LMFDB - Embedded newform 471.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,6,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("471.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	471.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:	$75.5407791319$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.5389 q^{2} -9.00000 q^{3} +79.0692 q^{4} -79.1689 q^{5} +94.8504 q^{6} +161.660 q^{7} -496.059 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.5389 q^{2} -9.00000 q^{3} +79.0692 q^{4} -79.1689 q^{5} +94.8504 q^{6} +161.660 q^{7} -496.059 q^{8} +81.0000 q^{9} +834.356 q^{10} +109.929 q^{11} -711.623 q^{12} -181.774 q^{13} -1703.73 q^{14} +712.520 q^{15} +2697.72 q^{16} +455.460 q^{17} -853.654 q^{18} -1089.34 q^{19} -6259.82 q^{20} -1454.94 q^{21} -1158.53 q^{22} -444.765 q^{23} +4464.53 q^{24} +3142.72 q^{25} +1915.70 q^{26} -729.000 q^{27} +12782.4 q^{28} -2059.79 q^{29} -7509.21 q^{30} +265.397 q^{31} -12557.2 q^{32} -989.360 q^{33} -4800.06 q^{34} -12798.5 q^{35} +6404.60 q^{36} -2458.75 q^{37} +11480.5 q^{38} +1635.96 q^{39} +39272.5 q^{40} -11942.9 q^{41} +15333.6 q^{42} +13431.1 q^{43} +8691.99 q^{44} -6412.68 q^{45} +4687.35 q^{46} -20537.1 q^{47} -24279.5 q^{48} +9327.08 q^{49} -33120.9 q^{50} -4099.14 q^{51} -14372.7 q^{52} -7918.14 q^{53} +7682.88 q^{54} -8702.96 q^{55} -80193.1 q^{56} +9804.04 q^{57} +21708.0 q^{58} +49244.6 q^{59} +56338.4 q^{60} +40099.6 q^{61} -2797.01 q^{62} +13094.5 q^{63} +46012.7 q^{64} +14390.8 q^{65} +10426.8 q^{66} +55600.6 q^{67} +36012.8 q^{68} +4002.88 q^{69} +134882. q^{70} +4109.05 q^{71} -40180.8 q^{72} +18672.2 q^{73} +25912.6 q^{74} -28284.5 q^{75} -86133.1 q^{76} +17771.2 q^{77} -17241.3 q^{78} -3418.52 q^{79} -213576. q^{80} +6561.00 q^{81} +125866. q^{82} +51751.3 q^{83} -115041. q^{84} -36058.3 q^{85} -141549. q^{86} +18538.1 q^{87} -54531.2 q^{88} +43865.4 q^{89} +67582.9 q^{90} -29385.6 q^{91} -35167.2 q^{92} -2388.58 q^{93} +216439. q^{94} +86241.7 q^{95} +113015. q^{96} -51613.3 q^{97} -98297.5 q^{98} +8904.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) $ 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * 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 $

$2$	−10.5389	−1.86304	−0.931519	−	0.363692i	$-0.881516\pi$
$2$	−10.5389	−1.86304	−0.931519	+	0.363692i	$0.881516\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	79.0692	2.47091
$5$	−79.1689	−1.41622	−0.708108	−	0.706104i	$-0.750451\pi$
$5$	−79.1689	−1.41622	−0.708108	+	0.706104i	$0.750451\pi$
$6$	94.8504	1.07563
$7$	161.660	1.24698	0.623489	−	0.781832i	$-0.285715\pi$
$7$	161.660	1.24698	0.623489	+	0.781832i	$0.285715\pi$
$8$	−496.059	−2.74037
$9$	81.0000	0.333333
$10$	834.356	2.63847
$11$	109.929	0.273924	0.136962	−	0.990576i	$-0.456266\pi$
$11$	109.929	0.273924	0.136962	+	0.990576i	$0.456266\pi$
$12$	−711.623	−1.42658
$13$	−181.774	−0.298314	−0.149157	−	0.988814i	$-0.547656\pi$
$13$	−181.774	−0.298314	−0.149157	+	0.988814i	$0.547656\pi$
$14$	−1703.73	−2.32317
$15$	712.520	0.817653
$16$	2697.72	2.63449
$17$	455.460	0.382233	0.191116	−	0.981567i	$-0.438789\pi$
$17$	455.460	0.382233	0.191116	+	0.981567i	$0.438789\pi$
$18$	−853.654	−0.621013
$19$	−1089.34	−0.692275	−0.346138	−	0.938184i	$-0.612507\pi$
$19$	−1089.34	−0.692275	−0.346138	+	0.938184i	$0.612507\pi$
$20$	−6259.82	−3.49935
$21$	−1454.94	−0.719943
$22$	−1158.53	−0.510331
$23$	−444.765	−0.175312	−0.0876558	−	0.996151i	$-0.527938\pi$
$23$	−444.765	−0.175312	−0.0876558	+	0.996151i	$0.527938\pi$
$24$	4464.53	1.58215
$25$	3142.72	1.00567
$26$	1915.70	0.555770
$27$	−729.000	−0.192450
$28$	12782.4	3.08117
$29$	−2059.79	−0.454808	−0.227404	−	0.973800i	$-0.573024\pi$
$29$	−2059.79	−0.454808	−0.227404	+	0.973800i	$0.573024\pi$
$30$	−7509.21	−1.52332
$31$	265.397	0.0496012	0.0248006	−	0.999692i	$-0.492105\pi$
$31$	265.397	0.0496012	0.0248006	+	0.999692i	$0.492105\pi$
$32$	−12557.2	−2.16780
$33$	−989.360	−0.158150
$34$	−4800.06	−0.712114
$35$	−12798.5	−1.76599
$36$	6404.60	0.823637
$37$	−2458.75	−0.295264	−0.147632	−	0.989042i	$-0.547165\pi$
$37$	−2458.75	−0.295264	−0.147632	+	0.989042i	$0.547165\pi$
$38$	11480.5	1.28973
$39$	1635.96	0.172231
$40$	39272.5	3.88095
$41$	−11942.9	−1.10956	−0.554781	−	0.831996i	$-0.687198\pi$
$41$	−11942.9	−1.10956	−0.554781	+	0.831996i	$0.687198\pi$
$42$	15333.6	1.34128
$43$	13431.1	1.10774	0.553872	−	0.832602i	$-0.313150\pi$
$43$	13431.1	1.10774	0.553872	+	0.832602i	$0.313150\pi$
$44$	8691.99	0.676842
$45$	−6412.68	−0.472072
$46$	4687.35	0.326612
$47$	−20537.1	−1.35611	−0.678053	−	0.735013i	$-0.737176\pi$
$47$	−20537.1	−1.35611	−0.678053	+	0.735013i	$0.737176\pi$
$48$	−24279.5	−1.52103
$49$	9327.08	0.554952
$50$	−33120.9	−1.87360
$51$	−4099.14	−0.220682
$52$	−14372.7	−0.737107
$53$	−7918.14	−0.387198	−0.193599	−	0.981081i	$-0.562016\pi$
$53$	−7918.14	−0.387198	−0.193599	+	0.981081i	$0.562016\pi$
$54$	7682.88	0.358542
$55$	−8702.96	−0.387936
$56$	−80193.1	−3.41717
$57$	9804.04	0.399685
$58$	21708.0	0.847325
$59$	49244.6	1.84174	0.920870	−	0.389870i	$-0.127480\pi$
$59$	49244.6	1.84174	0.920870	+	0.389870i	$0.127480\pi$
$60$	56338.4	2.02035
$61$	40099.6	1.37980	0.689900	−	0.723905i	$-0.257655\pi$
$61$	40099.6	1.37980	0.689900	+	0.723905i	$0.257655\pi$
$62$	−2797.01	−0.0924090
$63$	13094.5	0.415659
$64$	46012.7	1.40420
$65$	14390.8	0.422477
$66$	10426.8	0.294640
$67$	55600.6	1.51319	0.756593	−	0.653886i	$-0.226862\pi$
$67$	55600.6	1.51319	0.756593	+	0.653886i	$0.226862\pi$
$68$	36012.8	0.944464
$69$	4002.88	0.101216
$70$	134882.	3.29011
$71$	4109.05	0.0967377	0.0483688	−	0.998830i	$-0.484598\pi$
$71$	4109.05	0.0967377	0.0483688	+	0.998830i	$0.484598\pi$
$72$	−40180.8	−0.913455
$73$	18672.2	0.410098	0.205049	−	0.978752i	$-0.434265\pi$
$73$	18672.2	0.410098	0.205049	+	0.978752i	$0.434265\pi$
$74$	25912.6	0.550088
$75$	−28284.5	−0.580624
$76$	−86133.1	−1.71055
$77$	17771.2	0.341577
$78$	−17241.3	−0.320874
$79$	−3418.52	−0.0616269	−0.0308135	−	0.999525i	$-0.509810\pi$
$79$	−3418.52	−0.0616269	−0.0308135	+	0.999525i	$0.509810\pi$
$80$	−213576.	−3.73101
$81$	6561.00	0.111111
$82$	125866.	2.06716
$83$	51751.3	0.824567	0.412283	−	0.911056i	$-0.364731\pi$
$83$	51751.3	0.824567	0.412283	+	0.911056i	$0.364731\pi$
$84$	−115041.	−1.77891
$85$	−36058.3	−0.541325
$86$	−141549.	−2.06377
$87$	18538.1	0.262584
$88$	−54531.2	−0.750652
$89$	43865.4	0.587012	0.293506	−	0.955957i	$-0.405178\pi$
$89$	43865.4	0.587012	0.293506	+	0.955957i	$0.405178\pi$
$90$	67582.9	0.879489
$91$	−29385.6	−0.371990
$92$	−35167.2	−0.433179
$93$	−2388.58	−0.0286373
$94$	216439.	2.52648
$95$	86241.7	0.980412
$96$	113015.	1.25158
$97$	−51613.3	−0.556970	−0.278485	−	0.960441i	$-0.589832\pi$
$97$	−51613.3	−0.556970	−0.278485	+	0.960441i	$0.589832\pi$
$98$	−98297.5	−1.03390
$99$	8904.24	0.0913080
$100$	248492.	2.48492
$101$	148976.	1.45316	0.726581	−	0.687080i	$-0.241108\pi$
$101$	148976.	1.45316	0.726581	+	0.687080i	$0.241108\pi$
$102$	43200.6	0.411139
$103$	−14005.0	−0.130074	−0.0650369	−	0.997883i	$-0.520717\pi$
$103$	−14005.0	−0.130074	−0.0650369	+	0.997883i	$0.520717\pi$
$104$	90170.6	0.817488
$105$	115186.	1.01959
$106$	83448.8	0.721366
$107$	−43625.6	−0.368368	−0.184184	−	0.982892i	$-0.558964\pi$
$107$	−43625.6	−0.368368	−0.184184	+	0.982892i	$0.558964\pi$
$108$	−57641.4	−0.475527
$109$	64863.4	0.522918	0.261459	−	0.965215i	$-0.415796\pi$
$109$	64863.4	0.522918	0.261459	+	0.965215i	$0.415796\pi$
$110$	91719.9	0.722740
$111$	22128.8	0.170471
$112$	436115.	3.28515
$113$	−61757.7	−0.454983	−0.227491	−	0.973780i	$-0.573052\pi$
$113$	−61757.7	−0.454983	−0.227491	+	0.973780i	$0.573052\pi$
$114$	−103324.	−0.744629
$115$	35211.5	0.248279
$116$	−162866.	−1.12379
$117$	−14723.7	−0.0994379
$118$	−518985.	−3.43123
$119$	73629.8	0.476636
$120$	−353452.	−2.24067
$121$	−148967.	−0.924966
$122$	−422608.	−2.57062
$123$	107487.	0.640606
$124$	20984.8	0.122560
$125$	−1402.77	−0.00802993
$126$	−138002.	−0.774389
$127$	119980.	0.660084	0.330042	−	0.943966i	$-0.392937\pi$
$127$	119980.	0.660084	0.330042	+	0.943966i	$0.392937\pi$
$128$	−83093.6	−0.448273
$129$	−120880.	−0.639556
$130$	−151664.	−0.787090
$131$	−227336.	−1.15742	−0.578709	−	0.815534i	$-0.696443\pi$
$131$	−227336.	−1.15742	−0.578709	+	0.815534i	$0.696443\pi$
$132$	−78227.9	−0.390775
$133$	−176103.	−0.863251
$134$	−585971.	−2.81912
$135$	57714.1	0.272551
$136$	−225935.	−1.04746
$137$	247196.	1.12523	0.562614	−	0.826719i	$-0.309796\pi$
$137$	247196.	1.12523	0.562614	+	0.826719i	$0.309796\pi$
$138$	−42186.1	−0.188570
$139$	−422431.	−1.85446	−0.927232	−	0.374488i	$-0.877819\pi$
$139$	−422431.	−1.85446	−0.927232	+	0.374488i	$0.877819\pi$
$140$	−1.01197e6	−4.36361
$141$	184834.	0.782949
$142$	−43305.0	−0.180226
$143$	−19982.2	−0.0817153
$144$	218515.	0.878164
$145$	163072.	0.644107
$146$	−196785.	−0.764028
$147$	−83943.8	−0.320402
$148$	−194411.	−0.729571
$149$	−289463.	−1.06814	−0.534069	−	0.845441i	$-0.679338\pi$
$149$	−289463.	−1.06814	−0.534069	+	0.845441i	$0.679338\pi$
$150$	298088.	1.08172
$151$	−272896.	−0.973992	−0.486996	−	0.873404i	$-0.661907\pi$
$151$	−272896.	−0.973992	−0.486996	+	0.873404i	$0.661907\pi$
$152$	540376.	1.89709
$153$	36892.3	0.127411
$154$	−187289.	−0.636371
$155$	−21011.2	−0.0702461
$156$	129354.	0.425569
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	36027.6	0.114813
$159$	71263.3	0.223549
$160$	994142.	3.07007
$161$	−71900.8	−0.218610
$162$	−69146.0	−0.207004
$163$	−389487.	−1.14822	−0.574108	−	0.818779i	$-0.694651\pi$
$163$	−389487.	−1.14822	−0.574108	+	0.818779i	$0.694651\pi$
$164$	−944319.	−2.74163
$165$	78326.6	0.223975
$166$	−545403.	−1.53620
$167$	127438.	0.353597	0.176798	−	0.984247i	$-0.443426\pi$
$167$	127438.	0.353597	0.176798	+	0.984247i	$0.443426\pi$
$168$	721738.	1.97291
$169$	−338251.	−0.911009
$170$	380016.	1.00851
$171$	−88236.4	−0.230758
$172$	1.06198e6	2.73714
$173$	313003.	0.795122	0.397561	−	0.917576i	$-0.369857\pi$
$173$	313003.	0.795122	0.397561	+	0.917576i	$0.369857\pi$
$174$	−195372.	−0.489204
$175$	508053.	1.25405
$176$	296558.	0.721651
$177$	−443201.	−1.06333
$178$	−462295.	−1.09363
$179$	104652.	0.244126	0.122063	−	0.992522i	$-0.461049\pi$
$179$	104652.	0.244126	0.122063	+	0.992522i	$0.461049\pi$
$180$	−507046.	−1.16645
$181$	239363.	0.543077	0.271538	−	0.962428i	$-0.412468\pi$
$181$	239363.	0.543077	0.271538	+	0.962428i	$0.412468\pi$
$182$	309693.	0.693032
$183$	−360897.	−0.796627
$184$	220630.	0.480418
$185$	194657.	0.418157
$186$	25173.1	0.0533523
$187$	50068.2	0.104703
$188$	−1.62385e6	−3.35082
$189$	−117850.	−0.239981
$190$	−908896.	−1.82654
$191$	−254439.	−0.504662	−0.252331	−	0.967641i	$-0.581197\pi$
$191$	−254439.	−0.504662	−0.252331	+	0.967641i	$0.581197\pi$
$192$	−414114.	−0.810713
$193$	518.871	0.00100269	0.000501344	−	1.00000i	$-0.499840\pi$
$193$	518.871	0.00100269	0.000501344		1.00000i	$0.499840\pi$
$194$	543949.	1.03766
$195$	−129518.	−0.243917
$196$	737485.	1.37124
$197$	332020.	0.609536	0.304768	−	0.952427i	$-0.401421\pi$
$197$	332020.	0.609536	0.304768	+	0.952427i	$0.401421\pi$
$198$	−93841.3	−0.170110
$199$	−377726.	−0.676152	−0.338076	−	0.941119i	$-0.609776\pi$
$199$	−377726.	−0.676152	−0.338076	+	0.941119i	$0.609776\pi$
$200$	−1.55897e6	−2.75590
$201$	−500405.	−0.873638
$202$	−1.57005e6	−2.70730
$203$	−332987.	−0.567136
$204$	−324116.	−0.545286
$205$	945510.	1.57138
$206$	147598.	0.242333
$207$	−36025.9	−0.0584372
$208$	−490375.	−0.785905
$209$	−119750.	−0.189631
$210$	−1.21394e6	−1.89954
$211$	−1.05552e6	−1.63215	−0.816075	−	0.577945i	$-0.803855\pi$
$211$	−1.05552e6	−1.63215	−0.816075	+	0.577945i	$0.803855\pi$
$212$	−626081.	−0.956733
$213$	−36981.5	−0.0558515
$214$	459768.	0.686285
$215$	−1.06332e6	−1.56880
$216$	361627.	0.527383
$217$	42904.2	0.0618516
$218$	−683591.	−0.974216
$219$	−168050.	−0.236770
$220$	−688136.	−0.958556
$221$	−82790.7	−0.114025
$222$	−233214.	−0.317593
$223$	798770.	1.07562	0.537811	−	0.843066i	$-0.319251\pi$
$223$	798770.	1.07562	0.537811	+	0.843066i	$0.319251\pi$
$224$	−2.03001e6	−2.70319
$225$	254560.	0.335223
$226$	650860.	0.847650
$227$	−393997.	−0.507490	−0.253745	−	0.967271i	$-0.581662\pi$
$227$	−393997.	−0.507490	−0.253745	+	0.967271i	$0.581662\pi$
$228$	775198.	0.987587
$229$	−133197.	−0.167844	−0.0839218	−	0.996472i	$-0.526745\pi$
$229$	−133197.	−0.167844	−0.0839218	+	0.996472i	$0.526745\pi$
$230$	−371092.	−0.462554
$231$	−159940.	−0.197210
$232$	1.02178e6	1.24634
$233$	−634505.	−0.765677	−0.382838	−	0.923815i	$-0.625053\pi$
$233$	−634505.	−0.765677	−0.382838	+	0.923815i	$0.625053\pi$
$234$	155172.	0.185257
$235$	1.62590e6	1.92054
$236$	3.89373e6	4.55078
$237$	30766.7	0.0355803
$238$	−775980.	−0.887990
$239$	−893354.	−1.01165	−0.505824	−	0.862637i	$-0.668811\pi$
$239$	−893354.	−1.01165	−0.505824	+	0.862637i	$0.668811\pi$
$240$	1.92218e6	2.15410
$241$	1.66784e6	1.84974	0.924872	−	0.380278i	$-0.124172\pi$
$241$	1.66784e6	1.84974	0.924872	+	0.380278i	$0.124172\pi$
$242$	1.56995e6	1.72325
$243$	−59049.0	−0.0641500
$244$	3.17065e6	3.40936
$245$	−738415.	−0.785933
$246$	−1.13279e6	−1.19347
$247$	198013.	0.206515
$248$	−131653.	−0.135925
$249$	−465761.	−0.476064
$250$	14783.7	0.0149601
$251$	−243169.	−0.243626	−0.121813	−	0.992553i	$-0.538871\pi$
$251$	−243169.	−0.243626	−0.121813	+	0.992553i	$0.538871\pi$
$252$	1.03537e6	1.02706
$253$	−48892.5	−0.0480221
$254$	−1.26446e6	−1.22976
$255$	324525.	0.312534
$256$	−596688.	−0.569046
$257$	1.93680e6	1.82916	0.914581	−	0.404403i	$-0.132521\pi$
$257$	1.93680e6	1.82916	0.914581	+	0.404403i	$0.132521\pi$
$258$	1.27394e6	1.19152
$259$	−397483.	−0.368187
$260$	1.13787e6	1.04390
$261$	−166843.	−0.151603
$262$	2.39588e6	2.15631
$263$	2.13643e6	1.90458	0.952291	−	0.305190i	$-0.0987201\pi$
$263$	2.13643e6	1.90458	0.952291	+	0.305190i	$0.0987201\pi$
$264$	490781.	0.433389
$265$	626871.	0.548357
$266$	1.85594e6	1.60827
$267$	−394789.	−0.338912
$268$	4.39629e6	3.73895
$269$	−784030.	−0.660620	−0.330310	−	0.943872i	$-0.607153\pi$
$269$	−784030.	−0.660620	−0.330310	+	0.943872i	$0.607153\pi$
$270$	−608246.	−0.507773
$271$	−1.52329e6	−1.25997	−0.629984	−	0.776608i	$-0.716939\pi$
$271$	−1.52329e6	−1.25997	−0.629984	+	0.776608i	$0.716939\pi$
$272$	1.22870e6	1.00699
$273$	264471.	0.214769
$274$	−2.60519e6	−2.09634
$275$	345476.	0.275477
$276$	316505.	0.250096
$277$	814246.	0.637611	0.318806	−	0.947820i	$-0.396718\pi$
$277$	814246.	0.637611	0.318806	+	0.947820i	$0.396718\pi$
$278$	4.45197e6	3.45494
$279$	21497.2	0.0165337
$280$	6.34880e6	4.83946
$281$	−291928.	−0.220551	−0.110276	−	0.993901i	$-0.535173\pi$
$281$	−291928.	−0.220551	−0.110276	+	0.993901i	$0.535173\pi$
$282$	−1.94795e6	−1.45866
$283$	−211496.	−0.156977	−0.0784886	−	0.996915i	$-0.525009\pi$
$283$	−211496.	−0.156977	−0.0784886	+	0.996915i	$0.525009\pi$
$284$	324899.	0.239030
$285$	−776176.	−0.566041
$286$	210591.	0.152239
$287$	−1.93070e6	−1.38360
$288$	−1.01713e6	−0.722599
$289$	−1.21241e6	−0.853898
$290$	−1.71860e6	−1.20000
$291$	464519.	0.321567
$292$	1.47639e6	1.01332
$293$	1.27608e6	0.868379	0.434190	−	0.900821i	$-0.357035\pi$
$293$	1.27608e6	0.868379	0.434190	+	0.900821i	$0.357035\pi$
$294$	884678.	0.596921
$295$	−3.89864e6	−2.60830
$296$	1.21969e6	0.809130
$297$	−80138.2	−0.0527167
$298$	3.05063e6	1.98998
$299$	80846.6	0.0522978
$300$	−2.23643e6	−1.43467
$301$	2.17127e6	1.38133
$302$	2.87604e6	1.81458
$303$	−1.34079e6	−0.838984
$304$	−2.93873e6	−1.82379
$305$	−3.17465e6	−1.95409
$306$	−388805.	−0.237371
$307$	−1.86068e6	−1.12675	−0.563373	−	0.826203i	$-0.690497\pi$
$307$	−1.86068e6	−1.12675	−0.563373	+	0.826203i	$0.690497\pi$
$308$	1.40515e6	0.844007
$309$	126045.	0.0750982
$310$	221436.	0.130871
$311$	−309461.	−0.181428	−0.0907141	−	0.995877i	$-0.528915\pi$
$311$	−309461.	−0.181428	−0.0907141	+	0.995877i	$0.528915\pi$
$312$	−811535.	−0.471977
$313$	−2.85636e6	−1.64798	−0.823991	−	0.566603i	$-0.808257\pi$
$313$	−2.85636e6	−1.64798	−0.823991	+	0.566603i	$0.808257\pi$
$314$	259774.	0.148687
$315$	−1.03668e6	−0.588663
$316$	−270300.	−0.152275
$317$	3.55112e6	1.98480	0.992402	−	0.123037i	$-0.0392635\pi$
$317$	3.55112e6	1.98480	0.992402	+	0.123037i	$0.0392635\pi$
$318$	−751039.	−0.416481
$319$	−226431.	−0.124583
$320$	−3.64277e6	−1.98865
$321$	392631.	0.212678
$322$	757758.	0.407278
$323$	−496150.	−0.264610
$324$	518773.	0.274546
$325$	−571264.	−0.300005
$326$	4.10478e6	2.13917
$327$	−583771.	−0.301907
$328$	5.92441e6	3.04061
$329$	−3.32003e6	−1.69103
$330$	−825479.	−0.417274
$331$	2.32975e6	1.16880	0.584399	−	0.811466i	$-0.301330\pi$
$331$	2.32975e6	1.16880	0.584399	+	0.811466i	$0.301330\pi$
$332$	4.09193e6	2.03743
$333$	−199159.	−0.0984212
$334$	−1.34306e6	−0.658764
$335$	−4.40184e6	−2.14300
$336$	−3.92503e6	−1.89668
$337$	1.51731e6	0.727779	0.363890	−	0.931442i	$-0.381448\pi$
$337$	1.51731e6	0.727779	0.363890	+	0.931442i	$0.381448\pi$
$338$	3.56481e6	1.69724
$339$	555819.	0.262684
$340$	−2.85110e6	−1.33757
$341$	29174.8	0.0135870
$342$	929918.	0.429912
$343$	−1.20921e6	−0.554964
$344$	−6.66260e6	−3.03562
$345$	−316904.	−0.143344
$346$	−3.29872e6	−1.48134
$347$	−1.18828e6	−0.529780	−0.264890	−	0.964279i	$-0.585336\pi$
$347$	−1.18828e6	−0.529780	−0.264890	+	0.964279i	$0.585336\pi$
$348$	1.46579e6	0.648821
$349$	−2.31924e6	−1.01925	−0.509627	−	0.860395i	$-0.670217\pi$
$349$	−2.31924e6	−1.01925	−0.509627	+	0.860395i	$0.670217\pi$
$350$	−5.35434e6	−2.33634
$351$	132513.	0.0574105
$352$	−1.38040e6	−0.593812
$353$	−3.41633e6	−1.45923	−0.729613	−	0.683860i	$-0.760300\pi$
$353$	−3.41633e6	−1.45923	−0.729613	+	0.683860i	$0.760300\pi$
$354$	4.67087e6	1.98102
$355$	−325309.	−0.137002
$356$	3.46840e6	1.45046
$357$	−662669.	−0.275186
$358$	−1.10292e6	−0.454816
$359$	−1.00287e6	−0.410683	−0.205342	−	0.978690i	$-0.565831\pi$
$359$	−1.00287e6	−0.410683	−0.205342	+	0.978690i	$0.565831\pi$
$360$	3.18107e6	1.29365
$361$	−1.28944e6	−0.520755
$362$	−2.52263e6	−1.01177
$363$	1.34070e6	0.534029
$364$	−2.32350e6	−0.919155
$365$	−1.47826e6	−0.580788
$366$	3.80347e6	1.48415
$367$	−212256.	−0.0822612	−0.0411306	−	0.999154i	$-0.513096\pi$
$367$	−212256.	−0.0822612	−0.0411306	+	0.999154i	$0.513096\pi$
$368$	−1.19985e6	−0.461857
$369$	−967379.	−0.369854
$370$	−2.05147e6	−0.779043
$371$	−1.28005e6	−0.482828
$372$	−188863.	−0.0707602
$373$	78127.2	0.0290757	0.0145378	−	0.999894i	$-0.495372\pi$
$373$	78127.2	0.0290757	0.0145378	+	0.999894i	$0.495372\pi$
$374$	−527666.	−0.195065
$375$	12624.9	0.00463608
$376$	1.01876e7	3.71623
$377$	374416.	0.135676
$378$	1.24202e6	0.447094
$379$	2.62255e6	0.937834	0.468917	−	0.883242i	$-0.344644\pi$
$379$	2.62255e6	0.937834	0.468917	+	0.883242i	$0.344644\pi$
$380$	6.81906e6	2.42251
$381$	−1.07982e6	−0.381100
$382$	2.68152e6	0.940205
$383$	−4.41387e6	−1.53753	−0.768763	−	0.639534i	$-0.779127\pi$
$383$	−4.41387e6	−1.53753	−0.768763	+	0.639534i	$0.779127\pi$
$384$	747842.	0.258811
$385$	−1.40692e6	−0.483747
$386$	−5468.34	−0.00186805
$387$	1.08792e6	0.369248
$388$	−4.08102e6	−1.37622
$389$	−3.40479e6	−1.14082	−0.570409	−	0.821361i	$-0.693215\pi$
$389$	−3.40479e6	−1.14082	−0.570409	+	0.821361i	$0.693215\pi$
$390$	1.36498e6	0.454427
$391$	−202572.	−0.0670098
$392$	−4.62678e6	−1.52077
$393$	2.04603e6	0.668236
$394$	−3.49914e6	−1.13559
$395$	270641.	0.0872771
$396$	704051.	0.225614
$397$	−1.68730e6	−0.537300	−0.268650	−	0.963238i	$-0.586578\pi$
$397$	−1.68730e6	−0.537300	−0.268650	+	0.963238i	$0.586578\pi$
$398$	3.98083e6	1.25970
$399$	1.58493e6	0.498398
$400$	8.47818e6	2.64943
$401$	−3.55433e6	−1.10382	−0.551908	−	0.833905i	$-0.686100\pi$
$401$	−3.55433e6	−1.10382	−0.551908	+	0.833905i	$0.686100\pi$
$402$	5.27374e6	1.62762
$403$	−48242.3	−0.0147967
$404$	1.17794e7	3.59064
$405$	−519427.	−0.157357
$406$	3.50933e6	1.05660
$407$	−270288.	−0.0808799
$408$	2.03342e6	0.604750
$409$	−1.16165e6	−0.343372	−0.171686	−	0.985152i	$-0.554922\pi$
$409$	−1.16165e6	−0.343372	−0.171686	+	0.985152i	$0.554922\pi$
$410$	−9.96467e6	−2.92754
$411$	−2.22477e6	−0.649651
$412$	−1.10736e6	−0.321401
$413$	7.96090e6	2.29661
$414$	379675.	0.108871
$415$	−4.09709e6	−1.16777
$416$	2.28257e6	0.646683
$417$	3.80188e6	1.07068
$418$	1.26204e6	0.353290
$419$	−4.54190e6	−1.26387	−0.631935	−	0.775021i	$-0.717739\pi$
$419$	−4.54190e6	−1.26387	−0.631935	+	0.775021i	$0.717739\pi$
$420$	9.10769e6	2.51933
$421$	185490.	0.0510052	0.0255026	−	0.999675i	$-0.491881\pi$
$421$	185490.	0.0510052	0.0255026	+	0.999675i	$0.491881\pi$
$422$	1.11241e7	3.04076
$423$	−1.66350e6	−0.452036
$424$	3.92787e6	1.06107
$425$	1.43138e6	0.384400
$426$	389745.	0.104054
$427$	6.48252e6	1.72058
$428$	−3.44944e6	−0.910206
$429$	179840.	0.0471783
$430$	1.12063e7	2.92274
$431$	−362408.	−0.0939733	−0.0469867	−	0.998896i	$-0.514962\pi$
$431$	−362408.	−0.0939733	−0.0469867	+	0.998896i	$0.514962\pi$
$432$	−1.96664e6	−0.507008
$433$	−2.72039e6	−0.697287	−0.348644	−	0.937255i	$-0.613358\pi$
$433$	−2.72039e6	−0.697287	−0.348644	+	0.937255i	$0.613358\pi$
$434$	−452165.	−0.115232
$435$	−1.46764e6	−0.371876
$436$	5.12870e6	1.29208
$437$	484499.	0.121364
$438$	1.77106e6	0.441112
$439$	−3.55384e6	−0.880110	−0.440055	−	0.897971i	$-0.645041\pi$
$439$	−3.55384e6	−0.880110	−0.440055	+	0.897971i	$0.645041\pi$
$440$	4.31718e6	1.06309
$441$	755494.	0.184984
$442$	872526.	0.212433
$443$	811751.	0.196523	0.0982615	−	0.995161i	$-0.468672\pi$
$443$	811751.	0.196523	0.0982615	+	0.995161i	$0.468672\pi$
$444$	1.74970e6	0.421218
$445$	−3.47278e6	−0.831337
$446$	−8.41818e6	−2.00392
$447$	2.60517e6	0.616690
$448$	7.43843e6	1.75100
$449$	4.06286e6	0.951077	0.475539	−	0.879695i	$-0.342253\pi$
$449$	4.06286e6	0.951077	0.475539	+	0.879695i	$0.342253\pi$
$450$	−2.68279e6	−0.624534
$451$	−1.31288e6	−0.303936
$452$	−4.88313e6	−1.12422
$453$	2.45607e6	0.562335
$454$	4.15230e6	0.945474
$455$	2.32643e6	0.526819
$456$	−4.86338e6	−1.09528
$457$	7.90411e6	1.77036	0.885182	−	0.465245i	$-0.154034\pi$
$457$	7.90411e6	1.77036	0.885182	+	0.465245i	$0.154034\pi$
$458$	1.40375e6	0.312699
$459$	−332030.	−0.0735607
$460$	2.78415e6	0.613476
$461$	−5.30548e6	−1.16271	−0.581356	−	0.813649i	$-0.697478\pi$
$461$	−5.30548e6	−1.16271	−0.581356	+	0.813649i	$0.697478\pi$
$462$	1.68560e6	0.367409
$463$	2.72060e6	0.589811	0.294905	−	0.955526i	$-0.404712\pi$
$463$	2.72060e6	0.589811	0.294905	+	0.955526i	$0.404712\pi$
$464$	−5.55675e6	−1.19819
$465$	189101.	0.0405566
$466$	6.68701e6	1.42649
$467$	−1.39131e6	−0.295211	−0.147605	−	0.989046i	$-0.547157\pi$
$467$	−1.39131e6	−0.295211	−0.147605	+	0.989046i	$0.547157\pi$
$468$	−1.16419e6	−0.245702
$469$	8.98841e6	1.88691
$470$	−1.71352e7	−3.57804
$471$	221841.	0.0460776
$472$	−2.44282e7	−5.04704
$473$	1.47646e6	0.303438
$474$	−324248.	−0.0662875
$475$	−3.42348e6	−0.696200
$476$	5.82185e6	1.17772
$477$	−641369.	−0.129066
$478$	9.41500e6	1.88474
$479$	−2.54976e6	−0.507762	−0.253881	−	0.967235i	$-0.581707\pi$
$479$	−2.54976e6	−0.507762	−0.253881	+	0.967235i	$0.581707\pi$
$480$	−8.94728e6	−1.77251
$481$	446937.	0.0880812
$482$	−1.75773e7	−3.44614
$483$	647107.	0.126214
$484$	−1.17787e7	−2.28551
$485$	4.08617e6	0.788790
$486$	622314.	0.119514
$487$	−2.80152e6	−0.535268	−0.267634	−	0.963521i	$-0.586242\pi$
$487$	−2.80152e6	−0.535268	−0.267634	+	0.963521i	$0.586242\pi$
$488$	−1.98918e7	−3.78115
$489$	3.50538e6	0.662923
$490$	7.78211e6	1.46422
$491$	8.85049e6	1.65677	0.828387	−	0.560156i	$-0.189259\pi$
$491$	8.85049e6	1.65677	0.828387	+	0.560156i	$0.189259\pi$
$492$	8.49887e6	1.58288
$493$	−938153.	−0.173843
$494$	−2.08685e6	−0.384745
$495$	−704939.	−0.129312
$496$	715968.	0.130674
$497$	664271.	0.120630
$498$	4.90863e6	0.886925
$499$	8.02740e6	1.44319	0.721595	−	0.692316i	$-0.243409\pi$
$499$	8.02740e6	1.44319	0.721595	+	0.692316i	$0.243409\pi$
$500$	−110916.	−0.0198412
$501$	−1.14694e6	−0.204149
$502$	2.56274e6	0.453884
$503$	−6.32192e6	−1.11411	−0.557056	−	0.830475i	$-0.688069\pi$
$503$	−6.32192e6	−1.11411	−0.557056	+	0.830475i	$0.688069\pi$
$504$	−6.49564e6	−1.13906
$505$	−1.17943e7	−2.05799
$506$	515275.	0.0894670
$507$	3.04426e6	0.525971
$508$	9.48672e6	1.63101
$509$	−35769.9	−0.00611960	−0.00305980	−	0.999995i	$-0.500974\pi$
$509$	−35769.9	−0.00611960	−0.00305980	+	0.999995i	$0.500974\pi$
$510$	−3.42014e6	−0.582263
$511$	3.01855e6	0.511383
$512$	8.94745e6	1.50843
$513$	794127.	0.133228
$514$	−2.04118e7	−3.40780
$515$	1.10876e6	0.184213
$516$	−9.55784e6	−1.58029
$517$	−2.25762e6	−0.371470
$518$	4.18904e6	0.685947
$519$	−2.81703e6	−0.459064
$520$	−7.13871e6	−1.15774
$521$	−3.95592e6	−0.638489	−0.319244	−	0.947672i	$-0.603429\pi$
$521$	−3.95592e6	−0.638489	−0.319244	+	0.947672i	$0.603429\pi$
$522$	1.75835e6	0.282442
$523$	−6.17402e6	−0.986992	−0.493496	−	0.869748i	$-0.664281\pi$
$523$	−6.17402e6	−0.986992	−0.493496	+	0.869748i	$0.664281\pi$
$524$	−1.79753e7	−2.85988
$525$	−4.57248e6	−0.724025
$526$	−2.25157e7	−3.54831
$527$	120878.	0.0189592
$528$	−2.66902e6	−0.416646
$529$	−6.23853e6	−0.969266
$530$	−6.60655e6	−1.02161
$531$	3.98881e6	0.613913
$532$	−1.39243e7	−2.13302
$533$	2.17092e6	0.330998
$534$	4.16065e6	0.631405
$535$	3.45380e6	0.521690
$536$	−2.75812e7	−4.14668
$537$	−941865.	−0.140946
$538$	8.26284e6	1.23076
$539$	1.02532e6	0.152015
$540$	4.56341e6	0.673450
$541$	9.01397e6	1.32411	0.662053	−	0.749457i	$-0.269685\pi$
$541$	9.01397e6	1.32411	0.662053	+	0.749457i	$0.269685\pi$
$542$	1.60539e7	2.34737
$543$	−2.15427e6	−0.313545
$544$	−5.71931e6	−0.828603
$545$	−5.13517e6	−0.740565
$546$	−2.78724e6	−0.400122
$547$	−9.68766e6	−1.38437	−0.692183	−	0.721722i	$-0.743351\pi$
$547$	−9.68766e6	−1.38437	−0.692183	+	0.721722i	$0.743351\pi$
$548$	1.95456e7	2.78034
$549$	3.24807e6	0.459933
$550$	−3.64095e6	−0.513225
$551$	2.24381e6	0.314853
$552$	−1.98567e6	−0.277369
$553$	−552640.	−0.0768474
$554$	−8.58128e6	−1.18789
$555$	−1.75191e6	−0.241423
$556$	−3.34012e7	−4.58222
$557$	1.17355e7	1.60274	0.801372	−	0.598166i	$-0.204104\pi$
$557$	1.17355e7	1.60274	0.801372	+	0.598166i	$0.204104\pi$
$558$	−226557.	−0.0308030
$559$	−2.44141e6	−0.330455
$560$	−3.45267e7	−4.65249
$561$	−450614.	−0.0604502
$562$	3.07661e6	0.410896
$563$	9.96519e6	1.32500	0.662498	−	0.749064i	$-0.269496\pi$
$563$	9.96519e6	1.32500	0.662498	+	0.749064i	$0.269496\pi$
$564$	1.46146e7	1.93460
$565$	4.88929e6	0.644354
$566$	2.22894e6	0.292454
$567$	1.06065e6	0.138553
$568$	−2.03833e6	−0.265097
$569$	3.75755e6	0.486546	0.243273	−	0.969958i	$-0.421779\pi$
$569$	3.75755e6	0.486546	0.243273	+	0.969958i	$0.421779\pi$
$570$	8.18006e6	1.05456
$571$	3.73828e6	0.479824	0.239912	−	0.970795i	$-0.422881\pi$
$571$	3.73828e6	0.479824	0.239912	+	0.970795i	$0.422881\pi$
$572$	−1.57998e6	−0.201911
$573$	2.28995e6	0.291367
$574$	2.03475e7	2.57770
$575$	−1.39777e6	−0.176306
$576$	3.72703e6	0.468065
$577$	−6.44406e6	−0.805787	−0.402894	−	0.915247i	$-0.631996\pi$
$577$	−6.44406e6	−0.805787	−0.402894	+	0.915247i	$0.631996\pi$
$578$	1.27775e7	1.59084
$579$	−4669.83	−0.000578902 0
$580$	1.28939e7	1.59153
$581$	8.36613e6	1.02822
$582$	−4.89554e6	−0.599091
$583$	−870433.	−0.106063
$584$	−9.26250e6	−1.12382
$585$	1.16566e6	0.140826
$586$	−1.34485e7	−1.61782
$587$	−5.98263e6	−0.716633	−0.358316	−	0.933600i	$-0.616649\pi$
$587$	−5.98263e6	−0.716633	−0.358316	+	0.933600i	$0.616649\pi$
$588$	−6.63736e6	−0.791685
$589$	−289107.	−0.0343377
$590$	4.10875e7	4.85937
$591$	−2.98818e6	−0.351916
$592$	−6.63302e6	−0.777870
$593$	−1.22378e6	−0.142912	−0.0714559	−	0.997444i	$-0.522765\pi$
$593$	−1.22378e6	−0.142912	−0.0714559	+	0.997444i	$0.522765\pi$
$594$	844571.	0.0982133
$595$	−5.82920e6	−0.675019
$596$	−2.28876e7	−2.63928
$597$	3.39954e6	0.390377
$598$	−852037.	−0.0974329
$599$	1.24954e7	1.42293	0.711464	−	0.702723i	$-0.248033\pi$
$599$	1.24954e7	1.42293	0.711464	+	0.702723i	$0.248033\pi$
$600$	1.40308e7	1.59112
$601$	−9.72010e6	−1.09770	−0.548851	−	0.835920i	$-0.684935\pi$
$601$	−9.72010e6	−1.09770	−0.548851	+	0.835920i	$0.684935\pi$
$602$	−2.28829e7	−2.57347
$603$	4.50365e6	0.504395
$604$	−2.15777e7	−2.40665
$605$	1.17935e7	1.30995
$606$	1.41305e7	1.56306
$607$	−8.19732e6	−0.903025	−0.451513	−	0.892265i	$-0.649115\pi$
$607$	−8.19732e6	−0.903025	−0.451513	+	0.892265i	$0.649115\pi$
$608$	1.36791e7	1.50071
$609$	2.99688e6	0.327436
$610$	3.34574e7	3.64055
$611$	3.73310e6	0.404545
$612$	2.91704e6	0.314821
$613$	−3.44584e6	−0.370377	−0.185189	−	0.982703i	$-0.559290\pi$
$613$	−3.44584e6	−0.370377	−0.185189	+	0.982703i	$0.559290\pi$
$614$	1.96096e7	2.09917
$615$	−8.50959e6	−0.907238
$616$	−8.81554e6	−0.936046
$617$	−1.08253e7	−1.14479	−0.572397	−	0.819976i	$-0.693987\pi$
$617$	−1.08253e7	−1.14479	−0.572397	+	0.819976i	$0.693987\pi$
$618$	−1.32838e6	−0.139911
$619$	−1.58851e7	−1.66633	−0.833167	−	0.553022i	$-0.813475\pi$
$619$	−1.58851e7	−1.66633	−0.833167	+	0.553022i	$0.813475\pi$
$620$	−1.66134e6	−0.173572
$621$	324233.	0.0337387
$622$	3.26139e6	0.338008
$623$	7.09130e6	0.731991
$624$	4.41338e6	0.453743
$625$	−9.70994e6	−0.994298
$626$	3.01030e7	3.07025
$627$	1.07775e6	0.109483
$628$	−1.94898e6	−0.197200
$629$	−1.11986e6	−0.112859
$630$	1.09255e7	1.09670
$631$	−1.81921e7	−1.81891	−0.909453	−	0.415806i	$-0.863500\pi$
$631$	−1.81921e7	−1.81891	−0.909453	+	0.415806i	$0.863500\pi$
$632$	1.69579e6	0.168880
$633$	9.49968e6	0.942323
$634$	−3.74251e7	−3.69777
$635$	−9.49868e6	−0.934822
$636$	5.63473e6	0.552370
$637$	−1.69542e6	−0.165550
$638$	2.38634e6	0.232103
$639$	332833.	0.0322459
$640$	6.57843e6	0.634852
$641$	−1.12649e7	−1.08289	−0.541443	−	0.840738i	$-0.682122\pi$
$641$	−1.12649e7	−1.08289	−0.541443	+	0.840738i	$0.682122\pi$
$642$	−4.13791e6	−0.396227
$643$	2.00475e7	1.91220	0.956098	−	0.293048i	$-0.0946697\pi$
$643$	2.00475e7	1.91220	0.956098	+	0.293048i	$0.0946697\pi$
$644$	−5.68514e6	−0.540165
$645$	9.56990e6	0.905750
$646$	5.22889e6	0.492979
$647$	−9.43927e6	−0.886498	−0.443249	−	0.896399i	$-0.646174\pi$
$647$	−9.43927e6	−0.886498	−0.443249	+	0.896399i	$0.646174\pi$
$648$	−3.25464e6	−0.304485
$649$	5.41340e6	0.504497
$650$	6.02052e6	0.558921
$651$	−386138.	−0.0357100
$652$	−3.07964e7	−2.83714
$653$	−6.08108e6	−0.558082	−0.279041	−	0.960279i	$-0.590017\pi$
$653$	−6.08108e6	−0.558082	−0.279041	+	0.960279i	$0.590017\pi$
$654$	6.15232e6	0.562464
$655$	1.79980e7	1.63915
$656$	−3.22187e7	−2.92314
$657$	1.51245e6	0.136699
$658$	3.49896e7	3.15046
$659$	−3.71143e6	−0.332911	−0.166456	−	0.986049i	$-0.553232\pi$
$659$	−3.71143e6	−0.332911	−0.166456	+	0.986049i	$0.553232\pi$
$660$	6.19322e6	0.553422
$661$	8.79528e6	0.782971	0.391486	−	0.920184i	$-0.371961\pi$
$661$	8.79528e6	0.782971	0.391486	+	0.920184i	$0.371961\pi$
$662$	−2.45531e7	−2.17752
$663$	745117.	0.0658325
$664$	−2.56717e7	−2.25961
$665$	1.39419e7	1.22255
$666$	2.09892e6	0.183363
$667$	916123.	0.0797332
$668$	1.00764e7	0.873706
$669$	−7.18893e6	−0.621010
$670$	4.63907e7	3.99249
$671$	4.40811e6	0.377960
$672$	1.82700e7	1.56069
$673$	−6.52509e6	−0.555327	−0.277664	−	0.960678i	$-0.589560\pi$
$673$	−6.52509e6	−0.555327	−0.277664	+	0.960678i	$0.589560\pi$
$674$	−1.59908e7	−1.35588
$675$	−2.29104e6	−0.193541
$676$	−2.67452e7	−2.25102
$677$	−2.29449e7	−1.92404	−0.962019	−	0.272981i	$-0.911990\pi$
$677$	−2.29449e7	−1.92404	−0.962019	+	0.272981i	$0.911990\pi$
$678$	−5.85774e6	−0.489391
$679$	−8.34382e6	−0.694529
$680$	1.78870e7	1.48343
$681$	3.54597e6	0.293000
$682$	−307472.	−0.0253130
$683$	−1.02137e7	−0.837780	−0.418890	−	0.908037i	$-0.637581\pi$
$683$	−1.02137e7	−0.837780	−0.418890	+	0.908037i	$0.637581\pi$
$684$	−6.97678e6	−0.570184
$685$	−1.95703e7	−1.59357
$686$	1.27437e7	1.03392
$687$	1.19877e6	0.0969046
$688$	3.62332e7	2.91834
$689$	1.43931e6	0.115507
$690$	3.33983e6	0.267056
$691$	−1.69057e7	−1.34691	−0.673454	−	0.739229i	$-0.735190\pi$
$691$	−1.69057e7	−1.34691	−0.673454	+	0.739229i	$0.735190\pi$
$692$	2.47489e7	1.96468
$693$	1.43946e6	0.113859
$694$	1.25232e7	0.987000
$695$	3.34434e7	2.62632
$696$	−9.19601e6	−0.719575
$697$	−5.43954e6	−0.424111
$698$	2.44424e7	1.89891
$699$	5.71055e6	0.442064
$700$	4.01713e7	3.09864
$701$	4.93033e6	0.378949	0.189475	−	0.981886i	$-0.439322\pi$
$701$	4.93033e6	0.378949	0.189475	+	0.981886i	$0.439322\pi$
$702$	−1.39655e6	−0.106958
$703$	2.67841e6	0.204404
$704$	5.05812e6	0.384643
$705$	−1.46331e7	−1.10883
$706$	3.60045e7	2.71860
$707$	2.40836e7	1.81206
$708$	−3.50435e7	−2.62739
$709$	−2.33490e7	−1.74443	−0.872215	−	0.489122i	$-0.837317\pi$
$709$	−2.33490e7	−1.74443	−0.872215	+	0.489122i	$0.837317\pi$
$710$	3.42841e6	0.255239
$711$	−276900.	−0.0205423
$712$	−2.17598e7	−1.60863
$713$	−118039.	−0.00869567
$714$	6.98382e6	0.512682
$715$	1.58197e6	0.115727
$716$	8.27472e6	0.603213
$717$	8.04019e6	0.584075
$718$	1.05691e7	0.765118
$719$	1.94276e7	1.40151	0.700755	−	0.713402i	$-0.252846\pi$
$719$	1.94276e7	1.40151	0.700755	+	0.713402i	$0.252846\pi$
$720$	−1.72996e7	−1.24367
$721$	−2.26405e6	−0.162199
$722$	1.35893e7	0.970187
$723$	−1.50106e7	−1.06795
$724$	1.89263e7	1.34189
$725$	−6.47335e6	−0.457387
$726$	−1.41295e7	−0.994917
$727$	−1.04299e7	−0.731885	−0.365943	−	0.930637i	$-0.619253\pi$
$727$	−1.04299e7	−0.731885	−0.365943	+	0.930637i	$0.619253\pi$
$728$	1.45770e7	1.01939
$729$	531441.	0.0370370
$730$	1.55792e7	1.08203
$731$	6.11731e6	0.423416
$732$	−2.85358e7	−1.96840
$733$	1.32397e7	0.910158	0.455079	−	0.890451i	$-0.349611\pi$
$733$	1.32397e7	0.910158	0.455079	+	0.890451i	$0.349611\pi$
$734$	2.23695e6	0.153256
$735$	6.64574e6	0.453759
$736$	5.58501e6	0.380040
$737$	6.11211e6	0.414498
$738$	1.01951e7	0.689053
$739$	1.04920e7	0.706722	0.353361	−	0.935487i	$-0.385039\pi$
$739$	1.04920e7	0.706722	0.353361	+	0.935487i	$0.385039\pi$
$740$	1.53913e7	1.03323
$741$	−1.78212e6	−0.119232
$742$	1.34904e7	0.899526
$743$	−1.08294e6	−0.0719671	−0.0359835	−	0.999352i	$-0.511456\pi$
$743$	−1.08294e6	−0.0719671	−0.0359835	+	0.999352i	$0.511456\pi$
$744$	1.18487e6	0.0784766
$745$	2.29165e7	1.51272
$746$	−823378.	−0.0541691
$747$	4.19185e6	0.274856
$748$	3.95885e6	0.258711
$749$	−7.05254e6	−0.459347
$750$	−133053.	−0.00863720
$751$	6.64604e6	0.429995	0.214997	−	0.976615i	$-0.431026\pi$
$751$	6.64604e6	0.429995	0.214997	+	0.976615i	$0.431026\pi$
$752$	−5.54033e7	−3.57265
$753$	2.18852e6	0.140657
$754$	−3.94595e6	−0.252769
$755$	2.16049e7	1.37938
$756$	−9.31834e6	−0.592972
$757$	−1.28791e7	−0.816854	−0.408427	−	0.912791i	$-0.633922\pi$
$757$	−1.28791e7	−0.816854	−0.408427	+	0.912791i	$0.633922\pi$
$758$	−2.76389e7	−1.74722
$759$	440032.	0.0277256
$760$	−4.27810e7	−2.68669
$761$	1.67149e7	1.04626	0.523132	−	0.852252i	$-0.324764\pi$
$761$	1.67149e7	1.04626	0.523132	+	0.852252i	$0.324764\pi$
$762$	1.13801e7	0.710004
$763$	1.04858e7	0.652067
$764$	−2.01183e7	−1.24698
$765$	−2.92072e6	−0.180442
$766$	4.65175e7	2.86447
$767$	−8.95138e6	−0.549416
$768$	5.37019e6	0.328539
$769$	2.17361e6	0.132546	0.0662730	−	0.997802i	$-0.478889\pi$
$769$	2.17361e6	0.132546	0.0662730	+	0.997802i	$0.478889\pi$
$770$	1.48275e7	0.901240
$771$	−1.74312e7	−1.05607
$772$	41026.7	0.00247755
$773$	−1.61196e7	−0.970296	−0.485148	−	0.874432i	$-0.661234\pi$
$773$	−1.61196e7	−0.970296	−0.485148	+	0.874432i	$0.661234\pi$
$774$	−1.14655e7	−0.687923
$775$	834069.	0.0498825
$776$	2.56032e7	1.52630
$777$	3.57734e6	0.212573
$778$	3.58829e7	2.12539
$779$	1.30099e7	0.768123
$780$	−1.02408e7	−0.602698
$781$	451704.	0.0264988
$782$	2.13490e6	0.124842
$783$	1.50159e6	0.0875279
$784$	2.51619e7	1.46202
$785$	1.95143e6	0.113026
$786$	−2.15629e7	−1.24495
$787$	−7.30473e6	−0.420405	−0.210202	−	0.977658i	$-0.567412\pi$
$787$	−7.30473e6	−0.420405	−0.210202	+	0.977658i	$0.567412\pi$
$788$	2.62526e7	1.50611
$789$	−1.92279e7	−1.09961
$790$	−2.85227e6	−0.162601
$791$	−9.98377e6	−0.567353
$792$	−4.41703e6	−0.250217
$793$	−7.28907e6	−0.411613
$794$	1.77824e7	1.00101
$795$	−5.64184e6	−0.316594
$796$	−2.98665e7	−1.67071
$797$	1.57138e7	0.876266	0.438133	−	0.898910i	$-0.355640\pi$
$797$	1.57138e7	0.876266	0.438133	+	0.898910i	$0.355640\pi$
$798$	−1.67034e7	−0.928535
$799$	−9.35382e6	−0.518349
$800$	−3.94638e7	−2.18009
$801$	3.55310e6	0.195671
$802$	3.74588e7	2.05645
$803$	2.05261e6	0.112336
$804$	−3.95666e7	−2.15868
$805$	5.69231e6	0.309599
$806$	508423.	0.0275669
$807$	7.05627e6	0.381409
$808$	−7.39011e7	−3.98220
$809$	−3.03473e7	−1.63023	−0.815115	−	0.579299i	$-0.803326\pi$
$809$	−3.03473e7	−1.63023	−0.815115	+	0.579299i	$0.803326\pi$
$810$	5.47421e6	0.293163
$811$	−2.35898e7	−1.25942	−0.629712	−	0.776829i	$-0.716827\pi$
$811$	−2.35898e7	−1.25942	−0.629712	+	0.776829i	$0.716827\pi$
$812$	−2.63290e7	−1.40134
$813$	1.37096e7	0.727443
$814$	2.84855e6	0.150682
$815$	3.08353e7	1.62612
$816$	−1.10583e7	−0.581386
$817$	−1.46310e7	−0.766863
$818$	1.22425e7	0.639716
$819$	−2.38024e6	−0.123997
$820$	7.47607e7	3.88275
$821$	−1.90866e7	−0.988258	−0.494129	−	0.869389i	$-0.664513\pi$
$821$	−1.90866e7	−0.988258	−0.494129	+	0.869389i	$0.664513\pi$
$822$	2.34467e7	1.21033
$823$	9.11011e6	0.468839	0.234420	−	0.972136i	$-0.424681\pi$
$823$	9.11011e6	0.468839	0.234420	+	0.972136i	$0.424681\pi$
$824$	6.94731e6	0.356450
$825$	−3.10928e6	−0.159047
$826$	−8.38994e7	−4.27867
$827$	−1.56866e7	−0.797565	−0.398783	−	0.917045i	$-0.630567\pi$
$827$	−1.56866e7	−0.797565	−0.398783	+	0.917045i	$0.630567\pi$
$828$	−2.84854e6	−0.144393
$829$	−8.75588e6	−0.442500	−0.221250	−	0.975217i	$-0.571014\pi$
$829$	−8.75588e6	−0.442500	−0.221250	+	0.975217i	$0.571014\pi$
$830$	4.31790e7	2.17559
$831$	−7.32821e6	−0.368125
$832$	−8.36390e6	−0.418891
$833$	4.24811e6	0.212121
$834$	−4.00677e7	−1.99471
$835$	−1.00891e7	−0.500769
$836$	−9.46852e6	−0.468561
$837$	−193475.	−0.00954576
$838$	4.78668e7	2.35464
$839$	−6.17204e6	−0.302708	−0.151354	−	0.988480i	$-0.548363\pi$
$839$	−6.17204e6	−0.302708	−0.151354	+	0.988480i	$0.548363\pi$
$840$	−5.71392e7	−2.79406
$841$	−1.62684e7	−0.793149
$842$	−1.95486e6	−0.0950246
$843$	2.62735e6	0.127335
$844$	−8.34591e7	−4.03290
$845$	2.67790e7	1.29019
$846$	1.75316e7	0.842160
$847$	−2.40820e7	−1.15341
$848$	−2.13609e7	−1.02007
$849$	1.90347e6	0.0906308
$850$	−1.50853e7	−0.716152
$851$	1.09357e6	0.0517632
$852$	−2.92409e6	−0.138004
$853$	5.48679e6	0.258194	0.129097	−	0.991632i	$-0.458792\pi$
$853$	5.48679e6	0.258194	0.129097	+	0.991632i	$0.458792\pi$
$854$	−6.83189e7	−3.20550
$855$	6.98558e6	0.326804
$856$	2.16409e7	1.00946
$857$	1.58816e7	0.738655	0.369328	−	0.929299i	$-0.379588\pi$
$857$	1.58816e7	0.738655	0.369328	+	0.929299i	$0.379588\pi$
$858$	−1.89532e6	−0.0878951
$859$	1.93489e7	0.894693	0.447347	−	0.894361i	$-0.352369\pi$
$859$	1.93489e7	0.894693	0.447347	+	0.894361i	$0.352369\pi$
$860$	−8.40760e7	−3.87638
$861$	1.73763e7	0.798822
$862$	3.81939e6	0.175076
$863$	−1.27130e7	−0.581061	−0.290531	−	0.956866i	$-0.593832\pi$
$863$	−1.27130e7	−0.581061	−0.290531	+	0.956866i	$0.593832\pi$
$864$	9.15421e6	0.417193
$865$	−2.47801e7	−1.12606
$866$	2.86700e7	1.29907
$867$	1.09117e7	0.492998
$868$	3.39240e6	0.152830
$869$	−375794.	−0.0168811
$870$	1.54674e7	0.692818
$871$	−1.01067e7	−0.451404
$872$	−3.21761e7	−1.43299
$873$	−4.18067e6	−0.185657
$874$	−5.10610e6	−0.226105
$875$	−226773.	−0.0100131
$876$	−1.32875e7	−0.585038
$877$	3.63791e7	1.59718	0.798588	−	0.601878i	$-0.205581\pi$
$877$	3.63791e7	1.59718	0.798588	+	0.601878i	$0.205581\pi$
$878$	3.74537e7	1.63968
$879$	−1.14847e7	−0.501359
$880$	−2.34781e7	−1.02201
$881$	−7.84512e6	−0.340534	−0.170267	−	0.985398i	$-0.554463\pi$
$881$	−7.84512e6	−0.340534	−0.170267	+	0.985398i	$0.554463\pi$
$882$	−7.96210e6	−0.344633
$883$	4.15275e6	0.179240	0.0896198	−	0.995976i	$-0.471435\pi$
$883$	4.15275e6	0.179240	0.0896198	+	0.995976i	$0.471435\pi$
$884$	−6.54619e6	−0.281746
$885$	3.50878e7	1.50590
$886$	−8.55499e6	−0.366130
$887$	1.69003e7	0.721251	0.360626	−	0.932711i	$-0.382563\pi$
$887$	1.69003e7	0.721251	0.360626	+	0.932711i	$0.382563\pi$
$888$	−1.09772e7	−0.467152
$889$	1.93960e7	0.823110
$890$	3.65994e7	1.54881
$891$	721244.	0.0304360
$892$	6.31581e7	2.65777
$893$	2.23718e7	0.938799
$894$	−2.74557e7	−1.14892
$895$	−8.28516e6	−0.345735
$896$	−1.34329e7	−0.558986
$897$	−727619.	−0.0301942
$898$	−4.28182e7	−1.77189
$899$	−546664.	−0.0225591
$900$	2.01279e7	0.828307
$901$	−3.60640e6	−0.148000
$902$	1.38363e7	0.566245
$903$	−1.95414e7	−0.797511
$904$	3.06355e7	1.24682
$905$	−1.89501e7	−0.769114
$906$	−2.58843e7	−1.04765
$907$	2.40198e7	0.969507	0.484753	−	0.874651i	$-0.338909\pi$
$907$	2.40198e7	0.969507	0.484753	+	0.874651i	$0.338909\pi$
$908$	−3.11530e7	−1.25396
$909$	1.20671e7	0.484388
$910$	−2.45181e7	−0.981484
$911$	2.45461e7	0.979912	0.489956	−	0.871747i	$-0.337013\pi$
$911$	2.45461e7	0.979912	0.489956	+	0.871747i	$0.337013\pi$
$912$	2.64486e7	1.05297
$913$	5.68896e6	0.225869
$914$	−8.33009e7	−3.29826
$915$	2.85718e7	1.12820
$916$	−1.05318e7	−0.414727
$917$	−3.67512e7	−1.44327
$918$	3.49925e6	0.137046
$919$	3.36730e7	1.31520	0.657601	−	0.753366i	$-0.271571\pi$
$919$	3.36730e7	1.31520	0.657601	+	0.753366i	$0.271571\pi$
$920$	−1.74670e7	−0.680376
$921$	1.67461e7	0.650527
$922$	5.59141e7	2.16618
$923$	−746918.	−0.0288582
$924$	−1.26464e7	−0.487288
$925$	−7.72716e6	−0.296938
$926$	−2.86723e7	−1.09884
$927$	−1.13441e6	−0.0433580
$928$	2.58653e7	0.985932
$929$	−5.14211e7	−1.95480	−0.977399	−	0.211402i	$-0.932197\pi$
$929$	−5.14211e7	−1.95480	−0.977399	+	0.211402i	$0.932197\pi$
$930$	−1.99292e6	−0.0755585
$931$	−1.01603e7	−0.384180
$932$	−5.01698e7	−1.89192
$933$	2.78515e6	0.104748
$934$	1.46629e7	0.549989
$935$	−3.96385e6	−0.148282
$936$	7.30382e6	0.272496
$937$	4.02993e7	1.49951	0.749753	−	0.661718i	$-0.230172\pi$
$937$	4.02993e7	1.49951	0.749753	+	0.661718i	$0.230172\pi$
$938$	−9.47283e7	−3.51538
$939$	2.57073e7	0.951463
$940$	1.28558e8	4.74549
$941$	−3.36109e7	−1.23739	−0.618694	−	0.785632i	$-0.712338\pi$
$941$	−3.36109e7	−1.23739	−0.618694	+	0.785632i	$0.712338\pi$
$942$	−2.33797e6	−0.0858443
$943$	5.31180e6	0.194519
$944$	1.32848e8	4.85205
$945$	9.33009e6	0.339865
$946$	−1.55603e7	−0.565316
$947$	3.36843e7	1.22054	0.610270	−	0.792193i	$-0.291061\pi$
$947$	3.36843e7	1.22054	0.610270	+	0.792193i	$0.291061\pi$
$948$	2.43270e6	0.0879159
$949$	−3.39411e6	−0.122338
$950$	3.60799e7	1.29705
$951$	−3.19601e7	−1.14593
$952$	−3.65248e7	−1.30616
$953$	−9.83380e6	−0.350743	−0.175371	−	0.984502i	$-0.556113\pi$
$953$	−9.83380e6	−0.350743	−0.175371	+	0.984502i	$0.556113\pi$
$954$	6.75935e6	0.240455
$955$	2.01437e7	0.714711
$956$	−7.06368e7	−2.49969
$957$	2.03788e6	0.0719280
$958$	2.68717e7	0.945980
$959$	3.99619e7	1.40313
$960$	3.27850e7	1.14814
$961$	−2.85587e7	−0.997540
$962$	−4.71024e6	−0.164099
$963$	−3.53368e6	−0.122789
$964$	1.31875e8	4.57055
$965$	−41078.4	−0.00142002
$966$	−6.81982e6	−0.235142
$967$	3.90604e7	1.34329	0.671646	−	0.740872i	$-0.265588\pi$
$967$	3.90604e7	1.34329	0.671646	+	0.740872i	$0.265588\pi$
$968$	7.38962e7	2.53474
$969$	4.46535e6	0.152773
$970$	−4.30638e7	−1.46955
$971$	1.49067e7	0.507379	0.253689	−	0.967286i	$-0.418356\pi$
$971$	1.49067e7	0.507379	0.253689	+	0.967286i	$0.418356\pi$
$972$	−4.66896e6	−0.158509
$973$	−6.82903e7	−2.31247
$974$	2.95250e7	0.997224
$975$	5.14138e6	0.173208
$976$	1.08178e8	3.63507
$977$	−1.79320e7	−0.601026	−0.300513	−	0.953778i	$-0.597158\pi$
$977$	−1.79320e7	−0.601026	−0.300513	+	0.953778i	$0.597158\pi$
$978$	−3.69430e7	−1.23505
$979$	4.82208e6	0.160797
$980$	−5.83859e7	−1.94197
$981$	5.25394e6	0.174306
$982$	−9.32747e7	−3.08663
$983$	−5.24884e7	−1.73253	−0.866263	−	0.499588i	$-0.833485\pi$
$983$	−5.24884e7	−1.73253	−0.866263	+	0.499588i	$0.833485\pi$
$984$	−5.33197e7	−1.75550
$985$	−2.62857e7	−0.863234
$986$	9.88714e6	0.323876
$987$	2.98803e7	0.976319
$988$	1.56567e7	0.510281
$989$	−5.97366e6	−0.194200
$990$	7.42931e6	0.240913
$991$	−1.86323e7	−0.602674	−0.301337	−	0.953518i	$-0.597433\pi$
$991$	−1.86323e7	−0.602674	−0.301337	+	0.953518i	$0.597433\pi$
$992$	−3.33265e6	−0.107525
$993$	−2.09678e7	−0.674806
$994$	−7.00071e6	−0.224738
$995$	2.99042e7	0.957578
$996$	−3.68274e7	−1.17631
$997$	−5.33720e7	−1.70050	−0.850248	−	0.526382i	$-0.823548\pi$
$997$	−5.33720e7	−1.70050	−0.850248	+	0.526382i	$0.823548\pi$
$998$	−8.46002e7	−2.68872
$999$	1.79243e6	0.0568235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.2	✓	30	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-10.5389 q^{2} -9.00000 q^{3} +79.0692 q^{4} -79.1689 q^{5} +94.8504 q^{6} +161.660 q^{7} -496.059 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.5389 q^{2} -9.00000 q^{3} +79.0692 q^{4} -79.1689 q^{5} +94.8504 q^{6} +161.660 q^{7} -496.059 q^{8} +81.0000 q^{9} +834.356 q^{10} +109.929 q^{11} -711.623 q^{12} -181.774 q^{13} -1703.73 q^{14} +712.520 q^{15} +2697.72 q^{16} +455.460 q^{17} -853.654 q^{18} -1089.34 q^{19} -6259.82 q^{20} -1454.94 q^{21} -1158.53 q^{22} -444.765 q^{23} +4464.53 q^{24} +3142.72 q^{25} +1915.70 q^{26} -729.000 q^{27} +12782.4 q^{28} -2059.79 q^{29} -7509.21 q^{30} +265.397 q^{31} -12557.2 q^{32} -989.360 q^{33} -4800.06 q^{34} -12798.5 q^{35} +6404.60 q^{36} -2458.75 q^{37} +11480.5 q^{38} +1635.96 q^{39} +39272.5 q^{40} -11942.9 q^{41} +15333.6 q^{42} +13431.1 q^{43} +8691.99 q^{44} -6412.68 q^{45} +4687.35 q^{46} -20537.1 q^{47} -24279.5 q^{48} +9327.08 q^{49} -33120.9 q^{50} -4099.14 q^{51} -14372.7 q^{52} -7918.14 q^{53} +7682.88 q^{54} -8702.96 q^{55} -80193.1 q^{56} +9804.04 q^{57} +21708.0 q^{58} +49244.6 q^{59} +56338.4 q^{60} +40099.6 q^{61} -2797.01 q^{62} +13094.5 q^{63} +46012.7 q^{64} +14390.8 q^{65} +10426.8 q^{66} +55600.6 q^{67} +36012.8 q^{68} +4002.88 q^{69} +134882. q^{70} +4109.05 q^{71} -40180.8 q^{72} +18672.2 q^{73} +25912.6 q^{74} -28284.5 q^{75} -86133.1 q^{76} +17771.2 q^{77} -17241.3 q^{78} -3418.52 q^{79} -213576. q^{80} +6561.00 q^{81} +125866. q^{82} +51751.3 q^{83} -115041. q^{84} -36058.3 q^{85} -141549. q^{86} +18538.1 q^{87} -54531.2 q^{88} +43865.4 q^{89} +67582.9 q^{90} -29385.6 q^{91} -35167.2 q^{92} -2388.58 q^{93} +216439. q^{94} +86241.7 q^{95} +113015. q^{96} -51613.3 q^{97} -98297.5 q^{98} +8904.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * q^99

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