LMFDB - Embedded newform 43.8.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.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:	$13.4325560958$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 $ x^11 - 2x^10 - 977x^9 + 2592x^8 + 344686x^7 - 1160956x^6 - 53409536x^5 + 209758592x^4 + 3410917248x^3 - 14180732672x^2 - 60918607872x + 238240894976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$19.7860$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.7860 q^{2} +54.2998 q^{3} +346.631 q^{4} -409.924 q^{5} -1182.98 q^{6} +476.571 q^{7} -4763.10 q^{8} +761.467 q^{9} +O(q^{10})$	\(q-21.7860 q^{2} +54.2998 q^{3} +346.631 q^{4} -409.924 q^{5} -1182.98 q^{6} +476.571 q^{7} -4763.10 q^{8} +761.467 q^{9} +8930.61 q^{10} +6867.50 q^{11} +18822.0 q^{12} -8276.59 q^{13} -10382.6 q^{14} -22258.8 q^{15} +59400.2 q^{16} -16111.6 q^{17} -16589.3 q^{18} +27534.5 q^{19} -142092. q^{20} +25877.7 q^{21} -149616. q^{22} -69123.4 q^{23} -258635. q^{24} +89912.4 q^{25} +180314. q^{26} -77406.2 q^{27} +165194. q^{28} -111490. q^{29} +484930. q^{30} -169599. q^{31} -684418. q^{32} +372904. q^{33} +351008. q^{34} -195358. q^{35} +263948. q^{36} -60102.6 q^{37} -599867. q^{38} -449417. q^{39} +1.95251e6 q^{40} -813919. q^{41} -563772. q^{42} +79507.0 q^{43} +2.38049e6 q^{44} -312143. q^{45} +1.50592e6 q^{46} -624677. q^{47} +3.22542e6 q^{48} -596423. q^{49} -1.95883e6 q^{50} -874857. q^{51} -2.86892e6 q^{52} +365470. q^{53} +1.68637e6 q^{54} -2.81515e6 q^{55} -2.26995e6 q^{56} +1.49512e6 q^{57} +2.42892e6 q^{58} +1.43500e6 q^{59} -7.71558e6 q^{60} -153457. q^{61} +3.69489e6 q^{62} +362893. q^{63} +7.30752e6 q^{64} +3.39277e6 q^{65} -8.12409e6 q^{66} -1.27944e6 q^{67} -5.58478e6 q^{68} -3.75339e6 q^{69} +4.25607e6 q^{70} +821210. q^{71} -3.62694e6 q^{72} +4.08244e6 q^{73} +1.30940e6 q^{74} +4.88222e6 q^{75} +9.54431e6 q^{76} +3.27285e6 q^{77} +9.79101e6 q^{78} -6.74067e6 q^{79} -2.43496e7 q^{80} -5.86847e6 q^{81} +1.77321e7 q^{82} +281235. q^{83} +8.97001e6 q^{84} +6.60453e6 q^{85} -1.73214e6 q^{86} -6.05387e6 q^{87} -3.27106e7 q^{88} +9.40951e6 q^{89} +6.80036e6 q^{90} -3.94438e6 q^{91} -2.39603e7 q^{92} -9.20921e6 q^{93} +1.36092e7 q^{94} -1.12870e7 q^{95} -3.71638e7 q^{96} -6.78204e6 q^{97} +1.29937e7 q^{98} +5.22937e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) $ 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * 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 $

$2$	−21.7860	−1.92563	−0.962815	−	0.270160i	$-0.912923\pi$
$2$	−21.7860	−1.92563	−0.962815	+	0.270160i	$0.912923\pi$
$3$	54.2998	1.16111	0.580555	−	0.814221i	$-0.302835\pi$
$3$	54.2998	1.16111	0.580555	+	0.814221i	$0.302835\pi$
$4$	346.631	2.70805
$5$	−409.924	−1.46659	−0.733294	−	0.679912i	$-0.762018\pi$
$5$	−409.924	−1.46659	−0.733294	+	0.679912i	$0.762018\pi$
$6$	−1182.98	−2.23587
$7$	476.571	0.525151	0.262576	−	0.964911i	$-0.415428\pi$
$7$	476.571	0.525151	0.262576	+	0.964911i	$0.415428\pi$
$8$	−4763.10	−3.28908
$9$	761.467	0.348179
$10$	8930.61	2.82411
$11$	6867.50	1.55569	0.777847	−	0.628453i	$-0.216312\pi$
$11$	6867.50	1.55569	0.777847	+	0.628453i	$0.216312\pi$
$12$	18822.0	3.14435
$13$	−8276.59	−1.04484	−0.522420	−	0.852688i	$-0.674971\pi$
$13$	−8276.59	−1.04484	−0.522420	+	0.852688i	$0.674971\pi$
$14$	−10382.6	−1.01125
$15$	−22258.8	−1.70287
$16$	59400.2	3.62550
$17$	−16111.6	−0.795367	−0.397684	−	0.917523i	$-0.630186\pi$
$17$	−16111.6	−0.795367	−0.397684	+	0.917523i	$0.630186\pi$
$18$	−16589.3	−0.670463
$19$	27534.5	0.920957	0.460479	−	0.887671i	$-0.347678\pi$
$19$	27534.5	0.920957	0.460479	+	0.887671i	$0.347678\pi$
$20$	−142092.	−3.97160
$21$	25877.7	0.609759
$22$	−149616.	−2.99569
$23$	−69123.4	−1.18462	−0.592308	−	0.805711i	$-0.701783\pi$
$23$	−69123.4	−1.18462	−0.592308	+	0.805711i	$0.701783\pi$
$24$	−258635.	−3.81899
$25$	89912.4	1.15088
$26$	180314.	2.01198
$27$	−77406.2	−0.756837
$28$	165194.	1.42214
$29$	−111490.	−0.848871	−0.424435	−	0.905458i	$-0.639527\pi$
$29$	−111490.	−0.848871	−0.424435	+	0.905458i	$0.639527\pi$
$30$	484930.	3.27910
$31$	−169599.	−1.02249	−0.511244	−	0.859436i	$-0.670815\pi$
$31$	−169599.	−1.02249	−0.511244	+	0.859436i	$0.670815\pi$
$32$	−684418.	−3.69230
$33$	372904.	1.80633
$34$	351008.	1.53158
$35$	−195358.	−0.770180
$36$	263948.	0.942886
$37$	−60102.6	−0.195068	−0.0975342	−	0.995232i	$-0.531096\pi$
$37$	−60102.6	−0.195068	−0.0975342	+	0.995232i	$0.531096\pi$
$38$	−599867.	−1.77342
$39$	−449417.	−1.21317
$40$	1.95251e6	4.82372
$41$	−813919.	−1.84433	−0.922163	−	0.386802i	$-0.873580\pi$
$41$	−813919.	−1.84433	−0.922163	+	0.386802i	$0.873580\pi$
$42$	−563772.	−1.17417
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	2.38049e6	4.21290
$45$	−312143.	−0.510634
$46$	1.50592e6	2.28113
$47$	−624677.	−0.877633	−0.438817	−	0.898577i	$-0.644602\pi$
$47$	−624677.	−0.877633	−0.438817	+	0.898577i	$0.644602\pi$
$48$	3.22542e6	4.20961
$49$	−596423.	−0.724216
$50$	−1.95883e6	−2.21617
$51$	−874857.	−0.923510
$52$	−2.86892e6	−2.82948
$53$	365470.	0.337199	0.168600	−	0.985685i	$-0.446076\pi$
$53$	365470.	0.337199	0.168600	+	0.985685i	$0.446076\pi$
$54$	1.68637e6	1.45739
$55$	−2.81515e6	−2.28156
$56$	−2.26995e6	−1.72726
$57$	1.49512e6	1.06933
$58$	2.42892e6	1.63461
$59$	1.43500e6	0.909643	0.454822	−	0.890583i	$-0.349703\pi$
$59$	1.43500e6	0.909643	0.454822	+	0.890583i	$0.349703\pi$
$60$	−7.71558e6	−4.61147
$61$	−153457.	−0.0865630	−0.0432815	−	0.999063i	$-0.513781\pi$
$61$	−153457.	−0.0865630	−0.0432815	+	0.999063i	$0.513781\pi$
$62$	3.69489e6	1.96893
$63$	362893.	0.182846
$64$	7.30752e6	3.48450
$65$	3.39277e6	1.53235
$66$	−8.12409e6	−3.47833
$67$	−1.27944e6	−0.519708	−0.259854	−	0.965648i	$-0.583674\pi$
$67$	−1.27944e6	−0.519708	−0.259854	+	0.965648i	$0.583674\pi$
$68$	−5.58478e6	−2.15390
$69$	−3.75339e6	−1.37547
$70$	4.25607e6	1.48308
$71$	821210.	0.272302	0.136151	−	0.990688i	$-0.456527\pi$
$71$	821210.	0.272302	0.136151	+	0.990688i	$0.456527\pi$
$72$	−3.62694e6	−1.14519
$73$	4.08244e6	1.22826	0.614130	−	0.789205i	$-0.289507\pi$
$73$	4.08244e6	1.22826	0.614130	+	0.789205i	$0.289507\pi$
$74$	1.30940e6	0.375630
$75$	4.88222e6	1.33630
$76$	9.54431e6	2.49400
$77$	3.27285e6	0.816975
$78$	9.79101e6	2.33613
$79$	−6.74067e6	−1.53818	−0.769091	−	0.639139i	$-0.779291\pi$
$79$	−6.74067e6	−1.53818	−0.769091	+	0.639139i	$0.779291\pi$
$80$	−2.43496e7	−5.31712
$81$	−5.86847e6	−1.22695
$82$	1.77321e7	3.55149
$83$	281235.	0.0539878	0.0269939	−	0.999636i	$-0.491407\pi$
$83$	281235.	0.0539878	0.0269939	+	0.999636i	$0.491407\pi$
$84$	8.97001e6	1.65126
$85$	6.60453e6	1.16648
$86$	−1.73214e6	−0.293656
$87$	−6.05387e6	−0.985633
$88$	−3.27106e7	−5.11681
$89$	9.40951e6	1.41482	0.707411	−	0.706802i	$-0.249863\pi$
$89$	9.40951e6	1.41482	0.707411	+	0.706802i	$0.249863\pi$
$90$	6.80036e6	0.983293
$91$	−3.94438e6	−0.548699
$92$	−2.39603e7	−3.20801
$93$	−9.20921e6	−1.18722
$94$	1.36092e7	1.69000
$95$	−1.12870e7	−1.35066
$96$	−3.71638e7	−4.28717
$97$	−6.78204e6	−0.754500	−0.377250	−	0.926112i	$-0.623130\pi$
$97$	−6.78204e6	−0.754500	−0.377250	+	0.926112i	$0.623130\pi$
$98$	1.29937e7	1.39457
$99$	5.22937e6	0.541660
$100$	3.11664e7	3.11664
$101$	1.37928e7	1.33208	0.666038	−	0.745918i	$-0.267989\pi$
$101$	1.37928e7	1.33208	0.666038	+	0.745918i	$0.267989\pi$
$102$	1.90597e7	1.77834
$103$	−1.39555e7	−1.25839	−0.629197	−	0.777246i	$-0.716616\pi$
$103$	−1.39555e7	−1.25839	−0.629197	+	0.777246i	$0.716616\pi$
$104$	3.94222e7	3.43656
$105$	−1.06079e7	−0.894264
$106$	−7.96214e6	−0.649321
$107$	4.53042e6	0.357516	0.178758	−	0.983893i	$-0.442792\pi$
$107$	4.53042e6	0.357516	0.178758	+	0.983893i	$0.442792\pi$
$108$	−2.68314e7	−2.04956
$109$	1.43535e7	1.06161	0.530806	−	0.847493i	$-0.321889\pi$
$109$	1.43535e7	1.06161	0.530806	+	0.847493i	$0.321889\pi$
$110$	6.13310e7	4.39345
$111$	−3.26356e6	−0.226496
$112$	2.83084e7	1.90394
$113$	−1.27510e7	−0.831322	−0.415661	−	0.909520i	$-0.636450\pi$
$113$	−1.27510e7	−0.831322	−0.415661	+	0.909520i	$0.636450\pi$
$114$	−3.25727e7	−2.05914
$115$	2.83353e7	1.73734
$116$	−3.86458e7	−2.29879
$117$	−6.30235e6	−0.363791
$118$	−3.12630e7	−1.75164
$119$	−7.67832e6	−0.417688
$120$	1.06021e8	5.60088
$121$	2.76754e7	1.42019
$122$	3.34322e6	0.166688
$123$	−4.41956e7	−2.14147
$124$	−5.87884e7	−2.76895
$125$	−4.83193e6	−0.221277
$126$	−7.90599e6	−0.352095
$127$	−1.14084e7	−0.494210	−0.247105	−	0.968989i	$-0.579479\pi$
$127$	−1.14084e7	−0.494210	−0.247105	+	0.968989i	$0.579479\pi$
$128$	−7.15964e7	−3.01756
$129$	4.31721e6	0.177068
$130$	−7.39150e7	−2.95074
$131$	3.48381e6	0.135396	0.0676978	−	0.997706i	$-0.478435\pi$
$131$	3.48381e6	0.135396	0.0676978	+	0.997706i	$0.478435\pi$
$132$	1.29260e8	4.89165
$133$	1.31221e7	0.483642
$134$	2.78740e7	1.00077
$135$	3.17306e7	1.10997
$136$	7.67412e7	2.61603
$137$	2.52123e7	0.837703	0.418852	−	0.908055i	$-0.362433\pi$
$137$	2.52123e7	0.837703	0.418852	+	0.908055i	$0.362433\pi$
$138$	8.17714e7	2.64865
$139$	2.46536e7	0.778625	0.389313	−	0.921106i	$-0.372713\pi$
$139$	2.46536e7	0.778625	0.389313	+	0.921106i	$0.372713\pi$
$140$	−6.77170e7	−2.08569
$141$	−3.39198e7	−1.01903
$142$	−1.78909e7	−0.524352
$143$	−5.68395e7	−1.62545
$144$	4.52313e7	1.26232
$145$	4.57023e7	1.24494
$146$	−8.89402e7	−2.36518
$147$	−3.23857e7	−0.840896
$148$	−2.08334e7	−0.528256
$149$	−4.27780e7	−1.05942	−0.529710	−	0.848179i	$-0.677699\pi$
$149$	−4.27780e7	−1.05942	−0.529710	+	0.848179i	$0.677699\pi$
$150$	−1.06364e8	−2.57322
$151$	6.03840e7	1.42726	0.713629	−	0.700524i	$-0.247050\pi$
$151$	6.03840e7	1.42726	0.713629	+	0.700524i	$0.247050\pi$
$152$	−1.31149e8	−3.02910
$153$	−1.22685e7	−0.276930
$154$	−7.13024e7	−1.57319
$155$	6.95228e7	1.49957
$156$	−1.55782e8	−3.28534
$157$	−5.70927e7	−1.17742	−0.588711	−	0.808344i	$-0.700364\pi$
$157$	−5.70927e7	−1.17742	−0.588711	+	0.808344i	$0.700364\pi$
$158$	1.46852e8	2.96197
$159$	1.98450e7	0.391526
$160$	2.80559e8	5.41508
$161$	−3.29422e7	−0.622103
$162$	1.27851e8	2.36265
$163$	−2.03054e7	−0.367245	−0.183622	−	0.982997i	$-0.558782\pi$
$163$	−2.03054e7	−0.367245	−0.183622	+	0.982997i	$0.558782\pi$
$164$	−2.82129e8	−4.99453
$165$	−1.52862e8	−2.64915
$166$	−6.12699e6	−0.103961
$167$	3.18949e7	0.529925	0.264962	−	0.964259i	$-0.414640\pi$
$167$	3.18949e7	0.529925	0.264962	+	0.964259i	$0.414640\pi$
$168$	−1.23258e8	−2.00555
$169$	5.75340e6	0.0916898
$170$	−1.43886e8	−2.24620
$171$	2.09666e7	0.320658
$172$	2.75596e7	0.412974
$173$	−2.81474e7	−0.413311	−0.206656	−	0.978414i	$-0.566258\pi$
$173$	−2.81474e7	−0.413311	−0.206656	+	0.978414i	$0.566258\pi$
$174$	1.31890e8	1.89797
$175$	4.28496e7	0.604385
$176$	4.07931e8	5.64017
$177$	7.79204e7	1.05620
$178$	−2.04996e8	−2.72443
$179$	−3.87229e6	−0.0504641	−0.0252321	−	0.999682i	$-0.508032\pi$
$179$	−3.87229e6	−0.0504641	−0.0252321	+	0.999682i	$0.508032\pi$
$180$	−1.08198e8	−1.38283
$181$	−5.34400e7	−0.669871	−0.334935	−	0.942241i	$-0.608715\pi$
$181$	−5.34400e7	−0.669871	−0.334935	+	0.942241i	$0.608715\pi$
$182$	8.59324e7	1.05659
$183$	−8.33268e6	−0.100509
$184$	3.29242e8	3.89630
$185$	2.46375e7	0.286085
$186$	2.00632e8	2.28615
$187$	−1.10647e8	−1.23735
$188$	−2.16532e8	−2.37668
$189$	−3.68895e7	−0.397454
$190$	2.45900e8	2.60088
$191$	−1.82945e7	−0.189978	−0.0949891	−	0.995478i	$-0.530282\pi$
$191$	−1.82945e7	−0.189978	−0.0949891	+	0.995478i	$0.530282\pi$
$192$	3.96797e8	4.04589
$193$	8.24942e7	0.825986	0.412993	−	0.910734i	$-0.364483\pi$
$193$	8.24942e7	0.825986	0.412993	+	0.910734i	$0.364483\pi$
$194$	1.47754e8	1.45289
$195$	1.84227e8	1.77923
$196$	−2.06739e8	−1.96122
$197$	7.08196e7	0.659966	0.329983	−	0.943987i	$-0.392957\pi$
$197$	7.08196e7	0.659966	0.329983	+	0.943987i	$0.392957\pi$
$198$	−1.13927e8	−1.04304
$199$	1.61028e8	1.44849	0.724247	−	0.689540i	$-0.242187\pi$
$199$	1.61028e8	1.44849	0.724247	+	0.689540i	$0.242187\pi$
$200$	−4.28262e8	−3.78533
$201$	−6.94736e7	−0.603439
$202$	−3.00491e8	−2.56509
$203$	−5.31327e7	−0.445785
$204$	−3.03252e8	−2.50091
$205$	3.33645e8	2.70486
$206$	3.04036e8	2.42320
$207$	−5.26352e7	−0.412458
$208$	−4.91631e8	−3.78807
$209$	1.89093e8	1.43273
$210$	2.31103e8	1.72202
$211$	−2.05501e8	−1.50600	−0.753002	−	0.658018i	$-0.771395\pi$
$211$	−2.05501e8	−1.50600	−0.753002	+	0.658018i	$0.771395\pi$
$212$	1.26683e8	0.913153
$213$	4.45915e7	0.316172
$214$	−9.86999e7	−0.688444
$215$	−3.25918e7	−0.223652
$216$	3.68693e8	2.48930
$217$	−8.08261e7	−0.536961
$218$	−3.12706e8	−2.04427
$219$	2.21676e8	1.42615
$220$	−9.75818e8	−6.17859
$221$	1.33349e8	0.831031
$222$	7.10999e7	0.436148
$223$	−8.77217e7	−0.529712	−0.264856	−	0.964288i	$-0.585324\pi$
$223$	−8.77217e7	−0.529712	−0.264856	+	0.964288i	$0.585324\pi$
$224$	−3.26174e8	−1.93901
$225$	6.84653e7	0.400711
$226$	2.77793e8	1.60082
$227$	−1.96811e8	−1.11676	−0.558378	−	0.829586i	$-0.688576\pi$
$227$	−1.96811e8	−1.11676	−0.558378	+	0.829586i	$0.688576\pi$
$228$	5.18254e8	2.89581
$229$	−1.91603e8	−1.05434	−0.527168	−	0.849761i	$-0.676746\pi$
$229$	−1.91603e8	−1.05434	−0.527168	+	0.849761i	$0.676746\pi$
$230$	−6.17314e8	−3.34548
$231$	1.77715e8	0.948598
$232$	5.31036e8	2.79201
$233$	−7.48220e7	−0.387511	−0.193755	−	0.981050i	$-0.562067\pi$
$233$	−7.48220e7	−0.387511	−0.193755	+	0.981050i	$0.562067\pi$
$234$	1.37303e8	0.700527
$235$	2.56070e8	1.28713
$236$	4.97417e8	2.46336
$237$	−3.66017e8	−1.78600
$238$	1.67280e8	0.804313
$239$	3.09828e8	1.46801	0.734004	−	0.679145i	$-0.237649\pi$
$239$	3.09828e8	1.46801	0.734004	+	0.679145i	$0.237649\pi$
$240$	−1.32218e9	−6.17376
$241$	−2.29329e8	−1.05536	−0.527678	−	0.849445i	$-0.676937\pi$
$241$	−2.29329e8	−1.05536	−0.527678	+	0.849445i	$0.676937\pi$
$242$	−6.02937e8	−2.73475
$243$	−1.49369e8	−0.667788
$244$	−5.31929e7	−0.234417
$245$	2.44488e8	1.06213
$246$	9.62847e8	4.12367
$247$	−2.27892e8	−0.962253
$248$	8.07818e8	3.36305
$249$	1.52710e7	0.0626859
$250$	1.05269e8	0.426097
$251$	7.43216e7	0.296659	0.148329	−	0.988938i	$-0.452610\pi$
$251$	7.43216e7	0.296659	0.148329	+	0.988938i	$0.452610\pi$
$252$	1.25790e8	0.495158
$253$	−4.74705e8	−1.84290
$254$	2.48544e8	0.951666
$255$	3.58625e8	1.35441
$256$	6.24437e8	2.32621
$257$	8.21908e7	0.302035	0.151017	−	0.988531i	$-0.451745\pi$
$257$	8.21908e7	0.302035	0.151017	+	0.988531i	$0.451745\pi$
$258$	−9.40549e7	−0.340967
$259$	−2.86431e7	−0.102440
$260$	1.17604e9	4.14968
$261$	−8.48957e7	−0.295559
$262$	−7.58983e7	−0.260722
$263$	4.73912e8	1.60640	0.803198	−	0.595713i	$-0.203130\pi$
$263$	4.73912e8	1.60640	0.803198	+	0.595713i	$0.203130\pi$
$264$	−1.77618e9	−5.94118
$265$	−1.49815e8	−0.494532
$266$	−2.85879e8	−0.931315
$267$	5.10934e8	1.64277
$268$	−4.43495e8	−1.40740
$269$	−1.61866e8	−0.507016	−0.253508	−	0.967333i	$-0.581584\pi$
$269$	−1.61866e8	−0.507016	−0.253508	+	0.967333i	$0.581584\pi$
$270$	−6.91284e8	−2.13739
$271$	9.56080e7	0.291811	0.145905	−	0.989299i	$-0.453390\pi$
$271$	9.56080e7	0.291811	0.145905	+	0.989299i	$0.453390\pi$
$272$	−9.57033e8	−2.88361
$273$	−2.14179e8	−0.637100
$274$	−5.49275e8	−1.61311
$275$	6.17473e8	1.79042
$276$	−1.30104e9	−3.72485
$277$	5.77704e8	1.63315	0.816575	−	0.577240i	$-0.195870\pi$
$277$	5.77704e8	1.63315	0.816575	+	0.577240i	$0.195870\pi$
$278$	−5.37104e8	−1.49934
$279$	−1.29144e8	−0.356008
$280$	9.30507e8	2.53318
$281$	1.72244e8	0.463096	0.231548	−	0.972823i	$-0.425621\pi$
$281$	1.72244e8	0.463096	0.231548	+	0.972823i	$0.425621\pi$
$282$	7.38978e8	1.96227
$283$	−3.33472e8	−0.874595	−0.437298	−	0.899317i	$-0.644064\pi$
$283$	−3.33472e8	−0.874595	−0.437298	+	0.899317i	$0.644064\pi$
$284$	2.84657e8	0.737407
$285$	−6.12884e8	−1.56827
$286$	1.23831e9	3.13002
$287$	−3.87890e8	−0.968549
$288$	−5.21162e8	−1.28558
$289$	−1.50755e8	−0.367391
$290$	−9.95670e8	−2.39730
$291$	−3.68263e8	−0.876058
$292$	1.41510e9	3.32619
$293$	−2.96954e8	−0.689688	−0.344844	−	0.938660i	$-0.612068\pi$
$293$	−2.96954e8	−0.689688	−0.344844	+	0.938660i	$0.612068\pi$
$294$	7.05555e8	1.61925
$295$	−5.88242e8	−1.33407
$296$	2.86274e8	0.641596
$297$	−5.31587e8	−1.17741
$298$	9.31962e8	2.04005
$299$	5.72106e8	1.23773
$300$	1.69233e9	3.61877
$301$	3.78907e7	0.0800848
$302$	−1.31553e9	−2.74837
$303$	7.48949e8	1.54669
$304$	1.63555e9	3.33893
$305$	6.29056e7	0.126952
$306$	2.67281e8	0.533265
$307$	3.16973e8	0.625228	0.312614	−	0.949880i	$-0.398795\pi$
$307$	3.16973e8	0.625228	0.312614	+	0.949880i	$0.398795\pi$
$308$	1.13447e9	2.21241
$309$	−7.57783e8	−1.46113
$310$	−1.51462e9	−2.88761
$311$	−8.80151e8	−1.65919	−0.829594	−	0.558367i	$-0.811428\pi$
$311$	−8.80151e8	−1.65919	−0.829594	+	0.558367i	$0.811428\pi$
$312$	2.14062e9	3.99023
$313$	−8.29846e8	−1.52965	−0.764825	−	0.644238i	$-0.777175\pi$
$313$	−8.29846e8	−1.52965	−0.764825	+	0.644238i	$0.777175\pi$
$314$	1.24382e9	2.26728
$315$	−1.48758e8	−0.268160
$316$	−2.33652e9	−4.16548
$317$	−2.04074e8	−0.359817	−0.179908	−	0.983683i	$-0.557580\pi$
$317$	−2.04074e8	−0.359817	−0.179908	+	0.983683i	$0.557580\pi$
$318$	−4.32343e8	−0.753934
$319$	−7.65655e8	−1.32058
$320$	−2.99553e9	−5.11032
$321$	2.46001e8	0.415116
$322$	7.17680e8	1.19794
$323$	−4.43625e8	−0.732499
$324$	−2.03419e9	−3.32265
$325$	−7.44168e8	−1.20248
$326$	4.42375e8	0.707178
$327$	7.79393e8	1.23265
$328$	3.87677e9	6.06614
$329$	−2.97703e8	−0.460890
$330$	3.33026e9	5.10128
$331$	−4.43600e8	−0.672347	−0.336174	−	0.941800i	$-0.609133\pi$
$331$	−4.43600e8	−0.672347	−0.336174	+	0.941800i	$0.609133\pi$
$332$	9.74847e7	0.146202
$333$	−4.57661e7	−0.0679187
$334$	−6.94864e8	−1.02044
$335$	5.24475e8	0.762198
$336$	1.53714e9	2.21068
$337$	9.56240e8	1.36101	0.680506	−	0.732742i	$-0.261760\pi$
$337$	9.56240e8	1.36101	0.680506	+	0.732742i	$0.261760\pi$
$338$	−1.25344e8	−0.176561
$339$	−6.92376e8	−0.965257
$340$	2.28933e9	3.15888
$341$	−1.16472e9	−1.59068
$342$	−4.56779e8	−0.617468
$343$	−6.76714e8	−0.905474
$344$	−3.78700e8	−0.501580
$345$	1.53860e9	2.01725
$346$	6.13220e8	0.795885
$347$	7.21806e8	0.927401	0.463700	−	0.885992i	$-0.346521\pi$
$347$	7.21806e8	0.927401	0.463700	+	0.885992i	$0.346521\pi$
$348$	−2.09846e9	−2.66915
$349$	4.87486e8	0.613865	0.306933	−	0.951731i	$-0.400697\pi$
$349$	4.87486e8	0.613865	0.306933	+	0.951731i	$0.400697\pi$
$350$	−9.33523e8	−1.16382
$351$	6.40659e8	0.790773
$352$	−4.70024e9	−5.74409
$353$	2.31713e8	0.280375	0.140187	−	0.990125i	$-0.455229\pi$
$353$	2.31713e8	0.280375	0.140187	+	0.990125i	$0.455229\pi$
$354$	−1.69758e9	−2.03385
$355$	−3.36633e8	−0.399354
$356$	3.26163e9	3.83142
$357$	−4.16931e8	−0.484982
$358$	8.43619e7	0.0971753
$359$	−1.05857e8	−0.120750	−0.0603751	−	0.998176i	$-0.519230\pi$
$359$	−1.05857e8	−0.120750	−0.0603751	+	0.998176i	$0.519230\pi$
$360$	1.48677e9	1.67952
$361$	−1.35724e8	−0.151838
$362$	1.16424e9	1.28992
$363$	1.50277e9	1.64899
$364$	−1.36724e9	−1.48591
$365$	−1.67349e9	−1.80135
$366$	1.81536e8	0.193544
$367$	2.03126e8	0.214504	0.107252	−	0.994232i	$-0.465795\pi$
$367$	2.03126e8	0.214504	0.107252	+	0.994232i	$0.465795\pi$
$368$	−4.10595e9	−4.29483
$369$	−6.19772e8	−0.642155
$370$	−5.36752e8	−0.550894
$371$	1.74172e8	0.177080
$372$	−3.19220e9	−3.21506
$373$	−7.70434e8	−0.768696	−0.384348	−	0.923188i	$-0.625574\pi$
$373$	−7.70434e8	−0.768696	−0.384348	+	0.923188i	$0.625574\pi$
$374$	2.41055e9	2.38268
$375$	−2.62373e8	−0.256927
$376$	2.97540e9	2.88661
$377$	9.22754e8	0.886934
$378$	8.03676e8	0.765349
$379$	9.79682e8	0.924375	0.462187	−	0.886782i	$-0.347065\pi$
$379$	9.79682e8	0.924375	0.462187	+	0.886782i	$0.347065\pi$
$380$	−3.91244e9	−3.65767
$381$	−6.19473e8	−0.573833
$382$	3.98564e8	0.365828
$383$	−1.47413e9	−1.34072	−0.670362	−	0.742034i	$-0.733861\pi$
$383$	−1.47413e9	−1.34072	−0.670362	+	0.742034i	$0.733861\pi$
$384$	−3.88767e9	−3.50372
$385$	−1.34162e9	−1.19816
$386$	−1.79722e9	−1.59054
$387$	6.05419e7	0.0530967
$388$	−2.35086e9	−2.04323
$389$	1.14843e9	0.989194	0.494597	−	0.869122i	$-0.335316\pi$
$389$	1.14843e9	0.989194	0.494597	+	0.869122i	$0.335316\pi$
$390$	−4.01357e9	−3.42613
$391$	1.11369e9	0.942205
$392$	2.84082e9	2.38201
$393$	1.89170e8	0.157209
$394$	−1.54288e9	−1.27085
$395$	2.76316e9	2.25588
$396$	1.81266e9	1.46684
$397$	1.53079e9	1.22786	0.613928	−	0.789362i	$-0.289588\pi$
$397$	1.53079e9	1.22786	0.613928	+	0.789362i	$0.289588\pi$
$398$	−3.50817e9	−2.78927
$399$	7.12529e8	0.561562
$400$	5.34082e9	4.17251
$401$	−5.05503e8	−0.391488	−0.195744	−	0.980655i	$-0.562712\pi$
$401$	−5.05503e8	−0.391488	−0.195744	+	0.980655i	$0.562712\pi$
$402$	1.51355e9	1.16200
$403$	1.40370e9	1.06834
$404$	4.78103e9	3.60734
$405$	2.40562e9	1.79943
$406$	1.15755e9	0.858418
$407$	−4.12754e8	−0.303467
$408$	4.16703e9	3.03750
$409$	1.60782e9	1.16200	0.580998	−	0.813905i	$-0.302662\pi$
$409$	1.60782e9	1.16200	0.580998	+	0.813905i	$0.302662\pi$
$410$	−7.26879e9	−5.20857
$411$	1.36902e9	0.972666
$412$	−4.83742e9	−3.40780
$413$	6.83881e8	0.477700
$414$	1.14671e9	0.794242
$415$	−1.15285e8	−0.0791779
$416$	5.66465e9	3.85786
$417$	1.33868e9	0.904070
$418$	−4.11959e9	−2.75891
$419$	2.86738e9	1.90430	0.952152	−	0.305625i	$-0.0988654\pi$
$419$	2.86738e9	1.90430	0.952152	+	0.305625i	$0.0988654\pi$
$420$	−3.67702e9	−2.42172
$421$	1.98494e9	1.29646	0.648231	−	0.761444i	$-0.275509\pi$
$421$	1.98494e9	1.29646	0.648231	+	0.761444i	$0.275509\pi$
$422$	4.47706e9	2.90001
$423$	−4.75671e8	−0.305573
$424$	−1.74077e9	−1.10908
$425$	−1.44863e9	−0.915371
$426$	−9.71472e8	−0.608831
$427$	−7.31331e7	−0.0454586
$428$	1.57038e9	0.968172
$429$	−3.08637e9	−1.88733
$430$	7.10046e8	0.430672
$431$	7.78770e7	0.0468531	0.0234266	−	0.999726i	$-0.492542\pi$
$431$	7.78770e7	0.0468531	0.0234266	+	0.999726i	$0.492542\pi$
$432$	−4.59794e9	−2.74391
$433$	−1.06362e9	−0.629619	−0.314810	−	0.949155i	$-0.601941\pi$
$433$	−1.06362e9	−0.629619	−0.314810	+	0.949155i	$0.601941\pi$
$434$	1.76088e9	1.03399
$435$	2.48162e9	1.44552
$436$	4.97537e9	2.87490
$437$	−1.90328e9	−1.09098
$438$	−4.82944e9	−2.74623
$439$	−1.17090e9	−0.660531	−0.330266	−	0.943888i	$-0.607138\pi$
$439$	−1.17090e9	−0.660531	−0.330266	+	0.943888i	$0.607138\pi$
$440$	1.34088e10	7.50424
$441$	−4.54156e8	−0.252157
$442$	−2.90515e9	−1.60026
$443$	−1.61819e8	−0.0884335	−0.0442167	−	0.999022i	$-0.514079\pi$
$443$	−1.61819e8	−0.0884335	−0.0442167	+	0.999022i	$0.514079\pi$
$444$	−1.13125e9	−0.613364
$445$	−3.85718e9	−2.07496
$446$	1.91111e9	1.02003
$447$	−2.32283e9	−1.23010
$448$	3.48255e9	1.82989
$449$	1.17696e9	0.613618	0.306809	−	0.951771i	$-0.400739\pi$
$449$	1.17696e9	0.613618	0.306809	+	0.951771i	$0.400739\pi$
$450$	−1.49159e9	−0.771622
$451$	−5.58959e9	−2.86921
$452$	−4.41989e9	−2.25127
$453$	3.27884e9	1.65721
$454$	4.28773e9	2.15046
$455$	1.61689e9	0.804714
$456$	−7.12139e9	−3.51712
$457$	7.63423e8	0.374161	0.187081	−	0.982345i	$-0.440097\pi$
$457$	7.63423e8	0.374161	0.187081	+	0.982345i	$0.440097\pi$
$458$	4.17428e9	2.03026
$459$	1.24714e9	0.601963
$460$	9.82190e9	4.70482
$461$	−3.36981e9	−1.60196	−0.800980	−	0.598691i	$-0.795688\pi$
$461$	−3.36981e9	−1.60196	−0.800980	+	0.598691i	$0.795688\pi$
$462$	−3.87170e9	−1.82665
$463$	−2.92488e9	−1.36954	−0.684769	−	0.728761i	$-0.740097\pi$
$463$	−2.92488e9	−1.36954	−0.684769	+	0.728761i	$0.740097\pi$
$464$	−6.62251e9	−3.07758
$465$	3.77507e9	1.74116
$466$	1.63007e9	0.746202
$467$	−2.12116e9	−0.963748	−0.481874	−	0.876240i	$-0.660044\pi$
$467$	−2.12116e9	−0.963748	−0.481874	+	0.876240i	$0.660044\pi$
$468$	−2.18459e9	−0.985165
$469$	−6.09746e8	−0.272925
$470$	−5.57875e9	−2.47853
$471$	−3.10012e9	−1.36712
$472$	−6.83507e9	−2.99189
$473$	5.46014e8	0.237241
$474$	7.97405e9	3.43918
$475$	2.47569e9	1.05991
$476$	−2.66154e9	−1.13112
$477$	2.78293e8	0.117406
$478$	−6.74992e9	−2.82684
$479$	3.77482e8	0.156936	0.0784678	−	0.996917i	$-0.474997\pi$
$479$	3.77482e8	0.156936	0.0784678	+	0.996917i	$0.474997\pi$
$480$	1.52343e10	6.28750
$481$	4.97444e8	0.203815
$482$	4.99616e9	2.03223
$483$	−1.78875e9	−0.722330
$484$	9.59315e9	3.84594
$485$	2.78012e9	1.10654
$486$	3.25416e9	1.28591
$487$	−5.49674e8	−0.215652	−0.107826	−	0.994170i	$-0.534389\pi$
$487$	−5.49674e8	−0.215652	−0.107826	+	0.994170i	$0.534389\pi$
$488$	7.30931e8	0.284713
$489$	−1.10258e9	−0.426412
$490$	−5.32642e9	−2.04526
$491$	−3.90286e9	−1.48798	−0.743991	−	0.668190i	$-0.767069\pi$
$491$	−3.90286e9	−1.48798	−0.743991	+	0.668190i	$0.767069\pi$
$492$	−1.53196e10	−5.79921
$493$	1.79628e9	0.675164
$494$	4.96485e9	1.85294
$495$	−2.14364e9	−0.794391
$496$	−1.00742e10	−3.70703
$497$	3.91365e8	0.142999
$498$	−3.32694e8	−0.120710
$499$	5.05727e9	1.82207	0.911033	−	0.412334i	$-0.135286\pi$
$499$	5.05727e9	1.82207	0.911033	+	0.412334i	$0.135286\pi$
$500$	−1.67490e9	−0.599229
$501$	1.73189e9	0.615301
$502$	−1.61917e9	−0.571255
$503$	2.90093e9	1.01636	0.508182	−	0.861249i	$-0.330318\pi$
$503$	2.90093e9	1.01636	0.508182	+	0.861249i	$0.330318\pi$
$504$	−1.72849e9	−0.601396
$505$	−5.65402e9	−1.95361
$506$	1.03419e10	3.54875
$507$	3.12408e8	0.106462
$508$	−3.95450e9	−1.33835
$509$	−1.02191e9	−0.343479	−0.171739	−	0.985142i	$-0.554939\pi$
$509$	−1.02191e9	−0.343479	−0.171739	+	0.985142i	$0.554939\pi$
$510$	−7.81300e9	−2.60809
$511$	1.94557e9	0.645022
$512$	−4.43967e9	−1.46186
$513$	−2.13134e9	−0.697014
$514$	−1.79061e9	−0.581608
$515$	5.72071e9	1.84554
$516$	1.49648e9	0.479509
$517$	−4.28997e9	−1.36533
$518$	6.24020e8	0.197262
$519$	−1.52840e9	−0.479900
$520$	−1.61601e10	−5.04002
$521$	−5.15409e8	−0.159669	−0.0798344	−	0.996808i	$-0.525439\pi$
$521$	−5.15409e8	−0.159669	−0.0798344	+	0.996808i	$0.525439\pi$
$522$	1.84954e9	0.569137
$523$	4.99074e8	0.152549	0.0762745	−	0.997087i	$-0.475697\pi$
$523$	4.99074e8	0.152549	0.0762745	+	0.997087i	$0.475697\pi$
$524$	1.20760e9	0.366659
$525$	2.32672e9	0.701758
$526$	−1.03247e10	−3.09332
$527$	2.73252e9	0.813253
$528$	2.21506e10	6.54887
$529$	1.37322e9	0.403316
$530$	3.26387e9	0.952286
$531$	1.09271e9	0.316718
$532$	4.54854e9	1.30973
$533$	6.73647e9	1.92702
$534$	−1.11312e10	−3.16336
$535$	−1.85713e9	−0.524328
$536$	6.09412e9	1.70936
$537$	−2.10265e8	−0.0585944
$538$	3.52641e9	0.976325
$539$	−4.09594e9	−1.12666
$540$	1.09988e10	3.00585
$541$	3.98160e9	1.08110	0.540551	−	0.841311i	$-0.318216\pi$
$541$	3.98160e9	1.08110	0.540551	+	0.841311i	$0.318216\pi$
$542$	−2.08292e9	−0.561920
$543$	−2.90178e9	−0.777794
$544$	1.10271e10	2.93673
$545$	−5.88385e9	−1.55695
$546$	4.66611e9	1.22682
$547$	4.26163e9	1.11332	0.556660	−	0.830740i	$-0.312083\pi$
$547$	4.26163e9	1.11332	0.556660	+	0.830740i	$0.312083\pi$
$548$	8.73935e9	2.26854
$549$	−1.16852e8	−0.0301394
$550$	−1.34523e10	−3.44768
$551$	−3.06981e9	−0.781774
$552$	1.78777e10	4.52404
$553$	−3.21240e9	−0.807778
$554$	−1.25859e10	−3.14484
$555$	1.33781e9	0.332176
$556$	8.54570e9	2.10856
$557$	−6.93171e9	−1.69960	−0.849800	−	0.527104i	$-0.823278\pi$
$557$	−6.93171e9	−1.69960	−0.849800	+	0.527104i	$0.823278\pi$
$558$	2.81354e9	0.685541
$559$	−6.58047e8	−0.159337
$560$	−1.16043e10	−2.79229
$561$	−6.00808e9	−1.43670
$562$	−3.75250e9	−0.891752
$563$	8.38570e8	0.198043	0.0990216	−	0.995085i	$-0.468429\pi$
$563$	8.38570e8	0.198043	0.0990216	+	0.995085i	$0.468429\pi$
$564$	−1.17577e10	−2.75959
$565$	5.22693e9	1.21921
$566$	7.26503e9	1.68415
$567$	−2.79674e9	−0.644334
$568$	−3.91150e9	−0.895622
$569$	7.43736e9	1.69249	0.846244	−	0.532795i	$-0.178858\pi$
$569$	7.43736e9	1.69249	0.846244	+	0.532795i	$0.178858\pi$
$570$	1.33523e10	3.01991
$571$	−2.43113e9	−0.546490	−0.273245	−	0.961944i	$-0.588097\pi$
$571$	−2.43113e9	−0.546490	−0.273245	+	0.961944i	$0.588097\pi$
$572$	−1.97023e10	−4.40181
$573$	−9.93387e8	−0.220586
$574$	8.45058e9	1.86507
$575$	−6.21505e9	−1.36335
$576$	5.56443e9	1.21323
$577$	−2.78106e8	−0.0602692	−0.0301346	−	0.999546i	$-0.509594\pi$
$577$	−2.78106e8	−0.0602692	−0.0301346	+	0.999546i	$0.509594\pi$
$578$	3.28434e9	0.707459
$579$	4.47942e9	0.959061
$580$	1.58418e10	3.37137
$581$	1.34028e8	0.0283518
$582$	8.02299e9	1.68696
$583$	2.50987e9	0.524579
$584$	−1.94451e10	−4.03985
$585$	2.58348e9	0.533531
$586$	6.46945e9	1.32809
$587$	−4.32874e9	−0.883340	−0.441670	−	0.897178i	$-0.645614\pi$
$587$	−4.32874e9	−0.883340	−0.441670	+	0.897178i	$0.645614\pi$
$588$	−1.12259e10	−2.27719
$589$	−4.66983e9	−0.941668
$590$	1.28155e10	2.56893
$591$	3.84549e9	0.766294
$592$	−3.57011e9	−0.707221
$593$	−1.16343e9	−0.229112	−0.114556	−	0.993417i	$-0.536544\pi$
$593$	−1.16343e9	−0.229112	−0.114556	+	0.993417i	$0.536544\pi$
$594$	1.15812e10	2.26725
$595$	3.14753e9	0.612576
$596$	−1.48282e10	−2.86897
$597$	8.74381e9	1.68186
$598$	−1.24639e10	−2.38342
$599$	−6.78491e9	−1.28988	−0.644941	−	0.764232i	$-0.723118\pi$
$599$	−6.78491e9	−1.28988	−0.644941	+	0.764232i	$0.723118\pi$
$600$	−2.32545e10	−4.39519
$601$	2.61686e9	0.491723	0.245862	−	0.969305i	$-0.420929\pi$
$601$	2.61686e9	0.491723	0.245862	+	0.969305i	$0.420929\pi$
$602$	−8.25488e8	−0.154214
$603$	−9.74254e8	−0.180951
$604$	2.09310e10	3.86509
$605$	−1.13448e10	−2.08283
$606$	−1.63166e10	−2.97835
$607$	1.41096e9	0.256067	0.128034	−	0.991770i	$-0.459133\pi$
$607$	1.41096e9	0.256067	0.128034	+	0.991770i	$0.459133\pi$
$608$	−1.88451e10	−3.40045
$609$	−2.88509e9	−0.517606
$610$	−1.37046e9	−0.244463
$611$	5.17020e9	0.916986
$612$	−4.25263e9	−0.749941
$613$	2.52910e9	0.443459	0.221730	−	0.975108i	$-0.428830\pi$
$613$	2.52910e9	0.443459	0.221730	+	0.975108i	$0.428830\pi$
$614$	−6.90558e9	−1.20396
$615$	1.81168e10	3.14065
$616$	−1.55889e10	−2.68710
$617$	−3.77565e9	−0.647133	−0.323567	−	0.946205i	$-0.604882\pi$
$617$	−3.77565e9	−0.647133	−0.323567	+	0.946205i	$0.604882\pi$
$618$	1.65091e10	2.81360
$619$	−9.20238e9	−1.55949	−0.779746	−	0.626096i	$-0.784652\pi$
$619$	−9.20238e9	−1.55949	−0.779746	+	0.626096i	$0.784652\pi$
$620$	2.40987e10	4.06091
$621$	5.35058e9	0.896562
$622$	1.91750e10	3.19498
$623$	4.48430e9	0.742996
$624$	−2.66955e10	−4.39837
$625$	−5.04368e9	−0.826357
$626$	1.80790e10	2.94554
$627$	1.02677e10	1.66356
$628$	−1.97901e10	−3.18852
$629$	9.68349e8	0.155151
$630$	3.24085e9	0.516377
$631$	−4.06379e9	−0.643915	−0.321958	−	0.946754i	$-0.604341\pi$
$631$	−4.06379e9	−0.643915	−0.321958	+	0.946754i	$0.604341\pi$
$632$	3.21065e10	5.05921
$633$	−1.11587e10	−1.74864
$634$	4.44597e9	0.692874
$635$	4.67657e9	0.724802
$636$	6.87887e9	1.06027
$637$	4.93635e9	0.756690
$638$	1.66806e10	2.54296
$639$	6.25324e8	0.0948096
$640$	2.93490e10	4.42552
$641$	4.61167e9	0.691599	0.345800	−	0.938308i	$-0.387608\pi$
$641$	4.61167e9	0.691599	0.345800	+	0.938308i	$0.387608\pi$
$642$	−5.35938e9	−0.799359
$643$	−8.37065e9	−1.24171	−0.620856	−	0.783925i	$-0.713215\pi$
$643$	−8.37065e9	−1.24171	−0.620856	+	0.783925i	$0.713215\pi$
$644$	−1.14188e10	−1.68469
$645$	−1.76973e9	−0.259685
$646$	9.66483e9	1.41052
$647$	1.08886e10	1.58054	0.790272	−	0.612756i	$-0.209939\pi$
$647$	1.08886e10	1.58054	0.790272	+	0.612756i	$0.209939\pi$
$648$	2.79521e10	4.03554
$649$	9.85489e9	1.41513
$650$	1.62125e10	2.31554
$651$	−4.38884e9	−0.623471
$652$	−7.03849e9	−0.994518
$653$	4.93139e9	0.693064	0.346532	−	0.938038i	$-0.387359\pi$
$653$	4.93139e9	0.693064	0.346532	+	0.938038i	$0.387359\pi$
$654$	−1.69799e10	−2.37363
$655$	−1.42809e9	−0.198569
$656$	−4.83470e10	−6.68661
$657$	3.10865e9	0.427654
$658$	6.48576e9	0.887504
$659$	−9.90535e9	−1.34825	−0.674126	−	0.738616i	$-0.735480\pi$
$659$	−9.90535e9	−1.34825	−0.674126	+	0.738616i	$0.735480\pi$
$660$	−5.29867e10	−7.17403
$661$	−6.13396e9	−0.826107	−0.413053	−	0.910707i	$-0.635538\pi$
$661$	−6.13396e9	−0.826107	−0.413053	+	0.910707i	$0.635538\pi$
$662$	9.66428e9	1.29469
$663$	7.24083e9	0.964920
$664$	−1.33955e9	−0.177570
$665$	−5.37907e9	−0.709303
$666$	9.97061e8	0.130786
$667$	7.70655e9	1.00559
$668$	1.10558e10	1.43506
$669$	−4.76327e9	−0.615055
$670$	−1.14262e10	−1.46771
$671$	−1.05387e9	−0.134666
$672$	−1.77112e10	−2.25141
$673$	−5.75452e9	−0.727707	−0.363853	−	0.931456i	$-0.618539\pi$
$673$	−5.75452e9	−0.727707	−0.363853	+	0.931456i	$0.618539\pi$
$674$	−2.08327e10	−2.62081
$675$	−6.95977e9	−0.871027
$676$	1.99431e9	0.248301
$677$	−3.89999e9	−0.483062	−0.241531	−	0.970393i	$-0.577650\pi$
$677$	−3.89999e9	−0.483062	−0.241531	+	0.970393i	$0.577650\pi$
$678$	1.50841e10	1.85873
$679$	−3.23212e9	−0.396226
$680$	−3.14580e10	−3.83663
$681$	−1.06868e10	−1.29668
$682$	2.53747e10	3.06306
$683$	−1.93635e8	−0.0232547	−0.0116273	−	0.999932i	$-0.503701\pi$
$683$	−1.93635e8	−0.0232547	−0.0116273	+	0.999932i	$0.503701\pi$
$684$	7.26767e9	0.868358
$685$	−1.03351e10	−1.22856
$686$	1.47429e10	1.74361
$687$	−1.04040e10	−1.22420
$688$	4.72273e9	0.552884
$689$	−3.02485e9	−0.352319
$690$	−3.35200e10	−3.88448
$691$	1.72931e8	0.0199388	0.00996940	−	0.999950i	$-0.496827\pi$
$691$	1.72931e8	0.0199388	0.00996940	+	0.999950i	$0.496827\pi$
$692$	−9.75676e9	−1.11927
$693$	2.49217e9	0.284453
$694$	−1.57253e10	−1.78583
$695$	−1.01061e10	−1.14192
$696$	2.88352e10	3.24183
$697$	1.31135e10	1.46692
$698$	−1.06204e10	−1.18208
$699$	−4.06282e9	−0.449943
$700$	1.48530e10	1.63671
$701$	−1.41045e10	−1.54649	−0.773243	−	0.634110i	$-0.781367\pi$
$701$	−1.41045e10	−1.54649	−0.773243	+	0.634110i	$0.781367\pi$
$702$	−1.39574e10	−1.52274
$703$	−1.65489e9	−0.179650
$704$	5.01844e10	5.42082
$705$	1.39045e10	1.49450
$706$	−5.04811e9	−0.539898
$707$	6.57327e9	0.699541
$708$	2.70096e10	2.86024
$709$	7.26226e9	0.765262	0.382631	−	0.923901i	$-0.375018\pi$
$709$	7.26226e9	0.765262	0.382631	+	0.923901i	$0.375018\pi$
$710$	7.33391e9	0.769008
$711$	−5.13279e9	−0.535562
$712$	−4.48184e10	−4.65347
$713$	1.17233e10	1.21126
$714$	9.08327e9	0.933896
$715$	2.32998e10	2.38387
$716$	−1.34226e9	−0.136660
$717$	1.68236e10	1.70452
$718$	2.30620e9	0.232520
$719$	−5.40870e9	−0.542677	−0.271339	−	0.962484i	$-0.587466\pi$
$719$	−5.40870e9	−0.542677	−0.271339	+	0.962484i	$0.587466\pi$
$720$	−1.85414e10	−1.85131
$721$	−6.65080e9	−0.660846
$722$	2.95688e9	0.292384
$723$	−1.24525e10	−1.22538
$724$	−1.85239e10	−1.81405
$725$	−1.00243e10	−0.976947
$726$	−3.27393e10	−3.17535
$727$	−1.56561e10	−1.51116	−0.755582	−	0.655054i	$-0.772646\pi$
$727$	−1.56561e10	−1.51116	−0.755582	+	0.655054i	$0.772646\pi$
$728$	1.87875e10	1.80471
$729$	4.72362e9	0.451574
$730$	3.64587e10	3.46874
$731$	−1.28099e9	−0.121292
$732$	−2.88836e9	−0.272184
$733$	1.25157e10	1.17379	0.586895	−	0.809663i	$-0.300350\pi$
$733$	1.25157e10	1.17379	0.586895	+	0.809663i	$0.300350\pi$
$734$	−4.42531e9	−0.413055
$735$	1.32756e10	1.23325
$736$	4.73093e10	4.37396
$737$	−8.78659e9	−0.808507
$738$	1.35024e10	1.23655
$739$	−1.12760e10	−1.02778	−0.513888	−	0.857857i	$-0.671795\pi$
$739$	−1.12760e10	−1.02778	−0.513888	+	0.857857i	$0.671795\pi$
$740$	8.54011e9	0.774733
$741$	−1.23745e10	−1.11728
$742$	−3.79452e9	−0.340992
$743$	6.56019e9	0.586753	0.293377	−	0.955997i	$-0.405221\pi$
$743$	6.56019e9	0.586753	0.293377	+	0.955997i	$0.405221\pi$
$744$	4.38644e10	3.90487
$745$	1.75357e10	1.55373
$746$	1.67847e10	1.48022
$747$	2.14151e8	0.0187974
$748$	−3.83535e10	−3.35081
$749$	2.15907e9	0.187750
$750$	5.71606e9	0.494746
$751$	1.28366e10	1.10589	0.552943	−	0.833219i	$-0.313505\pi$
$751$	1.28366e10	1.10589	0.552943	+	0.833219i	$0.313505\pi$
$752$	−3.71060e10	−3.18186
$753$	4.03565e9	0.344454
$754$	−2.01031e10	−1.70791
$755$	−2.47528e10	−2.09320
$756$	−1.27870e10	−1.07633
$757$	−3.54032e9	−0.296624	−0.148312	−	0.988941i	$-0.547384\pi$
$757$	−3.54032e9	−0.296624	−0.148312	+	0.988941i	$0.547384\pi$
$758$	−2.13434e10	−1.78000
$759$	−2.57764e10	−2.13981
$760$	5.37613e10	4.44244
$761$	−1.14256e10	−0.939795	−0.469897	−	0.882721i	$-0.655709\pi$
$761$	−1.14256e10	−0.939795	−0.469897	+	0.882721i	$0.655709\pi$
$762$	1.34959e10	1.10499
$763$	6.84047e9	0.557506
$764$	−6.34144e9	−0.514471
$765$	5.02913e9	0.406142
$766$	3.21154e10	2.58174
$767$	−1.18769e10	−0.950431
$768$	3.39068e10	2.70099
$769$	1.70491e10	1.35195	0.675974	−	0.736926i	$-0.263723\pi$
$769$	1.70491e10	1.35195	0.675974	+	0.736926i	$0.263723\pi$
$770$	2.92285e10	2.30722
$771$	4.46294e9	0.350696
$772$	2.85950e10	2.23681
$773$	−1.14110e10	−0.888576	−0.444288	−	0.895884i	$-0.646543\pi$
$773$	−1.14110e10	−0.888576	−0.444288	+	0.895884i	$0.646543\pi$
$774$	−1.31897e9	−0.102245
$775$	−1.52491e10	−1.17676
$776$	3.23035e10	2.48161
$777$	−1.55532e9	−0.118945
$778$	−2.50198e10	−1.90482
$779$	−2.24108e10	−1.69854
$780$	6.38586e10	4.81824
$781$	5.63966e9	0.423618
$782$	−2.42629e10	−1.81434
$783$	8.62999e9	0.642457
$784$	−3.54277e10	−2.62565
$785$	2.34037e10	1.72679
$786$	−4.12126e9	−0.302727
$787$	−1.06817e10	−0.781142	−0.390571	−	0.920573i	$-0.627722\pi$
$787$	−1.06817e10	−0.781142	−0.390571	+	0.920573i	$0.627722\pi$
$788$	2.45483e10	1.78722
$789$	2.57333e10	1.86520
$790$	−6.01982e10	−4.34399
$791$	−6.07675e9	−0.436570
$792$	−2.49080e10	−1.78156
$793$	1.27010e9	0.0904444
$794$	−3.33497e10	−2.36440
$795$	−8.13492e9	−0.574206
$796$	5.58174e10	3.92260
$797$	1.80601e10	1.26362	0.631810	−	0.775123i	$-0.282312\pi$
$797$	1.80601e10	1.26362	0.631810	+	0.775123i	$0.282312\pi$
$798$	−1.55232e10	−1.08136
$799$	1.00646e10	0.698041
$800$	−6.15377e10	−4.24939
$801$	7.16503e9	0.492611
$802$	1.10129e10	0.753862
$803$	2.80362e10	1.91080
$804$	−2.40817e10	−1.63415
$805$	1.35038e10	0.912368
$806$	−3.05811e10	−2.05722
$807$	−8.78926e9	−0.588701
$808$	−6.56967e10	−4.38131
$809$	1.87987e10	1.24827	0.624134	−	0.781317i	$-0.285452\pi$
$809$	1.87987e10	1.24827	0.624134	+	0.781317i	$0.285452\pi$
$810$	−5.24090e10	−3.46504
$811$	−1.93491e9	−0.127376	−0.0636881	−	0.997970i	$-0.520286\pi$
$811$	−1.93491e9	−0.127376	−0.0636881	+	0.997970i	$0.520286\pi$
$812$	−1.84174e10	−1.20721
$813$	5.19149e9	0.338825
$814$	8.99228e9	0.584365
$815$	8.32368e9	0.538596
$816$	−5.19667e10	−3.34819
$817$	2.18918e9	0.140445
$818$	−3.50279e10	−2.23758
$819$	−3.00351e9	−0.191045
$820$	1.15652e11	7.32492
$821$	1.74599e10	1.10113	0.550567	−	0.834791i	$-0.314411\pi$
$821$	1.74599e10	1.10113	0.550567	+	0.834791i	$0.314411\pi$
$822$	−2.98255e10	−1.87300
$823$	−1.78070e10	−1.11350	−0.556752	−	0.830679i	$-0.687953\pi$
$823$	−1.78070e10	−1.11350	−0.556752	+	0.830679i	$0.687953\pi$
$824$	6.64716e10	4.13896
$825$	3.35287e10	2.07887
$826$	−1.48990e10	−0.919874
$827$	−2.44106e10	−1.50075	−0.750377	−	0.661010i	$-0.770128\pi$
$827$	−2.44106e10	−1.50075	−0.750377	+	0.661010i	$0.770128\pi$
$828$	−1.82450e10	−1.11696
$829$	1.80753e10	1.10191	0.550953	−	0.834536i	$-0.314264\pi$
$829$	1.80753e10	1.10191	0.550953	+	0.834536i	$0.314264\pi$
$830$	2.51160e9	0.152467
$831$	3.13692e10	1.89627
$832$	−6.04814e10	−3.64074
$833$	9.60934e9	0.576018
$834$	−2.91646e10	−1.74091
$835$	−1.30745e10	−0.777181
$836$	6.55455e10	3.87990
$837$	1.31280e10	0.773857
$838$	−6.24688e10	−3.66699
$839$	−3.99758e9	−0.233684	−0.116842	−	0.993150i	$-0.537277\pi$
$839$	−3.99758e9	−0.233684	−0.116842	+	0.993150i	$0.537277\pi$
$840$	5.05264e10	2.94131
$841$	−4.81993e9	−0.279418
$842$	−4.32439e10	−2.49651
$843$	9.35279e9	0.537706
$844$	−7.12331e10	−4.07834
$845$	−2.35846e9	−0.134471
$846$	1.03630e10	0.588421
$847$	1.31893e10	0.745812
$848$	2.17090e10	1.22252
$849$	−1.81075e10	−1.01550
$850$	3.15600e10	1.76267
$851$	4.15450e9	0.231081
$852$	1.54568e10	0.856212
$853$	1.49532e10	0.824923	0.412461	−	0.910975i	$-0.364669\pi$
$853$	1.49532e10	0.824923	0.412461	+	0.910975i	$0.364669\pi$
$854$	1.59328e9	0.0875366
$855$	−8.59470e9	−0.470272
$856$	−2.15788e10	−1.17590
$857$	−2.77267e10	−1.50475	−0.752377	−	0.658732i	$-0.771093\pi$
$857$	−2.77267e10	−1.50475	−0.752377	+	0.658732i	$0.771093\pi$
$858$	6.72398e10	3.63430
$859$	−1.83528e10	−0.987930	−0.493965	−	0.869482i	$-0.664453\pi$
$859$	−1.83528e10	−0.987930	−0.493965	+	0.869482i	$0.664453\pi$
$860$	−1.12973e10	−0.605663
$861$	−2.10623e10	−1.12459
$862$	−1.69663e9	−0.0902218
$863$	−5.98092e9	−0.316760	−0.158380	−	0.987378i	$-0.550627\pi$
$863$	−5.98092e9	−0.316760	−0.158380	+	0.987378i	$0.550627\pi$
$864$	5.29782e10	2.79447
$865$	1.15383e10	0.606157
$866$	2.31720e10	1.21241
$867$	−8.18594e9	−0.426581
$868$	−2.80168e10	−1.45412
$869$	−4.62915e10	−2.39294
$870$	−5.40647e10	−2.78353
$871$	1.05894e10	0.543012
$872$	−6.83672e10	−3.49173
$873$	−5.16429e9	−0.262701
$874$	4.14649e10	2.10083
$875$	−2.30276e9	−0.116204
$876$	7.68397e10	3.86208
$877$	2.39573e10	1.19933	0.599666	−	0.800251i	$-0.295300\pi$
$877$	2.39573e10	1.19933	0.599666	+	0.800251i	$0.295300\pi$
$878$	2.55092e10	1.27194
$879$	−1.61246e10	−0.800805
$880$	−1.67221e11	−8.27181
$881$	1.57373e9	0.0775380	0.0387690	−	0.999248i	$-0.487656\pi$
$881$	1.57373e9	0.0775380	0.0387690	+	0.999248i	$0.487656\pi$
$882$	9.89426e9	0.485561
$883$	1.75377e10	0.857254	0.428627	−	0.903482i	$-0.358998\pi$
$883$	1.75377e10	0.857254	0.428627	+	0.903482i	$0.358998\pi$
$884$	4.62229e10	2.25048
$885$	−3.19414e10	−1.54901
$886$	3.52539e9	0.170290
$887$	4.02646e10	1.93727	0.968637	−	0.248479i	$-0.0799307\pi$
$887$	4.02646e10	1.93727	0.968637	+	0.248479i	$0.0799307\pi$
$888$	1.55446e10	0.744964
$889$	−5.43691e9	−0.259535
$890$	8.40326e10	3.99561
$891$	−4.03017e10	−1.90876
$892$	−3.04070e10	−1.43449
$893$	−1.72002e10	−0.808263
$894$	5.06053e10	2.36873
$895$	1.58734e9	0.0740100
$896$	−3.41207e10	−1.58467
$897$	3.10652e10	1.43715
$898$	−2.56412e10	−1.18160
$899$	1.89086e10	0.867960
$900$	2.37322e10	1.08515
$901$	−5.88831e9	−0.268197
$902$	1.21775e11	5.52503
$903$	2.05746e9	0.0929873
$904$	6.07342e10	2.73429
$905$	2.19063e10	0.982424
$906$	−7.14329e10	−3.19117
$907$	2.96929e10	1.32138	0.660688	−	0.750660i	$-0.270264\pi$
$907$	2.96929e10	1.32138	0.660688	+	0.750660i	$0.270264\pi$
$908$	−6.82207e10	−3.02424
$909$	1.05028e10	0.463801
$910$	−3.52257e10	−1.54958
$911$	6.10006e9	0.267313	0.133656	−	0.991028i	$-0.457328\pi$
$911$	6.10006e9	0.267313	0.133656	+	0.991028i	$0.457328\pi$
$912$	8.88103e10	3.87687
$913$	1.93138e9	0.0839886
$914$	−1.66320e10	−0.720496
$915$	3.41576e9	0.147406
$916$	−6.64156e10	−2.85520
$917$	1.66028e9	0.0711031
$918$	−2.71702e10	−1.15916
$919$	−3.43035e10	−1.45792	−0.728960	−	0.684556i	$-0.759996\pi$
$919$	−3.43035e10	−1.45792	−0.728960	+	0.684556i	$0.759996\pi$
$920$	−1.34964e11	−5.71426
$921$	1.72116e10	0.725959
$922$	7.34147e10	3.08478
$923$	−6.79682e9	−0.284511
$924$	6.16015e10	2.56885
$925$	−5.40397e9	−0.224500
$926$	6.37214e10	2.63722
$927$	−1.06267e10	−0.438146
$928$	7.63056e10	3.13428
$929$	−1.04991e10	−0.429632	−0.214816	−	0.976655i	$-0.568915\pi$
$929$	−1.04991e10	−0.429632	−0.214816	+	0.976655i	$0.568915\pi$
$930$	−8.22438e10	−3.35284
$931$	−1.64222e10	−0.666972
$932$	−2.59356e10	−1.04940
$933$	−4.77920e10	−1.92650
$934$	4.62116e10	1.85582
$935$	4.53566e10	1.81468
$936$	3.00187e10	1.19654
$937$	3.00943e10	1.19507	0.597537	−	0.801841i	$-0.296146\pi$
$937$	3.00943e10	1.19507	0.597537	+	0.801841i	$0.296146\pi$
$938$	1.32839e10	0.525553
$939$	−4.50604e10	−1.77609
$940$	8.87617e10	3.48561
$941$	−1.94953e10	−0.762720	−0.381360	−	0.924427i	$-0.624544\pi$
$941$	−1.94953e10	−0.762720	−0.381360	+	0.924427i	$0.624544\pi$
$942$	6.75394e10	2.63256
$943$	5.62608e10	2.18482
$944$	8.52396e10	3.29791
$945$	1.51219e10	0.582901
$946$	−1.18955e10	−0.456839
$947$	2.51681e10	0.962998	0.481499	−	0.876447i	$-0.340092\pi$
$947$	2.51681e10	0.962998	0.481499	+	0.876447i	$0.340092\pi$
$948$	−1.26873e11	−4.83659
$949$	−3.37887e10	−1.28333
$950$	−5.39355e10	−2.04100
$951$	−1.10812e10	−0.417787
$952$	3.65726e10	1.37381
$953$	1.34093e10	0.501859	0.250929	−	0.968005i	$-0.419264\pi$
$953$	1.34093e10	0.501859	0.250929	+	0.968005i	$0.419264\pi$
$954$	−6.06291e9	−0.226080
$955$	7.49935e9	0.278620
$956$	1.07396e11	3.97544
$957$	−4.15749e10	−1.53334
$958$	−8.22383e9	−0.302200
$959$	1.20154e10	0.439921
$960$	−1.62656e11	−5.93365
$961$	1.25131e9	0.0454815
$962$	−1.08373e10	−0.392473
$963$	3.44976e9	0.124479
$964$	−7.94924e10	−2.85796
$965$	−3.38163e10	−1.21138
$966$	3.89698e10	1.39094
$967$	−4.92333e10	−1.75092	−0.875460	−	0.483291i	$-0.839441\pi$
$967$	−4.92333e10	−1.75092	−0.875460	+	0.483291i	$0.839441\pi$
$968$	−1.31821e11	−4.67111
$969$	−2.40887e10	−0.850513
$970$	−6.05677e10	−2.13079
$971$	1.64288e10	0.575889	0.287945	−	0.957647i	$-0.407028\pi$
$971$	1.64288e10	0.575889	0.287945	+	0.957647i	$0.407028\pi$
$972$	−5.17760e10	−1.80841
$973$	1.17492e10	0.408896
$974$	1.19752e10	0.415266
$975$	−4.04082e10	−1.39622
$976$	−9.11538e9	−0.313834
$977$	1.72848e10	0.592972	0.296486	−	0.955037i	$-0.404185\pi$
$977$	1.72848e10	0.592972	0.296486	+	0.955037i	$0.404185\pi$
$978$	2.40208e10	0.821112
$979$	6.46198e10	2.20103
$980$	8.47471e10	2.87630
$981$	1.09297e10	0.369630
$982$	8.50278e10	2.86530
$983$	−8.75111e9	−0.293850	−0.146925	−	0.989148i	$-0.546938\pi$
$983$	−8.75111e9	−0.293850	−0.146925	+	0.989148i	$0.546938\pi$
$984$	2.10508e11	7.04346
$985$	−2.90306e10	−0.967898
$986$	−3.91338e10	−1.30012
$987$	−1.61652e10	−0.535144
$988$	−7.89943e10	−2.60583
$989$	−5.49580e9	−0.180652
$990$	4.67015e10	1.52970
$991$	−2.33937e10	−0.763555	−0.381778	−	0.924254i	$-0.624688\pi$
$991$	−2.33937e10	−0.763555	−0.381778	+	0.924254i	$0.624688\pi$
$992$	1.16077e11	3.77533
$993$	−2.40874e10	−0.780670
$994$	−8.52628e9	−0.275364
$995$	−6.60094e10	−2.12434
$996$	5.29340e9	0.169757
$997$	−8.07234e9	−0.257968	−0.128984	−	0.991647i	$-0.541172\pi$
$997$	−8.07234e9	−0.257968	−0.128984	+	0.991647i	$0.541172\pi$
$998$	−1.10178e11	−3.50862
$999$	4.65231e9	0.147635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.a.1.1	✓	11
3.2	odd	2		387.8.a.b.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.1	✓	11	1.1	even	1	trivial
387.8.a.b.1.11		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-21.7860 q^{2} +54.2998 q^{3} +346.631 q^{4} -409.924 q^{5} -1182.98 q^{6} +476.571 q^{7} -4763.10 q^{8} +761.467 q^{9} +O(q^{10})\)	\(q-21.7860 q^{2} +54.2998 q^{3} +346.631 q^{4} -409.924 q^{5} -1182.98 q^{6} +476.571 q^{7} -4763.10 q^{8} +761.467 q^{9} +8930.61 q^{10} +6867.50 q^{11} +18822.0 q^{12} -8276.59 q^{13} -10382.6 q^{14} -22258.8 q^{15} +59400.2 q^{16} -16111.6 q^{17} -16589.3 q^{18} +27534.5 q^{19} -142092. q^{20} +25877.7 q^{21} -149616. q^{22} -69123.4 q^{23} -258635. q^{24} +89912.4 q^{25} +180314. q^{26} -77406.2 q^{27} +165194. q^{28} -111490. q^{29} +484930. q^{30} -169599. q^{31} -684418. q^{32} +372904. q^{33} +351008. q^{34} -195358. q^{35} +263948. q^{36} -60102.6 q^{37} -599867. q^{38} -449417. q^{39} +1.95251e6 q^{40} -813919. q^{41} -563772. q^{42} +79507.0 q^{43} +2.38049e6 q^{44} -312143. q^{45} +1.50592e6 q^{46} -624677. q^{47} +3.22542e6 q^{48} -596423. q^{49} -1.95883e6 q^{50} -874857. q^{51} -2.86892e6 q^{52} +365470. q^{53} +1.68637e6 q^{54} -2.81515e6 q^{55} -2.26995e6 q^{56} +1.49512e6 q^{57} +2.42892e6 q^{58} +1.43500e6 q^{59} -7.71558e6 q^{60} -153457. q^{61} +3.69489e6 q^{62} +362893. q^{63} +7.30752e6 q^{64} +3.39277e6 q^{65} -8.12409e6 q^{66} -1.27944e6 q^{67} -5.58478e6 q^{68} -3.75339e6 q^{69} +4.25607e6 q^{70} +821210. q^{71} -3.62694e6 q^{72} +4.08244e6 q^{73} +1.30940e6 q^{74} +4.88222e6 q^{75} +9.54431e6 q^{76} +3.27285e6 q^{77} +9.79101e6 q^{78} -6.74067e6 q^{79} -2.43496e7 q^{80} -5.86847e6 q^{81} +1.77321e7 q^{82} +281235. q^{83} +8.97001e6 q^{84} +6.60453e6 q^{85} -1.73214e6 q^{86} -6.05387e6 q^{87} -3.27106e7 q^{88} +9.40951e6 q^{89} +6.80036e6 q^{90} -3.94438e6 q^{91} -2.39603e7 q^{92} -9.20921e6 q^{93} +1.36092e7 q^{94} -1.12870e7 q^{95} -3.71638e7 q^{96} -6.78204e6 q^{97} +1.29937e7 q^{98} +5.22937e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9}+O(q^{10}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9	\( 11 q - 24 q^{2} - 68 q^{3} + 602 q^{4} - 752 q^{5} - 681 q^{6} - 12 q^{7} - 3810 q^{8} + 2721 q^{9} - 1333 q^{10} + 1333 q^{11} + 5089 q^{12} - 17967 q^{13} - 22352 q^{14} - 49504 q^{15} - 34406 q^{16} - 63095 q^{17} - 165931 q^{18} - 54524 q^{19} - 280995 q^{20} - 139788 q^{21} - 289358 q^{22} - 138139 q^{23} - 429583 q^{24} + 3455 q^{25} - 132946 q^{26} - 240356 q^{27} - 12704 q^{28} - 308658 q^{29} + 421284 q^{30} - 209523 q^{31} - 644934 q^{32} + 96814 q^{33} + 762435 q^{34} - 578892 q^{35} + 426161 q^{36} - 298472 q^{37} - 369707 q^{38} + 292298 q^{39} + 2633173 q^{40} - 1346735 q^{41} + 1173266 q^{42} + 874577 q^{43} + 3134292 q^{44} + 1893784 q^{45} + 3588111 q^{46} + 499284 q^{47} + 5647533 q^{48} + 2544563 q^{49} + 3049745 q^{50} + 1258424 q^{51} + 983088 q^{52} - 2210495 q^{53} + 6789698 q^{54} - 1855072 q^{55} - 469976 q^{56} - 1238444 q^{57} + 4397067 q^{58} - 5824216 q^{59} - 2889372 q^{60} - 4453034 q^{61} + 1002789 q^{62} - 6240564 q^{63} + 4757538 q^{64} - 2162872 q^{65} - 258940 q^{66} - 6859513 q^{67} - 9397005 q^{68} - 10040030 q^{69} + 845078 q^{70} - 10726554 q^{71} + 1199517 q^{72} - 4456898 q^{73} + 1046637 q^{74} - 3349114 q^{75} + 5861267 q^{76} - 17019816 q^{77} + 1999122 q^{78} - 15541320 q^{79} - 15680911 q^{80} - 12976697 q^{81} + 20233655 q^{82} - 11146767 q^{83} + 12348278 q^{84} - 12471976 q^{85} - 1908168 q^{86} - 18648900 q^{87} - 24463544 q^{88} - 13531356 q^{89} + 20858990 q^{90} - 19746448 q^{91} - 26023161 q^{92} - 21903110 q^{93} + 20288857 q^{94} - 12291624 q^{95} - 13954503 q^{96} - 10999901 q^{97} + 29909168 q^{98} + 29396057 q^{99}+O(q^{100}) \) 11 * q - 24 * q^2 - 68 * q^3 + 602 * q^4 - 752 * q^5 - 681 * q^6 - 12 * q^7 - 3810 * q^8 + 2721 * q^9 - 1333 * q^10 + 1333 * q^11 + 5089 * q^12 - 17967 * q^13 - 22352 * q^14 - 49504 * q^15 - 34406 * q^16 - 63095 * q^17 - 165931 * q^18 - 54524 * q^19 - 280995 * q^20 - 139788 * q^21 - 289358 * q^22 - 138139 * q^23 - 429583 * q^24 + 3455 * q^25 - 132946 * q^26 - 240356 * q^27 - 12704 * q^28 - 308658 * q^29 + 421284 * q^30 - 209523 * q^31 - 644934 * q^32 + 96814 * q^33 + 762435 * q^34 - 578892 * q^35 + 426161 * q^36 - 298472 * q^37 - 369707 * q^38 + 292298 * q^39 + 2633173 * q^40 - 1346735 * q^41 + 1173266 * q^42 + 874577 * q^43 + 3134292 * q^44 + 1893784 * q^45 + 3588111 * q^46 + 499284 * q^47 + 5647533 * q^48 + 2544563 * q^49 + 3049745 * q^50 + 1258424 * q^51 + 983088 * q^52 - 2210495 * q^53 + 6789698 * q^54 - 1855072 * q^55 - 469976 * q^56 - 1238444 * q^57 + 4397067 * q^58 - 5824216 * q^59 - 2889372 * q^60 - 4453034 * q^61 + 1002789 * q^62 - 6240564 * q^63 + 4757538 * q^64 - 2162872 * q^65 - 258940 * q^66 - 6859513 * q^67 - 9397005 * q^68 - 10040030 * q^69 + 845078 * q^70 - 10726554 * q^71 + 1199517 * q^72 - 4456898 * q^73 + 1046637 * q^74 - 3349114 * q^75 + 5861267 * q^76 - 17019816 * q^77 + 1999122 * q^78 - 15541320 * q^79 - 15680911 * q^80 - 12976697 * q^81 + 20233655 * q^82 - 11146767 * q^83 + 12348278 * q^84 - 12471976 * q^85 - 1908168 * q^86 - 18648900 * q^87 - 24463544 * q^88 - 13531356 * q^89 + 20858990 * q^90 - 19746448 * q^91 - 26023161 * q^92 - 21903110 * q^93 + 20288857 * q^94 - 12291624 * q^95 - 13954503 * q^96 - 10999901 * q^97 + 29909168 * q^98 + 29396057 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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