LMFDB - Embedded newform 547.6.a.b.1.8

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			1.8
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)

$f(q)$	$=$	$q-9.87295 q^{2} +20.2571 q^{3} +65.4751 q^{4} +73.8486 q^{5} -199.997 q^{6} -245.912 q^{7} -330.498 q^{8} +167.350 q^{9} +O(q^{10})$	\(q-9.87295 q^{2} +20.2571 q^{3} +65.4751 q^{4} +73.8486 q^{5} -199.997 q^{6} -245.912 q^{7} -330.498 q^{8} +167.350 q^{9} -729.104 q^{10} +298.531 q^{11} +1326.33 q^{12} +141.249 q^{13} +2427.88 q^{14} +1495.96 q^{15} +1167.78 q^{16} -2169.61 q^{17} -1652.23 q^{18} -806.214 q^{19} +4835.25 q^{20} -4981.46 q^{21} -2947.38 q^{22} +1581.36 q^{23} -6694.92 q^{24} +2328.62 q^{25} -1394.54 q^{26} -1532.46 q^{27} -16101.1 q^{28} -7210.03 q^{29} -14769.5 q^{30} +4705.15 q^{31} -953.540 q^{32} +6047.37 q^{33} +21420.5 q^{34} -18160.3 q^{35} +10957.2 q^{36} +5295.28 q^{37} +7959.71 q^{38} +2861.29 q^{39} -24406.8 q^{40} +15578.9 q^{41} +49181.7 q^{42} +9071.23 q^{43} +19546.3 q^{44} +12358.5 q^{45} -15612.7 q^{46} +10343.1 q^{47} +23655.9 q^{48} +43665.7 q^{49} -22990.4 q^{50} -43950.0 q^{51} +9248.28 q^{52} +17082.0 q^{53} +15129.9 q^{54} +22046.1 q^{55} +81273.4 q^{56} -16331.6 q^{57} +71184.2 q^{58} -33570.3 q^{59} +97948.0 q^{60} +14623.9 q^{61} -46453.7 q^{62} -41153.3 q^{63} -27954.8 q^{64} +10431.0 q^{65} -59705.3 q^{66} +54499.8 q^{67} -142056. q^{68} +32033.8 q^{69} +179295. q^{70} +14814.7 q^{71} -55308.7 q^{72} +58836.7 q^{73} -52280.0 q^{74} +47171.1 q^{75} -52787.0 q^{76} -73412.3 q^{77} -28249.4 q^{78} +71592.0 q^{79} +86239.2 q^{80} -71709.1 q^{81} -153810. q^{82} +9585.65 q^{83} -326162. q^{84} -160223. q^{85} -89559.8 q^{86} -146054. q^{87} -98663.8 q^{88} +81568.5 q^{89} -122015. q^{90} -34734.8 q^{91} +103540. q^{92} +95312.6 q^{93} -102117. q^{94} -59537.8 q^{95} -19316.0 q^{96} +45875.5 q^{97} -431109. q^{98} +49959.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.87295	−1.74531	−0.872653	−	0.488340i	$-0.837603\pi$
$2$	−9.87295	−1.74531	−0.872653	+	0.488340i	$0.837603\pi$
$3$	20.2571	1.29949	0.649746	−	0.760151i	$-0.274875\pi$
$3$	20.2571	1.29949	0.649746	+	0.760151i	$0.274875\pi$
$4$	65.4751	2.04610
$5$	73.8486	1.32104	0.660522	−	0.750806i	$-0.270335\pi$
$5$	73.8486	1.32104	0.660522	+	0.750806i	$0.270335\pi$
$6$	−199.997	−2.26801
$7$	−245.912	−1.89686	−0.948429	−	0.316991i	$-0.897328\pi$
$7$	−245.912	−1.89686	−0.948429	+	0.316991i	$0.897328\pi$
$8$	−330.498	−1.82576
$9$	167.350	0.688682
$10$	−729.104	−2.30563
$11$	298.531	0.743888	0.371944	−	0.928255i	$-0.378691\pi$
$11$	298.531	0.743888	0.371944	+	0.928255i	$0.378691\pi$
$12$	1326.33	2.65889
$13$	141.249	0.231807	0.115903	−	0.993260i	$-0.463024\pi$
$13$	141.249	0.231807	0.115903	+	0.993260i	$0.463024\pi$
$14$	2427.88	3.31060
$15$	1495.96	1.71669
$16$	1167.78	1.14041
$17$	−2169.61	−1.82079	−0.910395	−	0.413740i	$-0.864222\pi$
$17$	−2169.61	−1.82079	−0.910395	+	0.413740i	$0.864222\pi$
$18$	−1652.23	−1.20196
$19$	−806.214	−0.512350	−0.256175	−	0.966630i	$-0.582462\pi$
$19$	−806.214	−0.512350	−0.256175	+	0.966630i	$0.582462\pi$
$20$	4835.25	2.70298
$21$	−4981.46	−2.46495
$22$	−2947.38	−1.29831
$23$	1581.36	0.623322	0.311661	−	0.950193i	$-0.399115\pi$
$23$	1581.36	0.623322	0.311661	+	0.950193i	$0.399115\pi$
$24$	−6694.92	−2.37256
$25$	2328.62	0.745159
$26$	−1394.54	−0.404574
$27$	−1532.46	−0.404556
$28$	−16101.1	−3.88115
$29$	−7210.03	−1.59200	−0.795998	−	0.605299i	$-0.793054\pi$
$29$	−7210.03	−1.59200	−0.795998	+	0.605299i	$0.793054\pi$
$30$	−14769.5	−2.99615
$31$	4705.15	0.879364	0.439682	−	0.898153i	$-0.355091\pi$
$31$	4705.15	0.879364	0.439682	+	0.898153i	$0.355091\pi$
$32$	−953.540	−0.164613
$33$	6047.37	0.966677
$34$	21420.5	3.17784
$35$	−18160.3	−2.50583
$36$	10957.2	1.40911
$37$	5295.28	0.635894	0.317947	−	0.948109i	$-0.397007\pi$
$37$	5295.28	0.635894	0.317947	+	0.948109i	$0.397007\pi$
$38$	7959.71	0.894208
$39$	2861.29	0.301232
$40$	−24406.8	−2.41191
$41$	15578.9	1.44736	0.723680	−	0.690135i	$-0.242449\pi$
$41$	15578.9	1.44736	0.723680	+	0.690135i	$0.242449\pi$
$42$	49181.7	4.30210
$43$	9071.23	0.748161	0.374081	−	0.927396i	$-0.377958\pi$
$43$	9071.23	0.748161	0.374081	+	0.927396i	$0.377958\pi$
$44$	19546.3	1.52207
$45$	12358.5	0.909779
$46$	−15612.7	−1.08789
$47$	10343.1	0.682975	0.341488	−	0.939886i	$-0.389069\pi$
$47$	10343.1	0.682975	0.341488	+	0.939886i	$0.389069\pi$
$48$	23655.9	1.48196
$49$	43665.7	2.59807
$50$	−22990.4	−1.30053
$51$	−43950.0	−2.36610
$52$	9248.28	0.474299
$53$	17082.0	0.835313	0.417656	−	0.908605i	$-0.362852\pi$
$53$	17082.0	0.835313	0.417656	+	0.908605i	$0.362852\pi$
$54$	15129.9	0.706074
$55$	22046.1	0.982709
$56$	81273.4	3.46320
$57$	−16331.6	−0.665795
$58$	71184.2	2.77852
$59$	−33570.3	−1.25552	−0.627762	−	0.778405i	$-0.716029\pi$
$59$	−33570.3	−1.25552	−0.627762	+	0.778405i	$0.716029\pi$
$60$	97948.0	3.51251
$61$	14623.9	0.503198	0.251599	−	0.967832i	$-0.419044\pi$
$61$	14623.9	0.503198	0.251599	+	0.967832i	$0.419044\pi$
$62$	−46453.7	−1.53476
$63$	−41153.3	−1.30633
$64$	−27954.8	−0.853114
$65$	10431.0	0.306227
$66$	−59705.3	−1.68715
$67$	54499.8	1.48323	0.741614	−	0.670827i	$-0.234061\pi$
$67$	54499.8	1.48323	0.741614	+	0.670827i	$0.234061\pi$
$68$	−142056.	−3.72551
$69$	32033.8	0.810002
$70$	179295.	4.37345
$71$	14814.7	0.348776	0.174388	−	0.984677i	$-0.444205\pi$
$71$	14814.7	0.348776	0.174388	+	0.984677i	$0.444205\pi$
$72$	−55308.7	−1.25737
$73$	58836.7	1.29223	0.646117	−	0.763239i	$-0.276392\pi$
$73$	58836.7	1.29223	0.646117	+	0.763239i	$0.276392\pi$
$74$	−52280.0	−1.10983
$75$	47171.1	0.968328
$76$	−52787.0	−1.04832
$77$	−73412.3	−1.41105
$78$	−28249.4	−0.525741
$79$	71592.0	1.29062	0.645308	−	0.763923i	$-0.276729\pi$
$79$	71592.0	1.29062	0.645308	+	0.763923i	$0.276729\pi$
$80$	86239.2	1.50654
$81$	−71709.1	−1.21440
$82$	−153810.	−2.52609
$83$	9585.65	0.152731	0.0763654	−	0.997080i	$-0.475668\pi$
$83$	9585.65	0.152731	0.0763654	+	0.997080i	$0.475668\pi$
$84$	−326162.	−5.04353
$85$	−160223.	−2.40534
$86$	−89559.8	−1.30577
$87$	−146054.	−2.06879
$88$	−98663.8	−1.35816
$89$	81568.5	1.09156	0.545780	−	0.837929i	$-0.316234\pi$
$89$	81568.5	1.09156	0.545780	+	0.837929i	$0.316234\pi$
$90$	−122015.	−1.58784
$91$	−34734.8	−0.439705
$92$	103540.	1.27538
$93$	95312.6	1.14273
$94$	−102117.	−1.19200
$95$	−59537.8	−0.676837
$96$	−19316.0	−0.213913
$97$	45875.5	0.495053	0.247527	−	0.968881i	$-0.420382\pi$
$97$	45875.5	0.495053	0.247527	+	0.968881i	$0.420382\pi$
$98$	−431109.	−4.53443
$99$	49959.0	0.512302
$100$	152467.	1.52467
$101$	154791.	1.50988	0.754939	−	0.655795i	$-0.227666\pi$
$101$	154791.	1.50988	0.754939	+	0.655795i	$0.227666\pi$
$102$	433916.	4.12958
$103$	143978.	1.33722	0.668612	−	0.743611i	$-0.266889\pi$
$103$	143978.	1.33722	0.668612	+	0.743611i	$0.266889\pi$
$104$	−46682.4	−0.423224
$105$	−367874.	−3.25631
$106$	−168650.	−1.45788
$107$	132196.	1.11624	0.558121	−	0.829760i	$-0.311523\pi$
$107$	132196.	1.11624	0.558121	+	0.829760i	$0.311523\pi$
$108$	−100338.	−0.827760
$109$	−192793.	−1.55426	−0.777132	−	0.629337i	$-0.783326\pi$
$109$	−192793.	−1.55426	−0.777132	+	0.629337i	$0.783326\pi$
$110$	−217660.	−1.71513
$111$	107267.	0.826339
$112$	−287172.	−2.16320
$113$	189949.	1.39940	0.699699	−	0.714438i	$-0.253317\pi$
$113$	189949.	1.39940	0.699699	+	0.714438i	$0.253317\pi$
$114$	161241.	1.16202
$115$	116782.	0.823436
$116$	−472077.	−3.25738
$117$	23637.9	0.159641
$118$	331438.	2.19128
$119$	533534.	3.45378
$120$	−494411.	−3.13426
$121$	−71930.3	−0.446631
$122$	−144381.	−0.878234
$123$	315583.	1.88083
$124$	308070.	1.79926
$125$	−58811.5	−0.336657
$126$	406304.	2.27995
$127$	−290468.	−1.59805	−0.799023	−	0.601301i	$-0.794649\pi$
$127$	−290468.	−1.59805	−0.799023	+	0.601301i	$0.794649\pi$
$128$	306510.	1.65356
$129$	183757.	0.972230
$130$	−102985.	−0.534461
$131$	−249986.	−1.27273	−0.636366	−	0.771387i	$-0.719563\pi$
$131$	−249986.	−1.27273	−0.636366	+	0.771387i	$0.719563\pi$
$132$	395952.	1.97791
$133$	198258.	0.971855
$134$	−538074.	−2.58869
$135$	−113170.	−0.534436
$136$	717052.	3.32432
$137$	−161055.	−0.733117	−0.366558	−	0.930395i	$-0.619464\pi$
$137$	−161055.	−0.733117	−0.366558	+	0.930395i	$0.619464\pi$
$138$	−316268.	−1.41370
$139$	35162.1	0.154361	0.0771805	−	0.997017i	$-0.475408\pi$
$139$	35162.1	0.154361	0.0771805	+	0.997017i	$0.475408\pi$
$140$	−1.18905e6	−5.12718
$141$	209521.	0.887522
$142$	−146265.	−0.608721
$143$	42167.1	0.172438
$144$	195428.	0.785382
$145$	−532451.	−2.10310
$146$	−580891.	−2.25534
$147$	884541.	3.37617
$148$	346709.	1.30110
$149$	−245507.	−0.905939	−0.452969	−	0.891526i	$-0.649635\pi$
$149$	−245507.	−0.905939	−0.452969	+	0.891526i	$0.649635\pi$
$150$	−465718.	−1.69003
$151$	−50450.9	−0.180064	−0.0900319	−	0.995939i	$-0.528697\pi$
$151$	−50450.9	−0.180064	−0.0900319	+	0.995939i	$0.528697\pi$
$152$	266452.	0.935427
$153$	−363084.	−1.25394
$154$	724796.	2.46271
$155$	347469.	1.16168
$156$	187343.	0.616349
$157$	−140184.	−0.453888	−0.226944	−	0.973908i	$-0.572873\pi$
$157$	−140184.	−0.453888	−0.226944	+	0.973908i	$0.572873\pi$
$158$	−706824.	−2.25252
$159$	346032.	1.08548
$160$	−70417.7	−0.217461
$161$	−388876.	−1.18235
$162$	707980.	2.11950
$163$	388638.	1.14571	0.572857	−	0.819656i	$-0.305835\pi$
$163$	388638.	1.14571	0.572857	+	0.819656i	$0.305835\pi$
$164$	1.02003e6	2.96144
$165$	446590.	1.27702
$166$	−94638.7	−0.266562
$167$	327634.	0.909071	0.454535	−	0.890729i	$-0.349805\pi$
$167$	327634.	0.909071	0.454535	+	0.890729i	$0.349805\pi$
$168$	1.64636e6	4.50041
$169$	−351342.	−0.946266
$170$	1.58187e6	4.19806
$171$	−134920.	−0.352846
$172$	593940.	1.53081
$173$	87071.4	0.221187	0.110594	−	0.993866i	$-0.464725\pi$
$173$	87071.4	0.221187	0.110594	+	0.993866i	$0.464725\pi$
$174$	1.44199e6	3.61067
$175$	−572636.	−1.41346
$176$	348619.	0.848340
$177$	−680037.	−1.63155
$178$	−805321.	−1.90511
$179$	−489099.	−1.14094	−0.570472	−	0.821317i	$-0.693240\pi$
$179$	−489099.	−1.14094	−0.570472	+	0.821317i	$0.693240\pi$
$180$	809177.	1.86150
$181$	165848.	0.376282	0.188141	−	0.982142i	$-0.439754\pi$
$181$	165848.	0.376282	0.188141	+	0.982142i	$0.439754\pi$
$182$	342935.	0.767420
$183$	296238.	0.653902
$184$	−522637.	−1.13804
$185$	391049.	0.840044
$186$	−941016.	−1.99441
$187$	−647696.	−1.35446
$188$	677214.	1.39743
$189$	376849.	0.767385
$190$	587814.	1.18129
$191$	230924.	0.458020	0.229010	−	0.973424i	$-0.426451\pi$
$191$	230924.	0.458020	0.229010	+	0.973424i	$0.426451\pi$
$192$	−566283.	−1.10862
$193$	183551.	0.354703	0.177351	−	0.984148i	$-0.443247\pi$
$193$	183551.	0.354703	0.177351	+	0.984148i	$0.443247\pi$
$194$	−452927.	−0.864020
$195$	211302.	0.397940
$196$	2.85902e6	5.31590
$197$	235827.	0.432941	0.216471	−	0.976289i	$-0.430545\pi$
$197$	235827.	0.432941	0.216471	+	0.976289i	$0.430545\pi$
$198$	−493243.	−0.894124
$199$	−803609.	−1.43851	−0.719254	−	0.694748i	$-0.755516\pi$
$199$	−803609.	−1.43851	−0.719254	+	0.694748i	$0.755516\pi$
$200$	−769604.	−1.36048
$201$	1.10401e6	1.92744
$202$	−1.52824e6	−2.63520
$203$	1.77303e6	3.01979
$204$	−2.87763e6	−4.84128
$205$	1.15048e6	1.91203
$206$	−1.42149e6	−2.33387
$207$	264641.	0.429270
$208$	164948.	0.264356
$209$	−240680.	−0.381131
$210$	3.63200e6	5.68326
$211$	903785.	1.39752	0.698762	−	0.715355i	$-0.253735\pi$
$211$	903785.	1.39752	0.698762	+	0.715355i	$0.253735\pi$
$212$	1.11845e6	1.70913
$213$	300103.	0.453232
$214$	−1.30516e6	−1.94818
$215$	669898.	0.988354
$216$	506473.	0.738622
$217$	−1.15705e6	−1.66803
$218$	1.90344e6	2.71267
$219$	1.19186e6	1.67925
$220$	1.44347e6	2.01072
$221$	−306455.	−0.422072
$222$	−1.05904e6	−1.44222
$223$	−252686.	−0.340266	−0.170133	−	0.985421i	$-0.554420\pi$
$223$	−252686.	−0.340266	−0.170133	+	0.985421i	$0.554420\pi$
$224$	234487.	0.312247
$225$	389694.	0.513177
$226$	−1.87536e6	−2.44238
$227$	−48733.4	−0.0627715	−0.0313857	−	0.999507i	$-0.509992\pi$
$227$	−48733.4	−0.0627715	−0.0313857	+	0.999507i	$0.509992\pi$
$228$	−1.06931e6	−1.36228
$229$	−570244.	−0.718575	−0.359287	−	0.933227i	$-0.616980\pi$
$229$	−570244.	−0.718575	−0.359287	+	0.933227i	$0.616980\pi$
$230$	−1.15298e6	−1.43715
$231$	−1.48712e6	−1.83365
$232$	2.38290e6	2.90660
$233$	1.42890e6	1.72430	0.862151	−	0.506651i	$-0.169117\pi$
$233$	1.42890e6	1.72430	0.862151	+	0.506651i	$0.169117\pi$
$234$	−233376.	−0.278623
$235$	763822.	0.902241
$236$	−2.19802e6	−2.56892
$237$	1.45025e6	1.67715
$238$	−5.26755e6	−6.02790
$239$	−438855.	−0.496966	−0.248483	−	0.968636i	$-0.579932\pi$
$239$	−438855.	−0.496966	−0.248483	+	0.968636i	$0.579932\pi$
$240$	1.74696e6	1.95773
$241$	349734.	0.387878	0.193939	−	0.981014i	$-0.437874\pi$
$241$	349734.	0.387878	0.193939	+	0.981014i	$0.437874\pi$
$242$	710164.	0.779508
$243$	−1.08023e6	−1.17355
$244$	957501.	1.02959
$245$	3.22465e6	3.43216
$246$	−3.11573e6	−3.28263
$247$	−113877.	−0.118766
$248$	−1.55504e6	−1.60551
$249$	194177.	0.198473
$250$	580643.	0.587569
$251$	−46098.6	−0.0461853	−0.0230927	−	0.999733i	$-0.507351\pi$
$251$	−46098.6	−0.0461853	−0.0230927	+	0.999733i	$0.507351\pi$
$252$	−2.69452e6	−2.67288
$253$	472086.	0.463681
$254$	2.86778e6	2.78908
$255$	−3.24565e6	−3.12573
$256$	−2.13160e6	−2.03285
$257$	163637.	0.154543	0.0772715	−	0.997010i	$-0.475379\pi$
$257$	163637.	0.154543	0.0772715	+	0.997010i	$0.475379\pi$
$258$	−1.81422e6	−1.69684
$259$	−1.30217e6	−1.20620
$260$	682973.	0.626571
$261$	−1.20660e6	−1.09638
$262$	2.46810e6	2.22131
$263$	1.69566e6	1.51164	0.755820	−	0.654779i	$-0.227238\pi$
$263$	1.69566e6	1.51164	0.755820	+	0.654779i	$0.227238\pi$
$264$	−1.99864e6	−1.76492
$265$	1.26148e6	1.10349
$266$	−1.95739e6	−1.69618
$267$	1.65234e6	1.41847
$268$	3.56838e6	3.03483
$269$	−1.20008e6	−1.01118	−0.505591	−	0.862774i	$-0.668725\pi$
$269$	−1.20008e6	−1.01118	−0.505591	+	0.862774i	$0.668725\pi$
$270$	1.11732e6	0.932755
$271$	179204.	0.148226	0.0741132	−	0.997250i	$-0.476387\pi$
$271$	179204.	0.148226	0.0741132	+	0.997250i	$0.476387\pi$
$272$	−2.53364e6	−2.07645
$273$	−703626.	−0.571393
$274$	1.59009e6	1.27951
$275$	695165.	0.554315
$276$	2.09742e6	1.65734
$277$	761220.	0.596089	0.298044	−	0.954552i	$-0.403666\pi$
$277$	761220.	0.596089	0.298044	+	0.954552i	$0.403666\pi$
$278$	−347153.	−0.269407
$279$	787405.	0.605602
$280$	6.00193e6	4.57505
$281$	−1.37838e6	−1.04137	−0.520683	−	0.853750i	$-0.674323\pi$
$281$	−1.37838e6	−1.04137	−0.520683	+	0.853750i	$0.674323\pi$
$282$	−2.06859e6	−1.54900
$283$	−2.23630e6	−1.65983	−0.829915	−	0.557890i	$-0.811611\pi$
$283$	−2.23630e6	−1.65983	−0.829915	+	0.557890i	$0.811611\pi$
$284$	969993.	0.713630
$285$	−1.20606e6	−0.879545
$286$	−416314.	−0.300958
$287$	−3.83104e6	−2.74544
$288$	−159575.	−0.113366
$289$	3.28736e6	2.31528
$290$	5.25686e6	3.67055
$291$	929305.	0.643318
$292$	3.85234e6	2.64403
$293$	1.52554e6	1.03813	0.519067	−	0.854734i	$-0.326280\pi$
$293$	1.52554e6	1.03813	0.519067	+	0.854734i	$0.326280\pi$
$294$	−8.73302e6	−5.89245
$295$	−2.47912e6	−1.65860
$296$	−1.75008e6	−1.16099
$297$	−457485.	−0.300944
$298$	2.42388e6	1.58114
$299$	223366.	0.144490
$300$	3.08853e6	1.98129
$301$	−2.23072e6	−1.41915
$302$	498099.	0.314267
$303$	3.13561e6	1.96208
$304$	−941484.	−0.584291
$305$	1.07995e6	0.664746
$306$	3.58471e6	2.18852
$307$	2.58908e6	1.56783	0.783917	−	0.620865i	$-0.213219\pi$
$307$	2.58908e6	1.56783	0.783917	+	0.620865i	$0.213219\pi$
$308$	−4.80668e6	−2.88714
$309$	2.91658e6	1.73771
$310$	−3.43054e6	−2.02749
$311$	1.08033e6	0.633368	0.316684	−	0.948531i	$-0.397431\pi$
$311$	1.08033e6	0.633368	0.316684	+	0.948531i	$0.397431\pi$
$312$	−945650.	−0.549976
$313$	69040.8	0.0398332	0.0199166	−	0.999802i	$-0.493660\pi$
$313$	69040.8	0.0398332	0.0199166	+	0.999802i	$0.493660\pi$
$314$	1.38403e6	0.792173
$315$	−3.03911e6	−1.72572
$316$	4.68749e6	2.64072
$317$	764027.	0.427032	0.213516	−	0.976940i	$-0.431508\pi$
$317$	764027.	0.427032	0.213516	+	0.976940i	$0.431508\pi$
$318$	−3.41635e6	−1.89450
$319$	−2.15242e6	−1.18427
$320$	−2.06443e6	−1.12700
$321$	2.67790e6	1.45055
$322$	3.83936e6	2.06357
$323$	1.74917e6	0.932881
$324$	−4.69516e6	−2.48478
$325$	328915.	0.172733
$326$	−3.83700e6	−1.99962
$327$	−3.90543e6	−2.01976
$328$	−5.14879e6	−2.64253
$329$	−2.54349e6	−1.29551
$330$	−4.40916e6	−2.22880
$331$	−2.31411e6	−1.16095	−0.580477	−	0.814277i	$-0.697134\pi$
$331$	−2.31411e6	−1.16095	−0.580477	+	0.814277i	$0.697134\pi$
$332$	627622.	0.312502
$333$	886163.	0.437928
$334$	−3.23471e6	−1.58661
$335$	4.02474e6	1.95941
$336$	−5.81727e6	−2.81107
$337$	280630.	0.134604	0.0673022	−	0.997733i	$-0.478561\pi$
$337$	280630.	0.134604	0.0673022	+	0.997733i	$0.478561\pi$
$338$	3.46878e6	1.65152
$339$	3.84782e6	1.81851
$340$	−1.04906e7	−4.92157
$341$	1.40463e6	0.654148
$342$	1.33206e6	0.615825
$343$	−6.60488e6	−3.03131
$344$	−2.99802e6	−1.36596
$345$	2.36565e6	1.07005
$346$	−859651.	−0.386040
$347$	2.62709e6	1.17125	0.585627	−	0.810581i	$-0.300848\pi$
$347$	2.62709e6	1.17125	0.585627	+	0.810581i	$0.300848\pi$
$348$	−9.56291e6	−4.23294
$349$	707677.	0.311008	0.155504	−	0.987835i	$-0.450300\pi$
$349$	707677.	0.311008	0.155504	+	0.987835i	$0.450300\pi$
$350$	5.65360e6	2.46692
$351$	−216458.	−0.0937789
$352$	−284661.	−0.122454
$353$	675737.	0.288630	0.144315	−	0.989532i	$-0.453902\pi$
$353$	675737.	0.288630	0.144315	+	0.989532i	$0.453902\pi$
$354$	6.71397e6	2.84755
$355$	1.09404e6	0.460749
$356$	5.34070e6	2.23344
$357$	1.08078e7	4.48816
$358$	4.82885e6	1.99130
$359$	301503.	0.123468	0.0617341	−	0.998093i	$-0.480337\pi$
$359$	301503.	0.123468	0.0617341	+	0.998093i	$0.480337\pi$
$360$	−4.08447e6	−1.66104
$361$	−1.82612e6	−0.737498
$362$	−1.63741e6	−0.656727
$363$	−1.45710e6	−0.580394
$364$	−2.27426e6	−0.899678
$365$	4.34501e6	1.70710
$366$	−2.92474e6	−1.14126
$367$	−3.31653e6	−1.28534	−0.642671	−	0.766143i	$-0.722174\pi$
$367$	−3.31653e6	−1.28534	−0.642671	+	0.766143i	$0.722174\pi$
$368$	1.84669e6	0.710845
$369$	2.60712e6	0.996771
$370$	−3.86081e6	−1.46613
$371$	−4.20067e6	−1.58447
$372$	6.24060e6	2.33813
$373$	665140.	0.247537	0.123769	−	0.992311i	$-0.460502\pi$
$373$	665140.	0.247537	0.123769	+	0.992311i	$0.460502\pi$
$374$	6.39467e6	2.36395
$375$	−1.19135e6	−0.437483
$376$	−3.41836e6	−1.24695
$377$	−1.01841e6	−0.369036
$378$	−3.72061e6	−1.33932
$379$	5.01407e6	1.79305	0.896525	−	0.442993i	$-0.146083\pi$
$379$	5.01407e6	1.79305	0.896525	+	0.442993i	$0.146083\pi$
$380$	−3.89824e6	−1.38487
$381$	−5.88404e6	−2.07665
$382$	−2.27990e6	−0.799386
$383$	−3.33394e6	−1.16134	−0.580671	−	0.814138i	$-0.697210\pi$
$383$	−3.33394e6	−1.16134	−0.580671	+	0.814138i	$0.697210\pi$
$384$	6.20900e6	2.14879
$385$	−5.42140e6	−1.86406
$386$	−1.81219e6	−0.619065
$387$	1.51807e6	0.515245
$388$	3.00370e6	1.01293
$389$	−130873.	−0.0438507	−0.0219254	−	0.999760i	$-0.506980\pi$
$389$	−130873.	−0.0438507	−0.0219254	+	0.999760i	$0.506980\pi$
$390$	−2.08618e6	−0.694528
$391$	−3.43095e6	−1.13494
$392$	−1.44314e7	−4.74345
$393$	−5.06398e6	−1.65391
$394$	−2.32831e6	−0.755615
$395$	5.28697e6	1.70496
$396$	3.27107e6	1.04822
$397$	−2.76015e6	−0.878933	−0.439466	−	0.898259i	$-0.644832\pi$
$397$	−2.76015e6	−0.878933	−0.439466	+	0.898259i	$0.644832\pi$
$398$	7.93399e6	2.51064
$399$	4.01613e6	1.26292
$400$	2.71933e6	0.849789
$401$	−2.07299e6	−0.643778	−0.321889	−	0.946777i	$-0.604318\pi$
$401$	−2.07299e6	−0.643778	−0.321889	+	0.946777i	$0.604318\pi$
$402$	−1.08998e7	−3.36398
$403$	664596.	0.203843
$404$	1.01349e7	3.08936
$405$	−5.29562e6	−1.60428
$406$	−1.75051e7	−5.27046
$407$	1.58080e6	0.473034
$408$	1.45254e7	4.31994
$409$	6.00233e6	1.77424	0.887119	−	0.461542i	$-0.152703\pi$
$409$	6.00233e6	1.77424	0.887119	+	0.461542i	$0.152703\pi$
$410$	−1.13586e7	−3.33708
$411$	−3.26251e6	−0.952680
$412$	9.42700e6	2.73609
$413$	8.25534e6	2.38155
$414$	−2.61278e6	−0.749208
$415$	707888.	0.201764
$416$	−134686.	−0.0381584
$417$	712281.	0.200591
$418$	2.37622e6	0.665190
$419$	59419.6	0.0165346	0.00826731	−	0.999966i	$-0.497368\pi$
$419$	59419.6	0.0165346	0.00826731	+	0.999966i	$0.497368\pi$
$420$	−2.40866e7	−6.66273
$421$	5.25172e6	1.44410	0.722048	−	0.691843i	$-0.243201\pi$
$421$	5.25172e6	1.44410	0.722048	+	0.691843i	$0.243201\pi$
$422$	−8.92302e6	−2.43911
$423$	1.73091e6	0.470353
$424$	−5.64556e6	−1.52508
$425$	−5.05220e6	−1.35678
$426$	−2.96290e6	−0.791029
$427$	−3.59619e6	−0.954494
$428$	8.65553e6	2.28394
$429$	854183.	0.224082
$430$	−6.61387e6	−1.72498
$431$	−3.64834e6	−0.946024	−0.473012	−	0.881056i	$-0.656833\pi$
$431$	−3.64834e6	−0.946024	−0.473012	+	0.881056i	$0.656833\pi$
$432$	−1.78958e6	−0.461361
$433$	−7.21919e6	−1.85041	−0.925207	−	0.379464i	$-0.876108\pi$
$433$	−7.21919e6	−1.85041	−0.925207	+	0.379464i	$0.876108\pi$
$434$	1.14235e7	2.91122
$435$	−1.07859e7	−2.73296
$436$	−1.26231e7	−3.18018
$437$	−1.27492e6	−0.319359
$438$	−1.17672e7	−2.93080
$439$	1.45988e6	0.361540	0.180770	−	0.983525i	$-0.442141\pi$
$439$	1.45988e6	0.361540	0.180770	+	0.983525i	$0.442141\pi$
$440$	−7.28618e6	−1.79419
$441$	7.30744e6	1.78924
$442$	3.02562e6	0.736645
$443$	−6.55274e6	−1.58640	−0.793202	−	0.608959i	$-0.791587\pi$
$443$	−6.55274e6	−1.58640	−0.793202	+	0.608959i	$0.791587\pi$
$444$	7.02331e6	1.69077
$445$	6.02372e6	1.44200
$446$	2.49476e6	0.593869
$447$	−4.97326e6	−1.17726
$448$	6.87443e6	1.61823
$449$	7.10735e6	1.66377	0.831883	−	0.554952i	$-0.187263\pi$
$449$	7.10735e6	1.66377	0.831883	+	0.554952i	$0.187263\pi$
$450$	−3.84743e6	−0.895652
$451$	4.65078e6	1.07667
$452$	1.24369e7	2.86330
$453$	−1.02199e6	−0.233992
$454$	481143.	0.109555
$455$	−2.56512e6	−0.580870
$456$	5.39754e6	1.21558
$457$	1.30283e6	0.291808	0.145904	−	0.989299i	$-0.453391\pi$
$457$	1.30283e6	0.291808	0.145904	+	0.989299i	$0.453391\pi$
$458$	5.62999e6	1.25413
$459$	3.32483e6	0.736611
$460$	7.64628e6	1.68483
$461$	4.49015e6	0.984030	0.492015	−	0.870587i	$-0.336260\pi$
$461$	4.49015e6	0.984030	0.492015	+	0.870587i	$0.336260\pi$
$462$	1.46823e7	3.20028
$463$	−2.97572e6	−0.645119	−0.322560	−	0.946549i	$-0.604543\pi$
$463$	−2.97572e6	−0.645119	−0.322560	+	0.946549i	$0.604543\pi$
$464$	−8.41976e6	−1.81553
$465$	7.03870e6	1.50959
$466$	−1.41075e7	−3.00944
$467$	1.98673e6	0.421547	0.210774	−	0.977535i	$-0.432402\pi$
$467$	1.98673e6	0.421547	0.210774	+	0.977535i	$0.432402\pi$
$468$	1.54770e6	0.326641
$469$	−1.34022e7	−2.81347
$470$	−7.54117e6	−1.57469
$471$	−2.83971e6	−0.589824
$472$	1.10949e7	2.29229
$473$	2.70804e6	0.556548
$474$	−1.43182e7	−2.92713
$475$	−1.87737e6	−0.381782
$476$	3.49332e7	7.06676
$477$	2.85867e6	0.575265
$478$	4.33280e6	0.867358
$479$	3.12266e6	0.621850	0.310925	−	0.950434i	$-0.399361\pi$
$479$	3.12266e6	0.621850	0.310925	+	0.950434i	$0.399361\pi$
$480$	−1.42646e6	−0.282589
$481$	747952.	0.147405
$482$	−3.45290e6	−0.676966
$483$	−7.87750e6	−1.53646
$484$	−4.70964e6	−0.913850
$485$	3.38785e6	0.653987
$486$	1.06651e7	2.04820
$487$	−642214.	−0.122704	−0.0613518	−	0.998116i	$-0.519541\pi$
$487$	−642214.	−0.122704	−0.0613518	+	0.998116i	$0.519541\pi$
$488$	−4.83316e6	−0.918717
$489$	7.87267e6	1.48885
$490$	−3.18368e7	−5.99018
$491$	−4.32156e6	−0.808978	−0.404489	−	0.914543i	$-0.632551\pi$
$491$	−4.32156e6	−0.808978	−0.404489	+	0.914543i	$0.632551\pi$
$492$	2.06628e7	3.84837
$493$	1.56430e7	2.89869
$494$	1.12430e6	0.207284
$495$	3.68941e6	0.676774
$496$	5.49459e6	1.00284
$497$	−3.64311e6	−0.661579
$498$	−1.91710e6	−0.346396
$499$	−2.59688e6	−0.466874	−0.233437	−	0.972372i	$-0.574997\pi$
$499$	−2.59688e6	−0.466874	−0.233437	+	0.972372i	$0.574997\pi$
$500$	−3.85069e6	−0.688832
$501$	6.63691e6	1.18133
$502$	455129.	0.0806075
$503$	7.60819e6	1.34079	0.670396	−	0.742003i	$-0.266124\pi$
$503$	7.60819e6	1.34079	0.670396	+	0.742003i	$0.266124\pi$
$504$	1.36011e7	2.38505
$505$	1.14311e7	1.99462
$506$	−4.66088e6	−0.809266
$507$	−7.11716e6	−1.22967
$508$	−1.90184e7	−3.26975
$509$	−4.53635e6	−0.776090	−0.388045	−	0.921640i	$-0.626850\pi$
$509$	−4.53635e6	−0.776090	−0.388045	+	0.921640i	$0.626850\pi$
$510$	3.20441e7	5.45536
$511$	−1.44686e7	−2.45118
$512$	1.12369e7	1.89439
$513$	1.23549e6	0.207274
$514$	−1.61558e6	−0.269725
$515$	1.06326e7	1.76653
$516$	1.20315e7	1.98928
$517$	3.08773e6	0.508057
$518$	1.28563e7	2.10519
$519$	1.76381e6	0.287431
$520$	−3.44743e6	−0.559097
$521$	−5.25367e6	−0.847947	−0.423974	−	0.905675i	$-0.639365\pi$
$521$	−5.25367e6	−0.847947	−0.423974	+	0.905675i	$0.639365\pi$
$522$	1.19127e7	1.91352
$523$	9.63116e6	1.53966	0.769829	−	0.638250i	$-0.220341\pi$
$523$	9.63116e6	1.53966	0.769829	+	0.638250i	$0.220341\pi$
$524$	−1.63678e7	−2.60413
$525$	−1.15999e7	−1.83678
$526$	−1.67411e7	−2.63828
$527$	−1.02083e7	−1.60114
$528$	7.06202e6	1.10241
$529$	−3.93563e6	−0.611470
$530$	−1.24545e7	−1.92592
$531$	−5.61798e6	−0.864657
$532$	1.29809e7	1.98851
$533$	2.20050e6	0.335508
$534$	−1.63135e7	−2.47567
$535$	9.76248e6	1.47461
$536$	−1.80121e7	−2.70802
$537$	−9.90772e6	−1.48265
$538$	1.18483e7	1.76482
$539$	1.30356e7	1.93267
$540$	−7.40980e6	−1.09351
$541$	−6.06810e6	−0.891373	−0.445687	−	0.895189i	$-0.647040\pi$
$541$	−6.06810e6	−0.891373	−0.445687	+	0.895189i	$0.647040\pi$
$542$	−1.76928e6	−0.258701
$543$	3.35959e6	0.488975
$544$	2.06881e6	0.299726
$545$	−1.42375e7	−2.05325
$546$	6.94686e6	0.997257
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−1.05451e7	−1.50003
$549$	2.44730e6	0.346543
$550$	−6.86333e6	−0.967449
$551$	5.81283e6	0.815659
$552$	−1.05871e7	−1.47887
$553$	−1.76053e7	−2.44811
$554$	−7.51549e6	−1.04036
$555$	7.92152e6	1.09163
$556$	2.30224e6	0.315837
$557$	1.17818e7	1.60907	0.804533	−	0.593907i	$-0.202415\pi$
$557$	1.17818e7	1.60907	0.804533	+	0.593907i	$0.202415\pi$
$558$	−7.77400e6	−1.05696
$559$	1.28130e6	0.173429
$560$	−2.12073e7	−2.85769
$561$	−1.31204e7	−1.76012
$562$	1.36087e7	1.81750
$563$	6.96637e6	0.926265	0.463133	−	0.886289i	$-0.346725\pi$
$563$	6.96637e6	0.926265	0.463133	+	0.886289i	$0.346725\pi$
$564$	1.37184e7	1.81595
$565$	1.40275e7	1.84867
$566$	2.20789e7	2.89691
$567$	1.76341e7	2.30354
$568$	−4.89622e6	−0.636781
$569$	7.09174e6	0.918274	0.459137	−	0.888365i	$-0.348159\pi$
$569$	7.09174e6	0.918274	0.459137	+	0.888365i	$0.348159\pi$
$570$	1.19074e7	1.53508
$571$	−9.54998e6	−1.22578	−0.612889	−	0.790169i	$-0.709993\pi$
$571$	−9.54998e6	−1.22578	−0.612889	+	0.790169i	$0.709993\pi$
$572$	2.76090e6	0.352826
$573$	4.67784e6	0.595194
$574$	3.78236e7	4.79163
$575$	3.68240e6	0.464473
$576$	−4.67823e6	−0.587524
$577$	50831.8	0.00635618	0.00317809	−	0.999995i	$-0.498988\pi$
$577$	50831.8	0.00635618	0.00317809	+	0.999995i	$0.498988\pi$
$578$	−3.24559e7	−4.04087
$579$	3.71822e6	0.460934
$580$	−3.48623e7	−4.30314
$581$	−2.35723e6	−0.289708
$582$	−9.17498e6	−1.12279
$583$	5.09950e6	0.621379
$584$	−1.94454e7	−2.35931
$585$	1.74563e6	0.210893
$586$	−1.50615e7	−1.81186
$587$	−7.62195e6	−0.913001	−0.456500	−	0.889723i	$-0.650897\pi$
$587$	−7.62195e6	−0.913001	−0.456500	+	0.889723i	$0.650897\pi$
$588$	5.79154e7	6.90797
$589$	−3.79336e6	−0.450542
$590$	2.44762e7	2.89477
$591$	4.77718e6	0.562604
$592$	6.18374e6	0.725182
$593$	−5.33415e6	−0.622914	−0.311457	−	0.950260i	$-0.600817\pi$
$593$	−5.33415e6	−0.622914	−0.311457	+	0.950260i	$0.600817\pi$
$594$	4.51673e6	0.525240
$595$	3.94007e7	4.56260
$596$	−1.60746e7	−1.85364
$597$	−1.62788e7	−1.86933
$598$	−2.20528e6	−0.252180
$599$	7.96184e6	0.906664	0.453332	−	0.891342i	$-0.350235\pi$
$599$	7.96184e6	0.906664	0.453332	+	0.891342i	$0.350235\pi$
$600$	−1.55899e7	−1.76793
$601$	−2.55490e6	−0.288528	−0.144264	−	0.989539i	$-0.546081\pi$
$601$	−2.55490e6	−0.288528	−0.144264	+	0.989539i	$0.546081\pi$
$602$	2.20238e7	2.47686
$603$	9.12053e6	1.02147
$604$	−3.30328e6	−0.368428
$605$	−5.31196e6	−0.590019
$606$	−3.09577e7	−3.42442
$607$	8.42188e6	0.927764	0.463882	−	0.885897i	$-0.346456\pi$
$607$	8.42188e6	0.927764	0.463882	+	0.885897i	$0.346456\pi$
$608$	768758.	0.0843395
$609$	3.59165e7	3.92420
$610$	−1.06623e7	−1.16019
$611$	1.46095e6	0.158318
$612$	−2.37729e7	−2.56569
$613$	8.26695e6	0.888576	0.444288	−	0.895884i	$-0.353457\pi$
$613$	8.26695e6	0.888576	0.444288	+	0.895884i	$0.353457\pi$
$614$	−2.55619e7	−2.73635
$615$	2.33054e7	2.48467
$616$	2.42626e7	2.57624
$617$	1.88750e7	1.99606	0.998030	−	0.0627454i	$-0.0199856\pi$
$617$	1.88750e7	1.99606	0.998030	+	0.0627454i	$0.0199856\pi$
$618$	−2.87953e7	−3.03284
$619$	1.23783e7	1.29848	0.649241	−	0.760583i	$-0.275087\pi$
$619$	1.23783e7	1.29848	0.649241	+	0.760583i	$0.275087\pi$
$620$	2.27505e7	2.37691
$621$	−2.42337e6	−0.252168
$622$	−1.06660e7	−1.10542
$623$	−2.00587e7	−2.07053
$624$	3.34137e6	0.343529
$625$	−1.16201e7	−1.18990
$626$	−681637.	−0.0695212
$627$	−4.87547e6	−0.495277
$628$	−9.17854e6	−0.928698
$629$	−1.14887e7	−1.15783
$630$	3.00050e7	3.01191
$631$	340146.	0.0340089	0.0170044	−	0.999855i	$-0.494587\pi$
$631$	340146.	0.0340089	0.0170044	+	0.999855i	$0.494587\pi$
$632$	−2.36610e7	−2.35635
$633$	1.83081e7	1.81607
$634$	−7.54320e6	−0.745302
$635$	−2.14507e7	−2.11109
$636$	2.26564e7	2.22100
$637$	6.16773e6	0.602250
$638$	2.12507e7	2.06691
$639$	2.47923e6	0.240196
$640$	2.26353e7	2.18442
$641$	1.47756e7	1.42037	0.710184	−	0.704016i	$-0.248612\pi$
$641$	1.47756e7	1.42037	0.710184	+	0.704016i	$0.248612\pi$
$642$	−2.64388e7	−2.53165
$643$	−1.93221e7	−1.84301	−0.921505	−	0.388366i	$-0.873040\pi$
$643$	−1.93221e7	−1.84301	−0.921505	+	0.388366i	$0.873040\pi$
$644$	−2.54617e7	−2.41921
$645$	1.35702e7	1.28436
$646$	−1.72695e7	−1.62816
$647$	−3.26722e6	−0.306844	−0.153422	−	0.988161i	$-0.549029\pi$
$647$	−3.26722e6	−0.306844	−0.153422	+	0.988161i	$0.549029\pi$
$648$	2.36997e7	2.21720
$649$	−1.00218e7	−0.933970
$650$	−3.24736e6	−0.301472
$651$	−2.34385e7	−2.16759
$652$	2.54461e7	2.34424
$653$	9.00047e6	0.826004	0.413002	−	0.910730i	$-0.364480\pi$
$653$	9.00047e6	0.826004	0.413002	+	0.910730i	$0.364480\pi$
$654$	3.85581e7	3.52509
$655$	−1.84611e7	−1.68134
$656$	1.81928e7	1.65059
$657$	9.84630e6	0.889937
$658$	2.51117e7	2.26106
$659$	−1.71578e6	−0.153904	−0.0769518	−	0.997035i	$-0.524519\pi$
$659$	−1.71578e6	−0.153904	−0.0769518	+	0.997035i	$0.524519\pi$
$660$	2.92405e7	2.61291
$661$	1.11877e7	0.995945	0.497972	−	0.867193i	$-0.334078\pi$
$661$	1.11877e7	0.995945	0.497972	+	0.867193i	$0.334078\pi$
$662$	2.28471e7	2.02622
$663$	−6.20789e6	−0.548479
$664$	−3.16804e6	−0.278850
$665$	1.46411e7	1.28386
$666$	−8.74904e6	−0.764319
$667$	−1.14017e7	−0.992326
$668$	2.14519e7	1.86005
$669$	−5.11868e6	−0.442174
$670$	−3.97360e7	−3.41977
$671$	4.36568e6	0.374323
$672$	4.75003e6	0.405763
$673$	4.18819e6	0.356442	0.178221	−	0.983991i	$-0.442966\pi$
$673$	4.18819e6	0.356442	0.178221	+	0.983991i	$0.442966\pi$
$674$	−2.77064e6	−0.234926
$675$	−3.56851e6	−0.301458
$676$	−2.30041e7	−1.93615
$677$	−8.36016e6	−0.701040	−0.350520	−	0.936555i	$-0.613995\pi$
$677$	−8.36016e6	−0.701040	−0.350520	+	0.936555i	$0.613995\pi$
$678$	−3.79893e7	−3.17385
$679$	−1.12813e7	−0.939045
$680$	5.29533e7	4.39158
$681$	−987197.	−0.0815711
$682$	−1.38678e7	−1.14169
$683$	−1.35507e6	−0.111150	−0.0555750	−	0.998455i	$-0.517699\pi$
$683$	−1.35507e6	−0.111150	−0.0555750	+	0.998455i	$0.517699\pi$
$684$	−8.83388e6	−0.721957
$685$	−1.18937e7	−0.968480
$686$	6.52097e7	5.29056
$687$	−1.15515e7	−0.933783
$688$	1.05932e7	0.853213
$689$	2.41281e6	0.193631
$690$	−2.33560e7	−1.86756
$691$	−1.53869e7	−1.22590	−0.612950	−	0.790122i	$-0.710017\pi$
$691$	−1.53869e7	−1.22590	−0.612950	+	0.790122i	$0.710017\pi$
$692$	5.70101e6	0.452571
$693$	−1.22855e7	−0.971764
$694$	−2.59371e7	−2.04420
$695$	2.59667e6	0.203918
$696$	4.82706e7	3.77711
$697$	−3.38001e7	−2.63534
$698$	−6.98686e6	−0.542804
$699$	2.89454e7	2.24072
$700$	−3.74934e7	−2.89207
$701$	7.62295e6	0.585906	0.292953	−	0.956127i	$-0.405362\pi$
$701$	7.62295e6	0.585906	0.292953	+	0.956127i	$0.405362\pi$
$702$	2.13707e6	0.163673
$703$	−4.26913e6	−0.325800
$704$	−8.34538e6	−0.634621
$705$	1.54728e7	1.17246
$706$	−6.67152e6	−0.503747
$707$	−3.80649e7	−2.86402
$708$	−4.45255e7	−3.33830
$709$	4.64521e6	0.347048	0.173524	−	0.984830i	$-0.444485\pi$
$709$	4.64521e6	0.347048	0.173524	+	0.984830i	$0.444485\pi$
$710$	−1.08014e7	−0.804148
$711$	1.19809e7	0.888823
$712$	−2.69582e7	−1.99292
$713$	7.44055e6	0.548127
$714$	−1.06705e8	−7.83322
$715$	3.11399e6	0.227799
$716$	−3.20238e7	−2.33448
$717$	−8.88993e6	−0.645804
$718$	−2.97672e6	−0.215490
$719$	2.20841e7	1.59315	0.796577	−	0.604537i	$-0.206642\pi$
$719$	2.20841e7	1.59315	0.796577	+	0.604537i	$0.206642\pi$
$720$	1.44321e7	1.03752
$721$	−3.54060e7	−2.53652
$722$	1.80292e7	1.28716
$723$	7.08459e6	0.504045
$724$	1.08589e7	0.769909
$725$	−1.67894e7	−1.18629
$726$	1.43859e7	1.01296
$727$	1.61856e7	1.13577	0.567887	−	0.823107i	$-0.307761\pi$
$727$	1.61856e7	1.13577	0.567887	+	0.823107i	$0.307761\pi$
$728$	1.14798e7	0.802795
$729$	−4.45702e6	−0.310617
$730$	−4.28980e7	−2.97941
$731$	−1.96811e7	−1.36224
$732$	1.93962e7	1.33795
$733$	−2.30659e7	−1.58566	−0.792832	−	0.609440i	$-0.791394\pi$
$733$	−2.30659e7	−1.58566	−0.792832	+	0.609440i	$0.791394\pi$
$734$	3.27439e7	2.24332
$735$	6.53221e7	4.46007
$736$	−1.50789e6	−0.102607
$737$	1.62699e7	1.10336
$738$	−2.57400e7	−1.73967
$739$	−1.13073e7	−0.761640	−0.380820	−	0.924649i	$-0.624358\pi$
$739$	−1.13073e7	−0.761640	−0.380820	+	0.924649i	$0.624358\pi$
$740$	2.56040e7	1.71881
$741$	−2.30681e6	−0.154336
$742$	4.14730e7	2.76538
$743$	−2.73009e7	−1.81428	−0.907140	−	0.420830i	$-0.861739\pi$
$743$	−2.73009e7	−1.81428	−0.907140	+	0.420830i	$0.861739\pi$
$744$	−3.15006e7	−2.08635
$745$	−1.81304e7	−1.19679
$746$	−6.56689e6	−0.432029
$747$	1.60416e6	0.105183
$748$	−4.24080e7	−2.77136
$749$	−3.25085e7	−2.11735
$750$	1.17621e7	0.763542
$751$	818196.	0.0529368	0.0264684	−	0.999650i	$-0.491574\pi$
$751$	818196.	0.0529368	0.0264684	+	0.999650i	$0.491574\pi$
$752$	1.20785e7	0.778875
$753$	−933824.	−0.0600175
$754$	1.00547e7	0.644081
$755$	−3.72573e6	−0.237872
$756$	2.46742e7	1.57014
$757$	3.98467e6	0.252727	0.126364	−	0.991984i	$-0.459669\pi$
$757$	3.98467e6	0.252727	0.126364	+	0.991984i	$0.459669\pi$
$758$	−4.95036e7	−3.12942
$759$	9.56308e6	0.602551
$760$	1.96771e7	1.23574
$761$	9.75879e6	0.610849	0.305425	−	0.952216i	$-0.401202\pi$
$761$	9.75879e6	0.610849	0.305425	+	0.952216i	$0.401202\pi$
$762$	5.80928e7	3.62439
$763$	4.74101e7	2.94822
$764$	1.51197e7	0.937154
$765$	−2.68133e7	−1.65652
$766$	3.29158e7	2.02690
$767$	−4.74177e6	−0.291039
$768$	−4.31800e7	−2.64168
$769$	−5.97231e6	−0.364189	−0.182094	−	0.983281i	$-0.558288\pi$
$769$	−5.97231e6	−0.364189	−0.182094	+	0.983281i	$0.558288\pi$
$770$	5.35252e7	3.25335
$771$	3.31481e6	0.200827
$772$	1.20180e7	0.725756
$773$	−2.73692e6	−0.164745	−0.0823727	−	0.996602i	$-0.526250\pi$
$773$	−2.73692e6	−0.164745	−0.0823727	+	0.996602i	$0.526250\pi$
$774$	−1.49878e7	−0.899260
$775$	1.09565e7	0.655266
$776$	−1.51618e7	−0.903848
$777$	−2.63782e7	−1.56745
$778$	1.29210e6	0.0765330
$779$	−1.25599e7	−0.741555
$780$	1.38350e7	0.814224
$781$	4.42264e6	0.259450
$782$	3.38735e7	1.98081
$783$	1.10491e7	0.644051
$784$	5.09921e7	2.96287
$785$	−1.03524e7	−0.599606
$786$	4.99964e7	2.88657
$787$	−3.11591e7	−1.79328	−0.896641	−	0.442758i	$-0.854000\pi$
$787$	−3.11591e7	−1.79328	−0.896641	+	0.442758i	$0.854000\pi$
$788$	1.54408e7	0.885839
$789$	3.43491e7	1.96437
$790$	−5.21980e7	−2.97568
$791$	−4.67108e7	−2.65446
$792$	−1.65113e7	−0.935340
$793$	2.06561e6	0.116645
$794$	2.72508e7	1.53401
$795$	2.55540e7	1.43397
$796$	−5.26164e7	−2.94332
$797$	−1.44591e7	−0.806296	−0.403148	−	0.915135i	$-0.632084\pi$
$797$	−1.44591e7	−0.806296	−0.403148	+	0.915135i	$0.632084\pi$
$798$	−3.96510e7	−2.20418
$799$	−2.24405e7	−1.24355
$800$	−2.22043e6	−0.122663
$801$	1.36505e7	0.751737
$802$	2.04665e7	1.12359
$803$	1.75646e7	0.961277
$804$	7.22850e7	3.94374
$805$	−2.87180e7	−1.56194
$806$	−6.56152e6	−0.355768
$807$	−2.43101e7	−1.31402
$808$	−5.11580e7	−2.75667
$809$	−5.73231e6	−0.307934	−0.153967	−	0.988076i	$-0.549205\pi$
$809$	−5.73231e6	−0.307934	−0.153967	+	0.988076i	$0.549205\pi$
$810$	5.22833e7	2.79995
$811$	−1.81452e7	−0.968745	−0.484372	−	0.874862i	$-0.660952\pi$
$811$	−1.81452e7	−0.968745	−0.484372	+	0.874862i	$0.660952\pi$
$812$	1.16089e8	6.17878
$813$	3.63016e6	0.192619
$814$	−1.56072e7	−0.825589
$815$	2.87004e7	1.51354
$816$	−5.13241e7	−2.69834
$817$	−7.31336e6	−0.383320
$818$	−5.92607e7	−3.09659
$819$	−5.81286e6	−0.302817
$820$	7.53277e7	3.91219
$821$	3.00978e6	0.155839	0.0779196	−	0.996960i	$-0.475172\pi$
$821$	3.00978e6	0.155839	0.0779196	+	0.996960i	$0.475172\pi$
$822$	3.22106e7	1.66272
$823$	−2.00280e7	−1.03071	−0.515356	−	0.856976i	$-0.672340\pi$
$823$	−2.00280e7	−1.03071	−0.515356	+	0.856976i	$0.672340\pi$
$824$	−4.75845e7	−2.44145
$825$	1.40820e7	0.720328
$826$	−8.15046e7	−4.15654
$827$	−1.24180e7	−0.631375	−0.315688	−	0.948863i	$-0.602235\pi$
$827$	−1.24180e7	−0.631375	−0.315688	+	0.948863i	$0.602235\pi$
$828$	1.73274e7	0.878328
$829$	9.12786e6	0.461299	0.230649	−	0.973037i	$-0.425915\pi$
$829$	9.12786e6	0.461299	0.230649	+	0.973037i	$0.425915\pi$
$830$	−6.98894e6	−0.352140
$831$	1.54201e7	0.774613
$832$	−3.94859e6	−0.197758
$833$	−9.47377e7	−4.73054
$834$	−7.03231e6	−0.350093
$835$	2.41953e7	1.20092
$836$	−1.57585e7	−0.779830
$837$	−7.21043e6	−0.355752
$838$	−586646.	−0.0288580
$839$	4.05979e6	0.199113	0.0995563	−	0.995032i	$-0.468258\pi$
$839$	4.05979e6	0.199113	0.0995563	+	0.995032i	$0.468258\pi$
$840$	1.21582e8	5.94524
$841$	3.14734e7	1.53445
$842$	−5.18499e7	−2.52039
$843$	−2.79220e7	−1.35325
$844$	5.91754e7	2.85947
$845$	−2.59461e7	−1.25006
$846$	−1.70892e7	−0.820910
$847$	1.76885e7	0.847195
$848$	1.99481e7	0.952602
$849$	−4.53009e7	−2.15694
$850$	4.98802e7	2.36799
$851$	8.37376e6	0.396366
$852$	1.96492e7	0.927356
$853$	−3.00804e7	−1.41550	−0.707751	−	0.706462i	$-0.750290\pi$
$853$	−3.00804e7	−1.41550	−0.707751	+	0.706462i	$0.750290\pi$
$854$	3.55050e7	1.66588
$855$	−9.96364e6	−0.466125
$856$	−4.36904e7	−2.03799
$857$	−1.42344e7	−0.662044	−0.331022	−	0.943623i	$-0.607393\pi$
$857$	−1.42344e7	−0.662044	−0.331022	+	0.943623i	$0.607393\pi$
$858$	−8.43331e6	−0.391093
$859$	2.86769e7	1.32602	0.663010	−	0.748611i	$-0.269279\pi$
$859$	2.86769e7	1.32602	0.663010	+	0.748611i	$0.269279\pi$
$860$	4.38616e7	2.02227
$861$	−7.76056e7	−3.56768
$862$	3.60199e7	1.65110
$863$	−1.78624e7	−0.816420	−0.408210	−	0.912888i	$-0.633847\pi$
$863$	−1.78624e7	−0.816420	−0.408210	+	0.912888i	$0.633847\pi$
$864$	1.46126e6	0.0665952
$865$	6.43010e6	0.292198
$866$	7.12747e7	3.22954
$867$	6.65924e7	3.00868
$868$	−7.57581e7	−3.41295
$869$	2.13724e7	0.960073
$870$	1.06489e8	4.76986
$871$	7.69804e6	0.343823
$872$	6.37176e7	2.83771
$873$	7.67726e6	0.340934
$874$	1.25872e7	0.557379
$875$	1.44625e7	0.638590
$876$	7.80371e7	3.43590
$877$	−1.16348e6	−0.0510810	−0.0255405	−	0.999674i	$-0.508131\pi$
$877$	−1.16348e6	−0.0510810	−0.0255405	+	0.999674i	$0.508131\pi$
$878$	−1.44133e7	−0.630998
$879$	3.09029e7	1.34905
$880$	2.57451e7	1.12069
$881$	−7.57324e6	−0.328732	−0.164366	−	0.986399i	$-0.552558\pi$
$881$	−7.57324e6	−0.328732	−0.164366	+	0.986399i	$0.552558\pi$
$882$	−7.21460e7	−3.12278
$883$	1.27043e7	0.548341	0.274170	−	0.961681i	$-0.411597\pi$
$883$	1.27043e7	0.548341	0.274170	+	0.961681i	$0.411597\pi$
$884$	−2.00652e7	−0.863600
$885$	−5.02198e7	−2.15534
$886$	6.46949e7	2.76876
$887$	1.34984e7	0.576066	0.288033	−	0.957621i	$-0.406999\pi$
$887$	1.34984e7	0.576066	0.288033	+	0.957621i	$0.406999\pi$
$888$	−3.54515e7	−1.50870
$889$	7.14296e7	3.03126
$890$	−5.94719e7	−2.51673
$891$	−2.14074e7	−0.903377
$892$	−1.65446e7	−0.696218
$893$	−8.33874e6	−0.349922
$894$	4.91008e7	2.05468
$895$	−3.61193e7	−1.50724
$896$	−7.53744e7	−3.13656
$897$	4.52474e6	0.187764
$898$	−7.01705e7	−2.90378
$899$	−3.39242e7	−1.39994
$900$	2.55152e7	1.05001
$901$	−3.70613e7	−1.52093
$902$	−4.59169e7	−1.87913
$903$	−4.51880e7	−1.84418
$904$	−6.27778e7	−2.55496
$905$	1.22476e7	0.497085
$906$	1.00900e7	0.408387
$907$	−1.49711e7	−0.604276	−0.302138	−	0.953264i	$-0.597700\pi$
$907$	−1.49711e7	−0.604276	−0.302138	+	0.953264i	$0.597700\pi$
$908$	−3.19083e6	−0.128436
$909$	2.59042e7	1.03983
$910$	2.53253e7	1.01380
$911$	−4.26753e6	−0.170365	−0.0851825	−	0.996365i	$-0.527147\pi$
$911$	−4.26753e6	−0.170365	−0.0851825	+	0.996365i	$0.527147\pi$
$912$	−1.90717e7	−0.759282
$913$	2.86161e6	0.113615
$914$	−1.28627e7	−0.509294
$915$	2.18767e7	0.863833
$916$	−3.73368e7	−1.47027
$917$	6.14745e7	2.41419
$918$	−3.28259e7	−1.28561
$919$	−1.60034e7	−0.625063	−0.312531	−	0.949907i	$-0.601177\pi$
$919$	−1.60034e7	−0.625063	−0.312531	+	0.949907i	$0.601177\pi$
$920$	−3.85960e7	−1.50339
$921$	5.24473e7	2.03739
$922$	−4.43310e7	−1.71743
$923$	2.09256e6	0.0808487
$924$	−9.73693e7	−3.75182
$925$	1.23307e7	0.473842
$926$	2.93792e7	1.12593
$927$	2.40947e7	0.920922
$928$	6.87506e6	0.262063
$929$	−3.88856e6	−0.147825	−0.0739127	−	0.997265i	$-0.523549\pi$
$929$	−3.88856e6	−0.147825	−0.0739127	+	0.997265i	$0.523549\pi$
$930$	−6.94927e7	−2.63471
$931$	−3.52039e7	−1.33112
$932$	9.35576e7	3.52809
$933$	2.18844e7	0.823057
$934$	−1.96149e7	−0.735730
$935$	−4.78315e7	−1.78931
$936$	−7.81229e6	−0.291466
$937$	2.84486e7	1.05855	0.529276	−	0.848450i	$-0.322464\pi$
$937$	2.84486e7	1.05855	0.529276	+	0.848450i	$0.322464\pi$
$938$	1.32319e8	4.91037
$939$	1.39857e6	0.0517630
$940$	5.00113e7	1.84607
$941$	−1.72884e7	−0.636473	−0.318237	−	0.948011i	$-0.603091\pi$
$941$	−1.72884e7	−0.636473	−0.318237	+	0.948011i	$0.603091\pi$
$942$	2.80363e7	1.02942
$943$	2.46359e7	0.902171
$944$	−3.92029e7	−1.43182
$945$	2.78298e7	1.01375
$946$	−2.67364e7	−0.971347
$947$	1.52154e6	0.0551325	0.0275662	−	0.999620i	$-0.491224\pi$
$947$	1.52154e6	0.0551325	0.0275662	+	0.999620i	$0.491224\pi$
$948$	9.49549e7	3.43160
$949$	8.31061e6	0.299549
$950$	1.85352e7	0.666327
$951$	1.54770e7	0.554925
$952$	−1.76332e8	−6.30577
$953$	−3.32341e6	−0.118536	−0.0592682	−	0.998242i	$-0.518877\pi$
$953$	−3.32341e6	−0.118536	−0.0592682	+	0.998242i	$0.518877\pi$
$954$	−2.82235e7	−1.00401
$955$	1.70534e7	0.605065
$956$	−2.87341e7	−1.01684
$957$	−4.36017e7	−1.53895
$958$	−3.08298e7	−1.08532
$959$	3.96054e7	1.39062
$960$	−4.18193e7	−1.46453
$961$	−6.49076e6	−0.226718
$962$	−7.38449e6	−0.257266
$963$	2.21229e7	0.768735
$964$	2.28988e7	0.793635
$965$	1.35550e7	0.468578
$966$	7.77742e7	2.68159
$967$	7.15266e6	0.245981	0.122990	−	0.992408i	$-0.460752\pi$
$967$	7.15266e6	0.245981	0.122990	+	0.992408i	$0.460752\pi$
$968$	2.37728e7	0.815440
$969$	3.54332e7	1.21227
$970$	−3.34480e7	−1.14141
$971$	3.55880e7	1.21131	0.605655	−	0.795727i	$-0.292911\pi$
$971$	3.55880e7	1.21131	0.605655	+	0.795727i	$0.292911\pi$
$972$	−7.07282e7	−2.40119
$973$	−8.64678e6	−0.292801
$974$	6.34054e6	0.214155
$975$	6.66286e6	0.224465
$976$	1.70775e7	0.573853
$977$	−4.28769e7	−1.43710	−0.718550	−	0.695475i	$-0.755194\pi$
$977$	−4.28769e7	−1.43710	−0.718550	+	0.695475i	$0.755194\pi$
$978$	−7.77264e7	−2.59849
$979$	2.43507e7	0.811998
$980$	2.11135e8	7.02254
$981$	−3.22638e7	−1.07039
$982$	4.26665e7	1.41191
$983$	1.64307e7	0.542341	0.271170	−	0.962531i	$-0.412589\pi$
$983$	1.64307e7	0.542341	0.271170	+	0.962531i	$0.412589\pi$
$984$	−1.04299e8	−3.43395
$985$	1.74155e7	0.571934
$986$	−1.54442e8	−5.05911
$987$	−5.15236e7	−1.68350
$988$	−7.45610e6	−0.243007
$989$	1.43449e7	0.466345
$990$	−3.64253e7	−1.18118
$991$	8.90992e6	0.288197	0.144099	−	0.989563i	$-0.453972\pi$
$991$	8.90992e6	0.288197	0.144099	+	0.989563i	$0.453972\pi$
$992$	−4.48655e6	−0.144755
$993$	−4.68772e7	−1.50865
$994$	3.59682e7	1.15466
$995$	−5.93454e7	−1.90033
$996$	1.27138e7	0.406094
$997$	3.92350e7	1.25007	0.625036	−	0.780596i	$-0.285084\pi$
$997$	3.92350e7	1.25007	0.625036	+	0.780596i	$0.285084\pi$
$998$	2.56388e7	0.814839
$999$	−8.11478e6	−0.257255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.8	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-9.87295 q^{2} +20.2571 q^{3} +65.4751 q^{4} +73.8486 q^{5} -199.997 q^{6} -245.912 q^{7} -330.498 q^{8} +167.350 q^{9} +O(q^{10})\)	\(q-9.87295 q^{2} +20.2571 q^{3} +65.4751 q^{4} +73.8486 q^{5} -199.997 q^{6} -245.912 q^{7} -330.498 q^{8} +167.350 q^{9} -729.104 q^{10} +298.531 q^{11} +1326.33 q^{12} +141.249 q^{13} +2427.88 q^{14} +1495.96 q^{15} +1167.78 q^{16} -2169.61 q^{17} -1652.23 q^{18} -806.214 q^{19} +4835.25 q^{20} -4981.46 q^{21} -2947.38 q^{22} +1581.36 q^{23} -6694.92 q^{24} +2328.62 q^{25} -1394.54 q^{26} -1532.46 q^{27} -16101.1 q^{28} -7210.03 q^{29} -14769.5 q^{30} +4705.15 q^{31} -953.540 q^{32} +6047.37 q^{33} +21420.5 q^{34} -18160.3 q^{35} +10957.2 q^{36} +5295.28 q^{37} +7959.71 q^{38} +2861.29 q^{39} -24406.8 q^{40} +15578.9 q^{41} +49181.7 q^{42} +9071.23 q^{43} +19546.3 q^{44} +12358.5 q^{45} -15612.7 q^{46} +10343.1 q^{47} +23655.9 q^{48} +43665.7 q^{49} -22990.4 q^{50} -43950.0 q^{51} +9248.28 q^{52} +17082.0 q^{53} +15129.9 q^{54} +22046.1 q^{55} +81273.4 q^{56} -16331.6 q^{57} +71184.2 q^{58} -33570.3 q^{59} +97948.0 q^{60} +14623.9 q^{61} -46453.7 q^{62} -41153.3 q^{63} -27954.8 q^{64} +10431.0 q^{65} -59705.3 q^{66} +54499.8 q^{67} -142056. q^{68} +32033.8 q^{69} +179295. q^{70} +14814.7 q^{71} -55308.7 q^{72} +58836.7 q^{73} -52280.0 q^{74} +47171.1 q^{75} -52787.0 q^{76} -73412.3 q^{77} -28249.4 q^{78} +71592.0 q^{79} +86239.2 q^{80} -71709.1 q^{81} -153810. q^{82} +9585.65 q^{83} -326162. q^{84} -160223. q^{85} -89559.8 q^{86} -146054. q^{87} -98663.8 q^{88} +81568.5 q^{89} -122015. q^{90} -34734.8 q^{91} +103540. q^{92} +95312.6 q^{93} -102117. q^{94} -59537.8 q^{95} -19316.0 q^{96} +45875.5 q^{97} -431109. q^{98} +49959.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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