LMFDB - Embedded newform 1.40.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,40,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 40, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	1.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:	$9.63395513897$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 175630027x - 142249227846 $ x^3 - 175630027*x - 142249227846
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5}\cdot 5\cdot 13 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-12827.3$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +O(q^{10})$	\(q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +2.81604e19 q^{10} +7.53597e19 q^{11} +2.01573e21 q^{12} +3.07373e21 q^{13} -5.59707e22 q^{14} +7.60408e22 q^{15} -2.17987e23 q^{16} -4.56106e23 q^{17} +5.39430e24 q^{18} -1.63031e24 q^{19} +1.71691e25 q^{20} -1.51136e26 q^{21} +8.33870e25 q^{22} +2.17009e26 q^{23} +4.12858e26 q^{24} -1.17131e27 q^{25} +3.40114e27 q^{26} +2.45742e27 q^{27} -3.41246e28 q^{28} -6.88782e27 q^{29} +8.41407e28 q^{30} +1.62636e29 q^{31} -3.17170e29 q^{32} +2.25168e29 q^{33} -5.04690e29 q^{34} -1.28730e30 q^{35} +3.28883e30 q^{36} -1.23773e30 q^{37} -1.80397e30 q^{38} +9.18399e30 q^{39} +3.51653e30 q^{40} +1.60595e31 q^{41} -1.67235e32 q^{42} +1.28211e32 q^{43} +5.08400e31 q^{44} +1.24067e32 q^{45} +2.40125e32 q^{46} -6.09258e32 q^{47} -6.51324e32 q^{48} +1.64906e33 q^{49} -1.29608e33 q^{50} -1.36280e33 q^{51} +2.07363e33 q^{52} +1.51248e33 q^{53} +2.71918e33 q^{54} +1.91787e33 q^{55} -6.98933e33 q^{56} -4.87122e33 q^{57} -7.62152e33 q^{58} -4.73479e34 q^{59} +5.12995e34 q^{60} +7.02166e34 q^{61} +1.79960e35 q^{62} -2.46591e35 q^{63} -2.31116e35 q^{64} +7.82250e34 q^{65} +2.49152e35 q^{66} -9.34963e34 q^{67} -3.07703e35 q^{68} +6.48402e35 q^{69} -1.42443e36 q^{70} +2.40247e36 q^{71} +6.73613e35 q^{72} -7.72964e35 q^{73} -1.36958e36 q^{74} -3.49976e36 q^{75} -1.09986e36 q^{76} -3.81189e36 q^{77} +1.01623e37 q^{78} +1.44777e37 q^{79} -5.54767e36 q^{80} -1.24137e37 q^{81} +1.77702e37 q^{82} +1.12684e37 q^{83} -1.01961e38 q^{84} -1.16077e37 q^{85} +1.41868e38 q^{86} -2.05802e37 q^{87} +1.04129e37 q^{88} -1.09111e38 q^{89} +1.37282e38 q^{90} -1.55477e38 q^{91} +1.46401e38 q^{92} +4.85940e38 q^{93} -6.74156e38 q^{94} -4.14907e37 q^{95} -9.47674e38 q^{96} +7.84026e37 q^{97} +1.82471e39 q^{98} +3.67379e38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 83\!\cdots\!91 q^{9}+O(q^{10}) $ 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9	$ 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) $ 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9 + 90373081165367671440 * q^10 + 667814968265751536076 * q^11 + 3676571280854873162496 * q^12 + 3156080701447967254962 * q^13 - 63063724565889303463872 * q^14 - 171209278264452417200520 * q^15 - 351730940560369057001472 * q^16 + 890025791008793741893206 * q^17 + 8758537968130529168653272 * q^18 + 9227612185007697573518580 * q^19 - 14662452947108747596260480 * q^20 - 190208658572592931471251744 * q^21 - 122745877544387429034313248 * q^22 + 305308591470919570740188472 * q^23 + 1672960268636194560046295040 * q^24 + 1866127065486173095027030725 * q^25 + 283778605804595582169202896 * q^26 - 11508090459893795046427628760 * q^27 - 41794856371466593385827533312 * q^28 - 2492682219258648277296444030 * q^29 + 105977898643957401776506418880 * q^30 + 306107671747822704409554746016 * q^31 - 56572224161556180973554008064 * q^32 - 157376353761155567959844693616 * q^33 - 1683392869529765869103799245712 * q^34 - 1197259217905835166323668756560 * q^35 + 188684323073267404408057366848 * q^36 + 7599073412303579174888591086506 * q^37 + 2479871855304922949496616465440 * q^38 + 22252083518345402015145920059992 * q^39 - 32669995448979982796588503833600 * q^40 + 2391924206237769506232479990286 * q^41 - 195689966839404680756969540713728 * q^42 + 162865923671547339657067136304492 * q^43 - 45577647299113910363374898556672 * q^44 + 588908524142943445153326555470130 * q^45 - 24296541145531030477977021520704 * q^46 + 202683231875405841765643043683056 * q^47 - 1747281225742357435119054532067328 * q^48 + 368237681722499062385273201641179 * q^49 - 2624175085265540082696197615369400 * q^50 + 785651103815434341253216161914376 * q^51 + 3782687188757116950236456253499776 * q^52 + 5869079988764517679853946632443002 * q^53 + 7930814851979058696152103557167680 * q^54 - 4993109836111426485910134681304920 * q^55 - 6272116703248607238900430116679680 * q^56 - 46129102671186186415908500969957520 * q^57 + 2579097256656295554169870267982160 * q^58 - 56082681385621280317109288669637060 * q^59 + 127333179651658235430567238147607040 * q^60 + 39577675682126428331898689976833826 * q^61 + 262011550289381451529348830657714432 * q^62 - 174786720262353444072185876495505528 * q^63 - 169364906963561439583712861665099776 * q^64 - 264857762104053085095614223637519620 * q^65 - 287121760972609093376568794235255168 * q^66 - 140659929656119892877736400727430044 * q^67 - 130643133997460537100958647836349312 * q^68 + 1584175048695702801789842685209503392 * q^69 - 480338235822643784458804278358623360 * q^70 + 3849053210874068146700295241416217896 * q^71 - 1699150852984576616740529956276922880 * q^72 - 180754136492273067100959984036797778 * q^73 - 5070707041697857186532012041702753392 * q^74 - 4308561205008052508725896857031567300 * q^75 - 7362591710990284189025184136271151360 * q^76 + 5690389092595065468343565382905921952 * q^77 + 9330105385756793042468361274821534144 * q^78 + 13807772201216229289895673856694559120 * q^79 + 26839954555034162361105063302056304640 * q^80 - 18798023146176620962298765658838887237 * q^81 + 5068915865662526415092477483885831472 * q^82 - 20899400147905548803677768348186808268 * q^83 - 72152575898640813291791263837177976832 * q^84 - 105991789747453754784809897833488498060 * q^85 + 170012097580285110854272781787916483296 * q^86 - 73247996942640959139716393654519138280 * q^87 + 69412125637007165807333386173055825920 * q^88 + 205050039910109857136561853222076224510 * q^89 + 93221656611667223268126392859978755280 * q^90 - 165525104998331842571199169888366982544 * q^91 + 262356454404517646077951321169615264256 * q^92 - 167325068951627887866919523900021629056 * q^93 - 1127972668535151884588260809571286639232 * q^94 + 724803433705663618674774120451764528600 * q^95 - 1451094524490643350592064137029388468224 * q^96 + 173490888317728793437812209497231327206 * q^97 + 2246791677555180938475077451719860538808 * q^98 + 1057018158118568141770036034713090936572 * 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 $

$2$	1.10652e6	1.49236	0.746181	−	0.665743i	$-0.231885\pi$
$2$	1.10652e6	1.49236	0.746181	+	0.665743i	$0.231885\pi$
$3$	2.98790e9	1.48423	0.742116	−	0.670271i	$-0.233822\pi$
$3$	2.98790e9	1.48423	0.742116	+	0.670271i	$0.233822\pi$
$4$	6.74631e11	1.22715
$5$	2.54496e13	0.596713	0.298356	−	0.954455i	$-0.403562\pi$
$5$	2.54496e13	0.596713	0.298356	+	0.954455i	$0.403562\pi$
$6$	3.30617e15	2.21501
$7$	−5.05826e16	−1.67722	−0.838609	−	0.544734i	$-0.816631\pi$
$7$	−5.05826e16	−1.67722	−0.838609	+	0.544734i	$0.816631\pi$
$8$	1.38177e17	0.338984
$9$	4.87501e18	1.20295
$10$	2.81604e19	0.890511
$11$	7.53597e19	0.371520	0.185760	−	0.982595i	$-0.440525\pi$
$11$	7.53597e19	0.371520	0.185760	+	0.982595i	$0.440525\pi$
$12$	2.01573e21	1.82137
$13$	3.07373e21	0.583136	0.291568	−	0.956550i	$-0.405823\pi$
$13$	3.07373e21	0.583136	0.291568	+	0.956550i	$0.405823\pi$
$14$	−5.59707e22	−2.50302
$15$	7.60408e22	0.885660
$16$	−2.17987e23	−0.721258
$17$	−4.56106e23	−0.462713	−0.231357	−	0.972869i	$-0.574316\pi$
$17$	−4.56106e23	−0.462713	−0.231357	+	0.972869i	$0.574316\pi$
$18$	5.39430e24	1.79523
$19$	−1.63031e24	−0.189050	−0.0945248	−	0.995523i	$-0.530133\pi$
$19$	−1.63031e24	−0.189050	−0.0945248	+	0.995523i	$0.530133\pi$
$20$	1.71691e25	0.732253
$21$	−1.51136e26	−2.48938
$22$	8.33870e25	0.554442
$23$	2.17009e26	0.606436	0.303218	−	0.952921i	$-0.401939\pi$
$23$	2.17009e26	0.606436	0.303218	+	0.952921i	$0.401939\pi$
$24$	4.12858e26	0.503132
$25$	−1.17131e27	−0.643934
$26$	3.40114e27	0.870250
$27$	2.45742e27	0.301222
$28$	−3.41246e28	−2.05819
$29$	−6.88782e27	−0.209566	−0.104783	−	0.994495i	$-0.533415\pi$
$29$	−6.88782e27	−0.209566	−0.104783	+	0.994495i	$0.533415\pi$
$30$	8.41407e28	1.32173
$31$	1.62636e29	1.34792	0.673959	−	0.738769i	$-0.264593\pi$
$31$	1.62636e29	1.34792	0.673959	+	0.738769i	$0.264593\pi$
$32$	−3.17170e29	−1.41536
$33$	2.25168e29	0.551422
$34$	−5.04690e29	−0.690536
$35$	−1.28730e30	−1.00082
$36$	3.28883e30	1.47619
$37$	−1.23773e30	−0.325606	−0.162803	−	0.986659i	$-0.552054\pi$
$37$	−1.23773e30	−0.325606	−0.162803	+	0.986659i	$0.552054\pi$
$38$	−1.80397e30	−0.282130
$39$	9.18399e30	0.865509
$40$	3.51653e30	0.202276
$41$	1.60595e31	0.570751	0.285375	−	0.958416i	$-0.407882\pi$
$41$	1.60595e31	0.570751	0.285375	+	0.958416i	$0.407882\pi$
$42$	−1.67235e32	−3.71506
$43$	1.28211e32	1.80007	0.900036	−	0.435815i	$-0.143540\pi$
$43$	1.28211e32	1.80007	0.900036	+	0.435815i	$0.143540\pi$
$44$	5.08400e31	0.455909
$45$	1.24067e32	0.717814
$46$	2.40125e32	0.905022
$47$	−6.09258e32	−1.50971	−0.754854	−	0.655893i	$-0.772292\pi$
$47$	−6.09258e32	−1.50971	−0.754854	+	0.655893i	$0.772292\pi$
$48$	−6.51324e32	−1.07052
$49$	1.64906e33	1.81306
$50$	−1.29608e33	−0.960983
$51$	−1.36280e33	−0.686774
$52$	2.07363e33	0.715593
$53$	1.51248e33	0.360006	0.180003	−	0.983666i	$-0.442389\pi$
$53$	1.51248e33	0.360006	0.180003	+	0.983666i	$0.442389\pi$
$54$	2.71918e33	0.449532
$55$	1.91787e33	0.221690
$56$	−6.98933e33	−0.568551
$57$	−4.87122e33	−0.280594
$58$	−7.62152e33	−0.312749
$59$	−4.73479e34	−1.39215	−0.696076	−	0.717969i	$-0.745072\pi$
$59$	−4.73479e34	−1.39215	−0.696076	+	0.717969i	$0.745072\pi$
$60$	5.12995e34	1.08683
$61$	7.02166e34	1.07772	0.538862	−	0.842394i	$-0.318854\pi$
$61$	7.02166e34	1.07772	0.538862	+	0.842394i	$0.318854\pi$
$62$	1.79960e35	2.01158
$63$	−2.46591e35	−2.01760
$64$	−2.31116e35	−1.39098
$65$	7.82250e34	0.347964
$66$	2.49152e35	0.822921
$67$	−9.34963e34	−0.230322	−0.115161	−	0.993347i	$-0.536738\pi$
$67$	−9.34963e34	−0.230322	−0.115161	+	0.993347i	$0.536738\pi$
$68$	−3.07703e35	−0.567817
$69$	6.48402e35	0.900092
$70$	−1.42443e36	−1.49358
$71$	2.40247e36	1.91038	0.955190	−	0.295994i	$-0.0956509\pi$
$71$	2.40247e36	1.91038	0.955190	+	0.295994i	$0.0956509\pi$
$72$	6.73613e35	0.407781
$73$	−7.72964e35	−0.357572	−0.178786	−	0.983888i	$-0.557217\pi$
$73$	−7.72964e35	−0.357572	−0.178786	+	0.983888i	$0.557217\pi$
$74$	−1.36958e36	−0.485923
$75$	−3.49976e36	−0.955748
$76$	−1.09986e36	−0.231991
$77$	−3.81189e36	−0.623119
$78$	1.01623e37	1.29165
$79$	1.44777e37	1.43540	0.717699	−	0.696353i	$-0.245195\pi$
$79$	1.44777e37	1.43540	0.717699	+	0.696353i	$0.245195\pi$
$80$	−5.54767e36	−0.430384
$81$	−1.24137e37	−0.755865
$82$	1.77702e37	0.851767
$83$	1.12684e37	0.426423	0.213212	−	0.977006i	$-0.431608\pi$
$83$	1.12684e37	0.426423	0.213212	+	0.977006i	$0.431608\pi$
$84$	−1.01961e38	−3.05483
$85$	−1.16077e37	−0.276107
$86$	1.41868e38	2.68636
$87$	−2.05802e37	−0.311045
$88$	1.04129e37	0.125939
$89$	−1.09111e38	−1.05868	−0.529338	−	0.848411i	$-0.677560\pi$
$89$	−1.09111e38	−1.05868	−0.529338	+	0.848411i	$0.677560\pi$
$90$	1.37282e38	1.07124
$91$	−1.55477e38	−0.978045
$92$	1.46401e38	0.744185
$93$	4.85940e38	2.00062
$94$	−6.74156e38	−2.25303
$95$	−4.14907e37	−0.112808
$96$	−9.47674e38	−2.10073
$97$	7.84026e37	0.141998	0.0709989	−	0.997476i	$-0.477381\pi$
$97$	7.84026e37	0.141998	0.0709989	+	0.997476i	$0.477381\pi$
$98$	1.82471e39	2.70574
$99$	3.67379e38	0.446919
$100$	−7.90201e38	−0.790201
$101$	1.53402e39	1.26347	0.631734	−	0.775185i	$-0.282344\pi$
$101$	1.53402e39	1.26347	0.631734	+	0.775185i	$0.282344\pi$
$102$	−1.50797e39	−1.02492
$103$	−1.10618e39	−0.621586	−0.310793	−	0.950478i	$-0.600595\pi$
$103$	−1.10618e39	−0.621586	−0.310793	+	0.950478i	$0.600595\pi$
$104$	4.24717e38	0.197674
$105$	−3.84634e39	−1.48545
$106$	1.67359e39	0.537260
$107$	2.25314e39	0.602288	0.301144	−	0.953579i	$-0.402631\pi$
$107$	2.25314e39	0.602288	0.301144	+	0.953579i	$0.402631\pi$
$108$	1.65785e39	0.369643
$109$	−3.29726e38	−0.0614239	−0.0307119	−	0.999528i	$-0.509777\pi$
$109$	−3.29726e38	−0.0614239	−0.0307119	+	0.999528i	$0.509777\pi$
$110$	2.12216e39	0.330843
$111$	−3.69822e39	−0.483276
$112$	1.10263e40	1.20971
$113$	−9.62984e39	−0.888361	−0.444181	−	0.895937i	$-0.646505\pi$
$113$	−9.62984e39	−0.888361	−0.444181	+	0.895937i	$0.646505\pi$
$114$	−5.39010e39	−0.418747
$115$	5.52278e39	0.361868
$116$	−4.64674e39	−0.257168
$117$	1.49844e40	0.701482
$118$	−5.23914e40	−2.07759
$119$	2.30710e40	0.776070
$120$	1.05071e40	0.300225
$121$	−3.54657e40	−0.861973
$122$	7.76961e40	1.60836
$123$	4.79842e40	0.847127
$124$	1.09719e41	1.65409
$125$	−7.61018e40	−0.980956
$126$	−2.72858e41	−3.01100
$127$	−7.59694e40	−0.718565	−0.359282	−	0.933229i	$-0.616978\pi$
$127$	−7.59694e40	−0.718565	−0.359282	+	0.933229i	$0.616978\pi$
$128$	−8.13679e40	−0.660479
$129$	3.83082e41	2.67173
$130$	8.65575e40	0.519289
$131$	−2.08014e41	−1.07474	−0.537368	−	0.843348i	$-0.680581\pi$
$131$	−2.08014e41	−1.07474	−0.537368	+	0.843348i	$0.680581\pi$
$132$	1.51905e41	0.676675
$133$	8.24654e40	0.317077
$134$	−1.03456e41	−0.343724
$135$	6.25403e40	0.179743
$136$	−6.30232e40	−0.156853
$137$	−3.53926e41	−0.763592	−0.381796	−	0.924247i	$-0.624694\pi$
$137$	−3.53926e41	−0.763592	−0.381796	+	0.924247i	$0.624694\pi$
$138$	7.17470e41	1.34326
$139$	−5.01395e39	−0.00815438	−0.00407719	−	0.999992i	$-0.501298\pi$
$139$	−5.01395e39	−0.00815438	−0.00407719	+	0.999992i	$0.501298\pi$
$140$	−8.68455e41	−1.22815
$141$	−1.82040e42	−2.24076
$142$	2.65838e42	2.85098
$143$	2.31635e41	0.216646
$144$	−1.06269e42	−0.867636
$145$	−1.75292e41	−0.125051
$146$	−8.55300e41	−0.533627
$147$	4.92722e42	2.69100
$148$	−8.35012e41	−0.399567
$149$	1.36965e42	0.574749	0.287374	−	0.957818i	$-0.407218\pi$
$149$	1.36965e42	0.574749	0.287374	+	0.957818i	$0.407218\pi$
$150$	−3.87255e42	−1.42632
$151$	−2.28466e42	−0.739214	−0.369607	−	0.929188i	$-0.620508\pi$
$151$	−2.28466e42	−0.739214	−0.369607	+	0.929188i	$0.620508\pi$
$152$	−2.25271e41	−0.0640848
$153$	−2.22352e42	−0.556620
$154$	−4.21793e42	−0.929920
$155$	4.13901e42	0.804319
$156$	6.19580e42	1.06211
$157$	−3.22622e42	−0.488260	−0.244130	−	0.969743i	$-0.578502\pi$
$157$	−3.22622e42	−0.488260	−0.244130	+	0.969743i	$0.578502\pi$
$158$	1.60199e43	2.14213
$159$	4.51914e42	0.534333
$160$	−8.07185e42	−0.844565
$161$	−1.09769e43	−1.01712
$162$	−1.37360e43	−1.12802
$163$	−4.44788e42	−0.323963	−0.161981	−	0.986794i	$-0.551788\pi$
$163$	−4.44788e42	−0.323963	−0.161981	+	0.986794i	$0.551788\pi$
$164$	1.08342e43	0.700395
$165$	5.73041e42	0.329040
$166$	1.24688e43	0.636378
$167$	4.33425e42	0.196762	0.0983812	−	0.995149i	$-0.468634\pi$
$167$	4.33425e42	0.196762	0.0983812	+	0.995149i	$0.468634\pi$
$168$	−2.08834e43	−0.843862
$169$	−1.83360e43	−0.659953
$170$	−1.28441e43	−0.412051
$171$	−7.94779e42	−0.227417
$172$	8.64950e43	2.20895
$173$	2.21391e43	0.504965	0.252482	−	0.967601i	$-0.418753\pi$
$173$	2.21391e43	0.504965	0.252482	+	0.967601i	$0.418753\pi$
$174$	−2.27724e43	−0.464192
$175$	5.92479e43	1.08002
$176$	−1.64274e43	−0.267962
$177$	−1.41471e44	−2.06628
$178$	−1.20733e44	−1.57993
$179$	1.32994e44	1.56026	0.780130	−	0.625618i	$-0.215153\pi$
$179$	1.32994e44	1.56026	0.780130	+	0.625618i	$0.215153\pi$
$180$	8.36993e43	0.880863
$181$	−1.07254e44	−1.01317	−0.506584	−	0.862191i	$-0.669092\pi$
$181$	−1.07254e44	−1.01317	−0.506584	+	0.862191i	$0.669092\pi$
$182$	−1.72038e44	−1.45960
$183$	2.09800e44	1.59959
$184$	2.99856e43	0.205572
$185$	−3.14997e43	−0.194293
$186$	5.37703e44	2.98566
$187$	−3.43720e43	−0.171907
$188$	−4.11024e44	−1.85263
$189$	−1.24303e44	−0.505214
$190$	−4.59103e43	−0.168351
$191$	2.71109e44	0.897414	0.448707	−	0.893679i	$-0.351885\pi$
$191$	2.71109e44	0.897414	0.448707	+	0.893679i	$0.351885\pi$
$192$	−6.90551e44	−2.06453
$193$	−8.26925e43	−0.223408	−0.111704	−	0.993742i	$-0.535631\pi$
$193$	−8.26925e43	−0.223408	−0.111704	+	0.993742i	$0.535631\pi$
$194$	8.67541e43	0.211912
$195$	2.33729e44	0.516460
$196$	1.11250e45	2.22489
$197$	−5.36056e44	−0.970776	−0.485388	−	0.874299i	$-0.661322\pi$
$197$	−5.36056e44	−0.970776	−0.485388	+	0.874299i	$0.661322\pi$
$198$	4.06513e44	0.666965
$199$	−1.00046e45	−1.48787	−0.743935	−	0.668252i	$-0.767043\pi$
$199$	−1.00046e45	−1.48787	−0.743935	+	0.668252i	$0.767043\pi$
$200$	−1.61848e44	−0.218284
$201$	−2.79358e44	−0.341852
$202$	1.69742e45	1.88555
$203$	3.48404e44	0.351488
$204$	−9.19387e44	−0.842772
$205$	4.08707e44	0.340574
$206$	−1.22401e45	−0.927631
$207$	1.05792e45	0.729511
$208$	−6.70032e44	−0.420592
$209$	−1.22860e44	−0.0702356
$210$	−4.25605e45	−2.21682
$211$	−1.34673e45	−0.639402	−0.319701	−	0.947518i	$-0.603582\pi$
$211$	−1.34673e45	−0.639402	−0.319701	+	0.947518i	$0.603582\pi$
$212$	1.02037e45	0.441780
$213$	7.17834e45	2.83545
$214$	2.49314e45	0.898832
$215$	3.26291e45	1.07413
$216$	3.39558e44	0.102109
$217$	−8.22655e45	−2.26075
$218$	−3.64849e44	−0.0916667
$219$	−2.30954e45	−0.530720
$220$	1.29385e45	0.272047
$221$	−1.40194e45	−0.269825
$222$	−4.09216e45	−0.721223
$223$	−4.53007e45	−0.731409	−0.365705	−	0.930731i	$-0.619172\pi$
$223$	−4.53007e45	−0.731409	−0.365705	+	0.930731i	$0.619172\pi$
$224$	1.60433e46	2.37387
$225$	−5.71015e45	−0.774619
$226$	−1.06556e46	−1.32576
$227$	1.08195e46	1.23510	0.617550	−	0.786532i	$-0.288125\pi$
$227$	1.08195e46	1.23510	0.617550	+	0.786532i	$0.288125\pi$
$228$	−3.28627e45	−0.344329
$229$	1.83988e46	1.77010	0.885051	−	0.465494i	$-0.154123\pi$
$229$	1.83988e46	1.77010	0.885051	+	0.465494i	$0.154123\pi$
$230$	6.11107e45	0.540038
$231$	−1.13896e46	−0.924854
$232$	−9.51736e44	−0.0710397
$233$	−1.58389e46	−1.08714	−0.543570	−	0.839364i	$-0.682928\pi$
$233$	−1.58389e46	−1.08714	−0.543570	+	0.839364i	$0.682928\pi$
$234$	1.65806e46	1.04687
$235$	−1.55053e46	−0.900861
$236$	−3.19423e46	−1.70837
$237$	4.32581e46	2.13047
$238$	2.55285e46	1.15818
$239$	−2.86406e46	−1.19736	−0.598678	−	0.800990i	$-0.704307\pi$
$239$	−2.86406e46	−1.19736	−0.598678	+	0.800990i	$0.704307\pi$
$240$	−1.65759e46	−0.638790
$241$	1.94777e46	0.692159	0.346080	−	0.938205i	$-0.387513\pi$
$241$	1.94777e46	0.692159	0.346080	+	0.938205i	$0.387513\pi$
$242$	−3.92435e46	−1.28638
$243$	−4.70498e46	−1.42310
$244$	4.73703e46	1.32253
$245$	4.19677e46	1.08187
$246$	5.30955e46	1.26422
$247$	−5.01113e45	−0.110242
$248$	2.24725e46	0.456923
$249$	3.36690e46	0.632911
$250$	−8.42081e46	−1.46394
$251$	6.63788e46	1.06756	0.533779	−	0.845624i	$-0.320771\pi$
$251$	6.63788e46	1.06756	0.533779	+	0.845624i	$0.320771\pi$
$252$	−1.66358e47	−2.47590
$253$	1.63537e46	0.225303
$254$	−8.40616e46	−1.07236
$255$	−3.46827e46	−0.409807
$256$	3.70220e46	0.405303
$257$	−1.60889e47	−1.63241	−0.816206	−	0.577761i	$-0.803927\pi$
$257$	−1.60889e47	−1.63241	−0.816206	+	0.577761i	$0.803927\pi$
$258$	4.23888e47	3.98719
$259$	6.26077e46	0.546113
$260$	5.27730e46	0.427003
$261$	−3.35782e46	−0.252097
$262$	−2.30171e47	−1.60390
$263$	3.82398e46	0.247388	0.123694	−	0.992320i	$-0.460526\pi$
$263$	3.82398e46	0.247388	0.123694	+	0.992320i	$0.460526\pi$
$264$	3.11129e46	0.186923
$265$	3.84919e46	0.214820
$266$	9.12497e46	0.473194
$267$	−3.26013e47	−1.57132
$268$	−6.30755e46	−0.282639
$269$	7.76998e46	0.323780	0.161890	−	0.986809i	$-0.448241\pi$
$269$	7.76998e46	0.323780	0.161890	+	0.986809i	$0.448241\pi$
$270$	6.92020e46	0.268241
$271$	2.35011e47	0.847591	0.423796	−	0.905758i	$-0.360697\pi$
$271$	2.35011e47	0.847591	0.423796	+	0.905758i	$0.360697\pi$
$272$	9.94252e46	0.333736
$273$	−4.64550e47	−1.45165
$274$	−3.91626e47	−1.13956
$275$	−8.82695e46	−0.239234
$276$	4.37432e47	1.10454
$277$	4.19090e47	0.986170	0.493085	−	0.869981i	$-0.335869\pi$
$277$	4.19090e47	0.986170	0.493085	+	0.869981i	$0.335869\pi$
$278$	−5.54803e45	−0.0121693
$279$	7.92852e47	1.62147
$280$	−1.77875e47	−0.339261
$281$	2.30674e46	0.0410417	0.0205209	−	0.999789i	$-0.493468\pi$
$281$	2.30674e46	0.0410417	0.0205209	+	0.999789i	$0.493468\pi$
$282$	−2.01431e48	−3.34402
$283$	6.25956e47	0.969858	0.484929	−	0.874554i	$-0.338846\pi$
$283$	6.25956e47	0.969858	0.484929	+	0.874554i	$0.338846\pi$
$284$	1.62078e48	2.34431
$285$	−1.23970e47	−0.167434
$286$	2.56309e47	0.323315
$287$	−8.12331e47	−0.957273
$288$	−1.54621e48	−1.70261
$289$	−7.63613e47	−0.785897
$290$	−1.93964e47	−0.186621
$291$	2.34259e47	0.210758
$292$	−5.21465e47	−0.438793
$293$	4.49093e47	0.353523	0.176762	−	0.984254i	$-0.443438\pi$
$293$	4.49093e47	0.353523	0.176762	+	0.984254i	$0.443438\pi$
$294$	5.45207e48	4.01595
$295$	−1.20498e48	−0.830714
$296$	−1.71026e47	−0.110376
$297$	1.85190e47	0.111910
$298$	1.51555e48	0.857733
$299$	6.67026e47	0.353634
$300$	−2.36105e48	−1.17284
$301$	−6.48524e48	−3.01911
$302$	−2.52802e48	−1.10318
$303$	4.58350e48	1.87528
$304$	3.55387e47	0.136354
$305$	1.78698e48	0.643092
$306$	−2.46037e48	−0.830678
$307$	5.77022e48	1.82808	0.914038	−	0.405628i	$-0.132947\pi$
$307$	5.77022e48	1.82808	0.914038	+	0.405628i	$0.132947\pi$
$308$	−2.57162e48	−0.764659
$309$	−3.30517e48	−0.922578
$310$	4.57990e48	1.20034
$311$	−3.50073e48	−0.861651	−0.430826	−	0.902435i	$-0.641778\pi$
$311$	−3.50073e48	−0.861651	−0.430826	+	0.902435i	$0.641778\pi$
$312$	1.26901e48	0.293394
$313$	4.32088e48	0.938551	0.469276	−	0.883052i	$-0.344515\pi$
$313$	4.32088e48	0.938551	0.469276	+	0.883052i	$0.344515\pi$
$314$	−3.56988e48	−0.728661
$315$	−6.27563e48	−1.20393
$316$	9.76713e48	1.76144
$317$	−3.38834e47	−0.0574554	−0.0287277	−	0.999587i	$-0.509146\pi$
$317$	−3.38834e47	−0.0574554	−0.0287277	+	0.999587i	$0.509146\pi$
$318$	5.00052e48	0.797419
$319$	−5.19065e47	−0.0778580
$320$	−5.88179e48	−0.830014
$321$	6.73216e48	0.893936
$322$	−1.21461e49	−1.51792
$323$	7.43595e47	0.0874757
$324$	−8.37468e48	−0.927556
$325$	−3.60028e48	−0.375501
$326$	−4.92167e48	−0.483470
$327$	−9.85191e47	−0.0911673
$328$	2.21905e48	0.193476
$329$	3.08178e49	2.53211
$330$	6.34082e48	0.491047
$331$	−1.23716e49	−0.903189	−0.451595	−	0.892223i	$-0.649145\pi$
$331$	−1.23716e49	−0.903189	−0.451595	+	0.892223i	$0.649145\pi$
$332$	7.60203e48	0.523284
$333$	−6.03396e48	−0.391688
$334$	4.79593e48	0.293641
$335$	−2.37944e48	−0.137436
$336$	3.29457e49	1.79549
$337$	−1.65140e49	−0.849316	−0.424658	−	0.905354i	$-0.639606\pi$
$337$	−1.65140e49	−0.849316	−0.424658	+	0.905354i	$0.639606\pi$
$338$	−2.02891e49	−0.984889
$339$	−2.87730e49	−1.31853
$340$	−7.83091e48	−0.338823
$341$	1.22562e49	0.500778
$342$	−8.79439e48	−0.339388
$343$	−3.74064e49	−1.36368
$344$	1.77157e49	0.610197
$345$	1.65015e49	0.537096
$346$	2.44974e49	0.753591
$347$	3.18063e49	0.924885	0.462443	−	0.886649i	$-0.346973\pi$
$347$	3.18063e49	0.924885	0.462443	+	0.886649i	$0.346973\pi$
$348$	−1.38840e49	−0.381698
$349$	1.04623e49	0.271976	0.135988	−	0.990711i	$-0.456579\pi$
$349$	1.04623e49	0.271976	0.135988	+	0.990711i	$0.456579\pi$
$350$	6.55590e49	1.61178
$351$	7.55343e48	0.175653
$352$	−2.39019e49	−0.525835
$353$	−3.28850e49	−0.684527	−0.342263	−	0.939604i	$-0.611194\pi$
$353$	−3.28850e49	−0.684527	−0.342263	+	0.939604i	$0.611194\pi$
$354$	−1.56540e50	−3.08363
$355$	6.11417e49	1.13995
$356$	−7.36096e49	−1.29915
$357$	6.89340e49	1.15187
$358$	1.47160e50	2.32847
$359$	4.88065e49	0.731367	0.365684	−	0.930739i	$-0.380835\pi$
$359$	4.88065e49	0.731367	0.365684	+	0.930739i	$0.380835\pi$
$360$	1.71431e49	0.243328
$361$	−7.17108e49	−0.964260
$362$	−1.18679e50	−1.51201
$363$	−1.05968e50	−1.27937
$364$	−1.04890e50	−1.20020
$365$	−1.96716e49	−0.213368
$366$	2.32148e50	2.38718
$367$	7.14273e49	0.696428	0.348214	−	0.937415i	$-0.386788\pi$
$367$	7.14273e49	0.696428	0.348214	+	0.937415i	$0.386788\pi$
$368$	−4.73051e49	−0.437397
$369$	7.82902e49	0.686583
$370$	−3.48551e49	−0.289956
$371$	−7.65051e49	−0.603809
$372$	3.27830e50	2.45506
$373$	1.05915e50	0.752724	0.376362	−	0.926473i	$-0.377175\pi$
$373$	1.05915e50	0.752724	0.376362	+	0.926473i	$0.377175\pi$
$374$	−3.80333e49	−0.256548
$375$	−2.27385e50	−1.45597
$376$	−8.41852e49	−0.511767
$377$	−2.11713e49	−0.122206
$378$	−1.37543e50	−0.753962
$379$	−1.87195e50	−0.974605	−0.487302	−	0.873233i	$-0.662019\pi$
$379$	−1.87195e50	−0.974605	−0.487302	+	0.873233i	$0.662019\pi$
$380$	−2.79909e49	−0.138432
$381$	−2.26989e50	−1.06652
$382$	2.99987e50	1.33927
$383$	3.66531e50	1.55502	0.777508	−	0.628873i	$-0.216484\pi$
$383$	3.66531e50	1.55502	0.777508	+	0.628873i	$0.216484\pi$
$384$	−2.43120e50	−0.980305
$385$	−9.70109e49	−0.371823
$386$	−9.15009e49	−0.333406
$387$	6.25030e50	2.16539
$388$	5.28928e49	0.174252
$389$	−4.12272e49	−0.129171	−0.0645857	−	0.997912i	$-0.520573\pi$
$389$	−4.12272e49	−0.129171	−0.0645857	+	0.997912i	$0.520573\pi$
$390$	2.58625e50	0.770746
$391$	−9.89791e49	−0.280606
$392$	2.27861e50	0.614598
$393$	−6.21525e50	−1.59516
$394$	−5.93157e50	−1.44875
$395$	3.68452e50	0.856520
$396$	2.47845e50	0.548435
$397$	4.25670e50	0.896723	0.448361	−	0.893852i	$-0.352008\pi$
$397$	4.25670e50	0.896723	0.448361	+	0.893852i	$0.352008\pi$
$398$	−1.10703e51	−2.22044
$399$	2.46399e50	0.470616
$400$	2.55330e50	0.464443
$401$	−6.90511e50	−1.19634	−0.598171	−	0.801368i	$-0.704106\pi$
$401$	−6.90511e50	−1.19634	−0.598171	+	0.801368i	$0.704106\pi$
$402$	−3.09115e50	−0.510167
$403$	4.99898e50	0.786019
$404$	1.03490e51	1.55046
$405$	−3.15924e50	−0.451034
$406$	3.85516e50	0.524548
$407$	−9.32751e49	−0.120969
$408$	−1.88307e50	−0.232806
$409$	−5.24800e50	−0.618571	−0.309286	−	0.950969i	$-0.600090\pi$
$409$	−5.24800e50	−0.618571	−0.309286	+	0.950969i	$0.600090\pi$
$410$	4.52243e50	0.508260
$411$	−1.05750e51	−1.13335
$412$	−7.46265e50	−0.762776
$413$	2.39498e51	2.33494
$414$	1.17061e51	1.08869
$415$	2.86777e50	0.254452
$416$	−9.74895e50	−0.825349
$417$	−1.49812e49	−0.0121030
$418$	−1.35947e50	−0.104817
$419$	1.54729e51	1.13867	0.569334	−	0.822106i	$-0.307201\pi$
$419$	1.54729e51	1.13867	0.569334	+	0.822106i	$0.307201\pi$
$420$	−2.59486e51	−1.82286
$421$	−1.69195e51	−1.13472	−0.567359	−	0.823471i	$-0.692035\pi$
$421$	−1.69195e51	−1.13472	−0.567359	+	0.823471i	$0.692035\pi$
$422$	−1.49019e51	−0.954220
$423$	−2.97014e51	−1.81610
$424$	2.08989e50	0.122037
$425$	5.34241e50	0.297957
$426$	7.94298e51	4.23152
$427$	−3.55174e51	−1.80758
$428$	1.52004e51	0.739096
$429$	6.92103e50	0.321554
$430$	3.61048e51	1.60299
$431$	2.11949e51	0.899341	0.449670	−	0.893195i	$-0.351541\pi$
$431$	2.11949e51	0.899341	0.449670	+	0.893195i	$0.351541\pi$
$432$	−5.35686e50	−0.217259
$433$	1.57391e51	0.610193	0.305097	−	0.952321i	$-0.401311\pi$
$433$	1.57391e51	0.610193	0.305097	+	0.952321i	$0.401311\pi$
$434$	−9.10284e51	−3.37386
$435$	−5.23756e50	−0.185604
$436$	−2.22444e50	−0.0753761
$437$	−3.53792e50	−0.114646
$438$	−2.55555e51	−0.792027
$439$	7.36309e50	0.218274	0.109137	−	0.994027i	$-0.465191\pi$
$439$	7.36309e50	0.218274	0.109137	+	0.994027i	$0.465191\pi$
$440$	2.65005e50	0.0751496
$441$	8.03916e51	2.18101
$442$	−1.55128e51	−0.402676
$443$	−3.79349e51	−0.942251	−0.471125	−	0.882066i	$-0.656152\pi$
$443$	−3.79349e51	−0.942251	−0.471125	+	0.882066i	$0.656152\pi$
$444$	−2.49494e51	−0.593050
$445$	−2.77683e51	−0.631726
$446$	−5.01262e51	−1.09153
$447$	4.09239e51	0.853061
$448$	1.16904e52	2.33297
$449$	7.69430e51	1.47016	0.735081	−	0.677979i	$-0.237144\pi$
$449$	7.69430e51	1.47016	0.735081	+	0.677979i	$0.237144\pi$
$450$	−6.31839e51	−1.15601
$451$	1.21024e51	0.212045
$452$	−6.49659e51	−1.09015
$453$	−6.82633e51	−1.09717
$454$	1.19720e52	1.84322
$455$	−3.95682e51	−0.583612
$456$	−6.73088e50	−0.0951168
$457$	−9.48171e51	−1.28387	−0.641935	−	0.766759i	$-0.721868\pi$
$457$	−9.48171e51	−1.28387	−0.641935	+	0.766759i	$0.721868\pi$
$458$	2.03587e52	2.64163
$459$	−1.12084e51	−0.139379
$460$	3.72584e51	0.444065
$461$	−1.00315e52	−1.14604	−0.573018	−	0.819543i	$-0.694227\pi$
$461$	−1.00315e52	−1.14604	−0.573018	+	0.819543i	$0.694227\pi$
$462$	−1.26028e52	−1.38022
$463$	−6.38266e51	−0.670151	−0.335075	−	0.942191i	$-0.608762\pi$
$463$	−6.38266e51	−0.670151	−0.335075	+	0.942191i	$0.608762\pi$
$464$	1.50146e51	0.151151
$465$	1.23670e52	1.19380
$466$	−1.75261e52	−1.62241
$467$	8.44728e51	0.749960	0.374980	−	0.927033i	$-0.377650\pi$
$467$	8.44728e51	0.749960	0.374980	+	0.927033i	$0.377650\pi$
$468$	1.01090e52	0.860821
$469$	4.72929e51	0.386300
$470$	−1.71570e52	−1.34441
$471$	−9.63964e51	−0.724692
$472$	−6.54237e51	−0.471918
$473$	9.66194e51	0.668762
$474$	4.78659e52	3.17943
$475$	1.90960e51	0.121735
$476$	1.55644e52	0.952352
$477$	7.37335e51	0.433069
$478$	−3.16914e52	−1.78689
$479$	3.34415e51	0.181027	0.0905134	−	0.995895i	$-0.471149\pi$
$479$	3.34415e51	0.181027	0.0905134	+	0.995895i	$0.471149\pi$
$480$	−2.41179e52	−1.25353
$481$	−3.80445e51	−0.189873
$482$	2.15525e52	1.03295
$483$	−3.27978e52	−1.50965
$484$	−2.39262e52	−1.05777
$485$	1.99531e51	0.0847319
$486$	−5.20616e52	−2.12378
$487$	3.02586e52	1.18586	0.592931	−	0.805254i	$-0.297971\pi$
$487$	3.02586e52	1.18586	0.592931	+	0.805254i	$0.297971\pi$
$488$	9.70229e51	0.365332
$489$	−1.32898e52	−0.480836
$490$	4.64381e52	1.61455
$491$	5.39058e52	1.80114	0.900568	−	0.434715i	$-0.143151\pi$
$491$	5.39058e52	1.80114	0.900568	+	0.434715i	$0.143151\pi$
$492$	3.23716e52	1.03955
$493$	3.14158e51	0.0969690
$494$	−5.54492e51	−0.164520
$495$	9.34964e51	0.266682
$496$	−3.54525e52	−0.972197
$497$	−1.21523e53	−3.20412
$498$	3.72554e52	0.944533
$499$	4.77343e52	1.16378	0.581888	−	0.813269i	$-0.302314\pi$
$499$	4.77343e52	1.16378	0.581888	+	0.813269i	$0.302314\pi$
$500$	−5.13406e52	−1.20378
$501$	1.29503e52	0.292041
$502$	7.34494e52	1.59318
$503$	4.55769e51	0.0950974	0.0475487	−	0.998869i	$-0.484859\pi$
$503$	4.55769e51	0.0950974	0.0475487	+	0.998869i	$0.484859\pi$
$504$	−3.40731e52	−0.683937
$505$	3.90401e52	0.753927
$506$	1.80957e52	0.336234
$507$	−5.47861e52	−0.979524
$508$	−5.12513e52	−0.881784
$509$	−4.13304e52	−0.684341	−0.342170	−	0.939638i	$-0.611162\pi$
$509$	−4.13304e52	−0.684341	−0.342170	+	0.939638i	$0.611162\pi$
$510$	−3.83771e52	−0.611580
$511$	3.90985e52	0.599726
$512$	8.56980e52	1.26534
$513$	−4.00636e51	−0.0569458
$514$	−1.78027e53	−2.43615
$515$	−2.81519e52	−0.370908
$516$	2.58439e53	3.27860
$517$	−4.59135e52	−0.560886
$518$	6.92767e52	0.814998
$519$	6.61495e52	0.749486
$520$	1.08089e52	0.117955
$521$	−4.81863e52	−0.506510	−0.253255	−	0.967400i	$-0.581501\pi$
$521$	−4.81863e52	−0.506510	−0.253255	+	0.967400i	$0.581501\pi$
$522$	−3.71550e52	−0.376220
$523$	1.41580e52	0.138108	0.0690541	−	0.997613i	$-0.478002\pi$
$523$	1.41580e52	0.138108	0.0690541	+	0.997613i	$0.478002\pi$
$524$	−1.40333e53	−1.31886
$525$	1.77027e53	1.60300
$526$	4.23131e52	0.369193
$527$	−7.41792e52	−0.623699
$528$	−4.90836e52	−0.397718
$529$	−8.09589e52	−0.632236
$530$	4.25921e52	0.320590
$531$	−2.30821e53	−1.67468
$532$	5.56337e52	0.389100
$533$	4.93625e52	0.332825
$534$	−3.60740e53	−2.34498
$535$	5.73414e52	0.359393
$536$	−1.29190e52	−0.0780756
$537$	3.97372e53	2.31579
$538$	8.59763e52	0.483197
$539$	1.24272e53	0.673587
$540$	4.21916e52	0.220570
$541$	1.61080e53	0.812258	0.406129	−	0.913816i	$-0.366878\pi$
$541$	1.61080e53	0.812258	0.406129	+	0.913816i	$0.366878\pi$
$542$	2.60044e53	1.26491
$543$	−3.20465e53	−1.50378
$544$	1.44663e53	0.654907
$545$	−8.39139e51	−0.0366524
$546$	−5.14034e53	−2.16638
$547$	−2.03359e52	−0.0827010	−0.0413505	−	0.999145i	$-0.513166\pi$
$547$	−2.03359e52	−0.0827010	−0.0413505	+	0.999145i	$0.513166\pi$
$548$	−2.38769e53	−0.937039
$549$	3.42307e53	1.29645
$550$	−9.76720e52	−0.357024
$551$	1.12293e52	0.0396184
$552$	8.95940e52	0.305117
$553$	−7.32322e53	−2.40747
$554$	4.63731e53	1.47172
$555$	−9.41182e52	−0.288377
$556$	−3.38256e51	−0.0100066
$557$	−4.33061e53	−1.23701	−0.618505	−	0.785781i	$-0.712261\pi$
$557$	−4.33061e53	−1.23701	−0.618505	+	0.785781i	$0.712261\pi$
$558$	8.77306e53	2.41983
$559$	3.94085e53	1.04969
$560$	2.80616e53	0.721847
$561$	−1.02700e53	−0.255150
$562$	2.55246e52	0.0612491
$563$	−6.67730e53	−1.54770	−0.773851	−	0.633368i	$-0.781672\pi$
$563$	−6.67730e53	−1.54770	−0.773851	+	0.633368i	$0.781672\pi$
$564$	−1.22810e54	−2.74974
$565$	−2.45075e53	−0.530096
$566$	6.92632e53	1.44738
$567$	6.27918e53	1.26775
$568$	3.31965e53	0.647589
$569$	9.32793e53	1.75831	0.879156	−	0.476534i	$-0.158107\pi$
$569$	9.32793e53	1.75831	0.879156	+	0.476534i	$0.158107\pi$
$570$	−1.37176e53	−0.249872
$571$	−2.47736e53	−0.436099	−0.218049	−	0.975938i	$-0.569969\pi$
$571$	−2.47736e53	−0.436099	−0.218049	+	0.975938i	$0.569969\pi$
$572$	1.56268e53	0.265857
$573$	8.10046e53	1.33197
$574$	−8.98860e53	−1.42860
$575$	−2.54185e53	−0.390505
$576$	−1.12669e54	−1.67327
$577$	4.60066e53	0.660528	0.330264	−	0.943889i	$-0.392862\pi$
$577$	4.60066e53	0.660528	0.330264	+	0.943889i	$0.392862\pi$
$578$	−8.44953e53	−1.17284
$579$	−2.47077e53	−0.331590
$580$	−1.18257e53	−0.153456
$581$	−5.69987e53	−0.715204
$582$	2.59213e53	0.314527
$583$	1.13980e53	0.133749
$584$	−1.06806e53	−0.121211
$585$	3.81348e53	0.418583
$586$	4.96930e53	0.527585
$587$	1.03979e54	1.06783	0.533916	−	0.845537i	$-0.320720\pi$
$587$	1.03979e54	1.06783	0.533916	+	0.845537i	$0.320720\pi$
$588$	3.32405e54	3.30225
$589$	−2.65147e53	−0.254823
$590$	−1.33334e54	−1.23973
$591$	−1.60168e54	−1.44086
$592$	2.69809e53	0.234846
$593$	−4.68001e53	−0.394167	−0.197084	−	0.980387i	$-0.563147\pi$
$593$	−4.68001e53	−0.394167	−0.197084	+	0.980387i	$0.563147\pi$
$594$	2.04917e53	0.167010
$595$	5.87147e53	0.463091
$596$	9.24009e53	0.705301
$597$	−2.98928e54	−2.20835
$598$	7.38078e53	0.527751
$599$	1.95085e54	1.35021	0.675106	−	0.737721i	$-0.264098\pi$
$599$	1.95085e54	1.35021	0.675106	+	0.737721i	$0.264098\pi$
$600$	−4.83585e53	−0.323984
$601$	2.02439e54	1.31293	0.656467	−	0.754355i	$-0.272050\pi$
$601$	2.02439e54	1.31293	0.656467	+	0.754355i	$0.272050\pi$
$602$	−7.17605e54	−4.50561
$603$	−4.55796e53	−0.277066
$604$	−1.54130e54	−0.907124
$605$	−9.02586e53	−0.514350
$606$	5.07174e54	2.79860
$607$	2.12357e54	1.13472	0.567359	−	0.823471i	$-0.307965\pi$
$607$	2.12357e54	1.13472	0.567359	+	0.823471i	$0.307965\pi$
$608$	5.17087e53	0.267574
$609$	1.04100e54	0.521690
$610$	1.97733e54	0.959726
$611$	−1.87269e54	−0.880364
$612$	−1.50006e54	−0.683054
$613$	−3.14022e54	−1.38510	−0.692549	−	0.721371i	$-0.743512\pi$
$613$	−3.14022e54	−1.38510	−0.692549	+	0.721371i	$0.743512\pi$
$614$	6.38487e54	2.72815
$615$	1.22118e54	0.505492
$616$	−5.26714e53	−0.211228
$617$	−2.88947e54	−1.12268	−0.561341	−	0.827585i	$-0.689714\pi$
$617$	−2.88947e54	−1.12268	−0.561341	+	0.827585i	$0.689714\pi$
$618$	−3.65723e54	−1.37682
$619$	−8.69334e53	−0.317116	−0.158558	−	0.987350i	$-0.550685\pi$
$619$	−8.69334e53	−0.317116	−0.158558	+	0.987350i	$0.550685\pi$
$620$	2.79230e54	0.987017
$621$	5.33282e53	0.182672
$622$	−3.87363e54	−1.28590
$623$	5.51912e54	1.77563
$624$	−2.00199e54	−0.624256
$625$	1.93843e53	0.0585853
$626$	4.78114e54	1.40066
$627$	−3.67093e53	−0.104246
$628$	−2.17651e54	−0.599166
$629$	5.64537e53	0.150662
$630$	−6.94411e54	−1.79670
$631$	−2.40764e54	−0.603976	−0.301988	−	0.953312i	$-0.597650\pi$
$631$	−2.40764e54	−0.603976	−0.301988	+	0.953312i	$0.597650\pi$
$632$	2.00048e54	0.486578
$633$	−4.02391e54	−0.949022
$634$	−3.74926e53	−0.0857443
$635$	−1.93339e54	−0.428777
$636$	3.04875e54	0.655705
$637$	5.06874e54	1.05726
$638$	−5.74355e53	−0.116192
$639$	1.17121e55	2.29809
$640$	−2.07078e54	−0.394116
$641$	−2.69211e53	−0.0497005	−0.0248503	−	0.999691i	$-0.507911\pi$
$641$	−2.69211e53	−0.0497005	−0.0248503	+	0.999691i	$0.507911\pi$
$642$	7.44927e54	1.33408
$643$	−3.09318e54	−0.537393	−0.268696	−	0.963225i	$-0.586593\pi$
$643$	−3.09318e54	−0.537393	−0.268696	+	0.963225i	$0.586593\pi$
$644$	−7.40534e54	−1.24816
$645$	9.74926e54	1.59425
$646$	8.22803e53	0.130545
$647$	−1.66944e54	−0.257003	−0.128501	−	0.991709i	$-0.541017\pi$
$647$	−1.66944e54	−0.257003	−0.128501	+	0.991709i	$0.541017\pi$
$648$	−1.71529e54	−0.256226
$649$	−3.56812e54	−0.517212
$650$	−3.98379e54	−0.560384
$651$	−2.45801e55	−3.35548
$652$	−3.00068e54	−0.397549
$653$	1.05739e55	1.35965	0.679824	−	0.733375i	$-0.262056\pi$
$653$	1.05739e55	1.35965	0.679824	+	0.733375i	$0.262056\pi$
$654$	−1.09013e54	−0.136055
$655$	−5.29386e54	−0.641309
$656$	−3.50076e54	−0.411659
$657$	−3.76821e54	−0.430140
$658$	3.41006e55	3.77882
$659$	3.28150e54	0.353026	0.176513	−	0.984298i	$-0.443518\pi$
$659$	3.28150e54	0.353026	0.176513	+	0.984298i	$0.443518\pi$
$660$	3.86591e54	0.403781
$661$	1.10445e55	1.12000	0.560001	−	0.828492i	$-0.310801\pi$
$661$	1.10445e55	1.12000	0.560001	+	0.828492i	$0.310801\pi$
$662$	−1.36894e55	−1.34789
$663$	−4.18887e54	−0.400482
$664$	1.55703e54	0.144551
$665$	2.09871e54	0.189204
$666$	−6.67670e54	−0.584540
$667$	−1.49472e54	−0.127088
$668$	2.92402e54	0.241456
$669$	−1.35354e55	−1.08558
$670$	−2.63290e54	−0.205105
$671$	5.29150e54	0.400396
$672$	4.79358e55	3.52338
$673$	−1.32277e55	−0.944478	−0.472239	−	0.881471i	$-0.656554\pi$
$673$	−1.32277e55	−0.944478	−0.472239	+	0.881471i	$0.656554\pi$
$674$	−1.82731e55	−1.26749
$675$	−2.87840e54	−0.193967
$676$	−1.23700e55	−0.809858
$677$	1.10632e54	0.0703723	0.0351861	−	0.999381i	$-0.488798\pi$
$677$	1.10632e54	0.0703723	0.0351861	+	0.999381i	$0.488798\pi$
$678$	−3.18379e55	−1.96773
$679$	−3.96581e54	−0.238161
$680$	−1.60391e54	−0.0935959
$681$	3.23276e55	1.83318
$682$	1.35617e55	0.747342
$683$	1.00248e55	0.536873	0.268437	−	0.963297i	$-0.413493\pi$
$683$	1.00248e55	0.536873	0.268437	+	0.963297i	$0.413493\pi$
$684$	−5.36182e54	−0.279073
$685$	−9.00726e54	−0.455645
$686$	−4.13910e55	−2.03510
$687$	5.49739e55	2.62724
$688$	−2.79483e55	−1.29832
$689$	4.64895e54	0.209933
$690$	1.82593e55	0.801542
$691$	−1.51432e55	−0.646242	−0.323121	−	0.946358i	$-0.604732\pi$
$691$	−1.51432e55	−0.646242	−0.323121	+	0.946358i	$0.604732\pi$
$692$	1.49357e55	0.619666
$693$	−1.85830e55	−0.749580
$694$	3.51943e55	1.38026
$695$	−1.27603e53	−0.00486582
$696$	−2.84370e54	−0.105439
$697$	−7.32483e54	−0.264094
$698$	1.15767e55	0.405886
$699$	−4.73252e55	−1.61357
$700$	3.99704e55	1.32534
$701$	4.82172e55	1.55489	0.777447	−	0.628948i	$-0.216514\pi$
$701$	4.82172e55	1.55489	0.777447	+	0.628948i	$0.216514\pi$
$702$	8.35803e54	0.262138
$703$	2.01789e54	0.0615557
$704$	−1.74168e55	−0.516775
$705$	−4.63285e55	−1.33709
$706$	−3.63879e55	−1.02156
$707$	−7.75947e55	−2.11911
$708$	−9.54406e55	−2.53562
$709$	6.05445e53	0.0156485	0.00782426	−	0.999969i	$-0.497509\pi$
$709$	6.05445e53	0.0156485	0.00782426	+	0.999969i	$0.497509\pi$
$710$	6.76545e55	1.70121
$711$	7.05791e55	1.72671
$712$	−1.50766e55	−0.358875
$713$	3.52934e55	0.817425
$714$	7.62768e55	1.71901
$715$	5.89501e54	0.129276
$716$	8.97216e55	1.91467
$717$	−8.55754e55	−1.77716
$718$	5.40053e55	1.09147
$719$	−7.05056e54	−0.138679	−0.0693394	−	0.997593i	$-0.522089\pi$
$719$	−7.05056e54	−0.138679	−0.0693394	+	0.997593i	$0.522089\pi$
$720$	−2.70450e55	−0.517729
$721$	5.59536e55	1.04253
$722$	−7.93495e55	−1.43903
$723$	5.81976e55	1.02733
$724$	−7.23568e55	−1.24330
$725$	8.06777e54	0.134947
$726$	−1.17256e56	−1.90928
$727$	7.92077e55	1.25559	0.627793	−	0.778380i	$-0.283958\pi$
$727$	7.92077e55	1.25559	0.627793	+	0.778380i	$0.283958\pi$
$728$	−2.14833e55	−0.331542
$729$	−9.02730e55	−1.35635
$730$	−2.17670e55	−0.318422
$731$	−5.84777e55	−0.832917
$732$	1.41538e56	1.96294
$733$	−6.30225e55	−0.851076	−0.425538	−	0.904941i	$-0.639915\pi$
$733$	−6.30225e55	−0.851076	−0.425538	+	0.904941i	$0.639915\pi$
$734$	7.90358e55	1.03932
$735$	1.25396e56	1.60575
$736$	−6.88288e55	−0.858327
$737$	−7.04586e54	−0.0855692
$738$	8.66297e55	1.02463
$739$	−1.14548e56	−1.31954	−0.659768	−	0.751469i	$-0.729345\pi$
$739$	−1.14548e56	−1.31954	−0.659768	+	0.751469i	$0.729345\pi$
$740$	−2.12507e55	−0.238426
$741$	−1.49728e55	−0.163624
$742$	−8.46545e55	−0.901101
$743$	3.14628e55	0.326224	0.163112	−	0.986608i	$-0.447847\pi$
$743$	3.14628e55	0.326224	0.163112	+	0.986608i	$0.447847\pi$
$744$	6.71456e55	0.678180
$745$	3.48570e55	0.342960
$746$	1.17197e56	1.12334
$747$	5.49338e55	0.512965
$748$	−2.31884e55	−0.210955
$749$	−1.13970e56	−1.01017
$750$	−2.51606e56	−2.17283
$751$	1.74710e56	1.47007	0.735036	−	0.678028i	$-0.237165\pi$
$751$	1.74710e56	1.47007	0.735036	+	0.678028i	$0.237165\pi$
$752$	1.32810e56	1.08889
$753$	1.98333e56	1.58451
$754$	−2.34264e55	−0.182375
$755$	−5.81435e55	−0.441098
$756$	−8.38584e55	−0.619971
$757$	2.77438e55	0.199893	0.0999463	−	0.994993i	$-0.468133\pi$
$757$	2.77438e55	0.199893	0.0999463	+	0.994993i	$0.468133\pi$
$758$	−2.07134e56	−1.45446
$759$	4.88634e55	0.334402
$760$	−5.73305e54	−0.0382402
$761$	−2.40584e56	−1.56411	−0.782053	−	0.623212i	$-0.785827\pi$
$761$	−2.40584e56	−1.56411	−0.782053	+	0.623212i	$0.785827\pi$
$762$	−2.51168e56	−1.59163
$763$	1.66784e55	0.103021
$764$	1.82898e56	1.10126
$765$	−5.65876e55	−0.332142
$766$	4.05574e56	2.32065
$767$	−1.45534e56	−0.811813
$768$	1.10618e56	0.601565
$769$	3.04973e56	1.61695	0.808477	−	0.588528i	$-0.200292\pi$
$769$	3.04973e56	1.61695	0.808477	+	0.588528i	$0.200292\pi$
$770$	−1.07345e56	−0.554895
$771$	−4.80720e56	−2.42288
$772$	−5.57869e55	−0.274154
$773$	4.36657e55	0.209238	0.104619	−	0.994512i	$-0.466638\pi$
$773$	4.36657e55	0.209238	0.104619	+	0.994512i	$0.466638\pi$
$774$	6.91608e56	3.23155
$775$	−1.90497e56	−0.867970
$776$	1.08334e55	0.0481351
$777$	1.87066e56	0.810559
$778$	−4.56187e55	−0.192771
$779$	−2.61820e55	−0.107900
$780$	1.57680e56	0.633772
$781$	1.81049e56	0.709744
$782$	−1.09522e56	−0.418766
$783$	−1.69263e55	−0.0631258
$784$	−3.59473e56	−1.30768
$785$	−8.21060e55	−0.291351
$786$	−6.87730e56	−2.38056
$787$	−4.86747e56	−1.64360	−0.821800	−	0.569777i	$-0.807030\pi$
$787$	−4.86747e56	−1.64360	−0.821800	+	0.569777i	$0.807030\pi$
$788$	−3.61640e56	−1.19128
$789$	1.14257e56	0.367182
$790$	4.07700e56	1.27824
$791$	4.87102e56	1.48997
$792$	5.07632e55	0.151499
$793$	2.15827e56	0.628460
$794$	4.71012e56	1.33824
$795$	1.15010e56	0.318843
$796$	−6.74942e56	−1.82583
$797$	5.82796e56	1.53844	0.769218	−	0.638986i	$-0.220646\pi$
$797$	5.82796e56	1.53844	0.769218	+	0.638986i	$0.220646\pi$
$798$	2.72645e56	0.702330
$799$	2.77886e56	0.698561
$800$	3.71505e56	0.911401
$801$	−5.31917e56	−1.27353
$802$	−7.64064e56	−1.78538
$803$	−5.82503e55	−0.132845
$804$	−1.88463e56	−0.419502
$805$	−2.79357e56	−0.606931
$806$	5.53147e56	1.17303
$807$	2.32159e56	0.480565
$808$	2.11966e56	0.428296
$809$	−7.85718e56	−1.54978	−0.774891	−	0.632095i	$-0.782195\pi$
$809$	−7.85718e56	−1.54978	−0.774891	+	0.632095i	$0.782195\pi$
$810$	−3.49576e56	−0.673106
$811$	4.57812e56	0.860558	0.430279	−	0.902696i	$-0.358415\pi$
$811$	4.57812e56	0.860558	0.430279	+	0.902696i	$0.358415\pi$
$812$	2.35044e56	0.431327
$813$	7.02189e56	1.25802
$814$	−1.03211e56	−0.180530
$815$	−1.13197e56	−0.193312
$816$	2.97073e56	0.495342
$817$	−2.09024e56	−0.340303
$818$	−5.80702e56	−0.923132
$819$	−7.57952e56	−1.17654
$820$	2.75726e56	0.417934
$821$	5.79486e56	0.857731	0.428866	−	0.903368i	$-0.358913\pi$
$821$	5.79486e56	0.857731	0.428866	+	0.903368i	$0.358913\pi$
$822$	−1.17014e57	−1.69137
$823$	−1.26890e57	−1.79114	−0.895572	−	0.444916i	$-0.853233\pi$
$823$	−1.26890e57	−1.79114	−0.895572	+	0.444916i	$0.853233\pi$
$824$	−1.52849e56	−0.210708
$825$	−2.63741e56	−0.355079
$826$	2.65009e57	3.48458
$827$	3.04410e56	0.390932	0.195466	−	0.980710i	$-0.437378\pi$
$827$	3.04410e56	0.390932	0.195466	+	0.980710i	$0.437378\pi$
$828$	7.13706e56	0.895216
$829$	−4.36698e56	−0.535017	−0.267509	−	0.963555i	$-0.586200\pi$
$829$	−4.36698e56	−0.535017	−0.267509	+	0.963555i	$0.586200\pi$
$830$	3.17324e56	0.379735
$831$	1.25220e57	1.46371
$832$	−7.10386e56	−0.811129
$833$	−7.52144e56	−0.838926
$834$	−1.65770e55	−0.0180621
$835$	1.10305e56	0.117411
$836$	−8.28850e55	−0.0861894
$837$	3.99665e56	0.406022
$838$	1.71210e57	1.69931
$839$	1.05819e56	0.102614	0.0513070	−	0.998683i	$-0.483661\pi$
$839$	1.05819e56	0.102614	0.0513070	+	0.998683i	$0.483661\pi$
$840$	−5.31475e56	−0.503543
$841$	−1.03280e57	−0.956082
$842$	−1.87218e57	−1.69341
$843$	6.89232e55	0.0609155
$844$	−9.08549e56	−0.784640
$845$	−4.66642e56	−0.393802
$846$	−3.28652e57	−2.71028
$847$	1.79395e57	1.44572
$848$	−3.29701e56	−0.259658
$849$	1.87029e57	1.43949
$850$	5.91149e56	0.444660
$851$	−2.68599e56	−0.197459
$852$	4.84273e57	3.47951
$853$	−1.08758e57	−0.763756	−0.381878	−	0.924213i	$-0.624723\pi$
$853$	−1.08758e57	−0.763756	−0.381878	+	0.924213i	$0.624723\pi$
$854$	−3.93007e57	−2.69756
$855$	−2.02268e56	−0.135702
$856$	3.11331e56	0.204166
$857$	1.97964e57	1.26900	0.634498	−	0.772925i	$-0.281207\pi$
$857$	1.97964e57	1.26900	0.634498	+	0.772925i	$0.281207\pi$
$858$	7.65826e56	0.479875
$859$	5.66557e56	0.347038	0.173519	−	0.984831i	$-0.444486\pi$
$859$	5.66557e56	0.347038	0.173519	+	0.984831i	$0.444486\pi$
$860$	2.20126e57	1.31811
$861$	−2.42717e57	−1.42082
$862$	2.34526e57	1.34214
$863$	−5.59601e56	−0.313089	−0.156545	−	0.987671i	$-0.550036\pi$
$863$	−5.59601e56	−0.313089	−0.156545	+	0.987671i	$0.550036\pi$
$864$	−7.79421e56	−0.426338
$865$	5.63431e56	0.301319
$866$	1.74157e57	0.910629
$867$	−2.28160e57	−1.16645
$868$	−5.54988e57	−2.77427
$869$	1.09104e57	0.533279
$870$	−5.79546e56	−0.276989
$871$	−2.87382e56	−0.134309
$872$	−4.55605e55	−0.0208217
$873$	3.82214e56	0.170816
$874$	−3.91478e56	−0.171094
$875$	3.84943e57	1.64528
$876$	−1.55809e57	−0.651271
$877$	−3.51912e57	−1.43861	−0.719304	−	0.694695i	$-0.755539\pi$
$877$	−3.51912e57	−1.43861	−0.719304	+	0.694695i	$0.755539\pi$
$878$	8.14740e56	0.325744
$879$	1.34185e57	0.524711
$880$	−4.18071e56	−0.159896
$881$	−2.67197e57	−0.999542	−0.499771	−	0.866158i	$-0.666583\pi$
$881$	−2.67197e57	−0.999542	−0.499771	+	0.866158i	$0.666583\pi$
$882$	8.89550e57	3.25486
$883$	3.97981e57	1.42439	0.712194	−	0.701982i	$-0.247701\pi$
$883$	3.97981e57	1.42439	0.712194	+	0.701982i	$0.247701\pi$
$884$	−9.45795e56	−0.331114
$885$	−3.60037e57	−1.23297
$886$	−4.19757e57	−1.40618
$887$	−2.01262e57	−0.659555	−0.329778	−	0.944059i	$-0.606974\pi$
$887$	−2.01262e57	−0.659555	−0.329778	+	0.944059i	$0.606974\pi$
$888$	−5.11008e56	−0.163823
$889$	3.84273e57	1.20519
$890$	−3.07261e57	−0.942764
$891$	−9.35494e56	−0.280819
$892$	−3.05613e57	−0.897546
$893$	9.93280e56	0.285409
$894$	4.52831e57	1.27308
$895$	3.38463e57	0.931026
$896$	4.11580e57	1.10777
$897$	1.99301e57	0.524876
$898$	8.51389e57	2.19401
$899$	−1.12021e57	−0.282478
$900$	−3.85224e57	−0.950571
$901$	−6.89851e56	−0.166580
$902$	1.33915e57	0.316448
$903$	−1.93773e58	−4.48107
$904$	−1.33062e57	−0.301141
$905$	−2.72957e57	−0.604570
$906$	−7.55347e57	−1.63737
$907$	−1.92035e57	−0.407416	−0.203708	−	0.979032i	$-0.565299\pi$
$907$	−1.92035e57	−0.407416	−0.203708	+	0.979032i	$0.565299\pi$
$908$	7.29915e57	1.51565
$909$	7.47836e57	1.51989
$910$	−4.37830e57	−0.870961
$911$	5.42803e57	1.05690	0.528450	−	0.848964i	$-0.322773\pi$
$911$	5.42803e57	1.05690	0.528450	+	0.848964i	$0.322773\pi$
$912$	1.06186e57	0.202380
$913$	8.49186e56	0.158425
$914$	−1.04917e58	−1.91600
$915$	5.33933e57	0.954498
$916$	1.24124e58	2.17217
$917$	1.05219e58	1.80257
$918$	−1.24024e57	−0.208004
$919$	−1.06801e58	−1.75357	−0.876785	−	0.480883i	$-0.840316\pi$
$919$	−1.06801e58	−1.75357	−0.876785	+	0.480883i	$0.840316\pi$
$920$	7.63119e56	0.122668
$921$	1.72409e58	2.71329
$922$	−1.11001e58	−1.71030
$923$	7.38452e57	1.11401
$924$	−7.68375e57	−1.13493
$925$	1.44977e57	0.209669
$926$	−7.06255e57	−1.00011
$927$	−5.39265e57	−0.747735
$928$	2.18461e57	0.296612
$929$	−9.61260e57	−1.27801	−0.639005	−	0.769202i	$-0.720654\pi$
$929$	−9.61260e57	−1.27801	−0.639005	+	0.769202i	$0.720654\pi$
$930$	1.36843e58	1.78158
$931$	−2.68848e57	−0.342758
$932$	−1.06854e58	−1.33408
$933$	−1.04599e58	−1.27889
$934$	9.34709e57	1.11921
$935$	−8.74753e56	−0.102579
$936$	2.07050e57	0.237791
$937$	−6.32461e57	−0.711396	−0.355698	−	0.934601i	$-0.615757\pi$
$937$	−6.32461e57	−0.711396	−0.355698	+	0.934601i	$0.615757\pi$
$938$	5.23305e57	0.576500
$939$	1.29104e58	1.39303
$940$	−1.04604e58	−1.10549
$941$	4.44546e57	0.460171	0.230085	−	0.973170i	$-0.426099\pi$
$941$	4.44546e57	0.460171	0.230085	+	0.973170i	$0.426099\pi$
$942$	−1.06665e58	−1.08150
$943$	3.48505e57	0.346124
$944$	1.03212e58	1.00410
$945$	−3.16345e57	−0.301467
$946$	1.06911e58	0.998036
$947$	−2.02681e58	−1.85348	−0.926739	−	0.375705i	$-0.877401\pi$
$947$	−2.02681e58	−1.85348	−0.926739	+	0.375705i	$0.877401\pi$
$948$	2.91832e58	2.61439
$949$	−2.37588e57	−0.208513
$950$	2.11301e57	0.181673
$951$	−1.01240e57	−0.0852772
$952$	3.18788e57	0.263076
$953$	−2.18717e58	−1.76837	−0.884183	−	0.467141i	$-0.845284\pi$
$953$	−2.18717e58	−1.76837	−0.884183	+	0.467141i	$0.845284\pi$
$954$	8.15876e57	0.646295
$955$	6.89959e57	0.535498
$956$	−1.93218e58	−1.46933
$957$	−1.55091e57	−0.115559
$958$	3.70037e57	0.270158
$959$	1.79025e58	1.28071
$960$	−1.75742e58	−1.23193
$961$	1.18923e58	0.816882
$962$	−4.20970e57	−0.283359
$963$	1.09841e58	0.724521
$964$	1.31403e58	0.849381
$965$	−2.10449e57	−0.133310
$966$	−3.62915e58	−2.25295
$967$	−8.40382e57	−0.511282	−0.255641	−	0.966772i	$-0.582287\pi$
$967$	−8.40382e57	−0.511282	−0.255641	+	0.966772i	$0.582287\pi$
$968$	−4.90053e57	−0.292195
$969$	2.22179e57	0.129834
$970$	2.20785e57	0.126451
$971$	2.19465e58	1.23194	0.615972	−	0.787768i	$-0.288763\pi$
$971$	2.19465e58	1.23194	0.615972	+	0.787768i	$0.288763\pi$
$972$	−3.17413e58	−1.74635
$973$	2.53618e56	0.0136767
$974$	3.34817e58	1.76974
$975$	−1.07573e58	−0.557331
$976$	−1.53063e58	−0.777318
$977$	4.53213e57	0.225610	0.112805	−	0.993617i	$-0.464016\pi$
$977$	4.53213e57	0.225610	0.112805	+	0.993617i	$0.464016\pi$
$978$	−1.47055e58	−0.717581
$979$	−8.22257e57	−0.393319
$980$	2.83127e58	1.32762
$981$	−1.60742e57	−0.0738897
$982$	5.96479e58	2.68795
$983$	−3.96363e58	−1.75105	−0.875527	−	0.483169i	$-0.839486\pi$
$983$	−3.96363e58	−1.75105	−0.875527	+	0.483169i	$0.839486\pi$
$984$	6.63030e57	0.287163
$985$	−1.36424e58	−0.579274
$986$	3.47622e57	0.144713
$987$	9.20807e58	3.75824
$988$	−3.38066e57	−0.135282
$989$	2.78229e58	1.09163
$990$	1.03456e58	0.397986
$991$	−1.58403e58	−0.597486	−0.298743	−	0.954334i	$-0.596567\pi$
$991$	−1.58403e58	−0.597486	−0.298743	+	0.954334i	$0.596567\pi$
$992$	−5.15833e58	−1.90779
$993$	−3.69650e58	−1.34054
$994$	−1.34468e59	−4.78171
$995$	−2.54613e58	−0.887831
$996$	2.27141e58	0.776675
$997$	6.66270e57	0.223406	0.111703	−	0.993742i	$-0.464369\pi$
$997$	6.66270e57	0.223406	0.111703	+	0.993742i	$0.464369\pi$
$998$	5.28189e58	1.73678
$999$	−3.04163e57	−0.0980797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.40.a.a.1.3	✓	3
3.2	odd	2		9.40.a.b.1.1		3
4.3	odd	2		16.40.a.c.1.1		3
5.2	odd	4		25.40.b.a.24.6		6
5.3	odd	4		25.40.b.a.24.1		6
5.4	even	2		25.40.a.a.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.40.a.a.1.3	✓	3	1.1	even	1	trivial
9.40.a.b.1.1		3	3.2	odd	2
16.40.a.c.1.1		3	4.3	odd	2
25.40.a.a.1.1		3	5.4	even	2
25.40.b.a.24.1		6	5.3	odd	4
25.40.b.a.24.6		6	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +O(q^{10})\)	\(q+1.10652e6 q^{2} +2.98790e9 q^{3} +6.74631e11 q^{4} +2.54496e13 q^{5} +3.30617e15 q^{6} -5.05826e16 q^{7} +1.38177e17 q^{8} +4.87501e18 q^{9} +2.81604e19 q^{10} +7.53597e19 q^{11} +2.01573e21 q^{12} +3.07373e21 q^{13} -5.59707e22 q^{14} +7.60408e22 q^{15} -2.17987e23 q^{16} -4.56106e23 q^{17} +5.39430e24 q^{18} -1.63031e24 q^{19} +1.71691e25 q^{20} -1.51136e26 q^{21} +8.33870e25 q^{22} +2.17009e26 q^{23} +4.12858e26 q^{24} -1.17131e27 q^{25} +3.40114e27 q^{26} +2.45742e27 q^{27} -3.41246e28 q^{28} -6.88782e27 q^{29} +8.41407e28 q^{30} +1.62636e29 q^{31} -3.17170e29 q^{32} +2.25168e29 q^{33} -5.04690e29 q^{34} -1.28730e30 q^{35} +3.28883e30 q^{36} -1.23773e30 q^{37} -1.80397e30 q^{38} +9.18399e30 q^{39} +3.51653e30 q^{40} +1.60595e31 q^{41} -1.67235e32 q^{42} +1.28211e32 q^{43} +5.08400e31 q^{44} +1.24067e32 q^{45} +2.40125e32 q^{46} -6.09258e32 q^{47} -6.51324e32 q^{48} +1.64906e33 q^{49} -1.29608e33 q^{50} -1.36280e33 q^{51} +2.07363e33 q^{52} +1.51248e33 q^{53} +2.71918e33 q^{54} +1.91787e33 q^{55} -6.98933e33 q^{56} -4.87122e33 q^{57} -7.62152e33 q^{58} -4.73479e34 q^{59} +5.12995e34 q^{60} +7.02166e34 q^{61} +1.79960e35 q^{62} -2.46591e35 q^{63} -2.31116e35 q^{64} +7.82250e34 q^{65} +2.49152e35 q^{66} -9.34963e34 q^{67} -3.07703e35 q^{68} +6.48402e35 q^{69} -1.42443e36 q^{70} +2.40247e36 q^{71} +6.73613e35 q^{72} -7.72964e35 q^{73} -1.36958e36 q^{74} -3.49976e36 q^{75} -1.09986e36 q^{76} -3.81189e36 q^{77} +1.01623e37 q^{78} +1.44777e37 q^{79} -5.54767e36 q^{80} -1.24137e37 q^{81} +1.77702e37 q^{82} +1.12684e37 q^{83} -1.01961e38 q^{84} -1.16077e37 q^{85} +1.41868e38 q^{86} -2.05802e37 q^{87} +1.04129e37 q^{88} -1.09111e38 q^{89} +1.37282e38 q^{90} -1.55477e38 q^{91} +1.46401e38 q^{92} +4.85940e38 q^{93} -6.74156e38 q^{94} -4.14907e37 q^{95} -9.47674e38 q^{96} +7.84026e37 q^{97} +1.82471e39 q^{98} +3.67379e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 83\!\cdots\!91 q^{9}+O(q^{10}) \) 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9	\( 3 q + 548856 q^{2} + 1109442852 q^{3} + 272078981184 q^{4} + 17426916500490 q^{5} + 15\!\cdots\!96 q^{6}+ \cdots + 10\!\cdots\!72 q^{99}+O(q^{100}) \) 3 * q + 548856 * q^2 + 1109442852 * q^3 + 272078981184 * q^4 + 17426916500490 * q^5 + 1529727847867296 * q^6 - 17996297718635544 * q^7 + 255044243806133760 * q^8 + 8305879902078677391 * q^9 + 90373081165367671440 * q^10 + 667814968265751536076 * q^11 + 3676571280854873162496 * q^12 + 3156080701447967254962 * q^13 - 63063724565889303463872 * q^14 - 171209278264452417200520 * q^15 - 351730940560369057001472 * q^16 + 890025791008793741893206 * q^17 + 8758537968130529168653272 * q^18 + 9227612185007697573518580 * q^19 - 14662452947108747596260480 * q^20 - 190208658572592931471251744 * q^21 - 122745877544387429034313248 * q^22 + 305308591470919570740188472 * q^23 + 1672960268636194560046295040 * q^24 + 1866127065486173095027030725 * q^25 + 283778605804595582169202896 * q^26 - 11508090459893795046427628760 * q^27 - 41794856371466593385827533312 * q^28 - 2492682219258648277296444030 * q^29 + 105977898643957401776506418880 * q^30 + 306107671747822704409554746016 * q^31 - 56572224161556180973554008064 * q^32 - 157376353761155567959844693616 * q^33 - 1683392869529765869103799245712 * q^34 - 1197259217905835166323668756560 * q^35 + 188684323073267404408057366848 * q^36 + 7599073412303579174888591086506 * q^37 + 2479871855304922949496616465440 * q^38 + 22252083518345402015145920059992 * q^39 - 32669995448979982796588503833600 * q^40 + 2391924206237769506232479990286 * q^41 - 195689966839404680756969540713728 * q^42 + 162865923671547339657067136304492 * q^43 - 45577647299113910363374898556672 * q^44 + 588908524142943445153326555470130 * q^45 - 24296541145531030477977021520704 * q^46 + 202683231875405841765643043683056 * q^47 - 1747281225742357435119054532067328 * q^48 + 368237681722499062385273201641179 * q^49 - 2624175085265540082696197615369400 * q^50 + 785651103815434341253216161914376 * q^51 + 3782687188757116950236456253499776 * q^52 + 5869079988764517679853946632443002 * q^53 + 7930814851979058696152103557167680 * q^54 - 4993109836111426485910134681304920 * q^55 - 6272116703248607238900430116679680 * q^56 - 46129102671186186415908500969957520 * q^57 + 2579097256656295554169870267982160 * q^58 - 56082681385621280317109288669637060 * q^59 + 127333179651658235430567238147607040 * q^60 + 39577675682126428331898689976833826 * q^61 + 262011550289381451529348830657714432 * q^62 - 174786720262353444072185876495505528 * q^63 - 169364906963561439583712861665099776 * q^64 - 264857762104053085095614223637519620 * q^65 - 287121760972609093376568794235255168 * q^66 - 140659929656119892877736400727430044 * q^67 - 130643133997460537100958647836349312 * q^68 + 1584175048695702801789842685209503392 * q^69 - 480338235822643784458804278358623360 * q^70 + 3849053210874068146700295241416217896 * q^71 - 1699150852984576616740529956276922880 * q^72 - 180754136492273067100959984036797778 * q^73 - 5070707041697857186532012041702753392 * q^74 - 4308561205008052508725896857031567300 * q^75 - 7362591710990284189025184136271151360 * q^76 + 5690389092595065468343565382905921952 * q^77 + 9330105385756793042468361274821534144 * q^78 + 13807772201216229289895673856694559120 * q^79 + 26839954555034162361105063302056304640 * q^80 - 18798023146176620962298765658838887237 * q^81 + 5068915865662526415092477483885831472 * q^82 - 20899400147905548803677768348186808268 * q^83 - 72152575898640813291791263837177976832 * q^84 - 105991789747453754784809897833488498060 * q^85 + 170012097580285110854272781787916483296 * q^86 - 73247996942640959139716393654519138280 * q^87 + 69412125637007165807333386173055825920 * q^88 + 205050039910109857136561853222076224510 * q^89 + 93221656611667223268126392859978755280 * q^90 - 165525104998331842571199169888366982544 * q^91 + 262356454404517646077951321169615264256 * q^92 - 167325068951627887866919523900021629056 * q^93 - 1127972668535151884588260809571286639232 * q^94 + 724803433705663618674774120451764528600 * q^95 - 1451094524490643350592064137029388468224 * q^96 + 173490888317728793437812209497231327206 * q^97 + 2246791677555180938475077451719860538808 * q^98 + 1057018158118568141770036034713090936572 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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