LMFDB - Embedded newform 5.34.a.a.1.3

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			1.3
Root			$117.007$ 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)

$f(q)$	$=$	$q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} +O(q^{10})$	\(q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} -8.58760e14 q^{10} +9.39806e16 q^{11} +1.06640e18 q^{12} +9.95093e17 q^{13} +3.94836e17 q^{14} +1.90132e19 q^{15} +7.29717e19 q^{16} -2.59085e20 q^{17} +5.60955e19 q^{18} -1.31117e21 q^{19} +1.30589e21 q^{20} -8.74176e21 q^{21} +5.28920e20 q^{22} +5.44854e22 q^{23} +1.20255e22 q^{24} +2.32831e22 q^{25} +5.60036e21 q^{26} -5.49284e23 q^{27} -6.00413e23 q^{28} -9.77301e23 q^{29} +1.07006e23 q^{30} +6.82815e24 q^{31} +1.23969e24 q^{32} -1.17104e25 q^{33} -1.45812e24 q^{34} -1.07050e25 q^{35} -8.53025e25 q^{36} -7.50351e25 q^{37} -7.37925e24 q^{38} -1.23993e26 q^{39} +1.47262e25 q^{40} -2.94248e25 q^{41} -4.91984e25 q^{42} -1.00868e27 q^{43} -8.04311e26 q^{44} -1.52088e27 q^{45} +3.06642e26 q^{46} +1.91365e27 q^{47} -9.09262e27 q^{48} -2.80913e27 q^{49} +1.31036e26 q^{50} +3.22832e28 q^{51} -8.51627e27 q^{52} +4.33344e28 q^{53} -3.09135e27 q^{54} -1.43403e28 q^{55} -6.77072e27 q^{56} +1.63379e29 q^{57} -5.50022e27 q^{58} -1.21137e29 q^{59} -1.62720e29 q^{60} +4.03792e29 q^{61} +3.84287e28 q^{62} +6.99264e29 q^{63} -6.19846e29 q^{64} -1.51839e29 q^{65} -6.59060e28 q^{66} -1.33311e30 q^{67} +2.21732e30 q^{68} -6.78914e30 q^{69} -6.02472e28 q^{70} -4.10877e30 q^{71} -9.61937e29 q^{72} +8.64070e30 q^{73} -4.22295e29 q^{74} -2.90118e30 q^{75} +1.12214e31 q^{76} +6.59330e30 q^{77} -6.97831e29 q^{78} -1.76553e31 q^{79} -1.11346e31 q^{80} +1.30347e31 q^{81} -1.65602e29 q^{82} -6.43615e30 q^{83} +7.48143e31 q^{84} +3.95332e31 q^{85} -5.67680e30 q^{86} +1.21776e32 q^{87} -9.07003e30 q^{88} +1.32441e32 q^{89} -8.55950e30 q^{90} +6.98117e31 q^{91} -4.66300e32 q^{92} -8.50820e32 q^{93} +1.07700e31 q^{94} +2.00069e32 q^{95} -1.54472e32 q^{96} +2.90988e32 q^{97} -1.58097e31 q^{98} +9.36730e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5627.97	0.0607235	0.0303618	−	0.999539i	$-0.490334\pi$
$2$	5627.97	0.0607235	0.0303618	+	0.999539i	$0.490334\pi$
$3$	−1.24605e8	−1.67122	−0.835610	−	0.549323i	$-0.814886\pi$
$3$	−1.24605e8	−1.67122	−0.835610	+	0.549323i	$0.814886\pi$
$4$	−8.55826e9	−0.996313
$5$	−1.52588e11	−0.447214
$5$	−1.52588e11	−0.447214
$6$	−7.01272e11	−0.101482
$7$	7.01560e13	0.797897	0.398949	−	0.916973i	$-0.369375\pi$
$7$	7.01560e13	0.797897	0.398949	+	0.916973i	$0.369375\pi$
$8$	−9.65096e13	−0.121223
$9$	9.96727e15	1.79298
$10$	−8.58760e14	−0.0271564
$11$	9.39806e16	0.616679	0.308339	−	0.951276i	$-0.400227\pi$
$11$	9.39806e16	0.616679	0.308339	+	0.951276i	$0.400227\pi$
$12$	1.06640e18	1.66506
$13$	9.95093e17	0.414761	0.207381	−	0.978260i	$-0.433506\pi$
$13$	9.95093e17	0.414761	0.207381	+	0.978260i	$0.433506\pi$
$14$	3.94836e17	0.0484511
$15$	1.90132e19	0.747392
$16$	7.29717e19	0.988952
$17$	−2.59085e20	−1.29132	−0.645662	−	0.763624i	$-0.723418\pi$
$17$	−2.59085e20	−1.29132	−0.645662	+	0.763624i	$0.723418\pi$
$18$	5.60955e19	0.108876
$19$	−1.31117e21	−1.04286	−0.521430	−	0.853294i	$-0.674601\pi$
$19$	−1.31117e21	−1.04286	−0.521430	+	0.853294i	$0.674601\pi$
$20$	1.30589e21	0.445565
$21$	−8.74176e21	−1.33346
$22$	5.28920e20	0.0374469
$23$	5.44854e22	1.85255	0.926277	−	0.376843i	$-0.122990\pi$
$23$	5.44854e22	1.85255	0.926277	+	0.376843i	$0.122990\pi$
$24$	1.20255e22	0.202591
$25$	2.32831e22	0.200000
$26$	5.60036e21	0.0251858
$27$	−5.49284e23	−1.32524
$28$	−6.00413e23	−0.794955
$29$	−9.77301e23	−0.725206	−0.362603	−	0.931944i	$-0.618112\pi$
$29$	−9.77301e23	−0.725206	−0.362603	+	0.931944i	$0.618112\pi$
$30$	1.07006e23	0.0453843
$31$	6.82815e24	1.68591	0.842957	−	0.537981i	$-0.180813\pi$
$31$	6.82815e24	1.68591	0.842957	+	0.537981i	$0.180813\pi$
$32$	1.23969e24	0.181276
$33$	−1.17104e25	−1.03061
$34$	−1.45812e24	−0.0784137
$35$	−1.07050e25	−0.356831
$36$	−8.53025e25	−1.78637
$37$	−7.50351e25	−0.999852	−0.499926	−	0.866068i	$-0.666640\pi$
$37$	−7.50351e25	−0.999852	−0.499926	+	0.866068i	$0.666640\pi$
$38$	−7.37925e24	−0.0633262
$39$	−1.23993e26	−0.693158
$40$	1.47262e25	0.0542126
$41$	−2.94248e25	−0.0720741	−0.0360371	−	0.999350i	$-0.511473\pi$
$41$	−2.94248e25	−0.0720741	−0.0360371	+	0.999350i	$0.511473\pi$
$42$	−4.91984e25	−0.0809725
$43$	−1.00868e27	−1.12596	−0.562979	−	0.826471i	$-0.690345\pi$
$43$	−1.00868e27	−1.12596	−0.562979	+	0.826471i	$0.690345\pi$
$44$	−8.04311e26	−0.614405
$45$	−1.52088e27	−0.801844
$46$	3.06642e26	0.112494
$47$	1.91365e27	0.492321	0.246160	−	0.969229i	$-0.420831\pi$
$47$	1.91365e27	0.492321	0.246160	+	0.969229i	$0.420831\pi$
$48$	−9.09262e27	−1.65276
$49$	−2.80913e27	−0.363360
$50$	1.31036e26	0.0121447
$51$	3.22832e28	2.15809
$52$	−8.51627e27	−0.413232
$53$	4.33344e28	1.53561	0.767804	−	0.640684i	$-0.221349\pi$
$53$	4.33344e28	1.53561	0.767804	+	0.640684i	$0.221349\pi$
$54$	−3.09135e27	−0.0804733
$55$	−1.43403e28	−0.275787
$56$	−6.77072e27	−0.0967236
$57$	1.63379e29	1.74285
$58$	−5.50022e27	−0.0440371
$59$	−1.21137e29	−0.731507	−0.365754	−	0.930712i	$-0.619189\pi$
$59$	−1.21137e29	−0.731507	−0.365754	+	0.930712i	$0.619189\pi$
$60$	−1.62720e29	−0.744637
$61$	4.03792e29	1.40674	0.703372	−	0.710822i	$-0.251677\pi$
$61$	4.03792e29	1.40674	0.703372	+	0.710822i	$0.251677\pi$
$62$	3.84287e28	0.102375
$63$	6.99264e29	1.43061
$64$	−6.19846e29	−0.977944
$65$	−1.51839e29	−0.185487
$66$	−6.59060e28	−0.0625821
$67$	−1.33311e30	−0.987713	−0.493856	−	0.869543i	$-0.664413\pi$
$67$	−1.33311e30	−0.987713	−0.493856	+	0.869543i	$0.664413\pi$
$68$	2.21732e30	1.28656
$69$	−6.78914e30	−3.09603
$70$	−6.02472e28	−0.0216680
$71$	−4.10877e30	−1.16936	−0.584681	−	0.811263i	$-0.698780\pi$
$71$	−4.10877e30	−1.16936	−0.584681	+	0.811263i	$0.698780\pi$
$72$	−9.61937e29	−0.217350
$73$	8.64070e30	1.55497	0.777484	−	0.628902i	$-0.216495\pi$
$73$	8.64070e30	1.55497	0.777484	+	0.628902i	$0.216495\pi$
$74$	−4.22295e29	−0.0607146
$75$	−2.90118e30	−0.334244
$76$	1.12214e31	1.03901
$77$	6.59330e30	0.492046
$78$	−6.97831e29	−0.0420910
$79$	−1.76553e31	−0.863033	−0.431516	−	0.902105i	$-0.642021\pi$
$79$	−1.76553e31	−0.863033	−0.431516	+	0.902105i	$0.642021\pi$
$80$	−1.11346e31	−0.442273
$81$	1.30347e31	0.421790
$82$	−1.65602e29	−0.00437659
$83$	−6.43615e30	−0.139264	−0.0696318	−	0.997573i	$-0.522182\pi$
$83$	−6.43615e30	−0.139264	−0.0696318	+	0.997573i	$0.522182\pi$
$84$	7.48143e31	1.32855
$85$	3.95332e31	0.577497
$86$	−5.67680e30	−0.0683722
$87$	1.21776e32	1.21198
$88$	−9.07003e30	−0.0747558
$89$	1.32441e32	0.905911	0.452956	−	0.891533i	$-0.350370\pi$
$89$	1.32441e32	0.905911	0.452956	+	0.891533i	$0.350370\pi$
$90$	−8.55950e30	−0.0486908
$91$	6.98117e31	0.330937
$92$	−4.66300e32	−1.84572
$93$	−8.50820e32	−2.81753
$94$	1.07700e31	0.0298955
$95$	2.00069e32	0.466381
$96$	−1.54472e32	−0.302952
$97$	2.90988e32	0.480996	0.240498	−	0.970650i	$-0.422689\pi$
$97$	2.90988e32	0.480996	0.240498	+	0.970650i	$0.422689\pi$
$98$	−1.58097e31	−0.0220645
$99$	9.36730e32	1.10569
$100$	−1.99263e32	−0.199263
$101$	−2.11490e33	−1.79468	−0.897341	−	0.441338i	$-0.854504\pi$
$101$	−2.11490e33	−1.79468	−0.897341	+	0.441338i	$0.854504\pi$
$102$	1.81689e32	0.131047
$103$	9.19643e32	0.564684	0.282342	−	0.959314i	$-0.408889\pi$
$103$	9.19643e32	0.564684	0.282342	+	0.959314i	$0.408889\pi$
$104$	−9.60360e31	−0.0502787
$105$	1.33389e33	0.596342
$106$	2.43885e32	0.0932476
$107$	−3.10653e33	−1.01729	−0.508644	−	0.860977i	$-0.669853\pi$
$107$	−3.10653e33	−1.01729	−0.508644	+	0.860977i	$0.669853\pi$
$108$	4.70091e33	1.32035
$109$	−4.33103e33	−1.04485	−0.522425	−	0.852685i	$-0.674972\pi$
$109$	−4.33103e33	−1.04485	−0.522425	+	0.852685i	$0.674972\pi$
$110$	−8.07069e31	−0.0167468
$111$	9.34972e33	1.67097
$112$	5.11940e33	0.789082
$113$	1.60843e33	0.214096	0.107048	−	0.994254i	$-0.465860\pi$
$113$	1.60843e33	0.214096	0.107048	+	0.994254i	$0.465860\pi$
$114$	9.19490e32	0.105832
$115$	−8.31381e33	−0.828487
$116$	8.36400e33	0.722532
$117$	9.91836e33	0.743658
$118$	−6.81756e32	−0.0444197
$119$	−1.81764e34	−1.03034
$120$	−1.83495e33	−0.0906013
$121$	−1.43928e34	−0.619707
$122$	2.27253e33	0.0854225
$123$	3.66646e33	0.120452
$124$	−5.84371e34	−1.67970
$125$	−3.55271e33	−0.0894427
$126$	3.93544e33	0.0868718
$127$	−6.65683e34	−1.28975	−0.644876	−	0.764287i	$-0.723091\pi$
$127$	−6.65683e34	−1.28975	−0.644876	+	0.764287i	$0.723091\pi$
$128$	−1.41374e34	−0.240660
$129$	1.25686e35	1.88173
$130$	−8.54547e32	−0.0112634
$131$	−3.69750e34	−0.429469	−0.214734	−	0.976672i	$-0.568889\pi$
$131$	−3.69750e34	−0.429469	−0.214734	+	0.976672i	$0.568889\pi$
$132$	1.00221e35	1.02681
$133$	−9.19867e34	−0.832095
$134$	−7.50269e33	−0.0599774
$135$	8.38140e34	0.592665
$136$	2.50042e34	0.156538
$137$	−1.76237e34	−0.0977705	−0.0488853	−	0.998804i	$-0.515567\pi$
$137$	−1.76237e34	−0.0977705	−0.0488853	+	0.998804i	$0.515567\pi$
$138$	−3.82091e34	−0.188002
$139$	1.00540e35	0.439130	0.219565	−	0.975598i	$-0.429536\pi$
$139$	1.00540e35	0.439130	0.219565	+	0.975598i	$0.429536\pi$
$140$	9.16158e34	0.355515
$141$	−2.38450e35	−0.822776
$142$	−2.31240e34	−0.0710078
$143$	9.35195e34	0.255775
$144$	7.27329e35	1.77317
$145$	1.49124e35	0.324322
$146$	4.86296e34	0.0944232
$147$	3.50031e35	0.607254
$148$	6.42170e35	0.996165
$149$	−1.14557e36	−1.59019	−0.795093	−	0.606487i	$-0.792578\pi$
$149$	−1.14557e36	−1.59019	−0.795093	+	0.606487i	$0.792578\pi$
$150$	−1.63278e34	−0.0202965
$151$	−6.40257e35	−0.713239	−0.356619	−	0.934250i	$-0.616071\pi$
$151$	−6.40257e35	−0.713239	−0.356619	+	0.934250i	$0.616071\pi$
$152$	1.26541e35	0.126419
$153$	−2.58237e36	−2.31531
$154$	3.71069e34	0.0298788
$155$	−1.04189e36	−0.753964
$156$	1.06117e36	0.690602
$157$	1.01110e36	0.592172	0.296086	−	0.955161i	$-0.404319\pi$
$157$	1.01110e36	0.592172	0.296086	+	0.955161i	$0.404319\pi$
$158$	−9.93633e34	−0.0524064
$159$	−5.39967e36	−2.56634
$160$	−1.89162e35	−0.0810690
$161$	3.82248e36	1.47815
$162$	7.33587e34	0.0256126
$163$	4.84374e36	1.52786	0.763932	−	0.645296i	$-0.223266\pi$
$163$	4.84374e36	1.52786	0.763932	+	0.645296i	$0.223266\pi$
$164$	2.51825e35	0.0718083
$165$	1.78687e36	0.460901
$166$	−3.62225e34	−0.00845658
$167$	1.75726e36	0.371548	0.185774	−	0.982593i	$-0.440521\pi$
$167$	1.75726e36	0.371548	0.185774	+	0.982593i	$0.440521\pi$
$168$	8.43664e35	0.161647
$169$	−4.76592e36	−0.827973
$170$	2.22492e35	0.0350677
$171$	−1.30688e37	−1.86982
$172$	8.63252e36	1.12181
$173$	1.04480e36	0.123388	0.0616942	−	0.998095i	$-0.480350\pi$
$173$	1.04480e36	0.123388	0.0616942	+	0.998095i	$0.480350\pi$
$174$	6.85354e35	0.0735957
$175$	1.63345e36	0.159579
$176$	6.85793e36	0.609866
$177$	1.50942e37	1.22251
$178$	7.45372e35	0.0550101
$179$	6.89417e36	0.463881	0.231941	−	0.972730i	$-0.425492\pi$
$179$	6.89417e36	0.463881	0.231941	+	0.972730i	$0.425492\pi$
$180$	1.30161e37	0.798887
$181$	2.73403e36	0.153146	0.0765732	−	0.997064i	$-0.475602\pi$
$181$	2.73403e36	0.153146	0.0765732	+	0.997064i	$0.475602\pi$
$182$	3.92898e35	0.0200957
$183$	−5.03143e37	−2.35098
$184$	−5.25836e36	−0.224572
$185$	1.14494e37	0.447148
$186$	−4.78839e36	−0.171091
$187$	−2.43490e37	−0.796332
$188$	−1.63775e37	−0.490505
$189$	−3.85355e37	−1.05741
$190$	1.12598e36	0.0283203
$191$	−7.33764e37	−1.69241	−0.846206	−	0.532856i	$-0.821119\pi$
$191$	−7.33764e37	−1.69241	−0.846206	+	0.532856i	$0.821119\pi$
$192$	7.72357e37	1.63436
$193$	−3.39286e37	−0.658978	−0.329489	−	0.944159i	$-0.606876\pi$
$193$	−3.39286e37	−0.658978	−0.329489	+	0.944159i	$0.606876\pi$
$194$	1.63767e36	0.0292078
$195$	1.89199e37	0.309990
$196$	2.40413e37	0.362020
$197$	1.22669e38	1.69841	0.849205	−	0.528063i	$-0.177081\pi$
$197$	1.22669e38	1.69841	0.849205	+	0.528063i	$0.177081\pi$
$198$	5.27189e36	0.0671415
$199$	−4.90395e37	−0.574738	−0.287369	−	0.957820i	$-0.592781\pi$
$199$	−4.90395e37	−0.574738	−0.287369	+	0.957820i	$0.592781\pi$
$200$	−2.24704e36	−0.0242446
$201$	1.66111e38	1.65069
$202$	−1.19026e37	−0.108979
$203$	−6.85635e37	−0.578640
$204$	−2.76288e38	−2.15013
$205$	4.48986e36	0.0322325
$206$	5.17573e36	0.0342896
$207$	5.43071e38	3.32159
$208$	7.26137e37	0.410179
$209$	−1.23225e38	−0.643110
$210$	7.50708e36	0.0362120
$211$	−2.26597e38	−1.01063	−0.505316	−	0.862934i	$-0.668624\pi$
$211$	−2.26597e38	−1.01063	−0.505316	+	0.862934i	$0.668624\pi$
$212$	−3.70867e38	−1.52995
$213$	5.11972e38	1.95426
$214$	−1.74835e37	−0.0617733
$215$	1.53912e38	0.503544
$216$	5.30111e37	0.160650
$217$	4.79036e38	1.34519
$218$	−2.43749e37	−0.0634469
$219$	−1.07667e39	−2.59870
$220$	1.22728e38	0.274770
$221$	−2.57814e38	−0.535591
$222$	5.26200e37	0.101467
$223$	−7.70736e38	−1.37999	−0.689994	−	0.723815i	$-0.742387\pi$
$223$	−7.70736e38	−1.37999	−0.689994	+	0.723815i	$0.742387\pi$
$224$	8.69719e37	0.144639
$225$	2.32069e38	0.358595
$226$	9.05221e36	0.0130007
$227$	3.75970e38	0.502026	0.251013	−	0.967984i	$-0.419236\pi$
$227$	3.75970e38	0.502026	0.251013	+	0.967984i	$0.419236\pi$
$228$	−1.39824e39	−1.73642
$229$	8.87055e38	1.02486	0.512431	−	0.858729i	$-0.328745\pi$
$229$	8.87055e38	1.02486	0.512431	+	0.858729i	$0.328745\pi$
$230$	−4.67899e37	−0.0503087
$231$	−8.21557e38	−0.822318
$232$	9.43189e37	0.0879118
$233$	−9.06227e38	−0.786800	−0.393400	−	0.919367i	$-0.628701\pi$
$233$	−9.06227e38	−0.786800	−0.393400	+	0.919367i	$0.628701\pi$
$234$	5.58203e37	0.0451575
$235$	−2.92000e38	−0.220173
$236$	1.03672e39	0.728810
$237$	2.19993e39	1.44232
$238$	−1.02296e38	−0.0625661
$239$	2.67931e39	1.52918	0.764589	−	0.644518i	$-0.222942\pi$
$239$	2.67931e39	1.52918	0.764589	+	0.644518i	$0.222942\pi$
$240$	1.38742e39	0.739135
$241$	4.69772e38	0.233672	0.116836	−	0.993151i	$-0.462725\pi$
$241$	4.69772e38	0.233672	0.116836	+	0.993151i	$0.462725\pi$
$242$	−8.10022e37	−0.0376308
$243$	1.42932e39	0.620335
$244$	−3.45575e39	−1.40156
$245$	4.28640e38	0.162499
$246$	2.06348e37	0.00731425
$247$	−1.30474e39	−0.432538
$248$	−6.58982e38	−0.204372
$249$	8.01974e38	0.232740
$250$	−1.99946e37	−0.00543128
$251$	−1.31521e38	−0.0334486	−0.0167243	−	0.999860i	$-0.505324\pi$
$251$	−1.31521e38	−0.0334486	−0.0167243	+	0.999860i	$0.505324\pi$
$252$	−5.98448e39	−1.42534
$253$	5.12057e39	1.14243
$254$	−3.74645e38	−0.0783183
$255$	−4.92603e39	−0.965125
$256$	5.24487e39	0.963330
$257$	4.96495e39	0.855104	0.427552	−	0.903991i	$-0.359376\pi$
$257$	4.96495e39	0.855104	0.427552	+	0.903991i	$0.359376\pi$
$258$	7.07356e38	0.114265
$259$	−5.26416e39	−0.797779
$260$	1.29948e39	0.184803
$261$	−9.74103e39	−1.30028
$262$	−2.08094e38	−0.0260789
$263$	6.41705e39	0.755206	0.377603	−	0.925968i	$-0.376748\pi$
$263$	6.41705e39	0.755206	0.377603	+	0.925968i	$0.376748\pi$
$264$	1.13017e39	0.124933
$265$	−6.61230e39	−0.686745
$266$	−5.17699e38	−0.0505278
$267$	−1.65027e40	−1.51398
$268$	1.14091e40	0.984071
$269$	−1.97544e39	−0.160233	−0.0801164	−	0.996786i	$-0.525529\pi$
$269$	−1.97544e39	−0.160233	−0.0801164	+	0.996786i	$0.525529\pi$
$270$	4.71703e38	0.0359887
$271$	−1.48531e40	−1.06616	−0.533082	−	0.846063i	$-0.678966\pi$
$271$	−1.48531e40	−1.06616	−0.533082	+	0.846063i	$0.678966\pi$
$272$	−1.89059e40	−1.27706
$273$	−8.69887e39	−0.553069
$274$	−9.91858e37	−0.00593697
$275$	2.18816e39	0.123336
$276$	5.81032e40	3.08461
$277$	6.46494e39	0.323332	0.161666	−	0.986846i	$-0.448313\pi$
$277$	6.46494e39	0.323332	0.161666	+	0.986846i	$0.448313\pi$
$278$	5.65835e38	0.0266655
$279$	6.80581e40	3.02281
$280$	1.03313e39	0.0432561
$281$	−1.46554e40	−0.578554	−0.289277	−	0.957245i	$-0.593415\pi$
$281$	−1.46554e40	−0.578554	−0.289277	+	0.957245i	$0.593415\pi$
$282$	−1.34199e39	−0.0499619
$283$	−2.68962e40	−0.944529	−0.472265	−	0.881457i	$-0.656563\pi$
$283$	−2.68962e40	−0.944529	−0.472265	+	0.881457i	$0.656563\pi$
$284$	3.51639e40	1.16505
$285$	−2.49296e40	−0.779426
$286$	5.26325e38	0.0155315
$287$	−2.06432e39	−0.0575077
$288$	1.23564e40	0.325023
$289$	2.68705e40	0.667516
$290$	8.39268e38	0.0196940
$291$	−3.62584e40	−0.803850
$292$	−7.39493e40	−1.54923
$293$	−4.27715e40	−0.846912	−0.423456	−	0.905917i	$-0.639183\pi$
$293$	−4.27715e40	−0.846912	−0.423456	+	0.905917i	$0.639183\pi$
$294$	1.96997e39	0.0368746
$295$	1.84840e40	0.327140
$296$	7.24160e39	0.121205
$297$	−5.16220e40	−0.817248
$298$	−6.44723e39	−0.0965617
$299$	5.42181e40	0.768368
$300$	2.48290e40	0.333012
$301$	−7.07647e40	−0.898399
$302$	−3.60335e39	−0.0433104
$303$	2.63527e41	2.99931
$304$	−9.56787e40	−1.03134
$305$	−6.16137e40	−0.629115
$306$	−1.45335e40	−0.140594
$307$	−5.26223e40	−0.482377	−0.241189	−	0.970478i	$-0.577537\pi$
$307$	−5.26223e40	−0.482377	−0.241189	+	0.970478i	$0.577537\pi$
$308$	−5.64272e40	−0.490232
$309$	−1.14592e41	−0.943711
$310$	−5.86375e39	−0.0457833
$311$	3.83170e40	0.283691	0.141845	−	0.989889i	$-0.454696\pi$
$311$	3.83170e40	0.283691	0.141845	+	0.989889i	$0.454696\pi$
$312$	1.19665e40	0.0840268
$313$	−8.13055e40	−0.541550	−0.270775	−	0.962643i	$-0.587280\pi$
$313$	−8.13055e40	−0.541550	−0.270775	+	0.962643i	$0.587280\pi$
$314$	5.69042e39	0.0359588
$315$	−1.06699e41	−0.639789
$316$	1.51098e41	0.859850
$317$	7.49503e40	0.404852	0.202426	−	0.979298i	$-0.435118\pi$
$317$	7.49503e40	0.404852	0.202426	+	0.979298i	$0.435118\pi$
$318$	−3.03892e40	−0.155837
$319$	−9.18474e40	−0.447219
$320$	9.45809e40	0.437350
$321$	3.87089e41	1.70011
$322$	2.15128e40	0.0897584
$323$	3.39706e41	1.34667
$324$	−1.11554e41	−0.420235
$325$	2.31688e40	0.0829523
$326$	2.72604e40	0.0927774
$327$	5.39666e41	1.74617
$328$	2.83977e39	0.00873705
$329$	1.34254e41	0.392821
$330$	1.00565e40	0.0279875
$331$	−5.91449e41	−1.56587	−0.782935	−	0.622103i	$-0.786278\pi$
$331$	−5.91449e41	−1.56587	−0.782935	+	0.622103i	$0.786278\pi$
$332$	5.50822e40	0.138750
$333$	−7.47895e41	−1.79271
$334$	9.88982e39	0.0225617
$335$	2.03416e41	0.441719
$336$	−6.37902e41	−1.31873
$337$	1.33169e41	0.262126	0.131063	−	0.991374i	$-0.458161\pi$
$337$	1.33169e41	0.262126	0.131063	+	0.991374i	$0.458161\pi$
$338$	−2.68225e40	−0.0502774
$339$	−2.00418e41	−0.357801
$340$	−3.38336e41	−0.575368
$341$	6.41714e41	1.03967
$342$	−7.35510e40	−0.113542
$343$	−7.39453e41	−1.08782
$344$	9.73469e40	0.136492
$345$	1.03594e42	1.38458
$346$	5.88013e39	0.00749257
$347$	1.89271e41	0.229957	0.114979	−	0.993368i	$-0.463320\pi$
$347$	1.89271e41	0.229957	0.114979	+	0.993368i	$0.463320\pi$
$348$	−1.04219e42	−1.20751
$349$	−5.82757e41	−0.643974	−0.321987	−	0.946744i	$-0.604351\pi$
$349$	−5.82757e41	−0.643974	−0.321987	+	0.946744i	$0.604351\pi$
$350$	9.19299e39	0.00969023
$351$	−5.46588e41	−0.549658
$352$	1.16507e41	0.111789
$353$	5.33261e41	0.488267	0.244134	−	0.969742i	$-0.421496\pi$
$353$	5.33261e41	0.488267	0.244134	+	0.969742i	$0.421496\pi$
$354$	8.49500e40	0.0742351
$355$	6.26948e41	0.522954
$356$	−1.13346e42	−0.902571
$357$	2.26486e42	1.72193
$358$	3.88002e40	0.0281685
$359$	−1.28621e42	−0.891772	−0.445886	−	0.895090i	$-0.647111\pi$
$359$	−1.28621e42	−0.891772	−0.445886	+	0.895090i	$0.647111\pi$
$360$	1.46780e41	0.0972020
$361$	1.38408e41	0.0875575
$362$	1.53871e40	0.00929959
$363$	1.79341e42	1.03567
$364$	−5.97467e41	−0.329717
$365$	−1.31847e42	−0.695403
$366$	−2.83168e41	−0.142760
$367$	−1.99600e42	−0.961988	−0.480994	−	0.876724i	$-0.659724\pi$
$367$	−1.99600e42	−0.961988	−0.480994	+	0.876724i	$0.659724\pi$
$368$	3.97589e42	1.83209
$369$	−2.93284e41	−0.129227
$370$	6.44371e40	0.0271524
$371$	3.04017e42	1.22526
$372$	7.28154e42	2.80714
$373$	−4.88676e42	−1.80229	−0.901146	−	0.433516i	$-0.857273\pi$
$373$	−4.88676e42	−1.80229	−0.901146	+	0.433516i	$0.857273\pi$
$374$	−1.37035e41	−0.0483561
$375$	4.42685e41	0.149478
$376$	−1.84686e41	−0.0596807
$377$	−9.72506e41	−0.300788
$378$	−2.16877e41	−0.0642094
$379$	−6.55646e42	−1.85833	−0.929164	−	0.369667i	$-0.879472\pi$
$379$	−6.55646e42	−1.85833	−0.929164	+	0.369667i	$0.879472\pi$
$380$	−1.71225e42	−0.464662
$381$	8.29473e42	2.15546
$382$	−4.12961e41	−0.102769
$383$	−8.72699e41	−0.208010	−0.104005	−	0.994577i	$-0.533166\pi$
$383$	−8.72699e41	−0.208010	−0.104005	+	0.994577i	$0.533166\pi$
$384$	1.76158e42	0.402196
$385$	−1.00606e42	−0.220050
$386$	−1.90949e41	−0.0400155
$387$	−1.00538e43	−2.01882
$388$	−2.49035e42	−0.479222
$389$	1.58040e42	0.291474	0.145737	−	0.989323i	$-0.453445\pi$
$389$	1.58040e42	0.291474	0.145737	+	0.989323i	$0.453445\pi$
$390$	1.06481e41	0.0188237
$391$	−1.41164e43	−2.39225
$392$	2.71108e41	0.0440476
$393$	4.60726e42	0.717737
$394$	6.90379e41	0.103133
$395$	2.69398e42	0.385960
$396$	−8.01678e42	−1.10161
$397$	−5.01270e42	−0.660736	−0.330368	−	0.943852i	$-0.607173\pi$
$397$	−5.01270e42	−0.660736	−0.330368	+	0.943852i	$0.607173\pi$
$398$	−2.75993e41	−0.0349001
$399$	1.14620e43	1.39061
$400$	1.69901e42	0.197790
$401$	8.66109e42	0.967588	0.483794	−	0.875182i	$-0.339258\pi$
$401$	8.66109e42	0.967588	0.483794	+	0.875182i	$0.339258\pi$
$402$	9.34870e41	0.100235
$403$	6.79465e42	0.699252
$404$	1.80999e43	1.78806
$405$	−1.98893e42	−0.188630
$406$	−3.85874e41	−0.0351371
$407$	−7.05184e42	−0.616588
$408$	−3.11564e42	−0.261610
$409$	6.15808e42	0.496605	0.248302	−	0.968683i	$-0.420127\pi$
$409$	6.15808e42	0.496605	0.248302	+	0.968683i	$0.420127\pi$
$410$	2.52688e40	0.00195727
$411$	2.19600e42	0.163396
$412$	−7.87055e42	−0.562601
$413$	−8.49849e42	−0.583668
$414$	3.05639e42	0.201699
$415$	9.82078e41	0.0622806
$416$	1.23361e42	0.0751862
$417$	−1.25277e43	−0.733883
$418$	−6.93507e41	−0.0390519
$419$	1.55362e43	0.841031	0.420516	−	0.907285i	$-0.361849\pi$
$419$	1.55362e43	0.841031	0.420516	+	0.907285i	$0.361849\pi$
$420$	−1.14158e43	−0.594144
$421$	1.08104e43	0.540987	0.270494	−	0.962722i	$-0.412813\pi$
$421$	1.08104e43	0.540987	0.270494	+	0.962722i	$0.412813\pi$
$422$	−1.27528e42	−0.0613691
$423$	1.90739e43	0.882720
$424$	−4.18218e42	−0.186151
$425$	−6.03229e42	−0.258265
$426$	2.88136e42	0.118670
$427$	2.83284e43	1.12244
$428$	2.65865e43	1.01354
$429$	−1.16530e43	−0.427456
$430$	8.66212e41	0.0305770
$431$	−4.98547e42	−0.169368	−0.0846840	−	0.996408i	$-0.526988\pi$
$431$	−4.98547e42	−0.169368	−0.0846840	+	0.996408i	$0.526988\pi$
$432$	−4.00822e43	−1.31060
$433$	−1.01098e43	−0.318194	−0.159097	−	0.987263i	$-0.550858\pi$
$433$	−1.01098e43	−0.318194	−0.159097	+	0.987263i	$0.550858\pi$
$434$	2.69600e42	0.0816845
$435$	−1.85816e43	−0.542014
$436$	3.70661e43	1.04100
$437$	−7.14399e43	−1.93195
$438$	−6.05948e42	−0.157802
$439$	−4.36398e43	−1.09451	−0.547253	−	0.836967i	$-0.684326\pi$
$439$	−4.36398e43	−1.09451	−0.547253	+	0.836967i	$0.684326\pi$
$440$	1.38398e42	0.0334318
$441$	−2.79994e43	−0.651496
$442$	−1.45097e42	−0.0325230
$443$	1.22624e43	0.264798	0.132399	−	0.991196i	$-0.457732\pi$
$443$	1.22624e43	0.264798	0.132399	+	0.991196i	$0.457732\pi$
$444$	−8.00174e43	−1.66481
$445$	−2.02088e43	−0.405136
$446$	−4.33768e42	−0.0837978
$447$	1.42743e44	2.65755
$448$	−4.34859e43	−0.780299
$449$	8.39293e43	1.45161	0.725803	−	0.687903i	$-0.241468\pi$
$449$	8.39293e43	1.45161	0.725803	+	0.687903i	$0.241468\pi$
$450$	1.30608e42	0.0217752
$451$	−2.76536e42	−0.0444466
$452$	−1.37654e43	−0.213306
$453$	7.97791e43	1.19198
$454$	2.11595e42	0.0304848
$455$	−1.06524e43	−0.148000
$456$	−1.57676e43	−0.211274
$457$	9.02636e42	0.116653	0.0583264	−	0.998298i	$-0.481424\pi$
$457$	9.02636e42	0.116653	0.0583264	+	0.998298i	$0.481424\pi$
$458$	4.99232e42	0.0622332
$459$	1.42311e44	1.71131
$460$	7.11518e43	0.825432
$461$	−3.52096e42	−0.0394091	−0.0197045	−	0.999806i	$-0.506273\pi$
$461$	−3.52096e42	−0.0394091	−0.0197045	+	0.999806i	$0.506273\pi$
$462$	−4.62370e42	−0.0499341
$463$	2.80824e42	0.0292650	0.0146325	−	0.999893i	$-0.495342\pi$
$463$	2.80824e42	0.0292650	0.0146325	+	0.999893i	$0.495342\pi$
$464$	−7.13154e43	−0.717194
$465$	1.29825e44	1.26004
$466$	−5.10022e42	−0.0477773
$467$	−1.17834e44	−1.06547	−0.532736	−	0.846282i	$-0.678836\pi$
$467$	−1.17834e44	−1.06547	−0.532736	+	0.846282i	$0.678836\pi$
$468$	−8.48839e43	−0.740916
$469$	−9.35254e43	−0.788094
$470$	−1.64337e42	−0.0133697
$471$	−1.25987e44	−0.989650
$472$	1.16909e43	0.0886756
$473$	−9.47961e43	−0.694355
$474$	1.23811e43	0.0875826
$475$	−3.05282e43	−0.208572
$476$	1.55558e44	1.02654
$477$	4.31925e44	2.75331
$478$	1.50791e43	0.0928571
$479$	2.89874e43	0.172454	0.0862271	−	0.996276i	$-0.472519\pi$
$479$	2.89874e43	0.172454	0.0862271	+	0.996276i	$0.472519\pi$
$480$	2.35705e43	0.135484
$481$	−7.46669e43	−0.414700
$482$	2.64386e42	0.0141894
$483$	−4.76299e44	−2.47031
$484$	1.23177e44	0.617422
$485$	−4.44012e43	−0.215108
$486$	8.04418e42	0.0376689
$487$	2.41311e44	1.09232	0.546158	−	0.837682i	$-0.316090\pi$
$487$	2.41311e44	1.09232	0.546158	+	0.837682i	$0.316090\pi$
$488$	−3.89698e43	−0.170530
$489$	−6.03552e44	−2.55340
$490$	2.41237e42	0.00986754
$491$	−2.36480e44	−0.935297	−0.467648	−	0.883915i	$-0.654899\pi$
$491$	−2.36480e44	−0.935297	−0.467648	+	0.883915i	$0.654899\pi$
$492$	−3.13785e43	−0.120008
$493$	2.53204e44	0.936476
$494$	−7.34305e42	−0.0262653
$495$	−1.42934e44	−0.494480
$496$	4.98262e44	1.66729
$497$	−2.88255e44	−0.933031
$498$	4.51349e42	0.0141328
$499$	−4.17695e44	−1.26532	−0.632659	−	0.774430i	$-0.718037\pi$
$499$	−4.17695e44	−1.26532	−0.632659	+	0.774430i	$0.718037\pi$
$500$	3.04050e43	0.0891129
$501$	−2.18963e44	−0.620938
$502$	−7.40196e41	−0.00203112
$503$	1.63646e44	0.434543	0.217271	−	0.976111i	$-0.430284\pi$
$503$	1.63646e44	0.434543	0.217271	+	0.976111i	$0.430284\pi$
$504$	−6.74856e43	−0.173423
$505$	3.22708e44	0.802606
$506$	2.88184e43	0.0693724
$507$	5.93856e44	1.38373
$508$	5.69709e44	1.28500
$509$	−9.46414e43	−0.206651	−0.103326	−	0.994648i	$-0.532948\pi$
$509$	−9.46414e43	−0.206651	−0.103326	+	0.994648i	$0.532948\pi$
$510$	−2.77235e43	−0.0586058
$511$	6.06197e44	1.24071
$512$	1.50957e44	0.299157
$513$	7.20207e44	1.38204
$514$	2.79426e43	0.0519249
$515$	−1.40326e44	−0.252534
$516$	−1.07565e45	−1.87479
$517$	1.79846e44	0.303604
$518$	−2.96265e43	−0.0484440
$519$	−1.30187e44	−0.206209
$520$	1.46539e43	0.0224853
$521$	7.82192e44	1.16276	0.581381	−	0.813631i	$-0.302512\pi$
$521$	7.82192e44	1.16276	0.581381	+	0.813631i	$0.302512\pi$
$522$	−5.48222e43	−0.0789575
$523$	−8.02848e44	−1.12035	−0.560177	−	0.828373i	$-0.689267\pi$
$523$	−8.02848e44	−1.12035	−0.560177	+	0.828373i	$0.689267\pi$
$524$	3.16442e44	0.427885
$525$	−2.03535e44	−0.266692
$526$	3.61150e43	0.0458588
$527$	−1.76907e45	−2.17706
$528$	−8.54530e44	−1.01922
$529$	2.10365e45	2.43196
$530$	−3.72138e43	−0.0417016
$531$	−1.20741e45	−1.31158
$532$	7.87246e44	0.829027
$533$	−2.92804e43	−0.0298936
$534$	−9.28768e43	−0.0919341
$535$	4.74019e44	0.454945
$536$	1.28658e44	0.119734
$537$	−8.59046e44	−0.775248
$538$	−1.11177e43	−0.00972990
$539$	−2.64004e44	−0.224076
$540$	−7.17302e44	−0.590480
$541$	−2.90457e44	−0.231914	−0.115957	−	0.993254i	$-0.536994\pi$
$541$	−2.90457e44	−0.231914	−0.115957	+	0.993254i	$0.536994\pi$
$542$	−8.35929e43	−0.0647413
$543$	−3.40673e44	−0.255941
$544$	−3.21186e44	−0.234086
$545$	6.60862e44	0.467271
$546$	−4.89570e43	−0.0335843
$547$	−2.63690e45	−1.75511	−0.877553	−	0.479480i	$-0.840825\pi$
$547$	−2.63690e45	−1.75511	−0.877553	+	0.479480i	$0.840825\pi$
$548$	1.50828e44	0.0974100
$549$	4.02470e45	2.52226
$550$	1.23149e43	0.00748938
$551$	1.28141e45	0.756289
$552$	6.55217e44	0.375310
$553$	−1.23862e45	−0.688611
$554$	3.63845e43	0.0196338
$555$	−1.42665e45	−0.747282
$556$	−8.60445e44	−0.437511
$557$	−1.37430e45	−0.678378	−0.339189	−	0.940718i	$-0.610153\pi$
$557$	−1.37430e45	−0.678378	−0.339189	+	0.940718i	$0.610153\pi$
$558$	3.83029e44	0.183555
$559$	−1.00373e45	−0.467004
$560$	−7.81159e44	−0.352888
$561$	3.03400e45	1.33085
$562$	−8.24803e43	−0.0351319
$563$	1.83620e45	0.759505	0.379753	−	0.925088i	$-0.376009\pi$
$563$	1.83620e45	0.759505	0.379753	+	0.925088i	$0.376009\pi$
$564$	2.04072e45	0.819743
$565$	−2.45427e44	−0.0957466
$566$	−1.51371e44	−0.0573552
$567$	9.14459e44	0.336546
$568$	3.96535e44	0.141754
$569$	−5.13991e45	−1.78485	−0.892427	−	0.451192i	$-0.850999\pi$
$569$	−5.13991e45	−1.78485	−0.892427	+	0.451192i	$0.850999\pi$
$570$	−1.40303e44	−0.0473295
$571$	5.28676e45	1.73258	0.866291	−	0.499540i	$-0.166498\pi$
$571$	5.28676e45	1.73258	0.866291	+	0.499540i	$0.166498\pi$
$572$	−8.00364e44	−0.254832
$573$	9.14305e45	2.82839
$574$	−1.16180e43	−0.00349207
$575$	1.26859e45	0.370511
$576$	−6.17817e45	−1.75343
$577$	−1.37030e45	−0.377934	−0.188967	−	0.981983i	$-0.560514\pi$
$577$	−1.37030e45	−0.377934	−0.188967	+	0.981983i	$0.560514\pi$
$578$	1.51227e44	0.0405340
$579$	4.22767e45	1.10130
$580$	−1.27624e45	−0.323126
$581$	−4.51534e44	−0.111118
$582$	−2.04062e44	−0.0488126
$583$	4.07259e45	0.946978
$584$	−8.33910e44	−0.188498
$585$	−1.51342e45	−0.332574
$586$	−2.40717e44	−0.0514275
$587$	1.82654e45	0.379402	0.189701	−	0.981842i	$-0.439248\pi$
$587$	1.82654e45	0.379402	0.189701	+	0.981842i	$0.439248\pi$
$588$	−2.99566e45	−0.605015
$589$	−8.95290e45	−1.75817
$590$	1.04028e44	0.0198651
$591$	−1.52852e46	−2.83842
$592$	−5.47544e45	−0.988805
$593$	−9.10503e45	−1.59911	−0.799556	−	0.600592i	$-0.794932\pi$
$593$	−9.10503e45	−1.59911	−0.799556	+	0.600592i	$0.794932\pi$
$594$	−2.90527e44	−0.0496262
$595$	2.77349e45	0.460784
$596$	9.80408e45	1.58432
$597$	6.11055e45	0.960514
$598$	3.05138e44	0.0466580
$599$	1.51052e45	0.224690	0.112345	−	0.993669i	$-0.464164\pi$
$599$	1.51052e45	0.224690	0.112345	+	0.993669i	$0.464164\pi$
$600$	2.79992e44	0.0405181
$601$	1.17313e46	1.65165	0.825825	−	0.563927i	$-0.190710\pi$
$601$	1.17313e46	1.65165	0.825825	+	0.563927i	$0.190710\pi$
$602$	−3.98262e44	−0.0545540
$603$	−1.32874e46	−1.77095
$604$	5.47949e45	0.710609
$605$	2.19617e45	0.277141
$606$	1.48312e45	0.182129
$607$	−9.39432e45	−1.12267	−0.561335	−	0.827589i	$-0.689712\pi$
$607$	−9.39432e45	−1.12267	−0.561335	+	0.827589i	$0.689712\pi$
$608$	−1.62546e45	−0.189045
$609$	8.54334e45	0.967035
$610$	−3.46760e44	−0.0382021
$611$	1.90426e45	0.204196
$612$	2.21006e46	2.30678
$613$	−9.71928e45	−0.987498	−0.493749	−	0.869604i	$-0.664374\pi$
$613$	−9.71928e45	−0.987498	−0.493749	+	0.869604i	$0.664374\pi$
$614$	−2.96157e44	−0.0292916
$615$	−5.59458e44	−0.0538676
$616$	−6.36317e44	−0.0596474
$617$	1.24293e46	1.13433	0.567166	−	0.823603i	$-0.308040\pi$
$617$	1.24293e46	1.13433	0.567166	+	0.823603i	$0.308040\pi$
$618$	−6.44920e44	−0.0573054
$619$	−1.07266e46	−0.928043	−0.464021	−	0.885824i	$-0.653594\pi$
$619$	−1.07266e46	−0.928043	−0.464021	+	0.885824i	$0.653594\pi$
$620$	8.91680e45	0.751183
$621$	−2.99279e46	−2.45508
$622$	2.15647e44	0.0172267
$623$	9.29149e45	0.722824
$624$	−9.04801e45	−0.685499
$625$	5.42101e44	0.0400000
$626$	−4.57585e44	−0.0328848
$627$	1.53544e46	1.07478
$628$	−8.65322e45	−0.589988
$629$	1.94405e46	1.29113
$630$	−6.00500e44	−0.0388503
$631$	−1.79249e46	−1.12972	−0.564862	−	0.825186i	$-0.691071\pi$
$631$	−1.79249e46	−1.12972	−0.564862	+	0.825186i	$0.691071\pi$
$632$	1.70390e45	0.104620
$633$	2.82350e46	1.68899
$634$	4.21818e44	0.0245840
$635$	1.01575e46	0.576795
$636$	4.62117e46	2.55688
$637$	−2.79535e45	−0.150708
$638$	−5.16915e44	−0.0271567
$639$	−4.09532e46	−2.09664
$640$	2.15719e45	0.107626
$641$	2.31165e46	1.12400	0.561998	−	0.827138i	$-0.310033\pi$
$641$	2.31165e46	1.12400	0.561998	+	0.827138i	$0.310033\pi$
$642$	2.17852e45	0.103237
$643$	−3.13717e45	−0.144896	−0.0724480	−	0.997372i	$-0.523081\pi$
$643$	−3.13717e45	−0.144896	−0.0724480	+	0.997372i	$0.523081\pi$
$644$	−3.27138e46	−1.47270
$645$	−1.91781e46	−0.841533
$646$	1.91185e45	0.0817746
$647$	−1.23833e46	−0.516318	−0.258159	−	0.966102i	$-0.583116\pi$
$647$	−1.23833e46	−0.516318	−0.258159	+	0.966102i	$0.583116\pi$
$648$	−1.25797e45	−0.0511308
$649$	−1.13845e46	−0.451105
$650$	1.30393e44	0.00503716
$651$	−5.96901e46	−2.24810
$652$	−4.14540e46	−1.52223
$653$	−9.15492e45	−0.327784	−0.163892	−	0.986478i	$-0.552405\pi$
$653$	−9.15492e45	−0.327784	−0.163892	+	0.986478i	$0.552405\pi$
$654$	3.03723e45	0.106034
$655$	5.64194e45	0.192064
$656$	−2.14718e45	−0.0712778
$657$	8.61242e46	2.78802
$658$	7.55578e44	0.0238535
$659$	−4.32900e46	−1.33284	−0.666420	−	0.745577i	$-0.732174\pi$
$659$	−4.32900e46	−1.33284	−0.666420	+	0.745577i	$0.732174\pi$
$660$	−1.52925e46	−0.459202
$661$	1.40663e46	0.411961	0.205980	−	0.978556i	$-0.433962\pi$
$661$	1.40663e46	0.411961	0.205980	+	0.978556i	$0.433962\pi$
$662$	−3.32866e45	−0.0950852
$663$	3.21248e46	0.895091
$664$	6.21150e44	0.0168820
$665$	1.40361e46	0.372124
$666$	−4.20913e45	−0.108860
$667$	−5.32487e46	−1.34348
$668$	−1.50391e46	−0.370178
$669$	9.60373e46	2.30626
$670$	1.14482e45	0.0268227
$671$	3.79486e46	0.867509
$672$	−1.08371e46	−0.241724
$673$	2.27399e46	0.494926	0.247463	−	0.968897i	$-0.420403\pi$
$673$	2.27399e46	0.494926	0.247463	+	0.968897i	$0.420403\pi$
$674$	7.49473e44	0.0159172
$675$	−1.27890e46	−0.265048
$676$	4.07880e46	0.824920
$677$	4.02008e46	0.793453	0.396727	−	0.917937i	$-0.370146\pi$
$677$	4.02008e46	0.793453	0.396727	+	0.917937i	$0.370146\pi$
$678$	−1.12795e45	−0.0217270
$679$	2.04145e46	0.383785
$680$	−3.81534e45	−0.0700061
$681$	−4.68476e46	−0.838996
$682$	3.61155e45	0.0631323
$683$	−8.62730e46	−1.47209	−0.736043	−	0.676935i	$-0.763308\pi$
$683$	−8.62730e46	−1.47209	−0.736043	+	0.676935i	$0.763308\pi$
$684$	1.11846e47	1.86293
$685$	2.68917e45	0.0437243
$686$	−4.16162e45	−0.0660563
$687$	−1.10531e47	−1.71277
$688$	−7.36049e46	−1.11352
$689$	4.31217e46	0.636911
$690$	5.83024e45	0.0840769
$691$	2.76452e46	0.389252	0.194626	−	0.980877i	$-0.437651\pi$
$691$	2.76452e46	0.389252	0.194626	+	0.980877i	$0.437651\pi$
$692$	−8.94170e45	−0.122933
$693$	6.57172e46	0.882228
$694$	1.06521e45	0.0139638
$695$	−1.53411e46	−0.196385
$696$	−1.17526e46	−0.146920
$697$	7.62351e45	0.0930710
$698$	−3.27974e45	−0.0391043
$699$	1.12920e47	1.31492
$700$	−1.39795e46	−0.158991
$701$	5.83426e45	0.0648094	0.0324047	−	0.999475i	$-0.489683\pi$
$701$	5.83426e45	0.0648094	0.0324047	+	0.999475i	$0.489683\pi$
$702$	−3.07618e45	−0.0333772
$703$	9.83841e46	1.04271
$704$	−5.82535e46	−0.603077
$705$	3.63846e46	0.367957
$706$	3.00118e45	0.0296493
$707$	−1.48373e47	−1.43197
$708$	−1.29180e47	−1.21800
$709$	−3.21473e46	−0.296130	−0.148065	−	0.988978i	$-0.547304\pi$
$709$	−3.21473e46	−0.296130	−0.148065	+	0.988978i	$0.547304\pi$
$710$	3.52845e45	0.0317556
$711$	−1.75975e47	−1.54740
$712$	−1.27818e46	−0.109817
$713$	3.72035e47	3.12325
$714$	1.27466e46	0.104562
$715$	−1.42699e46	−0.114386
$716$	−5.90021e46	−0.462171
$717$	−3.33855e47	−2.55559
$718$	−7.23876e45	−0.0541515
$719$	−5.61687e46	−0.410646	−0.205323	−	0.978694i	$-0.565824\pi$
$719$	−5.61687e46	−0.410646	−0.205323	+	0.978694i	$0.565824\pi$
$720$	−1.10982e47	−0.792985
$721$	6.45185e46	0.450560
$722$	7.78958e44	0.00531680
$723$	−5.85358e46	−0.390517
$724$	−2.33986e46	−0.152582
$725$	−2.27546e46	−0.145041
$726$	1.00933e46	0.0628894
$727$	2.29582e47	1.39836	0.699181	−	0.714944i	$-0.253548\pi$
$727$	2.29582e47	1.39836	0.699181	+	0.714944i	$0.253548\pi$
$728$	−6.73750e45	−0.0401172
$729$	−2.50561e47	−1.45851
$730$	−7.42029e45	−0.0422273
$731$	2.61333e47	1.45398
$732$	4.30603e47	2.34231
$733$	1.21401e46	0.0645662	0.0322831	−	0.999479i	$-0.489722\pi$
$733$	1.21401e46	0.0645662	0.0322831	+	0.999479i	$0.489722\pi$
$734$	−1.12334e46	−0.0584153
$735$	−5.34105e46	−0.271572
$736$	6.75452e46	0.335823
$737$	−1.25286e47	−0.609102
$738$	−1.65060e45	−0.00784713
$739$	3.32044e47	1.54370	0.771848	−	0.635807i	$-0.219333\pi$
$739$	3.32044e47	1.54370	0.771848	+	0.635807i	$0.219333\pi$
$740$	−9.79873e46	−0.445499
$741$	1.62577e47	0.722867
$742$	1.71100e46	0.0744020
$743$	−1.84054e47	−0.782762	−0.391381	−	0.920229i	$-0.628003\pi$
$743$	−1.84054e47	−0.782762	−0.391381	+	0.920229i	$0.628003\pi$
$744$	8.21123e46	0.341550
$745$	1.74800e47	0.711153
$746$	−2.75025e46	−0.109442
$747$	−6.41508e46	−0.249696
$748$	2.08385e47	0.793396
$749$	−2.17942e47	−0.811691
$750$	2.49142e45	0.00907686
$751$	−7.67452e45	−0.0273522	−0.0136761	−	0.999906i	$-0.504353\pi$
$751$	−7.67452e45	−0.0273522	−0.0136761	+	0.999906i	$0.504353\pi$
$752$	1.39642e47	0.486881
$753$	1.63881e46	0.0559000
$754$	−5.47324e45	−0.0182649
$755$	9.76955e46	0.318970
$756$	3.29797e47	1.05351
$757$	−1.14623e47	−0.358254	−0.179127	−	0.983826i	$-0.557327\pi$
$757$	−1.14623e47	−0.358254	−0.179127	+	0.983826i	$0.557327\pi$
$758$	−3.68996e46	−0.112844
$759$	−6.38047e47	−1.90925
$760$	−1.93086e46	−0.0565362
$761$	−6.74831e47	−1.93352	−0.966759	−	0.255690i	$-0.917697\pi$
$761$	−6.74831e47	−1.93352	−0.966759	+	0.255690i	$0.917697\pi$
$762$	4.66825e46	0.130887
$763$	−3.03847e47	−0.833682
$764$	6.27975e47	1.68617
$765$	3.94038e47	1.03544
$766$	−4.91152e45	−0.0126311
$767$	−1.20543e47	−0.303401
$768$	−6.53535e47	−1.60994
$769$	1.58437e47	0.382007	0.191004	−	0.981589i	$-0.438826\pi$
$769$	1.58437e47	0.382007	0.191004	+	0.981589i	$0.438826\pi$
$770$	−5.66207e45	−0.0133622
$771$	−6.18657e47	−1.42907
$772$	2.90370e47	0.656548
$773$	−1.15351e47	−0.255305	−0.127652	−	0.991819i	$-0.540744\pi$
$773$	−1.15351e47	−0.255305	−0.127652	+	0.991819i	$0.540744\pi$
$774$	−5.65822e46	−0.122590
$775$	1.58980e47	0.337183
$776$	−2.80831e46	−0.0583078
$777$	6.55939e47	1.33327
$778$	8.89447e45	0.0176993
$779$	3.85810e46	0.0751632
$780$	−1.61921e47	−0.308847
$781$	−3.86145e47	−0.721121
$782$	−7.94464e46	−0.145266
$783$	5.36816e47	0.961072
$784$	−2.04987e47	−0.359345
$785$	−1.54281e47	−0.264827
$786$	2.59295e46	0.0435835
$787$	7.25057e47	1.19341	0.596704	−	0.802461i	$-0.296477\pi$
$787$	7.25057e47	1.19341	0.596704	+	0.802461i	$0.296477\pi$
$788$	−1.04983e48	−1.69215
$789$	−7.99595e47	−1.26212
$790$	1.51616e46	0.0234369
$791$	1.12841e47	0.170827
$792$	−9.04034e46	−0.134035
$793$	4.01810e47	0.583463
$794$	−2.82113e46	−0.0401222
$795$	8.23924e47	1.14770
$796$	4.19693e47	0.572619
$797$	−5.72072e47	−0.764519	−0.382260	−	0.924055i	$-0.624854\pi$
$797$	−5.72072e47	−0.764519	−0.382260	+	0.924055i	$0.624854\pi$
$798$	6.45077e46	0.0844430
$799$	−4.95798e47	−0.635745
$800$	2.88639e46	0.0362552
$801$	1.32007e48	1.62428
$802$	4.87444e46	0.0587553
$803$	8.12058e47	0.958916
$804$	−1.42162e48	−1.64460
$805$	−5.83264e47	−0.661048
$806$	3.82401e46	0.0424611
$807$	2.46149e47	0.267784
$808$	2.04108e47	0.217557
$809$	1.25233e48	1.30788	0.653939	−	0.756547i	$-0.273115\pi$
$809$	1.25233e48	1.30788	0.653939	+	0.756547i	$0.273115\pi$
$810$	−1.11936e46	−0.0114543
$811$	−1.43044e48	−1.43425	−0.717126	−	0.696944i	$-0.754543\pi$
$811$	−1.43044e48	−1.43425	−0.717126	+	0.696944i	$0.754543\pi$
$812$	5.86785e47	0.576506
$813$	1.85077e48	1.78180
$814$	−3.96876e46	−0.0374414
$815$	−7.39095e47	−0.683282
$816$	2.35576e48	2.13424
$817$	1.32255e48	1.17422
$818$	3.46575e46	0.0301556
$819$	6.95832e47	0.593363
$820$	−3.84254e46	−0.0321137
$821$	−7.52133e47	−0.616074	−0.308037	−	0.951374i	$-0.599672\pi$
$821$	−7.52133e47	−0.616074	−0.308037	+	0.951374i	$0.599672\pi$
$822$	1.23590e46	0.00992199
$823$	−2.11125e47	−0.166128	−0.0830638	−	0.996544i	$-0.526471\pi$
$823$	−2.11125e47	−0.166128	−0.0830638	+	0.996544i	$0.526471\pi$
$824$	−8.87544e46	−0.0684527
$825$	−2.72655e47	−0.206121
$826$	−4.78292e46	−0.0354424
$827$	−1.64488e47	−0.119480	−0.0597399	−	0.998214i	$-0.519027\pi$
$827$	−1.64488e47	−0.119480	−0.0597399	+	0.998214i	$0.519027\pi$
$828$	−4.64774e48	−3.30934
$829$	−2.28060e48	−1.59184	−0.795919	−	0.605404i	$-0.793012\pi$
$829$	−2.28060e48	−1.59184	−0.795919	+	0.605404i	$0.793012\pi$
$830$	5.52711e45	0.00378190
$831$	−8.05561e47	−0.540358
$832$	−6.16804e47	−0.405613
$833$	7.27804e47	0.469215
$834$	−7.05056e46	−0.0445640
$835$	−2.68137e47	−0.166161
$836$	1.05459e48	0.640739
$837$	−3.75059e48	−2.23424
$838$	8.74370e46	0.0510704
$839$	1.56509e48	0.896327	0.448163	−	0.893952i	$-0.352078\pi$
$839$	1.56509e48	0.896327	0.448163	+	0.893952i	$0.352078\pi$
$840$	−1.28733e47	−0.0722905
$841$	−8.60958e47	−0.474076
$842$	6.08406e46	0.0328506
$843$	1.82613e48	0.966892
$844$	1.93927e48	1.00691
$845$	7.27222e47	0.370281
$846$	1.07347e47	0.0536019
$847$	−1.00974e48	−0.494463
$848$	3.16218e48	1.51864
$849$	3.35140e48	1.57852
$850$	−3.39496e46	−0.0156827
$851$	−4.08832e48	−1.85228
$852$	−4.38159e48	−1.94706
$853$	−1.60296e48	−0.698657	−0.349329	−	0.937000i	$-0.613590\pi$
$853$	−1.60296e48	−0.698657	−0.349329	+	0.937000i	$0.613590\pi$
$854$	1.59431e47	0.0681584
$855$	1.99415e48	0.836211
$856$	2.99810e47	0.123319
$857$	3.00131e48	1.21095	0.605476	−	0.795864i	$-0.292983\pi$
$857$	3.00131e48	1.21095	0.605476	+	0.795864i	$0.292983\pi$
$858$	−6.55826e46	−0.0259566
$859$	4.48822e48	1.74256	0.871279	−	0.490788i	$-0.163291\pi$
$859$	4.48822e48	1.74256	0.871279	+	0.490788i	$0.163291\pi$
$860$	−1.31722e48	−0.501687
$861$	2.57224e47	0.0961081
$862$	−2.80581e46	−0.0102846
$863$	5.23525e47	0.188260	0.0941302	−	0.995560i	$-0.469993\pi$
$863$	5.23525e47	0.188260	0.0941302	+	0.995560i	$0.469993\pi$
$864$	−6.80943e47	−0.240234
$865$	−1.59424e47	−0.0551809
$866$	−5.68977e46	−0.0193219
$867$	−3.34819e48	−1.11557
$868$	−4.09971e48	−1.34023
$869$	−1.65925e48	−0.532214
$870$	−1.04577e47	−0.0329130
$871$	−1.32657e48	−0.409665
$872$	4.17985e47	0.126660
$873$	2.90035e48	0.862414
$874$	−4.02062e47	−0.117315
$875$	−2.49244e47	−0.0713661
$876$	9.21444e48	2.58911
$877$	−1.66421e48	−0.458898	−0.229449	−	0.973321i	$-0.573692\pi$
$877$	−1.66421e48	−0.458898	−0.229449	+	0.973321i	$0.573692\pi$
$878$	−2.45603e47	−0.0664622
$879$	5.32952e48	1.41538
$880$	−1.04644e48	−0.272740
$881$	1.63041e48	0.417055	0.208528	−	0.978016i	$-0.433133\pi$
$881$	1.63041e48	0.417055	0.208528	+	0.978016i	$0.433133\pi$
$882$	−1.57580e47	−0.0395611
$883$	3.57816e48	0.881674	0.440837	−	0.897587i	$-0.354682\pi$
$883$	3.57816e48	0.881674	0.440837	+	0.897587i	$0.354682\pi$
$884$	2.20644e48	0.533616
$885$	−2.30320e48	−0.546723
$886$	6.90126e46	0.0160795
$887$	3.83241e48	0.876461	0.438230	−	0.898863i	$-0.355605\pi$
$887$	3.83241e48	0.876461	0.438230	+	0.898863i	$0.355605\pi$
$888$	−9.02338e47	−0.202561
$889$	−4.67017e48	−1.02909
$890$	−1.13735e47	−0.0246013
$891$	1.22501e48	0.260109
$892$	6.59616e48	1.37490
$893$	−2.50913e48	−0.513422
$894$	8.03356e47	0.161376
$895$	−1.05197e48	−0.207454
$896$	−9.91821e47	−0.192022
$897$	−6.75582e48	−1.28411
$898$	4.72352e47	0.0881467
$899$	−6.67316e48	−1.22264
$900$	−1.98610e48	−0.357273
$901$	−1.12273e49	−1.98297
$902$	−1.55634e46	−0.00269895
$903$	8.81761e48	1.50142
$904$	−1.55229e47	−0.0259534
$905$	−4.17180e47	−0.0684892
$906$	4.48994e47	0.0723812
$907$	−9.46008e48	−1.49753	−0.748763	−	0.662838i	$-0.769352\pi$
$907$	−9.46008e48	−1.49753	−0.748763	+	0.662838i	$0.769352\pi$
$908$	−3.21765e48	−0.500175
$909$	−2.10798e49	−3.21782
$910$	−5.99516e46	−0.00898706
$911$	7.92211e48	1.16624	0.583120	−	0.812386i	$-0.301832\pi$
$911$	7.92211e48	1.16624	0.583120	+	0.812386i	$0.301832\pi$
$912$	1.19220e49	1.72359
$913$	−6.04873e47	−0.0858809
$914$	5.08001e46	0.00708357
$915$	7.67736e48	1.05139
$916$	−7.59165e48	−1.02108
$917$	−2.59402e48	−0.342672
$918$	8.00923e47	0.103917
$919$	4.92680e48	0.627854	0.313927	−	0.949447i	$-0.398355\pi$
$919$	4.92680e48	0.627854	0.313927	+	0.949447i	$0.398355\pi$
$920$	8.02362e47	0.100432
$921$	6.55699e48	0.806158
$922$	−1.98159e46	−0.00239306
$923$	−4.08861e48	−0.485006
$924$	7.03110e48	0.819286
$925$	−1.74705e48	−0.199970
$926$	1.58047e46	0.00177707
$927$	9.16633e48	1.01246
$928$	−1.21155e48	−0.131462
$929$	2.38059e48	0.253761	0.126881	−	0.991918i	$-0.459503\pi$
$929$	2.38059e48	0.253761	0.126881	+	0.991918i	$0.459503\pi$
$930$	7.30651e47	0.0765140
$931$	3.68326e48	0.378934
$932$	7.75573e48	0.783899
$933$	−4.77448e48	−0.474110
$934$	−6.63166e47	−0.0646992
$935$	3.71536e48	0.356130
$936$	−9.57217e47	−0.0901486
$937$	−4.20946e47	−0.0389514	−0.0194757	−	0.999810i	$-0.506200\pi$
$937$	−4.20946e47	−0.0389514	−0.0194757	+	0.999810i	$0.506200\pi$
$938$	−5.26358e47	−0.0478558
$939$	1.01310e49	0.905049
$940$	2.49901e48	0.219361
$941$	−1.57932e49	−1.36221	−0.681103	−	0.732188i	$-0.738499\pi$
$941$	−1.57932e49	−1.36221	−0.681103	+	0.732188i	$0.738499\pi$
$942$	−7.09053e47	−0.0600950
$943$	−1.60322e48	−0.133521
$944$	−8.83958e48	−0.723425
$945$	5.88005e48	0.472886
$946$	−5.33510e47	−0.0421637
$947$	1.67820e49	1.30337	0.651685	−	0.758490i	$-0.274062\pi$
$947$	1.67820e49	1.30337	0.651685	+	0.758490i	$0.274062\pi$
$948$	−1.88276e49	−1.43700
$949$	8.59830e48	0.644941
$950$	−1.71812e47	−0.0126652
$951$	−9.33916e48	−0.676596
$952$	1.75419e48	0.124902
$953$	2.07777e49	1.45400	0.726999	−	0.686639i	$-0.240915\pi$
$953$	2.07777e49	1.45400	0.726999	+	0.686639i	$0.240915\pi$
$954$	2.43086e48	0.167191
$955$	1.11964e49	0.756870
$956$	−2.29303e49	−1.52354
$957$	1.14446e49	0.747402
$958$	1.63141e47	0.0104720
$959$	−1.23641e48	−0.0780109
$960$	−1.17852e49	−0.730908
$961$	3.02202e49	1.84231
$962$	−4.20223e47	−0.0251821
$963$	−3.09637e49	−1.82397
$964$	−4.02043e48	−0.232810
$965$	5.17710e48	0.294704
$966$	−2.68060e48	−0.150006
$967$	1.42054e48	0.0781480	0.0390740	−	0.999236i	$-0.487559\pi$
$967$	1.42054e48	0.0781480	0.0390740	+	0.999236i	$0.487559\pi$
$968$	1.38904e48	0.0751229
$969$	−4.23289e49	−2.25058
$970$	−2.49889e47	−0.0130621
$971$	3.67703e49	1.88964	0.944821	−	0.327588i	$-0.106236\pi$
$971$	3.67703e49	1.88964	0.944821	+	0.327588i	$0.106236\pi$
$972$	−1.22325e49	−0.618048
$973$	7.05346e48	0.350381
$974$	1.35809e48	0.0663293
$975$	−2.88694e48	−0.138632
$976$	2.94654e49	1.39120
$977$	−5.91833e48	−0.274751	−0.137375	−	0.990519i	$-0.543867\pi$
$977$	−5.91833e48	−0.274751	−0.137375	+	0.990519i	$0.543867\pi$
$978$	−3.39678e48	−0.155051
$979$	1.24468e49	0.558657
$980$	−3.66841e48	−0.161900
$981$	−4.31685e49	−1.87339
$982$	−1.33090e48	−0.0567945
$983$	−4.20754e49	−1.76561	−0.882805	−	0.469740i	$-0.844348\pi$
$983$	−4.20754e49	−1.76561	−0.882805	+	0.469740i	$0.844348\pi$
$984$	−3.53849e47	−0.0146015
$985$	−1.87178e49	−0.759552
$986$	1.42503e48	0.0568661
$987$	−1.67287e49	−0.656491
$988$	1.11663e49	0.430943
$989$	−5.49582e49	−2.08590
$990$	−8.04427e47	−0.0300266
$991$	−8.36780e48	−0.307182	−0.153591	−	0.988134i	$-0.549084\pi$
$991$	−8.36780e48	−0.307182	−0.153591	+	0.988134i	$0.549084\pi$
$992$	8.46482e48	0.305615
$993$	7.36974e49	2.61691
$994$	−1.62229e48	−0.0566569
$995$	7.48283e48	0.257031
$996$	−6.86351e48	−0.231882
$997$	4.11174e49	1.36633	0.683166	−	0.730264i	$-0.260603\pi$
$997$	4.11174e49	1.36633	0.683166	+	0.730264i	$0.260603\pi$
$998$	−2.35077e48	−0.0768346
$999$	4.12155e49	1.32504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.a.1.3	✓	5
5.2	odd	4		25.34.b.b.24.6		10
5.3	odd	4		25.34.b.b.24.5		10
5.4	even	2		25.34.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.3	✓	5	1.1	even	1	trivial
25.34.a.b.1.3		5	5.4	even	2
25.34.b.b.24.5		10	5.3	odd	4
25.34.b.b.24.6		10	5.2	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)

\(f(q)\)	\(=\)	\(q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} +O(q^{10})\)	\(q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} -8.58760e14 q^{10} +9.39806e16 q^{11} +1.06640e18 q^{12} +9.95093e17 q^{13} +3.94836e17 q^{14} +1.90132e19 q^{15} +7.29717e19 q^{16} -2.59085e20 q^{17} +5.60955e19 q^{18} -1.31117e21 q^{19} +1.30589e21 q^{20} -8.74176e21 q^{21} +5.28920e20 q^{22} +5.44854e22 q^{23} +1.20255e22 q^{24} +2.32831e22 q^{25} +5.60036e21 q^{26} -5.49284e23 q^{27} -6.00413e23 q^{28} -9.77301e23 q^{29} +1.07006e23 q^{30} +6.82815e24 q^{31} +1.23969e24 q^{32} -1.17104e25 q^{33} -1.45812e24 q^{34} -1.07050e25 q^{35} -8.53025e25 q^{36} -7.50351e25 q^{37} -7.37925e24 q^{38} -1.23993e26 q^{39} +1.47262e25 q^{40} -2.94248e25 q^{41} -4.91984e25 q^{42} -1.00868e27 q^{43} -8.04311e26 q^{44} -1.52088e27 q^{45} +3.06642e26 q^{46} +1.91365e27 q^{47} -9.09262e27 q^{48} -2.80913e27 q^{49} +1.31036e26 q^{50} +3.22832e28 q^{51} -8.51627e27 q^{52} +4.33344e28 q^{53} -3.09135e27 q^{54} -1.43403e28 q^{55} -6.77072e27 q^{56} +1.63379e29 q^{57} -5.50022e27 q^{58} -1.21137e29 q^{59} -1.62720e29 q^{60} +4.03792e29 q^{61} +3.84287e28 q^{62} +6.99264e29 q^{63} -6.19846e29 q^{64} -1.51839e29 q^{65} -6.59060e28 q^{66} -1.33311e30 q^{67} +2.21732e30 q^{68} -6.78914e30 q^{69} -6.02472e28 q^{70} -4.10877e30 q^{71} -9.61937e29 q^{72} +8.64070e30 q^{73} -4.22295e29 q^{74} -2.90118e30 q^{75} +1.12214e31 q^{76} +6.59330e30 q^{77} -6.97831e29 q^{78} -1.76553e31 q^{79} -1.11346e31 q^{80} +1.30347e31 q^{81} -1.65602e29 q^{82} -6.43615e30 q^{83} +7.48143e31 q^{84} +3.95332e31 q^{85} -5.67680e30 q^{86} +1.21776e32 q^{87} -9.07003e30 q^{88} +1.32441e32 q^{89} -8.55950e30 q^{90} +6.98117e31 q^{91} -4.66300e32 q^{92} -8.50820e32 q^{93} +1.07700e31 q^{94} +2.00069e32 q^{95} -1.54472e32 q^{96} +2.90988e32 q^{97} -1.58097e31 q^{98} +9.36730e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 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

Varieties

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