LMFDB - Embedded newform 547.8.a.a.1.19

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			1.19
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)

$f(q)$	$=$	$q-18.3687 q^{2} -35.4413 q^{3} +209.409 q^{4} +105.765 q^{5} +651.010 q^{6} +751.780 q^{7} -1495.38 q^{8} -930.915 q^{9} +O(q^{10})$	\(q-18.3687 q^{2} -35.4413 q^{3} +209.409 q^{4} +105.765 q^{5} +651.010 q^{6} +751.780 q^{7} -1495.38 q^{8} -930.915 q^{9} -1942.76 q^{10} +7049.03 q^{11} -7421.72 q^{12} +2832.00 q^{13} -13809.2 q^{14} -3748.43 q^{15} +663.757 q^{16} +24800.1 q^{17} +17099.7 q^{18} -1366.17 q^{19} +22148.0 q^{20} -26644.0 q^{21} -129481. q^{22} +102460. q^{23} +52998.0 q^{24} -66938.9 q^{25} -52020.2 q^{26} +110503. q^{27} +157429. q^{28} +33050.4 q^{29} +68853.8 q^{30} -284660. q^{31} +179216. q^{32} -249827. q^{33} -455546. q^{34} +79511.7 q^{35} -194942. q^{36} +565419. q^{37} +25094.7 q^{38} -100370. q^{39} -158158. q^{40} -508160. q^{41} +489416. q^{42} -925419. q^{43} +1.47613e6 q^{44} -98457.8 q^{45} -1.88206e6 q^{46} -523665. q^{47} -23524.4 q^{48} -258370. q^{49} +1.22958e6 q^{50} -878948. q^{51} +593046. q^{52} -848843. q^{53} -2.02979e6 q^{54} +745537. q^{55} -1.12419e6 q^{56} +48418.8 q^{57} -607093. q^{58} +783426. q^{59} -784955. q^{60} -2.66604e6 q^{61} +5.22883e6 q^{62} -699843. q^{63} -3.37692e6 q^{64} +299525. q^{65} +4.58899e6 q^{66} -3.59932e6 q^{67} +5.19337e6 q^{68} -3.63133e6 q^{69} -1.46053e6 q^{70} -3.61933e6 q^{71} +1.39207e6 q^{72} -2.36957e6 q^{73} -1.03860e7 q^{74} +2.37240e6 q^{75} -286088. q^{76} +5.29932e6 q^{77} +1.84366e6 q^{78} +1.86182e6 q^{79} +70202.0 q^{80} -1.88045e6 q^{81} +9.33424e6 q^{82} -482902. q^{83} -5.57950e6 q^{84} +2.62297e6 q^{85} +1.69987e7 q^{86} -1.17135e6 q^{87} -1.05409e7 q^{88} -6.37247e6 q^{89} +1.80854e6 q^{90} +2.12904e6 q^{91} +2.14561e7 q^{92} +1.00887e7 q^{93} +9.61904e6 q^{94} -144492. q^{95} -6.35164e6 q^{96} +6.61670e6 q^{97} +4.74592e6 q^{98} -6.56205e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−18.3687	−1.62358	−0.811789	−	0.583950i	$-0.801506\pi$
$2$	−18.3687	−1.62358	−0.811789	+	0.583950i	$0.801506\pi$
$3$	−35.4413	−0.757853	−0.378927	−	0.925427i	$-0.623707\pi$
$3$	−35.4413	−0.757853	−0.378927	+	0.925427i	$0.623707\pi$
$4$	209.409	1.63601
$5$	105.765	0.378395	0.189197	−	0.981939i	$-0.439411\pi$
$5$	105.765	0.378395	0.189197	+	0.981939i	$0.439411\pi$
$6$	651.010	1.23043
$7$	751.780	0.828414	0.414207	−	0.910183i	$-0.364059\pi$
$7$	751.780	0.828414	0.414207	+	0.910183i	$0.364059\pi$
$8$	−1495.38	−1.03261
$9$	−930.915	−0.425659
$10$	−1942.76	−0.614354
$11$	7049.03	1.59682	0.798408	−	0.602117i	$-0.205676\pi$
$11$	7049.03	1.59682	0.798408	+	0.602117i	$0.205676\pi$
$12$	−7421.72	−1.23985
$13$	2832.00	0.357513	0.178756	−	0.983893i	$-0.442793\pi$
$13$	2832.00	0.357513	0.178756	+	0.983893i	$0.442793\pi$
$14$	−13809.2	−1.34500
$15$	−3748.43	−0.286768
$16$	663.757	0.0405125
$17$	24800.1	1.22429	0.612143	−	0.790747i	$-0.290308\pi$
$17$	24800.1	1.22429	0.612143	+	0.790747i	$0.290308\pi$
$18$	17099.7	0.691090
$19$	−1366.17	−0.0456948	−0.0228474	−	0.999739i	$-0.507273\pi$
$19$	−1366.17	−0.0456948	−0.0228474	+	0.999739i	$0.507273\pi$
$20$	22148.0	0.619057
$21$	−26644.0	−0.627816
$22$	−129481.	−2.59256
$23$	102460.	1.75594	0.877968	−	0.478719i	$-0.158899\pi$
$23$	102460.	1.75594	0.877968	+	0.478719i	$0.158899\pi$
$24$	52998.0	0.782565
$25$	−66938.9	−0.856817
$26$	−52020.2	−0.580450
$27$	110503.	1.08044
$28$	157429.	1.35529
$29$	33050.4	0.251642	0.125821	−	0.992053i	$-0.459843\pi$
$29$	33050.4	0.251642	0.125821	+	0.992053i	$0.459843\pi$
$30$	68853.8	0.465590
$31$	−284660.	−1.71617	−0.858085	−	0.513508i	$-0.828345\pi$
$31$	−284660.	−1.71617	−0.858085	+	0.513508i	$0.828345\pi$
$32$	179216.	0.966832
$33$	−249827.	−1.21015
$34$	−455546.	−1.98772
$35$	79511.7	0.313468
$36$	−194942.	−0.696381
$37$	565419.	1.83512	0.917559	−	0.397599i	$-0.130157\pi$
$37$	565419.	1.83512	0.917559	+	0.397599i	$0.130157\pi$
$38$	25094.7	0.0741891
$39$	−100370.	−0.270942
$40$	−158158.	−0.390733
$41$	−508160.	−1.15148	−0.575741	−	0.817632i	$-0.695286\pi$
$41$	−508160.	−1.15148	−0.575741	+	0.817632i	$0.695286\pi$
$42$	489416.	1.01931
$43$	−925419.	−1.77500	−0.887501	−	0.460806i	$-0.847560\pi$
$43$	−925419.	−1.77500	−0.887501	+	0.460806i	$0.847560\pi$
$44$	1.47613e6	2.61240
$45$	−98457.8	−0.161067
$46$	−1.88206e6	−2.85090
$47$	−523665.	−0.735718	−0.367859	−	0.929882i	$-0.619909\pi$
$47$	−523665.	−0.735718	−0.367859	+	0.929882i	$0.619909\pi$
$48$	−23524.4	−0.0307025
$49$	−258370.	−0.313730
$50$	1.22958e6	1.39111
$51$	−878948.	−0.927829
$52$	593046.	0.584894
$53$	−848843.	−0.783180	−0.391590	−	0.920140i	$-0.628075\pi$
$53$	−848843.	−0.783180	−0.391590	+	0.920140i	$0.628075\pi$
$54$	−2.02979e6	−1.75418
$55$	745537.	0.604227
$56$	−1.12419e6	−0.855427
$57$	48418.8	0.0346299
$58$	−607093.	−0.408561
$59$	783426.	0.496610	0.248305	−	0.968682i	$-0.420126\pi$
$59$	783426.	0.496610	0.248305	+	0.968682i	$0.420126\pi$
$60$	−784955.	−0.469154
$61$	−2.66604e6	−1.50388	−0.751939	−	0.659233i	$-0.770881\pi$
$61$	−2.66604e6	−1.50388	−0.751939	+	0.659233i	$0.770881\pi$
$62$	5.22883e6	2.78634
$63$	−699843.	−0.352622
$64$	−3.37692e6	−1.61024
$65$	299525.	0.135281
$66$	4.58899e6	1.96478
$67$	−3.59932e6	−1.46204	−0.731020	−	0.682356i	$-0.760955\pi$
$67$	−3.59932e6	−1.46204	−0.731020	+	0.682356i	$0.760955\pi$
$68$	5.19337e6	2.00294
$69$	−3.63133e6	−1.33074
$70$	−1.46053e6	−0.508939
$71$	−3.61933e6	−1.20012	−0.600059	−	0.799956i	$-0.704856\pi$
$71$	−3.61933e6	−1.20012	−0.600059	+	0.799956i	$0.704856\pi$
$72$	1.39207e6	0.439538
$73$	−2.36957e6	−0.712917	−0.356459	−	0.934311i	$-0.616016\pi$
$73$	−2.36957e6	−0.712917	−0.356459	+	0.934311i	$0.616016\pi$
$74$	−1.03860e7	−2.97946
$75$	2.37240e6	0.649342
$76$	−286088.	−0.0747570
$77$	5.29932e6	1.32282
$78$	1.84366e6	0.439896
$79$	1.86182e6	0.424857	0.212429	−	0.977177i	$-0.431863\pi$
$79$	1.86182e6	0.424857	0.212429	+	0.977177i	$0.431863\pi$
$80$	70202.0	0.0153297
$81$	−1.88045e6	−0.393156
$82$	9.33424e6	1.86952
$83$	−482902.	−0.0927012	−0.0463506	−	0.998925i	$-0.514759\pi$
$83$	−482902.	−0.0927012	−0.0463506	+	0.998925i	$0.514759\pi$
$84$	−5.57950e6	−1.02711
$85$	2.62297e6	0.463263
$86$	1.69987e7	2.88186
$87$	−1.17135e6	−0.190708
$88$	−1.05409e7	−1.64888
$89$	−6.37247e6	−0.958171	−0.479086	−	0.877768i	$-0.659032\pi$
$89$	−6.37247e6	−0.958171	−0.479086	+	0.877768i	$0.659032\pi$
$90$	1.80854e6	0.261505
$91$	2.12904e6	0.296169
$92$	2.14561e7	2.87272
$93$	1.00887e7	1.30060
$94$	9.61904e6	1.19450
$95$	−144492.	−0.0172907
$96$	−6.35164e6	−0.732717
$97$	6.61670e6	0.736106	0.368053	−	0.929805i	$-0.380024\pi$
$97$	6.61670e6	0.736106	0.368053	+	0.929805i	$0.380024\pi$
$98$	4.74592e6	0.509365
$99$	−6.56205e6	−0.679698
$100$	−1.40176e7	−1.40176
$101$	−1.12044e7	−1.08209	−0.541044	−	0.840994i	$-0.681971\pi$
$101$	−1.12044e7	−1.08209	−0.541044	+	0.840994i	$0.681971\pi$
$102$	1.61451e7	1.50640
$103$	−4.48215e6	−0.404162	−0.202081	−	0.979369i	$-0.564770\pi$
$103$	−4.48215e6	−0.404162	−0.202081	+	0.979369i	$0.564770\pi$
$104$	−4.23491e6	−0.369171
$105$	−2.81800e6	−0.237562
$106$	1.55921e7	1.27155
$107$	2.11688e7	1.67052	0.835262	−	0.549852i	$-0.185316\pi$
$107$	2.11688e7	1.67052	0.835262	+	0.549852i	$0.185316\pi$
$108$	2.31403e7	1.76761
$109$	9.69031e6	0.716713	0.358356	−	0.933585i	$-0.383337\pi$
$109$	9.69031e6	0.716713	0.358356	+	0.933585i	$0.383337\pi$
$110$	−1.36945e7	−0.981009
$111$	−2.00392e7	−1.39075
$112$	498999.	0.0335611
$113$	−2.65396e7	−1.73029	−0.865145	−	0.501521i	$-0.832774\pi$
$113$	−2.65396e7	−1.73029	−0.865145	+	0.501521i	$0.832774\pi$
$114$	−889389.	−0.0562244
$115$	1.08367e7	0.664437
$116$	6.92105e6	0.411689
$117$	−2.63635e6	−0.152178
$118$	−1.43905e7	−0.806286
$119$	1.86442e7	1.01422
$120$	5.60531e6	0.296118
$121$	3.02016e7	1.54982
$122$	4.89717e7	2.44166
$123$	1.80098e7	0.872654
$124$	−5.96103e7	−2.80767
$125$	−1.53426e7	−0.702610
$126$	1.28552e7	0.572509
$127$	1.87376e7	0.811712	0.405856	−	0.913937i	$-0.366974\pi$
$127$	1.87376e7	0.811712	0.405856	+	0.913937i	$0.366974\pi$
$128$	3.90900e7	1.64752
$129$	3.27980e7	1.34519
$130$	−5.50189e6	−0.219639
$131$	−2.03541e7	−0.791047	−0.395523	−	0.918456i	$-0.629437\pi$
$131$	−2.03541e7	−0.791047	−0.395523	+	0.918456i	$0.629437\pi$
$132$	−5.23159e7	−1.97982
$133$	−1.02706e6	−0.0378542
$134$	6.61149e7	2.37374
$135$	1.16873e7	0.408833
$136$	−3.70855e7	−1.26421
$137$	3.46250e7	1.15045	0.575225	−	0.817995i	$-0.304915\pi$
$137$	3.46250e7	1.15045	0.575225	+	0.817995i	$0.304915\pi$
$138$	6.67028e7	2.16056
$139$	−2.64363e7	−0.834927	−0.417463	−	0.908694i	$-0.637081\pi$
$139$	−2.64363e7	−0.834927	−0.417463	+	0.908694i	$0.637081\pi$
$140$	1.66505e7	0.512835
$141$	1.85594e7	0.557566
$142$	6.64823e7	1.94849
$143$	1.99629e7	0.570882
$144$	−617902.	−0.0172445
$145$	3.49556e6	0.0952201
$146$	4.35259e7	1.15748
$147$	9.15697e6	0.237761
$148$	1.18404e8	3.00227
$149$	1.16584e6	0.0288727	0.0144364	−	0.999896i	$-0.495405\pi$
$149$	1.16584e6	0.0288727	0.0144364	+	0.999896i	$0.495405\pi$
$150$	−4.35779e7	−1.05426
$151$	4.21117e7	0.995367	0.497684	−	0.867359i	$-0.334184\pi$
$151$	4.21117e7	0.995367	0.497684	+	0.867359i	$0.334184\pi$
$152$	2.04293e6	0.0471848
$153$	−2.30868e7	−0.521128
$154$	−9.73415e7	−2.14771
$155$	−3.01069e7	−0.649389
$156$	−2.10183e7	−0.443263
$157$	1.73037e7	0.356854	0.178427	−	0.983953i	$-0.442899\pi$
$157$	1.73037e7	0.356854	0.178427	+	0.983953i	$0.442899\pi$
$158$	−3.41992e7	−0.689789
$159$	3.00841e7	0.593535
$160$	1.89547e7	0.365844
$161$	7.70277e7	1.45464
$162$	3.45415e7	0.638320
$163$	−6.10027e7	−1.10330	−0.551648	−	0.834077i	$-0.686001\pi$
$163$	−6.10027e7	−1.10330	−0.551648	+	0.834077i	$0.686001\pi$
$164$	−1.06413e8	−1.88383
$165$	−2.64228e7	−0.457915
$166$	8.87027e6	0.150508
$167$	−1.05180e8	−1.74753	−0.873764	−	0.486350i	$-0.838328\pi$
$167$	−1.05180e8	−1.74753	−0.873764	+	0.486350i	$0.838328\pi$
$168$	3.98429e7	0.648288
$169$	−5.47283e7	−0.872185
$170$	−4.81806e7	−0.752144
$171$	1.27179e6	0.0194504
$172$	−1.93791e8	−2.90392
$173$	2.09920e7	0.308243	0.154122	−	0.988052i	$-0.450745\pi$
$173$	2.09920e7	0.308243	0.154122	+	0.988052i	$0.450745\pi$
$174$	2.15161e7	0.309629
$175$	−5.03233e7	−0.709800
$176$	4.67884e6	0.0646910
$177$	−2.77656e7	−0.376358
$178$	1.17054e8	1.55567
$179$	−1.00481e8	−1.30948	−0.654741	−	0.755853i	$-0.727222\pi$
$179$	−1.00481e8	−1.30948	−0.654741	+	0.755853i	$0.727222\pi$
$180$	−2.06180e7	−0.263507
$181$	5.17077e7	0.648157	0.324079	−	0.946030i	$-0.394946\pi$
$181$	5.17077e7	0.648157	0.324079	+	0.946030i	$0.394946\pi$
$182$	−3.91077e7	−0.480853
$183$	9.44880e7	1.13972
$184$	−1.53217e8	−1.81319
$185$	5.98012e7	0.694399
$186$	−1.85316e8	−2.11163
$187$	1.74817e8	1.95496
$188$	−1.09660e8	−1.20364
$189$	8.30739e7	0.895052
$190$	2.65413e6	0.0280728
$191$	1.33065e8	1.38181	0.690903	−	0.722947i	$-0.257213\pi$
$191$	1.33065e8	1.38181	0.690903	+	0.722947i	$0.257213\pi$
$192$	1.19682e8	1.22033
$193$	−6.29546e7	−0.630343	−0.315171	−	0.949035i	$-0.602062\pi$
$193$	−6.29546e7	−0.630343	−0.315171	+	0.949035i	$0.602062\pi$
$194$	−1.21540e8	−1.19513
$195$	−1.06156e7	−0.102523
$196$	−5.41050e7	−0.513264
$197$	−1.32634e8	−1.23601	−0.618006	−	0.786174i	$-0.712059\pi$
$197$	−1.32634e8	−1.23601	−0.618006	+	0.786174i	$0.712059\pi$
$198$	1.20536e8	1.10354
$199$	−2.55824e7	−0.230120	−0.115060	−	0.993359i	$-0.536706\pi$
$199$	−2.55824e7	−0.230120	−0.115060	+	0.993359i	$0.536706\pi$
$200$	1.00099e8	0.884756
$201$	1.27565e8	1.10801
$202$	2.05810e8	1.75685
$203$	2.48466e7	0.208464
$204$	−1.84060e8	−1.51793
$205$	−5.37453e7	−0.435715
$206$	8.23312e7	0.656189
$207$	−9.53820e7	−0.747429
$208$	1.87976e6	0.0144837
$209$	−9.63016e6	−0.0729661
$210$	5.17629e7	0.385701
$211$	5.99112e7	0.439056	0.219528	−	0.975606i	$-0.429548\pi$
$211$	5.99112e7	0.439056	0.219528	+	0.975606i	$0.429548\pi$
$212$	−1.77755e8	−1.28129
$213$	1.28274e8	0.909513
$214$	−3.88843e8	−2.71223
$215$	−9.78765e7	−0.671651
$216$	−1.65243e8	−1.11567
$217$	−2.14001e8	−1.42170
$218$	−1.77998e8	−1.16364
$219$	8.39805e7	0.540287
$220$	1.56122e8	0.988519
$221$	7.02340e7	0.437698
$222$	3.68093e8	2.25799
$223$	−6.23420e7	−0.376456	−0.188228	−	0.982125i	$-0.560274\pi$
$223$	−6.23420e7	−0.376456	−0.188228	+	0.982125i	$0.560274\pi$
$224$	1.34731e8	0.800938
$225$	6.23144e7	0.364712
$226$	4.87497e8	2.80926
$227$	1.04446e8	0.592652	0.296326	−	0.955087i	$-0.404239\pi$
$227$	1.04446e8	0.592652	0.296326	+	0.955087i	$0.404239\pi$
$228$	1.01393e7	0.0566548
$229$	1.73315e8	0.953703	0.476852	−	0.878984i	$-0.341778\pi$
$229$	1.73315e8	0.953703	0.476852	+	0.878984i	$0.341778\pi$
$230$	−1.99056e8	−1.07877
$231$	−1.87815e8	−1.00251
$232$	−4.94228e7	−0.259848
$233$	1.48497e8	0.769083	0.384542	−	0.923108i	$-0.374360\pi$
$233$	1.48497e8	0.769083	0.384542	+	0.923108i	$0.374360\pi$
$234$	4.84264e7	0.247074
$235$	−5.53852e7	−0.278392
$236$	1.64056e8	0.812458
$237$	−6.59853e7	−0.321979
$238$	−3.42470e8	−1.64666
$239$	−3.10935e8	−1.47325	−0.736625	−	0.676301i	$-0.763582\pi$
$239$	−3.10935e8	−1.47325	−0.736625	+	0.676301i	$0.763582\pi$
$240$	−2.48805e6	−0.0116177
$241$	1.95501e8	0.899683	0.449841	−	0.893108i	$-0.351481\pi$
$241$	1.95501e8	0.899683	0.449841	+	0.893108i	$0.351481\pi$
$242$	−5.54764e8	−2.51625
$243$	−1.75024e8	−0.782485
$244$	−5.58293e8	−2.46036
$245$	−2.73264e7	−0.118714
$246$	−3.30817e8	−1.41682
$247$	−3.86899e6	−0.0163365
$248$	4.25673e8	1.77213
$249$	1.71147e7	0.0702539
$250$	2.81824e8	1.14074
$251$	−2.35583e8	−0.940343	−0.470171	−	0.882575i	$-0.655808\pi$
$251$	−2.35583e8	−0.940343	−0.470171	+	0.882575i	$0.655808\pi$
$252$	−1.46553e8	−0.576892
$253$	7.22246e8	2.80391
$254$	−3.44186e8	−1.31788
$255$	−9.29616e7	−0.351085
$256$	−2.85786e8	−1.06464
$257$	−3.62477e8	−1.33203	−0.666015	−	0.745938i	$-0.732001\pi$
$257$	−3.62477e8	−1.33203	−0.666015	+	0.745938i	$0.732001\pi$
$258$	−6.02457e8	−2.18402
$259$	4.25070e8	1.52024
$260$	6.27233e7	0.221321
$261$	−3.07671e7	−0.107114
$262$	3.73878e8	1.28433
$263$	−1.00836e8	−0.341798	−0.170899	−	0.985289i	$-0.554667\pi$
$263$	−1.00836e8	−0.341798	−0.170899	+	0.985289i	$0.554667\pi$
$264$	3.73585e8	1.24961
$265$	−8.97775e7	−0.296351
$266$	1.88657e7	0.0614593
$267$	2.25849e8	0.726153
$268$	−7.53730e8	−2.39191
$269$	−5.18187e6	−0.0162313	−0.00811565	−	0.999967i	$-0.502583\pi$
$269$	−5.18187e6	−0.0162313	−0.00811565	+	0.999967i	$0.502583\pi$
$270$	−2.14680e8	−0.663772
$271$	−1.97491e8	−0.602773	−0.301386	−	0.953502i	$-0.597449\pi$
$271$	−1.97491e8	−0.602773	−0.301386	+	0.953502i	$0.597449\pi$
$272$	1.64613e7	0.0495989
$273$	−7.54560e7	−0.224452
$274$	−6.36016e8	−1.86784
$275$	−4.71854e8	−1.36818
$276$	−7.60433e8	−2.17710
$277$	6.14860e8	1.73819	0.869095	−	0.494645i	$-0.164702\pi$
$277$	6.14860e8	1.73819	0.869095	+	0.494645i	$0.164702\pi$
$278$	4.85600e8	1.35557
$279$	2.64994e8	0.730502
$280$	−1.18900e8	−0.323689
$281$	−5.64285e8	−1.51714	−0.758572	−	0.651590i	$-0.774102\pi$
$281$	−5.64285e8	−1.51714	−0.758572	+	0.651590i	$0.774102\pi$
$282$	−3.40911e8	−0.905252
$283$	−4.67652e8	−1.22651	−0.613254	−	0.789886i	$-0.710140\pi$
$283$	−4.67652e8	−1.22651	−0.613254	+	0.789886i	$0.710140\pi$
$284$	−7.57920e8	−1.96340
$285$	5.12099e6	0.0131038
$286$	−3.66692e8	−0.926872
$287$	−3.82025e8	−0.953904
$288$	−1.66835e8	−0.411541
$289$	2.04708e8	0.498875
$290$	−6.42089e7	−0.154597
$291$	−2.34504e8	−0.557861
$292$	−4.96209e8	−1.16634
$293$	−1.24393e8	−0.288909	−0.144454	−	0.989511i	$-0.546143\pi$
$293$	−1.24393e8	−0.288909	−0.144454	+	0.989511i	$0.546143\pi$
$294$	−1.68202e8	−0.386024
$295$	8.28586e7	0.187915
$296$	−8.45513e8	−1.89496
$297$	7.78938e8	1.72526
$298$	−2.14150e7	−0.0468771
$299$	2.90168e8	0.627770
$300$	4.96802e8	1.06233
$301$	−6.95711e8	−1.47044
$302$	−7.73537e8	−1.61606
$303$	3.97097e8	0.820064
$304$	−906804.	−0.00185121
$305$	−2.81973e8	−0.569059
$306$	4.24075e8	0.846092
$307$	−1.50393e8	−0.296650	−0.148325	−	0.988939i	$-0.547388\pi$
$307$	−1.50393e8	−0.296650	−0.148325	+	0.988939i	$0.547388\pi$
$308$	1.10972e9	2.16415
$309$	1.58853e8	0.306296
$310$	5.53025e8	1.05433
$311$	−2.39237e8	−0.450991	−0.225495	−	0.974244i	$-0.572400\pi$
$311$	−2.39237e8	−0.450991	−0.225495	+	0.974244i	$0.572400\pi$
$312$	1.50090e8	0.279777
$313$	−3.11130e8	−0.573505	−0.286753	−	0.958005i	$-0.592576\pi$
$313$	−3.11130e8	−0.573505	−0.286753	+	0.958005i	$0.592576\pi$
$314$	−3.17847e8	−0.579381
$315$	−7.40186e7	−0.133430
$316$	3.89882e8	0.695069
$317$	4.21230e8	0.742698	0.371349	−	0.928493i	$-0.378895\pi$
$317$	4.21230e8	0.742698	0.371349	+	0.928493i	$0.378895\pi$
$318$	−5.52605e8	−0.963651
$319$	2.32973e8	0.401826
$320$	−3.57158e8	−0.609307
$321$	−7.50249e8	−1.26601
$322$	−1.41490e9	−2.36173
$323$	−3.38811e7	−0.0559435
$324$	−3.93784e8	−0.643206
$325$	−1.89571e8	−0.306323
$326$	1.12054e9	1.79129
$327$	−3.43437e8	−0.543163
$328$	7.59890e8	1.18903
$329$	−3.93681e8	−0.609479
$330$	4.85352e8	0.743461
$331$	−4.73926e8	−0.718312	−0.359156	−	0.933278i	$-0.616935\pi$
$331$	−4.73926e8	−0.718312	−0.359156	+	0.933278i	$0.616935\pi$
$332$	−1.01124e8	−0.151660
$333$	−5.26357e8	−0.781134
$334$	1.93201e9	2.83725
$335$	−3.80681e8	−0.553228
$336$	−1.76852e7	−0.0254344
$337$	−6.84547e8	−0.974314	−0.487157	−	0.873314i	$-0.661966\pi$
$337$	−6.84547e8	−0.974314	−0.487157	+	0.873314i	$0.661966\pi$
$338$	1.00529e9	1.41606
$339$	9.40596e8	1.31131
$340$	5.49274e8	0.757902
$341$	−2.00657e9	−2.74041
$342$	−2.33611e7	−0.0315792
$343$	−8.13360e8	−1.08831
$344$	1.38385e9	1.83288
$345$	−3.84066e8	−0.503546
$346$	−3.85596e8	−0.500457
$347$	−1.08310e8	−0.139160	−0.0695801	−	0.997576i	$-0.522166\pi$
$347$	−1.08310e8	−0.139160	−0.0695801	+	0.997576i	$0.522166\pi$
$348$	−2.45291e8	−0.312000
$349$	6.30878e8	0.794432	0.397216	−	0.917725i	$-0.369976\pi$
$349$	6.30878e8	0.794432	0.397216	+	0.917725i	$0.369976\pi$
$350$	9.24373e8	1.15242
$351$	3.12944e8	0.386271
$352$	1.26330e9	1.54385
$353$	1.03748e9	1.25536	0.627680	−	0.778471i	$-0.284005\pi$
$353$	1.03748e9	1.25536	0.627680	+	0.778471i	$0.284005\pi$
$354$	5.10018e8	0.611046
$355$	−3.82797e8	−0.454118
$356$	−1.33445e9	−1.56757
$357$	−6.60776e8	−0.768626
$358$	1.84571e9	2.12605
$359$	4.38222e8	0.499877	0.249939	−	0.968262i	$-0.419590\pi$
$359$	4.38222e8	0.499877	0.249939	+	0.968262i	$0.419590\pi$
$360$	1.47231e8	0.166319
$361$	−8.92005e8	−0.997912
$362$	−9.49803e8	−1.05233
$363$	−1.07038e9	−1.17454
$364$	4.45840e8	0.484534
$365$	−2.50616e8	−0.269764
$366$	−1.73562e9	−1.85042
$367$	−1.25815e9	−1.32862	−0.664308	−	0.747459i	$-0.731274\pi$
$367$	−1.25815e9	−1.32862	−0.664308	+	0.747459i	$0.731274\pi$
$368$	6.80088e7	0.0711374
$369$	4.73054e8	0.490138
$370$	−1.09847e9	−1.12741
$371$	−6.38143e8	−0.648798
$372$	2.11266e9	2.12780
$373$	4.27257e8	0.426293	0.213147	−	0.977020i	$-0.431629\pi$
$373$	4.27257e8	0.426293	0.213147	+	0.977020i	$0.431629\pi$
$374$	−3.21116e9	−3.17403
$375$	5.43762e8	0.532475
$376$	7.83076e8	0.759708
$377$	9.35988e7	0.0899654
$378$	−1.52596e9	−1.45319
$379$	1.87247e9	1.76676	0.883380	−	0.468658i	$-0.155262\pi$
$379$	1.87247e9	1.76676	0.883380	+	0.468658i	$0.155262\pi$
$380$	−3.02579e7	−0.0282877
$381$	−6.64086e8	−0.615158
$382$	−2.44423e9	−2.24347
$383$	1.91626e8	0.174285	0.0871424	−	0.996196i	$-0.472226\pi$
$383$	1.91626e8	0.174285	0.0871424	+	0.996196i	$0.472226\pi$
$384$	−1.38540e9	−1.24858
$385$	5.60480e8	0.500550
$386$	1.15639e9	1.02341
$387$	8.61487e8	0.755545
$388$	1.38560e9	1.20428
$389$	1.54418e9	1.33007	0.665037	−	0.746811i	$-0.268416\pi$
$389$	1.54418e9	1.33007	0.665037	+	0.746811i	$0.268416\pi$
$390$	1.94994e8	0.166454
$391$	2.54103e9	2.14977
$392$	3.86360e8	0.323960
$393$	7.21375e8	0.599497
$394$	2.43631e9	2.00676
$395$	1.96915e8	0.160764
$396$	−1.37415e9	−1.11199
$397$	1.15252e9	0.924443	0.462221	−	0.886765i	$-0.347053\pi$
$397$	1.15252e9	0.924443	0.462221	+	0.886765i	$0.347053\pi$
$398$	4.69914e8	0.373618
$399$	3.64002e7	0.0286879
$400$	−4.44311e7	−0.0347118
$401$	−6.37647e8	−0.493828	−0.246914	−	0.969037i	$-0.579416\pi$
$401$	−6.37647e8	−0.493828	−0.246914	+	0.969037i	$0.579416\pi$
$402$	−2.34320e9	−1.79894
$403$	−8.06157e8	−0.613553
$404$	−2.34629e9	−1.77030
$405$	−1.98885e8	−0.148768
$406$	−4.56400e8	−0.338458
$407$	3.98565e9	2.93035
$408$	1.31436e9	0.958083
$409$	−5.54404e8	−0.400678	−0.200339	−	0.979727i	$-0.564204\pi$
$409$	−5.54404e8	−0.400678	−0.200339	+	0.979727i	$0.564204\pi$
$410$	9.87231e8	0.707417
$411$	−1.22715e9	−0.871872
$412$	−9.38602e8	−0.661213
$413$	5.88964e8	0.411399
$414$	1.75204e9	1.21351
$415$	−5.10739e7	−0.0350776
$416$	5.07539e8	0.345655
$417$	9.36935e8	0.632752
$418$	1.76893e8	0.118466
$419$	7.12135e8	0.472948	0.236474	−	0.971638i	$-0.424008\pi$
$419$	7.12135e8	0.472948	0.236474	+	0.971638i	$0.424008\pi$
$420$	−5.90113e8	−0.388654
$421$	−7.76060e7	−0.0506883	−0.0253442	−	0.999679i	$-0.508068\pi$
$421$	−7.76060e7	−0.0506883	−0.0253442	+	0.999679i	$0.508068\pi$
$422$	−1.10049e9	−0.712842
$423$	4.87488e8	0.313165
$424$	1.26934e9	0.808718
$425$	−1.66009e9	−1.04899
$426$	−2.35622e9	−1.47667
$427$	−2.00428e9	−1.24583
$428$	4.43293e9	2.73299
$429$	−7.07509e8	−0.432645
$430$	1.79786e9	1.09048
$431$	1.60074e9	0.963052	0.481526	−	0.876432i	$-0.340083\pi$
$431$	1.60074e9	0.963052	0.481526	+	0.876432i	$0.340083\pi$
$432$	7.33471e7	0.0437713
$433$	−2.30103e8	−0.136212	−0.0681060	−	0.997678i	$-0.521696\pi$
$433$	−2.30103e8	−0.136212	−0.0681060	+	0.997678i	$0.521696\pi$
$434$	3.93093e9	2.30824
$435$	−1.23887e8	−0.0721629
$436$	2.02924e9	1.17255
$437$	−1.39978e8	−0.0802371
$438$	−1.54261e9	−0.877198
$439$	−3.30995e9	−1.86722	−0.933611	−	0.358288i	$-0.883360\pi$
$439$	−3.30995e9	−1.86722	−0.933611	+	0.358288i	$0.883360\pi$
$440$	−1.11486e9	−0.623929
$441$	2.40521e8	0.133542
$442$	−1.29011e9	−0.710637
$443$	−5.67141e8	−0.309940	−0.154970	−	0.987919i	$-0.549528\pi$
$443$	−5.67141e8	−0.309940	−0.154970	+	0.987919i	$0.549528\pi$
$444$	−4.19638e9	−2.27528
$445$	−6.73982e8	−0.362567
$446$	1.14514e9	0.611205
$447$	−4.13189e7	−0.0218813
$448$	−2.53870e9	−1.33395
$449$	1.83955e9	0.959068	0.479534	−	0.877523i	$-0.340806\pi$
$449$	1.83955e9	0.959068	0.479534	+	0.877523i	$0.340806\pi$
$450$	−1.14463e9	−0.592138
$451$	−3.58203e9	−1.83870
$452$	−5.55762e9	−2.83077
$453$	−1.49249e9	−0.754342
$454$	−1.91853e9	−0.962216
$455$	2.25177e8	0.112069
$456$	−7.24042e7	−0.0357591
$457$	−7.38030e8	−0.361715	−0.180858	−	0.983509i	$-0.557887\pi$
$457$	−7.38030e8	−0.361715	−0.180858	+	0.983509i	$0.557887\pi$
$458$	−3.18358e9	−1.54841
$459$	2.74049e9	1.32277
$460$	2.26930e9	1.08702
$461$	2.84981e9	1.35476	0.677380	−	0.735633i	$-0.263115\pi$
$461$	2.84981e9	1.35476	0.677380	+	0.735633i	$0.263115\pi$
$462$	3.44991e9	1.62765
$463$	1.80202e9	0.843772	0.421886	−	0.906649i	$-0.361368\pi$
$463$	1.80202e9	0.843772	0.421886	+	0.906649i	$0.361368\pi$
$464$	2.19374e7	0.0101947
$465$	1.06703e9	0.492142
$466$	−2.72771e9	−1.24867
$467$	4.77834e8	0.217104	0.108552	−	0.994091i	$-0.465379\pi$
$467$	4.77834e8	0.217104	0.108552	+	0.994091i	$0.465379\pi$
$468$	−5.52076e8	−0.248965
$469$	−2.70590e9	−1.21117
$470$	1.01735e9	0.451991
$471$	−6.13266e8	−0.270443
$472$	−1.17152e9	−0.512804
$473$	−6.52330e9	−2.83435
$474$	1.21206e9	0.522759
$475$	9.14497e7	0.0391521
$476$	3.90427e9	1.65926
$477$	7.90201e8	0.333367
$478$	5.71147e9	2.39194
$479$	3.73444e6	0.00155257	0.000776286	−	1.00000i	$-0.499753\pi$
$479$	3.73444e6	0.00155257	0.000776286		1.00000i	$0.499753\pi$
$480$	−6.71778e8	−0.277256
$481$	1.60127e9	0.656078
$482$	−3.59110e9	−1.46071
$483$	−2.72996e9	−1.10241
$484$	6.32449e9	2.53552
$485$	6.99813e8	0.278539
$486$	3.21497e9	1.27043
$487$	−2.75258e9	−1.07991	−0.539955	−	0.841694i	$-0.681559\pi$
$487$	−2.75258e9	−1.07991	−0.539955	+	0.841694i	$0.681559\pi$
$488$	3.98673e9	1.55292
$489$	2.16201e9	0.836137
$490$	5.01950e8	0.192741
$491$	1.88292e9	0.717873	0.358936	−	0.933362i	$-0.383140\pi$
$491$	1.88292e9	0.717873	0.358936	+	0.933362i	$0.383140\pi$
$492$	3.77142e9	1.42767
$493$	8.19654e8	0.308082
$494$	7.10683e7	0.0265235
$495$	−6.94032e8	−0.257194
$496$	−1.88945e8	−0.0695263
$497$	−2.72094e9	−0.994195
$498$	−3.14374e8	−0.114063
$499$	−1.34298e9	−0.483856	−0.241928	−	0.970294i	$-0.577780\pi$
$499$	−1.34298e9	−0.483856	−0.241928	+	0.970294i	$0.577780\pi$
$500$	−3.21288e9	−1.14947
$501$	3.72770e9	1.32437
$502$	4.32735e9	1.52672
$503$	−1.35109e9	−0.473364	−0.236682	−	0.971587i	$-0.576060\pi$
$503$	−1.35109e9	−0.473364	−0.236682	+	0.971587i	$0.576060\pi$
$504$	1.04653e9	0.364120
$505$	−1.18502e9	−0.409456
$506$	−1.32667e10	−4.55236
$507$	1.93964e9	0.660988
$508$	3.92383e9	1.32797
$509$	3.18835e9	1.07165	0.535826	−	0.844329i	$-0.320000\pi$
$509$	3.18835e9	1.07165	0.535826	+	0.844329i	$0.320000\pi$
$510$	1.70758e9	0.570015
$511$	−1.78139e9	−0.590591
$512$	2.46004e8	0.0810024
$513$	−1.50966e8	−0.0493705
$514$	6.65822e9	2.16266
$515$	−4.74052e8	−0.152933
$516$	6.86820e9	2.20074
$517$	−3.69133e9	−1.17481
$518$	−7.80799e9	−2.46823
$519$	−7.43985e8	−0.233603
$520$	−4.47903e8	−0.139692
$521$	−4.03807e9	−1.25096	−0.625478	−	0.780242i	$-0.715096\pi$
$521$	−4.03807e9	−1.25096	−0.625478	+	0.780242i	$0.715096\pi$
$522$	5.65152e8	0.173908
$523$	−3.29144e9	−1.00607	−0.503037	−	0.864265i	$-0.667784\pi$
$523$	−3.29144e9	−1.00607	−0.503037	+	0.864265i	$0.667784\pi$
$524$	−4.26233e9	−1.29416
$525$	1.78352e9	0.537924
$526$	1.85222e9	0.554935
$527$	−7.05960e9	−2.10108
$528$	−1.65824e8	−0.0490263
$529$	7.09331e9	2.08331
$530$	1.64909e9	0.481150
$531$	−7.29303e8	−0.211386
$532$	−2.15075e8	−0.0619298
$533$	−1.43911e9	−0.411670
$534$	−4.14855e9	−1.17897
$535$	2.23891e9	0.632118
$536$	5.38234e9	1.50971
$537$	3.56119e9	0.992395
$538$	9.51842e7	0.0263528
$539$	−1.82126e9	−0.500969
$540$	2.44742e9	0.668853
$541$	5.74201e9	1.55910	0.779549	−	0.626342i	$-0.215449\pi$
$541$	5.74201e9	1.55910	0.779549	+	0.626342i	$0.215449\pi$
$542$	3.62764e9	0.978649
$543$	−1.83259e9	−0.491208
$544$	4.44457e9	1.18368
$545$	1.02489e9	0.271200
$546$	1.38603e9	0.364416
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	7.25078e9	1.88214
$549$	2.48186e9	0.640139
$550$	8.66734e9	2.22135
$551$	−4.51524e7	−0.0114987
$552$	5.43020e9	1.37413
$553$	1.39968e9	0.351958
$554$	−1.12942e10	−2.82209
$555$	−2.11943e9	−0.526253
$556$	−5.53599e9	−1.36595
$557$	−3.21281e9	−0.787757	−0.393879	−	0.919162i	$-0.628867\pi$
$557$	−3.21281e9	−0.787757	−0.393879	+	0.919162i	$0.628867\pi$
$558$	−4.86760e9	−1.18603
$559$	−2.62079e9	−0.634586
$560$	5.27764e7	0.0126994
$561$	−6.19573e9	−1.48157
$562$	1.03652e10	2.46320
$563$	−2.36105e9	−0.557605	−0.278803	−	0.960348i	$-0.589937\pi$
$563$	−2.36105e9	−0.557605	−0.278803	+	0.960348i	$0.589937\pi$
$564$	3.88650e9	0.912182
$565$	−2.80694e9	−0.654733
$566$	8.59016e9	1.99133
$567$	−1.41369e9	−0.325696
$568$	5.41226e9	1.23925
$569$	−4.48353e8	−0.102030	−0.0510150	−	0.998698i	$-0.516246\pi$
$569$	−4.48353e8	−0.102030	−0.0510150	+	0.998698i	$0.516246\pi$
$570$	−9.40659e7	−0.0212750
$571$	3.16527e9	0.711515	0.355758	−	0.934578i	$-0.384223\pi$
$571$	3.16527e9	0.711515	0.355758	+	0.934578i	$0.384223\pi$
$572$	4.18040e9	0.933967
$573$	−4.71600e9	−1.04721
$574$	7.01729e9	1.54874
$575$	−6.85858e9	−1.50452
$576$	3.14363e9	0.685413
$577$	−2.53992e9	−0.550433	−0.275217	−	0.961382i	$-0.588750\pi$
$577$	−2.53992e9	−0.550433	−0.275217	+	0.961382i	$0.588750\pi$
$578$	−3.76021e9	−0.809962
$579$	2.23119e9	0.477707
$580$	7.32002e8	0.155781
$581$	−3.63036e8	−0.0767950
$582$	4.30754e9	0.905730
$583$	−5.98351e9	−1.25059
$584$	3.54339e9	0.736164
$585$	−2.78833e8	−0.0575835
$586$	2.28494e9	0.469066
$587$	8.48385e9	1.73125	0.865625	−	0.500693i	$-0.166921\pi$
$587$	8.48385e9	1.73125	0.865625	+	0.500693i	$0.166921\pi$
$588$	1.91755e9	0.388979
$589$	3.88893e8	0.0784200
$590$	−1.52201e9	−0.305094
$591$	4.70071e9	0.936715
$592$	3.75301e8	0.0743453
$593$	−2.29144e9	−0.451249	−0.225625	−	0.974214i	$-0.572442\pi$
$593$	−2.29144e9	−0.451249	−0.225625	+	0.974214i	$0.572442\pi$
$594$	−1.43081e10	−2.80110
$595$	1.97190e9	0.383774
$596$	2.44138e8	0.0472360
$597$	9.06672e8	0.174397
$598$	−5.33001e9	−1.01923
$599$	7.85652e8	0.149361	0.0746804	−	0.997208i	$-0.476206\pi$
$599$	7.85652e8	0.149361	0.0746804	+	0.997208i	$0.476206\pi$
$600$	−3.54763e9	−0.670515
$601$	2.83291e9	0.532319	0.266160	−	0.963929i	$-0.414245\pi$
$601$	2.83291e9	0.532319	0.266160	+	0.963929i	$0.414245\pi$
$602$	1.27793e10	2.38737
$603$	3.35067e9	0.622330
$604$	8.81857e9	1.62843
$605$	3.19426e9	0.586444
$606$	−7.29416e9	−1.33144
$607$	−2.34413e9	−0.425423	−0.212712	−	0.977115i	$-0.568229\pi$
$607$	−2.34413e9	−0.425423	−0.212712	+	0.977115i	$0.568229\pi$
$608$	−2.44839e8	−0.0441792
$609$	−8.80596e8	−0.157985
$610$	5.17947e9	0.923913
$611$	−1.48302e9	−0.263029
$612$	−4.83459e9	−0.852569
$613$	9.83561e9	1.72461	0.862303	−	0.506393i	$-0.169021\pi$
$613$	9.83561e9	1.72461	0.862303	+	0.506393i	$0.169021\pi$
$614$	2.76253e9	0.481635
$615$	1.90480e9	0.330208
$616$	−7.92447e9	−1.36596
$617$	−2.87243e9	−0.492324	−0.246162	−	0.969229i	$-0.579170\pi$
$617$	−2.87243e9	−0.492324	−0.246162	+	0.969229i	$0.579170\pi$
$618$	−2.91792e9	−0.497295
$619$	−6.63007e9	−1.12357	−0.561786	−	0.827282i	$-0.689886\pi$
$619$	−6.63007e9	−1.12357	−0.561786	+	0.827282i	$0.689886\pi$
$620$	−6.30465e9	−1.06241
$621$	1.13222e10	1.89718
$622$	4.39448e9	0.732219
$623$	−4.79070e9	−0.793763
$624$	−6.66211e7	−0.0109766
$625$	3.60689e9	0.590954
$626$	5.71506e9	0.931131
$627$	3.41305e8	0.0552976
$628$	3.62356e9	0.583816
$629$	1.40225e10	2.24671
$630$	1.35963e9	0.216634
$631$	−7.46771e9	−1.18327	−0.591636	−	0.806205i	$-0.701518\pi$
$631$	−7.46771e9	−1.18327	−0.591636	+	0.806205i	$0.701518\pi$
$632$	−2.78412e9	−0.438711
$633$	−2.12333e9	−0.332740
$634$	−7.73745e9	−1.20583
$635$	1.98178e9	0.307147
$636$	6.29987e9	0.971028
$637$	−7.31704e8	−0.112162
$638$	−4.27941e9	−0.652397
$639$	3.36929e9	0.510840
$640$	4.13434e9	0.623413
$641$	1.85990e9	0.278925	0.139462	−	0.990227i	$-0.455463\pi$
$641$	1.85990e9	0.278925	0.139462	+	0.990227i	$0.455463\pi$
$642$	1.37811e10	2.05547
$643$	2.96035e9	0.439141	0.219571	−	0.975597i	$-0.429534\pi$
$643$	2.96035e9	0.439141	0.219571	+	0.975597i	$0.429534\pi$
$644$	1.61303e10	2.37981
$645$	3.46887e9	0.509013
$646$	6.22352e8	0.0908286
$647$	−1.06438e10	−1.54500	−0.772502	−	0.635012i	$-0.780995\pi$
$647$	−1.06438e10	−1.54500	−0.772502	+	0.635012i	$0.780995\pi$
$648$	2.81198e9	0.405976
$649$	5.52239e9	0.792995
$650$	3.48217e9	0.497340
$651$	7.58449e9	1.07744
$652$	−1.27745e10	−1.80500
$653$	6.84430e9	0.961906	0.480953	−	0.876746i	$-0.340291\pi$
$653$	6.84430e9	0.961906	0.480953	+	0.876746i	$0.340291\pi$
$654$	6.30849e9	0.881868
$655$	−2.15274e9	−0.299328
$656$	−3.37295e8	−0.0466494
$657$	2.20587e9	0.303459
$658$	7.23140e9	0.989537
$659$	−9.13042e8	−0.124277	−0.0621386	−	0.998068i	$-0.519792\pi$
$659$	−9.13042e8	−0.124277	−0.0621386	+	0.998068i	$0.519792\pi$
$660$	−5.53317e9	−0.749152
$661$	−7.61767e9	−1.02593	−0.512964	−	0.858410i	$-0.671453\pi$
$661$	−7.61767e9	−1.02593	−0.512964	+	0.858410i	$0.671453\pi$
$662$	8.70541e9	1.16624
$663$	−2.48918e9	−0.331711
$664$	7.22119e8	0.0957240
$665$	−1.08626e8	−0.0143238
$666$	9.66849e9	1.26823
$667$	3.38636e9	0.441868
$668$	−2.20256e10	−2.85897
$669$	2.20948e9	0.285298
$670$	6.99261e9	0.898209
$671$	−1.87930e10	−2.40142
$672$	−4.77503e9	−0.606993
$673$	−8.26300e8	−0.104493	−0.0522463	−	0.998634i	$-0.516638\pi$
$673$	−8.26300e8	−0.104493	−0.0522463	+	0.998634i	$0.516638\pi$
$674$	1.25742e10	1.58188
$675$	−7.39694e9	−0.925740
$676$	−1.14606e10	−1.42690
$677$	−6.99945e9	−0.866969	−0.433485	−	0.901161i	$-0.642716\pi$
$677$	−6.99945e9	−0.866969	−0.433485	+	0.901161i	$0.642716\pi$
$678$	−1.72775e10	−2.12901
$679$	4.97430e9	0.609801
$680$	−3.92233e9	−0.478369
$681$	−3.70168e9	−0.449143
$682$	3.68581e10	4.44926
$683$	6.98302e9	0.838630	0.419315	−	0.907841i	$-0.362270\pi$
$683$	6.98302e9	0.838630	0.419315	+	0.907841i	$0.362270\pi$
$684$	2.66324e8	0.0318210
$685$	3.66209e9	0.435324
$686$	1.49404e10	1.76696
$687$	−6.14252e9	−0.722767
$688$	−6.14253e8	−0.0719098
$689$	−2.40392e9	−0.279997
$690$	7.05479e9	0.817546
$691$	−1.32980e10	−1.53326	−0.766628	−	0.642092i	$-0.778067\pi$
$691$	−1.32980e10	−1.53326	−0.766628	+	0.642092i	$0.778067\pi$
$692$	4.39592e9	0.504288
$693$	−4.93322e9	−0.563072
$694$	1.98951e9	0.225937
$695$	−2.79602e9	−0.315932
$696$	1.75161e9	0.196927
$697$	−1.26024e10	−1.40974
$698$	−1.15884e10	−1.28982
$699$	−5.26294e9	−0.582852
$700$	−1.05381e10	−1.16124
$701$	−1.02613e9	−0.112509	−0.0562547	−	0.998416i	$-0.517916\pi$
$701$	−1.02613e9	−0.112509	−0.0562547	+	0.998416i	$0.517916\pi$
$702$	−5.74838e9	−0.627142
$703$	−7.72457e8	−0.0838553
$704$	−2.38040e10	−2.57126
$705$	1.96292e9	0.210980
$706$	−1.90572e10	−2.03818
$707$	−8.42322e9	−0.896417
$708$	−5.81437e9	−0.615724
$709$	−2.79888e9	−0.294933	−0.147466	−	0.989067i	$-0.547112\pi$
$709$	−2.79888e9	−0.294933	−0.147466	+	0.989067i	$0.547112\pi$
$710$	7.03148e9	0.737297
$711$	−1.73320e9	−0.180844
$712$	9.52924e9	0.989415
$713$	−2.91664e10	−3.01348
$714$	1.21376e10	1.24793
$715$	2.11136e9	0.216019
$716$	−2.10417e10	−2.14232
$717$	1.10199e10	1.11651
$718$	−8.04956e9	−0.811590
$719$	9.03134e9	0.906152	0.453076	−	0.891472i	$-0.350327\pi$
$719$	9.03134e9	0.906152	0.453076	+	0.891472i	$0.350327\pi$
$720$	−6.53521e7	−0.00652523
$721$	−3.36959e9	−0.334814
$722$	1.63850e10	1.62019
$723$	−6.92881e9	−0.681827
$724$	1.08281e10	1.06039
$725$	−2.21236e9	−0.215612
$726$	1.96616e10	1.90695
$727$	8.17627e9	0.789195	0.394598	−	0.918854i	$-0.370884\pi$
$727$	8.17627e9	0.789195	0.394598	+	0.918854i	$0.370884\pi$
$728$	−3.18372e9	−0.305826
$729$	1.03156e10	0.986165
$730$	4.60349e9	0.437983
$731$	−2.29505e10	−2.17311
$732$	1.97866e10	1.86459
$733$	−1.16933e10	−1.09666	−0.548330	−	0.836262i	$-0.684736\pi$
$733$	−1.16933e10	−1.09666	−0.548330	+	0.836262i	$0.684736\pi$
$734$	2.31105e10	2.15711
$735$	9.68482e8	0.0899676
$736$	1.83625e10	1.69770
$737$	−2.53717e10	−2.33461
$738$	−8.68939e9	−0.795778
$739$	−1.70855e10	−1.55730	−0.778648	−	0.627461i	$-0.784094\pi$
$739$	−1.70855e10	−1.55730	−0.778648	+	0.627461i	$0.784094\pi$
$740$	1.25229e10	1.13604
$741$	1.37122e8	0.0123806
$742$	1.17218e10	1.05337
$743$	2.01976e10	1.80650	0.903250	−	0.429115i	$-0.141174\pi$
$743$	2.01976e10	1.80650	0.903250	+	0.429115i	$0.141174\pi$
$744$	−1.50864e10	−1.34301
$745$	1.23305e8	0.0109253
$746$	−7.84815e9	−0.692120
$747$	4.49541e8	0.0394591
$748$	3.66082e10	3.19833
$749$	1.59143e10	1.38389
$750$	−9.98820e9	−0.864515
$751$	1.78273e8	0.0153584	0.00767918	−	0.999971i	$-0.497556\pi$
$751$	1.78273e8	0.0153584	0.00767918	+	0.999971i	$0.497556\pi$
$752$	−3.47586e8	−0.0298058
$753$	8.34937e9	0.712642
$754$	−1.71929e9	−0.146066
$755$	4.45392e9	0.376642
$756$	1.73964e10	1.46431
$757$	1.01481e10	0.850251	0.425126	−	0.905134i	$-0.360230\pi$
$757$	1.01481e10	0.850251	0.425126	+	0.905134i	$0.360230\pi$
$758$	−3.43948e10	−2.86847
$759$	−2.55973e10	−2.12495
$760$	2.16070e8	0.0178545
$761$	1.26407e9	0.103974	0.0519870	−	0.998648i	$-0.483445\pi$
$761$	1.26407e9	0.103974	0.0519870	+	0.998648i	$0.483445\pi$
$762$	1.21984e10	0.998758
$763$	7.28498e9	0.593735
$764$	2.78650e10	2.26065
$765$	−2.44177e9	−0.197192
$766$	−3.51993e9	−0.282965
$767$	2.21866e9	0.177545
$768$	1.01286e10	0.806839
$769$	−2.19577e10	−1.74118	−0.870591	−	0.492008i	$-0.836263\pi$
$769$	−2.19577e10	−1.74118	−0.870591	+	0.492008i	$0.836263\pi$
$770$	−1.02953e10	−0.812682
$771$	1.28466e10	1.00948
$772$	−1.31832e10	−1.03125
$773$	−1.56171e10	−1.21611	−0.608055	−	0.793895i	$-0.708050\pi$
$773$	−1.56171e10	−1.21611	−0.608055	+	0.793895i	$0.708050\pi$
$774$	−1.58244e10	−1.22669
$775$	1.90548e10	1.47044
$776$	−9.89446e9	−0.760109
$777$	−1.50650e10	−1.15212
$778$	−2.83647e10	−2.15948
$779$	6.94232e8	0.0526167
$780$	−2.22299e9	−0.167729
$781$	−2.55127e10	−1.91637
$782$	−4.66754e10	−3.49032
$783$	3.65217e9	0.271884
$784$	−1.71495e8	−0.0127100
$785$	1.83012e9	0.135032
$786$	−1.32507e10	−0.973331
$787$	2.15044e10	1.57259	0.786294	−	0.617853i	$-0.211997\pi$
$787$	2.15044e10	1.57259	0.786294	+	0.617853i	$0.211997\pi$
$788$	−2.77747e10	−2.02212
$789$	3.57374e9	0.259032
$790$	−3.61706e9	−0.261013
$791$	−1.99519e10	−1.43340
$792$	9.81273e9	0.701862
$793$	−7.55023e9	−0.537656
$794$	−2.11702e10	−1.50091
$795$	3.18183e9	0.224591
$796$	−5.35717e9	−0.376478
$797$	1.12709e10	0.788593	0.394297	−	0.918983i	$-0.370988\pi$
$797$	1.12709e10	0.788593	0.394297	+	0.918983i	$0.370988\pi$
$798$	−6.68625e8	−0.0465771
$799$	−1.29870e10	−0.900728
$800$	−1.19965e10	−0.828399
$801$	5.93223e9	0.407854
$802$	1.17128e10	0.801768
$803$	−1.67031e10	−1.13840
$804$	2.67132e10	1.81271
$805$	8.14680e9	0.550429
$806$	1.48080e10	0.996151
$807$	1.83652e8	0.0123009
$808$	1.67547e10	1.11737
$809$	−1.77264e10	−1.17706	−0.588532	−	0.808474i	$-0.700294\pi$
$809$	−1.77264e10	−1.17706	−0.588532	+	0.808474i	$0.700294\pi$
$810$	3.65326e9	0.241537
$811$	5.74783e9	0.378382	0.189191	−	0.981940i	$-0.439413\pi$
$811$	5.74783e9	0.378382	0.189191	+	0.981940i	$0.439413\pi$
$812$	5.20311e9	0.341049
$813$	6.99932e9	0.456813
$814$	−7.32112e10	−4.75765
$815$	−6.45192e9	−0.417482
$816$	−5.83408e8	−0.0375887
$817$	1.26428e9	0.0811083
$818$	1.01837e10	0.650532
$819$	−1.98196e9	−0.126067
$820$	−1.12548e10	−0.712832
$821$	−1.06549e10	−0.671971	−0.335985	−	0.941867i	$-0.609069\pi$
$821$	−1.06549e10	−0.671971	−0.335985	+	0.941867i	$0.609069\pi$
$822$	2.25412e10	1.41555
$823$	−1.22238e9	−0.0764375	−0.0382187	−	0.999269i	$-0.512168\pi$
$823$	−1.22238e9	−0.0764375	−0.0382187	+	0.999269i	$0.512168\pi$
$824$	6.70250e9	0.417341
$825$	1.67231e10	1.03688
$826$	−1.08185e10	−0.667939
$827$	−2.76817e10	−1.70186	−0.850930	−	0.525279i	$-0.823961\pi$
$827$	−2.76817e10	−1.70186	−0.850930	+	0.525279i	$0.823961\pi$
$828$	−1.99738e10	−1.22280
$829$	−1.11368e10	−0.678923	−0.339461	−	0.940620i	$-0.610245\pi$
$829$	−1.11368e10	−0.678923	−0.339461	+	0.940620i	$0.610245\pi$
$830$	9.38160e8	0.0569513
$831$	−2.17914e10	−1.31729
$832$	−9.56344e9	−0.575682
$833$	−6.40761e9	−0.384095
$834$	−1.72103e10	−1.02732
$835$	−1.11243e10	−0.661255
$836$	−2.01664e9	−0.119373
$837$	−3.14557e10	−1.85422
$838$	−1.30810e10	−0.767868
$839$	1.13747e10	0.664924	0.332462	−	0.943117i	$-0.392121\pi$
$839$	1.13747e10	0.664924	0.332462	+	0.943117i	$0.392121\pi$
$840$	4.21396e9	0.245309
$841$	−1.61575e10	−0.936676
$842$	1.42552e9	0.0822964
$843$	1.99990e10	1.14977
$844$	1.25459e10	0.718298
$845$	−5.78831e9	−0.330030
$846$	−8.95452e9	−0.508447
$847$	2.27050e10	1.28389
$848$	−5.63425e8	−0.0317286
$849$	1.65742e10	0.929513
$850$	3.04937e10	1.70312
$851$	5.79330e10	3.22235
$852$	2.68617e10	1.48797
$853$	−2.66204e10	−1.46856	−0.734282	−	0.678844i	$-0.762481\pi$
$853$	−2.66204e10	−1.46856	−0.734282	+	0.678844i	$0.762481\pi$
$854$	3.68159e10	2.02271
$855$	1.34510e8	0.00735992
$856$	−3.16553e10	−1.72500
$857$	2.99637e10	1.62616	0.813078	−	0.582155i	$-0.197790\pi$
$857$	2.99637e10	1.62616	0.813078	+	0.582155i	$0.197790\pi$
$858$	1.29960e10	0.702433
$859$	7.63212e9	0.410837	0.205418	−	0.978674i	$-0.434145\pi$
$859$	7.63212e9	0.410837	0.205418	+	0.978674i	$0.434145\pi$
$860$	−2.04962e10	−1.09883
$861$	1.35394e10	0.722919
$862$	−2.94035e10	−1.56359
$863$	−1.21950e9	−0.0645868	−0.0322934	−	0.999478i	$-0.510281\pi$
$863$	−1.21950e9	−0.0645868	−0.0322934	+	0.999478i	$0.510281\pi$
$864$	1.98039e10	1.04460
$865$	2.22021e9	0.116638
$866$	4.22670e9	0.221151
$867$	−7.25510e9	−0.378074
$868$	−4.48138e10	−2.32591
$869$	1.31240e10	0.678419
$870$	2.27565e9	0.117162
$871$	−1.01933e10	−0.522698
$872$	−1.44907e10	−0.740083
$873$	−6.15959e9	−0.313330
$874$	2.57122e9	0.130271
$875$	−1.15343e10	−0.582052
$876$	1.75863e10	0.883913
$877$	3.39001e9	0.169708	0.0848539	−	0.996393i	$-0.472958\pi$
$877$	3.39001e9	0.169708	0.0848539	+	0.996393i	$0.472958\pi$
$878$	6.07995e10	3.03158
$879$	4.40866e9	0.218950
$880$	4.94856e8	0.0244787
$881$	4.62755e9	0.228001	0.114000	−	0.993481i	$-0.463634\pi$
$881$	4.62755e9	0.228001	0.114000	+	0.993481i	$0.463634\pi$
$882$	−4.41805e9	−0.216816
$883$	3.00028e10	1.46656	0.733278	−	0.679929i	$-0.237989\pi$
$883$	3.00028e10	1.46656	0.733278	+	0.679929i	$0.237989\pi$
$884$	1.47076e10	0.716077
$885$	−2.93662e9	−0.142412
$886$	1.04176e10	0.503212
$887$	−1.84244e10	−0.886464	−0.443232	−	0.896407i	$-0.646168\pi$
$887$	−1.84244e10	−0.886464	−0.443232	+	0.896407i	$0.646168\pi$
$888$	2.99661e10	1.43610
$889$	1.40866e10	0.672433
$890$	1.23802e10	0.588656
$891$	−1.32554e10	−0.627798
$892$	−1.30550e10	−0.615884
$893$	7.15415e8	0.0336185
$894$	7.58975e8	0.0355260
$895$	−1.06274e10	−0.495501
$896$	2.93871e10	1.36483
$897$	−1.02839e10	−0.475757
$898$	−3.37901e10	−1.55712
$899$	−9.40812e9	−0.431861
$900$	1.30492e10	0.596671
$901$	−2.10514e10	−0.958836
$902$	6.57973e10	2.98528
$903$	2.46569e10	1.11438
$904$	3.96866e10	1.78671
$905$	5.46884e9	0.245259
$906$	2.74151e10	1.22473
$907$	−1.55989e10	−0.694174	−0.347087	−	0.937833i	$-0.612829\pi$
$907$	−1.55989e10	−0.694174	−0.347087	+	0.937833i	$0.612829\pi$
$908$	2.18718e10	0.969582
$909$	1.04303e10	0.460600
$910$	−4.13621e9	−0.181952
$911$	1.77001e10	0.775643	0.387822	−	0.921734i	$-0.373228\pi$
$911$	1.77001e10	0.775643	0.387822	+	0.921734i	$0.373228\pi$
$912$	3.21383e7	0.00140295
$913$	−3.40399e9	−0.148027
$914$	1.35566e10	0.587273
$915$	9.99348e9	0.431264
$916$	3.62938e10	1.56027
$917$	−1.53018e10	−0.655314
$918$	−5.03392e10	−2.14762
$919$	9.24832e9	0.393060	0.196530	−	0.980498i	$-0.437033\pi$
$919$	9.24832e9	0.393060	0.196530	+	0.980498i	$0.437033\pi$
$920$	−1.62049e10	−0.686103
$921$	5.33014e9	0.224817
$922$	−5.23473e10	−2.19956
$923$	−1.02499e10	−0.429058
$924$	−3.93300e10	−1.64011
$925$	−3.78485e10	−1.57236
$926$	−3.31007e10	−1.36993
$927$	4.17250e9	0.172035
$928$	5.92315e9	0.243296
$929$	−3.00628e10	−1.23020	−0.615098	−	0.788451i	$-0.710884\pi$
$929$	−3.00628e10	−1.23020	−0.615098	+	0.788451i	$0.710884\pi$
$930$	−1.95999e10	−0.799031
$931$	3.52977e8	0.0143358
$932$	3.10967e10	1.25823
$933$	8.47888e9	0.341785
$934$	−8.77719e9	−0.352486
$935$	1.84894e10	0.739746
$936$	3.94234e9	0.157141
$937$	2.75609e10	1.09447	0.547236	−	0.836978i	$-0.315680\pi$
$937$	2.75609e10	1.09447	0.547236	+	0.836978i	$0.315680\pi$
$938$	4.97038e10	1.96644
$939$	1.10269e10	0.434633
$940$	−1.15982e10	−0.455451
$941$	−2.80955e10	−1.09919	−0.549595	−	0.835432i	$-0.685218\pi$
$941$	−2.80955e10	−1.09919	−0.549595	+	0.835432i	$0.685218\pi$
$942$	1.12649e10	0.439086
$943$	−5.20663e10	−2.02193
$944$	5.20004e8	0.0201189
$945$	8.78627e9	0.338683
$946$	1.19825e11	4.60179
$947$	−1.33924e10	−0.512430	−0.256215	−	0.966620i	$-0.582476\pi$
$947$	−1.33924e10	−0.512430	−0.256215	+	0.966620i	$0.582476\pi$
$948$	−1.38179e10	−0.526761
$949$	−6.71062e9	−0.254877
$950$	−1.67981e9	−0.0635665
$951$	−1.49289e10	−0.562856
$952$	−2.78801e10	−1.04729
$953$	−1.82451e10	−0.682843	−0.341422	−	0.939910i	$-0.610908\pi$
$953$	−1.82451e10	−0.682843	−0.341422	+	0.939910i	$0.610908\pi$
$954$	−1.45150e10	−0.541248
$955$	1.40736e10	0.522868
$956$	−6.51125e10	−2.41025
$957$	−8.25687e9	−0.304525
$958$	−6.85969e7	−0.00252072
$959$	2.60304e10	0.953049
$960$	1.26582e10	0.461765
$961$	5.35185e10	1.94524
$962$	−2.94132e10	−1.06519
$963$	−1.97064e10	−0.711073
$964$	4.09397e10	1.47189
$965$	−6.65836e9	−0.238518
$966$	5.01458e10	1.78984
$967$	7.38736e9	0.262722	0.131361	−	0.991335i	$-0.458065\pi$
$967$	7.38736e9	0.262722	0.131361	+	0.991335i	$0.458065\pi$
$968$	−4.51627e10	−1.60036
$969$	1.20079e9	0.0423969
$970$	−1.28546e10	−0.452230
$971$	4.17449e10	1.46331	0.731654	−	0.681676i	$-0.238749\pi$
$971$	4.17449e10	1.46331	0.731654	+	0.681676i	$0.238749\pi$
$972$	−3.66516e10	−1.28015
$973$	−1.98742e10	−0.691665
$974$	5.05612e10	1.75332
$975$	6.71864e9	0.232148
$976$	−1.76960e9	−0.0609259
$977$	−1.52864e10	−0.524413	−0.262206	−	0.965012i	$-0.584450\pi$
$977$	−1.52864e10	−0.524413	−0.262206	+	0.965012i	$0.584450\pi$
$978$	−3.97134e10	−1.35753
$979$	−4.49197e10	−1.53002
$980$	−5.72239e9	−0.194217
$981$	−9.02086e9	−0.305075
$982$	−3.45868e10	−1.16552
$983$	5.38511e10	1.80824	0.904122	−	0.427275i	$-0.140526\pi$
$983$	5.38511e10	1.80824	0.904122	+	0.427275i	$0.140526\pi$
$984$	−2.69315e10	−0.901109
$985$	−1.40280e10	−0.467700
$986$	−1.50560e10	−0.500195
$987$	1.39526e10	0.461895
$988$	−8.10201e8	−0.0267266
$989$	−9.48188e10	−3.11679
$990$	1.27485e10	0.417575
$991$	−1.37805e10	−0.449788	−0.224894	−	0.974383i	$-0.572204\pi$
$991$	−1.37805e10	−0.449788	−0.224894	+	0.974383i	$0.572204\pi$
$992$	−5.10155e10	−1.65925
$993$	1.67966e10	0.544375
$994$	4.99801e10	1.61415
$995$	−2.70571e9	−0.0870763
$996$	3.58396e9	0.114936
$997$	−5.58497e10	−1.78479	−0.892396	−	0.451253i	$-0.850977\pi$
$997$	−5.58497e10	−1.78479	−0.892396	+	0.451253i	$0.850977\pi$
$998$	2.46687e10	0.785578
$999$	6.24804e10	1.98273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.19	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-18.3687 q^{2} -35.4413 q^{3} +209.409 q^{4} +105.765 q^{5} +651.010 q^{6} +751.780 q^{7} -1495.38 q^{8} -930.915 q^{9} +O(q^{10})\)	\(q-18.3687 q^{2} -35.4413 q^{3} +209.409 q^{4} +105.765 q^{5} +651.010 q^{6} +751.780 q^{7} -1495.38 q^{8} -930.915 q^{9} -1942.76 q^{10} +7049.03 q^{11} -7421.72 q^{12} +2832.00 q^{13} -13809.2 q^{14} -3748.43 q^{15} +663.757 q^{16} +24800.1 q^{17} +17099.7 q^{18} -1366.17 q^{19} +22148.0 q^{20} -26644.0 q^{21} -129481. q^{22} +102460. q^{23} +52998.0 q^{24} -66938.9 q^{25} -52020.2 q^{26} +110503. q^{27} +157429. q^{28} +33050.4 q^{29} +68853.8 q^{30} -284660. q^{31} +179216. q^{32} -249827. q^{33} -455546. q^{34} +79511.7 q^{35} -194942. q^{36} +565419. q^{37} +25094.7 q^{38} -100370. q^{39} -158158. q^{40} -508160. q^{41} +489416. q^{42} -925419. q^{43} +1.47613e6 q^{44} -98457.8 q^{45} -1.88206e6 q^{46} -523665. q^{47} -23524.4 q^{48} -258370. q^{49} +1.22958e6 q^{50} -878948. q^{51} +593046. q^{52} -848843. q^{53} -2.02979e6 q^{54} +745537. q^{55} -1.12419e6 q^{56} +48418.8 q^{57} -607093. q^{58} +783426. q^{59} -784955. q^{60} -2.66604e6 q^{61} +5.22883e6 q^{62} -699843. q^{63} -3.37692e6 q^{64} +299525. q^{65} +4.58899e6 q^{66} -3.59932e6 q^{67} +5.19337e6 q^{68} -3.63133e6 q^{69} -1.46053e6 q^{70} -3.61933e6 q^{71} +1.39207e6 q^{72} -2.36957e6 q^{73} -1.03860e7 q^{74} +2.37240e6 q^{75} -286088. q^{76} +5.29932e6 q^{77} +1.84366e6 q^{78} +1.86182e6 q^{79} +70202.0 q^{80} -1.88045e6 q^{81} +9.33424e6 q^{82} -482902. q^{83} -5.57950e6 q^{84} +2.62297e6 q^{85} +1.69987e7 q^{86} -1.17135e6 q^{87} -1.05409e7 q^{88} -6.37247e6 q^{89} +1.80854e6 q^{90} +2.12904e6 q^{91} +2.14561e7 q^{92} +1.00887e7 q^{93} +9.61904e6 q^{94} -144492. q^{95} -6.35164e6 q^{96} +6.61670e6 q^{97} +4.74592e6 q^{98} -6.56205e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 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

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