LMFDB - Embedded newform 547.8.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-20.6976 q^{2} +32.5628 q^{3} +300.390 q^{4} -462.112 q^{5} -673.972 q^{6} -452.526 q^{7} -3568.07 q^{8} -1126.66 q^{9} +O(q^{10})$	\(q-20.6976 q^{2} +32.5628 q^{3} +300.390 q^{4} -462.112 q^{5} -673.972 q^{6} -452.526 q^{7} -3568.07 q^{8} -1126.66 q^{9} +9564.62 q^{10} +5706.77 q^{11} +9781.56 q^{12} +13576.3 q^{13} +9366.19 q^{14} -15047.7 q^{15} +35400.4 q^{16} -250.572 q^{17} +23319.2 q^{18} -47393.5 q^{19} -138814. q^{20} -14735.5 q^{21} -118116. q^{22} -11730.8 q^{23} -116186. q^{24} +135423. q^{25} -280996. q^{26} -107902. q^{27} -135934. q^{28} -144917. q^{29} +311451. q^{30} +25022.5 q^{31} -275991. q^{32} +185828. q^{33} +5186.24 q^{34} +209118. q^{35} -338439. q^{36} +428389. q^{37} +980932. q^{38} +442082. q^{39} +1.64885e6 q^{40} -708444. q^{41} +304990. q^{42} -541986. q^{43} +1.71426e6 q^{44} +520645. q^{45} +242800. q^{46} +483710. q^{47} +1.15274e6 q^{48} -618764. q^{49} -2.80293e6 q^{50} -8159.34 q^{51} +4.07819e6 q^{52} +1.51440e6 q^{53} +2.23332e6 q^{54} -2.63717e6 q^{55} +1.61464e6 q^{56} -1.54327e6 q^{57} +2.99944e6 q^{58} -2.15802e6 q^{59} -4.52018e6 q^{60} +3.47244e6 q^{61} -517905. q^{62} +509844. q^{63} +1.18110e6 q^{64} -6.27377e6 q^{65} -3.84620e6 q^{66} +2.73868e6 q^{67} -75269.5 q^{68} -381989. q^{69} -4.32823e6 q^{70} +2.12071e6 q^{71} +4.02001e6 q^{72} +4.92614e6 q^{73} -8.86662e6 q^{74} +4.40975e6 q^{75} -1.42366e7 q^{76} -2.58246e6 q^{77} -9.15004e6 q^{78} -639874. q^{79} -1.63590e7 q^{80} -1.04959e6 q^{81} +1.46631e7 q^{82} +2.88015e6 q^{83} -4.42641e6 q^{84} +115793. q^{85} +1.12178e7 q^{86} -4.71892e6 q^{87} -2.03621e7 q^{88} -6.94291e6 q^{89} -1.07761e7 q^{90} -6.14362e6 q^{91} -3.52383e6 q^{92} +814803. q^{93} -1.00116e7 q^{94} +2.19011e7 q^{95} -8.98706e6 q^{96} +3.81505e6 q^{97} +1.28069e7 q^{98} -6.42960e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.6976	−1.82943	−0.914713	−	0.404104i	$-0.867583\pi$
$2$	−20.6976	−1.82943	−0.914713	+	0.404104i	$0.867583\pi$
$3$	32.5628	0.696302	0.348151	−	0.937438i	$-0.386810\pi$
$3$	32.5628	0.696302	0.348151	+	0.937438i	$0.386810\pi$
$4$	300.390	2.34680
$5$	−462.112	−1.65330	−0.826652	−	0.562714i	$-0.809757\pi$
$5$	−462.112	−1.65330	−0.826652	+	0.562714i	$0.809757\pi$
$6$	−673.972	−1.27383
$7$	−452.526	−0.498655	−0.249327	−	0.968419i	$-0.580210\pi$
$7$	−452.526	−0.498655	−0.249327	+	0.968419i	$0.580210\pi$
$8$	−3568.07	−2.46387
$9$	−1126.66	−0.515164
$10$	9564.62	3.02460
$11$	5706.77	1.29275	0.646377	−	0.763018i	$-0.276283\pi$
$11$	5706.77	1.29275	0.646377	+	0.763018i	$0.276283\pi$
$12$	9781.56	1.63408
$13$	13576.3	1.71388	0.856938	−	0.515420i	$-0.172364\pi$
$13$	13576.3	1.71388	0.856938	+	0.515420i	$0.172364\pi$
$14$	9366.19	0.912252
$15$	−15047.7	−1.15120
$16$	35400.4	2.16067
$17$	−250.572	−0.0123698	−0.00618489	−	0.999981i	$-0.501969\pi$
$17$	−250.572	−0.0123698	−0.00618489	+	0.999981i	$0.501969\pi$
$18$	23319.2	0.942454
$19$	−47393.5	−1.58519	−0.792595	−	0.609748i	$-0.791271\pi$
$19$	−47393.5	−1.58519	−0.792595	+	0.609748i	$0.791271\pi$
$20$	−138814.	−3.87997
$21$	−14735.5	−0.347214
$22$	−118116.	−2.36500
$23$	−11730.8	−0.201039	−0.100520	−	0.994935i	$-0.532051\pi$
$23$	−11730.8	−0.201039	−0.100520	+	0.994935i	$0.532051\pi$
$24$	−116186.	−1.71560
$25$	135423.	1.73341
$26$	−280996.	−3.13541
$27$	−107902.	−1.05501
$28$	−135934.	−1.17024
$29$	−144917.	−1.10339	−0.551693	−	0.834047i	$-0.686018\pi$
$29$	−144917.	−1.10339	−0.551693	+	0.834047i	$0.686018\pi$
$30$	311451.	2.10603
$31$	25022.5	0.150857	0.0754283	−	0.997151i	$-0.475968\pi$
$31$	25022.5	0.150857	0.0754283	+	0.997151i	$0.475968\pi$
$32$	−275991.	−1.48892
$33$	185828.	0.900147
$34$	5186.24	0.0226296
$35$	209118.	0.824428
$36$	−338439.	−1.20899
$37$	428389.	1.39038	0.695188	−	0.718828i	$-0.255321\pi$
$37$	428389.	1.39038	0.695188	+	0.718828i	$0.255321\pi$
$38$	980932.	2.89999
$39$	442082.	1.19337
$40$	1.64885e6	4.07353
$41$	−708444.	−1.60532	−0.802661	−	0.596435i	$-0.796583\pi$
$41$	−708444.	−1.60532	−0.802661	+	0.596435i	$0.796583\pi$
$42$	304990.	0.635203
$43$	−541986.	−1.03956	−0.519779	−	0.854301i	$-0.673986\pi$
$43$	−541986.	−1.03956	−0.519779	+	0.854301i	$0.673986\pi$
$44$	1.71426e6	3.03383
$45$	520645.	0.851722
$46$	242800.	0.367787
$47$	483710.	0.679583	0.339791	−	0.940501i	$-0.389644\pi$
$47$	483710.	0.679583	0.339791	+	0.940501i	$0.389644\pi$
$48$	1.15274e6	1.50448
$49$	−618764.	−0.751343
$50$	−2.80293e6	−3.17115
$51$	−8159.34	−0.00861310
$52$	4.07819e6	4.02212
$53$	1.51440e6	1.39725	0.698626	−	0.715487i	$-0.253795\pi$
$53$	1.51440e6	1.39725	0.698626	+	0.715487i	$0.253795\pi$
$54$	2.23332e6	1.93007
$55$	−2.63717e6	−2.13731
$56$	1.61464e6	1.22862
$57$	−1.54327e6	−1.10377
$58$	2.99944e6	2.01856
$59$	−2.15802e6	−1.36796	−0.683979	−	0.729502i	$-0.739752\pi$
$59$	−2.15802e6	−1.36796	−0.683979	+	0.729502i	$0.739752\pi$
$60$	−4.52018e6	−2.70163
$61$	3.47244e6	1.95876	0.979378	−	0.202039i	$-0.0647567\pi$
$61$	3.47244e6	1.95876	0.979378	+	0.202039i	$0.0647567\pi$
$62$	−517905.	−0.275981
$63$	509844.	0.256889
$64$	1.18110e6	0.563193
$65$	−6.27377e6	−2.83356
$66$	−3.84620e6	−1.64675
$67$	2.73868e6	1.11245	0.556223	−	0.831033i	$-0.312250\pi$
$67$	2.73868e6	1.11245	0.556223	+	0.831033i	$0.312250\pi$
$68$	−75269.5	−0.0290294
$69$	−381989.	−0.139984
$70$	−4.32823e6	−1.50823
$71$	2.12071e6	0.703196	0.351598	−	0.936151i	$-0.385638\pi$
$71$	2.12071e6	0.703196	0.351598	+	0.936151i	$0.385638\pi$
$72$	4.02001e6	1.26930
$73$	4.92614e6	1.48210	0.741049	−	0.671451i	$-0.234329\pi$
$73$	4.92614e6	1.48210	0.741049	+	0.671451i	$0.234329\pi$
$74$	−8.86662e6	−2.54359
$75$	4.40975e6	1.20698
$76$	−1.42366e7	−3.72013
$77$	−2.58246e6	−0.644638
$78$	−9.15004e6	−2.18319
$79$	−639874.	−0.146016	−0.0730079	−	0.997331i	$-0.523260\pi$
$79$	−639874.	−0.146016	−0.0730079	+	0.997331i	$0.523260\pi$
$80$	−1.63590e7	−3.57225
$81$	−1.04959e6	−0.219443
$82$	1.46631e7	2.93682
$83$	2.88015e6	0.552894	0.276447	−	0.961029i	$-0.410843\pi$
$83$	2.88015e6	0.552894	0.276447	+	0.961029i	$0.410843\pi$
$84$	−4.42641e6	−0.814842
$85$	115793.	0.0204510
$86$	1.12178e7	1.90179
$87$	−4.71892e6	−0.768290
$88$	−2.03621e7	−3.18518
$89$	−6.94291e6	−1.04394	−0.521971	−	0.852963i	$-0.674803\pi$
$89$	−6.94291e6	−1.04394	−0.521971	+	0.852963i	$0.674803\pi$
$90$	−1.07761e7	−1.55816
$91$	−6.14362e6	−0.854632
$92$	−3.52383e6	−0.471799
$93$	814803.	0.105042
$94$	−1.00116e7	−1.24325
$95$	2.19011e7	2.62080
$96$	−8.98706e6	−1.03674
$97$	3.81505e6	0.424423	0.212212	−	0.977224i	$-0.431933\pi$
$97$	3.81505e6	0.424423	0.212212	+	0.977224i	$0.431933\pi$
$98$	1.28069e7	1.37453
$99$	−6.42960e6	−0.665980
$100$	4.06797e7	4.06797
$101$	1.37787e7	1.33071	0.665356	−	0.746526i	$-0.268280\pi$
$101$	1.37787e7	1.33071	0.665356	+	0.746526i	$0.268280\pi$
$102$	168879.	0.0157570
$103$	−3.52774e6	−0.318102	−0.159051	−	0.987270i	$-0.550843\pi$
$103$	−3.52774e6	−0.318102	−0.159051	+	0.987270i	$0.550843\pi$
$104$	−4.84411e7	−4.22277
$105$	6.80946e6	0.574051
$106$	−3.13444e7	−2.55617
$107$	1.55655e7	1.22834	0.614172	−	0.789173i	$-0.289490\pi$
$107$	1.55655e7	1.22834	0.614172	+	0.789173i	$0.289490\pi$
$108$	−3.24128e7	−2.47590
$109$	1.09794e7	0.812054	0.406027	−	0.913861i	$-0.366914\pi$
$109$	1.09794e7	0.812054	0.406027	+	0.913861i	$0.366914\pi$
$110$	5.45830e7	3.91006
$111$	1.39495e7	0.968121
$112$	−1.60196e7	−1.07743
$113$	−2.46678e7	−1.60826	−0.804130	−	0.594453i	$-0.797369\pi$
$113$	−2.46678e7	−1.60826	−0.804130	+	0.594453i	$0.797369\pi$
$114$	3.19419e7	2.01927
$115$	5.42096e6	0.332379
$116$	−4.35318e7	−2.58943
$117$	−1.52959e7	−0.882926
$118$	4.46657e7	2.50258
$119$	113390.	0.00616825
$120$	5.36911e7	2.83641
$121$	1.30800e7	0.671212
$122$	−7.18711e7	−3.58340
$123$	−2.30689e7	−1.11779
$124$	7.51652e6	0.354030
$125$	−2.64781e7	−1.21255
$126$	−1.05525e7	−0.469959
$127$	3.90335e6	0.169093	0.0845464	−	0.996420i	$-0.473056\pi$
$127$	3.90335e6	0.169093	0.0845464	+	0.996420i	$0.473056\pi$
$128$	1.08809e7	0.458597
$129$	−1.76486e7	−0.723846
$130$	1.29852e8	5.18378
$131$	329102.	0.0127903	0.00639516	−	0.999980i	$-0.497964\pi$
$131$	329102.	0.0127903	0.00639516	+	0.999980i	$0.497964\pi$
$132$	5.58211e7	2.11246
$133$	2.14468e7	0.790463
$134$	−5.66840e7	−2.03514
$135$	4.98629e7	1.74425
$136$	894059.	0.0304775
$137$	4.63321e7	1.53943	0.769715	−	0.638388i	$-0.220398\pi$
$137$	4.63321e7	1.53943	0.769715	+	0.638388i	$0.220398\pi$
$138$	7.90625e6	0.256091
$139$	4.60022e7	1.45287	0.726435	−	0.687236i	$-0.241176\pi$
$139$	4.60022e7	1.45287	0.726435	+	0.687236i	$0.241176\pi$
$140$	6.28169e7	1.93477
$141$	1.57510e7	0.473195
$142$	−4.38935e7	−1.28645
$143$	7.74767e7	2.21562
$144$	−3.98844e7	−1.11310
$145$	6.69681e7	1.82423
$146$	−1.01959e8	−2.71139
$147$	−2.01487e7	−0.523162
$148$	1.28684e8	3.26293
$149$	−4.36169e7	−1.08020	−0.540099	−	0.841602i	$-0.681613\pi$
$149$	−4.36169e7	−1.08020	−0.540099	+	0.841602i	$0.681613\pi$
$150$	−9.12712e7	−2.20808
$151$	−8.48904e6	−0.200650	−0.100325	−	0.994955i	$-0.531988\pi$
$151$	−8.48904e6	−0.200650	−0.100325	+	0.994955i	$0.531988\pi$
$152$	1.69103e8	3.90571
$153$	282311.	0.00637246
$154$	5.34507e7	1.17932
$155$	−1.15632e7	−0.249412
$156$	1.32797e8	2.80061
$157$	−8.85252e7	−1.82565	−0.912826	−	0.408348i	$-0.866105\pi$
$157$	−8.85252e7	−1.82565	−0.912826	+	0.408348i	$0.866105\pi$
$158$	1.32439e7	0.267125
$159$	4.93131e7	0.972909
$160$	1.27539e8	2.46163
$161$	5.30850e6	0.100249
$162$	2.17239e7	0.401454
$163$	−3.32953e7	−0.602180	−0.301090	−	0.953596i	$-0.597350\pi$
$163$	−3.32953e7	−0.602180	−0.301090	+	0.953596i	$0.597350\pi$
$164$	−2.12810e8	−3.76737
$165$	−8.58736e7	−1.48822
$166$	−5.96121e7	−1.01148
$167$	−7.52087e7	−1.24957	−0.624785	−	0.780797i	$-0.714813\pi$
$167$	−7.52087e7	−1.24957	−0.624785	+	0.780797i	$0.714813\pi$
$168$	5.25773e7	0.855491
$169$	1.21567e8	1.93737
$170$	−2.39663e6	−0.0374136
$171$	5.33965e7	0.816633
$172$	−1.62807e8	−2.43963
$173$	4.38313e7	0.643610	0.321805	−	0.946806i	$-0.395710\pi$
$173$	4.38313e7	0.643610	0.321805	+	0.946806i	$0.395710\pi$
$174$	9.76703e7	1.40553
$175$	−6.12823e7	−0.864374
$176$	2.02022e8	2.79322
$177$	−7.02711e7	−0.952511
$178$	1.43702e8	1.90982
$179$	−6.52528e7	−0.850381	−0.425190	−	0.905104i	$-0.639793\pi$
$179$	−6.52528e7	−0.850381	−0.425190	+	0.905104i	$0.639793\pi$
$180$	1.56397e8	1.99882
$181$	−2.35902e7	−0.295704	−0.147852	−	0.989010i	$-0.547236\pi$
$181$	−2.35902e7	−0.295704	−0.147852	+	0.989010i	$0.547236\pi$
$182$	1.27158e8	1.56349
$183$	1.13072e8	1.36388
$184$	4.18564e7	0.495335
$185$	−1.97964e8	−2.29871
$186$	−1.68645e7	−0.192166
$187$	−1.42996e6	−0.0159911
$188$	1.45302e8	1.59485
$189$	4.88285e7	0.526086
$190$	−4.53301e8	−4.79456
$191$	−1.13802e8	−1.18177	−0.590883	−	0.806757i	$-0.701221\pi$
$191$	−1.13802e8	−1.18177	−0.590883	+	0.806757i	$0.701221\pi$
$192$	3.84600e7	0.392152
$193$	−1.55029e8	−1.55225	−0.776126	−	0.630578i	$-0.782818\pi$
$193$	−1.55029e8	−1.55225	−0.776126	+	0.630578i	$0.782818\pi$
$194$	−7.89623e7	−0.776451
$195$	−2.04292e8	−1.97301
$196$	−1.85871e8	−1.76325
$197$	1.30967e7	0.122048	0.0610238	−	0.998136i	$-0.480563\pi$
$197$	1.30967e7	0.122048	0.0610238	+	0.998136i	$0.480563\pi$
$198$	1.33077e8	1.21836
$199$	1.73246e8	1.55839	0.779195	−	0.626781i	$-0.215628\pi$
$199$	1.73246e8	1.55839	0.779195	+	0.626781i	$0.215628\pi$
$200$	−4.83198e8	−4.27091
$201$	8.91790e7	0.774598
$202$	−2.85186e8	−2.43444
$203$	6.55788e7	0.550209
$204$	−2.45099e6	−0.0202132
$205$	3.27381e8	2.65408
$206$	7.30157e7	0.581944
$207$	1.32167e7	0.103568
$208$	4.80607e8	3.70312
$209$	−2.70464e8	−2.04926
$210$	−1.40939e8	−1.05018
$211$	2.43285e8	1.78290	0.891449	−	0.453121i	$-0.149690\pi$
$211$	2.43285e8	1.78290	0.891449	+	0.453121i	$0.149690\pi$
$212$	4.54911e8	3.27907
$213$	6.90562e7	0.489637
$214$	−3.22168e8	−2.24716
$215$	2.50459e8	1.71870
$216$	3.85002e8	2.59941
$217$	−1.13233e7	−0.0752254
$218$	−2.27247e8	−1.48559
$219$	1.60409e8	1.03199
$220$	−7.92180e8	−5.01585
$221$	−3.40184e6	−0.0212003
$222$	−2.88722e8	−1.77111
$223$	1.99013e8	1.20175	0.600875	−	0.799343i	$-0.294819\pi$
$223$	1.99013e8	1.20175	0.600875	+	0.799343i	$0.294819\pi$
$224$	1.24893e8	0.742456
$225$	−1.52576e8	−0.892991
$226$	5.10565e8	2.94219
$227$	1.45302e8	0.824480	0.412240	−	0.911075i	$-0.364746\pi$
$227$	1.45302e8	0.824480	0.412240	+	0.911075i	$0.364746\pi$
$228$	−4.63583e8	−2.59033
$229$	1.64772e8	0.906688	0.453344	−	0.891336i	$-0.350231\pi$
$229$	1.64772e8	0.906688	0.453344	+	0.891336i	$0.350231\pi$
$230$	−1.12201e8	−0.608063
$231$	−8.40921e7	−0.448862
$232$	5.17075e8	2.71860
$233$	−1.44647e8	−0.749142	−0.374571	−	0.927198i	$-0.622210\pi$
$233$	−1.44647e8	−0.749142	−0.374571	+	0.927198i	$0.622210\pi$
$234$	3.16588e8	1.61525
$235$	−2.23528e8	−1.12356
$236$	−6.48247e8	−3.21032
$237$	−2.08361e7	−0.101671
$238$	−2.34691e6	−0.0112844
$239$	−7.23272e7	−0.342696	−0.171348	−	0.985211i	$-0.554812\pi$
$239$	−7.23272e7	−0.342696	−0.171348	+	0.985211i	$0.554812\pi$
$240$	−5.32695e8	−2.48736
$241$	−1.32868e7	−0.0611451	−0.0305726	−	0.999533i	$-0.509733\pi$
$241$	−1.32868e7	−0.0611451	−0.0305726	+	0.999533i	$0.509733\pi$
$242$	−2.70725e8	−1.22793
$243$	2.01805e8	0.902213
$244$	1.04309e9	4.59681
$245$	2.85938e8	1.24220
$246$	4.77472e8	2.04491
$247$	−6.43428e8	−2.71682
$248$	−8.92819e7	−0.371691
$249$	9.37857e7	0.384981
$250$	5.48032e8	2.21828
$251$	1.94047e8	0.774550	0.387275	−	0.921964i	$-0.373416\pi$
$251$	1.94047e8	0.774550	0.387275	+	0.921964i	$0.373416\pi$
$252$	1.53152e8	0.602867
$253$	−6.69451e7	−0.259894
$254$	−8.07901e7	−0.309343
$255$	3.77053e6	0.0142401
$256$	−3.76390e8	−1.40216
$257$	6.86558e6	0.0252297	0.0126148	−	0.999920i	$-0.495984\pi$
$257$	6.86558e6	0.0252297	0.0126148	+	0.999920i	$0.495984\pi$
$258$	3.65284e8	1.32422
$259$	−1.93857e8	−0.693317
$260$	−1.88458e9	−6.64979
$261$	1.63273e8	0.568424
$262$	−6.81162e6	−0.0233989
$263$	−3.22473e8	−1.09307	−0.546536	−	0.837436i	$-0.684054\pi$
$263$	−3.22473e8	−1.09307	−0.546536	+	0.837436i	$0.684054\pi$
$264$	−6.63048e8	−2.21785
$265$	−6.99823e8	−2.31008
$266$	−4.43897e8	−1.44609
$267$	−2.26081e8	−0.726899
$268$	8.22672e8	2.61069
$269$	4.42113e7	0.138484	0.0692421	−	0.997600i	$-0.477942\pi$
$269$	4.42113e7	0.138484	0.0692421	+	0.997600i	$0.477942\pi$
$270$	−1.03204e9	−3.19098
$271$	−4.37925e8	−1.33662	−0.668309	−	0.743884i	$-0.732982\pi$
$271$	−4.37925e8	−1.33662	−0.668309	+	0.743884i	$0.732982\pi$
$272$	−8.87037e6	−0.0267270
$273$	−2.00053e8	−0.595082
$274$	−9.58963e8	−2.81627
$275$	7.72827e8	2.24088
$276$	−1.14746e8	−0.328515
$277$	−5.17203e8	−1.46212	−0.731058	−	0.682315i	$-0.760973\pi$
$277$	−5.17203e8	−1.46212	−0.731058	+	0.682315i	$0.760973\pi$
$278$	−9.52134e8	−2.65792
$279$	−2.81919e7	−0.0777159
$280$	−7.46146e8	−2.03128
$281$	−5.70199e8	−1.53304	−0.766522	−	0.642218i	$-0.778014\pi$
$281$	−5.70199e8	−1.53304	−0.766522	+	0.642218i	$0.778014\pi$
$282$	−3.26007e8	−0.865675
$283$	1.56488e8	0.410419	0.205210	−	0.978718i	$-0.434212\pi$
$283$	1.56488e8	0.410419	0.205210	+	0.978718i	$0.434212\pi$
$284$	6.37040e8	1.65026
$285$	7.13163e8	1.82487
$286$	−1.60358e9	−4.05331
$287$	3.20589e8	0.800501
$288$	3.10949e8	0.767036
$289$	−4.10276e8	−0.999847
$290$	−1.38608e9	−3.33730
$291$	1.24229e8	0.295527
$292$	1.47977e9	3.47819
$293$	−5.66511e8	−1.31574	−0.657872	−	0.753130i	$-0.728543\pi$
$293$	−5.66511e8	−1.31574	−0.657872	+	0.753130i	$0.728543\pi$
$294$	4.17029e8	0.957086
$295$	9.97246e8	2.26165
$296$	−1.52852e9	−3.42571
$297$	−6.15773e8	−1.36387
$298$	9.02766e8	1.97614
$299$	−1.59261e8	−0.344556
$300$	1.32465e9	2.83254
$301$	2.45263e8	0.518380
$302$	1.75703e8	0.367074
$303$	4.48674e8	0.926577
$304$	−1.67775e9	−3.42508
$305$	−1.60466e9	−3.23842
$306$	−5.84315e6	−0.0116579
$307$	1.30923e8	0.258244	0.129122	−	0.991629i	$-0.458784\pi$
$307$	1.30923e8	0.258244	0.129122	+	0.991629i	$0.458784\pi$
$308$	−7.75746e8	−1.51284
$309$	−1.14873e8	−0.221495
$310$	2.39330e8	0.456281
$311$	6.75891e8	1.27413	0.637067	−	0.770808i	$-0.280147\pi$
$311$	6.75891e8	1.27413	0.637067	+	0.770808i	$0.280147\pi$
$312$	−1.57738e9	−2.94032
$313$	−1.03640e9	−1.91039	−0.955193	−	0.295985i	$-0.904352\pi$
$313$	−1.03640e9	−1.91039	−0.955193	+	0.295985i	$0.904352\pi$
$314$	1.83226e9	3.33990
$315$	−2.35605e8	−0.424715
$316$	−1.92212e8	−0.342670
$317$	−2.67791e7	−0.0472159	−0.0236080	−	0.999721i	$-0.507515\pi$
$317$	−2.67791e7	−0.0472159	−0.0236080	+	0.999721i	$0.507515\pi$
$318$	−1.02066e9	−1.77987
$319$	−8.27010e8	−1.42641
$320$	−5.45802e8	−0.931129
$321$	5.06856e8	0.855298
$322$	−1.09873e8	−0.183399
$323$	1.18755e7	0.0196085
$324$	−3.15286e8	−0.514988
$325$	1.83854e9	2.97085
$326$	6.89133e8	1.10164
$327$	3.57519e8	0.565435
$328$	2.52778e9	3.95531
$329$	−2.18891e8	−0.338877
$330$	1.77738e9	2.72258
$331$	3.66079e7	0.0554851	0.0277426	−	0.999615i	$-0.491168\pi$
$331$	3.66079e7	0.0554851	0.0277426	+	0.999615i	$0.491168\pi$
$332$	8.65169e8	1.29753
$333$	−4.82650e8	−0.716271
$334$	1.55664e9	2.28600
$335$	−1.26558e9	−1.83921
$336$	−5.21643e8	−0.750216
$337$	6.25249e8	0.889915	0.444957	−	0.895552i	$-0.353219\pi$
$337$	6.25249e8	0.889915	0.444957	+	0.895552i	$0.353219\pi$
$338$	−2.51614e9	−3.54427
$339$	−8.03254e8	−1.11984
$340$	3.47830e7	0.0479944
$341$	1.42797e8	0.195020
$342$	−1.10518e9	−1.49397
$343$	6.52681e8	0.873316
$344$	1.93384e9	2.56134
$345$	1.76522e8	0.231436
$346$	−9.07203e8	−1.17744
$347$	−8.08895e8	−1.03929	−0.519647	−	0.854381i	$-0.673937\pi$
$347$	−8.08895e8	−1.03929	−0.519647	+	0.854381i	$0.673937\pi$
$348$	−1.41752e9	−1.80302
$349$	3.34470e8	0.421180	0.210590	−	0.977574i	$-0.432461\pi$
$349$	3.34470e8	0.421180	0.210590	+	0.977574i	$0.432461\pi$
$350$	1.26840e9	1.58131
$351$	−1.46491e9	−1.80816
$352$	−1.57502e9	−1.92480
$353$	−8.21180e8	−0.993635	−0.496817	−	0.867855i	$-0.665498\pi$
$353$	−8.21180e8	−0.993635	−0.496817	+	0.867855i	$0.665498\pi$
$354$	1.45444e9	1.74255
$355$	−9.80005e8	−1.16260
$356$	−2.08558e9	−2.44993
$357$	3.69231e6	0.00429496
$358$	1.35058e9	1.55571
$359$	−3.47235e8	−0.396090	−0.198045	−	0.980193i	$-0.563459\pi$
$359$	−3.47235e8	−0.396090	−0.198045	+	0.980193i	$0.563459\pi$
$360$	−1.85770e9	−2.09853
$361$	1.35228e9	1.51283
$362$	4.88260e8	0.540968
$363$	4.25922e8	0.467366
$364$	−1.84548e9	−2.00565
$365$	−2.27643e9	−2.45036
$366$	−2.34033e9	−2.49513
$367$	6.27139e8	0.662266	0.331133	−	0.943584i	$-0.392569\pi$
$367$	6.27139e8	0.662266	0.331133	+	0.943584i	$0.392569\pi$
$368$	−4.15276e8	−0.434380
$369$	7.98178e8	0.827004
$370$	4.09737e9	4.20532
$371$	−6.85304e8	−0.696746
$372$	2.44759e8	0.246512
$373$	3.23033e8	0.322304	0.161152	−	0.986930i	$-0.448479\pi$
$373$	3.23033e8	0.322304	0.161152	+	0.986930i	$0.448479\pi$
$374$	2.95967e7	0.0292545
$375$	−8.62200e8	−0.844303
$376$	−1.72591e9	−1.67440
$377$	−1.96744e9	−1.89107
$378$	−1.01063e9	−0.962436
$379$	−1.08712e9	−1.02575	−0.512875	−	0.858463i	$-0.671420\pi$
$379$	−1.08712e9	−1.02575	−0.512875	+	0.858463i	$0.671420\pi$
$380$	6.57889e9	6.15050
$381$	1.27104e8	0.117740
$382$	2.35542e9	2.16196
$383$	9.19973e8	0.836718	0.418359	−	0.908282i	$-0.362605\pi$
$383$	9.19973e8	0.836718	0.418359	+	0.908282i	$0.362605\pi$
$384$	3.54314e8	0.319322
$385$	1.19339e9	1.06578
$386$	3.20873e9	2.83973
$387$	6.10636e8	0.535542
$388$	1.14600e9	0.996036
$389$	−2.09983e8	−0.180868	−0.0904339	−	0.995902i	$-0.528825\pi$
$389$	−2.09983e8	−0.180868	−0.0904339	+	0.995902i	$0.528825\pi$
$390$	4.22835e9	3.60948
$391$	2.93942e6	0.00248681
$392$	2.20779e9	1.85121
$393$	1.07165e7	0.00890592
$394$	−2.71070e8	−0.223277
$395$	2.95694e8	0.241408
$396$	−1.93139e9	−1.56292
$397$	3.19714e8	0.256446	0.128223	−	0.991745i	$-0.459073\pi$
$397$	3.19714e8	0.256446	0.128223	+	0.991745i	$0.459073\pi$
$398$	−3.58577e9	−2.85096
$399$	6.98368e8	0.550401
$400$	4.79403e9	3.74534
$401$	1.76539e8	0.136721	0.0683603	−	0.997661i	$-0.478223\pi$
$401$	1.76539e8	0.136721	0.0683603	+	0.997661i	$0.478223\pi$
$402$	−1.84579e9	−1.41707
$403$	3.39712e8	0.258550
$404$	4.13899e9	3.12291
$405$	4.85027e8	0.362805
$406$	−1.35732e9	−1.00657
$407$	2.44471e9	1.79741
$408$	2.91131e7	0.0212216
$409$	8.70079e8	0.628821	0.314411	−	0.949287i	$-0.398193\pi$
$409$	8.70079e8	0.628821	0.314411	+	0.949287i	$0.398193\pi$
$410$	−6.77600e9	−4.85545
$411$	1.50870e9	1.07191
$412$	−1.05970e9	−0.746521
$413$	9.76557e8	0.682138
$414$	−2.73554e8	−0.189470
$415$	−1.33095e9	−0.914101
$416$	−3.74694e9	−2.55182
$417$	1.49796e9	1.01164
$418$	5.59795e9	3.74897
$419$	1.81977e8	0.120856	0.0604280	−	0.998173i	$-0.480753\pi$
$419$	1.81977e8	0.120856	0.0604280	+	0.998173i	$0.480753\pi$
$420$	2.04550e9	1.34718
$421$	9.22851e8	0.602760	0.301380	−	0.953504i	$-0.402553\pi$
$421$	9.22851e8	0.602760	0.301380	+	0.953504i	$0.402553\pi$
$422$	−5.03541e9	−3.26168
$423$	−5.44978e8	−0.350096
$424$	−5.40348e9	−3.44265
$425$	−3.39332e7	−0.0214419
$426$	−1.42930e9	−0.895754
$427$	−1.57137e9	−0.976742
$428$	4.67573e9	2.88268
$429$	2.52286e9	1.54274
$430$	−5.18389e9	−3.14424
$431$	−1.69038e9	−1.01699	−0.508493	−	0.861066i	$-0.669797\pi$
$431$	−1.69038e9	−1.01699	−0.508493	+	0.861066i	$0.669797\pi$
$432$	−3.81979e9	−2.27953
$433$	−2.33674e9	−1.38326	−0.691629	−	0.722253i	$-0.743107\pi$
$433$	−2.33674e9	−1.38326	−0.691629	+	0.722253i	$0.743107\pi$
$434$	2.34365e8	0.137619
$435$	2.18067e9	1.27022
$436$	3.29810e9	1.90573
$437$	5.55965e8	0.318686
$438$	−3.32008e9	−1.88795
$439$	8.38580e8	0.473063	0.236531	−	0.971624i	$-0.423989\pi$
$439$	8.38580e8	0.473063	0.236531	+	0.971624i	$0.423989\pi$
$440$	9.40959e9	5.26607
$441$	6.97138e8	0.387065
$442$	7.04099e7	0.0387843
$443$	−2.76395e9	−1.51049	−0.755244	−	0.655444i	$-0.772482\pi$
$443$	−2.76395e9	−1.51049	−0.755244	+	0.655444i	$0.772482\pi$
$444$	4.19031e9	2.27199
$445$	3.20841e9	1.72595
$446$	−4.11909e9	−2.19851
$447$	−1.42029e9	−0.752144
$448$	−5.34478e8	−0.280839
$449$	2.59235e9	1.35155	0.675774	−	0.737109i	$-0.263809\pi$
$449$	2.59235e9	1.35155	0.675774	+	0.737109i	$0.263809\pi$
$450$	3.15795e9	1.63366
$451$	−4.04293e9	−2.07529
$452$	−7.40998e9	−3.77427
$453$	−2.76427e8	−0.139713
$454$	−3.00740e9	−1.50833
$455$	2.83904e9	1.41297
$456$	5.50648e9	2.71955
$457$	3.12466e9	1.53143	0.765713	−	0.643183i	$-0.222386\pi$
$457$	3.12466e9	1.53143	0.765713	+	0.643183i	$0.222386\pi$
$458$	−3.41037e9	−1.65872
$459$	2.70373e7	0.0130503
$460$	1.62840e9	0.780027
$461$	−1.31904e8	−0.0627053	−0.0313526	−	0.999508i	$-0.509981\pi$
$461$	−1.31904e8	−0.0627053	−0.0313526	+	0.999508i	$0.509981\pi$
$462$	1.74050e9	0.821161
$463$	6.90639e8	0.323383	0.161692	−	0.986841i	$-0.448305\pi$
$463$	6.90639e8	0.323383	0.161692	+	0.986841i	$0.448305\pi$
$464$	−5.13014e9	−2.38405
$465$	−3.76530e8	−0.173666
$466$	2.99385e9	1.37050
$467$	−1.62280e9	−0.737322	−0.368661	−	0.929564i	$-0.620184\pi$
$467$	−1.62280e9	−0.737322	−0.368661	+	0.929564i	$0.620184\pi$
$468$	−4.59474e9	−2.07205
$469$	−1.23932e9	−0.554726
$470$	4.62650e9	2.05546
$471$	−2.88263e9	−1.27121
$472$	7.69994e9	3.37047
$473$	−3.09299e9	−1.34389
$474$	4.31257e8	0.186000
$475$	−6.41817e9	−2.74779
$476$	3.40614e7	0.0144756
$477$	−1.70622e9	−0.719814
$478$	1.49700e9	0.626937
$479$	−1.59426e9	−0.662805	−0.331403	−	0.943489i	$-0.607522\pi$
$479$	−1.59426e9	−0.662805	−0.331403	+	0.943489i	$0.607522\pi$
$480$	4.15303e9	1.71404
$481$	5.81593e9	2.38293
$482$	2.75005e8	0.111860
$483$	1.72860e8	0.0698037
$484$	3.92911e9	1.57520
$485$	−1.76298e9	−0.701700
$486$	−4.17687e9	−1.65053
$487$	−7.80522e8	−0.306220	−0.153110	−	0.988209i	$-0.548929\pi$
$487$	−7.80522e8	−0.306220	−0.153110	+	0.988209i	$0.548929\pi$
$488$	−1.23899e10	−4.82612
$489$	−1.08419e9	−0.419299
$490$	−5.91824e9	−2.27251
$491$	−1.44603e9	−0.551306	−0.275653	−	0.961257i	$-0.588894\pi$
$491$	−1.44603e9	−0.551306	−0.275653	+	0.961257i	$0.588894\pi$
$492$	−6.92969e9	−2.62323
$493$	3.63123e7	0.0136486
$494$	1.33174e10	4.97022
$495$	2.97120e9	1.10107
$496$	8.85807e8	0.325952
$497$	−9.59674e8	−0.350652
$498$	−1.94114e9	−0.704294
$499$	7.96792e8	0.287074	0.143537	−	0.989645i	$-0.454152\pi$
$499$	7.96792e8	0.287074	0.143537	+	0.989645i	$0.454152\pi$
$500$	−7.95375e9	−2.84562
$501$	−2.44901e9	−0.870078
$502$	−4.01631e9	−1.41698
$503$	−4.30139e9	−1.50703	−0.753513	−	0.657433i	$-0.771642\pi$
$503$	−4.30139e9	−1.50703	−0.753513	+	0.657433i	$0.771642\pi$
$504$	−1.81916e9	−0.632941
$505$	−6.36732e9	−2.20007
$506$	1.38560e9	0.475458
$507$	3.95856e9	1.34899
$508$	1.17253e9	0.396827
$509$	−1.36307e9	−0.458147	−0.229073	−	0.973409i	$-0.573570\pi$
$509$	−1.36307e9	−0.458147	−0.229073	+	0.973409i	$0.573570\pi$
$510$	−7.80409e7	−0.0260511
$511$	−2.22921e9	−0.739055
$512$	6.39761e9	2.10656
$513$	5.11387e9	1.67239
$514$	−1.42101e8	−0.0461558
$515$	1.63021e9	0.525919
$516$	−5.30147e9	−1.69872
$517$	2.76042e9	0.878533
$518$	4.01237e9	1.26837
$519$	1.42727e9	0.448147
$520$	2.23852e10	6.98152
$521$	−1.09022e9	−0.337740	−0.168870	−	0.985638i	$-0.554012\pi$
$521$	−1.09022e9	−0.337740	−0.168870	+	0.985638i	$0.554012\pi$
$522$	−3.37936e9	−1.03989
$523$	−3.70961e9	−1.13389	−0.566946	−	0.823755i	$-0.691875\pi$
$523$	−3.70961e9	−1.13389	−0.566946	+	0.823755i	$0.691875\pi$
$524$	9.88591e7	0.0300163
$525$	−1.99552e9	−0.601866
$526$	6.67442e9	1.99969
$527$	−6.26994e6	−0.00186606
$528$	6.57841e9	1.94492
$529$	−3.26721e9	−0.959583
$530$	1.44846e10	4.22613
$531$	2.43136e9	0.704722
$532$	6.44241e9	1.85506
$533$	−9.61804e9	−2.75132
$534$	4.67933e9	1.32981
$535$	−7.19301e9	−2.03082
$536$	−9.77178e9	−2.74092
$537$	−2.12481e9	−0.592122
$538$	−9.15068e8	−0.253347
$539$	−3.53114e9	−0.971302
$540$	1.49784e10	4.09342
$541$	−5.55033e9	−1.50705	−0.753526	−	0.657419i	$-0.771648\pi$
$541$	−5.55033e9	−1.50705	−0.753526	+	0.657419i	$0.771648\pi$
$542$	9.06400e9	2.44524
$543$	−7.68163e8	−0.205899
$544$	6.91558e7	0.0184176
$545$	−5.07370e9	−1.34257
$546$	4.14062e9	1.08866
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	1.39177e10	3.61273
$549$	−3.91227e9	−1.00908
$550$	−1.59957e10	−4.09952
$551$	6.86815e9	1.74908
$552$	1.36296e9	0.344903
$553$	2.89559e8	0.0728115
$554$	1.07049e10	2.67483
$555$	−6.44626e9	−1.60060
$556$	1.38186e10	3.40959
$557$	1.63682e9	0.401336	0.200668	−	0.979659i	$-0.435689\pi$
$557$	1.63682e9	0.401336	0.200668	+	0.979659i	$0.435689\pi$
$558$	5.83505e8	0.142175
$559$	−7.35816e9	−1.78167
$560$	7.40286e9	1.78132
$561$	−4.65634e7	−0.0111346
$562$	1.18018e10	2.80459
$563$	−3.19509e9	−0.754578	−0.377289	−	0.926096i	$-0.623144\pi$
$563$	−3.19509e9	−0.754578	−0.377289	+	0.926096i	$0.623144\pi$
$564$	4.73144e9	1.11049
$565$	1.13993e10	2.65894
$566$	−3.23892e9	−0.750832
$567$	4.74965e8	0.109426
$568$	−7.56683e9	−1.73259
$569$	−4.31790e9	−0.982606	−0.491303	−	0.870989i	$-0.663479\pi$
$569$	−4.31790e9	−0.982606	−0.491303	+	0.870989i	$0.663479\pi$
$570$	−1.47608e10	−3.33846
$571$	4.70752e9	1.05819	0.529097	−	0.848561i	$-0.322531\pi$
$571$	4.70752e9	1.05819	0.529097	+	0.848561i	$0.322531\pi$
$572$	2.32733e10	5.19961
$573$	−3.70570e9	−0.822866
$574$	−6.63542e9	−1.46446
$575$	−1.58862e9	−0.348484
$576$	−1.33070e9	−0.290137
$577$	4.80790e9	1.04193	0.520967	−	0.853577i	$-0.325572\pi$
$577$	4.80790e9	1.04193	0.520967	+	0.853577i	$0.325572\pi$
$578$	8.49172e9	1.82915
$579$	−5.04818e9	−1.08084
$580$	2.01166e10	4.28111
$581$	−1.30334e9	−0.275703
$582$	−2.57124e9	−0.540644
$583$	8.64232e9	1.80630
$584$	−1.75768e10	−3.65170
$585$	7.06842e9	1.45975
$586$	1.17254e10	2.40706
$587$	−5.17570e9	−1.05617	−0.528087	−	0.849190i	$-0.677091\pi$
$587$	−5.17570e9	−1.05617	−0.528087	+	0.849190i	$0.677091\pi$
$588$	−6.05247e9	−1.22776
$589$	−1.18590e9	−0.239137
$590$	−2.06406e10	−4.13752
$591$	4.26465e8	0.0849820
$592$	1.51652e10	3.00414
$593$	−3.34397e9	−0.658523	−0.329261	−	0.944239i	$-0.606800\pi$
$593$	−3.34397e9	−0.658523	−0.329261	+	0.944239i	$0.606800\pi$
$594$	1.27450e10	2.49510
$595$	−5.23991e7	−0.0101980
$596$	−1.31021e10	−2.53501
$597$	5.64136e9	1.08511
$598$	3.29632e9	0.630340
$599$	8.75111e9	1.66368	0.831839	−	0.555017i	$-0.187288\pi$
$599$	8.75111e9	1.66368	0.831839	+	0.555017i	$0.187288\pi$
$600$	−1.57343e10	−2.97384
$601$	−3.85707e9	−0.724765	−0.362382	−	0.932030i	$-0.618037\pi$
$601$	−3.85707e9	−0.724765	−0.362382	+	0.932030i	$0.618037\pi$
$602$	−5.07635e9	−0.948339
$603$	−3.08556e9	−0.573092
$604$	−2.55003e9	−0.470885
$605$	−6.04444e9	−1.10972
$606$	−9.28647e9	−1.69510
$607$	−1.05738e10	−1.91899	−0.959493	−	0.281734i	$-0.909090\pi$
$607$	−1.05738e10	−1.91899	−0.959493	+	0.281734i	$0.909090\pi$
$608$	1.30802e10	2.36022
$609$	2.13543e9	0.383111
$610$	3.32125e10	5.92444
$611$	6.56698e9	1.16472
$612$	8.48034e7	0.0149549
$613$	8.72918e9	1.53060	0.765300	−	0.643674i	$-0.222591\pi$
$613$	8.72918e9	1.53060	0.765300	+	0.643674i	$0.222591\pi$
$614$	−2.70978e9	−0.472438
$615$	1.06604e10	1.84804
$616$	9.21438e9	1.58830
$617$	1.02587e9	0.175830	0.0879151	−	0.996128i	$-0.471980\pi$
$617$	1.02587e9	0.175830	0.0879151	+	0.996128i	$0.471980\pi$
$618$	2.37760e9	0.405209
$619$	−3.00461e9	−0.509180	−0.254590	−	0.967049i	$-0.581940\pi$
$619$	−3.00461e9	−0.509180	−0.254590	+	0.967049i	$0.581940\pi$
$620$	−3.47347e9	−0.585320
$621$	1.26578e9	0.212099
$622$	−1.39893e10	−2.33094
$623$	3.14185e9	0.520567
$624$	1.56499e10	2.57849
$625$	1.65592e9	0.271307
$626$	2.14509e10	3.49491
$627$	−8.80707e9	−1.42690
$628$	−2.65921e10	−4.28444
$629$	−1.07342e8	−0.0171986
$630$	4.87646e9	0.776985
$631$	−7.37106e9	−1.16796	−0.583979	−	0.811769i	$-0.698505\pi$
$631$	−7.37106e9	−1.16796	−0.583979	+	0.811769i	$0.698505\pi$
$632$	2.28311e9	0.359764
$633$	7.92204e9	1.24144
$634$	5.54263e8	0.0863781
$635$	−1.80379e9	−0.279562
$636$	1.48132e10	2.28322
$637$	−8.40051e9	−1.28771
$638$	1.71171e10	2.60951
$639$	−2.38932e9	−0.362261
$640$	−5.02822e9	−0.758201
$641$	7.21629e9	1.08221	0.541104	−	0.840956i	$-0.318007\pi$
$641$	7.21629e9	1.08221	0.541104	+	0.840956i	$0.318007\pi$
$642$	−1.04907e10	−1.56470
$643$	−6.52688e9	−0.968205	−0.484102	−	0.875011i	$-0.660854\pi$
$643$	−6.52688e9	−0.968205	−0.484102	+	0.875011i	$0.660854\pi$
$644$	1.59462e9	0.235265
$645$	8.15564e9	1.19674
$646$	−2.45794e8	−0.0358722
$647$	−6.37976e9	−0.926061	−0.463031	−	0.886342i	$-0.653238\pi$
$647$	−6.37976e9	−0.926061	−0.463031	+	0.886342i	$0.653238\pi$
$648$	3.74500e9	0.540679
$649$	−1.23153e10	−1.76843
$650$	−3.80533e10	−5.43496
$651$	−3.68719e8	−0.0523796
$652$	−1.00016e10	−1.41320
$653$	−3.21717e9	−0.452145	−0.226073	−	0.974110i	$-0.572589\pi$
$653$	−3.21717e9	−0.452145	−0.226073	+	0.974110i	$0.572589\pi$
$654$	−7.39979e9	−1.03442
$655$	−1.52082e8	−0.0211463
$656$	−2.50792e10	−3.46857
$657$	−5.55010e9	−0.763523
$658$	4.53052e9	0.619951
$659$	−9.49390e9	−1.29225	−0.646124	−	0.763233i	$-0.723611\pi$
$659$	−9.49390e9	−1.29225	−0.646124	+	0.763233i	$0.723611\pi$
$660$	−2.57956e10	−3.49255
$661$	4.23399e9	0.570223	0.285111	−	0.958494i	$-0.407969\pi$
$661$	4.23399e9	0.570223	0.285111	+	0.958494i	$0.407969\pi$
$662$	−7.57695e8	−0.101506
$663$	−1.10774e8	−0.0147618
$664$	−1.02766e10	−1.36226
$665$	−9.91083e9	−1.30688
$666$	9.98969e9	1.31036
$667$	1.70000e9	0.221824
$668$	−2.25920e10	−2.93249
$669$	6.48042e9	0.836780
$670$	2.61944e10	3.36470
$671$	1.98164e10	2.53219
$672$	4.06687e9	0.516973
$673$	−7.60272e9	−0.961427	−0.480713	−	0.876878i	$-0.659622\pi$
$673$	−7.60272e9	−0.961427	−0.480713	+	0.876878i	$0.659622\pi$
$674$	−1.29412e10	−1.62803
$675$	−1.46124e10	−1.82877
$676$	3.65176e10	4.54662
$677$	−2.00258e9	−0.248045	−0.124022	−	0.992279i	$-0.539579\pi$
$677$	−2.00258e9	−0.248045	−0.124022	+	0.992279i	$0.539579\pi$
$678$	1.66254e10	2.04866
$679$	−1.72641e9	−0.211641
$680$	−4.13156e8	−0.0503886
$681$	4.73143e9	0.574087
$682$	−2.95556e9	−0.356776
$683$	1.21297e10	1.45673	0.728364	−	0.685190i	$-0.240281\pi$
$683$	1.21297e10	1.45673	0.728364	+	0.685190i	$0.240281\pi$
$684$	1.60398e10	1.91647
$685$	−2.14106e10	−2.54514
$686$	−1.35089e10	−1.59767
$687$	5.36543e9	0.631329
$688$	−1.91866e10	−2.24614
$689$	2.05599e10	2.39472
$690$	−3.65357e9	−0.423395
$691$	2.08830e9	0.240780	0.120390	−	0.992727i	$-0.461586\pi$
$691$	2.08830e9	0.240780	0.120390	+	0.992727i	$0.461586\pi$
$692$	1.31665e10	1.51042
$693$	2.90956e9	0.332094
$694$	1.67422e10	1.90131
$695$	−2.12582e10	−2.40203
$696$	1.68374e10	1.89297
$697$	1.77516e8	0.0198575
$698$	−6.92272e9	−0.770518
$699$	−4.71012e9	−0.521629
$700$	−1.84086e10	−2.02851
$701$	1.12854e10	1.23739	0.618693	−	0.785633i	$-0.287662\pi$
$701$	1.12854e10	1.23739	0.618693	+	0.785633i	$0.287662\pi$
$702$	3.03201e10	3.30789
$703$	−2.03029e10	−2.20401
$704$	6.74027e9	0.728070
$705$	−7.27871e9	−0.782335
$706$	1.69964e10	1.81778
$707$	−6.23522e9	−0.663566
$708$	−2.11088e10	−2.23535
$709$	−7.37738e9	−0.777392	−0.388696	−	0.921366i	$-0.627074\pi$
$709$	−7.37738e9	−0.777392	−0.388696	+	0.921366i	$0.627074\pi$
$710$	2.02837e10	2.12688
$711$	7.20923e8	0.0752220
$712$	2.47728e10	2.57214
$713$	−2.93534e8	−0.0303281
$714$	−7.64219e7	−0.00785732
$715$	−3.58029e10	−3.66309
$716$	−1.96013e10	−1.99567
$717$	−2.35518e9	−0.238620
$718$	7.18694e9	0.724617
$719$	−7.07106e9	−0.709469	−0.354735	−	0.934967i	$-0.615429\pi$
$719$	−7.07106e9	−0.709469	−0.354735	+	0.934967i	$0.615429\pi$
$720$	1.84311e10	1.84029
$721$	1.59639e9	0.158623
$722$	−2.79889e10	−2.76761
$723$	−4.32657e8	−0.0425755
$724$	−7.08627e9	−0.693957
$725$	−1.96251e10	−1.91262
$726$	−8.81557e9	−0.855012
$727$	−1.10405e10	−1.06566	−0.532831	−	0.846222i	$-0.678872\pi$
$727$	−1.10405e10	−1.06566	−0.532831	+	0.846222i	$0.678872\pi$
$728$	2.19208e10	2.10570
$729$	8.86677e9	0.847655
$730$	4.71167e10	4.48275
$731$	1.35807e8	0.0128591
$732$	3.39659e10	3.20077
$733$	1.69069e10	1.58563	0.792814	−	0.609464i	$-0.208615\pi$
$733$	1.69069e10	1.58563	0.792814	+	0.609464i	$0.208615\pi$
$734$	−1.29803e10	−1.21157
$735$	9.31096e9	0.864945
$736$	3.23761e9	0.299331
$737$	1.56290e10	1.43812
$738$	−1.65204e10	−1.51294
$739$	1.38707e10	1.26428	0.632138	−	0.774856i	$-0.282178\pi$
$739$	1.38707e10	1.26428	0.632138	+	0.774856i	$0.282178\pi$
$740$	−5.94664e10	−5.39462
$741$	−2.09518e10	−1.89173
$742$	1.41842e10	1.27465
$743$	−8.38037e8	−0.0749553	−0.0374777	−	0.999297i	$-0.511932\pi$
$743$	−8.38037e8	−0.0749553	−0.0374777	+	0.999297i	$0.511932\pi$
$744$	−2.90727e9	−0.258809
$745$	2.01559e10	1.78589
$746$	−6.68600e9	−0.589631
$747$	−3.24496e9	−0.284831
$748$	−4.29546e8	−0.0375279
$749$	−7.04378e9	−0.612519
$750$	1.78455e10	1.54459
$751$	−7.83230e9	−0.674761	−0.337380	−	0.941368i	$-0.609541\pi$
$751$	−7.83230e9	−0.674761	−0.337380	+	0.941368i	$0.609541\pi$
$752$	1.71235e10	1.46836
$753$	6.31873e9	0.539321
$754$	4.07213e10	3.45957
$755$	3.92289e9	0.331735
$756$	1.46676e10	1.23462
$757$	−1.14880e10	−0.962515	−0.481258	−	0.876579i	$-0.659820\pi$
$757$	−1.14880e10	−0.962515	−0.481258	+	0.876579i	$0.659820\pi$
$758$	2.25008e10	1.87653
$759$	−2.17992e9	−0.180965
$760$	−7.81448e10	−6.45732
$761$	−1.85314e10	−1.52427	−0.762133	−	0.647420i	$-0.775848\pi$
$761$	−1.85314e10	−1.52427	−0.762133	+	0.647420i	$0.775848\pi$
$762$	−2.63075e9	−0.215396
$763$	−4.96845e9	−0.404934
$764$	−3.41849e10	−2.77337
$765$	−1.30459e8	−0.0105356
$766$	−1.90412e10	−1.53071
$767$	−2.92978e10	−2.34451
$768$	−1.22563e10	−0.976329
$769$	1.26418e8	0.0100246	0.00501230	−	0.999987i	$-0.498405\pi$
$769$	1.26418e8	0.0100246	0.00501230	+	0.999987i	$0.498405\pi$
$770$	−2.47002e10	−1.94977
$771$	2.23563e8	0.0175675
$772$	−4.65692e10	−3.64282
$773$	1.14152e10	0.888907	0.444453	−	0.895802i	$-0.353398\pi$
$773$	1.14152e10	0.888907	0.444453	+	0.895802i	$0.353398\pi$
$774$	−1.26387e10	−0.979735
$775$	3.38862e9	0.261497
$776$	−1.36124e10	−1.04572
$777$	−6.31253e9	−0.482758
$778$	4.34615e9	0.330884
$779$	3.35757e10	2.54474
$780$	−6.13672e10	−4.63026
$781$	1.21024e10	0.909059
$782$	−6.08389e7	−0.00454944
$783$	1.56369e10	1.16408
$784$	−2.19045e10	−1.62341
$785$	4.09086e10	3.01836
$786$	−2.21806e8	−0.0162927
$787$	1.99791e10	1.46105	0.730525	−	0.682886i	$-0.239275\pi$
$787$	1.99791e10	1.46105	0.730525	+	0.682886i	$0.239275\pi$
$788$	3.93412e9	0.286421
$789$	−1.05006e10	−0.761108
$790$	−6.12015e9	−0.441639
$791$	1.11628e10	0.801967
$792$	2.29413e10	1.64089
$793$	4.71428e10	3.35706
$794$	−6.61732e9	−0.469149
$795$	−2.27882e10	−1.60851
$796$	5.20413e10	3.65723
$797$	−1.44382e10	−1.01020	−0.505102	−	0.863060i	$-0.668545\pi$
$797$	−1.44382e10	−1.01020	−0.505102	+	0.863060i	$0.668545\pi$
$798$	−1.44545e10	−1.00692
$799$	−1.21204e8	−0.00840629
$800$	−3.73755e10	−2.58091
$801$	7.82232e9	0.537801
$802$	−3.65392e9	−0.250120
$803$	2.81123e10	1.91599
$804$	2.67885e10	1.81783
$805$	−2.45312e9	−0.165742
$806$	−7.03123e9	−0.472997
$807$	1.43964e9	0.0964268
$808$	−4.91634e10	−3.27870
$809$	9.38563e9	0.623223	0.311612	−	0.950210i	$-0.399131\pi$
$809$	9.38563e9	0.623223	0.311612	+	0.950210i	$0.399131\pi$
$810$	−1.00389e10	−0.663726
$811$	−2.53034e10	−1.66574	−0.832868	−	0.553471i	$-0.813303\pi$
$811$	−2.53034e10	−1.66574	−0.832868	+	0.553471i	$0.813303\pi$
$812$	1.96992e10	1.29123
$813$	−1.42601e10	−0.930690
$814$	−5.05997e10	−3.28823
$815$	1.53862e10	0.995586
$816$	−2.88844e8	−0.0186101
$817$	2.56866e10	1.64790
$818$	−1.80086e10	−1.15038
$819$	6.92178e9	0.440275
$820$	9.83421e10	6.22861
$821$	9.66997e9	0.609852	0.304926	−	0.952376i	$-0.401368\pi$
$821$	9.66997e9	0.609852	0.304926	+	0.952376i	$0.401368\pi$
$822$	−3.12265e10	−1.96098
$823$	−2.88661e10	−1.80505	−0.902523	−	0.430642i	$-0.858287\pi$
$823$	−2.88661e10	−1.80505	−0.902523	+	0.430642i	$0.858287\pi$
$824$	1.25872e10	0.783762
$825$	2.51654e10	1.56033
$826$	−2.02124e10	−1.24792
$827$	1.55360e10	0.955146	0.477573	−	0.878592i	$-0.341517\pi$
$827$	1.55360e10	0.955146	0.477573	+	0.878592i	$0.341517\pi$
$828$	3.97017e9	0.243054
$829$	−1.52392e10	−0.929012	−0.464506	−	0.885570i	$-0.653768\pi$
$829$	−1.52392e10	−0.929012	−0.464506	+	0.885570i	$0.653768\pi$
$830$	2.75475e10	1.67228
$831$	−1.68416e10	−1.01807
$832$	1.60350e10	0.965242
$833$	1.55045e8	0.00929395
$834$	−3.10042e10	−1.85071
$835$	3.47549e10	2.06592
$836$	−8.12448e10	−4.80921
$837$	−2.69998e9	−0.159155
$838$	−3.76649e9	−0.221097
$839$	−1.12064e10	−0.655087	−0.327543	−	0.944836i	$-0.606221\pi$
$839$	−1.12064e10	−0.655087	−0.327543	+	0.944836i	$0.606221\pi$
$840$	−2.42966e10	−1.41439
$841$	3.75117e9	0.217461
$842$	−1.91008e10	−1.10270
$843$	−1.85673e10	−1.06746
$844$	7.30804e10	4.18410
$845$	−5.61776e10	−3.20306
$846$	1.12797e10	0.640475
$847$	−5.91904e9	−0.334703
$848$	5.36104e10	3.01900
$849$	5.09568e9	0.285776
$850$	7.02336e8	0.0392264
$851$	−5.02535e9	−0.279520
$852$	2.07438e10	1.14908
$853$	−1.72110e10	−0.949478	−0.474739	−	0.880127i	$-0.657457\pi$
$853$	−1.72110e10	−0.949478	−0.474739	+	0.880127i	$0.657457\pi$
$854$	3.25235e10	1.78688
$855$	−2.46752e10	−1.35014
$856$	−5.55387e10	−3.02648
$857$	1.04986e10	0.569766	0.284883	−	0.958562i	$-0.408045\pi$
$857$	1.04986e10	0.569766	0.284883	+	0.958562i	$0.408045\pi$
$858$	−5.22171e10	−2.82233
$859$	−1.62591e10	−0.875228	−0.437614	−	0.899163i	$-0.644176\pi$
$859$	−1.62591e10	−0.875228	−0.437614	+	0.899163i	$0.644176\pi$
$860$	7.52353e10	4.03346
$861$	1.04393e10	0.557391
$862$	3.49869e10	1.86050
$863$	2.77008e10	1.46708	0.733540	−	0.679646i	$-0.237867\pi$
$863$	2.77008e10	1.46708	0.733540	+	0.679646i	$0.237867\pi$
$864$	2.97801e10	1.57082
$865$	−2.02550e10	−1.06408
$866$	4.83650e10	2.53057
$867$	−1.33597e10	−0.696195
$868$	−3.40141e9	−0.176539
$869$	−3.65161e9	−0.188762
$870$	−4.51346e10	−2.32377
$871$	3.71810e10	1.90659
$872$	−3.91751e10	−2.00080
$873$	−4.29827e9	−0.218647
$874$	−1.15071e10	−0.583012
$875$	1.19820e10	0.604646
$876$	4.81854e10	2.42187
$877$	−1.90485e10	−0.953590	−0.476795	−	0.879014i	$-0.658202\pi$
$877$	−1.90485e10	−0.953590	−0.476795	+	0.879014i	$0.658202\pi$
$878$	−1.73566e10	−0.865433
$879$	−1.84472e10	−0.916155
$880$	−9.33569e10	−4.61803
$881$	7.29599e9	0.359475	0.179737	−	0.983715i	$-0.442475\pi$
$881$	7.29599e9	0.359475	0.179737	+	0.983715i	$0.442475\pi$
$882$	−1.44291e10	−0.708107
$883$	2.50202e10	1.22301	0.611503	−	0.791242i	$-0.290565\pi$
$883$	2.50202e10	1.22301	0.611503	+	0.791242i	$0.290565\pi$
$884$	−1.02188e9	−0.0497528
$885$	3.24731e10	1.57479
$886$	5.72071e10	2.76333
$887$	−1.76793e10	−0.850614	−0.425307	−	0.905049i	$-0.639834\pi$
$887$	−1.76793e10	−0.850614	−0.425307	+	0.905049i	$0.639834\pi$
$888$	−4.97729e10	−2.38533
$889$	−1.76637e9	−0.0843189
$890$	−6.64063e10	−3.15751
$891$	−5.98975e9	−0.283685
$892$	5.97815e10	2.82027
$893$	−2.29247e10	−1.07727
$894$	2.93966e10	1.37599
$895$	3.01541e10	1.40594
$896$	−4.92390e9	−0.228682
$897$	−5.18599e9	−0.239915
$898$	−5.36554e10	−2.47256
$899$	−3.62619e9	−0.166453
$900$	−4.58323e10	−2.09567
$901$	−3.79466e8	−0.0172837
$902$	8.36789e10	3.79658
$903$	7.98644e9	0.360949
$904$	8.80165e10	3.96255
$905$	1.09013e10	0.488888
$906$	5.72137e9	0.255595
$907$	−4.36552e9	−0.194272	−0.0971361	−	0.995271i	$-0.530968\pi$
$907$	−4.36552e9	−0.194272	−0.0971361	+	0.995271i	$0.530968\pi$
$908$	4.36472e10	1.93489
$909$	−1.55240e10	−0.685534
$910$	−5.87613e10	−2.58492
$911$	9.43686e9	0.413536	0.206768	−	0.978390i	$-0.433705\pi$
$911$	9.43686e9	0.413536	0.206768	+	0.978390i	$0.433705\pi$
$912$	−5.46323e10	−2.38489
$913$	1.64363e10	0.714755
$914$	−6.46729e10	−2.80163
$915$	−5.22521e10	−2.25492
$916$	4.94958e10	2.12782
$917$	−1.48927e8	−0.00637795
$918$	−5.59607e8	−0.0238745
$919$	−1.14388e10	−0.486156	−0.243078	−	0.970007i	$-0.578157\pi$
$919$	−1.14388e10	−0.486156	−0.243078	+	0.970007i	$0.578157\pi$
$920$	−1.93423e10	−0.818939
$921$	4.26321e9	0.179816
$922$	2.73009e9	0.114715
$923$	2.87913e10	1.20519
$924$	−2.52605e10	−1.05339
$925$	5.80136e10	2.41009
$926$	−1.42946e10	−0.591606
$927$	3.97457e9	0.163874
$928$	3.99959e10	1.64285
$929$	2.77383e10	1.13508	0.567539	−	0.823347i	$-0.307896\pi$
$929$	2.77383e10	1.13508	0.567539	+	0.823347i	$0.307896\pi$
$930$	7.79327e9	0.317709
$931$	2.93254e10	1.19102
$932$	−4.34506e10	−1.75809
$933$	2.20089e10	0.887182
$934$	3.35881e10	1.34888
$935$	6.60801e8	0.0264381
$936$	5.45768e10	2.17542
$937$	−2.38147e10	−0.945705	−0.472852	−	0.881142i	$-0.656776\pi$
$937$	−2.38147e10	−0.945705	−0.472852	+	0.881142i	$0.656776\pi$
$938$	2.56510e10	1.01483
$939$	−3.37480e10	−1.33020
$940$	−6.71458e10	−2.63676
$941$	−1.04581e10	−0.409156	−0.204578	−	0.978850i	$-0.565582\pi$
$941$	−1.04581e10	−0.409156	−0.204578	+	0.978850i	$0.565582\pi$
$942$	5.96635e10	2.32558
$943$	8.31063e9	0.322733
$944$	−7.63947e10	−2.95571
$945$	−2.25643e10	−0.869780
$946$	6.40174e10	2.45855
$947$	4.63381e10	1.77302	0.886509	−	0.462711i	$-0.153123\pi$
$947$	4.63381e10	1.77302	0.886509	+	0.462711i	$0.153123\pi$
$948$	−6.25897e9	−0.238602
$949$	6.68787e10	2.54013
$950$	1.32841e11	5.02688
$951$	−8.72003e8	−0.0328766
$952$	−4.04584e8	−0.0151978
$953$	−5.95644e9	−0.222927	−0.111463	−	0.993769i	$-0.535554\pi$
$953$	−5.95644e9	−0.222927	−0.111463	+	0.993769i	$0.535554\pi$
$954$	3.53146e10	1.31685
$955$	5.25892e10	1.95382
$956$	−2.17264e10	−0.804239
$957$	−2.69298e10	−0.993209
$958$	3.29974e10	1.21255
$959$	−2.09665e10	−0.767644
$960$	−1.77728e10	−0.648347
$961$	−2.68865e10	−0.977242
$962$	−1.20376e11	−4.35939
$963$	−1.75371e10	−0.632798
$964$	−3.99124e9	−0.143495
$965$	7.16408e10	2.56634
$966$	−3.57778e9	−0.127701
$967$	4.39611e10	1.56342	0.781710	−	0.623642i	$-0.214348\pi$
$967$	4.39611e10	1.56342	0.781710	+	0.623642i	$0.214348\pi$
$968$	−4.66704e10	−1.65378
$969$	3.86700e8	0.0136534
$970$	3.64895e10	1.28371
$971$	2.05549e10	0.720522	0.360261	−	0.932852i	$-0.382688\pi$
$971$	2.05549e10	0.720522	0.360261	+	0.932852i	$0.382688\pi$
$972$	6.06202e10	2.11731
$973$	−2.08172e10	−0.724480
$974$	1.61549e10	0.560207
$975$	5.98680e10	2.06861
$976$	1.22926e11	4.23223
$977$	−4.60599e10	−1.58013	−0.790063	−	0.613026i	$-0.789952\pi$
$977$	−4.60599e10	−1.58013	−0.790063	+	0.613026i	$0.789952\pi$
$978$	2.24401e10	0.767077
$979$	−3.96216e10	−1.34956
$980$	8.58931e10	2.91519
$981$	−1.23701e10	−0.418341
$982$	2.99294e10	1.00857
$983$	−1.82755e10	−0.613666	−0.306833	−	0.951763i	$-0.599269\pi$
$983$	−1.82755e10	−0.613666	−0.306833	+	0.951763i	$0.599269\pi$
$984$	8.23115e10	2.75409
$985$	−6.05214e9	−0.201782
$986$	−7.51577e8	−0.0249692
$987$	−7.12771e9	−0.235961
$988$	−1.93280e11	−6.37583
$989$	6.35794e9	0.208992
$990$	−6.14967e10	−2.01432
$991$	1.66094e10	0.542120	0.271060	−	0.962562i	$-0.412626\pi$
$991$	1.66094e10	0.542120	0.271060	+	0.962562i	$0.412626\pi$
$992$	−6.90599e9	−0.224613
$993$	1.19206e9	0.0386344
$994$	1.98629e10	0.641492
$995$	−8.00589e10	−2.57649
$996$	2.81723e10	0.903473
$997$	2.04202e10	0.652568	0.326284	−	0.945272i	$-0.394203\pi$
$997$	2.04202e10	0.652568	0.326284	+	0.945272i	$0.394203\pi$
$998$	−1.64917e10	−0.525180
$999$	−4.62241e10	−1.46686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.10	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-20.6976 q^{2} +32.5628 q^{3} +300.390 q^{4} -462.112 q^{5} -673.972 q^{6} -452.526 q^{7} -3568.07 q^{8} -1126.66 q^{9} +O(q^{10})\)	\(q-20.6976 q^{2} +32.5628 q^{3} +300.390 q^{4} -462.112 q^{5} -673.972 q^{6} -452.526 q^{7} -3568.07 q^{8} -1126.66 q^{9} +9564.62 q^{10} +5706.77 q^{11} +9781.56 q^{12} +13576.3 q^{13} +9366.19 q^{14} -15047.7 q^{15} +35400.4 q^{16} -250.572 q^{17} +23319.2 q^{18} -47393.5 q^{19} -138814. q^{20} -14735.5 q^{21} -118116. q^{22} -11730.8 q^{23} -116186. q^{24} +135423. q^{25} -280996. q^{26} -107902. q^{27} -135934. q^{28} -144917. q^{29} +311451. q^{30} +25022.5 q^{31} -275991. q^{32} +185828. q^{33} +5186.24 q^{34} +209118. q^{35} -338439. q^{36} +428389. q^{37} +980932. q^{38} +442082. q^{39} +1.64885e6 q^{40} -708444. q^{41} +304990. q^{42} -541986. q^{43} +1.71426e6 q^{44} +520645. q^{45} +242800. q^{46} +483710. q^{47} +1.15274e6 q^{48} -618764. q^{49} -2.80293e6 q^{50} -8159.34 q^{51} +4.07819e6 q^{52} +1.51440e6 q^{53} +2.23332e6 q^{54} -2.63717e6 q^{55} +1.61464e6 q^{56} -1.54327e6 q^{57} +2.99944e6 q^{58} -2.15802e6 q^{59} -4.52018e6 q^{60} +3.47244e6 q^{61} -517905. q^{62} +509844. q^{63} +1.18110e6 q^{64} -6.27377e6 q^{65} -3.84620e6 q^{66} +2.73868e6 q^{67} -75269.5 q^{68} -381989. q^{69} -4.32823e6 q^{70} +2.12071e6 q^{71} +4.02001e6 q^{72} +4.92614e6 q^{73} -8.86662e6 q^{74} +4.40975e6 q^{75} -1.42366e7 q^{76} -2.58246e6 q^{77} -9.15004e6 q^{78} -639874. q^{79} -1.63590e7 q^{80} -1.04959e6 q^{81} +1.46631e7 q^{82} +2.88015e6 q^{83} -4.42641e6 q^{84} +115793. q^{85} +1.12178e7 q^{86} -4.71892e6 q^{87} -2.03621e7 q^{88} -6.94291e6 q^{89} -1.07761e7 q^{90} -6.14362e6 q^{91} -3.52383e6 q^{92} +814803. q^{93} -1.00116e7 q^{94} +2.19011e7 q^{95} -8.98706e6 q^{96} +3.81505e6 q^{97} +1.28069e7 q^{98} -6.42960e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 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

Fields

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Groups

Database

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