LMFDB - Embedded newform 547.8.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,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, 8, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
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:	$170.874608940$
Analytic rank:	$1$
Dimension:	$156$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-18.7781 q^{2} -27.5200 q^{3} +224.616 q^{4} +480.924 q^{5} +516.772 q^{6} -221.639 q^{7} -1814.26 q^{8} -1429.65 q^{9} +O(q^{10})$	\(q-18.7781 q^{2} -27.5200 q^{3} +224.616 q^{4} +480.924 q^{5} +516.772 q^{6} -221.639 q^{7} -1814.26 q^{8} -1429.65 q^{9} -9030.83 q^{10} -940.126 q^{11} -6181.42 q^{12} -6627.18 q^{13} +4161.95 q^{14} -13235.0 q^{15} +5317.40 q^{16} +6229.81 q^{17} +26846.1 q^{18} -25178.1 q^{19} +108023. q^{20} +6099.50 q^{21} +17653.7 q^{22} +71987.4 q^{23} +49928.3 q^{24} +153163. q^{25} +124446. q^{26} +99530.2 q^{27} -49783.5 q^{28} -108316. q^{29} +248528. q^{30} -83883.8 q^{31} +132374. q^{32} +25872.3 q^{33} -116984. q^{34} -106591. q^{35} -321122. q^{36} +97936.5 q^{37} +472797. q^{38} +182380. q^{39} -872520. q^{40} +614044. q^{41} -114537. q^{42} +534189. q^{43} -211167. q^{44} -687553. q^{45} -1.35178e6 q^{46} -1.15464e6 q^{47} -146335. q^{48} -774419. q^{49} -2.87611e6 q^{50} -171444. q^{51} -1.48857e6 q^{52} +1.20347e6 q^{53} -1.86898e6 q^{54} -452130. q^{55} +402109. q^{56} +692902. q^{57} +2.03397e6 q^{58} +1.62834e6 q^{59} -2.97280e6 q^{60} -2.08146e6 q^{61} +1.57518e6 q^{62} +316866. q^{63} -3.16636e6 q^{64} -3.18717e6 q^{65} -485831. q^{66} -3.67820e6 q^{67} +1.39931e6 q^{68} -1.98109e6 q^{69} +2.00158e6 q^{70} +4.99912e6 q^{71} +2.59375e6 q^{72} +1.42194e6 q^{73} -1.83906e6 q^{74} -4.21506e6 q^{75} -5.65540e6 q^{76} +208368. q^{77} -3.42474e6 q^{78} -1.58328e6 q^{79} +2.55727e6 q^{80} +387572. q^{81} -1.15306e7 q^{82} +3.58269e6 q^{83} +1.37004e6 q^{84} +2.99607e6 q^{85} -1.00310e7 q^{86} +2.98087e6 q^{87} +1.70563e6 q^{88} -6.29266e6 q^{89} +1.29109e7 q^{90} +1.46884e6 q^{91} +1.61695e7 q^{92} +2.30848e6 q^{93} +2.16818e7 q^{94} -1.21088e7 q^{95} -3.64294e6 q^{96} -1.50391e6 q^{97} +1.45421e7 q^{98} +1.34405e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) $ 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * 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 $

$2$	−18.7781	−1.65976	−0.829881	−	0.557940i	$-0.811592\pi$
$2$	−18.7781	−1.65976	−0.829881	+	0.557940i	$0.811592\pi$
$3$	−27.5200	−0.588470	−0.294235	−	0.955733i	$-0.595065\pi$
$3$	−27.5200	−0.588470	−0.294235	+	0.955733i	$0.595065\pi$
$4$	224.616	1.75481
$5$	480.924	1.72061	0.860304	−	0.509782i	$-0.170274\pi$
$5$	480.924	1.72061	0.860304	+	0.509782i	$0.170274\pi$
$6$	516.772	0.976720
$7$	−221.639	−0.244232	−0.122116	−	0.992516i	$-0.538968\pi$
$7$	−221.639	−0.244232	−0.122116	+	0.992516i	$0.538968\pi$
$8$	−1814.26	−1.25281
$9$	−1429.65	−0.653703
$10$	−9030.83	−2.85580
$11$	−940.126	−0.212967	−0.106483	−	0.994314i	$-0.533959\pi$
$11$	−940.126	−0.212967	−0.106483	+	0.994314i	$0.533959\pi$
$12$	−6181.42	−1.03265
$13$	−6627.18	−0.836618	−0.418309	−	0.908305i	$-0.637377\pi$
$13$	−6627.18	−0.836618	−0.418309	+	0.908305i	$0.637377\pi$
$14$	4161.95	0.405367
$15$	−13235.0	−1.01253
$16$	5317.40	0.324548
$17$	6229.81	0.307541	0.153771	−	0.988107i	$-0.450858\pi$
$17$	6229.81	0.307541	0.153771	+	0.988107i	$0.450858\pi$
$18$	26846.1	1.08499
$19$	−25178.1	−0.842143	−0.421072	−	0.907027i	$-0.638346\pi$
$19$	−25178.1	−0.842143	−0.421072	+	0.907027i	$0.638346\pi$
$20$	108023.	3.01934
$21$	6099.50	0.143723
$22$	17653.7	0.353474
$23$	71987.4	1.23370	0.616849	−	0.787082i	$-0.288409\pi$
$23$	71987.4	1.23370	0.616849	+	0.787082i	$0.288409\pi$
$24$	49928.3	0.737238
$25$	153163.	1.96049
$26$	124446.	1.38859
$27$	99530.2	0.973154
$28$	−49783.5	−0.428581
$29$	−108316.	−0.824710	−0.412355	−	0.911023i	$-0.635294\pi$
$29$	−108316.	−0.824710	−0.412355	+	0.911023i	$0.635294\pi$
$30$	248528.	1.68055
$31$	−83883.8	−0.505723	−0.252861	−	0.967503i	$-0.581372\pi$
$31$	−83883.8	−0.505723	−0.252861	+	0.967503i	$0.581372\pi$
$32$	132374.	0.714132
$33$	25872.3	0.125324
$34$	−116984.	−0.510445
$35$	−106591.	−0.420227
$36$	−321122.	−1.14713
$37$	97936.5	0.317862	0.158931	−	0.987290i	$-0.449195\pi$
$37$	97936.5	0.317862	0.158931	+	0.987290i	$0.449195\pi$
$38$	472797.	1.39776
$39$	182380.	0.492324
$40$	−872520.	−2.15559
$41$	614044.	1.39141	0.695706	−	0.718327i	$-0.255092\pi$
$41$	614044.	1.39141	0.695706	+	0.718327i	$0.255092\pi$
$42$	−114537.	−0.238546
$43$	534189.	1.02460	0.512301	−	0.858806i	$-0.328793\pi$
$43$	534189.	1.02460	0.512301	+	0.858806i	$0.328793\pi$
$44$	−211167.	−0.373716
$45$	−687553.	−1.12477
$46$	−1.35178e6	−2.04764
$47$	−1.15464e6	−1.62219	−0.811096	−	0.584913i	$-0.801129\pi$
$47$	−1.15464e6	−1.62219	−0.811096	+	0.584913i	$0.801129\pi$
$48$	−146335.	−0.190987
$49$	−774419.	−0.940351
$50$	−2.87611e6	−3.25395
$51$	−171444.	−0.180979
$52$	−1.48857e6	−1.46811
$53$	1.20347e6	1.11038	0.555188	−	0.831725i	$-0.312646\pi$
$53$	1.20347e6	1.11038	0.555188	+	0.831725i	$0.312646\pi$
$54$	−1.86898e6	−1.61520
$55$	−452130.	−0.366432
$56$	402109.	0.305975
$57$	692902.	0.495576
$58$	2.03397e6	1.36882
$59$	1.62834e6	1.03220	0.516099	−	0.856529i	$-0.327384\pi$
$59$	1.62834e6	1.03220	0.516099	+	0.856529i	$0.327384\pi$
$60$	−2.97280e6	−1.77679
$61$	−2.08146e6	−1.17412	−0.587061	−	0.809542i	$-0.699715\pi$
$61$	−2.08146e6	−1.17412	−0.587061	+	0.809542i	$0.699715\pi$
$62$	1.57518e6	0.839379
$63$	316866.	0.159655
$64$	−3.16636e6	−1.50984
$65$	−3.18717e6	−1.43949
$66$	−485831.	−0.208009
$67$	−3.67820e6	−1.49408	−0.747039	−	0.664780i	$-0.768525\pi$
$67$	−3.67820e6	−1.49408	−0.747039	+	0.664780i	$0.768525\pi$
$68$	1.39931e6	0.539676
$69$	−1.98109e6	−0.725994
$70$	2.00158e6	0.697477
$71$	4.99912e6	1.65764	0.828818	−	0.559518i	$-0.189014\pi$
$71$	4.99912e6	1.65764	0.828818	+	0.559518i	$0.189014\pi$
$72$	2.59375e6	0.818963
$73$	1.42194e6	0.427810	0.213905	−	0.976854i	$-0.431382\pi$
$73$	1.42194e6	0.427810	0.213905	+	0.976854i	$0.431382\pi$
$74$	−1.83906e6	−0.527575
$75$	−4.21506e6	−1.15369
$76$	−5.65540e6	−1.47780
$77$	208368.	0.0520133
$78$	−3.42474e6	−0.817141
$79$	−1.58328e6	−0.361296	−0.180648	−	0.983548i	$-0.557820\pi$
$79$	−1.58328e6	−0.361296	−0.180648	+	0.983548i	$0.557820\pi$
$80$	2.55727e6	0.558420
$81$	387572.	0.0810318
$82$	−1.15306e7	−2.30941
$83$	3.58269e6	0.687759	0.343879	−	0.939014i	$-0.388259\pi$
$83$	3.58269e6	0.687759	0.343879	+	0.939014i	$0.388259\pi$
$84$	1.37004e6	0.252207
$85$	2.99607e6	0.529158
$86$	−1.00310e7	−1.70060
$87$	2.98087e6	0.485317
$88$	1.70563e6	0.266806
$89$	−6.29266e6	−0.946171	−0.473085	−	0.881017i	$-0.656860\pi$
$89$	−6.29266e6	−0.946171	−0.473085	+	0.881017i	$0.656860\pi$
$90$	1.29109e7	1.86685
$91$	1.46884e6	0.204329
$92$	1.61695e7	2.16491
$93$	2.30848e6	0.297602
$94$	2.16818e7	2.69245
$95$	−1.21088e7	−1.44900
$96$	−3.64294e6	−0.420245
$97$	−1.50391e6	−0.167310	−0.0836548	−	0.996495i	$-0.526659\pi$
$97$	−1.50391e6	−0.167310	−0.0836548	+	0.996495i	$0.526659\pi$
$98$	1.45421e7	1.56076
$99$	1.34405e6	0.139217
$100$	3.44029e7	3.44029
$101$	1.66998e7	1.61283	0.806413	−	0.591353i	$-0.201406\pi$
$101$	1.66998e7	1.61283	0.806413	+	0.591353i	$0.201406\pi$
$102$	3.21939e6	0.300381
$103$	−8.64170e6	−0.779236	−0.389618	−	0.920977i	$-0.627393\pi$
$103$	−8.64170e6	−0.779236	−0.389618	+	0.920977i	$0.627393\pi$
$104$	1.20234e7	1.04812
$105$	2.93340e6	0.247291
$106$	−2.25988e7	−1.84296
$107$	−5.93449e6	−0.468317	−0.234159	−	0.972198i	$-0.575234\pi$
$107$	−5.93449e6	−0.468317	−0.234159	+	0.972198i	$0.575234\pi$
$108$	2.23560e7	1.70770
$109$	−3.18009e6	−0.235205	−0.117603	−	0.993061i	$-0.537521\pi$
$109$	−3.18009e6	−0.235205	−0.117603	+	0.993061i	$0.537521\pi$
$110$	8.49012e6	0.608190
$111$	−2.69521e6	−0.187052
$112$	−1.17854e6	−0.0792651
$113$	2.32155e7	1.51357	0.756786	−	0.653663i	$-0.226768\pi$
$113$	2.32155e7	1.51357	0.756786	+	0.653663i	$0.226768\pi$
$114$	−1.30114e7	−0.822538
$115$	3.46205e7	2.12271
$116$	−2.43296e7	−1.44721
$117$	9.47455e6	0.546900
$118$	−3.05770e7	−1.71320
$119$	−1.38077e6	−0.0751114
$120$	2.40117e7	1.26850
$121$	−1.86033e7	−0.954645
$122$	3.90858e7	1.94876
$123$	−1.68985e7	−0.818804
$124$	−1.88416e7	−0.887447
$125$	3.60878e7	1.65263
$126$	−5.95012e6	−0.264990
$127$	1.04164e7	0.451235	0.225617	−	0.974216i	$-0.427560\pi$
$127$	1.04164e7	0.451235	0.225617	+	0.974216i	$0.427560\pi$
$128$	4.25142e7	1.79184
$129$	−1.47009e7	−0.602948
$130$	5.98489e7	2.38921
$131$	2.72326e7	1.05838	0.529188	−	0.848505i	$-0.322497\pi$
$131$	2.72326e7	1.05838	0.529188	+	0.848505i	$0.322497\pi$
$132$	5.81132e6	0.219921
$133$	5.58045e6	0.205678
$134$	6.90695e7	2.47981
$135$	4.78665e7	1.67442
$136$	−1.13025e7	−0.385289
$137$	−3.51662e7	−1.16843	−0.584216	−	0.811598i	$-0.698598\pi$
$137$	−3.51662e7	−1.16843	−0.584216	+	0.811598i	$0.698598\pi$
$138$	3.72011e7	1.20498
$139$	3.49520e7	1.10388	0.551938	−	0.833885i	$-0.313889\pi$
$139$	3.49520e7	1.10388	0.551938	+	0.833885i	$0.313889\pi$
$140$	−2.39421e7	−0.737419
$141$	3.17756e7	0.954611
$142$	−9.38738e7	−2.75128
$143$	6.23038e6	0.178172
$144$	−7.60202e6	−0.212158
$145$	−5.20920e7	−1.41900
$146$	−2.67013e7	−0.710063
$147$	2.13120e7	0.553368
$148$	2.19981e7	0.557787
$149$	−5.83992e7	−1.44629	−0.723144	−	0.690697i	$-0.757304\pi$
$149$	−5.83992e7	−1.44629	−0.723144	+	0.690697i	$0.757304\pi$
$150$	7.91506e7	1.91485
$151$	−7.38296e7	−1.74506	−0.872532	−	0.488557i	$-0.837523\pi$
$151$	−7.38296e7	−1.74506	−0.872532	+	0.488557i	$0.837523\pi$
$152$	4.56796e7	1.05504
$153$	−8.90644e6	−0.201041
$154$	−3.91275e6	−0.0863296
$155$	−4.03418e7	−0.870150
$156$	4.09654e7	0.863935
$157$	−6.01920e7	−1.24134	−0.620669	−	0.784072i	$-0.713139\pi$
$157$	−6.01920e7	−1.24134	−0.620669	+	0.784072i	$0.713139\pi$
$158$	2.97310e7	0.599666
$159$	−3.31195e7	−0.653422
$160$	6.36620e7	1.22874
$161$	−1.59552e7	−0.301308
$162$	−7.27786e6	−0.134493
$163$	3.84369e7	0.695172	0.347586	−	0.937648i	$-0.387001\pi$
$163$	3.84369e7	0.695172	0.347586	+	0.937648i	$0.387001\pi$
$164$	1.37924e8	2.44166
$165$	1.24426e7	0.215634
$166$	−6.72760e7	−1.14152
$167$	−2.97792e7	−0.494773	−0.247386	−	0.968917i	$-0.579572\pi$
$167$	−2.97792e7	−0.494773	−0.247386	+	0.968917i	$0.579572\pi$
$168$	−1.10660e7	−0.180057
$169$	−1.88290e7	−0.300071
$170$	−5.62603e7	−0.878276
$171$	3.59959e7	0.550512
$172$	1.19987e8	1.79798
$173$	3.43081e7	0.503774	0.251887	−	0.967757i	$-0.418949\pi$
$173$	3.43081e7	0.503774	0.251887	+	0.967757i	$0.418949\pi$
$174$	−5.59749e7	−0.805510
$175$	−3.39469e7	−0.478815
$176$	−4.99903e6	−0.0691180
$177$	−4.48119e7	−0.607417
$178$	1.18164e8	1.57042
$179$	1.29346e8	1.68565	0.842826	−	0.538186i	$-0.180890\pi$
$179$	1.29346e8	1.68565	0.842826	+	0.538186i	$0.180890\pi$
$180$	−1.54435e8	−1.97375
$181$	−4.06029e7	−0.508959	−0.254479	−	0.967078i	$-0.581904\pi$
$181$	−4.06029e7	−0.508959	−0.254479	+	0.967078i	$0.581904\pi$
$182$	−2.75820e7	−0.339137
$183$	5.72818e7	0.690936
$184$	−1.30603e8	−1.54558
$185$	4.71001e7	0.546916
$186$	−4.33489e7	−0.493949
$187$	−5.85680e6	−0.0654960
$188$	−2.59349e8	−2.84664
$189$	−2.20597e7	−0.237675
$190$	2.27379e8	2.40499
$191$	−1.35318e8	−1.40520	−0.702602	−	0.711583i	$-0.747979\pi$
$191$	−1.35318e8	−1.40520	−0.702602	+	0.711583i	$0.747979\pi$
$192$	8.71382e7	0.888494
$193$	−9.66499e7	−0.967722	−0.483861	−	0.875145i	$-0.660766\pi$
$193$	−9.66499e7	−0.967722	−0.483861	+	0.875145i	$0.660766\pi$
$194$	2.82405e7	0.277694
$195$	8.77110e7	0.847097
$196$	−1.73947e8	−1.65014
$197$	1.01061e8	0.941789	0.470894	−	0.882190i	$-0.343931\pi$
$197$	1.01061e8	0.941789	0.470894	+	0.882190i	$0.343931\pi$
$198$	−2.52387e7	−0.231067
$199$	−6.33572e7	−0.569915	−0.284958	−	0.958540i	$-0.591980\pi$
$199$	−6.33572e7	−0.569915	−0.284958	+	0.958540i	$0.591980\pi$
$200$	−2.77877e8	−2.45611
$201$	1.01224e8	0.879220
$202$	−3.13591e8	−2.67691
$203$	2.40071e7	0.201420
$204$	−3.85091e7	−0.317583
$205$	2.95309e8	2.39407
$206$	1.62274e8	1.29335
$207$	−1.02917e8	−0.806473
$208$	−3.52394e7	−0.271523
$209$	2.36706e7	0.179348
$210$	−5.50835e7	−0.410444
$211$	−6.28727e7	−0.460759	−0.230379	−	0.973101i	$-0.573997\pi$
$211$	−6.28727e7	−0.460759	−0.230379	+	0.973101i	$0.573997\pi$
$212$	2.70318e8	1.94850
$213$	−1.37576e8	−0.975468
$214$	1.11438e8	0.777296
$215$	2.56905e8	1.76294
$216$	−1.80573e8	−1.21917
$217$	1.85919e7	0.123514
$218$	5.97160e7	0.390385
$219$	−3.91318e7	−0.251753
$220$	−1.01555e8	−0.643019
$221$	−4.12860e7	−0.257294
$222$	5.06109e7	0.310462
$223$	2.23581e8	1.35011	0.675053	−	0.737770i	$-0.264121\pi$
$223$	2.23581e8	1.35011	0.675053	+	0.737770i	$0.264121\pi$
$224$	−2.93393e7	−0.174414
$225$	−2.18970e8	−1.28158
$226$	−4.35942e8	−2.51217
$227$	−2.32033e8	−1.31662	−0.658309	−	0.752747i	$-0.728728\pi$
$227$	−2.32033e8	−1.31662	−0.658309	+	0.752747i	$0.728728\pi$
$228$	1.55637e8	0.869641
$229$	1.85357e6	0.0101997	0.00509983	−	0.999987i	$-0.498377\pi$
$229$	1.85357e6	0.0101997	0.00509983	+	0.999987i	$0.498377\pi$
$230$	−6.50106e8	−3.52319
$231$	−5.73430e6	−0.0306082
$232$	1.96514e8	1.03320
$233$	1.51941e8	0.786917	0.393458	−	0.919342i	$-0.371279\pi$
$233$	1.51941e8	0.786917	0.393458	+	0.919342i	$0.371279\pi$
$234$	−1.77914e8	−0.907724
$235$	−5.55292e8	−2.79116
$236$	3.65750e8	1.81131
$237$	4.35719e7	0.212612
$238$	2.59281e7	0.124667
$239$	−4.28187e7	−0.202881	−0.101440	−	0.994842i	$-0.532345\pi$
$239$	−4.28187e7	−0.202881	−0.101440	+	0.994842i	$0.532345\pi$
$240$	−7.03760e7	−0.328613
$241$	2.61073e8	1.20144	0.600719	−	0.799460i	$-0.294881\pi$
$241$	2.61073e8	1.20144	0.600719	+	0.799460i	$0.294881\pi$
$242$	3.49335e8	1.58448
$243$	−2.28339e8	−1.02084
$244$	−4.67528e8	−2.06036
$245$	−3.72437e8	−1.61797
$246$	3.17321e8	1.35902
$247$	1.66860e8	0.704552
$248$	1.52187e8	0.633572
$249$	−9.85957e7	−0.404725
$250$	−6.77659e8	−2.74297
$251$	3.39690e8	1.35589	0.677945	−	0.735113i	$-0.262871\pi$
$251$	3.39690e8	1.35589	0.677945	+	0.735113i	$0.262871\pi$
$252$	7.11730e7	0.280165
$253$	−6.76772e7	−0.262737
$254$	−1.95599e8	−0.748942
$255$	−8.24517e7	−0.311393
$256$	−3.93040e8	−1.46419
$257$	6.05398e7	0.222472	0.111236	−	0.993794i	$-0.464519\pi$
$257$	6.05398e7	0.222472	0.111236	+	0.993794i	$0.464519\pi$
$258$	2.76054e8	1.00075
$259$	−2.17065e7	−0.0776320
$260$	−7.15889e8	−2.52603
$261$	1.54854e8	0.539116
$262$	−5.11376e8	−1.75665
$263$	2.95228e8	1.00072	0.500360	−	0.865817i	$-0.333201\pi$
$263$	2.95228e8	1.00072	0.500360	+	0.865817i	$0.333201\pi$
$264$	−4.69389e7	−0.157007
$265$	5.78778e8	1.91052
$266$	−1.04790e8	−0.341377
$267$	1.73174e8	0.556793
$268$	−8.26181e8	−2.62182
$269$	−5.14170e8	−1.61055	−0.805275	−	0.592902i	$-0.797982\pi$
$269$	−5.14170e8	−1.61055	−0.805275	+	0.592902i	$0.797982\pi$
$270$	−8.98840e8	−2.77913
$271$	5.70046e8	1.73987	0.869936	−	0.493164i	$-0.164160\pi$
$271$	5.70046e8	1.73987	0.869936	+	0.493164i	$0.164160\pi$
$272$	3.31264e7	0.0998120
$273$	−4.04225e7	−0.120241
$274$	6.60353e8	1.93932
$275$	−1.43993e8	−0.417519
$276$	−4.44984e8	−1.27398
$277$	−1.24927e8	−0.353165	−0.176582	−	0.984286i	$-0.556504\pi$
$277$	−1.24927e8	−0.353165	−0.176582	+	0.984286i	$0.556504\pi$
$278$	−6.56331e8	−1.83217
$279$	1.19925e8	0.330593
$280$	1.93384e8	0.526463
$281$	2.78003e8	0.747442	0.373721	−	0.927541i	$-0.378082\pi$
$281$	2.78003e8	0.747442	0.373721	+	0.927541i	$0.378082\pi$
$282$	−5.96683e8	−1.58443
$283$	−4.70426e8	−1.23378	−0.616892	−	0.787048i	$-0.711608\pi$
$283$	−4.70426e8	−1.23378	−0.616892	+	0.787048i	$0.711608\pi$
$284$	1.12288e9	2.90884
$285$	3.33234e8	0.852691
$286$	−1.16995e8	−0.295723
$287$	−1.36096e8	−0.339827
$288$	−1.89249e8	−0.466831
$289$	−3.71528e8	−0.905418
$290$	9.78187e8	2.35521
$291$	4.13876e7	0.0984567
$292$	3.19390e8	0.750726
$293$	−6.90679e8	−1.60413	−0.802065	−	0.597236i	$-0.796266\pi$
$293$	−6.90679e8	−1.60413	−0.802065	+	0.597236i	$0.796266\pi$
$294$	−4.00198e8	−0.918459
$295$	7.83108e8	1.77601
$296$	−1.77682e8	−0.398219
$297$	−9.35709e7	−0.207249
$298$	1.09662e9	2.40050
$299$	−4.77073e8	−1.03213
$300$	−9.46768e8	−2.02451
$301$	−1.18397e8	−0.250241
$302$	1.38638e9	2.89639
$303$	−4.59579e8	−0.949099
$304$	−1.33882e8	−0.273316
$305$	−1.00102e9	−2.02020
$306$	1.67246e8	0.333680
$307$	−1.58743e8	−0.313119	−0.156560	−	0.987669i	$-0.550040\pi$
$307$	−1.58743e8	−0.313119	−0.156560	+	0.987669i	$0.550040\pi$
$308$	4.68028e7	0.0912734
$309$	2.37820e8	0.458556
$310$	7.57541e8	1.44424
$311$	−7.06563e8	−1.33196	−0.665978	−	0.745971i	$-0.731986\pi$
$311$	−7.06563e8	−1.33196	−0.665978	+	0.745971i	$0.731986\pi$
$312$	−3.30884e8	−0.616786
$313$	2.27028e8	0.418479	0.209240	−	0.977864i	$-0.432901\pi$
$313$	2.27028e8	0.418479	0.209240	+	0.977864i	$0.432901\pi$
$314$	1.13029e9	2.06033
$315$	1.52388e8	0.274704
$316$	−3.55630e8	−0.634006
$317$	−8.63213e8	−1.52199	−0.760993	−	0.648760i	$-0.775288\pi$
$317$	−8.63213e8	−1.52199	−0.760993	+	0.648760i	$0.775288\pi$
$318$	6.21920e8	1.08453
$319$	1.01831e8	0.175636
$320$	−1.52278e9	−2.59784
$321$	1.63317e8	0.275591
$322$	2.99608e8	0.500100
$323$	−1.56855e8	−0.258994
$324$	8.70548e7	0.142195
$325$	−1.01504e9	−1.64018
$326$	−7.21771e8	−1.15382
$327$	8.75162e7	0.138411
$328$	−1.11403e9	−1.74317
$329$	2.55912e8	0.396191
$330$	−2.33648e8	−0.357901
$331$	7.70507e8	1.16783	0.583914	−	0.811816i	$-0.301521\pi$
$331$	7.70507e8	1.16783	0.583914	+	0.811816i	$0.301521\pi$
$332$	8.04729e8	1.20689
$333$	−1.40015e8	−0.207787
$334$	5.59196e8	0.821205
$335$	−1.76894e9	−2.57072
$336$	3.24335e7	0.0466451
$337$	−7.23257e8	−1.02941	−0.514704	−	0.857368i	$-0.672098\pi$
$337$	−7.23257e8	−1.02941	−0.514704	+	0.857368i	$0.672098\pi$
$338$	3.53572e8	0.498046
$339$	−6.38890e8	−0.890691
$340$	6.72963e8	0.928571
$341$	7.88614e7	0.107702
$342$	−6.75933e8	−0.913719
$343$	3.54170e8	0.473896
$344$	−9.69156e8	−1.28363
$345$	−9.52756e8	−1.24915
$346$	−6.44241e8	−0.836145
$347$	7.95216e8	1.02172	0.510860	−	0.859664i	$-0.329327\pi$
$347$	7.95216e8	1.02172	0.510860	+	0.859664i	$0.329327\pi$
$348$	6.69549e8	0.851638
$349$	8.44336e7	0.106323	0.0531614	−	0.998586i	$-0.483070\pi$
$349$	8.44336e7	0.106323	0.0531614	+	0.998586i	$0.483070\pi$
$350$	6.37458e8	0.794718
$351$	−6.59605e8	−0.814158
$352$	−1.24448e8	−0.152086
$353$	1.01999e9	1.23420	0.617100	−	0.786885i	$-0.288307\pi$
$353$	1.01999e9	1.23420	0.617100	+	0.786885i	$0.288307\pi$
$354$	8.41480e8	1.00817
$355$	2.40420e9	2.85214
$356$	−1.41343e9	−1.66035
$357$	3.79987e7	0.0442008
$358$	−2.42887e9	−2.79778
$359$	−2.05562e8	−0.234483	−0.117242	−	0.993103i	$-0.537405\pi$
$359$	−2.05562e8	−0.234483	−0.117242	+	0.993103i	$0.537405\pi$
$360$	1.24740e9	1.40911
$361$	−2.59933e8	−0.290795
$362$	7.62444e8	0.844750
$363$	5.11964e8	0.561780
$364$	3.29925e8	0.358558
$365$	6.83846e8	0.736094
$366$	−1.07564e9	−1.14679
$367$	−1.32967e9	−1.40415	−0.702074	−	0.712104i	$-0.747742\pi$
$367$	−1.32967e9	−1.40415	−0.702074	+	0.712104i	$0.747742\pi$
$368$	3.82786e8	0.400395
$369$	−8.77867e8	−0.909571
$370$	−8.84448e8	−0.907750
$371$	−2.66736e8	−0.271189
$372$	5.18522e8	0.522236
$373$	−7.80807e8	−0.779045	−0.389523	−	0.921017i	$-0.627360\pi$
$373$	−7.80807e8	−0.779045	−0.389523	+	0.921017i	$0.627360\pi$
$374$	1.09979e8	0.108708
$375$	−9.93136e8	−0.972521
$376$	2.09480e9	2.03229
$377$	7.17832e8	0.689967
$378$	4.14239e8	0.394485
$379$	8.35441e8	0.788276	0.394138	−	0.919051i	$-0.371043\pi$
$379$	8.35441e8	0.788276	0.394138	+	0.919051i	$0.371043\pi$
$380$	−2.71982e9	−2.54272
$381$	−2.86658e8	−0.265538
$382$	2.54102e9	2.33231
$383$	−1.30231e9	−1.18445	−0.592226	−	0.805772i	$-0.701751\pi$
$383$	−1.30231e9	−1.18445	−0.592226	+	0.805772i	$0.701751\pi$
$384$	−1.16999e9	−1.05444
$385$	1.00209e8	0.0894944
$386$	1.81490e9	1.60619
$387$	−7.63703e8	−0.669786
$388$	−3.37802e8	−0.293597
$389$	1.61859e9	1.39417	0.697083	−	0.716990i	$-0.254481\pi$
$389$	1.61859e9	1.39417	0.697083	+	0.716990i	$0.254481\pi$
$390$	−1.64704e9	−1.40598
$391$	4.48467e8	0.379413
$392$	1.40499e9	1.17808
$393$	−7.49442e8	−0.622822
$394$	−1.89774e9	−1.56315
$395$	−7.61439e8	−0.621649
$396$	3.01895e8	0.244299
$397$	−5.33898e8	−0.428245	−0.214122	−	0.976807i	$-0.568689\pi$
$397$	−5.33898e8	−0.428245	−0.214122	+	0.976807i	$0.568689\pi$
$398$	1.18973e9	0.945924
$399$	−1.53574e8	−0.121035
$400$	8.14431e8	0.636274
$401$	1.27544e9	0.987771	0.493886	−	0.869527i	$-0.335576\pi$
$401$	1.27544e9	0.987771	0.493886	+	0.869527i	$0.335576\pi$
$402$	−1.90079e9	−1.45930
$403$	5.55913e8	0.423097
$404$	3.75104e9	2.83020
$405$	1.86393e8	0.139424
$406$	−4.50807e8	−0.334310
$407$	−9.20726e7	−0.0676940
$408$	3.11044e8	0.226731
$409$	2.31006e9	1.66952	0.834758	−	0.550616i	$-0.185607\pi$
$409$	2.31006e9	1.66952	0.834758	+	0.550616i	$0.185607\pi$
$410$	−5.54532e9	−3.97359
$411$	9.67774e8	0.687587
$412$	−1.94106e9	−1.36741
$413$	−3.60903e8	−0.252096
$414$	1.93258e9	1.33855
$415$	1.72300e9	1.18336
$416$	−8.77268e8	−0.597456
$417$	−9.61879e8	−0.649597
$418$	−4.44488e8	−0.297676
$419$	−2.01419e9	−1.33767	−0.668837	−	0.743409i	$-0.733208\pi$
$419$	−2.01419e9	−1.33767	−0.668837	+	0.743409i	$0.733208\pi$
$420$	6.58887e8	0.433949
$421$	−1.12669e9	−0.735896	−0.367948	−	0.929846i	$-0.619940\pi$
$421$	−1.12669e9	−0.735896	−0.367948	+	0.929846i	$0.619940\pi$
$422$	1.18063e9	0.764750
$423$	1.65072e9	1.06043
$424$	−2.18340e9	−1.39108
$425$	9.54178e8	0.602932
$426$	2.58341e9	1.61905
$427$	4.61332e8	0.286758
$428$	−1.33298e9	−0.821808
$429$	−1.71460e8	−0.104849
$430$	−4.82417e9	−2.92606
$431$	−8.75815e7	−0.0526917	−0.0263458	−	0.999653i	$-0.508387\pi$
$431$	−8.75815e7	−0.0526917	−0.0263458	+	0.999653i	$0.508387\pi$
$432$	5.29242e8	0.315836
$433$	−1.08500e9	−0.642278	−0.321139	−	0.947032i	$-0.604066\pi$
$433$	−1.08500e9	−0.642278	−0.321139	+	0.947032i	$0.604066\pi$
$434$	−3.49120e8	−0.205003
$435$	1.43357e9	0.835039
$436$	−7.14299e8	−0.412741
$437$	−1.81251e9	−1.03895
$438$	7.34819e8	0.417851
$439$	−1.29604e9	−0.731127	−0.365563	−	0.930786i	$-0.619124\pi$
$439$	−1.29604e9	−0.731127	−0.365563	+	0.930786i	$0.619124\pi$
$440$	8.20279e8	0.459068
$441$	1.10715e9	0.614711
$442$	7.75272e8	0.427047
$443$	−3.50559e9	−1.91579	−0.957896	−	0.287114i	$-0.907304\pi$
$443$	−3.50559e9	−1.91579	−0.957896	+	0.287114i	$0.907304\pi$
$444$	−6.05387e8	−0.328241
$445$	−3.02630e9	−1.62799
$446$	−4.19842e9	−2.24085
$447$	1.60715e9	0.851097
$448$	7.01788e8	0.368751
$449$	4.60817e8	0.240252	0.120126	−	0.992759i	$-0.461670\pi$
$449$	4.60817e8	0.240252	0.120126	+	0.992759i	$0.461670\pi$
$450$	4.11183e9	2.12712
$451$	−5.77278e8	−0.296324
$452$	5.21456e9	2.65603
$453$	2.03179e9	1.02692
$454$	4.35714e9	2.18527
$455$	7.06401e8	0.351570
$456$	−1.25710e9	−0.620860
$457$	2.08323e9	1.02101	0.510506	−	0.859874i	$-0.329458\pi$
$457$	2.08323e9	1.02101	0.510506	+	0.859874i	$0.329458\pi$
$458$	−3.48065e7	−0.0169290
$459$	6.20054e8	0.299285
$460$	7.77630e9	3.72495
$461$	−2.91226e9	−1.38445	−0.692224	−	0.721683i	$-0.743369\pi$
$461$	−2.91226e9	−1.38445	−0.692224	+	0.721683i	$0.743369\pi$
$462$	1.07679e8	0.0508024
$463$	−1.02719e9	−0.480967	−0.240484	−	0.970653i	$-0.577306\pi$
$463$	−1.02719e9	−0.480967	−0.240484	+	0.970653i	$0.577306\pi$
$464$	−5.75961e8	−0.267658
$465$	1.11021e9	0.512057
$466$	−2.85315e9	−1.30609
$467$	1.33615e9	0.607078	0.303539	−	0.952819i	$-0.401832\pi$
$467$	1.33615e9	0.607078	0.303539	+	0.952819i	$0.401832\pi$
$468$	2.12813e9	0.959706
$469$	8.15231e8	0.364902
$470$	1.04273e10	4.63265
$471$	1.65649e9	0.730490
$472$	−2.95422e9	−1.29314
$473$	−5.02205e8	−0.218206
$474$	−8.18196e8	−0.352885
$475$	−3.85637e9	−1.65101
$476$	−3.10142e8	−0.131806
$477$	−1.72054e9	−0.725856
$478$	8.04052e8	0.336733
$479$	8.29420e8	0.344826	0.172413	−	0.985025i	$-0.444844\pi$
$479$	8.29420e8	0.344826	0.172413	+	0.985025i	$0.444844\pi$
$480$	−1.75198e9	−0.723077
$481$	−6.49043e8	−0.265929
$482$	−4.90244e9	−1.99410
$483$	4.39087e8	0.177311
$484$	−4.17860e9	−1.67522
$485$	−7.23268e8	−0.287874
$486$	4.28776e9	1.69435
$487$	−2.54015e9	−0.996569	−0.498284	−	0.867014i	$-0.666036\pi$
$487$	−2.54015e9	−0.996569	−0.498284	+	0.867014i	$0.666036\pi$
$488$	3.77630e9	1.47095
$489$	−1.05778e9	−0.409088
$490$	6.99365e9	2.68545
$491$	2.92154e9	1.11385	0.556924	−	0.830563i	$-0.311981\pi$
$491$	2.92154e9	1.11385	0.556924	+	0.830563i	$0.311981\pi$
$492$	−3.79566e9	−1.43684
$493$	−6.74790e8	−0.253632
$494$	−3.13331e9	−1.16939
$495$	6.46387e8	0.239538
$496$	−4.46044e8	−0.164131
$497$	−1.10800e9	−0.404848
$498$	1.85144e9	0.671748
$499$	1.76525e9	0.635997	0.317998	−	0.948091i	$-0.396989\pi$
$499$	1.76525e9	0.635997	0.317998	+	0.948091i	$0.396989\pi$
$500$	8.10588e9	2.90005
$501$	8.19524e8	0.291159
$502$	−6.37871e9	−2.25045
$503$	−2.83197e9	−0.992202	−0.496101	−	0.868265i	$-0.665235\pi$
$503$	−2.83197e9	−0.992202	−0.496101	+	0.868265i	$0.665235\pi$
$504$	−5.74875e8	−0.200017
$505$	8.03136e9	2.77504
$506$	1.27085e9	0.436080
$507$	5.18174e8	0.176582
$508$	2.33968e9	0.791831
$509$	1.56587e8	0.0526311	0.0263155	−	0.999654i	$-0.491623\pi$
$509$	1.56587e8	0.0526311	0.0263155	+	0.999654i	$0.491623\pi$
$510$	1.54828e9	0.516839
$511$	−3.15157e8	−0.104485
$512$	1.93872e9	0.638366
$513$	−2.50598e9	−0.819535
$514$	−1.13682e9	−0.369250
$515$	−4.15600e9	−1.34076
$516$	−3.30205e9	−1.05806
$517$	1.08550e9	0.345473
$518$	4.07606e8	0.128851
$519$	−9.44160e8	−0.296456
$520$	5.78235e9	1.80340
$521$	−2.60591e9	−0.807287	−0.403644	−	0.914916i	$-0.632256\pi$
$521$	−2.60591e9	−0.807287	−0.403644	+	0.914916i	$0.632256\pi$
$522$	−2.90787e9	−0.894804
$523$	2.39107e8	0.0730864	0.0365432	−	0.999332i	$-0.488365\pi$
$523$	2.39107e8	0.0730864	0.0365432	+	0.999332i	$0.488365\pi$
$524$	6.11687e9	1.85725
$525$	9.34220e8	0.281768
$526$	−5.54381e9	−1.66096
$527$	−5.22580e8	−0.155531
$528$	1.37573e8	0.0406738
$529$	1.77735e9	0.522011
$530$	−1.08683e10	−3.17101
$531$	−2.32795e9	−0.674751
$532$	1.25346e9	0.360926
$533$	−4.06938e9	−1.16408
$534$	−3.25187e9	−0.924143
$535$	−2.85404e9	−0.805791
$536$	6.67319e9	1.87179
$537$	−3.55961e9	−0.991955
$538$	9.65512e9	2.67313
$539$	7.28052e8	0.200263
$540$	1.07516e10	2.93828
$541$	−5.93601e9	−1.61177	−0.805887	−	0.592069i	$-0.798311\pi$
$541$	−5.93601e9	−1.61177	−0.805887	+	0.592069i	$0.798311\pi$
$542$	−1.07044e10	−2.88777
$543$	1.11739e9	0.299507
$544$	8.24666e8	0.219625
$545$	−1.52938e9	−0.404696
$546$	7.59056e8	0.199572
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	−7.89888e9	−2.05038
$549$	2.97576e9	0.767528
$550$	2.70391e9	0.692982
$551$	2.72720e9	0.694524
$552$	3.59421e9	0.909529
$553$	3.50917e8	0.0882401
$554$	2.34589e9	0.586170
$555$	−1.29619e9	−0.321843
$556$	7.85077e9	1.93709
$557$	3.30704e8	0.0810861	0.0405430	−	0.999178i	$-0.487091\pi$
$557$	3.30704e8	0.0810861	0.0405430	+	0.999178i	$0.487091\pi$
$558$	−2.25195e9	−0.548705
$559$	−3.54017e9	−0.857201
$560$	−5.66790e8	−0.136384
$561$	1.61179e8	0.0385424
$562$	−5.22036e9	−1.24058
$563$	1.52349e9	0.359800	0.179900	−	0.983685i	$-0.442423\pi$
$563$	1.52349e9	0.359800	0.179900	+	0.983685i	$0.442423\pi$
$564$	7.13729e9	1.67516
$565$	1.11649e10	2.60426
$566$	8.83369e9	2.04779
$567$	−8.59011e7	−0.0197905
$568$	−9.06968e9	−2.07670
$569$	2.45494e9	0.558660	0.279330	−	0.960195i	$-0.409888\pi$
$569$	2.45494e9	0.558660	0.279330	+	0.960195i	$0.409888\pi$
$570$	−6.25748e9	−1.41526
$571$	6.49147e9	1.45921	0.729604	−	0.683870i	$-0.239705\pi$
$571$	6.49147e9	1.45921	0.729604	+	0.683870i	$0.239705\pi$
$572$	1.39944e9	0.312657
$573$	3.72396e9	0.826920
$574$	2.55562e9	0.564032
$575$	1.10258e10	2.41865
$576$	4.52678e9	0.986986
$577$	7.51580e9	1.62877	0.814385	−	0.580325i	$-0.197075\pi$
$577$	7.51580e9	1.62877	0.814385	+	0.580325i	$0.197075\pi$
$578$	6.97658e9	1.50278
$579$	2.65981e9	0.569475
$580$	−1.17007e10	−2.49008
$581$	−7.94063e8	−0.167973
$582$	−7.77180e8	−0.163415
$583$	−1.13141e9	−0.236473
$584$	−2.57976e9	−0.535963
$585$	4.55654e9	0.941000
$586$	1.29696e10	2.66248
$587$	−6.11190e9	−1.24722	−0.623610	−	0.781736i	$-0.714334\pi$
$587$	−6.11190e9	−1.24722	−0.623610	+	0.781736i	$0.714334\pi$
$588$	4.78701e9	0.971055
$589$	2.11204e9	0.425891
$590$	−1.47052e10	−2.94775
$591$	−2.78121e9	−0.554214
$592$	5.20768e8	0.103162
$593$	−7.39300e9	−1.45589	−0.727946	−	0.685634i	$-0.759525\pi$
$593$	−7.39300e9	−1.45589	−0.727946	+	0.685634i	$0.759525\pi$
$594$	1.75708e9	0.343985
$595$	−6.64044e8	−0.129237
$596$	−1.31174e10	−2.53796
$597$	1.74359e9	0.335378
$598$	8.95851e9	1.71310
$599$	4.15758e9	0.790400	0.395200	−	0.918595i	$-0.370675\pi$
$599$	4.15758e9	0.790400	0.395200	+	0.918595i	$0.370675\pi$
$600$	7.64719e9	1.44535
$601$	−1.54367e9	−0.290064	−0.145032	−	0.989427i	$-0.546329\pi$
$601$	−1.54367e9	−0.290064	−0.145032	+	0.989427i	$0.546329\pi$
$602$	2.22327e9	0.415340
$603$	5.25854e9	0.976684
$604$	−1.65833e10	−3.06226
$605$	−8.94680e9	−1.64257
$606$	8.63001e9	1.57528
$607$	−7.11088e9	−1.29052	−0.645258	−	0.763965i	$-0.723250\pi$
$607$	−7.11088e9	−1.29052	−0.645258	+	0.763965i	$0.723250\pi$
$608$	−3.33294e9	−0.601401
$609$	−6.60675e8	−0.118530
$610$	1.87973e10	3.35306
$611$	7.65198e9	1.35715
$612$	−2.00053e9	−0.352788
$613$	−1.08906e10	−1.90958	−0.954791	−	0.297277i	$-0.903922\pi$
$613$	−1.08906e10	−1.90958	−0.954791	+	0.297277i	$0.903922\pi$
$614$	2.98088e9	0.519703
$615$	−8.12689e9	−1.40884
$616$	−3.78033e8	−0.0651625
$617$	5.99636e9	1.02776	0.513878	−	0.857863i	$-0.328208\pi$
$617$	5.99636e9	1.02776	0.513878	+	0.857863i	$0.328208\pi$
$618$	−4.46579e9	−0.761095
$619$	3.22215e9	0.546045	0.273022	−	0.962008i	$-0.411977\pi$
$619$	3.22215e9	0.546045	0.273022	+	0.962008i	$0.411977\pi$
$620$	−9.06140e9	−1.52695
$621$	7.16492e9	1.20058
$622$	1.32679e10	2.21073
$623$	1.39470e9	0.231085
$624$	9.69788e8	0.159783
$625$	5.38961e9	0.883033
$626$	−4.26314e9	−0.694576
$627$	−6.51415e8	−0.105541
$628$	−1.35201e10	−2.17831
$629$	6.10125e8	0.0977556
$630$	−2.86156e9	−0.455943
$631$	−5.66566e9	−0.897734	−0.448867	−	0.893599i	$-0.648172\pi$
$631$	−5.66566e9	−0.897734	−0.448867	+	0.893599i	$0.648172\pi$
$632$	2.87248e9	0.452634
$633$	1.73026e9	0.271143
$634$	1.62095e10	2.52613
$635$	5.00948e9	0.776398
$636$	−7.43916e9	−1.14663
$637$	5.13222e9	0.786714
$638$	−1.91219e9	−0.291513
$639$	−7.14699e9	−1.08360
$640$	2.04461e10	3.08305
$641$	−8.63899e9	−1.29557	−0.647784	−	0.761824i	$-0.724304\pi$
$641$	−8.63899e9	−1.29557	−0.647784	+	0.761824i	$0.724304\pi$
$642$	−3.06678e9	−0.457415
$643$	8.88514e9	1.31803	0.659016	−	0.752129i	$-0.270973\pi$
$643$	8.88514e9	1.31803	0.659016	+	0.752129i	$0.270973\pi$
$644$	−3.58379e9	−0.528739
$645$	−7.07002e9	−1.03744
$646$	2.94543e9	0.429868
$647$	−8.91742e9	−1.29442	−0.647208	−	0.762313i	$-0.724064\pi$
$647$	−8.91742e9	−1.29442	−0.647208	+	0.762313i	$0.724064\pi$
$648$	−7.03155e8	−0.101517
$649$	−1.53084e9	−0.219824
$650$	1.90605e10	2.72231
$651$	−5.11649e8	−0.0726840
$652$	8.63354e9	1.21989
$653$	−1.38012e9	−0.193964	−0.0969822	−	0.995286i	$-0.530919\pi$
$653$	−1.38012e9	−0.193964	−0.0969822	+	0.995286i	$0.530919\pi$
$654$	−1.64338e9	−0.229730
$655$	1.30968e10	1.82105
$656$	3.26512e9	0.451580
$657$	−2.03288e9	−0.279661
$658$	−4.80553e9	−0.657583
$659$	1.52499e9	0.207572	0.103786	−	0.994600i	$-0.466904\pi$
$659$	1.52499e9	0.207572	0.103786	+	0.994600i	$0.466904\pi$
$660$	2.79480e9	0.378397
$661$	−6.90962e9	−0.930570	−0.465285	−	0.885161i	$-0.654048\pi$
$661$	−6.90962e9	−0.930570	−0.465285	+	0.885161i	$0.654048\pi$
$662$	−1.44686e10	−1.93832
$663$	1.13619e9	0.151410
$664$	−6.49992e9	−0.861628
$665$	2.68377e9	0.353892
$666$	2.62921e9	0.344878
$667$	−7.79741e9	−1.01744
$668$	−6.68888e9	−0.868232
$669$	−6.15294e9	−0.794496
$670$	3.32172e10	4.26679
$671$	1.95683e9	0.250049
$672$	8.07416e8	0.102637
$673$	−1.04926e10	−1.32687	−0.663435	−	0.748234i	$-0.730902\pi$
$673$	−1.04926e10	−1.32687	−0.663435	+	0.748234i	$0.730902\pi$
$674$	1.35814e10	1.70857
$675$	1.52444e10	1.90786
$676$	−4.22929e9	−0.526567
$677$	−1.13364e9	−0.140415	−0.0702074	−	0.997532i	$-0.522366\pi$
$677$	−1.13364e9	−0.140415	−0.0702074	+	0.997532i	$0.522366\pi$
$678$	1.19971e10	1.47834
$679$	3.33325e8	0.0408624
$680$	−5.43563e9	−0.662931
$681$	6.38556e9	0.774790
$682$	−1.48086e9	−0.178760
$683$	−8.11059e9	−0.974047	−0.487024	−	0.873389i	$-0.661917\pi$
$683$	−8.11059e9	−0.974047	−0.487024	+	0.873389i	$0.661917\pi$
$684$	8.08525e9	0.966044
$685$	−1.69123e10	−2.01041
$686$	−6.65063e9	−0.786554
$687$	−5.10103e7	−0.00600219
$688$	2.84050e9	0.332533
$689$	−7.97562e9	−0.928960
$690$	1.78909e10	2.07329
$691$	−1.10876e10	−1.27839	−0.639196	−	0.769044i	$-0.720733\pi$
$691$	−1.10876e10	−1.27839	−0.639196	+	0.769044i	$0.720733\pi$
$692$	7.70615e9	0.884028
$693$	−2.97894e8	−0.0340013
$694$	−1.49326e10	−1.69581
$695$	1.68093e10	1.89934
$696$	−5.40805e9	−0.608007
$697$	3.82537e9	0.427916
$698$	−1.58550e9	−0.176470
$699$	−4.18141e9	−0.463077
$700$	−7.62501e9	−0.840229
$701$	−8.70330e8	−0.0954270	−0.0477135	−	0.998861i	$-0.515193\pi$
$701$	−8.70330e8	−0.0954270	−0.0477135	+	0.998861i	$0.515193\pi$
$702$	1.23861e10	1.35131
$703$	−2.46586e9	−0.267685
$704$	2.97678e9	0.321545
$705$	1.52816e10	1.64251
$706$	−1.91535e10	−2.04848
$707$	−3.70133e9	−0.393904
$708$	−1.00654e10	−1.06590
$709$	−1.17853e10	−1.24188	−0.620940	−	0.783858i	$-0.713249\pi$
$709$	−1.17853e10	−1.24188	−0.620940	+	0.783858i	$0.713249\pi$
$710$	−4.51462e10	−4.73388
$711$	2.26354e9	0.236181
$712$	1.14165e10	1.18537
$713$	−6.03858e9	−0.623909
$714$	−7.13542e8	−0.0733628
$715$	2.99634e9	0.306564
$716$	2.90532e10	2.95800
$717$	1.17837e9	0.119389
$718$	3.86005e9	0.389186
$719$	−2.35448e8	−0.0236235	−0.0118117	−	0.999930i	$-0.503760\pi$
$719$	−2.35448e8	−0.0236235	−0.0118117	+	0.999930i	$0.503760\pi$
$720$	−3.65600e9	−0.365041
$721$	1.91533e9	0.190314
$722$	4.88104e9	0.482650
$723$	−7.18472e9	−0.707010
$724$	−9.12006e9	−0.893126
$725$	−1.65901e10	−1.61684
$726$	−9.61369e9	−0.932421
$727$	−1.64830e10	−1.59099	−0.795493	−	0.605962i	$-0.792788\pi$
$727$	−1.64830e10	−1.59099	−0.795493	+	0.605962i	$0.792788\pi$
$728$	−2.66485e9	−0.255984
$729$	5.43626e9	0.519701
$730$	−1.28413e10	−1.22174
$731$	3.32790e9	0.315108
$732$	1.28664e10	1.21246
$733$	2.57748e9	0.241730	0.120865	−	0.992669i	$-0.461433\pi$
$733$	2.57748e9	0.241730	0.120865	+	0.992669i	$0.461433\pi$
$734$	2.49686e10	2.33055
$735$	1.02495e10	0.952129
$736$	9.52927e9	0.881023
$737$	3.45797e9	0.318189
$738$	1.64846e10	1.50967
$739$	−4.24404e9	−0.386833	−0.193417	−	0.981117i	$-0.561957\pi$
$739$	−4.24404e9	−0.386833	−0.193417	+	0.981117i	$0.561957\pi$
$740$	1.05794e10	0.959733
$741$	−4.59199e9	−0.414607
$742$	5.00878e9	0.450110
$743$	−1.14691e10	−1.02581	−0.512906	−	0.858445i	$-0.671431\pi$
$743$	−1.14691e10	−1.02581	−0.512906	+	0.858445i	$0.671431\pi$
$744$	−4.18818e9	−0.372838
$745$	−2.80856e10	−2.48850
$746$	1.46620e10	1.29303
$747$	−5.12199e9	−0.449590
$748$	−1.31553e9	−0.114933
$749$	1.31531e9	0.114378
$750$	1.86492e10	1.61415
$751$	4.99744e9	0.430535	0.215267	−	0.976555i	$-0.430938\pi$
$751$	4.99744e9	0.430535	0.215267	+	0.976555i	$0.430938\pi$
$752$	−6.13966e9	−0.526480
$753$	−9.34826e9	−0.797900
$754$	−1.34795e10	−1.14518
$755$	−3.55065e10	−3.00257
$756$	−4.95497e9	−0.417075
$757$	−8.81443e9	−0.738514	−0.369257	−	0.929327i	$-0.620388\pi$
$757$	−8.81443e9	−0.738514	−0.369257	+	0.929327i	$0.620388\pi$
$758$	−1.56880e10	−1.30835
$759$	1.86248e9	0.154612
$760$	2.19684e10	1.81531
$761$	−7.11941e9	−0.585596	−0.292798	−	0.956174i	$-0.594586\pi$
$761$	−7.11941e9	−0.585596	−0.292798	+	0.956174i	$0.594586\pi$
$762$	5.38288e9	0.440730
$763$	7.04832e8	0.0574447
$764$	−3.03946e10	−2.46587
$765$	−4.28332e9	−0.345912
$766$	2.44548e10	1.96591
$767$	−1.07913e10	−0.863554
$768$	1.08165e10	0.861631
$769$	−6.41496e9	−0.508689	−0.254344	−	0.967114i	$-0.581860\pi$
$769$	−6.41496e9	−0.508689	−0.254344	+	0.967114i	$0.581860\pi$
$770$	−1.88174e9	−0.148539
$771$	−1.66605e9	−0.130918
$772$	−2.17091e10	−1.69817
$773$	−3.87431e9	−0.301694	−0.150847	−	0.988557i	$-0.548200\pi$
$773$	−3.87431e9	−0.301694	−0.150847	+	0.988557i	$0.548200\pi$
$774$	1.43409e10	1.11169
$775$	−1.28479e10	−0.991465
$776$	2.72848e9	0.209606
$777$	5.97363e8	0.0456841
$778$	−3.03941e10	−2.31398
$779$	−1.54605e10	−1.17177
$780$	1.97013e10	1.48649
$781$	−4.69980e9	−0.353021
$782$	−8.42135e9	−0.629735
$783$	−1.07807e10	−0.802570
$784$	−4.11790e9	−0.305189
$785$	−2.89478e10	−2.13586
$786$	1.40731e10	1.03374
$787$	6.99897e9	0.511826	0.255913	−	0.966700i	$-0.417624\pi$
$787$	6.99897e9	0.511826	0.255913	+	0.966700i	$0.417624\pi$
$788$	2.27000e10	1.65266
$789$	−8.12468e9	−0.588893
$790$	1.42984e10	1.03179
$791$	−5.14545e9	−0.369663
$792$	−2.43845e9	−0.174412
$793$	1.37942e10	0.982292
$794$	1.00256e10	0.710784
$795$	−1.59280e10	−1.12428
$796$	−1.42310e10	−1.00009
$797$	−1.19054e10	−0.832993	−0.416496	−	0.909137i	$-0.636742\pi$
$797$	−1.19054e10	−0.832993	−0.416496	+	0.909137i	$0.636742\pi$
$798$	2.88382e9	0.200890
$799$	−7.19315e9	−0.498891
$800$	2.02749e10	1.40005
$801$	8.99630e9	0.618515
$802$	−2.39504e10	−1.63947
$803$	−1.33680e9	−0.0911093
$804$	2.27365e10	1.54286
$805$	−7.67324e9	−0.518434
$806$	−1.04390e10	−0.702240
$807$	1.41500e10	0.947759
$808$	−3.02978e10	−2.02056
$809$	1.71071e10	1.13594	0.567970	−	0.823049i	$-0.307729\pi$
$809$	1.71071e10	1.13594	0.567970	+	0.823049i	$0.307729\pi$
$810$	−3.50010e9	−0.231410
$811$	4.48123e9	0.295001	0.147501	−	0.989062i	$-0.452877\pi$
$811$	4.48123e9	0.295001	0.147501	+	0.989062i	$0.452877\pi$
$812$	5.39237e9	0.353455
$813$	−1.56877e10	−1.02386
$814$	1.72895e9	0.112356
$815$	1.84853e10	1.19612
$816$	−9.11638e8	−0.0587363
$817$	−1.34499e10	−0.862862
$818$	−4.33784e10	−2.77100
$819$	−2.09993e9	−0.133570
$820$	6.63309e10	4.20115
$821$	−1.79535e10	−1.13227	−0.566134	−	0.824314i	$-0.691561\pi$
$821$	−1.79535e10	−1.13227	−0.566134	+	0.824314i	$0.691561\pi$
$822$	−1.81729e10	−1.14123
$823$	−4.03228e9	−0.252146	−0.126073	−	0.992021i	$-0.540237\pi$
$823$	−4.03228e9	−0.252146	−0.126073	+	0.992021i	$0.540237\pi$
$824$	1.56782e10	0.976230
$825$	3.96268e9	0.245697
$826$	6.77706e9	0.418419
$827$	1.64636e10	1.01217	0.506087	−	0.862482i	$-0.331091\pi$
$827$	1.64636e10	1.01217	0.506087	+	0.862482i	$0.331091\pi$
$828$	−2.31167e10	−1.41521
$829$	−3.51870e9	−0.214507	−0.107253	−	0.994232i	$-0.534206\pi$
$829$	−3.51870e9	−0.214507	−0.107253	+	0.994232i	$0.534206\pi$
$830$	−3.23547e10	−1.96410
$831$	3.43799e9	0.207827
$832$	2.09840e10	1.26316
$833$	−4.82448e9	−0.289197
$834$	1.80622e10	1.07818
$835$	−1.43216e10	−0.851310
$836$	5.31679e9	0.314722
$837$	−8.34898e9	−0.492146
$838$	3.78225e10	2.22022
$839$	6.84498e8	0.0400134	0.0200067	−	0.999800i	$-0.493631\pi$
$839$	6.84498e8	0.0400134	0.0200067	+	0.999800i	$0.493631\pi$
$840$	−5.32193e9	−0.309808
$841$	−5.51744e9	−0.319854
$842$	2.11570e10	1.22141
$843$	−7.65064e9	−0.439847
$844$	−1.41222e10	−0.808544
$845$	−9.05532e9	−0.516304
$846$	−3.09974e10	−1.76007
$847$	4.12322e9	0.233155
$848$	6.39933e9	0.360371
$849$	1.29461e10	0.726044
$850$	−1.79176e10	−1.00072
$851$	7.05019e9	0.392146
$852$	−3.09017e10	−1.71176
$853$	2.85698e9	0.157611	0.0788054	−	0.996890i	$-0.474889\pi$
$853$	2.85698e9	0.157611	0.0788054	+	0.996890i	$0.474889\pi$
$854$	−8.66292e9	−0.475951
$855$	1.73113e10	0.947215
$856$	1.07667e10	0.586711
$857$	−9.63967e9	−0.523154	−0.261577	−	0.965183i	$-0.584243\pi$
$857$	−9.63967e9	−0.523154	−0.261577	+	0.965183i	$0.584243\pi$
$858$	3.21969e9	0.174024
$859$	2.07001e10	1.11429	0.557144	−	0.830416i	$-0.311897\pi$
$859$	2.07001e10	1.11429	0.557144	+	0.830416i	$0.311897\pi$
$860$	5.77048e10	3.09362
$861$	3.74536e9	0.199978
$862$	1.64461e9	0.0874556
$863$	−3.29537e10	−1.74529	−0.872643	−	0.488358i	$-0.837596\pi$
$863$	−3.29537e10	−1.74529	−0.872643	+	0.488358i	$0.837596\pi$
$864$	1.31752e10	0.694961
$865$	1.64996e10	0.866798
$866$	2.03742e10	1.06603
$867$	1.02245e10	0.532811
$868$	4.17603e9	0.216743
$869$	1.48848e9	0.0769441
$870$	−2.69197e10	−1.38597
$871$	2.43761e10	1.24997
$872$	5.76950e9	0.294666
$873$	2.15007e9	0.109371
$874$	3.40354e10	1.72441
$875$	−7.99845e9	−0.403625
$876$	−8.78962e9	−0.441779
$877$	−2.54942e10	−1.27627	−0.638136	−	0.769924i	$-0.720294\pi$
$877$	−2.54942e10	−1.27627	−0.638136	+	0.769924i	$0.720294\pi$
$878$	2.43371e10	1.21350
$879$	1.90075e10	0.943982
$880$	−2.40415e9	−0.118925
$881$	−3.31787e10	−1.63472	−0.817361	−	0.576126i	$-0.804564\pi$
$881$	−3.31787e10	−1.63472	−0.817361	+	0.576126i	$0.804564\pi$
$882$	−2.07901e10	−1.02027
$883$	−1.10486e10	−0.540064	−0.270032	−	0.962851i	$-0.587034\pi$
$883$	−1.10486e10	−0.540064	−0.270032	+	0.962851i	$0.587034\pi$
$884$	−9.27349e9	−0.451503
$885$	−2.15511e10	−1.04513
$886$	6.58283e10	3.17976
$887$	3.17540e10	1.52780	0.763898	−	0.645337i	$-0.223283\pi$
$887$	3.17540e10	1.52780	0.763898	+	0.645337i	$0.223283\pi$
$888$	4.88980e9	0.234340
$889$	−2.30867e9	−0.110206
$890$	5.68280e10	2.70207
$891$	−3.64367e8	−0.0172571
$892$	5.02198e10	2.36918
$893$	2.90716e10	1.36612
$894$	−3.01791e10	−1.41262
$895$	6.22057e10	2.90035
$896$	−9.42279e9	−0.437624
$897$	1.31291e10	0.607379
$898$	−8.65325e9	−0.398760
$899$	9.08599e9	0.417074
$900$	−4.91841e10	−2.24893
$901$	7.49739e9	0.341486
$902$	1.08402e10	0.491828
$903$	3.25829e9	0.147259
$904$	−4.21188e10	−1.89621
$905$	−1.95269e10	−0.875718
$906$	−3.81531e10	−1.70444
$907$	−2.54489e10	−1.13251	−0.566257	−	0.824229i	$-0.691609\pi$
$907$	−2.54489e10	−1.13251	−0.566257	+	0.824229i	$0.691609\pi$
$908$	−5.21183e10	−2.31042
$909$	−2.38749e10	−1.05431
$910$	−1.32648e10	−0.583522
$911$	1.09414e10	0.479467	0.239733	−	0.970839i	$-0.422940\pi$
$911$	1.09414e10	0.479467	0.239733	+	0.970839i	$0.422940\pi$
$912$	3.68444e9	0.160838
$913$	−3.36818e9	−0.146470
$914$	−3.91190e10	−1.69464
$915$	2.75482e10	1.18883
$916$	4.16342e8	0.0178985
$917$	−6.03580e9	−0.258489
$918$	−1.16434e10	−0.496742
$919$	−2.48795e10	−1.05739	−0.528697	−	0.848811i	$-0.677319\pi$
$919$	−2.48795e10	−1.05739	−0.528697	+	0.848811i	$0.677319\pi$
$920$	−6.28104e10	−2.65934
$921$	4.36860e9	0.184261
$922$	5.46866e10	2.29785
$923$	−3.31301e10	−1.38681
$924$	−1.28801e9	−0.0537116
$925$	1.50003e10	0.623165
$926$	1.92886e10	0.798291
$927$	1.23546e10	0.509389
$928$	−1.43383e10	−0.588952
$929$	−1.68429e10	−0.689226	−0.344613	−	0.938745i	$-0.611990\pi$
$929$	−1.68429e10	−0.689226	−0.344613	+	0.938745i	$0.611990\pi$
$930$	−2.08475e10	−0.849893
$931$	1.94984e10	0.791910
$932$	3.41283e10	1.38089
$933$	1.94446e10	0.783816
$934$	−2.50902e10	−1.00761
$935$	−2.81668e9	−0.112693
$936$	−1.71892e10	−0.685159
$937$	−2.45264e10	−0.973971	−0.486986	−	0.873410i	$-0.661904\pi$
$937$	−2.45264e10	−0.973971	−0.486986	+	0.873410i	$0.661904\pi$
$938$	−1.53085e10	−0.605650
$939$	−6.24781e9	−0.246262
$940$	−1.24727e11	−4.89795
$941$	2.97899e10	1.16548	0.582740	−	0.812659i	$-0.301981\pi$
$941$	2.97899e10	1.16548	0.582740	+	0.812659i	$0.301981\pi$
$942$	−3.11056e10	−1.21244
$943$	4.42034e10	1.71658
$944$	8.65853e9	0.334998
$945$	−1.06091e10	−0.408946
$946$	9.43044e9	0.362170
$947$	5.10986e10	1.95517	0.977584	−	0.210547i	$-0.0675246\pi$
$947$	5.10986e10	1.95517	0.977584	+	0.210547i	$0.0675246\pi$
$948$	9.78694e9	0.373093
$949$	−9.42345e9	−0.357914
$950$	7.24151e10	2.74029
$951$	2.37556e10	0.895642
$952$	2.50506e9	0.0940999
$953$	−6.04439e9	−0.226218	−0.113109	−	0.993583i	$-0.536081\pi$
$953$	−6.04439e9	−0.226218	−0.113109	+	0.993583i	$0.536081\pi$
$954$	3.23084e10	1.20475
$955$	−6.50779e10	−2.41781
$956$	−9.61774e9	−0.356017
$957$	−2.80239e9	−0.103356
$958$	−1.55749e10	−0.572329
$959$	7.79419e9	0.285369
$960$	4.19069e10	1.52875
$961$	−2.04761e10	−0.744245
$962$	1.21878e10	0.441379
$963$	8.48424e9	0.306141
$964$	5.86410e10	2.10830
$965$	−4.64813e10	−1.66507
$966$	−8.24520e9	−0.294294
$967$	1.58690e10	0.564360	0.282180	−	0.959361i	$-0.408942\pi$
$967$	1.58690e10	0.564360	0.282180	+	0.959361i	$0.408942\pi$
$968$	3.37512e10	1.19598
$969$	4.31665e9	0.152410
$970$	1.35816e10	0.477803
$971$	−3.24388e10	−1.13710	−0.568548	−	0.822650i	$-0.692495\pi$
$971$	−3.24388e10	−1.13710	−0.568548	+	0.822650i	$0.692495\pi$
$972$	−5.12884e10	−1.79138
$973$	−7.74672e9	−0.269602
$974$	4.76990e10	1.65407
$975$	2.79339e10	0.965197
$976$	−1.10680e10	−0.381060
$977$	4.15807e8	0.0142646	0.00713232	−	0.999975i	$-0.497730\pi$
$977$	4.15807e8	0.0142646	0.00713232	+	0.999975i	$0.497730\pi$
$978$	1.98631e10	0.678988
$979$	5.91590e9	0.201503
$980$	−8.36552e10	−2.83924
$981$	4.54642e9	0.153755
$982$	−5.48608e10	−1.84872
$983$	1.60053e10	0.537437	0.268718	−	0.963219i	$-0.413400\pi$
$983$	1.60053e10	0.537437	0.268718	+	0.963219i	$0.413400\pi$
$984$	3.06582e10	1.02580
$985$	4.86029e10	1.62045
$986$	1.26712e10	0.420969
$987$	−7.04269e9	−0.233146
$988$	3.74794e10	1.23635
$989$	3.84549e10	1.26405
$990$	−1.21379e10	−0.397576
$991$	5.06048e10	1.65171	0.825855	−	0.563882i	$-0.190693\pi$
$991$	5.06048e10	1.65171	0.825855	+	0.563882i	$0.190693\pi$
$992$	−1.11041e10	−0.361153
$993$	−2.12044e10	−0.687231
$994$	2.08061e10	0.671951
$995$	−3.04700e10	−0.980601
$996$	−2.21461e10	−0.710216
$997$	−1.97433e10	−0.630939	−0.315469	−	0.948936i	$-0.602162\pi$
$997$	−1.97433e10	−0.630939	−0.315469	+	0.948936i	$0.602162\pi$
$998$	−3.31480e10	−1.05560
$999$	9.74764e9	0.309329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.18	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.18	✓	156	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-18.7781 q^{2} -27.5200 q^{3} +224.616 q^{4} +480.924 q^{5} +516.772 q^{6} -221.639 q^{7} -1814.26 q^{8} -1429.65 q^{9} +O(q^{10})\)	\(q-18.7781 q^{2} -27.5200 q^{3} +224.616 q^{4} +480.924 q^{5} +516.772 q^{6} -221.639 q^{7} -1814.26 q^{8} -1429.65 q^{9} -9030.83 q^{10} -940.126 q^{11} -6181.42 q^{12} -6627.18 q^{13} +4161.95 q^{14} -13235.0 q^{15} +5317.40 q^{16} +6229.81 q^{17} +26846.1 q^{18} -25178.1 q^{19} +108023. q^{20} +6099.50 q^{21} +17653.7 q^{22} +71987.4 q^{23} +49928.3 q^{24} +153163. q^{25} +124446. q^{26} +99530.2 q^{27} -49783.5 q^{28} -108316. q^{29} +248528. q^{30} -83883.8 q^{31} +132374. q^{32} +25872.3 q^{33} -116984. q^{34} -106591. q^{35} -321122. q^{36} +97936.5 q^{37} +472797. q^{38} +182380. q^{39} -872520. q^{40} +614044. q^{41} -114537. q^{42} +534189. q^{43} -211167. q^{44} -687553. q^{45} -1.35178e6 q^{46} -1.15464e6 q^{47} -146335. q^{48} -774419. q^{49} -2.87611e6 q^{50} -171444. q^{51} -1.48857e6 q^{52} +1.20347e6 q^{53} -1.86898e6 q^{54} -452130. q^{55} +402109. q^{56} +692902. q^{57} +2.03397e6 q^{58} +1.62834e6 q^{59} -2.97280e6 q^{60} -2.08146e6 q^{61} +1.57518e6 q^{62} +316866. q^{63} -3.16636e6 q^{64} -3.18717e6 q^{65} -485831. q^{66} -3.67820e6 q^{67} +1.39931e6 q^{68} -1.98109e6 q^{69} +2.00158e6 q^{70} +4.99912e6 q^{71} +2.59375e6 q^{72} +1.42194e6 q^{73} -1.83906e6 q^{74} -4.21506e6 q^{75} -5.65540e6 q^{76} +208368. q^{77} -3.42474e6 q^{78} -1.58328e6 q^{79} +2.55727e6 q^{80} +387572. q^{81} -1.15306e7 q^{82} +3.58269e6 q^{83} +1.37004e6 q^{84} +2.99607e6 q^{85} -1.00310e7 q^{86} +2.98087e6 q^{87} +1.70563e6 q^{88} -6.29266e6 q^{89} +1.29109e7 q^{90} +1.46884e6 q^{91} +1.61695e7 q^{92} +2.30848e6 q^{93} +2.16818e7 q^{94} -1.21088e7 q^{95} -3.64294e6 q^{96} -1.50391e6 q^{97} +1.45421e7 q^{98} +1.34405e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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