LMFDB - Embedded newform 5.34.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,34,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	5.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:	$34.4914144405$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 $ x^5 - 2x^4 - 1372039866x^3 - 648067657640x^2 + 285631173782445856x - 33409741805340964224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$33794.2$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +O(q^{10})$	\(q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +1.96961e16 q^{10} -1.11807e17 q^{11} -5.51213e17 q^{12} +3.82676e18 q^{13} +1.79859e19 q^{14} +1.04199e19 q^{15} -7.79687e19 q^{16} +1.35670e20 q^{17} +1.15630e20 q^{18} +1.50898e21 q^{19} -1.23167e21 q^{20} +9.51513e21 q^{21} +1.44321e22 q^{22} +2.26444e22 q^{23} -4.56653e21 q^{24} +2.32831e22 q^{25} -4.93961e23 q^{26} +4.40790e23 q^{27} -1.12472e24 q^{28} -6.82827e23 q^{29} -1.34501e24 q^{30} -5.41504e24 q^{31} +9.48983e24 q^{32} +7.63507e24 q^{33} -1.75124e25 q^{34} +2.12613e25 q^{35} -7.23078e24 q^{36} -7.55931e24 q^{37} -1.94780e26 q^{38} -2.61322e26 q^{39} -1.02038e25 q^{40} -1.95728e26 q^{41} -1.22822e27 q^{42} +5.44732e26 q^{43} -9.02490e26 q^{44} +1.36688e26 q^{45} -2.92295e27 q^{46} -3.58134e27 q^{47} +5.32433e27 q^{48} +1.16841e28 q^{49} -3.00539e27 q^{50} -9.26465e27 q^{51} +3.08891e28 q^{52} +4.28944e28 q^{53} -5.68974e28 q^{54} +1.70604e28 q^{55} -9.31777e27 q^{56} -1.03045e29 q^{57} +8.81397e28 q^{58} -2.15590e28 q^{59} +8.41084e28 q^{60} +5.24247e29 q^{61} +6.98976e29 q^{62} +1.24819e29 q^{63} -5.55207e29 q^{64} -5.83917e29 q^{65} -9.85539e29 q^{66} -1.47500e30 q^{67} +1.09511e30 q^{68} -1.54634e30 q^{69} -2.74442e30 q^{70} -1.24706e30 q^{71} -5.99036e28 q^{72} -9.14380e30 q^{73} +9.75760e29 q^{74} -1.58996e30 q^{75} +1.21803e31 q^{76} +1.55789e31 q^{77} +3.37316e31 q^{78} -2.52252e31 q^{79} +1.18971e31 q^{80} -2.51209e31 q^{81} +2.52647e31 q^{82} -1.28605e31 q^{83} +7.68050e31 q^{84} -2.07016e31 q^{85} -7.03143e31 q^{86} +4.66289e31 q^{87} -7.47670e30 q^{88} +1.22503e32 q^{89} -1.76438e31 q^{90} -5.33214e32 q^{91} +1.82783e32 q^{92} +3.69782e32 q^{93} +4.62282e32 q^{94} -2.30252e32 q^{95} -6.48042e32 q^{96} +2.05513e31 q^{97} -1.50819e33 q^{98} +1.00156e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q + 30472 * q^2 - 14988714 * q^3 + 1141311360 * q^4 - 762939453125 * q^5 + 12925063115760 * q^6 - 65452561787158 * q^7 + 155610638035200 * q^8 + 14541250990408965 * q^9	$ 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q + 30472 * q^2 - 14988714 * q^3 + 1141311360 * q^4 - 762939453125 * q^5 + 12925063115760 * q^6 - 65452561787158 * q^7 + 155610638035200 * q^8 + 14541250990408965 * q^9 - 4649658203125000 * q^10 - 287801801877976640 * q^11 - 405379955363513088 * q^12 + 2397201150889907466 * q^13 + 11676449916272482320 * q^14 + 2287096252441406250 * q^15 - 89180089543245957120 * q^16 - 308725634324001653918 * q^17 + 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 174150292968750000000 * q^20 - 10535115771712805413140 * q^21 - 13757888128329419319296 * q^22 + 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 + 116415321826934814453125 * q^25 - 424902360762721464761840 * q^26 + 679342131249712739644500 * q^27 - 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1972208117028808593750000 * q^30 - 1336046479411821372201940 * q^31 - 813043271605502937899008 * q^32 - 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 + 9987268339104919433593750 * q^35 - 180374200000978588488558720 * q^36 - 142836045294254023962738038 * q^37 - 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 23744299016601562500000000 * q^40 - 1325620030754525933329256290 * q^41 - 2645870671030939362357320736 * q^42 - 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2218818815675196075439453125 * q^45 - 2874649720834424257835685840 * q^46 - 7724956189479550762134222398 * q^47 - 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 709481537342071533203125000 * q^50 + 7346719218915268753088875260 * q^51 + 48963787841701555176191049472 * q^52 + 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 43915069866634619140625000000 * q^55 + 144880509244845944794630156800 * q^56 + 208512654554635835530896805800 * q^57 + 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 61856072290575117187500000000 * q^60 + 742889693167672203496619446410 * q^61 + 532537079706659761431026425824 * q^62 - 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 365783867018113321838378906250 * q^65 - 3327517517031282146197646561280 * q^66 - 3757683664783078488809531637718 * q^67 + 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 1781684862712475939941406250000 * q^70 - 5502085339682331744817794354940 * q^71 - 15971664273931445780329968326400 * q^72 - 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 - 348983192816376686096191406250 * q^75 + 7186339982587317558706196185600 * q^76 + 47237885671577674597763242652544 * q^77 + 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 13607801749152520312500000000000 * q^80 + 78583804836302041006582647314505 * q^81 + 27306575776891610455800103348784 * q^82 + 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 47107793323364510180358886718750 * q^85 + 65486114707827974097903540464560 * q^86 + 137286065258860195168416991536900 * q^87 + 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 82066451889727956368408203125000 * q^90 - 268937084803738847432203207735340 * q^91 - 697440932909638690403668496563968 * q^92 - 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 140131334258293754196166992187500 * q^95 - 344518603172836645970889894051840 * q^96 - 867959773515074594808067717684598 * q^97 - 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * 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 $

$2$	−129081.	−1.39273	−0.696364	−	0.717689i	$-0.745200\pi$
$2$	−129081.	−1.39273	−0.696364	+	0.717689i	$0.745200\pi$
$3$	−6.82881e7	−0.915892	−0.457946	−	0.888980i	$-0.651415\pi$
$3$	−6.82881e7	−0.915892	−0.457946	+	0.888980i	$0.651415\pi$
$4$	8.07187e9	0.939690
$5$	−1.52588e11	−0.447214
$5$	−1.52588e11	−0.447214
$6$	8.81467e12	1.27559
$7$	−1.39338e14	−1.58472	−0.792360	−	0.610054i	$-0.791148\pi$
$7$	−1.39338e14	−1.58472	−0.792360	+	0.610054i	$0.791148\pi$
$8$	6.68716e13	0.0839957
$9$	−8.95800e14	−0.161142
$10$	1.96961e16	0.622847
$11$	−1.11807e17	−0.733650	−0.366825	−	0.930290i	$-0.619555\pi$
$11$	−1.11807e17	−0.733650	−0.366825	+	0.930290i	$0.619555\pi$
$12$	−5.51213e17	−0.860654
$13$	3.82676e18	1.59502	0.797510	−	0.603306i	$-0.206150\pi$
$13$	3.82676e18	1.59502	0.797510	+	0.603306i	$0.206150\pi$
$14$	1.79859e19	2.20708
$15$	1.04199e19	0.409599
$16$	−7.79687e19	−1.05667
$17$	1.35670e20	0.676203	0.338101	−	0.941110i	$-0.390215\pi$
$17$	1.35670e20	0.676203	0.338101	+	0.941110i	$0.390215\pi$
$18$	1.15630e20	0.224427
$19$	1.50898e21	1.20019	0.600093	−	0.799930i	$-0.295130\pi$
$19$	1.50898e21	1.20019	0.600093	+	0.799930i	$0.295130\pi$
$20$	−1.23167e21	−0.420242
$21$	9.51513e21	1.45143
$22$	1.44321e22	1.02177
$23$	2.26444e22	0.769931	0.384965	−	0.922931i	$-0.374213\pi$
$23$	2.26444e22	0.769931	0.384965	+	0.922931i	$0.374213\pi$
$24$	−4.56653e21	−0.0769310
$25$	2.32831e22	0.200000
$26$	−4.93961e23	−2.22143
$27$	4.40790e23	1.06348
$28$	−1.12472e24	−1.48914
$29$	−6.82827e23	−0.506691	−0.253346	−	0.967376i	$-0.581531\pi$
$29$	−6.82827e23	−0.506691	−0.253346	+	0.967376i	$0.581531\pi$
$30$	−1.34501e24	−0.570460
$31$	−5.41504e24	−1.33701	−0.668503	−	0.743709i	$-0.733065\pi$
$31$	−5.41504e24	−1.33701	−0.668503	+	0.743709i	$0.733065\pi$
$32$	9.48983e24	1.38766
$33$	7.63507e24	0.671944
$34$	−1.75124e25	−0.941766
$35$	2.12613e25	0.708708
$36$	−7.23078e24	−0.151424
$37$	−7.55931e24	−0.100729	−0.0503644	−	0.998731i	$-0.516038\pi$
$37$	−7.55931e24	−0.100729	−0.0503644	+	0.998731i	$0.516038\pi$
$38$	−1.94780e26	−1.67153
$39$	−2.61322e26	−1.46087
$40$	−1.02038e25	−0.0375640
$41$	−1.95728e26	−0.479423	−0.239711	−	0.970844i	$-0.577053\pi$
$41$	−1.95728e26	−0.479423	−0.239711	+	0.970844i	$0.577053\pi$
$42$	−1.22822e27	−2.02145
$43$	5.44732e26	0.608069	0.304035	−	0.952661i	$-0.401666\pi$
$43$	5.44732e26	0.608069	0.304035	+	0.952661i	$0.401666\pi$
$44$	−9.02490e26	−0.689403
$45$	1.36688e26	0.0720650
$46$	−2.92295e27	−1.07230
$47$	−3.58134e27	−0.921363	−0.460682	−	0.887565i	$-0.652395\pi$
$47$	−3.58134e27	−0.921363	−0.460682	+	0.887565i	$0.652395\pi$
$48$	5.32433e27	0.967798
$49$	1.16841e28	1.51134
$50$	−3.00539e27	−0.278545
$51$	−9.26465e27	−0.619329
$52$	3.08891e28	1.49882
$53$	4.28944e28	1.52002	0.760010	−	0.649912i	$-0.225194\pi$
$53$	4.28944e28	1.52002	0.760010	+	0.649912i	$0.225194\pi$
$54$	−5.68974e28	−1.48114
$55$	1.70604e28	0.328098
$56$	−9.31777e27	−0.133110
$57$	−1.03045e29	−1.09924
$58$	8.81397e28	0.705683
$59$	−2.15590e28	−0.130188	−0.0650940	−	0.997879i	$-0.520735\pi$
$59$	−2.15590e28	−0.130188	−0.0650940	+	0.997879i	$0.520735\pi$
$60$	8.41084e28	0.384896
$61$	5.24247e29	1.82639	0.913196	−	0.407521i	$-0.133607\pi$
$61$	5.24247e29	1.82639	0.913196	+	0.407521i	$0.133607\pi$
$62$	6.98976e29	1.86209
$63$	1.24819e29	0.255365
$64$	−5.55207e29	−0.875962
$65$	−5.83917e29	−0.713314
$66$	−9.85539e29	−0.935834
$67$	−1.47500e30	−1.09284	−0.546422	−	0.837510i	$-0.684011\pi$
$67$	−1.47500e30	−1.09284	−0.546422	+	0.837510i	$0.684011\pi$
$68$	1.09511e30	0.635421
$69$	−1.54634e30	−0.705173
$70$	−2.74442e30	−0.987037
$71$	−1.24706e30	−0.354914	−0.177457	−	0.984129i	$-0.556787\pi$
$71$	−1.24706e30	−0.354914	−0.177457	+	0.984129i	$0.556787\pi$
$72$	−5.99036e28	−0.0135353
$73$	−9.14380e30	−1.64551	−0.822753	−	0.568398i	$-0.807563\pi$
$73$	−9.14380e30	−1.64551	−0.822753	+	0.568398i	$0.807563\pi$
$74$	9.75760e29	0.140288
$75$	−1.58996e30	−0.183178
$76$	1.21803e31	1.12780
$77$	1.55789e31	1.16263
$78$	3.37316e31	2.03459
$79$	−2.52252e31	−1.23307	−0.616536	−	0.787327i	$-0.711464\pi$
$79$	−2.52252e31	−1.23307	−0.616536	+	0.787327i	$0.711464\pi$
$80$	1.18971e31	0.472558
$81$	−2.51209e31	−0.812891
$82$	2.52647e31	0.667706
$83$	−1.28605e31	−0.278273	−0.139136	−	0.990273i	$-0.544433\pi$
$83$	−1.28605e31	−0.278273	−0.139136	+	0.990273i	$0.544433\pi$
$84$	7.68050e31	1.36390
$85$	−2.07016e31	−0.302407
$86$	−7.03143e31	−0.846875
$87$	4.66289e31	0.464074
$88$	−7.47670e30	−0.0616234
$89$	1.22503e32	0.837935	0.418967	−	0.908001i	$-0.362392\pi$
$89$	1.22503e32	0.837935	0.418967	+	0.908001i	$0.362392\pi$
$90$	−1.76438e31	−0.100367
$91$	−5.33214e32	−2.52766
$92$	1.82783e32	0.723496
$93$	3.69782e32	1.22455
$94$	4.62282e32	1.28321
$95$	−2.30252e32	−0.536739
$96$	−6.48042e32	−1.27095
$97$	2.05513e31	0.0339707	0.0169854	−	0.999856i	$-0.494593\pi$
$97$	2.05513e31	0.0339707	0.0169854	+	0.999856i	$0.494593\pi$
$98$	−1.50819e33	−2.10488
$99$	1.00156e32	0.118222
$100$	1.87938e32	0.187938
$101$	4.29097e32	0.364127	0.182064	−	0.983287i	$-0.441722\pi$
$101$	4.29097e32	0.364127	0.182064	+	0.983287i	$0.441722\pi$
$102$	1.19589e33	0.862556
$103$	−1.12430e33	−0.690346	−0.345173	−	0.938539i	$-0.612180\pi$
$103$	−1.12430e33	−0.690346	−0.345173	+	0.938539i	$0.612180\pi$
$104$	2.55902e32	0.133975
$105$	−1.45189e33	−0.649100
$106$	−5.53684e33	−2.11697
$107$	6.03479e33	1.97619	0.988097	−	0.153831i	$-0.0491611\pi$
$107$	6.03479e33	1.97619	0.988097	+	0.153831i	$0.0491611\pi$
$108$	3.55800e33	0.999342
$109$	−1.99935e32	−0.0482337	−0.0241169	−	0.999709i	$-0.507677\pi$
$109$	−1.99935e32	−0.0482337	−0.0241169	+	0.999709i	$0.507677\pi$
$110$	−2.20216e33	−0.456951
$111$	5.16211e32	0.0922567
$112$	1.08640e34	1.67453
$113$	9.03195e33	1.20223	0.601114	−	0.799163i	$-0.294724\pi$
$113$	9.03195e33	1.20223	0.601114	+	0.799163i	$0.294724\pi$
$114$	1.33011e34	1.53094
$115$	−3.45526e33	−0.344323
$116$	−5.51169e33	−0.476133
$117$	−3.42801e33	−0.257025
$118$	2.78285e33	0.181316
$119$	−1.89040e34	−1.07159
$120$	6.96798e32	0.0344046
$121$	−1.07244e34	−0.461758
$122$	−6.76702e34	−2.54367
$123$	1.33659e34	0.439100
$124$	−4.37095e34	−1.25637
$125$	−3.55271e33	−0.0894427
$126$	−1.61117e34	−0.355654
$127$	7.84484e34	1.51993	0.759963	−	0.649966i	$-0.225217\pi$
$127$	7.84484e34	1.51993	0.759963	+	0.649966i	$0.225217\pi$
$128$	−9.85056e33	−0.167686
$129$	−3.71987e34	−0.556926
$130$	7.53724e34	0.993453
$131$	1.29629e35	1.50566	0.752829	−	0.658216i	$-0.228689\pi$
$131$	1.29629e35	1.50566	0.752829	+	0.658216i	$0.228689\pi$
$132$	6.16293e34	0.631419
$133$	−2.10258e35	−1.90196
$134$	1.90394e35	1.52203
$135$	−6.72592e34	−0.475603
$136$	9.07248e33	0.0567981
$137$	−3.35566e35	−1.86161	−0.930804	−	0.365518i	$-0.880892\pi$
$137$	−3.35566e35	−1.86161	−0.930804	+	0.365518i	$0.880892\pi$
$138$	1.99603e35	0.982114
$139$	−1.22685e35	−0.535855	−0.267927	−	0.963439i	$-0.586339\pi$
$139$	−1.22685e35	−0.535855	−0.267927	+	0.963439i	$0.586339\pi$
$140$	1.71619e35	0.665966
$141$	2.44563e35	0.843869
$142$	1.60971e35	0.494299
$143$	−4.27858e35	−1.17019
$144$	6.98443e34	0.170275
$145$	1.04191e35	0.226599
$146$	1.18029e36	2.29174
$147$	−7.97887e35	−1.38422
$148$	−6.10178e34	−0.0946538
$149$	6.68791e34	0.0928361	0.0464181	−	0.998922i	$-0.485219\pi$
$149$	6.68791e34	0.0928361	0.0464181	+	0.998922i	$0.485219\pi$
$150$	2.05232e35	0.255118
$151$	−6.76462e34	−0.0753570	−0.0376785	−	0.999290i	$-0.511996\pi$
$151$	−6.76462e34	−0.0753570	−0.0376785	+	0.999290i	$0.511996\pi$
$152$	1.00908e35	0.100810
$153$	−1.21533e35	−0.108965
$154$	−2.01094e36	−1.61923
$155$	8.26269e35	0.597927
$156$	−2.10936e36	−1.37276
$157$	7.84957e35	0.459729	0.229864	−	0.973223i	$-0.426172\pi$
$157$	7.84957e35	0.459729	0.229864	+	0.973223i	$0.426172\pi$
$158$	3.25609e36	1.71733
$159$	−2.92918e36	−1.39217
$160$	−1.44803e36	−0.620581
$161$	−3.15523e36	−1.22012
$162$	3.24262e36	1.13214
$163$	−4.51268e36	−1.42344	−0.711720	−	0.702464i	$-0.752083\pi$
$163$	−4.51268e36	−1.42344	−0.711720	+	0.702464i	$0.752083\pi$
$164$	−1.57989e36	−0.450509
$165$	−1.16502e36	−0.300502
$166$	1.66005e36	0.387558
$167$	7.01398e36	1.48300	0.741502	−	0.670950i	$-0.234114\pi$
$167$	7.01398e36	1.48300	0.741502	+	0.670950i	$0.234114\pi$
$168$	6.36293e35	0.121914
$169$	8.88797e36	1.54409
$170$	2.67218e36	0.421171
$171$	−1.35174e36	−0.193401
$172$	4.39701e36	0.571397
$173$	1.06789e37	1.26115	0.630574	−	0.776129i	$-0.282819\pi$
$173$	1.06789e37	1.26115	0.630574	+	0.776129i	$0.282819\pi$
$174$	−6.01889e36	−0.646329
$175$	−3.24422e36	−0.316944
$176$	8.71743e36	0.775228
$177$	1.47222e36	0.119238
$178$	−1.58127e37	−1.16702
$179$	1.01966e36	0.0686086	0.0343043	−	0.999411i	$-0.489078\pi$
$179$	1.01966e36	0.0686086	0.0343043	+	0.999411i	$0.489078\pi$
$180$	1.10333e36	0.0677188
$181$	−3.22152e37	−1.80453	−0.902266	−	0.431180i	$-0.858097\pi$
$181$	−3.22152e37	−1.80453	−0.902266	+	0.431180i	$0.858097\pi$
$182$	6.88276e37	3.52034
$183$	−3.57998e37	−1.67278
$184$	1.51427e36	0.0646709
$185$	1.15346e36	0.0450473
$186$	−4.77318e37	−1.70547
$187$	−1.51688e37	−0.496096
$188$	−2.89081e37	−0.865796
$189$	−6.14189e37	−1.68532
$190$	2.97210e37	0.747532
$191$	−2.89210e37	−0.667057	−0.333529	−	0.942740i	$-0.608239\pi$
$191$	−2.89210e37	−0.667057	−0.333529	+	0.942740i	$0.608239\pi$
$192$	3.79140e37	0.802286
$193$	4.75455e37	0.923451	0.461726	−	0.887023i	$-0.347230\pi$
$193$	4.75455e37	0.923451	0.461726	+	0.887023i	$0.347230\pi$
$194$	−2.65277e36	−0.0473120
$195$	3.98746e37	0.653319
$196$	9.43128e37	1.42019
$197$	2.87965e37	0.398701	0.199350	−	0.979928i	$-0.436117\pi$
$197$	2.87965e37	0.398701	0.199350	+	0.979928i	$0.436117\pi$
$198$	−1.29283e37	−0.164651
$199$	−1.09912e38	−1.28815	−0.644076	−	0.764961i	$-0.722758\pi$
$199$	−1.09912e38	−1.28815	−0.644076	+	0.764961i	$0.722758\pi$
$200$	1.55698e36	0.0167991
$201$	1.00725e38	1.00093
$202$	−5.53881e37	−0.507130
$203$	9.51438e37	0.802964
$204$	−7.47831e37	−0.581977
$205$	2.98657e37	0.214404
$206$	1.45125e38	0.961464
$207$	−2.02848e37	−0.124068
$208$	−2.98368e38	−1.68541
$209$	−1.68714e38	−0.880516
$210$	1.87411e38	0.904019
$211$	9.20360e37	0.410485	0.205242	−	0.978711i	$-0.434202\pi$
$211$	9.20360e37	0.410485	0.205242	+	0.978711i	$0.434202\pi$
$212$	3.46238e38	1.42835
$213$	8.51591e37	0.325063
$214$	−7.78974e38	−2.75230
$215$	−8.31195e37	−0.271937
$216$	2.94763e37	0.0893278
$217$	7.54521e38	2.11878
$218$	2.58077e37	0.0671765
$219$	6.24413e38	1.50711
$220$	1.37709e38	0.308310
$221$	5.19177e38	1.07856
$222$	−6.66328e37	−0.128488
$223$	−8.19419e38	−1.46715	−0.733577	−	0.679606i	$-0.762151\pi$
$223$	−8.19419e38	−1.46715	−0.733577	+	0.679606i	$0.762151\pi$
$224$	−1.32229e39	−2.19905
$225$	−2.08570e37	−0.0322285
$226$	−1.16585e39	−1.67438
$227$	−3.68201e38	−0.491652	−0.245826	−	0.969314i	$-0.579059\pi$
$227$	−3.68201e38	−0.491652	−0.245826	+	0.969314i	$0.579059\pi$
$228$	−8.31768e38	−1.03294
$229$	5.37397e38	0.620883	0.310442	−	0.950592i	$-0.399523\pi$
$229$	5.37397e38	0.620883	0.310442	+	0.950592i	$0.399523\pi$
$230$	4.46007e38	0.479549
$231$	−1.06386e39	−1.06484
$232$	−4.56617e37	−0.0425599
$233$	5.60193e38	0.486368	0.243184	−	0.969980i	$-0.421808\pi$
$233$	5.60193e38	0.486368	0.243184	+	0.969980i	$0.421808\pi$
$234$	4.42490e38	0.357966
$235$	5.46469e38	0.412046
$236$	−1.74022e38	−0.122336
$237$	1.72258e39	1.12936
$238$	2.44014e39	1.49244
$239$	4.65466e38	0.265658	0.132829	−	0.991139i	$-0.457594\pi$
$239$	4.65466e38	0.265658	0.132829	+	0.991139i	$0.457594\pi$
$240$	−8.12429e38	−0.432812
$241$	−8.56759e38	−0.426165	−0.213082	−	0.977034i	$-0.568350\pi$
$241$	−8.56759e38	−0.426165	−0.213082	+	0.977034i	$0.568350\pi$
$242$	1.38431e39	0.643103
$243$	−7.34921e38	−0.318961
$244$	4.23166e39	1.71624
$245$	−1.78286e39	−0.675890
$246$	−1.72528e39	−0.611546
$247$	5.77450e39	1.91432
$248$	−3.62112e38	−0.112303
$249$	8.78222e38	0.254868
$250$	4.58587e38	0.124569
$251$	−5.15351e39	−1.31065	−0.655325	−	0.755347i	$-0.727468\pi$
$251$	−5.15351e39	−1.31065	−0.655325	+	0.755347i	$0.727468\pi$
$252$	1.00752e39	0.239964
$253$	−2.53180e39	−0.564859
$254$	−1.01262e40	−2.11684
$255$	1.41367e39	0.276972
$256$	6.04071e39	1.10950
$257$	−5.66916e39	−0.976388	−0.488194	−	0.872735i	$-0.662344\pi$
$257$	−5.66916e39	−0.976388	−0.488194	+	0.872735i	$0.662344\pi$
$258$	4.80163e39	0.775646
$259$	1.05330e39	0.159627
$260$	−4.71331e39	−0.670294
$261$	6.11676e38	0.0816494
$262$	−1.67326e40	−2.09697
$263$	−1.47291e39	−0.173343	−0.0866715	−	0.996237i	$-0.527623\pi$
$263$	−1.47291e39	−0.173343	−0.0866715	+	0.996237i	$0.527623\pi$
$264$	5.10569e38	0.0564404
$265$	−6.54517e39	−0.679773
$266$	2.71403e40	2.64891
$267$	−8.36547e39	−0.767458
$268$	−1.19060e40	−1.02693
$269$	−2.15538e39	−0.174828	−0.0874139	−	0.996172i	$-0.527860\pi$
$269$	−2.15538e39	−0.174828	−0.0874139	+	0.996172i	$0.527860\pi$
$270$	8.68186e39	0.662385
$271$	−6.55007e39	−0.470168	−0.235084	−	0.971975i	$-0.575536\pi$
$271$	−6.55007e39	−0.470168	−0.235084	+	0.971975i	$0.575536\pi$
$272$	−1.05780e40	−0.714525
$273$	3.64121e40	2.31506
$274$	4.33150e40	2.59271
$275$	−2.60320e39	−0.146730
$276$	−1.24819e40	−0.662644
$277$	−2.17785e40	−1.08921	−0.544604	−	0.838693i	$-0.683320\pi$
$277$	−2.17785e40	−1.08921	−0.544604	+	0.838693i	$0.683320\pi$
$278$	1.58362e40	0.746299
$279$	4.85079e39	0.215448
$280$	1.42178e39	0.0595284
$281$	4.97063e38	0.0196226	0.00981131	−	0.999952i	$-0.496877\pi$
$281$	4.97063e38	0.0196226	0.00981131	+	0.999952i	$0.496877\pi$
$282$	−3.15683e40	−1.17528
$283$	−2.67595e40	−0.939728	−0.469864	−	0.882739i	$-0.655697\pi$
$283$	−2.67595e40	−0.939728	−0.469864	+	0.882739i	$0.655697\pi$
$284$	−1.00661e40	−0.333509
$285$	1.57234e40	0.491595
$286$	5.52281e40	1.62975
$287$	2.72724e40	0.759751
$288$	−8.50098e39	−0.223611
$289$	−2.18481e40	−0.542750
$290$	−1.34490e40	−0.315591
$291$	−1.40341e39	−0.0311135
$292$	−7.38076e40	−1.54627
$293$	1.28487e40	0.254415	0.127207	−	0.991876i	$-0.459399\pi$
$293$	1.28487e40	0.254415	0.127207	+	0.991876i	$0.459399\pi$
$294$	1.02992e41	1.92784
$295$	3.28965e39	0.0582218
$296$	−5.05503e38	−0.00846079
$297$	−4.92833e40	−0.780222
$298$	−8.63280e39	−0.129295
$299$	8.66547e40	1.22805
$300$	−1.28339e40	−0.172131
$301$	−7.59019e40	−0.963619
$302$	8.73181e39	0.104952
$303$	−2.93022e40	−0.333501
$304$	−1.17653e41	−1.26820
$305$	−7.99938e40	−0.816787
$306$	1.56876e40	0.151758
$307$	5.95612e40	0.545984	0.272992	−	0.962016i	$-0.411987\pi$
$307$	5.95612e40	0.545984	0.272992	+	0.962016i	$0.411987\pi$
$308$	1.25751e41	1.09251
$309$	7.67761e40	0.632283
$310$	−1.06655e41	−0.832750
$311$	−3.80156e40	−0.281459	−0.140730	−	0.990048i	$-0.544945\pi$
$311$	−3.80156e40	−0.281459	−0.140730	+	0.990048i	$0.544945\pi$
$312$	−1.74750e40	−0.122706
$313$	−2.52982e41	−1.68503	−0.842515	−	0.538673i	$-0.818926\pi$
$313$	−2.52982e41	−1.68503	−0.842515	+	0.538673i	$0.818926\pi$
$314$	−1.01323e41	−0.640277
$315$	−1.90459e40	−0.114203
$316$	−2.03615e41	−1.15870
$317$	2.56047e41	1.38306	0.691530	−	0.722348i	$-0.256937\pi$
$317$	2.56047e41	1.38306	0.691530	+	0.722348i	$0.256937\pi$
$318$	3.78100e41	1.93892
$319$	7.63446e40	0.371734
$320$	8.47178e40	0.391742
$321$	−4.12104e41	−1.80998
$322$	4.07279e41	1.69930
$323$	2.04723e41	0.811569
$324$	−2.02773e41	−0.763865
$325$	8.90987e40	0.319004
$326$	5.82499e41	1.98246
$327$	1.36532e40	0.0441769
$328$	−1.30886e40	−0.0402695
$329$	4.99017e41	1.46010
$330$	1.50381e41	0.418518
$331$	3.97632e41	1.05274	0.526368	−	0.850257i	$-0.323553\pi$
$331$	3.97632e41	1.05274	0.526368	+	0.850257i	$0.323553\pi$
$332$	−1.03809e41	−0.261490
$333$	6.77163e39	0.0162317
$334$	−9.05368e41	−2.06542
$335$	2.25067e41	0.488735
$336$	−7.41883e41	−1.53369
$337$	−3.16941e41	−0.623857	−0.311928	−	0.950106i	$-0.600975\pi$
$337$	−3.16941e41	−0.623857	−0.311928	+	0.950106i	$0.600975\pi$
$338$	−1.14726e42	−2.15049
$339$	−6.16774e41	−1.10111
$340$	−1.67101e41	−0.284169
$341$	6.05438e41	0.980894
$342$	1.74484e41	0.269354
$343$	−5.50823e41	−0.810324
$344$	3.64271e40	0.0510752
$345$	2.35953e41	0.315363
$346$	−1.37844e42	−1.75644
$347$	3.65901e41	0.444557	0.222279	−	0.974983i	$-0.428651\pi$
$347$	3.65901e41	0.444557	0.222279	+	0.974983i	$0.428651\pi$
$348$	3.76383e41	0.436086
$349$	1.01851e42	1.12550	0.562752	−	0.826626i	$-0.309743\pi$
$349$	1.01851e42	1.12550	0.562752	+	0.826626i	$0.309743\pi$
$350$	4.18766e41	0.441416
$351$	1.68680e42	1.69627
$352$	−1.06103e42	−1.01806
$353$	−1.09904e42	−1.00631	−0.503153	−	0.864197i	$-0.667827\pi$
$353$	−1.09904e42	−1.00631	−0.503153	+	0.864197i	$0.667827\pi$
$354$	−1.90036e41	−0.166066
$355$	1.90286e41	0.158722
$356$	9.88826e41	0.787399
$357$	1.29092e42	0.981462
$358$	−1.31618e41	−0.0955531
$359$	−1.88943e42	−1.31000	−0.655002	−	0.755627i	$-0.727332\pi$
$359$	−1.88943e42	−1.31000	−0.655002	+	0.755627i	$0.727332\pi$
$360$	9.14056e39	0.00605315
$361$	6.96243e41	0.440445
$362$	4.15836e42	2.51322
$363$	7.32349e41	0.422921
$364$	−4.30403e42	−2.37522
$365$	1.39523e42	0.735893
$366$	4.62106e42	2.32972
$367$	−3.72944e42	−1.79744	−0.898718	−	0.438527i	$-0.855500\pi$
$367$	−3.72944e42	−1.79744	−0.898718	+	0.438527i	$0.855500\pi$
$368$	−1.76555e42	−0.813565
$369$	1.75333e41	0.0772553
$370$	−1.48889e41	−0.0627386
$371$	−5.97683e42	−2.40880
$372$	2.98484e42	1.15070
$373$	2.08286e42	0.768181	0.384091	−	0.923295i	$-0.374515\pi$
$373$	2.08286e42	0.768181	0.384091	+	0.923295i	$0.374515\pi$
$374$	1.95800e42	0.690926
$375$	2.42608e41	0.0819198
$376$	−2.39490e41	−0.0773906
$377$	−2.61301e42	−0.808183
$378$	7.92799e42	2.34719
$379$	1.44890e42	0.410668	0.205334	−	0.978692i	$-0.434172\pi$
$379$	1.44890e42	0.410668	0.205334	+	0.978692i	$0.434172\pi$
$380$	−1.85856e42	−0.504368
$381$	−5.35709e42	−1.39209
$382$	3.73314e42	0.929029
$383$	−3.31373e42	−0.789837	−0.394919	−	0.918716i	$-0.629227\pi$
$383$	−3.31373e42	−0.789837	−0.394919	+	0.918716i	$0.629227\pi$
$384$	6.72676e41	0.153582
$385$	−2.37716e42	−0.519943
$386$	−6.13721e42	−1.28612
$387$	−4.87970e41	−0.0979857
$388$	1.65887e41	0.0319219
$389$	3.52845e42	0.650752	0.325376	−	0.945585i	$-0.394509\pi$
$389$	3.52845e42	0.650752	0.325376	+	0.945585i	$0.394509\pi$
$390$	−5.14704e42	−0.909895
$391$	3.07217e42	0.520629
$392$	7.81337e41	0.126946
$393$	−8.85213e42	−1.37902
$394$	−3.71707e42	−0.555282
$395$	3.84907e42	0.551446
$396$	8.08450e41	0.111092
$397$	2.11298e42	0.278517	0.139258	−	0.990256i	$-0.455528\pi$
$397$	2.11298e42	0.278517	0.139258	+	0.990256i	$0.455528\pi$
$398$	1.41874e43	1.79405
$399$	1.43581e43	1.74199
$400$	−1.81535e42	−0.211335
$401$	−3.95709e42	−0.442073	−0.221037	−	0.975266i	$-0.570944\pi$
$401$	−3.95709e42	−0.442073	−0.221037	+	0.975266i	$0.570944\pi$
$402$	−1.30016e43	−1.39402
$403$	−2.07221e43	−2.13255
$404$	3.46362e42	0.342167
$405$	3.83314e42	0.363536
$406$	−1.22812e43	−1.11831
$407$	8.45182e41	0.0738996
$408$	−6.19542e41	−0.0520209
$409$	4.44989e42	0.358851	0.179426	−	0.983772i	$-0.442576\pi$
$409$	4.44989e42	0.358851	0.179426	+	0.983772i	$0.442576\pi$
$410$	−3.85508e42	−0.298607
$411$	2.29151e43	1.70503
$412$	−9.07519e42	−0.648711
$413$	3.00399e42	0.206311
$414$	2.61838e42	0.172793
$415$	1.96236e42	0.124447
$416$	3.63153e43	2.21335
$417$	8.37792e42	0.490785
$418$	2.17777e43	1.22632
$419$	2.01206e43	1.08920	0.544601	−	0.838695i	$-0.316681\pi$
$419$	2.01206e43	1.08920	0.544601	+	0.838695i	$0.316681\pi$
$420$	−1.17195e43	−0.609953
$421$	−1.46744e43	−0.734354	−0.367177	−	0.930151i	$-0.619676\pi$
$421$	−1.46744e43	−0.734354	−0.367177	+	0.930151i	$0.619676\pi$
$422$	−1.18801e43	−0.571694
$423$	3.20816e42	0.148471
$424$	2.86842e42	0.127675
$425$	3.15882e42	0.135241
$426$	−1.09924e43	−0.452724
$427$	−7.30476e43	−2.89432
$428$	4.87120e43	1.85701
$429$	2.92176e43	1.07176
$430$	1.07291e43	0.378734
$431$	9.38421e42	0.318803	0.159402	−	0.987214i	$-0.449044\pi$
$431$	9.38421e42	0.318803	0.159402	+	0.987214i	$0.449044\pi$
$432$	−3.43678e43	−1.12375
$433$	3.99047e42	0.125595	0.0627976	−	0.998026i	$-0.479998\pi$
$433$	3.99047e42	0.125595	0.0627976	+	0.998026i	$0.479998\pi$
$434$	−9.73941e43	−2.95088
$435$	−7.11501e42	−0.207540
$436$	−1.61385e42	−0.0453248
$437$	3.41699e43	0.924060
$438$	−8.05996e43	−2.09899
$439$	9.80249e42	0.245851	0.122925	−	0.992416i	$-0.460772\pi$
$439$	9.80249e42	0.245851	0.122925	+	0.992416i	$0.460772\pi$
$440$	1.14085e42	0.0275588
$441$	−1.04666e43	−0.243540
$442$	−6.70157e43	−1.50214
$443$	−2.57496e42	−0.0556044	−0.0278022	−	0.999613i	$-0.508851\pi$
$443$	−2.57496e42	−0.0556044	−0.0278022	+	0.999613i	$0.508851\pi$
$444$	4.16679e42	0.0866926
$445$	−1.86924e43	−0.374736
$446$	1.05771e44	2.04335
$447$	−4.56704e42	−0.0850278
$448$	7.73615e43	1.38815
$449$	−7.29533e43	−1.26177	−0.630885	−	0.775876i	$-0.717308\pi$
$449$	−7.29533e43	−1.26177	−0.630885	+	0.775876i	$0.717308\pi$
$450$	2.69223e42	0.0448855
$451$	2.18837e43	0.351728
$452$	7.29048e43	1.12972
$453$	4.61943e42	0.0690188
$454$	4.75276e43	0.684737
$455$	8.13620e43	1.13040
$456$	−6.89080e42	−0.0923315
$457$	1.18400e44	1.53015	0.765077	−	0.643939i	$-0.222701\pi$
$457$	1.18400e44	1.53015	0.765077	+	0.643939i	$0.222701\pi$
$458$	−6.93676e43	−0.864721
$459$	5.98020e43	0.719129
$460$	−2.78904e43	−0.323557
$461$	−1.64770e44	−1.84423	−0.922113	−	0.386921i	$-0.873539\pi$
$461$	−1.64770e44	−1.84423	−0.922113	+	0.386921i	$0.873539\pi$
$462$	1.37323e44	1.48303
$463$	−5.84287e43	−0.608892	−0.304446	−	0.952530i	$-0.598471\pi$
$463$	−5.84287e43	−0.608892	−0.304446	+	0.952530i	$0.598471\pi$
$464$	5.32391e43	0.535407
$465$	−5.64243e43	−0.547637
$466$	−7.23100e43	−0.677378
$467$	9.91255e43	0.896307	0.448154	−	0.893957i	$-0.352082\pi$
$467$	9.91255e43	0.896307	0.448154	+	0.893957i	$0.352082\pi$
$468$	−2.76705e43	−0.241524
$469$	2.05524e44	1.73185
$470$	−7.05386e43	−0.573868
$471$	−5.36032e43	−0.421062
$472$	−1.44169e42	−0.0109352
$473$	−6.09047e43	−0.446110
$474$	−2.22352e44	−1.57289
$475$	3.51336e43	0.240037
$476$	−1.52591e44	−1.00696
$477$	−3.84248e43	−0.244939
$478$	−6.00826e43	−0.369989
$479$	−1.45337e44	−0.864647	−0.432324	−	0.901719i	$-0.642306\pi$
$479$	−1.45337e44	−0.864647	−0.432324	+	0.901719i	$0.642306\pi$
$480$	9.88833e43	0.568385
$481$	−2.89277e43	−0.160664
$482$	1.10591e44	0.593531
$483$	2.15465e44	1.11750
$484$	−8.65661e43	−0.433910
$485$	−3.13587e42	−0.0151922
$486$	9.48640e43	0.444225
$487$	3.00271e43	0.135921	0.0679604	−	0.997688i	$-0.478351\pi$
$487$	3.00271e43	0.135921	0.0679604	+	0.997688i	$0.478351\pi$
$488$	3.50573e43	0.153409
$489$	3.08162e44	1.30372
$490$	2.30132e44	0.941331
$491$	−2.65183e44	−1.04882	−0.524410	−	0.851466i	$-0.675714\pi$
$491$	−2.65183e44	−1.04882	−0.524410	+	0.851466i	$0.675714\pi$
$492$	1.07888e44	0.412617
$493$	−9.26391e43	−0.342626
$494$	−7.45376e44	−2.66613
$495$	−1.52827e43	−0.0528705
$496$	4.22203e44	1.41278
$497$	1.73763e44	0.562439
$498$	−1.13361e44	−0.354961
$499$	−5.34386e44	−1.61881	−0.809405	−	0.587251i	$-0.800210\pi$
$499$	−5.34386e44	−1.61881	−0.809405	+	0.587251i	$0.800210\pi$
$500$	−2.86771e43	−0.0840484
$501$	−4.78971e44	−1.35827
$502$	6.65218e44	1.82538
$503$	−6.08597e44	−1.61606	−0.808031	−	0.589140i	$-0.799466\pi$
$503$	−6.08597e44	−1.61606	−0.808031	+	0.589140i	$0.799466\pi$
$504$	8.34686e42	0.0214496
$505$	−6.54750e43	−0.162843
$506$	3.26806e44	0.786695
$507$	−6.06942e44	−1.41422
$508$	6.33225e44	1.42826
$509$	1.32394e44	0.289084	0.144542	−	0.989499i	$-0.453829\pi$
$509$	1.32394e44	0.289084	0.144542	+	0.989499i	$0.453829\pi$
$510$	−1.82478e44	−0.385747
$511$	1.27408e45	2.60767
$512$	−6.95122e44	−1.37755
$513$	6.65142e44	1.27637
$514$	7.31779e44	1.35984
$515$	1.71554e44	0.308732
$516$	−3.00263e44	−0.523337
$517$	4.00418e44	0.675958
$518$	−1.35961e44	−0.222317
$519$	−7.29242e44	−1.15508
$520$	−3.90475e43	−0.0599154
$521$	7.67376e44	1.14074	0.570369	−	0.821389i	$-0.306800\pi$
$521$	7.67376e44	1.14074	0.570369	+	0.821389i	$0.306800\pi$
$522$	−7.89555e43	−0.113715
$523$	−4.46260e44	−0.622745	−0.311373	−	0.950288i	$-0.600789\pi$
$523$	−4.46260e44	−0.622745	−0.311373	+	0.950288i	$0.600789\pi$
$524$	1.04635e45	1.41485
$525$	2.21541e44	0.290286
$526$	1.90124e44	0.241420
$527$	−7.34659e44	−0.904087
$528$	−5.95296e44	−0.710025
$529$	−3.52236e44	−0.407207
$530$	8.44855e44	0.946739
$531$	1.93126e43	0.0209788
$532$	−1.69718e45	−1.78725
$533$	−7.49003e44	−0.764689
$534$	1.07982e45	1.06886
$535$	−9.20835e44	−0.883781
$536$	−9.86358e43	−0.0917942
$537$	−6.96303e43	−0.0628381
$538$	2.78217e44	0.243487
$539$	−1.30636e45	−1.10879
$540$	−5.42908e44	−0.446919
$541$	2.76410e44	0.220698	0.110349	−	0.993893i	$-0.464803\pi$
$541$	2.76410e44	0.220698	0.110349	+	0.993893i	$0.464803\pi$
$542$	8.45487e44	0.654815
$543$	2.19991e45	1.65276
$544$	1.28749e45	0.938341
$545$	3.05076e43	0.0215708
$546$	−4.70010e45	−3.22425
$547$	−1.10195e45	−0.733453	−0.366726	−	0.930329i	$-0.619521\pi$
$547$	−1.10195e45	−0.733453	−0.366726	+	0.930329i	$0.619521\pi$
$548$	−2.70864e45	−1.74933
$549$	−4.69620e44	−0.294309
$550$	3.36023e44	0.204355
$551$	−1.03037e45	−0.608124
$552$	−1.03406e44	−0.0592315
$553$	3.51484e45	1.95407
$554$	2.81118e45	1.51697
$555$	−7.87675e43	−0.0412584
$556$	−9.90297e44	−0.503537
$557$	9.98180e44	0.492718	0.246359	−	0.969179i	$-0.420766\pi$
$557$	9.98180e44	0.492718	0.246359	+	0.969179i	$0.420766\pi$
$558$	−6.26143e44	−0.300061
$559$	2.08456e45	0.969882
$560$	−1.65772e45	−0.748873
$561$	1.03585e45	0.454370
$562$	−6.41612e43	−0.0273290
$563$	2.41489e45	0.998870	0.499435	−	0.866351i	$-0.333541\pi$
$563$	2.41489e45	0.998870	0.499435	+	0.866351i	$0.333541\pi$
$564$	1.97408e45	0.792975
$565$	−1.37817e45	−0.537653
$566$	3.45414e45	1.30878
$567$	3.50030e45	1.28820
$568$	−8.33927e43	−0.0298113
$569$	3.12759e45	1.08607	0.543035	−	0.839710i	$-0.317275\pi$
$569$	3.12759e45	1.08607	0.543035	+	0.839710i	$0.317275\pi$
$570$	−2.02959e45	−0.684658
$571$	4.44750e44	0.145754	0.0728770	−	0.997341i	$-0.476782\pi$
$571$	4.44750e44	0.145754	0.0728770	+	0.997341i	$0.476782\pi$
$572$	−3.45361e45	−1.09961
$573$	1.97496e45	0.610952
$574$	−3.52033e45	−1.05813
$575$	5.27231e44	0.153986
$576$	4.97354e44	0.141154
$577$	−2.41991e45	−0.667420	−0.333710	−	0.942676i	$-0.608301\pi$
$577$	−2.41991e45	−0.667420	−0.333710	+	0.942676i	$0.608301\pi$
$578$	2.82017e45	0.755903
$579$	−3.24679e45	−0.845781
$580$	8.41017e44	0.212933
$581$	1.79197e45	0.440985
$582$	1.81153e44	0.0433326
$583$	−4.79589e45	−1.11516
$584$	−6.11461e44	−0.138216
$585$	5.23073e44	0.114945
$586$	−1.65851e45	−0.354330
$587$	−5.33169e45	−1.10748	−0.553741	−	0.832689i	$-0.686800\pi$
$587$	−5.33169e45	−1.10748	−0.553741	+	0.832689i	$0.686800\pi$
$588$	−6.44044e45	−1.30074
$589$	−8.17117e45	−1.60466
$590$	−4.24629e44	−0.0810871
$591$	−1.96646e45	−0.365167
$592$	5.89389e44	0.106437
$593$	4.45568e45	0.782549	0.391274	−	0.920274i	$-0.372034\pi$
$593$	4.45568e45	0.782549	0.391274	+	0.920274i	$0.372034\pi$
$594$	6.36152e45	1.08664
$595$	2.88452e45	0.479230
$596$	5.39840e44	0.0872372
$597$	7.50565e45	1.17981
$598$	−1.11854e46	−1.71035
$599$	−6.35076e44	−0.0944676	−0.0472338	−	0.998884i	$-0.515041\pi$
$599$	−6.35076e44	−0.0944676	−0.0472338	+	0.998884i	$0.515041\pi$
$600$	−1.06323e44	−0.0153862
$601$	5.17167e45	0.728119	0.364059	−	0.931376i	$-0.381390\pi$
$601$	5.17167e45	0.728119	0.364059	+	0.931376i	$0.381390\pi$
$602$	9.79747e45	1.34206
$603$	1.32131e45	0.176103
$604$	−5.46031e44	−0.0708122
$605$	1.63641e45	0.206505
$606$	3.78235e45	0.464476
$607$	−8.40877e45	−1.00489	−0.502446	−	0.864609i	$-0.667566\pi$
$607$	−8.40877e45	−1.00489	−0.502446	+	0.864609i	$0.667566\pi$
$608$	1.43199e46	1.66545
$609$	−6.49719e45	−0.735428
$610$	1.03256e46	1.13756
$611$	−1.37049e46	−1.46959
$612$	−9.81001e44	−0.102393
$613$	2.24884e45	0.228486	0.114243	−	0.993453i	$-0.463556\pi$
$613$	2.24884e45	0.228486	0.114243	+	0.993453i	$0.463556\pi$
$614$	−7.68820e45	−0.760408
$615$	−2.03947e45	−0.196371
$616$	1.04179e45	0.0976558
$617$	−2.01918e46	−1.84277	−0.921384	−	0.388654i	$-0.872940\pi$
$617$	−2.01918e46	−1.84277	−0.921384	+	0.388654i	$0.872940\pi$
$618$	−9.91031e45	−0.880597
$619$	−6.12733e44	−0.0530122	−0.0265061	−	0.999649i	$-0.508438\pi$
$619$	−6.12733e44	−0.0530122	−0.0265061	+	0.999649i	$0.508438\pi$
$620$	6.66954e45	0.561866
$621$	9.98143e45	0.818806
$622$	4.90708e45	0.391996
$623$	−1.70693e46	−1.32789
$624$	2.03749e46	1.54366
$625$	5.42101e44	0.0400000
$626$	3.26550e46	2.34679
$627$	1.15211e46	0.806457
$628$	6.33607e45	0.432002
$629$	−1.02557e45	−0.0681131
$630$	2.45845e45	0.159053
$631$	−3.45501e45	−0.217753	−0.108877	−	0.994055i	$-0.534725\pi$
$631$	−3.45501e45	−0.217753	−0.108877	+	0.994055i	$0.534725\pi$
$632$	−1.68685e45	−0.103573
$633$	−6.28496e45	−0.375960
$634$	−3.30507e46	−1.92623
$635$	−1.19703e46	−0.679732
$636$	−2.36440e46	−1.30821
$637$	4.47124e46	2.41061
$638$	−9.85461e45	−0.517724
$639$	1.11711e45	0.0571917
$640$	1.50308e45	0.0749914
$641$	−1.11074e44	−0.00540077	−0.00270039	−	0.999996i	$-0.500860\pi$
$641$	−1.11074e44	−0.00540077	−0.00270039	+	0.999996i	$0.500860\pi$
$642$	5.31946e46	2.52081
$643$	2.41519e46	1.11550	0.557751	−	0.830009i	$-0.311665\pi$
$643$	2.41519e46	1.11550	0.557751	+	0.830009i	$0.311665\pi$
$644$	−2.54686e46	−1.14654
$645$	5.67607e45	0.249065
$646$	−2.64258e46	−1.13029
$647$	2.20068e46	0.917563	0.458781	−	0.888549i	$-0.348286\pi$
$647$	2.20068e46	0.917563	0.458781	+	0.888549i	$0.348286\pi$
$648$	−1.67988e45	−0.0682794
$649$	2.41044e45	0.0955123
$650$	−1.15009e46	−0.444286
$651$	−5.15248e46	−1.94057
$652$	−3.64258e46	−1.33759
$653$	2.59836e46	0.930319	0.465159	−	0.885227i	$-0.345997\pi$
$653$	2.59836e46	0.930319	0.465159	+	0.885227i	$0.345997\pi$
$654$	−1.76236e45	−0.0615264
$655$	−1.97799e46	−0.673351
$656$	1.52606e46	0.506593
$657$	8.19102e45	0.265161
$658$	−6.44135e46	−2.03352
$659$	−8.95518e45	−0.275718	−0.137859	−	0.990452i	$-0.544022\pi$
$659$	−8.95518e45	−0.275718	−0.137859	+	0.990452i	$0.544022\pi$
$660$	−9.40388e45	−0.282379
$661$	5.29479e45	0.155069	0.0775345	−	0.996990i	$-0.475295\pi$
$661$	5.29479e45	0.155069	0.0775345	+	0.996990i	$0.475295\pi$
$662$	−5.13266e46	−1.46617
$663$	−3.54536e46	−0.987841
$664$	−8.60006e44	−0.0233737
$665$	3.20829e46	0.850581
$666$	−8.74086e44	−0.0226063
$667$	−1.54622e46	−0.390117
$668$	5.66159e46	1.39356
$669$	5.59565e46	1.34375
$670$	−2.90518e46	−0.680674
$671$	−5.86144e46	−1.33993
$672$	9.02970e46	2.01410
$673$	5.71426e46	1.24369	0.621844	−	0.783141i	$-0.286384\pi$
$673$	5.71426e46	1.24369	0.621844	+	0.783141i	$0.286384\pi$
$674$	4.09109e46	0.868862
$675$	1.02629e46	0.212696
$676$	7.17426e46	1.45096
$677$	−8.00955e46	−1.58087	−0.790433	−	0.612548i	$-0.790145\pi$
$677$	−8.00955e46	−1.58087	−0.790433	+	0.612548i	$0.790145\pi$
$678$	7.96136e46	1.53355
$679$	−2.86357e45	−0.0538341
$680$	−1.38435e45	−0.0254009
$681$	2.51437e46	0.450300
$682$	−7.81503e46	−1.36612
$683$	−1.21546e45	−0.0207395	−0.0103697	−	0.999946i	$-0.503301\pi$
$683$	−1.21546e45	−0.0207395	−0.0103697	+	0.999946i	$0.503301\pi$
$684$	−1.09111e46	−0.181737
$685$	5.12033e46	0.832537
$686$	7.11005e46	1.12856
$687$	−3.66978e46	−0.568662
$688$	−4.24720e46	−0.642530
$689$	1.64147e47	2.42446
$690$	−3.04570e46	−0.439215
$691$	−8.60411e46	−1.21149	−0.605743	−	0.795661i	$-0.707124\pi$
$691$	−8.60411e46	−1.21149	−0.605743	+	0.795661i	$0.707124\pi$
$692$	8.61988e46	1.18509
$693$	−1.39556e46	−0.187349
$694$	−4.72308e46	−0.619147
$695$	1.87202e46	0.239641
$696$	3.11815e45	0.0389803
$697$	−2.65544e46	−0.324187
$698$	−1.31470e47	−1.56752
$699$	−3.82545e46	−0.445460
$700$	−2.61869e46	−0.297829
$701$	2.40906e46	0.267609	0.133804	−	0.991008i	$-0.457281\pi$
$701$	2.40906e46	0.267609	0.133804	+	0.991008i	$0.457281\pi$
$702$	−2.17733e47	−2.36245
$703$	−1.14068e46	−0.120893
$704$	6.20758e46	0.642649
$705$	−3.73173e46	−0.377390
$706$	1.41864e47	1.40151
$707$	−5.97896e46	−0.577039
$708$	1.18836e46	0.112047
$709$	1.49721e46	0.137917	0.0689586	−	0.997620i	$-0.478032\pi$
$709$	1.49721e46	0.137917	0.0689586	+	0.997620i	$0.478032\pi$
$710$	−2.45622e46	−0.221057
$711$	2.25968e46	0.198700
$712$	8.19195e45	0.0703829
$713$	−1.22620e47	−1.02940
$714$	−1.66633e47	−1.36691
$715$	6.52859e46	0.523323
$716$	8.23053e45	0.0644708
$717$	−3.17858e46	−0.243314
$718$	2.43889e47	1.82448
$719$	4.37252e46	0.319673	0.159836	−	0.987144i	$-0.448903\pi$
$719$	4.37252e46	0.319673	0.159836	+	0.987144i	$0.448903\pi$
$720$	−1.06574e46	−0.0761492
$721$	1.56658e47	1.09401
$722$	−8.98715e46	−0.613420
$723$	5.85064e46	0.390321
$724$	−2.60037e47	−1.69570
$725$	−1.58983e46	−0.101338
$726$	−9.45321e46	−0.589013
$727$	−1.19298e47	−0.726634	−0.363317	−	0.931666i	$-0.618356\pi$
$727$	−1.19298e47	−0.726634	−0.363317	+	0.931666i	$0.618356\pi$
$728$	−3.56569e46	−0.212313
$729$	1.89835e47	1.10502
$730$	−1.80098e47	−1.02490
$731$	7.39038e46	0.411178
$732$	−2.88972e47	−1.57189
$733$	3.02145e47	1.60694	0.803471	−	0.595343i	$-0.202984\pi$
$733$	3.02145e47	1.60694	0.803471	+	0.595343i	$0.202984\pi$
$734$	4.81398e47	2.50334
$735$	1.21748e47	0.619042
$736$	2.14891e47	1.06840
$737$	1.64915e47	0.801765
$738$	−2.26321e46	−0.107596
$739$	−4.95875e46	−0.230536	−0.115268	−	0.993334i	$-0.536773\pi$
$739$	−4.95875e46	−0.230536	−0.115268	+	0.993334i	$0.536773\pi$
$740$	9.31057e45	0.0423305
$741$	−3.94329e47	−1.75331
$742$	7.71493e47	3.35481
$743$	−7.50450e46	−0.319158	−0.159579	−	0.987185i	$-0.551014\pi$
$743$	−7.50450e46	−0.319158	−0.159579	+	0.987185i	$0.551014\pi$
$744$	2.47280e46	0.102857
$745$	−1.02049e46	−0.0415176
$746$	−2.68856e47	−1.06987
$747$	1.15205e46	0.0448415
$748$	−1.22441e47	−0.466176
$749$	−8.40876e47	−3.13171
$750$	−3.13160e46	−0.114092
$751$	−2.61189e47	−0.930884	−0.465442	−	0.885078i	$-0.654105\pi$
$751$	−2.61189e47	−0.930884	−0.465442	+	0.885078i	$0.654105\pi$
$752$	2.79232e47	0.973580
$753$	3.51923e47	1.20041
$754$	3.37289e47	1.12558
$755$	1.03220e46	0.0337007
$756$	−4.95765e47	−1.58368
$757$	−7.29946e46	−0.228144	−0.114072	−	0.993472i	$-0.536389\pi$
$757$	−7.29946e46	−0.228144	−0.114072	+	0.993472i	$0.536389\pi$
$758$	−1.87025e47	−0.571948
$759$	1.72892e47	0.517350
$760$	−1.53973e46	−0.0450838
$761$	−3.25049e47	−0.931327	−0.465663	−	0.884962i	$-0.654184\pi$
$761$	−3.25049e47	−0.931327	−0.465663	+	0.884962i	$0.654184\pi$
$762$	6.91496e47	1.93880
$763$	2.78585e46	0.0764370
$764$	−2.33447e47	−0.626827
$765$	1.85445e46	0.0487306
$766$	4.27739e47	1.10003
$767$	−8.25012e46	−0.207652
$768$	−4.12508e47	−1.01618
$769$	4.28447e47	1.03303	0.516514	−	0.856279i	$-0.327229\pi$
$769$	4.28447e47	1.03303	0.516514	+	0.856279i	$0.327229\pi$
$770$	3.06845e47	0.724139
$771$	3.87136e47	0.894266
$772$	3.83781e47	0.867758
$773$	−8.22105e47	−1.81956	−0.909779	−	0.415094i	$-0.863749\pi$
$773$	−8.22105e47	−1.81956	−0.909779	+	0.415094i	$0.863749\pi$
$774$	6.29875e46	0.136467
$775$	−1.26079e47	−0.267401
$776$	1.37430e45	0.00285340
$777$	−7.19278e46	−0.146201
$778$	−4.55454e47	−0.906320
$779$	−2.95349e47	−0.575397
$780$	3.21863e47	0.613917
$781$	1.39429e47	0.260383
$782$	−3.96557e47	−0.725095
$783$	−3.00983e47	−0.538856
$784$	−9.10996e47	−1.59699
$785$	−1.19775e47	−0.205597
$786$	1.14264e48	1.92060
$787$	−9.92861e47	−1.63420	−0.817100	−	0.576496i	$-0.804420\pi$
$787$	−9.92861e47	−1.63420	−0.817100	+	0.576496i	$0.804420\pi$
$788$	2.32442e47	0.374655
$789$	1.00582e47	0.158763
$790$	−4.96840e47	−0.768014
$791$	−1.25850e48	−1.90520
$792$	6.69762e45	0.00993014
$793$	2.00617e48	2.91313
$794$	−2.72744e47	−0.387898
$795$	4.46957e47	0.622599
$796$	−8.87192e47	−1.21046
$797$	1.14954e48	1.53625	0.768124	−	0.640301i	$-0.221190\pi$
$797$	1.14954e48	1.53625	0.768124	+	0.640301i	$0.221190\pi$
$798$	−1.85336e48	−2.42611
$799$	−4.85881e47	−0.623028
$800$	2.20952e47	0.277532
$801$	−1.09738e47	−0.135027
$802$	5.10784e47	0.615687
$803$	1.02234e48	1.20723
$804$	8.13040e47	0.940561
$805$	4.81450e47	0.545656
$806$	2.67482e48	2.97006
$807$	1.47187e47	0.160123
$808$	2.86944e46	0.0305851
$809$	−1.50525e48	−1.57202	−0.786009	−	0.618215i	$-0.787856\pi$
$809$	−1.50525e48	−1.57202	−0.786009	+	0.618215i	$0.787856\pi$
$810$	−4.94785e47	−0.506306
$811$	1.19205e48	1.19522	0.597612	−	0.801786i	$-0.296116\pi$
$811$	1.19205e48	1.19522	0.597612	+	0.801786i	$0.296116\pi$
$812$	7.67989e47	0.754537
$813$	4.47292e47	0.430623
$814$	−1.09097e47	−0.102922
$815$	6.88580e47	0.636581
$816$	7.22353e47	0.654428
$817$	8.21988e47	0.729796
$818$	−5.74394e47	−0.499782
$819$	4.77653e47	0.407313
$820$	2.41072e47	0.201474
$821$	−1.82470e48	−1.49461	−0.747306	−	0.664480i	$-0.768653\pi$
$821$	−1.82470e48	−1.49461	−0.747306	+	0.664480i	$0.768653\pi$
$822$	−2.95790e48	−2.37464
$823$	1.63942e48	1.29001	0.645004	−	0.764180i	$-0.276856\pi$
$823$	1.63942e48	1.29001	0.645004	+	0.764180i	$0.276856\pi$
$824$	−7.51836e46	−0.0579861
$825$	1.77768e47	0.134389
$826$	−3.87757e47	−0.287336
$827$	−1.07814e48	−0.783129	−0.391565	−	0.920151i	$-0.628066\pi$
$827$	−1.07814e48	−0.783129	−0.391565	+	0.920151i	$0.628066\pi$
$828$	−1.63737e47	−0.116586
$829$	−1.12436e48	−0.784795	−0.392397	−	0.919796i	$-0.628354\pi$
$829$	−1.12436e48	−0.784795	−0.392397	+	0.919796i	$0.628354\pi$
$830$	−2.53303e47	−0.173321
$831$	1.48721e48	0.997597
$832$	−2.12464e48	−1.39718
$833$	1.58519e48	1.02197
$834$	−1.08143e48	−0.683530
$835$	−1.07025e48	−0.663220
$836$	−1.36184e48	−0.827412
$837$	−2.38689e48	−1.42188
$838$	−2.59717e48	−1.51696
$839$	2.27412e48	1.30239	0.651195	−	0.758911i	$-0.274268\pi$
$839$	2.27412e48	1.30239	0.651195	+	0.758911i	$0.274268\pi$
$840$	−9.70905e46	−0.0545216
$841$	−1.34982e48	−0.743264
$842$	1.89418e48	1.02275
$843$	−3.39435e46	−0.0179722
$844$	7.42903e47	0.385729
$845$	−1.35620e48	−0.690537
$846$	−4.14112e47	−0.206779
$847$	1.49432e48	0.731757
$848$	−3.34442e48	−1.60616
$849$	1.82736e48	0.860689
$850$	−4.07742e47	−0.188353
$851$	−1.71176e47	−0.0775542
$852$	6.87393e47	0.305458
$853$	1.39001e48	0.605840	0.302920	−	0.953016i	$-0.402038\pi$
$853$	1.39001e48	0.605840	0.302920	+	0.953016i	$0.402038\pi$
$854$	9.42904e48	4.03100
$855$	2.06259e47	0.0864914
$856$	4.03556e47	0.165992
$857$	7.18028e47	0.289706	0.144853	−	0.989453i	$-0.453729\pi$
$857$	7.18028e47	0.289706	0.144853	+	0.989453i	$0.453729\pi$
$858$	−3.77142e48	−1.49267
$859$	−4.63630e48	−1.80005	−0.900025	−	0.435838i	$-0.856452\pi$
$859$	−4.63630e48	−1.80005	−0.900025	+	0.435838i	$0.856452\pi$
$860$	−6.70930e47	−0.255536
$861$	−1.86238e48	−0.695850
$862$	−1.21132e48	−0.444006
$863$	4.88949e48	1.75827	0.879135	−	0.476572i	$-0.158121\pi$
$863$	4.88949e48	1.75827	0.879135	+	0.476572i	$0.158121\pi$
$864$	4.18302e48	1.47575
$865$	−1.62947e48	−0.564003
$866$	−5.15092e47	−0.174920
$867$	1.49197e48	0.497100
$868$	6.09040e48	1.99100
$869$	2.82035e48	0.904642
$870$	9.18410e47	0.289047
$871$	−5.64448e48	−1.74311
$872$	−1.33700e46	−0.00405143
$873$	−1.84098e46	−0.00547412
$874$	−4.41067e48	−1.28696
$875$	4.95029e47	0.141742
$876$	5.04018e48	1.41621
$877$	−7.15117e46	−0.0197189	−0.00985947	−	0.999951i	$-0.503138\pi$
$877$	−7.15117e46	−0.0197189	−0.00985947	+	0.999951i	$0.503138\pi$
$878$	−1.26531e48	−0.342403
$879$	−8.77410e47	−0.233016
$880$	−1.33017e48	−0.346692
$881$	−1.25763e48	−0.321698	−0.160849	−	0.986979i	$-0.551423\pi$
$881$	−1.25763e48	−0.321698	−0.160849	+	0.986979i	$0.551423\pi$
$882$	1.35104e48	0.339185
$883$	−6.34796e47	−0.156417	−0.0782083	−	0.996937i	$-0.524920\pi$
$883$	−6.34796e47	−0.156417	−0.0782083	+	0.996937i	$0.524920\pi$
$884$	4.19073e48	1.01351
$885$	−2.24644e47	−0.0533249
$886$	3.32378e47	0.0774418
$887$	−5.08980e47	−0.116402	−0.0582011	−	0.998305i	$-0.518536\pi$
$887$	−5.08980e47	−0.116402	−0.0582011	+	0.998305i	$0.518536\pi$
$888$	3.45198e46	0.00774916
$889$	−1.09309e49	−2.40866
$890$	2.41283e48	0.521905
$891$	2.80869e48	0.596377
$892$	−6.61425e48	−1.37867
$893$	−5.40416e48	−1.10581
$894$	5.89517e47	0.118421
$895$	−1.55587e47	−0.0306827
$896$	1.37256e48	0.265735
$897$	−5.91748e48	−1.12476
$898$	9.41686e48	1.75730
$899$	3.69753e48	0.677450
$900$	−1.68355e47	−0.0302847
$901$	5.81949e48	1.02784
$902$	−2.82476e48	−0.489862
$903$	5.18319e48	0.882571
$904$	6.03981e47	0.100982
$905$	4.91565e48	0.807011
$906$	−5.96278e47	−0.0961244
$907$	4.07509e47	0.0645085	0.0322543	−	0.999480i	$-0.489731\pi$
$907$	4.07509e47	0.0645085	0.0322543	+	0.999480i	$0.489731\pi$
$908$	−2.97207e48	−0.462001
$909$	−3.84385e47	−0.0586763
$910$	−1.05023e49	−1.57434
$911$	−5.53521e48	−0.814855	−0.407428	−	0.913237i	$-0.633574\pi$
$911$	−5.53521e48	−0.814855	−0.407428	+	0.913237i	$0.633574\pi$
$912$	8.03430e48	1.16154
$913$	1.43790e48	0.204155
$914$	−1.52832e49	−2.13109
$915$	5.46262e48	0.748089
$916$	4.33780e48	0.583438
$917$	−1.80623e49	−2.38605
$918$	−7.71928e48	−1.00155
$919$	5.10117e48	0.650075	0.325038	−	0.945701i	$-0.394623\pi$
$919$	5.10117e48	0.650075	0.325038	+	0.945701i	$0.394623\pi$
$920$	−2.31059e47	−0.0289217
$921$	−4.06732e48	−0.500063
$922$	2.12687e49	2.56850
$923$	−4.77219e48	−0.566095
$924$	−8.58731e48	−1.00062
$925$	−1.76004e47	−0.0201458
$926$	7.54202e48	0.848021
$927$	1.00715e48	0.111244
$928$	−6.47990e48	−0.703116
$929$	4.04144e48	0.430801	0.215401	−	0.976526i	$-0.430894\pi$
$929$	4.04144e48	0.430801	0.215401	+	0.976526i	$0.430894\pi$
$930$	7.28329e48	0.762709
$931$	1.76311e49	1.81388
$932$	4.52180e48	0.457035
$933$	2.59601e48	0.257786
$934$	−1.27952e49	−1.24831
$935$	2.31458e48	0.221861
$936$	−2.29237e47	−0.0215890
$937$	4.94756e48	0.457812	0.228906	−	0.973448i	$-0.426485\pi$
$937$	4.94756e48	0.457812	0.228906	+	0.973448i	$0.426485\pi$
$938$	−2.65292e49	−2.41200
$939$	1.72756e49	1.54331
$940$	4.41103e48	0.387196
$941$	−1.04427e49	−0.900712	−0.450356	−	0.892849i	$-0.648703\pi$
$941$	−1.04427e49	−0.900712	−0.450356	+	0.892849i	$0.648703\pi$
$942$	6.91913e48	0.586424
$943$	−4.43214e48	−0.369122
$944$	1.68093e48	0.137566
$945$	9.37177e48	0.753697
$946$	7.86161e48	0.621309
$947$	1.15016e49	0.893271	0.446636	−	0.894716i	$-0.352622\pi$
$947$	1.15016e49	0.893271	0.446636	+	0.894716i	$0.352622\pi$
$948$	1.39045e49	1.06125
$949$	−3.49912e49	−2.62462
$950$	−4.53507e48	−0.334306
$951$	−1.74849e49	−1.26673
$952$	−1.26414e48	−0.0900091
$953$	8.00029e48	0.559852	0.279926	−	0.960022i	$-0.409690\pi$
$953$	8.00029e48	0.559852	0.279926	+	0.960022i	$0.409690\pi$
$954$	4.95990e48	0.341134
$955$	4.41300e48	0.298317
$956$	3.75718e48	0.249636
$957$	−5.21343e48	−0.340468
$958$	1.87601e49	1.20422
$959$	4.67571e49	2.95013
$960$	−5.78522e48	−0.358793
$961$	1.29192e49	0.787586
$962$	3.73400e48	0.223762
$963$	−5.40596e48	−0.318448
$964$	−6.91565e48	−0.400463
$965$	−7.25487e48	−0.412980
$966$	−2.78123e49	−1.55638
$967$	2.45742e49	1.35190	0.675948	−	0.736949i	$-0.263734\pi$
$967$	2.45742e49	1.35190	0.675948	+	0.736949i	$0.263734\pi$
$968$	−7.17159e47	−0.0387857
$969$	−1.39801e49	−0.743309
$970$	4.04781e47	0.0211586
$971$	−3.60689e49	−1.85360	−0.926800	−	0.375556i	$-0.877452\pi$
$971$	−3.60689e49	−1.85360	−0.926800	+	0.375556i	$0.877452\pi$
$972$	−5.93219e48	−0.299724
$973$	1.70947e49	0.849179
$974$	−3.87592e48	−0.189301
$975$	−6.08438e48	−0.292173
$976$	−4.08749e49	−1.92990
$977$	1.33484e49	0.619683	0.309841	−	0.950788i	$-0.399724\pi$
$977$	1.33484e49	0.619683	0.309841	+	0.950788i	$0.399724\pi$
$978$	−3.97778e49	−1.81572
$979$	−1.36966e49	−0.614751
$980$	−1.43910e49	−0.635127
$981$	1.79101e47	0.00777250
$982$	3.42300e49	1.46072
$983$	−1.85345e49	−0.777765	−0.388882	−	0.921287i	$-0.627139\pi$
$983$	−1.85345e49	−0.777765	−0.388882	+	0.921287i	$0.627139\pi$
$984$	8.93798e47	0.0368825
$985$	−4.39400e48	−0.178304
$986$	1.19579e49	0.477185
$987$	−3.40769e49	−1.33730
$988$	4.66110e49	1.79887
$989$	1.23351e49	0.468171
$990$	1.97270e48	0.0736342
$991$	−1.48569e49	−0.545398	−0.272699	−	0.962099i	$-0.587916\pi$
$991$	−1.48569e49	−0.545398	−0.272699	+	0.962099i	$0.587916\pi$
$992$	−5.13878e49	−1.85531
$993$	−2.71535e49	−0.964192
$994$	−2.24294e49	−0.783325
$995$	1.67712e49	0.576079
$996$	7.08890e48	0.239497
$997$	−2.13570e49	−0.709694	−0.354847	−	0.934924i	$-0.615467\pi$
$997$	−2.13570e49	−0.709694	−0.354847	+	0.934924i	$0.615467\pi$
$998$	6.89789e49	2.25456
$999$	−3.33207e48	−0.107123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.a.1.1	✓	5
5.2	odd	4		25.34.b.b.24.2		10
5.3	odd	4		25.34.b.b.24.9		10
5.4	even	2		25.34.a.b.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.1	✓	5	1.1	even	1	trivial
25.34.a.b.1.5		5	5.4	even	2
25.34.b.b.24.2		10	5.2	odd	4
25.34.b.b.24.9		10	5.3	odd	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +O(q^{10})\)	\(q-129081. q^{2} -6.82881e7 q^{3} +8.07187e9 q^{4} -1.52588e11 q^{5} +8.81467e12 q^{6} -1.39338e14 q^{7} +6.68716e13 q^{8} -8.95800e14 q^{9} +1.96961e16 q^{10} -1.11807e17 q^{11} -5.51213e17 q^{12} +3.82676e18 q^{13} +1.79859e19 q^{14} +1.04199e19 q^{15} -7.79687e19 q^{16} +1.35670e20 q^{17} +1.15630e20 q^{18} +1.50898e21 q^{19} -1.23167e21 q^{20} +9.51513e21 q^{21} +1.44321e22 q^{22} +2.26444e22 q^{23} -4.56653e21 q^{24} +2.32831e22 q^{25} -4.93961e23 q^{26} +4.40790e23 q^{27} -1.12472e24 q^{28} -6.82827e23 q^{29} -1.34501e24 q^{30} -5.41504e24 q^{31} +9.48983e24 q^{32} +7.63507e24 q^{33} -1.75124e25 q^{34} +2.12613e25 q^{35} -7.23078e24 q^{36} -7.55931e24 q^{37} -1.94780e26 q^{38} -2.61322e26 q^{39} -1.02038e25 q^{40} -1.95728e26 q^{41} -1.22822e27 q^{42} +5.44732e26 q^{43} -9.02490e26 q^{44} +1.36688e26 q^{45} -2.92295e27 q^{46} -3.58134e27 q^{47} +5.32433e27 q^{48} +1.16841e28 q^{49} -3.00539e27 q^{50} -9.26465e27 q^{51} +3.08891e28 q^{52} +4.28944e28 q^{53} -5.68974e28 q^{54} +1.70604e28 q^{55} -9.31777e27 q^{56} -1.03045e29 q^{57} +8.81397e28 q^{58} -2.15590e28 q^{59} +8.41084e28 q^{60} +5.24247e29 q^{61} +6.98976e29 q^{62} +1.24819e29 q^{63} -5.55207e29 q^{64} -5.83917e29 q^{65} -9.85539e29 q^{66} -1.47500e30 q^{67} +1.09511e30 q^{68} -1.54634e30 q^{69} -2.74442e30 q^{70} -1.24706e30 q^{71} -5.99036e28 q^{72} -9.14380e30 q^{73} +9.75760e29 q^{74} -1.58996e30 q^{75} +1.21803e31 q^{76} +1.55789e31 q^{77} +3.37316e31 q^{78} -2.52252e31 q^{79} +1.18971e31 q^{80} -2.51209e31 q^{81} +2.52647e31 q^{82} -1.28605e31 q^{83} +7.68050e31 q^{84} -2.07016e31 q^{85} -7.03143e31 q^{86} +4.66289e31 q^{87} -7.47670e30 q^{88} +1.22503e32 q^{89} -1.76438e31 q^{90} -5.33214e32 q^{91} +1.82783e32 q^{92} +3.69782e32 q^{93} +4.62282e32 q^{94} -2.30252e32 q^{95} -6.48042e32 q^{96} +2.05513e31 q^{97} -1.50819e33 q^{98} +1.00156e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q + 30472 * q^2 - 14988714 * q^3 + 1141311360 * q^4 - 762939453125 * q^5 + 12925063115760 * q^6 - 65452561787158 * q^7 + 155610638035200 * q^8 + 14541250990408965 * q^9	\( 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q + 30472 * q^2 - 14988714 * q^3 + 1141311360 * q^4 - 762939453125 * q^5 + 12925063115760 * q^6 - 65452561787158 * q^7 + 155610638035200 * q^8 + 14541250990408965 * q^9 - 4649658203125000 * q^10 - 287801801877976640 * q^11 - 405379955363513088 * q^12 + 2397201150889907466 * q^13 + 11676449916272482320 * q^14 + 2287096252441406250 * q^15 - 89180089543245957120 * q^16 - 308725634324001653918 * q^17 + 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 174150292968750000000 * q^20 - 10535115771712805413140 * q^21 - 13757888128329419319296 * q^22 + 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 + 116415321826934814453125 * q^25 - 424902360762721464761840 * q^26 + 679342131249712739644500 * q^27 - 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1972208117028808593750000 * q^30 - 1336046479411821372201940 * q^31 - 813043271605502937899008 * q^32 - 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 + 9987268339104919433593750 * q^35 - 180374200000978588488558720 * q^36 - 142836045294254023962738038 * q^37 - 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 23744299016601562500000000 * q^40 - 1325620030754525933329256290 * q^41 - 2645870671030939362357320736 * q^42 - 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2218818815675196075439453125 * q^45 - 2874649720834424257835685840 * q^46 - 7724956189479550762134222398 * q^47 - 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 709481537342071533203125000 * q^50 + 7346719218915268753088875260 * q^51 + 48963787841701555176191049472 * q^52 + 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 43915069866634619140625000000 * q^55 + 144880509244845944794630156800 * q^56 + 208512654554635835530896805800 * q^57 + 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 61856072290575117187500000000 * q^60 + 742889693167672203496619446410 * q^61 + 532537079706659761431026425824 * q^62 - 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 365783867018113321838378906250 * q^65 - 3327517517031282146197646561280 * q^66 - 3757683664783078488809531637718 * q^67 + 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 1781684862712475939941406250000 * q^70 - 5502085339682331744817794354940 * q^71 - 15971664273931445780329968326400 * q^72 - 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 - 348983192816376686096191406250 * q^75 + 7186339982587317558706196185600 * q^76 + 47237885671577674597763242652544 * q^77 + 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 13607801749152520312500000000000 * q^80 + 78583804836302041006582647314505 * q^81 + 27306575776891610455800103348784 * q^82 + 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 47107793323364510180358886718750 * q^85 + 65486114707827974097903540464560 * q^86 + 137286065258860195168416991536900 * q^87 + 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 82066451889727956368408203125000 * q^90 - 268937084803738847432203207735340 * q^91 - 697440932909638690403668496563968 * q^92 - 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 140131334258293754196166992187500 * q^95 - 344518603172836645970889894051840 * q^96 - 867959773515074594808067717684598 * q^97 - 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * q^99

Introduction

L-functions

Modular forms

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