LMFDB - Embedded newform 177.8.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-3.09726$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.09726 q^{2} -27.0000 q^{3} -118.407 q^{4} -156.435 q^{5} -83.6261 q^{6} +11.3597 q^{7} -763.187 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+3.09726 q^{2} -27.0000 q^{3} -118.407 q^{4} -156.435 q^{5} -83.6261 q^{6} +11.3597 q^{7} -763.187 q^{8} +729.000 q^{9} -484.520 q^{10} +4296.19 q^{11} +3196.99 q^{12} +1741.86 q^{13} +35.1841 q^{14} +4223.74 q^{15} +12792.3 q^{16} -4764.38 q^{17} +2257.91 q^{18} +18278.8 q^{19} +18523.0 q^{20} -306.713 q^{21} +13306.4 q^{22} +82004.5 q^{23} +20606.1 q^{24} -53653.2 q^{25} +5395.00 q^{26} -19683.0 q^{27} -1345.07 q^{28} -157425. q^{29} +13082.0 q^{30} +37778.8 q^{31} +137309. q^{32} -115997. q^{33} -14756.5 q^{34} -1777.05 q^{35} -86318.7 q^{36} +450442. q^{37} +56614.3 q^{38} -47030.2 q^{39} +119389. q^{40} -437505. q^{41} -949.970 q^{42} -738856. q^{43} -508699. q^{44} -114041. q^{45} +253989. q^{46} +869122. q^{47} -345392. q^{48} -823414. q^{49} -166178. q^{50} +128638. q^{51} -206248. q^{52} -991560. q^{53} -60963.4 q^{54} -672074. q^{55} -8669.60 q^{56} -493528. q^{57} -487588. q^{58} +205379. q^{59} -500120. q^{60} -1.30896e6 q^{61} +117011. q^{62} +8281.24 q^{63} -1.21213e6 q^{64} -272487. q^{65} -359274. q^{66} +2.85617e6 q^{67} +564135. q^{68} -2.21412e6 q^{69} -5504.01 q^{70} -4.56945e6 q^{71} -556364. q^{72} +937053. q^{73} +1.39514e6 q^{74} +1.44864e6 q^{75} -2.16434e6 q^{76} +48803.6 q^{77} -145665. q^{78} +6.61566e6 q^{79} -2.00116e6 q^{80} +531441. q^{81} -1.35507e6 q^{82} -3.65210e6 q^{83} +36316.9 q^{84} +745314. q^{85} -2.28843e6 q^{86} +4.25049e6 q^{87} -3.27880e6 q^{88} -5.71107e6 q^{89} -353215. q^{90} +19787.0 q^{91} -9.70990e6 q^{92} -1.02003e6 q^{93} +2.69190e6 q^{94} -2.85944e6 q^{95} -3.70735e6 q^{96} -1.38687e7 q^{97} -2.55033e6 q^{98} +3.13193e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * 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 $

$2$	3.09726	0.273762	0.136881	−	0.990587i	$-0.456292\pi$
$2$	3.09726	0.273762	0.136881	+	0.990587i	$0.456292\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−118.407	−0.925054
$5$	−156.435	−0.559678	−0.279839	−	0.960047i	$-0.590281\pi$
$5$	−156.435	−0.559678	−0.279839	+	0.960047i	$0.590281\pi$
$6$	−83.6261	−0.158057
$7$	11.3597	0.0125177	0.00625885	−	0.999980i	$-0.498008\pi$
$7$	11.3597	0.0125177	0.00625885	+	0.999980i	$0.498008\pi$
$8$	−763.187	−0.527007
$9$	729.000	0.333333
$10$	−484.520	−0.153219
$11$	4296.19	0.973217	0.486608	−	0.873620i	$-0.338234\pi$
$11$	4296.19	0.973217	0.486608	+	0.873620i	$0.338234\pi$
$12$	3196.99	0.534080
$13$	1741.86	0.219893	0.109947	−	0.993938i	$-0.464932\pi$
$13$	1741.86	0.219893	0.109947	+	0.993938i	$0.464932\pi$
$14$	35.1841	0.00342687
$15$	4223.74	0.323130
$16$	12792.3	0.780780
$17$	−4764.38	−0.235199	−0.117599	−	0.993061i	$-0.537520\pi$
$17$	−4764.38	−0.235199	−0.117599	+	0.993061i	$0.537520\pi$
$18$	2257.91	0.0912540
$19$	18278.8	0.611379	0.305689	−	0.952131i	$-0.401113\pi$
$19$	18278.8	0.611379	0.305689	+	0.952131i	$0.401113\pi$
$20$	18523.0	0.517732
$21$	−306.713	−0.00722710
$22$	13306.4	0.266430
$23$	82004.5	1.40537	0.702684	−	0.711502i	$-0.251985\pi$
$23$	82004.5	1.40537	0.702684	+	0.711502i	$0.251985\pi$
$24$	20606.1	0.304268
$25$	−53653.2	−0.686761
$26$	5395.00	0.0601984
$27$	−19683.0	−0.192450
$28$	−1345.07	−0.0115796
$29$	−157425.	−1.19862	−0.599311	−	0.800517i	$-0.704559\pi$
$29$	−157425.	−1.19862	−0.599311	+	0.800517i	$0.704559\pi$
$30$	13082.0	0.0884608
$31$	37778.8	0.227762	0.113881	−	0.993494i	$-0.463672\pi$
$31$	37778.8	0.227762	0.113881	+	0.993494i	$0.463672\pi$
$32$	137309.	0.740755
$33$	−115997.	−0.561887
$34$	−14756.5	−0.0643885
$35$	−1777.05	−0.00700588
$36$	−86318.7	−0.308351
$37$	450442.	1.46195	0.730975	−	0.682404i	$-0.239066\pi$
$37$	450442.	1.46195	0.730975	+	0.682404i	$0.239066\pi$
$38$	56614.3	0.167372
$39$	−47030.2	−0.126955
$40$	119389.	0.294954
$41$	−437505.	−0.991378	−0.495689	−	0.868500i	$-0.665084\pi$
$41$	−437505.	−0.991378	−0.495689	+	0.868500i	$0.665084\pi$
$42$	−949.970	−0.00197851
$43$	−738856.	−1.41716	−0.708582	−	0.705629i	$-0.750665\pi$
$43$	−738856.	−1.41716	−0.708582	+	0.705629i	$0.750665\pi$
$44$	−508699.	−0.900278
$45$	−114041.	−0.186559
$46$	253989.	0.384736
$47$	869122.	1.22106	0.610532	−	0.791992i	$-0.290956\pi$
$47$	869122.	1.22106	0.610532	+	0.791992i	$0.290956\pi$
$48$	−345392.	−0.450783
$49$	−823414.	−0.999843
$50$	−166178.	−0.188009
$51$	128638.	0.135792
$52$	−206248.	−0.203413
$53$	−991560.	−0.914858	−0.457429	−	0.889246i	$-0.651230\pi$
$53$	−991560.	−0.914858	−0.457429	+	0.889246i	$0.651230\pi$
$54$	−60963.4	−0.0526855
$55$	−672074.	−0.544688
$56$	−8669.60	−0.00659691
$57$	−493528.	−0.352980
$58$	−487588.	−0.328137
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	−500120.	−0.298913
$61$	−1.30896e6	−0.738368	−0.369184	−	0.929356i	$-0.620363\pi$
$61$	−1.30896e6	−0.738368	−0.369184	+	0.929356i	$0.620363\pi$
$62$	117011.	0.0623527
$63$	8281.24	0.00417257
$64$	−1.21213e6	−0.577989
$65$	−272487.	−0.123069
$66$	−359274.	−0.153823
$67$	2.85617e6	1.16017	0.580085	−	0.814556i	$-0.303019\pi$
$67$	2.85617e6	1.16017	0.580085	+	0.814556i	$0.303019\pi$
$68$	564135.	0.217572
$69$	−2.21412e6	−0.811390
$70$	−5504.01	−0.00191794
$71$	−4.56945e6	−1.51516	−0.757582	−	0.652740i	$-0.773619\pi$
$71$	−4.56945e6	−1.51516	−0.757582	+	0.652740i	$0.773619\pi$
$72$	−556364.	−0.175669
$73$	937053.	0.281925	0.140963	−	0.990015i	$-0.454980\pi$
$73$	937053.	0.281925	0.140963	+	0.990015i	$0.454980\pi$
$74$	1.39514e6	0.400226
$75$	1.44864e6	0.396502
$76$	−2.16434e6	−0.565559
$77$	48803.6	0.0121824
$78$	−145665.	−0.0347555
$79$	6.61566e6	1.50966	0.754829	−	0.655922i	$-0.227720\pi$
$79$	6.61566e6	1.50966	0.754829	+	0.655922i	$0.227720\pi$
$80$	−2.00116e6	−0.436985
$81$	531441.	0.111111
$82$	−1.35507e6	−0.271402
$83$	−3.65210e6	−0.701082	−0.350541	−	0.936547i	$-0.614002\pi$
$83$	−3.65210e6	−0.701082	−0.350541	+	0.936547i	$0.614002\pi$
$84$	36316.9	0.00668546
$85$	745314.	0.131635
$86$	−2.28843e6	−0.387966
$87$	4.25049e6	0.692024
$88$	−3.27880e6	−0.512892
$89$	−5.71107e6	−0.858722	−0.429361	−	0.903133i	$-0.641261\pi$
$89$	−5.71107e6	−0.858722	−0.429361	+	0.903133i	$0.641261\pi$
$90$	−353215.	−0.0510728
$91$	19787.0	0.00275256
$92$	−9.70990e6	−1.30004
$93$	−1.02003e6	−0.131499
$94$	2.69190e6	0.334281
$95$	−2.85944e6	−0.342175
$96$	−3.70735e6	−0.427675
$97$	−1.38687e7	−1.54289	−0.771446	−	0.636295i	$-0.780466\pi$
$97$	−1.38687e7	−1.54289	−0.771446	+	0.636295i	$0.780466\pi$
$98$	−2.55033e6	−0.273719
$99$	3.13193e6	0.324406
$100$	6.35291e6	0.635291
$101$	1.27095e7	1.22745	0.613727	−	0.789518i	$-0.289670\pi$
$101$	1.27095e7	1.22745	0.613727	+	0.789518i	$0.289670\pi$
$102$	398426.	0.0371747
$103$	1.41595e7	1.27679	0.638394	−	0.769710i	$-0.279599\pi$
$103$	1.41595e7	1.27679	0.638394	+	0.769710i	$0.279599\pi$
$104$	−1.32937e6	−0.115885
$105$	47980.5	0.00404485
$106$	−3.07112e6	−0.250453
$107$	−7.44830e6	−0.587779	−0.293889	−	0.955839i	$-0.594950\pi$
$107$	−7.44830e6	−0.587779	−0.293889	+	0.955839i	$0.594950\pi$
$108$	2.33060e6	0.178027
$109$	−2.45904e7	−1.81875	−0.909374	−	0.415980i	$-0.863439\pi$
$109$	−2.45904e7	−1.81875	−0.909374	+	0.415980i	$0.863439\pi$
$110$	−2.08159e6	−0.149115
$111$	−1.21619e7	−0.844057
$112$	145317.	0.00977357
$113$	5.72325e6	0.373137	0.186569	−	0.982442i	$-0.440263\pi$
$113$	5.72325e6	0.373137	0.186569	+	0.982442i	$0.440263\pi$
$114$	−1.52859e6	−0.0966325
$115$	−1.28283e7	−0.786553
$116$	1.86403e7	1.10879
$117$	1.26982e6	0.0732977
$118$	636113.	0.0356408
$119$	−54122.0	−0.00294415
$120$	−3.22350e6	−0.170292
$121$	−1.02989e6	−0.0528495
$122$	−4.05420e6	−0.202137
$123$	1.18126e7	0.572372
$124$	−4.47327e6	−0.210693
$125$	2.06147e7	0.944043
$126$	25649.2	0.00114229
$127$	−1.29403e7	−0.560574	−0.280287	−	0.959916i	$-0.590430\pi$
$127$	−1.29403e7	−0.560574	−0.280287	+	0.959916i	$0.590430\pi$
$128$	−2.13299e7	−0.898986
$129$	1.99491e7	0.818200
$130$	−843965.	−0.0336917
$131$	−4.66242e7	−1.81201	−0.906007	−	0.423263i	$-0.860885\pi$
$131$	−4.66242e7	−1.81201	−0.906007	+	0.423263i	$0.860885\pi$
$132$	1.37349e7	0.519776
$133$	207642.	0.00765306
$134$	8.84630e6	0.317611
$135$	3.07910e6	0.107710
$136$	3.63611e6	0.123951
$137$	−2.07610e7	−0.689803	−0.344902	−	0.938639i	$-0.612088\pi$
$137$	−2.07610e7	−0.689803	−0.344902	+	0.938639i	$0.612088\pi$
$138$	−6.85772e6	−0.222128
$139$	−1.80615e6	−0.0570430	−0.0285215	−	0.999593i	$-0.509080\pi$
$139$	−1.80615e6	−0.0570430	−0.0285215	+	0.999593i	$0.509080\pi$
$140$	210416.	0.00648082
$141$	−2.34663e7	−0.704981
$142$	−1.41528e7	−0.414794
$143$	7.48337e6	0.214004
$144$	9.32558e6	0.260260
$145$	2.46268e7	0.670842
$146$	2.90230e6	0.0771805
$147$	2.22322e7	0.577260
$148$	−5.33354e7	−1.35238
$149$	7.35804e7	1.82226	0.911130	−	0.412119i	$-0.135211\pi$
$149$	7.35804e7	1.82226	0.911130	+	0.412119i	$0.135211\pi$
$150$	4.48681e6	0.108547
$151$	2.57500e6	0.0608636	0.0304318	−	0.999537i	$-0.490312\pi$
$151$	2.57500e6	0.0608636	0.0304318	+	0.999537i	$0.490312\pi$
$152$	−1.39502e7	−0.322201
$153$	−3.47323e6	−0.0783996
$154$	151158.	0.00333509
$155$	−5.90991e6	−0.127474
$156$	5.56871e6	0.117441
$157$	−2.53317e7	−0.522414	−0.261207	−	0.965283i	$-0.584121\pi$
$157$	−2.53317e7	−0.522414	−0.261207	+	0.965283i	$0.584121\pi$
$158$	2.04904e7	0.413287
$159$	2.67721e7	0.528193
$160$	−2.14799e7	−0.414584
$161$	931548.	0.0175920
$162$	1.64601e6	0.0304180
$163$	−1.12501e6	−0.0203470	−0.0101735	−	0.999948i	$-0.503238\pi$
$163$	−1.12501e6	−0.0203470	−0.0101735	+	0.999948i	$0.503238\pi$
$164$	5.18036e7	0.917078
$165$	1.81460e7	0.314476
$166$	−1.13115e7	−0.191930
$167$	−5.17400e7	−0.859645	−0.429823	−	0.902913i	$-0.641424\pi$
$167$	−5.17400e7	−0.859645	−0.429823	+	0.902913i	$0.641424\pi$
$168$	234079.	0.00380873
$169$	−5.97144e7	−0.951647
$170$	2.30843e6	0.0360368
$171$	1.33253e7	0.203793
$172$	8.74857e7	1.31095
$173$	−5.17329e7	−0.759636	−0.379818	−	0.925061i	$-0.624013\pi$
$173$	−5.17329e7	−0.759636	−0.379818	+	0.925061i	$0.624013\pi$
$174$	1.31649e7	0.189450
$175$	−609485.	−0.00859667
$176$	5.49582e7	0.759868
$177$	−5.54523e6	−0.0751646
$178$	−1.76887e7	−0.235086
$179$	4.40517e7	0.574086	0.287043	−	0.957918i	$-0.407328\pi$
$179$	4.40517e7	0.574086	0.287043	+	0.957918i	$0.407328\pi$
$180$	1.35032e7	0.172577
$181$	8.76285e7	1.09843	0.549213	−	0.835683i	$-0.314928\pi$
$181$	8.76285e7	1.09843	0.549213	+	0.835683i	$0.314928\pi$
$182$	61285.7	0.000753545 0
$183$	3.53420e7	0.426297
$184$	−6.25848e7	−0.740638
$185$	−7.04647e7	−0.818221
$186$	−3.15929e6	−0.0359993
$187$	−2.04687e7	−0.228899
$188$	−1.02910e8	−1.12955
$189$	−223593.	−0.00240903
$190$	−8.85644e6	−0.0936746
$191$	1.82917e8	1.89949	0.949744	−	0.313028i	$-0.101344\pi$
$191$	1.82917e8	1.89949	0.949744	+	0.313028i	$0.101344\pi$
$192$	3.27276e7	0.333702
$193$	−8.82731e7	−0.883848	−0.441924	−	0.897053i	$-0.645704\pi$
$193$	−8.82731e7	−0.883848	−0.441924	+	0.897053i	$0.645704\pi$
$194$	−4.29551e7	−0.422385
$195$	7.35716e6	0.0710541
$196$	9.74979e7	0.924909
$197$	1.70359e8	1.58757	0.793785	−	0.608198i	$-0.208107\pi$
$197$	1.70359e8	1.58757	0.793785	+	0.608198i	$0.208107\pi$
$198$	9.70040e6	0.0888099
$199$	9.62750e7	0.866020	0.433010	−	0.901389i	$-0.357451\pi$
$199$	9.62750e7	0.866020	0.433010	+	0.901389i	$0.357451\pi$
$200$	4.09474e7	0.361928
$201$	−7.71165e7	−0.669825
$202$	3.93648e7	0.336030
$203$	−1.78831e6	−0.0150040
$204$	−1.52317e7	−0.125615
$205$	6.84409e7	0.554852
$206$	4.38558e7	0.349536
$207$	5.97813e7	0.468456
$208$	2.22824e7	0.171688
$209$	7.85293e7	0.595004
$210$	148608.	0.00110733
$211$	−2.06758e8	−1.51521	−0.757605	−	0.652713i	$-0.773631\pi$
$211$	−2.06758e8	−1.51521	−0.757605	+	0.652713i	$0.773631\pi$
$212$	1.17408e8	0.846293
$213$	1.23375e8	0.874780
$214$	−2.30693e7	−0.160912
$215$	1.15583e8	0.793155
$216$	1.50218e7	0.101423
$217$	429156.	0.00285106
$218$	−7.61629e7	−0.497904
$219$	−2.53004e7	−0.162770
$220$	7.95782e7	0.503866
$221$	−8.29888e6	−0.0517186
$222$	−3.76687e7	−0.231071
$223$	−4.61080e7	−0.278426	−0.139213	−	0.990262i	$-0.544457\pi$
$223$	−4.61080e7	−0.278426	−0.139213	+	0.990262i	$0.544457\pi$
$224$	1.55979e6	0.00927255
$225$	−3.91132e7	−0.228920
$226$	1.77264e7	0.102151
$227$	1.52563e8	0.865683	0.432841	−	0.901470i	$-0.357511\pi$
$227$	1.52563e8	0.865683	0.432841	+	0.901470i	$0.357511\pi$
$228$	5.84371e7	0.326525
$229$	−2.88554e8	−1.58782	−0.793912	−	0.608033i	$-0.791959\pi$
$229$	−2.88554e8	−1.58782	−0.793912	+	0.608033i	$0.791959\pi$
$230$	−3.97328e7	−0.215328
$231$	−1.31770e6	−0.00703353
$232$	1.20145e8	0.631682
$233$	3.41845e7	0.177045	0.0885224	−	0.996074i	$-0.471786\pi$
$233$	3.41845e7	0.177045	0.0885224	+	0.996074i	$0.471786\pi$
$234$	3.93296e6	0.0200661
$235$	−1.35961e8	−0.683402
$236$	−2.43183e7	−0.120432
$237$	−1.78623e8	−0.871601
$238$	−167630.	−0.000805996 0
$239$	1.22378e8	0.579843	0.289922	−	0.957050i	$-0.406371\pi$
$239$	1.22378e8	0.579843	0.289922	+	0.957050i	$0.406371\pi$
$240$	5.40313e7	0.252293
$241$	−1.04747e8	−0.482040	−0.241020	−	0.970520i	$-0.577482\pi$
$241$	−1.04747e8	−0.482040	−0.241020	+	0.970520i	$0.577482\pi$
$242$	−3.18983e6	−0.0144682
$243$	−1.43489e7	−0.0641500
$244$	1.54990e8	0.683030
$245$	1.28811e8	0.559590
$246$	3.65868e7	0.156694
$247$	3.18391e7	0.134438
$248$	−2.88323e7	−0.120032
$249$	9.86066e7	0.404770
$250$	6.38491e7	0.258443
$251$	1.01531e8	0.405268	0.202634	−	0.979255i	$-0.435050\pi$
$251$	1.01531e8	0.405268	0.202634	+	0.979255i	$0.435050\pi$
$252$	−980556.	−0.00385985
$253$	3.52307e8	1.36773
$254$	−4.00797e7	−0.153464
$255$	−2.01235e7	−0.0759998
$256$	8.90886e7	0.331881
$257$	2.43506e8	0.894836	0.447418	−	0.894325i	$-0.352344\pi$
$257$	2.43506e8	0.894836	0.447418	+	0.894325i	$0.352344\pi$
$258$	6.17876e7	0.223992
$259$	5.11689e6	0.0183003
$260$	3.22644e7	0.113846
$261$	−1.14763e8	−0.399540
$262$	−1.44407e8	−0.496061
$263$	−5.30485e8	−1.79816	−0.899079	−	0.437787i	$-0.855762\pi$
$263$	−5.30485e8	−1.79816	−0.899079	+	0.437787i	$0.855762\pi$
$264$	8.85276e7	0.296118
$265$	1.55114e8	0.512026
$266$	643123.	0.00209512
$267$	1.54199e8	0.495784
$268$	−3.38190e8	−1.07322
$269$	−1.66365e8	−0.521110	−0.260555	−	0.965459i	$-0.583906\pi$
$269$	−1.66365e8	−0.521110	−0.260555	+	0.965459i	$0.583906\pi$
$270$	9.53680e6	0.0294869
$271$	−5.31604e8	−1.62254	−0.811271	−	0.584670i	$-0.801224\pi$
$271$	−5.31604e8	−1.62254	−0.811271	+	0.584670i	$0.801224\pi$
$272$	−6.09473e7	−0.183638
$273$	−534250.	−0.00158919
$274$	−6.43022e7	−0.188842
$275$	−2.30504e8	−0.668367
$276$	2.62167e8	0.750579
$277$	−3.03386e8	−0.857661	−0.428831	−	0.903385i	$-0.641074\pi$
$277$	−3.03386e8	−0.857661	−0.428831	+	0.903385i	$0.641074\pi$
$278$	−5.59412e6	−0.0156162
$279$	2.75407e7	0.0759208
$280$	1.35623e6	0.00369215
$281$	6.31916e7	0.169898	0.0849489	−	0.996385i	$-0.472927\pi$
$281$	6.31916e7	0.169898	0.0849489	+	0.996385i	$0.472927\pi$
$282$	−7.26813e7	−0.192997
$283$	−2.67112e8	−0.700552	−0.350276	−	0.936647i	$-0.613912\pi$
$283$	−2.67112e8	−0.700552	−0.350276	+	0.936647i	$0.613912\pi$
$284$	5.41054e8	1.40161
$285$	7.72049e7	0.197555
$286$	2.31780e7	0.0585861
$287$	−4.96993e6	−0.0124098
$288$	1.00098e8	0.246918
$289$	−3.87639e8	−0.944682
$290$	7.62757e7	0.183651
$291$	3.74455e8	0.890789
$292$	−1.10954e8	−0.260796
$293$	−4.43690e8	−1.03049	−0.515244	−	0.857043i	$-0.672299\pi$
$293$	−4.43690e8	−1.03049	−0.515244	+	0.857043i	$0.672299\pi$
$294$	6.88589e7	0.158032
$295$	−3.21284e7	−0.0728638
$296$	−3.43771e8	−0.770458
$297$	−8.45620e7	−0.187296
$298$	2.27898e8	0.498866
$299$	1.42840e8	0.309031
$300$	−1.71529e8	−0.366785
$301$	−8.39320e6	−0.0177396
$302$	7.97544e6	0.0166621
$303$	−3.43158e8	−0.708671
$304$	2.33828e8	0.477352
$305$	2.04767e8	0.413248
$306$	−1.07575e7	−0.0214628
$307$	−4.86871e8	−0.960351	−0.480175	−	0.877173i	$-0.659427\pi$
$307$	−4.86871e8	−0.960351	−0.480175	+	0.877173i	$0.659427\pi$
$308$	−5.77868e6	−0.0112694
$309$	−3.82307e8	−0.737153
$310$	−1.83046e7	−0.0348974
$311$	−5.91749e8	−1.11552	−0.557758	−	0.830003i	$-0.688338\pi$
$311$	−5.91749e8	−1.11552	−0.557758	+	0.830003i	$0.688338\pi$
$312$	3.58929e7	0.0669063
$313$	−6.83534e8	−1.25995	−0.629977	−	0.776614i	$-0.716936\pi$
$313$	−6.83534e8	−1.25995	−0.629977	+	0.776614i	$0.716936\pi$
$314$	−7.84589e7	−0.143017
$315$	−1.29547e6	−0.00233529
$316$	−7.83340e8	−1.39651
$317$	−3.17450e8	−0.559716	−0.279858	−	0.960041i	$-0.590287\pi$
$317$	−3.17450e8	−0.559716	−0.279858	+	0.960041i	$0.590287\pi$
$318$	8.29204e7	0.144599
$319$	−6.76330e8	−1.16652
$320$	1.89619e8	0.323488
$321$	2.01104e8	0.339354
$322$	2.88525e6	0.00481602
$323$	−8.70872e7	−0.143796
$324$	−6.29263e7	−0.102784
$325$	−9.34563e7	−0.151014
$326$	−3.48446e6	−0.00557024
$327$	6.63940e8	1.05005
$328$	3.33898e8	0.522463
$329$	9.87298e6	0.0152849
$330$	5.62029e7	0.0860915
$331$	1.88196e8	0.285242	0.142621	−	0.989777i	$-0.454447\pi$
$331$	1.88196e8	0.285242	0.142621	+	0.989777i	$0.454447\pi$
$332$	4.32434e8	0.648539
$333$	3.28372e8	0.487317
$334$	−1.60253e8	−0.235338
$335$	−4.46804e8	−0.649321
$336$	−3.92356e6	−0.00564277
$337$	−7.47824e8	−1.06438	−0.532188	−	0.846626i	$-0.678630\pi$
$337$	−7.47824e8	−1.06438	−0.532188	+	0.846626i	$0.678630\pi$
$338$	−1.84951e8	−0.260525
$339$	−1.54528e8	−0.215431
$340$	−8.82504e7	−0.121770
$341$	1.62305e8	0.221662
$342$	4.12718e7	0.0557908
$343$	−1.87090e7	−0.0250334
$344$	5.63885e8	0.746855
$345$	3.46365e8	0.454117
$346$	−1.60230e8	−0.207959
$347$	−1.23827e8	−0.159097	−0.0795483	−	0.996831i	$-0.525348\pi$
$347$	−1.23827e8	−0.159097	−0.0795483	+	0.996831i	$0.525348\pi$
$348$	−5.03287e8	−0.640160
$349$	−1.33403e9	−1.67987	−0.839935	−	0.542688i	$-0.817407\pi$
$349$	−1.33403e9	−1.67987	−0.839935	+	0.542688i	$0.817407\pi$
$350$	−1.88774e6	−0.00235344
$351$	−3.42850e7	−0.0423184
$352$	5.89907e8	0.720915
$353$	1.33244e9	1.61226	0.806132	−	0.591735i	$-0.201557\pi$
$353$	1.33244e9	1.61226	0.806132	+	0.591735i	$0.201557\pi$
$354$	−1.71751e7	−0.0205772
$355$	7.14820e8	0.848003
$356$	6.76231e8	0.794365
$357$	1.46129e6	0.00169980
$358$	1.36440e8	0.157163
$359$	7.56062e8	0.862435	0.431218	−	0.902248i	$-0.358084\pi$
$359$	7.56062e8	0.862435	0.431218	+	0.902248i	$0.358084\pi$
$360$	8.70346e7	0.0983180
$361$	−5.59757e8	−0.626216
$362$	2.71409e8	0.300707
$363$	2.78070e7	0.0305127
$364$	−2.34292e6	−0.00254626
$365$	−1.46588e8	−0.157787
$366$	1.09463e8	0.116704
$367$	−1.10105e9	−1.16272	−0.581358	−	0.813648i	$-0.697479\pi$
$367$	−1.10105e9	−1.16272	−0.581358	+	0.813648i	$0.697479\pi$
$368$	1.04903e9	1.09728
$369$	−3.18941e8	−0.330459
$370$	−2.18248e8	−0.223998
$371$	−1.12639e7	−0.0114519
$372$	1.20778e8	0.121643
$373$	−1.72328e9	−1.71940	−0.859698	−	0.510803i	$-0.829348\pi$
$373$	−1.72328e9	−1.71940	−0.859698	+	0.510803i	$0.829348\pi$
$374$	−6.33969e7	−0.0626639
$375$	−5.56596e8	−0.545043
$376$	−6.63303e8	−0.643509
$377$	−2.74213e8	−0.263569
$378$	−692528.	−0.000659502 0
$379$	3.29484e8	0.310883	0.155441	−	0.987845i	$-0.450320\pi$
$379$	3.29484e8	0.310883	0.155441	+	0.987845i	$0.450320\pi$
$380$	3.38578e8	0.316531
$381$	3.49389e8	0.323647
$382$	5.66541e8	0.520008
$383$	−6.36350e8	−0.578762	−0.289381	−	0.957214i	$-0.593449\pi$
$383$	−6.36350e8	−0.578762	−0.289381	+	0.957214i	$0.593449\pi$
$384$	5.75906e8	0.519030
$385$	−7.63457e6	−0.00681824
$386$	−2.73405e8	−0.241964
$387$	−5.38626e8	−0.472388
$388$	1.64215e9	1.42726
$389$	−9.45771e8	−0.814634	−0.407317	−	0.913287i	$-0.633536\pi$
$389$	−9.45771e8	−0.814634	−0.407317	+	0.913287i	$0.633536\pi$
$390$	2.27871e7	0.0194519
$391$	−3.90700e8	−0.330541
$392$	6.28419e8	0.526924
$393$	1.25885e9	1.04617
$394$	5.27647e8	0.434617
$395$	−1.03492e9	−0.844922
$396$	−3.70842e8	−0.300093
$397$	1.20371e9	0.965506	0.482753	−	0.875756i	$-0.339637\pi$
$397$	1.20371e9	0.965506	0.482753	+	0.875756i	$0.339637\pi$
$398$	2.98189e8	0.237083
$399$	−5.60634e6	−0.00441850
$400$	−6.86348e8	−0.536209
$401$	1.24141e9	0.961409	0.480705	−	0.876883i	$-0.340381\pi$
$401$	1.24141e9	0.961409	0.480705	+	0.876883i	$0.340381\pi$
$402$	−2.38850e8	−0.183373
$403$	6.58053e7	0.0500834
$404$	−1.50490e9	−1.13546
$405$	−8.31358e7	−0.0621864
$406$	−5.53887e6	−0.00410752
$407$	1.93518e9	1.42279
$408$	−9.81750e7	−0.0715633
$409$	−1.31447e9	−0.949990	−0.474995	−	0.879988i	$-0.657550\pi$
$409$	−1.31447e9	−0.949990	−0.474995	+	0.879988i	$0.657550\pi$
$410$	2.11980e8	0.151897
$411$	5.60546e8	0.398258
$412$	−1.67659e9	−1.18110
$413$	2.33305e6	0.00162967
$414$	1.85158e8	0.128245
$415$	5.71315e8	0.392380
$416$	2.39173e8	0.162887
$417$	4.87661e7	0.0329338
$418$	2.43226e8	0.162890
$419$	−1.30216e9	−0.864796	−0.432398	−	0.901683i	$-0.642333\pi$
$419$	−1.30216e9	−0.864796	−0.432398	+	0.901683i	$0.642333\pi$
$420$	−5.68122e6	−0.00374170
$421$	2.34962e9	1.53465	0.767327	−	0.641256i	$-0.221587\pi$
$421$	2.34962e9	1.53465	0.767327	+	0.641256i	$0.221587\pi$
$422$	−6.40383e8	−0.414807
$423$	6.33590e8	0.407021
$424$	7.56746e8	0.482136
$425$	2.55624e8	0.161525
$426$	3.82125e8	0.239482
$427$	−1.48694e7	−0.00924267
$428$	8.81930e8	0.543727
$429$	−2.02051e8	−0.123555
$430$	3.57990e8	0.217136
$431$	−1.37817e9	−0.829147	−0.414573	−	0.910016i	$-0.636069\pi$
$431$	−1.37817e9	−0.829147	−0.414573	+	0.910016i	$0.636069\pi$
$432$	−2.51791e8	−0.150261
$433$	−1.93157e9	−1.14341	−0.571705	−	0.820459i	$-0.693718\pi$
$433$	−1.93157e9	−1.14341	−0.571705	+	0.820459i	$0.693718\pi$
$434$	1.32921e6	0.000780512 0
$435$	−6.64924e8	−0.387311
$436$	2.91167e9	1.68244
$437$	1.49894e9	0.859212
$438$	−7.83621e7	−0.0445602
$439$	2.84522e9	1.60505	0.802526	−	0.596617i	$-0.203489\pi$
$439$	2.84522e9	1.60505	0.802526	+	0.596617i	$0.203489\pi$
$440$	5.12918e8	0.287054
$441$	−6.00269e8	−0.333281
$442$	−2.57038e7	−0.0141586
$443$	3.69126e8	0.201726	0.100863	−	0.994900i	$-0.467840\pi$
$443$	3.69126e8	0.201726	0.100863	+	0.994900i	$0.467840\pi$
$444$	1.44006e9	0.780799
$445$	8.93410e8	0.480608
$446$	−1.42809e8	−0.0762224
$447$	−1.98667e9	−1.05208
$448$	−1.37695e7	−0.00723510
$449$	−3.21750e8	−0.167748	−0.0838739	−	0.996476i	$-0.526729\pi$
$449$	−3.21750e8	−0.167748	−0.0838739	+	0.996476i	$0.526729\pi$
$450$	−1.21144e8	−0.0626697
$451$	−1.87961e9	−0.964825
$452$	−6.77673e8	−0.345172
$453$	−6.95249e7	−0.0351396
$454$	4.72528e8	0.236991
$455$	−3.09538e6	−0.00154054
$456$	3.76654e8	0.186023
$457$	3.67556e9	1.80143	0.900714	−	0.434413i	$-0.143044\pi$
$457$	3.67556e9	1.80143	0.900714	+	0.434413i	$0.143044\pi$
$458$	−8.93727e8	−0.434686
$459$	9.37772e7	0.0452640
$460$	1.51897e9	0.727604
$461$	−8.20164e8	−0.389895	−0.194947	−	0.980814i	$-0.562454\pi$
$461$	−8.20164e8	−0.389895	−0.194947	+	0.980814i	$0.562454\pi$
$462$	−4.08125e6	−0.00192551
$463$	−1.84327e9	−0.863089	−0.431544	−	0.902092i	$-0.642031\pi$
$463$	−1.84327e9	−0.863089	−0.431544	+	0.902092i	$0.642031\pi$
$464$	−2.01383e9	−0.935859
$465$	1.59568e8	0.0735969
$466$	1.05878e8	0.0484682
$467$	7.89693e8	0.358797	0.179399	−	0.983776i	$-0.442585\pi$
$467$	7.89693e8	0.358797	0.179399	+	0.983776i	$0.442585\pi$
$468$	−1.50355e8	−0.0678043
$469$	3.24453e7	0.0145227
$470$	−4.21107e8	−0.187090
$471$	6.83955e8	0.301616
$472$	−1.56743e8	−0.0686104
$473$	−3.17427e9	−1.37921
$474$	−5.53242e8	−0.238611
$475$	−9.80717e8	−0.419871
$476$	6.40842e6	0.00272350
$477$	−7.22848e8	−0.304953
$478$	3.79037e8	0.158739
$479$	3.05692e9	1.27089	0.635447	−	0.772144i	$-0.280816\pi$
$479$	3.05692e9	1.27089	0.635447	+	0.772144i	$0.280816\pi$
$480$	5.79958e8	0.239360
$481$	7.84606e8	0.321473
$482$	−3.24430e8	−0.131964
$483$	−2.51518e7	−0.0101567
$484$	1.21946e8	0.0488887
$485$	2.16955e9	0.863522
$486$	−4.44424e7	−0.0175618
$487$	2.29199e9	0.899209	0.449605	−	0.893228i	$-0.351565\pi$
$487$	2.29199e9	0.899209	0.449605	+	0.893228i	$0.351565\pi$
$488$	9.98983e8	0.389125
$489$	3.03753e7	0.0117473
$490$	3.98960e8	0.153195
$491$	−2.91988e9	−1.11322	−0.556608	−	0.830775i	$-0.687897\pi$
$491$	−2.91988e9	−1.11322	−0.556608	+	0.830775i	$0.687897\pi$
$492$	−1.39870e9	−0.529476
$493$	7.50034e8	0.281914
$494$	9.86142e7	0.0368040
$495$	−4.89942e8	−0.181563
$496$	4.83277e8	0.177832
$497$	−5.19077e7	−0.0189664
$498$	3.05411e8	0.110811
$499$	2.09323e9	0.754163	0.377082	−	0.926180i	$-0.376928\pi$
$499$	2.09323e9	0.754163	0.377082	+	0.926180i	$0.376928\pi$
$500$	−2.44092e9	−0.873291
$501$	1.39698e9	0.496316
$502$	3.14469e8	0.110947
$503$	2.06891e9	0.724860	0.362430	−	0.932011i	$-0.381947\pi$
$503$	2.06891e9	0.724860	0.362430	+	0.932011i	$0.381947\pi$
$504$	−6.32014e6	−0.00219897
$505$	−1.98821e9	−0.686979
$506$	1.09119e9	0.374432
$507$	1.61229e9	0.549434
$508$	1.53223e9	0.518561
$509$	−3.44598e9	−1.15824	−0.579122	−	0.815241i	$-0.696605\pi$
$509$	−3.44598e9	−1.15824	−0.579122	+	0.815241i	$0.696605\pi$
$510$	−6.23277e7	−0.0208059
$511$	1.06447e7	0.00352906
$512$	3.00615e9	0.989843
$513$	−3.59782e8	−0.117660
$514$	7.54202e8	0.244972
$515$	−2.21504e9	−0.714589
$516$	−2.36211e9	−0.756879
$517$	3.73392e9	1.18836
$518$	1.58484e7	0.00500992
$519$	1.39679e9	0.438576
$520$	2.07959e8	0.0648583
$521$	3.18767e9	0.987509	0.493755	−	0.869601i	$-0.335624\pi$
$521$	3.18767e9	0.987509	0.493755	+	0.869601i	$0.335624\pi$
$522$	−3.55452e8	−0.109379
$523$	4.05354e9	1.23902	0.619510	−	0.784988i	$-0.287331\pi$
$523$	4.05354e9	1.23902	0.619510	+	0.784988i	$0.287331\pi$
$524$	5.52062e9	1.67621
$525$	1.64561e7	0.00496329
$526$	−1.64305e9	−0.492267
$527$	−1.79992e8	−0.0535694
$528$	−1.48387e9	−0.438710
$529$	3.31991e9	0.975059
$530$	4.80430e8	0.140173
$531$	1.49721e8	0.0433963
$532$	−2.45863e7	−0.00707950
$533$	−7.62072e8	−0.217997
$534$	4.77595e8	0.135727
$535$	1.16517e9	0.328967
$536$	−2.17979e9	−0.611418
$537$	−1.18939e9	−0.331448
$538$	−5.15277e8	−0.142660
$539$	−3.53755e9	−0.973064
$540$	−3.64587e8	−0.0996376
$541$	−1.94039e9	−0.526865	−0.263432	−	0.964678i	$-0.584855\pi$
$541$	−1.94039e9	−0.526865	−0.263432	+	0.964678i	$0.584855\pi$
$542$	−1.64652e9	−0.444190
$543$	−2.36597e9	−0.634176
$544$	−6.54192e8	−0.174225
$545$	3.84679e9	1.01791
$546$	−1.65471e6	−0.000435060 0
$547$	3.90843e9	1.02105	0.510525	−	0.859863i	$-0.329451\pi$
$547$	3.90843e9	1.02105	0.510525	+	0.859863i	$0.329451\pi$
$548$	2.45824e9	0.638106
$549$	−9.54233e8	−0.246123
$550$	−7.13933e8	−0.182974
$551$	−2.87755e9	−0.732812
$552$	1.68979e9	0.427608
$553$	7.51521e7	0.0188974
$554$	−9.39665e8	−0.234795
$555$	1.90255e9	0.472400
$556$	2.13861e8	0.0527678
$557$	−1.37471e9	−0.337069	−0.168534	−	0.985696i	$-0.553903\pi$
$557$	−1.37471e9	−0.337069	−0.168534	+	0.985696i	$0.553903\pi$
$558$	8.53009e7	0.0207842
$559$	−1.28698e9	−0.311625
$560$	−2.27326e7	−0.00547005
$561$	5.52655e8	0.132155
$562$	1.95721e8	0.0465115
$563$	−7.49339e9	−1.76970	−0.884849	−	0.465879i	$-0.845738\pi$
$563$	−7.49339e9	−1.76970	−0.884849	+	0.465879i	$0.845738\pi$
$564$	2.77857e9	0.652146
$565$	−8.95316e8	−0.208837
$566$	−8.27315e8	−0.191785
$567$	6.03702e6	0.00139086
$568$	3.48734e9	0.798501
$569$	4.64326e9	1.05665	0.528324	−	0.849043i	$-0.322821\pi$
$569$	4.64326e9	1.05665	0.528324	+	0.849043i	$0.322821\pi$
$570$	2.39124e8	0.0540830
$571$	−7.07238e9	−1.58979	−0.794894	−	0.606748i	$-0.792474\pi$
$571$	−7.07238e9	−1.58979	−0.794894	+	0.606748i	$0.792474\pi$
$572$	−8.86083e8	−0.197965
$573$	−4.93875e9	−1.09667
$574$	−1.53932e7	−0.00339733
$575$	−4.39980e9	−0.965152
$576$	−8.83644e8	−0.192663
$577$	7.54152e8	0.163434	0.0817172	−	0.996656i	$-0.473960\pi$
$577$	7.54152e8	0.163434	0.0817172	+	0.996656i	$0.473960\pi$
$578$	−1.20062e9	−0.258618
$579$	2.38337e9	0.510290
$580$	−2.91599e9	−0.620565
$581$	−4.14868e7	−0.00877594
$582$	1.15979e9	0.243864
$583$	−4.25994e9	−0.890355
$584$	−7.15147e8	−0.148577
$585$	−1.98643e8	−0.0410231
$586$	−1.37423e9	−0.282109
$587$	4.19667e9	0.856389	0.428195	−	0.903687i	$-0.359150\pi$
$587$	4.19667e9	0.856389	0.428195	+	0.903687i	$0.359150\pi$
$588$	−2.63244e9	−0.533997
$589$	6.90551e8	0.139249
$590$	−9.95101e7	−0.0199474
$591$	−4.59969e9	−0.916584
$592$	5.76218e9	1.14146
$593$	−9.07288e8	−0.178671	−0.0893355	−	0.996002i	$-0.528474\pi$
$593$	−9.07288e8	−0.178671	−0.0893355	+	0.996002i	$0.528474\pi$
$594$	−2.61911e8	−0.0512744
$595$	8.46656e6	0.00164777
$596$	−8.71244e9	−1.68569
$597$	−2.59943e9	−0.499997
$598$	4.42414e8	0.0846009
$599$	−7.00263e9	−1.33127	−0.665637	−	0.746276i	$-0.731840\pi$
$599$	−7.00263e9	−1.33127	−0.665637	+	0.746276i	$0.731840\pi$
$600$	−1.10558e9	−0.208959
$601$	3.01689e7	0.00566890	0.00283445	−	0.999996i	$-0.499098\pi$
$601$	3.01689e7	0.00566890	0.00283445	+	0.999996i	$0.499098\pi$
$602$	−2.59959e7	−0.00485644
$603$	2.08215e9	0.386723
$604$	−3.04898e8	−0.0563021
$605$	1.61110e8	0.0295787
$606$	−1.06285e9	−0.194007
$607$	−1.46131e9	−0.265205	−0.132602	−	0.991169i	$-0.542333\pi$
$607$	−1.46131e9	−0.265205	−0.132602	+	0.991169i	$0.542333\pi$
$608$	2.50985e9	0.452882
$609$	4.82844e7	0.00866255
$610$	6.34218e8	0.113132
$611$	1.51389e9	0.268503
$612$	4.11255e8	0.0725239
$613$	−5.73275e9	−1.00520	−0.502599	−	0.864520i	$-0.667623\pi$
$613$	−5.73275e9	−1.00520	−0.502599	+	0.864520i	$0.667623\pi$
$614$	−1.50797e9	−0.262908
$615$	−1.84790e9	−0.320344
$616$	−3.72463e7	−0.00642023
$617$	3.48905e9	0.598010	0.299005	−	0.954251i	$-0.403345\pi$
$617$	3.48905e9	0.598010	0.299005	+	0.954251i	$0.403345\pi$
$618$	−1.18411e9	−0.201805
$619$	−5.02284e9	−0.851200	−0.425600	−	0.904911i	$-0.639937\pi$
$619$	−5.02284e9	−0.851200	−0.425600	+	0.904911i	$0.639937\pi$
$620$	6.99775e8	0.117920
$621$	−1.61409e9	−0.270463
$622$	−1.83280e9	−0.305386
$623$	−6.48762e7	−0.0107492
$624$	−6.01625e8	−0.0991242
$625$	9.66804e8	0.158401
$626$	−2.11708e9	−0.344928
$627$	−2.12029e9	−0.343526
$628$	2.99945e9	0.483262
$629$	−2.14607e9	−0.343849
$630$	−4.01242e6	−0.000639315 0
$631$	−7.21168e9	−1.14270	−0.571352	−	0.820705i	$-0.693581\pi$
$631$	−7.21168e9	−1.14270	−0.571352	+	0.820705i	$0.693581\pi$
$632$	−5.04899e9	−0.795600
$633$	5.58246e9	0.874807
$634$	−9.83226e8	−0.153229
$635$	2.02432e9	0.313741
$636$	−3.17001e9	−0.488608
$637$	−1.43427e9	−0.219859
$638$	−2.09477e9	−0.319348
$639$	−3.33113e9	−0.505055
$640$	3.33673e9	0.503143
$641$	1.16522e10	1.74746	0.873728	−	0.486415i	$-0.161696\pi$
$641$	1.16522e10	1.74746	0.873728	+	0.486415i	$0.161696\pi$
$642$	6.22872e8	0.0929023
$643$	−1.68105e9	−0.249369	−0.124684	−	0.992196i	$-0.539792\pi$
$643$	−1.68105e9	−0.249369	−0.124684	+	0.992196i	$0.539792\pi$
$644$	−1.10302e8	−0.0162735
$645$	−3.12073e9	−0.457928
$646$	−2.69732e8	−0.0393658
$647$	3.46626e9	0.503148	0.251574	−	0.967838i	$-0.419052\pi$
$647$	3.46626e9	0.503148	0.251574	+	0.967838i	$0.419052\pi$
$648$	−4.05589e8	−0.0585563
$649$	8.82348e8	0.126702
$650$	−2.89459e8	−0.0413419
$651$	−1.15872e7	−0.00164606
$652$	1.33209e8	0.0188221
$653$	8.92600e9	1.25447	0.627236	−	0.778830i	$-0.284186\pi$
$653$	8.92600e9	1.25447	0.627236	+	0.778830i	$0.284186\pi$
$654$	2.05640e9	0.287465
$655$	7.29364e9	1.01414
$656$	−5.59669e9	−0.774048
$657$	6.83112e8	0.0939751
$658$	3.05792e7	0.00418443
$659$	1.71451e8	0.0233368	0.0116684	−	0.999932i	$-0.496286\pi$
$659$	1.71451e8	0.0233368	0.0116684	+	0.999932i	$0.496286\pi$
$660$	−2.14861e9	−0.290907
$661$	1.10119e10	1.48305	0.741526	−	0.670924i	$-0.234102\pi$
$661$	1.10119e10	1.48305	0.741526	+	0.670924i	$0.234102\pi$
$662$	5.82894e8	0.0780884
$663$	2.24070e8	0.0298597
$664$	2.78723e9	0.369475
$665$	−3.24825e7	−0.00428325
$666$	1.01705e9	0.133409
$667$	−1.29096e10	−1.68450
$668$	6.12638e9	0.795218
$669$	1.24492e9	0.160749
$670$	−1.38387e9	−0.177760
$671$	−5.62356e9	−0.718592
$672$	−4.21144e7	−0.00535351
$673$	−5.18178e9	−0.655279	−0.327640	−	0.944803i	$-0.606253\pi$
$673$	−5.18178e9	−0.655279	−0.327640	+	0.944803i	$0.606253\pi$
$674$	−2.31621e9	−0.291386
$675$	1.05606e9	0.132167
$676$	7.07061e9	0.880325
$677$	−8.09065e9	−1.00213	−0.501064	−	0.865410i	$-0.667058\pi$
$677$	−8.09065e9	−1.00213	−0.501064	+	0.865410i	$0.667058\pi$
$678$	−4.78614e8	−0.0589768
$679$	−1.57545e8	−0.0193135
$680$	−5.68814e8	−0.0693728
$681$	−4.11920e9	−0.499802
$682$	5.02701e8	0.0606827
$683$	1.31475e9	0.157896	0.0789478	−	0.996879i	$-0.474844\pi$
$683$	1.31475e9	0.157896	0.0789478	+	0.996879i	$0.474844\pi$
$684$	−1.57780e9	−0.188520
$685$	3.24773e9	0.386068
$686$	−5.79466e7	−0.00685321
$687$	7.79095e9	0.916731
$688$	−9.45166e9	−1.10649
$689$	−1.72716e9	−0.201171
$690$	1.07278e9	0.124320
$691$	9.51511e9	1.09709	0.548543	−	0.836123i	$-0.315183\pi$
$691$	9.51511e9	1.09709	0.548543	+	0.836123i	$0.315183\pi$
$692$	6.12553e9	0.702704
$693$	3.55778e7	0.00406081
$694$	−3.83524e8	−0.0435546
$695$	2.82545e8	0.0319257
$696$	−3.24392e9	−0.364702
$697$	2.08444e9	0.233171
$698$	−4.13183e9	−0.459884
$699$	−9.22981e8	−0.102217
$700$	7.21673e7	0.00795238
$701$	−1.01482e10	−1.11270	−0.556349	−	0.830949i	$-0.687798\pi$
$701$	−1.01482e10	−1.11270	−0.556349	+	0.830949i	$0.687798\pi$
$702$	−1.06190e8	−0.0115852
$703$	8.23354e9	0.893805
$704$	−5.20755e9	−0.562509
$705$	3.67094e9	0.394562
$706$	4.12692e9	0.441377
$707$	1.44377e8	0.0153649
$708$	6.56594e8	0.0695313
$709$	1.71054e10	1.80248	0.901241	−	0.433319i	$-0.142658\pi$
$709$	1.71054e10	1.80248	0.901241	+	0.433319i	$0.142658\pi$
$710$	2.21399e9	0.232151
$711$	4.82282e9	0.503219
$712$	4.35862e9	0.452553
$713$	3.09803e9	0.320090
$714$	4.52601e6	0.000465342 0
$715$	−1.17066e9	−0.119773
$716$	−5.21602e9	−0.531060
$717$	−3.30421e9	−0.334773
$718$	2.34172e9	0.236102
$719$	4.37544e9	0.439006	0.219503	−	0.975612i	$-0.429556\pi$
$719$	4.37544e9	0.439006	0.219503	+	0.975612i	$0.429556\pi$
$720$	−1.45885e9	−0.145662
$721$	1.60848e8	0.0159824
$722$	−1.73371e9	−0.171434
$723$	2.82818e9	0.278306
$724$	−1.03758e10	−1.01610
$725$	8.44638e9	0.823166
$726$	8.61255e7	0.00835322
$727$	−1.22749e10	−1.18481	−0.592405	−	0.805641i	$-0.701821\pi$
$727$	−1.22749e10	−1.18481	−0.592405	+	0.805641i	$0.701821\pi$
$728$	−1.51012e7	−0.00145062
$729$	3.87420e8	0.0370370
$730$	−4.54020e8	−0.0431962
$731$	3.52019e9	0.333315
$732$	−4.18474e9	−0.394348
$733$	−7.53477e9	−0.706653	−0.353327	−	0.935500i	$-0.614950\pi$
$733$	−7.53477e9	−0.706653	−0.353327	+	0.935500i	$0.614950\pi$
$734$	−3.41023e9	−0.318308
$735$	−3.47788e9	−0.323079
$736$	1.12600e10	1.04103
$737$	1.22706e10	1.12910
$738$	−9.87844e8	−0.0904672
$739$	1.70023e10	1.54972	0.774858	−	0.632136i	$-0.217821\pi$
$739$	1.70023e10	1.54972	0.774858	+	0.632136i	$0.217821\pi$
$740$	8.34351e9	0.756899
$741$	−8.59657e8	−0.0776178
$742$	−3.48871e7	−0.00313510
$743$	−1.25008e10	−1.11809	−0.559045	−	0.829137i	$-0.688832\pi$
$743$	−1.25008e10	−1.11809	−0.559045	+	0.829137i	$0.688832\pi$
$744$	7.78472e8	0.0693007
$745$	−1.15105e10	−1.01988
$746$	−5.33747e9	−0.470705
$747$	−2.66238e9	−0.233694
$748$	2.42364e9	0.211744
$749$	−8.46106e7	−0.00735764
$750$	−1.72393e9	−0.149212
$751$	−6.82394e9	−0.587889	−0.293945	−	0.955822i	$-0.594968\pi$
$751$	−6.82394e9	−0.587889	−0.293945	+	0.955822i	$0.594968\pi$
$752$	1.11181e10	0.953382
$753$	−2.74135e9	−0.233981
$754$	−8.49311e8	−0.0721551
$755$	−4.02819e8	−0.0340640
$756$	2.64750e7	0.00222849
$757$	1.76261e10	1.47680	0.738400	−	0.674363i	$-0.235582\pi$
$757$	1.76261e10	1.47680	0.738400	+	0.674363i	$0.235582\pi$
$758$	1.02050e9	0.0851079
$759$	−9.51229e9	−0.789658
$760$	2.18229e9	0.180329
$761$	−8.48847e9	−0.698205	−0.349103	−	0.937084i	$-0.613514\pi$
$761$	−8.48847e9	−0.698205	−0.349103	+	0.937084i	$0.613514\pi$
$762$	1.08215e9	0.0886024
$763$	−2.79340e8	−0.0227665
$764$	−2.16586e10	−1.75713
$765$	5.43334e8	0.0438785
$766$	−1.97094e9	−0.158443
$767$	3.57741e8	0.0286276
$768$	−2.40539e9	−0.191612
$769$	1.91757e10	1.52058	0.760288	−	0.649586i	$-0.225058\pi$
$769$	1.91757e10	1.52058	0.760288	+	0.649586i	$0.225058\pi$
$770$	−2.36463e7	−0.00186657
$771$	−6.57466e9	−0.516634
$772$	1.04521e10	0.817607
$773$	−7.92188e8	−0.0616879	−0.0308440	−	0.999524i	$-0.509819\pi$
$773$	−7.92188e8	−0.0616879	−0.0308440	+	0.999524i	$0.509819\pi$
$774$	−1.66827e9	−0.129322
$775$	−2.02695e9	−0.156418
$776$	1.05844e10	0.813114
$777$	−1.38156e8	−0.0105657
$778$	−2.92930e9	−0.223016
$779$	−7.99707e9	−0.606108
$780$	−8.71139e8	−0.0657289
$781$	−1.96312e10	−1.47458
$782$	−1.21010e9	−0.0904895
$783$	3.09861e9	0.230675
$784$	−1.05334e10	−0.780658
$785$	3.96275e9	0.292384
$786$	3.89900e9	0.286401
$787$	2.00728e10	1.46790	0.733950	−	0.679203i	$-0.237675\pi$
$787$	2.00728e10	1.46790	0.733950	+	0.679203i	$0.237675\pi$
$788$	−2.01717e10	−1.46859
$789$	1.43231e10	1.03817
$790$	−3.20542e9	−0.231307
$791$	6.50146e7	0.00467082
$792$	−2.39025e9	−0.170964
$793$	−2.28003e9	−0.162362
$794$	3.72821e9	0.264319
$795$	−4.18809e9	−0.295618
$796$	−1.13996e10	−0.801115
$797$	1.65749e10	1.15971	0.579853	−	0.814721i	$-0.303110\pi$
$797$	1.65749e10	1.15971	0.579853	+	0.814721i	$0.303110\pi$
$798$	−1.73643e7	−0.00120962
$799$	−4.14082e9	−0.287192
$800$	−7.36707e9	−0.508721
$801$	−4.16337e9	−0.286241
$802$	3.84496e9	0.263197
$803$	4.02576e9	0.274374
$804$	9.13113e9	0.619624
$805$	−1.45726e8	−0.00984584
$806$	2.03817e8	0.0137109
$807$	4.49186e9	0.300863
$808$	−9.69977e9	−0.646877
$809$	−7.11284e9	−0.472305	−0.236153	−	0.971716i	$-0.575887\pi$
$809$	−7.11284e9	−0.472305	−0.236153	+	0.971716i	$0.575887\pi$
$810$	−2.57494e8	−0.0170243
$811$	1.80923e9	0.119102	0.0595511	−	0.998225i	$-0.481033\pi$
$811$	1.80923e9	0.119102	0.0595511	+	0.998225i	$0.481033\pi$
$812$	2.11748e8	0.0138795
$813$	1.43533e10	0.936775
$814$	5.99378e9	0.389507
$815$	1.75991e8	0.0113878
$816$	1.64558e9	0.106024
$817$	−1.35054e10	−0.866424
$818$	−4.07126e9	−0.260071
$819$	1.44248e7	0.000917519 0
$820$	−8.10388e9	−0.513268
$821$	1.91315e10	1.20655	0.603277	−	0.797531i	$-0.293861\pi$
$821$	1.91315e10	1.20655	0.603277	+	0.797531i	$0.293861\pi$
$822$	1.73616e9	0.109028
$823$	−1.55173e10	−0.970325	−0.485163	−	0.874424i	$-0.661240\pi$
$823$	−1.55173e10	−0.970325	−0.485163	+	0.874424i	$0.661240\pi$
$824$	−1.08064e10	−0.672876
$825$	6.22362e9	0.385882
$826$	7.22607e6	0.000446141 0
$827$	2.67848e10	1.64672	0.823360	−	0.567519i	$-0.192097\pi$
$827$	2.67848e10	1.64672	0.823360	+	0.567519i	$0.192097\pi$
$828$	−7.07852e9	−0.433347
$829$	1.50178e10	0.915515	0.457757	−	0.889077i	$-0.348653\pi$
$829$	1.50178e10	0.915515	0.457757	+	0.889077i	$0.348653\pi$
$830$	1.76951e9	0.107419
$831$	8.19141e9	0.495171
$832$	−2.11136e9	−0.127096
$833$	3.92305e9	0.235162
$834$	1.51041e8	0.00901602
$835$	8.09394e9	0.481124
$836$	−9.29842e9	−0.550411
$837$	−7.43600e8	−0.0438329
$838$	−4.03312e9	−0.236748
$839$	1.78661e10	1.04439	0.522197	−	0.852825i	$-0.325113\pi$
$839$	1.78661e10	1.04439	0.522197	+	0.852825i	$0.325113\pi$
$840$	−3.66181e7	−0.00213166
$841$	7.53290e9	0.436693
$842$	7.27739e9	0.420130
$843$	−1.70617e9	−0.0980905
$844$	2.44815e10	1.40165
$845$	9.34141e9	0.532616
$846$	1.96239e9	0.111427
$847$	−1.16992e7	−0.000661555 0
$848$	−1.26843e10	−0.714303
$849$	7.21201e9	0.404464
$850$	7.91735e8	0.0442195
$851$	3.69382e10	2.05458
$852$	−1.46085e10	−0.809219
$853$	−1.05414e10	−0.581538	−0.290769	−	0.956793i	$-0.593911\pi$
$853$	−1.05414e10	−0.581538	−0.290769	+	0.956793i	$0.593911\pi$
$854$	−4.60546e7	−0.00253029
$855$	−2.08453e9	−0.114058
$856$	5.68445e9	0.309763
$857$	−1.68053e10	−0.912037	−0.456018	−	0.889970i	$-0.650725\pi$
$857$	−1.68053e10	−0.912037	−0.456018	+	0.889970i	$0.650725\pi$
$858$	−6.25805e8	−0.0338247
$859$	−3.46312e9	−0.186420	−0.0932099	−	0.995646i	$-0.529713\pi$
$859$	−3.46312e9	−0.186420	−0.0932099	+	0.995646i	$0.529713\pi$
$860$	−1.36858e10	−0.733712
$861$	1.34188e8	0.00716479
$862$	−4.26855e9	−0.226989
$863$	1.26642e10	0.670716	0.335358	−	0.942091i	$-0.391143\pi$
$863$	1.26642e10	0.670716	0.335358	+	0.942091i	$0.391143\pi$
$864$	−2.70266e9	−0.142558
$865$	8.09282e9	0.425151
$866$	−5.98257e9	−0.313022
$867$	1.04663e10	0.545412
$868$	−5.08151e7	−0.00263739
$869$	2.84222e10	1.46922
$870$	−2.05944e9	−0.106031
$871$	4.97504e9	0.255113
$872$	1.87671e10	0.958492
$873$	−1.01103e10	−0.514297
$874$	4.64263e9	0.235220
$875$	2.34177e8	0.0118172
$876$	2.99575e9	0.150571
$877$	−1.35643e10	−0.679044	−0.339522	−	0.940598i	$-0.610265\pi$
$877$	−1.35643e10	−0.679044	−0.339522	+	0.940598i	$0.610265\pi$
$878$	8.81238e9	0.439403
$879$	1.19796e10	0.594953
$880$	−8.59737e9	−0.425281
$881$	3.52328e10	1.73593	0.867963	−	0.496630i	$-0.165429\pi$
$881$	3.52328e10	1.73593	0.867963	+	0.496630i	$0.165429\pi$
$882$	−1.85919e9	−0.0912397
$883$	1.37573e10	0.672469	0.336234	−	0.941778i	$-0.390847\pi$
$883$	1.37573e10	0.672469	0.336234	+	0.941778i	$0.390847\pi$
$884$	9.82645e8	0.0478425
$885$	8.67467e8	0.0420680
$886$	1.14328e9	0.0552248
$887$	−2.09679e10	−1.00884	−0.504420	−	0.863459i	$-0.668294\pi$
$887$	−2.09679e10	−1.00884	−0.504420	+	0.863459i	$0.668294\pi$
$888$	9.28183e9	0.444824
$889$	−1.46999e8	−0.00701709
$890$	2.76713e9	0.131572
$891$	2.28317e9	0.108135
$892$	5.45951e9	0.257559
$893$	1.58865e10	0.746532
$894$	−6.15325e9	−0.288020
$895$	−6.89121e9	−0.321303
$896$	−2.42301e8	−0.0112532
$897$	−3.85669e9	−0.178419
$898$	−9.96545e8	−0.0459230
$899$	−5.94734e9	−0.273001
$900$	4.63127e9	0.211764
$901$	4.72417e9	0.215173
$902$	−5.82163e9	−0.264133
$903$	2.26616e8	0.0102420
$904$	−4.36792e9	−0.196646
$905$	−1.37081e10	−0.614764
$906$	−2.15337e8	−0.00961989
$907$	−6.58180e9	−0.292900	−0.146450	−	0.989218i	$-0.546785\pi$
$907$	−6.58180e9	−0.292900	−0.146450	+	0.989218i	$0.546785\pi$
$908$	−1.80645e10	−0.800803
$909$	9.26526e9	0.409151
$910$	−9.58721e6	−0.000421743 0
$911$	2.97498e10	1.30368	0.651839	−	0.758357i	$-0.273998\pi$
$911$	2.97498e10	1.30368	0.651839	+	0.758357i	$0.273998\pi$
$912$	−6.31336e9	−0.275600
$913$	−1.56901e10	−0.682305
$914$	1.13842e10	0.493163
$915$	−5.52871e9	−0.238589
$916$	3.41668e10	1.46882
$917$	−5.29638e8	−0.0226822
$918$	2.90453e8	0.0123916
$919$	−9.95637e9	−0.423152	−0.211576	−	0.977361i	$-0.567860\pi$
$919$	−9.95637e9	−0.423152	−0.211576	+	0.977361i	$0.567860\pi$
$920$	9.79043e9	0.414519
$921$	1.31455e10	0.554459
$922$	−2.54027e9	−0.106738
$923$	−7.95934e9	−0.333174
$924$	1.56024e8	0.00650640
$925$	−2.41676e10	−1.00401
$926$	−5.70909e9	−0.236281
$927$	1.03223e10	0.425596
$928$	−2.16160e10	−0.887884
$929$	−6.90890e9	−0.282718	−0.141359	−	0.989958i	$-0.545147\pi$
$929$	−6.90890e9	−0.282718	−0.141359	+	0.989958i	$0.545147\pi$
$930$	4.94223e8	0.0201480
$931$	−1.50510e10	−0.611283
$932$	−4.04768e9	−0.163776
$933$	1.59772e10	0.644044
$934$	2.44589e9	0.0982251
$935$	3.20201e9	0.128110
$936$	−9.69108e8	−0.0386284
$937$	−6.04161e9	−0.239919	−0.119959	−	0.992779i	$-0.538276\pi$
$937$	−6.04161e9	−0.239919	−0.119959	+	0.992779i	$0.538276\pi$
$938$	1.00492e8	0.00397575
$939$	1.84554e10	0.727435
$940$	1.60987e10	0.632184
$941$	−1.95376e10	−0.764376	−0.382188	−	0.924085i	$-0.624829\pi$
$941$	−1.95376e10	−0.764376	−0.382188	+	0.924085i	$0.624829\pi$
$942$	2.11839e9	0.0825710
$943$	−3.58773e10	−1.39325
$944$	2.62727e9	0.101649
$945$	3.49778e7	0.00134828
$946$	−9.83154e9	−0.377575
$947$	−2.08163e10	−0.796486	−0.398243	−	0.917280i	$-0.630380\pi$
$947$	−2.08163e10	−0.796486	−0.398243	+	0.917280i	$0.630380\pi$
$948$	2.11502e10	0.806278
$949$	1.63222e9	0.0619934
$950$	−3.03754e9	−0.114945
$951$	8.57115e9	0.323152
$952$	4.13052e7	0.00155159
$953$	−2.45125e10	−0.917409	−0.458705	−	0.888589i	$-0.651686\pi$
$953$	−2.45125e10	−0.917409	−0.458705	+	0.888589i	$0.651686\pi$
$954$	−2.23885e9	−0.0834845
$955$	−2.86145e10	−1.06310
$956$	−1.44904e10	−0.536387
$957$	1.82609e10	0.673490
$958$	9.46808e9	0.347923
$959$	−2.35839e8	−0.00863475
$960$	−5.11972e9	−0.186766
$961$	−2.60854e10	−0.948124
$962$	2.43013e9	0.0880070
$963$	−5.42981e9	−0.195926
$964$	1.24028e10	0.445913
$965$	1.38090e10	0.494670
$966$	−7.79017e7	−0.00278053
$967$	−9.86699e9	−0.350907	−0.175454	−	0.984488i	$-0.556139\pi$
$967$	−9.86699e9	−0.350907	−0.175454	+	0.984488i	$0.556139\pi$
$968$	7.85997e8	0.0278521
$969$	2.35135e9	0.0830204
$970$	6.71967e9	0.236400
$971$	1.19828e10	0.420039	0.210020	−	0.977697i	$-0.432647\pi$
$971$	1.19828e10	0.420039	0.210020	+	0.977697i	$0.432647\pi$
$972$	1.69901e9	0.0593423
$973$	−2.05174e7	−0.000714047 0
$974$	7.09889e9	0.246169
$975$	2.52332e9	0.0871879
$976$	−1.67446e10	−0.576503
$977$	7.54352e9	0.258787	0.129394	−	0.991593i	$-0.458697\pi$
$977$	7.54352e9	0.258787	0.129394	+	0.991593i	$0.458697\pi$
$978$	9.40804e7	0.00321598
$979$	−2.45359e10	−0.835723
$980$	−1.52521e10	−0.517651
$981$	−1.79264e10	−0.606249
$982$	−9.04363e9	−0.304756
$983$	2.03133e10	0.682091	0.341045	−	0.940047i	$-0.389219\pi$
$983$	2.03133e10	0.682091	0.341045	+	0.940047i	$0.389219\pi$
$984$	−9.01525e9	−0.301644
$985$	−2.66500e10	−0.888528
$986$	2.32305e9	0.0771774
$987$	−2.66571e8	−0.00882474
$988$	−3.76998e9	−0.124362
$989$	−6.05895e10	−1.99164
$990$	−1.51748e9	−0.0497049
$991$	−3.47760e10	−1.13507	−0.567534	−	0.823350i	$-0.692103\pi$
$991$	−3.47760e10	−1.13507	−0.567534	+	0.823350i	$0.692103\pi$
$992$	5.18737e9	0.168716
$993$	−5.08130e9	−0.164685
$994$	−1.60772e8	−0.00519227
$995$	−1.50608e10	−0.484692
$996$	−1.16757e10	−0.374434
$997$	−1.31923e10	−0.421586	−0.210793	−	0.977531i	$-0.567605\pi$
$997$	−1.31923e10	−0.421586	−0.210793	+	0.977531i	$0.567605\pi$
$998$	6.48329e9	0.206461
$999$	−8.86604e9	−0.281352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.10	✓	16
3.2	odd	2		531.8.a.b.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.10	✓	16	1.1	even	1	trivial
531.8.a.b.1.7		16	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+3.09726 q^{2} -27.0000 q^{3} -118.407 q^{4} -156.435 q^{5} -83.6261 q^{6} +11.3597 q^{7} -763.187 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+3.09726 q^{2} -27.0000 q^{3} -118.407 q^{4} -156.435 q^{5} -83.6261 q^{6} +11.3597 q^{7} -763.187 q^{8} +729.000 q^{9} -484.520 q^{10} +4296.19 q^{11} +3196.99 q^{12} +1741.86 q^{13} +35.1841 q^{14} +4223.74 q^{15} +12792.3 q^{16} -4764.38 q^{17} +2257.91 q^{18} +18278.8 q^{19} +18523.0 q^{20} -306.713 q^{21} +13306.4 q^{22} +82004.5 q^{23} +20606.1 q^{24} -53653.2 q^{25} +5395.00 q^{26} -19683.0 q^{27} -1345.07 q^{28} -157425. q^{29} +13082.0 q^{30} +37778.8 q^{31} +137309. q^{32} -115997. q^{33} -14756.5 q^{34} -1777.05 q^{35} -86318.7 q^{36} +450442. q^{37} +56614.3 q^{38} -47030.2 q^{39} +119389. q^{40} -437505. q^{41} -949.970 q^{42} -738856. q^{43} -508699. q^{44} -114041. q^{45} +253989. q^{46} +869122. q^{47} -345392. q^{48} -823414. q^{49} -166178. q^{50} +128638. q^{51} -206248. q^{52} -991560. q^{53} -60963.4 q^{54} -672074. q^{55} -8669.60 q^{56} -493528. q^{57} -487588. q^{58} +205379. q^{59} -500120. q^{60} -1.30896e6 q^{61} +117011. q^{62} +8281.24 q^{63} -1.21213e6 q^{64} -272487. q^{65} -359274. q^{66} +2.85617e6 q^{67} +564135. q^{68} -2.21412e6 q^{69} -5504.01 q^{70} -4.56945e6 q^{71} -556364. q^{72} +937053. q^{73} +1.39514e6 q^{74} +1.44864e6 q^{75} -2.16434e6 q^{76} +48803.6 q^{77} -145665. q^{78} +6.61566e6 q^{79} -2.00116e6 q^{80} +531441. q^{81} -1.35507e6 q^{82} -3.65210e6 q^{83} +36316.9 q^{84} +745314. q^{85} -2.28843e6 q^{86} +4.25049e6 q^{87} -3.27880e6 q^{88} -5.71107e6 q^{89} -353215. q^{90} +19787.0 q^{91} -9.70990e6 q^{92} -1.02003e6 q^{93} +2.69190e6 q^{94} -2.85944e6 q^{95} -3.70735e6 q^{96} -1.38687e7 q^{97} -2.55033e6 q^{98} +3.13193e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9	\( 16 q - 6 q^{2} - 432 q^{3} + 974 q^{4} - 68 q^{5} + 162 q^{6} - 2343 q^{7} + 819 q^{8} + 11664 q^{9} - 3479 q^{10} + 898 q^{11} - 26298 q^{12} - 8172 q^{13} - 13315 q^{14} + 1836 q^{15} + 3138 q^{16} - 44985 q^{17} - 4374 q^{18} - 40137 q^{19} + 130657 q^{20} + 63261 q^{21} + 109394 q^{22} - 2833 q^{23} - 22113 q^{24} + 285746 q^{25} - 129420 q^{26} - 314928 q^{27} + 112890 q^{28} + 144375 q^{29} + 93933 q^{30} - 141759 q^{31} - 36224 q^{32} - 24246 q^{33} - 341332 q^{34} - 78859 q^{35} + 710046 q^{36} - 297971 q^{37} + 329075 q^{38} + 220644 q^{39} - 203048 q^{40} + 659077 q^{41} + 359505 q^{42} - 1431608 q^{43} + 254916 q^{44} - 49572 q^{45} + 873113 q^{46} - 1574073 q^{47} - 84726 q^{48} + 1893545 q^{49} + 302533 q^{50} + 1214595 q^{51} - 4972548 q^{52} + 587736 q^{53} + 118098 q^{54} - 4624036 q^{55} - 5798506 q^{56} + 1083699 q^{57} - 6991380 q^{58} + 3286064 q^{59} - 3527739 q^{60} - 6117131 q^{61} - 11570258 q^{62} - 1708047 q^{63} - 19063011 q^{64} - 5335514 q^{65} - 2953638 q^{66} - 16518710 q^{67} - 17284669 q^{68} + 76491 q^{69} - 39189486 q^{70} - 10882582 q^{71} + 597051 q^{72} - 21097441 q^{73} - 16717030 q^{74} - 7715142 q^{75} - 40864952 q^{76} - 3404601 q^{77} + 3494340 q^{78} - 3784458 q^{79} - 27466195 q^{80} + 8503056 q^{81} - 24990117 q^{82} - 1951425 q^{83} - 3048030 q^{84} - 23238675 q^{85} - 35910572 q^{86} - 3898125 q^{87} - 27843055 q^{88} + 10499443 q^{89} - 2536191 q^{90} + 699217 q^{91} - 20062766 q^{92} + 3827493 q^{93} - 59358988 q^{94} - 29236333 q^{95} + 978048 q^{96} - 25158976 q^{97} + 2120460 q^{98} + 654642 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 432 * q^3 + 974 * q^4 - 68 * q^5 + 162 * q^6 - 2343 * q^7 + 819 * q^8 + 11664 * q^9 - 3479 * q^10 + 898 * q^11 - 26298 * q^12 - 8172 * q^13 - 13315 * q^14 + 1836 * q^15 + 3138 * q^16 - 44985 * q^17 - 4374 * q^18 - 40137 * q^19 + 130657 * q^20 + 63261 * q^21 + 109394 * q^22 - 2833 * q^23 - 22113 * q^24 + 285746 * q^25 - 129420 * q^26 - 314928 * q^27 + 112890 * q^28 + 144375 * q^29 + 93933 * q^30 - 141759 * q^31 - 36224 * q^32 - 24246 * q^33 - 341332 * q^34 - 78859 * q^35 + 710046 * q^36 - 297971 * q^37 + 329075 * q^38 + 220644 * q^39 - 203048 * q^40 + 659077 * q^41 + 359505 * q^42 - 1431608 * q^43 + 254916 * q^44 - 49572 * q^45 + 873113 * q^46 - 1574073 * q^47 - 84726 * q^48 + 1893545 * q^49 + 302533 * q^50 + 1214595 * q^51 - 4972548 * q^52 + 587736 * q^53 + 118098 * q^54 - 4624036 * q^55 - 5798506 * q^56 + 1083699 * q^57 - 6991380 * q^58 + 3286064 * q^59 - 3527739 * q^60 - 6117131 * q^61 - 11570258 * q^62 - 1708047 * q^63 - 19063011 * q^64 - 5335514 * q^65 - 2953638 * q^66 - 16518710 * q^67 - 17284669 * q^68 + 76491 * q^69 - 39189486 * q^70 - 10882582 * q^71 + 597051 * q^72 - 21097441 * q^73 - 16717030 * q^74 - 7715142 * q^75 - 40864952 * q^76 - 3404601 * q^77 + 3494340 * q^78 - 3784458 * q^79 - 27466195 * q^80 + 8503056 * q^81 - 24990117 * q^82 - 1951425 * q^83 - 3048030 * q^84 - 23238675 * q^85 - 35910572 * q^86 - 3898125 * q^87 - 27843055 * q^88 + 10499443 * q^89 - 2536191 * q^90 + 699217 * q^91 - 20062766 * q^92 + 3827493 * q^93 - 59358988 * q^94 - 29236333 * q^95 + 978048 * q^96 - 25158976 * q^97 + 2120460 * q^98 + 654642 * q^99

Introduction

L-functions

Modular forms

Varieties

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