LMFDB - Embedded newform 43.8.a.b.1.10

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$15.0703$ 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)

$f(q)$	$=$	$q+16.0703 q^{2} +41.5098 q^{3} +130.256 q^{4} +431.884 q^{5} +667.077 q^{6} +218.970 q^{7} +36.2566 q^{8} -463.938 q^{9} +O(q^{10})$	\(q+16.0703 q^{2} +41.5098 q^{3} +130.256 q^{4} +431.884 q^{5} +667.077 q^{6} +218.970 q^{7} +36.2566 q^{8} -463.938 q^{9} +6940.53 q^{10} -7017.15 q^{11} +5406.90 q^{12} +7017.50 q^{13} +3518.93 q^{14} +17927.4 q^{15} -16090.1 q^{16} +37064.5 q^{17} -7455.64 q^{18} -39841.8 q^{19} +56255.5 q^{20} +9089.40 q^{21} -112768. q^{22} +29837.9 q^{23} +1505.01 q^{24} +108399. q^{25} +112774. q^{26} -110040. q^{27} +28522.2 q^{28} -72817.2 q^{29} +288100. q^{30} -103069. q^{31} -263215. q^{32} -291280. q^{33} +595639. q^{34} +94569.7 q^{35} -60430.7 q^{36} +330208. q^{37} -640272. q^{38} +291295. q^{39} +15658.7 q^{40} +387979. q^{41} +146070. q^{42} -79507.0 q^{43} -914026. q^{44} -200367. q^{45} +479505. q^{46} -1.39939e6 q^{47} -667898. q^{48} -775595. q^{49} +1.74201e6 q^{50} +1.53854e6 q^{51} +914072. q^{52} -300329. q^{53} -1.76838e6 q^{54} -3.03059e6 q^{55} +7939.12 q^{56} -1.65382e6 q^{57} -1.17020e6 q^{58} -440915. q^{59} +2.33515e6 q^{60} +1.72200e6 q^{61} -1.65635e6 q^{62} -101588. q^{63} -2.17042e6 q^{64} +3.03075e6 q^{65} -4.68098e6 q^{66} +3.45225e6 q^{67} +4.82787e6 q^{68} +1.23856e6 q^{69} +1.51977e6 q^{70} -1.85700e6 q^{71} -16820.8 q^{72} -673491. q^{73} +5.30655e6 q^{74} +4.49961e6 q^{75} -5.18964e6 q^{76} -1.53655e6 q^{77} +4.68121e6 q^{78} +5.44201e6 q^{79} -6.94907e6 q^{80} -3.55310e6 q^{81} +6.23496e6 q^{82} +4.84142e6 q^{83} +1.18395e6 q^{84} +1.60075e7 q^{85} -1.27771e6 q^{86} -3.02263e6 q^{87} -254418. q^{88} +8.98649e6 q^{89} -3.21997e6 q^{90} +1.53662e6 q^{91} +3.88656e6 q^{92} -4.27836e6 q^{93} -2.24887e7 q^{94} -1.72070e7 q^{95} -1.09260e7 q^{96} -7.64277e6 q^{97} -1.24641e7 q^{98} +3.25552e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) $ 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * 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 $

$2$	16.0703	1.42043	0.710216	−	0.703984i	$-0.248597\pi$
$2$	16.0703	1.42043	0.710216	+	0.703984i	$0.248597\pi$
$3$	41.5098	0.887618	0.443809	−	0.896121i	$-0.353627\pi$
$3$	41.5098	0.887618	0.443809	+	0.896121i	$0.353627\pi$
$4$	130.256	1.01763
$5$	431.884	1.54515	0.772577	−	0.634921i	$-0.218967\pi$
$5$	431.884	1.54515	0.772577	+	0.634921i	$0.218967\pi$
$6$	667.077	1.26080
$7$	218.970	0.241291	0.120646	−	0.992696i	$-0.461504\pi$
$7$	218.970	0.241291	0.120646	+	0.992696i	$0.461504\pi$
$8$	36.2566	0.0250364
$9$	−463.938	−0.212134
$10$	6940.53	2.19479
$11$	−7017.15	−1.58959	−0.794797	−	0.606875i	$-0.792423\pi$
$11$	−7017.15	−1.58959	−0.794797	+	0.606875i	$0.792423\pi$
$12$	5406.90	0.903263
$13$	7017.50	0.885892	0.442946	−	0.896548i	$-0.353933\pi$
$13$	7017.50	0.885892	0.442946	+	0.896548i	$0.353933\pi$
$14$	3518.93	0.342738
$15$	17927.4	1.37151
$16$	−16090.1	−0.982063
$17$	37064.5	1.82973	0.914864	−	0.403763i	$-0.132298\pi$
$17$	37064.5	1.82973	0.914864	+	0.403763i	$0.132298\pi$
$18$	−7455.64	−0.301322
$19$	−39841.8	−1.33260	−0.666302	−	0.745682i	$-0.732124\pi$
$19$	−39841.8	−1.33260	−0.666302	+	0.745682i	$0.732124\pi$
$20$	56255.5	1.57239
$21$	9089.40	0.214175
$22$	−112768.	−2.25791
$23$	29837.9	0.511352	0.255676	−	0.966762i	$-0.417702\pi$
$23$	29837.9	0.511352	0.255676	+	0.966762i	$0.417702\pi$
$24$	1505.01	0.0222228
$25$	108399.	1.38750
$26$	112774.	1.25835
$27$	−110040.	−1.07591
$28$	28522.2	0.245544
$29$	−72817.2	−0.554423	−0.277211	−	0.960809i	$-0.589410\pi$
$29$	−72817.2	−0.554423	−0.277211	+	0.960809i	$0.589410\pi$
$30$	288100.	1.94813
$31$	−103069.	−0.621386	−0.310693	−	0.950510i	$-0.600561\pi$
$31$	−103069.	−0.621386	−0.310693	+	0.950510i	$0.600561\pi$
$32$	−263215.	−1.41999
$33$	−291280.	−1.41095
$34$	595639.	2.59900
$35$	94569.7	0.372832
$36$	−60430.7	−0.215873
$37$	330208.	1.07172	0.535860	−	0.844307i	$-0.319988\pi$
$37$	330208.	1.07172	0.535860	+	0.844307i	$0.319988\pi$
$38$	−640272.	−1.89287
$39$	291295.	0.786334
$40$	15658.7	0.0386852
$41$	387979.	0.879154	0.439577	−	0.898205i	$-0.355128\pi$
$41$	387979.	0.879154	0.439577	+	0.898205i	$0.355128\pi$
$42$	146070.	0.304220
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−914026.	−1.61761
$45$	−200367.	−0.327780
$46$	479505.	0.726341
$47$	−1.39939e6	−1.96606	−0.983031	−	0.183440i	$-0.941277\pi$
$47$	−1.39939e6	−1.96606	−0.983031	+	0.183440i	$0.941277\pi$
$48$	−667898.	−0.871697
$49$	−775595.	−0.941778
$50$	1.74201e6	1.97085
$51$	1.53854e6	1.62410
$52$	914072.	0.901507
$53$	−300329.	−0.277097	−0.138548	−	0.990356i	$-0.544244\pi$
$53$	−300329.	−0.277097	−0.138548	+	0.990356i	$0.544244\pi$
$54$	−1.76838e6	−1.52826
$55$	−3.03059e6	−2.45617
$56$	7939.12	0.00604108
$57$	−1.65382e6	−1.18284
$58$	−1.17020e6	−0.787520
$59$	−440915.	−0.279494	−0.139747	−	0.990187i	$-0.544629\pi$
$59$	−440915.	−0.279494	−0.139747	+	0.990187i	$0.544629\pi$
$60$	2.33515e6	1.39568
$61$	1.72200e6	0.971356	0.485678	−	0.874138i	$-0.338573\pi$
$61$	1.72200e6	0.971356	0.485678	+	0.874138i	$0.338573\pi$
$62$	−1.65635e6	−0.882636
$63$	−101588.	−0.0511862
$64$	−2.17042e6	−1.03494
$65$	3.03075e6	1.36884
$66$	−4.68098e6	−2.00416
$67$	3.45225e6	1.40230	0.701149	−	0.713015i	$-0.252671\pi$
$67$	3.45225e6	1.40230	0.701149	+	0.713015i	$0.252671\pi$
$68$	4.82787e6	1.86198
$69$	1.23856e6	0.453885
$70$	1.51977e6	0.529583
$71$	−1.85700e6	−0.615756	−0.307878	−	0.951426i	$-0.599619\pi$
$71$	−1.85700e6	−0.615756	−0.307878	+	0.951426i	$0.599619\pi$
$72$	−16820.8	−0.00531109
$73$	−673491.	−0.202629	−0.101315	−	0.994854i	$-0.532305\pi$
$73$	−673491.	−0.202629	−0.101315	+	0.994854i	$0.532305\pi$
$74$	5.30655e6	1.52230
$75$	4.49961e6	1.23157
$76$	−5.18964e6	−1.35609
$77$	−1.53655e6	−0.383555
$78$	4.68121e6	1.11693
$79$	5.44201e6	1.24184	0.620918	−	0.783875i	$-0.286760\pi$
$79$	5.44201e6	1.24184	0.620918	+	0.783875i	$0.286760\pi$
$80$	−6.94907e6	−1.51744
$81$	−3.55310e6	−0.742865
$82$	6.23496e6	1.24878
$83$	4.84142e6	0.929394	0.464697	−	0.885470i	$-0.346163\pi$
$83$	4.84142e6	0.929394	0.464697	+	0.885470i	$0.346163\pi$
$84$	1.18395e6	0.217950
$85$	1.60075e7	2.82721
$86$	−1.27771e6	−0.216614
$87$	−3.02263e6	−0.492116
$88$	−254418.	−0.0397978
$89$	8.98649e6	1.35122	0.675609	−	0.737260i	$-0.263881\pi$
$89$	8.98649e6	1.35122	0.675609	+	0.737260i	$0.263881\pi$
$90$	−3.21997e6	−0.465589
$91$	1.53662e6	0.213758
$92$	3.88656e6	0.520365
$93$	−4.27836e6	−0.551553
$94$	−2.24887e7	−2.79266
$95$	−1.72070e7	−2.05908
$96$	−1.09260e7	−1.26041
$97$	−7.64277e6	−0.850256	−0.425128	−	0.905133i	$-0.639771\pi$
$97$	−7.64277e6	−0.850256	−0.425128	+	0.905133i	$0.639771\pi$
$98$	−1.24641e7	−1.33773
$99$	3.25552e6	0.337207
$100$	1.41196e7	1.41196
$101$	−4.72174e6	−0.456013	−0.228006	−	0.973660i	$-0.573221\pi$
$101$	−4.72174e6	−0.456013	−0.228006	+	0.973660i	$0.573221\pi$
$102$	2.47248e7	2.30692
$103$	5.07090e6	0.457251	0.228625	−	0.973514i	$-0.426577\pi$
$103$	5.07090e6	0.457251	0.228625	+	0.973514i	$0.426577\pi$
$104$	254431.	0.0221796
$105$	3.92557e6	0.330933
$106$	−4.82639e6	−0.393597
$107$	−3.42527e6	−0.270304	−0.135152	−	0.990825i	$-0.543152\pi$
$107$	−3.42527e6	−0.270304	−0.135152	+	0.990825i	$0.543152\pi$
$108$	−1.43334e7	−1.09488
$109$	−4.64829e6	−0.343795	−0.171898	−	0.985115i	$-0.554990\pi$
$109$	−4.64829e6	−0.343795	−0.171898	+	0.985115i	$0.554990\pi$
$110$	−4.87027e7	−3.48882
$111$	1.37069e7	0.951278
$112$	−3.52326e6	−0.236963
$113$	1.20722e7	0.787065	0.393533	−	0.919311i	$-0.371253\pi$
$113$	1.20722e7	0.787065	0.393533	+	0.919311i	$0.371253\pi$
$114$	−2.65775e7	−1.68015
$115$	1.28865e7	0.790118
$116$	−9.48489e6	−0.564195
$117$	−3.25568e6	−0.187928
$118$	−7.08566e6	−0.397003
$119$	8.11601e6	0.441497
$120$	649988.	0.0343377
$121$	2.97532e7	1.52681
$122$	2.76731e7	1.37974
$123$	1.61049e7	0.780353
$124$	−1.34253e7	−0.632338
$125$	1.30747e7	0.598753
$126$	−1.63256e6	−0.0727064
$127$	3.31970e6	0.143809	0.0719045	−	0.997412i	$-0.477092\pi$
$127$	3.31970e6	0.143809	0.0719045	+	0.997412i	$0.477092\pi$
$128$	−1.18787e6	−0.0500651
$129$	−3.30032e6	−0.135360
$130$	4.87051e7	1.94434
$131$	2.70388e7	1.05084	0.525421	−	0.850842i	$-0.323908\pi$
$131$	2.70388e7	1.05084	0.525421	+	0.850842i	$0.323908\pi$
$132$	−3.79410e7	−1.43582
$133$	−8.72417e6	−0.321546
$134$	5.54789e7	1.99187
$135$	−4.75244e7	−1.66245
$136$	1.34383e6	0.0458099
$137$	7.47994e6	0.248529	0.124264	−	0.992249i	$-0.460343\pi$
$137$	7.47994e6	0.248529	0.124264	+	0.992249i	$0.460343\pi$
$138$	1.99041e7	0.644713
$139$	3.21430e7	1.01516	0.507580	−	0.861605i	$-0.330540\pi$
$139$	3.21430e7	1.01516	0.507580	+	0.861605i	$0.330540\pi$
$140$	1.23183e7	0.379404
$141$	−5.80885e7	−1.74511
$142$	−2.98427e7	−0.874639
$143$	−4.92428e7	−1.40821
$144$	7.46481e6	0.208329
$145$	−3.14486e7	−0.856669
$146$	−1.08232e7	−0.287821
$147$	−3.21948e7	−0.835940
$148$	4.30116e7	1.09061
$149$	−5.81325e7	−1.43968	−0.719842	−	0.694138i	$-0.755786\pi$
$149$	−5.81325e7	−1.43968	−0.719842	+	0.694138i	$0.755786\pi$
$150$	7.23103e7	1.74937
$151$	3.73079e7	0.881824	0.440912	−	0.897550i	$-0.354655\pi$
$151$	3.73079e7	0.881824	0.440912	+	0.897550i	$0.354655\pi$
$152$	−1.44453e6	−0.0333637
$153$	−1.71956e7	−0.388148
$154$	−2.46928e7	−0.544814
$155$	−4.45137e7	−0.960137
$156$	3.79429e7	0.800193
$157$	1.77014e7	0.365055	0.182528	−	0.983201i	$-0.441572\pi$
$157$	1.77014e7	0.365055	0.182528	+	0.983201i	$0.441572\pi$
$158$	8.74550e7	1.76394
$159$	−1.24666e7	−0.245956
$160$	−1.13678e8	−2.19410
$161$	6.53360e6	0.123385
$162$	−5.70995e7	−1.05519
$163$	5.62209e7	1.01681	0.508407	−	0.861117i	$-0.330235\pi$
$163$	5.62209e7	1.01681	0.508407	+	0.861117i	$0.330235\pi$
$164$	5.05367e7	0.894650
$165$	−1.25799e8	−2.18014
$166$	7.78033e7	1.32014
$167$	9.11586e7	1.51457	0.757286	−	0.653083i	$-0.226525\pi$
$167$	9.11586e7	1.51457	0.757286	+	0.653083i	$0.226525\pi$
$168$	329551.	0.00536217
$169$	−1.35032e7	−0.215196
$170$	2.57247e8	4.01586
$171$	1.84841e7	0.282691
$172$	−1.03563e7	−0.155187
$173$	−1.16610e8	−1.71228	−0.856140	−	0.516744i	$-0.827144\pi$
$173$	−1.16610e8	−1.71228	−0.856140	+	0.516744i	$0.827144\pi$
$174$	−4.85747e7	−0.699017
$175$	2.37361e7	0.334793
$176$	1.12907e8	1.56108
$177$	−1.83023e7	−0.248084
$178$	1.44416e8	1.91931
$179$	8.45696e6	0.110212	0.0551060	−	0.998481i	$-0.482450\pi$
$179$	8.45696e6	0.110212	0.0551060	+	0.998481i	$0.482450\pi$
$180$	−2.60991e7	−0.333558
$181$	2.00697e7	0.251574	0.125787	−	0.992057i	$-0.459854\pi$
$181$	2.00697e7	0.251574	0.125787	+	0.992057i	$0.459854\pi$
$182$	2.46941e7	0.303629
$183$	7.14798e7	0.862193
$184$	1.08182e6	0.0128024
$185$	1.42611e8	1.65597
$186$	−6.87548e7	−0.783443
$187$	−2.60087e8	−2.90852
$188$	−1.82279e8	−2.00072
$189$	−2.40954e7	−0.259608
$190$	−2.76523e8	−2.92478
$191$	1.71659e7	0.178259	0.0891293	−	0.996020i	$-0.471592\pi$
$191$	1.71659e7	0.178259	0.0891293	+	0.996020i	$0.471592\pi$
$192$	−9.00936e7	−0.918628
$193$	−1.58315e8	−1.58515	−0.792575	−	0.609775i	$-0.791260\pi$
$193$	−1.58315e8	−1.58515	−0.792575	+	0.609775i	$0.791260\pi$
$194$	−1.22822e8	−1.20773
$195$	1.25806e8	1.21501
$196$	−1.01026e8	−0.958378
$197$	5.27998e7	0.492040	0.246020	−	0.969265i	$-0.420877\pi$
$197$	5.27998e7	0.492040	0.246020	+	0.969265i	$0.420877\pi$
$198$	5.23173e7	0.478980
$199$	−1.26904e8	−1.14154	−0.570768	−	0.821112i	$-0.693354\pi$
$199$	−1.26904e8	−1.14154	−0.570768	+	0.821112i	$0.693354\pi$
$200$	3.93017e6	0.0347382
$201$	1.43302e8	1.24471
$202$	−7.58800e7	−0.647735
$203$	−1.59448e7	−0.133777
$204$	2.00404e8	1.65273
$205$	1.67562e8	1.35843
$206$	8.14911e7	0.649494
$207$	−1.38429e7	−0.108475
$208$	−1.12912e8	−0.870002
$209$	2.79576e8	2.11830
$210$	6.30852e7	0.470067
$211$	−1.23497e8	−0.905040	−0.452520	−	0.891754i	$-0.649475\pi$
$211$	−1.23497e8	−0.905040	−0.452520	+	0.891754i	$0.649475\pi$
$212$	−3.91197e7	−0.281981
$213$	−7.70838e7	−0.546556
$214$	−5.50453e7	−0.383948
$215$	−3.43378e7	−0.235634
$216$	−3.98968e6	−0.0269370
$217$	−2.25690e7	−0.149935
$218$	−7.46996e7	−0.488338
$219$	−2.79565e7	−0.179857
$220$	−3.94753e8	−2.49946
$221$	2.60100e8	1.62094
$222$	2.20274e8	1.35122
$223$	−2.86561e8	−1.73041	−0.865207	−	0.501415i	$-0.832813\pi$
$223$	−2.86561e8	−1.73041	−0.865207	+	0.501415i	$0.832813\pi$
$224$	−5.76362e7	−0.342631
$225$	−5.02902e7	−0.294337
$226$	1.94004e8	1.11797
$227$	1.80796e7	0.102588	0.0512941	−	0.998684i	$-0.483665\pi$
$227$	1.80796e7	0.102588	0.0512941	+	0.998684i	$0.483665\pi$
$228$	−2.15421e8	−1.20369
$229$	3.18532e8	1.75279	0.876393	−	0.481597i	$-0.159943\pi$
$229$	3.18532e8	1.75279	0.876393	+	0.481597i	$0.159943\pi$
$230$	2.07090e8	1.12231
$231$	−6.37817e7	−0.340451
$232$	−2.64011e6	−0.0138808
$233$	38350.8	0.000198622 0	9.93112e−5	−	1.00000i	$-0.499968\pi$
$233$	38350.8	0.000198622 0	9.93112e−5		1.00000i	$0.499968\pi$
$234$	−5.23199e7	−0.266939
$235$	−6.04375e8	−3.03787
$236$	−5.74319e7	−0.284421
$237$	2.25897e8	1.10228
$238$	1.30427e8	0.627117
$239$	−2.35171e7	−0.111427	−0.0557136	−	0.998447i	$-0.517743\pi$
$239$	−2.35171e7	−0.111427	−0.0557136	+	0.998447i	$0.517743\pi$
$240$	−2.88454e8	−1.34691
$241$	2.36236e8	1.08714	0.543570	−	0.839364i	$-0.317072\pi$
$241$	2.36236e8	1.08714	0.543570	+	0.839364i	$0.317072\pi$
$242$	4.78144e8	2.16873
$243$	9.31688e7	0.416532
$244$	2.24301e8	0.988477
$245$	−3.34967e8	−1.45519
$246$	2.58812e8	1.10844
$247$	−2.79590e8	−1.18054
$248$	−3.73693e6	−0.0155573
$249$	2.00966e8	0.824946
$250$	2.10115e8	0.850488
$251$	5.78454e7	0.230893	0.115446	−	0.993314i	$-0.463170\pi$
$251$	5.78454e7	0.230893	0.115446	+	0.993314i	$0.463170\pi$
$252$	−1.32325e7	−0.0520884
$253$	−2.09377e8	−0.812843
$254$	5.33488e7	0.204271
$255$	6.64470e8	2.50948
$256$	2.58724e8	0.963822
$257$	1.20884e8	0.444226	0.222113	−	0.975021i	$-0.428705\pi$
$257$	1.20884e8	0.444226	0.222113	+	0.975021i	$0.428705\pi$
$258$	−5.30373e7	−0.192270
$259$	7.23056e7	0.258597
$260$	3.94773e8	1.39297
$261$	3.37826e7	0.117612
$262$	4.34523e8	1.49265
$263$	−3.92747e7	−0.133127	−0.0665637	−	0.997782i	$-0.521204\pi$
$263$	−3.92747e7	−0.133127	−0.0665637	+	0.997782i	$0.521204\pi$
$264$	−1.05608e7	−0.0353252
$265$	−1.29707e8	−0.428158
$266$	−1.40200e8	−0.456734
$267$	3.73027e8	1.19937
$268$	4.49677e8	1.42702
$269$	−2.04982e8	−0.642070	−0.321035	−	0.947067i	$-0.604031\pi$
$269$	−2.04982e8	−0.642070	−0.321035	+	0.947067i	$0.604031\pi$
$270$	−7.63734e8	−2.36140
$271$	−3.83850e8	−1.17157	−0.585787	−	0.810465i	$-0.699214\pi$
$271$	−3.83850e8	−1.17157	−0.585787	+	0.810465i	$0.699214\pi$
$272$	−5.96372e8	−1.79691
$273$	6.37849e7	0.189735
$274$	1.20205e8	0.353018
$275$	−7.60650e8	−2.20557
$276$	1.61330e8	0.461886
$277$	5.84462e8	1.65226	0.826128	−	0.563483i	$-0.190539\pi$
$277$	5.84462e8	1.65226	0.826128	+	0.563483i	$0.190539\pi$
$278$	5.16549e8	1.44196
$279$	4.78175e7	0.131817
$280$	3.42878e6	0.00933440
$281$	−1.50550e8	−0.404770	−0.202385	−	0.979306i	$-0.564869\pi$
$281$	−1.50550e8	−0.404770	−0.202385	+	0.979306i	$0.564869\pi$
$282$	−9.33503e8	−2.47881
$283$	3.43343e8	0.900483	0.450242	−	0.892907i	$-0.351338\pi$
$283$	3.43343e8	0.900483	0.450242	+	0.892907i	$0.351338\pi$
$284$	−2.41886e8	−0.626609
$285$	−7.14260e8	−1.82768
$286$	−7.91350e8	−2.00026
$287$	8.49558e7	0.212132
$288$	1.22115e8	0.301229
$289$	9.63435e8	2.34790
$290$	−5.05390e8	−1.21684
$291$	−3.17250e8	−0.754703
$292$	−8.77263e7	−0.206201
$293$	−4.31569e8	−1.00234	−0.501168	−	0.865350i	$-0.667096\pi$
$293$	−4.31569e8	−1.00234	−0.501168	+	0.865350i	$0.667096\pi$
$294$	−5.17381e8	−1.18739
$295$	−1.90424e8	−0.431862
$296$	1.19722e7	0.0268320
$297$	7.72166e8	1.71026
$298$	−9.34210e8	−2.04497
$299$	2.09387e8	0.453003
$300$	5.86101e8	1.25328
$301$	−1.74097e7	−0.0367966
$302$	5.99552e8	1.25257
$303$	−1.95998e8	−0.404765
$304$	6.41060e8	1.30870
$305$	7.43703e8	1.50089
$306$	−2.76339e8	−0.551337
$307$	−9.63326e8	−1.90016	−0.950078	−	0.312013i	$-0.898997\pi$
$307$	−9.63326e8	−1.90016	−0.950078	+	0.312013i	$0.898997\pi$
$308$	−2.00144e8	−0.390316
$309$	2.10492e8	0.405864
$310$	−7.15351e8	−1.36381
$311$	3.93814e8	0.742386	0.371193	−	0.928556i	$-0.378949\pi$
$311$	3.93814e8	0.742386	0.371193	+	0.928556i	$0.378949\pi$
$312$	1.05614e7	0.0196870
$313$	−1.05509e9	−1.94484	−0.972422	−	0.233227i	$-0.925071\pi$
$313$	−1.05509e9	−1.94484	−0.972422	+	0.233227i	$0.925071\pi$
$314$	2.84468e8	0.518536
$315$	−4.38744e7	−0.0790905
$316$	7.08855e8	1.26373
$317$	5.36072e8	0.945182	0.472591	−	0.881282i	$-0.343319\pi$
$317$	5.36072e8	0.945182	0.472591	+	0.881282i	$0.343319\pi$
$318$	−2.00342e8	−0.349364
$319$	5.10969e8	0.881307
$320$	−9.37368e8	−1.59914
$321$	−1.42182e8	−0.239926
$322$	1.04997e8	0.175260
$323$	−1.47671e9	−2.43830
$324$	−4.62813e8	−0.755959
$325$	7.60688e8	1.22918
$326$	9.03490e8	1.44431
$327$	−1.92949e8	−0.305159
$328$	1.40668e7	0.0220109
$329$	−3.06425e8	−0.474394
$330$	−2.02164e9	−3.09674
$331$	−6.83321e8	−1.03568	−0.517842	−	0.855476i	$-0.673264\pi$
$331$	−6.83321e8	−1.03568	−0.517842	+	0.855476i	$0.673264\pi$
$332$	6.30625e8	0.945775
$333$	−1.53196e8	−0.227348
$334$	1.46495e9	2.15135
$335$	1.49097e9	2.16677
$336$	−1.46250e8	−0.210333
$337$	9.38435e8	1.33567	0.667835	−	0.744309i	$-0.267221\pi$
$337$	9.38435e8	1.33567	0.667835	+	0.744309i	$0.267221\pi$
$338$	−2.17001e8	−0.305671
$339$	5.01113e8	0.698613
$340$	2.08508e9	2.87704
$341$	7.23249e8	0.987751
$342$	2.97046e8	0.401543
$343$	−3.50163e8	−0.468534
$344$	−2.88266e6	−0.00381802
$345$	5.34915e8	0.701323
$346$	−1.87396e9	−2.43218
$347$	8.64270e8	1.11044	0.555221	−	0.831703i	$-0.312634\pi$
$347$	8.64270e8	1.11044	0.555221	+	0.831703i	$0.312634\pi$
$348$	−3.93716e8	−0.500790
$349$	−1.00648e9	−1.26741	−0.633706	−	0.773574i	$-0.718467\pi$
$349$	−1.00648e9	−1.26741	−0.633706	+	0.773574i	$0.718467\pi$
$350$	3.81447e8	0.475550
$351$	−7.72205e8	−0.953142
$352$	1.84702e9	2.25721
$353$	−8.45245e8	−1.02275	−0.511377	−	0.859356i	$-0.670864\pi$
$353$	−8.45245e8	−1.02275	−0.511377	+	0.859356i	$0.670864\pi$
$354$	−2.94124e8	−0.352387
$355$	−8.02010e8	−0.951438
$356$	1.17055e9	1.37503
$357$	3.36894e8	0.391881
$358$	1.35906e8	0.156548
$359$	−1.65237e8	−0.188485	−0.0942423	−	0.995549i	$-0.530043\pi$
$359$	−1.65237e8	−0.188485	−0.0942423	+	0.995549i	$0.530043\pi$
$360$	−7.26464e6	−0.00820645
$361$	6.93498e8	0.775836
$362$	3.22527e8	0.357343
$363$	1.23505e9	1.35522
$364$	2.00155e8	0.217526
$365$	−2.90870e8	−0.313093
$366$	1.14870e9	1.22469
$367$	−8.00752e8	−0.845603	−0.422802	−	0.906222i	$-0.638953\pi$
$367$	−8.00752e8	−0.845603	−0.422802	+	0.906222i	$0.638953\pi$
$368$	−4.80095e8	−0.502180
$369$	−1.79998e8	−0.186499
$370$	2.29182e9	2.35220
$371$	−6.57631e7	−0.0668611
$372$	−5.57283e8	−0.561275
$373$	−4.62722e8	−0.461678	−0.230839	−	0.972992i	$-0.574147\pi$
$373$	−4.62722e8	−0.461678	−0.230839	+	0.972992i	$0.574147\pi$
$374$	−4.17969e9	−4.13136
$375$	5.42729e8	0.531464
$376$	−5.07373e7	−0.0492232
$377$	−5.10995e8	−0.491159
$378$	−3.87222e8	−0.368756
$379$	5.59662e8	0.528066	0.264033	−	0.964514i	$-0.414947\pi$
$379$	5.59662e8	0.528066	0.264033	+	0.964514i	$0.414947\pi$
$380$	−2.24132e9	−2.09537
$381$	1.37800e8	0.127647
$382$	2.75862e8	0.253204
$383$	2.55484e8	0.232364	0.116182	−	0.993228i	$-0.462934\pi$
$383$	2.55484e8	0.232364	0.116182	+	0.993228i	$0.462934\pi$
$384$	−4.93084e7	−0.0444387
$385$	−6.63609e8	−0.592652
$386$	−2.54417e9	−2.25160
$387$	3.68863e7	0.0323502
$388$	−9.95518e8	−0.865243
$389$	2.14983e9	1.85175	0.925873	−	0.377834i	$-0.123331\pi$
$389$	2.14983e9	1.85175	0.925873	+	0.377834i	$0.123331\pi$
$390$	2.02174e9	1.72583
$391$	1.10592e9	0.935635
$392$	−2.81205e7	−0.0235788
$393$	1.12237e9	0.932747
$394$	8.48512e8	0.698910
$395$	2.35032e9	1.91883
$396$	4.24051e8	0.343151
$397$	−7.29245e8	−0.584933	−0.292467	−	0.956276i	$-0.594476\pi$
$397$	−7.29245e8	−0.584933	−0.292467	+	0.956276i	$0.594476\pi$
$398$	−2.03939e9	−1.62147
$399$	−3.62138e8	−0.285410
$400$	−1.74415e9	−1.36262
$401$	−3.33153e8	−0.258011	−0.129006	−	0.991644i	$-0.541179\pi$
$401$	−3.33153e8	−0.258011	−0.129006	+	0.991644i	$0.541179\pi$
$402$	2.30292e9	1.76802
$403$	−7.23285e8	−0.550480
$404$	−6.15035e8	−0.464050
$405$	−1.53453e9	−1.14784
$406$	−2.56238e8	−0.190022
$407$	−2.31712e9	−1.70360
$408$	5.57822e7	0.0406617
$409$	−1.35727e9	−0.980923	−0.490461	−	0.871463i	$-0.663172\pi$
$409$	−1.35727e9	−0.980923	−0.490461	+	0.871463i	$0.663172\pi$
$410$	2.69278e9	1.92956
$411$	3.10491e8	0.220598
$412$	6.60516e8	0.465310
$413$	−9.65473e7	−0.0674396
$414$	−2.22460e8	−0.154082
$415$	2.09093e9	1.43606
$416$	−1.84711e9	−1.25796
$417$	1.33425e9	0.901074
$418$	4.49288e9	3.00890
$419$	−6.15909e8	−0.409041	−0.204521	−	0.978862i	$-0.565564\pi$
$419$	−6.15909e8	−0.409041	−0.204521	+	0.978862i	$0.565564\pi$
$420$	5.11329e8	0.336766
$421$	−2.78917e9	−1.82174	−0.910871	−	0.412690i	$-0.864589\pi$
$421$	−2.78917e9	−1.82174	−0.910871	+	0.412690i	$0.864589\pi$
$422$	−1.98464e9	−1.28555
$423$	6.49231e8	0.417069
$424$	−1.08889e7	−0.00693752
$425$	4.01774e9	2.53875
$426$	−1.23876e9	−0.776345
$427$	3.77066e8	0.234380
$428$	−4.46163e8	−0.275068
$429$	−2.04406e9	−1.24995
$430$	−5.51820e8	−0.334702
$431$	3.90368e8	0.234857	0.117429	−	0.993081i	$-0.462535\pi$
$431$	3.90368e8	0.234857	0.117429	+	0.993081i	$0.462535\pi$
$432$	1.77056e9	1.05661
$433$	1.71968e9	1.01798	0.508991	−	0.860772i	$-0.330019\pi$
$433$	1.71968e9	1.01798	0.508991	+	0.860772i	$0.330019\pi$
$434$	−3.62691e8	−0.212972
$435$	−1.30542e9	−0.760395
$436$	−6.05468e8	−0.349855
$437$	−1.18879e9	−0.681431
$438$	−4.49270e8	−0.255475
$439$	−1.48222e9	−0.836154	−0.418077	−	0.908412i	$-0.637296\pi$
$439$	−1.48222e9	−0.836154	−0.418077	+	0.908412i	$0.637296\pi$
$440$	−1.09879e8	−0.0614937
$441$	3.59828e8	0.199783
$442$	4.17990e9	2.30244
$443$	−3.10398e9	−1.69631	−0.848156	−	0.529747i	$-0.822287\pi$
$443$	−3.10398e9	−1.69631	−0.848156	+	0.529747i	$0.822287\pi$
$444$	1.78540e9	0.968045
$445$	3.88112e9	2.08784
$446$	−4.60513e9	−2.45793
$447$	−2.41307e9	−1.27789
$448$	−4.75257e8	−0.249721
$449$	−6.30366e8	−0.328648	−0.164324	−	0.986406i	$-0.552544\pi$
$449$	−6.30366e8	−0.328648	−0.164324	+	0.986406i	$0.552544\pi$
$450$	−8.08182e8	−0.418086
$451$	−2.72251e9	−1.39750
$452$	1.57247e9	0.800938
$453$	1.54864e9	0.782723
$454$	2.90545e8	0.145720
$455$	6.63643e8	0.330289
$456$	−5.99621e7	−0.0296142
$457$	−3.54718e9	−1.73851	−0.869255	−	0.494365i	$-0.835401\pi$
$457$	−3.54718e9	−1.73851	−0.869255	+	0.494365i	$0.835401\pi$
$458$	5.11892e9	2.48971
$459$	−4.07857e9	−1.96863
$460$	1.67854e9	0.804045
$461$	−9.13977e8	−0.434492	−0.217246	−	0.976117i	$-0.569707\pi$
$461$	−9.13977e8	−0.434492	−0.217246	+	0.976117i	$0.569707\pi$
$462$	−1.02499e9	−0.483587
$463$	−8.31986e8	−0.389567	−0.194784	−	0.980846i	$-0.562400\pi$
$463$	−8.31986e8	−0.389567	−0.194784	+	0.980846i	$0.562400\pi$
$464$	1.17164e9	0.544478
$465$	−1.84776e9	−0.852235
$466$	616310.	0.000282130 0
$467$	2.96829e9	1.34864	0.674322	−	0.738437i	$-0.264436\pi$
$467$	2.96829e9	1.34864	0.674322	+	0.738437i	$0.264436\pi$
$468$	−4.24073e8	−0.191240
$469$	7.55940e8	0.338362
$470$	−9.71252e9	−4.31509
$471$	7.34781e8	0.324030
$472$	−1.59861e7	−0.00699755
$473$	5.57912e8	0.242411
$474$	3.63024e9	1.56571
$475$	−4.31880e9	−1.84899
$476$	1.05716e9	0.449279
$477$	1.39334e8	0.0587817
$478$	−3.77928e8	−0.158275
$479$	3.69035e9	1.53424	0.767120	−	0.641504i	$-0.221689\pi$
$479$	3.69035e9	1.53424	0.767120	+	0.641504i	$0.221689\pi$
$480$	−4.71876e9	−1.94753
$481$	2.31723e9	0.949428
$482$	3.79639e9	1.54421
$483$	2.71208e8	0.109519
$484$	3.87554e9	1.55372
$485$	−3.30079e9	−1.31378
$486$	1.49725e9	0.591655
$487$	−2.04194e8	−0.0801107	−0.0400554	−	0.999197i	$-0.512753\pi$
$487$	−2.04194e8	−0.0801107	−0.0400554	+	0.999197i	$0.512753\pi$
$488$	6.24339e7	0.0243193
$489$	2.33372e9	0.902542
$490$	−5.38304e9	−2.06700
$491$	−1.33712e9	−0.509782	−0.254891	−	0.966970i	$-0.582040\pi$
$491$	−1.33712e9	−0.509782	−0.254891	+	0.966970i	$0.582040\pi$
$492$	2.09777e9	0.794107
$493$	−2.69893e9	−1.01444
$494$	−4.49311e9	−1.67688
$495$	1.40601e9	0.521038
$496$	1.65839e9	0.610240
$497$	−4.06628e8	−0.148577
$498$	3.22960e9	1.17178
$499$	−1.58060e9	−0.569469	−0.284734	−	0.958606i	$-0.591905\pi$
$499$	−1.58060e9	−0.569469	−0.284734	+	0.958606i	$0.591905\pi$
$500$	1.70306e9	0.609307
$501$	3.78397e9	1.34436
$502$	9.29595e8	0.327968
$503$	8.52354e8	0.298629	0.149315	−	0.988790i	$-0.452293\pi$
$503$	8.52354e8	0.298629	0.149315	+	0.988790i	$0.452293\pi$
$504$	−3.68326e6	−0.00128152
$505$	−2.03924e9	−0.704610
$506$	−3.36476e9	−1.15459
$507$	−5.60515e8	−0.191011
$508$	4.32412e8	0.146344
$509$	−2.02364e9	−0.680177	−0.340089	−	0.940393i	$-0.610457\pi$
$509$	−2.02364e9	−0.680177	−0.340089	+	0.940393i	$0.610457\pi$
$510$	1.06783e10	3.56455
$511$	−1.47474e8	−0.0488926
$512$	4.30983e9	1.41911
$513$	4.38419e9	1.43377
$514$	1.94265e9	0.630993
$515$	2.19004e9	0.706524
$516$	−4.29887e8	−0.137746
$517$	9.81975e9	3.12524
$518$	1.16198e9	0.367319
$519$	−4.84046e9	−1.51985
$520$	1.09885e8	0.0342709
$521$	1.77856e8	0.0550980	0.0275490	−	0.999620i	$-0.491230\pi$
$521$	1.77856e8	0.0550980	0.0275490	+	0.999620i	$0.491230\pi$
$522$	5.42899e8	0.167060
$523$	−1.80745e9	−0.552471	−0.276236	−	0.961090i	$-0.589087\pi$
$523$	−1.80745e9	−0.552471	−0.276236	+	0.961090i	$0.589087\pi$
$524$	3.52197e9	1.06936
$525$	9.85280e8	0.297168
$526$	−6.31158e8	−0.189098
$527$	−3.82019e9	−1.13697
$528$	4.68674e9	1.38564
$529$	−2.51453e9	−0.738519
$530$	−2.08444e9	−0.608169
$531$	2.04557e8	0.0592903
$532$	−1.13638e9	−0.327214
$533$	2.72264e9	0.778835
$534$	5.99468e9	1.70362
$535$	−1.47932e9	−0.417661
$536$	1.25167e8	0.0351086
$537$	3.51046e8	0.0978261
$538$	−3.29413e9	−0.912016
$539$	5.44247e9	1.49705
$540$	−6.19035e9	−1.69175
$541$	−1.63216e8	−0.0443172	−0.0221586	−	0.999754i	$-0.507054\pi$
$541$	−1.63216e8	−0.0443172	−0.0221586	+	0.999754i	$0.507054\pi$
$542$	−6.16861e9	−1.66414
$543$	8.33088e8	0.223301
$544$	−9.75591e9	−2.59820
$545$	−2.00752e9	−0.531217
$546$	1.02505e9	0.269506
$547$	1.75641e9	0.458849	0.229425	−	0.973326i	$-0.426316\pi$
$547$	1.75641e9	0.458849	0.229425	+	0.973326i	$0.426316\pi$
$548$	9.74308e8	0.252909
$549$	−7.98900e8	−0.206058
$550$	−1.22239e10	−3.13286
$551$	2.90117e9	0.738826
$552$	4.49061e7	0.0113637
$553$	1.19164e9	0.299644
$554$	9.39251e9	2.34692
$555$	5.91977e9	1.46987
$556$	4.18682e9	1.03305
$557$	3.96938e9	0.973262	0.486631	−	0.873608i	$-0.338226\pi$
$557$	3.96938e9	0.973262	0.486631	+	0.873608i	$0.338226\pi$
$558$	7.68443e8	0.187237
$559$	−5.57940e8	−0.135097
$560$	−1.52164e9	−0.366145
$561$	−1.07961e10	−2.58166
$562$	−2.41939e9	−0.574948
$563$	−7.01695e9	−1.65718	−0.828588	−	0.559858i	$-0.810855\pi$
$563$	−7.01695e9	−1.65718	−0.828588	+	0.559858i	$0.810855\pi$
$564$	−7.56638e9	−1.77587
$565$	5.21378e9	1.21614
$566$	5.51764e9	1.27907
$567$	−7.78023e8	−0.179247
$568$	−6.73287e7	−0.0154163
$569$	−3.72696e9	−0.848129	−0.424064	−	0.905632i	$-0.639397\pi$
$569$	−3.72696e9	−0.848129	−0.424064	+	0.905632i	$0.639397\pi$
$570$	−1.14784e10	−2.59609
$571$	−6.36851e9	−1.43157	−0.715783	−	0.698323i	$-0.753930\pi$
$571$	−6.36851e9	−1.43157	−0.715783	+	0.698323i	$0.753930\pi$
$572$	−6.41418e9	−1.43303
$573$	7.12554e8	0.158226
$574$	1.36527e9	0.301319
$575$	3.23439e9	0.709503
$576$	1.00694e9	0.219545
$577$	−4.84407e9	−1.04977	−0.524887	−	0.851172i	$-0.675892\pi$
$577$	−4.84407e9	−1.04977	−0.524887	+	0.851172i	$0.675892\pi$
$578$	1.54827e10	3.33503
$579$	−6.57160e9	−1.40701
$580$	−4.09637e9	−0.871769
$581$	1.06013e9	0.224255
$582$	−5.09832e9	−1.07200
$583$	2.10745e9	0.440472
$584$	−2.44185e7	−0.00507311
$585$	−1.40608e9	−0.290378
$586$	−6.93547e9	−1.42375
$587$	7.07809e9	1.44438	0.722192	−	0.691693i	$-0.243135\pi$
$587$	7.07809e9	1.44438	0.722192	+	0.691693i	$0.243135\pi$
$588$	−4.19357e9	−0.850674
$589$	4.10645e9	0.828061
$590$	−3.06018e9	−0.613431
$591$	2.19171e9	0.436744
$592$	−5.31308e9	−1.05250
$593$	−8.42138e9	−1.65841	−0.829205	−	0.558945i	$-0.811206\pi$
$593$	−8.42138e9	−1.65841	−0.829205	+	0.558945i	$0.811206\pi$
$594$	1.24090e10	2.42931
$595$	3.50517e9	0.682182
$596$	−7.57211e9	−1.46506
$597$	−5.26775e9	−1.01325
$598$	3.36492e9	0.643460
$599$	−3.43703e8	−0.0653416	−0.0326708	−	0.999466i	$-0.510401\pi$
$599$	−3.43703e8	−0.0653416	−0.0326708	+	0.999466i	$0.510401\pi$
$600$	1.63141e8	0.0308342
$601$	−3.45425e9	−0.649073	−0.324536	−	0.945873i	$-0.605208\pi$
$601$	−3.45425e9	−0.649073	−0.324536	+	0.945873i	$0.605208\pi$
$602$	−2.79779e8	−0.0522670
$603$	−1.60163e9	−0.297475
$604$	4.85959e9	0.897367
$605$	1.28499e10	2.35916
$606$	−3.14976e9	−0.574941
$607$	1.86343e9	0.338183	0.169092	−	0.985600i	$-0.445917\pi$
$607$	1.86343e9	0.338183	0.169092	+	0.985600i	$0.445917\pi$
$608$	1.04870e10	1.89229
$609$	−6.61865e8	−0.118743
$610$	1.19516e10	2.13192
$611$	−9.82024e9	−1.74172
$612$	−2.23983e9	−0.394989
$613$	4.59607e9	0.805888	0.402944	−	0.915225i	$-0.367987\pi$
$613$	4.59607e9	0.805888	0.402944	+	0.915225i	$0.367987\pi$
$614$	−1.54810e10	−2.69904
$615$	6.95546e9	1.20577
$616$	−5.57100e7	−0.00960286
$617$	9.17212e9	1.57207	0.786034	−	0.618183i	$-0.212131\pi$
$617$	9.17212e9	1.57207	0.786034	+	0.618183i	$0.212131\pi$
$618$	3.38268e9	0.576502
$619$	2.36759e9	0.401226	0.200613	−	0.979671i	$-0.435707\pi$
$619$	2.36759e9	0.401226	0.200613	+	0.979671i	$0.435707\pi$
$620$	−5.79819e9	−0.977060
$621$	−3.28335e9	−0.550170
$622$	6.32873e9	1.05451
$623$	1.96777e9	0.326037
$624$	−4.68697e9	−0.772229
$625$	−2.82188e9	−0.462337
$626$	−1.69557e10	−2.76252
$627$	1.16051e10	1.88024
$628$	2.30571e9	0.371490
$629$	1.22390e10	1.96095
$630$	−7.05077e8	−0.112343
$631$	−4.85631e9	−0.769491	−0.384746	−	0.923023i	$-0.625711\pi$
$631$	−4.85631e9	−0.769491	−0.384746	+	0.923023i	$0.625711\pi$
$632$	1.97309e8	0.0310912
$633$	−5.12633e9	−0.803330
$634$	8.61486e9	1.34257
$635$	1.43373e9	0.222207
$636$	−1.62385e9	−0.250291
$637$	−5.44274e9	−0.834314
$638$	8.21145e9	1.25184
$639$	8.61534e8	0.130623
$640$	−5.13023e8	−0.0773583
$641$	4.17538e9	0.626171	0.313086	−	0.949725i	$-0.398637\pi$
$641$	4.17538e9	0.626171	0.313086	+	0.949725i	$0.398637\pi$
$642$	−2.28492e9	−0.340799
$643$	6.67976e9	0.990884	0.495442	−	0.868641i	$-0.335006\pi$
$643$	6.67976e9	0.990884	0.495442	+	0.868641i	$0.335006\pi$
$644$	8.51041e8	0.125560
$645$	−1.42535e9	−0.209153
$646$	−2.37313e10	−3.46344
$647$	3.94085e9	0.572038	0.286019	−	0.958224i	$-0.407668\pi$
$647$	3.94085e9	0.572038	0.286019	+	0.958224i	$0.407668\pi$
$648$	−1.28823e8	−0.0185987
$649$	3.09397e9	0.444283
$650$	1.22245e10	1.74596
$651$	−9.36834e8	−0.133085
$652$	7.32312e9	1.03474
$653$	−3.11818e9	−0.438233	−0.219116	−	0.975699i	$-0.570317\pi$
$653$	−3.11818e9	−0.438233	−0.219116	+	0.975699i	$0.570317\pi$
$654$	−3.10076e9	−0.433457
$655$	1.16776e10	1.62371
$656$	−6.24263e9	−0.863385
$657$	3.12458e8	0.0429846
$658$	−4.92436e9	−0.673844
$659$	8.02376e9	1.09214	0.546071	−	0.837739i	$-0.316123\pi$
$659$	8.02376e9	1.09214	0.546071	+	0.837739i	$0.316123\pi$
$660$	−1.63861e10	−2.21857
$661$	9.19114e9	1.23784	0.618920	−	0.785454i	$-0.287571\pi$
$661$	9.19114e9	1.23784	0.618920	+	0.785454i	$0.287571\pi$
$662$	−1.09812e10	−1.47112
$663$	1.07967e10	1.43878
$664$	1.75534e8	0.0232687
$665$	−3.76783e9	−0.496838
$666$	−2.46191e9	−0.322933
$667$	−2.17271e9	−0.283505
$668$	1.18740e10	1.54127
$669$	−1.18951e10	−1.53595
$670$	2.39604e10	3.07775
$671$	−1.20835e10	−1.54406
$672$	−2.39247e9	−0.304126
$673$	−4.44798e8	−0.0562484	−0.0281242	−	0.999604i	$-0.508953\pi$
$673$	−4.44798e8	−0.0562484	−0.0281242	+	0.999604i	$0.508953\pi$
$674$	1.50810e10	1.89723
$675$	−1.19282e10	−1.49283
$676$	−1.75888e9	−0.218989
$677$	−7.64502e8	−0.0946931	−0.0473465	−	0.998879i	$-0.515077\pi$
$677$	−7.64502e8	−0.0946931	−0.0473465	+	0.998879i	$0.515077\pi$
$678$	8.05306e9	0.992333
$679$	−1.67354e9	−0.205160
$680$	5.80380e8	0.0707833
$681$	7.50479e8	0.0910592
$682$	1.16229e10	1.40303
$683$	−9.15944e9	−1.10001	−0.550005	−	0.835162i	$-0.685374\pi$
$683$	−9.15944e9	−1.10001	−0.550005	+	0.835162i	$0.685374\pi$
$684$	2.40767e9	0.287674
$685$	3.23047e9	0.384015
$686$	−5.62725e9	−0.665521
$687$	1.32222e10	1.55580
$688$	1.27928e9	0.149763
$689$	−2.10756e9	−0.245478
$690$	8.59628e9	0.996182
$691$	1.38604e10	1.59809	0.799047	−	0.601269i	$-0.205338\pi$
$691$	1.38604e10	1.59809	0.799047	+	0.601269i	$0.205338\pi$
$692$	−1.51892e10	−1.74246
$693$	7.12861e8	0.0813652
$694$	1.38891e10	1.57731
$695$	1.38820e10	1.56858
$696$	−1.09590e8	−0.0123208
$697$	1.43802e10	1.60861
$698$	−1.61745e10	−1.80027
$699$	1.59193e6	0.000176301 0
$700$	3.09177e9	0.340694
$701$	−1.37849e10	−1.51144	−0.755718	−	0.654897i	$-0.772712\pi$
$701$	−1.37849e10	−1.51144	−0.755718	+	0.654897i	$0.772712\pi$
$702$	−1.24096e10	−1.35387
$703$	−1.31561e10	−1.42818
$704$	1.52301e10	1.64513
$705$	−2.50875e10	−2.69647
$706$	−1.35834e10	−1.45275
$707$	−1.03392e9	−0.110032
$708$	−2.38399e9	−0.252457
$709$	5.66562e9	0.597015	0.298508	−	0.954407i	$-0.403511\pi$
$709$	5.66562e9	0.597015	0.298508	+	0.954407i	$0.403511\pi$
$710$	−1.28886e10	−1.35145
$711$	−2.52475e9	−0.263436
$712$	3.25820e8	0.0338297
$713$	−3.07535e9	−0.317747
$714$	5.41400e9	0.556640
$715$	−2.12672e10	−2.17590
$716$	1.10157e9	0.112154
$717$	−9.76190e8	−0.0989047
$718$	−2.65541e9	−0.267729
$719$	1.02176e10	1.02518	0.512588	−	0.858635i	$-0.328687\pi$
$719$	1.02176e10	1.02518	0.512588	+	0.858635i	$0.328687\pi$
$720$	3.22393e9	0.321901
$721$	1.11038e9	0.110331
$722$	1.11448e10	1.10202
$723$	9.80609e9	0.964965
$724$	2.61420e9	0.256008
$725$	−7.89329e9	−0.769263
$726$	1.98477e10	1.92500
$727$	−1.12746e10	−1.08826	−0.544128	−	0.839002i	$-0.683139\pi$
$727$	−1.12746e10	−1.08826	−0.544128	+	0.839002i	$0.683139\pi$
$728$	5.57128e7	0.00535174
$729$	1.16380e10	1.11259
$730$	−4.67438e9	−0.444727
$731$	−2.94688e9	−0.279031
$732$	9.31068e9	0.877390
$733$	−1.48284e10	−1.39069	−0.695345	−	0.718676i	$-0.744749\pi$
$733$	−1.48284e10	−1.39069	−0.695345	+	0.718676i	$0.744749\pi$
$734$	−1.28684e10	−1.20112
$735$	−1.39044e10	−1.29166
$736$	−7.85377e9	−0.726115
$737$	−2.42249e10	−2.22909
$738$	−2.89263e9	−0.264909
$739$	4.66823e9	0.425497	0.212749	−	0.977107i	$-0.431758\pi$
$739$	4.66823e9	0.425497	0.212749	+	0.977107i	$0.431758\pi$
$740$	1.85760e10	1.68516
$741$	−1.16057e10	−1.04787
$742$	−1.05684e9	−0.0949716
$743$	1.40086e10	1.25295	0.626477	−	0.779440i	$-0.284496\pi$
$743$	1.40086e10	1.25295	0.626477	+	0.779440i	$0.284496\pi$
$744$	−1.55119e8	−0.0138089
$745$	−2.51065e10	−2.22453
$746$	−7.43611e9	−0.655782
$747$	−2.24612e9	−0.197156
$748$	−3.38779e10	−2.95979
$749$	−7.50032e8	−0.0652219
$750$	8.72185e9	0.754908
$751$	1.52897e10	1.31722	0.658611	−	0.752484i	$-0.271144\pi$
$751$	1.52897e10	1.31722	0.658611	+	0.752484i	$0.271144\pi$
$752$	2.25164e10	1.93080
$753$	2.40115e9	0.204945
$754$	−8.21186e9	−0.697657
$755$	1.61127e10	1.36255
$756$	−3.13858e9	−0.264184
$757$	−3.72305e9	−0.311934	−0.155967	−	0.987762i	$-0.549849\pi$
$757$	−3.72305e9	−0.311934	−0.155967	+	0.987762i	$0.549849\pi$
$758$	8.99396e9	0.750082
$759$	−8.69118e9	−0.721494
$760$	−6.23869e8	−0.0515521
$761$	1.87206e10	1.53984	0.769918	−	0.638143i	$-0.220297\pi$
$761$	1.87206e10	1.53984	0.769918	+	0.638143i	$0.220297\pi$
$762$	2.21450e9	0.181315
$763$	−1.01784e9	−0.0829549
$764$	2.23597e9	0.181401
$765$	−7.42650e9	−0.599749
$766$	4.10572e9	0.330057
$767$	−3.09412e9	−0.247602
$768$	1.07396e10	0.855505
$769$	1.14386e10	0.907052	0.453526	−	0.891243i	$-0.350166\pi$
$769$	1.14386e10	0.907052	0.453526	+	0.891243i	$0.350166\pi$
$770$	−1.06644e10	−0.841822
$771$	5.01789e9	0.394303
$772$	−2.06214e10	−1.61309
$773$	2.03033e9	0.158103	0.0790513	−	0.996871i	$-0.474811\pi$
$773$	2.03033e9	0.158103	0.0790513	+	0.996871i	$0.474811\pi$
$774$	5.92775e8	0.0459512
$775$	−1.11725e10	−0.862175
$776$	−2.77101e8	−0.0212874
$777$	3.00139e9	0.229535
$778$	3.45486e10	2.63028
$779$	−1.54578e10	−1.17156
$780$	1.63869e10	1.23642
$781$	1.30309e10	0.978802
$782$	1.77726e10	1.32901
$783$	8.01279e9	0.596510
$784$	1.24794e10	0.924886
$785$	7.64495e9	0.564067
$786$	1.80369e10	1.32490
$787$	−2.52279e10	−1.84488	−0.922442	−	0.386135i	$-0.873810\pi$
$787$	−2.52279e10	−1.84488	−0.922442	+	0.386135i	$0.873810\pi$
$788$	6.87750e9	0.500713
$789$	−1.63028e9	−0.118166
$790$	3.77704e10	2.72557
$791$	2.64344e9	0.189912
$792$	1.18034e8	0.00844247
$793$	1.20841e10	0.860516
$794$	−1.17192e10	−0.830858
$795$	−5.38412e9	−0.380040
$796$	−1.65300e10	−1.16166
$797$	2.72322e10	1.90536	0.952682	−	0.303968i	$-0.0983115\pi$
$797$	2.72322e10	1.90536	0.952682	+	0.303968i	$0.0983115\pi$
$798$	−5.81969e9	−0.405405
$799$	−5.18677e10	−3.59736
$800$	−2.85321e10	−1.97024
$801$	−4.16917e9	−0.286640
$802$	−5.35389e9	−0.366487
$803$	4.72598e9	0.322098
$804$	1.86660e10	1.26664
$805$	2.82176e9	0.190649
$806$	−1.16234e10	−0.781920
$807$	−8.50875e9	−0.569913
$808$	−1.71194e8	−0.0114169
$809$	−6.22108e9	−0.413091	−0.206546	−	0.978437i	$-0.566222\pi$
$809$	−6.22108e9	−0.413091	−0.206546	+	0.978437i	$0.566222\pi$
$810$	−2.46604e10	−1.63043
$811$	7.83342e8	0.0515678	0.0257839	−	0.999668i	$-0.491792\pi$
$811$	7.83342e8	0.0515678	0.0257839	+	0.999668i	$0.491792\pi$
$812$	−2.07691e9	−0.136135
$813$	−1.59335e10	−1.03991
$814$	−3.72369e10	−2.41985
$815$	2.42809e10	1.57113
$816$	−2.47553e10	−1.59497
$817$	3.16770e9	0.203220
$818$	−2.18118e10	−1.39333
$819$	−7.12897e8	−0.0453454
$820$	2.18260e10	1.38237
$821$	−7.41002e9	−0.467324	−0.233662	−	0.972318i	$-0.575071\pi$
$821$	−7.41002e9	−0.467324	−0.233662	+	0.972318i	$0.575071\pi$
$822$	4.98970e9	0.313345
$823$	−1.21111e10	−0.757328	−0.378664	−	0.925534i	$-0.623616\pi$
$823$	−1.21111e10	−0.757328	−0.378664	+	0.925534i	$0.623616\pi$
$824$	1.83854e8	0.0114479
$825$	−3.15744e10	−1.95770
$826$	−1.55155e9	−0.0957933
$827$	1.37043e10	0.842533	0.421266	−	0.906937i	$-0.361586\pi$
$827$	1.37043e10	0.842533	0.421266	+	0.906937i	$0.361586\pi$
$828$	−1.80312e9	−0.110387
$829$	−1.81240e8	−0.0110487	−0.00552437	−	0.999985i	$-0.501758\pi$
$829$	−1.81240e8	−0.0110487	−0.00552437	+	0.999985i	$0.501758\pi$
$830$	3.36020e10	2.03982
$831$	2.42609e10	1.46657
$832$	−1.52309e10	−0.916841
$833$	−2.87470e10	−1.72320
$834$	2.14418e10	1.27991
$835$	3.93699e10	2.34025
$836$	3.64165e10	2.15564
$837$	1.13417e10	0.668556
$838$	−9.89787e9	−0.581015
$839$	−1.86015e9	−0.108738	−0.0543689	−	0.998521i	$-0.517315\pi$
$839$	−1.86015e9	−0.108738	−0.0543689	+	0.998521i	$0.517315\pi$
$840$	1.42328e8	0.00828538
$841$	−1.19475e10	−0.692615
$842$	−4.48229e10	−2.58766
$843$	−6.24929e9	−0.359281
$844$	−1.60862e10	−0.920992
$845$	−5.83182e9	−0.332511
$846$	1.04334e10	0.592418
$847$	6.51506e9	0.368406
$848$	4.83233e9	0.272127
$849$	1.42521e10	0.799285
$850$	6.45665e10	3.60613
$851$	9.85269e9	0.548026
$852$	−1.00406e10	−0.556189
$853$	8.00784e9	0.441768	0.220884	−	0.975300i	$-0.429106\pi$
$853$	8.00784e9	0.441768	0.220884	+	0.975300i	$0.429106\pi$
$854$	6.05958e9	0.332920
$855$	7.98299e9	0.436802
$856$	−1.24189e8	−0.00676744
$857$	3.09890e10	1.68180	0.840900	−	0.541190i	$-0.182026\pi$
$857$	3.09890e10	1.68180	0.840900	+	0.541190i	$0.182026\pi$
$858$	−3.28488e10	−1.77547
$859$	2.61801e10	1.40927	0.704636	−	0.709569i	$-0.251110\pi$
$859$	2.61801e10	1.40927	0.704636	+	0.709569i	$0.251110\pi$
$860$	−4.47271e9	−0.239787
$861$	3.52650e9	0.188292
$862$	6.27335e9	0.333598
$863$	−5.73619e9	−0.303799	−0.151899	−	0.988396i	$-0.548539\pi$
$863$	−5.73619e9	−0.303799	−0.151899	+	0.988396i	$0.548539\pi$
$864$	2.89641e10	1.52778
$865$	−5.03620e10	−2.64574
$866$	2.76359e10	1.44597
$867$	3.99920e10	2.08404
$868$	−2.93975e9	−0.152578
$869$	−3.81874e10	−1.97402
$870$	−2.09786e10	−1.08009
$871$	2.42262e10	1.24228
$872$	−1.68531e8	−0.00860741
$873$	3.54577e9	0.180369
$874$	−1.91043e10	−0.967926
$875$	2.86298e9	0.144474
$876$	−3.64150e9	−0.183027
$877$	−1.13135e10	−0.566369	−0.283184	−	0.959065i	$-0.591391\pi$
$877$	−1.13135e10	−0.566369	−0.283184	+	0.959065i	$0.591391\pi$
$878$	−2.38198e10	−1.18770
$879$	−1.79143e10	−0.889692
$880$	4.87626e10	2.41211
$881$	7.59277e9	0.374097	0.187049	−	0.982351i	$-0.440108\pi$
$881$	7.59277e9	0.374097	0.187049	+	0.982351i	$0.440108\pi$
$882$	5.78256e9	0.283779
$883$	−1.12205e10	−0.548466	−0.274233	−	0.961663i	$-0.588424\pi$
$883$	−1.12205e10	−0.548466	−0.274233	+	0.961663i	$0.588424\pi$
$884$	3.38796e10	1.64951
$885$	−7.90447e9	−0.383329
$886$	−4.98820e10	−2.40949
$887$	6.84701e8	0.0329434	0.0164717	−	0.999864i	$-0.494757\pi$
$887$	6.84701e8	0.0329434	0.0164717	+	0.999864i	$0.494757\pi$
$888$	4.96964e8	0.0238166
$889$	7.26916e8	0.0346999
$890$	6.23710e10	2.96563
$891$	2.49326e10	1.18085
$892$	−3.73263e10	−1.76091
$893$	5.57543e10	2.61998
$894$	−3.87788e10	−1.81515
$895$	3.65242e9	0.170294
$896$	−2.60109e8	−0.0120803
$897$	8.69162e9	0.402093
$898$	−1.01302e10	−0.466822
$899$	7.50518e9	0.344510
$900$	−6.55061e9	−0.299525
$901$	−1.11315e10	−0.507012
$902$	−4.37516e10	−1.98505
$903$	−7.22671e8	−0.0326613
$904$	4.37696e8	0.0197053
$905$	8.66777e9	0.388720
$906$	2.48873e10	1.11180
$907$	2.96670e8	0.0132022	0.00660112	−	0.999978i	$-0.497899\pi$
$907$	2.96670e8	0.0132022	0.00660112	+	0.999978i	$0.497899\pi$
$908$	2.35497e9	0.104396
$909$	2.19059e9	0.0967359
$910$	1.06650e10	0.469153
$911$	2.64975e10	1.16115	0.580577	−	0.814205i	$-0.302827\pi$
$911$	2.64975e10	1.16115	0.580577	+	0.814205i	$0.302827\pi$
$912$	2.66103e10	1.16163
$913$	−3.39730e10	−1.47736
$914$	−5.70045e10	−2.46943
$915$	3.08710e10	1.33222
$916$	4.14907e10	1.78368
$917$	5.92069e9	0.253559
$918$	−6.55440e10	−2.79630
$919$	9.31788e9	0.396016	0.198008	−	0.980200i	$-0.436553\pi$
$919$	9.31788e9	0.396016	0.198008	+	0.980200i	$0.436553\pi$
$920$	4.67221e8	0.0197818
$921$	−3.99875e10	−1.68661
$922$	−1.46879e10	−0.617166
$923$	−1.30315e10	−0.545493
$924$	−8.30796e9	−0.346451
$925$	3.57941e10	1.48701
$926$	−1.33703e10	−0.553354
$927$	−2.35258e9	−0.0969986
$928$	1.91666e10	0.787275
$929$	1.76298e10	0.721425	0.360713	−	0.932677i	$-0.382533\pi$
$929$	1.76298e10	0.721425	0.360713	+	0.932677i	$0.382533\pi$
$930$	−2.96941e10	−1.21054
$931$	3.09011e10	1.25502
$932$	4.99542e6	0.000202123 0
$933$	1.63471e10	0.658956
$934$	4.77015e10	1.91566
$935$	−1.12327e11	−4.49412
$936$	−1.18040e8	−0.00470505
$937$	1.86944e10	0.742373	0.371187	−	0.928558i	$-0.378951\pi$
$937$	1.86944e10	0.742373	0.371187	+	0.928558i	$0.378951\pi$
$938$	1.21482e10	0.480621
$939$	−4.37966e10	−1.72628
$940$	−7.87236e10	−3.09142
$941$	−3.37256e10	−1.31946	−0.659729	−	0.751504i	$-0.729329\pi$
$941$	−3.37256e10	−1.31946	−0.659729	+	0.751504i	$0.729329\pi$
$942$	1.18082e10	0.460262
$943$	1.15765e10	0.449557
$944$	7.09438e9	0.274481
$945$	−1.04064e10	−0.401135
$946$	8.96585e9	0.344328
$947$	2.90728e10	1.11240	0.556202	−	0.831047i	$-0.312258\pi$
$947$	2.90728e10	1.11240	0.556202	+	0.831047i	$0.312258\pi$
$948$	2.94244e10	1.12171
$949$	−4.72622e9	−0.179507
$950$	−6.94046e10	−2.62637
$951$	2.22522e10	0.838960
$952$	2.94259e8	0.0110535
$953$	3.91532e10	1.46535	0.732677	−	0.680577i	$-0.238271\pi$
$953$	3.91532e10	1.46535	0.732677	+	0.680577i	$0.238271\pi$
$954$	2.23914e9	0.0834954
$955$	7.41369e9	0.275437
$956$	−3.06325e9	−0.113391
$957$	2.12102e10	0.782264
$958$	5.93052e10	2.17928
$959$	1.63788e9	0.0599678
$960$	−3.89100e10	−1.41942
$961$	−1.68894e10	−0.613880
$962$	3.72387e10	1.34860
$963$	1.58911e9	0.0573406
$964$	3.07711e10	1.10630
$965$	−6.83735e10	−2.44930
$966$	4.35841e9	0.155564
$967$	2.39640e10	0.852248	0.426124	−	0.904665i	$-0.359879\pi$
$967$	2.39640e10	0.852248	0.426124	+	0.904665i	$0.359879\pi$
$968$	1.07875e9	0.0382259
$969$	−6.12981e10	−2.16428
$970$	−5.30449e10	−1.86613
$971$	−1.51230e10	−0.530114	−0.265057	−	0.964233i	$-0.585391\pi$
$971$	−1.51230e10	−0.530114	−0.265057	+	0.964233i	$0.585391\pi$
$972$	1.21358e10	0.423874
$973$	7.03835e9	0.244949
$974$	−3.28146e9	−0.113792
$975$	3.15760e10	1.09104
$976$	−2.77072e10	−0.953933
$977$	6.93989e9	0.238079	0.119040	−	0.992890i	$-0.462018\pi$
$977$	6.93989e9	0.238079	0.119040	+	0.992890i	$0.462018\pi$
$978$	3.75037e10	1.28200
$979$	−6.30596e10	−2.14789
$980$	−4.36315e10	−1.48084
$981$	2.15651e9	0.0729308
$982$	−2.14880e10	−0.724111
$983$	−3.16877e10	−1.06403	−0.532014	−	0.846736i	$-0.678565\pi$
$983$	−3.16877e10	−1.06403	−0.532014	+	0.846736i	$0.678565\pi$
$984$	5.83911e8	0.0195373
$985$	2.28034e10	0.760279
$986$	−4.33727e10	−1.44095
$987$	−1.27196e10	−0.421080
$988$	−3.64183e10	−1.20135
$989$	−2.37232e9	−0.0779805
$990$	2.25950e10	0.740098
$991$	8.97486e9	0.292934	0.146467	−	0.989216i	$-0.453210\pi$
$991$	8.97486e9	0.292934	0.146467	+	0.989216i	$0.453210\pi$
$992$	2.71292e10	0.882361
$993$	−2.83645e10	−0.919291
$994$	−6.53466e9	−0.211043
$995$	−5.48078e10	−1.76385
$996$	2.61771e10	0.839487
$997$	−3.06127e10	−0.978291	−0.489145	−	0.872202i	$-0.662691\pi$
$997$	−3.06127e10	−0.978291	−0.489145	+	0.872202i	$0.662691\pi$
$998$	−2.54008e10	−0.808891
$999$	−3.63360e10	−1.15308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.10	✓	13
3.2	odd	2		387.8.a.d.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.10	✓	13	1.1	even	1	trivial
387.8.a.d.1.4		13	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)

\(f(q)\)	\(=\)	\(q+16.0703 q^{2} +41.5098 q^{3} +130.256 q^{4} +431.884 q^{5} +667.077 q^{6} +218.970 q^{7} +36.2566 q^{8} -463.938 q^{9} +O(q^{10})\)	\(q+16.0703 q^{2} +41.5098 q^{3} +130.256 q^{4} +431.884 q^{5} +667.077 q^{6} +218.970 q^{7} +36.2566 q^{8} -463.938 q^{9} +6940.53 q^{10} -7017.15 q^{11} +5406.90 q^{12} +7017.50 q^{13} +3518.93 q^{14} +17927.4 q^{15} -16090.1 q^{16} +37064.5 q^{17} -7455.64 q^{18} -39841.8 q^{19} +56255.5 q^{20} +9089.40 q^{21} -112768. q^{22} +29837.9 q^{23} +1505.01 q^{24} +108399. q^{25} +112774. q^{26} -110040. q^{27} +28522.2 q^{28} -72817.2 q^{29} +288100. q^{30} -103069. q^{31} -263215. q^{32} -291280. q^{33} +595639. q^{34} +94569.7 q^{35} -60430.7 q^{36} +330208. q^{37} -640272. q^{38} +291295. q^{39} +15658.7 q^{40} +387979. q^{41} +146070. q^{42} -79507.0 q^{43} -914026. q^{44} -200367. q^{45} +479505. q^{46} -1.39939e6 q^{47} -667898. q^{48} -775595. q^{49} +1.74201e6 q^{50} +1.53854e6 q^{51} +914072. q^{52} -300329. q^{53} -1.76838e6 q^{54} -3.03059e6 q^{55} +7939.12 q^{56} -1.65382e6 q^{57} -1.17020e6 q^{58} -440915. q^{59} +2.33515e6 q^{60} +1.72200e6 q^{61} -1.65635e6 q^{62} -101588. q^{63} -2.17042e6 q^{64} +3.03075e6 q^{65} -4.68098e6 q^{66} +3.45225e6 q^{67} +4.82787e6 q^{68} +1.23856e6 q^{69} +1.51977e6 q^{70} -1.85700e6 q^{71} -16820.8 q^{72} -673491. q^{73} +5.30655e6 q^{74} +4.49961e6 q^{75} -5.18964e6 q^{76} -1.53655e6 q^{77} +4.68121e6 q^{78} +5.44201e6 q^{79} -6.94907e6 q^{80} -3.55310e6 q^{81} +6.23496e6 q^{82} +4.84142e6 q^{83} +1.18395e6 q^{84} +1.60075e7 q^{85} -1.27771e6 q^{86} -3.02263e6 q^{87} -254418. q^{88} +8.98649e6 q^{89} -3.21997e6 q^{90} +1.53662e6 q^{91} +3.88656e6 q^{92} -4.27836e6 q^{93} -2.24887e7 q^{94} -1.72070e7 q^{95} -1.09260e7 q^{96} -7.64277e6 q^{97} -1.24641e7 q^{98} +3.25552e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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