LMFDB - Embedded newform 1.48.a.a.1.2

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			1.2
Root			$-124721.$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} +O(q^{10})$	\(q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} -6.55837e22 q^{10} +2.66558e24 q^{11} -2.10331e25 q^{12} +2.26259e26 q^{13} +6.04405e25 q^{14} +6.44566e27 q^{15} +1.88024e28 q^{16} +8.41583e28 q^{17} +5.37476e27 q^{18} +3.16735e29 q^{19} -5.86528e30 q^{20} -5.94018e30 q^{21} -4.12345e30 q^{22} +2.26985e31 q^{23} +6.56359e31 q^{24} +1.08689e33 q^{25} -3.50006e32 q^{26} -4.57064e33 q^{27} +5.40532e33 q^{28} -3.39685e34 q^{29} -9.97095e33 q^{30} +1.81646e35 q^{31} -8.98449e34 q^{32} +4.05259e35 q^{33} -1.30186e35 q^{34} -1.65648e36 q^{35} +4.80676e35 q^{36} -7.13789e36 q^{37} -4.89965e35 q^{38} +3.43991e37 q^{39} +1.83032e37 q^{40} -2.78383e37 q^{41} +9.18901e36 q^{42} -4.92777e37 q^{43} -3.68769e38 q^{44} -1.47305e38 q^{45} -3.51128e37 q^{46} +1.86825e39 q^{47} +2.85861e39 q^{48} -3.71676e39 q^{49} -1.68134e39 q^{50} +1.27949e40 q^{51} -3.13017e40 q^{52} -2.48904e40 q^{53} +7.07044e39 q^{54} +1.13011e41 q^{55} -1.68679e40 q^{56} +4.81545e40 q^{57} +5.25467e40 q^{58} +3.69239e40 q^{59} -8.91722e41 q^{60} +3.52589e41 q^{61} -2.80993e41 q^{62} +1.35753e41 q^{63} -2.50722e42 q^{64} +9.59253e42 q^{65} -6.26905e41 q^{66} -1.26183e42 q^{67} -1.16428e43 q^{68} +3.45094e42 q^{69} +2.56245e42 q^{70} -3.26023e43 q^{71} -1.50000e42 q^{72} +3.59179e43 q^{73} +1.10418e43 q^{74} +1.65245e44 q^{75} -4.38186e43 q^{76} -1.04148e44 q^{77} -5.32128e43 q^{78} -5.82596e44 q^{79} +7.97151e44 q^{80} -6.02511e44 q^{81} +4.30637e43 q^{82} -3.51619e44 q^{83} +8.21792e44 q^{84} +3.56799e45 q^{85} +7.62288e43 q^{86} -5.16437e45 q^{87} +1.15078e45 q^{88} -2.92401e45 q^{89} +2.27869e44 q^{90} -8.84027e45 q^{91} -3.14021e45 q^{92} +2.76164e46 q^{93} -2.89005e45 q^{94} +1.34284e46 q^{95} -1.36595e46 q^{96} +2.17182e46 q^{97} +5.74955e45 q^{98} -9.26152e45 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.54692e6	−0.130396	−0.0651980	−	0.997872i	$-0.520768\pi$
$2$	−1.54692e6	−0.130396	−0.0651980	+	0.997872i	$0.520768\pi$
$3$	1.52034e11	0.932376	0.466188	−	0.884686i	$-0.345627\pi$
$3$	1.52034e11	0.932376	0.466188	+	0.884686i	$0.345627\pi$
$4$	−1.38345e14	−0.982997
$5$	4.23962e16	1.59049	0.795246	−	0.606286i	$-0.207341\pi$
$5$	4.23962e16	1.59049	0.795246	+	0.606286i	$0.207341\pi$
$6$	−2.35185e17	−0.121578
$7$	−3.90714e19	−0.539579	−0.269790	−	0.962919i	$-0.586954\pi$
$7$	−3.90714e19	−0.539579	−0.269790	+	0.962919i	$0.586954\pi$
$8$	4.31719e20	0.258575
$9$	−3.47448e21	−0.130675
$10$	−6.55837e22	−0.207394
$11$	2.66558e24	0.897561	0.448781	−	0.893642i	$-0.351858\pi$
$11$	2.66558e24	0.897561	0.448781	+	0.893642i	$0.351858\pi$
$12$	−2.10331e25	−0.916523
$13$	2.26259e26	1.50293	0.751463	−	0.659776i	$-0.229349\pi$
$13$	2.26259e26	1.50293	0.751463	+	0.659776i	$0.229349\pi$
$14$	6.04405e25	0.0703589
$15$	6.44566e27	1.48294
$16$	1.88024e28	0.949280
$17$	8.41583e28	1.02223	0.511114	−	0.859513i	$-0.329233\pi$
$17$	8.41583e28	1.02223	0.511114	+	0.859513i	$0.329233\pi$
$18$	5.37476e27	0.0170394
$19$	3.16735e29	0.281830	0.140915	−	0.990022i	$-0.454996\pi$
$19$	3.16735e29	0.281830	0.140915	+	0.990022i	$0.454996\pi$
$20$	−5.86528e30	−1.56345
$21$	−5.94018e30	−0.503091
$22$	−4.12345e30	−0.117038
$23$	2.26985e31	0.226669	0.113335	−	0.993557i	$-0.463847\pi$
$23$	2.26985e31	0.226669	0.113335	+	0.993557i	$0.463847\pi$
$24$	6.56359e31	0.241089
$25$	1.08689e33	1.52967
$26$	−3.50006e32	−0.195975
$27$	−4.57064e33	−1.05421
$28$	5.40532e33	0.530405
$29$	−3.39685e34	−1.46125	−0.730624	−	0.682780i	$-0.760771\pi$
$29$	−3.39685e34	−1.46125	−0.730624	+	0.682780i	$0.760771\pi$
$30$	−9.97095e33	−0.193369
$31$	1.81646e35	1.63015	0.815074	−	0.579357i	$-0.196696\pi$
$31$	1.81646e35	1.63015	0.815074	+	0.579357i	$0.196696\pi$
$32$	−8.98449e34	−0.382357
$33$	4.05259e35	0.836865
$34$	−1.30186e35	−0.133294
$35$	−1.65648e36	−0.858197
$36$	4.80676e35	0.128453
$37$	−7.13789e36	−1.00191	−0.500956	−	0.865473i	$-0.667018\pi$
$37$	−7.13789e36	−1.00191	−0.500956	+	0.865473i	$0.667018\pi$
$38$	−4.89965e35	−0.0367494
$39$	3.43991e37	1.40129
$40$	1.83032e37	0.411261
$41$	−2.78383e37	−0.350124	−0.175062	−	0.984557i	$-0.556013\pi$
$41$	−2.78383e37	−0.350124	−0.175062	+	0.984557i	$0.556013\pi$
$42$	9.18901e36	0.0656010
$43$	−4.92777e37	−0.202368	−0.101184	−	0.994868i	$-0.532263\pi$
$43$	−4.92777e37	−0.202368	−0.101184	+	0.994868i	$0.532263\pi$
$44$	−3.68769e38	−0.882300
$45$	−1.47305e38	−0.207837
$46$	−3.51128e37	−0.0295567
$47$	1.86825e39	0.948716	0.474358	−	0.880332i	$-0.342680\pi$
$47$	1.86825e39	0.948716	0.474358	+	0.880332i	$0.342680\pi$
$48$	2.85861e39	0.885086
$49$	−3.71676e39	−0.708854
$50$	−1.68134e39	−0.199462
$51$	1.27949e40	0.953100
$52$	−3.13017e40	−1.47737
$53$	−2.48904e40	−0.750843	−0.375421	−	0.926854i	$-0.622502\pi$
$53$	−2.48904e40	−0.750843	−0.375421	+	0.926854i	$0.622502\pi$
$54$	7.07044e39	0.137465
$55$	1.13011e41	1.42756
$56$	−1.68679e40	−0.139522
$57$	4.81545e40	0.262771
$58$	5.25467e40	0.190541
$59$	3.69239e40	0.0895953	0.0447976	−	0.998996i	$-0.485736\pi$
$59$	3.69239e40	0.0895953	0.0447976	+	0.998996i	$0.485736\pi$
$60$	−8.91722e41	−1.45772
$61$	3.52589e41	0.390857	0.195429	−	0.980718i	$-0.437390\pi$
$61$	3.52589e41	0.390857	0.195429	+	0.980718i	$0.437390\pi$
$62$	−2.80993e41	−0.212565
$63$	1.35753e41	0.0705093
$64$	−2.50722e42	−0.899422
$65$	9.59253e42	2.39039
$66$	−6.26905e41	−0.109124
$67$	−1.26183e42	−0.154257	−0.0771283	−	0.997021i	$-0.524575\pi$
$67$	−1.26183e42	−0.154257	−0.0771283	+	0.997021i	$0.524575\pi$
$68$	−1.16428e43	−1.00485
$69$	3.45094e42	0.211341
$70$	2.56245e42	0.111905
$71$	−3.26023e43	−1.02018	−0.510090	−	0.860121i	$-0.670388\pi$
$71$	−3.26023e43	−1.02018	−0.510090	+	0.860121i	$0.670388\pi$
$72$	−1.50000e42	−0.0337891
$73$	3.59179e43	0.585092	0.292546	−	0.956251i	$-0.405498\pi$
$73$	3.59179e43	0.585092	0.292546	+	0.956251i	$0.405498\pi$
$74$	1.10418e43	0.130645
$75$	1.65245e44	1.42623
$76$	−4.38186e43	−0.277038
$77$	−1.04148e44	−0.484305
$78$	−5.32128e43	−0.182723
$79$	−5.82596e44	−1.48297	−0.741483	−	0.670972i	$-0.765877\pi$
$79$	−5.82596e44	−1.48297	−0.741483	+	0.670972i	$0.765877\pi$
$80$	7.97151e44	1.50982
$81$	−6.02511e44	−0.852250
$82$	4.30637e43	0.0456547
$83$	−3.51619e44	−0.280373	−0.140187	−	0.990125i	$-0.544770\pi$
$83$	−3.51619e44	−0.280373	−0.140187	+	0.990125i	$0.544770\pi$
$84$	8.21792e44	0.494537
$85$	3.56799e45	1.62584
$86$	7.62288e43	0.0263879
$87$	−5.16437e45	−1.36243
$88$	1.15078e45	0.232087
$89$	−2.92401e45	−0.452182	−0.226091	−	0.974106i	$-0.572595\pi$
$89$	−2.92401e45	−0.452182	−0.226091	+	0.974106i	$0.572595\pi$
$90$	2.27869e44	0.0271011
$91$	−8.84027e45	−0.810947
$92$	−3.14021e45	−0.222815
$93$	2.76164e46	1.51991
$94$	−2.89005e45	−0.123709
$95$	1.34284e46	0.448248
$96$	−1.36595e46	−0.356500
$97$	2.17182e46	0.444311	0.222156	−	0.975011i	$-0.428691\pi$
$97$	2.17182e46	0.444311	0.222156	+	0.975011i	$0.428691\pi$
$98$	5.74955e45	0.0924317
$99$	−9.26152e45	−0.117288
$100$	−1.50366e47	−1.50366
$101$	−5.11557e46	−0.404894	−0.202447	−	0.979293i	$-0.564889\pi$
$101$	−5.11557e46	−0.404894	−0.202447	+	0.979293i	$0.564889\pi$
$102$	−1.97928e46	−0.124280
$103$	3.19569e47	1.59547	0.797736	−	0.603006i	$-0.206031\pi$
$103$	3.19569e47	1.59547	0.797736	+	0.603006i	$0.206031\pi$
$104$	9.76803e46	0.388618
$105$	−2.51841e47	−0.800162
$106$	3.85036e46	0.0979068
$107$	2.00584e47	0.409051	0.204526	−	0.978861i	$-0.434435\pi$
$107$	2.00584e47	0.409051	0.204526	+	0.978861i	$0.434435\pi$
$108$	6.32323e47	1.03629
$109$	−5.86410e47	−0.773888	−0.386944	−	0.922103i	$-0.626469\pi$
$109$	−5.86410e47	−0.773888	−0.386944	+	0.922103i	$0.626469\pi$
$110$	−1.74819e47	−0.186149
$111$	−1.08520e48	−0.934158
$112$	−7.34637e47	−0.512212
$113$	3.11593e47	0.176297	0.0881484	−	0.996107i	$-0.471905\pi$
$113$	3.11593e47	0.176297	0.0881484	+	0.996107i	$0.471905\pi$
$114$	−7.44914e46	−0.0342643
$115$	9.62329e47	0.360516
$116$	4.69936e48	1.43640
$117$	−7.86134e47	−0.196394
$118$	−5.71184e46	−0.0116829
$119$	−3.28818e48	−0.551572
$120$	2.78271e48	0.383450
$121$	−1.71442e48	−0.194384
$122$	−5.45429e47	−0.0509662
$123$	−4.23236e48	−0.326447
$124$	−2.51298e49	−1.60243
$125$	1.59559e49	0.842432
$126$	−2.09999e47	−0.00919412
$127$	2.66165e49	0.967749	0.483875	−	0.875137i	$-0.339229\pi$
$127$	2.66165e49	0.967749	0.483875	+	0.875137i	$0.339229\pi$
$128$	1.65230e49	0.499638
$129$	−7.49188e48	−0.188683
$130$	−1.48389e49	−0.311697
$131$	6.34924e49	1.11390	0.556950	−	0.830546i	$-0.311972\pi$
$131$	6.34924e49	1.11390	0.556950	+	0.830546i	$0.311972\pi$
$132$	−5.60654e49	−0.822636
$133$	−1.23753e49	−0.152069
$134$	1.95196e48	0.0201144
$135$	−1.93778e50	−1.67672
$136$	3.63327e49	0.264322
$137$	1.99734e50	1.22326	0.611631	−	0.791143i	$-0.290514\pi$
$137$	1.99734e50	1.22326	0.611631	+	0.791143i	$0.290514\pi$
$138$	−5.33834e48	−0.0275580
$139$	−3.16608e50	−1.37935	−0.689674	−	0.724120i	$-0.742246\pi$
$139$	−3.16608e50	−1.37935	−0.689674	+	0.724120i	$0.742246\pi$
$140$	2.29165e50	0.843605
$141$	2.84038e50	0.884560
$142$	5.04332e49	0.133027
$143$	6.03113e50	1.34897
$144$	−6.53287e49	−0.124047
$145$	−1.44014e51	−2.32410
$146$	−5.55623e49	−0.0762936
$147$	−5.65074e50	−0.660919
$148$	9.87488e50	0.984876
$149$	1.00267e50	0.0853651	0.0426826	−	0.999089i	$-0.486410\pi$
$149$	1.00267e50	0.0853651	0.0426826	+	0.999089i	$0.486410\pi$
$150$	−2.55621e50	−0.185974
$151$	−2.40479e49	−0.0149664	−0.00748321	−	0.999972i	$-0.502382\pi$
$151$	−2.40479e49	−0.0149664	−0.00748321	+	0.999972i	$0.502382\pi$
$152$	1.36740e50	0.0728740
$153$	−2.92407e50	−0.133579
$154$	1.61109e50	0.0631514
$155$	7.70111e51	2.59274
$156$	−4.75892e51	−1.37747
$157$	−1.42274e51	−0.354391	−0.177196	−	0.984176i	$-0.556702\pi$
$157$	−1.42274e51	−0.354391	−0.177196	+	0.984176i	$0.556702\pi$
$158$	9.01232e50	0.193373
$159$	−3.78419e51	−0.700068
$160$	−3.80908e51	−0.608136
$161$	−8.86862e50	−0.122306
$162$	9.32038e50	0.111130
$163$	−4.79256e51	−0.494492	−0.247246	−	0.968953i	$-0.579525\pi$
$163$	−4.79256e51	−0.494492	−0.247246	+	0.968953i	$0.579525\pi$
$164$	3.85127e51	0.344170
$165$	1.71814e52	1.33103
$166$	5.43927e50	0.0365596
$167$	−9.89736e51	−0.577673	−0.288837	−	0.957378i	$-0.593268\pi$
$167$	−9.89736e51	−0.577673	−0.288837	+	0.957378i	$0.593268\pi$
$168$	−2.56449e51	−0.130087
$169$	2.85292e52	1.25878
$170$	−5.51941e51	−0.212004
$171$	−1.10049e51	−0.0368280
$172$	6.81729e51	0.198927
$173$	−7.43991e52	−1.89446	−0.947228	−	0.320562i	$-0.896128\pi$
$173$	−7.43991e52	−1.89446	−0.947228	+	0.320562i	$0.896128\pi$
$174$	7.98889e51	0.177656
$175$	−4.24665e52	−0.825377
$176$	5.01194e52	0.852037
$177$	5.61369e51	0.0835365
$178$	4.52321e51	0.0589627
$179$	3.60632e52	0.412115	0.206057	−	0.978540i	$-0.433937\pi$
$179$	3.60632e52	0.412115	0.206057	+	0.978540i	$0.433937\pi$
$180$	2.03788e52	0.204303
$181$	6.19557e52	0.545299	0.272650	−	0.962113i	$-0.412100\pi$
$181$	6.19557e52	0.545299	0.272650	+	0.962113i	$0.412100\pi$
$182$	1.36752e52	0.105744
$183$	5.36056e52	0.364426
$184$	9.79935e51	0.0586109
$185$	−3.02619e53	−1.59353
$186$	−4.27205e52	−0.198190
$187$	2.24331e53	0.917511
$188$	−2.58463e53	−0.932585
$189$	1.78581e53	0.568832
$190$	−2.07727e52	−0.0584497
$191$	−3.09862e53	−0.770699	−0.385349	−	0.922771i	$-0.625919\pi$
$191$	−3.09862e53	−0.770699	−0.385349	+	0.922771i	$0.625919\pi$
$192$	−3.81183e53	−0.838600
$193$	4.75475e53	0.925829	0.462914	−	0.886403i	$-0.346804\pi$
$193$	4.75475e53	0.925829	0.462914	+	0.886403i	$0.346804\pi$
$194$	−3.35963e52	−0.0579364
$195$	1.45839e54	2.22874
$196$	5.14194e53	0.696802
$197$	−7.61644e53	−0.915790	−0.457895	−	0.889006i	$-0.651396\pi$
$197$	−7.61644e53	−0.915790	−0.457895	+	0.889006i	$0.651396\pi$
$198$	1.43269e52	0.0152939
$199$	−1.90631e54	−1.80778	−0.903890	−	0.427765i	$-0.859301\pi$
$199$	−1.90631e54	−1.80778	−0.903890	+	0.427765i	$0.859301\pi$
$200$	4.69232e53	0.395533
$201$	−1.91841e53	−0.143825
$202$	7.91339e52	0.0527965
$203$	1.32720e54	0.788459
$204$	−1.77011e54	−0.936895
$205$	−1.18024e54	−0.556869
$206$	−4.94348e53	−0.208043
$207$	−7.88655e52	−0.0296199
$208$	4.25422e54	1.42670
$209$	8.44284e53	0.252959
$210$	3.89579e53	0.104338
$211$	1.25520e54	0.300660	0.150330	−	0.988636i	$-0.451966\pi$
$211$	1.25520e54	0.300660	0.150330	+	0.988636i	$0.451966\pi$
$212$	3.44345e54	0.738076
$213$	−4.95665e54	−0.951191
$214$	−3.10288e53	−0.0533386
$215$	−2.08918e54	−0.321864
$216$	−1.97323e54	−0.272593
$217$	−7.09718e54	−0.879594
$218$	9.07131e53	0.100912
$219$	5.46075e54	0.545526
$220$	−1.56344e55	−1.40329
$221$	1.90416e55	1.53633
$222$	1.67872e54	0.121810
$223$	−1.43141e54	−0.0934545	−0.0467272	−	0.998908i	$-0.514879\pi$
$223$	−1.43141e54	−0.0934545	−0.0467272	+	0.998908i	$0.514879\pi$
$224$	3.51037e54	0.206312
$225$	−3.77639e54	−0.199889
$226$	−4.82011e53	−0.0229884
$227$	3.38487e55	1.45524	0.727619	−	0.685982i	$-0.240627\pi$
$227$	3.38487e55	1.45524	0.727619	+	0.685982i	$0.240627\pi$
$228$	−6.66191e54	−0.258303
$229$	−4.65218e54	−0.162750	−0.0813752	−	0.996684i	$-0.525931\pi$
$229$	−4.65218e54	−0.162750	−0.0813752	+	0.996684i	$0.525931\pi$
$230$	−1.48865e54	−0.0470098
$231$	−1.58341e55	−0.451555
$232$	−1.46649e55	−0.377842
$233$	−6.87236e55	−1.60045	−0.800225	−	0.599700i	$-0.795287\pi$
$233$	−6.87236e55	−1.60045	−0.800225	+	0.599700i	$0.795287\pi$
$234$	1.21609e54	0.0256090
$235$	7.92068e55	1.50893
$236$	−5.10822e54	−0.0880719
$237$	−8.85744e55	−1.38268
$238$	5.08657e54	0.0719228
$239$	1.09219e56	1.39942	0.699710	−	0.714427i	$-0.253313\pi$
$239$	1.09219e56	1.39942	0.699710	+	0.714427i	$0.253313\pi$
$240$	1.21194e56	1.40772
$241$	−4.82622e55	−0.508401	−0.254201	−	0.967152i	$-0.581812\pi$
$241$	−4.82622e55	−0.508401	−0.254201	+	0.967152i	$0.581812\pi$
$242$	2.65207e54	0.0253468
$243$	2.99259e55	0.259597
$244$	−4.87788e55	−0.384211
$245$	−1.57577e56	−1.12743
$246$	6.54714e54	0.0425674
$247$	7.16642e55	0.423569
$248$	7.84201e55	0.421515
$249$	−5.34580e55	−0.261414
$250$	−2.46825e55	−0.109850
$251$	−4.06217e56	−1.64599	−0.822993	−	0.568052i	$-0.807697\pi$
$251$	−4.06217e56	−1.64599	−0.822993	+	0.568052i	$0.807697\pi$
$252$	−1.87807e55	−0.0693104
$253$	6.05047e55	0.203450
$254$	−4.11736e55	−0.126191
$255$	5.42456e56	1.51590
$256$	3.27300e56	0.834271
$257$	1.93698e56	0.450501	0.225251	−	0.974301i	$-0.427680\pi$
$257$	1.93698e56	0.450501	0.225251	+	0.974301i	$0.427680\pi$
$258$	1.15894e55	0.0246035
$259$	2.78887e56	0.540611
$260$	−1.32707e57	−2.34975
$261$	1.18023e56	0.190948
$262$	−9.82178e55	−0.145248
$263$	8.33659e56	1.12727	0.563636	−	0.826023i	$-0.309402\pi$
$263$	8.33659e56	1.12727	0.563636	+	0.826023i	$0.309402\pi$
$264$	1.74958e56	0.216392
$265$	−1.05526e57	−1.19421
$266$	1.91436e55	0.0198292
$267$	−4.44548e56	−0.421604
$268$	1.74568e56	0.151634
$269$	−1.88490e57	−1.50006	−0.750032	−	0.661402i	$-0.769962\pi$
$269$	−1.88490e57	−1.50006	−0.750032	+	0.661402i	$0.769962\pi$
$270$	2.99759e56	0.218637
$271$	2.56612e57	1.71593	0.857963	−	0.513712i	$-0.171730\pi$
$271$	2.56612e57	1.71593	0.857963	+	0.513712i	$0.171730\pi$
$272$	1.58238e57	0.970380
$273$	−1.34402e57	−0.756108
$274$	−3.08974e56	−0.159508
$275$	2.89721e57	1.37297
$276$	−4.77419e56	−0.207748
$277$	−8.36679e56	−0.334414	−0.167207	−	0.985922i	$-0.553475\pi$
$277$	−8.36679e56	−0.334414	−0.167207	+	0.985922i	$0.553475\pi$
$278$	4.89768e56	0.179861
$279$	−6.31127e56	−0.213019
$280$	−7.15133e56	−0.221908
$281$	−3.96974e57	−1.13283	−0.566414	−	0.824121i	$-0.691670\pi$
$281$	−3.96974e57	−1.13283	−0.566414	+	0.824121i	$0.691670\pi$
$282$	−4.39385e56	−0.115343
$283$	−4.45361e57	−1.07580	−0.537900	−	0.843009i	$-0.680782\pi$
$283$	−4.45361e57	−1.07580	−0.537900	+	0.843009i	$0.680782\pi$
$284$	4.51034e57	1.00283
$285$	2.04157e57	0.417936
$286$	−9.32969e56	−0.175900
$287$	1.08768e57	0.188919
$288$	3.12165e56	0.0499643
$289$	3.04657e56	0.0449481
$290$	2.22778e57	0.303054
$291$	3.30190e57	0.414265
$292$	−4.96905e57	−0.575144
$293$	1.05167e58	1.12328	0.561641	−	0.827381i	$-0.310170\pi$
$293$	1.05167e58	1.12328	0.561641	+	0.827381i	$0.310170\pi$
$294$	8.74127e56	0.0861811
$295$	1.56543e57	0.142501
$296$	−3.08156e57	−0.259069
$297$	−1.21834e58	−0.946222
$298$	−1.55105e56	−0.0111313
$299$	5.13574e57	0.340667
$300$	−2.28607e58	−1.40198
$301$	1.92535e57	0.109193
$302$	3.72002e55	0.00195156
$303$	−7.77740e57	−0.377514
$304$	5.95539e57	0.267535
$305$	1.49484e58	0.621656
$306$	4.52331e56	0.0174182
$307$	5.43218e57	0.193741	0.0968707	−	0.995297i	$-0.469117\pi$
$307$	5.43218e57	0.193741	0.0968707	+	0.995297i	$0.469117\pi$
$308$	1.44083e58	0.476071
$309$	4.85853e58	1.48758
$310$	−1.19130e58	−0.338082
$311$	−4.80030e58	−1.26299	−0.631493	−	0.775381i	$-0.717558\pi$
$311$	−4.80030e58	−1.26299	−0.631493	+	0.775381i	$0.717558\pi$
$312$	1.48507e58	0.362339
$313$	−2.50321e58	−0.566507	−0.283253	−	0.959045i	$-0.591414\pi$
$313$	−2.50321e58	−0.566507	−0.283253	+	0.959045i	$0.591414\pi$
$314$	2.20087e57	0.0462111
$315$	5.75541e57	0.112145
$316$	8.05990e58	1.45775
$317$	−6.65301e58	−1.11719	−0.558593	−	0.829442i	$-0.688659\pi$
$317$	−6.65301e58	−1.11719	−0.558593	+	0.829442i	$0.688659\pi$
$318$	5.85385e57	0.0912860
$319$	−9.05460e58	−1.31156
$320$	−1.06297e59	−1.43052
$321$	3.04956e58	0.381390
$322$	1.37191e57	0.0159482
$323$	2.66559e58	0.288094
$324$	8.33540e58	0.837759
$325$	2.45920e59	2.29898
$326$	7.41372e57	0.0644797
$327$	−8.91542e58	−0.721555
$328$	−1.20183e58	−0.0905331
$329$	−7.29953e58	−0.511907
$330$	−2.65784e58	−0.173561
$331$	−1.52984e58	−0.0930438	−0.0465219	−	0.998917i	$-0.514814\pi$
$331$	−1.52984e58	−0.0930438	−0.0465219	+	0.998917i	$0.514814\pi$
$332$	4.86445e58	0.275606
$333$	2.48005e58	0.130924
$334$	1.53105e58	0.0753262
$335$	−5.34969e58	−0.245344
$336$	−1.11690e59	−0.477574
$337$	−1.19696e59	−0.477284	−0.238642	−	0.971108i	$-0.576702\pi$
$337$	−1.19696e59	−0.477284	−0.238642	+	0.971108i	$0.576702\pi$
$338$	−4.41324e58	−0.164140
$339$	4.73727e58	0.164375
$340$	−4.93612e59	−1.59820
$341$	4.84194e59	1.46316
$342$	1.70238e57	0.00480222
$343$	3.50084e59	0.922062
$344$	−2.12741e58	−0.0523272
$345$	1.46307e59	0.336136
$346$	1.15090e59	0.247029
$347$	−6.60768e59	−1.32528	−0.662638	−	0.748940i	$-0.730563\pi$
$347$	−6.60768e59	−1.32528	−0.662638	+	0.748940i	$0.730563\pi$
$348$	7.14463e59	1.33927
$349$	7.13810e59	1.25079	0.625396	−	0.780308i	$-0.284937\pi$
$349$	7.13810e59	1.25079	0.625396	+	0.780308i	$0.284937\pi$
$350$	6.56924e58	0.107626
$351$	−1.03415e60	−1.58441
$352$	−2.39489e59	−0.343189
$353$	4.98386e58	0.0668129	0.0334064	−	0.999442i	$-0.489364\pi$
$353$	4.98386e58	0.0668129	0.0334064	+	0.999442i	$0.489364\pi$
$354$	−8.68394e57	−0.0108928
$355$	−1.38221e60	−1.62259
$356$	4.04520e59	0.444493
$357$	−4.99916e59	−0.514273
$358$	−5.57870e58	−0.0537381
$359$	2.08989e60	1.88540	0.942700	−	0.333641i	$-0.108277\pi$
$359$	2.08989e60	1.88540	0.942700	+	0.333641i	$0.108277\pi$
$360$	−6.35942e58	−0.0537414
$361$	−1.16273e60	−0.920572
$362$	−9.58408e58	−0.0711048
$363$	−2.60649e59	−0.181239
$364$	1.22300e60	0.797159
$365$	1.52278e60	0.930585
$366$	−8.29237e58	−0.0475197
$367$	−1.22059e59	−0.0656021	−0.0328011	−	0.999462i	$-0.510443\pi$
$367$	−1.22059e59	−0.0656021	−0.0328011	+	0.999462i	$0.510443\pi$
$368$	4.26786e59	0.215173
$369$	9.67236e58	0.0457523
$370$	4.68129e59	0.207790
$371$	9.72503e59	0.405139
$372$	−3.82058e60	−1.49407
$373$	−2.41910e60	−0.888172	−0.444086	−	0.895984i	$-0.646472\pi$
$373$	−2.41910e60	−0.888172	−0.444086	+	0.895984i	$0.646472\pi$
$374$	−3.47023e59	−0.119640
$375$	2.42583e60	0.785463
$376$	8.06560e59	0.245314
$377$	−7.68569e60	−2.19615
$378$	−2.76252e59	−0.0741734
$379$	6.29795e60	1.58920	0.794598	−	0.607135i	$-0.207681\pi$
$379$	6.29795e60	1.58920	0.794598	+	0.607135i	$0.207681\pi$
$380$	−1.85774e60	−0.440626
$381$	4.04661e60	0.902306
$382$	4.79333e59	0.100496
$383$	3.88964e60	0.766898	0.383449	−	0.923562i	$-0.374736\pi$
$383$	3.88964e60	0.766898	0.383449	+	0.923562i	$0.374736\pi$
$384$	2.51206e60	0.465850
$385$	−4.41548e60	−0.770284
$386$	−7.35523e59	−0.120724
$387$	1.71214e59	0.0264443
$388$	−3.00459e60	−0.436757
$389$	5.15774e60	0.705739	0.352869	−	0.935673i	$-0.385206\pi$
$389$	5.15774e60	0.705739	0.352869	+	0.935673i	$0.385206\pi$
$390$	−2.25602e60	−0.290619
$391$	1.91027e60	0.231707
$392$	−1.60460e60	−0.183292
$393$	9.65300e60	1.03857
$394$	1.17821e60	0.119415
$395$	−2.46999e61	−2.35865
$396$	1.28128e60	0.115294
$397$	−1.92619e61	−1.63351	−0.816754	−	0.576986i	$-0.804229\pi$
$397$	−1.92619e61	−1.63351	−0.816754	+	0.576986i	$0.804229\pi$
$398$	2.94891e60	0.235727
$399$	−1.88146e60	−0.141786
$400$	2.04362e61	1.45208
$401$	5.06490e58	0.00339374	0.00169687	−	0.999999i	$-0.499460\pi$
$401$	5.06490e58	0.00339374	0.00169687	+	0.999999i	$0.499460\pi$
$402$	2.96764e59	0.0187542
$403$	4.10992e61	2.44999
$404$	7.07710e60	0.398010
$405$	−2.55442e61	−1.35550
$406$	−2.05308e60	−0.102812
$407$	−1.90266e61	−0.899277
$408$	5.52381e60	0.246448
$409$	1.50217e61	0.632733	0.316367	−	0.948637i	$-0.397537\pi$
$409$	1.50217e61	0.632733	0.316367	+	0.948637i	$0.397537\pi$
$410$	1.82574e60	0.0726135
$411$	3.03664e61	1.14054
$412$	−4.42106e61	−1.56834
$413$	−1.44267e60	−0.0483437
$414$	1.21999e59	0.00386232
$415$	−1.49073e61	−0.445932
$416$	−2.03282e61	−0.574654
$417$	−4.81352e61	−1.28607
$418$	−1.30604e60	−0.0329849
$419$	6.95944e61	1.66167	0.830835	−	0.556518i	$-0.187863\pi$
$419$	6.95944e61	1.66167	0.830835	+	0.556518i	$0.187863\pi$
$420$	3.48408e61	0.786557
$421$	−3.78966e61	−0.809042	−0.404521	−	0.914529i	$-0.632562\pi$
$421$	−3.78966e61	−0.809042	−0.404521	+	0.914529i	$0.632562\pi$
$422$	−1.94170e60	−0.0392049
$423$	−6.49121e60	−0.123973
$424$	−1.07457e61	−0.194149
$425$	9.14712e61	1.56367
$426$	7.66756e60	0.124031
$427$	−1.37762e61	−0.210898
$428$	−2.77497e61	−0.402096
$429$	9.16936e61	1.25775
$430$	3.23181e60	0.0419698
$431$	4.06747e60	0.0500160	0.0250080	−	0.999687i	$-0.492039\pi$
$431$	4.06747e60	0.0500160	0.0250080	+	0.999687i	$0.492039\pi$
$432$	−8.59392e61	−1.00074
$433$	−2.59125e61	−0.285788	−0.142894	−	0.989738i	$-0.545641\pi$
$433$	−2.59125e61	−0.285788	−0.142894	+	0.989738i	$0.545641\pi$
$434$	1.09788e61	0.114695
$435$	−2.18950e62	−2.16694
$436$	8.11265e61	0.760730
$437$	7.18941e60	0.0638821
$438$	−8.44736e60	−0.0711344
$439$	3.51058e61	0.280196	0.140098	−	0.990138i	$-0.455258\pi$
$439$	3.51058e61	0.280196	0.140098	+	0.990138i	$0.455258\pi$
$440$	4.87888e61	0.369132
$441$	1.29138e61	0.0926293
$442$	−2.94559e61	−0.200331
$443$	−4.43894e61	−0.286281	−0.143140	−	0.989702i	$-0.545720\pi$
$443$	−4.43894e61	−0.286281	−0.143140	+	0.989702i	$0.545720\pi$
$444$	1.50132e62	0.918275
$445$	−1.23967e62	−0.719192
$446$	2.21428e60	0.0121861
$447$	1.52440e61	0.0795924
$448$	9.79607e61	0.485309
$449$	3.43198e62	1.61345	0.806725	−	0.590927i	$-0.201238\pi$
$449$	3.43198e62	1.61345	0.806725	+	0.590927i	$0.201238\pi$
$450$	5.84179e60	0.0260647
$451$	−7.42052e61	−0.314257
$452$	−4.31072e61	−0.173299
$453$	−3.65609e60	−0.0139543
$454$	−5.23613e61	−0.189757
$455$	−3.74794e62	−1.28981
$456$	2.07892e61	0.0679460
$457$	−9.64466e60	−0.0299403	−0.0149701	−	0.999888i	$-0.504765\pi$
$457$	−9.64466e60	−0.0299403	−0.0149701	+	0.999888i	$0.504765\pi$
$458$	7.19656e60	0.0212220
$459$	−3.84658e62	−1.07765
$460$	−1.33133e62	−0.354386
$461$	−6.32143e61	−0.159898	−0.0799491	−	0.996799i	$-0.525476\pi$
$461$	−6.32143e61	−0.159898	−0.0799491	+	0.996799i	$0.525476\pi$
$462$	2.44941e61	0.0588809
$463$	6.86213e62	1.56785	0.783927	−	0.620853i	$-0.213214\pi$
$463$	6.86213e62	1.56785	0.783927	+	0.620853i	$0.213214\pi$
$464$	−6.38691e62	−1.38713
$465$	1.17083e63	2.41741
$466$	1.06310e62	0.208692
$467$	−2.91371e62	−0.543876	−0.271938	−	0.962315i	$-0.587665\pi$
$467$	−2.91371e62	−0.543876	−0.271938	+	0.962315i	$0.587665\pi$
$468$	1.08757e62	0.193055
$469$	4.93016e61	0.0832337
$470$	−1.22527e62	−0.196758
$471$	−2.16304e62	−0.330426
$472$	1.59407e61	0.0231671
$473$	−1.31354e62	−0.181637
$474$	1.37018e62	0.180296
$475$	3.44258e62	0.431106
$476$	4.54902e62	0.542194
$477$	8.64813e61	0.0981161
$478$	−1.68954e62	−0.182479
$479$	−9.39830e62	−0.966417	−0.483209	−	0.875505i	$-0.660529\pi$
$479$	−9.39830e62	−0.966417	−0.483209	+	0.875505i	$0.660529\pi$
$480$	−5.79110e62	−0.567011
$481$	−1.61501e63	−1.50580
$482$	7.46579e61	0.0662934
$483$	−1.34833e62	−0.114035
$484$	2.37180e62	0.191079
$485$	9.20767e62	0.706674
$486$	−4.62931e61	−0.0338504
$487$	2.39350e63	1.66764	0.833820	−	0.552037i	$-0.186149\pi$
$487$	2.39350e63	1.66764	0.833820	+	0.552037i	$0.186149\pi$
$488$	1.52219e62	0.101066
$489$	−7.28632e62	−0.461052
$490$	2.43759e62	0.147012
$491$	1.23586e63	0.710481	0.355241	−	0.934775i	$-0.384399\pi$
$491$	1.23586e63	0.710481	0.355241	+	0.934775i	$0.384399\pi$
$492$	5.85524e62	0.320896
$493$	−2.85874e63	−1.49373
$494$	−1.10859e62	−0.0552317
$495$	−3.92653e62	−0.186546
$496$	3.41539e63	1.54747
$497$	1.27382e63	0.550468
$498$	8.26955e61	0.0340873
$499$	−2.94657e63	−1.15865	−0.579327	−	0.815095i	$-0.696684\pi$
$499$	−2.94657e63	−1.15865	−0.579327	+	0.815095i	$0.696684\pi$
$500$	−2.20741e63	−0.828108
$501$	−1.50473e63	−0.538609
$502$	6.28387e62	0.214630
$503$	−1.27808e63	−0.416591	−0.208296	−	0.978066i	$-0.566792\pi$
$503$	−1.27808e63	−0.416591	−0.208296	+	0.978066i	$0.566792\pi$
$504$	5.86071e61	0.0182319
$505$	−2.16880e63	−0.643981
$506$	−9.35961e61	−0.0265290
$507$	4.33740e63	1.17366
$508$	−3.68224e63	−0.951294
$509$	7.25177e63	1.78886	0.894429	−	0.447209i	$-0.147582\pi$
$509$	7.25177e63	1.78886	0.894429	+	0.447209i	$0.147582\pi$
$510$	−8.39138e62	−0.197667
$511$	−1.40336e63	−0.315704
$512$	−2.83172e63	−0.608423
$513$	−1.44768e63	−0.297109
$514$	−2.99635e62	−0.0587435
$515$	1.35485e64	2.53759
$516$	1.03646e63	0.185475
$517$	4.97998e63	0.851531
$518$	−4.31418e62	−0.0704934
$519$	−1.13112e64	−1.76634
$520$	4.14127e63	0.618095
$521$	−9.84138e63	−1.40401	−0.702004	−	0.712173i	$-0.747711\pi$
$521$	−9.84138e63	−1.40401	−0.702004	+	0.712173i	$0.747711\pi$
$522$	−1.82573e62	−0.0248988
$523$	4.91409e62	0.0640698	0.0320349	−	0.999487i	$-0.489801\pi$
$523$	4.91409e62	0.0640698	0.0320349	+	0.999487i	$0.489801\pi$
$524$	−8.78382e63	−1.09496
$525$	−6.45635e63	−0.769561
$526$	−1.28961e63	−0.146992
$527$	1.52871e64	1.66638
$528$	7.61986e63	0.794419
$529$	−9.51264e63	−0.948621
$530$	1.63240e63	0.155720
$531$	−1.28291e62	−0.0117078
$532$	1.71205e63	0.149484
$533$	−6.29866e63	−0.526210
$534$	6.87682e62	0.0549754
$535$	8.50400e63	0.650593
$536$	−5.44756e62	−0.0398869
$537$	5.48283e63	0.384246
$538$	2.91580e63	0.195602
$539$	−9.90734e63	−0.636240
$540$	2.68081e64	1.64821
$541$	6.71742e61	0.00395428	0.00197714	−	0.999998i	$-0.499371\pi$
$541$	6.71742e61	0.00395428	0.00197714	+	0.999998i	$0.499371\pi$
$542$	−3.96959e63	−0.223750
$543$	9.41938e63	0.508424
$544$	−7.56119e63	−0.390856
$545$	−2.48615e64	−1.23086
$546$	2.07910e63	0.0985934
$547$	4.01645e62	0.0182449	0.00912243	−	0.999958i	$-0.497096\pi$
$547$	4.01645e62	0.0182449	0.00912243	+	0.999958i	$0.497096\pi$
$548$	−2.76322e64	−1.20246
$549$	−1.22507e63	−0.0510751
$550$	−4.48176e63	−0.179030
$551$	−1.07590e64	−0.411823
$552$	1.48983e63	0.0546474
$553$	2.27629e64	0.800177
$554$	1.29428e63	0.0436062
$555$	−4.60084e64	−1.48577
$556$	4.38010e64	1.35589
$557$	6.03614e64	1.79127	0.895637	−	0.444785i	$-0.146720\pi$
$557$	6.03614e64	1.79127	0.895637	+	0.444785i	$0.146720\pi$
$558$	9.76306e62	0.0277768
$559$	−1.11495e64	−0.304144
$560$	−3.11458e64	−0.814669
$561$	3.41059e64	0.855466
$562$	6.14089e63	0.147716
$563$	−3.47404e63	−0.0801470	−0.0400735	−	0.999197i	$-0.512759\pi$
$563$	−3.47404e63	−0.0801470	−0.0400735	+	0.999197i	$0.512759\pi$
$564$	−3.92951e64	−0.869520
$565$	1.32104e64	0.280399
$566$	6.88940e63	0.140280
$567$	2.35409e64	0.459856
$568$	−1.40750e64	−0.263793
$569$	9.25178e64	1.66375	0.831873	−	0.554966i	$-0.187269\pi$
$569$	9.25178e64	1.66375	0.831873	+	0.554966i	$0.187269\pi$
$570$	−3.15815e63	−0.0544971
$571$	−1.04188e65	−1.72532	−0.862658	−	0.505787i	$-0.831202\pi$
$571$	−1.04188e65	−1.72532	−0.862658	+	0.505787i	$0.831202\pi$
$572$	−8.34373e64	−1.32603
$573$	−4.71096e64	−0.718581
$574$	−1.68256e63	−0.0246343
$575$	2.46708e64	0.346728
$576$	8.71130e63	0.117532
$577$	−8.68105e64	−1.12445	−0.562225	−	0.826984i	$-0.690055\pi$
$577$	−8.68105e64	−1.12445	−0.562225	+	0.826984i	$0.690055\pi$
$578$	−4.71281e62	−0.00586105
$579$	7.22883e64	0.863221
$580$	1.99235e65	2.28459
$581$	1.37382e64	0.151284
$582$	−5.10778e63	−0.0540185
$583$	−6.63474e64	−0.673928
$584$	1.55064e64	0.151290
$585$	−3.33291e64	−0.312364
$586$	−1.62685e64	−0.146471
$587$	5.04453e64	0.436340	0.218170	−	0.975911i	$-0.429991\pi$
$587$	5.04453e64	0.436340	0.218170	+	0.975911i	$0.429991\pi$
$588$	7.81749e64	0.649681
$589$	5.75338e64	0.459424
$590$	−2.42160e63	−0.0185815
$591$	−1.15796e65	−0.853861
$592$	−1.34210e65	−0.951094
$593$	1.82757e65	1.24477	0.622385	−	0.782712i	$-0.286164\pi$
$593$	1.82757e65	1.24477	0.622385	+	0.782712i	$0.286164\pi$
$594$	1.88468e64	0.123383
$595$	−1.39406e65	−0.877272
$596$	−1.38714e64	−0.0839137
$597$	−2.89823e65	−1.68553
$598$	−7.94459e63	−0.0444216
$599$	6.30818e64	0.339136	0.169568	−	0.985519i	$-0.445763\pi$
$599$	6.30818e64	0.339136	0.169568	+	0.985519i	$0.445763\pi$
$600$	7.13392e64	0.368786
$601$	1.16613e65	0.579693	0.289847	−	0.957073i	$-0.406396\pi$
$601$	1.16613e65	0.579693	0.289847	+	0.957073i	$0.406396\pi$
$602$	−2.97837e63	−0.0142384
$603$	4.38422e63	0.0201574
$604$	3.32689e63	0.0147119
$605$	−7.26847e64	−0.309166
$606$	1.20310e64	0.0492262
$607$	−8.69736e64	−0.342337	−0.171168	−	0.985242i	$-0.554754\pi$
$607$	−8.69736e64	−0.342337	−0.171168	+	0.985242i	$0.554754\pi$
$608$	−2.84570e64	−0.107760
$609$	2.01779e65	0.735141
$610$	−2.31241e64	−0.0810614
$611$	4.22709e65	1.42585
$612$	4.04529e64	0.131308
$613$	3.95467e65	1.23535	0.617674	−	0.786435i	$-0.288075\pi$
$613$	3.95467e65	1.23535	0.617674	+	0.786435i	$0.288075\pi$
$614$	−8.40317e63	−0.0252631
$615$	−1.79436e65	−0.519212
$616$	−4.49627e64	−0.125229
$617$	−4.10300e65	−1.10002	−0.550009	−	0.835159i	$-0.685376\pi$
$617$	−4.10300e65	−1.10002	−0.550009	+	0.835159i	$0.685376\pi$
$618$	−7.51577e64	−0.193974
$619$	1.39273e65	0.346047	0.173024	−	0.984918i	$-0.444646\pi$
$619$	1.39273e65	0.346047	0.173024	+	0.984918i	$0.444646\pi$
$620$	−1.06541e66	−2.54865
$621$	−1.03747e65	−0.238958
$622$	7.42569e64	0.164688
$623$	1.14245e65	0.243988
$624$	6.46786e65	1.33022
$625$	−9.58171e64	−0.189785
$626$	3.87227e64	0.0738702
$627$	1.28360e65	0.235853
$628$	1.96828e65	0.348365
$629$	−6.00713e65	−1.02418
$630$	−8.90318e63	−0.0146232
$631$	1.54026e65	0.243728	0.121864	−	0.992547i	$-0.461113\pi$
$631$	1.54026e65	0.243728	0.121864	+	0.992547i	$0.461113\pi$
$632$	−2.51518e65	−0.383457
$633$	1.90833e65	0.280328
$634$	1.02917e65	0.145677
$635$	1.12844e66	1.53920
$636$	5.23522e65	0.688165
$637$	−8.40952e65	−1.06536
$638$	1.40068e65	0.171022
$639$	1.13276e65	0.133312
$640$	7.00513e65	0.794670
$641$	−1.65837e65	−0.181350	−0.0906752	−	0.995881i	$-0.528903\pi$
$641$	−1.65837e65	−0.181350	−0.0906752	+	0.995881i	$0.528903\pi$
$642$	−4.71743e64	−0.0497316
$643$	−1.22213e66	−1.24211	−0.621053	−	0.783768i	$-0.713295\pi$
$643$	−1.22213e66	−1.24211	−0.621053	+	0.783768i	$0.713295\pi$
$644$	1.22692e65	0.120226
$645$	−3.17627e65	−0.300099
$646$	−4.12346e64	−0.0375663
$647$	−9.62351e65	−0.845440	−0.422720	−	0.906260i	$-0.638925\pi$
$647$	−9.62351e65	−0.845440	−0.422720	+	0.906260i	$0.638925\pi$
$648$	−2.60115e65	−0.220370
$649$	9.84237e64	0.0804173
$650$	−3.80419e65	−0.299777
$651$	−1.07901e66	−0.820112
$652$	6.63024e65	0.486084
$653$	3.91841e65	0.277109	0.138554	−	0.990355i	$-0.455754\pi$
$653$	3.91841e65	0.277109	0.138554	+	0.990355i	$0.455754\pi$
$654$	1.37915e65	0.0940878
$655$	2.69183e66	1.77165
$656$	−5.23427e65	−0.332365
$657$	−1.24796e65	−0.0764567
$658$	1.12918e65	0.0667506
$659$	2.16961e66	1.23758	0.618792	−	0.785555i	$-0.287622\pi$
$659$	2.16961e66	1.23758	0.618792	+	0.785555i	$0.287622\pi$
$660$	−2.37696e66	−1.30840
$661$	−9.87453e65	−0.524544	−0.262272	−	0.964994i	$-0.584472\pi$
$661$	−9.87453e65	−0.524544	−0.262272	+	0.964994i	$0.584472\pi$
$662$	2.36654e64	0.0121325
$663$	2.89497e66	1.43244
$664$	−1.51800e65	−0.0724975
$665$	−5.24665e65	−0.241865
$666$	−3.83644e64	−0.0170720
$667$	−7.71034e65	−0.331220
$668$	1.36925e66	0.567851
$669$	−2.17623e65	−0.0871347
$670$	8.27556e64	0.0319919
$671$	9.39857e65	0.350818
$672$	5.33695e65	0.192360
$673$	−5.18176e66	−1.80353	−0.901765	−	0.432227i	$-0.857728\pi$
$673$	−5.18176e66	−1.80353	−0.901765	+	0.432227i	$0.857728\pi$
$674$	1.85161e65	0.0622359
$675$	−4.96780e66	−1.61260
$676$	−3.94685e66	−1.23738
$677$	5.62905e66	1.70452	0.852259	−	0.523120i	$-0.175232\pi$
$677$	5.62905e66	1.70452	0.852259	+	0.523120i	$0.175232\pi$
$678$	−7.32820e64	−0.0214338
$679$	−8.48559e65	−0.239741
$680$	1.54037e66	0.420402
$681$	5.14615e66	1.35683
$682$	−7.49010e65	−0.190790
$683$	−2.17309e66	−0.534800	−0.267400	−	0.963586i	$-0.586165\pi$
$683$	−2.17309e66	−0.534800	−0.267400	+	0.963586i	$0.586165\pi$
$684$	1.52247e65	0.0362018
$685$	8.46798e66	1.94559
$686$	−5.41553e65	−0.120233
$687$	−7.07289e65	−0.151745
$688$	−9.26539e65	−0.192104
$689$	−5.63168e66	−1.12846
$690$	−2.26325e65	−0.0438308
$691$	3.80507e66	0.712244	0.356122	−	0.934439i	$-0.384099\pi$
$691$	3.80507e66	0.712244	0.356122	+	0.934439i	$0.384099\pi$
$692$	1.02927e67	1.86224
$693$	3.61861e65	0.0632864
$694$	1.02216e66	0.172811
$695$	−1.34230e67	−2.19384
$696$	−2.22956e66	−0.352291
$697$	−2.34282e66	−0.357906
$698$	−1.10421e66	−0.163098
$699$	−1.04483e67	−1.49222
$700$	5.87500e66	0.811343
$701$	4.48575e66	0.599048	0.299524	−	0.954089i	$-0.403172\pi$
$701$	4.48575e66	0.599048	0.299524	+	0.954089i	$0.403172\pi$
$702$	1.59975e66	0.206600
$703$	−2.26082e66	−0.282368
$704$	−6.68321e66	−0.807286
$705$	1.20421e67	1.40689
$706$	−7.70965e64	−0.00871212
$707$	1.99872e66	0.218472
$708$	−7.76623e65	−0.0821161
$709$	−1.23589e67	−1.26414	−0.632068	−	0.774913i	$-0.717794\pi$
$709$	−1.23589e67	−1.26414	−0.632068	+	0.774913i	$0.717794\pi$
$710$	2.13818e66	0.211579
$711$	2.02422e66	0.193786
$712$	−1.26235e66	−0.116923
$713$	4.12310e66	0.369504
$714$	7.73331e65	0.0670591
$715$	2.55697e67	2.14552
$716$	−4.98915e66	−0.405108
$717$	1.66050e67	1.30479
$718$	−3.23290e66	−0.245848
$719$	−5.05205e66	−0.371825	−0.185913	−	0.982566i	$-0.559524\pi$
$719$	−5.05205e66	−0.371825	−0.185913	+	0.982566i	$0.559524\pi$
$720$	−2.76969e66	−0.197295
$721$	−1.24860e67	−0.860884
$722$	1.79865e66	0.120039
$723$	−7.33749e66	−0.474021
$724$	−8.57124e66	−0.536028
$725$	−3.69202e67	−2.23522
$726$	4.03205e65	0.0236328
$727$	2.10795e67	1.19619	0.598097	−	0.801424i	$-0.295924\pi$
$727$	2.10795e67	1.19619	0.598097	+	0.801424i	$0.295924\pi$
$728$	−3.81651e66	−0.209690
$729$	2.05698e67	1.09429
$730$	−2.35563e66	−0.121344
$731$	−4.14712e66	−0.206866
$732$	−7.41604e66	−0.358230
$733$	2.34941e67	1.09905	0.549523	−	0.835478i	$-0.314809\pi$
$733$	2.34941e67	1.09905	0.549523	+	0.835478i	$0.314809\pi$
$734$	1.88816e65	0.00855425
$735$	−2.39570e67	−1.05119
$736$	−2.03934e66	−0.0866685
$737$	−3.36352e66	−0.138455
$738$	−1.49624e65	−0.00596591
$739$	−8.69448e66	−0.335814	−0.167907	−	0.985803i	$-0.553701\pi$
$739$	−8.69448e66	−0.335814	−0.167907	+	0.985803i	$0.553701\pi$
$740$	4.18657e67	1.56644
$741$	1.08954e67	0.394926
$742$	−1.50439e66	−0.0528285
$743$	1.83903e67	0.625679	0.312840	−	0.949806i	$-0.398720\pi$
$743$	1.83903e67	0.625679	0.312840	+	0.949806i	$0.398720\pi$
$744$	1.19225e67	0.393011
$745$	4.25094e66	0.135773
$746$	3.74217e66	0.115814
$747$	1.22169e66	0.0366377
$748$	−3.10350e67	−0.901911
$749$	−7.83710e66	−0.220715
$750$	−3.75258e66	−0.102421
$751$	−2.92872e67	−0.774709	−0.387355	−	0.921931i	$-0.626611\pi$
$751$	−2.92872e67	−0.774709	−0.387355	+	0.921931i	$0.626611\pi$
$752$	3.51277e67	0.900597
$753$	−6.17588e67	−1.53468
$754$	1.18892e67	0.286369
$755$	−1.01954e66	−0.0238040
$756$	−2.47058e67	−0.559160
$757$	−3.60671e67	−0.791330	−0.395665	−	0.918395i	$-0.629486\pi$
$757$	−3.60671e67	−0.791330	−0.395665	+	0.918395i	$0.629486\pi$
$758$	−9.74245e66	−0.207225
$759$	9.19877e66	0.189691
$760$	5.79727e66	0.115906
$761$	6.36047e67	1.23296	0.616481	−	0.787370i	$-0.288558\pi$
$761$	6.36047e67	1.23296	0.616481	+	0.787370i	$0.288558\pi$
$762$	−6.25979e66	−0.117657
$763$	2.29118e67	0.417574
$764$	4.28678e67	0.757595
$765$	−1.23969e67	−0.212457
$766$	−6.01697e66	−0.100000
$767$	8.35437e66	0.134655
$768$	4.97608e67	0.777855
$769$	−1.58030e67	−0.239591	−0.119795	−	0.992799i	$-0.538224\pi$
$769$	−1.58030e67	−0.239591	−0.119795	+	0.992799i	$0.538224\pi$
$770$	6.83041e66	0.100442
$771$	2.94486e67	0.420037
$772$	−6.57793e67	−0.910087
$773$	−1.20430e68	−1.61628	−0.808142	−	0.588988i	$-0.799526\pi$
$773$	−1.20430e68	−1.61628	−0.808142	+	0.588988i	$0.799526\pi$
$774$	−2.64856e65	−0.00344823
$775$	1.97430e68	2.49358
$776$	9.37613e66	0.114888
$777$	4.24004e67	0.504052
$778$	−7.97864e66	−0.0920255
$779$	−8.81736e66	−0.0986752
$780$	−2.01760e68	−2.19085
$781$	−8.69040e67	−0.915674
$782$	−2.95503e66	−0.0302137
$783$	1.55258e68	1.54047
$784$	−6.98842e67	−0.672901
$785$	−6.03186e67	−0.563656
$786$	−1.49324e67	−0.135426
$787$	−1.72836e68	−1.52134	−0.760671	−	0.649137i	$-0.775130\pi$
$787$	−1.72836e68	−1.52134	−0.760671	+	0.649137i	$0.775130\pi$
$788$	1.05369e68	0.900219
$789$	1.26745e68	1.05104
$790$	3.82088e67	0.307558
$791$	−1.21744e67	−0.0951261
$792$	−3.99837e66	−0.0303278
$793$	7.97766e67	0.587429
$794$	2.97966e67	0.213003
$795$	−1.60435e68	−1.11345
$796$	2.63727e68	1.77704
$797$	−5.17743e67	−0.338722	−0.169361	−	0.985554i	$-0.554170\pi$
$797$	−5.17743e67	−0.338722	−0.169361	+	0.985554i	$0.554170\pi$
$798$	2.91048e66	0.0184883
$799$	1.57229e68	0.969803
$800$	−9.76519e67	−0.584879
$801$	1.01594e67	0.0590887
$802$	−7.83502e64	−0.000442530 0
$803$	9.57423e67	0.525156
$804$	2.65402e67	0.141380
$805$	−3.75995e67	−0.194527
$806$	−6.35773e67	−0.319469
$807$	−2.86569e68	−1.39862
$808$	−2.20848e67	−0.104695
$809$	−1.34819e68	−0.620812	−0.310406	−	0.950604i	$-0.600465\pi$
$809$	−1.34819e68	−0.620812	−0.310406	+	0.950604i	$0.600465\pi$
$810$	3.95149e67	0.176751
$811$	−1.29768e68	−0.563869	−0.281934	−	0.959434i	$-0.590976\pi$
$811$	−1.29768e68	−0.563869	−0.281934	+	0.959434i	$0.590976\pi$
$812$	−1.83611e68	−0.775053
$813$	3.90137e68	1.59989
$814$	2.94328e67	0.117262
$815$	−2.03186e68	−0.786485
$816$	2.40576e68	0.904759
$817$	−1.56080e67	−0.0570332
$818$	−2.32374e67	−0.0825059
$819$	3.07154e67	0.105970
$820$	1.63279e68	0.547401
$821$	−3.05518e68	−0.995342	−0.497671	−	0.867366i	$-0.665811\pi$
$821$	−3.05518e68	−0.995342	−0.497671	+	0.867366i	$0.665811\pi$
$822$	−4.69745e67	−0.148722
$823$	−3.54128e68	−1.08959	−0.544796	−	0.838568i	$-0.683393\pi$
$823$	−3.54128e68	−1.08959	−0.544796	+	0.838568i	$0.683393\pi$
$824$	1.37964e68	0.412549
$825$	4.40474e68	1.28012
$826$	2.23170e66	0.00630383
$827$	5.88899e68	1.61682	0.808410	−	0.588620i	$-0.200328\pi$
$827$	5.88899e68	1.61682	0.808410	+	0.588620i	$0.200328\pi$
$828$	1.09106e67	0.0291163
$829$	7.14204e68	1.85264	0.926319	−	0.376740i	$-0.122955\pi$
$829$	7.14204e68	1.85264	0.926319	+	0.376740i	$0.122955\pi$
$830$	2.30604e67	0.0581477
$831$	−1.27204e68	−0.311799
$832$	−5.67282e68	−1.35176
$833$	−3.12797e68	−0.724610
$834$	7.44614e67	0.167698
$835$	−4.19610e68	−0.918785
$836$	−1.16802e68	−0.248658
$837$	−8.30241e68	−1.71852
$838$	−1.07657e68	−0.216675
$839$	4.08251e68	0.798953	0.399477	−	0.916743i	$-0.369192\pi$
$839$	4.08251e68	0.798953	0.399477	+	0.916743i	$0.369192\pi$
$840$	−1.08724e68	−0.206902
$841$	6.13474e68	1.13525
$842$	5.86231e67	0.105496
$843$	−6.03536e68	−1.05622
$844$	−1.73650e68	−0.295548
$845$	1.20953e69	2.00209
$846$	1.00414e67	0.0161656
$847$	6.69846e67	0.104885
$848$	−4.68000e68	−0.712760
$849$	−6.77100e68	−1.00305
$850$	−1.41499e68	−0.203896
$851$	−1.62019e68	−0.227102
$852$	6.85726e68	0.935018
$853$	6.69695e68	0.888331	0.444166	−	0.895945i	$-0.353500\pi$
$853$	6.69695e68	0.888331	0.444166	+	0.895945i	$0.353500\pi$
$854$	2.13107e67	0.0275003
$855$	−4.66566e67	−0.0585746
$856$	8.65958e67	0.105770
$857$	1.01115e69	1.20162	0.600809	−	0.799393i	$-0.294845\pi$
$857$	1.01115e69	1.20162	0.600809	+	0.799393i	$0.294845\pi$
$858$	−1.41843e68	−0.164005
$859$	−4.13647e68	−0.465361	−0.232681	−	0.972553i	$-0.574750\pi$
$859$	−4.13647e68	−0.465361	−0.232681	+	0.972553i	$0.574750\pi$
$860$	2.89027e68	0.316392
$861$	1.65364e68	0.176144
$862$	−6.29207e66	−0.00652188
$863$	6.85332e68	0.691270	0.345635	−	0.938369i	$-0.387664\pi$
$863$	6.85332e68	0.691270	0.345635	+	0.938369i	$0.387664\pi$
$864$	4.10649e68	0.403086
$865$	−3.15424e69	−3.01312
$866$	4.00847e67	0.0372656
$867$	4.63182e67	0.0419086
$868$	9.81856e68	0.864638
$869$	−1.55296e69	−1.33105
$870$	3.38699e68	0.282560
$871$	−2.85501e68	−0.231836
$872$	−2.53164e68	−0.200108
$873$	−7.54594e67	−0.0580602
$874$	−1.11215e67	−0.00832997
$875$	−6.23418e68	−0.454559
$876$	−7.55464e68	−0.536250
$877$	6.43840e68	0.444925	0.222463	−	0.974941i	$-0.428590\pi$
$877$	6.43840e68	0.444925	0.222463	+	0.974941i	$0.428590\pi$
$878$	−5.43059e67	−0.0365364
$879$	1.59889e69	1.04732
$880$	2.12487e69	1.35516
$881$	8.86127e68	0.550253	0.275126	−	0.961408i	$-0.411280\pi$
$881$	8.86127e68	0.550253	0.275126	+	0.961408i	$0.411280\pi$
$882$	−1.99767e67	−0.0120785
$883$	4.16643e68	0.245294	0.122647	−	0.992450i	$-0.460862\pi$
$883$	4.16643e68	0.245294	0.122647	+	0.992450i	$0.460862\pi$
$884$	−2.63430e69	−1.51021
$885$	2.37999e68	0.132864
$886$	6.86670e67	0.0373298
$887$	2.94393e69	1.55856	0.779278	−	0.626679i	$-0.215586\pi$
$887$	2.94393e69	1.55856	0.779278	+	0.626679i	$0.215586\pi$
$888$	−4.68502e68	−0.241550
$889$	−1.03994e69	−0.522177
$890$	1.91767e68	0.0937797
$891$	−1.60604e69	−0.764946
$892$	1.98028e68	0.0918654
$893$	5.91742e68	0.267376
$894$	−2.35813e67	−0.0103785
$895$	1.52894e69	0.655466
$896$	−6.45578e68	−0.269594
$897$	7.80807e68	0.317630
$898$	−5.30901e68	−0.210387
$899$	−6.17026e69	−2.38205
$900$	5.22443e68	0.196490
$901$	−2.09473e69	−0.767532
$902$	1.14790e68	0.0409779
$903$	2.92718e68	0.101809
$904$	1.34521e68	0.0455859
$905$	2.62669e69	0.867295
$906$	5.65569e66	0.00181959
$907$	3.36233e69	1.05407	0.527034	−	0.849844i	$-0.323304\pi$
$907$	3.36233e69	1.05407	0.527034	+	0.849844i	$0.323304\pi$
$908$	−4.68278e69	−1.43049
$909$	1.77739e68	0.0529094
$910$	5.79777e68	0.168185
$911$	4.29823e69	1.21509	0.607544	−	0.794286i	$-0.292155\pi$
$911$	4.29823e69	1.21509	0.607544	+	0.794286i	$0.292155\pi$
$912$	9.05422e68	0.249443
$913$	−9.37269e68	−0.251652
$914$	1.49195e67	0.00390409
$915$	2.27267e69	0.579617
$916$	6.43603e68	0.159983
$917$	−2.48074e69	−0.601037
$918$	5.95036e68	0.140521
$919$	5.89124e69	1.35610	0.678050	−	0.735015i	$-0.262825\pi$
$919$	5.89124e69	1.35610	0.678050	+	0.735015i	$0.262825\pi$
$920$	4.15455e68	0.0932202
$921$	8.25876e68	0.180640
$922$	9.77877e67	0.0208501
$923$	−7.37656e69	−1.53325
$924$	2.19055e69	0.443877
$925$	−7.75813e69	−1.53259
$926$	−1.06152e69	−0.204442
$927$	−1.11034e69	−0.208488
$928$	3.05190e69	0.558718
$929$	−3.81127e69	−0.680301	−0.340150	−	0.940371i	$-0.610478\pi$
$929$	−3.81127e69	−0.680301	−0.340150	+	0.940371i	$0.610478\pi$
$930$	−1.81119e69	−0.315220
$931$	−1.17723e69	−0.199776
$932$	9.50754e69	1.57324
$933$	−7.29808e69	−1.17758
$934$	4.50729e68	0.0709192
$935$	9.51078e69	1.45930
$936$	−3.39388e68	−0.0507826
$937$	−3.18868e69	−0.465298	−0.232649	−	0.972561i	$-0.574739\pi$
$937$	−3.18868e69	−0.465298	−0.232649	+	0.972561i	$0.574739\pi$
$938$	−7.62658e67	−0.0108533
$939$	−3.80573e69	−0.528197
$940$	−1.09578e70	−1.48327
$941$	7.20176e69	0.950785	0.475393	−	0.879774i	$-0.342306\pi$
$941$	7.20176e69	0.950785	0.475393	+	0.879774i	$0.342306\pi$
$942$	3.34606e68	0.0430862
$943$	−6.31886e68	−0.0793623
$944$	6.94259e68	0.0850510
$945$	7.57117e69	0.904723
$946$	2.03194e68	0.0236848
$947$	7.19607e69	0.818222	0.409111	−	0.912485i	$-0.365839\pi$
$947$	7.19607e69	0.818222	0.409111	+	0.912485i	$0.365839\pi$
$948$	1.22538e70	1.35917
$949$	8.12676e69	0.879350
$950$	−5.32540e68	−0.0562144
$951$	−1.01148e70	−1.04164
$952$	−1.41957e69	−0.142623
$953$	1.03533e70	1.01483	0.507417	−	0.861700i	$-0.330600\pi$
$953$	1.03533e70	1.01483	0.507417	+	0.861700i	$0.330600\pi$
$954$	−1.33780e68	−0.0127939
$955$	−1.31370e70	−1.22579
$956$	−1.51099e70	−1.37563
$957$	−1.37661e70	−1.22287
$958$	1.45384e69	0.126017
$959$	−7.80391e69	−0.660047
$960$	−1.61607e70	−1.33379
$961$	2.05789e70	1.65738
$962$	2.49830e69	0.196350
$963$	−6.96926e68	−0.0534526
$964$	6.67681e69	0.499757
$965$	2.01583e70	1.47252
$966$	2.08576e68	0.0148697
$967$	−1.88655e70	−1.31264	−0.656321	−	0.754482i	$-0.727888\pi$
$967$	−1.88655e70	−1.31264	−0.656321	+	0.754482i	$0.727888\pi$
$968$	−7.40145e68	−0.0502627
$969$	4.05260e69	0.268612
$970$	−1.42436e69	−0.0921474
$971$	−1.54065e70	−0.972862	−0.486431	−	0.873719i	$-0.661701\pi$
$971$	−1.54065e70	−0.972862	−0.486431	+	0.873719i	$0.661701\pi$
$972$	−4.14008e69	−0.255183
$973$	1.23703e70	0.744268
$974$	−3.70256e69	−0.217453
$975$	3.73882e70	2.14351
$976$	6.62954e69	0.371033
$977$	−1.28077e70	−0.699760	−0.349880	−	0.936795i	$-0.613778\pi$
$977$	−1.28077e70	−0.699760	−0.349880	+	0.936795i	$0.613778\pi$
$978$	1.12714e69	0.0601193
$979$	−7.79418e69	−0.405861
$980$	2.17999e70	1.10826
$981$	2.03747e69	0.101128
$982$	−1.91177e69	−0.0926438
$983$	1.22658e70	0.580349	0.290174	−	0.956974i	$-0.406287\pi$
$983$	1.22658e70	0.580349	0.290174	+	0.956974i	$0.406287\pi$
$984$	−1.82719e69	−0.0844109
$985$	−3.22908e70	−1.45656
$986$	4.42225e69	0.194776
$987$	−1.10978e70	−0.477290
$988$	−9.91435e69	−0.416367
$989$	−1.11853e69	−0.0458705
$990$	6.07405e68	0.0243249
$991$	2.78865e70	1.09059	0.545296	−	0.838244i	$-0.316417\pi$
$991$	2.78865e70	1.09059	0.545296	+	0.838244i	$0.316417\pi$
$992$	−1.63200e70	−0.623298
$993$	−2.32587e69	−0.0867519
$994$	−1.97050e69	−0.0717787
$995$	−8.08202e70	−2.87526
$996$	7.39562e69	0.256969
$997$	2.05189e70	0.696336	0.348168	−	0.937432i	$-0.386804\pi$
$997$	2.05189e70	0.696336	0.348168	+	0.937432i	$0.386804\pi$
$998$	4.55812e69	0.151084
$999$	3.26247e70	1.05623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.48.a.a.1.2	✓	4
3.2	odd	2		9.48.a.c.1.3		4
4.3	odd	2		16.48.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.48.a.a.1.2	✓	4	1.1	even	1	trivial
9.48.a.c.1.3		4	3.2	odd	2
16.48.a.d.1.1		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)

\(f(q)\)	\(=\)	\(q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} +O(q^{10})\)	\(q-1.54692e6 q^{2} +1.52034e11 q^{3} -1.38345e14 q^{4} +4.23962e16 q^{5} -2.35185e17 q^{6} -3.90714e19 q^{7} +4.31719e20 q^{8} -3.47448e21 q^{9} -6.55837e22 q^{10} +2.66558e24 q^{11} -2.10331e25 q^{12} +2.26259e26 q^{13} +6.04405e25 q^{14} +6.44566e27 q^{15} +1.88024e28 q^{16} +8.41583e28 q^{17} +5.37476e27 q^{18} +3.16735e29 q^{19} -5.86528e30 q^{20} -5.94018e30 q^{21} -4.12345e30 q^{22} +2.26985e31 q^{23} +6.56359e31 q^{24} +1.08689e33 q^{25} -3.50006e32 q^{26} -4.57064e33 q^{27} +5.40532e33 q^{28} -3.39685e34 q^{29} -9.97095e33 q^{30} +1.81646e35 q^{31} -8.98449e34 q^{32} +4.05259e35 q^{33} -1.30186e35 q^{34} -1.65648e36 q^{35} +4.80676e35 q^{36} -7.13789e36 q^{37} -4.89965e35 q^{38} +3.43991e37 q^{39} +1.83032e37 q^{40} -2.78383e37 q^{41} +9.18901e36 q^{42} -4.92777e37 q^{43} -3.68769e38 q^{44} -1.47305e38 q^{45} -3.51128e37 q^{46} +1.86825e39 q^{47} +2.85861e39 q^{48} -3.71676e39 q^{49} -1.68134e39 q^{50} +1.27949e40 q^{51} -3.13017e40 q^{52} -2.48904e40 q^{53} +7.07044e39 q^{54} +1.13011e41 q^{55} -1.68679e40 q^{56} +4.81545e40 q^{57} +5.25467e40 q^{58} +3.69239e40 q^{59} -8.91722e41 q^{60} +3.52589e41 q^{61} -2.80993e41 q^{62} +1.35753e41 q^{63} -2.50722e42 q^{64} +9.59253e42 q^{65} -6.26905e41 q^{66} -1.26183e42 q^{67} -1.16428e43 q^{68} +3.45094e42 q^{69} +2.56245e42 q^{70} -3.26023e43 q^{71} -1.50000e42 q^{72} +3.59179e43 q^{73} +1.10418e43 q^{74} +1.65245e44 q^{75} -4.38186e43 q^{76} -1.04148e44 q^{77} -5.32128e43 q^{78} -5.82596e44 q^{79} +7.97151e44 q^{80} -6.02511e44 q^{81} +4.30637e43 q^{82} -3.51619e44 q^{83} +8.21792e44 q^{84} +3.56799e45 q^{85} +7.62288e43 q^{86} -5.16437e45 q^{87} +1.15078e45 q^{88} -2.92401e45 q^{89} +2.27869e44 q^{90} -8.84027e45 q^{91} -3.14021e45 q^{92} +2.76164e46 q^{93} -2.89005e45 q^{94} +1.34284e46 q^{95} -1.36595e46 q^{96} +2.17182e46 q^{97} +5.74955e45 q^{98} -9.26152e45 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5785560 q^{2} + 38461494960 q^{3} + 404807499161152 q^{4} - 31\!\cdots\!00 q^{5}+ \cdots - 17\!\cdots\!72 q^{9}+O(q^{10}) \) 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

L-functions

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