1.54249e6	0.520169
$389$	−2.63502e6	−0.882897	−0.441449	−	0.897287i	$-0.645535\pi$
$389$	−2.63502e6	−0.882897	−0.441449	+	0.897287i	$0.645535\pi$
$390$	−61908.6	−0.0206105
$391$	−126074.	−0.0417045
$392$	4.80885e6	1.58061
$393$	23607.3	0.00771019
$394$	820564.	0.266300
$395$	−6.79536e6	−2.19139
$396$	−489893.	−0.156987
$397$	1.36622e6	0.435054	0.217527	−	0.976054i	$-0.430201\pi$
$397$	1.36622e6	0.435054	0.217527	+	0.976054i	$0.430201\pi$
$398$	1.01213e6	0.320278
$399$	−43839.7	−0.0137859
$400$	−2.46683e6	−0.770884
$401$	−3.74930e6	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$401$	−3.74930e6	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$402$	897.515	0.000276998 0
$403$	6.42961e6	1.97207
$404$	21758.5	0.00663248
$405$	5.64637e6	1.71053
$406$	6.13669e6	1.84765
$407$	204400.	0.0611639
$408$	6335.29	0.00188415
$409$	−3.71159e6	−1.09711	−0.548557	−	0.836113i	$-0.684823\pi$
$409$	−3.71159e6	−1.09711	−0.548557	+	0.836113i	$0.684823\pi$
$410$	3.59497e6	1.05618
$411$	43910.9	0.0128224
$412$	2.74676e6	0.797220
$413$	−4.18578e6	−1.20754
$414$	614564.	0.176225
$415$	−2.20939e6	−0.629727
$416$	4.48579e6	1.27088
$417$	−47714.6	−0.0134373
$418$	−916386.	−0.256530
$419$	637348.	0.177354	0.0886772	−	0.996060i	$-0.471736\pi$
$419$	637348.	0.177354	0.0886772	+	0.996060i	$0.471736\pi$
$420$	−39677.5	−0.0109754
$421$	4.93191e6	1.35616	0.678078	−	0.734990i	$-0.262813\pi$
$421$	4.93191e6	1.35616	0.678078	+	0.734990i	$0.262813\pi$
$422$	−4.03330e6	−1.10250
$423$	4.75906e6	1.29321
$424$	6.68151e6	1.80493
$425$	−1.29129e6	−0.346779
$426$	27505.1	0.00734326
$427$	−422792.	−0.112216
$428$	−270567.	−0.0713945
$429$	−22470.3	−0.00589476
$430$	−1.55192e6	−0.404759
$431$	6.11134e6	1.58469	0.792343	−	0.610076i	$-0.208861\pi$
$431$	6.11134e6	1.58469	0.792343	+	0.610076i	$0.208861\pi$
$432$	−30054.3	−0.00774815
$433$	1.01248e6	0.259518	0.129759	−	0.991546i	$-0.458580\pi$
$433$	1.01248e6	0.259518	0.129759	+	0.991546i	$0.458580\pi$
$434$	−5.64418e6	−1.43839
$435$	−101320.	−0.0256726
$436$	−561135.	−0.141368
$437$	−839308.	−0.210241
$438$	−12184.9	−0.00303484
$439$	−2.65502e6	−0.657516	−0.328758	−	0.944414i	$-0.606630\pi$
$439$	−2.65502e6	−0.657516	−0.328758	+	0.944414i	$0.606630\pi$
$440$	−2.79477e6	−0.688199
$441$	−5.97060e6	−1.46191
$442$	−918801.	−0.223700
$443$	−4.12021e6	−0.997494	−0.498747	−	0.866748i	$-0.666206\pi$
$443$	−4.12021e6	−0.997494	−0.498747	+	0.866748i	$0.666206\pi$
$444$	−2791.74	−0.000672076 0
$445$	4.07012e6	0.974334
$446$	−271315.	−0.0645856
$447$	−7324.11	−0.00173375
$448$	−6.60358e6	−1.55448
$449$	−3.22691e6	−0.755389	−0.377694	−	0.925930i	$-0.623283\pi$
$449$	−3.22691e6	−0.755389	−0.377694	+	0.925930i	$0.623283\pi$
$450$	6.29459e6	1.46533
$451$	1.30483e6	0.302073
$452$	−1.24921e6	−0.287601
$453$	51877.3	0.0118777
$454$	2.90207e6	0.660797
$455$	1.93905e7	4.39098
$456$	42175.8	0.00949841
$457$	−168213.	−0.0376765	−0.0188382	−	0.999823i	$-0.505997\pi$
$457$	−168213.	−0.0376765	−0.0188382	+	0.999823i	$0.505997\pi$
$458$	−2.93920e6	−0.654734
$459$	−15732.3	−0.00348547
$460$	−759624.	−0.167380
$461$	−4.81966e6	−1.05624	−0.528122	−	0.849169i	$-0.677104\pi$
$461$	−4.81966e6	−1.05624	−0.528122	+	0.849169i	$0.677104\pi$
$462$	19725.4	0.00429953
$463$	4.22658e6	0.916297	0.458149	−	0.888876i	$-0.348513\pi$
$463$	4.22658e6	0.916297	0.458149	+	0.888876i	$0.348513\pi$
$464$	−2.87262e6	−0.619416
$465$	93188.1	0.0199861
$466$	−4.93279e6	−1.05227
$467$	9.34705e6	1.98327	0.991636	−	0.129067i	$-0.0411982\pi$
$467$	9.34705e6	1.98327	0.991636	+	0.129067i	$0.0411982\pi$
$468$	−3.26995e6	−0.690122
$469$	−281113.	−0.0590131
$470$	8.05704e6	1.68241
$471$	3849.96	0.000799657 0
$472$	4.02691e6	0.831987
$473$	−563283.	−0.115764
$474$	−46141.1	−0.00943283
$475$	−8.59650e6	−1.74819
$476$	−588864.	−0.119124
$477$	−8.29567e6	−1.66938
$478$	−2.08630e6	−0.417646
$479$	902678.	0.179760	0.0898802	−	0.995953i	$-0.471352\pi$
$479$	902678.	0.179760	0.0898802	+	0.995953i	$0.471352\pi$
$480$	65015.2	0.0128799
$481$	1.36433e6	0.268880
$482$	3.72580e6	0.730469
$483$	18066.3	0.00352372
$484$	1.87378e6	0.363584
$485$	−1.09256e7	−2.10907
$486$	115036.	0.0220924
$487$	9.23130e6	1.76376	0.881882	−	0.471470i	$-0.156276\pi$
$487$	9.23130e6	1.76376	0.881882	+	0.471470i	$0.156276\pi$
$488$	406744.	0.0773165
$489$	21104.6	0.00399122
$490$	−1.01082e7	−1.90187
$491$	1.08623e6	0.203337	0.101669	−	0.994818i	$-0.467582\pi$
$491$	1.08623e6	0.203337	0.101669	+	0.994818i	$0.467582\pi$
$492$	−17821.7	−0.00331921
$493$	−1.50371e6	−0.278642
$494$	−6.11671e6	−1.12772
$495$	3.46994e6	0.636516
$496$	2.64207e6	0.482214
$497$	−8.61493e6	−1.56445
$498$	−15002.0	−0.00271066
$499$	1.98800e6	0.357409	0.178705	−	0.983903i	$-0.442809\pi$
$499$	1.98800e6	0.357409	0.178705	+	0.983903i	$0.442809\pi$
$500$	−3.74401e6	−0.669749
$501$	29937.2	0.00532865
$502$	455490.	0.0806713
$503$	611569.	0.107777	0.0538884	−	0.998547i	$-0.482838\pi$
$503$	611569.	0.107777	0.0538884	+	0.998547i	$0.482838\pi$
$504$	9.67270e6	1.69618
$505$	−154117.	−0.0268919
$506$	377642.	0.0655698
$507$	−93915.2	−0.0162262
$508$	3.14834e6	0.541280
$509$	1.01190e6	0.173119	0.0865596	−	0.996247i	$-0.472413\pi$
$509$	1.01190e6	0.173119	0.0865596	+	0.996247i	$0.472413\pi$
$510$	−13316.7	−0.00226711
$511$	3.81646e6	0.646559
$512$	4.40789e6	0.743115
$513$	−104735.	−0.0175710
$514$	2.63115e6	0.439276
$515$	−1.94555e7	−3.23239
$516$	7693.44	0.00127203
$517$	2.92438e6	0.481180
$518$	−1.19767e6	−0.196116
$519$	71425.7	0.0116395
$520$	−1.86546e7	−3.02536
$521$	3.17332e6	0.512176	0.256088	−	0.966653i	$-0.417566\pi$
$521$	3.17332e6	0.512176	0.256088	+	0.966653i	$0.417566\pi$
$522$	7.33004e6	1.17742
$523$	32547.4	0.00520310	0.00260155	−	0.999997i	$-0.499172\pi$
$523$	32547.4	0.00520310	0.00260155	+	0.999997i	$0.499172\pi$
$524$	2.11101e6	0.335863
$525$	185042.	0.0293002
$526$	4.17540e6	0.658011
$527$	1.38303e6	0.216922
$528$	−9233.56	−0.00144140
$529$	−6.09047e6	−0.946262
$530$	−1.40445e7	−2.17178
$531$	−4.99975e6	−0.769506
$532$	−3.92023e6	−0.600527
$533$	8.70950e6	1.32793
$534$	27636.5	0.00419402
$535$	1.91644e6	0.289475
$536$	270443.	0.0406597
$537$	−96071.8	−0.0143767
$538$	4.40581e6	0.656250
$539$	−3.66885e6	−0.543949
$540$	−94791.0	−0.0139889
$541$	7.57322e6	1.11247	0.556234	−	0.831026i	$-0.312246\pi$
$541$	7.57322e6	1.11247	0.556234	+	0.831026i	$0.312246\pi$
$542$	2.78467e6	0.407170
$543$	−26773.1	−0.00389672
$544$	964907.	0.139794
$545$	3.97455e6	0.573188
$546$	131663.	0.0189010
$547$	−2.94803e6	−0.421273	−0.210636	−	0.977564i	$-0.567554\pi$
$547$	−2.94803e6	−0.421273	−0.210636	+	0.977564i	$0.567554\pi$
$548$	3.92660e6	0.558554
$549$	−505008.	−0.0715101
$550$	3.86794e6	0.545222
$551$	−1.00106e7	−1.40469
$552$	−17380.6	−0.00242782
$553$	1.44520e7	2.00962
$554$	2.12616e6	0.294321
$555$	19774.1	0.00272499
$556$	−4.26673e6	−0.585340
$557$	−165788.	−0.0226420	−0.0113210	−	0.999936i	$-0.503604\pi$
$557$	−165788.	−0.0226420	−0.0113210	+	0.999936i	$0.503604\pi$
$558$	−6.74176e6	−0.916617
$559$	−3.75981e6	−0.508904
$560$	7.96801e6	1.07369
$561$	−4833.43	−0.000648408 0
$562$	−6.54403e6	−0.873986
$563$	4.56719e6	0.607265	0.303633	−	0.952789i	$-0.401800\pi$
$563$	4.56719e6	0.607265	0.303633	+	0.952789i	$0.401800\pi$
$564$	−39941.8	−0.00528725
$565$	8.84824e6	1.16610
$566$	7.98467e6	1.04765
$567$	−1.20084e7	−1.56865
$568$	8.28794e6	1.07789
$569$	−3.99526e6	−0.517327	−0.258663	−	0.965968i	$-0.583282\pi$
$569$	−3.99526e6	−0.517327	−0.258663	+	0.965968i	$0.583282\pi$
$570$	−88653.1	−0.0114290
$571$	1.53839e6	0.197459	0.0987294	−	0.995114i	$-0.468522\pi$
$571$	1.53839e6	0.197459	0.0987294	+	0.995114i	$0.468522\pi$
$572$	−2.00934e6	−0.256781
$573$	−69792.0	−0.00888013
$574$	−7.64557e6	−0.968568
$575$	3.54261e6	0.446841
$576$	−7.88772e6	−0.990593
$577$	−1.26306e7	−1.57937	−0.789686	−	0.613511i	$-0.789756\pi$
$577$	−1.26306e7	−1.57937	−0.789686	+	0.613511i	$0.789756\pi$
$578$	5.90876e6	0.735660
$579$	83724.0	0.0103790
$580$	−9.06019e6	−1.11832
$581$	4.69880e6	0.577493
$582$	−74185.7	−0.00907847
$583$	−5.09758e6	−0.621144
$584$	−3.67160e6	−0.445475
$585$	2.31612e7	2.79816
$586$	−3.31336e6	−0.398588
$587$	1.51994e7	1.82067	0.910337	−	0.413867i	$-0.135822\pi$
$587$	1.51994e7	1.82067	0.910337	+	0.413867i	$0.135822\pi$
$588$	50110.0	0.00597697
$589$	9.20719e6	1.09355
$590$	−8.46453e6	−1.00109
$591$	28812.8	0.00339326
$592$	560636.	0.0657471
$593$	8.23623e6	0.961816	0.480908	−	0.876771i	$-0.340307\pi$
$593$	8.23623e6	0.961816	0.480908	+	0.876771i	$0.340307\pi$
$594$	47124.7	0.00548002
$595$	4.17096e6	0.482996
$596$	−654936.	−0.0755237
$597$	35539.3	0.00408106
$598$	2.52069e6	0.288248
$599$	1.38722e7	1.57972	0.789859	−	0.613289i	$-0.210154\pi$
$599$	1.38722e7	1.57972	0.789859	+	0.613289i	$0.210154\pi$
$600$	−178018.	−0.0201877
$601$	−314936.	−0.0355661	−0.0177830	−	0.999842i	$-0.505661\pi$
$601$	−314936.	−0.0355661	−0.0177830	+	0.999842i	$0.505661\pi$
$602$	3.30052e6	0.371186
$603$	−335778.	−0.0376062
$604$	4.63897e6	0.517403
$605$	−1.32721e7	−1.47418
$606$	−1046.47	−0.000115756 0
$607$	6.14693e6	0.677152	0.338576	−	0.940939i	$-0.390055\pi$
$607$	6.14693e6	0.677152	0.338576	+	0.940939i	$0.390055\pi$
$608$	6.42365e6	0.704730
$609$	215480.	0.0235432
$610$	−854973.	−0.0930310
$611$	1.95197e7	2.11529
$612$	−703375.	−0.0759117
$613$	−2.07446e6	−0.222974	−0.111487	−	0.993766i	$-0.535561\pi$
$613$	−2.07446e6	−0.222974	−0.111487	+	0.993766i	$0.535561\pi$
$614$	2.10285e6	0.225106
$615$	126232.	0.0134580
$616$	5.94375e6	0.631115
$617$	−9.20962e6	−0.973932	−0.486966	−	0.873421i	$-0.661896\pi$
$617$	−9.20962e6	−0.973932	−0.486966	+	0.873421i	$0.661896\pi$
$618$	−132105.	−0.0139138
$619$	−8.02849e6	−0.842184	−0.421092	−	0.907018i	$-0.638353\pi$
$619$	−8.02849e6	−0.842184	−0.421092	+	0.907018i	$0.638353\pi$
$620$	8.33306e6	0.870613
$621$	43161.0	0.00449120
$622$	−3.23632e6	−0.335410
$623$	−8.65610e6	−0.893515
$624$	−61632.3	−0.00633647
$625$	7.69506e6	0.787974
$626$	−8.21548e6	−0.837909
$627$	−32177.5	−0.00326876
$628$	344271.	0.0348338
$629$	293472.	0.0295761
$630$	−2.03319e7	−2.04093
$631$	−7.58834e6	−0.758705	−0.379353	−	0.925252i	$-0.623853\pi$
$631$	−7.58834e6	−0.758705	−0.379353	+	0.925252i	$0.623853\pi$
$632$	−1.39034e7	−1.38462
$633$	−141623.	−0.0140483
$634$	−4.95340e6	−0.489418
$635$	−2.22999e7	−2.19466
$636$	69623.8	0.00682520
$637$	−2.44889e7	−2.39123
$638$	4.50421e6	0.438094
$639$	−1.02902e7	−0.996946
$640$	423065.	0.0408279
$641$	9.29000e6	0.893039	0.446520	−	0.894774i	$-0.352663\pi$
$641$	9.29000e6	0.893039	0.446520	+	0.894774i	$0.352663\pi$
$642$	13012.8	0.00124604
$643$	1.19617e7	1.14094	0.570472	−	0.821317i	$-0.306760\pi$
$643$	1.19617e7	1.14094	0.570472	+	0.821317i	$0.306760\pi$
$644$	1.61552e6	0.153496
$645$	−54493.1	−0.00515754
$646$	−1.31572e6	−0.124046
$647$	−1.64374e7	−1.54373	−0.771866	−	0.635785i	$-0.780677\pi$
$647$	−1.64374e7	−1.54373	−0.771866	+	0.635785i	$0.780677\pi$
$648$	1.15526e7	1.08079
$649$	−3.07228e6	−0.286318
$650$	2.58178e7	2.39682
$651$	−198187.	−0.0183283
$652$	1.88722e6	0.173861
$653$	1.11326e7	1.02168	0.510840	−	0.859676i	$-0.329335\pi$
$653$	1.11326e7	1.02168	0.510840	+	0.859676i	$0.329335\pi$
$654$	26987.6	0.00246729
$655$	−1.49524e7	−1.36178
$656$	3.57893e6	0.324709
$657$	4.55861e6	0.412021
$658$	−1.71352e7	−1.54286
$659$	−1.28072e7	−1.14879	−0.574393	−	0.818580i	$-0.694762\pi$
$659$	−1.28072e7	−1.14879	−0.574393	+	0.818580i	$0.694762\pi$
$660$	−29122.5	−0.00260237
$661$	−1.51001e7	−1.34424	−0.672119	−	0.740444i	$-0.734615\pi$
$661$	−1.51001e7	−1.34424	−0.672119	+	0.740444i	$0.734615\pi$
$662$	1.06339e7	0.943074
$663$	−32262.3	−0.00285043
$664$	−4.52045e6	−0.397889
$665$	2.77672e7	2.43489
$666$	−1.43057e6	−0.124975
$667$	4.12536e6	0.359044
$668$	2.67704e6	0.232121
$669$	−9526.79	−0.000822965 0
$670$	−568469.	−0.0489237
$671$	−310321.	−0.0266075
$672$	−138270.	−0.0118115
$673$	−8.14830e6	−0.693473	−0.346737	−	0.937963i	$-0.612710\pi$
$673$	−8.14830e6	−0.693473	−0.346737	+	0.937963i	$0.612710\pi$
$674$	1.49605e7	1.26852
$675$	442071.	0.0373450
$676$	−8.39808e6	−0.706827
$677$	−9.48338e6	−0.795228	−0.397614	−	0.917553i	$-0.630162\pi$
$677$	−9.48338e6	−0.795228	−0.397614	+	0.917553i	$0.630162\pi$
$678$	60080.4	0.00501947
$679$	2.32359e7	1.93412
$680$	−4.01265e6	−0.332782
$681$	101902.	0.00842002
$682$	−4.14272e6	−0.341055
$683$	2.84549e6	0.233403	0.116701	−	0.993167i	$-0.462768\pi$
$683$	2.84549e6	0.233403	0.116701	+	0.993167i	$0.462768\pi$
$684$	−4.68256e6	−0.382687
$685$	−2.78124e7	−2.26470
$686$	6.79380e6	0.551192
$687$	−103205.	−0.00834277
$688$	−1.54499e6	−0.124438
$689$	−3.40254e7	−2.73058
$690$	36533.8	0.00292127
$691$	−1.93430e7	−1.54109	−0.770547	−	0.637383i	$-0.780017\pi$
$691$	−1.93430e7	−1.54109	−0.770547	+	0.637383i	$0.780017\pi$
$692$	6.38702e6	0.507029
$693$	−7.37967e6	−0.583719
$694$	−2.86118e6	−0.225500
$695$	3.02215e7	2.37331
$696$	−207302.	−0.0162211
$697$	1.87344e6	0.146069
$698$	−1.36008e7	−1.05663
$699$	−173207.	−0.0134083
$700$	1.65468e7	1.27634
$701$	1.15671e7	0.889060	0.444530	−	0.895764i	$-0.353371\pi$
$701$	1.15671e7	0.889060	0.444530	+	0.895764i	$0.353371\pi$
$702$	314549.	0.0240905
$703$	1.95373e6	0.149099
$704$	−4.84690e6	−0.368580
$705$	282911.	0.0214376
$706$	9.87972e6	0.745990
$707$	327767.	0.0246613
$708$	41961.9	0.00314610
$709$	1.26351e7	0.943978	0.471989	−	0.881604i	$-0.343536\pi$
$709$	1.26351e7	0.943978	0.471989	+	0.881604i	$0.343536\pi$
$710$	−1.74212e7	−1.29698
$711$	1.72623e7	1.28063
$712$	8.32755e6	0.615627
$713$	−3.79427e6	−0.279515
$714$	28321.2	0.00207906
$715$	1.42323e7	1.04114
$716$	−8.59092e6	−0.626264
$717$	−73257.4	−0.00532174
$718$	−5.41464e6	−0.391975
$719$	−2.96638e6	−0.213996	−0.106998	−	0.994259i	$-0.534124\pi$
$719$	−2.96638e6	−0.213996	−0.106998	+	0.994259i	$0.534124\pi$
$720$	9.51748e6	0.684212
$721$	4.13768e7	2.96428
$722$	1.88987e6	0.134924
$723$	130826.	0.00930781
$724$	−2.39410e6	−0.169745
$725$	4.22534e7	2.98550
$726$	−90118.6	−0.00634561
$727$	−3.67741e6	−0.258051	−0.129026	−	0.991641i	$-0.541185\pi$
$727$	−3.67741e6	−0.258051	−0.129026	+	0.991641i	$0.541185\pi$
$728$	3.96734e7	2.77441
$729$	−1.43408e7	−0.999437
$730$	7.71768e6	0.536018
$731$	−808746.	−0.0559782
$732$	4238.43	0.000292366 0
$733$	−2.74542e7	−1.88733	−0.943667	−	0.330897i	$-0.892649\pi$
$733$	−2.74542e7	−1.88733	−0.943667	+	0.330897i	$0.892649\pi$
$734$	−1.17689e7	−0.806296
$735$	−354932.	−0.0242341
$736$	−2.64718e6	−0.180131
$737$	−206331.	−0.0139925
$738$	−9.13234e6	−0.617222
$739$	−2.49009e7	−1.67728	−0.838638	−	0.544690i	$-0.816647\pi$
$739$	−2.49009e7	−1.67728	−0.838638	+	0.544690i	$0.816647\pi$
$740$	1.76824e6	0.118703
$741$	−214779.	−0.0143696
$742$	2.98689e7	1.99164
$743$	1.58518e7	1.05343	0.526717	−	0.850041i	$-0.323423\pi$
$743$	1.58518e7	1.05343	0.526717	+	0.850041i	$0.323423\pi$
$744$	190665.	0.0126281
$745$	4.63895e6	0.306217
$746$	−9.18392e6	−0.604200
$747$	5.61253e6	0.368008
$748$	−432215.	−0.0282453
$749$	−4.07577e6	−0.265464
$750$	180067.	0.0116891
$751$	−2.15921e6	−0.139700	−0.0698499	−	0.997558i	$-0.522252\pi$
$751$	−2.15921e6	−0.139700	−0.0698499	+	0.997558i	$0.522252\pi$
$752$	8.02109e6	0.517236
$753$	15993.8	0.00102793
$754$	3.00648e7	1.92588
$755$	−3.28581e7	−2.09785
$756$	201596.	0.0128285
$757$	−2.95151e6	−0.187199	−0.0935996	−	0.995610i	$-0.529837\pi$
$757$	−2.95151e6	−0.187199	−0.0935996	+	0.995610i	$0.529837\pi$
$758$	2.41888e6	0.152912
$759$	13260.3	0.000835505 0
$760$	−2.67133e7	−1.67762
$761$	−1.61385e7	−1.01019	−0.505093	−	0.863065i	$-0.668542\pi$
$761$	−1.61385e7	−1.01019	−0.505093	+	0.863065i	$0.668542\pi$
$762$	−151418.	−0.00944692
$763$	−8.45284e6	−0.525643
$764$	−6.24093e6	−0.386827
$765$	4.98205e6	0.307790
$766$	2.01112e7	1.23842
$767$	−2.05069e7	−1.25867
$768$	159746.	0.00977299
$769$	−1.00000e6	−0.0609798	−0.0304899	−	0.999535i	$-0.509707\pi$
$769$	−1.00000e6	−0.0609798	−0.0304899	+	0.999535i	$0.509707\pi$
$770$	−1.24937e7	−0.759389
$771$	92388.7	0.00559736
$772$	7.48676e6	0.452117
$773$	1.13390e7	0.682539	0.341269	−	0.939966i	$-0.389143\pi$
$773$	1.13390e7	0.682539	0.341269	+	0.939966i	$0.389143\pi$
$774$	3.94234e6	0.236539
$775$	−3.88623e7	−2.32421
$776$	−2.23539e7	−1.33260
$777$	−42054.4	−0.00249896
$778$	1.13325e7	0.671237
$779$	1.24720e7	0.736364
$780$	−194388.	−0.0114402
$781$	−6.32319e6	−0.370944
$782$	542208.	0.0317065
$783$	514790.	0.0300072
$784$	−1.00630e7	−0.584709
$785$	−2.43849e6	−0.141236
$786$	−101528.	−0.00586180
$787$	3.07454e7	1.76947	0.884735	−	0.466095i	$-0.154340\pi$
$787$	3.07454e7	1.76947	0.884735	+	0.466095i	$0.154340\pi$
$788$	2.57650e6	0.147814
$789$	146613.	0.00838453
$790$	2.92249e7	1.66604
$791$	−1.88179e7	−1.06938
$792$	7.09957e6	0.402179
$793$	−2.07133e6	−0.116968
$794$	−5.87571e6	−0.330757
$795$	−493150.	−0.0276733
$796$	3.17799e6	0.177775
$797$	2.20896e7	1.23180	0.615902	−	0.787823i	$-0.288792\pi$
$797$	2.20896e7	1.23180	0.615902	+	0.787823i	$0.288792\pi$
$798$	188542.	0.0104810
$799$	4.19875e6	0.232677
$800$	−2.71134e7	−1.49782
$801$	−1.03394e7	−0.569394
$802$	1.61247e7	0.885228
$803$	2.80121e6	0.153305
$804$	2818.12	0.000153751 0
$805$	−1.14428e7	−0.622364
$806$	−2.76519e7	−1.49930
$807$	154703.	0.00836209
$808$	−315326.	−0.0169915
$809$	2.81522e6	0.151231	0.0756156	−	0.997137i	$-0.475908\pi$
$809$	2.81522e6	0.151231	0.0756156	+	0.997137i	$0.475908\pi$
$810$	−2.42834e7	−1.30046
$811$	2.48228e7	1.32525	0.662626	−	0.748951i	$-0.269442\pi$
$811$	2.48228e7	1.32525	0.662626	+	0.748951i	$0.269442\pi$
$812$	1.92687e7	1.02556
$813$	97779.4	0.00518825
$814$	−879067.	−0.0465008
$815$	−1.33673e7	−0.704934
$816$	−13257.3	−0.000696995 0
$817$	−5.38404e6	−0.282198
$818$	1.59625e7	0.834099
$819$	−4.92579e7	−2.56606
$820$	1.12879e7	0.586244
$821$	1.61308e7	0.835214	0.417607	−	0.908628i	$-0.362869\pi$
$821$	1.61308e7	0.835214	0.417607	+	0.908628i	$0.362869\pi$
$822$	−188848.	−0.00974841
$823$	9.86776e6	0.507831	0.253915	−	0.967226i	$-0.418282\pi$
$823$	9.86776e6	0.507831	0.253915	+	0.967226i	$0.418282\pi$
$824$	−3.98063e7	−2.04237
$825$	135817.	0.00694734
$826$	1.80018e7	0.918051
$827$	−1.55899e7	−0.792648	−0.396324	−	0.918111i	$-0.629714\pi$
$827$	−1.55899e7	−0.792648	−0.396324	+	0.918111i	$0.629714\pi$
$828$	1.92968e6	0.0978158
$829$	8.82372e6	0.445929	0.222964	−	0.974827i	$-0.428427\pi$
$829$	8.82372e6	0.445929	0.222964	+	0.974827i	$0.428427\pi$
$830$	9.50195e6	0.478760
$831$	74656.9	0.00375031
$832$	−3.23521e7	−1.62030
$833$	−5.26764e6	−0.263029
$834$	205207.	0.0102159
$835$	−1.89617e7	−0.941153
$836$	−2.87737e6	−0.142390
$837$	−473475.	−0.0233606
$838$	−2.74105e6	−0.134836
$839$	5.18926e6	0.254508	0.127254	−	0.991870i	$-0.459384\pi$
$839$	5.18926e6	0.254508	0.127254	+	0.991870i	$0.459384\pi$
$840$	575010.	0.0281175
$841$	2.86929e7	1.39889
$842$	−2.12107e7	−1.03104
$843$	−229783.	−0.0111365
$844$	−1.26642e7	−0.611959
$845$	5.94841e7	2.86589
$846$	−2.04674e7	−0.983187
$847$	2.82263e7	1.35190
$848$	−1.39818e7	−0.667688
$849$	280369.	0.0133494
$850$	5.55349e6	0.263644
$851$	−805128.	−0.0381102
$852$	86363.5	0.00407597
$853$	9.97881e6	0.469576	0.234788	−	0.972047i	$-0.424560\pi$
$853$	9.97881e6	0.469576	0.234788	+	0.972047i	$0.424560\pi$
$854$	1.81831e6	0.0853144
$855$	3.31669e7	1.55163
$856$	3.92107e6	0.182903
$857$	2.49502e7	1.16044	0.580220	−	0.814460i	$-0.302967\pi$
$857$	2.49502e7	1.16044	0.580220	+	0.814460i	$0.302967\pi$
$858$	96638.4	0.00448158
$859$	−3.40165e7	−1.57292	−0.786461	−	0.617640i	$-0.788089\pi$
$859$	−3.40165e7	−1.57292	−0.786461	+	0.617640i	$0.788089\pi$
$860$	−4.87288e6	−0.224667
$861$	−268462.	−0.0123417
$862$	−2.62831e7	−1.20478
$863$	1.50989e7	0.690112	0.345056	−	0.938582i	$-0.387860\pi$
$863$	1.50989e7	0.690112	0.345056	+	0.938582i	$0.387860\pi$
$864$	−330333.	−0.0150545
$865$	−4.52397e7	−2.05579
$866$	−4.35439e6	−0.197303
$867$	207477.	0.00937394
$868$	−1.77222e7	−0.798398
$869$	1.06074e7	0.476498
$870$	435747.	0.0195180
$871$	−1.37722e6	−0.0615119
$872$	8.13201e6	0.362165
$873$	2.77543e7	1.23252
$874$	3.60962e6	0.159839
$875$	−5.63991e7	−2.49030
$876$	−38259.5	−0.00168453
$877$	−3.14737e7	−1.38181	−0.690905	−	0.722945i	$-0.742788\pi$
$877$	−3.14737e7	−1.38181	−0.690905	+	0.722945i	$0.742788\pi$
$878$	1.14185e7	0.499887
$879$	−116343.	−0.00507890
$880$	5.84836e6	0.254582
$881$	1.54322e7	0.669866	0.334933	−	0.942242i	$-0.391286\pi$
$881$	1.54322e7	0.669866	0.334933	+	0.942242i	$0.391286\pi$
$882$	2.56778e7	1.11144
$883$	2.74826e7	1.18620	0.593098	−	0.805130i	$-0.297905\pi$
$883$	2.74826e7	1.18620	0.593098	+	0.805130i	$0.297905\pi$
$884$	−2.88495e6	−0.124168
$885$	−297219.	−0.0127561
$886$	1.77198e7	0.758360
$887$	−3.34044e7	−1.42559	−0.712796	−	0.701372i	$-0.752571\pi$
$887$	−3.34044e7	−1.42559	−0.712796	+	0.701372i	$0.752571\pi$
$888$	40458.2	0.00172176
$889$	4.74260e7	2.01262
$890$	−1.75044e7	−0.740753
$891$	−8.81390e6	−0.371941
$892$	−851904.	−0.0358491
$893$	2.79522e7	1.17297
$894$	31498.9	0.00131811
$895$	6.08500e7	2.53924
$896$	−899749.	−0.0374413
$897$	88510.1	0.00367292
$898$	1.38780e7	0.574296
$899$	−4.52551e7	−1.86753
$900$	1.97645e7	0.813353
$901$	−7.31896e6	−0.300357
$902$	−5.61170e6	−0.229656
$903$	115893.	0.00472973
$904$	1.81037e7	0.736793
$905$	1.69576e7	0.688244
$906$	−223109.	−0.00903020
$907$	−1.19623e7	−0.482832	−0.241416	−	0.970422i	$-0.577612\pi$
$907$	−1.19623e7	−0.482832	−0.241416	+	0.970422i	$0.577612\pi$
$908$	9.11224e6	0.366784
$909$	391504.	0.0157155
$910$	−8.33932e7	−3.33831
$911$	4.70606e7	1.87872	0.939360	−	0.342934i	$-0.111421\pi$
$911$	4.70606e7	1.87872	0.939360	+	0.342934i	$0.111421\pi$
$912$	−88257.5	−0.00351370
$913$	3.44882e6	0.136929
$914$	723438.	0.0286441
$915$	−30021.1	−0.00118542
$916$	−9.22882e6	−0.363419
$917$	3.17999e7	1.24883
$918$	67660.3	0.00264989
$919$	−1.82926e6	−0.0714475	−0.0357238	−	0.999362i	$-0.511374\pi$
$919$	−1.82926e6	−0.0714475	−0.0357238	+	0.999362i	$0.511374\pi$
$920$	1.10085e7	0.428805
$921$	73838.2	0.00286835
$922$	2.07280e7	0.803026
$923$	−4.22061e7	−1.63069
$924$	61936.0	0.00238651
$925$	−8.24641e6	−0.316892
$926$	−1.81773e7	−0.696630
$927$	4.94230e7	1.88899
$928$	−3.15735e7	−1.20352
$929$	2.89438e7	1.10031	0.550157	−	0.835061i	$-0.314568\pi$
$929$	2.89438e7	1.10031	0.550157	+	0.835061i	$0.314568\pi$
$930$	−400775.	−0.0151947
$931$	−3.50681e7	−1.32598
$932$	−1.54885e7	−0.584077
$933$	−113638.	−0.00427387
$934$	−4.01990e7	−1.50781
$935$	3.06140e6	0.114523
$936$	4.73883e7	1.76800
$937$	−4.93895e7	−1.83775	−0.918874	−	0.394551i	$-0.870900\pi$
$937$	−4.93895e7	−1.83775	−0.918874	+	0.394551i	$0.870900\pi$
$938$	1.20899e6	0.0448656
$939$	−288474.	−0.0106768
$940$	2.52984e7	0.933842
$941$	7.31504e6	0.269304	0.134652	−	0.990893i	$-0.457008\pi$
$941$	7.31504e6	0.269304	0.134652	+	0.990893i	$0.457008\pi$
$942$	−16557.6	−0.000607952 0
$943$	−5.13970e6	−0.188217
$944$	−8.42675e6	−0.307773
$945$	−1.42792e6	−0.0520143
$946$	2.42252e6	0.0880114
$947$	−4.85078e7	−1.75767	−0.878834	−	0.477127i	$-0.841678\pi$
$947$	−4.85078e7	−1.75767	−0.878834	+	0.477127i	$0.841678\pi$
$948$	−144879.	−0.00523582
$949$	1.86975e7	0.673936
$950$	3.69711e7	1.32909
$951$	−173931.	−0.00623627
$952$	8.53387e6	0.305178
$953$	−1.91946e7	−0.684614	−0.342307	−	0.939588i	$-0.611208\pi$
$953$	−1.91946e7	−0.684614	−0.342307	+	0.939588i	$0.611208\pi$
$954$	3.56773e7	1.26917
$955$	4.42049e7	1.56842
$956$	−6.55081e6	−0.231820
$957$	158158.	0.00558229
$958$	−3.88216e6	−0.136666
$959$	5.91497e7	2.07685
$960$	−468899.	−0.0164211
$961$	1.29939e7	0.453871
$962$	−5.86761e6	−0.204420
$963$	−4.86835e6	−0.169167
$964$	1.16987e7	0.405457
$965$	−5.30292e7	−1.83315
$966$	−77697.9	−0.00267896
$967$	5.07946e7	1.74683	0.873416	−	0.486976i	$-0.161900\pi$
$967$	5.07946e7	1.74683	0.873416	+	0.486976i	$0.161900\pi$
$968$	−2.71549e7	−0.931452
$969$	−46199.6	−0.00158062
$970$	4.69878e7	1.60345
$971$	4.70774e7	1.60238	0.801188	−	0.598413i	$-0.204202\pi$
$971$	4.70774e7	1.60238	0.801188	+	0.598413i	$0.204202\pi$
$972$	361203.	0.0122627
$973$	−6.42733e7	−2.17645
$974$	−3.97012e7	−1.34093
$975$	906552.	0.0305409
$976$	−851158.	−0.0286013
$977$	−3.33595e7	−1.11811	−0.559053	−	0.829132i	$-0.688835\pi$
$977$	−3.33595e7	−1.11811	−0.559053	+	0.829132i	$0.688835\pi$
$978$	−90764.9	−0.00303439
$979$	−6.35340e6	−0.211860
$980$	−3.17387e7	−1.05566
$981$	−1.00966e7	−0.334967
$982$	−4.67155e6	−0.154590
$983$	2.87580e7	0.949237	0.474619	−	0.880191i	$-0.342586\pi$
$983$	2.87580e7	0.949237	0.474619	+	0.880191i	$0.342586\pi$
$984$	258273.	0.00850337
$985$	−1.82495e7	−0.599322
$986$	6.46702e6	0.211842
$987$	−601677.	−0.0196594
$988$	−1.92059e7	−0.625955
$989$	2.21876e6	0.0721305
$990$	−1.49232e7	−0.483922
$991$	3.21423e7	1.03966	0.519832	−	0.854268i	$-0.325994\pi$
$991$	3.21423e7	1.03966	0.519832	+	0.854268i	$0.325994\pi$
$992$	2.90395e7	0.936936
$993$	373391.	0.0120169
$994$	3.70503e7	1.18940
$995$	−2.25099e7	−0.720802
$996$	−47104.8	−0.00150459
$997$	3.54024e7	1.12796	0.563981	−	0.825788i	$-0.309269\pi$
$997$	3.54024e7	1.12796	0.563981	+	0.825788i	$0.309269\pi$
$998$	−8.54983e6	−0.271726
$999$	−100469.	−0.00318508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.a.a.1.3	✓	7
3.2	odd	2		333.6.a.c.1.5		7
4.3	odd	2		592.6.a.g.1.3		7
5.4	even	2		925.6.a.a.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.a.a.1.3	✓	7	1.1	even	1	trivial
333.6.a.c.1.5		7	3.2	odd	2
592.6.a.g.1.3		7	4.3	odd	2
925.6.a.a.1.5		7	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q-4.30071 q^{2} -0.151013 q^{3} -13.5039 q^{4} +95.6487 q^{5} +0.649463 q^{6} -203.420 q^{7} +195.699 q^{8} -242.977 q^{9} +O(q^{10})\)	\(q-4.30071 q^{2} -0.151013 q^{3} -13.5039 q^{4} +95.6487 q^{5} +0.649463 q^{6} -203.420 q^{7} +195.699 q^{8} -242.977 q^{9} -411.358 q^{10} -149.306 q^{11} +2.03926 q^{12} -996.592 q^{13} +874.851 q^{14} -14.4442 q^{15} -409.522 q^{16} -214.370 q^{17} +1044.98 q^{18} -1427.12 q^{19} -1291.63 q^{20} +30.7190 q^{21} +642.123 q^{22} +588.114 q^{23} -29.5531 q^{24} +6023.68 q^{25} +4286.06 q^{26} +73.3888 q^{27} +2746.95 q^{28} +7014.56 q^{29} +62.1203 q^{30} -6451.60 q^{31} -4501.13 q^{32} +22.5472 q^{33} +921.943 q^{34} -19456.9 q^{35} +3281.13 q^{36} -1369.00 q^{37} +6137.63 q^{38} +150.498 q^{39} +18718.4 q^{40} -8739.29 q^{41} -132.114 q^{42} +3772.67 q^{43} +2016.21 q^{44} -23240.5 q^{45} -2529.31 q^{46} -19586.5 q^{47} +61.8431 q^{48} +24572.7 q^{49} -25906.1 q^{50} +32.3726 q^{51} +13457.8 q^{52} +34141.8 q^{53} -315.624 q^{54} -14280.9 q^{55} -39809.1 q^{56} +215.513 q^{57} -30167.6 q^{58} +20577.0 q^{59} +195.052 q^{60} +2078.42 q^{61} +27746.5 q^{62} +49426.4 q^{63} +32462.8 q^{64} -95322.7 q^{65} -96.9689 q^{66} +1381.93 q^{67} +2894.82 q^{68} -88.8128 q^{69} +83678.4 q^{70} +42350.5 q^{71} -47550.4 q^{72} -18761.5 q^{73} +5887.68 q^{74} -909.653 q^{75} +19271.6 q^{76} +30371.9 q^{77} -647.250 q^{78} -71044.9 q^{79} -39170.3 q^{80} +59032.4 q^{81} +37585.2 q^{82} -23099.0 q^{83} -414.826 q^{84} -20504.2 q^{85} -16225.2 q^{86} -1059.29 q^{87} -29219.1 q^{88} +42552.8 q^{89} +99950.5 q^{90} +202727. q^{91} -7941.81 q^{92} +974.274 q^{93} +84235.7 q^{94} -136502. q^{95} +679.729 q^{96} -114226. q^{97} -105680. q^{98} +36278.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * q^99

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