LMFDB - Embedded newform 3.36.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,36,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, 36, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 36 $
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:	$23.2785391901$
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} - x^{2} - 1847580440x + 20051963761200 $ x^3 - x^2 - 1847580440*x + 20051963761200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{5}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-47629.1$ 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)

$f(q)$	$=$	$q-314887. q^{2} -1.29140e8 q^{3} +6.47940e10 q^{4} +2.58564e12 q^{5} +4.06645e13 q^{6} +8.89060e14 q^{7} -9.58334e15 q^{8} +1.66772e16 q^{9} +O(q^{10})$	\(q-314887. q^{2} -1.29140e8 q^{3} +6.47940e10 q^{4} +2.58564e12 q^{5} +4.06645e13 q^{6} +8.89060e14 q^{7} -9.58334e15 q^{8} +1.66772e16 q^{9} -8.14184e17 q^{10} +2.05240e18 q^{11} -8.36750e18 q^{12} -1.82090e19 q^{13} -2.79953e20 q^{14} -3.33910e20 q^{15} +7.91364e20 q^{16} +3.53481e21 q^{17} -5.25142e21 q^{18} +2.01653e22 q^{19} +1.67534e23 q^{20} -1.14813e23 q^{21} -6.46272e23 q^{22} +2.51478e23 q^{23} +1.23759e24 q^{24} +3.77515e24 q^{25} +5.73379e24 q^{26} -2.15369e24 q^{27} +5.76057e25 q^{28} -8.93017e24 q^{29} +1.05144e26 q^{30} -1.94629e26 q^{31} +8.00910e25 q^{32} -2.65047e26 q^{33} -1.11307e27 q^{34} +2.29879e27 q^{35} +1.08058e27 q^{36} -2.17467e27 q^{37} -6.34979e27 q^{38} +2.35152e27 q^{39} -2.47791e28 q^{40} -7.70191e27 q^{41} +3.61532e28 q^{42} -2.60169e28 q^{43} +1.32983e29 q^{44} +4.31212e28 q^{45} -7.91871e28 q^{46} +3.33024e29 q^{47} -1.02197e29 q^{48} +4.11609e29 q^{49} -1.18875e30 q^{50} -4.56486e29 q^{51} -1.17984e30 q^{52} +1.01164e30 q^{53} +6.78170e29 q^{54} +5.30676e30 q^{55} -8.52016e30 q^{56} -2.60415e30 q^{57} +2.81199e30 q^{58} +1.91584e30 q^{59} -2.16354e31 q^{60} +7.04823e30 q^{61} +6.12862e31 q^{62} +1.48270e31 q^{63} -5.24107e31 q^{64} -4.70820e31 q^{65} +8.34597e31 q^{66} +1.18905e32 q^{67} +2.29034e32 q^{68} -3.24759e31 q^{69} -7.23859e32 q^{70} -2.78716e32 q^{71} -1.59823e32 q^{72} -3.82719e32 q^{73} +6.84776e32 q^{74} -4.87524e32 q^{75} +1.30659e33 q^{76} +1.82470e33 q^{77} -7.40462e32 q^{78} -1.32234e33 q^{79} +2.04618e33 q^{80} +2.78128e32 q^{81} +2.42523e33 q^{82} -5.69848e33 q^{83} -7.43921e33 q^{84} +9.13975e33 q^{85} +8.19238e33 q^{86} +1.15324e33 q^{87} -1.96688e34 q^{88} +1.72108e34 q^{89} -1.35783e34 q^{90} -1.61889e34 q^{91} +1.62943e34 q^{92} +2.51344e34 q^{93} -1.04865e35 q^{94} +5.21402e34 q^{95} -1.03430e34 q^{96} +4.83801e34 q^{97} -1.29610e35 q^{98} +3.42282e34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 50\!\cdots\!07 q^{9}+O(q^{10}) $ 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9	$ 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 57\!\cdots\!76 q^{99}+O(q^{100}) $ 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9 - 1127779626928867020 * q^10 + 3426356175124224804 * q^11 - 4195602845172722700 * q^12 + 50087718431258539506 * q^13 - 217880362960444050144 * q^14 - 357547300335073771830 * q^15 + 606906765664363747344 * q^16 + 2730709287864549111942 * q^17 - 1456418277831881470770 * q^18 + 28794251065778257727292 * q^19 + 88477655809138293889560 * q^20 - 63051115342974896664432 * q^21 - 122741766765729403865496 * q^22 + 1806983834691084779311608 * q^23 + 2412744607366739676625176 * q^24 + 8598840806404444672708725 * q^25 + 12462234191474761114326516 * q^26 - 6461081889226673298932241 * q^27 + 88582873604432535904569792 * q^28 + 78927943791269118086922714 * q^29 + 145641644849673076368124260 * q^30 - 1597007179004406242679048 * q^31 + 212133152341134442715841504 * q^32 - 442480194951598936437203052 * q^33 - 1031323232079473133177847620 * q^34 - 1159830211565676145196532000 * q^35 + 541820835308869172631800100 * q^36 - 5102549932092597658956094086 * q^37 - 8724219045726720381610922664 * q^38 - 6468336122510832086946779478 * q^39 - 17377992868876213570860774960 * q^40 - 20208748955896036456754429058 * q^41 + 28137105587210907187976333472 * q^42 + 46721962642013867129638134372 * q^43 + 194349428414233101115805936688 * q^44 + 46173716645481381511151008290 * q^45 + 52087178478532028950981302192 * q^46 + 293197746513164578153478190816 * q^47 - 78376038643698737623294977072 * q^48 + 836105627836985614440420595707 * q^49 - 701125828082122697797800571950 * q^50 - 352644242540441794237695126546 * q^51 - 2520178249741268871517789030248 * q^52 - 108875909240521237104294715182 * q^53 + 188082093795388459731917535510 * q^54 - 6237008697722857733231584966440 * q^55 - 9347630291312236144016149603200 * q^56 - 3718494276097527924758498428596 * q^57 + 11382186268398399744329433517572 * q^58 + 11320340569522247618095325505348 * q^59 - 11426018893050016162439682398280 * q^60 + 12771547929195071355310409383218 * q^61 + 101447293741849863418951127675568 * q^62 + 8142431312723579060152904782416 * q^63 - 41280658033851993168324127190976 * q^64 - 7709579158673152743776325663060 * q^65 + 15850891767034278029082983515848 * q^66 + 175757710780078940305499908875612 * q^67 + 281442880096236379198382763169800 * q^68 - 233354186950371743047120084912104 * q^69 - 1040498682940112273466514884936000 * q^70 - 27474747461715252213775775690424 * q^71 - 311582231872711762617942518543688 * q^72 - 585184619829428568163757555870322 * q^73 + 134392541523566959843290841608516 * q^74 - 1110455703350121428958086398022175 * q^75 + 403477747366730076622590548780112 * q^76 + 5306726056931811905707525354511808 * q^77 - 1609374954831223860690187911462108 * q^78 - 2667396066634861458375845391576600 * q^79 + 7102490190805235743681469824979040 * q^80 + 834385168331080533771857328695283 * q^81 + 917242845604400818117266629806188 * q^82 + 6578360642441675208543593208203580 * q^83 - 11439606736284815209219495383756096 * q^84 + 3560960065600250795485268792239140 * q^85 + 18773659018851120901851911340565224 * q^86 - 10192767526459331886611447454362382 * q^87 - 34961215155916125706150543997131872 * q^88 + 11419551912179244059325275346141822 * q^89 - 18808185755474891578891014940654380 * q^90 - 40541093249602611010364470781007648 * q^91 - 19232540048657476273178638696239456 * q^92 + 206237767408799199897789815404824 * q^93 - 101336598951909608865466201817694528 * q^94 + 159588702835640097495158571410457960 * q^95 - 27394909871037933537237934508725152 * q^96 + 211792260572805448951439211684683142 * q^97 - 124471288129025507609829835395708786 * q^98 + 57141964500321263762127041399377476 * 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 $

$2$	−314887.	−1.69875	−0.849375	−	0.527790i	$-0.823021\pi$
$2$	−314887.	−1.69875	−0.849375	+	0.527790i	$0.823021\pi$
$3$	−1.29140e8	−0.577350
$3$	−1.29140e8	−0.577350
$4$	6.47940e10	1.88575
$5$	2.58564e12	1.51563	0.757815	−	0.652470i	$-0.226267\pi$
$5$	2.58564e12	1.51563	0.757815	+	0.652470i	$0.226267\pi$
$6$	4.06645e13	0.980774
$7$	8.89060e14	1.44449	0.722246	−	0.691636i	$-0.243110\pi$
$7$	8.89060e14	1.44449	0.722246	+	0.691636i	$0.243110\pi$
$8$	−9.58334e15	−1.50467
$9$	1.66772e16	0.333333
$10$	−8.14184e17	−2.57468
$11$	2.05240e18	1.22430	0.612152	−	0.790740i	$-0.290304\pi$
$11$	2.05240e18	1.22430	0.612152	+	0.790740i	$0.290304\pi$
$12$	−8.36750e18	−1.08874
$13$	−1.82090e19	−0.583819	−0.291910	−	0.956446i	$-0.594291\pi$
$13$	−1.82090e19	−0.583819	−0.291910	+	0.956446i	$0.594291\pi$
$14$	−2.79953e20	−2.45383
$15$	−3.33910e20	−0.875049
$16$	7.91364e20	0.670311
$17$	3.53481e21	1.03636	0.518179	−	0.855272i	$-0.326610\pi$
$17$	3.53481e21	1.03636	0.518179	+	0.855272i	$0.326610\pi$
$18$	−5.25142e21	−0.566250
$19$	2.01653e22	0.844144	0.422072	−	0.906562i	$-0.361303\pi$
$19$	2.01653e22	0.844144	0.422072	+	0.906562i	$0.361303\pi$
$20$	1.67534e23	2.85810
$21$	−1.14813e23	−0.833978
$22$	−6.46272e23	−2.07979
$23$	2.51478e23	0.371760	0.185880	−	0.982572i	$-0.440486\pi$
$23$	2.51478e23	0.371760	0.185880	+	0.982572i	$0.440486\pi$
$24$	1.23759e24	0.868723
$25$	3.77515e24	1.29713
$26$	5.73379e24	0.991763
$27$	−2.15369e24	−0.192450
$28$	5.76057e25	2.72396
$29$	−8.93017e24	−0.228505	−0.114252	−	0.993452i	$-0.536447\pi$
$29$	−8.93017e24	−0.228505	−0.114252	+	0.993452i	$0.536447\pi$
$30$	1.05144e26	1.48649
$31$	−1.94629e26	−1.55017	−0.775083	−	0.631859i	$-0.782292\pi$
$31$	−1.94629e26	−1.55017	−0.775083	+	0.631859i	$0.782292\pi$
$32$	8.00910e25	0.365982
$33$	−2.65047e26	−0.706852
$34$	−1.11307e27	−1.76051
$35$	2.29879e27	2.18932
$36$	1.08058e27	0.628584
$37$	−2.17467e27	−0.783184	−0.391592	−	0.920139i	$-0.628076\pi$
$37$	−2.17467e27	−0.783184	−0.391592	+	0.920139i	$0.628076\pi$
$38$	−6.34979e27	−1.43399
$39$	2.35152e27	0.337068
$40$	−2.47791e28	−2.28053
$41$	−7.70191e27	−0.460130	−0.230065	−	0.973175i	$-0.573894\pi$
$41$	−7.70191e27	−0.460130	−0.230065	+	0.973175i	$0.573894\pi$
$42$	3.61532e28	1.41672
$43$	−2.60169e28	−0.675394	−0.337697	−	0.941255i	$-0.609648\pi$
$43$	−2.60169e28	−0.675394	−0.337697	+	0.941255i	$0.609648\pi$
$44$	1.32983e29	2.30873
$45$	4.31212e28	0.505210
$46$	−7.91871e28	−0.631528
$47$	3.33024e29	1.82290	0.911449	−	0.411412i	$-0.134964\pi$
$47$	3.33024e29	1.82290	0.911449	+	0.411412i	$0.134964\pi$
$48$	−1.02197e29	−0.387004
$49$	4.11609e29	1.08656
$50$	−1.18875e30	−2.20351
$51$	−4.56486e29	−0.598342
$52$	−1.17984e30	−1.10094
$53$	1.01164e30	0.676390	0.338195	−	0.941076i	$-0.390184\pi$
$53$	1.01164e30	0.676390	0.338195	+	0.941076i	$0.390184\pi$
$54$	6.78170e29	0.326925
$55$	5.30676e30	1.85559
$56$	−8.52016e30	−2.17349
$57$	−2.60415e30	−0.487367
$58$	2.81199e30	0.388172
$59$	1.91584e30	0.196087	0.0980435	−	0.995182i	$-0.468742\pi$
$59$	1.91584e30	0.196087	0.0980435	+	0.995182i	$0.468742\pi$
$60$	−2.16354e31	−1.65013
$61$	7.04823e30	0.402539	0.201270	−	0.979536i	$-0.435493\pi$
$61$	7.04823e30	0.402539	0.201270	+	0.979536i	$0.435493\pi$
$62$	6.12862e31	2.63335
$63$	1.48270e31	0.481498
$64$	−5.24107e31	−1.29202
$65$	−4.70820e31	−0.884854
$66$	8.34597e31	1.20076
$67$	1.18905e32	1.31489	0.657445	−	0.753503i	$-0.271637\pi$
$67$	1.18905e32	1.31489	0.657445	+	0.753503i	$0.271637\pi$
$68$	2.29034e32	1.95432
$69$	−3.24759e31	−0.214636
$70$	−7.23859e32	−3.71910
$71$	−2.78716e32	−1.11723	−0.558613	−	0.829428i	$-0.688666\pi$
$71$	−2.78716e32	−1.11723	−0.558613	+	0.829428i	$0.688666\pi$
$72$	−1.59823e32	−0.501558
$73$	−3.82719e32	−0.943474	−0.471737	−	0.881739i	$-0.656373\pi$
$73$	−3.82719e32	−0.943474	−0.471737	+	0.881739i	$0.656373\pi$
$74$	6.84776e32	1.33043
$75$	−4.87524e32	−0.748900
$76$	1.30659e33	1.59185
$77$	1.82470e33	1.76850
$78$	−7.40462e32	−0.572595
$79$	−1.32234e33	−0.818218	−0.409109	−	0.912486i	$-0.634160\pi$
$79$	−1.32234e33	−0.818218	−0.409109	+	0.912486i	$0.634160\pi$
$80$	2.04618e33	1.01594
$81$	2.78128e32	0.111111
$82$	2.42523e33	0.781646
$83$	−5.69848e33	−1.48557	−0.742783	−	0.669532i	$-0.766495\pi$
$83$	−5.69848e33	−1.48557	−0.742783	+	0.669532i	$0.766495\pi$
$84$	−7.43921e33	−1.57268
$85$	9.13975e33	1.57074
$86$	8.19238e33	1.14733
$87$	1.15324e33	0.131927
$88$	−1.96688e34	−1.84218
$89$	1.72108e34	1.32274	0.661371	−	0.750059i	$-0.269975\pi$
$89$	1.72108e34	1.32274	0.661371	+	0.750059i	$0.269975\pi$
$90$	−1.35783e34	−0.858225
$91$	−1.61889e34	−0.843323
$92$	1.62943e34	0.701048
$93$	2.51344e34	0.894989
$94$	−1.04865e35	−3.09665
$95$	5.21402e34	1.27941
$96$	−1.03430e34	−0.211300
$97$	4.83801e34	0.824444	0.412222	−	0.911083i	$-0.364753\pi$
$97$	4.83801e34	0.824444	0.412222	+	0.911083i	$0.364753\pi$
$98$	−1.29610e35	−1.84579
$99$	3.42282e34	0.408101
$100$	2.44607e35	2.44607
$101$	3.38688e34	0.284561	0.142281	−	0.989826i	$-0.454556\pi$
$101$	3.38688e34	0.284561	0.142281	+	0.989826i	$0.454556\pi$
$102$	1.43741e35	1.01643
$103$	5.14533e34	0.306734	0.153367	−	0.988169i	$-0.450988\pi$
$103$	5.14533e34	0.306734	0.153367	+	0.988169i	$0.450988\pi$
$104$	1.74503e35	0.878457
$105$	−2.96866e35	−1.26400
$106$	−3.18551e35	−1.14902
$107$	−2.18093e35	−0.667461	−0.333731	−	0.942668i	$-0.608308\pi$
$107$	−2.18093e35	−0.667461	−0.333731	+	0.942668i	$0.608308\pi$
$108$	−1.39546e35	−0.362913
$109$	4.44389e35	0.983557	0.491778	−	0.870720i	$-0.336347\pi$
$109$	4.44389e35	0.983557	0.491778	+	0.870720i	$0.336347\pi$
$110$	−1.67103e36	−3.15218
$111$	2.80838e35	0.452172
$112$	7.03570e35	0.968260
$113$	−3.31993e35	−0.391071	−0.195536	−	0.980697i	$-0.562645\pi$
$113$	−3.31993e35	−0.391071	−0.195536	+	0.980697i	$0.562645\pi$
$114$	8.20012e35	0.827914
$115$	6.50232e35	0.563451
$116$	−5.78621e35	−0.430903
$117$	−3.03675e35	−0.194606
$118$	−6.03272e35	−0.333103
$119$	3.14266e36	1.49701
$120$	3.19997e36	1.31666
$121$	1.40208e36	0.498918
$122$	−2.21940e36	−0.683814
$123$	9.94625e35	0.265656
$124$	−1.26108e37	−2.92323
$125$	2.23599e36	0.450344
$126$	−4.66883e36	−0.817944
$127$	3.99299e35	0.0609162	0.0304581	−	0.999536i	$-0.490303\pi$
$127$	3.99299e35	0.0609162	0.0304581	+	0.999536i	$0.490303\pi$
$128$	1.37515e37	1.82884
$129$	3.35983e36	0.389939
$130$	1.48255e37	1.50315
$131$	−8.23775e36	−0.730400	−0.365200	−	0.930929i	$-0.618999\pi$
$131$	−8.23775e36	−0.730400	−0.365200	+	0.930929i	$0.618999\pi$
$132$	−1.71734e37	−1.33295
$133$	1.79282e37	1.21936
$134$	−3.74415e37	−2.23367
$135$	−5.56868e36	−0.291683
$136$	−3.38753e37	−1.55938
$137$	−5.87550e36	−0.237922	−0.118961	−	0.992899i	$-0.537956\pi$
$137$	−5.87550e36	−0.237922	−0.118961	+	0.992899i	$0.537956\pi$
$138$	1.02262e37	0.364613
$139$	−2.62173e37	−0.823813	−0.411907	−	0.911226i	$-0.635137\pi$
$139$	−2.62173e37	−0.823813	−0.411907	+	0.911226i	$0.635137\pi$
$140$	1.48948e38	4.12851
$141$	−4.30067e37	−1.05245
$142$	8.77641e37	1.89789
$143$	−3.73721e37	−0.714772
$144$	1.31977e37	0.223437
$145$	−2.30902e37	−0.346328
$146$	1.20513e38	1.60273
$147$	−5.31552e37	−0.627325
$148$	−1.40906e38	−1.47689
$149$	−1.56999e37	−0.146264	−0.0731320	−	0.997322i	$-0.523299\pi$
$149$	−1.56999e37	−0.146264	−0.0731320	+	0.997322i	$0.523299\pi$
$150$	1.53515e38	1.27219
$151$	8.16299e37	0.602217	0.301108	−	0.953590i	$-0.402643\pi$
$151$	8.16299e37	0.602217	0.301108	+	0.953590i	$0.402643\pi$
$152$	−1.93251e38	−1.27016
$153$	5.89507e37	0.345453
$154$	−5.74575e38	−3.00424
$155$	−5.03241e38	−2.34948
$156$	1.52364e38	0.635627
$157$	4.68779e38	1.74874	0.874369	−	0.485262i	$-0.161276\pi$
$157$	4.68779e38	1.74874	0.874369	+	0.485262i	$0.161276\pi$
$158$	4.16387e38	1.38995
$159$	−1.30643e38	−0.390514
$160$	2.07087e38	0.554693
$161$	2.23579e38	0.537005
$162$	−8.75790e37	−0.188750
$163$	5.22512e38	1.01114	0.505572	−	0.862784i	$-0.331281\pi$
$163$	5.22512e38	1.01114	0.505572	+	0.862784i	$0.331281\pi$
$164$	−4.99037e38	−0.867692
$165$	−6.85315e38	−1.07133
$166$	1.79437e39	2.52361
$167$	−3.40776e38	−0.431450	−0.215725	−	0.976454i	$-0.569212\pi$
$167$	−3.40776e38	−0.431450	−0.215725	+	0.976454i	$0.569212\pi$
$168$	1.10030e39	1.25486
$169$	−6.41217e38	−0.659155
$170$	−2.87799e39	−2.66829
$171$	3.36300e38	0.281381
$172$	−1.68574e39	−1.27363
$173$	2.05298e39	1.40145	0.700725	−	0.713432i	$-0.252860\pi$
$173$	2.05298e39	1.40145	0.700725	+	0.713432i	$0.252860\pi$
$174$	−3.63141e38	−0.224111
$175$	3.35634e39	1.87370
$176$	1.62419e39	0.820664
$177$	−2.47412e38	−0.113211
$178$	−5.41944e39	−2.24701
$179$	−1.59660e39	−0.600161	−0.300081	−	0.953914i	$-0.597014\pi$
$179$	−1.59660e39	−0.600161	−0.300081	+	0.953914i	$0.597014\pi$
$180$	2.79399e39	0.952701
$181$	−4.40686e39	−1.36381	−0.681906	−	0.731440i	$-0.738849\pi$
$181$	−4.40686e39	−1.36381	−0.681906	+	0.731440i	$0.738849\pi$
$182$	5.09768e39	1.43259
$183$	−9.10210e38	−0.232406
$184$	−2.41000e39	−0.559378
$185$	−5.62293e39	−1.18702
$186$	−7.91451e39	−1.52036
$187$	7.25483e39	1.26882
$188$	2.15779e40	3.43754
$189$	−1.91476e39	−0.277993
$190$	−1.64183e40	−2.17340
$191$	−2.10798e38	−0.0254555	−0.0127278	−	0.999919i	$-0.504051\pi$
$191$	−2.10798e38	−0.0254555	−0.0127278	+	0.999919i	$0.504051\pi$
$192$	6.76832e39	0.745950
$193$	1.90663e40	1.91873	0.959364	−	0.282170i	$-0.0910544\pi$
$193$	1.90663e40	1.91873	0.959364	+	0.282170i	$0.0910544\pi$
$194$	−1.52342e40	−1.40052
$195$	6.08018e39	0.510871
$196$	2.66698e40	2.04898
$197$	1.95633e40	1.37494	0.687471	−	0.726212i	$-0.258721\pi$
$197$	1.95633e40	1.37494	0.687471	+	0.726212i	$0.258721\pi$
$198$	−1.07780e40	−0.693262
$199$	−9.66419e39	−0.569163	−0.284582	−	0.958652i	$-0.591855\pi$
$199$	−9.66419e39	−0.569163	−0.284582	+	0.958652i	$0.591855\pi$
$200$	−3.61786e40	−1.95176
$201$	−1.53553e40	−0.759152
$202$	−1.06648e40	−0.483398
$203$	−7.93946e39	−0.330073
$204$	−2.95775e40	−1.12833
$205$	−1.99144e40	−0.697387
$206$	−1.62020e40	−0.521064
$207$	4.19395e39	0.123920
$208$	−1.44100e40	−0.391341
$209$	4.13872e40	1.03349
$210$	9.34792e40	2.14722
$211$	−6.88109e39	−0.145450	−0.0727251	−	0.997352i	$-0.523170\pi$
$211$	−6.88109e39	−0.145450	−0.0727251	+	0.997352i	$0.523170\pi$
$212$	6.55481e40	1.27551
$213$	3.59935e40	0.645031
$214$	6.86747e40	1.13385
$215$	−6.72703e40	−1.02365
$216$	2.06396e40	0.289574
$217$	−1.73037e41	−2.23920
$218$	−1.39932e41	−1.67082
$219$	4.94244e40	0.544715
$220$	3.43846e41	3.49918
$221$	−6.43655e40	−0.605046
$222$	−8.84321e40	−0.768127
$223$	−1.52790e41	−1.22676	−0.613378	−	0.789789i	$-0.710190\pi$
$223$	−1.52790e41	−1.22676	−0.613378	+	0.789789i	$0.710190\pi$
$224$	7.12057e40	0.528658
$225$	6.29589e40	0.432378
$226$	1.04540e41	0.664333
$227$	1.54327e41	0.907797	0.453898	−	0.891053i	$-0.350033\pi$
$227$	1.54327e41	0.907797	0.453898	+	0.891053i	$0.350033\pi$
$228$	−1.68733e41	−0.919053
$229$	−2.85667e41	−1.44125	−0.720625	−	0.693325i	$-0.756145\pi$
$229$	−2.85667e41	−1.44125	−0.720625	+	0.693325i	$0.756145\pi$
$230$	−2.04749e41	−0.957162
$231$	−2.35642e41	−1.02104
$232$	8.55809e40	0.343825
$233$	2.74988e40	0.102467	0.0512337	−	0.998687i	$-0.483685\pi$
$233$	2.74988e40	0.102467	0.0512337	+	0.998687i	$0.483685\pi$
$234$	9.56234e40	0.330588
$235$	8.61079e41	2.76284
$236$	1.24135e41	0.369772
$237$	1.70767e41	0.472398
$238$	−9.89582e41	−2.54305
$239$	9.13574e39	0.0218163	0.0109081	−	0.999941i	$-0.496528\pi$
$239$	9.13574e39	0.0218163	0.0109081	+	0.999941i	$0.496528\pi$
$240$	−2.64244e41	−0.586555
$241$	−1.74391e41	−0.359936	−0.179968	−	0.983672i	$-0.557599\pi$
$241$	−1.74391e41	−0.359936	−0.179968	+	0.983672i	$0.557599\pi$
$242$	−4.41497e41	−0.847538
$243$	−3.59175e40	−0.0641500
$244$	4.56683e41	0.759089
$245$	1.06427e42	1.64682
$246$	−3.13194e41	−0.451284
$247$	−3.67191e41	−0.492827
$248$	1.86520e42	2.33249
$249$	7.35902e41	0.857692
$250$	−7.04083e41	−0.765021
$251$	−9.25053e39	−0.00937296	−0.00468648	−	0.999989i	$-0.501492\pi$
$251$	−9.25053e39	−0.00937296	−0.00468648	+	0.999989i	$0.501492\pi$
$252$	9.60701e41	0.907985
$253$	5.16132e41	0.455147
$254$	−1.25734e41	−0.103481
$255$	−1.18031e42	−0.906865
$256$	−2.52936e42	−1.81472
$257$	8.65068e41	0.579723	0.289862	−	0.957069i	$-0.406391\pi$
$257$	8.65068e41	0.579723	0.289862	+	0.957069i	$0.406391\pi$
$258$	−1.05796e42	−0.662409
$259$	−1.93342e42	−1.13130
$260$	−3.05063e42	−1.66862
$261$	−1.48930e41	−0.0761682
$262$	2.59396e42	1.24077
$263$	−1.58951e42	−0.711277	−0.355639	−	0.934624i	$-0.615737\pi$
$263$	−1.58951e42	−0.711277	−0.355639	+	0.934624i	$0.615737\pi$
$264$	2.54003e42	1.06358
$265$	2.61573e42	1.02516
$266$	−5.64534e42	−2.07139
$267$	−2.22260e42	−0.763685
$268$	7.70430e42	2.47956
$269$	−4.32299e42	−1.30352	−0.651762	−	0.758423i	$-0.725970\pi$
$269$	−4.32299e42	−1.30352	−0.651762	+	0.758423i	$0.725970\pi$
$270$	1.75350e42	0.495497
$271$	6.45806e42	1.71056	0.855282	−	0.518163i	$-0.173384\pi$
$271$	6.45806e42	1.71056	0.855282	+	0.518163i	$0.173384\pi$
$272$	2.79732e42	0.694683
$273$	2.09064e42	0.486893
$274$	1.85012e42	0.404170
$275$	7.74811e42	1.58808
$276$	−2.10424e42	−0.404750
$277$	−1.05719e43	−1.90878	−0.954392	−	0.298555i	$-0.903495\pi$
$277$	−1.05719e43	−1.90878	−0.954392	+	0.298555i	$0.903495\pi$
$278$	8.25548e42	1.39945
$279$	−3.24587e42	−0.516722
$280$	−2.20301e43	−3.29420
$281$	−1.01596e42	−0.142730	−0.0713652	−	0.997450i	$-0.522736\pi$
$281$	−1.01596e42	−0.142730	−0.0713652	+	0.997450i	$0.522736\pi$
$282$	1.35423e43	1.78785
$283$	7.86611e42	0.976107	0.488054	−	0.872814i	$-0.337707\pi$
$283$	7.86611e42	0.976107	0.488054	+	0.872814i	$0.337707\pi$
$284$	−1.80591e43	−2.10681
$285$	−6.73339e42	−0.738667
$286$	1.17680e43	1.21422
$287$	−6.84746e42	−0.664655
$288$	1.33569e42	0.121994
$289$	8.61340e41	0.0740393
$290$	7.27080e42	0.588325
$291$	−6.24781e42	−0.475993
$292$	−2.47979e43	−1.77916
$293$	1.69976e43	1.14870	0.574348	−	0.818611i	$-0.305256\pi$
$293$	1.69976e43	1.14870	0.574348	+	0.818611i	$0.305256\pi$
$294$	1.67379e43	1.06567
$295$	4.95367e42	0.297195
$296$	2.08406e43	1.17844
$297$	−4.42023e42	−0.235617
$298$	4.94369e42	0.248466
$299$	−4.57917e42	−0.217041
$300$	−3.15886e43	−1.41224
$301$	−2.31306e43	−0.975602
$302$	−2.57042e43	−1.02302
$303$	−4.37382e42	−0.164291
$304$	1.59581e43	0.565839
$305$	1.82242e43	0.610100
$306$	−1.85628e43	−0.586838
$307$	−1.31155e43	−0.391619	−0.195810	−	0.980642i	$-0.562733\pi$
$307$	−1.31155e43	−0.391619	−0.195810	+	0.980642i	$0.562733\pi$
$308$	1.18230e44	3.33495
$309$	−6.64469e42	−0.177093
$310$	1.58464e44	3.99118
$311$	−3.73438e43	−0.889020	−0.444510	−	0.895774i	$-0.646622\pi$
$311$	−3.73438e43	−0.889020	−0.444510	+	0.895774i	$0.646622\pi$
$312$	−2.25354e43	−0.507177
$313$	−2.87704e43	−0.612238	−0.306119	−	0.951993i	$-0.599031\pi$
$313$	−2.87704e43	−0.612238	−0.306119	+	0.951993i	$0.599031\pi$
$314$	−1.47612e44	−2.97067
$315$	3.83373e43	0.729772
$316$	−8.56796e43	−1.54296
$317$	9.00125e43	1.53379	0.766894	−	0.641773i	$-0.221801\pi$
$317$	9.00125e43	1.53379	0.766894	+	0.641773i	$0.221801\pi$
$318$	4.11378e43	0.663386
$319$	−1.83282e43	−0.279759
$320$	−1.35515e44	−1.95823
$321$	2.81646e43	0.385359
$322$	−7.04021e43	−0.912237
$323$	7.12805e43	0.874836
$324$	1.80210e43	0.209528
$325$	−6.87419e43	−0.757291
$326$	−1.64532e44	−1.71768
$327$	−5.73884e43	−0.567857
$328$	7.38100e43	0.692346
$329$	2.96078e44	2.63316
$330$	2.15797e44	1.81991
$331$	−2.23808e44	−1.79014	−0.895068	−	0.445930i	$-0.852873\pi$
$331$	−2.23808e44	−1.79014	−0.895068	+	0.445930i	$0.852873\pi$
$332$	−3.69227e44	−2.80141
$333$	−3.62674e43	−0.261061
$334$	1.07306e44	0.732927
$335$	3.07444e44	1.99289
$336$	−9.08591e43	−0.559025
$337$	2.79105e44	1.63021	0.815106	−	0.579312i	$-0.196679\pi$
$337$	2.79105e44	1.63021	0.815106	+	0.579312i	$0.196679\pi$
$338$	2.01911e44	1.11974
$339$	4.28736e43	0.225785
$340$	5.92201e44	2.96202
$341$	−3.99456e44	−1.89787
$342$	−1.05897e44	−0.477997
$343$	2.91524e43	0.125034
$344$	2.49329e44	1.01625
$345$	−8.39710e43	−0.325309
$346$	−6.46456e44	−2.38071
$347$	−5.39083e44	−1.88751	−0.943756	−	0.330643i	$-0.892734\pi$
$347$	−5.39083e44	−1.88751	−0.943756	+	0.330643i	$0.892734\pi$
$348$	7.47233e43	0.248782
$349$	1.63788e44	0.518606	0.259303	−	0.965796i	$-0.416507\pi$
$349$	1.63788e44	0.518606	0.259303	+	0.965796i	$0.416507\pi$
$350$	−1.05687e45	−3.18295
$351$	3.92167e43	0.112356
$352$	1.64378e44	0.448073
$353$	5.00187e44	1.29740	0.648702	−	0.761043i	$-0.275312\pi$
$353$	5.00187e44	1.29740	0.648702	+	0.761043i	$0.275312\pi$
$354$	7.79067e43	0.192317
$355$	−7.20660e44	−1.69330
$356$	1.11515e45	2.49436
$357$	−4.05843e44	−0.864301
$358$	5.02748e44	1.01952
$359$	6.16722e44	1.19107	0.595534	−	0.803330i	$-0.296940\pi$
$359$	6.16722e44	1.19107	0.595534	+	0.803330i	$0.296940\pi$
$360$	−4.13245e44	−0.760176
$361$	−1.64019e44	−0.287421
$362$	1.38766e45	2.31678
$363$	−1.81065e44	−0.288051
$364$	−1.04895e45	−1.59030
$365$	−9.89574e44	−1.42996
$366$	2.86613e44	0.394800
$367$	−1.18610e45	−1.55764	−0.778818	−	0.627250i	$-0.784181\pi$
$367$	−1.18610e45	−1.55764	−0.778818	+	0.627250i	$0.784181\pi$
$368$	1.99011e44	0.249195
$369$	−1.28446e44	−0.153377
$370$	1.77059e45	2.01645
$371$	8.99407e44	0.977041
$372$	1.62856e45	1.68773
$373$	1.06538e45	1.05341	0.526706	−	0.850048i	$-0.323427\pi$
$373$	1.06538e45	1.05341	0.526706	+	0.850048i	$0.323427\pi$
$374$	−2.28445e45	−2.15540
$375$	−2.88756e44	−0.260006
$376$	−3.19148e45	−2.74287
$377$	1.62610e44	0.133405
$378$	6.02934e44	0.472240
$379$	1.24427e44	0.0930524	0.0465262	−	0.998917i	$-0.485185\pi$
$379$	1.24427e44	0.0930524	0.0465262	+	0.998917i	$0.485185\pi$
$380$	3.37837e45	2.41265
$381$	−5.15655e43	−0.0351700
$382$	6.63774e43	0.0432425
$383$	−2.30053e44	−0.143169	−0.0715846	−	0.997435i	$-0.522806\pi$
$383$	−2.30053e44	−0.143169	−0.0715846	+	0.997435i	$0.522806\pi$
$384$	−1.77587e45	−1.05588
$385$	4.71802e45	2.68039
$386$	−6.00373e45	−3.25944
$387$	−4.33888e44	−0.225131
$388$	3.13474e45	1.55470
$389$	1.23018e45	0.583243	0.291621	−	0.956534i	$-0.405805\pi$
$389$	1.23018e45	0.583243	0.291621	+	0.956534i	$0.405805\pi$
$390$	−1.91457e45	−0.867841
$391$	8.88927e44	0.385277
$392$	−3.94459e45	−1.63492
$393$	1.06382e45	0.421697
$394$	−6.16024e45	−2.33568
$395$	−3.41910e45	−1.24012
$396$	2.21778e45	0.769578
$397$	−2.62258e45	−0.870752	−0.435376	−	0.900249i	$-0.643385\pi$
$397$	−2.62258e45	−0.870752	−0.435376	+	0.900249i	$0.643385\pi$
$398$	3.04313e45	0.966866
$399$	−2.31524e45	−0.703998
$400$	2.98752e45	0.869483
$401$	2.22698e45	0.620425	0.310213	−	0.950667i	$-0.399600\pi$
$401$	2.22698e45	0.620425	0.310213	+	0.950667i	$0.399600\pi$
$402$	4.83520e45	1.28961
$403$	3.54401e45	0.905017
$404$	2.19449e45	0.536612
$405$	7.19140e44	0.168403
$406$	2.50003e45	0.560712
$407$	−4.46329e45	−0.958855
$408$	4.37466e45	0.900309
$409$	2.77503e44	0.0547155	0.0273577	−	0.999626i	$-0.491291\pi$
$409$	2.77503e44	0.0547155	0.0273577	+	0.999626i	$0.491291\pi$
$410$	6.27077e45	1.18469
$411$	7.58762e44	0.137364
$412$	3.33386e45	0.578425
$413$	1.70330e45	0.283246
$414$	−1.32062e45	−0.210509
$415$	−1.47342e46	−2.25157
$416$	−1.45838e45	−0.213667
$417$	3.38570e45	0.475629
$418$	−1.30323e46	−1.75564
$419$	2.74431e45	0.354559	0.177280	−	0.984161i	$-0.443270\pi$
$419$	2.74431e45	0.354559	0.177280	+	0.984161i	$0.443270\pi$
$420$	−1.92351e46	−2.38360
$421$	5.30191e45	0.630225	0.315112	−	0.949054i	$-0.397958\pi$
$421$	5.30191e45	0.630225	0.315112	+	0.949054i	$0.397958\pi$
$422$	2.16676e45	0.247084
$423$	5.55390e45	0.607633
$424$	−9.69487e45	−1.01775
$425$	1.33445e46	1.34430
$426$	−1.13339e46	−1.09575
$427$	6.26630e45	0.581465
$428$	−1.41311e46	−1.25867
$429$	4.82625e45	0.412674
$430$	2.11825e46	1.73892
$431$	−2.12281e46	−1.67324	−0.836621	−	0.547782i	$-0.815472\pi$
$431$	−2.12281e46	−1.67324	−0.836621	+	0.547782i	$0.815472\pi$
$432$	−1.70436e45	−0.129001
$433$	−2.59717e46	−1.88782	−0.943912	−	0.330196i	$-0.892885\pi$
$433$	−2.59717e46	−1.88782	−0.943912	+	0.330196i	$0.892885\pi$
$434$	5.44871e46	3.80385
$435$	2.98187e45	0.199953
$436$	2.87937e46	1.85474
$437$	5.07113e45	0.313819
$438$	−1.55631e46	−0.925335
$439$	−1.14491e45	−0.0654099	−0.0327049	−	0.999465i	$-0.510412\pi$
$439$	−1.14491e45	−0.0654099	−0.0327049	+	0.999465i	$0.510412\pi$
$440$	−5.08565e46	−2.79206
$441$	6.86448e45	0.362186
$442$	2.02679e46	1.02782
$443$	−3.09981e46	−1.51102	−0.755510	−	0.655137i	$-0.772611\pi$
$443$	−3.09981e46	−1.51102	−0.755510	+	0.655137i	$0.772611\pi$
$444$	1.81966e46	0.852684
$445$	4.45008e46	2.00479
$446$	4.81114e46	2.08395
$447$	2.02749e45	0.0844455
$448$	−4.65962e46	−1.86632
$449$	2.02968e46	0.781836	0.390918	−	0.920425i	$-0.372158\pi$
$449$	2.02968e46	0.781836	0.390918	+	0.920425i	$0.372158\pi$
$450$	−1.98249e46	−0.734502
$451$	−1.58074e46	−0.563339
$452$	−2.15111e46	−0.737464
$453$	−1.05417e46	−0.347690
$454$	−4.85955e46	−1.54212
$455$	−4.18587e46	−1.27816
$456$	2.49564e46	0.733328
$457$	−3.46406e46	−0.979607	−0.489803	−	0.871833i	$-0.662931\pi$
$457$	−3.46406e46	−0.979607	−0.489803	+	0.871833i	$0.662931\pi$
$458$	8.99528e46	2.44832
$459$	−7.61290e45	−0.199447
$460$	4.21311e46	1.06253
$461$	1.41927e46	0.344587	0.172294	−	0.985046i	$-0.444882\pi$
$461$	1.41927e46	0.344587	0.172294	+	0.985046i	$0.444882\pi$
$462$	7.42007e46	1.73450
$463$	−4.26132e46	−0.959129	−0.479565	−	0.877507i	$-0.659205\pi$
$463$	−4.26132e46	−0.959129	−0.479565	+	0.877507i	$0.659205\pi$
$464$	−7.06702e45	−0.153169
$465$	6.49886e46	1.35647
$466$	−8.65902e45	−0.174066
$467$	−7.98255e46	−1.54560	−0.772798	−	0.634652i	$-0.781143\pi$
$467$	−7.98255e46	−1.54560	−0.772798	+	0.634652i	$0.781143\pi$
$468$	−1.96763e46	−0.366980
$469$	1.05713e47	1.89935
$470$	−2.71143e47	−4.69337
$471$	−6.05382e46	−1.00963
$472$	−1.83601e46	−0.295047
$473$	−5.33969e46	−0.826888
$474$	−5.37723e46	−0.802487
$475$	7.61271e46	1.09497
$476$	2.03625e47	2.82300
$477$	1.68713e46	0.225463
$478$	−2.87672e45	−0.0370604
$479$	8.93537e46	1.10979	0.554895	−	0.831920i	$-0.312758\pi$
$479$	8.93537e46	1.10979	0.554895	+	0.831920i	$0.312758\pi$
$480$	−2.67432e46	−0.320252
$481$	3.95987e46	0.457238
$482$	5.49133e46	0.611441
$483$	−2.88730e46	−0.310040
$484$	9.08465e46	0.940837
$485$	1.25093e47	1.24955
$486$	1.13100e46	0.108975
$487$	1.97444e47	1.83522	0.917608	−	0.397486i	$-0.130117\pi$
$487$	1.97444e47	1.83522	0.917608	+	0.397486i	$0.130117\pi$
$488$	−6.75456e46	−0.605690
$489$	−6.74773e46	−0.583785
$490$	−3.35125e47	−2.79754
$491$	4.10668e46	0.330799	0.165400	−	0.986227i	$-0.447109\pi$
$491$	4.10668e46	0.330799	0.165400	+	0.986227i	$0.447109\pi$
$492$	6.44457e46	0.500962
$493$	−3.15665e46	−0.236813
$494$	1.15623e47	0.837191
$495$	8.85017e46	0.618530
$496$	−1.54022e47	−1.03909
$497$	−2.47795e47	−1.61383
$498$	−2.31726e47	−1.45700
$499$	−2.11891e47	−1.28633	−0.643167	−	0.765726i	$-0.722380\pi$
$499$	−2.11891e47	−1.28633	−0.643167	+	0.765726i	$0.722380\pi$
$500$	1.44878e47	0.849237
$501$	4.40079e46	0.249098
$502$	2.91287e45	0.0159223
$503$	1.10572e47	0.583720	0.291860	−	0.956461i	$-0.405726\pi$
$503$	1.10572e47	0.583720	0.291860	+	0.956461i	$0.405726\pi$
$504$	−1.42092e47	−0.724496
$505$	8.75725e46	0.431289
$506$	−1.62523e47	−0.773182
$507$	8.28069e46	0.380563
$508$	2.58721e46	0.114873
$509$	−2.45677e47	−1.05391	−0.526954	−	0.849894i	$-0.676666\pi$
$509$	−2.45677e47	−1.05391	−0.526954	+	0.849894i	$0.676666\pi$
$510$	3.71664e47	1.54054
$511$	−3.40260e47	−1.36284
$512$	3.23962e47	1.25392
$513$	−4.34299e46	−0.162456
$514$	−2.72399e47	−0.984805
$515$	1.33040e47	0.464895
$516$	2.17696e47	0.735329
$517$	6.83496e47	2.23178
$518$	6.08807e47	1.92180
$519$	−2.65122e47	−0.809127
$520$	4.51203e47	1.33142
$521$	4.14045e47	1.18137	0.590686	−	0.806901i	$-0.298857\pi$
$521$	4.14045e47	1.18137	0.590686	+	0.806901i	$0.298857\pi$
$522$	4.68961e46	0.129391
$523$	−5.96375e47	−1.59125	−0.795627	−	0.605787i	$-0.792858\pi$
$523$	−5.96375e47	−1.59125	−0.795627	+	0.605787i	$0.792858\pi$
$524$	−5.33756e47	−1.37735
$525$	−4.33438e47	−1.08178
$526$	5.00517e47	1.20828
$527$	−6.87977e47	−1.60653
$528$	−2.09748e47	−0.473811
$529$	−3.94346e47	−0.861794
$530$	−8.23660e47	−1.74149
$531$	3.19508e46	0.0653623
$532$	1.16164e48	2.29941
$533$	1.40244e47	0.268633
$534$	6.99868e47	1.29731
$535$	−5.63911e47	−1.01162
$536$	−1.13950e48	−1.97848
$537$	2.06185e47	0.346503
$538$	1.36125e48	2.21436
$539$	8.44784e47	1.33028
$540$	−3.60817e47	−0.550042
$541$	−3.26439e47	−0.481781	−0.240891	−	0.970552i	$-0.577439\pi$
$541$	−3.26439e47	−0.481781	−0.240891	+	0.970552i	$0.577439\pi$
$542$	−2.03356e48	−2.90582
$543$	5.69103e47	0.787397
$544$	2.83107e47	0.379288
$545$	1.14903e48	1.49071
$546$	−6.58315e47	−0.827109
$547$	5.93281e47	0.721909	0.360955	−	0.932583i	$-0.382451\pi$
$547$	5.93281e47	0.721909	0.360955	+	0.932583i	$0.382451\pi$
$548$	−3.80697e47	−0.448662
$549$	1.17545e47	0.134180
$550$	−2.43978e48	−2.69776
$551$	−1.80080e47	−0.192891
$552$	3.11228e47	0.322957
$553$	−1.17564e48	−1.18191
$554$	3.32895e48	3.24255
$555$	7.26146e47	0.685325
$556$	−1.69872e48	−1.55351
$557$	−6.26275e47	−0.555008	−0.277504	−	0.960724i	$-0.589507\pi$
$557$	−6.26275e47	−0.555008	−0.277504	+	0.960724i	$0.589507\pi$
$558$	1.02208e48	0.877782
$559$	4.73743e47	0.394308
$560$	1.81918e48	1.46752
$561$	−9.36890e47	−0.732552
$562$	3.19913e47	0.242463
$563$	1.90044e48	1.39623	0.698116	−	0.715985i	$-0.254022\pi$
$563$	1.90044e48	1.39623	0.698116	+	0.715985i	$0.254022\pi$
$564$	−2.78658e48	−1.98466
$565$	−8.58414e47	−0.592719
$566$	−2.47694e48	−1.65816
$567$	2.47273e47	0.160499
$568$	2.67103e48	1.68106
$569$	1.88708e48	1.15166	0.575832	−	0.817568i	$-0.304678\pi$
$569$	1.88708e48	1.15166	0.575832	+	0.817568i	$0.304678\pi$
$570$	2.12026e48	1.25481
$571$	1.45610e48	0.835720	0.417860	−	0.908511i	$-0.362780\pi$
$571$	1.45610e48	0.835720	0.417860	+	0.908511i	$0.362780\pi$
$572$	−2.42149e48	−1.34788
$573$	2.72224e46	0.0146967
$574$	2.15617e48	1.12908
$575$	9.49368e47	0.482223
$576$	−8.74062e47	−0.430674
$577$	−1.31602e48	−0.629051	−0.314526	−	0.949249i	$-0.601845\pi$
$577$	−1.31602e48	−0.629051	−0.314526	+	0.949249i	$0.601845\pi$
$578$	−2.71225e47	−0.125774
$579$	−2.46223e48	−1.10778
$580$	−1.49611e48	−0.653090
$581$	−5.06629e48	−2.14589
$582$	1.96735e48	0.808593
$583$	2.07628e48	0.828107
$584$	3.66773e48	1.41962
$585$	−7.85196e47	−0.294951
$586$	−5.35233e48	−1.95135
$587$	3.36632e48	1.19121	0.595606	−	0.803277i	$-0.296912\pi$
$587$	3.36632e48	1.19121	0.595606	+	0.803277i	$0.296912\pi$
$588$	−3.44414e48	−1.18298
$589$	−3.92475e48	−1.30856
$590$	−1.55985e48	−0.504861
$591$	−2.52641e48	−0.793823
$592$	−1.72096e48	−0.524977
$593$	−1.31507e48	−0.389486	−0.194743	−	0.980854i	$-0.562387\pi$
$593$	−1.31507e48	−0.389486	−0.194743	+	0.980854i	$0.562387\pi$
$594$	1.39187e48	0.400255
$595$	8.12579e48	2.26892
$596$	−1.01726e48	−0.275818
$597$	1.24804e48	0.328606
$598$	1.44192e48	0.368698
$599$	−5.62894e48	−1.39784	−0.698919	−	0.715201i	$-0.746335\pi$
$599$	−5.62894e48	−1.39784	−0.698919	+	0.715201i	$0.746335\pi$
$600$	4.67211e48	1.12685
$601$	6.95422e48	1.62909	0.814545	−	0.580101i	$-0.196987\pi$
$601$	6.95422e48	1.62909	0.814545	+	0.580101i	$0.196987\pi$
$602$	7.28351e48	1.65730
$603$	1.98299e48	0.438297
$604$	5.28913e48	1.13563
$605$	3.62528e48	0.756176
$606$	1.37726e48	0.279090
$607$	−3.70436e48	−0.729309	−0.364654	−	0.931143i	$-0.618813\pi$
$607$	−3.70436e48	−0.729309	−0.364654	+	0.931143i	$0.618813\pi$
$608$	1.61506e48	0.308941
$609$	1.02530e48	0.190568
$610$	−5.73856e48	−1.03641
$611$	−6.06404e48	−1.06424
$612$	3.81965e48	0.651439
$613$	−5.48390e48	−0.908932	−0.454466	−	0.890764i	$-0.650170\pi$
$613$	−5.48390e48	−0.908932	−0.454466	+	0.890764i	$0.650170\pi$
$614$	4.12991e48	0.665264
$615$	2.57174e48	0.402637
$616$	−1.74867e49	−2.66101
$617$	−5.61348e48	−0.830313	−0.415156	−	0.909750i	$-0.636273\pi$
$617$	−5.61348e48	−0.830313	−0.415156	+	0.909750i	$0.636273\pi$
$618$	2.09233e48	0.300837
$619$	2.35877e48	0.329684	0.164842	−	0.986320i	$-0.447289\pi$
$619$	2.35877e48	0.329684	0.164842	+	0.986320i	$0.447289\pi$
$620$	−3.26070e49	−4.43054
$621$	−5.41607e47	−0.0715453
$622$	1.17591e49	1.51022
$623$	1.53014e49	1.91069
$624$	1.86091e48	0.225941
$625$	−5.20569e48	−0.614579
$626$	9.05943e48	1.04004
$627$	−5.34474e48	−0.596685
$628$	3.03741e49	3.29769
$629$	−7.68706e48	−0.811660
$630$	−1.20719e49	−1.23970
$631$	2.89336e48	0.288994	0.144497	−	0.989505i	$-0.453844\pi$
$631$	2.89336e48	0.288994	0.144497	+	0.989505i	$0.453844\pi$
$632$	1.26724e49	1.23115
$633$	8.88625e47	0.0839757
$634$	−2.83437e49	−2.60552
$635$	1.03244e48	0.0923264
$636$	−8.46489e48	−0.736413
$637$	−7.49500e48	−0.634354
$638$	5.77132e48	0.475241
$639$	−4.64820e48	−0.372409
$640$	3.55565e49	2.77185
$641$	−1.08872e49	−0.825853	−0.412926	−	0.910764i	$-0.635493\pi$
$641$	−1.08872e49	−0.825853	−0.412926	+	0.910764i	$0.635493\pi$
$642$	−8.86866e48	−0.654629
$643$	5.30333e48	0.380940	0.190470	−	0.981693i	$-0.438999\pi$
$643$	5.30333e48	0.380940	0.190470	+	0.981693i	$0.438999\pi$
$644$	1.44866e49	1.01266
$645$	8.68730e48	0.591003
$646$	−2.24453e49	−1.48613
$647$	−8.64507e48	−0.557113	−0.278557	−	0.960420i	$-0.589856\pi$
$647$	−8.64507e48	−0.557113	−0.278557	+	0.960420i	$0.589856\pi$
$648$	−2.66540e48	−0.167186
$649$	3.93206e48	0.240070
$650$	2.16459e49	1.28645
$651$	2.23460e49	1.29281
$652$	3.38556e49	1.90677
$653$	−2.69906e49	−1.47990	−0.739948	−	0.672664i	$-0.765150\pi$
$653$	−2.69906e49	−1.47990	−0.739948	+	0.672664i	$0.765150\pi$
$654$	1.80709e49	0.964647
$655$	−2.12999e49	−1.10702
$656$	−6.09501e48	−0.308430
$657$	−6.38267e48	−0.314491
$658$	−9.32310e49	−4.47309
$659$	6.87234e48	0.321077	0.160539	−	0.987030i	$-0.448677\pi$
$659$	6.87234e48	0.321077	0.160539	+	0.987030i	$0.448677\pi$
$660$	−4.44043e49	−2.02026
$661$	3.16481e49	1.40224	0.701119	−	0.713045i	$-0.252684\pi$
$661$	3.16481e49	1.40224	0.701119	+	0.713045i	$0.252684\pi$
$662$	7.04742e49	3.04099
$663$	8.31217e48	0.349324
$664$	5.46104e49	2.23529
$665$	4.63558e49	1.84810
$666$	1.14201e49	0.443478
$667$	−2.24574e48	−0.0849489
$668$	−2.20802e49	−0.813609
$669$	1.97313e49	0.708268
$670$	−9.68102e49	−3.38542
$671$	1.44658e49	0.492830
$672$	−9.19552e48	−0.305221
$673$	−6.90752e48	−0.223387	−0.111694	−	0.993743i	$-0.535628\pi$
$673$	−6.90752e48	−0.223387	−0.111694	+	0.993743i	$0.535628\pi$
$674$	−8.78864e49	−2.76932
$675$	−8.13053e48	−0.249633
$676$	−4.15470e49	−1.24300
$677$	3.65968e49	1.06694	0.533471	−	0.845818i	$-0.320887\pi$
$677$	3.65968e49	1.06694	0.533471	+	0.845818i	$0.320887\pi$
$678$	−1.35003e49	−0.383553
$679$	4.30128e49	1.19090
$680$	−8.75894e49	−2.36344
$681$	−1.99298e49	−0.524117
$682$	1.25783e50	3.22401
$683$	−4.27715e49	−1.06854	−0.534272	−	0.845312i	$-0.679414\pi$
$683$	−4.27715e49	−1.06854	−0.534272	+	0.845312i	$0.679414\pi$
$684$	2.17902e49	0.530616
$685$	−1.51919e49	−0.360602
$686$	−9.17972e48	−0.212401
$687$	3.68911e49	0.832106
$688$	−2.05888e49	−0.452724
$689$	−1.84210e49	−0.394890
$690$	2.64414e49	0.552618
$691$	−4.11987e49	−0.839494	−0.419747	−	0.907641i	$-0.637881\pi$
$691$	−4.11987e49	−0.839494	−0.419747	+	0.907641i	$0.637881\pi$
$692$	1.33021e50	2.64279
$693$	3.04309e49	0.589499
$694$	1.69750e50	3.20641
$695$	−6.77885e49	−1.24860
$696$	−1.10519e49	−0.198507
$697$	−2.72248e49	−0.476860
$698$	−5.15748e49	−0.880982
$699$	−3.55120e48	−0.0591596
$700$	2.17471e50	3.53333
$701$	6.08013e48	0.0963491	0.0481745	−	0.998839i	$-0.484660\pi$
$701$	6.08013e48	0.0963491	0.0481745	+	0.998839i	$0.484660\pi$
$702$	−1.23488e49	−0.190865
$703$	−4.38529e49	−0.661120
$704$	−1.07567e50	−1.58183
$705$	−1.11200e50	−1.59513
$706$	−1.57502e50	−2.20397
$707$	3.01114e49	0.411046
$708$	−1.60308e49	−0.213488
$709$	1.16393e50	1.51224	0.756118	−	0.654436i	$-0.227094\pi$
$709$	1.16393e50	1.51224	0.756118	+	0.654436i	$0.227094\pi$
$710$	2.26926e50	2.87650
$711$	−2.20529e49	−0.272739
$712$	−1.64937e50	−1.99029
$713$	−4.89450e49	−0.576290
$714$	1.27795e50	1.46823
$715$	−9.66309e49	−1.08333
$716$	−1.03450e50	−1.13176
$717$	−1.17979e48	−0.0125956
$718$	−1.94198e50	−2.02333
$719$	−1.15725e49	−0.117672	−0.0588360	−	0.998268i	$-0.518739\pi$
$719$	−1.15725e49	−0.117672	−0.0588360	+	0.998268i	$0.518739\pi$
$720$	3.41246e49	0.338648
$721$	4.57451e49	0.443075
$722$	5.16475e49	0.488257
$723$	2.25208e49	0.207809
$724$	−2.85538e50	−2.57181
$725$	−3.37128e49	−0.296401
$726$	5.70150e49	0.489326
$727$	−3.49319e49	−0.292664	−0.146332	−	0.989236i	$-0.546747\pi$
$727$	−3.49319e49	−0.292664	−0.146332	+	0.989236i	$0.546747\pi$
$728$	1.55144e50	1.26892
$729$	4.63840e48	0.0370370
$730$	3.11604e50	2.42914
$731$	−9.19648e49	−0.699951
$732$	−5.89761e49	−0.438261
$733$	2.27403e50	1.64997	0.824986	−	0.565153i	$-0.191183\pi$
$733$	2.27403e50	1.64997	0.824986	+	0.565153i	$0.191183\pi$
$734$	3.73488e50	2.64604
$735$	−1.37440e50	−0.950793
$736$	2.01411e49	0.136057
$737$	2.44039e50	1.60982
$738$	4.04460e49	0.260549
$739$	4.83328e49	0.304063	0.152032	−	0.988376i	$-0.451418\pi$
$739$	4.83328e49	0.304063	0.152032	+	0.988376i	$0.451418\pi$
$740$	−3.64332e50	−2.23842
$741$	4.74191e49	0.284534
$742$	−2.83211e50	−1.65975
$743$	1.27541e50	0.730040	0.365020	−	0.931000i	$-0.381062\pi$
$743$	1.27541e50	0.730040	0.365020	+	0.931000i	$0.381062\pi$
$744$	−2.40872e50	−1.34667
$745$	−4.05943e49	−0.221682
$746$	−3.35473e50	−1.78948
$747$	−9.50345e49	−0.495189
$748$	4.70069e50	2.39268
$749$	−1.93898e50	−0.964143
$750$	9.09254e49	0.441685
$751$	−7.89850e49	−0.374840	−0.187420	−	0.982280i	$-0.560012\pi$
$751$	−7.89850e49	−0.374840	−0.187420	+	0.982280i	$0.560012\pi$
$752$	2.63543e50	1.22191
$753$	1.19462e48	0.00541148
$754$	−5.12037e49	−0.226622
$755$	2.11066e50	0.912738
$756$	−1.24065e50	−0.524226
$757$	6.60764e49	0.272815	0.136408	−	0.990653i	$-0.456444\pi$
$757$	6.60764e49	0.272815	0.136408	+	0.990653i	$0.456444\pi$
$758$	−3.91804e49	−0.158073
$759$	−6.66534e49	−0.262779
$760$	−4.99677e50	−1.92509
$761$	3.99863e50	1.50549	0.752747	−	0.658310i	$-0.228728\pi$
$761$	3.99863e50	1.50549	0.752747	+	0.658310i	$0.228728\pi$
$762$	1.62373e49	0.0597450
$763$	3.95088e50	1.42074
$764$	−1.36584e49	−0.0480028
$765$	1.52425e50	0.523579
$766$	7.24407e49	0.243209
$767$	−3.48856e49	−0.114479
$768$	3.26642e50	1.04773
$769$	−3.41036e50	−1.06928	−0.534638	−	0.845081i	$-0.679552\pi$
$769$	−3.41036e50	−1.06928	−0.534638	+	0.845081i	$0.679552\pi$
$770$	−1.48564e51	−4.55331
$771$	−1.11715e50	−0.334703
$772$	1.23538e51	3.61825
$773$	−5.59367e49	−0.160160	−0.0800802	−	0.996788i	$-0.525518\pi$
$773$	−5.59367e49	−0.160160	−0.0800802	+	0.996788i	$0.525518\pi$
$774$	1.36626e50	0.382442
$775$	−7.34755e50	−2.01077
$776$	−4.63643e50	−1.24052
$777$	2.49682e50	0.653159
$778$	−3.87366e50	−0.990784
$779$	−1.55311e50	−0.388416
$780$	3.93959e50	0.963376
$781$	−5.72036e50	−1.36782
$782$	−2.79912e50	−0.654489
$783$	1.92329e49	0.0439757
$784$	3.25732e50	0.728333
$785$	1.21209e51	2.65044
$786$	−3.34984e50	−0.716357
$787$	−5.37997e50	−1.12518	−0.562590	−	0.826736i	$-0.690195\pi$
$787$	−5.37997e50	−1.12518	−0.562590	+	0.826736i	$0.690195\pi$
$788$	1.26759e51	2.59280
$789$	2.05270e50	0.410656
$790$	1.07663e51	2.10665
$791$	−2.95162e50	−0.564900
$792$	−3.28020e50	−0.614059
$793$	−1.28342e50	−0.235010
$794$	8.25815e50	1.47919
$795$	−3.37796e50	−0.591875
$796$	−6.26181e50	−1.07330
$797$	−2.56980e50	−0.430902	−0.215451	−	0.976515i	$-0.569122\pi$
$797$	−2.56980e50	−0.430902	−0.215451	+	0.976515i	$0.569122\pi$
$798$	7.29040e50	1.19592
$799$	1.17718e51	1.88918
$800$	3.02356e50	0.474727
$801$	2.87027e50	0.440914
$802$	−7.01246e50	−1.05395
$803$	−7.85491e50	−1.15510
$804$	−9.94934e50	−1.43157
$805$	5.78095e50	0.813901
$806$	−1.11596e51	−1.53740
$807$	5.58272e50	0.752590
$808$	−3.24576e50	−0.428171
$809$	−5.38460e50	−0.695112	−0.347556	−	0.937659i	$-0.612988\pi$
$809$	−5.38460e50	−0.695112	−0.347556	+	0.937659i	$0.612988\pi$
$810$	−2.26448e50	−0.286075
$811$	1.74111e50	0.215259	0.107630	−	0.994191i	$-0.465674\pi$
$811$	1.74111e50	0.215259	0.107630	+	0.994191i	$0.465674\pi$
$812$	−5.14429e50	−0.622436
$813$	−8.33995e50	−0.987595
$814$	1.40543e51	1.62886
$815$	1.35103e51	1.53252
$816$	−3.61247e50	−0.401075
$817$	−5.24638e50	−0.570130
$818$	−8.73821e49	−0.0929479
$819$	−2.69986e50	−0.281108
$820$	−1.29033e51	−1.31510
$821$	−1.66594e51	−1.66209	−0.831046	−	0.556204i	$-0.812257\pi$
$821$	−1.66594e51	−1.66209	−0.831046	+	0.556204i	$0.812257\pi$
$822$	−2.38924e50	−0.233348
$823$	3.02282e50	0.289012	0.144506	−	0.989504i	$-0.453841\pi$
$823$	3.02282e50	0.289012	0.144506	+	0.989504i	$0.453841\pi$
$824$	−4.93095e50	−0.461534
$825$	−1.00059e51	−0.916881
$826$	−5.36345e50	−0.481165
$827$	−4.63022e50	−0.406682	−0.203341	−	0.979108i	$-0.565180\pi$
$827$	−4.63022e50	−0.406682	−0.203341	+	0.979108i	$0.565180\pi$
$828$	2.71742e50	0.233683
$829$	−3.82585e49	−0.0322124	−0.0161062	−	0.999870i	$-0.505127\pi$
$829$	−3.82585e49	−0.0322124	−0.0161062	+	0.999870i	$0.505127\pi$
$830$	4.63961e51	3.82485
$831$	1.36526e51	1.10204
$832$	9.54348e50	0.754308
$833$	1.45496e51	1.12606
$834$	−1.06611e51	−0.807975
$835$	−8.81124e50	−0.653919
$836$	2.68164e51	1.94890
$837$	4.19172e50	0.298330
$838$	−8.64149e50	−0.602307
$839$	1.51079e51	1.03127	0.515633	−	0.856809i	$-0.327557\pi$
$839$	1.51079e51	1.03127	0.515633	+	0.856809i	$0.327557\pi$
$840$	2.84497e51	1.90191
$841$	−1.44757e51	−0.947786
$842$	−1.66950e51	−1.07059
$843$	1.31201e50	0.0824055
$844$	−4.45853e50	−0.274283
$845$	−1.65796e51	−0.999035
$846$	−1.74885e51	−1.03222
$847$	1.24654e51	0.720684
$848$	8.00574e50	0.453392
$849$	−1.01583e51	−0.563556
$850$	−4.20199e51	−2.28362
$851$	−5.46883e50	−0.291157
$852$	2.33216e51	1.21637
$853$	4.42362e50	0.226032	0.113016	−	0.993593i	$-0.463949\pi$
$853$	4.42362e50	0.226032	0.113016	+	0.993593i	$0.463949\pi$
$854$	−1.97318e51	−0.987764
$855$	8.69552e50	0.426470
$856$	2.09006e51	1.00431
$857$	−4.10421e51	−1.93226	−0.966129	−	0.258059i	$-0.916917\pi$
$857$	−4.10421e51	−1.93226	−0.966129	+	0.258059i	$0.916917\pi$
$858$	−1.51972e51	−0.701030
$859$	3.05622e51	1.38135	0.690675	−	0.723165i	$-0.257313\pi$
$859$	3.05622e51	1.38135	0.690675	+	0.723165i	$0.257313\pi$
$860$	−4.35871e51	−1.93035
$861$	8.84282e50	0.383739
$862$	6.68445e51	2.84242
$863$	−2.21426e51	−0.922657	−0.461329	−	0.887229i	$-0.652627\pi$
$863$	−2.21426e51	−0.922657	−0.461329	+	0.887229i	$0.652627\pi$
$864$	−1.72492e50	−0.0704332
$865$	5.30826e51	2.12408
$866$	8.17814e51	3.20694
$867$	−1.11234e50	−0.0427466
$868$	−1.12118e52	−4.22259
$869$	−2.71396e51	−1.00175
$870$	−9.38953e50	−0.339670
$871$	−2.16514e51	−0.767658
$872$	−4.25873e51	−1.47993
$873$	8.06843e50	0.274815
$874$	−1.59683e51	−0.533100
$875$	1.98793e51	0.650518
$876$	3.20240e51	1.02720
$877$	1.01208e51	0.318215	0.159108	−	0.987261i	$-0.449138\pi$
$877$	1.01208e51	0.318215	0.159108	+	0.987261i	$0.449138\pi$
$878$	3.60518e50	0.111115
$879$	−2.19508e51	−0.663200
$880$	4.19958e51	1.24382
$881$	2.64312e51	0.767430	0.383715	−	0.923452i	$-0.374645\pi$
$881$	2.64312e51	0.767430	0.383715	+	0.923452i	$0.374645\pi$
$882$	−2.16153e51	−0.615264
$883$	3.39738e51	0.948050	0.474025	−	0.880511i	$-0.342801\pi$
$883$	3.39738e51	0.948050	0.474025	+	0.880511i	$0.342801\pi$
$884$	−4.17050e51	−1.14097
$885$	−6.39718e50	−0.171586
$886$	9.76091e51	2.56685
$887$	4.09378e51	1.05551	0.527754	−	0.849397i	$-0.323034\pi$
$887$	4.09378e51	1.05551	0.527754	+	0.849397i	$0.323034\pi$
$888$	−2.69136e51	−0.680371
$889$	3.55000e50	0.0879930
$890$	−1.40127e52	−3.40563
$891$	5.70829e50	0.136034
$892$	−9.89984e51	−2.31336
$893$	6.71552e51	1.53879
$894$	−6.38429e50	−0.143452
$895$	−4.12823e51	−0.909622
$896$	1.22259e52	2.64175
$897$	5.91355e50	0.125309
$898$	−6.39118e51	−1.32814
$899$	1.73807e51	0.354220
$900$	4.07936e51	0.815357
$901$	3.57595e51	0.700983
$902$	4.97753e51	0.956972
$903$	2.98709e51	0.563264
$904$	3.18160e51	0.588435
$905$	−1.13946e52	−2.06703
$906$	3.31944e51	0.590639
$907$	6.74690e50	0.117754	0.0588771	−	0.998265i	$-0.481248\pi$
$907$	6.74690e50	0.117754	0.0588771	+	0.998265i	$0.481248\pi$
$908$	9.99944e51	1.71188
$909$	5.64836e50	0.0948537
$910$	1.31808e52	2.17128
$911$	−4.50163e51	−0.727441	−0.363720	−	0.931508i	$-0.618494\pi$
$911$	−4.50163e51	−0.727441	−0.363720	+	0.931508i	$0.618494\pi$
$912$	−2.06083e51	−0.326687
$913$	−1.16955e52	−1.81878
$914$	1.09079e52	1.66411
$915$	−2.35348e51	−0.352242
$916$	−1.85095e52	−2.71784
$917$	−7.32385e51	−1.05506
$918$	2.39720e51	0.338811
$919$	−1.02476e52	−1.42102	−0.710511	−	0.703686i	$-0.751536\pi$
$919$	−1.02476e52	−1.42102	−0.710511	+	0.703686i	$0.751536\pi$
$920$	−6.23139e51	−0.847809
$921$	1.69374e51	0.226102
$922$	−4.46910e51	−0.585368
$923$	5.07515e51	0.652258
$924$	−1.52682e52	−1.92543
$925$	−8.20973e51	−1.01589
$926$	1.34183e52	1.62932
$927$	8.58096e50	0.102245
$928$	−7.15227e50	−0.0836285
$929$	−4.03684e51	−0.463198	−0.231599	−	0.972811i	$-0.574396\pi$
$929$	−4.03684e51	−0.463198	−0.231599	+	0.972811i	$0.574396\pi$
$930$	−2.04641e52	−2.30431
$931$	8.30021e51	0.917212
$932$	1.78176e51	0.193228
$933$	4.82258e51	0.513276
$934$	2.51360e52	2.62558
$935$	1.87584e52	1.92306
$936$	2.91023e51	0.292819
$937$	−1.56788e52	−1.54836	−0.774178	−	0.632968i	$-0.781836\pi$
$937$	−1.56788e52	−1.54836	−0.774178	+	0.632968i	$0.781836\pi$
$938$	−3.32877e52	−3.22652
$939$	3.71542e51	0.353476
$940$	5.57928e52	5.21003
$941$	8.58654e50	0.0787046	0.0393523	−	0.999225i	$-0.487471\pi$
$941$	8.58654e50	0.0787046	0.0393523	+	0.999225i	$0.487471\pi$
$942$	1.90627e52	1.71512
$943$	−1.93686e51	−0.171058
$944$	1.51613e51	0.131439
$945$	−4.95089e51	−0.421334
$946$	1.68140e52	1.40468
$947$	−6.34472e51	−0.520341	−0.260170	−	0.965563i	$-0.583779\pi$
$947$	−6.34472e51	−0.520341	−0.260170	+	0.965563i	$0.583779\pi$
$948$	1.10647e52	0.890826
$949$	6.96895e51	0.550818
$950$	−2.39714e52	−1.86008
$951$	−1.16242e52	−0.885533
$952$	−3.01172e52	−2.25251
$953$	1.01401e52	0.744587	0.372293	−	0.928115i	$-0.378572\pi$
$953$	1.01401e52	0.744587	0.372293	+	0.928115i	$0.378572\pi$
$954$	−5.31254e51	−0.383006
$955$	−5.45047e50	−0.0385811
$956$	5.91941e50	0.0411401
$957$	2.36691e51	0.161519
$958$	−2.81363e52	−1.88526
$959$	−5.22367e51	−0.343677
$960$	1.75004e52	1.13058
$961$	2.21168e52	1.40302
$962$	−1.24691e52	−0.776733
$963$	−3.63718e51	−0.222487
$964$	−1.12995e52	−0.678750
$965$	4.92986e52	2.90808
$966$	9.09174e51	0.526681
$967$	2.62715e50	0.0149459	0.00747294	−	0.999972i	$-0.497621\pi$
$967$	2.62715e50	0.0149459	0.00747294	+	0.999972i	$0.497621\pi$
$968$	−1.34366e52	−0.750709
$969$	−9.20518e51	−0.505087
$970$	−3.93903e52	−2.12268
$971$	−1.35550e52	−0.717405	−0.358702	−	0.933452i	$-0.616781\pi$
$971$	−1.35550e52	−0.717405	−0.358702	+	0.933452i	$0.616781\pi$
$972$	−2.32724e51	−0.120971
$973$	−2.33087e52	−1.18999
$974$	−6.21725e52	−3.11758
$975$	8.87734e51	0.437222
$976$	5.57772e51	0.269827
$977$	1.04794e52	0.497947	0.248973	−	0.968510i	$-0.419907\pi$
$977$	1.04794e52	0.497947	0.248973	+	0.968510i	$0.419907\pi$
$978$	2.12477e52	0.991704
$979$	3.53233e52	1.61944
$980$	6.89585e52	3.10550
$981$	7.41115e51	0.327852
$982$	−1.29314e52	−0.561945
$983$	−1.08382e52	−0.462668	−0.231334	−	0.972874i	$-0.574309\pi$
$983$	−1.08382e52	−0.462668	−0.231334	+	0.972874i	$0.574309\pi$
$984$	−9.53183e51	−0.399726
$985$	5.05838e52	2.08390
$986$	9.93987e51	0.402286
$987$	−3.82356e52	−1.52026
$988$	−2.37917e52	−0.929351
$989$	−6.54268e51	−0.251085
$990$	−2.78680e52	−1.05073
$991$	−4.54048e52	−1.68195	−0.840975	−	0.541074i	$-0.818018\pi$
$991$	−4.54048e52	−1.68195	−0.840975	+	0.541074i	$0.818018\pi$
$992$	−1.55881e52	−0.567333
$993$	2.89026e52	1.03354
$994$	7.80275e52	2.74149
$995$	−2.49881e52	−0.862640
$996$	4.76820e52	1.61740
$997$	−1.50067e52	−0.500174	−0.250087	−	0.968223i	$-0.580459\pi$
$997$	−1.50067e52	−0.500174	−0.250087	+	0.968223i	$0.580459\pi$
$998$	6.67218e52	2.18516
$999$	4.68358e51	0.150724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.36.a.b.1.1	✓	3
3.2	odd	2		9.36.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.b.1.1	✓	3	1.1	even	1	trivial
9.36.a.c.1.3		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:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-314887. q^{2} -1.29140e8 q^{3} +6.47940e10 q^{4} +2.58564e12 q^{5} +4.06645e13 q^{6} +8.89060e14 q^{7} -9.58334e15 q^{8} +1.66772e16 q^{9} +O(q^{10})\)	\(q-314887. q^{2} -1.29140e8 q^{3} +6.47940e10 q^{4} +2.58564e12 q^{5} +4.06645e13 q^{6} +8.89060e14 q^{7} -9.58334e15 q^{8} +1.66772e16 q^{9} -8.14184e17 q^{10} +2.05240e18 q^{11} -8.36750e18 q^{12} -1.82090e19 q^{13} -2.79953e20 q^{14} -3.33910e20 q^{15} +7.91364e20 q^{16} +3.53481e21 q^{17} -5.25142e21 q^{18} +2.01653e22 q^{19} +1.67534e23 q^{20} -1.14813e23 q^{21} -6.46272e23 q^{22} +2.51478e23 q^{23} +1.23759e24 q^{24} +3.77515e24 q^{25} +5.73379e24 q^{26} -2.15369e24 q^{27} +5.76057e25 q^{28} -8.93017e24 q^{29} +1.05144e26 q^{30} -1.94629e26 q^{31} +8.00910e25 q^{32} -2.65047e26 q^{33} -1.11307e27 q^{34} +2.29879e27 q^{35} +1.08058e27 q^{36} -2.17467e27 q^{37} -6.34979e27 q^{38} +2.35152e27 q^{39} -2.47791e28 q^{40} -7.70191e27 q^{41} +3.61532e28 q^{42} -2.60169e28 q^{43} +1.32983e29 q^{44} +4.31212e28 q^{45} -7.91871e28 q^{46} +3.33024e29 q^{47} -1.02197e29 q^{48} +4.11609e29 q^{49} -1.18875e30 q^{50} -4.56486e29 q^{51} -1.17984e30 q^{52} +1.01164e30 q^{53} +6.78170e29 q^{54} +5.30676e30 q^{55} -8.52016e30 q^{56} -2.60415e30 q^{57} +2.81199e30 q^{58} +1.91584e30 q^{59} -2.16354e31 q^{60} +7.04823e30 q^{61} +6.12862e31 q^{62} +1.48270e31 q^{63} -5.24107e31 q^{64} -4.70820e31 q^{65} +8.34597e31 q^{66} +1.18905e32 q^{67} +2.29034e32 q^{68} -3.24759e31 q^{69} -7.23859e32 q^{70} -2.78716e32 q^{71} -1.59823e32 q^{72} -3.82719e32 q^{73} +6.84776e32 q^{74} -4.87524e32 q^{75} +1.30659e33 q^{76} +1.82470e33 q^{77} -7.40462e32 q^{78} -1.32234e33 q^{79} +2.04618e33 q^{80} +2.78128e32 q^{81} +2.42523e33 q^{82} -5.69848e33 q^{83} -7.43921e33 q^{84} +9.13975e33 q^{85} +8.19238e33 q^{86} +1.15324e33 q^{87} -1.96688e34 q^{88} +1.72108e34 q^{89} -1.35783e34 q^{90} -1.61889e34 q^{91} +1.62943e34 q^{92} +2.51344e34 q^{93} -1.04865e35 q^{94} +5.21402e34 q^{95} -1.03430e34 q^{96} +4.83801e34 q^{97} -1.29610e35 q^{98} +3.42282e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 50\!\cdots\!07 q^{9}+O(q^{10}) \) 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9	\( 3 q - 87330 q^{2} - 387420489 q^{3} + 32488752900 q^{4} + 2768676235410 q^{5} + 11277810434790 q^{6} + 488237848538064 q^{7} - 18\!\cdots\!52 q^{8}+ \cdots + 57\!\cdots\!76 q^{99}+O(q^{100}) \) 3 * q - 87330 * q^2 - 387420489 * q^3 + 32488752900 * q^4 + 2768676235410 * q^5 + 11277810434790 * q^6 + 488237848538064 * q^7 - 18683146678130952 * q^8 + 50031545098999707 * q^9 - 1127779626928867020 * q^10 + 3426356175124224804 * q^11 - 4195602845172722700 * q^12 + 50087718431258539506 * q^13 - 217880362960444050144 * q^14 - 357547300335073771830 * q^15 + 606906765664363747344 * q^16 + 2730709287864549111942 * q^17 - 1456418277831881470770 * q^18 + 28794251065778257727292 * q^19 + 88477655809138293889560 * q^20 - 63051115342974896664432 * q^21 - 122741766765729403865496 * q^22 + 1806983834691084779311608 * q^23 + 2412744607366739676625176 * q^24 + 8598840806404444672708725 * q^25 + 12462234191474761114326516 * q^26 - 6461081889226673298932241 * q^27 + 88582873604432535904569792 * q^28 + 78927943791269118086922714 * q^29 + 145641644849673076368124260 * q^30 - 1597007179004406242679048 * q^31 + 212133152341134442715841504 * q^32 - 442480194951598936437203052 * q^33 - 1031323232079473133177847620 * q^34 - 1159830211565676145196532000 * q^35 + 541820835308869172631800100 * q^36 - 5102549932092597658956094086 * q^37 - 8724219045726720381610922664 * q^38 - 6468336122510832086946779478 * q^39 - 17377992868876213570860774960 * q^40 - 20208748955896036456754429058 * q^41 + 28137105587210907187976333472 * q^42 + 46721962642013867129638134372 * q^43 + 194349428414233101115805936688 * q^44 + 46173716645481381511151008290 * q^45 + 52087178478532028950981302192 * q^46 + 293197746513164578153478190816 * q^47 - 78376038643698737623294977072 * q^48 + 836105627836985614440420595707 * q^49 - 701125828082122697797800571950 * q^50 - 352644242540441794237695126546 * q^51 - 2520178249741268871517789030248 * q^52 - 108875909240521237104294715182 * q^53 + 188082093795388459731917535510 * q^54 - 6237008697722857733231584966440 * q^55 - 9347630291312236144016149603200 * q^56 - 3718494276097527924758498428596 * q^57 + 11382186268398399744329433517572 * q^58 + 11320340569522247618095325505348 * q^59 - 11426018893050016162439682398280 * q^60 + 12771547929195071355310409383218 * q^61 + 101447293741849863418951127675568 * q^62 + 8142431312723579060152904782416 * q^63 - 41280658033851993168324127190976 * q^64 - 7709579158673152743776325663060 * q^65 + 15850891767034278029082983515848 * q^66 + 175757710780078940305499908875612 * q^67 + 281442880096236379198382763169800 * q^68 - 233354186950371743047120084912104 * q^69 - 1040498682940112273466514884936000 * q^70 - 27474747461715252213775775690424 * q^71 - 311582231872711762617942518543688 * q^72 - 585184619829428568163757555870322 * q^73 + 134392541523566959843290841608516 * q^74 - 1110455703350121428958086398022175 * q^75 + 403477747366730076622590548780112 * q^76 + 5306726056931811905707525354511808 * q^77 - 1609374954831223860690187911462108 * q^78 - 2667396066634861458375845391576600 * q^79 + 7102490190805235743681469824979040 * q^80 + 834385168331080533771857328695283 * q^81 + 917242845604400818117266629806188 * q^82 + 6578360642441675208543593208203580 * q^83 - 11439606736284815209219495383756096 * q^84 + 3560960065600250795485268792239140 * q^85 + 18773659018851120901851911340565224 * q^86 - 10192767526459331886611447454362382 * q^87 - 34961215155916125706150543997131872 * q^88 + 11419551912179244059325275346141822 * q^89 - 18808185755474891578891014940654380 * q^90 - 40541093249602611010364470781007648 * q^91 - 19232540048657476273178638696239456 * q^92 + 206237767408799199897789815404824 * q^93 - 101336598951909608865466201817694528 * q^94 + 159588702835640097495158571410457960 * q^95 - 27394909871037933537237934508725152 * q^96 + 211792260572805448951439211684683142 * q^97 - 124471288129025507609829835395708786 * q^98 + 57141964500321263762127041399377476 * q^99

Introduction

L-functions

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