LMFDB - Embedded newform 1.48.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,48,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 48, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 48);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 48 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$13.9907662655$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 $ x^4 - x^3 - 832803191366x^2 + 3710135215485780x + 13175318942671469337000
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$901372.$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} +O(q^{10})$	\(q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} -2.65611e23 q^{10} -3.19474e24 q^{11} +5.03652e25 q^{12} +1.57743e25 q^{13} +3.55908e26 q^{14} -1.47897e27 q^{15} +7.86346e28 q^{16} -3.42618e28 q^{17} -2.32503e29 q^{18} +1.00019e30 q^{19} -4.51042e30 q^{20} +1.98176e30 q^{21} -7.37325e31 q^{22} +5.17765e31 q^{23} +7.44978e32 q^{24} -5.78095e32 q^{25} +3.64060e32 q^{26} -4.71154e33 q^{27} +6.04378e33 q^{28} -6.90432e33 q^{29} -3.41336e34 q^{30} -1.79630e35 q^{31} +9.98970e35 q^{32} -4.10556e35 q^{33} -7.90739e35 q^{34} -1.77475e35 q^{35} -3.94820e36 q^{36} -2.68894e36 q^{37} +2.30836e37 q^{38} +2.02715e36 q^{39} -6.67160e37 q^{40} +1.17249e38 q^{41} +4.57376e37 q^{42} +1.58085e38 q^{43} -1.25208e39 q^{44} +1.15938e38 q^{45} +1.19497e39 q^{46} -1.34555e39 q^{47} +1.01053e40 q^{48} -5.00553e39 q^{49} -1.33420e40 q^{50} -4.40298e39 q^{51} +6.18221e39 q^{52} +4.68526e40 q^{53} -1.08739e41 q^{54} +3.67670e40 q^{55} +8.93968e40 q^{56} +1.28534e41 q^{57} -1.59347e41 q^{58} +3.84916e41 q^{59} -5.79633e41 q^{60} +4.37844e41 q^{61} -4.14573e42 q^{62} -1.55353e41 q^{63} +1.19887e43 q^{64} -1.81540e41 q^{65} -9.47534e42 q^{66} +4.64892e42 q^{67} -1.34278e43 q^{68} +6.65378e42 q^{69} -4.09600e42 q^{70} +1.91856e43 q^{71} -5.83999e43 q^{72} +8.25143e43 q^{73} -6.20589e43 q^{74} -7.42908e43 q^{75} +3.91990e44 q^{76} -4.92663e43 q^{77} +4.67852e43 q^{78} -5.45765e44 q^{79} -9.04975e44 q^{80} -3.37621e44 q^{81} +2.70603e45 q^{82} -1.02727e45 q^{83} +7.76685e44 q^{84} +3.94306e44 q^{85} +3.64849e45 q^{86} -8.87272e44 q^{87} -1.85201e46 q^{88} +1.06667e46 q^{89} +2.67578e45 q^{90} +2.43256e44 q^{91} +2.02921e46 q^{92} -2.30842e46 q^{93} -3.10543e46 q^{94} -1.15107e46 q^{95} +1.28377e47 q^{96} +3.72976e46 q^{97} -1.15524e47 q^{98} +3.21841e46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots - 17\!\cdots\!72 q^{9}+O(q^{10}) $ 4 * q + 5785560 * q^2 + 38461494960 * q^3 + 404807499161152 * q^4 - 31114680242272200 * q^5 + 2130087053081157408 * q^6 - 39169218725888423200 * q^7 + 2392716988073784337920 * q^8 - 17071972417358142200172 * q^9	$ 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots + 53\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q + 5785560 * q^2 + 38461494960 * q^3 + 404807499161152 * q^4 - 31114680242272200 * q^5 + 2130087053081157408 * q^6 - 39169218725888423200 * q^7 + 2392716988073784337920 * q^8 - 17071972417358142200172 * q^9 + 161126302562215963534800 * q^10 - 1902165515717740404742512 * q^11 + 50498409864612604588081920 * q^12 + 126959149195199610466858520 * q^13 + 3491363489769461659480835904 * q^14 + 12437812896841241272880733600 * q^15 + 124527684040554167211817897984 * q^16 + 210426285758836687099688769480 * q^17 + 407430960534937802050318472760 * q^18 - 1059119811802437301721159140240 * q^19 - 15129514318106701401937782249600 * q^20 - 26054906182888686128940663165312 * q^21 - 79668451994083088127806382590880 * q^22 + 137531418344493639994288859179680 * q^23 + 1127389844243414442148606193633280 * q^24 + 1009909900344396506188154274977500 * q^25 + 2282338781897562472343866220387088 * q^26 - 7345952425324536073931587214783520 * q^27 - 36222097928665071743339635065479680 * q^28 - 22743132490172744184500850941726760 * q^29 - 25720928123802268640488729686158400 * q^30 + 75786540814706434901630981303934848 * q^31 + 1184674767018086471839527432906178560 * q^32 + 263381387470144952341649359926294720 * q^33 - 1261659118578465318749852382715620816 * q^34 - 1313148822925052387484546800067979200 * q^35 - 13289406181678982858450254524690284736 * q^36 - 11291457045120157869429951769632191560 * q^37 + 29667542464851305273548614410680536480 * q^38 + 39294375338503805226442587829551714336 * q^39 + 70753686685508718175919216681780352000 * q^40 + 130658126291089294119301677048020391528 * q^41 - 109062084819684721847642948723433304320 * q^42 - 445357287738427943170332944488133090800 * q^43 - 1525898906718917337200010663037616115456 * q^44 + 86022747271219179966948746072020632600 * q^45 + 1226146172325422687186041586267533291968 * q^46 + 2031912465958423919194866366997063590720 * q^47 + 10099193618530117215910418995824892231680 * q^48 + 9153745744156628626499502447643951451172 * q^49 - 19226200465513908889722489088356697935000 * q^50 - 18534366050002170683962116343746386369952 * q^51 - 55272350705889116147839999778699925596800 * q^52 + 29171719896619533806321793123448457437560 * q^53 - 119298079293441315567989538387565460341440 * q^54 + 192172580604633896452606078657416872901600 * q^55 + 276101696826518177934513744689489393111040 * q^56 + 558743644452458098451223285784560964733760 * q^57 - 732323136683092912071778597620095648941680 * q^58 + 478242858216320686410790860443879577596880 * q^59 - 2122170544542769609835673200272436380915200 * q^60 + 626683213833907852009669690320782900857688 * q^61 - 6870459615610782098804391369236375065946880 * q^62 + 5811636950821577036406237472810763671724640 * q^63 + 5525430481808418303700543890989262651523072 * q^64 + 12996735432890074297558542478104126872331600 * q^65 - 8968962593451471455705715472787747435620224 * q^66 + 18701411419127220668869505853739529194216880 * q^67 - 27469024204738931095482995064729717598496640 * q^68 - 2096956664577882726873494616728974107851904 * q^69 - 97207317904230285933067401805385458355395200 * q^70 + 22196594617762006008028198712153461686540768 * q^71 - 17423883005618236773493453708136577246773760 * q^72 + 104911201720506650033573412943840886878191080 * q^73 + 187734656069700274526204928907842421165646544 * q^74 + 32388703324174028323482311940739905891330000 * q^75 + 351694386032713991264839561028061045130100480 * q^76 - 263490744376507692433815778071300370399209600 * q^77 - 49672827098281461020739302707360391741486400 * q^78 - 1327995310109394234162785254414226288730352960 * q^79 - 948349663264469859337474495994045561022259200 * q^80 - 1061448205755511803861508510986654404170081116 * q^81 + 3821513842864797430908620724480935919685390320 * q^82 - 1439130627532364606968733068855111784504073360 * q^83 + 5249451328483250861794821516342136498695481344 * q^84 - 1001895286410663502447652611446390227458237200 * q^85 + 9578145533777866709022895861637903827077656928 * q^86 - 4326251093943206485496474339443178030108648160 * q^87 - 15478856320702836436797993507832298416714229760 * q^88 - 7960590522674945421108320896849737731421281880 * q^89 - 16839942698767843070418568109517409659960668400 * q^90 + 5325194479227227497182497798631911205603381568 * q^91 + 13058297350229360275908546071900174502239009280 * q^92 + 10728611999875738337226031496188630272675064320 * q^93 + 3475860200879106349192555645858186353201354624 * q^94 + 75421152415106939771624998522249518123547668000 * q^95 + 64914496577750590120454418039013206176753123328 * q^96 + 95066248961258904822565865801364599382905757320 * q^97 - 296344663186266398350742083591017164797938217320 * q^98 + 530900415919166351015781326273177630089784016 * 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 $

$2$	2.30793e7	1.94544	0.972720	−	0.231981i	$-0.0745207\pi$
$2$	2.30793e7	1.94544	0.972720	+	0.231981i	$0.0745207\pi$
$3$	1.28510e11	0.788109	0.394055	−	0.919087i	$-0.371072\pi$
$3$	1.28510e11	0.788109	0.394055	+	0.919087i	$0.371072\pi$
$4$	3.91917e14	2.78474
$5$	−1.15086e16	−0.431745	−0.215873	−	0.976422i	$-0.569260\pi$
$5$	−1.15086e16	−0.431745	−0.215873	+	0.976422i	$0.569260\pi$
$6$	2.96592e18	1.53322
$7$	1.54211e19	0.212966	0.106483	−	0.994315i	$-0.466041\pi$
$7$	1.54211e19	0.212966	0.106483	+	0.994315i	$0.466041\pi$
$8$	5.79706e21	3.47211
$9$	−1.00741e22	−0.378884
$10$	−2.65611e23	−0.839935
$11$	−3.19474e24	−1.07574	−0.537871	−	0.843027i	$-0.680771\pi$
$11$	−3.19474e24	−1.07574	−0.537871	+	0.843027i	$0.680771\pi$
$12$	5.03652e25	2.19468
$13$	1.57743e25	0.104781	0.0523903	−	0.998627i	$-0.483316\pi$
$13$	1.57743e25	0.104781	0.0523903	+	0.998627i	$0.483316\pi$
$14$	3.55908e26	0.414313
$15$	−1.47897e27	−0.340262
$16$	7.86346e28	3.97004
$17$	−3.42618e28	−0.416160	−0.208080	−	0.978112i	$-0.566722\pi$
$17$	−3.42618e28	−0.416160	−0.208080	+	0.978112i	$0.566722\pi$
$18$	−2.32503e29	−0.737096
$19$	1.00019e30	0.889961	0.444980	−	0.895540i	$-0.353211\pi$
$19$	1.00019e30	0.889961	0.444980	+	0.895540i	$0.353211\pi$
$20$	−4.51042e30	−1.20230
$21$	1.98176e30	0.167841
$22$	−7.37325e31	−2.09279
$23$	5.17765e31	0.517045	0.258522	−	0.966005i	$-0.416764\pi$
$23$	5.17765e31	0.517045	0.258522	+	0.966005i	$0.416764\pi$
$24$	7.44978e32	2.73640
$25$	−5.78095e32	−0.813596
$26$	3.64060e32	0.203844
$27$	−4.71154e33	−1.08671
$28$	6.04378e33	0.593055
$29$	−6.90432e33	−0.297008	−0.148504	−	0.988912i	$-0.547446\pi$
$29$	−6.90432e33	−0.297008	−0.148504	+	0.988912i	$0.547446\pi$
$30$	−3.41336e34	−0.661960
$31$	−1.79630e35	−1.61205	−0.806025	−	0.591882i	$-0.798385\pi$
$31$	−1.79630e35	−1.61205	−0.806025	+	0.591882i	$0.798385\pi$
$32$	9.98970e35	4.25136
$33$	−4.10556e35	−0.847802
$34$	−7.90739e35	−0.809615
$35$	−1.77475e35	−0.0919471
$36$	−3.94820e36	−1.05509
$37$	−2.68894e36	−0.377434	−0.188717	−	0.982032i	$-0.560433\pi$
$37$	−2.68894e36	−0.377434	−0.188717	+	0.982032i	$0.560433\pi$
$38$	2.30836e37	1.73137
$39$	2.02715e36	0.0825786
$40$	−6.67160e37	−1.49906
$41$	1.17249e38	1.47465	0.737325	−	0.675538i	$-0.236088\pi$
$41$	1.17249e38	1.47465	0.737325	+	0.675538i	$0.236088\pi$
$42$	4.57376e37	0.326524
$43$	1.58085e38	0.649204	0.324602	−	0.945851i	$-0.394770\pi$
$43$	1.58085e38	0.649204	0.324602	+	0.945851i	$0.394770\pi$
$44$	−1.25208e39	−2.99566
$45$	1.15938e38	0.163581
$46$	1.19497e39	1.00588
$47$	−1.34555e39	−0.683282	−0.341641	−	0.939831i	$-0.610983\pi$
$47$	−1.34555e39	−0.683282	−0.341641	+	0.939831i	$0.610983\pi$
$48$	1.01053e40	3.12882
$49$	−5.00553e39	−0.954645
$50$	−1.33420e40	−1.58280
$51$	−4.40298e39	−0.327980
$52$	6.18221e39	0.291787
$53$	4.68526e40	1.41335	0.706677	−	0.707536i	$-0.250193\pi$
$53$	4.68526e40	1.41335	0.706677	+	0.707536i	$0.250193\pi$
$54$	−1.08739e41	−2.11413
$55$	3.67670e40	0.464446
$56$	8.93968e40	0.739440
$57$	1.28534e41	0.701387
$58$	−1.59347e41	−0.577811
$59$	3.84916e41	0.933993	0.466997	−	0.884259i	$-0.345336\pi$
$59$	3.84916e41	0.933993	0.466997	+	0.884259i	$0.345336\pi$
$60$	−5.79633e41	−0.947542
$61$	4.37844e41	0.485365	0.242683	−	0.970106i	$-0.421973\pi$
$61$	4.37844e41	0.485365	0.242683	+	0.970106i	$0.421973\pi$
$62$	−4.14573e42	−3.13615
$63$	−1.55353e41	−0.0806893
$64$	1.19887e43	4.30074
$65$	−1.81540e41	−0.0452385
$66$	−9.47534e42	−1.64935
$67$	4.64892e42	0.568321	0.284161	−	0.958777i	$-0.408285\pi$
$67$	4.64892e42	0.568321	0.284161	+	0.958777i	$0.408285\pi$
$68$	−1.34278e43	−1.15890
$69$	6.65378e42	0.407488
$70$	−4.09600e42	−0.178878
$71$	1.91856e43	0.600349	0.300175	−	0.953884i	$-0.402955\pi$
$71$	1.91856e43	0.600349	0.300175	+	0.953884i	$0.402955\pi$
$72$	−5.83999e43	−1.31552
$73$	8.25143e43	1.34413	0.672066	−	0.740491i	$-0.265407\pi$
$73$	8.25143e43	1.34413	0.672066	+	0.740491i	$0.265407\pi$
$74$	−6.20589e43	−0.734275
$75$	−7.42908e43	−0.641203
$76$	3.91990e44	2.47831
$77$	−4.92663e43	−0.229096
$78$	4.67852e43	0.160652
$79$	−5.45765e44	−1.38921	−0.694607	−	0.719389i	$-0.744422\pi$
$79$	−5.45765e44	−1.38921	−0.694607	+	0.719389i	$0.744422\pi$
$80$	−9.04975e44	−1.71404
$81$	−3.37621e44	−0.477564
$82$	2.70603e45	2.86885
$83$	−1.02727e45	−0.819125	−0.409563	−	0.912282i	$-0.634319\pi$
$83$	−1.02727e45	−0.819125	−0.409563	+	0.912282i	$0.634319\pi$
$84$	7.76685e44	0.467392
$85$	3.94306e44	0.179675
$86$	3.64849e45	1.26299
$87$	−8.87272e44	−0.234075
$88$	−1.85201e46	−3.73509
$89$	1.06667e46	1.64954	0.824771	−	0.565467i	$-0.191304\pi$
$89$	1.06667e46	1.64954	0.824771	+	0.565467i	$0.191304\pi$
$90$	2.67578e45	0.318237
$91$	2.43256e44	0.0223147
$92$	2.02921e46	1.43984
$93$	−2.30842e46	−1.27047
$94$	−3.10543e46	−1.32928
$95$	−1.15107e46	−0.384236
$96$	1.28377e47	3.35054
$97$	3.72976e46	0.763037	0.381518	−	0.924361i	$-0.375401\pi$
$97$	3.72976e46	0.763037	0.381518	+	0.924361i	$0.375401\pi$
$98$	−1.15524e47	−1.85721
$99$	3.21841e46	0.407581
$100$	−2.26565e47	−2.26565
$101$	9.27720e46	0.734285	0.367142	−	0.930165i	$-0.380336\pi$
$101$	9.27720e46	0.734285	0.367142	+	0.930165i	$0.380336\pi$
$102$	−1.01618e47	−0.638065
$103$	1.00960e47	0.504051	0.252026	−	0.967721i	$-0.418903\pi$
$103$	1.00960e47	0.504051	0.252026	+	0.967721i	$0.418903\pi$
$104$	9.14444e46	0.363809
$105$	−2.28072e46	−0.0724643
$106$	1.08133e48	2.74960
$107$	1.99211e47	0.406252	0.203126	−	0.979153i	$-0.434890\pi$
$107$	1.99211e47	0.406252	0.203126	+	0.979153i	$0.434890\pi$
$108$	−1.84653e48	−3.02621
$109$	−6.24516e47	−0.824177	−0.412089	−	0.911144i	$-0.635201\pi$
$109$	−6.24516e47	−0.824177	−0.412089	+	0.911144i	$0.635201\pi$
$110$	8.48558e47	0.903553
$111$	−3.45555e47	−0.297459
$112$	1.21263e48	0.845483
$113$	−2.17631e48	−1.23134	−0.615669	−	0.788005i	$-0.711114\pi$
$113$	−2.17631e48	−1.23134	−0.615669	+	0.788005i	$0.711114\pi$
$114$	2.96647e48	1.36451
$115$	−5.95875e47	−0.223232
$116$	−2.70592e48	−0.827089
$117$	−1.58911e47	−0.0396996
$118$	8.88360e48	1.81703
$119$	−5.28354e47	−0.0886280
$120$	−8.57366e48	−1.18143
$121$	1.38664e48	0.157220
$122$	1.01051e49	0.944249
$123$	1.50677e49	1.16219
$124$	−7.04000e49	−4.48914
$125$	1.48304e49	0.783011
$126$	−3.58544e48	−0.156976
$127$	−1.42624e49	−0.518568	−0.259284	−	0.965801i	$-0.583487\pi$
$127$	−1.42624e49	−0.518568	−0.259284	+	0.965801i	$0.583487\pi$
$128$	1.36099e50	4.11547
$129$	2.03154e49	0.511644
$130$	−4.18982e48	−0.0880088
$131$	−7.28871e49	−1.27872	−0.639359	−	0.768908i	$-0.720800\pi$
$131$	−7.28871e49	−1.27872	−0.639359	+	0.768908i	$0.720800\pi$
$132$	−1.60904e50	−2.36091
$133$	1.54239e49	0.189531
$134$	1.07294e50	1.10564
$135$	5.42232e49	0.469182
$136$	−1.98618e50	−1.44495
$137$	2.99893e49	0.183668	0.0918338	−	0.995774i	$-0.470727\pi$
$137$	2.99893e49	0.183668	0.0918338	+	0.995774i	$0.470727\pi$
$138$	1.53565e50	0.792743
$139$	1.25821e50	0.548159	0.274079	−	0.961707i	$-0.411627\pi$
$139$	1.25821e50	0.548159	0.274079	+	0.961707i	$0.411627\pi$
$140$	−6.95555e49	−0.256049
$141$	−1.72916e50	−0.538501
$142$	4.42790e50	1.16794
$143$	−5.03948e49	−0.112717
$144$	−7.92171e50	−1.50418
$145$	7.94590e49	0.128232
$146$	1.90437e51	2.61493
$147$	−6.43259e50	−0.752365
$148$	−1.05384e51	−1.05106
$149$	−1.60599e51	−1.36730	−0.683652	−	0.729809i	$-0.739609\pi$
$149$	−1.60599e51	−1.36730	−0.683652	+	0.729809i	$0.739609\pi$
$150$	−1.71458e51	−1.24742
$151$	2.76267e49	0.0171938	0.00859689	−	0.999963i	$-0.497263\pi$
$151$	2.76267e49	0.0171938	0.00859689	+	0.999963i	$0.497263\pi$
$152$	5.79813e51	3.09004
$153$	3.45156e50	0.157676
$154$	−1.13703e51	−0.445693
$155$	2.06729e51	0.695995
$156$	7.94474e50	0.229960
$157$	3.26071e51	0.812214	0.406107	−	0.913825i	$-0.366886\pi$
$157$	3.26071e51	0.812214	0.406107	+	0.913825i	$0.366886\pi$
$158$	−1.25959e52	−2.70263
$159$	6.02102e51	1.11388
$160$	−1.14968e52	−1.83551
$161$	7.98448e50	0.110113
$162$	−7.79206e51	−0.929072
$163$	−1.71469e51	−0.176920	−0.0884602	−	0.996080i	$-0.528195\pi$
$163$	−1.71469e51	−0.176920	−0.0884602	+	0.996080i	$0.528195\pi$
$164$	4.59520e52	4.10652
$165$	4.72492e51	0.366034
$166$	−2.37087e52	−1.59356
$167$	−1.35054e52	−0.788264	−0.394132	−	0.919054i	$-0.628955\pi$
$167$	−1.35054e52	−0.788264	−0.394132	+	0.919054i	$0.628955\pi$
$168$	1.14884e52	0.582760
$169$	−2.24152e52	−0.989021
$170$	9.10030e51	0.349548
$171$	−1.00759e52	−0.337192
$172$	6.19562e52	1.80787
$173$	9.07124e51	0.230985	0.115492	−	0.993308i	$-0.463155\pi$
$173$	9.07124e51	0.230985	0.115492	+	0.993308i	$0.463155\pi$
$174$	−2.04776e52	−0.455378
$175$	−8.91484e51	−0.173268
$176$	−2.51218e53	−4.27073
$177$	4.94655e52	0.736089
$178$	2.46179e53	3.20908
$179$	−2.83103e52	−0.323518	−0.161759	−	0.986830i	$-0.551717\pi$
$179$	−2.83103e52	−0.323518	−0.161759	+	0.986830i	$0.551717\pi$
$180$	4.54383e52	0.455531
$181$	−7.28434e52	−0.641127	−0.320563	−	0.947227i	$-0.603872\pi$
$181$	−7.28434e52	−0.641127	−0.320563	+	0.947227i	$0.603872\pi$
$182$	5.61418e51	0.0434119
$183$	5.62672e52	0.382521
$184$	3.00151e53	1.79523
$185$	3.09460e52	0.162955
$186$	−5.32767e53	−2.47163
$187$	1.09458e53	0.447681
$188$	−5.27344e53	−1.90276
$189$	−7.26569e52	−0.231433
$190$	−2.65660e53	−0.747509
$191$	2.15414e53	0.535785	0.267893	−	0.963449i	$-0.413673\pi$
$191$	2.15414e53	0.535785	0.267893	+	0.963449i	$0.413673\pi$
$192$	1.54067e54	3.38945
$193$	−4.58281e53	−0.892351	−0.446175	−	0.894946i	$-0.647214\pi$
$193$	−4.58281e53	−0.892351	−0.446175	+	0.894946i	$0.647214\pi$
$194$	8.60804e53	1.48444
$195$	−2.33296e52	−0.0356529
$196$	−1.96175e54	−2.65844
$197$	2.29005e53	0.275353	0.137676	−	0.990477i	$-0.456037\pi$
$197$	2.29005e53	0.275353	0.137676	+	0.990477i	$0.456037\pi$
$198$	7.42786e53	0.792924
$199$	1.26295e54	1.19767	0.598835	−	0.800872i	$-0.295630\pi$
$199$	1.26295e54	1.19767	0.598835	+	0.800872i	$0.295630\pi$
$200$	−3.35125e54	−2.82489
$201$	5.97431e53	0.447899
$202$	2.14111e54	1.42851
$203$	−1.06472e53	−0.0632525
$204$	−1.72560e54	−0.913339
$205$	−1.34937e54	−0.636673
$206$	2.33009e54	0.980602
$207$	−5.21599e53	−0.195900
$208$	1.24040e54	0.415983
$209$	−3.19534e54	−0.957368
$210$	−5.26376e53	−0.140975
$211$	−4.97549e54	−1.19178	−0.595892	−	0.803064i	$-0.703201\pi$
$211$	−4.97549e54	−1.19178	−0.595892	+	0.803064i	$0.703201\pi$
$212$	1.83624e55	3.93582
$213$	2.46554e54	0.473141
$214$	4.59766e54	0.790339
$215$	−1.81934e54	−0.280291
$216$	−2.73130e55	−3.77318
$217$	−2.77008e54	−0.343312
$218$	−1.44134e55	−1.60339
$219$	1.06039e55	1.05932
$220$	1.44096e55	1.29336
$221$	−5.40455e53	−0.0436055
$222$	−7.97518e54	−0.578689
$223$	2.79892e55	1.82737	0.913686	−	0.406421i	$-0.133223\pi$
$223$	2.79892e55	1.82737	0.913686	+	0.406421i	$0.133223\pi$
$224$	1.54052e55	0.905396
$225$	5.82376e54	0.308258
$226$	−5.02277e55	−2.39549
$227$	1.40478e55	0.603949	0.301974	−	0.953316i	$-0.402354\pi$
$227$	1.40478e55	0.603949	0.301974	+	0.953316i	$0.402354\pi$
$228$	5.03745e55	1.95318
$229$	−4.09641e55	−1.43308	−0.716539	−	0.697547i	$-0.754275\pi$
$229$	−4.09641e55	−1.43308	−0.716539	+	0.697547i	$0.754275\pi$
$230$	−1.37524e55	−0.434284
$231$	−6.33120e54	−0.180553
$232$	−4.00247e55	−1.03124
$233$	−1.21897e55	−0.283876	−0.141938	−	0.989876i	$-0.545333\pi$
$233$	−1.21897e55	−0.283876	−0.141938	+	0.989876i	$0.545333\pi$
$234$	−3.66756e54	−0.0772333
$235$	1.54854e55	0.295004
$236$	1.50855e56	2.60093
$237$	−7.01362e55	−1.09485
$238$	−1.21940e55	−0.172421
$239$	6.34948e55	0.813556	0.406778	−	0.913527i	$-0.366652\pi$
$239$	6.34948e55	0.813556	0.406778	+	0.913527i	$0.366652\pi$
$240$	−1.16298e56	−1.35085
$241$	−1.11357e56	−1.17305	−0.586525	−	0.809931i	$-0.699504\pi$
$241$	−1.11357e56	−1.17305	−0.586525	+	0.809931i	$0.699504\pi$
$242$	3.20027e55	0.305862
$243$	8.18866e55	0.710339
$244$	1.71599e56	1.35162
$245$	5.76066e55	0.412164
$246$	3.47751e56	2.26096
$247$	1.57772e55	0.0932506
$248$	−1.04132e57	−5.59721
$249$	−1.32014e56	−0.645560
$250$	3.42276e56	1.52330
$251$	1.81960e56	0.737299	0.368649	−	0.929569i	$-0.379820\pi$
$251$	1.81960e56	0.737299	0.368649	+	0.929569i	$0.379820\pi$
$252$	−6.08854e55	−0.224699
$253$	−1.65413e56	−0.556207
$254$	−3.29167e56	−1.00884
$255$	5.06721e55	0.141604
$256$	1.45380e57	3.70566
$257$	−3.46416e56	−0.805694	−0.402847	−	0.915267i	$-0.631979\pi$
$257$	−3.46416e56	−0.805694	−0.402847	+	0.915267i	$0.631979\pi$
$258$	4.68866e56	0.995373
$259$	−4.14663e55	−0.0803806
$260$	−7.11486e55	−0.125977
$261$	6.95545e55	0.112531
$262$	−1.68218e57	−2.48767
$263$	1.25535e57	1.69748	0.848738	−	0.528814i	$-0.177363\pi$
$263$	1.25535e57	1.69748	0.848738	+	0.528814i	$0.177363\pi$
$264$	−2.38001e57	−2.94366
$265$	−5.39208e56	−0.610209
$266$	3.55974e56	0.368722
$267$	1.37077e57	1.30002
$268$	1.82199e57	1.58263
$269$	−2.60597e55	−0.0207391	−0.0103696	−	0.999946i	$-0.503301\pi$
$269$	−2.60597e55	−0.0207391	−0.0103696	+	0.999946i	$0.503301\pi$
$270$	1.25143e57	0.912766
$271$	−1.42492e57	−0.952822	−0.476411	−	0.879223i	$-0.658063\pi$
$271$	−1.42492e57	−0.952822	−0.476411	+	0.879223i	$0.658063\pi$
$272$	−2.69417e57	−1.65217
$273$	3.12608e55	0.0175864
$274$	6.92132e56	0.357314
$275$	1.84686e57	0.875219
$276$	2.60773e57	1.13475
$277$	−3.96329e57	−1.58409	−0.792047	−	0.610461i	$-0.790984\pi$
$277$	−3.96329e57	−1.58409	−0.792047	+	0.610461i	$0.790984\pi$
$278$	2.90387e57	1.06641
$279$	1.80960e57	0.610779
$280$	−1.02883e57	−0.319250
$281$	−4.27684e57	−1.22046	−0.610231	−	0.792223i	$-0.708924\pi$
$281$	−4.27684e57	−1.22046	−0.610231	+	0.792223i	$0.708924\pi$
$282$	−3.99078e57	−1.04762
$283$	−9.57574e56	−0.231308	−0.115654	−	0.993290i	$-0.536896\pi$
$283$	−9.57574e56	−0.231308	−0.115654	+	0.993290i	$0.536896\pi$
$284$	7.51917e57	1.67182
$285$	−1.47924e57	−0.302820
$286$	−1.16308e57	−0.219284
$287$	1.80811e57	0.314050
$288$	−1.00637e58	−1.61077
$289$	−5.60409e57	−0.826811
$290$	1.83386e57	0.249467
$291$	4.79311e57	0.601357
$292$	3.23388e58	3.74306
$293$	1.40107e58	1.49648	0.748241	−	0.663427i	$-0.230899\pi$
$293$	1.40107e58	1.49648	0.748241	+	0.663427i	$0.230899\pi$
$294$	−1.48460e58	−1.46368
$295$	−4.42985e57	−0.403247
$296$	−1.55880e58	−1.31049
$297$	1.50522e58	1.16902
$298$	−3.70651e58	−2.66001
$299$	8.16736e56	0.0541762
$300$	−2.91158e58	−1.78558
$301$	2.43784e57	0.138258
$302$	6.37606e56	0.0334495
$303$	1.19221e58	0.578697
$304$	7.86492e58	3.53318
$305$	−5.03897e57	−0.209554
$306$	7.96596e57	0.306750
$307$	−4.70339e58	−1.67749	−0.838743	−	0.544527i	$-0.816709\pi$
$307$	−4.70339e58	−1.67749	−0.838743	+	0.544527i	$0.816709\pi$
$308$	−1.93083e58	−0.637974
$309$	1.29743e58	0.397248
$310$	4.77116e58	1.35402
$311$	−2.66280e58	−0.700600	−0.350300	−	0.936638i	$-0.613920\pi$
$311$	−2.66280e58	−0.700600	−0.350300	+	0.936638i	$0.613920\pi$
$312$	1.17515e58	0.286721
$313$	−5.63252e58	−1.27471	−0.637354	−	0.770571i	$-0.719971\pi$
$313$	−5.63252e58	−1.27471	−0.637354	+	0.770571i	$0.719971\pi$
$314$	7.52550e58	1.58012
$315$	1.78789e57	0.0348372
$316$	−2.13895e59	−3.86860
$317$	9.99715e58	1.67874	0.839371	−	0.543560i	$-0.182924\pi$
$317$	9.99715e58	1.67874	0.839371	+	0.543560i	$0.182924\pi$
$318$	1.38961e59	2.16698
$319$	2.20575e58	0.319503
$320$	−1.37973e59	−1.85682
$321$	2.56006e58	0.320171
$322$	1.84276e58	0.214218
$323$	−3.42682e58	−0.370366
$324$	−1.32319e59	−1.32989
$325$	−9.11903e57	−0.0852491
$326$	−3.95740e58	−0.344188
$327$	−8.02563e58	−0.649542
$328$	6.79700e59	5.12014
$329$	−2.07498e58	−0.145516
$330$	1.09048e59	0.712098
$331$	−1.86524e58	−0.113443	−0.0567215	−	0.998390i	$-0.518065\pi$
$331$	−1.86524e58	−0.113443	−0.0567215	+	0.998390i	$0.518065\pi$
$332$	−4.02606e59	−2.28105
$333$	2.70886e58	0.143004
$334$	−3.11696e59	−1.53352
$335$	−5.35025e58	−0.245370
$336$	1.55835e59	0.666333
$337$	2.11425e59	0.843050	0.421525	−	0.906817i	$-0.361495\pi$
$337$	2.11425e59	0.843050	0.421525	+	0.906817i	$0.361495\pi$
$338$	−5.17328e59	−1.92408
$339$	−2.79677e59	−0.970429
$340$	1.54535e59	0.500349
$341$	5.73871e59	1.73415
$342$	−2.32546e59	−0.655986
$343$	−1.58048e59	−0.416273
$344$	9.16427e59	2.25411
$345$	−7.65757e58	−0.175931
$346$	2.09358e59	0.449367
$347$	1.60147e59	0.321200	0.160600	−	0.987020i	$-0.448657\pi$
$347$	1.60147e59	0.321200	0.160600	+	0.987020i	$0.448657\pi$
$348$	−3.47737e59	−0.651837
$349$	8.79943e59	1.54190	0.770951	−	0.636894i	$-0.219781\pi$
$349$	8.79943e59	1.54190	0.770951	+	0.636894i	$0.219781\pi$
$350$	−2.05748e59	−0.337083
$351$	−7.43211e58	−0.113866
$352$	−3.19145e60	−4.57337
$353$	−9.28528e59	−1.24477	−0.622386	−	0.782711i	$-0.713836\pi$
$353$	−9.28528e59	−1.24477	−0.622386	+	0.782711i	$0.713836\pi$
$354$	1.14163e60	1.43202
$355$	−2.20799e59	−0.259198
$356$	4.18045e60	4.59354
$357$	−6.78986e58	−0.0698486
$358$	−6.53382e59	−0.629385
$359$	−1.74133e60	−1.57095	−0.785475	−	0.618893i	$-0.787581\pi$
$359$	−1.74133e60	−1.57095	−0.785475	+	0.618893i	$0.787581\pi$
$360$	6.72102e59	0.567971
$361$	−2.62675e59	−0.207970
$362$	−1.68118e60	−1.24727
$363$	1.78197e59	0.123906
$364$	9.53363e58	0.0621406
$365$	−9.49624e59	−0.580323
$366$	1.29861e60	0.744171
$367$	2.18975e60	1.17691	0.588453	−	0.808531i	$-0.299737\pi$
$367$	2.18975e60	1.17691	0.588453	+	0.808531i	$0.299737\pi$
$368$	4.07142e60	2.05269
$369$	−1.18118e60	−0.558721
$370$	7.14212e59	0.317020
$371$	7.22517e59	0.300996
$372$	−9.04709e60	−3.53793
$373$	1.69293e60	0.621556	0.310778	−	0.950482i	$-0.399410\pi$
$373$	1.69293e60	0.621556	0.310778	+	0.950482i	$0.399410\pi$
$374$	2.52621e60	0.870937
$375$	1.90585e60	0.617099
$376$	−7.80022e60	−2.37243
$377$	−1.08911e59	−0.0311206
$378$	−1.67687e60	−0.450238
$379$	4.02001e60	1.01439	0.507196	−	0.861831i	$-0.330682\pi$
$379$	4.02001e60	1.01439	0.507196	+	0.861831i	$0.330682\pi$
$380$	−4.51126e60	−1.07000
$381$	−1.83286e60	−0.408688
$382$	4.97162e60	1.04234
$383$	2.58725e60	0.510113	0.255057	−	0.966926i	$-0.417906\pi$
$383$	2.58725e60	0.510113	0.255057	+	0.966926i	$0.417906\pi$
$384$	1.74900e61	3.24344
$385$	5.66987e59	0.0989113
$386$	−1.05768e61	−1.73602
$387$	−1.59256e60	−0.245973
$388$	1.46176e61	2.12486
$389$	−7.66990e60	−1.04948	−0.524740	−	0.851263i	$-0.675837\pi$
$389$	−7.66990e60	−1.04948	−0.524740	+	0.851263i	$0.675837\pi$
$390$	−5.38432e59	−0.0693606
$391$	−1.77396e60	−0.215174
$392$	−2.90173e61	−3.31463
$393$	−9.36670e60	−1.00777
$394$	5.28529e60	0.535683
$395$	6.28100e60	0.599787
$396$	1.26135e61	1.13501
$397$	2.69403e60	0.228468	0.114234	−	0.993454i	$-0.463559\pi$
$397$	2.69403e60	0.228468	0.114234	+	0.993454i	$0.463559\pi$
$398$	2.91479e61	2.33000
$399$	1.98212e60	0.149372
$400$	−4.54583e61	−3.23001
$401$	−8.61448e60	−0.577213	−0.288607	−	0.957448i	$-0.593192\pi$
$401$	−8.61448e60	−0.577213	−0.288607	+	0.957448i	$0.593192\pi$
$402$	1.37883e61	0.871362
$403$	−2.83353e60	−0.168912
$404$	3.63589e61	2.04479
$405$	3.88554e60	0.206186
$406$	−2.45730e60	−0.123054
$407$	8.59048e60	0.406021
$408$	−2.55243e61	−1.13878
$409$	−4.89023e60	−0.205983	−0.102992	−	0.994682i	$-0.532841\pi$
$409$	−4.89023e60	−0.205983	−0.102992	+	0.994682i	$0.532841\pi$
$410$	−3.11426e61	−1.23861
$411$	3.85391e60	0.144750
$412$	3.95680e61	1.40365
$413$	5.93581e60	0.198909
$414$	−1.20382e61	−0.381111
$415$	1.18225e61	0.353653
$416$	1.57580e61	0.445460
$417$	1.61693e61	0.432009
$418$	−7.37462e61	−1.86250
$419$	−4.08353e60	−0.0975003	−0.0487501	−	0.998811i	$-0.515524\pi$
$419$	−4.08353e60	−0.0975003	−0.0487501	+	0.998811i	$0.515524\pi$
$420$	−8.93855e60	−0.201794
$421$	−8.09919e61	−1.72907	−0.864534	−	0.502574i	$-0.832386\pi$
$421$	−8.09919e61	−1.72907	−0.864534	+	0.502574i	$0.832386\pi$
$422$	−1.14831e62	−2.31855
$423$	1.35551e61	0.258884
$424$	2.71607e62	4.90731
$425$	1.98066e61	0.338586
$426$	5.69029e61	0.920468
$427$	6.75202e60	0.103366
$428$	7.80744e61	1.13131
$429$	−6.47622e60	−0.0888332
$430$	−4.19890e61	−0.545289
$431$	5.41910e61	0.666364	0.333182	−	0.942863i	$-0.391878\pi$
$431$	5.41910e61	0.666364	0.333182	+	0.942863i	$0.391878\pi$
$432$	−3.70490e62	−4.31428
$433$	1.10085e62	1.21412	0.607060	−	0.794656i	$-0.292349\pi$
$433$	1.10085e62	1.21412	0.607060	+	0.794656i	$0.292349\pi$
$434$	−6.39316e61	−0.667893
$435$	1.02113e61	0.101061
$436$	−2.44758e62	−2.29512
$437$	5.17861e61	0.460150
$438$	2.44731e62	2.06085
$439$	−1.32013e62	−1.05366	−0.526832	−	0.849969i	$-0.676620\pi$
$439$	−1.32013e62	−1.05366	−0.526832	+	0.849969i	$0.676620\pi$
$440$	2.13141e62	1.61261
$441$	5.04260e61	0.361699
$442$	−1.24733e61	−0.0848320
$443$	−8.89175e61	−0.573455	−0.286728	−	0.958012i	$-0.592567\pi$
$443$	−8.89175e61	−0.573455	−0.286728	+	0.958012i	$0.592567\pi$
$444$	−1.35429e62	−0.828346
$445$	−1.22758e62	−0.712181
$446$	6.45973e62	3.55504
$447$	−2.06385e62	−1.07758
$448$	1.84879e62	0.915911
$449$	9.45855e61	0.444668	0.222334	−	0.974971i	$-0.428633\pi$
$449$	9.45855e61	0.444668	0.222334	+	0.974971i	$0.428633\pi$
$450$	1.34408e62	0.599698
$451$	−3.74581e62	−1.58634
$452$	−8.52933e62	−3.42896
$453$	3.55030e60	0.0135506
$454$	3.24213e62	1.17495
$455$	−2.79954e60	−0.00963426
$456$	7.45116e62	2.43529
$457$	3.37293e62	1.04707	0.523536	−	0.852003i	$-0.324612\pi$
$457$	3.37293e62	1.04707	0.523536	+	0.852003i	$0.324612\pi$
$458$	−9.45424e62	−2.78797
$459$	1.61426e62	0.452246
$460$	−2.33534e62	−0.621642
$461$	4.97092e62	1.25738	0.628688	−	0.777658i	$-0.283592\pi$
$461$	4.97092e62	1.25738	0.628688	+	0.777658i	$0.283592\pi$
$462$	−1.46120e62	−0.351255
$463$	−4.42973e62	−1.01210	−0.506051	−	0.862504i	$-0.668895\pi$
$463$	−4.42973e62	−1.01210	−0.506051	+	0.862504i	$0.668895\pi$
$464$	−5.42918e62	−1.17913
$465$	2.65667e62	0.548520
$466$	−2.81330e62	−0.552264
$467$	7.17000e62	1.33836	0.669179	−	0.743101i	$-0.266646\pi$
$467$	7.17000e62	1.33836	0.669179	+	0.743101i	$0.266646\pi$
$468$	−6.22800e61	−0.110553
$469$	7.16912e61	0.121033
$470$	3.57392e62	0.573912
$471$	4.19033e62	0.640114
$472$	2.23138e63	3.24292
$473$	−5.05040e62	−0.698376
$474$	−1.61869e63	−2.12997
$475$	−5.78202e62	−0.724069
$476$	−2.07071e62	−0.246806
$477$	−4.71996e62	−0.535497
$478$	1.46542e63	1.58273
$479$	−1.03149e62	−0.106067	−0.0530337	−	0.998593i	$-0.516889\pi$
$479$	−1.03149e62	−0.106067	−0.0530337	+	0.998593i	$0.516889\pi$
$480$	−1.47744e63	−1.44658
$481$	−4.24161e61	−0.0395477
$482$	−2.57004e63	−2.28210
$483$	1.02608e62	0.0867811
$484$	5.43448e62	0.437816
$485$	−4.29244e62	−0.329438
$486$	1.88989e63	1.38192
$487$	−2.41720e61	−0.0168415	−0.00842076	−	0.999965i	$-0.502680\pi$
$487$	−2.41720e61	−0.0168415	−0.00842076	+	0.999965i	$0.502680\pi$
$488$	2.53821e63	1.68524
$489$	−2.20355e62	−0.139433
$490$	1.32952e63	0.801840
$491$	−1.48334e63	−0.852760	−0.426380	−	0.904544i	$-0.640211\pi$
$491$	−1.48334e63	−0.852760	−0.426380	+	0.904544i	$0.640211\pi$
$492$	5.90528e63	3.23639
$493$	2.36554e62	0.123603
$494$	3.64127e62	0.181414
$495$	−3.70394e62	−0.175971
$496$	−1.41251e64	−6.39989
$497$	2.95862e62	0.127854
$498$	−3.04680e63	−1.25590
$499$	3.58476e63	1.40960	0.704802	−	0.709404i	$-0.251036\pi$
$499$	3.58476e63	1.40960	0.704802	+	0.709404i	$0.251036\pi$
$500$	5.81230e63	2.18048
$501$	−1.73558e63	−0.621238
$502$	4.19951e63	1.43437
$503$	3.59373e63	1.17138	0.585691	−	0.810535i	$-0.300823\pi$
$503$	3.59373e63	1.17138	0.585691	+	0.810535i	$0.300823\pi$
$504$	−9.00589e62	−0.280162
$505$	−1.06768e63	−0.317024
$506$	−3.81761e63	−1.08207
$507$	−2.88057e63	−0.779457
$508$	−5.58969e63	−1.44408
$509$	1.51124e63	0.372790	0.186395	−	0.982475i	$-0.440320\pi$
$509$	1.51124e63	0.372790	0.186395	+	0.982475i	$0.440320\pi$
$510$	1.16948e63	0.275482
$511$	1.27246e63	0.286255
$512$	1.43986e64	3.09368
$513$	−4.71241e63	−0.967130
$514$	−7.99505e63	−1.56743
$515$	−1.16191e63	−0.217622
$516$	7.96197e63	1.42480
$517$	4.29868e63	0.735034
$518$	−9.57015e62	−0.156376
$519$	1.16574e63	0.182041
$520$	−1.05240e63	−0.157073
$521$	−5.89563e63	−0.841093	−0.420546	−	0.907271i	$-0.638162\pi$
$521$	−5.89563e63	−0.841093	−0.420546	+	0.907271i	$0.638162\pi$
$522$	1.60527e63	0.218923
$523$	1.19071e64	1.55245	0.776224	−	0.630457i	$-0.217132\pi$
$523$	1.19071e64	1.55245	0.776224	+	0.630457i	$0.217132\pi$
$524$	−2.85657e64	−3.56090
$525$	−1.14564e63	−0.136554
$526$	2.89725e64	3.30234
$527$	6.15444e63	0.670871
$528$	−3.22839e64	−3.36580
$529$	−7.34706e63	−0.732665
$530$	−1.24446e64	−1.18712
$531$	−3.87767e63	−0.353875
$532$	6.04490e63	0.527796
$533$	1.84952e63	0.154515
$534$	3.16364e64	2.52911
$535$	−2.29264e63	−0.175397
$536$	2.69500e64	1.97327
$537$	−3.63815e63	−0.254968
$538$	−6.01439e62	−0.0403467
$539$	1.59914e64	1.02695
$540$	2.12510e64	1.30655
$541$	−1.24707e64	−0.734101	−0.367051	−	0.930201i	$-0.619632\pi$
$541$	−1.24707e64	−0.734101	−0.367051	+	0.930201i	$0.619632\pi$
$542$	−3.28861e64	−1.85366
$543$	−9.36109e63	−0.505278
$544$	−3.42265e64	−1.76925
$545$	7.18730e63	0.355835
$546$	7.21477e62	0.0342134
$547$	−3.38744e64	−1.53876	−0.769378	−	0.638794i	$-0.779434\pi$
$547$	−3.38744e64	−1.53876	−0.769378	+	0.638794i	$0.779434\pi$
$548$	1.17533e64	0.511467
$549$	−4.41087e63	−0.183897
$550$	4.26244e64	1.70269
$551$	−6.90560e63	−0.264325
$552$	3.85723e64	1.41484
$553$	−8.41628e63	−0.295856
$554$	−9.14699e64	−3.08176
$555$	3.97686e63	0.128427
$556$	4.93115e64	1.52648
$557$	4.80284e64	1.42528	0.712641	−	0.701528i	$-0.247499\pi$
$557$	4.80284e64	1.42528	0.712641	+	0.701528i	$0.247499\pi$
$558$	4.17644e64	1.18823
$559$	2.49367e63	0.0680240
$560$	−1.39557e64	−0.365033
$561$	1.40664e64	0.352822
$562$	−9.87066e64	−2.37434
$563$	3.05103e64	0.703882	0.351941	−	0.936022i	$-0.385522\pi$
$563$	3.05103e64	0.703882	0.351941	+	0.936022i	$0.385522\pi$
$564$	−6.77688e64	−1.49958
$565$	2.50463e64	0.531624
$566$	−2.21002e64	−0.449997
$567$	−5.20647e63	−0.101705
$568$	1.11220e65	2.08448
$569$	7.49437e64	1.34771	0.673856	−	0.738863i	$-0.264637\pi$
$569$	7.49437e64	1.34771	0.673856	+	0.738863i	$0.264637\pi$
$570$	−3.41399e64	−0.589119
$571$	−5.47320e64	−0.906344	−0.453172	−	0.891423i	$-0.649708\pi$
$571$	−5.47320e64	−0.906344	−0.453172	+	0.891423i	$0.649708\pi$
$572$	−1.97506e64	−0.313887
$573$	2.76828e64	0.422257
$574$	4.17299e64	0.610967
$575$	−2.99317e64	−0.420666
$576$	−1.20775e65	−1.62948
$577$	−4.19523e63	−0.0543406	−0.0271703	−	0.999631i	$-0.508650\pi$
$577$	−4.19523e63	−0.0543406	−0.0271703	+	0.999631i	$0.508650\pi$
$578$	−1.29339e65	−1.60851
$579$	−5.88936e64	−0.703270
$580$	3.11414e64	0.357092
$581$	−1.58416e64	−0.174446
$582$	1.10622e65	1.16990
$583$	−1.49682e65	−1.52040
$584$	4.78340e65	4.66697
$585$	1.82884e63	0.0171401
$586$	3.23358e65	2.91132
$587$	3.17978e64	0.275043	0.137522	−	0.990499i	$-0.456086\pi$
$587$	3.17978e64	0.275043	0.137522	+	0.990499i	$0.456086\pi$
$588$	−2.52104e65	−2.09514
$589$	−1.79663e65	−1.43466
$590$	−1.02238e65	−0.784493
$591$	2.94294e64	0.217008
$592$	−2.11444e65	−1.49843
$593$	4.66511e64	0.317744	0.158872	−	0.987299i	$-0.449214\pi$
$593$	4.66511e64	0.317744	0.158872	+	0.987299i	$0.449214\pi$
$594$	3.47393e65	2.27426
$595$	6.08061e63	0.0382647
$596$	−6.29414e65	−3.80758
$597$	1.62301e65	0.943896
$598$	1.88497e64	0.105397
$599$	2.50137e65	1.34477	0.672384	−	0.740202i	$-0.265270\pi$
$599$	2.50137e65	1.34477	0.672384	+	0.740202i	$0.265270\pi$
$600$	−4.30668e65	−2.22632
$601$	4.33262e64	0.215377	0.107689	−	0.994185i	$-0.465655\pi$
$601$	4.33262e64	0.215377	0.107689	+	0.994185i	$0.465655\pi$
$602$	5.62636e64	0.268974
$603$	−4.68335e64	−0.215328
$604$	1.08274e64	0.0478802
$605$	−1.59583e64	−0.0678789
$606$	2.75154e65	1.12582
$607$	−2.09462e64	−0.0824464	−0.0412232	−	0.999150i	$-0.513125\pi$
$607$	−2.09462e64	−0.0824464	−0.0412232	+	0.999150i	$0.513125\pi$
$608$	9.99156e65	3.78355
$609$	−1.36827e64	−0.0498499
$610$	−1.16296e65	−0.407675
$611$	−2.12251e64	−0.0715946
$612$	1.35273e65	0.439088
$613$	−4.02606e65	−1.25765	−0.628824	−	0.777548i	$-0.716463\pi$
$613$	−4.02606e65	−1.25765	−0.628824	+	0.777548i	$0.716463\pi$
$614$	−1.08551e66	−3.26345
$615$	−1.73408e65	−0.501768
$616$	−2.85600e65	−0.795447
$617$	4.25894e65	1.14183	0.570914	−	0.821010i	$-0.306589\pi$
$617$	4.25894e65	1.14183	0.570914	+	0.821010i	$0.306589\pi$
$618$	2.99439e65	0.772821
$619$	3.05847e65	0.759931	0.379965	−	0.925001i	$-0.375936\pi$
$619$	3.05847e65	0.759931	0.379965	+	0.925001i	$0.375936\pi$
$620$	8.10206e65	1.93816
$621$	−2.43947e65	−0.561878
$622$	−6.14557e65	−1.36298
$623$	1.64491e65	0.351296
$624$	1.59404e65	0.327840
$625$	2.40084e65	0.475535
$626$	−1.29995e66	−2.47987
$627$	−4.10632e65	−0.754511
$628$	1.27793e66	2.26181
$629$	9.21280e64	0.157073
$630$	4.12634e64	0.0677738
$631$	6.21302e65	0.983134	0.491567	−	0.870840i	$-0.336424\pi$
$631$	6.21302e65	0.983134	0.491567	+	0.870840i	$0.336424\pi$
$632$	−3.16383e66	−4.82350
$633$	−6.39398e65	−0.939257
$634$	2.30727e66	3.26589
$635$	1.64141e65	0.223889
$636$	2.35974e66	3.10186
$637$	−7.89586e64	−0.100028
$638$	5.09072e65	0.621575
$639$	−1.93277e65	−0.227463
$640$	−1.56631e66	−1.77683
$641$	−6.05212e65	−0.661826	−0.330913	−	0.943661i	$-0.607357\pi$
$641$	−6.05212e65	−0.661826	−0.330913	+	0.943661i	$0.607357\pi$
$642$	5.90844e65	0.622873
$643$	8.65041e65	0.879183	0.439591	−	0.898198i	$-0.355123\pi$
$643$	8.65041e65	0.879183	0.439591	+	0.898198i	$0.355123\pi$
$644$	3.12926e65	0.306636
$645$	−2.33802e65	−0.220900
$646$	−7.90886e65	−0.720526
$647$	2.75625e65	0.242141	0.121070	−	0.992644i	$-0.461367\pi$
$647$	2.75625e65	0.242141	0.121070	+	0.992644i	$0.461367\pi$
$648$	−1.95721e66	−1.65815
$649$	−1.22971e66	−1.00474
$650$	−2.10461e65	−0.165847
$651$	−3.55982e65	−0.270567
$652$	−6.72018e65	−0.492677
$653$	−1.27020e66	−0.898282	−0.449141	−	0.893461i	$-0.648270\pi$
$653$	−1.27020e66	−0.898282	−0.449141	+	0.893461i	$0.648270\pi$
$654$	−1.85226e66	−1.26365
$655$	8.38828e65	0.552081
$656$	9.21985e66	5.85441
$657$	−8.31254e65	−0.509270
$658$	−4.78891e65	−0.283092
$659$	1.08832e66	0.620794	0.310397	−	0.950607i	$-0.399538\pi$
$659$	1.08832e66	0.620794	0.310397	+	0.950607i	$0.399538\pi$
$660$	1.85178e66	1.01931
$661$	1.19166e66	0.633020	0.316510	−	0.948589i	$-0.397489\pi$
$661$	1.19166e66	0.633020	0.316510	+	0.948589i	$0.397489\pi$
$662$	−4.30485e65	−0.220697
$663$	−6.94538e64	−0.0343659
$664$	−5.95515e66	−2.84409
$665$	−1.77508e65	−0.0818293
$666$	6.25186e65	0.278205
$667$	−3.57481e65	−0.153566
$668$	−5.29301e66	−2.19511
$669$	3.59689e66	1.44017
$670$	−1.23480e66	−0.477353
$671$	−1.39880e66	−0.522127
$672$	1.97972e66	0.713551
$673$	2.35019e66	0.817993	0.408997	−	0.912536i	$-0.365879\pi$
$673$	2.35019e66	0.817993	0.408997	+	0.912536i	$0.365879\pi$
$674$	4.87954e66	1.64010
$675$	2.72371e66	0.884144
$676$	−8.78491e66	−2.75417
$677$	−1.35609e66	−0.410633	−0.205316	−	0.978696i	$-0.565822\pi$
$677$	−1.35609e66	−0.410633	−0.205316	+	0.978696i	$0.565822\pi$
$678$	−6.45475e66	−1.88791
$679$	5.75169e65	0.162501
$680$	2.28581e66	0.623851
$681$	1.80528e66	0.475978
$682$	1.32446e67	3.37368
$683$	−2.30165e66	−0.566438	−0.283219	−	0.959055i	$-0.591402\pi$
$683$	−2.30165e66	−0.566438	−0.283219	+	0.959055i	$0.591402\pi$
$684$	−3.94893e66	−0.938991
$685$	−3.45135e65	−0.0792976
$686$	−3.64765e66	−0.809835
$687$	−5.26429e66	−1.12942
$688$	1.24309e67	2.57736
$689$	7.39066e65	0.148092
$690$	−1.76731e66	−0.342263
$691$	−8.06352e66	−1.50935	−0.754676	−	0.656098i	$-0.772206\pi$
$691$	−8.06352e66	−1.50935	−0.754676	+	0.656098i	$0.772206\pi$
$692$	3.55517e66	0.643232
$693$	4.96312e65	0.0868009
$694$	3.69608e66	0.624876
$695$	−1.44803e66	−0.236665
$696$	−5.14356e66	−0.812731
$697$	−4.01717e66	−0.613691
$698$	2.03085e67	2.99968
$699$	−1.56649e66	−0.223725
$700$	−3.49388e66	−0.482507
$701$	5.85991e66	0.782560	0.391280	−	0.920272i	$-0.372032\pi$
$701$	5.85991e66	0.782560	0.391280	+	0.920272i	$0.372032\pi$
$702$	−1.71528e66	−0.221520
$703$	−2.68944e66	−0.335901
$704$	−3.83009e67	−4.62648
$705$	1.99002e66	0.232495
$706$	−2.14298e67	−2.42163
$707$	1.43064e66	0.156378
$708$	1.93864e67	2.04982
$709$	1.17722e67	1.20413	0.602064	−	0.798448i	$-0.294345\pi$
$709$	1.17722e67	1.20413	0.602064	+	0.798448i	$0.294345\pi$
$710$	−5.09590e66	−0.504254
$711$	5.49808e66	0.526351
$712$	6.18352e67	5.72738
$713$	−9.30059e66	−0.833502
$714$	−1.56705e66	−0.135886
$715$	5.79974e65	0.0486649
$716$	−1.10953e67	−0.900913
$717$	8.15970e66	0.641171
$718$	−4.01888e67	−3.05619
$719$	1.34473e67	0.989709	0.494854	−	0.868976i	$-0.335221\pi$
$719$	1.34473e67	0.989709	0.494854	+	0.868976i	$0.335221\pi$
$720$	9.11678e66	0.649423
$721$	1.55691e66	0.107346
$722$	−6.06236e66	−0.404593
$723$	−1.43104e67	−0.924491
$724$	−2.85486e67	−1.78537
$725$	3.99135e66	0.241644
$726$	4.11266e66	0.241053
$727$	−6.52974e66	−0.370542	−0.185271	−	0.982687i	$-0.559316\pi$
$727$	−6.52974e66	−0.370542	−0.185271	+	0.982687i	$0.559316\pi$
$728$	1.41017e66	0.0774790
$729$	1.95002e67	1.03739
$730$	−2.19167e67	−1.12898
$731$	−5.41627e66	−0.270173
$732$	2.20521e67	1.06522
$733$	−4.16163e67	−1.94679	−0.973397	−	0.229127i	$-0.926413\pi$
$733$	−4.16163e67	−1.94679	−0.973397	+	0.229127i	$0.926413\pi$
$734$	5.05379e67	2.28960
$735$	7.40301e66	0.324830
$736$	5.17232e67	2.19815
$737$	−1.48521e67	−0.611367
$738$	−2.72607e67	−1.08696
$739$	1.83231e67	0.707709	0.353854	−	0.935301i	$-0.384871\pi$
$739$	1.83231e67	0.707709	0.353854	+	0.935301i	$0.384871\pi$
$740$	1.21283e67	0.453788
$741$	2.02752e66	0.0734917
$742$	1.66752e67	0.585571
$743$	−2.26817e67	−0.771681	−0.385840	−	0.922566i	$-0.626088\pi$
$743$	−2.26817e67	−0.771681	−0.385840	+	0.922566i	$0.626088\pi$
$744$	−1.33820e68	−4.41121
$745$	1.84827e67	0.590327
$746$	3.90716e67	1.20920
$747$	1.03488e67	0.310353
$748$	4.28984e67	1.24668
$749$	3.07205e66	0.0865178
$750$	4.39858e67	1.20053
$751$	3.95970e67	1.04743	0.523713	−	0.851895i	$-0.324546\pi$
$751$	3.95970e67	1.04743	0.523713	+	0.851895i	$0.324546\pi$
$752$	−1.05807e68	−2.71265
$753$	2.33836e67	0.581072
$754$	−2.51358e66	−0.0605433
$755$	−3.17945e65	−0.00742333
$756$	−2.84755e67	−0.644479
$757$	−3.90670e67	−0.857149	−0.428575	−	0.903506i	$-0.640984\pi$
$757$	−3.90670e67	−0.857149	−0.428575	+	0.903506i	$0.640984\pi$
$758$	9.27790e67	1.97344
$759$	−2.12571e67	−0.438352
$760$	−6.67284e67	−1.33411
$761$	−8.64597e67	−1.67600	−0.838001	−	0.545669i	$-0.816276\pi$
$761$	−8.64597e67	−1.67600	−0.838001	+	0.545669i	$0.816276\pi$
$762$	−4.23012e67	−0.795079
$763$	−9.63069e66	−0.175522
$764$	8.44246e67	1.49202
$765$	−3.97226e66	−0.0680760
$766$	5.97119e67	0.992395
$767$	6.07177e66	0.0978643
$768$	1.86828e68	2.92047
$769$	8.45845e67	1.28240	0.641198	−	0.767376i	$-0.278438\pi$
$769$	8.45845e67	1.28240	0.641198	+	0.767376i	$0.278438\pi$
$770$	1.30857e67	0.192426
$771$	−4.45179e67	−0.634975
$772$	−1.79608e68	−2.48496
$773$	−9.32204e67	−1.25110	−0.625551	−	0.780183i	$-0.715126\pi$
$773$	−9.32204e67	−1.25110	−0.625551	+	0.780183i	$0.715126\pi$
$774$	−3.67551e67	−0.478526
$775$	1.03843e68	1.31156
$776$	2.16217e68	2.64934
$777$	−5.32883e66	−0.0633487
$778$	−1.77016e68	−2.04170
$779$	1.17271e68	1.31238
$780$	−9.14329e66	−0.0992840
$781$	−6.12931e67	−0.645821
$782$	−4.09417e67	−0.418607
$783$	3.25299e67	0.322762
$784$	−3.93608e68	−3.78998
$785$	−3.75262e67	−0.350670
$786$	−2.16177e68	−1.96056
$787$	1.40543e68	1.23709	0.618547	−	0.785748i	$-0.287722\pi$
$787$	1.40543e68	1.23709	0.618547	+	0.785748i	$0.287722\pi$
$788$	8.97512e67	0.766786
$789$	1.61324e68	1.33780
$790$	1.44961e68	1.16685
$791$	−3.35610e67	−0.262233
$792$	1.86573e68	1.41516
$793$	6.90668e66	0.0508568
$794$	6.21764e67	0.444471
$795$	−6.92935e67	−0.480911
$796$	4.94970e68	3.33520
$797$	−6.41377e67	−0.419607	−0.209804	−	0.977744i	$-0.567282\pi$
$797$	−6.41377e67	−0.419607	−0.209804	+	0.977744i	$0.567282\pi$
$798$	4.57461e67	0.290593
$799$	4.61009e67	0.284355
$800$	−5.77500e68	−3.45889
$801$	−1.07457e68	−0.624984
$802$	−1.98816e68	−1.12293
$803$	−2.63612e68	−1.44594
$804$	2.34144e68	1.24728
$805$	−9.18902e66	−0.0475407
$806$	−6.53959e67	−0.328607
$807$	−3.34892e66	−0.0163447
$808$	5.37805e68	2.54951
$809$	7.54417e67	0.347393	0.173696	−	0.984799i	$-0.444429\pi$
$809$	7.54417e67	0.347393	0.173696	+	0.984799i	$0.444429\pi$
$810$	8.96757e67	0.401122
$811$	−2.25843e68	−0.981332	−0.490666	−	0.871348i	$-0.663247\pi$
$811$	−2.25843e68	−0.981332	−0.490666	+	0.871348i	$0.663247\pi$
$812$	−4.17282e67	−0.176142
$813$	−1.83116e68	−0.750928
$814$	1.98262e68	0.789890
$815$	1.97337e67	0.0763845
$816$	−3.46227e68	−1.30209
$817$	1.58114e68	0.577766
$818$	−1.12863e68	−0.400728
$819$	−2.45058e66	−0.00845467
$820$	−5.28843e68	−1.77297
$821$	2.57889e68	0.840174	0.420087	−	0.907484i	$-0.362000\pi$
$821$	2.57889e68	0.840174	0.420087	+	0.907484i	$0.362000\pi$
$822$	8.89457e67	0.281603
$823$	−8.83986e67	−0.271988	−0.135994	−	0.990710i	$-0.543423\pi$
$823$	−8.83986e67	−0.271988	−0.135994	+	0.990710i	$0.543423\pi$
$824$	5.85271e68	1.75012
$825$	2.37340e68	0.689768
$826$	1.36995e68	0.386965
$827$	−2.82593e68	−0.775856	−0.387928	−	0.921690i	$-0.626809\pi$
$827$	−2.82593e68	−0.775856	−0.387928	+	0.921690i	$0.626809\pi$
$828$	−2.04424e68	−0.545530
$829$	2.91606e68	0.756423	0.378211	−	0.925719i	$-0.376539\pi$
$829$	2.91606e68	0.756423	0.378211	+	0.925719i	$0.376539\pi$
$830$	2.72854e68	0.688012
$831$	−5.09321e68	−1.24844
$832$	1.89113e68	0.450634
$833$	1.71499e68	0.397286
$834$	3.73175e68	0.840448
$835$	1.55429e68	0.340329
$836$	−1.25231e69	−2.66602
$837$	8.46332e68	1.75183
$838$	−9.42450e67	−0.189681
$839$	9.42111e68	1.84372	0.921862	−	0.387518i	$-0.126667\pi$
$839$	9.42111e68	1.84372	0.921862	+	0.387518i	$0.126667\pi$
$840$	−1.32215e68	−0.251604
$841$	−4.92719e68	−0.911786
$842$	−1.86924e69	−3.36380
$843$	−5.49616e68	−0.961858
$844$	−1.94998e69	−3.31881
$845$	2.57968e68	0.427005
$846$	3.12843e68	0.503644
$847$	2.13835e67	0.0334825
$848$	3.68424e69	5.61106
$849$	−1.23058e68	−0.182296
$850$	4.57122e68	0.658700
$851$	−1.39224e68	−0.195150
$852$	9.66286e68	1.31757
$853$	−1.22430e69	−1.62400	−0.811999	−	0.583659i	$-0.801620\pi$
$853$	−1.22430e69	−1.62400	−0.811999	+	0.583659i	$0.801620\pi$
$854$	1.55832e68	0.201093
$855$	1.15960e68	0.145581
$856$	1.15484e69	1.41055
$857$	−4.45209e68	−0.529071	−0.264536	−	0.964376i	$-0.585219\pi$
$857$	−4.45209e68	−0.529071	−0.264536	+	0.964376i	$0.585219\pi$
$858$	−1.49467e68	−0.172820
$859$	−2.77149e68	−0.311799	−0.155899	−	0.987773i	$-0.549828\pi$
$859$	−2.77149e68	−0.311799	−0.155899	+	0.987773i	$0.549828\pi$
$860$	−7.13029e68	−0.780537
$861$	2.32359e68	0.247506
$862$	1.25069e69	1.29637
$863$	2.86475e68	0.288957	0.144479	−	0.989508i	$-0.453850\pi$
$863$	2.86475e68	0.288957	0.144479	+	0.989508i	$0.453850\pi$
$864$	−4.70669e69	−4.62000
$865$	−1.04397e68	−0.0997265
$866$	2.54068e69	2.36200
$867$	−7.20180e68	−0.651617
$868$	−1.08564e69	−0.956034
$869$	1.74358e69	1.49444
$870$	2.35669e68	0.196607
$871$	7.33333e67	0.0595490
$872$	−3.62035e69	−2.86163
$873$	−3.75739e68	−0.289102
$874$	1.19519e69	0.895194
$875$	2.28701e68	0.166755
$876$	4.15585e69	2.94994
$877$	−6.75109e68	−0.466534	−0.233267	−	0.972413i	$-0.574942\pi$
$877$	−6.75109e68	−0.466534	−0.233267	+	0.972413i	$0.574942\pi$
$878$	−3.04678e69	−2.04984
$879$	1.80052e69	1.17939
$880$	2.89116e69	1.84387
$881$	−2.56812e67	−0.0159471	−0.00797354	−	0.999968i	$-0.502538\pi$
$881$	−2.56812e67	−0.0159471	−0.00797354	+	0.999968i	$0.502538\pi$
$882$	1.16380e69	0.703665
$883$	−1.81395e69	−1.06794	−0.533972	−	0.845502i	$-0.679301\pi$
$883$	−1.81395e69	−1.06794	−0.533972	+	0.845502i	$0.679301\pi$
$884$	−2.11814e68	−0.121430
$885$	−5.69278e68	−0.317803
$886$	−2.05215e69	−1.11562
$887$	1.74355e68	0.0923059	0.0461529	−	0.998934i	$-0.485304\pi$
$887$	1.74355e68	0.0923059	0.0461529	+	0.998934i	$0.485304\pi$
$888$	−2.00320e69	−1.03281
$889$	−2.19942e68	−0.110437
$890$	−2.83318e69	−1.38551
$891$	1.07861e69	0.513735
$892$	1.09695e70	5.08875
$893$	−1.34580e69	−0.608094
$894$	−4.76322e69	−2.09638
$895$	3.25812e68	0.139677
$896$	2.09879e69	0.876455
$897$	1.04959e68	0.0426968
$898$	2.18297e69	0.865074
$899$	1.24022e69	0.478791
$900$	2.28243e69	0.858419
$901$	−1.60526e69	−0.588182
$902$	−8.64507e69	−3.08614
$903$	3.13286e68	0.108963
$904$	−1.26162e70	−4.27533
$905$	8.38326e68	0.276803
$906$	8.19386e67	0.0263618
$907$	−7.97555e68	−0.250028	−0.125014	−	0.992155i	$-0.539898\pi$
$907$	−7.97555e68	−0.250028	−0.125014	+	0.992155i	$0.539898\pi$
$908$	5.50557e69	1.68184
$909$	−9.34591e68	−0.278208
$910$	−6.46114e67	−0.0187429
$911$	6.39008e69	1.80644	0.903222	−	0.429173i	$-0.141195\pi$
$911$	6.39008e69	1.80644	0.903222	+	0.429173i	$0.141195\pi$
$912$	1.01072e70	2.78453
$913$	3.28187e69	0.881167
$914$	7.78449e69	2.03702
$915$	−6.47557e68	−0.165151
$916$	−1.60546e70	−3.99075
$917$	−1.12400e69	−0.272324
$918$	3.72560e69	0.879818
$919$	3.86963e69	0.890747	0.445373	−	0.895345i	$-0.353071\pi$
$919$	3.86963e69	0.890747	0.445373	+	0.895345i	$0.353071\pi$
$920$	−3.45432e69	−0.775084
$921$	−6.04431e69	−1.32204
$922$	1.14725e70	2.44615
$923$	3.02639e68	0.0629050
$924$	−2.48131e69	−0.502793
$925$	1.55446e69	0.307079
$926$	−1.02235e70	−1.96898
$927$	−1.01708e69	−0.190977
$928$	−6.89721e69	−1.26269
$929$	−4.53114e69	−0.808795	−0.404398	−	0.914583i	$-0.632519\pi$
$929$	−4.53114e69	−0.808795	−0.404398	+	0.914583i	$0.632519\pi$
$930$	6.13140e69	1.06711
$931$	−5.00646e69	−0.849597
$932$	−4.77735e69	−0.790520
$933$	−3.42196e69	−0.552149
$934$	1.65479e70	2.60370
$935$	−1.25971e69	−0.193284
$936$	−9.21217e68	−0.137841
$937$	2.69082e69	0.392648	0.196324	−	0.980539i	$-0.437100\pi$
$937$	2.69082e69	0.392648	0.196324	+	0.980539i	$0.437100\pi$
$938$	1.65458e69	0.235463
$939$	−7.23833e69	−1.00461
$940$	6.06899e69	0.821508
$941$	−3.38983e69	−0.447530	−0.223765	−	0.974643i	$-0.571835\pi$
$941$	−3.38983e69	−0.447530	−0.223765	+	0.974643i	$0.571835\pi$
$942$	9.67100e69	1.24530
$943$	6.07075e69	0.762460
$944$	3.02677e70	3.70799
$945$	8.36179e68	0.0999199
$946$	−1.16560e70	−1.35865
$947$	−1.24658e70	−1.41742	−0.708708	−	0.705502i	$-0.750721\pi$
$947$	−1.24658e70	−1.41742	−0.708708	+	0.705502i	$0.750721\pi$
$948$	−2.74876e70	−3.04888
$949$	1.30160e69	0.140839
$950$	−1.33445e70	−1.40863
$951$	1.28473e70	1.32303
$952$	−3.06290e69	−0.307726
$953$	1.47472e70	1.44553	0.722766	−	0.691093i	$-0.242870\pi$
$953$	1.47472e70	1.44553	0.722766	+	0.691093i	$0.242870\pi$
$954$	−1.08934e70	−1.04178
$955$	−2.47912e69	−0.231323
$956$	2.48847e70	2.26554
$957$	2.83461e69	0.251804
$958$	−2.38062e69	−0.206348
$959$	4.62466e68	0.0391150
$960$	−1.77309e70	−1.46338
$961$	1.98503e70	1.59871
$962$	−9.78935e68	−0.0769378
$963$	−2.00687e69	−0.153922
$964$	−4.36427e70	−3.26664
$965$	5.27418e69	0.385268
$966$	2.36813e69	0.168827
$967$	9.72062e69	0.676351	0.338175	−	0.941083i	$-0.390190\pi$
$967$	9.72062e69	0.676351	0.338175	+	0.941083i	$0.390190\pi$
$968$	8.03843e69	0.545884
$969$	−4.40379e69	−0.291889
$970$	−9.90665e69	−0.640901
$971$	−2.15826e70	−1.36286	−0.681431	−	0.731883i	$-0.738642\pi$
$971$	−2.15826e70	−1.36286	−0.681431	+	0.731883i	$0.738642\pi$
$972$	3.20928e70	1.97811
$973$	1.94030e69	0.116739
$974$	−5.57872e68	−0.0327642
$975$	−1.17188e69	−0.0671856
$976$	3.44297e70	1.92692
$977$	−1.11352e69	−0.0608384	−0.0304192	−	0.999537i	$-0.509684\pi$
$977$	−1.11352e69	−0.0608384	−0.0304192	+	0.999537i	$0.509684\pi$
$978$	−5.08564e69	−0.271258
$979$	−3.40772e70	−1.77448
$980$	2.25770e70	1.14777
$981$	6.29141e69	0.312267
$982$	−3.42345e70	−1.65899
$983$	−3.46672e69	−0.164025	−0.0820127	−	0.996631i	$-0.526135\pi$
$983$	−3.46672e69	−0.164025	−0.0820127	+	0.996631i	$0.526135\pi$
$984$	8.73481e70	4.03523
$985$	−2.63553e69	−0.118882
$986$	5.45951e69	0.240462
$987$	−2.66655e69	−0.114682
$988$	6.18336e69	0.259679
$989$	8.18507e69	0.335668
$990$	−8.54843e69	−0.342341
$991$	1.50226e70	0.587510	0.293755	−	0.955881i	$-0.405095\pi$
$991$	1.50226e70	0.587510	0.293755	+	0.955881i	$0.405095\pi$
$992$	−1.79445e71	−6.85341
$993$	−2.39702e69	−0.0894055
$994$	6.82830e69	0.248732
$995$	−1.45347e70	−0.517089
$996$	−5.17387e70	−1.79772
$997$	−9.94591e69	−0.337527	−0.168763	−	0.985657i	$-0.553977\pi$
$997$	−9.94591e69	−0.337527	−0.168763	+	0.985657i	$0.553977\pi$
$998$	8.27338e70	2.74230
$999$	1.26690e70	0.410162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.48.a.a.1.4	✓	4
3.2	odd	2		9.48.a.c.1.1		4
4.3	odd	2		16.48.a.d.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.48.a.a.1.4	✓	4	1.1	even	1	trivial
9.48.a.c.1.1		4	3.2	odd	2
16.48.a.d.1.2		4	4.3	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} +O(q^{10})\)	\(q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} -2.65611e23 q^{10} -3.19474e24 q^{11} +5.03652e25 q^{12} +1.57743e25 q^{13} +3.55908e26 q^{14} -1.47897e27 q^{15} +7.86346e28 q^{16} -3.42618e28 q^{17} -2.32503e29 q^{18} +1.00019e30 q^{19} -4.51042e30 q^{20} +1.98176e30 q^{21} -7.37325e31 q^{22} +5.17765e31 q^{23} +7.44978e32 q^{24} -5.78095e32 q^{25} +3.64060e32 q^{26} -4.71154e33 q^{27} +6.04378e33 q^{28} -6.90432e33 q^{29} -3.41336e34 q^{30} -1.79630e35 q^{31} +9.98970e35 q^{32} -4.10556e35 q^{33} -7.90739e35 q^{34} -1.77475e35 q^{35} -3.94820e36 q^{36} -2.68894e36 q^{37} +2.30836e37 q^{38} +2.02715e36 q^{39} -6.67160e37 q^{40} +1.17249e38 q^{41} +4.57376e37 q^{42} +1.58085e38 q^{43} -1.25208e39 q^{44} +1.15938e38 q^{45} +1.19497e39 q^{46} -1.34555e39 q^{47} +1.01053e40 q^{48} -5.00553e39 q^{49} -1.33420e40 q^{50} -4.40298e39 q^{51} +6.18221e39 q^{52} +4.68526e40 q^{53} -1.08739e41 q^{54} +3.67670e40 q^{55} +8.93968e40 q^{56} +1.28534e41 q^{57} -1.59347e41 q^{58} +3.84916e41 q^{59} -5.79633e41 q^{60} +4.37844e41 q^{61} -4.14573e42 q^{62} -1.55353e41 q^{63} +1.19887e43 q^{64} -1.81540e41 q^{65} -9.47534e42 q^{66} +4.64892e42 q^{67} -1.34278e43 q^{68} +6.65378e42 q^{69} -4.09600e42 q^{70} +1.91856e43 q^{71} -5.83999e43 q^{72} +8.25143e43 q^{73} -6.20589e43 q^{74} -7.42908e43 q^{75} +3.91990e44 q^{76} -4.92663e43 q^{77} +4.67852e43 q^{78} -5.45765e44 q^{79} -9.04975e44 q^{80} -3.37621e44 q^{81} +2.70603e45 q^{82} -1.02727e45 q^{83} +7.76685e44 q^{84} +3.94306e44 q^{85} +3.64849e45 q^{86} -8.87272e44 q^{87} -1.85201e46 q^{88} +1.06667e46 q^{89} +2.67578e45 q^{90} +2.43256e44 q^{91} +2.02921e46 q^{92} -2.30842e46 q^{93} -3.10543e46 q^{94} -1.15107e46 q^{95} +1.28377e47 q^{96} +3.72976e46 q^{97} -1.15524e47 q^{98} +3.21841e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots - 17\!\cdots\!72 q^{9}+O(q^{10}) \) 4 * q + 5785560 * q^2 + 38461494960 * q^3 + 404807499161152 * q^4 - 31114680242272200 * q^5 + 2130087053081157408 * q^6 - 39169218725888423200 * q^7 + 2392716988073784337920 * q^8 - 17071972417358142200172 * q^9	\( 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots + 53\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q + 5785560 * q^2 + 38461494960 * q^3 + 404807499161152 * q^4 - 31114680242272200 * q^5 + 2130087053081157408 * q^6 - 39169218725888423200 * q^7 + 2392716988073784337920 * q^8 - 17071972417358142200172 * q^9 + 161126302562215963534800 * q^10 - 1902165515717740404742512 * q^11 + 50498409864612604588081920 * q^12 + 126959149195199610466858520 * q^13 + 3491363489769461659480835904 * q^14 + 12437812896841241272880733600 * q^15 + 124527684040554167211817897984 * q^16 + 210426285758836687099688769480 * q^17 + 407430960534937802050318472760 * q^18 - 1059119811802437301721159140240 * q^19 - 15129514318106701401937782249600 * q^20 - 26054906182888686128940663165312 * q^21 - 79668451994083088127806382590880 * q^22 + 137531418344493639994288859179680 * q^23 + 1127389844243414442148606193633280 * q^24 + 1009909900344396506188154274977500 * q^25 + 2282338781897562472343866220387088 * q^26 - 7345952425324536073931587214783520 * q^27 - 36222097928665071743339635065479680 * q^28 - 22743132490172744184500850941726760 * q^29 - 25720928123802268640488729686158400 * q^30 + 75786540814706434901630981303934848 * q^31 + 1184674767018086471839527432906178560 * q^32 + 263381387470144952341649359926294720 * q^33 - 1261659118578465318749852382715620816 * q^34 - 1313148822925052387484546800067979200 * q^35 - 13289406181678982858450254524690284736 * q^36 - 11291457045120157869429951769632191560 * q^37 + 29667542464851305273548614410680536480 * q^38 + 39294375338503805226442587829551714336 * q^39 + 70753686685508718175919216681780352000 * q^40 + 130658126291089294119301677048020391528 * q^41 - 109062084819684721847642948723433304320 * q^42 - 445357287738427943170332944488133090800 * q^43 - 1525898906718917337200010663037616115456 * q^44 + 86022747271219179966948746072020632600 * q^45 + 1226146172325422687186041586267533291968 * q^46 + 2031912465958423919194866366997063590720 * q^47 + 10099193618530117215910418995824892231680 * q^48 + 9153745744156628626499502447643951451172 * q^49 - 19226200465513908889722489088356697935000 * q^50 - 18534366050002170683962116343746386369952 * q^51 - 55272350705889116147839999778699925596800 * q^52 + 29171719896619533806321793123448457437560 * q^53 - 119298079293441315567989538387565460341440 * q^54 + 192172580604633896452606078657416872901600 * q^55 + 276101696826518177934513744689489393111040 * q^56 + 558743644452458098451223285784560964733760 * q^57 - 732323136683092912071778597620095648941680 * q^58 + 478242858216320686410790860443879577596880 * q^59 - 2122170544542769609835673200272436380915200 * q^60 + 626683213833907852009669690320782900857688 * q^61 - 6870459615610782098804391369236375065946880 * q^62 + 5811636950821577036406237472810763671724640 * q^63 + 5525430481808418303700543890989262651523072 * q^64 + 12996735432890074297558542478104126872331600 * q^65 - 8968962593451471455705715472787747435620224 * q^66 + 18701411419127220668869505853739529194216880 * q^67 - 27469024204738931095482995064729717598496640 * q^68 - 2096956664577882726873494616728974107851904 * q^69 - 97207317904230285933067401805385458355395200 * q^70 + 22196594617762006008028198712153461686540768 * q^71 - 17423883005618236773493453708136577246773760 * q^72 + 104911201720506650033573412943840886878191080 * q^73 + 187734656069700274526204928907842421165646544 * q^74 + 32388703324174028323482311940739905891330000 * q^75 + 351694386032713991264839561028061045130100480 * q^76 - 263490744376507692433815778071300370399209600 * q^77 - 49672827098281461020739302707360391741486400 * q^78 - 1327995310109394234162785254414226288730352960 * q^79 - 948349663264469859337474495994045561022259200 * q^80 - 1061448205755511803861508510986654404170081116 * q^81 + 3821513842864797430908620724480935919685390320 * q^82 - 1439130627532364606968733068855111784504073360 * q^83 + 5249451328483250861794821516342136498695481344 * q^84 - 1001895286410663502447652611446390227458237200 * q^85 + 9578145533777866709022895861637903827077656928 * q^86 - 4326251093943206485496474339443178030108648160 * q^87 - 15478856320702836436797993507832298416714229760 * q^88 - 7960590522674945421108320896849737731421281880 * q^89 - 16839942698767843070418568109517409659960668400 * q^90 + 5325194479227227497182497798631911205603381568 * q^91 + 13058297350229360275908546071900174502239009280 * q^92 + 10728611999875738337226031496188630272675064320 * q^93 + 3475860200879106349192555645858186353201354624 * q^94 + 75421152415106939771624998522249518123547668000 * q^95 + 64914496577750590120454418039013206176753123328 * q^96 + 95066248961258904822565865801364599382905757320 * q^97 - 296344663186266398350742083591017164797938217320 * q^98 + 530900415919166351015781326273177630089784016 * q^99

Introduction

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