LMFDB - Embedded newform 471.6.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-9.06695 q^{2} -9.00000 q^{3} +50.2095 q^{4} -0.166632 q^{5} +81.6025 q^{6} -235.849 q^{7} -165.105 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.06695 q^{2} -9.00000 q^{3} +50.2095 q^{4} -0.166632 q^{5} +81.6025 q^{6} -235.849 q^{7} -165.105 q^{8} +81.0000 q^{9} +1.51084 q^{10} -232.290 q^{11} -451.886 q^{12} -315.051 q^{13} +2138.43 q^{14} +1.49969 q^{15} -109.708 q^{16} +1006.66 q^{17} -734.423 q^{18} +1338.94 q^{19} -8.36651 q^{20} +2122.64 q^{21} +2106.17 q^{22} +253.578 q^{23} +1485.94 q^{24} -3124.97 q^{25} +2856.55 q^{26} -729.000 q^{27} -11841.9 q^{28} -1965.26 q^{29} -13.5976 q^{30} +40.3615 q^{31} +6278.07 q^{32} +2090.61 q^{33} -9127.32 q^{34} +39.3000 q^{35} +4066.97 q^{36} +6134.45 q^{37} -12140.1 q^{38} +2835.46 q^{39} +27.5117 q^{40} -19793.8 q^{41} -19245.9 q^{42} +17413.9 q^{43} -11663.2 q^{44} -13.4972 q^{45} -2299.18 q^{46} -3171.34 q^{47} +987.376 q^{48} +38817.9 q^{49} +28334.0 q^{50} -9059.93 q^{51} -15818.6 q^{52} +11419.0 q^{53} +6609.80 q^{54} +38.7070 q^{55} +38939.9 q^{56} -12050.5 q^{57} +17818.9 q^{58} +3189.32 q^{59} +75.2985 q^{60} +10586.7 q^{61} -365.956 q^{62} -19103.8 q^{63} -53412.3 q^{64} +52.4975 q^{65} -18955.5 q^{66} +21129.5 q^{67} +50543.8 q^{68} -2282.20 q^{69} -356.331 q^{70} +72862.7 q^{71} -13373.5 q^{72} +78511.9 q^{73} -55620.8 q^{74} +28124.8 q^{75} +67227.7 q^{76} +54785.6 q^{77} -25709.0 q^{78} -1487.14 q^{79} +18.2809 q^{80} +6561.00 q^{81} +179469. q^{82} +11260.3 q^{83} +106577. q^{84} -167.741 q^{85} -157891. q^{86} +17687.3 q^{87} +38352.3 q^{88} -72837.0 q^{89} +122.378 q^{90} +74304.6 q^{91} +12732.0 q^{92} -363.254 q^{93} +28754.4 q^{94} -223.111 q^{95} -56502.7 q^{96} +10681.4 q^{97} -351960. q^{98} -18815.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.06695	−1.60282	−0.801412	−	0.598112i	$-0.795918\pi$
$2$	−9.06695	−1.60282	−0.801412	+	0.598112i	$0.795918\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	50.2095	1.56905
$5$	−0.166632	−0.00298080	−0.00149040	−	0.999999i	$-0.500474\pi$
$5$	−0.166632	−0.00298080	−0.00149040	+	0.999999i	$0.500474\pi$
$6$	81.6025	0.925391
$7$	−235.849	−1.81924	−0.909619	−	0.415443i	$-0.863627\pi$
$7$	−235.849	−1.81924	−0.909619	+	0.415443i	$0.863627\pi$
$8$	−165.105	−0.912084
$9$	81.0000	0.333333
$10$	1.51084	0.00477770
$11$	−232.290	−0.578828	−0.289414	−	0.957204i	$-0.593460\pi$
$11$	−232.290	−0.578828	−0.289414	+	0.957204i	$0.593460\pi$
$12$	−451.886	−0.905890
$13$	−315.051	−0.517038	−0.258519	−	0.966006i	$-0.583234\pi$
$13$	−315.051	−0.517038	−0.258519	+	0.966006i	$0.583234\pi$
$14$	2138.43	2.91592
$15$	1.49969	0.00172097
$16$	−109.708	−0.107137
$17$	1006.66	0.844811	0.422406	−	0.906407i	$-0.361186\pi$
$17$	1006.66	0.844811	0.422406	+	0.906407i	$0.361186\pi$
$18$	−734.423	−0.534275
$19$	1338.94	0.850899	0.425450	−	0.904982i	$-0.360116\pi$
$19$	1338.94	0.850899	0.425450	+	0.904982i	$0.360116\pi$
$20$	−8.36651	−0.00467702
$21$	2122.64	1.05034
$22$	2106.17	0.927760
$23$	253.578	0.0999520	0.0499760	−	0.998750i	$-0.484086\pi$
$23$	253.578	0.0999520	0.0499760	+	0.998750i	$0.484086\pi$
$24$	1485.94	0.526592
$25$	−3124.97	−0.999991
$26$	2856.55	0.828721
$27$	−729.000	−0.192450
$28$	−11841.9	−2.85447
$29$	−1965.26	−0.433935	−0.216967	−	0.976179i	$-0.569616\pi$
$29$	−1965.26	−0.433935	−0.216967	+	0.976179i	$0.569616\pi$
$30$	−13.5976	−0.00275841
$31$	40.3615	0.00754333	0.00377167	−	0.999993i	$-0.498799\pi$
$31$	40.3615	0.00754333	0.00377167	+	0.999993i	$0.498799\pi$
$32$	6278.07	1.08381
$33$	2090.61	0.334187
$34$	−9127.32	−1.35408
$35$	39.3000	0.00542279
$36$	4066.97	0.523016
$37$	6134.45	0.736668	0.368334	−	0.929694i	$-0.379928\pi$
$37$	6134.45	0.736668	0.368334	+	0.929694i	$0.379928\pi$
$38$	−12140.1	−1.36384
$39$	2835.46	0.298512
$40$	27.5117	0.00271874
$41$	−19793.8	−1.83895	−0.919475	−	0.393149i	$-0.871386\pi$
$41$	−19793.8	−1.83895	−0.919475	+	0.393149i	$0.871386\pi$
$42$	−19245.9	−1.68351
$43$	17413.9	1.43623	0.718116	−	0.695923i	$-0.245005\pi$
$43$	17413.9	1.43623	0.718116	+	0.695923i	$0.245005\pi$
$44$	−11663.2	−0.908209
$45$	−13.4972	−0.000993600 0
$46$	−2299.18	−0.160206
$47$	−3171.34	−0.209411	−0.104705	−	0.994503i	$-0.533390\pi$
$47$	−3171.34	−0.209411	−0.104705	+	0.994503i	$0.533390\pi$
$48$	987.376	0.0618557
$49$	38817.9	2.30963
$50$	28334.0	1.60281
$51$	−9059.93	−0.487752
$52$	−15818.6	−0.811257
$53$	11419.0	0.558393	0.279197	−	0.960234i	$-0.409932\pi$
$53$	11419.0	0.558393	0.279197	+	0.960234i	$0.409932\pi$
$54$	6609.80	0.308464
$55$	38.7070	0.00172537
$56$	38939.9	1.65930
$57$	−12050.5	−0.491267
$58$	17818.9	0.695521
$59$	3189.32	0.119280	0.0596400	−	0.998220i	$-0.481005\pi$
$59$	3189.32	0.119280	0.0596400	+	0.998220i	$0.481005\pi$
$60$	75.2985	0.00270028
$61$	10586.7	0.364282	0.182141	−	0.983272i	$-0.441697\pi$
$61$	10586.7	0.364282	0.182141	+	0.983272i	$0.441697\pi$
$62$	−365.956	−0.0120906
$63$	−19103.8	−0.606413
$64$	−53412.3	−1.63001
$65$	52.4975	0.00154119
$66$	−18955.5	−0.535643
$67$	21129.5	0.575047	0.287523	−	0.957774i	$-0.407168\pi$
$67$	21129.5	0.575047	0.287523	+	0.957774i	$0.407168\pi$
$68$	50543.8	1.32555
$69$	−2282.20	−0.0577073
$70$	−356.331	−0.00869178
$71$	72862.7	1.71538	0.857688	−	0.514170i	$-0.171900\pi$
$71$	72862.7	1.71538	0.857688	+	0.514170i	$0.171900\pi$
$72$	−13373.5	−0.304028
$73$	78511.9	1.72436	0.862181	−	0.506600i	$-0.169098\pi$
$73$	78511.9	1.72436	0.862181	+	0.506600i	$0.169098\pi$
$74$	−55620.8	−1.18075
$75$	28124.8	0.577345
$76$	67227.7	1.33510
$77$	54785.6	1.05303
$78$	−25709.0	−0.478462
$79$	−1487.14	−0.0268092	−0.0134046	−	0.999910i	$-0.504267\pi$
$79$	−1487.14	−0.0268092	−0.0134046	+	0.999910i	$0.504267\pi$
$80$	18.2809	0.000319355 0
$81$	6561.00	0.111111
$82$	179469.	2.94751
$83$	11260.3	0.179414	0.0897070	−	0.995968i	$-0.471407\pi$
$83$	11260.3	0.179414	0.0897070	+	0.995968i	$0.471407\pi$
$84$	106577.	1.64803
$85$	−167.741	−0.00251821
$86$	−157891.	−2.30203
$87$	17687.3	0.250532
$88$	38352.3	0.527940
$89$	−72837.0	−0.974714	−0.487357	−	0.873203i	$-0.662039\pi$
$89$	−72837.0	−0.974714	−0.487357	+	0.873203i	$0.662039\pi$
$90$	122.378	0.00159257
$91$	74304.6	0.940615
$92$	12732.0	0.156830
$93$	−363.254	−0.00435515
$94$	28754.4	0.335649
$95$	−223.111	−0.00253636
$96$	−56502.7	−0.625736
$97$	10681.4	0.115266	0.0576328	−	0.998338i	$-0.481645\pi$
$97$	10681.4	0.115266	0.0576328	+	0.998338i	$0.481645\pi$
$98$	−351960.	−3.70193
$99$	−18815.5	−0.192943
$100$	−156903.	−1.56903
$101$	62850.7	0.613065	0.306533	−	0.951860i	$-0.400831\pi$
$101$	62850.7	0.613065	0.306533	+	0.951860i	$0.400831\pi$
$102$	82145.9	0.781781
$103$	195741.	1.81798	0.908991	−	0.416815i	$-0.136854\pi$
$103$	195741.	1.81798	0.908991	+	0.416815i	$0.136854\pi$
$104$	52016.4	0.471582
$105$	−353.700	−0.00313085
$106$	−103536.	−0.895007
$107$	−127008.	−1.07244	−0.536218	−	0.844080i	$-0.680147\pi$
$107$	−127008.	−1.07244	−0.536218	+	0.844080i	$0.680147\pi$
$108$	−36602.7	−0.301963
$109$	−19248.1	−0.155175	−0.0775873	−	0.996986i	$-0.524722\pi$
$109$	−19248.1	−0.155175	−0.0775873	+	0.996986i	$0.524722\pi$
$110$	−350.954	−0.00276547
$111$	−55210.1	−0.425315
$112$	25874.7	0.194908
$113$	220639.	1.62550	0.812750	−	0.582613i	$-0.197969\pi$
$113$	220639.	1.62550	0.812750	+	0.582613i	$0.197969\pi$
$114$	109261.	0.787415
$115$	−42.2541	−0.000297937 0
$116$	−98674.6	−0.680864
$117$	−25519.1	−0.172346
$118$	−28917.4	−0.191185
$119$	−237420.	−1.53691
$120$	−247.605	−0.00156967
$121$	−107092.	−0.664958
$122$	−95989.3	−0.583880
$123$	178144.	1.06172
$124$	2026.53	0.0118359
$125$	1041.44	0.00596158
$126$	173213.	0.971973
$127$	−194634.	−1.07080	−0.535401	−	0.844598i	$-0.679840\pi$
$127$	−194634.	−1.07080	−0.535401	+	0.844598i	$0.679840\pi$
$128$	283388.	1.52882
$129$	−156725.	−0.829209
$130$	−475.992	−0.00247025
$131$	−147110.	−0.748969	−0.374485	−	0.927233i	$-0.622180\pi$
$131$	−147110.	−0.748969	−0.374485	+	0.927233i	$0.622180\pi$
$132$	104969.	0.524355
$133$	−315789.	−1.54799
$134$	−191580.	−0.921699
$135$	121.475	0.000573655 0
$136$	−166204.	−0.770539
$137$	−203513.	−0.926382	−0.463191	−	0.886259i	$-0.653296\pi$
$137$	−203513.	−0.926382	−0.463191	+	0.886259i	$0.653296\pi$
$138$	20692.6	0.0924948
$139$	−240313.	−1.05497	−0.527484	−	0.849565i	$-0.676865\pi$
$139$	−240313.	−1.05497	−0.527484	+	0.849565i	$0.676865\pi$
$140$	1973.23	0.00850861
$141$	28542.1	0.120903
$142$	−660642.	−2.74945
$143$	73183.3	0.299276
$144$	−8886.38	−0.0357124
$145$	327.474	0.00129347
$146$	−711863.	−2.76385
$147$	−349361.	−1.33346
$148$	308008.	1.15587
$149$	−445458.	−1.64377	−0.821884	−	0.569655i	$-0.807077\pi$
$149$	−445458.	−1.64377	−0.821884	+	0.569655i	$0.807077\pi$
$150$	−255006.	−0.925383
$151$	433666.	1.54779	0.773896	−	0.633312i	$-0.218305\pi$
$151$	433666.	1.54779	0.773896	+	0.633312i	$0.218305\pi$
$152$	−221066.	−0.776091
$153$	81539.3	0.281604
$154$	−496738.	−1.68782
$155$	−6.72552	−2.24852e−5 0
$156$	142367.	0.468380
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	13483.8	0.0429705
$159$	−102771.	−0.322389
$160$	−1046.13	−0.00323061
$161$	−59806.2	−0.181837
$162$	−59488.2	−0.178092
$163$	631988.	1.86311	0.931557	−	0.363595i	$-0.118451\pi$
$163$	631988.	1.86311	0.931557	+	0.363595i	$0.118451\pi$
$164$	−993838.	−2.88540
$165$	−348.363	−0.000996144 0
$166$	−102097.	−0.287569
$167$	−156046.	−0.432974	−0.216487	−	0.976286i	$-0.569460\pi$
$167$	−156046.	−0.432974	−0.216487	+	0.976286i	$0.569460\pi$
$168$	−350459.	−0.957996
$169$	−272036.	−0.732672
$170$	1520.90	0.00403626
$171$	108454.	0.283633
$172$	874343.	2.25352
$173$	−494241.	−1.25552	−0.627759	−	0.778407i	$-0.716028\pi$
$173$	−494241.	−1.25552	−0.627759	+	0.778407i	$0.716028\pi$
$174$	−160370.	−0.401559
$175$	737023.	1.81922
$176$	25484.2	0.0620140
$177$	−28703.9	−0.0688664
$178$	660409.	1.56230
$179$	−246098.	−0.574083	−0.287042	−	0.957918i	$-0.592672\pi$
$179$	−246098.	−0.574083	−0.287042	+	0.957918i	$0.592672\pi$
$180$	−677.687	−0.00155901
$181$	−194915.	−0.442230	−0.221115	−	0.975248i	$-0.570970\pi$
$181$	−194915.	−0.442230	−0.221115	+	0.975248i	$0.570970\pi$
$182$	−673715.	−1.50764
$183$	−95280.6	−0.210318
$184$	−41866.9	−0.0911646
$185$	−1022.20	−0.00219586
$186$	3293.60	0.00698054
$187$	−233837.	−0.489001
$188$	−159232.	−0.328575
$189$	171934.	0.350113
$190$	2022.93	0.00406534
$191$	472176.	0.936527	0.468263	−	0.883589i	$-0.344880\pi$
$191$	472176.	0.936527	0.468263	+	0.883589i	$0.344880\pi$
$192$	480711.	0.941089
$193$	195827.	0.378424	0.189212	−	0.981936i	$-0.439407\pi$
$193$	195827.	0.378424	0.189212	+	0.981936i	$0.439407\pi$
$194$	−96847.8	−0.184750
$195$	−472.478	−0.000889805 0
$196$	1.94903e6	3.62392
$197$	−163895.	−0.300885	−0.150443	−	0.988619i	$-0.548070\pi$
$197$	−163895.	−0.300885	−0.150443	+	0.988619i	$0.548070\pi$
$198$	170599.	0.309253
$199$	−396710.	−0.710134	−0.355067	−	0.934841i	$-0.615542\pi$
$199$	−396710.	−0.710134	−0.355067	+	0.934841i	$0.615542\pi$
$200$	515948.	0.912076
$201$	−190166.	−0.332003
$202$	−569864.	−0.982636
$203$	463504.	0.789430
$204$	−454895.	−0.765306
$205$	3298.28	0.00548154
$206$	−1.77478e6	−2.91391
$207$	20539.8	0.0333173
$208$	34563.7	0.0553940
$209$	−311024.	−0.492524
$210$	3206.98	0.00501820
$211$	447531.	0.692018	0.346009	−	0.938231i	$-0.387537\pi$
$211$	447531.	0.692018	0.346009	+	0.938231i	$0.387537\pi$
$212$	573345.	0.876146
$213$	−655764.	−0.990373
$214$	1.15157e6	1.71893
$215$	−2901.71	−0.00428112
$216$	120361.	0.175531
$217$	−9519.24	−0.0137231
$218$	174521.	0.248718
$219$	−706607.	−0.995561
$220$	1943.46	0.00270719
$221$	−317149.	−0.436800
$222$	500587.	0.681706
$223$	−390619.	−0.526006	−0.263003	−	0.964795i	$-0.584713\pi$
$223$	−390619.	−0.526006	−0.263003	+	0.964795i	$0.584713\pi$
$224$	−1.48068e6	−1.97170
$225$	−253123.	−0.333330
$226$	−2.00053e6	−2.60539
$227$	204231.	0.263061	0.131530	−	0.991312i	$-0.458011\pi$
$227$	204231.	0.263061	0.131530	+	0.991312i	$0.458011\pi$
$228$	−605049.	−0.770821
$229$	132125.	0.166493	0.0832463	−	0.996529i	$-0.473471\pi$
$229$	132125.	0.166493	0.0832463	+	0.996529i	$0.473471\pi$
$230$	383.116	0.000477541 0
$231$	−493070.	−0.607965
$232$	324473.	0.395785
$233$	239473.	0.288979	0.144489	−	0.989506i	$-0.453846\pi$
$233$	239473.	0.288979	0.144489	+	0.989506i	$0.453846\pi$
$234$	231381.	0.276240
$235$	528.447	0.000624211 0
$236$	160134.	0.187156
$237$	13384.3	0.0154783
$238$	2.15267e6	2.46340
$239$	1.29339e6	1.46465	0.732325	−	0.680955i	$-0.238435\pi$
$239$	1.29339e6	1.46465	0.732325	+	0.680955i	$0.238435\pi$
$240$	−164.528	−0.000184379 0
$241$	−453889.	−0.503393	−0.251696	−	0.967806i	$-0.580988\pi$
$241$	−453889.	−0.503393	−0.251696	+	0.967806i	$0.580988\pi$
$242$	970999.	1.06581
$243$	−59049.0	−0.0641500
$244$	531555.	0.571575
$245$	−6468.30	−0.00688454
$246$	−1.61522e6	−1.70175
$247$	−421835.	−0.439947
$248$	−6663.88	−0.00688015
$249$	−101343.	−0.103585
$250$	−9442.72	−0.00955536
$251$	−1.19782e6	−1.20008	−0.600038	−	0.799972i	$-0.704848\pi$
$251$	−1.19782e6	−1.20008	−0.600038	+	0.799972i	$0.704848\pi$
$252$	−959193.	−0.951491
$253$	−58903.7	−0.0578551
$254$	1.76474e6	1.71631
$255$	1509.67	0.00145389
$256$	−860271.	−0.820418
$257$	−1.24531e6	−1.17610	−0.588049	−	0.808825i	$-0.700104\pi$
$257$	−1.24531e6	−1.17610	−0.588049	+	0.808825i	$0.700104\pi$
$258$	1.42102e6	1.32908
$259$	−1.44681e6	−1.34017
$260$	2635.88	0.00241820
$261$	−159186.	−0.144645
$262$	1.33384e6	1.20047
$263$	−1.27706e6	−1.13847	−0.569235	−	0.822175i	$-0.692761\pi$
$263$	−1.27706e6	−1.13847	−0.569235	+	0.822175i	$0.692761\pi$
$264$	−345170.	−0.304806
$265$	−1902.78	−0.00166446
$266$	2.86324e6	2.48115
$267$	655533.	0.562751
$268$	1.06090e6	0.902276
$269$	−562069.	−0.473597	−0.236798	−	0.971559i	$-0.576098\pi$
$269$	−562069.	−0.473597	−0.236798	+	0.971559i	$0.576098\pi$
$270$	−1101.40	−0.000919469 0
$271$	−1.96283e6	−1.62353	−0.811765	−	0.583985i	$-0.801493\pi$
$271$	−1.96283e6	−1.62353	−0.811765	+	0.583985i	$0.801493\pi$
$272$	−110439.	−0.0905107
$273$	−668741.	−0.543064
$274$	1.84524e6	1.48483
$275$	725901.	0.578823
$276$	−114588.	−0.0905456
$277$	223121.	0.174719	0.0873596	−	0.996177i	$-0.472157\pi$
$277$	223121.	0.174719	0.0873596	+	0.996177i	$0.472157\pi$
$278$	2.17890e6	1.69093
$279$	3269.28	0.00251444
$280$	−6488.62	−0.00494604
$281$	−610565.	−0.461282	−0.230641	−	0.973039i	$-0.574082\pi$
$281$	−610565.	−0.461282	−0.230641	+	0.973039i	$0.574082\pi$
$282$	−258790.	−0.193787
$283$	−646123.	−0.479567	−0.239784	−	0.970826i	$-0.577076\pi$
$283$	−646123.	−0.479567	−0.239784	+	0.970826i	$0.577076\pi$
$284$	3.65840e6	2.69151
$285$	2007.99	0.00146437
$286$	−663549.	−0.479687
$287$	4.66836e6	3.34549
$288$	508524.	0.361269
$289$	−406496.	−0.286294
$290$	−2969.19	−0.00207321
$291$	−96132.7	−0.0665486
$292$	3.94205e6	2.70561
$293$	2.04521e6	1.39177	0.695886	−	0.718153i	$-0.255012\pi$
$293$	2.04521e6	1.39177	0.695886	+	0.718153i	$0.255012\pi$
$294$	3.16764e6	2.13731
$295$	−531.442	−0.000355550 0
$296$	−1.01283e6	−0.671903
$297$	169340.	0.111396
$298$	4.03894e6	2.63467
$299$	−79889.9	−0.0516790
$300$	1.41213e6	0.905882
$301$	−4.10706e6	−2.61285
$302$	−3.93202e6	−2.48084
$303$	−565656.	−0.353953
$304$	−146893.	−0.0911629
$305$	−1764.09	−0.00108585
$306$	−739313.	−0.451362
$307$	1.61764e6	0.979569	0.489785	−	0.871843i	$-0.337075\pi$
$307$	1.61764e6	0.979569	0.489785	+	0.871843i	$0.337075\pi$
$308$	2.75076e6	1.65225
$309$	−1.76167e6	−1.04961
$310$	60.9799	3.60398e−5 0
$311$	427044.	0.250364	0.125182	−	0.992134i	$-0.460049\pi$
$311$	427044.	0.250364	0.125182	+	0.992134i	$0.460049\pi$
$312$	−468148.	−0.272268
$313$	2.53076e6	1.46012	0.730061	−	0.683382i	$-0.239492\pi$
$313$	2.53076e6	1.46012	0.730061	+	0.683382i	$0.239492\pi$
$314$	223491.	0.127919
$315$	3183.30	0.00180760
$316$	−74668.7	−0.0420650
$317$	−3.38893e6	−1.89415	−0.947074	−	0.321015i	$-0.895976\pi$
$317$	−3.38893e6	−1.89415	−0.947074	+	0.321015i	$0.895976\pi$
$318$	931823.	0.516732
$319$	456510.	0.251174
$320$	8900.19	0.00485875
$321$	1.14307e6	0.619171
$322$	542259.	0.291452
$323$	1.34786e6	0.718849
$324$	329425.	0.174339
$325$	984525.	0.517033
$326$	−5.73020e6	−2.98625
$327$	173233.	0.0895901
$328$	3.26805e6	1.67728
$329$	747959.	0.380968
$330$	3158.59	0.00159664
$331$	−543410.	−0.272620	−0.136310	−	0.990666i	$-0.543524\pi$
$331$	−543410.	−0.272620	−0.136310	+	0.990666i	$0.543524\pi$
$332$	565377.	0.281509
$333$	496891.	0.245556
$334$	1.41486e6	0.693981
$335$	−3520.85	−0.00171410
$336$	−232872.	−0.112530
$337$	−2.78614e6	−1.33638	−0.668188	−	0.743992i	$-0.732930\pi$
$337$	−2.78614e6	−1.33638	−0.668188	+	0.743992i	$0.732930\pi$
$338$	2.46654e6	1.17434
$339$	−1.98575e6	−0.938483
$340$	−8422.21	−0.00395120
$341$	−9375.60	−0.00436630
$342$	−983350.	−0.454614
$343$	−5.19126e6	−2.38253
$344$	−2.87512e6	−1.30996
$345$	380.287	0.000172014 0
$346$	4.48125e6	2.01238
$347$	781860.	0.348582	0.174291	−	0.984694i	$-0.444237\pi$
$347$	781860.	0.348582	0.174291	+	0.984694i	$0.444237\pi$
$348$	888071.	0.393097
$349$	−938859.	−0.412607	−0.206304	−	0.978488i	$-0.566143\pi$
$349$	−938859.	−0.412607	−0.206304	+	0.978488i	$0.566143\pi$
$350$	−6.68255e6	−2.91589
$351$	229672.	0.0995040
$352$	−1.45834e6	−0.627337
$353$	−2.61354e6	−1.11633	−0.558166	−	0.829730i	$-0.688495\pi$
$353$	−2.61354e6	−1.11633	−0.558166	+	0.829730i	$0.688495\pi$
$354$	260256.	0.110381
$355$	−12141.2	−0.00511319
$356$	−3.65711e6	−1.52937
$357$	2.13678e6	0.887337
$358$	2.23135e6	0.920155
$359$	3.31806e6	1.35878	0.679389	−	0.733779i	$-0.262245\pi$
$359$	3.31806e6	1.35878	0.679389	+	0.733779i	$0.262245\pi$
$360$	2228.45	0.000906247 0
$361$	−683330.	−0.275971
$362$	1.76728e6	0.708818
$363$	963829.	0.383914
$364$	3.73080e6	1.47587
$365$	−13082.6	−0.00513998
$366$	863904.	0.337103
$367$	3.08860e6	1.19700	0.598502	−	0.801121i	$-0.295763\pi$
$367$	3.08860e6	1.19700	0.598502	+	0.801121i	$0.295763\pi$
$368$	−27819.6	−0.0107086
$369$	−1.60330e6	−0.612983
$370$	9268.19	0.00351958
$371$	−2.69318e6	−1.01585
$372$	−18238.8	−0.00683343
$373$	1.03468e6	0.385064	0.192532	−	0.981291i	$-0.438330\pi$
$373$	1.03468e6	0.385064	0.192532	+	0.981291i	$0.438330\pi$
$374$	2.12019e6	0.783783
$375$	−9373.00	−0.00344192
$376$	523604.	0.191000
$377$	619156.	0.224361
$378$	−1.55892e6	−0.561169
$379$	3.56413e6	1.27455	0.637273	−	0.770638i	$-0.280062\pi$
$379$	3.56413e6	1.27455	0.637273	+	0.770638i	$0.280062\pi$
$380$	−11202.3	−0.00397967
$381$	1.75171e6	0.618228
$382$	−4.28119e6	−1.50109
$383$	2.07272e6	0.722011	0.361006	−	0.932564i	$-0.382434\pi$
$383$	2.07272e6	0.722011	0.361006	+	0.932564i	$0.382434\pi$
$384$	−2.55049e6	−0.882665
$385$	−9129.02	−0.00313886
$386$	−1.77555e6	−0.606547
$387$	1.41053e6	0.478744
$388$	536309.	0.180857
$389$	−3.35691e6	−1.12478	−0.562388	−	0.826874i	$-0.690117\pi$
$389$	−3.35691e6	−1.12478	−0.562388	+	0.826874i	$0.690117\pi$
$390$	4283.93	0.00142620
$391$	255266.	0.0844406
$392$	−6.40902e6	−2.10657
$393$	1.32399e6	0.432418
$394$	1.48603e6	0.482267
$395$	247.805	7.99130e−5 0
$396$	−944719.	−0.302736
$397$	−2.26190e6	−0.720273	−0.360137	−	0.932900i	$-0.617270\pi$
$397$	−2.26190e6	−0.720273	−0.360137	+	0.932900i	$0.617270\pi$
$398$	3.59695e6	1.13822
$399$	2.84210e6	0.893732
$400$	342836.	0.107136
$401$	157149.	0.0488035	0.0244017	−	0.999702i	$-0.492232\pi$
$401$	157149.	0.0488035	0.0244017	+	0.999702i	$0.492232\pi$
$402$	1.72422e6	0.532143
$403$	−12715.9	−0.00390019
$404$	3.15570e6	0.961928
$405$	−1093.27	−0.000331200 0
$406$	−4.20257e6	−1.26532
$407$	−1.42498e6	−0.426404
$408$	1.49584e6	0.444871
$409$	4.34050e6	1.28301	0.641507	−	0.767117i	$-0.278309\pi$
$409$	4.34050e6	1.28301	0.641507	+	0.767117i	$0.278309\pi$
$410$	−29905.3	−0.00878595
$411$	1.83161e6	0.534847
$412$	9.82808e6	2.85250
$413$	−752198.	−0.216999
$414$	−186233.	−0.0534019
$415$	−1876.33	−0.000534798 0
$416$	−1.97791e6	−0.560369
$417$	2.16281e6	0.609087
$418$	2.82004e6	0.789431
$419$	2.07994e6	0.578783	0.289391	−	0.957211i	$-0.406547\pi$
$419$	2.07994e6	0.578783	0.289391	+	0.957211i	$0.406547\pi$
$420$	−17759.1	−0.00491245
$421$	−5.58085e6	−1.53460	−0.767300	−	0.641288i	$-0.778400\pi$
$421$	−5.58085e6	−1.53460	−0.767300	+	0.641288i	$0.778400\pi$
$422$	−4.05774e6	−1.10918
$423$	−256879.	−0.0698035
$424$	−1.88534e6	−0.509302
$425$	−3.14578e6	−0.844804
$426$	5.94578e6	1.58739
$427$	−2.49687e6	−0.662715
$428$	−6.37700e6	−1.68270
$429$	−658650.	−0.172787
$430$	26309.6	0.00686189
$431$	1.41659e6	0.367324	0.183662	−	0.982989i	$-0.441205\pi$
$431$	1.41659e6	0.367324	0.183662	+	0.982989i	$0.441205\pi$
$432$	79977.5	0.0206186
$433$	−2.82817e6	−0.724913	−0.362457	−	0.932001i	$-0.618062\pi$
$433$	−2.82817e6	−0.724913	−0.362457	+	0.932001i	$0.618062\pi$
$434$	86310.5	0.0219958
$435$	−2947.27	−0.000746787 0
$436$	−966436.	−0.243476
$437$	339526.	0.0850491
$438$	6.40677e6	1.59571
$439$	−1.75466e6	−0.434543	−0.217271	−	0.976111i	$-0.569716\pi$
$439$	−1.75466e6	−0.434543	−0.217271	+	0.976111i	$0.569716\pi$
$440$	−6390.71	−0.00157368
$441$	3.14425e6	0.769876
$442$	2.87557e6	0.700113
$443$	−5.65130e6	−1.36817	−0.684083	−	0.729404i	$-0.739797\pi$
$443$	−5.65130e6	−1.36817	−0.684083	+	0.729404i	$0.739797\pi$
$444$	−2.77207e6	−0.667340
$445$	12137.0	0.00290543
$446$	3.54172e6	0.843096
$447$	4.00912e6	0.949030
$448$	1.25973e7	2.96538
$449$	−3.70601e6	−0.867542	−0.433771	−	0.901023i	$-0.642817\pi$
$449$	−3.70601e6	−0.867542	−0.433771	+	0.901023i	$0.642817\pi$
$450$	2.29505e6	0.534270
$451$	4.59791e6	1.06444
$452$	1.10782e7	2.55049
$453$	−3.90299e6	−0.893618
$454$	−1.85175e6	−0.421641
$455$	−12381.5	−0.00280379
$456$	1.98959e6	0.448077
$457$	3.67739e6	0.823663	0.411831	−	0.911260i	$-0.364889\pi$
$457$	3.67739e6	0.823663	0.411831	+	0.911260i	$0.364889\pi$
$458$	−1.19797e6	−0.266859
$459$	−733854.	−0.162584
$460$	−2121.56	−0.000467478 0
$461$	7.94334e6	1.74081	0.870404	−	0.492339i	$-0.163858\pi$
$461$	7.94334e6	1.74081	0.870404	+	0.492339i	$0.163858\pi$
$462$	4.47064e6	0.974462
$463$	−2.17114e6	−0.470690	−0.235345	−	0.971912i	$-0.575622\pi$
$463$	−2.17114e6	−0.470690	−0.235345	+	0.971912i	$0.575622\pi$
$464$	215605.	0.0464905
$465$	60.5296	1.29818e−5 0
$466$	−2.17128e6	−0.463182
$467$	−3.22329e6	−0.683922	−0.341961	−	0.939714i	$-0.611091\pi$
$467$	−3.22329e6	−0.683922	−0.341961	+	0.939714i	$0.611091\pi$
$468$	−1.28130e6	−0.270419
$469$	−4.98339e6	−1.04615
$470$	−4791.40	−0.00100050
$471$	221841.	0.0460776
$472$	−526572.	−0.108793
$473$	−4.04508e6	−0.831332
$474$	−121354.	−0.0248090
$475$	−4.18416e6	−0.850892
$476$	−1.19207e7	−2.41149
$477$	924943.	0.186131
$478$	−1.17271e7	−2.34758
$479$	−4.80404e6	−0.956682	−0.478341	−	0.878174i	$-0.658762\pi$
$479$	−4.80404e6	−0.956682	−0.478341	+	0.878174i	$0.658762\pi$
$480$	9415.14	0.00186519
$481$	−1.93267e6	−0.380885
$482$	4.11539e6	0.806850
$483$	538255.	0.104983
$484$	−5.37704e6	−1.04335
$485$	−1779.86	−0.000343584 0
$486$	535394.	0.102821
$487$	−102991.	−0.0196779	−0.00983893	−	0.999952i	$-0.503132\pi$
$487$	−102991.	−0.0196779	−0.00983893	+	0.999952i	$0.503132\pi$
$488$	−1.74792e6	−0.332255
$489$	−5.68789e6	−1.07567
$490$	58647.7	0.0110347
$491$	−1.88880e6	−0.353576	−0.176788	−	0.984249i	$-0.556571\pi$
$491$	−1.88880e6	−0.353576	−0.176788	+	0.984249i	$0.556571\pi$
$492$	8.94454e6	1.66589
$493$	−1.97834e6	−0.366593
$494$	3.82476e6	0.705158
$495$	3135.27	0.000575124 0
$496$	−4428.00	−0.000808171 0
$497$	−1.71846e7	−3.12068
$498$	918873.	0.166028
$499$	9.00002e6	1.61805	0.809026	−	0.587773i	$-0.199995\pi$
$499$	9.00002e6	1.61805	0.809026	+	0.587773i	$0.199995\pi$
$500$	52290.4	0.00935400
$501$	1.40441e6	0.249977
$502$	1.08606e7	1.92351
$503$	540205.	0.0952003	0.0476002	−	0.998866i	$-0.484843\pi$
$503$	540205.	0.0952003	0.0476002	+	0.998866i	$0.484843\pi$
$504$	3.15413e6	0.553099
$505$	−10472.9	−0.00182743
$506$	534077.	0.0927315
$507$	2.44832e6	0.423008
$508$	−9.77248e6	−1.68014
$509$	−2.38424e6	−0.407902	−0.203951	−	0.978981i	$-0.565378\pi$
$509$	−2.38424e6	−0.407902	−0.203951	+	0.978981i	$0.565378\pi$
$510$	−13688.1	−0.00233033
$511$	−1.85170e7	−3.13703
$512$	−1.26839e6	−0.213834
$513$	−976089.	−0.163756
$514$	1.12911e7	1.88508
$515$	−32616.8	−0.00541904
$516$	−7.86909e6	−1.30107
$517$	736673.	0.121213
$518$	1.31181e7	2.14806
$519$	4.44817e6	0.724874
$520$	−8667.59	−0.00140569
$521$	6.15337e6	0.993159	0.496580	−	0.867991i	$-0.334589\pi$
$521$	6.15337e6	0.993159	0.496580	+	0.867991i	$0.334589\pi$
$522$	1.44333e6	0.231840
$523$	−6.52959e6	−1.04384	−0.521918	−	0.852996i	$-0.674783\pi$
$523$	−6.52959e6	−1.04384	−0.521918	+	0.852996i	$0.674783\pi$
$524$	−7.38632e6	−1.17517
$525$	−6.63320e6	−1.05033
$526$	1.15790e7	1.82477
$527$	40630.3	0.00637270
$528$	−229358.	−0.0358038
$529$	−6.37204e6	−0.990010
$530$	17252.4	0.00266784
$531$	258335.	0.0397600
$532$	−1.58556e7	−2.42887
$533$	6.23606e6	0.950807
$534$	−5.94368e6	−0.901992
$535$	21163.5	0.00319672
$536$	−3.48859e6	−0.524491
$537$	2.21488e6	0.331447
$538$	5.09625e6	0.759092
$539$	−9.01703e6	−1.33688
$540$	6099.18	0.000900093 0
$541$	7.94032e6	1.16639	0.583196	−	0.812331i	$-0.301802\pi$
$541$	7.94032e6	1.16639	0.583196	+	0.812331i	$0.301802\pi$
$542$	1.77969e7	2.60223
$543$	1.75423e6	0.255322
$544$	6.31988e6	0.915612
$545$	3207.34	0.000462545 0
$546$	6.06344e6	0.870437
$547$	2.42439e6	0.346445	0.173223	−	0.984883i	$-0.444582\pi$
$547$	2.42439e6	0.346445	0.173223	+	0.984883i	$0.444582\pi$
$548$	−1.02183e7	−1.45354
$549$	857525.	0.121427
$550$	−6.58171e6	−0.927752
$551$	−2.63137e6	−0.369235
$552$	376802.	0.0526339
$553$	350741.	0.0487724
$554$	−2.02302e6	−0.280044
$555$	9199.76	0.00126778
$556$	−1.20660e7	−1.65530
$557$	−1.23158e7	−1.68200	−0.840999	−	0.541037i	$-0.818032\pi$
$557$	−1.23158e7	−1.68200	−0.840999	+	0.541037i	$0.818032\pi$
$558$	−29642.4	−0.00403022
$559$	−5.48626e6	−0.742587
$560$	−4311.54	−0.000580982 0
$561$	2.10453e6	0.282325
$562$	5.53596e6	0.739354
$563$	203953.	0.0271180	0.0135590	−	0.999908i	$-0.495684\pi$
$563$	203953.	0.0271180	0.0135590	+	0.999908i	$0.495684\pi$
$564$	1.43309e6	0.189703
$565$	−36765.5	−0.00484529
$566$	5.85837e6	0.768662
$567$	−1.54741e6	−0.202138
$568$	−1.20300e7	−1.56457
$569$	−6.62735e6	−0.858142	−0.429071	−	0.903271i	$-0.641159\pi$
$569$	−6.62735e6	−0.858142	−0.429071	+	0.903271i	$0.641159\pi$
$570$	−18206.4	−0.00234713
$571$	−5.07441e6	−0.651321	−0.325660	−	0.945487i	$-0.605587\pi$
$571$	−5.07441e6	−0.651321	−0.325660	+	0.945487i	$0.605587\pi$
$572$	3.67450e6	0.469579
$573$	−4.24958e6	−0.540704
$574$	−4.23277e7	−5.36223
$575$	−792424.	−0.0999511
$576$	−4.32640e6	−0.543338
$577$	−248791.	−0.0311097	−0.0155548	−	0.999879i	$-0.504951\pi$
$577$	−248791.	−0.0311097	−0.0155548	+	0.999879i	$0.504951\pi$
$578$	3.68568e6	0.458878
$579$	−1.76244e6	−0.218483
$580$	16442.3	0.00202952
$581$	−2.65575e6	−0.326397
$582$	871630.	0.106666
$583$	−2.65254e6	−0.323214
$584$	−1.29627e7	−1.57276
$585$	4252.30	0.000513729 0
$586$	−1.85438e7	−2.23077
$587$	−5.63092e6	−0.674503	−0.337252	−	0.941415i	$-0.609497\pi$
$587$	−5.63092e6	−0.674503	−0.337252	+	0.941415i	$0.609497\pi$
$588$	−1.75413e7	−2.09227
$589$	54041.8	0.00641862
$590$	4818.55	0.000569884 0
$591$	1.47506e6	0.173716
$592$	−673001.	−0.0789245
$593$	8.86128e6	1.03481	0.517404	−	0.855741i	$-0.326898\pi$
$593$	8.86128e6	1.03481	0.517404	+	0.855741i	$0.326898\pi$
$594$	−1.53539e6	−0.178548
$595$	39561.7	0.00458123
$596$	−2.23662e7	−2.57915
$597$	3.57039e6	0.409996
$598$	724358.	0.0828324
$599$	−1.17521e7	−1.33829	−0.669144	−	0.743133i	$-0.733339\pi$
$599$	−1.17521e7	−1.33829	−0.669144	+	0.743133i	$0.733339\pi$
$600$	−4.64353e6	−0.526587
$601$	4.44217e6	0.501659	0.250830	−	0.968031i	$-0.419297\pi$
$601$	4.44217e6	0.501659	0.250830	+	0.968031i	$0.419297\pi$
$602$	3.72385e7	4.18794
$603$	1.71149e6	0.191682
$604$	2.17742e7	2.42856
$605$	17845.0	0.00198211
$606$	5.12878e6	0.567325
$607$	−542930.	−0.0598098	−0.0299049	−	0.999553i	$-0.509520\pi$
$607$	−542930.	−0.0598098	−0.0299049	+	0.999553i	$0.509520\pi$
$608$	8.40598e6	0.922209
$609$	−4.17154e6	−0.455778
$610$	15994.9	0.00174043
$611$	999135.	0.108273
$612$	4.09405e6	0.441850
$613$	6.99790e6	0.752171	0.376086	−	0.926585i	$-0.377270\pi$
$613$	6.99790e6	0.752171	0.376086	+	0.926585i	$0.377270\pi$
$614$	−1.46670e7	−1.57008
$615$	−29684.5	−0.00316477
$616$	−9.04536e6	−0.960448
$617$	−3.65455e6	−0.386475	−0.193237	−	0.981152i	$-0.561899\pi$
$617$	−3.65455e6	−0.386475	−0.193237	+	0.981152i	$0.561899\pi$
$618$	1.59730e7	1.68235
$619$	−1.55139e7	−1.62740	−0.813702	−	0.581282i	$-0.802551\pi$
$619$	−1.55139e7	−1.62740	−0.813702	+	0.581282i	$0.802551\pi$
$620$	−337.685	−3.52803e−5 0
$621$	−184858.	−0.0192358
$622$	−3.87199e6	−0.401290
$623$	1.71786e7	1.77324
$624$	−311074.	−0.0319817
$625$	9.76536e6	0.999973
$626$	−2.29462e7	−2.34032
$627$	2.79921e6	0.284359
$628$	−1.23761e6	−0.125224
$629$	6.17530e6	0.622345
$630$	−28862.8	−0.00289726
$631$	1.88005e7	1.87973	0.939867	−	0.341541i	$-0.110949\pi$
$631$	1.88005e7	1.87973	0.939867	+	0.341541i	$0.110949\pi$
$632$	245534.	0.0244523
$633$	−4.02778e6	−0.399537
$634$	3.07272e7	3.03599
$635$	32432.2	0.00319185
$636$	−5.16011e6	−0.505843
$637$	−1.22296e7	−1.19417
$638$	−4.13916e6	−0.402587
$639$	5.90188e6	0.571792
$640$	−47221.5	−0.00455711
$641$	−4.55614e6	−0.437977	−0.218989	−	0.975727i	$-0.570276\pi$
$641$	−4.55614e6	−0.437977	−0.218989	+	0.975727i	$0.570276\pi$
$642$	−1.03642e7	−0.992422
$643$	1.50072e7	1.43144	0.715720	−	0.698388i	$-0.246099\pi$
$643$	1.50072e7	1.43144	0.715720	+	0.698388i	$0.246099\pi$
$644$	−3.00284e6	−0.285310
$645$	26115.4	0.00247171
$646$	−1.22210e7	−1.15219
$647$	1.37203e7	1.28855	0.644277	−	0.764792i	$-0.277158\pi$
$647$	1.37203e7	1.28855	0.644277	+	0.764792i	$0.277158\pi$
$648$	−1.08325e6	−0.101343
$649$	−740848.	−0.0690426
$650$	−8.92664e6	−0.828714
$651$	85673.2	0.00792305
$652$	3.17318e7	2.92332
$653$	1.14043e7	1.04662	0.523308	−	0.852144i	$-0.324698\pi$
$653$	1.14043e7	1.04662	0.523308	+	0.852144i	$0.324698\pi$
$654$	−1.57069e6	−0.143597
$655$	24513.2	0.00223253
$656$	2.17155e6	0.197020
$657$	6.35947e6	0.574787
$658$	−6.78171e6	−0.610625
$659$	1.41702e7	1.27105	0.635527	−	0.772079i	$-0.280783\pi$
$659$	1.41702e7	1.27105	0.635527	+	0.772079i	$0.280783\pi$
$660$	−17491.1	−0.00156300
$661$	2.11936e6	0.188669	0.0943344	−	0.995541i	$-0.469928\pi$
$661$	2.11936e6	0.188669	0.0943344	+	0.995541i	$0.469928\pi$
$662$	4.92707e6	0.436962
$663$	2.85434e6	0.252186
$664$	−1.85914e6	−0.163641
$665$	52620.5	0.00461425
$666$	−4.50528e6	−0.393583
$667$	−498345.	−0.0433726
$668$	−7.83499e6	−0.679356
$669$	3.51557e6	0.303690
$670$	31923.4	0.00274740
$671$	−2.45920e6	−0.210856
$672$	1.33261e7	1.13836
$673$	3.06185e6	0.260583	0.130292	−	0.991476i	$-0.458409\pi$
$673$	3.06185e6	0.260583	0.130292	+	0.991476i	$0.458409\pi$
$674$	2.52618e7	2.14198
$675$	2.27810e6	0.192448
$676$	−1.36588e7	−1.14960
$677$	9.23040e6	0.774014	0.387007	−	0.922077i	$-0.373509\pi$
$677$	9.23040e6	0.774014	0.387007	+	0.922077i	$0.373509\pi$
$678$	1.80047e7	1.50422
$679$	−2.51920e6	−0.209695
$680$	27694.9	0.00229682
$681$	−1.83808e6	−0.151878
$682$	85008.1	0.00699841
$683$	1.14530e7	0.939433	0.469716	−	0.882817i	$-0.344356\pi$
$683$	1.14530e7	0.939433	0.469716	+	0.882817i	$0.344356\pi$
$684$	5.44544e6	0.445034
$685$	33911.7	0.00276136
$686$	4.70689e7	3.81877
$687$	−1.18912e6	−0.0961246
$688$	−1.91045e6	−0.153874
$689$	−3.59758e6	−0.288711
$690$	−3448.04	−0.000275708 0
$691$	−3.31137e6	−0.263823	−0.131911	−	0.991261i	$-0.542111\pi$
$691$	−3.31137e6	−0.263823	−0.131911	+	0.991261i	$0.542111\pi$
$692$	−2.48156e7	−1.96997
$693$	4.43763e6	0.351009
$694$	−7.08908e6	−0.558716
$695$	40043.7	0.00314465
$696$	−2.92026e6	−0.228506
$697$	−1.99256e7	−1.55357
$698$	8.51259e6	0.661337
$699$	−2.15525e6	−0.166842
$700$	3.70056e7	2.85445
$701$	1.80374e7	1.38637	0.693183	−	0.720761i	$-0.256208\pi$
$701$	1.80374e7	1.38637	0.693183	+	0.720761i	$0.256208\pi$
$702$	−2.08243e6	−0.159487
$703$	8.21368e6	0.626830
$704$	1.24072e7	0.943498
$705$	−4756.02	−0.000360389 0
$706$	2.36969e7	1.78928
$707$	−1.48233e7	−1.11531
$708$	−1.44121e6	−0.108055
$709$	6.58975e6	0.492327	0.246163	−	0.969228i	$-0.420830\pi$
$709$	6.58975e6	0.492327	0.246163	+	0.969228i	$0.420830\pi$
$710$	110084.	0.00819556
$711$	−120458.	−0.00893641
$712$	1.20257e7	0.889020
$713$	10234.8	0.000753972 0
$714$	−1.93740e7	−1.42225
$715$	−12194.7	−0.000892083 0
$716$	−1.23564e7	−0.900764
$717$	−1.16405e7	−0.845617
$718$	−3.00847e7	−2.17788
$719$	2.73541e7	1.97333	0.986665	−	0.162761i	$-0.0520400\pi$
$719$	2.73541e7	1.97333	0.986665	+	0.162761i	$0.0520400\pi$
$720$	1480.75	0.000106452 0
$721$	−4.61655e7	−3.30734
$722$	6.19572e6	0.442333
$723$	4.08500e6	0.290634
$724$	−9.78658e6	−0.693881
$725$	6.14137e6	0.433931
$726$	−8.73899e6	−0.615346
$727$	1.29667e7	0.909897	0.454949	−	0.890518i	$-0.349658\pi$
$727$	1.29667e7	0.909897	0.454949	+	0.890518i	$0.349658\pi$
$728$	−1.22680e7	−0.857920
$729$	531441.	0.0370370
$730$	118619.	0.00823849
$731$	1.75298e7	1.21335
$732$	−4.78399e6	−0.329999
$733$	2.24499e6	0.154332	0.0771659	−	0.997018i	$-0.475413\pi$
$733$	2.24499e6	0.154332	0.0771659	+	0.997018i	$0.475413\pi$
$734$	−2.80041e7	−1.91859
$735$	58214.7	0.00397479
$736$	1.59198e6	0.108329
$737$	−4.90819e6	−0.332853
$738$	1.45370e7	0.982505
$739$	−1.04930e7	−0.706785	−0.353393	−	0.935475i	$-0.614972\pi$
$739$	−1.04930e7	−0.706785	−0.353393	+	0.935475i	$0.614972\pi$
$740$	−51323.9	−0.00344541
$741$	3.79652e6	0.254004
$742$	2.44189e7	1.62823
$743$	−7.66322e6	−0.509259	−0.254630	−	0.967039i	$-0.581954\pi$
$743$	−7.66322e6	−0.509259	−0.254630	+	0.967039i	$0.581954\pi$
$744$	59974.9	0.00397226
$745$	74227.4	0.00489975
$746$	−9.38137e6	−0.617190
$747$	912088.	0.0598047
$748$	−1.17409e7	−0.767265
$749$	2.99547e7	1.95102
$750$	84984.5	0.00551679
$751$	8.66839e6	0.560840	0.280420	−	0.959877i	$-0.409526\pi$
$751$	8.66839e6	0.560840	0.280420	+	0.959877i	$0.409526\pi$
$752$	347923.	0.0224357
$753$	1.07804e7	0.692864
$754$	−5.61385e6	−0.359611
$755$	−72262.5	−0.00461366
$756$	8.63273e6	0.549343
$757$	−7.08188e6	−0.449168	−0.224584	−	0.974455i	$-0.572102\pi$
$757$	−7.08188e6	−0.449168	−0.224584	+	0.974455i	$0.572102\pi$
$758$	−3.23158e7	−2.04287
$759$	530133.	0.0334026
$760$	36836.6	0.00231337
$761$	2.43642e7	1.52507	0.762535	−	0.646947i	$-0.223955\pi$
$761$	2.43642e7	1.52507	0.762535	+	0.646947i	$0.223955\pi$
$762$	−1.58826e7	−0.990912
$763$	4.53964e6	0.282300
$764$	2.37077e7	1.46946
$765$	−13587.0	−0.000839405 0
$766$	−1.87933e7	−1.15726
$767$	−1.00480e6	−0.0616723
$768$	7.74244e6	0.473669
$769$	530453.	0.0323468	0.0161734	−	0.999869i	$-0.494852\pi$
$769$	530453.	0.0323468	0.0161734	+	0.999869i	$0.494852\pi$
$770$	82772.3	0.00503105
$771$	1.12078e7	0.679020
$772$	9.83237e6	0.593765
$773$	−9.56457e6	−0.575727	−0.287864	−	0.957671i	$-0.592945\pi$
$773$	−9.56457e6	−0.575727	−0.287864	+	0.957671i	$0.592945\pi$
$774$	−1.27892e7	−0.767343
$775$	−126129.	−0.00754327
$776$	−1.76355e6	−0.105132
$777$	1.30213e7	0.773750
$778$	3.04369e7	1.80282
$779$	−2.65028e7	−1.56476
$780$	−23722.9	−0.00139615
$781$	−1.69253e7	−0.992908
$782$	−2.31449e6	−0.135344
$783$	1.43267e6	0.0835107
$784$	−4.25865e6	−0.247447
$785$	4107.31	0.000237894 0
$786$	−1.20045e7	−0.693090
$787$	−2.07766e7	−1.19574	−0.597872	−	0.801591i	$-0.703987\pi$
$787$	−2.07766e7	−1.19574	−0.597872	+	0.801591i	$0.703987\pi$
$788$	−8.22911e6	−0.472104
$789$	1.14935e7	0.657297
$790$	−2246.84	−0.000128087 0
$791$	−5.20377e7	−2.95717
$792$	3.10653e6	0.175980
$793$	−3.33536e6	−0.188347
$794$	2.05085e7	1.15447
$795$	17125.0	0.000960976 0
$796$	−1.99186e7	−1.11423
$797$	1.84720e7	1.03007	0.515037	−	0.857168i	$-0.327778\pi$
$797$	1.84720e7	1.03007	0.515037	+	0.857168i	$0.327778\pi$
$798$	−2.57692e7	−1.43250
$799$	−3.19246e6	−0.176912
$800$	−1.96188e7	−1.08380
$801$	−5.89980e6	−0.324905
$802$	−1.42486e6	−0.0782235
$803$	−1.82376e7	−0.998109
$804$	−9.54814e6	−0.520929
$805$	9965.61	0.000542019 0
$806$	115295.	0.00625132
$807$	5.05862e6	0.273431
$808$	−1.03770e7	−0.559167
$809$	56404.3	0.00302999	0.00151500	−	0.999999i	$-0.499518\pi$
$809$	56404.3	0.00302999	0.00151500	+	0.999999i	$0.499518\pi$
$810$	9912.63	0.000530856 0
$811$	−8.95732e6	−0.478218	−0.239109	−	0.970993i	$-0.576855\pi$
$811$	−8.95732e6	−0.478218	−0.239109	+	0.970993i	$0.576855\pi$
$812$	2.32723e7	1.23865
$813$	1.76655e7	0.937345
$814$	1.29202e7	0.683451
$815$	−105309.	−0.00555357
$816$	993950.	0.0522564
$817$	2.33162e7	1.22209
$818$	−3.93551e7	−2.05645
$819$	6.01867e6	0.313538
$820$	165605.	0.00860080
$821$	−7.97271e6	−0.412808	−0.206404	−	0.978467i	$-0.566176\pi$
$821$	−7.97271e6	−0.412808	−0.206404	+	0.978467i	$0.566176\pi$
$822$	−1.66071e7	−0.857265
$823$	1.71254e7	0.881338	0.440669	−	0.897670i	$-0.354741\pi$
$823$	1.71254e7	0.881338	0.440669	+	0.897670i	$0.354741\pi$
$824$	−3.23178e7	−1.65815
$825$	−6.53311e6	−0.334184
$826$	6.82014e6	0.347811
$827$	−2.12587e7	−1.08087	−0.540436	−	0.841385i	$-0.681741\pi$
$827$	−2.12587e7	−1.08087	−0.540436	+	0.841385i	$0.681741\pi$
$828$	1.03129e6	0.0522765
$829$	3.55835e7	1.79830	0.899150	−	0.437640i	$-0.144186\pi$
$829$	3.55835e7	1.79830	0.899150	+	0.437640i	$0.144186\pi$
$830$	17012.6	0.000857187 0
$831$	−2.00809e6	−0.100874
$832$	1.68276e7	0.842779
$833$	3.90764e7	1.95120
$834$	−1.96101e7	−0.976259
$835$	26002.2	0.00129061
$836$	−1.56164e7	−0.772794
$837$	−29423.6	−0.00145172
$838$	−1.88587e7	−0.927688
$839$	−2.66380e7	−1.30646	−0.653230	−	0.757159i	$-0.726587\pi$
$839$	−2.66380e7	−1.30646	−0.653230	+	0.757159i	$0.726587\pi$
$840$	58397.6	0.00285560
$841$	−1.66489e7	−0.811701
$842$	5.06013e7	2.45970
$843$	5.49509e6	0.266321
$844$	2.24703e7	1.08581
$845$	45329.8	0.00218395
$846$	2.32911e6	0.111883
$847$	2.52576e7	1.20972
$848$	−1.25277e6	−0.0598247
$849$	5.81511e6	0.276878
$850$	2.85226e7	1.35407
$851$	1.55556e6	0.0736314
$852$	−3.29256e7	−1.55394
$853$	−4.13446e7	−1.94557	−0.972783	−	0.231717i	$-0.925566\pi$
$853$	−4.13446e7	−1.94557	−0.972783	+	0.231717i	$0.925566\pi$
$854$	2.26390e7	1.06222
$855$	−18072.0	−0.000845454 0
$856$	2.09696e7	0.978151
$857$	−4.21725e6	−0.196145	−0.0980724	−	0.995179i	$-0.531268\pi$
$857$	−4.21725e6	−0.196145	−0.0980724	+	0.995179i	$0.531268\pi$
$858$	5.97195e6	0.276948
$859$	−1.02492e6	−0.0473923	−0.0236962	−	0.999719i	$-0.507543\pi$
$859$	−1.02492e6	−0.0473923	−0.0236962	+	0.999719i	$0.507543\pi$
$860$	−145693.	−0.00671729
$861$	−4.20152e7	−1.93152
$862$	−1.28441e7	−0.588757
$863$	−5.30989e6	−0.242694	−0.121347	−	0.992610i	$-0.538721\pi$
$863$	−5.30989e6	−0.242694	−0.121347	+	0.992610i	$0.538721\pi$
$864$	−4.57672e6	−0.208579
$865$	82356.2	0.00374245
$866$	2.56429e7	1.16191
$867$	3.65846e6	0.165292
$868$	−477957.	−0.0215322
$869$	345449.	0.0155179
$870$	26722.7	0.00119697
$871$	−6.65688e6	−0.297321
$872$	3.17795e6	0.141532
$873$	865194.	0.0384218
$874$	−3.07847e6	−0.136319
$875$	−245624.	−0.0108455
$876$	−3.54784e7	−1.56208
$877$	2.09744e7	0.920855	0.460428	−	0.887697i	$-0.347696\pi$
$877$	2.09744e7	0.920855	0.460428	+	0.887697i	$0.347696\pi$
$878$	1.59094e7	0.696496
$879$	−1.84069e7	−0.803540
$880$	−4246.48	−0.000184851 0
$881$	−7.46605e6	−0.324079	−0.162040	−	0.986784i	$-0.551807\pi$
$881$	−7.46605e6	−0.324079	−0.162040	+	0.986784i	$0.551807\pi$
$882$	−2.85088e7	−1.23398
$883$	1.92000e7	0.828705	0.414353	−	0.910116i	$-0.364008\pi$
$883$	1.92000e7	0.828705	0.414353	+	0.910116i	$0.364008\pi$
$884$	−1.59239e7	−0.685359
$885$	4782.98	0.000205277 0
$886$	5.12400e7	2.19293
$887$	−2.64369e7	−1.12824	−0.564121	−	0.825692i	$-0.690785\pi$
$887$	−2.64369e7	−1.12824	−0.564121	+	0.825692i	$0.690785\pi$
$888$	9.11545e6	0.387923
$889$	4.59043e7	1.94805
$890$	−110045.	−0.00465689
$891$	−1.52406e6	−0.0643143
$892$	−1.96128e7	−0.825329
$893$	−4.24625e6	−0.178187
$894$	−3.63505e7	−1.52113
$895$	41007.7	0.00171123
$896$	−6.68369e7	−2.78129
$897$	719009.	0.0298369
$898$	3.36022e7	1.39052
$899$	−79320.8	−0.00327331
$900$	−1.27092e7	−0.523011
$901$	1.14951e7	0.471737
$902$	−4.16890e7	−1.70610
$903$	3.69635e7	1.50853
$904$	−3.64286e7	−1.48259
$905$	32479.0	0.00131820
$906$	3.53882e7	1.43231
$907$	−3.62300e7	−1.46235	−0.731173	−	0.682192i	$-0.761027\pi$
$907$	−3.62300e7	−1.46235	−0.731173	+	0.682192i	$0.761027\pi$
$908$	1.02543e7	0.412755
$909$	5.09091e6	0.204355
$910$	112262.	0.00449398
$911$	−1.17627e7	−0.469580	−0.234790	−	0.972046i	$-0.575440\pi$
$911$	−1.17627e7	−0.469580	−0.234790	+	0.972046i	$0.575440\pi$
$912$	1.32204e6	0.0526329
$913$	−2.61567e6	−0.103850
$914$	−3.33427e7	−1.32019
$915$	15876.8	0.000626916 0
$916$	6.63392e6	0.261235
$917$	3.46958e7	1.36255
$918$	6.65381e6	0.260594
$919$	−3.11827e7	−1.21794	−0.608969	−	0.793194i	$-0.708417\pi$
$919$	−3.11827e7	−1.21794	−0.608969	+	0.793194i	$0.708417\pi$
$920$	6976.36	0.000271744 0
$921$	−1.45587e7	−0.565555
$922$	−7.20218e7	−2.79021
$923$	−2.29555e7	−0.886914
$924$	−2.47568e7	−0.953926
$925$	−1.91700e7	−0.736661
$926$	1.96856e7	0.754434
$927$	1.58551e7	0.605994
$928$	−1.23380e7	−0.470301
$929$	−1.01462e7	−0.385712	−0.192856	−	0.981227i	$-0.561775\pi$
$929$	−1.01462e7	−0.385712	−0.192856	+	0.981227i	$0.561775\pi$
$930$	−548.819	−2.08076e−5 0
$931$	5.19750e7	1.96526
$932$	1.20238e7	0.453421
$933$	−3.84340e6	−0.144548
$934$	2.92254e7	1.09621
$935$	38964.7	0.00145761
$936$	4.21333e6	0.157194
$937$	−2.65346e7	−0.987334	−0.493667	−	0.869651i	$-0.664344\pi$
$937$	−2.65346e7	−0.987334	−0.493667	+	0.869651i	$0.664344\pi$
$938$	4.51841e7	1.67679
$939$	−2.27768e7	−0.843002
$940$	26533.1	0.000979417 0
$941$	−2.85355e6	−0.105054	−0.0525268	−	0.998620i	$-0.516727\pi$
$941$	−2.85355e6	−0.105054	−0.0525268	+	0.998620i	$0.516727\pi$
$942$	−2.01142e6	−0.0738543
$943$	−5.01927e6	−0.183807
$944$	−349895.	−0.0127793
$945$	−28649.7	−0.00104362
$946$	3.66765e7	1.33248
$947$	3.35810e7	1.21680	0.608399	−	0.793631i	$-0.291812\pi$
$947$	3.35810e7	1.21680	0.608399	+	0.793631i	$0.291812\pi$
$948$	672018.	0.0242862
$949$	−2.47353e7	−0.891560
$950$	3.79376e7	1.36383
$951$	3.05003e7	1.09359
$952$	3.91991e7	1.40179
$953$	−2.51007e7	−0.895270	−0.447635	−	0.894216i	$-0.647734\pi$
$953$	−2.51007e7	−0.895270	−0.447635	+	0.894216i	$0.647734\pi$
$954$	−8.38641e6	−0.298336
$955$	−78679.5	−0.00279160
$956$	6.49404e7	2.29811
$957$	−4.10859e6	−0.145015
$958$	4.35580e7	1.53339
$959$	4.79983e7	1.68531
$960$	−80101.7	−0.00280520
$961$	−2.86275e7	−0.999943
$962$	1.75234e7	0.610492
$963$	−1.02876e7	−0.357478
$964$	−2.27895e7	−0.789847
$965$	−32631.0	−0.00112801
$966$	−4.88033e6	−0.168270
$967$	−6.67124e6	−0.229425	−0.114712	−	0.993399i	$-0.536595\pi$
$967$	−6.67124e6	−0.229425	−0.114712	+	0.993399i	$0.536595\pi$
$968$	1.76814e7	0.606497
$969$	−1.21307e7	−0.415028
$970$	16137.9	0.000550704 0
$971$	−3.04329e7	−1.03585	−0.517923	−	0.855427i	$-0.673295\pi$
$971$	−3.04329e7	−1.03585	−0.517923	+	0.855427i	$0.673295\pi$
$972$	−2.96482e6	−0.100654
$973$	5.66776e7	1.91924
$974$	933816.	0.0315402
$975$	−8.86073e6	−0.298509
$976$	−1.16145e6	−0.0390281
$977$	−1.43545e7	−0.481118	−0.240559	−	0.970635i	$-0.577331\pi$
$977$	−1.43545e7	−0.481118	−0.240559	+	0.970635i	$0.577331\pi$
$978$	5.15718e7	1.72411
$979$	1.69193e7	0.564192
$980$	−324770.	−0.0108022
$981$	−1.55909e6	−0.0517249
$982$	1.71257e7	0.566721
$983$	1.37134e7	0.452649	0.226324	−	0.974052i	$-0.427329\pi$
$983$	1.37134e7	0.452649	0.226324	+	0.974052i	$0.427329\pi$
$984$	−2.94125e7	−0.968376
$985$	27310.2	0.000896880 0
$986$	1.79375e7	0.587584
$987$	−6.73163e6	−0.219952
$988$	−2.11801e7	−0.690298
$989$	4.41578e6	0.143554
$990$	−28427.3	−0.000921823 0
$991$	−1.77736e7	−0.574897	−0.287449	−	0.957796i	$-0.592807\pi$
$991$	−1.77736e7	−0.574897	−0.287449	+	0.957796i	$0.592807\pi$
$992$	253393.	0.00817551
$993$	4.89069e6	0.157397
$994$	1.55812e8	5.00190
$995$	66104.5	0.00211677
$996$	−5.08839e6	−0.162529
$997$	−1.83988e6	−0.0586207	−0.0293104	−	0.999570i	$-0.509331\pi$
$997$	−1.83988e6	−0.0586207	−0.0293104	+	0.999570i	$0.509331\pi$
$998$	−8.16027e7	−2.59345
$999$	−4.47202e6	−0.141772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-9.06695 q^{2} -9.00000 q^{3} +50.2095 q^{4} -0.166632 q^{5} +81.6025 q^{6} -235.849 q^{7} -165.105 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.06695 q^{2} -9.00000 q^{3} +50.2095 q^{4} -0.166632 q^{5} +81.6025 q^{6} -235.849 q^{7} -165.105 q^{8} +81.0000 q^{9} +1.51084 q^{10} -232.290 q^{11} -451.886 q^{12} -315.051 q^{13} +2138.43 q^{14} +1.49969 q^{15} -109.708 q^{16} +1006.66 q^{17} -734.423 q^{18} +1338.94 q^{19} -8.36651 q^{20} +2122.64 q^{21} +2106.17 q^{22} +253.578 q^{23} +1485.94 q^{24} -3124.97 q^{25} +2856.55 q^{26} -729.000 q^{27} -11841.9 q^{28} -1965.26 q^{29} -13.5976 q^{30} +40.3615 q^{31} +6278.07 q^{32} +2090.61 q^{33} -9127.32 q^{34} +39.3000 q^{35} +4066.97 q^{36} +6134.45 q^{37} -12140.1 q^{38} +2835.46 q^{39} +27.5117 q^{40} -19793.8 q^{41} -19245.9 q^{42} +17413.9 q^{43} -11663.2 q^{44} -13.4972 q^{45} -2299.18 q^{46} -3171.34 q^{47} +987.376 q^{48} +38817.9 q^{49} +28334.0 q^{50} -9059.93 q^{51} -15818.6 q^{52} +11419.0 q^{53} +6609.80 q^{54} +38.7070 q^{55} +38939.9 q^{56} -12050.5 q^{57} +17818.9 q^{58} +3189.32 q^{59} +75.2985 q^{60} +10586.7 q^{61} -365.956 q^{62} -19103.8 q^{63} -53412.3 q^{64} +52.4975 q^{65} -18955.5 q^{66} +21129.5 q^{67} +50543.8 q^{68} -2282.20 q^{69} -356.331 q^{70} +72862.7 q^{71} -13373.5 q^{72} +78511.9 q^{73} -55620.8 q^{74} +28124.8 q^{75} +67227.7 q^{76} +54785.6 q^{77} -25709.0 q^{78} -1487.14 q^{79} +18.2809 q^{80} +6561.00 q^{81} +179469. q^{82} +11260.3 q^{83} +106577. q^{84} -167.741 q^{85} -157891. q^{86} +17687.3 q^{87} +38352.3 q^{88} -72837.0 q^{89} +122.378 q^{90} +74304.6 q^{91} +12732.0 q^{92} -363.254 q^{93} +28754.4 q^{94} -223.111 q^{95} -56502.7 q^{96} +10681.4 q^{97} -351960. q^{98} -18815.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 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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