LMFDB - Embedded newform 547.6.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-10.9789 q^{2} +22.9161 q^{3} +88.5367 q^{4} -41.5403 q^{5} -251.594 q^{6} -192.368 q^{7} -620.712 q^{8} +282.146 q^{9} +O(q^{10})$	\(q-10.9789 q^{2} +22.9161 q^{3} +88.5367 q^{4} -41.5403 q^{5} -251.594 q^{6} -192.368 q^{7} -620.712 q^{8} +282.146 q^{9} +456.068 q^{10} -577.336 q^{11} +2028.91 q^{12} -826.892 q^{13} +2112.00 q^{14} -951.941 q^{15} +3981.58 q^{16} +1360.74 q^{17} -3097.66 q^{18} -1388.91 q^{19} -3677.85 q^{20} -4408.32 q^{21} +6338.53 q^{22} -1079.02 q^{23} -14224.3 q^{24} -1399.40 q^{25} +9078.38 q^{26} +897.069 q^{27} -17031.7 q^{28} -3673.52 q^{29} +10451.3 q^{30} -8338.55 q^{31} -23850.6 q^{32} -13230.3 q^{33} -14939.5 q^{34} +7991.05 q^{35} +24980.3 q^{36} +15771.8 q^{37} +15248.8 q^{38} -18949.1 q^{39} +25784.6 q^{40} -5256.74 q^{41} +48398.7 q^{42} -9504.87 q^{43} -51115.4 q^{44} -11720.4 q^{45} +11846.5 q^{46} +13088.4 q^{47} +91242.1 q^{48} +20198.6 q^{49} +15363.9 q^{50} +31182.8 q^{51} -73210.3 q^{52} -15865.7 q^{53} -9848.85 q^{54} +23982.7 q^{55} +119405. q^{56} -31828.4 q^{57} +40331.2 q^{58} +10059.4 q^{59} -84281.7 q^{60} +42772.5 q^{61} +91548.3 q^{62} -54275.9 q^{63} +134444. q^{64} +34349.4 q^{65} +145254. q^{66} -16074.6 q^{67} +120476. q^{68} -24726.9 q^{69} -87733.1 q^{70} +26174.0 q^{71} -175131. q^{72} -61802.3 q^{73} -173158. q^{74} -32068.7 q^{75} -122970. q^{76} +111061. q^{77} +208041. q^{78} -30199.5 q^{79} -165396. q^{80} -48004.2 q^{81} +57713.4 q^{82} -90025.4 q^{83} -390299. q^{84} -56525.7 q^{85} +104353. q^{86} -84182.5 q^{87} +358360. q^{88} +122079. q^{89} +128678. q^{90} +159068. q^{91} -95532.9 q^{92} -191087. q^{93} -143697. q^{94} +57695.9 q^{95} -546563. q^{96} -103991. q^{97} -221759. q^{98} -162893. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.9789	−1.94082	−0.970409	−	0.241468i	$-0.922371\pi$
$2$	−10.9789	−1.94082	−0.970409	+	0.241468i	$0.922371\pi$
$3$	22.9161	1.47007	0.735033	−	0.678031i	$-0.237167\pi$
$3$	22.9161	1.47007	0.735033	+	0.678031i	$0.237167\pi$
$4$	88.5367	2.76677
$5$	−41.5403	−0.743096	−0.371548	−	0.928414i	$-0.621173\pi$
$5$	−41.5403	−0.743096	−0.371548	+	0.928414i	$0.621173\pi$
$6$	−251.594	−2.85313
$7$	−192.368	−1.48384	−0.741922	−	0.670486i	$-0.766086\pi$
$7$	−192.368	−1.48384	−0.741922	+	0.670486i	$0.766086\pi$
$8$	−620.712	−3.42898
$9$	282.146	1.16109
$10$	456.068	1.44221
$11$	−577.336	−1.43862	−0.719311	−	0.694688i	$-0.755542\pi$
$11$	−577.336	−1.43862	−0.719311	+	0.694688i	$0.755542\pi$
$12$	2028.91	4.06734
$13$	−826.892	−1.35703	−0.678517	−	0.734585i	$-0.737377\pi$
$13$	−826.892	−1.35703	−0.678517	+	0.734585i	$0.737377\pi$
$14$	2112.00	2.87987
$15$	−951.941	−1.09240
$16$	3981.58	3.88826
$17$	1360.74	1.14197	0.570983	−	0.820962i	$-0.306562\pi$
$17$	1360.74	1.14197	0.570983	+	0.820962i	$0.306562\pi$
$18$	−3097.66	−2.25347
$19$	−1388.91	−0.882655	−0.441327	−	0.897346i	$-0.645492\pi$
$19$	−1388.91	−0.882655	−0.441327	+	0.897346i	$0.645492\pi$
$20$	−3677.85	−2.05598
$21$	−4408.32	−2.18135
$22$	6338.53	2.79210
$23$	−1079.02	−0.425314	−0.212657	−	0.977127i	$-0.568212\pi$
$23$	−1079.02	−0.425314	−0.212657	+	0.977127i	$0.568212\pi$
$24$	−14224.3	−5.04083
$25$	−1399.40	−0.447808
$26$	9078.38	2.63375
$27$	897.069	0.236819
$28$	−17031.7	−4.10546
$29$	−3673.52	−0.811123	−0.405562	−	0.914068i	$-0.632924\pi$
$29$	−3673.52	−0.811123	−0.405562	+	0.914068i	$0.632924\pi$
$30$	10451.3	2.12015
$31$	−8338.55	−1.55843	−0.779213	−	0.626759i	$-0.784381\pi$
$31$	−8338.55	−1.55843	−0.779213	+	0.626759i	$0.784381\pi$
$32$	−23850.6	−4.11742
$33$	−13230.3	−2.11487
$34$	−14939.5	−2.21635
$35$	7991.05	1.10264
$36$	24980.3	3.21248
$37$	15771.8	1.89399	0.946995	−	0.321249i	$-0.104103\pi$
$37$	15771.8	1.89399	0.946995	+	0.321249i	$0.104103\pi$
$38$	15248.8	1.71307
$39$	−18949.1	−1.99493
$40$	25784.6	2.54806
$41$	−5256.74	−0.488379	−0.244190	−	0.969728i	$-0.578522\pi$
$41$	−5256.74	−0.488379	−0.244190	+	0.969728i	$0.578522\pi$
$42$	48398.7	4.23360
$43$	−9504.87	−0.783926	−0.391963	−	0.919981i	$-0.628204\pi$
$43$	−9504.87	−0.783926	−0.391963	+	0.919981i	$0.628204\pi$
$44$	−51115.4	−3.98034
$45$	−11720.4	−0.862805
$46$	11846.5	0.825458
$47$	13088.4	0.864256	0.432128	−	0.901812i	$-0.357763\pi$
$47$	13088.4	0.864256	0.432128	+	0.901812i	$0.357763\pi$
$48$	91242.1	5.71600
$49$	20198.6	1.20180
$50$	15363.9	0.869114
$51$	31182.8	1.67877
$52$	−73210.3	−3.75460
$53$	−15865.7	−0.775838	−0.387919	−	0.921694i	$-0.626806\pi$
$53$	−15865.7	−0.775838	−0.387919	+	0.921694i	$0.626806\pi$
$54$	−9848.85	−0.459622
$55$	23982.7	1.06903
$56$	119405.	5.08808
$57$	−31828.4	−1.29756
$58$	40331.2	1.57424
$59$	10059.4	0.376221	0.188110	−	0.982148i	$-0.439764\pi$
$59$	10059.4	0.376221	0.188110	+	0.982148i	$0.439764\pi$
$60$	−84281.7	−3.02242
$61$	42772.5	1.47177	0.735885	−	0.677107i	$-0.236766\pi$
$61$	42772.5	1.47177	0.735885	+	0.677107i	$0.236766\pi$
$62$	91548.3	3.02462
$63$	−54275.9	−1.72288
$64$	134444.	4.10290
$65$	34349.4	1.00841
$66$	145254.	4.10458
$67$	−16074.6	−0.437474	−0.218737	−	0.975784i	$-0.570194\pi$
$67$	−16074.6	−0.437474	−0.218737	+	0.975784i	$0.570194\pi$
$68$	120476.	3.15956
$69$	−24726.9	−0.625240
$70$	−87733.1	−2.14002
$71$	26174.0	0.616203	0.308102	−	0.951353i	$-0.400306\pi$
$71$	26174.0	0.616203	0.308102	+	0.951353i	$0.400306\pi$
$72$	−175131.	−3.98137
$73$	−61802.3	−1.35737	−0.678684	−	0.734430i	$-0.737449\pi$
$73$	−61802.3	−1.35737	−0.678684	+	0.734430i	$0.737449\pi$
$74$	−173158.	−3.67589
$75$	−32068.7	−0.658308
$76$	−122970.	−2.44211
$77$	111061.	2.13469
$78$	208041.	3.87179
$79$	−30199.5	−0.544418	−0.272209	−	0.962238i	$-0.587754\pi$
$79$	−30199.5	−0.544418	−0.272209	+	0.962238i	$0.587754\pi$
$80$	−165396.	−2.88935
$81$	−48004.2	−0.812955
$82$	57713.4	0.947855
$83$	−90025.4	−1.43440	−0.717199	−	0.696868i	$-0.754576\pi$
$83$	−90025.4	−1.43440	−0.717199	+	0.696868i	$0.754576\pi$
$84$	−390299.	−6.03530
$85$	−56525.7	−0.848591
$86$	104353.	1.52146
$87$	−84182.5	−1.19240
$88$	358360.	4.93301
$89$	122079.	1.63367	0.816836	−	0.576870i	$-0.195726\pi$
$89$	122079.	1.63367	0.816836	+	0.576870i	$0.195726\pi$
$90$	128678.	1.67455
$91$	159068.	2.01363
$92$	−95532.9	−1.17675
$93$	−191087.	−2.29099
$94$	−143697.	−1.67736
$95$	57695.9	0.655897
$96$	−546563.	−6.05288
$97$	−103991.	−1.12219	−0.561097	−	0.827750i	$-0.689620\pi$
$97$	−103991.	−1.12219	−0.561097	+	0.827750i	$0.689620\pi$
$98$	−221759.	−2.33247
$99$	−162893.	−1.67038
$100$	−123898.	−1.23898
$101$	124401.	1.21344	0.606721	−	0.794915i	$-0.292484\pi$
$101$	124401.	1.21344	0.606721	+	0.794915i	$0.292484\pi$
$102$	−342354.	−3.25818
$103$	125334.	1.16406	0.582031	−	0.813167i	$-0.302258\pi$
$103$	125334.	1.16406	0.582031	+	0.813167i	$0.302258\pi$
$104$	513262.	4.65324
$105$	183123.	1.62095
$106$	174189.	1.50576
$107$	100854.	0.851596	0.425798	−	0.904818i	$-0.359994\pi$
$107$	100854.	0.851596	0.425798	+	0.904818i	$0.359994\pi$
$108$	79423.6	0.655224
$109$	−8850.03	−0.0713475	−0.0356737	−	0.999363i	$-0.511358\pi$
$109$	−8850.03	−0.0713475	−0.0356737	+	0.999363i	$0.511358\pi$
$110$	−263305.	−2.07480
$111$	361428.	2.78429
$112$	−765929.	−5.76957
$113$	−106213.	−0.782492	−0.391246	−	0.920286i	$-0.627956\pi$
$113$	−106213.	−0.782492	−0.391246	+	0.920286i	$0.627956\pi$
$114$	349442.	2.51833
$115$	44822.9	0.316049
$116$	−325241.	−2.24419
$117$	−233304.	−1.57564
$118$	−110442.	−0.730176
$119$	−261764.	−1.69450
$120$	590881.	3.74582
$121$	172266.	1.06963
$122$	−469596.	−2.85644
$123$	−120464.	−0.717949
$124$	−738268.	−4.31181
$125$	187945.	1.07586
$126$	595891.	3.34380
$127$	74062.1	0.407461	0.203731	−	0.979027i	$-0.434693\pi$
$127$	74062.1	0.407461	0.203731	+	0.979027i	$0.434693\pi$
$128$	−712827.	−3.84556
$129$	−217814.	−1.15242
$130$	−377119.	−1.95713
$131$	26154.9	0.133161	0.0665803	−	0.997781i	$-0.478791\pi$
$131$	26154.9	0.133161	0.0665803	+	0.997781i	$0.478791\pi$
$132$	−1.17136e6	−5.85137
$133$	267183.	1.30972
$134$	176481.	0.849057
$135$	−37264.6	−0.175979
$136$	−844629.	−3.91579
$137$	404382.	1.84073	0.920367	−	0.391057i	$-0.127890\pi$
$137$	404382.	1.84073	0.920367	+	0.391057i	$0.127890\pi$
$138$	271475.	1.21348
$139$	−332319.	−1.45887	−0.729437	−	0.684048i	$-0.760218\pi$
$139$	−332319.	−1.45887	−0.729437	+	0.684048i	$0.760218\pi$
$140$	707501.	3.05075
$141$	299935.	1.27051
$142$	−287362.	−1.19594
$143$	477394.	1.95226
$144$	1.12339e6	4.51463
$145$	152599.	0.602743
$146$	678523.	2.63440
$147$	462872.	1.76672
$148$	1.39639e6	5.24024
$149$	−73107.5	−0.269771	−0.134886	−	0.990861i	$-0.543067\pi$
$149$	−73107.5	−0.269771	−0.134886	+	0.990861i	$0.543067\pi$
$150$	352080.	1.27765
$151$	−320527.	−1.14399	−0.571995	−	0.820257i	$-0.693830\pi$
$151$	−320527.	−1.14399	−0.571995	+	0.820257i	$0.693830\pi$
$152$	862115.	3.02661
$153$	383928.	1.32593
$154$	−1.21933e6	−4.14305
$155$	346386.	1.15806
$156$	−1.67769e6	−5.51951
$157$	−324189.	−1.04966	−0.524830	−	0.851207i	$-0.675871\pi$
$157$	−324189.	−1.04966	−0.524830	+	0.851207i	$0.675871\pi$
$158$	331558.	1.05662
$159$	−363580.	−1.14053
$160$	990763.	3.05964
$161$	207569.	0.631101
$162$	527034.	1.57780
$163$	−398977.	−1.17619	−0.588096	−	0.808791i	$-0.700122\pi$
$163$	−398977.	−1.17619	−0.588096	+	0.808791i	$0.700122\pi$
$164$	−465415.	−1.35123
$165$	549590.	1.57155
$166$	988382.	2.78391
$167$	−206992.	−0.574332	−0.287166	−	0.957881i	$-0.592713\pi$
$167$	−206992.	−0.574332	−0.287166	+	0.957881i	$0.592713\pi$
$168$	2.73630e6	7.47981
$169$	312457.	0.841539
$170$	620591.	1.64696
$171$	−391876.	−1.02485
$172$	−841531.	−2.16895
$173$	688085.	1.74794	0.873971	−	0.485979i	$-0.161537\pi$
$173$	688085.	1.74794	0.873971	+	0.485979i	$0.161537\pi$
$174$	924233.	2.31424
$175$	269200.	0.664478
$176$	−2.29871e6	−5.59374
$177$	230522.	0.553069
$178$	−1.34029e6	−3.17066
$179$	662488.	1.54542	0.772708	−	0.634762i	$-0.218902\pi$
$179$	662488.	1.54542	0.772708	+	0.634762i	$0.218902\pi$
$180$	−1.03769e6	−2.38718
$181$	−402544.	−0.913308	−0.456654	−	0.889644i	$-0.650952\pi$
$181$	−402544.	−0.913308	−0.456654	+	0.889644i	$0.650952\pi$
$182$	−1.74639e6	−3.90808
$183$	980177.	2.16360
$184$	669761.	1.45840
$185$	−655167.	−1.40742
$186$	2.09793e6	4.44639
$187$	−785605.	−1.64286
$188$	1.15881e6	2.39120
$189$	−172568.	−0.351403
$190$	−633439.	−1.27298
$191$	−765459.	−1.51823	−0.759117	−	0.650955i	$-0.774369\pi$
$191$	−765459.	−1.51823	−0.759117	+	0.650955i	$0.774369\pi$
$192$	3.08092e6	6.03153
$193$	126874.	0.245177	0.122588	−	0.992458i	$-0.460881\pi$
$193$	126874.	0.245177	0.122588	+	0.992458i	$0.460881\pi$
$194$	1.14171e6	2.17797
$195$	787152.	1.48242
$196$	1.78832e6	3.32510
$197$	772040.	1.41734	0.708670	−	0.705540i	$-0.249296\pi$
$197$	772040.	1.41734	0.708670	+	0.705540i	$0.249296\pi$
$198$	1.78839e6	3.24190
$199$	−341919.	−0.612055	−0.306027	−	0.952023i	$-0.599000\pi$
$199$	−341919.	−0.612055	−0.306027	+	0.952023i	$0.599000\pi$
$200$	868625.	1.53553
$201$	−368366.	−0.643115
$202$	−1.36579e6	−2.35507
$203$	706668.	1.20358
$204$	2.76083e6	4.64477
$205$	218367.	0.362913
$206$	−1.37603e6	−2.25923
$207$	−304441.	−0.493830
$208$	−3.29233e6	−5.27650
$209$	801869.	1.26981
$210$	−2.01050e6	−3.14597
$211$	−57452.7	−0.0888391	−0.0444196	−	0.999013i	$-0.514144\pi$
$211$	−57452.7	−0.0888391	−0.0444196	+	0.999013i	$0.514144\pi$
$212$	−1.40470e6	−2.14657
$213$	599805.	0.905860
$214$	−1.10727e6	−1.65279
$215$	394836.	0.582533
$216$	−556822.	−0.812048
$217$	1.60407e6	2.31246
$218$	97163.8	0.138472
$219$	−1.41627e6	−1.99542
$220$	2.12335e6	2.95778
$221$	−1.12519e6	−1.54969
$222$	−3.96809e6	−5.40380
$223$	508584.	0.684858	0.342429	−	0.939544i	$-0.388750\pi$
$223$	508584.	0.684858	0.342429	+	0.939544i	$0.388750\pi$
$224$	4.58811e6	6.10961
$225$	−394835.	−0.519947
$226$	1.16610e6	1.51867
$227$	−878261.	−1.13125	−0.565625	−	0.824662i	$-0.691365\pi$
$227$	−878261.	−1.13125	−0.565625	+	0.824662i	$0.691365\pi$
$228$	−2.81798e6	−3.59006
$229$	−117517.	−0.148085	−0.0740425	−	0.997255i	$-0.523590\pi$
$229$	−117517.	−0.148085	−0.0740425	+	0.997255i	$0.523590\pi$
$230$	−492107.	−0.613394
$231$	2.54508e6	3.13814
$232$	2.28020e6	2.78133
$233$	−969278.	−1.16966	−0.584828	−	0.811157i	$-0.698838\pi$
$233$	−969278.	−1.16966	−0.584828	+	0.811157i	$0.698838\pi$
$234$	2.56143e6	3.05804
$235$	−543697.	−0.642225
$236$	890628.	1.04092
$237$	−692055.	−0.800331
$238$	2.87388e6	3.28872
$239$	−101696.	−0.115162	−0.0575812	−	0.998341i	$-0.518339\pi$
$239$	−101696.	−0.115162	−0.0575812	+	0.998341i	$0.518339\pi$
$240$	−3.79023e6	−4.24754
$241$	−408762.	−0.453345	−0.226672	−	0.973971i	$-0.572785\pi$
$241$	−408762.	−0.453345	−0.226672	+	0.973971i	$0.572785\pi$
$242$	−1.89129e6	−2.07597
$243$	−1.31805e6	−1.43192
$244$	3.78694e6	4.07205
$245$	−839056.	−0.893050
$246$	1.32256e6	1.39341
$247$	1.14848e6	1.19779
$248$	5.17584e6	5.34382
$249$	−2.06303e6	−2.10866
$250$	−2.06343e6	−2.08805
$251$	−1.24572e6	−1.24806	−0.624029	−	0.781401i	$-0.714505\pi$
$251$	−1.24572e6	−1.24806	−0.624029	+	0.781401i	$0.714505\pi$
$252$	−4.80541e6	−4.76683
$253$	622957.	0.611867
$254$	−813121.	−0.790808
$255$	−1.29535e6	−1.24748
$256$	3.52387e6	3.36063
$257$	1.31807e6	1.24481	0.622407	−	0.782694i	$-0.286155\pi$
$257$	1.31807e6	1.24481	0.622407	+	0.782694i	$0.286155\pi$
$258$	2.39137e6	2.23664
$259$	−3.03400e6	−2.81039
$260$	3.04118e6	2.79003
$261$	−1.03647e6	−0.941790
$262$	−287153.	−0.258440
$263$	−1.11857e6	−0.997180	−0.498590	−	0.866838i	$-0.666149\pi$
$263$	−1.11857e6	−0.997180	−0.498590	+	0.866838i	$0.666149\pi$
$264$	8.21219e6	7.25186
$265$	659069.	0.576522
$266$	−2.93338e6	−2.54193
$267$	2.79756e6	2.40161
$268$	−1.42319e6	−1.21039
$269$	−704480.	−0.593592	−0.296796	−	0.954941i	$-0.595918\pi$
$269$	−704480.	−0.593592	−0.296796	+	0.954941i	$0.595918\pi$
$270$	409125.	0.341544
$271$	510428.	0.422193	0.211096	−	0.977465i	$-0.432297\pi$
$271$	510428.	0.422193	0.211096	+	0.977465i	$0.432297\pi$
$272$	5.41790e6	4.44026
$273$	3.64521e6	2.96016
$274$	−4.43968e6	−3.57253
$275$	807924.	0.644227
$276$	−2.18924e6	−1.72990
$277$	860466.	0.673805	0.336902	−	0.941540i	$-0.390621\pi$
$277$	860466.	0.673805	0.336902	+	0.941540i	$0.390621\pi$
$278$	3.64850e6	2.83141
$279$	−2.35269e6	−1.80948
$280$	−4.96014e6	−3.78093
$281$	1.37148e6	1.03616	0.518078	−	0.855333i	$-0.326648\pi$
$281$	1.37148e6	1.03616	0.518078	+	0.855333i	$0.326648\pi$
$282$	−3.29296e6	−2.46583
$283$	−836552.	−0.620908	−0.310454	−	0.950588i	$-0.600481\pi$
$283$	−836552.	−0.620908	−0.310454	+	0.950588i	$0.600481\pi$
$284$	2.31736e6	1.70489
$285$	1.32216e6	0.964212
$286$	−5.24128e6	−3.78898
$287$	1.01123e6	0.724679
$288$	−6.72936e6	−4.78071
$289$	431762.	0.304088
$290$	−1.67537e6	−1.16981
$291$	−2.38307e6	−1.64970
$292$	−5.47178e6	−3.75553
$293$	−1.03938e6	−0.707304	−0.353652	−	0.935377i	$-0.615060\pi$
$293$	−1.03938e6	−0.707304	−0.353652	+	0.935377i	$0.615060\pi$
$294$	−5.08183e6	−3.42888
$295$	−417871.	−0.279568
$296$	−9.78977e6	−6.49446
$297$	−517910.	−0.340693
$298$	802641.	0.523577
$299$	892233.	0.577166
$300$	−2.83926e6	−1.82139
$301$	1.82844e6	1.16323
$302$	3.51904e6	2.22028
$303$	2.85077e6	1.78384
$304$	−5.53006e6	−3.43199
$305$	−1.77678e6	−1.09367
$306$	−4.21511e6	−2.57339
$307$	−69996.5	−0.0423868	−0.0211934	−	0.999775i	$-0.506747\pi$
$307$	−69996.5	−0.0423868	−0.0211934	+	0.999775i	$0.506747\pi$
$308$	9.83299e6	5.90621
$309$	2.87216e6	1.71125
$310$	−3.80295e6	−2.24758
$311$	1.37491e6	0.806071	0.403036	−	0.915184i	$-0.367955\pi$
$311$	1.37491e6	0.806071	0.403036	+	0.915184i	$0.367955\pi$
$312$	1.17619e7	6.84058
$313$	2.80029e6	1.61563	0.807816	−	0.589435i	$-0.200649\pi$
$313$	2.80029e6	1.61563	0.807816	+	0.589435i	$0.200649\pi$
$314$	3.55924e6	2.03720
$315$	2.25464e6	1.28027
$316$	−2.67377e6	−1.50628
$317$	2.14021e6	1.19621	0.598105	−	0.801418i	$-0.295921\pi$
$317$	2.14021e6	1.19621	0.598105	+	0.801418i	$0.295921\pi$
$318$	3.99172e6	2.21357
$319$	2.12085e6	1.16690
$320$	−5.58484e6	−3.04885
$321$	2.31117e6	1.25190
$322$	−2.27889e6	−1.22485
$323$	−1.88995e6	−1.00796
$324$	−4.25013e6	−2.24926
$325$	1.15715e6	0.607690
$326$	4.38033e6	2.28278
$327$	−202808.	−0.104886
$328$	3.26292e6	1.67464
$329$	−2.51780e6	−1.28242
$330$	−6.03390e6	−3.05010
$331$	−616817.	−0.309447	−0.154723	−	0.987958i	$-0.549449\pi$
$331$	−616817.	−0.309447	−0.154723	+	0.987958i	$0.549449\pi$
$332$	−7.97055e6	−3.96865
$333$	4.44995e6	2.19910
$334$	2.27255e6	1.11467
$335$	667743.	0.325085
$336$	−1.75521e7	−8.48165
$337$	1.90898e6	0.915643	0.457822	−	0.889044i	$-0.348630\pi$
$337$	1.90898e6	0.915643	0.457822	+	0.889044i	$0.348630\pi$
$338$	−3.43045e6	−1.63327
$339$	−2.43398e6	−1.15032
$340$	−5.00460e6	−2.34786
$341$	4.81414e6	2.24199
$342$	4.30237e6	1.98904
$343$	−652432.	−0.299433
$344$	5.89979e6	2.68807
$345$	1.02716e6	0.464614
$346$	−7.55443e6	−3.39244
$347$	−1.44574e6	−0.644562	−0.322281	−	0.946644i	$-0.604450\pi$
$347$	−1.44574e6	−0.644562	−0.322281	+	0.946644i	$0.604450\pi$
$348$	−7.45324e6	−3.29911
$349$	−841869.	−0.369982	−0.184991	−	0.982740i	$-0.559226\pi$
$349$	−841869.	−0.369982	−0.184991	+	0.982740i	$0.559226\pi$
$350$	−2.95553e6	−1.28963
$351$	−741779.	−0.321371
$352$	1.37698e7	5.92341
$353$	2.31535e6	0.988963	0.494482	−	0.869188i	$-0.335358\pi$
$353$	2.31535e6	0.988963	0.494482	+	0.869188i	$0.335358\pi$
$354$	−2.53088e6	−1.07341
$355$	−1.08728e6	−0.457898
$356$	1.08085e7	4.52000
$357$	−5.99859e6	−2.49103
$358$	−7.27340e6	−2.99937
$359$	421058.	0.172427	0.0862136	−	0.996277i	$-0.472523\pi$
$359$	421058.	0.172427	0.0862136	+	0.996277i	$0.472523\pi$
$360$	7.27502e6	2.95854
$361$	−547021.	−0.220921
$362$	4.41950e6	1.77257
$363$	3.94765e6	1.57243
$364$	1.40833e7	5.57125
$365$	2.56729e6	1.00866
$366$	−1.07613e7	−4.19915
$367$	2.23963e6	0.867981	0.433990	−	0.900917i	$-0.357105\pi$
$367$	2.23963e6	0.867981	0.433990	+	0.900917i	$0.357105\pi$
$368$	−4.29620e6	−1.65373
$369$	−1.48317e6	−0.567054
$370$	7.19303e6	2.73154
$371$	3.05207e6	1.15122
$372$	−1.69182e7	−6.33865
$373$	−3.25401e6	−1.21101	−0.605504	−	0.795843i	$-0.707028\pi$
$373$	−3.25401e6	−1.21101	−0.605504	+	0.795843i	$0.707028\pi$
$374$	8.62510e6	3.18849
$375$	4.30696e6	1.58159
$376$	−8.12414e6	−2.96352
$377$	3.03760e6	1.10072
$378$	1.89461e6	0.682008
$379$	329919.	0.117980	0.0589901	−	0.998259i	$-0.481212\pi$
$379$	329919.	0.117980	0.0589901	+	0.998259i	$0.481212\pi$
$380$	5.10821e6	1.81472
$381$	1.69721e6	0.598995
$382$	8.40391e6	2.94661
$383$	−81331.0	−0.0283308	−0.0141654	−	0.999900i	$-0.504509\pi$
$383$	−81331.0	−0.0283308	−0.0141654	+	0.999900i	$0.504509\pi$
$384$	−1.63352e7	−5.65322
$385$	−4.61352e6	−1.58628
$386$	−1.39294e6	−0.475843
$387$	−2.68176e6	−0.910212
$388$	−9.20705e6	−3.10485
$389$	2.56343e6	0.858911	0.429455	−	0.903088i	$-0.358706\pi$
$389$	2.56343e6	0.858911	0.429455	+	0.903088i	$0.358706\pi$
$390$	−8.64208e6	−2.87711
$391$	−1.46827e6	−0.485695
$392$	−1.25375e7	−4.12094
$393$	599368.	0.195755
$394$	−8.47616e6	−2.75080
$395$	1.25450e6	0.404555
$396$	−1.44220e7	−4.62155
$397$	6.25131e6	1.99065	0.995325	−	0.0965791i	$-0.0307901\pi$
$397$	6.25131e6	1.99065	0.995325	+	0.0965791i	$0.0307901\pi$
$398$	3.75390e6	1.18789
$399$	6.12278e6	1.92538
$400$	−5.57182e6	−1.74119
$401$	−5.80903e6	−1.80402	−0.902012	−	0.431710i	$-0.857910\pi$
$401$	−5.80903e6	−1.80402	−0.902012	+	0.431710i	$0.857910\pi$
$402$	4.04426e6	1.24817
$403$	6.89508e6	2.11484
$404$	1.10140e7	3.35732
$405$	1.99411e6	0.604103
$406$	−7.75845e6	−2.33593
$407$	−9.10564e6	−2.72474
$408$	−1.93556e7	−5.75646
$409$	991636.	0.293119	0.146559	−	0.989202i	$-0.453180\pi$
$409$	991636.	0.293119	0.146559	+	0.989202i	$0.453180\pi$
$410$	−2.39743e6	−0.704347
$411$	9.26685e6	2.70600
$412$	1.10967e7	3.22069
$413$	−1.93511e6	−0.558253
$414$	3.34244e6	0.958434
$415$	3.73969e6	1.06590
$416$	1.97219e7	5.58747
$417$	−7.61544e6	−2.14464
$418$	−8.80366e6	−2.46446
$419$	−4.38815e6	−1.22109	−0.610543	−	0.791983i	$-0.709049\pi$
$419$	−4.38815e6	−1.22109	−0.610543	+	0.791983i	$0.709049\pi$
$420$	1.62131e7	4.48481
$421$	−1.72695e6	−0.474871	−0.237435	−	0.971403i	$-0.576307\pi$
$421$	−1.72695e6	−0.474871	−0.237435	+	0.971403i	$0.576307\pi$
$422$	630769.	0.172421
$423$	3.69284e6	1.00348
$424$	9.84807e6	2.66033
$425$	−1.90422e6	−0.511382
$426$	−6.58521e6	−1.75811
$427$	−8.22807e6	−2.18388
$428$	8.92928e6	2.35617
$429$	1.09400e7	2.86995
$430$	−4.33487e6	−1.13059
$431$	4.63731e6	1.20247	0.601234	−	0.799073i	$-0.294676\pi$
$431$	4.63731e6	1.20247	0.601234	+	0.799073i	$0.294676\pi$
$432$	3.57175e6	0.920813
$433$	−568186.	−0.145637	−0.0728184	−	0.997345i	$-0.523199\pi$
$433$	−568186.	−0.145637	−0.0728184	+	0.997345i	$0.523199\pi$
$434$	−1.76110e7	−4.48807
$435$	3.49697e6	0.886071
$436$	−783553.	−0.197402
$437$	1.49866e6	0.375406
$438$	1.55491e7	3.87275
$439$	1.07522e6	0.266278	0.133139	−	0.991097i	$-0.457494\pi$
$439$	1.07522e6	0.266278	0.133139	+	0.991097i	$0.457494\pi$
$440$	−1.48864e7	−3.66570
$441$	5.69895e6	1.39540
$442$	1.23533e7	3.00766
$443$	1.51721e6	0.367314	0.183657	−	0.982990i	$-0.441206\pi$
$443$	1.51721e6	0.367314	0.183657	+	0.982990i	$0.441206\pi$
$444$	3.19997e7	7.70350
$445$	−5.07119e6	−1.21398
$446$	−5.58370e6	−1.32918
$447$	−1.67533e6	−0.396582
$448$	−2.58627e7	−6.08806
$449$	−3.62166e6	−0.847797	−0.423898	−	0.905710i	$-0.639339\pi$
$449$	−3.62166e6	−0.847797	−0.423898	+	0.905710i	$0.639339\pi$
$450$	4.33486e6	1.00912
$451$	3.03491e6	0.702593
$452$	−9.40372e6	−2.16498
$453$	−7.34522e6	−1.68174
$454$	9.64236e6	2.19555
$455$	−6.60773e6	−1.49632
$456$	1.97563e7	4.44931
$457$	−467219.	−0.104648	−0.0523239	−	0.998630i	$-0.516663\pi$
$457$	−467219.	−0.104648	−0.0523239	+	0.998630i	$0.516663\pi$
$458$	1.29021e6	0.287406
$459$	1.22068e6	0.270439
$460$	3.96847e6	0.874437
$461$	−1.95855e6	−0.429222	−0.214611	−	0.976700i	$-0.568848\pi$
$461$	−1.95855e6	−0.429222	−0.214611	+	0.976700i	$0.568848\pi$
$462$	−2.79423e7	−6.09056
$463$	4.22626e6	0.916229	0.458115	−	0.888893i	$-0.348525\pi$
$463$	4.22626e6	0.916229	0.458115	+	0.888893i	$0.348525\pi$
$464$	−1.46264e7	−3.15386
$465$	7.93780e6	1.70243
$466$	1.06416e7	2.27009
$467$	6.03337e6	1.28017	0.640085	−	0.768304i	$-0.278899\pi$
$467$	6.03337e6	1.28017	0.640085	+	0.768304i	$0.278899\pi$
$468$	−2.06560e7	−4.35945
$469$	3.09224e6	0.649143
$470$	5.96921e6	1.24644
$471$	−7.42913e6	−1.54307
$472$	−6.24400e6	−1.29005
$473$	5.48751e6	1.12777
$474$	7.59801e6	1.55330
$475$	1.94364e6	0.395260
$476$	−2.31757e7	−4.68830
$477$	−4.47646e6	−0.900821
$478$	1.11652e6	0.223509
$479$	2.26027e6	0.450113	0.225057	−	0.974346i	$-0.427743\pi$
$479$	2.26027e6	0.450113	0.225057	+	0.974346i	$0.427743\pi$
$480$	2.27044e7	4.49787
$481$	−1.30416e7	−2.57021
$482$	4.48777e6	0.879859
$483$	4.75667e6	0.927760
$484$	1.52518e7	2.95944
$485$	4.31983e6	0.833898
$486$	1.44708e7	2.77909
$487$	−6.40263e6	−1.22331	−0.611655	−	0.791125i	$-0.709496\pi$
$487$	−6.40263e6	−1.22331	−0.611655	+	0.791125i	$0.709496\pi$
$488$	−2.65494e7	−5.04667
$489$	−9.14297e6	−1.72908
$490$	9.21193e6	1.73325
$491$	−482290.	−0.0902828	−0.0451414	−	0.998981i	$-0.514374\pi$
$491$	−482290.	−0.0902828	−0.0451414	+	0.998981i	$0.514374\pi$
$492$	−1.06655e7	−1.98640
$493$	−4.99871e6	−0.926276
$494$	−1.26091e7	−2.32469
$495$	6.76663e6	1.24125
$496$	−3.32006e7	−6.05956
$497$	−5.03505e6	−0.914350
$498$	2.26498e7	4.09253
$499$	−8.67899e6	−1.56034	−0.780168	−	0.625571i	$-0.784866\pi$
$499$	−8.67899e6	−1.56034	−0.780168	+	0.625571i	$0.784866\pi$
$500$	1.66400e7	2.97666
$501$	−4.74345e6	−0.844306
$502$	1.36766e7	2.42225
$503$	−7.30267e6	−1.28695	−0.643475	−	0.765467i	$-0.722508\pi$
$503$	−7.30267e6	−1.28695	−0.643475	+	0.765467i	$0.722508\pi$
$504$	3.36897e7	5.90774
$505$	−5.16765e6	−0.901705
$506$	−6.83940e6	−1.18752
$507$	7.16029e6	1.23712
$508$	6.55721e6	1.12735
$509$	−5.50437e6	−0.941702	−0.470851	−	0.882213i	$-0.656053\pi$
$509$	−5.50437e6	−0.941702	−0.470851	+	0.882213i	$0.656053\pi$
$510$	1.42215e7	2.42114
$511$	1.18888e7	2.01412
$512$	−1.58779e7	−2.67681
$513$	−1.24595e6	−0.209029
$514$	−1.44710e7	−2.41596
$515$	−5.20642e6	−0.865010
$516$	−1.92846e7	−3.18849
$517$	−7.55641e6	−1.24334
$518$	3.33100e7	5.45445
$519$	1.57682e7	2.56959
$520$	−2.13211e7	−3.45781
$521$	−1.08905e7	−1.75773	−0.878865	−	0.477071i	$-0.841698\pi$
$521$	−1.08905e7	−1.75773	−0.878865	+	0.477071i	$0.841698\pi$
$522$	1.13793e7	1.82784
$523$	3.96278e6	0.633499	0.316749	−	0.948509i	$-0.397409\pi$
$523$	3.96278e6	0.633499	0.316749	+	0.948509i	$0.397409\pi$
$524$	2.31567e6	0.368425
$525$	6.16901e6	0.976826
$526$	1.22807e7	1.93534
$527$	−1.13466e7	−1.77967
$528$	−5.26773e7	−8.22316
$529$	−5.27206e6	−0.819108
$530$	−7.23586e6	−1.11892
$531$	2.83822e6	0.436828
$532$	2.36555e7	3.62371
$533$	4.34676e6	0.662747
$534$	−3.07142e7	−4.66108
$535$	−4.18951e6	−0.632817
$536$	9.97768e6	1.50009
$537$	1.51816e7	2.27186
$538$	7.73444e6	1.15205
$539$	−1.16614e7	−1.72893
$540$	−3.29928e6	−0.486895
$541$	9.77015e6	1.43519	0.717593	−	0.696463i	$-0.245244\pi$
$541$	9.77015e6	1.43519	0.717593	+	0.696463i	$0.245244\pi$
$542$	−5.60394e6	−0.819399
$543$	−9.22473e6	−1.34262
$544$	−3.24546e7	−4.70195
$545$	367633.	0.0530180
$546$	−4.00205e7	−5.74514
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	3.58027e7	5.09289
$549$	1.20681e7	1.70886
$550$	−8.87014e6	−1.25033
$551$	5.10219e6	0.715942
$552$	1.53483e7	2.14394
$553$	5.80944e6	0.807832
$554$	−9.44699e6	−1.30773
$555$	−1.50138e7	−2.06899
$556$	−2.94224e7	−4.03638
$557$	1.17713e7	1.60764	0.803818	−	0.594876i	$-0.202799\pi$
$557$	1.17713e7	1.60764	0.803818	+	0.594876i	$0.202799\pi$
$558$	2.58300e7	3.51187
$559$	7.85950e6	1.06381
$560$	3.18170e7	4.28735
$561$	−1.80030e7	−2.41511
$562$	−1.50574e7	−2.01099
$563$	4.13358e6	0.549611	0.274805	−	0.961500i	$-0.411387\pi$
$563$	4.13358e6	0.549611	0.274805	+	0.961500i	$0.411387\pi$
$564$	2.65553e7	3.51522
$565$	4.41211e6	0.581467
$566$	9.18444e6	1.20507
$567$	9.23448e6	1.20630
$568$	−1.62465e7	−2.11295
$569$	−606374.	−0.0785163	−0.0392582	−	0.999229i	$-0.512499\pi$
$569$	−606374.	−0.0785163	−0.0392582	+	0.999229i	$0.512499\pi$
$570$	−1.45159e7	−1.87136
$571$	−2.58654e6	−0.331993	−0.165997	−	0.986126i	$-0.553084\pi$
$571$	−2.58654e6	−0.331993	−0.165997	+	0.986126i	$0.553084\pi$
$572$	4.22669e7	5.40146
$573$	−1.75413e7	−2.23190
$574$	−1.11022e7	−1.40647
$575$	1.50998e6	0.190459
$576$	3.79327e7	4.76385
$577$	−1.08379e6	−0.135520	−0.0677602	−	0.997702i	$-0.521585\pi$
$577$	−1.08379e6	−0.135520	−0.0677602	+	0.997702i	$0.521585\pi$
$578$	−4.74028e6	−0.590179
$579$	2.90745e6	0.360426
$580$	1.35106e7	1.66765
$581$	1.73180e7	2.12842
$582$	2.61636e7	3.20176
$583$	9.15987e6	1.11614
$584$	3.83615e7	4.65439
$585$	9.69153e6	1.17085
$586$	1.14113e7	1.37275
$587$	−2.33977e6	−0.280271	−0.140135	−	0.990132i	$-0.544754\pi$
$587$	−2.33977e6	−0.280271	−0.140135	+	0.990132i	$0.544754\pi$
$588$	4.09812e7	4.88811
$589$	1.15815e7	1.37555
$590$	4.58778e6	0.542591
$591$	1.76921e7	2.08358
$592$	6.27967e7	7.36432
$593$	−2.82123e6	−0.329459	−0.164730	−	0.986339i	$-0.552675\pi$
$593$	−2.82123e6	−0.329459	−0.164730	+	0.986339i	$0.552675\pi$
$594$	5.68610e6	0.661223
$595$	1.08738e7	1.25918
$596$	−6.47270e6	−0.746396
$597$	−7.83543e6	−0.899761
$598$	−9.79576e6	−1.12017
$599$	−3.07377e6	−0.350030	−0.175015	−	0.984566i	$-0.555997\pi$
$599$	−3.07377e6	−0.350030	−0.175015	+	0.984566i	$0.555997\pi$
$600$	1.99055e7	2.25733
$601$	−8.40502e6	−0.949189	−0.474594	−	0.880205i	$-0.657405\pi$
$601$	−8.40502e6	−0.949189	−0.474594	+	0.880205i	$0.657405\pi$
$602$	−2.00743e7	−2.25761
$603$	−4.53537e6	−0.507948
$604$	−2.83784e7	−3.16516
$605$	−7.15598e6	−0.794842
$606$	−3.12984e7	−3.46211
$607$	2.45068e6	0.269970	0.134985	−	0.990848i	$-0.456901\pi$
$607$	2.45068e6	0.269970	0.134985	+	0.990848i	$0.456901\pi$
$608$	3.31264e7	3.63426
$609$	1.61940e7	1.76934
$610$	1.95072e7	2.12261
$611$	−1.08227e7	−1.17282
$612$	3.39917e7	3.66855
$613$	9.37253e6	1.00741	0.503704	−	0.863876i	$-0.331970\pi$
$613$	9.37253e6	1.00741	0.503704	+	0.863876i	$0.331970\pi$
$614$	768486.	0.0822650
$615$	5.00411e6	0.533505
$616$	−6.89370e7	−7.31983
$617$	4.78239e6	0.505745	0.252873	−	0.967500i	$-0.418625\pi$
$617$	4.78239e6	0.505745	0.252873	+	0.967500i	$0.418625\pi$
$618$	−3.15333e7	−3.32122
$619$	559030.	0.0586420	0.0293210	−	0.999570i	$-0.490666\pi$
$619$	559030.	0.0586420	0.0293210	+	0.999570i	$0.490666\pi$
$620$	3.06679e7	3.20409
$621$	−967956.	−0.100723
$622$	−1.50950e7	−1.56444
$623$	−2.34841e7	−2.42412
$624$	−7.54473e7	−7.75680
$625$	−3.43418e6	−0.351660
$626$	−3.07442e7	−3.13565
$627$	1.83757e7	1.86670
$628$	−2.87026e7	−2.90417
$629$	2.14614e7	2.16287
$630$	−2.47535e7	−2.48477
$631$	−692802.	−0.0692685	−0.0346342	−	0.999400i	$-0.511027\pi$
$631$	−692802.	−0.0692685	−0.0346342	+	0.999400i	$0.511027\pi$
$632$	1.87452e7	1.86680
$633$	−1.31659e6	−0.130599
$634$	−2.34972e7	−2.32163
$635$	−3.07656e6	−0.302783
$636$	−3.21902e7	−3.15559
$637$	−1.67020e7	−1.63088
$638$	−2.32847e7	−2.26474
$639$	7.38488e6	0.715470
$640$	2.96111e7	2.85762
$641$	3.79039e6	0.364367	0.182183	−	0.983265i	$-0.441684\pi$
$641$	3.79039e6	0.364367	0.182183	+	0.983265i	$0.441684\pi$
$642$	−2.53742e7	−2.42971
$643$	6.04686e6	0.576770	0.288385	−	0.957515i	$-0.406882\pi$
$643$	6.04686e6	0.576770	0.288385	+	0.957515i	$0.406882\pi$
$644$	1.83775e7	1.74611
$645$	9.04808e6	0.856361
$646$	2.07496e7	1.95627
$647$	1.90110e7	1.78543	0.892716	−	0.450619i	$-0.148797\pi$
$647$	1.90110e7	1.78543	0.892716	+	0.450619i	$0.148797\pi$
$648$	2.97968e7	2.78761
$649$	−5.80766e6	−0.541240
$650$	−1.27043e7	−1.17942
$651$	3.67590e7	3.39947
$652$	−3.53241e7	−3.25426
$653$	1.33577e7	1.22588	0.612942	−	0.790128i	$-0.289986\pi$
$653$	1.33577e7	1.22588	0.612942	+	0.790128i	$0.289986\pi$
$654$	2.22661e6	0.203564
$655$	−1.08649e6	−0.0989511
$656$	−2.09301e7	−1.89894
$657$	−1.74373e7	−1.57603
$658$	2.76427e7	2.48895
$659$	7.56374e6	0.678458	0.339229	−	0.940704i	$-0.389834\pi$
$659$	7.56374e6	0.678458	0.339229	+	0.940704i	$0.389834\pi$
$660$	4.86589e7	4.34813
$661$	−1.89042e7	−1.68289	−0.841445	−	0.540343i	$-0.818294\pi$
$661$	−1.89042e7	−1.68289	−0.841445	+	0.540343i	$0.818294\pi$
$662$	6.77198e6	0.600580
$663$	−2.57848e7	−2.27814
$664$	5.58799e7	4.91853
$665$	−1.10989e7	−0.973250
$666$	−4.88557e7	−4.26805
$667$	3.96380e6	0.344982
$668$	−1.83264e7	−1.58905
$669$	1.16547e7	1.00679
$670$	−7.33109e6	−0.630931
$671$	−2.46941e7	−2.11732
$672$	1.05141e8	8.98153
$673$	−9.85946e6	−0.839103	−0.419552	−	0.907731i	$-0.637813\pi$
$673$	−9.85946e6	−0.839103	−0.419552	+	0.907731i	$0.637813\pi$
$674$	−2.09585e7	−1.77710
$675$	−1.25536e6	−0.106049
$676$	2.76640e7	2.32835
$677$	−1.00986e7	−0.846819	−0.423410	−	0.905938i	$-0.639167\pi$
$677$	−1.00986e7	−0.846819	−0.423410	+	0.905938i	$0.639167\pi$
$678$	2.67224e7	2.23255
$679$	2.00046e7	1.66516
$680$	3.50862e7	2.90980
$681$	−2.01263e7	−1.66301
$682$	−5.28541e7	−4.35129
$683$	8.14926e6	0.668446	0.334223	−	0.942494i	$-0.391526\pi$
$683$	8.14926e6	0.668446	0.334223	+	0.942494i	$0.391526\pi$
$684$	−3.46954e7	−2.83551
$685$	−1.67982e7	−1.36784
$686$	7.16300e6	0.581145
$687$	−2.69302e6	−0.217695
$688$	−3.78444e7	−3.04811
$689$	1.31193e7	1.05284
$690$	−1.12772e7	−0.901730
$691$	−3.27880e6	−0.261228	−0.130614	−	0.991433i	$-0.541695\pi$
$691$	−3.27880e6	−0.261228	−0.130614	+	0.991433i	$0.541695\pi$
$692$	6.09208e7	4.83616
$693$	3.13354e7	2.47858
$694$	1.58726e7	1.25098
$695$	1.38046e7	1.08408
$696$	5.22531e7	4.08874
$697$	−7.15307e6	−0.557713
$698$	9.24282e6	0.718068
$699$	−2.22120e7	−1.71947
$700$	2.38341e7	1.83846
$701$	−1.51033e7	−1.16086	−0.580428	−	0.814312i	$-0.697115\pi$
$701$	−1.51033e7	−1.16086	−0.580428	+	0.814312i	$0.697115\pi$
$702$	8.14394e6	0.623723
$703$	−2.19057e7	−1.67174
$704$	−7.76192e7	−5.90252
$705$	−1.24594e7	−0.944114
$706$	−2.54201e7	−1.91940
$707$	−2.39308e7	−1.80056
$708$	2.04097e7	1.53022
$709$	1.76206e7	1.31645	0.658225	−	0.752822i	$-0.271308\pi$
$709$	1.76206e7	1.31645	0.658225	+	0.752822i	$0.271308\pi$
$710$	1.19371e7	0.888697
$711$	−8.52068e6	−0.632121
$712$	−7.57758e7	−5.60184
$713$	8.99746e6	0.662821
$714$	6.58581e7	4.83463
$715$	−1.98311e7	−1.45072
$716$	5.86545e7	4.27581
$717$	−2.33048e6	−0.169296
$718$	−4.62276e6	−0.334650
$719$	−2.01542e7	−1.45393	−0.726965	−	0.686675i	$-0.759070\pi$
$719$	−2.01542e7	−1.45393	−0.726965	+	0.686675i	$0.759070\pi$
$720$	−4.66658e7	−3.35481
$721$	−2.41103e7	−1.72729
$722$	6.00570e6	0.428767
$723$	−9.36723e6	−0.666446
$724$	−3.56400e7	−2.52692
$725$	5.14072e6	0.363228
$726$	−4.33410e7	−3.05181
$727$	−1.94520e7	−1.36498	−0.682491	−	0.730894i	$-0.739104\pi$
$727$	−1.94520e7	−1.36498	−0.682491	+	0.730894i	$0.739104\pi$
$728$	−9.87354e7	−6.90469
$729$	−1.85396e7	−1.29206
$730$	−2.81861e7	−1.95762
$731$	−1.29337e7	−0.895218
$732$	8.67816e7	5.98619
$733$	−1.06109e7	−0.729446	−0.364723	−	0.931116i	$-0.618836\pi$
$733$	−1.06109e7	−0.729446	−0.364723	+	0.931116i	$0.618836\pi$
$734$	−2.45887e7	−1.68459
$735$	−1.92279e7	−1.31284
$736$	2.57353e7	1.75120
$737$	9.28042e6	0.629360
$738$	1.62836e7	1.10055
$739$	1.58649e7	1.06863	0.534313	−	0.845286i	$-0.320570\pi$
$739$	1.58649e7	1.06863	0.534313	+	0.845286i	$0.320570\pi$
$740$	−5.80063e7	−3.89400
$741$	2.63187e7	1.76083
$742$	−3.35084e7	−2.23431
$743$	−1.73254e7	−1.15136	−0.575680	−	0.817675i	$-0.695263\pi$
$743$	−1.73254e7	−1.15136	−0.575680	+	0.817675i	$0.695263\pi$
$744$	1.18610e8	7.85576
$745$	3.03691e6	0.200466
$746$	3.57255e7	2.35034
$747$	−2.54003e7	−1.66547
$748$	−6.95549e7	−4.54542
$749$	−1.94011e7	−1.26364
$750$	−4.72858e7	−3.06957
$751$	2.58864e7	1.67483	0.837417	−	0.546564i	$-0.184065\pi$
$751$	2.58864e7	1.67483	0.837417	+	0.546564i	$0.184065\pi$
$752$	5.21125e7	3.36045
$753$	−2.85469e7	−1.83473
$754$	−3.33496e7	−2.13630
$755$	1.33148e7	0.850095
$756$	−1.52786e7	−0.972251
$757$	−1.12729e7	−0.714985	−0.357492	−	0.933916i	$-0.616368\pi$
$757$	−1.12729e7	−0.714985	−0.357492	+	0.933916i	$0.616368\pi$
$758$	−3.62215e6	−0.228978
$759$	1.42757e7	0.899485
$760$	−3.58126e7	−2.24906
$761$	−59757.0	−0.00374048	−0.00187024	−	0.999998i	$-0.500595\pi$
$761$	−59757.0	−0.00374048	−0.00187024	+	0.999998i	$0.500595\pi$
$762$	−1.86335e7	−1.16254
$763$	1.70247e6	0.105869
$764$	−6.77712e7	−4.20061
$765$	−1.59485e7	−0.985294
$766$	892926.	0.0549849
$767$	−8.31805e6	−0.510544
$768$	8.07533e7	4.94035
$769$	−1.95081e7	−1.18959	−0.594796	−	0.803876i	$-0.702767\pi$
$769$	−1.95081e7	−1.18959	−0.594796	+	0.803876i	$0.702767\pi$
$770$	5.06515e7	3.07868
$771$	3.02049e7	1.82996
$772$	1.12330e7	0.678348
$773$	−1.33958e7	−0.806340	−0.403170	−	0.915125i	$-0.632092\pi$
$773$	−1.33958e7	−0.806340	−0.403170	+	0.915125i	$0.632092\pi$
$774$	2.94428e7	1.76656
$775$	1.16690e7	0.697876
$776$	6.45487e7	3.84798
$777$	−6.95273e7	−4.13145
$778$	−2.81437e7	−1.66699
$779$	7.30115e6	0.431070
$780$	6.96919e7	4.10153
$781$	−1.51112e7	−0.886484
$782$	1.61200e7	0.942645
$783$	−3.29540e6	−0.192089
$784$	8.04222e7	4.67289
$785$	1.34669e7	0.779998
$786$	−6.58042e6	−0.379924
$787$	2.10375e7	1.21076	0.605380	−	0.795937i	$-0.293021\pi$
$787$	2.10375e7	1.21076	0.605380	+	0.795937i	$0.293021\pi$
$788$	6.83539e7	3.92146
$789$	−2.56332e7	−1.46592
$790$	−1.37731e7	−0.785168
$791$	2.04319e7	1.16110
$792$	1.01110e8	5.72769
$793$	−3.53682e7	−1.99724
$794$	−6.86327e7	−3.86349
$795$	1.51033e7	0.847525
$796$	−3.02724e7	−1.69342
$797$	3.09640e7	1.72668	0.863338	−	0.504626i	$-0.168369\pi$
$797$	3.09640e7	1.72668	0.863338	+	0.504626i	$0.168369\pi$
$798$	−6.72215e7	−3.73681
$799$	1.78100e7	0.986952
$800$	3.33766e7	1.84381
$801$	3.44440e7	1.89685
$802$	6.37769e7	3.50128
$803$	3.56807e7	1.95274
$804$	−3.26139e7	−1.77935
$805$	−8.62250e6	−0.468968
$806$	−7.57005e7	−4.10451
$807$	−1.61439e7	−0.872620
$808$	−7.72170e7	−4.16088
$809$	−3.60414e7	−1.93611	−0.968056	−	0.250734i	$-0.919328\pi$
$809$	−3.60414e7	−1.93611	−0.968056	+	0.250734i	$0.919328\pi$
$810$	−2.18932e7	−1.17245
$811$	2.02262e7	1.07985	0.539925	−	0.841713i	$-0.318453\pi$
$811$	2.02262e7	1.07985	0.539925	+	0.841713i	$0.318453\pi$
$812$	6.25661e7	3.33004
$813$	1.16970e7	0.620651
$814$	9.99701e7	5.28822
$815$	1.65736e7	0.874024
$816$	1.24157e8	6.52748
$817$	1.32014e7	0.691936
$818$	−1.08871e7	−0.568890
$819$	4.48803e7	2.33801
$820$	1.93335e7	1.00410
$821$	2.00951e7	1.04048	0.520238	−	0.854022i	$-0.325843\pi$
$821$	2.00951e7	1.04048	0.520238	+	0.854022i	$0.325843\pi$
$822$	−1.01740e8	−5.25185
$823$	2.76764e7	1.42433	0.712164	−	0.702013i	$-0.247715\pi$
$823$	2.76764e7	1.42433	0.712164	+	0.702013i	$0.247715\pi$
$824$	−7.77964e7	−3.99155
$825$	1.85144e7	0.947056
$826$	2.12455e7	1.08347
$827$	−1.50446e7	−0.764921	−0.382460	−	0.923972i	$-0.624923\pi$
$827$	−1.50446e7	−0.764921	−0.382460	+	0.923972i	$0.624923\pi$
$828$	−2.69542e7	−1.36632
$829$	2.35433e7	1.18982	0.594910	−	0.803792i	$-0.297188\pi$
$829$	2.35433e7	1.18982	0.594910	+	0.803792i	$0.297188\pi$
$830$	−4.10577e7	−2.06871
$831$	1.97185e7	0.990538
$832$	−1.11170e8	−5.56777
$833$	2.74851e7	1.37241
$834$	8.36093e7	4.16236
$835$	8.59854e6	0.426784
$836$	7.09949e7	3.51327
$837$	−7.48025e6	−0.369065
$838$	4.81771e7	2.36990
$839$	−1.92294e7	−0.943106	−0.471553	−	0.881838i	$-0.656306\pi$
$839$	−1.92294e7	−0.943106	−0.471553	+	0.881838i	$0.656306\pi$
$840$	−1.13667e8	−5.55822
$841$	−7.01643e6	−0.342079
$842$	1.89601e7	0.921638
$843$	3.14290e7	1.52322
$844$	−5.08667e6	−0.245798
$845$	−1.29796e7	−0.625344
$846$	−4.05434e7	−1.94758
$847$	−3.31385e7	−1.58717
$848$	−6.31707e7	−3.01666
$849$	−1.91705e7	−0.912775
$850$	2.09063e7	0.992499
$851$	−1.70181e7	−0.805541
$852$	5.31047e7	2.50631
$853$	−2.28326e7	−1.07444	−0.537221	−	0.843442i	$-0.680526\pi$
$853$	−2.28326e7	−1.07444	−0.537221	+	0.843442i	$0.680526\pi$
$854$	9.03353e7	4.23851
$855$	1.62787e7	0.761558
$856$	−6.26013e7	−2.92011
$857$	−1.64327e7	−0.764289	−0.382144	−	0.924103i	$-0.624814\pi$
$857$	−1.64327e7	−0.764289	−0.382144	+	0.924103i	$0.624814\pi$
$858$	−1.20109e8	−5.57005
$859$	−1.23286e7	−0.570076	−0.285038	−	0.958516i	$-0.592006\pi$
$859$	−1.23286e7	−0.570076	−0.285038	+	0.958516i	$0.592006\pi$
$860$	3.49575e7	1.61174
$861$	2.31734e7	1.06533
$862$	−5.09127e7	−2.33377
$863$	1.09122e7	0.498752	0.249376	−	0.968407i	$-0.419774\pi$
$863$	1.09122e7	0.498752	0.249376	+	0.968407i	$0.419774\pi$
$864$	−2.13957e7	−0.975083
$865$	−2.85833e7	−1.29889
$866$	6.23807e6	0.282654
$867$	9.89427e6	0.447029
$868$	1.42019e8	6.39806
$869$	1.74353e7	0.783212
$870$	−3.83930e7	−1.71970
$871$	1.32919e7	0.593666
$872$	5.49333e6	0.244649
$873$	−2.93407e7	−1.30297
$874$	−1.64537e7	−0.728594
$875$	−3.61547e7	−1.59641
$876$	−1.25392e8	−5.52088
$877$	−6.38728e6	−0.280425	−0.140213	−	0.990121i	$-0.544779\pi$
$877$	−6.38728e6	−0.280425	−0.140213	+	0.990121i	$0.544779\pi$
$878$	−1.18048e7	−0.516798
$879$	−2.38185e7	−1.03978
$880$	9.54891e7	4.15668
$881$	−2.20280e7	−0.956168	−0.478084	−	0.878314i	$-0.658669\pi$
$881$	−2.20280e7	−0.956168	−0.478084	+	0.878314i	$0.658669\pi$
$882$	−6.25683e7	−2.70821
$883$	−1.39751e7	−0.603188	−0.301594	−	0.953436i	$-0.597519\pi$
$883$	−1.39751e7	−0.603188	−0.301594	+	0.953436i	$0.597519\pi$
$884$	−9.96203e7	−4.28763
$885$	−9.57597e6	−0.410984
$886$	−1.66574e7	−0.712889
$887$	3.72855e7	1.59122	0.795611	−	0.605808i	$-0.207150\pi$
$887$	3.72855e7	1.59122	0.795611	+	0.605808i	$0.207150\pi$
$888$	−2.24343e8	−9.54728
$889$	−1.42472e7	−0.604609
$890$	5.56762e7	2.35611
$891$	2.77145e7	1.16953
$892$	4.50283e7	1.89485
$893$	−1.81787e7	−0.762840
$894$	1.83934e7	0.769693
$895$	−2.75200e7	−1.14839
$896$	1.37125e8	5.70621
$897$	2.04465e7	0.848472
$898$	3.97619e7	1.64542
$899$	3.06318e7	1.26408
$900$	−3.49574e7	−1.43858
$901$	−2.15892e7	−0.885981
$902$	−3.33200e7	−1.36361
$903$	4.19006e7	1.71002
$904$	6.59275e7	2.68315
$905$	1.67218e7	0.678676
$906$	8.06426e7	3.26395
$907$	−3.92336e6	−0.158358	−0.0791790	−	0.996860i	$-0.525230\pi$
$907$	−3.92336e6	−0.158358	−0.0791790	+	0.996860i	$0.525230\pi$
$908$	−7.77583e7	−3.12991
$909$	3.50991e7	1.40892
$910$	7.25458e7	2.90408
$911$	−3.58121e7	−1.42966	−0.714832	−	0.699297i	$-0.753497\pi$
$911$	−3.58121e7	−1.42966	−0.714832	+	0.699297i	$0.753497\pi$
$912$	−1.26727e8	−5.04525
$913$	5.19749e7	2.06356
$914$	5.12956e6	0.203102
$915$	−4.07169e7	−1.60776
$916$	−1.04046e7	−0.409718
$917$	−5.03138e6	−0.197590
$918$	−1.34017e7	−0.524873
$919$	−7.95393e6	−0.310666	−0.155333	−	0.987862i	$-0.549645\pi$
$919$	−7.95393e6	−0.310666	−0.155333	+	0.987862i	$0.549645\pi$
$920$	−2.78221e7	−1.08373
$921$	−1.60404e6	−0.0623114
$922$	2.15028e7	0.833042
$923$	−2.16431e7	−0.836208
$924$	2.25333e8	8.68252
$925$	−2.20711e7	−0.848144
$926$	−4.63998e7	−1.77823
$927$	3.53625e7	1.35159
$928$	8.76157e7	3.33973
$929$	−3.03536e7	−1.15391	−0.576953	−	0.816777i	$-0.695759\pi$
$929$	−3.03536e7	−1.15391	−0.576953	+	0.816777i	$0.695759\pi$
$930$	−8.71485e7	−3.30410
$931$	−2.80541e7	−1.06077
$932$	−8.58167e7	−3.23617
$933$	3.15075e7	1.18498
$934$	−6.62399e7	−2.48458
$935$	3.26343e7	1.22080
$936$	1.44815e8	5.40285
$937$	9.91460e6	0.368915	0.184457	−	0.982841i	$-0.440947\pi$
$937$	9.91460e6	0.368915	0.184457	+	0.982841i	$0.440947\pi$
$938$	−3.39494e7	−1.25987
$939$	6.41717e7	2.37509
$940$	−4.81372e7	−1.77689
$941$	8.29336e6	0.305321	0.152660	−	0.988279i	$-0.451216\pi$
$941$	8.29336e6	0.305321	0.152660	+	0.988279i	$0.451216\pi$
$942$	8.15638e7	2.99482
$943$	5.67213e6	0.207715
$944$	4.00523e7	1.46284
$945$	7.16852e6	0.261126
$946$	−6.02469e7	−2.18880
$947$	−2.54654e6	−0.0922733	−0.0461367	−	0.998935i	$-0.514691\pi$
$947$	−2.54654e6	−0.0922733	−0.0461367	+	0.998935i	$0.514691\pi$
$948$	−6.12723e7	−2.21433
$949$	5.11039e7	1.84199
$950$	−2.13391e7	−0.767127
$951$	4.90451e7	1.75851
$952$	1.62480e8	5.81042
$953$	−4.69033e7	−1.67290	−0.836452	−	0.548040i	$-0.815374\pi$
$953$	−4.69033e7	−1.67290	−0.836452	+	0.548040i	$0.815374\pi$
$954$	4.91467e7	1.74833
$955$	3.17974e7	1.12819
$956$	−9.00387e6	−0.318628
$957$	4.86016e7	1.71542
$958$	−2.48153e7	−0.873588
$959$	−7.77904e7	−2.73136
$960$	−1.27983e8	−4.48201
$961$	4.09022e7	1.42869
$962$	1.43183e8	4.98830
$963$	2.84555e7	0.988783
$964$	−3.61905e7	−1.25430
$965$	−5.27038e6	−0.182190
$966$	−5.22231e7	−1.80061
$967$	−3.08421e7	−1.06066	−0.530332	−	0.847790i	$-0.677933\pi$
$967$	−3.08421e7	−1.06066	−0.530332	+	0.847790i	$0.677933\pi$
$968$	−1.06927e8	−3.66776
$969$	−4.33102e7	−1.48177
$970$	−4.74271e7	−1.61844
$971$	−1.60031e7	−0.544699	−0.272350	−	0.962198i	$-0.587801\pi$
$971$	−1.60031e7	−0.544699	−0.272350	+	0.962198i	$0.587801\pi$
$972$	−1.16696e8	−3.96179
$973$	6.39276e7	2.16474
$974$	7.02940e7	2.37422
$975$	2.65174e7	0.893345
$976$	1.70302e8	5.72262
$977$	−1.86560e6	−0.0625291	−0.0312645	−	0.999511i	$-0.509953\pi$
$977$	−1.86560e6	−0.0625291	−0.0312645	+	0.999511i	$0.509953\pi$
$978$	1.00380e8	3.35583
$979$	−7.04804e7	−2.35024
$980$	−7.42872e7	−2.47087
$981$	−2.49700e6	−0.0828412
$982$	5.29503e6	0.175222
$983$	2.12052e7	0.699936	0.349968	−	0.936762i	$-0.386192\pi$
$983$	2.12052e7	0.699936	0.349968	+	0.936762i	$0.386192\pi$
$984$	7.47734e7	2.46184
$985$	−3.20708e7	−1.05322
$986$	5.48804e7	1.79773
$987$	−5.76980e7	−1.88524
$988$	1.01683e8	3.31402
$989$	1.02560e7	0.333415
$990$	−7.42903e7	−2.40904
$991$	1.19203e7	0.385569	0.192785	−	0.981241i	$-0.438248\pi$
$991$	1.19203e7	0.385569	0.192785	+	0.981241i	$0.438248\pi$
$992$	1.98880e8	6.41669
$993$	−1.41350e7	−0.454907
$994$	5.52794e7	1.77459
$995$	1.42034e7	0.454816
$996$	−1.82654e8	−5.83418
$997$	3.63128e7	1.15697	0.578485	−	0.815693i	$-0.303644\pi$
$997$	3.63128e7	1.15697	0.578485	+	0.815693i	$0.303644\pi$
$998$	9.52860e7	3.02833
$999$	1.41484e7	0.448533

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-10.9789 q^{2} +22.9161 q^{3} +88.5367 q^{4} -41.5403 q^{5} -251.594 q^{6} -192.368 q^{7} -620.712 q^{8} +282.146 q^{9} +O(q^{10})\)	\(q-10.9789 q^{2} +22.9161 q^{3} +88.5367 q^{4} -41.5403 q^{5} -251.594 q^{6} -192.368 q^{7} -620.712 q^{8} +282.146 q^{9} +456.068 q^{10} -577.336 q^{11} +2028.91 q^{12} -826.892 q^{13} +2112.00 q^{14} -951.941 q^{15} +3981.58 q^{16} +1360.74 q^{17} -3097.66 q^{18} -1388.91 q^{19} -3677.85 q^{20} -4408.32 q^{21} +6338.53 q^{22} -1079.02 q^{23} -14224.3 q^{24} -1399.40 q^{25} +9078.38 q^{26} +897.069 q^{27} -17031.7 q^{28} -3673.52 q^{29} +10451.3 q^{30} -8338.55 q^{31} -23850.6 q^{32} -13230.3 q^{33} -14939.5 q^{34} +7991.05 q^{35} +24980.3 q^{36} +15771.8 q^{37} +15248.8 q^{38} -18949.1 q^{39} +25784.6 q^{40} -5256.74 q^{41} +48398.7 q^{42} -9504.87 q^{43} -51115.4 q^{44} -11720.4 q^{45} +11846.5 q^{46} +13088.4 q^{47} +91242.1 q^{48} +20198.6 q^{49} +15363.9 q^{50} +31182.8 q^{51} -73210.3 q^{52} -15865.7 q^{53} -9848.85 q^{54} +23982.7 q^{55} +119405. q^{56} -31828.4 q^{57} +40331.2 q^{58} +10059.4 q^{59} -84281.7 q^{60} +42772.5 q^{61} +91548.3 q^{62} -54275.9 q^{63} +134444. q^{64} +34349.4 q^{65} +145254. q^{66} -16074.6 q^{67} +120476. q^{68} -24726.9 q^{69} -87733.1 q^{70} +26174.0 q^{71} -175131. q^{72} -61802.3 q^{73} -173158. q^{74} -32068.7 q^{75} -122970. q^{76} +111061. q^{77} +208041. q^{78} -30199.5 q^{79} -165396. q^{80} -48004.2 q^{81} +57713.4 q^{82} -90025.4 q^{83} -390299. q^{84} -56525.7 q^{85} +104353. q^{86} -84182.5 q^{87} +358360. q^{88} +122079. q^{89} +128678. q^{90} +159068. q^{91} -95532.9 q^{92} -191087. q^{93} -143697. q^{94} +57695.9 q^{95} -546563. q^{96} -103991. q^{97} -221759. q^{98} -162893. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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