LMFDB - Embedded newform 547.6.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,6,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	547.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:	$87.7299494377$
Analytic rank:	$0$
Dimension:	$117$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.84956 q^{2} +5.64544 q^{3} +46.3147 q^{4} -23.6980 q^{5} -49.9597 q^{6} -115.238 q^{7} -126.678 q^{8} -211.129 q^{9} +O(q^{10})$	\(q-8.84956 q^{2} +5.64544 q^{3} +46.3147 q^{4} -23.6980 q^{5} -49.9597 q^{6} -115.238 q^{7} -126.678 q^{8} -211.129 q^{9} +209.717 q^{10} -62.0590 q^{11} +261.467 q^{12} -448.303 q^{13} +1019.80 q^{14} -133.786 q^{15} -361.022 q^{16} -452.680 q^{17} +1868.40 q^{18} +115.074 q^{19} -1097.57 q^{20} -650.569 q^{21} +549.195 q^{22} -4523.01 q^{23} -715.156 q^{24} -2563.40 q^{25} +3967.28 q^{26} -2563.76 q^{27} -5337.20 q^{28} -6665.11 q^{29} +1183.94 q^{30} +2458.38 q^{31} +7248.59 q^{32} -350.351 q^{33} +4006.01 q^{34} +2730.91 q^{35} -9778.37 q^{36} +826.603 q^{37} -1018.36 q^{38} -2530.87 q^{39} +3002.03 q^{40} +2155.90 q^{41} +5757.25 q^{42} -4045.10 q^{43} -2874.24 q^{44} +5003.34 q^{45} +40026.6 q^{46} -571.672 q^{47} -2038.13 q^{48} -3527.23 q^{49} +22685.0 q^{50} -2555.58 q^{51} -20763.0 q^{52} +2303.70 q^{53} +22688.1 q^{54} +1470.67 q^{55} +14598.1 q^{56} +649.646 q^{57} +58983.3 q^{58} -21518.1 q^{59} -6196.24 q^{60} -45223.9 q^{61} -21755.5 q^{62} +24330.1 q^{63} -52594.1 q^{64} +10623.9 q^{65} +3100.45 q^{66} -23066.5 q^{67} -20965.7 q^{68} -25534.4 q^{69} -24167.3 q^{70} +77787.8 q^{71} +26745.5 q^{72} +31851.5 q^{73} -7315.07 q^{74} -14471.6 q^{75} +5329.63 q^{76} +7151.55 q^{77} +22397.1 q^{78} -51435.8 q^{79} +8555.49 q^{80} +36830.8 q^{81} -19078.8 q^{82} -55292.9 q^{83} -30130.9 q^{84} +10727.6 q^{85} +35797.4 q^{86} -37627.5 q^{87} +7861.53 q^{88} -137382. q^{89} -44277.3 q^{90} +51661.5 q^{91} -209481. q^{92} +13878.6 q^{93} +5059.05 q^{94} -2727.04 q^{95} +40921.5 q^{96} +88802.8 q^{97} +31214.4 q^{98} +13102.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) $ 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * 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 $

$2$	−8.84956	−1.56440	−0.782198	−	0.623030i	$-0.785901\pi$
$2$	−8.84956	−1.56440	−0.782198	+	0.623030i	$0.785901\pi$
$3$	5.64544	0.362155	0.181078	−	0.983469i	$-0.442041\pi$
$3$	5.64544	0.362155	0.181078	+	0.983469i	$0.442041\pi$
$4$	46.3147	1.44733
$5$	−23.6980	−0.423923	−0.211961	−	0.977278i	$-0.567985\pi$
$5$	−23.6980	−0.423923	−0.211961	+	0.977278i	$0.567985\pi$
$6$	−49.9597	−0.566554
$7$	−115.238	−0.888894	−0.444447	−	0.895805i	$-0.646600\pi$
$7$	−115.238	−0.888894	−0.444447	+	0.895805i	$0.646600\pi$
$8$	−126.678	−0.699806
$9$	−211.129	−0.868843
$10$	209.717	0.663183
$11$	−62.0590	−0.154640	−0.0773202	−	0.997006i	$-0.524636\pi$
$11$	−62.0590	−0.154640	−0.0773202	+	0.997006i	$0.524636\pi$
$12$	261.467	0.524159
$13$	−448.303	−0.735721	−0.367861	−	0.929881i	$-0.619910\pi$
$13$	−448.303	−0.735721	−0.367861	+	0.929881i	$0.619910\pi$
$14$	1019.80	1.39058
$15$	−133.786	−0.153526
$16$	−361.022	−0.352560
$17$	−452.680	−0.379899	−0.189950	−	0.981794i	$-0.560832\pi$
$17$	−452.680	−0.379899	−0.189950	+	0.981794i	$0.560832\pi$
$18$	1868.40	1.35921
$19$	115.074	0.0731299	0.0365649	−	0.999331i	$-0.488358\pi$
$19$	115.074	0.0731299	0.0365649	+	0.999331i	$0.488358\pi$
$20$	−1097.57	−0.613558
$21$	−650.569	−0.321918
$22$	549.195	0.241919
$23$	−4523.01	−1.78282	−0.891410	−	0.453198i	$-0.850283\pi$
$23$	−4523.01	−1.78282	−0.891410	+	0.453198i	$0.850283\pi$
$24$	−715.156	−0.253438
$25$	−2563.40	−0.820289
$26$	3967.28	1.15096
$27$	−2563.76	−0.676812
$28$	−5337.20	−1.28653
$29$	−6665.11	−1.47168	−0.735838	−	0.677157i	$-0.763212\pi$
$29$	−6665.11	−1.47168	−0.735838	+	0.677157i	$0.763212\pi$
$30$	1183.94	0.240175
$31$	2458.38	0.459456	0.229728	−	0.973255i	$-0.426216\pi$
$31$	2458.38	0.459456	0.229728	+	0.973255i	$0.426216\pi$
$32$	7248.59	1.25135
$33$	−350.351	−0.0560039
$34$	4006.01	0.594313
$35$	2730.91	0.376823
$36$	−9778.37	−1.25751
$37$	826.603	0.0992642	0.0496321	−	0.998768i	$-0.484195\pi$
$37$	826.603	0.0992642	0.0496321	+	0.998768i	$0.484195\pi$
$38$	−1018.36	−0.114404
$39$	−2530.87	−0.266446
$40$	3002.03	0.296664
$41$	2155.90	0.200295	0.100147	−	0.994973i	$-0.468069\pi$
$41$	2155.90	0.200295	0.100147	+	0.994973i	$0.468069\pi$
$42$	5757.25	0.503607
$43$	−4045.10	−0.333625	−0.166812	−	0.985989i	$-0.553347\pi$
$43$	−4045.10	−0.333625	−0.166812	+	0.985989i	$0.553347\pi$
$44$	−2874.24	−0.223816
$45$	5003.34	0.368323
$46$	40026.6	2.78904
$47$	−571.672	−0.0377487	−0.0188744	−	0.999822i	$-0.506008\pi$
$47$	−571.672	−0.0377487	−0.0188744	+	0.999822i	$0.506008\pi$
$48$	−2038.13	−0.127682
$49$	−3527.23	−0.209867
$50$	22685.0	1.28326
$51$	−2555.58	−0.137583
$52$	−20763.0	−1.06483
$53$	2303.70	0.112651	0.0563257	−	0.998412i	$-0.482061\pi$
$53$	2303.70	0.112651	0.0563257	+	0.998412i	$0.482061\pi$
$54$	22688.1	1.05880
$55$	1470.67	0.0655556
$56$	14598.1	0.622053
$57$	649.646	0.0264844
$58$	58983.3	2.30228
$59$	−21518.1	−0.804775	−0.402388	−	0.915469i	$-0.631820\pi$
$59$	−21518.1	−0.804775	−0.402388	+	0.915469i	$0.631820\pi$
$60$	−6196.24	−0.222203
$61$	−45223.9	−1.55612	−0.778061	−	0.628189i	$-0.783796\pi$
$61$	−45223.9	−1.55612	−0.778061	+	0.628189i	$0.783796\pi$
$62$	−21755.5	−0.718771
$63$	24330.1	0.772310
$64$	−52594.1	−1.60504
$65$	10623.9	0.311889
$66$	3100.45	0.0876122
$67$	−23066.5	−0.627762	−0.313881	−	0.949462i	$-0.601629\pi$
$67$	−23066.5	−0.627762	−0.313881	+	0.949462i	$0.601629\pi$
$68$	−20965.7	−0.549841
$69$	−25534.4	−0.645658
$70$	−24167.3	−0.589500
$71$	77787.8	1.83133	0.915663	−	0.401947i	$-0.131666\pi$
$71$	77787.8	1.83133	0.915663	+	0.401947i	$0.131666\pi$
$72$	26745.5	0.608022
$73$	31851.5	0.699557	0.349778	−	0.936832i	$-0.386257\pi$
$73$	31851.5	0.699557	0.349778	+	0.936832i	$0.386257\pi$
$74$	−7315.07	−0.155288
$75$	−14471.6	−0.297072
$76$	5329.63	0.105843
$77$	7151.55	0.137459
$78$	22397.1	0.416826
$79$	−51435.8	−0.927253	−0.463626	−	0.886031i	$-0.653452\pi$
$79$	−51435.8	−0.927253	−0.463626	+	0.886031i	$0.653452\pi$
$80$	8555.49	0.149458
$81$	36830.8	0.623732
$82$	−19078.8	−0.313340
$83$	−55292.9	−0.880996	−0.440498	−	0.897754i	$-0.645198\pi$
$83$	−55292.9	−0.880996	−0.440498	+	0.897754i	$0.645198\pi$
$84$	−30130.9	−0.465922
$85$	10727.6	0.161048
$86$	35797.4	0.521921
$87$	−37627.5	−0.532976
$88$	7861.53	0.108218
$89$	−137382.	−1.83846	−0.919229	−	0.393724i	$-0.871187\pi$
$89$	−137382.	−1.83846	−0.919229	+	0.393724i	$0.871187\pi$
$90$	−44277.3	−0.576202
$91$	51661.5	0.653979
$92$	−209481.	−2.58033
$93$	13878.6	0.166395
$94$	5059.05	0.0590539
$95$	−2727.04	−0.0310014
$96$	40921.5	0.453183
$97$	88802.8	0.958291	0.479146	−	0.877735i	$-0.340947\pi$
$97$	88802.8	0.958291	0.479146	+	0.877735i	$0.340947\pi$
$98$	31214.4	0.328314
$99$	13102.5	0.134358
$100$	−118723.	−1.18723
$101$	−107774.	−1.05126	−0.525631	−	0.850712i	$-0.676171\pi$
$101$	−107774.	−1.05126	−0.525631	+	0.850712i	$0.676171\pi$
$102$	22615.7	0.215234
$103$	−138064.	−1.28229	−0.641147	−	0.767418i	$-0.721541\pi$
$103$	−138064.	−1.28229	−0.641147	+	0.767418i	$0.721541\pi$
$104$	56790.3	0.514862
$105$	15417.2	0.136468
$106$	−20386.7	−0.176231
$107$	−13199.6	−0.111455	−0.0557277	−	0.998446i	$-0.517748\pi$
$107$	−13199.6	−0.111455	−0.0557277	+	0.998446i	$0.517748\pi$
$108$	−118740.	−0.979572
$109$	−138455.	−1.11620	−0.558101	−	0.829773i	$-0.688470\pi$
$109$	−138455.	−1.11620	−0.558101	+	0.829773i	$0.688470\pi$
$110$	−13014.8	−0.102555
$111$	4666.54	0.0359491
$112$	41603.4	0.313389
$113$	−249831.	−1.84056	−0.920282	−	0.391256i	$-0.872041\pi$
$113$	−249831.	−1.84056	−0.920282	+	0.391256i	$0.872041\pi$
$114$	−5749.08	−0.0414320
$115$	107186.	0.755778
$116$	−308692.	−2.13001
$117$	94649.8	0.639227
$118$	190426.	1.25899
$119$	52165.8	0.337691
$120$	16947.8	0.107438
$121$	−157200.	−0.976086
$122$	400211.	2.43439
$123$	12171.0	0.0725378
$124$	113859.	0.664986
$125$	134804.	0.771662
$126$	−215310.	−1.20820
$127$	−83588.6	−0.459873	−0.229936	−	0.973206i	$-0.573852\pi$
$127$	−83588.6	−0.459873	−0.229936	+	0.973206i	$0.573852\pi$
$128$	233480.	1.25958
$129$	−22836.4	−0.120824
$130$	−94016.7	−0.487918
$131$	23854.1	0.121446	0.0607232	−	0.998155i	$-0.480659\pi$
$131$	23854.1	0.121446	0.0607232	+	0.998155i	$0.480659\pi$
$132$	−16226.4	−0.0810563
$133$	−13260.9	−0.0650047
$134$	204128.	0.982068
$135$	60756.0	0.286916
$136$	57344.7	0.265856
$137$	−40069.8	−0.182396	−0.0911981	−	0.995833i	$-0.529070\pi$
$137$	−40069.8	−0.182396	−0.0911981	+	0.995833i	$0.529070\pi$
$138$	225968.	1.01006
$139$	218569.	0.959513	0.479757	−	0.877402i	$-0.340725\pi$
$139$	218569.	0.959513	0.479757	+	0.877402i	$0.340725\pi$
$140$	126481.	0.545388
$141$	−3227.34	−0.0136709
$142$	−688388.	−2.86492
$143$	27821.2	0.113772
$144$	76222.1	0.306320
$145$	157950.	0.623877
$146$	−281872.	−1.09438
$147$	−19912.8	−0.0760043
$148$	38283.8	0.143668
$149$	347159.	1.28104	0.640521	−	0.767941i	$-0.278719\pi$
$149$	347159.	1.28104	0.640521	+	0.767941i	$0.278719\pi$
$150$	128067.	0.464738
$151$	−72509.6	−0.258793	−0.129397	−	0.991593i	$-0.541304\pi$
$151$	−72509.6	−0.258793	−0.129397	+	0.991593i	$0.541304\pi$
$152$	−14577.4	−0.0511767
$153$	95573.8	0.330073
$154$	−63288.0	−0.215040
$155$	−58258.6	−0.194774
$156$	−117216.	−0.385635
$157$	559767.	1.81242	0.906209	−	0.422830i	$-0.138963\pi$
$157$	559767.	1.81242	0.906209	+	0.422830i	$0.138963\pi$
$158$	455184.	1.45059
$159$	13005.4	0.0407973
$160$	−171777.	−0.530476
$161$	521222.	1.58474
$162$	−325936.	−0.975764
$163$	461010.	1.35907	0.679535	−	0.733643i	$-0.262182\pi$
$163$	461010.	1.35907	0.679535	+	0.733643i	$0.262182\pi$
$164$	99849.9	0.289893
$165$	8302.61	0.0237413
$166$	489318.	1.37823
$167$	84163.8	0.233525	0.116763	−	0.993160i	$-0.462748\pi$
$167$	84163.8	0.233525	0.116763	+	0.993160i	$0.462748\pi$
$168$	82413.0	0.225280
$169$	−170317.	−0.458714
$170$	−94934.6	−0.251943
$171$	−24295.5	−0.0635384
$172$	−187348.	−0.482866
$173$	426612.	1.08372	0.541860	−	0.840468i	$-0.317720\pi$
$173$	426612.	1.08372	0.541860	+	0.840468i	$0.317720\pi$
$174$	332987.	0.833785
$175$	295401.	0.729151
$176$	22404.6	0.0545201
$177$	−121479.	−0.291454
$178$	1.21577e6	2.87607
$179$	639320.	1.49137	0.745685	−	0.666298i	$-0.232122\pi$
$179$	639320.	1.49137	0.745685	+	0.666298i	$0.232122\pi$
$180$	231728.	0.533085
$181$	−453319.	−1.02851	−0.514254	−	0.857638i	$-0.671931\pi$
$181$	−453319.	−1.02851	−0.514254	+	0.857638i	$0.671931\pi$
$182$	−457181.	−1.02308
$183$	−255309.	−0.563558
$184$	572967.	1.24763
$185$	−19588.8	−0.0420804
$186$	−122820.	−0.260307
$187$	28092.8	0.0587478
$188$	−26476.8	−0.0546350
$189$	295442.	0.601614
$190$	24133.1	0.0484985
$191$	−205490.	−0.407574	−0.203787	−	0.979015i	$-0.565325\pi$
$191$	−205490.	−0.407574	−0.203787	+	0.979015i	$0.565325\pi$
$192$	−296917.	−0.581276
$193$	−505444.	−0.976742	−0.488371	−	0.872636i	$-0.662409\pi$
$193$	−505444.	−0.976742	−0.488371	+	0.872636i	$0.662409\pi$
$194$	−785866.	−1.49915
$195$	59976.6	0.112952
$196$	−163362.	−0.303747
$197$	213280.	0.391547	0.195774	−	0.980649i	$-0.437278\pi$
$197$	213280.	0.391547	0.195774	+	0.980649i	$0.437278\pi$
$198$	−115951.	−0.210190
$199$	478426.	0.856410	0.428205	−	0.903682i	$-0.359146\pi$
$199$	478426.	0.856410	0.428205	+	0.903682i	$0.359146\pi$
$200$	324728.	0.574043
$201$	−130221.	−0.227347
$202$	953754.	1.64459
$203$	768073.	1.30817
$204$	−118361.	−0.199128
$205$	−51090.6	−0.0849095
$206$	1.22181e6	2.00601
$207$	954937.	1.54899
$208$	161847.	0.259386
$209$	−7141.40	−0.0113088
$210$	−136435.	−0.213491
$211$	−324328.	−0.501509	−0.250754	−	0.968051i	$-0.580679\pi$
$211$	−324328.	−0.501509	−0.250754	+	0.968051i	$0.580679\pi$
$212$	106695.	0.163044
$213$	439147.	0.663225
$214$	116811.	0.174360
$215$	95860.9	0.141431
$216$	324773.	0.473637
$217$	−283298.	−0.408408
$218$	1.22527e6	1.74618
$219$	179816.	0.253348
$220$	68113.8	0.0948808
$221$	202938.	0.279500
$222$	−41296.8	−0.0562385
$223$	−1.10674e6	−1.49033	−0.745164	−	0.666881i	$-0.767629\pi$
$223$	−1.10674e6	−1.49033	−0.745164	+	0.666881i	$0.767629\pi$
$224$	−835312.	−1.11232
$225$	541209.	0.712703
$226$	2.21090e6	2.87937
$227$	909837.	1.17192	0.585961	−	0.810339i	$-0.300717\pi$
$227$	909837.	1.17192	0.585961	+	0.810339i	$0.300717\pi$
$228$	30088.1	0.0383317
$229$	−342500.	−0.431590	−0.215795	−	0.976439i	$-0.569234\pi$
$229$	−342500.	−0.431590	−0.215795	+	0.976439i	$0.569234\pi$
$230$	−948551.	−1.18234
$231$	40373.7	0.0497815
$232$	844325.	1.02989
$233$	42691.5	0.0515171	0.0257586	−	0.999668i	$-0.491800\pi$
$233$	42691.5	0.0515171	0.0257586	+	0.999668i	$0.491800\pi$
$234$	−837609.	−1.00000
$235$	13547.5	0.0160026
$236$	−996605.	−1.16478
$237$	−290378.	−0.335810
$238$	−461645.	−0.528281
$239$	1.33771e6	1.51484	0.757421	−	0.652927i	$-0.226459\pi$
$239$	1.33771e6	1.51484	0.757421	+	0.652927i	$0.226459\pi$
$240$	48299.6	0.0541271
$241$	548919.	0.608787	0.304394	−	0.952546i	$-0.401546\pi$
$241$	548919.	0.608787	0.304394	+	0.952546i	$0.401546\pi$
$242$	1.39115e6	1.52698
$243$	830920.	0.902700
$244$	−2.09453e6	−2.25223
$245$	83588.3	0.0889673
$246$	−107708.	−0.113478
$247$	−51588.2	−0.0538032
$248$	−311423.	−0.321530
$249$	−312153.	−0.319058
$250$	−1.19295e6	−1.20719
$251$	−1.61359e6	−1.61662	−0.808309	−	0.588758i	$-0.799617\pi$
$251$	−1.61359e6	−1.61662	−0.808309	+	0.588758i	$0.799617\pi$
$252$	1.12684e6	1.11779
$253$	280693.	0.275696
$254$	739722.	0.719423
$255$	60562.1	0.0583244
$256$	−383181.	−0.365429
$257$	−110037.	−0.103921	−0.0519607	−	0.998649i	$-0.516547\pi$
$257$	−110037.	−0.103921	−0.0519607	+	0.998649i	$0.516547\pi$
$258$	202092.	0.189017
$259$	−95256.0	−0.0882354
$260$	492042.	0.451408
$261$	1.40720e6	1.27866
$262$	−211098.	−0.189990
$263$	−696037.	−0.620502	−0.310251	−	0.950655i	$-0.600413\pi$
$263$	−696037.	−0.620502	−0.310251	+	0.950655i	$0.600413\pi$
$264$	44381.8	0.0391918
$265$	−54593.1	−0.0477555
$266$	117353.	0.101693
$267$	−775580.	−0.665807
$268$	−1.06832e6	−0.908580
$269$	1.28999e6	1.08694	0.543469	−	0.839429i	$-0.317110\pi$
$269$	1.28999e6	1.08694	0.543469	+	0.839429i	$0.317110\pi$
$270$	−537664.	−0.448850
$271$	−1.55067e6	−1.28262	−0.641309	−	0.767283i	$-0.721608\pi$
$271$	−1.55067e6	−1.28262	−0.641309	+	0.767283i	$0.721608\pi$
$272$	163427.	0.133937
$273$	291652.	0.236842
$274$	354600.	0.285340
$275$	159082.	0.126850
$276$	−1.18262e6	−0.934482
$277$	−1.85284e6	−1.45090	−0.725450	−	0.688275i	$-0.758368\pi$
$277$	−1.85284e6	−1.45090	−0.725450	+	0.688275i	$0.758368\pi$
$278$	−1.93424e6	−1.50106
$279$	−519034.	−0.399196
$280$	−345947.	−0.263703
$281$	2.56962e6	1.94135	0.970673	−	0.240403i	$-0.0772795\pi$
$281$	2.56962e6	1.94135	0.970673	+	0.240403i	$0.0772795\pi$
$282$	28560.6	0.0213867
$283$	89779.7	0.0666364	0.0333182	−	0.999445i	$-0.489393\pi$
$283$	89779.7	0.0666364	0.0333182	+	0.999445i	$0.489393\pi$
$284$	3.60272e6	2.65054
$285$	−15395.3	−0.0112273
$286$	−246206.	−0.177985
$287$	−248442.	−0.178041
$288$	−1.53039e6	−1.08723
$289$	−1.21494e6	−0.855676
$290$	−1.39779e6	−0.975991
$291$	501331.	0.347050
$292$	1.47519e6	1.01249
$293$	−278268.	−0.189362	−0.0946812	−	0.995508i	$-0.530183\pi$
$293$	−278268.	−0.189362	−0.0946812	+	0.995508i	$0.530183\pi$
$294$	176219.	0.118901
$295$	509937.	0.341163
$296$	−104713.	−0.0694656
$297$	159104.	0.104662
$298$	−3.07221e6	−2.00406
$299$	2.02768e6	1.31166
$300$	−670245.	−0.429962
$301$	466149.	0.296557
$302$	641678.	0.404855
$303$	−608433.	−0.380721
$304$	−41544.4	−0.0257827
$305$	1.07172e6	0.659675
$306$	−845786.	−0.516365
$307$	2.84171e6	1.72081	0.860407	−	0.509608i	$-0.170210\pi$
$307$	2.84171e6	1.72081	0.860407	+	0.509608i	$0.170210\pi$
$308$	331222.	0.198949
$309$	−779433.	−0.464389
$310$	515563.	0.304704
$311$	2.62652e6	1.53986	0.769928	−	0.638130i	$-0.220292\pi$
$311$	2.62652e6	1.53986	0.769928	+	0.638130i	$0.220292\pi$
$312$	320607.	0.186460
$313$	−1.03717e6	−0.598398	−0.299199	−	0.954191i	$-0.596719\pi$
$313$	−1.03717e6	−0.598398	−0.299199	+	0.954191i	$0.596719\pi$
$314$	−4.95369e6	−2.83534
$315$	−576574.	−0.327400
$316$	−2.38223e6	−1.34204
$317$	−314716.	−0.175902	−0.0879510	−	0.996125i	$-0.528032\pi$
$317$	−314716.	−0.175902	−0.0879510	+	0.996125i	$0.528032\pi$
$318$	−115092.	−0.0638231
$319$	413630.	0.227581
$320$	1.24638e6	0.680415
$321$	−74517.6	−0.0403642
$322$	−4.61258e6	−2.47916
$323$	−52091.9	−0.0277820
$324$	1.70580e6	0.902749
$325$	1.14918e6	0.603505
$326$	−4.07974e6	−2.12612
$327$	−781640.	−0.404238
$328$	−273106.	−0.140167
$329$	65878.3	0.0335546
$330$	−73474.4	−0.0371408
$331$	−3.79673e6	−1.90476	−0.952380	−	0.304915i	$-0.901372\pi$
$331$	−3.79673e6	−1.90476	−0.952380	+	0.304915i	$0.901372\pi$
$332$	−2.56087e6	−1.27509
$333$	−174520.	−0.0862450
$334$	−744812.	−0.365326
$335$	546630.	0.266123
$336$	234869.	0.113495
$337$	−683223.	−0.327708	−0.163854	−	0.986485i	$-0.552393\pi$
$337$	−683223.	−0.327708	−0.163854	+	0.986485i	$0.552393\pi$
$338$	1.50723e6	0.717610
$339$	−1.41041e6	−0.666570
$340$	496845.	0.233090
$341$	−152564.	−0.0710505
$342$	215005.	0.0993992
$343$	2.34327e6	1.07544
$344$	512427.	0.233473
$345$	605114.	0.273709
$346$	−3.77532e6	−1.69537
$347$	−545981.	−0.243419	−0.121709	−	0.992566i	$-0.538838\pi$
$347$	−545981.	−0.243419	−0.121709	+	0.992566i	$0.538838\pi$
$348$	−1.74271e6	−0.771393
$349$	−1.66133e6	−0.730116	−0.365058	−	0.930985i	$-0.618951\pi$
$349$	−1.66133e6	−0.730116	−0.365058	+	0.930985i	$0.618951\pi$
$350$	−2.61417e6	−1.14068
$351$	1.14934e6	0.497945
$352$	−449840.	−0.193509
$353$	101047.	0.0431604	0.0215802	−	0.999767i	$-0.493130\pi$
$353$	101047.	0.0431604	0.0215802	+	0.999767i	$0.493130\pi$
$354$	1.07504e6	0.455949
$355$	−1.84342e6	−0.776341
$356$	−6.36278e6	−2.66086
$357$	294499.	0.122296
$358$	−5.65770e6	−2.33309
$359$	4.00859e6	1.64155	0.820777	−	0.571249i	$-0.193541\pi$
$359$	4.00859e6	1.64155	0.820777	+	0.571249i	$0.193541\pi$
$360$	−633814.	−0.257754
$361$	−2.46286e6	−0.994652
$362$	4.01167e6	1.60899
$363$	−887462.	−0.353495
$364$	2.39269e6	0.946525
$365$	−754818.	−0.296558
$366$	2.25937e6	0.881627
$367$	2.75576e6	1.06801	0.534005	−	0.845481i	$-0.320686\pi$
$367$	2.75576e6	1.06801	0.534005	+	0.845481i	$0.320686\pi$
$368$	1.63290e6	0.628551
$369$	−455173.	−0.174025
$370$	173353.	0.0658303
$371$	−265474.	−0.100135
$372$	642784.	0.240828
$373$	−53730.1	−0.0199961	−0.00999806	−	0.999950i	$-0.503183\pi$
$373$	−53730.1	−0.0199961	−0.00999806	+	0.999950i	$0.503183\pi$
$374$	−248609.	−0.0919048
$375$	761028.	0.279462
$376$	72418.5	0.0264168
$377$	2.98799e6	1.08274
$378$	−2.61453e6	−0.941163
$379$	1.00800e6	0.360463	0.180231	−	0.983624i	$-0.442315\pi$
$379$	1.00800e6	0.360463	0.180231	+	0.983624i	$0.442315\pi$
$380$	−126302.	−0.0448694
$381$	−471895.	−0.166545
$382$	1.81849e6	0.637607
$383$	1.35478e6	0.471923	0.235961	−	0.971762i	$-0.424176\pi$
$383$	1.35478e6	0.471923	0.235961	+	0.971762i	$0.424176\pi$
$384$	1.31810e6	0.456162
$385$	−169477.	−0.0582720
$386$	4.47296e6	1.52801
$387$	854038.	0.289868
$388$	4.11287e6	1.38697
$389$	−52320.6	−0.0175307	−0.00876534	−	0.999962i	$-0.502790\pi$
$389$	−52320.6	−0.0175307	−0.00876534	+	0.999962i	$0.502790\pi$
$390$	−530766.	−0.176702
$391$	2.04747e6	0.677292
$392$	446824.	0.146866
$393$	134667.	0.0439825
$394$	−1.88743e6	−0.612535
$395$	1.21893e6	0.393084
$396$	606836.	0.194461
$397$	−4.94236e6	−1.57383	−0.786915	−	0.617061i	$-0.788323\pi$
$397$	−4.94236e6	−1.57383	−0.786915	+	0.617061i	$0.788323\pi$
$398$	−4.23385e6	−1.33976
$399$	−74863.9	−0.0235418
$400$	925444.	0.289201
$401$	832621.	0.258575	0.129287	−	0.991607i	$-0.458731\pi$
$401$	832621.	0.258575	0.129287	+	0.991607i	$0.458731\pi$
$402$	1.15240e6	0.355661
$403$	−1.10210e6	−0.338032
$404$	−4.99152e6	−1.52153
$405$	−872816.	−0.264414
$406$	−6.79711e6	−2.04649
$407$	−51298.1	−0.0153503
$408$	323736.	0.0962811
$409$	−447600.	−0.132307	−0.0661534	−	0.997809i	$-0.521073\pi$
$409$	−447600.	−0.132307	−0.0661534	+	0.997809i	$0.521073\pi$
$410$	452129.	0.132832
$411$	−226212.	−0.0660558
$412$	−6.39439e6	−1.85591
$413$	2.47970e6	0.715360
$414$	−8.45077e6	−2.42324
$415$	1.31033e6	0.373474
$416$	−3.24957e6	−0.920644
$417$	1.23392e6	0.347493
$418$	63198.3	0.0176915
$419$	−2.11506e6	−0.588557	−0.294279	−	0.955720i	$-0.595079\pi$
$419$	−2.11506e6	−0.588557	−0.294279	+	0.955720i	$0.595079\pi$
$420$	714042.	0.197515
$421$	5.68633e6	1.56360	0.781802	−	0.623527i	$-0.214301\pi$
$421$	5.68633e6	1.56360	0.781802	+	0.623527i	$0.214301\pi$
$422$	2.87016e6	0.784558
$423$	120697.	0.0327977
$424$	−291829.	−0.0788340
$425$	1.16040e6	0.311627
$426$	−3.88625e6	−1.03755
$427$	5.21151e6	1.38323
$428$	−611335.	−0.161313
$429$	157063.	0.0412033
$430$	−848326.	−0.221254
$431$	176341.	0.0457258	0.0228629	−	0.999739i	$-0.492722\pi$
$431$	176341.	0.0457258	0.0228629	+	0.999739i	$0.492722\pi$
$432$	925573.	0.238617
$433$	−1.31044e6	−0.335890	−0.167945	−	0.985796i	$-0.553713\pi$
$433$	−1.31044e6	−0.335890	−0.167945	+	0.985796i	$0.553713\pi$
$434$	2.50706e6	0.638912
$435$	891697.	0.225941
$436$	−6.41250e6	−1.61551
$437$	−520482.	−0.130377
$438$	−1.59129e6	−0.396337
$439$	−4.19530e6	−1.03897	−0.519484	−	0.854480i	$-0.673876\pi$
$439$	−4.19530e6	−1.03897	−0.519484	+	0.854480i	$0.673876\pi$
$440$	−186303.	−0.0458762
$441$	744700.	0.182341
$442$	−1.79591e6	−0.437249
$443$	−3.26823e6	−0.791232	−0.395616	−	0.918416i	$-0.629469\pi$
$443$	−3.26823e6	−0.791232	−0.395616	+	0.918416i	$0.629469\pi$
$444$	216129.	0.0520303
$445$	3.25567e6	0.779364
$446$	9.79413e6	2.33146
$447$	1.95987e6	0.463936
$448$	6.06083e6	1.42672
$449$	2.79072e6	0.653283	0.326641	−	0.945148i	$-0.394083\pi$
$449$	2.79072e6	0.653283	0.326641	+	0.945148i	$0.394083\pi$
$450$	−4.78946e6	−1.11495
$451$	−133793.	−0.0309737
$452$	−1.15709e7	−2.66391
$453$	−409349.	−0.0937234
$454$	−8.05166e6	−1.83335
$455$	−1.22428e6	−0.277237
$456$	−82296.1	−0.0185339
$457$	3.28197e6	0.735097	0.367548	−	0.930004i	$-0.380197\pi$
$457$	3.28197e6	0.735097	0.367548	+	0.930004i	$0.380197\pi$
$458$	3.03097e6	0.675178
$459$	1.16056e6	0.257120
$460$	4.96429e6	1.09386
$461$	−3.66421e6	−0.803024	−0.401512	−	0.915854i	$-0.631515\pi$
$461$	−3.66421e6	−0.803024	−0.401512	+	0.915854i	$0.631515\pi$
$462$	−357289.	−0.0778780
$463$	−3.21500e6	−0.696992	−0.348496	−	0.937310i	$-0.613308\pi$
$463$	−3.21500e6	−0.696992	−0.348496	+	0.937310i	$0.613308\pi$
$464$	2.40625e6	0.518855
$465$	−328896.	−0.0705385
$466$	−377801.	−0.0805931
$467$	−6.63224e6	−1.40724	−0.703620	−	0.710577i	$-0.748434\pi$
$467$	−6.63224e6	−1.40724	−0.703620	+	0.710577i	$0.748434\pi$
$468$	4.38367e6	0.925174
$469$	2.65814e6	0.558014
$470$	−119889.	−0.0250343
$471$	3.16014e6	0.656377
$472$	2.72588e6	0.563186
$473$	251035.	0.0515919
$474$	2.56972e6	0.525339
$475$	−294982.	−0.0599877
$476$	2.41604e6	0.488751
$477$	−486378.	−0.0978764
$478$	−1.18381e7	−2.36981
$479$	−2.13150e6	−0.424469	−0.212235	−	0.977219i	$-0.568074\pi$
$479$	−2.13150e6	−0.424469	−0.212235	+	0.977219i	$0.568074\pi$
$480$	−969758.	−0.192115
$481$	−370569.	−0.0730308
$482$	−4.85769e6	−0.952384
$483$	2.94253e6	0.573922
$484$	−7.28065e6	−1.41272
$485$	−2.10445e6	−0.406242
$486$	−7.35327e6	−1.41218
$487$	7.10349e6	1.35722	0.678609	−	0.734500i	$-0.262583\pi$
$487$	7.10349e6	1.35722	0.678609	+	0.734500i	$0.262583\pi$
$488$	5.72889e6	1.08898
$489$	2.60261e6	0.492195
$490$	−739719.	−0.139180
$491$	−4.89557e6	−0.916431	−0.458215	−	0.888841i	$-0.651511\pi$
$491$	−4.89557e6	−0.916431	−0.458215	+	0.888841i	$0.651511\pi$
$492$	563697.	0.104986
$493$	3.01716e6	0.559089
$494$	456533.	0.0841695
$495$	−310502.	−0.0569576
$496$	−887527.	−0.161986
$497$	−8.96410e6	−1.62786
$498$	2.76241e6	0.499132
$499$	−6.89386e6	−1.23940	−0.619699	−	0.784839i	$-0.712745\pi$
$499$	−6.89386e6	−1.23940	−0.619699	+	0.784839i	$0.712745\pi$
$500$	6.24339e6	1.11685
$501$	475142.	0.0845725
$502$	1.42795e7	2.52903
$503$	5.89132e6	1.03823	0.519114	−	0.854705i	$-0.326262\pi$
$503$	5.89132e6	1.03823	0.519114	+	0.854705i	$0.326262\pi$
$504$	−3.08209e6	−0.540467
$505$	2.55403e6	0.445654
$506$	−2.48401e6	−0.431298
$507$	−961517.	−0.166126
$508$	−3.87138e6	−0.665589
$509$	4.64990e6	0.795516	0.397758	−	0.917490i	$-0.369788\pi$
$509$	4.64990e6	0.795516	0.397758	+	0.917490i	$0.369788\pi$
$510$	−535948.	−0.0912425
$511$	−3.67050e6	−0.621832
$512$	−4.08037e6	−0.687899
$513$	−295023.	−0.0494952
$514$	973776.	0.162574
$515$	3.27184e6	0.543594
$516$	−1.05766e6	−0.174873
$517$	35477.4	0.00583748
$518$	842973.	0.138035
$519$	2.40841e6	0.392475
$520$	−1.34582e6	−0.218262
$521$	−8.16865e6	−1.31843	−0.659213	−	0.751956i	$-0.729111\pi$
$521$	−8.16865e6	−1.31843	−0.659213	+	0.751956i	$0.729111\pi$
$522$	−1.24531e7	−2.00032
$523$	4.45085e6	0.711523	0.355762	−	0.934577i	$-0.384221\pi$
$523$	4.45085e6	0.711523	0.355762	+	0.934577i	$0.384221\pi$
$524$	1.10479e6	0.175773
$525$	1.66767e6	0.264066
$526$	6.15962e6	0.970710
$527$	−1.11286e6	−0.174547
$528$	126484.	0.0197447
$529$	1.40212e7	2.17845
$530$	483125.	0.0747084
$531$	4.54310e6	0.699224
$532$	−614176.	−0.0940835
$533$	−966498.	−0.147361
$534$	6.86354e6	1.04159
$535$	312804.	0.0472485
$536$	2.92203e6	0.439311
$537$	3.60925e6	0.540108
$538$	−1.14158e7	−1.70040
$539$	218896.	0.0324539
$540$	2.81389e6	0.415263
$541$	−9.77661e6	−1.43613	−0.718067	−	0.695974i	$-0.754973\pi$
$541$	−9.77661e6	−1.43613	−0.718067	+	0.695974i	$0.754973\pi$
$542$	1.37228e7	2.00652
$543$	−2.55919e6	−0.372479
$544$	−3.28129e6	−0.475387
$545$	3.28111e6	0.473183
$546$	−2.58099e6	−0.370514
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−1.85582e6	−0.263988
$549$	9.54807e6	1.35203
$550$	−1.40781e6	−0.198443
$551$	−766984.	−0.107624
$552$	3.23465e6	0.451835
$553$	5.92736e6	0.824230
$554$	1.63968e7	2.26978
$555$	−110588.	−0.0152396
$556$	1.01229e7	1.38874
$557$	9.63282e6	1.31557	0.657787	−	0.753204i	$-0.271493\pi$
$557$	9.63282e6	1.31557	0.657787	+	0.753204i	$0.271493\pi$
$558$	4.59322e6	0.624500
$559$	1.81343e6	0.245455
$560$	−985917.	−0.132853
$561$	158597.	0.0212758
$562$	−2.27400e7	−3.03703
$563$	−6.52868e6	−0.868069	−0.434035	−	0.900896i	$-0.642910\pi$
$563$	−6.52868e6	−0.868069	−0.434035	+	0.900896i	$0.642910\pi$
$564$	−149473.	−0.0197864
$565$	5.92051e6	0.780257
$566$	−794510.	−0.104246
$567$	−4.24430e6	−0.554432
$568$	−9.85403e6	−1.28157
$569$	7.19227e6	0.931291	0.465645	−	0.884971i	$-0.345822\pi$
$569$	7.19227e6	0.931291	0.465645	+	0.884971i	$0.345822\pi$
$570$	136242.	0.0175640
$571$	−1.35029e7	−1.73315	−0.866576	−	0.499046i	$-0.833684\pi$
$571$	−1.35029e7	−1.73315	−0.866576	+	0.499046i	$0.833684\pi$
$572$	1.28853e6	0.164666
$573$	−1.16008e6	−0.147605
$574$	2.19860e6	0.278526
$575$	1.15943e7	1.46243
$576$	1.11041e7	1.39453
$577$	59100.4	0.00739010	0.00369505	−	0.999993i	$-0.498824\pi$
$577$	59100.4	0.00739010	0.00369505	+	0.999993i	$0.498824\pi$
$578$	1.07517e7	1.33862
$579$	−2.85346e6	−0.353732
$580$	7.31539e6	0.902958
$581$	6.37184e6	0.783113
$582$	−4.43656e6	−0.542924
$583$	−142965.	−0.0174205
$584$	−4.03490e6	−0.489554
$585$	−2.24301e6	−0.270983
$586$	2.46255e6	0.296238
$587$	1.17830e7	1.41143	0.705717	−	0.708494i	$-0.250625\pi$
$587$	1.17830e7	1.41143	0.705717	+	0.708494i	$0.250625\pi$
$588$	−922253.	−0.110004
$589$	282896.	0.0336000
$590$	−4.51272e6	−0.533713
$591$	1.20406e6	0.141801
$592$	−298421.	−0.0349966
$593$	562978.	0.0657437	0.0328719	−	0.999460i	$-0.489535\pi$
$593$	562978.	0.0657437	0.0328719	+	0.999460i	$0.489535\pi$
$594$	−1.40800e6	−0.163733
$595$	−1.23623e6	−0.143155
$596$	1.60786e7	1.85409
$597$	2.70092e6	0.310153
$598$	−1.79440e7	−2.05195
$599$	5.26074e6	0.599073	0.299537	−	0.954085i	$-0.403168\pi$
$599$	5.26074e6	0.599073	0.299537	+	0.954085i	$0.403168\pi$
$600$	1.83323e6	0.207893
$601$	−3.76376e6	−0.425046	−0.212523	−	0.977156i	$-0.568168\pi$
$601$	−3.76376e6	−0.425046	−0.212523	+	0.977156i	$0.568168\pi$
$602$	−4.12521e6	−0.463933
$603$	4.87001e6	0.545427
$604$	−3.35826e6	−0.374560
$605$	3.72532e6	0.413785
$606$	5.38436e6	0.595598
$607$	−8.84077e6	−0.973909	−0.486954	−	0.873427i	$-0.661892\pi$
$607$	−8.84077e6	−0.973909	−0.486954	+	0.873427i	$0.661892\pi$
$608$	834127.	0.0915110
$609$	4.33612e6	0.473759
$610$	−9.48421e6	−1.03199
$611$	256282.	0.0277726
$612$	4.42647e6	0.477726
$613$	−7.33862e6	−0.788793	−0.394396	−	0.918940i	$-0.629046\pi$
$613$	−7.33862e6	−0.788793	−0.394396	+	0.918940i	$0.629046\pi$
$614$	−2.51479e7	−2.69203
$615$	−288429.	−0.0307504
$616$	−905947.	−0.0961946
$617$	−1.69331e7	−1.79070	−0.895351	−	0.445361i	$-0.853075\pi$
$617$	−1.69331e7	−1.79070	−0.895351	+	0.445361i	$0.853075\pi$
$618$	6.89763e6	0.726489
$619$	−1.78270e7	−1.87004	−0.935019	−	0.354598i	$-0.884618\pi$
$619$	−1.78270e7	−1.87004	−0.935019	+	0.354598i	$0.884618\pi$
$620$	−2.69823e6	−0.281903
$621$	1.15959e7	1.20663
$622$	−2.32436e7	−2.40894
$623$	1.58316e7	1.63419
$624$	913699.	0.0939381
$625$	4.81606e6	0.493164
$626$	9.17851e6	0.936130
$627$	−40316.4	−0.00409556
$628$	2.59254e7	2.62317
$629$	−374186.	−0.0377104
$630$	5.10242e6	0.512183
$631$	4.65644e6	0.465565	0.232783	−	0.972529i	$-0.425217\pi$
$631$	4.65644e6	0.465565	0.232783	+	0.972529i	$0.425217\pi$
$632$	6.51581e6	0.648897
$633$	−1.83098e6	−0.181624
$634$	2.78510e6	0.275180
$635$	1.98088e6	0.194951
$636$	602341.	0.0590473
$637$	1.58127e6	0.154403
$638$	−3.66044e6	−0.356026
$639$	−1.64233e7	−1.59114
$640$	−5.53300e6	−0.533963
$641$	−1.33581e7	−1.28410	−0.642052	−	0.766661i	$-0.721917\pi$
$641$	−1.33581e7	−1.28410	−0.642052	+	0.766661i	$0.721917\pi$
$642$	659448.	0.0631456
$643$	1.45952e7	1.39214	0.696070	−	0.717974i	$-0.254930\pi$
$643$	1.45952e7	1.39214	0.696070	+	0.717974i	$0.254930\pi$
$644$	2.41402e7	2.29364
$645$	541177.	0.0512201
$646$	460990.	0.0434620
$647$	1.04580e7	0.982171	0.491086	−	0.871111i	$-0.336600\pi$
$647$	1.04580e7	0.982171	0.491086	+	0.871111i	$0.336600\pi$
$648$	−4.66566e6	−0.436492
$649$	1.33539e6	0.124451
$650$	−1.01698e7	−0.944120
$651$	−1.59934e6	−0.147907
$652$	2.13515e7	1.96703
$653$	−1997.82	−0.000183347 0	−9.16735e−5	−	1.00000i	$-0.500029\pi$
$653$	−1997.82	−0.000183347 0	−9.16735e−5		1.00000i	$0.500029\pi$
$654$	6.91717e6	0.632388
$655$	−565294.	−0.0514839
$656$	−778327.	−0.0706159
$657$	−6.72478e6	−0.607805
$658$	−582994.	−0.0524927
$659$	−3.10911e6	−0.278884	−0.139442	−	0.990230i	$-0.544531\pi$
$659$	−3.10911e6	−0.278884	−0.139442	+	0.990230i	$0.544531\pi$
$660$	384533.	0.0343616
$661$	−1.71673e7	−1.52826	−0.764131	−	0.645061i	$-0.776832\pi$
$661$	−1.71673e7	−1.52826	−0.764131	+	0.645061i	$0.776832\pi$
$662$	3.35994e7	2.97980
$663$	1.14567e6	0.101223
$664$	7.00441e6	0.616526
$665$	314258.	0.0275570
$666$	1.54442e6	0.134921
$667$	3.01463e7	2.62373
$668$	3.89802e6	0.337989
$669$	−6.24802e6	−0.539731
$670$	−4.83744e6	−0.416321
$671$	2.80655e6	0.240639
$672$	−4.71571e6	−0.402832
$673$	2.96722e6	0.252529	0.126265	−	0.991997i	$-0.459701\pi$
$673$	2.96722e6	0.252529	0.126265	+	0.991997i	$0.459701\pi$
$674$	6.04622e6	0.512666
$675$	6.57195e6	0.555182
$676$	−7.88819e6	−0.663912
$677$	−7.05384e6	−0.591499	−0.295750	−	0.955266i	$-0.595569\pi$
$677$	−7.05384e6	−0.591499	−0.295750	+	0.955266i	$0.595569\pi$
$678$	1.24815e7	1.04278
$679$	−1.02335e7	−0.851820
$680$	−1.35896e6	−0.112702
$681$	5.13643e6	0.424418
$682$	1.35013e6	0.111151
$683$	1.45787e6	0.119582	0.0597912	−	0.998211i	$-0.480957\pi$
$683$	1.45787e6	0.119582	0.0597912	+	0.998211i	$0.480957\pi$
$684$	−1.12524e6	−0.0919612
$685$	949574.	0.0773219
$686$	−2.07369e7	−1.68242
$687$	−1.93356e6	−0.156303
$688$	1.46037e6	0.117623
$689$	−1.03276e6	−0.0828800
$690$	−5.35499e6	−0.428189
$691$	−1.74004e7	−1.38632	−0.693160	−	0.720784i	$-0.743782\pi$
$691$	−1.74004e7	−1.38632	−0.693160	+	0.720784i	$0.743782\pi$
$692$	1.97584e7	1.56851
$693$	−1.50990e6	−0.119430
$694$	4.83169e6	0.380803
$695$	−5.17964e6	−0.406760
$696$	4.76659e6	0.372979
$697$	−975933.	−0.0760918
$698$	1.47020e7	1.14219
$699$	241012.	0.0186572
$700$	1.36814e7	1.05532
$701$	−837145.	−0.0643436	−0.0321718	−	0.999482i	$-0.510242\pi$
$701$	−837145.	−0.0643436	−0.0321718	+	0.999482i	$0.510242\pi$
$702$	−1.01712e7	−0.778983
$703$	95120.8	0.00725918
$704$	3.26394e6	0.248205
$705$	76481.6	0.00579541
$706$	−894218.	−0.0675199
$707$	1.24197e7	0.934462
$708$	−5.62628e6	−0.421831
$709$	6.57861e6	0.491494	0.245747	−	0.969334i	$-0.420967\pi$
$709$	6.57861e6	0.491494	0.245747	+	0.969334i	$0.420967\pi$
$710$	1.63134e7	1.21450
$711$	1.08596e7	0.805637
$712$	1.74033e7	1.28656
$713$	−1.11192e7	−0.819128
$714$	−2.60619e6	−0.191320
$715$	−659308.	−0.0482307
$716$	2.96099e7	2.15851
$717$	7.55197e6	0.548608
$718$	−3.54742e7	−2.56804
$719$	−1.03978e7	−0.750097	−0.375048	−	0.927005i	$-0.622374\pi$
$719$	−1.03978e7	−0.750097	−0.375048	+	0.927005i	$0.622374\pi$
$720$	−1.80631e6	−0.129856
$721$	1.59102e7	1.13982
$722$	2.17952e7	1.55603
$723$	3.09889e6	0.220476
$724$	−2.09953e7	−1.48859
$725$	1.70854e7	1.20720
$726$	7.85365e6	0.553006
$727$	−1.43924e7	−1.00994	−0.504972	−	0.863136i	$-0.668497\pi$
$727$	−1.43924e7	−1.00994	−0.504972	+	0.863136i	$0.668497\pi$
$728$	−6.54440e6	−0.457658
$729$	−4.25897e6	−0.296815
$730$	6.67980e6	0.463934
$731$	1.83114e6	0.126744
$732$	−1.18245e7	−0.815656
$733$	−2.19192e7	−1.50683	−0.753417	−	0.657543i	$-0.771596\pi$
$733$	−2.19192e7	−1.50683	−0.753417	+	0.657543i	$0.771596\pi$
$734$	−2.43872e7	−1.67079
$735$	471893.	0.0322200
$736$	−3.27854e7	−2.23093
$737$	1.43148e6	0.0970774
$738$	4.02808e6	0.272243
$739$	−1.38926e7	−0.935780	−0.467890	−	0.883787i	$-0.654986\pi$
$739$	−1.38926e7	−0.935780	−0.467890	+	0.883787i	$0.654986\pi$
$740$	−907250.	−0.0609043
$741$	−291239.	−0.0194851
$742$	2.34932e6	0.156651
$743$	−2.23092e7	−1.48256	−0.741279	−	0.671197i	$-0.765780\pi$
$743$	−2.23092e7	−1.48256	−0.741279	+	0.671197i	$0.765780\pi$
$744$	−1.75812e6	−0.116444
$745$	−8.22699e6	−0.543063
$746$	475488.	0.0312819
$747$	1.16739e7	0.765448
$748$	1.30111e6	0.0850277
$749$	1.52109e6	0.0990722
$750$	−6.73476e6	−0.437189
$751$	−2.41124e7	−1.56006	−0.780029	−	0.625744i	$-0.784796\pi$
$751$	−2.41124e7	−1.56006	−0.780029	+	0.625744i	$0.784796\pi$
$752$	206386.	0.0133087
$753$	−9.10940e6	−0.585467
$754$	−2.64424e7	−1.69384
$755$	1.71833e6	0.109708
$756$	1.36833e7	0.870736
$757$	427476.	0.0271126	0.0135563	−	0.999908i	$-0.495685\pi$
$757$	427476.	0.0271126	0.0135563	+	0.999908i	$0.495685\pi$
$758$	−8.92031e6	−0.563907
$759$	1.58464e6	0.0998448
$760$	345456.	0.0216950
$761$	−2.05600e7	−1.28695	−0.643475	−	0.765467i	$-0.722508\pi$
$761$	−2.05600e7	−1.28695	−0.643475	+	0.765467i	$0.722508\pi$
$762$	4.17606e6	0.260543
$763$	1.59553e7	0.992185
$764$	−9.51719e6	−0.589896
$765$	−2.26491e6	−0.139926
$766$	−1.19892e7	−0.738274
$767$	9.64665e6	0.592090
$768$	−2.16322e6	−0.132342
$769$	−1.40457e7	−0.856501	−0.428250	−	0.903660i	$-0.640870\pi$
$769$	−1.40457e7	−0.856501	−0.428250	+	0.903660i	$0.640870\pi$
$770$	1.49980e6	0.0911605
$771$	−621206.	−0.0376357
$772$	−2.34095e7	−1.41367
$773$	−7.17675e6	−0.431995	−0.215998	−	0.976394i	$-0.569300\pi$
$773$	−7.17675e6	−0.431995	−0.215998	+	0.976394i	$0.569300\pi$
$774$	−7.55786e6	−0.453468
$775$	−6.30181e6	−0.376887
$776$	−1.12494e7	−0.670618
$777$	−537762.	−0.0319549
$778$	463014.	0.0274249
$779$	248089.	0.0146475
$780$	2.77780e6	0.163480
$781$	−4.82743e6	−0.283197
$782$	−1.81192e7	−1.05955
$783$	1.70877e7	0.996048
$784$	1.27341e6	0.0739906
$785$	−1.32654e7	−0.768326
$786$	−1.19174e6	−0.0688060
$787$	2.86907e7	1.65122	0.825608	−	0.564243i	$-0.190832\pi$
$787$	2.86907e7	1.65122	0.825608	+	0.564243i	$0.190832\pi$
$788$	9.87799e6	0.566700
$789$	−3.92944e6	−0.224718
$790$	−1.07870e7	−0.614938
$791$	2.87900e7	1.63607
$792$	−1.65980e6	−0.0940247
$793$	2.02740e7	1.14487
$794$	4.37377e7	2.46209
$795$	−308202.	−0.0172949
$796$	2.21581e7	1.23951
$797$	579135.	0.0322949	0.0161474	−	0.999870i	$-0.494860\pi$
$797$	579135.	0.0322949	0.0161474	+	0.999870i	$0.494860\pi$
$798$	662512.	0.0368287
$799$	258784.	0.0143407
$800$	−1.85811e7	−1.02647
$801$	2.90052e7	1.59733
$802$	−7.36832e6	−0.404513
$803$	−1.97667e6	−0.108180
$804$	−6.03113e6	−0.329047
$805$	−1.23519e7	−0.671807
$806$	9.75308e6	0.528815
$807$	7.28256e6	0.393641
$808$	1.36527e7	0.735680
$809$	3.28776e6	0.176616	0.0883079	−	0.996093i	$-0.471854\pi$
$809$	3.28776e6	0.176616	0.0883079	+	0.996093i	$0.471854\pi$
$810$	7.72404e6	0.413649
$811$	−3.18034e7	−1.69793	−0.848967	−	0.528445i	$-0.822775\pi$
$811$	−3.18034e7	−1.69793	−0.848967	+	0.528445i	$0.822775\pi$
$812$	3.55731e7	1.89335
$813$	−8.75424e6	−0.464507
$814$	453966.	0.0240139
$815$	−1.09250e7	−0.576141
$816$	922619.	0.0485062
$817$	−465488.	−0.0243979
$818$	3.96106e6	0.206980
$819$	−1.09072e7	−0.568205
$820$	−2.36624e6	−0.122892
$821$	−2.62490e7	−1.35911	−0.679556	−	0.733623i	$-0.737828\pi$
$821$	−2.62490e7	−1.35911	−0.679556	+	0.733623i	$0.737828\pi$
$822$	2.00187e6	0.103337
$823$	−9.01176e6	−0.463778	−0.231889	−	0.972742i	$-0.574491\pi$
$823$	−9.01176e6	−0.463778	−0.231889	+	0.972742i	$0.574491\pi$
$824$	1.74897e7	0.897356
$825$	898090.	0.0459394
$826$	−2.19443e7	−1.11911
$827$	−3.03879e7	−1.54503	−0.772515	−	0.634996i	$-0.781002\pi$
$827$	−3.03879e7	−1.54503	−0.772515	+	0.634996i	$0.781002\pi$
$828$	4.42276e7	2.24191
$829$	837211.	0.0423105	0.0211553	−	0.999776i	$-0.493266\pi$
$829$	837211.	0.0423105	0.0211553	+	0.999776i	$0.493266\pi$
$830$	−1.15959e7	−0.584262
$831$	−1.04601e7	−0.525451
$832$	2.35781e7	1.18087
$833$	1.59670e6	0.0797282
$834$	−1.09196e7	−0.543616
$835$	−1.99451e6	−0.0989968
$836$	−330752.	−0.0163677
$837$	−6.30269e6	−0.310965
$838$	1.87174e7	0.920736
$839$	1.82820e6	0.0896642	0.0448321	−	0.998995i	$-0.485725\pi$
$839$	1.82820e6	0.0896642	0.0448321	+	0.998995i	$0.485725\pi$
$840$	−1.95302e6	−0.0955014
$841$	2.39126e7	1.16583
$842$	−5.03215e7	−2.44609
$843$	1.45066e7	0.703069
$844$	−1.50211e7	−0.725850
$845$	4.03618e6	0.194459
$846$	−1.06811e6	−0.0513086
$847$	1.81154e7	0.867638
$848$	−831686.	−0.0397164
$849$	506846.	0.0241328
$850$	−1.02690e7	−0.487509
$851$	−3.73873e6	−0.176970
$852$	2.03389e7	0.959907
$853$	−2.25891e7	−1.06298	−0.531491	−	0.847064i	$-0.678368\pi$
$853$	−2.25891e7	−1.06298	−0.531491	+	0.847064i	$0.678368\pi$
$854$	−4.61195e7	−2.16391
$855$	575756.	0.0269354
$856$	1.67210e6	0.0779972
$857$	−1.28000e7	−0.595331	−0.297665	−	0.954670i	$-0.596208\pi$
$857$	−1.28000e7	−0.595331	−0.297665	+	0.954670i	$0.596208\pi$
$858$	−1.38994e6	−0.0644582
$859$	1.88524e7	0.871733	0.435866	−	0.900011i	$-0.356442\pi$
$859$	1.88524e7	0.871733	0.435866	+	0.900011i	$0.356442\pi$
$860$	4.43976e6	0.204698
$861$	−1.40256e6	−0.0644784
$862$	−1.56054e6	−0.0715332
$863$	3.04645e7	1.39241	0.696206	−	0.717842i	$-0.254870\pi$
$863$	3.04645e7	1.39241	0.696206	+	0.717842i	$0.254870\pi$
$864$	−1.85836e7	−0.846928
$865$	−1.01098e7	−0.459414
$866$	1.15968e7	0.525464
$867$	−6.85887e6	−0.309888
$868$	−1.31209e7	−0.591103
$869$	3.19206e6	0.143391
$870$	−7.89113e6	−0.353460
$871$	1.03408e7	0.461858
$872$	1.75393e7	0.781124
$873$	−1.87488e7	−0.832605
$874$	4.60604e6	0.203962
$875$	−1.55345e7	−0.685926
$876$	8.32812e6	0.366679
$877$	3.09479e7	1.35873	0.679365	−	0.733801i	$-0.262256\pi$
$877$	3.09479e7	1.35873	0.679365	+	0.733801i	$0.262256\pi$
$878$	3.71266e7	1.62536
$879$	−1.57095e6	−0.0685786
$880$	−530945.	−0.0231123
$881$	−4.21286e7	−1.82868	−0.914339	−	0.404949i	$-0.867289\pi$
$881$	−4.21286e7	−1.82868	−0.914339	+	0.404949i	$0.867289\pi$
$882$	−6.59027e6	−0.285254
$883$	−3.77359e7	−1.62874	−0.814372	−	0.580343i	$-0.802919\pi$
$883$	−3.77359e7	−1.62874	−0.814372	+	0.580343i	$0.802919\pi$
$884$	9.39899e6	0.404530
$885$	2.87882e6	0.123554
$886$	2.89224e7	1.23780
$887$	774168.	0.0330390	0.0165195	−	0.999864i	$-0.494741\pi$
$887$	774168.	0.0330390	0.0165195	+	0.999864i	$0.494741\pi$
$888$	−591150.	−0.0251574
$889$	9.63257e6	0.408778
$890$	−2.88112e7	−1.21923
$891$	−2.28568e6	−0.0964543
$892$	−5.12581e7	−2.15700
$893$	−65784.8	−0.00276056
$894$	−1.73440e7	−0.725780
$895$	−1.51506e7	−0.632226
$896$	−2.69057e7	−1.11963
$897$	1.14471e7	0.475024
$898$	−2.46967e7	−1.02199
$899$	−1.63854e7	−0.676171
$900$	2.50659e7	1.03152
$901$	−1.04284e6	−0.0427962
$902$	1.18401e6	0.0484550
$903$	2.63162e6	0.107400
$904$	3.16482e7	1.28804
$905$	1.07428e7	0.436008
$906$	3.62256e6	0.146620
$907$	4.27651e7	1.72612	0.863061	−	0.505100i	$-0.168544\pi$
$907$	4.27651e7	1.72612	0.863061	+	0.505100i	$0.168544\pi$
$908$	4.21388e7	1.69616
$909$	2.27543e7	0.913383
$910$	1.08343e7	0.433708
$911$	−5.83566e6	−0.232967	−0.116483	−	0.993193i	$-0.537162\pi$
$911$	−5.83566e6	−0.232967	−0.116483	+	0.993193i	$0.537162\pi$
$912$	−234536.	−0.00933734
$913$	3.43142e6	0.136238
$914$	−2.90440e7	−1.14998
$915$	6.05031e6	0.238905
$916$	−1.58628e7	−0.624655
$917$	−2.74889e6	−0.107953
$918$	−1.02705e7	−0.402238
$919$	4.17680e7	1.63138	0.815689	−	0.578491i	$-0.196358\pi$
$919$	4.17680e7	1.63138	0.815689	+	0.578491i	$0.196358\pi$
$920$	−1.35782e7	−0.528898
$921$	1.60427e7	0.623202
$922$	3.24267e7	1.25625
$923$	−3.48725e7	−1.34735
$924$	1.86989e6	0.0720505
$925$	−2.11892e6	−0.0814253
$926$	2.84513e7	1.09037
$927$	2.91493e7	1.11411
$928$	−4.83127e7	−1.84158
$929$	2.22314e7	0.845139	0.422569	−	0.906331i	$-0.361128\pi$
$929$	2.22314e7	0.845139	0.422569	+	0.906331i	$0.361128\pi$
$930$	2.91058e6	0.110350
$931$	−405894.	−0.0153475
$932$	1.97724e6	0.0745624
$933$	1.48279e7	0.557667
$934$	5.86924e7	2.20148
$935$	−665745.	−0.0249045
$936$	−1.19901e7	−0.447335
$937$	−3.12728e7	−1.16364	−0.581818	−	0.813319i	$-0.697659\pi$
$937$	−3.12728e7	−1.16364	−0.581818	+	0.813319i	$0.697659\pi$
$938$	−2.35233e7	−0.872954
$939$	−5.85529e6	−0.216713
$940$	627447.	0.0231610
$941$	−3.62149e7	−1.33326	−0.666628	−	0.745391i	$-0.732263\pi$
$941$	−3.62149e7	−1.33326	−0.666628	+	0.745391i	$0.732263\pi$
$942$	−2.79658e7	−1.02683
$943$	−9.75116e6	−0.357089
$944$	7.76851e6	0.283732
$945$	−7.00139e6	−0.255038
$946$	−2.22155e6	−0.0807101
$947$	3.14916e7	1.14109	0.570545	−	0.821266i	$-0.306732\pi$
$947$	3.14916e7	1.14109	0.570545	+	0.821266i	$0.306732\pi$
$948$	−1.34488e7	−0.486028
$949$	−1.42791e7	−0.514679
$950$	2.61046e6	0.0938444
$951$	−1.77671e6	−0.0637038
$952$	−6.60828e6	−0.236318
$953$	3.37673e7	1.20438	0.602190	−	0.798353i	$-0.294295\pi$
$953$	3.37673e7	1.20438	0.602190	+	0.798353i	$0.294295\pi$
$954$	4.30423e6	0.153117
$955$	4.86970e6	0.172780
$956$	6.19556e7	2.19248
$957$	2.33513e6	0.0824196
$958$	1.88628e7	0.664037
$959$	4.61756e6	0.162131
$960$	7.03634e6	0.246416
$961$	−2.25855e7	−0.788900
$962$	3.27937e6	0.114249
$963$	2.78682e6	0.0968374
$964$	2.54230e7	0.881118
$965$	1.19780e7	0.414063
$966$	−2.60401e7	−0.897841
$967$	1.56676e7	0.538812	0.269406	−	0.963027i	$-0.413173\pi$
$967$	1.56676e7	0.538812	0.269406	+	0.963027i	$0.413173\pi$
$968$	1.99138e7	0.683071
$969$	−294082.	−0.0100614
$970$	1.86235e7	0.635522
$971$	1.88686e7	0.642232	0.321116	−	0.947040i	$-0.395942\pi$
$971$	1.88686e7	0.642232	0.321116	+	0.947040i	$0.395942\pi$
$972$	3.84838e7	1.30651
$973$	−2.51874e7	−0.852906
$974$	−6.28628e7	−2.12323
$975$	6.48764e6	0.218562
$976$	1.63268e7	0.548626
$977$	3.79952e7	1.27348	0.636740	−	0.771078i	$-0.280282\pi$
$977$	3.79952e7	1.27348	0.636740	+	0.771078i	$0.280282\pi$
$978$	−2.30319e7	−0.769987
$979$	8.52577e6	0.284300
$980$	3.87136e6	0.128765
$981$	2.92319e7	0.969804
$982$	4.33236e7	1.43366
$983$	4.13482e7	1.36481	0.682407	−	0.730973i	$-0.260933\pi$
$983$	4.13482e7	1.36481	0.682407	+	0.730973i	$0.260933\pi$
$984$	−1.54181e6	−0.0507624
$985$	−5.05431e6	−0.165986
$986$	−2.67005e7	−0.874637
$987$	371912.	0.0121520
$988$	−2.38929e6	−0.0778712
$989$	1.82960e7	0.594793
$990$	2.74781e6	0.0891042
$991$	−2.51693e7	−0.814116	−0.407058	−	0.913402i	$-0.633445\pi$
$991$	−2.51693e7	−0.814116	−0.407058	+	0.913402i	$0.633445\pi$
$992$	1.78198e7	0.574940
$993$	−2.14342e7	−0.689819
$994$	7.93284e7	2.54661
$995$	−1.13377e7	−0.363052
$996$	−1.44573e7	−0.461782
$997$	−1.05201e7	−0.335183	−0.167592	−	0.985857i	$-0.553599\pi$
$997$	−1.05201e7	−0.335183	−0.167592	+	0.985857i	$0.553599\pi$
$998$	6.10076e7	1.93891
$999$	−2.11921e6	−0.0671832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.17	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.17	✓	117	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-8.84956 q^{2} +5.64544 q^{3} +46.3147 q^{4} -23.6980 q^{5} -49.9597 q^{6} -115.238 q^{7} -126.678 q^{8} -211.129 q^{9} +O(q^{10})\)	\(q-8.84956 q^{2} +5.64544 q^{3} +46.3147 q^{4} -23.6980 q^{5} -49.9597 q^{6} -115.238 q^{7} -126.678 q^{8} -211.129 q^{9} +209.717 q^{10} -62.0590 q^{11} +261.467 q^{12} -448.303 q^{13} +1019.80 q^{14} -133.786 q^{15} -361.022 q^{16} -452.680 q^{17} +1868.40 q^{18} +115.074 q^{19} -1097.57 q^{20} -650.569 q^{21} +549.195 q^{22} -4523.01 q^{23} -715.156 q^{24} -2563.40 q^{25} +3967.28 q^{26} -2563.76 q^{27} -5337.20 q^{28} -6665.11 q^{29} +1183.94 q^{30} +2458.38 q^{31} +7248.59 q^{32} -350.351 q^{33} +4006.01 q^{34} +2730.91 q^{35} -9778.37 q^{36} +826.603 q^{37} -1018.36 q^{38} -2530.87 q^{39} +3002.03 q^{40} +2155.90 q^{41} +5757.25 q^{42} -4045.10 q^{43} -2874.24 q^{44} +5003.34 q^{45} +40026.6 q^{46} -571.672 q^{47} -2038.13 q^{48} -3527.23 q^{49} +22685.0 q^{50} -2555.58 q^{51} -20763.0 q^{52} +2303.70 q^{53} +22688.1 q^{54} +1470.67 q^{55} +14598.1 q^{56} +649.646 q^{57} +58983.3 q^{58} -21518.1 q^{59} -6196.24 q^{60} -45223.9 q^{61} -21755.5 q^{62} +24330.1 q^{63} -52594.1 q^{64} +10623.9 q^{65} +3100.45 q^{66} -23066.5 q^{67} -20965.7 q^{68} -25534.4 q^{69} -24167.3 q^{70} +77787.8 q^{71} +26745.5 q^{72} +31851.5 q^{73} -7315.07 q^{74} -14471.6 q^{75} +5329.63 q^{76} +7151.55 q^{77} +22397.1 q^{78} -51435.8 q^{79} +8555.49 q^{80} +36830.8 q^{81} -19078.8 q^{82} -55292.9 q^{83} -30130.9 q^{84} +10727.6 q^{85} +35797.4 q^{86} -37627.5 q^{87} +7861.53 q^{88} -137382. q^{89} -44277.3 q^{90} +51661.5 q^{91} -209481. q^{92} +13878.6 q^{93} +5059.05 q^{94} -2727.04 q^{95} +40921.5 q^{96} +88802.8 q^{97} +31214.4 q^{98} +13102.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * q^99

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