LMFDB - Embedded newform 1045.6.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.86064 q^{2} +3.26128 q^{3} +65.2322 q^{4} -25.0000 q^{5} -32.1583 q^{6} -108.556 q^{7} -327.690 q^{8} -232.364 q^{9} +O(q^{10})$	\(q-9.86064 q^{2} +3.26128 q^{3} +65.2322 q^{4} -25.0000 q^{5} -32.1583 q^{6} -108.556 q^{7} -327.690 q^{8} -232.364 q^{9} +246.516 q^{10} -121.000 q^{11} +212.741 q^{12} -276.822 q^{13} +1070.43 q^{14} -81.5321 q^{15} +1143.81 q^{16} -520.094 q^{17} +2291.26 q^{18} +361.000 q^{19} -1630.80 q^{20} -354.030 q^{21} +1193.14 q^{22} +3090.77 q^{23} -1068.69 q^{24} +625.000 q^{25} +2729.64 q^{26} -1550.30 q^{27} -7081.31 q^{28} -7682.09 q^{29} +803.958 q^{30} +2876.40 q^{31} -792.565 q^{32} -394.615 q^{33} +5128.45 q^{34} +2713.89 q^{35} -15157.6 q^{36} -3486.45 q^{37} -3559.69 q^{38} -902.796 q^{39} +8192.26 q^{40} -12848.4 q^{41} +3490.97 q^{42} -18633.6 q^{43} -7893.09 q^{44} +5809.10 q^{45} -30477.0 q^{46} +2242.05 q^{47} +3730.28 q^{48} -5022.69 q^{49} -6162.90 q^{50} -1696.17 q^{51} -18057.7 q^{52} -12365.5 q^{53} +15286.9 q^{54} +3025.00 q^{55} +35572.6 q^{56} +1177.32 q^{57} +75750.3 q^{58} -23835.1 q^{59} -5318.52 q^{60} -15066.7 q^{61} -28363.2 q^{62} +25224.4 q^{63} -28786.6 q^{64} +6920.56 q^{65} +3891.16 q^{66} -64794.4 q^{67} -33926.8 q^{68} +10079.9 q^{69} -26760.7 q^{70} +23354.2 q^{71} +76143.4 q^{72} -41080.2 q^{73} +34378.6 q^{74} +2038.30 q^{75} +23548.8 q^{76} +13135.2 q^{77} +8902.14 q^{78} +81330.7 q^{79} -28595.1 q^{80} +51408.5 q^{81} +126694. q^{82} -120352. q^{83} -23094.2 q^{84} +13002.3 q^{85} +183739. q^{86} -25053.5 q^{87} +39650.5 q^{88} +45442.4 q^{89} -57281.4 q^{90} +30050.6 q^{91} +201618. q^{92} +9380.77 q^{93} -22108.0 q^{94} -9025.00 q^{95} -2584.78 q^{96} -110897. q^{97} +49527.0 q^{98} +28116.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−9.86064	−1.74313	−0.871565	−	0.490279i	$-0.836895\pi$
$2$	−9.86064	−1.74313	−0.871565	+	0.490279i	$0.836895\pi$
$3$	3.26128	0.209211	0.104606	−	0.994514i	$-0.466642\pi$
$3$	3.26128	0.209211	0.104606	+	0.994514i	$0.466642\pi$
$4$	65.2322	2.03851
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−32.1583	−0.364683
$7$	−108.556	−0.837350	−0.418675	−	0.908136i	$-0.637505\pi$
$7$	−108.556	−0.837350	−0.418675	+	0.908136i	$0.637505\pi$
$8$	−327.690	−1.81025
$9$	−232.364	−0.956231
$10$	246.516	0.779552
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	212.741	0.426479
$13$	−276.822	−0.454300	−0.227150	−	0.973860i	$-0.572941\pi$
$13$	−276.822	−0.454300	−0.227150	+	0.973860i	$0.572941\pi$
$14$	1070.43	1.45961
$15$	−81.5321	−0.0935622
$16$	1143.81	1.11700
$17$	−520.094	−0.436475	−0.218237	−	0.975896i	$-0.570031\pi$
$17$	−520.094	−0.436475	−0.218237	+	0.975896i	$0.570031\pi$
$18$	2291.26	1.66683
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−1630.80	−0.911647
$21$	−354.030	−0.175183
$22$	1193.14	0.525574
$23$	3090.77	1.21828	0.609140	−	0.793062i	$-0.291515\pi$
$23$	3090.77	1.21828	0.609140	+	0.793062i	$0.291515\pi$
$24$	−1068.69	−0.378725
$25$	625.000	0.200000
$26$	2729.64	0.791904
$27$	−1550.30	−0.409266
$28$	−7081.31	−1.70694
$29$	−7682.09	−1.69623	−0.848115	−	0.529813i	$-0.822262\pi$
$29$	−7682.09	−1.69623	−0.848115	+	0.529813i	$0.822262\pi$
$30$	803.958	0.163091
$31$	2876.40	0.537583	0.268791	−	0.963198i	$-0.413376\pi$
$31$	2876.40	0.537583	0.268791	+	0.963198i	$0.413376\pi$
$32$	−792.565	−0.136823
$33$	−394.615	−0.0630796
$34$	5128.45	0.760833
$35$	2713.89	0.374474
$36$	−15157.6	−1.94928
$37$	−3486.45	−0.418676	−0.209338	−	0.977843i	$-0.567131\pi$
$37$	−3486.45	−0.418676	−0.209338	+	0.977843i	$0.567131\pi$
$38$	−3559.69	−0.399902
$39$	−902.796	−0.0950447
$40$	8192.26	0.809569
$41$	−12848.4	−1.19369	−0.596843	−	0.802358i	$-0.703578\pi$
$41$	−12848.4	−1.19369	−0.596843	+	0.802358i	$0.703578\pi$
$42$	3490.97	0.305367
$43$	−18633.6	−1.53683	−0.768414	−	0.639954i	$-0.778954\pi$
$43$	−18633.6	−1.53683	−0.768414	+	0.639954i	$0.778954\pi$
$44$	−7893.09	−0.614632
$45$	5809.10	0.427639
$46$	−30477.0	−2.12362
$47$	2242.05	0.148047	0.0740237	−	0.997256i	$-0.476416\pi$
$47$	2242.05	0.148047	0.0740237	+	0.997256i	$0.476416\pi$
$48$	3730.28	0.233689
$49$	−5022.69	−0.298845
$50$	−6162.90	−0.348626
$51$	−1696.17	−0.0913155
$52$	−18057.7	−0.926093
$53$	−12365.5	−0.604673	−0.302337	−	0.953201i	$-0.597767\pi$
$53$	−12365.5	−0.604673	−0.302337	+	0.953201i	$0.597767\pi$
$54$	15286.9	0.713404
$55$	3025.00	0.134840
$56$	35572.6	1.51581
$57$	1177.32	0.0479964
$58$	75750.3	2.95675
$59$	−23835.1	−0.891428	−0.445714	−	0.895175i	$-0.647050\pi$
$59$	−23835.1	−0.891428	−0.445714	+	0.895175i	$0.647050\pi$
$60$	−5318.52	−0.190727
$61$	−15066.7	−0.518433	−0.259217	−	0.965819i	$-0.583464\pi$
$61$	−15066.7	−0.518433	−0.259217	+	0.965819i	$0.583464\pi$
$62$	−28363.2	−0.937077
$63$	25224.4	0.800699
$64$	−28786.6	−0.878497
$65$	6920.56	0.203169
$66$	3891.16	0.109956
$67$	−64794.4	−1.76340	−0.881699	−	0.471812i	$-0.843600\pi$
$67$	−64794.4	−1.76340	−0.881699	+	0.471812i	$0.843600\pi$
$68$	−33926.8	−0.889756
$69$	10079.9	0.254878
$70$	−26760.7	−0.652758
$71$	23354.2	0.549818	0.274909	−	0.961470i	$-0.411352\pi$
$71$	23354.2	0.549818	0.274909	+	0.961470i	$0.411352\pi$
$72$	76143.4	1.73102
$73$	−41080.2	−0.902247	−0.451123	−	0.892462i	$-0.648977\pi$
$73$	−41080.2	−0.902247	−0.451123	+	0.892462i	$0.648977\pi$
$74$	34378.6	0.729808
$75$	2038.30	0.0418423
$76$	23548.8	0.467665
$77$	13135.2	0.252470
$78$	8902.14	0.165675
$79$	81330.7	1.46618	0.733089	−	0.680133i	$-0.238078\pi$
$79$	81330.7	1.46618	0.733089	+	0.680133i	$0.238078\pi$
$80$	−28595.1	−0.499537
$81$	51408.5	0.870607
$82$	126694.	2.08075
$83$	−120352.	−1.91760	−0.958799	−	0.284087i	$-0.908310\pi$
$83$	−120352.	−1.91760	−0.958799	+	0.284087i	$0.908310\pi$
$84$	−23094.2	−0.357112
$85$	13002.3	0.195197
$86$	183739.	2.67889
$87$	−25053.5	−0.354871
$88$	39650.5	0.545811
$89$	45442.4	0.608116	0.304058	−	0.952653i	$-0.401658\pi$
$89$	45442.4	0.608116	0.304058	+	0.952653i	$0.401658\pi$
$90$	−57281.4	−0.745431
$91$	30050.6	0.380408
$92$	201618.	2.48347
$93$	9380.77	0.112469
$94$	−22108.0	−0.258066
$95$	−9025.00	−0.102598
$96$	−2584.78	−0.0286250
$97$	−110897.	−1.19672	−0.598360	−	0.801228i	$-0.704181\pi$
$97$	−110897.	−1.19672	−0.598360	+	0.801228i	$0.704181\pi$
$98$	49527.0	0.520927
$99$	28116.0	0.288314
$100$	40770.1	0.407701
$101$	32809.9	0.320038	0.160019	−	0.987114i	$-0.448844\pi$
$101$	32809.9	0.320038	0.160019	+	0.987114i	$0.448844\pi$
$102$	16725.3	0.159175
$103$	−86388.7	−0.802350	−0.401175	−	0.916001i	$-0.631398\pi$
$103$	−86388.7	−0.802350	−0.401175	+	0.916001i	$0.631398\pi$
$104$	90712.0	0.822397
$105$	8850.76	0.0783443
$106$	121931.	1.05402
$107$	−44003.0	−0.371554	−0.185777	−	0.982592i	$-0.559480\pi$
$107$	−44003.0	−0.371554	−0.185777	+	0.982592i	$0.559480\pi$
$108$	−101129.	−0.834291
$109$	92725.3	0.747536	0.373768	−	0.927522i	$-0.378066\pi$
$109$	92725.3	0.747536	0.373768	+	0.927522i	$0.378066\pi$
$110$	−29828.4	−0.235044
$111$	−11370.3	−0.0875919
$112$	−124166.	−0.935318
$113$	11383.1	0.0838618	0.0419309	−	0.999121i	$-0.486649\pi$
$113$	11383.1	0.0838618	0.0419309	+	0.999121i	$0.486649\pi$
$114$	−11609.2	−0.0836640
$115$	−77269.3	−0.544832
$116$	−501120.	−3.45777
$117$	64323.5	0.434415
$118$	235029.	1.55388
$119$	56459.0	0.365482
$120$	26717.3	0.169371
$121$	14641.0	0.0909091
$122$	148567.	0.903697
$123$	−41902.3	−0.249733
$124$	187634.	1.09587
$125$	−15625.0	−0.0894427
$126$	−248729.	−1.39572
$127$	−44649.6	−0.245645	−0.122823	−	0.992429i	$-0.539195\pi$
$127$	−44649.6	−0.245645	−0.122823	+	0.992429i	$0.539195\pi$
$128$	309216.	1.66816
$129$	−60769.4	−0.321522
$130$	−68241.1	−0.354150
$131$	−131044.	−0.667173	−0.333587	−	0.942719i	$-0.608259\pi$
$131$	−131044.	−0.667173	−0.333587	+	0.942719i	$0.608259\pi$
$132$	−25741.6	−0.128588
$133$	−39188.6	−0.192101
$134$	638914.	3.07383
$135$	38757.4	0.183029
$136$	170430.	0.790129
$137$	−146134.	−0.665199	−0.332599	−	0.943068i	$-0.607926\pi$
$137$	−146134.	−0.665199	−0.332599	+	0.943068i	$0.607926\pi$
$138$	−99394.1	−0.444286
$139$	−317529.	−1.39395	−0.696973	−	0.717097i	$-0.745470\pi$
$139$	−317529.	−1.39395	−0.696973	+	0.717097i	$0.745470\pi$
$140$	177033.	0.763368
$141$	7311.96	0.0309732
$142$	−230287.	−0.958404
$143$	33495.5	0.136977
$144$	−265779.	−1.06811
$145$	192052.	0.758577
$146$	405077.	1.57273
$147$	−16380.4	−0.0625219
$148$	−227428.	−0.853474
$149$	−71193.0	−0.262707	−0.131354	−	0.991336i	$-0.541932\pi$
$149$	−71193.0	−0.262707	−0.131354	+	0.991336i	$0.541932\pi$
$150$	−20099.0	−0.0729366
$151$	−288606.	−1.03006	−0.515031	−	0.857172i	$-0.672220\pi$
$151$	−288606.	−1.03006	−0.515031	+	0.857172i	$0.672220\pi$
$152$	−118296.	−0.415300
$153$	120851.	0.417371
$154$	−129522.	−0.440089
$155$	−71910.1	−0.240414
$156$	−58891.3	−0.193749
$157$	−262798.	−0.850888	−0.425444	−	0.904985i	$-0.639882\pi$
$157$	−262798.	−0.850888	−0.425444	+	0.904985i	$0.639882\pi$
$158$	−801972.	−2.55574
$159$	−40327.3	−0.126505
$160$	19814.1	0.0611893
$161$	−335520.	−1.02013
$162$	−506921.	−1.51758
$163$	23023.3	0.0678733	0.0339366	−	0.999424i	$-0.489196\pi$
$163$	23023.3	0.0678733	0.0339366	+	0.999424i	$0.489196\pi$
$164$	−838130.	−2.43333
$165$	9865.38	0.0282101
$166$	1.18675e6	3.34262
$167$	−471147.	−1.30727	−0.653634	−	0.756811i	$-0.726757\pi$
$167$	−471147.	−1.30727	−0.653634	+	0.756811i	$0.726757\pi$
$168$	116012.	0.317125
$169$	−294662.	−0.793612
$170$	−128211.	−0.340255
$171$	−83883.4	−0.219374
$172$	−1.21551e6	−3.13283
$173$	643973.	1.63588	0.817941	−	0.575301i	$-0.195115\pi$
$173$	643973.	1.63588	0.817941	+	0.575301i	$0.195115\pi$
$174$	247043.	0.618586
$175$	−67847.2	−0.167470
$176$	−138401.	−0.336788
$177$	−77732.9	−0.186497
$178$	−448091.	−1.06003
$179$	−95783.8	−0.223439	−0.111720	−	0.993740i	$-0.535636\pi$
$179$	−95783.8	−0.223439	−0.111720	+	0.993740i	$0.535636\pi$
$180$	378940.	0.871745
$181$	286968.	0.651084	0.325542	−	0.945528i	$-0.394453\pi$
$181$	286968.	0.651084	0.325542	+	0.945528i	$0.394453\pi$
$182$	−296318.	−0.663101
$183$	−49136.7	−0.108462
$184$	−1.01282e6	−2.20539
$185$	87161.1	0.187238
$186$	−92500.3	−0.196047
$187$	62931.3	0.131602
$188$	146254.	0.301795
$189$	168293.	0.342699
$190$	88992.2	0.178841
$191$	−129140.	−0.256139	−0.128070	−	0.991765i	$-0.540878\pi$
$191$	−129140.	−0.256139	−0.128070	+	0.991765i	$0.540878\pi$
$192$	−93881.2	−0.183792
$193$	363908.	0.703231	0.351615	−	0.936145i	$-0.385632\pi$
$193$	363908.	0.703231	0.351615	+	0.936145i	$0.385632\pi$
$194$	1.09352e6	2.08604
$195$	22569.9	0.0425053
$196$	−327641.	−0.609198
$197$	−415165.	−0.762175	−0.381088	−	0.924539i	$-0.624450\pi$
$197$	−415165.	−0.762175	−0.381088	+	0.924539i	$0.624450\pi$
$198$	−277242.	−0.502570
$199$	−858603.	−1.53695	−0.768475	−	0.639880i	$-0.778984\pi$
$199$	−858603.	−1.53695	−0.768475	+	0.639880i	$0.778984\pi$
$200$	−204806.	−0.362050
$201$	−211313.	−0.368923
$202$	−323526.	−0.557868
$203$	833934.	1.42034
$204$	−110645.	−0.186147
$205$	321210.	0.533832
$206$	851847.	1.39860
$207$	−718184.	−1.16496
$208$	−316631.	−0.507452
$209$	−43681.0	−0.0691714
$210$	−87274.1	−0.136564
$211$	−923392.	−1.42784	−0.713921	−	0.700226i	$-0.753082\pi$
$211$	−923392.	−1.42784	−0.713921	+	0.700226i	$0.753082\pi$
$212$	−806626.	−1.23263
$213$	76164.6	0.115028
$214$	433897.	0.647668
$215$	465839.	0.687290
$216$	508017.	0.740874
$217$	−312249.	−0.450145
$218$	−914330.	−1.30305
$219$	−133974.	−0.188760
$220$	197327.	0.274872
$221$	143973.	0.198290
$222$	112118.	0.152684
$223$	−596161.	−0.802788	−0.401394	−	0.915905i	$-0.631474\pi$
$223$	−596161.	−0.802788	−0.401394	+	0.915905i	$0.631474\pi$
$224$	86037.4	0.114569
$225$	−145228.	−0.191246
$226$	−112245.	−0.146182
$227$	−774598.	−0.997726	−0.498863	−	0.866681i	$-0.666249\pi$
$227$	−774598.	−0.997726	−0.498863	+	0.866681i	$0.666249\pi$
$228$	76799.4	0.0978409
$229$	884626.	1.11473	0.557367	−	0.830266i	$-0.311812\pi$
$229$	884626.	1.11473	0.557367	+	0.830266i	$0.311812\pi$
$230$	761924.	0.949713
$231$	42837.7	0.0528197
$232$	2.51735e6	3.07060
$233$	−1.17248e6	−1.41487	−0.707435	−	0.706779i	$-0.750148\pi$
$233$	−1.17248e6	−1.41487	−0.707435	+	0.706779i	$0.750148\pi$
$234$	−634271.	−0.757243
$235$	−56051.2	−0.0662088
$236$	−1.55481e6	−1.81718
$237$	265242.	0.306741
$238$	−556722.	−0.637083
$239$	1.40110e6	1.58662	0.793312	−	0.608816i	$-0.208355\pi$
$239$	1.40110e6	1.58662	0.793312	+	0.608816i	$0.208355\pi$
$240$	−93256.9	−0.104509
$241$	1.17514e6	1.30331	0.651655	−	0.758516i	$-0.274075\pi$
$241$	1.17514e6	1.30331	0.651655	+	0.758516i	$0.274075\pi$
$242$	−144370.	−0.158466
$243$	544380.	0.591407
$244$	−982832.	−1.05683
$245$	125567.	0.133648
$246$	413184.	0.435317
$247$	−99932.8	−0.104224
$248$	−942569.	−0.973160
$249$	−392501.	−0.401183
$250$	154072.	0.155910
$251$	1.73068e6	1.73393	0.866965	−	0.498370i	$-0.166068\pi$
$251$	1.73068e6	1.73393	0.866965	+	0.498370i	$0.166068\pi$
$252$	1.64544e6	1.63223
$253$	−373983.	−0.367325
$254$	440274.	0.428192
$255$	42404.3	0.0408376
$256$	−2.12790e6	−2.02932
$257$	−1.72152e6	−1.62585	−0.812923	−	0.582371i	$-0.802125\pi$
$257$	−1.72152e6	−1.62585	−0.812923	+	0.582371i	$0.802125\pi$
$258$	599225.	0.560455
$259$	378473.	0.350579
$260$	451443.	0.414161
$261$	1.78504e6	1.62199
$262$	1.29218e6	1.16297
$263$	−387957.	−0.345855	−0.172927	−	0.984935i	$-0.555323\pi$
$263$	−387957.	−0.345855	−0.172927	+	0.984935i	$0.555323\pi$
$264$	129312.	0.114190
$265$	309137.	0.270418
$266$	386424.	0.334858
$267$	148201.	0.127225
$268$	−4.22668e6	−3.59470
$269$	1.83809e6	1.54877	0.774384	−	0.632716i	$-0.218060\pi$
$269$	1.83809e6	1.54877	0.774384	+	0.632716i	$0.218060\pi$
$270$	−382173.	−0.319044
$271$	−103775.	−0.0858357	−0.0429179	−	0.999079i	$-0.513665\pi$
$271$	−103775.	−0.0858357	−0.0429179	+	0.999079i	$0.513665\pi$
$272$	−594886.	−0.487542
$273$	98003.5	0.0795857
$274$	1.44098e6	1.15953
$275$	−75625.0	−0.0603023
$276$	657533.	0.519571
$277$	1.11131e6	0.870236	0.435118	−	0.900373i	$-0.356707\pi$
$277$	1.11131e6	0.870236	0.435118	+	0.900373i	$0.356707\pi$
$278$	3.13104e6	2.42983
$279$	−668373.	−0.514053
$280$	−889315.	−0.677892
$281$	−1.47380e6	−1.11345	−0.556726	−	0.830696i	$-0.687943\pi$
$281$	−1.47380e6	−1.11345	−0.556726	+	0.830696i	$0.687943\pi$
$282$	−72100.6	−0.0539903
$283$	413404.	0.306838	0.153419	−	0.988161i	$-0.450972\pi$
$283$	413404.	0.306838	0.153419	+	0.988161i	$0.450972\pi$
$284$	1.52344e6	1.12081
$285$	−29433.1	−0.0214646
$286$	−330287.	−0.238768
$287$	1.39477e6	0.999532
$288$	184164.	0.130835
$289$	−1.14936e6	−0.809490
$290$	−1.89376e6	−1.32230
$291$	−361668.	−0.250367
$292$	−2.67975e6	−1.83923
$293$	2.79344e6	1.90095	0.950474	−	0.310804i	$-0.100598\pi$
$293$	2.79344e6	1.90095	0.950474	+	0.310804i	$0.100598\pi$
$294$	161522.	0.108984
$295$	595876.	0.398659
$296$	1.14247e6	0.757909
$297$	187586.	0.123398
$298$	702009.	0.457933
$299$	−855594.	−0.553465
$300$	132963.	0.0852957
$301$	2.02278e6	1.28686
$302$	2.84584e6	1.79553
$303$	107002.	0.0669556
$304$	412914.	0.256257
$305$	376667.	0.231850
$306$	−1.19167e6	−0.727532
$307$	−1.10600e6	−0.669743	−0.334872	−	0.942264i	$-0.608693\pi$
$307$	−1.10600e6	−0.669743	−0.334872	+	0.942264i	$0.608693\pi$
$308$	856839.	0.514662
$309$	−281738.	−0.167861
$310$	709079.	0.419074
$311$	1.12923e6	0.662036	0.331018	−	0.943624i	$-0.392608\pi$
$311$	1.12923e6	0.662036	0.331018	+	0.943624i	$0.392608\pi$
$312$	295838.	0.172055
$313$	1.07547e6	0.620494	0.310247	−	0.950656i	$-0.399588\pi$
$313$	1.07547e6	0.620494	0.310247	+	0.950656i	$0.399588\pi$
$314$	2.59135e6	1.48321
$315$	−630610.	−0.358084
$316$	5.30538e6	2.98881
$317$	2.76185e6	1.54366	0.771830	−	0.635828i	$-0.219341\pi$
$317$	2.76185e6	1.54366	0.771830	+	0.635828i	$0.219341\pi$
$318$	397653.	0.220514
$319$	929533.	0.511432
$320$	719665.	0.392876
$321$	−143506.	−0.0777335
$322$	3.30844e6	1.77821
$323$	−187754.	−0.100134
$324$	3.35349e6	1.77474
$325$	−173014.	−0.0908600
$326$	−227024.	−0.118312
$327$	302403.	0.156393
$328$	4.21030e6	2.16087
$329$	−243387.	−0.123967
$330$	−97279.0	−0.0491738
$331$	−1.26241e6	−0.633328	−0.316664	−	0.948538i	$-0.602563\pi$
$331$	−1.26241e6	−0.633328	−0.316664	+	0.948538i	$0.602563\pi$
$332$	−7.85081e6	−3.90903
$333$	810125.	0.400351
$334$	4.64580e6	2.27874
$335$	1.61986e6	0.788616
$336$	−404942.	−0.195679
$337$	−1.95370e6	−0.937093	−0.468547	−	0.883439i	$-0.655222\pi$
$337$	−1.95370e6	−0.937093	−0.468547	+	0.883439i	$0.655222\pi$
$338$	2.90556e6	1.38337
$339$	37123.5	0.0175448
$340$	848171.	0.397911
$341$	−348045.	−0.162087
$342$	827144.	0.382398
$343$	2.36973e6	1.08759
$344$	6.10604e6	2.78204
$345$	−251997.	−0.113985
$346$	−6.34998e6	−2.85156
$347$	−735554.	−0.327937	−0.163969	−	0.986466i	$-0.552430\pi$
$347$	−735554.	−0.327937	−0.163969	+	0.986466i	$0.552430\pi$
$348$	−1.63429e6	−0.723406
$349$	−1.13505e6	−0.498829	−0.249415	−	0.968397i	$-0.580238\pi$
$349$	−1.13505e6	−0.498829	−0.249415	+	0.968397i	$0.580238\pi$
$350$	669017.	0.291922
$351$	429157.	0.185929
$352$	95900.4	0.0412538
$353$	−2.65399e6	−1.13361	−0.566804	−	0.823853i	$-0.691820\pi$
$353$	−2.65399e6	−1.13361	−0.566804	+	0.823853i	$0.691820\pi$
$354$	766496.	0.325089
$355$	−583855.	−0.245886
$356$	2.96431e6	1.23965
$357$	184129.	0.0764630
$358$	944489.	0.389484
$359$	−3.06168e6	−1.25379	−0.626893	−	0.779105i	$-0.715674\pi$
$359$	−3.06168e6	−1.25379	−0.626893	+	0.779105i	$0.715674\pi$
$360$	−1.90359e6	−0.774134
$361$	130321.	0.0526316
$362$	−2.82969e6	−1.13492
$363$	47748.5	0.0190192
$364$	1.96027e6	0.775463
$365$	1.02700e6	0.403497
$366$	484519.	0.189064
$367$	−1.93575e6	−0.750211	−0.375105	−	0.926982i	$-0.622394\pi$
$367$	−1.93575e6	−0.750211	−0.375105	+	0.926982i	$0.622394\pi$
$368$	3.53524e6	1.36082
$369$	2.98551e6	1.14144
$370$	−859464.	−0.326380
$371$	1.34234e6	0.506323
$372$	611928.	0.229268
$373$	−2.41416e6	−0.898449	−0.449225	−	0.893419i	$-0.648300\pi$
$373$	−2.41416e6	−0.898449	−0.449225	+	0.893419i	$0.648300\pi$
$374$	−620543.	−0.229400
$375$	−50957.6	−0.0187124
$376$	−734698.	−0.268003
$377$	2.12657e6	0.770597
$378$	−1.65948e6	−0.597369
$379$	593688.	0.212305	0.106152	−	0.994350i	$-0.466147\pi$
$379$	593688.	0.212305	0.106152	+	0.994350i	$0.466147\pi$
$380$	−588720.	−0.209146
$381$	−145615.	−0.0513918
$382$	1.27340e6	0.446484
$383$	3.43023e6	1.19488	0.597442	−	0.801912i	$-0.296184\pi$
$383$	3.43023e6	1.19488	0.597442	+	0.801912i	$0.296184\pi$
$384$	1.00844e6	0.348998
$385$	−328381.	−0.112908
$386$	−3.58836e6	−1.22582
$387$	4.32977e6	1.46956
$388$	−7.23408e6	−2.43952
$389$	5.51055e6	1.84638	0.923190	−	0.384344i	$-0.125572\pi$
$389$	5.51055e6	1.84638	0.923190	+	0.384344i	$0.125572\pi$
$390$	−222554.	−0.0740923
$391$	−1.60749e6	−0.531749
$392$	1.64589e6	0.540985
$393$	−427372.	−0.139580
$394$	4.09379e6	1.32857
$395$	−2.03327e6	−0.655695
$396$	1.83407e6	0.587730
$397$	−4.75040e6	−1.51270	−0.756352	−	0.654165i	$-0.773020\pi$
$397$	−4.75040e6	−1.51270	−0.756352	+	0.654165i	$0.773020\pi$
$398$	8.46637e6	2.67911
$399$	−127805.	−0.0401898
$400$	714879.	0.223400
$401$	−183872.	−0.0571023	−0.0285511	−	0.999592i	$-0.509089\pi$
$401$	−183872.	−0.0571023	−0.0285511	+	0.999592i	$0.509089\pi$
$402$	2.08368e6	0.643081
$403$	−796252.	−0.244224
$404$	2.14026e6	0.652399
$405$	−1.28521e6	−0.389347
$406$	−8.22312e6	−2.47583
$407$	421860.	0.126236
$408$	555819.	0.165304
$409$	2.90195e6	0.857792	0.428896	−	0.903354i	$-0.358903\pi$
$409$	2.90195e6	0.857792	0.428896	+	0.903354i	$0.358903\pi$
$410$	−3.16734e6	−0.930540
$411$	−476586.	−0.139167
$412$	−5.63532e6	−1.63559
$413$	2.58743e6	0.746437
$414$	7.08175e6	2.03067
$415$	3.00880e6	0.857576
$416$	219400.	0.0621588
$417$	−1.03555e6	−0.291630
$418$	430722.	0.120575
$419$	6.41323e6	1.78460	0.892302	−	0.451438i	$-0.149089\pi$
$419$	6.41323e6	1.78460	0.892302	+	0.451438i	$0.149089\pi$
$420$	577354.	0.159705
$421$	−522369.	−0.143639	−0.0718195	−	0.997418i	$-0.522881\pi$
$421$	−522369.	−0.143639	−0.0718195	+	0.997418i	$0.522881\pi$
$422$	9.10523e6	2.48891
$423$	−520972.	−0.141567
$424$	4.05204e6	1.09461
$425$	−325059.	−0.0872950
$426$	−751032.	−0.200509
$427$	1.63557e6	0.434110
$428$	−2.87041e6	−0.757416
$429$	109238.	0.0286571
$430$	−4.59347e6	−1.19804
$431$	−3.75858e6	−0.974610	−0.487305	−	0.873232i	$-0.662020\pi$
$431$	−3.75858e6	−0.974610	−0.487305	+	0.873232i	$0.662020\pi$
$432$	−1.77324e6	−0.457149
$433$	−4.36672e6	−1.11927	−0.559636	−	0.828739i	$-0.689059\pi$
$433$	−4.36672e6	−1.11927	−0.559636	+	0.828739i	$0.689059\pi$
$434$	3.07898e6	0.784662
$435$	626337.	0.158703
$436$	6.04867e6	1.52386
$437$	1.11577e6	0.279493
$438$	1.32107e6	0.329034
$439$	3.02656e6	0.749529	0.374765	−	0.927120i	$-0.377724\pi$
$439$	3.02656e6	0.749529	0.374765	+	0.927120i	$0.377724\pi$
$440$	−991263.	−0.244094
$441$	1.16709e6	0.285765
$442$	−1.41967e6	−0.345646
$443$	5.14703e6	1.24608	0.623042	−	0.782188i	$-0.285897\pi$
$443$	5.14703e6	1.24608	0.623042	+	0.782188i	$0.285897\pi$
$444$	−741709.	−0.178557
$445$	−1.13606e6	−0.271958
$446$	5.87852e6	1.39937
$447$	−232181.	−0.0549613
$448$	3.12494e6	0.735609
$449$	6.88709e6	1.61220	0.806102	−	0.591776i	$-0.201573\pi$
$449$	6.88709e6	1.61220	0.806102	+	0.591776i	$0.201573\pi$
$450$	1.43204e6	0.333367
$451$	1.55466e6	0.359910
$452$	742543.	0.170953
$453$	−941227.	−0.215501
$454$	7.63803e6	1.73917
$455$	−751265.	−0.170124
$456$	−385797.	−0.0868855
$457$	−2.58435e6	−0.578844	−0.289422	−	0.957202i	$-0.593463\pi$
$457$	−2.58435e6	−0.578844	−0.289422	+	0.957202i	$0.593463\pi$
$458$	−8.72298e6	−1.94313
$459$	806300.	0.178634
$460$	−5.04044e6	−1.11064
$461$	−1.26095e6	−0.276341	−0.138170	−	0.990408i	$-0.544122\pi$
$461$	−1.26095e6	−0.276341	−0.138170	+	0.990408i	$0.544122\pi$
$462$	−422407.	−0.0920717
$463$	6.07047e6	1.31604	0.658021	−	0.753000i	$-0.271394\pi$
$463$	6.07047e6	1.31604	0.658021	+	0.753000i	$0.271394\pi$
$464$	−8.78682e6	−1.89468
$465$	−234519.	−0.0502975
$466$	1.15614e7	2.46630
$467$	3.99265e6	0.847168	0.423584	−	0.905857i	$-0.360772\pi$
$467$	3.99265e6	0.847168	0.423584	+	0.905857i	$0.360772\pi$
$468$	4.19596e6	0.885558
$469$	7.03379e6	1.47658
$470$	552701.	0.115411
$471$	−857058.	−0.178016
$472$	7.81052e6	1.61371
$473$	2.25466e6	0.463371
$474$	−2.61546e6	−0.534690
$475$	225625.	0.0458831
$476$	3.68295e6	0.745037
$477$	2.87329e6	0.578207
$478$	−1.38157e7	−2.76569
$479$	−1.55563e6	−0.309790	−0.154895	−	0.987931i	$-0.549504\pi$
$479$	−1.55563e6	−0.309790	−0.154895	+	0.987931i	$0.549504\pi$
$480$	64619.5	0.0128015
$481$	965126.	0.190205
$482$	−1.15876e7	−2.27184
$483$	−1.09423e6	−0.213422
$484$	955064.	0.185319
$485$	2.77244e6	0.535189
$486$	−5.36793e6	−1.03090
$487$	−6.21129e6	−1.18675	−0.593375	−	0.804926i	$-0.702205\pi$
$487$	−6.21129e6	−1.18675	−0.593375	+	0.804926i	$0.702205\pi$
$488$	4.93721e6	0.938494
$489$	75085.5	0.0141999
$490$	−1.23817e6	−0.232965
$491$	−3.63983e6	−0.681362	−0.340681	−	0.940179i	$-0.610658\pi$
$491$	−3.63983e6	−0.681362	−0.340681	+	0.940179i	$0.610658\pi$
$492$	−2.73338e6	−0.509081
$493$	3.99541e6	0.740361
$494$	985401.	0.181675
$495$	−702901.	−0.128938
$496$	3.29005e6	0.600479
$497$	−2.53523e6	−0.460390
$498$	3.87031e6	0.699315
$499$	7.24831e6	1.30312	0.651561	−	0.758596i	$-0.274114\pi$
$499$	7.24831e6	1.30312	0.651561	+	0.758596i	$0.274114\pi$
$500$	−1.01925e6	−0.182329
$501$	−1.53654e6	−0.273496
$502$	−1.70656e7	−3.02247
$503$	−6.42041e6	−1.13147	−0.565735	−	0.824587i	$-0.691407\pi$
$503$	−6.42041e6	−1.13147	−0.565735	+	0.824587i	$0.691407\pi$
$504$	−8.26579e6	−1.44947
$505$	−820247.	−0.143125
$506$	3.68771e6	0.640296
$507$	−960978.	−0.166033
$508$	−2.91259e6	−0.500749
$509$	−3.10263e6	−0.530806	−0.265403	−	0.964138i	$-0.585505\pi$
$509$	−3.10263e6	−0.530806	−0.265403	+	0.964138i	$0.585505\pi$
$510$	−418134.	−0.0711852
$511$	4.45948e6	0.755496
$512$	1.10875e7	1.86921
$513$	−559657.	−0.0938920
$514$	1.69753e7	2.83406
$515$	2.15972e6	0.358822
$516$	−3.96412e6	−0.655424
$517$	−271288.	−0.0446379
$518$	−3.73198e6	−0.611104
$519$	2.10018e6	0.342245
$520$	−2.26780e6	−0.367787
$521$	−610826.	−0.0985878	−0.0492939	−	0.998784i	$-0.515697\pi$
$521$	−610826.	−0.0985878	−0.0492939	+	0.998784i	$0.515697\pi$
$522$	−1.76017e7	−2.82733
$523$	−3.62809e6	−0.579995	−0.289998	−	0.957027i	$-0.593654\pi$
$523$	−3.62809e6	−0.579995	−0.289998	+	0.957027i	$0.593654\pi$
$524$	−8.54828e6	−1.36004
$525$	−221269.	−0.0350366
$526$	3.82550e6	0.602870
$527$	−1.49600e6	−0.234641
$528$	−451363.	−0.0704598
$529$	3.11653e6	0.484208
$530$	−3.04828e6	−0.471374
$531$	5.53841e6	0.852411
$532$	−2.55635e6	−0.391599
$533$	3.55673e6	0.542291
$534$	−1.46135e6	−0.221770
$535$	1.10007e6	0.166164
$536$	2.12325e7	3.19219
$537$	−312378.	−0.0467460
$538$	−1.81247e7	−2.69970
$539$	607746.	0.0901053
$540$	2.52823e6	0.373106
$541$	−1.20647e7	−1.77224	−0.886122	−	0.463453i	$-0.846610\pi$
$541$	−1.20647e7	−1.77224	−0.886122	+	0.463453i	$0.846610\pi$
$542$	1.02328e6	0.149623
$543$	935884.	0.136214
$544$	412208.	0.0597199
$545$	−2.31813e6	−0.334308
$546$	−966377.	−0.138728
$547$	−1.28619e7	−1.83796	−0.918980	−	0.394304i	$-0.870986\pi$
$547$	−1.28619e7	−1.83796	−0.918980	+	0.394304i	$0.870986\pi$
$548$	−9.53267e6	−1.35601
$549$	3.50095e6	0.495742
$550$	745711.	0.105115
$551$	−2.77324e6	−0.389142
$552$	−3.30308e6	−0.461393
$553$	−8.82890e6	−1.22770
$554$	−1.09583e7	−1.51694
$555$	284257.	0.0391723
$556$	−2.07131e7	−2.84157
$557$	6.58955e6	0.899949	0.449975	−	0.893041i	$-0.351433\pi$
$557$	6.58955e6	0.899949	0.449975	+	0.893041i	$0.351433\pi$
$558$	6.59058e6	0.896062
$559$	5.15819e6	0.698180
$560$	3.10416e6	0.418287
$561$	205237.	0.0275327
$562$	1.45326e7	1.94089
$563$	4.24095e6	0.563887	0.281944	−	0.959431i	$-0.409021\pi$
$563$	4.24095e6	0.563887	0.281944	+	0.959431i	$0.409021\pi$
$564$	476975.	0.0631390
$565$	−284577.	−0.0375041
$566$	−4.07643e6	−0.534858
$567$	−5.58068e6	−0.729003
$568$	−7.65294e6	−0.995308
$569$	860436.	0.111413	0.0557067	−	0.998447i	$-0.482259\pi$
$569$	860436.	0.111413	0.0557067	+	0.998447i	$0.482259\pi$
$570$	290229.	0.0374157
$571$	157019.	0.0201540	0.0100770	−	0.999949i	$-0.496792\pi$
$571$	157019.	0.0201540	0.0100770	+	0.999949i	$0.496792\pi$
$572$	2.18498e6	0.279227
$573$	−421161.	−0.0535872
$574$	−1.37533e7	−1.74232
$575$	1.93173e6	0.243656
$576$	6.68897e6	0.840046
$577$	1.33818e6	0.167331	0.0836654	−	0.996494i	$-0.473337\pi$
$577$	1.33818e6	0.167331	0.0836654	+	0.996494i	$0.473337\pi$
$578$	1.13334e7	1.41105
$579$	1.18681e6	0.147124
$580$	1.25280e7	1.54636
$581$	1.30649e7	1.60570
$582$	3.56628e6	0.436423
$583$	1.49622e6	0.182316
$584$	1.34616e7	1.63329
$585$	−1.60809e6	−0.194276
$586$	−2.75451e7	−3.31360
$587$	1.32105e7	1.58243	0.791216	−	0.611537i	$-0.209448\pi$
$587$	1.32105e7	1.58243	0.791216	+	0.611537i	$0.209448\pi$
$588$	−1.06853e6	−0.127451
$589$	1.03838e6	0.123330
$590$	−5.87572e6	−0.694914
$591$	−1.35397e6	−0.159456
$592$	−3.98782e6	−0.467661
$593$	3.82075e6	0.446182	0.223091	−	0.974798i	$-0.428385\pi$
$593$	3.82075e6	0.446182	0.223091	+	0.974798i	$0.428385\pi$
$594$	−1.84972e6	−0.215099
$595$	−1.41148e6	−0.163449
$596$	−4.64408e6	−0.535530
$597$	−2.80015e6	−0.321548
$598$	8.43671e6	0.964761
$599$	−5.03443e6	−0.573301	−0.286651	−	0.958035i	$-0.592542\pi$
$599$	−5.03443e6	−0.573301	−0.286651	+	0.958035i	$0.592542\pi$
$600$	−667932.	−0.0757450
$601$	−1.12990e7	−1.27600	−0.638002	−	0.770034i	$-0.720239\pi$
$601$	−1.12990e7	−1.27600	−0.638002	+	0.770034i	$0.720239\pi$
$602$	−1.99459e7	−2.24317
$603$	1.50559e7	1.68622
$604$	−1.88264e7	−2.09979
$605$	−366025.	−0.0406558
$606$	−1.05511e6	−0.116712
$607$	1.52342e7	1.67822	0.839108	−	0.543965i	$-0.183077\pi$
$607$	1.52342e7	1.67822	0.839108	+	0.543965i	$0.183077\pi$
$608$	−286116.	−0.0313894
$609$	2.71969e6	0.297151
$610$	−3.71418e6	−0.404146
$611$	−620649.	−0.0672579
$612$	7.88338e6	0.850812
$613$	−4.71940e6	−0.507266	−0.253633	−	0.967301i	$-0.581626\pi$
$613$	−4.71940e6	−0.507266	−0.253633	+	0.967301i	$0.581626\pi$
$614$	1.09058e7	1.16745
$615$	1.04756e6	0.111684
$616$	−4.30428e6	−0.457035
$617$	905327.	0.0957399	0.0478699	−	0.998854i	$-0.484757\pi$
$617$	905327.	0.0957399	0.0478699	+	0.998854i	$0.484757\pi$
$618$	2.77812e6	0.292603
$619$	598020.	0.0627320	0.0313660	−	0.999508i	$-0.490014\pi$
$619$	598020.	0.0627320	0.0313660	+	0.999508i	$0.490014\pi$
$620$	−4.69085e6	−0.490086
$621$	−4.79161e6	−0.498601
$622$	−1.11349e7	−1.15401
$623$	−4.93303e6	−0.509206
$624$	−1.03262e6	−0.106165
$625$	390625.	0.0400000
$626$	−1.06048e7	−1.08160
$627$	−142456.	−0.0144715
$628$	−1.71429e7	−1.73454
$629$	1.81328e6	0.182742
$630$	6.21822e6	0.624187
$631$	1.41547e6	0.141523	0.0707613	−	0.997493i	$-0.477457\pi$
$631$	1.41547e6	0.141523	0.0707613	+	0.997493i	$0.477457\pi$
$632$	−2.66513e7	−2.65415
$633$	−3.01144e6	−0.298721
$634$	−2.72336e7	−2.69080
$635$	1.11624e6	0.109856
$636$	−2.63064e6	−0.257880
$637$	1.39039e6	0.135765
$638$	−9.16579e6	−0.891494
$639$	−5.42667e6	−0.525753
$640$	−7.73041e6	−0.746023
$641$	1.06209e7	1.02097	0.510487	−	0.859885i	$-0.329465\pi$
$641$	1.06209e7	1.02097	0.510487	+	0.859885i	$0.329465\pi$
$642$	1.41506e6	0.135500
$643$	−1.15844e7	−1.10496	−0.552479	−	0.833527i	$-0.686318\pi$
$643$	−1.15844e7	−1.10496	−0.552479	+	0.833527i	$0.686318\pi$
$644$	−2.18867e7	−2.07953
$645$	1.51923e6	0.143789
$646$	1.85137e6	0.174547
$647$	2.12834e6	0.199885	0.0999425	−	0.994993i	$-0.468134\pi$
$647$	2.12834e6	0.199885	0.0999425	+	0.994993i	$0.468134\pi$
$648$	−1.68461e7	−1.57602
$649$	2.88404e6	0.268776
$650$	1.70603e6	0.158381
$651$	−1.01833e6	−0.0941755
$652$	1.50186e6	0.138360
$653$	1.06383e7	0.976311	0.488156	−	0.872757i	$-0.337670\pi$
$653$	1.06383e7	0.976311	0.488156	+	0.872757i	$0.337670\pi$
$654$	−2.98189e6	−0.272614
$655$	3.27610e6	0.298369
$656$	−1.46961e7	−1.33334
$657$	9.54556e6	0.862756
$658$	2.39995e6	0.216091
$659$	−2.73333e6	−0.245176	−0.122588	−	0.992458i	$-0.539119\pi$
$659$	−2.73333e6	−0.245176	−0.122588	+	0.992458i	$0.539119\pi$
$660$	643540.	0.0575064
$661$	1.83491e7	1.63347	0.816736	−	0.577011i	$-0.195781\pi$
$661$	1.83491e7	1.63347	0.816736	+	0.577011i	$0.195781\pi$
$662$	1.24481e7	1.10397
$663$	469538.	0.0414846
$664$	3.94381e7	3.47133
$665$	979714.	0.0859103
$666$	−7.98834e6	−0.697865
$667$	−2.37436e7	−2.06648
$668$	−3.07339e7	−2.66487
$669$	−1.94425e6	−0.167953
$670$	−1.59729e7	−1.37466
$671$	1.82307e6	0.156314
$672$	280592.	0.0239691
$673$	−1.66203e7	−1.41449	−0.707245	−	0.706969i	$-0.750062\pi$
$673$	−1.66203e7	−1.41449	−0.707245	+	0.706969i	$0.750062\pi$
$674$	1.92647e7	1.63348
$675$	−968936.	−0.0818532
$676$	−1.92215e7	−1.61778
$677$	−1.41379e7	−1.18553	−0.592767	−	0.805374i	$-0.701964\pi$
$677$	−1.41379e7	−1.18553	−0.592767	+	0.805374i	$0.701964\pi$
$678$	−366061.	−0.0305830
$679$	1.20385e7	1.00207
$680$	−4.26074e6	−0.353356
$681$	−2.52618e6	−0.208736
$682$	3.43194e6	0.282539
$683$	783438.	0.0642618	0.0321309	−	0.999484i	$-0.489771\pi$
$683$	783438.	0.0642618	0.0321309	+	0.999484i	$0.489771\pi$
$684$	−5.47190e6	−0.447196
$685$	3.65336e6	0.297486
$686$	−2.33671e7	−1.89581
$687$	2.88502e6	0.233215
$688$	−2.13132e7	−1.71663
$689$	3.42304e6	0.274703
$690$	2.48485e6	0.198691
$691$	−256430.	−0.0204302	−0.0102151	−	0.999948i	$-0.503252\pi$
$691$	−256430.	−0.0204302	−0.0102151	+	0.999948i	$0.503252\pi$
$692$	4.20077e7	3.33476
$693$	−3.05215e6	−0.241420
$694$	7.25303e6	0.571637
$695$	7.93822e6	0.623392
$696$	8.20979e6	0.642405
$697$	6.68238e6	0.521014
$698$	1.11923e7	0.869525
$699$	−3.82380e6	−0.296007
$700$	−4.42582e6	−0.341388
$701$	−1.49662e7	−1.15032	−0.575158	−	0.818042i	$-0.695059\pi$
$701$	−1.49662e7	−1.15032	−0.575158	+	0.818042i	$0.695059\pi$
$702$	−4.23176e6	−0.324099
$703$	−1.25861e6	−0.0960510
$704$	3.48318e6	0.264877
$705$	−182799.	−0.0138516
$706$	2.61701e7	1.97603
$707$	−3.56170e6	−0.267984
$708$	−5.07068e6	−0.380175
$709$	1.00216e7	0.748724	0.374362	−	0.927283i	$-0.377862\pi$
$709$	1.00216e7	0.748724	0.374362	+	0.927283i	$0.377862\pi$
$710$	5.75718e6	0.428611
$711$	−1.88983e7	−1.40200
$712$	−1.48910e7	−1.10084
$713$	8.89031e6	0.654927
$714$	−1.81563e6	−0.133285
$715$	−837387.	−0.0612578
$716$	−6.24818e6	−0.455482
$717$	4.56938e6	0.331940
$718$	3.01901e7	2.18551
$719$	−8.77388e6	−0.632950	−0.316475	−	0.948601i	$-0.602499\pi$
$719$	−8.77388e6	−0.632950	−0.316475	+	0.948601i	$0.602499\pi$
$720$	6.64448e6	0.477672
$721$	9.37797e6	0.671847
$722$	−1.28505e6	−0.0917437
$723$	3.83247e6	0.272667
$724$	1.87195e7	1.32724
$725$	−4.80131e6	−0.339246
$726$	−470830.	−0.0331530
$727$	−1.34788e7	−0.945831	−0.472916	−	0.881108i	$-0.656798\pi$
$727$	−1.34788e7	−0.945831	−0.472916	+	0.881108i	$0.656798\pi$
$728$	−9.84729e6	−0.688634
$729$	−1.07169e7	−0.746878
$730$	−1.01269e7	−0.703348
$731$	9.69120e6	0.670786
$732$	−3.20529e6	−0.221101
$733$	2.45041e7	1.68453	0.842264	−	0.539065i	$-0.181222\pi$
$733$	2.45041e7	1.68453	0.842264	+	0.539065i	$0.181222\pi$
$734$	1.90877e7	1.30772
$735$	409511.	0.0279606
$736$	−2.44964e6	−0.166689
$737$	7.84012e6	0.531685
$738$	−2.94390e7	−1.98968
$739$	9.12928e6	0.614929	0.307465	−	0.951559i	$-0.400519\pi$
$739$	9.12928e6	0.614929	0.307465	+	0.951559i	$0.400519\pi$
$740$	5.68571e6	0.381685
$741$	−325909.	−0.0218048
$742$	−1.32363e7	−0.882587
$743$	2.41370e7	1.60402	0.802012	−	0.597307i	$-0.203763\pi$
$743$	2.41370e7	1.60402	0.802012	+	0.597307i	$0.203763\pi$
$744$	−3.07399e6	−0.203596
$745$	1.77983e6	0.117486
$746$	2.38051e7	1.56611
$747$	2.79654e7	1.83367
$748$	4.10515e6	0.268272
$749$	4.77677e6	0.311121
$750$	502474.	0.0326182
$751$	−1.52330e7	−0.985563	−0.492781	−	0.870153i	$-0.664020\pi$
$751$	−1.52330e7	−0.985563	−0.492781	+	0.870153i	$0.664020\pi$
$752$	2.56447e6	0.165369
$753$	5.64422e6	0.362758
$754$	−2.09694e7	−1.34325
$755$	7.21515e6	0.460658
$756$	1.09781e7	0.698593
$757$	−1.93637e7	−1.22814	−0.614071	−	0.789251i	$-0.710469\pi$
$757$	−1.93637e7	−1.22814	−0.614071	+	0.789251i	$0.710469\pi$
$758$	−5.85414e6	−0.370075
$759$	−1.21967e6	−0.0768487
$760$	2.95740e6	0.185728
$761$	2.95831e6	0.185175	0.0925874	−	0.995705i	$-0.470486\pi$
$761$	2.95831e6	0.185175	0.0925874	+	0.995705i	$0.470486\pi$
$762$	1.43586e6	0.0895827
$763$	−1.00658e7	−0.625949
$764$	−8.42405e6	−0.522141
$765$	−3.02128e6	−0.186654
$766$	−3.38242e7	−2.08284
$767$	6.59807e6	0.404976
$768$	−6.93968e6	−0.424557
$769$	−1.34425e6	−0.0819717	−0.0409858	−	0.999160i	$-0.513050\pi$
$769$	−1.34425e6	−0.0819717	−0.0409858	+	0.999160i	$0.513050\pi$
$770$	3.23804e6	0.196814
$771$	−5.61437e6	−0.340146
$772$	2.37385e7	1.43354
$773$	−7.91280e6	−0.476301	−0.238150	−	0.971228i	$-0.576541\pi$
$773$	−7.91280e6	−0.476301	−0.238150	+	0.971228i	$0.576541\pi$
$774$	−4.26943e7	−2.56164
$775$	1.79775e6	0.107517
$776$	3.63400e7	2.16636
$777$	1.23431e6	0.0733451
$778$	−5.43375e7	−3.21848
$779$	−4.63828e6	−0.273850
$780$	1.47228e6	0.0866473
$781$	−2.82586e6	−0.165776
$782$	1.58509e7	0.926908
$783$	1.19095e7	0.694209
$784$	−5.74499e6	−0.333810
$785$	6.56994e6	0.380529
$786$	4.21416e6	0.243307
$787$	−1.48434e7	−0.854275	−0.427137	−	0.904187i	$-0.640478\pi$
$787$	−1.48434e7	−0.854275	−0.427137	+	0.904187i	$0.640478\pi$
$788$	−2.70821e7	−1.55370
$789$	−1.26524e6	−0.0723568
$790$	2.00493e7	1.14296
$791$	−1.23570e6	−0.0702216
$792$	−9.21336e6	−0.521921
$793$	4.17079e6	0.235524
$794$	4.68420e7	2.63684
$795$	1.00818e6	0.0565746
$796$	−5.60085e7	−3.13308
$797$	−8.83710e6	−0.492793	−0.246396	−	0.969169i	$-0.579246\pi$
$797$	−8.83710e6	−0.492793	−0.246396	+	0.969169i	$0.579246\pi$
$798$	1.26024e6	0.0700560
$799$	−1.16608e6	−0.0646189
$800$	−495353.	−0.0273647
$801$	−1.05592e7	−0.581499
$802$	1.81309e6	0.0995368
$803$	4.97070e6	0.272038
$804$	−1.37844e7	−0.752052
$805$	8.38801e6	0.456215
$806$	7.85156e6	0.425714
$807$	5.99453e6	0.324020
$808$	−1.07515e7	−0.579349
$809$	2.63401e7	1.41497	0.707483	−	0.706731i	$-0.249831\pi$
$809$	2.63401e7	1.41497	0.707483	+	0.706731i	$0.249831\pi$
$810$	1.26730e7	0.678684
$811$	1.64281e7	0.877069	0.438535	−	0.898714i	$-0.355498\pi$
$811$	1.64281e7	0.877069	0.438535	+	0.898714i	$0.355498\pi$
$812$	5.43993e7	2.89536
$813$	−338439.	−0.0179578
$814$	−4.15981e6	−0.220045
$815$	−575583.	−0.0303538
$816$	−1.94009e6	−0.101999
$817$	−6.72672e6	−0.352572
$818$	−2.86151e7	−1.49524
$819$	−6.98268e6	−0.363758
$820$	2.09532e7	1.08822
$821$	1.49971e7	0.776516	0.388258	−	0.921551i	$-0.373077\pi$
$821$	1.49971e7	0.776516	0.388258	+	0.921551i	$0.373077\pi$
$822$	4.69944e6	0.242587
$823$	−3.78193e6	−0.194632	−0.0973158	−	0.995254i	$-0.531026\pi$
$823$	−3.78193e6	−0.194632	−0.0973158	+	0.995254i	$0.531026\pi$
$824$	2.83087e7	1.45245
$825$	−246635.	−0.0126159
$826$	−2.55137e7	−1.30114
$827$	3.71705e7	1.88988	0.944942	−	0.327239i	$-0.106118\pi$
$827$	3.71705e7	1.88988	0.944942	+	0.327239i	$0.106118\pi$
$828$	−4.68487e7	−2.37477
$829$	1.95984e7	0.990453	0.495226	−	0.868764i	$-0.335085\pi$
$829$	1.95984e7	0.990453	0.495226	+	0.868764i	$0.335085\pi$
$830$	−2.96686e7	−1.49487
$831$	3.62431e6	0.182063
$832$	7.96877e6	0.399101
$833$	2.61227e6	0.130438
$834$	1.02112e7	0.508348
$835$	1.17787e7	0.584628
$836$	−2.84941e6	−0.141006
$837$	−4.45928e6	−0.220014
$838$	−6.32386e7	−3.11080
$839$	−530306.	−0.0260089	−0.0130044	−	0.999915i	$-0.504140\pi$
$839$	−530306.	−0.0260089	−0.0130044	+	0.999915i	$0.504140\pi$
$840$	−2.90031e6	−0.141823
$841$	3.85034e7	1.87719
$842$	5.15089e6	0.250382
$843$	−4.80647e6	−0.232947
$844$	−6.02349e7	−2.91066
$845$	7.36656e6	0.354914
$846$	5.13711e6	0.246770
$847$	−1.58936e6	−0.0761227
$848$	−1.41437e7	−0.675419
$849$	1.34823e6	0.0641940
$850$	3.20528e6	0.152167
$851$	−1.07758e7	−0.510065
$852$	4.96838e6	0.234486
$853$	−2.41248e7	−1.13525	−0.567624	−	0.823288i	$-0.692137\pi$
$853$	−2.41248e7	−1.13525	−0.567624	+	0.823288i	$0.692137\pi$
$854$	−1.61278e7	−0.756711
$855$	2.09709e6	0.0981072
$856$	1.44193e7	0.672607
$857$	−1.71270e7	−0.796582	−0.398291	−	0.917259i	$-0.630396\pi$
$857$	−1.71270e7	−0.796582	−0.398291	+	0.917259i	$0.630396\pi$
$858$	−1.07716e6	−0.0499530
$859$	2.59337e7	1.19917	0.599587	−	0.800310i	$-0.295332\pi$
$859$	2.59337e7	1.19917	0.599587	+	0.800310i	$0.295332\pi$
$860$	3.03877e7	1.40104
$861$	4.54873e6	0.209114
$862$	3.70620e7	1.69887
$863$	−1.82577e7	−0.834485	−0.417243	−	0.908795i	$-0.637003\pi$
$863$	−1.82577e7	−0.834485	−0.417243	+	0.908795i	$0.637003\pi$
$864$	1.22871e6	0.0559971
$865$	−1.60993e7	−0.731589
$866$	4.30586e7	1.95104
$867$	−3.74839e6	−0.169355
$868$	−2.03687e7	−0.917623
$869$	−9.84101e6	−0.442069
$870$	−6.17608e6	−0.276640
$871$	1.79365e7	0.801112
$872$	−3.03852e7	−1.35323
$873$	2.57686e7	1.14434
$874$	−1.10022e7	−0.487192
$875$	1.69618e6	0.0748948
$876$	−8.73943e6	−0.384789
$877$	2.82150e7	1.23874	0.619372	−	0.785098i	$-0.287387\pi$
$877$	2.82150e7	1.23874	0.619372	+	0.785098i	$0.287387\pi$
$878$	−2.98438e7	−1.30653
$879$	9.11020e6	0.397700
$880$	3.46001e6	0.150616
$881$	4.36351e7	1.89407	0.947035	−	0.321130i	$-0.104063\pi$
$881$	4.36351e7	1.89407	0.947035	+	0.321130i	$0.104063\pi$
$882$	−1.15083e7	−0.498126
$883$	4.61050e6	0.198997	0.0994984	−	0.995038i	$-0.468276\pi$
$883$	4.61050e6	0.198997	0.0994984	+	0.995038i	$0.468276\pi$
$884$	9.39170e6	0.404216
$885$	1.94332e6	0.0834040
$886$	−5.07530e7	−2.17209
$887$	−2.31448e7	−0.987746	−0.493873	−	0.869534i	$-0.664419\pi$
$887$	−2.31448e7	−0.987746	−0.493873	+	0.869534i	$0.664419\pi$
$888$	3.72593e6	0.158563
$889$	4.84697e6	0.205691
$890$	1.12023e7	0.474058
$891$	−6.22043e6	−0.262498
$892$	−3.88888e7	−1.63649
$893$	809380.	0.0339644
$894$	2.28945e6	0.0958048
$895$	2.39459e6	0.0999250
$896$	−3.35671e7	−1.39683
$897$	−2.79034e6	−0.115791
$898$	−6.79111e7	−2.81028
$899$	−2.20968e7	−0.911864
$900$	−9.47351e6	−0.389856
$901$	6.43120e6	0.263925
$902$	−1.53299e7	−0.627370
$903$	6.59685e6	0.269226
$904$	−3.73013e6	−0.151811
$905$	−7.17420e6	−0.291173
$906$	9.28110e6	0.375646
$907$	−3.92019e6	−0.158230	−0.0791151	−	0.996865i	$-0.525209\pi$
$907$	−3.92019e6	−0.158230	−0.0791151	+	0.996865i	$0.525209\pi$
$908$	−5.05287e7	−2.03387
$909$	−7.62384e6	−0.306030
$910$	7.40795e6	0.296548
$911$	1.25369e7	0.500487	0.250244	−	0.968183i	$-0.419489\pi$
$911$	1.25369e7	0.500487	0.250244	+	0.968183i	$0.419489\pi$
$912$	1.34663e6	0.0536119
$913$	1.45626e7	0.578177
$914$	2.54834e7	1.00900
$915$	1.22842e6	0.0485058
$916$	5.77061e7	2.27239
$917$	1.42255e7	0.558658
$918$	−7.95063e6	−0.311383
$919$	−1.05285e7	−0.411222	−0.205611	−	0.978634i	$-0.565918\pi$
$919$	−1.05285e7	−0.411222	−0.205611	+	0.978634i	$0.565918\pi$
$920$	2.53204e7	0.986282
$921$	−3.60697e6	−0.140118
$922$	1.24337e7	0.481698
$923$	−6.46496e6	−0.249782
$924$	2.79439e6	0.107673
$925$	−2.17903e6	−0.0837353
$926$	−5.98587e7	−2.29403
$927$	2.00736e7	0.767231
$928$	6.08856e6	0.232084
$929$	−2.91547e7	−1.10833	−0.554164	−	0.832407i	$-0.686962\pi$
$929$	−2.91547e7	−1.10833	−0.554164	+	0.832407i	$0.686962\pi$
$930$	2.31251e6	0.0876750
$931$	−1.81319e6	−0.0685598
$932$	−7.64835e7	−2.88422
$933$	3.68274e6	0.138505
$934$	−3.93701e7	−1.47672
$935$	−1.57328e6	−0.0588543
$936$	−2.10782e7	−0.786401
$937$	3.09479e7	1.15155	0.575774	−	0.817609i	$-0.304701\pi$
$937$	3.09479e7	1.15155	0.575774	+	0.817609i	$0.304701\pi$
$938$	−6.93577e7	−2.57387
$939$	3.50741e6	0.129814
$940$	−3.65634e6	−0.134967
$941$	−3.16695e7	−1.16592	−0.582958	−	0.812502i	$-0.698105\pi$
$941$	−3.16695e7	−1.16592	−0.582958	+	0.812502i	$0.698105\pi$
$942$	8.45114e6	0.310304
$943$	−3.97115e7	−1.45424
$944$	−2.72627e7	−0.995723
$945$	−4.20733e6	−0.153260
$946$	−2.22324e7	−0.807716
$947$	4.62125e7	1.67450	0.837249	−	0.546821i	$-0.184162\pi$
$947$	4.62125e7	1.67450	0.837249	+	0.546821i	$0.184162\pi$
$948$	1.73023e7	0.625294
$949$	1.13719e7	0.409891
$950$	−2.22481e6	−0.0799803
$951$	9.00718e6	0.322952
$952$	−1.85011e7	−0.661614
$953$	−1.48391e7	−0.529266	−0.264633	−	0.964349i	$-0.585251\pi$
$953$	−1.48391e7	−0.529266	−0.264633	+	0.964349i	$0.585251\pi$
$954$	−2.83325e7	−1.00789
$955$	3.22849e6	0.114549
$956$	9.13967e7	3.23434
$957$	3.03147e6	0.106998
$958$	1.53395e7	0.540004
$959$	1.58637e7	0.557004
$960$	2.34703e6	0.0821941
$961$	−2.03555e7	−0.711005
$962$	−9.51676e6	−0.331552
$963$	1.02247e7	0.355292
$964$	7.66570e7	2.65680
$965$	−9.09769e6	−0.314494
$966$	1.07898e7	0.372023
$967$	6.34906e6	0.218345	0.109173	−	0.994023i	$-0.465180\pi$
$967$	6.34906e6	0.218345	0.109173	+	0.994023i	$0.465180\pi$
$968$	−4.79771e6	−0.164568
$969$	−612318.	−0.0209492
$970$	−2.73380e7	−0.932905
$971$	1.82826e7	0.622287	0.311144	−	0.950363i	$-0.399288\pi$
$971$	1.82826e7	0.622287	0.311144	+	0.950363i	$0.399288\pi$
$972$	3.55111e7	1.20559
$973$	3.44695e7	1.16722
$974$	6.12472e7	2.06866
$975$	−564248.	−0.0190089
$976$	−1.72334e7	−0.579089
$977$	−3.32189e7	−1.11339	−0.556697	−	0.830716i	$-0.687932\pi$
$977$	−3.32189e7	−1.11339	−0.556697	+	0.830716i	$0.687932\pi$
$978$	−740391.	−0.0247522
$979$	−5.49854e6	−0.183354
$980$	8.19103e6	0.272442
$981$	−2.15460e7	−0.714816
$982$	3.58911e7	1.18770
$983$	−4.12371e7	−1.36114	−0.680572	−	0.732681i	$-0.738269\pi$
$983$	−4.12371e7	−1.36114	−0.680572	+	0.732681i	$0.738269\pi$
$984$	1.37310e7	0.452079
$985$	1.03791e7	0.340855
$986$	−3.93973e7	−1.29055
$987$	−793754.	−0.0259354
$988$	−6.51884e6	−0.212460
$989$	−5.75921e7	−1.87229
$990$	6.93105e6	0.224756
$991$	3.60094e7	1.16475	0.582373	−	0.812922i	$-0.302124\pi$
$991$	3.60094e7	1.16475	0.582373	+	0.812922i	$0.302124\pi$
$992$	−2.27974e6	−0.0735539
$993$	−4.11706e6	−0.132500
$994$	2.49989e7	0.802520
$995$	2.14651e7	0.687345
$996$	−2.56037e7	−0.817814
$997$	3.05148e7	0.972238	0.486119	−	0.873893i	$-0.338412\pi$
$997$	3.05148e7	0.972238	0.486119	+	0.873893i	$0.338412\pi$
$998$	−7.14729e7	−2.27151
$999$	5.40503e6	0.171350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.4	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.4	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-9.86064 q^{2} +3.26128 q^{3} +65.2322 q^{4} -25.0000 q^{5} -32.1583 q^{6} -108.556 q^{7} -327.690 q^{8} -232.364 q^{9} +O(q^{10})\)	\(q-9.86064 q^{2} +3.26128 q^{3} +65.2322 q^{4} -25.0000 q^{5} -32.1583 q^{6} -108.556 q^{7} -327.690 q^{8} -232.364 q^{9} +246.516 q^{10} -121.000 q^{11} +212.741 q^{12} -276.822 q^{13} +1070.43 q^{14} -81.5321 q^{15} +1143.81 q^{16} -520.094 q^{17} +2291.26 q^{18} +361.000 q^{19} -1630.80 q^{20} -354.030 q^{21} +1193.14 q^{22} +3090.77 q^{23} -1068.69 q^{24} +625.000 q^{25} +2729.64 q^{26} -1550.30 q^{27} -7081.31 q^{28} -7682.09 q^{29} +803.958 q^{30} +2876.40 q^{31} -792.565 q^{32} -394.615 q^{33} +5128.45 q^{34} +2713.89 q^{35} -15157.6 q^{36} -3486.45 q^{37} -3559.69 q^{38} -902.796 q^{39} +8192.26 q^{40} -12848.4 q^{41} +3490.97 q^{42} -18633.6 q^{43} -7893.09 q^{44} +5809.10 q^{45} -30477.0 q^{46} +2242.05 q^{47} +3730.28 q^{48} -5022.69 q^{49} -6162.90 q^{50} -1696.17 q^{51} -18057.7 q^{52} -12365.5 q^{53} +15286.9 q^{54} +3025.00 q^{55} +35572.6 q^{56} +1177.32 q^{57} +75750.3 q^{58} -23835.1 q^{59} -5318.52 q^{60} -15066.7 q^{61} -28363.2 q^{62} +25224.4 q^{63} -28786.6 q^{64} +6920.56 q^{65} +3891.16 q^{66} -64794.4 q^{67} -33926.8 q^{68} +10079.9 q^{69} -26760.7 q^{70} +23354.2 q^{71} +76143.4 q^{72} -41080.2 q^{73} +34378.6 q^{74} +2038.30 q^{75} +23548.8 q^{76} +13135.2 q^{77} +8902.14 q^{78} +81330.7 q^{79} -28595.1 q^{80} +51408.5 q^{81} +126694. q^{82} -120352. q^{83} -23094.2 q^{84} +13002.3 q^{85} +183739. q^{86} -25053.5 q^{87} +39650.5 q^{88} +45442.4 q^{89} -57281.4 q^{90} +30050.6 q^{91} +201618. q^{92} +9380.77 q^{93} -22108.0 q^{94} -9025.00 q^{95} -2584.78 q^{96} -110897. q^{97} +49527.0 q^{98} +28116.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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