LMFDB - Embedded newform 3.40.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,40,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	3.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:	$28.9018654169$
Analytic rank:	$1$
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} - 216694123x - 94580724378 $ x^3 - 216694123*x - 94580724378
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-436.856$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-337546. q^{2} +1.16226e9 q^{3} -4.35818e11 q^{4} +2.60351e13 q^{5} -3.92317e14 q^{6} -1.06972e16 q^{7} +3.32677e17 q^{8} +1.35085e18 q^{9} +O(q^{10})$	\(q-337546. q^{2} +1.16226e9 q^{3} -4.35818e11 q^{4} +2.60351e13 q^{5} -3.92317e14 q^{6} -1.06972e16 q^{7} +3.32677e17 q^{8} +1.35085e18 q^{9} -8.78806e18 q^{10} -2.32202e20 q^{11} -5.06535e20 q^{12} +4.99617e21 q^{13} +3.61079e21 q^{14} +3.02596e22 q^{15} +1.27300e23 q^{16} +1.94633e23 q^{17} -4.55975e23 q^{18} +5.09059e24 q^{19} -1.13466e25 q^{20} -1.24329e25 q^{21} +7.83790e25 q^{22} -4.20533e26 q^{23} +3.86658e26 q^{24} -1.14116e27 q^{25} -1.68644e27 q^{26} +1.57004e27 q^{27} +4.66202e27 q^{28} -2.15883e28 q^{29} -1.02140e28 q^{30} -2.23682e29 q^{31} -2.25861e29 q^{32} -2.69880e29 q^{33} -6.56978e28 q^{34} -2.78502e29 q^{35} -5.88726e29 q^{36} -5.80126e30 q^{37} -1.71831e30 q^{38} +5.80686e30 q^{39} +8.66129e30 q^{40} -9.08797e30 q^{41} +4.19669e30 q^{42} +2.60188e31 q^{43} +1.01198e32 q^{44} +3.51696e31 q^{45} +1.41949e32 q^{46} +4.64891e32 q^{47} +1.47956e32 q^{48} -7.95114e32 q^{49} +3.85195e32 q^{50} +2.26215e32 q^{51} -2.17742e33 q^{52} -4.59023e33 q^{53} -5.29962e32 q^{54} -6.04541e33 q^{55} -3.55870e33 q^{56} +5.91660e33 q^{57} +7.28704e33 q^{58} +6.43676e32 q^{59} -1.31877e34 q^{60} +1.61101e33 q^{61} +7.55031e34 q^{62} -1.44503e34 q^{63} +6.25468e33 q^{64} +1.30076e35 q^{65} +9.10969e34 q^{66} +5.84042e35 q^{67} -8.48248e34 q^{68} -4.88769e35 q^{69} +9.40074e34 q^{70} -1.82793e36 q^{71} +4.49397e35 q^{72} -2.99198e36 q^{73} +1.95819e36 q^{74} -1.32633e36 q^{75} -2.21857e36 q^{76} +2.48391e36 q^{77} -1.96008e36 q^{78} +1.10201e36 q^{79} +3.31426e36 q^{80} +1.82480e36 q^{81} +3.06761e36 q^{82} +4.80060e37 q^{83} +5.41849e36 q^{84} +5.06731e36 q^{85} -8.78254e36 q^{86} -2.50912e37 q^{87} -7.72483e37 q^{88} +3.02726e37 q^{89} -1.18714e37 q^{90} -5.34449e37 q^{91} +1.83276e38 q^{92} -2.59977e38 q^{93} -1.56922e38 q^{94} +1.32534e38 q^{95} -2.62509e38 q^{96} -3.29185e38 q^{97} +2.68388e38 q^{98} -3.13671e38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots + 40\!\cdots\!67 q^{9}+O(q^{10}) $ 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9	$ 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots - 54\!\cdots\!44 q^{99}+O(q^{100}) $ 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9 - 76029599179042436880 * q^10 - 40050327611147243796 * q^11 + 1169119071861486955200 * q^12 - 13932702500978393486094 * q^13 + 64143032386415214972096 * q^14 + 10875337996478108168430 * q^15 + 1098810764821648805597184 * q^16 - 169700805136994180103018 * q^17 - 1495392851464002242523000 * q^18 - 6957470542505489016962988 * q^19 + 33307320359730090833619840 * q^20 + 16087888842591162209012568 * q^21 - 182808419494676144863843296 * q^22 - 257172639984224911978099272 * q^23 - 1774258355442000609859705344 * q^24 - 2223570708999165320980345275 * q^25 + 6420909995769964414290523056 * q^26 + 4710128697246244834921603689 * q^27 - 31489800993928145336514267648 * q^28 - 46272789498091624686435987486 * q^29 - 88366273477255858343403702960 * q^30 - 282753969983174411853352917888 * q^31 - 1118437222052144608340712062976 * q^32 - 46548952523162601127345608732 * q^33 - 2020045599738440464009480297200 * q^34 - 2778733015107044038012367571600 * q^35 + 1358822047559410249352115278400 * q^36 - 5239395449699583862273344438486 * q^37 - 4077508380452877314541820882464 * q^38 - 16193443248061716548450856539898 * q^39 - 10242585699763810314758557271040 * q^40 + 47673397400045140822464268984782 * q^41 + 74550974919263458624588661024832 * q^42 - 14936449213367655469478076825588 * q^43 + 383801287439893621552232462293248 * q^44 + 12639986293907486833224134886810 * q^45 + 646689351161727342528587792407872 * q^46 - 13040685113470292045769719198544 * q^47 + 1277105411477001534152180886908928 * q^48 - 132364363537073708245470314514213 * q^49 + 2030100946651365938753014066519800 * q^50 - 197236706729603991736995911807406 * q^51 - 16457201727541975997405015057804928 * q^52 - 11047064078175508118010662971794342 * q^53 - 1738037489283864344086071761241000 * q^54 - 1504305246366733376700435214523160 * q^55 + 6316090378583898308960601541324800 * q^56 - 8086399919341715520407790317583396 * q^57 - 23720839646010288107197368475070928 * q^58 + 35633406741119515209244171316491548 * q^59 + 38711815023138863096326248158705280 * q^60 - 26245828903346977727221409425735902 * q^61 - 98335445202496226432366585960435712 * q^62 + 18698333287122936270281907905117256 * q^63 + 922428812776307390107790824712699904 * q^64 + 260861961831082759405211612047737660 * q^65 - 212471181821833694819355024467075232 * q^66 - 200741546976450474071235708204779388 * q^67 + 1264175105126717513162323757007619200 * q^68 - 298901849820328103053611531746352024 * q^69 - 431344371239166538676321844662332800 * q^70 - 3140665348656484831244609799236867544 * q^71 - 2062152119033027062230435797305179648 * q^72 - 3825610182002392515733100347600509522 * q^73 - 2544605510256173934291855124681995024 * q^74 - 2584370554219599987738141977488018425 * q^75 - 5521658898639443517674491687212787968 * q^76 - 994601047124972255067887751426792672 * q^77 + 7462776271158562634691099091263883152 * q^78 - 1038716953120555158347640895730970000 * q^79 + 45766070974584297712698519042271272960 * q^80 + 5474401089420219382077155933569751763 * q^81 - 16726391180845396277548112611717202352 * q^82 + 69227326737654458476356626745129089940 * q^83 - 36599382298740984291406281382995119616 * q^84 + 76820078772499304751574061990694660660 * q^85 + 159762376422294357818512142478616905504 * q^86 - 53781080204234165408470505817072001962 * q^87 - 343351801449478884201073068755288881152 * q^88 + 136597710245735759116899165769855535742 * q^89 - 102704714644998585052548577575521842320 * q^90 - 259984668223904357182500109993449632208 * q^91 - 135698237299460735254844067932094260736 * q^92 - 328634043952718257237540151213237421696 * q^93 + 457887889864219720177610385758047412352 * q^94 + 462468326274179393065716948072305471640 * q^95 - 1299916486449730342986216438139082145792 * q^96 - 1338928527743499267936157260425715870618 * q^97 + 1730483839907526080834886072855293848584 * q^98 - 54102053846884316265804561020862329844 * 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 $

$2$	−337546.	−0.455249	−0.227624	−	0.973749i	$-0.573096\pi$
$2$	−337546.	−0.455249	−0.227624	+	0.973749i	$0.573096\pi$
$3$	1.16226e9	0.577350
$3$	1.16226e9	0.577350
$4$	−4.35818e11	−0.792749
$5$	2.60351e13	0.610442	0.305221	−	0.952282i	$-0.401270\pi$
$5$	2.60351e13	0.610442	0.305221	+	0.952282i	$0.401270\pi$
$6$	−3.92317e14	−0.262838
$7$	−1.06972e16	−0.354697	−0.177348	−	0.984148i	$-0.556752\pi$
$7$	−1.06972e16	−0.354697	−0.177348	+	0.984148i	$0.556752\pi$
$8$	3.32677e17	0.816146
$9$	1.35085e18	0.333333
$10$	−8.78806e18	−0.277903
$11$	−2.32202e20	−1.14475	−0.572373	−	0.819994i	$-0.693977\pi$
$11$	−2.32202e20	−1.14475	−0.572373	+	0.819994i	$0.693977\pi$
$12$	−5.06535e20	−0.457694
$13$	4.99617e21	0.947855	0.473928	−	0.880564i	$-0.342836\pi$
$13$	4.99617e21	0.947855	0.473928	+	0.880564i	$0.342836\pi$
$14$	3.61079e21	0.161475
$15$	3.02596e22	0.352439
$16$	1.27300e23	0.421199
$17$	1.94633e23	0.197453	0.0987265	−	0.995115i	$-0.468523\pi$
$17$	1.94633e23	0.197453	0.0987265	+	0.995115i	$0.468523\pi$
$18$	−4.55975e23	−0.151750
$19$	5.09059e24	0.590301	0.295150	−	0.955451i	$-0.404630\pi$
$19$	5.09059e24	0.590301	0.295150	+	0.955451i	$0.404630\pi$
$20$	−1.13466e25	−0.483927
$21$	−1.24329e25	−0.204784
$22$	7.83790e25	0.521143
$23$	−4.20533e26	−1.17519	−0.587593	−	0.809156i	$-0.699924\pi$
$23$	−4.20533e26	−1.17519	−0.587593	+	0.809156i	$0.699924\pi$
$24$	3.86658e26	0.471202
$25$	−1.14116e27	−0.627360
$26$	−1.68644e27	−0.431510
$27$	1.57004e27	0.192450
$28$	4.66202e27	0.281186
$29$	−2.15883e28	−0.656836	−0.328418	−	0.944533i	$-0.606515\pi$
$29$	−2.15883e28	−0.656836	−0.328418	+	0.944533i	$0.606515\pi$
$30$	−1.02140e28	−0.160447
$31$	−2.23682e29	−1.85386	−0.926932	−	0.375228i	$-0.877564\pi$
$31$	−2.23682e29	−1.85386	−0.926932	+	0.375228i	$0.877564\pi$
$32$	−2.25861e29	−1.00790
$33$	−2.69880e29	−0.660919
$34$	−6.56978e28	−0.0898901
$35$	−2.78502e29	−0.216522
$36$	−5.88726e29	−0.264250
$37$	−5.80126e30	−1.52612	−0.763060	−	0.646328i	$-0.776304\pi$
$37$	−5.80126e30	−1.52612	−0.763060	+	0.646328i	$0.776304\pi$
$38$	−1.71831e30	−0.268734
$39$	5.80686e30	0.547244
$40$	8.66129e30	0.498210
$41$	−9.08797e30	−0.322985	−0.161492	−	0.986874i	$-0.551631\pi$
$41$	−9.08797e30	−0.322985	−0.161492	+	0.986874i	$0.551631\pi$
$42$	4.19669e30	0.0932278
$43$	2.60188e31	0.365302	0.182651	−	0.983178i	$-0.441532\pi$
$43$	2.60188e31	0.365302	0.182651	+	0.983178i	$0.441532\pi$
$44$	1.01198e32	0.907495
$45$	3.51696e31	0.203481
$46$	1.41949e32	0.535002
$47$	4.64891e32	1.15198	0.575988	−	0.817458i	$-0.304618\pi$
$47$	4.64891e32	1.15198	0.575988	+	0.817458i	$0.304618\pi$
$48$	1.47956e32	0.243180
$49$	−7.95114e32	−0.874190
$50$	3.85195e32	0.285605
$51$	2.26215e32	0.113999
$52$	−2.17742e33	−0.751411
$53$	−4.59023e33	−1.09258	−0.546292	−	0.837595i	$-0.683961\pi$
$53$	−4.59023e33	−1.09258	−0.546292	+	0.837595i	$0.683961\pi$
$54$	−5.29962e32	−0.0876126
$55$	−6.04541e33	−0.698801
$56$	−3.55870e33	−0.289485
$57$	5.91660e33	0.340810
$58$	7.28704e33	0.299023
$59$	6.43676e32	0.0189258	0.00946288	−	0.999955i	$-0.496988\pi$
$59$	6.43676e32	0.0189258	0.00946288	+	0.999955i	$0.496988\pi$
$60$	−1.31877e34	−0.279396
$61$	1.61101e33	0.0247267	0.0123633	−	0.999924i	$-0.496065\pi$
$61$	1.61101e33	0.0247267	0.0123633	+	0.999924i	$0.496065\pi$
$62$	7.55031e34	0.843969
$63$	−1.44503e34	−0.118232
$64$	6.25468e33	0.0376440
$65$	1.30076e35	0.578611
$66$	9.10969e34	0.300882
$67$	5.84042e35	1.43875	0.719375	−	0.694622i	$-0.244428\pi$
$67$	5.84042e35	1.43875	0.719375	+	0.694622i	$0.244428\pi$
$68$	−8.48248e34	−0.156531
$69$	−4.88769e35	−0.678494
$70$	9.40074e34	0.0985713
$71$	−1.82793e36	−1.45352	−0.726760	−	0.686892i	$-0.758975\pi$
$71$	−1.82793e36	−1.45352	−0.726760	+	0.686892i	$0.758975\pi$
$72$	4.49397e35	0.272049
$73$	−2.99198e36	−1.38409	−0.692043	−	0.721856i	$-0.743289\pi$
$73$	−2.99198e36	−1.38409	−0.692043	+	0.721856i	$0.743289\pi$
$74$	1.95819e36	0.694764
$75$	−1.32633e36	−0.362207
$76$	−2.21857e36	−0.467960
$77$	2.48391e36	0.406038
$78$	−1.96008e36	−0.249132
$79$	1.10201e36	0.109259	0.0546295	−	0.998507i	$-0.482602\pi$
$79$	1.10201e36	0.109259	0.0546295	+	0.998507i	$0.482602\pi$
$80$	3.31426e36	0.257118
$81$	1.82480e36	0.111111
$82$	3.06761e36	0.147038
$83$	4.80060e37	1.81665	0.908327	−	0.418260i	$-0.137360\pi$
$83$	4.80060e37	1.81665	0.908327	+	0.418260i	$0.137360\pi$
$84$	5.41849e36	0.162343
$85$	5.06731e36	0.120534
$86$	−8.78254e36	−0.166303
$87$	−2.50912e37	−0.379224
$88$	−7.72483e37	−0.934279
$89$	3.02726e37	0.293728	0.146864	−	0.989157i	$-0.453082\pi$
$89$	3.02726e37	0.293728	0.146864	+	0.989157i	$0.453082\pi$
$90$	−1.18714e37	−0.0926343
$91$	−5.34449e37	−0.336201
$92$	1.83276e38	0.931628
$93$	−2.59977e38	−1.07033
$94$	−1.56922e38	−0.524435
$95$	1.32534e38	0.360344
$96$	−2.62509e38	−0.581909
$97$	−3.29185e38	−0.596198	−0.298099	−	0.954535i	$-0.596353\pi$
$97$	−3.29185e38	−0.596198	−0.298099	+	0.954535i	$0.596353\pi$
$98$	2.68388e38	0.397974
$99$	−3.13671e38	−0.381582
$100$	4.97339e38	0.497339
$101$	1.49140e39	1.22837	0.614184	−	0.789163i	$-0.289485\pi$
$101$	1.49140e39	1.22837	0.614184	+	0.789163i	$0.289485\pi$
$102$	−7.63580e37	−0.0518981
$103$	−7.64549e38	−0.429615	−0.214807	−	0.976656i	$-0.568912\pi$
$103$	−7.64549e38	−0.429615	−0.214807	+	0.976656i	$0.568912\pi$
$104$	1.66211e39	0.773588
$105$	−3.23693e38	−0.125009
$106$	1.54941e39	0.497397
$107$	6.60376e39	1.76525	0.882627	−	0.470073i	$-0.155773\pi$
$107$	6.60376e39	1.76525	0.882627	+	0.470073i	$0.155773\pi$
$108$	−6.84253e38	−0.152565
$109$	−9.49528e39	−1.76885	−0.884425	−	0.466682i	$-0.845449\pi$
$109$	−9.49528e39	−1.76885	−0.884425	+	0.466682i	$0.845449\pi$
$110$	2.04061e39	0.318128
$111$	−6.74258e39	−0.881106
$112$	−1.36175e39	−0.149398
$113$	−8.42869e39	−0.777554	−0.388777	−	0.921332i	$-0.627102\pi$
$113$	−8.42869e39	−0.777554	−0.388777	+	0.921332i	$0.627102\pi$
$114$	−1.99713e39	−0.155153
$115$	−1.09486e40	−0.717383
$116$	9.40856e39	0.520706
$117$	6.74909e39	0.315952
$118$	−2.17271e38	−0.00861592
$119$	−2.08203e39	−0.0700359
$120$	1.00667e40	0.287642
$121$	1.27730e40	0.310441
$122$	−5.43790e38	−0.0112568
$123$	−1.05626e40	−0.186475
$124$	9.74847e40	1.46965
$125$	−7.70679e40	−0.993409
$126$	4.87765e39	0.0538251
$127$	6.18344e40	0.584867	0.292434	−	0.956286i	$-0.405535\pi$
$127$	6.18344e40	0.584867	0.292434	+	0.956286i	$0.405535\pi$
$128$	1.22057e41	0.990759
$129$	3.02406e40	0.210907
$130$	−4.39067e40	−0.263412
$131$	−2.67012e41	−1.37956	−0.689781	−	0.724018i	$-0.742293\pi$
$131$	−2.67012e41	−1.37956	−0.689781	+	0.724018i	$0.742293\pi$
$132$	1.17618e41	0.523943
$133$	−5.44550e40	−0.209378
$134$	−1.97141e41	−0.654989
$135$	4.08763e40	0.117480
$136$	6.47501e40	0.161150
$137$	−6.62395e41	−1.42911	−0.714556	−	0.699579i	$-0.753371\pi$
$137$	−6.62395e41	−1.42911	−0.714556	+	0.699579i	$0.753371\pi$
$138$	1.64982e41	0.308883
$139$	−2.13466e41	−0.347168	−0.173584	−	0.984819i	$-0.555535\pi$
$139$	−2.13466e41	−0.347168	−0.173584	+	0.984819i	$0.555535\pi$
$140$	1.21376e41	0.171648
$141$	5.40325e41	0.665094
$142$	6.17010e41	0.661712
$143$	−1.16012e42	−1.08505
$144$	1.71963e41	0.140400
$145$	−5.62053e41	−0.400960
$146$	1.00993e42	0.630103
$147$	−9.24130e41	−0.504714
$148$	2.52829e42	1.20983
$149$	3.20841e42	1.34635	0.673175	−	0.739483i	$-0.264930\pi$
$149$	3.20841e42	1.34635	0.673175	+	0.739483i	$0.264930\pi$
$150$	4.47697e41	0.164894
$151$	−5.17647e41	−0.167488	−0.0837439	−	0.996487i	$-0.526688\pi$
$151$	−5.17647e41	−0.167488	−0.0837439	+	0.996487i	$0.526688\pi$
$152$	1.69352e42	0.481772
$153$	2.62921e41	0.0658176
$154$	−8.38434e41	−0.184848
$155$	−5.82359e42	−1.13168
$156$	−2.53073e42	−0.433827
$157$	−3.82609e42	−0.579045	−0.289522	−	0.957171i	$-0.593496\pi$
$157$	−3.82609e42	−0.579045	−0.289522	+	0.957171i	$0.593496\pi$
$158$	−3.71980e41	−0.0497400
$159$	−5.33504e42	−0.630803
$160$	−5.88031e42	−0.615263
$161$	4.49851e42	0.416835
$162$	−6.15955e41	−0.0505832
$163$	5.49177e42	0.399995	0.199997	−	0.979796i	$-0.435907\pi$
$163$	5.49177e42	0.399995	0.199997	+	0.979796i	$0.435907\pi$
$164$	3.96070e42	0.256046
$165$	−7.02635e42	−0.403453
$166$	−1.62042e43	−0.827029
$167$	4.38972e43	1.99281	0.996404	−	0.0847334i	$-0.0270039\pi$
$167$	4.38972e43	1.99281	0.996404	+	0.0847334i	$0.0270039\pi$
$168$	−4.13614e42	−0.167134
$169$	−2.82202e42	−0.101571
$170$	−1.71045e42	−0.0548727
$171$	6.87664e42	0.196767
$172$	−1.13395e43	−0.289593
$173$	5.99267e43	1.36685	0.683425	−	0.730020i	$-0.260489\pi$
$173$	5.99267e43	1.36685	0.683425	+	0.730020i	$0.260489\pi$
$174$	8.46945e42	0.172641
$175$	1.22072e43	0.222523
$176$	−2.95593e43	−0.482166
$177$	7.48120e41	0.0109268
$178$	−1.02184e43	−0.133719
$179$	−1.11942e44	−1.31328	−0.656641	−	0.754203i	$-0.728023\pi$
$179$	−1.11942e44	−1.31328	−0.656641	+	0.754203i	$0.728023\pi$
$180$	−1.53275e43	−0.161309
$181$	1.53297e44	1.44811	0.724054	−	0.689743i	$-0.242277\pi$
$181$	1.53297e44	1.44811	0.724054	+	0.689743i	$0.242277\pi$
$182$	1.80401e43	0.153055
$183$	1.87241e42	0.0142760
$184$	−1.39901e44	−0.959124
$185$	−1.51037e44	−0.931608
$186$	8.77543e43	0.487266
$187$	−4.51943e43	−0.226033
$188$	−2.02608e44	−0.913227
$189$	−1.67950e43	−0.0682615
$190$	−4.47365e43	−0.164046
$191$	−6.17066e43	−0.204259	−0.102129	−	0.994771i	$-0.532566\pi$
$191$	−6.17066e43	−0.204259	−0.102129	+	0.994771i	$0.532566\pi$
$192$	7.26958e42	0.0217338
$193$	4.94468e44	1.33589	0.667945	−	0.744210i	$-0.267174\pi$
$193$	4.94468e44	1.33589	0.667945	+	0.744210i	$0.267174\pi$
$194$	1.11115e44	0.271418
$195$	1.51182e44	0.334061
$196$	3.46525e44	0.693013
$197$	−1.06923e44	−0.193633	−0.0968163	−	0.995302i	$-0.530866\pi$
$197$	−1.06923e44	−0.193633	−0.0968163	+	0.995302i	$0.530866\pi$
$198$	1.05878e44	0.173714
$199$	2.71083e44	0.403151	0.201576	−	0.979473i	$-0.435394\pi$
$199$	2.71083e44	0.403151	0.201576	+	0.979473i	$0.435394\pi$
$200$	−3.79638e44	−0.512018
$201$	6.78809e44	0.830663
$202$	−5.03418e44	−0.559213
$203$	2.30933e44	0.232978
$204$	−9.85886e43	−0.0903730
$205$	−2.36606e44	−0.197163
$206$	2.58071e44	0.195582
$207$	−5.68077e44	−0.391729
$208$	6.36011e44	0.399236
$209$	−1.18205e45	−0.675744
$210$	1.09261e44	0.0569102
$211$	−3.90011e45	−1.85169	−0.925846	−	0.377902i	$-0.876646\pi$
$211$	−3.90011e45	−1.85169	−0.925846	+	0.377902i	$0.876646\pi$
$212$	2.00050e45	0.866144
$213$	−2.12453e45	−0.839190
$214$	−2.22907e45	−0.803630
$215$	6.77402e44	0.222996
$216$	5.22317e44	0.157067
$217$	2.39277e45	0.657560
$218$	3.20510e45	0.805266
$219$	−3.47746e45	−0.799102
$220$	2.63470e45	0.553973
$221$	9.72422e44	0.187157
$222$	2.27593e45	0.401122
$223$	5.59176e45	0.902825	0.451412	−	0.892315i	$-0.350920\pi$
$223$	5.59176e45	0.902825	0.451412	+	0.892315i	$0.350920\pi$
$224$	2.41607e45	0.357498
$225$	−1.54154e45	−0.209120
$226$	2.84507e45	0.353980
$227$	4.01061e45	0.457832	0.228916	−	0.973446i	$-0.426482\pi$
$227$	4.01061e45	0.457832	0.228916	+	0.973446i	$0.426482\pi$
$228$	−2.57856e45	−0.270177
$229$	−1.62578e46	−1.56412	−0.782058	−	0.623206i	$-0.785830\pi$
$229$	−1.62578e46	−1.56412	−0.782058	+	0.623206i	$0.785830\pi$
$230$	3.69567e45	0.326588
$231$	2.88695e45	0.234426
$232$	−7.18192e45	−0.536074
$233$	6.55628e44	0.0450005	0.0225002	−	0.999747i	$-0.492837\pi$
$233$	6.55628e44	0.0450005	0.0225002	+	0.999747i	$0.492837\pi$
$234$	−2.27813e45	−0.143837
$235$	1.21035e46	0.703215
$236$	−2.80526e44	−0.0150034
$237$	1.28082e45	0.0630807
$238$	7.02781e44	0.0318838
$239$	−2.43505e46	−1.01800	−0.509001	−	0.860766i	$-0.669985\pi$
$239$	−2.43505e46	−1.01800	−0.509001	+	0.860766i	$0.669985\pi$
$240$	3.85204e45	0.148447
$241$	−2.11017e46	−0.749870	−0.374935	−	0.927051i	$-0.622335\pi$
$241$	−2.11017e46	−0.749870	−0.374935	+	0.927051i	$0.622335\pi$
$242$	−4.31149e45	−0.141328
$243$	2.12090e45	0.0641500
$244$	−7.02107e44	−0.0196021
$245$	−2.07009e46	−0.533643
$246$	3.56537e45	0.0848926
$247$	2.54335e46	0.559520
$248$	−7.44139e46	−1.51302
$249$	5.57955e46	1.04885
$250$	2.60140e46	0.452248
$251$	6.54085e46	1.05195	0.525977	−	0.850499i	$-0.323700\pi$
$251$	6.54085e46	1.05195	0.525977	+	0.850499i	$0.323700\pi$
$252$	6.29770e45	0.0937285
$253$	9.76485e46	1.34529
$254$	−2.08720e46	−0.266260
$255$	5.88953e45	0.0695901
$256$	−4.46384e46	−0.488686
$257$	1.64706e46	0.167114	0.0835570	−	0.996503i	$-0.473372\pi$
$257$	1.64706e46	0.167114	0.0835570	+	0.996503i	$0.473372\pi$
$258$	−1.02076e46	−0.0960152
$259$	6.20571e46	0.541310
$260$	−5.66895e46	−0.458693
$261$	−2.91625e46	−0.218945
$262$	9.01290e46	0.628043
$263$	−3.48367e46	−0.225372	−0.112686	−	0.993631i	$-0.535945\pi$
$263$	−3.48367e46	−0.225372	−0.112686	+	0.993631i	$0.535945\pi$
$264$	−8.97827e46	−0.539406
$265$	−1.19507e47	−0.666959
$266$	1.83811e46	0.0953189
$267$	3.51847e46	0.169584
$268$	−2.54536e47	−1.14057
$269$	−1.94339e46	−0.0809822	−0.0404911	−	0.999180i	$-0.512892\pi$
$269$	−1.94339e46	−0.0809822	−0.0404911	+	0.999180i	$0.512892\pi$
$270$	−1.37976e46	−0.0534824
$271$	−3.43747e47	−1.23976	−0.619879	−	0.784697i	$-0.712818\pi$
$271$	−3.43747e47	−1.23976	−0.619879	+	0.784697i	$0.712818\pi$
$272$	2.47768e46	0.0831671
$273$	−6.21170e46	−0.194106
$274$	2.23589e47	0.650601
$275$	2.64980e47	0.718168
$276$	2.13014e47	0.537875
$277$	1.76062e47	0.414296	0.207148	−	0.978310i	$-0.433582\pi$
$277$	1.76062e47	0.414296	0.207148	+	0.978310i	$0.433582\pi$
$278$	7.20546e46	0.158048
$279$	−3.02161e47	−0.617955
$280$	−9.26513e46	−0.176714
$281$	6.60026e47	1.17432	0.587162	−	0.809470i	$-0.300245\pi$
$281$	6.60026e47	1.17432	0.587162	+	0.809470i	$0.300245\pi$
$282$	−1.82385e47	−0.302783
$283$	−3.04981e47	−0.472539	−0.236269	−	0.971688i	$-0.575925\pi$
$283$	−3.04981e47	−0.472539	−0.236269	+	0.971688i	$0.575925\pi$
$284$	7.96644e47	1.15228
$285$	1.54039e47	0.208045
$286$	3.91595e47	0.493968
$287$	9.72156e46	0.114562
$288$	−3.05104e47	−0.335966
$289$	−9.33764e47	−0.961012
$290$	1.89719e47	0.182537
$291$	−3.82599e47	−0.344215
$292$	1.30396e48	1.09723
$293$	−3.48541e47	−0.274369	−0.137185	−	0.990545i	$-0.543805\pi$
$293$	−3.48541e47	−0.274369	−0.137185	+	0.990545i	$0.543805\pi$
$294$	3.11937e47	0.229770
$295$	1.67582e46	0.0115531
$296$	−1.92995e48	−1.24554
$297$	−3.64567e47	−0.220306
$298$	−1.08299e48	−0.612924
$299$	−2.10105e48	−1.11391
$300$	5.78038e47	0.287139
$301$	−2.78327e47	−0.129571
$302$	1.74730e47	0.0762486
$303$	1.73340e48	0.709198
$304$	6.48031e47	0.248634
$305$	4.19428e46	0.0150942
$306$	−8.87480e46	−0.0299634
$307$	2.59439e48	0.821933	0.410966	−	0.911651i	$-0.365191\pi$
$307$	2.59439e48	0.821933	0.410966	+	0.911651i	$0.365191\pi$
$308$	−1.08253e48	−0.321886
$309$	−8.88606e47	−0.248038
$310$	1.96573e48	0.515194
$311$	−3.40239e48	−0.837445	−0.418723	−	0.908114i	$-0.637522\pi$
$311$	−3.40239e48	−0.837445	−0.418723	+	0.908114i	$0.637522\pi$
$312$	1.93181e48	0.446631
$313$	−1.47821e48	−0.321086	−0.160543	−	0.987029i	$-0.551325\pi$
$313$	−1.47821e48	−0.321086	−0.160543	+	0.987029i	$0.551325\pi$
$314$	1.29148e48	0.263609
$315$	−3.76215e47	−0.0721740
$316$	−4.80276e47	−0.0866150
$317$	4.26922e48	0.723924	0.361962	−	0.932193i	$-0.382107\pi$
$317$	4.26922e48	0.723924	0.361962	+	0.932193i	$0.382107\pi$
$318$	1.80082e48	0.287172
$319$	5.01284e48	0.751909
$320$	1.62841e47	0.0229795
$321$	7.67529e48	1.01917
$322$	−1.51846e48	−0.189764
$323$	9.90800e47	0.116557
$324$	−7.95281e47	−0.0880832
$325$	−5.70144e48	−0.594647
$326$	−1.85373e48	−0.182097
$327$	−1.10360e49	−1.02125
$328$	−3.02336e48	−0.263603
$329$	−4.97303e48	−0.408602
$330$	2.37172e48	0.183671
$331$	5.94232e48	0.433821	0.216910	−	0.976192i	$-0.430402\pi$
$331$	5.94232e48	0.433821	0.216910	+	0.976192i	$0.430402\pi$
$332$	−2.09219e49	−1.44015
$333$	−7.83664e48	−0.508707
$334$	−1.48173e49	−0.907223
$335$	1.52056e49	0.878274
$336$	−1.58271e48	−0.0862551
$337$	2.24473e48	0.115447	0.0577233	−	0.998333i	$-0.481616\pi$
$337$	2.24473e48	0.115447	0.0577233	+	0.998333i	$0.481616\pi$
$338$	9.52561e47	0.0462399
$339$	−9.79634e48	−0.448921
$340$	−2.20842e48	−0.0955529
$341$	5.19394e49	2.12220
$342$	−2.32118e48	−0.0895778
$343$	1.82350e49	0.664769
$344$	8.65585e48	0.298140
$345$	−1.27252e49	−0.414181
$346$	−2.02280e49	−0.622257
$347$	3.87297e49	1.12621	0.563104	−	0.826386i	$-0.309607\pi$
$347$	3.87297e49	1.12621	0.563104	+	0.826386i	$0.309607\pi$
$348$	1.09352e49	0.300630
$349$	−1.88515e49	−0.490060	−0.245030	−	0.969515i	$-0.578798\pi$
$349$	−1.88515e49	−0.490060	−0.245030	+	0.969515i	$0.578798\pi$
$350$	−4.12050e48	−0.101303
$351$	7.84420e48	0.182415
$352$	5.24453e49	1.15378
$353$	−2.34165e49	−0.487432	−0.243716	−	0.969847i	$-0.578367\pi$
$353$	−2.34165e49	−0.487432	−0.243716	+	0.969847i	$0.578367\pi$
$354$	−2.52525e47	−0.00497441
$355$	−4.75903e49	−0.887290
$356$	−1.31934e49	−0.232852
$357$	−2.41986e48	−0.0404353
$358$	3.77855e49	0.597869
$359$	5.36357e48	0.0803733	0.0401867	−	0.999192i	$-0.487205\pi$
$359$	5.36357e48	0.0803733	0.0401867	+	0.999192i	$0.487205\pi$
$360$	1.17001e49	0.166070
$361$	−4.84546e49	−0.651545
$362$	−5.17448e49	−0.659249
$363$	1.48456e49	0.179233
$364$	2.32923e49	0.266523
$365$	−7.78966e49	−0.844904
$366$	−6.32026e47	−0.00649911
$367$	−1.01560e50	−0.990230	−0.495115	−	0.868828i	$-0.664874\pi$
$367$	−1.01560e50	−0.990230	−0.495115	+	0.868828i	$0.664874\pi$
$368$	−5.35337e49	−0.494988
$369$	−1.22765e49	−0.107662
$370$	5.09818e49	0.424113
$371$	4.91025e49	0.387536
$372$	1.13303e50	0.848502
$373$	−3.11556e48	−0.0221418	−0.0110709	−	0.999939i	$-0.503524\pi$
$373$	−3.11556e48	−0.0221418	−0.0110709	+	0.999939i	$0.503524\pi$
$374$	1.52552e49	0.102901
$375$	−8.95731e49	−0.573545
$376$	1.54659e50	0.940181
$377$	−1.07859e50	−0.622585
$378$	5.66910e48	0.0310759
$379$	1.84377e50	0.959936	0.479968	−	0.877286i	$-0.340648\pi$
$379$	1.84377e50	0.959936	0.479968	+	0.877286i	$0.340648\pi$
$380$	−5.77608e49	−0.285663
$381$	7.18677e49	0.337673
$382$	2.08288e49	0.0929885
$383$	−1.12810e50	−0.478599	−0.239299	−	0.970946i	$-0.576918\pi$
$383$	−1.12810e50	−0.478599	−0.239299	+	0.970946i	$0.576918\pi$
$384$	1.41862e50	0.572015
$385$	6.46688e49	0.247862
$386$	−1.66906e50	−0.608162
$387$	3.51475e49	0.121767
$388$	1.43465e50	0.472636
$389$	5.29551e50	1.65917	0.829584	−	0.558381i	$-0.188577\pi$
$389$	5.29551e50	1.65917	0.829584	+	0.558381i	$0.188577\pi$
$390$	−5.10310e49	−0.152081
$391$	−8.18497e49	−0.232044
$392$	−2.64516e50	−0.713467
$393$	−3.10338e50	−0.796490
$394$	3.60914e49	0.0881510
$395$	2.86910e49	0.0666963
$396$	1.36703e50	0.302498
$397$	−5.56529e50	−1.17239	−0.586196	−	0.810169i	$-0.699375\pi$
$397$	−5.56529e50	−1.17239	−0.586196	+	0.810169i	$0.699375\pi$
$398$	−9.15033e49	−0.183534
$399$	−6.32909e49	−0.120884
$400$	−1.45270e50	−0.264244
$401$	8.16865e50	1.41526	0.707628	−	0.706585i	$-0.249765\pi$
$401$	8.16865e50	1.41526	0.707628	+	0.706585i	$0.249765\pi$
$402$	−2.29130e50	−0.378158
$403$	−1.11755e51	−1.75720
$404$	−6.49981e50	−0.973787
$405$	4.75089e49	0.0678269
$406$	−7.79508e49	−0.106063
$407$	1.34706e51	1.74702
$408$	7.52565e49	0.0930403
$409$	−8.80468e49	−0.103779	−0.0518894	−	0.998653i	$-0.516524\pi$
$409$	−8.80468e49	−0.103779	−0.0518894	+	0.998653i	$0.516524\pi$
$410$	7.98657e49	0.0897584
$411$	−7.69876e50	−0.825098
$412$	3.33204e50	0.340577
$413$	−6.88552e48	−0.00671291
$414$	1.91752e50	0.178334
$415$	1.24984e51	1.10896
$416$	−1.12844e51	−0.955340
$417$	−2.48103e50	−0.200438
$418$	3.98996e50	0.307631
$419$	2.08362e51	1.53336	0.766682	−	0.642027i	$-0.221906\pi$
$419$	2.08362e51	1.53336	0.766682	+	0.642027i	$0.221906\pi$
$420$	1.41071e50	0.0991007
$421$	1.50555e51	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$421$	1.50555e51	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$422$	1.31647e51	0.842980
$423$	6.27999e50	0.383992
$424$	−1.52706e51	−0.891708
$425$	−2.22108e50	−0.123874
$426$	7.17127e50	0.382040
$427$	−1.72332e49	−0.00877048
$428$	−2.87804e51	−1.39940
$429$	−1.34836e51	−0.626455
$430$	−2.28655e50	−0.101518
$431$	−8.32491e50	−0.353242	−0.176621	−	0.984279i	$-0.556517\pi$
$431$	−8.32491e50	−0.353242	−0.176621	+	0.984279i	$0.556517\pi$
$432$	1.99866e50	0.0810599
$433$	−3.85277e51	−1.49369	−0.746843	−	0.665001i	$-0.768431\pi$
$433$	−3.85277e51	−1.49369	−0.746843	+	0.665001i	$0.768431\pi$
$434$	−8.07670e50	−0.299353
$435$	−6.53253e50	−0.231494
$436$	4.13822e51	1.40225
$437$	−2.14076e51	−0.693713
$438$	1.17381e51	0.363790
$439$	5.69942e50	0.168956	0.0844778	−	0.996425i	$-0.473078\pi$
$439$	5.69942e50	0.168956	0.0844778	+	0.996425i	$0.473078\pi$
$440$	−2.01117e51	−0.570324
$441$	−1.07408e51	−0.291397
$442$	−3.28238e50	−0.0852028
$443$	2.79741e51	0.694839	0.347419	−	0.937710i	$-0.387058\pi$
$443$	2.79741e51	0.694839	0.347419	+	0.937710i	$0.387058\pi$
$444$	2.93854e51	0.698496
$445$	7.88152e50	0.179304
$446$	−1.88748e51	−0.411010
$447$	3.72902e51	0.777316
$448$	−6.69075e49	−0.0133522
$449$	−8.12722e51	−1.55288	−0.776441	−	0.630190i	$-0.782977\pi$
$449$	−8.12722e51	−1.55288	−0.776441	+	0.630190i	$0.782977\pi$
$450$	5.20341e50	0.0952016
$451$	2.11025e51	0.369735
$452$	3.67338e51	0.616405
$453$	−6.01641e50	−0.0966992
$454$	−1.35377e51	−0.208427
$455$	−1.39145e51	−0.205231
$456$	1.96832e51	0.278151
$457$	1.73638e51	0.235114	0.117557	−	0.993066i	$-0.462494\pi$
$457$	1.73638e51	0.235114	0.117557	+	0.993066i	$0.462494\pi$
$458$	5.48775e51	0.712061
$459$	3.05583e50	0.0379998
$460$	4.77161e51	0.568705
$461$	1.14780e52	1.31128	0.655642	−	0.755072i	$-0.272398\pi$
$461$	1.14780e52	1.31128	0.655642	+	0.755072i	$0.272398\pi$
$462$	−9.74479e50	−0.106722
$463$	−3.44010e51	−0.361195	−0.180598	−	0.983557i	$-0.557803\pi$
$463$	−3.44010e51	−0.361195	−0.180598	+	0.983557i	$0.557803\pi$
$464$	−2.74818e51	−0.276659
$465$	−6.76853e51	−0.653374
$466$	−2.21305e50	−0.0204864
$467$	3.70446e51	0.328886	0.164443	−	0.986387i	$-0.447417\pi$
$467$	3.70446e51	0.328886	0.164443	+	0.986387i	$0.447417\pi$
$468$	−2.94138e51	−0.250470
$469$	−6.24760e51	−0.510320
$470$	−4.08549e51	−0.320137
$471$	−4.44692e51	−0.334312
$472$	2.14136e50	0.0154462
$473$	−6.04161e51	−0.418178
$474$	−4.32338e50	−0.0287174
$475$	−5.80919e51	−0.370331
$476$	9.07386e50	0.0555209
$477$	−6.20072e51	−0.364195
$478$	8.21942e51	0.463444
$479$	9.78827e51	0.529863	0.264931	−	0.964267i	$-0.414651\pi$
$479$	9.78827e51	0.529863	0.264931	+	0.964267i	$0.414651\pi$
$480$	−6.83446e51	−0.355222
$481$	−2.89841e52	−1.44654
$482$	7.12282e51	0.341377
$483$	5.22845e51	0.240660
$484$	−5.56672e51	−0.246102
$485$	−8.57036e51	−0.363945
$486$	−7.15900e50	−0.0292042
$487$	2.08492e52	0.817098	0.408549	−	0.912736i	$-0.366035\pi$
$487$	2.08492e52	0.817098	0.408549	+	0.912736i	$0.366035\pi$
$488$	5.35945e50	0.0201806
$489$	6.38287e51	0.230937
$490$	6.98751e51	0.242940
$491$	4.58188e52	1.53093	0.765464	−	0.643478i	$-0.222509\pi$
$491$	4.58188e52	1.53093	0.765464	+	0.643478i	$0.222509\pi$
$492$	4.60337e51	0.147828
$493$	−4.20180e51	−0.129694
$494$	−8.58498e51	−0.254720
$495$	−8.16645e51	−0.232934
$496$	−2.84747e52	−0.780847
$497$	1.95536e52	0.515559
$498$	−1.88336e52	−0.477486
$499$	4.96255e52	1.20988	0.604942	−	0.796269i	$-0.293196\pi$
$499$	4.96255e52	1.20988	0.604942	+	0.796269i	$0.293196\pi$
$500$	3.35876e52	0.787524
$501$	5.10200e52	1.15055
$502$	−2.20784e52	−0.478901
$503$	−2.14641e52	−0.447854	−0.223927	−	0.974606i	$-0.571888\pi$
$503$	−2.14641e52	−0.447854	−0.223927	+	0.974606i	$0.571888\pi$
$504$	−4.80728e51	−0.0964948
$505$	3.88289e52	0.749848
$506$	−3.29609e52	−0.612441
$507$	−3.27992e51	−0.0586419
$508$	−2.69485e52	−0.463653
$509$	−9.64802e52	−1.59750	−0.798751	−	0.601661i	$-0.794506\pi$
$509$	−9.64802e52	−1.59750	−0.798751	+	0.601661i	$0.794506\pi$
$510$	−1.98799e51	−0.0316808
$511$	3.20057e52	0.490931
$512$	−5.20340e52	−0.768286
$513$	7.99245e51	0.113603
$514$	−5.55958e51	−0.0760784
$515$	−1.99051e52	−0.262255
$516$	−1.31794e52	−0.167196
$517$	−1.07949e53	−1.31872
$518$	−2.09472e52	−0.246431
$519$	6.96505e52	0.789152
$520$	4.32733e52	0.472231
$521$	−1.34313e53	−1.41183	−0.705917	−	0.708294i	$-0.749465\pi$
$521$	−1.34313e53	−1.41183	−0.705917	+	0.708294i	$0.749465\pi$
$522$	9.84371e51	0.0996745
$523$	1.09949e53	1.07253	0.536265	−	0.844050i	$-0.319835\pi$
$523$	1.09949e53	1.07253	0.536265	+	0.844050i	$0.319835\pi$
$524$	1.16369e53	1.09365
$525$	1.41880e52	0.128474
$526$	1.17590e52	0.102600
$527$	−4.35360e52	−0.366051
$528$	−3.43556e52	−0.278379
$529$	4.87958e52	0.381063
$530$	4.03392e52	0.303632
$531$	8.69511e50	0.00630859
$532$	2.37325e52	0.165984
$533$	−4.54051e52	−0.306143
$534$	−1.18765e52	−0.0772028
$535$	1.71930e53	1.07759
$536$	1.94297e53	1.17423
$537$	−1.30106e53	−0.758223
$538$	6.55983e51	0.0368670
$539$	1.84627e53	1.00072
$540$	−1.78146e52	−0.0931319
$541$	−3.63090e53	−1.83091	−0.915455	−	0.402420i	$-0.868169\pi$
$541$	−3.63090e53	−1.83091	−0.915455	+	0.402420i	$0.868169\pi$
$542$	1.16030e53	0.564398
$543$	1.78171e53	0.836066
$544$	−4.39600e52	−0.199012
$545$	−2.47211e53	−1.07978
$546$	2.09674e52	0.0883664
$547$	−1.73690e53	−0.706353	−0.353176	−	0.935557i	$-0.614898\pi$
$547$	−1.73690e53	−0.706353	−0.353176	+	0.935557i	$0.614898\pi$
$548$	2.88684e53	1.13293
$549$	2.17623e51	0.00824223
$550$	−8.94431e52	−0.326945
$551$	−1.09897e53	−0.387731
$552$	−1.62602e53	−0.553750
$553$	−1.17884e52	−0.0387538
$554$	−5.94292e52	−0.188608
$555$	−1.75544e53	−0.537864
$556$	9.30323e52	0.275217
$557$	1.22542e53	0.350032	0.175016	−	0.984566i	$-0.444002\pi$
$557$	1.22542e53	0.350032	0.175016	+	0.984566i	$0.444002\pi$
$558$	1.01993e53	0.281323
$559$	1.29994e53	0.346253
$560$	−3.54533e52	−0.0911989
$561$	−5.25276e52	−0.130500
$562$	−2.22789e53	−0.534609
$563$	1.74387e53	0.404205	0.202102	−	0.979364i	$-0.435223\pi$
$563$	1.74387e53	0.404205	0.202102	+	0.979364i	$0.435223\pi$
$564$	−2.35484e53	−0.527252
$565$	−2.19442e53	−0.474652
$566$	1.02945e53	0.215123
$567$	−1.95202e52	−0.0394108
$568$	−6.08109e53	−1.18628
$569$	−5.15053e53	−0.970874	−0.485437	−	0.874272i	$-0.661339\pi$
$569$	−5.15053e53	−0.970874	−0.485437	+	0.874272i	$0.661339\pi$
$570$	−5.19955e52	−0.0947122
$571$	8.94621e53	1.57483	0.787417	−	0.616421i	$-0.211418\pi$
$571$	8.94621e53	1.57483	0.787417	+	0.616421i	$0.211418\pi$
$572$	5.05602e53	0.860174
$573$	−7.17192e52	−0.117929
$574$	−3.28148e52	−0.0521540
$575$	4.79896e53	0.737265
$576$	8.44915e51	0.0125480
$577$	6.62311e53	0.950897	0.475449	−	0.879744i	$-0.342286\pi$
$577$	6.62311e53	0.950897	0.475449	+	0.879744i	$0.342286\pi$
$578$	3.15188e53	0.437499
$579$	5.74702e53	0.771277
$580$	2.44953e53	0.317861
$581$	−5.13528e53	−0.644362
$582$	1.29145e53	0.156704
$583$	1.06586e54	1.25073
$584$	−9.95363e53	−1.12962
$585$	1.75713e53	0.192870
$586$	1.17649e53	0.124906
$587$	−3.25143e53	−0.333911	−0.166956	−	0.985964i	$-0.553394\pi$
$587$	−3.25143e53	−0.333911	−0.166956	+	0.985964i	$0.553394\pi$
$588$	4.02753e53	0.400111
$589$	−1.13867e54	−1.09434
$590$	−5.65667e51	−0.00525952
$591$	−1.24272e53	−0.111794
$592$	−7.38499e53	−0.642801
$593$	−1.04178e54	−0.877426	−0.438713	−	0.898627i	$-0.644566\pi$
$593$	−1.04178e54	−0.877426	−0.438713	+	0.898627i	$0.644566\pi$
$594$	1.23058e53	0.100294
$595$	−5.42059e52	−0.0427529
$596$	−1.39829e54	−1.06732
$597$	3.15070e53	0.232760
$598$	7.09203e53	0.507104
$599$	−8.95920e51	−0.00620078	−0.00310039	−	0.999995i	$-0.500987\pi$
$599$	−8.95920e51	−0.00620078	−0.00310039	+	0.999995i	$0.500987\pi$
$600$	−4.41239e53	−0.295614
$601$	9.79675e52	0.0635375	0.0317687	−	0.999495i	$-0.489886\pi$
$601$	9.79675e52	0.0635375	0.0317687	+	0.999495i	$0.489886\pi$
$602$	9.39484e52	0.0589872
$603$	7.88954e53	0.479583
$604$	2.25600e53	0.132776
$605$	3.32547e53	0.189506
$606$	−5.85103e53	−0.322862
$607$	−2.35816e54	−1.26007	−0.630035	−	0.776567i	$-0.716959\pi$
$607$	−2.35816e54	−1.26007	−0.630035	+	0.776567i	$0.716959\pi$
$608$	−1.14977e54	−0.594962
$609$	2.68405e53	0.134510
$610$	−1.41576e52	−0.00687162
$611$	2.32268e54	1.09191
$612$	−1.14586e53	−0.0521769
$613$	4.03801e53	0.178110	0.0890550	−	0.996027i	$-0.471615\pi$
$613$	4.03801e53	0.178110	0.0890550	+	0.996027i	$0.471615\pi$
$614$	−8.75725e53	−0.374184
$615$	−2.74999e53	−0.113832
$616$	8.26339e53	0.331386
$617$	2.82430e54	1.09736	0.548682	−	0.836031i	$-0.315130\pi$
$617$	2.82430e54	1.09736	0.548682	+	0.836031i	$0.315130\pi$
$618$	2.99946e53	0.112919
$619$	1.46203e54	0.533321	0.266660	−	0.963791i	$-0.414080\pi$
$619$	1.46203e54	0.533321	0.266660	+	0.963791i	$0.414080\pi$
$620$	2.53803e54	0.897136
$621$	−6.60254e53	−0.226165
$622$	1.14846e54	0.381246
$623$	−3.23832e53	−0.104184
$624$	7.39211e53	0.230499
$625$	6.92890e52	0.0209413
$626$	4.98964e53	0.146174
$627$	−1.37385e54	−0.390141
$628$	1.66748e54	0.459037
$629$	−1.12912e54	−0.301337
$630$	1.26990e53	0.0328571
$631$	−1.85775e54	−0.466031	−0.233016	−	0.972473i	$-0.574859\pi$
$631$	−1.85775e54	−0.466031	−0.233016	+	0.972473i	$0.574859\pi$
$632$	3.66613e53	0.0891714
$633$	−4.53294e54	−1.06907
$634$	−1.44106e54	−0.329565
$635$	1.60986e54	0.357028
$636$	2.32511e54	0.500069
$637$	−3.97253e54	−0.828606
$638$	−1.69207e54	−0.342306
$639$	−2.46926e54	−0.484506
$640$	3.17777e54	0.604801
$641$	2.51010e54	0.463403	0.231702	−	0.972787i	$-0.425571\pi$
$641$	2.51010e54	0.463403	0.231702	+	0.972787i	$0.425571\pi$
$642$	−2.59077e54	−0.463976
$643$	−7.23422e54	−1.25683	−0.628416	−	0.777877i	$-0.716297\pi$
$643$	−7.23422e54	−1.25683	−0.628416	+	0.777877i	$0.716297\pi$
$644$	−1.96053e54	−0.330445
$645$	7.87318e53	0.128747
$646$	−3.34441e53	−0.0530622
$647$	5.07753e54	0.781661	0.390831	−	0.920463i	$-0.372188\pi$
$647$	5.07753e54	0.781661	0.390831	+	0.920463i	$0.372188\pi$
$648$	6.07069e53	0.0906829
$649$	−1.49463e53	−0.0216652
$650$	1.92450e54	0.270712
$651$	2.78102e54	0.379643
$652$	−2.39341e54	−0.317095
$653$	6.07495e52	0.00781152	0.00390576	−	0.999992i	$-0.498757\pi$
$653$	6.07495e52	0.00781152	0.00390576	+	0.999992i	$0.498757\pi$
$654$	3.72516e54	0.464921
$655$	−6.95170e54	−0.842143
$656$	−1.15690e54	−0.136041
$657$	−4.04172e54	−0.461362
$658$	1.67863e54	0.186016
$659$	−2.66302e54	−0.286489	−0.143245	−	0.989687i	$-0.545754\pi$
$659$	−2.66302e54	−0.286489	−0.143245	+	0.989687i	$0.545754\pi$
$660$	3.06221e54	0.319837
$661$	8.51695e54	0.863686	0.431843	−	0.901949i	$-0.357864\pi$
$661$	8.51695e54	0.863686	0.431843	+	0.901949i	$0.357864\pi$
$662$	−2.00581e54	−0.197496
$663$	1.13021e54	0.108055
$664$	1.59705e55	1.48266
$665$	−1.41774e54	−0.127813
$666$	2.64523e54	0.231588
$667$	9.07857e54	0.771904
$668$	−1.91312e55	−1.57980
$669$	6.49908e54	0.521246
$670$	−5.13260e54	−0.399833
$671$	−3.74079e53	−0.0283058
$672$	2.80811e54	0.206401
$673$	7.69147e54	0.549181	0.274590	−	0.961561i	$-0.411458\pi$
$673$	7.69147e54	0.549181	0.274590	+	0.961561i	$0.411458\pi$
$674$	−7.57700e53	−0.0525568
$675$	−1.79167e54	−0.120736
$676$	1.22989e54	0.0805201
$677$	1.10266e55	0.701396	0.350698	−	0.936489i	$-0.385944\pi$
$677$	1.10266e55	0.701396	0.350698	+	0.936489i	$0.385944\pi$
$678$	3.30672e54	0.204371
$679$	3.52135e54	0.211470
$680$	1.68578e54	0.0983730
$681$	4.66138e54	0.264330
$682$	−1.75320e55	−0.966130
$683$	−3.73234e54	−0.199883	−0.0999417	−	0.994993i	$-0.531866\pi$
$683$	−3.73234e54	−0.199883	−0.0999417	+	0.994993i	$0.531866\pi$
$684$	−2.99696e54	−0.155987
$685$	−1.72455e55	−0.872390
$686$	−6.15517e54	−0.302635
$687$	−1.88958e55	−0.903042
$688$	3.31218e54	0.153865
$689$	−2.29336e55	−1.03561
$690$	4.29533e54	0.188556
$691$	2.98683e55	1.27464	0.637322	−	0.770598i	$-0.280042\pi$
$691$	2.98683e55	1.27464	0.637322	+	0.770598i	$0.280042\pi$
$692$	−2.61171e55	−1.08357
$693$	3.35539e54	0.135346
$694$	−1.30731e55	−0.512705
$695$	−5.55761e54	−0.211926
$696$	−8.34727e54	−0.309502
$697$	−1.76882e54	−0.0637742
$698$	6.36324e54	0.223099
$699$	7.62011e53	0.0259810
$700$	−5.32012e54	−0.176405
$701$	6.15481e55	1.98478	0.992392	−	0.123116i	$-0.0392886\pi$
$701$	6.15481e55	1.98478	0.992392	+	0.123116i	$0.0392886\pi$
$702$	−2.64778e54	−0.0830441
$703$	−2.95319e55	−0.900870
$704$	−1.45235e54	−0.0430928
$705$	1.40674e55	0.406001
$706$	7.90414e54	0.221903
$707$	−1.59538e55	−0.435698
$708$	−3.26044e53	−0.00866220
$709$	3.95407e55	1.02198	0.510990	−	0.859587i	$-0.329279\pi$
$709$	3.95407e55	1.02198	0.510990	+	0.859587i	$0.329279\pi$
$710$	1.60639e55	0.403937
$711$	1.48865e54	0.0364197
$712$	1.00710e55	0.239725
$713$	9.40656e55	2.17864
$714$	8.16816e53	0.0184081
$715$	−3.02039e55	−0.662362
$716$	4.87862e55	1.04110
$717$	−2.83016e55	−0.587744
$718$	−1.81045e54	−0.0365898
$719$	−5.63244e55	−1.10786	−0.553928	−	0.832564i	$-0.686872\pi$
$719$	−5.63244e55	−1.10786	−0.553928	+	0.832564i	$0.686872\pi$
$720$	4.47708e54	0.0857060
$721$	8.17852e54	0.152383
$722$	1.63557e55	0.296615
$723$	−2.45257e55	−0.432938
$724$	−6.68096e55	−1.14799
$725$	2.46357e55	0.412073
$726$	−5.01108e54	−0.0815957
$727$	−8.02277e55	−1.27175	−0.635877	−	0.771790i	$-0.719361\pi$
$727$	−8.02277e55	−1.27175	−0.635877	+	0.771790i	$0.719361\pi$
$728$	−1.77799e55	−0.274389
$729$	2.46503e54	0.0370370
$730$	2.62937e55	0.384641
$731$	5.06412e54	0.0721299
$732$	−8.16032e53	−0.0113173
$733$	−8.87618e54	−0.119867	−0.0599334	−	0.998202i	$-0.519089\pi$
$733$	−8.87618e54	−0.119867	−0.0599334	+	0.998202i	$0.519089\pi$
$734$	3.42813e55	0.450801
$735$	−2.40599e55	−0.308099
$736$	9.49817e55	1.18447
$737$	−1.35616e56	−1.64700
$738$	4.14389e54	0.0490127
$739$	−9.22862e54	−0.106309	−0.0531545	−	0.998586i	$-0.516928\pi$
$739$	−9.22862e54	−0.106309	−0.0531545	+	0.998586i	$0.516928\pi$
$740$	6.58245e55	0.738531
$741$	2.95604e55	0.323039
$742$	−1.65744e55	−0.176425
$743$	−1.70176e56	−1.76448	−0.882239	−	0.470802i	$-0.843965\pi$
$743$	−1.70176e56	−1.76448	−0.882239	+	0.470802i	$0.843965\pi$
$744$	−8.64884e55	−0.873545
$745$	8.35314e55	0.821869
$746$	1.05164e54	0.0100800
$747$	6.48489e55	0.605551
$748$	1.96965e55	0.179188
$749$	−7.06415e55	−0.626130
$750$	3.02351e55	0.261106
$751$	−6.42817e55	−0.540889	−0.270445	−	0.962736i	$-0.587171\pi$
$751$	−6.42817e55	−0.540889	−0.270445	+	0.962736i	$0.587171\pi$
$752$	5.91806e55	0.485212
$753$	7.60218e55	0.607346
$754$	3.64073e55	0.283431
$755$	−1.34770e55	−0.102242
$756$	7.31958e54	0.0541142
$757$	1.12756e56	0.812398	0.406199	−	0.913785i	$-0.366854\pi$
$757$	1.12756e56	0.812398	0.406199	+	0.913785i	$0.366854\pi$
$758$	−6.22358e55	−0.437009
$759$	1.13493e56	0.776703
$760$	4.40911e55	0.294094
$761$	1.09744e56	0.713480	0.356740	−	0.934204i	$-0.383888\pi$
$761$	1.09744e56	0.713480	0.356740	+	0.934204i	$0.383888\pi$
$762$	−2.42587e55	−0.153725
$763$	1.01573e56	0.627406
$764$	2.68928e55	0.161926
$765$	6.84518e54	0.0401779
$766$	3.80786e55	0.217881
$767$	3.21592e54	0.0179389
$768$	−5.18815e55	−0.282143
$769$	−2.26789e56	−1.20243	−0.601213	−	0.799089i	$-0.705316\pi$
$769$	−2.26789e56	−1.20243	−0.601213	+	0.799089i	$0.705316\pi$
$770$	−2.18287e55	−0.112839
$771$	1.91431e55	0.0964834
$772$	−2.15498e56	−1.05903
$773$	−6.35461e55	−0.304501	−0.152251	−	0.988342i	$-0.548652\pi$
$773$	−6.35461e55	−0.304501	−0.152251	+	0.988342i	$0.548652\pi$
$774$	−1.18639e55	−0.0554344
$775$	2.55257e56	1.16304
$776$	−1.09512e56	−0.486585
$777$	7.21266e55	0.312526
$778$	−1.78748e56	−0.755334
$779$	−4.62632e55	−0.190658
$780$	−6.58880e55	−0.264827
$781$	4.24448e56	1.66391
$782$	2.76281e55	0.105638
$783$	−3.38945e55	−0.126408
$784$	−1.01218e56	−0.368208
$785$	−9.96127e55	−0.353473
$786$	1.04754e56	0.362601
$787$	−5.30511e56	−1.79138	−0.895688	−	0.444683i	$-0.853316\pi$
$787$	−5.30511e56	−1.79138	−0.895688	+	0.444683i	$0.853316\pi$
$788$	4.65989e55	0.153502
$789$	−4.04894e55	−0.130119
$790$	−9.68454e54	−0.0303634
$791$	9.01632e55	0.275796
$792$	−1.04351e56	−0.311426
$793$	8.04887e54	0.0234373
$794$	1.87854e56	0.533730
$795$	−1.38899e56	−0.385069
$796$	−1.18143e56	−0.319598
$797$	−5.56073e56	−1.46789	−0.733947	−	0.679207i	$-0.762324\pi$
$797$	−5.56073e56	−1.46789	−0.733947	+	0.679207i	$0.762324\pi$
$798$	2.13636e55	0.0550324
$799$	9.04834e55	0.227461
$800$	2.57744e56	0.632314
$801$	4.08938e55	0.0979092
$802$	−2.75730e56	−0.644294
$803$	6.94744e56	1.58443
$804$	−2.95837e56	−0.658507
$805$	1.17119e56	0.254454
$806$	3.77226e56	0.799960
$807$	−2.25872e55	−0.0467551
$808$	4.96156e56	1.00253
$809$	5.83597e56	1.15111	0.575555	−	0.817763i	$-0.304786\pi$
$809$	5.83597e56	1.15111	0.575555	+	0.817763i	$0.304786\pi$
$810$	−1.60365e55	−0.0308781
$811$	7.13909e56	1.34195	0.670975	−	0.741480i	$-0.265876\pi$
$811$	7.13909e56	1.34195	0.670975	+	0.741480i	$0.265876\pi$
$812$	−1.00645e56	−0.184693
$813$	−3.99523e56	−0.715775
$814$	−4.54697e56	−0.795327
$815$	1.42979e56	0.244174
$816$	2.87971e55	0.0480165
$817$	1.32451e56	0.215638
$818$	2.97199e55	0.0472452
$819$	−7.21962e55	−0.112067
$820$	1.03117e56	0.156301
$821$	3.39371e56	0.502324	0.251162	−	0.967945i	$-0.419187\pi$
$821$	3.39371e56	0.502324	0.251162	+	0.967945i	$0.419187\pi$
$822$	2.59869e56	0.375625
$823$	−6.34753e56	−0.896000	−0.448000	−	0.894034i	$-0.647863\pi$
$823$	−6.34753e56	−0.896000	−0.448000	+	0.894034i	$0.647863\pi$
$824$	−2.54348e56	−0.350629
$825$	3.07976e56	0.414634
$826$	2.32418e54	0.00305604
$827$	−1.20117e57	−1.54258	−0.771290	−	0.636484i	$-0.780388\pi$
$827$	−1.20117e57	−1.54258	−0.771290	+	0.636484i	$0.780388\pi$
$828$	2.47578e56	0.310543
$829$	−1.44460e57	−1.76984	−0.884922	−	0.465739i	$-0.845788\pi$
$829$	−1.44460e57	−1.76984	−0.884922	+	0.465739i	$0.845788\pi$
$830$	−4.21879e56	−0.504854
$831$	2.04631e56	0.239194
$832$	3.12495e55	0.0356811
$833$	−1.54756e56	−0.172611
$834$	8.37463e55	0.0912489
$835$	1.14287e57	1.21649
$836$	5.15158e56	0.535695
$837$	−3.51190e56	−0.356776
$838$	−7.03318e56	−0.698061
$839$	−1.29612e57	−1.25686	−0.628431	−	0.777865i	$-0.716303\pi$
$839$	−1.29612e57	−1.25686	−0.628431	+	0.777865i	$0.716303\pi$
$840$	−1.07685e56	−0.102026
$841$	−6.14191e56	−0.568567
$842$	−5.08194e56	−0.459667
$843$	7.67123e56	0.677996
$844$	1.69974e57	1.46793
$845$	−7.34715e55	−0.0620031
$846$	−2.11979e56	−0.174812
$847$	−1.36635e56	−0.110113
$848$	−5.84335e56	−0.460196
$849$	−3.54468e56	−0.272820
$850$	7.49718e55	0.0563935
$851$	2.43962e57	1.79348
$852$	9.25908e56	0.665267
$853$	5.58199e56	0.391997	0.195999	−	0.980604i	$-0.437205\pi$
$853$	5.58199e56	0.391997	0.195999	+	0.980604i	$0.437205\pi$
$854$	5.81702e54	0.00399275
$855$	1.79034e56	0.120115
$856$	2.19692e57	1.44071
$857$	−2.91108e57	−1.86607	−0.933035	−	0.359786i	$-0.882850\pi$
$857$	−2.91108e57	−1.86607	−0.933035	+	0.359786i	$0.882850\pi$
$858$	4.55136e56	0.285193
$859$	−1.72483e57	−1.05652	−0.528262	−	0.849082i	$-0.677156\pi$
$859$	−1.72483e57	−1.05652	−0.528262	+	0.849082i	$0.677156\pi$
$860$	−2.95224e56	−0.176780
$861$	1.12990e56	0.0661422
$862$	2.81004e56	0.160813
$863$	1.62824e57	0.910977	0.455488	−	0.890242i	$-0.349465\pi$
$863$	1.62824e57	0.910977	0.455488	+	0.890242i	$0.349465\pi$
$864$	−3.54611e56	−0.193970
$865$	1.56020e57	0.834383
$866$	1.30049e57	0.679998
$867$	−1.08528e57	−0.554841
$868$	−1.04281e57	−0.521280
$869$	−2.55889e56	−0.125074
$870$	2.20503e56	0.105388
$871$	2.91797e57	1.36373
$872$	−3.15886e57	−1.44364
$873$	−4.44680e56	−0.198733
$874$	7.22606e56	0.315812
$875$	8.24409e56	0.352359
$876$	1.51554e57	0.633487
$877$	−4.11574e57	−1.68250	−0.841252	−	0.540642i	$-0.818181\pi$
$877$	−4.11574e57	−1.68250	−0.841252	+	0.540642i	$0.818181\pi$
$878$	−1.92382e56	−0.0769168
$879$	−4.05096e56	−0.158407
$880$	−7.69579e56	−0.294334
$881$	1.71796e57	0.642663	0.321332	−	0.946967i	$-0.395870\pi$
$881$	1.71796e57	0.642663	0.321332	+	0.946967i	$0.395870\pi$
$882$	3.62552e56	0.132658
$883$	−2.54131e56	−0.0909543	−0.0454771	−	0.998965i	$-0.514481\pi$
$883$	−2.54131e56	−0.0909543	−0.0454771	+	0.998965i	$0.514481\pi$
$884$	−4.23799e56	−0.148368
$885$	1.94774e55	0.00667017
$886$	−9.44257e56	−0.316324
$887$	6.92788e56	0.227034	0.113517	−	0.993536i	$-0.463788\pi$
$887$	6.92788e56	0.227034	0.113517	+	0.993536i	$0.463788\pi$
$888$	−2.24310e57	−0.719111
$889$	−6.61453e56	−0.207451
$890$	−2.66038e56	−0.0816278
$891$	−4.23722e56	−0.127194
$892$	−2.43699e57	−0.715713
$893$	2.36657e57	0.680012
$894$	−1.25872e57	−0.353872
$895$	−2.91442e57	−0.801682
$896$	−1.30566e57	−0.351419
$897$	−2.44197e57	−0.643114
$898$	2.74331e57	0.706947
$899$	4.82891e57	1.21768
$900$	6.71831e56	0.165780
$901$	−8.93412e56	−0.215734
$902$	−7.12306e56	−0.168321
$903$	−3.23489e56	−0.0748081
$904$	−2.80403e57	−0.634598
$905$	3.99110e57	0.883986
$906$	2.03082e56	0.0440221
$907$	5.29598e57	1.12358	0.561791	−	0.827279i	$-0.310113\pi$
$907$	5.29598e57	1.12358	0.561791	+	0.827279i	$0.310113\pi$
$908$	−1.74790e57	−0.362946
$909$	2.01467e57	0.409456
$910$	4.69677e56	0.0934313
$911$	8.97639e57	1.74781	0.873903	−	0.486099i	$-0.161581\pi$
$911$	8.97639e57	1.74781	0.873903	+	0.486099i	$0.161581\pi$
$912$	7.53182e56	0.143549
$913$	−1.11471e58	−2.07961
$914$	−5.86109e56	−0.107035
$915$	4.87485e55	0.00871465
$916$	7.08543e57	1.23995
$917$	2.85628e57	0.489326
$918$	−1.03148e56	−0.0172994
$919$	8.31649e57	1.36549	0.682743	−	0.730658i	$-0.260787\pi$
$919$	8.31649e57	1.36549	0.682743	+	0.730658i	$0.260787\pi$
$920$	−3.64235e57	−0.585490
$921$	3.01535e57	0.474543
$922$	−3.87434e57	−0.596960
$923$	−9.13263e57	−1.37773
$924$	−1.25819e57	−0.185841
$925$	6.62018e57	0.957427
$926$	1.16119e57	0.164434
$927$	−1.03279e57	−0.143205
$928$	4.87594e57	0.662022
$929$	−1.24197e58	−1.65121	−0.825607	−	0.564246i	$-0.809167\pi$
$929$	−1.24197e58	−1.65121	−0.825607	+	0.564246i	$0.809167\pi$
$930$	2.28469e57	0.297448
$931$	−4.04760e57	−0.516035
$932$	−2.85735e56	−0.0356741
$933$	−3.95446e57	−0.483499
$934$	−1.25043e57	−0.149725
$935$	−1.17664e57	−0.137980
$936$	2.24527e57	0.257863
$937$	2.05999e57	0.231709	0.115854	−	0.993266i	$-0.463039\pi$
$937$	2.05999e57	0.231709	0.115854	+	0.993266i	$0.463039\pi$
$938$	2.10885e57	0.232322
$939$	−1.71807e57	−0.185379
$940$	−5.27493e57	−0.557473
$941$	−3.80737e57	−0.394119	−0.197060	−	0.980391i	$-0.563139\pi$
$941$	−3.80737e57	−0.394119	−0.197060	+	0.980391i	$0.563139\pi$
$942$	1.50104e57	0.152195
$943$	3.82179e57	0.379567
$944$	8.19398e55	0.00797152
$945$	−4.37261e56	−0.0416697
$946$	2.03932e57	0.190375
$947$	−1.53584e58	−1.40450	−0.702251	−	0.711929i	$-0.747822\pi$
$947$	−1.53584e58	−1.40450	−0.702251	+	0.711929i	$0.747822\pi$
$948$	−5.58207e56	−0.0500072
$949$	−1.49484e58	−1.31191
$950$	1.96087e57	0.168593
$951$	4.96195e57	0.417958
$952$	−6.92643e56	−0.0571596
$953$	−1.33994e58	−1.08337	−0.541683	−	0.840583i	$-0.682213\pi$
$953$	−1.33994e58	−1.08337	−0.541683	+	0.840583i	$0.682213\pi$
$954$	2.09303e57	0.165799
$955$	−1.60654e57	−0.124688
$956$	1.06124e58	0.807020
$957$	5.82623e57	0.434115
$958$	−3.30399e57	−0.241219
$959$	7.08576e57	0.506901
$960$	1.89264e56	0.0132672
$961$	3.54755e58	2.43681
$962$	9.78347e57	0.658535
$963$	8.92070e57	0.588418
$964$	9.19653e57	0.594459
$965$	1.28735e58	0.815484
$966$	−1.76484e57	−0.109560
$967$	−1.56161e58	−0.950069	−0.475035	−	0.879967i	$-0.657564\pi$
$967$	−1.56161e58	−0.950069	−0.475035	+	0.879967i	$0.657564\pi$
$968$	4.24929e57	0.253365
$969$	1.15157e57	0.0672940
$970$	2.89290e57	0.165685
$971$	−1.63785e58	−0.919390	−0.459695	−	0.888077i	$-0.652041\pi$
$971$	−1.63785e58	−0.919390	−0.459695	+	0.888077i	$0.652041\pi$
$972$	−9.24325e56	−0.0508549
$973$	2.28348e57	0.123139
$974$	−7.03756e57	−0.371983
$975$	−6.62656e57	−0.343319
$976$	2.05081e56	0.0104149
$977$	1.41094e57	0.0702369	0.0351185	−	0.999383i	$-0.488819\pi$
$977$	1.41094e57	0.0702369	0.0351185	+	0.999383i	$0.488819\pi$
$978$	−2.15452e57	−0.105134
$979$	−7.02937e57	−0.336243
$980$	9.02183e57	0.423044
$981$	−1.28267e58	−0.589617
$982$	−1.54660e58	−0.696953
$983$	1.33223e58	0.588551	0.294276	−	0.955721i	$-0.404922\pi$
$983$	1.33223e58	0.588551	0.294276	+	0.955721i	$0.404922\pi$
$984$	−3.51393e57	−0.152191
$985$	−2.78375e57	−0.118202
$986$	1.41830e57	0.0590431
$987$	−5.77996e57	−0.235907
$988$	−1.10844e58	−0.443558
$989$	−1.09417e58	−0.429298
$990$	2.75656e57	0.106043
$991$	−2.84242e58	−1.07214	−0.536071	−	0.844173i	$-0.680092\pi$
$991$	−2.84242e58	−1.07214	−0.536071	+	0.844173i	$0.680092\pi$
$992$	5.05210e58	1.86850
$993$	6.90653e57	0.250466
$994$	−6.60026e57	−0.234707
$995$	7.05769e57	0.246101
$996$	−2.43167e58	−0.831471
$997$	3.57370e58	1.19829	0.599146	−	0.800640i	$-0.295507\pi$
$997$	3.57370e58	1.19829	0.599146	+	0.800640i	$0.295507\pi$
$998$	−1.67509e58	−0.550798
$999$	−9.10823e57	−0.293702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.40.a.a.1.2	✓	3
3.2	odd	2		9.40.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.40.a.a.1.2	✓	3	1.1	even	1	trivial
9.40.a.d.1.2		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-337546. q^{2} +1.16226e9 q^{3} -4.35818e11 q^{4} +2.60351e13 q^{5} -3.92317e14 q^{6} -1.06972e16 q^{7} +3.32677e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\)	\(q-337546. q^{2} +1.16226e9 q^{3} -4.35818e11 q^{4} +2.60351e13 q^{5} -3.92317e14 q^{6} -1.06972e16 q^{7} +3.32677e17 q^{8} +1.35085e18 q^{9} -8.78806e18 q^{10} -2.32202e20 q^{11} -5.06535e20 q^{12} +4.99617e21 q^{13} +3.61079e21 q^{14} +3.02596e22 q^{15} +1.27300e23 q^{16} +1.94633e23 q^{17} -4.55975e23 q^{18} +5.09059e24 q^{19} -1.13466e25 q^{20} -1.24329e25 q^{21} +7.83790e25 q^{22} -4.20533e26 q^{23} +3.86658e26 q^{24} -1.14116e27 q^{25} -1.68644e27 q^{26} +1.57004e27 q^{27} +4.66202e27 q^{28} -2.15883e28 q^{29} -1.02140e28 q^{30} -2.23682e29 q^{31} -2.25861e29 q^{32} -2.69880e29 q^{33} -6.56978e28 q^{34} -2.78502e29 q^{35} -5.88726e29 q^{36} -5.80126e30 q^{37} -1.71831e30 q^{38} +5.80686e30 q^{39} +8.66129e30 q^{40} -9.08797e30 q^{41} +4.19669e30 q^{42} +2.60188e31 q^{43} +1.01198e32 q^{44} +3.51696e31 q^{45} +1.41949e32 q^{46} +4.64891e32 q^{47} +1.47956e32 q^{48} -7.95114e32 q^{49} +3.85195e32 q^{50} +2.26215e32 q^{51} -2.17742e33 q^{52} -4.59023e33 q^{53} -5.29962e32 q^{54} -6.04541e33 q^{55} -3.55870e33 q^{56} +5.91660e33 q^{57} +7.28704e33 q^{58} +6.43676e32 q^{59} -1.31877e34 q^{60} +1.61101e33 q^{61} +7.55031e34 q^{62} -1.44503e34 q^{63} +6.25468e33 q^{64} +1.30076e35 q^{65} +9.10969e34 q^{66} +5.84042e35 q^{67} -8.48248e34 q^{68} -4.88769e35 q^{69} +9.40074e34 q^{70} -1.82793e36 q^{71} +4.49397e35 q^{72} -2.99198e36 q^{73} +1.95819e36 q^{74} -1.32633e36 q^{75} -2.21857e36 q^{76} +2.48391e36 q^{77} -1.96008e36 q^{78} +1.10201e36 q^{79} +3.31426e36 q^{80} +1.82480e36 q^{81} +3.06761e36 q^{82} +4.80060e37 q^{83} +5.41849e36 q^{84} +5.06731e36 q^{85} -8.78254e36 q^{86} -2.50912e37 q^{87} -7.72483e37 q^{88} +3.02726e37 q^{89} -1.18714e37 q^{90} -5.34449e37 q^{91} +1.83276e38 q^{92} -2.59977e38 q^{93} -1.56922e38 q^{94} +1.32534e38 q^{95} -2.62509e38 q^{96} -3.29185e38 q^{97} +2.68388e38 q^{98} -3.13671e38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots + 40\!\cdots\!67 q^{9}+O(q^{10}) \) 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9	\( 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots - 54\!\cdots\!44 q^{99}+O(q^{100}) \) 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9 - 76029599179042436880 * q^10 - 40050327611147243796 * q^11 + 1169119071861486955200 * q^12 - 13932702500978393486094 * q^13 + 64143032386415214972096 * q^14 + 10875337996478108168430 * q^15 + 1098810764821648805597184 * q^16 - 169700805136994180103018 * q^17 - 1495392851464002242523000 * q^18 - 6957470542505489016962988 * q^19 + 33307320359730090833619840 * q^20 + 16087888842591162209012568 * q^21 - 182808419494676144863843296 * q^22 - 257172639984224911978099272 * q^23 - 1774258355442000609859705344 * q^24 - 2223570708999165320980345275 * q^25 + 6420909995769964414290523056 * q^26 + 4710128697246244834921603689 * q^27 - 31489800993928145336514267648 * q^28 - 46272789498091624686435987486 * q^29 - 88366273477255858343403702960 * q^30 - 282753969983174411853352917888 * q^31 - 1118437222052144608340712062976 * q^32 - 46548952523162601127345608732 * q^33 - 2020045599738440464009480297200 * q^34 - 2778733015107044038012367571600 * q^35 + 1358822047559410249352115278400 * q^36 - 5239395449699583862273344438486 * q^37 - 4077508380452877314541820882464 * q^38 - 16193443248061716548450856539898 * q^39 - 10242585699763810314758557271040 * q^40 + 47673397400045140822464268984782 * q^41 + 74550974919263458624588661024832 * q^42 - 14936449213367655469478076825588 * q^43 + 383801287439893621552232462293248 * q^44 + 12639986293907486833224134886810 * q^45 + 646689351161727342528587792407872 * q^46 - 13040685113470292045769719198544 * q^47 + 1277105411477001534152180886908928 * q^48 - 132364363537073708245470314514213 * q^49 + 2030100946651365938753014066519800 * q^50 - 197236706729603991736995911807406 * q^51 - 16457201727541975997405015057804928 * q^52 - 11047064078175508118010662971794342 * q^53 - 1738037489283864344086071761241000 * q^54 - 1504305246366733376700435214523160 * q^55 + 6316090378583898308960601541324800 * q^56 - 8086399919341715520407790317583396 * q^57 - 23720839646010288107197368475070928 * q^58 + 35633406741119515209244171316491548 * q^59 + 38711815023138863096326248158705280 * q^60 - 26245828903346977727221409425735902 * q^61 - 98335445202496226432366585960435712 * q^62 + 18698333287122936270281907905117256 * q^63 + 922428812776307390107790824712699904 * q^64 + 260861961831082759405211612047737660 * q^65 - 212471181821833694819355024467075232 * q^66 - 200741546976450474071235708204779388 * q^67 + 1264175105126717513162323757007619200 * q^68 - 298901849820328103053611531746352024 * q^69 - 431344371239166538676321844662332800 * q^70 - 3140665348656484831244609799236867544 * q^71 - 2062152119033027062230435797305179648 * q^72 - 3825610182002392515733100347600509522 * q^73 - 2544605510256173934291855124681995024 * q^74 - 2584370554219599987738141977488018425 * q^75 - 5521658898639443517674491687212787968 * q^76 - 994601047124972255067887751426792672 * q^77 + 7462776271158562634691099091263883152 * q^78 - 1038716953120555158347640895730970000 * q^79 + 45766070974584297712698519042271272960 * q^80 + 5474401089420219382077155933569751763 * q^81 - 16726391180845396277548112611717202352 * q^82 + 69227326737654458476356626745129089940 * q^83 - 36599382298740984291406281382995119616 * q^84 + 76820078772499304751574061990694660660 * q^85 + 159762376422294357818512142478616905504 * q^86 - 53781080204234165408470505817072001962 * q^87 - 343351801449478884201073068755288881152 * q^88 + 136597710245735759116899165769855535742 * q^89 - 102704714644998585052548577575521842320 * q^90 - 259984668223904357182500109993449632208 * q^91 - 135698237299460735254844067932094260736 * q^92 - 328634043952718257237540151213237421696 * q^93 + 457887889864219720177610385758047412352 * q^94 + 462468326274179393065716948072305471640 * q^95 - 1299916486449730342986216438139082145792 * q^96 - 1338928527743499267936157260425715870618 * q^97 + 1730483839907526080834886072855293848584 * q^98 - 54102053846884316265804561020862329844 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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