LMFDB - Embedded newform 5.34.a.a.1.4

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			1.4
Root			$-16460.4$ 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)

$f(q)$	$=$	$q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} +O(q^{10})$	\(q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} -1.09768e16 q^{10} -2.33530e17 q^{11} -4.69797e17 q^{12} -2.28395e18 q^{13} -7.74658e18 q^{14} -2.09920e19 q^{15} -3.27918e19 q^{16} -2.09885e20 q^{17} +9.61615e20 q^{18} +6.01644e20 q^{19} +5.21071e20 q^{20} -1.48145e22 q^{21} -1.67997e22 q^{22} +4.84991e22 q^{23} -1.18808e23 q^{24} +2.32831e22 q^{25} -1.64302e23 q^{26} +1.07421e24 q^{27} +3.67730e23 q^{28} -8.15476e22 q^{29} -1.51012e24 q^{30} -1.49925e24 q^{31} +5.05930e24 q^{32} -3.21275e25 q^{33} -1.50986e25 q^{34} +1.64313e25 q^{35} -4.56479e25 q^{36} +1.78708e25 q^{37} +4.32809e25 q^{38} -3.14210e26 q^{39} +1.31775e26 q^{40} -1.94621e26 q^{41} -1.06572e27 q^{42} -9.48110e26 q^{43} +7.97481e26 q^{44} -2.03969e27 q^{45} +3.48891e27 q^{46} -6.29157e26 q^{47} -4.51128e27 q^{48} +3.86494e27 q^{49} +1.67493e27 q^{50} -2.88745e28 q^{51} +7.79943e27 q^{52} -8.56042e27 q^{53} +7.72760e28 q^{54} +3.56339e28 q^{55} +9.29963e28 q^{56} +8.27701e28 q^{57} -5.86635e27 q^{58} +5.43089e27 q^{59} +7.16853e28 q^{60} +1.79220e29 q^{61} -1.07853e29 q^{62} -1.43945e30 q^{63} +6.45635e29 q^{64} +3.48503e29 q^{65} -2.31118e30 q^{66} -3.33703e29 q^{67} +7.16732e29 q^{68} +6.67217e30 q^{69} +1.18203e30 q^{70} -3.44997e30 q^{71} -1.15440e31 q^{72} -7.11823e30 q^{73} +1.28559e30 q^{74} +3.20312e30 q^{75} -2.05455e30 q^{76} +2.51476e31 q^{77} -2.26036e31 q^{78} -1.57830e31 q^{79} +5.00364e30 q^{80} +7.34723e31 q^{81} -1.40006e31 q^{82} +3.45599e31 q^{83} +5.05898e31 q^{84} +3.20258e31 q^{85} -6.82049e31 q^{86} -1.12188e31 q^{87} +2.01677e32 q^{88} -2.35733e32 q^{89} -1.46731e32 q^{90} +2.45946e32 q^{91} -1.65619e32 q^{92} -2.06256e32 q^{93} -4.52602e31 q^{94} -9.18036e31 q^{95} +6.96024e32 q^{96} -3.55763e32 q^{97} +2.78035e32 q^{98} -3.12168e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	71937.8	0.776180	0.388090	−	0.921622i	$-0.373135\pi$
$2$	71937.8	0.776180	0.388090	+	0.921622i	$0.373135\pi$
$3$	1.37573e8	1.84516	0.922578	−	0.385811i	$-0.126078\pi$
$3$	1.37573e8	1.84516	0.922578	+	0.385811i	$0.126078\pi$
$4$	−3.41489e9	−0.397545
$5$	−1.52588e11	−0.447214
$5$	−1.52588e11	−0.447214
$6$	9.89671e12	1.43217
$7$	−1.07684e14	−1.22472	−0.612358	−	0.790581i	$-0.709779\pi$
$7$	−1.07684e14	−1.22472	−0.612358	+	0.790581i	$0.709779\pi$
$8$	−8.63600e14	−1.08475
$9$	1.33673e16	2.40460
$10$	−1.09768e16	−0.347118
$11$	−2.33530e17	−1.53237	−0.766186	−	0.642619i	$-0.777848\pi$
$11$	−2.33530e17	−1.53237	−0.766186	+	0.642619i	$0.777848\pi$
$12$	−4.69797e17	−0.733533
$13$	−2.28395e18	−0.951965	−0.475983	−	0.879455i	$-0.657908\pi$
$13$	−2.28395e18	−0.951965	−0.475983	+	0.879455i	$0.657908\pi$
$14$	−7.74658e18	−0.950599
$15$	−2.09920e19	−0.825179
$16$	−3.27918e19	−0.444412
$17$	−2.09885e20	−1.04610	−0.523050	−	0.852302i	$-0.675206\pi$
$17$	−2.09885e20	−1.04610	−0.523050	+	0.852302i	$0.675206\pi$
$18$	9.61615e20	1.86640
$19$	6.01644e20	0.478526	0.239263	−	0.970955i	$-0.423094\pi$
$19$	6.01644e20	0.478526	0.239263	+	0.970955i	$0.423094\pi$
$20$	5.21071e20	0.177788
$21$	−1.48145e22	−2.25979
$22$	−1.67997e22	−1.18940
$23$	4.84991e22	1.64901	0.824506	−	0.565853i	$-0.191453\pi$
$23$	4.84991e22	1.64901	0.824506	+	0.565853i	$0.191453\pi$
$24$	−1.18808e23	−2.00153
$25$	2.32831e22	0.200000
$26$	−1.64302e23	−0.738896
$27$	1.07421e24	2.59171
$28$	3.67730e23	0.486880
$29$	−8.15476e22	−0.0605124	−0.0302562	−	0.999542i	$-0.509632\pi$
$29$	−8.15476e22	−0.0605124	−0.0302562	+	0.999542i	$0.509632\pi$
$30$	−1.51012e24	−0.640487
$31$	−1.49925e24	−0.370174	−0.185087	−	0.982722i	$-0.559257\pi$
$31$	−1.49925e24	−0.370174	−0.185087	+	0.982722i	$0.559257\pi$
$32$	5.05930e24	0.739802
$33$	−3.21275e25	−2.82747
$34$	−1.50986e25	−0.811961
$35$	1.64313e25	0.547709
$36$	−4.56479e25	−0.955938
$37$	1.78708e25	0.238131	0.119066	−	0.992886i	$-0.462010\pi$
$37$	1.78708e25	0.238131	0.119066	+	0.992886i	$0.462010\pi$
$38$	4.32809e25	0.371422
$39$	−3.14210e26	−1.75652
$40$	1.31775e26	0.485113
$41$	−1.94621e26	−0.476712	−0.238356	−	0.971178i	$-0.576608\pi$
$41$	−1.94621e26	−0.476712	−0.238356	+	0.971178i	$0.576608\pi$
$42$	−1.06572e27	−1.75400
$43$	−9.48110e26	−1.05835	−0.529175	−	0.848513i	$-0.677498\pi$
$43$	−9.48110e26	−1.05835	−0.529175	+	0.848513i	$0.677498\pi$
$44$	7.97481e26	0.609187
$45$	−2.03969e27	−1.07537
$46$	3.48891e27	1.27993
$47$	−6.29157e26	−0.161862	−0.0809309	−	0.996720i	$-0.525789\pi$
$47$	−6.29157e26	−0.161862	−0.0809309	+	0.996720i	$0.525789\pi$
$48$	−4.51128e27	−0.820010
$49$	3.86494e27	0.499927
$50$	1.67493e27	0.155236
$51$	−2.88745e28	−1.93022
$52$	7.79943e27	0.378449
$53$	−8.56042e27	−0.303350	−0.151675	−	0.988430i	$-0.548467\pi$
$53$	−8.56042e27	−0.303350	−0.151675	+	0.988430i	$0.548467\pi$
$54$	7.72760e28	2.01163
$55$	3.56339e28	0.685298
$56$	9.29963e28	1.32851
$57$	8.27701e28	0.882954
$58$	−5.86635e27	−0.0469685
$59$	5.43089e27	0.0327954	0.0163977	−	0.999866i	$-0.494780\pi$
$59$	5.43089e27	0.0327954	0.0163977	+	0.999866i	$0.494780\pi$
$60$	7.16853e28	0.328046
$61$	1.79220e29	0.624373	0.312186	−	0.950021i	$-0.398939\pi$
$61$	1.79220e29	0.624373	0.312186	+	0.950021i	$0.398939\pi$
$62$	−1.07853e29	−0.287321
$63$	−1.43945e30	−2.94495
$64$	6.45635e29	1.01863
$65$	3.48503e29	0.425732
$66$	−2.31118e30	−2.19462
$67$	−3.33703e29	−0.247244	−0.123622	−	0.992329i	$-0.539451\pi$
$67$	−3.33703e29	−0.247244	−0.123622	+	0.992329i	$0.539451\pi$
$68$	7.16732e29	0.415872
$69$	6.67217e30	3.04269
$70$	1.18203e30	0.425121
$71$	−3.44997e30	−0.981866	−0.490933	−	0.871197i	$-0.663344\pi$
$71$	−3.44997e30	−0.981866	−0.490933	+	0.871197i	$0.663344\pi$
$72$	−1.15440e31	−2.60838
$73$	−7.11823e30	−1.28099	−0.640494	−	0.767963i	$-0.721270\pi$
$73$	−7.11823e30	−1.28099	−0.640494	+	0.767963i	$0.721270\pi$
$74$	1.28559e30	0.184833
$75$	3.20312e30	0.369031
$76$	−2.05455e30	−0.190236
$77$	2.51476e31	1.87672
$78$	−2.26036e31	−1.36338
$79$	−1.57830e31	−0.771510	−0.385755	−	0.922601i	$-0.626059\pi$
$79$	−1.57830e31	−0.771510	−0.385755	+	0.922601i	$0.626059\pi$
$80$	5.00364e30	0.198747
$81$	7.34723e31	2.37750
$82$	−1.40006e31	−0.370014
$83$	3.45599e31	0.747798	0.373899	−	0.927470i	$-0.378021\pi$
$83$	3.45599e31	0.747798	0.373899	+	0.927470i	$0.378021\pi$
$84$	5.05898e31	0.898369
$85$	3.20258e31	0.467830
$86$	−6.82049e31	−0.821469
$87$	−1.12188e31	−0.111655
$88$	2.01677e32	1.66223
$89$	−2.35733e32	−1.61244	−0.806222	−	0.591613i	$-0.798491\pi$
$89$	−2.35733e32	−1.61244	−0.806222	+	0.591613i	$0.798491\pi$
$90$	−1.46731e32	−0.834680
$91$	2.45946e32	1.16589
$92$	−1.65619e32	−0.655557
$93$	−2.06256e32	−0.683029
$94$	−4.52602e31	−0.125634
$95$	−9.18036e31	−0.214003
$96$	6.96024e32	1.36505
$97$	−3.55763e32	−0.588067	−0.294033	−	0.955795i	$-0.594998\pi$
$97$	−3.55763e32	−0.588067	−0.294033	+	0.955795i	$0.594998\pi$
$98$	2.78035e32	0.388033
$99$	−3.12168e33	−3.68474
$100$	−7.95091e31	−0.0795091
$101$	9.03859e32	0.767004	0.383502	−	0.923540i	$-0.374718\pi$
$101$	9.03859e32	0.767004	0.383502	+	0.923540i	$0.374718\pi$
$102$	−2.07717e33	−1.49820
$103$	2.36642e33	1.45304	0.726519	−	0.687146i	$-0.241137\pi$
$103$	2.36642e33	1.45304	0.726519	+	0.687146i	$0.241137\pi$
$104$	1.97242e33	1.03264
$105$	2.26051e33	1.01061
$106$	−6.15818e32	−0.235454
$107$	2.84756e33	0.932482	0.466241	−	0.884658i	$-0.345608\pi$
$107$	2.84756e33	0.932482	0.466241	+	0.884658i	$0.345608\pi$
$108$	−3.66830e33	−1.03032
$109$	3.46217e33	0.835241	0.417620	−	0.908622i	$-0.362864\pi$
$109$	3.46217e33	0.835241	0.417620	+	0.908622i	$0.362864\pi$
$110$	2.56343e33	0.531914
$111$	2.45855e33	0.439389
$112$	3.53117e33	0.544279
$113$	−9.04247e33	−1.20363	−0.601815	−	0.798636i	$-0.705556\pi$
$113$	−9.04247e33	−1.20363	−0.601815	+	0.798636i	$0.705556\pi$
$114$	5.95430e33	0.685331
$115$	−7.40037e33	−0.737461
$116$	2.78476e32	0.0240564
$117$	−3.05303e34	−2.28910
$118$	3.90687e32	0.0254551
$119$	2.26013e34	1.28117
$120$	1.81287e34	0.895109
$121$	3.13113e34	1.34816
$122$	1.28927e34	0.484626
$123$	−2.67746e34	−0.879608
$124$	5.11977e33	0.147161
$125$	−3.55271e33	−0.0894427
$126$	−1.03551e35	−2.28581
$127$	−4.59458e33	−0.0890194	−0.0445097	−	0.999009i	$-0.514173\pi$
$127$	−4.59458e33	−0.0890194	−0.0445097	+	0.999009i	$0.514173\pi$
$128$	2.98648e33	0.0508388
$129$	−1.30434e35	−1.95282
$130$	2.50705e34	0.330444
$131$	−2.50614e34	−0.291091	−0.145545	−	0.989352i	$-0.546494\pi$
$131$	−2.50614e34	−0.291091	−0.145545	+	0.989352i	$0.546494\pi$
$132$	1.09712e35	1.12405
$133$	−6.47877e34	−0.586058
$134$	−2.40059e34	−0.191906
$135$	−1.63911e35	−1.15905
$136$	1.81256e35	1.13475
$137$	2.78859e35	1.54702	0.773510	−	0.633784i	$-0.218499\pi$
$137$	2.78859e35	1.54702	0.773510	+	0.633784i	$0.218499\pi$
$138$	4.79981e35	2.36167
$139$	1.40995e35	0.615827	0.307914	−	0.951414i	$-0.400369\pi$
$139$	1.40995e35	0.615827	0.307914	+	0.951414i	$0.400369\pi$
$140$	−5.61112e34	−0.217739
$141$	−8.65551e34	−0.298660
$142$	−2.48183e35	−0.762104
$143$	5.33372e35	1.45877
$144$	−4.38339e35	−1.06863
$145$	1.24432e34	0.0270620
$146$	−5.12070e35	−0.994277
$147$	5.31711e35	0.922444
$148$	−6.10269e34	−0.0946680
$149$	−4.84716e35	−0.672844	−0.336422	−	0.941711i	$-0.609217\pi$
$149$	−4.84716e35	−0.672844	−0.336422	+	0.941711i	$0.609217\pi$
$150$	2.30426e35	0.286434
$151$	−1.29129e35	−0.143848	−0.0719238	−	0.997410i	$-0.522914\pi$
$151$	−1.29129e35	−0.143848	−0.0719238	+	0.997410i	$0.522914\pi$
$152$	−5.19580e35	−0.519079
$153$	−2.80559e36	−2.51545
$154$	1.80906e36	1.45667
$155$	2.28767e35	0.165547
$156$	1.07299e36	0.698298
$157$	1.48727e36	0.871052	0.435526	−	0.900176i	$-0.356562\pi$
$157$	1.48727e36	0.871052	0.435526	+	0.900176i	$0.356562\pi$
$158$	−1.13539e36	−0.598830
$159$	−1.17768e36	−0.559727
$160$	−7.71988e35	−0.330850
$161$	−5.22259e36	−2.01957
$162$	5.28543e36	1.84537
$163$	−5.65066e36	−1.78240	−0.891198	−	0.453615i	$-0.850134\pi$
$163$	−5.65066e36	−1.78240	−0.891198	+	0.453615i	$0.850134\pi$
$164$	6.64609e35	0.189515
$165$	4.90227e36	1.26448
$166$	2.48616e36	0.580425
$167$	−8.79383e36	−1.85933	−0.929665	−	0.368407i	$-0.879903\pi$
$167$	−8.79383e36	−1.85933	−0.929665	+	0.368407i	$0.879903\pi$
$168$	1.27938e37	2.45130
$169$	−5.39705e35	−0.0937617
$170$	2.30387e36	0.363120
$171$	8.04237e36	1.15066
$172$	3.23769e36	0.420742
$173$	−5.34130e36	−0.630792	−0.315396	−	0.948960i	$-0.602137\pi$
$173$	−5.34130e36	−0.630792	−0.315396	+	0.948960i	$0.602137\pi$
$174$	−8.07053e35	−0.0866641
$175$	−2.50722e36	−0.244943
$176$	7.65790e36	0.681005
$177$	7.47145e35	0.0605127
$178$	−1.69581e37	−1.25155
$179$	−1.75097e37	−1.17816	−0.589080	−	0.808075i	$-0.700510\pi$
$179$	−1.75097e37	−1.17816	−0.589080	+	0.808075i	$0.700510\pi$
$180$	6.96532e36	0.427508
$181$	1.00404e37	0.562411	0.281205	−	0.959648i	$-0.409266\pi$
$181$	1.00404e37	0.562411	0.281205	+	0.959648i	$0.409266\pi$
$182$	1.76928e37	0.904937
$183$	2.46559e37	1.15207
$184$	−4.18838e37	−1.78876
$185$	−2.72687e36	−0.106496
$186$	−1.48376e37	−0.530153
$187$	4.90144e37	1.60301
$188$	2.14850e36	0.0643474
$189$	−1.15675e38	−3.17410
$190$	−6.60415e36	−0.166105
$191$	−1.96610e37	−0.453477	−0.226739	−	0.973956i	$-0.572806\pi$
$191$	−1.96610e37	−0.453477	−0.226739	+	0.973956i	$0.572806\pi$
$192$	8.88220e37	1.87953
$193$	3.92456e37	0.762246	0.381123	−	0.924524i	$-0.375537\pi$
$193$	3.92456e37	0.762246	0.381123	+	0.924524i	$0.375537\pi$
$194$	−2.55928e37	−0.456446
$195$	4.79447e37	0.785542
$196$	−1.31983e37	−0.198744
$197$	−1.18069e38	−1.63471	−0.817357	−	0.576131i	$-0.804562\pi$
$197$	−1.18069e38	−1.63471	−0.817357	+	0.576131i	$0.804562\pi$
$198$	−2.24566e38	−2.86002
$199$	1.43693e38	1.68407	0.842035	−	0.539423i	$-0.181358\pi$
$199$	1.43693e38	1.68407	0.842035	+	0.539423i	$0.181358\pi$
$200$	−2.01073e37	−0.216949
$201$	−4.59086e37	−0.456204
$202$	6.50216e37	0.595333
$203$	8.78140e36	0.0741104
$204$	9.86031e37	0.767349
$205$	2.96968e37	0.213192
$206$	1.70235e38	1.12782
$207$	6.48302e38	3.96522
$208$	7.48949e37	0.423065
$209$	−1.40502e38	−0.733279
$210$	1.62616e38	0.784414
$211$	−2.97825e38	−1.32831	−0.664157	−	0.747593i	$-0.731210\pi$
$211$	−2.97825e38	−1.32831	−0.664157	+	0.747593i	$0.731210\pi$
$212$	2.92329e37	0.120595
$213$	−4.74623e38	−1.81170
$214$	2.04847e38	0.723773
$215$	1.44670e38	0.473308
$216$	−9.27685e38	−2.81134
$217$	1.61446e38	0.453358
$218$	2.49061e38	0.648297
$219$	−9.79278e38	−2.36362
$220$	−1.21686e38	−0.272437
$221$	4.79366e38	0.995851
$222$	1.76863e38	0.341045
$223$	−1.05983e38	−0.189761	−0.0948804	−	0.995489i	$-0.530247\pi$
$223$	−1.05983e38	−0.189761	−0.0948804	+	0.995489i	$0.530247\pi$
$224$	−5.44808e38	−0.906047
$225$	3.11232e38	0.480920
$226$	−6.50496e38	−0.934233
$227$	7.63192e38	1.01908	0.509538	−	0.860448i	$-0.329816\pi$
$227$	7.63192e38	1.01908	0.509538	+	0.860448i	$0.329816\pi$
$228$	−2.82651e38	−0.351014
$229$	2.74424e38	0.317057	0.158528	−	0.987354i	$-0.449325\pi$
$229$	2.74424e38	0.317057	0.158528	+	0.987354i	$0.449325\pi$
$230$	−5.32366e38	−0.572402
$231$	3.45963e39	3.46284
$232$	7.04245e37	0.0656406
$233$	−7.50623e38	−0.651702	−0.325851	−	0.945421i	$-0.605651\pi$
$233$	−7.50623e38	−0.651702	−0.325851	+	0.945421i	$0.605651\pi$
$234$	−2.19628e39	−1.77675
$235$	9.60017e37	0.0723868
$236$	−1.85459e37	−0.0130377
$237$	−2.17131e39	−1.42356
$238$	1.62589e39	0.994422
$239$	−9.41651e38	−0.537434	−0.268717	−	0.963219i	$-0.586600\pi$
$239$	−9.41651e38	−0.537434	−0.268717	+	0.963219i	$0.586600\pi$
$240$	6.88366e38	0.366720
$241$	−4.90507e38	−0.243985	−0.121993	−	0.992531i	$-0.538928\pi$
$241$	−4.90507e38	−0.243985	−0.121993	+	0.992531i	$0.538928\pi$
$242$	2.25247e39	1.04642
$243$	4.13623e39	1.79515
$244$	−6.12016e38	−0.248217
$245$	−5.89742e38	−0.223574
$246$	−1.92611e39	−0.682734
$247$	−1.37412e39	−0.455540
$248$	1.29475e39	0.401545
$249$	4.75452e39	1.37980
$250$	−2.55574e38	−0.0694236
$251$	5.96650e39	1.51741	0.758705	−	0.651434i	$-0.225832\pi$
$251$	5.96650e39	1.51741	0.758705	+	0.651434i	$0.225832\pi$
$252$	4.91557e39	1.17075
$253$	−1.13260e40	−2.52690
$254$	−3.30524e38	−0.0690950
$255$	4.40590e39	0.863220
$256$	−5.33112e39	−0.979172
$257$	−8.25525e39	−1.42178	−0.710892	−	0.703301i	$-0.751709\pi$
$257$	−8.25525e39	−1.42178	−0.710892	+	0.703301i	$0.751709\pi$
$258$	−9.38317e39	−1.51574
$259$	−1.92441e39	−0.291643
$260$	−1.19010e39	−0.169248
$261$	−1.09007e39	−0.145508
$262$	−1.80286e39	−0.225939
$263$	6.74712e39	0.794051	0.397026	−	0.917808i	$-0.370042\pi$
$263$	6.74712e39	0.794051	0.397026	+	0.917808i	$0.370042\pi$
$264$	2.77454e40	3.06708
$265$	1.30622e39	0.135662
$266$	−4.66068e39	−0.454886
$267$	−3.24305e40	−2.97521
$268$	1.13956e39	0.0982907
$269$	−2.97390e39	−0.241220	−0.120610	−	0.992700i	$-0.538485\pi$
$269$	−2.97390e39	−0.241220	−0.120610	+	0.992700i	$0.538485\pi$
$270$	−1.17914e40	−0.899628
$271$	−7.89524e39	−0.566725	−0.283362	−	0.959013i	$-0.591450\pi$
$271$	−7.89524e39	−0.566725	−0.283362	+	0.959013i	$0.591450\pi$
$272$	6.88250e39	0.464900
$273$	3.38355e40	2.15124
$274$	2.00605e40	1.20076
$275$	−5.43731e39	−0.306474
$276$	−2.27847e40	−1.20961
$277$	2.12171e40	1.06113	0.530566	−	0.847644i	$-0.321980\pi$
$277$	2.12171e40	1.06113	0.530566	+	0.847644i	$0.321980\pi$
$278$	1.01429e40	0.477993
$279$	−2.00409e40	−0.890120
$280$	−1.41901e40	−0.594126
$281$	4.91397e40	1.93989	0.969947	−	0.243317i	$-0.0782355\pi$
$281$	4.91397e40	1.93989	0.969947	+	0.243317i	$0.0782355\pi$
$282$	−6.22658e39	−0.231814
$283$	−4.22019e40	−1.48203	−0.741013	−	0.671491i	$-0.765654\pi$
$283$	−4.22019e40	−1.48203	−0.741013	+	0.671491i	$0.765654\pi$
$284$	1.17813e40	0.390336
$285$	−1.26297e40	−0.394869
$286$	3.83696e40	1.13226
$287$	2.09576e40	0.583836
$288$	6.76292e40	1.77893
$289$	3.79702e39	0.0943253
$290$	8.95135e38	0.0210049
$291$	−4.89434e40	−1.08508
$292$	2.43080e40	0.509251
$293$	2.96004e40	0.586115	0.293057	−	0.956095i	$-0.405327\pi$
$293$	2.96004e40	0.586115	0.293057	+	0.956095i	$0.405327\pi$
$294$	3.82502e40	0.715982
$295$	−8.28689e38	−0.0146666
$296$	−1.54333e40	−0.258312
$297$	−2.50860e41	−3.97146
$298$	−3.48694e40	−0.522248
$299$	−1.10769e41	−1.56980
$300$	−1.09383e40	−0.146707
$301$	1.02097e41	1.29618
$302$	−9.28922e39	−0.111652
$303$	1.24347e41	1.41524
$304$	−1.97290e40	−0.212663
$305$	−2.73468e40	−0.279228
$306$	−2.01828e41	−1.95244
$307$	−1.70501e41	−1.56295	−0.781474	−	0.623938i	$-0.785532\pi$
$307$	−1.70501e41	−1.56295	−0.781474	+	0.623938i	$0.785532\pi$
$308$	−8.58762e40	−0.746081
$309$	3.25556e41	2.68108
$310$	1.64570e40	0.128494
$311$	1.09238e41	0.808774	0.404387	−	0.914588i	$-0.367485\pi$
$311$	1.09238e41	0.808774	0.404387	+	0.914588i	$0.367485\pi$
$312$	2.71352e41	1.90538
$313$	−2.55151e41	−1.69948	−0.849738	−	0.527205i	$-0.823240\pi$
$313$	−2.55151e41	−1.69948	−0.849738	+	0.527205i	$0.823240\pi$
$314$	1.06991e41	0.676093
$315$	2.19643e41	1.31702
$316$	5.38971e40	0.306710
$317$	1.40033e41	0.756400	0.378200	−	0.925724i	$-0.376543\pi$
$317$	1.40033e41	0.756400	0.378200	+	0.925724i	$0.376543\pi$
$318$	−8.47200e40	−0.434449
$319$	1.90438e40	0.0927275
$320$	−9.85160e40	−0.455546
$321$	3.91748e41	1.72057
$322$	−3.75702e41	−1.56755
$323$	−1.26276e41	−0.500586
$324$	−2.50900e41	−0.945164
$325$	−5.31773e40	−0.190393
$326$	−4.06496e41	−1.38346
$327$	4.76302e41	1.54115
$328$	1.68075e41	0.517111
$329$	6.77504e40	0.198235
$330$	3.52659e41	0.981464
$331$	−2.36103e41	−0.625086	−0.312543	−	0.949904i	$-0.601181\pi$
$331$	−2.36103e41	−0.625086	−0.312543	+	0.949904i	$0.601181\pi$
$332$	−1.18018e41	−0.297283
$333$	2.38885e41	0.572611
$334$	−6.32609e41	−1.44317
$335$	5.09190e40	0.110571
$336$	4.85794e41	1.00428
$337$	5.72695e41	1.12728	0.563638	−	0.826022i	$-0.309401\pi$
$337$	5.72695e41	1.12728	0.563638	+	0.826022i	$0.309401\pi$
$338$	−3.88252e40	−0.0727759
$339$	−1.24400e42	−2.22088
$340$	−1.09365e41	−0.185984
$341$	3.50120e41	0.567244
$342$	5.78550e41	0.893121
$343$	4.16314e41	0.612446
$344$	8.18788e41	1.14804
$345$	−1.01809e42	−1.36073
$346$	−3.84241e41	−0.489608
$347$	7.23409e41	0.878917	0.439458	−	0.898263i	$-0.355170\pi$
$347$	7.23409e41	0.878917	0.439458	+	0.898263i	$0.355170\pi$
$348$	3.83108e40	0.0443878
$349$	−1.72145e42	−1.90228	−0.951140	−	0.308761i	$-0.900086\pi$
$349$	−1.72145e42	−1.90228	−0.951140	+	0.308761i	$0.900086\pi$
$350$	−1.80364e41	−0.190120
$351$	−2.45343e42	−2.46721
$352$	−1.18150e42	−1.13365
$353$	−1.10466e42	−1.01145	−0.505725	−	0.862695i	$-0.668775\pi$
$353$	−1.10466e42	−1.01145	−0.505725	+	0.862695i	$0.668775\pi$
$354$	5.37480e40	0.0469687
$355$	5.26423e41	0.439104
$356$	8.05001e41	0.641020
$357$	3.10933e42	2.36397
$358$	−1.25961e42	−0.914464
$359$	1.24115e42	0.860528	0.430264	−	0.902703i	$-0.358420\pi$
$359$	1.24115e42	0.860528	0.430264	+	0.902703i	$0.358420\pi$
$360$	1.76148e42	1.16650
$361$	−1.21880e42	−0.771013
$362$	7.22283e41	0.436532
$363$	4.30760e42	2.48757
$364$	−8.39877e41	−0.463493
$365$	1.08616e42	0.572875
$366$	1.77369e42	0.894210
$367$	7.83869e41	0.377792	0.188896	−	0.981997i	$-0.439509\pi$
$367$	7.83869e41	0.377792	0.188896	+	0.981997i	$0.439509\pi$
$368$	−1.59037e42	−0.732842
$369$	−2.60156e42	−1.14630
$370$	−1.96165e41	−0.0826597
$371$	9.21824e41	0.371517
$372$	7.04343e41	0.271535
$373$	−4.48131e42	−1.65276	−0.826378	−	0.563116i	$-0.809603\pi$
$373$	−4.48131e42	−1.65276	−0.826378	+	0.563116i	$0.809603\pi$
$374$	3.52599e42	1.24423
$375$	−4.88758e41	−0.165036
$376$	5.43340e41	0.175579
$377$	1.86251e41	0.0576057
$378$	−8.32142e42	−2.46367
$379$	5.32753e42	1.51001	0.755003	−	0.655721i	$-0.227635\pi$
$379$	5.32753e42	1.51001	0.755003	+	0.655721i	$0.227635\pi$
$380$	3.13499e41	0.0850760
$381$	−6.32091e41	−0.164255
$382$	−1.41437e42	−0.351980
$383$	7.66000e42	1.82578	0.912891	−	0.408203i	$-0.133844\pi$
$383$	7.66000e42	1.82578	0.912891	+	0.408203i	$0.133844\pi$
$384$	4.10860e41	0.0938055
$385$	−3.83722e42	−0.839295
$386$	2.82324e42	0.591640
$387$	−1.26737e43	−2.54491
$388$	1.21489e42	0.233783
$389$	2.42415e42	0.447085	0.223543	−	0.974694i	$-0.428238\pi$
$389$	2.42415e42	0.447085	0.223543	+	0.974694i	$0.428238\pi$
$390$	3.44903e42	0.609721
$391$	−1.01792e43	−1.72503
$392$	−3.33776e42	−0.542294
$393$	−3.44777e42	−0.537108
$394$	−8.49360e42	−1.26883
$395$	2.40829e42	0.345030
$396$	1.06602e43	1.46485
$397$	4.43937e42	0.585164	0.292582	−	0.956240i	$-0.405486\pi$
$397$	4.43937e42	0.585164	0.292582	+	0.956240i	$0.405486\pi$
$398$	1.03370e43	1.30714
$399$	−8.91304e42	−1.08137
$400$	−7.63495e41	−0.0888825
$401$	6.39786e41	0.0714747	0.0357374	−	0.999361i	$-0.488622\pi$
$401$	6.39786e41	0.0714747	0.0357374	+	0.999361i	$0.488622\pi$
$402$	−3.30256e42	−0.354096
$403$	3.42421e42	0.352393
$404$	−3.08658e42	−0.304919
$405$	−1.12110e43	−1.06325
$406$	6.31715e41	0.0575230
$407$	−4.17339e42	−0.364906
$408$	2.49360e43	2.09380
$409$	−1.16096e43	−0.936227	−0.468114	−	0.883668i	$-0.655066\pi$
$409$	−1.16096e43	−0.936227	−0.468114	+	0.883668i	$0.655066\pi$
$410$	2.13632e42	0.165475
$411$	3.83636e43	2.85449
$412$	−8.08105e42	−0.577649
$413$	−5.84823e41	−0.0401650
$414$	4.66374e43	3.07772
$415$	−5.27342e42	−0.334425
$416$	−1.15552e43	−0.704266
$417$	1.93971e43	1.13630
$418$	−1.01074e43	−0.569156
$419$	−7.07188e42	−0.382828	−0.191414	−	0.981509i	$-0.561307\pi$
$419$	−7.07188e42	−0.382828	−0.191414	+	0.981509i	$0.561307\pi$
$420$	−7.71939e42	−0.401763
$421$	−2.32219e43	−1.16210	−0.581050	−	0.813868i	$-0.697358\pi$
$421$	−2.32219e43	−1.16210	−0.581050	+	0.813868i	$0.697358\pi$
$422$	−2.14249e43	−1.03101
$423$	−8.41014e42	−0.389213
$424$	7.39279e42	0.329057
$425$	−4.88676e42	−0.209220
$426$	−3.41433e43	−1.40620
$427$	−1.92992e43	−0.764679
$428$	−9.72410e42	−0.370704
$429$	7.33777e43	2.69165
$430$	1.04072e43	0.367372
$431$	−3.01488e43	−1.02422	−0.512112	−	0.858919i	$-0.671137\pi$
$431$	−3.01488e43	−1.02422	−0.512112	+	0.858919i	$0.671137\pi$
$432$	−3.52252e43	−1.15179
$433$	3.63888e43	1.14530	0.572648	−	0.819802i	$-0.305916\pi$
$433$	3.63888e43	1.14530	0.572648	+	0.819802i	$0.305916\pi$
$434$	1.16141e43	0.351887
$435$	1.71185e42	0.0499335
$436$	−1.18229e43	−0.332046
$437$	2.91792e43	0.789095
$438$	−7.04471e43	−1.83460
$439$	−3.62391e42	−0.0908893	−0.0454446	−	0.998967i	$-0.514470\pi$
$439$	−3.62391e42	−0.0908893	−0.0454446	+	0.998967i	$0.514470\pi$
$440$	−3.07735e43	−0.743374
$441$	5.16638e43	1.20213
$442$	3.44845e43	0.772959
$443$	2.84653e43	0.614686	0.307343	−	0.951599i	$-0.400560\pi$
$443$	2.84653e43	0.614686	0.307343	+	0.951599i	$0.400560\pi$
$444$	−8.39567e42	−0.174677
$445$	3.59699e43	0.721107
$446$	−7.62419e42	−0.147288
$447$	−6.66840e43	−1.24150
$448$	−6.95248e43	−1.24753
$449$	−3.05597e43	−0.528548	−0.264274	−	0.964448i	$-0.585132\pi$
$449$	−3.05597e43	−0.528548	−0.264274	+	0.964448i	$0.585132\pi$
$450$	2.23893e43	0.373280
$451$	4.54499e43	0.730500
$452$	3.08790e43	0.478497
$453$	−1.77646e43	−0.265421
$454$	5.49023e43	0.790987
$455$	−3.75283e43	−0.521400
$456$	−7.14803e43	−0.957781
$457$	−8.70256e42	−0.112468	−0.0562341	−	0.998418i	$-0.517909\pi$
$457$	−8.70256e42	−0.112468	−0.0562341	+	0.998418i	$0.517909\pi$
$458$	1.97415e43	0.246093
$459$	−2.25459e44	−2.71118
$460$	2.52714e43	0.293174
$461$	7.28964e43	0.815907	0.407954	−	0.913003i	$-0.366243\pi$
$461$	7.28964e43	0.815907	0.407954	+	0.913003i	$0.366243\pi$
$462$	2.48878e44	2.68779
$463$	1.54940e44	1.61465	0.807324	−	0.590108i	$-0.200915\pi$
$463$	1.54940e44	1.61465	0.807324	+	0.590108i	$0.200915\pi$
$464$	2.67410e42	0.0268924
$465$	3.14722e43	0.305460
$466$	−5.39982e43	−0.505838
$467$	−9.15725e43	−0.828011	−0.414006	−	0.910274i	$-0.635871\pi$
$467$	−9.15725e43	−0.828011	−0.414006	+	0.910274i	$0.635871\pi$
$468$	1.04257e44	0.910020
$469$	3.59346e43	0.302804
$470$	6.90615e42	0.0561852
$471$	2.04608e44	1.60723
$472$	−4.69012e42	−0.0355747
$473$	2.21413e44	1.62179
$474$	−1.56199e44	−1.10494
$475$	1.40081e43	0.0957051
$476$	−7.71809e43	−0.509325
$477$	−1.14430e44	−0.729434
$478$	−6.77403e43	−0.417145
$479$	3.67745e43	0.218782	0.109391	−	0.993999i	$-0.465110\pi$
$479$	3.67745e43	0.218782	0.109391	+	0.993999i	$0.465110\pi$
$480$	−1.06205e44	−0.610469
$481$	−4.08161e43	−0.226693
$482$	−3.52860e43	−0.189376
$483$	−7.18488e44	−3.72642
$484$	−1.06925e44	−0.535957
$485$	5.42851e43	0.262992
$486$	2.97552e44	1.39336
$487$	2.46290e44	1.11485	0.557427	−	0.830226i	$-0.311789\pi$
$487$	2.46290e44	1.11485	0.557427	+	0.830226i	$0.311789\pi$
$488$	−1.54774e44	−0.677286
$489$	−7.77380e44	−3.28880
$490$	−4.24248e43	−0.173534
$491$	1.21128e44	0.479071	0.239535	−	0.970888i	$-0.423005\pi$
$491$	1.21128e44	0.479071	0.239535	+	0.970888i	$0.423005\pi$
$492$	9.14324e43	0.349684
$493$	1.71156e43	0.0633020
$494$	−9.88515e43	−0.353581
$495$	4.76330e44	1.64787
$496$	4.91632e43	0.164510
$497$	3.71508e44	1.20251
$498$	3.42029e44	1.07097
$499$	4.07835e44	1.23545	0.617726	−	0.786393i	$-0.288054\pi$
$499$	4.07835e44	1.23545	0.617726	+	0.786393i	$0.288054\pi$
$500$	1.21321e43	0.0355575
$501$	−1.20980e45	−3.43075
$502$	4.29217e44	1.17778
$503$	−5.88791e44	−1.56347	−0.781734	−	0.623612i	$-0.785665\pi$
$503$	−5.88791e44	−1.56347	−0.781734	+	0.623612i	$0.785665\pi$
$504$	1.24311e45	3.19452
$505$	−1.37918e44	−0.343015
$506$	−8.14768e44	−1.96133
$507$	−7.42489e43	−0.173005
$508$	1.56900e43	0.0353892
$509$	7.13633e44	1.55823	0.779115	−	0.626881i	$-0.215669\pi$
$509$	7.13633e44	1.55823	0.779115	+	0.626881i	$0.215669\pi$
$510$	3.16950e44	0.670013
$511$	7.66523e44	1.56885
$512$	−4.09163e44	−0.810852
$513$	6.46290e44	1.24020
$514$	−5.93864e44	−1.10356
$515$	−3.61087e44	−0.649819
$516$	4.45419e44	0.776335
$517$	1.46927e44	0.248033
$518$	−1.38438e44	−0.226367
$519$	−7.34820e44	−1.16391
$520$	−3.00967e44	−0.461811
$521$	−1.39893e44	−0.207957	−0.103978	−	0.994580i	$-0.533157\pi$
$521$	−1.39893e44	−0.207957	−0.103978	+	0.994580i	$0.533157\pi$
$522$	−7.84174e43	−0.112940
$523$	−4.12677e44	−0.575880	−0.287940	−	0.957648i	$-0.592970\pi$
$523$	−4.12677e44	−0.575880	−0.287940	+	0.957648i	$0.592970\pi$
$524$	8.55818e43	0.115722
$525$	−3.44927e44	−0.451958
$526$	4.85373e44	0.616326
$527$	3.14669e44	0.387239
$528$	1.05352e45	1.25656
$529$	1.48715e45	1.71924
$530$	9.39664e43	0.105298
$531$	7.25965e43	0.0788599
$532$	2.21243e44	0.232984
$533$	4.44504e44	0.453813
$534$	−2.33298e45	−2.30930
$535$	−4.34503e44	−0.417019
$536$	2.88186e44	0.268197
$537$	−2.40887e45	−2.17389
$538$	−2.13936e44	−0.187230
$539$	−9.02580e44	−0.766075
$540$	5.59737e44	0.460773
$541$	−2.35683e45	−1.88180	−0.940899	−	0.338687i	$-0.890017\pi$
$541$	−2.35683e45	−1.88180	−0.940899	+	0.338687i	$0.890017\pi$
$542$	−5.67966e44	−0.439880
$543$	1.38129e45	1.03774
$544$	−1.06187e45	−0.773907
$545$	−5.28286e44	−0.373531
$546$	2.43405e45	1.66975
$547$	2.11321e45	1.40654	0.703270	−	0.710923i	$-0.251723\pi$
$547$	2.11321e45	1.40654	0.703270	+	0.710923i	$0.251723\pi$
$548$	−9.52274e44	−0.615010
$549$	2.39569e45	1.50137
$550$	−3.91148e44	−0.237879
$551$	−4.90626e43	−0.0289567
$552$	−5.76209e45	−3.30054
$553$	1.69958e45	0.944880
$554$	1.52631e45	0.823628
$555$	−3.75145e44	−0.196501
$556$	−4.81482e44	−0.244819
$557$	2.27438e45	1.12267	0.561335	−	0.827589i	$-0.310288\pi$
$557$	2.27438e45	1.12267	0.561335	+	0.827589i	$0.310288\pi$
$558$	−1.44170e45	−0.690893
$559$	2.16544e45	1.00751
$560$	−5.38814e44	−0.243409
$561$	6.74307e45	2.95781
$562$	3.53500e45	1.50571
$563$	−1.75752e45	−0.726962	−0.363481	−	0.931602i	$-0.618412\pi$
$563$	−1.75752e45	−0.726962	−0.363481	+	0.931602i	$0.618412\pi$
$564$	2.95576e44	0.118731
$565$	1.37977e45	0.538280
$566$	−3.03591e45	−1.15032
$567$	−7.91182e45	−2.91176
$568$	2.97939e45	1.06508
$569$	9.61177e44	0.333773	0.166886	−	0.985976i	$-0.446629\pi$
$569$	9.61177e44	0.333773	0.166886	+	0.985976i	$0.446629\pi$
$570$	−9.08553e44	−0.306489
$571$	−5.28842e45	−1.73313	−0.866563	−	0.499067i	$-0.833676\pi$
$571$	−5.28842e45	−1.73313	−0.866563	+	0.499067i	$0.833676\pi$
$572$	−1.82141e45	−0.579925
$573$	−2.70483e45	−0.836737
$574$	1.50765e45	0.453162
$575$	1.12921e45	0.329803
$576$	8.63040e45	2.44940
$577$	−1.11538e45	−0.307626	−0.153813	−	0.988100i	$-0.549155\pi$
$577$	−1.11538e45	−0.307626	−0.153813	+	0.988100i	$0.549155\pi$
$578$	2.73149e44	0.0732134
$579$	5.39914e45	1.40646
$580$	−4.24921e43	−0.0107584
$581$	−3.72156e45	−0.915839
$582$	−3.52088e45	−0.842213
$583$	1.99912e45	0.464845
$584$	6.14731e45	1.38955
$585$	4.65855e45	1.02371
$586$	2.12939e45	0.454930
$587$	3.02679e45	0.628714	0.314357	−	0.949305i	$-0.398211\pi$
$587$	3.02679e45	0.628714	0.314357	+	0.949305i	$0.398211\pi$
$588$	−1.81574e45	−0.366713
$589$	−9.02014e44	−0.177138
$590$	−5.96140e43	−0.0113839
$591$	−1.62431e46	−3.01630
$592$	−5.86018e44	−0.105829
$593$	2.02049e45	0.354857	0.177428	−	0.984134i	$-0.443222\pi$
$593$	2.02049e45	0.354857	0.177428	+	0.984134i	$0.443222\pi$
$594$	−1.80463e46	−3.08256
$595$	−3.44868e45	−0.572959
$596$	1.65525e45	0.267486
$597$	1.97683e46	3.10737
$598$	−7.96851e45	−1.21845
$599$	−7.17593e45	−1.06742	−0.533710	−	0.845667i	$-0.679203\pi$
$599$	−7.17593e45	−1.06742	−0.533710	+	0.845667i	$0.679203\pi$
$600$	−2.76622e45	−0.400305
$601$	−8.79572e44	−0.123835	−0.0619174	−	0.998081i	$-0.519722\pi$
$601$	−8.79572e44	−0.123835	−0.0619174	+	0.998081i	$0.519722\pi$
$602$	7.34461e45	1.00607
$603$	−4.46071e45	−0.594523
$604$	4.40960e44	0.0571859
$605$	−4.77773e45	−0.602918
$606$	8.94523e45	1.09848
$607$	−1.35040e46	−1.61380	−0.806902	−	0.590686i	$-0.798857\pi$
$607$	−1.35040e46	−1.61380	−0.806902	+	0.590686i	$0.798857\pi$
$608$	3.04390e45	0.354014
$609$	1.20809e45	0.136745
$610$	−1.96727e45	−0.216731
$611$	1.43696e45	0.154087
$612$	9.58079e45	1.00001
$613$	−1.09063e45	−0.110810	−0.0554052	−	0.998464i	$-0.517645\pi$
$613$	−1.09063e45	−0.110810	−0.0554052	+	0.998464i	$0.517645\pi$
$614$	−1.22655e46	−1.21313
$615$	4.08548e45	0.393373
$616$	−2.17175e46	−2.03576
$617$	1.20780e46	1.10227	0.551137	−	0.834415i	$-0.314194\pi$
$617$	1.20780e46	1.10227	0.551137	+	0.834415i	$0.314194\pi$
$618$	2.34197e46	2.08100
$619$	−3.00533e45	−0.260014	−0.130007	−	0.991513i	$-0.541500\pi$
$619$	−3.00533e45	−0.260014	−0.130007	+	0.991513i	$0.541500\pi$
$620$	−7.81215e44	−0.0658124
$621$	5.20980e46	4.27376
$622$	7.85834e45	0.627754
$623$	2.53847e46	1.97478
$624$	1.03035e46	0.780621
$625$	5.42101e44	0.0400000
$626$	−1.83550e46	−1.31910
$627$	−1.93293e46	−1.35301
$628$	−5.07885e45	−0.346283
$629$	−3.75081e45	−0.249109
$630$	1.58006e46	1.02225
$631$	−2.08614e46	−1.31480	−0.657400	−	0.753542i	$-0.728344\pi$
$631$	−2.08614e46	−1.31480	−0.657400	+	0.753542i	$0.728344\pi$
$632$	1.36302e46	0.836892
$633$	−4.09728e46	−2.45095
$634$	1.00736e46	0.587102
$635$	7.01077e44	0.0398107
$636$	4.02166e45	0.222517
$637$	−8.82732e45	−0.475914
$638$	1.36997e45	0.0719732
$639$	−4.61168e46	−2.36099
$640$	−4.55701e44	−0.0227358
$641$	−1.91329e46	−0.930299	−0.465149	−	0.885232i	$-0.653999\pi$
$641$	−1.91329e46	−0.930299	−0.465149	+	0.885232i	$0.653999\pi$
$642$	2.81815e46	1.33547
$643$	−3.18460e46	−1.47087	−0.735434	−	0.677597i	$-0.763022\pi$
$643$	−3.18460e46	−1.47087	−0.735434	+	0.677597i	$0.763022\pi$
$644$	1.78346e46	0.802871
$645$	1.99027e46	0.873328
$646$	−9.08400e45	−0.388544
$647$	3.25342e46	1.35650	0.678250	−	0.734831i	$-0.262739\pi$
$647$	3.25342e46	1.35650	0.678250	+	0.734831i	$0.262739\pi$
$648$	−6.34507e46	−2.57898
$649$	−1.26828e45	−0.0502548
$650$	−3.82546e45	−0.147779
$651$	2.22106e46	0.836516
$652$	1.92964e46	0.708583
$653$	1.98304e46	0.710009	0.355005	−	0.934865i	$-0.384479\pi$
$653$	1.98304e46	0.710009	0.355005	+	0.934865i	$0.384479\pi$
$654$	3.42641e46	1.19621
$655$	3.82406e45	0.130180
$656$	6.38198e45	0.211857
$657$	−9.51517e46	−3.08026
$658$	4.87381e45	0.153866
$659$	2.96542e45	0.0913011	0.0456506	−	0.998957i	$-0.485464\pi$
$659$	2.96542e45	0.0913011	0.0456506	+	0.998957i	$0.485464\pi$
$660$	−1.67407e46	−0.502689
$661$	1.20833e46	0.353886	0.176943	−	0.984221i	$-0.443379\pi$
$661$	1.20833e46	0.353886	0.176943	+	0.984221i	$0.443379\pi$
$662$	−1.69847e46	−0.485179
$663$	6.59479e46	1.83750
$664$	−2.98460e46	−0.811170
$665$	9.88581e45	0.262093
$666$	1.71849e46	0.444449
$667$	−3.95498e45	−0.0997857
$668$	3.00300e46	0.739168
$669$	−1.45804e46	−0.350138
$670$	3.66300e45	0.0858229
$671$	−4.18533e46	−0.956772
$672$	−7.49509e46	−1.67180
$673$	2.52503e46	0.549565	0.274782	−	0.961506i	$-0.411394\pi$
$673$	2.52503e46	0.549565	0.274782	+	0.961506i	$0.411394\pi$
$674$	4.11984e46	0.874968
$675$	2.50108e46	0.518341
$676$	1.84303e45	0.0372745
$677$	3.98633e46	0.786793	0.393396	−	0.919369i	$-0.371300\pi$
$677$	3.98633e46	0.786793	0.393396	+	0.919369i	$0.371300\pi$
$678$	−8.94908e46	−1.72381
$679$	3.83101e46	0.720215
$680$	−2.76575e46	−0.507477
$681$	1.04995e47	1.88036
$682$	2.51869e46	0.440284
$683$	−3.89128e46	−0.663973	−0.331986	−	0.943284i	$-0.607719\pi$
$683$	−3.89128e46	−0.663973	−0.331986	+	0.943284i	$0.607719\pi$
$684$	−2.74638e46	−0.457441
$685$	−4.25506e46	−0.691848
$686$	2.99487e46	0.475368
$687$	3.77534e46	0.585019
$688$	3.10903e46	0.470344
$689$	1.95516e46	0.288778
$690$	−7.32393e46	−1.05617
$691$	−3.16293e46	−0.445350	−0.222675	−	0.974893i	$-0.571479\pi$
$691$	−3.16293e46	−0.445350	−0.222675	+	0.974893i	$0.571479\pi$
$692$	1.82399e46	0.250769
$693$	3.36156e47	4.51276
$694$	5.20405e46	0.682197
$695$	−2.15141e46	−0.275406
$696$	9.68853e45	0.121117
$697$	4.08479e46	0.498688
$698$	−1.23837e47	−1.47651
$699$	−1.03266e47	−1.20249
$700$	8.56189e45	0.0973760
$701$	−5.26072e46	−0.584384	−0.292192	−	0.956360i	$-0.594385\pi$
$701$	−5.26072e46	−0.584384	−0.292192	+	0.956360i	$0.594385\pi$
$702$	−1.76495e47	−1.91500
$703$	1.07519e46	0.113952
$704$	−1.50775e47	−1.56092
$705$	1.32073e46	0.133565
$706$	−7.94665e46	−0.785066
$707$	−9.73315e46	−0.939362
$708$	−2.55142e45	−0.0240565
$709$	1.31306e47	1.20954	0.604771	−	0.796399i	$-0.293265\pi$
$709$	1.31306e47	1.20954	0.604771	+	0.796399i	$0.293265\pi$
$710$	3.78697e46	0.340823
$711$	−2.10976e47	−1.85517
$712$	2.03579e47	1.74909
$713$	−7.27122e46	−0.610422
$714$	2.23678e47	1.83486
$715$	−8.13861e46	−0.652380
$716$	5.97938e46	0.468372
$717$	−1.29546e47	−0.991649
$718$	8.92855e46	0.667925
$719$	1.58298e47	1.15731	0.578653	−	0.815574i	$-0.303579\pi$
$719$	1.58298e47	1.15731	0.578653	+	0.815574i	$0.303579\pi$
$720$	6.68852e46	0.477908
$721$	−2.54826e47	−1.77956
$722$	−8.76774e46	−0.598445
$723$	−6.74806e46	−0.450191
$724$	−3.42868e46	−0.223584
$725$	−1.89868e45	−0.0121025
$726$	3.09879e47	1.93080
$727$	−2.56013e47	−1.55935	−0.779676	−	0.626184i	$-0.784616\pi$
$727$	−2.56013e47	−1.55935	−0.779676	+	0.626184i	$0.784616\pi$
$728$	−2.12399e47	−1.26469
$729$	1.60598e47	0.934838
$730$	7.81357e46	0.444654
$731$	1.98994e47	1.10714
$732$	−8.41970e46	−0.457998
$733$	−5.58232e46	−0.296893	−0.148446	−	0.988920i	$-0.547427\pi$
$733$	−5.58232e46	−0.296893	−0.148446	+	0.988920i	$0.547427\pi$
$734$	5.63898e46	0.293235
$735$	−8.11327e46	−0.412529
$736$	2.45371e47	1.21994
$737$	7.79298e46	0.378870
$738$	−1.87150e47	−0.889736
$739$	1.40164e47	0.651634	0.325817	−	0.945433i	$-0.394361\pi$
$739$	1.40164e47	0.651634	0.325817	+	0.945433i	$0.394361\pi$
$740$	9.31197e45	0.0423368
$741$	−1.89043e47	−0.840542
$742$	6.63140e46	0.288364
$743$	3.74285e46	0.159180	0.0795898	−	0.996828i	$-0.474639\pi$
$743$	3.74285e46	0.159180	0.0795898	+	0.996828i	$0.474639\pi$
$744$	1.78123e47	0.740913
$745$	7.39618e46	0.300905
$746$	−3.22375e47	−1.28284
$747$	4.61973e47	1.79815
$748$	−1.67379e47	−0.637271
$749$	−3.06638e47	−1.14202
$750$	−3.51602e46	−0.128097
$751$	2.45331e47	0.874365	0.437182	−	0.899373i	$-0.355976\pi$
$751$	2.45331e47	0.874365	0.437182	+	0.899373i	$0.355976\pi$
$752$	2.06312e46	0.0719334
$753$	8.20830e47	2.79986
$754$	1.33985e46	0.0447124
$755$	1.97035e46	0.0643306
$756$	3.95018e47	1.26185
$757$	3.89117e47	1.21618	0.608090	−	0.793868i	$-0.291936\pi$
$757$	3.89117e47	1.21618	0.608090	+	0.793868i	$0.291936\pi$
$758$	3.83251e47	1.17204
$759$	−1.55815e48	−4.66253
$760$	7.92816e46	0.232139
$761$	−2.57108e47	−0.736662	−0.368331	−	0.929695i	$-0.620071\pi$
$761$	−2.57108e47	−0.736662	−0.368331	+	0.929695i	$0.620071\pi$
$762$	−4.54712e46	−0.127491
$763$	−3.72822e47	−1.02293
$764$	6.71402e46	0.180278
$765$	4.28100e47	1.12494
$766$	5.51044e47	1.41714
$767$	−1.24039e46	−0.0312201
$768$	−7.33419e47	−1.80672
$769$	1.74753e47	0.421348	0.210674	−	0.977556i	$-0.432434\pi$
$769$	1.74753e47	0.421348	0.210674	+	0.977556i	$0.432434\pi$
$770$	−2.76041e47	−0.651443
$771$	−1.13570e48	−2.62341
$772$	−1.34019e47	−0.303027
$773$	1.07838e47	0.238676	0.119338	−	0.992854i	$-0.461923\pi$
$773$	1.07838e47	0.238676	0.119338	+	0.992854i	$0.461923\pi$
$774$	−9.11717e47	−1.97531
$775$	−3.49071e46	−0.0740348
$776$	3.07237e47	0.637903
$777$	−2.64747e47	−0.538127
$778$	1.74388e47	0.347019
$779$	−1.17093e47	−0.228119
$780$	−1.63726e47	−0.312288
$781$	8.05672e47	1.50458
$782$	−7.32269e47	−1.33893
$783$	−8.75990e46	−0.156830
$784$	−1.26738e47	−0.222174
$785$	−2.26939e47	−0.389546
$786$	−2.48025e47	−0.416892
$787$	−2.21953e47	−0.365324	−0.182662	−	0.983176i	$-0.558471\pi$
$787$	−2.21953e47	−0.365324	−0.182662	+	0.983176i	$0.558471\pi$
$788$	4.03191e47	0.649873
$789$	9.28223e47	1.46515
$790$	1.73247e47	0.267805
$791$	9.73733e47	1.47410
$792$	2.69588e48	3.99701
$793$	−4.09329e47	−0.594382
$794$	3.19358e47	0.454192
$795$	1.79700e47	0.250318
$796$	−4.90696e47	−0.669494
$797$	9.77934e47	1.30691	0.653457	−	0.756963i	$-0.273318\pi$
$797$	9.77934e47	1.30691	0.653457	+	0.756963i	$0.273318\pi$
$798$	−6.41185e47	−0.839335
$799$	1.32050e47	0.169324
$800$	1.17796e47	0.147960
$801$	−3.15111e48	−3.87728
$802$	4.60248e46	0.0554772
$803$	1.66232e48	1.96295
$804$	1.56773e47	0.181362
$805$	7.96904e47	0.903180
$806$	2.46330e47	0.273520
$807$	−4.09129e47	−0.445089
$808$	−7.80573e47	−0.832005
$809$	−6.43989e47	−0.672555	−0.336278	−	0.941763i	$-0.609168\pi$
$809$	−6.43989e47	−0.672555	−0.336278	+	0.941763i	$0.609168\pi$
$810$	−8.06493e47	−0.825273
$811$	−3.92035e47	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$811$	−3.92035e47	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$812$	−2.99875e46	−0.0294623
$813$	−1.08617e48	−1.04570
$814$	−3.00224e47	−0.283232
$815$	8.62223e47	0.797111
$816$	9.46847e47	0.857813
$817$	−5.70425e47	−0.506447
$818$	−8.35166e47	−0.726680
$819$	3.28763e48	2.80349
$820$	−1.01411e47	−0.0847535
$821$	−3.66301e47	−0.300038	−0.150019	−	0.988683i	$-0.547934\pi$
$821$	−3.66301e47	−0.300038	−0.150019	+	0.988683i	$0.547934\pi$
$822$	2.75979e48	2.21560
$823$	6.74278e47	0.530569	0.265284	−	0.964170i	$-0.414534\pi$
$823$	6.74278e47	0.530569	0.265284	+	0.964170i	$0.414534\pi$
$824$	−2.04364e48	−1.57618
$825$	−7.48027e47	−0.565493
$826$	−4.20708e46	−0.0311753
$827$	−1.83329e48	−1.33165	−0.665827	−	0.746106i	$-0.731921\pi$
$827$	−1.83329e48	−1.33165	−0.665827	+	0.746106i	$0.731921\pi$
$828$	−2.21388e48	−1.57635
$829$	1.99989e48	1.39591	0.697954	−	0.716142i	$-0.254094\pi$
$829$	1.99989e48	1.39591	0.697954	+	0.716142i	$0.254094\pi$
$830$	−3.79358e47	−0.259574
$831$	2.91890e48	1.95795
$832$	−1.47460e48	−0.969702
$833$	−8.11190e47	−0.522974
$834$	1.39539e48	0.881971
$835$	1.34183e48	0.831517
$836$	4.79799e47	0.291512
$837$	−1.61050e48	−0.959382
$838$	−5.08735e47	−0.297143
$839$	−7.68878e47	−0.440337	−0.220168	−	0.975462i	$-0.570661\pi$
$839$	−7.68878e47	−0.440337	−0.220168	+	0.975462i	$0.570661\pi$
$840$	−1.95218e48	−1.09625
$841$	−1.80943e48	−0.996338
$842$	−1.67053e48	−0.901998
$843$	6.76030e48	3.57941
$844$	1.01704e48	0.528065
$845$	8.23524e46	0.0419315
$846$	−6.05007e47	−0.302099
$847$	−3.37174e48	−1.65112
$848$	2.80712e47	0.134812
$849$	−5.80585e48	−2.73457
$850$	−3.51542e47	−0.162392
$851$	8.66719e47	0.392682
$852$	1.62078e48	0.720231
$853$	1.63399e47	0.0712180	0.0356090	−	0.999366i	$-0.488663\pi$
$853$	1.63399e47	0.0712180	0.0356090	+	0.999366i	$0.488663\pi$
$854$	−1.38834e48	−0.593528
$855$	−1.22717e48	−0.514592
$856$	−2.45915e48	−1.01151
$857$	−5.35960e47	−0.216247	−0.108123	−	0.994137i	$-0.534484\pi$
$857$	−5.35960e47	−0.216247	−0.108123	+	0.994137i	$0.534484\pi$
$858$	5.27863e48	2.08920
$859$	−3.45793e48	−1.34255	−0.671273	−	0.741210i	$-0.734252\pi$
$859$	−3.45793e48	−1.34255	−0.671273	+	0.741210i	$0.734252\pi$
$860$	−4.94032e47	−0.188162
$861$	2.88321e48	1.07727
$862$	−2.16884e48	−0.794982
$863$	1.95932e48	0.704574	0.352287	−	0.935892i	$-0.385404\pi$
$863$	1.95932e48	0.704574	0.352287	+	0.935892i	$0.385404\pi$
$864$	5.43473e48	1.91735
$865$	8.15018e47	0.282099
$866$	2.61773e48	0.888955
$867$	5.22368e47	0.174045
$868$	−5.51319e47	−0.180230
$869$	3.68580e48	1.18224
$870$	1.23146e47	0.0387574
$871$	7.62161e47	0.235368
$872$	−2.98994e48	−0.906024
$873$	−4.75559e48	−1.41407
$874$	2.09908e48	0.612479
$875$	3.82572e47	0.109542
$876$	3.34413e48	0.939647
$877$	1.31812e48	0.363464	0.181732	−	0.983348i	$-0.441830\pi$
$877$	1.31812e48	0.363464	0.181732	+	0.983348i	$0.441830\pi$
$878$	−2.60696e47	−0.0705464
$879$	4.07223e48	1.08147
$880$	−1.16850e48	−0.304555
$881$	6.02351e48	1.54080	0.770401	−	0.637559i	$-0.220056\pi$
$881$	6.02351e48	1.54080	0.770401	+	0.637559i	$0.220056\pi$
$882$	3.71658e48	0.933065
$883$	−5.51914e48	−1.35994	−0.679970	−	0.733240i	$-0.738007\pi$
$883$	−5.51914e48	−1.35994	−0.679970	+	0.733240i	$0.738007\pi$
$884$	−1.63698e48	−0.395896
$885$	−1.14005e47	−0.0270621
$886$	2.04773e48	0.477107
$887$	2.46908e48	0.564672	0.282336	−	0.959316i	$-0.408891\pi$
$887$	2.46908e48	0.564672	0.282336	+	0.959316i	$0.408891\pi$
$888$	−2.12320e48	−0.476626
$889$	4.94765e47	0.109023
$890$	2.58760e48	0.559708
$891$	−1.71580e49	−3.64322
$892$	3.61921e47	0.0754385
$893$	−3.78528e47	−0.0774550
$894$	−4.79710e48	−0.963628
$895$	2.67177e48	0.526889
$896$	−3.21597e47	−0.0622631
$897$	−1.52389e49	−2.89653
$898$	−2.19840e48	−0.410248
$899$	1.22260e47	0.0224001
$900$	−1.06282e48	−0.191188
$901$	1.79670e48	0.317334
$902$	3.26957e48	0.566999
$903$	1.40458e49	2.39165
$904$	7.80909e48	1.30563
$905$	−1.53204e48	−0.251518
$906$	−1.27795e48	−0.206015
$907$	1.76568e48	0.279507	0.139753	−	0.990186i	$-0.455369\pi$
$907$	1.76568e48	0.279507	0.139753	+	0.990186i	$0.455369\pi$
$908$	−2.60621e48	−0.405129
$909$	1.20822e49	1.84434
$910$	−2.69971e48	−0.404700
$911$	−4.90626e48	−0.722266	−0.361133	−	0.932514i	$-0.617610\pi$
$911$	−4.90626e48	−0.722266	−0.361133	+	0.932514i	$0.617610\pi$
$912$	−2.71418e48	−0.392396
$913$	−8.07079e48	−1.14590
$914$	−6.26043e47	−0.0872955
$915$	−3.76219e48	−0.515219
$916$	−9.37128e47	−0.126044
$917$	2.69872e48	0.356503
$918$	−1.62190e49	−2.10437
$919$	−7.03091e48	−0.895994	−0.447997	−	0.894035i	$-0.647863\pi$
$919$	−7.03091e48	−0.895994	−0.447997	+	0.894035i	$0.647863\pi$
$920$	6.39096e48	0.799958
$921$	−2.34564e49	−2.88388
$922$	5.24400e48	0.633290
$923$	7.87955e48	0.934702
$924$	−1.18143e49	−1.37664
$925$	4.16088e47	0.0476263
$926$	1.11461e49	1.25326
$927$	3.16327e49	3.49398
$928$	−4.12574e47	−0.0447672
$929$	3.42900e48	0.365517	0.182759	−	0.983158i	$-0.441497\pi$
$929$	3.42900e48	0.365517	0.182759	+	0.983158i	$0.441497\pi$
$930$	2.26404e48	0.237092
$931$	2.32532e48	0.239228
$932$	2.56329e48	0.259081
$933$	1.50282e49	1.49231
$934$	−6.58752e48	−0.642686
$935$	−7.47901e48	−0.716890
$936$	2.63660e49	2.48309
$937$	−2.88611e48	−0.267060	−0.133530	−	0.991045i	$-0.542631\pi$
$937$	−2.88611e48	−0.267060	−0.133530	+	0.991045i	$0.542631\pi$
$938$	2.58506e48	0.235030
$939$	−3.51019e49	−3.13580
$940$	−3.27835e47	−0.0287770
$941$	−1.90690e49	−1.64475	−0.822373	−	0.568949i	$-0.807350\pi$
$941$	−1.90690e49	−1.64475	−0.822373	+	0.568949i	$0.807350\pi$
$942$	1.47190e49	1.24750
$943$	−9.43893e48	−0.786104
$944$	−1.78089e47	−0.0145747
$945$	1.76506e49	1.41950
$946$	1.59279e49	1.25880
$947$	7.16410e48	0.556400	0.278200	−	0.960523i	$-0.410262\pi$
$947$	7.16410e48	0.556400	0.278200	+	0.960523i	$0.410262\pi$
$948$	7.41479e48	0.565928
$949$	1.62577e49	1.21946
$950$	1.00771e48	0.0742843
$951$	1.92647e49	1.39568
$952$	−1.95185e49	−1.38975
$953$	3.01662e48	0.211100	0.105550	−	0.994414i	$-0.466340\pi$
$953$	3.01662e48	0.211100	0.105550	+	0.994414i	$0.466340\pi$
$954$	−8.23183e48	−0.566172
$955$	3.00004e48	0.202801
$956$	3.21563e48	0.213654
$957$	2.61992e48	0.171097
$958$	2.64548e48	0.169814
$959$	−3.00288e49	−1.89466
$960$	−1.35532e49	−0.840553
$961$	−1.41557e49	−0.862971
$962$	−2.93622e48	−0.175954
$963$	3.80642e49	2.24225
$964$	1.67503e48	0.0969952
$965$	−5.98840e48	−0.340887
$966$	−5.16865e49	−2.89237
$967$	−9.56534e48	−0.526216	−0.263108	−	0.964766i	$-0.584748\pi$
$967$	−9.56534e48	−0.526216	−0.263108	+	0.964766i	$0.584748\pi$
$968$	−2.70405e49	−1.46242
$969$	−1.73722e49	−0.923658
$970$	3.90515e48	0.204129
$971$	3.02376e49	1.55392	0.776961	−	0.629548i	$-0.216760\pi$
$971$	3.02376e49	1.55392	0.776961	+	0.629548i	$0.216760\pi$
$972$	−1.41248e49	−0.713655
$973$	−1.51829e49	−0.754213
$974$	1.77175e49	0.865327
$975$	−7.31578e48	−0.351305
$976$	−5.87695e48	−0.277479
$977$	5.10941e48	0.237198	0.118599	−	0.992942i	$-0.462160\pi$
$977$	5.10941e48	0.237198	0.118599	+	0.992942i	$0.462160\pi$
$978$	−5.59230e49	−2.55270
$979$	5.50508e49	2.47086
$980$	2.01390e48	0.0888809
$981$	4.62800e49	2.00842
$982$	8.71368e48	0.371845
$983$	−1.15145e49	−0.483183	−0.241591	−	0.970378i	$-0.577669\pi$
$983$	−1.15145e49	−0.483183	−0.241591	+	0.970378i	$0.577669\pi$
$984$	2.31226e49	0.954151
$985$	1.80159e49	0.731067
$986$	1.23126e48	0.0491337
$987$	9.32064e48	0.365774
$988$	4.69248e48	0.181098
$989$	−4.59824e49	−1.74523
$990$	3.42661e49	1.27904
$991$	6.06784e48	0.222751	0.111375	−	0.993778i	$-0.464474\pi$
$991$	6.06784e48	0.222751	0.111375	+	0.993778i	$0.464474\pi$
$992$	−7.58515e48	−0.273856
$993$	−3.24815e49	−1.15338
$994$	2.67254e49	0.933361
$995$	−2.19258e49	−0.753139
$996$	−1.62361e49	−0.548534
$997$	3.14175e49	1.04400	0.522000	−	0.852945i	$-0.325186\pi$
$997$	3.14175e49	1.04400	0.522000	+	0.852945i	$0.325186\pi$
$998$	2.93388e49	0.958932
$999$	1.91970e49	0.617166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.a.1.4	✓	5
5.2	odd	4		25.34.b.b.24.8		10
5.3	odd	4		25.34.b.b.24.3		10
5.4	even	2		25.34.a.b.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.4	✓	5	1.1	even	1	trivial
25.34.a.b.1.2		5	5.4	even	2
25.34.b.b.24.3		10	5.3	odd	4
25.34.b.b.24.8		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)

\(f(q)\)	\(=\)	\(q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} +O(q^{10})\)	\(q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} -1.09768e16 q^{10} -2.33530e17 q^{11} -4.69797e17 q^{12} -2.28395e18 q^{13} -7.74658e18 q^{14} -2.09920e19 q^{15} -3.27918e19 q^{16} -2.09885e20 q^{17} +9.61615e20 q^{18} +6.01644e20 q^{19} +5.21071e20 q^{20} -1.48145e22 q^{21} -1.67997e22 q^{22} +4.84991e22 q^{23} -1.18808e23 q^{24} +2.32831e22 q^{25} -1.64302e23 q^{26} +1.07421e24 q^{27} +3.67730e23 q^{28} -8.15476e22 q^{29} -1.51012e24 q^{30} -1.49925e24 q^{31} +5.05930e24 q^{32} -3.21275e25 q^{33} -1.50986e25 q^{34} +1.64313e25 q^{35} -4.56479e25 q^{36} +1.78708e25 q^{37} +4.32809e25 q^{38} -3.14210e26 q^{39} +1.31775e26 q^{40} -1.94621e26 q^{41} -1.06572e27 q^{42} -9.48110e26 q^{43} +7.97481e26 q^{44} -2.03969e27 q^{45} +3.48891e27 q^{46} -6.29157e26 q^{47} -4.51128e27 q^{48} +3.86494e27 q^{49} +1.67493e27 q^{50} -2.88745e28 q^{51} +7.79943e27 q^{52} -8.56042e27 q^{53} +7.72760e28 q^{54} +3.56339e28 q^{55} +9.29963e28 q^{56} +8.27701e28 q^{57} -5.86635e27 q^{58} +5.43089e27 q^{59} +7.16853e28 q^{60} +1.79220e29 q^{61} -1.07853e29 q^{62} -1.43945e30 q^{63} +6.45635e29 q^{64} +3.48503e29 q^{65} -2.31118e30 q^{66} -3.33703e29 q^{67} +7.16732e29 q^{68} +6.67217e30 q^{69} +1.18203e30 q^{70} -3.44997e30 q^{71} -1.15440e31 q^{72} -7.11823e30 q^{73} +1.28559e30 q^{74} +3.20312e30 q^{75} -2.05455e30 q^{76} +2.51476e31 q^{77} -2.26036e31 q^{78} -1.57830e31 q^{79} +5.00364e30 q^{80} +7.34723e31 q^{81} -1.40006e31 q^{82} +3.45599e31 q^{83} +5.05898e31 q^{84} +3.20258e31 q^{85} -6.82049e31 q^{86} -1.12188e31 q^{87} +2.01677e32 q^{88} -2.35733e32 q^{89} -1.46731e32 q^{90} +2.45946e32 q^{91} -1.65619e32 q^{92} -2.06256e32 q^{93} -4.52602e31 q^{94} -9.18036e31 q^{95} +6.96024e32 q^{96} -3.55763e32 q^{97} +2.78035e32 q^{98} -3.12168e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 30472 q^{2} - 14988714 q^{3} + 1141311360 q^{4} - 762939453125 q^{5} + 12925063115760 q^{6} - 65452561787158 q^{7} + 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 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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